LMFDB - Embedded newform 637.2.u.i.30.5

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			30.5
Root			$0.759479 - 1.19298i$ of defining polynomial
Character	$\chi$	$=$	637.30
Dual form			637.2.u.i.361.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20027 - 0.692976i) q^{2} +2.82577 q^{3} +(-0.0395678 + 0.0685334i) q^{4} +(0.449430 + 0.259479i) q^{5} +(3.39169 - 1.95819i) q^{6} +2.88158i q^{8} +4.98500 q^{9} +O(q^{10})$	\(q+(1.20027 - 0.692976i) q^{2} +2.82577 q^{3} +(-0.0395678 + 0.0685334i) q^{4} +(0.449430 + 0.259479i) q^{5} +(3.39169 - 1.95819i) q^{6} +2.88158i q^{8} +4.98500 q^{9} +0.719250 q^{10} -1.62416i q^{11} +(-0.111810 + 0.193660i) q^{12} +(-1.42641 + 3.31140i) q^{13} +(1.26999 + 0.733228i) q^{15} +(1.91773 + 3.32161i) q^{16} +(-0.974127 + 1.68724i) q^{17} +(5.98335 - 3.45449i) q^{18} -2.49115i q^{19} +(-0.0355659 + 0.0205340i) q^{20} +(-1.12550 - 1.94943i) q^{22} +(-4.57029 - 7.91598i) q^{23} +8.14270i q^{24} +(-2.36534 - 4.09689i) q^{25} +(0.582637 + 4.96304i) q^{26} +5.60916 q^{27} +(2.61498 - 4.52928i) q^{29} +2.03244 q^{30} +(-5.01767 + 2.89695i) q^{31} +(-0.387453 - 0.223696i) q^{32} -4.58951i q^{33} +2.70019i q^{34} +(-0.197245 + 0.341639i) q^{36} +(8.85879 - 5.11463i) q^{37} +(-1.72631 - 2.99006i) q^{38} +(-4.03072 + 9.35726i) q^{39} +(-0.747709 + 1.29507i) q^{40} +(-3.64513 - 2.10452i) q^{41} +(-0.498655 - 0.863697i) q^{43} +(0.111309 + 0.0642644i) q^{44} +(2.24041 + 1.29350i) q^{45} +(-10.9712 - 6.33421i) q^{46} +(3.91206 + 2.25863i) q^{47} +(5.41908 + 9.38612i) q^{48} +(-5.67810 - 3.27825i) q^{50} +(-2.75266 + 4.76775i) q^{51} +(-0.170501 - 0.228782i) q^{52} +(4.44825 + 7.70460i) q^{53} +(6.73251 - 3.88701i) q^{54} +(0.421434 - 0.729946i) q^{55} -7.03944i q^{57} -7.24847i q^{58} +(-5.37392 - 3.10263i) q^{59} +(-0.100501 + 0.0580244i) q^{60} +13.4707 q^{61} +(-4.01504 + 6.95426i) q^{62} -8.29100 q^{64} +(-1.50031 + 1.11812i) q^{65} +(-3.18042 - 5.50865i) q^{66} +8.37266i q^{67} +(-0.0770880 - 0.133520i) q^{68} +(-12.9146 - 22.3688i) q^{69} +(-4.50168 + 2.59905i) q^{71} +14.3647i q^{72} +(-10.2533 + 5.91976i) q^{73} +(7.08863 - 12.2779i) q^{74} +(-6.68392 - 11.5769i) q^{75} +(0.170727 + 0.0985694i) q^{76} +(1.64640 + 14.0244i) q^{78} +(-0.491155 + 0.850705i) q^{79} +1.99044i q^{80} +0.895217 q^{81} -5.83352 q^{82} +8.91851i q^{83} +(-0.875603 + 0.505530i) q^{85} +(-1.19704 - 0.691113i) q^{86} +(7.38934 - 12.7987i) q^{87} +4.68015 q^{88} +(-10.4087 + 6.00949i) q^{89} +3.58546 q^{90} +0.723345 q^{92} +(-14.1788 + 8.18614i) q^{93} +6.26070 q^{94} +(0.646401 - 1.11960i) q^{95} +(-1.09485 - 0.632114i) q^{96} +(-3.82981 + 2.21114i) q^{97} -8.09643i 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 $

$2$	1.20027	−	0.692976i	0.848719	−	0.490008i	−0.0114993	−	0.999934i	$-0.503660\pi$
$2$	1.20027	−	0.692976i	0.848719	−	0.490008i	0.860218	+	0.509926i	$0.170327\pi$
$3$	2.82577			1.63146			0.815731	−	0.578432i	$-0.196335\pi$
$3$	2.82577			1.63146			0.815731	+	0.578432i	$0.196335\pi$
$4$	−0.0395678	+	0.0685334i	−0.0197839	+	0.0342667i
$5$	0.449430	+	0.259479i	0.200991	+	0.116042i	0.597118	−	0.802154i	$-0.296313\pi$
$5$	0.449430	+	0.259479i	0.200991	+	0.116042i	−0.396127	+	0.918196i	$0.629646\pi$
$6$	3.39169	−	1.95819i	1.38465	−	0.799429i
$7$		0			0
$7$		0			0
$8$			2.88158i			1.01879i
$9$	4.98500			1.66167
$10$	0.719250			0.227447
$11$		−	1.62416i		−	0.489702i	−0.969561	−	0.244851i	$-0.921261\pi$
$11$		−	1.62416i		−	0.489702i	0.969561	−	0.244851i	$-0.0787391\pi$
$12$	−0.111810	+	0.193660i	−0.0322766	+	0.0559048i
$13$	−1.42641	+	3.31140i	−0.395616	+	0.918416i
$13$	−1.42641	+	3.31140i	−0.395616	+	0.918416i
$14$		0			0
$15$	1.26999	+	0.733228i	0.327909	+	0.189319i
$16$	1.91773	+	3.32161i	0.479433	+	0.830403i
$17$	−0.974127	+	1.68724i	−0.236260	+	0.409215i	−0.959638	−	0.281237i	$-0.909255\pi$
$17$	−0.974127	+	1.68724i	−0.236260	+	0.409215i	0.723378	+	0.690452i	$0.242589\pi$
$18$	5.98335	−	3.45449i	1.41029	−	0.814230i
$19$		−	2.49115i		−	0.571510i	−0.958303	−	0.285755i	$-0.907756\pi$
$19$		−	2.49115i		−	0.571510i	0.958303	−	0.285755i	$-0.0922444\pi$
$20$	−0.0355659	+	0.0205340i	−0.00795277	+	0.00459154i
$21$		0			0
$22$	−1.12550	−	1.94943i	−0.239958	−	0.415620i
$23$	−4.57029	−	7.91598i	−0.952971	−	1.65059i	−0.738943	−	0.673767i	$-0.764675\pi$
$23$	−4.57029	−	7.91598i	−0.952971	−	1.65059i	−0.214028	−	0.976828i	$-0.568658\pi$
$24$			8.14270i			1.66212i
$25$	−2.36534	−	4.09689i	−0.473068	−	0.819378i
$26$	0.582637	+	4.96304i	0.114265	+	0.973332i
$27$	5.60916			1.07948
$28$		0			0
$29$	2.61498	−	4.52928i	0.485589	−	0.841065i	−0.514274	−	0.857626i	$-0.671938\pi$
$29$	2.61498	−	4.52928i	0.485589	−	0.841065i	0.999863	+	0.0165608i	$0.00527172\pi$
$30$	2.03244			0.371071
$31$	−5.01767	+	2.89695i	−0.901201	+	0.520308i	−0.877590	−	0.479413i	$-0.840850\pi$
$31$	−5.01767	+	2.89695i	−0.901201	+	0.520308i	−0.0236111	+	0.999721i	$0.507516\pi$
$32$	−0.387453	−	0.223696i	−0.0684926	−	0.0395442i
$33$		−	4.58951i		−	0.798931i
$34$			2.70019i			0.463078i
$35$		0			0
$36$	−0.197245	+	0.341639i	−0.0328742	+	0.0569398i
$37$	8.85879	−	5.11463i	1.45638	−	0.840840i	0.457546	−	0.889186i	$-0.348728\pi$
$37$	8.85879	−	5.11463i	1.45638	−	0.840840i	0.998831	+	0.0483462i	$0.0153951\pi$
$38$	−1.72631	−	2.99006i	−0.280045	−	0.485052i
$39$	−4.03072	+	9.35726i	−0.645432	+	1.49836i
$40$	−0.747709	+	1.29507i	−0.118223	+	0.204769i
$41$	−3.64513	−	2.10452i	−0.569273	−	0.328670i	0.187586	−	0.982248i	$-0.439934\pi$
$41$	−3.64513	−	2.10452i	−0.569273	−	0.328670i	−0.756859	+	0.653578i	$0.773267\pi$
$42$		0			0
$43$	−0.498655	−	0.863697i	−0.0760442	−	0.131712i	0.825496	−	0.564408i	$-0.190896\pi$
$43$	−0.498655	−	0.863697i	−0.0760442	−	0.131712i	−0.901540	+	0.432696i	$0.857562\pi$
$44$	0.111309	+	0.0642644i	0.0167805	+	0.00968822i
$45$	2.24041	+	1.29350i	0.333980	+	0.192824i
$46$	−10.9712	−	6.33421i	−1.61761	−	0.933928i
$47$	3.91206	+	2.25863i	0.570632	+	0.329455i	0.757402	−	0.652949i	$-0.226468\pi$
$47$	3.91206	+	2.25863i	0.570632	+	0.329455i	−0.186770	+	0.982404i	$0.559802\pi$
$48$	5.41908	+	9.38612i	0.782177	+	1.35477i
$49$		0			0
$50$	−5.67810	−	3.27825i	−0.803004	−	0.463615i
$51$	−2.75266	+	4.76775i	−0.385450	+	0.667618i
$52$	−0.170501	−	0.228782i	−0.0236443	−	0.0317263i
$53$	4.44825	+	7.70460i	0.611015	+	1.05831i	0.991070	+	0.133344i	$0.0425717\pi$
$53$	4.44825	+	7.70460i	0.611015	+	1.05831i	−0.380055	+	0.924964i	$0.624095\pi$
$54$	6.73251	−	3.88701i	0.916178	−	0.528956i
$55$	0.421434	−	0.729946i	0.0568262	−	0.0984259i
$56$		0			0
$57$		−	7.03944i		−	0.932397i
$58$		−	7.24847i		−	0.951771i
$59$	−5.37392	−	3.10263i	−0.699624	−	0.403928i	0.107583	−	0.994196i	$-0.465689\pi$
$59$	−5.37392	−	3.10263i	−0.699624	−	0.403928i	−0.807207	+	0.590268i	$0.799022\pi$
$60$	−0.100501	+	0.0580244i	−0.0129746	+	0.00749091i
$61$	13.4707			1.72475			0.862375	−	0.506270i	$-0.168976\pi$
$61$	13.4707			1.72475			0.862375	+	0.506270i	$0.168976\pi$
$62$	−4.01504	+	6.95426i	−0.509911	+	0.883191i
$63$		0			0
$64$	−8.29100			−1.03637
$65$	−1.50031	+	1.11812i	−0.186090	+	0.138685i
$66$	−3.18042	−	5.50865i	−0.391483	−	0.678068i
$67$			8.37266i			1.02288i	0.859318	+	0.511442i	$0.170888\pi$
$67$			8.37266i			1.02288i	−0.859318	+	0.511442i	$0.829112\pi$
$68$	−0.0770880	−	0.133520i	−0.00934830	−	0.0161917i
$69$	−12.9146	−	22.3688i	−1.55474	−	2.69288i
$70$		0			0
$71$	−4.50168	+	2.59905i	−0.534251	+	0.308450i	−0.742746	−	0.669573i	$-0.766477\pi$
$71$	−4.50168	+	2.59905i	−0.534251	+	0.308450i	0.208495	+	0.978023i	$0.433144\pi$
$72$			14.3647i			1.69289i
$73$	−10.2533	+	5.91976i	−1.20006	+	0.692856i	−0.960569	−	0.278042i	$-0.910315\pi$
$73$	−10.2533	+	5.91976i	−1.20006	+	0.692856i	−0.239493	+	0.970898i	$0.576981\pi$
$74$	7.08863	−	12.2779i	0.824037	−	1.42727i
$75$	−6.68392	−	11.5769i	−0.771793	−	1.33678i
$76$	0.170727	+	0.0985694i	0.0195838	+	0.0113067i
$77$		0			0
$78$	1.64640	+	14.0244i	0.186418	+	1.58795i
$79$	−0.491155	+	0.850705i	−0.0552592	+	0.0957118i	−0.892332	−	0.451380i	$-0.850932\pi$
$79$	−0.491155	+	0.850705i	−0.0552592	+	0.0957118i	0.837073	+	0.547092i	$0.184265\pi$
$80$			1.99044i			0.222538i
$81$	0.895217			0.0994686
$82$	−5.83352			−0.644204
$83$			8.91851i			0.978934i	0.872022	+	0.489467i	$0.162809\pi$
$83$			8.91851i			0.978934i	−0.872022	+	0.489467i	$0.837191\pi$
$84$		0			0
$85$	−0.875603	+	0.505530i	−0.0949725	+	0.0548324i
$86$	−1.19704	−	0.691113i	−0.129080	−	0.0745246i
$87$	7.38934	−	12.7987i	0.792220	−	1.37217i
$88$	4.68015			0.498906
$89$	−10.4087	+	6.00949i	−1.10332	+	0.637005i	−0.937092	−	0.349082i	$-0.886494\pi$
$89$	−10.4087	+	6.00949i	−1.10332	+	0.637005i	−0.166233	+	0.986087i	$0.553160\pi$
$90$	3.58546			0.377941
$91$		0			0
$92$	0.723345			0.0754139
$93$	−14.1788	+	8.18614i	−1.47027	+	0.848863i
$94$	6.26070			0.645742
$95$	0.646401	−	1.11960i	0.0663194	−	0.114869i
$96$	−1.09485	−	0.632114i	−0.111743	−	0.0645149i
$97$	−3.82981	+	2.21114i	−0.388858	+	0.224507i	−0.681665	−	0.731664i	$-0.738744\pi$
$97$	−3.82981	+	2.21114i	−0.388858	+	0.224507i	0.292807	+	0.956172i	$0.405411\pi$
$98$		0			0
$99$		−	8.09643i		−	0.813722i
$100$	0.374365			0.0374365
$101$	18.3026			1.82118			0.910591	−	0.413309i	$-0.135627\pi$
$101$	18.3026			1.82118			0.910591	+	0.413309i	$0.135627\pi$
$102$			7.63012i			0.755494i
$103$	−2.51023	+	4.34784i	−0.247340	+	0.428406i	−0.962787	−	0.270262i	$-0.912890\pi$
$103$	−2.51023	+	4.34784i	−0.247340	+	0.428406i	0.715447	+	0.698667i	$0.246223\pi$
$104$	−9.54206	−	4.11033i	−0.935676	−	0.403051i
$105$		0			0
$106$	10.6782	+	6.16507i	1.03716	+	0.598804i
$107$	−3.07228	−	5.32134i	−0.297008	−	0.514434i	0.678442	−	0.734654i	$-0.262656\pi$
$107$	−3.07228	−	5.32134i	−0.297008	−	0.514434i	−0.975450	+	0.220221i	$0.929322\pi$
$108$	−0.221942	+	0.384415i	−0.0213564	+	0.0369903i
$109$	10.3025	−	5.94812i	0.986796	−	0.569727i	0.0824809	−	0.996593i	$-0.473716\pi$
$109$	10.3025	−	5.94812i	0.986796	−	0.569727i	0.904315	+	0.426866i	$0.140382\pi$
$110$		−	1.16818i		−	0.111381i
$111$	25.0330	−	14.4528i	2.37602	−	1.37180i
$112$		0			0
$113$	−1.77806	−	3.07969i	−0.167266	−	0.289713i	0.770192	−	0.637812i	$-0.220161\pi$
$113$	−1.77806	−	3.07969i	−0.167266	−	0.289713i	−0.937458	+	0.348099i	$0.886827\pi$
$114$	−4.87817	−	8.44923i	−0.456882	−	0.791343i
$115$		−	4.74357i		−	0.442340i
$116$	0.206938	+	0.358427i	0.0192137	+	0.0332791i
$117$	−7.11067	+	16.5073i	−0.657382	+	1.52610i
$118$	−8.60020			−0.791713
$119$		0			0
$120$	−2.11286	+	3.65957i	−0.192877	+	0.334072i
$121$	8.36211			0.760191
$122$	16.1685	−	9.33489i	1.46383	−	0.845141i
$123$	−10.3003	−	5.94689i	−0.928748	−	0.536213i
$124$		−	0.458504i		−	0.0411749i
$125$		−	5.04981i		−	0.451668i
$126$		0			0
$127$	−0.711749	+	1.23279i	−0.0631575	+	0.109392i	−0.895875	−	0.444306i	$-0.853450\pi$
$127$	−0.711749	+	1.23279i	−0.0631575	+	0.109392i	0.832718	+	0.553698i	$0.186784\pi$
$128$	−9.17653	+	5.29807i	−0.811098	+	0.468288i
$129$	−1.40909	−	2.44061i	−0.124063	−	0.214884i
$130$	−1.02595	+	2.38172i	−0.0899816	+	0.208891i
$131$	4.33687	−	7.51168i	0.378914	−	0.656298i	−0.611990	−	0.790865i	$-0.709631\pi$
$131$	4.33687	−	7.51168i	0.378914	−	0.656298i	0.990905	+	0.134567i	$0.0429643\pi$
$132$	0.314535	+	0.181597i	0.0273767	+	0.0158060i
$133$		0			0
$134$	5.80205	+	10.0495i	0.501221	+	0.868141i
$135$	2.52092	+	1.45546i	0.216967	+	0.125266i
$136$	−4.86191	−	2.80703i	−0.416906	−	0.240701i
$137$	−7.37667	−	4.25892i	−0.630231	−	0.363864i	0.150611	−	0.988593i	$-0.451876\pi$
$137$	−7.37667	−	4.25892i	−0.630231	−	0.363864i	−0.780842	+	0.624729i	$0.785209\pi$
$138$	−31.0020	−	17.8990i	−2.63907	−	1.52367i
$139$	−2.51922	−	4.36342i	−0.213677	−	0.370100i	0.739185	−	0.673502i	$-0.235211\pi$
$139$	−2.51922	−	4.36342i	−0.213677	−	0.370100i	−0.952863	+	0.303402i	$0.901877\pi$
$140$		0			0
$141$	11.0546	+	6.38237i	0.930964	+	0.537493i
$142$	−3.60215	+	6.23912i	−0.302286	+	0.523575i
$143$	5.37824	+	2.31672i	0.449751	+	0.193734i
$144$	9.55990	+	16.5582i	0.796658	+	1.37985i
$145$	2.35050	−	1.35706i	0.195198	−	0.112698i
$146$	−8.20451	+	14.2106i	−0.679010	+	1.17608i
$147$		0			0
$148$			0.809498i			0.0665403i
$149$			3.36490i			0.275663i	0.990456	+	0.137832i	$0.0440133\pi$
$149$			3.36490i			0.275663i	−0.990456	+	0.137832i	$0.955987\pi$
$150$	−16.0450	−	9.26360i	−1.31007	−	0.756370i
$151$	−10.9610	+	6.32831i	−0.891990	+	0.514991i	−0.874593	−	0.484858i	$-0.838871\pi$
$151$	−10.9610	+	6.32831i	−0.891990	+	0.514991i	−0.0173971	+	0.999849i	$0.505538\pi$
$152$	7.17847			0.582251
$153$	−4.85602	+	8.41087i	−0.392586	+	0.679979i
$154$		0			0
$155$	−3.00679			−0.241511
$156$	−0.481798	−	0.646485i	−0.0385747	−	0.0517602i
$157$	5.18457	+	8.97993i	0.413773	+	0.716677i	0.995299	−	0.0968517i	$-0.0308772\pi$
$157$	5.18457	+	8.97993i	0.413773	+	0.716677i	−0.581525	+	0.813528i	$0.697544\pi$
$158$			1.36143i			0.108310i
$159$	12.5698	+	21.7715i	0.996847	+	1.72659i
$160$	−0.116089	−	0.201071i	−0.00917761	−	0.0158961i
$161$		0			0
$162$	1.07450	−	0.620364i	0.0844209	−	0.0487404i
$163$			15.7534i			1.23390i	0.787002	+	0.616950i	$0.211632\pi$
$163$			15.7534i			1.23390i	−0.787002	+	0.616950i	$0.788368\pi$
$164$	0.288459	−	0.166542i	0.0225249	−	0.0130047i
$165$	1.19088	−	2.06266i	0.0927098	−	0.160578i
$166$	6.18032	+	10.7046i	0.479686	+	0.830840i
$167$	14.2016	+	8.19930i	1.09895	+	0.634481i	0.935946	−	0.352144i	$-0.114547\pi$
$167$	14.2016	+	8.19930i	1.09895	+	0.634481i	0.163007	+	0.986625i	$0.447881\pi$
$168$		0			0
$169$	−8.93069	−	9.44684i	−0.686976	−	0.726680i
$170$	−0.700640	+	1.21354i	−0.0537367	+	0.0930746i
$171$		−	12.4184i		−	0.949659i
$172$	0.0789227			0.00601780
$173$	−0.301355			−0.0229116			−0.0114558	−	0.999934i	$-0.503647\pi$
$173$	−0.301355			−0.0229116			−0.0114558	+	0.999934i	$0.503647\pi$
$174$		−	20.4825i		−	1.55278i
$175$		0			0
$176$	5.39483	−	3.11470i	0.406650	−	0.234780i
$177$	−15.1855	−	8.76734i	−1.14141	−	0.658993i
$178$	−8.32887	+	14.4260i	−0.624275	+	1.08128i
$179$	9.81582			0.733669			0.366834	−	0.930286i	$-0.380442\pi$
$179$	9.81582			0.733669			0.366834	+	0.930286i	$0.380442\pi$
$180$	−0.177296	+	0.102362i	−0.0132149	+	0.00762960i
$181$	−12.4320			−0.924062			−0.462031	−	0.886864i	$-0.652879\pi$
$181$	−12.4320			−0.924062			−0.462031	+	0.886864i	$0.652879\pi$
$182$		0			0
$183$	38.0652			2.81386
$184$	22.8105	−	13.1697i	1.68162	−	0.970881i
$185$	5.30854			0.390292
$186$	−11.3456	+	19.6512i	−0.831900	+	1.44089i
$187$	2.74034	+	1.58214i	0.200394	+	0.115697i
$188$	−0.309583	+	0.178738i	−0.0225786	+	0.0130358i
$189$		0			0
$190$		−	1.79176i		−	0.129988i
$191$	−12.2469			−0.886156			−0.443078	−	0.896483i	$-0.646114\pi$
$191$	−12.2469			−0.886156			−0.443078	+	0.896483i	$0.646114\pi$
$192$	−23.4285			−1.69081
$193$			11.6338i			0.837422i	0.908119	+	0.418711i	$0.137518\pi$
$193$			11.6338i			0.837422i	−0.908119	+	0.418711i	$0.862482\pi$
$194$	−3.06454	+	5.30794i	−0.220021	+	0.381088i
$195$	−4.23953	+	3.15955i	−0.303599	+	0.226260i
$196$		0			0
$197$	−1.55984	−	0.900572i	−0.111134	−	0.0641631i	0.443403	−	0.896322i	$-0.353771\pi$
$197$	−1.55984	−	0.900572i	−0.111134	−	0.0641631i	−0.554537	+	0.832159i	$0.687104\pi$
$198$	−5.61064	−	9.71791i	−0.398731	−	0.690622i
$199$	−3.29657	+	5.70982i	−0.233687	+	0.404759i	−0.958890	−	0.283777i	$-0.908413\pi$
$199$	−3.29657	+	5.70982i	−0.233687	+	0.404759i	0.725203	+	0.688535i	$0.241746\pi$
$200$	11.8055	−	6.81593i	0.834777	−	0.481959i
$201$			23.6592i			1.66879i
$202$	21.9681	−	12.6833i	1.54567	−	0.892394i
$203$		0			0
$204$	−0.217833	−	0.377298i	−0.0152514	−	0.0264162i
$205$	−1.09215	−	1.89166i	−0.0762793	−	0.132120i
$206$			6.95811i			0.484795i
$207$	−22.7829	−	39.4611i	−1.58352	−	2.74274i
$208$	−13.7347	+	1.61238i	−0.952327	+	0.111799i
$209$	−4.04603			−0.279870
$210$		0			0
$211$	−5.35996	+	9.28373i	−0.368995	+	0.639118i	−0.989409	−	0.145157i	$-0.953631\pi$
$211$	−5.35996	+	9.28373i	−0.368995	+	0.639118i	0.620414	+	0.784275i	$0.286965\pi$
$212$	−0.704030			−0.0483530
$213$	−12.7207	+	7.34432i	−0.871610	+	0.503224i
$214$	−7.37513	−	4.25803i	−0.504154	−	0.291073i
$215$		−	0.517562i		−	0.0352974i
$216$			16.1633i			1.09977i
$217$		0			0
$218$	8.24382	−	14.2787i	0.558342	−	0.967076i
$219$	−28.9736	+	16.7279i	−1.95785	+	1.13037i
$220$	0.0333504	+	0.0577647i	0.00224849	+	0.00389449i
$221$	−4.19760	−	5.63242i	−0.282361	−	0.378877i
$222$	20.0309	−	34.6945i	1.34438	−	2.32854i
$223$	11.1612	+	6.44392i	0.747409	+	0.431517i	0.824757	−	0.565487i	$-0.191312\pi$
$223$	11.1612	+	6.44392i	0.747409	+	0.431517i	−0.0773480	+	0.997004i	$0.524645\pi$
$224$		0			0
$225$	−11.7912	−	20.4230i	−0.786082	−	1.36153i
$226$	−4.26831	−	2.46431i	−0.283924	−	0.163923i
$227$	−0.605486	−	0.349577i	−0.0401875	−	0.0232023i	0.479772	−	0.877393i	$-0.340720\pi$
$227$	−0.605486	−	0.349577i	−0.0401875	−	0.0232023i	−0.519959	+	0.854191i	$0.674053\pi$
$228$	0.482437	+	0.278535i	0.0319502	+	0.0184464i
$229$	−15.8369	−	9.14342i	−1.04653	−	0.604214i	−0.124854	−	0.992175i	$-0.539846\pi$
$229$	−15.8369	−	9.14342i	−1.04653	−	0.604214i	−0.921676	+	0.387961i	$0.873180\pi$
$230$	−3.28718	−	5.69356i	−0.216750	−	0.375422i
$231$		0			0
$232$	13.0515	+	7.53528i	0.856872	+	0.494715i
$233$	13.3898	−	23.1918i	0.877194	−	1.51934i	0.0227864	−	0.999740i	$-0.492746\pi$
$233$	13.3898	−	23.1918i	0.877194	−	1.51934i	0.854407	−	0.519604i	$-0.173920\pi$
$234$	2.90445	+	24.7408i	0.189870	+	1.61735i
$235$	1.17213	+	2.03019i	0.0764614	+	0.132435i
$236$	0.425268	−	0.245528i	0.0276826	−	0.0159825i
$237$	−1.38789	+	2.40390i	−0.0901533	+	0.156150i
$238$		0			0
$239$		−	16.6177i		−	1.07491i	−0.843293	−	0.537454i	$-0.819386\pi$
$239$		−	16.6177i		−	1.07491i	0.843293	−	0.537454i	$-0.180614\pi$
$240$			5.62454i			0.363063i
$241$	15.0800	+	8.70643i	0.971387	+	0.560830i	0.899659	−	0.436594i	$-0.143815\pi$
$241$	15.0800	+	8.70643i	0.971387	+	0.560830i	0.0717279	+	0.997424i	$0.477149\pi$
$242$	10.0368	−	5.79474i	0.645189	−	0.372500i
$243$	−14.2978			−0.917204
$244$	−0.533007	+	0.923194i	−0.0341222	+	0.0591015i
$245$		0			0
$246$	−16.4842			−1.05099
$247$	8.24920	+	3.55342i	0.524884	+	0.226099i
$248$	−8.34782	−	14.4588i	−0.530087	−	0.918137i
$249$			25.2017i			1.59709i
$250$	−3.49940	−	6.06113i	−0.221321	−	0.383340i
$251$	3.22491	+	5.58571i	0.203554	+	0.352567i	0.949671	−	0.313249i	$-0.101417\pi$
$251$	3.22491	+	5.58571i	0.203554	+	0.352567i	−0.746117	+	0.665815i	$0.768084\pi$
$252$		0			0
$253$	−12.8568	+	7.42288i	−0.808300	+	0.466672i
$254$			1.97290i			0.123791i
$255$	−2.47426	+	1.42851i	−0.154944	+	0.0894570i
$256$	0.948120	−	1.64219i	0.0592575	−	0.102637i
$257$	1.83578	+	3.17966i	0.114513	+	0.198342i	0.917585	−	0.397540i	$-0.130136\pi$
$257$	1.83578	+	3.17966i	0.114513	+	0.198342i	−0.803072	+	0.595882i	$0.796803\pi$
$258$	−3.38257	−	1.95293i	−0.210590	−	0.121584i
$259$		0			0
$260$	−0.0172645	−	0.147063i	−0.00107070	−	0.00912044i
$261$	13.0357	−	22.5784i	0.806887	−	1.39757i
$262$		−	12.0214i		−	0.742684i
$263$	18.3193			1.12961			0.564807	−	0.825223i	$-0.308950\pi$
$263$	18.3193			1.12961			0.564807	+	0.825223i	$0.308950\pi$
$264$	13.2250			0.813945
$265$			4.61690i			0.283614i
$266$		0			0
$267$	−29.4128	+	16.9815i	−1.80003	+	1.03925i
$268$	−0.573807	−	0.331287i	−0.0350508	−	0.0202366i
$269$	13.7715	−	23.8529i	0.839661	−	1.45434i	−0.0505171	−	0.998723i	$-0.516087\pi$
$269$	13.7715	−	23.8529i	0.839661	−	1.45434i	0.890178	−	0.455613i	$-0.150580\pi$
$270$	4.03439			0.245525
$271$	5.64582	−	3.25961i	0.342959	−	0.198007i	−0.318621	−	0.947882i	$-0.603220\pi$
$271$	5.64582	−	3.25961i	0.342959	−	0.198007i	0.661580	+	0.749875i	$0.269886\pi$
$272$	−7.47246			−0.453084
$273$		0			0
$274$	−11.8053			−0.713186
$275$	−6.65401	+	3.84169i	−0.401252	+	0.231663i
$276$	2.04401			0.123035
$277$	2.72093	−	4.71279i	0.163485	−	0.283164i	−0.772631	−	0.634855i	$-0.781060\pi$
$277$	2.72093	−	4.71279i	0.163485	−	0.283164i	0.936116	+	0.351691i	$0.114393\pi$
$278$	−6.04749	−	3.49152i	−0.362704	−	0.209407i
$279$	−25.0131	+	14.4413i	−1.49749	+	0.864579i
$280$		0			0
$281$		−	3.54237i		−	0.211320i	−0.994402	−	0.105660i	$-0.966304\pi$
$281$		−	3.54237i		−	0.211320i	0.994402	−	0.105660i	$-0.0336955\pi$
$282$	17.6913			1.05350
$283$	−14.1391			−0.840484			−0.420242	−	0.907412i	$-0.638055\pi$
$283$	−14.1391			−0.840484			−0.420242	+	0.907412i	$0.638055\pi$
$284$		−	0.411354i		−	0.0244094i
$285$	1.82658	−	3.16374i	0.108197	−	0.187404i
$286$	8.06077	−	0.946296i	0.476643	−	0.0559556i
$287$		0			0
$288$	−1.93145	−	1.11512i	−0.113812	−	0.0657093i
$289$	6.60215	+	11.4353i	0.388362	+	0.672663i
$290$	1.88082	−	3.25768i	0.110446	−	0.191298i
$291$	−10.8222	+	6.24819i	−0.634407	+	0.366275i
$292$		−	0.936928i		−	0.0548295i
$293$	7.23071	−	4.17465i	0.422423	−	0.243886i	−0.273691	−	0.961818i	$-0.588244\pi$
$293$	7.23071	−	4.17465i	0.422423	−	0.243886i	0.696113	+	0.717932i	$0.254911\pi$
$294$		0			0
$295$	−1.61013	−	2.78883i	−0.0937455	−	0.162372i
$296$	14.7382	+	25.5274i	0.856642	+	1.48375i
$297$		−	9.11017i		−	0.528626i
$298$	2.33180	+	4.03879i	0.135077	+	0.233961i
$299$	32.7321	−	3.84259i	1.89294	−	0.222223i
$300$	1.05787			0.0610762
$301$		0			0
$302$	−8.77074	+	15.1914i	−0.504699	+	0.874165i
$303$	51.7192			2.97119
$304$	8.27465	−	4.77737i	0.474584	−	0.274001i
$305$	6.05415	+	3.49536i	0.346659	+	0.200144i
$306$			13.4604i			0.769481i
$307$		−	8.33362i		−	0.475625i	−0.971311	−	0.237813i	$-0.923570\pi$
$307$		−	8.33362i		−	0.475625i	0.971311	−	0.237813i	$-0.0764304\pi$
$308$		0			0
$309$	−7.09334	+	12.2860i	−0.403526	+	0.698927i
$310$	−3.60896	+	2.08363i	−0.204975	+	0.118342i
$311$	7.31134	+	12.6636i	0.414588	+	0.718088i	0.995385	−	0.0959606i	$-0.0305923\pi$
$311$	7.31134	+	12.6636i	0.414588	+	0.718088i	−0.580797	+	0.814048i	$0.697259\pi$
$312$	−26.9637	−	11.6149i	−1.52652	−	0.657562i
$313$	8.56641	−	14.8375i	0.484202	−	0.838663i	−0.515633	−	0.856809i	$-0.672443\pi$
$313$	8.56641	−	14.8375i	0.484202	−	0.838663i	0.999835	+	0.0181467i	$0.00577661\pi$
$314$	12.4458	+	7.18556i	0.702355	+	0.405505i
$315$		0			0
$316$	−0.0388678	−	0.0673210i	−0.00218649	−	0.00378710i
$317$	12.1244	+	7.00002i	0.680973	+	0.393160i	0.800222	−	0.599704i	$-0.204715\pi$
$317$	12.1244	+	7.00002i	0.680973	+	0.393160i	−0.119248	+	0.992864i	$0.538048\pi$
$318$	30.1742	+	17.4211i	1.69209	+	0.976926i
$319$	−7.35627	−	4.24714i	−0.411872	−	0.237794i
$320$	−3.72622	−	2.15134i	−0.208302	−	0.120263i
$321$	−8.68157	−	15.0369i	−0.484558	−	0.839279i
$322$		0			0
$323$	4.20317	+	2.42670i	0.233871	+	0.135025i
$324$	−0.0354217	+	0.0613523i	−0.00196787	+	0.00340846i
$325$	16.9404	−	1.98872i	0.939684	−	0.110314i
$326$	10.9167	+	18.9083i	0.604621	+	1.04724i
$327$	29.1124	−	16.8081i	1.60992	−	0.929487i
$328$	6.06434	−	10.5037i	0.334847	−	0.579972i
$329$		0			0
$330$		−	3.30100i		−	0.181714i
$331$			6.91996i			0.380355i	0.981750	+	0.190178i	$0.0609064\pi$
$331$			6.91996i			0.380355i	−0.981750	+	0.190178i	$0.939094\pi$
$332$	−0.611216	−	0.352886i	−0.0335448	−	0.0193671i
$333$	44.1611	−	25.4964i	2.42001	−	1.39719i
$334$	22.7277			1.24360
$335$	−2.17253	+	3.76292i	−0.118698	+	0.205591i
$336$		0			0
$337$	11.1559			0.607703			0.303852	−	0.952719i	$-0.401727\pi$
$337$	11.1559			0.607703			0.303852	+	0.952719i	$0.401727\pi$
$338$	−17.2657	−	5.15001i	−0.939129	−	0.280123i
$339$	−5.02440	−	8.70251i	−0.272888	−	0.472656i
$340$		−	0.0800108i		−	0.00433919i
$341$	4.70512	+	8.14950i	0.254796	+	0.441320i
$342$	−8.60566	−	14.9054i	−0.465341	−	0.805994i
$343$		0			0
$344$	2.48881	−	1.43692i	0.134188	−	0.0774734i
$345$		−	13.4043i		−	0.721661i
$346$	−0.361707	+	0.208832i	−0.0194455	+	0.0112269i
$347$	2.46255	−	4.26527i	0.132197	−	0.228971i	−0.792326	−	0.610097i	$-0.791130\pi$
$347$	2.46255	−	4.26527i	0.132197	−	0.228971i	0.924523	+	0.381126i	$0.124464\pi$
$348$	0.584759	+	1.01283i	0.0313464	+	0.0542935i
$349$	−1.31926	−	0.761675i	−0.0706183	−	0.0407715i	0.464275	−	0.885691i	$-0.346315\pi$
$349$	−1.31926	−	0.761675i	−0.0706183	−	0.0407715i	−0.534893	+	0.844920i	$0.679648\pi$
$350$		0			0
$351$	−8.00098	+	18.5741i	−0.427061	+	0.991415i
$352$	−0.363318	+	0.629285i	−0.0193649	+	0.0335410i
$353$			17.9280i			0.954212i	0.878846	+	0.477106i	$0.158314\pi$
$353$			17.9280i			0.954212i	−0.878846	+	0.477106i	$0.841686\pi$
$354$	−24.3022			−1.29165
$355$	−2.69759			−0.143173
$356$		−	0.951129i		−	0.0504097i
$357$		0			0
$358$	11.7816	−	6.80213i	0.622679	−	0.359504i
$359$	−17.3217	−	10.0007i	−0.914204	−	0.527816i	−0.0324227	−	0.999474i	$-0.510322\pi$
$359$	−17.3217	−	10.0007i	−0.914204	−	0.527816i	−0.881781	+	0.471658i	$0.843656\pi$
$360$	−3.72733	+	6.45592i	−0.196447	+	0.340257i
$361$	12.7941			0.673376
$362$	−14.9217	+	8.61507i	−0.784269	+	0.452798i
$363$	23.6294			1.24022
$364$		0			0
$365$	−6.14421			−0.321602
$366$	45.6885	−	26.3783i	2.38818	−	1.37882i
$367$	−27.4157			−1.43109			−0.715544	−	0.698568i	$-0.753821\pi$
$367$	−27.4157			−1.43109			−0.715544	+	0.698568i	$0.753821\pi$
$368$	17.5292	−	30.3615i	0.913772	−	1.58270i
$369$	−18.1710	−	10.4910i	−0.945942	−	0.546140i
$370$	6.37169	−	3.67870i	0.331248	−	0.191246i
$371$		0			0
$372$		−	1.29563i		−	0.0671752i
$373$	−15.8929			−0.822901			−0.411451	−	0.911432i	$-0.634978\pi$
$373$	−15.8929			−0.822901			−0.411451	+	0.911432i	$0.634978\pi$
$374$	4.38553			0.226771
$375$		−	14.2696i		−	0.736880i
$376$	−6.50842	+	11.2729i	−0.335646	+	0.581356i
$377$	11.2682	+	15.1199i	0.580341	+	0.778712i
$378$		0			0
$379$	7.60284	+	4.38950i	0.390532	+	0.225474i	0.682390	−	0.730988i	$-0.260940\pi$
$379$	7.60284	+	4.38950i	0.390532	+	0.225474i	−0.291859	+	0.956461i	$0.594274\pi$
$380$	0.0511533	+	0.0886001i	0.00262411	+	0.00454509i
$381$	−2.01124	+	3.48357i	−0.103039	+	0.178469i
$382$	−14.6996	+	8.48682i	−0.752098	+	0.434224i
$383$		−	7.96237i		−	0.406858i	−0.979090	−	0.203429i	$-0.934791\pi$
$383$		−	7.96237i		−	0.406858i	0.979090	−	0.203429i	$-0.0652086\pi$
$384$	−25.9308	+	14.9712i	−1.32328	+	0.763994i
$385$		0			0
$386$	8.06198	+	13.9638i	0.410344	+	0.710736i
$387$	−2.48580	−	4.30553i	−0.126360	−	0.218862i
$388$		−	0.349960i		−	0.0177665i
$389$	16.0217	+	27.7504i	0.812333	+	1.40700i	0.911227	+	0.411904i	$0.135136\pi$
$389$	16.0217	+	27.7504i	0.812333	+	1.40700i	−0.0988938	+	0.995098i	$0.531530\pi$
$390$	−2.89910	+	6.73021i	−0.146801	+	0.340797i
$391$	17.8082			0.900598
$392$		0			0
$393$	12.2550	−	21.2263i	0.618184	−	1.07073i
$394$	−2.49630			−0.125762
$395$	−0.441479	+	0.254888i	−0.0222132	+	0.0128248i
$396$	0.554876	+	0.320358i	0.0278836	+	0.0160986i
$397$		−	6.43457i		−	0.322942i	−0.986877	−	0.161471i	$-0.948376\pi$
$397$		−	6.43457i		−	0.322942i	0.986877	−	0.161471i	$-0.0516238\pi$
$398$			9.13777i			0.458035i
$399$		0			0
$400$	9.07219	−	15.7135i	0.453609	−	0.785675i
$401$	0.462092	−	0.266789i	0.0230758	−	0.0133228i	−0.488418	−	0.872610i	$-0.662426\pi$
$401$	0.462092	−	0.266789i	0.0230758	−	0.0133228i	0.511494	+	0.859287i	$0.329092\pi$
$402$	16.3953	+	28.3975i	0.817723	+	1.41634i
$403$	−2.43569	−	20.7478i	−0.121330	−	1.03352i
$404$	−0.724195	+	1.25434i	−0.0360301	+	0.0624059i
$405$	0.402337	+	0.232290i	0.0199923	+	0.0115426i
$406$		0			0
$407$	−8.30697	−	14.3881i	−0.411761	−	0.713191i
$408$	−13.7387	−	7.93202i	−0.680165	−	0.392694i
$409$	−34.4269	−	19.8764i	−1.70230	−	0.982824i	−0.943424	−	0.331590i	$-0.892415\pi$
$409$	−34.4269	−	19.8764i	−1.70230	−	0.982824i	−0.758877	−	0.651234i	$-0.774252\pi$
$410$	−2.62176	−	1.51367i	−0.129479	−	0.0747550i
$411$	−20.8448	−	12.0347i	−1.02820	−	0.593630i
$412$	−0.198648	−	0.344069i	−0.00978670	−	0.0169511i
$413$		0			0
$414$	−54.6913	−	31.5760i	−2.68793	−	1.55188i
$415$	−2.31416	+	4.00825i	−0.113598	+	0.196757i
$416$	1.29341	−	0.963926i	0.0634148	−	0.0472604i
$417$	−7.11875	−	12.3300i	−0.348607	−	0.603804i
$418$	−4.85633	+	2.80380i	−0.237531	+	0.137139i
$419$	11.9088	−	20.6266i	0.581783	−	1.00768i	−0.413485	−	0.910511i	$-0.635689\pi$
$419$	11.9088	−	20.6266i	0.581783	−	1.00768i	0.995268	−	0.0971665i	$-0.0309779\pi$
$420$		0			0
$421$			23.2419i			1.13274i	0.824151	+	0.566370i	$0.191653\pi$
$421$			23.2419i			1.13274i	−0.824151	+	0.566370i	$0.808347\pi$
$422$			14.8573i			0.723243i
$423$	19.5016	+	11.2593i	0.948200	+	0.547444i
$424$	−22.2014	+	12.8180i	−1.07820	+	0.622498i
$425$	9.21657			0.447069
$426$	−10.1789	+	17.6303i	−0.493168	+	0.854192i
$427$		0			0
$428$	0.486253			0.0235039
$429$	15.1977	+	6.54654i	0.733751	+	0.316070i
$430$	−0.358658	−	0.621214i	−0.0172960	−	0.0299576i
$431$			2.70689i			0.130386i	0.997873	+	0.0651932i	$0.0207664\pi$
$431$			2.70689i			0.130386i	−0.997873	+	0.0651932i	$0.979234\pi$
$432$	10.7569	+	18.6314i	0.517540	+	0.896406i
$433$	2.90945	+	5.03932i	0.139819	+	0.242174i	0.927428	−	0.374002i	$-0.122015\pi$
$433$	2.90945	+	5.03932i	0.139819	+	0.242174i	−0.787609	+	0.616176i	$0.788681\pi$
$434$		0			0
$435$	6.64198	−	3.83475i	0.318459	−	0.183862i
$436$			0.941416i			0.0450856i
$437$	−19.7199	+	11.3853i	−0.943332	+	0.544633i
$438$	−23.1841	+	40.1560i	−1.10778	+	1.91873i
$439$	−19.0851	−	33.0563i	−0.910882	−	1.57769i	−0.812822	−	0.582513i	$-0.802070\pi$
$439$	−19.0851	−	33.0563i	−0.910882	−	1.57769i	−0.0980599	−	0.995181i	$-0.531264\pi$
$440$	2.10340	+	1.21440i	0.100276	+	0.0578942i
$441$		0			0
$442$	−8.94139	−	3.85158i	−0.425298	−	0.183201i
$443$	15.8370	−	27.4305i	0.752440	−	1.30326i	−0.194198	−	0.980962i	$-0.562210\pi$
$443$	15.8370	−	27.4305i	0.752440	−	1.30326i	0.946637	−	0.322301i	$-0.104456\pi$
$444$			2.28746i			0.108558i
$445$	−6.23734			−0.295678
$446$	17.8619			0.845787
$447$			9.50845i			0.449734i
$448$		0			0
$449$	27.1975	−	15.7025i	1.28353	−	0.741045i	0.306036	−	0.952020i	$-0.400997\pi$
$449$	27.1975	−	15.7025i	1.28353	−	0.741045i	0.977491	+	0.210975i	$0.0676638\pi$
$450$	−28.3053	−	16.3421i	−1.33433	−	0.770373i
$451$	−3.41807	+	5.92027i	−0.160951	+	0.278775i
$452$	0.281416			0.0132367
$453$	−30.9732	+	17.8824i	−1.45525	+	0.840187i
$454$	−0.968995			−0.0454772
$455$		0			0
$456$	20.2847			0.949920
$457$	−27.5640	+	15.9141i	−1.28939	+	0.744429i	−0.978545	−	0.206032i	$-0.933945\pi$
$457$	−27.5640	+	15.9141i	−1.28939	+	0.744429i	−0.310844	+	0.950461i	$0.600612\pi$
$458$	−25.3447			−1.18428
$459$	−5.46403	+	9.46398i	−0.255039	+	0.441741i
$460$	0.325093	+	0.187692i	0.0151575	+	0.00875121i
$461$	−1.01005	+	0.583153i	−0.0470427	+	0.0271601i	−0.523337	−	0.852126i	$-0.675313\pi$
$461$	−1.01005	+	0.583153i	−0.0470427	+	0.0271601i	0.476294	+	0.879286i	$0.341980\pi$
$462$		0			0
$463$		−	20.3441i		−	0.945469i	−0.881205	−	0.472734i	$-0.843267\pi$
$463$		−	20.3441i		−	0.945469i	0.881205	−	0.472734i	$-0.156733\pi$
$464$	20.0593			0.931231
$465$	−8.49651			−0.394016
$466$		−	37.1152i		−	1.71933i
$467$	0.784697	−	1.35913i	0.0363114	−	0.0628932i	−0.847299	−	0.531117i	$-0.821773\pi$
$467$	0.784697	−	1.35913i	0.0363114	−	0.0628932i	0.883610	+	0.468224i	$0.155106\pi$
$468$	−0.849948	−	1.14048i	−0.0392889	−	0.0527185i
$469$		0			0
$470$	2.81375	+	1.62452i	0.129788	+	0.0749334i
$471$	14.6504	+	25.3753i	0.675055	+	1.16923i
$472$	8.94049	−	15.4854i	0.411519	−	0.712773i
$473$	−1.40278	+	0.809896i	−0.0644999	+	0.0372391i
$474$			3.84711i			0.176703i
$475$	−10.2060	+	5.89243i	−0.468283	+	0.270363i
$476$		0			0
$477$	22.1745	+	38.4074i	1.01530	+	1.75856i
$478$	−11.5157	−	19.9457i	−0.526714	−	0.912295i
$479$			7.71918i			0.352699i	0.984328	+	0.176349i	$0.0564288\pi$
$479$			7.71918i			0.352699i	−0.984328	+	0.176349i	$0.943571\pi$
$480$	−0.328040	−	0.568182i	−0.0149729	−	0.0259338i
$481$	4.30025	+	36.6306i	0.196075	+	1.67021i
$482$	24.1334			1.09925
$483$		0			0
$484$	−0.330870	+	0.573083i	−0.0150395	+	0.0260492i
$485$	−2.29498			−0.104209
$486$	−17.1612	+	9.90803i	−0.778448	+	0.449437i
$487$	0.0659739	+	0.0380900i	0.00298956	+	0.00172602i	0.501494	−	0.865161i	$-0.332784\pi$
$487$	0.0659739	+	0.0380900i	0.00298956	+	0.00172602i	−0.498504	+	0.866887i	$0.666117\pi$
$488$			38.8170i			1.75716i
$489$			44.5155i			2.01306i
$490$		0			0
$491$	0.893574	−	1.54772i	0.0403264	−	0.0698474i	−0.845158	−	0.534517i	$-0.820494\pi$
$491$	0.893574	−	1.54772i	0.0403264	−	0.0698474i	0.885484	+	0.464670i	$0.153827\pi$
$492$	0.815121	−	0.470610i	0.0367485	−	0.0212167i
$493$	5.09464	+	8.82418i	0.229451	+	0.397421i
$494$	12.3637	−	1.45144i	0.556269	−	0.0653034i
$495$	2.10085	−	3.63878i	0.0944262	−	0.163551i
$496$	−19.2451	−	11.1112i	−0.864131	−	0.498906i
$497$		0			0
$498$	17.4642	+	30.2488i	0.782589	+	1.35548i
$499$	−7.21826	−	4.16747i	−0.323134	−	0.186561i	0.329655	−	0.944102i	$-0.393068\pi$
$499$	−7.21826	−	4.16747i	−0.323134	−	0.186561i	−0.652789	+	0.757540i	$0.726401\pi$
$500$	0.346080	+	0.199810i	0.0154772	+	0.00893576i
$501$	40.1305	+	23.1694i	1.79290	+	1.03513i
$502$	7.74152	+	4.46957i	0.345521	+	0.199487i
$503$	0.720238	+	1.24749i	0.0321138	+	0.0556228i	0.881636	−	0.471931i	$-0.156443\pi$
$503$	0.720238	+	1.24749i	0.0321138	+	0.0556228i	−0.849522	+	0.527554i	$0.823109\pi$
$504$		0			0
$505$	8.22576	+	4.74914i	0.366041	+	0.211334i
$506$	−10.2878	+	17.8189i	−0.457347	+	0.792148i
$507$	−25.2361	−	26.6946i	−1.12077	−	1.18555i
$508$	−0.0563247	−	0.0975572i	−0.00249900	−	0.00432840i
$509$	12.8394	−	7.41282i	0.569096	−	0.328568i	−0.187692	−	0.982228i	$-0.560101\pi$
$509$	12.8394	−	7.41282i	0.569096	−	0.328568i	0.756788	+	0.653660i	$0.226767\pi$
$510$	−1.97985	+	3.42920i	−0.0876693	+	0.151848i
$511$		0			0
$512$		−	23.8204i		−	1.05272i
$513$		−	13.9733i		−	0.616935i
$514$	4.40686	+	2.54430i	0.194378	+	0.112224i
$515$	−2.25634	+	1.30270i	−0.0994264	+	0.0574038i
$516$	0.223018			0.00981781
$517$	3.66837	−	6.35380i	0.161335	−	0.279440i
$518$		0			0
$519$	−0.851561			−0.0373794
$520$	−3.22195	−	4.32327i	−0.141292	−	0.189588i
$521$	−0.167194	−	0.289588i	−0.00732489	−	0.0126871i	0.862340	−	0.506330i	$-0.168998\pi$
$521$	−0.167194	−	0.289588i	−0.00732489	−	0.0126871i	−0.869665	+	0.493643i	$0.835665\pi$
$522$		−	36.1336i		−	1.58153i
$523$	−16.2533	−	28.1515i	−0.710705	−	1.23098i	−0.964593	−	0.263744i	$-0.915043\pi$
$523$	−16.2533	−	28.1515i	−0.710705	−	1.23098i	0.253887	−	0.967234i	$-0.418291\pi$
$524$	0.343201	+	0.594441i	0.0149928	+	0.0259683i
$525$		0			0
$526$	21.9881	−	12.6948i	0.958726	−	0.553521i
$527$		−	11.2880i		−	0.491713i
$528$	15.2446	−	8.80145i	0.663434	−	0.383034i
$529$	−30.2751	+	52.4380i	−1.31631	+	2.27991i
$530$	3.19941	+	5.54153i	0.138973	+	0.240709i
$531$	−26.7890	−	15.4666i	−1.16254	−	0.671194i
$532$		0			0
$533$	12.1683	−	9.06855i	0.527070	−	0.392803i
$534$	−23.5355	+	40.7647i	−1.01848	+	1.76406i
$535$		−	3.18876i		−	0.137862i
$536$	−24.1265			−1.04211
$537$	27.7373			1.19695
$538$		−	38.1732i		−	1.64576i
$539$		0			0
$540$	−0.199495	+	0.115178i	−0.00858488	+	0.00495649i
$541$	9.18120	+	5.30077i	0.394731	+	0.227898i	0.684208	−	0.729287i	$-0.260148\pi$
$541$	9.18120	+	5.30077i	0.394731	+	0.227898i	−0.289477	+	0.957185i	$0.593481\pi$
$542$	4.51767	−	7.82483i	0.194051	−	0.336105i
$543$	−35.1300			−1.50757
$544$	0.754856	−	0.435816i	0.0323642	−	0.0186855i
$545$	6.17364			0.264450
$546$		0			0
$547$	10.2327			0.437519			0.218760	−	0.975779i	$-0.429799\pi$
$547$	10.2327			0.437519			0.218760	+	0.975779i	$0.429799\pi$
$548$	0.583756	−	0.337032i	0.0249368	−	0.0143973i
$549$	67.1515			2.86596
$550$	−5.32440	+	9.22214i	−0.227033	+	0.393233i
$551$	−11.2831	−	6.51432i	−0.480677	−	0.277519i
$552$	64.4574	−	37.2145i	2.74349	−	1.58396i
$553$		0			0
$554$		−	7.54216i		−	0.320436i
$555$	15.0007			0.636746
$556$	0.398720			0.0169095
$557$		−	31.9930i		−	1.35559i	−0.735253	−	0.677793i	$-0.762937\pi$
$557$		−	31.9930i		−	1.35559i	0.735253	−	0.677793i	$-0.237063\pi$
$558$	−20.0150	+	34.6670i	−0.847302	+	1.46757i
$559$	3.57133	−	0.419257i	0.151051	−	0.0177327i
$560$		0			0
$561$	7.74359	+	4.47076i	0.326934	+	0.188756i
$562$	−2.45478	−	4.25180i	−0.103549	−	0.179351i
$563$	−5.39566	+	9.34556i	−0.227400	+	0.393868i	−0.957037	−	0.289967i	$-0.906356\pi$
$563$	−5.39566	+	9.34556i	−0.227400	+	0.393868i	0.729637	+	0.683835i	$0.239689\pi$
$564$	−0.874811	+	0.505072i	−0.0368362	+	0.0212674i
$565$		−	1.84547i		−	0.0776397i
$566$	−16.9708	+	9.79808i	−0.713335	+	0.411844i
$567$		0			0
$568$	−7.48937	−	12.9720i	−0.314247	−	0.544292i
$569$	−12.3007	−	21.3054i	−0.515672	−	0.893170i	−0.999835	−	0.0181917i	$-0.994209\pi$
$569$	−12.3007	−	21.3054i	−0.515672	−	0.893170i	0.484163	−	0.874978i	$-0.339124\pi$
$570$		−	5.06312i		−	0.212071i
$571$	8.28621	+	14.3521i	0.346767	+	0.600618i	0.985673	−	0.168667i	$-0.0539461\pi$
$571$	8.28621	+	14.3521i	0.346767	+	0.600618i	−0.638906	+	0.769285i	$0.720613\pi$
$572$	−0.371578	+	0.276921i	−0.0155364	+	0.0115787i
$573$	−34.6070			−1.44573
$574$		0			0
$575$	−21.6206	+	37.4480i	−0.901641	+	1.56169i
$576$	−41.3306			−1.72211
$577$	−12.6969	+	7.33053i	−0.528577	+	0.305174i	−0.740437	−	0.672126i	$-0.765381\pi$
$577$	−12.6969	+	7.33053i	−0.528577	+	0.305174i	0.211860	+	0.977300i	$0.432048\pi$
$578$	15.8487	+	9.15027i	0.659221	+	0.380601i
$579$			32.8746i			1.36622i
$580$			0.214784i			0.00891840i
$581$		0			0
$582$	−8.65969	+	14.9990i	−0.358956	+	0.621730i
$583$	12.5135	−	7.22467i	0.518256	−	0.299215i
$584$	−17.0583	−	29.5458i	−0.705877	−	1.22262i
$585$	−7.47904	+	5.57381i	−0.309220	+	0.230449i
$586$	5.78587	−	10.0214i	0.239012	−	0.413981i
$587$	−30.5998	−	17.6668i	−1.26299	−	0.729186i	−0.289336	−	0.957227i	$-0.593435\pi$
$587$	−30.5998	−	17.6668i	−1.26299	−	0.729186i	−0.973652	+	0.228041i	$0.926768\pi$
$588$		0			0
$589$	7.21676	+	12.4998i	0.297362	+	0.515045i
$590$	−3.86519	−	2.23157i	−0.159127	−	0.0918722i
$591$	−4.40775	−	2.54481i	−0.181310	−	0.104680i
$592$	33.9776	+	19.6170i	1.39647	+	0.806253i
$593$	−14.2283	−	8.21471i	−0.584286	−	0.337338i	0.178549	−	0.983931i	$-0.442860\pi$
$593$	−14.2283	−	8.21471i	−0.584286	−	0.337338i	−0.762835	+	0.646593i	$0.776193\pi$
$594$	−6.31313	−	10.9347i	−0.259031	−	0.448655i
$595$		0			0
$596$	−0.230608	−	0.133142i	−0.00944608	−	0.00545370i
$597$	−9.31535	+	16.1347i	−0.381252	+	0.660348i
$598$	36.6245	−	27.2947i	1.49769	−	1.11616i
$599$	−6.04094	−	10.4632i	−0.246826	−	0.427516i	0.715817	−	0.698288i	$-0.246054\pi$
$599$	−6.04094	−	10.4632i	−0.246826	−	0.427516i	−0.962644	+	0.270772i	$0.912721\pi$
$600$	33.3598	−	19.2603i	1.36191	−	0.786297i
$601$	3.90743	−	6.76787i	0.159387	−	0.276067i	−0.775261	−	0.631642i	$-0.782381\pi$
$601$	3.90743	−	6.76787i	0.159387	−	0.276067i	0.934648	+	0.355574i	$0.115715\pi$
$602$		0			0
$603$			41.7377i			1.69969i
$604$		−	1.00159i		−	0.0407541i
$605$	3.75818	+	2.16979i	0.152792	+	0.0882144i
$606$	62.0770	−	35.8401i	2.52170	−	1.45591i
$607$	−35.5649			−1.44354			−0.721768	−	0.692135i	$-0.756670\pi$
$607$	−35.5649			−1.44354			−0.721768	+	0.692135i	$0.756670\pi$
$608$	−0.557261	+	0.965205i	−0.0225999	+	0.0391442i
$609$		0			0
$610$	9.68882			0.392289
$611$	−13.0594	+	9.73263i	−0.528328	+	0.393740i
$612$	−0.384284	−	0.665599i	−0.0155338	−	0.0269052i
$613$			11.9368i			0.482122i	0.970510	+	0.241061i	$0.0774954\pi$
$613$			11.9368i			0.482122i	−0.970510	+	0.241061i	$0.922505\pi$
$614$	−5.77500	−	10.0026i	−0.233060	−	0.403672i
$615$	−3.08618	−	5.34542i	−0.124447	−	0.215548i
$616$		0			0
$617$	−20.4124	+	11.7851i	−0.821772	+	0.474450i	−0.851027	−	0.525122i	$-0.824020\pi$
$617$	−20.4124	+	11.7851i	−0.821772	+	0.474450i	0.0292550	+	0.999572i	$0.490687\pi$
$618$			19.6621i			0.790924i
$619$	24.7312	−	14.2786i	0.994031	−	0.573904i	0.0875541	−	0.996160i	$-0.472095\pi$
$619$	24.7312	−	14.2786i	0.994031	−	0.573904i	0.906477	+	0.422256i	$0.138762\pi$
$620$	0.118972	−	0.206066i	0.00477803	−	0.00827579i
$621$	−25.6355	−	44.4020i	−1.02872	−	1.78179i
$622$	17.5512	+	10.1332i	0.703738	+	0.406303i
$623$		0			0
$624$	−38.8110	+	4.55623i	−1.55368	+	0.182395i
$625$	−10.5164	+	18.2149i	−0.420656	+	0.728597i
$626$		−	23.7453i		−	0.949052i
$627$	−11.4332			−0.456597
$628$	−0.820567			−0.0327442
$629$			19.9292i			0.794628i
$630$		0			0
$631$	−38.9646	+	22.4962i	−1.55116	+	0.895561i	−0.553109	+	0.833109i	$0.686559\pi$
$631$	−38.9646	+	22.4962i	−1.55116	+	0.895561i	−0.998048	+	0.0624526i	$0.980108\pi$
$632$	−2.45138	−	1.41530i	−0.0975106	−	0.0562978i
$633$	−15.1460	+	26.2337i	−0.602001	+	1.04270i
$634$	19.4034			0.770607
$635$	−0.639763	+	0.369367i	−0.0253882	+	0.0146579i
$636$	−1.98943			−0.0788860
$637$		0			0
$638$	−11.7727			−0.466085
$639$	−22.4409	+	12.9562i	−0.887747	+	0.512541i
$640$	−5.49894			−0.217365
$641$	−1.26650	+	2.19364i	−0.0500238	+	0.0866437i	−0.889953	−	0.456052i	$-0.849263\pi$
$641$	−1.26650	+	2.19364i	−0.0500238	+	0.0866437i	0.839929	+	0.542696i	$0.182596\pi$
$642$	−20.8405	−	12.0322i	−0.822507	−	0.474875i
$643$	−15.9150	+	9.18853i	−0.627627	+	0.362360i	−0.779832	−	0.625988i	$-0.784696\pi$
$643$	−15.9150	+	9.18853i	−0.627627	+	0.362360i	0.152206	+	0.988349i	$0.451362\pi$
$644$		0			0
$645$		−	1.46251i		−	0.0575863i
$646$	6.72658			0.264654
$647$	20.9287			0.822791			0.411396	−	0.911457i	$-0.365041\pi$
$647$	20.9287			0.822791			0.411396	+	0.911457i	$0.365041\pi$
$648$			2.57964i			0.101338i
$649$	−5.03917	+	8.72810i	−0.197805	+	0.342608i
$650$	18.9549	−	14.1263i	0.743473	−	0.554079i
$651$		0			0
$652$	−1.07963	−	0.623326i	−0.0422817	−	0.0244113i
$653$	24.0580	+	41.6696i	0.941461	+	1.63066i	0.762686	+	0.646769i	$0.223880\pi$
$653$	24.0580	+	41.6696i	0.941461	+	1.63066i	0.178775	+	0.983890i	$0.442786\pi$
$654$	23.2952	−	40.3484i	0.910913	−	1.57775i
$655$	3.89824	−	2.25065i	0.152317	−	0.0879401i
$656$		−	16.1436i		−	0.630302i
$657$	−51.1129	+	29.5100i	−1.99410	+	1.15130i
$658$		0			0
$659$	1.10819	+	1.91944i	0.0431690	+	0.0747708i	0.886803	−	0.462148i	$-0.152921\pi$
$659$	1.10819	+	1.91944i	0.0431690	+	0.0747708i	−0.843634	+	0.536919i	$0.819588\pi$
$660$	0.0942408	+	0.163230i	0.00366832	+	0.00635371i
$661$		−	0.637434i		−	0.0247933i	−0.999923	−	0.0123966i	$-0.996054\pi$
$661$		−	0.637434i		−	0.0247933i	0.999923	−	0.0123966i	$-0.00394608\pi$
$662$	4.79537	+	8.30582i	0.186377	+	0.322815i
$663$	−11.8615	−	15.9159i	−0.460661	−	0.618124i
$664$	−25.6994			−0.997331
$665$		0			0
$666$	35.3368	−	61.2052i	1.36927	−	2.37165i
$667$	−47.8048			−1.85101
$668$	−1.12385	+	0.648856i	−0.0434831	+	0.0251050i
$669$	31.5390	+	18.2091i	1.21937	+	0.704003i
$670$			6.02203i			0.232651i
$671$		−	21.8786i		−	0.844614i
$672$		0			0
$673$	7.70343	−	13.3427i	0.296945	−	0.514324i	−0.678490	−	0.734609i	$-0.737365\pi$
$673$	7.70343	−	13.3427i	0.296945	−	0.514324i	0.975436	+	0.220285i	$0.0706988\pi$
$674$	13.3901	−	7.73081i	0.515769	−	0.297780i
$675$	−13.2676	−	22.9801i	−0.510669	−	0.884505i
$676$	1.00079	−	0.238260i	0.0384920	−	0.00916384i
$677$	−5.84060	+	10.1162i	−0.224473	+	0.388798i	−0.956161	−	0.292841i	$-0.905399\pi$
$677$	−5.84060	+	10.1162i	−0.224473	+	0.388798i	0.731689	+	0.681639i	$0.238733\pi$
$678$	−12.0613	−	6.96358i	−0.463210	−	0.267435i
$679$		0			0
$680$	−1.45673	−	2.52312i	−0.0558629	−	0.0967574i
$681$	−1.71097	−	0.987826i	−0.0655643	−	0.0378536i
$682$	11.2948	+	6.52107i	0.432501	+	0.249705i
$683$	−19.8419	−	11.4557i	−0.759227	−	0.438340i	0.0697909	−	0.997562i	$-0.477767\pi$
$683$	−19.8419	−	11.4557i	−0.759227	−	0.438340i	−0.829018	+	0.559221i	$0.811100\pi$
$684$	0.851075	+	0.491369i	0.0325417	+	0.0187879i
$685$	−2.21020	−	3.82817i	−0.0844473	−	0.146267i
$686$		0			0
$687$	−44.7514	−	25.8372i	−1.70737	−	0.985752i
$688$	1.91258	−	3.31268i	0.0729163	−	0.126295i
$689$	−31.8580	+	3.73998i	−1.21369	+	0.142482i
$690$	−9.28883	−	16.0887i	−0.353620	−	0.612487i
$691$	−40.9046	+	23.6163i	−1.55608	+	0.898405i	−0.558458	+	0.829533i	$0.688607\pi$
$691$	−40.9046	+	23.6163i	−1.55608	+	0.898405i	−0.997625	+	0.0688729i	$0.978060\pi$
$692$	0.0119239	−	0.0206529i	0.000453280	−	0.000785104i
$693$		0			0
$694$		−	6.82596i		−	0.259110i
$695$		−	2.61473i		−	0.0991825i
$696$	36.8805	+	21.2930i	1.39795	+	0.807109i
$697$	7.10163	−	4.10013i	0.268994	−	0.155303i
$698$	−2.11129			−0.0799135
$699$	37.8365	−	65.5347i	1.43111	−	2.47875i
$700$		0			0
$701$	12.2098			0.461158			0.230579	−	0.973054i	$-0.425938\pi$
$701$	12.2098			0.461158			0.230579	+	0.973054i	$0.425938\pi$
$702$	3.26810	+	27.8385i	0.123347	+	1.05070i
$703$	−12.7413	−	22.0686i	−0.480548	−	0.832334i
$704$			13.4659i			0.507515i
$705$	3.31218	+	5.73686i	0.124744	+	0.216063i
$706$	12.4237	+	21.5185i	0.467572	+	0.809858i
$707$		0			0
$708$	1.20171	−	0.693808i	0.0451630	−	0.0260749i
$709$		−	17.8875i		−	0.671778i	−0.941902	−	0.335889i	$-0.890963\pi$
$709$		−	17.8875i		−	0.671778i	0.941902	−	0.335889i	$-0.109037\pi$
$710$	−3.23783	+	1.86936i	−0.121514	+	0.0701560i
$711$	−2.44841	+	4.24076i	−0.0918224	+	0.159041i
$712$	−17.3169	−	29.9937i	−0.648977	−	1.12406i
$713$	45.8644	+	26.4798i	1.71764	+	0.991678i
$714$		0			0
$715$	1.81600	+	2.43674i	0.0679146	+	0.0911290i
$716$	−0.388390	+	0.672711i	−0.0145148	+	0.0251404i
$717$		−	46.9578i		−	1.75367i
$718$	−27.7210			−1.03454
$719$	9.12634			0.340355			0.170178	−	0.985413i	$-0.445566\pi$
$719$	9.12634			0.340355			0.170178	+	0.985413i	$0.445566\pi$
$720$			9.92235i			0.369784i
$721$		0			0
$722$	15.3564	−	8.86604i	0.571507	−	0.329960i
$723$	42.6126	+	24.6024i	1.58478	+	0.914973i
$724$	0.491906	−	0.852006i	0.0182815	−	0.0316646i
$725$	−24.7413			−0.918868
$726$	28.3617	−	16.3746i	1.05260	−	0.607719i
$727$	−33.6859			−1.24934			−0.624670	−	0.780889i	$-0.714767\pi$
$727$	−33.6859			−1.24934			−0.624670	+	0.780889i	$0.714767\pi$
$728$		0			0
$729$	−43.0880			−1.59585
$730$	−7.37471	+	4.25779i	−0.272950	+	0.157588i
$731$	1.94301			0.0718650
$732$	−1.50616	+	2.60874i	−0.0556691	+	0.0964218i
$733$	40.2134	+	23.2172i	1.48532	+	0.857547i	0.999860	−	0.0167147i	$-0.00532072\pi$
$733$	40.2134	+	23.2172i	1.48532	+	0.857547i	0.485455	+	0.874262i	$0.338654\pi$
$734$	−32.9062	+	18.9984i	−1.21459	+	0.701245i
$735$		0			0
$736$			4.08942i			0.150738i
$737$	13.5985			0.500908
$738$	−29.0801			−1.07045
$739$			1.85025i			0.0680627i	0.999421	+	0.0340314i	$0.0108346\pi$
$739$			1.85025i			0.0680627i	−0.999421	+	0.0340314i	$0.989165\pi$
$740$	−0.210047	+	0.363813i	−0.00772149	+	0.0133740i
$741$	23.3104	+	10.0412i	0.856328	+	0.368871i
$742$		0			0
$743$	28.7095	+	16.5755i	1.05325	+	0.608094i	0.923558	−	0.383460i	$-0.125268\pi$
$743$	28.7095	+	16.5755i	1.05325	+	0.608094i	0.129693	+	0.991554i	$0.458601\pi$
$744$	−23.5890	−	40.8574i	−0.864816	−	1.49791i
$745$	−0.873120	+	1.51229i	−0.0319886	+	0.0554059i
$746$	−19.0757	+	11.0134i	−0.698412	+	0.403228i
$747$			44.4588i			1.62666i
$748$	−0.216858	+	0.125203i	−0.00792913	+	0.00457788i
$749$		0			0
$750$	−9.88850	−	17.1274i	−0.361077	−	0.625404i
$751$	−10.3871	−	17.9910i	−0.379032	−	0.656503i	0.611890	−	0.790943i	$-0.290410\pi$
$751$	−10.3871	−	17.9910i	−0.379032	−	0.656503i	−0.990922	+	0.134441i	$0.957076\pi$
$752$			17.3258i			0.631806i
$753$	9.11286	+	15.7839i	0.332091	+	0.575199i
$754$	24.0026	+	10.3393i	0.874122	+	0.376536i
$755$	−6.56824			−0.239043
$756$		0			0
$757$	−21.8075	+	37.7717i	−0.792607	+	1.37283i	0.131741	+	0.991284i	$0.457943\pi$
$757$	−21.8075	+	37.7717i	−0.792607	+	1.37283i	−0.924348	+	0.381551i	$0.875390\pi$
$758$	12.1673			0.441936
$759$	−36.3304	+	20.9754i	−1.31871	+	0.761358i
$760$	3.22622	+	1.86266i	0.117027	+	0.0675657i
$761$		−	12.3902i		−	0.449145i	−0.974457	−	0.224573i	$-0.927901\pi$
$761$		−	12.3902i		−	0.449145i	0.974457	−	0.224573i	$-0.0720986\pi$
$762$			5.57497i			0.201960i
$763$		0			0
$764$	0.484583	−	0.839323i	0.0175316	−	0.0303656i
$765$	−4.36488	+	2.52007i	−0.157813	+	0.0911132i
$766$	−5.51773	−	9.55700i	−0.199364	−	0.345308i
$767$	17.9395	−	13.3695i	0.647757	−	0.482746i
$768$	2.67917	−	4.64046i	0.0966763	−	0.167448i
$769$	4.80955	+	2.77680i	0.173437	+	0.100134i	0.584205	−	0.811606i	$-0.301406\pi$
$769$	4.80955	+	2.77680i	0.173437	+	0.100134i	−0.410769	+	0.911740i	$0.634740\pi$
$770$		0			0
$771$	5.18750	+	8.98501i	0.186823	+	0.323587i
$772$	−0.797307	−	0.460325i	−0.0286957	−	0.0165675i
$773$	37.9355	+	21.9021i	1.36445	+	0.787764i	0.990212	−	0.139570i	$-0.0445721\pi$
$773$	37.9355	+	21.9021i	1.36445	+	0.787764i	0.374235	+	0.927334i	$0.377905\pi$
$774$	−5.96726	−	3.44520i	−0.214489	−	0.123835i
$775$	23.7370	+	13.7046i	0.852659	+	0.492283i
$776$	−6.37159	−	11.0359i	−0.228727	−	0.396166i
$777$		0			0
$778$	38.4608	+	22.2053i	1.37889	+	0.796100i
$779$	−5.24267	+	9.08058i	−0.187838	+	0.325346i
$780$	−0.0487854	−	0.415566i	−0.00174680	−	0.0148796i
$781$	4.22127	+	7.31145i	0.151049	+	0.261624i
$782$	21.3746	−	12.3406i	0.764354	−	0.441300i
$783$	14.6678	−	25.4054i	0.524185	−	0.907916i
$784$		0			0
$785$			5.38113i			0.192061i
$786$		−	33.9697i		−	1.21166i
$787$	21.4782	+	12.4005i	0.765616	+	0.442029i	0.831309	−	0.555811i	$-0.187592\pi$
$787$	21.4782	+	12.4005i	0.765616	+	0.442029i	−0.0656923	+	0.997840i	$0.520926\pi$
$788$	0.123439	−	0.0712673i	0.00439732	−	0.00253879i
$789$	51.7661			1.84292
$790$	−0.353263	+	0.611870i	−0.0125685	+	0.0217693i
$791$		0			0
$792$	23.3305			0.829015
$793$	−19.2148	+	44.6069i	−0.682338	+	1.58404i
$794$	−4.45901	−	7.72323i	−0.158244	−	0.274087i
$795$			13.0463i			0.462706i
$796$	−0.260876	−	0.451850i	−0.00924649	−	0.0160154i
$797$	8.23575	+	14.2647i	0.291725	+	0.505283i	0.974218	−	0.225610i	$-0.0724373\pi$
$797$	8.23575	+	14.2647i	0.291725	+	0.505283i	−0.682492	+	0.730893i	$0.739104\pi$
$798$		0			0
$799$	−7.62168	+	4.40038i	−0.269636	+	0.155674i
$800$			2.11647i			0.0748285i
$801$	−51.8876	+	29.9573i	−1.83336	+	1.05849i
$802$	0.369756	−	0.640437i	0.0130566	−	0.0226146i
$803$	9.61464	+	16.6530i	0.339293	+	0.587673i
$804$	−1.62145	−	0.936144i	−0.0571841	−	0.0330152i
$805$		0			0
$806$	−17.3012	−	23.2150i	−0.609408	−	0.817715i
$807$	38.9151	−	67.4028i	1.36987	−	2.37269i
$808$			52.7406i			1.85541i
$809$	1.38194			0.0485863			0.0242932	−	0.999705i	$-0.492266\pi$
$809$	1.38194			0.0485863			0.0242932	+	0.999705i	$0.492266\pi$
$810$	0.643885			0.0226238
$811$			6.83571i			0.240034i	0.992772	+	0.120017i	$0.0382950\pi$
$811$			6.83571i			0.240034i	−0.992772	+	0.120017i	$0.961705\pi$
$812$		0			0
$813$	15.9538	−	9.21093i	0.559524	−	0.323041i
$814$	−19.9412	−	11.5131i	−0.698939	−	0.403533i
$815$	−4.08767	+	7.08004i	−0.143185	+	0.248003i
$816$	−21.1155			−0.739190
$817$	−2.15160	+	1.24223i	−0.0752750	+	0.0434601i
$818$	−55.0954			−1.92637
$819$		0			0
$820$	0.172856			0.00603640
$821$	9.13009	−	5.27126i	0.318642	−	0.183968i	−0.332145	−	0.943228i	$-0.607772\pi$
$821$	9.13009	−	5.27126i	0.318642	−	0.183968i	0.650787	+	0.759260i	$0.274439\pi$
$822$	−33.3592			−1.16353
$823$	7.41652	−	12.8458i	0.258524	−	0.447776i	−0.707323	−	0.706891i	$-0.750097\pi$
$823$	7.41652	−	12.8458i	0.258524	−	0.447776i	0.965847	+	0.259114i	$0.0834307\pi$
$824$	−12.5287	−	7.23343i	−0.436457	−	0.251988i
$825$	−18.8027	+	10.8558i	−0.654627	+	0.377949i
$826$		0			0
$827$		−	55.6758i		−	1.93604i	−0.250879	−	0.968018i	$-0.580720\pi$
$827$		−	55.6758i		−	1.93604i	0.250879	−	0.968018i	$-0.419280\pi$
$828$	3.60587			0.125313
$829$	−0.0464848			−0.00161448			−0.000807242	−	1.00000i	$-0.500257\pi$
$829$	−0.0464848			−0.00161448			−0.000807242		1.00000i	$0.500257\pi$
$830$			6.41464i			0.222655i
$831$	7.68873	−	13.3173i	0.266719	−	0.461971i
$832$	11.8264	−	27.4548i	0.410006	−	0.951823i
$833$		0			0
$834$	−17.0888	−	9.86624i	−0.591738	−	0.341640i
$835$	4.25508	+	7.37002i	0.147253	+	0.255050i
$836$	0.160092	−	0.277288i	0.00553691	−	0.00959022i
$837$	−28.1449	+	16.2495i	−0.972831	+	0.561664i
$838$		−	33.0100i		−	1.14031i
$839$	−22.1248	+	12.7738i	−0.763833	+	0.440999i	−0.830670	−	0.556765i	$-0.812043\pi$
$839$	−22.1248	+	12.7738i	−0.763833	+	0.440999i	0.0668370	+	0.997764i	$0.478709\pi$
$840$		0			0
$841$	0.823775	+	1.42682i	0.0284060	+	0.0492007i
$842$	16.1061	+	27.8965i	0.555052	+	0.961378i
$843$		−	10.0099i		−	0.344761i
$844$	−0.424164	−	0.734673i	−0.0146003	−	0.0252885i
$845$	−1.56247	−	6.56302i	−0.0537505	−	0.225775i
$846$	31.2096			1.07301
$847$		0			0
$848$	−17.0611	+	29.5507i	−0.585881	+	1.01478i
$849$	−39.9540			−1.37122
$850$	11.0624	−	6.38686i	0.379436	−	0.219068i
$851$	−80.9745	−	46.7507i	−2.77577	−	1.60259i
$852$		−	1.16239i		−	0.0398229i
$853$		−	22.6671i		−	0.776105i	−0.921637	−	0.388053i	$-0.873148\pi$
$853$		−	22.6671i		−	0.776105i	0.921637	−	0.388053i	$-0.126852\pi$
$854$		0			0
$855$	3.22231	−	5.58120i	0.110201	−	0.190873i
$856$	15.3339	−	8.85303i	0.524102	−	0.302590i
$857$	18.5268	+	32.0893i	0.632862	+	1.09615i	0.986964	+	0.160943i	$0.0514534\pi$
$857$	18.5268	+	32.0893i	0.632862	+	1.09615i	−0.354101	+	0.935207i	$0.615213\pi$
$858$	22.7779	−	2.67402i	0.777625	−	0.0912895i
$859$	−2.12169	+	3.67488i	−0.0723912	+	0.125385i	−0.899949	−	0.435996i	$-0.856396\pi$
$859$	−2.12169	+	3.67488i	−0.0723912	+	0.125385i	0.827558	+	0.561381i	$0.189730\pi$
$860$	0.0354702	+	0.0204788i	0.00120953	+	0.000698320i
$861$		0			0
$862$	1.87581	+	3.24900i	0.0638904	+	0.110661i
$863$	6.49563	+	3.75025i	0.221114	+	0.127660i	0.606466	−	0.795110i	$-0.292587\pi$
$863$	6.49563	+	3.75025i	0.221114	+	0.127660i	−0.385352	+	0.922770i	$0.625920\pi$
$864$	−2.17328	−	1.25475i	−0.0739366	−	0.0426873i
$865$	−0.135438	−	0.0781951i	−0.00460503	−	0.00265871i
$866$	6.98425	+	4.03236i	0.237335	+	0.137025i
$867$	18.6562	+	32.3135i	0.633598	+	1.09742i
$868$		0			0
$869$	1.38168	+	0.797714i	0.0468703	+	0.0270606i
$870$	5.31478	−	9.20547i	0.180188	−	0.312095i
$871$	−27.7252	−	11.9429i	−0.939432	−	0.404669i
$872$	17.1400	+	29.6874i	0.580434	+	1.00534i
$873$	−19.0916	+	11.0225i	−0.646153	+	0.373057i
$874$	−15.7795	+	27.3309i	−0.533749	+	0.924481i
$875$		0			0
$876$		−	2.64755i		−	0.0894523i
$877$		−	28.2897i		−	0.955274i	−0.878557	−	0.477637i	$-0.841493\pi$
$877$		−	28.2897i		−	0.955274i	0.878557	−	0.477637i	$-0.158507\pi$
$878$	−45.8145	−	26.4510i	−1.54617	−	0.892679i
$879$	20.4324	−	11.7966i	0.689166	−	0.397890i
$880$	3.23280			0.108978
$881$	19.7860	−	34.2704i	0.666609	−	1.15460i	−0.312238	−	0.950004i	$-0.601079\pi$
$881$	19.7860	−	34.2704i	0.666609	−	1.15460i	0.978846	−	0.204596i	$-0.0655882\pi$
$882$		0			0
$883$	−28.3609			−0.954419			−0.477209	−	0.878790i	$-0.658352\pi$
$883$	−28.3609			−0.954419			−0.477209	+	0.878790i	$0.658352\pi$
$884$	0.552098	−	0.0648137i	0.0185691	−	0.00217992i
$885$	−4.54987	−	7.88061i	−0.152942	−	0.264904i
$886$		−	43.8987i		−	1.47481i
$887$	−21.8593	−	37.8614i	−0.733963	−	1.27126i	−0.955177	−	0.296036i	$-0.904335\pi$
$887$	−21.8593	−	37.8614i	−0.733963	−	1.27126i	0.221214	−	0.975225i	$-0.428998\pi$
$888$	41.6469	+	72.1345i	1.39758	+	2.42068i
$889$		0			0
$890$	−7.48649	+	4.32233i	−0.250948	+	0.144885i
$891$		−	1.45398i		−	0.0487100i
$892$	−0.883247	+	0.509943i	−0.0295733	+	0.0170742i
$893$	5.62659	−	9.74554i	0.188287	−	0.326122i
$894$	6.58913	+	11.4127i	0.220374	+	0.381698i
$895$	4.41152	+	2.54699i	0.147461	+	0.0851366i
$896$		0			0
$897$	92.4934	−	10.8583i	3.08826	−	0.362547i
$898$	21.7629	−	37.6944i	0.726236	−	1.25788i
$899$			30.3019i			1.01062i
$900$	1.86621			0.0622070
$901$	−17.3326			−0.577434
$902$			9.47456i			0.315468i
$903$		0			0
$904$	8.87439	−	5.12363i	0.295158	−	0.170409i
$905$	−5.58731	−	3.22583i	−0.185728	−	0.107230i
$906$	−24.7841	+	42.9274i	−0.823397	+	1.42617i
$907$	36.6985			1.21855			0.609277	−	0.792957i	$-0.291460\pi$
$907$	36.6985			1.21855			0.609277	+	0.792957i	$0.291460\pi$
$908$	0.0479154	−	0.0276640i	0.00159013	−	0.000918062i
$909$	91.2387			3.02620
$910$		0			0
$911$	−35.5211			−1.17686			−0.588432	−	0.808546i	$-0.700255\pi$
$911$	−35.5211			−1.17686			−0.588432	+	0.808546i	$0.700255\pi$
$912$	23.3823	−	13.4998i	0.774265	−	0.447022i
$913$	14.4851			0.479386
$914$	−22.0562	+	38.2024i	−0.729553	+	1.26362i
$915$	17.1077	+	9.87711i	0.565562	+	0.326527i
$916$	1.25326	−	0.723569i	0.0414088	−	0.0239074i
$917$		0			0
$918$			15.1458i			0.499885i
$919$	21.9334			0.723516			0.361758	−	0.932272i	$-0.382177\pi$
$919$	21.9334			0.723516			0.361758	+	0.932272i	$0.382177\pi$
$920$	13.6690			0.450653
$921$		−	23.5489i		−	0.775964i
$922$	−0.808222	+	1.39988i	−0.0266174	+	0.0461026i
$923$	−2.18521	−	18.6142i	−0.0719272	−	0.612693i
$924$		0			0
$925$	−41.9082	−	24.1957i	−1.37793	−	0.795549i
$926$	−14.0980	−	24.4184i	−0.463287	−	0.802437i
$927$	−12.5135	+	21.6740i	−0.410997	+	0.711867i
$928$	−2.02636	+	1.16992i	−0.0665186	+	0.0384045i
$929$			15.5172i			0.509102i	0.967059	+	0.254551i	$0.0819276\pi$
$929$			15.5172i			0.509102i	−0.967059	+	0.254551i	$0.918072\pi$
$930$	−10.1981	+	5.88788i	−0.334409	+	0.193071i
$931$		0			0
$932$	1.05961	+	1.83529i	0.0347086	+	0.0601171i
$933$	20.6602	+	35.7845i	0.676385	+	1.17153i
$934$		−	2.17510i		−	0.0711716i
$935$	0.821061	+	1.42212i	0.0268516	+	0.0465083i
$936$	−47.5672	−	20.4900i	−1.55478	−	0.669736i
$937$	−40.8110			−1.33324			−0.666618	−	0.745399i	$-0.732259\pi$
$937$	−40.8110			−1.33324			−0.666618	+	0.745399i	$0.732259\pi$
$938$		0			0
$939$	24.2067	−	41.9273i	0.789957	−	1.36825i
$940$	−0.185514			−0.00605081
$941$	44.6814	−	25.7968i	1.45657	−	0.840952i	0.457731	−	0.889091i	$-0.348662\pi$
$941$	44.6814	−	25.7968i	1.45657	−	0.840952i	0.998841	+	0.0481384i	$0.0153288\pi$
$942$	35.1689	+	20.3048i	1.14586	+	0.661565i
$943$			38.4730i			1.25285i
$944$		−	23.8001i		−	0.774627i
$945$		0			0
$946$	−1.12248	+	1.94419i	−0.0364949	+	0.0632110i
$947$	4.31462	−	2.49105i	0.140206	−	0.0809482i	−0.428256	−	0.903657i	$-0.640872\pi$
$947$	4.31462	−	2.49105i	0.140206	−	0.0809482i	0.568462	+	0.822709i	$0.307539\pi$
$948$	−0.109832	−	0.190234i	−0.00356717	−	0.00617851i
$949$	−4.97719	−	42.3969i	−0.161566	−	1.37626i
$950$	−8.16663	+	14.1450i	−0.264961	+	0.458925i
$951$	34.2608	+	19.7805i	1.11098	+	0.641426i
$952$		0			0
$953$	15.1163	+	26.1822i	0.489664	+	0.848123i	0.999929	−	0.0118941i	$-0.00378608\pi$
$953$	15.1163	+	26.1822i	0.489664	+	0.848123i	−0.510265	+	0.860017i	$0.670453\pi$
$954$	53.2309	+	30.7329i	1.72341	+	0.995013i
$955$	−5.50413	−	3.17781i	−0.178110	−	0.102832i
$956$	1.13887	+	0.657525i	0.0368336	+	0.0212659i
$957$	−20.7871	−	12.0015i	−0.671953	−	0.387952i
$958$	5.34921	+	9.26511i	0.172825	+	0.299342i
$959$		0			0
$960$	−10.5295	−	6.07919i	−0.339837	−	0.196205i
$961$	1.28469	−	2.22516i	0.0414418	−	0.0717792i
$962$	30.5456	+	40.9866i	0.984829	+	1.32146i
$963$	−15.3153	−	26.5269i	−0.493529	−	0.854817i
$964$	−1.19336	+	0.688988i	−0.0384356	+	0.0221908i
$965$	−3.01873	+	5.22860i	−0.0971764	+	0.168315i
$966$		0			0
$967$		−	29.9990i		−	0.964703i	−0.875978	−	0.482352i	$-0.839783\pi$
$967$		−	29.9990i		−	0.964703i	0.875978	−	0.482352i	$-0.160217\pi$
$968$			24.0961i			0.774478i
$969$	11.8772	+	6.85731i	0.381551	+	0.220288i
$970$	−2.75459	+	1.59036i	−0.0884446	+	0.0510635i
$971$	−44.1240			−1.41601			−0.708003	−	0.706209i	$-0.750404\pi$
$971$	−44.1240			−1.41601			−0.708003	+	0.706209i	$0.750404\pi$
$972$	0.565732	−	0.979876i	0.0181459	−	0.0314295i
$973$		0			0
$974$	0.105582			0.00338306
$975$	47.8697	−	5.61968i	1.53306	−	0.179974i
$976$	25.8333	+	44.7445i	0.826902	+	1.43224i
$977$			15.0024i			0.479970i	0.970777	+	0.239985i	$0.0771425\pi$
$977$			15.0024i			0.479970i	−0.970777	+	0.239985i	$0.922858\pi$
$978$	30.8482	+	53.4306i	0.986417	+	1.70852i
$979$	9.76037	+	16.9055i	0.311943	+	0.540301i
$980$		0			0
$981$	51.3577	−	29.6514i	1.63973	−	0.946696i
$982$		−	2.47690i		−	0.0790411i
$983$	−5.21223	+	3.00928i	−0.166244	+	0.0959812i	−0.580814	−	0.814037i	$-0.697266\pi$
$983$	−5.21223	+	3.00928i	−0.166244	+	0.0959812i	0.414569	+	0.910018i	$0.363932\pi$
$984$	17.1364	−	29.6812i	0.546290	−	0.946202i
$985$	−0.467358	−	0.809488i	−0.0148913	−	0.0257924i
$986$	12.2299	+	7.06093i	0.389479	+	0.224866i
$987$		0			0
$988$	−0.569930	+	0.424745i	−0.0181319	+	0.0135129i
$989$	−4.55800	+	7.89469i	−0.144936	+	0.251036i
$990$		−	5.82336i		−	0.185078i
$991$	33.8400			1.07496			0.537482	−	0.843275i	$-0.319376\pi$
$991$	33.8400			1.07496			0.537482	+	0.843275i	$0.319376\pi$
$992$	2.59215			0.0823008
$993$			19.5542i			0.620535i
$994$		0			0
$995$	−2.96315	+	1.71078i	−0.0939382	+	0.0542353i
$996$	−1.72716	−	0.997175i	−0.0547271	−	0.0315967i
$997$	13.1608	−	22.7951i	0.416805	−	0.721928i	−0.578811	−	0.815462i	$-0.696483\pi$
$997$	13.1608	−	22.7951i	0.416805	−	0.721928i	0.995616	+	0.0935340i	$0.0298164\pi$
$998$	−11.5518			−0.365666
$999$	49.6904	−	28.6888i	1.57213	−	0.907672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.u.i.30.5		12
7.2	even	3		637.2.q.h.589.2		12
7.3	odd	6		637.2.k.h.459.5		12
7.4	even	3		637.2.k.g.459.5		12
7.5	odd	6		91.2.q.a.43.2	yes	12
7.6	odd	2		637.2.u.h.30.5		12
13.10	even	6		637.2.k.g.569.2		12
21.5	even	6		819.2.ct.a.316.5		12
28.19	even	6		1456.2.cc.c.225.1		12
91.10	odd	6		637.2.u.h.361.5		12
91.19	even	12		1183.2.a.m.1.6		6
91.23	even	6		637.2.q.h.491.2		12
91.33	even	12		1183.2.a.p.1.1		6
91.58	odd	12		8281.2.a.by.1.6		6
91.61	odd	6		1183.2.c.i.337.10		12
91.62	odd	6		637.2.k.h.569.2		12
91.72	odd	12		8281.2.a.ch.1.1		6
91.75	odd	6		91.2.q.a.36.2	✓	12
91.82	odd	6		1183.2.c.i.337.3		12
91.88	even	6	inner	637.2.u.i.361.5		12
273.257	even	6		819.2.ct.a.127.5		12
364.75	even	6		1456.2.cc.c.673.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.2	✓	12	91.75	odd	6
91.2.q.a.43.2	yes	12	7.5	odd	6
637.2.k.g.459.5		12	7.4	even	3
637.2.k.g.569.2		12	13.10	even	6
637.2.k.h.459.5		12	7.3	odd	6
637.2.k.h.569.2		12	91.62	odd	6
637.2.q.h.491.2		12	91.23	even	6
637.2.q.h.589.2		12	7.2	even	3
637.2.u.h.30.5		12	7.6	odd	2
637.2.u.h.361.5		12	91.10	odd	6
637.2.u.i.30.5		12	1.1	even	1	trivial
637.2.u.i.361.5		12	91.88	even	6	inner
819.2.ct.a.127.5		12	273.257	even	6
819.2.ct.a.316.5		12	21.5	even	6
1183.2.a.m.1.6		6	91.19	even	12
1183.2.a.p.1.1		6	91.33	even	12
1183.2.c.i.337.3		12	91.82	odd	6
1183.2.c.i.337.10		12	91.61	odd	6
1456.2.cc.c.225.1		12	28.19	even	6
1456.2.cc.c.673.1		12	364.75	even	6
8281.2.a.by.1.6		6	91.58	odd	12
8281.2.a.ch.1.1		6	91.72	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)

\(f(q)\)	\(=\)	\(q+(1.20027 - 0.692976i) q^{2} +2.82577 q^{3} +(-0.0395678 + 0.0685334i) q^{4} +(0.449430 + 0.259479i) q^{5} +(3.39169 - 1.95819i) q^{6} +2.88158i q^{8} +4.98500 q^{9} +O(q^{10})\)	\(q+(1.20027 - 0.692976i) q^{2} +2.82577 q^{3} +(-0.0395678 + 0.0685334i) q^{4} +(0.449430 + 0.259479i) q^{5} +(3.39169 - 1.95819i) q^{6} +2.88158i q^{8} +4.98500 q^{9} +0.719250 q^{10} -1.62416i q^{11} +(-0.111810 + 0.193660i) q^{12} +(-1.42641 + 3.31140i) q^{13} +(1.26999 + 0.733228i) q^{15} +(1.91773 + 3.32161i) q^{16} +(-0.974127 + 1.68724i) q^{17} +(5.98335 - 3.45449i) q^{18} -2.49115i q^{19} +(-0.0355659 + 0.0205340i) q^{20} +(-1.12550 - 1.94943i) q^{22} +(-4.57029 - 7.91598i) q^{23} +8.14270i q^{24} +(-2.36534 - 4.09689i) q^{25} +(0.582637 + 4.96304i) q^{26} +5.60916 q^{27} +(2.61498 - 4.52928i) q^{29} +2.03244 q^{30} +(-5.01767 + 2.89695i) q^{31} +(-0.387453 - 0.223696i) q^{32} -4.58951i q^{33} +2.70019i q^{34} +(-0.197245 + 0.341639i) q^{36} +(8.85879 - 5.11463i) q^{37} +(-1.72631 - 2.99006i) q^{38} +(-4.03072 + 9.35726i) q^{39} +(-0.747709 + 1.29507i) q^{40} +(-3.64513 - 2.10452i) q^{41} +(-0.498655 - 0.863697i) q^{43} +(0.111309 + 0.0642644i) q^{44} +(2.24041 + 1.29350i) q^{45} +(-10.9712 - 6.33421i) q^{46} +(3.91206 + 2.25863i) q^{47} +(5.41908 + 9.38612i) q^{48} +(-5.67810 - 3.27825i) q^{50} +(-2.75266 + 4.76775i) q^{51} +(-0.170501 - 0.228782i) q^{52} +(4.44825 + 7.70460i) q^{53} +(6.73251 - 3.88701i) q^{54} +(0.421434 - 0.729946i) q^{55} -7.03944i q^{57} -7.24847i q^{58} +(-5.37392 - 3.10263i) q^{59} +(-0.100501 + 0.0580244i) q^{60} +13.4707 q^{61} +(-4.01504 + 6.95426i) q^{62} -8.29100 q^{64} +(-1.50031 + 1.11812i) q^{65} +(-3.18042 - 5.50865i) q^{66} +8.37266i q^{67} +(-0.0770880 - 0.133520i) q^{68} +(-12.9146 - 22.3688i) q^{69} +(-4.50168 + 2.59905i) q^{71} +14.3647i q^{72} +(-10.2533 + 5.91976i) q^{73} +(7.08863 - 12.2779i) q^{74} +(-6.68392 - 11.5769i) q^{75} +(0.170727 + 0.0985694i) q^{76} +(1.64640 + 14.0244i) q^{78} +(-0.491155 + 0.850705i) q^{79} +1.99044i q^{80} +0.895217 q^{81} -5.83352 q^{82} +8.91851i q^{83} +(-0.875603 + 0.505530i) q^{85} +(-1.19704 - 0.691113i) q^{86} +(7.38934 - 12.7987i) q^{87} +4.68015 q^{88} +(-10.4087 + 6.00949i) q^{89} +3.58546 q^{90} +0.723345 q^{92} +(-14.1788 + 8.18614i) q^{93} +6.26070 q^{94} +(0.646401 - 1.11960i) q^{95} +(-1.09485 - 0.632114i) q^{96} +(-3.82981 + 2.21114i) q^{97} -8.09643i 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

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Representations

Groups

Database

Properties

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