LMFDB - Embedded newform 462.2.p.a.439.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(241,462)]

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([0, 1, 3]))

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

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

chi := DirichletCharacter("462.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.p (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 $ x^16 - 8x^15 + 74x^14 - 378x^13 + 1878x^12 - 6718x^11 + 22086x^10 - 56904x^9 + 130215x^8 - 239606x^7 + 378750x^6 - 477124x^5 + 493030x^4 - 386266x^3 + 223844x^2 - 82874*x + 13417
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.7
Root			$0.500000 + 0.921602i$ of defining polynomial
Character	$\chi$	$=$	462.439
Dual form			462.2.p.a.241.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.54813 + 0.893814i) q^{5} -1.00000 q^{6} +(0.165362 - 2.64058i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.54813 + 0.893814i) q^{5} -1.00000 q^{6} +(0.165362 - 2.64058i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.893814 + 1.54813i) q^{10} +(0.692408 + 3.24354i) q^{11} +(-0.866025 - 0.500000i) q^{12} +6.37742 q^{13} +(1.46350 - 2.20413i) q^{14} -1.78763 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.0530476 + 0.0918811i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.07581 + 3.59541i) q^{19} +1.78763i q^{20} +(1.17708 + 2.36949i) q^{21} +(-1.02213 + 3.15519i) q^{22} +(-3.97933 + 6.89240i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.902194 - 1.56265i) q^{25} +(5.52301 + 3.18871i) q^{26} +1.00000i q^{27} +(2.36949 - 1.17708i) q^{28} -7.65230i q^{29} +(-1.54813 - 0.893814i) q^{30} +(1.10740 - 0.639360i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.22141 - 2.46279i) q^{33} +0.106095i q^{34} +(2.61619 - 3.94016i) q^{35} +1.00000 q^{36} +(-2.26092 + 3.91603i) q^{37} +(-3.59541 + 2.07581i) q^{38} +(-5.52301 + 3.18871i) q^{39} +(-0.893814 + 1.54813i) q^{40} +0.0321383 q^{41} +(-0.165362 + 2.64058i) q^{42} -6.87723i q^{43} +(-2.46279 + 2.22141i) q^{44} +(1.54813 - 0.893814i) q^{45} +(-6.89240 + 3.97933i) q^{46} +(8.55805 + 4.94099i) q^{47} -1.00000i q^{48} +(-6.94531 - 0.873304i) q^{49} -1.80439i q^{50} +(-0.0918811 - 0.0530476i) q^{51} +(3.18871 + 5.52301i) q^{52} +(0.313720 + 0.543380i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.82718 + 5.64031i) q^{55} +(2.64058 + 0.165362i) q^{56} -4.15162i q^{57} +(3.82615 - 6.62708i) q^{58} +(10.7863 - 6.22747i) q^{59} +(-0.893814 - 1.54813i) q^{60} +(4.97512 - 8.61716i) q^{61} +1.27872 q^{62} +(-2.20413 - 1.46350i) q^{63} -1.00000 q^{64} +(9.87308 + 5.70022i) q^{65} +(-0.692408 - 3.24354i) q^{66} +(-5.43609 - 9.41558i) q^{67} +(-0.0530476 + 0.0918811i) q^{68} -7.95866i q^{69} +(4.23576 - 2.10418i) q^{70} -8.42785 q^{71} +(0.866025 + 0.500000i) q^{72} +(0.0625042 + 0.108260i) q^{73} +(-3.91603 + 2.26092i) q^{74} +(1.56265 + 0.902194i) q^{75} -4.15162 q^{76} +(8.67933 - 1.29200i) q^{77} -6.37742 q^{78} +(-8.80673 - 5.08457i) q^{79} +(-1.54813 + 0.893814i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.0278326 + 0.0160691i) q^{82} -12.0657 q^{83} +(-1.46350 + 2.20413i) q^{84} +0.189659i q^{85} +(3.43862 - 5.95586i) q^{86} +(3.82615 + 6.62708i) q^{87} +(-3.24354 + 0.692408i) q^{88} +(-4.64198 - 2.68005i) q^{89} +1.78763 q^{90} +(1.05458 - 16.8401i) q^{91} -7.95866 q^{92} +(-0.639360 + 1.10740i) q^{93} +(4.94099 + 8.55805i) q^{94} +(-6.42726 + 3.71078i) q^{95} +(0.500000 - 0.866025i) q^{96} -15.7498i q^{97} +(-5.57816 - 4.22896i) q^{98} +(3.15519 + 1.02213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9	$ 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9} + 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 10 q^{19} - 4 q^{21} + 2 q^{22} - 4 q^{23} - 8 q^{24} + 10 q^{25} + 12 q^{26} - 12 q^{30} + 6 q^{31} + 2 q^{33} - 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} - 12 q^{39} - 2 q^{40} + 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} + 18 q^{46} - 24 q^{47} - 6 q^{49} + 6 q^{51} - 8 q^{54} - 14 q^{55} + 4 q^{56} - 2 q^{60} + 28 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 72 q^{65} + 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} - 44 q^{73} + 24 q^{74} - 12 q^{75} - 20 q^{76} + 32 q^{77} - 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} + 8 q^{83} - 8 q^{84} - 12 q^{86} + 4 q^{88} - 36 q^{89} + 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} + 14 q^{94} + 72 q^{95} + 8 q^{96} - 40 q^{98} - 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9 + 2 * q^10 - 4 * q^11 + 8 * q^14 - 4 * q^15 - 8 * q^16 - 10 * q^19 - 4 * q^21 + 2 * q^22 - 4 * q^23 - 8 * q^24 + 10 * q^25 + 12 * q^26 - 12 * q^30 + 6 * q^31 + 2 * q^33 - 8 * q^35 + 16 * q^36 + 14 * q^37 - 12 * q^38 - 12 * q^39 - 2 * q^40 + 32 * q^41 + 6 * q^42 + 4 * q^44 + 12 * q^45 + 18 * q^46 - 24 * q^47 - 6 * q^49 + 6 * q^51 - 8 * q^54 - 14 * q^55 + 4 * q^56 - 2 * q^60 + 28 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 72 * q^65 + 4 * q^66 - 16 * q^67 - 30 * q^70 - 56 * q^71 - 44 * q^73 + 24 * q^74 - 12 * q^75 - 20 * q^76 + 32 * q^77 - 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 + 8 * q^83 - 8 * q^84 - 12 * q^86 + 4 * q^88 - 36 * q^89 + 4 * q^90 - 8 * q^91 - 8 * q^92 + 4 * q^93 + 14 * q^94 + 72 * q^95 + 8 * q^96 - 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.54813	+	0.893814i	0.692345	+	0.399726i	0.804490	−	0.593966i	$-0.202439\pi$
$5$	1.54813	+	0.893814i	0.692345	+	0.399726i	−0.112145	+	0.993692i	$0.535772\pi$
$6$	−1.00000			−0.408248
$7$	0.165362	−	2.64058i	0.0625011	−	0.998045i
$7$	0.165362	−	2.64058i	0.0625011	−	0.998045i
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	0.893814	+	1.54813i	0.282649	+	0.489562i
$11$	0.692408	+	3.24354i	0.208769	+	0.977965i
$11$	0.692408	+	3.24354i	0.208769	+	0.977965i
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$	6.37742			1.76878			0.884389	−	0.466751i	$-0.154576\pi$
$13$	6.37742			1.76878			0.884389	+	0.466751i	$0.154576\pi$
$14$	1.46350	−	2.20413i	0.391136	−	0.589078i
$15$	−1.78763			−0.461563
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.0530476	+	0.0918811i	0.0128659	+	0.0222844i	0.872387	−	0.488816i	$-0.162571\pi$
$17$	0.0530476	+	0.0918811i	0.0128659	+	0.0222844i	−0.859521	+	0.511101i	$0.829238\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−2.07581	+	3.59541i	−0.476224	+	0.824844i	−0.999629	−	0.0272400i	$-0.991328\pi$
$19$	−2.07581	+	3.59541i	−0.476224	+	0.824844i	0.523405	+	0.852084i	$0.324661\pi$
$20$			1.78763i			0.399726i
$21$	1.17708	+	2.36949i	0.256860	+	0.517065i
$22$	−1.02213	+	3.15519i	−0.217919	+	0.672690i
$23$	−3.97933	+	6.89240i	−0.829748	+	1.43717i	0.0684879	+	0.997652i	$0.478183\pi$
$23$	−3.97933	+	6.89240i	−0.829748	+	1.43717i	−0.898236	+	0.439514i	$0.855151\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.902194	−	1.56265i	−0.180439	−	0.312529i
$26$	5.52301	+	3.18871i	1.08315	+	0.625357i
$27$			1.00000i			0.192450i
$28$	2.36949	−	1.17708i	0.447791	−	0.222447i
$29$		−	7.65230i		−	1.42100i	−0.703699	−	0.710498i	$-0.748470\pi$
$29$		−	7.65230i		−	1.42100i	0.703699	−	0.710498i	$-0.251530\pi$
$30$	−1.54813	−	0.893814i	−0.282649	−	0.163187i
$31$	1.10740	−	0.639360i	0.198896	−	0.114833i	−0.397245	−	0.917713i	$-0.630034\pi$
$31$	1.10740	−	0.639360i	0.198896	−	0.114833i	0.596140	+	0.802880i	$0.296700\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−2.22141	−	2.46279i	−0.386699	−	0.428716i
$34$			0.106095i			0.0181952i
$35$	2.61619	−	3.94016i	0.442216	−	0.666008i
$36$	1.00000			0.166667
$37$	−2.26092	+	3.91603i	−0.371693	+	0.643792i	−0.989826	−	0.142282i	$-0.954556\pi$
$37$	−2.26092	+	3.91603i	−0.371693	+	0.643792i	0.618133	+	0.786074i	$0.287889\pi$
$38$	−3.59541	+	2.07581i	−0.583253	+	0.336741i
$39$	−5.52301	+	3.18871i	−0.884389	+	0.510602i
$40$	−0.893814	+	1.54813i	−0.141324	+	0.244781i
$41$	0.0321383			0.00501915			0.00250958	−	0.999997i	$-0.499201\pi$
$41$	0.0321383			0.00501915			0.00250958	+	0.999997i	$0.499201\pi$
$42$	−0.165362	+	2.64058i	−0.0255160	+	0.407450i
$43$		−	6.87723i		−	1.04877i	−0.851482	−	0.524384i	$-0.824296\pi$
$43$		−	6.87723i		−	1.04877i	0.851482	−	0.524384i	$-0.175704\pi$
$44$	−2.46279	+	2.22141i	−0.371279	+	0.334891i
$45$	1.54813	−	0.893814i	0.230782	−	0.133242i
$46$	−6.89240	+	3.97933i	−1.01623	+	0.586720i
$47$	8.55805	+	4.94099i	1.24832	+	0.720718i	0.970774	−	0.239995i	$-0.0771458\pi$
$47$	8.55805	+	4.94099i	1.24832	+	0.720718i	0.277545	+	0.960713i	$0.410479\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−6.94531	−	0.873304i	−0.992187	−	0.124758i
$50$		−	1.80439i		−	0.255179i
$51$	−0.0918811	−	0.0530476i	−0.0128659	−	0.00742815i
$52$	3.18871	+	5.52301i	0.442194	+	0.765903i
$53$	0.313720	+	0.543380i	0.0430928	+	0.0746389i	0.886767	−	0.462216i	$-0.152946\pi$
$53$	0.313720	+	0.543380i	0.0430928	+	0.0746389i	−0.843675	+	0.536855i	$0.819612\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−1.82718	+	5.64031i	−0.246378	+	0.760539i
$56$	2.64058	+	0.165362i	0.352862	+	0.0220975i
$57$		−	4.15162i		−	0.549896i
$58$	3.82615	−	6.62708i	0.502398	−	0.870179i
$59$	10.7863	−	6.22747i	1.40426	−	0.810748i	0.409431	−	0.912341i	$-0.365727\pi$
$59$	10.7863	−	6.22747i	1.40426	−	0.810748i	0.994826	+	0.101593i	$0.0323940\pi$
$60$	−0.893814	−	1.54813i	−0.115391	−	0.199863i
$61$	4.97512	−	8.61716i	0.636999	−	1.10331i	−0.349089	−	0.937089i	$-0.613509\pi$
$61$	4.97512	−	8.61716i	0.636999	−	1.10331i	0.986088	−	0.166224i	$-0.0531576\pi$
$62$	1.27872			0.162398
$63$	−2.20413	−	1.46350i	−0.277694	−	0.184383i
$64$	−1.00000			−0.125000
$65$	9.87308	+	5.70022i	1.22460	+	0.707026i
$66$	−0.692408	−	3.24354i	−0.0852295	−	0.399253i
$67$	−5.43609	−	9.41558i	−0.664124	−	1.15030i	−0.979522	−	0.201337i	$-0.935471\pi$
$67$	−5.43609	−	9.41558i	−0.664124	−	1.15030i	0.315398	−	0.948959i	$-0.397862\pi$
$68$	−0.0530476	+	0.0918811i	−0.00643296	+	0.0111422i
$69$		−	7.95866i		−	0.958110i
$70$	4.23576	−	2.10418i	0.506271	−	0.251498i
$71$	−8.42785			−1.00020			−0.500101	−	0.865967i	$-0.666704\pi$
$71$	−8.42785			−1.00020			−0.500101	+	0.865967i	$0.666704\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	0.0625042	+	0.108260i	0.00731556	+	0.0126709i	0.869660	−	0.493651i	$-0.164338\pi$
$73$	0.0625042	+	0.108260i	0.00731556	+	0.0126709i	−0.862344	+	0.506322i	$0.831005\pi$
$74$	−3.91603	+	2.26092i	−0.455229	+	0.262827i
$75$	1.56265	+	0.902194i	0.180439	+	0.104176i
$76$	−4.15162			−0.476224
$77$	8.67933	−	1.29200i	0.989101	−	0.147237i
$78$	−6.37742			−0.722100
$79$	−8.80673	−	5.08457i	−0.990835	−	0.572059i	−0.0853112	−	0.996354i	$-0.527188\pi$
$79$	−8.80673	−	5.08457i	−0.990835	−	0.572059i	−0.905524	+	0.424295i	$0.860522\pi$
$80$	−1.54813	+	0.893814i	−0.173086	+	0.0999314i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.0278326	+	0.0160691i	0.00307359	+	0.00177454i
$83$	−12.0657			−1.32438			−0.662191	−	0.749335i	$-0.730373\pi$
$83$	−12.0657			−1.32438			−0.662191	+	0.749335i	$0.730373\pi$
$84$	−1.46350	+	2.20413i	−0.159681	+	0.240490i
$85$			0.189659i			0.0205714i
$86$	3.43862	−	5.95586i	0.370795	−	0.642237i
$87$	3.82615	+	6.62708i	0.410206	+	0.710498i
$88$	−3.24354	+	0.692408i	−0.345763	+	0.0738109i
$89$	−4.64198	−	2.68005i	−0.492049	−	0.284084i	0.233375	−	0.972387i	$-0.425023\pi$
$89$	−4.64198	−	2.68005i	−0.492049	−	0.284084i	−0.725424	+	0.688302i	$0.758356\pi$
$90$	1.78763			0.188432
$91$	1.05458	−	16.8401i	0.110550	−	1.76532i
$92$	−7.95866			−0.829748
$93$	−0.639360	+	1.10740i	−0.0662986	+	0.114833i
$94$	4.94099	+	8.55805i	0.509624	+	0.882695i
$95$	−6.42726	+	3.71078i	−0.659423	+	0.380718i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$		−	15.7498i		−	1.59915i	−0.600569	−	0.799573i	$-0.705059\pi$
$97$		−	15.7498i		−	1.59915i	0.600569	−	0.799573i	$-0.294941\pi$
$98$	−5.57816	−	4.22896i	−0.563480	−	0.427189i
$99$	3.15519	+	1.02213i	0.317109	+	0.102728i
$100$	0.902194	−	1.56265i	0.0902194	−	0.156265i
$101$	3.78650	+	6.55841i	0.376771	+	0.652586i	0.990590	−	0.136860i	$-0.0437012\pi$
$101$	3.78650	+	6.55841i	0.376771	+	0.652586i	−0.613820	+	0.789446i	$0.710368\pi$
$102$	−0.0530476	−	0.0918811i	−0.00525249	−	0.00909758i
$103$	−4.53550	−	2.61857i	−0.446896	−	0.258016i	0.259622	−	0.965710i	$-0.416402\pi$
$103$	−4.53550	−	2.61857i	−0.446896	−	0.258016i	−0.706519	+	0.707695i	$0.749735\pi$
$104$			6.37742i			0.625357i
$105$	−0.295606	+	4.72037i	−0.0288482	+	0.460661i
$106$			0.627441i			0.0609424i
$107$	−4.12912	−	2.38395i	−0.399177	−	0.230465i	0.286952	−	0.957945i	$-0.407358\pi$
$107$	−4.12912	−	2.38395i	−0.399177	−	0.230465i	−0.686129	+	0.727480i	$0.740691\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−7.36585	+	4.25268i	−0.705521	+	0.407332i	−0.809400	−	0.587257i	$-0.800208\pi$
$109$	−7.36585	+	4.25268i	−0.705521	+	0.407332i	0.103880	+	0.994590i	$0.466874\pi$
$110$	−4.40254	+	3.97106i	−0.419766	+	0.378626i
$111$		−	4.52184i		−	0.429194i
$112$	2.20413	+	1.46350i	0.208270	+	0.138287i
$113$	10.3003			0.968969			0.484484	−	0.874800i	$-0.339007\pi$
$113$	10.3003			0.968969			0.484484	+	0.874800i	$0.339007\pi$
$114$	2.07581	−	3.59541i	0.194418	−	0.336741i
$115$	−12.3210	+	7.11356i	−1.14894	+	0.663343i
$116$	6.62708	−	3.82615i	0.615309	−	0.355249i
$117$	3.18871	−	5.52301i	0.294796	−	0.510602i
$118$	12.4549			1.14657
$119$	0.251391	−	0.124883i	0.0230450	−	0.0114480i
$120$		−	1.78763i		−	0.163187i
$121$	−10.0411	+	4.49171i	−0.912831	+	0.408337i
$122$	8.61716	−	4.97512i	0.780161	−	0.450426i
$123$	−0.0278326	+	0.0160691i	−0.00250958	+	0.00144891i
$124$	1.10740	+	0.639360i	0.0994479	+	0.0574163i
$125$		−	12.1637i		−	1.08796i
$126$	−1.17708	−	2.36949i	−0.104863	−	0.211091i
$127$			3.18422i			0.282553i	0.989970	+	0.141277i	$0.0451207\pi$
$127$			3.18422i			0.282553i	−0.989970	+	0.141277i	$0.954879\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	3.43862	+	5.95586i	0.302753	+	0.524384i
$130$	5.70022	+	9.87308i	0.499943	+	0.865926i
$131$	0.543099	−	0.940675i	0.0474508	−	0.0821872i	−0.841324	−	0.540530i	$-0.818224\pi$
$131$	0.543099	−	0.940675i	0.0474508	−	0.0821872i	0.888775	+	0.458343i	$0.151557\pi$
$132$	1.02213	−	3.15519i	0.0889649	−	0.274624i
$133$	9.15071	+	6.07589i	0.793467	+	0.526846i
$134$		−	10.8722i		−	0.939213i
$135$	−0.893814	+	1.54813i	−0.0769272	+	0.133242i
$136$	−0.0918811	+	0.0530476i	−0.00787874	+	0.00454879i
$137$	3.79098	+	6.56617i	0.323885	+	0.560986i	0.981286	−	0.192555i	$-0.0616774\pi$
$137$	3.79098	+	6.56617i	0.323885	+	0.560986i	−0.657401	+	0.753541i	$0.728344\pi$
$138$	3.97933	−	6.89240i	0.338743	−	0.586720i
$139$	−1.34643			−0.114203			−0.0571013	−	0.998368i	$-0.518186\pi$
$139$	−1.34643			−0.114203			−0.0571013	+	0.998368i	$0.518186\pi$
$140$	4.72037	+	0.295606i	0.398944	+	0.0249833i
$141$	−9.88198			−0.832213
$142$	−7.29873	−	4.21392i	−0.612496	−	0.353625i
$143$	4.41578	+	20.6854i	0.369266	+	1.72980i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	6.83973	−	11.8468i	0.568008	−	0.983819i
$146$			0.125008i			0.0103458i
$147$	6.45147	−	2.71635i	0.532108	−	0.224041i
$148$	−4.52184			−0.371693
$149$	0.424489	+	0.245079i	0.0347755	+	0.0200776i	0.517287	−	0.855812i	$-0.326942\pi$
$149$	0.424489	+	0.245079i	0.0347755	+	0.0200776i	−0.482511	+	0.875890i	$0.660275\pi$
$150$	0.902194	+	1.56265i	0.0736639	+	0.127590i
$151$	−2.92130	+	1.68661i	−0.237732	+	0.137255i	−0.614134	−	0.789202i	$-0.710495\pi$
$151$	−2.92130	+	1.68661i	−0.237732	+	0.137255i	0.376402	+	0.926456i	$0.377161\pi$
$152$	−3.59541	−	2.07581i	−0.291626	−	0.168371i
$153$	0.106095			0.00857728
$154$	8.16252	+	3.22076i	0.657754	+	0.259536i
$155$	2.28588			0.183606
$156$	−5.52301	−	3.18871i	−0.442194	−	0.255301i
$157$	3.51865	−	2.03150i	0.280819	−	0.162131i	−0.352975	−	0.935633i	$-0.614830\pi$
$157$	3.51865	−	2.03150i	0.280819	−	0.162131i	0.633794	+	0.773502i	$0.281497\pi$
$158$	−5.08457	−	8.80673i	−0.404507	−	0.700626i
$159$	−0.543380	−	0.313720i	−0.0430928	−	0.0248796i
$160$	−1.78763			−0.141324
$161$	17.5419	+	11.6475i	1.38250	+	0.917950i
$162$		−	1.00000i		−	0.0785674i
$163$	−10.3707	+	17.9626i	−0.812297	+	1.40694i	0.0989554	+	0.995092i	$0.468450\pi$
$163$	−10.3707	+	17.9626i	−0.812297	+	1.40694i	−0.911253	+	0.411848i	$0.864883\pi$
$164$	0.0160691	+	0.0278326i	0.00125479	+	0.00217336i
$165$	−1.23777	−	5.79825i	−0.0963601	−	0.451393i
$166$	−10.4492	−	6.03285i	−0.811015	−	0.468240i
$167$	−3.42870			−0.265321			−0.132660	−	0.991162i	$-0.542352\pi$
$167$	−3.42870			−0.265321			−0.132660	+	0.991162i	$0.542352\pi$
$168$	−2.36949	+	1.17708i	−0.182810	+	0.0908138i
$169$	27.6715			2.12857
$170$	−0.0948293	+	0.164249i	−0.00727307	+	0.0125973i
$171$	2.07581	+	3.59541i	0.158741	+	0.274948i
$172$	5.95586	−	3.43862i	0.454130	−	0.262192i
$173$	−10.5762	+	18.3185i	−0.804094	+	1.39273i	0.112807	+	0.993617i	$0.464016\pi$
$173$	−10.5762	+	18.3185i	−0.804094	+	1.39273i	−0.916901	+	0.399115i	$0.869317\pi$
$174$			7.65230i			0.580119i
$175$	−4.27548	+	2.12391i	−0.323196	+	0.160553i
$176$	−3.15519	−	1.02213i	−0.237832	−	0.0770458i
$177$	−6.22747	+	10.7863i	−0.468086	+	0.810748i
$178$	−2.68005	−	4.64198i	−0.200878	−	0.347931i
$179$	7.04330	+	12.1994i	0.526441	+	0.911822i	0.999525	+	0.0308052i	$0.00980716\pi$
$179$	7.04330	+	12.1994i	0.526441	+	0.911822i	−0.473085	+	0.881017i	$0.656860\pi$
$180$	1.54813	+	0.893814i	0.115391	+	0.0666209i
$181$			12.4579i			0.925992i	0.886360	+	0.462996i	$0.153225\pi$
$181$			12.4579i			0.925992i	−0.886360	+	0.462996i	$0.846775\pi$
$182$	9.33333	−	14.0566i	0.691833	−	1.04195i
$183$			9.95024i			0.735543i
$184$	−6.89240	−	3.97933i	−0.508115	−	0.293360i
$185$	−7.00040	+	4.04169i	−0.514680	+	0.297151i
$186$	−1.10740	+	0.639360i	−0.0811988	+	0.0468802i
$187$	−0.261290	+	0.235681i	−0.0191074	+	0.0172347i
$188$			9.88198i			0.720718i
$189$	2.64058	+	0.165362i	0.192074	+	0.0120283i
$190$	−7.42156			−0.538416
$191$	13.6147	−	23.5813i	0.985122	−	1.70628i	0.343731	−	0.939068i	$-0.388309\pi$
$191$	13.6147	−	23.5813i	0.985122	−	1.70628i	0.641391	−	0.767214i	$-0.278358\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−23.0692	+	13.3190i	−1.66056	+	0.958724i	−0.688111	+	0.725605i	$0.741560\pi$
$193$	−23.0692	+	13.3190i	−1.66056	+	0.958724i	−0.972448	+	0.233119i	$0.925107\pi$
$194$	7.87488	−	13.6397i	0.565384	−	0.979273i
$195$	−11.4004			−0.816403
$196$	−2.71635	−	6.45147i	−0.194025	−	0.460819i
$197$		−	11.7764i		−	0.839031i	−0.907748	−	0.419515i	$-0.862200\pi$
$197$		−	11.7764i		−	0.839031i	0.907748	−	0.419515i	$-0.137800\pi$
$198$	2.22141	+	2.46279i	0.157869	+	0.175023i
$199$	18.5336	−	10.7004i	1.31381	−	0.758531i	0.331089	−	0.943600i	$-0.392584\pi$
$199$	18.5336	−	10.7004i	1.31381	−	0.758531i	0.982726	+	0.185069i	$0.0592508\pi$
$200$	1.56265	−	0.902194i	0.110496	−	0.0637948i
$201$	9.41558	+	5.43609i	0.664124	+	0.383432i
$202$			7.57300i			0.532834i
$203$	−20.2065	−	1.26540i	−1.41822	−	0.0888137i
$204$		−	0.106095i		−	0.00742815i
$205$	0.0497542	+	0.0287256i	0.00347499	+	0.00200628i
$206$	−2.61857	−	4.53550i	−0.182445	−	0.316004i
$207$	3.97933	+	6.89240i	0.276583	+	0.479055i
$208$	−3.18871	+	5.52301i	−0.221097	+	0.382952i
$209$	−13.0992	−	4.24349i	−0.906089	−	0.293529i
$210$	−2.61619	+	3.94016i	−0.180534	+	0.271897i
$211$		−	25.2654i		−	1.73934i	−0.493630	−	0.869672i	$-0.664330\pi$
$211$		−	25.2654i		−	1.73934i	0.493630	−	0.869672i	$-0.335670\pi$
$212$	−0.313720	+	0.543380i	−0.0215464	+	0.0373195i
$213$	7.29873	−	4.21392i	0.500101	−	0.288733i
$214$	−2.38395	−	4.12912i	−0.162963	−	0.282261i
$215$	6.14696	−	10.6469i	0.419219	−	0.726109i
$216$	−1.00000			−0.0680414
$217$	−1.50516	−	3.02992i	−0.102177	−	0.205684i
$218$	−8.50535			−0.576055
$219$	−0.108260	−	0.0625042i	−0.00731556	−	0.00422364i
$220$	−5.79825	+	1.23777i	−0.390918	+	0.0834503i
$221$	0.338307	+	0.585964i	0.0227570	+	0.0394162i
$222$	2.26092	−	3.91603i	0.151743	−	0.262827i
$223$			9.80133i			0.656346i	0.944618	+	0.328173i	$0.106433\pi$
$223$			9.80133i			0.656346i	−0.944618	+	0.328173i	$0.893567\pi$
$224$	1.17708	+	2.36949i	0.0786471	+	0.158318i
$225$	−1.80439			−0.120293
$226$	8.92030	+	5.15014i	0.593370	+	0.342582i
$227$	−11.6454	−	20.1704i	−0.772931	−	1.33875i	−0.935950	−	0.352132i	$-0.885457\pi$
$227$	−11.6454	−	20.1704i	−0.772931	−	1.33875i	0.163020	−	0.986623i	$-0.447877\pi$
$228$	3.59541	−	2.07581i	0.238112	−	0.137474i
$229$	−5.65569	−	3.26531i	−0.373739	−	0.215778i	0.301352	−	0.953513i	$-0.402562\pi$
$229$	−5.65569	−	3.26531i	−0.373739	−	0.215778i	−0.675090	+	0.737735i	$0.735895\pi$
$230$	−14.2271			−0.938109
$231$	−6.87052	+	5.45857i	−0.452047	+	0.359147i
$232$	7.65230			0.502398
$233$	9.41166	+	5.43383i	0.616579	+	0.355982i	0.775536	−	0.631304i	$-0.217480\pi$
$233$	9.41166	+	5.43383i	0.616579	+	0.355982i	−0.158957	+	0.987285i	$0.550813\pi$
$234$	5.52301	−	3.18871i	0.361050	−	0.208452i
$235$	8.83265	+	15.2986i	0.576179	+	0.997971i
$236$	10.7863	+	6.22747i	0.702128	+	0.405374i
$237$	10.1691			0.660557
$238$	0.280153	+	0.0175441i	0.0181596	+	0.00113722i
$239$			7.69148i			0.497521i	0.968565	+	0.248760i	$0.0800231\pi$
$239$			7.69148i			0.497521i	−0.968565	+	0.248760i	$0.919977\pi$
$240$	0.893814	−	1.54813i	0.0576954	−	0.0999314i
$241$	11.4067	+	19.7571i	0.734773	+	1.27266i	0.954823	+	0.297176i	$0.0960447\pi$
$241$	11.4067	+	19.7571i	0.734773	+	1.27266i	−0.220050	+	0.975489i	$0.570622\pi$
$242$	−10.9417	−	1.13064i	−0.703362	−	0.0726801i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	9.95024			0.636999
$245$	−9.97168	−	7.55980i	−0.637067	−	0.482978i
$246$	−0.0321383			−0.00204906
$247$	−13.2383	+	22.9294i	−0.842334	+	1.45897i
$248$	0.639360	+	1.10740i	0.0405994	+	0.0703203i
$249$	10.4492	−	6.03285i	0.662191	−	0.382316i
$250$	6.08186	−	10.5341i	0.384650	−	0.666234i
$251$			18.1111i			1.14317i	0.820544	+	0.571583i	$0.193670\pi$
$251$			18.1111i			1.14317i	−0.820544	+	0.571583i	$0.806330\pi$
$252$	0.165362	−	2.64058i	0.0104168	−	0.166341i
$253$	−25.1111	−	8.13478i	−1.57872	−	0.511429i
$254$	−1.59211	+	2.75761i	−0.0998977	+	0.173028i
$255$	−0.0948293	−	0.164249i	−0.00593844	−	0.0102857i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.41428	−	1.97123i	−0.212977	−	0.122962i	0.389717	−	0.920935i	$-0.372573\pi$
$257$	−3.41428	−	1.97123i	−0.212977	−	0.122962i	−0.602694	+	0.797972i	$0.705906\pi$
$258$			6.87723i			0.428158i
$259$	9.96672	+	6.61771i	0.619302	+	0.411204i
$260$			11.4004i			0.707026i
$261$	−6.62708	−	3.82615i	−0.410206	−	0.236833i
$262$	0.940675	−	0.543099i	0.0581151	−	0.0335528i
$263$	−1.79020	+	1.03357i	−0.110389	+	0.0637329i	−0.554178	−	0.832398i	$-0.686967\pi$
$263$	−1.79020	+	1.03357i	−0.110389	+	0.0637329i	0.443789	+	0.896131i	$0.353634\pi$
$264$	2.46279	−	2.22141i	0.151574	−	0.136719i
$265$			1.12163i			0.0689012i
$266$	4.88680	+	9.83723i	0.299629	+	0.603159i
$267$	5.36009			0.328032
$268$	5.43609	−	9.41558i	0.332062	−	0.575148i
$269$	2.42902	−	1.40240i	0.148100	−	0.0855057i	−0.424119	−	0.905607i	$-0.639416\pi$
$269$	2.42902	−	1.40240i	0.148100	−	0.0855057i	0.572219	+	0.820101i	$0.306083\pi$
$270$	−1.54813	+	0.893814i	−0.0942162	+	0.0543958i
$271$	4.64046	−	8.03751i	0.281888	−	0.488244i	−0.689962	−	0.723846i	$-0.742373\pi$
$271$	4.64046	−	8.03751i	0.281888	−	0.488244i	0.971850	+	0.235602i	$0.0757061\pi$
$272$	−0.106095			−0.00643296
$273$	7.50674	+	15.1112i	0.454329	+	0.914573i
$274$			7.58196i			0.458043i
$275$	4.44383	−	4.00830i	0.267973	−	0.241709i
$276$	6.89240	−	3.97933i	0.414874	−	0.239528i
$277$	4.53015	−	2.61548i	0.272190	−	0.157149i	−0.357692	−	0.933839i	$-0.616436\pi$
$277$	4.53015	−	2.61548i	0.272190	−	0.157149i	0.629883	+	0.776690i	$0.283103\pi$
$278$	−1.16604	−	0.673214i	−0.0699345	−	0.0403767i
$279$		−	1.27872i		−	0.0765550i
$280$	3.94016	+	2.61619i	0.235469	+	0.156347i
$281$		−	6.87281i		−	0.409998i	−0.978762	−	0.204999i	$-0.934281\pi$
$281$		−	6.87281i		−	0.409998i	0.978762	−	0.204999i	$-0.0657190\pi$
$282$	−8.55805	−	4.94099i	−0.509624	−	0.294232i
$283$	6.00542	+	10.4017i	0.356985	+	0.618316i	0.987456	−	0.157897i	$-0.0504714\pi$
$283$	6.00542	+	10.4017i	0.356985	+	0.618316i	−0.630471	+	0.776213i	$0.717138\pi$
$284$	−4.21392	−	7.29873i	−0.250050	−	0.433100i
$285$	3.71078	−	6.42726i	0.219808	−	0.380718i
$286$	−6.51854	+	20.1220i	−0.385449	+	1.18984i
$287$	0.00531446	−	0.0848636i	0.000313703	−	0.00500934i
$288$			1.00000i			0.0589256i
$289$	8.49437	−	14.7127i	0.499669	−	0.865452i
$290$	11.8468	−	6.83973i	0.695665	−	0.401643i
$291$	7.87488	+	13.6397i	0.461634	+	0.799573i
$292$	−0.0625042	+	0.108260i	−0.00365778	+	0.00633546i
$293$	−14.1147			−0.824592			−0.412296	−	0.911050i	$-0.635273\pi$
$293$	−14.1147			−0.824592			−0.412296	+	0.911050i	$0.635273\pi$
$294$	6.94531	+	0.873304i	0.405059	+	0.0509321i
$295$	22.2648			1.29631
$296$	−3.91603	−	2.26092i	−0.227615	−	0.131413i
$297$	−3.24354	+	0.692408i	−0.188209	+	0.0401776i
$298$	0.245079	+	0.424489i	0.0141970	+	0.0245900i
$299$	−25.3779	+	43.9557i	−1.46764	+	2.54203i
$300$			1.80439i			0.104176i
$301$	−18.1599	−	1.13723i	−1.04672	−	0.0655491i
$302$	−3.37323			−0.194107
$303$	−6.55841	−	3.78650i	−0.376771	−	0.217529i
$304$	−2.07581	−	3.59541i	−0.119056	−	0.206211i
$305$	15.4043	−	8.89366i	0.882046	−	0.509249i
$306$	0.0918811	+	0.0530476i	0.00525249	+	0.00303253i
$307$	21.0753			1.20283			0.601417	−	0.798936i	$-0.294603\pi$
$307$	21.0753			1.20283			0.601417	+	0.798936i	$0.294603\pi$
$308$	5.45857	+	6.87052i	0.311031	+	0.391484i
$309$	5.23715			0.297931
$310$	1.97963	+	1.14294i	0.112435	+	0.0649145i
$311$	−12.0806	+	6.97475i	−0.685029	+	0.395502i	−0.801747	−	0.597663i	$-0.796096\pi$
$311$	−12.0806	+	6.97475i	−0.685029	+	0.395502i	0.116718	+	0.993165i	$0.462763\pi$
$312$	−3.18871	−	5.52301i	−0.180525	−	0.312679i
$313$	3.45030	+	1.99203i	0.195023	+	0.112596i	0.594332	−	0.804220i	$-0.297417\pi$
$313$	3.45030	+	1.99203i	0.195023	+	0.112596i	−0.399309	+	0.916816i	$0.630750\pi$
$314$	4.06299			0.229288
$315$	−2.10418	−	4.23576i	−0.118557	−	0.238658i
$316$		−	10.1691i		−	0.572059i
$317$	−6.14927	+	10.6509i	−0.345377	+	0.598211i	−0.985422	−	0.170126i	$-0.945582\pi$
$317$	−6.14927	+	10.6509i	−0.345377	+	0.598211i	0.640045	+	0.768338i	$0.278916\pi$
$318$	−0.313720	−	0.543380i	−0.0175926	−	0.0304712i
$319$	24.8205	−	5.29851i	1.38968	−	0.296660i
$320$	−1.54813	−	0.893814i	−0.0865431	−	0.0499657i
$321$	4.76790			0.266118
$322$	9.36799	+	18.8580i	0.522058	+	1.05091i
$323$	−0.440467			−0.0245082
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−5.75367	−	9.96565i	−0.319156	−	0.552795i
$326$	−17.9626	+	10.3707i	−0.994857	+	0.574381i
$327$	4.25268	−	7.36585i	0.235174	−	0.407332i
$328$			0.0321383i			0.00177454i
$329$	14.4623	−	21.7811i	0.797330	−	1.20083i
$330$	1.82718	−	5.64031i	0.100583	−	0.310489i
$331$	15.5066	−	26.8582i	0.852319	−	1.47626i	−0.0267909	−	0.999641i	$-0.508529\pi$
$331$	15.5066	−	26.8582i	0.852319	−	1.47626i	0.879110	−	0.476619i	$-0.158138\pi$
$332$	−6.03285	−	10.4492i	−0.331096	−	0.573474i
$333$	2.26092	+	3.91603i	0.123898	+	0.214597i
$334$	−2.96934	−	1.71435i	−0.162475	−	0.0938051i
$335$		−	19.4354i		−	1.06187i
$336$	−2.64058	−	0.165362i	−0.144055	−	0.00902125i
$337$			13.6161i			0.741718i	0.928689	+	0.370859i	$0.120937\pi$
$337$			13.6161i			0.741718i	−0.928689	+	0.370859i	$0.879063\pi$
$338$	23.9642	+	13.8357i	1.30348	+	0.752565i
$339$	−8.92030	+	5.15014i	−0.484484	+	0.279717i
$340$	−0.164249	+	0.0948293i	−0.00890766	+	0.00514284i
$341$	2.84057	+	3.14922i	0.153825	+	0.170540i
$342$			4.15162i			0.224494i
$343$	−3.45452	+	18.1952i	−0.186527	+	0.982450i
$344$	6.87723			0.370795
$345$	7.11356	−	12.3210i	0.382981	−	0.663343i
$346$	−18.3185	+	10.5762i	−0.984810	+	0.568580i
$347$	−24.1708	+	13.9550i	−1.29756	+	0.749144i	−0.979981	−	0.199090i	$-0.936201\pi$
$347$	−24.1708	+	13.9550i	−1.29756	+	0.749144i	−0.317574	+	0.948234i	$0.602868\pi$
$348$	−3.82615	+	6.62708i	−0.205103	+	0.355249i
$349$	−27.8147			−1.48888			−0.744442	−	0.667687i	$-0.767285\pi$
$349$	−27.8147			−1.48888			−0.744442	+	0.667687i	$0.767285\pi$
$350$	−4.76463	−	0.298378i	−0.254680	−	0.0159490i
$351$			6.37742i			0.340401i
$352$	−2.22141	−	2.46279i	−0.118402	−	0.131267i
$353$	−18.6325	+	10.7575i	−0.991706	+	0.572562i	−0.905784	−	0.423740i	$-0.860717\pi$
$353$	−18.6325	+	10.7575i	−0.991706	+	0.572562i	−0.0859222	+	0.996302i	$0.527384\pi$
$354$	−10.7863	+	6.22747i	−0.573285	+	0.330987i
$355$	−13.0474	−	7.53293i	−0.692485	−	0.399806i
$356$		−	5.36009i		−	0.284084i
$357$	−0.155270	+	0.233847i	−0.00821776	+	0.0123765i
$358$			14.0866i			0.744500i
$359$	18.0949	+	10.4471i	0.955015	+	0.551378i	0.894635	−	0.446798i	$-0.147436\pi$
$359$	18.0949	+	10.4471i	0.955015	+	0.551378i	0.0603796	+	0.998175i	$0.480769\pi$
$360$	0.893814	+	1.54813i	0.0471081	+	0.0815936i
$361$	0.882009	+	1.52769i	0.0464215	+	0.0804045i
$362$	−6.22897	+	10.7889i	−0.327387	+	0.567052i
$363$	6.45003	−	8.91051i	0.338539	−	0.467680i
$364$	15.1112	−	7.50674i	0.792043	−	0.393460i
$365$			0.223468i			0.0116969i
$366$	−4.97512	+	8.61716i	−0.260054	+	0.450426i
$367$	4.62731	−	2.67158i	0.241543	−	0.139455i	−0.374342	−	0.927291i	$-0.622132\pi$
$367$	4.62731	−	2.67158i	0.241543	−	0.139455i	0.615886	+	0.787835i	$0.288798\pi$
$368$	−3.97933	−	6.89240i	−0.207437	−	0.359291i
$369$	0.0160691	−	0.0278326i	0.000836526	−	0.00144891i
$370$	−8.08337			−0.420234
$371$	1.48671	−	0.738549i	0.0771864	−	0.0383435i
$372$	−1.27872			−0.0662986
$373$	21.9741	+	12.6868i	1.13778	+	0.656895i	0.945879	−	0.324520i	$-0.105203\pi$
$373$	21.9741	+	12.6868i	1.13778	+	0.656895i	0.191897	+	0.981415i	$0.438536\pi$
$374$	−0.344124	+	0.0734611i	−0.0177942	+	0.00379858i
$375$	6.08186	+	10.5341i	0.314066	+	0.543978i
$376$	−4.94099	+	8.55805i	−0.254812	+	0.441348i
$377$		−	48.8019i		−	2.51343i
$378$	2.20413	+	1.46350i	0.113368	+	0.0752742i
$379$	22.7532			1.16875			0.584377	−	0.811483i	$-0.301339\pi$
$379$	22.7532			1.16875			0.584377	+	0.811483i	$0.301339\pi$
$380$	−6.42726	−	3.71078i	−0.329711	−	0.190359i
$381$	−1.59211	−	2.75761i	−0.0815662	−	0.141277i
$382$	23.5813	−	13.6147i	1.20652	−	0.696587i
$383$	−14.3310	−	8.27402i	−0.732281	−	0.422783i	0.0869750	−	0.996210i	$-0.472280\pi$
$383$	−14.3310	−	8.27402i	−0.732281	−	0.422783i	−0.819256	+	0.573428i	$0.805613\pi$
$384$	1.00000			0.0510310
$385$	14.5915	+	5.75752i	0.743654	+	0.293430i
$386$	−26.6381			−1.35584
$387$	−5.95586	−	3.43862i	−0.302753	−	0.174795i
$388$	13.6397	−	7.87488i	0.692451	−	0.399787i
$389$	−3.69906	−	6.40696i	−0.187550	−	0.324846i	0.756883	−	0.653550i	$-0.226721\pi$
$389$	−3.69906	−	6.40696i	−0.187550	−	0.324846i	−0.944433	+	0.328705i	$0.893388\pi$
$390$	−9.87308	−	5.70022i	−0.499943	−	0.288642i
$391$	−0.844376			−0.0427019
$392$	0.873304	−	6.94531i	0.0441085	−	0.350791i
$393$			1.08620i			0.0547915i
$394$	5.88818	−	10.1986i	0.296642	−	0.513799i
$395$	−9.08932	−	15.7432i	−0.457333	−	0.792124i
$396$	0.692408	+	3.24354i	0.0347948	+	0.162994i
$397$	3.34925	+	1.93369i	0.168094	+	0.0970492i	0.581687	−	0.813413i	$-0.302393\pi$
$397$	3.34925	+	1.93369i	0.168094	+	0.0970492i	−0.413593	+	0.910462i	$0.635726\pi$
$398$	21.4008			1.07272
$399$	−10.9627	−	0.686522i	−0.548821	−	0.0343691i
$400$	1.80439			0.0902194
$401$	−1.56681	+	2.71379i	−0.0782426	+	0.135520i	−0.902492	−	0.430707i	$-0.858264\pi$
$401$	−1.56681	+	2.71379i	−0.0782426	+	0.135520i	0.824249	+	0.566227i	$0.191598\pi$
$402$	5.43609	+	9.41558i	0.271127	+	0.469606i
$403$	7.06238	−	4.07747i	0.351802	−	0.203113i
$404$	−3.78650	+	6.55841i	−0.188385	+	0.326293i
$405$		−	1.78763i		−	0.0888279i
$406$	−16.8666	−	11.1991i	−0.837077	−	0.555803i
$407$	−14.2673	−	4.62191i	−0.707204	−	0.229099i
$408$	0.0530476	−	0.0918811i	0.00262625	−	0.00454879i
$409$	10.0511	+	17.4091i	0.496996	+	0.860822i	0.999994	−	0.00346526i	$-0.00110303\pi$
$409$	10.0511	+	17.4091i	0.496996	+	0.860822i	−0.502998	+	0.864288i	$0.667770\pi$
$410$	0.0287256	+	0.0497542i	0.00141866	+	0.00245719i
$411$	−6.56617	−	3.79098i	−0.323885	−	0.186995i
$412$		−	5.23715i		−	0.258016i
$413$	−14.6605	−	29.5119i	−0.721395	−	1.45218i
$414$			7.95866i			0.391147i
$415$	−18.6793	−	10.7845i	−0.916929	−	0.529389i
$416$	−5.52301	+	3.18871i	−0.270788	+	0.156339i
$417$	1.16604	−	0.673214i	0.0571013	−	0.0329674i
$418$	−9.22248	−	10.2246i	−0.451086	−	0.500100i
$419$			2.63035i			0.128501i	0.997934	+	0.0642506i	$0.0204657\pi$
$419$			2.63035i			0.128501i	−0.997934	+	0.0642506i	$0.979534\pi$
$420$	−4.23576	+	2.10418i	−0.206684	+	0.102674i
$421$	24.9232			1.21468			0.607341	−	0.794441i	$-0.292236\pi$
$421$	24.9232			1.21468			0.607341	+	0.794441i	$0.292236\pi$
$422$	12.6327	−	21.8805i	0.614951	−	1.06513i
$423$	8.55805	−	4.94099i	0.416107	−	0.240239i
$424$	−0.543380	+	0.313720i	−0.0263888	+	0.0152356i
$425$	0.0957185	−	0.165789i	0.00464303	−	0.00804196i
$426$	8.42785			0.408331
$427$	−21.9316	−	14.5621i	−1.06134	−	0.704712i
$428$		−	4.76790i		−	0.230465i
$429$	−14.1669	−	15.7062i	−0.683984	−	0.758303i
$430$	10.6469	−	6.14696i	0.513437	−	0.296433i
$431$	−11.8175	+	6.82282i	−0.569227	+	0.328644i	−0.756841	−	0.653599i	$-0.773258\pi$
$431$	−11.8175	+	6.82282i	−0.569227	+	0.328644i	0.187613	+	0.982243i	$0.439925\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$			10.4001i			0.499795i	0.968272	+	0.249897i	$0.0803969\pi$
$433$			10.4001i			0.499795i	−0.968272	+	0.249897i	$0.919603\pi$
$434$	0.211452	−	3.37656i	0.0101500	−	0.162080i
$435$			13.6795i			0.655879i
$436$	−7.36585	−	4.25268i	−0.352760	−	0.203666i
$437$	−16.5207	−	28.6147i	−0.790292	−	1.36883i
$438$	−0.0625042	−	0.108260i	−0.00298656	−	0.00517288i
$439$	11.6619	−	20.1991i	0.556594	−	0.964049i	−0.441183	−	0.897417i	$-0.645441\pi$
$439$	11.6619	−	20.1991i	0.556594	−	0.964049i	0.997778	−	0.0666324i	$-0.0212255\pi$
$440$	−5.64031	−	1.82718i	−0.268891	−	0.0871076i
$441$	−4.22896	+	5.57816i	−0.201379	+	0.265627i
$442$			0.676613i			0.0321832i
$443$	−4.91726	+	8.51694i	−0.233626	+	0.404652i	−0.958872	−	0.283837i	$-0.908392\pi$
$443$	−4.91726	+	8.51694i	−0.233626	+	0.404652i	0.725247	+	0.688489i	$0.241726\pi$
$444$	3.91603	−	2.26092i	0.185847	−	0.107299i
$445$	−4.79092	−	8.29813i	−0.227112	−	0.393369i
$446$	−4.90067	+	8.48820i	−0.232053	+	0.401928i
$447$	−0.490157			−0.0231836
$448$	−0.165362	+	2.64058i	−0.00781263	+	0.124756i
$449$	9.26223			0.437112			0.218556	−	0.975824i	$-0.429865\pi$
$449$	9.26223			0.437112			0.218556	+	0.975824i	$0.429865\pi$
$450$	−1.56265	−	0.902194i	−0.0736639	−	0.0425299i
$451$	0.0222528	+	0.104242i	0.00104784	+	0.00490856i
$452$	5.15014	+	8.92030i	0.242242	+	0.419576i
$453$	1.68661	−	2.92130i	0.0792440	−	0.137255i
$454$		−	23.2907i		−	1.09309i
$455$	16.6845	−	25.1280i	0.782182	−	1.17802i
$456$	4.15162			0.194418
$457$	−2.21387	−	1.27818i	−0.103560	−	0.0597906i	0.447325	−	0.894371i	$-0.352377\pi$
$457$	−2.21387	−	1.27818i	−0.103560	−	0.0597906i	−0.550886	+	0.834581i	$0.685710\pi$
$458$	−3.26531	−	5.65569i	−0.152578	−	0.264273i
$459$	−0.0918811	+	0.0530476i	−0.00428864	+	0.00247605i
$460$	−12.3210	−	7.11356i	−0.574472	−	0.331672i
$461$	29.5798			1.37767			0.688834	−	0.724919i	$-0.258123\pi$
$461$	29.5798			1.37767			0.688834	+	0.724919i	$0.258123\pi$
$462$	−8.67933	+	1.29200i	−0.403799	+	0.0601092i
$463$	−9.24447			−0.429627			−0.214813	−	0.976655i	$-0.568914\pi$
$463$	−9.24447			−0.429627			−0.214813	+	0.976655i	$0.568914\pi$
$464$	6.62708	+	3.82615i	0.307655	+	0.177624i
$465$	−1.97963	+	1.14294i	−0.0918030	+	0.0530025i
$466$	5.43383	+	9.41166i	0.251717	+	0.435987i
$467$	−10.0889	−	5.82484i	−0.466859	−	0.269541i	0.248065	−	0.968743i	$-0.420205\pi$
$467$	−10.0889	−	5.82484i	−0.466859	−	0.269541i	−0.714924	+	0.699202i	$0.753539\pi$
$468$	6.37742			0.294796
$469$	−25.7615	+	12.7974i	−1.18956	+	0.590931i
$470$			17.6653i			0.814840i
$471$	−2.03150	+	3.51865i	−0.0936064	+	0.162131i
$472$	6.22747	+	10.7863i	0.286643	+	0.496480i
$473$	22.3066	−	4.76185i	1.02566	−	0.218950i
$474$	8.80673	+	5.08457i	0.404507	+	0.233542i
$475$	7.49114			0.343717
$476$	0.233847	+	0.155270i	0.0107184	+	0.00711679i
$477$	0.627441			0.0287285
$478$	−3.84574	+	6.66102i	−0.175900	+	0.304668i
$479$	−5.02758	−	8.70803i	−0.229716	−	0.397880i	0.728008	−	0.685569i	$-0.240446\pi$
$479$	−5.02758	−	8.70803i	−0.229716	−	0.397880i	−0.957724	+	0.287689i	$0.907113\pi$
$480$	1.54813	−	0.893814i	0.0706622	−	0.0407968i
$481$	−14.4188	+	24.9742i	−0.657443	+	1.13872i
$482$			22.8135i			1.03913i
$483$	−21.0155	−	1.31606i	−0.956237	−	0.0598829i
$484$	−8.91051	−	6.45003i	−0.405023	−	0.293183i
$485$	14.0774	−	24.3827i	0.639220	−	1.10716i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−8.65731	−	14.9949i	−0.392300	−	0.679484i	0.600452	−	0.799661i	$-0.294987\pi$
$487$	−8.65731	−	14.9949i	−0.392300	−	0.679484i	−0.992753	+	0.120176i	$0.961654\pi$
$488$	8.61716	+	4.97512i	0.390080	+	0.225213i
$489$		−	20.7414i		−	0.937960i
$490$	−4.85582	−	11.5328i	−0.219364	−	0.521000i
$491$			8.44002i			0.380893i	0.981698	+	0.190446i	$0.0609935\pi$
$491$			8.44002i			0.380893i	−0.981698	+	0.190446i	$0.939006\pi$
$492$	−0.0278326	−	0.0160691i	−0.00125479	−	0.000724453i
$493$	0.703101	−	0.405936i	0.0316661	−	0.0182824i
$494$	−22.9294	+	13.2383i	−1.03164	+	0.595620i
$495$	3.97106	+	4.40254i	0.178486	+	0.197880i
$496$			1.27872i			0.0574163i
$497$	−1.39365	+	22.2544i	−0.0625137	+	0.998246i
$498$	12.0657			0.540677
$499$	−9.53597	+	16.5168i	−0.426889	+	0.739393i	−0.996595	−	0.0824555i	$-0.973724\pi$
$499$	−9.53597	+	16.5168i	−0.426889	+	0.739393i	0.569706	+	0.821849i	$0.307057\pi$
$500$	10.5341	−	6.08186i	0.471098	−	0.271989i
$501$	2.96934	−	1.71435i	0.132660	−	0.0765915i
$502$	−9.05557	+	15.6847i	−0.404170	+	0.700043i
$503$	3.32018			0.148039			0.0740197	−	0.997257i	$-0.476417\pi$
$503$	3.32018			0.148039			0.0740197	+	0.997257i	$0.476417\pi$
$504$	1.46350	−	2.20413i	0.0651893	−	0.0981796i
$505$			13.5377i			0.602419i
$506$	−17.6795	−	19.6005i	−0.785949	−	0.871348i
$507$	−23.9642	+	13.8357i	−1.06429	+	0.614466i
$508$	−2.75761	+	1.59211i	−0.122349	+	0.0706384i
$509$	3.91339	+	2.25939i	0.173458	+	0.100146i	0.584215	−	0.811599i	$-0.301402\pi$
$509$	3.91339	+	2.25939i	0.173458	+	0.100146i	−0.410758	+	0.911745i	$0.634736\pi$
$510$		−	0.189659i		−	0.00839822i
$511$	0.296206	−	0.147145i	0.0131034	−	0.00650931i
$512$		−	1.00000i		−	0.0441942i
$513$	−3.59541	−	2.07581i	−0.158741	−	0.0916493i
$514$	−1.97123	−	3.41428i	−0.0869474	−	0.150597i
$515$	−4.68103	−	8.10779i	−0.206271	−	0.357272i
$516$	−3.43862	+	5.95586i	−0.151377	+	0.262192i
$517$	−10.1007	+	31.1796i	−0.444226	+	1.37128i
$518$	5.32258	+	10.7145i	0.233861	+	0.470766i
$519$		−	21.1524i		−	0.928488i
$520$	−5.70022	+	9.87308i	−0.249971	+	0.432963i
$521$	−8.10705	+	4.68061i	−0.355176	+	0.205061i	−0.666963	−	0.745091i	$-0.732406\pi$
$521$	−8.10705	+	4.68061i	−0.355176	+	0.205061i	0.311786	+	0.950152i	$0.399073\pi$
$522$	−3.82615	−	6.62708i	−0.167466	−	0.290060i
$523$	8.70477	−	15.0771i	0.380633	−	0.659276i	−0.610520	−	0.792001i	$-0.709039\pi$
$523$	8.70477	−	15.0771i	0.380633	−	0.659276i	0.991153	+	0.132725i	$0.0423728\pi$
$524$	1.08620			0.0474508
$525$	2.64072	−	3.97710i	0.115250	−	0.173575i
$526$	−2.06715			−0.0901320
$527$	0.117490	+	0.0678330i	0.00511796	+	0.00295485i
$528$	3.24354	−	0.692408i	0.141157	−	0.0301332i
$529$	−20.1702	−	34.9357i	−0.876963	−	1.51895i
$530$	−0.560815	+	0.971360i	−0.0243603	+	0.0421932i
$531$		−	12.4549i		−	0.540499i
$532$	−0.686522	+	10.9627i	−0.0297645	+	0.475293i
$533$	0.204959			0.00887777
$534$	4.64198	+	2.68005i	0.200878	+	0.115977i
$535$	−4.26161	−	7.38132i	−0.184245	−	0.319122i
$536$	9.41558	−	5.43609i	0.406691	−	0.234803i
$537$	−12.1994	−	7.04330i	−0.526441	−	0.303941i
$538$	2.80480			0.120923
$539$	−1.97639	−	23.1321i	−0.0851291	−	0.996370i
$540$	−1.78763			−0.0769272
$541$	−34.0973	−	19.6861i	−1.46596	−	0.846370i	−0.466681	−	0.884426i	$-0.654550\pi$
$541$	−34.0973	−	19.6861i	−1.46596	−	0.846370i	−0.999276	+	0.0380552i	$0.987884\pi$
$542$	8.03751	−	4.64046i	0.345241	−	0.199325i
$543$	−6.22897	−	10.7889i	−0.267311	−	0.462996i
$544$	−0.0918811	−	0.0530476i	−0.00393937	−	0.00227440i
$545$	−15.2044			−0.651285
$546$	−1.05458	+	16.8401i	−0.0451321	+	0.720689i
$547$		−	20.3539i		−	0.870271i	−0.900365	−	0.435135i	$-0.856701\pi$
$547$		−	20.3539i		−	0.870271i	0.900365	−	0.435135i	$-0.143299\pi$
$548$	−3.79098	+	6.56617i	−0.161943	+	0.280493i
$549$	−4.97512	−	8.61716i	−0.212333	−	0.367771i
$550$	5.85261	−	1.24937i	0.249556	−	0.0532735i
$551$	27.5132	+	15.8847i	1.17210	+	0.676712i
$552$	7.95866			0.338743
$553$	−14.8825	+	22.4141i	−0.632869	+	0.953144i
$554$	5.23096			0.222242
$555$	4.04169	−	7.00040i	0.171560	−	0.297151i
$556$	−0.673214	−	1.16604i	−0.0285506	−	0.0494512i
$557$	11.2830	−	6.51425i	0.478076	−	0.276017i	−0.241538	−	0.970391i	$-0.577652\pi$
$557$	11.2830	−	6.51425i	0.478076	−	0.276017i	0.719614	+	0.694374i	$0.244319\pi$
$558$	0.639360	−	1.10740i	0.0270663	−	0.0468802i
$559$		−	43.8590i		−	1.85504i
$560$	2.10418	+	4.23576i	0.0889179	+	0.178994i
$561$	0.108443	−	0.334751i	0.00457846	−	0.0141332i
$562$	3.43641	−	5.95203i	0.144956	−	0.251071i
$563$	−16.7817	−	29.0667i	−0.707262	−	1.22501i	−0.965869	−	0.259032i	$-0.916597\pi$
$563$	−16.7817	−	29.0667i	−0.707262	−	1.22501i	0.258607	−	0.965983i	$-0.416737\pi$
$564$	−4.94099	−	8.55805i	−0.208053	−	0.360359i
$565$	15.9462	+	9.20653i	0.670861	+	0.387322i
$566$			12.0108i			0.504853i
$567$	−2.36949	+	1.17708i	−0.0995092	+	0.0494328i
$568$		−	8.42785i		−	0.353625i
$569$	4.80366	+	2.77340i	0.201380	+	0.116267i	0.597299	−	0.802019i	$-0.296241\pi$
$569$	4.80366	+	2.77340i	0.201380	+	0.116267i	−0.395919	+	0.918285i	$0.629574\pi$
$570$	6.42726	−	3.71078i	0.269208	−	0.155427i
$571$	32.1228	−	18.5461i	1.34430	−	0.776132i	0.356864	−	0.934156i	$-0.383846\pi$
$571$	32.1228	−	18.5461i	1.34430	−	0.776132i	0.987435	+	0.158025i	$0.0505126\pi$
$572$	−15.7062	+	14.1669i	−0.656710	+	0.592347i
$573$			27.2293i			1.13752i
$574$	0.0470343	−	0.0708368i	0.00196317	−	0.00295667i
$575$	14.3605			0.598875
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	2.66926	−	1.54110i	0.111123	−	0.0641567i	−0.443409	−	0.896320i	$-0.646231\pi$
$577$	2.66926	−	1.54110i	0.111123	−	0.0641567i	0.554531	+	0.832163i	$0.312898\pi$
$578$	14.7127	−	8.49437i	0.611967	−	0.353319i
$579$	13.3190	−	23.0692i	0.553520	−	0.958724i
$580$	13.6795			0.568008
$581$	−1.99521	+	31.8604i	−0.0827753	+	1.32179i
$582$			15.7498i			0.652849i
$583$	−1.54525	+	1.39381i	−0.0639978	+	0.0577255i
$584$	−0.108260	+	0.0625042i	−0.00447985	+	0.00258644i
$585$	9.87308	−	5.70022i	0.408201	−	0.235675i
$586$	−12.2237	−	7.05737i	−0.504957	−	0.291537i
$587$			46.9255i			1.93682i	0.249356	+	0.968412i	$0.419781\pi$
$587$			46.9255i			1.93682i	−0.249356	+	0.968412i	$0.580219\pi$
$588$	5.57816	+	4.22896i	0.230040	+	0.174399i
$589$			5.30877i			0.218744i
$590$	19.2819	+	11.1324i	0.793823	+	0.458314i
$591$	5.88818	+	10.1986i	0.242207	+	0.419515i
$592$	−2.26092	−	3.91603i	−0.0929233	−	0.160948i
$593$	2.57479	−	4.45967i	0.105734	−	0.183137i	−0.808304	−	0.588766i	$-0.799614\pi$
$593$	2.57479	−	4.45967i	0.105734	−	0.183137i	0.914038	+	0.405629i	$0.132947\pi$
$594$	−3.15519	−	1.02213i	−0.129459	−	0.0419384i
$595$	0.500808	+	0.0313624i	0.0205311	+	0.00128573i
$596$			0.490157i			0.0200776i
$597$	−10.7004	+	18.5336i	−0.437938	+	0.758531i
$598$	−43.9557	+	25.3779i	−1.79748	+	1.03778i
$599$	17.5731	+	30.4375i	0.718017	+	1.24364i	0.961784	+	0.273808i	$0.0882832\pi$
$599$	17.5731	+	30.4375i	0.718017	+	1.24364i	−0.243768	+	0.969834i	$0.578384\pi$
$600$	−0.902194	+	1.56265i	−0.0368319	+	0.0637948i
$601$	42.8385			1.74742			0.873710	−	0.486447i	$-0.161707\pi$
$601$	42.8385			1.74742			0.873710	+	0.486447i	$0.161707\pi$
$602$	−15.1583	−	10.0648i	−0.617806	−	0.410211i
$603$	−10.8722			−0.442749
$604$	−2.92130	−	1.68661i	−0.118866	−	0.0686273i
$605$	−19.5598	−	2.02116i	−0.795217	−	0.0821717i
$606$	−3.78650	−	6.55841i	−0.153816	−	0.266417i
$607$	−8.33275	+	14.4328i	−0.338216	+	0.585807i	−0.984097	−	0.177631i	$-0.943157\pi$
$607$	−8.33275	+	14.4328i	−0.338216	+	0.585807i	0.645881	+	0.763438i	$0.276490\pi$
$608$		−	4.15162i		−	0.168371i
$609$	18.1320	−	9.00737i	0.734747	−	0.364997i
$610$	17.7873			0.720187
$611$	54.5783	+	31.5108i	2.20800	+	1.27479i
$612$	0.0530476	+	0.0918811i	0.00214432	+	0.00371407i
$613$	−10.3018	+	5.94776i	−0.416087	+	0.240228i	−0.693402	−	0.720551i	$-0.743889\pi$
$613$	−10.3018	+	5.94776i	−0.416087	+	0.240228i	0.277315	+	0.960779i	$0.410555\pi$
$614$	18.2518	+	10.5377i	0.736582	+	0.425266i
$615$	−0.0574512			−0.00231666
$616$	1.29200	+	8.67933i	0.0520561	+	0.349700i
$617$	−0.0716192			−0.00288328			−0.00144164	−	0.999999i	$-0.500459\pi$
$617$	−0.0716192			−0.00288328			−0.00144164	+	0.999999i	$0.500459\pi$
$618$	4.53550	+	2.61857i	0.182445	+	0.105335i
$619$	25.3042	−	14.6094i	1.01706	−	0.587200i	0.103809	−	0.994597i	$-0.466897\pi$
$619$	25.3042	−	14.6094i	1.01706	−	0.587200i	0.913251	+	0.407397i	$0.133563\pi$
$620$	1.14294	+	1.97963i	0.0459015	+	0.0795037i
$621$	−6.89240	−	3.97933i	−0.276583	−	0.159685i
$622$	−13.9495			−0.559324
$623$	−7.84448	+	11.8143i	−0.314283	+	0.473331i
$624$		−	6.37742i		−	0.255301i
$625$	6.36112	−	11.0178i	0.254445	−	0.440711i
$626$	1.99203	+	3.45030i	0.0796177	+	0.137902i
$627$	13.4660	−	2.87462i	0.537779	−	0.114801i
$628$	3.51865	+	2.03150i	0.140410	+	0.0810655i
$629$	−0.479746			−0.0191287
$630$	0.295606	−	4.72037i	0.0117772	−	0.188064i
$631$	−43.3663			−1.72638			−0.863192	−	0.504876i	$-0.831538\pi$
$631$	−43.3663			−1.72638			−0.863192	+	0.504876i	$0.831538\pi$
$632$	5.08457	−	8.80673i	0.202253	−	0.350313i
$633$	12.6327	+	21.8805i	0.502106	+	0.869672i
$634$	−10.6509	+	6.14927i	−0.422999	+	0.244219i
$635$	−2.84610	+	4.92958i	−0.112944	+	0.195624i
$636$		−	0.627441i		−	0.0248796i
$637$	−44.2932	−	5.56943i	−1.75496	−	0.220669i
$638$	24.1445	+	7.82163i	0.955889	+	0.309661i
$639$	−4.21392	+	7.29873i	−0.166700	+	0.288733i
$640$	−0.893814	−	1.54813i	−0.0353311	−	0.0611952i
$641$	2.72745	+	4.72408i	0.107728	+	0.186590i	0.914849	−	0.403795i	$-0.132309\pi$
$641$	2.72745	+	4.72408i	0.107728	+	0.186590i	−0.807122	+	0.590385i	$0.798976\pi$
$642$	4.12912	+	2.38395i	0.162963	+	0.0940869i
$643$		−	4.26488i		−	0.168190i	−0.996458	−	0.0840952i	$-0.973200\pi$
$643$		−	4.26488i		−	0.168190i	0.996458	−	0.0840952i	$-0.0268000\pi$
$644$	−1.31606	+	21.0155i	−0.0518601	+	0.828126i
$645$			12.2939i			0.484073i
$646$	−0.381456	−	0.220234i	−0.0150082	−	0.00866497i
$647$	20.5525	−	11.8660i	0.808004	−	0.466501i	−0.0382582	−	0.999268i	$-0.512181\pi$
$647$	20.5525	−	11.8660i	0.808004	−	0.466501i	0.846262	+	0.532767i	$0.178848\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	27.6676	+	30.6739i	1.08605	+	1.20406i
$650$		−	11.5073i		−	0.451355i
$651$	2.81846	+	1.87140i	0.110464	+	0.0733461i
$652$	−20.7414			−0.812297
$653$	−16.8093	+	29.1145i	−0.657797	+	1.13934i	0.323388	+	0.946266i	$0.395178\pi$
$653$	−16.8093	+	29.1145i	−0.657797	+	1.13934i	−0.981185	+	0.193071i	$0.938155\pi$
$654$	7.36585	−	4.25268i	0.288028	−	0.166293i
$655$	1.68158	−	0.970859i	0.0657047	−	0.0379346i
$656$	−0.0160691	+	0.0278326i	−0.000627394	+	0.00108668i
$657$	0.125008			0.00487704
$658$	23.4153	−	11.6319i	0.912822	−	0.453459i
$659$		−	28.9405i		−	1.12736i	−0.825993	−	0.563681i	$-0.809385\pi$
$659$		−	28.9405i		−	1.12736i	0.825993	−	0.563681i	$-0.190615\pi$
$660$	4.40254	−	3.97106i	0.171369	−	0.154573i
$661$	−0.518650	+	0.299443i	−0.0201732	+	0.0116470i	−0.510053	−	0.860143i	$-0.670374\pi$
$661$	−0.518650	+	0.299443i	−0.0201732	+	0.0116470i	0.489880	+	0.871790i	$0.337041\pi$
$662$	26.8582	−	15.5066i	1.04387	−	0.602681i
$663$	−0.585964	−	0.338307i	−0.0227570	−	0.0131387i
$664$		−	12.0657i		−	0.468240i
$665$	8.73578	+	17.5853i	0.338759	+	0.681929i
$666$			4.52184i			0.175218i
$667$	52.7427	+	30.4510i	2.04221	+	1.17907i
$668$	−1.71435	−	2.96934i	−0.0663302	−	0.114887i
$669$	−4.90067	−	8.48820i	−0.189471	−	0.328173i
$670$	9.71770	−	16.8315i	0.375427	−	0.650259i
$671$	31.3949	+	10.1704i	1.21199	+	0.392625i
$672$	−2.20413	−	1.46350i	−0.0850260	−	0.0564556i
$673$			36.3353i			1.40062i	0.713837	+	0.700312i	$0.246956\pi$
$673$			36.3353i			1.40062i	−0.713837	+	0.700312i	$0.753044\pi$
$674$	−6.80807	+	11.7919i	−0.262237	+	0.454208i
$675$	1.56265	−	0.902194i	0.0601463	−	0.0347255i
$676$	13.8357	+	23.9642i	0.532144	+	0.921700i
$677$	9.99570	−	17.3131i	0.384166	−	0.665395i	−0.607487	−	0.794329i	$-0.707822\pi$
$677$	9.99570	−	17.3131i	0.384166	−	0.665395i	0.991653	+	0.128935i	$0.0411558\pi$
$678$	−10.3003			−0.395580
$679$	−41.5885	−	2.60442i	−1.59602	−	0.0999484i
$680$	−0.189659			−0.00727307
$681$	20.1704	+	11.6454i	0.772931	+	0.446252i
$682$	0.885396	+	4.14759i	0.0339036	+	0.158819i
$683$	11.0162	+	19.0807i	0.421524	+	0.730102i	0.996089	−	0.0883577i	$-0.0281619\pi$
$683$	11.0162	+	19.0807i	0.421524	+	0.730102i	−0.574564	+	0.818459i	$0.694829\pi$
$684$	−2.07581	+	3.59541i	−0.0793707	+	0.137474i
$685$			13.5537i			0.517861i
$686$	−12.0893	+	14.0303i	−0.461572	+	0.535678i
$687$	6.53063			0.249159
$688$	5.95586	+	3.43862i	0.227065	+	0.131096i
$689$	2.00073	+	3.46536i	0.0762216	+	0.132020i
$690$	12.3210	−	7.11356i	0.469054	−	0.270809i
$691$	9.88161	+	5.70515i	0.375914	+	0.217034i	0.676039	−	0.736866i	$-0.263695\pi$
$691$	9.88161	+	5.70515i	0.375914	+	0.217034i	−0.300125	+	0.953900i	$0.597028\pi$
$692$	−21.1524			−0.804094
$693$	3.22076	−	8.16252i	0.122347	−	0.310068i
$694$	−27.9100			−1.05945
$695$	−2.08445	−	1.20346i	−0.0790676	−	0.0456497i
$696$	−6.62708	+	3.82615i	−0.251199	+	0.145030i
$697$	0.00170486	+	0.00295290i	6.45761e−5	+	0.000111849i
$698$	−24.0882	−	13.9073i	−0.911752	−	0.526400i
$699$	−10.8677			−0.411052
$700$	−3.97710	−	2.64072i	−0.150320	−	0.0998098i
$701$		−	1.92874i		−	0.0728474i	−0.999336	−	0.0364237i	$-0.988403\pi$
$701$		−	1.92874i		−	0.0728474i	0.999336	−	0.0364237i	$-0.0115966\pi$
$702$	−3.18871	+	5.52301i	−0.120350	+	0.208452i
$703$	−9.38650	−	16.2579i	−0.354018	−	0.613178i
$704$	−0.692408	−	3.24354i	−0.0260961	−	0.122246i
$705$	−15.2986	−	8.83265i	−0.576179	−	0.332657i
$706$	−21.5149			−0.809725
$707$	17.9441	−	8.91403i	0.674859	−	0.335247i
$708$	−12.4549			−0.468086
$709$	−9.50162	+	16.4573i	−0.356841	+	0.618066i	−0.987431	−	0.158050i	$-0.949479\pi$
$709$	−9.50162	+	16.4573i	−0.356841	+	0.618066i	0.630590	+	0.776116i	$0.282813\pi$
$710$	−7.53293	−	13.0474i	−0.282706	−	0.489661i
$711$	−8.80673	+	5.08457i	−0.330278	+	0.190686i
$712$	2.68005	−	4.64198i	0.100439	−	0.173965i
$713$			10.1769i			0.381128i
$714$	−0.251391	+	0.124883i	−0.00940808	+	0.00467361i
$715$	−11.6527	+	35.9706i	−0.435787	+	1.34523i
$716$	−7.04330	+	12.1994i	−0.263220	+	0.455911i
$717$	−3.84574	−	6.66102i	−0.143622	−	0.248760i
$718$	10.4471	+	18.0949i	0.389883	+	0.675297i
$719$	17.8998	+	10.3345i	0.667551	+	0.385411i	0.795148	−	0.606415i	$-0.207393\pi$
$719$	17.8998	+	10.3345i	0.667551	+	0.385411i	−0.127597	+	0.991826i	$0.540726\pi$
$720$			1.78763i			0.0666209i
$721$	−7.66455	+	11.5433i	−0.285443	+	0.429896i
$722$			1.76402i			0.0656500i
$723$	−19.7571	−	11.4067i	−0.734773	−	0.424221i
$724$	−10.7889	+	6.22897i	−0.400966	+	0.231498i
$725$	−11.9578	+	6.90386i	−0.444103	+	0.256403i
$726$	10.0411	−	4.49171i	0.372662	−	0.166703i
$727$		−	1.72185i		−	0.0638600i	−0.999490	−	0.0319300i	$-0.989835\pi$
$727$		−	1.72185i		−	0.0638600i	0.999490	−	0.0319300i	$-0.0101654\pi$
$728$	16.8401	+	1.05458i	0.624135	+	0.0390855i
$729$	−1.00000			−0.0370370
$730$	−0.111734	+	0.193529i	−0.00413547	+	0.00716284i
$731$	0.631887	−	0.364820i	0.0233712	−	0.0134934i
$732$	−8.61716	+	4.97512i	−0.318499	+	0.183886i
$733$	0.597125	−	1.03425i	0.0220553	−	0.0382009i	−0.854787	−	0.518979i	$-0.826312\pi$
$733$	0.597125	−	1.03425i	0.0220553	−	0.0382009i	0.876842	+	0.480778i	$0.159646\pi$
$734$	5.34315			0.197219
$735$	12.4156	+	1.56114i	0.457957	+	0.0575836i
$736$		−	7.95866i		−	0.293360i
$737$	26.7758	−	24.1516i	0.986301	−	0.889636i
$738$	0.0278326	−	0.0160691i	0.00102453	−	0.000591513i
$739$	10.7713	−	6.21881i	0.396228	−	0.228763i	−0.288627	−	0.957442i	$-0.593199\pi$
$739$	10.7713	−	6.21881i	0.396228	−	0.228763i	0.684855	+	0.728679i	$0.259865\pi$
$740$	−7.00040	−	4.04169i	−0.257340	−	0.148575i
$741$		−	26.4766i		−	0.972644i
$742$	1.65681	+	0.103755i	0.0608233	+	0.00380897i
$743$			19.1754i			0.703479i	0.936098	+	0.351739i	$0.114410\pi$
$743$			19.1754i			0.703479i	−0.936098	+	0.351739i	$0.885590\pi$
$744$	−1.10740	−	0.639360i	−0.0405994	−	0.0234401i
$745$	0.438109	+	0.758827i	0.0160511	+	0.0278013i
$746$	12.6868	+	21.9741i	0.464495	+	0.804529i
$747$	−6.03285	+	10.4492i	−0.220730	+	0.382316i
$748$	−0.334751	−	0.108443i	−0.0122397	−	0.00396506i
$749$	−6.97780	+	10.5090i	−0.254963	+	0.383992i
$750$			12.1637i			0.444156i
$751$	−22.9870	+	39.8146i	−0.838807	+	1.45286i	0.0520865	+	0.998643i	$0.483413\pi$
$751$	−22.9870	+	39.8146i	−0.838807	+	1.45286i	−0.890893	+	0.454213i	$0.849921\pi$
$752$	−8.55805	+	4.94099i	−0.312080	+	0.180179i
$753$	−9.05557	−	15.6847i	−0.330003	−	0.571583i
$754$	24.4009	−	42.2637i	0.888630	−	1.53915i
$755$	−6.03007			−0.219457
$756$	1.17708	+	2.36949i	0.0428100	+	0.0861775i
$757$	32.1348			1.16796			0.583979	−	0.811768i	$-0.301495\pi$
$757$	32.1348			1.16796			0.583979	+	0.811768i	$0.301495\pi$
$758$	19.7048	+	11.3766i	0.715712	+	0.413217i
$759$	25.8143	−	5.51064i	0.936998	−	0.200024i
$760$	−3.71078	−	6.42726i	−0.134604	−	0.233141i
$761$	−10.2499	+	17.7533i	−0.371558	+	0.643558i	−0.989805	−	0.142426i	$-0.954510\pi$
$761$	−10.2499	+	17.7533i	−0.371558	+	0.643558i	0.618247	+	0.785984i	$0.287843\pi$
$762$		−	3.18422i		−	0.115352i
$763$	10.0115	+	20.1533i	0.362440	+	0.729600i
$764$	27.2293			0.985122
$765$	0.164249	+	0.0948293i	0.00593844	+	0.00342856i
$766$	−8.27402	−	14.3310i	−0.298953	−	0.517801i
$767$	68.7888	−	39.7152i	2.48382	−	1.43403i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	−14.3312			−0.516796			−0.258398	−	0.966039i	$-0.583195\pi$
$769$	−14.3312			−0.516796			−0.258398	+	0.966039i	$0.583195\pi$
$770$	9.75788	+	12.2819i	0.351650	+	0.442610i
$771$	3.94247			0.141984
$772$	−23.0692	−	13.3190i	−0.830280	−	0.479362i
$773$	−25.6118	+	14.7870i	−0.921193	+	0.531851i	−0.884016	−	0.467457i	$-0.845170\pi$
$773$	−25.6118	+	14.7870i	−0.921193	+	0.531851i	−0.0371778	+	0.999309i	$0.511837\pi$
$774$	−3.43862	−	5.95586i	−0.123598	−	0.214079i
$775$	−1.99819	−	1.15365i	−0.0717771	−	0.0414405i
$776$	15.7498			0.565384
$777$	−11.9403	−	0.747742i	−0.428355	−	0.0268251i
$778$		−	7.39812i		−	0.265235i
$779$	−0.0667130	+	0.115550i	−0.00239024	+	0.00414002i
$780$	−5.70022	−	9.87308i	−0.204101	−	0.353513i
$781$	−5.83551	−	27.3361i	−0.208811	−	0.978162i
$782$	−0.731251	−	0.422188i	−0.0261495	−	0.0150974i
$783$	7.65230			0.273471
$784$	4.22896	−	5.57816i	0.151034	−	0.199220i
$785$	7.26311			0.259232
$786$	−0.543099	+	0.940675i	−0.0193717	+	0.0335528i
$787$	13.3487	+	23.1207i	0.475831	+	0.824164i	0.999617	−	0.0276865i	$-0.00881401\pi$
$787$	13.3487	+	23.1207i	0.475831	+	0.824164i	−0.523786	+	0.851850i	$0.675481\pi$
$788$	10.1986	−	5.88818i	0.363311	−	0.209758i
$789$	1.03357	−	1.79020i	0.0367962	−	0.0637329i
$790$		−	18.1786i		−	0.646767i
$791$	1.70328	−	27.1987i	0.0605616	−	0.967074i
$792$	−1.02213	+	3.15519i	−0.0363198	+	0.112115i
$793$	31.7284	−	54.9552i	1.12671	−	1.95152i
$794$	1.93369	+	3.34925i	0.0686241	+	0.118860i
$795$	−0.560815	−	0.971360i	−0.0198901	−	0.0344506i
$796$	18.5336	+	10.7004i	0.656907	+	0.379265i
$797$		−	47.2556i		−	1.67388i	−0.547294	−	0.836940i	$-0.684342\pi$
$797$		−	47.2556i		−	1.67388i	0.547294	−	0.836940i	$-0.315658\pi$
$798$	−9.15071	−	6.07589i	−0.323931	−	0.215084i
$799$			1.04843i			0.0370908i
$800$	1.56265	+	0.902194i	0.0552479	+	0.0318974i
$801$	−4.64198	+	2.68005i	−0.164016	+	0.0946948i
$802$	−2.71379	+	1.56681i	−0.0958272	+	0.0553259i
$803$	−0.307869	+	0.277695i	−0.0108645	+	0.00979965i
$804$			10.8722i			0.383432i
$805$	16.7465	+	33.7110i	0.590236	+	1.18816i
$806$	8.15494			0.287245
$807$	−1.40240	+	2.42902i	−0.0493667	+	0.0855057i
$808$	−6.55841	+	3.78650i	−0.230724	+	0.133209i
$809$	−18.2536	+	10.5387i	−0.641763	+	0.370522i	−0.785293	−	0.619124i	$-0.787488\pi$
$809$	−18.2536	+	10.5387i	−0.641763	+	0.370522i	0.143530	+	0.989646i	$0.454155\pi$
$810$	0.893814	−	1.54813i	0.0314054	−	0.0543958i
$811$	38.7457			1.36055			0.680273	−	0.732959i	$-0.261861\pi$
$811$	38.7457			1.36055			0.680273	+	0.732959i	$0.261861\pi$
$812$	−9.00737	−	18.1320i	−0.316097	−	0.636310i
$813$			9.28092i			0.325496i
$814$	−10.0449	−	11.1363i	−0.352073	−	0.390328i
$815$	−32.1104	+	18.5390i	−1.12478	+	0.649392i
$816$	0.0918811	−	0.0530476i	0.00321648	−	0.00185704i
$817$	24.7265	+	14.2758i	0.865070	+	0.499448i
$818$			20.1022i			0.702858i
$819$	−14.0566	−	9.33333i	−0.491179	−	0.326133i
$820$			0.0574512i			0.00200628i
$821$	−37.0933	−	21.4158i	−1.29456	−	0.747417i	−0.315105	−	0.949057i	$-0.602040\pi$
$821$	−37.0933	−	21.4158i	−1.29456	−	0.747417i	−0.979460	+	0.201639i	$0.935373\pi$
$822$	−3.79098	−	6.56617i	−0.132226	−	0.229022i
$823$	−16.9309	−	29.3253i	−0.590176	−	1.02221i	−0.994208	−	0.107469i	$-0.965725\pi$
$823$	−16.9309	−	29.3253i	−0.590176	−	1.02221i	0.404033	−	0.914744i	$-0.367608\pi$
$824$	2.61857	−	4.53550i	0.0912224	−	0.158002i
$825$	−1.84432	+	5.69320i	−0.0642109	+	0.198212i
$826$	2.05958	−	32.8883i	0.0716619	−	1.14433i
$827$			15.2572i			0.530544i	0.964174	+	0.265272i	$0.0854618\pi$
$827$			15.2572i			0.530544i	−0.964174	+	0.265272i	$0.914538\pi$
$828$	−3.97933	+	6.89240i	−0.138291	+	0.239528i
$829$	−14.9375	+	8.62414i	−0.518799	+	0.299529i	−0.736443	−	0.676499i	$-0.763496\pi$
$829$	−14.9375	+	8.62414i	−0.518799	+	0.299529i	0.217644	+	0.976028i	$0.430163\pi$
$830$	−10.7845	−	18.6793i	−0.374335	−	0.648367i
$831$	−2.61548	+	4.53015i	−0.0907300	+	0.157149i
$832$	−6.37742			−0.221097
$833$	−0.288192	−	0.684469i	−0.00998525	−	0.0237155i
$834$	1.34643			0.0466230
$835$	−5.30808	−	3.06462i	−0.183694	−	0.106056i
$836$	−2.87462	−	13.4660i	−0.0994207	−	0.465730i
$837$	0.639360	+	1.10740i	0.0220995	+	0.0382775i
$838$	−1.31518	+	2.27795i	−0.0454320	+	0.0786906i
$839$			9.80607i			0.338543i	0.985569	+	0.169272i	$0.0541415\pi$
$839$			9.80607i			0.338543i	−0.985569	+	0.169272i	$0.945859\pi$
$840$	−4.72037	−	0.295606i	−0.162868	−	0.0101994i
$841$	−29.5576			−1.01923
$842$	21.5841	+	12.4616i	0.743838	+	0.429455i
$843$	3.43641	+	5.95203i	0.118356	+	0.204999i
$844$	21.8805	−	12.6327i	0.753158	−	0.434836i
$845$	42.8390	+	24.7331i	1.47371	+	0.850846i
$846$	9.88198			0.339750
$847$	10.2003	+	27.2572i	0.350486	+	0.936568i
$848$	−0.627441			−0.0215464
$849$	−10.4017	−	6.00542i	−0.356985	−	0.206105i
$850$	0.165789	−	0.0957185i	0.00568652	−	0.00328312i
$851$	−17.9939	−	31.1664i	−0.616823	−	1.06837i
$852$	7.29873	+	4.21392i	0.250050	+	0.144367i
$853$	−58.0237			−1.98669			−0.993346	−	0.115168i	$-0.963259\pi$
$853$	−58.0237			−1.98669			−0.993346	+	0.115168i	$0.963259\pi$
$854$	−11.7122	−	23.5770i	−0.400785	−	0.806788i
$855$			7.42156i			0.253812i
$856$	2.38395	−	4.12912i	0.0814817	−	0.141130i
$857$	20.5434	+	35.5821i	0.701748	+	1.21546i	0.967853	+	0.251518i	$0.0809299\pi$
$857$	20.5434	+	35.5821i	0.701748	+	1.21546i	−0.266105	+	0.963944i	$0.585737\pi$
$858$	−4.41578	−	20.6854i	−0.150752	−	0.706189i
$859$	−23.0028	−	13.2807i	−0.784845	−	0.453130i	0.0532999	−	0.998579i	$-0.483026\pi$
$859$	−23.0028	−	13.2807i	−0.784845	−	0.453130i	−0.838144	+	0.545448i	$0.816359\pi$
$860$	12.2939			0.419219
$861$	0.0378294	+	0.0761513i	0.00128922	+	0.00259523i
$862$	−13.6456			−0.464772
$863$	−4.54395	+	7.87036i	−0.154678	+	0.267910i	−0.932942	−	0.360027i	$-0.882767\pi$
$863$	−4.54395	+	7.87036i	−0.154678	+	0.267910i	0.778264	+	0.627938i	$0.216101\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−32.7467	+	18.9063i	−1.11342	+	0.642834i
$866$	−5.20003	+	9.00671i	−0.176704	+	0.306061i
$867$			16.9887i			0.576968i
$868$	1.87140	−	2.81846i	0.0635196	−	0.0956649i
$869$	10.3942	−	32.0856i	0.352598	−	1.08843i
$870$	−6.83973	+	11.8468i	−0.231888	+	0.401643i
$871$	−34.6682	−	60.0471i	−1.17469	−	2.03462i
$872$	−4.25268	−	7.36585i	−0.144014	−	0.249439i
$873$	−13.6397	−	7.87488i	−0.461634	−	0.266524i
$874$		−	33.0414i		−	1.11764i
$875$	−32.1192	−	2.01142i	−1.08583	−	0.0679984i
$876$		−	0.125008i		−	0.00422364i
$877$	3.95476	+	2.28328i	0.133543	+	0.0771009i	0.565283	−	0.824897i	$-0.308767\pi$
$877$	3.95476	+	2.28328i	0.133543	+	0.0771009i	−0.431740	+	0.901998i	$0.642100\pi$
$878$	20.1991	−	11.6619i	0.681686	−	0.393572i
$879$	12.2237	−	7.05737i	0.412296	−	0.238039i
$880$	−3.97106	−	4.40254i	−0.133864	−	0.148410i
$881$			35.4288i			1.19363i	0.802380	+	0.596813i	$0.203567\pi$
$881$			35.4288i			1.19363i	−0.802380	+	0.596813i	$0.796433\pi$
$882$	−6.45147	+	2.71635i	−0.217232	+	0.0914643i
$883$	25.2987			0.851368			0.425684	−	0.904872i	$-0.360033\pi$
$883$	25.2987			0.851368			0.425684	+	0.904872i	$0.360033\pi$
$884$	−0.338307	+	0.585964i	−0.0113785	+	0.0197081i
$885$	−19.2819	+	11.1324i	−0.648153	+	0.374212i
$886$	−8.51694	+	4.91726i	−0.286132	+	0.165198i
$887$	−22.4831	+	38.9419i	−0.754909	+	1.30754i	0.190511	+	0.981685i	$0.438986\pi$
$887$	−22.4831	+	38.9419i	−0.754909	+	1.30754i	−0.945420	+	0.325855i	$0.894348\pi$
$888$	4.52184			0.151743
$889$	8.40817	+	0.526549i	0.282001	+	0.0176599i
$890$		−	9.58185i		−	0.321184i
$891$	2.46279	−	2.22141i	0.0825065	−	0.0744202i
$892$	−8.48820	+	4.90067i	−0.284206	+	0.164086i
$893$	−35.5298	+	20.5131i	−1.18896	+	0.686446i
$894$	−0.424489	−	0.245079i	−0.0141970	−	0.00819666i
$895$			25.1816i			0.841727i
$896$	−1.46350	+	2.20413i	−0.0488920	+	0.0736347i
$897$		−	50.7557i		−	1.69468i
$898$	8.02133	+	4.63112i	0.267675	+	0.154542i
$899$	−4.89257	−	8.47419i	−0.163176	−	0.282630i
$900$	−0.902194	−	1.56265i	−0.0300731	−	0.0520882i
$901$	−0.0332842	+	0.0576499i	−0.00110886	+	0.00192060i
$902$	−0.0328494	+	0.101403i	−0.00109377	+	0.00337633i
$903$	16.2955	−	8.09506i	0.542281	−	0.269387i
$904$			10.3003i			0.342582i
$905$	−11.1351	+	19.2865i	−0.370143	+	0.641106i
$906$	2.92130	−	1.68661i	0.0970537	−	0.0560340i
$907$	8.63064	+	14.9487i	0.286576	+	0.496364i	0.972990	−	0.230847i	$-0.0741497\pi$
$907$	8.63064	+	14.9487i	0.286576	+	0.496364i	−0.686414	+	0.727211i	$0.740816\pi$
$908$	11.6454	−	20.1704i	0.386465	−	0.669377i
$909$	7.57300			0.251180
$910$	27.0132	−	13.4193i	0.895480	−	0.444844i
$911$	−18.9606			−0.628194			−0.314097	−	0.949391i	$-0.601702\pi$
$911$	−18.9606			−0.628194			−0.314097	+	0.949391i	$0.601702\pi$
$912$	3.59541	+	2.07581i	0.119056	+	0.0687370i
$913$	−8.35438	−	39.1356i	−0.276490	−	1.29520i
$914$	−1.27818	−	2.21387i	−0.0422783	−	0.0732282i
$915$	−8.89366	+	15.4043i	−0.294015	+	0.509249i
$916$		−	6.53063i		−	0.215778i
$917$	−2.39412	−	1.58965i	−0.0790608	−	0.0524948i
$918$	−0.106095			−0.00350166
$919$	30.9373	+	17.8617i	1.02053	+	0.589203i	0.914257	−	0.405134i	$-0.132775\pi$
$919$	30.9373	+	17.8617i	1.02053	+	0.589203i	0.106272	+	0.994337i	$0.466109\pi$
$920$	−7.11356	−	12.3210i	−0.234527	−	0.406213i
$921$	−18.2518	+	10.5377i	−0.601417	+	0.347228i
$922$	25.6168	+	14.7899i	0.843645	+	0.487079i
$923$	−53.7479			−1.76913
$924$	−8.16252	−	3.22076i	−0.268527	−	0.105955i
$925$	8.15916			0.268272
$926$	−8.00595	−	4.62224i	−0.263092	−	0.151896i
$927$	−4.53550	+	2.61857i	−0.148965	+	0.0860053i
$928$	3.82615	+	6.62708i	0.125599	+	0.217545i
$929$	35.0844	+	20.2560i	1.15108	+	0.664577i	0.949150	−	0.314823i	$-0.101945\pi$
$929$	35.0844	+	20.2560i	1.15108	+	0.664577i	0.201930	+	0.979400i	$0.435279\pi$
$930$	−2.28588			−0.0749568
$931$	17.5570	−	23.1584i	0.575409	−	0.758987i
$932$			10.8677i			0.355982i
$933$	6.97475	−	12.0806i	0.228343	−	0.395502i
$934$	−5.82484	−	10.0889i	−0.190595	−	0.330119i
$935$	−0.615166	+	0.131321i	−0.0201181	+	0.00429466i
$936$	5.52301	+	3.18871i	0.180525	+	0.104226i
$937$	36.2513			1.18428			0.592140	−	0.805835i	$-0.298283\pi$
$937$	36.2513			1.18428			0.592140	+	0.805835i	$0.298283\pi$
$938$	−28.7088	−	1.79785i	−0.937376	−	0.0587018i
$939$	−3.98407			−0.130015
$940$	−8.83265	+	15.2986i	−0.288089	+	0.498985i
$941$	−22.3898	−	38.7803i	−0.729887	−	1.26420i	−0.956931	−	0.290316i	$-0.906239\pi$
$941$	−22.3898	−	38.7803i	−0.729887	−	1.26420i	0.227044	−	0.973884i	$-0.427094\pi$
$942$	−3.51865	+	2.03150i	−0.114644	+	0.0661897i
$943$	−0.127889	+	0.221510i	−0.00416463	+	0.00721336i
$944$			12.4549i			0.405374i
$945$	3.94016	+	2.61619i	0.128173	+	0.0851046i
$946$	21.6990	+	7.02941i	0.705495	+	0.228546i
$947$	7.35348	−	12.7366i	0.238956	−	0.413884i	−0.721459	−	0.692457i	$-0.756528\pi$
$947$	7.35348	−	12.7366i	0.238956	−	0.413884i	0.960415	+	0.278573i	$0.0898615\pi$
$948$	5.08457	+	8.80673i	0.165139	+	0.286029i
$949$	0.398615	+	0.690422i	0.0129396	+	0.0224120i
$950$	6.48752	+	3.74557i	0.210483	+	0.121522i
$951$		−	12.2985i		−	0.398808i
$952$	0.124883	+	0.251391i	0.00404747	+	0.00814764i
$953$			23.4615i			0.759991i	0.924988	+	0.379996i	$0.124074\pi$
$953$			23.4615i			0.759991i	−0.924988	+	0.379996i	$0.875926\pi$
$954$	0.543380	+	0.313720i	0.0175926	+	0.0101571i
$955$	42.1546	−	24.3379i	1.36409	−	0.787557i
$956$	−6.66102	+	3.84574i	−0.215433	+	0.124380i
$957$	−18.8460	+	16.9989i	−0.609204	+	0.549497i
$958$		−	10.0552i		−	0.324868i
$959$	17.9654	−	8.92459i	0.580133	−	0.288190i
$960$	1.78763			0.0576954
$961$	−14.6824	+	25.4307i	−0.473627	+	0.820346i
$962$	−24.9742	+	14.4188i	−0.805200	+	0.464882i
$963$	−4.12912	+	2.38395i	−0.133059	+	0.0768216i
$964$	−11.4067	+	19.7571i	−0.367387	+	0.636332i
$965$	−47.6189			−1.53291
$966$	−17.5419	−	11.6475i	−0.564402	−	0.374752i
$967$			57.3317i			1.84366i	0.387589	+	0.921832i	$0.373308\pi$
$967$			57.3317i			1.84366i	−0.387589	+	0.921832i	$0.626692\pi$
$968$	−4.49171	−	10.0411i	−0.144369	−	0.322735i
$969$	0.381456	−	0.220234i	0.0122541	−	0.00707492i
$970$	24.3827	−	14.0774i	0.782881	−	0.451997i
$971$	−42.1712	−	24.3476i	−1.35334	−	0.781351i	−0.364623	−	0.931155i	$-0.618802\pi$
$971$	−42.1712	−	24.3476i	−1.35334	−	0.781351i	−0.988716	+	0.149805i	$0.952136\pi$
$972$			1.00000i			0.0320750i
$973$	−0.222649	+	3.55535i	−0.00713778	+	0.113979i
$974$		−	17.3146i		−	0.554797i
$975$	9.96565	+	5.75367i	0.319156	+	0.184265i
$976$	4.97512	+	8.61716i	0.159250	+	0.275828i
$977$	−21.1278	−	36.5945i	−0.675939	−	1.17076i	−0.976193	−	0.216902i	$-0.930405\pi$
$977$	−21.1278	−	36.5945i	−0.675939	−	1.17076i	0.300255	−	0.953859i	$-0.402928\pi$
$978$	10.3707	−	17.9626i	0.331619	−	0.574381i
$979$	5.47871	−	16.9121i	0.175100	−	0.540514i
$980$	1.56114	−	12.4156i	0.0498689	−	0.396603i
$981$			8.50535i			0.271555i
$982$	−4.22001	+	7.30927i	−0.134666	+	0.233248i
$983$	20.4533	−	11.8087i	0.652359	−	0.376639i	−0.137001	−	0.990571i	$-0.543746\pi$
$983$	20.4533	−	11.8087i	0.652359	−	0.376639i	0.789359	+	0.613931i	$0.210413\pi$
$984$	−0.0160691	−	0.0278326i	−0.000512265	−	0.000887270i
$985$	10.5259	−	18.2313i	0.335382	−	0.580899i
$986$	0.811871			0.0258553
$987$	−1.63411	+	26.0942i	−0.0520142	+	0.830586i
$988$	−26.4766			−0.842334
$989$	47.4007	+	27.3668i	1.50725	+	0.870213i
$990$	1.23777	+	5.79825i	0.0393388	+	0.184280i
$991$	−13.4870	−	23.3602i	−0.428429	−	0.742060i	0.568305	−	0.822818i	$-0.307599\pi$
$991$	−13.4870	−	23.3602i	−0.428429	−	0.742060i	−0.996734	+	0.0807577i	$0.974266\pi$
$992$	−0.639360	+	1.10740i	−0.0202997	+	0.0351601i
$993$			31.0132i			0.984173i
$994$	−12.3341	+	18.5760i	−0.391215	+	0.589196i
$995$	38.2566			1.21282
$996$	10.4492	+	6.03285i	0.331096	+	0.191158i
$997$	−11.1707	−	19.3483i	−0.353781	−	0.612766i	0.633128	−	0.774047i	$-0.281771\pi$
$997$	−11.1707	−	19.3483i	−0.353781	−	0.612766i	−0.986909	+	0.161281i	$0.948437\pi$
$998$	−16.5168	+	9.53597i	−0.522830	+	0.301856i
$999$	−3.91603	−	2.26092i	−0.123898	−	0.0715324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.p.a.439.7	yes	16
3.2	odd	2		1386.2.bk.a.901.2		16
7.2	even	3		3234.2.e.a.2155.3		16
7.3	odd	6		462.2.p.b.241.3	yes	16
7.5	odd	6		3234.2.e.b.2155.6		16
11.10	odd	2		462.2.p.b.439.3	yes	16
21.17	even	6		1386.2.bk.b.703.6		16
33.32	even	2		1386.2.bk.b.901.6		16
77.10	even	6	inner	462.2.p.a.241.7	✓	16
77.54	even	6		3234.2.e.a.2155.14		16
77.65	odd	6		3234.2.e.b.2155.11		16
231.164	odd	6		1386.2.bk.a.703.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.p.a.241.7	✓	16	77.10	even	6	inner
462.2.p.a.439.7	yes	16	1.1	even	1	trivial
462.2.p.b.241.3	yes	16	7.3	odd	6
462.2.p.b.439.3	yes	16	11.10	odd	2
1386.2.bk.a.703.2		16	231.164	odd	6
1386.2.bk.a.901.2		16	3.2	odd	2
1386.2.bk.b.703.6		16	21.17	even	6
1386.2.bk.b.901.6		16	33.32	even	2
3234.2.e.a.2155.3		16	7.2	even	3
3234.2.e.a.2155.14		16	77.54	even	6
3234.2.e.b.2155.6		16	7.5	odd	6
3234.2.e.b.2155.11		16	77.65	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.54813 + 0.893814i) q^{5} -1.00000 q^{6} +(0.165362 - 2.64058i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.54813 + 0.893814i) q^{5} -1.00000 q^{6} +(0.165362 - 2.64058i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(0.893814 + 1.54813i) q^{10} +(0.692408 + 3.24354i) q^{11} +(-0.866025 - 0.500000i) q^{12} +6.37742 q^{13} +(1.46350 - 2.20413i) q^{14} -1.78763 q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.0530476 + 0.0918811i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.07581 + 3.59541i) q^{19} +1.78763i q^{20} +(1.17708 + 2.36949i) q^{21} +(-1.02213 + 3.15519i) q^{22} +(-3.97933 + 6.89240i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.902194 - 1.56265i) q^{25} +(5.52301 + 3.18871i) q^{26} +1.00000i q^{27} +(2.36949 - 1.17708i) q^{28} -7.65230i q^{29} +(-1.54813 - 0.893814i) q^{30} +(1.10740 - 0.639360i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.22141 - 2.46279i) q^{33} +0.106095i q^{34} +(2.61619 - 3.94016i) q^{35} +1.00000 q^{36} +(-2.26092 + 3.91603i) q^{37} +(-3.59541 + 2.07581i) q^{38} +(-5.52301 + 3.18871i) q^{39} +(-0.893814 + 1.54813i) q^{40} +0.0321383 q^{41} +(-0.165362 + 2.64058i) q^{42} -6.87723i q^{43} +(-2.46279 + 2.22141i) q^{44} +(1.54813 - 0.893814i) q^{45} +(-6.89240 + 3.97933i) q^{46} +(8.55805 + 4.94099i) q^{47} -1.00000i q^{48} +(-6.94531 - 0.873304i) q^{49} -1.80439i q^{50} +(-0.0918811 - 0.0530476i) q^{51} +(3.18871 + 5.52301i) q^{52} +(0.313720 + 0.543380i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.82718 + 5.64031i) q^{55} +(2.64058 + 0.165362i) q^{56} -4.15162i q^{57} +(3.82615 - 6.62708i) q^{58} +(10.7863 - 6.22747i) q^{59} +(-0.893814 - 1.54813i) q^{60} +(4.97512 - 8.61716i) q^{61} +1.27872 q^{62} +(-2.20413 - 1.46350i) q^{63} -1.00000 q^{64} +(9.87308 + 5.70022i) q^{65} +(-0.692408 - 3.24354i) q^{66} +(-5.43609 - 9.41558i) q^{67} +(-0.0530476 + 0.0918811i) q^{68} -7.95866i q^{69} +(4.23576 - 2.10418i) q^{70} -8.42785 q^{71} +(0.866025 + 0.500000i) q^{72} +(0.0625042 + 0.108260i) q^{73} +(-3.91603 + 2.26092i) q^{74} +(1.56265 + 0.902194i) q^{75} -4.15162 q^{76} +(8.67933 - 1.29200i) q^{77} -6.37742 q^{78} +(-8.80673 - 5.08457i) q^{79} +(-1.54813 + 0.893814i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.0278326 + 0.0160691i) q^{82} -12.0657 q^{83} +(-1.46350 + 2.20413i) q^{84} +0.189659i q^{85} +(3.43862 - 5.95586i) q^{86} +(3.82615 + 6.62708i) q^{87} +(-3.24354 + 0.692408i) q^{88} +(-4.64198 - 2.68005i) q^{89} +1.78763 q^{90} +(1.05458 - 16.8401i) q^{91} -7.95866 q^{92} +(-0.639360 + 1.10740i) q^{93} +(4.94099 + 8.55805i) q^{94} +(-6.42726 + 3.71078i) q^{95} +(0.500000 - 0.866025i) q^{96} -15.7498i q^{97} +(-5.57816 - 4.22896i) q^{98} +(3.15519 + 1.02213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9	\( 16 q + 8 q^{4} + 12 q^{5} - 16 q^{6} - 6 q^{7} + 8 q^{9} + 2 q^{10} - 4 q^{11} + 8 q^{14} - 4 q^{15} - 8 q^{16} - 10 q^{19} - 4 q^{21} + 2 q^{22} - 4 q^{23} - 8 q^{24} + 10 q^{25} + 12 q^{26} - 12 q^{30} + 6 q^{31} + 2 q^{33} - 8 q^{35} + 16 q^{36} + 14 q^{37} - 12 q^{38} - 12 q^{39} - 2 q^{40} + 32 q^{41} + 6 q^{42} + 4 q^{44} + 12 q^{45} + 18 q^{46} - 24 q^{47} - 6 q^{49} + 6 q^{51} - 8 q^{54} - 14 q^{55} + 4 q^{56} - 2 q^{60} + 28 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 72 q^{65} + 4 q^{66} - 16 q^{67} - 30 q^{70} - 56 q^{71} - 44 q^{73} + 24 q^{74} - 12 q^{75} - 20 q^{76} + 32 q^{77} - 30 q^{79} - 12 q^{80} - 8 q^{81} - 12 q^{82} + 8 q^{83} - 8 q^{84} - 12 q^{86} + 4 q^{88} - 36 q^{89} + 4 q^{90} - 8 q^{91} - 8 q^{92} + 4 q^{93} + 14 q^{94} + 72 q^{95} + 8 q^{96} - 40 q^{98} - 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^5 - 16 * q^6 - 6 * q^7 + 8 * q^9 + 2 * q^10 - 4 * q^11 + 8 * q^14 - 4 * q^15 - 8 * q^16 - 10 * q^19 - 4 * q^21 + 2 * q^22 - 4 * q^23 - 8 * q^24 + 10 * q^25 + 12 * q^26 - 12 * q^30 + 6 * q^31 + 2 * q^33 - 8 * q^35 + 16 * q^36 + 14 * q^37 - 12 * q^38 - 12 * q^39 - 2 * q^40 + 32 * q^41 + 6 * q^42 + 4 * q^44 + 12 * q^45 + 18 * q^46 - 24 * q^47 - 6 * q^49 + 6 * q^51 - 8 * q^54 - 14 * q^55 + 4 * q^56 - 2 * q^60 + 28 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 72 * q^65 + 4 * q^66 - 16 * q^67 - 30 * q^70 - 56 * q^71 - 44 * q^73 + 24 * q^74 - 12 * q^75 - 20 * q^76 + 32 * q^77 - 30 * q^79 - 12 * q^80 - 8 * q^81 - 12 * q^82 + 8 * q^83 - 8 * q^84 - 12 * q^86 + 4 * q^88 - 36 * q^89 + 4 * q^90 - 8 * q^91 - 8 * q^92 + 4 * q^93 + 14 * q^94 + 72 * q^95 + 8 * q^96 - 40 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more