LMFDB - Embedded newform 637.2.u.i.30.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(30,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("637.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.u (of order $6$, degree $2$, not 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			30.4
Root			$1.34408 + 0.439820i$ of defining polynomial
Character	$\chi$	$=$	637.30
Dual form			637.2.u.i.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104235 - 0.0601799i) q^{2} +0.582292 q^{3} +(-0.992757 + 1.71951i) q^{4} +(-1.46199 - 0.844083i) q^{5} +(0.0606950 - 0.0350423i) q^{6} +0.479696i q^{8} -2.66094 q^{9} +O(q^{10})$	\(q+(0.104235 - 0.0601799i) q^{2} +0.582292 q^{3} +(-0.992757 + 1.71951i) q^{4} +(-1.46199 - 0.844083i) q^{5} +(0.0606950 - 0.0350423i) q^{6} +0.479696i q^{8} -2.66094 q^{9} -0.203187 q^{10} +0.364618i q^{11} +(-0.578074 + 1.00125i) q^{12} +(-1.80124 - 3.12338i) q^{13} +(-0.851308 - 0.491503i) q^{15} +(-1.95665 - 3.38901i) q^{16} +(1.59277 - 2.75877i) q^{17} +(-0.277362 + 0.160135i) q^{18} -1.44391i q^{19} +(2.90281 - 1.67594i) q^{20} +(0.0219427 + 0.0380059i) q^{22} +(-2.54161 - 4.40219i) q^{23} +0.279323i q^{24} +(-1.07505 - 1.86204i) q^{25} +(-0.375717 - 0.217166i) q^{26} -3.29632 q^{27} +(-4.09831 + 7.09848i) q^{29} -0.118314 q^{30} +(4.06838 - 2.34888i) q^{31} +(-1.23876 - 0.715198i) q^{32} +0.212314i q^{33} -0.383412i q^{34} +(2.64166 - 4.57549i) q^{36} +(-5.46967 + 3.15792i) q^{37} +(-0.0868943 - 0.150505i) q^{38} +(-1.04885 - 1.81872i) q^{39} +(0.404903 - 0.701313i) q^{40} +(5.04661 + 2.91366i) q^{41} +(-0.386561 - 0.669543i) q^{43} +(-0.626963 - 0.361977i) q^{44} +(3.89027 + 2.24605i) q^{45} +(-0.529847 - 0.305907i) q^{46} +(-11.0769 - 6.39527i) q^{47} +(-1.13934 - 1.97339i) q^{48} +(-0.224115 - 0.129393i) q^{50} +(0.927459 - 1.60641i) q^{51} +(7.15887 + 0.00351282i) q^{52} +(-0.685548 - 1.18740i) q^{53} +(-0.343591 + 0.198372i) q^{54} +(0.307768 - 0.533070i) q^{55} -0.840776i q^{57} +0.986544i q^{58} +(-8.10770 - 4.68098i) q^{59} +(1.69028 - 0.975885i) q^{60} +9.02484 q^{61} +(0.282711 - 0.489669i) q^{62} +7.65442 q^{64} +(-0.00298674 + 6.08677i) q^{65} +(0.0127771 + 0.0221305i) q^{66} +13.4759i q^{67} +(3.16247 + 5.47757i) q^{68} +(-1.47996 - 2.56336i) q^{69} +(-6.13246 + 3.54058i) q^{71} -1.27644i q^{72} +(-1.87133 + 1.08041i) q^{73} +(-0.380087 + 0.658329i) q^{74} +(-0.625992 - 1.08425i) q^{75} +(2.48281 + 1.43345i) q^{76} +(-0.218777 - 0.126454i) q^{78} +(3.44391 - 5.96502i) q^{79} +6.60628i q^{80} +6.06339 q^{81} +0.701376 q^{82} -0.567380i q^{83} +(-4.65725 + 2.68887i) q^{85} +(-0.0805861 - 0.0465264i) q^{86} +(-2.38641 + 4.13339i) q^{87} -0.174906 q^{88} +(-0.986346 + 0.569467i) q^{89} +0.540669 q^{90} +10.0928 q^{92} +(2.36898 - 1.36773i) q^{93} -1.53947 q^{94} +(-1.21878 + 2.11098i) q^{95} +(-0.721319 - 0.416454i) q^{96} +(-6.86572 + 3.96393i) q^{97} -0.970225i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9}+O(q^{10}) $ 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9	$ 12 q + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9} + 24 q^{10} - 2 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} - 12 q^{18} + 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} - 24 q^{26} - 12 q^{27} + 8 q^{29} - 16 q^{30} - 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} + 2 q^{38} - 10 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} - 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} - 26 q^{52} + 22 q^{53} + 12 q^{54} + 6 q^{55} + 18 q^{59} + 66 q^{60} + 28 q^{61} + 4 q^{62} - 52 q^{64} - 42 q^{65} - 26 q^{66} + 8 q^{68} - 4 q^{69} - 24 q^{71} - 30 q^{73} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} + 28 q^{82} - 48 q^{85} - 60 q^{86} + 2 q^{87} + 28 q^{88} - 12 q^{89} - 24 q^{90} + 24 q^{92} + 18 q^{93} + 8 q^{94} - 22 q^{95} - 6 q^{96} - 6 q^{97}+O(q^{100}) $ 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9 + 24 * q^10 - 2 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 - 12 * q^18 + 12 * q^20 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 12 * q^27 + 8 * q^29 - 16 * q^30 - 18 * q^31 - 36 * q^32 - 10 * q^36 + 42 * q^37 + 2 * q^38 - 10 * q^39 + 46 * q^40 - 30 * q^41 + 2 * q^43 + 24 * q^44 - 12 * q^46 - 42 * q^47 + 2 * q^48 - 18 * q^50 - 26 * q^51 - 26 * q^52 + 22 * q^53 + 12 * q^54 + 6 * q^55 + 18 * q^59 + 66 * q^60 + 28 * q^61 + 4 * q^62 - 52 * q^64 - 42 * q^65 - 26 * q^66 + 8 * q^68 - 4 * q^69 - 24 * q^71 - 30 * q^73 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 + 28 * q^79 - 4 * q^81 + 28 * q^82 - 48 * q^85 - 60 * q^86 + 2 * q^87 + 28 * q^88 - 12 * q^89 - 24 * q^90 + 24 * q^92 + 18 * q^93 + 8 * q^94 - 22 * q^95 - 6 * q^96 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.104235	−	0.0601799i	0.0737051	−	0.0425536i	−0.462695	−	0.886518i	$-0.653117\pi$
$2$	0.104235	−	0.0601799i	0.0737051	−	0.0425536i	0.536400	+	0.843964i	$0.319784\pi$
$3$	0.582292			0.336186			0.168093	−	0.985771i	$-0.446239\pi$
$3$	0.582292			0.336186			0.168093	+	0.985771i	$0.446239\pi$
$4$	−0.992757	+	1.71951i	−0.496378	+	0.859753i
$5$	−1.46199	−	0.844083i	−0.653824	−	0.377485i	0.136096	−	0.990696i	$-0.456544\pi$
$5$	−1.46199	−	0.844083i	−0.653824	−	0.377485i	−0.789920	+	0.613210i	$0.789878\pi$
$6$	0.0606950	−	0.0350423i	0.0247786	−	0.0143060i
$7$		0			0
$7$		0			0
$8$			0.479696i			0.169598i
$9$	−2.66094			−0.886979
$10$	−0.203187			−0.0642535
$11$			0.364618i			0.109936i	0.998488	+	0.0549682i	$0.0175058\pi$
$11$			0.364618i			0.109936i	−0.998488	+	0.0549682i	$0.982494\pi$
$12$	−0.578074	+	1.00125i	−0.166876	+	0.289037i
$13$	−1.80124	−	3.12338i	−0.499575	−	0.866271i
$13$	−1.80124	−	3.12338i	−0.499575	−	0.866271i
$14$		0			0
$15$	−0.851308	−	0.491503i	−0.219807	−	0.126905i
$16$	−1.95665	−	3.38901i	−0.489161	−	0.847252i
$17$	1.59277	−	2.75877i	0.386304	−	0.669099i	−0.605645	−	0.795735i	$-0.707085\pi$
$17$	1.59277	−	2.75877i	0.386304	−	0.669099i	0.991949	+	0.126636i	$0.0404181\pi$
$18$	−0.277362	+	0.160135i	−0.0653748	+	0.0377442i
$19$		−	1.44391i		−	0.331255i	−0.986188	−	0.165628i	$-0.947035\pi$
$19$		−	1.44391i		−	0.331255i	0.986188	−	0.165628i	$-0.0529649\pi$
$20$	2.90281	−	1.67594i	0.649088	−	0.374751i
$21$		0			0
$22$	0.0219427	+	0.0380059i	0.00467820	+	0.00810288i
$23$	−2.54161	−	4.40219i	−0.529962	−	0.917920i	−0.999389	−	0.0349493i	$-0.988873\pi$
$23$	−2.54161	−	4.40219i	−0.529962	−	0.917920i	0.469428	−	0.882971i	$-0.344460\pi$
$24$			0.279323i			0.0570166i
$25$	−1.07505	−	1.86204i	−0.215010	−	0.372408i
$26$	−0.375717	−	0.217166i	−0.0736842	−	0.0425898i
$27$	−3.29632			−0.634377
$28$		0			0
$29$	−4.09831	+	7.09848i	−0.761037	+	1.31815i	0.181280	+	0.983432i	$0.441976\pi$
$29$	−4.09831	+	7.09848i	−0.761037	+	1.31815i	−0.942317	+	0.334723i	$0.891357\pi$
$30$	−0.118314			−0.0216012
$31$	4.06838	−	2.34888i	0.730702	−	0.421871i	−0.0879771	−	0.996122i	$-0.528040\pi$
$31$	4.06838	−	2.34888i	0.730702	−	0.421871i	0.818679	+	0.574252i	$0.194707\pi$
$32$	−1.23876	−	0.715198i	−0.218984	−	0.126430i
$33$			0.212314i			0.0369592i
$34$		−	0.383412i		−	0.0657546i
$35$		0			0
$36$	2.64166	−	4.57549i	0.440277	−	0.762582i
$37$	−5.46967	+	3.15792i	−0.899209	+	0.519159i	−0.876943	−	0.480594i	$-0.840421\pi$
$37$	−5.46967	+	3.15792i	−0.899209	+	0.519159i	−0.0222655	+	0.999752i	$0.507088\pi$
$38$	−0.0868943	−	0.150505i	−0.0140961	−	0.0244152i
$39$	−1.04885	−	1.81872i	−0.167950	−	0.291228i
$40$	0.404903	−	0.701313i	0.0640208	−	0.110887i
$41$	5.04661	+	2.91366i	0.788148	+	0.455037i	0.839310	−	0.543653i	$-0.182959\pi$
$41$	5.04661	+	2.91366i	0.788148	+	0.455037i	−0.0511624	+	0.998690i	$0.516293\pi$
$42$		0			0
$43$	−0.386561	−	0.669543i	−0.0589500	−	0.102104i	0.835044	−	0.550183i	$-0.185442\pi$
$43$	−0.386561	−	0.669543i	−0.0589500	−	0.102104i	−0.893994	+	0.448078i	$0.852109\pi$
$44$	−0.626963	−	0.361977i	−0.0945182	−	0.0545701i
$45$	3.89027	+	2.24605i	0.579928	+	0.334821i
$46$	−0.529847	−	0.305907i	−0.0781217	−	0.0451036i
$47$	−11.0769	−	6.39527i	−1.61574	−	0.932846i	−0.988006	−	0.154416i	$-0.950650\pi$
$47$	−11.0769	−	6.39527i	−1.61574	−	0.932846i	−0.627731	−	0.778430i	$-0.716016\pi$
$48$	−1.13934	−	1.97339i	−0.164449	−	0.284835i
$49$		0			0
$50$	−0.224115	−	0.129393i	−0.0316946	−	0.0182989i
$51$	0.927459	−	1.60641i	0.129870	−	0.224942i
$52$	7.15887	+	0.00351282i	0.992757	+	0.000487140i
$53$	−0.685548	−	1.18740i	−0.0941672	−	0.163102i	0.815094	−	0.579329i	$-0.196685\pi$
$53$	−0.685548	−	1.18740i	−0.0941672	−	0.163102i	−0.909261	+	0.416227i	$0.863352\pi$
$54$	−0.343591	+	0.198372i	−0.0467568	+	0.0269950i
$55$	0.307768	−	0.533070i	0.0414994	−	0.0718791i
$56$		0			0
$57$		−	0.840776i		−	0.111363i
$58$			0.986544i			0.129540i
$59$	−8.10770	−	4.68098i	−1.05553	−	0.609412i	−0.131340	−	0.991337i	$-0.541928\pi$
$59$	−8.10770	−	4.68098i	−1.05553	−	0.609412i	−0.924193	+	0.381925i	$0.875261\pi$
$60$	1.69028	−	0.975885i	0.218215	−	0.125986i
$61$	9.02484			1.15551			0.577756	−	0.816209i	$-0.303928\pi$
$61$	9.02484			1.15551			0.577756	+	0.816209i	$0.303928\pi$
$62$	0.282711	−	0.489669i	0.0359043	−	0.0621880i
$63$		0			0
$64$	7.65442			0.956802
$65$	−0.00298674	+	6.08677i	−0.000370460	+	0.754970i
$66$	0.0127771	+	0.0221305i	0.00157275	+	0.00272408i
$67$			13.4759i			1.64635i	0.567789	+	0.823174i	$0.307799\pi$
$67$			13.4759i			1.64635i	−0.567789	+	0.823174i	$0.692201\pi$
$68$	3.16247	+	5.47757i	0.383506	+	0.664252i
$69$	−1.47996	−	2.56336i	−0.178166	−	0.308592i
$70$		0			0
$71$	−6.13246	+	3.54058i	−0.727789	+	0.420189i	−0.817613	−	0.575769i	$-0.804703\pi$
$71$	−6.13246	+	3.54058i	−0.727789	+	0.420189i	0.0898239	+	0.995958i	$0.471370\pi$
$72$		−	1.27644i		−	0.150430i
$73$	−1.87133	+	1.08041i	−0.219023	+	0.126453i	−0.605498	−	0.795847i	$-0.707026\pi$
$73$	−1.87133	+	1.08041i	−0.219023	+	0.126453i	0.386475	+	0.922300i	$0.373693\pi$
$74$	−0.380087	+	0.658329i	−0.0441842	+	0.0765292i
$75$	−0.625992	−	1.08425i	−0.0722834	−	0.125198i
$76$	2.48281	+	1.43345i	0.284797	+	0.164428i
$77$		0			0
$78$	−0.218777	−	0.126454i	−0.0247716	−	0.0143181i
$79$	3.44391	−	5.96502i	0.387470	−	0.671117i	−0.604639	−	0.796500i	$-0.706682\pi$
$79$	3.44391	−	5.96502i	0.387470	−	0.671117i	0.992108	+	0.125382i	$0.0400158\pi$
$80$			6.60628i			0.738605i
$81$	6.06339			0.673710
$82$	0.701376			0.0774540
$83$		−	0.567380i		−	0.0622780i	−0.999515	−	0.0311390i	$-0.990087\pi$
$83$		−	0.567380i		−	0.0622780i	0.999515	−	0.0311390i	$-0.00991345\pi$
$84$		0			0
$85$	−4.65725	+	2.68887i	−0.505150	+	0.291648i
$86$	−0.0805861	−	0.0465264i	−0.00868982	−	0.00501707i
$87$	−2.38641	+	4.13339i	−0.255850	+	0.443146i
$88$	−0.174906			−0.0186450
$89$	−0.986346	+	0.569467i	−0.104553	+	0.0603634i	−0.551364	−	0.834264i	$-0.685893\pi$
$89$	−0.986346	+	0.569467i	−0.104553	+	0.0603634i	0.446812	+	0.894628i	$0.352559\pi$
$90$	0.540669			0.0569915
$91$		0			0
$92$	10.0928			1.05225
$93$	2.36898	−	1.36773i	0.245652	−	0.141827i
$94$	−1.53947			−0.158784
$95$	−1.21878	+	2.11098i	−0.125044	+	0.216582i
$96$	−0.721319	−	0.416454i	−0.0736193	−	0.0425041i
$97$	−6.86572	+	3.96393i	−0.697109	+	0.402476i	−0.806270	−	0.591548i	$-0.798517\pi$
$97$	−6.86572	+	3.96393i	−0.697109	+	0.402476i	0.109161	+	0.994024i	$0.465184\pi$
$98$		0			0
$99$		−	0.970225i		−	0.0975113i
$100$	4.26905			0.426905
$101$	−15.5464			−1.54693			−0.773465	−	0.633839i	$-0.781478\pi$
$101$	−15.5464			−1.54693			−0.773465	+	0.633839i	$0.781478\pi$
$102$		−	0.223258i		−	0.0221058i
$103$	−5.14908	+	8.91847i	−0.507354	+	0.878763i	0.492610	+	0.870250i	$0.336043\pi$
$103$	−5.14908	+	8.91847i	−0.507354	+	0.878763i	−0.999964	+	0.00851245i	$0.997290\pi$
$104$	1.49827	−	0.864049i	0.146918	−	0.0847270i
$105$		0			0
$106$	−0.142916	−	0.0825124i	−0.0138812	−	0.00801432i
$107$	6.56220	+	11.3661i	0.634391	+	1.09880i	0.986644	+	0.162893i	$0.0520826\pi$
$107$	6.56220	+	11.3661i	0.634391	+	1.09880i	−0.352252	+	0.935905i	$0.614584\pi$
$108$	3.27244	−	5.66804i	0.314891	−	0.545407i
$109$	9.04641	−	5.22295i	0.866489	−	0.500268i	0.000309035	−	1.00000i	$-0.499902\pi$
$109$	9.04641	−	5.22295i	0.866489	−	0.500268i	0.866180	+	0.499732i	$0.166568\pi$
$110$		−	0.0740858i		−	0.00706380i
$111$	−3.18495	+	1.83883i	−0.302302	+	0.174534i
$112$		0			0
$113$	−2.47631	−	4.28909i	−0.232952	−	0.403484i	0.725724	−	0.687986i	$-0.241505\pi$
$113$	−2.47631	−	4.28909i	−0.232952	−	0.403484i	−0.958675	+	0.284502i	$0.908172\pi$
$114$	−0.0505978	−	0.0876380i	−0.00473892	−	0.00820805i
$115$			8.58130i			0.800211i
$116$	−8.13725	−	14.0941i	−0.755524	−	1.30861i
$117$	4.79299	+	8.31112i	0.443112	+	0.768364i
$118$	−1.12681			−0.103731
$119$		0			0
$120$	0.235772	−	0.408369i	0.0215229	−	0.0372788i
$121$	10.8671			0.987914
$122$	0.940702	−	0.543114i	0.0851671	−	0.0491713i
$123$	2.93860	+	1.69660i	0.264965	+	0.152977i
$124$			9.32746i			0.837630i
$125$			12.0705i			1.07962i
$126$		0			0
$127$	4.03366	−	6.98650i	0.357929	−	0.619951i	−0.629686	−	0.776850i	$-0.716816\pi$
$127$	4.03366	−	6.98650i	0.357929	−	0.619951i	0.987615	+	0.156899i	$0.0501496\pi$
$128$	3.27537	−	1.89104i	0.289505	−	0.167146i
$129$	−0.225091	−	0.389870i	−0.0198182	−	0.0343261i
$130$	0.365990	+	0.634632i	0.0320994	+	0.0556609i
$131$	9.45194	−	16.3712i	0.825820	−	1.43036i	−0.0754716	−	0.997148i	$-0.524046\pi$
$131$	9.45194	−	16.3712i	0.825820	−	1.43036i	0.901291	−	0.433214i	$-0.142620\pi$
$132$	−0.365075	−	0.210776i	−0.0317757	−	0.0183457i
$133$		0			0
$134$	0.810981	+	1.40466i	0.0700581	+	0.121344i
$135$	4.81920	+	2.78236i	0.414770	+	0.239468i
$136$	1.32337	+	0.764047i	0.113478	+	0.0655165i
$137$	−15.7837	−	9.11274i	−1.34850	−	0.778554i	−0.360459	−	0.932775i	$-0.617380\pi$
$137$	−15.7837	−	9.11274i	−1.34850	−	0.778554i	−0.988036	+	0.154221i	$0.950713\pi$
$138$	−0.308526	−	0.178127i	−0.0262635	−	0.0151632i
$139$	2.62542	+	4.54737i	0.222686	+	0.385703i	0.955623	−	0.294594i	$-0.0951843\pi$
$139$	2.62542	+	4.54737i	0.222686	+	0.385703i	−0.732937	+	0.680297i	$0.761851\pi$
$140$		0			0
$141$	−6.45001	−	3.72392i	−0.543189	−	0.313610i
$142$	−0.426143	+	0.738102i	−0.0357612	+	0.0619401i
$143$	1.13884	−	0.656766i	0.0952348	−	0.0549215i
$144$	5.20651	+	9.01794i	0.433876	+	0.751495i
$145$	11.9834	−	6.91862i	0.995167	−	0.574560i
$146$	−0.130038	+	0.225233i	−0.0107621	+	0.0186404i
$147$		0			0
$148$		−	12.5402i		−	1.03080i
$149$			9.27309i			0.759681i	0.925052	+	0.379841i	$0.124021\pi$
$149$			9.27309i			0.759681i	−0.925052	+	0.379841i	$0.875979\pi$
$150$	−0.130500	−	0.0753444i	−0.0106553	−	0.00615184i
$151$	12.1358	−	7.00661i	0.987597	−	0.570189i	0.0830419	−	0.996546i	$-0.473536\pi$
$151$	12.1358	−	7.00661i	0.987597	−	0.570189i	0.904555	+	0.426357i	$0.140203\pi$
$152$	0.692636			0.0561802
$153$	−4.23827	+	7.34090i	−0.342644	+	0.593476i
$154$		0			0
$155$	−7.93059			−0.637000
$156$	4.16855	+	0.00204549i	0.333751	+	0.000163770i
$157$	−8.59125	−	14.8805i	−0.685656	−	1.18759i	−0.973230	−	0.229833i	$-0.926182\pi$
$157$	−8.59125	−	14.8805i	−0.685656	−	1.18759i	0.287574	−	0.957759i	$-0.407151\pi$
$158$		−	0.829017i		−	0.0659530i
$159$	−0.399189	−	0.691415i	−0.0316577	−	0.0548328i
$160$	1.20737	+	2.09123i	0.0954511	+	0.165326i
$161$		0			0
$162$	0.632016	−	0.364894i	0.0496558	−	0.0286688i
$163$			11.7927i			0.923679i	0.886963	+	0.461840i	$0.152810\pi$
$163$			11.7927i			0.923679i	−0.886963	+	0.461840i	$0.847190\pi$
$164$	−10.0201	+	5.78511i	−0.782439	+	0.451741i
$165$	0.179211	−	0.310402i	0.0139515	−	0.0241648i
$166$	−0.0341449	−	0.0591407i	−0.00265016	−	0.00459021i
$167$	−3.73852	−	2.15843i	−0.289295	−	0.167025i	0.348329	−	0.937372i	$-0.386749\pi$
$167$	−3.73852	−	2.15843i	−0.289295	−	0.167025i	−0.637624	+	0.770348i	$0.720083\pi$
$168$		0			0
$169$	−6.51105	+	11.2519i	−0.500850	+	0.865534i
$170$	−0.323632	+	0.560546i	−0.0248214	+	0.0429919i
$171$			3.84214i			0.293816i
$172$	1.53504			0.117046
$173$	12.5197			0.951855			0.475928	−	0.879484i	$-0.342112\pi$
$173$	12.5197			0.951855			0.475928	+	0.879484i	$0.342112\pi$
$174$			0.574457i			0.0435494i
$175$		0			0
$176$	1.23569	−	0.713428i	0.0931440	−	0.0537767i
$177$	−4.72105	−	2.72570i	−0.354856	−	0.204876i
$178$	−0.0685410	+	0.118717i	−0.00513737	+	0.00889818i
$179$	6.59534			0.492959			0.246479	−	0.969148i	$-0.420726\pi$
$179$	6.59534			0.492959			0.246479	+	0.969148i	$0.420726\pi$
$180$	−7.72419	+	4.45956i	−0.575727	+	0.332396i
$181$	11.0157			0.818791			0.409395	−	0.912357i	$-0.365740\pi$
$181$	11.0157			0.818791			0.409395	+	0.912357i	$0.365740\pi$
$182$		0			0
$183$	5.25509			0.388468
$184$	2.11171	−	1.21920i	0.155678	−	0.0898805i
$185$	10.6622			0.783899
$186$	0.164620	−	0.285130i	0.0120705	−	0.0209068i
$187$	1.00590	+	0.580754i	0.0735584	+	0.0424690i
$188$	21.9934	−	12.6979i	1.60403	−	0.926089i
$189$		0			0
$190$			0.293384i			0.0212843i
$191$	5.93213			0.429234			0.214617	−	0.976698i	$-0.431150\pi$
$191$	5.93213			0.429234			0.214617	+	0.976698i	$0.431150\pi$
$192$	4.45711			0.321664
$193$		−	4.19595i		−	0.302031i	−0.988531	−	0.151016i	$-0.951746\pi$
$193$		−	4.19595i		−	0.302031i	0.988531	−	0.151016i	$-0.0482544\pi$
$194$	−0.477098	+	0.826358i	−0.0342536	+	0.0593290i
$195$	−0.00173916	+	3.54428i	−0.000124544	+	0.253811i
$196$		0			0
$197$	5.00990	+	2.89247i	0.356941	+	0.206080i	0.667738	−	0.744396i	$-0.267263\pi$
$197$	5.00990	+	2.89247i	0.356941	+	0.206080i	−0.310797	+	0.950476i	$0.600596\pi$
$198$	−0.0583881	−	0.101131i	−0.00414946	−	0.00718708i
$199$	−5.97988	+	10.3575i	−0.423903	+	0.734221i	−0.996317	−	0.0857435i	$-0.972673\pi$
$199$	−5.97988	+	10.3575i	−0.423903	+	0.734221i	0.572415	+	0.819964i	$0.306007\pi$
$200$	0.893213	−	0.515697i	0.0631597	−	0.0364653i
$201$			7.84693i			0.553480i
$202$	−1.62048	+	0.935584i	−0.114017	+	0.0658275i
$203$		0			0
$204$	1.84148	+	3.18954i	0.128930	+	0.223313i
$205$	−4.91874	−	8.51951i	−0.343540	−	0.595028i
$206$			1.23949i			0.0863590i
$207$	6.76305	+	11.7139i	0.470065	+	0.814176i
$208$	−7.06078	+	12.2158i	−0.489577	+	0.847012i
$209$	0.526475			0.0364170
$210$		0			0
$211$	4.11795	−	7.13251i	0.283492	−	0.491022i	−0.688751	−	0.724998i	$-0.741840\pi$
$211$	4.11795	−	7.13251i	0.283492	−	0.491022i	0.972242	+	0.233976i	$0.0751738\pi$
$212$	2.72233			0.186970
$213$	−3.57088	+	2.06165i	−0.244673	+	0.141262i
$214$	1.36802	+	0.789825i	0.0935157	+	0.0539913i
$215$			1.30516i			0.0890110i
$216$		−	1.58123i		−	0.107589i
$217$		0			0
$218$	0.628633	−	1.08882i	0.0425764	−	0.0737445i
$219$	−1.08966	+	0.629116i	−0.0736325	+	0.0425117i
$220$	0.611077	+	1.05842i	0.0411988	+	0.0713584i
$221$	−11.4857	−	0.00563595i	−0.772609	−	0.000379115i
$222$	−0.221321	+	0.383340i	−0.0148541	+	0.0257281i
$223$	−13.2515	−	7.65073i	−0.887383	−	0.512331i	−0.0142977	−	0.999898i	$-0.504551\pi$
$223$	−13.2515	−	7.65073i	−0.887383	−	0.512331i	−0.873086	+	0.487567i	$0.837885\pi$
$224$		0			0
$225$	2.86064	+	4.95477i	0.190709	+	0.330318i
$226$	−0.516235	−	0.298048i	−0.0343394	−	0.0198259i
$227$	−6.02292	−	3.47733i	−0.399755	−	0.230799i	0.286623	−	0.958043i	$-0.407467\pi$
$227$	−6.02292	−	3.47733i	−0.399755	−	0.230799i	−0.686378	+	0.727245i	$0.740801\pi$
$228$	1.44572	+	0.834686i	0.0957450	+	0.0552784i
$229$	−23.7481	−	13.7110i	−1.56932	−	0.906045i	−0.996249	−	0.0865377i	$-0.972420\pi$
$229$	−23.7481	−	13.7110i	−1.56932	−	0.906045i	−0.573068	−	0.819508i	$-0.694247\pi$
$230$	0.516422	+	0.894470i	0.0340519	+	0.0589796i
$231$		0			0
$232$	−3.40511	−	1.96594i	−0.223556	−	0.129070i
$233$	−3.42666	+	5.93515i	−0.224488	+	0.388825i	−0.956166	−	0.292826i	$-0.905404\pi$
$233$	−3.42666	+	5.93515i	−0.224488	+	0.388825i	0.731678	+	0.681651i	$0.238738\pi$
$234$	0.999759	+	0.577866i	0.0653563	+	0.0377763i
$235$	10.7963	+	18.6997i	0.704271	+	1.21983i
$236$	16.0980	−	9.29416i	1.04789	−	0.604998i
$237$	2.00536	−	3.47338i	0.130262	−	0.225621i
$238$		0			0
$239$			22.0754i			1.42794i	0.700177	+	0.713970i	$0.253105\pi$
$239$			22.0754i			1.42794i	−0.700177	+	0.713970i	$0.746895\pi$
$240$			3.84679i			0.248309i
$241$	13.6807	+	7.89855i	0.881251	+	0.508790i	0.871071	−	0.491158i	$-0.163426\pi$
$241$	13.6807	+	7.89855i	0.881251	+	0.508790i	0.0101802	+	0.999948i	$0.496759\pi$
$242$	1.13272	−	0.653979i	0.0728143	−	0.0420393i
$243$	13.4196			0.860869
$244$	−8.95947	+	15.5183i	−0.573571	+	0.993455i
$245$		0			0
$246$	0.408405			0.0260390
$247$	−4.50988	+	2.60083i	−0.286957	+	0.165487i
$248$	1.12675	+	1.95158i	0.0715485	+	0.123926i
$249$		−	0.330381i		−	0.0209370i
$250$	0.726405	+	1.25817i	0.0459419	+	0.0795737i
$251$	−11.2783	−	19.5346i	−0.711882	−	1.23302i	−0.964150	−	0.265359i	$-0.914510\pi$
$251$	−11.2783	−	19.5346i	−0.711882	−	1.23302i	0.252268	−	0.967658i	$-0.418824\pi$
$252$		0			0
$253$	1.60512	−	0.926716i	0.100913	−	0.0582621i
$254$		−	0.970981i		−	0.0609247i
$255$	−2.71188	+	1.56570i	−0.169825	+	0.0980483i
$256$	−7.42681	+	12.8636i	−0.464176	+	0.803976i
$257$	−10.2064	−	17.6781i	−0.636660	−	1.10273i	−0.986161	−	0.165791i	$-0.946982\pi$
$257$	−10.2064	−	17.6781i	−0.636660	−	1.10273i	0.349501	−	0.936936i	$-0.386351\pi$
$258$	−0.0469247	−	0.0270920i	−0.00292140	−	0.00168667i
$259$		0			0
$260$	−10.4633	−	6.04781i	−0.648904	−	0.375069i
$261$	10.9053	−	18.8886i	0.675023	−	1.16917i
$262$		−	2.27527i		−	0.140567i
$263$	−29.5402			−1.82153			−0.910764	−	0.412927i	$-0.864506\pi$
$263$	−29.5402			−1.82153			−0.910764	+	0.412927i	$0.864506\pi$
$264$	−0.101846			−0.00626820
$265$			2.31464i			0.142187i
$266$		0			0
$267$	−0.574342	+	0.331596i	−0.0351491	+	0.0202934i
$268$	−23.1719	−	13.3783i	−1.41545	−	0.817211i
$269$	13.9581	−	24.1762i	0.851043	−	1.47405i	−0.0292252	−	0.999573i	$-0.509304\pi$
$269$	13.9581	−	24.1762i	0.851043	−	1.47405i	0.880268	−	0.474477i	$-0.157363\pi$
$270$	0.669770			0.0407609
$271$	−25.5036	+	14.7245i	−1.54924	+	0.894451i	−0.551035	+	0.834482i	$0.685767\pi$
$271$	−25.5036	+	14.7245i	−1.54924	+	0.894451i	−0.998200	+	0.0599690i	$0.980900\pi$
$272$	−12.4660			−0.755861
$273$		0			0
$274$	−2.19362			−0.132521
$275$	0.678933	−	0.391982i	0.0409412	−	0.0236374i
$276$	5.87695			0.353751
$277$	3.42927	−	5.93967i	0.206045	−	0.356880i	−0.744420	−	0.667711i	$-0.767274\pi$
$277$	3.42927	−	5.93967i	0.206045	−	0.356880i	0.950465	+	0.310831i	$0.100607\pi$
$278$	0.547321	+	0.315996i	0.0328261	+	0.0189522i
$279$	−10.8257	+	6.25021i	−0.648117	+	0.374190i
$280$		0			0
$281$		−	29.0940i		−	1.73561i	−0.496909	−	0.867803i	$-0.665532\pi$
$281$		−	29.0940i		−	1.73561i	0.496909	−	0.867803i	$-0.334468\pi$
$282$	−0.896420			−0.0533810
$283$	11.6102			0.690156			0.345078	−	0.938574i	$-0.387853\pi$
$283$	11.6102			0.690156			0.345078	+	0.938574i	$0.387853\pi$
$284$		−	14.0597i		−	0.834291i
$285$	−0.709684	+	1.22921i	−0.0420381	+	0.0728121i
$286$	0.0791828	−	0.136993i	0.00468217	−	0.00810058i
$287$		0			0
$288$	3.29626	+	1.90310i	0.194234	+	0.112141i
$289$	3.42614	+	5.93425i	0.201538	+	0.349074i
$290$	0.832724	−	1.44232i	0.0488993	−	0.0846960i
$291$	−3.99786	+	2.30816i	−0.234358	+	0.135307i
$292$		−	4.29035i		−	0.251074i
$293$	15.4054	−	8.89430i	0.899992	−	0.519610i	0.0227942	−	0.999740i	$-0.492744\pi$
$293$	15.4054	−	8.89430i	0.899992	−	0.519610i	0.877197	+	0.480130i	$0.159410\pi$
$294$		0			0
$295$	7.90228	+	13.6871i	0.460088	+	0.796896i
$296$	−1.51484	−	2.62378i	−0.0880483	−	0.152504i
$297$		−	1.20190i		−	0.0697412i
$298$	0.558054	+	0.966578i	0.0323272	+	0.0559924i
$299$	−9.17168	+	15.8678i	−0.530412	+	0.917660i
$300$	2.48583			0.143520
$301$		0			0
$302$	0.843314	−	1.46066i	0.0485273	−	0.0840517i
$303$	−9.05257			−0.520057
$304$	−4.89341	+	2.82521i	−0.280657	+	0.162037i
$305$	−13.1943	−	7.61771i	−0.755501	−	0.436189i
$306$			1.02024i			0.0583230i
$307$		−	9.07966i		−	0.518204i	−0.965850	−	0.259102i	$-0.916573\pi$
$307$		−	9.07966i		−	0.518204i	0.965850	−	0.259102i	$-0.0834265\pi$
$308$		0			0
$309$	−2.99827	+	5.19315i	−0.170566	+	0.295428i
$310$	−0.826643	+	0.477262i	−0.0469501	+	0.0271067i
$311$	−0.785363	−	1.36029i	−0.0445338	−	0.0771349i	0.842899	−	0.538071i	$-0.180847\pi$
$311$	−0.785363	−	1.36029i	−0.0445338	−	0.0771349i	−0.887433	+	0.460937i	$0.847514\pi$
$312$	0.872433	−	0.503129i	0.0493918	−	0.0284841i
$313$	10.3116	−	17.8602i	0.582846	−	1.00952i	−0.412294	−	0.911051i	$-0.635272\pi$
$313$	10.3116	−	17.8602i	0.582846	−	1.00952i	0.995140	−	0.0984686i	$-0.0313944\pi$
$314$	−1.79101	−	1.03404i	−0.101073	−	0.0583544i
$315$		0			0
$316$	6.83792	+	11.8436i	0.384663	+	0.666256i
$317$	−26.4515	−	15.2718i	−1.48566	−	0.857747i	−0.485795	−	0.874073i	$-0.661470\pi$
$317$	−26.4515	−	15.2718i	−1.48566	−	0.857747i	−0.999867	+	0.0163255i	$0.994803\pi$
$318$	−0.0832187	−	0.0480463i	−0.00466667	−	0.00269430i
$319$	−2.58823	−	1.49432i	−0.144913	−	0.0836657i
$320$	−11.1907	−	6.46096i	−0.625580	−	0.361179i
$321$	3.82111	+	6.61836i	0.213274	+	0.369401i
$322$		0			0
$323$	−3.98340	−	2.29982i	−0.221642	−	0.127965i
$324$	−6.01947	+	10.4260i	−0.334415	+	0.579224i
$325$	−3.87944	+	6.71177i	−0.215192	+	0.372302i
$326$	0.709687	+	1.22921i	0.0393059	+	0.0680799i
$327$	5.26765	−	3.04128i	0.291302	−	0.168183i
$328$	−1.39767	+	2.42084i	−0.0771735	+	0.133668i
$329$		0			0
$330$		−	0.0431396i		−	0.00237476i
$331$		−	25.8531i		−	1.42101i	−0.703690	−	0.710507i	$-0.748466\pi$
$331$		−	25.8531i		−	1.42101i	0.703690	−	0.710507i	$-0.251534\pi$
$332$	0.975612	+	0.563270i	0.0535437	+	0.0309135i
$333$	14.5545	−	8.40302i	0.797579	−	0.460483i
$334$	−0.519578			−0.0284300
$335$	11.3748	−	19.7017i	0.621472	−	1.07642i
$336$		0			0
$337$	−21.3954			−1.16548			−0.582742	−	0.812657i	$-0.698020\pi$
$337$	−21.3954			−1.16548			−0.582742	+	0.812657i	$0.698020\pi$
$338$	−0.00153556	+	1.56468i	−8.35233e−5	+	0.0851073i
$339$	−1.44194	−	2.49750i	−0.0783152	−	0.135646i
$340$		−	10.6776i		−	0.579072i
$341$	0.856443	+	1.48340i	0.0463790	+	0.0803308i
$342$	0.231220	+	0.400485i	0.0125029	+	0.0216557i
$343$		0			0
$344$	0.321177	−	0.185432i	0.0173167	−	0.00999781i
$345$			4.99682i			0.269020i
$346$	1.30499	−	0.753435i	0.0701566	−	0.0405049i
$347$	−1.10442	+	1.91291i	−0.0592882	+	0.102690i	−0.894146	−	0.447775i	$-0.852216\pi$
$347$	−1.10442	+	1.91291i	−0.0592882	+	0.102690i	0.834858	+	0.550466i	$0.185550\pi$
$348$	−4.73825	−	8.20689i	−0.253997	−	0.439936i
$349$	9.77843	+	5.64558i	0.523427	+	0.302201i	0.738336	−	0.674433i	$-0.235612\pi$
$349$	9.77843	+	5.64558i	0.523427	+	0.302201i	−0.214908	+	0.976634i	$0.568945\pi$
$350$		0			0
$351$	5.93747	+	10.2957i	0.316919	+	0.549542i
$352$	0.260774	−	0.451674i	0.0138993	−	0.0240743i
$353$		−	35.6433i		−	1.89710i	−0.316623	−	0.948552i	$-0.602549\pi$
$353$		−	35.6433i		−	1.89710i	0.316623	−	0.948552i	$-0.397451\pi$
$354$	−0.656130			−0.0348729
$355$	11.9542			0.634461
$356$		−	2.26137i		−	0.119852i
$357$		0			0
$358$	0.687464	−	0.396907i	0.0363336	−	0.0209772i
$359$	−16.7331	−	9.66089i	−0.883142	−	0.509882i	−0.0114488	−	0.999934i	$-0.503644\pi$
$359$	−16.7331	−	9.66089i	−0.883142	−	0.509882i	−0.871693	+	0.490052i	$0.836978\pi$
$360$	−1.07742	+	1.86615i	−0.0567851	+	0.0983546i
$361$	16.9151			0.890270
$362$	1.14822	−	0.662924i	0.0603490	−	0.0348425i
$363$	6.32780			0.332123
$364$		0			0
$365$	3.64783			0.190936
$366$	0.547763	−	0.316251i	0.0286320	−	0.0165307i
$367$	3.72065			0.194216			0.0971082	−	0.995274i	$-0.469041\pi$
$367$	3.72065			0.194216			0.0971082	+	0.995274i	$0.469041\pi$
$368$	−9.94604	+	17.2271i	−0.518473	+	0.898022i
$369$	−13.4287	−	7.75306i	−0.699070	−	0.403608i
$370$	1.11137	−	0.641649i	0.0577773	−	0.0333578i
$371$		0			0
$372$			5.43130i			0.281600i
$373$	−3.51276			−0.181884			−0.0909420	−	0.995856i	$-0.528988\pi$
$373$	−3.51276			−0.181884			−0.0909420	+	0.995856i	$0.528988\pi$
$374$	0.139799			0.00722884
$375$			7.02858i			0.362954i
$376$	3.06779	−	5.31356i	0.158209	−	0.274026i
$377$	29.5533	+	0.0145016i	1.52207	+	0.000746873i
$378$		0			0
$379$	21.6647	+	12.5081i	1.11284	+	0.642500i	0.939564	−	0.342373i	$-0.111230\pi$
$379$	21.6647	+	12.5081i	1.11284	+	0.642500i	0.173279	+	0.984873i	$0.444564\pi$
$380$	−2.41990	−	4.19139i	−0.124138	−	0.215014i
$381$	2.34877	−	4.06818i	0.120331	−	0.208419i
$382$	0.618333	−	0.356995i	0.0316367	−	0.0182655i
$383$			22.4654i			1.14793i	0.818881	+	0.573964i	$0.194595\pi$
$383$			22.4654i			1.14793i	−0.818881	+	0.573964i	$0.805405\pi$
$384$	1.90722	−	1.10114i	0.0973276	−	0.0561921i
$385$		0			0
$386$	−0.252512	−	0.437364i	−0.0128525	−	0.0222612i
$387$	1.02861	+	1.78161i	0.0522874	+	0.0905644i
$388$		−	15.7409i		−	0.799121i
$389$	−6.66822	−	11.5497i	−0.338092	−	0.585592i	0.645982	−	0.763353i	$-0.276448\pi$
$389$	−6.66822	−	11.5497i	−0.338092	−	0.585592i	−0.984074	+	0.177760i	$0.943115\pi$
$390$	0.213113	+	0.369541i	0.0107914	+	0.0187124i
$391$	−16.1928			−0.818906
$392$		0			0
$393$	5.50379	−	9.53284i	0.277629	−	0.480868i
$394$	0.696274			0.0350778
$395$	−10.0699	+	5.81388i	−0.506674	+	0.292528i
$396$	1.66831	+	0.963198i	0.0838356	+	0.0484025i
$397$			25.8333i			1.29654i	0.761412	+	0.648268i	$0.224506\pi$
$397$			25.8333i			1.29654i	−0.761412	+	0.648268i	$0.775494\pi$
$398$			1.43948i			0.0721544i
$399$		0			0
$400$	−4.20698	+	7.28670i	−0.210349	+	0.364335i
$401$	−15.2078	+	8.78025i	−0.759443	+	0.438465i	−0.829096	−	0.559106i	$-0.811144\pi$
$401$	−15.2078	+	8.78025i	−0.759443	+	0.438465i	0.0696524	+	0.997571i	$0.477811\pi$
$402$	0.472228	+	0.817923i	0.0235526	+	0.0407943i
$403$	−14.6646	−	8.47620i	−0.730495	−	0.422229i
$404$	15.4338	−	26.7322i	0.767862	−	1.32998i
$405$	−8.86464	−	5.11800i	−0.440487	−	0.254316i
$406$		0			0
$407$	−1.15143	−	1.99434i	−0.0570745	−	0.0988559i
$408$	0.770587	+	0.444899i	0.0381497	+	0.0220258i
$409$	12.5818	+	7.26410i	0.622129	+	0.359186i	0.777698	−	0.628639i	$-0.216388\pi$
$409$	12.5818	+	7.26410i	0.622129	+	0.359186i	−0.155568	+	0.987825i	$0.549721\pi$
$410$	−1.02541	−	0.592019i	−0.0506412	−	0.0292377i
$411$	−9.19074	−	5.30628i	−0.453346	−	0.261739i
$412$	−10.2236	−	17.7077i	−0.503679	−	0.872398i
$413$		0			0
$414$	1.40989	+	0.814000i	0.0692923	+	0.0400059i
$415$	−0.478915	+	0.829506i	−0.0235090	+	0.0407188i
$416$	−0.00253069	+	5.15736i	−0.000124077	+	0.252861i
$417$	1.52876	+	2.64790i	0.0748639	+	0.129668i
$418$	0.0548769	−	0.0316832i	0.00268412	−	0.00154968i
$419$	−2.30096	+	3.98538i	−0.112409	+	0.194699i	−0.916741	−	0.399482i	$-0.869190\pi$
$419$	−2.30096	+	3.98538i	−0.112409	+	0.194699i	0.804332	+	0.594180i	$0.202523\pi$
$420$		0			0
$421$		−	19.2645i		−	0.938895i	−0.882960	−	0.469447i	$-0.844453\pi$
$421$		−	19.2645i		−	0.938895i	0.882960	−	0.469447i	$-0.155547\pi$
$422$		−	0.991273i		−	0.0482544i
$423$	29.4750	+	17.0174i	1.43312	+	0.827415i
$424$	0.569593	−	0.328854i	0.0276619	−	0.0159706i
$425$	−6.84924			−0.332237
$426$	−0.248140	+	0.429791i	−0.0120224	+	0.0208234i
$427$		0			0
$428$	−26.0587			−1.25959
$429$	0.663139	−	0.382430i	0.0320166	−	0.0184639i
$430$	0.0785443	+	0.136043i	0.00378774	+	0.00656056i
$431$			28.3651i			1.36630i	0.730279	+	0.683149i	$0.239390\pi$
$431$			28.3651i			1.36630i	−0.730279	+	0.683149i	$0.760610\pi$
$432$	6.44973	+	11.1713i	0.310313	+	0.537477i
$433$	6.26014	+	10.8429i	0.300843	+	0.521076i	0.976327	−	0.216299i	$-0.0693986\pi$
$433$	6.26014	+	10.8429i	0.300843	+	0.521076i	−0.675484	+	0.737375i	$0.736065\pi$
$434$		0			0
$435$	6.97784	−	4.02866i	0.334562	−	0.193159i
$436$			20.7405i			0.993288i
$437$	−6.35636	+	3.66984i	−0.304066	+	0.175552i
$438$	−0.0757203	+	0.131151i	−0.00361806	+	0.00626666i
$439$	−15.8637	−	27.4767i	−0.757132	−	1.31139i	−0.944307	−	0.329064i	$-0.893267\pi$
$439$	−15.8637	−	27.4767i	−0.757132	−	1.31139i	0.187176	−	0.982326i	$-0.440067\pi$
$440$	0.255711	+	0.147635i	0.0121906	+	0.00703822i
$441$		0			0
$442$	−1.19754	+	0.690619i	−0.0569613	+	0.0328494i
$443$	−0.865241	+	1.49864i	−0.0411088	+	0.0712026i	−0.885848	−	0.463976i	$-0.846422\pi$
$443$	−0.865241	+	1.49864i	−0.0411088	+	0.0712026i	0.844739	+	0.535179i	$0.179756\pi$
$444$		−	7.30205i		−	0.346540i
$445$	1.92271			0.0911452
$446$	−1.84168			−0.0872062
$447$			5.39965i			0.255394i
$448$		0			0
$449$	−9.14208	+	5.27818i	−0.431442	+	0.249093i	−0.699961	−	0.714181i	$-0.746799\pi$
$449$	−9.14208	+	5.27818i	−0.431442	+	0.249093i	0.268519	+	0.963274i	$0.413466\pi$
$450$	0.596355	+	0.344306i	0.0281125	+	0.0162307i
$451$	−1.06237	+	1.84008i	−0.0500252	+	0.0866462i
$452$	9.83349			0.462528
$453$	7.06658	−	4.07989i	0.332017	−	0.191690i
$454$	−0.837063			−0.0392853
$455$		0			0
$456$	0.403317			0.0188870
$457$	6.88399	−	3.97447i	0.322019	−	0.185918i	−0.330273	−	0.943885i	$-0.607141\pi$
$457$	6.88399	−	3.97447i	0.322019	−	0.185918i	0.652292	+	0.757968i	$0.273807\pi$
$458$	−3.30050			−0.154222
$459$	−5.25029	+	9.09377i	−0.245062	+	0.424461i
$460$	−14.7556	−	8.51915i	−0.687983	−	0.397207i
$461$	−9.43262	+	5.44592i	−0.439321	+	0.253642i	−0.703309	−	0.710884i	$-0.748295\pi$
$461$	−9.43262	+	5.44592i	−0.439321	+	0.253642i	0.263989	+	0.964526i	$0.414962\pi$
$462$		0			0
$463$		−	35.8227i		−	1.66482i	−0.554158	−	0.832411i	$-0.686960\pi$
$463$		−	35.8227i		−	1.66482i	0.554158	−	0.832411i	$-0.313040\pi$
$464$	32.0757			1.48908
$465$	−4.61792			−0.214151
$466$			0.824866i			0.0382112i
$467$	−9.94917	+	17.2325i	−0.460393	+	0.797423i	−0.998980	−	0.0451460i	$-0.985625\pi$
$467$	−9.94917	+	17.2325i	−0.460393	+	0.797423i	0.538588	+	0.842569i	$0.318958\pi$
$468$	−19.0493	−	0.00934738i	−0.880554	−	0.000432083i
$469$		0			0
$470$	2.25069	+	1.29944i	0.103817	+	0.0599386i
$471$	−5.00262	−	8.66479i	−0.230508	−	0.399252i
$472$	2.24545	−	3.88923i	0.103355	−	0.179016i
$473$	0.244127	−	0.140947i	0.0112250	−	0.00648075i
$474$		−	0.482730i		−	0.0221725i
$475$	−2.68861	+	1.55227i	−0.123362	+	0.0712231i
$476$		0			0
$477$	1.82420	+	3.15960i	0.0835243	+	0.144668i
$478$	1.32850	+	2.30102i	0.0607640	+	0.105246i
$479$			26.2902i			1.20123i	0.799538	+	0.600615i	$0.205078\pi$
$479$			26.2902i			1.20123i	−0.799538	+	0.600615i	$0.794922\pi$
$480$	0.703043	+	1.21771i	0.0320894	+	0.0555804i
$481$	19.7156	+	11.3957i	0.898954	+	0.519600i
$482$	1.90134			0.0866035
$483$		0			0
$484$	−10.7883	+	18.6860i	−0.490379	+	0.849362i
$485$	13.3835			0.607715
$486$	1.39879	−	0.807592i	0.0634504	−	0.0366331i
$487$	−5.52491	−	3.18981i	−0.250358	−	0.144544i	0.369570	−	0.929203i	$-0.379505\pi$
$487$	−5.52491	−	3.18981i	−0.250358	−	0.144544i	−0.619928	+	0.784659i	$0.712838\pi$
$488$			4.32918i			0.195973i
$489$			6.86682i			0.310528i
$490$		0			0
$491$	−1.48384	+	2.57008i	−0.0669647	+	0.115986i	−0.897564	−	0.440885i	$-0.854665\pi$
$491$	−1.48384	+	2.57008i	−0.0669647	+	0.115986i	0.830599	+	0.556871i	$0.187998\pi$
$492$	−5.83463	+	3.36862i	−0.263045	+	0.151869i
$493$	13.0554	+	22.6125i	0.587984	+	1.01842i
$494$	−0.313568	+	0.542501i	−0.0141081	+	0.0244083i
$495$	−0.818951	+	1.41846i	−0.0368091	+	0.0637552i
$496$	−15.9207	−	9.19184i	−0.714862	−	0.412726i
$497$		0			0
$498$	−0.0198823	−	0.0344371i	−0.000890947	−	0.00154316i
$499$	24.3639	+	14.0665i	1.09068	+	0.629704i	0.933757	−	0.357906i	$-0.116509\pi$
$499$	24.3639	+	14.0665i	1.09068	+	0.629704i	0.156923	+	0.987611i	$0.449843\pi$
$500$	−20.7554	−	11.9831i	−0.928208	−	0.535901i
$501$	−2.17691	−	1.25684i	−0.0972571	−	0.0561514i
$502$	−2.35119	−	1.35746i	−0.104939	−	0.0605864i
$503$	−15.7688	−	27.3124i	−0.703097	−	1.21780i	−0.967374	−	0.253353i	$-0.918467\pi$
$503$	−15.7688	−	27.3124i	−0.703097	−	1.21780i	0.264277	−	0.964447i	$-0.414867\pi$
$504$		0			0
$505$	22.7288	+	13.1225i	1.01142	+	0.583943i
$506$	0.111539	−	0.193192i	0.00495853	−	0.00858843i
$507$	−3.79133	+	6.55192i	−0.168379	+	0.290981i
$508$	8.00888	+	13.8718i	0.355336	+	0.615461i
$509$	11.7731	−	6.79719i	0.521832	−	0.301280i	−0.215852	−	0.976426i	$-0.569253\pi$
$509$	11.7731	−	6.79719i	0.521832	−	0.301280i	0.737684	+	0.675146i	$0.235919\pi$
$510$	−0.188448	+	0.326402i	−0.00834462	+	0.0144533i
$511$		0			0
$512$			9.35193i			0.413301i
$513$			4.75958i			0.210140i
$514$	−2.12773	−	1.22845i	−0.0938502	−	0.0541844i
$515$	15.0558	−	8.69250i	0.663440	−	0.383037i
$516$	0.893844			0.0393493
$517$	2.33183	−	4.03885i	0.102554	−	0.177628i
$518$		0			0
$519$	7.29012			0.320001
$520$	−2.91980	−	0.00143273i	−0.128042	−	6.28293e-5i
$521$	4.39172	+	7.60669i	0.192405	+	0.333255i	0.946047	−	0.324030i	$-0.105038\pi$
$521$	4.39172	+	7.60669i	0.192405	+	0.333255i	−0.753642	+	0.657285i	$0.771705\pi$
$522$		−	2.62513i		−	0.114899i
$523$	16.2849	+	28.2063i	0.712088	+	1.23337i	0.964072	+	0.265642i	$0.0855839\pi$
$523$	16.2849	+	28.2063i	0.712088	+	1.23337i	−0.251983	+	0.967732i	$0.581083\pi$
$524$	18.7670	+	32.5053i	0.819838	+	1.42000i
$525$		0			0
$526$	−3.07912	+	1.77773i	−0.134256	+	0.0775127i
$527$		−	14.9649i		−	0.651882i
$528$	0.719535	−	0.415424i	0.0313137	−	0.0180790i
$529$	−1.41953	+	2.45869i	−0.0617185	+	0.106900i
$530$	0.139295	+	0.241265i	0.00605057	+	0.0104799i
$531$	21.5741	+	12.4558i	0.936235	+	0.540536i
$532$		0			0
$533$	0.0103098	−	21.0107i	0.000446568	−	0.910074i
$534$	−0.0399109	+	0.0691277i	−0.00172711	+	0.00299145i
$535$		−	22.1561i		−	0.957894i
$536$	−6.46435			−0.279218
$537$	3.84041			0.165726
$538$		−	3.36000i		−	0.144860i
$539$		0			0
$540$	−9.56858	+	5.52442i	−0.411766	+	0.237733i
$541$	6.01775	+	3.47435i	0.258723	+	0.149374i	0.623752	−	0.781622i	$-0.285608\pi$
$541$	6.01775	+	3.47435i	0.258723	+	0.149374i	−0.365029	+	0.930996i	$0.618941\pi$
$542$	−1.77224	+	3.06961i	−0.0761243	+	0.131851i
$543$	6.41436			0.275266
$544$	−3.94612	+	2.27830i	−0.169189	+	0.0976811i
$545$	−17.6344			−0.755375
$546$		0			0
$547$	10.9095			0.466457			0.233229	−	0.972422i	$-0.425071\pi$
$547$	10.9095			0.466457			0.233229	+	0.972422i	$0.425071\pi$
$548$	31.3388	−	18.0935i	1.33873	−	0.772915i
$549$	−24.0145			−1.02491
$550$	0.0471789	−	0.0817163i	0.00201172	−	0.00348440i
$551$	10.2495	+	5.91758i	0.436645	+	0.252097i
$552$	1.22963	−	0.709929i	0.0523367	−	0.0302166i
$553$		0			0
$554$		−	0.825493i		−	0.0350718i
$555$	6.20850			0.263536
$556$	−10.4256			−0.442145
$557$		−	34.6295i		−	1.46730i	−0.679527	−	0.733650i	$-0.737815\pi$
$557$		−	34.6295i		−	1.46730i	0.679527	−	0.733650i	$-0.262185\pi$
$558$	−0.752275	+	1.30298i	−0.0318463	+	0.0551595i
$559$	−1.39495	+	2.41339i	−0.0590001	+	0.102075i
$560$		0			0
$561$	0.585725	+	0.338169i	0.0247293	+	0.0142775i
$562$	−1.75088	−	3.03261i	−0.0738563	−	0.127923i
$563$	−4.56839	+	7.91269i	−0.192535	+	0.333480i	−0.946090	−	0.323905i	$-0.895004\pi$
$563$	−4.56839	+	7.91269i	−0.192535	+	0.333480i	0.753555	+	0.657385i	$0.228338\pi$
$564$	12.8066	−	7.39388i	0.539254	−	0.311339i
$565$			8.36084i			0.351743i
$566$	1.21019	−	0.698702i	0.0508680	−	0.0293686i
$567$		0			0
$568$	−1.69840	−	2.94172i	−0.0712633	−	0.123432i
$569$	9.15000	+	15.8483i	0.383588	+	0.664394i	0.991572	−	0.129555i	$-0.0413549\pi$
$569$	9.15000	+	15.8483i	0.383588	+	0.664394i	−0.607984	+	0.793949i	$0.708022\pi$
$570$			0.170835i			0.00715549i
$571$	5.08954	+	8.81533i	0.212990	+	0.368910i	0.952649	−	0.304072i	$-0.0983464\pi$
$571$	5.08954	+	8.81533i	0.212990	+	0.368910i	−0.739659	+	0.672982i	$0.765013\pi$
$572$	−0.00128084	+	2.61025i	−5.35545e−5	+	0.109140i
$573$	3.45423			0.144303
$574$		0			0
$575$	−5.46470	+	9.46514i	−0.227894	+	0.394724i
$576$	−20.3679			−0.848663
$577$	−16.9018	+	9.75824i	−0.703630	+	0.406241i	−0.808698	−	0.588224i	$-0.799827\pi$
$577$	−16.9018	+	9.75824i	−0.703630	+	0.406241i	0.105068	+	0.994465i	$0.466494\pi$
$578$	0.714246	+	0.412370i	0.0297087	+	0.0171523i
$579$		−	2.44327i		−	0.101539i
$580$			27.4740i			1.14080i
$581$		0			0
$582$	−0.277810	+	0.481182i	−0.0115156	+	0.0199456i
$583$	0.432949	−	0.249963i	0.0179309	−	0.0103524i
$584$	−0.518270	−	0.897670i	−0.0214462	−	0.0371458i
$585$	0.00794753	−	16.1965i	0.000328590	−	0.669643i
$586$	1.07052	−	1.85419i	0.0442226	−	0.0765959i
$587$	30.6486	+	17.6950i	1.26501	+	0.730351i	0.974039	−	0.226382i	$-0.0726898\pi$
$587$	30.6486	+	17.6950i	1.26501	+	0.730351i	0.290967	+	0.956733i	$0.406023\pi$
$588$		0			0
$589$	−3.39156	−	5.87436i	−0.139747	−	0.242049i
$590$	1.64738	+	0.951117i	0.0678217	+	0.0391569i
$591$	2.91723	+	1.68426i	0.119999	+	0.0692812i
$592$	21.4044	+	12.3579i	0.879716	+	0.507905i
$593$	−15.6648	−	9.04406i	−0.643275	−	0.371395i	0.142600	−	0.989780i	$-0.454454\pi$
$593$	−15.6648	−	9.04406i	−0.643275	−	0.371395i	−0.785875	+	0.618385i	$0.787787\pi$
$594$	−0.0723301	−	0.125279i	−0.00296774	−	0.00514028i
$595$		0			0
$596$	−15.9451	−	9.20592i	−0.653138	−	0.377089i
$597$	−3.48204	+	6.03107i	−0.142510	+	0.246835i
$598$	−0.00108244	+	2.20593i	−4.42642e−5	+	0.0902072i
$599$	−4.52996	−	7.84612i	−0.185089	−	0.320584i	0.758517	−	0.651653i	$-0.225924\pi$
$599$	−4.52996	−	7.84612i	−0.185089	−	0.320584i	−0.943607	+	0.331069i	$0.892591\pi$
$600$	0.520111	−	0.300286i	0.0212334	−	0.0122591i
$601$	14.6440	−	25.3642i	0.597343	−	1.03463i	−0.395869	−	0.918307i	$-0.629556\pi$
$601$	14.6440	−	25.3642i	0.597343	−	1.03463i	0.993212	−	0.116321i	$-0.0371102\pi$
$602$		0			0
$603$		−	35.8586i		−	1.46028i
$604$			27.8234i			1.13212i
$605$	−15.8876	−	9.17269i	−0.645922	−	0.372923i
$606$	−0.943592	+	0.544783i	−0.0383308	+	0.0221303i
$607$	39.3650			1.59777			0.798887	−	0.601481i	$-0.205422\pi$
$607$	39.3650			1.59777			0.798887	+	0.601481i	$0.205422\pi$
$608$	−1.03268	+	1.78865i	−0.0418807	+	0.0725394i
$609$		0			0
$610$	−1.83373			−0.0742457
$611$	−0.0226293	+	46.1170i	−0.000915485	+	1.86569i
$612$	−8.41514	−	14.5755i	−0.340162	−	0.589178i
$613$		−	5.53316i		−	0.223482i	−0.993737	−	0.111741i	$-0.964357\pi$
$613$		−	5.53316i		−	0.223482i	0.993737	−	0.111741i	$-0.0356427\pi$
$614$	−0.546413	−	0.946416i	−0.0220514	−	0.0381942i
$615$	−2.86414	−	4.96084i	−0.115493	−	0.200040i
$616$		0			0
$617$	10.8959	−	6.29077i	0.438654	−	0.253257i	−0.264373	−	0.964421i	$-0.585165\pi$
$617$	10.8959	−	6.29077i	0.438654	−	0.253257i	0.703026	+	0.711164i	$0.251832\pi$
$618$			0.721742i			0.0290327i
$619$	−19.3950	+	11.1977i	−0.779552	+	0.450075i	−0.836272	−	0.548316i	$-0.815269\pi$
$619$	−19.3950	+	11.1977i	−0.779552	+	0.450075i	0.0567194	+	0.998390i	$0.481936\pi$
$620$	7.87314	−	13.6367i	0.316193	−	0.547662i
$621$	8.37794	+	14.5110i	0.336195	+	0.582307i
$622$	−0.163724	−	0.0945262i	−0.00656474	−	0.00379015i
$623$		0			0
$624$	−4.11144	+	7.11315i	−0.164589	+	0.284754i
$625$	4.81330	−	8.33687i	0.192532	−	0.333475i
$626$		−	2.48221i		−	0.0992090i
$627$	0.306562			0.0122429
$628$	34.1161			1.36138
$629$			20.1194i			0.802213i
$630$		0			0
$631$	1.68778	−	0.974439i	0.0671894	−	0.0387918i	−0.466029	−	0.884769i	$-0.654316\pi$
$631$	1.68778	−	0.974439i	0.0671894	−	0.0387918i	0.533218	+	0.845978i	$0.320982\pi$
$632$	2.86140	+	1.65203i	0.113820	+	0.0657142i
$633$	2.39785	−	4.15320i	0.0953061	−	0.165075i
$634$	−3.67621			−0.146001
$635$	−11.7944	+	6.80948i	−0.468045	+	0.270226i
$636$	1.58519			0.0628569
$637$		0			0
$638$	−0.359712			−0.0142411
$639$	16.3181	−	9.42125i	0.645533	−	0.372699i
$640$	−6.38477			−0.252380
$641$	5.21051	−	9.02487i	0.205803	−	0.356461i	−0.744585	−	0.667527i	$-0.767353\pi$
$641$	5.21051	−	9.02487i	0.205803	−	0.356461i	0.950388	+	0.311066i	$0.100686\pi$
$642$	0.796586	+	0.459909i	0.0314387	+	0.0181512i
$643$	−13.2247	+	7.63531i	−0.521533	+	0.301107i	−0.737562	−	0.675280i	$-0.764023\pi$
$643$	−13.2247	+	7.63531i	−0.521533	+	0.301107i	0.216029	+	0.976387i	$0.430690\pi$
$644$		0			0
$645$			0.759983i			0.0299243i
$646$	−0.553612			−0.0217816
$647$	17.5066			0.688254			0.344127	−	0.938923i	$-0.388175\pi$
$647$	17.5066			0.688254			0.344127	+	0.938923i	$0.388175\pi$
$648$			2.90858i			0.114260i
$649$	1.70677	−	2.95622i	0.0669966	−	0.116042i
$650$	−0.000457849		0.933064i	−1.79583e−5		0.0365978i
$651$		0			0
$652$	−20.2777	−	11.7073i	−0.794136	−	0.458494i
$653$	5.09169	+	8.81906i	0.199253	+	0.345117i	0.948287	−	0.317416i	$-0.102815\pi$
$653$	5.09169	+	8.81906i	0.199253	+	0.345117i	−0.749033	+	0.662532i	$0.769482\pi$
$654$	0.366048	−	0.634014i	0.0143136	−	0.0247919i
$655$	−27.6374	+	15.9564i	−1.07988	+	0.623470i
$656$		−	22.8040i		−	0.890346i
$657$	4.97949	−	2.87491i	0.194268	−	0.112161i
$658$		0			0
$659$	21.9294	+	37.9828i	0.854247	+	1.47960i	0.877342	+	0.479866i	$0.159315\pi$
$659$	21.9294	+	37.9828i	0.854247	+	1.47960i	−0.0230945	+	0.999733i	$0.507352\pi$
$660$	0.355825	+	0.616308i	0.0138505	+	0.0239897i
$661$		−	32.9270i		−	1.28071i	−0.768078	−	0.640356i	$-0.778787\pi$
$661$		−	32.9270i		−	1.28071i	0.768078	−	0.640356i	$-0.221213\pi$
$662$	−1.55584	−	2.69479i	−0.0604693	−	0.104736i
$663$	−6.68800	−	0.00328177i	−0.259741	−	0.000127453i
$664$	0.272170			0.0105622
$665$		0			0
$666$	1.01139	−	1.75177i	0.0391904	−	0.0678798i
$667$	41.6651			1.61328
$668$	7.42287	−	4.28560i	0.287200	−	0.165815i
$669$	−7.71622	−	4.45496i	−0.298326	−	0.172239i
$670$		−	2.73814i		−	0.105784i
$671$			3.29062i			0.127033i
$672$		0			0
$673$	13.3423	−	23.1095i	0.514307	−	0.890806i	−0.485555	−	0.874206i	$-0.661383\pi$
$673$	13.3423	−	23.1095i	0.514307	−	0.890806i	0.999862	−	0.0165997i	$-0.00528409\pi$
$674$	−2.23015	+	1.28758i	−0.0859021	+	0.0495956i
$675$	3.54370	+	6.13787i	0.136397	+	0.236247i
$676$	−12.8839	−	22.3662i	−0.495534	−	0.860239i
$677$	14.7664	−	25.5761i	0.567519	−	0.982971i	−0.429292	−	0.903166i	$-0.641237\pi$
$677$	14.7664	−	25.5761i	0.567519	−	0.982971i	0.996810	−	0.0798052i	$-0.0254298\pi$
$678$	−0.300599	−	0.173551i	−0.0115444	−	0.00666519i
$679$		0			0
$680$	−1.28984	−	2.23406i	−0.0494630	−	0.0856725i
$681$	−3.50710	−	2.02482i	−0.134392	−	0.0775914i
$682$	0.178542	+	0.103081i	0.00683674	+	0.00394719i
$683$	15.8379	+	9.14400i	0.606019	+	0.349885i	0.771406	−	0.636343i	$-0.219554\pi$
$683$	15.8379	+	9.14400i	0.606019	+	0.349885i	−0.165387	+	0.986229i	$0.552887\pi$
$684$	−6.60659	−	3.81431i	−0.252609	−	0.145844i
$685$	15.3838	+	26.6456i	0.587786	+	1.01807i
$686$		0			0
$687$	−13.8283	−	7.98378i	−0.527583	−	0.304600i
$688$	−1.51272	+	2.62012i	−0.0576721	+	0.0998910i
$689$	−2.47388	+	4.28003i	−0.0942472	+	0.163056i
$690$	0.300709	+	0.520843i	0.0114478	+	0.0198281i
$691$	−8.95525	+	5.17031i	−0.340674	+	0.196688i	−0.660570	−	0.750765i	$-0.729685\pi$
$691$	−8.95525	+	5.17031i	−0.340674	+	0.196688i	0.319896	+	0.947453i	$0.396352\pi$
$692$	−12.4290	+	21.5277i	−0.472480	+	0.818360i
$693$		0			0
$694$			0.265855i			0.0100917i
$695$		−	8.86430i		−	0.336242i
$696$	−1.98277	−	1.14475i	−0.0751567	−	0.0433917i
$697$	16.0762	−	9.28160i	0.608930	−	0.351566i
$698$	1.35900			0.0514390
$699$	−1.99532	+	3.45599i	−0.0754699	+	0.130718i
$700$		0			0
$701$	41.6959			1.57483			0.787415	−	0.616423i	$-0.211419\pi$
$701$	41.6959			1.57483			0.787415	+	0.616423i	$0.211419\pi$
$702$	1.23848	+	0.715849i	0.0467435	+	0.0270180i
$703$	4.55974	+	7.89770i	0.171974	+	0.297867i
$704$			2.79094i			0.105188i
$705$	6.28659	+	10.8887i	0.236766	+	0.410092i
$706$	−2.14501	−	3.71527i	−0.0807287	−	0.139826i
$707$		0			0
$708$	9.37371	−	5.41191i	0.352286	−	0.203392i
$709$			0.0109463i			0.000411095i	1.00000		0.000205548i	$6.54279e-5\pi$
$709$			0.0109463i			0.000411095i	−1.00000		0.000205548i	$0.999935\pi$
$710$	1.24604	−	0.719400i	0.0467630	−	0.0269986i
$711$	−9.16402	+	15.8725i	−0.343677	+	0.595267i
$712$	−0.273171	−	0.473146i	−0.0102375	−	0.0177319i
$713$	−20.6804	−	11.9398i	−0.774488	−	0.447151i
$714$		0			0
$715$	−2.21935	−	0.00108902i	−0.0829988	−	4.07271e-5i
$716$	−6.54757	+	11.3407i	−0.244694	+	0.423823i
$717$			12.8543i			0.480054i
$718$	−2.32557			−0.0867894
$719$	−25.4660			−0.949722			−0.474861	−	0.880061i	$-0.657502\pi$
$719$	−25.4660			−0.949722			−0.474861	+	0.880061i	$0.657502\pi$
$720$		−	17.5789i		−	0.655127i
$721$		0			0
$722$	1.76314	−	1.01795i	0.0656174	−	0.0378842i
$723$	7.96616	+	4.59926i	0.296265	+	0.171048i
$724$	−10.9359	+	18.9416i	−0.406430	+	0.703957i
$725$	17.6235			0.654521
$726$	0.659576	−	0.380807i	0.0244792	−	0.0141331i
$727$	23.5565			0.873663			0.436831	−	0.899543i	$-0.356101\pi$
$727$	23.5565			0.873663			0.436831	+	0.899543i	$0.356101\pi$
$728$		0			0
$729$	−10.3760			−0.384297
$730$	0.380231	−	0.219526i	0.0140730	−	0.00812503i
$731$	−2.46282			−0.0910905
$732$	−5.21703	+	9.03616i	−0.192827	+	0.333986i
$733$	5.39750	+	3.11625i	0.199361	+	0.115101i	0.596357	−	0.802719i	$-0.296614\pi$
$733$	5.39750	+	3.11625i	0.199361	+	0.115101i	−0.396996	+	0.917820i	$0.629947\pi$
$734$	0.387821	−	0.223909i	0.0143147	−	0.00826461i
$735$		0			0
$736$			7.27100i			0.268013i
$737$	−4.91357			−0.180994
$738$	−1.86632			−0.0687000
$739$		−	1.29718i		−	0.0477174i	−0.999715	−	0.0238587i	$-0.992405\pi$
$739$		−	1.29718i		−	0.0477174i	0.999715	−	0.0238587i	$-0.00759517\pi$
$740$	−10.5849	+	18.3337i	−0.389110	+	0.673959i
$741$	−2.62606	+	1.51444i	−0.0964709	+	0.0556344i
$742$		0			0
$743$	5.25627	+	3.03471i	0.192834	+	0.111333i	0.593309	−	0.804975i	$-0.297821\pi$
$743$	5.25627	+	3.03471i	0.192834	+	0.111333i	−0.400475	+	0.916308i	$0.631155\pi$
$744$	0.656096	+	1.13639i	0.0240536	+	0.0416621i
$745$	7.82725	−	13.5572i	0.286768	−	0.496697i
$746$	−0.366152	+	0.211398i	−0.0134058	+	0.00773983i
$747$			1.50976i			0.0552393i
$748$	−1.99722	+	1.15310i	−0.0730256	+	0.0421613i
$749$		0			0
$750$	0.422980	+	0.732622i	0.0154450	+	0.0267516i
$751$	−18.3023	−	31.7005i	−0.667860	−	1.15677i	−0.978501	−	0.206241i	$-0.933877\pi$
$751$	−18.3023	−	31.7005i	−0.667860	−	1.15677i	0.310641	−	0.950527i	$-0.399456\pi$
$752$			50.0531i			1.82525i
$753$	−6.56728	−	11.3749i	−0.239325	−	0.414523i
$754$	3.08135	−	1.77701i	0.112216	−	0.0647147i
$755$	−23.6566			−0.860952
$756$		0			0
$757$	−5.83991	+	10.1150i	−0.212255	+	0.367636i	−0.952420	−	0.304789i	$-0.901414\pi$
$757$	−5.83991	+	10.1150i	−0.212255	+	0.367636i	0.740165	+	0.672425i	$0.234747\pi$
$758$	3.01096			0.109363
$759$	0.934648	−	0.539619i	0.0339256	−	0.0195869i
$760$	−1.01263	−	0.584642i	−0.0367320	−	0.0212072i
$761$			39.7688i			1.44162i	0.693133	+	0.720810i	$0.256230\pi$
$761$			39.7688i			1.44162i	−0.693133	+	0.720810i	$0.743770\pi$
$762$		−	0.565394i		−	0.0204821i
$763$		0			0
$764$	−5.88916	+	10.2003i	−0.213062	+	0.369035i
$765$	12.3926	−	7.15490i	0.448057	−	0.258686i
$766$	1.35197	+	2.34167i	0.0488485	+	0.0846081i
$767$	−0.0165634	+	33.7551i	−0.000598070	+	1.21882i
$768$	−4.32457	+	7.49038i	−0.156050	+	0.270286i
$769$	8.62507	+	4.97969i	0.311028	+	0.179572i	0.647386	−	0.762162i	$-0.275862\pi$
$769$	8.62507	+	4.97969i	0.311028	+	0.179572i	−0.336358	+	0.941734i	$0.609195\pi$
$770$		0			0
$771$	−5.94313	−	10.2938i	−0.214036	−	0.370722i
$772$	7.21496	+	4.16556i	0.259672	+	0.149922i
$773$	11.0433	+	6.37588i	0.397201	+	0.229324i	0.685276	−	0.728284i	$-0.259682\pi$
$773$	11.0433	+	6.37588i	0.397201	+	0.229324i	−0.288074	+	0.957608i	$0.593015\pi$
$774$	0.214435	+	0.123804i	0.00770769	+	0.00445004i
$775$	−8.74740	−	5.05032i	−0.314216	−	0.181413i
$776$	−1.90148	−	3.29346i	−0.0682592	−	0.118228i
$777$		0			0
$778$	−1.39012	−	0.802586i	−0.0498382	−	0.0287741i
$779$	4.20705	−	7.28683i	0.150733	−	0.261078i
$780$	−6.09267	−	3.52159i	−0.218153	−	0.126093i
$781$	−1.29096	−	2.23601i	−0.0461941	−	0.0800106i
$782$	−1.68785	+	0.974483i	−0.0603575	+	0.0348474i
$783$	13.5093	−	23.3988i	0.482784	−	0.836206i
$784$		0			0
$785$			29.0069i			1.03530i
$786$		−	1.32487i		−	0.0472566i
$787$	7.52380	+	4.34387i	0.268194	+	0.154842i	0.628067	−	0.778159i	$-0.283846\pi$
$787$	7.52380	+	4.34387i	0.268194	+	0.154842i	−0.359872	+	0.933002i	$0.617180\pi$
$788$	−9.94723	+	5.74303i	−0.354355	+	0.204587i
$789$	−17.2010			−0.612373
$790$	−0.699759	+	1.21202i	−0.0248963	+	0.0431216i
$791$		0			0
$792$	0.465413			0.0165377
$793$	−16.2559	−	28.1880i	−0.577265	−	1.00099i
$794$	1.55465	+	2.69273i	0.0551723	+	0.0955613i
$795$			1.34779i			0.0478013i
$796$	−11.8731	−	20.5649i	−0.420832	−	0.728903i
$797$	−19.3719	−	33.5531i	−0.686187	−	1.18851i	−0.973062	−	0.230543i	$-0.925950\pi$
$797$	−19.3719	−	33.5531i	−0.686187	−	1.18851i	0.286875	−	0.957968i	$-0.407384\pi$
$798$		0			0
$799$	−35.2861	+	20.3724i	−1.24833	+	0.720725i
$800$			3.07549i			0.108735i
$801$	2.62460	−	1.51532i	0.0927358	−	0.0535411i
$802$	−1.05679	+	1.83041i	−0.0373166	+	0.0646342i
$803$	−0.393938	−	0.682321i	−0.0139018	−	0.0240786i
$804$	−13.4928	−	7.79009i	−0.475856	−	0.274735i
$805$		0			0
$806$	−2.03866	−	0.00100036i	−0.0718086	−	3.52361e-5i
$807$	8.12771	−	14.0776i	0.286109	−	0.495555i
$808$		−	7.45757i		−	0.262356i
$809$	28.8550			1.01449			0.507244	−	0.861802i	$-0.330664\pi$
$809$	28.8550			1.01449			0.507244	+	0.861802i	$0.330664\pi$
$810$	−1.23200			−0.0432882
$811$			12.3917i			0.435131i	0.976046	+	0.217566i	$0.0698116\pi$
$811$			12.3917i			0.435131i	−0.976046	+	0.217566i	$0.930188\pi$
$812$		0			0
$813$	−14.8506	+	8.57397i	−0.520832	+	0.300702i
$814$	−0.240039	−	0.138586i	−0.00841336	−	0.00485745i
$815$	9.95405	−	17.2409i	0.348675	−	0.603923i
$816$	−7.25884			−0.254110
$817$	−0.966758	+	0.558158i	−0.0338226	+	0.0195275i
$818$	1.74861			0.0611388
$819$		0			0
$820$	19.5324			0.682103
$821$	−35.5277	+	20.5119i	−1.23992	+	0.715870i	−0.969079	−	0.246753i	$-0.920636\pi$
$821$	−35.5277	+	20.5119i	−1.23992	+	0.715870i	−0.270845	+	0.962623i	$0.587303\pi$
$822$	−1.27733			−0.0445519
$823$	−1.06806	+	1.84994i	−0.0372304	+	0.0644849i	−0.884040	−	0.467411i	$-0.845187\pi$
$823$	−1.06806	+	1.84994i	−0.0372304	+	0.0644849i	0.846810	+	0.531896i	$0.178520\pi$
$824$	−4.27815	−	2.46999i	−0.149037	−	0.0860463i
$825$	0.395337	−	0.228248i	0.0137639	−	0.00794658i
$826$		0			0
$827$			8.54938i			0.297291i	0.988891	+	0.148645i	$0.0474913\pi$
$827$			8.54938i			0.297291i	−0.988891	+	0.148645i	$0.952509\pi$
$828$	−26.8563			−0.933320
$829$	−14.7569			−0.512528			−0.256264	−	0.966607i	$-0.582492\pi$
$829$	−14.7569			−0.512528			−0.256264	+	0.966607i	$0.582492\pi$
$830$			0.115284i			0.00400158i
$831$	1.99684	−	3.45862i	0.0692695	−	0.119978i
$832$	−13.7875	−	23.9077i	−0.477995	−	0.828850i
$833$		0			0
$834$	0.318701	+	0.184002i	0.0110357	+	0.00637146i
$835$	3.64379	+	6.31123i	0.126099	+	0.218409i
$836$	−0.522661	+	0.905276i	−0.0180766	+	0.0313096i
$837$	−13.4107	+	7.74265i	−0.463540	+	0.267625i
$838$			0.553887i			0.0191337i
$839$	−23.3581	+	13.4858i	−0.806411	+	0.465582i	−0.845708	−	0.533646i	$-0.820822\pi$
$839$	−23.3581	+	13.4858i	−0.806411	+	0.465582i	0.0392968	+	0.999228i	$0.487488\pi$
$840$		0			0
$841$	−19.0923	−	33.0687i	−0.658353	−	1.14030i
$842$	−1.15934	−	2.00803i	−0.0399534	−	0.0692013i
$843$		−	16.9412i		−	0.583487i
$844$	8.17626	+	14.1617i	0.281438	+	0.487465i
$845$	19.0167	−	10.9544i	0.654194	−	0.376843i
$846$	4.09643			0.140838
$847$		0			0
$848$	−2.68275	+	4.64665i	−0.0921259	+	0.159567i
$849$	6.76053			0.232021
$850$	−0.713928	+	0.412187i	−0.0244875	+	0.0141379i
$851$	27.8035	+	16.0524i	0.953092	+	0.550268i
$852$		−	8.18686i		−	0.280477i
$853$		−	25.6332i		−	0.877665i	−0.898569	−	0.438832i	$-0.855392\pi$
$853$		−	25.6332i		−	0.877665i	0.898569	−	0.438832i	$-0.144608\pi$
$854$		0			0
$855$	3.24309	−	5.61719i	0.110911	−	0.192104i
$856$	−5.45225	+	3.14786i	−0.186354	+	0.107592i
$857$	−5.88263	−	10.1890i	−0.200947	−	0.348050i	0.747887	−	0.663826i	$-0.231068\pi$
$857$	−5.88263	−	10.1890i	−0.200947	−	0.348050i	−0.948834	+	0.315776i	$0.897735\pi$
$858$	0.0461075	−	0.0797701i	0.00157408	−	0.00272331i
$859$	−10.8881	+	18.8587i	−0.371496	+	0.643450i	−0.989796	−	0.142492i	$-0.954488\pi$
$859$	−10.8881	+	18.8587i	−0.371496	+	0.643450i	0.618300	+	0.785942i	$0.287822\pi$
$860$	−2.24422	−	1.29570i	−0.0765274	−	0.0441831i
$861$		0			0
$862$	1.70701	+	2.95663i	0.0581410	+	0.100703i
$863$	−35.5569	−	20.5288i	−1.21037	−	0.698807i	−0.247530	−	0.968880i	$-0.579619\pi$
$863$	−35.5569	−	20.5288i	−1.21037	−	0.698807i	−0.962840	+	0.270073i	$0.912952\pi$
$864$	4.08334	+	2.35752i	0.138918	+	0.0802044i
$865$	−18.3037	−	10.5677i	−0.622345	−	0.359311i
$866$	1.30505	+	0.753470i	0.0443473	+	0.0256040i
$867$	1.99502	+	3.45547i	0.0677543	+	0.117354i
$868$		0			0
$869$	2.17496	+	1.25571i	0.0737803	+	0.0425971i
$870$	0.484889	−	0.839852i	0.0164393	−	0.0284737i
$871$	42.0905	−	24.2734i	1.42618	−	0.822474i
$872$	2.50543	+	4.33953i	0.0848445	+	0.146955i
$873$	18.2693	−	10.5478i	0.618320	−	0.356987i
$874$	−0.441702	+	0.765050i	−0.0149408	+	0.0258782i
$875$		0			0
$876$		−	2.49824i		−	0.0844076i
$877$			6.89112i			0.232696i	0.993208	+	0.116348i	$0.0371189\pi$
$877$			6.89112i			0.232696i	−0.993208	+	0.116348i	$0.962881\pi$
$878$	−3.30709	−	1.90935i	−0.111609	−	0.0644374i
$879$	8.97043	−	5.17908i	0.302565	−	0.174686i
$880$	−2.40877			−0.0811996
$881$	5.32288	−	9.21950i	0.179332	−	0.310613i	−0.762320	−	0.647201i	$-0.775940\pi$
$881$	5.32288	−	9.21950i	0.179332	−	0.310613i	0.941652	+	0.336588i	$0.109273\pi$
$882$		0			0
$883$	21.3844			0.719641			0.359821	−	0.933022i	$-0.382838\pi$
$883$	21.3844			0.719641			0.359821	+	0.933022i	$0.382838\pi$
$884$	11.4122	−	19.7440i	0.383832	−	0.664064i
$885$	4.60143	+	7.96991i	0.154675	+	0.267906i
$886$			0.208281i			0.00699732i
$887$	−17.0575	−	29.5445i	−0.572735	−	0.992007i	−0.996284	−	0.0861333i	$-0.972549\pi$
$887$	−17.0575	−	29.5445i	−0.572735	−	0.992007i	0.423548	−	0.905874i	$-0.360784\pi$
$888$	−0.882080	−	1.52781i	−0.0296007	−	0.0512698i
$889$		0			0
$890$	0.200413	−	0.115709i	0.00671786	−	0.00387856i
$891$			2.21082i			0.0740653i
$892$	26.3110	−	15.1906i	0.880956	−	0.508620i
$893$	−9.23418	+	15.9941i	−0.309010	+	0.535221i
$894$	0.324950	+	0.562831i	0.0108680	+	0.0188239i
$895$	−9.64235	−	5.56701i	−0.322308	−	0.186085i
$896$		0			0
$897$	−5.34060	+	9.23971i	−0.178317	+	0.308505i
$898$	−0.635282	+	1.10034i	−0.0211996	+	0.0367188i
$899$			38.5057i			1.28424i
$900$	−11.3597			−0.378655
$901$	−4.36769			−0.145509
$902$			0.255734i			0.00851502i
$903$		0			0
$904$	2.05746	−	1.18788i	0.0684301	−	0.0395081i
$905$	−16.1049	−	9.29816i	−0.535345	−	0.309081i
$906$	0.491055	−	0.850532i	0.0163142	−	0.0282570i
$907$	−42.1515			−1.39962			−0.699810	−	0.714329i	$-0.746732\pi$
$907$	−42.1515			−1.39962			−0.699810	+	0.714329i	$0.746732\pi$
$908$	11.9586	−	6.90429i	0.396860	−	0.229127i
$909$	41.3681			1.37209
$910$		0			0
$911$	20.9947			0.695584			0.347792	−	0.937572i	$-0.386932\pi$
$911$	20.9947			0.695584			0.347792	+	0.937572i	$0.386932\pi$
$912$	−2.84940	+	1.64510i	−0.0943529	+	0.0544747i
$913$	0.206877			0.00684663
$914$	0.478367	−	0.828556i	0.0158230	−	0.0274062i
$915$	−7.68291	−	4.43573i	−0.253989	−	0.146641i
$916$	47.1521	−	27.2233i	1.55795	−	0.899483i
$917$		0			0
$918$			1.26385i			0.0417132i
$919$	−14.2940			−0.471515			−0.235757	−	0.971812i	$-0.575757\pi$
$919$	−14.2940			−0.471515			−0.235757	+	0.971812i	$0.575757\pi$
$920$	−4.11642			−0.135714
$921$		−	5.28701i		−	0.174213i
$922$	−0.655471	+	1.13531i	−0.0215868	+	0.0373894i
$923$	22.1046	+	12.7766i	0.727583	+	0.420546i
$924$		0			0
$925$	11.7603	+	6.78983i	0.386677	+	0.223248i
$926$	−2.15581	−	3.73397i	−0.0708443	−	0.122706i
$927$	13.7014	−	23.7315i	0.450012	−	0.779444i
$928$	10.1536	−	5.86220i	0.333309	−	0.192436i
$929$		−	6.80723i		−	0.223338i	−0.993745	−	0.111669i	$-0.964380\pi$
$929$		−	6.80723i		−	0.223338i	0.993745	−	0.111669i	$-0.0356197\pi$
$930$	−0.481347	+	0.277906i	−0.0157840	+	0.00911290i
$931$		0			0
$932$	−6.80369	−	11.7843i	−0.222862	−	0.386009i
$933$	−0.457310	−	0.792085i	−0.0149717	−	0.0259317i
$934$			2.39496i			0.0783655i
$935$	−0.980409	−	1.69812i	−0.0320628	−	0.0555344i
$936$	−3.98681	+	2.29918i	−0.130313	+	0.0751510i
$937$	5.22890			0.170821			0.0854104	−	0.996346i	$-0.472780\pi$
$937$	5.22890			0.170821			0.0854104	+	0.996346i	$0.472780\pi$
$938$		0			0
$939$	6.00437	−	10.3999i	0.195945	−	0.339387i
$940$	−42.8723			−1.39834
$941$	48.8788	−	28.2202i	1.59340	−	0.919951i	0.600685	−	0.799486i	$-0.294895\pi$
$941$	48.8788	−	28.2202i	1.59340	−	0.919951i	0.992718	−	0.120465i	$-0.0384386\pi$
$942$	−1.04289	−	0.602114i	−0.0339793	−	0.0196179i
$943$		−	29.6215i		−	0.964609i
$944$			36.6361i			1.19240i
$945$		0			0
$946$	0.0169644	−	0.0293832i	0.000551559	−	0.000955329i
$947$	5.06648	−	2.92513i	0.164639	−	0.0950541i	−0.415417	−	0.909631i	$-0.636364\pi$
$947$	5.06648	−	2.92513i	0.164639	−	0.0950541i	0.580055	+	0.814577i	$0.303031\pi$
$948$	3.98167	+	6.89645i	0.129319	+	0.223986i
$949$	6.74527	+	3.89880i	0.218961	+	0.126560i
$950$	−0.186831	+	0.323601i	−0.00606160	+	0.0104990i
$951$	−15.4025	−	8.89262i	−0.499459	−	0.288363i
$952$		0			0
$953$	−10.8742	−	18.8346i	−0.352249	−	0.610114i	0.634394	−	0.773010i	$-0.281250\pi$
$953$	−10.8742	−	18.8346i	−0.352249	−	0.610114i	−0.986643	+	0.162896i	$0.947916\pi$
$954$	0.380290	+	0.219560i	0.0123123	+	0.00710853i
$955$	−8.67273	−	5.00720i	−0.280643	−	0.162029i
$956$	−37.9588	−	21.9155i	−1.22767	−	0.708798i
$957$	−1.50711	−	0.870129i	−0.0487179	−	0.0281273i
$958$	1.58214	+	2.74035i	0.0511167	+	0.0885368i
$959$		0			0
$960$	−6.51626	−	3.76217i	−0.210312	−	0.121423i
$961$	−4.46555	+	7.73456i	−0.144050	+	0.249502i
$962$	2.74084	+	0.00134492i	0.0883683	+	4.33619e-5i
$963$	−17.4616	−	30.2444i	−0.562692	−	0.974611i
$964$	−27.1632	+	15.6827i	−0.874868	+	0.505105i
$965$	−3.54173	+	6.13446i	−0.114012	+	0.197475i
$966$		0			0
$967$			13.3251i			0.428507i	0.976778	+	0.214253i	$0.0687318\pi$
$967$			13.3251i			0.428507i	−0.976778	+	0.214253i	$0.931268\pi$
$968$			5.21288i			0.167548i
$969$	−2.31950	−	1.33917i	−0.0745132	−	0.0430202i
$970$	1.39503	−	0.805420i	0.0447917	−	0.0258605i
$971$	−7.46185			−0.239462			−0.119731	−	0.992806i	$-0.538203\pi$
$971$	−7.46185			−0.239462			−0.119731	+	0.992806i	$0.538203\pi$
$972$	−13.3224	+	23.0751i	−0.427317	+	0.740134i
$973$		0			0
$974$	−0.767850			−0.0246035
$975$	−2.25897	+	3.90821i	−0.0723448	+	0.125163i
$976$	−17.6584	−	30.5853i	−0.565232	−	0.979011i
$977$			10.9605i			0.350656i	0.984510	+	0.175328i	$0.0560986\pi$
$977$			10.9605i			0.350656i	−0.984510	+	0.175328i	$0.943901\pi$
$978$	0.413245	+	0.715761i	0.0132141	+	0.0228875i
$979$	−0.207638	−	0.359640i	−0.00663614	−	0.0114941i
$980$		0			0
$981$	−24.0719	+	13.8979i	−0.768557	+	0.443727i
$982$			0.357189i			0.0113984i
$983$	−13.9812	+	8.07206i	−0.445932	+	0.257459i	−0.706111	−	0.708102i	$-0.749552\pi$
$983$	−13.9812	+	8.07206i	−0.445932	+	0.257459i	0.260179	+	0.965560i	$0.416219\pi$
$984$	−0.813853	+	1.40963i	−0.0259447	+	0.0449375i
$985$	−4.88296	−	8.45754i	−0.155584	−	0.269480i
$986$	2.72164	+	1.57134i	0.0866747	+	0.0500417i
$987$		0			0
$988$	0.00507218	−	10.3367i	0.000161368	−	0.328856i
$989$	−1.96497	+	3.40343i	−0.0624824	+	0.108223i
$990$			0.197138i			0.00626544i
$991$	6.71496			0.213308			0.106654	−	0.994296i	$-0.465986\pi$
$991$	6.71496			0.213308			0.106654	+	0.994296i	$0.465986\pi$
$992$	−6.71965			−0.213349
$993$		−	15.0540i		−	0.477725i
$994$		0			0
$995$	17.4851	−	10.0950i	0.554315	−	0.320034i
$996$	0.568091	+	0.327988i	0.0180007	+	0.0103927i
$997$	−9.22057	+	15.9705i	−0.292018	+	0.505791i	−0.974287	−	0.225311i	$-0.927660\pi$
$997$	−9.22057	+	15.9705i	−0.292018	+	0.505791i	0.682269	+	0.731102i	$0.260993\pi$
$998$	3.38609			0.107185
$999$	18.0298	−	10.4095i	0.570437	−	0.329342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.u.i.30.4		12
7.2	even	3		637.2.q.h.589.3		12
7.3	odd	6		637.2.k.h.459.4		12
7.4	even	3		637.2.k.g.459.4		12
7.5	odd	6		91.2.q.a.43.3	yes	12
7.6	odd	2		637.2.u.h.30.4		12
13.10	even	6		637.2.k.g.569.3		12
21.5	even	6		819.2.ct.a.316.4		12
28.19	even	6		1456.2.cc.c.225.3		12
91.10	odd	6		637.2.u.h.361.4		12
91.19	even	12		1183.2.a.p.1.3		6
91.23	even	6		637.2.q.h.491.3		12
91.33	even	12		1183.2.a.m.1.4		6
91.58	odd	12		8281.2.a.ch.1.3		6
91.61	odd	6		1183.2.c.i.337.7		12
91.62	odd	6		637.2.k.h.569.3		12
91.72	odd	12		8281.2.a.by.1.4		6
91.75	odd	6		91.2.q.a.36.3	✓	12
91.82	odd	6		1183.2.c.i.337.6		12
91.88	even	6	inner	637.2.u.i.361.4		12
273.257	even	6		819.2.ct.a.127.4		12
364.75	even	6		1456.2.cc.c.673.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.3	✓	12	91.75	odd	6
91.2.q.a.43.3	yes	12	7.5	odd	6
637.2.k.g.459.4		12	7.4	even	3
637.2.k.g.569.3		12	13.10	even	6
637.2.k.h.459.4		12	7.3	odd	6
637.2.k.h.569.3		12	91.62	odd	6
637.2.q.h.491.3		12	91.23	even	6
637.2.q.h.589.3		12	7.2	even	3
637.2.u.h.30.4		12	7.6	odd	2
637.2.u.h.361.4		12	91.10	odd	6
637.2.u.i.30.4		12	1.1	even	1	trivial
637.2.u.i.361.4		12	91.88	even	6	inner
819.2.ct.a.127.4		12	273.257	even	6
819.2.ct.a.316.4		12	21.5	even	6
1183.2.a.m.1.4		6	91.33	even	12
1183.2.a.p.1.3		6	91.19	even	12
1183.2.c.i.337.6		12	91.82	odd	6
1183.2.c.i.337.7		12	91.61	odd	6
1456.2.cc.c.225.3		12	28.19	even	6
1456.2.cc.c.673.3		12	364.75	even	6
8281.2.a.by.1.4		6	91.72	odd	12
8281.2.a.ch.1.3		6	91.58	odd	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.104235 - 0.0601799i) q^{2} +0.582292 q^{3} +(-0.992757 + 1.71951i) q^{4} +(-1.46199 - 0.844083i) q^{5} +(0.0606950 - 0.0350423i) q^{6} +0.479696i q^{8} -2.66094 q^{9} +O(q^{10})\)	\(q+(0.104235 - 0.0601799i) q^{2} +0.582292 q^{3} +(-0.992757 + 1.71951i) q^{4} +(-1.46199 - 0.844083i) q^{5} +(0.0606950 - 0.0350423i) q^{6} +0.479696i q^{8} -2.66094 q^{9} -0.203187 q^{10} +0.364618i q^{11} +(-0.578074 + 1.00125i) q^{12} +(-1.80124 - 3.12338i) q^{13} +(-0.851308 - 0.491503i) q^{15} +(-1.95665 - 3.38901i) q^{16} +(1.59277 - 2.75877i) q^{17} +(-0.277362 + 0.160135i) q^{18} -1.44391i q^{19} +(2.90281 - 1.67594i) q^{20} +(0.0219427 + 0.0380059i) q^{22} +(-2.54161 - 4.40219i) q^{23} +0.279323i q^{24} +(-1.07505 - 1.86204i) q^{25} +(-0.375717 - 0.217166i) q^{26} -3.29632 q^{27} +(-4.09831 + 7.09848i) q^{29} -0.118314 q^{30} +(4.06838 - 2.34888i) q^{31} +(-1.23876 - 0.715198i) q^{32} +0.212314i q^{33} -0.383412i q^{34} +(2.64166 - 4.57549i) q^{36} +(-5.46967 + 3.15792i) q^{37} +(-0.0868943 - 0.150505i) q^{38} +(-1.04885 - 1.81872i) q^{39} +(0.404903 - 0.701313i) q^{40} +(5.04661 + 2.91366i) q^{41} +(-0.386561 - 0.669543i) q^{43} +(-0.626963 - 0.361977i) q^{44} +(3.89027 + 2.24605i) q^{45} +(-0.529847 - 0.305907i) q^{46} +(-11.0769 - 6.39527i) q^{47} +(-1.13934 - 1.97339i) q^{48} +(-0.224115 - 0.129393i) q^{50} +(0.927459 - 1.60641i) q^{51} +(7.15887 + 0.00351282i) q^{52} +(-0.685548 - 1.18740i) q^{53} +(-0.343591 + 0.198372i) q^{54} +(0.307768 - 0.533070i) q^{55} -0.840776i q^{57} +0.986544i q^{58} +(-8.10770 - 4.68098i) q^{59} +(1.69028 - 0.975885i) q^{60} +9.02484 q^{61} +(0.282711 - 0.489669i) q^{62} +7.65442 q^{64} +(-0.00298674 + 6.08677i) q^{65} +(0.0127771 + 0.0221305i) q^{66} +13.4759i q^{67} +(3.16247 + 5.47757i) q^{68} +(-1.47996 - 2.56336i) q^{69} +(-6.13246 + 3.54058i) q^{71} -1.27644i q^{72} +(-1.87133 + 1.08041i) q^{73} +(-0.380087 + 0.658329i) q^{74} +(-0.625992 - 1.08425i) q^{75} +(2.48281 + 1.43345i) q^{76} +(-0.218777 - 0.126454i) q^{78} +(3.44391 - 5.96502i) q^{79} +6.60628i q^{80} +6.06339 q^{81} +0.701376 q^{82} -0.567380i q^{83} +(-4.65725 + 2.68887i) q^{85} +(-0.0805861 - 0.0465264i) q^{86} +(-2.38641 + 4.13339i) q^{87} -0.174906 q^{88} +(-0.986346 + 0.569467i) q^{89} +0.540669 q^{90} +10.0928 q^{92} +(2.36898 - 1.36773i) q^{93} -1.53947 q^{94} +(-1.21878 + 2.11098i) q^{95} +(-0.721319 - 0.416454i) q^{96} +(-6.86572 + 3.96393i) q^{97} -0.970225i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9}+O(q^{10}) \) 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9	\( 12 q + 4 q^{4} + 6 q^{5} + 18 q^{6} + 8 q^{9} + 24 q^{10} - 2 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} - 12 q^{18} + 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} - 24 q^{26} - 12 q^{27} + 8 q^{29} - 16 q^{30} - 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} + 2 q^{38} - 10 q^{39} + 46 q^{40} - 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} - 42 q^{47} + 2 q^{48} - 18 q^{50} - 26 q^{51} - 26 q^{52} + 22 q^{53} + 12 q^{54} + 6 q^{55} + 18 q^{59} + 66 q^{60} + 28 q^{61} + 4 q^{62} - 52 q^{64} - 42 q^{65} - 26 q^{66} + 8 q^{68} - 4 q^{69} - 24 q^{71} - 30 q^{73} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} + 28 q^{82} - 48 q^{85} - 60 q^{86} + 2 q^{87} + 28 q^{88} - 12 q^{89} - 24 q^{90} + 24 q^{92} + 18 q^{93} + 8 q^{94} - 22 q^{95} - 6 q^{96} - 6 q^{97}+O(q^{100}) \) 12 * q + 4 * q^4 + 6 * q^5 + 18 * q^6 + 8 * q^9 + 24 * q^10 - 2 * q^12 - 4 * q^13 + 6 * q^15 - 8 * q^16 + 4 * q^17 - 12 * q^18 + 12 * q^20 + 6 * q^22 - 12 * q^23 + 10 * q^25 - 24 * q^26 - 12 * q^27 + 8 * q^29 - 16 * q^30 - 18 * q^31 - 36 * q^32 - 10 * q^36 + 42 * q^37 + 2 * q^38 - 10 * q^39 + 46 * q^40 - 30 * q^41 + 2 * q^43 + 24 * q^44 - 12 * q^46 - 42 * q^47 + 2 * q^48 - 18 * q^50 - 26 * q^51 - 26 * q^52 + 22 * q^53 + 12 * q^54 + 6 * q^55 + 18 * q^59 + 66 * q^60 + 28 * q^61 + 4 * q^62 - 52 * q^64 - 42 * q^65 - 26 * q^66 + 8 * q^68 - 4 * q^69 - 24 * q^71 - 30 * q^73 + 6 * q^74 - 46 * q^75 + 18 * q^76 - 10 * q^78 + 28 * q^79 - 4 * q^81 + 28 * q^82 - 48 * q^85 - 60 * q^86 + 2 * q^87 + 28 * q^88 - 12 * q^89 - 24 * q^90 + 24 * q^92 + 18 * q^93 + 8 * q^94 - 22 * q^95 - 6 * q^96 - 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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