LMFDB - Embedded newform 128.3.l.a.43.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,3,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, 3, names="a")

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

chi := DirichletCharacter("128.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 3 $
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:	$3.48774738381$
Analytic rank:	$0$
Dimension:	$496$
Relative dimension:	$31$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			43.13
Character	$\chi$	$=$	128.43
Dual form			128.3.l.a.3.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.630182 - 1.89812i) q^{2} +(-2.02704 - 1.66355i) q^{3} +(-3.20574 + 2.39233i) q^{4} +(-2.42484 + 0.735568i) q^{5} +(-1.88021 + 4.89591i) q^{6} +(-0.539873 + 2.71413i) q^{7} +(6.56113 + 4.57729i) q^{8} +(-0.414318 - 2.08292i) q^{9} +O(q^{10})$	\(q+(-0.630182 - 1.89812i) q^{2} +(-2.02704 - 1.66355i) q^{3} +(-3.20574 + 2.39233i) q^{4} +(-2.42484 + 0.735568i) q^{5} +(-1.88021 + 4.89591i) q^{6} +(-0.539873 + 2.71413i) q^{7} +(6.56113 + 4.57729i) q^{8} +(-0.414318 - 2.08292i) q^{9} +(2.92429 + 4.13911i) q^{10} +(-1.71554 + 17.4182i) q^{11} +(10.4779 + 0.483563i) q^{12} +(-0.950147 + 3.13221i) q^{13} +(5.49196 - 0.685648i) q^{14} +(6.13890 + 2.54282i) q^{15} +(4.55355 - 15.3384i) q^{16} +(-2.88229 - 6.95847i) q^{17} +(-3.69253 + 2.09904i) q^{18} +(12.6094 + 23.5904i) q^{19} +(6.01370 - 8.15906i) q^{20} +(5.60942 - 4.60353i) q^{21} +(34.1430 - 7.72032i) q^{22} +(-22.5962 - 15.0983i) q^{23} +(-5.68513 - 20.1931i) q^{24} +(-15.4479 + 10.3220i) q^{25} +(6.54409 - 0.170371i) q^{26} +(-13.7503 + 25.7251i) q^{27} +(-4.76238 - 9.99233i) q^{28} +(-0.0540521 - 0.548800i) q^{29} +(0.957951 - 13.2548i) q^{30} +(-29.1550 + 29.1550i) q^{31} +(-31.9837 + 1.02277i) q^{32} +(32.4535 - 32.4535i) q^{33} +(-11.3917 + 9.85604i) q^{34} +(-0.687316 - 6.97844i) q^{35} +(6.31121 + 5.68610i) q^{36} +(-0.0272610 + 0.0510018i) q^{37} +(36.8314 - 38.8004i) q^{38} +(7.13657 - 4.76851i) q^{39} +(-19.2766 - 6.27304i) q^{40} +(-31.0621 - 20.7550i) q^{41} +(-12.2730 - 7.74631i) q^{42} +(-30.8908 + 25.3514i) q^{43} +(-36.1704 - 59.9423i) q^{44} +(2.53678 + 4.74598i) q^{45} +(-14.4187 + 52.4051i) q^{46} +(-19.1031 - 46.1190i) q^{47} +(-34.7463 + 23.5164i) q^{48} +(38.1951 + 15.8209i) q^{49} +(29.3274 + 22.8174i) q^{50} +(-5.73322 + 18.8999i) q^{51} +(-4.44736 - 12.3141i) q^{52} +(0.466326 - 4.73468i) q^{53} +(57.4946 + 9.88835i) q^{54} +(-8.65234 - 43.4983i) q^{55} +(-15.9655 + 15.3366i) q^{56} +(13.6842 - 68.7950i) q^{57} +(-1.00763 + 0.448441i) q^{58} +(18.9420 - 5.74600i) q^{59} +(-25.7630 + 6.53465i) q^{60} +(-33.0210 - 27.0997i) q^{61} +(73.7127 + 36.9668i) q^{62} +5.87697 q^{63} +(22.0969 + 60.0644i) q^{64} -8.29403i q^{65} +(-82.0522 - 41.1491i) q^{66} +(28.9288 - 35.2498i) q^{67} +(25.8868 + 15.4117i) q^{68} +(20.6867 + 68.1948i) q^{69} +(-12.8128 + 5.70230i) q^{70} +(64.2669 + 12.7835i) q^{71} +(6.81571 - 15.5627i) q^{72} +(76.8910 - 15.2946i) q^{73} +(0.113987 + 0.0196043i) q^{74} +(48.4847 + 4.77532i) q^{75} +(-96.8584 - 45.4592i) q^{76} +(-46.3490 - 14.0598i) q^{77} +(-13.5486 - 10.5411i) q^{78} +(-34.1007 + 82.3263i) q^{79} +(0.240774 + 40.5425i) q^{80} +(53.0088 - 21.9570i) q^{81} +(-19.8208 + 72.0391i) q^{82} +(0.388254 - 0.207526i) q^{83} +(-6.96919 + 28.1773i) q^{84} +(12.1075 + 14.7531i) q^{85} +(67.5870 + 42.6585i) q^{86} +(-0.803389 + 1.20236i) q^{87} +(-90.9839 + 106.430i) q^{88} +(-10.5423 - 15.7777i) q^{89} +(7.40983 - 7.80596i) q^{90} +(-7.98826 - 4.26982i) q^{91} +(108.558 - 5.65627i) q^{92} +(107.599 - 10.5976i) q^{93} +(-75.5011 + 65.3235i) q^{94} +(-47.9281 - 47.9281i) q^{95} +(66.5335 + 51.1331i) q^{96} +(113.647 + 113.647i) q^{97} +(5.96019 - 82.4690i) q^{98} +(36.9914 - 3.64333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 496 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}) $ 496 * 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	\( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 640 q^{50} - 16 q^{51} - 1072 q^{52} - 16 q^{53} - 1168 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 736 q^{58} - 16 q^{59} - 592 q^{60} - 16 q^{61} - 112 q^{62} - 32 q^{63} + 176 q^{64} + 560 q^{66} - 16 q^{67} + 464 q^{68} - 16 q^{69} + 1328 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 1216 q^{74} - 16 q^{75} + 1648 q^{76} - 16 q^{77} + 1424 q^{78} - 16 q^{79} + 800 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 496 * 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 - 640 * q^50 - 16 * q^51 - 1072 * q^52 - 16 * q^53 - 1168 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 736 * q^58 - 16 * q^59 - 592 * q^60 - 16 * q^61 - 112 * q^62 - 32 * q^63 + 176 * q^64 + 560 * q^66 - 16 * q^67 + 464 * q^68 - 16 * q^69 + 1328 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 1216 * q^74 - 16 * q^75 + 1648 * q^76 - 16 * q^77 + 1424 * q^78 - 16 * q^79 + 800 * 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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{29}{32}\right)$	$-1$

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 $

$2$	−0.630182	−	1.89812i	−0.315091	−	0.949061i
$2$	−0.630182	−	1.89812i	−0.315091	−	0.949061i
$3$	−2.02704	−	1.66355i	−0.675680	−	0.554516i	0.232759	−	0.972534i	$-0.425225\pi$
$3$	−2.02704	−	1.66355i	−0.675680	−	0.554516i	−0.908438	+	0.418019i	$0.862725\pi$
$4$	−3.20574	+	2.39233i	−0.801435	+	0.598082i
$5$	−2.42484	+	0.735568i	−0.484969	+	0.147114i	−0.523295	−	0.852152i	$-0.675297\pi$
$5$	−2.42484	+	0.735568i	−0.484969	+	0.147114i	0.0383263	+	0.999265i	$0.487797\pi$
$6$	−1.88021	+	4.89591i	−0.313369	+	0.815985i
$7$	−0.539873	+	2.71413i	−0.0771247	+	0.387732i	0.922872	+	0.385107i	$0.125836\pi$
$7$	−0.539873	+	2.71413i	−0.0771247	+	0.387732i	−0.999997	+	0.00262495i	$0.999164\pi$
$8$	6.56113	+	4.57729i	0.820141	+	0.572161i
$9$	−0.414318	−	2.08292i	−0.0460353	−	0.231435i
$10$	2.92429	+	4.13911i	0.292429	+	0.413911i
$11$	−1.71554	+	17.4182i	−0.155958	+	1.58347i	0.524969	+	0.851121i	$0.324077\pi$
$11$	−1.71554	+	17.4182i	−0.155958	+	1.58347i	−0.680928	+	0.732351i	$0.738423\pi$
$12$	10.4779	+	0.483563i	0.873159	+	0.0402969i
$13$	−0.950147	+	3.13221i	−0.0730882	+	0.240940i	−0.985871	−	0.167505i	$-0.946429\pi$
$13$	−0.950147	+	3.13221i	−0.0730882	+	0.240940i	0.912783	+	0.408445i	$0.133929\pi$
$14$	5.49196	−	0.685648i	0.392283	−	0.0489749i
$15$	6.13890	+	2.54282i	0.409260	+	0.169521i
$16$	4.55355	−	15.3384i	0.284597	−	0.958647i
$17$	−2.88229	−	6.95847i	−0.169547	−	0.409321i	0.816153	−	0.577836i	$-0.196103\pi$
$17$	−2.88229	−	6.95847i	−0.169547	−	0.409321i	−0.985699	+	0.168515i	$0.946103\pi$
$18$	−3.69253	+	2.09904i	−0.205141	+	0.116613i
$19$	12.6094	+	23.5904i	0.663650	+	1.24160i	0.958236	+	0.285978i	$0.0923183\pi$
$19$	12.6094	+	23.5904i	0.663650	+	1.24160i	−0.294586	+	0.955625i	$0.595182\pi$
$20$	6.01370	−	8.15906i	0.300685	−	0.407953i
$21$	5.60942	−	4.60353i	0.267115	−	0.219216i
$22$	34.1430	−	7.72032i	1.55195	−	0.350924i
$23$	−22.5962	−	15.0983i	−0.982444	−	0.656448i	−0.0429732	−	0.999076i	$-0.513683\pi$
$23$	−22.5962	−	15.0983i	−0.982444	−	0.656448i	−0.939471	+	0.342628i	$0.888683\pi$
$24$	−5.68513	−	20.1931i	−0.236880	−	0.841379i
$25$	−15.4479	+	10.3220i	−0.617918	+	0.412879i
$26$	6.54409	−	0.170371i	0.251696	−	0.00655272i
$27$	−13.7503	+	25.7251i	−0.509272	+	0.952781i
$28$	−4.76238	−	9.99233i	−0.170085	−	0.356869i
$29$	−0.0540521	−	0.548800i	−0.00186386	−	0.0189241i	0.994208	−	0.107475i	$-0.0342765\pi$
$29$	−0.0540521	−	0.548800i	−0.00186386	−	0.0189241i	−0.996072	+	0.0885506i	$0.971776\pi$
$30$	0.957951	−	13.2548i	0.0319317	−	0.441828i
$31$	−29.1550	+	29.1550i	−0.940484	+	0.940484i	−0.998326	−	0.0578418i	$-0.981578\pi$
$31$	−29.1550	+	29.1550i	−0.940484	+	0.940484i	0.0578418	+	0.998326i	$0.481578\pi$
$32$	−31.9837	+	1.02277i	−0.999489	+	0.0319617i
$33$	32.4535	−	32.4535i	0.983438	−	0.983438i
$34$	−11.3917	+	9.85604i	−0.335049	+	0.289884i
$35$	−0.687316	−	6.97844i	−0.0196376	−	0.199384i
$36$	6.31121	+	5.68610i	0.175311	+	0.157947i
$37$	−0.0272610	+	0.0510018i	−0.000736784	+	0.00137843i	−0.882289	−	0.470707i	$-0.843999\pi$
$37$	−0.0272610	+	0.0510018i	−0.000736784	+	0.00137843i	0.881553	+	0.472086i	$0.156499\pi$
$38$	36.8314	−	38.8004i	0.969247	−	1.02106i
$39$	7.13657	−	4.76851i	0.182989	−	0.122269i
$40$	−19.2766	−	6.27304i	−0.481915	−	0.156826i
$41$	−31.0621	−	20.7550i	−0.757612	−	0.506220i	0.115758	−	0.993277i	$-0.463070\pi$
$41$	−31.0621	−	20.7550i	−0.757612	−	0.506220i	−0.873370	+	0.487057i	$0.838070\pi$
$42$	−12.2730	−	7.74631i	−0.292215	−	0.184436i
$43$	−30.8908	+	25.3514i	−0.718391	+	0.589568i	−0.920940	−	0.389704i	$-0.872577\pi$
$43$	−30.8908	+	25.3514i	−0.718391	+	0.589568i	0.202549	+	0.979272i	$0.435077\pi$
$44$	−36.1704	−	59.9423i	−0.822055	−	1.36233i
$45$	2.53678	+	4.74598i	0.0563729	+	0.105466i
$46$	−14.4187	+	52.4051i	−0.313450	+	1.13924i
$47$	−19.1031	−	46.1190i	−0.406450	−	0.981256i	−0.986064	−	0.166365i	$-0.946797\pi$
$47$	−19.1031	−	46.1190i	−0.406450	−	0.981256i	0.579615	−	0.814891i	$-0.303203\pi$
$48$	−34.7463	+	23.5164i	−0.723881	+	0.489925i
$49$	38.1951	+	15.8209i	0.779491	+	0.322876i
$50$	29.3274	+	22.8174i	0.586548	+	0.456347i
$51$	−5.73322	+	18.8999i	−0.112416	+	0.370586i
$52$	−4.44736	−	12.3141i	−0.0855261	−	0.236810i
$53$	0.466326	−	4.73468i	0.00879860	−	0.0893337i	−0.989783	−	0.142585i	$-0.954459\pi$
$53$	0.466326	−	4.73468i	0.00879860	−	0.0893337i	0.998581	+	0.0532515i	$0.0169585\pi$
$54$	57.4946	+	9.88835i	1.06471	+	0.183118i
$55$	−8.65234	−	43.4983i	−0.157315	−	0.790878i
$56$	−15.9655	+	15.3366i	−0.285098	+	0.273867i
$57$	13.6842	−	68.7950i	0.240073	−	1.20693i
$58$	−1.00763	+	0.448441i	−0.0173729	+	0.00773175i
$59$	18.9420	−	5.74600i	0.321051	−	0.0973898i	−0.125646	−	0.992075i	$-0.540100\pi$
$59$	18.9420	−	5.74600i	0.321051	−	0.0973898i	0.446697	+	0.894685i	$0.352600\pi$
$60$	−25.7630	+	6.53465i	−0.429383	+	0.108911i
$61$	−33.0210	−	27.0997i	−0.541329	−	0.444257i	0.323570	−	0.946204i	$-0.395117\pi$
$61$	−33.0210	−	27.0997i	−0.541329	−	0.444257i	−0.864898	+	0.501948i	$0.832617\pi$
$62$	73.7127	+	36.9668i	1.18892	+	0.596239i
$63$	5.87697			0.0932853
$64$	22.0969	+	60.0644i	0.345264	+	0.938506i
$65$		−	8.29403i		−	0.127600i
$66$	−82.0522	−	41.1491i	−1.24322	−	0.623471i
$67$	28.9288	−	35.2498i	0.431772	−	0.526116i	−0.510988	−	0.859588i	$-0.670720\pi$
$67$	28.9288	−	35.2498i	0.431772	−	0.526116i	0.942760	+	0.333472i	$0.108220\pi$
$68$	25.8868	+	15.4117i	0.380688	+	0.226642i
$69$	20.6867	+	68.1948i	0.299807	+	0.988330i
$70$	−12.8128	+	5.70230i	−0.183040	+	0.0814614i
$71$	64.2669	+	12.7835i	0.905167	+	0.180049i	0.625661	−	0.780095i	$-0.284829\pi$
$71$	64.2669	+	12.7835i	0.905167	+	0.180049i	0.279506	+	0.960144i	$0.409829\pi$
$72$	6.81571	−	15.5627i	0.0946627	−	0.216149i
$73$	76.8910	−	15.2946i	1.05330	−	0.209515i	0.362072	−	0.932150i	$-0.382069\pi$
$73$	76.8910	−	15.2946i	1.05330	−	0.209515i	0.691229	+	0.722635i	$0.257069\pi$
$74$	0.113987	+	0.0196043i	0.00154037	+	0.000264924i
$75$	48.4847	+	4.77532i	0.646462	+	0.0636710i
$76$	−96.8584	−	45.4592i	−1.27445	−	0.598147i
$77$	−46.3490	−	14.0598i	−0.601935	−	0.182595i
$78$	−13.5486	−	10.5411i	−0.173699	−	0.135142i
$79$	−34.1007	+	82.3263i	−0.431654	+	1.04210i	0.547100	+	0.837067i	$0.315732\pi$
$79$	−34.1007	+	82.3263i	−0.431654	+	1.04210i	−0.978754	+	0.205038i	$0.934268\pi$
$80$	0.240774	+	40.5425i	0.00300967	+	0.506782i
$81$	53.0088	−	21.9570i	0.654430	−	0.271074i
$82$	−19.8208	+	72.0391i	−0.241717	+	0.878526i
$83$	0.388254	−	0.207526i	0.00467776	−	0.00250032i	−0.469056	−	0.883168i	$-0.655406\pi$
$83$	0.388254	−	0.207526i	0.00467776	−	0.00250032i	0.473734	+	0.880668i	$0.342906\pi$
$84$	−6.96919	+	28.1773i	−0.0829666	+	0.335444i
$85$	12.1075	+	14.7531i	0.142441	+	0.173565i
$86$	67.5870	+	42.6585i	0.785895	+	0.496029i
$87$	−0.803389	+	1.20236i	−0.00923436	+	0.0138202i
$88$	−90.9839	+	106.430i	−1.03391	+	1.20944i
$89$	−10.5423	−	15.7777i	−0.118453	−	0.177277i	0.767505	−	0.641043i	$-0.221498\pi$
$89$	−10.5423	−	15.7777i	−0.118453	−	0.177277i	−0.885958	+	0.463766i	$0.846498\pi$
$90$	7.40983	−	7.80596i	0.0823314	−	0.0867329i
$91$	−7.98826	−	4.26982i	−0.0877831	−	0.0469211i
$92$	108.558	−	5.65627i	1.17998	−	0.0614812i
$93$	107.599	−	10.5976i	1.15698	−	0.113953i
$94$	−75.5011	+	65.3235i	−0.803204	+	0.694931i
$95$	−47.9281	−	47.9281i	−0.504506	−	0.504506i
$96$	66.5335	+	51.1331i	0.693058	+	0.532637i
$97$	113.647	+	113.647i	1.17161	+	1.17161i	0.981825	+	0.189789i	$0.0607806\pi$
$97$	113.647	+	113.647i	1.17161	+	1.17161i	0.189789	+	0.981825i	$0.439219\pi$
$98$	5.96019	−	82.4690i	0.0608182	−	0.841521i
$99$	36.9914	−	3.64333i	0.373650	−	0.0368014i
$100$	24.8285	−	70.0461i	0.248285	−	0.700461i
$101$	−124.689	−	66.6475i	−1.23454	−	0.659876i	−0.280587	−	0.959829i	$-0.590529\pi$
$101$	−124.689	−	66.6475i	−1.23454	−	0.659876i	−0.953954	+	0.299953i	$0.903029\pi$
$102$	39.4873	−	1.02802i	0.387131	−	0.0100787i
$103$	−58.7335	−	87.9009i	−0.570228	−	0.853407i	0.428515	−	0.903535i	$-0.359037\pi$
$103$	−58.7335	−	87.9009i	−0.570228	−	0.853407i	−0.998743	+	0.0501281i	$0.984037\pi$
$104$	−20.5711	+	16.2018i	−0.197799	+	0.155786i
$105$	−10.2158	+	15.2890i	−0.0972929	+	0.145609i
$106$	−9.28088	+	2.09857i	−0.0875555	+	0.0197978i
$107$	122.739	+	149.558i	1.14709	+	1.39774i	0.903893	+	0.427759i	$0.140697\pi$
$107$	122.739	+	149.558i	1.14709	+	1.39774i	0.243199	+	0.969976i	$0.421803\pi$
$108$	−17.4628	−	115.363i	−0.161692	−	1.06818i
$109$	−139.755	+	74.7008i	−1.28216	+	0.685328i	−0.964802	−	0.262978i	$-0.915295\pi$
$109$	−139.755	+	74.7008i	−1.28216	+	0.685328i	−0.317357	+	0.948306i	$0.602795\pi$
$110$	−77.1125	+	43.8350i	−0.701023	+	0.398500i
$111$	0.140103	−	0.0580326i	0.00126219	−	0.000522816i
$112$	39.1719	+	20.6397i	0.349749	+	0.184283i
$113$	37.9796	−	91.6908i	0.336102	−	0.811423i	−0.661980	−	0.749522i	$-0.730284\pi$
$113$	37.9796	−	91.6908i	0.336102	−	0.811423i	0.998082	−	0.0619013i	$-0.0197164\pi$
$114$	−139.205	+	17.3791i	−1.22110	+	0.152449i
$115$	65.8981	+	19.9900i	0.573027	+	0.173826i
$116$	1.48619	+	1.63000i	0.0128119	+	0.0140517i
$117$	6.91780	+	0.681344i	0.0591265	+	0.00582345i
$118$	−22.8435	−	32.3333i	−0.193589	−	0.274011i
$119$	20.4422	−	4.06621i	0.171783	−	0.0341698i
$120$	28.6389	+	44.7833i	0.238658	+	0.373194i
$121$	−181.775	−	36.1573i	−1.50227	−	0.298821i
$122$	−30.6292	+	79.7557i	−0.251059	+	0.653735i
$123$	28.4371	+	93.7445i	0.231196	+	0.762150i
$124$	23.7151	−	163.212i	0.191251	−	1.31622i
$125$	70.0544	−	85.3615i	0.560435	−	0.682892i
$126$	−3.70356	−	11.1552i	−0.0293934	−	0.0885335i
$127$			65.4306i			0.515202i	0.966251	+	0.257601i	$0.0829320\pi$
$127$			65.4306i			0.515202i	−0.966251	+	0.257601i	$0.917068\pi$
$128$	100.084	−	79.7941i	0.781910	−	0.623391i
$129$	104.790			0.812327
$130$	−15.7431	+	5.22675i	−0.121101	+	0.0402058i
$131$	−126.054	−	103.450i	−0.962244	−	0.789693i	0.0154171	−	0.999881i	$-0.495092\pi$
$131$	−126.054	−	103.450i	−0.962244	−	0.789693i	−0.977661	+	0.210188i	$0.932592\pi$
$132$	−26.3981	+	181.677i	−0.199986	+	1.37634i
$133$	−70.8349	+	21.4875i	−0.532593	+	0.161560i
$134$	−85.1388	−	32.6965i	−0.635364	−	0.244004i
$135$	14.4199	−	72.4936i	0.106814	−	0.536989i
$136$	12.9398	−	58.8485i	0.0951457	−	0.432709i
$137$	−2.02256	−	10.1681i	−0.0147632	−	0.0742198i	0.972701	−	0.232061i	$-0.0745467\pi$
$137$	−2.02256	−	10.1681i	−0.0147632	−	0.0742198i	−0.987465	+	0.157841i	$0.949547\pi$
$138$	116.406	−	82.2409i	0.843519	−	0.595949i
$139$	−2.85176	+	28.9544i	−0.0205162	+	0.208305i	0.979461	+	0.201631i	$0.0646243\pi$
$139$	−2.85176	+	28.9544i	−0.0205162	+	0.208305i	−0.999978	+	0.00667359i	$0.997876\pi$
$140$	18.8981	+	20.7268i	0.134986	+	0.148048i
$141$	−37.9984	+	125.264i	−0.269492	+	0.888397i
$142$	−16.2352	−	130.042i	−0.114333	−	0.915791i
$143$	−52.9275	−	21.9233i	−0.370122	−	0.153310i
$144$	−33.8351	−	3.12970i	−0.234966	−	0.0217340i
$145$	0.534747	+	1.29099i	0.00368791	+	0.00890341i
$146$	−77.4863	−	136.310i	−0.530728	−	0.933632i
$147$	−51.1041	−	95.6090i	−0.347647	−	0.650401i
$148$	−0.0346212	−	0.228716i	−0.000233927	−	0.00154538i
$149$	−150.951	+	123.882i	−1.01309	+	0.831423i	−0.985752	−	0.168203i	$-0.946203\pi$
$149$	−150.951	+	123.882i	−1.01309	+	0.831423i	−0.0273393	+	0.999626i	$0.508703\pi$
$150$	−21.4900	−	95.0392i	−0.143267	−	0.633595i
$151$	−140.980	−	94.1996i	−0.933641	−	0.623839i	−0.00707617	−	0.999975i	$-0.502252\pi$
$151$	−140.980	−	94.1996i	−0.933641	−	0.623839i	−0.926564	+	0.376136i	$0.877252\pi$
$152$	−25.2486	+	212.497i	−0.166109	+	1.39800i
$153$	−13.2997	+	8.88658i	−0.0869262	+	0.0580822i
$154$	2.52106	+	96.8363i	0.0163705	+	0.628807i
$155$	49.2508	−	92.1418i	0.317747	−	0.594463i
$156$	−11.4702	+	32.3596i	−0.0735268	+	0.207433i
$157$	−7.84770	−	79.6790i	−0.0499853	−	0.507510i	−0.987282	−	0.158978i	$-0.949180\pi$
$157$	−7.84770	−	79.6790i	−0.0499853	−	0.507510i	0.937297	−	0.348532i	$-0.113320\pi$
$158$	177.755	+	12.8467i	1.12503	+	0.0813081i
$159$	−8.82163	+	8.82163i	−0.0554820	+	0.0554820i
$160$	76.8030	−	26.0062i	0.480019	−	0.162539i
$161$	53.1778	−	53.1778i	0.330297	−	0.330297i
$162$	−75.0822	−	86.7803i	−0.463470	−	0.535681i
$163$	−18.0851	−	183.621i	−0.110952	−	1.12651i	−0.875924	−	0.482448i	$-0.839748\pi$
$163$	−18.0851	−	183.621i	−0.110952	−	1.12651i	0.764973	−	0.644063i	$-0.222752\pi$
$164$	149.230	−	7.77544i	0.909938	−	0.0474112i
$165$	−54.8228	+	102.566i	−0.332259	+	0.621614i
$166$	−0.638581	−	0.606175i	−0.00384688	−	0.00365166i
$167$	180.808	−	120.812i	1.08268	−	0.723426i	0.119653	−	0.992816i	$-0.461822\pi$
$167$	180.808	−	120.812i	1.08268	−	0.723426i	0.963031	+	0.269390i	$0.0868219\pi$
$168$	57.8758	−	4.52845i	0.344499	−	0.0269551i
$169$	131.610	+	87.9392i	0.778760	+	0.520351i
$170$	20.3732	−	32.2787i	0.119842	−	0.189875i
$171$	43.9126	−	36.0382i	0.256799	−	0.210750i
$172$	38.3790	−	155.171i	0.223134	−	0.902157i
$173$	−66.4439	−	124.308i	−0.384069	−	0.718543i	0.613390	−	0.789780i	$-0.289805\pi$
$173$	−66.4439	−	124.308i	−0.384069	−	0.718543i	−0.997459	+	0.0712372i	$0.977305\pi$
$174$	2.78850	+	0.767227i	0.0160259	+	0.00440935i
$175$	−19.6752	−	47.5002i	−0.112430	−	0.271430i
$176$	259.355	+	105.628i	1.47361	+	0.600160i
$177$	−47.9550	−	19.8636i	−0.270932	−	0.112224i
$178$	−23.3044	+	29.9534i	−0.130923	+	0.168277i
$179$	−39.1538	+	129.073i	−0.218736	+	0.721077i	0.777055	+	0.629432i	$0.216712\pi$
$179$	−39.1538	+	129.073i	−0.218736	+	0.721077i	−0.995792	+	0.0916449i	$0.970788\pi$
$180$	−19.4862	−	9.14558i	−0.108257	−	0.0508088i
$181$	−21.4804	+	218.094i	−0.118676	+	1.20494i	0.732762	+	0.680485i	$0.238231\pi$
$181$	−21.4804	+	218.094i	−0.118676	+	1.20494i	−0.851438	+	0.524455i	$0.824269\pi$
$182$	−3.07057	+	17.8535i	−0.0168713	+	0.0980960i
$183$	21.8533	+	109.864i	0.119417	+	0.600351i
$184$	−79.1475	−	202.491i	−0.430149	−	1.10050i
$185$	0.0285884	−	0.143724i	0.000154532	−	0.000776884i
$186$	−87.9225	−	197.558i	−0.472702	−	1.06214i
$187$	126.149	−	38.2667i	0.674591	−	0.204635i
$188$	171.571	+	102.145i	0.912614	+	0.543323i
$189$	−62.3976	−	51.2084i	−0.330146	−	0.270944i
$190$	−60.7700	+	121.177i	−0.319842	+	0.637773i
$191$	−88.7294			−0.464552			−0.232276	−	0.972650i	$-0.574617\pi$
$191$	−88.7294			−0.464552			−0.232276	+	0.972650i	$0.574617\pi$
$192$	55.1287	−	158.512i	0.287129	−	0.825583i
$193$			280.329i			1.45248i	0.687442	+	0.726240i	$0.258734\pi$
$193$			280.329i			1.45248i	−0.687442	+	0.726240i	$0.741266\pi$
$194$	144.097	−	287.333i	0.742769	−	1.48110i
$195$	−13.7975	+	16.8123i	−0.0707565	+	0.0862170i
$196$	−160.292	+	40.6573i	−0.817818	+	0.207435i
$197$	105.186	+	346.752i	0.533939	+	1.76016i	0.642727	+	0.766095i	$0.277803\pi$
$197$	105.186	+	346.752i	0.533939	+	1.76016i	−0.108788	+	0.994065i	$0.534697\pi$
$198$	−30.2268	−	67.9182i	−0.152661	−	0.343021i
$199$	357.966	+	71.2039i	1.79883	+	0.357809i	0.977217	−	0.212243i	$-0.0680769\pi$
$199$	357.966	+	71.2039i	1.79883	+	0.357809i	0.821609	+	0.570052i	$0.193077\pi$
$200$	−148.603	−	2.98578i	−0.743013	−	0.0149289i
$201$	−117.279	+	23.3283i	−0.583480	+	0.116061i
$202$	−47.9285	+	278.674i	−0.237270	+	1.37958i
$203$	1.51869	+	0.149578i	0.00748125	+	0.000736838i
$204$	−26.8355	−	74.3039i	−0.131547	−	0.364235i
$205$	90.5874	+	27.4794i	0.441890	+	0.134046i
$206$	−129.834	+	166.877i	−0.630262	+	0.810082i
$207$	−22.0865	+	53.3215i	−0.106698	+	0.257592i
$208$	43.7165	+	28.8364i	0.210175	+	0.138636i
$209$	−432.535	+	179.162i	−2.06954	+	0.857233i
$210$	35.4581	+	9.75592i	0.168848	+	0.0464568i
$211$	−270.913	+	144.806i	−1.28395	+	0.686285i	−0.965190	−	0.261550i	$-0.915766\pi$
$211$	−270.913	+	144.806i	−1.28395	+	0.686285i	−0.318759	+	0.947836i	$0.603266\pi$
$212$	9.83199	+	16.2938i	0.0463773	+	0.0768574i
$213$	−109.006	−	132.824i	−0.511763	−	0.623585i
$214$	206.531	−	327.222i	0.965098	−	1.52907i
$215$	56.2577	−	84.1955i	0.261664	−	0.391607i
$216$	−207.969	+	105.846i	−0.962819	+	0.490029i
$217$	−63.3903	−	94.8703i	−0.292121	−	0.437190i
$218$	229.863	+	218.198i	1.05442	+	1.00091i
$219$	−181.304	−	96.9092i	−0.827874	−	0.442508i
$220$	131.799	+	118.745i	0.599087	+	0.539750i
$221$	24.5340	−	2.41639i	0.111014	−	0.0109339i
$222$	−0.198443	−	0.229362i	−0.000893889	−	0.00103316i
$223$	−236.549	−	236.549i	−1.06076	−	1.06076i	−0.998031	−	0.0627254i	$-0.980021\pi$
$223$	−236.549	−	236.549i	−1.06076	−	1.06076i	−0.0627254	−	0.998031i	$-0.519979\pi$
$224$	14.4912	−	87.3598i	0.0646928	−	0.389999i
$225$	27.9002	+	27.9002i	0.124001	+	0.124001i
$226$	−197.974	−	14.3080i	−0.875993	−	0.0633096i
$227$	76.3084	−	7.51573i	0.336161	−	0.0331089i	0.0714712	−	0.997443i	$-0.477231\pi$
$227$	76.3084	−	7.51573i	0.336161	−	0.0331089i	0.264689	+	0.964334i	$0.414731\pi$
$228$	120.712	+	253.276i	0.529440	+	1.11086i
$229$	347.586	+	185.789i	1.51784	+	0.811304i	0.999049	−	0.0435945i	$-0.0138810\pi$
$229$	347.586	+	185.789i	1.51784	+	0.811304i	0.518795	+	0.854899i	$0.326381\pi$
$230$	−3.58440	−	137.680i	−0.0155843	−	0.598609i
$231$	70.5620	+	105.604i	0.305463	+	0.457158i
$232$	2.15737	−	3.84816i	0.00929902	−	0.0165869i
$233$	−235.394	+	352.292i	−1.01027	+	1.51198i	−0.158986	+	0.987281i	$0.550823\pi$
$233$	−235.394	+	352.292i	−1.01027	+	1.51198i	−0.851287	+	0.524700i	$0.824177\pi$
$234$	−3.06620	−	13.5602i	−0.0131034	−	0.0579496i
$235$	80.2458	+	97.7797i	0.341471	+	0.416084i
$236$	−46.9769	+	63.7357i	−0.199055	+	0.270066i
$237$	206.077	−	110.150i	0.869523	−	0.464770i
$238$	−20.6005	−	36.2394i	−0.0865567	−	0.152266i
$239$	−165.184	+	68.4214i	−0.691146	+	0.286282i	−0.700477	−	0.713675i	$-0.747030\pi$
$239$	−165.184	+	68.4214i	−0.691146	+	0.286282i	0.00933182	+	0.999956i	$0.497030\pi$
$240$	66.9564	−	82.5819i	0.278985	−	0.344091i
$241$	79.7412	−	192.512i	0.330876	−	0.798806i	−0.667647	−	0.744478i	$-0.732698\pi$
$241$	79.7412	−	192.512i	0.330876	−	0.798806i	0.998523	−	0.0543279i	$-0.0173016\pi$
$242$	45.9204	+	367.817i	0.189754	+	1.51991i
$243$	107.243	+	32.5317i	0.441328	+	0.133875i
$244$	170.688	+	7.87739i	0.699542	+	0.0322844i
$245$	−104.254	−	10.2682i	−0.425528	−	0.0419109i
$246$	160.018	−	113.053i	0.650480	−	0.459566i
$247$	−85.8711	+	17.0808i	−0.347656	+	0.0691531i
$248$	−324.741	+	57.8390i	−1.30944	+	0.233222i
$249$	−1.13224	−	0.225216i	−0.00454714	−	0.000904481i
$250$	−206.174	−	79.1785i	−0.824695	−	0.316714i
$251$	61.2009	+	201.752i	0.243828	+	0.803794i	0.990369	+	0.138454i	$0.0442133\pi$
$251$	61.2009	+	201.752i	0.243828	+	0.803794i	−0.746541	+	0.665340i	$0.768287\pi$
$252$	−18.8401	+	14.0596i	−0.0747621	+	0.0557922i
$253$	301.750	−	367.683i	1.19269	−	1.45329i
$254$	124.195	−	41.2332i	0.488958	−	0.162336i
$255$		−	50.0465i		−	0.196261i
$256$	−214.530	−	139.688i	−0.838010	−	0.545656i
$257$	12.9544			0.0504061			0.0252030	−	0.999682i	$-0.491977\pi$
$257$	12.9544			0.0504061			0.0252030	+	0.999682i	$0.491977\pi$
$258$	−66.0369	−	198.905i	−0.255957	−	0.770948i
$259$	−0.123708	−	0.101524i	−0.000477636	−	0.000391986i
$260$	19.8420	+	26.5885i	0.0763155	+	0.102263i
$261$	−1.12071	+	0.339963i	−0.00429391	+	0.00130254i
$262$	−116.923	+	304.458i	−0.446273	+	1.16205i
$263$	11.9887	−	60.2710i	0.0455842	−	0.229167i	−0.951277	−	0.308338i	$-0.900227\pi$
$263$	11.9887	−	60.2710i	0.0455842	−	0.229167i	0.996861	+	0.0791706i	$0.0252272\pi$
$264$	361.480	−	64.3826i	1.36924	−	0.243873i
$265$	2.35192	+	11.8239i	0.00887515	+	0.0446184i
$266$	85.4249	+	120.912i	0.321146	+	0.454557i
$267$	−4.87725	+	49.5195i	−0.0182669	+	0.185466i
$268$	−8.40907	+	182.209i	−0.0313771	+	0.679883i
$269$	56.1905	−	185.235i	0.208887	−	0.688607i	−0.788412	−	0.615148i	$-0.789096\pi$
$269$	56.1905	−	185.235i	0.208887	−	0.688607i	0.997298	−	0.0734589i	$-0.0234038\pi$
$270$	−146.689	+	18.3135i	−0.543292	+	0.0678277i
$271$	354.000	+	146.631i	1.30627	+	0.541075i	0.923794	−	0.382889i	$-0.125071\pi$
$271$	354.000	+	146.631i	1.30627	+	0.541075i	0.382478	+	0.923965i	$0.375071\pi$
$272$	−119.856	+	12.5239i	−0.440647	+	0.0460438i
$273$	9.08948	+	21.9439i	0.0332948	+	0.0803807i
$274$	−18.0257	+	10.2468i	−0.0657873	+	0.0373972i
$275$	−153.289	−	286.783i	−0.557413	−	1.04285i
$276$	−229.460	−	169.125i	−0.831378	−	0.612773i
$277$	373.611	−	306.615i	1.34878	−	1.10691i	0.364323	−	0.931272i	$-0.381300\pi$
$277$	373.611	−	306.615i	1.34878	−	1.10691i	0.984454	−	0.175641i	$-0.0561997\pi$
$278$	56.7561	−	12.8336i	0.204159	−	0.0461639i
$279$	72.8068	+	48.6480i	0.260956	+	0.174366i
$280$	27.4328	−	48.9325i	0.0979741	−	0.174759i
$281$	243.548	−	162.734i	0.866720	−	0.579124i	−0.0407837	−	0.999168i	$-0.512985\pi$
$281$	243.548	−	162.734i	0.866720	−	0.579124i	0.907504	+	0.420044i	$0.137985\pi$
$282$	261.712	−	6.81349i	0.928058	−	0.0241613i
$283$	−1.05914	+	1.98150i	−0.00374253	+	0.00700177i	−0.883786	−	0.467892i	$-0.845014\pi$
$283$	−1.05914	+	1.98150i	−0.00374253	+	0.00700177i	0.880043	+	0.474894i	$0.157514\pi$
$284$	−236.605	+	112.767i	−0.833117	+	0.397066i
$285$	17.4214	+	176.883i	0.0611278	+	0.620641i
$286$	−8.25912	+	114.279i	−0.0288780	+	0.399575i
$287$	73.1013	−	73.1013i	0.254708	−	0.254708i
$288$	15.3817	+	66.1955i	0.0534088	+	0.229845i
$289$	164.241	−	164.241i	0.568309	−	0.568309i
$290$	2.11348	−	1.82858i	0.00728785	−	0.00630544i
$291$	−41.3095	−	419.423i	−0.141957	−	1.44131i
$292$	−209.903	+	232.979i	−0.718846	+	0.797873i
$293$	115.636	−	216.339i	0.394660	−	0.738358i	−0.603602	−	0.797286i	$-0.706268\pi$
$293$	115.636	−	216.339i	0.394660	−	0.738358i	0.998262	+	0.0589281i	$0.0187683\pi$
$294$	−149.273	+	157.253i	−0.507730	+	0.534874i
$295$	−41.7049	+	27.8663i	−0.141372	+	0.0944620i
$296$	−0.412313	+	0.209848i	−0.00139295	+	0.000708945i
$297$	−424.495	−	283.638i	−1.42928	−	0.955012i
$298$	330.270	+	208.455i	1.10829	+	0.699512i
$299$	68.7609	−	56.4306i	0.229970	−	0.188731i
$300$	−166.853	+	100.683i	−0.556178	+	0.335609i
$301$	−52.1299	−	97.5281i	−0.173189	−	0.324014i
$302$	−89.9596	+	326.960i	−0.297879	+	1.08265i
$303$	141.877	+	342.522i	0.468242	+	1.13044i
$304$	419.256	−	85.9867i	1.37913	−	0.282851i
$305$	100.004	+	41.4232i	0.327884	+	0.135814i
$306$	25.2491	+	19.6443i	0.0825133	+	0.0641971i
$307$	−34.7147	+	114.439i	−0.113077	+	0.372765i	−0.995153	−	0.0983428i	$-0.968646\pi$
$307$	−34.7147	+	114.439i	−0.113077	+	0.372765i	0.882075	+	0.471108i	$0.156146\pi$
$308$	182.218	−	65.8098i	0.591618	−	0.213668i
$309$	−27.1723	+	275.885i	−0.0879361	+	0.892830i
$310$	−205.933	−	35.4180i	−0.664301	−	0.114252i
$311$	46.6640	+	234.596i	0.150045	+	0.754328i	0.980388	+	0.197076i	$0.0631444\pi$
$311$	46.6640	+	234.596i	0.150045	+	0.754328i	−0.830343	+	0.557252i	$0.811856\pi$
$312$	68.6508	+	1.37936i	0.220035	+	0.00442101i
$313$	5.22010	−	26.2432i	0.0166776	−	0.0838442i	−0.971550	−	0.236834i	$-0.923890\pi$
$313$	5.22010	−	26.2432i	0.0166776	−	0.0838442i	0.988228	+	0.152990i	$0.0488902\pi$
$314$	−146.295	+	65.1082i	−0.465908	+	0.207351i
$315$	−14.2507	+	4.32291i	−0.0452404	+	0.0137235i
$316$	−87.6335	−	345.497i	−0.277321	−	1.09334i
$317$	−344.710	−	282.896i	−1.08741	−	0.892418i	−0.0927610	−	0.995688i	$-0.529569\pi$
$317$	−344.710	−	282.896i	−1.08741	−	0.892418i	−0.994653	+	0.103271i	$0.967069\pi$
$318$	22.3038	+	11.1853i	0.0701377	+	0.0351739i
$319$	9.65183			0.0302565
$320$	−97.7629	−	129.393i	−0.305509	−	0.404353i
$321$		−	507.341i		−	1.58050i
$322$	−134.450	−	67.4263i	−0.417546	−	0.209398i
$323$	127.809	−	155.736i	0.395695	−	0.482156i
$324$	−117.404	+	197.203i	−0.362359	+	0.608650i
$325$	−17.6529	−	58.1937i	−0.0543165	−	0.179057i
$326$	−337.139	+	150.043i	−1.03417	+	0.460254i
$327$	407.558	+	81.0683i	1.24635	+	0.247915i
$328$	−108.801	−	278.357i	−0.331709	−	0.848648i
$329$	135.486	−	26.9499i	0.411812	−	0.0819145i
$330$	229.232	+	39.4250i	0.694642	+	0.119470i
$331$	−109.972	−	10.8313i	−0.332242	−	0.0327230i	−0.0694791	−	0.997583i	$-0.522134\pi$
$331$	−109.972	−	10.8313i	−0.332242	−	0.0327230i	−0.262763	+	0.964860i	$0.584634\pi$
$332$	−0.748172	+	1.59411i	−0.00225353	+	0.00480153i
$333$	0.117527	+	0.0356515i	0.000352934	+	0.000107061i
$334$	−343.259	−	267.063i	−1.02772	−	0.799588i
$335$	−44.2191	+	106.754i	−0.131997	+	0.318669i
$336$	−45.0679	−	107.002i	−0.134131	−	0.318457i
$337$	−189.990	+	78.6964i	−0.563768	+	0.233520i	−0.646320	−	0.763066i	$-0.723693\pi$
$337$	−189.990	+	78.6964i	−0.563768	+	0.233520i	0.0825521	+	0.996587i	$0.473693\pi$
$338$	83.9810	−	305.230i	0.248464	−	0.903049i
$339$	−229.518	+	122.680i	−0.677044	+	0.361888i
$340$	−74.1077	−	18.3293i	−0.217964	−	0.0539098i
$341$	−457.811	−	557.844i	−1.34255	−	1.63591i
$342$	−96.0778	−	60.6410i	−0.280929	−	0.177313i
$343$	−138.894	+	207.870i	−0.404940	+	0.606036i
$344$	−318.719	+	24.9380i	−0.926510	+	0.0724940i
$345$	−100.324	−	150.145i	−0.290794	−	0.435203i
$346$	−194.080	+	204.455i	−0.560924	+	0.590912i
$347$	−451.550	−	241.359i	−1.30130	−	0.695558i	−0.332427	−	0.943129i	$-0.607868\pi$
$347$	−451.550	−	241.359i	−1.30130	−	0.695558i	−0.968870	+	0.247571i	$0.920368\pi$
$348$	−0.300973	−	5.77641i	−0.000864866	−	0.0165989i
$349$	547.319	−	53.9062i	1.56825	−	0.154459i	0.723768	−	0.690043i	$-0.242409\pi$
$349$	547.319	−	53.9062i	1.56825	−	0.154459i	0.844482	+	0.535584i	$0.179909\pi$
$350$	−77.7622	+	67.2798i	−0.222178	+	0.192228i
$351$	−67.5116	−	67.5116i	−0.192341	−	0.192341i
$352$	37.0544	−	558.852i	0.105268	−	1.58765i
$353$	266.488	+	266.488i	0.754924	+	0.754924i	0.975394	−	0.220470i	$-0.0707590\pi$
$353$	266.488	+	266.488i	0.754924	+	0.754924i	−0.220470	+	0.975394i	$0.570759\pi$
$354$	−7.48318	+	103.542i	−0.0211389	+	0.292492i
$355$	−165.240	+	16.2747i	−0.465465	+	0.0458443i
$356$	71.5412	+	25.3585i	0.200958	+	0.0712317i
$357$	−48.2015	−	25.7642i	−0.135018	−	0.0721687i
$358$	269.670	−	7.02066i	0.753268	−	0.0196108i
$359$	−87.8884	−	131.534i	−0.244814	−	0.366391i	0.688630	−	0.725113i	$-0.258213\pi$
$359$	−87.8884	−	131.534i	−0.244814	−	0.366391i	−0.933444	+	0.358722i	$0.883213\pi$
$360$	−5.07958	+	42.7506i	−0.0141099	+	0.118752i
$361$	−196.953	+	294.760i	−0.545575	+	0.816511i
$362$	427.506	−	96.6667i	1.18096	−	0.267035i
$363$	308.316	+	375.684i	0.849355	+	1.03494i
$364$	35.8231	−	5.42262i	0.0984151	−	0.0148973i
$365$	−175.198	+	93.6455i	−0.479996	+	0.256563i
$366$	194.764	−	110.715i	0.532142	−	0.302499i
$367$	−244.363	+	101.219i	−0.665840	+	0.275800i	−0.689894	−	0.723911i	$-0.742343\pi$
$367$	−244.363	+	101.219i	−0.665840	+	0.275800i	0.0240536	+	0.999711i	$0.492343\pi$
$368$	−334.476	+	277.838i	−0.908903	+	0.754995i
$369$	−30.3614	+	73.2989i	−0.0822802	+	0.198642i
$370$	−0.290821	+	0.0363078i	−0.000786003	+	9.81291e-5i
$371$	12.5988	+	3.82179i	0.0339589	+	0.0103013i
$372$	−319.582	+	291.385i	−0.859091	+	0.783294i
$373$	222.186	+	21.8834i	0.595672	+	0.0586686i	0.391361	−	0.920237i	$-0.372004\pi$
$373$	222.186	+	21.8834i	0.595672	+	0.0586686i	0.204311	+	0.978906i	$0.434504\pi$
$374$	−152.132	−	215.330i	−0.406769	−	0.575750i
$375$	−284.006	+	56.4923i	−0.757349	+	0.150646i
$376$	85.7619	−	390.033i	0.228090	−	1.03732i
$377$	1.77032	+	0.352138i	0.00469580	+	0.000934053i
$378$	−57.8780	+	150.709i	−0.153116	+	0.398701i
$379$	−62.3073	−	205.400i	−0.164399	−	0.541951i	0.835573	−	0.549379i	$-0.185136\pi$
$379$	−62.3073	−	205.400i	−0.164399	−	0.541951i	−0.999972	+	0.00742767i	$0.997636\pi$
$380$	268.305	+	38.9854i	0.706065	+	0.102593i
$381$	108.847	−	132.630i	0.285688	−	0.348111i
$382$	55.9157	+	168.419i	0.146376	+	0.440888i
$383$			49.1325i			0.128283i	0.997941	+	0.0641416i	$0.0204309\pi$
$383$			49.1325i			0.128283i	−0.997941	+	0.0641416i	$0.979569\pi$
$384$	−335.616	−	4.74960i	−0.874001	−	0.0123687i
$385$	122.731			0.318782
$386$	532.098	−	176.658i	1.37849	−	0.457663i
$387$	65.6035	+	53.8394i	0.169518	+	0.139120i
$388$	−636.201	−	92.4417i	−1.63969	−	0.238252i
$389$	467.630	−	141.854i	1.20213	−	0.364663i	0.375190	−	0.926948i	$-0.377577\pi$
$389$	467.630	−	141.854i	1.20213	−	0.364663i	0.826944	+	0.562284i	$0.190077\pi$
$390$	40.6068	+	15.5945i	0.104120	+	0.0399860i
$391$	−39.9322	+	200.753i	−0.102128	+	0.513434i
$392$	178.186	+	278.633i	0.454556	+	0.710799i
$393$	83.4226	+	419.394i	0.212271	+	1.06716i
$394$	591.891	−	418.172i	1.50226	−	1.06135i
$395$	22.1322	−	224.712i	0.0560308	−	0.568890i
$396$	−109.869	+	100.175i	−0.277446	+	0.252967i
$397$	−125.692	+	414.352i	−0.316605	+	1.04371i	0.643822	+	0.765175i	$0.277348\pi$
$397$	−125.692	+	414.352i	−0.316605	+	1.04371i	−0.960427	+	0.278532i	$0.910152\pi$
$398$	−90.4302	−	724.335i	−0.227212	−	1.81994i
$399$	179.331	+	74.2812i	0.449450	+	0.186168i
$400$	87.9794	+	283.948i	0.219948	+	0.709869i
$401$	−0.590213	−	1.42490i	−0.00147185	−	0.00355337i	0.923142	−	0.384459i	$-0.125612\pi$
$401$	−0.590213	−	1.42490i	−0.00147185	−	0.00355337i	−0.924614	+	0.380906i	$0.875612\pi$
$402$	118.187	+	207.910i	0.293999	+	0.517188i
$403$	−63.6182	−	119.021i	−0.157862	−	0.295338i
$404$	559.162	−	84.6415i	1.38406	−	0.209509i
$405$	−112.387	+	92.2337i	−0.277499	+	0.227738i
$406$	−0.673136	−	2.97693i	−0.00165797	−	0.00733233i
$407$	−0.841591	−	0.562333i	−0.00206779	−	0.00138165i
$408$	−124.127	+	97.7622i	−0.304232	+	0.239613i
$409$	55.4088	−	37.0230i	0.135474	−	0.0905208i	−0.485987	−	0.873966i	$-0.661540\pi$
$409$	55.4088	−	37.0230i	0.135474	−	0.0905208i	0.621461	+	0.783445i	$0.286540\pi$
$410$	−4.92732	−	189.263i	−0.0120179	−	0.461617i
$411$	−12.8153	+	23.9758i	−0.0311808	+	0.0583352i
$412$	398.572	+	141.278i	0.967408	+	0.342907i
$413$	5.36908	+	54.5131i	0.0130002	+	0.131993i
$414$	115.129	+	8.32061i	0.278090	+	0.0200981i
$415$	−0.788806	+	0.788806i	−0.00190074	+	0.00190074i
$416$	27.1856	−	101.151i	0.0653501	−	0.243153i
$417$	53.9476	−	53.9476i	0.129371	−	0.129371i
$418$	612.647	+	708.100i	1.46566	+	1.69402i
$419$	60.7136	+	616.436i	0.144901	+	1.47121i	0.742734	+	0.669586i	$0.233529\pi$
$419$	60.7136	+	616.436i	0.144901	+	1.47121i	−0.597833	+	0.801621i	$0.703971\pi$
$420$	−3.82712	−	73.4518i	−0.00911219	−	0.174885i
$421$	−121.908	+	228.074i	−0.289568	+	0.541744i	−0.984078	−	0.177739i	$-0.943122\pi$
$421$	−121.908	+	228.074i	−0.289568	+	0.541744i	0.694509	+	0.719484i	$0.255622\pi$
$422$	445.585	+	422.972i	1.05589	+	1.00230i
$423$	−88.1473	+	58.8981i	−0.208386	+	0.139239i
$424$	24.7316	−	28.9304i	0.0583293	−	0.0682320i
$425$	116.351	+	77.7430i	0.273766	+	0.182925i
$426$	−183.422	+	290.609i	−0.430569	+	0.682181i
$427$	91.3791	−	74.9929i	0.214002	−	0.175627i
$428$	−751.260	−	185.812i	−1.75528	−	0.434140i
$429$	70.8156	+	132.487i	0.165071	+	0.308827i
$430$	−195.266	−	53.7254i	−0.454107	−	0.124943i
$431$	209.295	+	505.282i	0.485603	+	1.17235i	0.956911	+	0.290381i	$0.0937819\pi$
$431$	209.295	+	505.282i	0.485603	+	1.17235i	−0.471308	+	0.881969i	$0.656218\pi$
$432$	331.968	+	328.048i	0.768444	+	0.759370i
$433$	−30.1896	−	12.5049i	−0.0697220	−	0.0288798i	0.347550	−	0.937661i	$-0.387014\pi$
$433$	−30.1896	−	12.5049i	−0.0697220	−	0.0288798i	−0.417272	+	0.908782i	$0.637014\pi$
$434$	−140.128	+	180.108i	−0.322876	+	0.414996i
$435$	1.06368	−	3.50647i	0.00244524	−	0.00806086i
$436$	269.311	−	573.812i	0.617685	−	1.31608i
$437$	71.2521	−	723.435i	0.163048	−	1.65546i
$438$	−69.6908	+	405.208i	−0.159111	+	0.925133i
$439$	5.81257	+	29.2218i	0.0132405	+	0.0665644i	0.986841	−	0.161696i	$-0.0516963\pi$
$439$	5.81257	+	29.2218i	0.0132405	+	0.0665644i	−0.973600	+	0.228260i	$0.926696\pi$
$440$	142.335	−	325.002i	0.323488	−	0.738641i
$441$	17.1287	−	86.1120i	0.0388407	−	0.195265i
$442$	−20.0475	−	45.0458i	−0.0453563	−	0.101914i
$443$	−665.503	+	201.878i	−1.50226	+	0.455707i	−0.930987	−	0.365052i	$-0.881051\pi$
$443$	−665.503	+	201.878i	−1.50226	+	0.455707i	−0.571276	+	0.820758i	$0.693551\pi$
$444$	−0.310301	+	0.521210i	−0.000698876	+	0.00117390i
$445$	37.1690	+	30.5038i	0.0835257	+	0.0685478i
$446$	−299.930	+	598.067i	−0.672488	+	1.34096i
$447$	512.066			1.14556
$448$	−174.952	+	27.5466i	−0.390517	+	0.0614879i
$449$			685.174i			1.52600i	0.646398	+	0.763000i	$0.276274\pi$
$449$			685.174i			1.52600i	−0.646398	+	0.763000i	$0.723726\pi$
$450$	35.3758	−	70.5401i	0.0786128	−	0.156756i
$451$	414.803	−	505.439i	0.919741	−	1.12071i
$452$	97.6017	+	384.796i	0.215933	+	0.851319i
$453$	129.066	+	425.473i	0.284913	+	0.939234i
$454$	−62.3540	−	140.107i	−0.137344	−	0.308605i
$455$	22.5110	+	4.47772i	0.0494748	+	0.00984115i
$456$	404.678	−	388.737i	0.887452	−	0.852493i
$457$	412.329	−	82.0173i	0.902252	−	0.179469i	0.277898	−	0.960611i	$-0.410362\pi$
$457$	412.329	−	82.0173i	0.902252	−	0.179469i	0.624354	+	0.781142i	$0.285362\pi$
$458$	133.607	−	776.842i	0.291719	−	1.69616i
$459$	218.640	+	21.5341i	0.476339	+	0.0469153i
$460$	−259.075	+	93.5672i	−0.563206	+	0.203407i
$461$	−417.673	−	126.700i	−0.906015	−	0.274837i	−0.197310	−	0.980341i	$-0.563221\pi$
$461$	−417.673	−	126.700i	−0.906015	−	0.274837i	−0.708706	+	0.705504i	$0.750721\pi$
$462$	155.981	−	200.485i	0.337622	−	0.433950i
$463$	−192.797	+	465.453i	−0.416408	+	1.00530i	0.566972	+	0.823737i	$0.308115\pi$
$463$	−192.797	+	465.453i	−0.416408	+	1.00530i	−0.983380	+	0.181560i	$0.941885\pi$
$464$	−8.66382	−	1.66992i	−0.0186720	−	0.00359896i
$465$	−253.116	+	104.844i	−0.544335	+	0.225471i
$466$	817.034	+	224.798i	1.75329	+	0.482400i
$467$	189.198	−	101.128i	0.405134	−	0.216549i	−0.256227	−	0.966617i	$-0.582479\pi$
$467$	189.198	−	101.128i	0.405134	−	0.216549i	0.661361	+	0.750068i	$0.269979\pi$
$468$	−23.8067	+	14.3654i	−0.0508690	+	0.0306954i
$469$	80.0545	+	97.5467i	0.170692	+	0.207989i
$470$	135.029	−	213.935i	0.287295	−	0.455182i
$471$	−116.642	+	174.567i	−0.247648	+	0.370632i
$472$	150.582	+	49.0028i	0.319030	+	0.103820i
$473$	−388.582	−	581.553i	−0.821526	−	1.22950i
$474$	−338.945	−	321.745i	−0.715074	−	0.678786i
$475$	−438.289	−	234.270i	−0.922713	−	0.493201i
$476$	−55.8047	+	61.9397i	−0.117237	+	0.130125i
$477$	−10.0552	+	0.990346i	−0.0210800	+	0.00207620i
$478$	233.968	+	270.421i	0.489473	+	0.565735i
$479$	−475.879	−	475.879i	−0.993484	−	0.993484i	0.00649522	−	0.999979i	$-0.497932\pi$
$479$	−475.879	−	475.879i	−0.993484	−	0.993484i	−0.999979	+	0.00649522i	$0.997932\pi$
$480$	−198.945	−	75.0499i	−0.414469	−	0.156354i
$481$	−0.133847	−	0.133847i	−0.000278267	−	0.000278267i
$482$	−415.663	−	30.0408i	−0.862372	−	0.0623252i
$483$	−196.257	+	19.3297i	−0.406330	+	0.0400200i
$484$	669.224	−	318.955i	1.38269	−	0.658997i
$485$	−359.170	−	191.980i	−0.740556	−	0.395836i
$486$	−5.83325	−	224.061i	−0.0120026	−	0.461030i
$487$	−523.675	−	783.734i	−1.07531	−	1.60931i	−0.747109	−	0.664702i	$-0.768559\pi$
$487$	−523.675	−	783.734i	−1.07531	−	1.60931i	−0.328198	−	0.944609i	$-0.606441\pi$
$488$	−92.6124	−	328.951i	−0.189780	−	0.674080i
$489$	−268.804	+	402.293i	−0.549700	+	0.822685i
$490$	46.2091	+	204.359i	0.0943042	+	0.417058i
$491$	192.251	+	234.258i	0.391550	+	0.477105i	0.931056	−	0.364877i	$-0.118889\pi$
$491$	192.251	+	234.258i	0.391550	+	0.477105i	−0.539506	+	0.841982i	$0.681389\pi$
$492$	−315.429	−	232.490i	−0.641117	−	0.472540i
$493$	−3.66301	+	1.95792i	−0.00743004	+	0.00397144i
$494$	86.5359	+	152.230i	0.175174	+	0.308158i
$495$	−87.0184	+	36.0442i	−0.175795	+	0.0728166i
$496$	314.431	+	579.949i	0.633934	+	1.16925i
$497$	−69.3919	+	167.527i	−0.139622	+	0.337076i
$498$	0.286028	+	2.29105i	0.000574354	+	0.00460050i
$499$	−140.822	−	42.7177i	−0.282207	−	0.0856067i	0.146008	−	0.989283i	$-0.453358\pi$
$499$	−140.822	−	42.7177i	−0.282207	−	0.0856067i	−0.428215	+	0.903677i	$0.640858\pi$
$500$	−20.3635	+	441.240i	−0.0407271	+	0.882480i
$501$	−567.482	−	55.8921i	−1.13270	−	0.111561i
$502$	344.383	−	243.307i	0.686022	−	0.484676i
$503$	414.693	−	82.4876i	0.824439	−	0.163991i	0.235197	−	0.971948i	$-0.424426\pi$
$503$	414.693	−	82.4876i	0.824439	−	0.163991i	0.589242	+	0.807957i	$0.299426\pi$
$504$	38.5596	+	26.9006i	0.0765071	+	0.0533742i
$505$	351.374	+	69.8926i	0.695790	+	0.138401i
$506$	−888.066	−	341.051i	−1.75507	−	0.674014i
$507$	−120.488	−	397.196i	−0.237649	−	0.783425i
$508$	−156.531	−	209.754i	−0.308133	−	0.412901i
$509$	−323.135	+	393.741i	−0.634843	+	0.773558i	−0.986710	−	0.162492i	$-0.948047\pi$
$509$	−323.135	+	393.741i	−0.634843	+	0.773558i	0.351867	+	0.936050i	$0.385547\pi$
$510$	−94.9944	+	31.5384i	−0.186263	+	0.0618400i
$511$			216.949i			0.424558i
$512$	−129.951	+	495.234i	−0.253811	+	0.967254i
$513$	−780.249			−1.52095
$514$	−8.16361	−	24.5890i	−0.0158825	−	0.0478385i
$515$	207.077	+	169.943i	0.402090	+	0.329987i
$516$	−335.930	+	250.692i	−0.651027	+	0.485838i
$517$	836.082	−	253.623i	1.61718	−	0.490566i
$518$	−0.114747	+	0.298791i	−0.000221520	+	0.000576817i
$519$	−72.1076	+	362.510i	−0.138936	+	0.698477i
$520$	37.9641	−	54.4182i	0.0730080	−	0.104650i
$521$	−18.2252	−	91.6241i	−0.0349811	−	0.175862i	0.959345	−	0.282236i	$-0.0910760\pi$
$521$	−18.2252	−	91.6241i	−0.0349811	−	0.175862i	−0.994326	+	0.106374i	$0.966076\pi$
$522$	1.35154	+	1.91300i	0.00258916	+	0.00366476i
$523$	81.4263	−	826.735i	0.155691	−	1.58076i	−0.526882	−	0.849938i	$-0.676639\pi$
$523$	81.4263	−	826.735i	0.155691	−	1.58076i	0.682573	−	0.730817i	$-0.260861\pi$
$524$	651.582	+	30.0710i	1.24348	+	0.0573874i
$525$	−39.1364	+	129.015i	−0.0745455	+	0.245744i
$526$	−121.957	+	15.2258i	−0.231857	+	0.0289464i
$527$	286.907	+	118.841i	0.544416	+	0.225505i
$528$	−350.004	−	645.561i	−0.662887	−	1.22265i
$529$	80.1906	+	193.597i	0.151589	+	0.365968i
$530$	20.9610	−	11.9154i	0.0395491	−	0.0224819i
$531$	−19.8164	−	37.0740i	−0.0373191	−	0.0698191i
$532$	175.673	−	238.344i	0.330213	−	0.448014i
$533$	94.5227	−	77.5728i	0.177341	−	0.145540i
$534$	97.0677	−	21.9487i	0.181775	−	0.0411025i
$535$	−407.632	−	272.371i	−0.761929	−	0.509105i
$536$	351.154	−	98.8633i	0.655138	−	0.184446i
$537$	294.085	−	196.501i	0.547644	−	0.365924i
$538$	−387.010	+	10.0755i	−0.719349	+	0.0187277i
$539$	−341.097	+	638.148i	−0.632833	+	1.18395i
$540$	127.202	+	266.893i	0.235559	+	0.494246i
$541$	53.9348	+	547.610i	0.0996947	+	1.01222i	0.906729	+	0.421713i	$0.138571\pi$
$541$	53.9348	+	547.610i	0.0996947	+	1.01222i	−0.807034	+	0.590504i	$0.798929\pi$
$542$	55.2402	−	764.339i	0.101919	−	1.41022i
$543$	406.352	−	406.352i	0.748346	−	0.748346i
$544$	99.3031	+	219.609i	0.182542	+	0.403693i
$545$	283.937	−	283.937i	0.520986	−	0.520986i
$546$	35.9243	−	31.0816i	0.0657954	−	0.0569261i
$547$	54.0206	+	548.481i	0.0987580	+	1.00271i	0.909052	+	0.416683i	$0.136808\pi$
$547$	54.0206	+	548.481i	0.0987580	+	1.00271i	−0.810294	+	0.586024i	$0.800692\pi$
$548$	30.8092	+	27.7577i	0.0562213	+	0.0506527i
$549$	−42.7651	+	80.0079i	−0.0778964	+	0.145734i
$550$	−447.749	+	471.686i	−0.814090	+	0.857611i
$551$	12.2649	−	8.19513i	0.0222593	−	0.0148732i
$552$	−176.419	+	542.124i	−0.319600	+	0.982108i
$553$	−205.034	−	136.999i	−0.370766	−	0.247738i
$554$	−817.436	−	515.937i	−1.47552	−	0.931294i
$555$	−0.297041	+	0.243775i	−0.000535209	+	0.000439235i
$556$	−60.1264	−	99.6426i	−0.108141	−	0.179213i
$557$	366.652	+	685.958i	0.658263	+	1.23152i	0.960497	+	0.278289i	$0.0897674\pi$
$557$	366.652	+	685.958i	0.658263	+	1.23152i	−0.302235	+	0.953234i	$0.597733\pi$
$558$	46.4583	−	168.853i	0.0832585	−	0.302605i
$559$	−50.0553	−	120.844i	−0.0895444	−	0.216179i
$560$	−110.168	−	21.2343i	−0.196728	−	0.0379185i
$561$	−319.367	−	132.286i	−0.569281	−	0.235804i
$562$	−462.368	−	359.733i	−0.822720	−	0.640094i
$563$	−218.971	+	721.852i	−0.388937	+	1.28215i	0.515993	+	0.856593i	$0.327423\pi$
$563$	−218.971	+	721.852i	−0.388937	+	1.28215i	−0.904930	+	0.425560i	$0.860077\pi$
$564$	−177.859	−	492.469i	−0.315354	−	0.873171i
$565$	−24.6497	+	250.272i	−0.0436277	+	0.442960i
$566$	4.42858	+	0.761661i	0.00782435	+	0.00134569i
$567$	30.9759	+	155.726i	0.0546313	+	0.274650i
$568$	363.150	+	378.042i	0.639348	+	0.665567i
$569$	−67.9157	+	341.435i	−0.119360	+	0.600062i	0.874087	+	0.485769i	$0.161460\pi$
$569$	−67.9157	+	341.435i	−0.119360	+	0.600062i	−0.993447	+	0.114293i	$0.963540\pi$
$570$	324.767	−	144.536i	0.569766	−	0.253573i
$571$	487.424	−	147.859i	0.853633	−	0.258947i	0.167005	−	0.985956i	$-0.446590\pi$
$571$	487.424	−	147.859i	0.853633	−	0.258947i	0.686628	+	0.727009i	$0.259090\pi$
$572$	222.119	−	56.3395i	0.388321	−	0.0984956i
$573$	179.858	+	147.606i	0.313888	+	0.257602i
$574$	−184.822	−	92.6881i	−0.321990	−	0.161478i
$575$	504.910			0.878104
$576$	115.954	−	70.9117i	0.201309	−	0.123111i
$577$		−	1016.60i		−	1.76188i	−0.473228	−	0.880940i	$-0.656911\pi$
$577$		−	1016.60i		−	1.76188i	0.473228	−	0.880940i	$-0.343089\pi$
$578$	−415.252	−	208.248i	−0.718429	−	0.360291i
$579$	466.340	−	568.237i	0.805423	−	0.981411i
$580$	−4.80274	−	2.85930i	−0.00828059	−	0.00492983i
$581$	0.353644	+	1.16581i	0.000608682	+	0.00200656i
$582$	−770.083	+	342.723i	−1.32317	+	0.588871i
$583$	81.6696	+	16.2451i	0.140085	+	0.0278647i
$584$	574.500	+	251.603i	0.983732	+	0.430826i
$585$	−17.2758	+	3.43636i	−0.0295312	+	0.00587412i
$586$	−483.509	−	83.1575i	−0.825101	−	0.141907i
$587$	375.288	+	36.9626i	0.639332	+	0.0629687i	0.412489	−	0.910963i	$-0.364660\pi$
$587$	375.288	+	36.9626i	0.639332	+	0.0629687i	0.226843	+	0.973931i	$0.427160\pi$
$588$	392.554	+	184.240i	0.667609	+	0.313333i
$589$	−1055.41	−	320.154i	−1.79186	−	0.543555i
$590$	79.1753	+	61.6001i	0.134195	+	0.104407i
$591$	363.622	−	877.861i	0.615265	−	1.48538i
$592$	0.658149	+	0.650378i	0.00111174	+	0.00109861i
$593$	−568.621	+	235.530i	−0.958888	+	0.397185i	−0.806565	−	0.591146i	$-0.798676\pi$
$593$	−568.621	+	235.530i	−0.958888	+	0.397185i	−0.152324	+	0.988331i	$0.548676\pi$
$594$	−270.871	+	984.487i	−0.456012	+	1.65739i
$595$	−46.5782	+	24.8966i	−0.0782827	+	0.0418430i
$596$	187.542	−	758.257i	0.314668	−	1.27224i
$597$	−607.160	−	739.827i	−1.01702	−	1.23924i
$598$	−150.444	−	94.9550i	−0.251579	−	0.158788i
$599$	572.935	−	857.457i	0.956485	−	1.43148i	0.0550915	−	0.998481i	$-0.482455\pi$
$599$	572.935	−	857.457i	0.956485	−	1.43148i	0.901394	−	0.433000i	$-0.142545\pi$
$600$	296.256	+	253.260i	0.493761	+	0.422100i
$601$	112.001	+	167.622i	0.186358	+	0.278905i	0.912871	−	0.408248i	$-0.133860\pi$
$601$	112.001	+	167.622i	0.186358	+	0.278905i	−0.726513	+	0.687153i	$0.758860\pi$
$602$	−152.269	+	160.409i	−0.252939	+	0.266461i
$603$	−85.4080	−	45.6515i	−0.141639	−	0.0757074i
$604$	677.301	−	35.2900i	1.12136	−	0.0584271i
$605$	467.372	−	46.0322i	0.772516	−	0.0760862i
$606$	560.741	−	485.152i	0.925315	−	0.800582i
$607$	−482.164	−	482.164i	−0.794340	−	0.794340i	0.187857	−	0.982196i	$-0.439846\pi$
$607$	−482.164	−	482.164i	−0.794340	−	0.794340i	−0.982196	+	0.187857i	$0.939846\pi$
$608$	−427.421	−	741.612i	−0.702995	−	1.21976i
$609$	−2.82962	−	2.82962i	−0.00464634	−	0.00464634i
$610$	15.6053	−	215.925i	0.0255824	−	0.353975i
$611$	162.605	−	16.0152i	0.266130	−	0.0262115i
$612$	21.3758	−	60.3053i	0.0349278	−	0.0985381i
$613$	−174.685	−	93.3709i	−0.284967	−	0.152318i	0.322720	−	0.946494i	$-0.395403\pi$
$613$	−174.685	−	93.3709i	−0.284967	−	0.152318i	−0.607687	+	0.794176i	$0.707903\pi$
$614$	239.096	−	6.22468i	0.389407	−	0.0101379i
$615$	−137.911	−	206.398i	−0.224245	−	0.335607i
$616$	−239.746	−	304.401i	−0.389198	−	0.494157i
$617$	7.73494	−	11.5761i	0.0125364	−	0.0187620i	−0.825149	−	0.564916i	$-0.808909\pi$
$617$	7.73494	−	11.5761i	0.0125364	−	0.0187620i	0.837685	+	0.546154i	$0.183909\pi$
$618$	540.786	−	122.281i	0.875059	−	0.197866i
$619$	−177.591	−	216.395i	−0.286899	−	0.349588i	0.609539	−	0.792756i	$-0.291354\pi$
$619$	−177.591	−	216.395i	−0.286899	−	0.349588i	−0.896439	+	0.443168i	$0.853854\pi$
$620$	62.5479	+	413.207i	0.100884	+	0.666462i
$621$	699.111	−	373.683i	1.12578	−	0.601743i
$622$	415.885	−	236.412i	0.668626	−	0.380084i
$623$	48.5141	−	20.0952i	0.0778717	−	0.0322555i
$624$	−40.6443	−	131.177i	−0.0651352	−	0.210219i
$625$	70.6660	−	170.603i	0.113066	−	0.272964i
$626$	−53.1025	+	6.62962i	−0.0848283	+	0.0105904i
$627$	1174.81	+	356.374i	1.87370	+	0.568380i
$628$	215.776	+	236.656i	0.343592	+	0.376841i
$629$	0.433468	+	0.0426929i	0.000689139	+	6.78742e-5i
$630$	17.1860	+	24.3254i	0.0272793	+	0.0386118i
$631$	−1139.11	+	226.582i	−1.80524	+	0.359085i	−0.978941	−	0.204146i	$-0.934558\pi$
$631$	−1139.11	+	226.582i	−1.80524	+	0.359085i	−0.826300	+	0.563230i	$0.809558\pi$
$632$	−600.570	+	384.065i	−0.950269	+	0.607698i
$633$	790.044	+	157.149i	1.24809	+	0.248261i
$634$	−319.742	+	832.579i	−0.504325	+	1.31322i
$635$	−48.1287	−	158.659i	−0.0757932	−	0.249857i
$636$	7.17564	−	49.3841i	0.0112825	−	0.0776480i
$637$	−85.8455	+	104.603i	−0.134765	+	0.164212i
$638$	−6.08241	−	18.3204i	−0.00953356	−	0.0287153i
$639$		−	139.159i		−	0.217776i
$640$	−183.995	+	267.107i	−0.287492	+	0.417355i
$641$	604.251			0.942669			0.471334	−	0.881955i	$-0.343772\pi$
$641$	604.251			0.942669			0.471334	+	0.881955i	$0.343772\pi$
$642$	−962.996	+	319.717i	−1.49999	+	0.498002i
$643$	282.336	+	231.707i	0.439091	+	0.360353i	0.827815	−	0.561002i	$-0.189584\pi$
$643$	282.336	+	231.707i	0.439091	+	0.360353i	−0.388724	+	0.921354i	$0.627084\pi$
$644$	−43.2556	+	297.693i	−0.0671670	+	0.462256i
$645$	−254.100	+	77.0803i	−0.393953	+	0.119504i
$646$	−376.150	−	144.456i	−0.582275	−	0.223616i
$647$	34.9923	−	175.918i	0.0540839	−	0.271898i	−0.944275	−	0.329156i	$-0.893236\pi$
$647$	34.9923	−	175.918i	0.0540839	−	0.271898i	0.998359	+	0.0572579i	$0.0182357\pi$
$648$	448.301	+	98.5740i	0.691822	+	0.152120i
$649$	67.5891	+	339.793i	0.104143	+	0.523564i
$650$	−99.3342	+	70.1799i	−0.152822	+	0.107969i
$651$	−29.3267	+	297.759i	−0.0450487	+	0.457387i
$652$	497.258	+	545.377i	0.762666	+	0.836467i
$653$	−209.919	+	692.010i	−0.321469	+	1.05974i	0.636117	+	0.771592i	$0.280539\pi$
$653$	−209.919	+	692.010i	−0.321469	+	1.05974i	−0.957586	+	0.288148i	$0.906961\pi$
$654$	−102.958	−	824.683i	−0.157428	−	1.26098i
$655$	381.755	+	158.128i	0.582833	+	0.241417i
$656$	−459.791	+	381.932i	−0.700900	+	0.582214i
$657$	−63.7146	−	153.821i	−0.0969781	−	0.234126i
$658$	−136.535	−	240.186i	−0.207500	−	0.365024i
$659$	82.1706	+	153.730i	0.124690	+	0.233278i	0.936519	−	0.350617i	$-0.114028\pi$
$659$	82.1706	+	153.730i	0.124690	+	0.233278i	−0.811829	+	0.583895i	$0.801528\pi$
$660$	−69.6243	−	459.955i	−0.105491	−	0.696901i
$661$	598.406	−	491.099i	0.905304	−	0.742964i	−0.0616009	−	0.998101i	$-0.519621\pi$
$661$	598.406	−	491.099i	0.905304	−	0.742964i	0.966905	+	0.255137i	$0.0821206\pi$
$662$	48.7433	+	215.566i	0.0736304	+	0.325629i
$663$	−53.7512	−	35.9154i	−0.0810726	−	0.0541710i
$664$	3.49730	+	0.415545i	0.00526701	+	0.000625820i
$665$	155.958	−	104.208i	0.234523	−	0.156703i
$666$	−0.00639265	−	0.245548i	−9.59858e−6	−	0.000368690i
$667$	−7.06458	+	13.2169i	−0.0105916	+	0.0198154i
$668$	−290.602	+	819.845i	−0.435033	+	1.22731i
$669$	85.9833	+	873.003i	0.128525	+	1.30494i
$670$	230.499	+	16.6586i	0.344028	+	0.0248635i
$671$	528.676	−	528.676i	0.787893	−	0.787893i
$672$	−174.701	+	152.975i	−0.259972	+	0.227641i
$673$	−136.795	+	136.795i	−0.203262	+	0.203262i	−0.801396	−	0.598134i	$-0.795909\pi$
$673$	−136.795	+	136.795i	−0.203262	+	0.203262i	0.598134	+	0.801396i	$0.295909\pi$
$674$	269.104	+	311.031i	0.399263	+	0.461470i
$675$	−53.1194	−	539.330i	−0.0786954	−	0.799008i
$676$	−632.288	+	32.9446i	−0.935337	+	0.0487347i
$677$	−279.688	+	523.259i	−0.413128	+	0.772908i	−0.999305	−	0.0372749i	$-0.988132\pi$
$677$	−279.688	+	523.259i	−0.413128	+	0.772908i	0.586177	+	0.810183i	$0.300632\pi$
$678$	377.500	+	358.343i	0.556784	+	0.528529i
$679$	−369.806	+	247.096i	−0.544633	+	0.363912i
$680$	11.9101	+	152.216i	0.0175148	+	0.223848i
$681$	−167.183	−	111.708i	−0.245496	−	0.164035i
$682$	−770.352	+	1220.52i	−1.12955	+	1.78963i
$683$	−1011.01	+	829.717i	−1.48025	+	1.21481i	−0.557063	+	0.830471i	$0.688072\pi$
$683$	−1011.01	+	829.717i	−1.48025	+	1.21481i	−0.923191	+	0.384342i	$0.874428\pi$
$684$	−54.5574	+	220.582i	−0.0797623	+	0.322489i
$685$	12.3837	+	23.1683i	0.0180784	+	0.0338224i
$686$	482.092	+	132.643i	0.702758	+	0.193357i
$687$	−395.502	−	954.827i	−0.575695	−	1.38985i
$688$	248.187	+	589.253i	0.360736	+	0.856473i
$689$	14.3870	+	5.95928i	0.0208809	+	0.00864917i
$690$	−221.772	+	285.046i	−0.321408	+	0.413110i
$691$	−195.920	+	645.863i	−0.283532	+	0.934679i	0.693296	+	0.720653i	$0.256158\pi$
$691$	−195.920	+	645.863i	−0.283532	+	0.934679i	−0.976828	+	0.214026i	$0.931342\pi$
$692$	510.387	+	239.543i	0.737554	+	0.346161i
$693$	−10.0822	+	102.366i	−0.0145486	+	0.147715i
$694$	−173.569	+	1009.20i	−0.250100	+	1.45418i
$695$	−14.3829	−	72.3075i	−0.0206948	−	0.104040i
$696$	−10.7747	+	4.21148i	−0.0154809	+	0.00605097i
$697$	−54.8931	+	275.966i	−0.0787563	+	0.395935i
$698$	−447.232	−	1004.91i	−0.640733	−	1.43970i
$699$	1063.21	−	322.520i	1.52104	−	0.461402i
$700$	176.710	+	105.204i	0.252442	+	0.150291i
$701$	−562.956	−	462.006i	−0.803076	−	0.659067i	0.140553	−	0.990073i	$-0.455112\pi$
$701$	−562.956	−	462.006i	−0.803076	−	0.659067i	−0.943629	+	0.331006i	$0.892612\pi$
$702$	−85.6007	+	170.690i	−0.121938	+	0.243148i
$703$	−1.54690			−0.00220042
$704$	−1084.12	+	281.845i	−1.53994	+	0.400348i
$705$		−	331.696i		−	0.470491i
$706$	337.891	−	673.764i	0.478599	−	0.954339i
$707$	248.206	−	302.439i	0.351069	−	0.427778i
$708$	201.251	−	51.0464i	0.284253	−	0.0720994i
$709$	134.346	+	442.880i	0.189487	+	0.624654i	0.999280	+	0.0379389i	$0.0120792\pi$
$709$	134.346	+	442.880i	0.189487	+	0.624654i	−0.809793	+	0.586715i	$0.800421\pi$
$710$	135.023	+	303.390i	0.190173	+	0.427310i
$711$	185.607	+	36.9196i	0.261051	+	0.0519262i
$712$	3.04951	−	151.774i	0.00428301	−	0.213166i
$713$	1098.98	−	218.602i	1.54135	−	0.306594i
$714$	−18.5280	+	107.729i	−0.0259495	+	0.150880i
$715$	144.467	+	14.2287i	0.202052	+	0.0199003i
$716$	−183.267	−	507.443i	−0.255960	−	0.708719i
$717$	448.656	+	136.098i	0.625741	+	0.189816i
$718$	−194.282	+	249.714i	−0.270588	+	0.347790i
$719$	515.678	−	1244.96i	0.717216	−	1.73151i	0.0360865	−	0.999349i	$-0.488511\pi$
$719$	515.678	−	1244.96i	0.717216	−	1.73151i	0.681129	−	0.732163i	$-0.261489\pi$
$720$	84.3469	−	17.2990i	0.117149	−	0.0240264i
$721$	270.283	−	111.955i	0.374872	−	0.155277i
$722$	683.607	+	188.087i	0.946825	+	0.260509i
$723$	−481.892	+	257.577i	−0.666517	+	0.356261i
$724$	−452.892	−	750.542i	−0.625542	−	1.03666i
$725$	6.49970	+	7.91990i	0.00896510	+	0.0109240i
$726$	518.799	−	821.971i	0.714599	−	1.13219i
$727$	−12.8063	+	19.1660i	−0.0176153	+	0.0263632i	−0.840173	−	0.542319i	$-0.817546\pi$
$727$	−12.8063	+	19.1660i	−0.0176153	+	0.0263632i	0.822557	+	0.568682i	$0.192546\pi$
$728$	−32.8679	−	64.5794i	−0.0451482	−	0.0887080i
$729$	−450.156	−	673.706i	−0.617498	−	0.924151i
$730$	288.158	+	273.534i	0.394736	+	0.374705i
$731$	265.443	+	141.882i	0.363124	+	0.194094i
$732$	−332.887	−	299.916i	−0.454764	−	0.409721i
$733$	−1104.50	+	108.783i	−1.50681	+	0.148408i	−0.817447	−	0.576003i	$-0.804611\pi$
$733$	−1104.50	+	108.783i	−1.50681	+	0.148408i	−0.689368	+	0.724412i	$0.742111\pi$
$734$	346.119	+	400.045i	0.471552	+	0.545021i
$735$	194.246	+	194.246i	0.264281	+	0.264281i
$736$	738.152	+	459.788i	1.00292	+	0.624712i
$737$	564.359	+	564.359i	0.765752	+	0.765752i
$738$	158.263	+	11.4380i	0.214449	+	0.0154986i
$739$	−382.330	+	37.6562i	−0.517361	+	0.0509556i	−0.353328	−	0.935499i	$-0.614950\pi$
$739$	−382.330	+	37.6562i	−0.517361	+	0.0509556i	−0.164032	+	0.986455i	$0.552450\pi$
$740$	0.252187	+	0.529133i	0.000340793	+	0.000715045i
$741$	202.479	+	108.227i	0.273251	+	0.146056i
$742$	−0.685285	−	26.3224i	−0.000923565	−	0.0354750i
$743$	586.641	+	877.970i	0.789557	+	1.18166i	0.979812	+	0.199920i	$0.0640684\pi$
$743$	586.641	+	877.970i	0.789557	+	1.18166i	−0.190255	+	0.981735i	$0.560932\pi$
$744$	754.480	+	422.980i	1.01409	+	0.568521i
$745$	274.908	−	411.429i	0.369004	−	0.552253i
$746$	−98.4802	−	435.526i	−0.132011	−	0.583815i
$747$	−0.593120	−	0.722719i	−0.000794003	−	0.000967496i
$748$	−312.853	+	424.462i	−0.418253	+	0.567462i
$749$	−472.182	+	252.386i	−0.630416	+	0.336964i
$750$	286.205	+	503.478i	0.381606	+	0.671304i
$751$	−744.704	+	308.466i	−0.991616	+	0.410741i	−0.818716	−	0.574198i	$-0.805314\pi$
$751$	−744.704	+	308.466i	−0.991616	+	0.410741i	−0.172900	+	0.984939i	$0.555314\pi$
$752$	−794.377	+	83.0055i	−1.05635	+	0.110380i
$753$	211.568	−	510.770i	0.280967	−	0.678314i
$754$	−0.447221	−	3.58219i	−0.000593132	−	0.00475091i
$755$	411.144	+	124.719i	0.544561	+	0.165191i
$756$	322.538	+	14.8854i	0.426637	+	0.0196896i
$757$	−64.2740	−	6.33043i	−0.0849062	−	0.00836253i	0.0554748	−	0.998460i	$-0.482333\pi$
$757$	−64.2740	−	6.33043i	−0.0849062	−	0.00836253i	−0.140381	+	0.990098i	$0.544833\pi$
$758$	−350.609	+	247.706i	−0.462544	+	0.326789i
$759$	−1223.32	+	243.333i	−1.61175	+	0.320597i
$760$	−95.0818	−	533.843i	−0.125108	−	0.702425i
$761$	501.010	+	99.6572i	0.658358	+	0.130956i	0.512953	−	0.858417i	$-0.328552\pi$
$761$	501.010	+	99.6572i	0.658358	+	0.130956i	0.145405	+	0.989372i	$0.453552\pi$
$762$	−320.342	−	123.024i	−0.420397	−	0.161448i
$763$	−127.297	−	419.642i	−0.166838	−	0.549990i
$764$	284.444	−	212.270i	0.372308	−	0.277840i
$765$	25.7130	−	31.3314i	0.0336118	−	0.0409561i
$766$	93.2595	−	30.9624i	0.121749	−	0.0404209i
$767$			64.7900i			0.0844720i
$768$	202.484	+	640.034i	0.263651	+	0.833378i
$769$	−1324.27			−1.72207			−0.861033	−	0.508549i	$-0.830182\pi$
$769$	−1324.27			−1.72207			−0.861033	+	0.508549i	$0.830182\pi$
$770$	−77.3428	−	232.958i	−0.100445	−	0.302543i
$771$	−26.2590	−	21.5502i	−0.0340584	−	0.0279510i
$772$	−670.637	−	898.660i	−0.868701	−	1.16407i
$773$	457.899	−	138.902i	0.592366	−	0.179692i	0.0201524	−	0.999797i	$-0.493585\pi$
$773$	457.899	−	138.902i	0.592366	−	0.179692i	0.572214	+	0.820105i	$0.306085\pi$
$774$	60.8516	−	158.452i	0.0786197	−	0.204719i
$775$	149.447	−	751.322i	0.192835	−	0.969448i
$776$	225.457	+	1265.84i	0.290537	+	1.63124i
$777$	0.0818698	+	0.411587i	0.000105367	+	0.000529714i
$778$	−563.949	−	798.226i	−0.724870	−	1.02600i
$779$	97.9473	−	994.476i	0.125735	−	1.27661i
$780$	4.01069	−	86.9041i	0.00514191	−	0.111415i
$781$	−332.918	+	1097.48i	−0.426271	+	1.40523i
$782$	406.218	−	50.7146i	0.519460	−	0.0648524i
$783$	14.8612	+	6.15569i	0.0189798	+	0.00786167i
$784$	416.590	−	513.809i	0.531365	−	0.655368i
$785$	77.6388	+	187.437i	0.0989029	+	0.238773i
$786$	743.489	−	422.641i	0.945915	−	0.537711i
$787$	129.800	+	242.838i	0.164930	+	0.308562i	0.950787	−	0.309847i	$-0.100278\pi$
$787$	129.800	+	242.838i	0.164930	+	0.308562i	−0.785857	+	0.618409i	$0.787778\pi$
$788$	−1166.74	−	859.956i	−1.48064	−	1.09132i
$789$	−124.565	+	102.228i	−0.157877	+	0.129567i
$790$	−440.477	+	99.5997i	−0.557566	+	0.126076i
$791$	228.356	+	152.583i	0.288693	+	0.192898i
$792$	259.382	+	145.416i	0.327503	+	0.183606i
$793$	116.257	−	77.6803i	0.146604	−	0.0979575i
$794$	865.699	−	22.5378i	1.09030	−	0.0283852i
$795$	14.9022	−	27.8800i	0.0187449	−	0.0350692i
$796$	−1317.89	+	628.111i	−1.65564	+	0.789084i
$797$	−48.8321	−	495.801i	−0.0612699	−	0.622084i	−0.975963	−	0.217935i	$-0.930068\pi$
$797$	−48.8321	−	495.801i	−0.0612699	−	0.622084i	0.914693	−	0.404149i	$-0.132432\pi$
$798$	27.9838	−	387.202i	0.0350674	−	0.485216i
$799$	−265.857	+	265.857i	−0.332737	+	0.332737i
$800$	483.524	−	345.934i	0.604406	−	0.432418i
$801$	−28.4957	+	28.4957i	−0.0355751	+	0.0355751i
$802$	−2.33269	+	2.01824i	−0.00290860	+	0.00251651i
$803$	134.494	+	1365.54i	0.167489	+	1.70055i
$804$	320.158	−	355.355i	0.398207	−	0.441984i
$805$	−89.8319	+	168.064i	−0.111592	+	0.208775i
$806$	−185.826	+	195.760i	−0.230553	+	0.242879i
$807$	−422.048	+	282.004i	−0.522984	+	0.349447i
$808$	−513.034	−	1008.02i	−0.634943	−	1.24755i
$809$	1099.96	+	734.968i	1.35965	+	0.908490i	0.999700	−	0.0244817i	$-0.00779356\pi$
$809$	1099.96	+	734.968i	1.35965	+	0.908490i	0.359951	+	0.932971i	$0.382794\pi$
$810$	245.895	+	155.201i	0.303575	+	0.191606i
$811$	611.823	−	502.110i	0.754406	−	0.619125i	−0.176535	−	0.984294i	$-0.556489\pi$
$811$	611.823	−	502.110i	0.754406	−	0.619125i	0.930941	+	0.365169i	$0.118989\pi$
$812$	−5.22638	+	3.15370i	−0.00643642	+	0.00388387i
$813$	−473.643	−	886.123i	−0.582586	−	1.08994i
$814$	−0.537022	+	1.95182i	−0.000659732	+	0.00239781i
$815$	178.919	+	431.950i	0.219533	+	0.530000i
$816$	263.787	+	174.000i	0.323268	+	0.213235i
$817$	−987.565	−	409.063i	−1.20877	−	0.500689i
$818$	−105.192	−	81.8415i	−0.128596	−	0.100051i
$819$	−5.58399	+	18.4079i	−0.00681806	+	0.0224761i
$820$	−356.139	+	128.623i	−0.434316	+	0.156857i
$821$	−122.654	+	1245.33i	−0.149396	+	1.51684i	0.569654	+	0.821885i	$0.307077\pi$
$821$	−122.654	+	1245.33i	−0.149396	+	1.51684i	−0.719050	+	0.694959i	$0.755423\pi$
$822$	53.5850	+	9.21594i	0.0651885	+	0.0112116i
$823$	188.685	+	948.581i	0.229264	+	1.15259i	0.908247	+	0.418435i	$0.137421\pi$
$823$	188.685	+	948.581i	0.229264	+	1.15259i	−0.678982	+	0.734154i	$0.737579\pi$
$824$	16.9895	−	845.569i	0.0206183	−	1.02618i
$825$	−166.355	+	836.323i	−0.201642	+	1.01372i
$826$	100.089	−	44.5444i	0.121173	−	0.0539278i
$827$	387.518	−	117.552i	0.468583	−	0.142143i	−0.0471583	−	0.998887i	$-0.515017\pi$
$827$	387.518	−	117.552i	0.468583	−	0.142143i	0.515741	+	0.856744i	$0.327517\pi$
$828$	−56.7589	−	223.773i	−0.0685494	−	0.270257i
$829$	95.0103	+	77.9729i	0.114608	+	0.0940566i	0.689952	−	0.723855i	$-0.257632\pi$
$829$	95.0103	+	77.9729i	0.114608	+	0.0940566i	−0.575344	+	0.817912i	$0.695132\pi$
$830$	1.99434	+	1.00016i	0.00240282	+	0.00120501i
$831$	−1267.39			−1.52514
$832$	−209.130	+	12.1422i	−0.251358	+	0.0145940i
$833$		−	311.380i		−	0.373805i
$834$	−136.396	−	68.4024i	−0.163544	−	0.0820172i
$835$	−349.566	+	425.947i	−0.418642	+	0.510117i
$836$	957.981	−	1609.11i	1.14591	−	1.92477i
$837$	−349.123	−	1150.91i	−0.417113	−	1.37504i
$838$	1131.81	−	503.709i	1.35061	−	0.601084i
$839$	−300.777	−	59.8283i	−0.358495	−	0.0713090i	0.0125572	−	0.999921i	$-0.496003\pi$
$839$	−300.777	−	59.8283i	−0.358495	−	0.0713090i	−0.371052	+	0.928612i	$0.621003\pi$
$840$	−137.009	+	53.5524i	−0.163106	+	0.0637528i
$841$	824.542	−	164.012i	0.980431	−	0.195020i
$842$	509.738	+	87.6685i	0.605389	+	0.104119i
$843$	−764.397	−	75.2866i	−0.906758	−	0.0893079i
$844$	522.054	−	1112.32i	0.618547	−	1.31792i
$845$	−383.820	−	116.430i	−0.454225	−	0.137788i
$846$	167.345	+	130.198i	0.197807	+	0.153898i
$847$	196.271	−	473.840i	0.231725	−	0.559434i
$848$	−70.4988	−	28.7123i	−0.0831354	−	0.0338588i
$849$	5.44323	−	2.25466i	0.00641134	−	0.00265567i
$850$	74.2437	−	269.840i	0.0873455	−	0.317459i
$851$	1.38604	−	0.740852i	0.00162872	−	0.000870566i
$852$	667.201	+	165.021i	0.783100	+	0.193687i
$853$	375.128	+	457.094i	0.439774	+	0.535867i	0.944978	−	0.327133i	$-0.106083\pi$
$853$	375.128	+	457.094i	0.439774	+	0.535867i	−0.505204	+	0.863000i	$0.668583\pi$
$854$	−199.931	−	126.190i	−0.234111	−	0.147763i
$855$	−79.9727	+	119.688i	−0.0935353	+	0.139986i
$856$	120.737	+	1543.08i	0.141048	+	1.80266i
$857$	200.036	+	299.375i	0.233414	+	0.349329i	0.929624	−	0.368509i	$-0.120132\pi$
$857$	200.036	+	299.375i	0.233414	+	0.349329i	−0.696210	+	0.717838i	$0.745132\pi$
$858$	206.849	−	217.908i	0.241083	−	0.253972i
$859$	−697.551	−	372.849i	−0.812050	−	0.434050i	0.0124428	−	0.999923i	$-0.496039\pi$
$859$	−697.551	−	372.849i	−0.812050	−	0.434050i	−0.824492	+	0.565873i	$0.808539\pi$
$860$	21.0758	+	404.496i	0.0245067	+	0.470344i
$861$	−269.787	+	26.5717i	−0.313341	+	0.0308614i
$862$	827.194	−	715.687i	0.959622	−	0.830264i
$863$	201.325	+	201.325i	0.233285	+	0.233285i	0.814062	−	0.580777i	$-0.197251\pi$
$863$	201.325	+	201.325i	0.233285	+	0.233285i	−0.580777	+	0.814062i	$0.697251\pi$
$864$	413.475	−	836.845i	0.478559	−	0.968571i
$865$	252.553	+	252.553i	0.291969	+	0.291969i
$866$	−4.71097	+	65.1840i	−0.00543991	+	0.0752702i
$867$	−606.146	+	59.7002i	−0.699131	+	0.0688584i
$868$	430.174	+	152.479i	0.495592	+	0.175667i
$869$	−1375.47	−	735.206i	−1.58282	−	0.846037i
$870$	−7.32603	+	0.190728i	−0.00842072	+	0.000219227i
$871$	82.9233	+	124.104i	0.0952048	+	0.142484i
$872$	−1258.88	−	149.579i	−1.44367	−	0.171535i
$873$	189.630	−	283.802i	0.217217	−	0.325088i
$874$	−1418.07	+	320.651i	−1.62251	+	0.366877i
$875$	193.861	+	236.221i	0.221556	+	0.269967i
$876$	813.053	−	123.073i	0.928143	−	0.140495i
$877$	1141.89	−	610.356i	1.30205	−	0.695958i	0.333021	−	0.942919i	$-0.391932\pi$
$877$	1141.89	−	610.356i	1.30205	−	0.695958i	0.969025	+	0.246961i	$0.0794319\pi$
$878$	51.8035	−	29.4480i	0.0590017	−	0.0335399i
$879$	−594.288	+	246.162i	−0.676095	+	0.280048i
$880$	−706.591	−	65.3586i	−0.802944	−	0.0742711i
$881$	327.721	−	791.189i	0.371988	−	0.898058i	−0.621426	−	0.783473i	$-0.713446\pi$
$881$	327.721	−	791.189i	0.371988	−	0.898058i	0.993413	−	0.114585i	$-0.0365538\pi$
$882$	−174.245	+	21.7538i	−0.197557	+	0.0246642i
$883$	−370.887	−	112.507i	−0.420030	−	0.127415i	0.0731925	−	0.997318i	$-0.476681\pi$
$883$	−370.887	−	112.507i	−0.420030	−	0.127415i	−0.493223	+	0.869903i	$0.664181\pi$
$884$	−72.8689	+	66.4397i	−0.0824308	+	0.0751580i
$885$	130.894	+	12.8920i	0.147903	+	0.0145672i
$886$	802.577	+	1135.99i	0.905843	+	1.28215i
$887$	−32.0703	+	6.37919i	−0.0361560	+	0.00719187i	−0.213135	−	0.977023i	$-0.568367\pi$
$887$	−32.0703	+	6.37919i	−0.0361560	+	0.00719187i	0.176979	+	0.984215i	$0.443367\pi$
$888$	1.18487	+	0.260533i	0.00133431	+	0.000293392i
$889$	−177.587	−	35.3242i	−0.199760	−	0.0397348i
$890$	34.4767	−	89.7742i	0.0387379	−	0.100870i
$891$	291.512	+	960.985i	0.327174	+	1.07855i
$892$	1324.22	+	192.412i	1.48455	+	0.215708i
$893$	847.090	−	1032.18i	0.948590	−	1.15586i
$894$	−322.695	−	971.965i	−0.360957	−	1.08721i
$895$		−	341.781i		−	0.381879i
$896$	162.538	+	314.721i	0.181404	+	0.351251i
$897$	−233.256			−0.260040
$898$	1300.54	−	431.785i	1.44827	−	0.480829i
$899$	17.5762	+	14.4244i	0.0195508	+	0.0160449i
$900$	−156.187	−	22.6944i	−0.173541	−	0.0252160i
$901$	−34.2902	+	10.4018i	−0.0380580	+	0.0115448i
$902$	−1220.79	−	468.829i	−1.35342	−	0.519766i
$903$	−56.5734	+	284.414i	−0.0626505	+	0.314965i
$904$	668.884	−	427.752i	0.739916	−	0.473177i
$905$	−108.337	−	544.645i	−0.119709	−	0.601817i
$906$	726.265	−	513.108i	0.801617	−	0.566344i
$907$	−45.2851	+	459.788i	−0.0499285	+	0.506932i	0.937401	+	0.348251i	$0.113224\pi$
$907$	−45.2851	+	459.788i	−0.0499285	+	0.506932i	−0.987330	+	0.158681i	$0.949276\pi$
$908$	−226.645	+	206.648i	−0.249609	+	0.227586i
$909$	−87.1603	+	287.329i	−0.0958859	+	0.316094i
$910$	−5.68678	−	45.5505i	−0.00624921	−	0.0500555i
$911$	−692.637	−	286.900i	−0.760304	−	0.314928i	−0.0313660	−	0.999508i	$-0.509986\pi$
$911$	−692.637	−	286.900i	−0.760304	−	0.314928i	−0.728938	+	0.684580i	$0.759986\pi$
$912$	−992.891	−	523.154i	−1.08870	−	0.573634i
$913$	2.94867	+	7.11871i	0.00322964	+	0.00779705i
$914$	−415.521	−	730.965i	−0.454619	−	0.799743i
$915$	−133.803	−	250.329i	−0.146233	−	0.273583i
$916$	−1558.74	+	235.949i	−1.70168	+	0.257587i
$917$	348.829	−	286.276i	0.380402	−	0.312188i
$918$	−96.9084	−	428.575i	−0.105565	−	0.466857i
$919$	303.924	+	203.075i	0.330711	+	0.220974i	0.709829	−	0.704374i	$-0.248772\pi$
$919$	303.924	+	203.075i	0.330711	+	0.220974i	−0.379117	+	0.925349i	$0.623772\pi$
$920$	340.866	+	432.791i	0.370507	+	0.470426i
$921$	260.743	−	174.223i	0.283108	−	0.189167i
$922$	22.7185	+	872.639i	0.0246405	+	0.946463i
$923$	−101.104	+	189.152i	−0.109538	+	0.204931i
$924$	−478.842	−	169.730i	−0.518227	−	0.183691i
$925$	−0.105313	−	1.06926i	−0.000113852	−	0.00115596i
$926$	1004.98	+	72.6320i	1.08530	+	0.0784363i
$927$	−158.756	+	158.756i	−0.171258	+	0.171258i
$928$	2.29008	+	17.4973i	0.00246776	+	0.0188549i
$929$	−1296.64	+	1296.64i	−1.39574	+	1.39574i	−0.583946	+	0.811793i	$0.698492\pi$
$929$	−1296.64	+	1296.64i	−1.39574	+	1.39574i	−0.811793	+	0.583946i	$0.801508\pi$
$930$	358.516	+	414.374i	0.385501	+	0.445563i
$931$	108.393	+	1100.53i	0.116426	+	1.18210i
$932$	−88.1854	−	1692.49i	−0.0946195	−	1.81598i
$933$	295.672	−	553.163i	0.316904	−	0.592886i
$934$	−311.183	−	295.391i	−0.333172	−	0.316264i
$935$	−277.743	+	185.582i	−0.297051	+	0.198483i
$936$	42.2699	+	36.1352i	0.0451601	+	0.0386059i
$937$	−843.789	−	563.802i	−0.900522	−	0.601710i	0.0167987	−	0.999859i	$-0.494653\pi$
$937$	−843.789	−	563.802i	−0.900522	−	0.601710i	−0.917321	+	0.398149i	$0.869653\pi$
$938$	134.707	−	213.425i	0.143611	−	0.227532i
$939$	−54.2382	+	44.5122i	−0.0577617	+	0.0474038i
$940$	−491.168	−	121.482i	−0.522519	−	0.129237i
$941$	−289.289	−	541.221i	−0.307427	−	0.575155i	0.680004	−	0.733209i	$-0.261978\pi$
$941$	−289.289	−	541.221i	−0.307427	−	0.575155i	−0.987431	+	0.158053i	$0.949478\pi$
$942$	404.856	+	111.392i	0.429784	+	0.118251i
$943$	388.520	+	937.970i	0.412004	+	0.994666i
$944$	−1.88084	−	316.704i	−0.00199242	−	0.335492i
$945$	188.972	+	78.2747i	0.199970	+	0.0828303i
$946$	−858.983	+	1104.06i	−0.908015	+	1.16708i
$947$	188.848	−	622.550i	0.199418	−	0.657391i	−0.799009	−	0.601319i	$-0.794642\pi$
$947$	188.848	−	622.550i	0.199418	−	0.657391i	0.998427	−	0.0560726i	$-0.0178578\pi$
$948$	−397.114	+	846.117i	−0.418896	+	0.892529i
$949$	−25.1519	+	255.371i	−0.0265036	+	0.269095i
$950$	−168.472	+	979.559i	−0.177339	+	1.03111i
$951$	228.129	+	1146.88i	0.239884	+	1.20598i
$952$	152.736	+	66.8910i	0.160437	+	0.0702636i
$953$	−47.2457	+	237.520i	−0.0495758	+	0.249234i	−0.997624	−	0.0688920i	$-0.978054\pi$
$953$	−47.2457	+	237.520i	−0.0495758	+	0.249234i	0.948048	+	0.318126i	$0.103054\pi$
$954$	8.21638	+	18.4618i	0.00861256	+	0.0193520i
$955$	215.155	−	65.2665i	0.225293	−	0.0683419i
$956$	365.850	−	614.515i	0.382688	−	0.642798i
$957$	−19.5646	−	16.0563i	−0.0204437	−	0.0167777i
$958$	−603.386	+	1203.17i	−0.629839	+	1.25591i
$959$	28.6894			0.0299160
$960$	−17.0821	+	424.918i	−0.0177938	+	0.442623i
$961$		−	739.028i		−	0.769020i
$962$	−0.169709	+	0.338405i	−0.000176413	+	0.000351772i
$963$	260.663	−	317.619i	0.270678	−	0.329822i
$964$	204.923	+	807.911i	0.212575	+	0.838082i
$965$	−206.201	−	679.753i	−0.213679	−	0.704407i
$966$	160.368	+	360.339i	0.166012	+	0.373022i
$967$	−184.426	−	36.6847i	−0.190720	−	0.0379366i	0.0988060	−	0.995107i	$-0.468498\pi$
$967$	−184.426	−	36.6847i	−0.190720	−	0.0379366i	−0.289526	+	0.957170i	$0.593498\pi$
$968$	−1027.15	−	1069.27i	−1.06110	−	1.10462i
$969$	−518.150	+	103.066i	−0.534726	+	0.106364i
$970$	−138.060	+	802.731i	−0.142330	+	0.827558i
$971$	−280.042	−	27.5817i	−0.288405	−	0.0284054i	−0.0472199	−	0.998885i	$-0.515036\pi$
$971$	−280.042	−	27.5817i	−0.288405	−	0.0284054i	−0.241185	+	0.970479i	$0.577536\pi$
$972$	−421.619	+	152.271i	−0.433764	+	0.156658i
$973$	−77.0462	−	23.3717i	−0.0791842	−	0.0240203i
$974$	−1157.61	+	1487.89i	−1.18851	+	1.52761i
$975$	−61.0249	+	147.327i	−0.0625897	+	0.151105i
$976$	−566.027	+	383.089i	−0.579946	+	0.392509i
$977$	216.480	−	89.6691i	0.221577	−	0.0917801i	−0.269134	−	0.963103i	$-0.586737\pi$
$977$	216.480	−	89.6691i	0.221577	−	0.0917801i	0.490710	+	0.871323i	$0.336737\pi$
$978$	932.997	+	256.704i	0.953984	+	0.262479i
$979$	292.904	−	156.560i	0.299187	−	0.159919i
$980$	358.777	−	216.494i	0.366099	−	0.220912i
$981$	213.499	+	260.149i	0.217634	+	0.265187i
$982$	323.498	−	512.541i	0.329428	−	0.521936i
$983$	624.030	−	933.926i	0.634822	−	0.950078i	−0.364997	−	0.931009i	$-0.618930\pi$
$983$	624.030	−	933.926i	0.634822	−	0.950078i	0.999818	−	0.0190688i	$-0.00607015\pi$
$984$	−242.516	+	745.235i	−0.246459	+	0.757352i
$985$	−510.119	−	763.447i	−0.517887	−	0.775073i
$986$	6.02474	+	5.71900i	0.00611028	+	0.00580020i
$987$	−319.468	−	170.759i	−0.323676	−	0.173008i
$988$	234.418	−	260.188i	0.237265	−	0.263349i
$989$	1080.78	−	106.447i	1.09280	−	0.107631i
$990$	123.254	+	142.457i	0.124499	+	0.143896i
$991$	665.611	+	665.611i	0.671656	+	0.671656i	0.958098	−	0.286442i	$-0.0924725\pi$
$991$	665.611	+	665.611i	0.671656	+	0.671656i	−0.286442	+	0.958098i	$0.592472\pi$
$992$	902.665	−	962.302i	0.909944	−	0.970063i
$993$	204.899	+	204.899i	0.206344	+	0.206344i
$994$	361.716	+	26.1419i	0.363900	+	0.0262997i
$995$	−920.387	+	90.6502i	−0.925012	+	0.0911058i
$996$	4.16845	−	1.98670i	0.00418519	−	0.00199468i
$997$	−682.827	−	364.978i	−0.684881	−	0.366077i	0.0919692	−	0.995762i	$-0.470684\pi$
$997$	−682.827	−	364.978i	−0.684881	−	0.366077i	−0.776850	+	0.629685i	$0.783184\pi$
$998$	7.65971	+	294.216i	0.00767506	+	0.294806i
$999$	−0.937176	−	1.40258i	−0.000938114	−	0.00140399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.l.a.43.13	yes	496
128.3	odd	32	inner	128.3.l.a.3.13	✓	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.3.l.a.3.13	✓	496	128.3	odd	32	inner
128.3.l.a.43.13	yes	496	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.l (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.630182 - 1.89812i) q^{2} +(-2.02704 - 1.66355i) q^{3} +(-3.20574 + 2.39233i) q^{4} +(-2.42484 + 0.735568i) q^{5} +(-1.88021 + 4.89591i) q^{6} +(-0.539873 + 2.71413i) q^{7} +(6.56113 + 4.57729i) q^{8} +(-0.414318 - 2.08292i) q^{9} +O(q^{10})\)	\(q+(-0.630182 - 1.89812i) q^{2} +(-2.02704 - 1.66355i) q^{3} +(-3.20574 + 2.39233i) q^{4} +(-2.42484 + 0.735568i) q^{5} +(-1.88021 + 4.89591i) q^{6} +(-0.539873 + 2.71413i) q^{7} +(6.56113 + 4.57729i) q^{8} +(-0.414318 - 2.08292i) q^{9} +(2.92429 + 4.13911i) q^{10} +(-1.71554 + 17.4182i) q^{11} +(10.4779 + 0.483563i) q^{12} +(-0.950147 + 3.13221i) q^{13} +(5.49196 - 0.685648i) q^{14} +(6.13890 + 2.54282i) q^{15} +(4.55355 - 15.3384i) q^{16} +(-2.88229 - 6.95847i) q^{17} +(-3.69253 + 2.09904i) q^{18} +(12.6094 + 23.5904i) q^{19} +(6.01370 - 8.15906i) q^{20} +(5.60942 - 4.60353i) q^{21} +(34.1430 - 7.72032i) q^{22} +(-22.5962 - 15.0983i) q^{23} +(-5.68513 - 20.1931i) q^{24} +(-15.4479 + 10.3220i) q^{25} +(6.54409 - 0.170371i) q^{26} +(-13.7503 + 25.7251i) q^{27} +(-4.76238 - 9.99233i) q^{28} +(-0.0540521 - 0.548800i) q^{29} +(0.957951 - 13.2548i) q^{30} +(-29.1550 + 29.1550i) q^{31} +(-31.9837 + 1.02277i) q^{32} +(32.4535 - 32.4535i) q^{33} +(-11.3917 + 9.85604i) q^{34} +(-0.687316 - 6.97844i) q^{35} +(6.31121 + 5.68610i) q^{36} +(-0.0272610 + 0.0510018i) q^{37} +(36.8314 - 38.8004i) q^{38} +(7.13657 - 4.76851i) q^{39} +(-19.2766 - 6.27304i) q^{40} +(-31.0621 - 20.7550i) q^{41} +(-12.2730 - 7.74631i) q^{42} +(-30.8908 + 25.3514i) q^{43} +(-36.1704 - 59.9423i) q^{44} +(2.53678 + 4.74598i) q^{45} +(-14.4187 + 52.4051i) q^{46} +(-19.1031 - 46.1190i) q^{47} +(-34.7463 + 23.5164i) q^{48} +(38.1951 + 15.8209i) q^{49} +(29.3274 + 22.8174i) q^{50} +(-5.73322 + 18.8999i) q^{51} +(-4.44736 - 12.3141i) q^{52} +(0.466326 - 4.73468i) q^{53} +(57.4946 + 9.88835i) q^{54} +(-8.65234 - 43.4983i) q^{55} +(-15.9655 + 15.3366i) q^{56} +(13.6842 - 68.7950i) q^{57} +(-1.00763 + 0.448441i) q^{58} +(18.9420 - 5.74600i) q^{59} +(-25.7630 + 6.53465i) q^{60} +(-33.0210 - 27.0997i) q^{61} +(73.7127 + 36.9668i) q^{62} +5.87697 q^{63} +(22.0969 + 60.0644i) q^{64} -8.29403i q^{65} +(-82.0522 - 41.1491i) q^{66} +(28.9288 - 35.2498i) q^{67} +(25.8868 + 15.4117i) q^{68} +(20.6867 + 68.1948i) q^{69} +(-12.8128 + 5.70230i) q^{70} +(64.2669 + 12.7835i) q^{71} +(6.81571 - 15.5627i) q^{72} +(76.8910 - 15.2946i) q^{73} +(0.113987 + 0.0196043i) q^{74} +(48.4847 + 4.77532i) q^{75} +(-96.8584 - 45.4592i) q^{76} +(-46.3490 - 14.0598i) q^{77} +(-13.5486 - 10.5411i) q^{78} +(-34.1007 + 82.3263i) q^{79} +(0.240774 + 40.5425i) q^{80} +(53.0088 - 21.9570i) q^{81} +(-19.8208 + 72.0391i) q^{82} +(0.388254 - 0.207526i) q^{83} +(-6.96919 + 28.1773i) q^{84} +(12.1075 + 14.7531i) q^{85} +(67.5870 + 42.6585i) q^{86} +(-0.803389 + 1.20236i) q^{87} +(-90.9839 + 106.430i) q^{88} +(-10.5423 - 15.7777i) q^{89} +(7.40983 - 7.80596i) q^{90} +(-7.98826 - 4.26982i) q^{91} +(108.558 - 5.65627i) q^{92} +(107.599 - 10.5976i) q^{93} +(-75.5011 + 65.3235i) q^{94} +(-47.9281 - 47.9281i) q^{95} +(66.5335 + 51.1331i) q^{96} +(113.647 + 113.647i) q^{97} +(5.96019 - 82.4690i) q^{98} +(36.9914 - 3.64333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 496 * 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	\( 496 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} - 640 q^{50} - 16 q^{51} - 1072 q^{52} - 16 q^{53} - 1168 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 736 q^{58} - 16 q^{59} - 592 q^{60} - 16 q^{61} - 112 q^{62} - 32 q^{63} + 176 q^{64} + 560 q^{66} - 16 q^{67} + 464 q^{68} - 16 q^{69} + 1328 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 1216 q^{74} - 16 q^{75} + 1648 q^{76} - 16 q^{77} + 1424 q^{78} - 16 q^{79} + 800 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 496 * 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 - 640 * q^50 - 16 * q^51 - 1072 * q^52 - 16 * q^53 - 1168 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 736 * q^58 - 16 * q^59 - 592 * q^60 - 16 * q^61 - 112 * q^62 - 32 * q^63 + 176 * q^64 + 560 * q^66 - 16 * q^67 + 464 * q^68 - 16 * q^69 + 1328 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 1216 * q^74 - 16 * q^75 + 1648 * q^76 - 16 * q^77 + 1424 * q^78 - 16 * q^79 + 800 * 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

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