LMFDB - Embedded newform 128.3.l.a.3.11

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			3.11
Character	$\chi$	$=$	128.3
Dual form			128.3.l.a.43.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.849476 - 1.81063i) q^{2} +(-0.740915 + 0.608053i) q^{3} +(-2.55678 + 3.07618i) q^{4} +(-2.60449 - 0.790064i) q^{5} +(1.73035 + 0.824998i) q^{6} +(-0.481425 - 2.42029i) q^{7} +(7.74175 + 2.01625i) q^{8} +(-1.57659 + 7.92604i) q^{9} +O(q^{10})$	\(q+(-0.849476 - 1.81063i) q^{2} +(-0.740915 + 0.608053i) q^{3} +(-2.55678 + 3.07618i) q^{4} +(-2.60449 - 0.790064i) q^{5} +(1.73035 + 0.824998i) q^{6} +(-0.481425 - 2.42029i) q^{7} +(7.74175 + 2.01625i) q^{8} +(-1.57659 + 7.92604i) q^{9} +(0.781937 + 5.38692i) q^{10} +(1.38820 + 14.0946i) q^{11} +(0.0238782 - 3.83384i) q^{12} +(3.31551 + 10.9298i) q^{13} +(-3.97329 + 2.92766i) q^{14} +(2.41011 - 0.998299i) q^{15} +(-2.92574 - 15.7302i) q^{16} +(-5.67490 + 13.7004i) q^{17} +(15.6904 - 3.87836i) q^{18} +(-0.788950 + 1.47602i) q^{19} +(9.08949 - 5.99186i) q^{20} +(1.82836 + 1.50049i) q^{21} +(24.3410 - 14.4866i) q^{22} +(15.3342 - 10.2460i) q^{23} +(-6.96197 + 3.21352i) q^{24} +(-14.6276 - 9.77383i) q^{25} +(16.9734 - 15.2878i) q^{26} +(-7.71775 - 14.4389i) q^{27} +(8.67613 + 4.70719i) q^{28} +(-4.87645 + 49.5115i) q^{29} +(-3.85488 - 3.51579i) q^{30} +(-22.7164 - 22.7164i) q^{31} +(-25.9963 + 18.6599i) q^{32} +(-9.59882 - 9.59882i) q^{33} +(29.6271 - 1.36302i) q^{34} +(-0.658314 + 6.68397i) q^{35} +(-20.3509 - 25.1150i) q^{36} +(0.562008 + 1.05144i) q^{37} +(3.34273 + 0.174654i) q^{38} +(-9.10240 - 6.08203i) q^{39} +(-18.5704 - 11.3678i) q^{40} +(-42.1875 + 28.1888i) q^{41} +(1.16370 - 4.58512i) q^{42} +(-5.77105 - 4.73618i) q^{43} +(-46.9069 - 31.7666i) q^{44} +(10.3683 - 19.3977i) q^{45} +(-31.5777 - 19.0609i) q^{46} +(10.8542 - 26.2043i) q^{47} +(11.7325 + 9.87576i) q^{48} +(39.6441 - 16.4211i) q^{49} +(-5.27105 + 34.7878i) q^{50} +(-4.12596 - 13.6015i) q^{51} +(-42.0990 - 17.7460i) q^{52} +(5.17075 + 52.4995i) q^{53} +(-19.5875 + 26.2395i) q^{54} +(7.52011 - 37.8061i) q^{55} +(1.15284 - 19.7079i) q^{56} +(-0.312955 - 1.57333i) q^{57} +(93.7895 - 33.2293i) q^{58} +(-74.3666 - 22.5589i) q^{59} +(-3.09117 + 9.96635i) q^{60} +(18.4632 - 15.1524i) q^{61} +(-21.8341 + 60.4282i) q^{62} +19.9423 q^{63} +(55.8694 + 31.2187i) q^{64} -31.0860i q^{65} +(-9.22598 + 25.5339i) q^{66} +(26.7709 + 32.6205i) q^{67} +(-27.6354 - 52.4860i) q^{68} +(-5.13122 + 16.9154i) q^{69} +(12.6614 - 4.48591i) q^{70} +(100.537 - 19.9980i) q^{71} +(-28.1864 + 58.1826i) q^{72} +(27.5345 + 5.47695i) q^{73} +(1.42636 - 1.91076i) q^{74} +(16.7808 - 1.65276i) q^{75} +(-2.52333 - 6.20082i) q^{76} +(33.4447 - 10.1454i) q^{77} +(-3.28005 + 21.6476i) q^{78} +(-9.90450 - 23.9116i) q^{79} +(-4.80783 + 43.2808i) q^{80} +(-52.6977 - 21.8281i) q^{81} +(86.8769 + 52.4404i) q^{82} +(132.576 + 70.8633i) q^{83} +(-9.29050 + 1.78792i) q^{84} +(25.6044 - 31.1991i) q^{85} +(-3.67311 + 14.4725i) q^{86} +(-26.4926 - 39.6489i) q^{87} +(-17.6713 + 111.916i) q^{88} +(-44.7450 + 66.9656i) q^{89} +(-43.9297 - 2.29528i) q^{90} +(24.8570 - 13.2864i) q^{91} +(-7.68772 + 73.3673i) q^{92} +(30.6437 + 3.01814i) q^{93} +(-56.6666 + 2.60699i) q^{94} +(3.22097 - 3.22097i) q^{95} +(7.91486 - 29.6325i) q^{96} +(-3.34959 + 3.34959i) q^{97} +(-63.4093 - 57.8315i) q^{98} +(-113.903 - 11.2185i) 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 $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.849476	−	1.81063i	−0.424738	−	0.905316i
$2$	−0.849476	−	1.81063i	−0.424738	−	0.905316i
$3$	−0.740915	+	0.608053i	−0.246972	+	0.202684i	−0.749732	−	0.661741i	$-0.769818\pi$
$3$	−0.740915	+	0.608053i	−0.246972	+	0.202684i	0.502761	+	0.864426i	$0.332318\pi$
$4$	−2.55678	+	3.07618i	−0.639195	+	0.769044i
$5$	−2.60449	−	0.790064i	−0.520898	−	0.158013i	0.0188771	−	0.999822i	$-0.493991\pi$
$5$	−2.60449	−	0.790064i	−0.520898	−	0.158013i	−0.539775	+	0.841809i	$0.681491\pi$
$6$	1.73035	+	0.824998i	0.288392	+	0.137500i
$7$	−0.481425	−	2.42029i	−0.0687750	−	0.345755i	0.931041	−	0.364913i	$-0.118901\pi$
$7$	−0.481425	−	2.42029i	−0.0687750	−	0.345755i	−0.999816	+	0.0191582i	$0.993901\pi$
$8$	7.74175	+	2.01625i	0.967719	+	0.252032i
$9$	−1.57659	+	7.92604i	−0.175176	+	0.880671i
$10$	0.781937	+	5.38692i	0.0781937	+	0.538692i
$11$	1.38820	+	14.0946i	0.126200	+	1.28133i	0.824638	+	0.565660i	$0.191379\pi$
$11$	1.38820	+	14.0946i	0.126200	+	1.28133i	−0.698438	+	0.715670i	$0.746121\pi$
$12$	0.0238782	−	3.83384i	0.00198985	−	0.319487i
$13$	3.31551	+	10.9298i	0.255039	+	0.840752i	0.987182	+	0.159601i	$0.0510206\pi$
$13$	3.31551	+	10.9298i	0.255039	+	0.840752i	−0.732142	+	0.681152i	$0.761479\pi$
$14$	−3.97329	+	2.92766i	−0.283806	+	0.209118i
$15$	2.41011	−	0.998299i	0.160674	−	0.0665533i
$16$	−2.92574	−	15.7302i	−0.182858	−	0.983139i
$17$	−5.67490	+	13.7004i	−0.333818	+	0.805907i	0.664465	+	0.747320i	$0.268660\pi$
$17$	−5.67490	+	13.7004i	−0.333818	+	0.805907i	−0.998282	+	0.0585873i	$0.981340\pi$
$18$	15.6904	−	3.87836i	0.871690	−	0.215464i
$19$	−0.788950	+	1.47602i	−0.0415237	+	0.0776854i	−0.901827	−	0.432097i	$-0.857774\pi$
$19$	−0.788950	+	1.47602i	−0.0415237	+	0.0776854i	0.860304	+	0.509782i	$0.170274\pi$
$20$	9.08949	−	5.99186i	0.454475	−	0.299593i
$21$	1.82836	+	1.50049i	0.0870646	+	0.0714521i
$22$	24.3410	−	14.4866i	1.10641	−	0.658481i
$23$	15.3342	−	10.2460i	0.666703	−	0.445477i	−0.175614	−	0.984459i	$-0.556191\pi$
$23$	15.3342	−	10.2460i	0.666703	−	0.445477i	0.842317	+	0.538982i	$0.181191\pi$
$24$	−6.96197	+	3.21352i	−0.290082	+	0.133897i
$25$	−14.6276	−	9.77383i	−0.585103	−	0.390953i
$26$	16.9734	−	15.2878i	0.652822	−	0.587991i
$27$	−7.71775	−	14.4389i	−0.285843	−	0.534774i
$28$	8.67613	+	4.70719i	0.309862	+	0.168114i
$29$	−4.87645	+	49.5115i	−0.168154	+	1.70729i	0.427471	+	0.904029i	$0.359405\pi$
$29$	−4.87645	+	49.5115i	−0.168154	+	1.70729i	−0.595625	+	0.803263i	$0.703095\pi$
$30$	−3.85488	−	3.51579i	−0.128496	−	0.117193i
$31$	−22.7164	−	22.7164i	−0.732788	−	0.732788i	0.238383	−	0.971171i	$-0.423383\pi$
$31$	−22.7164	−	22.7164i	−0.732788	−	0.732788i	−0.971171	+	0.238383i	$0.923383\pi$
$32$	−25.9963	+	18.6599i	−0.812385	+	0.583121i
$33$	−9.59882	−	9.59882i	−0.290873	−	0.290873i
$34$	29.6271	−	1.36302i	0.871386	−	0.0400887i
$35$	−0.658314	+	6.68397i	−0.0188090	+	0.190971i
$36$	−20.3509	−	25.1150i	−0.565303	−	0.697639i
$37$	0.562008	+	1.05144i	0.0151894	+	0.0284174i	0.889401	−	0.457127i	$-0.151121\pi$
$37$	0.562008	+	1.05144i	0.0151894	+	0.0284174i	−0.874212	+	0.485544i	$0.838621\pi$
$38$	3.34273	+	0.174654i	0.0879665	+	0.00459616i
$39$	−9.10240	−	6.08203i	−0.233395	−	0.155949i
$40$	−18.5704	−	11.3678i	−0.464259	−	0.284195i
$41$	−42.1875	+	28.1888i	−1.02896	+	0.687532i	−0.950926	−	0.309418i	$-0.899866\pi$
$41$	−42.1875	+	28.1888i	−1.02896	+	0.687532i	−0.0780384	+	0.996950i	$0.524866\pi$
$42$	1.16370	−	4.58512i	0.0277071	−	0.109169i
$43$	−5.77105	−	4.73618i	−0.134211	−	0.110144i	0.564893	−	0.825164i	$-0.308917\pi$
$43$	−5.77105	−	4.73618i	−0.134211	−	0.110144i	−0.699104	+	0.715020i	$0.746417\pi$
$44$	−46.9069	−	31.7666i	−1.06607	−	0.721967i
$45$	10.3683	−	19.3977i	0.230406	−	0.431060i
$46$	−31.5777	−	19.0609i	−0.686471	−	0.414366i
$47$	10.8542	−	26.2043i	0.230940	−	0.557537i	−0.765349	−	0.643616i	$-0.777434\pi$
$47$	10.8542	−	26.2043i	0.230940	−	0.557537i	0.996288	+	0.0860783i	$0.0274335\pi$
$48$	11.7325	+	9.87576i	0.244428	+	0.205745i
$49$	39.6441	−	16.4211i	0.809063	−	0.335125i
$50$	−5.27105	+	34.7878i	−0.105421	+	0.695755i
$51$	−4.12596	−	13.6015i	−0.0809013	−	0.266696i
$52$	−42.0990	−	17.7460i	−0.809596	−	0.341268i
$53$	5.17075	+	52.4995i	0.0975614	+	0.990557i	0.911968	+	0.410262i	$0.134563\pi$
$53$	5.17075	+	52.4995i	0.0975614	+	0.990557i	−0.814406	+	0.580295i	$0.802937\pi$
$54$	−19.5875	+	26.2395i	−0.362731	+	0.485917i
$55$	7.52011	−	37.8061i	0.136729	−	0.687384i
$56$	1.15284	−	19.7079i	0.0205864	−	0.351927i
$57$	−0.312955	−	1.57333i	−0.00549043	−	0.0276023i
$58$	93.7895	−	33.2293i	1.61706	−	0.572919i
$59$	−74.3666	−	22.5589i	−1.26045	−	0.382354i	−0.411784	−	0.911281i	$-0.635094\pi$
$59$	−74.3666	−	22.5589i	−1.26045	−	0.382354i	−0.848667	+	0.528928i	$0.822594\pi$
$60$	−3.09117	+	9.96635i	−0.0515195	+	0.166106i
$61$	18.4632	−	15.1524i	0.302676	−	0.248400i	−0.470779	−	0.882251i	$-0.656027\pi$
$61$	18.4632	−	15.1524i	0.302676	−	0.248400i	0.773455	+	0.633851i	$0.218527\pi$
$62$	−21.8341	+	60.4282i	−0.352162	+	0.974648i
$63$	19.9423			0.316544
$64$	55.8694	+	31.2187i	0.872960	+	0.487792i
$65$		−	31.0860i		−	0.478246i
$66$	−9.22598	+	25.5339i	−0.139788	+	0.386878i
$67$	26.7709	+	32.6205i	0.399566	+	0.486873i	0.933461	−	0.358678i	$-0.116772\pi$
$67$	26.7709	+	32.6205i	0.399566	+	0.486873i	−0.533895	+	0.845551i	$0.679272\pi$
$68$	−27.6354	−	52.4860i	−0.406404	−	0.771853i
$69$	−5.13122	+	16.9154i	−0.0743655	+	0.245150i
$70$	12.6614	−	4.48591i	0.180878	−	0.0640844i
$71$	100.537	−	19.9980i	1.41601	−	0.281662i	0.572999	−	0.819556i	$-0.305780\pi$
$71$	100.537	−	19.9980i	1.41601	−	0.281662i	0.843013	+	0.537894i	$0.180780\pi$
$72$	−28.1864	+	58.1826i	−0.391478	+	0.808092i
$73$	27.5345	+	5.47695i	0.377185	+	0.0750267i	0.380042	−	0.924969i	$-0.375910\pi$
$73$	27.5345	+	5.47695i	0.377185	+	0.0750267i	−0.00285740	+	0.999996i	$0.500910\pi$
$74$	1.42636	−	1.91076i	0.0192752	−	0.0258211i
$75$	16.7808	−	1.65276i	0.223744	−	0.0220368i
$76$	−2.52333	−	6.20082i	−0.0332017	−	0.0815897i
$77$	33.4447	−	10.1454i	0.434347	−	0.131758i
$78$	−3.28005	+	21.6476i	−0.0420519	+	0.277534i
$79$	−9.90450	−	23.9116i	−0.125373	−	0.302678i	0.848713	−	0.528853i	$-0.177378\pi$
$79$	−9.90450	−	23.9116i	−0.125373	−	0.302678i	−0.974087	+	0.226175i	$0.927378\pi$
$80$	−4.80783	+	43.2808i	−0.0600979	+	0.541010i
$81$	−52.6977	−	21.8281i	−0.650588	−	0.269483i
$82$	86.8769	+	52.4404i	1.05947	+	0.639517i
$83$	132.576	+	70.8633i	1.59730	+	0.853774i	0.998605	+	0.0527969i	$0.0168136\pi$
$83$	132.576	+	70.8633i	1.59730	+	0.853774i	0.598694	+	0.800978i	$0.295686\pi$
$84$	−9.29050	+	1.78792i	−0.110601	+	0.0212847i
$85$	25.6044	−	31.1991i	0.301229	−	0.367048i
$86$	−3.67311	+	14.4725i	−0.0427106	+	0.168285i
$87$	−26.4926	−	39.6489i	−0.304512	−	0.455735i
$88$	−17.6713	+	111.916i	−0.200810	+	1.27177i
$89$	−44.7450	+	66.9656i	−0.502753	+	0.752423i	−0.992866	−	0.119236i	$-0.961955\pi$
$89$	−44.7450	+	66.9656i	−0.502753	+	0.752423i	0.490113	+	0.871659i	$0.336955\pi$
$90$	−43.9297	−	2.29528i	−0.488108	−	0.0255031i
$91$	24.8570	−	13.2864i	0.273154	−	0.146004i
$92$	−7.68772	+	73.3673i	−0.0835621	+	0.797471i
$93$	30.6437	+	3.01814i	0.329502	+	0.0324532i
$94$	−56.6666	+	2.60699i	−0.602837	+	0.0277339i
$95$	3.22097	−	3.22097i	0.0339049	−	0.0339049i
$96$	7.91486	−	29.6325i	0.0824465	−	0.308672i
$97$	−3.34959	+	3.34959i	−0.0345318	+	0.0345318i	−0.724162	−	0.689630i	$-0.757773\pi$
$97$	−3.34959	+	3.34959i	−0.0345318	+	0.0345318i	0.689630	+	0.724162i	$0.257773\pi$
$98$	−63.4093	−	57.8315i	−0.647034	−	0.590118i
$99$	−113.903	−	11.2185i	−1.15054	−	0.113318i
$100$	67.4655	−	20.0074i	0.674655	−	0.200074i
$101$	80.3983	−	42.9738i	0.796022	−	0.425483i	−0.0226502	−	0.999743i	$-0.507210\pi$
$101$	80.3983	−	42.9738i	0.796022	−	0.425483i	0.818673	+	0.574261i	$0.194710\pi$
$102$	−21.1224	+	19.0247i	−0.207082	+	0.186517i
$103$	16.3335	−	24.4448i	0.158577	−	0.237328i	−0.743670	−	0.668547i	$-0.766917\pi$
$103$	16.3335	−	24.4448i	0.158577	−	0.237328i	0.902247	+	0.431219i	$0.141917\pi$
$104$	3.63066	+	91.3006i	0.0349102	+	0.877890i
$105$	−3.57645	−	5.35254i	−0.0340615	−	0.0509766i
$106$	90.6649	−	53.9594i	0.855330	−	0.509051i
$107$	−39.7348	+	48.4170i	−0.371353	+	0.452495i	−0.924836	−	0.380365i	$-0.875798\pi$
$107$	−39.7348	+	48.4170i	−0.371353	+	0.452495i	0.553483	+	0.832860i	$0.313298\pi$
$108$	64.1492	+	13.1759i	0.593974	+	0.121999i
$109$	105.352	+	56.3118i	0.966532	+	0.516622i	0.877589	−	0.479414i	$-0.159151\pi$
$109$	105.352	+	56.3118i	0.966532	+	0.516622i	0.0889435	+	0.996037i	$0.471651\pi$
$110$	−74.8412	+	18.4992i	−0.680374	+	0.168175i
$111$	−1.05573	−	0.437299i	−0.00951110	−	0.00393963i
$112$	−36.6631	+	14.6540i	−0.327349	+	0.130840i
$113$	−65.3591	−	157.791i	−0.578399	−	1.39638i	−0.894249	−	0.447570i	$-0.852289\pi$
$113$	−65.3591	−	157.791i	−0.578399	−	1.39638i	0.315849	−	0.948809i	$-0.397711\pi$
$114$	−2.58287	+	1.90315i	−0.0226568	+	0.0166943i
$115$	−48.0327	+	14.5706i	−0.417676	+	0.126700i
$116$	−139.838	−	141.591i	−1.20550	−	1.22061i
$117$	−91.8570	+	9.04713i	−0.785103	+	0.0773259i
$118$	22.3268	+	153.814i	0.189210	+	1.30351i
$119$	35.8910	+	7.13916i	0.301605	+	0.0599929i
$120$	20.6713	−	2.86920i	0.172261	−	0.0239100i
$121$	−78.0567	+	15.5264i	−0.645096	+	0.128318i
$122$	−43.1195	−	20.5586i	−0.353439	−	0.168513i
$123$	14.1171	−	46.5378i	0.114773	−	0.378356i
$124$	127.961	−	11.7988i	1.03194	−	0.0951518i
$125$	73.5409	+	89.6099i	0.588327	+	0.716879i
$126$	−16.9405	−	36.1082i	−0.134448	−	0.286573i
$127$		−	4.82698i		−	0.0380077i	−0.999819	−	0.0190039i	$-0.993951\pi$
$127$		−	4.82698i		−	0.0380077i	0.999819	−	0.0190039i	$-0.00604948\pi$
$128$	9.06581	−	127.679i	0.0708267	−	0.997489i
$129$	7.15571			0.0554706
$130$	−56.2853	+	26.4068i	−0.432964	+	0.203129i
$131$	−107.532	+	88.2493i	−0.820856	+	0.673659i	−0.948016	−	0.318223i	$-0.896914\pi$
$131$	−107.532	+	88.2493i	−0.820856	+	0.673659i	0.127160	+	0.991882i	$0.459414\pi$
$132$	54.0698	−	4.98559i	0.409620	−	0.0377696i
$133$	3.95222	+	1.19889i	0.0297159	+	0.00901422i
$134$	36.3225	−	76.1827i	0.271063	−	0.568527i
$135$	8.69317	+	43.7035i	0.0643938	+	0.323730i
$136$	−71.5572	+	94.6232i	−0.526156	+	0.695759i
$137$	−2.10698	+	10.5925i	−0.0153794	+	0.0773175i	−0.987713	−	0.156280i	$-0.950050\pi$
$137$	−2.10698	+	10.5925i	−0.0153794	+	0.0773175i	0.972333	+	0.233597i	$0.0750498\pi$
$138$	34.9864	−	5.07844i	0.253524	−	0.0368003i
$139$	−7.63402	−	77.5095i	−0.0549210	−	0.557623i	−0.982791	−	0.184719i	$-0.940862\pi$
$139$	−7.63402	−	77.5095i	−0.0549210	−	0.557623i	0.927870	−	0.372903i	$-0.121638\pi$
$140$	−18.8779	−	19.1145i	−0.134842	−	0.136532i
$141$	7.89157	+	26.0150i	0.0559686	+	0.184504i
$142$	−121.613	−	165.047i	−0.856427	−	1.16231i
$143$	−149.449	+	61.9037i	−1.04510	+	0.432893i
$144$	129.291	+	1.61058i	0.897854	+	0.0111846i
$145$	51.8179	−	125.099i	0.357365	−	0.862755i
$146$	−13.4731	−	54.5074i	−0.0922817	−	0.373338i
$147$	−19.3880	+	36.2724i	−0.131891	+	0.246751i
$148$	−4.67135	−	0.959473i	−0.0315632	−	0.00648293i
$149$	−136.859	−	112.317i	−0.918518	−	0.753808i	0.0510333	−	0.998697i	$-0.483749\pi$
$149$	−136.859	−	112.317i	−0.918518	−	0.753808i	−0.969551	+	0.244889i	$0.921249\pi$
$150$	−17.2474	−	28.9798i	−0.114983	−	0.193199i
$151$	187.744	−	125.447i	1.24334	−	0.830772i	0.252734	−	0.967536i	$-0.418670\pi$
$151$	187.744	−	125.447i	1.24334	−	0.830772i	0.990604	+	0.136764i	$0.0436702\pi$
$152$	−9.08389	+	9.83627i	−0.0597624	+	0.0647123i
$153$	−99.6431	−	66.5794i	−0.651262	−	0.435159i
$154$	−46.7800	−	51.9379i	−0.303766	−	0.337259i
$155$	41.2173	+	77.1122i	0.265918	+	0.497498i
$156$	41.9822	−	12.4502i	0.269117	−	0.0798088i
$157$	−6.36612	+	64.6363i	−0.0405485	+	0.411696i	0.953389	+	0.301745i	$0.0975693\pi$
$157$	−6.36612	+	64.6363i	−0.0405485	+	0.411696i	−0.993937	+	0.109951i	$0.964931\pi$
$158$	−34.8814	+	38.2457i	−0.220769	+	0.242061i
$159$	−35.7536	−	35.7536i	−0.224865	−	0.224865i
$160$	82.4497	−	28.0608i	0.515311	−	0.175380i
$161$	−32.1804	−	32.1804i	−0.199878	−	0.199878i
$162$	5.24274	+	113.959i	0.0323626	+	0.703448i
$163$	−21.2101	+	215.350i	−0.130123	+	1.32116i	0.679266	+	0.733892i	$0.262298\pi$
$163$	−21.2101	+	215.350i	−0.130123	+	1.32116i	−0.809389	+	0.587272i	$0.800202\pi$
$164$	21.1505	−	201.849i	0.128967	−	1.23079i
$165$	17.4164	+	32.5837i	0.105554	+	0.197477i
$166$	15.6874	−	300.243i	0.0945022	−	1.80869i
$167$	228.954	+	152.982i	1.37098	+	0.916059i	0.999921	−	0.0125499i	$-0.00399488\pi$
$167$	228.954	+	152.982i	1.37098	+	0.916059i	0.371059	+	0.928609i	$0.378995\pi$
$168$	11.1293	+	15.3029i	0.0662459	+	0.0910886i
$169$	32.0509	−	21.4157i	0.189650	−	0.126720i
$170$	−78.2405	−	19.8574i	−0.460238	−	0.116808i
$171$	−10.4552	−	8.58032i	−0.0611413	−	0.0501773i
$172$	29.3247	−	5.64341i	0.170492	−	0.0328105i
$173$	111.125	−	207.901i	0.642344	−	1.20174i	−0.324382	−	0.945926i	$-0.605156\pi$
$173$	111.125	−	207.901i	0.642344	−	1.20174i	0.966726	−	0.255814i	$-0.0823436\pi$
$174$	−49.2848	+	81.6491i	−0.283246	+	0.469248i
$175$	−16.6134	+	40.1083i	−0.0949336	+	0.229190i
$176$	217.650	−	63.0739i	1.23665	−	0.358374i
$177$	68.8163	−	28.5047i	0.388793	−	0.161043i
$178$	159.260	+	24.1311i	0.894719	+	0.135568i
$179$	61.0280	+	201.182i	0.340939	+	1.12392i	0.945023	+	0.327004i	$0.106039\pi$
$179$	61.0280	+	201.182i	0.340939	+	1.12392i	−0.604084	+	0.796920i	$0.706461\pi$
$180$	33.1613	+	81.4903i	0.184230	+	0.452724i
$181$	−20.0243	−	203.310i	−0.110632	−	1.12326i	−0.876877	−	0.480714i	$-0.840378\pi$
$181$	−20.0243	−	203.310i	−0.110632	−	1.12326i	0.766246	−	0.642547i	$-0.222122\pi$
$182$	−45.1722	−	33.7205i	−0.248199	−	0.185277i
$183$	−4.46623	+	22.4533i	−0.0244056	+	0.122695i
$184$	139.372	−	48.4041i	0.757455	−	0.263066i
$185$	−0.633038	−	3.18250i	−0.00342183	−	0.0172027i
$186$	−20.5664	−	58.0484i	−0.110572	−	0.312088i
$187$	−200.980	−	60.9667i	−1.07476	−	0.326025i
$188$	52.8572	+	100.388i	0.281156	+	0.533978i
$189$	−31.2307	+	25.6304i	−0.165242	+	0.135611i
$190$	−8.56812	−	3.09585i	−0.0450954	−	0.0162940i
$191$	−309.050			−1.61806			−0.809031	−	0.587766i	$-0.800008\pi$
$191$	−309.050			−1.61806			−0.809031	+	0.587766i	$0.800008\pi$
$192$	−60.3771	+	10.8412i	−0.314464	+	0.0564646i
$193$			203.949i			1.05673i	0.849017	+	0.528366i	$0.177195\pi$
$193$			203.949i			1.05673i	−0.849017	+	0.528366i	$0.822805\pi$
$194$	8.91027	+	3.21948i	0.0459292	+	0.0165953i
$195$	18.9019	+	23.0321i	0.0969330	+	0.118113i
$196$	−50.8470	+	163.937i	−0.259423	+	0.836416i
$197$	−33.1233	+	109.193i	−0.168138	+	0.554278i	−1.00000		0.000705386i	$-0.999775\pi$
$197$	−33.1233	+	109.193i	−0.168138	+	0.554278i	0.831861	+	0.554984i	$0.187275\pi$
$198$	76.4455	+	215.767i	0.386088	+	1.08973i
$199$	−350.149	+	69.6491i	−1.75954	+	0.349995i	−0.966005	−	0.258523i	$-0.916764\pi$
$199$	−350.149	+	69.6491i	−1.75954	+	0.349995i	−0.793540	+	0.608518i	$0.791764\pi$
$200$	−93.5365	−	105.159i	−0.467682	−	0.525797i
$201$	−39.6700	−	7.89085i	−0.197363	−	0.0392579i
$202$	−146.106	−	109.067i	−0.723297	−	0.539933i
$203$	122.180	−	12.0336i	0.601870	−	0.0592790i
$204$	52.3898	+	22.0838i	0.256813	+	0.108254i
$205$	132.148	−	40.0867i	0.644625	−	0.195545i
$206$	−58.1354	−	8.80867i	−0.282210	−	0.0427606i
$207$	57.0342	+	137.693i	0.275528	+	0.665183i
$208$	162.228	−	84.1314i	0.779940	−	0.404478i
$209$	−21.8992	−	9.07095i	−0.104781	−	0.0434017i
$210$	−6.65338	+	11.0225i	−0.0316828	+	0.0524881i
$211$	−18.7955	−	10.0464i	−0.0890783	−	0.0476133i	0.426256	−	0.904603i	$-0.359832\pi$
$211$	−18.7955	−	10.0464i	−0.0890783	−	0.0476133i	−0.515334	+	0.856989i	$0.672332\pi$
$212$	−174.718	−	118.324i	−0.824143	−	0.558131i
$213$	−62.3294	+	75.9485i	−0.292626	+	0.356566i
$214$	121.419	+	30.8160i	0.567379	+	0.144000i
$215$	11.2888	+	16.8949i	0.0525059	+	0.0785807i
$216$	−30.6364	−	127.343i	−0.141835	−	0.589552i
$217$	−44.0440	+	65.9165i	−0.202968	+	0.303763i
$218$	12.4660	−	238.589i	0.0571837	−	1.09445i
$219$	−23.7310	+	12.6845i	−0.108361	+	0.0579199i
$220$	97.0711	+	119.795i	0.441232	+	0.544524i
$221$	−168.558	−	16.6015i	−0.762705	−	0.0751199i
$222$	0.105032	+	2.28302i	0.000473117	+	0.0102839i
$223$	−114.570	+	114.570i	−0.513766	+	0.513766i	−0.915678	−	0.401912i	$-0.868346\pi$
$223$	−114.570	+	114.570i	−0.513766	+	0.513766i	0.401912	+	0.915678i	$0.368346\pi$
$224$	57.6775	+	53.9352i	0.257489	+	0.240782i
$225$	100.529	−	100.529i	0.446797	−	0.446797i
$226$	−230.180	+	252.381i	−1.01850	+	1.11673i
$227$	157.721	+	15.5342i	0.694807	+	0.0684325i	0.439254	−	0.898363i	$-0.355243\pi$
$227$	157.721	+	15.5342i	0.694807	+	0.0684325i	0.255552	+	0.966795i	$0.417743\pi$
$228$	5.64000	+	3.05996i	0.0247368	+	0.0134209i
$229$	31.2540	−	16.7056i	0.136480	−	0.0729502i	−0.401743	−	0.915752i	$-0.631596\pi$
$229$	31.2540	−	16.7056i	0.136480	−	0.0729502i	0.538224	+	0.842802i	$0.319096\pi$
$230$	67.1845	+	74.5922i	0.292107	+	0.324314i
$231$	−18.6108	+	27.8530i	−0.0805662	+	0.120576i
$232$	−137.580	+	373.473i	−0.593017	+	1.60980i
$233$	221.967	+	332.197i	0.952648	+	1.42574i	0.904295	+	0.426908i	$0.140397\pi$
$233$	221.967	+	332.197i	0.952648	+	1.42574i	0.0483531	+	0.998830i	$0.484603\pi$
$234$	94.4114	+	158.634i	0.403467	+	0.677923i
$235$	−48.9726	+	59.6733i	−0.208394	+	0.253929i
$236$	259.534	−	171.087i	1.09972	−	0.724944i
$237$	21.8779	+	11.6940i	0.0923118	+	0.0493417i
$238$	−17.5621	−	71.0499i	−0.0737904	−	0.298529i
$239$	177.075	+	73.3467i	0.740898	+	0.306890i	0.721022	−	0.692913i	$-0.243673\pi$
$239$	177.075	+	73.3467i	0.740898	+	0.306890i	0.0198760	+	0.999802i	$0.493673\pi$
$240$	−22.7548	−	34.9908i	−0.0948117	−	0.145795i
$241$	−79.7765	−	192.598i	−0.331023	−	0.799160i	−0.998512	−	0.0545400i	$-0.982631\pi$
$241$	−79.7765	−	192.598i	−0.331023	−	0.799160i	0.667489	−	0.744620i	$-0.267369\pi$
$242$	94.4199	+	128.143i	0.390165	+	0.529515i
$243$	193.321	−	58.6433i	0.795560	−	0.241331i
$244$	−0.595033	+	95.5376i	−0.00243866	+	0.391547i
$245$	−116.226	+	11.4473i	−0.474394	+	0.0467237i
$246$	−96.2549	+	13.9719i	−0.391280	+	0.0567962i
$247$	−18.7484	−	3.72928i	−0.0759043	−	0.0150983i
$248$	−130.063	−	221.667i	−0.524447	−	0.893819i
$249$	−141.316	+	28.1095i	−0.567534	+	0.112890i
$250$	99.7793	−	209.277i	0.399117	−	0.837108i
$251$	71.3509	−	235.213i	0.284267	−	0.937102i	−0.692250	−	0.721658i	$-0.743380\pi$
$251$	71.3509	−	235.213i	0.284267	−	0.937102i	0.976516	−	0.215444i	$-0.0691197\pi$
$252$	−50.9881	+	61.3460i	−0.202334	+	0.243437i
$253$	165.700	+	201.906i	0.654941	+	0.798048i
$254$	−8.73989	+	4.10041i	−0.0344090	+	0.0161433i
$255$			38.6847i			0.151705i
$256$	−238.880	+	92.0450i	−0.933126	+	0.359551i
$257$	508.297			1.97781			0.988904	−	0.148555i	$-0.0474623\pi$
$257$	508.297			1.97781			0.988904	+	0.148555i	$0.0474623\pi$
$258$	−6.07860	−	12.9564i	−0.0235605	−	0.0502185i
$259$	2.27423	−	1.86641i	0.00878080	−	0.00720622i
$260$	95.6260	+	79.4801i	0.367792	+	0.305693i
$261$	−384.741	−	116.710i	−1.47411	−	0.447165i
$262$	251.133	+	119.735i	0.958523	+	0.457006i
$263$	−20.0310	−	100.703i	−0.0761634	−	0.382899i	−1.00000		0.000112257i	$-0.999964\pi$
$263$	−20.0310	−	100.703i	−0.0761634	−	0.382899i	0.923837	−	0.382787i	$-0.125036\pi$
$264$	−54.9581	−	93.6654i	−0.208174	−	0.354793i
$265$	28.0108	−	140.820i	0.105701	−	0.531396i
$266$	−1.18656	−	8.17444i	−0.00446075	−	0.0307310i
$267$	−7.56642	−	76.8232i	−0.0283387	−	0.287727i
$268$	−168.794	−	1.05129i	−0.629828	−	0.00392273i
$269$	−9.69646	−	31.9649i	−0.0360463	−	0.118829i	0.937071	−	0.349139i	$-0.113526\pi$
$269$	−9.69646	−	31.9649i	−0.0360463	−	0.118829i	−0.973117	+	0.230310i	$0.926026\pi$
$270$	71.7464	−	52.8652i	0.265727	−	0.195797i
$271$	225.699	−	93.4876i	0.832837	−	0.344973i	0.0748121	−	0.997198i	$-0.476164\pi$
$271$	225.699	−	93.4876i	0.832837	−	0.344973i	0.758025	+	0.652225i	$0.226164\pi$
$272$	232.114	+	49.1837i	0.853360	+	0.180822i
$273$	−10.3381	+	24.9584i	−0.0378686	+	0.0914229i
$274$	20.9690	−	5.18311i	0.0765290	−	0.0189165i
$275$	117.453	−	219.738i	0.427100	−	0.799048i
$276$	−38.9153	−	59.0335i	−0.140997	−	0.213889i
$277$	−163.769	−	134.402i	−0.591225	−	0.485205i	0.290561	−	0.956857i	$-0.406158\pi$
$277$	−163.769	−	134.402i	−0.591225	−	0.485205i	−0.881785	+	0.471651i	$0.843658\pi$
$278$	−133.856	+	79.6649i	−0.481498	+	0.286564i
$279$	215.866	−	144.237i	0.773712	−	0.516978i
$280$	−18.5731	+	50.4183i	−0.0663325	+	0.180065i
$281$	67.9421	+	45.3975i	0.241787	+	0.161557i	0.670560	−	0.741855i	$-0.266054\pi$
$281$	67.9421	+	45.3975i	0.241787	+	0.161557i	−0.428773	+	0.903412i	$0.641054\pi$
$282$	40.4000	−	36.3879i	0.143262	−	0.129035i
$283$	−217.366	−	406.663i	−0.768078	−	1.43697i	−0.895471	−	0.445120i	$-0.853161\pi$
$283$	−217.366	−	406.663i	−0.768078	−	1.43697i	0.127393	−	0.991852i	$-0.459339\pi$
$284$	−195.533	+	360.400i	−0.688497	+	1.26901i
$285$	−0.427943	+	4.34498i	−0.00150155	+	0.0152455i
$286$	239.038	+	218.011i	0.835797	+	0.762276i
$287$	88.5351	+	88.5351i	0.308485	+	0.308485i
$288$	−106.913	−	235.467i	−0.371227	−	0.817593i
$289$	48.8569	+	48.8569i	0.169055	+	0.169055i
$290$	−270.527	+	12.4458i	−0.932853	+	0.0429166i
$291$	0.445032	−	4.51849i	0.00152932	−	0.0155274i
$292$	−87.2477	+	70.6976i	−0.298793	+	0.242115i
$293$	32.0352	+	59.9336i	0.109335	+	0.204551i	0.930638	−	0.365940i	$-0.119253\pi$
$293$	32.0352	+	59.9336i	0.109335	+	0.204551i	−0.821303	+	0.570492i	$0.806753\pi$
$294$	82.1455	+	4.29202i	0.279407	+	0.0145987i
$295$	175.864	+	117.509i	0.596150	+	0.398335i
$296$	2.23095	+	9.27316i	0.00753699	+	0.0313282i
$297$	192.797	−	128.823i	0.649149	−	0.433747i
$298$	−87.1070	+	343.213i	−0.292305	+	1.15172i
$299$	162.827	+	133.628i	0.544571	+	0.446918i
$300$	−37.8206	+	55.8464i	−0.126069	+	0.186155i
$301$	−8.68459	+	16.2477i	−0.0288524	+	0.0539791i
$302$	−386.622	−	233.372i	−1.28020	−	0.772754i
$303$	−33.4379	+	80.7263i	−0.110356	+	0.266423i
$304$	25.5264	+	8.09191i	0.0839685	+	0.0266181i
$305$	−60.0587	+	24.8771i	−0.196914	+	0.0815644i
$306$	−35.9064	+	236.975i	−0.117341	+	0.774427i
$307$	−125.513	−	413.759i	−0.408836	−	1.34775i	−0.883849	−	0.467772i	$-0.845057\pi$
$307$	−125.513	−	413.759i	−0.408836	−	1.34775i	0.475014	−	0.879978i	$-0.342443\pi$
$308$	−54.3020	+	128.821i	−0.176305	+	0.418251i
$309$	2.76200	+	28.0431i	0.00893852	+	0.0907543i
$310$	104.609	−	140.134i	0.337448	−	0.452046i
$311$	90.0214	−	452.568i	0.289458	−	1.45520i	−0.512946	−	0.858421i	$-0.671446\pi$
$311$	90.0214	−	452.568i	0.289458	−	1.45520i	0.802403	−	0.596782i	$-0.203554\pi$
$312$	−58.2056	−	65.4383i	−0.186556	−	0.209738i
$313$	59.2547	+	297.894i	0.189312	+	0.951737i	0.952263	+	0.305280i	$0.0987500\pi$
$313$	59.2547	+	297.894i	0.189312	+	0.951737i	−0.762951	+	0.646457i	$0.776250\pi$
$314$	122.440	−	43.3802i	0.389938	−	0.138154i
$315$	−51.9395	−	15.7557i	−0.164887	−	0.0500180i
$316$	98.8799	+	30.6687i	0.312911	+	0.0970528i
$317$	−49.1156	+	40.3082i	−0.154939	+	0.127155i	−0.708669	−	0.705541i	$-0.750704\pi$
$317$	−49.1156	+	40.3082i	−0.154939	+	0.127155i	0.553730	+	0.832696i	$0.313204\pi$
$318$	−34.3648	+	95.1084i	−0.108065	+	0.299083i
$319$	−704.616			−2.20883
$320$	−120.847	−	125.449i	−0.377646	−	0.392029i
$321$		−	60.0337i		−	0.187021i
$322$	−30.9304	+	85.6034i	−0.0960572	+	0.265849i
$323$	−15.7449	−	19.1852i	−0.0487458	−	0.0593970i
$324$	201.883	−	106.298i	0.623097	−	0.328079i
$325$	58.3279	−	192.281i	0.179470	−	0.591635i
$326$	407.937	−	144.531i	1.25134	−	0.443346i
$327$	−112.297	+	22.3373i	−0.343417	+	0.0683099i
$328$	−383.441	+	133.170i	−1.16903	+	0.406006i
$329$	−68.6473	−	13.6548i	−0.208654	−	0.0415039i
$330$	44.2024	−	59.2138i	0.133947	−	0.179436i
$331$	204.632	−	20.1545i	0.618225	−	0.0608898i	0.215943	−	0.976406i	$-0.430717\pi$
$331$	204.632	−	20.1545i	0.618225	−	0.0608898i	0.402281	+	0.915516i	$0.368217\pi$
$332$	−556.956	+	226.645i	−1.67758	+	0.682666i
$333$	−9.21983	+	2.79680i	−0.0276872	+	0.00839881i
$334$	82.5035	−	544.505i	0.247016	−	1.63026i
$335$	−43.9524	−	106.111i	−0.131201	−	0.316748i
$336$	18.2538	−	33.1505i	0.0543268	−	0.0986623i
$337$	379.360	+	157.136i	1.12570	+	0.466279i	0.866316	−	0.499496i	$-0.166482\pi$
$337$	379.360	+	157.136i	1.12570	+	0.466279i	0.259381	+	0.965775i	$0.416482\pi$
$338$	−66.0025	−	39.8403i	−0.195274	−	0.117871i
$339$	144.371	+	77.1678i	0.425872	+	0.227634i
$340$	30.5090	+	158.533i	0.0897324	+	0.466274i
$341$	288.645	−	351.715i	0.846466	−	1.03142i
$342$	−6.65441	+	26.2192i	−0.0194573	+	0.0766644i
$343$	−126.008	−	188.584i	−0.367369	−	0.549807i
$344$	−35.1287	−	48.3023i	−0.102118	−	0.140414i
$345$	26.7285	−	40.0020i	0.0774738	−	0.115948i
$346$	−470.831	−	24.6004i	−1.36078	−	0.0710995i
$347$	319.237	−	170.636i	0.919993	−	0.491746i	0.0578007	−	0.998328i	$-0.481591\pi$
$347$	319.237	−	170.636i	0.919993	−	0.491746i	0.862192	+	0.506582i	$0.169091\pi$
$348$	189.703	+	19.8778i	0.545123	+	0.0571201i
$349$	−402.672	−	39.6598i	−1.15379	−	0.113638i	−0.497026	−	0.867736i	$-0.665575\pi$
$349$	−402.672	−	39.6598i	−1.15379	−	0.113638i	−0.656763	+	0.754097i	$0.728075\pi$
$350$	86.7340	−	3.99026i	0.247811	−	0.0114007i
$351$	132.226	−	132.226i	0.376711	−	0.376711i
$352$	−299.092	−	340.505i	−0.849694	−	0.967344i
$353$	−425.623	+	425.623i	−1.20573	+	1.20573i	−0.233336	+	0.972396i	$0.574964\pi$
$353$	−425.623	+	425.623i	−1.20573	+	1.20573i	−0.972396	+	0.233336i	$0.925036\pi$
$354$	−110.069	−	100.387i	−0.310930	−	0.283579i
$355$	−277.647	−	27.3458i	−0.782104	−	0.0770306i
$356$	−91.5950	−	308.860i	−0.257289	−	0.867584i
$357$	−30.9331	+	16.5341i	−0.0866474	+	0.0463140i
$358$	312.426	−	281.399i	0.872697	−	0.786030i
$359$	−159.665	+	238.955i	−0.444749	+	0.665614i	−0.984333	−	0.176318i	$-0.943581\pi$
$359$	−159.665	+	238.955i	−0.444749	+	0.665614i	0.539585	+	0.841931i	$0.318581\pi$
$360$	119.379	−	129.267i	0.331609	−	0.359075i
$361$	199.005	+	297.832i	0.551259	+	0.825018i
$362$	−351.110	+	208.964i	−0.969917	+	0.577248i
$363$	48.3924	−	58.9664i	0.133313	−	0.162442i
$364$	−22.6828	+	110.435i	−0.0623154	+	0.303393i
$365$	−67.3862	−	36.0187i	−0.184620	−	0.0986813i
$366$	44.4486	−	10.9868i	0.121444	−	0.0300186i
$367$	360.049	+	149.137i	0.981059	+	0.406368i	0.814818	−	0.579717i	$-0.196837\pi$
$367$	360.049	+	149.137i	0.981059	+	0.406368i	0.166241	+	0.986085i	$0.446837\pi$
$368$	−206.035	−	211.233i	−0.559878	−	0.574003i
$369$	−156.913	−	378.822i	−0.425239	−	1.02662i
$370$	−5.22458	+	3.84965i	−0.0141205	+	0.0104045i
$371$	124.575	−	37.7893i	0.335780	−	0.101858i
$372$	−87.6337	+	86.5488i	−0.235574	+	0.232658i
$373$	−629.632	+	62.0134i	−1.68802	+	0.166256i	−0.895945	−	0.444165i	$-0.853500\pi$
$373$	−629.632	+	62.0134i	−1.68802	+	0.166256i	−0.792078	+	0.610420i	$0.791000\pi$
$374$	60.3396	+	415.691i	0.161336	+	1.11147i
$375$	−108.975	−	21.6765i	−0.290600	−	0.0578040i
$376$	136.865	−	180.982i	0.364002	−	0.481335i
$377$	−557.317	+	110.857i	−1.47830	+	0.294051i
$378$	72.9370	+	34.7750i	0.192955	+	0.0919973i
$379$	56.2372	−	185.389i	0.148383	−	0.489154i	−0.850966	−	0.525221i	$-0.823983\pi$
$379$	56.2372	−	185.389i	0.148383	−	0.489154i	0.999349	+	0.0360666i	$0.0114828\pi$
$380$	1.67296	+	18.1436i	0.00440252	+	0.0477462i
$381$	2.93506	+	3.57638i	0.00770357	+	0.00938683i
$382$	262.530	+	559.576i	0.687252	+	1.46486i
$383$			49.0013i			0.127941i	0.997952	+	0.0639704i	$0.0203763\pi$
$383$			49.0013i			0.127941i	−0.997952	+	0.0639704i	$0.979624\pi$
$384$	70.9183	+	100.111i	0.184683	+	0.260707i
$385$	−95.1220			−0.247070
$386$	369.277	−	173.250i	0.956677	−	0.448834i
$387$	46.6377	−	38.2746i	0.120511	−	0.0989007i
$388$	−1.73976	−	18.8681i	−0.00448392	−	0.0486291i
$389$	372.403	+	112.967i	0.957335	+	0.290404i	0.730027	−	0.683418i	$-0.239507\pi$
$389$	372.403	+	112.967i	0.957335	+	0.290404i	0.227308	+	0.973823i	$0.427007\pi$
$390$	25.6459	−	53.7896i	0.0657587	−	0.137922i
$391$	53.3541	+	268.229i	0.136456	+	0.686009i
$392$	340.024	−	47.1957i	0.867408	−	0.120397i
$393$	26.0118	−	130.770i	0.0661879	−	0.332749i
$394$	225.845	−	32.7826i	0.573212	−	0.0832045i
$395$	6.90451	+	70.1027i	0.0174798	+	0.177475i
$396$	325.736	−	321.703i	0.822565	−	0.812382i
$397$	54.4339	+	179.444i	0.137113	+	0.452001i	0.998427	−	0.0560725i	$-0.0178578\pi$
$397$	54.4339	+	179.444i	0.137113	+	0.452001i	−0.861314	+	0.508074i	$0.830358\pi$
$398$	423.552	+	574.827i	1.06420	+	1.44429i
$399$	−3.65724	+	1.51488i	−0.00916603	+	0.00379669i
$400$	−110.948	+	258.691i	−0.277370	+	0.646726i
$401$	−84.6399	+	204.339i	−0.211072	+	0.509573i	−0.993589	−	0.113057i	$-0.963936\pi$
$401$	−84.6399	+	204.339i	−0.211072	+	0.509573i	0.782516	+	0.622630i	$0.213936\pi$
$402$	19.4113	+	78.5308i	0.0482867	+	0.195350i
$403$	172.969	−	323.602i	0.429203	−	0.802983i
$404$	−73.3659	+	357.194i	−0.181599	+	0.884143i
$405$	120.005	+	98.4856i	0.296309	+	0.243174i
$406$	−125.577	−	211.000i	−0.309303	−	0.519704i
$407$	−14.0395	+	9.38091i	−0.0344951	+	0.0230489i
$408$	−4.51815	−	113.618i	−0.0110739	−	0.278476i
$409$	73.1896	+	48.9037i	0.178948	+	0.119569i	0.641818	−	0.766857i	$-0.278180\pi$
$409$	73.1896	+	48.9037i	0.178948	+	0.119569i	−0.462870	+	0.886426i	$0.653180\pi$
$410$	−184.839	−	205.219i	−0.450826	−	0.500534i
$411$	−4.87971	−	9.12930i	−0.0118728	−	0.0222124i
$412$	33.4353	+	112.745i	0.0811537	+	0.273652i
$413$	−18.7970	+	190.849i	−0.0455133	+	0.462104i
$414$	200.862	−	220.235i	0.485174	−	0.531968i
$415$	−289.306	−	289.306i	−0.697123	−	0.697123i
$416$	−290.140	−	222.267i	−0.697451	−	0.534296i
$417$	52.7861	+	52.7861i	0.126585	+	0.126585i
$418$	2.17869	+	47.3570i	0.00521218	+	0.113294i
$419$	−29.5693	+	300.222i	−0.0705712	+	0.716521i	0.893177	+	0.449706i	$0.148471\pi$
$419$	−29.5693	+	300.222i	−0.0705712	+	0.716521i	−0.963748	+	0.266815i	$0.914029\pi$
$420$	25.6096	+	2.68347i	0.0609752	+	0.00638922i
$421$	316.000	+	591.195i	0.750594	+	1.40426i	0.908960	+	0.416883i	$0.136877\pi$
$421$	316.000	+	591.195i	0.750594	+	1.40426i	−0.158366	+	0.987380i	$0.550623\pi$
$422$	−2.22403	+	42.5660i	−0.00527021	+	0.100867i
$423$	190.583	+	127.344i	0.450552	+	0.301049i
$424$	−65.8217	+	416.864i	−0.155240	+	0.983169i
$425$	216.915	−	144.938i	0.510389	−	0.341031i
$426$	190.462	+	48.3391i	0.447094	+	0.113472i
$427$	−45.5618	−	37.3916i	−0.106702	−	0.0875682i
$428$	−47.3460	−	246.023i	−0.110622	−	0.574820i
$429$	73.0880	−	136.738i	0.170368	−	0.318737i
$430$	21.0008	−	34.7916i	0.0488391	−	0.0809107i
$431$	−174.297	+	420.789i	−0.404401	+	0.976309i	0.582184	+	0.813057i	$0.302198\pi$
$431$	−174.297	+	420.789i	−0.404401	+	0.976309i	−0.986584	+	0.163252i	$0.947802\pi$
$432$	−204.547	+	163.646i	−0.473489	+	0.378811i
$433$	497.173	−	205.936i	1.14820	−	0.475602i	0.274274	−	0.961652i	$-0.411563\pi$
$433$	497.173	−	205.936i	1.14820	−	0.475602i	0.873931	+	0.486050i	$0.161563\pi$
$434$	156.765	+	23.7530i	0.361209	+	0.0547305i
$435$	37.6745	+	124.196i	0.0866080	+	0.285508i
$436$	−442.587	+	180.104i	−1.01511	+	0.413084i
$437$	3.02537	+	30.7171i	0.00692305	+	0.0702909i
$438$	43.1258	+	32.1929i	0.0984607	+	0.0734998i
$439$	−156.019	+	784.363i	−0.355397	+	1.78670i	0.227100	+	0.973871i	$0.427075\pi$
$439$	−156.019	+	784.363i	−0.355397	+	1.78670i	−0.582498	+	0.812832i	$0.697925\pi$
$440$	134.446	−	277.523i	0.305558	−	0.630735i
$441$	67.6520	+	340.110i	0.153406	+	0.771224i
$442$	113.127	+	319.299i	0.255942	+	0.722395i
$443$	−501.107	−	152.009i	−1.13117	−	0.343136i	−0.331426	−	0.943481i	$-0.607530\pi$
$443$	−501.107	−	152.009i	−1.13117	−	0.343136i	−0.799741	+	0.600346i	$0.795030\pi$
$444$	4.04449	−	2.12954i	0.00910920	−	0.00479627i
$445$	169.445	−	139.060i	0.380776	−	0.312494i
$446$	304.768	+	110.120i	0.683337	+	0.246905i
$447$	169.696			0.379633
$448$	48.6612	−	150.249i	0.108619	−	0.335378i
$449$			822.028i			1.83080i	0.402548	+	0.915399i	$0.368125\pi$
$449$			822.028i			1.83080i	−0.402548	+	0.915399i	$0.631875\pi$
$450$	−267.419	−	96.6244i	−0.594264	−	0.214721i
$451$	−455.876	−	555.486i	−1.01081	−	1.23168i
$452$	652.502	+	202.381i	1.44359	+	0.447745i
$453$	−62.8242	+	207.103i	−0.138685	+	0.457182i
$454$	−105.854	−	298.771i	−0.233158	−	0.658086i
$455$	−75.2370	+	14.9656i	−0.165356	+	0.0328914i
$456$	0.749414	−	12.8113i	0.00164345	−	0.0280950i
$457$	255.232	+	50.7688i	0.558494	+	0.111091i	0.466263	−	0.884646i	$-0.345600\pi$
$457$	255.232	+	50.7688i	0.558494	+	0.111091i	0.0922314	+	0.995738i	$0.470600\pi$
$458$	−56.7972	−	42.3985i	−0.124011	−	0.0925731i
$459$	241.616	−	23.7971i	0.526397	−	0.0518456i
$460$	77.9875	−	185.011i	0.169538	−	0.402197i
$461$	134.298	−	40.7390i	0.291320	−	0.0883709i	−0.141242	−	0.989975i	$-0.545110\pi$
$461$	134.298	−	40.7390i	0.291320	−	0.0883709i	0.432562	+	0.901604i	$0.357610\pi$
$462$	66.2410	+	10.0368i	0.143379	+	0.0217248i
$463$	−156.508	−	377.843i	−0.338030	−	0.816076i	−0.997905	−	0.0647005i	$-0.979391\pi$
$463$	−156.508	−	377.843i	−0.338030	−	0.816076i	0.659875	−	0.751375i	$-0.270609\pi$
$464$	793.094	−	68.1497i	1.70925	−	0.146874i
$465$	−77.4268	−	32.0712i	−0.166509	−	0.0689704i
$466$	412.931	−	684.094i	0.886119	−	1.46801i
$467$	730.162	+	390.280i	1.56352	+	0.835716i	0.999954	+	0.00964279i	$0.00306944\pi$
$467$	730.162	+	390.280i	1.56352	+	0.835716i	0.563562	+	0.826074i	$0.309431\pi$
$468$	207.028	−	305.700i	0.442367	−	0.653205i
$469$	66.0627	−	80.4977i	0.140859	−	0.171637i
$470$	149.647	+	37.9804i	0.318399	+	0.0808093i
$471$	−34.5855	−	51.7609i	−0.0734300	−	0.109896i
$472$	−530.244	−	324.587i	−1.12340	−	0.687685i
$473$	58.7434	−	87.9157i	0.124193	−	0.185868i
$474$	2.58876	−	49.5466i	0.00546151	−	0.104529i
$475$	25.9668	−	13.8795i	0.0546669	−	0.0292201i
$476$	−113.727	+	92.1537i	−0.238922	+	0.193600i
$477$	−424.265	−	41.7865i	−0.889445	−	0.0876027i
$478$	−17.6167	−	382.923i	−0.0368549	−	0.801094i
$479$	104.497	−	104.497i	0.218157	−	0.218157i	−0.589564	−	0.807722i	$-0.700700\pi$
$479$	104.497	−	104.497i	0.218157	−	0.218157i	0.807722	+	0.589564i	$0.200700\pi$
$480$	−44.0258	+	70.9244i	−0.0917204	+	0.147759i
$481$	−9.62869	+	9.62869i	−0.0200181	+	0.0200181i
$482$	−280.955	+	308.053i	−0.582895	+	0.639114i
$483$	43.4103	+	4.27555i	0.0898765	+	0.00885206i
$484$	151.812	−	279.814i	0.313661	−	0.578128i
$485$	11.3704	−	6.07759i	0.0234441	−	0.0125311i
$486$	−270.403	−	300.218i	−0.556385	−	0.617732i
$487$	−6.21597	+	9.30285i	−0.0127638	+	0.0191024i	−0.837797	−	0.545982i	$-0.816157\pi$
$487$	−6.21597	+	9.30285i	−0.0127638	+	0.0191024i	0.825033	+	0.565085i	$0.191157\pi$
$488$	173.489	−	80.0795i	0.355510	−	0.164097i
$489$	−115.229	−	172.453i	−0.235643	−	0.352664i
$490$	119.458	+	200.719i	0.243793	+	0.409631i
$491$	−376.418	+	458.667i	−0.766635	+	0.934148i	−0.999262	−	0.0384183i	$-0.987768\pi$
$491$	−376.418	+	458.667i	−0.766635	+	0.934148i	0.232626	+	0.972566i	$0.425268\pi$
$492$	107.064	+	162.414i	0.217610	+	0.330109i
$493$	−650.654	−	347.782i	−1.31979	−	0.705440i
$494$	9.17392	+	37.1143i	0.0185707	+	0.0751302i
$495$	287.797	+	119.209i	0.581407	+	0.240827i
$496$	−290.872	+	423.797i	−0.586436	+	0.854429i
$497$	−96.8018	−	233.700i	−0.194772	−	0.470222i
$498$	170.941	+	231.993i	0.343254	+	0.465850i
$499$	−881.562	+	267.419i	−1.76666	+	0.535909i	−0.994977	−	0.100102i	$-0.968083\pi$
$499$	−881.562	+	267.419i	−1.76666	+	0.535909i	−0.771680	+	0.636011i	$0.780583\pi$
$500$	−463.684	−	2.88794i	−0.927368	−	0.00577589i
$501$	−262.656	+	25.8694i	−0.524264	+	0.0516355i
$502$	−486.494	+	70.6170i	−0.969112	+	0.140671i
$503$	−198.782	−	39.5403i	−0.395194	−	0.0786089i	−0.00650688	−	0.999979i	$-0.502071\pi$
$503$	−198.782	−	39.5403i	−0.395194	−	0.0786089i	−0.388687	+	0.921370i	$0.627071\pi$
$504$	154.388	+	40.2087i	0.306326	+	0.0797792i
$505$	−243.349	+	48.4050i	−0.481878	+	0.0958516i
$506$	224.820	−	471.536i	0.444308	−	0.931890i
$507$	−10.7251	+	35.3559i	−0.0211540	+	0.0697354i
$508$	14.8487	+	12.3415i	0.0292296	+	0.0242944i
$509$	−366.633	−	446.743i	−0.720300	−	0.877688i	0.276216	−	0.961096i	$-0.410920\pi$
$509$	−366.633	−	446.743i	−0.720300	−	0.877688i	−0.996515	+	0.0834079i	$0.973420\pi$
$510$	70.0438	−	32.8617i	0.137341	−	0.0644348i
$511$		−	69.2780i		−	0.135573i
$512$	369.583	+	354.334i	0.721841	+	0.692059i
$513$	27.4010			0.0534133
$514$	−431.786	−	920.339i	−0.840050	−	1.79054i
$515$	−61.8533	+	50.7617i	−0.120103	+	0.0985664i
$516$	−18.2956	+	22.0122i	−0.0354566	+	0.0426594i
$517$	384.407	+	116.609i	0.743534	+	0.225549i
$518$	−5.31128	−	2.53232i	−0.0102534	−	0.00488865i
$519$	44.0804	+	221.607i	0.0849333	+	0.426989i
$520$	62.6772	−	240.660i	0.120533	−	0.462808i
$521$	74.4963	−	374.518i	0.142987	−	0.718845i	−0.841061	−	0.540941i	$-0.818068\pi$
$521$	74.4963	−	374.518i	0.142987	−	0.718845i	0.984048	−	0.177904i	$-0.0569318\pi$
$522$	115.510	+	795.768i	0.221283	+	1.52446i
$523$	67.5243	+	685.586i	0.129110	+	1.31087i	0.813418	+	0.581680i	$0.197604\pi$
$523$	67.5243	+	685.586i	0.129110	+	1.31087i	−0.684308	+	0.729193i	$0.739896\pi$
$524$	3.46554	−	556.422i	0.00661363	−	1.06187i
$525$	−12.0788	−	39.8186i	−0.0230073	−	0.0758450i
$526$	−165.319	+	121.813i	−0.314296	+	0.231584i
$527$	440.138	−	182.311i	0.835177	−	0.345941i
$528$	−122.908	+	179.075i	−0.232780	+	0.339158i
$529$	−72.2826	+	174.506i	−0.136640	+	0.329878i
$530$	−278.767	+	68.9058i	−0.525976	+	0.130011i
$531$	296.048	−	553.867i	0.557529	−	1.04306i
$532$	−13.7930	+	9.09241i	−0.0259266	+	0.0170910i
$533$	−447.971	−	367.640i	−0.840471	−	0.689756i
$534$	−132.671	+	78.9594i	−0.248448	+	0.147864i
$535$	141.741	−	94.7086i	0.264937	−	0.177025i
$536$	141.483	+	306.517i	0.263960	+	0.571860i
$537$	−167.546	−	111.951i	−0.312004	−	0.208474i
$538$	−49.6399	+	44.7102i	−0.0922674	+	0.0831044i
$539$	286.484	+	535.973i	0.531509	+	0.994384i
$540$	−156.666	−	84.9986i	−0.290123	−	0.157405i
$541$	−89.9942	+	913.726i	−0.166348	+	1.68896i	0.443370	+	0.896339i	$0.353783\pi$
$541$	−89.9942	+	913.726i	−0.166348	+	1.68896i	−0.609717	+	0.792619i	$0.708717\pi$
$542$	−360.997	−	329.242i	−0.666047	−	0.607458i
$543$	138.460	+	138.460i	0.254990	+	0.254990i
$544$	−108.122	−	462.053i	−0.198753	−	0.849363i
$545$	−229.898	−	229.898i	−0.421832	−	0.421832i
$546$	53.9726	−	2.48305i	0.0988509	−	0.00454770i
$547$	−54.4402	+	552.741i	−0.0995251	+	1.01049i	0.807628	+	0.589693i	$0.200751\pi$
$547$	−54.4402	+	552.741i	−0.0995251	+	1.01049i	−0.907153	+	0.420802i	$0.861749\pi$
$548$	−27.1973	−	33.5642i	−0.0496302	−	0.0612485i
$549$	90.9895	+	170.229i	0.165737	+	0.310072i
$550$	−497.638	−	26.0011i	−0.904797	−	0.0472747i
$551$	−69.2327	−	46.2598i	−0.125649	−	0.0839561i
$552$	−73.8303	+	120.609i	−0.133751	+	0.218494i
$553$	−53.1046	+	35.4833i	−0.0960300	+	0.0641652i
$554$	−104.235	+	410.697i	−0.188149	+	0.741330i
$555$	2.40415	+	1.97304i	0.00433181	+	0.00355502i
$556$	257.952	+	174.691i	0.463942	+	0.314193i
$557$	486.225	−	909.664i	0.872936	−	1.63315i	0.103314	−	0.994649i	$-0.467055\pi$
$557$	486.225	−	909.664i	0.872936	−	1.63315i	0.769622	−	0.638500i	$-0.220445\pi$
$558$	−444.533	−	268.328i	−0.796653	−	0.480874i
$559$	32.6314	−	78.7792i	0.0583746	−	0.140929i
$560$	107.066	−	9.20011i	0.191190	−	0.0164288i
$561$	185.980	−	77.0356i	0.331516	−	0.137318i
$562$	24.4830	−	161.582i	0.0435640	−	0.287513i
$563$	−232.269	−	765.687i	−0.412556	−	1.36001i	−0.879572	−	0.475765i	$-0.842171\pi$
$563$	−232.269	−	765.687i	−0.412556	−	1.36001i	0.467017	−	0.884248i	$-0.345329\pi$
$564$	−100.204	−	42.2389i	−0.177666	−	0.0748916i
$565$	45.5624	+	462.603i	0.0806414	+	0.818766i
$566$	−551.670	+	739.020i	−0.974683	+	1.30569i
$567$	−27.4602	+	138.052i	−0.0484308	+	0.243478i
$568$	818.652	+	47.8881i	1.44129	+	0.0843100i
$569$	−91.4814	−	459.908i	−0.160776	−	0.808275i	−0.974039	−	0.226379i	$-0.927311\pi$
$569$	−91.4814	−	459.908i	−0.160776	−	0.808275i	0.813263	−	0.581896i	$-0.197689\pi$
$570$	8.23069	−	2.91611i	0.0144398	−	0.00511598i
$571$	12.0842	+	3.66570i	0.0211632	+	0.00641978i	0.300849	−	0.953672i	$-0.402730\pi$
$571$	12.0842	+	3.66570i	0.0211632	+	0.00641978i	−0.279685	+	0.960092i	$0.590230\pi$
$572$	191.681	−	618.005i	0.335107	−	1.08043i
$573$	228.980	−	187.919i	0.399615	−	0.327956i
$574$	85.0961	−	235.513i	0.148251	−	0.410301i
$575$	−324.444			−0.564250
$576$	−335.523	+	393.604i	−0.582506	+	0.683341i
$577$		−	363.204i		−	0.629470i	−0.949179	−	0.314735i	$-0.898084\pi$
$577$		−	363.204i		−	0.629470i	0.949179	−	0.314735i	$-0.101916\pi$
$578$	46.9591	−	129.965i	0.0812441	−	0.224852i
$579$	−124.012	−	151.109i	−0.214183	−	0.260983i
$580$	252.341	+	479.253i	0.435071	+	0.826298i
$581$	107.684	−	354.987i	0.185343	−	0.610993i
$582$	−8.55937	+	3.03256i	−0.0147068	+	0.00521058i
$583$	−732.784	+	145.760i	−1.25692	+	0.250017i
$584$	202.122	+	97.9177i	0.346100	+	0.167667i
$585$	246.389	+	49.0098i	0.421177	+	0.0837774i
$586$	81.3046	−	108.916i	0.138745	−	0.185864i
$587$	317.764	−	31.2970i	0.541336	−	0.0533169i	0.176346	−	0.984328i	$-0.443572\pi$
$587$	317.764	−	31.2970i	0.541336	−	0.0533169i	0.364990	+	0.931011i	$0.381072\pi$
$588$	−62.0094	−	152.381i	−0.105458	−	0.259152i
$589$	51.4521	−	15.6078i	0.0873550	−	0.0264988i
$590$	63.3728	−	418.247i	0.107411	−	0.708893i
$591$	−41.8535	−	101.043i	−0.0708181	−	0.170970i
$592$	14.8951	−	11.9168i	0.0251607	−	0.0201296i
$593$	−712.396	−	295.084i	−1.20134	−	0.497613i	−0.309910	−	0.950766i	$-0.600299\pi$
$593$	−712.396	−	295.084i	−1.20134	−	0.497613i	−0.891433	+	0.453153i	$0.850299\pi$
$594$	−397.028	−	239.653i	−0.668397	−	0.403456i
$595$	−87.8374	−	46.9500i	−0.147626	−	0.0789076i
$596$	695.427	−	133.832i	1.16682	−	0.224550i
$597$	217.081	−	264.513i	0.363619	−	0.443071i
$598$	103.635	−	408.334i	0.173302	−	0.682832i
$599$	−350.737	−	524.915i	−0.585537	−	0.876319i	0.413884	−	0.910330i	$-0.364172\pi$
$599$	−350.737	−	524.915i	−0.585537	−	0.876319i	−0.999421	+	0.0340109i	$0.989172\pi$
$600$	133.245	+	21.0390i	0.222075	+	0.0350651i
$601$	577.365	−	864.088i	0.960674	−	1.43775i	0.0625338	−	0.998043i	$-0.480082\pi$
$601$	577.365	−	864.088i	0.960674	−	1.43775i	0.898141	−	0.439708i	$-0.144918\pi$
$602$	36.7960	+	1.92255i	0.0611229	+	0.00319361i
$603$	−300.758	+	160.758i	−0.498769	+	0.266598i
$604$	−94.1246	+	898.273i	−0.155835	+	1.48721i
$605$	215.565	+	21.2313i	0.356306	+	0.0350930i
$606$	174.570	−	8.03123i	0.288070	−	0.0132529i
$607$	601.711	−	601.711i	0.991287	−	0.991287i	−0.00867515	−	0.999962i	$-0.502761\pi$
$607$	601.711	−	601.711i	0.991287	−	0.991287i	0.999962	+	0.00867515i	$0.00276142\pi$
$608$	−7.03259	−	53.0929i	−0.0115668	−	0.0873238i
$609$	−83.2075	+	83.2075i	−0.136630	+	0.136630i
$610$	96.0618	+	87.6118i	0.157478	+	0.143626i
$611$	322.394	+	31.7530i	0.527650	+	0.0519690i
$612$	459.575	−	136.291i	0.750940	−	0.222697i
$613$	922.356	−	493.010i	1.50466	−	0.804257i	0.506347	−	0.862330i	$-0.330996\pi$
$613$	922.356	−	493.010i	1.50466	−	0.804257i	0.998312	+	0.0580728i	$0.0184955\pi$
$614$	−642.546	+	578.736i	−1.04649	+	0.942566i
$615$	−73.5356	+	110.054i	−0.119570	+	0.178949i
$616$	279.376	−	11.1097i	0.453533	−	0.0180352i
$617$	207.377	+	310.361i	0.336105	+	0.503016i	0.960571	−	0.278036i	$-0.0896834\pi$
$617$	207.377	+	310.361i	0.336105	+	0.503016i	−0.624466	+	0.781052i	$0.714683\pi$
$618$	48.4295	−	28.8229i	0.0783649	−	0.0466390i
$619$	−392.408	+	478.151i	−0.633939	+	0.772456i	−0.986576	−	0.163304i	$-0.947785\pi$
$619$	−392.408	+	478.151i	−0.633939	+	0.772456i	0.352637	+	0.935760i	$0.385285\pi$
$620$	−342.594	−	70.3672i	−0.552572	−	0.113496i
$621$	−266.286	−	142.333i	−0.428802	−	0.229199i
$622$	−895.906	+	221.450i	−1.44036	+	0.356029i
$623$	183.617	+	76.0568i	0.294731	+	0.122082i
$624$	−69.0405	+	160.977i	−0.110642	+	0.257976i
$625$	47.5690	+	114.842i	0.0761104	+	0.183747i
$626$	489.040	−	360.342i	0.781215	−	0.575626i
$627$	21.7411	−	6.59508i	0.0346747	−	0.0105185i
$628$	−182.556	−	184.844i	−0.290694	−	0.294338i
$629$	−17.5945	+	1.73291i	−0.0279722	+	0.00275503i
$630$	15.5936	+	107.427i	0.0247518	+	0.170520i
$631$	561.779	+	111.745i	0.890299	+	0.177092i	0.618988	−	0.785400i	$-0.287543\pi$
$631$	561.779	+	111.745i	0.890299	+	0.177092i	0.271311	+	0.962492i	$0.412543\pi$
$632$	−28.4664	−	205.087i	−0.0450417	−	0.324505i
$633$	20.0346	−	3.98514i	0.0316503	−	0.00629563i
$634$	114.706	+	54.6896i	0.180924	+	0.0862612i
$635$	−3.81363	+	12.5718i	−0.00600571	+	0.0197982i
$636$	201.398	−	18.5703i	0.316664	−	0.0291985i
$637$	310.920	+	378.857i	0.488100	+	0.594751i
$638$	598.554	+	1275.80i	0.938172	+	1.99969i
$639$			828.387i			1.29638i
$640$	−124.486	+	325.375i	−0.194509	+	0.508399i
$641$	−516.859			−0.806332			−0.403166	−	0.915127i	$-0.632090\pi$
$641$	−516.859			−0.806332			−0.403166	+	0.915127i	$0.632090\pi$
$642$	−108.699	+	50.9972i	−0.169313	+	0.0794349i
$643$	351.694	−	288.628i	0.546958	−	0.448877i	−0.319886	−	0.947456i	$-0.603645\pi$
$643$	351.694	−	288.628i	0.546958	−	0.448877i	0.866844	+	0.498579i	$0.166145\pi$
$644$	181.271	−	16.7144i	0.281477	−	0.0259540i
$645$	−18.6370	−	5.65347i	−0.0288946	−	0.00876507i
$646$	−21.3625	+	44.8056i	−0.0330688	+	0.0693585i
$647$	−183.042	−	920.214i	−0.282909	−	1.42228i	−0.816896	−	0.576785i	$-0.804307\pi$
$647$	−183.042	−	920.214i	−0.282909	−	1.42228i	0.533987	−	0.845493i	$-0.320693\pi$
$648$	−363.961	−	275.239i	−0.561669	−	0.424752i
$649$	214.723	−	1079.49i	0.330853	−	1.66331i
$650$	−397.699	+	57.7279i	−0.611845	+	0.0888122i
$651$	−7.44788	−	75.6196i	−0.0114407	−	0.116159i
$652$	−608.225	−	615.848i	−0.932860	−	0.944553i
$653$	−38.9327	−	128.344i	−0.0596214	−	0.196545i	0.922070	−	0.387023i	$-0.126496\pi$
$653$	−38.9327	−	128.344i	−0.0596214	−	0.196545i	−0.981692	+	0.190477i	$0.938996\pi$
$654$	135.839	+	184.354i	0.207704	+	0.281887i
$655$	349.789	−	144.887i	0.534029	−	0.221202i
$656$	566.846	+	581.147i	0.864095	+	0.885894i
$657$	−86.8210	+	209.604i	−0.132148	+	0.319033i
$658$	33.5904	+	135.894i	0.0510492	+	0.206526i
$659$	−216.542	+	405.122i	−0.328593	+	0.614753i	−0.990919	−	0.134462i	$-0.957069\pi$
$659$	−216.542	+	405.122i	−0.328593	+	0.614753i	0.662326	+	0.749216i	$0.269569\pi$
$660$	−144.763	−	29.7337i	−0.219338	−	0.0450510i
$661$	515.458	+	423.025i	0.779815	+	0.639978i	0.937687	−	0.347482i	$-0.112963\pi$
$661$	515.458	+	423.025i	0.779815	+	0.639978i	−0.157872	+	0.987460i	$0.550463\pi$
$662$	−210.323	−	353.393i	−0.317708	−	0.533827i
$663$	134.982	−	90.1918i	0.203592	−	0.136036i
$664$	883.491	+	815.913i	1.33056	+	1.22878i
$665$	−9.34631	−	6.24501i	−0.0140546	−	0.00939099i
$666$	12.8960	+	14.3179i	0.0193634	+	0.0214983i
$667$	432.516	+	809.181i	0.648450	+	1.21317i
$668$	−1055.98	+	313.161i	−1.58081	+	0.468803i
$669$	15.2219	−	154.551i	0.0227533	−	0.231018i
$670$	−154.791	+	169.720i	−0.231031	+	0.253314i
$671$	239.198	+	239.198i	0.356480	+	0.356480i
$672$	−75.5296	−	4.89040i	−0.112395	−	0.00727738i
$673$	158.655	+	158.655i	0.235743	+	0.235743i	0.815085	−	0.579341i	$-0.196690\pi$
$673$	158.655	+	158.655i	0.235743	+	0.235743i	−0.579341	+	0.815085i	$0.696690\pi$
$674$	−37.7415	−	820.365i	−0.0559962	−	1.21716i
$675$	−28.2314	+	286.638i	−0.0418242	+	0.424649i
$676$	−16.0686	+	153.350i	−0.0237701	+	0.226849i
$677$	473.699	+	886.228i	0.699703	+	1.30905i	0.940936	+	0.338584i	$0.109948\pi$
$677$	473.699	+	886.228i	0.699703	+	1.30905i	−0.241233	+	0.970467i	$0.577552\pi$
$678$	17.0830	−	326.955i	0.0251962	−	0.482234i
$679$	9.71954	+	6.49439i	0.0143145	+	0.00956464i
$680$	261.128	−	189.911i	0.384012	−	0.279280i
$681$	−126.303	+	84.3933i	−0.185468	+	0.123926i
$682$	−882.023	−	223.857i	−1.29329	−	0.328236i
$683$	458.251	+	376.077i	0.670938	+	0.550625i	0.907009	−	0.421111i	$-0.138360\pi$
$683$	458.251	+	376.077i	0.670938	+	0.550625i	−0.236071	+	0.971736i	$0.575860\pi$
$684$	53.1261	−	10.2239i	0.0776698	−	0.0149472i
$685$	13.8564	−	25.9234i	0.0202283	−	0.0378444i
$686$	−234.415	+	388.351i	−0.341713	+	0.566109i
$687$	−12.9986	+	31.3815i	−0.0189209	+	0.0456791i
$688$	−57.6166	+	104.637i	−0.0837451	+	0.152088i
$689$	−556.665	+	230.578i	−0.807931	+	0.334656i
$690$	−95.1340	−	14.4147i	−0.137875	−	0.0208909i
$691$	75.0882	+	247.533i	0.108666	+	0.358224i	0.994362	−	0.106043i	$-0.0338180\pi$
$691$	75.0882	+	247.533i	0.108666	+	0.358224i	−0.885696	+	0.464266i	$0.846318\pi$
$692$	355.417	+	873.399i	0.513609	+	1.26214i
$693$	27.6839	+	281.079i	0.0399479	+	0.405598i
$694$	−580.144	−	433.071i	−0.835942	−	0.624021i
$695$	−41.3547	+	207.904i	−0.0595032	+	0.299143i
$696$	−125.157	−	360.368i	−0.179823	−	0.517770i
$697$	−146.789	−	737.956i	−0.210600	−	1.05876i
$698$	270.251	+	762.782i	0.387179	+	1.09281i
$699$	−366.452	−	111.162i	−0.524252	−	0.159030i
$700$	−80.9033	−	153.654i	−0.115576	−	0.219505i
$701$	89.9705	−	73.8369i	0.128346	−	0.105331i	−0.568030	−	0.823008i	$-0.692294\pi$
$701$	89.9705	−	73.8369i	0.128346	−	0.105331i	0.696376	+	0.717677i	$0.254794\pi$
$702$	−351.735	−	127.090i	−0.501046	−	0.181039i
$703$	−1.99535			−0.00283833
$704$	−362.458	+	830.797i	−0.514855	+	1.18011i
$705$		−	73.9908i		−	0.104951i
$706$	1132.20	+	409.091i	1.60369	+	0.579449i
$707$	−142.715	−	173.898i	−0.201859	−	0.245966i
$708$	−88.2629	+	284.571i	−0.124665	+	0.401937i
$709$	28.4030	−	93.6322i	0.0400607	−	0.132062i	−0.934629	−	0.355624i	$-0.884268\pi$
$709$	28.4030	−	93.6322i	0.0400607	−	0.132062i	0.974690	+	0.223562i	$0.0717684\pi$
$710$	186.341	+	525.946i	0.262452	+	0.740770i
$711$	205.139	−	40.8047i	0.288522	−	0.0573906i
$712$	−481.424	+	428.214i	−0.676158	+	0.601424i
$713$	−581.089	−	115.586i	−0.814992	−	0.162112i
$714$	56.2141	+	41.9632i	0.0787313	+	0.0587720i
$715$	438.146	−	43.1536i	0.612791	−	0.0603547i
$716$	−774.908	−	326.646i	−1.08227	−	0.456210i
$717$	−175.796	+	53.3271i	−0.245182	+	0.0743753i
$718$	568.292	+	86.1076i	0.791493	+	0.119927i
$719$	−301.609	−	728.148i	−0.419484	−	1.01272i	−0.982497	−	0.186276i	$-0.940358\pi$
$719$	−301.609	−	728.148i	−0.419484	−	1.01272i	0.563013	−	0.826448i	$-0.309642\pi$
$720$	−335.465	−	106.343i	−0.465924	−	0.147699i
$721$	−67.0266	−	27.7633i	−0.0929634	−	0.0385067i
$722$	370.214	−	613.325i	0.512762	−	0.849481i
$723$	176.217	+	94.1900i	0.243730	+	0.130277i
$724$	676.616	+	458.222i	0.934553	+	0.632903i
$725$	555.247	−	676.570i	0.765858	−	0.933201i
$726$	−147.875	−	37.5304i	−0.203684	−	0.0516948i
$727$	−285.500	−	427.282i	−0.392710	−	0.587733i	0.581452	−	0.813581i	$-0.302485\pi$
$727$	−285.500	−	427.282i	−0.392710	−	0.587733i	−0.974163	+	0.225848i	$0.927485\pi$
$728$	219.226	−	52.7416i	0.301134	−	0.0724473i
$729$	177.629	−	265.841i	0.243661	−	0.364665i
$730$	−7.97364	+	152.609i	−0.0109228	+	0.209053i
$731$	97.6378	−	52.1885i	0.133567	−	0.0713933i
$732$	−57.6510	−	71.1470i	−0.0787583	−	0.0971954i
$733$	−939.072	−	92.4905i	−1.28113	−	0.126181i	−0.565554	−	0.824711i	$-0.691338\pi$
$733$	−939.072	−	92.4905i	−1.28113	−	0.126181i	−0.715580	+	0.698530i	$0.753838\pi$
$734$	−35.8202	−	778.604i	−0.0488014	−	1.06077i
$735$	79.1533	−	79.1533i	0.107692	−	0.107692i
$736$	−207.444	+	552.491i	−0.281853	+	0.750667i
$737$	−422.610	+	422.610i	−0.573420	+	0.573420i
$738$	−552.614	+	605.912i	−0.748799	+	0.821020i
$739$	−1013.55	−	99.8264i	−1.37152	−	0.135083i	−0.614729	−	0.788738i	$-0.710735\pi$
$739$	−1013.55	−	99.8264i	−1.37152	−	0.135083i	−0.756792	+	0.653655i	$0.773235\pi$
$740$	11.4085	+	6.18961i	0.0154168	+	0.00836434i
$741$	16.1585	−	8.63692i	0.0218064	−	0.0116558i
$742$	−174.246	−	193.458i	−0.234832	−	0.260725i
$743$	356.221	−	533.123i	0.479437	−	0.717527i	−0.510369	−	0.859956i	$-0.670491\pi$
$743$	356.221	−	533.123i	0.479437	−	0.717527i	0.989805	+	0.142428i	$0.0454910\pi$
$744$	231.151	+	85.1513i	0.310687	+	0.114451i
$745$	267.711	+	400.657i	0.359343	+	0.537795i
$746$	647.141	+	1087.35i	0.867481	+	1.45758i
$747$	−770.682	+	939.079i	−1.03170	+	1.25713i
$748$	701.407	−	462.373i	0.937710	−	0.618145i
$749$	136.312	+	72.8604i	0.181992	+	0.0972769i
$750$	53.3235	+	215.728i	0.0710981	+	0.287637i
$751$	683.862	+	283.265i	0.910601	+	0.377183i	0.788287	−	0.615308i	$-0.210968\pi$
$751$	683.862	+	283.265i	0.910601	+	0.377183i	0.122315	+	0.992491i	$0.460968\pi$
$752$	−443.955	−	94.0717i	−0.590366	−	0.125095i
$753$	90.1567	+	217.658i	0.119730	+	0.289054i
$754$	674.149	+	914.926i	0.894097	+	1.21343i
$755$	−588.089	+	178.395i	−0.778925	+	0.236284i
$756$	1.00650	−	161.603i	0.00133135	−	0.213760i
$757$	1161.34	−	114.382i	1.53414	−	0.151099i	0.704623	−	0.709582i	$-0.251116\pi$
$757$	1161.34	−	114.382i	1.53414	−	0.151099i	0.829516	+	0.558483i	$0.188616\pi$
$758$	−383.444	+	55.6588i	−0.505863	+	0.0734285i
$759$	−245.539	−	48.8408i	−0.323504	−	0.0643489i
$760$	31.4302	−	18.4416i	0.0413555	−	0.0242653i
$761$	−1100.17	+	218.837i	−1.44568	+	0.287564i	−0.854701	−	0.519120i	$-0.826260\pi$
$761$	−1100.17	+	218.837i	−1.44568	+	0.287564i	−0.590983	+	0.806684i	$0.701260\pi$
$762$	3.98225	−	8.35237i	0.00522605	−	0.0109611i
$763$	85.5716	−	282.092i	0.112152	−	0.369714i
$764$	790.173	−	950.692i	1.03426	−	1.24436i
$765$	206.918	+	252.130i	0.270480	+	0.329581i
$766$	88.7234	−	41.6254i	0.115827	−	0.0543413i
$767$		−	887.605i		−	1.15724i
$768$	121.022	−	213.449i	0.157580	−	0.277929i
$769$	1462.40			1.90169			0.950844	−	0.309671i	$-0.100219\pi$
$769$	1462.40			1.90169			0.950844	+	0.309671i	$0.100219\pi$
$770$	80.8039	+	172.231i	0.104940	+	0.223677i
$771$	−376.605	+	309.071i	−0.488462	+	0.400871i
$772$	−627.384	−	521.454i	−0.812674	−	0.675459i
$773$	−1169.01	−	354.616i	−1.51231	−	0.458753i	−0.578243	−	0.815864i	$-0.696262\pi$
$773$	−1169.01	−	354.616i	−1.51231	−	0.458753i	−0.934062	+	0.357112i	$0.883762\pi$
$774$	−108.919	−	51.9304i	−0.140722	−	0.0670936i
$775$	110.260	+	554.312i	0.142270	+	0.715242i
$776$	−32.6853	+	19.1781i	−0.0421202	+	0.0247140i
$777$	−0.550132	+	2.76570i	−0.000708021	+	0.00355946i
$778$	−111.805	−	770.249i	−0.143709	−	0.990037i
$779$	−8.32344	−	84.5093i	−0.0106848	−	0.108484i
$780$	−119.179	−	0.742277i	−0.152793	−	0.000951637i
$781$	421.430	+	1389.27i	0.539603	+	1.77883i
$782$	440.342	−	324.459i	0.563097	−	0.414909i
$783$	752.526	−	311.707i	0.961081	−	0.398093i
$784$	−374.296	−	575.567i	−0.477418	−	0.734141i
$785$	67.6473	−	163.315i	0.0861749	−	0.208045i
$786$	−258.874	+	63.9884i	−0.329356	+	0.0814102i
$787$	304.362	−	569.421i	0.386737	−	0.723533i	−0.610939	−	0.791678i	$-0.709208\pi$
$787$	304.362	−	569.421i	0.386737	−	0.723533i	0.997675	+	0.0681444i	$0.0217079\pi$
$788$	−251.207	−	381.075i	−0.318791	−	0.483598i
$789$	76.0737	+	62.4321i	0.0964179	+	0.0791281i
$790$	121.065	−	72.0521i	0.153247	−	0.0912051i
$791$	−350.434	+	234.152i	−0.443026	+	0.296021i
$792$	−859.191	−	316.509i	−1.08484	−	0.399632i
$793$	226.827	+	151.561i	0.286037	+	0.191124i
$794$	278.668	−	250.993i	0.350967	−	0.316113i
$795$	64.8723	+	121.368i	0.0816004	+	0.152664i
$796$	681.003	−	1255.20i	0.855531	−	1.57688i
$797$	60.3772	−	613.020i	0.0757555	−	0.769159i	−0.879995	−	0.474982i	$-0.842455\pi$
$797$	60.3772	−	613.020i	0.0757555	−	0.769159i	0.955751	−	0.294177i	$-0.0950454\pi$
$798$	5.84963	+	5.33507i	0.00733037	+	0.00668555i
$799$	297.413	+	297.413i	0.372232	+	0.372232i
$800$	562.641	−	18.8651i	0.703302	−	0.0235813i
$801$	−460.228	−	460.228i	−0.574566	−	0.574566i
$802$	441.882	−	20.3291i	0.550975	−	0.0253480i
$803$	−38.9722	+	395.692i	−0.0485333	+	0.492767i
$804$	125.701	−	101.857i	0.156345	−	0.126687i
$805$	58.3890	+	109.238i	0.0725330	+	0.135700i
$806$	−732.858	−	38.2910i	−0.909253	−	0.0475075i
$807$	26.6206	+	17.7873i	0.0329871	+	0.0220413i
$808$	709.069	−	170.589i	0.877561	−	0.211125i
$809$	336.606	−	224.913i	0.416077	−	0.278014i	−0.329861	−	0.944030i	$-0.607002\pi$
$809$	336.606	−	224.913i	0.416077	−	0.278014i	0.745937	+	0.666016i	$0.232002\pi$
$810$	76.3798	−	300.946i	0.0942961	−	0.371538i
$811$	74.5565	+	61.1869i	0.0919315	+	0.0754462i	0.679236	−	0.733919i	$-0.262311\pi$
$811$	74.5565	+	61.1869i	0.0919315	+	0.0754462i	−0.587305	+	0.809366i	$0.699811\pi$
$812$	−275.369	+	406.613i	−0.339124	+	0.500755i
$813$	−110.378	+	206.503i	−0.135767	+	0.254002i
$814$	28.9116	+	17.4516i	0.0355179	+	0.0214393i
$815$	225.382	−	544.119i	0.276542	−	0.667631i
$816$	−201.883	+	104.697i	−0.247406	+	0.128305i
$817$	11.5438	−	4.78159i	0.0141295	−	0.00585262i
$818$	26.3739	−	174.062i	0.0322419	−	0.212790i
$819$	66.1189	+	217.965i	0.0807313	+	0.266135i
$820$	−214.560	+	509.004i	−0.261659	+	0.620736i
$821$	71.7209	+	728.194i	0.0873579	+	0.886960i	0.934588	+	0.355733i	$0.115769\pi$
$821$	71.7209	+	728.194i	0.0873579	+	0.886960i	−0.847230	+	0.531227i	$0.821731\pi$
$822$	−12.3846	+	16.5905i	−0.0150664	+	0.0201831i
$823$	−39.5741	+	198.952i	−0.0480851	+	0.241740i	−0.997351	−	0.0727330i	$-0.976828\pi$
$823$	−39.5741	+	198.952i	−0.0480851	+	0.241740i	0.949266	+	0.314473i	$0.101828\pi$
$824$	175.736	−	156.313i	0.213272	−	0.189700i
$825$	46.5902	+	234.225i	0.0564729	+	0.283909i
$826$	361.525	−	128.087i	0.437681	−	0.155069i
$827$	−267.948	−	81.2811i	−0.324000	−	0.0982843i	0.124095	−	0.992270i	$-0.460397\pi$
$827$	−267.948	−	81.2811i	−0.324000	−	0.0982843i	−0.448095	+	0.893986i	$0.647897\pi$
$828$	−569.392	−	176.603i	−0.687671	−	0.213289i
$829$	79.7330	−	65.4352i	0.0961797	−	0.0789327i	−0.585075	−	0.810979i	$-0.698935\pi$
$829$	79.7330	−	65.4352i	0.0961797	−	0.0789327i	0.681254	+	0.732047i	$0.261435\pi$
$830$	−278.069	+	769.586i	−0.335023	+	0.927212i
$831$	203.063			0.244359
$832$	−155.977	+	714.147i	−0.187473	+	0.858349i
$833$			636.329i			0.763900i
$834$	50.7357	−	140.417i	0.0608342	−	0.168365i
$835$	−475.442	−	579.328i	−0.569392	−	0.693806i
$836$	83.8954	−	44.1734i	0.100353	−	0.0528390i
$837$	−152.680	+	503.320i	−0.182414	+	0.601338i
$838$	568.711	−	201.492i	0.678652	−	0.240444i
$839$	−1048.84	+	208.627i	−1.25010	+	0.248661i	−0.775392	−	0.631480i	$-0.782448\pi$
$839$	−1048.84	+	208.627i	−1.25010	+	0.248661i	−0.474712	+	0.880141i	$0.657448\pi$
$840$	−16.8959	−	48.6491i	−0.0201142	−	0.0579156i
$841$	−1602.76	−	318.810i	−1.90578	−	0.379084i
$842$	802.002	−	1074.37i	0.952497	−	1.27597i
$843$	−77.9434	+	7.67675i	−0.0924595	+	0.00910647i
$844$	78.9606	−	32.1319i	0.0935552	−	0.0380709i
$845$	−100.396	+	30.4548i	−0.118812	+	0.0360412i
$846$	68.6768	−	453.252i	0.0811782	−	0.535759i
$847$	75.1568	+	181.445i	0.0887330	+	0.214220i
$848$	810.701	−	234.937i	0.956016	−	0.277048i
$849$	408.322	+	169.133i	0.480945	+	0.199214i
$850$	−446.694	−	269.633i	−0.525523	−	0.317215i
$851$	19.3910	+	10.3647i	0.0227861	+	0.0121794i
$852$	−74.2686	−	385.920i	−0.0871698	−	0.452958i
$853$	−111.939	+	136.398i	−0.131230	+	0.159904i	−0.834480	−	0.551039i	$-0.814232\pi$
$853$	−111.939	+	136.398i	−0.131230	+	0.159904i	0.703250	+	0.710943i	$0.251732\pi$
$854$	−28.9988	+	114.259i	−0.0339565	+	0.133793i
$855$	20.4514	+	30.6076i	0.0239197	+	0.0357984i
$856$	−405.238	+	294.717i	−0.473409	+	0.344295i
$857$	200.057	−	299.407i	0.233439	−	0.349366i	−0.696193	−	0.717854i	$-0.745124\pi$
$857$	200.057	−	299.407i	0.233439	−	0.349366i	0.929633	+	0.368488i	$0.120124\pi$
$858$	−309.669	−	16.1799i	−0.360919	−	0.0188577i
$859$	−640.857	+	342.545i	−0.746051	+	0.398772i	−0.800179	−	0.599762i	$-0.795262\pi$
$859$	−640.857	+	342.545i	−0.746051	+	0.398772i	0.0541281	+	0.998534i	$0.482762\pi$
$860$	−80.8345	−	8.47016i	−0.0939936	−	0.00984902i
$861$	−119.431	−	11.7629i	−0.138712	−	0.0136619i
$862$	909.956	−	41.8632i	1.05563	−	0.0485651i
$863$	47.4148	−	47.4148i	0.0549418	−	0.0549418i	−0.679102	−	0.734044i	$-0.737631\pi$
$863$	47.4148	−	47.4148i	0.0549418	−	0.0549418i	0.734044	+	0.679102i	$0.237631\pi$
$864$	470.061	+	231.346i	0.544052	+	0.267761i
$865$	−453.680	+	453.680i	−0.524486	+	0.524486i
$866$	−795.210	−	725.260i	−0.918256	−	0.837482i
$867$	−65.9063	−	6.49121i	−0.0760165	−	0.00748697i
$868$	−90.1600	−	304.021i	−0.103871	−	0.350255i
$869$	323.275	−	172.794i	0.372009	−	0.198843i
$870$	192.870	−	173.716i	0.221690	−	0.199674i
$871$	−267.775	+	400.754i	−0.307434	+	0.460108i
$872$	702.070	+	648.369i	0.805126	+	0.743542i
$873$	−21.2680	−	31.8299i	−0.0243620	−	0.0364603i
$874$	53.0474	−	31.5713i	0.0606950	−	0.0361228i
$875$	181.477	−	221.130i	0.207402	−	0.252721i
$876$	21.6552	−	105.432i	0.0247206	−	0.120356i
$877$	−763.374	−	408.032i	−0.870438	−	0.465259i	−0.0252209	−	0.999682i	$-0.508029\pi$
$877$	−763.374	−	408.032i	−0.870438	−	0.465259i	−0.845217	+	0.534423i	$0.820529\pi$
$878$	1552.73	−	383.803i	1.76848	−	0.437134i
$879$	−60.1781	−	24.9266i	−0.0684620	−	0.0283579i
$880$	−616.701	−	7.68225i	−0.700797	−	0.00872983i
$881$	−196.071	−	473.358i	−0.222556	−	0.537297i	0.772680	−	0.634796i	$-0.218916\pi$
$881$	−196.071	−	473.358i	−0.222556	−	0.537297i	−0.995236	+	0.0974990i	$0.968916\pi$
$882$	558.345	−	411.408i	0.633044	−	0.466449i
$883$	399.394	−	121.155i	0.452315	−	0.137208i	−0.0559041	−	0.998436i	$-0.517804\pi$
$883$	399.394	−	121.155i	0.452315	−	0.137208i	0.508219	+	0.861228i	$0.330304\pi$
$884$	482.035	−	476.067i	0.545288	−	0.538538i
$885$	−201.752	+	19.8708i	−0.227968	+	0.0224529i
$886$	150.445	+	1036.45i	0.169803	+	1.16981i
$887$	−931.135	−	185.214i	−1.04976	−	0.208810i	−0.360076	−	0.932923i	$-0.617249\pi$
$887$	−931.135	−	185.214i	−1.04976	−	0.208810i	−0.689681	+	0.724113i	$0.742249\pi$
$888$	−7.29151	−	5.51408i	−0.00821116	−	0.00620955i
$889$	−11.6827	+	2.32383i	−0.0131414	+	0.00261398i
$890$	−395.726	−	188.675i	−0.444636	−	0.211994i
$891$	234.504	−	773.056i	0.263192	−	0.867628i
$892$	−59.5071	−	645.367i	−0.0667120	−	0.723506i
$893$	30.1147	+	36.6948i	0.0337230	+	0.0410916i
$894$	−144.153	−	307.257i	−0.161244	−	0.343688i
$895$		−	572.194i		−	0.639323i
$896$	−313.383	+	39.5258i	−0.349758	+	0.0441136i
$897$	−201.894			−0.225077
$898$	1488.39	−	698.293i	1.65745	−	0.777609i
$899$	1235.50	−	1013.95i	1.37430	−	1.12786i
$900$	52.2145	+	566.278i	0.0580161	+	0.629197i
$901$	−748.609	−	227.088i	−0.830865	−	0.252040i
$902$	−618.526	+	1297.30i	−0.685727	+	1.43824i
$903$	−3.44494	−	17.3189i	−0.00381499	−	0.0191793i
$904$	−187.848	−	1353.36i	−0.207796	−	1.49708i
$905$	−108.475	+	545.341i	−0.119862	+	0.602586i
$906$	428.356	−	62.1779i	0.472799	−	0.0686291i
$907$	−150.464	−	1527.68i	−0.165891	−	1.68432i	−0.613187	−	0.789938i	$-0.710113\pi$
$907$	−150.464	−	1527.68i	−0.165891	−	1.68432i	0.447295	−	0.894386i	$-0.352387\pi$
$908$	−451.044	+	445.461i	−0.496745	+	0.490595i
$909$	213.857	+	704.991i	0.235266	+	0.775568i
$910$	91.0092	+	123.514i	0.100010	+	0.135729i
$911$	−1535.29	+	635.939i	−1.68528	+	0.698067i	−0.999556	−	0.0297924i	$-0.990515\pi$
$911$	−1535.29	+	635.939i	−1.68528	+	0.698067i	−0.685726	+	0.727859i	$0.740515\pi$
$912$	−23.8332	+	9.52600i	−0.0261329	+	0.0104452i
$913$	−814.750	+	1966.98i	−0.892388	+	2.15442i
$914$	−124.890	−	505.258i	−0.136641	−	0.552799i
$915$	29.3718	−	54.9507i	0.0321003	−	0.0600555i
$916$	−28.5202	+	138.855i	−0.0311356	+	0.151589i
$917$	265.357	+	217.773i	0.289375	+	0.237484i
$918$	−248.335	−	417.263i	−0.270518	−	0.454535i
$919$	1255.24	−	838.722i	1.36587	−	0.912646i	0.366033	−	0.930602i	$-0.380716\pi$
$919$	1255.24	−	838.722i	1.36587	−	0.912646i	0.999839	+	0.0179558i	$0.00571582\pi$
$920$	−401.235	+	15.9555i	−0.436125	+	0.0173430i
$921$	344.582	+	230.242i	0.374139	+	0.249991i
$922$	−187.847	−	208.558i	−0.203738	−	0.226202i
$923$	551.905	+	1032.54i	0.597947	+	1.11868i
$924$	−38.0971	−	128.464i	−0.0412306	−	0.139030i
$925$	2.05581	−	20.8730i	0.00222250	−	0.0225654i
$926$	−551.186	+	604.347i	−0.595233	+	0.652642i
$927$	167.999	+	167.999i	0.181229	+	0.181229i
$928$	−797.108	−	1378.11i	−0.858953	−	1.48503i
$929$	−642.884	−	642.884i	−0.692017	−	0.692017i	0.270658	−	0.962675i	$-0.412759\pi$
$929$	−642.884	−	642.884i	−0.692017	−	0.692017i	−0.962675	+	0.270658i	$0.912759\pi$
$930$	7.70298	+	167.435i	0.00828277	+	0.180038i
$931$	−7.03928	+	71.4710i	−0.00756098	+	0.0767680i
$932$	−1589.42	−	166.546i	−1.70538	−	0.178697i
$933$	208.487	+	390.052i	0.223459	+	0.418062i
$934$	86.3982	−	1653.59i	0.0925034	−	1.77044i
$935$	475.284	+	317.575i	0.508325	+	0.339652i
$936$	−729.376	−	115.166i	−0.779247	−	0.123041i
$937$	15.6853	−	10.4806i	0.0167399	−	0.0111852i	−0.547172	−	0.837020i	$-0.684296\pi$
$937$	15.6853	−	10.4806i	0.0167399	−	0.0111852i	0.563912	+	0.825835i	$0.309296\pi$
$938$	−201.870	−	51.2345i	−0.215214	−	0.0546210i
$939$	−225.038	−	184.684i	−0.239657	−	0.196681i
$940$	−58.3534	−	303.220i	−0.0620781	−	0.322575i
$941$	32.3570	−	60.5357i	0.0343857	−	0.0643312i	−0.864142	−	0.503249i	$-0.832138\pi$
$941$	32.3570	−	60.5357i	0.0343857	−	0.0643312i	0.898527	+	0.438918i	$0.144638\pi$
$942$	−64.3404	+	106.591i	−0.0683019	+	0.113154i
$943$	−358.089	+	864.504i	−0.379734	+	0.916759i
$944$	−137.279	+	1235.81i	−0.145423	+	1.30912i
$945$	101.590	−	42.0799i	0.107503	−	0.0445290i
$946$	−209.084	−	31.6804i	−0.221019	−	0.0334888i
$947$	−49.5767	−	163.432i	−0.0523513	−	0.172579i	0.926866	−	0.375392i	$-0.122492\pi$
$947$	−49.5767	−	163.432i	−0.0523513	−	0.172579i	−0.979218	+	0.202813i	$0.934992\pi$
$948$	−91.9097	+	37.4013i	−0.0969512	+	0.0394529i
$949$	31.4291	+	319.105i	0.0331181	+	0.336254i
$950$	−47.1889	−	35.2260i	−0.0496725	−	0.0370800i
$951$	11.8810	−	59.7298i	0.0124932	−	0.0628074i
$952$	263.465	+	127.635i	0.276749	+	0.134070i
$953$	260.210	+	1308.16i	0.273043	+	1.37268i	0.837148	+	0.546977i	$0.184221\pi$
$953$	260.210	+	1308.16i	0.273043	+	1.37268i	−0.564105	+	0.825703i	$0.690779\pi$
$954$	284.743	+	803.685i	0.298473	+	0.842437i
$955$	804.918	+	244.169i	0.842846	+	0.255675i
$956$	−678.368	+	357.181i	−0.709590	+	0.373621i
$957$	522.060	−	428.444i	0.545517	−	0.447694i
$958$	−277.974	−	100.438i	−0.290161	−	0.104842i
$959$	26.6512			0.0277907
$960$	165.817	+	19.4659i	0.172726	+	0.0202770i
$961$			71.0723i			0.0739566i
$962$	25.6134	+	9.25468i	0.0266251	+	0.00962025i
$963$	−321.109	−	391.273i	−0.333447	−	0.406306i
$964$	796.435	+	247.023i	0.826178	+	0.256248i
$965$	161.133	−	531.184i	0.166977	−	0.550450i
$966$	−29.1346	−	82.2322i	−0.0301600	−	0.0851265i
$967$	458.714	−	91.2438i	0.474368	−	0.0943576i	0.0478841	−	0.998853i	$-0.484752\pi$
$967$	458.714	−	91.2438i	0.474368	−	0.0943576i	0.426484	+	0.904495i	$0.359752\pi$
$968$	−635.601	−	37.1802i	−0.656612	−	0.0384093i
$969$	23.3313	+	4.64088i	0.0240777	+	0.00478935i
$970$	−20.6631	−	15.4248i	−0.0213022	−	0.0159019i
$971$	−274.242	+	27.0105i	−0.282432	+	0.0278172i	−0.238241	−	0.971206i	$-0.576571\pi$
$971$	−274.242	+	27.0105i	−0.282432	+	0.0278172i	−0.0441908	+	0.999023i	$0.514071\pi$
$972$	−313.883	+	744.628i	−0.322925	+	0.766079i
$973$	−183.920	+	55.7915i	−0.189024	+	0.0573397i
$974$	22.1244	+	3.35228i	0.0227149	+	0.00344177i
$975$	73.7012	+	177.930i	0.0755910	+	0.182493i
$976$	−292.369	−	246.099i	−0.299559	−	0.252151i
$977$	157.533	+	65.2523i	0.161241	+	0.0667884i	0.461844	−	0.886961i	$-0.347188\pi$
$977$	157.533	+	65.2523i	0.161241	+	0.0667884i	−0.300603	+	0.953749i	$0.597188\pi$
$978$	−214.364	+	355.132i	−0.219186	+	0.363121i
$979$	−1005.97	−	537.703i	−1.02755	−	0.549237i
$980$	261.952	−	386.801i	0.267298	−	0.394695i
$981$	−612.426	+	746.243i	−0.624288	+	0.760697i
$982$	1150.23	+	291.928i	1.17132	+	0.297279i
$983$	−275.347	−	412.086i	−0.280109	−	0.419213i	0.664561	−	0.747234i	$-0.268618\pi$
$983$	−275.347	−	412.086i	−0.280109	−	0.419213i	−0.944671	+	0.328021i	$0.893618\pi$
$984$	203.123	−	331.820i	0.206426	−	0.337216i
$985$	172.539	−	258.222i	0.175166	−	0.262155i
$986$	−76.9903	+	1473.53i	−0.0780835	+	1.49445i
$987$	59.1646	−	31.6241i	0.0599439	−	0.0320407i
$988$	59.4074	−	48.1383i	0.0601290	−	0.0487230i
$989$	−137.021	−	13.4954i	−0.138545	−	0.0136455i
$990$	−28.6321	−	622.360i	−0.0289213	−	0.628646i
$991$	695.365	−	695.365i	0.701680	−	0.701680i	−0.263091	−	0.964771i	$-0.584742\pi$
$991$	695.365	−	695.365i	0.701680	−	0.701680i	0.964771	+	0.263091i	$0.0847419\pi$
$992$	1014.43	+	166.658i	1.02261	+	0.168002i
$993$	−139.360	+	139.360i	−0.140343	+	0.140343i
$994$	−340.915	+	373.795i	−0.342972	+	0.376052i
$995$	966.989	+	95.2401i	0.971848	+	0.0957187i
$996$	274.844	−	506.583i	0.275948	−	0.508618i
$997$	−627.541	+	335.428i	−0.629429	+	0.336437i	−0.755075	−	0.655638i	$-0.772400\pi$
$997$	−627.541	+	335.428i	−0.629429	+	0.336437i	0.125646	+	0.992075i	$0.459900\pi$
$998$	1233.06	+	1369.02i	1.23553	+	1.37176i
$999$	10.8442	−	16.2295i	0.0108551	−	0.0162458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.3.l.a.3.11	✓	496
128.43	odd	32	inner	128.3.l.a.43.11	yes	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.3.l.a.3.11	✓	496	1.1	even	1	trivial
128.3.l.a.43.11	yes	496	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	128.l (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.849476 - 1.81063i) q^{2} +(-0.740915 + 0.608053i) q^{3} +(-2.55678 + 3.07618i) q^{4} +(-2.60449 - 0.790064i) q^{5} +(1.73035 + 0.824998i) q^{6} +(-0.481425 - 2.42029i) q^{7} +(7.74175 + 2.01625i) q^{8} +(-1.57659 + 7.92604i) q^{9} +O(q^{10})\)	\(q+(-0.849476 - 1.81063i) q^{2} +(-0.740915 + 0.608053i) q^{3} +(-2.55678 + 3.07618i) q^{4} +(-2.60449 - 0.790064i) q^{5} +(1.73035 + 0.824998i) q^{6} +(-0.481425 - 2.42029i) q^{7} +(7.74175 + 2.01625i) q^{8} +(-1.57659 + 7.92604i) q^{9} +(0.781937 + 5.38692i) q^{10} +(1.38820 + 14.0946i) q^{11} +(0.0238782 - 3.83384i) q^{12} +(3.31551 + 10.9298i) q^{13} +(-3.97329 + 2.92766i) q^{14} +(2.41011 - 0.998299i) q^{15} +(-2.92574 - 15.7302i) q^{16} +(-5.67490 + 13.7004i) q^{17} +(15.6904 - 3.87836i) q^{18} +(-0.788950 + 1.47602i) q^{19} +(9.08949 - 5.99186i) q^{20} +(1.82836 + 1.50049i) q^{21} +(24.3410 - 14.4866i) q^{22} +(15.3342 - 10.2460i) q^{23} +(-6.96197 + 3.21352i) q^{24} +(-14.6276 - 9.77383i) q^{25} +(16.9734 - 15.2878i) q^{26} +(-7.71775 - 14.4389i) q^{27} +(8.67613 + 4.70719i) q^{28} +(-4.87645 + 49.5115i) q^{29} +(-3.85488 - 3.51579i) q^{30} +(-22.7164 - 22.7164i) q^{31} +(-25.9963 + 18.6599i) q^{32} +(-9.59882 - 9.59882i) q^{33} +(29.6271 - 1.36302i) q^{34} +(-0.658314 + 6.68397i) q^{35} +(-20.3509 - 25.1150i) q^{36} +(0.562008 + 1.05144i) q^{37} +(3.34273 + 0.174654i) q^{38} +(-9.10240 - 6.08203i) q^{39} +(-18.5704 - 11.3678i) q^{40} +(-42.1875 + 28.1888i) q^{41} +(1.16370 - 4.58512i) q^{42} +(-5.77105 - 4.73618i) q^{43} +(-46.9069 - 31.7666i) q^{44} +(10.3683 - 19.3977i) q^{45} +(-31.5777 - 19.0609i) q^{46} +(10.8542 - 26.2043i) q^{47} +(11.7325 + 9.87576i) q^{48} +(39.6441 - 16.4211i) q^{49} +(-5.27105 + 34.7878i) q^{50} +(-4.12596 - 13.6015i) q^{51} +(-42.0990 - 17.7460i) q^{52} +(5.17075 + 52.4995i) q^{53} +(-19.5875 + 26.2395i) q^{54} +(7.52011 - 37.8061i) q^{55} +(1.15284 - 19.7079i) q^{56} +(-0.312955 - 1.57333i) q^{57} +(93.7895 - 33.2293i) q^{58} +(-74.3666 - 22.5589i) q^{59} +(-3.09117 + 9.96635i) q^{60} +(18.4632 - 15.1524i) q^{61} +(-21.8341 + 60.4282i) q^{62} +19.9423 q^{63} +(55.8694 + 31.2187i) q^{64} -31.0860i q^{65} +(-9.22598 + 25.5339i) q^{66} +(26.7709 + 32.6205i) q^{67} +(-27.6354 - 52.4860i) q^{68} +(-5.13122 + 16.9154i) q^{69} +(12.6614 - 4.48591i) q^{70} +(100.537 - 19.9980i) q^{71} +(-28.1864 + 58.1826i) q^{72} +(27.5345 + 5.47695i) q^{73} +(1.42636 - 1.91076i) q^{74} +(16.7808 - 1.65276i) q^{75} +(-2.52333 - 6.20082i) q^{76} +(33.4447 - 10.1454i) q^{77} +(-3.28005 + 21.6476i) q^{78} +(-9.90450 - 23.9116i) q^{79} +(-4.80783 + 43.2808i) q^{80} +(-52.6977 - 21.8281i) q^{81} +(86.8769 + 52.4404i) q^{82} +(132.576 + 70.8633i) q^{83} +(-9.29050 + 1.78792i) q^{84} +(25.6044 - 31.1991i) q^{85} +(-3.67311 + 14.4725i) q^{86} +(-26.4926 - 39.6489i) q^{87} +(-17.6713 + 111.916i) q^{88} +(-44.7450 + 66.9656i) q^{89} +(-43.9297 - 2.29528i) q^{90} +(24.8570 - 13.2864i) q^{91} +(-7.68772 + 73.3673i) q^{92} +(30.6437 + 3.01814i) q^{93} +(-56.6666 + 2.60699i) q^{94} +(3.22097 - 3.22097i) q^{95} +(7.91486 - 29.6325i) q^{96} +(-3.34959 + 3.34959i) q^{97} +(-63.4093 - 57.8315i) q^{98} +(-113.903 - 11.2185i) 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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