LMFDB - Embedded newform 714.2.ba.e.361.2

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			361.2
Character	$\chi$	$=$	714.361
Dual form			714.2.ba.e.625.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.400100 + 0.107206i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.01225 - 2.44445i) q^{7} -1.00000i q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.400100 + 0.107206i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.01225 - 2.44445i) q^{7} -1.00000i q^{8} +(-0.866025 + 0.500000i) q^{9} +(0.400100 - 0.107206i) q^{10} +(3.81183 - 1.02138i) q^{11} +(-0.965926 - 0.258819i) q^{12} +3.53208 q^{13} +(-2.09886 - 1.61083i) q^{14} -0.414214i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.23523 - 2.55603i) 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} +(-0.0575273 + 0.214695i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(-4.18154 - 2.41421i) q^{25} +(3.05888 - 1.76604i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.62308 - 0.345588i) q^{28} +(0.292893 - 0.292893i) q^{29} +(-0.207107 - 0.358719i) q^{30} +(-2.53105 - 9.44602i) 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} +(8.04387 + 2.15535i) q^{37} +(-2.11113 + 3.65659i) q^{38} +(-0.914171 - 3.41173i) q^{39} +(0.107206 - 0.400100i) q^{40} +(0.965476 + 0.965476i) q^{41} +(-1.01272 + 2.44426i) q^{42} +2.16670i q^{43} +(1.02138 - 3.81183i) q^{44} +(-0.400100 + 0.107206i) q^{45} +(0.0575273 + 0.214695i) q^{46} +(-3.11161 - 5.38947i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(-4.95068 + 4.94881i) q^{49} -4.82843 q^{50} +(-1.63160 + 3.78654i) q^{51} +(1.76604 - 3.05888i) q^{52} +(4.45538 + 2.57232i) q^{53} +(0.965926 + 0.258819i) q^{54} +1.63461 q^{55} +(-2.44445 + 1.01225i) q^{56} +(2.98559 + 2.98559i) q^{57} +(0.107206 - 0.400100i) q^{58} +(11.4009 + 6.58232i) q^{59} +(-0.358719 - 0.207107i) q^{60} +(-3.77455 + 14.0868i) q^{61} +(-6.91497 - 6.91497i) q^{62} +(2.09886 + 1.61083i) q^{63} -1.00000 q^{64} +(1.41319 + 0.378662i) q^{65} +(-3.41759 - 1.97315i) q^{66} +(4.01338 - 6.95138i) q^{67} +(-3.83120 + 1.52378i) q^{68} +0.222269 q^{69} +(-0.667063 - 0.869504i) q^{70} +(10.8348 - 10.8348i) q^{71} +(0.500000 + 0.866025i) q^{72} +(4.32308 + 16.1340i) q^{73} +(8.04387 - 2.15535i) q^{74} +(-1.24969 + 4.66390i) q^{75} +4.22227i q^{76} +(-6.35525 - 8.28394i) q^{77} +(-2.49756 - 2.49756i) q^{78} +(-2.19205 + 8.18084i) q^{79} +(-0.107206 - 0.400100i) q^{80} +(0.500000 - 0.866025i) q^{81} +(1.31887 + 0.353389i) 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} +(-1.02138 - 3.81183i) q^{88} +(-7.12903 - 12.3479i) q^{89} +(-0.292893 + 0.292893i) q^{90} +(-3.57537 - 8.63401i) q^{91} +(0.157168 + 0.157168i) q^{92} +(-8.46907 + 4.88962i) q^{93} +(-5.38947 - 3.11161i) q^{94} +(-1.68933 + 0.452654i) q^{95} +(-0.258819 + 0.965926i) 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 $\left(\mathbb{Z}/714\mathbb{Z}\right)^\times$.

$n$	$239$	$409$	$547$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$3$	−0.258819	−	0.965926i	−0.149429	−	0.557678i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.400100	+	0.107206i	0.178930	+	0.0479441i	0.347171	−	0.937802i	$-0.387142\pi$
$5$	0.400100	+	0.107206i	0.178930	+	0.0479441i	−0.168242	+	0.985746i	$0.553809\pi$
$6$	−0.707107	−	0.707107i	−0.288675	−	0.288675i
$7$	−1.01225	−	2.44445i	−0.382596	−	0.923916i
$7$	−1.01225	−	2.44445i	−0.382596	−	0.923916i
$8$		−	1.00000i		−	0.353553i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	0.400100	−	0.107206i	0.126523	−	0.0339016i
$11$	3.81183	−	1.02138i	1.14931	−	0.307957i	0.366622	−	0.930370i	$-0.380514\pi$
$11$	3.81183	−	1.02138i	1.14931	−	0.307957i	0.782689	+	0.622413i	$0.213848\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	3.53208			0.979624			0.489812	−	0.871828i	$-0.337065\pi$
$13$	3.53208			0.979624			0.489812	+	0.871828i	$0.337065\pi$
$14$	−2.09886	−	1.61083i	−0.560945	−	0.430512i
$15$		−	0.414214i		−	0.106949i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.23523	−	2.55603i	−0.784658	−	0.619928i
$17$	−3.23523	−	2.55603i	−0.784658	−	0.619928i
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−3.65659	+	2.11113i	−0.838880	+	0.484327i	−0.856883	−	0.515511i	$-0.827602\pi$
$19$	−3.65659	+	2.11113i	−0.838880	+	0.484327i	0.0180036	+	0.999838i	$0.494269\pi$
$20$	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
$23$	−0.0575273	+	0.214695i	−0.0119953	+	0.0447670i	−0.971664	−	0.236366i	$-0.924044\pi$
$23$	−0.0575273	+	0.214695i	−0.0119953	+	0.0447670i	0.959669	+	0.281133i	$0.0907102\pi$
$24$	−0.965926	+	0.258819i	−0.197169	+	0.0528312i
$25$	−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
$28$	−2.62308	−	0.345588i	−0.495716	−	0.0653100i
$29$	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
$31$	−2.53105	−	9.44602i	−0.454591	−	1.69656i	−0.689288	−	0.724488i	$-0.742076\pi$
$31$	−2.53105	−	9.44602i	−0.454591	−	1.69656i	0.234697	−	0.972069i	$-0.424590\pi$
$32$	−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
$37$	8.04387	+	2.15535i	1.32240	+	0.354337i	0.849878	−	0.526980i	$-0.176676\pi$
$37$	8.04387	+	2.15535i	1.32240	+	0.354337i	0.472526	+	0.881317i	$0.343342\pi$
$38$	−2.11113	+	3.65659i	−0.342471	+	0.593178i
$39$	−0.914171	−	3.41173i	−0.146384	−	0.546314i
$40$	0.107206	−	0.400100i	0.0169508	−	0.0632613i
$41$	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	$0.947170\pi$
$44$	1.02138	−	3.81183i	0.153978	−	0.574655i
$45$	−0.400100	+	0.107206i	−0.0596433	+	0.0159814i
$46$	0.0575273	+	0.214695i	0.00848194	+	0.0316550i
$47$	−3.11161	−	5.38947i	−0.453875	−	0.786135i	0.544747	−	0.838600i	$-0.316626\pi$
$47$	−3.11161	−	5.38947i	−0.453875	−	0.786135i	−0.998623	+	0.0524649i	$0.983292\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$	−4.95068	+	4.94881i	−0.707240	+	0.706973i
$50$	−4.82843			−0.682843
$51$	−1.63160	+	3.78654i	−0.228469	+	0.530222i
$52$	1.76604	−	3.05888i	0.244906	−	0.424190i
$53$	4.45538	+	2.57232i	0.611994	+	0.353335i	0.773745	−	0.633497i	$-0.218381\pi$
$53$	4.45538	+	2.57232i	0.611994	+	0.353335i	−0.161751	+	0.986832i	$0.551714\pi$
$54$	0.965926	+	0.258819i	0.131446	+	0.0352208i
$55$	1.63461			0.220411
$56$	−2.44445	+	1.01225i	−0.326654	+	0.135268i
$57$	2.98559	+	2.98559i	0.395452	+	0.395452i
$58$	0.107206	−	0.400100i	0.0140769	−	0.0525356i
$59$	11.4009	+	6.58232i	1.48427	+	0.856946i	0.999840	−	0.0178827i	$-0.00569255\pi$
$59$	11.4009	+	6.58232i	1.48427	+	0.856946i	0.484433	+	0.874828i	$0.339026\pi$
$60$	−0.358719	−	0.207107i	−0.0463105	−	0.0267374i
$61$	−3.77455	+	14.0868i	−0.483282	+	1.80363i	0.104396	+	0.994536i	$0.466709\pi$
$61$	−3.77455	+	14.0868i	−0.483282	+	1.80363i	−0.587677	+	0.809095i	$0.699958\pi$
$62$	−6.91497	−	6.91497i	−0.878202	−	0.878202i
$63$	2.09886	+	1.61083i	0.264432	+	0.202945i
$64$	−1.00000			−0.125000
$65$	1.41319	+	0.378662i	0.175284	+	0.0469672i
$66$	−3.41759	−	1.97315i	−0.420677	−	0.242878i
$67$	4.01338	−	6.95138i	0.490313	−	0.849246i	−0.509625	−	0.860396i	$-0.670216\pi$
$67$	4.01338	−	6.95138i	0.490313	−	0.849246i	0.999938	+	0.0111502i	$0.00354928\pi$
$68$	−3.83120	+	1.52378i	−0.464601	+	0.184785i
$69$	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
$73$	4.32308	+	16.1340i	0.505979	+	1.88834i	0.456846	+	0.889546i	$0.348979\pi$
$73$	4.32308	+	16.1340i	0.505979	+	1.88834i	0.0491331	+	0.998792i	$0.484354\pi$
$74$	8.04387	−	2.15535i	0.935081	−	0.250554i
$75$	−1.24969	+	4.66390i	−0.144302	+	0.538541i
$76$			4.22227i			0.484327i
$77$	−6.35525	−	8.28394i	−0.724248	−	0.944043i
$78$	−2.49756	−	2.49756i	−0.282793	−	0.282793i
$79$	−2.19205	+	8.18084i	−0.246625	+	0.920416i	0.725935	+	0.687763i	$0.241407\pi$
$79$	−2.19205	+	8.18084i	−0.246625	+	0.920416i	−0.972560	+	0.232653i	$0.925259\pi$
$80$	−0.107206	−	0.400100i	−0.0119860	−	0.0447325i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	1.31887	+	0.353389i	0.145644	+	0.0390253i
$83$		−	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
$88$	−1.02138	−	3.81183i	−0.108879	−	0.406343i
$89$	−7.12903	−	12.3479i	−0.755676	−	1.30887i	−0.945037	−	0.326962i	$-0.893975\pi$
$89$	−7.12903	−	12.3479i	−0.755676	−	1.30887i	0.189361	−	0.981907i	$-0.439358\pi$
$90$	−0.292893	+	0.292893i	−0.0308737	+	0.0308737i
$91$	−3.57537	−	8.63401i	−0.374800	−	0.905090i
$92$	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
$95$	−1.68933	+	0.452654i	−0.173321	+	0.0464413i
$96$	−0.258819	+	0.965926i	−0.0264156	+	0.0985844i
$97$	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	−0.992904	−	0.118920i	$-0.962057\pi$
$101$	−3.95427	+	6.84899i	−0.393464	+	0.681500i	0.599440	+	0.800420i	$0.295390\pi$
$102$	0.480266	+	4.09504i	0.0475534	+	0.405469i
$103$	0.906062	+	1.56934i	0.0892769	+	0.154632i	0.907206	−	0.420687i	$-0.138211\pi$
$103$	0.906062	+	1.56934i	0.0892769	+	0.154632i	−0.817929	+	0.575319i	$0.804878\pi$
$104$		−	3.53208i		−	0.346349i
$105$	−1.01252	+	0.419289i	−0.0988123	+	0.0409185i
$106$	5.14463			0.499691
$107$	19.7904	+	5.30281i	1.91321	+	0.512642i	0.992476	+	0.122442i	$0.0390726\pi$
$107$	19.7904	+	5.30281i	1.91321	+	0.512642i	0.920730	+	0.390200i	$0.127594\pi$
$108$	0.965926	−	0.258819i	0.0929463	−	0.0249049i
$109$	5.72280	−	1.53342i	0.548145	−	0.146875i	0.0258906	−	0.999665i	$-0.491758\pi$
$109$	5.72280	−	1.53342i	0.548145	−	0.146875i	0.522254	+	0.852790i	$0.325091\pi$
$110$	1.41561	−	0.817305i	0.134974	−	0.0779270i
$111$		−	8.32762i		−	0.790423i
$112$	−1.61083	+	2.09886i	−0.152209	+	0.198324i
$113$	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	$0.558463\pi$
$114$	4.07840	+	1.09280i	0.381977	+	0.102350i
$115$	−0.0460333	+	0.0797321i	−0.00429263	+	0.00743505i
$116$	−0.107206	−	0.400100i	−0.00995386	−	0.0371483i
$117$	−3.05888	+	1.76604i	−0.282793	+	0.163271i
$118$	13.1646			1.21190
$119$	−2.97322	+	10.4957i	−0.272554	+	0.962140i
$120$	−0.414214			−0.0378124
$121$	3.96057	−	2.28664i	0.360052	−	0.207876i
$122$	3.77455	+	14.0868i	0.341732	+	1.27536i
$123$	0.682695	−	1.18246i	0.0615565	−	0.106619i
$124$	−9.44602	−	2.53105i	−0.848278	−	0.227295i
$125$	−2.87868	−	2.87868i	−0.257477	−	0.257477i
$126$	2.62308	+	0.345588i	0.233683	+	0.0307874i
$127$			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
$129$	2.09287	−	0.560782i	0.184267	−	0.0493741i
$130$	1.41319	−	0.378662i	0.123945	−	0.0332109i
$131$	−7.81669	−	2.09448i	−0.682948	−	0.182995i	−0.0993675	−	0.995051i	$-0.531682\pi$
$131$	−7.81669	−	2.09448i	−0.682948	−	0.182995i	−0.583580	+	0.812056i	$0.698349\pi$
$132$	−3.94630			−0.343481
$133$	8.86196	+	6.80136i	0.768430	+	0.589752i
$134$		−	8.02676i		−	0.693407i
$135$	0.207107	+	0.358719i	0.0178249	+	0.0308737i
$136$	−2.55603	+	3.23523i	−0.219178	+	0.277419i
$137$	2.39096	−	4.14126i	0.204273	−	0.353812i	−0.745628	−	0.666363i	$-0.767850\pi$
$137$	2.39096	−	4.14126i	0.204273	−	0.353812i	0.949901	+	0.312551i	$0.101184\pi$
$138$	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
$142$	3.96582	−	14.8006i	0.332804	−	1.24204i
$143$	13.4637	−	3.60759i	1.12589	−	0.301682i
$144$	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
$147$	6.06152	+	3.50115i	0.499945	+	0.288770i
$148$	5.88852	−	5.88852i	0.484033	−	0.484033i
$149$	−4.82498	−	8.35711i	−0.395278	−	0.684641i	0.597859	−	0.801601i	$-0.296018\pi$
$149$	−4.82498	−	8.35711i	−0.395278	−	0.684641i	−0.993137	+	0.116960i	$0.962685\pi$
$150$	1.24969	+	4.66390i	0.102037	+	0.380806i
$151$	19.6913	+	11.3688i	1.60245	+	0.925176i	0.990995	+	0.133899i	$0.0427498\pi$
$151$	19.6913	+	11.3688i	1.60245	+	0.925176i	0.611457	+	0.791277i	$0.290584\pi$
$152$	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
$156$	−3.41173	−	0.914171i	−0.273157	−	0.0731922i
$157$	−9.04705	+	15.6699i	−0.722033	+	1.25060i	0.238151	+	0.971228i	$0.423459\pi$
$157$	−9.04705	+	15.6699i	−0.722033	+	1.25060i	−0.960184	+	0.279370i	$0.909875\pi$
$158$	2.19205	+	8.18084i	0.174390	+	0.650833i
$159$	1.33153	−	4.96933i	0.105597	−	0.394094i
$160$	−0.292893	−	0.292893i	−0.0231552	−	0.0231552i
$161$	0.583044	−	0.0767031i	0.0459503	−	0.00604505i
$162$		−	1.00000i		−	0.0785674i
$163$	−1.37270	+	5.12297i	−0.107518	+	0.401262i	−0.998619	−	0.0525433i	$-0.983267\pi$
$163$	−1.37270	+	5.12297i	−0.107518	+	0.401262i	0.891101	+	0.453805i	$0.149934\pi$
$164$	1.31887	−	0.353389i	0.102986	−	0.0275950i
$165$	−0.423068	−	1.57891i	−0.0329358	−	0.122918i
$166$	−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
$170$	−1.56844	−	0.675829i	−0.120294	−	0.0518338i
$171$	2.11113	−	3.65659i	0.161442	−	0.279627i
$172$	1.87641	+	1.08335i	0.143075	+	0.0826045i
$173$	12.4114	+	3.32563i	0.943623	+	0.252843i	0.697654	−	0.716435i	$-0.254227\pi$
$173$	12.4114	+	3.32563i	0.943623	+	0.252843i	0.245969	+	0.969278i	$0.420894\pi$
$174$	−0.414214			−0.0314014
$175$	−1.66865	+	12.6654i	−0.126138	+	0.957412i
$176$	−2.79045	−	2.79045i	−0.210338	−	0.210338i
$177$	3.40726	−	12.7161i	0.256105	−	0.955799i
$178$	−12.3479	−	7.12903i	−0.925511	−	0.534344i
$179$	7.54125	+	4.35394i	0.563659	+	0.325429i	0.754613	−	0.656170i	$-0.227825\pi$
$179$	7.54125	+	4.35394i	0.563659	+	0.325429i	−0.190954	+	0.981599i	$0.561158\pi$
$180$	−0.107206	+	0.400100i	−0.00799069	+	0.0298217i
$181$	−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	$-0.560007\pi$
$182$	−7.41336	−	5.68959i	−0.549515	−	0.421740i
$183$	14.5837			1.07806
$184$	0.214695	+	0.0575273i	0.0158275	+	0.00424097i
$185$	2.98728	+	1.72471i	0.219629	+	0.126803i
$186$	−4.88962	+	8.46907i	−0.358524	+	0.620983i
$187$	−14.9428	−	6.43877i	−1.09273	−	0.470849i
$188$	−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	0.697554	−	0.716532i	$-0.254272\pi$
$191$	−3.75576	−	6.50517i	−0.271758	−	0.470698i	−0.969312	+	0.245834i	$0.920938\pi$
$192$	0.258819	+	0.965926i	0.0186787	+	0.0697097i
$193$	−4.58001	+	1.22721i	−0.329676	+	0.0883364i	−0.419861	−	0.907589i	$-0.637921\pi$
$193$	−4.58001	+	1.22721i	−0.329676	+	0.0883364i	0.0901844	+	0.995925i	$0.471254\pi$
$194$	0.233453	−	0.871259i	0.0167610	−	0.0625527i
$195$		−	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	$0.617831\pi$
$198$	−1.02138	+	3.81183i	−0.0725861	+	0.270895i
$199$	4.75515	+	17.7465i	0.337084	+	1.25801i	0.901593	+	0.432586i	$0.142399\pi$
$199$	4.75515	+	17.7465i	0.337084	+	1.25801i	−0.564509	+	0.825427i	$0.690934\pi$
$200$	−2.41421	+	4.18154i	−0.170711	+	0.295680i
$201$	−7.75326	−	2.07748i	−0.546873	−	0.146534i
$202$			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
$207$	−0.0575273	−	0.214695i	−0.00399843	−	0.0149223i
$208$	−1.76604	−	3.05888i	−0.122453	−	0.212095i
$209$	−11.7820	+	11.7820i	−0.814981	+	0.814981i
$210$	−0.667228	+	0.869378i	−0.0460431	+	0.0599928i
$211$	−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
$214$	19.7904	−	5.30281i	1.35284	−	0.362493i
$215$	−0.232283	+	0.866894i	−0.0158416	+	0.0591217i
$216$	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
$221$	−11.4271	−	9.02812i	−0.768670	−	0.607297i
$222$	−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	$-0.212306\pi$
$224$	−0.345588	+	2.62308i	−0.0230906	+	0.175262i
$225$	4.82843			0.321895
$226$	11.6248	+	3.11485i	0.773268	+	0.207197i
$227$	10.4809	−	2.80836i	0.695645	−	0.186397i	0.106366	−	0.994327i	$-0.466079\pi$
$227$	10.4809	−	2.80836i	0.695645	−	0.186397i	0.589279	+	0.807930i	$0.299412\pi$
$228$	4.07840	−	1.09280i	0.270099	−	0.0723727i
$229$	−9.40287	+	5.42875i	−0.621359	+	0.358742i	−0.777398	−	0.629009i	$-0.783461\pi$
$229$	−9.40287	+	5.42875i	−0.621359	+	0.358742i	0.156039	+	0.987751i	$0.450128\pi$
$230$			0.0920666i			0.00607070i
$231$	−6.35681	+	8.28274i	−0.418248	+	0.544964i
$232$	−0.292893	−	0.292893i	−0.0192294	−	0.0192294i
$233$	−7.96274	−	2.13361i	−0.521657	−	0.139777i	−0.0116238	−	0.999932i	$-0.503700\pi$
$233$	−7.96274	−	2.13361i	−0.521657	−	0.139777i	−0.510033	+	0.860155i	$0.670367\pi$
$234$	−1.76604	+	3.05888i	−0.115450	+	0.199965i
$235$	−0.667169	−	2.48991i	−0.0435213	−	0.162424i
$236$	11.4009	−	6.58232i	0.742137	−	0.428473i
$237$	8.46943			0.550148
$238$	2.67297	+	10.5762i	0.173263	+	0.685551i
$239$	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
$241$	−3.67751	−	13.7247i	−0.236889	−	0.884082i	−0.977288	−	0.211915i	$-0.932030\pi$
$241$	−3.67751	−	13.7247i	−0.236889	−	0.884082i	0.740399	−	0.672168i	$-0.234637\pi$
$242$	2.28664	−	3.96057i	0.146990	−	0.254595i
$243$	−0.965926	−	0.258819i	−0.0619642	−	0.0166032i
$244$	10.3123	+	10.3123i	0.660175	+	0.660175i
$245$	−2.51131	+	1.44927i	−0.160442	+	0.0925906i
$246$		−	1.36539i		−	0.0870541i
$247$	−12.9154	+	7.45671i	−0.821787	+	0.474459i
$248$	−9.44602	+	2.53105i	−0.599823	+	0.160722i
$249$	−6.92994	+	1.85687i	−0.439167	+	0.117674i
$250$	−3.93235	−	1.05367i	−0.248704	−	0.0666399i
$251$	−3.89994			−0.246162			−0.123081	−	0.992397i	$-0.539277\pi$
$251$	−3.89994			−0.246162			−0.123081	+	0.992397i	$0.539277\pi$
$252$	2.44445	−	1.01225i	0.153986	−	0.0637660i
$253$			0.877138i			0.0551452i
$254$	8.50367	+	14.7288i	0.533568	+	0.924167i
$255$	−1.05874	+	1.34008i	−0.0663010	+	0.0839188i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.4435	−	6.60688i	0.713823	−	0.412126i	−0.0986519	−	0.995122i	$-0.531453\pi$
$257$	11.4435	−	6.60688i	0.713823	−	0.412126i	0.812475	+	0.582996i	$0.198120\pi$
$258$	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
$261$	−0.107206	+	0.400100i	−0.00663591	+	0.0247655i
$262$	−7.81669	+	2.09448i	−0.482917	+	0.129397i
$263$	−21.0565	−	12.1570i	−1.29840	−	0.749630i	−0.318270	−	0.948000i	$-0.603102\pi$
$263$	−21.0565	−	12.1570i	−1.29840	−	0.749630i	−0.980127	+	0.198370i	$0.936435\pi$
$264$	−3.41759	+	1.97315i	−0.210338	+	0.121439i
$265$	1.50683	+	1.50683i	0.0925637	+	0.0925637i
$266$	11.0754	+	1.45916i	0.679074	+	0.0894671i
$267$	−10.0820	+	10.0820i	−0.617007	+	0.617007i
$268$	−4.01338	−	6.95138i	−0.245156	−	0.424623i
$269$	6.66521	+	24.8749i	0.406385	+	1.51665i	0.801487	+	0.598012i	$0.204043\pi$
$269$	6.66521	+	24.8749i	0.406385	+	1.51665i	−0.395102	+	0.918637i	$0.629291\pi$
$270$	0.358719	+	0.207107i	0.0218310	+	0.0126041i
$271$	−6.42498	−	11.1284i	−0.390290	−	0.676001i	0.602198	−	0.798347i	$-0.294292\pi$
$271$	−6.42498	−	11.1284i	−0.390290	−	0.676001i	−0.992488	+	0.122345i	$0.960958\pi$
$272$	−0.595973	+	4.07981i	−0.0361361	+	0.247375i
$273$	−7.41444	+	5.68819i	−0.448742	+	0.344265i
$274$		−	4.78192i		−	0.288886i
$275$	−18.4052	−	4.93165i	−1.10987	−	0.297389i
$276$	0.111134	−	0.192490i	0.00668950	−	0.0115865i
$277$	−0.580276	−	2.16562i	−0.0348654	−	0.130120i	0.946300	−	0.323291i	$-0.104789\pi$
$277$	−0.580276	−	2.16562i	−0.0348654	−	0.130120i	−0.981165	+	0.193172i	$0.938123\pi$
$278$	0.141705	−	0.528849i	0.00849887	−	0.0317182i
$279$	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	$-0.326321\pi$
$282$	−1.61069	+	6.01118i	−0.0959152	+	0.357960i
$283$	3.15895	−	0.846439i	0.187780	−	0.0503156i	−0.163703	−	0.986510i	$-0.552344\pi$
$283$	3.15895	−	0.846439i	0.187780	−	0.0503156i	0.351484	+	0.936194i	$0.385677\pi$
$284$	−3.96582	−	14.8006i	−0.235328	−	0.878256i
$285$	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
$289$	3.93342	+	16.5387i	0.231378	+	0.972864i
$290$	0.0857864	−	0.148586i	0.00503755	−	0.00872530i
$291$	−0.781149	−	0.450997i	−0.0457918	−	0.0264379i
$292$	16.1340	+	4.32308i	0.944169	+	0.252989i
$293$	4.91330			0.287038			0.143519	−	0.989648i	$-0.454158\pi$
$293$	4.91330			0.287038			0.143519	+	0.989648i	$0.454158\pi$
$294$	7.00000	+	0.00132345i	0.408248	+	7.71849e-5i
$295$	3.85584	+	3.85584i	0.224495	+	0.224495i
$296$	2.15535	−	8.04387i	0.125277	−	0.467540i
$297$	3.41759	+	1.97315i	0.198309	+	0.114494i
$298$	−8.35711	−	4.82498i	−0.484114	−	0.279503i
$299$	−0.203191	+	0.758321i	−0.0117509	+	0.0438548i
$300$	3.41421	+	3.41421i	0.197120	+	0.197120i
$301$	5.29638	−	2.19325i	0.305278	−	0.126417i
$302$	22.7375			1.30840
$303$	7.63906	+	2.04688i	0.438852	+	0.117590i
$304$	3.65659	+	2.11113i	0.209720	+	0.121082i
$305$	−3.02039	+	5.23147i	−0.172947	+	0.299553i
$306$	3.83120	−	1.52378i	0.219015	−	0.0871085i
$307$	−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
$311$	0.461920	+	1.72391i	0.0261931	+	0.0977539i	0.977785	−	0.209611i	$-0.0672196\pi$
$311$	0.461920	+	1.72391i	0.0261931	+	0.0977539i	−0.951592	+	0.307364i	$0.900553\pi$
$312$	−3.41173	+	0.914171i	−0.193151	+	0.0517547i
$313$	5.64998	−	21.0860i	0.319356	−	1.19185i	−0.600510	−	0.799617i	$-0.705036\pi$
$313$	5.64998	−	21.0860i	0.319356	−	1.19185i	0.919865	−	0.392234i	$-0.128298\pi$
$314$			18.0941i			1.02111i
$315$	0.667063	+	0.869504i	0.0375848	+	0.0489910i
$316$	5.98879	+	5.98879i	0.336896	+	0.336896i
$317$	−2.10454	+	7.85427i	−0.118203	+	0.441140i	−0.999507	−	0.0314110i	$-0.990000\pi$
$317$	−2.10454	+	7.85427i	−0.118203	+	0.441140i	0.881304	+	0.472551i	$0.156667\pi$
$318$	−1.33153	−	4.96933i	−0.0746685	−	0.278666i
$319$	0.817305	−	1.41561i	0.0457603	−	0.0792592i
$320$	−0.400100	−	0.107206i	−0.0223662	−	0.00599302i
$321$		−	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
$326$	1.37270	+	5.12297i	0.0760266	+	0.283735i
$327$	−2.96234	−	5.13092i	−0.163818	−	0.283741i
$328$	0.965476	−	0.965476i	0.0533095	−	0.0533095i
$329$	−10.0246	+	13.0617i	−0.552672	+	0.720115i
$330$	−1.15584	−	1.15584i	−0.0636271	−	0.0636271i
$331$	−6.47739	+	3.73972i	−0.356030	+	0.205554i	−0.667338	−	0.744755i	$-0.732566\pi$
$331$	−6.47739	+	3.73972i	−0.356030	+	0.205554i	0.311308	+	0.950309i	$0.399233\pi$
$332$	−6.21322	−	3.58720i	−0.340994	−	0.196873i
$333$	−8.04387	+	2.15535i	−0.440801	+	0.118112i
$334$	0.928944	−	3.46686i	0.0508295	−	0.189698i
$335$	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
$340$	−1.69622	+	0.198933i	−0.0919905	+	0.0107886i
$341$	−19.2959	−	33.4215i	−1.04493	−	1.80988i
$342$		−	4.22227i		−	0.228314i
$343$	17.1085	+	7.09225i	0.923771	+	0.382945i
$344$	2.16670			0.116820
$345$	0.0889296	+	0.0238286i	0.00478781	+	0.00128289i
$346$	12.4114	−	3.32563i	0.667242	−	0.178787i
$347$	0.894520	−	0.239686i	0.0480203	−	0.0128670i	−0.234729	−	0.972061i	$-0.575420\pi$
$347$	0.894520	−	0.239686i	0.0480203	−	0.0128670i	0.282749	+	0.959194i	$0.408754\pi$
$348$	−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	$-0.0106989\pi$
$350$	4.88760	+	11.8029i	0.261253	+	0.630889i
$351$	2.49756	+	2.49756i	0.133310	+	0.133310i
$352$	−3.81183	−	1.02138i	−0.203171	−	0.0544396i
$353$	−10.7917	+	18.6918i	−0.574387	+	0.994867i	0.421721	+	0.906725i	$0.361426\pi$
$353$	−10.7917	+	18.6918i	−0.574387	+	0.994867i	−0.996108	+	0.0881413i	$0.971907\pi$
$354$	−3.40726	−	12.7161i	−0.181094	−	0.675852i
$355$	5.49657	−	3.17344i	0.291728	−	0.168429i
$356$	−14.2581			−0.755676
$357$	10.9076	+	0.155417i	0.577292	+	0.00822553i
$358$	8.70788			0.460226
$359$	−9.21420	+	5.31982i	−0.486307	+	0.280770i	−0.723041	−	0.690805i	$-0.757256\pi$
$359$	−9.21420	+	5.31982i	−0.486307	+	0.280770i	0.236734	+	0.971574i	$0.423923\pi$
$360$	0.107206	+	0.400100i	0.00565027	+	0.0210871i
$361$	−0.586224	+	1.01537i	−0.0308539	+	0.0534405i
$362$	−21.4965	−	5.75997i	−1.12983	−	0.302737i
$363$	−3.23379	−	3.23379i	−0.169730	−	0.169730i
$364$	−9.26495	−	1.22065i	−0.485616	−	0.0639792i
$365$			6.91866i			0.362139i
$366$	12.6299	−	7.29187i	0.660175	−	0.381152i
$367$	−16.3367	+	4.37740i	−0.852768	+	0.228498i	−0.658622	−	0.752474i	$-0.728860\pi$
$367$	−16.3367	+	4.37740i	−0.852768	+	0.228498i	−0.194146	+	0.980973i	$0.562194\pi$
$368$	0.214695	−	0.0575273i	0.0111917	−	0.00299882i
$369$	−1.31887	−	0.353389i	−0.0686574	−	0.0183967i
$370$	3.44941			0.179327
$371$	1.77792	−	13.4948i	0.0923052	−	0.700615i
$372$			9.77924i			0.507030i
$373$	13.7292	+	23.7797i	0.710871	+	1.23126i	0.964531	+	0.263970i	$0.0850322\pi$
$373$	13.7292	+	23.7797i	0.710871	+	1.23126i	−0.253660	+	0.967293i	$0.581635\pi$
$374$	−16.1602	+	1.89527i	−0.835626	+	0.0980023i
$375$	−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	$0.318536\pi$
$380$	−0.452654	+	1.68933i	−0.0232207	+	0.0866607i
$381$	16.4278	−	4.40183i	0.841624	−	0.225512i
$382$	−6.50517	−	3.75576i	−0.332834	−	0.192162i
$383$	−27.6865	+	15.9848i	−1.41471	+	0.816785i	−0.995828	−	0.0912533i	$-0.970913\pi$
$383$	−27.6865	+	15.9848i	−1.41471	+	0.816785i	−0.418886	+	0.908039i	$0.637579\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	−1.65464	−	3.99573i	−0.0843283	−	0.203641i
$386$	−3.35280	+	3.35280i	−0.170653	+	0.170653i
$387$	−1.08335	−	1.87641i	−0.0550697	−	0.0953834i
$388$	−0.233453	−	0.871259i	−0.0118518	−	0.0442315i
$389$	−18.9296	−	10.9290i	−0.959769	−	0.554123i	−0.0636674	−	0.997971i	$-0.520280\pi$
$389$	−18.9296	−	10.9290i	−0.959769	−	0.554123i	−0.896102	+	0.443848i	$0.853613\pi$
$390$	−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
$394$	10.9379	+	2.93080i	0.551043	+	0.147652i
$395$	−1.75408	+	3.03815i	−0.0882571	+	0.152866i
$396$	1.02138	+	3.81183i	0.0513261	+	0.191552i
$397$	−0.367119	+	1.37011i	−0.0184252	+	0.0687637i	−0.974526	−	0.224273i	$-0.927999\pi$
$397$	−0.367119	+	1.37011i	−0.0184252	+	0.0687637i	0.956101	+	0.293037i	$0.0946659\pi$
$398$	12.9913	+	12.9913i	0.651195	+	0.651195i
$399$	4.27596	−	10.3203i	0.214066	−	0.516662i
$400$			4.82843i			0.241421i
$401$	−6.44818	+	24.0649i	−0.322007	+	1.20175i	0.595280	+	0.803518i	$0.297041\pi$
$401$	−6.44818	+	24.0649i	−0.322007	+	1.20175i	−0.917287	+	0.398227i	$0.869625\pi$
$402$	−7.75326	+	2.07748i	−0.386697	+	0.103615i
$403$	−8.93990	−	33.3642i	−0.445328	−	1.66199i
$404$	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
$408$	3.78654	+	1.63160i	0.187462	+	0.0807761i
$409$	4.84577	−	8.39312i	0.239608	−	0.415013i	−0.720994	−	0.692941i	$-0.756314\pi$
$409$	4.84577	−	8.39312i	0.239608	−	0.415013i	0.960602	+	0.277928i	$0.0896478\pi$
$410$	0.489792	+	0.282781i	0.0241891	+	0.0139656i
$411$	−4.61898	−	1.23765i	−0.227837	−	0.0610488i
$412$	1.81212			0.0892769
$413$	4.54954	−	34.5320i	0.223868	−	1.69921i
$414$	−0.157168	−	0.157168i	−0.00772437	−	0.00772437i
$415$	0.769142	−	2.87048i	0.0377557	−	0.140906i
$416$	−3.05888	−	1.76604i	−0.149974	−	0.0865874i
$417$	−0.474153	−	0.273752i	−0.0232194	−	0.0134057i
$418$	−4.31253	+	16.0946i	−0.210933	+	0.787211i
$419$	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	$0.718323\pi$
$420$	−0.143147	+	1.08652i	−0.00698487	+	0.0530166i
$421$	−28.1922			−1.37400			−0.687002	−	0.726655i	$-0.741074\pi$
$421$	−28.1922			−1.37400			−0.687002	+	0.726655i	$0.741074\pi$
$422$	−11.5976	−	3.10758i	−0.564564	−	0.151274i
$423$	5.38947	+	3.11161i	0.262045	+	0.151292i
$424$	2.57232	−	4.45538i	0.124923	−	0.216373i
$425$	7.35744	+	18.4987i	0.356888	+	0.897318i
$426$	−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
$430$	0.232283	+	0.866894i	0.0112017	+	0.0418053i
$431$	−18.2320	+	4.88524i	−0.878203	+	0.235314i	−0.669632	−	0.742693i	$-0.733548\pi$
$431$	−18.2320	+	4.88524i	−0.878203	+	0.235314i	−0.208572	+	0.978007i	$0.566881\pi$
$432$	0.258819	−	0.965926i	0.0124524	−	0.0464731i
$433$			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
$436$	1.53342	−	5.72280i	0.0734375	−	0.274072i
$437$	−0.242896	−	0.906500i	−0.0116193	−	0.0433638i
$438$	8.35156	−	14.4653i	0.399053	−	0.691180i
$439$	−20.7303	−	5.55466i	−0.989401	−	0.265109i	−0.272402	−	0.962183i	$-0.587818\pi$
$439$	−20.7303	−	5.55466i	−0.989401	−	0.265109i	−0.716999	+	0.697074i	$0.754485\pi$
$440$		−	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	−0.925882	−	0.377813i	$-0.876676\pi$
$443$	−16.6305	−	28.8048i	−0.790137	−	1.36856i	0.135745	−	0.990744i	$-0.456657\pi$
$444$	−7.21193	−	4.16381i	−0.342263	−	0.197606i
$445$	−1.52856	−	5.70465i	−0.0724605	−	0.270426i
$446$	−9.23791	−	16.0005i	−0.437428	−	0.757647i
$447$	−6.82355	+	6.82355i	−0.322743	+	0.322743i
$448$	1.01225	+	2.44445i	0.0478245	+	0.115489i
$449$	−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
$452$	11.6248	−	3.11485i	0.546783	−	0.146510i
$453$	5.88490	−	21.9628i	0.276497	−	1.03190i
$454$	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	$-0.734858\pi$
$457$	−7.87175	+	4.54476i	−0.368225	+	0.212595i	0.304458	+	0.952526i	$0.401525\pi$
$458$	−5.42875	+	9.40287i	−0.253669	+	0.439367i
$459$	−0.480266	−	4.09504i	−0.0224169	−	0.191140i
$460$	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	$0.949608\pi$
$462$	−1.36379	+	10.3515i	−0.0634494	+	0.481594i
$463$	−22.5692			−1.04888			−0.524441	−	0.851447i	$-0.675726\pi$
$463$	−22.5692			−1.04888			−0.524441	+	0.851447i	$0.675726\pi$
$464$	−0.400100	−	0.107206i	−0.0185742	−	0.00497693i
$465$	−3.91267	+	1.04840i	−0.181446	+	0.0486183i
$466$	−7.96274	+	2.13361i	−0.368867	+	0.0988376i
$467$	9.47354	−	5.46955i	0.438383	−	0.253101i	−0.264528	−	0.964378i	$-0.585216\pi$
$467$	9.47354	−	5.46955i	0.438383	−	0.253101i	0.702911	+	0.711277i	$0.251883\pi$
$468$			3.53208i			0.163271i
$469$	−21.0549	−	2.77395i	−0.972224	−	0.128089i
$470$	−1.82274	−	1.82274i	−0.0840768	−	0.0840768i
$471$	17.4776	+	4.68310i	0.805323	+	0.215786i
$472$	6.58232	−	11.4009i	0.302976	−	0.524770i
$473$	2.21301	+	8.25908i	0.101754	+	0.379753i
$474$	7.33474	−	4.23471i	0.336896	−	0.194507i
$475$	20.3869			0.935416
$476$	7.60295	+	7.82274i	0.348480	+	0.358555i
$477$	−5.14463			−0.235557
$478$	4.05568	−	2.34155i	0.185503	−	0.107100i
$479$	4.58305	+	17.1042i	0.209405	+	0.781511i	0.988062	+	0.154060i	$0.0492349\pi$
$479$	4.58305	+	17.1042i	0.209405	+	0.781511i	−0.778656	+	0.627451i	$0.784098\pi$
$480$	−0.207107	+	0.358719i	−0.00945309	+	0.0163732i
$481$	28.4116	+	7.61287i	1.29546	+	0.347117i
$482$	−10.0471	−	10.0471i	−0.457635	−	0.457635i
$483$	−0.224992	−	0.543325i	−0.0102375	−	0.0247221i
$484$		−	4.57327i		−	0.207876i
$485$	0.323563	−	0.186809i	0.0146922	−	0.00848256i
$486$	−0.965926	+	0.258819i	−0.0438153	+	0.0117403i
$487$	27.9088	−	7.47814i	1.26467	−	0.338867i	0.436682	−	0.899616i	$-0.356153\pi$
$487$	27.9088	−	7.47814i	1.26467	−	0.338867i	0.827986	+	0.560749i	$0.189487\pi$
$488$	14.0868	+	3.77455i	0.637680	+	0.170866i
$489$	5.30369			0.239841
$490$	−1.45022	+	2.51076i	−0.0655144	+	0.113425i
$491$		−	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
$493$	−1.69622	+	0.198933i	−0.0763939	+	0.00895948i
$494$	−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
$499$	6.28060	−	23.4395i	0.281158	−	1.04930i	−0.670443	−	0.741961i	$-0.733896\pi$
$499$	6.28060	−	23.4395i	0.281158	−	1.04930i	0.951601	−	0.307335i	$-0.0994373\pi$
$500$	−3.93235	+	1.05367i	−0.175860	+	0.0471215i
$501$	−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	$0.565083\pi$
$504$	1.61083	−	2.09886i	0.0717521	−	0.0934908i
$505$	−2.31636	+	2.31636i	−0.103076	+	0.103076i
$506$	0.438569	+	0.759624i	0.0194968	+	0.0337694i
$507$	0.135719	+	0.506509i	0.00602748	+	0.0224949i
$508$	14.7288	+	8.50367i	0.653485	+	0.377290i
$509$	−2.69371	−	4.66564i	−0.119397	−	0.206801i	0.800132	−	0.599824i	$-0.204763\pi$
$509$	−2.69371	−	4.66564i	−0.119397	−	0.206801i	−0.919529	+	0.393023i	$0.871429\pi$
$510$	−0.246860	+	1.68991i	−0.0109311	+	0.0748305i
$511$	35.0626	−	26.8992i	1.55108	−	1.18995i
$512$			1.00000i			0.0441942i
$513$	−4.07840	−	1.09280i	−0.180066	−	0.0482485i
$514$	6.60688	−	11.4435i	0.291417	−	0.504749i
$515$	0.194271	+	0.725030i	0.00856061	+	0.0319486i
$516$	0.560782	−	2.09287i	0.0246870	−	0.0921333i
$517$	−17.3656	−	17.3656i	−0.763740	−	0.763740i
$518$	−13.4111	−	17.4811i	−0.589249	−	0.768075i
$519$		−	12.8493i		−	0.564019i
$520$	0.378662	−	1.41319i	0.0166054	−	0.0619723i
$521$	17.4348	−	4.67164i	0.763832	−	0.204668i	0.144187	−	0.989550i	$-0.453943\pi$
$521$	17.4348	−	4.67164i	0.763832	−	0.204668i	0.619645	+	0.784882i	$0.287277\pi$
$522$	0.107206	+	0.400100i	0.00469229	+	0.0175119i
$523$	−3.15034	−	5.45655i	−0.137755	−	0.238598i	0.788892	−	0.614532i	$-0.210655\pi$
$523$	−3.15034	−	5.45655i	−0.137755	−	0.238598i	−0.926646	+	0.375934i	$0.877322\pi$
$524$	−5.72222	+	5.72222i	−0.249976	+	0.249976i
$525$	12.6657	−	1.66625i	0.552776	−	0.0727212i
$526$	−24.3139			−1.06014
$527$	−15.9558	+	37.0295i	−0.695045	+	1.61303i
$528$	−1.97315	+	3.41759i	−0.0858703	+	0.148732i
$529$	19.8758	+	11.4753i	0.864165	+	0.498926i
$530$	2.05837	+	0.551537i	0.0894097	+	0.0239573i
$531$	−13.1646			−0.571297
$532$	10.3211	−	4.27401i	0.447478	−	0.185302i
$533$	3.41014	+	3.41014i	0.147710	+	0.147710i
$534$	−3.69026	+	13.7722i	−0.159693	+	0.595983i
$535$	7.34962	+	4.24330i	0.317752	+	0.183454i
$536$	−6.95138	−	4.01338i	−0.300254	−	0.173352i
$537$	2.25377	−	8.41117i	0.0972572	−	0.362969i
$538$	18.2097	+	18.2097i	0.785075	+	0.785075i
$539$	−13.8166	+	23.9206i	−0.595122	+	1.03033i
$540$	0.414214			0.0178249
$541$	2.07599	+	0.556259i	0.0892536	+	0.0239154i	0.303169	−	0.952937i	$-0.401955\pi$
$541$	2.07599	+	0.556259i	0.0892536	+	0.0239154i	−0.213916	+	0.976852i	$0.568622\pi$
$542$	−11.1284	−	6.42498i	−0.478005	−	0.275976i
$543$	−11.1274	+	19.2732i	−0.477522	+	0.827093i
$544$	1.52378	+	3.83120i	0.0653313	+	0.164261i
$545$	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
$549$	−3.77455	−	14.0868i	−0.161094	−	0.601210i
$550$	−18.4052	+	4.93165i	−0.784798	+	0.210286i
$551$	−0.452654	+	1.68933i	−0.0192837	+	0.0719678i
$552$		−	0.222269i		−	0.00946038i
$553$	22.2166	−	2.92273i	0.944745	−	0.124287i
$554$	−1.58534	−	1.58534i	−0.0673548	−	0.0673548i
$555$	0.892774	−	3.33188i	0.0378962	−	0.141430i
$556$	−0.141705	−	0.528849i	−0.00600961	−	0.0224282i
$557$	−5.38489	+	9.32690i	−0.228165	+	0.395194i	−0.957264	−	0.289214i	$-0.906606\pi$
$557$	−5.38489	+	9.32690i	−0.228165	+	0.395194i	0.729099	+	0.684408i	$0.239939\pi$
$558$	9.44602	+	2.53105i	0.399882	+	0.107148i
$559$			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	$-0.0971544\pi$
$563$	27.7715	+	16.0339i	1.17043	+	0.675747i	0.216647	+	0.976250i	$0.430488\pi$
$564$	1.61069	+	6.01118i	0.0678223	+	0.253116i
$565$	2.49250	+	4.31713i	0.104860	+	0.181623i
$566$	2.31251	−	2.31251i	0.0972022	−	0.0972022i
$567$	−2.62308	−	0.345588i	−0.110159	−	0.0145133i
$568$	−10.8348	−	10.8348i	−0.454619	−	0.454619i
$569$	−33.1177	+	19.1205i	−1.38836	+	0.801572i	−0.993131	−	0.117008i	$-0.962670\pi$
$569$	−33.1177	+	19.1205i	−1.38836	+	0.801572i	−0.395233	+	0.918581i	$0.629336\pi$
$570$	1.51461	+	0.874460i	0.0634400	+	0.0366271i
$571$	−30.6004	+	8.19936i	−1.28059	+	0.343133i	−0.834078	−	0.551646i	$-0.814000\pi$
$571$	−30.6004	+	8.19936i	−1.28059	+	0.343133i	−0.446510	+	0.894779i	$0.647333\pi$
$572$	3.60759	−	13.4637i	0.150841	−	0.562946i
$573$	−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	−0.887865	−	0.460104i	$-0.847812\pi$
$577$	−1.09225	+	1.89183i	−0.0454709	+	0.0787580i	0.842394	+	0.538862i	$0.181146\pi$
$578$	11.6758	+	12.3562i	0.485649	+	0.513951i
$579$	2.37079	+	4.10632i	0.0985265	+	0.170653i
$580$		−	0.171573i		−	0.00712418i
$581$	−17.5375	+	7.26232i	−0.727577	+	0.301292i
$582$	−0.901993			−0.0373888
$583$	19.6105	+	5.25461i	0.812183	+	0.217624i
$584$	16.1340	−	4.32308i	0.667628	−	0.178890i
$585$	−1.41319	+	0.378662i	−0.0584280	+	0.0156557i
$586$	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	$-0.0790623\pi$
$588$	6.06284	−	3.49885i	0.250027	−	0.144290i
$589$	29.1969	+	29.1969i	1.20304	+	1.20304i
$590$	5.26717	+	1.41133i	0.216846	+	0.0581037i
$591$	5.66187	−	9.80665i	0.232898	−	0.403392i
$592$	−2.15535	−	8.04387i	−0.0885842	−	0.330601i
$593$	1.87212	−	1.08087i	0.0768788	−	0.0443860i	−0.461068	−	0.887365i	$-0.652534\pi$
$593$	1.87212	−	1.08087i	0.0768788	−	0.0443860i	0.537947	+	0.842979i	$0.319200\pi$
$594$	3.94630			0.161919
$595$	−2.31479	+	3.88058i	−0.0948971	+	0.159088i
$596$	−9.64996			−0.395278
$597$	15.9110	−	9.18624i	0.651195	−	0.375968i
$598$	0.203191	+	0.758321i	0.00830912	+	0.0310100i
$599$	−10.1460	+	17.5734i	−0.414556	+	0.718031i	−0.995382	−	0.0959963i	$-0.969396\pi$
$599$	−10.1460	+	17.5734i	−0.414556	+	0.718031i	0.580826	+	0.814028i	$0.302730\pi$
$600$	4.66390	+	1.24969i	0.190403	+	0.0510183i
$601$	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	$0.615402\pi$
$602$	3.49018	−	4.54760i	0.142249	−	0.185346i
$603$			8.02676i			0.326875i
$604$	19.6913	−	11.3688i	0.801226	−	0.462588i
$605$	1.82976	−	0.490284i	0.0743905	−	0.0199329i
$606$	7.63906	−	2.04688i	0.310315	−	0.0831488i
$607$	−22.3535	−	5.98959i	−0.907299	−	0.243110i	−0.225151	−	0.974324i	$-0.572288\pi$
$607$	−22.3535	−	5.98959i	−0.907299	−	0.243110i	−0.682148	+	0.731214i	$0.738954\pi$
$608$	4.22227			0.171236
$609$	−0.143147	+	1.08652i	−0.00580062	+	0.0440279i
$610$			6.04078i			0.244584i
$611$	−10.9905	−	19.0361i	−0.444627	−	0.770117i
$612$	2.55603	−	3.23523i	0.103321	−	0.130776i
$613$	1.98752	−	3.44249i	0.0802753	−	0.139041i	−0.823093	−	0.567907i	$-0.807753\pi$
$613$	1.98752	−	3.44249i	0.0802753	−	0.139041i	0.903368	+	0.428866i	$0.141087\pi$
$614$	−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	$0.385190\pi$
$618$	0.469012	−	1.75038i	0.0188664	−	0.0704105i
$619$	44.8503	−	12.0176i	1.80269	−	0.483028i	0.808294	−	0.588779i	$-0.200391\pi$
$619$	44.8503	−	12.0176i	1.80269	−	0.483028i	0.994393	+	0.105751i	$0.0337246\pi$
$620$	−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
$623$	−22.9673	+	29.9257i	−0.920166	+	1.19895i
$624$	−2.49756	+	2.49756i	−0.0999825	+	0.0999825i
$625$	11.2279	+	19.4473i	0.449117	+	0.777893i
$626$	−5.64998	−	21.0860i	−0.225819	−	0.842766i
$627$	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	$-0.146263\pi$
$632$	8.18084	+	2.19205i	0.325416	+	0.0871950i
$633$	−6.00337	+	10.3982i	−0.238613	+	0.413289i
$634$	2.10454	+	7.85427i	0.0835821	+	0.311933i
$635$	−1.82330	+	6.80463i	−0.0723553	+	0.270034i
$636$	−3.63781	−	3.63781i	−0.144248	−	0.144248i
$637$	−17.4862	+	17.4796i	−0.692830	+	0.692568i
$638$		−	1.63461i		−	0.0647148i
$639$	−3.96582	+	14.8006i	−0.156885	+	0.585504i
$640$	−0.400100	+	0.107206i	−0.0158153	+	0.00423770i
$641$	−6.98429	−	26.0657i	−0.275863	−	1.02953i	−0.955261	−	0.295764i	$-0.904426\pi$
$641$	−6.98429	−	26.0657i	−0.275863	−	1.02953i	0.679398	−	0.733770i	$-0.262241\pi$
$642$	−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
$646$	16.1764	−	6.43379i	0.636450	−	0.253134i
$647$	4.60750	−	7.98043i	0.181140	−	0.313743i	−0.761129	−	0.648600i	$-0.775355\pi$
$647$	4.60750	−	7.98043i	0.181140	−	0.313743i	0.942269	+	0.334857i	$0.108688\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	50.1814	+	13.4461i	1.96979	+	0.527804i
$650$	−17.0544			−0.668929
$651$	20.5253	+	15.7527i	0.804450	+	0.617397i
$652$	3.75028	+	3.75028i	0.146872	+	0.146872i
$653$	−6.28568	+	23.4585i	−0.245978	+	0.918001i	0.726912	+	0.686731i	$0.240955\pi$
$653$	−6.28568	+	23.4585i	−0.245978	+	0.918001i	−0.972890	+	0.231270i	$0.925712\pi$
$654$	−5.13092	−	2.96234i	−0.200635	−	0.115837i
$655$	−2.90291	−	1.67600i	−0.113426	−	0.0654867i
$656$	0.353389	−	1.31887i	0.0137975	−	0.0514930i
$657$	−11.8109	−	11.8109i	−0.460787	−	0.460787i
$658$	−2.15067	+	16.3240i	−0.0838419	+	0.636378i
$659$	−15.4667			−0.602499			−0.301249	−	0.953545i	$-0.597404\pi$
$659$	−15.4667			−0.602499			−0.301249	+	0.953545i	$0.597404\pi$
$660$	−1.57891	−	0.423068i	−0.0614591	−	0.0164679i
$661$	11.1725	+	6.45045i	0.434560	+	0.250894i	0.701288	−	0.712879i	$-0.252609\pi$
$661$	11.1725	+	6.45045i	0.434560	+	0.250894i	−0.266727	+	0.963772i	$0.585942\pi$
$662$	−3.73972	+	6.47739i	−0.145349	+	0.251751i
$663$	−5.76294	+	13.3744i	−0.223814	+	0.519418i
$664$	−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
$668$	−0.928944	−	3.46686i	−0.0359419	−	0.134137i
$669$	−17.8463	+	4.78189i	−0.689977	+	0.184879i
$670$	0.860520	−	3.21150i	0.0332448	−	0.124071i
$671$			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	$0.710950\pi$
$674$	2.19991	−	8.21019i	0.0847375	−	0.316245i
$675$	−1.24969	−	4.66390i	−0.0481005	−	0.179514i
$676$	−0.262188	+	0.454124i	−0.0100842	+	0.0174663i
$677$	46.0329	+	12.3345i	1.76919	+	0.474053i	0.988545	−	0.150925i	$-0.0482251\pi$
$677$	46.0329	+	12.3345i	1.76919	+	0.474053i	0.780643	+	0.624977i	$0.214892\pi$
$678$		−	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
$683$	10.8813	+	40.6094i	0.416360	+	1.55388i	0.782096	+	0.623158i	$0.214151\pi$
$683$	10.8813	+	40.6094i	0.416360	+	1.55388i	−0.365736	+	0.930719i	$0.619183\pi$
$684$	−2.11113	−	3.65659i	−0.0807212	−	0.139813i
$685$	1.40059	−	1.40059i	0.0535138	−	0.0535138i
$686$	18.3625	−	2.41217i	0.701084	−	0.0920971i
$687$	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
$690$	0.0889296	−	0.0238286i	0.00338549	−	0.000907139i
$691$	8.52138	−	31.8022i	0.324169	−	1.20981i	−0.590976	−	0.806689i	$-0.701257\pi$
$691$	8.52138	−	31.8022i	0.324169	−	1.20981i	0.915145	−	0.403125i	$-0.132076\pi$
$692$	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
$697$	−0.655751	−	5.59132i	−0.0248383	−	0.211786i
$698$	−0.627799	−	1.08738i	−0.0237625	−	0.0411579i
$699$			8.24364i			0.311803i
$700$	10.1342	+	7.77777i	0.383037	+	0.293972i
$701$	20.0411			0.756942			0.378471	−	0.925613i	$-0.376450\pi$
$701$	20.0411			0.756942			0.378471	+	0.925613i	$0.376450\pi$
$702$	3.41173	+	0.914171i	0.128768	+	0.0345032i
$703$	−33.9634	+	9.10046i	−1.28095	+	0.343230i
$704$	−3.81183	+	1.02138i	−0.143664	+	0.0384946i
$705$	−2.23239	+	1.28887i	−0.0840768	+	0.0485417i
$706$			21.5835i			0.812305i
$707$	20.7447	+	2.73309i	0.780186	+	0.102789i
$708$	−9.30881	−	9.30881i	−0.349847	−	0.349847i
$709$	−1.36147	−	0.364804i	−0.0511309	−	0.0137005i	0.233163	−	0.972438i	$-0.425092\pi$
$709$	−1.36147	−	0.364804i	−0.0511309	−	0.0137005i	−0.284294	+	0.958737i	$0.591759\pi$
$710$	3.17344	−	5.49657i	0.119097	−	0.206282i
$711$	−2.19205	−	8.18084i	−0.0822083	−	0.306805i
$712$	−12.3479	+	7.12903i	−0.462755	+	0.267172i
$713$	2.17362			0.0814027
$714$	9.52397	−	5.31921i	0.356426	−	0.199066i
$715$	5.77358			0.215920
$716$	7.54125	−	4.35394i	0.281830	−	0.162714i
$717$	−1.21208	−	4.52353i	−0.0452658	−	0.168934i
$718$	−5.31982	+	9.21420i	−0.198534	+	0.343871i
$719$	25.5247	+	6.83932i	0.951910	+	0.255063i	0.701172	−	0.712992i	$-0.252660\pi$
$719$	25.5247	+	6.83932i	0.951910	+	0.255063i	0.250737	+	0.968055i	$0.419327\pi$
$720$	0.292893	+	0.292893i	0.0109155	+	0.0109155i
$721$	2.91902	−	3.80340i	0.108710	−	0.141646i
$722$			1.17245i			0.0436340i
$723$	−12.3052	+	7.10440i	−0.457635	+	0.264216i
$724$	−21.4965	+	5.75997i	−0.798911	+	0.214067i
$725$	−1.93185	+	0.517638i	−0.0717472	+	0.0192246i
$726$	−4.41744	−	1.18365i	−0.163947	−	0.0439294i
$727$	−18.4677			−0.684928			−0.342464	−	0.939531i	$-0.611261\pi$
$727$	−18.4677			−0.684928			−0.342464	+	0.939531i	$0.611261\pi$
$728$	−8.63401	+	3.57537i	−0.319998	+	0.132512i
$729$			1.00000i			0.0370370i
$730$	3.45933	+	5.99173i	0.128035	+	0.221764i
$731$	5.53814	−	7.00976i	0.204835	−	0.259265i
$732$	7.29187	−	12.6299i	0.269515	−	0.466814i
$733$	−2.51288	+	1.45081i	−0.0928153	+	0.0535869i	−0.545689	−	0.837988i	$-0.683732\pi$
$733$	−2.51288	+	1.45081i	−0.0928153	+	0.0535869i	0.452874	+	0.891575i	$0.350399\pi$
$734$	−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
$737$	8.19835	−	30.5967i	0.301990	−	1.12704i
$738$	−1.31887	+	0.353389i	−0.0485481	+	0.0130084i
$739$	−1.35581	−	0.782780i	−0.0498744	−	0.0287950i	0.474855	−	0.880064i	$-0.342500\pi$
$739$	−1.35581	−	0.782780i	−0.0498744	−	0.0287950i	−0.524730	+	0.851269i	$0.675834\pi$
$740$	2.98728	−	1.72471i	0.109815	−	0.0634015i
$741$	10.5454	+	10.5454i	0.387394	+	0.387394i
$742$	−5.20768	−	12.5758i	−0.191180	−	0.461672i
$743$	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
$745$	−1.03454	−	3.86094i	−0.0379025	−	0.141454i
$746$	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
$751$	3.40702	+	0.912909i	0.124324	+	0.0333125i	0.320445	−	0.947267i	$-0.396168\pi$
$751$	3.40702	+	0.912909i	0.124324	+	0.0333125i	−0.196120	+	0.980580i	$0.562834\pi$
$752$	−3.11161	+	5.38947i	−0.113469	+	0.196534i
$753$	1.00938	+	3.76705i	0.0367838	+	0.137279i
$754$	0.378662	−	1.41319i	0.0137901	−	0.0514652i
$755$	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	$0.803358\pi$
$758$	−2.15306	+	8.03532i	−0.0782025	+	0.291856i
$759$	0.847250	−	0.227020i	0.0307532	−	0.00824030i
$760$	0.452654	+	1.68933i	0.0164195	+	0.0612784i
$761$	13.9540	+	24.1690i	0.505831	+	0.876125i	0.999977	+	0.00674606i	$0.00214735\pi$
$761$	13.9540	+	24.1690i	0.505831	+	0.876125i	−0.494146	+	0.869379i	$0.664519\pi$
$762$	12.0260	−	12.0260i	0.435656	−	0.435656i
$763$	−9.54130	−	12.4369i	−0.345418	−	0.450246i
$764$	−7.51153			−0.271758
$765$	1.56844	+	0.675829i	0.0567069	+	0.0244347i
$766$	−15.9848	+	27.6865i	−0.577555	+	1.00035i
$767$	40.2690	+	23.2493i	1.45403	+	0.839484i
$768$	0.965926	+	0.258819i	0.0348548	+	0.00933933i
$769$	54.0208			1.94804			0.974021	−	0.226460i	$-0.0727151\pi$
$769$	54.0208			1.94804			0.974021	+	0.226460i	$0.0727151\pi$
$770$	−3.43082	−	2.63308i	−0.123638	−	0.0948896i
$771$	−9.34354	−	9.34354i	−0.336499	−	0.336499i
$772$	−1.22721	+	4.58001i	−0.0441682	+	0.164838i
$773$	−31.0380	−	17.9198i	−1.11636	−	0.644530i	−0.175890	−	0.984410i	$-0.556280\pi$
$773$	−31.0380	−	17.9198i	−1.11636	−	0.644530i	−0.940469	+	0.339879i	$0.889614\pi$
$774$	−1.87641	−	1.08335i	−0.0674463	−	0.0389401i
$775$	−12.2210	+	45.6094i	−0.438992	+	1.63834i
$776$	−0.637806	−	0.637806i	−0.0228959	−	0.0228959i
$777$	−20.3565	+	8.42967i	−0.730284	+	0.302413i
$778$	−21.8580			−0.783648
$779$	−5.56860	−	1.49210i	−0.199516	−	0.0534601i
$780$	−1.26703	−	0.731519i	−0.0453669	−	0.0261926i
$781$	30.2341	−	52.3669i	1.08186	−	1.87384i
$782$	0.362653	−	0.841629i	0.0129684	−	0.0300966i
$783$	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
$787$	−4.84052	−	18.0651i	−0.172546	−	0.643950i	−0.996957	−	0.0779582i	$-0.975160\pi$
$787$	−4.84052	−	18.0651i	−0.172546	−	0.643950i	0.824411	−	0.565992i	$-0.191507\pi$
$788$	10.9379	−	2.93080i	0.389646	−	0.104405i
$789$	−6.29290	+	23.4854i	−0.224033	+	0.836103i
$790$			3.50815i			0.124814i
$791$	12.1879	−	29.4163i	0.433351	−	1.04592i
$792$	2.79045	+	2.79045i	0.0991545	+	0.0991545i
$793$	−13.3320	+	49.7558i	−0.473434	+	1.76688i
$794$	0.367119	+	1.37011i	0.0130286	+	0.0486233i
$795$	1.06549	−	1.84548i	0.0377890	−	0.0654524i
$796$	17.7465	+	4.75515i	0.629006	+	0.168542i
$797$			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
$802$	6.44818	+	24.0649i	0.227693	+	0.849763i
$803$	32.9577	+	57.0845i	1.16305	+	2.01447i
$804$	−5.67578	+	5.67578i	−0.200169	+	0.200169i
$805$	0.241499	+	0.0318171i	0.00851171	+	0.00112141i
$806$	−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
$809$	−3.41727	+	0.915654i	−0.120145	+	0.0321927i	−0.318390	−	0.947960i	$-0.603142\pi$
$809$	−3.41727	+	0.915654i	−0.120145	+	0.0321927i	0.198246	+	0.980152i	$0.436476\pi$
$810$	0.107206	−	0.400100i	0.00376685	−	0.0140581i
$811$	−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
$816$	4.09504	−	0.480266i	0.143355	−	0.0168127i
$817$	−4.57418	−	7.92272i	−0.160030	−	0.277181i
$818$		−	9.69154i		−	0.338857i
$819$	7.41336	+	5.68959i	0.259044	+	0.198810i
$820$	0.565563			0.0197503
$821$	−17.5583	−	4.70474i	−0.612790	−	0.164197i	−0.0609420	−	0.998141i	$-0.519410\pi$
$821$	−17.5583	−	4.70474i	−0.612790	−	0.164197i	−0.551848	+	0.833945i	$0.686077\pi$
$822$	−4.61898	+	1.23765i	−0.161105	+	0.0431680i
$823$	−34.8150	+	9.32865i	−1.21358	+	0.325176i	−0.808164	−	0.588958i	$-0.799538\pi$
$823$	−34.8150	+	9.32865i	−1.21358	+	0.325176i	−0.405411	+	0.914134i	$0.632872\pi$
$824$	1.56934	−	0.906062i	0.0546707	−	0.0315641i
$825$			19.0544i			0.663390i
$826$	−13.3260	−	32.1803i	−0.463670	−	1.11970i
$827$	−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	$-0.579432\pi$
$828$	−0.214695	−	0.0575273i	−0.00746116	−	0.00199921i
$829$	−8.39025	+	14.5323i	−0.291406	+	0.504729i	−0.974142	−	0.225935i	$-0.927456\pi$
$829$	−8.39025	+	14.5323i	−0.291406	+	0.504729i	0.682737	+	0.730664i	$0.260790\pi$
$830$	−0.769142	−	2.87048i	−0.0266973	−	0.0996357i
$831$	−1.94164	+	1.12101i	−0.0673548	+	0.0388873i
$832$	−3.53208			−0.122453
$833$	28.6659	−	3.35644i	0.993215	−	0.116294i
$834$	−0.547504			−0.0189585
$835$	1.28750	−	0.743340i	0.0445559	−	0.0257243i
$836$	4.31253	+	16.0946i	0.149152	+	0.556643i
$837$	4.88962	−	8.46907i	0.169010	−	0.292734i
$838$	3.92873	+	1.05270i	0.135716	+	0.0363649i
$839$	−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	$0.987164\pi$
$840$	0.419289	+	1.01252i	0.0144669	+	0.0349354i
$841$			28.8284i			0.994084i
$842$	−24.4152	+	14.0961i	−0.841403	+	0.485784i
$843$	−27.6817	+	7.41728i	−0.953408	+	0.255465i
$844$	−11.5976	+	3.10758i	−0.399207	+	0.106967i
$845$	−0.209803	−	0.0562165i	−0.00721744	−	0.00193391i
$846$	6.22323			0.213959
$847$	−9.59867	−	7.36676i	−0.329814	−	0.253125i
$848$		−	5.14463i		−	0.176667i
$849$	−1.63519	−	2.83224i	−0.0561197	−	0.0972022i
$850$	15.6211	+	12.3416i	0.535798	+	0.423314i
$851$	−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
$856$	5.30281	−	19.7904i	0.181246	−	0.676420i
$857$	37.8069	−	10.1303i	1.29146	−	0.346045i	0.453244	−	0.891386i	$-0.350267\pi$
$857$	37.8069	−	10.1303i	1.29146	−	0.346045i	0.838214	+	0.545341i	$0.183600\pi$
$858$	−12.0712	−	6.96933i	−0.412105	−	0.237929i
$859$	−31.7966	+	18.3578i	−1.08488	+	0.626358i	−0.932210	−	0.361918i	$-0.882122\pi$
$859$	−31.7966	+	18.3578i	−1.08488	+	0.626358i	−0.152675	+	0.988277i	$0.548789\pi$
$860$	0.634610	+	0.634610i	0.0216400	+	0.0216400i
$861$	−3.58153	−	0.471862i	−0.122058	−	0.0160810i
$862$	−13.3467	+	13.3467i	−0.454591	+	0.454591i
$863$	17.2622	+	29.8991i	0.587613	+	1.01778i	0.994544	+	0.104317i	$0.0332656\pi$
$863$	17.2622	+	29.8991i	0.587613	+	1.01778i	−0.406931	+	0.913459i	$0.633401\pi$
$864$	−0.258819	−	0.965926i	−0.00880520	−	0.0328615i
$865$	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
$870$	−0.165727	−	0.0444063i	−0.00561866	−	0.00150552i
$871$	14.1756	−	24.5529i	0.480322	−	0.831942i
$872$	−1.53342	−	5.72280i	−0.0519281	−	0.193798i
$873$	−0.233453	+	0.871259i	−0.00790119	+	0.0294876i
$874$	−0.663604	−	0.663604i	−0.0224467	−	0.0224467i
$875$	−4.12284	+	9.95075i	−0.139377	+	0.336397i
$876$		−	16.7031i		−	0.564346i
$877$	6.46415	−	24.1245i	0.218279	−	0.814628i	−0.766708	−	0.641996i	$-0.778106\pi$
$877$	6.46415	−	24.1245i	0.218279	−	0.814628i	0.984987	−	0.172631i	$-0.0552269\pi$
$878$	−20.7303	+	5.55466i	−0.699612	+	0.187461i
$879$	−1.27166	−	4.74589i	−0.0428919	−	0.160075i
$880$	−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	$0.705296\pi$
$884$	−13.5321	+	5.38210i	−0.455135	+	0.181020i
$885$	2.72649	−	4.72242i	0.0916499	−	0.158742i
$886$	−28.8048	−	16.6305i	−0.967716	−	0.558711i
$887$	16.8240	+	4.50797i	0.564893	+	0.151363i	0.529954	−	0.848027i	$-0.322209\pi$
$887$	16.8240	+	4.50797i	0.564893	+	0.151363i	0.0349399	+	0.999389i	$0.488876\pi$
$888$	−8.32762			−0.279457
$889$	41.5736	−	17.2158i	1.39433	−	0.577398i
$890$	−4.17609	−	4.17609i	−0.139983	−	0.139983i
$891$	1.02138	−	3.81183i	0.0342174	−	0.127701i
$892$	−16.0005	−	9.23791i	−0.535737	−	0.309308i
$893$	22.7558	+	13.1381i	0.761494	+	0.439649i
$894$	−2.49759	+	9.32114i	−0.0835320	+	0.311746i
$895$	2.55048	+	2.55048i	0.0852531	+	0.0852531i
$896$	2.09886	+	1.61083i	0.0701181	+	0.0538140i
$897$	0.785071			0.0262128
$898$	−13.0353	−	3.49279i	−0.434993	−	0.116556i
$899$	−3.50801	−	2.02535i	−0.116999	−	0.0675491i
$900$	2.41421	−	4.18154i	0.0804738	−	0.139385i
$901$	−7.83927	−	19.7101i	−0.261164	−	0.656640i
$902$	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
$906$	−5.88490	−	21.9628i	−0.195513	−	0.729664i
$907$	0.405386	−	0.108623i	0.0134606	−	0.00360676i	−0.252082	−	0.967706i	$-0.581115\pi$
$907$	0.405386	−	0.108623i	0.0134606	−	0.00360676i	0.265543	+	0.964099i	$0.414449\pi$
$908$	2.80836	−	10.4809i	0.0931987	−	0.347822i
$909$		−	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	$0.913844\pi$
$912$	1.09280	−	4.07840i	0.0361863	−	0.135049i
$913$	−7.32777	−	27.3476i	−0.242514	−	0.905074i
$914$	−4.54476	+	7.87175i	−0.150327	+	0.260374i
$915$	5.83495	+	1.56347i	0.192897	+	0.0516867i
$916$			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	0.903086	−	0.429459i	$-0.141296\pi$
$919$	2.41370	+	4.18065i	0.0796205	+	0.137907i	−0.823466	+	0.567366i	$0.807962\pi$
$920$	0.0797321	+	0.0460333i	0.00262869	+	0.00151767i
$921$	1.42445	+	5.31610i	0.0469371	+	0.175171i
$922$	3.38489	+	5.86280i	0.111475	+	0.193081i
$923$	38.2695	−	38.2695i	1.25966	−	1.25966i
$924$	3.99466	+	9.64653i	0.131415	+	0.317348i
$925$	−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
$928$	−0.400100	+	0.107206i	−0.0131339	+	0.00351922i
$929$	12.7903	−	47.7342i	0.419638	−	1.56611i	−0.355724	−	0.934591i	$-0.615766\pi$
$929$	12.7903	−	47.7342i	0.419638	−	1.56611i	0.775361	−	0.631518i	$-0.217568\pi$
$930$	−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
$935$	−5.28834	−	4.17811i	−0.172947	−	0.136639i
$936$	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	$-0.139640\pi$
$938$	−19.6210	+	8.12512i	−0.640649	+	0.265295i
$939$	−21.8298			−0.712390
$940$	−2.48991	−	0.667169i	−0.0812119	−	0.0217607i
$941$	14.2234	−	3.81115i	0.463670	−	0.124240i	−0.0194186	−	0.999811i	$-0.506182\pi$
$941$	14.2234	−	3.81115i	0.463670	−	0.124240i	0.483089	+	0.875571i	$0.339515\pi$
$942$	17.4776	−	4.68310i	0.569450	−	0.152584i
$943$	−0.262824	+	0.151742i	−0.00855873	+	0.00494139i
$944$		−	13.1646i		−	0.428473i
$945$	0.667228	−	0.869378i	0.0217049	−	0.0282809i
$946$	6.04606	+	6.04606i	0.196574	+	0.196574i
$947$	−30.2342	−	8.10123i	−0.982479	−	0.263255i	−0.268391	−	0.963310i	$-0.586492\pi$
$947$	−30.2342	−	8.10123i	−0.982479	−	0.263255i	−0.714088	+	0.700056i	$0.753159\pi$
$948$	4.23471	−	7.33474i	0.137537	−	0.238221i
$949$	15.2695	+	56.9865i	0.495669	+	1.84986i
$950$	17.6556	−	10.1935i	0.572823	−	0.330719i
$951$	8.13134			0.263677
$952$	10.4957	+	2.97322i	0.340168	+	0.0963625i
$953$	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
$955$	−0.805284	−	3.00536i	−0.0260584	−	0.0972511i
$956$	2.34155	−	4.05568i	0.0757311	−	0.131170i
$957$	−1.57891	−	0.423068i	−0.0510390	−	0.0136759i
$958$	12.5211	+	12.5211i	0.404540	+	0.404540i
$959$	−12.5434	−	1.65257i	−0.405047	−	0.0533643i
$960$			0.414214i			0.0133687i
$961$	−55.9744	+	32.3168i	−1.80562	+	1.04248i
$962$	28.4116	−	7.61287i	0.916027	−	0.245449i
$963$	−19.7904	+	5.30281i	−0.637735	+	0.170881i
$964$	−13.7247	−	3.67751i	−0.442041	−	0.118445i
$965$	−1.96402			−0.0632241
$966$	−0.466511	−	0.358037i	−0.0150098	−	0.0115196i
$967$			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
$969$	−2.02781	−	17.2904i	−0.0651427	−	0.555446i
$970$	0.186809	−	0.323563i	0.00599807	−	0.0103890i
$971$	−7.35159	+	4.24444i	−0.235924	+	0.136211i	−0.613302	−	0.789849i	$-0.710159\pi$
$971$	−7.35159	+	4.24444i	−0.235924	+	0.136211i	0.377378	+	0.926059i	$0.376826\pi$
$972$	−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
$975$	−4.41401	+	16.4733i	−0.141361	+	0.527568i
$976$	14.0868	−	3.77455i	0.450908	−	0.120820i
$977$	−2.82261	−	1.62963i	−0.0903032	−	0.0521366i	0.454168	−	0.890916i	$-0.349936\pi$
$977$	−2.82261	−	1.62963i	−0.0903032	−	0.0521366i	−0.544472	+	0.838779i	$0.683270\pi$
$978$	4.59313	−	2.65185i	0.146872	−	0.0847967i
$979$	−39.7865	−	39.7865i	−1.27158	−	1.27158i
$980$	−0.000548189		2.89949i	−1.75113e−5		0.0926210i
$981$	−4.18938	+	4.18938i	−0.133757	+	0.133757i
$982$	−13.2978	−	23.0324i	−0.424349	−	0.734995i
$983$	14.0113	+	52.2909i	0.446891	+	1.66782i	0.710894	+	0.703299i	$0.248290\pi$
$983$	14.0113	+	52.2909i	0.446891	+	1.66782i	−0.264003	+	0.964522i	$0.585043\pi$
$984$	−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
$989$	−0.465178	−	0.124644i	−0.0147918	−	0.00396345i
$990$	−0.817305	+	1.41561i	−0.0259757	+	0.0449912i
$991$	−5.26043	−	19.6322i	−0.167103	−	0.623638i	−0.997763	−	0.0668567i	$-0.978703\pi$
$991$	−5.26043	−	19.6322i	−0.167103	−	0.623638i	0.830659	−	0.556781i	$-0.187964\pi$
$992$	−2.53105	+	9.44602i	−0.0803611	+	0.299912i
$993$	5.28877	+	5.28877i	0.167834	+	0.167834i
$994$	−40.1938	+	5.28776i	−1.27487	+	0.167717i
$995$			7.61013i			0.241257i
$996$	−1.85687	+	6.92994i	−0.0588372	+	0.219584i
$997$	29.8324	−	7.99357i	0.944802	−	0.253159i	0.246647	−	0.969105i	$-0.420671\pi$
$997$	29.8324	−	7.99357i	0.944802	−	0.253159i	0.698155	+	0.715947i	$0.254005\pi$
$998$	−6.28060	−	23.4395i	−0.198809	−	0.741965i
$999$	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.361.2	yes	24
7.2	even	3	inner	714.2.ba.e.667.4	yes	24
17.13	even	4	inner	714.2.ba.e.319.4	✓	24
119.30	even	12	inner	714.2.ba.e.625.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.ba.e.319.4	✓	24	17.13	even	4	inner
714.2.ba.e.361.2	yes	24	1.1	even	1	trivial
714.2.ba.e.625.2	yes	24	119.30	even	12	inner
714.2.ba.e.667.4	yes	24	7.2	even	3	inner

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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.400100 + 0.107206i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.01225 - 2.44445i) q^{7} -1.00000i q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.400100 + 0.107206i) q^{5} +(-0.707107 - 0.707107i) q^{6} +(-1.01225 - 2.44445i) q^{7} -1.00000i q^{8} +(-0.866025 + 0.500000i) q^{9} +(0.400100 - 0.107206i) q^{10} +(3.81183 - 1.02138i) q^{11} +(-0.965926 - 0.258819i) q^{12} +3.53208 q^{13} +(-2.09886 - 1.61083i) q^{14} -0.414214i q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.23523 - 2.55603i) 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} +(-0.0575273 + 0.214695i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(-4.18154 - 2.41421i) q^{25} +(3.05888 - 1.76604i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.62308 - 0.345588i) q^{28} +(0.292893 - 0.292893i) q^{29} +(-0.207107 - 0.358719i) q^{30} +(-2.53105 - 9.44602i) 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} +(8.04387 + 2.15535i) q^{37} +(-2.11113 + 3.65659i) q^{38} +(-0.914171 - 3.41173i) q^{39} +(0.107206 - 0.400100i) q^{40} +(0.965476 + 0.965476i) q^{41} +(-1.01272 + 2.44426i) q^{42} +2.16670i q^{43} +(1.02138 - 3.81183i) q^{44} +(-0.400100 + 0.107206i) q^{45} +(0.0575273 + 0.214695i) q^{46} +(-3.11161 - 5.38947i) q^{47} +(-0.707107 + 0.707107i) q^{48} +(-4.95068 + 4.94881i) q^{49} -4.82843 q^{50} +(-1.63160 + 3.78654i) q^{51} +(1.76604 - 3.05888i) q^{52} +(4.45538 + 2.57232i) q^{53} +(0.965926 + 0.258819i) q^{54} +1.63461 q^{55} +(-2.44445 + 1.01225i) q^{56} +(2.98559 + 2.98559i) q^{57} +(0.107206 - 0.400100i) q^{58} +(11.4009 + 6.58232i) q^{59} +(-0.358719 - 0.207107i) q^{60} +(-3.77455 + 14.0868i) q^{61} +(-6.91497 - 6.91497i) q^{62} +(2.09886 + 1.61083i) q^{63} -1.00000 q^{64} +(1.41319 + 0.378662i) q^{65} +(-3.41759 - 1.97315i) q^{66} +(4.01338 - 6.95138i) q^{67} +(-3.83120 + 1.52378i) q^{68} +0.222269 q^{69} +(-0.667063 - 0.869504i) q^{70} +(10.8348 - 10.8348i) q^{71} +(0.500000 + 0.866025i) q^{72} +(4.32308 + 16.1340i) q^{73} +(8.04387 - 2.15535i) q^{74} +(-1.24969 + 4.66390i) q^{75} +4.22227i q^{76} +(-6.35525 - 8.28394i) q^{77} +(-2.49756 - 2.49756i) q^{78} +(-2.19205 + 8.18084i) q^{79} +(-0.107206 - 0.400100i) q^{80} +(0.500000 - 0.866025i) q^{81} +(1.31887 + 0.353389i) 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} +(-1.02138 - 3.81183i) q^{88} +(-7.12903 - 12.3479i) q^{89} +(-0.292893 + 0.292893i) q^{90} +(-3.57537 - 8.63401i) q^{91} +(0.157168 + 0.157168i) q^{92} +(-8.46907 + 4.88962i) q^{93} +(-5.38947 - 3.11161i) q^{94} +(-1.68933 + 0.452654i) q^{95} +(-0.258819 + 0.965926i) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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