LMFDB - Embedded newform 637.2.k.h.569.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(459,637)]

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([4, 1]))

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

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

chi := DirichletCharacter("637.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.k (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:	$\Z[a_1, \ldots, a_{5}]$
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			569.3
Root			$1.34408 + 0.439820i$ of defining polynomial
Character	$\chi$	$=$	637.569
Dual form			637.2.k.h.459.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.120360i q^{2} +(0.291146 - 0.504280i) q^{3} +1.98551 q^{4} +(-1.46199 - 0.844083i) q^{5} +(-0.0606950 - 0.0350423i) q^{6} -0.479696i q^{8} +(1.33047 + 2.30444i) q^{9} +O(q^{10})$	\(q-0.120360i q^{2} +(0.291146 - 0.504280i) q^{3} +1.98551 q^{4} +(-1.46199 - 0.844083i) q^{5} +(-0.0606950 - 0.0350423i) q^{6} -0.479696i q^{8} +(1.33047 + 2.30444i) q^{9} +(-0.101594 + 0.175965i) q^{10} +(0.315769 + 0.182309i) q^{11} +(0.578074 - 1.00125i) q^{12} +(1.80124 - 3.12338i) q^{13} +(-0.851308 + 0.491503i) q^{15} +3.91329 q^{16} +3.18555 q^{17} +(0.277362 - 0.160135i) q^{18} +(-1.25046 + 0.721954i) q^{19} +(-2.90281 - 1.67594i) q^{20} +(0.0219427 - 0.0380059i) q^{22} +5.08321 q^{23} +(-0.241901 - 0.139662i) q^{24} +(-1.07505 - 1.86204i) q^{25} +(-0.375930 - 0.216797i) q^{26} +3.29632 q^{27} +(-4.09831 - 7.09848i) q^{29} +(0.0591572 + 0.102463i) q^{30} +(4.06838 - 2.34888i) q^{31} -1.43040i q^{32} +(0.183870 - 0.106157i) q^{33} -0.383412i q^{34} +(2.64166 + 4.57549i) q^{36} +6.31584i q^{37} +(0.0868943 + 0.150505i) q^{38} +(-1.05063 - 1.81769i) 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} -4.49210i q^{45} -0.611815i 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} +(3.57639 - 6.20152i) q^{52} +(-0.685548 - 1.18740i) q^{53} -0.396744i q^{54} +(-0.307768 - 0.533070i) q^{55} +0.840776i q^{57} +(-0.854372 + 0.493272i) q^{58} +9.36197i q^{59} +(-1.69028 + 0.975885i) q^{60} +(4.51242 + 7.81574i) q^{61} +(-0.282711 - 0.489669i) q^{62} +7.65442 q^{64} +(-5.26980 + 3.04597i) q^{65} +(-0.0127771 - 0.0221305i) q^{66} +(11.6705 + 6.73797i) q^{67} +6.32495 q^{68} +(1.47996 - 2.56336i) q^{69} +(-6.13246 - 3.54058i) q^{71} +(1.10543 - 0.638220i) q^{72} +(-1.87133 + 1.08041i) q^{73} +0.760173 q^{74} -1.25198 q^{75} +(-2.48281 + 1.43345i) q^{76} +(-0.218777 + 0.126454i) q^{78} +(3.44391 - 5.96502i) q^{79} +(-5.72121 - 3.30314i) q^{80} +(-3.03169 + 5.25105i) q^{81} +(0.350688 + 0.607409i) q^{82} -0.567380i q^{83} +(-4.65725 - 2.68887i) q^{85} +(0.0805861 + 0.0465264i) q^{86} -4.77282 q^{87} +(0.0874529 - 0.151473i) q^{88} -1.13893i q^{89} -0.540669 q^{90} +10.0928 q^{92} -2.73547i q^{93} +(-0.769734 + 1.33322i) q^{94} +2.43755 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 - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q - 8 * q^4 + 6 * q^5 - 18 * q^6 - 4 * q^9	$ 12 q - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9} + 12 q^{10} - 6 q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{15} + 16 q^{16} + 8 q^{17} + 12 q^{18} - 12 q^{20} + 6 q^{22} + 24 q^{23} - 12 q^{24} + 10 q^{25} + 18 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} - 18 q^{31} + 30 q^{33} - 10 q^{36} - 2 q^{38} + 14 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} - 24 q^{44} - 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} - 28 q^{52} + 22 q^{53} - 6 q^{55} + 12 q^{58} - 66 q^{60} + 14 q^{61} - 4 q^{62} - 52 q^{64} - 18 q^{65} + 26 q^{66} + 24 q^{67} + 16 q^{68} + 4 q^{69} - 24 q^{71} - 60 q^{72} - 30 q^{73} - 12 q^{74} - 92 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} + 72 q^{80} + 2 q^{81} + 14 q^{82} - 48 q^{85} + 60 q^{86} + 4 q^{87} - 14 q^{88} + 24 q^{90} + 24 q^{92} + 4 q^{94} + 44 q^{95} - 6 q^{96} + 6 q^{97}+O(q^{100}) $ 12 * q - 8 * q^4 + 6 * q^5 - 18 * q^6 - 4 * q^9 + 12 * q^10 - 6 * q^11 + 2 * q^12 + 4 * q^13 + 6 * q^15 + 16 * q^16 + 8 * q^17 + 12 * q^18 - 12 * q^20 + 6 * q^22 + 24 * q^23 - 12 * q^24 + 10 * q^25 + 18 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 - 18 * q^31 + 30 * q^33 - 10 * q^36 - 2 * q^38 + 14 * q^39 - 46 * q^40 + 30 * q^41 + 2 * q^43 - 24 * q^44 - 42 * q^47 - 2 * q^48 - 18 * q^50 - 26 * q^51 - 28 * q^52 + 22 * q^53 - 6 * q^55 + 12 * q^58 - 66 * q^60 + 14 * q^61 - 4 * q^62 - 52 * q^64 - 18 * q^65 + 26 * q^66 + 24 * q^67 + 16 * q^68 + 4 * q^69 - 24 * q^71 - 60 * q^72 - 30 * q^73 - 12 * q^74 - 92 * q^75 - 18 * q^76 - 10 * q^78 + 28 * q^79 + 72 * q^80 + 2 * q^81 + 14 * q^82 - 48 * q^85 + 60 * q^86 + 4 * q^87 - 14 * q^88 + 24 * q^90 + 24 * q^92 + 4 * q^94 + 44 * q^95 - 6 * q^96 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	0.120360i		−	0.0851073i	−0.999094	−	0.0425536i	$-0.986451\pi$
$2$		−	0.120360i		−	0.0851073i	0.999094	−	0.0425536i	$-0.0135493\pi$
$3$	0.291146	−	0.504280i	0.168093	−	0.291146i	−0.769656	−	0.638459i	$-0.779572\pi$
$3$	0.291146	−	0.504280i	0.168093	−	0.291146i	0.937749	+	0.347313i	$0.112906\pi$
$4$	1.98551			0.992757
$5$	−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
$9$	1.33047	+	2.30444i	0.443489	+	0.768146i
$10$	−0.101594	+	0.175965i	−0.0321267	+	0.0556452i
$11$	0.315769	+	0.182309i	0.0952078	+	0.0549682i	0.546848	−	0.837232i	$-0.315828\pi$
$11$	0.315769	+	0.182309i	0.0952078	+	0.0549682i	−0.451640	+	0.892200i	$0.649161\pi$
$12$	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
$16$	3.91329			0.978323
$17$	3.18555			0.772609			0.386304	−	0.922371i	$-0.373751\pi$
$17$	3.18555			0.772609			0.386304	+	0.922371i	$0.373751\pi$
$18$	0.277362	−	0.160135i	0.0653748	−	0.0377442i
$19$	−1.25046	+	0.721954i	−0.286875	+	0.165628i	−0.636532	−	0.771250i	$-0.719632\pi$
$19$	−1.25046	+	0.721954i	−0.286875	+	0.165628i	0.349657	+	0.936878i	$0.386298\pi$
$20$	−2.90281	−	1.67594i	−0.649088	−	0.374751i
$21$		0			0
$22$	0.0219427	−	0.0380059i	0.00467820	−	0.00810288i
$23$	5.08321			1.05992			0.529962	−	0.848022i	$-0.322206\pi$
$23$	5.08321			1.05992			0.529962	+	0.848022i	$0.322206\pi$
$24$	−0.241901	−	0.139662i	−0.0493778	−	0.0285083i
$25$	−1.07505	−	1.86204i	−0.215010	−	0.372408i
$26$	−0.375930	−	0.216797i	−0.0737260	−	0.0425175i
$27$	3.29632			0.634377
$28$		0			0
$29$	−4.09831	−	7.09848i	−0.761037	−	1.31815i	−0.942317	−	0.334723i	$-0.891357\pi$
$29$	−4.09831	−	7.09848i	−0.761037	−	1.31815i	0.181280	−	0.983432i	$-0.441976\pi$
$30$	0.0591572	+	0.102463i	0.0108006	+	0.0187071i
$31$	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	$0.194707\pi$
$32$		−	1.43040i		−	0.252861i
$33$	0.183870	−	0.106157i	0.0320076	−	0.0184796i
$34$		−	0.383412i		−	0.0657546i
$35$		0			0
$36$	2.64166	+	4.57549i	0.440277	+	0.762582i
$37$			6.31584i			1.03832i	0.854678	+	0.519159i	$0.173755\pi$
$37$			6.31584i			1.03832i	−0.854678	+	0.519159i	$0.826245\pi$
$38$	0.0868943	+	0.150505i	0.0140961	+	0.0244152i
$39$	−1.05063	−	1.81769i	−0.168236	−	0.291063i
$40$	−0.404903	+	0.701313i	−0.0640208	+	0.110887i
$41$	−5.04661	+	2.91366i	−0.788148	+	0.455037i	−0.839310	−	0.543653i	$-0.817041\pi$
$41$	−5.04661	+	2.91366i	−0.788148	+	0.455037i	0.0511624	+	0.998690i	$0.483707\pi$
$42$		0			0
$43$	−0.386561	+	0.669543i	−0.0589500	+	0.102104i	−0.893994	−	0.448078i	$-0.852109\pi$
$43$	−0.386561	+	0.669543i	−0.0589500	+	0.102104i	0.835044	+	0.550183i	$0.185442\pi$
$44$	0.626963	+	0.361977i	0.0945182	+	0.0545701i
$45$		−	4.49210i		−	0.669643i
$46$		−	0.611815i		−	0.0902072i
$47$	−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
$52$	3.57639	−	6.20152i	0.495956	−	0.859996i
$53$	−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	$0.863352\pi$
$54$		−	0.396744i		−	0.0539901i
$55$	−0.307768	−	0.533070i	−0.0414994	−	0.0718791i
$56$		0			0
$57$			0.840776i			0.111363i
$58$	−0.854372	+	0.493272i	−0.112185	+	0.0647698i
$59$			9.36197i			1.21882i	0.792854	+	0.609412i	$0.208595\pi$
$59$			9.36197i			1.21882i	−0.792854	+	0.609412i	$0.791405\pi$
$60$	−1.69028	+	0.975885i	−0.218215	+	0.125986i
$61$	4.51242	+	7.81574i	0.577756	+	1.00070i	0.995736	+	0.0922469i	$0.0294049\pi$
$61$	4.51242	+	7.81574i	0.577756	+	1.00070i	−0.417980	+	0.908456i	$0.637262\pi$
$62$	−0.282711	−	0.489669i	−0.0359043	−	0.0621880i
$63$		0			0
$64$	7.65442			0.956802
$65$	−5.26980	+	3.04597i	−0.653638	+	0.377806i
$66$	−0.0127771	−	0.0221305i	−0.00157275	−	0.00272408i
$67$	11.6705	+	6.73797i	1.42578	+	0.823174i	0.996784	−	0.0801330i	$-0.0255345\pi$
$67$	11.6705	+	6.73797i	1.42578	+	0.823174i	0.428995	+	0.903307i	$0.358868\pi$
$68$	6.32495			0.767013
$69$	1.47996	−	2.56336i	0.178166	−	0.308592i
$70$		0			0
$71$	−6.13246	−	3.54058i	−0.727789	−	0.420189i	0.0898239	−	0.995958i	$-0.471370\pi$
$71$	−6.13246	−	3.54058i	−0.727789	−	0.420189i	−0.817613	+	0.575769i	$0.804703\pi$
$72$	1.10543	−	0.638220i	0.130276	−	0.0752150i
$73$	−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	$0.373693\pi$
$74$	0.760173			0.0883684
$75$	−1.25198			−0.144567
$76$	−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	$0.0400158\pi$
$80$	−5.72121	−	3.30314i	−0.639651	−	0.369302i
$81$	−3.03169	+	5.25105i	−0.336855	+	0.583450i
$82$	0.350688	+	0.607409i	0.0387270	+	0.0670771i
$83$		−	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
$87$	−4.77282			−0.511700
$88$	0.0874529	−	0.151473i	0.00932251	−	0.0161471i
$89$		−	1.13893i		−	0.120727i	−0.998176	−	0.0603634i	$-0.980774\pi$
$89$		−	1.13893i		−	0.120727i	0.998176	−	0.0603634i	$-0.0192260\pi$
$90$	−0.540669			−0.0569915
$91$		0			0
$92$	10.0928			1.05225
$93$		−	2.73547i		−	0.283655i
$94$	−0.769734	+	1.33322i	−0.0793920	+	0.137511i
$95$	2.43755			0.250088
$96$	−0.721319	−	0.416454i	−0.0736193	−	0.0425041i
$97$	6.86572	+	3.96393i	0.697109	+	0.402476i	0.806270	−	0.591548i	$-0.201483\pi$
$97$	6.86572	+	3.96393i	0.697109	+	0.402476i	−0.109161	+	0.994024i	$0.534816\pi$
$98$		0			0
$99$			0.970225i			0.0975113i
$100$	−2.13452	−	3.69710i	−0.213452	−	0.369710i
$101$	−7.77322	+	13.4636i	−0.773465	+	1.33968i	0.162189	+	0.986760i	$0.448145\pi$
$101$	−7.77322	+	13.4636i	−0.773465	+	1.33968i	−0.935653	+	0.352920i	$0.885189\pi$
$102$	−0.193347	−	0.111629i	−0.0191442	−	0.0110529i
$103$	5.14908	−	8.91847i	0.507354	−	0.878763i	−0.492610	−	0.870250i	$-0.663957\pi$
$103$	5.14908	−	8.91847i	0.507354	−	0.878763i	0.999964	−	0.00851245i	$-0.00270963\pi$
$104$	−1.49827	−	0.864049i	−0.146918	−	0.0847270i
$105$		0			0
$106$	−0.142916	+	0.0825124i	−0.0138812	+	0.00801432i
$107$	−13.1244			−1.26878			−0.634391	−	0.773012i	$-0.718749\pi$
$107$	−13.1244			−1.26878			−0.634391	+	0.773012i	$0.718749\pi$
$108$	6.54488			0.629782
$109$	−9.04641	+	5.22295i	−0.866489	+	0.500268i	−0.866180	−	0.499732i	$-0.833432\pi$
$109$	−9.04641	+	5.22295i	−0.866489	+	0.500268i	−0.000309035		1.00000i	$0.500098\pi$
$110$	−0.0641602	+	0.0370429i	−0.00611743	+	0.00353190i
$111$	3.18495	+	1.83883i	0.302302	+	0.174534i
$112$		0			0
$113$	−2.47631	+	4.28909i	−0.232952	+	0.403484i	−0.958675	−	0.284502i	$-0.908172\pi$
$113$	−2.47631	+	4.28909i	−0.232952	+	0.403484i	0.725724	+	0.687986i	$0.241505\pi$
$114$	0.101196			0.00947784
$115$	−7.43163	−	4.29065i	−0.693003	−	0.400105i
$116$	−8.13725	−	14.0941i	−0.755524	−	1.30861i
$117$	9.59414	−	0.00470779i	0.886979	−	0.000435235i
$118$	1.12681			0.103731
$119$		0			0
$120$	0.235772	+	0.408369i	0.0215229	+	0.0372788i
$121$	−5.43353	−	9.41114i	−0.493957	−	0.855559i
$122$	0.940702	−	0.543114i	0.0851671	−	0.0491713i
$123$			3.39320i			0.305955i
$124$	8.07781	−	4.66373i	0.725409	−	0.418815i
$125$			12.0705i			1.07962i
$126$		0			0
$127$	4.03366	+	6.98650i	0.357929	+	0.619951i	0.987615	−	0.156899i	$-0.0501496\pi$
$127$	4.03366	+	6.98650i	0.357929	+	0.619951i	−0.629686	+	0.776850i	$0.716816\pi$
$128$		−	3.78208i		−	0.334291i
$129$	0.225091	+	0.389870i	0.0198182	+	0.0343261i
$130$	0.366613	+	0.634273i	0.0321541	+	0.0556294i
$131$	−9.45194	+	16.3712i	−0.825820	+	1.43036i	0.0754716	+	0.997148i	$0.475954\pi$
$131$	−9.45194	+	16.3712i	−0.825820	+	1.43036i	−0.901291	+	0.433214i	$0.857380\pi$
$132$	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
$136$		−	1.52809i		−	0.131033i
$137$		−	18.2255i		−	1.55711i	−0.627577	−	0.778554i	$-0.715953\pi$
$137$		−	18.2255i		−	1.55711i	0.627577	−	0.778554i	$-0.284047\pi$
$138$	−0.308526	−	0.178127i	−0.0262635	−	0.0151632i
$139$	−2.62542	+	4.54737i	−0.222686	+	0.385703i	−0.955623	−	0.294594i	$-0.904816\pi$
$139$	−2.62542	+	4.54737i	−0.222686	+	0.385703i	0.732937	+	0.680297i	$0.238149\pi$
$140$		0			0
$141$	−6.45001	+	3.72392i	−0.543189	+	0.313610i
$142$	−0.426143	+	0.738102i	−0.0357612	+	0.0619401i
$143$	1.13820	−	0.657883i	0.0951808	−	0.0550150i
$144$	5.20651	+	9.01794i	0.433876	+	0.751495i
$145$			13.8372i			1.14912i
$146$	0.130038	+	0.225233i	0.0107621	+	0.0186404i
$147$		0			0
$148$			12.5402i			1.03080i
$149$	−8.03073	+	4.63654i	−0.657903	+	0.379841i	−0.791478	−	0.611198i	$-0.790688\pi$
$149$	−8.03073	+	4.63654i	−0.657903	+	0.379841i	0.133574	+	0.991039i	$0.457354\pi$
$150$			0.150689i			0.0123037i
$151$	−12.1358	+	7.00661i	−0.987597	+	0.570189i	−0.904555	−	0.426357i	$-0.859797\pi$
$151$	−12.1358	+	7.00661i	−0.987597	+	0.570189i	−0.0830419	+	0.996546i	$0.526464\pi$
$152$	0.346318	+	0.599841i	0.0280901	+	0.0486535i
$153$	4.23827	+	7.34090i	0.342644	+	0.593476i
$154$		0			0
$155$	−7.93059			−0.637000
$156$	−2.08605	−	3.60905i	−0.167017	−	0.288955i
$157$	8.59125	+	14.8805i	0.685656	+	1.18759i	0.973230	+	0.229833i	$0.0738180\pi$
$157$	8.59125	+	14.8805i	0.685656	+	1.18759i	−0.287574	+	0.957759i	$0.592849\pi$
$158$	−0.717949	−	0.414508i	−0.0571170	−	0.0329765i
$159$	−0.798378			−0.0633155
$160$	−1.20737	+	2.09123i	−0.0954511	+	0.165326i
$161$		0			0
$162$	0.632016	+	0.364894i	0.0496558	+	0.0286688i
$163$	−10.2128	+	5.89637i	−0.799930	+	0.461840i	−0.843447	−	0.537213i	$-0.819477\pi$
$163$	−10.2128	+	5.89637i	−0.799930	+	0.461840i	0.0435169	+	0.999053i	$0.486144\pi$
$164$	−10.0201	+	5.78511i	−0.782439	+	0.451741i
$165$	−0.358422			−0.0279031
$166$	−0.0682898			−0.00530031
$167$	3.73852	−	2.15843i	0.289295	−	0.167025i	−0.348329	−	0.937372i	$-0.613251\pi$
$167$	3.73852	−	2.15843i	0.289295	−	0.167025i	0.637624	+	0.770348i	$0.279917\pi$
$168$		0			0
$169$	−6.51105	−	11.2519i	−0.500850	−	0.865534i
$170$	−0.323632	+	0.560546i	−0.0248214	+	0.0429919i
$171$	−3.32739	−	1.92107i	−0.254452	−	0.146908i
$172$	−0.767522	+	1.32939i	−0.0585230	+	0.101365i
$173$	6.25985	+	10.8424i	0.475928	+	0.824331i	0.999620	−	0.0275769i	$-0.00877910\pi$
$173$	6.25985	+	10.8424i	0.475928	+	0.824331i	−0.523692	+	0.851908i	$0.675446\pi$
$174$			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
$178$	−0.137082			−0.0102747
$179$	−3.29767	+	5.71173i	−0.246479	+	0.426915i	−0.962547	−	0.271117i	$-0.912607\pi$
$179$	−3.29767	+	5.71173i	−0.246479	+	0.426915i	0.716067	+	0.698031i	$0.245940\pi$
$180$		−	8.91913i		−	0.664792i
$181$	−11.0157			−0.818791			−0.409395	−	0.912357i	$-0.634260\pi$
$181$	−11.0157			−0.818791			−0.409395	+	0.912357i	$0.634260\pi$
$182$		0			0
$183$	5.25509			0.388468
$184$		−	2.43840i		−	0.179761i
$185$	5.33109	−	9.23371i	0.391949	−	0.678876i
$186$	−0.329240			−0.0241411
$187$	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
$191$	−2.96606	−	5.13737i	−0.214617	−	0.371727i	0.738537	−	0.674213i	$-0.235517\pi$
$191$	−2.96606	−	5.13737i	−0.214617	−	0.371727i	−0.953154	+	0.302486i	$0.902184\pi$
$192$	2.22855	−	3.85997i	0.160832	−	0.278569i
$193$	−3.63380	−	2.09798i	−0.261567	−	0.151016i	0.363482	−	0.931601i	$-0.381588\pi$
$193$	−3.63380	−	2.09798i	−0.261567	−	0.151016i	−0.625049	+	0.780586i	$0.714921\pi$
$194$	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	−0.310797	−	0.950476i	$-0.600596\pi$
$197$	5.00990	−	2.89247i	0.356941	−	0.206080i	0.667738	+	0.744396i	$0.267263\pi$
$198$	0.116776			0.00829893
$199$	−11.9598			−0.847805			−0.423903	−	0.905708i	$-0.639340\pi$
$199$	−11.9598			−0.847805			−0.423903	+	0.905708i	$0.639340\pi$
$200$	−0.893213	+	0.515697i	−0.0631597	+	0.0364653i
$201$	6.79564	−	3.92347i	0.479328	−	0.276740i
$202$	1.62048	+	0.935584i	0.114017	+	0.0658275i
$203$		0			0
$204$	1.84148	−	3.18954i	0.128930	−	0.223313i
$205$	9.83748			0.687079
$206$	−1.07343	−	0.619743i	−0.0747891	−	0.0431795i
$207$	6.76305	+	11.7139i	0.470065	+	0.814176i
$208$	7.04879	−	12.2227i	0.488746	−	0.847492i
$209$	−0.526475			−0.0364170
$210$		0			0
$211$	4.11795	+	7.13251i	0.283492	+	0.491022i	0.972242	−	0.233976i	$-0.0751738\pi$
$211$	4.11795	+	7.13251i	0.283492	+	0.491022i	−0.688751	+	0.724998i	$0.741840\pi$
$212$	−1.36116	−	2.35761i	−0.0934851	−	0.161921i
$213$	−3.57088	+	2.06165i	−0.244673	+	0.141262i
$214$			1.57965i			0.107983i
$215$	1.13030	−	0.652579i	0.0770858	−	0.0445055i
$216$		−	1.58123i		−	0.107589i
$217$		0			0
$218$	0.628633	+	1.08882i	0.0425764	+	0.0737445i
$219$			1.25823i			0.0850234i
$220$	−0.611077	−	1.05842i	−0.0411988	−	0.0713584i
$221$	5.73795	−	9.94969i	0.385976	−	0.669288i
$222$	0.221321	−	0.383340i	0.0148541	−	0.0257281i
$223$	13.2515	−	7.65073i	0.887383	−	0.512331i	0.0142977	−	0.999898i	$-0.495449\pi$
$223$	13.2515	−	7.65073i	0.887383	−	0.512331i	0.873086	+	0.487567i	$0.162115\pi$
$224$		0			0
$225$	2.86064	−	4.95477i	0.190709	−	0.330318i
$226$	0.516235	+	0.298048i	0.0343394	+	0.0198259i
$227$			6.95467i			0.461598i	0.973002	+	0.230799i	$0.0741339\pi$
$227$			6.95467i			0.461598i	−0.973002	+	0.230799i	$0.925866\pi$
$228$			1.66937i			0.110557i
$229$	−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	$0.238738\pi$
$234$	−0.000566629	−	1.15475i	−3.70417e−5	−	0.0754883i
$235$	10.7963	+	18.6997i	0.704271	+	1.21983i
$236$			18.5883i			1.21000i
$237$	−2.00536	−	3.47338i	−0.130262	−	0.225621i
$238$		0			0
$239$		−	22.0754i		−	1.42794i	−0.700177	−	0.713970i	$-0.746895\pi$
$239$		−	22.0754i		−	1.42794i	0.700177	−	0.713970i	$-0.253105\pi$
$240$	−3.33141	+	1.92339i	−0.215042	+	0.124154i
$241$		−	15.7971i		−	1.01758i	−0.860890	−	0.508790i	$-0.830093\pi$
$241$		−	15.7971i		−	1.01758i	0.860890	−	0.508790i	$-0.169907\pi$
$242$	−1.13272	+	0.653979i	−0.0728143	+	0.0420393i
$243$	6.70981	+	11.6217i	0.430434	+	0.745534i
$244$	8.95947	+	15.5183i	0.573571	+	0.993455i
$245$		0			0
$246$	0.408405			0.0260390
$247$	0.00255459	+	5.20608i	0.000162545	+	0.331255i
$248$	−1.12675	−	1.95158i	−0.0715485	−	0.123926i
$249$	−0.286118	−	0.165190i	−0.0181320	−	0.0104685i
$250$	1.45281			0.0918838
$251$	11.2783	−	19.5346i	0.711882	−	1.23302i	−0.252268	−	0.967658i	$-0.581176\pi$
$251$	11.2783	−	19.5346i	0.711882	−	1.23302i	0.964150	−	0.265359i	$-0.0854903\pi$
$252$		0			0
$253$	1.60512	+	0.926716i	0.100913	+	0.0582621i
$254$	0.840894	−	0.485490i	0.0527624	−	0.0304624i
$255$	−2.71188	+	1.56570i	−0.169825	+	0.0980483i
$256$	14.8536			0.928352
$257$	−20.4129			−1.27332			−0.636660	−	0.771145i	$-0.719685\pi$
$257$	−20.4129			−1.27332			−0.636660	+	0.771145i	$0.719685\pi$
$258$	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
$262$	1.97044	+	1.13763i	0.121734	+	0.0702833i
$263$	14.7701	−	25.5826i	0.910764	−	1.57749i	0.0977768	−	0.995208i	$-0.468827\pi$
$263$	14.7701	−	25.5826i	0.910764	−	1.57749i	0.812987	−	0.582281i	$-0.197840\pi$
$264$	−0.0509231	−	0.0882015i	−0.00313410	−	0.00542842i
$265$			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
$269$	27.9163			1.70209			0.851043	−	0.525096i	$-0.175971\pi$
$269$	27.9163			1.70209			0.851043	+	0.525096i	$0.175971\pi$
$270$	−0.334885	+	0.580038i	−0.0203805	+	0.0353000i
$271$		−	29.4491i		−	1.78890i	−0.447165	−	0.894451i	$-0.647566\pi$
$271$		−	29.4491i		−	1.78890i	0.447165	−	0.894451i	$-0.352434\pi$
$272$	12.4660			0.755861
$273$		0			0
$274$	−2.19362			−0.132521
$275$		−	0.783965i		−	0.0472748i
$276$	2.93847	−	5.08959i	0.176875	−	0.306357i
$277$	−6.85854			−0.412090			−0.206045	−	0.978543i	$-0.566059\pi$
$277$	−6.85854			−0.412090			−0.206045	+	0.978543i	$0.566059\pi$
$278$	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	$0.334468\pi$
$281$			29.0940i			1.73561i	−0.496909	+	0.867803i	$0.665532\pi$
$282$	0.448210	+	0.776323i	0.0266905	+	0.0462293i
$283$	5.80511	−	10.0547i	0.345078	−	0.597692i	−0.640290	−	0.768133i	$-0.721186\pi$
$283$	5.80511	−	10.0547i	0.345078	−	0.597692i	0.985368	+	0.170441i	$0.0545192\pi$
$284$	−12.1761	−	7.02986i	−0.722517	−	0.417146i
$285$	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
$289$	−6.85229			−0.403076
$290$	1.66545			0.0977985
$291$	3.99786	−	2.30816i	0.234358	−	0.135307i
$292$	−3.71555	+	2.14517i	−0.217436	+	0.125537i
$293$	−15.4054	−	8.89430i	−0.899992	−	0.519610i	−0.0227942	−	0.999740i	$-0.507256\pi$
$293$	−15.4054	−	8.89430i	−0.899992	−	0.519610i	−0.877197	+	0.480130i	$0.840590\pi$
$294$		0			0
$295$	7.90228	−	13.6871i	0.460088	−	0.796896i
$296$	3.02968			0.176097
$297$	1.04087	+	0.600949i	0.0603976	+	0.0348706i
$298$	0.558054	+	0.966578i	0.0323272	+	0.0559924i
$299$	9.15610	−	15.8768i	0.529511	−	0.918180i
$300$	−2.48583			−0.143520
$301$		0			0
$302$	0.843314	+	1.46066i	0.0485273	+	0.0840517i
$303$	4.52629	+	7.83976i	0.260028	+	0.450382i
$304$	−4.89341	+	2.82521i	−0.280657	+	0.162037i
$305$		−	15.2354i		−	0.872378i
$306$	0.883550	−	0.510118i	0.0505092	−	0.0291615i
$307$		−	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
$310$			0.954525i			0.0542134i
$311$	0.785363	+	1.36029i	0.0445338	+	0.0771349i	0.887433	−	0.460937i	$-0.152486\pi$
$311$	0.785363	+	1.36029i	0.0445338	+	0.0771349i	−0.842899	+	0.538071i	$0.819153\pi$
$312$	−0.871939	+	0.503985i	−0.0493638	+	0.0285325i
$313$	−10.3116	+	17.8602i	−0.582846	+	1.00952i	0.412294	+	0.911051i	$0.364728\pi$
$313$	−10.3116	+	17.8602i	−0.582846	+	1.00952i	−0.995140	+	0.0984686i	$0.968606\pi$
$314$	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	0.999867	−	0.0163255i	$-0.00519681\pi$
$317$	26.4515	+	15.2718i	1.48566	+	0.857747i	0.485795	+	0.874073i	$0.338530\pi$
$318$			0.0960927i			0.00538861i
$319$		−	2.98863i		−	0.167331i
$320$	−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
$325$	−7.75229	+	0.00380400i	−0.430019	+	0.000211008i
$326$	0.709687	+	1.22921i	0.0393059	+	0.0680799i
$327$			6.08256i			0.336366i
$328$	1.39767	+	2.42084i	0.0771735	+	0.133668i
$329$		0			0
$330$			0.0431396i			0.00237476i
$331$	22.3894	−	12.9265i	1.23063	−	0.710507i	0.263472	−	0.964667i	$-0.415132\pi$
$331$	22.3894	−	12.9265i	1.23063	−	0.710507i	0.967162	+	0.254161i	$0.0817992\pi$
$332$		−	1.12654i		−	0.0618269i
$333$	−14.5545	+	8.40302i	−0.797579	+	0.460483i
$334$	−0.259789	−	0.449967i	−0.0142150	−	0.0246211i
$335$	−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	$0.698020\pi$
$338$	−1.35428	+	0.783669i	−0.0736633	+	0.0426260i
$339$	1.44194	+	2.49750i	0.0783152	+	0.135646i
$340$	−9.24704	−	5.33878i	−0.501491	−	0.289536i
$341$	1.71289			0.0927580
$342$	−0.231220	+	0.400485i	−0.0125029	+	0.0216557i
$343$		0			0
$344$	0.321177	+	0.185432i	0.0173167	+	0.00999781i
$345$	−4.32738	+	2.49841i	−0.232978	+	0.134510i
$346$	1.30499	−	0.753435i	0.0701566	−	0.0405049i
$347$	2.20883			0.118576			0.0592882	−	0.998241i	$-0.481117\pi$
$347$	2.20883			0.118576			0.0592882	+	0.998241i	$0.481117\pi$
$348$	−9.47651			−0.507994
$349$	−9.77843	+	5.64558i	−0.523427	+	0.302201i	−0.738336	−	0.674433i	$-0.764388\pi$
$349$	−9.77843	+	5.64558i	−0.523427	+	0.302201i	0.214908	+	0.976634i	$0.431055\pi$
$350$		0			0
$351$	5.93747	−	10.2957i	0.316919	−	0.549542i
$352$	0.260774	−	0.451674i	0.0138993	−	0.0240743i
$353$	30.8680	+	17.8217i	1.64294	+	0.948552i	0.979781	+	0.200072i	$0.0641177\pi$
$353$	30.8680	+	17.8217i	1.64294	+	0.948552i	0.663158	+	0.748479i	$0.269216\pi$
$354$	0.328065	−	0.568225i	0.0174365	−	0.0302008i
$355$	5.97708	+	10.3526i	0.317230	+	0.549459i
$356$		−	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	0.871693	−	0.490052i	$-0.163022\pi$
$359$	16.7331	+	9.66089i	0.883142	+	0.509882i	0.0114488	+	0.999934i	$0.496356\pi$
$360$	−2.15484			−0.113570
$361$	−8.45757	+	14.6489i	−0.445135	+	0.770997i
$362$			1.32585i			0.0696851i
$363$	−6.32780			−0.332123
$364$		0			0
$365$	3.64783			0.190936
$366$		−	0.632502i		−	0.0330614i
$367$	1.86032	−	3.22218i	0.0971082	−	0.168196i	−0.813378	−	0.581735i	$-0.802374\pi$
$367$	1.86032	−	3.22218i	0.0971082	−	0.168196i	0.910487	+	0.413539i	$0.135707\pi$
$368$	19.8921			1.03695
$369$	−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
$373$	1.75638	+	3.04214i	0.0909420	+	0.157516i	0.907908	−	0.419170i	$-0.137679\pi$
$373$	1.75638	+	3.04214i	0.0909420	+	0.157516i	−0.816966	+	0.576686i	$0.804346\pi$
$374$	0.0698995	−	0.121070i	0.00361442	−	0.00626035i
$375$	6.08693	+	3.51429i	0.314328	+	0.181477i
$376$	−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	0.173279	−	0.984873i	$-0.444564\pi$
$379$	21.6647	−	12.5081i	1.11284	−	0.642500i	0.939564	+	0.342373i	$0.111230\pi$
$380$	4.83980			0.248276
$381$	4.69753			0.240662
$382$	−0.618333	+	0.356995i	−0.0316367	+	0.0182655i
$383$	19.4556	−	11.2327i	0.994134	−	0.573964i	0.0876266	−	0.996153i	$-0.472072\pi$
$383$	19.4556	−	11.2327i	0.994134	−	0.573964i	0.906507	+	0.422190i	$0.138738\pi$
$384$	−1.90722	−	1.10114i	−0.0973276	−	0.0561921i
$385$		0			0
$386$	−0.252512	+	0.437364i	−0.0128525	+	0.0222612i
$387$	−2.05723			−0.104575
$388$	13.6320	+	7.87043i	0.692059	+	0.399561i
$389$	−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	$0.943115\pi$
$390$	0.426589		0.000209325i	0.0216012		1.05996e-5i
$391$	16.1928			0.818906
$392$		0			0
$393$	5.50379	+	9.53284i	0.277629	+	0.480868i
$394$	−0.348137	−	0.602991i	−0.0175389	−	0.0303783i
$395$	−10.0699	+	5.81388i	−0.506674	+	0.292528i
$396$			1.92640i			0.0968050i
$397$	22.3723	−	12.9166i	1.12283	−	0.648268i	0.180710	−	0.983536i	$-0.442160\pi$
$397$	22.3723	−	12.9166i	1.12283	−	0.648268i	0.942123	+	0.335268i	$0.108827\pi$
$398$			1.43948i			0.0721544i
$399$		0			0
$400$	−4.20698	−	7.28670i	−0.210349	−	0.364335i
$401$			17.5605i			0.876930i	0.898748	+	0.438465i	$0.144478\pi$
$401$			17.5605i			0.876930i	−0.898748	+	0.438465i	$0.855522\pi$
$402$	−0.472228	−	0.817923i	−0.0235526	−	0.0407943i
$403$	−0.00831138	−	16.9380i	−0.000414019	−	0.843742i
$404$	−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
$409$		−	14.5282i		−	0.718373i	−0.933266	−	0.359186i	$-0.883054\pi$
$409$		−	14.5282i		−	0.718373i	0.933266	−	0.359186i	$-0.116946\pi$
$410$		−	1.18404i		−	0.0584755i
$411$	−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
$416$	−4.46767	−	2.57649i	−0.219046	−	0.126323i
$417$	1.52876	+	2.64790i	0.0748639	+	0.129668i
$418$			0.0633664i			0.00309935i
$419$	2.30096	+	3.98538i	0.112409	+	0.194699i	0.916741	−	0.399482i	$-0.130810\pi$
$419$	2.30096	+	3.98538i	0.112409	+	0.194699i	−0.804332	+	0.594180i	$0.797477\pi$
$420$		0			0
$421$			19.2645i			0.938895i	0.882960	+	0.469447i	$0.155547\pi$
$421$			19.2645i			0.938895i	−0.882960	+	0.469447i	$0.844453\pi$
$422$	0.858468	−	0.495637i	0.0417896	−	0.0241272i
$423$		−	34.0348i		−	1.65483i
$424$	−0.569593	+	0.328854i	−0.0276619	+	0.0159706i
$425$	−3.42462	−	5.93161i	−0.166118	−	0.287726i
$426$	0.248140	+	0.429791i	0.0120224	+	0.0208234i
$427$		0			0
$428$	−26.0587			−1.25959
$429$	−0.000375631	−	0.765510i	−1.81357e−5	−	0.0369592i
$430$	−0.0785443	−	0.136043i	−0.00378774	−	0.00656056i
$431$	24.5649	+	14.1825i	1.18325	+	0.683149i	0.956764	−	0.290865i	$-0.0939432\pi$
$431$	24.5649	+	14.1825i	1.18325	+	0.683149i	0.226485	+	0.974015i	$0.427277\pi$
$432$	12.8995			0.620625
$433$	−6.26014	+	10.8429i	−0.300843	+	0.521076i	−0.976327	−	0.216299i	$-0.930601\pi$
$433$	−6.26014	+	10.8429i	−0.300843	+	0.521076i	0.675484	+	0.737375i	$0.263935\pi$
$434$		0			0
$435$	6.97784	+	4.02866i	0.334562	+	0.193159i
$436$	−17.9618	+	10.3702i	−0.860213	+	0.496644i
$437$	−6.35636	+	3.66984i	−0.304066	+	0.175552i
$438$	0.151441			0.00723611
$439$	−31.7273			−1.51426			−0.757132	−	0.653262i	$-0.773400\pi$
$439$	−31.7273			−1.51426			−0.757132	+	0.653262i	$0.773400\pi$
$440$	−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	$0.179756\pi$
$444$	6.32376	+	3.65102i	0.300112	+	0.173270i
$445$	−0.961355	+	1.66512i	−0.0455726	+	0.0789341i
$446$	−0.920842	−	1.59494i	−0.0436031	−	0.0755228i
$447$			5.39965i			0.255394i
$448$		0			0
$449$	−9.14208	−	5.27818i	−0.431442	−	0.249093i	0.268519	−	0.963274i	$-0.413466\pi$
$449$	−9.14208	−	5.27818i	−0.431442	−	0.249093i	−0.699961	+	0.714181i	$0.746799\pi$
$450$	−0.596355	−	0.344306i	−0.0281125	−	0.0162307i
$451$	−2.12475			−0.100050
$452$	−4.91675	+	8.51605i	−0.231264	+	0.400561i
$453$			8.15978i			0.383380i
$454$	0.837063			0.0392853
$455$		0			0
$456$	0.403317			0.0188870
$457$		−	7.94894i		−	0.371836i	−0.982565	−	0.185918i	$-0.940474\pi$
$457$		−	7.94894i		−	0.371836i	0.982565	−	0.185918i	$-0.0595259\pi$
$458$	−1.65025	+	2.85832i	−0.0771111	+	0.133560i
$459$	10.5006			0.490125
$460$	−14.7556	−	8.51915i	−0.687983	−	0.397207i
$461$	9.43262	+	5.44592i	0.439321	+	0.253642i	0.703309	−	0.710884i	$-0.251705\pi$
$461$	9.43262	+	5.44592i	0.439321	+	0.253642i	−0.263989	+	0.964526i	$0.585038\pi$
$462$		0			0
$463$			35.8227i			1.66482i	0.554158	+	0.832411i	$0.313040\pi$
$463$			35.8227i			1.66482i	−0.554158	+	0.832411i	$0.686960\pi$
$464$	−16.0379	−	27.7784i	−0.744539	−	1.28958i
$465$	−2.30896	+	3.99923i	−0.107075	+	0.185460i
$466$	0.714355	+	0.412433i	0.0330918	+	0.0191056i
$467$	9.94917	−	17.2325i	0.460393	−	0.797423i	−0.538588	−	0.842569i	$-0.681042\pi$
$467$	9.94917	−	17.2325i	0.460393	−	0.797423i	0.998980	+	0.0451460i	$0.0143753\pi$
$468$	19.0493	−	0.00934738i	0.880554	−	0.000432083i
$469$		0			0
$470$	2.25069	−	1.29944i	0.103817	−	0.0599386i
$471$	10.0052			0.461017
$472$	4.49090			0.206710
$473$	−0.244127	+	0.140947i	−0.0112250	+	0.00648075i
$474$	−0.418056	+	0.241365i	−0.0192020	+	0.0110863i
$475$	2.68861	+	1.55227i	0.123362	+	0.0712231i
$476$		0			0
$477$	1.82420	−	3.15960i	0.0835243	−	0.144668i
$478$	−2.65699			−0.121528
$479$	−22.7680	−	13.1451i	−1.04030	−	0.600615i	−0.120379	−	0.992728i	$-0.538411\pi$
$479$	−22.7680	−	13.1451i	−1.04030	−	0.600615i	−0.919917	+	0.392113i	$0.871744\pi$
$480$	0.703043	+	1.21771i	0.0320894	+	0.0555804i
$481$	19.7268	+	11.3764i	0.899464	+	0.518717i
$482$	−1.90134			−0.0866035
$483$		0			0
$484$	−10.7883	−	18.6860i	−0.490379	−	0.849362i
$485$	−6.69177	−	11.5905i	−0.303857	−	0.526296i
$486$	1.39879	−	0.807592i	0.0634504	−	0.0366331i
$487$		−	6.37962i		−	0.289088i	−0.989498	−	0.144544i	$-0.953828\pi$
$487$		−	6.37962i		−	0.289088i	0.989498	−	0.144544i	$-0.0461716\pi$
$488$	3.74918	−	2.16459i	0.169717	−	0.0979864i
$489$			6.86682i			0.310528i
$490$		0			0
$491$	−1.48384	−	2.57008i	−0.0669647	−	0.115986i	0.830599	−	0.556871i	$-0.187998\pi$
$491$	−1.48384	−	2.57008i	−0.0669647	−	0.115986i	−0.897564	+	0.440885i	$0.854665\pi$
$492$			6.73725i			0.303739i
$493$	−13.0554	−	22.6125i	−0.587984	−	1.01842i
$494$	0.626603		0.000307471i	0.0281922		1.38338e-5i
$495$	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	−0.156923	−	0.987611i	$-0.550157\pi$
$499$	−24.3639	−	14.0665i	−1.09068	−	0.629704i	−0.933757	+	0.357906i	$0.883491\pi$
$500$			23.9662i			1.07180i
$501$		−	2.51368i		−	0.112303i
$502$	−2.35119	−	1.35746i	−0.104939	−	0.0605864i
$503$	15.7688	−	27.3124i	0.703097	−	1.21780i	−0.264277	−	0.964447i	$-0.585133\pi$
$503$	15.7688	−	27.3124i	0.703097	−	1.21780i	0.967374	−	0.253353i	$-0.0815334\pi$
$504$		0			0
$505$	22.7288	−	13.1225i	1.01142	−	0.583943i
$506$	0.111539	−	0.193192i	0.00495853	−	0.00858843i
$507$	−7.56979	+	0.00742891i	−0.336186	+	0.000329930i
$508$	8.00888	+	13.8718i	0.355336	+	0.615461i
$509$			13.5944i			0.602560i	0.953536	+	0.301280i	$0.0974139\pi$
$509$			13.5944i			0.602560i	−0.953536	+	0.301280i	$0.902586\pi$
$510$	0.188448	+	0.326402i	0.00834462	+	0.0144533i
$511$		0			0
$512$		−	9.35193i		−	0.413301i
$513$	−4.12191	+	2.37979i	−0.181987	+	0.105070i
$514$			2.45689i			0.108369i
$515$	−15.0558	+	8.69250i	−0.663440	+	0.383037i
$516$	0.446922	+	0.774091i	0.0196746	+	0.0340775i
$517$	−2.33183	−	4.03885i	−0.102554	−	0.177628i
$518$		0			0
$519$	7.29012			0.320001
$520$	1.46114	+	2.52790i	0.0640752	+	0.110856i
$521$	−4.39172	−	7.60669i	−0.192405	−	0.333255i	0.753642	−	0.657285i	$-0.228295\pi$
$521$	−4.39172	−	7.60669i	−0.192405	−	0.333255i	−0.946047	+	0.324030i	$0.894962\pi$
$522$	−2.27343	−	1.31256i	−0.0995053	−	0.0574494i
$523$	32.5698			1.42418			0.712088	−	0.702090i	$-0.247749\pi$
$523$	32.5698			1.42418			0.712088	+	0.702090i	$0.247749\pi$
$524$	−18.7670	+	32.5053i	−0.819838	+	1.42000i
$525$		0			0
$526$	−3.07912	−	1.77773i	−0.134256	−	0.0775127i
$527$	12.9600	−	7.48246i	0.564547	−	0.325941i
$528$	0.719535	−	0.415424i	0.0313137	−	0.0180790i
$529$	2.83905			0.123437
$530$	0.278589			0.0121011
$531$	−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
$535$	19.1878	+	11.0781i	0.829560	+	0.478947i
$536$	3.23218	−	5.59829i	0.139609	−	0.241809i
$537$	1.92021	+	3.32590i	0.0828631	+	0.143523i
$538$		−	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	0.365029	−	0.930996i	$-0.381059\pi$
$541$	−6.01775	−	3.47435i	−0.258723	−	0.149374i	−0.623752	+	0.781622i	$0.714392\pi$
$542$	−3.54448			−0.152249
$543$	−3.20718	+	5.55500i	−0.137633	+	0.238388i
$544$		−	4.55659i		−	0.195362i
$545$	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	$0.425071\pi$
$548$		−	36.1870i		−	1.54583i
$549$	−12.0073	+	20.7972i	−0.512457	+	0.887602i
$550$	−0.0943579			−0.00402343
$551$	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
$555$	−3.10425	−	5.37672i	−0.131768	−	0.228229i
$556$	−5.21282	+	9.02886i	−0.221073	+	0.382909i
$557$	−29.9901	−	17.3148i	−1.27072	−	0.733650i	−0.295596	−	0.955313i	$-0.595518\pi$
$557$	−29.9901	−	17.3148i	−1.27072	−	0.733650i	−0.975123	+	0.221662i	$0.928852\pi$
$558$	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
$562$	3.50176			0.147713
$563$	−9.13679			−0.385070			−0.192535	−	0.981290i	$-0.561671\pi$
$563$	−9.13679			−0.385070			−0.192535	+	0.981290i	$0.561671\pi$
$564$	−12.8066	+	7.39388i	−0.539254	+	0.311339i
$565$	7.24070	−	4.18042i	0.304618	−	0.175872i
$566$	−1.21019	−	0.698702i	−0.0508680	−	0.0293686i
$567$		0			0
$568$	−1.69840	+	2.94172i	−0.0712633	+	0.123432i
$569$	−18.3000			−0.767176			−0.383588	−	0.923504i	$-0.625312\pi$
$569$	−18.3000			−0.767176			−0.383588	+	0.923504i	$0.625312\pi$
$570$	−0.147947	−	0.0854175i	−0.00619684	−	0.00357775i
$571$	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	$0.765013\pi$
$572$	2.25991	−	1.30624i	0.0944914	−	0.0546165i
$573$	−3.45423			−0.144303
$574$		0			0
$575$	−5.46470	−	9.46514i	−0.227894	−	0.394724i
$576$	10.1840	+	17.6391i	0.424332	+	0.734964i
$577$	−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	$0.466494\pi$
$578$			0.824740i			0.0343047i
$579$	−2.11593	+	1.22163i	−0.0879352	+	0.0507694i
$580$			27.4740i			1.14080i
$581$		0			0
$582$	−0.277810	−	0.481182i	−0.0115156	−	0.0199456i
$583$		−	0.499926i		−	0.0207048i
$584$	0.518270	+	0.897670i	0.0214462	+	0.0371458i
$585$	−14.0306	−	8.09136i	−0.580092	−	0.334537i
$586$	−1.07052	+	1.85419i	−0.0442226	+	0.0765959i
$587$	−30.6486	+	17.6950i	−1.26501	+	0.730351i	−0.974039	−	0.226382i	$-0.927310\pi$
$587$	−30.6486	+	17.6950i	−1.26501	+	0.730351i	−0.290967	+	0.956733i	$0.593977\pi$
$588$		0			0
$589$	−3.39156	+	5.87436i	−0.139747	+	0.242049i
$590$	−1.64738	−	0.951117i	−0.0678217	−	0.0391569i
$591$		−	3.36852i		−	0.138562i
$592$			24.7157i			1.01581i
$593$	−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
$598$	−1.91093	−	1.10203i	−0.0781438	−	0.0450653i
$599$	−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	$0.892591\pi$
$600$			0.600572i			0.0245182i
$601$	−14.6440	−	25.3642i	−0.597343	−	1.03463i	−0.993212	−	0.116321i	$-0.962890\pi$
$601$	−14.6440	−	25.3642i	−0.597343	−	1.03463i	0.395869	−	0.918307i	$-0.370444\pi$
$602$		0			0
$603$			35.8586i			1.46028i
$604$	−24.0958	+	13.9117i	−0.980444	+	0.566059i
$605$			18.3454i			0.745846i
$606$	0.943592	−	0.544783i	0.0383308	−	0.0221303i
$607$	19.6825	+	34.0911i	0.798887	+	1.38371i	0.920341	+	0.391116i	$0.127911\pi$
$607$	19.6825	+	34.0911i	0.798887	+	1.38371i	−0.121454	+	0.992597i	$0.538756\pi$
$608$	1.03268	+	1.78865i	0.0418807	+	0.0725394i
$609$		0			0
$610$	−1.83373			−0.0742457
$611$	−39.9271	+	23.0781i	−1.61528	+	0.933639i
$612$	8.41514	+	14.5755i	0.340162	+	0.589178i
$613$	−4.79186	−	2.76658i	−0.193541	−	0.111741i	0.400098	−	0.916472i	$-0.368976\pi$
$613$	−4.79186	−	2.76658i	−0.193541	−	0.111741i	−0.593639	+	0.804731i	$0.702309\pi$
$614$	−1.09283			−0.0441029
$615$	2.86414	−	4.96084i	0.115493	−	0.200040i
$616$		0			0
$617$	10.8959	+	6.29077i	0.438654	+	0.253257i	0.703026	−	0.711164i	$-0.251832\pi$
$617$	10.8959	+	6.29077i	0.438654	+	0.253257i	−0.264373	+	0.964421i	$0.585165\pi$
$618$	−0.625047	+	0.360871i	−0.0251431	+	0.0145164i
$619$	−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	$0.481936\pi$
$620$	−15.7463			−0.632386
$621$	16.7559			0.672390
$622$	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
$626$	2.14965	+	1.24110i	0.0859175	+	0.0496045i
$627$	−0.153281	+	0.265491i	−0.00612145	+	0.0106027i
$628$	17.0580	+	29.5454i	0.680690	+	1.17899i
$629$			20.1194i			0.802213i
$630$		0			0
$631$	1.68778	+	0.974439i	0.0671894	+	0.0387918i	0.533218	−	0.845978i	$-0.320982\pi$
$631$	1.68778	+	0.974439i	0.0671894	+	0.0387918i	−0.466029	+	0.884769i	$0.654316\pi$
$632$	−2.86140	−	1.65203i	−0.113820	−	0.0657142i
$633$	4.79570			0.190612
$634$	1.83811	−	3.18369i	0.0730005	−	0.126441i
$635$		−	13.6190i		−	0.540452i
$636$	−1.58519			−0.0628569
$637$		0			0
$638$	−0.359712			−0.0142411
$639$		−	18.8425i		−	0.745397i
$640$	−3.19238	+	5.52937i	−0.126190	+	0.218568i
$641$	−10.4210			−0.411605			−0.205803	−	0.978594i	$-0.565981\pi$
$641$	−10.4210			−0.411605			−0.205803	+	0.978594i	$0.565981\pi$
$642$	0.796586	+	0.459909i	0.0314387	+	0.0181512i
$643$	13.2247	+	7.63531i	0.521533	+	0.301107i	0.737562	−	0.675280i	$-0.235977\pi$
$643$	13.2247	+	7.63531i	0.521533	+	0.301107i	−0.216029	+	0.976387i	$0.569310\pi$
$644$		0			0
$645$		−	0.759983i		−	0.0299243i
$646$	0.276806	+	0.479442i	0.0108908	+	0.0188634i
$647$	8.75328	−	15.1611i	0.344127	−	0.596045i	−0.641068	−	0.767484i	$-0.721508\pi$
$647$	8.75328	−	15.1611i	0.344127	−	0.596045i	0.985195	+	0.171439i	$0.0548417\pi$
$648$	2.51891	+	1.45429i	0.0989520	+	0.0571300i
$649$	−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
$653$	−10.1834			−0.398506			−0.199253	−	0.979948i	$-0.563852\pi$
$653$	−10.1834			−0.398506			−0.199253	+	0.979948i	$0.563852\pi$
$654$	0.732096			0.0286272
$655$	27.6374	−	15.9564i	1.07988	−	0.623470i
$656$	−19.7488	+	11.4020i	−0.771063	+	0.445173i
$657$	−4.97949	−	2.87491i	−0.194268	−	0.112161i
$658$		0			0
$659$	21.9294	−	37.9828i	0.854247	−	1.47960i	−0.0230945	−	0.999733i	$-0.507352\pi$
$659$	21.9294	−	37.9828i	0.854247	−	1.47960i	0.877342	−	0.479866i	$-0.159315\pi$
$660$	−0.711651			−0.0277010
$661$	28.5156	+	16.4635i	1.10913	+	0.640356i	0.938604	−	0.344997i	$-0.112120\pi$
$661$	28.5156	+	16.4635i	1.10913	+	0.640356i	0.170526	+	0.985353i	$0.445453\pi$
$662$	−1.55584	−	2.69479i	−0.0604693	−	0.104736i
$663$	−3.34684	−	5.79034i	−0.129981	−	0.224878i
$664$	−0.272170			−0.0105622
$665$		0			0
$666$	1.01139	+	1.75177i	0.0391904	+	0.0678798i
$667$	−20.8326	−	36.0831i	−0.806640	−	1.39714i
$668$	7.42287	−	4.28560i	0.287200	−	0.165815i
$669$		−	8.90992i		−	0.344478i
$670$	−2.37130	+	1.36907i	−0.0916113	+	0.0528918i
$671$			3.29062i			0.127033i
$672$		0			0
$673$	13.3423	+	23.1095i	0.514307	+	0.890806i	0.999862	+	0.0165997i	$0.00528409\pi$
$673$	13.3423	+	23.1095i	0.514307	+	0.890806i	−0.485555	+	0.874206i	$0.661383\pi$
$674$			2.57515i			0.0991912i
$675$	−3.54370	−	6.13787i	−0.136397	−	0.236247i
$676$	−12.9278	−	22.3409i	−0.497222	−	0.859265i
$677$	−14.7664	+	25.5761i	−0.567519	+	0.982971i	0.429292	+	0.903166i	$0.358763\pi$
$677$	−14.7664	+	25.5761i	−0.567519	+	0.982971i	−0.996810	+	0.0798052i	$0.974570\pi$
$678$	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
$682$		−	0.206163i		−	0.00789438i
$683$			18.2880i			0.699771i	0.936793	+	0.349885i	$0.113779\pi$
$683$			18.2880i			0.699771i	−0.936793	+	0.349885i	$0.886221\pi$
$684$	−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
$689$	−4.94355	+	0.00242577i	−0.188334	+	9.24146e-5i
$690$	0.300709	+	0.520843i	0.0114478	+	0.0198281i
$691$		−	10.3406i		−	0.393376i	−0.980466	−	0.196688i	$-0.936981\pi$
$691$		−	10.3406i		−	0.393376i	0.980466	−	0.196688i	$-0.0630186\pi$
$692$	12.4290	+	21.5277i	0.472480	+	0.818360i
$693$		0			0
$694$		−	0.265855i		−	0.0100917i
$695$	7.67671	−	4.43215i	0.291194	−	0.168121i
$696$			2.28950i			0.0867834i
$697$	−16.0762	+	9.28160i	−0.608930	+	0.351566i
$698$	0.679501	+	1.17693i	0.0257195	+	0.0445475i
$699$	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	$0.211419\pi$
$702$	−1.23918	−	0.714633i	−0.0467700	−	0.0269721i
$703$	−4.55974	−	7.89770i	−0.171974	−	0.297867i
$704$	2.41702	+	1.39547i	0.0910951	+	0.0525938i
$705$	12.5732			0.473533
$706$	2.14501	−	3.71527i	0.0807287	−	0.139826i
$707$		0			0
$708$	9.37371	+	5.41191i	0.352286	+	0.203392i
$709$	−0.00947974	+	0.00547313i	−0.000356019	+	0.000205548i	−0.500178	−	0.865923i	$-0.666732\pi$
$709$	−0.00947974	+	0.00547313i	−0.000356019	+	0.000205548i	0.499822	+	0.866128i	$0.333399\pi$
$710$	1.24604	−	0.719400i	0.0467630	−	0.0269986i
$711$	18.3280			0.687355
$712$	−0.546342			−0.0204750
$713$	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
$717$	−11.1322	−	6.42717i	−0.415739	−	0.240027i
$718$	1.16278	−	2.01400i	0.0433947	−	0.0751618i
$719$	−12.7330	−	22.0542i	−0.474861	−	0.822484i	0.524724	−	0.851272i	$-0.324168\pi$
$719$	−12.7330	−	22.0542i	−0.474861	−	0.822484i	−0.999586	+	0.0287885i	$0.990835\pi$
$720$		−	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
$724$	−21.8718			−0.812860
$725$	−8.81176	+	15.2624i	−0.327261	+	0.566832i
$726$			0.761613i			0.0282661i
$727$	−23.5565			−0.873663			−0.436831	−	0.899543i	$-0.643899\pi$
$727$	−23.5565			−0.873663			−0.436831	+	0.899543i	$0.643899\pi$
$728$		0			0
$729$	−10.3760			−0.384297
$730$		−	0.439053i		−	0.0162501i
$731$	−1.23141	+	2.13286i	−0.0455453	+	0.0788867i
$732$	10.4341			0.385654
$733$	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
$737$	2.45679	+	4.25528i	0.0904969	+	0.156745i
$738$	−0.933158	+	1.61628i	−0.0343500	+	0.0594960i
$739$	−1.12339	−	0.648588i	−0.0413244	−	0.0238587i	0.479195	−	0.877708i	$-0.340929\pi$
$739$	−1.12339	−	0.648588i	−0.0413244	−	0.0238587i	−0.520520	+	0.853850i	$0.674262\pi$
$740$	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	−0.400475	−	0.916308i	$-0.631155\pi$
$743$	5.25627	−	3.03471i	0.192834	−	0.111333i	0.593309	+	0.804975i	$0.297821\pi$
$744$	−1.31219			−0.0481073
$745$	15.6545			0.573537
$746$	0.366152	−	0.211398i	0.0134058	−	0.00773983i
$747$	1.30749	−	0.754880i	0.0478386	−	0.0276196i
$748$	1.99722	+	1.15310i	0.0730256	+	0.0421613i
$749$		0			0
$750$	0.422980	−	0.732622i	0.0154450	−	0.0267516i
$751$	36.6046			1.33572			0.667860	−	0.744287i	$-0.267210\pi$
$751$	36.6046			1.33572			0.667860	+	0.744287i	$0.267210\pi$
$752$	−43.3473	−	25.0266i	−1.58071	−	0.912625i
$753$	−6.56728	−	11.3749i	−0.239325	−	0.414523i
$754$	0.00174542	+	3.55703i	6.35643e−5	+	0.129540i
$755$	23.6566			0.860952
$756$		0			0
$757$	−5.83991	−	10.1150i	−0.212255	−	0.367636i	0.740165	−	0.672425i	$-0.234747\pi$
$757$	−5.83991	−	10.1150i	−0.212255	−	0.367636i	−0.952420	+	0.304789i	$0.901414\pi$
$758$	−1.50548	−	2.60757i	−0.0546815	−	0.0947111i
$759$	0.934648	−	0.539619i	0.0339256	−	0.0195869i
$760$		−	1.16928i		−	0.0424144i
$761$	34.4408	−	19.8844i	1.24848	−	0.720810i	0.277673	−	0.960676i	$-0.410437\pi$
$761$	34.4408	−	19.8844i	1.24848	−	0.720810i	0.970806	+	0.239866i	$0.0771035\pi$
$762$		−	0.565394i		−	0.0204821i
$763$		0			0
$764$	−5.88916	−	10.2003i	−0.213062	−	0.369035i
$765$		−	14.3098i		−	0.517372i
$766$	−1.35197	−	2.34167i	−0.0488485	−	0.0846081i
$767$	29.2410	+	16.8632i	1.05583	+	0.608894i
$768$	4.32457	−	7.49038i	0.156050	−	0.270286i
$769$	−8.62507	+	4.97969i	−0.311028	+	0.179572i	−0.647386	−	0.762162i	$-0.724138\pi$
$769$	−8.62507	+	4.97969i	−0.311028	+	0.179572i	0.336358	+	0.941734i	$0.390805\pi$
$770$		0			0
$771$	−5.94313	+	10.2938i	−0.214036	+	0.370722i
$772$	−7.21496	−	4.16556i	−0.259672	−	0.149922i
$773$		−	12.7518i		−	0.458649i	−0.973350	−	0.229324i	$-0.926348\pi$
$773$		−	12.7518i		−	0.458649i	0.973350	−	0.229324i	$-0.0736517\pi$
$774$			0.247608i			0.00890007i
$775$	−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
$780$	0.00345312	+	7.03721i	0.000123641	+	0.251972i
$781$	−1.29096	−	2.23601i	−0.0461941	−	0.0800106i
$782$		−	1.94897i		−	0.0696949i
$783$	−13.5093	−	23.3988i	−0.482784	−	0.836206i
$784$		0			0
$785$		−	29.0069i		−	1.03530i
$786$	1.14737	−	0.662435i	0.0409254	−	0.0236283i
$787$		−	8.68773i		−	0.309684i	−0.987939	−	0.154842i	$-0.950513\pi$
$787$		−	8.68773i		−	0.309684i	0.987939	−	0.154842i	$-0.0494869\pi$
$788$	9.94723	−	5.74303i	0.354355	−	0.204587i
$789$	−8.60052	−	14.8965i	−0.306187	−	0.530331i
$790$	0.699759	+	1.21202i	0.0248963	+	0.0431216i
$791$		0			0
$792$	0.465413			0.0165377
$793$	32.5395	−	0.0159670i	1.15551	−	0.000567003i
$794$	−1.55465	−	2.69273i	−0.0551723	−	0.0955613i
$795$	1.16722	+	0.673897i	0.0413972	+	0.0239007i
$796$	−23.7463			−0.841664
$797$	19.3719	−	33.5531i	0.686187	−	1.18851i	−0.286875	−	0.957968i	$-0.592616\pi$
$797$	19.3719	−	33.5531i	0.686187	−	1.18851i	0.973062	−	0.230543i	$-0.0740503\pi$
$798$		0			0
$799$	−35.2861	−	20.3724i	−1.24833	−	0.720725i
$800$	−2.66345	+	1.53774i	−0.0941672	+	0.0543675i
$801$	2.62460	−	1.51532i	0.0927358	−	0.0535411i
$802$	2.11358			0.0746331
$803$	−0.787876			−0.0278036
$804$	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
$808$	6.45844	+	3.72878i	0.227207	+	0.131178i
$809$	−14.4275	+	24.9892i	−0.507244	+	0.878573i	0.492721	+	0.870188i	$0.336002\pi$
$809$	−14.4275	+	24.9892i	−0.507244	+	0.878573i	−0.999965	+	0.00838530i	$0.997331\pi$
$810$	−0.616002	−	1.06695i	−0.0216441	−	0.0374887i
$811$			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
$815$	19.9081			0.697351
$816$	3.62942	−	6.28634i	0.127055	−	0.220066i
$817$		−	1.11632i		−	0.0390549i
$818$	−1.74861			−0.0611388
$819$		0			0
$820$	19.5324			0.682103
$821$			41.0238i			1.43174i	0.698233	+	0.715870i	$0.253970\pi$
$821$			41.0238i			1.43174i	−0.698233	+	0.715870i	$0.746030\pi$
$822$	−0.638663	+	1.10620i	−0.0222759	+	0.0385830i
$823$	2.13613			0.0744608			0.0372304	−	0.999307i	$-0.488146\pi$
$823$	2.13613			0.0744608			0.0372304	+	0.999307i	$0.488146\pi$
$824$	−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	$-0.952509\pi$
$827$		−	8.54938i		−	0.297291i	0.988891	−	0.148645i	$-0.0474913\pi$
$828$	13.4281	+	23.2582i	0.466660	+	0.808278i
$829$	−7.37844	+	12.7798i	−0.256264	+	0.443862i	−0.965238	−	0.261373i	$-0.915825\pi$
$829$	−7.37844	+	12.7798i	−0.256264	+	0.443862i	0.708974	+	0.705234i	$0.249158\pi$
$830$	0.0998392	+	0.0576422i	0.00346547	+	0.00200079i
$831$	−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
$835$	−7.28758			−0.252197
$836$	−1.04532			−0.0361532
$837$	13.4107	−	7.74265i	0.463540	−	0.267625i
$838$	0.479680	−	0.276943i	0.0165703	−	0.00956685i
$839$	23.3581	+	13.4858i	0.806411	+	0.465582i	0.845708	−	0.533646i	$-0.179178\pi$
$839$	23.3581	+	13.4858i	0.806411	+	0.465582i	−0.0392968	+	0.999228i	$0.512512\pi$
$840$		0			0
$841$	−19.0923	+	33.0687i	−0.658353	+	1.14030i
$842$	2.31867			0.0799068
$843$	14.6715	+	8.47062i	0.505315	+	0.291743i
$844$	8.17626	+	14.1617i	0.281438	+	0.487465i
$845$	0.0215377	+	21.9461i	0.000740920	+	0.754970i
$846$	−4.09643			−0.140838
$847$		0			0
$848$	−2.68275	−	4.64665i	−0.0921259	−	0.159567i
$849$	−3.38027	−	5.85479i	−0.116010	−	0.200936i
$850$	−0.713928	+	0.412187i	−0.0244875	+	0.0141379i
$851$			32.1047i			1.10054i
$852$	−7.09003	+	4.09343i	−0.242901	+	0.140239i
$853$		−	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
$856$			6.29572i			0.215183i
$857$	5.88263	+	10.1890i	0.200947	+	0.348050i	0.948834	−	0.315776i	$-0.102265\pi$
$857$	5.88263	+	10.1890i	0.200947	+	0.348050i	−0.747887	+	0.663826i	$0.768932\pi$
$858$	−0.0921367		4.52110e-5i	−0.00314549		1.54348e-6i
$859$	10.8881	−	18.8587i	0.371496	−	0.643450i	−0.618300	−	0.785942i	$-0.712178\pi$
$859$	10.8881	−	18.8587i	0.371496	−	0.643450i	0.989796	+	0.142492i	$0.0455117\pi$
$860$	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	0.962840	−	0.270073i	$-0.0870479\pi$
$863$	35.5569	+	20.5288i	1.21037	+	0.698807i	0.247530	+	0.968880i	$0.420381\pi$
$864$		−	4.71504i		−	0.160409i
$865$		−	21.1353i		−	0.718623i
$866$	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
$871$	42.0667	−	24.3147i	1.42538	−	0.823873i
$872$	2.50543	+	4.33953i	0.0848445	+	0.146955i
$873$			21.0955i			0.713975i
$874$	0.441702	+	0.765050i	0.0149408	+	0.0258782i
$875$		0			0
$876$			2.49824i			0.0844076i
$877$	−5.96788	+	3.44556i	−0.201521	+	0.116348i	−0.597365	−	0.801970i	$-0.703786\pi$
$877$	−5.96788	+	3.44556i	−0.201521	+	0.116348i	0.395844	+	0.918318i	$0.370452\pi$
$878$			3.81870i			0.128875i
$879$	−8.97043	+	5.17908i	−0.302565	+	0.174686i
$880$	−1.20439	−	2.08606i	−0.0405998	−	0.0703209i
$881$	−5.32288	−	9.21950i	−0.179332	−	0.310613i	0.762320	−	0.647201i	$-0.224060\pi$
$881$	−5.32288	−	9.21950i	−0.179332	−	0.310613i	−0.941652	+	0.336588i	$0.890727\pi$
$882$		0			0
$883$	21.3844			0.719641			0.359821	−	0.933022i	$-0.382838\pi$
$883$	21.3844			0.719641			0.359821	+	0.933022i	$0.382838\pi$
$884$	11.3928	−	19.7552i	0.383180	−	0.664440i
$885$	−4.60143	−	7.96991i	−0.154675	−	0.267906i
$886$	0.180376	+	0.104140i	0.00605986	+	0.00349866i
$887$	−34.1150			−1.14547			−0.572735	−	0.819740i	$-0.694118\pi$
$887$	−34.1150			−1.14547			−0.572735	+	0.819740i	$0.694118\pi$
$888$	0.882080	−	1.52781i	0.0296007	−	0.0512698i
$889$		0			0
$890$	0.200413	+	0.115709i	0.00671786	+	0.00387856i
$891$	−1.91463	+	1.10541i	−0.0641424	+	0.0370326i
$892$	26.3110	−	15.1906i	0.880956	−	0.508620i
$893$	18.4684			0.618020
$894$	0.649901			0.0217359
$895$	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
$899$	−33.3469	−	19.2528i	−1.11218	−	0.642118i
$900$	5.67983	−	9.83776i	0.189328	−	0.327925i
$901$	−2.18384	−	3.78253i	−0.0727544	−	0.126014i
$902$			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
$906$	0.982110			0.0326284
$907$	21.0758	−	36.5043i	0.699810	−	1.21211i	−0.268723	−	0.963218i	$-0.586601\pi$
$907$	21.0758	−	36.5043i	0.699810	−	1.21211i	0.968532	−	0.248888i	$-0.0800652\pi$
$908$			13.8086i			0.458254i
$909$	−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	$0.386932\pi$
$912$			3.29020i			0.108949i
$913$	0.103438	−	0.179161i	0.00342331	−	0.00592935i
$914$	−0.956734			−0.0316459
$915$	−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
$919$	7.14699	+	12.3789i	0.235757	+	0.408344i	0.959493	−	0.281734i	$-0.0909096\pi$
$919$	7.14699	+	12.3789i	0.235757	+	0.408344i	−0.723735	+	0.690078i	$0.757576\pi$
$920$	−2.05821	+	3.56492i	−0.0678571	+	0.117532i
$921$	−4.57869	−	2.64351i	−0.150873	−	0.0871065i
$922$	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
$926$	4.31162			0.141689
$927$	27.4027			0.900024
$928$	−10.1536	+	5.86220i	−0.333309	+	0.192436i
$929$	−5.89524	+	3.40362i	−0.193416	+	0.111669i	−0.593581	−	0.804774i	$-0.702286\pi$
$929$	−5.89524	+	3.40362i	−0.193416	+	0.111669i	0.400164	+	0.916443i	$0.368953\pi$
$930$	0.481347	+	0.277906i	0.0157840	+	0.00911290i
$931$		0			0
$932$	−6.80369	+	11.7843i	−0.222862	+	0.386009i
$933$	0.914621			0.0299433
$934$	−2.07410	−	1.19748i	−0.0678666	−	0.0391828i
$935$	−0.980409	−	1.69812i	−0.0320628	−	0.0555344i
$936$	−0.00225831	−	4.60227i	−7.38151e−5	−	0.150430i
$937$	−5.22890			−0.170821			−0.0854104	−	0.996346i	$-0.527220\pi$
$937$	−5.22890			−0.170821			−0.0854104	+	0.996346i	$0.527220\pi$
$938$		0			0
$939$	6.00437	+	10.3999i	0.195945	+	0.339387i
$940$	21.4362	+	37.1285i	0.699170	+	1.21100i
$941$	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	$-0.0384386\pi$
$942$		−	1.20423i		−	0.0392359i
$943$	−25.6530	+	14.8108i	−0.835376	+	0.482304i
$944$			36.6361i			1.19240i
$945$		0			0
$946$	0.0169644	+	0.0293832i	0.000551559	+	0.000955329i
$947$		−	5.85027i		−	0.190108i	−0.995472	−	0.0950541i	$-0.969698\pi$
$947$		−	5.85027i		−	0.190108i	0.995472	−	0.0950541i	$-0.0303024\pi$
$948$	−3.98167	−	6.89645i	−0.129319	−	0.223986i
$949$	0.00382299	+	7.79097i	0.000124099	+	0.252906i
$950$	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	−0.986643	−	0.162896i	$-0.947916\pi$
$953$	−10.8742	+	18.8346i	−0.352249	+	0.610114i	0.634394	+	0.773010i	$0.281250\pi$
$954$	−0.380290	−	0.219560i	−0.0123123	−	0.00710853i
$955$			10.0144i			0.324059i
$956$		−	43.8310i		−	1.41760i
$957$	−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
$962$	1.36926	−	2.37431i	0.0441466	−	0.0765509i
$963$	−17.4616	−	30.2444i	−0.562692	−	0.974611i
$964$		−	31.3654i		−	1.01021i
$965$	3.54173	+	6.13446i	0.114012	+	0.197475i
$966$		0			0
$967$		−	13.3251i		−	0.428507i	−0.976778	−	0.214253i	$-0.931268\pi$
$967$		−	13.3251i		−	0.428507i	0.976778	−	0.214253i	$-0.0687318\pi$
$968$	−4.51449	+	2.60644i	−0.145101	+	0.0837742i
$969$			2.67833i			0.0860404i
$970$	−1.39503	+	0.805420i	−0.0447917	+	0.0258605i
$971$	−3.73092	−	6.46215i	−0.119731	−	0.207380i	0.799930	−	0.600093i	$-0.204870\pi$
$971$	−3.73092	−	6.46215i	−0.119731	−	0.207380i	−0.919661	+	0.392713i	$0.871537\pi$
$972$	13.3224	+	23.0751i	0.427317	+	0.740134i
$973$		0			0
$974$	−0.767850			−0.0246035
$975$	−2.25513	+	3.91043i	−0.0722219	+	0.125234i
$976$	17.6584	+	30.5853i	0.565232	+	0.979011i
$977$	9.49204	+	5.48023i	0.303677	+	0.175328i	0.644094	−	0.764947i	$-0.277235\pi$
$977$	9.49204	+	5.48023i	0.303677	+	0.175328i	−0.340416	+	0.940275i	$0.610568\pi$
$978$	0.826490			0.0264282
$979$	0.207638	−	0.359640i	0.00663614	−	0.0114941i
$980$		0			0
$981$	−24.0719	−	13.8979i	−0.768557	−	0.443727i
$982$	−0.309335	+	0.178595i	−0.00987127	+	0.00569918i
$983$	−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	$0.416219\pi$
$984$	1.62771			0.0518893
$985$	−9.76593			−0.311168
$986$	−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
$990$	−0.170726	−	0.0985688i	−0.00542603	−	0.00313272i
$991$	−3.35748	+	5.81533i	−0.106654	+	0.184730i	−0.914413	−	0.404783i	$-0.867347\pi$
$991$	−3.35748	+	5.81533i	−0.106654	+	0.184730i	0.807759	+	0.589513i	$0.200680\pi$
$992$	−3.35982	−	5.81938i	−0.106674	−	0.184766i
$993$		−	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
$997$	−18.4411			−0.584037			−0.292018	−	0.956413i	$-0.594327\pi$
$997$	−18.4411			−0.584037			−0.292018	+	0.956413i	$0.594327\pi$
$998$	−1.69305	+	2.93244i	−0.0535924	+	0.0928248i
$999$			20.8190i			0.658684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.k.h.569.3		12
7.2	even	3		91.2.q.a.36.3	✓	12
7.3	odd	6		637.2.u.i.361.4		12
7.4	even	3		637.2.u.h.361.4		12
7.5	odd	6		637.2.q.h.491.3		12
7.6	odd	2		637.2.k.g.569.3		12
13.4	even	6		637.2.u.h.30.4		12
21.2	odd	6		819.2.ct.a.127.4		12
28.23	odd	6		1456.2.cc.c.673.3		12
91.2	odd	12		1183.2.a.m.1.4		6
91.4	even	6	inner	637.2.k.h.459.4		12
91.16	even	3		1183.2.c.i.337.6		12
91.17	odd	6		637.2.k.g.459.4		12
91.23	even	6		1183.2.c.i.337.7		12
91.30	even	6		91.2.q.a.43.3	yes	12
91.37	odd	12		1183.2.a.p.1.3		6
91.54	even	12		8281.2.a.by.1.4		6
91.69	odd	6		637.2.u.i.30.4		12
91.82	odd	6		637.2.q.h.589.3		12
91.89	even	12		8281.2.a.ch.1.3		6
273.212	odd	6		819.2.ct.a.316.4		12
364.303	odd	6		1456.2.cc.c.225.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.3	✓	12	7.2	even	3
91.2.q.a.43.3	yes	12	91.30	even	6
637.2.k.g.459.4		12	91.17	odd	6
637.2.k.g.569.3		12	7.6	odd	2
637.2.k.h.459.4		12	91.4	even	6	inner
637.2.k.h.569.3		12	1.1	even	1	trivial
637.2.q.h.491.3		12	7.5	odd	6
637.2.q.h.589.3		12	91.82	odd	6
637.2.u.h.30.4		12	13.4	even	6
637.2.u.h.361.4		12	7.4	even	3
637.2.u.i.30.4		12	91.69	odd	6
637.2.u.i.361.4		12	7.3	odd	6
819.2.ct.a.127.4		12	21.2	odd	6
819.2.ct.a.316.4		12	273.212	odd	6
1183.2.a.m.1.4		6	91.2	odd	12
1183.2.a.p.1.3		6	91.37	odd	12
1183.2.c.i.337.6		12	91.16	even	3
1183.2.c.i.337.7		12	91.23	even	6
1456.2.cc.c.225.3		12	364.303	odd	6
1456.2.cc.c.673.3		12	28.23	odd	6
8281.2.a.by.1.4		6	91.54	even	12
8281.2.a.ch.1.3		6	91.89	even	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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.120360i q^{2} +(0.291146 - 0.504280i) q^{3} +1.98551 q^{4} +(-1.46199 - 0.844083i) q^{5} +(-0.0606950 - 0.0350423i) q^{6} -0.479696i q^{8} +(1.33047 + 2.30444i) q^{9} +O(q^{10})\)	\(q-0.120360i q^{2} +(0.291146 - 0.504280i) q^{3} +1.98551 q^{4} +(-1.46199 - 0.844083i) q^{5} +(-0.0606950 - 0.0350423i) q^{6} -0.479696i q^{8} +(1.33047 + 2.30444i) q^{9} +(-0.101594 + 0.175965i) q^{10} +(0.315769 + 0.182309i) q^{11} +(0.578074 - 1.00125i) q^{12} +(1.80124 - 3.12338i) q^{13} +(-0.851308 + 0.491503i) q^{15} +3.91329 q^{16} +3.18555 q^{17} +(0.277362 - 0.160135i) q^{18} +(-1.25046 + 0.721954i) q^{19} +(-2.90281 - 1.67594i) q^{20} +(0.0219427 - 0.0380059i) q^{22} +5.08321 q^{23} +(-0.241901 - 0.139662i) q^{24} +(-1.07505 - 1.86204i) q^{25} +(-0.375930 - 0.216797i) q^{26} +3.29632 q^{27} +(-4.09831 - 7.09848i) q^{29} +(0.0591572 + 0.102463i) q^{30} +(4.06838 - 2.34888i) q^{31} -1.43040i q^{32} +(0.183870 - 0.106157i) q^{33} -0.383412i q^{34} +(2.64166 + 4.57549i) q^{36} +6.31584i q^{37} +(0.0868943 + 0.150505i) q^{38} +(-1.05063 - 1.81769i) 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} -4.49210i q^{45} -0.611815i 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} +(3.57639 - 6.20152i) q^{52} +(-0.685548 - 1.18740i) q^{53} -0.396744i q^{54} +(-0.307768 - 0.533070i) q^{55} +0.840776i q^{57} +(-0.854372 + 0.493272i) q^{58} +9.36197i q^{59} +(-1.69028 + 0.975885i) q^{60} +(4.51242 + 7.81574i) q^{61} +(-0.282711 - 0.489669i) q^{62} +7.65442 q^{64} +(-5.26980 + 3.04597i) q^{65} +(-0.0127771 - 0.0221305i) q^{66} +(11.6705 + 6.73797i) q^{67} +6.32495 q^{68} +(1.47996 - 2.56336i) q^{69} +(-6.13246 - 3.54058i) q^{71} +(1.10543 - 0.638220i) q^{72} +(-1.87133 + 1.08041i) q^{73} +0.760173 q^{74} -1.25198 q^{75} +(-2.48281 + 1.43345i) q^{76} +(-0.218777 + 0.126454i) q^{78} +(3.44391 - 5.96502i) q^{79} +(-5.72121 - 3.30314i) q^{80} +(-3.03169 + 5.25105i) q^{81} +(0.350688 + 0.607409i) q^{82} -0.567380i q^{83} +(-4.65725 - 2.68887i) q^{85} +(0.0805861 + 0.0465264i) q^{86} -4.77282 q^{87} +(0.0874529 - 0.151473i) q^{88} -1.13893i q^{89} -0.540669 q^{90} +10.0928 q^{92} -2.73547i q^{93} +(-0.769734 + 1.33322i) q^{94} +2.43755 q^{95} +(-0.721319 - 0.416454i) q^{96} +(6.86572 + 3.96393i) q^{97} +0.970225i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q - 8 * q^4 + 6 * q^5 - 18 * q^6 - 4 * q^9	\( 12 q - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9} + 12 q^{10} - 6 q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{15} + 16 q^{16} + 8 q^{17} + 12 q^{18} - 12 q^{20} + 6 q^{22} + 24 q^{23} - 12 q^{24} + 10 q^{25} + 18 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} - 18 q^{31} + 30 q^{33} - 10 q^{36} - 2 q^{38} + 14 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} - 24 q^{44} - 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} - 28 q^{52} + 22 q^{53} - 6 q^{55} + 12 q^{58} - 66 q^{60} + 14 q^{61} - 4 q^{62} - 52 q^{64} - 18 q^{65} + 26 q^{66} + 24 q^{67} + 16 q^{68} + 4 q^{69} - 24 q^{71} - 60 q^{72} - 30 q^{73} - 12 q^{74} - 92 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} + 72 q^{80} + 2 q^{81} + 14 q^{82} - 48 q^{85} + 60 q^{86} + 4 q^{87} - 14 q^{88} + 24 q^{90} + 24 q^{92} + 4 q^{94} + 44 q^{95} - 6 q^{96} + 6 q^{97}+O(q^{100}) \) 12 * q - 8 * q^4 + 6 * q^5 - 18 * q^6 - 4 * q^9 + 12 * q^10 - 6 * q^11 + 2 * q^12 + 4 * q^13 + 6 * q^15 + 16 * q^16 + 8 * q^17 + 12 * q^18 - 12 * q^20 + 6 * q^22 + 24 * q^23 - 12 * q^24 + 10 * q^25 + 18 * q^26 + 12 * q^27 + 8 * q^29 + 8 * q^30 - 18 * q^31 + 30 * q^33 - 10 * q^36 - 2 * q^38 + 14 * q^39 - 46 * q^40 + 30 * q^41 + 2 * q^43 - 24 * q^44 - 42 * q^47 - 2 * q^48 - 18 * q^50 - 26 * q^51 - 28 * q^52 + 22 * q^53 - 6 * q^55 + 12 * q^58 - 66 * q^60 + 14 * q^61 - 4 * q^62 - 52 * q^64 - 18 * q^65 + 26 * q^66 + 24 * q^67 + 16 * q^68 + 4 * q^69 - 24 * q^71 - 60 * q^72 - 30 * q^73 - 12 * q^74 - 92 * q^75 - 18 * q^76 - 10 * q^78 + 28 * q^79 + 72 * q^80 + 2 * q^81 + 14 * q^82 - 48 * q^85 + 60 * q^86 + 4 * q^87 - 14 * q^88 + 24 * q^90 + 24 * q^92 + 4 * q^94 + 44 * q^95 - 6 * q^96 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more