LMFDB - Embedded newform 128.5.l.a.3.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,5,Mod(3,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([16, 3]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("128.3");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	128.l (of order $32$, degree $16$, 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:	$13.2313552747$
Analytic rank:	$0$
Dimension:	$1008$
Relative dimension:	$63$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			3.7
Character	$\chi$	$=$	128.3
Dual form			128.5.l.a.43.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.87689 + 0.984756i) q^{2} +(3.81952 - 3.13460i) q^{3} +(14.0605 - 7.63558i) q^{4} +(27.8176 + 8.43838i) q^{5} +(-11.7210 + 15.9138i) q^{6} +(7.96282 + 40.0318i) q^{7} +(-46.9918 + 43.4484i) q^{8} +(-11.0393 + 55.4983i) q^{9} +O(q^{10})$	\(q+(-3.87689 + 0.984756i) q^{2} +(3.81952 - 3.13460i) q^{3} +(14.0605 - 7.63558i) q^{4} +(27.8176 + 8.43838i) q^{5} +(-11.7210 + 15.9138i) q^{6} +(7.96282 + 40.0318i) q^{7} +(-46.9918 + 43.4484i) q^{8} +(-11.0393 + 55.4983i) q^{9} +(-116.155 - 5.32109i) q^{10} +(2.91910 + 29.6381i) q^{11} +(29.7699 - 73.2382i) q^{12} +(-8.11634 - 26.7560i) q^{13} +(-70.2925 - 147.357i) q^{14} +(132.701 - 54.9664i) q^{15} +(139.396 - 214.720i) q^{16} +(27.2487 - 65.7842i) q^{17} +(-11.8542 - 226.032i) q^{18} +(-185.060 + 346.222i) q^{19} +(455.562 - 93.7555i) q^{20} +(155.898 + 127.942i) q^{21} +(-40.5034 - 112.029i) q^{22} +(-231.629 + 154.769i) q^{23} +(-43.2928 + 313.252i) q^{24} +(182.945 + 122.240i) q^{25} +(57.8143 + 95.7373i) q^{26} +(320.466 + 599.551i) q^{27} +(417.627 + 502.067i) q^{28} +(-1.62561 + 16.5051i) q^{29} +(-460.337 + 343.777i) q^{30} +(48.8233 + 48.8233i) q^{31} +(-328.975 + 969.717i) q^{32} +(104.053 + 104.053i) q^{33} +(-40.8588 + 281.871i) q^{34} +(-116.297 + 1180.78i) q^{35} +(268.543 + 864.626i) q^{36} +(499.498 + 934.495i) q^{37} +(376.511 - 1524.50i) q^{38} +(-114.870 - 76.7535i) q^{39} +(-1673.84 + 812.097i) q^{40} +(-310.025 + 207.152i) q^{41} +(-730.389 - 342.495i) q^{42} +(2331.72 + 1913.60i) q^{43} +(267.348 + 394.438i) q^{44} +(-775.403 + 1450.68i) q^{45} +(745.588 - 828.120i) q^{46} +(118.274 - 285.540i) q^{47} +(-140.636 - 1257.08i) q^{48} +(679.097 - 281.291i) q^{49} +(-829.632 - 293.754i) q^{50} +(-102.130 - 336.677i) q^{51} +(-318.417 - 314.230i) q^{52} +(-142.139 - 1443.16i) q^{53} +(-1832.82 - 2008.81i) q^{54} +(-168.895 + 849.094i) q^{55} +(-2113.51 - 1535.20i) q^{56} +(378.429 + 1902.49i) q^{57} +(-9.95121 - 65.5894i) q^{58} +(2790.26 + 846.416i) q^{59} +(1446.14 - 1786.10i) q^{60} +(3528.98 - 2896.16i) q^{61} +(-237.361 - 141.203i) q^{62} -2309.60 q^{63} +(320.466 - 4083.44i) q^{64} -812.777i q^{65} +(-505.869 - 300.935i) q^{66} +(-1275.06 - 1553.66i) q^{67} +(-119.169 - 1133.02i) q^{68} +(-399.570 + 1317.21i) q^{69} +(-711.912 - 4692.28i) q^{70} +(-320.710 + 63.7932i) q^{71} +(-1892.56 - 3087.61i) q^{72} +(2665.01 + 530.103i) q^{73} +(-2856.75 - 3131.05i) q^{74} +(1081.93 - 106.561i) q^{75} +(41.5731 + 6281.10i) q^{76} +(-1163.22 + 352.860i) q^{77} +(520.920 + 184.446i) q^{78} +(176.280 + 425.577i) q^{79} +(5689.55 - 4796.73i) q^{80} +(-1131.17 - 468.544i) q^{81} +(997.938 - 1108.40i) q^{82} +(-8601.87 - 4597.79i) q^{83} +(3168.91 + 608.560i) q^{84} +(1313.11 - 1600.02i) q^{85} +(-10924.3 - 5122.62i) q^{86} +(45.5279 + 68.1373i) q^{87} +(-1424.90 - 1265.92i) q^{88} +(3670.19 - 5492.83i) q^{89} +(1577.59 - 6387.69i) q^{90} +(1006.46 - 537.965i) q^{91} +(-2075.06 + 3944.75i) q^{92} +(339.523 + 33.4401i) q^{93} +(-177.350 + 1223.48i) q^{94} +(-8069.48 + 8069.48i) q^{95} +(1783.14 + 4735.05i) q^{96} +(12478.3 - 12478.3i) q^{97} +(-2355.78 + 1759.28i) q^{98} +(-1677.09 - 165.179i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1008 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 1008 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 1008 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 43072 q^{50} - 16 q^{51} - 17968 q^{52} - 16 q^{53} + 31088 q^{54} - 16 q^{55} + 49376 q^{56} - 16 q^{57} + 65504 q^{58} - 16 q^{59} + 63920 q^{60} - 16 q^{61} + 11792 q^{62} - 32 q^{63} - 24400 q^{64} - 70864 q^{66} - 16 q^{67} - 53296 q^{68} - 16 q^{69} - 122320 q^{70} - 16 q^{71} - 81664 q^{72} - 16 q^{73} - 33280 q^{74} - 16 q^{75} + 28272 q^{76} - 16 q^{77} + 99344 q^{78} - 16 q^{79} + 105248 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 1008 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 - 43072 * q^50 - 16 * q^51 - 17968 * q^52 - 16 * q^53 + 31088 * q^54 - 16 * q^55 + 49376 * q^56 - 16 * q^57 + 65504 * q^58 - 16 * q^59 + 63920 * q^60 - 16 * q^61 + 11792 * q^62 - 32 * q^63 - 24400 * q^64 - 70864 * q^66 - 16 * q^67 - 53296 * q^68 - 16 * q^69 - 122320 * q^70 - 16 * q^71 - 81664 * q^72 - 16 * q^73 - 33280 * q^74 - 16 * q^75 + 28272 * q^76 - 16 * q^77 + 99344 * q^78 - 16 * q^79 + 105248 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{32}\right)$	$-1$

Coefficient data

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

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

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

$2$	−3.87689	+	0.984756i	−0.969222	+	0.246189i
$2$	−3.87689	+	0.984756i	−0.969222	+	0.246189i
$3$	3.81952	−	3.13460i	0.424391	−	0.348288i	−0.397828	−	0.917460i	$-0.630236\pi$
$3$	3.81952	−	3.13460i	0.424391	−	0.348288i	0.822219	+	0.569172i	$0.192736\pi$
$4$	14.0605	−	7.63558i	0.878782	−	0.477224i
$5$	27.8176	+	8.43838i	1.11270	+	0.337535i	0.792536	−	0.609825i	$-0.208760\pi$
$5$	27.8176	+	8.43838i	1.11270	+	0.337535i	0.320169	+	0.947361i	$0.396260\pi$
$6$	−11.7210	+	15.9138i	−0.325584	+	0.442049i
$7$	7.96282	+	40.0318i	0.162506	+	0.816975i	0.972925	+	0.231123i	$0.0742400\pi$
$7$	7.96282	+	40.0318i	0.162506	+	0.816975i	−0.810418	+	0.585852i	$0.800760\pi$
$8$	−46.9918	+	43.4484i	−0.734247	+	0.678882i
$9$	−11.0393	+	55.4983i	−0.136288	+	0.685165i
$10$	−116.155	−	5.32109i	−1.16155	−	0.0532109i
$11$	2.91910	+	29.6381i	0.0241248	+	0.244943i	0.999682	+	0.0251995i	$0.00802211\pi$
$11$	2.91910	+	29.6381i	0.0241248	+	0.244943i	−0.975558	+	0.219744i	$0.929478\pi$
$12$	29.7699	−	73.2382i	0.206735	−	0.508599i
$13$	−8.11634	−	26.7560i	−0.0480257	−	0.158319i	0.929648	−	0.368450i	$-0.120111\pi$
$13$	−8.11634	−	26.7560i	−0.0480257	−	0.158319i	−0.977673	+	0.210130i	$0.932611\pi$
$14$	−70.2925	−	147.357i	−0.358635	−	0.751823i
$15$	132.701	−	54.9664i	0.589781	−	0.244295i
$16$	139.396	−	214.720i	0.544515	−	0.838751i
$17$	27.2487	−	65.7842i	0.0942862	−	0.227627i	−0.869699	−	0.493582i	$-0.835687\pi$
$17$	27.2487	−	65.7842i	0.0942862	−	0.227627i	0.963985	+	0.265955i	$0.0856873\pi$
$18$	−11.8542	−	226.032i	−0.0365870	−	0.697629i
$19$	−185.060	+	346.222i	−0.512631	+	0.959065i	0.483843	+	0.875155i	$0.339241\pi$
$19$	−185.060	+	346.222i	−0.512631	+	0.959065i	−0.996473	+	0.0839097i	$0.973259\pi$
$20$	455.562	−	93.7555i	1.13890	−	0.234389i
$21$	155.898	+	127.942i	0.353509	+	0.290118i
$22$	−40.5034	−	112.029i	−0.0836846	−	0.231465i
$23$	−231.629	+	154.769i	−0.437861	+	0.292569i	−0.754896	−	0.655844i	$-0.772313\pi$
$23$	−231.629	+	154.769i	−0.437861	+	0.292569i	0.317035	+	0.948414i	$0.397313\pi$
$24$	−43.2928	+	313.252i	−0.0751611	+	0.543841i
$25$	182.945	+	122.240i	0.292711	+	0.195584i
$26$	57.8143	+	95.7373i	0.0855241	+	0.141623i
$27$	320.466	+	599.551i	0.439597	+	0.822429i
$28$	417.627	+	502.067i	0.532688	+	0.640391i
$29$	−1.62561	+	16.5051i	−0.00193295	+	0.0196256i	−0.996103	−	0.0881996i	$-0.971889\pi$
$29$	−1.62561	+	16.5051i	−0.00193295	+	0.0196256i	0.994170	+	0.107825i	$0.0343887\pi$
$30$	−460.337	+	343.777i	−0.511486	+	0.381974i
$31$	48.8233	+	48.8233i	0.0508047	+	0.0508047i	0.732053	−	0.681248i	$-0.238562\pi$
$31$	48.8233	+	48.8233i	0.0508047	+	0.0508047i	−0.681248	+	0.732053i	$0.738562\pi$
$32$	−328.975	+	969.717i	−0.321265	+	0.946989i
$33$	104.053	+	104.053i	0.0955492	+	0.0955492i
$34$	−40.8588	+	281.871i	−0.0353450	+	0.243833i
$35$	−116.297	+	1180.78i	−0.0949362	+	0.963904i
$36$	268.543	+	864.626i	0.207209	+	0.667150i
$37$	499.498	+	934.495i	0.364863	+	0.682611i	0.995632	−	0.0933592i	$-0.0297605\pi$
$37$	499.498	+	934.495i	0.364863	+	0.682611i	−0.630769	+	0.775971i	$0.717261\pi$
$38$	376.511	−	1524.50i	0.260742	−	1.05575i
$39$	−114.870	−	76.7535i	−0.0755225	−	0.0504625i
$40$	−1673.84	+	812.097i	−1.04615	+	0.507561i
$41$	−310.025	+	207.152i	−0.184429	+	0.123232i	−0.644357	−	0.764724i	$-0.722875\pi$
$41$	−310.025	+	207.152i	−0.184429	+	0.123232i	0.459928	+	0.887956i	$0.347875\pi$
$42$	−730.389	−	342.495i	−0.414053	−	0.194158i
$43$	2331.72	+	1913.60i	1.26107	+	1.03494i	0.997527	+	0.0702897i	$0.0223924\pi$
$43$	2331.72	+	1913.60i	1.26107	+	1.03494i	0.263547	+	0.964647i	$0.415108\pi$
$44$	267.348	+	394.438i	0.138093	+	0.203739i
$45$	−775.403	+	1450.68i	−0.382915	+	0.716384i
$46$	745.588	−	828.120i	0.352357	−	0.391361i
$47$	118.274	−	285.540i	0.0535420	−	0.129262i	−0.894845	−	0.446377i	$-0.852714\pi$
$47$	118.274	−	285.540i	0.0535420	−	0.129262i	0.948387	+	0.317115i	$0.102714\pi$
$48$	−140.636	−	1257.08i	−0.0610399	−	0.545606i
$49$	679.097	−	281.291i	0.282839	−	0.117156i
$50$	−829.632	−	293.754i	−0.331853	−	0.117502i
$51$	−102.130	−	336.677i	−0.0392657	−	0.129442i
$52$	−318.417	−	314.230i	−0.117758	−	0.116209i
$53$	−142.139	−	1443.16i	−0.0506013	−	0.513764i	−0.986760	−	0.162186i	$-0.948145\pi$
$53$	−142.139	−	1443.16i	−0.0506013	−	0.513764i	0.936159	−	0.351577i	$-0.114355\pi$
$54$	−1832.82	−	2008.81i	−0.628540	−	0.688892i
$55$	−168.895	+	849.094i	−0.0558332	+	0.280692i
$56$	−2113.51	−	1535.20i	−0.673950	−	0.489539i
$57$	378.429	+	1902.49i	0.116475	+	0.585562i
$58$	−9.95121	−	65.5894i	−0.00295815	−	0.0194974i
$59$	2790.26	+	846.416i	0.801568	+	0.243153i	0.664383	−	0.747392i	$-0.268694\pi$
$59$	2790.26	+	846.416i	0.801568	+	0.243153i	0.137185	+	0.990545i	$0.456194\pi$
$60$	1446.14	−	1786.10i	0.401705	−	0.496140i
$61$	3528.98	−	2896.16i	0.948397	−	0.778329i	−0.0268064	−	0.999641i	$-0.508534\pi$
$61$	3528.98	−	2896.16i	0.948397	−	0.778329i	0.975203	+	0.221312i	$0.0710338\pi$
$62$	−237.361	−	141.203i	−0.0617486	−	0.0367335i
$63$	−2309.60			−0.581910
$64$	320.466	−	4083.44i	0.0782388	−	0.996935i
$65$		−	812.777i		−	0.192373i
$66$	−505.869	−	300.935i	−0.116132	−	0.0690852i
$67$	−1275.06	−	1553.66i	−0.284041	−	0.346104i	0.611371	−	0.791344i	$-0.290618\pi$
$67$	−1275.06	−	1553.66i	−0.284041	−	0.346104i	−0.895411	+	0.445240i	$0.853118\pi$
$68$	−119.169	−	1133.02i	−0.0257719	−	0.245030i
$69$	−399.570	+	1317.21i	−0.0839256	+	0.276666i
$70$	−711.912	−	4692.28i	−0.145288	−	0.957609i
$71$	−320.710	+	63.7932i	−0.0636203	+	0.0126549i	−0.226798	−	0.973942i	$-0.572826\pi$
$71$	−320.710	+	63.7932i	−0.0636203	+	0.0126549i	0.163178	+	0.986597i	$0.447826\pi$
$72$	−1892.56	−	3087.61i	−0.365077	−	0.595604i
$73$	2665.01	+	530.103i	0.500095	+	0.0994751i	0.438691	−	0.898638i	$-0.355442\pi$
$73$	2665.01	+	530.103i	0.500095	+	0.0994751i	0.0614041	+	0.998113i	$0.480442\pi$
$74$	−2856.75	−	3131.05i	−0.521685	−	0.571776i
$75$	1081.93	−	106.561i	0.192344	−	0.0189442i
$76$	41.5731	+	6281.10i	0.00719755	+	1.08745i
$77$	−1163.22	+	352.860i	−0.196192	+	0.0595142i
$78$	520.920	+	184.446i	0.0856214	+	0.0303166i
$79$	176.280	+	425.577i	0.0282454	+	0.0681905i	0.937373	−	0.348328i	$-0.113250\pi$
$79$	176.280	+	425.577i	0.0282454	+	0.0681905i	−0.909127	+	0.416518i	$0.863250\pi$
$80$	5689.55	−	4796.73i	0.888993	−	0.749489i
$81$	−1131.17	−	468.544i	−0.172407	−	0.0714135i
$82$	997.938	−	1108.40i	0.148414	−	0.164843i
$83$	−8601.87	−	4597.79i	−1.24864	−	0.667411i	−0.291369	−	0.956611i	$-0.594111\pi$
$83$	−8601.87	−	4597.79i	−1.24864	−	0.667411i	−0.957269	+	0.289200i	$0.906611\pi$
$84$	3168.91	+	608.560i	0.449108	+	0.0862471i
$85$	1313.11	−	1600.02i	0.181745	−	0.221457i
$86$	−10924.3	−	5122.62i	−1.47705	−	0.692620i
$87$	45.5279	+	68.1373i	0.00601504	+	0.00900215i
$88$	−1424.90	−	1265.92i	−0.184001	−	0.163471i
$89$	3670.19	−	5492.83i	0.463349	−	0.693451i	−0.524052	−	0.851686i	$-0.675580\pi$
$89$	3670.19	−	5492.83i	0.463349	−	0.693451i	0.987401	+	0.158235i	$0.0505804\pi$
$90$	1577.59	−	6387.69i	0.194764	−	0.788604i
$91$	1006.46	−	537.965i	0.121539	−	0.0649637i
$92$	−2075.06	+	3944.75i	−0.245163	+	0.466062i
$93$	339.523	+	33.4401i	0.0392557	+	0.00386635i
$94$	−177.350	+	1223.48i	−0.0200713	+	0.138465i
$95$	−8069.48	+	8069.48i	−0.894125	+	0.894125i
$96$	1783.14	+	4735.05i	0.193484	+	0.513786i
$97$	12478.3	−	12478.3i	1.32621	−	1.32621i	0.417563	−	0.908648i	$-0.362884\pi$
$97$	12478.3	−	12478.3i	1.32621	−	1.32621i	0.908648	−	0.417563i	$-0.137116\pi$
$98$	−2355.78	+	1759.28i	−0.245292	+	0.183182i
$99$	−1677.09	−	165.179i	−0.171114	−	0.0168533i
$100$	3505.67	+	321.865i	0.350567	+	0.0321865i
$101$	−5590.65	+	2988.27i	−0.548049	+	0.292939i	−0.722089	−	0.691800i	$-0.756818\pi$
$101$	−5590.65	+	2988.27i	−0.548049	+	0.292939i	0.174040	+	0.984739i	$0.444318\pi$
$102$	727.492	+	1204.69i	0.0699242	+	0.115791i
$103$	−11155.2	+	16694.9i	−1.05148	+	1.57365i	−0.256957	+	0.966423i	$0.582720\pi$
$103$	−11155.2	+	16694.9i	−1.05148	+	1.57365i	−0.794525	+	0.607231i	$0.792280\pi$
$104$	1543.91	+	904.671i	0.142743	+	0.0836419i
$105$	3257.08	+	4874.56i	0.295426	+	0.442137i
$106$	1972.22	+	5455.01i	0.175527	+	0.485494i
$107$	−4496.44	+	5478.93i	−0.392736	+	0.478551i	−0.931414	−	0.363961i	$-0.881424\pi$
$107$	−4496.44	+	5478.93i	−0.392736	+	0.478551i	0.538678	+	0.842512i	$0.318924\pi$
$108$	9083.84	+	5983.04i	0.778793	+	0.512949i
$109$	13832.1	+	7393.41i	1.16422	+	0.622289i	0.936235	−	0.351375i	$-0.114286\pi$
$109$	13832.1	+	7393.41i	1.16422	+	0.622289i	0.227986	+	0.973664i	$0.426786\pi$
$110$	−181.362	−	3458.16i	−0.0149886	−	0.285799i
$111$	4837.10	+	2003.59i	0.392590	+	0.162616i
$112$	9705.62	+	3870.49i	0.773726	+	0.308553i
$113$	−4204.70	−	10151.0i	−0.329289	−	0.794975i	−0.998645	−	0.0520331i	$-0.983430\pi$
$113$	−4204.70	−	10151.0i	−0.329289	−	0.794975i	0.669356	−	0.742942i	$-0.266570\pi$
$114$	−3340.61	−	7003.08i	−0.257049	−	0.538864i
$115$	−7749.35	+	2350.74i	−0.585962	+	0.177750i
$116$	103.169	+	244.483i	0.00766715	+	0.0181691i
$117$	1574.51	−	155.076i	0.115020	−	0.0113285i
$118$	−11651.0	−	533.735i	−0.836759	−	0.0383320i
$119$	2850.43	+	566.987i	0.201288	+	0.0400386i
$120$	−3847.64	+	8348.61i	−0.267198	+	0.579765i
$121$	13489.8	−	2683.28i	0.921370	−	0.183272i
$122$	−10829.5	+	14703.3i	−0.727591	+	0.987858i
$123$	−534.808	+	1763.02i	−0.0353498	+	0.116533i
$124$	1059.27	+	313.687i	0.0688914	+	0.0204010i
$125$	−7468.29	−	9100.13i	−0.477970	−	0.582409i
$126$	8954.06	−	2274.39i	0.564000	−	0.143260i
$127$			8916.05i			0.552796i	0.961043	+	0.276398i	$0.0891408\pi$
$127$			8916.05i			0.552796i	−0.961043	+	0.276398i	$0.910859\pi$
$128$	2778.79	+	16146.6i	0.169604	+	0.985512i
$129$	14904.4			0.895644
$130$	800.387	+	3151.04i	0.0473601	+	0.186452i
$131$	−12821.4	+	10522.2i	−0.747123	+	0.613148i	−0.928960	−	0.370181i	$-0.879296\pi$
$131$	−12821.4	+	10522.2i	−0.747123	+	0.613148i	0.181837	+	0.983329i	$0.441796\pi$
$132$	2257.55	+	668.535i	0.129565	+	0.0383686i
$133$	−15333.5	−	4651.37i	−0.866838	−	0.262952i
$134$	6473.24	+	4767.75i	0.360505	+	0.265524i
$135$	3855.38	+	19382.3i	0.211543	+	1.06350i
$136$	1577.75	+	4275.23i	0.0853024	+	0.231144i
$137$	3322.37	−	16702.7i	0.177014	−	0.889908i	−0.785539	−	0.618813i	$-0.787614\pi$
$137$	3322.37	−	16702.7i	0.177014	−	0.889908i	0.962552	−	0.271096i	$-0.0873860\pi$
$138$	251.962	−	5500.14i	0.0132305	−	0.288812i
$139$	−2905.92	−	29504.3i	−0.150402	−	1.52706i	−0.713492	−	0.700663i	$-0.752888\pi$
$139$	−2905.92	−	29504.3i	−0.150402	−	1.52706i	0.563090	−	0.826395i	$-0.309612\pi$
$140$	7380.76	+	17490.4i	0.376569	+	0.892367i
$141$	−443.300	−	1461.37i	−0.0222977	−	0.0735056i
$142$	1180.54	−	563.140i	0.0585467	−	0.0279280i
$143$	769.305	−	318.657i	0.0376207	−	0.0155830i
$144$	10377.8	+	10106.6i	0.500472	+	0.487394i
$145$	−184.497	+	445.416i	−0.00877514	+	0.0211851i
$146$	−10854.0	+	569.233i	−0.509193	+	0.0267045i
$147$	1712.09	−	3203.09i	0.0792304	−	0.148230i
$148$	14158.6	+	9325.52i	0.646393	+	0.425745i
$149$	−23341.6	−	19155.9i	−1.05137	−	0.862840i	−0.0605726	−	0.998164i	$-0.519293\pi$
$149$	−23341.6	−	19155.9i	−1.05137	−	0.862840i	−0.990801	+	0.135323i	$0.956793\pi$
$150$	−4089.59	+	1478.56i	−0.181760	+	0.0657140i
$151$	14982.2	−	10010.8i	0.657087	−	0.439051i	−0.181816	−	0.983333i	$-0.558198\pi$
$151$	14982.2	−	10010.8i	0.657087	−	0.439051i	0.838903	+	0.544281i	$0.183198\pi$
$152$	−6346.53	−	24310.2i	−0.274694	−	1.05221i
$153$	3350.11	+	2238.47i	0.143112	+	0.0956243i
$154$	4162.20	−	2513.49i	0.175502	−	0.105983i
$155$	946.158	+	1770.14i	0.0393822	+	0.0736790i
$156$	−2201.18	−	202.097i	−0.0904497	−	0.00830444i
$157$	259.831	−	2638.11i	0.0105413	−	0.107027i	−0.988474	−	0.151389i	$-0.951625\pi$
$157$	259.831	−	2638.11i	0.0105413	−	0.107027i	0.999016	+	0.0443618i	$0.0141254\pi$
$158$	−1102.51	−	1476.32i	−0.0441638	−	0.0591380i
$159$	−5066.63	−	5066.63i	−0.200413	−	0.200413i
$160$	−17334.2	+	24199.2i	−0.677115	+	0.945281i
$161$	−8040.10	−	8040.10i	−0.310177	−	0.310177i
$162$	4846.80	+	702.571i	0.184682	+	0.0267707i
$163$	1931.85	−	19614.4i	0.0727105	−	0.738242i	−0.887843	−	0.460147i	$-0.847797\pi$
$163$	1931.85	−	19614.4i	0.0727105	−	0.738242i	0.960553	−	0.278096i	$-0.0897032\pi$
$164$	−2777.39	+	5279.89i	−0.103264	+	0.196307i
$165$	2016.47	+	3772.55i	0.0740668	+	0.138569i
$166$	37876.2	+	9354.39i	1.37452	+	0.339468i
$167$	−3853.65	−	2574.93i	−0.138178	−	0.0923276i	0.484560	−	0.874758i	$-0.338980\pi$
$167$	−3853.65	−	2574.93i	−0.138178	−	0.0923276i	−0.622738	+	0.782430i	$0.713980\pi$
$168$	−12884.8	+	761.285i	−0.456519	+	0.0269730i
$169$	23097.6	−	15433.3i	0.808711	−	0.540363i
$170$	−3515.13	+	7496.20i	−0.121631	+	0.259384i
$171$	−17171.8	−	14092.6i	−0.587252	−	0.481945i
$172$	47396.7	+	9102.09i	1.60210	+	0.307669i
$173$	−21219.4	+	39698.8i	−0.708992	+	1.32643i	0.226821	+	0.973936i	$0.427167\pi$
$173$	−21219.4	+	39698.8i	−0.708992	+	1.32643i	−0.935814	+	0.352495i	$0.885333\pi$
$174$	−243.605	−	219.327i	−0.00804614	−	0.00724424i
$175$	−3436.72	+	8296.97i	−0.112219	+	0.270922i
$176$	6770.82	+	3504.65i	0.218583	+	0.113141i
$177$	13310.6	−	5513.44i	0.424866	−	0.175985i
$178$	−8819.82	+	24909.3i	−0.278368	+	0.786179i
$179$	−6856.85	−	22604.0i	−0.214002	−	0.705471i	−0.996559	−	0.0828914i	$-0.973585\pi$
$179$	−6856.85	−	22604.0i	−0.214002	−	0.705471i	0.782556	−	0.622580i	$-0.213915\pi$
$180$	174.192	+	26317.9i	0.00537629	+	0.812281i
$181$	−4670.28	−	47418.1i	−0.142556	−	1.44740i	−0.754399	−	0.656417i	$-0.772071\pi$
$181$	−4670.28	−	47418.1i	−0.142556	−	1.44740i	0.611843	−	0.790980i	$-0.290429\pi$
$182$	−3372.17	+	3076.75i	−0.101805	+	0.0928857i
$183$	4400.71	−	22123.9i	0.131408	−	0.660631i
$184$	4160.17	−	17336.8i	0.122878	−	0.512074i
$185$	6009.22	+	30210.4i	0.175580	+	0.882699i
$186$	−1349.22	+	204.704i	−0.0389994	+	0.00591697i
$187$	2029.26	+	615.570i	0.0580303	+	0.0176033i
$188$	−517.261	−	4917.93i	−0.0146350	−	0.139145i
$189$	−21449.3	+	17603.0i	−0.600466	+	0.492790i
$190$	23338.0	−	39230.9i	0.646482	−	1.08673i
$191$	−28702.8			−0.786788			−0.393394	−	0.919370i	$-0.628699\pi$
$191$	−28702.8			−0.786788			−0.393394	+	0.919370i	$0.628699\pi$
$192$	−11575.9	−	16601.3i	−0.314017	−	0.450339i
$193$			40660.9i			1.09160i	0.837916	+	0.545799i	$0.183774\pi$
$193$			40660.9i			1.09160i	−0.837916	+	0.545799i	$0.816226\pi$
$194$	−36088.9	+	60665.1i	−0.958894	+	1.61189i
$195$	−2547.73	−	3104.41i	−0.0670013	−	0.0816414i
$196$	7400.64	−	9140.40i	0.192645	−	0.237932i
$197$	3676.67	−	12120.4i	0.0947376	−	0.312308i	−0.896745	−	0.442548i	$-0.854075\pi$
$197$	3676.67	−	12120.4i	0.0947376	−	0.312308i	0.991483	+	0.130240i	$0.0415747\pi$
$198$	6664.56	−	1011.15i	0.169997	−	0.0257919i
$199$	14155.3	−	2815.67i	0.357449	−	0.0711010i	−0.0130993	−	0.999914i	$-0.504170\pi$
$199$	14155.3	−	2815.67i	0.357449	−	0.0711010i	0.370548	+	0.928813i	$0.379170\pi$
$200$	−13908.0	+	2204.39i	−0.347701	+	0.0551098i
$201$	−9740.21	−	1937.45i	−0.241088	−	0.0479555i
$202$	18731.6	−	17090.6i	0.459063	−	0.418846i
$203$	−673.674	+	66.3511i	−0.0163477	+	0.00161011i
$204$	−4006.73	−	3954.04i	−0.0962785	−	0.0950124i
$205$	−10372.2	+	3146.37i	−0.246810	+	0.0748690i
$206$	26807.0	−	75709.4i	0.631703	−	1.78408i
$207$	−6032.42	−	14563.5i	−0.140783	−	0.339881i
$208$	−6876.44	−	1986.93i	−0.158941	−	0.0459258i
$209$	−10801.6	−	4474.17i	−0.247284	−	0.102428i
$210$	−17427.6	−	15690.7i	−0.395183	−	0.355798i
$211$	−14426.6	−	7711.20i	−0.324041	−	0.173204i	0.301353	−	0.953513i	$-0.402562\pi$
$211$	−14426.6	−	7711.20i	−0.324041	−	0.173204i	−0.625394	+	0.780309i	$0.715062\pi$
$212$	−13017.9	−	19206.3i	−0.289648	−	0.427338i
$213$	−1024.99	+	1248.96i	−0.0225923	+	0.0275288i
$214$	12036.8	−	25669.1i	0.262835	−	0.560509i
$215$	48715.4	+	72907.7i	1.05387	+	1.57723i
$216$	−41108.8	−	14250.2i	−0.881105	−	0.305432i
$217$	−1565.71	+	2343.25i	−0.0332501	+	0.0497623i
$218$	−60906.2	−	15042.2i	−1.28159	−	0.316518i
$219$	11840.7	−	6328.99i	0.246882	−	0.131961i
$220$	4108.57	+	13228.3i	0.0848878	+	0.273312i
$221$	−1981.28	−	195.139i	−0.0405659	−	0.00399540i
$222$	−20726.0	−	3004.34i	−0.420541	−	0.0609598i
$223$	−36614.1	+	36614.1i	−0.736272	+	0.736272i	−0.971854	−	0.235582i	$-0.924300\pi$
$223$	−36614.1	+	36614.1i	−0.736272	+	0.736272i	0.235582	+	0.971854i	$0.424300\pi$
$224$	−41439.1	−	5447.79i	−0.825874	−	0.108574i
$225$	−8803.68	+	8803.68i	−0.173900	+	0.173900i
$226$	26297.4	+	35213.8i	0.514869	+	0.689440i
$227$	80376.2	+	7916.36i	1.55982	+	0.153629i	0.840796	−	0.541352i	$-0.182087\pi$
$227$	80376.2	+	7916.36i	1.55982	+	0.153629i	0.719028	+	0.694981i	$0.244587\pi$
$228$	19847.5	+	23860.5i	0.381800	+	0.458996i
$229$	17352.7	−	9275.22i	0.330900	−	0.176870i	−0.297577	−	0.954698i	$-0.596179\pi$
$229$	17352.7	−	9275.22i	0.330900	−	0.176870i	0.628477	+	0.777828i	$0.283679\pi$
$230$	27728.5	−	16744.8i	0.524168	−	0.316536i
$231$	−3336.88	+	4993.99i	−0.0625340	+	0.0935887i
$232$	−640.732	−	846.237i	−0.0119042	−	0.0157223i
$233$	−31346.0	−	46912.6i	−0.577391	−	0.864126i	0.421701	−	0.906735i	$-0.361433\pi$
$233$	−31346.0	−	46912.6i	−0.577391	−	0.864126i	−0.999092	+	0.0426086i	$0.986433\pi$
$234$	−5951.49	+	2151.72i	−0.108691	+	0.0392965i
$235$	5699.60	−	6944.99i	0.103207	−	0.125758i
$236$	45695.3	−	9404.20i	0.820442	−	0.168849i
$237$	2007.31	+	1072.93i	0.0357371	+	0.0191019i
$238$	−11609.2	+	608.839i	−0.204949	+	0.0107485i
$239$	85115.8	+	35256.1i	1.49010	+	0.617218i	0.971338	−	0.237703i	$-0.0763946\pi$
$239$	85115.8	+	35256.1i	1.49010	+	0.617218i	0.518758	+	0.854921i	$0.326395\pi$
$240$	6695.54	−	36155.6i	0.116242	−	0.627702i
$241$	20643.9	+	49838.8i	0.355433	+	0.858091i	0.995930	+	0.0901301i	$0.0287283\pi$
$241$	20643.9	+	49838.8i	0.355433	+	0.858091i	−0.640497	+	0.767960i	$0.721272\pi$
$242$	−49656.0	+	23686.9i	−0.847892	+	0.404462i
$243$	−58483.8	+	17740.9i	−0.990428	+	0.300443i
$244$	27505.5	−	67667.4i	0.461997	−	1.13658i
$245$	21264.5	−	2094.37i	0.354261	−	0.0348917i
$246$	337.240	−	7361.70i	0.00557274	−	0.121649i
$247$	10765.5	+	2141.40i	0.176458	+	0.0350997i
$248$	−4415.59	−	173.000i	−0.0717936	−	0.00281283i
$249$	−47267.2	+	9402.03i	−0.762362	+	0.151643i
$250$	37915.1	+	27925.8i	0.606642	+	0.446812i
$251$	29408.1	−	96945.4i	0.466787	−	1.53879i	−0.335610	−	0.942001i	$-0.608942\pi$
$251$	29408.1	−	96945.4i	0.466787	−	1.53879i	0.802397	−	0.596791i	$-0.203558\pi$
$252$	−32474.2	+	17635.1i	−0.511372	+	0.277701i
$253$	−5263.22	−	6413.25i	−0.0822262	−	0.100193i
$254$	−8780.13	−	34566.5i	−0.136092	−	0.535782i
$255$		−	10227.4i		−	0.157284i
$256$	−26673.5	−	59862.3i	−0.407006	−	0.913426i
$257$	93482.3			1.41535			0.707674	−	0.706539i	$-0.249745\pi$
$257$	93482.3			1.41535			0.707674	+	0.706539i	$0.249745\pi$
$258$	−57782.7	+	14677.2i	−0.868078	+	0.220498i
$259$	−33432.1	+	27437.0i	−0.498384	+	0.409013i
$260$	−6206.02	−	11428.1i	−0.0918050	−	0.169054i
$261$	−898.062	−	272.424i	−0.0131833	−	0.00399912i
$262$	39345.2	−	53419.4i	0.573177	−	0.778210i
$263$	2702.10	+	13584.4i	0.0390651	+	0.196394i	0.995390	−	0.0959132i	$-0.0305771\pi$
$263$	2702.10	+	13584.4i	0.0390651	+	0.196394i	−0.956325	+	0.292307i	$0.905577\pi$
$264$	−9410.59	−	368.702i	−0.135023	−	0.00529014i
$265$	8223.98	−	41344.8i	0.117109	−	0.588747i
$266$	64026.7	+	2933.07i	0.904894	+	0.0414533i
$267$	−3199.44	−	32484.5i	−0.0448799	−	0.455673i
$268$	−29791.1	−	12109.5i	−0.414779	−	0.168599i
$269$	497.073	+	1638.63i	0.00686935	+	0.0226452i	0.960308	−	0.278942i	$-0.0899836\pi$
$269$	497.073	+	1638.63i	0.00686935	+	0.0226452i	−0.953439	+	0.301587i	$0.902484\pi$
$270$	−34033.7	−	71346.3i	−0.466854	−	0.978687i
$271$	−20080.9	+	8317.77i	−0.273429	+	0.113258i	−0.515185	−	0.857079i	$-0.672277\pi$
$271$	−20080.9	+	8317.77i	−0.273429	+	0.113258i	0.241756	+	0.970337i	$0.422277\pi$
$272$	−10326.8	−	15020.9i	−0.139582	−	0.203029i
$273$	2157.89	−	5209.61i	0.0289537	−	0.0699005i
$274$	3567.61	+	68026.2i	0.0475200	+	0.906098i
$275$	−3088.92	+	5778.97i	−0.0408453	+	0.0764161i
$276$	4439.47	+	21571.5i	0.0582791	+	0.283180i
$277$	−77775.7	−	63828.9i	−1.01364	−	0.831875i	−0.0278106	−	0.999613i	$-0.508854\pi$
$277$	−77775.7	−	63828.9i	−1.01364	−	0.831875i	−0.985831	+	0.167739i	$0.946354\pi$
$278$	40320.5	+	111523.i	0.521718	+	1.44303i
$279$	−3248.59	+	2170.64i	−0.0417336	+	0.0278855i
$280$	−45838.1	−	60540.0i	−0.584670	−	0.772194i
$281$	−56480.8	−	37739.2i	−0.715299	−	0.477948i	0.143898	−	0.989593i	$-0.454036\pi$
$281$	−56480.8	−	37739.2i	−0.715299	−	0.477948i	−0.859197	+	0.511645i	$0.829036\pi$
$282$	3157.71	+	5229.01i	0.0397077	+	0.0657538i
$283$	−4147.87	−	7760.12i	−0.0517908	−	0.0968937i	0.854694	−	0.519132i	$-0.173745\pi$
$283$	−4147.87	−	7760.12i	−0.0517908	−	0.0968937i	−0.906485	+	0.422238i	$0.861245\pi$
$284$	−4022.25	+	3345.77i	−0.0498692	+	0.0414820i
$285$	−5526.95	+	56116.0i	−0.0680449	+	0.690871i
$286$	−2668.71	+	1992.97i	−0.0326264	+	0.0243652i
$287$	−10761.3	−	10761.3i	−0.130648	−	0.130648i
$288$	−50186.0	−	28962.6i	−0.605059	−	0.349182i
$289$	55473.2	+	55473.2i	0.664183	+	0.664183i
$290$	276.649	−	1908.51i	0.00328953	−	0.0226934i
$291$	8546.65	−	86775.6i	0.100928	−	1.02474i
$292$	41519.0	−	12895.4i	0.486947	−	0.151240i
$293$	40188.8	+	75188.0i	0.468134	+	0.875817i	0.999587	+	0.0287294i	$0.00914610\pi$
$293$	40188.8	+	75188.0i	0.468134	+	0.875817i	−0.531453	+	0.847088i	$0.678354\pi$
$294$	−3483.31	+	14104.0i	−0.0402993	+	0.163173i
$295$	70476.0	+	47090.5i	0.809836	+	0.541115i
$296$	−64074.7	−	22211.2i	−0.731312	−	0.253507i
$297$	−16834.1	+	11248.2i	−0.190843	+	0.127517i
$298$	109356.	+	51279.6i	1.23144	+	0.577447i
$299$	6020.98	+	4941.29i	0.0673480	+	0.0552711i
$300$	14398.9	−	9759.48i	0.159987	−	0.108439i
$301$	−58037.6	+	108581.i	−0.640585	+	1.19845i
$302$	−48226.2	+	53564.6i	−0.528773	+	0.587306i
$303$	−11986.6	+	28938.2i	−0.130560	+	0.315200i
$304$	48544.4	+	87998.1i	0.525281	+	0.952195i
$305$	122607.	−	50785.4i	1.31800	−	0.545933i
$306$	−15192.3	−	5379.26i	−0.162249	−	0.0574486i
$307$	20806.4	+	68589.4i	0.220759	+	0.727746i	0.995440	+	0.0953931i	$0.0304108\pi$
$307$	20806.4	+	68589.4i	0.220759	+	0.727746i	−0.774680	+	0.632353i	$0.782089\pi$
$308$	−13661.2	+	13843.3i	−0.144009	+	0.145928i
$309$	9724.39	+	98733.4i	0.101846	+	1.03406i
$310$	−5411.30	−	5930.89i	−0.0563091	−	0.0617158i
$311$	11081.5	−	55710.6i	0.114572	−	0.575993i	−0.880263	−	0.474486i	$-0.842634\pi$
$311$	11081.5	−	55710.6i	0.114572	−	0.575993i	0.994835	−	0.101506i	$-0.0323662\pi$
$312$	8732.76	−	1384.12i	0.0897103	−	0.0142189i
$313$	37992.1	+	190999.i	0.387797	+	1.94959i	0.302145	+	0.953262i	$0.402297\pi$
$313$	37992.1	+	190999.i	0.387797	+	1.94959i	0.0856517	+	0.996325i	$0.472703\pi$
$314$	1590.56	+	10483.5i	0.0161321	+	0.106328i
$315$	−64247.6	−	19489.3i	−0.647494	−	0.196415i
$316$	5728.11	+	4637.83i	0.0573637	+	0.0464452i
$317$	−137346.	+	112717.i	−1.36678	+	1.12169i	−0.386892	+	0.922125i	$0.626451\pi$
$317$	−137346.	+	112717.i	−1.36678	+	1.12169i	−0.979886	+	0.199561i	$0.936049\pi$
$318$	24632.2	+	14653.4i	0.243584	+	0.144905i
$319$	−493.927			−0.00485379
$320$	43372.3	−	110887.i	0.423557	−	1.08289i
$321$			35021.4i			0.339878i
$322$	39088.1	+	23253.0i	0.376993	+	0.224268i
$323$	17733.3	+	21608.1i	0.169975	+	0.207115i
$324$	−19482.4	+	2049.13i	−0.185589	+	0.0195200i
$325$	1785.80	−	5887.01i	0.0169070	−	0.0557350i
$326$	11825.8	+	77945.1i	0.111275	+	0.733421i
$327$	76007.3	−	15118.8i	0.710820	−	0.141391i
$328$	5568.21	−	23204.6i	0.0517569	−	0.215688i
$329$	12372.5	+	2461.03i	0.114305	+	0.0227366i
$330$	−11532.7	−	12640.0i	−0.105901	−	0.116070i
$331$	141526.	−	13939.1i	1.29176	−	0.127227i	0.571310	−	0.820735i	$-0.306436\pi$
$331$	141526.	−	13939.1i	1.29176	−	0.127227i	0.720449	+	0.693507i	$0.243936\pi$
$332$	−156053.	+	1032.88i	−1.41578	+	0.00937074i
$333$	−57377.0	+	17405.1i	−0.517427	+	0.156960i
$334$	17475.8	+	6187.79i	0.156655	+	0.0554680i
$335$	−22358.7	−	53978.6i	−0.199231	−	0.480986i
$336$	49203.2	−	15639.8i	0.435828	−	0.138533i
$337$	31624.6	+	13099.4i	0.278462	+	0.115343i	0.517544	−	0.855657i	$-0.326846\pi$
$337$	31624.6	+	13099.4i	0.278462	+	0.115343i	−0.239082	+	0.970999i	$0.576846\pi$
$338$	−74348.7	+	82578.7i	−0.650789	+	0.722828i
$339$	−47879.3	−	25592.0i	−0.416628	−	0.222692i
$340$	6245.83	−	32523.5i	0.0540297	−	0.281345i
$341$	−1304.51	+	1589.55i	−0.0112186	+	0.0136699i
$342$	80451.0	+	37725.2i	0.687827	+	0.322537i
$343$	71113.6	+	106429.i	0.604456	+	0.904632i
$344$	−192715.	+	11386.4i	−1.62854	+	0.0962206i
$345$	−22230.2	+	33269.8i	−0.186769	+	0.279519i
$346$	43171.8	−	174804.i	0.360618	−	1.46015i
$347$	60992.5	−	32601.2i	0.506544	−	0.270754i	−0.198267	−	0.980148i	$-0.563531\pi$
$347$	60992.5	−	32601.2i	0.506544	−	0.270754i	0.704812	+	0.709394i	$0.251031\pi$
$348$	1160.41	+	610.413i	0.00958195	+	0.00504041i
$349$	8206.97	+	808.316i	0.0673802	+	0.00663637i	0.131651	−	0.991296i	$-0.457972\pi$
$349$	8206.97	+	808.316i	0.0673802	+	0.00663637i	−0.0642709	+	0.997932i	$0.520472\pi$
$350$	5153.28	−	35550.8i	0.0420676	−	0.290210i
$351$	13440.6	−	13440.6i	0.109095	−	0.109095i
$352$	−29700.9	−	6919.51i	−0.239709	−	0.0558458i
$353$	60806.7	−	60806.7i	0.487980	−	0.487980i	−0.419688	−	0.907668i	$-0.637861\pi$
$353$	60806.7	−	60806.7i	0.487980	−	0.487980i	0.907668	+	0.419688i	$0.137861\pi$
$354$	−46174.4	+	34482.7i	−0.368463	+	0.275166i
$355$	−9459.70	−	931.699i	−0.0750621	−	0.00739297i
$356$	9663.84	−	105256.i	0.0762518	−	0.830513i
$357$	12664.6	−	6769.35i	0.0993696	−	0.0531142i
$358$	48842.7	+	80880.9i	0.381095	+	0.631073i
$359$	−11897.6	+	17806.0i	−0.0923146	+	0.138159i	−0.874752	−	0.484570i	$-0.838976\pi$
$359$	−11897.6	+	17806.0i	−0.0923146	+	0.138159i	0.782438	+	0.622729i	$0.213976\pi$
$360$	−26592.0	−	101860.i	−0.205186	−	0.785957i
$361$	−13220.4	−	19785.7i	−0.101445	−	0.151823i
$362$	64801.4	+	179236.i	0.494501	+	1.36775i
$363$	43113.4	−	52533.9i	0.327189	−	0.398681i
$364$	10043.7	−	15249.0i	0.0758037	−	0.115090i
$365$	69660.9	+	37234.6i	0.522882	+	0.279486i
$366$	4725.55	+	90105.4i	0.0352769	+	0.672649i
$367$	54965.4	+	22767.4i	0.408091	+	0.169037i	0.577279	−	0.816547i	$-0.304114\pi$
$367$	54965.4	+	22767.4i	0.408091	+	0.169037i	−0.169188	+	0.985584i	$0.554114\pi$
$368$	944.002	+	71309.5i	0.00697072	+	0.526565i
$369$	−8074.14	−	19492.7i	−0.0592985	−	0.143159i
$370$	−53046.9	−	111205.i	−0.387486	−	0.812305i
$371$	56640.5	−	17181.7i	0.411509	−	0.124830i
$372$	5029.20	−	2122.27i	0.0363423	−	0.0153361i
$373$	−216171.	+	21291.0i	−1.55374	+	0.153030i	−0.838132	−	0.545468i	$-0.816352\pi$
$373$	−216171.	+	21291.0i	−1.55374	+	0.153030i	−0.715612	+	0.698498i	$0.753852\pi$
$374$	−8473.41	−	388.167i	−0.0605780	−	0.00277508i
$375$	−57050.5	−	11348.0i	−0.405692	−	0.0806972i
$376$	6848.32	+	18556.9i	0.0484405	+	0.131259i
$377$	454.805	−	90.4664i	0.00319995	−	0.000636509i
$378$	65821.8	−	89367.0i	0.460666	−	0.625451i
$379$	64433.8	−	212410.i	0.448575	−	1.47875i	−0.383213	−	0.923660i	$-0.625182\pi$
$379$	64433.8	−	212410.i	0.448575	−	1.47875i	0.831788	−	0.555094i	$-0.187318\pi$
$380$	−51845.9	+	175076.i	−0.359043	+	1.21244i
$381$	27948.2	+	34055.0i	0.192532	+	0.234601i
$382$	111278.	−	28265.3i	0.762572	−	0.193699i
$383$		−	5148.49i		−	0.0350980i	−0.999846	−	0.0175490i	$-0.994414\pi$
$383$		−	5148.49i		−	0.0350980i	0.999846	−	0.0175490i	$-0.00558631\pi$
$384$	61226.8	+	52962.0i	0.415221	+	0.359171i
$385$	−35335.7			−0.238392
$386$	−40041.1	−	157638.i	−0.268739	−	1.05800i
$387$	−131942.	+	108282.i	−0.880970	+	0.722994i
$388$	80172.4	−	270731.i	0.532551	−	1.79835i
$389$	−166672.	−	50559.5i	−1.10145	−	0.334121i	−0.313330	−	0.949644i	$-0.601445\pi$
$389$	−166672.	−	50559.5i	−1.10145	−	0.334121i	−0.788118	+	0.615524i	$0.788945\pi$
$390$	12934.3	+	9526.57i	0.0850384	+	0.0626336i
$391$	3869.79	+	19454.8i	0.0253124	+	0.127254i
$392$	−19690.4	+	42724.1i	−0.128139	+	0.278036i
$393$	−15988.5	+	80379.7i	−0.103520	+	0.520428i
$394$	−2318.44	+	50609.9i	−0.0149349	+	0.326019i
$395$	1312.50	+	13326.0i	0.00841212	+	0.0854097i
$396$	−24842.0	+	10483.1i	−0.158415	+	0.0668494i
$397$	−69036.0	−	227581.i	−0.438021	−	1.44396i	−0.847086	−	0.531456i	$-0.821645\pi$
$397$	−69036.0	−	227581.i	−0.438021	−	1.44396i	0.409065	−	0.912505i	$-0.365855\pi$
$398$	−52105.9	+	24855.6i	−0.328943	+	0.156913i
$399$	−73146.7	+	30298.4i	−0.459461	+	0.190315i
$400$	51749.1	−	22242.2i	0.323432	−	0.139014i
$401$	93178.1	−	224952.i	0.579462	−	1.39895i	−0.313834	−	0.949478i	$-0.601614\pi$
$401$	93178.1	−	224952.i	0.579462	−	1.39895i	0.893296	−	0.449468i	$-0.148386\pi$
$402$	39669.6	−	2080.46i	0.245474	−	0.0128738i
$403$	910.049	−	1702.58i	0.00560344	−	0.0104833i
$404$	−55790.3	+	84704.4i	−0.341819	+	0.518971i
$405$	−27512.6	−	22579.0i	−0.167734	−	0.137656i
$406$	2546.42	−	920.641i	0.0154482	−	0.00558519i
$407$	−26238.6	+	17532.1i	−0.158399	+	0.105839i
$408$	19427.4	+	11383.7i	0.116706	+	0.0683854i
$409$	−269729.	−	180227.i	−1.61243	−	1.07739i	−0.942100	−	0.335331i	$-0.891152\pi$
$409$	−269729.	−	180227.i	−1.61243	−	1.07739i	−0.670332	−	0.742062i	$-0.733848\pi$
$410$	37113.4	−	22412.2i	0.220782	−	0.133327i
$411$	−39666.3	−	74210.5i	−0.234822	−	0.439321i
$412$	−29372.3	+	319915.i	−0.173039	+	1.88469i
$413$	−11665.2	+	118439.i	−0.0683900	+	0.694375i
$414$	37728.5	+	50520.7i	0.220125	+	0.294760i
$415$	−200485.	−	200485.i	−1.16409	−	1.16409i
$416$	28615.8	+	931.509i	0.165356	+	0.00538270i
$417$	−103583.	−	103583.i	−0.595686	−	0.595686i
$418$	46282.5	+	6708.91i	0.264889	+	0.0383972i
$419$	−11583.4	+	117608.i	−0.0659793	+	0.669899i	0.904134	+	0.427248i	$0.140517\pi$
$419$	−11583.4	+	117608.i	−0.0659793	+	0.669899i	−0.970114	+	0.242651i	$0.921983\pi$
$420$	83016.2	+	43669.1i	0.470614	+	0.247557i
$421$	−39698.2	−	74270.1i	−0.223979	−	0.419035i	0.744683	−	0.667418i	$-0.232601\pi$
$421$	−39698.2	−	74270.1i	−0.223979	−	0.419035i	−0.968662	+	0.248384i	$0.920101\pi$
$422$	63524.1	+	15688.7i	0.356709	+	0.0880974i
$423$	14541.3	+	9716.19i	0.0812686	+	0.0543019i
$424$	69382.5	+	61641.1i	0.385939	+	0.342877i
$425$	13026.4	−	8703.99i	0.0721187	−	0.0481882i
$426$	2743.86	−	5851.42i	0.0151197	−	0.0322435i
$427$	144039.	+	118210.i	0.789996	+	0.648333i
$428$	−21387.5	+	111369.i	−0.116754	+	0.607965i
$429$	1939.51	−	3628.57i	0.0105385	−	0.0197161i
$430$	−260660.	−	234682.i	−1.40974	−	1.26924i
$431$	125421.	−	302793.i	0.675175	−	1.63002i	−0.0975160	−	0.995234i	$-0.531090\pi$
$431$	125421.	−	302793.i	0.675175	−	1.63002i	0.772691	−	0.634782i	$-0.218910\pi$
$432$	173407.	+	14764.3i	0.929180	+	0.0791125i
$433$	163896.	−	67888.1i	0.874165	−	0.362091i	0.0999338	−	0.994994i	$-0.468137\pi$
$433$	163896.	−	67888.1i	0.874165	−	0.362091i	0.774231	+	0.632903i	$0.218137\pi$
$434$	3762.56	−	10626.4i	0.0199758	−	0.0564165i
$435$	691.508	+	2279.60i	0.00365442	+	0.0120470i
$436$	250939.	−	1660.91i	1.32007	−	0.00873720i
$437$	−10719.5	−	108837.i	−0.0561320	−	0.569917i
$438$	−39672.6	+	36197.0i	−0.206796	+	0.188679i
$439$	−22930.0	+	115277.i	−0.118980	+	0.598154i	0.874583	+	0.484876i	$0.161135\pi$
$439$	−22930.0	+	115277.i	−0.118980	+	0.598154i	−0.993563	+	0.113278i	$0.963865\pi$
$440$	−28955.1	−	47238.8i	−0.149562	−	0.244002i
$441$	8114.44	+	40794.0i	0.0417235	+	0.209758i
$442$	7873.37	−	1194.55i	0.0403010	−	0.00611446i
$443$	−167745.	−	50885.0i	−0.854758	−	0.259288i	−0.167653	−	0.985846i	$-0.553619\pi$
$443$	−167745.	−	50885.0i	−0.854758	−	0.259288i	−0.687105	+	0.726558i	$0.741119\pi$
$444$	83310.8	−	8762.52i	0.422605	−	0.0444491i
$445$	148446.	−	121827.i	0.749635	−	0.615209i
$446$	105893.	−	178005.i	0.532349	−	0.894873i
$447$	−149200.			−0.746711
$448$	166019.	−	19686.9i	0.827185	−	0.0980892i
$449$			38663.7i			0.191783i	0.995392	+	0.0958917i	$0.0305703\pi$
$449$			38663.7i			0.191783i	−0.995392	+	0.0958917i	$0.969430\pi$
$450$	25461.4	−	42800.4i	0.125735	−	0.211360i
$451$	−7044.60	−	8583.87i	−0.0346340	−	0.0422017i
$452$	−136629.	−	110623.i	−0.668754	−	0.541465i
$453$	25845.1	−	85199.7i	0.125945	−	0.415185i
$454$	−319405.	+	48460.1i	−1.54964	+	0.235111i
$455$	32536.9	−	6471.99i	0.157164	−	0.0312619i
$456$	−100443.	−	72959.3i	−0.483049	−	0.350874i
$457$	−155197.	−	30870.6i	−0.743105	−	0.147813i	−0.191003	−	0.981589i	$-0.561174\pi$
$457$	−155197.	−	30870.6i	−0.743105	−	0.147813i	−0.552102	+	0.833777i	$0.686174\pi$
$458$	−58140.7	+	53047.2i	−0.277172	+	0.252890i
$459$	48173.2	−	4744.65i	0.228655	−	0.0225205i
$460$	−91010.6	+	92223.4i	−0.430107	+	0.435838i
$461$	319634.	−	96960.0i	1.50401	−	0.456237i	0.572488	−	0.819913i	$-0.305978\pi$
$461$	319634.	−	96960.0i	1.50401	−	0.456237i	0.931526	+	0.363676i	$0.118478\pi$
$462$	8018.83	−	22647.1i	0.0375688	−	0.106103i
$463$	−134928.	−	325746.i	−0.629422	−	1.51956i	−0.840343	−	0.542055i	$-0.817646\pi$
$463$	−134928.	−	325746.i	−0.629422	−	1.51956i	0.210921	−	0.977503i	$-0.432354\pi$
$464$	3317.38	+	2649.80i	0.0154085	+	0.0123077i
$465$	9162.53	+	3795.24i	0.0423750	+	0.0175523i
$466$	167722.	+	151007.i	0.772358	+	0.695383i
$467$	−54462.0	−	29110.5i	−0.249724	−	0.133480i	0.341786	−	0.939778i	$-0.388968\pi$
$467$	−54462.0	−	29110.5i	−0.249724	−	0.133480i	−0.591510	+	0.806298i	$0.701468\pi$
$468$	20954.3	−	14202.7i	0.0956714	−	0.0648456i
$469$	52042.8	−	63414.4i	0.236600	−	0.288298i
$470$	−15257.6	+	32537.6i	−0.0690702	+	0.147296i
$471$	−7276.99	−	10890.8i	−0.0328027	−	0.0490927i
$472$	−167895.	+	81457.8i	−0.753622	+	0.365636i
$473$	−49908.9	+	74694.0i	−0.223077	+	0.333859i
$474$	−8838.71	−	2182.92i	−0.0393398	−	0.00971586i
$475$	−76177.8	+	40717.9i	−0.337630	+	0.180467i
$476$	44407.8	−	13792.6i	0.195995	−	0.0608740i
$477$	81662.2	+	8043.03i	0.358909	+	0.0353495i
$478$	−364703.	−	52865.7i	−1.59619	−	0.231376i
$479$	75487.1	−	75487.1i	0.329005	−	0.329005i	−0.523203	−	0.852208i	$-0.675263\pi$
$479$	75487.1	−	75487.1i	0.329005	−	0.329005i	0.852208	+	0.523203i	$0.175263\pi$
$480$	9646.62	+	146765.i	0.0418690	+	0.637000i
$481$	20949.2	−	20949.2i	0.0905479	−	0.0905479i
$482$	−129113.	−	172890.i	−0.555746	−	0.744176i
$483$	−55911.8	−	5506.83i	−0.239667	−	0.0236052i
$484$	169185.	−	140731.i	0.722222	−	0.600756i
$485$	452414.	−	241820.i	1.92332	−	1.02804i
$486$	209265.	−	126372.i	0.885978	−	0.535028i
$487$	−98288.5	+	147099.i	−0.414424	+	0.620229i	−0.978685	−	0.205367i	$-0.934161\pi$
$487$	−98288.5	+	147099.i	−0.414424	+	0.620229i	0.564261	+	0.825596i	$0.309161\pi$
$488$	−39999.7	+	289425.i	−0.167964	+	1.21534i
$489$	−54104.4	−	80972.9i	−0.226264	−	0.338627i
$490$	−80377.7	+	29060.0i	−0.334767	+	0.121033i
$491$	4895.46	−	5965.14i	0.0203063	−	0.0247433i	−0.762758	−	0.646684i	$-0.776155\pi$
$491$	4895.46	−	5965.14i	0.0203063	−	0.0247433i	0.783065	+	0.621940i	$0.213655\pi$
$492$	5942.04	+	28872.6i	0.0245474	+	0.119277i
$493$	1041.48	+	556.683i	0.00428507	+	0.00229041i
$494$	−43845.5	+	2299.47i	−0.179668	+	0.00942265i
$495$	−45258.8	−	18746.8i	−0.184711	−	0.0765098i
$496$	17289.1	−	3677.58i	0.0702764	−	0.0149485i
$497$	−5107.51	−	12330.6i	−0.0206774	−	0.0499197i
$498$	173991.	−	82997.3i	0.701565	−	0.334661i
$499$	226859.	−	68817.0i	0.911078	−	0.276373i	0.200255	−	0.979744i	$-0.435823\pi$
$499$	226859.	−	68817.0i	0.911078	−	0.276373i	0.710823	+	0.703371i	$0.248323\pi$
$500$	−174493.	−	70927.9i	−0.697971	−	0.283711i
$501$	−22790.4	+	2244.66i	−0.0907981	+	0.00894284i
$502$	−18544.2	+	404806.i	−0.0735869	+	1.60635i
$503$	213006.	+	42369.4i	0.841889	+	0.167462i	0.597153	−	0.802128i	$-0.296299\pi$
$503$	213006.	+	42369.4i	0.841889	+	0.167462i	0.244736	+	0.969590i	$0.421299\pi$
$504$	108532.	−	100349.i	0.427266	−	0.395048i
$505$	−180735.	+	35950.4i	−0.708694	+	0.140968i
$506$	26720.4	+	19680.5i	0.104362	+	0.0768660i
$507$	39844.4	−	131349.i	0.155007	−	0.510990i
$508$	68079.2	+	125364.i	0.263807	+	0.485787i
$509$	299867.	+	365389.i	1.15743	+	1.41033i	0.895397	+	0.445268i	$0.146892\pi$
$509$	299867.	+	365389.i	1.15743	+	1.41033i	0.262029	+	0.965060i	$0.415608\pi$
$510$	10071.5	+	39650.4i	0.0387215	+	0.152443i
$511$			110906.i			0.424731i
$512$	162360.	+	205812.i	0.619354	+	0.785112i
$513$	−266883.			−1.01411
$514$	−362420.	+	92057.2i	−1.37179	+	0.348443i
$515$	−451188.	+	370281.i	−1.70115	+	1.39610i
$516$	209564.	−	113804.i	0.787076	−	0.427422i
$517$	8808.12	+	2671.91i	0.0329535	+	0.00999634i
$518$	102594.	−	139293.i	0.382350	−	0.519121i
$519$	43391.6	+	218144.i	0.161091	+	0.809859i
$520$	35313.9	+	38193.9i	0.130599	+	0.141249i
$521$	−34139.1	+	171629.i	−0.125770	+	0.632288i	0.865551	+	0.500821i	$0.166969\pi$
$521$	−34139.1	+	171629.i	−0.125770	+	0.632288i	−0.991321	+	0.131466i	$0.958031\pi$
$522$	3749.95	+	171.786i	0.0137621	+	0.000630443i
$523$	42585.8	+	432381.i	0.155690	+	1.58075i	0.682577	+	0.730814i	$0.260859\pi$
$523$	42585.8	+	432381.i	0.155690	+	1.58075i	−0.526887	+	0.849935i	$0.676641\pi$
$524$	−99931.8	+	245847.i	−0.363949	+	0.895368i
$525$	12881.1	+	42463.2i	0.0467340	+	0.154061i
$526$	−23853.0	−	50004.1i	−0.0862127	−	0.180732i
$527$	4542.17	−	1881.43i	0.0163547	−	0.00677434i
$528$	36846.9	−	7837.72i	0.132170	−	0.0281140i
$529$	−77392.3	+	186841.i	−0.276558	+	0.667670i
$530$	8831.04	+	168388.i	0.0314384	+	0.599457i
$531$	−77777.2	+	145511.i	−0.275844	+	0.516067i
$532$	−251113.	+	51679.5i	−0.887249	+	0.182598i
$533$	8058.83	+	6613.71i	0.0283673	+	0.0232804i
$534$	44393.2	+	122788.i	0.155680	+	0.430600i
$535$	−171313.	+	114468.i	−0.598527	+	0.399923i
$536$	127422.	+	17610.2i	0.443520	+	0.0612963i
$537$	−97044.3	−	64842.9i	−0.336528	−	0.224861i
$538$	−3540.75	−	5863.29i	−0.0122329	−	0.0202571i
$539$	10319.3	+	19306.1i	0.0355200	+	0.0664532i
$540$	202203.	+	243087.i	0.693427	+	0.833631i
$541$	2462.79	−	25005.1i	0.00841459	−	0.0854347i	−0.990060	−	0.140644i	$-0.955083\pi$
$541$	2462.79	−	25005.1i	0.00841459	−	0.0854347i	0.998475	+	0.0552094i	$0.0175826\pi$
$542$	69660.3	−	52021.8i	0.237130	−	0.177087i
$543$	−166475.	−	166475.i	−0.564611	−	0.564611i
$544$	54827.9	+	48064.9i	0.185269	+	0.162417i
$545$	322388.	+	322388.i	1.08539	+	1.08539i
$546$	−3235.71	+	22322.1i	−0.0108539	+	0.0748772i
$547$	−46289.3	+	469983.i	−0.154705	+	1.57075i	0.533857	+	0.845575i	$0.320742\pi$
$547$	−46289.3	+	469983.i	−0.154705	+	1.57075i	−0.688563	+	0.725177i	$0.741758\pi$
$548$	−80820.4	−	260217.i	−0.269129	−	0.866511i
$549$	121775.	+	227824.i	0.404029	+	0.755885i
$550$	6284.53	−	25446.2i	0.0207753	−	0.0841198i
$551$	−5413.61	−	3617.26i	−0.0178313	−	0.0119145i
$552$	−38454.0	−	79258.6i	−0.126201	−	0.260117i
$553$	−15632.9	+	10445.6i	−0.0511199	+	0.0341572i
$554$	364384.	+	170867.i	1.18724	+	0.556723i
$555$	117650.	+	96552.5i	0.381948	+	0.313457i
$556$	−266141.	−	392657.i	−0.860919	−	1.27018i
$557$	−39596.6	+	74080.0i	−0.127628	+	0.238776i	−0.937617	−	0.347670i	$-0.886973\pi$
$557$	−39596.6	+	74080.0i	−0.127628	+	0.238776i	0.809989	+	0.586445i	$0.199473\pi$
$558$	10456.9	−	11614.4i	0.0335840	−	0.0373016i
$559$	32275.1	−	77919.0i	0.103287	−	0.249356i
$560$	237326.	+	189568.i	0.756781	+	0.604488i
$561$	9680.36	−	4009.74i	0.0307586	−	0.0127406i
$562$	256133.	+	90691.0i	0.810949	+	0.287139i
$563$	−27635.8	−	91103.1i	−0.0871878	−	0.287420i	0.902494	−	0.430702i	$-0.141734\pi$
$563$	−27635.8	−	91103.1i	−0.0871878	−	0.287420i	−0.989682	+	0.143283i	$0.954234\pi$
$564$	−17391.4	−	17162.7i	−0.0546734	−	0.0539544i
$565$	−31306.3	−	317858.i	−0.0980698	−	0.995719i
$566$	23722.7	+	26000.5i	0.0740509	+	0.0811612i
$567$	9749.39	−	49013.5i	0.0303257	−	0.152458i
$568$	12299.0	−	16932.1i	0.0381219	−	0.0524825i
$569$	−18328.0	−	92141.3i	−0.0566098	−	0.284597i	0.942103	−	0.335324i	$-0.108846\pi$
$569$	−18328.0	−	92141.3i	−0.0566098	−	0.284597i	−0.998713	+	0.0507278i	$0.983846\pi$
$570$	−33833.3	−	222998.i	−0.104134	−	0.686360i
$571$	−42481.8	−	12886.7i	−0.130296	−	0.0395248i	0.224463	−	0.974483i	$-0.427937\pi$
$571$	−42481.8	−	12886.7i	−0.130296	−	0.0395248i	−0.354759	+	0.934958i	$0.615437\pi$
$572$	8383.70	−	10354.6i	0.0256238	−	0.0316475i
$573$	−109631.	+	89971.7i	−0.333906	+	0.274029i
$574$	52317.8	+	31123.2i	0.158791	+	0.0944628i
$575$	−61294.2			−0.185389
$576$	223087.	+	62863.7i	0.672401	+	0.189476i
$577$		−	22107.2i		−	0.0664021i	−0.999449	−	0.0332010i	$-0.989430\pi$
$577$		−	22107.2i		−	0.0664021i	0.999449	−	0.0332010i	$-0.0105702\pi$
$578$	−269691.	−	160436.i	−0.807255	−	0.480226i
$579$	127455.	+	155305.i	0.380191	+	0.463264i
$580$	806.880	+	7671.52i	0.00239857	+	0.0228047i
$581$	115563.	−	380960.i	0.342346	−	1.12857i
$582$	52318.4	+	344836.i	0.154457	+	1.01804i
$583$	42357.7	−	8425.48i	0.124622	−	0.0247889i
$584$	−148266.	+	90879.9i	−0.434726	+	0.266466i
$585$	45107.7	+	8972.49i	0.131807	+	0.0262181i
$586$	−229849.	−	251919.i	−0.669342	−	0.733612i
$587$	112622.	−	11092.3i	0.326850	−	0.0321919i	0.0667384	−	0.997771i	$-0.478741\pi$
$587$	112622.	−	11092.3i	0.326850	−	0.0321919i	0.260111	+	0.965579i	$0.416241\pi$
$588$	−384.615	−	58109.9i	−0.00111243	−	0.168072i
$589$	−25938.9	+	7868.49i	−0.0747690	+	0.0226809i
$590$	−319600.	−	113163.i	−0.918127	−	0.325088i
$591$	−23949.3	−	57818.8i	−0.0685675	−	0.165537i
$592$	270283.	+	23012.5i	0.771215	+	0.0656630i
$593$	183890.	+	76169.5i	0.522935	+	0.216607i	0.628506	−	0.777805i	$-0.283667\pi$
$593$	183890.	+	76169.5i	0.522935	+	0.216607i	−0.105571	+	0.994412i	$0.533667\pi$
$594$	54187.1	−	60185.4i	0.153576	−	0.170576i
$595$	74507.8	+	39825.3i	0.210459	+	0.112493i
$596$	−474461.	−	91115.8i	−1.33570	−	0.256508i
$597$	45240.6	−	55125.8i	0.126934	−	0.154670i
$598$	−28208.6	−	13227.6i	−0.0788823	−	0.0369896i
$599$	−277561.	−	415400.i	−0.773581	−	1.15775i	−0.983656	−	0.180060i	$-0.942371\pi$
$599$	−277561.	−	415400.i	−0.773581	−	1.15775i	0.210075	−	0.977685i	$-0.432629\pi$
$600$	−46212.1	+	52015.8i	−0.128367	+	0.144488i
$601$	−27347.0	+	40927.7i	−0.0757113	+	0.113310i	−0.867393	−	0.497624i	$-0.834206\pi$
$601$	−27347.0	+	40927.7i	−0.0757113	+	0.113310i	0.791682	+	0.610934i	$0.209206\pi$
$602$	118080.	−	478108.i	0.325824	−	1.31927i
$603$	100301.	−	53612.2i	0.275850	−	0.147445i
$604$	134220.	−	255155.i	0.367910	−	0.699408i
$605$	397896.	+	39189.3i	1.08707	+	0.107067i
$606$	17973.6	−	123994.i	0.0489429	−	0.337641i
$607$	−226165.	+	226165.i	−0.613831	+	0.613831i	−0.943942	−	0.330111i	$-0.892914\pi$
$607$	−226165.	+	226165.i	−0.613831	+	0.613831i	0.330111	+	0.943942i	$0.392914\pi$
$608$	−274858.	−	293354.i	−0.743534	−	0.793570i
$609$	−2365.13	+	2365.13i	−0.00637705	+	0.00637705i
$610$	−425322.	+	317627.i	−1.14303	+	0.853607i
$611$	−8599.85	−	847.011i	−0.0230361	−	0.00226886i
$612$	64196.2	+	5894.03i	0.171398	+	0.0157366i
$613$	455901.	−	243684.i	1.21325	−	0.648495i	0.264457	−	0.964397i	$-0.414807\pi$
$613$	455901.	−	243684.i	1.21325	−	0.648495i	0.948792	+	0.315902i	$0.102307\pi$
$614$	−148208.	−	245424.i	−0.393128	−	0.650999i
$615$	−29754.1	+	44530.2i	−0.0786678	+	0.117735i
$616$	39330.8	−	67121.8i	0.103650	−	0.176889i
$617$	133638.	+	200004.i	0.351044	+	0.525374i	0.964405	−	0.264428i	$-0.0851832\pi$
$617$	133638.	+	200004.i	0.351044	+	0.525374i	−0.613362	+	0.789802i	$0.710183\pi$
$618$	−134929.	−	373202.i	−0.353287	−	0.977163i
$619$	46533.3	−	56701.0i	0.121446	−	0.147982i	−0.708738	−	0.705472i	$-0.750735\pi$
$619$	46533.3	−	56701.0i	0.121446	−	0.147982i	0.830184	+	0.557489i	$0.188235\pi$
$620$	26819.5	+	17664.6i	0.0697697	+	0.0459536i
$621$	−167021.	−	89274.7i	−0.433100	−	0.231497i
$622$	11899.5	+	226896.i	0.0307573	+	0.586471i
$623$	249113.	+	103186.i	0.641830	+	0.265855i
$624$	−32492.9	+	13965.7i	−0.0834486	+	0.0358669i
$625$	−183585.	−	443213.i	−0.469977	−	1.13462i
$626$	−335379.	−	703069.i	−0.855828	−	1.79411i
$627$	−55281.6	+	16769.5i	−0.140619	+	0.0426564i
$628$	−16490.1	−	39077.2i	−0.0418124	−	0.0990841i
$629$	75085.7	−	7395.29i	0.189782	−	0.0186919i
$630$	268273.	+	12289.6i	0.675920	+	0.0309640i
$631$	420989.	+	83739.9i	1.05733	+	0.210317i	0.692990	−	0.720948i	$-0.256293\pi$
$631$	420989.	+	83739.9i	1.05733	+	0.210317i	0.364344	+	0.931264i	$0.381293\pi$
$632$	−26774.4	−	12339.6i	−0.0670324	−	0.0308934i
$633$	−79274.3	+	15768.6i	−0.197845	+	0.0393538i
$634$	421477.	−	572244.i	1.04856	−	1.42365i
$635$	−75237.0	+	248023.i	−0.186588	+	0.615099i
$636$	−109926.	−	32552.8i	−0.271761	−	0.0804774i
$637$	−13038.0	−	15886.9i	−0.0321316	−	0.0391525i
$638$	1914.90	−	486.397i	0.00470440	−	0.00119495i
$639$		−	18503.1i		−	0.0453151i
$640$	−58952.2	+	472609.i	−0.143926	+	1.15383i
$641$	224271.			0.545830			0.272915	−	0.962038i	$-0.412012\pi$
$641$	224271.			0.545830			0.272915	+	0.962038i	$0.412012\pi$
$642$	−34487.5	−	135774.i	−0.0836742	−	0.329417i
$643$	−435216.	+	357173.i	−1.05265	+	0.863886i	−0.990953	−	0.134209i	$-0.957151\pi$
$643$	−435216.	+	357173.i	−1.05265	+	0.863886i	−0.0616950	+	0.998095i	$0.519651\pi$
$644$	−174439.	−	51657.1i	−0.420602	−	0.124554i
$645$	414605.	+	125769.i	0.996587	+	0.302311i
$646$	−90028.8	−	66309.2i	−0.215733	−	0.158895i
$647$	1994.94	+	10029.2i	0.00476563	+	0.0239585i	0.983095	−	0.183097i	$-0.0586121\pi$
$647$	1994.94	+	10029.2i	0.00476563	+	0.0239585i	−0.978329	+	0.207055i	$0.933612\pi$
$648$	73513.1	−	27129.6i	0.175071	−	0.0646091i
$649$	−16941.1	+	85168.8i	−0.0402210	+	0.202205i
$650$	−1126.10	+	24581.8i	−0.00266531	+	0.0581819i
$651$	1364.89	+	13858.0i	0.00322060	+	0.0326993i
$652$	−122604.	−	290539.i	−0.288410	−	0.683453i
$653$	52629.2	+	173495.i	0.123424	+	0.406875i	0.996778	−	0.0802117i	$-0.0255596\pi$
$653$	52629.2	+	173495.i	0.123424	+	0.406875i	−0.873354	+	0.487087i	$0.838060\pi$
$654$	−279784.	+	133463.i	−0.654134	+	0.312035i
$655$	−445451.	+	184512.i	−1.03829	+	0.430072i
$656$	1263.51	+	95444.8i	0.00293610	+	0.221791i
$657$	−58839.7	+	142052.i	−0.136314	+	0.329090i
$658$	−50390.1	+	2642.70i	−0.116384	+	0.00610373i
$659$	44050.7	−	82413.1i	0.101434	−	0.189769i	−0.826085	−	0.563545i	$-0.809437\pi$
$659$	44050.7	−	82413.1i	0.101434	−	0.189769i	0.927519	+	0.373776i	$0.121937\pi$
$660$	57158.2	+	37647.1i	0.131217	+	0.0864258i
$661$	−362629.	−	297602.i	−0.829965	−	0.681135i	0.120245	−	0.992744i	$-0.461632\pi$
$661$	−362629.	−	297602.i	−0.829965	−	0.681135i	−0.950210	+	0.311610i	$0.899132\pi$
$662$	−534955.	+	193409.i	−1.22068	+	0.441328i
$663$	−8179.22	+	5465.18i	−0.0186074	+	0.0124330i
$664$	603985.	−	157679.i	1.36990	−	0.357633i
$665$	−387291.	−	258780.i	−0.875779	−	0.585177i
$666$	205304.	−	123980.i	0.462860	−	0.279514i
$667$	−2177.95	−	4074.65i	−0.00489549	−	0.00915881i
$668$	−73845.3	−	6779.94i	−0.165489	−	0.0151940i
$669$	−25077.7	+	254618.i	−0.0560320	+	0.568902i
$670$	139838.	+	187251.i	0.311512	+	0.417133i
$671$	96138.3	+	96138.3i	0.213526	+	0.213526i
$672$	−175354.	+	109087.i	−0.388308	+	0.241565i
$673$	638260.	+	638260.i	1.40918	+	1.40918i	0.764181	+	0.645002i	$0.223144\pi$
$673$	638260.	+	638260.i	1.40918	+	1.40918i	0.645002	+	0.764181i	$0.276856\pi$
$674$	−135505.	−	19642.2i	−0.298288	−	0.0432384i
$675$	−14661.3	+	148858.i	−0.0321784	+	0.326712i
$676$	206922.	−	393364.i	0.452807	−	0.860798i
$677$	−57592.0	−	107747.i	−0.125656	−	0.235087i	0.811225	−	0.584734i	$-0.198801\pi$
$677$	−57592.0	−	107747.i	−0.125656	−	0.235087i	−0.936881	+	0.349648i	$0.886301\pi$
$678$	210825.	+	52068.0i	0.458629	+	0.113269i
$679$	598892.	+	400167.i	1.29900	+	0.867964i
$680$	7813.29	+	132240.i	0.0168973	+	0.285987i
$681$	331813.	−	221710.i	0.715482	−	0.478070i
$682$	3492.12	−	7447.14i	0.00750794	−	0.0160111i
$683$	−110749.	−	90889.0i	−0.237409	−	0.194836i	0.508164	−	0.861260i	$-0.330324\pi$
$683$	−110749.	−	90889.0i	−0.237409	−	0.194836i	−0.745573	+	0.666424i	$0.767824\pi$
$684$	−349050.	−	67031.8i	−0.746062	−	0.143274i
$685$	233364.	−	436594.i	0.497339	−	0.930457i
$686$	−380506.	−	342584.i	−0.808562	−	0.727979i
$687$	37204.9	−	89820.6i	0.0788292	−	0.190310i
$688$	735921.	−	233921.i	1.55473	−	0.494188i
$689$	−37459.6	+	15516.3i	−0.0789087	+	0.0326850i
$690$	53421.2	−	150874.i	0.112206	−	0.316897i
$691$	70270.0	+	231649.i	0.147168	+	0.485149i	0.999269	−	0.0382291i	$-0.0121717\pi$
$691$	70270.0	+	231649.i	0.147168	+	0.485149i	−0.852101	+	0.523378i	$0.824672\pi$
$692$	4766.88	+	720208.i	0.00995456	+	1.50399i
$693$	−6741.96	−	68452.3i	−0.0140385	−	0.142535i
$694$	−204357.	+	186454.i	−0.424297	+	0.387126i
$695$	168133.	−	845260.i	0.348083	−	1.74993i
$696$	−5099.90	−	1223.78i	−0.0105279	−	0.00252630i
$697$	5179.55	+	26039.4i	0.0106617	+	0.0536000i
$698$	−32613.5	+	4948.11i	−0.0669401	+	0.0101561i
$699$	−266778.	−	80926.3i	−0.546004	−	0.165629i
$700$	15030.1	+	142901.i	0.0306738	+	0.291635i
$701$	−293124.	+	240560.i	−0.596506	+	0.489540i	−0.883524	−	0.468385i	$-0.844836\pi$
$701$	−293124.	+	240560.i	−0.596506	+	0.489540i	0.287018	+	0.957925i	$0.407336\pi$
$702$	−38871.8	+	65343.2i	−0.0788789	+	0.132595i
$703$	−415980.			−0.841709
$704$	121961.	−	2421.98i	0.246080	−	0.00488680i
$705$		−	44392.4i		−	0.0893163i
$706$	−175861.	+	295621.i	−0.352826	+	0.593097i
$707$	−164143.	−	200009.i	−0.328385	−	0.400138i
$708$	145056.	−	179156.i	0.289380	−	0.357408i
$709$	−212181.	+	699468.i	−0.422100	+	1.39148i	0.445977	+	0.895045i	$0.352856\pi$
$709$	−212181.	+	699468.i	−0.422100	+	1.39148i	−0.868076	+	0.496431i	$0.834644\pi$
$710$	37591.7	−	5703.40i	0.0745718	−	0.0113140i
$711$	−25564.8	+	5085.16i	−0.0505712	+	0.0100592i
$712$	66185.8	+	417582.i	0.130558	+	0.823724i
$713$	−18865.2	−	3752.52i	−0.0371093	−	0.00738150i
$714$	−42432.9	+	38715.5i	−0.0832351	+	0.0759431i
$715$	24089.2	−	2372.58i	0.0471205	−	0.00464096i
$716$	−269005.	−	265468.i	−0.524729	−	0.517829i
$717$	435615.	−	132142.i	0.847353	−	0.257042i
$718$	28591.1	−	80748.2i	0.0554602	−	0.156633i
$719$	152582.	+	368365.i	0.295152	+	0.712560i	0.999995	+	0.00319625i	$0.00101740\pi$
$719$	152582.	+	368365.i	0.295152	+	0.712560i	−0.704843	+	0.709363i	$0.748983\pi$
$720$	203402.	+	368713.i	0.392364	+	0.711252i
$721$	−757153.	−	313623.i	−1.45651	−	0.603306i
$722$	70738.0	+	63688.0i	0.135699	+	0.122175i
$723$	235074.	+	125650.i	0.449705	+	0.240373i
$724$	−427731.	−	631063.i	−0.816007	−	1.20391i
$725$	−2314.98	+	2820.81i	−0.00440424	+	0.00536659i
$726$	−115413.	+	246124.i	−0.218968	+	0.466961i
$727$	−247312.	−	370128.i	−0.467925	−	0.700299i	0.520184	−	0.854054i	$-0.325863\pi$
$727$	−247312.	−	370128.i	−0.467925	−	0.700299i	−0.988109	+	0.153755i	$0.950863\pi$
$728$	−23921.7	+	69009.1i	−0.0451367	+	0.130210i
$729$	−112671.	+	168625.i	−0.212011	+	0.317297i
$730$	−306735.	−	75755.1i	−0.575595	−	0.142156i
$731$	189421.	−	101248.i	0.354481	−	0.189474i
$732$	−107052.	−	344675.i	−0.199790	−	0.643262i
$733$	−568273.	−	55970.0i	−1.05767	−	0.104171i	−0.445800	−	0.895132i	$-0.647081\pi$
$733$	−568273.	−	55970.0i	−1.05767	−	0.104171i	−0.611866	+	0.790961i	$0.709581\pi$
$734$	−235515.	−	34139.2i	−0.437146	−	0.0633667i
$735$	74655.1	−	74655.1i	0.138193	−	0.138193i
$736$	−73882.3	−	275529.i	−0.136391	−	0.508642i
$737$	42325.6	−	42325.6i	0.0779235	−	0.0779235i
$738$	50498.1	+	67619.9i	0.0927176	+	0.124154i
$739$	−236929.	−	23335.4i	−0.433839	−	0.0427294i	−0.121259	−	0.992621i	$-0.538693\pi$
$739$	−236929.	−	23335.4i	−0.433839	−	0.0427294i	−0.312580	+	0.949891i	$0.601193\pi$
$740$	315166.	+	378889.i	0.575541	+	0.691909i
$741$	47831.5	−	25566.5i	0.0871120	−	0.0465623i
$742$	−202669.	+	122389.i	−0.368112	+	0.222297i
$743$	143931.	−	215408.i	0.260722	−	0.390198i	−0.677895	−	0.735158i	$-0.737108\pi$
$743$	143931.	−	215408.i	0.260722	−	0.390198i	0.938617	+	0.344961i	$0.112108\pi$
$744$	−17407.7	+	13180.3i	−0.0314482	+	0.0238111i
$745$	−487661.	−	729837.i	−0.878630	−	1.31496i
$746$	817103.	−	295418.i	1.46825	−	0.530835i
$747$	350129.	−	426633.i	0.627460	−	0.764563i
$748$	33232.7	−	6839.36i	0.0593967	−	0.0122240i
$749$	−255136.	−	136373.i	−0.454786	−	0.243088i
$750$	232353.	−	12185.7i	0.413073	−	0.0216635i
$751$	−68938.3	−	28555.2i	−0.122231	−	0.0506297i	0.320730	−	0.947171i	$-0.396072\pi$
$751$	−68938.3	−	28555.2i	−0.122231	−	0.0506297i	−0.442961	+	0.896541i	$0.646072\pi$
$752$	−44824.2	−	65199.0i	−0.0792641	−	0.115294i
$753$	−191560.	−	462467.i	−0.337843	−	0.815625i
$754$	−1674.14	+	798.600i	−0.00294476	+	0.00140471i
$755$	501245.	−	152051.i	0.879339	−	0.266745i
$756$	−167179.	+	411284.i	−0.292508	+	0.719612i
$757$	−18592.0	+	1831.15i	−0.0324440	+	0.00319546i	−0.114226	−	0.993455i	$-0.536439\pi$
$757$	−18592.0	+	1831.15i	−0.0324440	+	0.00319546i	0.0817821	+	0.996650i	$0.473939\pi$
$758$	−40630.8	+	886940.i	−0.0707158	+	1.54367i
$759$	−40205.9	−	7997.45i	−0.0697921	−	0.0138825i
$760$	28593.4	−	729806.i	0.0495037	−	1.26351i
$761$	−533561.	+	106132.i	−0.921329	+	0.183264i	−0.632896	−	0.774237i	$-0.718134\pi$
$761$	−533561.	+	106132.i	−0.921329	+	0.183264i	−0.288432	+	0.957500i	$0.593134\pi$
$762$	−141888.	−	104505.i	−0.244363	−	0.179982i
$763$	−185829.	+	612596.i	−0.319201	+	1.05227i
$764$	−403576.	+	219163.i	−0.691415	+	0.375474i
$765$	74302.9	+	90538.3i	0.126965	+	0.154707i
$766$	5070.01	+	19960.1i	0.00864074	+	0.0340177i
$767$		−	81526.0i		−	0.138581i
$768$	−289524.	−	145034.i	−0.490865	−	0.245894i
$769$	268383.			0.453839			0.226920	−	0.973914i	$-0.427135\pi$
$769$	268383.			0.453839			0.226920	+	0.973914i	$0.427135\pi$
$770$	136992.	−	34797.0i	0.231055	−	0.0586895i
$771$	357057.	−	293029.i	0.600660	−	0.492949i
$772$	310469.	+	571713.i	0.520936	+	0.959276i
$773$	271346.	+	82311.8i	0.454113	+	0.137754i	0.509051	−	0.860736i	$-0.329996\pi$
$773$	271346.	+	82311.8i	0.454113	+	0.137754i	−0.0549385	+	0.998490i	$0.517496\pi$
$774$	404893.	−	549728.i	0.675863	−	0.917627i
$775$	2963.82	+	14900.1i	0.00493455	+	0.0248077i
$776$	−44215.7	+	1.12854e6i	−0.0734265	+	1.87411i
$777$	−41690.5	+	209592.i	−0.0690549	+	0.347163i
$778$	695958.	+	31881.9i	1.14980	+	0.0526726i
$779$	−14347.6	−	145673.i	−0.0236430	−	0.240052i
$780$	−59526.3	−	24196.3i	−0.0978407	−	0.0397703i
$781$	−2826.90	−	9319.02i	−0.00463455	−	0.0152781i
$782$	−34160.9	−	71613.1i	−0.0558620	−	0.117106i
$783$	−10416.6	+	4314.70i	−0.0169904	+	0.00703765i
$784$	34264.5	−	185027.i	0.0557458	−	0.301025i
$785$	29489.3	−	71193.4i	0.0478547	−	0.115532i
$786$	−17168.7	−	327368.i	−0.0277902	−	0.529896i
$787$	254559.	−	476247.i	0.410998	−	0.768923i	−0.588210	−	0.808708i	$-0.700167\pi$
$787$	254559.	−	476247.i	0.410998	−	0.768923i	0.999208	+	0.0397851i	$0.0126673\pi$
$788$	−40850.0	−	198492.i	−0.0657870	−	0.319662i
$789$	52902.1	+	43415.7i	0.0849805	+	0.0697417i
$790$	−18211.3	−	50371.1i	−0.0291801	−	0.0807100i
$791$	372883.	−	249152.i	0.595963	−	0.398210i
$792$	85986.4	−	65104.9i	0.137082	−	0.103792i
$793$	−106132.	−	70915.2i	−0.168772	−	0.112770i
$794$	491757.	+	814323.i	0.780027	+	1.29168i
$795$	−98187.5	−	183696.i	−0.155354	−	0.290646i
$796$	177532.	−	147674.i	0.280189	−	0.233065i
$797$	−93193.9	+	946214.i	−0.146714	+	1.48961i	0.586687	+	0.809814i	$0.300432\pi$
$797$	−93193.9	+	946214.i	−0.146714	+	1.48961i	−0.733401	+	0.679797i	$0.762068\pi$
$798$	253745.	−	189495.i	0.398466	−	0.297572i
$799$	−15561.2	−	15561.2i	−0.0243752	−	0.0243752i
$800$	−178722.	+	137191.i	−0.279254	+	0.214360i
$801$	264326.	+	264326.i	0.411979	+	0.411979i
$802$	−139718.	+	963871.i	−0.217223	+	1.49855i
$803$	−7931.84	+	80533.3i	−0.0123011	+	0.124895i
$804$	−151746.	+	47130.6i	−0.234750	+	0.0729106i
$805$	−155811.	−	291502.i	−0.240440	−	0.449831i
$806$	−1851.53	+	7496.90i	−0.00285010	+	0.0115401i
$807$	7035.03	+	4700.65i	0.0108024	+	0.00721791i
$808$	132880.	−	383329.i	0.203533	−	0.587150i
$809$	112335.	−	75060.0i	0.171640	−	0.114686i	−0.466783	−	0.884372i	$-0.654587\pi$
$809$	112335.	−	75060.0i	0.171640	−	0.114686i	0.638423	+	0.769686i	$0.279587\pi$
$810$	128898.	+	60443.0i	0.196461	+	0.0921247i
$811$	638128.	+	523698.i	0.970211	+	0.796231i	0.979027	−	0.203730i	$-0.0653064\pi$
$811$	638128.	+	523698.i	0.970211	+	0.796231i	−0.00881647	+	0.999961i	$0.502806\pi$
$812$	−8965.58	+	6076.82i	−0.0135977	+	0.00921647i
$813$	−50626.4	+	94715.3i	−0.0765942	+	0.143298i
$814$	84459.3	−	93808.5i	0.127467	−	0.141577i
$815$	219253.	−	529323.i	0.330088	−	0.796903i
$816$	−86528.0	−	25002.1i	−0.129950	−	0.0375488i
$817$	−1.09404e6	+	453166.i	−1.63904	+	0.678911i
$818$	1.22319e6	+	433104.i	1.82805	+	0.647269i
$819$	18745.5	+	61795.7i	0.0279466	+	0.0921277i
$820$	−121814.	+	123437.i	−0.181163	+	0.183577i
$821$	−20506.7	−	208208.i	−0.0304235	−	0.308895i	−0.998339	−	0.0576179i	$-0.981649\pi$
$821$	−20506.7	−	208208.i	−0.0304235	−	0.308895i	0.967915	−	0.251277i	$-0.0808505\pi$
$822$	226861.	+	248644.i	0.335750	+	0.367989i
$823$	184062.	−	925340.i	0.271746	−	1.36616i	−0.567932	−	0.823076i	$-0.692256\pi$
$823$	184062.	−	925340.i	0.271746	−	1.36616i	0.839678	−	0.543084i	$-0.182744\pi$
$824$	−201165.	−	1.26920e6i	−0.296277	−	1.86928i
$825$	6316.54	+	31755.4i	0.00928050	+	0.0466562i
$826$	−71408.7	−	470662.i	−0.104662	−	0.689841i
$827$	−201813.	−	61219.4i	−0.295079	−	0.0895113i	0.139274	−	0.990254i	$-0.455523\pi$
$827$	−201813.	−	61219.4i	−0.295079	−	0.0895113i	−0.434353	+	0.900743i	$0.643023\pi$
$828$	−196020.	−	158710.i	−0.285917	−	0.231496i
$829$	−358039.	+	293835.i	−0.520981	+	0.427558i	−0.857779	−	0.514019i	$-0.828156\pi$
$829$	−358039.	+	293835.i	−0.520981	+	0.427558i	0.336798	+	0.941577i	$0.390656\pi$
$830$	974689.	+	579830.i	1.41485	+	0.841676i
$831$	−497144.			−0.719913
$832$	−111858.	+	24568.2i	−0.161592	+	0.0354918i
$833$		−	52338.7i		−	0.0754280i
$834$	503585.	+	299576.i	0.724003	+	0.430701i
$835$	−85471.1	−	104147.i	−0.122588	−	0.149373i
$836$	−186039.	+	19567.3i	−0.266189	+	0.0279975i
$837$	−13625.8	+	44918.3i	−0.0194496	+	0.0641168i
$838$	−70907.8	−	467360.i	−0.100973	−	0.665524i
$839$	−557460.	+	110886.i	−0.791936	+	0.157526i	−0.574452	−	0.818538i	$-0.694785\pi$
$839$	−557460.	+	110886.i	−0.791936	+	0.157526i	−0.217484	+	0.976064i	$0.569785\pi$
$840$	−364848.	−	87549.6i	−0.517075	−	0.124078i
$841$	693421.	+	137930.i	0.980404	+	0.195014i
$842$	227043.	+	248844.i	0.320247	+	0.350996i
$843$	−334026.	+	32898.7i	−0.470030	+	0.0462939i
$844$	−261725.	+	1732.30i	−0.367418	+	0.00243185i
$845$	772752.	−	234412.i	1.08225	−	0.328296i
$846$	−65943.1	−	23348.9i	−0.0921358	−	0.0326232i
$847$	214833.	+	518653.i	0.299457	+	0.722954i
$848$	−329690.	−	170651.i	−0.458473	−	0.237310i
$849$	−40167.7	−	16638.0i	−0.0557265	−	0.0230827i
$850$	−41930.8	+	46572.3i	−0.0580356	+	0.0644599i
$851$	−260329.	−	139149.i	−0.359471	−	0.192141i
$852$	−4875.41	+	25387.3i	−0.00671632	+	0.0349734i
$853$	−431681.	+	526005.i	−0.593287	+	0.722923i	−0.979938	−	0.199304i	$-0.936132\pi$
$853$	−431681.	+	526005.i	−0.593287	+	0.722923i	0.386650	+	0.922226i	$0.373632\pi$
$854$	−674832.	−	316443.i	−0.925294	−	0.433890i
$855$	−358761.	−	536924.i	−0.490764	−	0.734481i
$856$	−26754.9	−	452828.i	−0.0365137	−	0.617996i
$857$	−459490.	+	687676.i	−0.625626	+	0.936315i	0.374333	+	0.927294i	$0.377872\pi$
$857$	−459490.	+	687676.i	−0.625626	+	0.936315i	−0.999959	+	0.00902123i	$0.997128\pi$
$858$	−3946.02	+	15977.5i	−0.00536024	+	0.0217038i
$859$	664681.	−	355280.i	0.900798	−	0.481486i	0.0451117	−	0.998982i	$-0.485636\pi$
$859$	664681.	−	355280.i	0.900798	−	0.481486i	0.855686	+	0.517496i	$0.173136\pi$
$860$	1.24165e6	+	653149.i	1.67882	+	0.883112i
$861$	−74835.6	−	7370.66i	−0.100949	−	0.00994261i
$862$	−188066.	+	1.29741e6i	−0.253102	+	1.74607i
$863$	−424214.	+	424214.i	−0.569591	+	0.569591i	−0.932014	−	0.362423i	$-0.881950\pi$
$863$	−424214.	+	424214.i	−0.569591	+	0.569591i	0.362423	+	0.932014i	$0.381950\pi$
$864$	−686820.	+	113524.i	−0.920058	+	0.152076i
$865$	−925267.	+	925267.i	−1.23662	+	1.23662i
$866$	−568554.	+	424592.i	−0.758117	+	0.566156i
$867$	385767.	+	37994.7i	0.513200	+	0.0505458i
$868$	−4122.62	+	44902.5i	−0.00547185	+	0.0595979i
$869$	−12098.7	+	6466.90i	−0.0160214	+	0.00856361i
$870$	−4925.75	−	8156.77i	−0.00650779	−	0.0107766i
$871$	−31221.0	+	46725.5i	−0.0411538	+	0.0615911i
$872$	−971228.	+	253553.i	−1.27729	+	0.333454i
$873$	554774.	+	830278.i	0.727927	+	1.08942i
$874$	148736.	+	411391.i	0.194712	+	0.538557i
$875$	304826.	−	371432.i	0.398140	−	0.485135i
$876$	118161.	−	179399.i	0.153980	−	0.233783i
$877$	−543253.	−	290375.i	−0.706322	−	0.377537i	0.0787897	−	0.996891i	$-0.474894\pi$
$877$	−543253.	−	290375.i	−0.706322	−	0.377537i	−0.785112	+	0.619354i	$0.787394\pi$
$878$	−24622.6	−	469496.i	−0.0319407	−	0.609036i
$879$	389186.	+	161206.i	0.503709	+	0.208643i
$880$	158774.	+	154626.i	0.205029	+	0.199671i
$881$	−276510.	−	667555.i	−0.356254	−	0.860073i	−0.995820	−	0.0913367i	$-0.970886\pi$
$881$	−276510.	−	667555.i	−0.356254	−	0.860073i	0.639566	−	0.768736i	$-0.279114\pi$
$882$	−71630.9	−	150163.i	−0.0920796	−	0.193031i
$883$	−321463.	+	97514.7i	−0.412296	+	0.125069i	−0.489617	−	0.871938i	$-0.662863\pi$
$883$	−321463.	+	97514.7i	−0.412296	+	0.125069i	0.0773208	+	0.997006i	$0.475363\pi$
$884$	−29347.8	+	12384.5i	−0.0375553	+	0.0158479i
$885$	416794.	−	41050.6i	0.532151	−	0.0524123i
$886$	700440.	+	32087.2i	0.892284	+	0.0408756i
$887$	424149.	+	84368.5i	0.539102	+	0.107234i	0.457129	−	0.889400i	$-0.348878\pi$
$887$	424149.	+	84368.5i	0.539102	+	0.107234i	0.0819732	+	0.996635i	$0.473878\pi$
$888$	−314357.	+	116012.i	−0.398656	+	0.147122i
$889$	−356925.	+	70996.9i	−0.451621	+	0.0898329i
$890$	−455540.	+	618492.i	−0.575105	+	0.780826i
$891$	10584.8	−	34893.4i	0.0133330	−	0.0439529i
$892$	−235243.	+	794383.i	−0.295656	+	0.998389i
$893$	76972.4	+	93791.1i	0.0965233	+	0.117614i
$894$	578430.	−	146925.i	0.723728	−	0.183832i
$895$		−	686650.i		−	0.857215i
$896$	−624252.	+	239812.i	−0.777577	+	0.298714i
$897$	38486.2			0.0478322
$898$	−38074.3	−	149895.i	−0.0472150	−	0.185881i
$899$	−885.203	+	726.467i	−0.00109528	+	0.000898869i
$900$	−56563.1	+	191005.i	−0.0698310	+	0.235809i
$901$	−98810.4	−	29973.8i	−0.121717	−	0.0369226i
$902$	35764.1	+	26341.5i	0.0439577	+	0.0323763i
$903$	118681.	+	596650.i	0.145548	+	0.731719i
$904$	638633.	+	294328.i	0.781474	+	0.360160i
$905$	270216.	−	1.35847e6i	0.329924	−	1.65864i
$906$	−16297.4	+	355761.i	−0.0198547	+	0.433413i
$907$	16960.4	+	172202.i	0.0206168	+	0.209326i	0.999974	+	0.00718963i	$0.00228855\pi$
$907$	16960.4	+	172202.i	0.0206168	+	0.209326i	−0.979357	+	0.202137i	$0.935211\pi$
$908$	1.19058e6	−	502410.i	1.44406	−	0.609378i
$909$	−104127.	−	343260.i	−0.126019	−	0.415428i
$910$	−119769.	+	57132.1i	−0.144631	+	0.0689918i
$911$	1.27912e6	−	529827.i	1.54125	−	0.638407i	0.559543	−	0.828801i	$-0.310977\pi$
$911$	1.27912e6	−	529827.i	1.54125	−	0.638407i	0.981708	+	0.190394i	$0.0609767\pi$
$912$	461254.	+	183943.i	0.554563	+	0.221153i
$913$	111160.	−	268365.i	0.133355	−	0.321947i
$914$	632080.	−	33149.3i	0.756624	−	0.0396809i
$915$	309107.	−	578299.i	0.369204	−	0.690733i
$916$	173166.	−	262912.i	0.206382	−	0.313343i
$917$	−523318.	−	429476.i	−0.622339	−	0.510740i
$918$	−182090.	+	65833.4i	−0.216073	+	0.0781197i
$919$	−587122.	+	392302.i	−0.695180	+	0.464504i	−0.852285	−	0.523077i	$-0.824784\pi$
$919$	−587122.	+	392302.i	−0.695180	+	0.464504i	0.157105	+	0.987582i	$0.449784\pi$
$920$	262020.	−	447163.i	0.309570	−	0.528312i
$921$	294470.	+	196759.i	0.347154	+	0.231961i
$922$	−1.14370e6	+	690665.i	−1.34540	+	0.812467i
$923$	4309.84	+	8063.15i	0.00505892	+	0.00946457i
$924$	−8786.21	+	95697.0i	−0.0102910	+	0.112087i
$925$	−22851.9	+	232019.i	−0.0267079	+	0.271169i
$926$	843883.	+	1.13001e6i	0.984148	+	1.31783i
$927$	−803394.	−	803394.i	−0.934908	−	0.934908i
$928$	−15470.5	−	7006.17i	−0.0179642	−	0.00813551i
$929$	269088.	+	269088.i	0.311791	+	0.311791i	0.845603	−	0.533812i	$-0.179241\pi$
$929$	269088.	+	269088.i	0.311791	+	0.311791i	−0.533812	+	0.845603i	$0.679241\pi$
$930$	−39259.5	−	5690.88i	−0.0453919	−	0.00657981i
$931$	−28284.2	+	287174.i	−0.0326321	+	0.331319i
$932$	−798945.	−	420270.i	−0.919782	−	0.483834i
$933$	−132304.	−	247524.i	−0.151988	−	0.284350i
$934$	239810.	+	59226.5i	0.274899	+	0.0678926i
$935$	51254.8	+	34247.4i	0.0586289	+	0.0391745i
$936$	−67251.4	+	75697.4i	−0.0767626	+	0.0864031i
$937$	808008.	−	539893.i	0.920314	−	0.614934i	−0.00257619	−	0.999997i	$-0.500820\pi$
$937$	808008.	−	539893.i	0.920314	−	0.614934i	0.922891	+	0.385062i	$0.125820\pi$
$938$	−139317.	+	297100.i	−0.158342	+	0.337673i
$939$	743816.	+	610434.i	0.843596	+	0.692321i
$940$	27110.4	−	141170.i	0.0306817	−	0.159767i
$941$	135224.	−	252987.i	0.152713	−	0.285706i	−0.793918	−	0.608024i	$-0.791962\pi$
$941$	135224.	−	252987.i	0.152713	−	0.285706i	0.946631	+	0.322319i	$0.104462\pi$
$942$	38936.8	+	35056.3i	0.0438792	+	0.0395061i
$943$	39749.9	−	95964.7i	0.0447005	−	0.107917i
$944$	570693.	−	481138.i	0.640411	−	0.539915i
$945$	−745208.	+	308675.i	−0.834476	+	0.345651i
$946$	119936.	−	338728.i	0.134019	−	0.378503i
$947$	−282038.	−	929755.i	−0.314491	−	1.03674i	−0.961626	−	0.274362i	$-0.911533\pi$
$947$	−282038.	−	929755.i	−0.314491	−	1.03674i	0.647136	−	0.762375i	$-0.275967\pi$
$948$	36416.3	−	241.031i	0.0405209	−	0.000268198i
$949$	−7446.68	−	75607.4i	−0.00826857	−	0.0839522i
$950$	255236.	−	232875.i	0.282810	−	0.258034i
$951$	−171273.	+	861049.i	−0.189378	+	0.952066i
$952$	−158582.	+	97203.2i	−0.174976	+	0.107252i
$953$	283855.	+	1.42703e6i	0.312543	+	1.57126i	0.743404	+	0.668842i	$0.233210\pi$
$953$	283855.	+	1.42703e6i	0.312543	+	1.57126i	−0.430861	+	0.902418i	$0.641790\pi$
$954$	−324516.	+	49235.5i	−0.356565	+	0.0540980i
$955$	−798444.	−	242205.i	−0.875463	−	0.265569i
$956$	1.46597e6	−	154189.i	1.60402	−	0.168709i
$957$	−1886.56	+	1548.26i	−0.00205990	+	0.00169052i
$958$	−218319.	+	366992.i	−0.237881	+	0.399876i
$959$	695094.			0.755799
$960$	−181926.	−	559491.i	−0.197403	−	0.607086i
$961$		−	918754.i		−	0.994838i
$962$	−60588.0	+	101848.i	−0.0654691	+	0.110053i
$963$	−254434.	−	310028.i	−0.274361	−	0.334310i
$964$	670811.	+	543130.i	0.721849	+	0.584454i
$965$	−343112.	+	1.13109e6i	−0.368452	+	1.21462i
$966$	222187.	−	33710.1i	0.238102	−	0.0361248i
$967$	−637127.	+	126732.i	−0.681354	+	0.135530i	−0.523620	−	0.851952i	$-0.675419\pi$
$967$	−637127.	+	126732.i	−0.681354	+	0.135530i	−0.157734	+	0.987482i	$0.550419\pi$
$968$	−517325.	+	712202.i	−0.552094	+	0.760068i
$969$	135465.	+	26945.7i	0.144272	+	0.0286974i
$970$	−1.51582e6	+	1.38303e6i	−1.61104	+	1.46990i
$971$	−731604.	+	72056.7i	−0.775957	+	0.0764251i	−0.478240	−	0.878229i	$-0.658725\pi$
$971$	−731604.	+	72056.7i	−0.775957	+	0.0764251i	−0.297717	+	0.954654i	$0.596225\pi$
$972$	−686850.	+	696003.i	−0.726992	+	0.736679i
$973$	1.15797e6	−	351266.i	1.22313	−	0.371032i
$974$	236197.	−	667077.i	0.248975	−	0.703166i
$975$	−11632.5	−	28083.3i	−0.0122367	−	0.0295419i
$976$	−129938.	−	1.16146e6i	−0.136407	−	1.21928i
$977$	886992.	+	367404.i	0.929246	+	0.384906i	0.795392	−	0.606095i	$-0.207265\pi$
$977$	886992.	+	367404.i	0.929246	+	0.384906i	0.133854	+	0.991001i	$0.457265\pi$
$978$	289495.	+	260643.i	0.302666	+	0.272501i
$979$	173511.	+	92743.4i	0.181034	+	0.0967649i
$980$	282998.	−	191815.i	0.294667	−	0.199724i
$981$	−563019.	+	686041.i	−0.585039	+	0.712872i
$982$	−13105.0	+	27947.0i	−0.0135898	+	0.0289809i
$983$	−997162.	−	1.49236e6i	−1.03195	−	1.54442i	−0.824247	−	0.566231i	$-0.808401\pi$
$983$	−997162.	−	1.49236e6i	−1.03195	−	1.54442i	−0.207703	−	0.978192i	$-0.566599\pi$
$984$	−51469.1	−	106084.i	−0.0531565	−	0.109562i
$985$	204552.	−	306134.i	0.210830	−	0.315529i
$986$	−4585.90	−	1132.59i	−0.00471705	−	0.00116498i
$987$	54971.2	−	29382.7i	0.0564288	−	0.0301618i
$988$	167720.	−	52091.9i	0.171819	−	0.0533650i
$989$	−836260.	−	82364.4i	−0.854966	−	0.0842068i
$990$	193924.	+	28110.4i	0.197862	+	0.0286812i
$991$	−414567.	+	414567.i	−0.422131	+	0.422131i	−0.885937	−	0.463806i	$-0.846484\pi$
$991$	−414567.	+	414567.i	−0.422131	+	0.422131i	0.463806	+	0.885937i	$0.346484\pi$
$992$	−63406.5	+	31283.1i	−0.0644333	+	0.0317897i
$993$	496869.	−	496869.i	0.503899	−	0.503899i
$994$	31943.9	+	42774.8i	0.0323307	+	0.0432927i
$995$	417527.	+	41122.9i	0.421734	+	0.0415372i
$996$	−592811.	+	493110.i	−0.597582	+	0.497078i
$997$	−752132.	+	402023.i	−0.756665	+	0.404446i	−0.804150	−	0.594426i	$-0.797379\pi$
$997$	−752132.	+	402023.i	−0.756665	+	0.404446i	0.0474852	+	0.998872i	$0.484879\pi$
$998$	−811740.	+	490197.i	−0.814997	+	0.492164i
$999$	−400205.	+	598948.i	−0.401006	+	0.600148i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.5.l.a.3.7	✓	1008
128.43	odd	32	inner	128.5.l.a.43.7	yes	1008

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.5.l.a.3.7	✓	1008	1.1	even	1	trivial
128.5.l.a.43.7	yes	1008	128.43	odd	32	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	128.l (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.87689 + 0.984756i) q^{2} +(3.81952 - 3.13460i) q^{3} +(14.0605 - 7.63558i) q^{4} +(27.8176 + 8.43838i) q^{5} +(-11.7210 + 15.9138i) q^{6} +(7.96282 + 40.0318i) q^{7} +(-46.9918 + 43.4484i) q^{8} +(-11.0393 + 55.4983i) q^{9} +O(q^{10})\)	\(q+(-3.87689 + 0.984756i) q^{2} +(3.81952 - 3.13460i) q^{3} +(14.0605 - 7.63558i) q^{4} +(27.8176 + 8.43838i) q^{5} +(-11.7210 + 15.9138i) q^{6} +(7.96282 + 40.0318i) q^{7} +(-46.9918 + 43.4484i) q^{8} +(-11.0393 + 55.4983i) q^{9} +(-116.155 - 5.32109i) q^{10} +(2.91910 + 29.6381i) q^{11} +(29.7699 - 73.2382i) q^{12} +(-8.11634 - 26.7560i) q^{13} +(-70.2925 - 147.357i) q^{14} +(132.701 - 54.9664i) q^{15} +(139.396 - 214.720i) q^{16} +(27.2487 - 65.7842i) q^{17} +(-11.8542 - 226.032i) q^{18} +(-185.060 + 346.222i) q^{19} +(455.562 - 93.7555i) q^{20} +(155.898 + 127.942i) q^{21} +(-40.5034 - 112.029i) q^{22} +(-231.629 + 154.769i) q^{23} +(-43.2928 + 313.252i) q^{24} +(182.945 + 122.240i) q^{25} +(57.8143 + 95.7373i) q^{26} +(320.466 + 599.551i) q^{27} +(417.627 + 502.067i) q^{28} +(-1.62561 + 16.5051i) q^{29} +(-460.337 + 343.777i) q^{30} +(48.8233 + 48.8233i) q^{31} +(-328.975 + 969.717i) q^{32} +(104.053 + 104.053i) q^{33} +(-40.8588 + 281.871i) q^{34} +(-116.297 + 1180.78i) q^{35} +(268.543 + 864.626i) q^{36} +(499.498 + 934.495i) q^{37} +(376.511 - 1524.50i) q^{38} +(-114.870 - 76.7535i) q^{39} +(-1673.84 + 812.097i) q^{40} +(-310.025 + 207.152i) q^{41} +(-730.389 - 342.495i) q^{42} +(2331.72 + 1913.60i) q^{43} +(267.348 + 394.438i) q^{44} +(-775.403 + 1450.68i) q^{45} +(745.588 - 828.120i) q^{46} +(118.274 - 285.540i) q^{47} +(-140.636 - 1257.08i) q^{48} +(679.097 - 281.291i) q^{49} +(-829.632 - 293.754i) q^{50} +(-102.130 - 336.677i) q^{51} +(-318.417 - 314.230i) q^{52} +(-142.139 - 1443.16i) q^{53} +(-1832.82 - 2008.81i) q^{54} +(-168.895 + 849.094i) q^{55} +(-2113.51 - 1535.20i) q^{56} +(378.429 + 1902.49i) q^{57} +(-9.95121 - 65.5894i) q^{58} +(2790.26 + 846.416i) q^{59} +(1446.14 - 1786.10i) q^{60} +(3528.98 - 2896.16i) q^{61} +(-237.361 - 141.203i) q^{62} -2309.60 q^{63} +(320.466 - 4083.44i) q^{64} -812.777i q^{65} +(-505.869 - 300.935i) q^{66} +(-1275.06 - 1553.66i) q^{67} +(-119.169 - 1133.02i) q^{68} +(-399.570 + 1317.21i) q^{69} +(-711.912 - 4692.28i) q^{70} +(-320.710 + 63.7932i) q^{71} +(-1892.56 - 3087.61i) q^{72} +(2665.01 + 530.103i) q^{73} +(-2856.75 - 3131.05i) q^{74} +(1081.93 - 106.561i) q^{75} +(41.5731 + 6281.10i) q^{76} +(-1163.22 + 352.860i) q^{77} +(520.920 + 184.446i) q^{78} +(176.280 + 425.577i) q^{79} +(5689.55 - 4796.73i) q^{80} +(-1131.17 - 468.544i) q^{81} +(997.938 - 1108.40i) q^{82} +(-8601.87 - 4597.79i) q^{83} +(3168.91 + 608.560i) q^{84} +(1313.11 - 1600.02i) q^{85} +(-10924.3 - 5122.62i) q^{86} +(45.5279 + 68.1373i) q^{87} +(-1424.90 - 1265.92i) q^{88} +(3670.19 - 5492.83i) q^{89} +(1577.59 - 6387.69i) q^{90} +(1006.46 - 537.965i) q^{91} +(-2075.06 + 3944.75i) q^{92} +(339.523 + 33.4401i) q^{93} +(-177.350 + 1223.48i) q^{94} +(-8069.48 + 8069.48i) q^{95} +(1783.14 + 4735.05i) q^{96} +(12478.3 - 12478.3i) q^{97} +(-2355.78 + 1759.28i) q^{98} +(-1677.09 - 165.179i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1008 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 1008 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 1008 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 43072 q^{50} - 16 q^{51} - 17968 q^{52} - 16 q^{53} + 31088 q^{54} - 16 q^{55} + 49376 q^{56} - 16 q^{57} + 65504 q^{58} - 16 q^{59} + 63920 q^{60} - 16 q^{61} + 11792 q^{62} - 32 q^{63} - 24400 q^{64} - 70864 q^{66} - 16 q^{67} - 53296 q^{68} - 16 q^{69} - 122320 q^{70} - 16 q^{71} - 81664 q^{72} - 16 q^{73} - 33280 q^{74} - 16 q^{75} + 28272 q^{76} - 16 q^{77} + 99344 q^{78} - 16 q^{79} + 105248 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 1008 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 - 43072 * q^50 - 16 * q^51 - 17968 * q^52 - 16 * q^53 + 31088 * q^54 - 16 * q^55 + 49376 * q^56 - 16 * q^57 + 65504 * q^58 - 16 * q^59 + 63920 * q^60 - 16 * q^61 + 11792 * q^62 - 32 * q^63 - 24400 * q^64 - 70864 * q^66 - 16 * q^67 - 53296 * q^68 - 16 * q^69 - 122320 * q^70 - 16 * q^71 - 81664 * q^72 - 16 * q^73 - 33280 * q^74 - 16 * q^75 + 28272 * q^76 - 16 * q^77 + 99344 * q^78 - 16 * q^79 + 105248 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

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