LMFDB - Embedded newform 133.2.g.a.102.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [133,2,Mod(30,133)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(133, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("133.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 133 = 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	133.g (of order $3$, degree $2$, 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:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			102.3
Character	$\chi$	$=$	133.102
Dual form			133.2.g.a.30.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.797467 + 1.38125i) q^{2} -1.48377 q^{3} +(-0.271907 - 0.470957i) q^{4} +(-0.310056 + 0.537033i) q^{5} +(1.18326 - 2.04946i) q^{6} +(-2.33703 + 1.24028i) q^{7} -2.32252 q^{8} -0.798426 q^{9} +O(q^{10})$	\(q+(-0.797467 + 1.38125i) q^{2} -1.48377 q^{3} +(-0.271907 - 0.470957i) q^{4} +(-0.310056 + 0.537033i) q^{5} +(1.18326 - 2.04946i) q^{6} +(-2.33703 + 1.24028i) q^{7} -2.32252 q^{8} -0.798426 q^{9} +(-0.494519 - 0.856532i) q^{10} +(2.47691 - 4.29013i) q^{11} +(0.403448 + 0.698793i) q^{12} +(-2.32535 + 4.02762i) q^{13} +(0.150568 - 4.21711i) q^{14} +(0.460052 - 0.796833i) q^{15} +(2.39595 - 4.14990i) q^{16} -5.70797 q^{17} +(0.636718 - 1.10283i) q^{18} +(0.609015 + 4.31614i) q^{19} +0.337226 q^{20} +(3.46762 - 1.84029i) q^{21} +(3.95051 + 6.84248i) q^{22} +5.34418 q^{23} +3.44609 q^{24} +(2.30773 + 3.99711i) q^{25} +(-3.70878 - 6.42379i) q^{26} +5.63599 q^{27} +(1.21957 + 0.763402i) q^{28} +(-4.35913 + 7.55024i) q^{29} +(0.733752 + 1.27090i) q^{30} +(-1.94719 + 3.37263i) q^{31} +(1.49886 + 2.59610i) q^{32} +(-3.67517 + 6.36557i) q^{33} +(4.55192 - 7.88415i) q^{34} +(0.0585411 - 1.63962i) q^{35} +(0.217098 + 0.376025i) q^{36} +(1.69296 + 2.93229i) q^{37} +(-6.44736 - 2.60078i) q^{38} +(3.45028 - 5.97607i) q^{39} +(0.720111 - 1.24727i) q^{40} +(-2.13757 - 3.70239i) q^{41} +(-0.223409 + 6.25722i) q^{42} +(-0.790620 - 1.36939i) q^{43} -2.69396 q^{44} +(0.247557 - 0.428781i) q^{45} +(-4.26181 + 7.38167i) q^{46} +5.77039 q^{47} +(-3.55504 + 6.15750i) q^{48} +(3.92343 - 5.79713i) q^{49} -7.36136 q^{50} +8.46931 q^{51} +2.52912 q^{52} +(-1.94482 - 3.36853i) q^{53} +(-4.49452 + 7.78473i) q^{54} +(1.53596 + 2.66036i) q^{55} +(5.42780 - 2.88057i) q^{56} +(-0.903639 - 6.40417i) q^{57} +(-6.95253 - 12.0421i) q^{58} -2.52167 q^{59} -0.500366 q^{60} -4.29946 q^{61} +(-3.10564 - 5.37913i) q^{62} +(1.86595 - 0.990269i) q^{63} +4.80263 q^{64} +(-1.44198 - 2.49758i) q^{65} +(-5.86165 - 10.1527i) q^{66} +(-5.86924 - 10.1658i) q^{67} +(1.55204 + 2.68821i) q^{68} -7.92953 q^{69} +(2.21804 + 1.38840i) q^{70} +(2.34846 + 4.06765i) q^{71} +1.85436 q^{72} +6.98698 q^{73} -5.40031 q^{74} +(-3.42414 - 5.93079i) q^{75} +(1.86712 - 1.46041i) q^{76} +(-0.467661 + 13.0982i) q^{77} +(5.50297 + 9.53143i) q^{78} +(-5.32729 + 9.22714i) q^{79} +(1.48576 + 2.57340i) q^{80} -5.96724 q^{81} +6.81858 q^{82} -12.3296 q^{83} +(-1.80957 - 1.13271i) q^{84} +(1.76979 - 3.06537i) q^{85} +2.52197 q^{86} +(6.46795 - 11.2028i) q^{87} +(-5.75267 + 9.96392i) q^{88} +2.38744 q^{89} +(0.394837 + 0.683877i) q^{90} +(0.439045 - 12.2968i) q^{91} +(-1.45312 - 2.51688i) q^{92} +(2.88918 - 5.00421i) q^{93} +(-4.60170 + 7.97037i) q^{94} +(-2.50674 - 1.01119i) q^{95} +(-2.22396 - 3.85202i) q^{96} +(7.45741 + 12.9166i) q^{97} +(4.87850 + 10.0423i) q^{98} +(-1.97763 + 3.42536i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9}+O(q^{10}) $ 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9} + 16 q^{10} - q^{11} - 2 q^{12} + 6 q^{13} - q^{14} - 9 q^{15} - 9 q^{16} - 16 q^{17} + 5 q^{18} - 4 q^{19} - 21 q^{21} - 2 q^{22} + 18 q^{23} + 16 q^{24} - 14 q^{25} + q^{26} - 18 q^{27} - 14 q^{28} - 2 q^{29} - 9 q^{30} + 11 q^{31} + 24 q^{32} + 3 q^{33} + 6 q^{34} + 38 q^{35} - 7 q^{36} - 14 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 20 q^{41} - 36 q^{42} + 2 q^{43} - 4 q^{44} - 12 q^{45} - 6 q^{46} + 39 q^{48} + 18 q^{49} + 22 q^{50} - 42 q^{51} - 22 q^{52} + 7 q^{53} - 43 q^{54} + 9 q^{55} - 21 q^{56} + 21 q^{57} + 35 q^{58} - 84 q^{59} + 12 q^{60} - 12 q^{61} - 19 q^{62} + 9 q^{63} - 2 q^{64} - 27 q^{65} + 3 q^{66} - 14 q^{67} + 51 q^{68} - 34 q^{69} + 33 q^{70} + q^{71} - 36 q^{72} + 42 q^{73} + 50 q^{74} + 31 q^{75} - 70 q^{76} - 20 q^{77} + 57 q^{78} - 5 q^{79} + 13 q^{80} - 56 q^{81} + 24 q^{82} + 10 q^{83} + 129 q^{84} - 27 q^{85} - 36 q^{86} + 53 q^{87} - 36 q^{88} + 2 q^{89} + 27 q^{90} - 9 q^{91} - 72 q^{92} + 34 q^{93} + 12 q^{94} - 11 q^{95} - 94 q^{96} + 31 q^{97} - 26 q^{98} + 43 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9 + 16 * q^10 - q^11 - 2 * q^12 + 6 * q^13 - q^14 - 9 * q^15 - 9 * q^16 - 16 * q^17 + 5 * q^18 - 4 * q^19 - 21 * q^21 - 2 * q^22 + 18 * q^23 + 16 * q^24 - 14 * q^25 + q^26 - 18 * q^27 - 14 * q^28 - 2 * q^29 - 9 * q^30 + 11 * q^31 + 24 * q^32 + 3 * q^33 + 6 * q^34 + 38 * q^35 - 7 * q^36 - 14 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 20 * q^41 - 36 * q^42 + 2 * q^43 - 4 * q^44 - 12 * q^45 - 6 * q^46 + 39 * q^48 + 18 * q^49 + 22 * q^50 - 42 * q^51 - 22 * q^52 + 7 * q^53 - 43 * q^54 + 9 * q^55 - 21 * q^56 + 21 * q^57 + 35 * q^58 - 84 * q^59 + 12 * q^60 - 12 * q^61 - 19 * q^62 + 9 * q^63 - 2 * q^64 - 27 * q^65 + 3 * q^66 - 14 * q^67 + 51 * q^68 - 34 * q^69 + 33 * q^70 + q^71 - 36 * q^72 + 42 * q^73 + 50 * q^74 + 31 * q^75 - 70 * q^76 - 20 * q^77 + 57 * q^78 - 5 * q^79 + 13 * q^80 - 56 * q^81 + 24 * q^82 + 10 * q^83 + 129 * q^84 - 27 * q^85 - 36 * q^86 + 53 * q^87 - 36 * q^88 + 2 * q^89 + 27 * q^90 - 9 * q^91 - 72 * q^92 + 34 * q^93 + 12 * q^94 - 11 * q^95 - 94 * q^96 + 31 * q^97 - 26 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$.

$n$	$78$	$115$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.797467	+	1.38125i	−0.563894	+	0.976694i	0.433257	+	0.901270i	$0.357364\pi$
$2$	−0.797467	+	1.38125i	−0.563894	+	0.976694i	−0.997152	+	0.0754234i	$0.975969\pi$
$3$	−1.48377			−0.856655			−0.428328	−	0.903624i	$-0.640897\pi$
$3$	−1.48377			−0.856655			−0.428328	+	0.903624i	$0.640897\pi$
$4$	−0.271907	−	0.470957i	−0.135954	−	0.235479i
$5$	−0.310056	+	0.537033i	−0.138661	+	0.240168i	−0.926990	−	0.375086i	$-0.877613\pi$
$5$	−0.310056	+	0.537033i	−0.138661	+	0.240168i	0.788329	+	0.615254i	$0.210947\pi$
$6$	1.18326	−	2.04946i	0.483063	−	0.836690i
$7$	−2.33703	+	1.24028i	−0.883315	+	0.468781i
$7$	−2.33703	+	1.24028i	−0.883315	+	0.468781i
$8$	−2.32252			−0.821135
$9$	−0.798426			−0.266142
$10$	−0.494519	−	0.856532i	−0.156381	−	0.270859i
$11$	2.47691	−	4.29013i	0.746817	−	1.29352i	−0.202525	−	0.979277i	$-0.564915\pi$
$11$	2.47691	−	4.29013i	0.746817	−	1.29352i	0.949341	−	0.314247i	$-0.101752\pi$
$12$	0.403448	+	0.698793i	0.116465	+	0.201724i
$13$	−2.32535	+	4.02762i	−0.644936	+	1.11706i	0.339381	+	0.940649i	$0.389783\pi$
$13$	−2.32535	+	4.02762i	−0.644936	+	1.11706i	−0.984316	+	0.176412i	$0.943551\pi$
$14$	0.150568	−	4.21711i	0.0402411	−	1.12707i
$15$	0.460052	−	0.796833i	0.118785	−	0.205741i
$16$	2.39595	−	4.14990i	0.598987	−	1.03748i
$17$	−5.70797			−1.38439			−0.692193	−	0.721713i	$-0.743355\pi$
$17$	−5.70797			−1.38439			−0.692193	+	0.721713i	$0.743355\pi$
$18$	0.636718	−	1.10283i	0.150076	−	0.259939i
$19$	0.609015	+	4.31614i	0.139718	+	0.990191i
$19$	0.609015	+	4.31614i	0.139718	+	0.990191i
$20$	0.337226			0.0754061
$21$	3.46762	−	1.84029i	0.756696	−	0.401583i
$22$	3.95051	+	6.84248i	0.842251	+	1.45882i
$23$	5.34418			1.11434			0.557169	−	0.830399i	$-0.311887\pi$
$23$	5.34418			1.11434			0.557169	+	0.830399i	$0.311887\pi$
$24$	3.44609			0.703429
$25$	2.30773	+	3.99711i	0.461546	+	0.799421i
$26$	−3.70878	−	6.42379i	−0.727351	−	1.25981i
$27$	5.63599			1.08465
$28$	1.21957	+	0.763402i	0.230478	+	0.144269i
$29$	−4.35913	+	7.55024i	−0.809471	+	1.40204i	0.103760	+	0.994602i	$0.466913\pi$
$29$	−4.35913	+	7.55024i	−0.809471	+	1.40204i	−0.913231	+	0.407443i	$0.866421\pi$
$30$	0.733752	+	1.27090i	0.133964	+	0.232033i
$31$	−1.94719	+	3.37263i	−0.349726	+	0.605743i	−0.986201	−	0.165555i	$-0.947059\pi$
$31$	−1.94719	+	3.37263i	−0.349726	+	0.605743i	0.636475	+	0.771298i	$0.280392\pi$
$32$	1.49886	+	2.59610i	0.264963	+	0.458930i
$33$	−3.67517	+	6.36557i	−0.639764	+	1.10810i
$34$	4.55192	−	7.88415i	0.780647	−	1.35212i
$35$	0.0585411	−	1.63962i	0.00989526	−	0.277146i
$36$	0.217098	+	0.376025i	0.0361830	+	0.0626708i
$37$	1.69296	+	2.93229i	0.278320	+	0.482065i	0.970967	−	0.239212i	$-0.0768890\pi$
$37$	1.69296	+	2.93229i	0.278320	+	0.482065i	−0.692647	+	0.721277i	$0.743556\pi$
$38$	−6.44736	−	2.60078i	−1.04590	−	0.421902i
$39$	3.45028	−	5.97607i	0.552488	−	0.956936i
$40$	0.720111	−	1.24727i	0.113860	−	0.197211i
$41$	−2.13757	−	3.70239i	−0.333833	−	0.578215i	0.649427	−	0.760424i	$-0.275009\pi$
$41$	−2.13757	−	3.70239i	−0.333833	−	0.578215i	−0.983260	+	0.182208i	$0.941675\pi$
$42$	−0.223409	+	6.25722i	−0.0344727	+	0.965511i
$43$	−0.790620	−	1.36939i	−0.120568	−	0.208831i	0.799424	−	0.600768i	$-0.205138\pi$
$43$	−0.790620	−	1.36939i	−0.120568	−	0.208831i	−0.919992	+	0.391937i	$0.871805\pi$
$44$	−2.69396			−0.406130
$45$	0.247557	−	0.428781i	0.0369036	−	0.0639189i
$46$	−4.26181	+	7.38167i	−0.628369	+	1.08837i
$47$	5.77039			0.841698			0.420849	−	0.907131i	$-0.361732\pi$
$47$	5.77039			0.841698			0.420849	+	0.907131i	$0.361732\pi$
$48$	−3.55504	+	6.15750i	−0.513125	+	0.888759i
$49$	3.92343	−	5.79713i	0.560489	−	0.828162i
$50$	−7.36136			−1.04105
$51$	8.46931			1.18594
$52$	2.52912			0.350726
$53$	−1.94482	−	3.36853i	−0.267142	−	0.462704i	0.700981	−	0.713180i	$-0.252746\pi$
$53$	−1.94482	−	3.36853i	−0.267142	−	0.462704i	−0.968123	+	0.250477i	$0.919413\pi$
$54$	−4.49452	+	7.78473i	−0.611626	+	1.05937i
$55$	1.53596	+	2.66036i	0.207109	+	0.358723i
$56$	5.42780	−	2.88057i	0.725320	−	0.384932i
$57$	−0.903639	−	6.40417i	−0.119690	−	0.848253i
$58$	−6.95253	−	12.0421i	−0.912912	−	1.58121i
$59$	−2.52167			−0.328294			−0.164147	−	0.986436i	$-0.552487\pi$
$59$	−2.52167			−0.328294			−0.164147	+	0.986436i	$0.552487\pi$
$60$	−0.500366			−0.0645970
$61$	−4.29946			−0.550490			−0.275245	−	0.961374i	$-0.588759\pi$
$61$	−4.29946			−0.550490			−0.275245	+	0.961374i	$0.588759\pi$
$62$	−3.10564	−	5.37913i	−0.394417	−	0.683150i
$63$	1.86595	−	0.990269i	0.235087	−	0.124762i
$64$	4.80263			0.600328
$65$	−1.44198	−	2.49758i	−0.178855	−	0.309786i
$66$	−5.86165	−	10.1527i	−0.721519	−	1.24971i
$67$	−5.86924	−	10.1658i	−0.717042	−	1.24195i	−0.962167	−	0.272461i	$-0.912162\pi$
$67$	−5.86924	−	10.1658i	−0.717042	−	1.24195i	0.245125	−	0.969491i	$-0.421171\pi$
$68$	1.55204	+	2.68821i	0.188212	+	0.325993i
$69$	−7.92953			−0.954604
$70$	2.21804	+	1.38840i	0.265107	+	0.165946i
$71$	2.34846	+	4.06765i	0.278711	+	0.482741i	0.971065	−	0.238817i	$-0.0767596\pi$
$71$	2.34846	+	4.06765i	0.278711	+	0.482741i	−0.692354	+	0.721558i	$0.743426\pi$
$72$	1.85436			0.218538
$73$	6.98698			0.817765			0.408882	−	0.912587i	$-0.365919\pi$
$73$	6.98698			0.817765			0.408882	+	0.912587i	$0.365919\pi$
$74$	−5.40031			−0.627773
$75$	−3.42414	−	5.93079i	−0.395386	−	0.684828i
$76$	1.86712	−	1.46041i	0.214174	−	0.167521i
$77$	−0.467661	+	13.0982i	−0.0532949	+	1.49268i
$78$	5.50297	+	9.53143i	0.623089	+	1.07922i
$79$	−5.32729	+	9.22714i	−0.599367	+	1.03813i	0.393547	+	0.919304i	$0.371248\pi$
$79$	−5.32729	+	9.22714i	−0.599367	+	1.03813i	−0.992915	+	0.118830i	$0.962086\pi$
$80$	1.48576	+	2.57340i	0.166113	+	0.287715i
$81$	−5.96724			−0.663026
$82$	6.81858			0.752986
$83$	−12.3296			−1.35335			−0.676676	−	0.736281i	$-0.736580\pi$
$83$	−12.3296			−1.35335			−0.676676	+	0.736281i	$0.736580\pi$
$84$	−1.80957	−	1.13271i	−0.197440	−	0.123589i
$85$	1.76979	−	3.06537i	0.191961	−	0.332486i
$86$	2.52197			0.271952
$87$	6.46795	−	11.2028i	0.693437	−	1.20107i
$88$	−5.75267	+	9.96392i	−0.613237	+	1.06216i
$89$	2.38744			0.253068			0.126534	−	0.991962i	$-0.459615\pi$
$89$	2.38744			0.253068			0.126534	+	0.991962i	$0.459615\pi$
$90$	0.394837	+	0.683877i	0.0416195	+	0.0720870i
$91$	0.439045	−	12.2968i	0.0460244	−	1.28905i
$92$	−1.45312	−	2.51688i	−0.151498	−	0.262403i
$93$	2.88918	−	5.00421i	0.299594	−	0.518913i
$94$	−4.60170	+	7.97037i	−0.474629	+	0.822081i
$95$	−2.50674	−	1.01119i	−0.257186	−	0.103745i
$96$	−2.22396	−	3.85202i	−0.226982	−	0.393145i
$97$	7.45741	+	12.9166i	0.757185	+	1.31148i	0.944281	+	0.329141i	$0.106759\pi$
$97$	7.45741	+	12.9166i	0.757185	+	1.31148i	−0.187096	+	0.982342i	$0.559908\pi$
$98$	4.87850	+	10.0423i	0.492803	+	1.01442i
$99$	−1.97763	+	3.42536i	−0.198759	+	0.344261i
$100$	1.25498	−	2.17369i	0.125498	−	0.217369i
$101$	0.613994	+	1.06347i	0.0610947	+	0.105819i	0.894955	−	0.446156i	$-0.147207\pi$
$101$	0.613994	+	1.06347i	0.0610947	+	0.105819i	−0.833860	+	0.551976i	$0.813874\pi$
$102$	−6.75400	+	11.6983i	−0.668746	+	1.15830i
$103$	−0.997055	−	1.72695i	−0.0982427	−	0.170161i	0.812715	−	0.582662i	$-0.197989\pi$
$103$	−0.997055	−	1.72695i	−0.0982427	−	0.170161i	−0.910957	+	0.412501i	$0.864655\pi$
$104$	5.40067	−	9.35423i	0.529579	−	0.917258i
$105$	−0.0868616	+	2.43282i	−0.00847682	+	0.237418i
$106$	6.20373			0.602559
$107$	0.205204	+	0.355424i	0.0198378	+	0.0343601i	0.875774	−	0.482722i	$-0.160352\pi$
$107$	0.205204	+	0.355424i	0.0198378	+	0.0343601i	−0.855936	+	0.517082i	$0.827018\pi$
$108$	−1.53247	−	2.65431i	−0.147462	−	0.255411i
$109$	7.53582			0.721800			0.360900	−	0.932604i	$-0.382470\pi$
$109$	7.53582			0.721800			0.360900	+	0.932604i	$0.382470\pi$
$110$	−4.89952			−0.467151
$111$	−2.51196	−	4.35084i	−0.238424	−	0.412963i
$112$	−0.452375	+	12.6701i	−0.0427454	+	1.19721i
$113$	−2.67416			−0.251564			−0.125782	−	0.992058i	$-0.540144\pi$
$113$	−2.67416			−0.251564			−0.125782	+	0.992058i	$0.540144\pi$
$114$	9.56640	+	3.85896i	0.895975	+	0.361424i
$115$	−1.65700	+	2.87000i	−0.154516	+	0.267629i
$116$	4.74112			0.440202
$117$	1.85662	−	3.21576i	0.171645	−	0.297297i
$118$	2.01095	−	3.48307i	0.185123	−	0.320642i
$119$	13.3397	−	7.07946i	1.22285	−	0.648973i
$120$	−1.06848	+	1.85066i	−0.0975384	+	0.168941i
$121$	−6.77017	−	11.7263i	−0.615470	−	1.06603i
$122$	3.42868	−	5.93865i	0.310418	−	0.537660i
$123$	3.17167	+	5.49349i	0.285980	+	0.495331i
$124$	2.11782			0.190186
$125$	−5.96266			−0.533317
$126$	−0.120218	+	3.36705i	−0.0107098	+	0.299961i
$127$	0.168896	−	0.292537i	0.0149871	−	0.0259584i	−0.858435	−	0.512923i	$-0.828563\pi$
$127$	0.168896	−	0.292537i	0.0149871	−	0.0259584i	0.873422	+	0.486965i	$0.161896\pi$
$128$	−6.82766	+	11.8258i	−0.603485	+	1.04527i
$129$	1.17310	+	2.03187i	0.103286	+	0.178896i
$130$	4.59972			0.403422
$131$	0.720679	−	1.24825i	0.0629660	−	0.109060i	−0.832824	−	0.553538i	$-0.813277\pi$
$131$	0.720679	−	1.24825i	0.0629660	−	0.109060i	0.895790	+	0.444478i	$0.146611\pi$
$132$	3.99722			0.347913
$133$	−6.77650	−	9.33161i	−0.587597	−	0.809154i
$134$	18.7221			1.61734
$135$	−1.74747	+	3.02671i	−0.150399	+	0.260498i
$136$	13.2569			1.13677
$137$	8.63754	+	14.9607i	0.737955	+	1.27818i	0.953415	+	0.301663i	$0.0975417\pi$
$137$	8.63754	+	14.9607i	0.737955	+	1.27818i	−0.215460	+	0.976513i	$0.569125\pi$
$138$	6.32354	−	10.9527i	0.538296	−	0.932356i
$139$	4.08381	−	7.07336i	0.346384	−	0.599954i	−0.639220	−	0.769024i	$-0.720743\pi$
$139$	4.08381	−	7.07336i	0.346384	−	0.599954i	0.985604	+	0.169069i	$0.0540761\pi$
$140$	−0.788108	+	0.418254i	−0.0666073	+	0.0353489i
$141$	−8.56193			−0.721045
$142$	−7.49128			−0.628654
$143$	11.5194	+	19.9521i	0.963297	+	1.66848i
$144$	−1.91299	+	3.31339i	−0.159416	+	0.276116i
$145$	−2.70315	−	4.68200i	−0.224485	−	0.388819i
$146$	−5.57189	+	9.65079i	−0.461133	+	0.798705i
$147$	−5.82146	+	8.60161i	−0.480146	+	0.709449i
$148$	0.920655	−	1.59462i	0.0756773	−	0.131077i
$149$	0.378556	−	0.655677i	0.0310125	−	0.0537152i	−0.850103	−	0.526617i	$-0.823460\pi$
$149$	0.378556	−	0.655677i	0.0310125	−	0.0537152i	0.881115	+	0.472902i	$0.156794\pi$
$150$	10.9226			0.891823
$151$	10.0696	−	17.4411i	0.819453	−	1.41933i	−0.0866334	−	0.996240i	$-0.527611\pi$
$151$	10.0696	−	17.4411i	0.819453	−	1.41933i	0.906086	−	0.423093i	$-0.139056\pi$
$152$	−1.41445	−	10.0243i	−0.114727	−	0.813080i
$153$	4.55739			0.368443
$154$	−17.7190	−	11.0914i	−1.42784	−	0.893768i
$155$	−1.20748	−	2.09141i	−0.0969869	−	0.167986i
$156$	−3.75263			−0.300451
$157$	−20.3815			−1.62662			−0.813312	−	0.581828i	$-0.802338\pi$
$157$	−20.3815			−1.62662			−0.813312	+	0.581828i	$0.802338\pi$
$158$	−8.49668	−	14.7167i	−0.675960	−	1.17080i
$159$	2.88567	+	4.99813i	0.228849	+	0.396377i
$160$	−1.85892			−0.146961
$161$	−12.4895	+	6.62826i	−0.984312	+	0.522380i
$162$	4.75868	−	8.24227i	0.373877	−	0.647574i
$163$	0.0627234	+	0.108640i	0.00491288	+	0.00850936i	0.868471	−	0.495739i	$-0.165103\pi$
$163$	0.0627234	+	0.108640i	0.00491288	+	0.00850936i	−0.863559	+	0.504249i	$0.831770\pi$
$164$	−1.16244	+	2.01341i	−0.0907716	+	0.157221i
$165$	−2.27901	−	3.94737i	−0.177421	−	0.307302i
$166$	9.83247	−	17.0303i	0.763148	−	1.32181i
$167$	3.56690	−	6.17806i	0.276015	−	0.478072i	−0.694376	−	0.719613i	$-0.744319\pi$
$167$	3.56690	−	6.17806i	0.276015	−	0.478072i	0.970391	+	0.241540i	$0.0776526\pi$
$168$	−8.05361	+	4.27410i	−0.621349	+	0.329754i
$169$	−4.31450	−	7.47293i	−0.331884	−	0.574840i
$170$	2.82270	+	4.88906i	0.216491	+	0.374974i
$171$	−0.486254	−	3.44612i	−0.0371847	−	0.263532i
$172$	−0.429951	+	0.744697i	−0.0327835	+	0.0567826i
$173$	8.58352	−	14.8671i	0.652593	−	1.13032i	−0.329898	−	0.944016i	$-0.607014\pi$
$173$	8.58352	−	14.8671i	0.652593	−	1.13032i	0.982491	−	0.186308i	$-0.0596522\pi$
$174$	10.3160	+	17.8678i	0.782051	+	1.35455i
$175$	−10.3508	−	6.47914i	−0.782444	−	0.489777i
$176$	−11.8691	−	20.5579i	−0.894667	−	1.54961i
$177$	3.74158			0.281234
$178$	−1.90390	+	3.29766i	−0.142704	+	0.247170i
$179$	−4.08221	+	7.07059i	−0.305118	+	0.528481i	−0.977288	−	0.211917i	$-0.932029\pi$
$179$	−4.08221	+	7.07059i	−0.305118	+	0.528481i	0.672169	+	0.740398i	$0.265363\pi$
$180$	−0.269250			−0.0200687
$181$	−7.22251	+	12.5098i	−0.536845	+	0.929842i	0.462227	+	0.886762i	$0.347051\pi$
$181$	−7.22251	+	12.5098i	−0.536845	+	0.929842i	−0.999072	+	0.0430807i	$0.986283\pi$
$182$	16.6348	+	10.4127i	1.23305	+	0.771840i
$183$	6.37942			0.471580
$184$	−12.4120			−0.915022
$185$	−2.09964			−0.154369
$186$	4.60806	+	7.98139i	0.337879	+	0.585224i
$187$	−14.1381	+	24.4880i	−1.03388	+	1.79074i
$188$	−1.56901	−	2.71761i	−0.114432	−	0.198202i
$189$	−13.1715	+	6.99019i	−0.958085	+	0.508461i
$190$	3.39575	−	2.65606i	0.246353	−	0.192691i
$191$	11.0006	+	19.0536i	0.795975	+	1.37867i	0.922218	+	0.386670i	$0.126375\pi$
$191$	11.0006	+	19.0536i	0.795975	+	1.37867i	−0.126243	+	0.991999i	$0.540292\pi$
$192$	−7.12600			−0.514274
$193$	3.48593			0.250923			0.125462	−	0.992098i	$-0.459959\pi$
$193$	3.48593			0.250923			0.125462	+	0.992098i	$0.459959\pi$
$194$	−23.7881			−1.70789
$195$	2.13956	+	3.70583i	0.153217	+	0.265380i
$196$	−3.79701	−	0.271484i	−0.271215	−	0.0193917i
$197$	−2.48557			−0.177090			−0.0885448	−	0.996072i	$-0.528222\pi$
$197$	−2.48557			−0.177090			−0.0885448	+	0.996072i	$0.528222\pi$
$198$	−3.15419	−	5.46322i	−0.224158	−	0.388254i
$199$	8.16937	+	14.1498i	0.579111	+	1.00305i	0.995582	+	0.0939005i	$0.0299335\pi$
$199$	8.16937	+	14.1498i	0.579111	+	1.00305i	−0.416471	+	0.909149i	$0.636733\pi$
$200$	−5.35975	−	9.28336i	−0.378991	−	0.656433i
$201$	8.70860	+	15.0837i	0.614257	+	1.06393i
$202$	−1.95856			−0.137804
$203$	0.823041	−	23.0517i	0.0577661	−	1.61791i
$204$	−2.30287	−	3.98869i	−0.161233	−	0.279264i
$205$	2.65107			0.185159
$206$	3.18047			0.221594
$207$	−4.26693			−0.296572
$208$	11.1428	+	19.2999i	0.772616	+	1.33821i
$209$	20.0253	+	8.07794i	1.38518	+	0.558763i
$210$	−3.29107	−	2.06007i	−0.227105	−	0.142158i
$211$	−2.02045	−	3.49953i	−0.139094	−	0.240917i	0.788060	−	0.615598i	$-0.211086\pi$
$211$	−2.02045	−	3.49953i	−0.139094	−	0.240917i	−0.927154	+	0.374681i	$0.877752\pi$
$212$	−1.05762	+	1.83186i	−0.0726379	+	0.125813i
$213$	−3.48457	−	6.03546i	−0.238759	−	0.413543i
$214$	−0.654574			−0.0447458
$215$	0.980546			0.0668727
$216$	−13.0897			−0.890641
$217$	0.367646	−	10.2970i	0.0249574	−	0.699006i
$218$	−6.00957	+	10.4089i	−0.407019	+	0.704978i
$219$	−10.3671			−0.700542
$220$	0.835279	−	1.44675i	0.0563145	−	0.0975396i
$221$	13.2730	−	22.9895i	0.892840	−	1.54644i
$222$	8.01281			0.537785
$223$	−2.07218	−	3.58912i	−0.138763	−	0.240345i	0.788265	−	0.615335i	$-0.210979\pi$
$223$	−2.07218	−	3.58912i	−0.138763	−	0.240345i	−0.927029	+	0.374990i	$0.877646\pi$
$224$	−6.72276	−	4.20817i	−0.449183	−	0.281170i
$225$	−1.84255	−	3.19139i	−0.122837	−	0.212760i
$226$	2.13256	−	3.69369i	0.141856	−	0.245701i
$227$	3.73290	−	6.46557i	0.247761	−	0.429135i	−0.715143	−	0.698978i	$-0.753639\pi$
$227$	3.73290	−	6.46557i	0.247761	−	0.429135i	0.962904	+	0.269843i	$0.0869719\pi$
$228$	−2.77038	+	2.16692i	−0.183473	+	0.143507i
$229$	6.08831	+	10.5453i	0.402327	+	0.696851i	0.994006	−	0.109323i	$-0.0348682\pi$
$229$	6.08831	+	10.5453i	0.402327	+	0.696851i	−0.591679	+	0.806173i	$0.701535\pi$
$230$	−2.64280	−	4.57746i	−0.174261	−	0.301829i
$231$	0.693902	−	19.4348i	0.0456554	−	1.27871i
$232$	10.1242	−	17.5356i	0.664685	−	1.15127i
$233$	−14.7587	+	25.5628i	−0.966873	+	1.67467i	−0.262375	+	0.964966i	$0.584506\pi$
$233$	−14.7587	+	25.5628i	−0.966873	+	1.67467i	−0.704497	+	0.709706i	$0.748828\pi$
$234$	2.96119	+	5.12892i	0.193579	+	0.335288i
$235$	−1.78914	+	3.09889i	−0.116711	+	0.202149i
$236$	0.685661	+	1.18760i	0.0446327	+	0.0773062i
$237$	7.90448	−	13.6910i	0.513451	−	0.889324i
$238$	−0.859440	+	24.0711i	−0.0557092	+	1.56030i
$239$	−15.4563			−0.999786			−0.499893	−	0.866087i	$-0.666627\pi$
$239$	−15.4563			−0.999786			−0.499893	+	0.866087i	$0.666627\pi$
$240$	−2.20452	−	3.81834i	−0.142301	−	0.246473i
$241$	4.28084	+	7.41464i	0.275753	+	0.477619i	0.970325	−	0.241805i	$-0.0777394\pi$
$241$	4.28084	+	7.41464i	0.275753	+	0.477619i	−0.694572	+	0.719424i	$0.744406\pi$
$242$	21.5960			1.38824
$243$	−8.05396			−0.516662
$244$	1.16906	+	2.02486i	0.0748412	+	0.129629i
$245$	1.89677	+	3.90444i	0.121180	+	0.249446i
$246$	−10.1172			−0.645049
$247$	−18.8000	−	7.58366i	−1.19621	−	0.482537i
$248$	4.52239	−	7.83301i	0.287172	−	0.497397i
$249$	18.2943			1.15936
$250$	4.75503	−	8.23595i	0.300734	−	0.520887i
$251$	−2.15448	+	3.73167i	−0.135990	+	0.235541i	−0.925975	−	0.377585i	$-0.876755\pi$
$251$	−2.15448	+	3.73167i	−0.135990	+	0.235541i	0.789985	+	0.613126i	$0.210088\pi$
$252$	−0.973739	−	0.609520i	−0.0613398	−	0.0383961i
$253$	13.2371	−	22.9273i	0.832207	−	1.44142i
$254$	0.269378	+	0.466577i	0.0169023	+	0.0292756i
$255$	−2.62596	+	4.54830i	−0.164444	+	0.284826i
$256$	−6.08703	−	10.5430i	−0.380440	−	0.658941i
$257$	2.37935			0.148420			0.0742099	−	0.997243i	$-0.476357\pi$
$257$	2.37935			0.148420			0.0742099	+	0.997243i	$0.476357\pi$
$258$	−3.74203			−0.232969
$259$	−7.59334	−	4.75311i	−0.471827	−	0.295344i
$260$	−0.784168	+	1.35822i	−0.0486321	+	0.0842332i
$261$	3.48045	−	6.02831i	0.215434	−	0.373143i
$262$	1.14943	+	1.99088i	0.0710123	+	0.122997i
$263$	19.0149			1.17251			0.586255	−	0.810127i	$-0.300602\pi$
$263$	19.0149			1.17251			0.586255	+	0.810127i	$0.300602\pi$
$264$	8.53564	−	14.7842i	0.525333	−	0.909903i
$265$	2.41202			0.148169
$266$	18.2934	−	1.91841i	1.12164	−	0.117625i
$267$	−3.54241			−0.216792
$268$	−3.19178	+	5.52832i	−0.194969	+	0.337696i
$269$	−11.7206			−0.714619			−0.357310	−	0.933986i	$-0.616306\pi$
$269$	−11.7206			−0.714619			−0.357310	+	0.933986i	$0.616306\pi$
$270$	−2.78710	−	4.82741i	−0.169618	−	0.293787i
$271$	3.22656	−	5.58856i	0.195999	−	0.339481i	−0.751228	−	0.660042i	$-0.770538\pi$
$271$	3.22656	−	5.58856i	0.195999	−	0.339481i	0.947228	+	0.320562i	$0.103872\pi$
$272$	−13.6760	+	23.6875i	−0.829229	+	1.43627i
$273$	−0.651442	+	18.2456i	−0.0394271	+	1.10427i
$274$	−27.5526			−1.66451
$275$	22.8642			1.37876
$276$	2.15610	+	3.73447i	0.129782	+	0.224789i
$277$	−10.8480	+	18.7892i	−0.651791	+	1.12894i	0.330897	+	0.943667i	$0.392649\pi$
$277$	−10.8480	+	18.7892i	−0.651791	+	1.12894i	−0.982688	+	0.185268i	$0.940685\pi$
$278$	6.51340	+	11.2815i	0.390648	+	0.676622i
$279$	1.55469	−	2.69280i	0.0930768	−	0.161214i
$280$	−0.135963	+	3.80804i	−0.00812534	+	0.227574i
$281$	−3.03520	+	5.25711i	−0.181065	+	0.313613i	−0.942243	−	0.334929i	$-0.891288\pi$
$281$	−3.03520	+	5.25711i	−0.181065	+	0.313613i	0.761179	+	0.648542i	$0.224621\pi$
$282$	6.82786	−	11.8262i	0.406593	−	0.704240i
$283$	11.0059			0.654230			0.327115	−	0.944984i	$-0.393923\pi$
$283$	11.0059			0.654230			0.327115	+	0.944984i	$0.393923\pi$
$284$	1.27713	−	2.21205i	0.0757835	−	0.131261i
$285$	3.71943	+	1.50037i	0.220320	+	0.0888740i
$286$	−36.7452			−2.17279
$287$	9.58756	+	6.00141i	0.565936	+	0.354252i
$288$	−1.19673	−	2.07279i	−0.0705179	−	0.122141i
$289$	15.5809			0.916524
$290$	8.62270			0.506342
$291$	−11.0651	−	19.1653i	−0.648646	−	1.12349i
$292$	−1.89981	−	3.29057i	−0.111178	−	0.192566i
$293$	24.6780			1.44171			0.720853	−	0.693088i	$-0.243750\pi$
$293$	24.6780			1.44171			0.720853	+	0.693088i	$0.243750\pi$
$294$	−7.23858	−	14.9004i	−0.422162	−	0.869010i
$295$	0.781859	−	1.35422i	0.0455216	−	0.0788457i
$296$	−3.93192	−	6.81029i	−0.228538	−	0.395840i
$297$	13.9598	−	24.1792i	0.810032	−	1.40302i
$298$	0.603771	+	1.04576i	0.0349755	+	0.0605794i
$299$	−12.4271	+	21.5243i	−0.718677	+	1.24478i
$300$	−1.86210	+	3.22525i	−0.107508	+	0.186210i
$301$	3.54613	+	2.21973i	0.204396	+	0.127943i
$302$	16.0604	+	27.8173i	0.924169	+	1.60071i
$303$	−0.911027	−	1.57794i	−0.0523371	−	0.0906505i
$304$	19.3707	+	7.81390i	1.11099	+	0.448158i
$305$	1.33307	−	2.30895i	0.0763317	−	0.132210i
$306$	−3.63437	+	6.29491i	−0.207763	+	0.359856i
$307$	5.12650	+	8.87936i	0.292585	+	0.506772i	0.974420	−	0.224734i	$-0.0721513\pi$
$307$	5.12650	+	8.87936i	0.292585	+	0.506772i	−0.681835	+	0.731506i	$0.738818\pi$
$308$	6.29587	−	3.34126i	0.358741	−	0.190386i
$309$	1.47940	+	2.56240i	0.0841601	+	0.145770i
$310$	3.85169			0.218761
$311$	−2.88364	+	4.99461i	−0.163516	+	0.283218i	−0.936127	−	0.351661i	$-0.885617\pi$
$311$	−2.88364	+	4.99461i	−0.163516	+	0.283218i	0.772611	+	0.634879i	$0.218950\pi$
$312$	−8.01335	+	13.8795i	−0.453667	+	0.785774i
$313$	5.99465			0.338838			0.169419	−	0.985544i	$-0.445811\pi$
$313$	5.99465			0.338838			0.169419	+	0.985544i	$0.445811\pi$
$314$	16.2536	−	28.1521i	0.917244	−	1.58871i
$315$	−0.0467408	+	1.30911i	−0.00263354	+	0.0737602i
$316$	5.79412			0.325945
$317$	−22.6797			−1.27382			−0.636910	−	0.770938i	$-0.719788\pi$
$317$	−22.6797			−1.27382			−0.636910	+	0.770938i	$0.719788\pi$
$318$	−9.20491			−0.516186
$319$	21.5944	+	37.4026i	1.20905	+	2.09414i
$320$	−1.48908	+	2.57917i	−0.0832423	+	0.144180i
$321$	−0.304476	−	0.527367i	−0.0169942	−	0.0294348i
$322$	0.804664	−	22.5370i	0.0448422	−	1.25594i
$323$	−3.47624	−	24.6364i	−0.193423	−	1.37081i
$324$	1.62254	+	2.81031i	0.0901409	+	0.156129i
$325$	−21.4651			−1.19067
$326$	−0.200079			−0.0110814
$327$	−11.1814			−0.618334
$328$	4.96455	+	8.59886i	0.274122	+	0.474793i
$329$	−13.4856	+	7.15688i	−0.743484	+	0.394572i
$330$	7.26976			0.400187
$331$	0.243673	+	0.422055i	0.0133935	+	0.0231982i	0.872644	−	0.488356i	$-0.162403\pi$
$331$	0.243673	+	0.422055i	0.0133935	+	0.0231982i	−0.859251	+	0.511554i	$0.829070\pi$
$332$	3.35252	+	5.80673i	0.183993	+	0.318686i
$333$	−1.35170	−	2.34121i	−0.0740727	−	0.128298i
$334$	5.68898	+	9.85359i	0.311287	+	0.539165i
$335$	7.27917			0.397704
$336$	0.671220	−	18.7995i	0.0366181	−	1.02560i
$337$	1.04786	+	1.81494i	0.0570804	+	0.0988661i	0.893154	−	0.449752i	$-0.148488\pi$
$337$	1.04786	+	1.81494i	0.0570804	+	0.0988661i	−0.836073	+	0.548618i	$0.815154\pi$
$338$	13.7627			0.748591
$339$	3.96784			0.215504
$340$	−1.92488			−0.104391
$341$	9.64604	+	16.7074i	0.522362	+	0.904758i
$342$	5.14774	+	2.07653i	0.278358	+	0.112286i
$343$	−1.97912	+	18.4142i	−0.106863	+	0.994274i
$344$	1.83623	+	3.18045i	0.0990030	+	0.171478i
$345$	2.45860	−	4.25842i	0.132367	−	0.229266i
$346$	13.6902	+	23.7120i	0.735987	+	1.27477i
$347$	−22.7975			−1.22384			−0.611918	−	0.790921i	$-0.709602\pi$
$347$	−22.7975			−1.22384			−0.611918	+	0.790921i	$0.709602\pi$
$348$	−7.03474			−0.377102
$349$	24.8271			1.32896			0.664481	−	0.747305i	$-0.268653\pi$
$349$	24.8271			1.32896			0.664481	+	0.747305i	$0.268653\pi$
$350$	17.2037	−	9.13012i	0.919577	−	0.488025i
$351$	−13.1056	+	22.6996i	−0.699528	+	1.21162i
$352$	14.8502			0.791516
$353$	1.80239	−	3.12184i	0.0959317	−	0.166159i	−0.814065	−	0.580773i	$-0.802750\pi$
$353$	1.80239	−	3.12184i	0.0959317	−	0.166159i	0.909997	+	0.414615i	$0.136084\pi$
$354$	−2.98379	+	5.16807i	−0.158587	+	0.274680i
$355$	−2.91262			−0.154586
$356$	−0.649162	−	1.12438i	−0.0344055	−	0.0595921i
$357$	−19.7930	+	10.5043i	−1.04756	+	0.555946i
$358$	−6.51085	−	11.2771i	−0.344109	−	0.596015i
$359$	−5.50384	+	9.53293i	−0.290482	+	0.503129i	−0.973924	−	0.226876i	$-0.927149\pi$
$359$	−5.50384	+	9.53293i	−0.290482	+	0.503129i	0.683442	+	0.730005i	$0.260482\pi$
$360$	−0.574955	+	0.995852i	−0.0303028	+	0.0524860i
$361$	−18.2582	+	5.25720i	−0.960958	+	0.276695i
$362$	−11.5194	−	19.9522i	−0.605447	−	1.04867i
$363$	10.0454	+	17.3991i	0.527246	+	0.913216i
$364$	−5.91063	+	3.13681i	−0.309801	+	0.164413i
$365$	−2.16636	+	3.75224i	−0.113392	+	0.196401i
$366$	−5.08738	+	8.81159i	−0.265921	+	0.460589i
$367$	−0.140329	−	0.243057i	−0.00732510	−	0.0126874i	0.862340	−	0.506330i	$-0.168998\pi$
$367$	−0.140329	−	0.243057i	−0.00732510	−	0.0126874i	−0.869665	+	0.493643i	$0.835665\pi$
$368$	12.8044	−	22.1778i	0.667474	−	1.15610i
$369$	1.70669	+	2.95608i	0.0888469	+	0.153887i
$370$	1.67440	−	2.90014i	0.0870478	−	0.150771i
$371$	8.72302	+	5.46024i	0.452877	+	0.283482i
$372$	−3.14236			−0.162924
$373$	−4.63478	−	8.02767i	−0.239980	−	0.415657i	0.720728	−	0.693218i	$-0.243807\pi$
$373$	−4.63478	−	8.02767i	−0.239980	−	0.415657i	−0.960708	+	0.277560i	$0.910474\pi$
$374$	−22.5494	−	39.0567i	−1.16600	−	2.01957i
$375$	8.84722			0.456869
$376$	−13.4018			−0.691147
$377$	−20.2730	−	35.1139i	−1.04411	−	1.80846i
$378$	0.848602	−	23.7676i	0.0436474	−	1.22247i
$379$	−13.6131			−0.699256			−0.349628	−	0.936889i	$-0.613692\pi$
$379$	−13.6131			−0.699256			−0.349628	+	0.936889i	$0.613692\pi$
$380$	0.205376	+	1.45552i	0.0105356	+	0.0746664i
$381$	−0.250603	+	0.434057i	−0.0128388	+	0.0222374i
$382$	−35.0904			−1.79538
$383$	14.4423	−	25.0149i	0.737969	−	1.27820i	−0.215440	−	0.976517i	$-0.569119\pi$
$383$	14.4423	−	25.0149i	0.737969	−	1.27820i	0.953409	−	0.301682i	$-0.0975482\pi$
$384$	10.1307	−	17.5468i	0.516979	−	0.895433i
$385$	−6.88918	−	4.31234i	−0.351105	−	0.219777i
$386$	−2.77992	+	4.81496i	−0.141494	+	0.245075i
$387$	0.631252	+	1.09336i	0.0320883	+	0.0555786i
$388$	4.05545	−	7.02424i	0.205884	−	0.356602i
$389$	4.22218	+	7.31302i	0.214073	+	0.370785i	0.952985	−	0.303016i	$-0.0979937\pi$
$389$	4.22218	+	7.31302i	0.214073	+	0.370785i	−0.738913	+	0.673801i	$0.764660\pi$
$390$	−6.82492			−0.345593
$391$	−30.5044			−1.54267
$392$	−9.11223	+	13.4639i	−0.460237	+	0.680032i
$393$	−1.06932	+	1.85212i	−0.0539401	+	0.0934270i
$394$	1.98216	−	3.43321i	0.0998599	−	0.172962i
$395$	−3.30352	−	5.72186i	−0.166218	−	0.287898i
$396$	2.15093			0.108088
$397$	6.52211	−	11.2966i	0.327335	−	0.566961i	−0.654647	−	0.755935i	$-0.727183\pi$
$397$	6.52211	−	11.2966i	0.327335	−	0.566961i	0.981982	+	0.188974i	$0.0605160\pi$
$398$	−26.0592			−1.30623
$399$	10.0548	+	13.8460i	0.503368	+	0.693166i
$400$	22.1168			1.10584
$401$	1.75805	−	3.04504i	0.0877929	−	0.152062i	−0.818785	−	0.574100i	$-0.805352\pi$
$401$	1.75805	−	3.04504i	0.0877929	−	0.152062i	0.906578	+	0.422038i	$0.138685\pi$
$402$	−27.7793			−1.38551
$403$	−9.05580	−	15.6851i	−0.451101	−	0.781331i
$404$	0.333899	−	0.578330i	0.0166121	−	0.0287730i
$405$	1.85018	−	3.20460i	0.0919361	−	0.159238i
$406$	31.1839	+	19.5198i	1.54763	+	0.968751i
$407$	16.7732			0.831417
$408$	−19.6701			−0.973817
$409$	−10.4818	−	18.1549i	−0.518290	−	0.897704i	−0.999774	−	0.0212493i	$-0.993236\pi$
$409$	−10.4818	−	18.1549i	−0.518290	−	0.897704i	0.481485	−	0.876455i	$-0.340098\pi$
$410$	−2.11414	+	3.66180i	−0.104410	+	0.180843i
$411$	−12.8161	−	22.1982i	−0.632173	−	1.09496i
$412$	−0.542213	+	0.939141i	−0.0267129	+	0.0462681i
$413$	5.89322	−	3.12757i	0.289987	−	0.153898i
$414$	3.40274	−	5.89372i	0.167235	−	0.289660i
$415$	3.82288	−	6.62141i	0.187658	−	0.325032i
$416$	−13.9415			−0.683537
$417$	−6.05943	+	10.4952i	−0.296731	+	0.513954i
$418$	−27.1272	+	21.2181i	−1.32684	+	1.03781i
$419$	−38.0730			−1.85999			−0.929993	−	0.367577i	$-0.880187\pi$
$419$	−38.0730			−1.85999			−0.929993	+	0.367577i	$0.880187\pi$
$420$	1.16937	−	0.620592i	0.0570595	−	0.0302818i
$421$	17.0430	+	29.5193i	0.830623	+	1.43868i	0.897545	+	0.440923i	$0.145349\pi$
$421$	17.0430	+	29.5193i	0.830623	+	1.43868i	−0.0669217	+	0.997758i	$0.521318\pi$
$422$	6.44498			0.313737
$423$	−4.60723			−0.224011
$424$	4.51689	+	7.82348i	0.219360	+	0.379942i
$425$	−13.1725	−	22.8154i	−0.638958	−	1.10671i
$426$	11.1153			0.538540
$427$	10.0480	−	5.33253i	0.486256	−	0.258059i
$428$	0.111593	−	0.193285i	0.00539405	−	0.00934277i
$429$	−17.0921	−	29.6044i	−0.825214	−	1.42931i
$430$	−0.781954	+	1.35438i	−0.0377091	+	0.0653142i
$431$	11.6753	+	20.2221i	0.562377	+	0.974066i	0.997288	+	0.0735928i	$0.0234465\pi$
$431$	11.6753	+	20.2221i	0.562377	+	0.974066i	−0.434911	+	0.900473i	$0.643220\pi$
$432$	13.5035	−	23.3888i	0.649689	−	1.12529i
$433$	17.0834	−	29.5894i	0.820977	−	1.42197i	−0.0839780	−	0.996468i	$-0.526763\pi$
$433$	17.0834	−	29.5894i	0.820977	−	1.42197i	0.904955	−	0.425507i	$-0.139904\pi$
$434$	13.9296	+	8.71934i	0.668642	+	0.418542i
$435$	4.01086	+	6.94701i	0.192306	+	0.333083i
$436$	−2.04904	−	3.54905i	−0.0981314	−	0.169969i
$437$	3.25469	+	23.0663i	0.155693	+	1.10341i
$438$	8.26740	−	14.3196i	0.395032	−	0.684215i
$439$	17.9956	−	31.1693i	0.858882	−	1.48763i	−0.0141134	−	0.999900i	$-0.504493\pi$
$439$	17.9956	−	31.1693i	0.858882	−	1.48763i	0.872996	−	0.487728i	$-0.162174\pi$
$440$	−3.56730	−	6.17875i	−0.170064	−	0.294560i
$441$	−3.13257	+	4.62858i	−0.149170	+	0.220409i
$442$	21.1696	+	36.6668i	1.00693	+	1.74406i
$443$	0.470106			0.0223354			0.0111677	−	0.999938i	$-0.496445\pi$
$443$	0.470106			0.0223354			0.0111677	+	0.999938i	$0.496445\pi$
$444$	−1.36604	+	2.36605i	−0.0648294	+	0.112288i
$445$	−0.740240	+	1.28213i	−0.0350907	+	0.0607789i
$446$	6.60998			0.312991
$447$	−0.561689	+	0.972875i	−0.0265670	+	0.0460154i
$448$	−11.2239	+	5.95659i	−0.530279	+	0.281422i
$449$	12.3072			0.580812			0.290406	−	0.956904i	$-0.406210\pi$
$449$	12.3072			0.580812			0.290406	+	0.956904i	$0.406210\pi$
$450$	5.87750			0.277068
$451$	−21.1783			−0.997248
$452$	0.727124	+	1.25942i	0.0342011	+	0.0592380i
$453$	−14.9410	+	25.8785i	−0.701988	+	1.21588i
$454$	5.95372	+	10.3122i	0.279422	+	0.483973i
$455$	6.46763	+	4.04846i	0.303207	+	0.189795i
$456$	2.09872	+	14.8738i	0.0982815	+	0.696529i
$457$	−11.3576	−	19.6719i	−0.531286	−	0.920215i	−0.999333	−	0.0365110i	$-0.988376\pi$
$457$	−11.3576	−	19.6719i	−0.531286	−	0.920215i	0.468047	−	0.883704i	$-0.344958\pi$
$458$	−19.4209			−0.907479
$459$	−32.1701			−1.50157
$460$	1.80220			0.0840279
$461$	12.7499	+	22.0834i	0.593820	+	1.02853i	0.993712	+	0.111965i	$0.0357143\pi$
$461$	12.7499	+	22.0834i	0.593820	+	1.02853i	−0.399892	+	0.916562i	$0.630952\pi$
$462$	26.2910	+	16.4570i	1.22317	+	0.765651i
$463$	33.1237			1.53939			0.769694	−	0.638413i	$-0.220409\pi$
$463$	33.1237			1.53939			0.769694	+	0.638413i	$0.220409\pi$
$464$	20.8885	+	36.1800i	0.969725	+	1.67961i
$465$	1.79162	+	3.10317i	0.0830843	+	0.143906i
$466$	−23.5391	−	40.7709i	−1.09043	−	1.88868i
$467$	10.4826	+	18.1563i	0.485075	+	0.840175i	0.999853	−	0.0171487i	$-0.00545886\pi$
$467$	10.4826	+	18.1563i	0.485075	+	0.840175i	−0.514778	+	0.857324i	$0.672126\pi$
$468$	−2.01931			−0.0933428
$469$	26.3250	+	16.4784i	1.21558	+	0.760900i
$470$	−2.85357	−	4.94252i	−0.131625	−	0.227982i
$471$	30.2415			1.39346
$472$	5.85663			0.269573
$473$	−7.83318			−0.360170
$474$	12.6071	+	21.8362i	0.579064	+	1.00297i
$475$	−15.8466	+	12.3948i	−0.727094	+	0.568712i
$476$	−6.96129	−	4.35747i	−0.319070	−	0.199724i
$477$	1.55280	+	2.68952i	0.0710977	+	0.123145i
$478$	12.3259	−	21.3491i	0.563774	−	0.976485i
$479$	−6.90895	−	11.9666i	−0.315678	−	0.546770i	0.663904	−	0.747818i	$-0.268899\pi$
$479$	−6.90895	−	11.9666i	−0.315678	−	0.546770i	−0.979581	+	0.201048i	$0.935565\pi$
$480$	2.75821			0.125895
$481$	−15.7469			−0.717995
$482$	−13.6553			−0.621983
$483$	18.5316	−	9.83482i	0.843216	−	0.447500i
$484$	−3.68172	+	6.37692i	−0.167351	+	0.289860i
$485$	−9.24886			−0.419969
$486$	6.42277	−	11.1246i	0.291343	−	0.504621i
$487$	−3.21087	+	5.56139i	−0.145498	+	0.252011i	−0.929559	−	0.368674i	$-0.879812\pi$
$487$	−3.21087	+	5.56139i	−0.145498	+	0.252011i	0.784060	+	0.620685i	$0.213145\pi$
$488$	9.98559			0.452026
$489$	−0.0930672	−	0.161197i	−0.00420864	−	0.00728958i
$490$	−6.90564	−	0.493749i	−0.311965	−	0.0223053i
$491$	−5.01834	−	8.69203i	−0.226475	−	0.392266i	0.730286	−	0.683141i	$-0.239387\pi$
$491$	−5.01834	−	8.69203i	−0.226475	−	0.392266i	−0.956761	+	0.290876i	$0.906053\pi$
$492$	1.72480	−	2.98744i	0.0777600	−	0.134684i
$493$	24.8818	−	43.0966i	1.12062	−	1.94097i
$494$	25.4673	−	19.9198i	1.14583	−	0.896235i
$495$	−1.22635	−	2.12410i	−0.0551204	−	0.0954714i
$496$	9.33074	+	16.1613i	0.418962	+	0.725664i
$497$	−10.5334	−	6.59349i	−0.472489	−	0.295758i
$498$	−14.5891	+	25.2691i	−0.653755	+	1.13234i
$499$	9.66784	−	16.7452i	0.432792	−	0.749618i	−0.564321	−	0.825556i	$-0.690862\pi$
$499$	9.66784	−	16.7452i	0.432792	−	0.749618i	0.997113	+	0.0759381i	$0.0241951\pi$
$500$	1.62129	+	2.80816i	0.0725064	+	0.125585i
$501$	−5.29246	+	9.16682i	−0.236450	+	0.409543i
$502$	−3.43626	−	5.95177i	−0.153368	−	0.265641i
$503$	−10.2265	+	17.7127i	−0.455975	+	0.789772i	−0.998744	−	0.0501105i	$-0.984043\pi$
$503$	−10.2265	+	17.7127i	−0.455975	+	0.789772i	0.542769	+	0.839882i	$0.317376\pi$
$504$	−4.33370	+	2.29992i	−0.193038	+	0.102447i
$505$	−0.761491			−0.0338859
$506$	21.1122	+	36.5675i	0.938553	+	1.62562i
$507$	6.40172	+	11.0881i	0.284310	+	0.492440i
$508$	−0.183696			−0.00815021
$509$	−19.5073			−0.864646			−0.432323	−	0.901719i	$-0.642306\pi$
$509$	−19.5073			−0.864646			−0.432323	+	0.901719i	$0.642306\pi$
$510$	−4.18824	−	7.25424i	−0.185458	−	0.321223i
$511$	−16.3288	+	8.66579i	−0.722343	+	0.383352i
$512$	−7.89379			−0.348859
$513$	3.43240	+	24.3258i	0.151544	+	1.07401i
$514$	−1.89745	+	3.28649i	−0.0836931	+	0.144961i
$515$	1.23657			0.0544898
$516$	0.637949	−	1.10496i	0.0280841	−	0.0486431i
$517$	14.2927	−	24.7557i	0.628594	−	1.08876i
$518$	12.6207	−	6.69788i	0.554521	−	0.294288i
$519$	−12.7360	+	22.0594i	−0.559047	+	0.968298i
$520$	3.34902	+	5.80067i	0.146864	+	0.254376i
$521$	−8.96299	+	15.5243i	−0.392676	+	0.680134i	−0.992801	−	0.119772i	$-0.961784\pi$
$521$	−8.96299	+	15.5243i	−0.392676	+	0.680134i	0.600126	+	0.799906i	$0.295117\pi$
$522$	5.55108	+	9.61476i	0.242964	+	0.420827i
$523$	17.1072			0.748044			0.374022	−	0.927420i	$-0.377979\pi$
$523$	17.1072			0.748044			0.374022	+	0.927420i	$0.377979\pi$
$524$	−0.783831			−0.0342418
$525$	15.3581	+	9.61355i	0.670284	+	0.419570i
$526$	−15.1638	+	26.2644i	−0.661171	+	1.14518i
$527$	11.1145	−	19.2509i	0.484156	−	0.838582i
$528$	17.6110	+	30.5032i	0.766421	+	1.32748i
$529$	5.56026			0.241750
$530$	−1.92350	+	3.33161i	−0.0835517	+	0.144716i
$531$	2.01337			0.0873727
$532$	−2.55221	+	5.72878i	−0.110652	+	0.248374i
$533$	19.8824			0.861203
$534$	2.82496	−	4.89297i	0.122248	−	0.211739i
$535$	−0.254499			−0.0110030
$536$	13.6314	+	23.6103i	0.588788	+	1.01981i
$537$	6.05706	−	10.4911i	0.261381	−	0.452726i
$538$	9.34682	−	16.1892i	0.402970	−	0.697964i
$539$	−15.1525	−	31.1910i	−0.652664	−	1.34349i
$540$	1.90060			0.0817890
$541$	11.4653			0.492932			0.246466	−	0.969151i	$-0.420731\pi$
$541$	11.4653			0.492932			0.246466	+	0.969151i	$0.420731\pi$
$542$	5.14614	+	8.91338i	0.221046	+	0.382863i
$543$	10.7165	−	18.5616i	0.459891	−	0.796554i
$544$	−8.55544	−	14.8185i	−0.366811	−	0.635336i
$545$	−2.33653	+	4.04698i	−0.100086	+	0.173354i
$546$	−24.6822	−	15.4500i	−1.05630	−	0.661201i
$547$	−18.0790	+	31.3138i	−0.773004	+	1.33888i	0.162905	+	0.986642i	$0.447913\pi$
$547$	−18.0790	+	31.3138i	−0.773004	+	1.33888i	−0.935909	+	0.352241i	$0.885420\pi$
$548$	4.69722	−	8.13583i	0.200655	−	0.347545i
$549$	3.43280			0.146509
$550$	−18.2334	+	31.5812i	−0.777476	+	1.34663i
$551$	−35.2427	−	14.2164i	−1.50139	−	0.605641i
$552$	18.4165			0.783858
$553$	1.00584	−	28.1714i	0.0427725	−	1.19797i
$554$	−17.3018	−	29.9676i	−0.735083	−	1.27320i
$555$	3.11539			0.132241
$556$	−4.44167			−0.188369
$557$	3.63891	+	6.30277i	0.154185	+	0.267057i	0.932762	−	0.360492i	$-0.117391\pi$
$557$	3.63891	+	6.30277i	0.154185	+	0.267057i	−0.778577	+	0.627550i	$0.784058\pi$
$558$	2.47963	+	4.29484i	0.104971	+	0.181815i
$559$	7.35387			0.311036
$560$	−6.66399	−	4.17138i	−0.281605	−	0.176273i
$561$	20.9777	−	36.3345i	0.885681	−	1.53404i
$562$	−4.84094	−	8.38475i	−0.204203	−	0.353689i
$563$	−12.1894	+	21.1127i	−0.513723	+	0.889794i	0.486151	+	0.873875i	$0.338401\pi$
$563$	−12.1894	+	21.1127i	−0.513723	+	0.889794i	−0.999873	+	0.0159188i	$0.994933\pi$
$564$	2.32805	+	4.03231i	0.0980287	+	0.169791i
$565$	0.829140	−	1.43611i	0.0348822	−	0.0604177i
$566$	−8.77681	+	15.2019i	−0.368917	+	0.638983i
$567$	13.9456	−	7.40103i	0.585661	−	0.310814i
$568$	−5.45434	−	9.44720i	−0.228859	−	0.396396i
$569$	−8.64675	−	14.9766i	−0.362491	−	0.627852i	0.625879	−	0.779920i	$-0.284740\pi$
$569$	−8.64675	−	14.9766i	−0.362491	−	0.627852i	−0.988370	+	0.152068i	$0.951407\pi$
$570$	−5.03851	+	3.94098i	−0.211040	+	0.165069i
$571$	9.88598	−	17.1230i	0.413716	−	0.716576i	−0.581577	−	0.813491i	$-0.697564\pi$
$571$	9.88598	−	17.1230i	0.413716	−	0.716576i	0.995293	+	0.0969149i	$0.0308975\pi$
$572$	6.26440	−	10.8503i	0.261928	−	0.453672i
$573$	−16.3223	−	28.2711i	−0.681876	−	1.18104i
$574$	−15.9352	+	8.45692i	−0.665123	+	0.352985i
$575$	12.3329	+	21.3613i	0.514319	+	0.890826i
$576$	−3.83454			−0.159773
$577$	15.3068	−	26.5121i	0.637230	−	1.10371i	−0.348808	−	0.937194i	$-0.613414\pi$
$577$	15.3068	−	26.5121i	0.637230	−	1.10371i	0.986038	−	0.166520i	$-0.0532531\pi$
$578$	−12.4253	+	21.5212i	−0.516823	+	0.895163i
$579$	−5.17233			−0.214955
$580$	−1.47001	+	2.54614i	−0.0610390	+	0.105723i
$581$	28.8147	−	15.2922i	1.19544	−	0.634425i
$582$	35.2961			1.46307
$583$	−19.2686			−0.798024
$584$	−16.2274			−0.671495
$585$	1.15131	+	1.99413i	0.0476009	+	0.0824472i
$586$	−19.6799	+	34.0866i	−0.812970	+	1.40810i
$587$	−21.6781	−	37.5475i	−0.894749	−	1.54975i	−0.834115	−	0.551591i	$-0.814021\pi$
$587$	−21.6781	−	37.5475i	−0.894749	−	1.54975i	−0.0606347	−	0.998160i	$-0.519312\pi$
$588$	5.63389	+	0.402820i	0.232338	+	0.0166120i
$589$	−15.7426	−	6.35037i	−0.648664	−	0.261663i
$590$	1.24701	+	2.15989i	0.0513388	+	0.0889213i
$591$	3.68802			0.151705
$592$	16.2249			0.666841
$593$	37.0835			1.52284			0.761418	−	0.648261i	$-0.224503\pi$
$593$	37.0835			1.52284			0.761418	+	0.648261i	$0.224503\pi$
$594$	22.2650	+	38.5642i	0.913545	+	1.58231i
$595$	−0.334151	+	9.35889i	−0.0136989	+	0.383677i
$596$	−0.411728			−0.0168650
$597$	−12.1215	−	20.9950i	−0.496098	−	0.859268i
$598$	−19.8204	−	34.3299i	−0.810516	−	1.40385i
$599$	−11.2841	−	19.5447i	−0.461058	−	0.798575i	0.537956	−	0.842973i	$-0.319196\pi$
$599$	−11.2841	−	19.5447i	−0.461058	−	0.798575i	−0.999014	+	0.0443976i	$0.985863\pi$
$600$	7.95264	+	13.7744i	0.324665	+	0.562336i
$601$	22.7154			0.926581			0.463290	−	0.886206i	$-0.346669\pi$
$601$	22.7154			0.926581			0.463290	+	0.886206i	$0.346669\pi$
$602$	−5.89393	+	3.12795i	−0.240219	+	0.127486i
$603$	4.68615	+	8.11666i	0.190835	+	0.330536i
$604$	−10.9520			−0.445630
$605$	8.39653			0.341367
$606$	2.90605			0.118050
$607$	−6.11589	−	10.5930i	−0.248236	−	0.429958i	0.714800	−	0.699329i	$-0.246518\pi$
$607$	−6.11589	−	10.5930i	−0.248236	−	0.429958i	−0.963037	+	0.269371i	$0.913184\pi$
$608$	−10.2923	+	8.05036i	−0.417408	+	0.326485i
$609$	−1.22120	+	34.2034i	−0.0494857	+	1.38599i
$610$	2.12617	+	3.68263i	0.0860860	+	0.149105i
$611$	−13.4182	+	23.2410i	−0.542841	+	0.940228i
$612$	−1.23919	−	2.14634i	−0.0500912	−	0.0867605i
$613$	17.6334			0.712206			0.356103	−	0.934447i	$-0.384105\pi$
$613$	17.6334			0.712206			0.356103	+	0.934447i	$0.384105\pi$
$614$	−16.3529			−0.659948
$615$	−3.93358			−0.158617
$616$	1.08615	−	30.4209i	0.0437623	−	1.22569i
$617$	2.23038	−	3.86313i	0.0897917	−	0.155524i	−0.817631	−	0.575742i	$-0.804713\pi$
$617$	2.23038	−	3.86313i	0.0897917	−	0.155524i	0.907423	+	0.420218i	$0.138047\pi$
$618$	−4.71909			−0.189830
$619$	5.25957	−	9.10984i	0.211400	−	0.366156i	−0.740753	−	0.671778i	$-0.765531\pi$
$619$	5.25957	−	9.10984i	0.211400	−	0.366156i	0.952153	+	0.305622i	$0.0988644\pi$
$620$	−0.656644	+	1.13734i	−0.0263714	+	0.0456767i
$621$	30.1198			1.20866
$622$	−4.59921	−	7.96607i	−0.184412	−	0.319410i
$623$	−5.57952	+	2.96109i	−0.223539	+	0.118633i
$624$	−16.5334	−	28.6367i	−0.661866	−	1.14638i
$625$	−9.68989	+	16.7834i	−0.387596	+	0.671335i
$626$	−4.78054	+	8.28014i	−0.191069	+	0.330941i
$627$	−29.7130	−	11.9858i	−1.18662	−	0.478667i
$628$	5.54189	+	9.59884i	0.221146	+	0.383035i
$629$	−9.66334	−	16.7374i	−0.385303	−	0.667364i
$630$	−1.77094	−	1.10854i	−0.0705561	−	0.0441651i
$631$	11.9526	−	20.7025i	0.475824	−	0.824152i	−0.523792	−	0.851846i	$-0.675483\pi$
$631$	11.9526	−	20.7025i	0.475824	−	0.824152i	0.999616	+	0.0276944i	$0.00881653\pi$
$632$	12.3727	−	21.4302i	0.492161	−	0.852448i
$633$	2.99789	+	5.19249i	0.119155	+	0.206383i
$634$	18.0863	−	31.3265i	0.718300	−	1.24413i
$635$	0.104734	+	0.181405i	0.00415626	+	0.00719886i
$636$	1.56927	−	2.71806i	0.0622256	−	0.107778i
$637$	14.2253	+	29.2824i	0.563628	+	1.16021i
$638$	−68.8832			−2.72711
$639$	−1.87507	−	3.24772i	−0.0741767	−	0.128478i
$640$	−4.23391	−	7.33335i	−0.167360	−	0.289876i
$641$	−20.7163			−0.818245			−0.409122	−	0.912480i	$-0.634165\pi$
$641$	−20.7163			−0.818245			−0.409122	+	0.912480i	$0.634165\pi$
$642$	0.971237			0.0383317
$643$	12.9443	+	22.4203i	0.510475	+	0.884169i	0.999926	+	0.0121383i	$0.00386384\pi$
$643$	12.9443	+	22.4203i	0.510475	+	0.884169i	−0.489451	+	0.872031i	$0.662803\pi$
$644$	6.51762	+	4.07976i	0.256830	+	0.160765i
$645$	−1.45491			−0.0572869
$646$	36.8013	+	14.8452i	1.44793	+	0.584075i
$647$	−3.45064	+	5.97668i	−0.135659	+	0.234967i	−0.925849	−	0.377894i	$-0.876648\pi$
$647$	−3.45064	+	5.97668i	−0.135659	+	0.234967i	0.790190	+	0.612862i	$0.209982\pi$
$648$	13.8590			0.544434
$649$	−6.24595	+	10.8183i	−0.245175	+	0.424656i
$650$	17.1177	−	29.6488i	0.671412	−	1.16292i
$651$	−0.545502	+	15.2784i	−0.0213799	+	0.598807i
$652$	0.0341099	−	0.0590801i	0.00133585	−	0.00231376i
$653$	4.63374	+	8.02588i	0.181332	+	0.314077i	0.942335	−	0.334672i	$-0.108626\pi$
$653$	4.63374	+	8.02588i	0.181332	+	0.314077i	−0.761002	+	0.648749i	$0.775292\pi$
$654$	8.91681	−	15.4444i	0.348675	−	0.603923i
$655$	0.446901	+	0.774056i	0.0174619	+	0.0302449i
$656$	−20.4861			−0.799846
$657$	−5.57859			−0.217641
$658$	0.868838	−	24.3344i	0.0338708	−	0.948653i
$659$	−8.94100	+	15.4863i	−0.348292	+	0.603259i	−0.985946	−	0.167063i	$-0.946572\pi$
$659$	−8.94100	+	15.4863i	−0.348292	+	0.603259i	0.637654	+	0.770323i	$0.279905\pi$
$660$	−1.23936	+	2.14664i	−0.0482421	+	0.0835578i
$661$	−19.3762	−	33.5606i	−0.753648	−	1.30536i	−0.946043	−	0.324040i	$-0.894959\pi$
$661$	−19.3762	−	33.5606i	−0.753648	−	1.30536i	0.192395	−	0.981318i	$-0.438375\pi$
$662$	−0.777286			−0.0302101
$663$	−19.6941	+	34.1112i	−0.764856	+	1.32477i
$664$	28.6358			1.11128
$665$	7.11248	−	0.745880i	0.275810	−	0.0289240i
$666$	4.31175			0.167077
$667$	−23.2960	+	40.3499i	−0.902025	+	1.56235i
$668$	−3.87947			−0.150101
$669$	3.07464	+	5.32543i	0.118872	+	0.205893i
$670$	−5.80490	+	10.0544i	−0.224263	+	0.388435i
$671$	−10.6494	+	18.4453i	−0.411115	+	0.712072i
$672$	9.97503	+	6.24395i	0.384795	+	0.240866i
$673$	−39.7523			−1.53234			−0.766170	−	0.642638i	$-0.777840\pi$
$673$	−39.7523			−1.53234			−0.766170	+	0.642638i	$0.777840\pi$
$674$	−3.34252			−0.128749
$675$	13.0063	+	22.5277i	0.500615	+	0.867090i
$676$	−2.34629	+	4.06389i	−0.0902418	+	0.156303i
$677$	15.2549	+	26.4222i	0.586293	+	1.01549i	0.994713	+	0.102695i	$0.0327466\pi$
$677$	15.2549	+	26.4222i	0.586293	+	1.01549i	−0.408420	+	0.912794i	$0.633920\pi$
$678$	−3.16422	+	5.48059i	−0.121521	+	0.210481i
$679$	−33.4484	−	20.9373i	−1.28363	−	0.803498i
$680$	−4.11037	+	7.11937i	−0.157626	+	0.273015i
$681$	−5.53876	+	9.59341i	−0.212246	+	0.367620i
$682$	−30.7696			−1.17823
$683$	−0.0144815	+	0.0250828i	−0.000554120	+	0.000959765i	−0.866302	−	0.499520i	$-0.833510\pi$
$683$	−0.0144815	+	0.0250828i	−0.000554120	+	0.000959765i	0.865748	+	0.500480i	$0.166843\pi$
$684$	−1.49076	+	1.16603i	−0.0570007	+	0.0445843i
$685$	−10.7125			−0.409303
$686$	−23.8564	−	17.4184i	−0.910842	−	0.665037i
$687$	−9.03365	−	15.6467i	−0.344655	−	0.596961i
$688$	−7.57714			−0.288876
$689$	18.0896			0.689158
$690$	3.92131	+	6.79190i	0.149282	+	0.258563i
$691$	25.9092	+	44.8760i	0.985631	+	1.70716i	0.639099	+	0.769125i	$0.279307\pi$
$691$	25.9092	+	44.8760i	0.985631	+	1.70716i	0.346532	+	0.938038i	$0.387359\pi$
$692$	−9.33569			−0.354890
$693$	0.373393	−	10.4580i	0.0141840	−	0.397265i
$694$	18.1803	−	31.4892i	0.690114	−	1.19531i
$695$	2.53242	+	4.38627i	0.0960600	+	0.166381i
$696$	−15.0219	+	26.0188i	−0.569406	+	0.986239i
$697$	12.2012	+	21.1331i	0.462153	+	0.800473i
$698$	−19.7988	+	34.2925i	−0.749394	+	1.29799i
$699$	21.8985	−	37.9293i	0.828276	−	1.43462i
$700$	−0.236950	+	6.63649i	−0.00895588	+	0.250836i
$701$	−12.9862	−	22.4928i	−0.490484	−	0.849543i	0.509456	−	0.860497i	$-0.329847\pi$
$701$	−12.9862	−	22.4928i	−0.490484	−	0.849543i	−0.999940	+	0.0109538i	$0.996513\pi$
$702$	−20.9026	−	36.2044i	−0.788919	−	1.36645i
$703$	−11.6251	+	9.09285i	−0.438450	+	0.342943i
$704$	11.8957	−	20.6039i	0.448335	−	0.776539i
$705$	2.65468	−	4.59804i	0.0999810	−	0.173172i
$706$	2.87470	+	4.97912i	0.108191	+	0.187392i
$707$	−2.75392	−	1.72384i	−0.103572	−	0.0648316i
$708$	−1.01736	−	1.76213i	−0.0382349	−	0.0662247i
$709$	24.5938			0.923640			0.461820	−	0.886974i	$-0.347197\pi$
$709$	24.5938			0.923640			0.461820	+	0.886974i	$0.347197\pi$
$710$	2.32272	−	4.02306i	0.0871700	−	0.150983i
$711$	4.25345	−	7.36719i	0.159517	−	0.276291i
$712$	−5.54487			−0.207803
$713$	−10.4061	+	18.0240i	−0.389713	+	0.675003i
$714$	1.27521	−	35.7160i	0.0477236	−	1.33664i
$715$	−14.2866			−0.534288
$716$	4.43993			0.165928
$717$	22.9336			0.856472
$718$	−8.77827	−	15.2044i	−0.327602	−	0.567423i
$719$	9.92145	−	17.1845i	0.370008	−	0.640872i	−0.619559	−	0.784950i	$-0.712688\pi$
$719$	9.92145	−	17.1845i	0.370008	−	0.640872i	0.989566	+	0.144078i	$0.0460217\pi$
$720$	−1.18627	−	2.05467i	−0.0442095	−	0.0765732i
$721$	4.47204	+	2.79931i	0.166548	+	0.104252i
$722$	7.29879	−	29.4116i	0.271633	−	1.09459i
$723$	−6.35179	−	11.0016i	−0.236225	−	0.409155i
$724$	7.85541			0.291944
$725$	−40.2388			−1.49443
$726$	−32.0434			−1.18924
$727$	7.63755	+	13.2286i	0.283261	+	0.490623i	0.972186	−	0.234210i	$-0.0752504\pi$
$727$	7.63755	+	13.2286i	0.283261	+	0.490623i	−0.688925	+	0.724833i	$0.741917\pi$
$728$	−1.01969	+	28.5595i	−0.0377923	+	1.05848i
$729$	29.8519			1.10563
$730$	−3.45520	−	5.98457i	−0.127883	−	0.221499i
$731$	4.51284	+	7.81646i	0.166913	+	0.289102i
$732$	−1.73461	−	3.00443i	−0.0641131	−	0.111047i
$733$	−3.43625	−	5.95176i	−0.126921	−	0.219833i	0.795561	−	0.605873i	$-0.207176\pi$
$733$	−3.43625	−	5.95176i	−0.126921	−	0.219833i	−0.922482	+	0.386040i	$0.873843\pi$
$734$	0.447630			0.0165223
$735$	−2.81437	−	5.79330i	−0.103809	−	0.213689i
$736$	8.01017	+	13.8740i	0.295259	+	0.511403i
$737$	−58.1503			−2.14199
$738$	−5.44413			−0.200401
$739$	29.7471			1.09426			0.547132	−	0.837046i	$-0.315719\pi$
$739$	29.7471			1.09426			0.547132	+	0.837046i	$0.315719\pi$
$740$	0.570909	+	0.988843i	0.0209870	+	0.0363506i
$741$	27.8948	+	11.2524i	1.02474	+	0.413367i
$742$	−14.4983	+	7.69434i	−0.532250	+	0.282468i
$743$	2.43249	+	4.21319i	0.0892393	+	0.154567i	0.907190	−	0.420722i	$-0.138223\pi$
$743$	2.43249	+	4.21319i	0.0892393	+	0.154567i	−0.817950	+	0.575289i	$0.804890\pi$
$744$	−6.71019	+	11.6224i	−0.246007	+	0.426097i
$745$	0.234747	+	0.406593i	0.00860046	+	0.0148964i
$746$	14.7843			0.541293
$747$	9.84430			0.360184
$748$	15.3770			0.562240
$749$	−0.920392	−	0.576127i	−0.0336304	−	0.0210512i
$750$	−7.05537	+	12.2203i	−0.257626	+	0.446221i
$751$	48.9211			1.78516			0.892578	−	0.450894i	$-0.148895\pi$
$751$	48.9211			1.78516			0.892578	+	0.450894i	$0.148895\pi$
$752$	13.8256	−	23.9466i	0.504166	−	0.873241i
$753$	3.19676	−	5.53694i	0.116496	−	0.201777i
$754$	64.6683			2.35508
$755$	6.24428	+	10.8154i	0.227253	+	0.393613i
$756$	6.87351	+	4.30252i	0.249987	+	0.156481i
$757$	11.7791	+	20.4020i	0.428119	+	0.741523i	0.996706	−	0.0810996i	$-0.0258432\pi$
$757$	11.7791	+	20.4020i	0.428119	+	0.741523i	−0.568587	+	0.822623i	$0.692510\pi$
$758$	10.8560	−	18.8031i	0.394307	−	0.682959i
$759$	−19.6407	+	34.0188i	−0.712914	+	1.23480i
$760$	5.82195	+	2.34850i	0.211184	+	0.0851890i
$761$	−2.91294	−	5.04535i	−0.105594	−	0.182894i	0.808387	−	0.588652i	$-0.200341\pi$
$761$	−2.91294	−	5.04535i	−0.105594	−	0.182894i	−0.913981	+	0.405758i	$0.867008\pi$
$762$	−0.399695	−	0.692292i	−0.0144794	−	0.0250791i
$763$	−17.6114	+	9.34650i	−0.637577	+	0.338366i
$764$	5.98228	−	10.3616i	0.216431	−	0.374870i
$765$	−1.41305	+	2.44747i	−0.0510888	+	0.0884884i
$766$	23.0346	+	39.8970i	0.832273	+	1.44154i
$767$	5.86377	−	10.1563i	0.211728	−	0.366724i
$768$	9.03176	+	15.6435i	0.325905	+	0.564485i
$769$	−27.6166	+	47.8334i	−0.995881	+	1.72492i	−0.419418	+	0.907793i	$0.637766\pi$
$769$	−27.6166	+	47.8334i	−0.995881	+	1.72492i	−0.576463	+	0.817123i	$0.695567\pi$
$770$	11.4503	−	6.07676i	0.412641	−	0.218991i
$771$	−3.53041			−0.127145
$772$	−0.947851	−	1.64173i	−0.0341139	−	0.0590870i
$773$	−4.03797	−	6.99397i	−0.145236	−	0.251555i	0.784225	−	0.620476i	$-0.213061\pi$
$773$	−4.03797	−	6.99397i	−0.145236	−	0.251555i	−0.929461	+	0.368921i	$0.879727\pi$
$774$	−2.01361			−0.0723777
$775$	−17.9744			−0.645659
$776$	−17.3200	−	29.9991i	−0.621751	−	1.07690i
$777$	11.2668	+	7.05252i	0.404193	+	0.253008i
$778$	−13.4682			−0.482858
$779$	14.6782	−	11.4809i	0.525902	−	0.411345i
$780$	1.16353	−	2.01529i	0.0416609	−	0.0721588i
$781$	23.2677			0.832584
$782$	24.3263	−	42.1343i	0.869905	−	1.50672i
$783$	−24.5680	+	42.5531i	−0.877990	+	1.52072i
$784$	−14.6572	−	30.1715i	−0.523472	−	1.07755i
$785$	6.31942	−	10.9456i	0.225550	−	0.390664i
$786$	−1.70550	−	2.95401i	−0.0608331	−	0.105366i
$787$	17.0775	−	29.5791i	0.608748	−	1.05438i	−0.382699	−	0.923873i	$-0.625005\pi$
$787$	17.0775	−	29.5791i	0.608748	−	1.05438i	0.991447	−	0.130509i	$-0.0416613\pi$
$788$	0.675845	+	1.17060i	0.0240760	+	0.0417009i
$789$	−28.2138			−1.00444
$790$	10.5378			0.374918
$791$	6.24960	−	3.31670i	0.222210	−	0.117928i
$792$	4.59308	−	7.95545i	0.163208	−	0.282685i
$793$	9.99776	−	17.3166i	0.355031	−	0.614931i
$794$	10.4023	+	18.0174i	0.369165	+	0.639412i
$795$	−3.57888			−0.126930
$796$	4.44262	−	7.69485i	0.157465	−	0.272737i
$797$	6.95622			0.246402			0.123201	−	0.992382i	$-0.460684\pi$
$797$	6.95622			0.246402			0.123201	+	0.992382i	$0.460684\pi$
$798$	−27.1431	+	2.84648i	−0.960857	+	0.100764i
$799$	−32.9372			−1.16523
$800$	−6.91793	+	11.9822i	−0.244586	+	0.423635i
$801$	−1.90619			−0.0673520
$802$	2.80398	+	4.85663i	0.0990119	+	0.171494i
$803$	17.3061	−	29.9751i	0.610720	−	1.05780i
$804$	4.73587	−	8.20276i	0.167021	−	0.289289i
$805$	0.312854	−	8.76241i	0.0110267	−	0.308834i
$806$	28.8868			1.01749
$807$	17.3907			0.612182
$808$	−1.42601	−	2.46993i	−0.0501670	−	0.0868918i
$809$	2.03456	−	3.52397i	0.0715315	−	0.123896i	−0.828041	−	0.560667i	$-0.810545\pi$
$809$	2.03456	−	3.52397i	0.0715315	−	0.123896i	0.899573	+	0.436771i	$0.143878\pi$
$810$	2.95091	+	5.11113i	0.103684	+	0.179587i
$811$	−0.177349	+	0.307177i	−0.00622756	+	0.0107865i	−0.869122	−	0.494597i	$-0.835316\pi$
$811$	−0.177349	+	0.307177i	−0.00622756	+	0.0107865i	0.862895	+	0.505384i	$0.168649\pi$
$812$	−11.0802	+	5.88031i	−0.388837	+	0.206358i
$813$	−4.78747	+	8.29214i	−0.167904	+	0.290818i
$814$	−13.3761	+	23.1680i	−0.468831	+	0.812040i
$815$	−0.0777911			−0.00272490
$816$	20.2920	−	35.1468i	0.710363	−	1.23039i
$817$	5.42901	−	4.24641i	0.189937	−	0.148563i
$818$	33.4354			1.16904
$819$	−0.350545	+	9.81805i	−0.0122490	+	0.343070i
$820$	−0.720845	−	1.24854i	−0.0251730	−	0.0436009i
$821$	7.51454			0.262259			0.131130	−	0.991365i	$-0.458140\pi$
$821$	7.51454			0.262259			0.131130	+	0.991365i	$0.458140\pi$
$822$	40.8818			1.42592
$823$	−3.45019	−	5.97591i	−0.120266	−	0.208307i	0.799606	−	0.600524i	$-0.205041\pi$
$823$	−3.45019	−	5.97591i	−0.120266	−	0.208307i	−0.919873	+	0.392217i	$0.871708\pi$
$824$	2.31568	+	4.01087i	0.0806705	+	0.139725i
$825$	−33.9252			−1.18112
$826$	−0.379684	+	10.6342i	−0.0132109	+	0.370010i
$827$	17.7177	−	30.6880i	0.616106	−	1.06713i	−0.374084	−	0.927395i	$-0.622043\pi$
$827$	17.7177	−	30.6880i	0.616106	−	1.06713i	0.990189	−	0.139731i	$-0.0446239\pi$
$828$	1.16021	+	2.00954i	0.0403201	+	0.0698365i
$829$	−8.72719	+	15.1159i	−0.303108	+	0.524998i	−0.976838	−	0.213979i	$-0.931358\pi$
$829$	−8.72719	+	15.1159i	−0.303108	+	0.524998i	0.673730	+	0.738977i	$0.264691\pi$
$830$	6.09723	+	10.5607i	0.211638	+	0.366568i
$831$	16.0959	−	27.8789i	0.558360	−	0.967108i
$832$	−11.1678	+	19.3432i	−0.387173	+	0.670604i
$833$	−22.3948	+	33.0898i	−0.775934	+	1.14650i
$834$	−9.66439	−	16.7392i	−0.334650	−	0.579632i
$835$	2.21188	+	3.83109i	0.0765452	+	0.132580i
$836$	−1.64066	−	11.6275i	−0.0567435	−	0.402146i
$837$	−10.9744	+	19.0081i	−0.379329	+	0.657017i
$838$	30.3619	−	52.5884i	1.04884	−	1.81664i
$839$	8.90263	+	15.4198i	0.307353	+	0.532351i	0.977782	−	0.209622i	$-0.0672235\pi$
$839$	8.90263	+	15.4198i	0.307353	+	0.532351i	−0.670430	+	0.741973i	$0.733890\pi$
$840$	0.201738	−	5.65026i	0.00696061	−	0.194953i
$841$	−23.5041	−	40.7103i	−0.810487	−	1.40380i
$842$	−54.3648			−1.87353
$843$	4.50353	−	7.80035i	0.155110	−	0.268658i
$844$	−1.09875	+	1.90309i	−0.0378206	+	0.0655072i
$845$	5.35094			0.184078
$846$	3.67411	−	6.36375i	0.126319	−	0.218790i
$847$	30.3659	+	19.0078i	1.04339	+	0.653115i
$848$	−18.6388			−0.640058
$849$	−16.3302			−0.560450
$850$	42.0184			1.44122
$851$	9.04746	+	15.6707i	0.310143	+	0.537183i
$852$	−1.89496	+	3.28217i	−0.0649204	+	0.112445i
$853$	−3.39083	−	5.87309i	−0.116100	−	0.201091i	0.802119	−	0.597164i	$-0.203706\pi$
$853$	−3.39083	−	5.87309i	−0.116100	−	0.201091i	−0.918219	+	0.396073i	$0.870373\pi$
$854$	−0.647363	+	18.1313i	−0.0221523	+	0.620441i
$855$	2.00145	+	0.807357i	0.0684480	+	0.0276110i
$856$	−0.476590	−	0.825479i	−0.0162895	−	0.0282143i
$857$	0.160896			0.00549610			0.00274805	−	0.999996i	$-0.499125\pi$
$857$	0.160896			0.00549610			0.00274805	+	0.999996i	$0.499125\pi$
$858$	54.5215			1.86133
$859$	−57.7257			−1.96958			−0.984788	−	0.173758i	$-0.944409\pi$
$859$	−57.7257			−1.96958			−0.984788	+	0.173758i	$0.944409\pi$
$860$	−0.266618	−	0.461796i	−0.00909159	−	0.0157471i
$861$	−14.2257	−	8.90471i	−0.484812	−	0.303472i
$862$	−37.2425			−1.26849
$863$	11.4080	+	19.7593i	0.388333	+	0.672613i	0.992226	−	0.124453i	$-0.0397176\pi$
$863$	11.4080	+	19.7593i	0.388333	+	0.672613i	−0.603892	+	0.797066i	$0.706384\pi$
$864$	8.44756	+	14.6316i	0.287392	+	0.497777i
$865$	5.32275	+	9.21927i	0.180979	+	0.313464i
$866$	27.2469	+	47.1931i	0.925889	+	1.60369i
$867$	−23.1185			−0.785145
$868$	−4.94942	+	2.62669i	−0.167994	+	0.0891556i
$869$	26.3905	+	45.7096i	0.895235	+	1.55059i
$870$	−12.7941			−0.433761
$871$	54.5921			1.84978
$872$	−17.5021			−0.592695
$873$	−5.95419	−	10.3130i	−0.201519	−	0.349041i
$874$	−34.4558	−	13.8990i	−1.16549	−	0.470142i
$875$	13.9349	−	7.39535i	0.471087	−	0.250009i
$876$	2.81889	+	4.88245i	0.0952413	+	0.164963i
$877$	−2.53005	+	4.38218i	−0.0854338	+	0.147976i	−0.905576	−	0.424184i	$-0.860561\pi$
$877$	−2.53005	+	4.38218i	−0.0854338	+	0.147976i	0.820142	+	0.572160i	$0.193894\pi$
$878$	28.7018	+	49.7129i	0.968638	+	1.67773i
$879$	−36.6165			−1.23504
$880$	14.7203			0.496222
$881$	5.75777			0.193984			0.0969921	−	0.995285i	$-0.469078\pi$
$881$	5.75777			0.193984			0.0969921	+	0.995285i	$0.469078\pi$
$882$	−3.89512	−	8.01801i	−0.131156	−	0.269980i
$883$	21.1105	−	36.5644i	0.710424	−	1.23049i	−0.254274	−	0.967132i	$-0.581837\pi$
$883$	21.1105	−	36.5644i	0.710424	−	1.23049i	0.964698	−	0.263358i	$-0.0848300\pi$
$884$	−14.4361			−0.485540
$885$	−1.16010	+	2.00935i	−0.0389963	+	0.0675436i
$886$	−0.374894	+	0.649335i	−0.0125948	+	0.0218148i
$887$	26.1326			0.877446			0.438723	−	0.898622i	$-0.355431\pi$
$887$	26.1326			0.877446			0.438723	+	0.898622i	$0.355431\pi$
$888$	5.83407	+	10.1049i	0.195779	+	0.339098i
$889$	−0.0318890	+	0.893145i	−0.00106952	+	0.0299551i
$890$	−1.18063	−	2.04492i	−0.0395749	−	0.0685458i
$891$	−14.7803	+	25.6003i	−0.495159	+	0.857641i
$892$	−1.12688	+	1.95182i	−0.0377308	+	0.0653516i
$893$	3.51426	+	24.9058i	0.117600	+	0.833442i
$894$	−0.895858	−	1.55167i	−0.0299620	−	0.0518956i
$895$	−2.53143	−	4.38456i	−0.0846162	−	0.146560i
$896$	1.28912	−	36.1055i	0.0430664	−	1.20620i
$897$	18.4389	−	31.9372i	0.615658	−	1.06635i
$898$	−9.81458	+	16.9993i	−0.327517	+	0.567276i
$899$	−16.9761	−	29.4035i	−0.566186	−	0.980663i
$900$	−1.00201	+	1.73553i	−0.0334002	+	0.0578509i
$901$	11.1010	+	19.2275i	0.369828	+	0.640560i
$902$	16.8890	−	29.2526i	0.562342	−	0.974005i
$903$	−5.26165	−	3.29357i	−0.175097	−	0.109603i
$904$	6.21079			0.206568
$905$	−4.47876	−	7.75745i	−0.148879	−	0.257866i
$906$	−23.8299	−	41.2746i	−0.791694	−	1.37126i
$907$	−23.9733			−0.796019			−0.398010	−	0.917381i	$-0.630299\pi$
$907$	−23.9733			−0.796019			−0.398010	+	0.917381i	$0.630299\pi$
$908$	−4.06001			−0.134736
$909$	−0.490229	−	0.849102i	−0.0162599	−	0.0281629i
$910$	−10.7497	+	5.70492i	−0.356348	+	0.189116i
$911$	28.4961			0.944119			0.472060	−	0.881567i	$-0.343511\pi$
$911$	28.4961			0.944119			0.472060	+	0.881567i	$0.343511\pi$
$912$	−28.7417	−	11.5940i	−0.951734	−	0.383917i
$913$	−30.5394	+	52.8958i	−1.01071	+	1.75059i
$914$	36.2292			1.19836
$915$	−1.97798	+	3.42596i	−0.0653899	+	0.113259i
$916$	3.31091	−	5.73467i	0.109396	−	0.189479i
$917$	−0.136070	+	3.81104i	−0.00449343	+	0.125852i
$918$	25.6546	−	44.4350i	0.846727	−	1.46657i
$919$	24.6893	+	42.7631i	0.814424	+	1.41062i	0.909741	+	0.415177i	$0.136280\pi$
$919$	24.6893	+	42.7631i	0.814424	+	1.41062i	−0.0953164	+	0.995447i	$0.530386\pi$
$920$	3.84840	−	6.66563i	0.126878	−	0.219759i
$921$	−7.60655	−	13.1749i	−0.250644	−	0.434128i
$922$	−40.6704			−1.33941
$923$	−21.8440			−0.719002
$924$	−9.34162	+	4.95766i	−0.307317	+	0.163095i
$925$	−7.81377	+	13.5339i	−0.256915	+	0.444990i
$926$	−26.4150	+	45.7522i	−0.868052	+	1.50351i
$927$	0.796075	+	1.37884i	0.0261465	+	0.0452871i
$928$	−26.1349			−0.857921
$929$	15.8754	−	27.4970i	0.520856	−	0.902148i	−0.478850	−	0.877897i	$-0.658946\pi$
$929$	15.8754	−	27.4970i	0.520856	−	0.902148i	0.999706	−	0.0242517i	$-0.00772033\pi$
$930$	−5.71503			−0.187403
$931$	27.4107	+	13.4035i	0.898349	+	0.439283i
$932$	16.0520			0.525800
$933$	4.27866	−	7.41085i	0.140077	−	0.242620i
$934$	−33.4380			−1.09412
$935$	−8.76722	−	15.1853i	−0.286719	−	0.496612i
$936$	−4.31203	+	7.46866i	−0.140943	+	0.244121i
$937$	8.16984	−	14.1506i	0.266897	−	0.462280i	−0.701162	−	0.713002i	$-0.747335\pi$
$937$	8.16984	−	14.1506i	0.266897	−	0.462280i	0.968059	+	0.250723i	$0.0806682\pi$
$938$	−43.7541	+	23.2206i	−1.42862	+	0.758179i
$939$	−8.89469			−0.290267
$940$	1.94593			0.0634691
$941$	−4.64341	−	8.04262i	−0.151371	−	0.262182i	0.780361	−	0.625329i	$-0.215035\pi$
$941$	−4.64341	−	8.04262i	−0.151371	−	0.262182i	−0.931732	+	0.363148i	$0.881702\pi$
$942$	−24.1166	+	41.7712i	−0.785762	+	1.36098i
$943$	−11.4236	−	19.7862i	−0.372003	−	0.644328i
$944$	−6.04179	+	10.4647i	−0.196644	+	0.340597i
$945$	0.329937	−	9.24087i	0.0107329	−	0.300606i
$946$	6.24671	−	10.8196i	0.203098	−	0.351776i
$947$	19.4959	−	33.7679i	0.633531	−	1.09731i	−0.353293	−	0.935513i	$-0.614938\pi$
$947$	19.4959	−	33.7679i	0.633531	−	1.09731i	0.986824	−	0.161795i	$-0.0517284\pi$
$948$	−8.59715			−0.279222
$949$	−16.2472	+	28.1409i	−0.527406	+	0.913493i
$950$	−4.48318	−	31.7727i	−0.145454	−	1.03084i
$951$	33.6515			1.09122
$952$	−30.9817	+	16.4422i	−1.00412	+	0.532894i
$953$	23.7771	+	41.1832i	0.770217	+	1.33406i	0.937444	+	0.348137i	$0.113185\pi$
$953$	23.7771	+	41.1832i	0.770217	+	1.33406i	−0.167227	+	0.985918i	$0.553481\pi$
$954$	−4.95322			−0.160366
$955$	−13.6432			−0.441484
$956$	4.20269	+	7.27927i	0.135925	+	0.235428i
$957$	−32.0411	−	55.4968i	−1.03574	−	1.79396i
$958$	22.0386			0.712036
$959$	−38.7416	−	24.2506i	−1.25103	−	0.783092i
$960$	2.20946	−	3.82689i	0.0713099	−	0.123512i
$961$	7.91689	+	13.7125i	0.255384	+	0.442337i
$962$	12.5576	−	21.7504i	0.404873	−	0.701261i
$963$	−0.163840	−	0.283780i	−0.00527968	−	0.00914467i
$964$	2.32799	−	4.03219i	0.0749794	−	0.129868i
$965$	−1.08084	+	1.87206i	−0.0347933	+	0.0602638i
$966$	−1.19394	+	33.4397i	−0.0384143	+	1.07591i
$967$	20.6731	+	35.8069i	0.664802	+	1.15147i	0.979339	+	0.202226i	$0.0648175\pi$
$967$	20.6731	+	35.8069i	0.664802	+	1.15147i	−0.314537	+	0.949245i	$0.601849\pi$
$968$	15.7239	+	27.2345i	0.505384	+	0.875350i
$969$	5.15794	+	36.5548i	0.165697	+	1.17431i
$970$	7.37566	−	12.7750i	0.236818	−	0.410181i
$971$	10.1547	−	17.5885i	0.325880	−	0.564441i	−0.655810	−	0.754926i	$-0.727673\pi$
$971$	10.1547	−	17.5885i	0.325880	−	0.564441i	0.981690	+	0.190485i	$0.0610061\pi$
$972$	2.18993	+	3.79307i	0.0702421	+	0.121663i
$973$	−0.771056	+	21.5957i	−0.0247189	+	0.692327i
$974$	−5.12113	−	8.87005i	−0.164091	−	0.284215i
$975$	31.8493			1.01999
$976$	−10.3013	+	17.8424i	−0.329736	+	0.571120i
$977$	4.43628	−	7.68386i	0.141929	−	0.245828i	−0.786294	−	0.617853i	$-0.788003\pi$
$977$	4.43628	−	7.68386i	0.141929	−	0.245828i	0.928223	+	0.372024i	$0.121336\pi$
$978$	0.296872			0.00949292
$979$	5.91347	−	10.2424i	0.188995	−	0.327350i
$980$	1.32308	−	1.95494i	0.0422643	−	0.0624484i
$981$	−6.01679			−0.192101
$982$	16.0079			0.510831
$983$	−24.2074			−0.772096			−0.386048	−	0.922479i	$-0.626160\pi$
$983$	−24.2074			−0.772096			−0.386048	+	0.922479i	$0.626160\pi$
$984$	−7.36626	−	12.7587i	−0.234828	−	0.406734i
$985$	0.770667	−	1.33483i	0.0245555	−	0.0425313i
$986$	39.6848	+	68.7362i	1.26382	+	2.18901i
$987$	20.0095	−	10.6192i	0.636909	−	0.338012i
$988$	1.54027	+	10.9160i	0.0490026	+	0.347285i
$989$	−4.22522	−	7.31829i	−0.134354	−	0.232708i
$990$	3.91190			0.124328
$991$	3.49663			0.111074			0.0555371	−	0.998457i	$-0.482313\pi$
$991$	3.49663			0.111074			0.0555371	+	0.998457i	$0.482313\pi$
$992$	−11.6743			−0.370658
$993$	−0.361555	−	0.626232i	−0.0114736	−	0.0198729i
$994$	17.5073	−	9.29126i	0.555299	−	0.294701i
$995$	−10.1318			−0.321201
$996$	−4.97437	−	8.61585i	−0.157619	−	0.273004i
$997$	0.283358	+	0.490791i	0.00897405	+	0.0155435i	0.870478	−	0.492208i	$-0.163810\pi$
$997$	0.283358	+	0.490791i	0.00897405	+	0.0155435i	−0.861504	+	0.507752i	$0.830477\pi$
$998$	15.4196	+	26.7075i	0.488098	+	0.845410i
$999$	9.54149	+	16.5263i	0.301879	+	0.522870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.g.a.102.3	yes	24
7.2	even	3		133.2.h.a.121.10	yes	24
7.3	odd	6		931.2.e.e.197.3		24
7.4	even	3		931.2.e.f.197.3		24
7.5	odd	6		931.2.h.h.520.10		24
7.6	odd	2		931.2.g.h.900.3		24
19.11	even	3		133.2.h.a.11.10	yes	24
133.11	even	3		931.2.e.f.638.3		24
133.30	even	3	inner	133.2.g.a.30.3	✓	24
133.68	odd	6		931.2.g.h.30.3		24
133.87	odd	6		931.2.e.e.638.3		24
133.125	odd	6		931.2.h.h.410.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.g.a.30.3	✓	24	133.30	even	3	inner
133.2.g.a.102.3	yes	24	1.1	even	1	trivial
133.2.h.a.11.10	yes	24	19.11	even	3
133.2.h.a.121.10	yes	24	7.2	even	3
931.2.e.e.197.3		24	7.3	odd	6
931.2.e.e.638.3		24	133.87	odd	6
931.2.e.f.197.3		24	7.4	even	3
931.2.e.f.638.3		24	133.11	even	3
931.2.g.h.30.3		24	133.68	odd	6
931.2.g.h.900.3		24	7.6	odd	2
931.2.h.h.410.10		24	133.125	odd	6
931.2.h.h.520.10		24	7.5	odd	6

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:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.797467 + 1.38125i) q^{2} -1.48377 q^{3} +(-0.271907 - 0.470957i) q^{4} +(-0.310056 + 0.537033i) q^{5} +(1.18326 - 2.04946i) q^{6} +(-2.33703 + 1.24028i) q^{7} -2.32252 q^{8} -0.798426 q^{9} +O(q^{10})\)	\(q+(-0.797467 + 1.38125i) q^{2} -1.48377 q^{3} +(-0.271907 - 0.470957i) q^{4} +(-0.310056 + 0.537033i) q^{5} +(1.18326 - 2.04946i) q^{6} +(-2.33703 + 1.24028i) q^{7} -2.32252 q^{8} -0.798426 q^{9} +(-0.494519 - 0.856532i) q^{10} +(2.47691 - 4.29013i) q^{11} +(0.403448 + 0.698793i) q^{12} +(-2.32535 + 4.02762i) q^{13} +(0.150568 - 4.21711i) q^{14} +(0.460052 - 0.796833i) q^{15} +(2.39595 - 4.14990i) q^{16} -5.70797 q^{17} +(0.636718 - 1.10283i) q^{18} +(0.609015 + 4.31614i) q^{19} +0.337226 q^{20} +(3.46762 - 1.84029i) q^{21} +(3.95051 + 6.84248i) q^{22} +5.34418 q^{23} +3.44609 q^{24} +(2.30773 + 3.99711i) q^{25} +(-3.70878 - 6.42379i) q^{26} +5.63599 q^{27} +(1.21957 + 0.763402i) q^{28} +(-4.35913 + 7.55024i) q^{29} +(0.733752 + 1.27090i) q^{30} +(-1.94719 + 3.37263i) q^{31} +(1.49886 + 2.59610i) q^{32} +(-3.67517 + 6.36557i) q^{33} +(4.55192 - 7.88415i) q^{34} +(0.0585411 - 1.63962i) q^{35} +(0.217098 + 0.376025i) q^{36} +(1.69296 + 2.93229i) q^{37} +(-6.44736 - 2.60078i) q^{38} +(3.45028 - 5.97607i) q^{39} +(0.720111 - 1.24727i) q^{40} +(-2.13757 - 3.70239i) q^{41} +(-0.223409 + 6.25722i) q^{42} +(-0.790620 - 1.36939i) q^{43} -2.69396 q^{44} +(0.247557 - 0.428781i) q^{45} +(-4.26181 + 7.38167i) q^{46} +5.77039 q^{47} +(-3.55504 + 6.15750i) q^{48} +(3.92343 - 5.79713i) q^{49} -7.36136 q^{50} +8.46931 q^{51} +2.52912 q^{52} +(-1.94482 - 3.36853i) q^{53} +(-4.49452 + 7.78473i) q^{54} +(1.53596 + 2.66036i) q^{55} +(5.42780 - 2.88057i) q^{56} +(-0.903639 - 6.40417i) q^{57} +(-6.95253 - 12.0421i) q^{58} -2.52167 q^{59} -0.500366 q^{60} -4.29946 q^{61} +(-3.10564 - 5.37913i) q^{62} +(1.86595 - 0.990269i) q^{63} +4.80263 q^{64} +(-1.44198 - 2.49758i) q^{65} +(-5.86165 - 10.1527i) q^{66} +(-5.86924 - 10.1658i) q^{67} +(1.55204 + 2.68821i) q^{68} -7.92953 q^{69} +(2.21804 + 1.38840i) q^{70} +(2.34846 + 4.06765i) q^{71} +1.85436 q^{72} +6.98698 q^{73} -5.40031 q^{74} +(-3.42414 - 5.93079i) q^{75} +(1.86712 - 1.46041i) q^{76} +(-0.467661 + 13.0982i) q^{77} +(5.50297 + 9.53143i) q^{78} +(-5.32729 + 9.22714i) q^{79} +(1.48576 + 2.57340i) q^{80} -5.96724 q^{81} +6.81858 q^{82} -12.3296 q^{83} +(-1.80957 - 1.13271i) q^{84} +(1.76979 - 3.06537i) q^{85} +2.52197 q^{86} +(6.46795 - 11.2028i) q^{87} +(-5.75267 + 9.96392i) q^{88} +2.38744 q^{89} +(0.394837 + 0.683877i) q^{90} +(0.439045 - 12.2968i) q^{91} +(-1.45312 - 2.51688i) q^{92} +(2.88918 - 5.00421i) q^{93} +(-4.60170 + 7.97037i) q^{94} +(-2.50674 - 1.01119i) q^{95} +(-2.22396 - 3.85202i) q^{96} +(7.45741 + 12.9166i) q^{97} +(4.87850 + 10.0423i) q^{98} +(-1.97763 + 3.42536i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9}+O(q^{10}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9	\( 24 q + q^{2} - 6 q^{3} - 11 q^{4} - 6 q^{6} - 2 q^{7} - 18 q^{8} + 18 q^{9} + 16 q^{10} - q^{11} - 2 q^{12} + 6 q^{13} - q^{14} - 9 q^{15} - 9 q^{16} - 16 q^{17} + 5 q^{18} - 4 q^{19} - 21 q^{21} - 2 q^{22} + 18 q^{23} + 16 q^{24} - 14 q^{25} + q^{26} - 18 q^{27} - 14 q^{28} - 2 q^{29} - 9 q^{30} + 11 q^{31} + 24 q^{32} + 3 q^{33} + 6 q^{34} + 38 q^{35} - 7 q^{36} - 14 q^{37} + 12 q^{38} - 10 q^{39} + 42 q^{40} + 20 q^{41} - 36 q^{42} + 2 q^{43} - 4 q^{44} - 12 q^{45} - 6 q^{46} + 39 q^{48} + 18 q^{49} + 22 q^{50} - 42 q^{51} - 22 q^{52} + 7 q^{53} - 43 q^{54} + 9 q^{55} - 21 q^{56} + 21 q^{57} + 35 q^{58} - 84 q^{59} + 12 q^{60} - 12 q^{61} - 19 q^{62} + 9 q^{63} - 2 q^{64} - 27 q^{65} + 3 q^{66} - 14 q^{67} + 51 q^{68} - 34 q^{69} + 33 q^{70} + q^{71} - 36 q^{72} + 42 q^{73} + 50 q^{74} + 31 q^{75} - 70 q^{76} - 20 q^{77} + 57 q^{78} - 5 q^{79} + 13 q^{80} - 56 q^{81} + 24 q^{82} + 10 q^{83} + 129 q^{84} - 27 q^{85} - 36 q^{86} + 53 q^{87} - 36 q^{88} + 2 q^{89} + 27 q^{90} - 9 q^{91} - 72 q^{92} + 34 q^{93} + 12 q^{94} - 11 q^{95} - 94 q^{96} + 31 q^{97} - 26 q^{98} + 43 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 11 * q^4 - 6 * q^6 - 2 * q^7 - 18 * q^8 + 18 * q^9 + 16 * q^10 - q^11 - 2 * q^12 + 6 * q^13 - q^14 - 9 * q^15 - 9 * q^16 - 16 * q^17 + 5 * q^18 - 4 * q^19 - 21 * q^21 - 2 * q^22 + 18 * q^23 + 16 * q^24 - 14 * q^25 + q^26 - 18 * q^27 - 14 * q^28 - 2 * q^29 - 9 * q^30 + 11 * q^31 + 24 * q^32 + 3 * q^33 + 6 * q^34 + 38 * q^35 - 7 * q^36 - 14 * q^37 + 12 * q^38 - 10 * q^39 + 42 * q^40 + 20 * q^41 - 36 * q^42 + 2 * q^43 - 4 * q^44 - 12 * q^45 - 6 * q^46 + 39 * q^48 + 18 * q^49 + 22 * q^50 - 42 * q^51 - 22 * q^52 + 7 * q^53 - 43 * q^54 + 9 * q^55 - 21 * q^56 + 21 * q^57 + 35 * q^58 - 84 * q^59 + 12 * q^60 - 12 * q^61 - 19 * q^62 + 9 * q^63 - 2 * q^64 - 27 * q^65 + 3 * q^66 - 14 * q^67 + 51 * q^68 - 34 * q^69 + 33 * q^70 + q^71 - 36 * q^72 + 42 * q^73 + 50 * q^74 + 31 * q^75 - 70 * q^76 - 20 * q^77 + 57 * q^78 - 5 * q^79 + 13 * q^80 - 56 * q^81 + 24 * q^82 + 10 * q^83 + 129 * q^84 - 27 * q^85 - 36 * q^86 + 53 * q^87 - 36 * q^88 + 2 * q^89 + 27 * q^90 - 9 * q^91 - 72 * q^92 + 34 * q^93 + 12 * q^94 - 11 * q^95 - 94 * q^96 + 31 * q^97 - 26 * q^98 + 43 * q^99

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