LMFDB - Embedded newform 633.2.k.a.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [633,2,Mod(23,633)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(633, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1]))

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

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

chi := DirichletCharacter("633.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 633 = 3 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	633.k (of order $10$, degree $4$, 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:	$5.05453044795$
Analytic rank:	$0$
Dimension:	$272$
Relative dimension:	$68$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			23.4
Character	$\chi$	$=$	633.23
Dual form			633.2.k.a.578.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.799825 + 2.46161i) q^{2} +(1.66620 - 0.473050i) q^{3} +(-3.80176 - 2.76214i) q^{4} +(0.419853 - 0.577878i) q^{5} +(-0.168205 + 4.47989i) q^{6} +(-2.14759 + 0.697796i) q^{7} +(5.65212 - 4.10650i) q^{8} +(2.55245 - 1.57639i) q^{9} +O(q^{10})$	\(q+(-0.799825 + 2.46161i) q^{2} +(1.66620 - 0.473050i) q^{3} +(-3.80176 - 2.76214i) q^{4} +(0.419853 - 0.577878i) q^{5} +(-0.168205 + 4.47989i) q^{6} +(-2.14759 + 0.697796i) q^{7} +(5.65212 - 4.10650i) q^{8} +(2.55245 - 1.57639i) q^{9} +(1.08670 + 1.49572i) q^{10} +(-1.10482 + 1.52066i) q^{11} +(-7.64113 - 2.80386i) q^{12} +(1.68986 + 5.20087i) q^{13} -5.84465i q^{14} +(0.426194 - 1.16147i) q^{15} +(2.68361 + 8.25930i) q^{16} +(0.220305 + 0.678028i) q^{17} +(1.83895 + 7.54396i) q^{18} +(2.29110 + 7.05127i) q^{19} +(-3.19236 + 1.03726i) q^{20} +(-3.24823 + 2.17859i) q^{21} +(-2.85960 - 3.93590i) q^{22} +(0.604908 - 1.86171i) q^{23} +(7.47498 - 9.51599i) q^{24} +(1.38742 + 4.27003i) q^{25} -14.1541 q^{26} +(3.50718 - 3.83402i) q^{27} +(10.0921 + 3.27911i) q^{28} +(-0.125004 - 0.384722i) q^{29} +(2.51821 + 1.97810i) q^{30} +4.16171i q^{31} -8.50479 q^{32} +(-1.12151 + 3.05636i) q^{33} -1.84524 q^{34} +(-0.498433 + 1.53402i) q^{35} +(-14.0580 - 1.05716i) q^{36} +(0.494890 - 0.359559i) q^{37} -19.1899 q^{38} +(5.27592 + 7.86629i) q^{39} -4.99036i q^{40} +(-0.391785 - 0.284648i) q^{41} +(-2.76481 - 9.73836i) q^{42} -9.36274 q^{43} +(8.40054 - 2.72950i) q^{44} +(0.160691 - 2.13686i) q^{45} +(4.09899 + 2.97809i) q^{46} +(2.17336 - 0.706168i) q^{47} +(8.37849 + 12.4922i) q^{48} +(-1.53787 + 1.11733i) q^{49} -11.6208 q^{50} +(0.687813 + 1.02552i) q^{51} +(7.94107 - 24.4401i) q^{52} +(7.93908 + 10.9272i) q^{53} +(6.63273 + 11.6998i) q^{54} +(0.414892 + 1.27691i) q^{55} +(-9.27295 + 12.7631i) q^{56} +(7.15303 + 10.6650i) q^{57} +1.04702 q^{58} +(5.64530 - 7.77009i) q^{59} +(-4.82844 + 3.23843i) q^{60} +(0.246363 + 0.339090i) q^{61} +(-10.2445 - 3.32864i) q^{62} +(-4.38162 + 5.16654i) q^{63} +(1.43512 - 4.41685i) q^{64} +(3.71496 + 1.20706i) q^{65} +(-6.62654 - 5.20526i) q^{66} -13.5379i q^{67} +(1.03526 - 3.18621i) q^{68} +(0.127214 - 3.38814i) q^{69} +(-3.37750 - 2.45390i) q^{70} +(-5.24741 - 7.22244i) q^{71} +(7.95327 - 19.3916i) q^{72} +5.58735 q^{73} +(0.489267 + 1.50581i) q^{74} +(4.33166 + 6.45842i) q^{75} +(10.7664 - 33.1356i) q^{76} +(1.31160 - 4.03670i) q^{77} +(-23.5835 + 6.69559i) q^{78} +(-0.149910 - 0.108916i) q^{79} +(5.89959 + 1.91689i) q^{80} +(4.02998 - 8.04732i) q^{81} +(1.01405 - 0.736752i) q^{82} +(4.97696 - 6.85020i) q^{83} +(18.3666 + 0.689605i) q^{84} +(0.484313 + 0.157363i) q^{85} +(7.48855 - 23.0474i) q^{86} +(-0.390274 - 0.581891i) q^{87} +13.1319i q^{88} +(-4.33913 - 13.3545i) q^{89} +(5.13158 + 2.10467i) q^{90} +(-7.25828 - 9.99017i) q^{91} +(-7.44203 + 5.40695i) q^{92} +(1.96870 + 6.93425i) q^{93} +5.91478i q^{94} +(5.03670 + 1.63652i) q^{95} +(-14.1707 + 4.02319i) q^{96} +(-5.43893 - 7.48605i) q^{97} +(-1.52040 - 4.67931i) q^{98} +(-0.422849 + 5.62303i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9}+O(q^{10}) $ 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9	$ 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9} - 20 q^{10} + 6 q^{13} - 46 q^{16} - 20 q^{18} + 6 q^{19} - 3 q^{21} - 10 q^{22} + 23 q^{24} + 50 q^{25} - 40 q^{27} + 80 q^{28} - q^{30} + 12 q^{34} + 13 q^{36} - 42 q^{37} + 25 q^{39} - 10 q^{42} + 40 q^{43} - 23 q^{45} - 2 q^{46} - 15 q^{48} + 30 q^{49} - 11 q^{51} - 34 q^{52} + 128 q^{54} + 14 q^{55} + 20 q^{57} + 60 q^{58} + 30 q^{60} - 10 q^{61} - 108 q^{64} - 73 q^{66} + 40 q^{69} + 70 q^{70} - 105 q^{72} - 20 q^{73} - 10 q^{75} - 12 q^{76} - 82 q^{78} - 30 q^{79} - 42 q^{81} - 106 q^{82} + 121 q^{84} - 110 q^{85} - 11 q^{87} + 60 q^{90} - 40 q^{91} - 45 q^{93} - 114 q^{96} - 80 q^{97} - 18 q^{99}+O(q^{100}) $ 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9 - 20 * q^10 + 6 * q^13 - 46 * q^16 - 20 * q^18 + 6 * q^19 - 3 * q^21 - 10 * q^22 + 23 * q^24 + 50 * q^25 - 40 * q^27 + 80 * q^28 - q^30 + 12 * q^34 + 13 * q^36 - 42 * q^37 + 25 * q^39 - 10 * q^42 + 40 * q^43 - 23 * q^45 - 2 * q^46 - 15 * q^48 + 30 * q^49 - 11 * q^51 - 34 * q^52 + 128 * q^54 + 14 * q^55 + 20 * q^57 + 60 * q^58 + 30 * q^60 - 10 * q^61 - 108 * q^64 - 73 * q^66 + 40 * q^69 + 70 * q^70 - 105 * q^72 - 20 * q^73 - 10 * q^75 - 12 * q^76 - 82 * q^78 - 30 * q^79 - 42 * q^81 - 106 * q^82 + 121 * q^84 - 110 * q^85 - 11 * q^87 + 60 * q^90 - 40 * q^91 - 45 * q^93 - 114 * q^96 - 80 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/633\mathbb{Z}\right)^\times$.

$n$	$212$	$424$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.799825	+	2.46161i	−0.565562	+	1.74062i	0.100715	+	0.994915i	$0.467887\pi$
$2$	−0.799825	+	2.46161i	−0.565562	+	1.74062i	−0.666277	+	0.745705i	$0.732113\pi$
$3$	1.66620	−	0.473050i	0.961981	−	0.273115i
$3$	1.66620	−	0.473050i	0.961981	−	0.273115i
$4$	−3.80176	−	2.76214i	−1.90088	−	1.38107i
$5$	0.419853	−	0.577878i	0.187764	−	0.258435i	−0.704749	−	0.709457i	$-0.748940\pi$
$5$	0.419853	−	0.577878i	0.187764	−	0.258435i	0.892513	+	0.451022i	$0.148940\pi$
$6$	−0.168205	+	4.47989i	−0.0686695	+	1.82891i
$7$	−2.14759	+	0.697796i	−0.811715	+	0.263742i	−0.685324	−	0.728238i	$-0.740339\pi$
$7$	−2.14759	+	0.697796i	−0.811715	+	0.263742i	−0.126391	+	0.991981i	$0.540339\pi$
$8$	5.65212	−	4.10650i	1.99832	−	1.45187i
$9$	2.55245	−	1.57639i	0.850816	−	0.525464i
$10$	1.08670	+	1.49572i	0.343645	+	0.472987i
$11$	−1.10482	+	1.52066i	−0.333116	+	0.458495i	−0.942415	−	0.334445i	$-0.891451\pi$
$11$	−1.10482	+	1.52066i	−0.333116	+	0.458495i	0.609299	+	0.792941i	$0.291451\pi$
$12$	−7.64113	−	2.80386i	−2.20580	−	0.809404i
$13$	1.68986	+	5.20087i	0.468684	+	1.44246i	0.854290	+	0.519797i	$0.173992\pi$
$13$	1.68986	+	5.20087i	0.468684	+	1.44246i	−0.385606	+	0.922664i	$0.626008\pi$
$14$		−	5.84465i		−	1.56205i
$15$	0.426194	−	1.16147i	0.110043	−	0.299891i
$16$	2.68361	+	8.25930i	0.670903	+	2.06483i
$17$	0.220305	+	0.678028i	0.0534317	+	0.164446i	0.974211	−	0.225637i	$-0.0724463\pi$
$17$	0.220305	+	0.678028i	0.0534317	+	0.164446i	−0.920780	+	0.390083i	$0.872446\pi$
$18$	1.83895	+	7.54396i	0.433444	+	1.77813i
$19$	2.29110	+	7.05127i	0.525614	+	1.61767i	0.763099	+	0.646281i	$0.223677\pi$
$19$	2.29110	+	7.05127i	0.525614	+	1.61767i	−0.237486	+	0.971391i	$0.576323\pi$
$20$	−3.19236	+	1.03726i	−0.713834	+	0.231939i
$21$	−3.24823	+	2.17859i	−0.708822	+	0.475407i
$22$	−2.85960	−	3.93590i	−0.609668	−	0.839136i
$23$	0.604908	−	1.86171i	0.126132	−	0.388194i	−0.867974	−	0.496610i	$-0.834578\pi$
$23$	0.604908	−	1.86171i	0.126132	−	0.388194i	0.994106	+	0.108416i	$0.0345778\pi$
$24$	7.47498	−	9.51599i	1.52582	−	1.94244i
$25$	1.38742	+	4.27003i	0.277484	+	0.854007i
$26$	−14.1541			−2.77585
$27$	3.50718	−	3.83402i	0.674957	−	0.737857i
$28$	10.0921	+	3.27911i	1.90722	+	0.619693i
$29$	−0.125004	−	0.384722i	−0.0232126	−	0.0714411i	0.938779	−	0.344520i	$-0.111958\pi$
$29$	−0.125004	−	0.384722i	−0.0232126	−	0.0714411i	−0.961992	+	0.273078i	$0.911958\pi$
$30$	2.51821	+	1.97810i	0.459760	+	0.361150i
$31$			4.16171i			0.747466i	0.927536	+	0.373733i	$0.121922\pi$
$31$			4.16171i			0.747466i	−0.927536	+	0.373733i	$0.878078\pi$
$32$	−8.50479			−1.50345
$33$	−1.12151	+	3.05636i	−0.195230	+	0.532043i
$34$	−1.84524			−0.316457
$35$	−0.498433	+	1.53402i	−0.0842506	+	0.259297i
$36$	−14.0580	−	1.05716i	−2.34300	−	0.176193i
$37$	0.494890	−	0.359559i	0.0813594	−	0.0591111i	−0.546362	−	0.837549i	$-0.683988\pi$
$37$	0.494890	−	0.359559i	0.0813594	−	0.0591111i	0.627721	+	0.778438i	$0.283988\pi$
$38$	−19.1899			−3.11302
$39$	5.27592	+	7.86629i	0.844823	+	1.25962i
$40$		−	4.99036i		−	0.789046i
$41$	−0.391785	−	0.284648i	−0.0611865	−	0.0444546i	0.556772	−	0.830666i	$-0.312040\pi$
$41$	−0.391785	−	0.284648i	−0.0611865	−	0.0444546i	−0.617958	+	0.786211i	$0.712040\pi$
$42$	−2.76481	−	9.73836i	−0.426620	−	1.50266i
$43$	−9.36274			−1.42780			−0.713902	−	0.700246i	$-0.753074\pi$
$43$	−9.36274			−1.42780			−0.713902	+	0.700246i	$0.753074\pi$
$44$	8.40054	−	2.72950i	1.26643	−	0.411488i
$45$	0.160691	−	2.13686i	0.0239543	−	0.318544i
$46$	4.09899	+	2.97809i	0.604363	+	0.439096i
$47$	2.17336	−	0.706168i	0.317018	−	0.103005i	−0.146186	−	0.989257i	$-0.546700\pi$
$47$	2.17336	−	0.706168i	0.317018	−	0.103005i	0.463204	+	0.886252i	$0.346700\pi$
$48$	8.37849	+	12.4922i	1.20933	+	1.80309i
$49$	−1.53787	+	1.11733i	−0.219696	+	0.159619i
$50$	−11.6208			−1.64344
$51$	0.687813	+	1.02552i	0.0963130	+	0.143601i
$52$	7.94107	−	24.4401i	1.10123	−	3.38923i
$53$	7.93908	+	10.9272i	1.09052	+	1.50097i	0.847389	+	0.530972i	$0.178173\pi$
$53$	7.93908	+	10.9272i	1.09052	+	1.50097i	0.243127	+	0.969994i	$0.421827\pi$
$54$	6.63273	+	11.6998i	0.902600	+	1.59215i
$55$	0.414892	+	1.27691i	0.0559440	+	0.172178i
$56$	−9.27295	+	12.7631i	−1.23915	+	1.70554i
$57$	7.15303	+	10.6650i	0.947442	+	1.41262i
$58$	1.04702			0.137480
$59$	5.64530	−	7.77009i	0.734955	−	1.01158i	−0.263938	−	0.964540i	$-0.585021\pi$
$59$	5.64530	−	7.77009i	0.734955	−	1.01158i	0.998893	−	0.0470394i	$-0.0149786\pi$
$60$	−4.82844	+	3.23843i	−0.623349	+	0.418080i
$61$	0.246363	+	0.339090i	0.0315436	+	0.0434160i	0.824497	−	0.565866i	$-0.191458\pi$
$61$	0.246363	+	0.339090i	0.0315436	+	0.0434160i	−0.792954	+	0.609282i	$0.791458\pi$
$62$	−10.2445	−	3.32864i	−1.30105	−	0.422738i
$63$	−4.38162	+	5.16654i	−0.552033	+	0.650923i
$64$	1.43512	−	4.41685i	0.179390	−	0.552106i
$65$	3.71496	+	1.20706i	0.460784	+	0.149718i
$66$	−6.62654	−	5.20526i	−0.815671	−	0.640724i
$67$		−	13.5379i		−	1.65392i	−0.562264	−	0.826958i	$-0.690069\pi$
$67$		−	13.5379i		−	1.65392i	0.562264	−	0.826958i	$-0.309931\pi$
$68$	1.03526	−	3.18621i	0.125544	−	0.386385i
$69$	0.127214	−	3.38814i	0.0153147	−	0.407884i
$70$	−3.37750	−	2.45390i	−0.403688	−	0.293297i
$71$	−5.24741	−	7.22244i	−0.622753	−	0.857146i	0.374797	−	0.927107i	$-0.377712\pi$
$71$	−5.24741	−	7.22244i	−0.622753	−	0.857146i	−0.997550	+	0.0699612i	$0.977712\pi$
$72$	7.95327	−	19.3916i	0.937302	−	2.28532i
$73$	5.58735			0.653949			0.326975	−	0.945033i	$-0.393971\pi$
$73$	5.58735			0.653949			0.326975	+	0.945033i	$0.393971\pi$
$74$	0.489267	+	1.50581i	0.0568762	+	0.175047i
$75$	4.33166	+	6.45842i	0.500177	+	0.745754i
$76$	10.7664	−	33.1356i	1.23499	−	3.80091i
$77$	1.31160	−	4.03670i	0.149471	−	0.460024i
$78$	−23.5835	+	6.69559i	−2.67031	+	0.758126i
$79$	−0.149910	−	0.108916i	−0.0168662	−	0.0122540i	0.579320	−	0.815100i	$-0.303318\pi$
$79$	−0.149910	−	0.108916i	−0.0168662	−	0.0122540i	−0.596186	+	0.802846i	$0.703318\pi$
$80$	5.89959	+	1.91689i	0.659595	+	0.214315i
$81$	4.02998	−	8.04732i	0.447775	−	0.894146i
$82$	1.01405	−	0.736752i	0.111983	−	0.0813606i
$83$	4.97696	−	6.85020i	0.546293	−	0.751907i	−0.443211	−	0.896418i	$-0.646161\pi$
$83$	4.97696	−	6.85020i	0.546293	−	0.751907i	0.989503	+	0.144510i	$0.0461606\pi$
$84$	18.3666	+	0.689605i	2.00396	+	0.0752420i
$85$	0.484313	+	0.157363i	0.0525311	+	0.0170684i
$86$	7.48855	−	23.0474i	0.807511	−	2.48526i
$87$	−0.390274	−	0.581891i	−0.0418418	−	0.0623853i
$88$			13.1319i			1.39986i
$89$	−4.33913	−	13.3545i	−0.459947	−	1.41557i	−0.865227	−	0.501380i	$-0.832826\pi$
$89$	−4.33913	−	13.3545i	−0.459947	−	1.41557i	0.405280	−	0.914193i	$-0.367174\pi$
$90$	5.13158	+	2.10467i	0.540916	+	0.221852i
$91$	−7.25828	−	9.99017i	−0.760875	−	1.04725i
$92$	−7.44203	+	5.40695i	−0.775886	+	0.563714i
$93$	1.96870	+	6.93425i	0.204144	+	0.719048i
$94$			5.91478i			0.610063i
$95$	5.03670	+	1.63652i	0.516754	+	0.167904i
$96$	−14.1707	+	4.02319i	−1.44629	+	0.410615i
$97$	−5.43893	−	7.48605i	−0.552240	−	0.760093i	0.438074	−	0.898939i	$-0.355661\pi$
$97$	−5.43893	−	7.48605i	−0.552240	−	0.760093i	−0.990314	+	0.138846i	$0.955661\pi$
$98$	−1.52040	−	4.67931i	−0.153584	−	0.472682i
$99$	−0.422849	+	5.62303i	−0.0424979	+	0.565136i
$100$	6.51981	−	20.0659i	0.651981	−	2.00659i
$101$			15.5077i			1.54307i	0.636185	+	0.771537i	$0.280512\pi$
$101$			15.5077i			1.54307i	−0.636185	+	0.771537i	$0.719488\pi$
$102$	−3.07455	+	0.872893i	−0.304426	+	0.0864292i
$103$	0.799744	−	2.46136i	0.0788012	−	0.242525i	−0.903894	−	0.427757i	$-0.859304\pi$
$103$	0.799744	−	2.46136i	0.0788012	−	0.242525i	0.982695	+	0.185232i	$0.0593038\pi$
$104$	30.9087	+	22.4565i	3.03084	+	2.20204i
$105$	−0.104822	+	2.79177i	−0.0102296	+	0.272449i
$106$	−33.2484	+	10.8030i	−3.22937	+	1.04928i
$107$	−2.02930	+	2.79310i	−0.196180	+	0.270019i	−0.895762	−	0.444533i	$-0.853370\pi$
$107$	−2.02930	+	2.79310i	−0.196180	+	0.270019i	0.699582	+	0.714552i	$0.253370\pi$
$108$	−23.9236	+	4.88871i	−2.30205	+	0.470416i
$109$	8.98573	−	6.52851i	0.860676	−	0.625318i	−0.0673925	−	0.997727i	$-0.521468\pi$
$109$	8.98573	−	6.52851i	0.860676	−	0.625318i	0.928069	+	0.372409i	$0.121468\pi$
$110$	−3.47508			−0.331336
$111$	0.654497	−	0.833204i	0.0621221	−	0.0790843i
$112$	−11.5266	−	15.8650i	−1.08916	−	1.49910i
$113$	0.445864	−	0.144870i	0.0419434	−	0.0136282i	−0.287970	−	0.957639i	$-0.592980\pi$
$113$	0.445864	−	0.144870i	0.0419434	−	0.0136282i	0.329914	+	0.944011i	$0.392980\pi$
$114$	−31.9743	+	9.07780i	−2.99467	+	0.850214i
$115$	−0.821872	−	1.13121i	−0.0766399	−	0.105486i
$116$	−0.587422	+	1.80790i	−0.0545408	+	0.167859i
$117$	12.5119	+	10.6110i	1.15672	+	0.980992i
$118$	14.6117	+	20.1112i	1.34511	+	1.85139i
$119$	−0.946250	−	1.30240i	−0.0867426	−	0.119391i
$120$	−2.36069	−	8.31494i	−0.215501	−	0.759047i
$121$	2.30742	+	7.10151i	0.209766	+	0.645592i
$122$	−1.03175	+	0.335237i	−0.0934106	+	0.0303510i
$123$	−0.787444	−	0.288947i	−0.0710015	−	0.0260535i
$124$	11.4952	−	15.8218i	1.03230	−	1.42084i
$125$	6.44675	+	2.09468i	0.576615	+	0.187354i
$126$	−9.21346	−	14.9182i	−0.820800	−	1.32902i
$127$	−8.76884	+	2.84917i	−0.778108	+	0.252823i	−0.671032	−	0.741428i	$-0.734149\pi$
$127$	−8.76884	+	2.84917i	−0.778108	+	0.252823i	−0.107076	+	0.994251i	$0.534149\pi$
$128$	−4.03633	−	2.93256i	−0.356764	−	0.259204i
$129$	−15.6002	+	4.42904i	−1.37352	+	0.389955i
$130$	−5.94264	+	8.17934i	−0.521204	+	0.717376i
$131$	6.23808	−	19.1988i	0.545023	−	1.67741i	−0.175911	−	0.984406i	$-0.556287\pi$
$131$	6.23808	−	19.1988i	0.545023	−	1.67741i	0.720934	−	0.693004i	$-0.243713\pi$
$132$	12.7058	−	8.52177i	1.10590	−	0.741725i
$133$	−9.84069	−	13.5446i	−0.853296	−	1.17446i
$134$	33.3250	+	10.8279i	2.87884	+	0.935391i
$135$	−0.743097	−	3.63645i	−0.0639556	−	0.312975i
$136$	4.02951	+	2.92761i	0.345528	+	0.251041i
$137$	−15.3762	+	4.99604i	−1.31368	+	0.426841i	−0.880320	−	0.474380i	$-0.842672\pi$
$137$	−15.3762	+	4.99604i	−1.31368	+	0.426841i	−0.433360	+	0.901221i	$0.642672\pi$
$138$	8.23853	+	3.02307i	0.701310	+	0.257341i
$139$	5.33633	+	16.4235i	0.452621	+	1.39303i	0.873905	+	0.486096i	$0.161580\pi$
$139$	5.33633	+	16.4235i	0.452621	+	1.39303i	−0.421284	+	0.906929i	$0.638420\pi$
$140$	6.13210	−	4.45523i	0.518257	−	0.376536i
$141$	3.28721	−	2.20473i	0.276833	−	0.185672i
$142$	21.9758	−	7.14038i	1.84417	−	0.599207i
$143$	−9.77573	−	3.17633i	−0.817488	−	0.265618i
$144$	19.8697	+	16.8510i	1.65581	+	1.40425i
$145$	−0.274806	−	0.0892898i	−0.0228214	−	0.00741511i
$146$	−4.46890	+	13.7539i	−0.369849	+	1.13828i
$147$	−2.03385	+	2.58919i	−0.167749	+	0.213553i
$148$	−2.87461			−0.236291
$149$	1.22715	−	3.77679i	0.100532	−	0.309407i	−0.888124	−	0.459605i	$-0.847991\pi$
$149$	1.22715	−	3.77679i	0.100532	−	0.309407i	0.988656	+	0.150198i	$0.0479911\pi$
$150$	−19.3627	+	5.49724i	−1.58095	+	0.448848i
$151$	18.0271	+	13.0975i	1.46703	+	1.06586i	0.981462	+	0.191659i	$0.0613867\pi$
$151$	18.0271	+	13.0975i	1.46703	+	1.06586i	0.485567	+	0.874200i	$0.338613\pi$
$152$	41.9056	+	30.4462i	3.39899	+	2.46951i
$153$	1.63115	+	1.38334i	0.131871	+	0.111837i
$154$	8.88771	+	6.45730i	0.716192	+	0.520344i
$155$	2.40496	+	1.74731i	0.193171	+	0.140347i
$156$	1.67003	−	44.4786i	0.133709	−	3.56114i
$157$		−	1.48426i		−	0.118457i	−0.998244	−	0.0592286i	$-0.981136\pi$
$157$		−	1.48426i		−	0.118457i	0.998244	−	0.0592286i	$-0.0188641\pi$
$158$	0.388010	−	0.281906i	0.0308684	−	0.0224272i
$159$	18.3972	+	14.4513i	1.45899	+	1.14607i
$160$	−3.57076	+	4.91473i	−0.282293	+	0.388544i
$161$			4.42031i			0.348369i
$162$	16.5861	+	16.3567i	1.30312	+	1.28510i
$163$	−5.99335	−	4.35442i	−0.469435	−	0.341065i	0.327786	−	0.944752i	$-0.393698\pi$
$163$	−5.99335	−	4.35442i	−0.469435	−	0.341065i	−0.797221	+	0.603687i	$0.793698\pi$
$164$	0.703233	+	2.16433i	0.0549133	+	0.169006i
$165$	1.29533	+	1.93132i	0.100842	+	0.150353i
$166$	12.8818	+	17.7303i	0.999823	+	1.37614i
$167$	−4.70261	−	14.4731i	−0.363899	−	1.11997i	−0.950668	−	0.310211i	$-0.899600\pi$
$167$	−4.70261	−	14.4731i	−0.363899	−	1.11997i	0.586769	−	0.809754i	$-0.300400\pi$
$168$	−9.41301	+	25.6525i	−0.726229	+	1.97913i
$169$	−13.6761	+	9.93630i	−1.05201	+	0.764330i
$170$	−0.774732	+	1.06633i	−0.0594192	+	0.0817835i
$171$	16.9635	+	14.3863i	1.29723	+	1.10015i
$172$	35.5949	+	25.8612i	2.71409	+	1.97190i
$173$			8.98836i			0.683373i	0.939814	+	0.341686i	$0.110998\pi$
$173$			8.98836i			0.683373i	−0.939814	+	0.341686i	$0.889002\pi$
$174$	1.74454	−	0.495291i	0.132253	−	0.0375479i
$175$	−5.95922	−	8.20217i	−0.450475	−	0.620026i
$176$	−15.5245	−	5.04421i	−1.17020	−	0.380222i
$177$	5.73056	−	15.6170i	0.430735	−	1.17385i
$178$	36.3440			2.72410
$179$			4.26373i			0.318686i	0.987223	+	0.159343i	$0.0509376\pi$
$179$			4.26373i			0.318686i	−0.987223	+	0.159343i	$0.949062\pi$
$180$	−6.51321	+	7.67997i	−0.485466	+	0.572431i
$181$	17.4036	+	5.65479i	1.29360	+	0.420317i	0.873351	−	0.487091i	$-0.161942\pi$
$181$	17.4036	+	5.65479i	1.29360	+	0.420317i	0.420251	+	0.907408i	$0.361942\pi$
$182$	30.3972	−	9.87666i	2.25319	−	0.732107i
$183$	0.570897	+	0.448450i	0.0422019	+	0.0331504i
$184$	−4.22613	−	13.0067i	−0.311554	−	0.958865i
$185$		−	0.436948i		−	0.0321251i
$186$	−18.6440	−	0.700022i	−1.36705	−	0.0513281i
$187$	−1.27445	−	0.414092i	−0.0931967	−	0.0302814i
$188$	−10.2131	−	3.31845i	−0.744870	−	0.242023i
$189$	−4.85663	+	10.6812i	−0.353268	+	0.776944i
$190$	−8.05696	+	11.0894i	−0.584513	+	0.804513i
$191$	2.81852	+	8.67450i	0.203941	+	0.627665i	0.999755	+	0.0221246i	$0.00704305\pi$
$191$	2.81852	+	8.67450i	0.203941	+	0.627665i	−0.795814	+	0.605541i	$0.792957\pi$
$192$	0.301810	−	8.03824i	0.0217812	−	0.580110i
$193$	−1.23879	−	0.900031i	−0.0891698	−	0.0647857i	0.542307	−	0.840180i	$-0.317551\pi$
$193$	−1.23879	−	0.900031i	−0.0891698	−	0.0647857i	−0.631477	+	0.775395i	$0.717551\pi$
$194$	22.7779	−	7.40099i	1.63536	−	0.531360i
$195$	6.76087	+	0.253849i	0.484156	+	0.0181785i
$196$	8.93286			0.638061
$197$	−17.2660			−1.23015			−0.615077	−	0.788467i	$-0.710875\pi$
$197$	−17.2660			−1.23015			−0.615077	+	0.788467i	$0.710875\pi$
$198$	−13.5035	−	5.53833i	−0.959651	−	0.393592i
$199$	−18.6373			−1.32116			−0.660580	−	0.750755i	$-0.729690\pi$
$199$	−18.6373			−1.32116			−0.660580	+	0.750755i	$0.729690\pi$
$200$	25.3768	+	18.4373i	1.79441	+	1.30371i
$201$	−6.40409	−	22.5568i	−0.451710	−	1.59104i
$202$	−38.1739	−	12.4034i	−2.68590	−	0.872703i
$203$	0.536915	+	0.739000i	0.0376840	+	0.0518676i
$204$	0.217719	−	5.79860i	0.0152433	−	0.405983i
$205$	−0.328984	+	0.106893i	−0.0229772	+	0.00746576i
$206$	5.41925	+	3.93731i	0.377577	+	0.274326i
$207$	−1.39080	−	5.70550i	−0.0966670	−	0.396560i
$208$	−38.4206	+	27.9142i	−2.66399	+	1.93550i
$209$	−13.2538	−	4.30643i	−0.916786	−	0.297882i
$210$	−6.78840	−	2.49096i	−0.468444	−	0.171892i
$211$	−13.8859	+	4.26393i	−0.955946	+	0.293541i
$211$	−13.8859	+	4.26393i	−0.955946	+	0.293541i
$212$		−	63.4715i		−	4.35924i
$213$	−12.1598	−	9.55174i	−0.833176	−	0.654475i
$214$	−5.25242	−	7.22934i	−0.359048	−	0.494188i
$215$	−3.93097	+	5.41052i	−0.268090	+	0.368995i
$216$	4.07856	−	36.0726i	0.277511	−	2.45443i
$217$	−2.90403	−	8.93767i	−0.197138	−	0.606729i
$218$	8.88363	+	27.3410i	0.601675	+	1.85177i
$219$	9.30964	−	2.64309i	0.629087	−	0.178604i
$220$	1.94967	−	6.00048i	0.131447	−	0.404552i
$221$	−3.15405	+	2.29155i	−0.212164	+	0.154146i
$222$	1.52754	+	2.27753i	0.102522	+	0.152858i
$223$		−	1.99410i		−	0.133535i	−0.997769	−	0.0667675i	$-0.978731\pi$
$223$		−	1.99410i		−	0.133535i	0.997769	−	0.0667675i	$-0.0212686\pi$
$224$	18.2648	−	5.93460i	1.22037	−	0.396522i
$225$	10.2726	+	8.71192i	0.684837	+	0.580795i
$226$			1.21341i			0.0807150i
$227$	17.4723	−	5.67708i	1.15967	−	0.376801i	0.334895	−	0.942256i	$-0.391299\pi$
$227$	17.4723	−	5.67708i	1.15967	−	0.376801i	0.824780	+	0.565454i	$0.191299\pi$
$228$	2.26420	−	60.3036i	0.149950	−	3.99370i
$229$	10.0544	−	13.8387i	0.664414	−	0.914487i	−0.335203	−	0.942146i	$-0.608805\pi$
$229$	10.0544	−	13.8387i	0.664414	−	0.914487i	0.999617	+	0.0276583i	$0.00880504\pi$
$230$	3.44195	−	1.11836i	0.226955	−	0.0737423i
$231$	0.275833	−	7.34640i	0.0181485	−	0.483357i
$232$	−2.28640	−	1.66117i	−0.150109	−	0.109061i
$233$	7.45252	−	5.41458i	0.488231	−	0.354721i	−0.316273	−	0.948668i	$-0.602431\pi$
$233$	7.45252	−	5.41458i	0.488231	−	0.354721i	0.804504	+	0.593948i	$0.202431\pi$
$234$	−36.1276	+	22.3124i	−2.36173	+	1.45861i
$235$	0.504414	−	1.55243i	0.0329043	−	0.101269i
$236$	−42.9242	+	13.9469i	−2.79412	+	0.907866i
$237$	−0.301303	−	0.110561i	−0.0195717	−	0.00718170i
$238$	3.96284	−	1.28760i	0.256873	−	0.0834630i
$239$	−7.50010	+	23.0829i	−0.485141	+	1.49311i	0.346635	+	0.938000i	$0.387324\pi$
$239$	−7.50010	+	23.0829i	−0.485141	+	1.49311i	−0.831776	+	0.555111i	$0.812676\pi$
$240$	10.7367	+	0.403128i	0.693050	+	0.0260218i
$241$	7.08042	−	21.7913i	0.456090	−	1.40370i	−0.413761	−	0.910386i	$-0.635785\pi$
$241$	7.08042	−	21.7913i	0.456090	−	1.40370i	0.869851	−	0.493315i	$-0.164215\pi$
$242$	−19.3267			−1.24237
$243$	2.90797	−	15.3148i	0.186546	−	0.982446i
$244$		−	1.96963i		−	0.126093i
$245$			1.35782i			0.0867479i
$246$	1.34109	−	1.70727i	0.0855049	−	0.108852i
$247$	−32.8011	+	23.8314i	−2.08708	+	1.51635i
$248$	17.0901	+	23.5225i	1.08522	+	1.49368i
$249$	5.05213	−	13.7682i	0.320166	−	0.872522i
$250$	−10.3126	+	14.1940i	−0.652223	+	0.897708i
$251$	9.43190			0.595336			0.297668	−	0.954669i	$-0.403791\pi$
$251$	9.43190			0.595336			0.297668	+	0.954669i	$0.403791\pi$
$252$	30.9286	−	7.53928i	1.94832	−	0.474930i
$253$	2.16271	+	2.97672i	0.135969	+	0.187145i
$254$		−	23.8643i		−	1.49738i
$255$	0.881403	+	0.0330938i	0.0551956	+	0.00207242i
$256$	17.9616	−	13.0498i	1.12260	−	0.815615i
$257$	4.16753	−	5.73612i	0.259964	−	0.357809i	−0.659006	−	0.752138i	$-0.729023\pi$
$257$	4.16753	−	5.73612i	0.259964	−	0.357809i	0.918970	+	0.394328i	$0.129023\pi$
$258$	1.57486	−	41.9440i	0.0980466	−	2.61132i
$259$	−0.811925	+	1.11752i	−0.0504505	+	0.0694392i
$260$	−10.7893	−	14.8502i	−0.669125	−	0.920971i
$261$	−0.925538	−	0.784928i	−0.0572894	−	0.0485858i
$262$	42.2706	+	30.7114i	2.61149	+	1.89736i
$263$	−29.6454	−	9.63238i	−1.82802	−	0.593958i	−0.999418	−	0.0341136i	$-0.989139\pi$
$263$	−29.6454	−	9.63238i	−1.82802	−	0.593958i	−0.828598	−	0.559845i	$-0.810861\pi$
$264$	6.21204	+	21.8804i	0.382324	+	1.34664i
$265$	9.64784			0.592662
$266$	41.2122	−	13.3907i	2.52688	−	0.821034i
$267$	−13.5472	−	20.1986i	−0.829075	−	1.23614i
$268$	−37.3936	+	51.4678i	−2.28417	+	3.14390i
$269$		−	11.2392i		−	0.685268i	−0.939469	−	0.342634i	$-0.888681\pi$
$269$		−	11.2392i		−	0.685268i	0.939469	−	0.342634i	$-0.111319\pi$
$270$	9.54585	+	1.07931i	0.580942	+	0.0656845i
$271$	2.74065	−	3.77218i	0.166483	−	0.229144i	−0.717622	−	0.696433i	$-0.754769\pi$
$271$	2.74065	−	3.77218i	0.166483	−	0.229144i	0.884104	+	0.467289i	$0.154769\pi$
$272$	−5.00883	+	3.63913i	−0.303705	+	0.220654i
$273$	−16.8196	−	13.2121i	−1.01797	−	0.799632i
$274$		−	41.8462i		−	2.52802i
$275$	−8.02611	−	2.60784i	−0.483993	−	0.157259i
$276$	−9.84216	+	12.5295i	−0.592428	+	0.754189i
$277$	−7.20664	+	22.1797i	−0.433005	+	1.33265i	0.462113	+	0.886821i	$0.347092\pi$
$277$	−7.20664	+	22.1797i	−0.433005	+	1.33265i	−0.895117	+	0.445830i	$0.852908\pi$
$278$	−44.6964			−2.68071
$279$	6.56049	+	10.6226i	0.392766	+	0.635956i
$280$	3.48225	+	10.7173i	0.208105	+	0.640480i
$281$	11.6073	−	15.9760i	0.692431	−	0.953049i	−0.307568	−	0.951526i	$-0.599515\pi$
$281$	11.6073	−	15.9760i	0.692431	−	0.953049i	0.999999	−	0.00152323i	$-0.000484858\pi$
$282$	2.79799	+	9.85521i	0.166618	+	0.586869i
$283$	−0.676935	+	0.219949i	−0.0402396	+	0.0130746i	−0.329068	−	0.944306i	$-0.606734\pi$
$283$	−0.676935	+	0.219949i	−0.0402396	+	0.0130746i	0.288828	+	0.957381i	$0.406734\pi$
$284$			41.9521i			2.48940i
$285$	9.16631	+	0.344165i	0.542965	+	0.0203866i
$286$	15.6377	−	21.5235i	0.924679	−	1.27271i
$287$	1.04002	+	0.337923i	0.0613905	+	0.0199470i
$288$	−21.7080	+	13.4069i	−1.27916	+	0.790008i
$289$	13.3421	−	9.69360i	0.784829	−	0.570212i
$290$	0.439593	−	0.605048i	0.0258138	−	0.0355296i
$291$	−12.6036	−	9.90037i	−0.738838	−	0.580370i
$292$	−21.2418	−	15.4330i	−1.24308	−	0.903150i
$293$	15.1076	+	20.7938i	0.882593	+	1.21479i	0.975696	+	0.219129i	$0.0703216\pi$
$293$	15.1076	+	20.7938i	0.882593	+	1.21479i	−0.0931024	+	0.995657i	$0.529678\pi$
$294$	−4.74684	−	7.07745i	−0.276842	−	0.412765i
$295$	−2.11997	−	6.52459i	−0.123429	−	0.379876i
$296$	1.32065	−	4.06453i	0.0767611	−	0.236246i
$297$	1.95542	+	9.56912i	0.113465	+	0.555257i
$298$	8.31547	+	6.04154i	0.481702	+	0.349977i
$299$	10.7047			0.619071
$300$	1.37113	−	36.5180i	0.0791623	−	2.10837i
$301$	20.1074	−	6.53328i	1.15897	−	0.376572i
$302$	−46.6594	+	33.9001i	−2.68495	+	1.95073i
$303$	7.33591	+	25.8389i	0.421437	+	1.48441i
$304$	−52.0902	+	37.8457i	−2.98758	+	2.17060i
$305$	0.299389			0.0171430
$306$	−4.70989	+	2.90883i	−0.269246	+	0.166287i
$307$	11.7783	−	8.55741i	0.672221	−	0.488397i	−0.198547	−	0.980091i	$-0.563622\pi$
$307$	11.7783	−	8.55741i	0.672221	−	0.488397i	0.870768	+	0.491694i	$0.163622\pi$
$308$	−16.1363	+	11.7237i	−0.919452	+	0.668021i
$309$	0.168188	−	4.47944i	0.00956790	−	0.254826i
$310$	−6.22474	+	4.52254i	−0.353541	+	0.256863i
$311$	15.4375	+	5.01594i	0.875379	+	0.284428i	0.712037	−	0.702142i	$-0.247773\pi$
$311$	15.4375	+	5.01594i	0.875379	+	0.284428i	0.163342	+	0.986570i	$0.447773\pi$
$312$	62.1231	+	22.7956i	3.51703	+	1.29055i
$313$	−10.5909	−	14.5772i	−0.598635	−	0.823951i	0.396947	−	0.917841i	$-0.370070\pi$
$313$	−10.5909	−	14.5772i	−0.598635	−	0.823951i	−0.995583	+	0.0938907i	$0.970070\pi$
$314$	3.65368	+	1.18715i	0.206189	+	0.0669948i
$315$	1.14599	+	4.70123i	0.0645693	+	0.264884i
$316$	0.269080	+	0.828144i	0.0151370	+	0.0465868i
$317$	−3.15989	−	9.72515i	−0.177477	−	0.546219i	0.822261	−	0.569111i	$-0.192713\pi$
$317$	−3.15989	−	9.72515i	−0.177477	−	0.546219i	−0.999738	+	0.0228921i	$0.992713\pi$
$318$	−50.2881	+	33.7282i	−2.82001	+	1.89138i
$319$	0.723137	+	0.234962i	0.0404879	+	0.0131553i
$320$	−1.94986	−	2.68375i	−0.109001	−	0.150026i
$321$	−2.05995	+	5.61382i	−0.114975	+	0.313333i
$322$	−10.8811	−	3.53547i	−0.606378	−	0.197024i
$323$	−4.27622	+	3.10685i	−0.237935	+	0.172870i
$324$	−37.5488	+	19.4626i	−2.08605	+	1.08126i
$325$	−19.8633	+	14.4316i	−1.10182	+	0.800518i
$326$	15.5125	−	11.2705i	0.859159	−	0.624216i
$327$	11.8837	−	15.1285i	0.657171	−	0.836608i
$328$	−3.38332			−0.186813
$329$	−4.17474	+	3.03313i	−0.230161	+	0.167222i
$330$	−5.79018	+	1.64389i	−0.318739	+	0.0904930i
$331$	9.75450	−	7.08706i	0.536156	−	0.389540i	−0.286500	−	0.958080i	$-0.592492\pi$
$331$	9.75450	−	7.08706i	0.536156	−	0.389540i	0.822655	+	0.568540i	$0.192492\pi$
$332$	−37.8425	+	12.2958i	−2.07687	+	0.674817i
$333$	0.696376	−	1.69790i	0.0381611	−	0.0930441i
$334$	39.3885			2.15524
$335$	−7.82325	−	5.68392i	−0.427430	−	0.310546i
$336$	−26.7106	−	20.9816i	−1.45718	−	1.14464i
$337$	7.74105	−	23.8245i	0.421682	−	1.29780i	−0.484454	−	0.874817i	$-0.660982\pi$
$337$	7.74105	−	23.8245i	0.421682	−	1.29780i	0.906136	−	0.422986i	$-0.139018\pi$
$338$	−13.5208	−	41.6126i	−0.735432	−	2.26343i
$339$	0.674368	−	0.452298i	0.0366266	−	0.0245655i
$340$	−1.40658	−	1.93600i	−0.0762828	−	0.104994i
$341$	−6.32854	−	4.59795i	−0.342709	−	0.248993i
$342$	−48.9813	+	30.2509i	−2.64861	+	1.63578i
$343$	11.8141	−	16.2607i	0.637900	−	0.877994i
$344$	−52.9193	+	38.4481i	−2.85322	+	2.07298i
$345$	−1.90452	−	1.49604i	−0.102536	−	0.0805438i
$346$	−22.1258	−	7.18912i	−1.18949	−	0.386489i
$347$	7.82022	−	10.7636i	0.419811	−	0.577821i	−0.545766	−	0.837938i	$-0.683761\pi$
$347$	7.82022	−	10.7636i	0.419811	−	0.577821i	0.965577	+	0.260117i	$0.0837611\pi$
$348$	−0.123536	+	3.29020i	−0.00662225	+	0.176373i
$349$		−	13.6809i		−	0.732320i	−0.930552	−	0.366160i	$-0.880672\pi$
$349$		−	13.6809i		−	0.732320i	0.930552	−	0.366160i	$-0.119328\pi$
$350$	24.9569	−	8.10898i	1.33400	−	0.433443i
$351$	25.8669	+	11.7614i	1.38067	+	0.627776i
$352$	9.39628	−	12.9329i	0.500823	−	0.689324i
$353$	10.8331	+	33.3407i	0.576586	+	1.77455i	0.630716	+	0.776014i	$0.282761\pi$
$353$	10.8331	+	33.3407i	0.576586	+	1.77455i	−0.0541302	+	0.998534i	$0.517239\pi$
$354$	33.8596	+	26.5973i	1.79962	+	1.41363i
$355$	−6.37683			−0.338447
$356$	−20.3906	+	62.7558i	−1.08070	+	3.32605i
$357$	−2.19274	−	1.72244i	−0.116052	−	0.0911611i
$358$	−10.4956	−	3.41024i	−0.554712	−	0.180237i
$359$		−	27.3611i		−	1.44406i	−0.691860	−	0.722032i	$-0.743209\pi$
$359$		−	27.3611i		−	1.44406i	0.691860	−	0.722032i	$-0.256791\pi$
$360$	−7.86677	−	12.7376i	−0.414615	−	0.671333i
$361$	−29.1000	+	21.1424i	−1.53158	+	1.11276i
$362$	−27.8397	+	38.3181i	−1.46322	+	2.01396i
$363$	7.20399	+	10.7410i	0.378112	+	0.563757i
$364$			58.0287i			3.04153i
$365$	2.34586	−	3.22881i	0.122788	−	0.169003i
$366$	−1.56053	+	1.04664i	−0.0815700	+	0.0547089i
$367$	−15.8205	+	5.14039i	−0.825823	+	0.268326i	−0.691285	−	0.722582i	$-0.742955\pi$
$367$	−15.8205	+	5.14039i	−0.825823	+	0.268326i	−0.134538	+	0.990908i	$0.542955\pi$
$368$	16.9998			0.886176
$369$	−1.44873	−	0.108944i	−0.0754177	−	0.00567137i
$370$	1.07559	+	0.349482i	0.0559175	+	0.0181687i
$371$	−24.6749	−	17.9273i	−1.28106	−	0.930742i
$372$	11.6689	−	31.8002i	0.605002	−	1.64876i
$373$	1.24850	+	1.71841i	0.0646446	+	0.0889757i	0.840115	−	0.542408i	$-0.182487\pi$
$373$	1.24850	+	1.71841i	0.0646446	+	0.0889757i	−0.775471	+	0.631384i	$0.782487\pi$
$374$	2.03867	−	2.80598i	0.105417	−	0.145094i
$375$	11.7325	+	0.440516i	0.605862	+	0.0227482i
$376$	9.38422	−	12.9163i	0.483954	−	0.666106i
$377$	1.78965	−	1.30026i	0.0921716	−	0.0669666i
$378$	−22.4085	−	20.4982i	−1.15257	−	1.05432i
$379$		−	24.1561i		−	1.24082i	−0.784279	−	0.620408i	$-0.786967\pi$
$379$		−	24.1561i		−	1.24082i	0.784279	−	0.620408i	$-0.213033\pi$
$380$	−14.6280	−	20.1337i	−0.750402	−	1.03284i
$381$	−13.2628	+	8.89538i	−0.679476	+	0.455724i
$382$	−23.6076			−1.20787
$383$	−8.10588	+	11.1568i	−0.414191	+	0.570085i	−0.964234	−	0.265051i	$-0.914611\pi$
$383$	−8.10588	+	11.1568i	−0.414191	+	0.570085i	0.550043	+	0.835136i	$0.314611\pi$
$384$	−8.11258	−	2.97685i	−0.413993	−	0.151912i
$385$	−1.78204	−	2.45277i	−0.0908211	−	0.125005i
$386$	3.20634	−	2.32954i	0.163198	−	0.118570i
$387$	−23.8979	+	14.7593i	−1.21480	+	0.750259i
$388$			43.4833i			2.20753i
$389$			12.7091i			0.644377i	0.946676	+	0.322188i	$0.104418\pi$
$389$			12.7091i			0.644377i	−0.946676	+	0.322188i	$0.895582\pi$
$390$	−6.03239	+	16.4396i	−0.305462	+	0.832451i
$391$	1.39556			0.0705764
$392$	−4.10392	+	12.6306i	−0.207279	+	0.637940i
$393$	1.31188	−	34.9400i	0.0661758	−	1.76249i
$394$	13.8098	−	42.5022i	0.695728	−	2.14123i
$395$	−0.125880	+	0.0409010i	−0.00633372	+	0.00205795i
$396$	17.1392	−	20.2095i	0.861276	−	1.01556i
$397$	−26.6394	+	8.65566i	−1.33699	+	0.434415i	−0.888297	−	0.459270i	$-0.848111\pi$
$397$	−26.6394	+	8.65566i	−1.33699	+	0.434415i	−0.448696	+	0.893685i	$0.648111\pi$
$398$	14.9066	−	45.8777i	0.747198	−	2.29964i
$399$	−22.8038	−	17.9128i	−1.14162	−	0.896762i
$400$	−31.5442	+	22.9182i	−1.57721	+	1.14591i
$401$	27.1440	+	19.7212i	1.35551	+	0.984832i	0.998717	+	0.0506469i	$0.0161283\pi$
$401$	27.1440	+	19.7212i	1.35551	+	0.984832i	0.356788	+	0.934185i	$0.383872\pi$
$402$	60.6482	+	2.27714i	3.02486	+	0.113574i
$403$	−21.6445	+	7.03273i	−1.07819	+	0.350325i
$404$	42.8344	−	58.9566i	2.13109	−	2.93320i
$405$	−2.95837	−	5.70753i	−0.147003	−	0.283609i
$406$	−2.24857	+	0.730604i	−0.111594	+	0.0362592i
$407$			1.14981i			0.0569938i
$408$	8.09888	+	2.97183i	0.400954	+	0.147127i
$409$	8.88278	−	2.88619i	0.439225	−	0.142713i	−0.0810529	−	0.996710i	$-0.525828\pi$
$409$	8.88278	−	2.88619i	0.439225	−	0.142713i	0.520278	+	0.853997i	$0.325828\pi$
$410$		−	0.895326i		−	0.0442170i
$411$	−23.2565	+	15.5981i	−1.14716	+	0.769399i
$412$	−9.83906	+	7.14850i	−0.484736	+	0.352181i
$413$	−6.70188	+	20.6263i	−0.329778	+	1.01495i
$414$	15.1571	+	1.13981i	0.744931	+	0.0560184i
$415$	−1.86899	−	5.75216i	−0.0917451	−	0.282362i
$416$	−14.3719	−	44.2322i	−0.704642	−	2.16866i
$417$	16.6605	+	24.8405i	0.815870	+	1.21645i
$418$	21.2015	−	29.1813i	1.03700	−	1.42730i
$419$	1.74209	+	2.39778i	0.0851067	+	0.117139i	0.849447	−	0.527673i	$-0.176935\pi$
$419$	1.74209	+	2.39778i	0.0851067	+	0.117139i	−0.764341	+	0.644813i	$0.776935\pi$
$420$	8.10977	−	10.3241i	0.395716	−	0.503765i
$421$			3.91818i			0.190960i	0.995431	+	0.0954802i	$0.0304387\pi$
$421$			3.91818i			0.190960i	−0.995431	+	0.0954802i	$0.969561\pi$
$422$	0.610186	−	37.5921i	0.0297034	−	1.82996i
$423$	4.43420	−	5.22853i	0.215598	−	0.254220i
$424$	89.7452	+	29.1600i	4.35841	+	1.41613i
$425$	−2.58955	+	1.88142i	−0.125612	+	0.0912621i
$426$	33.2384	−	22.2930i	1.61040	−	1.08010i
$427$	−0.765704	−	0.556317i	−0.0370550	−	0.0269220i
$428$	15.4299	−	5.01347i	0.745831	−	0.242335i
$429$	−17.7909	−	0.667990i	−0.858952	−	0.0322509i
$430$	−10.1745	−	14.0040i	−0.490658	−	0.675332i
$431$	−0.139267	−	0.0452506i	−0.00670826	−	0.00217965i	0.305661	−	0.952140i	$-0.401123\pi$
$431$	−0.139267	−	0.0452506i	−0.00670826	−	0.00217965i	−0.312369	+	0.949961i	$0.601123\pi$
$432$	41.0782	+	18.6778i	1.97638	+	0.898637i
$433$	23.2291	+	16.8769i	1.11632	+	0.811052i	0.983647	−	0.180108i	$-0.0576448\pi$
$433$	23.2291	+	16.8769i	1.11632	+	0.811052i	0.132670	+	0.991160i	$0.457645\pi$
$434$	24.3238			1.16758
$435$	−0.500120	−	0.0187779i	−0.0239789	−	0.000900330i
$436$	−52.1943			−2.49965
$437$	14.5134			0.694268
$438$	−0.939821	+	25.0307i	−0.0449064	+	1.19601i
$439$	26.4164	−	8.58321i	1.26079	−	0.409654i	0.399012	−	0.916946i	$-0.369353\pi$
$439$	26.4164	−	8.58321i	1.26079	−	0.409654i	0.861775	+	0.507291i	$0.169353\pi$
$440$	7.58863	+	5.51346i	0.361774	+	0.262844i
$441$	−2.16399	+	5.27622i	−0.103047	+	0.251249i
$442$	−3.11821	−	9.59687i	−0.148318	−	0.456476i
$443$	6.86277	−	9.44579i	0.326060	−	0.448783i	−0.614245	−	0.789115i	$-0.710539\pi$
$443$	6.86277	−	9.44579i	0.326060	−	0.448783i	0.940305	+	0.340332i	$0.110539\pi$
$444$	−4.78967	+	1.35983i	−0.227308	+	0.0645348i
$445$	−9.53906	−	3.09943i	−0.452195	−	0.146927i
$446$	4.90870	+	1.59493i	0.232434	+	0.0755223i
$447$	0.258073	−	6.87339i	0.0122065	−	0.325100i
$448$			10.4870i			0.495465i
$449$	−9.68034	−	29.7930i	−0.456843	−	1.40602i	−0.868957	−	0.494887i	$-0.835209\pi$
$449$	−9.68034	−	29.7930i	−0.456843	−	1.40602i	0.412114	−	0.911132i	$-0.364791\pi$
$450$	−29.6616	+	18.3190i	−1.39826	+	0.863566i
$451$	0.865705	−	0.281284i	0.0407644	−	0.0132452i
$452$	−2.09522	−	0.680778i	−0.0985509	−	0.0320211i
$453$	36.2326	+	13.2953i	1.70236	+	0.624668i
$454$			47.5505i			2.23166i
$455$	−8.82052			−0.413512
$456$	84.2257	+	30.9060i	3.94423	+	1.44731i
$457$	31.8192	+	10.3387i	1.48844	+	0.483623i	0.936622	−	0.350341i	$-0.113934\pi$
$457$	31.8192	+	10.3387i	1.48844	+	0.483623i	0.551818	+	0.833965i	$0.313934\pi$
$458$	26.0237	+	35.8186i	1.21601	+	1.67369i
$459$	3.37222	+	1.53331i	0.157402	+	0.0715689i
$460$			6.57072i			0.306361i
$461$	−19.2049	−	13.9532i	−0.894463	−	0.649866i	0.0425746	−	0.999093i	$-0.486444\pi$
$461$	−19.2049	−	13.9532i	−0.894463	−	0.649866i	−0.937038	+	0.349228i	$0.886444\pi$
$462$	17.8633	+	6.55483i	0.831078	+	0.304958i
$463$	−0.829848	+	1.14219i	−0.0385663	+	0.0530820i	−0.827865	−	0.560928i	$-0.810444\pi$
$463$	−0.829848	+	1.14219i	−0.0385663	+	0.0530820i	0.789298	+	0.614010i	$0.210444\pi$
$464$	2.84207	−	2.06489i	0.131940	−	0.0958600i
$465$	4.83371	+	1.77370i	0.224158	+	0.0822533i
$466$	7.36785	+	22.6759i	0.341309	+	1.05044i
$467$	−24.9430	−	34.3311i	−1.15422	−	1.58865i	−0.730585	−	0.682822i	$-0.760753\pi$
$467$	−24.9430	−	34.3311i	−1.15422	−	1.58865i	−0.423639	−	0.905831i	$-0.639247\pi$
$468$	−18.2580	−	74.9003i	−0.843976	−	3.46227i
$469$	9.44668	+	29.0739i	0.436207	+	1.34251i
$470$	3.41802	+	2.48334i	0.157662	+	0.114548i
$471$	−0.702131	−	2.47308i	−0.0323525	−	0.113954i
$472$		−	67.0999i		−	3.08852i
$473$	10.3442	−	14.2375i	0.475625	−	0.654642i
$474$	0.513147	−	0.653259i	0.0235696	−	0.0300052i
$475$	−26.9305	+	19.5661i	−1.23565	+	0.897755i
$476$			7.56510i			0.346746i
$477$	37.4896	+	15.3760i	1.71653	+	0.704019i
$478$	−50.8224	−	36.9246i	−2.32456	−	1.68889i
$479$	4.45280	+	3.23515i	0.203454	+	0.147818i	0.684847	−	0.728687i	$-0.259869\pi$
$479$	4.45280	+	3.23515i	0.203454	+	0.147818i	−0.481393	+	0.876505i	$0.659869\pi$
$480$	−3.62469	+	9.87808i	−0.165444	+	0.450870i
$481$	2.70631	+	1.96625i	0.123397	+	0.0896533i
$482$	47.9785	+	34.8584i	2.18536	+	1.58776i
$483$	2.09103	+	7.36512i	0.0951450	+	0.335125i
$484$	10.8431	−	33.3717i	0.492869	−	1.51689i
$485$	−6.60958			−0.300125
$486$	35.3732	+	19.4075i	1.60456	+	0.880340i
$487$	1.87306	−	5.76470i	0.0848766	−	0.261223i	−0.899607	−	0.436701i	$-0.856147\pi$
$487$	1.87306	−	5.76470i	0.0848766	−	0.261223i	0.984483	+	0.175477i	$0.0561469\pi$
$488$	2.78495	+	0.904884i	0.126069	+	0.0409622i
$489$	−12.0460	−	4.42019i	−0.544738	−	0.199888i
$490$	−3.34242	−	1.08602i	−0.150995	−	0.0490613i
$491$	0.614062	−	0.199521i	0.0277122	−	0.00900425i	−0.295128	−	0.955458i	$-0.595362\pi$
$491$	0.614062	−	0.199521i	0.0277122	−	0.00900425i	0.322840	+	0.946453i	$0.395362\pi$
$492$	2.19556	+	3.27354i	0.0989836	+	0.147583i
$493$	0.233313	−	0.169512i	0.0105079	−	0.00763444i
$494$	−32.4284	−	99.8043i	−1.45902	−	4.49041i
$495$	3.07189	+	2.60520i	0.138071	+	0.117095i
$496$	−34.3728	+	11.1684i	−1.54339	+	0.501477i
$497$	16.3091	+	11.8493i	0.731563	+	0.531512i
$498$	29.8510	+	23.4485i	1.33766	+	1.05075i
$499$	26.5919	+	8.64024i	1.19042	+	0.386790i	0.836228	−	0.548383i	$-0.184756\pi$
$499$	26.5919	+	8.64024i	1.19042	+	0.386790i	0.354191	+	0.935173i	$0.384756\pi$
$500$	−18.7232	−	25.7703i	−0.837328	−	1.15248i
$501$	−14.6820	−	21.8906i	−0.655944	−	0.977999i
$502$	−7.54387	+	23.2176i	−0.336699	+	1.03625i
$503$	−1.79060	+	2.46455i	−0.0798390	+	0.109889i	−0.847069	−	0.531484i	$-0.821635\pi$
$503$	−1.79060	+	2.46455i	−0.0798390	+	0.109889i	0.767230	+	0.641373i	$0.221635\pi$
$504$	−3.54904	+	47.1950i	−0.158087	+	2.10223i
$505$	8.96156	+	6.51095i	0.398784	+	0.289734i
$506$	−9.05731	+	2.94290i	−0.402647	+	0.130828i
$507$	−18.0868	+	23.0254i	−0.803264	+	1.02259i
$508$	41.2068	+	13.3889i	1.82826	+	0.594037i
$509$	−8.59222	+	11.8262i	−0.380844	+	0.524186i	−0.955808	−	0.293992i	$-0.905016\pi$
$509$	−8.59222	+	11.8262i	−0.380844	+	0.524186i	0.574964	+	0.818179i	$0.305016\pi$
$510$	−0.786432	+	2.14320i	−0.0348238	+	0.0949025i
$511$	−11.9994	+	3.89883i	−0.530820	+	0.172474i
$512$	14.6740	+	45.1620i	0.648506	+	1.99590i
$513$	35.0700	+	15.9459i	1.54838	+	0.704031i
$514$	10.7868	+	14.8467i	0.475785	+	0.654861i
$515$	−1.08659	−	1.49556i	−0.0478809	−	0.0659024i
$516$	71.5419	+	26.2518i	3.14945	+	1.15567i
$517$	−1.32734	+	4.08513i	−0.0583763	+	0.179664i
$518$	−2.10150	−	2.89246i	−0.0923344	−	0.127087i
$519$	4.25194	+	14.9764i	0.186640	+	0.657392i
$520$	25.9542	−	8.43303i	1.13817	−	0.369813i
$521$	−8.29783	−	11.4210i	−0.363534	−	0.500362i	0.587595	−	0.809155i	$-0.300075\pi$
$521$	−8.29783	−	11.4210i	−0.363534	−	0.500362i	−0.951129	+	0.308793i	$0.900075\pi$
$522$	2.67245	−	1.65051i	0.116970	−	0.0722408i
$523$	3.40637			0.148950			0.0744751	−	0.997223i	$-0.476272\pi$
$523$	3.40637			0.148950			0.0744751	+	0.997223i	$0.476272\pi$
$524$	−76.7456	+	55.7589i	−3.35265	+	2.43584i
$525$	−13.8093	−	10.8474i	−0.602687	−	0.473421i
$526$	47.4223	−	65.2712i	2.06771	−	2.84596i
$527$	−2.82176	+	0.916844i	−0.122918	+	0.0399384i
$528$	−28.2531	−	1.06081i	−1.22956	−	0.0461658i
$529$	15.5073	+	11.2667i	0.674231	+	0.489858i
$530$	−7.71658	+	23.7492i	−0.335187	+	1.03160i
$531$	2.16063	−	28.7319i	0.0937632	−	1.24686i
$532$			78.6745i			3.41097i
$533$	0.818354	−	2.51864i	0.0354469	−	0.109094i
$534$	60.5565	−	17.1925i	2.62053	−	0.743994i
$535$	0.762061	+	2.34538i	0.0329468	+	0.101400i
$536$	−55.5934	−	76.5177i	−2.40127	−	3.30506i
$537$	2.01696	+	7.10423i	0.0870381	+	0.306570i
$538$	27.6666	+	8.98942i	1.19279	+	0.387562i
$539$		−	3.57303i		−	0.153901i
$540$	−7.21930	+	15.8774i	−0.310669	+	0.683256i
$541$	19.5121	−	14.1764i	0.838891	−	0.609490i	−0.0831699	−	0.996535i	$-0.526504\pi$
$541$	19.5121	−	14.1764i	0.838891	−	0.609490i	0.922061	+	0.387046i	$0.126504\pi$
$542$	7.09359	+	9.76349i	0.304696	+	0.419378i
$543$	31.6730	+	1.18922i	1.35922	+	0.0510342i
$544$	−1.87364	−	5.76648i	−0.0803318	−	0.247236i
$545$		−	7.93367i		−	0.339841i
$546$	45.9757	−	30.8359i	1.96758	−	1.31966i
$547$	−7.92210	+	24.3817i	−0.338725	+	1.04249i	0.626133	+	0.779716i	$0.284637\pi$
$547$	−7.92210	+	24.3817i	−0.338725	+	1.04249i	−0.964858	+	0.262772i	$0.915363\pi$
$548$	72.2566	+	23.4776i	3.08665	+	1.00291i
$549$	1.16337	+	0.477144i	0.0496513	+	0.0203640i
$550$	12.8390	−	17.6713i	0.547455	−	0.753508i
$551$	2.42638	−	1.76287i	0.103367	−	0.0751008i
$552$	−13.1944	−	19.6726i	−0.561590	−	0.837320i
$553$	0.397947	+	0.129301i	0.0169224	+	0.00549843i
$554$	−48.8338	−	35.4798i	−2.07475	−	1.50739i
$555$	−0.206698	−	0.728043i	−0.00877385	−	0.0309037i
$556$	25.0767	−	77.1780i	1.06349	−	3.27308i
$557$	−3.40672	+	10.4848i	−0.144347	+	0.444255i	−0.996926	−	0.0783427i	$-0.975037\pi$
$557$	−3.40672	+	10.4848i	−0.144347	+	0.444255i	0.852579	+	0.522598i	$0.175037\pi$
$558$	−31.3958	+	7.65317i	−1.32909	+	0.323985i
$559$	−15.8217	−	48.6943i	−0.669189	−	2.05955i
$560$	−14.0075			−0.591926
$561$	−2.31937	−	0.0870847i	−0.0979238	−	0.00367672i
$562$	30.0429	+	41.3505i	1.26728	+	1.74427i
$563$	−22.2912	−	16.1955i	−0.939464	−	0.682561i	0.00882754	−	0.999961i	$-0.497190\pi$
$563$	−22.2912	−	16.1955i	−0.939464	−	0.682561i	−0.948292	+	0.317400i	$0.897190\pi$
$564$	−18.5869	−	0.697879i	−0.782651	−	0.0293860i
$565$	0.103480	−	0.318479i	0.00435344	−	0.0133985i
$566$		−	1.84227i		−	0.0774363i
$567$	−3.03938	+	20.0945i	−0.127642	+	0.843889i
$568$	−59.3179	−	19.2736i	−2.48892	−	0.808701i
$569$	3.63062	−	11.1739i	0.152203	−	0.468434i	−0.845663	−	0.533717i	$-0.820795\pi$
$569$	3.63062	−	11.1739i	0.152203	−	0.468434i	0.997867	+	0.0652827i	$0.0207949\pi$
$570$	−8.17864	+	22.2886i	−0.342566	+	0.933566i
$571$	−17.1375	−	5.56830i	−0.717181	−	0.233026i	−0.0723806	−	0.997377i	$-0.523060\pi$
$571$	−17.1375	−	5.56830i	−0.717181	−	0.233026i	−0.644801	+	0.764351i	$0.723060\pi$
$572$	28.3915	+	39.0776i	1.18711	+	1.63392i
$573$	8.79969	+	13.1202i	0.367612	+	0.548103i
$574$	−1.66367	+	2.28984i	−0.0694402	+	0.0955763i
$575$	8.78885			0.366520
$576$	−3.29961	−	13.5361i	−0.137484	−	0.564004i
$577$	−5.85370	+	8.05693i	−0.243693	+	0.335414i	−0.913290	−	0.407310i	$-0.866467\pi$
$577$	−5.85370	+	8.05693i	−0.243693	+	0.335414i	0.669597	+	0.742725i	$0.266467\pi$
$578$	13.1905	+	40.5962i	0.548653	+	1.68858i
$579$	−2.48983	−	0.913625i	−0.103474	−	0.0379689i
$580$	0.798115	+	1.09851i	0.0331399	+	0.0456132i
$581$	−5.90846	+	18.1844i	−0.245124	+	0.754415i
$582$	34.4515	−	23.1066i	1.42806	−	0.957801i
$583$	−25.3878			−1.05146
$584$	31.5803	−	22.9445i	1.30680	−	0.949448i
$585$	11.3850	−	2.77527i	0.470714	−	0.114743i
$586$	−63.2696	+	20.5575i	−2.61364	+	0.849224i
$587$	−20.6760	−	15.0220i	−0.853392	−	0.620025i	0.0726875	−	0.997355i	$-0.476842\pi$
$587$	−20.6760	−	15.0220i	−0.853392	−	0.620025i	−0.926079	+	0.377330i	$0.876842\pi$
$588$	14.8839	−	4.22569i	0.613803	−	0.174264i
$589$	−29.3454	+	9.53488i	−1.20915	+	0.392878i
$590$	17.7566			0.731027
$591$	−28.7687	+	8.16769i	−1.18338	+	0.335974i
$592$	4.29780	+	3.12253i	0.176638	+	0.128335i
$593$		−	3.56345i		−	0.146333i	−0.997320	−	0.0731666i	$-0.976690\pi$
$593$		−	3.56345i		−	0.146333i	0.997320	−	0.0731666i	$-0.0233105\pi$
$594$	−25.1194	−	2.84014i	−1.03066	−	0.116532i
$595$	−1.14992			−0.0471419
$596$	−15.0974	+	10.9689i	−0.618412	+	0.449303i
$597$	−31.0534	+	8.81636i	−1.27093	+	0.360829i
$598$	−8.56192	+	26.3509i	−0.350123	+	1.07757i
$599$	−40.2112			−1.64298			−0.821492	−	0.570221i	$-0.806858\pi$
$599$	−40.2112			−1.64298			−0.821492	+	0.570221i	$0.806858\pi$
$600$	51.0045	+	18.7158i	2.08225	+	0.764068i
$601$	−33.1977			−1.35416			−0.677081	−	0.735909i	$-0.736755\pi$
$601$	−33.1977			−1.35416			−0.677081	+	0.735909i	$0.736755\pi$
$602$			54.7219i			2.23030i
$603$	−21.3410	−	34.5547i	−0.869073	−	1.40718i
$604$	−32.3578	−	99.5871i	−1.31662	−	4.05214i
$605$	5.07259	+	1.64818i	0.206230	+	0.0670082i
$606$	−69.4728	−	2.60848i	−2.82214	−	0.105962i
$607$	−18.5887			−0.754492			−0.377246	−	0.926113i	$-0.623129\pi$
$607$	−18.5887			−0.754492			−0.377246	+	0.926113i	$0.623129\pi$
$608$	−19.4853	−	59.9695i	−0.790233	−	2.43209i
$609$	1.24419	+	0.977335i	0.0504172	+	0.0396036i
$610$	−0.239459	+	0.736979i	−0.00969541	+	0.0298394i
$611$	7.34537	+	10.1100i	0.297162	+	0.409008i
$612$	−2.38026	−	9.76462i	−0.0962165	−	0.394711i
$613$	15.5228	−	5.04366i	0.626959	−	0.203711i	0.0217317	−	0.999764i	$-0.493082\pi$
$613$	15.5228	−	5.04366i	0.626959	−	0.203711i	0.605228	+	0.796052i	$0.293082\pi$
$614$	11.6444	+	35.8379i	0.469932	+	1.44630i
$615$	−0.497587	+	0.333732i	−0.0200647	+	0.0134574i
$616$	−9.16338	−	28.2020i	−0.369203	−	1.13629i
$617$	6.39024	+	19.6671i	0.257261	+	0.791769i	0.993376	+	0.114912i	$0.0366585\pi$
$617$	6.39024	+	19.6671i	0.257261	+	0.791769i	−0.736114	+	0.676857i	$0.763341\pi$
$618$	10.8921	+	3.99678i	0.438145	+	0.160774i
$619$			19.0818i			0.766962i	0.923549	+	0.383481i	$0.125275\pi$
$619$			19.0818i			0.766962i	−0.923549	+	0.383481i	$0.874725\pi$
$620$	−4.31678	−	13.2857i	−0.173366	−	0.533566i
$621$	−5.01633	−	8.84859i	−0.201298	−	0.355082i
$622$	−24.6946	+	33.9892i	−0.990162	+	1.36284i
$623$	18.6374	+	25.6522i	0.746692	+	1.02773i
$624$	−50.8116	+	64.6855i	−2.03409	+	2.58949i
$625$	−14.2444	+	10.3492i	−0.569775	+	0.413966i
$626$	44.3542	−	14.4116i	1.77275	−	0.576001i
$627$	−24.1207	−	0.905653i	−0.963287	−	0.0361683i
$628$	−4.09975	+	5.64282i	−0.163598	+	0.225173i
$629$	0.352817	+	0.256337i	0.0140678	+	0.0102208i
$630$	−12.4892	−	0.939180i	−0.497581	−	0.0374178i
$631$	6.13103	−	18.8694i	0.244072	−	0.751177i	−0.751715	−	0.659488i	$-0.770773\pi$
$631$	6.13103	−	18.8694i	0.244072	−	0.751177i	0.995788	−	0.0916896i	$-0.0292268\pi$
$632$	−1.29457			−0.0514953
$633$	−21.1197	+	13.6733i	−0.839432	+	0.543465i
$634$	26.4669			1.05113
$635$	−2.03515	+	6.26355i	−0.0807625	+	0.248561i
$636$	−30.0252	−	105.756i	−1.19058	−	4.19351i
$637$	−8.40989	−	6.11014i	−0.333212	−	0.242093i
$638$	−1.15677	+	1.59215i	−0.0457968	+	0.0630339i
$639$	−24.7791	−	10.1629i	−0.980247	−	0.402039i
$640$	−3.38933	+	1.10126i	−0.133975	+	0.0435311i
$641$	4.72935	−	3.43607i	0.186798	−	0.135717i	−0.490456	−	0.871466i	$-0.663170\pi$
$641$	4.72935	−	3.43607i	0.186798	−	0.135717i	0.677254	+	0.735749i	$0.263170\pi$
$642$	−12.1714	−	9.56087i	−0.480368	−	0.377338i
$643$	14.7525	+	20.3051i	0.581783	+	0.800756i	0.993889	−	0.110380i	$-0.0352068\pi$
$643$	14.7525	+	20.3051i	0.581783	+	0.800756i	−0.412106	+	0.911136i	$0.635207\pi$
$644$	12.2095	−	16.8050i	0.481123	−	0.662208i
$645$	−3.99034	+	10.8746i	−0.157120	+	0.428185i
$646$	−4.22763	−	13.0113i	−0.166334	−	0.511923i
$647$		−	21.0275i		−	0.826675i	−0.910578	−	0.413338i	$-0.864363\pi$
$647$		−	21.0275i		−	0.826675i	0.910578	−	0.413338i	$-0.135637\pi$
$648$	−10.2684	−	62.0335i	−0.403382	−	2.43691i
$649$	5.57859	+	17.1691i	0.218979	+	0.673947i
$650$	−19.6376	−	60.4384i	−0.770252	−	2.37059i
$651$	−9.06665	−	13.5182i	−0.355350	−	0.529820i
$652$	10.7578	+	33.1090i	0.421306	+	1.29665i
$653$	7.73515	−	2.51330i	0.302700	−	0.0983531i	−0.153729	−	0.988113i	$-0.549128\pi$
$653$	7.73515	−	2.51330i	0.302700	−	0.0983531i	0.456429	+	0.889760i	$0.349128\pi$
$654$	27.7356	+	41.3532i	1.08455	+	1.61704i
$655$	−8.47551	−	11.6655i	−0.331166	−	0.455810i
$656$	1.29960	−	3.99975i	0.0507408	−	0.156164i
$657$	14.2614	−	8.80785i	0.556391	−	0.343627i
$658$	−4.12731	−	12.7026i	−0.160899	−	0.495197i
$659$	−0.600671			−0.0233988			−0.0116994	−	0.999932i	$-0.503724\pi$
$659$	−0.600671			−0.0233988			−0.0116994	+	0.999932i	$0.503724\pi$
$660$	0.410021	−	10.9203i	0.0159601	−	0.425072i
$661$	20.0429	+	6.51234i	0.779579	+	0.253301i	0.671660	−	0.740859i	$-0.265581\pi$
$661$	20.0429	+	6.51234i	0.779579	+	0.253301i	0.107919	+	0.994160i	$0.465581\pi$
$662$	9.64367	+	29.6802i	0.374812	+	1.15355i
$663$	−4.17126	+	5.31020i	−0.161998	+	0.206231i
$664$		−	59.1561i		−	2.29570i
$665$	−11.9587			−0.463740
$666$	3.62257	+	3.07222i	0.140372	+	0.119046i
$667$	−0.791858			−0.0306609
$668$	−22.0987	+	68.0127i	−0.855023	+	2.63149i
$669$	−0.943310	−	3.32258i	−0.0364705	−	0.128458i
$670$	20.2488	−	14.7116i	0.782280	−	0.568360i
$671$	−0.787827			−0.0304137
$672$	27.6255	−	18.5284i	1.06568	−	0.714749i
$673$			49.3971i			1.90412i	0.305916	+	0.952058i	$0.401037\pi$
$673$			49.3971i			1.90412i	−0.305916	+	0.952058i	$0.598963\pi$
$674$	52.4551	+	38.1109i	2.02049	+	1.46798i
$675$	21.2373	+	9.65638i	0.817425	+	0.371674i
$676$	79.4389			3.05534
$677$	28.4760	−	9.25240i	1.09442	−	0.355599i	0.294467	−	0.955662i	$-0.404858\pi$
$677$	28.4760	−	9.25240i	1.09442	−	0.355599i	0.799953	+	0.600063i	$0.204858\pi$
$678$	0.574005	+	2.02179i	0.0220445	+	0.0776464i
$679$	16.9044	+	12.2817i	0.648730	+	0.471330i
$680$	3.38361	−	1.09940i	0.129755	−	0.0421601i
$681$	26.4267	−	17.7244i	1.01267	−	0.679201i
$682$	16.3801	−	11.9008i	0.627226	−	0.455706i
$683$	26.4935			1.01374			0.506872	−	0.862021i	$-0.330802\pi$
$683$	26.4935			1.01374			0.506872	+	0.862021i	$0.330802\pi$
$684$	−24.7540	−	101.549i	−0.946492	−	3.88282i
$685$	−3.56866	+	10.9832i	−0.136351	+	0.419646i
$686$	30.5782	+	42.0873i	1.16748	+	1.60690i
$687$	10.2063	−	27.8143i	0.389393	−	1.06118i
$688$	−25.1259	−	77.3297i	−0.957917	−	2.94817i
$689$	−43.4149	+	59.7556i	−1.65398	+	2.27651i
$690$	5.20594	−	3.49162i	0.198187	−	0.132924i
$691$	27.2449			1.03644			0.518222	−	0.855246i	$-0.326594\pi$
$691$	27.2449			1.03644			0.518222	+	0.855246i	$0.326594\pi$
$692$	24.8271	−	34.1716i	0.943786	−	1.29901i
$693$	−3.01562	−	12.3711i	−0.114554	−	0.469937i
$694$	20.2410	+	27.8593i	0.768337	+	1.05753i
$695$	11.7313	+	3.81172i	0.444992	+	0.144587i
$696$	−4.59541	−	1.68625i	−0.174189	−	0.0639173i
$697$	0.106687	−	0.328350i	0.00404108	−	0.0124372i
$698$	33.6769	+	10.9423i	1.27469	+	0.414172i
$699$	9.85603	−	12.5472i	0.372789	−	0.474578i
$700$			47.6429i			1.80073i
$701$	−11.0861	+	34.1196i	−0.418717	+	1.28868i	0.490166	+	0.871629i	$0.336936\pi$
$701$	−11.0861	+	34.1196i	−0.418717	+	1.28868i	−0.908883	+	0.417050i	$0.863064\pi$
$702$	−49.6409	+	54.2671i	−1.87357	+	2.04818i
$703$	3.66919	+	2.66582i	0.138386	+	0.100543i
$704$	5.13096	+	7.06216i	0.193380	+	0.266165i
$705$	0.106080	−	2.82527i	0.00399519	−	0.106406i
$706$	−90.7364			−3.41491
$707$	−10.8212	−	33.3042i	−0.406973	−	1.25253i
$708$	−64.9227	+	43.5436i	−2.43994	+	1.63647i
$709$	−12.4449	+	38.3014i	−0.467378	+	1.43844i	0.388590	+	0.921411i	$0.372962\pi$
$709$	−12.4449	+	38.3014i	−0.467378	+	1.43844i	−0.855967	+	0.517030i	$0.827038\pi$
$710$	5.10035	−	15.6973i	0.191413	−	0.589108i
$711$	−0.554331	−	0.0416854i	−0.0207890	−	0.00156333i
$712$	−79.3655	−	57.6624i	−2.97435	−	2.16099i
$713$	7.74792	+	2.51745i	0.290162	+	0.0942793i
$714$	5.99378	−	4.02003i	0.224312	−	0.150446i
$715$	−5.93990	+	4.31559i	−0.222140	+	0.161394i
$716$	11.7770	−	16.2097i	0.440128	−	0.605784i
$717$	−1.57729	+	42.0087i	−0.0589050	+	1.56884i
$718$	67.3523	+	21.8841i	2.51357	+	0.816707i
$719$	−14.1485	+	43.5446i	−0.527650	+	1.62394i	0.231366	+	0.972867i	$0.425681\pi$
$719$	−14.1485	+	43.5446i	−0.527650	+	1.62394i	−0.759016	+	0.651072i	$0.774319\pi$
$720$	18.0802	−	4.40730i	0.673808	−	0.164250i
$721$			5.84406i			0.217644i
$722$	−28.7693	−	88.5429i	−1.07068	−	3.29522i
$723$	1.48903	−	39.6581i	0.0553777	−	1.47490i
$724$	−50.5452	−	69.5695i	−1.87850	−	2.58553i
$725$	1.46934	−	1.06754i	0.0545701	−	0.0396475i
$726$	−32.2021	+	9.14248i	−1.19513	+	0.339309i
$727$			21.0126i			0.779314i	0.920960	+	0.389657i	$0.127406\pi$
$727$			21.0126i			0.779314i	−0.920960	+	0.389657i	$0.872594\pi$
$728$	−82.0493	−	26.6594i	−3.04095	−	0.988065i
$729$	−2.39941	−	26.8932i	−0.0888672	−	0.996043i
$730$	6.07177	+	8.35708i	0.224726	+	0.309309i
$731$	−2.06265	−	6.34820i	−0.0762900	−	0.234797i
$732$	−0.931733	−	3.28180i	−0.0344378	−	0.121299i
$733$	−2.57582	+	7.92757i	−0.0951402	+	0.292812i	−0.987290	−	0.158928i	$-0.949196\pi$
$733$	−2.57582	+	7.92757i	−0.0951402	+	0.292812i	0.892150	+	0.451739i	$0.149196\pi$
$734$		−	43.0553i		−	1.58920i
$735$	0.642316	+	2.26240i	0.0236922	+	0.0834499i
$736$	−5.14461	+	15.8335i	−0.189633	+	0.583630i
$737$	20.5865	+	14.9570i	0.758313	+	0.550947i
$738$	1.42690	−	3.47906i	0.0525251	−	0.128066i
$739$	1.26339	−	0.410501i	0.0464747	−	0.0151005i	−0.285687	−	0.958323i	$-0.592222\pi$
$739$	1.26339	−	0.410501i	0.0464747	−	0.0151005i	0.332162	+	0.943222i	$0.392222\pi$
$740$	−1.20691	+	1.66117i	−0.0443670	+	0.0610659i
$741$	−43.3797	+	55.2244i	−1.59359	+	2.02872i
$742$	63.8657	−	46.4011i	2.34458	−	1.70344i
$743$	24.7579			0.908278			0.454139	−	0.890931i	$-0.349947\pi$
$743$	24.7579			0.908278			0.454139	+	0.890931i	$0.349947\pi$
$744$	39.6028	+	31.1087i	1.45191	+	1.14050i
$745$	−1.66730	−	2.29484i	−0.0610851	−	0.0840765i
$746$	−5.22862	+	1.69888i	−0.191433	+	0.0622005i
$747$	1.90484	−	25.3304i	0.0696943	−	0.926792i
$748$	3.70136	+	5.09448i	0.135335	+	0.186273i
$749$	2.40911	−	7.41448i	0.0880270	−	0.270919i
$750$	−10.4683	+	28.5284i	−0.382248	+	1.04171i
$751$	4.78939	+	6.59202i	0.174767	+	0.240546i	0.887410	−	0.460980i	$-0.152502\pi$
$751$	4.78939	+	6.59202i	0.174767	+	0.240546i	−0.712643	+	0.701527i	$0.752502\pi$
$752$	11.6649	+	16.0554i	0.425376	+	0.585480i
$753$	15.7154	−	4.46176i	0.572702	−	0.162595i
$754$	1.76931	+	5.44539i	0.0644346	+	0.198309i
$755$	15.1375	−	4.91847i	0.550910	−	0.179002i
$756$	47.9668	−	27.1927i	1.74454	−	0.988990i
$757$	15.0543	−	20.7204i	0.547157	−	0.753096i	−0.442466	−	0.896785i	$-0.645896\pi$
$757$	15.0543	−	20.7204i	0.547157	−	0.753096i	0.989623	+	0.143689i	$0.0458964\pi$
$758$	59.4629	+	19.3207i	2.15979	+	0.701758i
$759$	5.01165	+	3.93674i	0.181911	+	0.142895i
$760$	35.1884	−	11.4334i	1.27642	−	0.414733i
$761$	6.64995	+	4.83147i	0.241061	+	0.175141i	0.701756	−	0.712418i	$-0.252400\pi$
$761$	6.64995	+	4.83147i	0.241061	+	0.175141i	−0.460695	+	0.887558i	$0.652400\pi$
$762$	−11.2890	−	39.7627i	−0.408957	−	1.44045i
$763$	−14.7421	+	20.2908i	−0.533701	+	0.734576i
$764$	13.2449	−	40.7635i	0.479183	−	1.47477i
$765$	1.48425	−	0.361807i	0.0536632	−	0.0130812i
$766$	−20.9804	−	28.8770i	−0.758051	−	1.04337i
$767$	49.9510	+	16.2300i	1.80362	+	0.586033i
$768$	23.7543	−	30.2404i	0.857161	−	1.09121i
$769$	10.2729	+	7.46371i	0.370451	+	0.269148i	0.757398	−	0.652954i	$-0.226470\pi$
$769$	10.2729	+	7.46371i	0.370451	+	0.269148i	−0.386947	+	0.922102i	$0.626470\pi$
$770$	7.46307	−	2.42490i	0.268950	−	0.0873872i
$771$	4.23048	−	11.5290i	0.152357	−	0.415206i
$772$	2.22356	+	6.84341i	0.0800276	+	0.246300i
$773$	−14.0978	+	10.2426i	−0.507062	+	0.368402i	−0.811708	−	0.584063i	$-0.801462\pi$
$773$	−14.0978	+	10.2426i	−0.507062	+	0.368402i	0.304646	+	0.952466i	$0.401462\pi$
$774$	−17.2176	−	70.6321i	−0.618873	−	2.53882i
$775$	−17.7707	+	5.77404i	−0.638341	+	0.207409i
$776$	−61.4830	−	19.9770i	−2.20711	−	0.717133i
$777$	−0.824187	+	2.24609i	−0.0295676	+	0.0805781i
$778$	−31.2848	−	10.1651i	−1.12162	−	0.364435i
$779$	1.10951	−	3.41474i	0.0397525	−	0.122346i
$780$	−25.0021	−	19.6396i	−0.895217	−	0.703209i
$781$	16.7803			0.600447
$782$	−1.11620	+	3.43532i	−0.0399153	+	0.122847i
$783$	−1.91344	−	0.870022i	−0.0683809	−	0.0310920i
$784$	−13.3554	−	9.70329i	−0.476980	−	0.346546i
$785$	−0.857724	−	0.623173i	−0.0306135	−	0.0222420i
$786$	84.9594	+	31.1753i	3.03040	+	1.11198i
$787$	−25.4294	−	18.4756i	−0.906461	−	0.658583i	0.0336562	−	0.999433i	$-0.489285\pi$
$787$	−25.4294	−	18.4756i	−0.906461	−	0.658583i	−0.940117	+	0.340851i	$0.889285\pi$
$788$	65.6413	+	47.6912i	2.33838	+	1.69893i
$789$	−53.9518	−	2.02572i	−1.92074	−	0.0721174i
$790$		−	0.342581i		−	0.0121885i
$791$	−0.856446	+	0.622244i	−0.0304517	+	0.0221245i
$792$	20.7010	+	33.5185i	0.735578	+	1.19103i
$793$	−1.34724	+	1.85432i	−0.0478419	+	0.0658488i
$794$		−	72.4988i		−	2.57288i
$795$	16.0752	−	4.56391i	0.570130	−	0.161865i
$796$	70.8544	+	51.4788i	2.51137	+	1.82462i
$797$	−3.16484	−	9.74039i	−0.112105	−	0.345022i	0.879228	−	0.476402i	$-0.158059\pi$
$797$	−3.16484	−	9.74039i	−0.112105	−	0.345022i	−0.991332	+	0.131380i	$0.958059\pi$
$798$	62.3334	−	41.8070i	2.20658	−	1.47995i
$799$	0.957604	+	1.31803i	0.0338776	+	0.0466285i
$800$	−11.7997	−	36.3157i	−0.417182	−	1.28396i
$801$	−32.1273	−	27.2464i	−1.13516	−	0.962705i
$802$	−70.2564	+	51.0443i	−2.48084	+	1.80244i
$803$	−6.17302	+	8.49644i	−0.217841	+	0.299833i
$804$	−37.9583	+	103.445i	−1.33869	+	3.64821i
$805$	2.55440	+	1.85588i	0.0900308	+	0.0654112i
$806$		−	58.9052i		−	2.07485i
$807$	−5.31672	−	18.7268i	−0.187157	−	0.659215i
$808$	63.6824	+	87.6513i	2.24034	+	3.08356i
$809$	7.16399	+	2.32772i	0.251873	+	0.0818383i	0.432232	−	0.901762i	$-0.357726\pi$
$809$	7.16399	+	2.32772i	0.251873	+	0.0818383i	−0.180360	+	0.983601i	$0.557726\pi$
$810$	16.4159	−	2.71732i	0.576795	−	0.0954770i
$811$	−51.9788			−1.82522			−0.912611	−	0.408828i	$-0.865937\pi$
$811$	−51.9788			−1.82522			−0.912611	+	0.408828i	$0.865937\pi$
$812$		−	4.29254i		−	0.150639i
$813$	2.78204	−	7.58167i	0.0975705	−	0.265901i
$814$	−2.83037	−	0.919644i	−0.0992045	−	0.0322335i
$815$	−5.03265	+	1.63521i	−0.176286	+	0.0572789i
$816$	−6.62422	+	8.43294i	−0.231894	+	0.295212i
$817$	−21.4509	−	66.0192i	−0.750473	−	2.30972i
$818$			24.1744i			0.845237i
$819$	−34.2748	−	14.0575i	−1.19766	−	0.491208i
$820$	1.54597	+	0.502317i	0.0539877	+	0.0175417i
$821$	21.6394	+	7.03108i	0.755222	+	0.245386i	0.661227	−	0.750186i	$-0.270036\pi$
$821$	21.6394	+	7.03108i	0.755222	+	0.245386i	0.0939952	+	0.995573i	$0.470036\pi$
$822$	−19.7954	−	69.7242i	−0.690442	−	2.43191i
$823$	23.4620	−	32.2926i	0.817833	−	1.12565i	−0.172235	−	0.985056i	$-0.555099\pi$
$823$	23.4620	−	32.2926i	0.817833	−	1.12565i	0.990067	−	0.140594i	$-0.0449013\pi$
$824$	−5.58733	−	17.1960i	−0.194644	−	0.599053i
$825$	−14.6067	−	0.548436i	−0.508542	−	0.0190941i
$826$	−45.4134	−	32.9948i	−1.58014	−	1.14804i
$827$	−52.9203	+	17.1949i	−1.84022	+	0.597924i	−0.841923	+	0.539598i	$0.818576\pi$
$827$	−52.9203	+	17.1949i	−1.84022	+	0.597924i	−0.998298	+	0.0583257i	$0.981424\pi$
$828$	−10.4719	+	25.5325i	−0.363924	+	0.887317i
$829$	−7.18709			−0.249618			−0.124809	−	0.992181i	$-0.539832\pi$
$829$	−7.18709			−0.249618			−0.124809	+	0.992181i	$0.539832\pi$
$830$	15.6544			0.543373
$831$	−1.51557	+	40.3650i	−0.0525747	+	1.40025i
$832$	25.3966			0.880469
$833$	−1.09638	−	0.796569i	−0.0379874	−	0.0275995i
$834$	−74.4732	+	21.1436i	−2.57880	+	0.732144i
$835$	−10.3381	−	3.35906i	−0.357765	−	0.116245i
$836$	38.4929	+	52.9809i	1.33130	+	1.83238i
$837$	15.9561	+	14.5959i	0.551523	+	0.504507i
$838$	−7.29576	+	2.37054i	−0.252028	+	0.0818889i
$839$	−7.38674	−	5.36678i	−0.255019	−	0.185282i	0.452929	−	0.891546i	$-0.350379\pi$
$839$	−7.38674	−	5.36678i	−0.255019	−	0.185282i	−0.707948	+	0.706264i	$0.750379\pi$
$840$	10.8719	+	16.2099i	0.375118	+	0.559293i
$841$	23.3291	−	16.9496i	0.804452	−	0.584469i
$842$	−9.64502	−	3.13386i	−0.332389	−	0.108000i
$843$	11.7826	−	32.1101i	0.405813	−	1.10593i
$844$	64.5686	+	22.1444i	2.22254	+	0.762243i
$845$			12.0749i			0.415390i
$846$	9.32401	+	15.0972i	0.320566	+	0.519051i
$847$	−9.91081	−	13.6411i	−0.340539	−	0.468712i
$848$	−68.9457	+	94.8956i	−2.36760	+	3.25873i
$849$	−1.02386	+	0.686704i	−0.0351388	+	0.0235676i
$850$	−2.56013	−	7.87926i	−0.0878116	−	0.270256i
$851$	−0.370033	−	1.13884i	−0.0126846	−	0.0390391i
$852$	19.8454	+	69.9006i	0.679893	+	2.39475i
$853$	−14.2177	+	43.7577i	−0.486806	+	1.49823i	0.342543	+	0.939502i	$0.388712\pi$
$853$	−14.2177	+	43.7577i	−0.486806	+	1.49823i	−0.829349	+	0.558731i	$0.811288\pi$
$854$	1.98186	−	1.43991i	0.0678179	−	0.0492726i
$855$	15.4357	−	3.76267i	0.527890	−	0.128681i
$856$			24.1203i			0.824413i
$857$	−9.60909	+	3.12218i	−0.328240	+	0.106652i	−0.468501	−	0.883463i	$-0.655206\pi$
$857$	−9.60909	+	3.12218i	−0.328240	+	0.106652i	0.140261	+	0.990115i	$0.455206\pi$
$858$	15.8739	−	43.2599i	0.541927	−	1.47687i
$859$		−	4.48323i		−	0.152966i	−0.997071	−	0.0764829i	$-0.975631\pi$
$859$		−	4.48323i		−	0.152966i	0.997071	−	0.0764829i	$-0.0243691\pi$
$860$	29.8893	−	9.71161i	1.01922	−	0.331163i
$861$	1.89274	+	0.0710661i	0.0645043	+	0.00242193i
$862$	0.222779	−	0.306629i	0.00758787	−	0.0104438i
$863$	14.3387	−	4.65891i	0.488093	−	0.158591i	−0.0546232	−	0.998507i	$-0.517396\pi$
$863$	14.3387	−	4.65891i	0.488093	−	0.158591i	0.542717	+	0.839916i	$0.317396\pi$
$864$	−29.8278	+	32.6075i	−1.01476	+	1.10933i
$865$	5.19418	+	3.77379i	0.176607	+	0.128313i
$866$	−60.1235	+	43.6823i	−2.04308	+	1.48438i
$867$	17.6451	−	22.4630i	0.599258	−	0.762882i
$868$	−13.6467	+	42.0002i	−0.463199	+	1.42558i
$869$	0.331247	−	0.107629i	0.0112368	−	0.00365106i
$870$	0.446232	−	1.21608i	0.0151287	−	0.0412290i
$871$	70.4087	−	22.8772i	2.38571	−	0.775164i
$872$	23.9790	−	73.7998i	0.812032	−	2.49918i
$873$	−25.6835	−	10.5339i	−0.869256	−	0.356517i
$874$	−11.6081	+	35.7262i	−0.392651	+	1.20846i
$875$	−15.3067			−0.517460
$876$	−42.6936	−	15.6661i	−1.44248	−	0.529309i
$877$		−	29.2589i		−	0.988002i	−0.869461	−	0.494001i	$-0.835534\pi$
$877$		−	29.2589i		−	0.988002i	0.869461	−	0.494001i	$-0.164466\pi$
$878$			71.8919i			2.42624i
$879$	35.0087	+	27.5000i	1.18082	+	0.927551i
$880$	−9.43294	+	6.85343i	−0.317984	+	0.231029i
$881$	−15.0834	−	20.7605i	−0.508172	−	0.699439i	0.475438	−	0.879749i	$-0.342290\pi$
$881$	−15.0834	−	20.7605i	−0.508172	−	0.699439i	−0.983610	+	0.180310i	$0.942290\pi$
$882$	−11.2572	−	9.54696i	−0.379049	−	0.321463i
$883$	−31.5955	+	43.4874i	−1.06327	+	1.46347i	−0.186566	+	0.982442i	$0.559736\pi$
$883$	−31.5955	+	43.4874i	−1.06327	+	1.46347i	−0.876706	+	0.481026i	$0.840264\pi$
$884$	18.3205			0.616186
$885$	−6.61875	−	9.86842i	−0.222487	−	0.331723i
$886$	17.7628	+	24.4484i	0.596754	+	0.821361i
$887$			47.7976i			1.60489i	0.596729	+	0.802443i	$0.296467\pi$
$887$			47.7976i			1.60489i	−0.596729	+	0.802443i	$0.703533\pi$
$888$	0.277736	−	7.39706i	0.00932020	−	0.248229i
$889$	16.8438	−	12.2377i	0.564922	−	0.410440i
$890$	15.2592	−	21.0024i	0.511488	−	0.704003i
$891$	7.78480	+	15.0191i	0.260801	+	0.503158i
$892$	−5.50799	+	7.58110i	−0.184421	+	0.253834i
$893$	9.95877	+	13.7071i	0.333257	+	0.458690i
$894$	16.7132	+	6.13279i	0.558972	+	0.205111i
$895$	2.46392	+	1.79014i	0.0823597	+	0.0598378i
$896$	10.7147	+	3.48143i	0.357954	+	0.116306i
$897$	17.8362	−	5.06387i	0.595535	−	0.169078i
$898$	81.0813			2.70572
$899$	1.60110	−	0.520230i	0.0533998	−	0.0173506i
$900$	−14.9903	−	61.4949i	−0.499675	−	2.04983i
$901$	−5.65993	+	7.79023i	−0.188560	+	0.259530i
$902$			2.35600i			0.0784464i
$903$	30.4123	−	20.3975i	1.01206	−	0.678788i
$904$	1.92517	−	2.64976i	0.0640301	−	0.0881298i
$905$	10.5748	−	7.68301i	0.351517	−	0.255392i
$906$	−61.7076	+	78.5566i	−2.05010	+	2.60987i
$907$		−	37.1550i		−	1.23371i	−0.787076	−	0.616856i	$-0.788406\pi$
$907$		−	37.1550i		−	1.23371i	0.787076	−	0.616856i	$-0.211594\pi$
$908$	−82.1062	−	26.6779i	−2.72479	−	0.885338i
$909$	24.4462	+	39.5826i	0.810829	+	1.31287i
$910$	7.05487	−	21.7127i	0.233867	−	0.719767i
$911$	−16.6858			−0.552824			−0.276412	−	0.961039i	$-0.589145\pi$
$911$	−16.6858			−0.552824			−0.276412	+	0.961039i	$0.589145\pi$
$912$	−68.8897	+	87.6998i	−2.28117	+	2.90403i
$913$	4.91815	+	15.1365i	0.162767	+	0.500945i
$914$	−50.8996	+	70.0573i	−1.68361	+	2.31729i
$915$	0.498842	−	0.141626i	0.0164912	−	0.00468201i
$916$	−76.4489	+	24.8398i	−2.52594	+	0.820729i
$917$			45.5842i			1.50532i
$918$	−6.47160	+	7.07470i	−0.213595	+	0.233500i
$919$	29.7409	−	40.9348i	0.981060	−	1.35031i	0.0448039	−	0.998996i	$-0.485734\pi$
$919$	29.7409	−	40.9348i	0.981060	−	1.35031i	0.936256	−	0.351318i	$-0.114266\pi$
$920$	−9.29063	−	3.01871i	−0.306303	−	0.0995239i
$921$	15.5769	−	19.8301i	0.513275	−	0.653423i
$922$	49.7079	−	36.1149i	1.63704	−	1.18938i
$923$	28.6955	−	39.4960i	0.944525	−	1.30003i
$924$	−21.3404	+	27.1674i	−0.702049	+	0.893740i
$925$	2.22195	+	1.61434i	0.0730572	+	0.0530791i
$926$	−2.14789	−	2.95631i	−0.0705839	−	0.0971504i
$927$	−1.83876	−	7.54320i	−0.0603929	−	0.247751i
$928$	1.06313	+	3.27198i	0.0348990	+	0.107408i
$929$	13.2318	−	40.7234i	0.434123	−	1.33609i	−0.459861	−	0.887991i	$-0.652101\pi$
$929$	13.2318	−	40.7234i	0.434123	−	1.33609i	0.893983	−	0.448101i	$-0.147899\pi$
$930$	−8.23227	+	10.4801i	−0.269947	+	0.343655i
$931$	−11.4020	−	8.28406i	−0.373686	−	0.271499i
$932$	−43.2885			−1.41796
$933$	28.0947	+	1.05487i	0.919780	+	0.0345347i
$934$	104.460	−	33.9410i	3.41803	−	1.11058i
$935$	−0.774375	+	0.562616i	−0.0253248	+	0.0183995i
$936$	114.293	+	8.59477i	3.73578	+	0.280929i
$937$	1.96113	−	1.42484i	0.0640673	−	0.0465476i	−0.555291	−	0.831656i	$-0.687393\pi$
$937$	1.96113	−	1.42484i	0.0640673	−	0.0465476i	0.619358	+	0.785109i	$0.287393\pi$
$938$	−79.1242			−2.58350
$939$	−24.5424	−	19.2785i	−0.800910	−	0.629129i
$940$	−6.20568	+	4.50869i	−0.202407	+	0.147057i
$941$	40.2419	−	29.2375i	1.31185	−	0.953114i	0.311854	−	0.950130i	$-0.399050\pi$
$941$	40.2419	−	29.2375i	1.31185	−	0.953114i	0.999996	−	0.00298404i	$-0.000949850\pi$
$942$	6.64934	+	0.249661i	0.216647	+	0.00813440i
$943$	−0.766927	+	0.557205i	−0.0249746	+	0.0181451i
$944$	79.3253	+	25.7743i	2.58182	+	0.838883i
$945$	4.13337	+	7.29108i	0.134459	+	0.237179i
$946$	26.7737	+	36.8508i	0.870487	+	1.19812i
$947$	−11.5584	−	3.75556i	−0.375599	−	0.122039i	0.115133	−	0.993350i	$-0.463271\pi$
$947$	−11.5584	−	3.75556i	−0.375599	−	0.122039i	−0.490732	+	0.871311i	$0.663271\pi$
$948$	0.840096	+	1.25257i	0.0272850	+	0.0406815i
$949$	9.44185	+	29.0590i	0.306496	+	0.943296i
$950$	−26.6245	−	81.9417i	−0.863812	−	2.65854i
$951$	−9.86550	−	14.7093i	−0.319911	−	0.476981i
$952$	−10.6966	−	3.47555i	−0.346680	−	0.112643i
$953$	−11.1684	−	15.3719i	−0.361779	−	0.497946i	0.588864	−	0.808232i	$-0.299575\pi$
$953$	−11.1684	−	15.3719i	−0.361779	−	0.497946i	−0.950643	+	0.310286i	$0.899575\pi$
$954$	−67.8349	+	79.9867i	−2.19624	+	2.58966i
$955$	6.19617	+	2.01326i	0.200503	+	0.0651475i
$956$	92.2719	−	67.0395i	2.98429	−	2.16821i
$957$	1.31604	+	0.0494130i	0.0425415	+	0.00159730i
$958$	−11.5251	+	8.37349i	−0.372360	+	0.270535i
$959$	29.5357	−	21.4589i	0.953758	−	0.692946i
$960$	−4.51841	−	3.54929i	−0.145831	−	0.114553i
$961$	13.6802			0.441295
$962$	−7.00472	+	5.08922i	−0.225841	+	0.164083i
$963$	−0.776677	+	10.3282i	−0.0250281	+	0.332822i
$964$	−87.1087	+	63.2882i	−2.80558	+	2.03838i
$965$	−1.04022	+	0.337987i	−0.0334858	+	0.0108802i
$966$	−19.8025	−	0.743520i	−0.637135	−	0.0239223i
$967$	3.24738			0.104429			0.0522144	−	0.998636i	$-0.483372\pi$
$967$	3.24738			0.104429			0.0522144	+	0.998636i	$0.483372\pi$
$968$	42.2042	+	30.6631i	1.35649	+	0.985550i
$969$	−5.65534	+	7.19951i	−0.181676	+	0.231281i
$970$	5.28651	−	16.2702i	0.169739	−	0.522404i
$971$	−3.57331	−	10.9975i	−0.114673	−	0.352927i	0.877206	−	0.480115i	$-0.159405\pi$
$971$	−3.57331	−	10.9975i	−0.114673	−	0.352927i	−0.991879	+	0.127188i	$0.959405\pi$
$972$	−53.3571	+	50.1911i	−1.71143	+	1.60988i
$973$	−22.9205	−	31.5474i	−0.734799	−	1.01136i
$974$	12.6923	+	9.22150i	0.406688	+	0.295476i
$975$	−26.2694	+	33.4422i	−0.841295	+	1.07101i
$976$	−2.13950	+	2.94477i	−0.0684838	+	0.0942599i
$977$	−35.2406	+	25.6038i	−1.12745	+	0.819139i	−0.985321	−	0.170709i	$-0.945394\pi$
$977$	−35.2406	+	25.6038i	−1.12745	+	0.819139i	−0.142127	+	0.989848i	$0.545394\pi$
$978$	20.5155	−	26.1171i	0.656012	−	0.835133i
$979$	25.1016	+	8.15599i	0.802249	+	0.260667i
$980$	3.75049	−	5.16211i	0.119805	−	0.164897i
$981$	12.6441	−	30.8287i	0.403695	−	0.984285i
$982$			1.67116i			0.0533289i
$983$	48.1569	−	15.6471i	1.53597	−	0.499066i	0.585706	−	0.810524i	$-0.300817\pi$
$983$	48.1569	−	15.6471i	1.53597	−	0.499066i	0.950260	+	0.311458i	$0.100817\pi$
$984$	−5.63729	+	1.60048i	−0.179710	+	0.0510214i
$985$	−7.24920	+	9.97766i	−0.230979	+	0.317915i
$986$	0.230663	+	0.709906i	0.00734579	+	0.0226080i
$987$	−5.52114	+	7.02866i	−0.175740	+	0.223725i
$988$	190.527			6.06148
$989$	−5.66359	+	17.4307i	−0.180092	+	0.554265i
$990$	−8.86996	+	5.47809i	−0.281906	+	0.174105i
$991$	−23.4466	−	7.61826i	−0.744805	−	0.242002i	−0.0880608	−	0.996115i	$-0.528067\pi$
$991$	−23.4466	−	7.61826i	−0.744805	−	0.242002i	−0.656744	+	0.754113i	$0.728067\pi$
$992$		−	35.3945i		−	1.12378i
$993$	12.9004	−	16.4228i	0.409382	−	0.521163i
$994$	−42.2126	+	30.6693i	−1.33890	+	0.972770i
$995$	−7.82491	+	10.7701i	−0.248066	+	0.341434i
$996$	−57.2366	+	38.3886i	−1.81361	+	1.21639i
$997$		−	16.1234i		−	0.510632i	−0.966858	−	0.255316i	$-0.917820\pi$
$997$		−	16.1234i		−	0.510632i	0.966858	−	0.255316i	$-0.0821795\pi$
$998$	−42.5378	+	58.5482i	−1.34651	+	1.85331i
$999$	0.357112	−	3.15845i	0.0112985	−	0.0999291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	633.2.k.a.23.4	✓	272
3.2	odd	2	inner	633.2.k.a.23.65	yes	272
211.156	odd	10	inner	633.2.k.a.578.65	yes	272
633.578	even	10	inner	633.2.k.a.578.4	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
633.2.k.a.23.4	✓	272	1.1	even	1	trivial
633.2.k.a.23.65	yes	272	3.2	odd	2	inner
633.2.k.a.578.4	yes	272	633.578	even	10	inner
633.2.k.a.578.65	yes	272	211.156	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 633 = 3 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	633.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.799825 + 2.46161i) q^{2} +(1.66620 - 0.473050i) q^{3} +(-3.80176 - 2.76214i) q^{4} +(0.419853 - 0.577878i) q^{5} +(-0.168205 + 4.47989i) q^{6} +(-2.14759 + 0.697796i) q^{7} +(5.65212 - 4.10650i) q^{8} +(2.55245 - 1.57639i) q^{9} +O(q^{10})\)	\(q+(-0.799825 + 2.46161i) q^{2} +(1.66620 - 0.473050i) q^{3} +(-3.80176 - 2.76214i) q^{4} +(0.419853 - 0.577878i) q^{5} +(-0.168205 + 4.47989i) q^{6} +(-2.14759 + 0.697796i) q^{7} +(5.65212 - 4.10650i) q^{8} +(2.55245 - 1.57639i) q^{9} +(1.08670 + 1.49572i) q^{10} +(-1.10482 + 1.52066i) q^{11} +(-7.64113 - 2.80386i) q^{12} +(1.68986 + 5.20087i) q^{13} -5.84465i q^{14} +(0.426194 - 1.16147i) q^{15} +(2.68361 + 8.25930i) q^{16} +(0.220305 + 0.678028i) q^{17} +(1.83895 + 7.54396i) q^{18} +(2.29110 + 7.05127i) q^{19} +(-3.19236 + 1.03726i) q^{20} +(-3.24823 + 2.17859i) q^{21} +(-2.85960 - 3.93590i) q^{22} +(0.604908 - 1.86171i) q^{23} +(7.47498 - 9.51599i) q^{24} +(1.38742 + 4.27003i) q^{25} -14.1541 q^{26} +(3.50718 - 3.83402i) q^{27} +(10.0921 + 3.27911i) q^{28} +(-0.125004 - 0.384722i) q^{29} +(2.51821 + 1.97810i) q^{30} +4.16171i q^{31} -8.50479 q^{32} +(-1.12151 + 3.05636i) q^{33} -1.84524 q^{34} +(-0.498433 + 1.53402i) q^{35} +(-14.0580 - 1.05716i) q^{36} +(0.494890 - 0.359559i) q^{37} -19.1899 q^{38} +(5.27592 + 7.86629i) q^{39} -4.99036i q^{40} +(-0.391785 - 0.284648i) q^{41} +(-2.76481 - 9.73836i) q^{42} -9.36274 q^{43} +(8.40054 - 2.72950i) q^{44} +(0.160691 - 2.13686i) q^{45} +(4.09899 + 2.97809i) q^{46} +(2.17336 - 0.706168i) q^{47} +(8.37849 + 12.4922i) q^{48} +(-1.53787 + 1.11733i) q^{49} -11.6208 q^{50} +(0.687813 + 1.02552i) q^{51} +(7.94107 - 24.4401i) q^{52} +(7.93908 + 10.9272i) q^{53} +(6.63273 + 11.6998i) q^{54} +(0.414892 + 1.27691i) q^{55} +(-9.27295 + 12.7631i) q^{56} +(7.15303 + 10.6650i) q^{57} +1.04702 q^{58} +(5.64530 - 7.77009i) q^{59} +(-4.82844 + 3.23843i) q^{60} +(0.246363 + 0.339090i) q^{61} +(-10.2445 - 3.32864i) q^{62} +(-4.38162 + 5.16654i) q^{63} +(1.43512 - 4.41685i) q^{64} +(3.71496 + 1.20706i) q^{65} +(-6.62654 - 5.20526i) q^{66} -13.5379i q^{67} +(1.03526 - 3.18621i) q^{68} +(0.127214 - 3.38814i) q^{69} +(-3.37750 - 2.45390i) q^{70} +(-5.24741 - 7.22244i) q^{71} +(7.95327 - 19.3916i) q^{72} +5.58735 q^{73} +(0.489267 + 1.50581i) q^{74} +(4.33166 + 6.45842i) q^{75} +(10.7664 - 33.1356i) q^{76} +(1.31160 - 4.03670i) q^{77} +(-23.5835 + 6.69559i) q^{78} +(-0.149910 - 0.108916i) q^{79} +(5.89959 + 1.91689i) q^{80} +(4.02998 - 8.04732i) q^{81} +(1.01405 - 0.736752i) q^{82} +(4.97696 - 6.85020i) q^{83} +(18.3666 + 0.689605i) q^{84} +(0.484313 + 0.157363i) q^{85} +(7.48855 - 23.0474i) q^{86} +(-0.390274 - 0.581891i) q^{87} +13.1319i q^{88} +(-4.33913 - 13.3545i) q^{89} +(5.13158 + 2.10467i) q^{90} +(-7.25828 - 9.99017i) q^{91} +(-7.44203 + 5.40695i) q^{92} +(1.96870 + 6.93425i) q^{93} +5.91478i q^{94} +(5.03670 + 1.63652i) q^{95} +(-14.1707 + 4.02319i) q^{96} +(-5.43893 - 7.48605i) q^{97} +(-1.52040 - 4.67931i) q^{98} +(-0.422849 + 5.62303i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9}+O(q^{10}) \) 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9	\( 272 q - 10 q^{3} - 74 q^{4} + 9 q^{6} - 30 q^{7} - 6 q^{9} - 20 q^{10} + 6 q^{13} - 46 q^{16} - 20 q^{18} + 6 q^{19} - 3 q^{21} - 10 q^{22} + 23 q^{24} + 50 q^{25} - 40 q^{27} + 80 q^{28} - q^{30} + 12 q^{34} + 13 q^{36} - 42 q^{37} + 25 q^{39} - 10 q^{42} + 40 q^{43} - 23 q^{45} - 2 q^{46} - 15 q^{48} + 30 q^{49} - 11 q^{51} - 34 q^{52} + 128 q^{54} + 14 q^{55} + 20 q^{57} + 60 q^{58} + 30 q^{60} - 10 q^{61} - 108 q^{64} - 73 q^{66} + 40 q^{69} + 70 q^{70} - 105 q^{72} - 20 q^{73} - 10 q^{75} - 12 q^{76} - 82 q^{78} - 30 q^{79} - 42 q^{81} - 106 q^{82} + 121 q^{84} - 110 q^{85} - 11 q^{87} + 60 q^{90} - 40 q^{91} - 45 q^{93} - 114 q^{96} - 80 q^{97} - 18 q^{99}+O(q^{100}) \) 272 * q - 10 * q^3 - 74 * q^4 + 9 * q^6 - 30 * q^7 - 6 * q^9 - 20 * q^10 + 6 * q^13 - 46 * q^16 - 20 * q^18 + 6 * q^19 - 3 * q^21 - 10 * q^22 + 23 * q^24 + 50 * q^25 - 40 * q^27 + 80 * q^28 - q^30 + 12 * q^34 + 13 * q^36 - 42 * q^37 + 25 * q^39 - 10 * q^42 + 40 * q^43 - 23 * q^45 - 2 * q^46 - 15 * q^48 + 30 * q^49 - 11 * q^51 - 34 * q^52 + 128 * q^54 + 14 * q^55 + 20 * q^57 + 60 * q^58 + 30 * q^60 - 10 * q^61 - 108 * q^64 - 73 * q^66 + 40 * q^69 + 70 * q^70 - 105 * q^72 - 20 * q^73 - 10 * q^75 - 12 * q^76 - 82 * q^78 - 30 * q^79 - 42 * q^81 - 106 * q^82 + 121 * q^84 - 110 * q^85 - 11 * q^87 + 60 * q^90 - 40 * q^91 - 45 * q^93 - 114 * q^96 - 80 * q^97 - 18 * q^99

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