LMFDB - Embedded newform 630.2.cd.a.23.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(23,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 4]))

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

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

chi := DirichletCharacter("630.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.cd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.7
Character	$\chi$	$=$	630.23
Dual form			630.2.cd.a.137.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.913950 + 1.47129i) q^{3} +1.00000i q^{4} +(0.187599 + 2.22818i) q^{5} +(1.68662 - 0.394099i) q^{6} +(1.77346 - 1.96337i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.32939 - 2.68937i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.913950 + 1.47129i) q^{3} +1.00000i q^{4} +(0.187599 + 2.22818i) q^{5} +(1.68662 - 0.394099i) q^{6} +(1.77346 - 1.96337i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.32939 - 2.68937i) q^{9} +(1.44291 - 1.70822i) q^{10} +(3.93553 + 2.27218i) q^{11} +(-1.47129 - 0.913950i) q^{12} +(4.22459 - 1.13198i) q^{13} +(-2.64234 + 0.134290i) q^{14} +(-3.44976 - 1.76044i) q^{15} -1.00000 q^{16} +(0.304112 - 1.13496i) q^{17} +(-0.961652 + 2.84169i) q^{18} +(-5.35282 - 3.09045i) q^{19} +(-2.22818 + 0.187599i) q^{20} +(1.26784 + 4.40370i) q^{21} +(-1.17617 - 4.38951i) q^{22} +(7.27337 + 1.94889i) q^{23} +(0.394099 + 1.68662i) q^{24} +(-4.92961 + 0.836011i) q^{25} +(-3.78767 - 2.18681i) q^{26} +(5.17184 + 0.502033i) q^{27} +(1.96337 + 1.77346i) q^{28} +(3.13342 + 5.42724i) q^{29} +(1.19453 + 3.68417i) q^{30} -0.358961 q^{31} +(0.707107 + 0.707107i) q^{32} +(-6.93992 + 3.71365i) q^{33} +(-1.01758 + 0.587499i) q^{34} +(4.70746 + 3.58327i) q^{35} +(2.68937 - 1.32939i) q^{36} +(2.46721 + 9.20775i) q^{37} +(1.59973 + 5.97029i) q^{38} +(-2.19560 + 7.25017i) q^{39} +(1.70822 + 1.44291i) q^{40} +(-8.04851 - 4.64681i) q^{41} +(2.21739 - 4.01038i) q^{42} +(-2.19596 + 8.19545i) q^{43} +(-2.27218 + 3.93553i) q^{44} +(5.74302 - 3.46665i) q^{45} +(-3.76497 - 6.52113i) q^{46} +(2.15351 + 2.15351i) q^{47} +(0.913950 - 1.47129i) q^{48} +(-0.709677 - 6.96393i) q^{49} +(4.07691 + 2.89461i) q^{50} +(1.39191 + 1.48474i) q^{51} +(1.13198 + 4.22459i) q^{52} +(0.0705647 + 0.0189078i) q^{53} +(-3.30205 - 4.01204i) q^{54} +(-4.32453 + 9.19535i) q^{55} +(-0.134290 - 2.64234i) q^{56} +(9.43915 - 5.05103i) q^{57} +(1.62198 - 6.05330i) q^{58} +8.50788 q^{59} +(1.76044 - 3.44976i) q^{60} -5.89163 q^{61} +(0.253824 + 0.253824i) q^{62} +(-7.63786 - 2.15940i) q^{63} -1.00000i q^{64} +(3.31478 + 9.20082i) q^{65} +(7.53321 + 2.28131i) q^{66} +(6.76808 - 6.76808i) q^{67} +(1.13496 + 0.304112i) q^{68} +(-9.51489 + 8.92005i) q^{69} +(-0.794923 - 5.86243i) q^{70} +13.2021i q^{71} +(-2.84169 - 0.961652i) q^{72} +(2.45665 - 9.16835i) q^{73} +(4.76628 - 8.25544i) q^{74} +(3.27541 - 8.01696i) q^{75} +(3.09045 - 5.35282i) q^{76} +(11.4406 - 3.69730i) q^{77} +(6.67917 - 3.57412i) q^{78} -5.26884i q^{79} +(-0.187599 - 2.22818i) q^{80} +(-5.46544 + 7.15045i) q^{81} +(2.40536 + 8.97694i) q^{82} +(3.57191 + 0.957089i) q^{83} +(-4.40370 + 1.26784i) q^{84} +(2.58596 + 0.464700i) q^{85} +(7.34784 - 4.24228i) q^{86} +(-10.8488 - 0.350059i) q^{87} +(4.38951 - 1.17617i) q^{88} +(-2.74487 + 4.75426i) q^{89} +(-6.51222 - 1.60964i) q^{90} +(5.26966 - 10.3020i) q^{91} +(-1.94889 + 7.27337i) q^{92} +(0.328073 - 0.528136i) q^{93} -3.04553i q^{94} +(5.88191 - 12.5068i) q^{95} +(-1.68662 + 0.394099i) q^{96} +(-3.37208 - 0.903546i) q^{97} +(-4.42243 + 5.42606i) q^{98} +(0.878880 - 13.6047i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{6}+O(q^{10}) $ 192 * q + 8 * q^6	$ 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.913950	+	1.47129i	−0.527669	+	0.849450i
$3$	−0.913950	+	1.47129i	−0.527669	+	0.849450i
$4$			1.00000i			0.500000i
$5$	0.187599	+	2.22818i	0.0838969	+	0.996474i
$5$	0.187599	+	2.22818i	0.0838969	+	0.996474i
$6$	1.68662	−	0.394099i	0.688560	−	0.160890i
$7$	1.77346	−	1.96337i	0.670305	−	0.742086i
$7$	1.77346	−	1.96337i	0.670305	−	0.742086i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.32939	−	2.68937i	−0.443130	−	0.896457i
$10$	1.44291	−	1.70822i	0.456289	−	0.540186i
$11$	3.93553	+	2.27218i	1.18661	+	0.685088i	0.957534	−	0.288321i	$-0.0930971\pi$
$11$	3.93553	+	2.27218i	1.18661	+	0.685088i	0.229073	+	0.973409i	$0.426430\pi$
$12$	−1.47129	−	0.913950i	−0.424725	−	0.263835i
$13$	4.22459	−	1.13198i	1.17169	−	0.313954i	0.380065	−	0.924960i	$-0.375901\pi$
$13$	4.22459	−	1.13198i	1.17169	−	0.313954i	0.791626	+	0.611006i	$0.209235\pi$
$14$	−2.64234	+	0.134290i	−0.706195	+	0.0358904i
$15$	−3.44976	−	1.76044i	−0.890725	−	0.454543i
$16$	−1.00000			−0.250000
$17$	0.304112	−	1.13496i	0.0737580	−	0.275269i	−0.919191	−	0.393812i	$-0.871156\pi$
$17$	0.304112	−	1.13496i	0.0737580	−	0.275269i	0.992949	+	0.118544i	$0.0378226\pi$
$18$	−0.961652	+	2.84169i	−0.226664	+	0.669794i
$19$	−5.35282	−	3.09045i	−1.22802	−	0.708998i	−0.261405	−	0.965229i	$-0.584186\pi$
$19$	−5.35282	−	3.09045i	−1.22802	−	0.708998i	−0.966615	+	0.256232i	$0.917519\pi$
$20$	−2.22818	+	0.187599i	−0.498237	+	0.0419484i
$21$	1.26784	+	4.40370i	0.276665	+	0.960966i
$22$	−1.17617	−	4.38951i	−0.250760	−	0.935848i
$23$	7.27337	+	1.94889i	1.51660	+	0.406373i	0.918622	−	0.395138i	$-0.129303\pi$
$23$	7.27337	+	1.94889i	1.51660	+	0.406373i	0.597981	+	0.801510i	$0.295970\pi$
$24$	0.394099	+	1.68662i	0.0804451	+	0.344280i
$25$	−4.92961	+	0.836011i	−0.985923	+	0.167202i
$26$	−3.78767	−	2.18681i	−0.742823	−	0.428869i
$27$	5.17184	+	0.502033i	0.995322	+	0.0966163i
$28$	1.96337	+	1.77346i	0.371043	+	0.335152i
$29$	3.13342	+	5.42724i	0.581861	+	1.00781i	0.995259	+	0.0972625i	$0.0310086\pi$
$29$	3.13342	+	5.42724i	0.581861	+	1.00781i	−0.413398	+	0.910551i	$0.635658\pi$
$30$	1.19453	+	3.68417i	0.218091	+	0.672634i
$31$	−0.358961			−0.0644714			−0.0322357	−	0.999480i	$-0.510263\pi$
$31$	−0.358961			−0.0644714			−0.0322357	+	0.999480i	$0.510263\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−6.93992	+	3.71365i	−1.20808	+	0.646463i
$34$	−1.01758	+	0.587499i	−0.174513	+	0.100755i
$35$	4.70746	+	3.58327i	0.795706	+	0.605683i
$36$	2.68937	−	1.32939i	0.448229	−	0.221565i
$37$	2.46721	+	9.20775i	0.405607	+	1.51374i	0.802934	+	0.596068i	$0.203271\pi$
$37$	2.46721	+	9.20775i	0.405607	+	1.51374i	−0.397328	+	0.917677i	$0.630062\pi$
$38$	1.59973	+	5.97029i	0.259511	+	0.968509i
$39$	−2.19560	+	7.25017i	−0.351578	+	1.16096i
$40$	1.70822	+	1.44291i	0.270093	+	0.228144i
$41$	−8.04851	−	4.64681i	−1.25697	−	0.725709i	−0.284482	−	0.958681i	$-0.591822\pi$
$41$	−8.04851	−	4.64681i	−1.25697	−	0.725709i	−0.972483	+	0.232972i	$0.925155\pi$
$42$	2.21739	−	4.01038i	0.342151	−	0.618816i
$43$	−2.19596	+	8.19545i	−0.334881	+	1.24979i	0.569116	+	0.822257i	$0.307285\pi$
$43$	−2.19596	+	8.19545i	−0.334881	+	1.24979i	−0.903998	+	0.427537i	$0.859381\pi$
$44$	−2.27218	+	3.93553i	−0.342544	+	0.593304i
$45$	5.74302	−	3.46665i	0.856120	−	0.516778i
$46$	−3.76497	−	6.52113i	−0.555115	−	0.961488i
$47$	2.15351	+	2.15351i	0.314122	+	0.314122i	0.846504	−	0.532382i	$-0.178703\pi$
$47$	2.15351	+	2.15351i	0.314122	+	0.314122i	−0.532382	+	0.846504i	$0.678703\pi$
$48$	0.913950	−	1.47129i	0.131917	−	0.212362i
$49$	−0.709677	−	6.96393i	−0.101382	−	0.994848i
$50$	4.07691	+	2.89461i	0.576562	+	0.409360i
$51$	1.39191	+	1.48474i	0.194907	+	0.207905i
$52$	1.13198	+	4.22459i	0.156977	+	0.585846i
$53$	0.0705647	+	0.0189078i	0.00969281	+	0.00259718i	0.263662	−	0.964615i	$-0.415070\pi$
$53$	0.0705647	+	0.0189078i	0.00969281	+	0.00259718i	−0.253969	+	0.967212i	$0.581736\pi$
$54$	−3.30205	−	4.01204i	−0.449353	−	0.545969i
$55$	−4.32453	+	9.19535i	−0.583120	+	1.23990i
$56$	−0.134290	−	2.64234i	−0.0179452	−	0.353098i
$57$	9.43915	−	5.05103i	1.25025	−	0.669025i
$58$	1.62198	−	6.05330i	0.212976	−	0.794837i
$59$	8.50788			1.10763			0.553816	−	0.832639i	$-0.313171\pi$
$59$	8.50788			1.10763			0.553816	+	0.832639i	$0.313171\pi$
$60$	1.76044	−	3.44976i	0.227271	−	0.445362i
$61$	−5.89163			−0.754346			−0.377173	−	0.926143i	$-0.623104\pi$
$61$	−5.89163			−0.754346			−0.377173	+	0.926143i	$0.623104\pi$
$62$	0.253824	+	0.253824i	0.0322357	+	0.0322357i
$63$	−7.63786	−	2.15940i	−0.962280	−	0.272059i
$64$		−	1.00000i		−	0.125000i
$65$	3.31478	+	9.20082i	0.411148	+	1.14122i
$66$	7.53321	+	2.28131i	0.927274	+	0.280810i
$67$	6.76808	−	6.76808i	0.826853	−	0.826853i	−0.160227	−	0.987080i	$-0.551223\pi$
$67$	6.76808	−	6.76808i	0.826853	−	0.826853i	0.987080	+	0.160227i	$0.0512226\pi$
$68$	1.13496	+	0.304112i	0.137634	+	0.0368790i
$69$	−9.51489	+	8.92005i	−1.14546	+	1.07385i
$70$	−0.794923	−	5.86243i	−0.0950114	−	0.700695i
$71$			13.2021i			1.56680i	0.621520	+	0.783398i	$0.286515\pi$
$71$			13.2021i			1.56680i	−0.621520	+	0.783398i	$0.713485\pi$
$72$	−2.84169	−	0.961652i	−0.334897	−	0.113332i
$73$	2.45665	−	9.16835i	0.287529	−	1.07307i	−0.659442	−	0.751756i	$-0.729207\pi$
$73$	2.45665	−	9.16835i	0.287529	−	1.07307i	0.946971	−	0.321319i	$-0.104126\pi$
$74$	4.76628	−	8.25544i	0.554069	−	0.959675i
$75$	3.27541	−	8.01696i	0.378211	−	0.925719i
$76$	3.09045	−	5.35282i	0.354499	−	0.614010i
$77$	11.4406	−	3.69730i	1.30378	−	0.421346i
$78$	6.67917	−	3.57412i	0.756267	−	0.404690i
$79$		−	5.26884i		−	0.592791i	−0.955065	−	0.296395i	$-0.904215\pi$
$79$		−	5.26884i		−	0.592791i	0.955065	−	0.296395i	$-0.0957846\pi$
$80$	−0.187599	−	2.22818i	−0.0209742	−	0.249119i
$81$	−5.46544	+	7.15045i	−0.607271	+	0.794494i
$82$	2.40536	+	8.97694i	0.265628	+	0.991338i
$83$	3.57191	+	0.957089i	0.392068	+	0.105054i	0.449467	−	0.893297i	$-0.351614\pi$
$83$	3.57191	+	0.957089i	0.392068	+	0.105054i	−0.0573990	+	0.998351i	$0.518281\pi$
$84$	−4.40370	+	1.26784i	−0.480483	+	0.138333i
$85$	2.58596	+	0.464700i	0.280486	+	0.0504038i
$86$	7.34784	−	4.24228i	0.792338	−	0.457457i
$87$	−10.8488	−	0.350059i	−1.16312	−	0.0375302i
$88$	4.38951	−	1.17617i	0.467924	−	0.125380i
$89$	−2.74487	+	4.75426i	−0.290956	+	0.503951i	−0.974036	−	0.226393i	$-0.927307\pi$
$89$	−2.74487	+	4.75426i	−0.290956	+	0.503951i	0.683080	+	0.730344i	$0.260640\pi$
$90$	−6.51222	−	1.60964i	−0.686449	−	0.169671i
$91$	5.26966	−	10.3020i	0.552410	−	1.07994i
$92$	−1.94889	+	7.27337i	−0.203186	+	0.758301i
$93$	0.328073	−	0.528136i	0.0340196	−	0.0547652i
$94$		−	3.04553i		−	0.314122i
$95$	5.88191	−	12.5068i	0.603471	−	1.28317i
$96$	−1.68662	+	0.394099i	−0.172140	+	0.0402226i
$97$	−3.37208	−	0.903546i	−0.342383	−	0.0917412i	0.0835303	−	0.996505i	$-0.473380\pi$
$97$	−3.37208	−	0.903546i	−0.342383	−	0.0917412i	−0.425913	+	0.904764i	$0.640047\pi$
$98$	−4.42243	+	5.42606i	−0.446733	+	0.548115i
$99$	0.878880	−	13.6047i	0.0883308	−	1.36733i
$100$	−0.836011	−	4.92961i	−0.0836011	−	0.492961i
$101$	−8.23544	−	4.75473i	−0.819457	−	0.473114i	0.0307724	−	0.999526i	$-0.490203\pi$
$101$	−8.23544	−	4.75473i	−0.819457	−	0.473114i	−0.850229	+	0.526413i	$0.823537\pi$
$102$	0.0656341	−	2.03410i	0.00649875	−	0.201406i
$103$	0.796349	−	2.97201i	0.0784666	−	0.292841i	−0.915530	−	0.402249i	$-0.868229\pi$
$103$	0.796349	−	2.97201i	0.0784666	−	0.292841i	0.993997	+	0.109408i	$0.0348954\pi$
$104$	2.18681	−	3.78767i	0.214434	−	0.371411i
$105$	−9.57441	+	3.65111i	−0.934367	+	0.356312i
$106$	−0.0365270	−	0.0632666i	−0.00354782	−	0.00614500i
$107$	−13.1662	+	3.52788i	−1.27283	+	0.341053i	−0.831113	−	0.556104i	$-0.812296\pi$
$107$	−13.1662	+	3.52788i	−1.27283	+	0.341053i	−0.441713	+	0.897156i	$0.645629\pi$
$108$	−0.502033	+	5.17184i	−0.0483081	+	0.497661i
$109$	0.421534	−	0.243373i	0.0403756	−	0.0233109i	−0.479676	−	0.877446i	$-0.659246\pi$
$109$	0.421534	−	0.243373i	0.0403756	−	0.0233109i	0.520052	+	0.854135i	$0.325913\pi$
$110$	9.56000	−	3.44419i	0.911510	−	0.328390i
$111$	−15.8022	−	4.78544i	−1.49988	−	0.454214i
$112$	−1.77346	+	1.96337i	−0.167576	+	0.185521i
$113$	0.762725	+	2.84653i	0.0717511	+	0.267779i	0.992477	−	0.122431i	$-0.0390691\pi$
$113$	0.762725	+	2.84653i	0.0717511	+	0.267779i	−0.920726	+	0.390210i	$0.872402\pi$
$114$	−10.2461	−	3.10287i	−0.959636	−	0.290611i
$115$	−2.97802	+	16.5720i	−0.277702	+	1.54535i
$116$	−5.42724	+	3.13342i	−0.503907	+	0.290931i
$117$	−8.66044	−	9.85667i	−0.800658	−	0.911249i
$118$	−6.01598	−	6.01598i	−0.553816	−	0.553816i
$119$	−1.68902	−	2.60990i	−0.154833	−	0.239249i
$120$	−3.68417	+	1.19453i	−0.336317	+	0.109046i
$121$	4.82560	+	8.35819i	0.438691	+	0.759835i
$122$	4.16601	+	4.16601i	0.377173	+	0.377173i
$123$	14.1927	−	7.59474i	1.27972	−	0.684795i
$124$		−	0.358961i		−	0.0322357i
$125$	−2.78758	−	10.8273i	−0.249329	−	0.968419i
$126$	3.87386	+	6.92771i	0.345111	+	0.617170i
$127$	8.13579	−	8.13579i	0.721935	−	0.721935i	−0.247064	−	0.968999i	$-0.579466\pi$
$127$	8.13579	−	8.13579i	0.721935	−	0.721935i	0.968999	+	0.247064i	$0.0794659\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−10.0509	−	10.7211i	−0.884931	−	0.943943i
$130$	4.16206	−	8.84987i	0.365036	−	0.776185i
$131$	−8.06148	+	4.65430i	−0.704335	+	0.406648i	−0.808960	−	0.587864i	$-0.799969\pi$
$131$	−8.06148	+	4.65430i	−0.704335	+	0.406648i	0.104625	+	0.994512i	$0.466636\pi$
$132$	−3.71365	−	6.93992i	−0.323232	−	0.604042i
$133$	−15.5607	+	5.02879i	−1.34928	+	0.436051i
$134$	−9.57152			−0.826853
$135$	−0.148389	+	11.6180i	−0.0127713	+	0.999918i
$136$	−0.587499	−	1.01758i	−0.0503777	−	0.0872567i
$137$	−17.9769	+	4.81689i	−1.53587	+	0.411535i	−0.924929	−	0.380141i	$-0.875876\pi$
$137$	−17.9769	+	4.81689i	−1.53587	+	0.411535i	−0.610941	+	0.791676i	$0.709209\pi$
$138$	13.0355	+	0.420615i	1.10965	+	0.0358051i
$139$	14.1952	+	8.19559i	1.20402	+	0.695141i	0.961446	−	0.274992i	$-0.0886754\pi$
$139$	14.1952	+	8.19559i	1.20402	+	0.695141i	0.242573	+	0.970133i	$0.422009\pi$
$140$	−3.58327	+	4.70746i	−0.302842	+	0.397853i
$141$	−5.13665	+	1.20024i	−0.432584	+	0.101078i
$142$	9.33527	−	9.33527i	0.783398	−	0.783398i
$143$	19.1981	+	5.14411i	1.60542	+	0.430172i
$144$	1.32939	+	2.68937i	0.110783	+	0.224114i
$145$	−11.5051	+	7.99998i	−0.955444	+	0.664362i
$146$	−8.22012	+	4.74589i	−0.680302	+	0.392772i
$147$	10.8946	+	5.32055i	0.898570	+	0.438831i
$148$	−9.20775	+	2.46721i	−0.756872	+	0.202803i
$149$	−2.24301	−	3.88501i	−0.183754	−	0.318272i	0.759402	−	0.650622i	$-0.225492\pi$
$149$	−2.24301	−	3.88501i	−0.183754	−	0.318272i	−0.943156	+	0.332350i	$0.892158\pi$
$150$	−7.98491	+	3.35279i	−0.651965	+	0.273754i
$151$	0.594012	−	1.02886i	0.0483400	−	0.0837273i	−0.840843	−	0.541279i	$-0.817940\pi$
$151$	0.594012	−	1.02886i	0.0483400	−	0.0837273i	0.889183	+	0.457552i	$0.151274\pi$
$152$	−5.97029	+	1.59973i	−0.484254	+	0.129756i
$153$	−3.45662	+	0.690937i	−0.279451	+	0.0558589i
$154$	−10.7041	−	5.47537i	−0.862565	−	0.441218i
$155$	−0.0673408	−	0.799832i	−0.00540895	−	0.0642441i
$156$	−7.25017	−	2.19560i	−0.580479	−	0.175789i
$157$	3.09903	−	3.09903i	0.247329	−	0.247329i	−0.572545	−	0.819874i	$-0.694044\pi$
$157$	3.09903	−	3.09903i	0.247329	−	0.247329i	0.819874	+	0.572545i	$0.194044\pi$
$158$	−3.72563	+	3.72563i	−0.296395	+	0.296395i
$159$	−0.0923115	+	0.0865405i	−0.00732077	+	0.00686310i
$160$	−1.44291	+	1.70822i	−0.114072	+	0.135046i
$161$	16.7254	−	10.8241i	1.31815	−	0.853056i
$162$	8.92078	−	1.19148i	0.700883	−	0.0936115i
$163$	17.1899	−	4.60602i	1.34642	−	0.360771i	0.487606	−	0.873064i	$-0.337870\pi$
$163$	17.1899	−	4.60602i	1.34642	−	0.360771i	0.858811	+	0.512293i	$0.171204\pi$
$164$	4.64681	−	8.04851i	0.362855	−	0.628483i
$165$	−9.57662	−	14.7667i	−0.745539	−	1.14959i
$166$	−1.84895	−	3.20248i	−0.143507	−	0.248561i
$167$	12.4613	−	3.33901i	0.964287	−	0.258380i	0.257873	−	0.966179i	$-0.416978\pi$
$167$	12.4613	−	3.33901i	0.964287	−	0.258380i	0.706414	+	0.707799i	$0.250312\pi$
$168$	4.01038	+	2.21739i	0.309408	+	0.171075i
$169$	5.30750	−	3.06428i	0.408269	−	0.235714i
$170$	−1.49995	−	2.15714i	−0.115041	−	0.165445i
$171$	−1.19539	+	18.5041i	−0.0914135	+	1.41505i
$172$	−8.19545	−	2.19596i	−0.624897	−	0.167441i
$173$	10.8173	−	10.8173i	0.822426	−	0.822426i	−0.164029	−	0.986456i	$-0.552449\pi$
$173$	10.8173	−	10.8173i	0.822426	−	0.822426i	0.986456	+	0.164029i	$0.0524491\pi$
$174$	7.42375	+	7.91881i	0.562793	+	0.600324i
$175$	−7.10107	+	11.1613i	−0.536791	+	0.843716i
$176$	−3.93553	−	2.27218i	−0.296652	−	0.171272i
$177$	−7.77578	+	12.5176i	−0.584463	+	0.940877i
$178$	5.30269	−	1.42085i	0.397453	−	0.106497i
$179$	−5.38279	−	9.32327i	−0.402329	−	0.696854i	0.591678	−	0.806175i	$-0.298466\pi$
$179$	−5.38279	−	9.32327i	−0.402329	−	0.696854i	−0.994007	+	0.109321i	$0.965132\pi$
$180$	3.46665	+	5.74302i	0.258389	+	0.428060i
$181$	0.210492			0.0156458			0.00782288	−	0.999969i	$-0.497510\pi$
$181$	0.210492			0.0156458			0.00782288	+	0.999969i	$0.497510\pi$
$182$	−11.0108	+	3.55839i	−0.816175	+	0.263765i
$183$	5.38466	−	8.66830i	0.398045	−	0.640779i
$184$	6.52113	−	3.76497i	0.480744	−	0.277558i
$185$	−20.0537	+	7.22476i	−1.47438	+	0.531175i
$186$	−0.605431	+	0.141466i	−0.0443924	+	0.0103728i
$187$	3.77568	−	3.77568i	0.276105	−	0.276105i
$188$	−2.15351	+	2.15351i	−0.157061	+	0.157061i
$189$	10.1577	−	9.26393i	0.738867	−	0.673852i
$190$	−13.0028	+	4.68452i	−0.943322	+	0.339851i
$191$			21.6280i			1.56495i	0.622685	+	0.782473i	$0.286042\pi$
$191$			21.6280i			1.56495i	−0.622685	+	0.782473i	$0.713958\pi$
$192$	1.47129	+	0.913950i	0.106181	+	0.0659587i
$193$	−15.2559	−	15.2559i	−1.09815	−	1.09815i	−0.994627	−	0.103520i	$-0.966989\pi$
$193$	−15.2559	−	15.2559i	−1.09815	−	1.09815i	−0.103520	−	0.994627i	$-0.533011\pi$
$194$	1.74552	+	3.02332i	0.125321	+	0.217062i
$195$	−16.5666	−	3.53208i	−1.18636	−	0.252938i
$196$	6.96393	−	0.709677i	0.497424	−	0.0506912i
$197$	−3.69607	−	3.69607i	−0.263334	−	0.263334i	0.563073	−	0.826407i	$-0.309619\pi$
$197$	−3.69607	−	3.69607i	−0.263334	−	0.263334i	−0.826407	+	0.563073i	$0.809619\pi$
$198$	−10.2415	+	8.99853i	−0.727828	+	0.639498i
$199$	3.82151	−	2.20635i	0.270900	−	0.156404i	−0.358397	−	0.933569i	$-0.616677\pi$
$199$	3.82151	−	2.20635i	0.270900	−	0.156404i	0.629296	+	0.777165i	$0.283343\pi$
$200$	−2.89461	+	4.07691i	−0.204680	+	0.288281i
$201$	3.77213	+	16.1435i	0.266065	+	1.13868i
$202$	2.46123	+	9.18544i	0.173172	+	0.646285i
$203$	16.2127	+	3.47292i	1.13791	+	0.243751i
$204$	−1.48474	+	1.39191i	−0.103952	+	0.0974535i
$205$	8.84405	−	18.8053i	0.617695	−	1.31342i
$206$	−2.66463	+	1.53843i	−0.185654	+	0.107187i
$207$	−4.42785	−	22.1516i	−0.307757	−	1.53965i
$208$	−4.22459	+	1.13198i	−0.292923	+	0.0784885i
$209$	−14.0441	−	24.3251i	−0.971452	−	1.68260i
$210$	9.35186	+	4.18841i	0.645339	+	0.289028i
$211$	7.09284	−	12.2852i	0.488291	−	0.845745i	−0.511618	−	0.859213i	$-0.670954\pi$
$211$	7.09284	−	12.2852i	0.488291	−	0.845745i	0.999909	+	0.0134680i	$0.00428714\pi$
$212$	−0.0189078	+	0.0705647i	−0.00129859	+	0.00484641i
$213$	−19.4241	−	12.0660i	−1.33091	−	0.826750i
$214$	11.8045	+	6.81534i	0.806940	+	0.465887i
$215$	−18.6729	−	3.35555i	−1.27348	−	0.228847i
$216$	4.01204	−	3.30205i	0.272984	−	0.224676i
$217$	−0.636604	+	0.704776i	−0.0432155	+	0.0478433i
$218$	−0.470160	−	0.125979i	−0.0318433	−	0.00853238i
$219$	11.2440	+	11.9939i	0.759802	+	0.810470i
$220$	−9.19535	−	4.32453i	−0.619950	−	0.291560i
$221$		−	5.13900i		−	0.345687i
$222$	7.79001	+	14.5576i	0.522831	+	0.977045i
$223$	0.613728	−	2.29046i	0.0410982	−	0.153381i	−0.942327	−	0.334692i	$-0.891368\pi$
$223$	0.613728	−	2.29046i	0.0410982	−	0.153381i	0.983426	+	0.181312i	$0.0580343\pi$
$224$	2.64234	−	0.134290i	0.176549	−	0.00897260i
$225$	8.80172	+	12.1462i	0.586782	+	0.809745i
$226$	1.47347	−	2.55213i	0.0980139	−	0.169765i
$227$	−0.531375	+	0.142382i	−0.0352686	+	0.00945019i	−0.276410	−	0.961040i	$-0.589145\pi$
$227$	−0.531375	+	0.142382i	−0.0352686	+	0.00945019i	0.241142	+	0.970490i	$0.422478\pi$
$228$	5.05103	+	9.43915i	0.334513	+	0.625123i
$229$	−17.0459	+	9.84143i	−1.12642	+	0.650340i	−0.943033	−	0.332700i	$-0.892040\pi$
$229$	−17.0459	+	9.84143i	−1.12642	+	0.650340i	−0.183389	+	0.983040i	$0.558707\pi$
$230$	13.8240	−	9.61242i	0.911526	−	0.633824i
$231$	−5.01638	+	20.2117i	−0.330054	+	1.32983i
$232$	6.05330	+	1.62198i	0.397419	+	0.106488i
$233$	1.56548	+	5.84244i	0.102558	+	0.382751i	0.998057	−	0.0623128i	$-0.0198476\pi$
$233$	1.56548	+	5.84244i	0.102558	+	0.382751i	−0.895499	+	0.445064i	$0.853181\pi$
$234$	−0.845859	+	13.0936i	−0.0552956	+	0.855954i
$235$	−4.39443	+	5.20242i	−0.286661	+	0.339369i
$236$			8.50788i			0.553816i
$237$	7.75199	+	4.81546i	0.503546	+	0.312798i
$238$	−0.651154	+	3.03979i	−0.0422081	+	0.197041i
$239$	10.1819	−	17.6355i	0.658610	−	1.14075i	−0.322365	−	0.946615i	$-0.604478\pi$
$239$	10.1819	−	17.6355i	0.658610	−	1.14075i	0.980976	−	0.194131i	$-0.0621888\pi$
$240$	3.44976	+	1.76044i	0.222681	+	0.113636i
$241$	4.74276	−	8.21469i	0.305508	−	0.529155i	−0.671866	−	0.740672i	$-0.734507\pi$
$241$	4.74276	−	8.21469i	0.305508	−	0.529155i	0.977374	+	0.211517i	$0.0678405\pi$
$242$	2.49792	−	9.32235i	0.160572	−	0.599263i
$243$	−5.52525	−	14.5764i	−0.354445	−	0.935077i
$244$		−	5.89163i		−	0.377173i
$245$	15.3838	−	2.88772i	0.982834	−	0.184490i
$246$	−15.4061	−	4.66549i	−0.982255	−	0.297461i
$247$	−26.1118	−	6.99663i	−1.66145	−	0.445185i
$248$	−0.253824	+	0.253824i	−0.0161178	+	0.0161178i
$249$	−4.67270	+	4.38058i	−0.296120	+	0.277608i
$250$	−5.68491	+	9.62714i	−0.359545	+	0.608874i
$251$		−	12.4751i		−	0.787419i	−0.919235	−	0.393710i	$-0.871192\pi$
$251$		−	12.4751i		−	0.787419i	0.919235	−	0.393710i	$-0.128808\pi$
$252$	2.15940	−	7.63786i	0.136030	−	0.481140i
$253$	24.1963	+	24.1963i	1.52121	+	1.52121i
$254$	−11.5057			−0.721935
$255$	−3.04714	+	3.37998i	−0.190819	+	0.211662i
$256$	1.00000			0.0625000
$257$	2.83403	−	10.5768i	0.176782	−	0.659760i	−0.819459	−	0.573138i	$-0.805726\pi$
$257$	2.83403	−	10.5768i	0.176782	−	0.659760i	0.996241	−	0.0866223i	$-0.0276073\pi$
$258$	−0.473938	+	14.6880i	−0.0295061	+	0.914437i
$259$	22.4538	+	11.4855i	1.39521	+	0.713676i
$260$	−9.20082	+	3.31478i	−0.570611	+	0.205574i
$261$	10.4303	−	15.6418i	0.645621	−	0.968206i
$262$	8.99141	+	2.40924i	0.555491	+	0.148843i
$263$	2.21106	+	8.25180i	0.136340	+	0.508828i	0.999989	+	0.00473372i	$0.00150680\pi$
$263$	2.21106	+	8.25180i	0.136340	+	0.508828i	−0.863649	+	0.504094i	$0.831827\pi$
$264$	−2.28131	+	7.53321i	−0.140405	+	0.463637i
$265$	−0.0288921	+	0.160778i	−0.00177483	+	0.00987653i
$266$	14.5590	+	7.44719i	0.892668	+	0.456617i
$267$	−4.48622	−	8.38366i	−0.274552	−	0.513072i
$268$	6.76808	+	6.76808i	0.413427	+	0.413427i
$269$	−1.89941	−	3.28987i	−0.115809	−	0.200587i	0.802294	−	0.596929i	$-0.203613\pi$
$269$	−1.89941	−	3.28987i	−0.115809	−	0.200587i	−0.918103	+	0.396342i	$0.870279\pi$
$270$	8.32009	−	8.11024i	0.506345	−	0.493574i
$271$	−9.26483	+	16.0472i	−0.562798	+	0.974795i	0.434452	+	0.900695i	$0.356942\pi$
$271$	−9.26483	+	16.0472i	−0.562798	+	0.974795i	−0.997251	+	0.0741005i	$0.976391\pi$
$272$	−0.304112	+	1.13496i	−0.0184395	+	0.0688172i
$273$	10.3410	+	17.1687i	0.625865	+	1.03910i
$274$	16.1176	+	9.30553i	0.973702	+	0.562167i
$275$	−21.3002	−	7.91082i	−1.28445	−	0.477040i
$276$	−8.92005	−	9.51489i	−0.536924	−	0.572729i
$277$	−5.13308	−	19.1569i	−0.308417	−	1.15103i	−0.929964	−	0.367651i	$-0.880162\pi$
$277$	−5.13308	−	19.1569i	−0.308417	−	1.15103i	0.621547	−	0.783377i	$-0.286504\pi$
$278$	−4.24235	−	15.8327i	−0.254439	−	0.949580i
$279$	0.477200	+	0.965381i	0.0285692	+	0.0577958i
$280$	5.86243	−	0.794923i	0.350347	−	0.0475057i
$281$	10.0568	−	5.80629i	0.599938	−	0.346374i	−0.169079	−	0.985602i	$-0.554079\pi$
$281$	10.0568	−	5.80629i	0.599938	−	0.346374i	0.769017	+	0.639228i	$0.220746\pi$
$282$	4.48085	+	2.78346i	0.266831	+	0.165753i
$283$	18.3438	+	18.3438i	1.09042	+	1.09042i	0.995483	+	0.0949410i	$0.0302663\pi$
$283$	18.3438	+	18.3438i	1.09042	+	1.09042i	0.0949410	+	0.995483i	$0.469734\pi$
$284$	−13.2021			−0.783398
$285$	13.0254	+	20.0846i	0.771558	+	1.18971i
$286$	−9.93766	−	17.2125i	−0.587626	−	1.01780i
$287$	−23.3971	+	7.56130i	−1.38109	+	0.446330i
$288$	0.961652	−	2.84169i	0.0566659	−	0.167448i
$289$	13.5268	+	7.80969i	0.795693	+	0.459393i
$290$	13.7922	+	2.47847i	0.809903	+	0.145541i
$291$	4.41129	−	4.13551i	0.258595	−	0.242428i
$292$	9.16835	+	2.45665i	0.536537	+	0.143765i
$293$	1.79568	+	6.70156i	0.104905	+	0.391510i	0.998334	−	0.0576935i	$-0.0183746\pi$
$293$	1.79568	+	6.70156i	0.104905	+	0.391510i	−0.893430	+	0.449203i	$0.851708\pi$
$294$	−3.94143	−	11.4658i	−0.229869	−	0.668700i
$295$	1.59607	+	18.9571i	0.0929268	+	1.10373i
$296$	8.25544	+	4.76628i	0.479838	+	0.277034i
$297$	19.2132	+	13.7271i	1.11487	+	0.796529i
$298$	−1.16107	+	4.33316i	−0.0672588	+	0.251013i
$299$	32.9331			1.90457
$300$	8.01696	+	3.27541i	0.462860	+	0.189106i
$301$	12.1963	+	18.8458i	0.702982	+	1.08625i
$302$	−1.14754	+	0.307483i	−0.0660337	+	0.0176937i
$303$	14.5224	−	7.77113i	0.834288	−	0.446440i
$304$	5.35282	+	3.09045i	0.307005	+	0.177249i
$305$	−1.10526	−	13.1276i	−0.0632873	−	0.751687i
$306$	2.93276	+	1.95563i	0.167655	+	0.111796i
$307$	6.86513	−	6.86513i	0.391814	−	0.391814i	−0.483520	−	0.875333i	$-0.660642\pi$
$307$	6.86513	−	6.86513i	0.391814	−	0.391814i	0.875333	+	0.483520i	$0.160642\pi$
$308$	3.69730	+	11.4406i	0.210673	+	0.651891i
$309$	3.64487	+	3.88793i	0.207349	+	0.221177i
$310$	−0.517950	+	0.613184i	−0.0294176	+	0.0348265i
$311$		−	0.941850i		−	0.0534074i	−0.999643	−	0.0267037i	$-0.991499\pi$
$311$		−	0.941850i		−	0.0534074i	0.999643	−	0.0267037i	$-0.00850106\pi$
$312$	3.57412	+	6.67917i	0.202345	+	0.378134i
$313$	−11.8339	−	11.8339i	−0.668890	−	0.668890i	0.288569	−	0.957459i	$-0.406820\pi$
$313$	−11.8339	−	11.8339i	−0.668890	−	0.668890i	−0.957459	+	0.288569i	$0.906820\pi$
$314$	−4.38268			−0.247329
$315$	3.37869	−	17.4237i	0.190368	−	0.981713i
$316$	5.26884			0.296395
$317$	−8.55250	−	8.55250i	−0.480356	−	0.480356i	0.424889	−	0.905245i	$-0.360313\pi$
$317$	−8.55250	−	8.55250i	−0.480356	−	0.480356i	−0.905245	+	0.424889i	$0.860313\pi$
$318$	0.126467	+	0.00408071i	0.00709194	+	0.000228835i
$319$			28.4788i			1.59450i
$320$	2.22818	−	0.187599i	0.124559	−	0.0104871i
$321$	6.84273	−	22.5956i	0.381924	−	1.26117i
$322$	−19.4804	−	4.17291i	−1.08560	−	0.232547i
$323$	−5.13540	+	5.13540i	−0.285741	+	0.285741i
$324$	−7.15045	−	5.46544i	−0.397247	−	0.303636i
$325$	−19.8793	+	9.11201i	−1.10270	+	0.505444i
$326$	−15.4120	−	8.89815i	−0.853594	−	0.492823i
$327$	−0.0271891	+	0.842629i	−0.00150356	+	0.0465975i
$328$	−8.97694	+	2.40536i	−0.495669	+	0.132814i
$329$	8.04732	−	0.408982i	0.443663	−	0.0225479i
$330$	−3.66997	+	17.2134i	−0.202025	+	0.947564i
$331$	−18.1440			−0.997285			−0.498643	−	0.866808i	$-0.666168\pi$
$331$	−18.1440			−0.997285			−0.498643	+	0.866808i	$0.666168\pi$
$332$	−0.957089	+	3.57191i	−0.0525271	+	0.196034i
$333$	21.4832	−	18.8759i	1.17727	−	1.03439i
$334$	−11.1725	−	6.45046i	−0.611334	−	0.352954i
$335$	16.3502	+	13.8109i	0.893308	+	0.754568i
$336$	−1.26784	−	4.40370i	−0.0691663	−	0.240242i
$337$	−3.01532	−	11.2533i	−0.164255	−	0.613007i	−0.998134	−	0.0610603i	$-0.980552\pi$
$337$	−3.01532	−	11.2533i	−0.164255	−	0.613007i	0.833879	−	0.551947i	$-0.186115\pi$
$338$	−5.91974	−	1.58619i	−0.321992	−	0.0862774i
$339$	−4.88516	−	1.47940i	−0.265326	−	0.0803497i
$340$	−0.464700	+	2.58596i	−0.0252019	+	0.140243i
$341$	−1.41270	−	0.815625i	−0.0765022	−	0.0441686i
$342$	13.9297	−	12.2391i	0.753230	−	0.661816i
$343$	−14.9314	−	10.9569i	−0.806219	−	0.591617i
$344$	4.24228	+	7.34784i	0.228728	+	0.396169i
$345$	−21.6605	−	19.5275i	−1.16616	−	1.05133i
$346$	−15.2980			−0.822426
$347$	−5.91862	−	5.91862i	−0.317728	−	0.317728i	0.530166	−	0.847894i	$-0.322130\pi$
$347$	−5.91862	−	5.91862i	−0.317728	−	0.317728i	−0.847894	+	0.530166i	$0.822130\pi$
$348$	0.350059	−	10.8488i	0.0187651	−	0.581559i
$349$	−13.2937	+	7.67509i	−0.711593	+	0.410838i	−0.811651	−	0.584143i	$-0.801431\pi$
$349$	−13.2937	+	7.67509i	−0.711593	+	0.410838i	0.100058	+	0.994982i	$0.468097\pi$
$350$	12.9135	−	2.87102i	0.690253	−	0.153463i
$351$	22.4172	−	3.73352i	1.19654	−	0.199281i
$352$	1.17617	+	4.38951i	0.0626899	+	0.233962i
$353$	4.36332	+	16.2841i	0.232236	+	0.866717i	0.979375	+	0.202049i	$0.0647602\pi$
$353$	4.36332	+	16.2841i	0.232236	+	0.866717i	−0.747139	+	0.664668i	$0.768573\pi$
$354$	14.3496	−	3.35295i	0.762670	−	0.178207i
$355$	−29.4166	+	2.47669i	−1.56127	+	0.131449i
$356$	−4.75426	−	2.74487i	−0.251975	−	0.145478i
$357$	5.38360	−	0.0997304i	0.284930	−	0.00527829i
$358$	−2.78634	+	10.3988i	−0.147263	+	0.549591i
$359$	14.1397	−	24.4907i	0.746264	−	1.29257i	−0.203337	−	0.979109i	$-0.565179\pi$
$359$	14.1397	−	24.4907i	0.746264	−	1.29257i	0.949602	−	0.313459i	$-0.101488\pi$
$360$	1.60964	−	6.51222i	0.0848355	−	0.343224i
$361$	9.60175	+	16.6307i	0.505355	+	0.875301i
$362$	−0.148840	−	0.148840i	−0.00782288	−	0.00782288i
$363$	−16.7077	−	0.539106i	−0.876926	−	0.0282957i
$364$	10.3020	+	5.26966i	0.539970	+	0.276205i
$365$	20.8896	+	3.75390i	1.09341	+	0.196488i
$366$	−9.93694	+	2.32189i	−0.519412	+	0.121367i
$367$	−5.08813	−	18.9891i	−0.265598	−	0.991225i	−0.961883	−	0.273460i	$-0.911832\pi$
$367$	−5.08813	−	18.9891i	−0.265598	−	0.991225i	0.696285	−	0.717765i	$-0.254835\pi$
$368$	−7.27337	−	1.94889i	−0.379151	−	0.101593i
$369$	−1.79739	+	27.8229i	−0.0935682	+	1.44840i
$370$	19.2888	+	9.07144i	1.00278	+	0.471602i
$371$	0.162267	−	0.105013i	0.00842447	−	0.00545199i
$372$	0.528136	+	0.328073i	0.0273826	+	0.0170098i
$373$	1.39402	−	5.20254i	0.0721794	−	0.269377i	−0.920400	−	0.390979i	$-0.872136\pi$
$373$	1.39402	−	5.20254i	0.0721794	−	0.269377i	0.992579	+	0.121602i	$0.0388031\pi$
$374$	−5.33962			−0.276105
$375$	18.4777	+	5.79423i	0.954186	+	0.299213i
$376$	3.04553			0.157061
$377$	19.3809	+	19.3809i	0.998169	+	0.998169i
$378$	−13.7332	−	0.632018i	−0.706359	−	0.0325075i
$379$		−	19.4353i		−	0.998326i	−0.866508	−	0.499163i	$-0.833641\pi$
$379$		−	19.4353i		−	0.998326i	0.866508	−	0.499163i	$-0.166359\pi$
$380$	12.5068	+	5.88191i	0.641587	+	0.301736i
$381$	4.53440	+	19.4058i	0.232305	+	0.994190i
$382$	15.2933	−	15.2933i	0.782473	−	0.782473i
$383$	−13.8998	−	3.72445i	−0.710249	−	0.190311i	−0.114432	−	0.993431i	$-0.536505\pi$
$383$	−13.8998	−	3.72445i	−0.710249	−	0.190311i	−0.595817	+	0.803121i	$0.703171\pi$
$384$	−0.394099	−	1.68662i	−0.0201113	−	0.0860700i
$385$	10.3845	+	24.7983i	0.529244	+	1.26384i
$386$			21.5752i			1.09815i
$387$	24.9599	−	4.98919i	1.26878	−	0.253615i
$388$	0.903546	−	3.37208i	0.0458706	−	0.171191i
$389$	3.14536	−	5.44791i	0.159476	−	0.276220i	−0.775204	−	0.631711i	$-0.782353\pi$
$389$	3.14536	−	5.44791i	0.159476	−	0.276220i	0.934680	+	0.355491i	$0.115686\pi$
$390$	9.21681	+	14.2119i	0.466711	+	0.719649i
$391$	4.42384	−	7.66232i	0.223723	−	0.387500i
$392$	−5.42606	−	4.42243i	−0.274058	−	0.223366i
$393$	0.519968	−	16.1146i	0.0262289	−	0.812872i
$394$			5.22703i			0.263334i
$395$	11.7399	−	0.988430i	0.590701	−	0.0497333i
$396$	13.6047	+	0.878880i	0.683663	+	0.0441654i
$397$	4.00301	+	14.9394i	0.200905	+	0.749788i	0.990659	+	0.136364i	$0.0435417\pi$
$397$	4.00301	+	14.9394i	0.200905	+	0.749788i	−0.789754	+	0.613424i	$0.789792\pi$
$398$	−4.26234	−	1.14209i	−0.213652	−	0.0572478i
$399$	6.82291	−	27.4904i	0.341572	−	1.37624i
$400$	4.92961	−	0.836011i	0.246481	−	0.0418005i
$401$	−5.27255	+	3.04411i	−0.263299	+	0.152015i	−0.625838	−	0.779953i	$-0.715243\pi$
$401$	−5.27255	+	3.04411i	−0.263299	+	0.152015i	0.362540	+	0.931968i	$0.381910\pi$
$402$	8.74789	−	14.0825i	0.436305	−	0.702370i
$403$	−1.51647	+	0.406336i	−0.0755406	+	0.0202410i
$404$	4.75473	−	8.23544i	0.236557	−	0.409728i
$405$	−16.9578	−	10.8366i	−0.842642	−	0.538475i
$406$	−9.00838	−	13.9198i	−0.447078	−	0.690830i
$407$	−11.2119	+	41.8433i	−0.555752	+	2.07410i
$408$	2.03410	+	0.0656341i	0.100703	+	0.00324937i
$409$		−	1.69471i		−	0.0837981i	−0.999122	−	0.0418991i	$-0.986659\pi$
$409$		−	1.69471i		−	0.0837981i	0.999122	−	0.0418991i	$-0.0133408\pi$
$410$	−19.5510	+	7.04366i	−0.965557	+	0.347862i
$411$	9.34294	−	30.8516i	0.460853	−	1.52180i
$412$	2.97201	+	0.796349i	0.146421	+	0.0392333i
$413$	15.0884	−	16.7042i	0.742451	−	0.821958i
$414$	−12.5326	+	18.7945i	−0.615944	+	0.923701i
$415$	−1.46249	+	8.13841i	−0.0717906	+	0.399499i
$416$	3.78767	+	2.18681i	0.185706	+	0.107217i
$417$	−25.0318	+	13.3949i	−1.22581	+	0.655949i
$418$	−7.26977	+	27.1311i	−0.355576	+	1.32703i
$419$	2.28863	−	3.96402i	0.111807	−	0.193655i	−0.804692	−	0.593693i	$-0.797670\pi$
$419$	2.28863	−	3.96402i	0.111807	−	0.193655i	0.916499	+	0.400037i	$0.131003\pi$
$420$	−3.65111	−	9.57441i	−0.178156	−	0.467184i
$421$	5.63946	+	9.76784i	0.274851	+	0.476055i	0.970097	−	0.242716i	$-0.0780383\pi$
$421$	5.63946	+	9.76784i	0.274851	+	0.476055i	−0.695247	+	0.718771i	$0.744705\pi$
$422$	−13.7023	+	3.67152i	−0.667018	+	0.178727i
$423$	2.92874	−	8.65446i	0.142400	−	0.420794i
$424$	0.0632666	−	0.0365270i	0.00307250	−	0.00177391i
$425$	−0.550315	+	5.84916i	−0.0266942	+	0.283726i
$426$	5.20292	+	22.2669i	0.252082	+	1.07883i
$427$	−10.4486	+	11.5675i	−0.505642	+	0.559790i
$428$	−3.52788	−	13.1662i	−0.170526	−	0.636413i
$429$	−25.1146	+	23.5445i	−1.21254	+	1.13674i
$430$	10.8310	+	15.5765i	0.522318	+	0.751165i
$431$	−1.92684	+	1.11246i	−0.0928126	+	0.0535854i	−0.545688	−	0.837988i	$-0.683732\pi$
$431$	−1.92684	+	1.11246i	−0.0928126	+	0.0535854i	0.452875	+	0.891574i	$0.350398\pi$
$432$	−5.17184	−	0.502033i	−0.248830	−	0.0241541i
$433$	21.7168	+	21.7168i	1.04364	+	1.04364i	0.999003	+	0.0446415i	$0.0142146\pi$
$433$	21.7168	+	21.7168i	1.04364	+	1.04364i	0.0446415	+	0.999003i	$0.485785\pi$
$434$	0.948498	−	0.0482048i	0.0455294	−	0.00231390i
$435$	−1.25524	−	24.2389i	−0.0601840	−	1.16217i
$436$	0.243373	+	0.421534i	0.0116554	+	0.0201878i
$437$	−32.9101	−	32.9101i	−1.57430	−	1.57430i
$438$	0.530200	−	16.4317i	0.0253339	−	0.785136i
$439$		−	14.3639i		−	0.685553i	−0.939417	−	0.342776i	$-0.888633\pi$
$439$		−	14.3639i		−	0.685553i	0.939417	−	0.342776i	$-0.111367\pi$
$440$	3.44419	+	9.56000i	0.164195	+	0.455755i
$441$	−17.7852	+	11.1664i	−0.846913	+	0.531732i
$442$	−3.63382	+	3.63382i	−0.172843	+	0.172843i
$443$	−6.74697	+	6.74697i	−0.320558	+	0.320558i	−0.848981	−	0.528423i	$-0.822784\pi$
$443$	−6.74697	+	6.74697i	−0.320558	+	0.320558i	0.528423	+	0.848981i	$0.322784\pi$
$444$	4.78544	−	15.8022i	0.227107	−	0.749938i
$445$	−11.1083	−	5.22419i	−0.526584	−	0.247650i
$446$	−2.05357	+	1.18563i	−0.0972395	+	0.0561412i
$447$	7.76597	+	0.250584i	0.367318	+	0.0118522i
$448$	−1.96337	−	1.77346i	−0.0927607	−	0.0837881i
$449$	−40.8669			−1.92863			−0.964313	−	0.264764i	$-0.914706\pi$
$449$	−40.8669			−1.92863			−0.964313	+	0.264764i	$0.914706\pi$
$450$	2.36489	−	14.8124i	0.111482	−	0.698263i
$451$	−21.1168	−	36.5753i	−0.994350	−	1.72226i
$452$	−2.84653	+	0.762725i	−0.133889	+	0.0358756i
$453$	0.970853	+	1.81429i	0.0456146	+	0.0852427i
$454$	0.476418	+	0.275060i	0.0223594	+	0.0129092i
$455$	23.9433	+	9.80913i	1.12248	+	0.459859i
$456$	3.10287	−	10.2461i	0.145305	−	0.479818i
$457$	−16.4449	+	16.4449i	−0.769259	+	0.769259i	−0.977976	−	0.208717i	$-0.933071\pi$
$457$	−16.4449	+	16.4449i	−0.769259	+	0.769259i	0.208717	+	0.977976i	$0.433071\pi$
$458$	19.0122	+	5.09430i	0.888381	+	0.238041i
$459$	2.14261	−	5.71717i	0.100008	−	0.266855i
$460$	−16.5720	−	2.97802i	−0.772675	−	0.138851i
$461$	−15.9837	+	9.22818i	−0.744434	+	0.429799i	−0.823679	−	0.567056i	$-0.808082\pi$
$461$	−15.9837	+	9.22818i	−0.744434	+	0.429799i	0.0792453	+	0.996855i	$0.474749\pi$
$462$	17.8389	−	10.7447i	0.829942	−	0.499888i
$463$	17.9673	−	4.81433i	0.835012	−	0.223741i	0.184113	−	0.982905i	$-0.441059\pi$
$463$	17.9673	−	4.81433i	0.835012	−	0.223741i	0.650899	+	0.759164i	$0.274392\pi$
$464$	−3.13342	−	5.42724i	−0.145465	−	0.251953i
$465$	1.23833	+	0.631929i	0.0574263	+	0.0293050i
$466$	3.02427	−	5.23819i	0.140097	−	0.242654i
$467$	−2.83925	+	0.760775i	−0.131385	+	0.0352045i	−0.323912	−	0.946087i	$-0.604998\pi$
$467$	−2.83925	+	0.760775i	−0.131385	+	0.0352045i	0.192527	+	0.981292i	$0.438332\pi$
$468$	9.85667	−	8.66044i	0.455625	−	0.400329i
$469$	−1.28535	−	25.2912i	−0.0593521	−	1.16784i
$470$	6.78600	−	0.571338i	0.313015	−	0.0263539i
$471$	1.72721	+	7.39192i	0.0795857	+	0.340602i
$472$	6.01598	−	6.01598i	0.276908	−	0.276908i
$473$	−27.2638	+	27.2638i	−1.25359	+	1.25359i
$474$	−2.07644	−	8.88653i	−0.0953743	−	0.408172i
$475$	28.9710	+	10.7597i	1.32928	+	0.493689i
$476$	2.60990	−	1.68902i	0.119624	−	0.0774163i
$477$	−0.0429581	−	0.214911i	−0.00196691	−	0.00984008i
$478$	−19.6699	+	5.27052i	−0.899679	+	0.241068i
$479$	0.117676	−	0.203821i	0.00537676	−	0.00931282i	−0.863325	−	0.504649i	$-0.831622\pi$
$479$	0.117676	−	0.203821i	0.00537676	−	0.00931282i	0.868701	+	0.495336i	$0.164955\pi$
$480$	−1.19453	−	3.68417i	−0.0545228	−	0.168158i
$481$	20.8459	+	36.1062i	0.950492	+	1.64630i
$482$	−9.16230	+	2.45503i	−0.417331	+	0.111824i
$483$	0.639120	+	34.5006i	0.0290810	+	1.56983i
$484$	−8.35819	+	4.82560i	−0.379918	+	0.219346i
$485$	1.38067	−	7.68312i	0.0626929	−	0.348873i
$486$	−6.40014	+	14.2140i	−0.290316	+	0.644761i
$487$	−14.6577	−	3.92751i	−0.664202	−	0.177973i	−0.0890606	−	0.996026i	$-0.528386\pi$
$487$	−14.6577	−	3.92751i	−0.664202	−	0.177973i	−0.575142	+	0.818054i	$0.695053\pi$
$488$	−4.16601	+	4.16601i	−0.188587	+	0.188587i
$489$	−8.93392	+	29.5010i	−0.404006	+	1.33408i
$490$	−12.9199	−	8.83606i	−0.583662	−	0.399172i
$491$	−2.37876	−	1.37337i	−0.107352	−	0.0619795i	0.445363	−	0.895350i	$-0.353075\pi$
$491$	−2.37876	−	1.37337i	−0.107352	−	0.0619795i	−0.552715	+	0.833371i	$0.686408\pi$
$492$	7.59474	+	14.1927i	0.342397	+	0.639858i
$493$	7.11262	−	1.90582i	0.320336	−	0.0858338i
$494$	13.5165	+	23.4112i	0.608134	+	1.05332i
$495$	30.4787	−	0.593926i	1.36992	−	0.0266950i
$496$	0.358961			0.0161178
$497$	25.9206	+	23.4133i	1.16270	+	1.05023i
$498$	6.40163	+	0.206561i	0.286864	+	0.00925622i
$499$	−30.0413	+	17.3443i	−1.34483	+	0.776439i	−0.987512	−	0.157543i	$-0.949643\pi$
$499$	−30.0413	+	17.3443i	−1.34483	+	0.776439i	−0.357320	+	0.933982i	$0.616309\pi$
$500$	10.8273	−	2.78758i	0.484209	−	0.124664i
$501$	−6.47640	+	21.3859i	−0.289344	+	0.955453i
$502$	−8.82121	+	8.82121i	−0.393710	+	0.393710i
$503$	−23.1452	+	23.1452i	−1.03199	+	1.03199i	−0.0325210	+	0.999471i	$0.510354\pi$
$503$	−23.1452	+	23.1452i	−1.03199	+	1.03199i	−0.999471	+	0.0325210i	$0.989646\pi$
$504$	−6.92771	+	3.87386i	−0.308585	+	0.172555i
$505$	9.04946	−	19.2421i	0.402696	−	0.856260i
$506$		−	34.2188i		−	1.52121i
$507$	−0.342335	+	10.6095i	−0.0152036	+	0.471183i
$508$	8.13579	+	8.13579i	0.360967	+	0.360967i
$509$	−18.7316	−	32.4440i	−0.830262	−	1.43806i	−0.897830	−	0.440341i	$-0.854857\pi$
$509$	−18.7316	−	32.4440i	−0.830262	−	1.43806i	0.0675684	−	0.997715i	$-0.478476\pi$
$510$	4.54466	−	0.235350i	0.201241	−	0.0104215i
$511$	−13.6441	−	21.0830i	−0.603581	−	0.932659i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−26.1324	−	18.6706i	−1.15377	−	0.824327i
$514$	−9.48286	+	5.47493i	−0.418271	+	0.241489i
$515$	6.77159	+	1.21686i	0.298392	+	0.0536215i
$516$	10.7211	−	10.0509i	0.471972	−	0.442466i
$517$	3.58205	+	13.3684i	0.157538	+	0.587941i
$518$	−7.75571	−	23.9987i	−0.340766	−	1.05444i
$519$	6.02893	+	25.8019i	0.264641	+	1.13258i
$520$	8.84987	+	4.16206i	0.388092	+	0.182518i
$521$	−28.8826	+	16.6754i	−1.26537	+	0.730562i	−0.974109	−	0.226081i	$-0.927409\pi$
$521$	−28.8826	+	16.6754i	−1.26537	+	0.730562i	−0.291263	+	0.956643i	$0.594075\pi$
$522$	−18.4358	+	3.68510i	−0.806914	+	0.161292i
$523$	−39.0426	+	10.4614i	−1.70722	+	0.457447i	−0.974739	−	0.223346i	$-0.928302\pi$
$523$	−39.0426	+	10.4614i	−1.70722	+	0.457447i	−0.732476	+	0.680793i	$0.761635\pi$
$524$	−4.65430	−	8.06148i	−0.203324	−	0.352167i
$525$	−9.93150	−	20.6486i	−0.433446	−	0.901179i
$526$	4.27144	−	7.39836i	0.186244	−	0.322584i
$527$	−0.109164	+	0.407407i	−0.00475528	+	0.0177469i
$528$	6.93992	−	3.71365i	0.302021	−	0.161616i
$529$	29.1852	+	16.8501i	1.26892	+	0.732612i
$530$	0.134117	−	0.0932576i	0.00582568	−	0.00405085i
$531$	−11.3103	−	22.8809i	−0.490825	−	0.992944i
$532$	−5.02879	−	15.5607i	−0.218026	−	0.674642i
$533$	−39.2618	−	10.5202i	−1.70062	−	0.455679i
$534$	−2.75591	+	9.10038i	−0.119260	+	0.393812i
$535$	−10.3307	−	28.6749i	−0.446637	−	1.23973i
$536$		−	9.57152i		−	0.413427i
$537$	18.6368	+	0.601354i	0.804239	+	0.0259503i
$538$	−0.983206	+	3.66937i	−0.0423890	+	0.158198i
$539$	13.0304	−	29.0193i	0.561257	−	1.24995i
$540$	−11.6180	−	0.148389i	−0.499959	−	0.00638563i
$541$	15.8159	−	27.3939i	0.679977	−	1.17776i	−0.295010	−	0.955494i	$-0.595323\pi$
$541$	15.8159	−	27.3939i	0.679977	−	1.17776i	0.974987	−	0.222261i	$-0.0713438\pi$
$542$	17.8983	−	4.79583i	0.768797	−	0.205998i
$543$	−0.192379	+	0.309695i	−0.00825579	+	0.0132903i
$544$	1.01758	−	0.587499i	0.0436283	−	0.0251888i
$545$	0.621359	+	0.893599i	0.0266161	+	0.0382776i
$546$	4.82791	−	19.4523i	0.206615	−	0.832481i
$547$	−20.4222	−	5.47211i	−0.873190	−	0.233971i	−0.205723	−	0.978610i	$-0.565955\pi$
$547$	−20.4222	−	5.47211i	−0.873190	−	0.233971i	−0.667467	+	0.744640i	$0.732621\pi$
$548$	−4.81689	−	17.9769i	−0.205768	−	0.767935i
$549$	7.83228	+	15.8448i	0.334274	+	0.676239i
$550$	9.46773	+	20.6553i	0.403705	+	0.880746i
$551$		−	38.7347i		−	1.65015i
$552$	−0.420615	+	13.0355i	−0.0179025	+	0.554826i
$553$	−10.3447	−	9.34408i	−0.439902	−	0.397351i
$554$	−9.91635	+	17.1756i	−0.421305	+	0.729722i
$555$	7.69837	−	36.1079i	0.326778	−	1.53270i
$556$	−8.19559	+	14.1952i	−0.347570	+	0.602010i
$557$	0.450534	−	1.68142i	0.0190898	−	0.0712439i	−0.955724	−	0.294265i	$-0.904925\pi$
$557$	0.450534	−	1.68142i	0.0190898	−	0.0712439i	0.974814	+	0.223021i	$0.0715919\pi$
$558$	0.345196	−	1.02006i	0.0146133	−	0.0431825i
$559$			37.1082i			1.56951i
$560$	−4.70746	−	3.58327i	−0.198926	−	0.151421i
$561$	2.10434	+	9.00590i	0.0888452	+	0.380230i
$562$	−11.2169	−	3.00556i	−0.473156	−	0.126782i
$563$	−9.75124	+	9.75124i	−0.410966	+	0.410966i	−0.882075	−	0.471109i	$-0.843854\pi$
$563$	−9.75124	+	9.75124i	−0.410966	+	0.410966i	0.471109	+	0.882075i	$0.343854\pi$
$564$	−1.20024	−	5.13665i	−0.0505392	−	0.216292i
$565$	−6.19950	+	2.23350i	−0.260815	+	0.0939640i
$566$		−	25.9420i		−	1.09042i
$567$	4.34626	+	23.4117i	0.182526	+	0.983201i
$568$	9.33527	+	9.33527i	0.391699	+	0.391699i
$569$	16.6912			0.699731			0.349866	−	0.936800i	$-0.386227\pi$
$569$	16.6912			0.699731			0.349866	+	0.936800i	$0.386227\pi$
$570$	4.99161	−	23.4123i	0.209076	−	0.980634i
$571$	20.3215			0.850428			0.425214	−	0.905093i	$-0.360199\pi$
$571$	20.3215			0.850428			0.425214	+	0.905093i	$0.360199\pi$
$572$	−5.14411	+	19.1981i	−0.215086	+	0.802712i
$573$	−31.8210	−	19.7669i	−1.32934	−	0.825774i
$574$	21.8909	+	11.1976i	0.913709	+	0.467380i
$575$	−37.4842	−	3.52668i	−1.56320	−	0.147073i
$576$	−2.68937	+	1.32939i	−0.112057	+	0.0553913i
$577$	20.5594	+	5.50888i	0.855900	+	0.229338i	0.659981	−	0.751282i	$-0.270564\pi$
$577$	20.5594	+	5.50888i	0.855900	+	0.229338i	0.195919	+	0.980620i	$0.437231\pi$
$578$	−4.04259	−	15.0872i	−0.168150	−	0.627543i
$579$	36.3891	−	8.50275i	1.51228	−	0.353362i
$580$	−7.99998	−	11.5051i	−0.332181	−	0.477722i
$581$	8.21376	−	5.31563i	0.340764	−	0.220529i
$582$	−6.04350	−	0.195005i	−0.250511	−	0.00808323i
$583$	0.234748	+	0.234748i	0.00972226	+	0.00972226i
$584$	−4.74589	−	8.22012i	−0.196386	−	0.340151i
$585$	20.3378	−	21.1462i	0.840864	−	0.874286i
$586$	3.46898	−	6.00846i	0.143302	−	0.248207i
$587$	−0.793359	+	2.96086i	−0.0327455	+	0.122208i	−0.980364	−	0.197197i	$-0.936816\pi$
$587$	−0.793359	+	2.96086i	−0.0327455	+	0.122208i	0.947618	+	0.319405i	$0.103483\pi$
$588$	−5.32055	+	10.8946i	−0.219416	+	0.449285i
$589$	1.92145	+	1.10935i	0.0791721	+	0.0457101i
$590$	12.2761	−	14.5333i	0.505400	−	0.598327i
$591$	8.81601	−	2.05997i	0.362642	−	0.0847357i
$592$	−2.46721	−	9.20775i	−0.101402	−	0.378436i
$593$	−6.34257	−	23.6708i	−0.260458	−	0.972042i	−0.964972	−	0.262352i	$-0.915502\pi$
$593$	−6.34257	−	23.6708i	−0.260458	−	0.972042i	0.704514	−	0.709690i	$-0.251165\pi$
$594$	−3.87927	−	23.2924i	−0.159168	−	0.955697i
$595$	5.49847	−	4.25307i	0.225415	−	0.174359i
$596$	3.88501	−	2.24301i	0.159136	−	0.0918772i
$597$	−0.246488	+	7.63904i	−0.0100881	+	0.312645i
$598$	−23.2873	−	23.2873i	−0.952287	−	0.952287i
$599$	29.8865			1.22113			0.610565	−	0.791966i	$-0.290942\pi$
$599$	29.8865			1.22113			0.610565	+	0.791966i	$0.290942\pi$
$600$	−3.35279	−	7.98491i	−0.136877	−	0.325983i
$601$	0.0345488	+	0.0598402i	0.00140927	+	0.00244093i	0.866729	−	0.498779i	$-0.166218\pi$
$601$	0.0345488	+	0.0598402i	0.00140927	+	0.00244093i	−0.865320	+	0.501220i	$0.832885\pi$
$602$	4.70192	−	21.9501i	0.191636	−	0.894618i
$603$	−27.1993	−	9.20447i	−1.10764	−	0.374835i
$604$	1.02886	+	0.594012i	0.0418637	+	0.0241700i
$605$	−17.7183	+	12.3203i	−0.720352	+	0.500892i
$606$	−15.7639	−	4.77385i	−0.640364	−	0.193924i
$607$	−36.4335	−	9.76233i	−1.47879	−	0.396241i	−0.572855	−	0.819657i	$-0.694164\pi$
$607$	−36.4335	−	9.76233i	−1.47879	−	0.396241i	−0.905935	+	0.423416i	$0.860831\pi$
$608$	−1.59973	−	5.97029i	−0.0648778	−	0.242127i
$609$	−19.9273	+	20.6795i	−0.807494	+	0.837976i
$610$	−8.50111	+	10.0642i	−0.344200	+	0.407487i
$611$	11.5354	+	6.65999i	0.466674	+	0.269434i
$612$	−0.690937	−	3.45662i	−0.0279295	−	0.139725i
$613$	9.75789	−	36.4169i	0.394117	−	1.47087i	−0.429161	−	0.903228i	$-0.641191\pi$
$613$	9.75789	−	36.4169i	0.394117	−	1.47087i	0.823278	−	0.567638i	$-0.192143\pi$
$614$	−9.70876			−0.391814
$615$	19.5850	+	30.1993i	0.789745	+	1.21775i
$616$	5.47537	−	10.7041i	0.220609	−	0.431282i
$617$	20.1462	−	5.39816i	0.811056	−	0.217322i	0.170624	−	0.985336i	$-0.445422\pi$
$617$	20.1462	−	5.39816i	0.811056	−	0.217322i	0.640433	+	0.768014i	$0.278755\pi$
$618$	0.171870	−	5.32650i	0.00691361	−	0.214263i
$619$	−27.1475	−	15.6736i	−1.09115	−	0.629977i	−0.157269	−	0.987556i	$-0.550269\pi$
$619$	−27.1475	−	15.6736i	−1.09115	−	0.629977i	−0.933883	+	0.357579i	$0.883602\pi$
$620$	0.799832	−	0.0673408i	0.0321220	−	0.00270447i
$621$	36.6383	+	13.7308i	1.47025	+	0.551000i
$622$	−0.665989	+	0.665989i	−0.0267037	+	0.0267037i
$623$	4.46647	+	13.8207i	0.178945	+	0.553715i
$624$	2.19560	−	7.25017i	0.0878944	−	0.290239i
$625$	23.6022	−	8.24242i	0.944087	−	0.329697i
$626$			16.7356i			0.668890i
$627$	48.6249	+	1.56898i	1.94189	+	0.0626589i
$628$	3.09903	+	3.09903i	0.123665	+	0.123665i
$629$	11.2007			0.446603
$630$	−14.7095	+	9.93130i	−0.586040	+	0.395673i
$631$	1.35271			0.0538504			0.0269252	−	0.999637i	$-0.491428\pi$
$631$	1.35271			0.0538504			0.0269252	+	0.999637i	$0.491428\pi$
$632$	−3.72563	−	3.72563i	−0.148198	−	0.148198i
$633$	11.5925	+	21.6636i	0.460762	+	0.861052i
$634$			12.0951i			0.480356i
$635$	19.6543	+	16.6018i	0.779958	+	0.658821i
$636$	−0.0865405	−	0.0923115i	−0.00343155	−	0.00366039i
$637$	−10.8811	−	28.6165i	−0.431125	−	1.13383i
$638$	20.1375	−	20.1375i	0.797252	−	0.797252i
$639$	35.5052	−	17.5507i	1.40457	−	0.694295i
$640$	−1.70822	−	1.44291i	−0.0675232	−	0.0570361i
$641$	−26.0320	−	15.0296i	−1.02820	−	0.593632i	−0.111732	−	0.993738i	$-0.535640\pi$
$641$	−26.0320	−	15.0296i	−1.02820	−	0.593632i	−0.916469	+	0.400107i	$0.868973\pi$
$642$	−20.8161	+	11.1390i	−0.821545	+	0.439621i
$643$	−36.7798	+	9.85511i	−1.45045	+	0.388648i	−0.896181	−	0.443688i	$-0.853670\pi$
$643$	−36.7798	+	9.85511i	−1.45045	+	0.388648i	−0.554272	+	0.832336i	$0.687003\pi$
$644$	10.8241	+	16.7254i	0.426528	+	0.659075i
$645$	22.0031	−	24.4065i	0.866372	−	0.961005i
$646$	7.26255			0.285741
$647$	−7.64948	+	28.5483i	−0.300732	+	1.12235i	0.635825	+	0.771833i	$0.280660\pi$
$647$	−7.64948	+	28.5483i	−0.300732	+	1.12235i	−0.936557	+	0.350515i	$0.886007\pi$
$648$	1.19148	+	8.92078i	0.0468057	+	0.350441i
$649$	33.4830	+	19.3314i	1.31432	+	0.758825i
$650$	20.4999	+	7.61360i	0.804074	+	0.298630i
$651$	−0.455105	−	1.58076i	−0.0178370	−	0.0619548i
$652$	4.60602	+	17.1899i	0.180386	+	0.673208i
$653$	26.6274	+	7.13480i	1.04201	+	0.279206i	0.738947	−	0.673764i	$-0.235323\pi$
$653$	26.6274	+	7.13480i	1.04201	+	0.279206i	0.303065	+	0.952970i	$0.401990\pi$
$654$	0.615055	−	0.576603i	0.0240505	−	0.0225470i
$655$	−11.8830	−	17.0893i	−0.464306	−	0.667735i
$656$	8.04851	+	4.64681i	0.314241	+	0.181427i
$657$	−27.9230	+	5.58147i	−1.08938	+	0.217754i
$658$	−5.97951	−	5.40112i	−0.233106	−	0.210558i
$659$	−16.0689	−	27.8321i	−0.625954	−	1.08418i	−0.988356	−	0.152162i	$-0.951377\pi$
$659$	−16.0689	−	27.8321i	−0.625954	−	1.08418i	0.362402	−	0.932022i	$-0.381957\pi$
$660$	14.7667	−	9.57662i	0.574794	−	0.372769i
$661$	7.17196			0.278957			0.139479	−	0.990225i	$-0.455457\pi$
$661$	7.17196			0.278957			0.139479	+	0.990225i	$0.455457\pi$
$662$	12.8298	+	12.8298i	0.498643	+	0.498643i
$663$	7.56096	+	4.69679i	0.293643	+	0.182408i
$664$	3.20248	−	1.84895i	0.124280	−	0.0717534i
$665$	−14.1242	−	33.7287i	−0.547715	−	1.30794i
$666$	−28.5382	−	1.84360i	−1.10583	−	0.0714380i
$667$	12.2134	+	45.5810i	0.472905	+	1.76490i
$668$	3.33901	+	12.4613i	0.129190	+	0.482144i
$669$	2.80902	+	2.99634i	0.108603	+	0.115845i
$670$	−1.79561	−	21.3271i	−0.0693704	−	0.823938i
$671$	−23.1867	−	13.3868i	−0.895113	−	0.516794i
$672$	−2.21739	+	4.01038i	−0.0855376	+	0.154704i
$673$	11.7689	−	43.9221i	0.453658	−	1.69307i	−0.238346	−	0.971180i	$-0.576605\pi$
$673$	11.7689	−	43.9221i	0.453658	−	1.69307i	0.692004	−	0.721894i	$-0.256728\pi$
$674$	−5.82514	+	10.0894i	−0.224376	+	0.388631i
$675$	−25.9149	+	1.84889i	−0.997465	+	0.0711638i
$676$	3.06428	+	5.30750i	0.117857	+	0.204134i
$677$	−7.30344	−	7.30344i	−0.280694	−	0.280694i	0.552692	−	0.833386i	$-0.313601\pi$
$677$	−7.30344	−	7.30344i	−0.280694	−	0.280694i	−0.833386	+	0.552692i	$0.813601\pi$
$678$	2.40824	+	4.50042i	0.0924879	+	0.172838i
$679$	−7.75425	+	5.01825i	−0.297581	+	0.192583i
$680$	2.15714	−	1.49995i	0.0827225	−	0.0575206i
$681$	0.276166	−	0.911937i	0.0105827	−	0.0349455i
$682$	0.422199	+	1.57567i	0.0161668	+	0.0603354i
$683$	−3.02083	−	0.809428i	−0.115589	−	0.0309719i	0.200561	−	0.979681i	$-0.435724\pi$
$683$	−3.02083	−	0.809428i	−0.115589	−	0.0309719i	−0.316150	+	0.948709i	$0.602390\pi$
$684$	−18.5041	−	1.19539i	−0.707523	−	0.0457068i
$685$	−14.1054	−	39.1522i	−0.538939	−	1.49593i
$686$	2.81039	+	18.3058i	0.107301	+	0.698918i
$687$	1.09946	−	34.0740i	0.0419471	−	1.30000i
$688$	2.19596	−	8.19545i	0.0837204	−	0.312449i
$689$	0.319511			0.0121724
$690$	1.50824	+	29.1243i	0.0574175	+	1.10874i
$691$	30.8285			1.17277			0.586386	−	0.810032i	$-0.300550\pi$
$691$	30.8285			1.17277			0.586386	+	0.810032i	$0.300550\pi$
$692$	10.8173	+	10.8173i	0.411213	+	0.411213i
$693$	−25.1525	−	25.8530i	−0.955464	−	0.982074i
$694$			8.37019i			0.317728i
$695$	−15.5983	+	33.1670i	−0.591677	+	1.25809i
$696$	−7.91881	+	7.42375i	−0.300162	+	0.281397i
$697$	−7.72160	+	7.72160i	−0.292476	+	0.292476i
$698$	14.8271	+	3.97292i	0.561216	+	0.150377i
$699$	−10.0267	−	3.03643i	−0.379244	−	0.114848i
$700$	−11.1613	−	7.10107i	−0.421858	−	0.268395i
$701$			40.5025i			1.52976i	0.644174	+	0.764879i	$0.277201\pi$
$701$			40.5025i			1.52976i	−0.644174	+	0.764879i	$0.722799\pi$
$702$	−18.4914	−	13.2114i	−0.697912	−	0.498631i
$703$	15.2496	−	56.9122i	0.575148	−	2.14648i
$704$	2.27218	−	3.93553i	0.0856360	−	0.148326i
$705$	−3.63798	−	11.2202i	−0.137014	−	0.422578i
$706$	8.42929	−	14.6000i	0.317240	−	0.549477i
$707$	−23.9405	+	7.73692i	−0.900377	+	0.290977i
$708$	−12.5176	−	7.77578i	−0.470439	−	0.292232i
$709$			13.4311i			0.504416i	0.967673	+	0.252208i	$0.0811567\pi$
$709$			13.4311i			0.504416i	−0.967673	+	0.252208i	$0.918843\pi$
$710$	22.5520	+	19.0494i	0.846361	+	0.714912i
$711$	−14.1699	+	7.00434i	−0.531412	+	0.262683i
$712$	1.42085	+	5.30269i	0.0532487	+	0.198727i
$713$	−2.61086	−	0.699578i	−0.0977775	−	0.0261994i
$714$	−3.87730	−	3.73626i	−0.145104	−	0.139826i
$715$	−7.86048	+	43.7419i	−0.293965	+	1.63585i
$716$	9.32327	−	5.38279i	0.348427	−	0.201164i
$717$	16.6412	+	31.0985i	0.621479	+	1.16139i
$718$	−27.3158	+	7.31924i	−1.01942	+	0.273152i
$719$	−2.12346	+	3.67795i	−0.0791919	+	0.137164i	−0.902901	−	0.429848i	$-0.858567\pi$
$719$	−2.12346	+	3.67795i	−0.0791919	+	0.137164i	0.823710	+	0.567012i	$0.191901\pi$
$720$	−5.74302	+	3.46665i	−0.214030	+	0.129194i
$721$	−4.42288	−	6.83428i	−0.164717	−	0.254522i
$722$	4.97023	−	18.5492i	0.184973	−	0.690328i
$723$	7.75156	+	14.4858i	0.288284	+	0.538732i
$724$			0.210492i			0.00782288i
$725$	−19.9838	−	24.1346i	−0.742179	−	0.896337i
$726$	11.4329	+	12.1953i	0.424315	+	0.452611i
$727$	13.0179	+	3.48815i	0.482809	+	0.129368i	0.492010	−	0.870589i	$-0.336262\pi$
$727$	13.0179	+	3.48815i	0.482809	+	0.129368i	−0.00920135	+	0.999958i	$0.502929\pi$
$728$	−3.55839	−	11.0108i	−0.131883	−	0.408088i
$729$	26.4959	+	5.19287i	0.981331	+	0.192329i
$730$	−12.1168	−	17.4256i	−0.448463	−	0.644951i
$731$	8.63370	+	4.98467i	0.319329	+	0.184365i
$732$	8.66830	+	5.38466i	0.320390	+	0.199023i
$733$	−6.37620	+	23.7963i	−0.235510	+	0.878937i	0.742408	+	0.669948i	$0.233684\pi$
$733$	−6.37620	+	23.7963i	−0.235510	+	0.878937i	−0.977918	+	0.208989i	$0.932983\pi$
$734$	−9.82951	+	17.0252i	−0.362814	+	0.628412i
$735$	−9.81135	+	25.2733i	−0.361897	+	0.932218i
$736$	3.76497	+	6.52113i	0.138779	+	0.240372i
$737$	42.0143	−	11.2577i	1.54762	−	0.414683i
$738$	20.9447	−	18.4028i	0.770984	−	0.677416i
$739$	−21.0639	+	12.1612i	−0.774847	+	0.447358i	−0.834601	−	0.550855i	$-0.814302\pi$
$739$	−21.0639	+	12.1612i	−0.774847	+	0.447358i	0.0597540	+	0.998213i	$0.480968\pi$
$740$	−7.22476	−	20.0537i	−0.265587	−	0.737189i
$741$	34.1589	−	32.0234i	1.25486	−	1.17641i
$742$	−0.188995	−	0.0404847i	−0.00693823	−	0.00148624i
$743$	−5.25592	−	19.6154i	−0.192821	−	0.719618i	−0.992820	−	0.119617i	$-0.961833\pi$
$743$	−5.25592	−	19.6154i	−0.192821	−	0.719618i	0.799999	−	0.600001i	$-0.204833\pi$
$744$	−0.141466	−	0.605431i	−0.00518641	−	0.0221962i
$745$	8.23572	−	5.72666i	0.301734	−	0.209809i
$746$	−4.66447	+	2.69303i	−0.170778	+	0.0985990i
$747$	−2.17449	−	10.8785i	−0.0795603	−	0.398025i
$748$	3.77568	+	3.77568i	0.138053	+	0.138053i
$749$	−16.4232	+	32.1068i	−0.600091	+	1.17316i
$750$	−8.96859	−	17.1629i	−0.327487	−	0.626700i
$751$	−15.8277	−	27.4144i	−0.577562	−	1.00037i	−0.995758	−	0.0920100i	$-0.970671\pi$
$751$	−15.8277	−	27.4144i	−0.577562	−	1.00037i	0.418196	−	0.908357i	$-0.362663\pi$
$752$	−2.15351	−	2.15351i	−0.0785305	−	0.0785305i
$753$	18.3545	+	11.4016i	0.668873	+	0.415497i
$754$		−	27.4088i		−	0.998169i
$755$	2.40392	+	1.13055i	0.0874877	+	0.0411451i
$756$	9.26393	+	10.1577i	0.336926	+	0.369433i
$757$	−4.79302	+	4.79302i	−0.174205	+	0.174205i	−0.788824	−	0.614619i	$-0.789310\pi$
$757$	−4.79302	+	4.79302i	−0.174205	+	0.174205i	0.614619	+	0.788824i	$0.289310\pi$
$758$	−13.7429	+	13.7429i	−0.499163	+	0.499163i
$759$	−57.7141	+	13.4856i	−2.09489	+	0.489496i
$760$	−4.68452	−	13.0028i	−0.169926	−	0.471661i
$761$	9.12740	−	5.26971i	0.330868	−	0.191027i	−0.325358	−	0.945591i	$-0.605485\pi$
$761$	9.12740	−	5.26971i	0.330868	−	0.191027i	0.656226	+	0.754564i	$0.272152\pi$
$762$	10.5157	−	16.9283i	0.380943	−	0.613247i
$763$	0.269742	−	1.25924i	0.00976531	−	0.0455876i
$764$	−21.6280			−0.782473
$765$	−2.18799	−	7.57236i	−0.0791070	−	0.273779i
$766$	7.19509	+	12.4623i	0.259969	+	0.450280i
$767$	35.9423	−	9.63072i	1.29780	−	0.347745i
$768$	−0.913950	+	1.47129i	−0.0329793	+	0.0530906i
$769$	15.0585	+	8.69401i	0.543022	+	0.313514i	0.746303	−	0.665607i	$-0.231827\pi$
$769$	15.0585	+	8.69401i	0.543022	+	0.313514i	−0.203281	+	0.979121i	$0.565160\pi$
$770$	10.1921	−	24.8780i	0.367296	−	0.896540i
$771$	12.9713	+	13.8363i	0.467150	+	0.498303i
$772$	15.2559	−	15.2559i	0.549074	−	0.549074i
$773$	29.8801	+	8.00635i	1.07471	+	0.287968i	0.752428	−	0.658674i	$-0.228882\pi$
$773$	29.8801	+	8.00635i	1.07471	+	0.287968i	0.322285	+	0.946643i	$0.395549\pi$
$774$	−21.1772	−	14.1214i	−0.761199	−	0.507584i
$775$	1.76954	−	0.300096i	0.0635638	−	0.0107798i
$776$	−3.02332	+	1.74552i	−0.108531	+	0.0626604i
$777$	−37.4201	+	22.5388i	−1.34244	+	0.808575i
$778$	−6.07636	+	1.62816i	−0.217848	+	0.0583722i
$779$	28.7214	+	49.7470i	1.02905	+	1.78237i
$780$	3.53208	−	16.5666i	0.126469	−	0.593180i
$781$	−29.9975	+	51.9571i	−1.07339	+	1.85917i
$782$	−8.54620	+	2.28995i	−0.305612	+	0.0818884i
$783$	13.4809	+	29.6419i	0.481768	+	1.05932i
$784$	0.709677	+	6.96393i	0.0253456	+	0.248712i
$785$	7.48657	+	6.32383i	0.267207	+	0.225707i
$786$	−11.7624	+	11.0270i	−0.419551	+	0.393322i
$787$	−4.78870	+	4.78870i	−0.170699	+	0.170699i	−0.787286	−	0.616588i	$-0.788515\pi$
$787$	−4.78870	+	4.78870i	−0.170699	+	0.170699i	0.616588	+	0.787286i	$0.288515\pi$
$788$	3.69607	−	3.69607i	0.131667	−	0.131667i
$789$	−14.1616	−	4.28862i	−0.504166	−	0.152679i
$790$	−9.00032	−	7.60247i	−0.320217	−	0.270484i
$791$	6.94146	+	3.55069i	0.246810	+	0.126248i
$792$	−8.99853	−	10.2415i	−0.319749	−	0.363914i
$793$	−24.8898	+	6.66919i	−0.883861	+	0.236830i
$794$	7.73321	−	13.3943i	0.274441	−	0.475347i
$795$	−0.210146	−	0.189452i	−0.00745310	−	0.00671917i
$796$	2.20635	+	3.82151i	0.0782020	+	0.135450i
$797$	−9.79545	+	2.62468i	−0.346973	+	0.0929710i	−0.428097	−	0.903733i	$-0.640816\pi$
$797$	−9.79545	+	2.62468i	−0.346973	+	0.0929710i	0.0811240	+	0.996704i	$0.474149\pi$
$798$	−24.2632	+	14.6141i	−0.858907	+	0.517334i
$799$	3.09906	−	1.78925i	0.109637	−	0.0632989i
$800$	−4.07691	−	2.89461i	−0.144141	−	0.102340i
$801$	16.4350	+	1.06172i	0.580702	+	0.0375140i
$802$	5.88077	+	1.57575i	0.207657	+	0.0556415i
$803$	30.5004	−	30.5004i	1.07633	−	1.07633i
$804$	−16.1435	+	3.77213i	−0.569338	+	0.133033i
$805$	27.2557	+	35.2368i	0.960637	+	1.24193i
$806$	1.35963	+	0.784981i	0.0478908	+	0.0276498i
$807$	6.57632	+	0.212198i	0.231497	+	0.00746971i
$808$	−9.18544	+	2.46123i	−0.323143	+	0.0865858i
$809$	−1.25982	−	2.18207i	−0.0442929	−	0.0767175i	0.843029	−	0.537868i	$-0.180770\pi$
$809$	−1.25982	−	2.18207i	−0.0442929	−	0.0767175i	−0.887322	+	0.461151i	$0.847437\pi$
$810$	4.32837	+	19.6536i	0.152083	+	0.690558i
$811$	−6.87827			−0.241529			−0.120764	−	0.992681i	$-0.538535\pi$
$811$	−6.87827			−0.241529			−0.120764	+	0.992681i	$0.538535\pi$
$812$	−3.47292	+	16.2127i	−0.121876	+	0.568954i
$813$	−15.1424	−	28.2976i	−0.531068	−	0.992439i
$814$	37.5157	−	21.6597i	1.31492	−	0.759172i
$815$	13.4879	+	37.4382i	0.472459	+	1.31140i
$816$	−1.39191	−	1.48474i	−0.0487268	−	0.0519761i
$817$	37.0822	−	37.0822i	1.29734	−	1.29734i
$818$	−1.19834	+	1.19834i	−0.0418991	+	0.0418991i
$819$	−34.7113	−	0.476720i	−1.21291	−	0.0166579i
$820$	18.8053	+	8.84405i	0.656709	+	0.308848i
$821$			14.9316i			0.521116i	0.965458	+	0.260558i	$0.0839065\pi$
$821$			14.9316i			0.521116i	−0.965458	+	0.260558i	$0.916093\pi$
$822$	−28.4219	+	15.2089i	−0.991326	+	0.530473i
$823$	19.0072	+	19.0072i	0.662550	+	0.662550i	0.955980	−	0.293431i	$-0.0947969\pi$
$823$	19.0072	+	19.0072i	0.662550	+	0.662550i	−0.293431	+	0.955980i	$0.594797\pi$
$824$	−1.53843	−	2.66463i	−0.0535937	−	0.0928269i
$825$	31.1064	−	24.1087i	1.08299	−	0.839357i
$826$	−22.4807	+	1.14252i	−0.782204	+	0.0397533i
$827$	5.42032	+	5.42032i	0.188483	+	0.188483i	0.795040	−	0.606557i	$-0.207450\pi$
$827$	5.42032	+	5.42032i	0.188483	+	0.188483i	−0.606557	+	0.795040i	$0.707450\pi$
$828$	22.1516	−	4.42785i	0.769823	−	0.153878i
$829$	12.1226	−	6.99901i	0.421037	−	0.243086i	−0.274484	−	0.961592i	$-0.588507\pi$
$829$	12.1226	−	6.99901i	0.421037	−	0.243086i	0.695521	+	0.718506i	$0.255174\pi$
$830$	6.78886	−	4.72059i	0.235645	−	0.163854i
$831$	32.8768	+	9.95621i	1.14048	+	0.345377i
$832$	−1.13198	−	4.22459i	−0.0392442	−	0.146461i
$833$	−8.11962	−	1.31236i	−0.281328	−	0.0454706i
$834$	27.1717	+	8.22854i	0.940880	+	0.284931i
$835$	9.77766	+	27.1398i	0.338370	+	0.939210i
$836$	24.3251	−	14.0441i	0.841302	−	0.485726i
$837$	−1.85649	−	0.180210i	−0.0641698	−	0.00622898i
$838$	−4.42129	+	1.18468i	−0.152731	+	0.0409241i
$839$	−16.7773	−	29.0592i	−0.579217	−	1.00323i	−0.995569	−	0.0940302i	$-0.970025\pi$
$839$	−16.7773	−	29.0592i	−0.579217	−	1.00323i	0.416352	−	0.909203i	$-0.363308\pi$
$840$	−4.18841	+	9.35186i	−0.144514	+	0.322670i
$841$	−5.13662	+	8.89689i	−0.177125	+	0.306789i
$842$	2.91920	−	10.8946i	0.100602	−	0.375453i
$843$	−0.648666	+	20.1031i	−0.0223412	+	0.692388i
$844$	12.2852	+	7.09284i	0.422872	+	0.244145i
$845$	7.82347	+	11.2512i	0.269136	+	0.387054i
$846$	−8.19055	+	4.04869i	−0.281597	+	0.139197i
$847$	24.9683	+	5.34845i	0.857920	+	0.183775i
$848$	−0.0705647	−	0.0189078i	−0.00242320	−	0.000649295i
$849$	−43.7543	+	10.2237i	−1.50164	+	0.350877i
$850$	4.52511	−	3.74685i	0.155210	−	0.128516i
$851$			71.7797i			2.46058i
$852$	12.0660	−	19.4241i	0.413375	−	0.665457i
$853$	1.52862	−	5.70488i	0.0523389	−	0.195331i	−0.934806	−	0.355158i	$-0.884427\pi$
$853$	1.52862	−	5.70488i	0.0523389	−	0.195331i	0.987145	+	0.159827i	$0.0510936\pi$
$854$	15.5677	−	0.791184i	0.532716	−	0.0270738i
$855$	−41.4549	+	0.807814i	−1.41773	+	0.0276266i
$856$	−6.81534	+	11.8045i	−0.232943	+	0.403470i
$857$	0.683192	−	0.183061i	0.0233374	−	0.00625324i	−0.247131	−	0.968982i	$-0.579488\pi$
$857$	0.683192	−	0.183061i	0.0233374	−	0.00625324i	0.270469	+	0.962729i	$0.412821\pi$
$858$	34.4071	+	1.11021i	1.17464	+	0.0379020i
$859$	33.5325	−	19.3600i	1.14411	−	0.660555i	0.196668	−	0.980470i	$-0.436988\pi$
$859$	33.5325	−	19.3600i	1.14411	−	0.660555i	0.947446	+	0.319915i	$0.103654\pi$
$860$	3.35555	−	18.6729i	0.114423	−	0.636742i
$861$	10.2589	−	41.3346i	0.349624	−	1.40868i
$862$	2.14911	+	0.575852i	0.0731990	+	0.0196136i
$863$	−1.27101	−	4.74346i	−0.0432655	−	0.161469i	0.940913	−	0.338648i	$-0.109970\pi$
$863$	−1.27101	−	4.74346i	−0.0432655	−	0.161469i	−0.984179	+	0.177179i	$0.943303\pi$
$864$	3.30205	+	4.01204i	0.112338	+	0.136492i
$865$	26.1323	+	22.0737i	0.888526	+	0.750528i
$866$		−	30.7122i		−	1.04364i
$867$	−23.8531	+	12.7642i	−0.810094	+	0.433493i
$868$	−0.704776	−	0.636604i	−0.0239216	−	0.0216077i
$869$	11.9718	−	20.7357i	0.406114	−	0.703410i
$870$	−16.2519	+	18.0271i	−0.550991	+	0.611175i
$871$	20.9311	−	36.2537i	0.709223	−	1.22841i
$872$	0.125979	−	0.470160i	0.00426619	−	0.0159216i
$873$	2.05284	+	10.2699i	0.0694781	+	0.347585i
$874$			46.5419i			1.57430i
$875$	−26.2016	−	13.7286i	−0.885776	−	0.464113i
$876$	−11.9939	+	11.2440i	−0.405235	+	0.379901i
$877$	1.77174	+	0.474735i	0.0598273	+	0.0160307i	0.288609	−	0.957447i	$-0.406807\pi$
$877$	1.77174	+	0.474735i	0.0598273	+	0.0160307i	−0.228781	+	0.973478i	$0.573474\pi$
$878$	−10.1568	+	10.1568i	−0.342776	+	0.342776i
$879$	−11.5011	−	3.48293i	−0.387923	−	0.117476i
$880$	4.32453	−	9.19535i	0.145780	−	0.309975i
$881$			9.87338i			0.332643i	0.986072	+	0.166321i	$0.0531889\pi$
$881$			9.87338i			0.332643i	−0.986072	+	0.166321i	$0.946811\pi$
$882$	20.4718	+	4.68020i	0.689322	+	0.157590i
$883$	20.1725	+	20.1725i	0.678857	+	0.678857i	0.959742	−	0.280884i	$-0.0906277\pi$
$883$	20.1725	+	20.1725i	0.678857	+	0.678857i	−0.280884	+	0.959742i	$0.590628\pi$
$884$	5.13900			0.172843
$885$	−29.3502	−	14.9776i	−0.986595	−	0.503466i
$886$	9.54166			0.320558
$887$	3.21711	−	12.0064i	0.108020	−	0.403136i	−0.890650	−	0.454689i	$-0.849750\pi$
$887$	3.21711	−	12.0064i	0.108020	−	0.403136i	0.998670	+	0.0515529i	$0.0164171\pi$
$888$	−14.5576	+	7.79001i	−0.488523	+	0.261415i
$889$	−1.54510	−	30.4021i	−0.0518210	−	1.01965i
$890$	4.16070	+	11.5488i	0.139467	+	0.387117i
$891$	−37.7565	+	15.7223i	−1.26489	+	0.526718i
$892$	2.29046	+	0.613728i	0.0766904	+	0.0205491i
$893$	−4.87203	−	18.1827i	−0.163036	−	0.608460i
$894$	−5.31418	−	5.66856i	−0.177733	−	0.189585i
$895$	19.7642	−	13.7429i	0.660643	−	0.459374i
$896$	0.134290	+	2.64234i	0.00448630	+	0.0882744i
$897$	−30.0993	+	48.4542i	−1.00498	+	1.61784i
$898$	28.8972	+	28.8972i	0.964313	+	0.964313i
$899$	−1.12478	−	1.94817i	−0.0375134	−	0.0649751i
$900$	−12.1462	+	8.80172i	−0.404873	+	0.293391i
$901$	0.0429192	−	0.0743382i	0.00142985	−	0.00247656i
$902$	−10.9308	+	40.7945i	−0.363957	+	1.35831i
$903$	−38.8744	+	0.720144i	−1.29366	+	0.0239649i
$904$	2.55213	+	1.47347i	0.0848825	+	0.0490069i
$905$	0.0394881	+	0.469015i	0.00131263	+	0.0155906i
$906$	0.596400	−	1.96939i	0.0198141	−	0.0654287i
$907$	8.63256	+	32.2171i	0.286639	+	1.06975i	0.947633	+	0.319361i	$0.103468\pi$
$907$	8.63256	+	32.2171i	0.286639	+	1.06975i	−0.660994	+	0.750391i	$0.729865\pi$
$908$	−0.142382	−	0.531375i	−0.00472510	−	0.0176343i
$909$	−1.83913	+	28.4690i	−0.0610002	+	0.944259i
$910$	−9.99436	−	23.8666i	−0.331310	−	0.791169i
$911$	−18.7417	+	10.8205i	−0.620941	+	0.358501i	−0.777235	−	0.629210i	$-0.783379\pi$
$911$	−18.7417	+	10.8205i	−0.620941	+	0.358501i	0.156294	+	0.987711i	$0.450045\pi$
$912$	−9.43915	+	5.05103i	−0.312562	+	0.167256i
$913$	11.8827	+	11.8827i	0.393259	+	0.393259i
$914$	23.2566			0.769259
$915$	20.3247	+	10.3718i	0.671915	+	0.342883i
$916$	−9.84143	−	17.0459i	−0.325170	−	0.563211i
$917$	−5.15858	+	24.0819i	−0.170351	+	0.795255i
$918$	−5.55770	+	2.52760i	−0.183432	+	0.0834231i
$919$	−21.8011	−	12.5868i	−0.719150	−	0.415202i	0.0952895	−	0.995450i	$-0.469622\pi$
$919$	−21.8011	−	12.5868i	−0.719150	−	0.415202i	−0.814440	+	0.580248i	$0.802956\pi$
$920$	9.61242	+	13.8240i	0.316912	+	0.455763i
$921$	3.82621	+	16.3750i	0.126078	+	0.539574i
$922$	17.8275	+	4.77686i	0.587117	+	0.157317i
$923$	14.9444	+	55.7733i	0.491902	+	1.83580i
$924$	−20.2117	−	5.01638i	−0.664915	−	0.165027i
$925$	−19.8602	−	43.3280i	−0.652998	−	1.42462i
$926$	−16.1091	−	9.30057i	−0.529377	−	0.305636i
$927$	−9.05151	+	1.80929i	−0.297290	+	0.0594248i
$928$	−1.62198	+	6.05330i	−0.0532440	+	0.198709i
$929$	−33.2557			−1.09108			−0.545541	−	0.838084i	$-0.683676\pi$
$929$	−33.2557			−1.09108			−0.545541	+	0.838084i	$0.683676\pi$
$930$	−0.428791	−	1.32247i	−0.0140606	−	0.0433656i
$931$	−17.7229	+	39.4699i	−0.580845	+	1.29357i
$932$	−5.84244	+	1.56548i	−0.191376	+	0.0512789i
$933$	1.38573	+	0.860804i	0.0453669	+	0.0281815i
$934$	2.54560	+	1.46970i	0.0832947	+	0.0480902i
$935$	9.12123	+	7.70460i	0.298296	+	0.251967i
$936$	−13.0936	−	0.845859i	−0.427977	−	0.0276478i
$937$	6.44273	−	6.44273i	0.210475	−	0.210475i	−0.593994	−	0.804469i	$-0.702450\pi$
$937$	6.44273	−	6.44273i	0.210475	−	0.210475i	0.804469	+	0.593994i	$0.202450\pi$
$938$	−16.9747	+	18.7925i	−0.554244	+	0.613596i
$939$	28.2266	−	6.59549i	0.921141	−	0.215236i
$940$	−5.20242	−	4.39443i	−0.169684	−	0.143330i
$941$		−	46.7275i		−	1.52327i	−0.648005	−	0.761636i	$-0.724396\pi$
$941$		−	46.7275i		−	1.52327i	0.648005	−	0.761636i	$-0.275604\pi$
$942$	4.00555	−	6.44820i	0.130508	−	0.210094i
$943$	−49.4837	−	49.4837i	−1.61141	−	1.61141i
$944$	−8.50788			−0.276908
$945$	22.5473	+	20.8954i	0.733465	+	0.679728i
$946$	38.5569			1.25359
$947$	−20.1451	−	20.1451i	−0.654627	−	0.654627i	0.299477	−	0.954104i	$-0.403188\pi$
$947$	−20.1451	−	20.1451i	−0.654627	−	0.654627i	−0.954104	+	0.299477i	$0.903188\pi$
$948$	−4.81546	+	7.75199i	−0.156399	+	0.251773i
$949$		−	41.5134i		−	1.34758i
$950$	−12.8773	−	28.0938i	−0.417795	−	0.911484i
$951$	20.3998	−	4.76665i	0.661508	−	0.154569i
$952$	−3.03979	−	0.651154i	−0.0985203	−	0.0211040i
$953$	−10.3138	+	10.3138i	−0.334098	+	0.334098i	−0.854140	−	0.520042i	$-0.825916\pi$
$953$	−10.3138	+	10.3138i	−0.334098	+	0.334098i	0.520042	+	0.854140i	$0.325916\pi$
$954$	−0.121589	+	0.182341i	−0.00393658	+	0.00590350i
$955$	−48.1911	+	4.05739i	−1.55943	+	0.131294i
$956$	17.6355	+	10.1819i	0.570373	+	0.329305i
$957$	−41.9005	−	26.0282i	−1.35445	−	0.841371i
$958$	−0.227333	+	0.0609136i	−0.00734479	+	0.00196803i
$959$	−22.4239	+	43.8379i	−0.724107	+	1.41560i
$960$	−1.76044	+	3.44976i	−0.0568179	+	0.111341i
$961$	−30.8711			−0.995843
$962$	10.7906	−	40.2712i	0.347904	−	1.29840i
$963$	26.9908	+	30.7189i	0.869767	+	0.989904i
$964$	8.21469	+	4.74276i	0.264577	+	0.152754i
$965$	31.1311	−	36.8551i	1.00214	−	1.18641i
$966$	23.9437	−	24.8476i	0.770376	−	0.799457i
$967$	−12.2705	−	45.7943i	−0.394594	−	1.47265i	−0.822470	−	0.568808i	$-0.807405\pi$
$967$	−12.2705	−	45.7943i	−0.394594	−	1.47265i	0.427876	−	0.903837i	$-0.359262\pi$
$968$	9.32235	+	2.49792i	0.299632	+	0.0802861i
$969$	−2.86216	−	12.2492i	−0.0919459	−	0.393500i
$970$	−6.40907	+	4.45651i	−0.205783	+	0.143090i
$971$	−29.2801	−	16.9049i	−0.939642	−	0.542503i	−0.0497939	−	0.998760i	$-0.515856\pi$
$971$	−29.2801	−	16.9049i	−0.939642	−	0.542503i	−0.889848	+	0.456257i	$0.849190\pi$
$972$	14.5764	−	5.52525i	0.467538	−	0.177222i
$973$	41.2656	−	13.3359i	1.32291	−	0.427529i
$974$	7.58737	+	13.1417i	0.243115	+	0.421087i
$975$	4.76225	−	37.5761i	0.152514	−	1.20340i
$976$	5.89163			0.188587
$977$	37.6141	+	37.6141i	1.20338	+	1.20338i	0.973131	+	0.230250i	$0.0739544\pi$
$977$	37.6141	+	37.6141i	1.20338	+	1.20338i	0.230250	+	0.973131i	$0.426046\pi$
$978$	27.1776	−	14.5431i	0.869044	−	0.465038i
$979$	−21.6051	+	12.4737i	−0.690501	+	0.398661i
$980$	2.88772	+	15.3838i	0.0922448	+	0.491417i
$981$	−1.21490	−	0.810124i	−0.0387889	−	0.0258653i
$982$	0.710911	+	2.65316i	0.0226861	+	0.0846656i
$983$	−13.9935	−	52.2246i	−0.446324	−	1.66571i	−0.712416	−	0.701758i	$-0.752399\pi$
$983$	−13.9935	−	52.2246i	−0.446324	−	1.66571i	0.266091	−	0.963948i	$-0.414268\pi$
$984$	4.66549	−	15.4061i	0.148730	−	0.491128i
$985$	7.54214	−	8.92890i	0.240313	−	0.284498i
$986$	−6.37700	−	3.68176i	−0.203085	−	0.117251i
$987$	−6.75312	+	12.2137i	−0.214954	+	0.388767i
$988$	6.99663	−	26.1118i	0.222593	−	0.830727i
$989$	−31.9441	+	55.3289i	−1.01576	+	1.75936i
$990$	−21.9717	−	21.1317i	−0.698305	−	0.671611i
$991$	7.91050	+	13.7014i	0.251285	+	0.435239i	0.963880	−	0.266337i	$-0.0858134\pi$
$991$	7.91050	+	13.7014i	0.251285	+	0.435239i	−0.712595	+	0.701576i	$0.752480\pi$
$992$	−0.253824	−	0.253824i	−0.00805892	−	0.00805892i
$993$	16.5827	−	26.6951i	0.526237	−	0.847144i
$994$	−1.77290	−	34.8843i	−0.0562329	−	1.10646i
$995$	5.63306	+	8.10112i	0.178580	+	0.256823i
$996$	−4.38058	−	4.67270i	−0.138804	−	0.148060i
$997$	−12.7422	−	47.5545i	−0.403549	−	1.50607i	−0.806715	−	0.590940i	$-0.798757\pi$
$997$	−12.7422	−	47.5545i	−0.403549	−	1.50607i	0.403166	−	0.915127i	$-0.367910\pi$
$998$	33.5067	+	8.97809i	1.06064	+	0.284196i
$999$	8.13742	+	48.8596i	0.257457	+	1.54585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.cd.a.23.7	yes	192
5.2	odd	4	inner	630.2.cd.a.527.43	yes	192
7.4	even	3		630.2.bt.a.473.47	yes	192
9.2	odd	6		630.2.bt.a.443.38	yes	192
35.32	odd	12		630.2.bt.a.347.38	yes	192
45.2	even	12		630.2.bt.a.317.47	✓	192
63.11	odd	6	inner	630.2.cd.a.263.43	yes	192
315.137	even	12	inner	630.2.cd.a.137.7	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.47	✓	192	45.2	even	12
630.2.bt.a.347.38	yes	192	35.32	odd	12
630.2.bt.a.443.38	yes	192	9.2	odd	6
630.2.bt.a.473.47	yes	192	7.4	even	3
630.2.cd.a.23.7	yes	192	1.1	even	1	trivial
630.2.cd.a.137.7	yes	192	315.137	even	12	inner
630.2.cd.a.263.43	yes	192	63.11	odd	6	inner
630.2.cd.a.527.43	yes	192	5.2	odd	4	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.cd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.913950 + 1.47129i) q^{3} +1.00000i q^{4} +(0.187599 + 2.22818i) q^{5} +(1.68662 - 0.394099i) q^{6} +(1.77346 - 1.96337i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.32939 - 2.68937i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.913950 + 1.47129i) q^{3} +1.00000i q^{4} +(0.187599 + 2.22818i) q^{5} +(1.68662 - 0.394099i) q^{6} +(1.77346 - 1.96337i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.32939 - 2.68937i) q^{9} +(1.44291 - 1.70822i) q^{10} +(3.93553 + 2.27218i) q^{11} +(-1.47129 - 0.913950i) q^{12} +(4.22459 - 1.13198i) q^{13} +(-2.64234 + 0.134290i) q^{14} +(-3.44976 - 1.76044i) q^{15} -1.00000 q^{16} +(0.304112 - 1.13496i) q^{17} +(-0.961652 + 2.84169i) q^{18} +(-5.35282 - 3.09045i) q^{19} +(-2.22818 + 0.187599i) q^{20} +(1.26784 + 4.40370i) q^{21} +(-1.17617 - 4.38951i) q^{22} +(7.27337 + 1.94889i) q^{23} +(0.394099 + 1.68662i) q^{24} +(-4.92961 + 0.836011i) q^{25} +(-3.78767 - 2.18681i) q^{26} +(5.17184 + 0.502033i) q^{27} +(1.96337 + 1.77346i) q^{28} +(3.13342 + 5.42724i) q^{29} +(1.19453 + 3.68417i) q^{30} -0.358961 q^{31} +(0.707107 + 0.707107i) q^{32} +(-6.93992 + 3.71365i) q^{33} +(-1.01758 + 0.587499i) q^{34} +(4.70746 + 3.58327i) q^{35} +(2.68937 - 1.32939i) q^{36} +(2.46721 + 9.20775i) q^{37} +(1.59973 + 5.97029i) q^{38} +(-2.19560 + 7.25017i) q^{39} +(1.70822 + 1.44291i) q^{40} +(-8.04851 - 4.64681i) q^{41} +(2.21739 - 4.01038i) q^{42} +(-2.19596 + 8.19545i) q^{43} +(-2.27218 + 3.93553i) q^{44} +(5.74302 - 3.46665i) q^{45} +(-3.76497 - 6.52113i) q^{46} +(2.15351 + 2.15351i) q^{47} +(0.913950 - 1.47129i) q^{48} +(-0.709677 - 6.96393i) q^{49} +(4.07691 + 2.89461i) q^{50} +(1.39191 + 1.48474i) q^{51} +(1.13198 + 4.22459i) q^{52} +(0.0705647 + 0.0189078i) q^{53} +(-3.30205 - 4.01204i) q^{54} +(-4.32453 + 9.19535i) q^{55} +(-0.134290 - 2.64234i) q^{56} +(9.43915 - 5.05103i) q^{57} +(1.62198 - 6.05330i) q^{58} +8.50788 q^{59} +(1.76044 - 3.44976i) q^{60} -5.89163 q^{61} +(0.253824 + 0.253824i) q^{62} +(-7.63786 - 2.15940i) q^{63} -1.00000i q^{64} +(3.31478 + 9.20082i) q^{65} +(7.53321 + 2.28131i) q^{66} +(6.76808 - 6.76808i) q^{67} +(1.13496 + 0.304112i) q^{68} +(-9.51489 + 8.92005i) q^{69} +(-0.794923 - 5.86243i) q^{70} +13.2021i q^{71} +(-2.84169 - 0.961652i) q^{72} +(2.45665 - 9.16835i) q^{73} +(4.76628 - 8.25544i) q^{74} +(3.27541 - 8.01696i) q^{75} +(3.09045 - 5.35282i) q^{76} +(11.4406 - 3.69730i) q^{77} +(6.67917 - 3.57412i) q^{78} -5.26884i q^{79} +(-0.187599 - 2.22818i) q^{80} +(-5.46544 + 7.15045i) q^{81} +(2.40536 + 8.97694i) q^{82} +(3.57191 + 0.957089i) q^{83} +(-4.40370 + 1.26784i) q^{84} +(2.58596 + 0.464700i) q^{85} +(7.34784 - 4.24228i) q^{86} +(-10.8488 - 0.350059i) q^{87} +(4.38951 - 1.17617i) q^{88} +(-2.74487 + 4.75426i) q^{89} +(-6.51222 - 1.60964i) q^{90} +(5.26966 - 10.3020i) q^{91} +(-1.94889 + 7.27337i) q^{92} +(0.328073 - 0.528136i) q^{93} -3.04553i q^{94} +(5.88191 - 12.5068i) q^{95} +(-1.68662 + 0.394099i) q^{96} +(-3.37208 - 0.903546i) q^{97} +(-4.42243 + 5.42606i) q^{98} +(0.878880 - 13.6047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{6}+O(q^{10}) \) 192 * q + 8 * q^6	\( 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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