LMFDB - Embedded newform 462.2.n.f.65.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(65,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("462.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.n (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.9
Character	$\chi$	$=$	462.65
Dual form			462.2.n.f.263.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.783456 - 1.54473i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.23623 + 1.86844i) q^{5} +(-0.946049 - 1.45086i) q^{6} +(-0.830341 + 2.51208i) q^{7} -1.00000 q^{8} +(-1.77239 - 2.42046i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.783456 - 1.54473i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.23623 + 1.86844i) q^{5} +(-0.946049 - 1.45086i) q^{6} +(-0.830341 + 2.51208i) q^{7} -1.00000 q^{8} +(-1.77239 - 2.42046i) q^{9} +(3.23623 - 1.86844i) q^{10} +(3.31609 - 0.0598058i) q^{11} +(-1.72951 + 0.0938734i) q^{12} -4.64070i q^{13} +(1.76035 + 1.97514i) q^{14} +(5.42167 - 3.53527i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.460807 - 0.798142i) q^{17} +(-2.98238 + 0.324709i) q^{18} +(4.14430 + 2.39271i) q^{19} -3.73687i q^{20} +(3.22995 + 3.25076i) q^{21} +(1.60625 - 2.90172i) q^{22} +(-4.94452 - 2.85472i) q^{23} +(-0.783456 + 1.54473i) q^{24} +(4.48211 + 7.76324i) q^{25} +(-4.01896 - 2.32035i) q^{26} +(-5.12755 + 0.841552i) q^{27} +(2.59069 - 0.536942i) q^{28} -7.73875 q^{29} +(-0.350793 - 6.46294i) q^{30} +(1.26564 + 2.19216i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.50562 - 5.16932i) q^{33} -0.921615 q^{34} +(-7.38083 + 6.57821i) q^{35} +(-1.20998 + 2.74517i) q^{36} +(-1.29412 + 2.24149i) q^{37} +(4.14430 - 2.39271i) q^{38} +(-7.16863 - 3.63578i) q^{39} +(-3.23623 - 1.86844i) q^{40} -4.10460 q^{41} +(4.43021 - 1.17184i) q^{42} +2.19681i q^{43} +(-1.70984 - 2.84191i) q^{44} +(-1.21340 - 11.1448i) q^{45} +(-4.94452 + 2.85472i) q^{46} +(4.96151 + 2.86453i) q^{47} +(0.946049 + 1.45086i) q^{48} +(-5.62107 - 4.17176i) q^{49} +8.96422 q^{50} +(-1.59394 + 0.0865151i) q^{51} +(-4.01896 + 2.32035i) q^{52} +(3.30063 - 1.90562i) q^{53} +(-1.83497 + 4.86137i) q^{54} +(10.8433 + 6.00235i) q^{55} +(0.830341 - 2.51208i) q^{56} +(6.94298 - 4.52725i) q^{57} +(-3.86938 + 6.70196i) q^{58} +(-7.65662 + 4.42055i) q^{59} +(-5.77247 - 2.92767i) q^{60} +(-6.52747 - 3.76863i) q^{61} +2.53129 q^{62} +(7.55207 - 2.44259i) q^{63} +1.00000 q^{64} +(8.67085 - 15.0184i) q^{65} +(-3.22395 - 4.75459i) q^{66} +(0.390387 + 0.676170i) q^{67} +(-0.460807 + 0.798142i) q^{68} +(-8.28358 + 5.40141i) q^{69} +(2.00648 + 9.68109i) q^{70} +11.4978i q^{71} +(1.77239 + 2.42046i) q^{72} +(9.35455 - 5.40085i) q^{73} +(1.29412 + 2.24149i) q^{74} +(15.5037 - 0.841502i) q^{75} -4.78543i q^{76} +(-2.60325 + 8.37992i) q^{77} +(-6.73300 + 4.39033i) q^{78} +(14.9095 + 8.60802i) q^{79} +(-3.23623 + 1.86844i) q^{80} +(-2.71724 + 8.58001i) q^{81} +(-2.05230 + 3.55469i) q^{82} -12.6784 q^{83} +(1.20026 - 4.42260i) q^{84} -3.44396i q^{85} +(1.90249 + 1.09840i) q^{86} +(-6.06297 + 11.9543i) q^{87} +(-3.31609 + 0.0598058i) q^{88} +(-7.44976 - 4.30112i) q^{89} +(-10.2583 - 4.52155i) q^{90} +(11.6578 + 3.85336i) q^{91} +5.70943i q^{92} +(4.37787 - 0.237621i) q^{93} +(4.96151 - 2.86453i) q^{94} +(8.94127 + 15.4867i) q^{95} +(1.72951 - 0.0938734i) q^{96} -12.1684 q^{97} +(-6.42339 + 2.78211i) q^{98} +(-6.02217 - 7.92045i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9	$ 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9} + 4 q^{11} + 4 q^{15} - 12 q^{16} - 4 q^{17} + 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} - 40 q^{29} + 2 q^{30} - 28 q^{31} + 12 q^{32} + 24 q^{33} - 8 q^{34} + 32 q^{35} + 16 q^{36} - 16 q^{37} + 8 q^{41} + 6 q^{42} + 4 q^{44} - 28 q^{45} - 8 q^{49} + 40 q^{50} + 34 q^{51} - 6 q^{54} + 8 q^{55} - 40 q^{57} - 20 q^{58} - 2 q^{60} - 56 q^{62} + 14 q^{63} + 24 q^{64} + 44 q^{65} - 24 q^{66} - 4 q^{68} - 20 q^{69} + 64 q^{70} + 8 q^{72} + 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} - 144 q^{83} + 6 q^{84} - 8 q^{87} - 4 q^{88} - 56 q^{90} - 32 q^{91} - 22 q^{93} + 44 q^{95} + 64 q^{97} + 8 q^{98} + 28 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9 + 4 * q^11 + 4 * q^15 - 12 * q^16 - 4 * q^17 + 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 - 40 * q^29 + 2 * q^30 - 28 * q^31 + 12 * q^32 + 24 * q^33 - 8 * q^34 + 32 * q^35 + 16 * q^36 - 16 * q^37 + 8 * q^41 + 6 * q^42 + 4 * q^44 - 28 * q^45 - 8 * q^49 + 40 * q^50 + 34 * q^51 - 6 * q^54 + 8 * q^55 - 40 * q^57 - 20 * q^58 - 2 * q^60 - 56 * q^62 + 14 * q^63 + 24 * q^64 + 44 * q^65 - 24 * q^66 - 4 * q^68 - 20 * q^69 + 64 * q^70 + 8 * q^72 + 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 - 144 * q^83 + 6 * q^84 - 8 * q^87 - 4 * q^88 - 56 * q^90 - 32 * q^91 - 22 * q^93 + 44 * q^95 + 64 * q^97 + 8 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.783456	−	1.54473i	0.452328	−	0.891851i
$3$	0.783456	−	1.54473i	0.452328	−	0.891851i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	3.23623	+	1.86844i	1.44728	+	0.835590i	0.998319	−	0.0579588i	$-0.0184592\pi$
$5$	3.23623	+	1.86844i	1.44728	+	0.835590i	0.448966	+	0.893549i	$0.351793\pi$
$6$	−0.946049	−	1.45086i	−0.386223	−	0.592311i
$7$	−0.830341	+	2.51208i	−0.313839	+	0.949476i
$7$	−0.830341	+	2.51208i	−0.313839	+	0.949476i
$8$	−1.00000			−0.353553
$9$	−1.77239	−	2.42046i	−0.590798	−	0.806819i
$10$	3.23623	−	1.86844i	1.02338	−	0.590852i
$11$	3.31609	−	0.0598058i	0.999837	−	0.0180321i
$11$	3.31609	−	0.0598058i	0.999837	−	0.0180321i
$12$	−1.72951	+	0.0938734i	−0.499265	+	0.0270989i
$13$		−	4.64070i		−	1.28710i	−0.765405	−	0.643549i	$-0.777461\pi$
$13$		−	4.64070i		−	1.28710i	0.765405	−	0.643549i	$-0.222539\pi$
$14$	1.76035	+	1.97514i	0.470474	+	0.527877i
$15$	5.42167	−	3.53527i	1.39987	−	0.912802i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.460807	−	0.798142i	−0.111762	−	0.193578i	0.804719	−	0.593656i	$-0.202316\pi$
$17$	−0.460807	−	0.798142i	−0.111762	−	0.193578i	−0.916481	+	0.400079i	$0.868983\pi$
$18$	−2.98238	+	0.324709i	−0.702953	+	0.0765347i
$19$	4.14430	+	2.39271i	0.950768	+	0.548926i	0.893319	−	0.449422i	$-0.148370\pi$
$19$	4.14430	+	2.39271i	0.950768	+	0.548926i	0.0574485	+	0.998348i	$0.481704\pi$
$20$		−	3.73687i		−	0.835590i
$21$	3.22995	+	3.25076i	0.704833	+	0.709373i
$22$	1.60625	−	2.90172i	0.342454	−	0.618648i
$23$	−4.94452	−	2.85472i	−1.03100	−	0.595250i	−0.113731	−	0.993512i	$-0.536280\pi$
$23$	−4.94452	−	2.85472i	−1.03100	−	0.595250i	−0.917272	+	0.398262i	$0.869614\pi$
$24$	−0.783456	+	1.54473i	−0.159922	+	0.315317i
$25$	4.48211	+	7.76324i	0.896422	+	1.55265i
$26$	−4.01896	−	2.32035i	−0.788183	−	0.455058i
$27$	−5.12755	+	0.841552i	−0.986798	+	0.161957i
$28$	2.59069	−	0.536942i	0.489595	−	0.101473i
$29$	−7.73875			−1.43705			−0.718525	−	0.695501i	$-0.755182\pi$
$29$	−7.73875			−1.43705			−0.718525	+	0.695501i	$0.755182\pi$
$30$	−0.350793	−	6.46294i	−0.0640458	−	1.17997i
$31$	1.26564	+	2.19216i	0.227316	+	0.393723i	0.957012	−	0.290049i	$-0.0936715\pi$
$31$	1.26564	+	2.19216i	0.227316	+	0.393723i	−0.729696	+	0.683772i	$0.760338\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.50562	−	5.16932i	0.436173	−	0.899863i
$34$	−0.921615			−0.158056
$35$	−7.38083	+	6.57821i	−1.24759	+	1.11192i
$36$	−1.20998	+	2.74517i	−0.201664	+	0.457528i
$37$	−1.29412	+	2.24149i	−0.212752	+	0.368498i	−0.952575	−	0.304304i	$-0.901576\pi$
$37$	−1.29412	+	2.24149i	−0.212752	+	0.368498i	0.739823	+	0.672802i	$0.234909\pi$
$38$	4.14430	−	2.39271i	0.672294	−	0.388149i
$39$	−7.16863	−	3.63578i	−1.14790	−	0.582191i
$40$	−3.23623	−	1.86844i	−0.511692	−	0.295426i
$41$	−4.10460			−0.641030			−0.320515	−	0.947243i	$-0.603856\pi$
$41$	−4.10460			−0.641030			−0.320515	+	0.947243i	$0.603856\pi$
$42$	4.43021	−	1.17184i	0.683597	−	0.180819i
$43$			2.19681i			0.335010i	0.985871	+	0.167505i	$0.0535711\pi$
$43$			2.19681i			0.335010i	−0.985871	+	0.167505i	$0.946429\pi$
$44$	−1.70984	−	2.84191i	−0.257767	−	0.428434i
$45$	−1.21340	−	11.1448i	−0.180883	−	1.66136i
$46$	−4.94452	+	2.85472i	−0.729029	+	0.420905i
$47$	4.96151	+	2.86453i	0.723711	+	0.417835i	0.816117	−	0.577887i	$-0.196122\pi$
$47$	4.96151	+	2.86453i	0.723711	+	0.417835i	−0.0924058	+	0.995721i	$0.529456\pi$
$48$	0.946049	+	1.45086i	0.136550	+	0.209413i
$49$	−5.62107	−	4.17176i	−0.803010	−	0.595966i
$50$	8.96422			1.26773
$51$	−1.59394	+	0.0865151i	−0.223196	+	0.0121145i
$52$	−4.01896	+	2.32035i	−0.557330	+	0.321774i
$53$	3.30063	−	1.90562i	0.453377	−	0.261757i	−0.255878	−	0.966709i	$-0.582365\pi$
$53$	3.30063	−	1.90562i	0.453377	−	0.261757i	0.709255	+	0.704952i	$0.249031\pi$
$54$	−1.83497	+	4.86137i	−0.249708	+	0.661548i
$55$	10.8433	+	6.00235i	1.46212	+	0.809357i
$56$	0.830341	−	2.51208i	0.110959	−	0.335690i
$57$	6.94298	−	4.52725i	0.919620	−	0.599649i
$58$	−3.86938	+	6.70196i	−0.508074	+	0.880010i
$59$	−7.65662	+	4.42055i	−0.996807	+	0.575507i	−0.907302	−	0.420480i	$-0.861862\pi$
$59$	−7.65662	+	4.42055i	−0.996807	+	0.575507i	−0.0895048	+	0.995986i	$0.528528\pi$
$60$	−5.77247	−	2.92767i	−0.745222	−	0.377961i
$61$	−6.52747	−	3.76863i	−0.835756	−	0.482524i	0.0200632	−	0.999799i	$-0.493613\pi$
$61$	−6.52747	−	3.76863i	−0.835756	−	0.482524i	−0.855819	+	0.517275i	$0.826947\pi$
$62$	2.53129			0.321474
$63$	7.55207	−	2.44259i	0.951472	−	0.307737i
$64$	1.00000			0.125000
$65$	8.67085	−	15.0184i	1.07549	−	1.86280i
$66$	−3.22395	−	4.75459i	−0.396841	−	0.585250i
$67$	0.390387	+	0.676170i	0.0476934	+	0.0826073i	0.888887	−	0.458127i	$-0.151480\pi$
$67$	0.390387	+	0.676170i	0.0476934	+	0.0826073i	−0.841193	+	0.540735i	$0.818146\pi$
$68$	−0.460807	+	0.798142i	−0.0558811	+	0.0967889i
$69$	−8.28358	+	5.40141i	−0.997226	+	0.650253i
$70$	2.00648	+	9.68109i	0.239821	+	1.15711i
$71$			11.4978i			1.36454i	0.731100	+	0.682271i	$0.239007\pi$
$71$			11.4978i			1.36454i	−0.731100	+	0.682271i	$0.760993\pi$
$72$	1.77239	+	2.42046i	0.208879	+	0.285254i
$73$	9.35455	−	5.40085i	1.09487	−	0.632122i	0.159999	−	0.987117i	$-0.448851\pi$
$73$	9.35455	−	5.40085i	1.09487	−	0.632122i	0.934868	+	0.354995i	$0.115518\pi$
$74$	1.29412	+	2.24149i	0.150439	+	0.260567i
$75$	15.5037	−	0.841502i	1.79021	−	0.0971683i
$76$		−	4.78543i		−	0.548926i
$77$	−2.60325	+	8.37992i	−0.296667	+	0.954981i
$78$	−6.73300	+	4.39033i	−0.762362	+	0.497107i
$79$	14.9095	+	8.60802i	1.67745	+	0.968478i	0.963276	+	0.268514i	$0.0865325\pi$
$79$	14.9095	+	8.60802i	1.67745	+	0.968478i	0.714178	+	0.699964i	$0.246801\pi$
$80$	−3.23623	+	1.86844i	−0.361821	+	0.208898i
$81$	−2.71724	+	8.58001i	−0.301915	+	0.953335i
$82$	−2.05230	+	3.55469i	−0.226638	+	0.392549i
$83$	−12.6784			−1.39163			−0.695816	−	0.718220i	$-0.744957\pi$
$83$	−12.6784			−1.39163			−0.695816	+	0.718220i	$0.744957\pi$
$84$	1.20026	−	4.42260i	0.130959	−	0.482545i
$85$		−	3.44396i		−	0.373550i
$86$	1.90249	+	1.09840i	0.205151	+	0.118444i
$87$	−6.06297	+	11.9543i	−0.650019	+	1.28164i
$88$	−3.31609	+	0.0598058i	−0.353496	+	0.00637532i
$89$	−7.44976	−	4.30112i	−0.789673	−	0.455918i	0.0501742	−	0.998740i	$-0.484022\pi$
$89$	−7.44976	−	4.30112i	−0.789673	−	0.455918i	−0.839848	+	0.542822i	$0.817356\pi$
$90$	−10.2583	−	4.52155i	−1.08132	−	0.476613i
$91$	11.6578	+	3.85336i	1.22207	+	0.403942i
$92$			5.70943i			0.595250i
$93$	4.37787	−	0.237621i	0.453964	−	0.0246401i
$94$	4.96151	−	2.86453i	0.511741	−	0.295454i
$95$	8.94127	+	15.4867i	0.917354	+	1.58890i
$96$	1.72951	−	0.0938734i	0.176517	−	0.00958092i
$97$	−12.1684			−1.23551			−0.617756	−	0.786370i	$-0.711958\pi$
$97$	−12.1684			−1.23551			−0.617756	+	0.786370i	$0.711958\pi$
$98$	−6.42339	+	2.78211i	−0.648860	+	0.281035i
$99$	−6.02217	−	7.92045i	−0.605251	−	0.796035i
$100$	4.48211	−	7.76324i	0.448211	−	0.776324i
$101$	0.661912	+	1.14646i	0.0658627	+	0.114077i	0.897076	−	0.441876i	$-0.145687\pi$
$101$	0.661912	+	1.14646i	0.0658627	+	0.114077i	−0.831214	+	0.555953i	$0.812353\pi$
$102$	−0.722045	+	1.42365i	−0.0714931	+	0.140962i
$103$	−4.94954	+	8.57285i	−0.487693	+	0.844708i	−0.999900	−	0.0141536i	$-0.995495\pi$
$103$	−4.94954	+	8.57285i	−0.487693	+	0.844708i	0.512207	+	0.858862i	$0.328828\pi$
$104$			4.64070i			0.455058i
$105$	4.37902	+	16.5551i	0.427349	+	1.61562i
$106$		−	3.81124i		−	0.370181i
$107$	5.61684	−	9.72865i	0.543000	−	0.940504i	−0.455730	−	0.890118i	$-0.650622\pi$
$107$	5.61684	−	9.72865i	0.543000	−	0.940504i	0.998730	−	0.0503857i	$-0.0160451\pi$
$108$	3.29258	+	4.01981i	0.316829	+	0.386807i
$109$	3.95986	−	2.28623i	0.379286	−	0.218981i	−0.298221	−	0.954497i	$-0.596393\pi$
$109$	3.95986	−	2.28623i	0.379286	−	0.218981i	0.677508	+	0.735516i	$0.263060\pi$
$110$	10.6199	−	6.38944i	1.01256	−	0.609209i
$111$	2.44861	+	3.75518i	0.232412	+	0.356426i
$112$	−1.76035	−	1.97514i	−0.166338	−	0.186633i
$113$		−	7.52223i		−	0.707632i	−0.935315	−	0.353816i	$-0.884884\pi$
$113$		−	7.52223i		−	0.707632i	0.935315	−	0.353816i	$-0.115116\pi$
$114$	−0.449224	−	8.27642i	−0.0420737	−	0.775158i
$115$	−10.6677	−	18.4770i	−0.994770	−	1.72299i
$116$	3.86938	+	6.70196i	0.359263	+	0.622261i
$117$	−11.2326	+	8.22514i	−1.03846	+	0.760415i
$118$			8.84110i			0.813889i
$119$	2.38762	−	0.494854i	0.218873	−	0.0453632i
$120$	−5.42167	+	3.53527i	−0.494929	+	0.322724i
$121$	10.9928	−	0.396643i	0.999350	−	0.0360584i
$122$	−6.52747	+	3.76863i	−0.590969	+	0.341196i
$123$	−3.21577	+	6.34050i	−0.289956	+	0.571704i
$124$	1.26564	−	2.19216i	0.113658	−	0.196862i
$125$			14.8138i			1.32499i
$126$	1.66069	−	7.76158i	0.147946	−	0.691456i
$127$		−	5.14870i		−	0.456873i	−0.973559	−	0.228437i	$-0.926639\pi$
$127$		−	5.14870i		−	0.456873i	0.973559	−	0.228437i	$-0.0733614\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	3.39348	+	1.72110i	0.298779	+	0.151535i
$130$	−8.67085	−	15.0184i	−0.760484	−	1.31720i
$131$	7.91279	−	13.7053i	0.691343	−	1.19744i	−0.280054	−	0.959984i	$-0.590353\pi$
$131$	7.91279	−	13.7053i	0.691343	−	1.19744i	0.971398	−	0.237458i	$-0.0763141\pi$
$132$	−5.72957	+	0.414727i	−0.498695	+	0.0360973i
$133$	−9.45186	+	8.42404i	−0.819581	+	0.730457i
$134$	0.780774			0.0674486
$135$	−18.1663	−	6.85705i	−1.56351	−	0.590161i
$136$	0.460807	+	0.798142i	0.0395139	+	0.0684401i
$137$	11.1932	−	6.46241i	0.956302	−	0.552121i	0.0612689	−	0.998121i	$-0.480485\pi$
$137$	11.1932	−	6.46241i	0.956302	−	0.552121i	0.895033	+	0.446000i	$0.147152\pi$
$138$	0.535964	+	9.87450i	0.0456243	+	0.840573i
$139$			8.08854i			0.686061i	0.939324	+	0.343031i	$0.111453\pi$
$139$			8.08854i			0.686061i	−0.939324	+	0.343031i	$0.888547\pi$
$140$	9.38731	+	3.10288i	0.793373	+	0.262241i
$141$	8.31206	−	5.41998i	0.700002	−	0.456444i
$142$	9.95741	+	5.74892i	0.835608	+	0.482438i
$143$	−0.277541	−	15.3889i	−0.0232091	−	1.28689i
$144$	2.98238	−	0.324709i	0.248531	−	0.0270591i
$145$	−25.0444	−	14.4594i	−2.07982	−	1.20079i
$146$		−	10.8017i		−	0.893955i
$147$	−10.8481	+	5.41465i	−0.894737	+	0.446593i
$148$	2.58824			0.212752
$149$	−6.60066	+	11.4327i	−0.540747	+	0.936602i	0.458114	+	0.888893i	$0.348525\pi$
$149$	−6.60066	+	11.4327i	−0.540747	+	0.936602i	−0.998861	+	0.0477082i	$0.984808\pi$
$150$	7.02307	−	13.8473i	0.573431	−	1.13063i
$151$	10.3132	−	5.95435i	0.839279	−	0.484558i	−0.0177403	−	0.999843i	$-0.505647\pi$
$151$	10.3132	−	5.95435i	0.839279	−	0.484558i	0.857019	+	0.515285i	$0.172314\pi$
$152$	−4.14430	−	2.39271i	−0.336147	−	0.194075i
$153$	−1.11514	+	2.52999i	−0.0901535	+	0.204537i
$154$	5.95560	+	6.44444i	0.479916	+	0.519308i
$155$			9.45910i			0.759773i
$156$	0.435638	+	8.02611i	0.0348790	+	0.642603i
$157$	6.04984	+	10.4786i	0.482830	+	0.836286i	0.999806	−	0.0197142i	$-0.00627562\pi$
$157$	6.04984	+	10.4786i	0.482830	+	0.836286i	−0.516976	+	0.856000i	$0.672942\pi$
$158$	14.9095	−	8.60802i	1.18614	−	0.684818i
$159$	−0.357774	−	6.59157i	−0.0283734	−	0.522745i
$160$			3.73687i			0.295426i
$161$	11.2769	−	10.0506i	0.888745	−	0.792100i
$162$	6.07189	+	6.64320i	0.477053	+	0.521939i
$163$	0.770417	−	1.33440i	0.0603437	−	0.104518i	−0.834275	−	0.551348i	$-0.814114\pi$
$163$	0.770417	−	1.33440i	0.0603437	−	0.104518i	0.894619	+	0.446830i	$0.147447\pi$
$164$	2.05230	+	3.55469i	0.160258	+	0.277574i
$165$	17.7673	−	12.0475i	1.38318	−	0.937896i
$166$	−6.33919	+	10.9798i	−0.492016	+	0.852197i
$167$	−10.2207			−0.790902			−0.395451	−	0.918487i	$-0.629412\pi$
$167$	−10.2207			−0.790902			−0.395451	+	0.918487i	$0.629412\pi$
$168$	−3.22995	−	3.25076i	−0.249196	−	0.250801i
$169$	−8.53607			−0.656621
$170$	−2.98256	−	1.72198i	−0.228752	−	0.132070i
$171$	−1.55387	−	14.2719i	−0.118828	−	1.09140i
$172$	1.90249	−	1.09840i	0.145064	−	0.0837525i
$173$	−3.49761	+	6.05803i	−0.265918	+	0.460584i	−0.967804	−	0.251706i	$-0.919008\pi$
$173$	−3.49761	+	6.05803i	−0.265918	+	0.460584i	0.701886	+	0.712290i	$0.252342\pi$
$174$	7.32124	+	11.2278i	0.555022	+	0.851180i
$175$	−23.2235	+	4.81327i	−1.75554	+	0.363849i
$176$	−1.60625	+	2.90172i	−0.121076	+	0.218725i
$177$	0.829944	+	15.2907i	0.0623824	+	1.14932i
$178$	−7.44976	+	4.30112i	−0.558383	+	0.322383i
$179$	−20.0703	+	11.5876i	−1.50012	+	0.866097i	−0.500125	+	0.865953i	$0.666713\pi$
$179$	−20.0703	+	11.5876i	−1.50012	+	0.866097i	−1.00000		0.000143992i	$0.999954\pi$
$180$	−9.04495	+	6.62321i	−0.674170	+	0.493665i
$181$	−6.34142			−0.471354			−0.235677	−	0.971831i	$-0.575731\pi$
$181$	−6.34142			−0.471354			−0.235677	+	0.971831i	$0.575731\pi$
$182$	9.16601	−	8.16926i	0.679430	−	0.605546i
$183$	−10.9355	+	7.13063i	−0.808376	+	0.527111i
$184$	4.94452	+	2.85472i	0.364515	+	0.210453i
$185$	−8.37615	+	4.83597i	−0.615827	+	0.355548i
$186$	1.98315	−	3.91016i	0.145412	−	0.286707i
$187$	−1.57581	−	2.61915i	−0.115235	−	0.191531i
$188$		−	5.72906i		−	0.417835i
$189$	2.14357	−	13.5796i	0.155922	−	0.987769i
$190$	17.8825			1.29734
$191$	6.08888	+	3.51541i	0.440576	+	0.254366i	0.703842	−	0.710357i	$-0.251466\pi$
$191$	6.08888	+	3.51541i	0.440576	+	0.254366i	−0.263266	+	0.964723i	$0.584800\pi$
$192$	0.783456	−	1.54473i	0.0565410	−	0.111481i
$193$	7.54828	−	4.35800i	0.543337	−	0.313696i	−0.203093	−	0.979159i	$-0.565099\pi$
$193$	7.54828	−	4.35800i	0.543337	−	0.313696i	0.746430	+	0.665464i	$0.231766\pi$
$194$	−6.08419	+	10.5381i	−0.436819	+	0.756593i
$195$	−16.4061	−	25.1604i	−1.17487	−	1.80177i
$196$	−0.802319	+	6.95387i	−0.0573085	+	0.496705i
$197$	−0.556764			−0.0396678			−0.0198339	−	0.999803i	$-0.506314\pi$
$197$	−0.556764			−0.0396678			−0.0198339	+	0.999803i	$0.506314\pi$
$198$	−9.87039	+	1.25513i	−0.701458	+	0.0891980i
$199$	3.23869	+	5.60958i	0.229585	+	0.397653i	0.957685	−	0.287818i	$-0.0929298\pi$
$199$	3.23869	+	5.60958i	0.229585	+	0.397653i	−0.728100	+	0.685471i	$0.759597\pi$
$200$	−4.48211	−	7.76324i	−0.316933	−	0.548944i
$201$	1.35035	−	0.0732939i	0.0952465	−	0.00516975i
$202$	1.32382			0.0931439
$203$	6.42580	−	19.4403i	0.451003	−	1.36444i
$204$	0.871893	+	1.33713i	0.0610447	+	0.0936180i
$205$	−13.2834	−	7.66918i	−0.927754	−	0.535639i
$206$	4.94954	+	8.57285i	0.344851	+	0.597299i
$207$	1.85391	+	17.0277i	0.128855	+	1.18351i
$208$	4.01896	+	2.32035i	0.278665	+	0.160887i
$209$	13.8860	+	7.68659i	0.960512	+	0.531692i
$210$	16.5267	+	4.48523i	1.14045	+	0.309510i
$211$			17.8142i			1.22638i	0.789936	+	0.613189i	$0.210114\pi$
$211$			17.8142i			1.22638i	−0.789936	+	0.613189i	$0.789886\pi$
$212$	−3.30063	−	1.90562i	−0.226688	−	0.130879i
$213$	17.7611	+	9.00804i	1.21697	+	0.617221i
$214$	−5.61684	−	9.72865i	−0.383959	−	0.665037i
$215$	−4.10460	+	7.10937i	−0.279931	+	0.484855i
$216$	5.12755	−	0.841552i	0.348886	−	0.0572603i
$217$	−6.55779	+	1.35916i	−0.445172	+	0.0922655i
$218$		−	4.57246i		−	0.309686i
$219$	−1.01399	−	18.6816i	−0.0685193	−	1.26239i
$220$	−0.223487	−	12.3918i	−0.0150675	−	0.835454i
$221$	−3.70394	+	2.13847i	−0.249154	+	0.143849i
$222$	4.47638	−	0.242967i	0.300435	−	0.0163069i
$223$	9.10963			0.610026			0.305013	−	0.952348i	$-0.401339\pi$
$223$	9.10963			0.610026			0.305013	+	0.952348i	$0.401339\pi$
$224$	−2.59069	+	0.536942i	−0.173098	+	0.0358760i
$225$	10.8465	−	24.6083i	0.723103	−	1.64055i
$226$	−6.51444	−	3.76112i	−0.433334	−	0.250186i
$227$	−12.5369	−	21.7145i	−0.832101	−	1.44124i	−0.896369	−	0.443308i	$-0.853805\pi$
$227$	−12.5369	−	21.7145i	−0.832101	−	1.44124i	0.0642687	−	0.997933i	$-0.479529\pi$
$228$	−7.39220	−	3.74917i	−0.489561	−	0.248295i
$229$	11.5525	−	20.0095i	0.763408	−	1.32226i	−0.177676	−	0.984089i	$-0.556858\pi$
$229$	11.5525	−	20.0095i	0.763408	−	1.32226i	0.941084	−	0.338173i	$-0.109809\pi$
$230$	−21.3354			−1.40682
$231$	10.9052	+	10.5866i	0.717510	+	0.696548i
$232$	7.73875			0.508074
$233$	11.6393	−	20.1599i	0.762517	−	1.32072i	−0.179033	−	0.983843i	$-0.557297\pi$
$233$	11.6393	−	20.1599i	0.762517	−	1.32072i	0.941549	−	0.336875i	$-0.109370\pi$
$234$	1.50688	+	13.8403i	0.0985076	+	0.904769i
$235$	10.7044	+	18.5406i	0.698278	+	1.20945i
$236$	7.65662	+	4.42055i	0.498403	+	0.287753i
$237$	24.9780	−	16.2872i	1.62250	−	1.05797i
$238$	0.765255	−	2.31517i	0.0496041	−	0.150070i
$239$	2.95273			0.190996			0.0954981	−	0.995430i	$-0.469556\pi$
$239$	2.95273			0.190996			0.0954981	+	0.995430i	$0.469556\pi$
$240$	0.350793	+	6.46294i	0.0226436	+	0.417181i
$241$	−3.18416	+	1.83837i	−0.205110	+	0.118420i	−0.599037	−	0.800722i	$-0.704450\pi$
$241$	−3.18416	+	1.83837i	−0.205110	+	0.118420i	0.393927	+	0.919142i	$0.371116\pi$
$242$	5.15292	−	9.71841i	0.331242	−	0.624723i
$243$	11.1250	+	10.9195i	0.713668	+	0.700484i
$244$			7.53727i			0.482524i
$245$	−10.3964	−	24.0034i	−0.664200	−	1.53352i
$246$	3.88315	+	5.95519i	0.247581	+	0.379689i
$247$	11.1039	−	19.2324i	0.706522	−	1.22373i
$248$	−1.26564	−	2.19216i	−0.0803685	−	0.139202i
$249$	−9.93294	+	19.5847i	−0.629475	+	1.24113i
$250$	12.8291	+	7.40689i	0.811385	+	0.468453i
$251$		−	27.0815i		−	1.70937i	−0.519147	−	0.854685i	$-0.673750\pi$
$251$		−	27.0815i		−	1.70937i	0.519147	−	0.854685i	$-0.326250\pi$
$252$	−5.89138	−	5.31899i	−0.371122	−	0.335065i
$253$	−16.5672	−	9.17078i	−1.04157	−	0.576562i
$254$	−4.45890	−	2.57435i	−0.279777	−	0.161529i
$255$	−5.31999	−	2.69819i	−0.333151	−	0.168967i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.5519	−	7.24684i	−0.782965	−	0.452045i	0.0545147	−	0.998513i	$-0.482639\pi$
$257$	−12.5519	−	7.24684i	−0.782965	−	0.452045i	−0.837480	+	0.546468i	$0.815972\pi$
$258$	3.18726	−	2.07829i	0.198430	−	0.129389i
$259$	−4.55622	−	5.11213i	−0.283110	−	0.317653i
$260$	−17.3417			−1.07549
$261$	13.7161	+	18.7313i	0.849006	+	1.15944i
$262$	−7.91279	−	13.7053i	−0.488854	−	0.846719i
$263$	7.25088	+	12.5589i	0.447108	+	0.774414i	0.998196	−	0.0600330i	$-0.0191206\pi$
$263$	7.25088	+	12.5589i	0.447108	+	0.774414i	−0.551088	+	0.834447i	$0.685787\pi$
$264$	−2.50562	+	5.16932i	−0.154210	+	0.318150i
$265$	14.2421			0.874887
$266$	2.56950	+	12.3976i	0.157546	+	0.760144i
$267$	−12.4806	+	8.13815i	−0.763803	+	0.498047i
$268$	0.390387	−	0.676170i	0.0238467	−	0.0413037i
$269$	6.66567	−	3.84843i	0.406413	−	0.234643i	−0.282834	−	0.959169i	$-0.591275\pi$
$269$	6.66567	−	3.84843i	0.406413	−	0.234643i	0.689248	+	0.724526i	$0.257941\pi$
$270$	−15.0215	+	12.3040i	−0.914182	+	0.748795i
$271$	−2.86928	−	1.65658i	−0.174296	−	0.100630i	0.410314	−	0.911944i	$-0.365419\pi$
$271$	−2.86928	−	1.65658i	−0.174296	−	0.100630i	−0.584610	+	0.811314i	$0.698752\pi$
$272$	0.921615			0.0558811
$273$	15.0858	−	14.9892i	0.913033	−	0.907189i
$274$		−	12.9248i		−	0.780817i
$275$	15.3273	+	25.4755i	0.924274	+	1.53623i
$276$	8.81955	+	4.47309i	0.530874	+	0.269248i
$277$	7.75856	−	4.47940i	0.466166	−	0.269141i	−0.248467	−	0.968640i	$-0.579927\pi$
$277$	7.75856	−	4.47940i	0.466166	−	0.269141i	0.714634	+	0.699499i	$0.246593\pi$
$278$	7.00488	+	4.04427i	0.420125	+	0.242559i
$279$	3.06281	−	6.94881i	0.183366	−	0.416014i
$280$	7.38083	−	6.57821i	0.441089	−	0.393123i
$281$	−22.9477			−1.36894			−0.684471	−	0.729040i	$-0.739967\pi$
$281$	−22.9477			−1.36894			−0.684471	+	0.729040i	$0.739967\pi$
$282$	−0.537807	−	9.90844i	−0.0320259	−	0.590039i
$283$	−22.4674	+	12.9715i	−1.33555	+	0.771078i	−0.986143	−	0.165895i	$-0.946949\pi$
$283$	−22.4674	+	12.9715i	−1.33555	+	0.771078i	−0.349402	+	0.936973i	$0.613615\pi$
$284$	9.95741	−	5.74892i	0.590864	−	0.341135i
$285$	30.9279	−	1.67869i	1.83201	−	0.0994373i
$286$	−13.4660	−	7.45412i	−0.796261	−	0.440771i
$287$	3.40822	−	10.3111i	0.201181	−	0.608643i
$288$	1.20998	−	2.74517i	0.0712988	−	0.161761i
$289$	8.07531	−	13.9869i	0.475018	−	0.822756i
$290$	−25.0444	+	14.4594i	−1.47066	+	0.849083i
$291$	−9.53339	+	18.7969i	−0.558857	+	1.10189i
$292$	−9.35455	−	5.40085i	−0.547434	−	0.316061i
$293$	5.56705			0.325230			0.162615	−	0.986690i	$-0.448007\pi$
$293$	5.56705			0.325230			0.162615	+	0.986690i	$0.448007\pi$
$294$	−0.734831	+	12.1021i	−0.0428562	+	0.705807i
$295$	−33.0381			−1.92355
$296$	1.29412	−	2.24149i	0.0752193	−	0.130284i
$297$	−16.9531	+	3.09732i	−0.983717	+	0.179724i
$298$	6.60066	+	11.4327i	0.382366	+	0.662277i
$299$	−13.2479	+	22.9460i	−0.766145	+	1.32700i
$300$	−8.48059	−	13.0058i	−0.489627	−	0.750891i
$301$	−5.51855	−	1.82410i	−0.318084	−	0.105139i
$302$		−	11.9087i		−	0.685268i
$303$	2.28956	−	0.124272i	0.131532	−	0.00713923i
$304$	−4.14430	+	2.39271i	−0.237692	+	0.137232i
$305$	−14.0829	−	24.3923i	−0.806385	−	1.39670i
$306$	1.63346	+	2.23073i	0.0933790	+	0.127522i
$307$		−	30.2069i		−	1.72400i	−0.506909	−	0.862000i	$-0.669212\pi$
$307$		−	30.2069i		−	1.72400i	0.506909	−	0.862000i	$-0.330788\pi$
$308$	8.55885	−	1.93548i	0.487686	−	0.110284i
$309$	9.36502	+	14.3622i	0.532757	+	0.817035i
$310$	8.19182	+	4.72955i	0.465264	+	0.268620i
$311$	−0.793092	+	0.457892i	−0.0449721	+	0.0259647i	−0.522318	−	0.852751i	$-0.674932\pi$
$311$	−0.793092	+	0.457892i	−0.0449721	+	0.0259647i	0.477345	+	0.878716i	$0.341599\pi$
$312$	7.16863	+	3.63578i	0.405844	+	0.205836i
$313$	2.87594	−	4.98127i	0.162558	−	0.281558i	−0.773228	−	0.634129i	$-0.781359\pi$
$313$	2.87594	−	4.98127i	0.162558	−	0.281558i	0.935785	+	0.352571i	$0.114692\pi$
$314$	12.0997			0.682825
$315$	29.0040	+	6.20581i	1.63419	+	0.349658i
$316$		−	17.2160i		−	0.968478i
$317$	−9.09364	−	5.25022i	−0.510750	−	0.294882i	0.222392	−	0.974957i	$-0.428614\pi$
$317$	−9.09364	−	5.25022i	−0.510750	−	0.294882i	−0.733142	+	0.680076i	$0.761947\pi$
$318$	−5.88735	−	2.98594i	−0.330146	−	0.167443i
$319$	−25.6624	+	0.462823i	−1.43682	+	0.0259131i
$320$	3.23623	+	1.86844i	0.180911	+	0.104449i
$321$	−10.6276	−	16.2985i	−0.593175	−	0.909692i
$322$	−3.06564	−	14.7914i	−0.170841	−	0.824292i
$323$		−	4.41032i		−	0.245397i
$324$	8.78913	−	1.93681i	0.488285	−	0.107601i
$325$	36.0269	−	20.8001i	1.99841	−	1.15378i
$326$	−0.770417	−	1.33440i	−0.0426695	−	0.0739057i
$327$	−0.429232	−	7.90809i	−0.0237366	−	0.437318i
$328$	4.10460			0.226638
$329$	−11.3157	+	10.0852i	−0.623853	+	0.556013i
$330$	−1.54978	−	21.4107i	−0.0853127	−	1.17862i
$331$	7.54164	−	13.0625i	0.414526	−	0.717981i	−0.580852	−	0.814009i	$-0.697281\pi$
$331$	7.54164	−	13.0625i	0.414526	−	0.717981i	0.995379	+	0.0960284i	$0.0306140\pi$
$332$	6.33919	+	10.9798i	0.347908	+	0.602594i
$333$	7.71912	−	0.840427i	0.423005	−	0.0460551i
$334$	−5.11035	+	8.85139i	−0.279626	+	0.484327i
$335$			2.91765i			0.159408i
$336$	−4.43021	+	1.17184i	−0.241688	+	0.0639292i
$337$			14.8370i			0.808223i	0.914710	+	0.404111i	$0.132419\pi$
$337$			14.8370i			0.808223i	−0.914710	+	0.404111i	$0.867581\pi$
$338$	−4.26804	+	7.39246i	−0.232151	+	0.402097i
$339$	−11.6198	−	5.89333i	−0.631103	−	0.320082i
$340$	−2.98256	+	1.72198i	−0.161752	+	0.0933874i
$341$	4.32809	+	7.19369i	0.234379	+	0.389560i
$342$	−13.1368	−	5.79028i	−0.710357	−	0.313102i
$343$	15.1472	−	10.6566i	0.817872	−	0.575401i
$344$		−	2.19681i		−	0.118444i
$345$	−36.8997	+	2.00283i	−1.98662	+	0.107829i
$346$	3.49761	+	6.05803i	0.188033	+	0.325682i
$347$	−0.849785	−	1.47187i	−0.0456188	−	0.0790141i	0.842314	−	0.538987i	$-0.181193\pi$
$347$	−0.849785	−	1.47187i	−0.0456188	−	0.0790141i	−0.887933	+	0.459972i	$0.847859\pi$
$348$	13.3842	−	0.726463i	0.717469	−	0.0389425i
$349$			20.1684i			1.07959i	0.841796	+	0.539796i	$0.181498\pi$
$349$			20.1684i			1.07959i	−0.841796	+	0.539796i	$0.818502\pi$
$350$	−7.44336	+	22.5188i	−0.397864	+	1.20368i
$351$	3.90539	+	23.7954i	0.208454	+	1.27011i
$352$	1.70984	+	2.84191i	0.0911346	+	0.151474i
$353$	−9.88903	+	5.70943i	−0.526340	+	0.303883i	−0.739525	−	0.673129i	$-0.764950\pi$
$353$	−9.88903	+	5.70943i	−0.526340	+	0.303883i	0.213185	+	0.977012i	$0.431616\pi$
$354$	13.6571	+	6.92661i	0.725868	+	0.368145i
$355$	−21.4830	+	37.2096i	−1.14020	+	1.97488i
$356$			8.60225i			0.455918i
$357$	1.10618	−	4.07593i	0.0585452	−	0.215721i
$358$			23.1752i			1.22485i
$359$	−4.22498	+	7.31788i	−0.222986	+	0.386223i	−0.955713	−	0.294299i	$-0.904914\pi$
$359$	−4.22498	+	7.31788i	−0.222986	+	0.386223i	0.732727	+	0.680522i	$0.238247\pi$
$360$	1.21340	+	11.1448i	0.0639516	+	0.587380i
$361$	1.95015	+	3.37776i	0.102640	+	0.177777i
$362$	−3.17071	+	5.49183i	−0.166649	+	0.288644i
$363$	7.99970	−	17.2918i	0.419875	−	0.907582i
$364$	−2.49179	−	12.0226i	−0.130605	−	0.630157i
$365$	40.3646			2.11278
$366$	0.707549	+	13.0357i	0.0369842	+	0.681389i
$367$	−0.156031	−	0.270253i	−0.00814474	−	0.0141071i	0.861924	−	0.507037i	$-0.169259\pi$
$367$	−0.156031	−	0.270253i	−0.00814474	−	0.0141071i	−0.870069	+	0.492930i	$0.835926\pi$
$368$	4.94452	−	2.85472i	0.257751	−	0.148812i
$369$	7.27496	+	9.93501i	0.378720	+	0.517196i
$370$			9.67194i			0.502820i
$371$	2.04642	+	9.87376i	0.106245	+	0.512620i
$372$	−2.39472	−	3.67254i	−0.124161	−	0.190412i
$373$	29.1559	+	16.8331i	1.50963	+	0.871587i	0.999937	+	0.0112328i	$0.00357558\pi$
$373$	29.1559	+	16.8331i	1.50963	+	0.871587i	0.509696	+	0.860354i	$0.329758\pi$
$374$	−3.05615	+	0.0551180i	−0.158030	+	0.00285008i
$375$	22.8833	+	11.6059i	1.18169	+	0.599329i
$376$	−4.96151	−	2.86453i	−0.255871	−	0.147727i
$377$			35.9132i			1.84962i
$378$	−10.6885	−	8.64618i	−0.549756	−	0.444712i
$379$	8.97243			0.460883			0.230441	−	0.973086i	$-0.425983\pi$
$379$	8.97243			0.460883			0.230441	+	0.973086i	$0.425983\pi$
$380$	8.94127	−	15.4867i	0.458677	−	0.794452i
$381$	−7.95336	−	4.03378i	−0.407463	−	0.206657i
$382$	6.08888	−	3.51541i	0.311534	−	0.179864i
$383$	6.48945	+	3.74669i	0.331596	+	0.191447i	0.656549	−	0.754283i	$-0.272015\pi$
$383$	6.48945	+	3.74669i	0.331596	+	0.191447i	−0.324954	+	0.945730i	$0.605349\pi$
$384$	−0.946049	−	1.45086i	−0.0482779	−	0.0740388i
$385$	−24.0820	+	22.2553i	−1.22733	+	1.13424i
$386$		−	8.71600i		−	0.443633i
$387$	5.31728	−	3.89361i	0.270293	−	0.197923i
$388$	6.08419	+	10.5381i	0.308878	+	0.534992i
$389$	−9.97406	+	5.75853i	−0.505705	+	0.291969i	−0.731066	−	0.682306i	$-0.760977\pi$
$389$	−9.97406	+	5.75853i	−0.505705	+	0.291969i	0.225361	+	0.974275i	$0.427644\pi$
$390$	−29.9926	+	1.62792i	−1.51873	+	0.0824332i
$391$			5.26190i			0.266106i
$392$	5.62107	+	4.17176i	0.283907	+	0.210706i
$393$	−14.9718	−	22.9607i	−0.755226	−	1.15821i
$394$	−0.278382	+	0.482171i	−0.0140247	+	0.0242914i
$395$	32.1671	+	55.7150i	1.61850	+	2.80333i
$396$	−3.84822	+	9.17557i	−0.193381	+	0.461090i
$397$	10.4828	−	18.1567i	0.526115	−	0.911258i	−0.473422	−	0.880836i	$-0.656981\pi$
$397$	10.4828	−	18.1567i	0.526115	−	0.911258i	0.999537	−	0.0304226i	$-0.00968532\pi$
$398$	6.47738			0.324682
$399$	5.60776	+	21.2005i	0.280739	+	1.06135i
$400$	−8.96422			−0.448211
$401$	20.3964	+	11.7758i	1.01855	+	0.588057i	0.913682	−	0.406429i	$-0.133226\pi$
$401$	20.3964	+	11.7758i	1.01855	+	0.588057i	0.104863	+	0.994487i	$0.466560\pi$
$402$	0.611702	−	1.20609i	0.0305089	−	0.0601541i
$403$	10.1731	−	5.87347i	0.506761	−	0.292578i
$404$	0.661912	−	1.14646i	0.0329313	−	0.0570387i
$405$	−24.8248	+	22.6899i	−1.23355	+	1.12747i
$406$	−13.6229	−	15.2851i	−0.676095	−	0.758586i
$407$	−4.15737	+	7.51035i	−0.206073	+	0.372274i
$408$	1.59394	−	0.0865151i	0.0789117	−	0.00428314i
$409$	−10.2853	+	5.93820i	−0.508573	+	0.293625i	−0.732247	−	0.681039i	$-0.761528\pi$
$409$	−10.2853	+	5.93820i	−0.508573	+	0.293625i	0.223674	+	0.974664i	$0.428195\pi$
$410$	−13.2834	+	7.66918i	−0.656021	+	0.378754i
$411$	−1.21330	−	22.3535i	−0.0598475	−	1.10262i
$412$	9.89908			0.487693
$413$	−4.74716	−	22.9046i	−0.233593	−	1.12706i
$414$	15.6734	+	6.90831i	0.770303	+	0.339525i
$415$	−41.0301	−	23.6887i	−2.01409	−	1.16283i
$416$	4.01896	−	2.32035i	0.197046	−	0.113764i
$417$	12.4946	+	6.33701i	0.611865	+	0.310325i
$418$	13.5998	−	8.18230i	0.665186	−	0.400209i
$419$		−	21.5571i		−	1.05313i	−0.850134	−	0.526567i	$-0.823479\pi$
$419$		−	21.5571i		−	1.05313i	0.850134	−	0.526567i	$-0.176521\pi$
$420$	12.1477	−	12.0699i	0.592745	−	0.588952i
$421$	−12.1688			−0.593070			−0.296535	−	0.955022i	$-0.595831\pi$
$421$	−12.1688			−0.593070			−0.296535	+	0.955022i	$0.595831\pi$
$422$	15.4275	+	8.90708i	0.751000	+	0.433590i
$423$	−1.86028	−	17.0862i	−0.0904499	−	0.830760i
$424$	−3.30063	+	1.90562i	−0.160293	+	0.0925452i
$425$	4.13078	−	7.15472i	0.200372	−	0.347055i
$426$	16.6817	−	10.8775i	0.808232	−	0.527017i
$427$	14.8871	−	13.2682i	0.720438	−	0.642095i
$428$	−11.2337			−0.543000
$429$	−23.9892	−	11.6278i	−1.15821	−	0.561397i
$430$	4.10460	+	7.10937i	0.197941	+	0.342844i
$431$	−6.76221	−	11.7125i	−0.325724	−	0.564171i	0.655934	−	0.754818i	$-0.272275\pi$
$431$	−6.76221	−	11.7125i	−0.325724	−	0.564171i	−0.981659	+	0.190647i	$0.938941\pi$
$432$	1.83497	−	4.86137i	0.0882851	−	0.233893i
$433$	34.3316			1.64987			0.824937	−	0.565225i	$-0.191211\pi$
$433$	34.3316			1.64987			0.824937	+	0.565225i	$0.191211\pi$
$434$	−2.10183	+	6.35879i	−0.100891	+	0.305232i
$435$	−41.9570	+	27.3585i	−2.01168	+	1.31174i
$436$	−3.95986	−	2.28623i	−0.189643	−	0.109490i
$437$	−13.6610	−	23.6616i	−0.653496	−	1.13189i
$438$	−16.6857	−	8.46266i	−0.797275	−	0.404361i
$439$	2.95877	+	1.70824i	0.141214	+	0.0815301i	0.568943	−	0.822377i	$-0.307353\pi$
$439$	2.95877	+	1.70824i	0.141214	+	0.0815301i	−0.427728	+	0.903907i	$0.640686\pi$
$440$	−10.8433	−	6.00235i	−0.516936	−	0.286151i
$441$	−0.134832	+	20.9996i	−0.00642057	+	0.999979i
$442$			4.27694i			0.203433i
$443$	21.5391	+	12.4356i	1.02336	+	0.590835i	0.915074	−	0.403286i	$-0.132132\pi$
$443$	21.5391	+	12.4356i	1.02336	+	0.590835i	0.108281	+	0.994120i	$0.465465\pi$
$444$	2.02778	−	3.99814i	0.0962340	−	0.189744i
$445$	−16.0727	−	27.8388i	−0.761921	−	1.31969i
$446$	4.55482	−	7.88917i	0.215677	−	0.373563i
$447$	12.4891	+	19.1532i	0.590714	+	0.905918i
$448$	−0.830341	+	2.51208i	−0.0392299	+	0.118685i
$449$			12.2457i			0.577908i	0.957343	+	0.288954i	$0.0933075\pi$
$449$			12.2457i			0.577908i	−0.957343	+	0.288954i	$0.906693\pi$
$450$	−15.8881	−	21.6975i	−0.748974	−	1.02283i
$451$	−13.6112	+	0.245479i	−0.640926	+	0.0115591i
$452$	−6.51444	+	3.76112i	−0.306414	+	0.176908i
$453$	−1.11791	−	20.5961i	−0.0525240	−	0.967691i
$454$	−25.0737			−1.17677
$455$	30.5275	+	34.2522i	1.43115	+	1.60577i
$456$	−6.94298	+	4.52725i	−0.325135	+	0.212008i
$457$	−26.7154	−	15.4241i	−1.24969	−	0.721511i	−0.278645	−	0.960394i	$-0.589885\pi$
$457$	−26.7154	−	15.4241i	−1.24969	−	0.721511i	−0.971048	+	0.238883i	$0.923219\pi$
$458$	−11.5525	−	20.0095i	−0.539811	−	0.934980i
$459$	3.03449	+	3.70472i	0.141638	+	0.172922i
$460$	−10.6677	+	18.4770i	−0.497385	+	0.861496i
$461$	3.40330			0.158507			0.0792537	−	0.996854i	$-0.474746\pi$
$461$	3.40330			0.158507			0.0792537	+	0.996854i	$0.474746\pi$
$462$	14.6209	−	4.15088i	0.680225	−	0.193116i
$463$	−15.8266			−0.735522			−0.367761	−	0.929920i	$-0.619876\pi$
$463$	−15.8266			−0.735522			−0.367761	+	0.929920i	$0.619876\pi$
$464$	3.86938	−	6.70196i	0.179631	−	0.311130i
$465$	14.6118	+	7.41079i	0.677605	+	0.343667i
$466$	−11.6393	−	20.1599i	−0.539181	−	0.933889i
$467$	18.9467	+	10.9389i	0.876750	+	0.506192i	0.869586	−	0.493782i	$-0.164386\pi$
$467$	18.9467	+	10.9389i	0.876750	+	0.506192i	0.00716472	+	0.999974i	$0.497719\pi$
$468$	12.7395	+	5.61516i	0.588883	+	0.259561i
$469$	−2.02275	+	0.419231i	−0.0934017	+	0.0193583i
$470$	21.4088			0.987514
$471$	20.9265	−	1.13584i	0.964240	−	0.0523367i
$472$	7.65662	−	4.42055i	0.352424	−	0.203472i
$473$	0.131382	+	7.28481i	0.00604095	+	0.334956i
$474$	−1.61613	−	29.7752i	−0.0742313	−	1.36762i
$475$			42.8976i			1.96828i
$476$	−1.62237	−	1.82031i	−0.0743611	−	0.0834340i
$477$	−10.4625	−	4.61153i	−0.479045	−	0.211148i
$478$	1.47636	−	2.55714i	0.0675273	−	0.116961i
$479$	12.2718	+	21.2553i	0.560711	+	0.971180i	0.997435	+	0.0715839i	$0.0228054\pi$
$479$	12.2718	+	21.2553i	0.560711	+	0.971180i	−0.436724	+	0.899596i	$0.643861\pi$
$480$	5.77247	+	2.92767i	0.263476	+	0.133629i
$481$	10.4021	+	6.00563i	0.474293	+	0.273833i
$482$			3.67675i			0.167471i
$483$	−6.69055	−	25.2940i	−0.304431	−	1.15092i
$484$	−5.83993	−	9.32176i	−0.265451	−	0.423717i
$485$	−39.3796	−	22.7358i	−1.78814	−	1.03238i
$486$	15.0190	−	4.17479i	0.681277	−	0.189372i
$487$	−18.0891	−	31.3313i	−0.819697	−	1.41976i	−0.905905	−	0.423480i	$-0.860808\pi$
$487$	−18.0891	−	31.3313i	−0.819697	−	1.41976i	0.0862081	−	0.996277i	$-0.472525\pi$
$488$	6.52747	+	3.76863i	0.295484	+	0.170598i
$489$	−1.45771	−	2.23553i	−0.0659197	−	0.101094i
$490$	−25.9857	−	2.99816i	−1.17392	−	0.135443i
$491$	39.6660			1.79010			0.895050	−	0.445965i	$-0.147139\pi$
$491$	39.6660			1.79010			0.895050	+	0.445965i	$0.147139\pi$
$492$	7.09892	−	0.385313i	0.320044	−	0.0173712i
$493$	3.56607	+	6.17662i	0.160608	+	0.278181i
$494$	−11.1039	−	19.2324i	−0.499586	−	0.865309i
$495$	−4.69025	−	36.8844i	−0.210811	−	1.65783i
$496$	−2.53129			−0.113658
$497$	−28.8834	−	9.54712i	−1.29560	−	0.428247i
$498$	11.9944	+	18.3945i	0.537480	+	0.824278i
$499$	−16.0605	+	27.8176i	−0.718966	+	1.24529i	0.242444	+	0.970165i	$0.422051\pi$
$499$	−16.0605	+	27.8176i	−0.718966	+	1.24529i	−0.961410	+	0.275120i	$0.911282\pi$
$500$	12.8291	−	7.40689i	0.573736	−	0.331246i
$501$	−8.00747	+	15.7883i	−0.357747	+	0.705367i
$502$	−23.4533	−	13.5408i	−1.04677	−	0.604353i
$503$	−8.24994			−0.367847			−0.183923	−	0.982941i	$-0.558880\pi$
$503$	−8.24994			−0.367847			−0.183923	+	0.982941i	$0.558880\pi$
$504$	−7.55207	+	2.44259i	−0.336396	+	0.108801i
$505$			4.94696i			0.220137i
$506$	−16.2257	+	9.76220i	−0.721321	+	0.433983i
$507$	−6.68763	+	13.1859i	−0.297008	+	0.585608i
$508$	−4.45890	+	2.57435i	−0.197832	+	0.114218i
$509$	3.24742	+	1.87490i	0.143939	+	0.0831033i	0.570240	−	0.821478i	$-0.306850\pi$
$509$	3.24742	+	1.87490i	0.143939	+	0.0831033i	−0.426301	+	0.904581i	$0.640184\pi$
$510$	−4.99670	+	3.25815i	−0.221257	+	0.144273i
$511$	5.79989	+	27.9839i	0.256572	+	1.23793i
$512$	−1.00000			−0.0441942
$513$	−23.2637	−	8.78112i	−1.02712	−	0.387696i
$514$	−12.5519	+	7.24684i	−0.553640	+	0.319644i
$515$	−32.0357	+	18.4958i	−1.41166	+	0.815022i
$516$	−0.206222	−	3.79939i	−0.00907841	−	0.167259i
$517$	16.6241	+	9.20231i	0.731128	+	0.404717i
$518$	−6.70535	+	1.38974i	−0.294616	+	0.0610616i
$519$	6.61782	+	10.1491i	0.290490	+	0.445495i
$520$	−8.67085	+	15.0184i	−0.380242	+	0.658598i
$521$	20.4859	−	11.8275i	0.897504	−	0.518174i	0.0211142	−	0.999777i	$-0.493279\pi$
$521$	20.4859	−	11.8275i	0.897504	−	0.518174i	0.876389	+	0.481603i	$0.159945\pi$
$522$	23.0799	−	2.51284i	1.01018	−	0.109984i
$523$	16.3582	+	9.44443i	0.715295	+	0.412976i	0.813019	−	0.582238i	$-0.197823\pi$
$523$	16.3582	+	9.44443i	0.715295	+	0.412976i	−0.0977232	+	0.995214i	$0.531156\pi$
$524$	−15.8256			−0.691343
$525$	−10.7594	+	39.6451i	−0.469579	+	1.73026i
$526$	14.5018			0.632306
$527$	1.16644	−	2.02033i	0.0508108	−	0.0880068i
$528$	3.22395	+	4.75459i	0.140304	+	0.206917i
$529$	4.79882	+	8.31181i	0.208645	+	0.361383i
$530$	7.12107	−	12.3341i	0.309319	−	0.535757i
$531$	24.2703	+	10.6976i	1.05324	+	0.464235i
$532$	12.0214	+	3.97354i	0.521192	+	0.172275i
$533$			19.0482i			0.825069i
$534$	0.807522	+	14.8776i	0.0349449	+	0.643818i
$535$	36.3547	−	20.9894i	1.57175	−	0.907451i
$536$	−0.390387	−	0.676170i	−0.0168622	−	0.0292061i
$537$	2.17553	+	40.0816i	0.0938812	+	1.72965i
$538$		−	7.69686i		−	0.331835i
$539$	−18.8894	−	13.4977i	−0.813626	−	0.581389i
$540$	3.14477	+	19.1610i	0.135329	+	0.824559i
$541$	30.8245	+	17.7966i	1.32525	+	0.765134i	0.984561	−	0.175042i	$-0.0560061\pi$
$541$	30.8245	+	17.7966i	1.32525	+	0.765134i	0.340690	+	0.940176i	$0.389339\pi$
$542$	−2.86928	+	1.65658i	−0.123246	+	0.0711561i
$543$	−4.96823	+	9.79580i	−0.213207	+	0.420378i
$544$	0.460807	−	0.798142i	0.0197570	−	0.0342201i
$545$	17.0867			0.731913
$546$	−5.43816	−	20.5593i	−0.232732	−	0.879856i
$547$		−	31.2280i		−	1.33521i	−0.744514	−	0.667607i	$-0.767319\pi$
$547$		−	31.2280i		−	1.33521i	0.744514	−	0.667607i	$-0.232681\pi$
$548$	−11.1932	−	6.46241i	−0.478151	−	0.276061i
$549$	2.44742	+	22.4790i	0.104453	+	0.959379i
$550$	29.7261	−	0.536113i	1.26753	−	0.0228599i
$551$	−32.0717	−	18.5166i	−1.36630	−	0.788834i
$552$	8.28358	−	5.40141i	0.352573	−	0.229899i
$553$	−34.0040	+	30.3063i	−1.44600	+	1.28876i
$554$		−	8.95881i		−	0.380623i
$555$	0.907938	+	16.7277i	0.0385398	+	0.710050i
$556$	7.00488	−	4.04427i	0.297073	−	0.171515i
$557$	7.73600	+	13.3991i	0.327785	+	0.567740i	0.982072	−	0.188506i	$-0.0603645\pi$
$557$	7.73600	+	13.3991i	0.327785	+	0.567740i	−0.654287	+	0.756246i	$0.727031\pi$
$558$	−4.48644	−	6.12688i	−0.189926	−	0.259371i
$559$	10.1947			0.431191
$560$	−2.00648	−	9.68109i	−0.0847895	−	0.409101i
$561$	−5.28046	+	0.382218i	−0.222941	+	0.0161373i
$562$	−11.4738	+	19.8733i	−0.483994	+	0.838303i
$563$	−0.771946	−	1.33705i	−0.0325336	−	0.0563499i	0.849300	−	0.527910i	$-0.177024\pi$
$563$	−0.771946	−	1.33705i	−0.0325336	−	0.0563499i	−0.881834	+	0.471560i	$0.843691\pi$
$564$	−8.84987	−	4.48847i	−0.372647	−	0.188999i
$565$	14.0548	−	24.3436i	0.591290	−	1.02414i
$566$			25.9431i			1.09047i
$567$	−19.2974	−	13.9503i	−0.810416	−	0.585855i
$568$		−	11.4978i		−	0.482438i
$569$	−11.5873	+	20.0697i	−0.485763	+	0.841366i	−0.999866	−	0.0163623i	$-0.994791\pi$
$569$	−11.5873	+	20.0697i	−0.485763	+	0.841366i	0.514103	+	0.857728i	$0.328125\pi$
$570$	14.0102	−	27.6237i	0.586822	−	1.15703i
$571$	7.03226	−	4.06008i	0.294291	−	0.169909i	−0.345584	−	0.938388i	$-0.612319\pi$
$571$	7.03226	−	4.06008i	0.294291	−	0.169909i	0.639875	+	0.768479i	$0.278986\pi$
$572$	−13.1885	+	7.93483i	−0.551437	+	0.331772i
$573$	10.2007	−	6.65151i	0.426142	−	0.277871i
$574$	−7.22554	−	8.10714i	−0.301588	−	0.338385i
$575$		−	51.1806i		−	2.13438i
$576$	−1.77239	−	2.42046i	−0.0738498	−	0.100852i
$577$	22.9056	+	39.6736i	0.953571	+	1.65163i	0.737605	+	0.675232i	$0.235957\pi$
$577$	22.9056	+	39.6736i	0.953571	+	1.65163i	0.215965	+	0.976401i	$0.430710\pi$
$578$	−8.07531	−	13.9869i	−0.335889	−	0.581776i
$579$	−0.818201	−	15.0744i	−0.0340033	−	0.626469i
$580$			28.9187i			1.20079i
$581$	10.5274	−	31.8491i	0.436749	−	1.32132i
$582$	11.5119	+	17.6546i	0.477183	+	0.731807i
$583$	10.8312	−	6.51660i	0.448583	−	0.269890i
$584$	−9.35455	+	5.40085i	−0.387094	+	0.223489i
$585$	−51.7195	+	5.63101i	−2.13834	+	0.232813i
$586$	2.78352	−	4.82120i	0.114986	−	0.199162i
$587$		−	8.71794i		−	0.359828i	−0.983682	−	0.179914i	$-0.942418\pi$
$587$		−	8.71794i		−	0.359828i	0.983682	−	0.179914i	$-0.0575820\pi$
$588$	10.1133	+	6.68742i	0.417065	+	0.275784i
$589$			12.1133i			0.499119i
$590$	−16.5190	+	28.6118i	−0.680078	+	1.17793i
$591$	−0.436200	+	0.860050i	−0.0179429	+	0.0353777i
$592$	−1.29412	−	2.24149i	−0.0531881	−	0.0921245i
$593$	−11.1048	+	19.2340i	−0.456019	+	0.789848i	−0.998746	−	0.0500613i	$-0.984058\pi$
$593$	−11.1048	+	19.2340i	−0.456019	+	0.789848i	0.542727	+	0.839909i	$0.317392\pi$
$594$	−5.79418	+	16.2304i	−0.237738	+	0.665943i
$595$	8.65149	+	2.85966i	0.354676	+	0.117235i
$596$	13.2013			0.540747
$597$	11.2027	−	0.608054i	0.458495	−	0.0248860i
$598$	13.2479	+	22.9460i	0.541746	+	0.938332i
$599$	−6.10885	+	3.52694i	−0.249601	+	0.144107i	−0.619581	−	0.784932i	$-0.712698\pi$
$599$	−6.10885	+	3.52694i	−0.249601	+	0.144107i	0.369981	+	0.929039i	$0.379364\pi$
$600$	−15.5037	+	0.841502i	−0.632934	+	0.0343542i
$601$			19.4191i			0.792122i	0.918224	+	0.396061i	$0.129623\pi$
$601$			19.4191i			0.792122i	−0.918224	+	0.396061i	$0.870377\pi$
$602$	−4.33899	+	3.86716i	−0.176844	+	0.157614i
$603$	0.944722	−	2.14336i	0.0384721	−	0.0872842i
$604$	−10.3132	−	5.95435i	−0.419639	−	0.242279i
$605$	36.3164	+	19.2558i	1.47647	+	0.782860i
$606$	1.03716	−	2.04495i	0.0421316	−	0.0830705i
$607$	−17.1496	−	9.90133i	−0.696081	−	0.401882i	0.109805	−	0.993953i	$-0.464977\pi$
$607$	−17.1496	−	9.90133i	−0.696081	−	0.401882i	−0.805886	+	0.592071i	$0.798311\pi$
$608$			4.78543i			0.194075i
$609$	−24.9958	−	25.1568i	−1.01288	−	1.01940i
$610$	−28.1658			−1.14040
$611$	13.2934	−	23.0249i	0.537794	−	0.931487i
$612$	2.74860	−	0.299257i	0.111106	−	0.0120967i
$613$	41.1230	−	23.7424i	1.66094	−	0.958945i	0.688675	−	0.725070i	$-0.258193\pi$
$613$	41.1230	−	23.7424i	1.66094	−	0.958945i	0.972267	−	0.233875i	$-0.0751405\pi$
$614$	−26.1600	−	15.1035i	−1.05573	−	0.609526i
$615$	−22.2538	+	14.5108i	−0.897359	+	0.585134i
$616$	2.60325	−	8.37992i	0.104888	−	0.337637i
$617$		−	38.1302i		−	1.53506i	−0.641011	−	0.767532i	$-0.721485\pi$
$617$		−	38.1302i		−	1.53506i	0.641011	−	0.767532i	$-0.278515\pi$
$618$	17.1205	−	0.929260i	0.688688	−	0.0373803i
$619$	−23.0035	−	39.8432i	−0.924588	−	1.60143i	−0.792222	−	0.610233i	$-0.791076\pi$
$619$	−23.0035	−	39.8432i	−0.924588	−	1.60143i	−0.132366	−	0.991201i	$-0.542257\pi$
$620$	8.19182	−	4.72955i	0.328991	−	0.189943i
$621$	27.7557	+	10.4766i	1.11380	+	0.420413i
$622$			0.915784i			0.0367196i
$623$	16.9906	−	15.1430i	0.680714	−	0.606691i
$624$	6.73300	−	4.39033i	0.269536	−	0.175754i
$625$	−5.26807	+	9.12457i	−0.210723	+	0.364983i
$626$	−2.87594	−	4.98127i	−0.114946	−	0.199092i
$627$	22.7528	−	15.4280i	0.908657	−	0.616134i
$628$	6.04984	−	10.4786i	0.241415	−	0.418143i
$629$	2.38536			0.0951107
$630$	19.8764	−	22.0153i	0.791895	−	0.877112i
$631$	30.5055			1.21441			0.607203	−	0.794547i	$-0.292292\pi$
$631$	30.5055			1.21441			0.607203	+	0.794547i	$0.292292\pi$
$632$	−14.9095	−	8.60802i	−0.593069	−	0.342409i
$633$	27.5181	+	13.9566i	1.09375	+	0.554725i
$634$	−9.09364	+	5.25022i	−0.361155	+	0.208513i
$635$	9.62002	−	16.6624i	0.381759	−	0.661226i
$636$	−5.52958	+	3.60562i	−0.219262	+	0.142972i
$637$	−19.3599	+	26.0857i	−0.767067	+	1.03355i
$638$	−12.4304	+	22.4557i	−0.492123	+	0.889028i
$639$	27.8300	−	20.3787i	1.10094	−	0.806169i
$640$	3.23623	−	1.86844i	0.127923	−	0.0738564i
$641$	−10.5012	+	6.06289i	−0.414774	+	0.239470i	−0.692839	−	0.721092i	$-0.743640\pi$
$641$	−10.5012	+	6.06289i	−0.414774	+	0.239470i	0.278065	+	0.960562i	$0.410307\pi$
$642$	−19.4287	+	1.05454i	−0.766790	+	0.0416195i
$643$	11.5883			0.456999			0.228499	−	0.973544i	$-0.426618\pi$
$643$	11.5883			0.456999			0.228499	+	0.973544i	$0.426618\pi$
$644$	−14.3425	−	4.74078i	−0.565175	−	0.186813i
$645$	7.76630	+	11.9104i	0.305798	+	0.468971i
$646$	−3.81945	−	2.20516i	−0.150274	−	0.0867609i
$647$	17.3213	−	10.0004i	0.680969	−	0.393158i	−0.119251	−	0.992864i	$-0.538049\pi$
$647$	17.3213	−	10.0004i	0.680969	−	0.393158i	0.800220	+	0.599707i	$0.204716\pi$
$648$	2.71724	−	8.58001i	0.106743	−	0.337055i
$649$	−25.1256	+	15.1168i	−0.986267	+	0.593388i
$650$		−	41.6002i		−	1.63170i
$651$	−3.03821	+	11.1949i	−0.119077	+	0.438761i
$652$	−1.54083			−0.0603437
$653$	18.1507	+	10.4793i	0.710291	+	0.410087i	0.811169	−	0.584812i	$-0.198832\pi$
$653$	18.1507	+	10.4793i	0.710291	+	0.410087i	−0.100878	+	0.994899i	$0.532165\pi$
$654$	−7.06322	−	3.58232i	−0.276194	−	0.140080i
$655$	51.2151	−	29.5691i	2.00114	−	1.15536i
$656$	2.05230	−	3.55469i	0.0801288	−	0.138787i
$657$	−29.6525	−	13.0699i	−1.15685	−	0.509904i
$658$	3.07618	+	14.8422i	0.119922	+	0.578611i
$659$	8.15565			0.317699			0.158850	−	0.987303i	$-0.449222\pi$
$659$	8.15565			0.317699			0.158850	+	0.987303i	$0.449222\pi$
$660$	−19.3171	−	9.36319i	−0.751917	−	0.364462i
$661$	−17.6023	−	30.4881i	−0.684650	−	1.18585i	−0.973547	−	0.228489i	$-0.926622\pi$
$661$	−17.6023	−	30.4881i	−0.684650	−	1.18585i	0.288896	−	0.957360i	$-0.406712\pi$
$662$	−7.54164	−	13.0625i	−0.293114	−	0.507689i
$663$	0.401491	+	7.39698i	0.0155926	+	0.287275i
$664$	12.6784			0.492016
$665$	−46.3282	+	9.60189i	−1.79653	+	0.372345i
$666$	3.13173	−	7.10517i	0.121352	−	0.275320i
$667$	38.2644	+	22.0919i	1.48160	+	0.855404i
$668$	5.11035	+	8.85139i	0.197726	+	0.342471i
$669$	7.13699	−	14.0719i	0.275932	−	0.544053i
$670$	2.52676	+	1.45883i	0.0976173	+	0.0563594i
$671$	−21.8710	−	12.1067i	−0.844321	−	0.467375i
$672$	−1.20026	+	4.42260i	−0.0463011	+	0.170605i
$673$		−	20.2008i		−	0.778685i	−0.921093	−	0.389342i	$-0.872702\pi$
$673$		−	20.2008i		−	0.778685i	0.921093	−	0.389342i	$-0.127298\pi$
$674$	12.8492	+	7.41850i	0.494933	+	0.285750i
$675$	−29.5154	−	36.0345i	−1.13605	−	1.38697i
$676$	4.26804	+	7.39246i	0.164155	+	0.284325i
$677$	−0.814387	+	1.41056i	−0.0312995	+	0.0542122i	−0.881251	−	0.472649i	$-0.843298\pi$
$677$	−0.814387	+	1.41056i	−0.0312995	+	0.0542122i	0.849951	+	0.526861i	$0.176631\pi$
$678$	−10.9137	+	7.11640i	−0.419138	+	0.273304i
$679$	10.1039	−	30.5679i	0.387752	−	1.17309i
$680$			3.44396i			0.132070i
$681$	−43.3651	+	2.35376i	−1.66176	+	0.0901961i
$682$	8.39397	−	0.151386i	0.321422	−	0.00579686i
$683$	26.5384	−	15.3220i	1.01546	−	0.586278i	0.102677	−	0.994715i	$-0.467259\pi$
$683$	26.5384	−	15.3220i	1.01546	−	0.586278i	0.912787	+	0.408436i	$0.133926\pi$
$684$	−11.5829	+	8.48166i	−0.442884	+	0.324304i
$685$	48.2984			1.84539
$686$	−1.65526	−	18.4461i	−0.0631982	−	0.704277i
$687$	−21.8584	−	33.5220i	−0.833950	−	1.27894i
$688$	−1.90249	−	1.09840i	−0.0725318	−	0.0418763i
$689$	−8.84341	−	15.3172i	−0.336907	−	0.583540i
$690$	−16.7154	+	32.9575i	−0.636343	+	1.25467i
$691$	−0.398760	+	0.690673i	−0.0151696	+	0.0262744i	−0.873511	−	0.486805i	$-0.838162\pi$
$691$	−0.398760	+	0.690673i	−0.0151696	+	0.0262744i	0.858341	+	0.513080i	$0.171495\pi$
$692$	6.99522			0.265918
$693$	24.8972	−	8.55148i	0.945768	−	0.324844i
$694$	−1.69957			−0.0645148
$695$	−15.1129	+	26.1764i	−0.573266	+	0.992926i
$696$	6.06297	−	11.9543i	0.229816	−	0.453126i
$697$	1.89143	+	3.27605i	0.0716430	+	0.124089i
$698$	17.4664	+	10.0842i	0.661112	+	0.381693i
$699$	−22.0227	−	33.7740i	−0.832976	−	1.27745i
$700$	15.7802	+	17.7055i	0.596435	+	0.669207i
$701$	−31.8559			−1.20318			−0.601591	−	0.798804i	$-0.705466\pi$
$701$	−31.8559			−1.20318			−0.601591	+	0.798804i	$0.705466\pi$
$702$	22.5601	+	8.51554i	0.851477	+	0.321398i
$703$	−10.7265	+	6.19293i	−0.404556	+	0.233571i
$704$	3.31609	−	0.0598058i	0.124980	−	0.00225402i
$705$	37.0266	−	2.00972i	1.39450	−	0.0756903i
$706$			11.4189i			0.429755i
$707$	−3.42962	+	0.710817i	−0.128984	+	0.0267330i
$708$	12.8272	−	8.36412i	0.482075	−	0.314343i
$709$	−15.7500	+	27.2797i	−0.591502	+	1.02451i	0.402528	+	0.915408i	$0.368132\pi$
$709$	−15.7500	+	27.2797i	−0.591502	+	1.02451i	−0.994030	+	0.109104i	$0.965202\pi$
$710$	21.4830	+	37.2096i	0.806241	+	1.39645i
$711$	−5.59021	−	51.3447i	−0.209649	−	1.92558i
$712$	7.44976	+	4.30112i	0.279192	+	0.161191i
$713$		−	14.4522i		−	0.541240i
$714$	−2.97677	−	2.99595i	−0.111403	−	0.112120i
$715$	27.8551	−	50.3207i	1.04172	−	1.88189i
$716$	20.0703	+	11.5876i	0.750062	+	0.433049i
$717$	2.31333	−	4.56118i	0.0863930	−	0.170340i
$718$	4.22498	+	7.31788i	0.157675	+	0.273101i
$719$	−6.04825	−	3.49196i	−0.225562	−	0.130228i	0.382961	−	0.923764i	$-0.374904\pi$
$719$	−6.04825	−	3.49196i	−0.225562	−	0.130228i	−0.608523	+	0.793536i	$0.708238\pi$
$720$	10.2583	+	4.52155i	0.382306	+	0.168508i
$721$	−17.4259	−	19.5520i	−0.648973	−	0.728155i
$722$	3.90031			0.145154
$723$	0.345149	+	6.35896i	0.0128362	+	0.236492i
$724$	3.17071	+	5.49183i	0.117839	+	0.204102i
$725$	−34.6859	−	60.0778i	−1.28820	−	2.23123i
$726$	−10.9752	−	15.5738i	−0.407330	−	0.577999i
$727$	−33.1623			−1.22992			−0.614960	−	0.788558i	$-0.710828\pi$
$727$	−33.1623			−1.22992			−0.614960	+	0.788558i	$0.710828\pi$
$728$	−11.6578	−	3.85336i	−0.432067	−	0.142815i
$729$	25.5836	−	8.63020i	0.947540	−	0.319637i
$730$	20.1823	−	34.9568i	0.746980	−	1.29381i
$731$	1.75336	−	1.01231i	0.0648505	−	0.0374415i
$732$	11.6431	+	5.90512i	0.430340	+	0.218259i
$733$	−21.5001	−	12.4131i	−0.794123	−	0.458487i	0.0472893	−	0.998881i	$-0.484942\pi$
$733$	−21.5001	−	12.4131i	−0.794123	−	0.458487i	−0.841412	+	0.540394i	$0.818275\pi$
$734$	−0.312061			−0.0115184
$735$	−45.2239	−	2.74597i	−1.66811	−	0.101287i
$736$		−	5.70943i		−	0.210453i
$737$	1.33500	+	2.21889i	0.0491752	+	0.0817339i
$738$	12.2415	−	1.33280i	0.450614	−	0.0490611i
$739$	−1.10754	+	0.639441i	−0.0407417	+	0.0235222i	−0.520233	−	0.854025i	$-0.674155\pi$
$739$	−1.10754	+	0.639441i	−0.0407417	+	0.0235222i	0.479491	+	0.877547i	$0.340821\pi$
$740$	8.37615	+	4.83597i	0.307913	+	0.177774i
$741$	−21.0096	−	32.2203i	−0.771807	−	1.18364i
$742$	9.57414	+	3.16463i	0.351478	+	0.116177i
$743$	0.935605			0.0343240			0.0171620	−	0.999853i	$-0.494537\pi$
$743$	0.935605			0.0343240			0.0171620	+	0.999853i	$0.494537\pi$
$744$	−4.37787	+	0.237621i	−0.160501	+	0.00871159i
$745$	−42.7225	+	24.6658i	−1.56523	+	0.903686i
$746$	29.1559	−	16.8331i	1.06747	−	0.616305i
$747$	22.4711	+	30.6875i	0.822173	+	1.12280i
$748$	−1.48034	+	2.67427i	−0.0541267	+	0.0977808i
$749$	19.7752	+	22.1880i	0.722571	+	0.810733i
$750$	21.4927	−	14.0146i	0.784803	−	0.511740i
$751$	−3.90274	+	6.75974i	−0.142413	+	0.246666i	−0.928405	−	0.371570i	$-0.878819\pi$
$751$	−3.90274	+	6.75974i	−0.142413	+	0.246666i	0.785992	+	0.618237i	$0.212153\pi$
$752$	−4.96151	+	2.86453i	−0.180928	+	0.104459i
$753$	−41.8337	−	21.2172i	−1.52450	−	0.773196i
$754$	31.1017	+	17.9566i	1.13266	+	0.653941i
$755$	44.5013			1.61957
$756$	−12.8321	+	4.93340i	−0.466697	+	0.179426i
$757$	48.4080			1.75942			0.879710	−	0.475510i	$-0.157737\pi$
$757$	48.4080			1.75942			0.879710	+	0.475510i	$0.157737\pi$
$758$	4.48621	−	7.77035i	0.162947	−	0.282232i
$759$	−27.1460	+	18.4069i	−0.985339	+	0.668129i
$760$	−8.94127	−	15.4867i	−0.324334	−	0.561763i
$761$	25.7356	−	44.5754i	0.932915	−	1.61586i	0.154604	−	0.987977i	$-0.450590\pi$
$761$	25.7356	−	44.5754i	0.932915	−	1.61586i	0.778311	−	0.627879i	$-0.216077\pi$
$762$	−7.47004	+	4.87092i	−0.270611	+	0.176455i
$763$	2.45515	+	11.8458i	0.0888822	+	0.428848i
$764$		−	7.03083i		−	0.254366i
$765$	−8.33596	+	6.10405i	−0.301387	+	0.220692i
$766$	6.48945	−	3.74669i	0.234473	−	0.135373i
$767$	20.5144	+	35.5320i	0.740733	+	1.28299i
$768$	−1.72951	+	0.0938734i	−0.0624081	+	0.00338737i
$769$		−	2.65444i		−	0.0957217i	−0.998854	−	0.0478609i	$-0.984760\pi$
$769$		−	2.65444i		−	0.0957217i	0.998854	−	0.0478609i	$-0.0152404\pi$
$770$	7.23266	+	31.9833i	0.260647	+	1.15260i
$771$	−21.0283	+	13.7117i	−0.757315	+	0.493816i
$772$	−7.54828	−	4.35800i	−0.271668	−	0.156848i
$773$	19.4199	−	11.2121i	0.698487	−	0.403272i	−0.108297	−	0.994119i	$-0.534540\pi$
$773$	19.4199	−	11.2121i	0.698487	−	0.403272i	0.806784	+	0.590847i	$0.201206\pi$
$774$	−0.713324	−	6.55171i	−0.0256399	−	0.235496i
$775$	−11.3455	+	19.6510i	−0.407543	+	0.705885i
$776$	12.1684			0.436819
$777$	−11.4665	+	3.03301i	−0.411358	+	0.108809i
$778$			11.5171i			0.412906i
$779$	−17.0107	−	9.82112i	−0.609471	−	0.351878i
$780$	−13.5865	+	26.7883i	−0.486473	+	0.959174i
$781$	0.687637	+	38.1278i	0.0246056	+	1.36432i
$782$	4.55694	+	2.63095i	0.162956	+	0.0940826i
$783$	39.6809	−	6.51256i	1.41808	−	0.232740i
$784$	6.42339	−	2.78211i	0.229407	−	0.0993609i
$785$			45.2150i			1.61379i
$786$	−27.3704	+	1.48560i	−0.976270	+	0.0529896i
$787$	−15.3260	+	8.84845i	−0.546312	+	0.315413i	−0.747633	−	0.664112i	$-0.768810\pi$
$787$	−15.3260	+	8.84845i	−0.546312	+	0.315413i	0.201321	+	0.979525i	$0.435476\pi$
$788$	0.278382	+	0.482171i	0.00991694	+	0.0171766i
$789$	25.0809	−	1.36133i	0.892902	−	0.0484646i
$790$	64.3342			2.28891
$791$	18.8964	+	6.24602i	0.671880	+	0.222083i
$792$	6.02217	+	7.92045i	0.213988	+	0.281441i
$793$	−17.4891	+	30.2920i	−0.621056	+	1.07570i
$794$	−10.4828	−	18.1567i	−0.372020	−	0.644357i
$795$	11.1581	−	22.0003i	0.395736	−	0.780270i
$796$	3.23869	−	5.60958i	0.114792	−	0.198826i
$797$		−	28.8638i		−	1.02241i	−0.859459	−	0.511205i	$-0.829199\pi$
$797$		−	28.8638i		−	1.02241i	0.859459	−	0.511205i	$-0.170801\pi$
$798$	21.1640	+	5.74377i	0.749198	+	0.203327i
$799$		−	5.27999i		−	0.186793i
$800$	−4.48211	+	7.76324i	−0.158467	+	0.274472i
$801$	2.79323	+	25.6551i	0.0986938	+	0.906479i
$802$	20.3964	−	11.7758i	0.720220	−	0.415819i
$803$	30.6975	−	18.4691i	1.08329	−	0.651762i
$804$	−0.738651	−	1.13279i	−0.0260502	−	0.0399505i
$805$	55.2736	−	11.4559i	1.94814	−	0.403767i
$806$		−	11.7469i		−	0.413768i
$807$	−0.722530	−	13.3118i	−0.0254343	−	0.468596i
$808$	−0.661912	−	1.14646i	−0.0232860	−	0.0403325i
$809$	4.95952	+	8.59014i	0.174367	+	0.302013i	0.939942	−	0.341334i	$-0.110879\pi$
$809$	4.95952	+	8.59014i	0.174367	+	0.302013i	−0.765575	+	0.643347i	$0.777545\pi$
$810$	7.23761	+	32.8439i	0.254304	+	1.15402i
$811$			47.8705i			1.68096i	0.541841	+	0.840481i	$0.317727\pi$
$811$			47.8705i			1.68096i	−0.541841	+	0.840481i	$0.682273\pi$
$812$	−20.0487	+	4.15526i	−0.703573	+	0.145821i
$813$	−4.80692	+	3.13441i	−0.168586	+	0.109928i
$814$	4.42547	+	7.35556i	0.155113	+	0.257812i
$815$	4.98649	−	2.87895i	0.174669	−	0.100845i
$816$	0.722045	−	1.42365i	0.0252766	−	0.0498377i
$817$	−5.25633	+	9.10424i	−0.183896	+	0.318517i
$818$			11.8764i			0.415248i
$819$	−11.3353	−	35.0469i	−0.396087	−	1.22464i
$820$			15.3384i			0.535639i
$821$	−14.3341	+	24.8274i	−0.500264	+	0.866482i	0.499736	+	0.866178i	$0.333430\pi$
$821$	−14.3341	+	24.8274i	−0.500264	+	0.866482i	−1.00000		0.000304753i	$0.999903\pi$
$822$	−19.9654	−	10.1260i	−0.696373	−	0.353186i
$823$	20.0175	+	34.6713i	0.697766	+	1.20857i	0.969239	+	0.246120i	$0.0791556\pi$
$823$	20.0175	+	34.6713i	0.697766	+	1.20857i	−0.271474	+	0.962446i	$0.587511\pi$
$824$	4.94954	−	8.57285i	0.172425	−	0.298649i
$825$	51.3612	−	3.71770i	1.78817	−	0.129434i
$826$	−22.2095	−	7.34113i	−0.772768	−	0.255431i
$827$	−5.40955			−0.188109			−0.0940543	−	0.995567i	$-0.529983\pi$
$827$	−5.40955			−0.188109			−0.0940543	+	0.995567i	$0.529983\pi$
$828$	13.8194	−	10.1194i	0.480259	−	0.351672i
$829$	4.25136	+	7.36358i	0.147656	+	0.255748i	0.930361	−	0.366646i	$-0.119494\pi$
$829$	4.25136	+	7.36358i	0.147656	+	0.255748i	−0.782705	+	0.622393i	$0.786160\pi$
$830$	−41.0301	+	23.6887i	−1.42418	+	0.822248i
$831$	−0.840994	−	15.4943i	−0.0291738	−	0.537492i
$832$		−	4.64070i		−	0.160887i
$833$	−0.739429	+	6.40879i	−0.0256197	+	0.222051i
$834$	11.7353	−	7.65216i	0.406361	−	0.264973i
$835$	−33.0765	−	19.0967i	−1.14466	−	0.660870i
$836$	−0.286196	−	15.8689i	−0.00989831	−	0.548837i
$837$	−8.33447	−	10.1753i	−0.288081	−	0.351710i
$838$	−18.6690	−	10.7785i	−0.644910	−	0.372339i
$839$			6.66926i			0.230248i	0.993351	+	0.115124i	$0.0367266\pi$
$839$			6.66926i			0.230248i	−0.993351	+	0.115124i	$0.963273\pi$
$840$	−4.37902	−	16.5551i	−0.151091	−	0.571207i
$841$	30.8883			1.06511
$842$	−6.08439	+	10.5385i	−0.209682	+	0.363180i
$843$	−17.9785	+	35.4480i	−0.619212	+	1.22089i
$844$	15.4275	−	8.90708i	0.531037	−	0.306594i
$845$	−27.6247	−	15.9491i	−0.950317	−	0.548666i
$846$	−15.7272	−	6.93206i	−0.540714	−	0.238329i
$847$	−8.13142	+	27.9442i	−0.279399	+	0.960175i
$848$			3.81124i			0.130879i
$849$	2.43536	+	44.8687i	0.0835815	+	1.53989i
$850$	−4.13078	−	7.15472i	−0.141685	−	0.245405i
$851$	12.7976	−	7.38871i	0.438697	−	0.253282i
$852$	−1.07934	−	19.8856i	−0.0369776	−	0.681268i
$853$		−	14.2558i		−	0.488109i	−0.969761	−	0.244055i	$-0.921522\pi$
$853$		−	14.2558i		−	0.488109i	0.969761	−	0.244055i	$-0.0784776\pi$
$854$	−4.04708	−	19.5268i	−0.138488	−	0.668192i
$855$	21.6375	−	49.0905i	0.739988	−	1.67886i
$856$	−5.61684	+	9.72865i	−0.191980	+	0.332518i
$857$	−18.2335	−	31.5813i	−0.622844	−	1.07880i	−0.988954	−	0.148225i	$-0.952644\pi$
$857$	−18.2335	−	31.5813i	−0.622844	−	1.07880i	0.366110	−	0.930572i	$-0.380689\pi$
$858$	−22.0646	+	14.9614i	−0.753274	+	0.510773i
$859$	−10.1170	+	17.5232i	−0.345189	+	0.597884i	−0.985388	−	0.170325i	$-0.945518\pi$
$859$	−10.1170	+	17.5232i	−0.345189	+	0.597884i	0.640199	+	0.768209i	$0.278852\pi$
$860$	8.20919			0.279931
$861$	−13.2576	−	13.3430i	−0.451819	−	0.454730i
$862$	−13.5244			−0.460644
$863$	6.55825	+	3.78641i	0.223245	+	0.128891i	0.607452	−	0.794356i	$-0.292192\pi$
$863$	6.55825	+	3.78641i	0.223245	+	0.128891i	−0.384207	+	0.923247i	$0.625525\pi$
$864$	−3.29258	−	4.01981i	−0.112016	−	0.136757i
$865$	−22.6381	+	13.0701i	−0.769719	+	0.444397i
$866$	17.1658	−	29.7321i	0.583318	−	1.01034i
$867$	−15.2793	−	23.4323i	−0.518912	−	0.795802i
$868$	4.45596	+	4.99964i	0.151245	+	0.169699i
$869$	49.9561	+	27.6533i	1.69464	+	0.938073i
$870$	2.71470	+	50.0151i	0.0920370	+	1.69567i
$871$	3.13790	−	1.81167i	0.106324	−	0.0613860i
$872$	−3.95986	+	2.28623i	−0.134098	+	0.0774215i
$873$	21.5672	+	29.4531i	0.729938	+	0.996835i
$874$	−27.3221			−0.924183
$875$	−37.2134	−	12.3005i	−1.25804	−	0.415833i
$876$	−15.6717	+	10.2189i	−0.529499	+	0.345266i
$877$	−33.6074	−	19.4033i	−1.13484	−	0.655202i	−0.189694	−	0.981843i	$-0.560750\pi$
$877$	−33.6074	−	19.4033i	−1.13484	−	0.655202i	−0.945148	+	0.326641i	$0.894083\pi$
$878$	2.95877	−	1.70824i	0.0998536	−	0.0576505i
$879$	4.36153	−	8.59960i	0.147111	−	0.290057i
$880$	−10.6199	+	6.38944i	−0.357995	+	0.215388i
$881$			38.0866i			1.28317i	0.767052	+	0.641584i	$0.221723\pi$
$881$			38.0866i			1.28317i	−0.767052	+	0.641584i	$0.778277\pi$
$882$	18.1187	+	10.6166i	0.610090	+	0.357478i
$883$	17.6201			0.592964			0.296482	−	0.955038i	$-0.404187\pi$
$883$	17.6201			0.592964			0.296482	+	0.955038i	$0.404187\pi$
$884$	3.70394	+	2.13847i	0.124577	+	0.0719245i
$885$	−25.8839	+	51.0350i	−0.870077	+	1.71552i
$886$	21.5391	−	12.4356i	0.723622	−	0.417783i
$887$	−13.6872	+	23.7070i	−0.459572	+	0.796002i	−0.998938	−	0.0460690i	$-0.985331\pi$
$887$	−13.6872	+	23.7070i	−0.459572	+	0.796002i	0.539366	+	0.842071i	$0.318664\pi$
$888$	−2.44861	−	3.75518i	−0.0821699	−	0.126015i
$889$	12.9339	+	4.27518i	0.433790	+	0.143385i
$890$	−32.1455			−1.07752
$891$	−8.49746	+	28.6146i	−0.284676	+	0.958624i
$892$	−4.55482	−	7.88917i	−0.152507	−	0.264149i
$893$	13.7080	+	23.7430i	0.458721	+	0.794528i
$894$	22.8317	−	1.23925i	0.763608	−	0.0414468i
$895$	−86.6027			−2.89481
$896$	1.76035	+	1.97514i	0.0588092	+	0.0659846i
$897$	25.0663	+	38.4416i	0.836939	+	1.28353i
$898$	10.6050	+	6.12283i	0.353895	+	0.204321i
$899$	−9.79450	−	16.9646i	−0.326665	−	0.565800i
$900$	−26.7347	+	2.91076i	−0.891156	+	0.0970255i
$901$	−3.04191	−	1.75625i	−0.101341	−	0.0585092i
$902$	−6.59301	+	11.9104i	−0.219523	+	0.396572i
$903$	−7.14129	+	7.09558i	−0.237647	+	0.236126i
$904$			7.52223i			0.250186i
$905$	−20.5223	−	11.8485i	−0.682184	−	0.393859i
$906$	−18.3957	−	9.32993i	−0.611157	−	0.309966i
$907$	−6.46073	−	11.1903i	−0.214525	−	0.371568i	0.738600	−	0.674143i	$-0.235487\pi$
$907$	−6.46073	−	11.1903i	−0.214525	−	0.371568i	−0.953126	+	0.302575i	$0.902154\pi$
$908$	−12.5369	+	21.7145i	−0.416050	+	0.720620i
$909$	1.60180	−	3.63412i	0.0531284	−	0.120536i
$910$	44.9270	−	9.31149i	1.48932	−	0.308673i
$911$		−	2.02350i		−	0.0670416i	−0.999438	−	0.0335208i	$-0.989328\pi$
$911$		−	2.02350i		−	0.0670416i	0.999438	−	0.0335208i	$-0.0106720\pi$
$912$	0.449224	+	8.27642i	0.0148753	+	0.274060i
$913$	−42.0426	+	0.758241i	−1.39141	+	0.0250941i
$914$	−26.7154	+	15.4241i	−0.883667	+	0.510185i
$915$	−48.7129	+	2.64402i	−1.61040	+	0.0874086i
$916$	−23.1049			−0.763408
$917$	27.8586	+	31.2576i	0.919972	+	1.03222i
$918$	4.72563	−	0.775587i	0.155969	−	0.0255982i
$919$	−23.8097	−	13.7465i	−0.785410	−	0.453457i	0.0529342	−	0.998598i	$-0.483143\pi$
$919$	−23.8097	−	13.7465i	−0.785410	−	0.453457i	−0.838344	+	0.545141i	$0.816476\pi$
$920$	10.6677	+	18.4770i	0.351704	+	0.609170i
$921$	−46.6616	−	23.6658i	−1.53755	−	0.779814i
$922$	1.70165	−	2.94734i	0.0560408	−	0.0970655i
$923$	53.3580			1.75630
$924$	3.71567	−	14.7375i	0.122237	−	0.484828i
$925$	−23.2016			−0.762864
$926$	−7.91328	+	13.7062i	−0.260046	+	0.450414i
$927$	29.5228	−	3.21432i	0.969655	−	0.105572i
$928$	−3.86938	−	6.70196i	−0.127018	−	0.220002i
$929$	−16.7462	−	9.66845i	−0.549426	−	0.317212i	0.199464	−	0.979905i	$-0.436080\pi$
$929$	−16.7462	−	9.66845i	−0.549426	−	0.317212i	−0.748891	+	0.662694i	$0.769413\pi$
$930$	13.7238	−	8.94877i	0.450022	−	0.293442i
$931$	−13.3136	−	30.7386i	−0.436334	−	1.00742i
$932$	−23.2786			−0.762517
$933$	0.0859678	+	1.58385i	0.00281446	+	0.0518530i
$934$	18.9467	−	10.9389i	0.619956	−	0.357932i
$935$	−0.205969	−	11.4205i	−0.00673590	−	0.373489i
$936$	11.2326	−	8.22514i	0.367150	−	0.268847i
$937$		−	6.07745i		−	0.198542i	−0.995060	−	0.0992708i	$-0.968349\pi$
$937$		−	6.07745i		−	0.198542i	0.995060	−	0.0992708i	$-0.0316510\pi$
$938$	−0.648309	+	1.96136i	−0.0211680	+	0.0640408i
$939$	−5.44156	−	8.34516i	−0.177579	−	0.272334i
$940$	10.7044	−	18.5406i	0.349139	−	0.604726i
$941$	−1.16233	−	2.01322i	−0.0378910	−	0.0656292i	0.846458	−	0.532456i	$-0.178731\pi$
$941$	−1.16233	−	2.01322i	−0.0378910	−	0.0656292i	−0.884349	+	0.466826i	$0.845397\pi$
$942$	9.47957	−	18.6908i	0.308861	−	0.608978i
$943$	20.2952	+	11.7175i	0.660904	+	0.381573i
$944$		−	8.84110i		−	0.287753i
$945$	32.3097	−	39.9415i	1.05103	−	1.29930i
$946$	6.37452	+	3.52862i	0.207253	+	0.114725i
$947$	−7.66708	−	4.42659i	−0.249147	−	0.143845i	0.370227	−	0.928941i	$-0.379280\pi$
$947$	−7.66708	−	4.42659i	−0.249147	−	0.143845i	−0.619374	+	0.785096i	$0.712613\pi$
$948$	−26.5942	−	13.4880i	−0.863739	−	0.438070i
$949$	−25.0637	−	43.4116i	−0.813603	−	1.40920i
$950$	37.1504	+	21.4488i	1.20532	+	0.695891i
$951$	−15.2346	+	9.93393i	−0.494017	+	0.322130i
$952$	−2.38762	+	0.494854i	−0.0773833	+	0.0160383i
$953$	−15.5373			−0.503303			−0.251651	−	0.967818i	$-0.580974\pi$
$953$	−15.5373			−0.503303			−0.251651	+	0.967818i	$0.580974\pi$
$954$	−9.22496	+	6.75503i	−0.298669	+	0.218702i
$955$	13.1367	+	22.7534i	0.425092	+	0.736281i
$956$	−1.47636	−	2.55714i	−0.0477490	−	0.0827038i
$957$	−19.3904	+	40.0041i	−0.626802	+	1.29315i
$958$	24.5435			0.792965
$959$	6.93988	+	33.4843i	0.224101	+	1.08126i
$960$	5.42167	−	3.53527i	0.174984	−	0.114100i
$961$	12.2963	−	21.2978i	0.396655	−	0.687026i
$962$	10.4021	−	6.00563i	0.335376	−	0.193629i
$963$	−33.5030	+	3.64768i	−1.07962	+	0.117545i
$964$	3.18416	+	1.83837i	0.102555	+	0.0592100i
$965$	32.5706			1.04848
$966$	−25.2505	−	6.85282i	−0.812423	−	0.220486i
$967$			50.7815i			1.63302i	0.577329	+	0.816512i	$0.304095\pi$
$967$			50.7815i			1.63302i	−0.577329	+	0.816512i	$0.695905\pi$
$968$	−10.9928	+	0.396643i	−0.353323	+	0.0127486i
$969$	−6.81276	−	3.45529i	−0.218857	−	0.111000i
$970$	−39.3796	+	22.7358i	−1.26440	+	0.730004i
$971$	−31.0032	−	17.8997i	−0.994941	−	0.574429i	−0.0881935	−	0.996103i	$-0.528109\pi$
$971$	−31.0032	−	17.8997i	−0.994941	−	0.574429i	−0.906748	+	0.421674i	$0.861443\pi$
$972$	3.89404	−	15.0943i	0.124901	−	0.484148i
$973$	−20.3190	−	6.71625i	−0.651399	−	0.215313i
$974$	−36.1783			−1.15923
$975$	−3.90516	−	71.9478i	−0.125065	−	2.30417i
$976$	6.52747	−	3.76863i	0.208939	−	0.120631i
$977$	−15.2247	+	8.79000i	−0.487082	+	0.281217i	−0.723363	−	0.690468i	$-0.757405\pi$
$977$	−15.2247	+	8.79000i	−0.487082	+	0.281217i	0.236281	+	0.971685i	$0.424071\pi$
$978$	−2.66488	+	0.144643i	−0.0852135	+	0.00462519i
$979$	−24.9613	−	13.8174i	−0.797766	−	0.441604i
$980$	−15.5893	+	21.0052i	−0.497983	+	0.670987i
$981$	−12.5522	−	5.53259i	−0.400760	−	0.176642i
$982$	19.8330	−	34.3518i	0.632896	−	1.09621i
$983$	31.5232	−	18.1999i	1.00543	−	0.580487i	0.0955818	−	0.995422i	$-0.469529\pi$
$983$	31.5232	−	18.1999i	1.00543	−	0.580487i	0.909851	+	0.414935i	$0.136196\pi$
$984$	3.21577	−	6.34050i	0.102515	−	0.202128i
$985$	−1.80181	−	1.04028i	−0.0574105	−	0.0331460i
$986$	7.13215			0.227134
$987$	6.71356	+	25.3810i	0.213695	+	0.807885i
$988$	−22.2077			−0.706522
$989$	6.27127	−	10.8622i	0.199415	−	0.345396i
$990$	−34.2880	−	14.3803i	−1.08974	−	0.457037i
$991$	4.46111	+	7.72687i	0.141712	+	0.245452i	0.928141	−	0.372228i	$-0.121406\pi$
$991$	4.46111	+	7.72687i	0.141712	+	0.245452i	−0.786429	+	0.617680i	$0.788073\pi$
$992$	−1.26564	+	2.19216i	−0.0401842	+	0.0696011i
$993$	−14.2695	−	21.8837i	−0.452830	−	0.694459i
$994$	−22.7098	+	20.2402i	−0.720310	+	0.641981i
$995$			24.2052i			0.767355i
$996$	21.9273	−	1.19016i	0.694793	−	0.0377117i
$997$	0.0417701	−	0.0241160i	0.00132287	−	0.000763761i	−0.499338	−	0.866407i	$-0.666424\pi$
$997$	0.0417701	−	0.0241160i	0.00132287	−	0.000763761i	0.500661	+	0.865643i	$0.333090\pi$
$998$	16.0605	+	27.8176i	0.508386	+	0.880550i
$999$	4.74935	−	12.5824i	0.150263	−	0.398090i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.n.f.65.9	yes	24
3.2	odd	2		462.2.n.e.65.1	✓	24
7.4	even	3	inner	462.2.n.f.263.1	yes	24
11.10	odd	2		462.2.n.e.65.9	yes	24
21.11	odd	6		462.2.n.e.263.9	yes	24
33.32	even	2	inner	462.2.n.f.65.1	yes	24
77.32	odd	6		462.2.n.e.263.1	yes	24
231.32	even	6	inner	462.2.n.f.263.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.n.e.65.1	✓	24	3.2	odd	2
462.2.n.e.65.9	yes	24	11.10	odd	2
462.2.n.e.263.1	yes	24	77.32	odd	6
462.2.n.e.263.9	yes	24	21.11	odd	6
462.2.n.f.65.1	yes	24	33.32	even	2	inner
462.2.n.f.65.9	yes	24	1.1	even	1	trivial
462.2.n.f.263.1	yes	24	7.4	even	3	inner
462.2.n.f.263.9	yes	24	231.32	even	6	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.783456 - 1.54473i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.23623 + 1.86844i) q^{5} +(-0.946049 - 1.45086i) q^{6} +(-0.830341 + 2.51208i) q^{7} -1.00000 q^{8} +(-1.77239 - 2.42046i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.783456 - 1.54473i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.23623 + 1.86844i) q^{5} +(-0.946049 - 1.45086i) q^{6} +(-0.830341 + 2.51208i) q^{7} -1.00000 q^{8} +(-1.77239 - 2.42046i) q^{9} +(3.23623 - 1.86844i) q^{10} +(3.31609 - 0.0598058i) q^{11} +(-1.72951 + 0.0938734i) q^{12} -4.64070i q^{13} +(1.76035 + 1.97514i) q^{14} +(5.42167 - 3.53527i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.460807 - 0.798142i) q^{17} +(-2.98238 + 0.324709i) q^{18} +(4.14430 + 2.39271i) q^{19} -3.73687i q^{20} +(3.22995 + 3.25076i) q^{21} +(1.60625 - 2.90172i) q^{22} +(-4.94452 - 2.85472i) q^{23} +(-0.783456 + 1.54473i) q^{24} +(4.48211 + 7.76324i) q^{25} +(-4.01896 - 2.32035i) q^{26} +(-5.12755 + 0.841552i) q^{27} +(2.59069 - 0.536942i) q^{28} -7.73875 q^{29} +(-0.350793 - 6.46294i) q^{30} +(1.26564 + 2.19216i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.50562 - 5.16932i) q^{33} -0.921615 q^{34} +(-7.38083 + 6.57821i) q^{35} +(-1.20998 + 2.74517i) q^{36} +(-1.29412 + 2.24149i) q^{37} +(4.14430 - 2.39271i) q^{38} +(-7.16863 - 3.63578i) q^{39} +(-3.23623 - 1.86844i) q^{40} -4.10460 q^{41} +(4.43021 - 1.17184i) q^{42} +2.19681i q^{43} +(-1.70984 - 2.84191i) q^{44} +(-1.21340 - 11.1448i) q^{45} +(-4.94452 + 2.85472i) q^{46} +(4.96151 + 2.86453i) q^{47} +(0.946049 + 1.45086i) q^{48} +(-5.62107 - 4.17176i) q^{49} +8.96422 q^{50} +(-1.59394 + 0.0865151i) q^{51} +(-4.01896 + 2.32035i) q^{52} +(3.30063 - 1.90562i) q^{53} +(-1.83497 + 4.86137i) q^{54} +(10.8433 + 6.00235i) q^{55} +(0.830341 - 2.51208i) q^{56} +(6.94298 - 4.52725i) q^{57} +(-3.86938 + 6.70196i) q^{58} +(-7.65662 + 4.42055i) q^{59} +(-5.77247 - 2.92767i) q^{60} +(-6.52747 - 3.76863i) q^{61} +2.53129 q^{62} +(7.55207 - 2.44259i) q^{63} +1.00000 q^{64} +(8.67085 - 15.0184i) q^{65} +(-3.22395 - 4.75459i) q^{66} +(0.390387 + 0.676170i) q^{67} +(-0.460807 + 0.798142i) q^{68} +(-8.28358 + 5.40141i) q^{69} +(2.00648 + 9.68109i) q^{70} +11.4978i q^{71} +(1.77239 + 2.42046i) q^{72} +(9.35455 - 5.40085i) q^{73} +(1.29412 + 2.24149i) q^{74} +(15.5037 - 0.841502i) q^{75} -4.78543i q^{76} +(-2.60325 + 8.37992i) q^{77} +(-6.73300 + 4.39033i) q^{78} +(14.9095 + 8.60802i) q^{79} +(-3.23623 + 1.86844i) q^{80} +(-2.71724 + 8.58001i) q^{81} +(-2.05230 + 3.55469i) q^{82} -12.6784 q^{83} +(1.20026 - 4.42260i) q^{84} -3.44396i q^{85} +(1.90249 + 1.09840i) q^{86} +(-6.06297 + 11.9543i) q^{87} +(-3.31609 + 0.0598058i) q^{88} +(-7.44976 - 4.30112i) q^{89} +(-10.2583 - 4.52155i) q^{90} +(11.6578 + 3.85336i) q^{91} +5.70943i q^{92} +(4.37787 - 0.237621i) q^{93} +(4.96151 - 2.86453i) q^{94} +(8.94127 + 15.4867i) q^{95} +(1.72951 - 0.0938734i) q^{96} -12.1684 q^{97} +(-6.42339 + 2.78211i) q^{98} +(-6.02217 - 7.92045i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9	\( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} - 8 q^{9} + 4 q^{11} + 4 q^{15} - 12 q^{16} - 4 q^{17} + 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} - 40 q^{29} + 2 q^{30} - 28 q^{31} + 12 q^{32} + 24 q^{33} - 8 q^{34} + 32 q^{35} + 16 q^{36} - 16 q^{37} + 8 q^{41} + 6 q^{42} + 4 q^{44} - 28 q^{45} - 8 q^{49} + 40 q^{50} + 34 q^{51} - 6 q^{54} + 8 q^{55} - 40 q^{57} - 20 q^{58} - 2 q^{60} - 56 q^{62} + 14 q^{63} + 24 q^{64} + 44 q^{65} - 24 q^{66} - 4 q^{68} - 20 q^{69} + 64 q^{70} + 8 q^{72} + 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} - 144 q^{83} + 6 q^{84} - 8 q^{87} - 4 q^{88} - 56 q^{90} - 32 q^{91} - 22 q^{93} + 44 q^{95} + 64 q^{97} + 8 q^{98} + 28 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 - 8 * q^9 + 4 * q^11 + 4 * q^15 - 12 * q^16 - 4 * q^17 + 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 - 40 * q^29 + 2 * q^30 - 28 * q^31 + 12 * q^32 + 24 * q^33 - 8 * q^34 + 32 * q^35 + 16 * q^36 - 16 * q^37 + 8 * q^41 + 6 * q^42 + 4 * q^44 - 28 * q^45 - 8 * q^49 + 40 * q^50 + 34 * q^51 - 6 * q^54 + 8 * q^55 - 40 * q^57 - 20 * q^58 - 2 * q^60 - 56 * q^62 + 14 * q^63 + 24 * q^64 + 44 * q^65 - 24 * q^66 - 4 * q^68 - 20 * q^69 + 64 * q^70 + 8 * q^72 + 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 - 144 * q^83 + 6 * q^84 - 8 * q^87 - 4 * q^88 - 56 * q^90 - 32 * q^91 - 22 * q^93 + 44 * q^95 + 64 * q^97 + 8 * q^98 + 28 * q^99

Introduction

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