LMFDB - Embedded newform 504.2.cs.b.421.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			421.33
Character	$\chi$	$=$	504.421
Dual form			504.2.cs.b.85.33

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37539 + 0.329083i) q^{2} +(-0.821098 + 1.52506i) q^{3} +(1.78341 + 0.905236i) q^{4} +(-2.72052 + 1.57069i) q^{5} +(-1.63120 + 1.82734i) q^{6} +(-0.500000 + 0.866025i) q^{7} +(2.15499 + 1.83194i) q^{8} +(-1.65160 - 2.50444i) q^{9} +O(q^{10})$	\(q+(1.37539 + 0.329083i) q^{2} +(-0.821098 + 1.52506i) q^{3} +(1.78341 + 0.905236i) q^{4} +(-2.72052 + 1.57069i) q^{5} +(-1.63120 + 1.82734i) q^{6} +(-0.500000 + 0.866025i) q^{7} +(2.15499 + 1.83194i) q^{8} +(-1.65160 - 2.50444i) q^{9} +(-4.25867 + 1.26504i) q^{10} +(-2.21426 - 1.27840i) q^{11} +(-2.84489 + 1.97651i) q^{12} +(-0.964474 + 0.556840i) q^{13} +(-0.972690 + 1.02658i) q^{14} +(-0.161584 - 5.43864i) q^{15} +(2.36110 + 3.22881i) q^{16} +1.14970 q^{17} +(-1.44743 - 3.98810i) q^{18} +4.46665i q^{19} +(-6.27365 + 0.338477i) q^{20} +(-0.910189 - 1.47362i) q^{21} +(-2.62478 - 2.48698i) q^{22} +(-0.842409 - 1.45909i) q^{23} +(-4.56328 + 1.78228i) q^{24} +(2.43416 - 4.21608i) q^{25} +(-1.50978 + 0.448481i) q^{26} +(5.17554 - 0.462390i) q^{27} +(-1.67566 + 1.09186i) q^{28} +(-4.17557 - 2.41077i) q^{29} +(1.56752 - 7.53344i) q^{30} +(3.39388 + 5.87838i) q^{31} +(2.18489 + 5.21788i) q^{32} +(3.76776 - 2.32718i) q^{33} +(1.58130 + 0.378348i) q^{34} -3.14139i q^{35} +(-0.678366 - 5.96153i) q^{36} +3.26969i q^{37} +(-1.46990 + 6.14339i) q^{38} +(-0.0572845 - 1.92810i) q^{39} +(-8.74012 - 1.59901i) q^{40} +(-1.46544 - 2.53822i) q^{41} +(-0.766925 - 2.32633i) q^{42} +(9.14833 + 5.28179i) q^{43} +(-2.79168 - 4.28435i) q^{44} +(8.42692 + 4.21923i) q^{45} +(-0.678480 - 2.28405i) q^{46} +(-5.80079 + 10.0473i) q^{47} +(-6.86281 + 0.949639i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(4.73536 - 4.99773i) q^{50} +(-0.944020 + 1.75337i) q^{51} +(-2.22412 + 0.119996i) q^{52} +9.23136i q^{53} +(7.27056 + 1.06721i) q^{54} +8.03193 q^{55} +(-2.66400 + 0.950305i) q^{56} +(-6.81189 - 3.66755i) q^{57} +(-4.94971 - 4.68986i) q^{58} +(11.4997 - 6.63933i) q^{59} +(4.63508 - 9.84560i) q^{60} +(-2.64571 - 1.52750i) q^{61} +(2.73345 + 9.20195i) q^{62} +(2.99471 - 0.178105i) q^{63} +(1.28797 + 7.89564i) q^{64} +(1.74925 - 3.02979i) q^{65} +(5.94799 - 1.96088i) q^{66} +(9.47390 - 5.46976i) q^{67} +(2.05039 + 1.04075i) q^{68} +(2.91690 - 0.0866623i) q^{69} +(1.03378 - 4.32064i) q^{70} +13.2125 q^{71} +(1.02882 - 8.42268i) q^{72} -7.16456 q^{73} +(-1.07600 + 4.49711i) q^{74} +(4.43109 + 7.17404i) q^{75} +(-4.04337 + 7.96586i) q^{76} +(2.21426 - 1.27840i) q^{77} +(0.555715 - 2.67074i) q^{78} +(-2.48070 + 4.29670i) q^{79} +(-11.4949 - 5.07549i) q^{80} +(-3.54445 + 8.27266i) q^{81} +(-1.18027 - 3.97330i) q^{82} +(-10.8973 - 6.29154i) q^{83} +(-0.289267 - 3.45200i) q^{84} +(-3.12780 + 1.80583i) q^{85} +(10.8444 + 10.2751i) q^{86} +(7.10511 - 4.38851i) q^{87} +(-2.42975 - 6.81135i) q^{88} +6.04820 q^{89} +(10.2018 + 8.57625i) q^{90} -1.11368i q^{91} +(-0.181535 - 3.36474i) q^{92} +(-11.7516 + 0.349144i) q^{93} +(-11.2847 + 11.9100i) q^{94} +(-7.01573 - 12.1516i) q^{95} +(-9.75157 - 0.952305i) q^{96} +(5.01036 - 8.67820i) q^{97} +(-0.402702 - 1.35567i) q^{98} +(0.455381 + 7.65690i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.37539	+	0.329083i	0.972549	+	0.232697i
$2$	1.37539	+	0.329083i	0.972549	+	0.232697i
$3$	−0.821098	+	1.52506i	−0.474061	+	0.880492i
$3$	−0.821098	+	1.52506i	−0.474061	+	0.880492i
$4$	1.78341	+	0.905236i	0.891705	+	0.452618i
$5$	−2.72052	+	1.57069i	−1.21665	+	0.702436i	−0.964201	−	0.265174i	$-0.914571\pi$
$5$	−2.72052	+	1.57069i	−1.21665	+	0.702436i	−0.252453	+	0.967609i	$0.581237\pi$
$6$	−1.63120	+	1.82734i	−0.665935	+	0.746010i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	2.15499	+	1.83194i	0.761904	+	0.647690i
$9$	−1.65160	−	2.50444i	−0.550533	−	0.834814i
$10$	−4.25867	+	1.26504i	−1.34671	+	0.400042i
$11$	−2.21426	−	1.27840i	−0.667625	−	0.385453i	0.127551	−	0.991832i	$-0.459288\pi$
$11$	−2.21426	−	1.27840i	−0.667625	−	0.385453i	−0.795176	+	0.606379i	$0.792622\pi$
$12$	−2.84489	+	1.97651i	−0.821249	+	0.570570i
$13$	−0.964474	+	0.556840i	−0.267497	+	0.154439i	−0.627750	−	0.778415i	$-0.716024\pi$
$13$	−0.964474	+	0.556840i	−0.267497	+	0.154439i	0.360253	+	0.932855i	$0.382691\pi$
$14$	−0.972690	+	1.02658i	−0.259962	+	0.274366i
$15$	−0.161584	−	5.43864i	−0.0417208	−	1.40425i
$16$	2.36110	+	3.22881i	0.590274	+	0.807203i
$17$	1.14970			0.278844			0.139422	−	0.990233i	$-0.455475\pi$
$17$	1.14970			0.278844			0.139422	+	0.990233i	$0.455475\pi$
$18$	−1.44743	−	3.98810i	−0.341162	−	0.940005i
$19$			4.46665i			1.02472i	0.858771	+	0.512359i	$0.171228\pi$
$19$			4.46665i			1.02472i	−0.858771	+	0.512359i	$0.828772\pi$
$20$	−6.27365	+	0.338477i	−1.40283	+	0.0756858i
$21$	−0.910189	−	1.47362i	−0.198620	−	0.321570i
$22$	−2.62478	−	2.48698i	−0.559605	−	0.530226i
$23$	−0.842409	−	1.45909i	−0.175654	−	0.304242i	0.764733	−	0.644347i	$-0.222871\pi$
$23$	−0.842409	−	1.45909i	−0.175654	−	0.304242i	−0.940388	+	0.340105i	$0.889537\pi$
$24$	−4.56328	+	1.78228i	−0.931475	+	0.363806i
$25$	2.43416	−	4.21608i	0.486831	−	0.843216i
$26$	−1.50978	+	0.448481i	−0.296092	+	0.0879544i
$27$	5.17554	−	0.462390i	0.996033	−	0.0889871i
$28$	−1.67566	+	1.09186i	−0.316670	+	0.206342i
$29$	−4.17557	−	2.41077i	−0.775384	−	0.447668i	0.0594077	−	0.998234i	$-0.481079\pi$
$29$	−4.17557	−	2.41077i	−0.775384	−	0.447668i	−0.834792	+	0.550565i	$0.814412\pi$
$30$	1.56752	−	7.53344i	0.286189	−	1.37541i
$31$	3.39388	+	5.87838i	0.609560	+	1.05579i	0.991313	+	0.131524i	$0.0419870\pi$
$31$	3.39388	+	5.87838i	0.609560	+	1.05579i	−0.381753	+	0.924264i	$0.624680\pi$
$32$	2.18489	+	5.21788i	0.386238	+	0.922399i
$33$	3.76776	−	2.32718i	0.655884	−	0.405110i
$34$	1.58130	+	0.378348i	0.271190	+	0.0648861i
$35$		−	3.14139i		−	0.530991i
$36$	−0.678366	−	5.96153i	−0.113061	−	0.993588i
$37$			3.26969i			0.537534i	0.963205	+	0.268767i	$0.0866162\pi$
$37$			3.26969i			0.537534i	−0.963205	+	0.268767i	$0.913384\pi$
$38$	−1.46990	+	6.14339i	−0.238449	+	0.996590i
$39$	−0.0572845	−	1.92810i	−0.00917287	−	0.308743i
$40$	−8.74012	−	1.59901i	−1.38193	−	0.252826i
$41$	−1.46544	−	2.53822i	−0.228864	−	0.396403i	0.728608	−	0.684931i	$-0.240168\pi$
$41$	−1.46544	−	2.53822i	−0.228864	−	0.396403i	−0.957472	+	0.288527i	$0.906834\pi$
$42$	−0.766925	−	2.32633i	−0.118339	−	0.358961i
$43$	9.14833	+	5.28179i	1.39511	+	0.805466i	0.993875	−	0.110510i	$-0.0352485\pi$
$43$	9.14833	+	5.28179i	1.39511	+	0.805466i	0.401233	+	0.915976i	$0.368582\pi$
$44$	−2.79168	−	4.28435i	−0.420861	−	0.645889i
$45$	8.42692	+	4.21923i	1.25621	+	0.628966i
$46$	−0.678480	−	2.28405i	−0.100036	−	0.336765i
$47$	−5.80079	+	10.0473i	−0.846132	+	1.46554i	0.0385022	+	0.999259i	$0.487741\pi$
$47$	−5.80079	+	10.0473i	−0.846132	+	1.46554i	−0.884634	+	0.466285i	$0.845592\pi$
$48$	−6.86281	+	0.949639i	−0.990562	+	0.137069i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	4.73536	−	4.99773i	0.669681	−	0.706786i
$51$	−0.944020	+	1.75337i	−0.132189	+	0.245520i
$52$	−2.22412	+	0.119996i	−0.308430	+	0.0166405i
$53$			9.23136i			1.26802i	0.773323	+	0.634012i	$0.218593\pi$
$53$			9.23136i			1.26802i	−0.773323	+	0.634012i	$0.781407\pi$
$54$	7.27056	+	1.06721i	0.989398	+	0.145229i
$55$	8.03193			1.08302
$56$	−2.66400	+	0.950305i	−0.355993	+	0.126990i
$57$	−6.81189	−	3.66755i	−0.902257	−	0.485779i
$58$	−4.94971	−	4.68986i	−0.649929	−	0.615809i
$59$	11.4997	−	6.63933i	1.49713	−	0.864367i	0.497134	−	0.867674i	$-0.334386\pi$
$59$	11.4997	−	6.63933i	1.49713	−	0.864367i	0.999995	+	0.00330678i	$0.00105258\pi$
$60$	4.63508	−	9.84560i	0.598386	−	1.27106i
$61$	−2.64571	−	1.52750i	−0.338749	−	0.195577i	0.320970	−	0.947089i	$-0.395991\pi$
$61$	−2.64571	−	1.52750i	−0.338749	−	0.195577i	−0.659719	+	0.751513i	$0.729325\pi$
$62$	2.73345	+	9.20195i	0.347149	+	1.16865i
$63$	2.99471	−	0.178105i	0.377298	−	0.0224391i
$64$	1.28797	+	7.89564i	0.160996	+	0.986955i
$65$	1.74925	−	3.02979i	0.216968	−	0.375799i
$66$	5.94799	−	1.96088i	0.732147	−	0.241368i
$67$	9.47390	−	5.46976i	1.15742	−	0.668238i	0.206737	−	0.978397i	$-0.433716\pi$
$67$	9.47390	−	5.46976i	1.15742	−	0.668238i	0.950685	+	0.310159i	$0.100382\pi$
$68$	2.05039	+	1.04075i	0.248647	+	0.126210i
$69$	2.91690	−	0.0866623i	0.351154	−	0.0104329i
$70$	1.03378	−	4.32064i	0.123560	−	0.516415i
$71$	13.2125			1.56803			0.784015	−	0.620742i	$-0.213168\pi$
$71$	13.2125			1.56803			0.784015	+	0.620742i	$0.213168\pi$
$72$	1.02882	−	8.42268i	0.121247	−	0.992622i
$73$	−7.16456			−0.838548			−0.419274	−	0.907860i	$-0.637715\pi$
$73$	−7.16456			−0.838548			−0.419274	+	0.907860i	$0.637715\pi$
$74$	−1.07600	+	4.49711i	−0.125082	+	0.522779i
$75$	4.43109	+	7.17404i	0.511658	+	0.828387i
$76$	−4.04337	+	7.96586i	−0.463806	+	0.913747i
$77$	2.21426	−	1.27840i	0.252338	−	0.145688i
$78$	0.555715	−	2.67074i	0.0629223	−	0.302402i
$79$	−2.48070	+	4.29670i	−0.279101	+	0.483417i	−0.971162	−	0.238422i	$-0.923370\pi$
$79$	−2.48070	+	4.29670i	−0.279101	+	0.483417i	0.692061	+	0.721839i	$0.256703\pi$
$80$	−11.4949	−	5.07549i	−1.28517	−	0.567457i
$81$	−3.54445	+	8.27266i	−0.393828	+	0.919184i
$82$	−1.18027	−	3.97330i	−0.130339	−	0.438778i
$83$	−10.8973	−	6.29154i	−1.19613	−	0.690586i	−0.236440	−	0.971646i	$-0.575981\pi$
$83$	−10.8973	−	6.29154i	−1.19613	−	0.690586i	−0.959690	+	0.281060i	$0.909314\pi$
$84$	−0.289267	−	3.45200i	−0.0315616	−	0.376644i
$85$	−3.12780	+	1.80583i	−0.339257	+	0.195870i
$86$	10.8444	+	10.2751i	1.16938	+	1.10799i
$87$	7.10511	−	4.38851i	0.761748	−	0.470498i
$88$	−2.42975	−	6.81135i	−0.259012	−	0.726092i
$89$	6.04820			0.641108			0.320554	−	0.947230i	$-0.396131\pi$
$89$	6.04820			0.641108			0.320554	+	0.947230i	$0.396131\pi$
$90$	10.2018	+	8.57625i	1.07537	+	0.904016i
$91$		−	1.11368i		−	0.116745i
$92$	−0.181535	−	3.36474i	−0.0189263	−	0.350799i
$93$	−11.7516	+	0.349144i	−1.21858	+	0.0362045i
$94$	−11.2847	+	11.9100i	−1.16393	+	1.22842i
$95$	−7.01573	−	12.1516i	−0.719799	−	1.24673i
$96$	−9.75157	−	0.952305i	−0.995265	−	0.0971943i
$97$	5.01036	−	8.67820i	0.508725	−	0.881138i	−0.491224	−	0.871033i	$-0.663450\pi$
$97$	5.01036	−	8.67820i	0.508725	−	0.881138i	0.999949	−	0.0101046i	$-0.00321645\pi$
$98$	−0.402702	−	1.35567i	−0.0406791	−	0.136943i
$99$	0.455381	+	7.65690i	0.0457675	+	0.769547i
$100$	8.15764	−	5.31552i	0.815764	−	0.531552i
$101$	−10.3557	−	5.97887i	−1.03043	−	0.594920i	−0.113323	−	0.993558i	$-0.536149\pi$
$101$	−10.3557	−	5.97887i	−1.03043	−	0.594920i	−0.917108	+	0.398638i	$0.869483\pi$
$102$	−1.87540	+	2.10091i	−0.185692	+	0.208021i
$103$	3.87345	+	6.70902i	0.381663	+	0.661059i	0.991300	−	0.131621i	$-0.0420183\pi$
$103$	3.87345	+	6.70902i	0.381663	+	0.661059i	−0.609637	+	0.792680i	$0.708685\pi$
$104$	−3.09853	−	0.566878i	−0.303836	−	0.0555870i
$105$	4.79079	+	2.57939i	0.467534	+	0.251722i
$106$	−3.03788	+	12.6967i	−0.295065	+	1.23322i
$107$			5.46939i			0.528746i	0.964421	+	0.264373i	$0.0851650\pi$
$107$			5.46939i			0.528746i	−0.964421	+	0.264373i	$0.914835\pi$
$108$	9.64867	+	3.86045i	0.928444	+	0.371472i
$109$		−	10.1589i		−	0.973049i	−0.873667	−	0.486524i	$-0.838264\pi$
$109$		−	10.1589i		−	0.973049i	0.873667	−	0.486524i	$-0.161736\pi$
$110$	11.0471	+	2.64317i	1.05329	+	0.252016i
$111$	−4.98647	−	2.68474i	−0.473295	−	0.254824i
$112$	−3.97678	+	0.430365i	−0.375770	+	0.0406656i
$113$	7.92723	+	13.7304i	0.745731	+	1.29164i	0.949852	+	0.312699i	$0.101233\pi$
$113$	7.92723	+	13.7304i	0.745731	+	1.29164i	−0.204121	+	0.978946i	$0.565434\pi$
$114$	−8.16209	−	7.28600i	−0.764450	−	0.682396i
$115$	4.58358	+	2.64633i	0.427421	+	0.246772i
$116$	−5.26444	−	8.07926i	−0.488791	−	0.750141i
$117$	2.98750	+	1.49579i	0.276194	+	0.138286i
$118$	18.0014	−	5.34735i	1.65717	−	0.492263i
$119$	−0.574852	+	0.995674i	−0.0526966	+	0.0912733i
$120$	9.61507	−	12.0162i	0.877732	−	1.09693i
$121$	−2.23136	−	3.86484i	−0.202851	−	0.351349i
$122$	−3.13622	−	2.97157i	−0.283940	−	0.269034i
$123$	5.07420	−	0.150757i	0.457525	−	0.0135933i
$124$	0.731366	+	13.5558i	0.0656786	+	1.21735i
$125$		−	0.413681i		−	0.0370007i
$126$	4.17751	+	0.740542i	0.372162	+	0.0659727i
$127$	16.1006			1.42869			0.714347	−	0.699791i	$-0.246724\pi$
$127$	16.1006			1.42869			0.714347	+	0.699791i	$0.246724\pi$
$128$	−0.826856	+	11.2835i	−0.0730845	+	0.997326i
$129$	−15.5667	+	9.61486i	−1.37057	+	0.846542i
$130$	3.40295	−	3.59150i	0.298459	−	0.314995i
$131$	−5.63758	+	3.25486i	−0.492557	+	0.284378i	−0.725635	−	0.688080i	$-0.758454\pi$
$131$	−5.63758	+	3.25486i	−0.492557	+	0.284378i	0.233077	+	0.972458i	$0.425120\pi$
$132$	8.82611	−	0.739601i	0.768214	−	0.0643740i
$133$	−3.86823	−	2.23332i	−0.335418	−	0.193654i
$134$	14.8303	−	4.40537i	1.28115	−	0.380566i
$135$	−13.3539	+	9.38713i	−1.14932	+	0.807915i
$136$	2.47760	+	2.10619i	0.212453	+	0.180605i
$137$	8.94475	−	15.4928i	0.764202	−	1.32364i	−0.176466	−	0.984307i	$-0.556466\pi$
$137$	8.94475	−	15.4928i	0.764202	−	1.32364i	0.940668	−	0.339330i	$-0.110200\pi$
$138$	4.04040	+	0.840707i	0.343942	+	0.0715657i
$139$	8.01173	−	4.62558i	0.679546	−	0.392336i	−0.120138	−	0.992757i	$-0.538334\pi$
$139$	8.01173	−	4.62558i	0.679546	−	0.392336i	0.799684	+	0.600421i	$0.205000\pi$
$140$	2.84370	−	5.60238i	0.240336	−	0.473487i
$141$	−10.5596	−	17.0963i	−0.889282	−	1.43977i
$142$	18.1723	+	4.34799i	1.52499	+	0.364875i
$143$	2.84746			0.238117
$144$	4.18678	−	11.2459i	0.348899	−	0.937160i
$145$	15.1463			1.25783
$146$	−9.85408	−	2.35773i	−0.815529	−	0.195127i
$147$	1.73129	−	0.0514372i	0.142794	−	0.00424247i
$148$	−2.95984	+	5.83120i	−0.243298	+	0.479322i
$149$	−18.0266	+	10.4077i	−1.47680	+	0.852629i	−0.999657	−	0.0261974i	$-0.991660\pi$
$149$	−18.0266	+	10.4077i	−1.47680	+	0.852629i	−0.477141	+	0.878827i	$0.658327\pi$
$150$	3.73363	+	11.3253i	0.304850	+	0.924708i
$151$	−3.29469	+	5.70657i	−0.268118	+	0.464394i	−0.968376	−	0.249496i	$-0.919735\pi$
$151$	−3.29469	+	5.70657i	−0.268118	+	0.464394i	0.700258	+	0.713890i	$0.253068\pi$
$152$	−8.18264	+	9.62558i	−0.663700	+	0.780738i
$153$	−1.89885	−	2.87937i	−0.153513	−	0.232783i
$154$	3.46618	−	1.02963i	0.279313	−	0.0829702i
$155$	−18.4663	−	10.6615i	−1.48325	−	0.856353i
$156$	1.64322	−	3.49044i	0.131563	−	0.279459i
$157$	14.8869	−	8.59497i	1.18811	−	0.685954i	0.230231	−	0.973136i	$-0.426052\pi$
$157$	14.8869	−	8.59497i	1.18811	−	0.685954i	0.957876	+	0.287183i	$0.0927186\pi$
$158$	−4.82591	+	5.09330i	−0.383929	+	0.405201i
$159$	−14.0783	−	7.57984i	−1.11649	−	0.601121i
$160$	−14.1397	−	10.7636i	−1.11784	−	0.850934i
$161$	1.68482			0.132782
$162$	−7.59740	+	10.2117i	−0.596908	+	0.802310i
$163$		−	9.53517i		−	0.746852i	−0.927660	−	0.373426i	$-0.878183\pi$
$163$		−	9.53517i		−	0.746852i	0.927660	−	0.373426i	$-0.121817\pi$
$164$	−0.315796	−	5.85326i	−0.0246595	−	0.457063i
$165$	−6.59499	+	12.2491i	−0.513420	+	0.953595i
$166$	−12.9176	−	12.2394i	−1.00260	−	0.949965i
$167$	−7.95846	−	13.7845i	−0.615844	−	1.06667i	−0.990236	−	0.139403i	$-0.955482\pi$
$167$	−7.95846	−	13.7845i	−0.615844	−	1.06667i	0.374392	−	0.927271i	$-0.377852\pi$
$168$	0.738138	−	4.84305i	0.0569486	−	0.373650i
$169$	−5.87986	+	10.1842i	−0.452297	+	0.783401i
$170$	−4.89622	+	1.45443i	−0.375523	+	0.111549i
$171$	11.1865	−	7.37710i	0.855449	−	0.564141i
$172$	11.5340	+	17.7010i	0.879456	+	1.34969i
$173$	−4.25768	−	2.45817i	−0.323705	−	0.186891i	0.329338	−	0.944212i	$-0.393175\pi$
$173$	−4.25768	−	2.45817i	−0.323705	−	0.186891i	−0.653043	+	0.757321i	$0.726508\pi$
$174$	11.2165	−	3.69776i	0.850321	−	0.280326i
$175$	2.43416	+	4.21608i	0.184005	+	0.318706i
$176$	−1.10036	−	10.1679i	−0.0829428	−	0.766432i
$177$	0.683017	+	22.9892i	0.0513387	+	1.72797i
$178$	8.31865	+	1.99036i	0.623509	+	0.149184i
$179$		−	7.84907i		−	0.586667i	−0.956010	−	0.293334i	$-0.905235\pi$
$179$		−	7.84907i		−	0.586667i	0.956010	−	0.293334i	$-0.0947647\pi$
$180$	11.2092	+	15.1530i	0.835488	+	1.12943i
$181$			1.16256i			0.0864122i	0.999066	+	0.0432061i	$0.0137572\pi$
$181$			1.16256i			0.0864122i	−0.999066	+	0.0432061i	$0.986243\pi$
$182$	0.366492	−	1.53175i	0.0271662	−	0.113541i
$183$	4.50192	−	2.78063i	0.332791	−	0.205550i
$184$	0.857596	−	4.68758i	0.0632228	−	0.345573i
$185$	−5.13569	−	8.89527i	−0.377583	−	0.653993i
$186$	−16.2779	−	3.38703i	−1.19356	−	0.248349i
$187$	−2.54575	−	1.46979i	−0.186163	−	0.107482i
$188$	−19.4403	+	12.6673i	−1.41783	+	0.923858i
$189$	−2.18733	+	4.71334i	−0.159105	+	0.342845i
$190$	−5.65050	−	19.0220i	−0.409931	−	1.38000i
$191$	−10.9574	+	18.9788i	−0.792852	+	1.37326i	0.131342	+	0.991337i	$0.458071\pi$
$191$	−10.9574	+	18.9788i	−0.792852	+	1.37326i	−0.924194	+	0.381923i	$0.875262\pi$
$192$	−13.0988	−	4.51887i	−0.945328	−	0.326121i
$193$	−0.00294224	−	0.00509610i	−0.000211787	−	0.000366826i	0.865919	−	0.500183i	$-0.166734\pi$
$193$	−0.00294224	−	0.00509610i	−0.000211787	−	0.000366826i	−0.866131	+	0.499817i	$0.833401\pi$
$194$	9.74706	−	10.2871i	0.699798	−	0.738572i
$195$	3.18429	+	5.15545i	0.228032	+	0.369190i
$196$	−0.107748	−	1.99710i	−0.00769626	−	0.142650i
$197$		−	6.08721i		−	0.433696i	−0.976205	−	0.216848i	$-0.930422\pi$
$197$		−	6.08721i		−	0.433696i	0.976205	−	0.216848i	$-0.0695776\pi$
$198$	−1.89342	+	10.6811i	−0.134560	+	0.759072i
$199$	−12.7449			−0.903459			−0.451729	−	0.892155i	$-0.649193\pi$
$199$	−12.7449			−0.903459			−0.451729	+	0.892155i	$0.649193\pi$
$200$	12.9692	−	4.62638i	0.917061	−	0.327135i
$201$	0.562698	+	18.9395i	0.0396897	+	1.33589i
$202$	−12.2756	−	11.6312i	−0.863709	−	0.818367i
$203$	4.17557	−	2.41077i	0.293068	−	0.169203i
$204$	−3.27078	+	2.27241i	−0.229001	+	0.159100i
$205$	7.97353	+	4.60352i	0.556896	+	0.321524i
$206$	3.11970	+	10.5022i	0.217360	+	0.731724i
$207$	−2.26290	+	4.51960i	−0.157282	+	0.314134i
$208$	−4.07515	−	1.79935i	−0.282561	−	0.124763i
$209$	5.71018	−	9.89032i	0.394981	−	0.684128i
$210$	5.74039	+	5.12423i	0.396125	+	0.353606i
$211$	−14.1689	+	8.18044i	−0.975430	+	0.563165i	−0.900887	−	0.434053i	$-0.857083\pi$
$211$	−14.1689	+	8.18044i	−0.975430	+	0.563165i	−0.0745426	+	0.997218i	$0.523750\pi$
$212$	−8.35655	+	16.4633i	−0.573930	+	1.13070i
$213$	−10.8487	+	20.1497i	−0.743342	+	1.38064i
$214$	−1.79988	+	7.52256i	−0.123037	+	0.514231i
$215$	−33.1843			−2.26315
$216$	12.0003	+	8.48485i	0.816518	+	0.577321i
$217$	−6.78777			−0.460784
$218$	3.34313	−	13.9725i	0.226425	−	0.946338i
$219$	5.88280	−	10.9264i	0.397523	−	0.738335i
$220$	14.3242	+	7.27078i	0.965738	+	0.490196i
$221$	−1.10886	+	0.640201i	−0.0745901	+	0.0430646i
$222$	−5.97485	−	5.33353i	−0.401006	−	0.357963i
$223$	7.54800	−	13.0735i	0.505451	−	0.875467i	−0.494529	−	0.869161i	$-0.664659\pi$
$223$	7.54800	−	13.0735i	0.505451	−	0.875467i	0.999980	−	0.00630607i	$-0.00200730\pi$
$224$	−5.61126	−	0.716769i	−0.374918	−	0.0478911i
$225$	−14.5792	+	0.867071i	−0.971945	+	0.0578047i
$226$	6.38463	+	21.4934i	0.424699	+	1.42972i
$227$	22.9345	+	13.2412i	1.52222	+	0.878852i	0.999655	+	0.0262499i	$0.00835658\pi$
$227$	22.9345	+	13.2412i	1.52222	+	0.878852i	0.522561	+	0.852602i	$0.324977\pi$
$228$	−8.82839	−	12.7071i	−0.584674	−	0.841549i
$229$	17.9709	−	10.3755i	1.18755	−	0.685632i	0.229801	−	0.973238i	$-0.426192\pi$
$229$	17.9709	−	10.3755i	1.18755	−	0.685632i	0.957749	+	0.287605i	$0.0928591\pi$
$230$	5.43336	+	5.14812i	0.358265	+	0.339457i
$231$	0.131515	+	4.42657i	0.00865306	+	0.291247i
$232$	−4.58193	−	12.8446i	−0.300818	−	0.843289i
$233$	13.1760			0.863191			0.431596	−	0.902067i	$-0.357951\pi$
$233$	13.1760			0.863191			0.431596	+	0.902067i	$0.357951\pi$
$234$	3.61674	+	3.04044i	0.236434	+	0.198760i
$235$		−	36.4451i		−	2.37741i
$236$	26.5188	−	1.43074i	1.72622	−	0.0931335i
$237$	−4.51582	−	7.31123i	−0.293334	−	0.474915i
$238$	−1.11831	+	1.18027i	−0.0724891	+	0.0765054i
$239$	−3.75351	−	6.50127i	−0.242794	−	0.420532i	0.718715	−	0.695305i	$-0.244731\pi$
$239$	−3.75351	−	6.50127i	−0.242794	−	0.420532i	−0.961509	+	0.274773i	$0.911397\pi$
$240$	17.1788	−	13.3629i	1.10889	−	0.862571i
$241$	−10.4970	+	18.1813i	−0.676171	+	1.17116i	0.299954	+	0.953954i	$0.403029\pi$
$241$	−10.4970	+	18.1813i	−0.676171	+	1.17116i	−0.976125	+	0.217209i	$0.930305\pi$
$242$	−1.79715	−	6.04997i	−0.115525	−	0.388907i
$243$	−9.70594	−	12.1981i	−0.622636	−	0.782512i
$244$	−3.33564	−	5.11916i	−0.213542	−	0.327720i
$245$	2.72052	+	1.57069i	0.173808	+	0.100348i
$246$	7.02863	+	1.46248i	0.448129	+	0.0932445i
$247$	−2.48720	−	4.30797i	−0.158257	−	0.274109i
$248$	−3.45507	+	18.8853i	−0.219397	+	1.19921i
$249$	18.5427	−	11.4530i	1.17509	−	0.725803i
$250$	0.136135	−	0.568974i	0.00860994	−	0.0359850i
$251$			15.9379i			1.00599i	0.864289	+	0.502996i	$0.167769\pi$
$251$			15.9379i			1.00599i	−0.864289	+	0.502996i	$0.832231\pi$
$252$	5.50202	+	2.39328i	0.346595	+	0.150763i
$253$			4.30776i			0.270826i
$254$	22.1446	+	5.29842i	1.38948	+	0.332452i
$255$	−0.185774	−	6.25283i	−0.0116336	−	0.391568i
$256$	−4.85044	+	15.2471i	−0.303153	+	0.952942i
$257$	−1.09021	−	1.88830i	−0.0680054	−	0.117789i	0.830018	−	0.557737i	$-0.188330\pi$
$257$	−1.09021	−	1.88830i	−0.0680054	−	0.117789i	−0.898023	+	0.439948i	$0.854997\pi$
$258$	−24.5744	+	8.10148i	−1.52994	+	0.504376i
$259$	−2.83164	−	1.63485i	−0.175949	−	0.101584i
$260$	5.86230	−	3.81987i	0.363564	−	0.236898i
$261$	0.858740	+	14.4391i	0.0531547	+	0.893757i
$262$	−8.82500	+	2.62148i	−0.545210	+	0.161955i
$263$	5.79496	−	10.0372i	0.357332	−	0.618918i	−0.630182	−	0.776448i	$-0.717020\pi$
$263$	5.79496	−	10.0372i	0.357332	−	0.618918i	0.987514	+	0.157530i	$0.0503530\pi$
$264$	12.3828	+	1.88728i	0.762106	+	0.116154i
$265$	−14.4996	−	25.1141i	−0.890705	−	1.54275i
$266$	−4.58539	−	4.34466i	−0.281148	−	0.266388i
$267$	−4.96616	+	9.22385i	−0.303924	+	0.564491i
$268$	21.8473	−	1.17871i	1.33453	−	0.0720010i
$269$		−	2.15568i		−	0.131434i	−0.997838	−	0.0657171i	$-0.979067\pi$
$269$		−	2.15568i		−	0.131434i	0.997838	−	0.0657171i	$-0.0209335\pi$
$270$	−21.4560	+	8.51645i	−1.30577	+	0.518295i
$271$	14.7673			0.897051			0.448526	−	0.893770i	$-0.351949\pi$
$271$	14.7673			0.897051			0.448526	+	0.893770i	$0.351949\pi$
$272$	2.71457	+	3.71218i	0.164595	+	0.225084i
$273$	1.69842	+	0.914439i	0.102793	+	0.0553444i
$274$	17.4009	−	18.3651i	1.05123	−	1.10947i
$275$	−10.7797	+	6.22367i	−0.650041	+	0.375302i
$276$	5.28048	+	2.48593i	0.317848	+	0.149635i
$277$	−7.34491	−	4.24059i	−0.441313	−	0.254792i	0.262841	−	0.964839i	$-0.415340\pi$
$277$	−7.34491	−	4.24059i	−0.441313	−	0.254792i	−0.704154	+	0.710047i	$0.748674\pi$
$278$	12.5415	−	3.72546i	0.752188	−	0.223438i
$279$	9.11672	−	18.2085i	0.545804	−	1.09011i
$280$	5.75484	−	6.76966i	0.343918	−	0.404565i
$281$	−7.88091	+	13.6501i	−0.470136	+	0.814299i	−0.999417	−	0.0341477i	$-0.989128\pi$
$281$	−7.88091	+	13.6501i	−0.470136	+	0.814299i	0.529281	+	0.848446i	$0.322462\pi$
$282$	−8.89754	−	26.9891i	−0.529841	−	1.60718i
$283$	−28.0432	+	16.1907i	−1.66699	+	0.962439i	−0.697748	+	0.716344i	$0.745814\pi$
$283$	−28.0432	+	16.1907i	−1.66699	+	0.962439i	−0.969246	+	0.246095i	$0.920852\pi$
$284$	23.5632	+	11.9604i	1.39822	+	0.709718i
$285$	24.2925	−	0.721739i	1.43896	−	0.0427521i
$286$	3.91638	+	0.937051i	0.231580	+	0.0554090i
$287$	2.93088			0.173005
$288$	9.45931	−	14.0898i	0.557395	−	0.830247i
$289$	−15.6782			−0.922246
$290$	20.8321	+	4.98439i	1.22330	+	0.292693i
$291$	9.12076	+	14.7667i	0.534668	+	0.865642i
$292$	−12.7773	−	6.48561i	−0.747737	−	0.379542i
$293$	20.4389	−	11.8004i	1.19406	−	0.689388i	0.234832	−	0.972036i	$-0.424546\pi$
$293$	20.4389	−	11.8004i	1.19406	−	0.689388i	0.959224	+	0.282647i	$0.0912127\pi$
$294$	2.39813	+	0.498990i	0.139862	+	0.0291017i
$295$	−20.8567	+	36.1249i	−1.21432	+	2.10327i
$296$	−5.98989	+	7.04616i	−0.348156	+	0.409550i
$297$	−12.0511	−	5.59258i	−0.699277	−	0.324514i
$298$	−28.2186	+	8.38239i	−1.63466	+	0.485579i
$299$	1.62496	+	0.938173i	0.0939740	+	0.0542559i
$300$	1.40824	+	16.8054i	0.0813049	+	0.970262i
$301$	−9.14833	+	5.28179i	−0.527301	+	0.304437i
$302$	−6.40942	+	6.76454i	−0.368821	+	0.389256i
$303$	17.6212	−	10.8838i	1.01231	−	0.625258i
$304$	−14.4220	+	10.5462i	−0.827156	+	0.604865i
$305$	9.59696			0.549520
$306$	−1.66411	−	4.58514i	−0.0951311	−	0.262115i
$307$			22.9528i			1.30998i	0.755636	+	0.654991i	$0.227328\pi$
$307$			22.9528i			1.30998i	−0.755636	+	0.654991i	$0.772672\pi$
$308$	5.10619	−	0.275490i	0.290952	−	0.0156975i
$309$	−13.4121	+	0.398479i	−0.762989	+	0.0226687i
$310$	−21.8898	−	20.7407i	−1.24326	−	1.17799i
$311$	−3.06168	−	5.30299i	−0.173612	−	0.300705i	0.766068	−	0.642759i	$-0.222211\pi$
$311$	−3.06168	−	5.30299i	−0.173612	−	0.300705i	−0.939680	+	0.342055i	$0.888877\pi$
$312$	3.40872	−	4.25997i	0.192981	−	0.241174i
$313$	0.163360	−	0.282948i	0.00923366	−	0.0159932i	−0.861372	−	0.507975i	$-0.830394\pi$
$313$	0.163360	−	0.282948i	0.00923366	−	0.0159932i	0.870605	+	0.491982i	$0.163727\pi$
$314$	23.3038	−	6.92243i	1.31511	−	0.390655i
$315$	−7.86742	+	5.18831i	−0.443279	+	0.292328i
$316$	−8.31364	+	5.41716i	−0.467679	+	0.304739i
$317$	0.988446	+	0.570680i	0.0555167	+	0.0320526i	0.527501	−	0.849554i	$-0.323129\pi$
$317$	0.988446	+	0.570680i	0.0555167	+	0.0320526i	−0.471985	+	0.881607i	$0.656462\pi$
$318$	−16.8689	−	15.0582i	−0.945958	−	0.844422i
$319$	6.16387	+	10.6761i	0.345111	+	0.597749i
$320$	−15.9056	−	19.4573i	−0.889149	−	1.08769i
$321$	−8.34113	−	4.49090i	−0.465556	−	0.250658i
$322$	2.31729	+	0.554444i	0.129137	+	0.0308980i
$323$			5.13532i			0.285737i
$324$	−13.8099	+	11.5450i	−0.767217	+	0.641387i
$325$			5.42174i			0.300744i
$326$	3.13786	−	13.1146i	0.173790	−	0.726350i
$327$	15.4929	+	8.34147i	0.856762	+	0.461284i
$328$	1.49186	−	8.15445i	0.0823743	−	0.450254i
$329$	−5.80079	−	10.0473i	−0.319808	−	0.553924i
$330$	−13.1017	+	14.6771i	−0.721224	+	0.807947i
$331$	0.734494	+	0.424060i	0.0403715	+	0.0233085i	0.520050	−	0.854136i	$-0.325913\pi$
$331$	0.734494	+	0.424060i	0.0403715	+	0.0233085i	−0.479678	+	0.877444i	$0.659247\pi$
$332$	−13.7390	−	21.0850i	−0.754023	−	1.15719i
$333$	8.18876	−	5.40022i	0.448741	−	0.295930i
$334$	−6.40978	−	21.5780i	−0.350728	−	1.18070i
$335$	−17.1826	+	29.7612i	−0.938788	+	1.62603i
$336$	2.60899	−	6.41819i	0.142332	−	0.350141i
$337$	−4.90148	−	8.48961i	−0.267001	−	0.462459i	0.701085	−	0.713077i	$-0.252699\pi$
$337$	−4.90148	−	8.48961i	−0.267001	−	0.462459i	−0.968086	+	0.250619i	$0.919366\pi$
$338$	−11.4386	+	12.0723i	−0.622176	+	0.656648i
$339$	−27.4486	+	0.815509i	−1.49080	+	0.0442924i
$340$	−7.21285	+	0.389149i	−0.391172	+	0.0211046i
$341$		−	17.3550i		−	0.939827i
$342$	17.8134	−	6.46514i	0.963240	−	0.349595i
$343$	1.00000			0.0539949
$344$	10.0386	+	28.1414i	0.541247	+	1.51728i
$345$	−7.79937	+	4.81733i	−0.419904	+	0.259356i
$346$	−5.04704	−	4.78208i	−0.271330	−	0.257086i
$347$	0.898387	−	0.518684i	0.0482279	−	0.0278444i	−0.475692	−	0.879612i	$-0.657802\pi$
$347$	0.898387	−	0.518684i	0.0482279	−	0.0278444i	0.523920	+	0.851767i	$0.324469\pi$
$348$	16.6440	−	1.39471i	0.892210	−	0.0747644i
$349$	10.5858	+	6.11171i	0.566644	+	0.327152i	0.755808	−	0.654793i	$-0.227244\pi$
$349$	10.5858	+	6.11171i	0.566644	+	0.327152i	−0.189164	+	0.981946i	$0.560578\pi$
$350$	1.96048	+	6.59981i	0.104792	+	0.352775i
$351$	−4.73420	+	3.32791i	−0.252693	+	0.177631i
$352$	1.83264	−	14.3469i	0.0976801	−	0.764693i
$353$	−1.22662	+	2.12456i	−0.0652863	+	0.113079i	−0.896821	−	0.442394i	$-0.854129\pi$
$353$	−1.22662	+	2.12456i	−0.0652863	+	0.113079i	0.831535	+	0.555473i	$0.187463\pi$
$354$	−6.62592	+	31.8439i	−0.352164	+	1.69248i
$355$	−35.9448	+	20.7527i	−1.90775	+	1.10144i
$356$	10.7864	+	5.47505i	0.571679	+	0.290177i
$357$	−1.04645	−	1.69423i	−0.0553840	−	0.0896681i
$358$	2.58299	−	10.7956i	0.136515	−	0.570563i
$359$	4.44789			0.234750			0.117375	−	0.993088i	$-0.462552\pi$
$359$	4.44789			0.234750			0.117375	+	0.993088i	$0.462552\pi$
$360$	10.4305	+	24.5300i	0.549737	+	1.29285i
$361$	−0.950925			−0.0500487
$362$	−0.382577	+	1.59897i	−0.0201078	+	0.0840401i
$363$	7.72626	−	0.229550i	0.405524	−	0.0120483i
$364$	1.00814	−	1.98615i	0.0528410	−	0.104102i
$365$	19.4913	−	11.2533i	1.02022	−	0.589026i
$366$	7.10696	−	2.34296i	0.371487	−	0.122468i
$367$	−8.48896	+	14.7033i	−0.443120	+	0.767507i	−0.997919	−	0.0644776i	$-0.979462\pi$
$367$	−8.48896	+	14.7033i	−0.443120	+	0.767507i	0.554799	+	0.831985i	$0.312795\pi$
$368$	2.72213	−	6.16504i	0.141901	−	0.321375i
$369$	−3.93650	+	7.86223i	−0.204926	+	0.409292i
$370$	−4.13631	−	13.9246i	−0.215036	−	0.723903i
$371$	−7.99459	−	4.61568i	−0.415058	−	0.239634i
$372$	−21.2739	−	10.0153i	−1.10300	−	0.519268i
$373$	21.8343	−	12.6060i	1.13054	−	0.652716i	0.186468	−	0.982461i	$-0.440296\pi$
$373$	21.8343	−	12.6060i	1.13054	−	0.652716i	0.944070	+	0.329745i	$0.106963\pi$
$374$	−3.01772	−	2.85930i	−0.156043	−	0.147851i
$375$	0.630887	+	0.339672i	0.0325789	+	0.0175406i
$376$	−30.9067	+	11.0250i	−1.59389	+	0.568573i
$377$	5.36964			0.276551
$378$	−4.55951	+	5.76289i	−0.234516	+	0.296411i
$379$		−	34.4947i		−	1.77187i	−0.463806	−	0.885937i	$-0.653516\pi$
$379$		−	34.4947i		−	1.77187i	0.463806	−	0.885937i	$-0.346484\pi$
$380$	−1.51186	−	28.0222i	−0.0775566	−	1.43751i
$381$	−13.2201	+	24.5543i	−0.677288	+	1.25795i
$382$	−21.3164	+	22.4974i	−1.09064	+	1.15107i
$383$	3.23187	+	5.59776i	0.165141	+	0.286032i	0.936705	−	0.350119i	$-0.113859\pi$
$383$	3.23187	+	5.59776i	0.165141	+	0.286032i	−0.771565	+	0.636151i	$0.780525\pi$
$384$	−16.5290	−	10.5258i	−0.843491	−	0.537143i
$385$	−4.01596	+	6.95585i	−0.204672	+	0.354503i
$386$	−0.00236969	−	0.00797738i	−0.000120614	−	0.000406038i
$387$	−1.88143	−	31.6349i	−0.0956384	−	1.60809i
$388$	16.7913	−	10.9412i	0.852451	−	0.555457i
$389$	11.5957	+	6.69480i	0.587927	+	0.339440i	0.764277	−	0.644888i	$-0.223096\pi$
$389$	11.5957	+	6.69480i	0.587927	+	0.339440i	−0.176350	+	0.984327i	$0.556429\pi$
$390$	2.68308	+	8.13867i	0.135863	+	0.412118i
$391$	−0.968521	−	1.67753i	−0.0489802	−	0.0848363i
$392$	0.509014	−	2.78225i	0.0257091	−	0.140525i
$393$	−0.334841	−	11.2702i	−0.0168905	−	0.568505i
$394$	2.00320	−	8.37231i	0.100920	−	0.421791i
$395$		−	15.5857i		−	0.784201i
$396$	−6.11916	+	14.0676i	−0.307500	+	0.706924i
$397$		−	31.1981i		−	1.56579i	−0.622155	−	0.782894i	$-0.713742\pi$
$397$		−	31.1981i		−	1.56579i	0.622155	−	0.782894i	$-0.286258\pi$
$398$	−17.5292	−	4.19411i	−0.878658	−	0.210232i
$399$	6.58214	−	4.06549i	0.329519	−	0.203529i
$400$	19.3602	−	2.09515i	0.968011	−	0.104757i
$401$	8.43370	+	14.6076i	0.421159	+	0.729469i	0.996053	−	0.0887591i	$-0.0282901\pi$
$401$	8.43370	+	14.6076i	0.421159	+	0.729469i	−0.574894	+	0.818228i	$0.694957\pi$
$402$	−5.45871	+	26.2344i	−0.272256	+	1.30845i
$403$	−6.54663	−	3.77970i	−0.326111	−	0.188280i
$404$	−13.0562	−	20.0371i	−0.649569	−	0.996884i
$405$	−3.35106	−	28.0732i	−0.166516	−	1.39497i
$406$	6.53639	−	1.94164i	0.324396	−	0.0963622i
$407$	4.17999	−	7.23996i	0.207194	−	0.358871i
$408$	−5.24642	+	2.04910i	−0.259736	+	0.101445i
$409$	−1.08388	−	1.87733i	−0.0535944	−	0.0928282i	0.837984	−	0.545695i	$-0.183734\pi$
$409$	−1.08388	−	1.87733i	−0.0535944	−	0.0928282i	−0.891578	+	0.452867i	$0.850401\pi$
$410$	9.45180	+	8.95560i	0.466791	+	0.442286i
$411$	16.2828	+	26.3623i	0.803173	+	1.30036i
$412$	0.834711	+	15.4713i	0.0411233	+	0.762217i
$413$			13.2787i			0.653400i
$414$	−4.59969	+	5.47154i	−0.226063	+	0.268912i
$415$	39.5283			1.94037
$416$	−5.01279	−	3.81588i	−0.245772	−	0.187089i
$417$	0.475853	+	16.0164i	0.0233026	+	0.784326i
$418$	11.1085	−	11.7240i	0.543333	−	0.573437i
$419$	19.8122	−	11.4386i	0.967890	−	0.558812i	0.0692976	−	0.997596i	$-0.477924\pi$
$419$	19.8122	−	11.4386i	0.967890	−	0.558812i	0.898592	+	0.438785i	$0.144591\pi$
$420$	6.20900	+	8.93690i	0.302968	+	0.436076i
$421$	21.0770	+	12.1688i	1.02723	+	0.593070i	0.916189	−	0.400746i	$-0.131249\pi$
$421$	21.0770	+	12.1688i	1.02723	+	0.593070i	0.111039	+	0.993816i	$0.464582\pi$
$422$	−22.1799	+	6.58857i	−1.07970	+	0.320726i
$423$	34.7433	−	2.06630i	1.68928	−	0.100467i
$424$	−16.9113	+	19.8935i	−0.821286	+	0.966113i
$425$	2.79856	−	4.84725i	0.135750	−	0.235126i
$426$	−21.5522	+	24.1437i	−1.04421	+	1.16977i
$427$	2.64571	−	1.52750i	0.128035	−	0.0739210i
$428$	−4.95109	+	9.75416i	−0.239320	+	0.471485i
$429$	−2.33805	+	4.34255i	−0.112882	+	0.209660i
$430$	−45.6415	−	10.9204i	−2.20103	−	0.526628i
$431$	−11.5368			−0.555710			−0.277855	−	0.960623i	$-0.589623\pi$
$431$	−11.5368			−0.555710			−0.277855	+	0.960623i	$0.589623\pi$
$432$	13.7129	+	15.6191i	0.659763	+	0.751474i
$433$	−36.9204			−1.77428			−0.887141	−	0.461498i	$-0.847312\pi$
$433$	−36.9204			−1.77428			−0.887141	+	0.461498i	$0.847312\pi$
$434$	−9.33585	−	2.23374i	−0.448135	−	0.107223i
$435$	−12.4366	+	23.0990i	−0.596289	+	1.10751i
$436$	9.19622	−	18.1175i	0.440419	−	0.867672i
$437$	6.51726	−	3.76274i	0.311763	−	0.179996i
$438$	11.6868	−	13.0921i	0.558419	−	0.625565i
$439$	−1.37686	+	2.38479i	−0.0657138	+	0.113820i	−0.897010	−	0.442009i	$-0.854266\pi$
$439$	−1.37686	+	2.38479i	−0.0657138	+	0.113820i	0.831297	+	0.555829i	$0.187599\pi$
$440$	17.3087	+	14.7140i	0.825161	+	0.701464i
$441$	−1.34311	+	2.68255i	−0.0639577	+	0.127740i
$442$	−1.73580	+	0.515621i	−0.0825635	+	0.0245256i
$443$	−2.23105	−	1.28810i	−0.106000	−	0.0611993i	0.446063	−	0.895002i	$-0.352826\pi$
$443$	−2.23105	−	1.28810i	−0.106000	−	0.0611993i	−0.552063	+	0.833802i	$0.686159\pi$
$444$	−6.46260	−	9.30192i	−0.306701	−	0.441449i
$445$	−16.4543	+	9.49987i	−0.780007	+	0.450337i
$446$	14.6837	−	15.4973i	0.695295	−	0.733818i
$447$	−1.07068	−	36.0373i	−0.0506415	−	1.70451i
$448$	−7.48181	−	2.83241i	−0.353482	−	0.133819i
$449$	29.7950			1.40611			0.703057	−	0.711133i	$-0.251818\pi$
$449$	29.7950			1.40611			0.703057	+	0.711133i	$0.251818\pi$
$450$	−20.3374	−	3.60519i	−0.958716	−	0.169950i
$451$			7.49371i			0.352865i
$452$	1.70828	+	31.6629i	0.0803508	+	1.48930i
$453$	−5.99758	−	9.71023i	−0.281791	−	0.456226i
$454$	27.1865	+	25.7592i	1.27592	+	1.20894i
$455$	1.74925	+	3.02979i	0.0820060	+	0.142039i
$456$	−7.96081	−	20.3825i	−0.372799	−	0.954500i
$457$	14.6563	−	25.3855i	0.685593	−	1.18748i	−0.287657	−	0.957733i	$-0.592876\pi$
$457$	14.6563	−	25.3855i	0.685593	−	1.18748i	0.973250	−	0.229748i	$-0.0737902\pi$
$458$	28.1314	−	8.35648i	1.31450	−	0.390473i
$459$	5.95034	−	0.531613i	0.277738	−	0.0248135i
$460$	5.77885	+	8.86871i	0.269440	+	0.413506i
$461$	20.1446	+	11.6305i	0.938226	+	0.541685i	0.889404	−	0.457122i	$-0.151120\pi$
$461$	20.1446	+	11.6305i	0.938226	+	0.541685i	0.0488222	+	0.998807i	$0.484453\pi$
$462$	−1.27582	+	6.13155i	−0.0593566	+	0.285266i
$463$	−5.91766	−	10.2497i	−0.275017	−	0.476344i	0.695122	−	0.718892i	$-0.255350\pi$
$463$	−5.91766	−	10.2497i	−0.275017	−	0.476344i	−0.970139	+	0.242548i	$0.922017\pi$
$464$	−2.07502	−	19.1742i	−0.0963303	−	0.890139i
$465$	31.4220	−	19.4080i	1.45716	−	0.900023i
$466$	18.1222	+	4.33601i	0.839496	+	0.200862i
$467$			11.1239i			0.514752i	0.966311	+	0.257376i	$0.0828579\pi$
$467$			11.1239i			0.514752i	−0.966311	+	0.257376i	$0.917142\pi$
$468$	3.97388	+	5.37200i	0.183693	+	0.248321i
$469$			10.9395i			0.505140i
$470$	11.9934	−	50.1263i	0.553216	−	2.31215i
$471$	0.884203	+	29.7607i	0.0407419	+	1.37130i
$472$	36.9445	+	6.75903i	1.70051	+	0.311109i
$473$	−13.5045	−	23.3905i	−0.620939	−	1.07550i
$474$	−3.80503	−	11.5419i	−0.174771	−	0.530136i
$475$	18.8317	+	10.8725i	0.864060	+	0.498865i
$476$	−1.92652	+	1.25532i	−0.0883017	+	0.0575373i
$477$	23.1194	−	15.2465i	1.05856	−	0.698089i
$478$	−3.02309	−	10.1770i	−0.138273	−	0.465485i
$479$	7.09183	−	12.2834i	0.324034	−	0.561243i	−0.657282	−	0.753644i	$-0.728294\pi$
$479$	7.09183	−	12.2834i	0.324034	−	0.561243i	0.981316	+	0.192401i	$0.0616275\pi$
$480$	28.0251	−	12.7260i	1.27917	−	0.580858i
$481$	−1.82070	−	3.15354i	−0.0830166	−	0.143789i
$482$	−20.4207	+	21.5521i	−0.930136	+	0.981671i
$483$	−1.38340	+	2.56944i	−0.0629469	+	0.116914i
$484$	−0.480849	−	8.91250i	−0.0218568	−	0.405113i
$485$			31.4790i			1.42939i
$486$	−9.33527	−	19.9713i	−0.423457	−	0.905916i
$487$	−1.07391			−0.0486634			−0.0243317	−	0.999704i	$-0.507746\pi$
$487$	−1.07391			−0.0486634			−0.0243317	+	0.999704i	$0.507746\pi$
$488$	−2.90319	−	8.13855i	−0.131421	−	0.368415i
$489$	14.5417	+	7.82930i	0.657597	+	0.354053i
$490$	3.22490	+	3.05560i	0.145686	+	0.138038i
$491$	−11.1376	+	6.43031i	−0.502634	+	0.290196i	−0.729801	−	0.683660i	$-0.760387\pi$
$491$	−11.1376	+	6.43031i	−0.502634	+	0.290196i	0.227167	+	0.973856i	$0.427054\pi$
$492$	9.18585	+	4.32449i	0.414130	+	0.194963i
$493$	−4.80068	−	2.77167i	−0.216212	−	0.124830i
$494$	−2.00321	−	6.74364i	−0.0901285	−	0.303411i
$495$	−13.2655	−	20.1155i	−0.596240	−	0.904124i
$496$	−10.9669	+	24.8376i	−0.492428	+	1.11524i
$497$	−6.60623	+	11.4423i	−0.296330	+	0.513258i
$498$	29.2724	−	9.65028i	1.31173	−	0.432439i
$499$	−9.13839	+	5.27605i	−0.409090	+	0.236188i	−0.690399	−	0.723429i	$-0.742565\pi$
$499$	−9.13839	+	5.27605i	−0.409090	+	0.236188i	0.281308	+	0.959617i	$0.409232\pi$
$500$	0.374479	−	0.737762i	0.0167472	−	0.0329937i
$501$	27.5568	−	0.818722i	1.23114	−	0.0365778i
$502$	−5.24489	+	21.9209i	−0.234091	+	0.978377i
$503$	40.4074			1.80168			0.900838	−	0.434155i	$-0.142953\pi$
$503$	40.4074			1.80168			0.900838	+	0.434155i	$0.142953\pi$
$504$	6.77985	+	5.10232i	0.301998	+	0.227275i
$505$	37.5639			1.67157
$506$	−1.41761	+	5.92486i	−0.0630203	+	0.263392i
$507$	−10.7036	−	17.3294i	−0.475362	−	0.769624i
$508$	28.7139	+	14.5748i	1.27397	+	0.646652i
$509$	6.56409	−	3.78978i	0.290948	−	0.167979i	−0.347421	−	0.937709i	$-0.612943\pi$
$509$	6.56409	−	3.78978i	0.290948	−	0.167979i	0.638369	+	0.769730i	$0.279609\pi$
$510$	1.80219	−	8.66124i	0.0798022	−	0.383526i
$511$	3.58228	−	6.20469i	0.158471	−	0.274479i
$512$	−11.6888	+	19.3745i	−0.516577	+	0.856241i
$513$	2.06533	+	23.1173i	0.0911867	+	1.02065i
$514$	−0.878060	−	2.95592i	−0.0387296	−	0.130380i
$515$	−21.0756	−	12.1680i	−0.928703	−	0.536187i
$516$	−36.4655	+	3.05570i	−1.60531	+	0.134520i
$517$	25.6889	−	14.8315i	1.12980	−	0.652289i
$518$	−3.35661	−	3.18040i	−0.147481	−	0.139739i
$519$	7.24482	−	4.47480i	0.318012	−	0.196422i
$520$	9.32001	−	3.32464i	0.408710	−	0.145795i
$521$	26.4340			1.15809			0.579047	−	0.815294i	$-0.303425\pi$
$521$	26.4340			1.15809			0.579047	+	0.815294i	$0.303425\pi$
$522$	−3.57055	+	20.1420i	−0.156279	+	0.881592i
$523$			6.40721i			0.280168i	0.990140	+	0.140084i	$0.0447372\pi$
$523$			6.40721i			0.280168i	−0.990140	+	0.140084i	$0.955263\pi$
$524$	−13.0005	+	0.701406i	−0.567930	+	0.0306411i
$525$	−8.42845	+	0.250412i	−0.367848	+	0.0109289i
$526$	11.2734	−	11.8980i	0.491543	−	0.518778i
$527$	3.90197	+	6.75840i	0.169972	+	0.294401i
$528$	16.4101	+	6.67070i	0.714157	+	0.290305i
$529$	10.0807	−	17.4603i	0.438291	−	0.759142i
$530$	−11.6781	−	39.3133i	−0.507263	−	1.70766i
$531$	−35.6206	−	17.8347i	−1.54580	−	0.773961i
$532$	−4.87695	−	7.48459i	−0.211443	−	0.324498i
$533$	2.82676	+	1.63203i	0.122441	+	0.0706912i
$534$	−9.86584	+	11.0521i	−0.426936	+	0.478273i
$535$	−8.59073	−	14.8796i	−0.371410	−	0.643301i
$536$	30.4365	+	5.56837i	1.31466	+	0.240517i
$537$	11.9703	+	6.44486i	0.516556	+	0.278116i
$538$	0.709397	−	2.96491i	0.0305843	−	0.127826i
$539$			2.55681i			0.110130i
$540$	−32.3130	+	4.65268i	−1.39053	+	0.200219i
$541$			6.31237i			0.271390i	0.990751	+	0.135695i	$0.0433267\pi$
$541$			6.31237i			0.271390i	−0.990751	+	0.135695i	$0.956673\pi$
$542$	20.3109	+	4.85967i	0.872426	+	0.208741i
$543$	−1.77297	−	0.954573i	−0.0760852	−	0.0409646i
$544$	2.51198	+	5.99902i	0.107700	+	0.257206i
$545$	15.9566	+	27.6376i	0.683504	+	1.18386i
$546$	2.03507	+	1.81663i	0.0870931	+	0.0777448i
$547$	31.9762	+	18.4615i	1.36720	+	0.789356i	0.990570	−	0.137007i	$-0.0437482\pi$
$547$	31.9762	+	18.4615i	1.36720	+	0.789356i	0.376634	+	0.926362i	$0.377082\pi$
$548$	29.9768	−	19.5328i	1.28054	−	0.834401i
$549$	0.544112	+	9.14885i	0.0232221	+	0.390463i
$550$	−16.8744	+	5.01257i	−0.719529	+	0.213737i
$551$	10.7680	−	18.6508i	0.458734	−	0.794551i
$552$	6.44466	+	5.15684i	0.274303	+	0.219490i
$553$	−2.48070	−	4.29670i	−0.105490	−	0.182714i
$554$	−8.70663	−	8.24956i	−0.369909	−	0.350490i
$555$	17.7827	−	0.528331i	0.754834	−	0.0224264i
$556$	18.4754	−	0.996790i	0.783533	−	0.0422733i
$557$			29.4941i			1.24970i	0.780743	+	0.624852i	$0.214841\pi$
$557$			29.4941i			1.24970i	−0.780743	+	0.624852i	$0.785159\pi$
$558$	18.5312	−	22.0437i	0.784487	−	0.933183i
$559$	−11.7644			−0.497583
$560$	10.1429	−	7.41712i	0.428618	−	0.313431i
$561$	4.33182	−	2.67557i	0.182889	−	0.112963i
$562$	−15.3314	+	16.1808i	−0.646715	+	0.682547i
$563$	27.1145	−	15.6546i	1.14274	−	0.659761i	0.195632	−	0.980677i	$-0.437324\pi$
$563$	27.1145	−	15.6546i	1.14274	−	0.659761i	0.947108	+	0.320916i	$0.103991\pi$
$564$	−3.35596	−	40.0487i	−0.141311	−	1.68635i
$565$	−43.1324	−	24.9025i	−1.81459	−	1.04766i
$566$	−43.8984	+	13.0401i	−1.84519	+	0.548116i
$567$	−5.39211	−	7.20591i	−0.226447	−	0.302620i
$568$	28.4727	+	24.2045i	1.19469	+	1.01560i
$569$	3.81743	−	6.61199i	0.160035	−	0.277189i	−0.774846	−	0.632150i	$-0.782173\pi$
$569$	3.81743	−	6.61199i	0.160035	−	0.277189i	0.934881	+	0.354961i	$0.115506\pi$
$570$	33.6492	+	7.00156i	1.40941	+	0.293263i
$571$	−0.877928	+	0.506872i	−0.0367402	+	0.0212119i	−0.518258	−	0.855225i	$-0.673419\pi$
$571$	−0.877928	+	0.506872i	−0.0367402	+	0.0212119i	0.481517	+	0.876437i	$0.340086\pi$
$572$	5.07819	+	2.57763i	0.212330	+	0.107776i
$573$	−19.9467	−	32.2942i	−0.833284	−	1.34911i
$574$	4.03112	+	0.964503i	0.168256	+	0.0402576i
$575$	−8.20222			−0.342056
$576$	17.6470	−	16.2661i	0.735290	−	0.677753i
$577$	4.43655			0.184696			0.0923481	−	0.995727i	$-0.470563\pi$
$577$	4.43655			0.184696			0.0923481	+	0.995727i	$0.470563\pi$
$578$	−21.5636	−	5.15942i	−0.896930	−	0.214603i
$579$	0.0101877		0.000302681i	0.000423387		1.25790e-5i
$580$	27.0121	+	13.7110i	1.12162	+	0.569317i
$581$	10.8973	−	6.29154i	0.452095	−	0.261017i
$582$	7.68515	+	23.3115i	0.318560	+	0.966295i
$583$	11.8014	−	20.4406i	0.488764	−	0.846565i
$584$	−15.4396	−	13.1251i	−0.638893	−	0.543119i
$585$	−10.4770	+	0.623100i	−0.433170	+	0.0257620i
$586$	31.9949	−	9.50412i	1.32170	−	0.392612i
$587$	2.66824	+	1.54051i	0.110130	+	0.0635837i	0.554053	−	0.832481i	$-0.313080\pi$
$587$	2.66824	+	1.54051i	0.110130	+	0.0635837i	−0.443923	+	0.896065i	$0.646414\pi$
$588$	3.13416	+	1.47549i	0.129250	+	0.0608481i
$589$	−26.2566	+	15.1593i	−1.08189	+	0.624627i
$590$	−40.5742	+	42.8223i	−1.67041	+	1.76297i
$591$	9.28335	+	4.99820i	0.381866	+	0.205598i
$592$	−10.5572	+	7.72007i	−0.433899	+	0.317293i
$593$	−7.07396			−0.290493			−0.145246	−	0.989396i	$-0.546398\pi$
$593$	−7.07396			−0.290493			−0.145246	+	0.989396i	$0.546398\pi$
$594$	−14.7346	−	11.6578i	−0.604568	−	0.478325i
$595$		−	3.61167i		−	0.148064i
$596$	−41.5702	+	2.24280i	−1.70278	+	0.0918688i
$597$	10.4648	−	19.4366i	0.428294	−	0.795488i
$598$	1.92623	+	1.82510i	0.0787692	+	0.0746340i
$599$	−15.1086	−	26.1689i	−0.617323	−	1.06923i	−0.989972	−	0.141262i	$-0.954884\pi$
$599$	−15.1086	−	26.1689i	−0.617323	−	1.06923i	0.372650	−	0.927972i	$-0.378449\pi$
$600$	−3.59349	+	23.5775i	−0.146704	+	0.962547i
$601$	1.20922	−	2.09443i	0.0493250	−	0.0854334i	−0.840309	−	0.542108i	$-0.817626\pi$
$601$	1.20922	−	2.09443i	0.0493250	−	0.0854334i	0.889634	+	0.456675i	$0.150960\pi$
$602$	−14.3207	+	4.25398i	−0.583668	+	0.173379i
$603$	−29.3458	−	14.6930i	−1.19505	−	0.598345i
$604$	−11.0416	+	7.19467i	−0.449275	+	0.292747i
$605$	12.1409	+	7.00958i	0.493600	+	0.284980i
$606$	27.8177	−	9.17069i	1.13002	−	0.372534i
$607$	−11.5566	−	20.0165i	−0.469066	−	0.812446i	0.530309	−	0.847805i	$-0.322076\pi$
$607$	−11.5566	−	20.0165i	−0.469066	−	0.812446i	−0.999375	+	0.0353585i	$0.988743\pi$
$608$	−23.3064	+	9.75913i	−0.945200	+	0.395785i
$609$	0.248006	+	8.34746i	0.0100497	+	0.338256i
$610$	13.1996	+	3.15819i	0.534435	+	0.127871i
$611$		−	12.9204i		−	0.522705i
$612$	−0.779920	−	6.85400i	−0.0315264	−	0.277056i
$613$			43.2417i			1.74651i	0.487260	+	0.873257i	$0.337997\pi$
$613$			43.2417i			1.74651i	−0.487260	+	0.873257i	$0.662003\pi$
$614$	−7.55335	+	31.5690i	−0.304829	+	1.27402i
$615$	−13.5677	+	8.38015i	−0.547102	+	0.337920i
$616$	7.11368	+	1.30145i	0.286618	+	0.0524370i
$617$	2.24846	+	3.89445i	0.0905198	+	0.156785i	0.907730	−	0.419555i	$-0.137814\pi$
$617$	2.24846	+	3.89445i	0.0905198	+	0.156785i	−0.817210	+	0.576340i	$0.804481\pi$
$618$	−18.5781	−	3.86563i	−0.747319	−	0.155498i
$619$	−5.80594	−	3.35206i	−0.233361	−	0.134731i	0.378761	−	0.925495i	$-0.376350\pi$
$619$	−5.80594	−	3.35206i	−0.233361	−	0.134731i	−0.612121	+	0.790764i	$0.709684\pi$
$620$	−23.2817	−	35.7301i	−0.935017	−	1.43496i
$621$	−5.03459	−	7.16208i	−0.202031	−	0.287404i
$622$	−2.46589	−	8.30124i	−0.0988733	−	0.332849i
$623$	−3.02410	+	5.23790i	−0.121158	+	0.209852i
$624$	6.09021	−	4.73739i	0.243803	−	0.189647i
$625$	12.8205	+	22.2058i	0.512822	+	0.888234i
$626$	0.317798	−	0.335406i	0.0127017	−	0.0134055i
$627$	10.3947	+	16.8293i	0.415124	+	0.672096i
$628$	34.3300	−	1.85218i	1.36991	−	0.0739099i
$629$			3.75918i			0.149888i
$630$	−12.5282	+	4.54693i	−0.499134	+	0.181154i
$631$	−44.2673			−1.76225			−0.881126	−	0.472881i	$-0.843214\pi$
$631$	−44.2673			−1.76225			−0.881126	+	0.472881i	$0.843214\pi$
$632$	−13.2172	+	4.71485i	−0.525752	+	0.187547i
$633$	−0.841558	−	28.3254i	−0.0334489	−	1.12583i
$634$	1.17170	+	1.11019i	0.0465342	+	0.0440912i
$635$	−43.8019	+	25.2891i	−1.73823	+	1.00357i
$636$	−18.2459	−	26.2622i	−0.723497	−	1.04136i
$637$	0.964474	+	0.556840i	0.0382139	+	0.0220628i
$638$	4.96441	+	16.7123i	0.196543	+	0.661647i
$639$	−21.8217	−	33.0898i	−0.863252	−	1.30901i
$640$	−15.4734	−	31.9956i	−0.611639	−	1.26474i
$641$	−24.1643	+	41.8538i	−0.954433	+	1.65313i	−0.218772	+	0.975776i	$0.570205\pi$
$641$	−24.1643	+	41.8538i	−0.954433	+	1.65313i	−0.735661	+	0.677350i	$0.763128\pi$
$642$	−9.99445	−	8.92167i	−0.394449	−	0.352110i
$643$	7.88176	−	4.55054i	0.310826	−	0.179456i	−0.336470	−	0.941694i	$-0.609233\pi$
$643$	7.88176	−	4.55054i	0.310826	−	0.179456i	0.647296	+	0.762239i	$0.275900\pi$
$644$	3.00472	+	1.52516i	0.118403	+	0.0600996i
$645$	27.2476	−	50.6080i	1.07287	−	1.99269i
$646$	−1.68995	+	7.06309i	−0.0664900	+	0.277893i
$647$	−19.5917			−0.770229			−0.385115	−	0.922869i	$-0.625838\pi$
$647$	−19.5917			−0.770229			−0.385115	+	0.922869i	$0.625838\pi$
$648$	−22.7933	+	11.3343i	−0.895405	+	0.445252i
$649$	−33.9510			−1.33269
$650$	−1.78420	+	7.45702i	−0.0699821	+	0.292488i
$651$	5.57342	−	10.3517i	0.218440	−	0.405716i
$652$	8.63157	−	17.0051i	0.338038	−	0.665971i
$653$	−20.1514	+	11.6344i	−0.788585	+	0.455290i	−0.839464	−	0.543415i	$-0.817131\pi$
$653$	−20.1514	+	11.6344i	−0.788585	+	0.455290i	0.0508794	+	0.998705i	$0.483798\pi$
$654$	18.5638	+	16.5713i	0.725904	+	0.647987i
$655$	10.2248	−	17.7098i	0.399514	−	0.691979i
$656$	4.73538	−	10.7246i	0.184886	−	0.418726i
$657$	11.8330	+	17.9432i	0.461648	+	0.700031i
$658$	−4.67198	−	15.7279i	−0.182133	−	0.613136i
$659$	28.0008	+	16.1663i	1.09076	+	0.629748i	0.933778	−	0.357854i	$-0.116491\pi$
$659$	28.0008	+	16.1663i	1.09076	+	0.629748i	0.156979	+	0.987602i	$0.449825\pi$
$660$	−22.8499	+	15.8752i	−0.889433	+	0.617942i
$661$	4.82385	−	2.78505i	0.187626	−	0.108326i	−0.403245	−	0.915092i	$-0.632118\pi$
$661$	4.82385	−	2.78505i	0.187626	−	0.108326i	0.590871	+	0.806766i	$0.298784\pi$
$662$	0.870667	+	0.824959i	0.0338394	+	0.0320629i
$663$	−0.0658603	−	2.21674i	−0.00255780	−	0.0860912i
$664$	−11.9578	−	33.5214i	−0.464051	−	1.30088i
$665$	14.0315			0.544117
$666$	13.0399	−	4.73264i	0.505285	−	0.183386i
$667$			8.12341i			0.314540i
$668$	−1.71501	−	31.7876i	−0.0663558	−	1.22990i
$669$	13.7402	+	22.2458i	0.531227	+	0.860071i
$670$	−33.4268	+	35.2788i	−1.29139	+	1.36294i
$671$	3.90553	+	6.76458i	0.150771	+	0.261144i
$672$	5.70051	−	7.96895i	0.219902	−	0.307409i
$673$	9.75438	−	16.8951i	0.376004	−	0.651258i	−0.614473	−	0.788938i	$-0.710631\pi$
$673$	9.75438	−	16.8951i	0.376004	−	0.651258i	0.990477	+	0.137680i	$0.0439647\pi$
$674$	−3.94767	−	13.2895i	−0.152059	−	0.511894i
$675$	10.6486	−	22.9460i	0.409865	−	0.883193i
$676$	−19.7053	+	12.8400i	−0.757897	+	0.493845i
$677$	21.1081	+	12.1868i	0.811249	+	0.468375i	0.847390	−	0.530972i	$-0.178173\pi$
$677$	21.1081	+	12.1868i	0.811249	+	0.468375i	−0.0361403	+	0.999347i	$0.511506\pi$
$678$	−38.0210	−	7.91122i	−1.46019	−	0.303829i
$679$	5.01036	+	8.67820i	0.192280	+	0.333039i
$680$	−10.0486	−	1.83839i	−0.385345	−	0.0704990i
$681$	−39.0251	+	24.1041i	−1.49545	+	0.923670i
$682$	5.71124	−	23.8700i	0.218695	−	0.914028i
$683$			9.84739i			0.376800i	0.982092	+	0.188400i	$0.0603301\pi$
$683$			9.84739i			0.376800i	−0.982092	+	0.188400i	$0.939670\pi$
$684$	26.6280	−	3.03002i	1.01815	−	0.115856i
$685$			56.1979i			2.14721i
$686$	1.37539	+	0.329083i	0.0525127	+	0.0125644i
$687$	1.06737	+	35.9259i	0.0407228	+	1.37066i
$688$	4.54619	+	42.0091i	0.173322	+	1.60158i
$689$	−5.14038	−	8.90341i	−0.195833	−	0.339193i
$690$	−12.3125	+	4.05908i	−0.468729	+	0.154526i
$691$	−8.36113	−	4.82730i	−0.318072	−	0.183639i	0.332461	−	0.943117i	$-0.392121\pi$
$691$	−8.36113	−	4.82730i	−0.318072	−	0.183639i	−0.650533	+	0.759478i	$0.725454\pi$
$692$	−5.36796	−	8.23813i	−0.204059	−	0.313167i
$693$	−6.85876	−	3.43408i	−0.260543	−	0.130450i
$694$	1.40632	−	0.417751i	0.0533834	−	0.0158576i
$695$	−14.5307	+	25.1680i	−0.551182	+	0.954675i
$696$	23.3509	+	3.55896i	0.885115	+	0.134902i
$697$	−1.68483	−	2.91820i	−0.0638174	−	0.110535i
$698$	12.5484	+	11.8896i	0.474962	+	0.450028i
$699$	−10.8188	+	20.0942i	−0.409205	+	0.760033i
$700$	0.524549	+	9.72249i	0.0198261	+	0.367475i
$701$			28.5557i			1.07853i	0.842135	+	0.539266i	$0.181298\pi$
$701$			28.5557i			1.07853i	−0.842135	+	0.539266i	$0.818702\pi$
$702$	−7.60654	+	3.01924i	−0.287090	+	0.113954i
$703$	−14.6046			−0.550822
$704$	7.24192	−	19.1296i	0.272940	−	0.720972i
$705$	55.5808	+	29.9249i	2.09329	+	1.12704i
$706$	−2.38624	+	2.51845i	−0.0898072	+	0.0947831i
$707$	10.3557	−	5.97887i	0.389466	−	0.224859i
$708$	−19.5925	+	41.6174i	−0.736332	+	1.56408i
$709$	−31.9698	−	18.4578i	−1.20065	−	0.693197i	−0.239952	−	0.970785i	$-0.577132\pi$
$709$	−31.9698	−	18.4578i	−1.20065	−	0.693197i	−0.960700	+	0.277588i	$0.910465\pi$
$710$	−56.2675	+	16.7143i	−2.11168	+	0.627278i
$711$	14.8580	−	0.883652i	0.557217	−	0.0331395i
$712$	13.0338	+	11.0800i	0.488463	+	0.415239i
$713$	5.71808	−	9.90400i	0.214144	−	0.370908i
$714$	−0.881737	−	2.67460i	−0.0329982	−	0.100094i
$715$	−7.74659	+	4.47249i	−0.289706	+	0.167262i
$716$	7.10526	−	13.9981i	0.265536	−	0.523134i
$717$	12.9968	−	0.386140i	0.485374	−	0.0144207i
$718$	6.11759	+	1.46372i	0.228306	+	0.0546256i
$719$	−28.5055			−1.06308			−0.531539	−	0.847034i	$-0.678386\pi$
$719$	−28.5055			−1.06308			−0.531539	+	0.847034i	$0.678386\pi$
$720$	6.27367	+	37.1709i	0.233806	+	1.38528i
$721$	−7.74691			−0.288510
$722$	−1.30790	−	0.312933i	−0.0486748	−	0.0116462i
$723$	−19.1085	−	30.9372i	−0.710653	−	1.15057i
$724$	−1.05239	+	2.07331i	−0.0391117	+	0.0770541i
$725$	−20.3280	+	11.7364i	−0.754963	+	0.435878i
$726$	10.7022	+	2.22686i	0.397195	+	0.0826464i
$727$	15.3515	−	26.5896i	0.569356	−	0.986153i	−0.427274	−	0.904122i	$-0.640526\pi$
$727$	15.3515	−	26.5896i	0.569356	−	0.986153i	0.996630	−	0.0820310i	$-0.0261406\pi$
$728$	2.04020	−	2.39997i	0.0756147	−	0.0889487i
$729$	26.5724	−	4.78624i	0.984163	−	0.177268i
$730$	30.5115	−	9.06348i	1.12928	−	0.335454i
$731$	10.5179	+	6.07250i	0.389018	+	0.224600i
$732$	10.5459	−	0.883713i	0.389787	−	0.0326630i
$733$	19.2294	−	11.1021i	0.710253	−	0.410065i	−0.100902	−	0.994896i	$-0.532173\pi$
$733$	19.2294	−	11.1021i	0.710253	−	0.410065i	0.811155	+	0.584832i	$0.198839\pi$
$734$	−16.5143	+	17.4293i	−0.609553	+	0.643326i
$735$	−4.62921	+	2.85926i	−0.170751	+	0.105465i
$736$	5.77281	−	7.58355i	0.212789	−	0.279533i
$737$	−27.9703			−1.03030
$738$	−8.00156	+	9.51822i	−0.294542	+	0.350371i
$739$		−	7.42933i		−	0.273292i	−0.990620	−	0.136646i	$-0.956368\pi$
$739$		−	7.42933i		−	0.273292i	0.990620	−	0.136646i	$-0.0436323\pi$
$740$	−1.10672	−	20.5129i	−0.0406837	−	0.754070i
$741$	8.61213	−	0.255870i	0.316375	−	0.00939961i
$742$	−9.47676	−	8.97925i	−0.347903	−	0.329639i
$743$	−0.0239107	−	0.0414146i	−0.000877200	−	0.00151935i	0.865586	−	0.500759i	$-0.166946\pi$
$743$	−0.0239107	−	0.0414146i	−0.000877200	−	0.00151935i	−0.866464	+	0.499240i	$0.833613\pi$
$744$	−25.9641	−	20.7758i	−0.951892	−	0.761678i
$745$	32.6945	−	56.6286i	1.19783	−	2.07471i
$746$	34.1792	−	10.1530i	1.25139	−	0.371727i
$747$	2.24111	+	37.6827i	0.0819979	+	1.37874i
$748$	−3.20960	−	4.92573i	−0.117355	−	0.180103i
$749$	−4.73663	−	2.73469i	−0.173073	−	0.0999236i
$750$	0.755937	+	0.674797i	0.0276029	+	0.0246401i
$751$	7.44702	+	12.8986i	0.271746	+	0.470677i	0.969309	−	0.245846i	$-0.0790657\pi$
$751$	7.44702	+	12.8986i	0.271746	+	0.470677i	−0.697563	+	0.716523i	$0.745732\pi$
$752$	−46.1369	+	4.99291i	−1.68244	+	0.182073i
$753$	−24.3062	−	13.0866i	−0.885769	−	0.476902i
$754$	7.38537	+	1.76706i	0.268959	+	0.0643524i
$755$		−	20.6998i		−	0.753342i
$756$	−8.16759	+	6.42577i	−0.297052	+	0.233703i
$757$		−	15.4496i		−	0.561525i	−0.959777	−	0.280762i	$-0.909413\pi$
$757$		−	15.4496i		−	0.561525i	0.959777	−	0.280762i	$-0.0905873\pi$
$758$	11.3516	−	47.4438i	0.412309	−	1.72323i
$759$	−6.56957	−	3.53709i	−0.238460	−	0.128388i
$760$	7.14221	−	39.0390i	0.259075	−	1.41609i
$761$	−19.3223	−	33.4672i	−0.700433	−	1.21318i	−0.968315	−	0.249733i	$-0.919657\pi$
$761$	−19.3223	−	33.4672i	−0.700433	−	1.21318i	0.267882	−	0.963452i	$-0.413676\pi$
$762$	−26.2633	+	29.4213i	−0.951418	+	1.06582i
$763$	8.79789	+	5.07946i	0.318505	+	0.183889i
$764$	−36.7219	+	23.9280i	−1.32855	+	0.865683i
$765$	9.68847	+	4.85087i	0.350287	+	0.175384i
$766$	2.60296	+	8.76267i	0.0940488	+	0.316608i
$767$	−7.39408	+	12.8069i	−0.266985	+	0.462431i
$768$	−19.2700	−	19.9165i	−0.695345	−	0.718676i
$769$	21.7548	+	37.6804i	0.784499	+	1.35879i	0.929298	+	0.369330i	$0.120413\pi$
$769$	21.7548	+	37.6804i	0.784499	+	1.35879i	−0.144800	+	0.989461i	$0.546254\pi$
$770$	−7.81258	+	8.24544i	−0.281546	+	0.297145i
$771$	3.77493	−	0.112155i	0.135951	−	0.00403915i
$772$	−0.000634038	−	0.0117519i	−2.28195e−5	−	0.000422959i
$773$		−	30.5921i		−	1.10032i	−0.835059	−	0.550161i	$-0.814566\pi$
$773$		−	30.5921i		−	1.10032i	0.835059	−	0.550161i	$-0.185434\pi$
$774$	7.82278	−	44.1295i	0.281184	−	1.58620i
$775$	33.0450			1.18701
$776$	26.6953	−	9.52275i	0.958304	−	0.341847i
$777$	4.81829	−	2.97604i	0.172855	−	0.106765i
$778$	13.7455	+	13.0239i	0.492801	+	0.466930i
$779$	11.3373	−	6.54561i	0.406202	−	0.234521i
$780$	1.01200	+	12.0768i	0.0362354	+	0.432420i
$781$	−29.2558	−	16.8909i	−1.04686	−	0.604403i
$782$	−0.780052	−	2.62598i	−0.0278946	−	0.0939050i
$783$	−22.7255	−	10.5463i	−0.812145	−	0.376893i
$784$	1.61568	−	3.65918i	0.0577030	−	0.130685i
$785$	−27.0001	+	46.7656i	−0.963676	+	1.66914i
$786$	3.24828	−	15.6111i	0.115862	−	0.556830i
$787$	−25.2543	+	14.5806i	−0.900220	+	0.519742i	−0.877271	−	0.479995i	$-0.840639\pi$
$787$	−25.2543	+	14.5806i	−0.900220	+	0.519742i	−0.0229483	+	0.999737i	$0.507305\pi$
$788$	5.51036	−	10.8560i	0.196299	−	0.386729i
$789$	10.5490	+	17.0791i	0.375555	+	0.608033i
$790$	5.12898	−	21.4365i	0.182481	−	0.762675i
$791$	−15.8545			−0.563720
$792$	−13.0457	+	17.3348i	−0.463557	+	0.615964i
$793$	3.40230			0.120819
$794$	10.2668	−	42.9097i	0.364354	−	1.52281i
$795$	50.2060	−	1.49164i	1.78062	−	0.0529030i
$796$	−22.7293	−	11.5371i	−0.805618	−	0.408921i
$797$	7.46331	−	4.30894i	0.264364	−	0.152631i	−0.361960	−	0.932194i	$-0.617892\pi$
$797$	7.46331	−	4.30894i	0.264364	−	0.152631i	0.626324	+	0.779563i	$0.284559\pi$
$798$	10.3909	−	3.42558i	0.367834	−	0.121264i
$799$	−6.66920	+	11.5514i	−0.235939	+	0.408659i
$800$	27.3174	+	3.48946i	0.965815	+	0.123371i
$801$	−9.98920	−	15.1474i	−0.352951	−	0.535206i
$802$	6.79254	+	22.8666i	0.239853	+	0.807446i
$803$	15.8642	+	9.15920i	0.559836	+	0.323221i
$804$	−16.1411	+	34.2862i	−0.569254	+	1.20918i
$805$	−4.58358	+	2.64633i	−0.161550	+	0.0932709i
$806$	−7.76035	−	7.35295i	−0.273347	−	0.258997i
$807$	3.28754	+	1.77002i	0.115727	+	0.0623078i
$808$	−11.3635	−	31.8555i	−0.399766	−	1.12067i
$809$	−30.6847			−1.07882			−0.539409	−	0.842044i	$-0.681352\pi$
$809$	−30.6847			−1.07882			−0.539409	+	0.842044i	$0.681352\pi$
$810$	4.62937	−	39.7144i	0.162660	−	1.39542i
$811$			22.8266i			0.801549i	0.916177	+	0.400774i	$0.131259\pi$
$811$			22.8266i			0.801549i	−0.916177	+	0.400774i	$0.868741\pi$
$812$	9.62907	−	0.519509i	0.337914	−	0.0182312i
$813$	−12.1254	+	22.5210i	−0.425257	+	0.789846i
$814$	8.13167	−	8.58222i	0.285015	−	0.300807i
$815$	14.9768	+	25.9406i	0.524615	+	0.908660i
$816$	−7.89021	+	1.09180i	−0.276213	+	0.0382208i
$817$	−23.5919	+	40.8624i	−0.825376	+	1.42959i
$818$	−0.872961	−	2.93876i	−0.0305224	−	0.102751i
$819$	−2.78914	+	1.83935i	−0.0974606	+	0.0642721i
$820$	10.0528	+	15.4279i	0.351059	+	0.538765i
$821$	−35.7103	−	20.6174i	−1.24630	−	0.719551i	−0.275930	−	0.961178i	$-0.588986\pi$
$821$	−35.7103	−	20.6174i	−1.24630	−	0.719551i	−0.970369	+	0.241627i	$0.922319\pi$
$822$	13.7199	+	41.6169i	0.478537	+	1.45156i
$823$	6.17838	+	10.7013i	0.215365	+	0.373023i	0.953385	−	0.301755i	$-0.0975726\pi$
$823$	6.17838	+	10.7013i	0.215365	+	0.373023i	−0.738021	+	0.674778i	$0.764239\pi$
$824$	−3.94328	+	21.5538i	−0.137371	+	0.750863i
$825$	−0.640256	−	21.5499i	−0.0222909	−	0.750272i
$826$	−4.36978	+	18.2634i	−0.152044	+	0.635464i
$827$			7.53865i			0.262145i	0.991373	+	0.131072i	$0.0418420\pi$
$827$			7.53865i			0.262145i	−0.991373	+	0.131072i	$0.958158\pi$
$828$	−8.12697	+	6.01184i	−0.282432	+	0.208926i
$829$			42.2972i			1.46904i	0.678585	+	0.734522i	$0.262593\pi$
$829$			42.2972i			1.46904i	−0.678585	+	0.734522i	$0.737407\pi$
$830$	54.3670	+	13.0081i	1.88710	+	0.451517i
$831$	12.4980	−	7.71948i	0.433552	−	0.267786i
$832$	−5.63882	−	6.89795i	−0.195491	−	0.239143i
$833$	−0.574852	−	0.995674i	−0.0199175	−	0.0344980i
$834$	−4.61623	+	22.1854i	−0.159847	+	0.768219i
$835$	43.3023	+	25.0006i	1.49854	+	0.865181i
$836$	19.1367	−	12.4694i	0.661855	−	0.431264i
$837$	20.2833	+	28.8545i	0.701093	+	0.997357i
$838$	31.0138	−	9.21269i	1.07135	−	0.318247i
$839$	−4.34598	+	7.52746i	−0.150040	+	0.259877i	−0.931242	−	0.364402i	$-0.881274\pi$
$839$	−4.34598	+	7.52746i	−0.150040	+	0.259877i	0.781202	+	0.624278i	$0.214607\pi$
$840$	5.59883	+	14.3350i	0.193178	+	0.494605i
$841$	−2.87640	−	4.98207i	−0.0991861	−	0.171795i
$842$	24.9845	+	23.6729i	0.861024	+	0.815822i
$843$	−14.3462	−	23.2269i	−0.494111	−	0.799978i
$844$	−32.6742	+	1.76285i	−1.12469	+	0.0606797i
$845$		−	36.9418i		−	1.27084i
$846$	48.4657	+	8.59146i	1.66629	+	0.295380i
$847$	4.46273			0.153341
$848$	−29.8063	+	21.7961i	−1.02355	+	0.748482i
$849$	−1.66561	−	56.0616i	−0.0571636	−	1.92403i
$850$	5.44427	−	5.74591i	0.186737	−	0.197083i
$851$	4.77079	−	2.75442i	0.163541	−	0.0944203i
$852$	−37.5880	+	26.1146i	−1.28774	+	0.894672i
$853$	−42.8080	−	24.7152i	−1.46572	−	0.846232i	−0.466451	−	0.884547i	$-0.654468\pi$
$853$	−42.8080	−	24.7152i	−1.46572	−	0.846232i	−0.999266	+	0.0383147i	$0.987801\pi$
$854$	4.14157	−	1.23026i	0.141722	−	0.0420986i
$855$	−18.8458	+	37.6400i	−0.644513	+	1.28726i
$856$	−10.0196	+	11.7865i	−0.342463	+	0.402854i
$857$	−18.9793	+	32.8732i	−0.648321	+	1.12293i	0.335202	+	0.942146i	$0.391195\pi$
$857$	−18.9793	+	32.8732i	−0.648321	+	1.12293i	−0.983524	+	0.180779i	$0.942138\pi$
$858$	−4.64479	+	5.20329i	−0.158570	+	0.177638i
$859$	−10.2126	+	5.89622i	−0.348448	+	0.201176i	−0.664001	−	0.747731i	$-0.731143\pi$
$859$	−10.2126	+	5.89622i	−0.348448	+	0.201176i	0.315554	+	0.948908i	$0.397810\pi$
$860$	−59.1812	−	30.0396i	−2.01806	−	1.02434i
$861$	−2.40654	+	4.46977i	−0.0820147	+	0.152329i
$862$	−15.8677	−	3.79657i	−0.540455	−	0.129312i
$863$	53.5701			1.82355			0.911774	−	0.410693i	$-0.134713\pi$
$863$	53.5701			1.82355			0.911774	+	0.410693i	$0.134713\pi$
$864$	13.7207	+	25.9951i	0.466787	+	0.884370i
$865$	15.4441			0.525117
$866$	−50.7801	−	12.1499i	−1.72558	−	0.412869i
$867$	12.8733	−	23.9101i	0.437201	−	0.812030i
$868$	−12.1054	−	6.14453i	−0.410883	−	0.208559i
$869$	10.9858	−	6.34268i	0.372669	−	0.215161i
$870$	−24.7067	+	27.6775i	−0.837635	+	0.938355i
$871$	−6.09156	+	10.5509i	−0.206405	+	0.357503i
$872$	18.6106	−	21.8924i	0.630234	−	0.741370i
$873$	−30.0092	+	1.78474i	−1.01566	+	0.0604044i
$874$	10.2020	−	3.03053i	0.345089	−	0.102509i
$875$	0.358258	+	0.206840i	0.0121113	+	0.00699248i
$876$	20.3824	−	14.1608i	0.688656	−	0.478451i
$877$	−1.42863	+	0.824823i	−0.0482416	+	0.0278523i	−0.523927	−	0.851763i	$-0.675533\pi$
$877$	−1.42863	+	0.824823i	−0.0482416	+	0.0278523i	0.475685	+	0.879616i	$0.342200\pi$
$878$	−2.67851	+	2.82692i	−0.0903953	+	0.0954038i
$879$	1.21396	+	40.8599i	0.0409459	+	1.37817i
$880$	18.9642	+	25.9336i	0.639282	+	0.874220i
$881$	−9.02450			−0.304043			−0.152022	−	0.988377i	$-0.548578\pi$
$881$	−9.02450			−0.304043			−0.152022	+	0.988377i	$0.548578\pi$
$882$	−2.73008	+	3.24756i	−0.0919267	+	0.109351i
$883$			54.0475i			1.81884i	0.415875	+	0.909422i	$0.363475\pi$
$883$			54.0475i			1.81884i	−0.415875	+	0.909422i	$0.636525\pi$
$884$	−2.55709	+	0.137960i	−0.0860041	+	0.00464011i
$885$	−37.9671	−	61.4697i	−1.27625	−	2.06628i
$886$	−2.64468	−	2.50584i	−0.0888497	−	0.0841853i
$887$	18.4551	+	31.9652i	0.619661	+	1.07328i	0.989547	+	0.144208i	$0.0460634\pi$
$887$	18.4551	+	31.9652i	0.619661	+	1.07328i	−0.369886	+	0.929077i	$0.620603\pi$
$888$	−5.82751	−	14.9205i	−0.195558	−	0.500700i
$889$	−8.05028	+	13.9435i	−0.269998	+	0.467650i
$890$	−25.7573	+	7.65124i	−0.863387	+	0.256470i
$891$	18.4241	−	13.7866i	0.617232	−	0.461868i
$892$	25.2958	−	16.4827i	0.846965	−	0.551882i
$893$	−44.8776	−	25.9101i	−1.50177	−	0.867048i
$894$	10.3866	−	49.9178i	0.347381	−	1.66950i
$895$	12.3285	+	21.3536i	0.412096	+	0.713771i
$896$	−9.35833	−	6.35780i	−0.312640	−	0.212399i
$897$	−2.76502	+	1.70783i	−0.0923213	+	0.0570228i
$898$	40.9799	+	9.80503i	1.36752	+	0.327198i
$899$		−	32.7275i		−	1.09152i
$900$	−26.7855	−	11.6512i	−0.892851	−	0.388375i
$901$			10.6133i			0.353581i
$902$	−2.46605	+	10.3068i	−0.0821105	+	0.343179i
$903$	−0.543361	−	18.2886i	−0.0180819	−	0.608606i
$904$	−8.07015	+	44.1111i	−0.268409	+	1.46711i
$905$	−1.82602	−	3.16276i	−0.0606990	−	0.105134i
$906$	−5.05356	−	15.3291i	−0.167893	−	0.509275i
$907$	−26.7112	−	15.4217i	−0.886931	−	0.512070i	−0.0139934	−	0.999902i	$-0.504454\pi$
$907$	−26.7112	−	15.4217i	−0.886931	−	0.512070i	−0.872937	+	0.487832i	$0.837788\pi$
$908$	28.9152	+	44.3757i	0.959583	+	1.47266i
$909$	2.12973	+	35.8099i	0.0706388	+	1.18774i
$910$	1.40885	+	4.74279i	0.0467030	+	0.157222i
$911$	6.79661	−	11.7721i	0.225182	−	0.390026i	−0.731192	−	0.682172i	$-0.761036\pi$
$911$	6.79661	−	11.7721i	0.225182	−	0.390026i	0.956374	+	0.292145i	$0.0943691\pi$
$912$	−4.24170	−	30.6537i	−0.140457	−	1.01505i
$913$	16.0863	+	27.8622i	0.532378	+	0.922105i
$914$	28.5121	−	30.0918i	0.943096	−	0.995349i
$915$	−7.88004	+	14.6359i	−0.260506	+	0.483848i
$916$	41.4417	−	2.23587i	1.36927	−	0.0738753i
$917$		−	6.50971i		−	0.214970i
$918$	8.35900	+	1.22698i	0.275888	+	0.0404963i
$919$	−11.6627			−0.384715			−0.192358	−	0.981325i	$-0.561613\pi$
$919$	−11.6627			−0.384715			−0.192358	+	0.981325i	$0.561613\pi$
$920$	5.02964	+	14.0997i	0.165822	+	0.464853i
$921$	−35.0043	−	18.8465i	−1.15343	−	0.621012i
$922$	23.8793	+	22.6257i	0.786423	+	0.745137i
$923$	−12.7431	+	7.35722i	−0.419443	+	0.242166i
$924$	−3.77254	+	8.01344i	−0.124108	+	0.263623i
$925$	13.7853	+	7.95895i	0.453258	+	0.261689i
$926$	−4.76612	−	16.0448i	−0.156624	−	0.527263i
$927$	10.4050	−	20.7814i	0.341743	−	0.682552i
$928$	3.45593	−	27.0549i	0.113446	−	0.888120i
$929$	20.0169	−	34.6702i	0.656732	−	1.13749i	−0.324724	−	0.945809i	$-0.605271\pi$
$929$	20.0169	−	34.6702i	0.656732	−	1.13749i	0.981456	−	0.191685i	$-0.0613952\pi$
$930$	49.6044	−	16.3531i	1.62659	−	0.536241i
$931$	3.86823	−	2.23332i	0.126776	−	0.0731942i
$932$	23.4983	+	11.9274i	0.769711	+	0.390696i
$933$	10.6013	−	0.314969i	0.347071	−	0.0103116i
$934$	−3.66068	+	15.2997i	−0.119781	+	0.500622i
$935$	9.23434			0.301995
$936$	3.69781	+	8.69634i	0.120867	+	0.284249i
$937$	−46.9538			−1.53391			−0.766956	−	0.641699i	$-0.778230\pi$
$937$	−46.9538			−1.53391			−0.766956	+	0.641699i	$0.778230\pi$
$938$	−3.60001	+	15.0461i	−0.117544	+	0.491274i
$939$	0.297377	+	0.481462i	0.00970454	+	0.0157119i
$940$	32.9914	−	64.9964i	1.07606	−	2.11995i
$941$	−26.0233	+	15.0246i	−0.848336	+	0.489787i	−0.860089	−	0.510144i	$-0.829592\pi$
$941$	−26.0233	+	15.0246i	−0.848336	+	0.489787i	0.0117532	+	0.999931i	$0.496259\pi$
$942$	−8.57761	+	41.2237i	−0.279474	+	1.34314i
$943$	−2.46900	+	4.27644i	−0.0804018	+	0.139260i
$944$	48.5890	+	21.4541i	1.58144	+	0.698272i
$945$	−1.45255	−	16.2584i	−0.0472514	−	0.528885i
$946$	−10.8766	−	36.6153i	−0.353629	−	1.19047i
$947$	−20.5354	−	11.8561i	−0.667311	−	0.385272i	0.127746	−	0.991807i	$-0.459226\pi$
$947$	−20.5354	−	11.8561i	−0.667311	−	0.385272i	−0.795057	+	0.606535i	$0.792559\pi$
$948$	−1.43517	−	17.1268i	−0.0466122	−	0.556252i
$949$	6.91003	−	3.98951i	0.224309	−	0.129505i
$950$	22.3231	+	21.1512i	0.724257	+	0.686235i
$951$	−1.68193	+	1.03885i	−0.0545403	+	0.0336871i
$952$	−3.06282	+	1.09257i	−0.0992665	+	0.0354104i
$953$	−49.9460			−1.61791			−0.808955	−	0.587871i	$-0.799966\pi$
$953$	−49.9460			−1.61791			−0.808955	+	0.587871i	$0.799966\pi$
$954$	36.8156	−	13.3617i	1.19195	−	0.432601i
$955$		−	68.8431i		−	2.22771i
$956$	−0.808863	−	14.9922i	−0.0261605	−	0.484883i
$957$	−21.3429	+	0.634105i	−0.689917	+	0.0204977i
$958$	13.7963	−	14.5607i	0.445738	−	0.470435i
$959$	8.94475	+	15.4928i	0.288841	+	0.500287i
$960$	42.7334	−	8.28061i	1.37922	−	0.267255i
$961$	−7.53690	+	13.0543i	−0.243126	+	0.421106i
$962$	−1.46640	−	4.93651i	−0.0472785	−	0.159159i
$963$	13.6978	−	9.03323i	0.441404	−	0.291092i
$964$	−35.1788	+	22.9225i	−1.13303	+	0.738284i
$965$	0.0160088	+	0.00924271i	0.000515343	+	0.000297533i
$966$	−2.74828	+	3.07874i	−0.0884243	+	0.0990568i
$967$	−23.1224	−	40.0491i	−0.743566	−	1.28789i	−0.950862	−	0.309615i	$-0.899800\pi$
$967$	−23.1224	−	40.0491i	−0.743566	−	1.28789i	0.207296	−	0.978278i	$-0.433534\pi$
$968$	2.27159	−	12.4164i	0.0730117	−	0.399079i
$969$	−7.83166	−	4.21660i	−0.251589	−	0.135457i
$970$	−10.3592	+	43.2960i	−0.332613	+	1.39015i
$971$			29.1228i			0.934596i	0.884100	+	0.467298i	$0.154773\pi$
$971$			29.1228i			0.934596i	−0.884100	+	0.467298i	$0.845227\pi$
$972$	−6.26746	−	30.5404i	−0.201029	−	0.979585i
$973$			9.25115i			0.296578i
$974$	−1.47704	−	0.353404i	−0.0473276	−	0.0113238i
$975$	−8.26846	−	4.45178i	−0.264803	−	0.142571i
$976$	−1.31477	−	12.1491i	−0.0420847	−	0.388883i
$977$	−22.6511	−	39.2328i	−0.724672	−	1.25517i	−0.959109	−	0.283038i	$-0.908658\pi$
$977$	−22.6511	−	39.2328i	−0.724672	−	1.25517i	0.234437	−	0.972131i	$-0.424675\pi$
$978$	17.4240	+	15.5538i	0.557159	+	0.497355i
$979$	−13.3923	−	7.73205i	−0.428020	−	0.247117i
$980$	3.42995	+	5.26390i	0.109566	+	0.168149i
$981$	−25.4424	+	16.7785i	−0.812314	+	0.535695i
$982$	−17.4347	+	5.17901i	−0.556364	+	0.165269i
$983$	−0.389552	+	0.674724i	−0.0124248	+	0.0215204i	−0.872171	−	0.489201i	$-0.837288\pi$
$983$	−0.389552	+	0.674724i	−0.0124248	+	0.0215204i	0.859746	+	0.510722i	$0.170622\pi$
$984$	11.2110	+	8.97077i	0.357395	+	0.285978i
$985$	9.56115	+	16.5604i	0.304643	+	0.527658i
$986$	−5.69070	−	5.39196i	−0.181229	−	0.171715i
$987$	20.0857	−	0.596753i	0.639334	−	0.0189948i
$988$	−0.535981	−	9.93437i	−0.0170518	−	0.316054i
$989$		−	17.7977i		−	0.565934i
$990$	−11.6256	−	32.0321i	−0.369487	−	1.01805i
$991$	41.5739			1.32064			0.660320	−	0.750985i	$-0.270421\pi$
$991$	41.5739			1.32064			0.660320	+	0.750985i	$0.270421\pi$
$992$	−23.2574	+	30.5525i	−0.738423	+	0.970042i
$993$	−1.24981	+	0.771951i	−0.0396614	+	0.0244971i
$994$	−12.8516	+	13.5637i	−0.407629	+	0.430214i
$995$	34.6726	−	20.0183i	1.09920	−	0.634621i
$996$	43.4368	−	3.63987i	1.37635	−	0.115334i
$997$	−5.90652	−	3.41013i	−0.187061	−	0.108000i	0.403545	−	0.914960i	$-0.367778\pi$
$997$	−5.90652	−	3.41013i	−0.187061	−	0.108000i	−0.590606	+	0.806960i	$0.701111\pi$
$998$	−14.3051	+	4.24936i	−0.452821	+	0.134511i
$999$	1.51188	+	16.9224i	0.0478336	+	0.535402i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.b.421.33	yes	72
8.5	even	2	inner	504.2.cs.b.421.9	yes	72
9.4	even	3	inner	504.2.cs.b.85.9	✓	72
72.13	even	6	inner	504.2.cs.b.85.33	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.b.85.9	✓	72	9.4	even	3	inner
504.2.cs.b.85.33	yes	72	72.13	even	6	inner
504.2.cs.b.421.9	yes	72	8.5	even	2	inner
504.2.cs.b.421.33	yes	72	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37539 + 0.329083i) q^{2} +(-0.821098 + 1.52506i) q^{3} +(1.78341 + 0.905236i) q^{4} +(-2.72052 + 1.57069i) q^{5} +(-1.63120 + 1.82734i) q^{6} +(-0.500000 + 0.866025i) q^{7} +(2.15499 + 1.83194i) q^{8} +(-1.65160 - 2.50444i) q^{9} +O(q^{10})\)	\(q+(1.37539 + 0.329083i) q^{2} +(-0.821098 + 1.52506i) q^{3} +(1.78341 + 0.905236i) q^{4} +(-2.72052 + 1.57069i) q^{5} +(-1.63120 + 1.82734i) q^{6} +(-0.500000 + 0.866025i) q^{7} +(2.15499 + 1.83194i) q^{8} +(-1.65160 - 2.50444i) q^{9} +(-4.25867 + 1.26504i) q^{10} +(-2.21426 - 1.27840i) q^{11} +(-2.84489 + 1.97651i) q^{12} +(-0.964474 + 0.556840i) q^{13} +(-0.972690 + 1.02658i) q^{14} +(-0.161584 - 5.43864i) q^{15} +(2.36110 + 3.22881i) q^{16} +1.14970 q^{17} +(-1.44743 - 3.98810i) q^{18} +4.46665i q^{19} +(-6.27365 + 0.338477i) q^{20} +(-0.910189 - 1.47362i) q^{21} +(-2.62478 - 2.48698i) q^{22} +(-0.842409 - 1.45909i) q^{23} +(-4.56328 + 1.78228i) q^{24} +(2.43416 - 4.21608i) q^{25} +(-1.50978 + 0.448481i) q^{26} +(5.17554 - 0.462390i) q^{27} +(-1.67566 + 1.09186i) q^{28} +(-4.17557 - 2.41077i) q^{29} +(1.56752 - 7.53344i) q^{30} +(3.39388 + 5.87838i) q^{31} +(2.18489 + 5.21788i) q^{32} +(3.76776 - 2.32718i) q^{33} +(1.58130 + 0.378348i) q^{34} -3.14139i q^{35} +(-0.678366 - 5.96153i) q^{36} +3.26969i q^{37} +(-1.46990 + 6.14339i) q^{38} +(-0.0572845 - 1.92810i) q^{39} +(-8.74012 - 1.59901i) q^{40} +(-1.46544 - 2.53822i) q^{41} +(-0.766925 - 2.32633i) q^{42} +(9.14833 + 5.28179i) q^{43} +(-2.79168 - 4.28435i) q^{44} +(8.42692 + 4.21923i) q^{45} +(-0.678480 - 2.28405i) q^{46} +(-5.80079 + 10.0473i) q^{47} +(-6.86281 + 0.949639i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(4.73536 - 4.99773i) q^{50} +(-0.944020 + 1.75337i) q^{51} +(-2.22412 + 0.119996i) q^{52} +9.23136i q^{53} +(7.27056 + 1.06721i) q^{54} +8.03193 q^{55} +(-2.66400 + 0.950305i) q^{56} +(-6.81189 - 3.66755i) q^{57} +(-4.94971 - 4.68986i) q^{58} +(11.4997 - 6.63933i) q^{59} +(4.63508 - 9.84560i) q^{60} +(-2.64571 - 1.52750i) q^{61} +(2.73345 + 9.20195i) q^{62} +(2.99471 - 0.178105i) q^{63} +(1.28797 + 7.89564i) q^{64} +(1.74925 - 3.02979i) q^{65} +(5.94799 - 1.96088i) q^{66} +(9.47390 - 5.46976i) q^{67} +(2.05039 + 1.04075i) q^{68} +(2.91690 - 0.0866623i) q^{69} +(1.03378 - 4.32064i) q^{70} +13.2125 q^{71} +(1.02882 - 8.42268i) q^{72} -7.16456 q^{73} +(-1.07600 + 4.49711i) q^{74} +(4.43109 + 7.17404i) q^{75} +(-4.04337 + 7.96586i) q^{76} +(2.21426 - 1.27840i) q^{77} +(0.555715 - 2.67074i) q^{78} +(-2.48070 + 4.29670i) q^{79} +(-11.4949 - 5.07549i) q^{80} +(-3.54445 + 8.27266i) q^{81} +(-1.18027 - 3.97330i) q^{82} +(-10.8973 - 6.29154i) q^{83} +(-0.289267 - 3.45200i) q^{84} +(-3.12780 + 1.80583i) q^{85} +(10.8444 + 10.2751i) q^{86} +(7.10511 - 4.38851i) q^{87} +(-2.42975 - 6.81135i) q^{88} +6.04820 q^{89} +(10.2018 + 8.57625i) q^{90} -1.11368i q^{91} +(-0.181535 - 3.36474i) q^{92} +(-11.7516 + 0.349144i) q^{93} +(-11.2847 + 11.9100i) q^{94} +(-7.01573 - 12.1516i) q^{95} +(-9.75157 - 0.952305i) q^{96} +(5.01036 - 8.67820i) q^{97} +(-0.402702 - 1.35567i) q^{98} +(0.455381 + 7.65690i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more