LMFDB - Embedded newform 798.2.bu.a.527.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(53,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 12, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.53"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bu (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [162,0,0,0,0,0,0,-81] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			527.13
Character	$\chi$	$=$	798.527
Dual form			798.2.bu.a.53.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 - 0.984808i) q^{2} +(-0.111227 - 1.72848i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.359967 - 0.989002i) q^{5} +(-1.72153 - 0.190609i) q^{6} +(-2.21348 + 1.44931i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.97526 + 0.384507i) q^{9} +(-1.03648 + 0.182760i) q^{10} +1.87185i q^{11} +(-0.486654 + 1.66228i) q^{12} +(0.976245 - 0.172138i) q^{13} +(1.04293 + 2.43152i) q^{14} +(-1.66943 + 0.732199i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-3.66571 + 4.36863i) q^{17} +(-0.137982 + 2.99683i) q^{18} +(-4.34667 + 0.326348i) q^{19} +1.05247i q^{20} +(2.75130 + 3.66474i) q^{21} +(1.84341 + 0.325044i) q^{22} +(0.876717 - 0.154589i) q^{23} +(1.55252 + 0.767912i) q^{24} +(2.98167 - 2.50192i) q^{25} -0.991305i q^{26} +(0.995541 + 5.09989i) q^{27} +(2.57568 - 0.604855i) q^{28} +(0.502368 + 0.182847i) q^{29} +(0.431182 + 1.77121i) q^{30} +(-3.84081 - 2.21749i) q^{31} +(0.766044 - 0.642788i) q^{32} +(3.23545 - 0.208201i) q^{33} +(3.66571 + 4.36863i) q^{34} +(2.23015 + 1.66743i) q^{35} +(2.92734 + 0.656279i) q^{36} +(-3.78576 - 2.18571i) q^{37} +(-0.433401 + 4.33730i) q^{38} +(-0.406122 - 1.66827i) q^{39} +(1.03648 + 0.182760i) q^{40} +(-2.05365 + 11.6468i) q^{41} +(4.08682 - 2.07313i) q^{42} +(-5.48400 - 4.60163i) q^{43} +(0.640211 - 1.75897i) q^{44} +(1.45127 + 2.80412i) q^{45} -0.890242i q^{46} +(4.05494 + 4.83249i) q^{47} +(1.02584 - 1.39558i) q^{48} +(2.79898 - 6.41605i) q^{49} +(-1.94615 - 3.37083i) q^{50} +(7.95879 + 5.85019i) q^{51} +(-0.976245 - 0.172138i) q^{52} +(-2.38323 - 0.867425i) q^{53} +(5.19529 - 0.0948299i) q^{54} +(1.85126 - 0.673805i) q^{55} +(-0.148403 - 2.64159i) q^{56} +(1.04755 + 7.47681i) q^{57} +(0.267305 - 0.462985i) q^{58} +(-6.88449 - 5.77678i) q^{59} +(1.81918 - 0.117064i) q^{60} +(-1.92328 - 10.9075i) q^{61} +(-2.85076 + 3.39740i) q^{62} +(6.02840 - 5.16318i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.521661 - 0.903544i) q^{65} +(0.356792 - 3.22245i) q^{66} +(5.33161 - 0.940107i) q^{67} +(4.93880 - 2.85142i) q^{68} +(-0.364718 - 1.49819i) q^{69} +(2.02936 - 1.90673i) q^{70} +(5.23292 + 4.39094i) q^{71} +(1.15464 - 2.76890i) q^{72} +(0.322091 - 0.117232i) q^{73} +(-2.80989 + 3.34870i) q^{74} +(-4.65615 - 4.87547i) q^{75} +(4.19615 + 1.17998i) q^{76} +(-2.71290 - 4.14330i) q^{77} +(-1.71345 + 0.110260i) q^{78} +(-7.89065 + 9.40371i) q^{79} +(0.359967 - 0.989002i) q^{80} +(8.70431 - 2.28802i) q^{81} +(11.1133 + 4.04489i) q^{82} +(-11.1341 + 6.42827i) q^{83} +(-1.33196 - 4.38473i) q^{84} +(5.64012 + 2.05283i) q^{85} +(-5.48400 + 4.60163i) q^{86} +(0.260170 - 0.888669i) q^{87} +(-1.62107 - 0.935926i) q^{88} +(-6.57724 - 2.39392i) q^{89} +(3.01353 - 0.942294i) q^{90} +(-1.91142 + 1.79591i) q^{91} +(-0.876717 - 0.154589i) q^{92} +(-3.40568 + 6.88540i) q^{93} +(5.46321 - 3.15419i) q^{94} +(1.88742 + 4.18139i) q^{95} +(-1.19625 - 1.25259i) q^{96} +(1.99972 + 5.49418i) q^{97} +(-5.83254 - 3.87059i) q^{98} +(-0.719741 - 5.56924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q - 81 q^{8} + 15 q^{13} + 6 q^{14} + 27 q^{15} - 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} - 9 q^{27} + 9 q^{28} + 6 q^{29} - 24 q^{33} + 6 q^{34} + 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) $ 162 * q - 81 * q^8 + 15 * q^13 + 6 * q^14 + 27 * q^15 - 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 - 9 * q^27 + 9 * q^28 + 6 * q^29 - 24 * q^33 + 6 * q^34 + 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 - 12 * q^44 - 63 * q^45 + 12 * q^47 - 48 * q^49 + 87 * q^50 - 24 * q^51 - 15 * q^52 - 18 * q^54 - 18 * q^57 - 48 * q^59 + 6 * q^60 + 45 * q^61 + 36 * q^62 - 15 * q^63 - 81 * q^64 + 36 * q^65 + 12 * q^66 + 9 * q^67 + 9 * q^69 - 24 * q^70 + 12 * q^71 + 102 * q^73 + 39 * q^74 - 6 * q^78 - 42 * q^79 + 84 * q^81 - 3 * q^84 - 6 * q^85 - 9 * q^86 + 60 * q^87 + 54 * q^89 + 36 * q^90 - 18 * q^91 - 21 * q^93 - 72 * q^94 - 12 * q^97 - 27 * q^98 - 57 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	−0.111227	−	1.72848i	−0.0642171	−	0.997936i
$3$	−0.111227	−	1.72848i	−0.0642171	−	0.997936i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	−0.359967	−	0.989002i	−0.160982	−	0.442295i	0.832808	−	0.553561i	$-0.186732\pi$
$5$	−0.359967	−	0.989002i	−0.160982	−	0.442295i	−0.993791	+	0.111266i	$0.964509\pi$
$6$	−1.72153	−	0.190609i	−0.702812	−	0.0778159i
$7$	−2.21348	+	1.44931i	−0.836616	+	0.547789i
$7$	−2.21348	+	1.44931i	−0.836616	+	0.547789i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−2.97526	+	0.384507i	−0.991752	+	0.128169i
$10$	−1.03648	+	0.182760i	−0.327765	+	0.0577938i
$11$			1.87185i			0.564384i	0.959358	+	0.282192i	$0.0910616\pi$
$11$			1.87185i			0.564384i	−0.959358	+	0.282192i	$0.908938\pi$
$12$	−0.486654	+	1.66228i	−0.140485	+	0.479858i
$13$	0.976245	−	0.172138i	0.270762	−	0.0477426i	−0.0366187	−	0.999329i	$-0.511659\pi$
$13$	0.976245	−	0.172138i	0.270762	−	0.0477426i	0.307380	+	0.951587i	$0.400548\pi$
$14$	1.04293	+	2.43152i	0.278734	+	0.649852i
$15$	−1.66943	+	0.732199i	−0.431044	+	0.189053i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−3.66571	+	4.36863i	−0.889066	+	1.05955i	0.108788	+	0.994065i	$0.465303\pi$
$17$	−3.66571	+	4.36863i	−0.889066	+	1.05955i	−0.997854	+	0.0654828i	$0.979141\pi$
$18$	−0.137982	+	2.99683i	−0.0325227	+	0.706358i
$19$	−4.34667	+	0.326348i	−0.997193	+	0.0748693i
$19$	−4.34667	+	0.326348i	−0.997193	+	0.0748693i
$20$			1.05247i			0.235340i
$21$	2.75130	+	3.66474i	0.600384	+	0.799712i
$22$	1.84341	+	0.325044i	0.393017	+	0.0692995i
$23$	0.876717	−	0.154589i	0.182808	−	0.0322340i	−0.0814946	−	0.996674i	$-0.525969\pi$
$23$	0.876717	−	0.154589i	0.182808	−	0.0322340i	0.264303	+	0.964440i	$0.414858\pi$
$24$	1.55252	+	0.767912i	0.316906	+	0.156749i
$25$	2.98167	−	2.50192i	0.596335	−	0.500384i
$26$		−	0.991305i		−	0.194411i
$27$	0.995541	+	5.09989i	0.191592	+	0.981475i
$28$	2.57568	−	0.604855i	0.486759	−	0.114307i
$29$	0.502368	+	0.182847i	0.0932874	+	0.0339538i	0.388242	−	0.921557i	$-0.373082\pi$
$29$	0.502368	+	0.182847i	0.0932874	+	0.0339538i	−0.294955	+	0.955511i	$0.595305\pi$
$30$	0.431182	+	1.77121i	0.0787227	+	0.323377i
$31$	−3.84081	−	2.21749i	−0.689830	−	0.398274i	0.113718	−	0.993513i	$-0.463724\pi$
$31$	−3.84081	−	2.21749i	−0.689830	−	0.398274i	−0.803548	+	0.595239i	$0.797057\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	3.23545	−	0.208201i	0.563220	−	0.0362431i
$34$	3.66571	+	4.36863i	0.628665	+	0.749213i
$35$	2.23015	+	1.66743i	0.376965	+	0.281847i
$36$	2.92734	+	0.656279i	0.487889	+	0.109380i
$37$	−3.78576	−	2.18571i	−0.622374	−	0.359328i	0.155419	−	0.987849i	$-0.450327\pi$
$37$	−3.78576	−	2.18571i	−0.622374	−	0.359328i	−0.777793	+	0.628521i	$0.783661\pi$
$38$	−0.433401	+	4.33730i	−0.0703069	+	0.703603i
$39$	−0.406122	−	1.66827i	−0.0650316	−	0.267137i
$40$	1.03648	+	0.182760i	0.163883	+	0.0288969i
$41$	−2.05365	+	11.6468i	−0.320726	+	1.81893i	0.217424	+	0.976077i	$0.430234\pi$
$41$	−2.05365	+	11.6468i	−0.320726	+	1.81893i	−0.538150	+	0.842849i	$0.680877\pi$
$42$	4.08682	−	2.07313i	0.630611	−	0.319891i
$43$	−5.48400	−	4.60163i	−0.836303	−	0.701741i	0.120426	−	0.992722i	$-0.461574\pi$
$43$	−5.48400	−	4.60163i	−0.836303	−	0.701741i	−0.956729	+	0.290981i	$0.906018\pi$
$44$	0.640211	−	1.75897i	0.0965154	−	0.265174i
$45$	1.45127	+	2.80412i	0.216343	+	0.418014i
$46$		−	0.890242i		−	0.131259i
$47$	4.05494	+	4.83249i	0.591474	+	0.704892i	0.975889	−	0.218269i	$-0.0700410\pi$
$47$	4.05494	+	4.83249i	0.591474	+	0.704892i	−0.384414	+	0.923161i	$0.625597\pi$
$48$	1.02584	−	1.39558i	0.148067	−	0.201435i
$49$	2.79898	−	6.41605i	0.399854	−	0.916579i
$50$	−1.94615	−	3.37083i	−0.275227	−	0.476707i
$51$	7.95879	+	5.85019i	1.11445	+	0.819190i
$52$	−0.976245	−	0.172138i	−0.135381	−	0.0238713i
$53$	−2.38323	−	0.867425i	−0.327362	−	0.119150i	0.173111	−	0.984902i	$-0.444618\pi$
$53$	−2.38323	−	0.867425i	−0.327362	−	0.119150i	−0.500473	+	0.865752i	$0.666840\pi$
$54$	5.19529	−	0.0948299i	0.706989	−	0.0129047i
$55$	1.85126	−	0.673805i	0.249624	−	0.0908559i
$56$	−0.148403	−	2.64159i	−0.0198312	−	0.352997i
$57$	1.04755	+	7.47681i	0.138752	+	0.990327i
$58$	0.267305	−	0.462985i	0.0350988	−	0.0607929i
$59$	−6.88449	−	5.77678i	−0.896285	−	0.752072i	0.0731758	−	0.997319i	$-0.476687\pi$
$59$	−6.88449	−	5.77678i	−0.896285	−	0.752072i	−0.969461	+	0.245247i	$0.921131\pi$
$60$	1.81918	−	0.117064i	0.234855	−	0.0151129i
$61$	−1.92328	−	10.9075i	−0.246251	−	1.39656i	−0.817570	−	0.575830i	$-0.804679\pi$
$61$	−1.92328	−	10.9075i	−0.246251	−	1.39656i	0.571319	−	0.820728i	$-0.306432\pi$
$62$	−2.85076	+	3.39740i	−0.362046	+	0.431470i
$63$	6.02840	−	5.16318i	0.759507	−	0.650500i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.521661	−	0.903544i	−0.0647041	−	0.112071i
$66$	0.356792	−	3.22245i	0.0439181	−	0.396656i
$67$	5.33161	−	0.940107i	0.651360	−	0.114852i	0.161802	−	0.986823i	$-0.448269\pi$
$67$	5.33161	−	0.940107i	0.651360	−	0.114852i	0.489558	+	0.871971i	$0.337158\pi$
$68$	4.93880	−	2.85142i	0.598918	−	0.345785i
$69$	−0.364718	−	1.49819i	−0.0439069	−	0.180361i
$70$	2.02936	−	1.90673i	0.242555	−	0.227897i
$71$	5.23292	+	4.39094i	0.621034	+	0.521109i	0.898128	−	0.439733i	$-0.144927\pi$
$71$	5.23292	+	4.39094i	0.621034	+	0.521109i	−0.277095	+	0.960843i	$0.589372\pi$
$72$	1.15464	−	2.76890i	0.136075	−	0.326318i
$73$	0.322091	−	0.117232i	0.0376979	−	0.0137209i	−0.323102	−	0.946364i	$-0.604726\pi$
$73$	0.322091	−	0.117232i	0.0376979	−	0.0137209i	0.360800	+	0.932643i	$0.382504\pi$
$74$	−2.80989	+	3.34870i	−0.326643	+	0.389278i
$75$	−4.65615	−	4.87547i	−0.537646	−	0.562971i
$76$	4.19615	+	1.17998i	0.481331	+	0.135353i
$77$	−2.71290	−	4.14330i	−0.309164	−	0.472173i
$78$	−1.71345	+	0.110260i	−0.194010	+	0.0124845i
$79$	−7.89065	+	9.40371i	−0.887768	+	1.05800i	0.110176	+	0.993912i	$0.464858\pi$
$79$	−7.89065	+	9.40371i	−0.887768	+	1.05800i	−0.997944	+	0.0640885i	$0.979586\pi$
$80$	0.359967	−	0.989002i	0.0402456	−	0.110574i
$81$	8.70431	−	2.28802i	0.967145	−	0.254224i
$82$	11.1133	+	4.04489i	1.22725	+	0.446684i
$83$	−11.1341	+	6.42827i	−1.22213	+	0.705595i	−0.965371	−	0.260882i	$-0.915987\pi$
$83$	−11.1341	+	6.42827i	−1.22213	+	0.705595i	−0.256755	+	0.966477i	$0.582653\pi$
$84$	−1.33196	−	4.38473i	−0.145329	−	0.478413i
$85$	5.64012	+	2.05283i	0.611757	+	0.222661i
$86$	−5.48400	+	4.60163i	−0.591355	+	0.496206i
$87$	0.260170	−	0.888669i	0.0278931	−	0.0952753i
$88$	−1.62107	−	0.935926i	−0.172807	−	0.0997700i
$89$	−6.57724	−	2.39392i	−0.697186	−	0.253755i	−0.0309770	−	0.999520i	$-0.509862\pi$
$89$	−6.57724	−	2.39392i	−0.697186	−	0.253755i	−0.666209	+	0.745765i	$0.732084\pi$
$90$	3.01353	−	0.942294i	0.317654	−	0.0993265i
$91$	−1.91142	+	1.79591i	−0.200371	+	0.188263i
$92$	−0.876717	−	0.154589i	−0.0914040	−	0.0161170i
$93$	−3.40568	+	6.88540i	−0.353153	+	0.713982i
$94$	5.46321	−	3.15419i	0.563487	−	0.325329i
$95$	1.88742	+	4.18139i	0.193645	+	0.429001i
$96$	−1.19625	−	1.25259i	−0.122092	−	0.127842i
$97$	1.99972	+	5.49418i	0.203041	+	0.557849i	0.998863	−	0.0476813i	$-0.0151832\pi$
$97$	1.99972	+	5.49418i	0.203041	+	0.557849i	−0.795822	+	0.605531i	$0.792961\pi$
$98$	−5.83254	−	3.87059i	−0.589175	−	0.390989i
$99$	−0.719741	−	5.56924i	−0.0723367	−	0.559730i
$100$	−3.65756	+	1.33124i	−0.365756	+	0.133124i
$101$	5.74902	+	6.85142i	0.572049	+	0.681742i	0.972050	−	0.234773i	$-0.0754347\pi$
$101$	5.74902	+	6.85142i	0.572049	+	0.681742i	−0.400001	+	0.916515i	$0.630990\pi$
$102$	7.14334	−	6.82201i	0.707296	−	0.675479i
$103$	−8.05579	+	4.65101i	−0.793761	+	0.458278i	−0.841285	−	0.540592i	$-0.818200\pi$
$103$	−8.05579	+	4.65101i	−0.793761	+	0.458278i	0.0475241	+	0.998870i	$0.484867\pi$
$104$	−0.339046	+	0.931522i	−0.0332462	+	0.0913433i
$105$	2.63406	−	4.04023i	0.257058	−	0.394286i
$106$	−1.26809	+	2.19640i	−0.123168	+	0.213333i
$107$	−6.77269			−0.654741			−0.327370	−	0.944896i	$-0.606162\pi$
$107$	−6.77269			−0.654741			−0.327370	+	0.944896i	$0.606162\pi$
$108$	0.808763	−	5.13283i	0.0778232	−	0.493906i
$109$	−1.18309	−	0.208611i	−0.113319	−	0.0199813i	0.116701	−	0.993167i	$-0.462768\pi$
$109$	−1.18309	−	0.208611i	−0.113319	−	0.0199813i	−0.230020	+	0.973186i	$0.573879\pi$
$110$	−0.342100	−	1.94014i	−0.0326179	−	0.184986i
$111$	−3.35686	+	6.78670i	−0.318619	+	0.644165i
$112$	−2.62722	−	0.312558i	−0.248249	−	0.0295340i
$113$	8.69260			0.817731			0.408866	−	0.912595i	$-0.365925\pi$
$113$	8.69260			0.817731			0.408866	+	0.912595i	$0.365925\pi$
$114$	7.54512	+	0.266697i	0.706665	+	0.0249784i
$115$	−0.468478	−	0.811428i	−0.0436858	−	0.0756660i
$116$	−0.409534	−	0.343640i	−0.0380243	−	0.0319062i
$117$	−2.83839	+	0.887529i	−0.262409	+	0.0820521i
$118$	−6.88449	+	5.77678i	−0.633769	+	0.531795i
$119$	1.78247	−	14.9826i	0.163399	−	1.37346i
$120$	0.200611	−	1.81187i	0.0183132	−	0.165400i
$121$	7.49617			0.681470
$122$	−11.0757			−1.00275
$123$	20.3597	+	2.25424i	1.83577	+	0.203258i
$124$	2.85076	+	3.39740i	0.256005	+	0.305095i
$125$	−8.10506	−	4.67946i	−0.724938	−	0.418543i
$126$	−4.03792	−	6.83339i	−0.359726	−	0.608767i
$127$	−17.0116	+	2.99960i	−1.50954	+	0.266172i	−0.866311	−	0.499506i	$-0.833515\pi$
$127$	−17.0116	+	2.99960i	−1.50954	+	0.266172i	−0.643225	+	0.765677i	$0.722404\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	−7.34383	+	9.99080i	−0.646588	+	0.879640i
$130$	−0.980403	+	0.356837i	−0.0859870	+	0.0312967i
$131$	−16.6047	−	2.92785i	−1.45076	−	0.255807i	−0.607928	−	0.793992i	$-0.707999\pi$
$131$	−16.6047	−	2.92785i	−1.45076	−	0.255807i	−0.842827	+	0.538185i	$0.819110\pi$
$132$	−3.11154	−	0.910944i	−0.270825	−	0.0792875i
$133$	9.14827	−	7.02205i	0.793256	−	0.608889i
$134$		−	5.41386i		−	0.467686i
$135$	4.68544	−	2.82039i	0.403259	−	0.242740i
$136$	−1.95049	−	5.35892i	−0.167253	−	0.459523i
$137$	6.62563	−	18.2038i	0.566066	−	1.55525i	−0.244527	−	0.969642i	$-0.578633\pi$
$137$	6.62563	−	18.2038i	0.566066	−	1.55525i	0.810593	−	0.585610i	$-0.199145\pi$
$138$	−1.53876	+	0.0990192i	−0.130988	+	0.00842907i
$139$	−2.32747	−	13.1998i	−0.197414	−	1.11959i	−0.908939	−	0.416928i	$-0.863107\pi$
$139$	−2.32747	−	13.1998i	−0.197414	−	1.11959i	0.711526	−	0.702660i	$-0.248005\pi$
$140$	−1.52536	−	2.32963i	−0.128917	−	0.196890i
$141$	7.90183	−	7.54638i	0.665454	−	0.635520i
$142$	5.23292	−	4.39094i	0.439137	−	0.368480i
$143$	0.322217	+	1.82739i	0.0269452	+	0.152814i
$144$	−2.52634	−	1.61791i	−0.210528	−	0.134826i
$145$		−	0.562662i		−	0.0467265i
$146$	−0.0595200	−	0.337555i	−0.00492591	−	0.0279362i
$147$	−11.4013	−	4.12433i	−0.940364	−	0.340169i
$148$	2.80989	+	3.34870i	0.230972	+	0.275261i
$149$	−7.00196	+	8.34461i	−0.573623	+	0.683617i	−0.972370	−	0.233444i	$-0.925001\pi$
$149$	−7.00196	+	8.34461i	−0.573623	+	0.683617i	0.398747	+	0.917061i	$0.369445\pi$
$150$	−5.60993	+	3.73880i	−0.458049	+	0.305272i
$151$	0.738010	−	0.426090i	0.0600584	−	0.0346747i	−0.469670	−	0.882842i	$-0.655627\pi$
$151$	0.738010	−	0.426090i	0.0600584	−	0.0346747i	0.529729	+	0.848167i	$0.322294\pi$
$152$	1.89071	−	3.92750i	0.153357	−	0.318562i
$153$	9.22667	−	14.4073i	0.745932	−	1.16476i
$154$	−4.55145	+	1.95221i	−0.366766	+	0.157313i
$155$	−0.810539	+	4.59680i	−0.0651041	+	0.369223i
$156$	−0.188952	+	1.70656i	−0.0151283	+	0.136634i
$157$	−2.31948	+	13.1544i	−0.185115	+	1.04984i	0.740693	+	0.671844i	$0.234497\pi$
$157$	−2.31948	+	13.1544i	−0.185115	+	1.04984i	−0.925808	+	0.377995i	$0.876614\pi$
$158$	7.89065	+	9.40371i	0.627747	+	0.748119i
$159$	−1.23424	+	4.21584i	−0.0978818	+	0.334338i
$160$	−0.911469	−	0.526237i	−0.0720580	−	0.0416027i
$161$	−1.71655	+	1.61282i	−0.135283	+	0.127108i
$162$	−0.741769	−	8.96938i	−0.0582789	−	0.704701i
$163$	0.236322	+	0.409322i	0.0185102	+	0.0320606i	0.875132	−	0.483884i	$-0.160774\pi$
$163$	0.236322	+	0.409322i	0.0185102	+	0.0320606i	−0.856622	+	0.515945i	$0.827441\pi$
$164$	5.91324	−	10.2420i	0.461747	−	0.799768i
$165$	−1.37057	−	3.12492i	−0.106699	−	0.243275i
$166$	4.39720	+	12.0812i	0.341289	+	0.937683i
$167$	−14.4091	+	12.0906i	−1.11501	+	0.935601i	−0.998341	−	0.0575705i	$-0.981665\pi$
$167$	−14.4091	+	12.0906i	−1.11501	+	0.935601i	−0.116664	+	0.993171i	$0.537220\pi$
$168$	−4.54941	+	0.550328i	−0.350995	+	0.0424587i
$169$	−11.2926	+	4.11016i	−0.868660	+	0.316166i
$170$	3.00104	−	5.19796i	0.230170	−	0.398665i
$171$	12.8070	−	2.64229i	0.979373	−	0.202061i
$172$	3.57943	+	6.19975i	0.272929	+	0.472727i
$173$	3.16408	−	17.9444i	0.240561	−	1.36429i	−0.590020	−	0.807389i	$-0.700880\pi$
$173$	3.16408	−	17.9444i	0.240561	−	1.36429i	0.830581	−	0.556899i	$-0.188009\pi$
$174$	−0.829990	−	0.410533i	−0.0629214	−	0.0311224i
$175$	−2.97380	+	9.85933i	−0.224798	+	0.745295i
$176$	−1.20320	+	1.43392i	−0.0906948	+	0.108086i
$177$	−9.21928	+	12.5422i	−0.692963	+	0.942731i
$178$	−3.49968	+	6.06162i	−0.262312	+	0.454337i
$179$	9.21550			0.688798			0.344399	−	0.938823i	$-0.388083\pi$
$179$	9.21550			0.688798			0.344399	+	0.938823i	$0.388083\pi$
$180$	−0.404684	−	3.13138i	−0.0301634	−	0.233399i
$181$	4.87189	−	13.3854i	0.362125	−	0.994930i	−0.616152	−	0.787627i	$-0.711309\pi$
$181$	4.87189	−	13.3854i	0.362125	−	0.994930i	0.978277	−	0.207303i	$-0.0664686\pi$
$182$	1.43671	+	2.19423i	0.106496	+	0.162647i
$183$	−18.6394	+	4.53755i	−1.37786	+	0.335425i
$184$	−0.304481	+	0.836553i	−0.0224466	+	0.0616715i
$185$	−0.798920	+	4.53090i	−0.0587378	+	0.333119i
$186$	6.18940	+	4.54958i	0.453829	+	0.333591i
$187$	−8.17742	−	6.86167i	−0.597992	−	0.501775i
$188$	−2.15759	−	5.92793i	−0.157358	−	0.432339i
$189$	−9.59495	−	9.84565i	−0.697930	−	0.716166i
$190$	4.44561	−	1.13265i	0.322518	−	0.0821712i
$191$	5.58459	+	3.22427i	0.404087	+	0.233300i	0.688246	−	0.725477i	$-0.258381\pi$
$191$	5.58459	+	3.22427i	0.404087	+	0.233300i	−0.284159	+	0.958777i	$0.591714\pi$
$192$	−1.44129	+	0.960564i	−0.104016	+	0.0693227i
$193$	1.39549	+	3.83407i	0.100449	+	0.275983i	0.979730	−	0.200321i	$-0.0641985\pi$
$193$	1.39549	+	3.83407i	0.100449	+	0.275983i	−0.879281	+	0.476304i	$0.841976\pi$
$194$	5.75796	−	1.01528i	0.413397	−	0.0728931i
$195$	−1.50373	+	1.00218i	−0.107684	+	0.0717675i
$196$	−4.82460	+	5.07181i	−0.344614	+	0.362272i
$197$	9.84238	−	5.68250i	0.701241	−	0.404861i	−0.106569	−	0.994305i	$-0.533986\pi$
$197$	9.84238	−	5.68250i	0.701241	−	0.404861i	0.807809	+	0.589444i	$0.200653\pi$
$198$	−5.60961	−	0.258282i	−0.398658	−	0.0183553i
$199$	−3.50429	−	19.8738i	−0.248413	−	1.40882i	−0.812432	−	0.583056i	$-0.801857\pi$
$199$	−3.50429	−	19.8738i	−0.248413	−	1.40882i	0.564019	−	0.825762i	$-0.309254\pi$
$200$	0.675891	+	3.83317i	0.0477927	+	0.271046i
$201$	−2.21797	−	9.11100i	−0.156444	−	0.642640i
$202$	7.74564	−	4.47195i	0.544981	−	0.314645i
$203$	−1.37698	+	0.323361i	−0.0966453	+	0.0226955i
$204$	−5.47794	−	8.21945i	−0.383532	−	0.575476i
$205$	12.2580	−	2.16141i	0.856133	−	0.150959i
$206$	3.18148	+	8.74105i	0.221664	+	0.609018i
$207$	−2.54902	+	0.797046i	−0.177169	+	0.0553985i
$208$	0.858496	+	0.495653i	0.0595260	+	0.0343673i
$209$	−0.610874	−	8.13631i	−0.0422551	−	0.562800i
$210$	−3.52145	−	3.29562i	−0.243003	−	0.227419i
$211$	−1.22419	−	3.36344i	−0.0842769	−	0.231549i	0.890395	−	0.455189i	$-0.150428\pi$
$211$	−1.22419	−	3.36344i	−0.0842769	−	0.231549i	−0.974672	+	0.223640i	$0.928206\pi$
$212$	1.94283	+	1.63023i	0.133434	+	0.111964i
$213$	7.00760	−	9.53337i	0.480153	−	0.653216i
$214$	−1.17607	+	6.66980i	−0.0803942	+	0.455938i
$215$	−2.57695	+	7.08013i	−0.175747	+	0.482861i
$216$	−4.91441	−	1.68778i	−0.334383	−	0.114839i
$217$	11.7154	−	0.658166i	0.795293	−	0.0446792i
$218$	−0.410883	+	1.12889i	−0.0278285	+	0.0764582i
$219$	−0.238457	−	0.543687i	−0.0161135	−	0.0367390i
$220$	−1.97007			−0.132822
$221$	−2.82663	+	4.89586i	−0.190140	+	0.329331i
$222$	6.10068	+	4.48436i	0.409451	+	0.300971i
$223$	−12.2269	+	14.5714i	−0.818773	+	0.975776i	−0.999971	−	0.00767088i	$-0.997558\pi$
$223$	−12.2269	+	14.5714i	−0.818773	+	0.975776i	0.181197	+	0.983447i	$0.442003\pi$
$224$	−0.764022	+	2.53304i	−0.0510484	+	0.169246i
$225$	−7.90924	+	8.59033i	−0.527283	+	0.572689i
$226$	1.50945	−	8.56054i	0.100407	−	0.569439i
$227$	−7.22767	−	12.5187i	−0.479718	−	0.830895i	0.520012	−	0.854159i	$-0.325928\pi$
$227$	−7.22767	−	12.5187i	−0.479718	−	0.830895i	−0.999729	+	0.0232638i	$0.992594\pi$
$228$	1.57284	−	7.38418i	0.104164	−	0.489030i
$229$	3.58839	−	6.21527i	0.237127	−	0.410716i	−0.722762	−	0.691098i	$-0.757127\pi$
$229$	3.58839	−	6.21527i	0.237127	−	0.410716i	0.959889	+	0.280381i	$0.0904608\pi$
$230$	−0.880451	+	0.320458i	−0.0580552	+	0.0211304i
$231$	−6.85985	+	5.15003i	−0.451345	+	0.338847i
$232$	−0.409534	+	0.343640i	−0.0268872	+	0.0225611i
$233$	−3.58117	−	9.83917i	−0.234610	−	0.644585i	−0.999999	−	0.00101822i	$-0.999676\pi$
$233$	−3.58117	−	9.83917i	−0.234610	−	0.644585i	0.765390	−	0.643567i	$-0.222546\pi$
$234$	0.381164	+	2.94939i	0.0249175	+	0.192808i
$235$	3.31970	−	5.74989i	0.216553	−	0.375081i
$236$	4.49353	+	7.78303i	0.292504	+	0.506632i
$237$	17.1317	+	12.5929i	1.11283	+	0.817994i
$238$	−14.4455	−	4.35710i	−0.936362	−	0.282429i
$239$	13.5839	+	7.84269i	0.878672	+	0.507302i	0.870220	−	0.492663i	$-0.163976\pi$
$239$	13.5839	+	7.84269i	0.878672	+	0.507302i	0.00845179	+	0.999964i	$0.497310\pi$
$240$	−1.74950	−	0.512191i	−0.112930	−	0.0330618i
$241$	−15.2525	−	18.1772i	−0.982500	−	1.17090i	−0.985288	−	0.170902i	$-0.945332\pi$
$241$	−15.2525	−	18.1772i	−0.982500	−	1.17090i	0.00278816	−	0.999996i	$-0.499112\pi$
$242$	1.30170	−	7.38229i	0.0836762	−	0.474551i
$243$	−4.92294	−	14.7907i	−0.315807	−	0.948824i
$244$	−1.92328	+	10.9075i	−0.123125	+	0.698279i
$245$	−7.35303	−	0.458627i	−0.469768	−	0.0293006i
$246$	5.75541	−	19.6589i	0.366951	−	1.25341i
$247$	−4.18723	+	1.06682i	−0.266427	+	0.0678803i
$248$	3.84081	−	2.21749i	0.243892	−	0.140811i
$249$	12.3495	+	18.5300i	0.782620	+	1.17429i
$250$	−6.01579	+	7.16934i	−0.380472	+	0.453429i
$251$	−6.44090	−	7.67596i	−0.406546	−	0.484503i	0.523458	−	0.852051i	$-0.324642\pi$
$251$	−6.44090	−	7.67596i	−0.406546	−	0.484503i	−0.930004	+	0.367549i	$0.880197\pi$
$252$	−7.43075	+	2.78997i	−0.468093	+	0.175752i
$253$	0.289367	+	1.64108i	0.0181924	+	0.103174i
$254$			17.2740i			1.08387i
$255$	2.92094	−	9.97714i	0.182916	−	0.624793i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−4.99546	+	4.19169i	−0.311608	+	0.261470i	−0.785156	−	0.619298i	$-0.787417\pi$
$257$	−4.99546	+	4.19169i	−0.311608	+	0.261470i	0.473548	+	0.880768i	$0.342973\pi$
$258$	8.56377	+	8.96714i	0.533157	+	0.558270i
$259$	11.5475	−	0.648731i	0.717525	−	0.0403102i
$260$	0.181171	+	1.02747i	0.0112358	+	0.0637211i
$261$	−1.56498	−	0.350853i	−0.0968699	−	0.0217172i
$262$	−5.76674	+	15.8440i	−0.356270	+	0.978844i
$263$	4.27603	+	11.7483i	0.263671	+	0.724431i	0.998912	+	0.0466256i	$0.0148468\pi$
$263$	4.27603	+	11.7483i	0.263671	+	0.724431i	−0.735241	+	0.677806i	$0.762931\pi$
$264$	−1.43742	+	2.90608i	−0.0884669	+	0.178857i
$265$			2.66926i			0.163972i
$266$	−5.32678	−	10.2287i	−0.326606	−	0.627159i
$267$	−3.40626	+	11.6349i	−0.208460	+	0.712042i
$268$	−5.33161	−	0.940107i	−0.325680	−	0.0574262i
$269$	24.1712	−	8.79760i	1.47374	−	0.536399i	0.524630	−	0.851331i	$-0.324204\pi$
$269$	24.1712	−	8.79760i	1.47374	−	0.536399i	0.949114	+	0.314932i	$0.101982\pi$
$270$	−1.96392	−	5.10401i	−0.119520	−	0.310620i
$271$	12.2404	−	4.45512i	0.743548	−	0.270629i	0.0576601	−	0.998336i	$-0.481636\pi$
$271$	12.2404	−	4.45512i	0.743548	−	0.270629i	0.685888	+	0.727707i	$0.259414\pi$
$272$	−5.61620	+	0.990287i	−0.340532	+	0.0600450i
$273$	3.31679	+	3.10408i	0.200741	+	0.187868i
$274$	−16.7767	−	9.68602i	−1.01352	−	0.585154i
$275$	4.68323	+	5.58125i	0.282409	+	0.336562i
$276$	−0.169688	+	1.53258i	−0.0102140	+	0.0922504i
$277$	−0.0911836			−0.00547869			−0.00273935	−	0.999996i	$-0.500872\pi$
$277$	−0.0911836			−0.00547869			−0.00273935	+	0.999996i	$0.500872\pi$
$278$	−13.4034			−0.803881
$279$	12.2800	+	5.12079i	0.735187	+	0.306574i
$280$	−2.55911	+	1.09766i	−0.152936	+	0.0655975i
$281$	11.4306	−	9.59138i	0.681890	−	0.572174i	−0.234668	−	0.972076i	$-0.575400\pi$
$281$	11.4306	−	9.59138i	0.681890	−	0.572174i	0.916558	+	0.399902i	$0.130956\pi$
$282$	−6.05959	−	9.09220i	−0.360843	−	0.541432i
$283$	17.9900	+	15.0954i	1.06939	+	0.897329i	0.994997	−	0.0999000i	$-0.0318523\pi$
$283$	17.9900	+	15.0954i	1.06939	+	0.897329i	0.0743972	+	0.997229i	$0.476297\pi$
$284$	−3.41555	−	5.91590i	−0.202675	−	0.351044i
$285$	7.01749	−	3.72744i	0.415680	−	0.220794i
$286$	1.85558			0.109723
$287$	−12.3342	−	28.7563i	−0.728064	−	1.69743i
$288$	−2.03202	+	2.20701i	−0.119738	+	0.130049i
$289$	−2.69543	−	15.2865i	−0.158555	−	0.899208i
$290$	−0.554114	−	0.0977052i	−0.0325387	−	0.00573745i
$291$	9.27413	−	4.06756i	0.543659	−	0.238445i
$292$	−0.342762			−0.0200586
$293$	−13.2074	+	22.8760i	−0.771587	+	1.33643i	0.165106	+	0.986276i	$0.447203\pi$
$293$	−13.2074	+	22.8760i	−0.771587	+	1.33643i	−0.936693	+	0.350152i	$0.886130\pi$
$294$	−6.04149	+	10.5119i	−0.352347	+	0.613068i
$295$	−3.23505	+	8.88823i	−0.188352	+	0.517493i
$296$	3.78576	−	2.18571i	0.220043	−	0.127042i
$297$	−9.54624	+	1.86351i	−0.553929	+	0.108132i
$298$	7.00196	+	8.34461i	0.405613	+	0.483390i
$299$	0.829280	−	0.301833i	0.0479585	−	0.0174555i
$300$	2.70785	+	6.17394i	0.156338	+	0.356453i
$301$	18.8079	+	2.23756i	1.08407	+	0.128971i
$302$	−0.291463	−	0.800788i	−0.0167718	−	0.0460802i
$303$	11.2031	−	10.6991i	0.643599	−	0.614648i
$304$	−3.53951	−	2.54399i	−0.203005	−	0.145908i
$305$	−10.0952	+	5.82846i	−0.578049	+	0.333737i
$306$	−12.5862	−	11.5883i	−0.719506	−	0.662459i
$307$	−4.14587	−	0.731029i	−0.236618	−	0.0417221i	0.0540818	−	0.998537i	$-0.482777\pi$
$307$	−4.14587	−	0.731029i	−0.236618	−	0.0417221i	−0.290699	+	0.956814i	$0.593888\pi$
$308$	1.13220	+	4.82130i	0.0645130	+	0.274719i
$309$	8.93519	+	13.4069i	0.508305	+	0.762693i
$310$	4.38621	+	1.59645i	0.249120	+	0.0906723i
$311$	5.67622	+	3.27717i	0.321869	+	0.185831i	0.652225	−	0.758025i	$-0.273836\pi$
$311$	5.67622	+	3.27717i	0.321869	+	0.185831i	−0.330356	+	0.943856i	$0.607169\pi$
$312$	1.64783	+	0.482423i	0.0932897	+	0.0273118i
$313$	3.11054	−	2.61005i	0.175818	−	0.147529i	−0.550632	−	0.834748i	$-0.685613\pi$
$313$	3.11054	−	2.61005i	0.175818	−	0.147529i	0.726450	+	0.687219i	$0.241169\pi$
$314$	12.5518	+	4.56849i	0.708340	+	0.257815i
$315$	−7.27642	−	4.10352i	−0.409980	−	0.231207i
$316$	10.6310	−	6.13784i	0.598043	−	0.345280i
$317$	25.5363	+	9.29444i	1.43426	+	0.522028i	0.938149	−	0.346232i	$-0.112539\pi$
$317$	25.5363	+	9.29444i	1.43426	+	0.522028i	0.496110	+	0.868259i	$0.334761\pi$
$318$	3.93746	+	1.94756i	0.220802	+	0.109214i
$319$	−0.342263	+	0.940359i	−0.0191630	+	0.0526500i
$320$	−0.676517	+	0.806242i	−0.0378185	+	0.0450703i
$321$	0.753308	+	11.7064i	0.0420456	+	0.653389i
$322$	1.29024	+	1.97053i	0.0719022	+	0.109813i
$323$	14.5079	−	20.1853i	0.807243	−	1.12314i
$324$	−8.96192	−	0.827017i	−0.497885	−	0.0459454i
$325$	2.48017	−	2.95575i	0.137575	−	0.163955i
$326$	0.444141	−	0.161654i	0.0245987	−	0.00895318i
$327$	−0.228987	+	2.06815i	−0.0126630	+	0.114369i
$328$	−9.05961	−	7.60192i	−0.500233	−	0.419746i
$329$	−15.9793	−	4.81974i	−0.880969	−	0.265721i
$330$	−3.31544	+	0.807108i	−0.182509	+	0.0444299i
$331$	4.90269	−	2.83057i	0.269476	−	0.155582i	−0.359173	−	0.933271i	$-0.616941\pi$
$331$	4.90269	−	2.83057i	0.269476	−	0.155582i	0.628650	+	0.777689i	$0.283608\pi$
$332$	12.6612	−	2.23252i	0.694875	−	0.122525i
$333$	12.1040	+	5.04739i	0.663296	+	0.276595i
$334$	9.40484	+	16.2897i	0.514610	+	0.891331i
$335$	−2.84897	−	4.93457i	−0.155656	−	0.269604i
$336$	−0.248030	+	4.57586i	−0.0135312	+	0.249634i
$337$	−3.91473	+	4.66539i	−0.213249	+	0.254140i	−0.862056	−	0.506812i	$-0.830824\pi$
$337$	−3.91473	+	4.66539i	−0.213249	+	0.254140i	0.648807	+	0.760953i	$0.275268\pi$
$338$	2.08678	+	11.8347i	0.113506	+	0.643725i
$339$	−0.966854	−	15.0249i	−0.0525123	−	0.816043i
$340$	−4.59787	−	3.85807i	−0.249354	−	0.209233i
$341$	4.15082	−	7.18943i	0.224779	−	0.389329i
$342$	−0.378244	−	13.0712i	−0.0204531	−	0.706811i
$343$	3.10339	+	18.2584i	0.167567	+	0.985861i
$344$	6.72713	−	2.44847i	0.362702	−	0.132013i
$345$	−1.35043	+	0.900006i	−0.0727045	+	0.0484547i
$346$	−17.1223	−	6.23202i	−0.920503	−	0.335036i
$347$	−32.4947	−	5.72969i	−1.74441	−	0.307586i	−0.791572	−	0.611076i	$-0.790737\pi$
$347$	−32.4947	−	5.72969i	−1.74441	−	0.307586i	−0.952835	+	0.303490i	$0.901848\pi$
$348$	−0.548422	+	0.746092i	−0.0293985	+	0.0399947i
$349$	9.07276	+	15.7145i	0.485654	+	0.841177i	0.999864	−	0.0164873i	$-0.00524830\pi$
$349$	9.07276	+	15.7145i	0.485654	+	0.841177i	−0.514210	+	0.857664i	$0.671915\pi$
$350$	9.19315	+	4.64068i	0.491395	+	0.248055i
$351$	1.84978	+	4.80737i	0.0987339	+	0.256599i
$352$	1.20320	+	1.43392i	0.0641309	+	0.0764283i
$353$			8.08519i			0.430331i	0.976578	+	0.215166i	$0.0690292\pi$
$353$			8.08519i			0.430331i	−0.976578	+	0.215166i	$0.930971\pi$
$354$	10.7508	+	11.2571i	0.571397	+	0.598311i
$355$	2.45897	−	6.75597i	0.130509	−	0.358569i
$356$	5.36181	+	4.49910i	0.284176	+	0.238452i
$357$	−26.0954	−	1.41448i	−1.38111	−	0.0748620i
$358$	1.60025	−	9.07549i	0.0845761	−	0.479655i
$359$	−9.18060	−	1.61879i	−0.484533	−	0.0854363i	−0.0739549	−	0.997262i	$-0.523562\pi$
$359$	−9.18060	−	1.61879i	−0.484533	−	0.0854363i	−0.410578	+	0.911825i	$0.634673\pi$
$360$	−3.15408	−	0.145223i	−0.166235	−	0.00765390i
$361$	18.7870	−	2.83705i	0.988789	−	0.149318i
$362$	−12.3361	−	7.12223i	−0.648369	−	0.374336i
$363$	−0.833779	−	12.9570i	−0.0437620	−	0.680064i
$364$	2.41038	−	1.03386i	0.126338	−	0.0541890i
$365$	−0.231885	−	0.276349i	−0.0121374	−	0.0144648i
$366$	1.23192	+	19.1441i	0.0643937	+	1.00068i
$367$	19.2714	−	16.1706i	1.00596	−	0.844099i	0.0181588	−	0.999835i	$-0.494220\pi$
$367$	19.2714	−	16.1706i	1.00596	−	0.844099i	0.987799	+	0.155737i	$0.0497751\pi$
$368$	0.770972	+	0.445121i	0.0401897	+	0.0232035i
$369$	1.63184	−	35.4419i	0.0849504	−	1.84503i
$370$	4.32334	+	1.57357i	0.224760	+	0.0818058i
$371$	6.53240	−	1.53402i	0.339145	−	0.0796424i
$372$	5.55524	−	5.30534i	0.288026	−	0.275069i
$373$			27.0309i			1.39960i	0.714337	+	0.699802i	$0.246729\pi$
$373$			27.0309i			1.39960i	−0.714337	+	0.699802i	$0.753271\pi$
$374$	−8.17742	+	6.86167i	−0.422844	+	0.354809i
$375$	−7.18682	+	14.5299i	−0.371126	+	0.750320i
$376$	−6.21253	+	1.09544i	−0.320387	+	0.0564929i
$377$	0.521909	+	0.0920267i	0.0268797	+	0.00473962i
$378$	−11.3622	+	7.73951i	−0.584410	+	0.398077i
$379$		−	23.7656i		−	1.22076i	−0.792109	−	0.610379i	$-0.791017\pi$
$379$		−	23.7656i		−	1.22076i	0.792109	−	0.610379i	$-0.208983\pi$
$380$	−0.343472	−	4.57475i	−0.0176198	−	0.234680i
$381$	7.07690	+	29.0705i	0.362560	+	1.48933i
$382$	4.14504	−	4.93986i	0.212079	−	0.252745i
$383$	13.0357	+	10.9382i	0.666091	+	0.558917i	0.911906	−	0.410400i	$-0.134611\pi$
$383$	13.0357	+	10.9382i	0.666091	+	0.558917i	−0.245815	+	0.969317i	$0.579055\pi$
$384$	0.695693	+	1.58619i	0.0355019	+	0.0809451i
$385$	−3.12118	+	4.17452i	−0.159070	+	0.212753i
$386$	4.01815	−	0.708508i	0.204518	−	0.0360621i
$387$	18.0857	+	11.5824i	0.919347	+	0.588765i
$388$		−	5.84678i		−	0.296825i
$389$	9.06475	−	1.59836i	0.459601	−	0.0810401i	0.0609461	−	0.998141i	$-0.480588\pi$
$389$	9.06475	−	1.59836i	0.459601	−	0.0810401i	0.398655	+	0.917101i	$0.369477\pi$
$390$	0.725832	+	1.65491i	0.0367540	+	0.0837998i
$391$	−2.53845	+	4.39673i	−0.128375	+	0.222352i
$392$	4.15697	+	5.63201i	0.209959	+	0.284460i
$393$	−3.21382	+	29.0264i	−0.162116	+	1.46419i
$394$	−3.88706	−	10.6796i	−0.195827	−	0.538031i
$395$	12.1407	+	4.41884i	0.610863	+	0.222336i
$396$	−1.22846	+	5.47954i	−0.0617323	+	0.275357i
$397$	−3.38529	+	19.1989i	−0.169903	+	0.963567i	0.773961	+	0.633233i	$0.218273\pi$
$397$	−3.38529	+	19.1989i	−0.169903	+	0.963567i	−0.943864	+	0.330334i	$0.892839\pi$
$398$	−20.1804			−1.01155
$399$	−13.1550	−	15.0315i	−0.658572	−	0.752517i
$400$	3.89230			0.194615
$401$	−2.81272	+	15.9517i	−0.140460	+	0.796590i	0.830440	+	0.557108i	$0.188089\pi$
$401$	−2.81272	+	15.9517i	−0.140460	+	0.796590i	−0.970901	+	0.239483i	$0.923022\pi$
$402$	−9.35773	+	0.602169i	−0.466721	+	0.0300335i
$403$	−4.13129	−	1.50367i	−0.205794	−	0.0749030i
$404$	−3.05899	−	8.40451i	−0.152191	−	0.418140i
$405$	−5.39612	−	7.78497i	−0.268135	−	0.386838i
$406$	0.0793376	+	1.41222i	0.00393746	+	0.0700871i
$407$	4.09132	−	7.08637i	0.202799	−	0.351258i
$408$	−9.04581	+	3.96742i	−0.447834	+	0.196417i
$409$	23.7841	−	4.19377i	1.17605	−	0.207369i	0.448728	−	0.893668i	$-0.351877\pi$
$409$	23.7841	−	4.19377i	1.17605	−	0.207369i	0.727319	+	0.686300i	$0.240766\pi$
$410$		−	12.4471i		−	0.614717i
$411$	−32.2017	−	9.42748i	−1.58839	−	0.465023i
$412$	9.16071	−	1.61528i	0.451316	−	0.0795791i
$413$	23.6110	+	2.80898i	1.16182	+	0.138221i
$414$	0.342304	+	2.64870i	0.0168233	+	0.130176i
$415$	10.3655	+	8.69767i	0.508822	+	0.426952i
$416$	0.637199	−	0.759384i	0.0312412	−	0.0372319i
$417$	−22.5566	+	5.49115i	−1.10460	+	0.268903i
$418$	−8.11878	−	0.811262i	−0.397103	−	0.0396801i
$419$			16.9464i			0.827887i	0.910303	+	0.413944i	$0.135849\pi$
$419$			16.9464i			0.827887i	−0.910303	+	0.413944i	$0.864151\pi$
$420$	−3.85704	+	2.89567i	−0.188205	+	0.141294i
$421$	15.2275	+	2.68502i	0.742144	+	0.130860i	0.531922	−	0.846794i	$-0.321470\pi$
$421$	15.2275	+	2.68502i	0.742144	+	0.130860i	0.210222	+	0.977654i	$0.432581\pi$
$422$	−3.52492	+	0.621539i	−0.171590	+	0.0302560i
$423$	−13.9226	−	12.8188i	−0.676941	−	0.623269i
$424$	1.94283	−	1.63023i	0.0943520	−	0.0791707i
$425$			22.1972i			1.07672i
$426$	−8.17168	−	8.55659i	−0.395919	−	0.414568i
$427$	20.0655	+	21.3560i	0.971037	+	1.03349i
$428$	6.36425	+	2.31640i	0.307628	+	0.111967i
$429$	3.12275	−	0.760200i	0.150768	−	0.0367028i
$430$	6.52508	+	3.76726i	0.314667	+	0.181673i
$431$	5.98267	−	5.02006i	0.288175	−	0.241808i	−0.487227	−	0.873275i	$-0.661992\pi$
$431$	5.98267	−	5.02006i	0.288175	−	0.241808i	0.775402	+	0.631468i	$0.217547\pi$
$432$	−2.51552	+	4.54667i	−0.121028	+	0.218752i
$433$	−8.93963	−	10.6538i	−0.429611	−	0.511991i	0.507199	−	0.861829i	$-0.330681\pi$
$433$	−8.93963	−	10.6538i	−0.429611	−	0.511991i	−0.936810	+	0.349838i	$0.886237\pi$
$434$	1.38619	−	11.6517i	0.0665393	−	0.559300i
$435$	−0.972548	+	0.0625834i	−0.0466301	+	0.00300064i
$436$	1.04039	+	0.600671i	0.0498257	+	0.0287669i
$437$	−3.76034	+	0.958060i	−0.179882	+	0.0458302i
$438$	−0.576835	+	0.140424i	−0.0275623	+	0.00670973i
$439$	−28.6338	−	5.04892i	−1.36662	−	0.240972i	−0.558262	−	0.829665i	$-0.688532\pi$
$439$	−28.6338	−	5.04892i	−1.36662	−	0.240972i	−0.808357	+	0.588693i	$0.799643\pi$
$440$	−0.342100	+	1.94014i	−0.0163090	+	0.0924928i
$441$	−5.86066	+	20.1656i	−0.279079	+	0.960268i
$442$	4.33064	+	3.63384i	0.205988	+	0.172844i
$443$	−12.2672	+	33.7038i	−0.582832	+	1.60132i	0.200486	+	0.979697i	$0.435748\pi$
$443$	−12.2672	+	33.7038i	−0.582832	+	1.60132i	−0.783318	+	0.621621i	$0.786474\pi$
$444$	5.47561	−	5.22929i	0.259861	−	0.248171i
$445$			7.36663i			0.349212i
$446$	12.2269	+	14.5714i	0.578960	+	0.689978i
$447$	15.2023	+	11.1746i	0.719043	+	0.528539i
$448$	2.36188	+	1.19227i	0.111588	+	0.0563296i
$449$	−11.6109	−	20.1106i	−0.547951	−	0.949079i	−0.998415	−	0.0562844i	$-0.982075\pi$
$449$	−11.6109	−	20.1106i	−0.547951	−	0.949079i	0.450464	−	0.892795i	$-0.351259\pi$
$450$	7.08640	+	9.28078i	0.334056	+	0.437500i
$451$	−21.8011	−	3.84412i	−1.02657	−	0.181013i
$452$	−8.16837	−	2.97304i	−0.384208	−	0.139840i
$453$	−0.818574	−	1.22824i	−0.0384599	−	0.0577077i
$454$	−13.5836	+	4.94402i	−0.637509	+	0.232034i
$455$	2.46421	+	1.24392i	0.115524	+	0.0583161i
$456$	−6.99888	−	2.83120i	−0.327753	−	0.132583i
$457$	15.7196	−	27.2272i	0.735334	−	1.27364i	−0.219243	−	0.975670i	$-0.570359\pi$
$457$	15.7196	−	27.2272i	0.735334	−	1.27364i	0.954577	−	0.297965i	$-0.0963080\pi$
$458$	−5.49773	−	4.61314i	−0.256892	−	0.215558i
$459$	−25.9289	−	14.3456i	−1.21026	−	0.669595i
$460$	0.162701	+	0.922722i	0.00758596	+	0.0430221i
$461$	7.20753	−	8.58960i	0.335688	−	0.400058i	−0.571624	−	0.820516i	$-0.693686\pi$
$461$	7.20753	−	8.58960i	0.335688	−	0.400058i	0.907312	+	0.420458i	$0.138131\pi$
$462$	3.88059	+	7.64993i	0.180541	+	0.355907i
$463$	6.03312	+	10.4497i	0.280383	+	0.485637i	0.971479	−	0.237126i	$-0.0762053\pi$
$463$	6.03312	+	10.4497i	0.280383	+	0.485637i	−0.691096	+	0.722763i	$0.742872\pi$
$464$	0.267305	+	0.462985i	0.0124093	+	0.0214935i
$465$	8.03560	+	0.889708i	0.372642	+	0.0412592i
$466$	−10.3116	+	1.81821i	−0.477674	+	0.0842267i
$467$	16.8168	−	9.70918i	0.778188	−	0.449287i	−0.0575997	−	0.998340i	$-0.518345\pi$
$467$	16.8168	−	9.70918i	0.778188	−	0.449287i	0.835788	+	0.549053i	$0.185011\pi$
$468$	2.97077	+	0.136782i	0.137324	+	0.00632277i
$469$	−10.4389	+	9.80809i	−0.482024	+	0.452895i
$470$	−5.08607	−	4.26772i	−0.234603	−	0.196855i
$471$	22.9951	+	2.54604i	1.05956	+	0.117315i
$472$	8.44508	−	3.07376i	0.388716	−	0.141481i
$473$	8.61356	−	10.2652i	0.396052	−	0.471996i
$474$	15.3764	−	14.6848i	0.706263	−	0.674493i
$475$	−12.1438	+	11.8481i	−0.557198	+	0.543627i
$476$	−6.79934	+	13.4694i	−0.311647	+	0.617370i
$477$	7.42425	+	1.66444i	0.339933	+	0.0762096i
$478$	10.0824	−	12.0157i	0.461157	−	0.549585i
$479$	−8.54178	+	23.4683i	−0.390284	+	1.07230i	0.576588	+	0.817035i	$0.304384\pi$
$479$	−8.54178	+	23.4683i	−0.390284	+	1.07230i	−0.966872	+	0.255261i	$0.917839\pi$
$480$	−0.808208	+	1.63398i	−0.0368895	+	0.0745808i
$481$	−4.07207	−	1.48211i	−0.185670	−	0.0675785i
$482$	−20.5496	+	11.8643i	−0.936010	+	0.540406i
$483$	2.97864	+	2.78762i	0.135533	+	0.126841i
$484$	−7.04410	−	2.56384i	−0.320186	−	0.116538i
$485$	4.71392	−	3.95545i	0.214048	−	0.179608i
$486$	−15.4209	+	2.27977i	−0.699504	+	0.103412i
$487$	−15.2365	−	8.79681i	−0.690432	−	0.398621i	0.113342	−	0.993556i	$-0.463845\pi$
$487$	−15.2365	−	8.79681i	−0.690432	−	0.398621i	−0.803774	+	0.594935i	$0.797178\pi$
$488$	10.4078	+	3.78812i	0.471138	+	0.171480i
$489$	0.681218	−	0.454005i	0.0308057	−	0.0205308i
$490$	−1.72850	+	7.16168i	−0.0780856	+	0.323532i
$491$	24.0923	+	4.24813i	1.08727	+	0.191715i	0.688429	−	0.725304i	$-0.258301\pi$
$491$	24.0923	+	4.24813i	1.08727	+	0.191715i	0.398843	+	0.917019i	$0.369412\pi$
$492$	−18.3608	−	9.08170i	−0.827770	−	0.409435i
$493$	−2.64033	+	1.52439i	−0.118914	+	0.0686553i
$494$	0.323510	+	4.30887i	0.0145554	+	0.193865i
$495$	−5.24891	+	2.71657i	−0.235921	+	0.122101i
$496$	−1.51686	−	4.16753i	−0.0681088	−	0.187127i
$497$	−17.9468	−	2.13511i	−0.805025	−	0.0957730i
$498$	20.3930	−	8.94421i	0.913831	−	0.400800i
$499$	33.2049	−	12.0856i	1.48646	−	0.541026i	0.533943	−	0.845521i	$-0.320710\pi$
$499$	33.2049	−	12.0856i	1.48646	−	0.541026i	0.952514	+	0.304495i	$0.0984875\pi$
$500$	6.01579	+	7.16934i	0.269034	+	0.320623i
$501$	22.5010	+	23.5609i	1.00527	+	1.05262i
$502$	−8.67780	+	5.01013i	−0.387309	+	0.223613i
$503$	−7.45363	+	20.4787i	−0.332341	+	0.913099i	0.655161	+	0.755490i	$0.272601\pi$
$503$	−7.45363	+	20.4787i	−0.332341	+	0.913099i	−0.987502	+	0.157610i	$0.949621\pi$
$504$	1.45725	+	7.80234i	0.0649109	+	0.347544i
$505$	4.70661	−	8.15208i	0.209441	−	0.362763i
$506$	1.66640			0.0740805
$507$	8.36036	+	19.0618i	0.371297	+	0.846564i
$508$	17.0116	+	2.99960i	0.754768	+	0.133086i
$509$	2.97926	+	16.8962i	0.132053	+	0.748911i	0.976867	+	0.213850i	$0.0686003\pi$
$509$	2.97926	+	16.8962i	0.132053	+	0.748911i	−0.844813	+	0.535061i	$0.820289\pi$
$510$	−9.31835	−	4.60908i	−0.412623	−	0.204093i
$511$	−0.543037	+	0.726301i	−0.0240225	+	0.0321297i
$512$	1.00000			0.0441942
$513$	−5.99162	−	21.8426i	−0.264537	−	0.964376i
$514$	3.26055	+	5.64744i	0.143817	+	0.249098i
$515$	7.49968	+	6.29298i	0.330475	+	0.277302i
$516$	10.3180	−	6.87654i	0.454224	−	0.302723i
$517$	−9.04571	+	7.59025i	−0.397830	+	0.333819i
$518$	1.36632	−	11.4847i	0.0600327	−	0.504608i
$519$	−31.3684	−	3.47313i	−1.37692	−	0.152454i
$520$	1.04332			0.0457527
$521$	29.1163			1.27561			0.637804	−	0.770199i	$-0.279843\pi$
$521$	29.1163			1.27561			0.637804	+	0.770199i	$0.279843\pi$
$522$	−0.617278	+	1.48028i	−0.0270175	+	0.0647901i
$523$	−18.8838	−	22.5048i	−0.825731	−	0.984068i	0.174269	−	0.984698i	$-0.444244\pi$
$523$	−18.8838	−	22.5048i	−0.825731	−	0.984068i	−1.00000		0.000630178i	$0.999799\pi$
$524$	14.6019	+	8.43040i	0.637886	+	0.368284i
$525$	17.3724	+	4.04352i	0.758193	+	0.176474i
$526$	12.3123	−	2.17100i	0.536844	−	0.0946600i
$527$	23.7667	−	8.65038i	1.03529	−	0.376816i
$528$	2.61233	+	1.92022i	0.113687	+	0.0835667i
$529$	−20.8682	+	7.59540i	−0.907313	+	0.330235i
$530$	2.62871	+	0.463513i	0.114184	+	0.0201337i
$531$	22.7044	+	14.5403i	0.985285	+	0.630993i
$532$	−10.9982	+	3.46967i	−0.476834	+	0.150429i
$533$			11.7237i			0.507808i
$534$	10.8666	+	5.37489i	0.470245	+	0.232594i
$535$	2.43795	+	6.69820i	0.105402	+	0.289589i
$536$	−1.85165	+	5.08737i	−0.0799791	+	0.219741i
$537$	−1.02501	−	15.9288i	−0.0442326	−	0.687377i
$538$	−4.46666	−	25.3317i	−0.192571	−	1.09213i
$539$	12.0099	+	5.23927i	0.517303	+	0.225671i
$540$	−5.36750	+	1.04778i	−0.230981	+	0.0450893i
$541$	−3.88423	+	3.25926i	−0.166996	+	0.140127i	−0.722456	−	0.691417i	$-0.756987\pi$
$541$	−3.88423	+	3.25926i	−0.166996	+	0.140127i	0.555460	+	0.831544i	$0.312542\pi$
$542$	−2.26193	−	12.8280i	−0.0971580	−	0.551011i
$543$	−23.6783	−	6.93213i	−1.01613	−	0.297486i
$544$			5.70284i			0.244507i
$545$	0.219557	+	1.24517i	0.00940480	+	0.0533373i
$546$	3.63288	−	2.72738i	0.155473	−	0.116721i
$547$	1.44754	+	1.72511i	0.0618922	+	0.0737603i	0.796102	−	0.605162i	$-0.206892\pi$
$547$	1.44754	+	1.72511i	0.0618922	+	0.0737603i	−0.734210	+	0.678922i	$0.762447\pi$
$548$	−12.4521	+	14.8398i	−0.531928	+	0.633927i
$549$	9.91626	+	31.7130i	0.423215	+	1.35348i
$550$	6.30969	−	3.64290i	0.269046	−	0.155334i
$551$	−2.24330	−	0.630828i	−0.0955677	−	0.0268742i
$552$	1.47983	+	0.433240i	0.0629857	+	0.0184399i
$553$	3.83686	−	32.2510i	0.163160	−	1.37145i
$554$	−0.0158339	+	0.0897984i	−0.000672717	+	0.00381517i
$555$	7.92042	+	0.876954i	0.336203	+	0.0372246i
$556$	−2.32747	+	13.1998i	−0.0987068	+	0.559794i
$557$	−7.40307	−	8.82264i	−0.313678	−	0.373827i	0.586052	−	0.810273i	$-0.300681\pi$
$557$	−7.40307	−	8.82264i	−0.313678	−	0.373827i	−0.899730	+	0.436446i	$0.856237\pi$
$558$	7.17540	−	11.2043i	0.303759	−	0.474314i
$559$	−6.14585	−	3.54831i	−0.259942	−	0.150077i
$560$	0.636594	+	2.71084i	0.0269010	+	0.114554i
$561$	−10.9507	+	14.8977i	−0.462338	+	0.628981i
$562$	−7.46077	−	12.9224i	−0.314714	−	0.545100i
$563$	4.28352	−	7.41927i	0.180529	−	0.312685i	−0.761532	−	0.648127i	$-0.775552\pi$
$563$	4.28352	−	7.41927i	0.180529	−	0.312685i	0.942061	+	0.335442i	$0.108886\pi$
$564$	−10.0063	+	4.38869i	−0.421341	+	0.184797i
$565$	−3.12905	−	8.59700i	−0.131640	−	0.361678i
$566$	17.9900	−	15.0954i	0.756176	−	0.634507i
$567$	−15.9508	+	17.6798i	−0.669869	+	0.742480i
$568$	−6.41913	+	2.33637i	−0.269341	+	0.0980320i
$569$	14.2910	−	24.7527i	0.599109	−	1.03769i	−0.393843	−	0.919178i	$-0.628855\pi$
$569$	14.2910	−	24.7527i	0.599109	−	1.03769i	0.992953	−	0.118510i	$-0.0378119\pi$
$570$	−2.45223	−	7.55814i	−0.102713	−	0.316576i
$571$	−2.53556	−	4.39171i	−0.106110	−	0.183788i	0.808081	−	0.589071i	$-0.200506\pi$
$571$	−2.53556	−	4.39171i	−0.106110	−	0.183788i	−0.914191	+	0.405283i	$0.867173\pi$
$572$	0.322217	−	1.82739i	0.0134726	−	0.0764069i
$573$	4.95191	−	10.0115i	0.206869	−	0.418235i
$574$	−30.4613	+	7.15331i	−1.27143	+	0.298573i
$575$	2.22731	−	2.65441i	0.0928854	−	0.110697i
$576$	1.82062	+	2.38439i	0.0758592	+	0.0993498i
$577$	−17.3353	+	30.0257i	−0.721679	+	1.24998i	0.238648	+	0.971106i	$0.423296\pi$
$577$	−17.3353	+	30.0257i	−0.721679	+	1.24998i	−0.960326	+	0.278878i	$0.910037\pi$
$578$	−15.5224			−0.645645
$579$	6.47189	−	2.83852i	0.268963	−	0.117965i
$580$	−0.192442	+	0.528729i	−0.00799071	+	0.0219543i
$581$	15.3285	−	30.3656i	0.635933	−	1.25978i
$582$	−2.39533	−	9.83956i	−0.0992898	−	0.407863i
$583$	1.62369	−	4.46105i	0.0672464	−	0.184758i
$584$	−0.0595200	+	0.337555i	−0.00246296	+	0.0139681i
$585$	1.89950	+	2.48769i	0.0785345	+	0.102853i
$586$	20.2350	+	16.9792i	0.835899	+	0.701402i
$587$	−14.3723	−	39.4875i	−0.593207	−	1.62982i	−0.764515	−	0.644606i	$-0.777021\pi$
$587$	−14.3723	−	39.4875i	−0.593207	−	1.62982i	0.171307	−	0.985218i	$-0.445201\pi$
$588$	9.30313	+	7.77508i	0.383654	+	0.320639i
$589$	17.4184	+	8.38526i	0.717713	+	0.345509i
$590$	8.19144	+	4.72933i	0.337236	+	0.194703i
$591$	−10.9168	−	16.3803i	−0.449057	−	0.673794i
$592$	−1.49511	−	4.10779i	−0.0614487	−	0.168829i
$593$	15.9065	−	2.80475i	0.653203	−	0.115177i	0.162781	−	0.986662i	$-0.447954\pi$
$593$	15.9065	−	2.80475i	0.653203	−	0.115177i	0.490422	+	0.871485i	$0.336843\pi$
$594$	0.177507	+	9.72481i	0.00728322	+	0.399014i
$595$	−15.4595	+	3.63039i	−0.633777	+	0.148832i
$596$	9.43372	−	5.44656i	0.386420	−	0.223100i
$597$	−33.9617	+	8.26760i	−1.38996	+	0.338370i
$598$	−0.153245	−	0.869094i	−0.00626664	−	0.0355399i
$599$	−4.63783	−	26.3025i	−0.189497	−	1.07469i	−0.920040	−	0.391823i	$-0.871844\pi$
$599$	−4.63783	−	26.3025i	−0.189497	−	1.07469i	0.730544	−	0.682866i	$-0.239267\pi$
$600$	6.55036	−	1.59461i	0.267417	−	0.0650998i
$601$	−24.0442	+	13.8819i	−0.980783	+	0.566256i	−0.902507	−	0.430676i	$-0.858275\pi$
$601$	−24.0442	+	13.8819i	−0.980783	+	0.566256i	−0.0782768	+	0.996932i	$0.524942\pi$
$602$	5.46953	−	18.1336i	0.222921	−	0.739072i
$603$	−15.5014	+	4.84710i	−0.631267	+	0.197389i
$604$	−0.839234	+	0.147980i	−0.0341480	+	0.00602120i
$605$	−2.69838	−	7.41373i	−0.109705	−	0.301411i
$606$	−8.59118	−	12.8907i	−0.348993	−	0.523651i
$607$	−31.6139	−	18.2523i	−1.28317	−	0.740838i	−0.305742	−	0.952114i	$-0.598905\pi$
$607$	−31.6139	−	18.2523i	−1.28317	−	0.740838i	−0.977426	+	0.211277i	$0.932238\pi$
$608$	−3.11997	+	3.04398i	−0.126531	+	0.123450i
$609$	0.712080	+	2.34412i	0.0288549	+	0.0949884i
$610$	3.98690	+	10.9539i	0.161425	+	0.443511i
$611$	4.79048	+	4.01969i	0.193802	+	0.162619i
$612$	−13.5978	+	10.3827i	−0.549659	+	0.419696i
$613$	−1.43409	+	8.13314i	−0.0579224	+	0.328494i	−0.999976	−	0.00696891i	$-0.997782\pi$
$613$	−1.43409	+	8.13314i	−0.0579224	+	0.328494i	0.942053	+	0.335463i	$0.108893\pi$
$614$	−1.43985	+	3.95595i	−0.0581075	+	0.159649i
$615$	−5.09936	−	20.9472i	−0.205626	−	0.844672i
$616$	4.94466	−	0.277789i	0.199226	−	0.0111924i
$617$	−13.1198	+	36.0464i	−0.528184	+	1.45117i	0.333023	+	0.942919i	$0.391931\pi$
$617$	−13.1198	+	36.0464i	−0.528184	+	1.45117i	−0.861207	+	0.508254i	$0.830291\pi$
$618$	14.7548	−	6.47135i	0.593526	−	0.260316i
$619$	0.660794			0.0265595			0.0132798	−	0.999912i	$-0.495773\pi$
$619$	0.660794			0.0265595			0.0132798	+	0.999912i	$0.495773\pi$
$620$	2.33385	−	4.04235i	0.0937298	−	0.162345i
$621$	1.66119	+	4.31726i	0.0666614	+	0.173246i
$622$	4.21305	−	5.02091i	0.168928	−	0.201320i
$623$	18.0281	−	4.23359i	0.722281	−	0.169615i
$624$	0.761236	−	1.53902i	0.0304738	−	0.0616101i
$625$	1.66902	−	9.46546i	0.0667607	−	0.378619i
$626$	−2.03026	−	3.51651i	−0.0811455	−	0.140548i
$627$	−13.9955	+	1.96086i	−0.558925	+	0.0783093i
$628$	6.67868	−	11.5678i	0.266508	−	0.461606i
$629$	23.4260	−	8.52638i	0.934057	−	0.339969i
$630$	−5.30472	+	6.45331i	−0.211345	+	0.257106i
$631$	30.5970	−	25.6739i	1.21805	−	1.02206i	0.219122	−	0.975697i	$-0.429681\pi$
$631$	30.5970	−	25.6739i	1.21805	−	1.02206i	0.998925	−	0.0463650i	$-0.0147637\pi$
$632$	−4.19853	−	11.5354i	−0.167009	−	0.458852i
$633$	−5.67746	+	2.49009i	−0.225659	+	0.0989723i
$634$	13.5876	−	23.5343i	0.539631	−	0.934668i
$635$	9.09023	+	15.7447i	0.360735	+	0.624811i
$636$	2.60171	−	3.53945i	0.103164	−	0.140349i
$637$	1.62804	−	6.74545i	0.0645053	−	0.267265i
$638$	0.866639	+	0.500354i	0.0343106	+	0.0198092i
$639$	−17.2576	−	11.0521i	−0.682702	−	0.437214i
$640$	0.676517	+	0.806242i	0.0267417	+	0.0318695i
$641$	−4.68205	+	26.5532i	−0.184930	+	1.04879i	0.741116	+	0.671377i	$0.234297\pi$
$641$	−4.68205	+	26.5532i	−0.184930	+	1.04879i	−0.926046	+	0.377412i	$0.876814\pi$
$642$	11.6594	+	1.29094i	0.460160	+	0.0509492i
$643$	−3.68150	+	20.8788i	−0.145184	+	0.823380i	0.822035	+	0.569437i	$0.192839\pi$
$643$	−3.68150	+	20.8788i	−0.145184	+	0.823380i	−0.967219	+	0.253943i	$0.918272\pi$
$644$	2.16464	−	0.928459i	0.0852988	−	0.0365864i
$645$	12.5245	+	3.66670i	0.493150	+	0.144376i
$646$	−17.3593	−	17.7927i	−0.682993	−	0.700043i
$647$	10.7066	−	6.18146i	0.420920	−	0.243018i	−0.274551	−	0.961573i	$-0.588529\pi$
$647$	10.7066	−	6.18146i	0.420920	−	0.243018i	0.695471	+	0.718554i	$0.255196\pi$
$648$	−2.37067	+	8.68216i	−0.0931289	+	0.341067i
$649$	10.8133	−	12.8868i	0.424458	−	0.505849i
$650$	−2.48017	−	2.95575i	−0.0972802	−	0.115934i
$651$	−2.44070	−	20.1766i	−0.0956584	−	0.790783i
$652$	−0.0820739	−	0.465464i	−0.00321426	−	0.0182290i
$653$			41.8445i			1.63750i	0.574148	+	0.818751i	$0.305333\pi$
$653$			41.8445i			1.63750i	−0.574148	+	0.818751i	$0.694667\pi$
$654$	1.99696	+	0.584638i	0.0780874	+	0.0228611i
$655$	3.08148	+	17.4760i	0.120404	+	0.682842i
$656$	−9.05961	+	7.60192i	−0.353718	+	0.296805i
$657$	−0.913228	+	0.472641i	−0.0356284	+	0.0184395i
$658$	−7.52130	+	14.8996i	−0.293211	+	0.580848i
$659$	−4.25222	−	24.1156i	−0.165643	−	0.939409i	−0.948399	−	0.317080i	$-0.897298\pi$
$659$	−4.25222	−	24.1156i	−0.165643	−	0.939409i	0.782756	−	0.622329i	$-0.213813\pi$
$660$	0.219126	+	3.40523i	0.00852947	+	0.132548i
$661$	7.14974	−	19.6438i	0.278093	−	0.764054i	−0.719486	−	0.694507i	$-0.755623\pi$
$661$	7.14974	−	19.6438i	0.278093	−	0.764054i	0.997579	−	0.0695466i	$-0.0221553\pi$
$662$	−1.93622	−	5.31973i	−0.0752534	−	0.206757i
$663$	8.77678	+	4.34120i	0.340862	+	0.168598i
$664$		−	12.8565i		−	0.498931i
$665$	−10.2379	−	6.51995i	−0.397009	−	0.252833i
$666$	7.07255	−	11.0437i	0.274056	−	0.427933i
$667$	0.468701	+	0.0826446i	0.0181482	+	0.00320001i
$668$	17.6753	−	6.43329i	0.683879	−	0.248911i
$669$	26.5463	+	19.5131i	1.02634	+	0.754422i
$670$	−5.35432	+	1.94881i	−0.206855	+	0.0752892i
$671$	20.4172	−	3.60010i	0.788196	−	0.138980i
$672$	4.46327	+	1.03885i	0.172174	+	0.0400746i
$673$	6.07430	+	3.50700i	0.234147	+	0.135185i	0.612484	−	0.790483i	$-0.290171\pi$
$673$	6.07430	+	3.50700i	0.234147	+	0.135185i	−0.378337	+	0.925668i	$0.623504\pi$
$674$	3.91473	+	4.66539i	0.150790	+	0.179704i
$675$	15.7279	+	12.7154i	0.605367	+	0.489418i
$676$	12.0173			0.462204
$677$	−40.8056			−1.56828			−0.784142	−	0.620581i	$-0.786897\pi$
$677$	−40.8056			−1.56828			−0.784142	+	0.620581i	$0.786897\pi$
$678$	−14.9646	−	1.65689i	−0.574711	−	0.0636325i
$679$	−12.3891	−	9.26303i	−0.475451	−	0.355482i
$680$	−4.59787	+	3.85807i	−0.176320	+	0.147950i
$681$	−20.8344	+	13.8853i	−0.798374	+	0.532085i
$682$	−6.35942	−	5.33619i	−0.243515	−	0.204333i
$683$	−15.6213	−	27.0569i	−0.597732	−	1.03530i	−0.993155	−	0.116803i	$-0.962735\pi$
$683$	−15.6213	−	27.0569i	−0.597732	−	1.03530i	0.395423	−	0.918499i	$-0.370598\pi$
$684$	−12.9383	−	1.89730i	−0.494709	−	0.0725449i
$685$	−20.3886			−0.779007
$686$	18.5199	+	0.114293i	0.707093	+	0.00436373i
$687$	−11.1421	−	5.51113i	−0.425096	−	0.210263i
$688$	−1.24312	−	7.05010i	−0.0473936	−	0.268783i
$689$	−2.47593	−	0.436574i	−0.0943256	−	0.0166321i
$690$	0.651834	+	1.48619i	0.0248149	+	0.0565784i
$691$	−0.308250			−0.0117264			−0.00586320	−	0.999983i	$-0.501866\pi$
$691$	−0.308250			−0.0117264			−0.00586320	+	0.999983i	$0.501866\pi$
$692$	−9.11061	+	15.7800i	−0.346333	+	0.599867i
$693$	9.66471	+	11.2843i	0.367132	+	0.428654i
$694$	−11.2853	+	31.0061i	−0.428384	+	1.17697i
$695$	−12.2168	+	7.05335i	−0.463408	+	0.267549i
$696$	0.639525	+	0.669648i	0.0242411	+	0.0253829i
$697$	−43.3525	−	51.6655i	−1.64209	−	1.95697i
$698$	17.0512	−	6.20613i	0.645398	−	0.234906i
$699$	−16.6084	+	7.28434i	−0.628189	+	0.275519i
$700$	6.16655	−	8.24764i	0.233074	−	0.311732i
$701$	−15.5894	−	42.8316i	−0.588805	−	1.61773i	−0.772692	−	0.634781i	$-0.781091\pi$
$701$	−15.5894	−	42.8316i	−0.588805	−	1.61773i	0.183888	−	0.982947i	$-0.441132\pi$
$702$	5.05555	−	0.986885i	0.190809	−	0.0372476i
$703$	17.1687	+	8.26506i	0.647530	+	0.311723i
$704$	1.62107	−	0.935926i	0.0610964	−	0.0352740i
$705$	−10.3078	−	5.09847i	−0.388213	−	0.192020i
$706$	7.96236	+	1.40398i	0.299667	+	0.0528395i
$707$	−22.6552	−	6.83334i	−0.852037	−	0.256994i
$708$	12.9530	−	8.63265i	0.486803	−	0.324435i
$709$	−34.7035	−	12.6310i	−1.30332	−	0.474369i	−0.405242	−	0.914210i	$-0.632813\pi$
$709$	−34.7035	−	12.6310i	−1.30332	−	0.474369i	−0.898076	+	0.439841i	$0.855035\pi$
$710$	−6.22633	−	3.59477i	−0.233670	−	0.134909i
$711$	19.8609	−	31.0125i	0.744843	−	1.16306i
$712$	5.36181	−	4.49910i	0.200942	−	0.168611i
$713$	−3.71010	−	1.35037i	−0.138944	−	0.0505717i
$714$	−5.92440	+	25.4533i	−0.221715	+	0.952566i
$715$	1.69130	−	0.976473i	0.0632511	−	0.0365180i
$716$	−8.65973	−	3.15189i	−0.323629	−	0.117791i
$717$	12.0450	−	24.3518i	0.449829	−	0.909436i
$718$	−3.18839	+	8.76002i	−0.118990	+	0.326921i
$719$	−23.6103	+	28.1377i	−0.880516	+	1.04936i	0.117897	+	0.993026i	$0.462385\pi$
$719$	−23.6103	+	28.1377i	−0.880516	+	1.04936i	−0.998412	+	0.0563317i	$0.982060\pi$
$720$	−0.690717	+	3.08094i	−0.0257415	+	0.114820i
$721$	11.0905	−	21.9703i	0.413034	−	0.818216i
$722$	0.468381	−	18.9942i	0.0174313	−	0.706892i
$723$	−29.7224	+	28.3854i	−1.10539	+	1.05566i
$724$	−9.15617	+	10.9119i	−0.340286	+	0.405537i
$725$	1.95537	−	0.711695i	0.0726205	−	0.0264317i
$726$	−12.9049	−	1.42884i	−0.478945	−	0.0530292i
$727$	−5.65877	−	4.74827i	−0.209872	−	0.176104i	0.531792	−	0.846875i	$-0.321519\pi$
$727$	−5.65877	−	4.74827i	−0.209872	−	0.176104i	−0.741664	+	0.670771i	$0.765963\pi$
$728$	−0.599596	−	2.55329i	−0.0222225	−	0.0946312i
$729$	−25.0178	+	10.1543i	−0.926585	+	0.376085i
$730$	−0.312417	+	0.180374i	−0.0115631	+	0.00667595i
$731$	40.2056	−	7.08933i	1.48706	−	0.262208i
$732$	19.0672	+	2.11114i	0.704744	+	0.0780298i
$733$	13.5650	+	23.4953i	0.501036	+	0.867820i	0.999999	+	0.00119677i	$0.000380945\pi$
$733$	13.5650	+	23.4953i	0.501036	+	0.867820i	−0.498963	+	0.866623i	$0.666286\pi$
$734$	−12.5785	−	21.7866i	−0.464281	−	0.804158i
$735$	0.0251317	+	12.7605i	0.000926997	+	0.470680i
$736$	0.572236	−	0.681965i	0.0210929	−	0.0251375i
$737$	1.75974	+	9.97999i	0.0648209	+	0.367618i
$738$	−34.6201	−	7.76147i	−1.27438	−	0.285704i
$739$	24.8247	+	20.8304i	0.913191	+	0.766258i	0.972723	−	0.231968i	$-0.0745164\pi$
$739$	24.8247	+	20.8304i	0.913191	+	0.766258i	−0.0595322	+	0.998226i	$0.518961\pi$
$740$	2.30040	−	3.98441i	0.0845644	−	0.146470i
$741$	2.30971	+	7.11887i	0.0848494	+	0.261518i
$742$	−0.376377	−	6.69954i	−0.0138172	−	0.245948i
$743$	−38.4964	+	14.0116i	−1.41230	+	0.514034i	−0.931803	−	0.362964i	$-0.881765\pi$
$743$	−38.4964	+	14.0116i	−1.41230	+	0.514034i	−0.480494	+	0.876998i	$0.659543\pi$
$744$	−4.26009	−	6.39210i	−0.156182	−	0.234346i
$745$	10.7733	+	3.92117i	0.394704	+	0.143660i
$746$	26.6202	+	4.69386i	0.974634	+	0.171854i
$747$	30.6551	−	23.4069i	1.12161	−	0.856414i
$748$	5.33743	+	9.24471i	0.195156	+	0.338020i
$749$	14.9912	−	9.81576i	0.547767	−	0.358660i
$750$	13.0612	+	9.60073i	0.476926	+	0.350569i
$751$	13.9813	+	16.6622i	0.510184	+	0.608014i	0.958231	−	0.285996i	$-0.0923245\pi$
$751$	13.9813	+	16.6622i	0.510184	+	0.608014i	−0.448046	+	0.894010i	$0.647880\pi$
$752$			6.30837i			0.230043i
$753$	−12.5513	+	11.9867i	−0.457395	+	0.436820i
$754$	0.181257	−	0.498000i	0.00660100	−	0.0181361i
$755$	−0.687064	−	0.576515i	−0.0250048	−	0.0209815i
$756$	5.64890	+	12.5336i	0.205448	+	0.455841i
$757$	−2.92526	+	16.5900i	−0.106320	+	0.602972i	0.884364	+	0.466797i	$0.154592\pi$
$757$	−2.92526	+	16.5900i	−0.106320	+	0.602972i	−0.990685	+	0.136175i	$0.956519\pi$
$758$	−23.4046	−	4.12686i	−0.850092	−	0.149894i
$759$	2.80439	−	0.682698i	0.101793	−	0.0247804i
$760$	−4.56489	−	0.456143i	−0.165586	−	0.0165460i
$761$	−14.7467	−	8.51399i	−0.534566	−	0.308632i	0.208308	−	0.978063i	$-0.433204\pi$
$761$	−14.7467	−	8.51399i	−0.534566	−	0.308632i	−0.742874	+	0.669431i	$0.766538\pi$
$762$	29.8577	−	1.92134i	1.08163	−	0.0696029i
$763$	2.92109	−	1.25291i	0.105750	−	0.0453585i
$764$	−4.14504	−	4.93986i	−0.149962	−	0.178718i
$765$	−17.5701	−	3.93905i	−0.635249	−	0.142416i
$766$	13.0357	−	10.9382i	0.470997	−	0.395214i
$767$	−7.71536	−	4.45447i	−0.278585	−	0.160841i
$768$	1.68290	−	0.409684i	0.0607265	−	0.0147832i
$769$	−0.999831	−	0.363909i	−0.0360548	−	0.0131229i	0.323930	−	0.946081i	$-0.394996\pi$
$769$	−0.999831	−	0.363909i	−0.0360548	−	0.0131229i	−0.359985	+	0.932958i	$0.617218\pi$
$770$	3.56911	+	3.79866i	0.128622	+	0.136894i
$771$	7.80086	+	8.16830i	0.280941	+	0.294174i
$772$		−	4.08014i		−	0.146847i
$773$	−8.54964	+	7.17400i	−0.307509	+	0.258031i	−0.783462	−	0.621440i	$-0.786548\pi$
$773$	−8.54964	+	7.17400i	−0.307509	+	0.258031i	0.475952	+	0.879471i	$0.342103\pi$
$774$	14.5470	−	15.7997i	0.522880	−	0.567907i
$775$	−17.0000	+	2.99757i	−0.610660	+	0.107676i
$776$	−5.75796	−	1.01528i	−0.206699	−	0.0364465i
$777$	−2.40571	−	19.8874i	−0.0863043	−	0.713455i
$778$		−	9.20459i		−	0.330000i
$779$	5.12561	−	51.2950i	0.183644	−	1.83783i
$780$	1.75581	−	0.427433i	0.0628681	−	0.0153046i
$781$	−8.21920	+	9.79526i	−0.294106	+	0.350502i
$782$	3.88913	+	3.26337i	0.139075	+	0.116698i
$783$	−0.432372	+	2.74405i	−0.0154517	+	0.0980645i
$784$	6.26830	−	3.11583i	0.223868	−	0.111280i
$785$	13.8447	−	2.44119i	0.494138	−	0.0871299i
$786$	28.0273	+	8.20538i	0.999702	+	0.292676i
$787$			27.2058i			0.969783i	0.874574	+	0.484891i	$0.161141\pi$
$787$			27.2058i			0.969783i	−0.874574	+	0.484891i	$0.838859\pi$
$788$	−11.1923	+	1.97351i	−0.398711	+	0.0703035i
$789$	19.8310	−	8.69775i	0.706004	−	0.309648i
$790$	6.45991	−	11.1889i	0.229833	−	0.398083i
$791$	−19.2409	+	12.5983i	−0.684127	+	0.447944i
$792$	5.18297	+	2.16131i	0.184169	+	0.0767987i
$793$	−3.75519	−	10.3173i	−0.133351	−	0.366378i
$794$	18.3194	+	6.66772i	0.650132	+	0.236629i
$795$	4.61376	−	0.296895i	0.163633	−	0.0105298i
$796$	−3.50429	+	19.8738i	−0.124206	+	0.704409i
$797$	−3.81264			−0.135051			−0.0675253	−	0.997718i	$-0.521510\pi$
$797$	−3.81264			−0.135051			−0.0675253	+	0.997718i	$0.521510\pi$
$798$	−17.0875	+	10.3449i	−0.604891	+	0.366206i
$799$	−35.9756			−1.27273
$800$	0.675891	−	3.83317i	0.0238963	−	0.135523i
$801$	20.4895	+	4.59353i	0.723959	+	0.162304i
$802$	15.2209	+	5.53997i	0.537470	+	0.195623i
$803$	0.219440	+	0.602907i	0.00774388	+	0.0212761i
$804$	−1.03193	+	9.32013i	−0.0363934	+	0.328696i
$805$	2.21298	+	1.11711i	0.0779973	+	0.0393728i
$806$	−2.19821	+	3.80742i	−0.0774288	+	0.134111i
$807$	−17.8949	−	40.8008i	−0.629931	−	1.43626i
$808$	−8.80802	+	1.55309i	−0.309865	+	0.0546375i
$809$		−	17.5773i		−	0.617986i	−0.951064	−	0.308993i	$-0.900008\pi$
$809$		−	17.5773i		−	0.617986i	0.951064	−	0.308993i	$-0.0999920\pi$
$810$	−8.60372	+	3.96229i	−0.302304	+	0.139221i
$811$	18.4511	−	3.25343i	0.647907	−	0.114243i	0.159969	−	0.987122i	$-0.448861\pi$
$811$	18.4511	−	3.25343i	0.647907	−	0.114243i	0.487937	+	0.872879i	$0.337749\pi$
$812$	1.40454	+	0.167096i	0.0492896	+	0.00586393i
$813$	−9.06203	−	20.6616i	−0.317819	−	0.724635i
$814$	−6.26826	−	5.25970i	−0.219703	−	0.184352i
$815$	0.319752	−	0.381066i	0.0112004	−	0.0133482i
$816$	2.33636	+	9.59732i	0.0817890	+	0.335973i
$817$	25.3389	+	18.2120i	0.886495	+	0.637158i
$818$		−	24.1510i		−	0.844419i
$819$	4.99641	−	6.07825i	0.174589	−	0.212391i
$820$	−12.2580	−	2.16141i	−0.428067	−	0.0754797i
$821$	−14.9659	+	2.63890i	−0.522314	+	0.0920981i	−0.428588	−	0.903500i	$-0.640989\pi$
$821$	−14.9659	+	2.63890i	−0.522314	+	0.0920981i	−0.0937260	+	0.995598i	$0.529878\pi$
$822$	−14.8760	+	30.0754i	−0.518861	+	1.04900i
$823$	−7.48809	+	6.28326i	−0.261018	+	0.219021i	−0.763900	−	0.645335i	$-0.776718\pi$
$823$	−7.48809	+	6.28326i	−0.261018	+	0.219021i	0.502881	+	0.864356i	$0.332273\pi$
$824$		−	9.30203i		−	0.324051i
$825$	9.12615	−	8.71563i	0.317732	−	0.303439i
$826$	6.86632	−	22.7646i	0.238910	−	0.792081i
$827$	−9.82428	−	3.57574i	−0.341624	−	0.124341i	0.165510	−	0.986208i	$-0.447073\pi$
$827$	−9.82428	−	3.57574i	−0.341624	−	0.124341i	−0.507134	+	0.861867i	$0.669295\pi$
$828$	2.66790	+	0.122837i	0.0927159	+	0.00426890i
$829$	−3.55872	−	2.05463i	−0.123599	−	0.0713602i	0.436926	−	0.899498i	$-0.356067\pi$
$829$	−3.55872	−	2.05463i	−0.123599	−	0.0713602i	−0.560525	+	0.828137i	$0.689401\pi$
$830$	10.3655	−	8.69767i	0.359791	−	0.301901i
$831$	0.0101421	+	0.157609i	0.000351826	+	0.00546739i
$832$	−0.637199	−	0.759384i	−0.0220909	−	0.0263269i
$833$	17.7691	+	35.7471i	0.615662	+	1.23856i
$834$	1.49082	+	23.1674i	0.0516229	+	0.802222i
$835$	17.1444	+	9.89835i	0.593308	+	0.342546i
$836$	−2.20875	+	7.85456i	−0.0763912	+	0.271656i
$837$	7.48529	−	21.7953i	0.258730	−	0.753357i
$838$	16.6890	+	2.94272i	0.576511	+	0.101654i
$839$	−0.993776	+	5.63598i	−0.0343090	+	0.194576i	−0.997145	−	0.0755109i	$-0.975941\pi$
$839$	−0.993776	+	5.63598i	−0.0343090	+	0.194576i	0.962836	+	0.270087i	$0.0870523\pi$
$840$	2.18191	+	4.30128i	0.0752832	+	0.148408i
$841$	−21.9963	−	18.4571i	−0.758495	−	0.636453i
$842$	5.28846	−	14.5299i	0.182252	−	0.500735i
$843$	−17.8499	−	18.6906i	−0.614782	−	0.643739i
$844$			3.57930i			0.123205i
$845$	8.12992	+	9.68886i	0.279678	+	0.333307i
$846$	−15.0416	+	11.4852i	−0.517142	+	0.394868i
$847$	−16.5926	+	10.8643i	−0.570129	+	0.373302i
$848$	−1.26809	−	2.19640i	−0.0435464	−	0.0754246i
$849$	24.0911	−	32.7743i	0.826803	−	1.12481i
$850$	21.8599	+	3.85449i	0.749789	+	0.132208i
$851$	−3.65692	−	1.33101i	−0.125358	−	0.0456265i
$852$	−9.84559	+	6.56170i	−0.337304	+	0.224800i
$853$	2.42726	−	0.883452i	0.0831079	−	0.0302488i	−0.300132	−	0.953898i	$-0.597031\pi$
$853$	2.42726	−	0.883452i	0.0831079	−	0.0302488i	0.383240	+	0.923649i	$0.374808\pi$
$854$	24.5159	−	16.0522i	0.838917	−	0.549295i
$855$	−7.22332	−	11.7150i	−0.247032	−	0.400644i
$856$	3.38635	−	5.86532i	0.115743	−	0.200473i
$857$	−23.7062	−	19.8919i	−0.809789	−	0.679494i	0.140768	−	0.990043i	$-0.455043\pi$
$857$	−23.7062	−	19.8919i	−0.809789	−	0.679494i	−0.950557	+	0.310549i	$0.899487\pi$
$858$	−0.206391	−	3.20732i	−0.00704606	−	0.109496i
$859$	−1.11231	−	6.30824i	−0.0379516	−	0.215234i	0.959934	−	0.280225i	$-0.0904092\pi$
$859$	−1.11231	−	6.30824i	−0.0379516	−	0.215234i	−0.997886	+	0.0649910i	$0.979298\pi$
$860$	4.84309	−	5.77177i	0.165148	−	0.196816i
$861$	−48.3328	+	24.5178i	−1.64718	+	0.835565i
$862$	−3.90491	−	6.76351i	−0.133002	−	0.230366i
$863$	−23.8597	−	41.3262i	−0.812194	−	1.40676i	−0.911325	−	0.411687i	$-0.864940\pi$
$863$	−23.8597	−	41.3262i	−0.812194	−	1.40676i	0.0991316	−	0.995074i	$-0.468394\pi$
$864$	4.04078	+	3.26682i	0.137470	+	0.111140i
$865$	−18.8860	+	3.33011i	−0.642144	+	0.113227i
$866$	−12.0443	+	6.95380i	−0.409283	+	0.236300i
$867$	−26.1226	+	6.35927i	−0.887171	+	0.215972i
$868$	−11.2340	−	3.38843i	−0.381306	−	0.115011i
$869$	−17.6024	−	14.7701i	−0.597119	−	0.501042i
$870$	−0.107249	+	0.968640i	−0.00363607	+	0.0328400i
$871$	5.04313	−	1.83555i	0.170880	−	0.0621953i
$872$	0.772207	−	0.920281i	0.0261502	−	0.0311646i
$873$	−8.06222	−	15.5777i	−0.272865	−	0.527225i
$874$	0.290528	+	3.86958i	0.00982726	+	0.130891i
$875$	24.7224	−	1.38889i	0.835769	−	0.0469531i
$876$	0.0381245	+	0.592456i	0.00128811	+	0.0200172i
$877$	−27.3400	+	32.5825i	−0.923205	+	1.10023i	0.0714973	+	0.997441i	$0.477222\pi$
$877$	−27.3400	+	32.5825i	−0.923205	+	1.10023i	−0.994703	+	0.102793i	$0.967222\pi$
$878$	−9.94443	+	27.3221i	−0.335608	+	0.922076i
$879$	41.0096	+	20.2843i	1.38322	+	0.684173i
$880$	1.85126	+	0.673805i	0.0624061	+	0.0227140i
$881$	0.125123	−	0.0722396i	0.00421549	−	0.00243381i	−0.497891	−	0.867240i	$-0.665892\pi$
$881$	0.125123	−	0.0722396i	0.00421549	−	0.00243381i	0.502106	+	0.864806i	$0.332559\pi$
$882$	18.8416	+	9.27335i	0.634429	+	0.312250i
$883$	19.7625	+	7.19298i	0.665062	+	0.242063i	0.652420	−	0.757857i	$-0.273754\pi$
$883$	19.7625	+	7.19298i	0.665062	+	0.242063i	0.0126418	+	0.999920i	$0.495976\pi$
$884$	4.33064	−	3.63384i	0.145655	−	0.122219i
$885$	15.7229	+	4.60309i	0.528520	+	0.154731i
$886$	31.0616	+	17.9334i	1.04354	+	0.602486i
$887$	38.1604	+	13.8892i	1.28130	+	0.466355i	0.890862	−	0.454274i	$-0.150101\pi$
$887$	38.1604	+	13.8892i	1.28130	+	0.466355i	0.390438	+	0.920629i	$0.372324\pi$
$888$	−4.19902	−	6.30048i	−0.140910	−	0.211430i
$889$	33.3075	−	31.2947i	1.11710	−	1.04959i
$890$	7.25472	+	1.27920i	0.243179	+	0.0428790i
$891$	4.28283	+	16.2932i	0.143480	+	0.545842i
$892$	16.4732	−	9.51083i	0.551565	−	0.318446i
$893$	−19.2026	−	19.6819i	−0.642589	−	0.658630i
$894$	13.6446	−	13.0309i	0.456345	−	0.435817i
$895$	−3.31728	−	9.11414i	−0.110884	−	0.304652i
$896$	1.58430	−	2.11896i	0.0529276	−	0.0707896i
$897$	−0.613950	−	1.39982i	−0.0204992	−	0.0467386i
$898$	−21.8213	+	7.94231i	−0.728186	+	0.265038i
$899$	−1.52404	−	1.81628i	−0.0508296	−	0.0605763i
$900$	10.3703	−	5.36716i	0.345677	−	0.178905i
$901$	12.5257	−	7.23171i	0.417291	−	0.240923i
$902$	−7.57144	+	20.8024i	−0.252101	+	0.692643i
$903$	1.77561	−	32.7579i	0.0590887	−	1.09012i
$904$	−4.34630	+	7.52801i	−0.144556	+	0.250378i
$905$	−14.9919			−0.498349
$906$	−1.35172	+	0.592856i	−0.0449080	+	0.0196963i
$907$	−10.2465	−	1.80673i	−0.340229	−	0.0599916i	0.000923325	−	1.00000i	$-0.499706\pi$
$907$	−10.2465	−	1.80673i	−0.340229	−	0.0599916i	−0.341152	+	0.940008i	$0.610817\pi$
$908$	2.51015	+	14.2357i	0.0833021	+	0.472430i
$909$	−19.7392	−	18.1742i	−0.654709	−	0.602800i
$910$	1.65293	−	2.21076i	0.0547942	−	0.0732861i
$911$	30.7585			1.01907			0.509537	−	0.860449i	$-0.329817\pi$
$911$	30.7585			1.01907			0.509537	+	0.860449i	$0.329817\pi$
$912$	−4.00353	+	6.40092i	−0.132570	+	0.211956i
$913$	−12.0328	−	20.8414i	−0.398227	−	0.689749i
$914$	−24.0839	−	20.2088i	−0.796624	−	0.668447i
$915$	11.1972	+	16.8010i	0.370168	+	0.555424i
$916$	−5.49773	+	4.61314i	−0.181650	+	0.152422i
$917$	40.9974	−	17.5846i	1.35385	−	0.580695i
$918$	−18.6302	+	23.0439i	−0.614887	+	0.760562i
$919$	−44.2142			−1.45849			−0.729246	−	0.684251i	$-0.760129\pi$
$919$	−44.2142			−1.45849			−0.729246	+	0.684251i	$0.760129\pi$
$920$	0.936956			0.0308905
$921$	−0.802432	+	7.24735i	−0.0264410	+	0.238808i
$922$	−7.20753	−	8.58960i	−0.237367	−	0.282884i
$923$	5.86447	+	3.38585i	0.193031	+	0.111447i
$924$	8.20757	−	2.49324i	0.270009	−	0.0820215i
$925$	−16.7564	+	2.95460i	−0.550946	+	0.0971466i
$926$	11.3386	−	4.12690i	0.372608	−	0.135618i
$927$	22.1797	−	16.9355i	0.728477	−	0.556234i
$928$	0.502368	−	0.182847i	0.0164910	−	0.00600225i
$929$	−24.6787	−	4.35152i	−0.809681	−	0.142769i	−0.246544	−	0.969132i	$-0.579295\pi$
$929$	−24.6787	−	4.35152i	−0.809681	−	0.142769i	−0.563138	+	0.826363i	$0.690406\pi$
$930$	2.27156	−	7.75903i	0.0744874	−	0.254429i
$931$	−10.0724	+	28.8019i	−0.330108	+	0.943943i
$932$			10.4706i			0.342977i
$933$	5.03315	−	10.1757i	0.164778	−	0.333138i
$934$	−6.64147	−	18.2473i	−0.217315	−	0.597069i
$935$	−3.84260	+	10.5575i	−0.125667	+	0.345266i
$936$	0.650573	−	2.90188i	0.0212646	−	0.0948511i
$937$	−0.329237	−	1.86720i	−0.0107557	−	0.0609987i	0.978958	−	0.204064i	$-0.0654151\pi$
$937$	−0.329237	−	1.86720i	−0.0107557	−	0.0609987i	−0.989713	+	0.143066i	$0.954304\pi$
$938$	7.84638	+	11.9835i	0.256194	+	0.391274i
$939$	−4.85739	−	5.08618i	−0.158515	−	0.165981i
$940$	−5.08607	+	4.26772i	−0.165889	+	0.139198i
$941$	−6.27452	−	35.5845i	−0.204543	−	1.16002i	−0.898157	−	0.439676i	$-0.855093\pi$
$941$	−6.27452	−	35.5845i	−0.204543	−	1.16002i	0.693613	−	0.720348i	$-0.256018\pi$
$942$	6.50041	−	22.2036i	0.211795	−	0.723434i
$943$			10.5284i			0.342853i
$944$	−1.56059	−	8.85054i	−0.0507928	−	0.288060i
$945$	−6.28350	+	13.0335i	−0.204402	+	0.423981i
$946$	−8.61356	−	10.2652i	−0.280051	−	0.333752i
$947$	31.6033	−	37.6634i	1.02697	−	1.22390i	0.0526766	−	0.998612i	$-0.483225\pi$
$947$	31.6033	−	37.6634i	1.02697	−	1.22390i	0.974293	−	0.225283i	$-0.0723308\pi$
$948$	−11.7916	−	17.6928i	−0.382972	−	0.574636i
$949$	0.294260	−	0.169891i	0.00955208	−	0.00551490i
$950$	9.55932	+	14.0167i	0.310145	+	0.454763i
$951$	13.2249	−	45.1726i	0.428846	−	1.46482i
$952$	12.0841	+	9.03498i	0.391648	+	0.292825i
$953$	−0.0958865	+	0.543800i	−0.00310607	+	0.0176154i	−0.986321	−	0.164834i	$-0.947291\pi$
$953$	−0.0958865	+	0.543800i	−0.00310607	+	0.0176154i	0.983215	+	0.182449i	$0.0584024\pi$
$954$	2.92836	−	7.02243i	0.0948093	−	0.227360i
$955$	1.17853	−	6.68380i	0.0381365	−	0.216283i
$956$	−10.0824	−	12.0157i	−0.326087	−	0.388616i
$957$	1.66346	+	0.486999i	0.0537719	+	0.0157424i
$958$	21.6285	+	12.4872i	0.698786	+	0.403444i
$959$	11.7173	+	49.8963i	0.378371	+	1.61123i
$960$	1.46882	+	1.07967i	0.0474058	+	0.0348461i
$961$	−5.66544	−	9.81283i	−0.182756	−	0.316543i
$962$	−2.16670	+	3.75284i	−0.0698573	+	0.120996i
$963$	20.1505	−	2.60415i	0.649341	−	0.0839175i
$964$	8.11569	+	22.2977i	0.261389	+	0.718159i
$965$	3.28958	−	2.76028i	0.105895	−	0.0888566i
$966$	3.26251	−	2.44932i	0.104969	−	0.0788057i
$967$	25.2632	−	9.19504i	0.812409	−	0.295693i	0.0977902	−	0.995207i	$-0.468823\pi$
$967$	25.2632	−	9.19504i	0.812409	−	0.295693i	0.714618	+	0.699515i	$0.246600\pi$
$968$	−3.74809	+	6.49188i	−0.120468	+	0.208657i
$969$	−36.5034	−	22.8315i	−1.17266	−	0.733452i
$970$	−3.07679	−	5.32916i	−0.0987898	−	0.171109i
$971$	−5.96943	+	33.8543i	−0.191568	+	1.08644i	0.725654	+	0.688060i	$0.241537\pi$
$971$	−5.96943	+	33.8543i	−0.191568	+	1.08644i	−0.917222	+	0.398377i	$0.869574\pi$
$972$	−0.432668	+	15.5825i	−0.0138778	+	0.499807i
$973$	24.2824	+	25.8441i	0.778458	+	0.828525i
$974$	−11.3090	+	13.4775i	−0.362362	+	0.431847i
$975$	−5.38480	−	3.95815i	−0.172452	−	0.126762i
$976$	5.53787	−	9.59187i	0.177263	−	0.307028i
$977$	−49.4276			−1.58133			−0.790665	−	0.612249i	$-0.790265\pi$
$977$	−49.4276			−1.58133			−0.790665	+	0.612249i	$0.790265\pi$
$978$	−0.328815	−	0.749706i	−0.0105144	−	0.0239730i
$979$	4.48106	−	12.3116i	0.143215	−	0.393481i
$980$	6.75273	+	2.94585i	0.215708	+	0.0941018i
$981$	3.60021	+	0.165764i	0.114946	+	0.00529243i
$982$	8.36718	−	22.9886i	0.267007	−	0.733597i
$983$	0.0273352	−	0.155026i	0.000871859	−	0.00494456i	−0.984369	−	0.176120i	$-0.943645\pi$
$983$	0.0273352	−	0.155026i	0.000871859	−	0.00494456i	0.985241	+	0.171175i	$0.0547565\pi$
$984$	−12.1321	+	16.5049i	−0.386756	+	0.526156i
$985$	−9.16294	−	7.68862i	−0.291956	−	0.244980i
$986$	1.04275	+	2.86492i	0.0332078	+	0.0912378i
$987$	−6.55346	+	28.1560i	−0.208599	+	0.896215i
$988$	4.29959	+	0.429633i	0.136788	+	0.0136684i
$989$	−5.51928	−	3.18656i	−0.175503	−	0.101327i
$990$	1.76384	+	5.64089i	0.0560584	+	0.179279i
$991$	14.3908	+	39.5383i	0.457138	+	1.25598i	0.927606	+	0.373560i	$0.121863\pi$
$991$	14.3908	+	39.5383i	0.457138	+	1.25598i	−0.470468	+	0.882417i	$0.655915\pi$
$992$	−4.36761	+	0.770128i	−0.138672	+	0.0244516i
$993$	−5.43788	−	8.15934i	−0.172566	−	0.258929i
$994$	−5.21911	+	17.3034i	−0.165540	+	0.548831i
$995$	−18.3938	+	10.6197i	−0.583123	+	0.336666i
$996$	−5.26712	−	21.6363i	−0.166895	−	0.685572i
$997$	−6.96013	−	39.4729i	−0.220430	−	1.25012i	−0.871232	−	0.490871i	$-0.836679\pi$
$997$	−6.96013	−	39.4729i	−0.220430	−	1.25012i	0.650802	−	0.759247i	$-0.274433\pi$
$998$	−6.13602	−	34.7991i	−0.194232	−	1.10155i
$999$	7.37799	−	21.4829i	0.233429	−	0.679689i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bu.a.527.13	yes	162
3.2	odd	2		798.2.bu.b.527.8	yes	162
7.4	even	3		798.2.cc.a.641.6	yes	162
19.15	odd	18		798.2.cc.b.737.10	yes	162
21.11	odd	6		798.2.cc.b.641.10	yes	162
57.53	even	18		798.2.cc.a.737.6	yes	162
133.53	odd	18		798.2.bu.b.53.8	yes	162
399.53	even	18	inner	798.2.bu.a.53.13	✓	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.53.13	✓	162	399.53	even	18	inner
798.2.bu.a.527.13	yes	162	1.1	even	1	trivial
798.2.bu.b.53.8	yes	162	133.53	odd	18
798.2.bu.b.527.8	yes	162	3.2	odd	2
798.2.cc.a.641.6	yes	162	7.4	even	3
798.2.cc.a.737.6	yes	162	57.53	even	18
798.2.cc.b.641.10	yes	162	21.11	odd	6
798.2.cc.b.737.10	yes	162	19.15	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bu (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.111227 - 1.72848i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.359967 - 0.989002i) q^{5} +(-1.72153 - 0.190609i) q^{6} +(-2.21348 + 1.44931i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-2.97526 + 0.384507i) q^{9} +(-1.03648 + 0.182760i) q^{10} +1.87185i q^{11} +(-0.486654 + 1.66228i) q^{12} +(0.976245 - 0.172138i) q^{13} +(1.04293 + 2.43152i) q^{14} +(-1.66943 + 0.732199i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-3.66571 + 4.36863i) q^{17} +(-0.137982 + 2.99683i) q^{18} +(-4.34667 + 0.326348i) q^{19} +1.05247i q^{20} +(2.75130 + 3.66474i) q^{21} +(1.84341 + 0.325044i) q^{22} +(0.876717 - 0.154589i) q^{23} +(1.55252 + 0.767912i) q^{24} +(2.98167 - 2.50192i) q^{25} -0.991305i q^{26} +(0.995541 + 5.09989i) q^{27} +(2.57568 - 0.604855i) q^{28} +(0.502368 + 0.182847i) q^{29} +(0.431182 + 1.77121i) q^{30} +(-3.84081 - 2.21749i) q^{31} +(0.766044 - 0.642788i) q^{32} +(3.23545 - 0.208201i) q^{33} +(3.66571 + 4.36863i) q^{34} +(2.23015 + 1.66743i) q^{35} +(2.92734 + 0.656279i) q^{36} +(-3.78576 - 2.18571i) q^{37} +(-0.433401 + 4.33730i) q^{38} +(-0.406122 - 1.66827i) q^{39} +(1.03648 + 0.182760i) q^{40} +(-2.05365 + 11.6468i) q^{41} +(4.08682 - 2.07313i) q^{42} +(-5.48400 - 4.60163i) q^{43} +(0.640211 - 1.75897i) q^{44} +(1.45127 + 2.80412i) q^{45} -0.890242i q^{46} +(4.05494 + 4.83249i) q^{47} +(1.02584 - 1.39558i) q^{48} +(2.79898 - 6.41605i) q^{49} +(-1.94615 - 3.37083i) q^{50} +(7.95879 + 5.85019i) q^{51} +(-0.976245 - 0.172138i) q^{52} +(-2.38323 - 0.867425i) q^{53} +(5.19529 - 0.0948299i) q^{54} +(1.85126 - 0.673805i) q^{55} +(-0.148403 - 2.64159i) q^{56} +(1.04755 + 7.47681i) q^{57} +(0.267305 - 0.462985i) q^{58} +(-6.88449 - 5.77678i) q^{59} +(1.81918 - 0.117064i) q^{60} +(-1.92328 - 10.9075i) q^{61} +(-2.85076 + 3.39740i) q^{62} +(6.02840 - 5.16318i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.521661 - 0.903544i) q^{65} +(0.356792 - 3.22245i) q^{66} +(5.33161 - 0.940107i) q^{67} +(4.93880 - 2.85142i) q^{68} +(-0.364718 - 1.49819i) q^{69} +(2.02936 - 1.90673i) q^{70} +(5.23292 + 4.39094i) q^{71} +(1.15464 - 2.76890i) q^{72} +(0.322091 - 0.117232i) q^{73} +(-2.80989 + 3.34870i) q^{74} +(-4.65615 - 4.87547i) q^{75} +(4.19615 + 1.17998i) q^{76} +(-2.71290 - 4.14330i) q^{77} +(-1.71345 + 0.110260i) q^{78} +(-7.89065 + 9.40371i) q^{79} +(0.359967 - 0.989002i) q^{80} +(8.70431 - 2.28802i) q^{81} +(11.1133 + 4.04489i) q^{82} +(-11.1341 + 6.42827i) q^{83} +(-1.33196 - 4.38473i) q^{84} +(5.64012 + 2.05283i) q^{85} +(-5.48400 + 4.60163i) q^{86} +(0.260170 - 0.888669i) q^{87} +(-1.62107 - 0.935926i) q^{88} +(-6.57724 - 2.39392i) q^{89} +(3.01353 - 0.942294i) q^{90} +(-1.91142 + 1.79591i) q^{91} +(-0.876717 - 0.154589i) q^{92} +(-3.40568 + 6.88540i) q^{93} +(5.46321 - 3.15419i) q^{94} +(1.88742 + 4.18139i) q^{95} +(-1.19625 - 1.25259i) q^{96} +(1.99972 + 5.49418i) q^{97} +(-5.83254 - 3.87059i) q^{98} +(-0.719741 - 5.56924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q - 81 q^{8} + 15 q^{13} + 6 q^{14} + 27 q^{15} - 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} - 9 q^{27} + 9 q^{28} + 6 q^{29} - 24 q^{33} + 6 q^{34} + 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) \) 162 * q - 81 * q^8 + 15 * q^13 + 6 * q^14 + 27 * q^15 - 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 - 9 * q^27 + 9 * q^28 + 6 * q^29 - 24 * q^33 + 6 * q^34 + 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 - 12 * q^44 - 63 * q^45 + 12 * q^47 - 48 * q^49 + 87 * q^50 - 24 * q^51 - 15 * q^52 - 18 * q^54 - 18 * q^57 - 48 * q^59 + 6 * q^60 + 45 * q^61 + 36 * q^62 - 15 * q^63 - 81 * q^64 + 36 * q^65 + 12 * q^66 + 9 * q^67 + 9 * q^69 - 24 * q^70 + 12 * q^71 + 102 * q^73 + 39 * q^74 - 6 * q^78 - 42 * q^79 + 84 * q^81 - 3 * q^84 - 6 * q^85 - 9 * q^86 + 60 * q^87 + 54 * q^89 + 36 * q^90 - 18 * q^91 - 21 * q^93 - 72 * q^94 - 12 * q^97 - 27 * q^98 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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