LMFDB - Embedded newform 372.2.p.a.191.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [372,2,Mod(191,372)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("372.191"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(372, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 372 = 2^{2} \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	372.p (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.97043495519$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$60$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			191.6
Character	$\chi$	$=$	372.191
Dual form			372.2.p.a.335.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37366 + 0.336245i) q^{2} +(1.45754 + 0.935726i) q^{3} +(1.77388 - 0.923772i) q^{4} +(3.42031 - 1.97472i) q^{5} +(-2.31679 - 0.795278i) q^{6} +(2.26131 + 1.30557i) q^{7} +(-2.12609 + 1.86541i) q^{8} +(1.24884 + 2.72771i) q^{9} +(-4.03435 + 3.86265i) q^{10} +(0.103767 + 0.179731i) q^{11} +(3.44989 + 0.313431i) q^{12} +(-1.71430 - 2.96925i) q^{13} +(-3.54526 - 1.03305i) q^{14} +(6.83302 + 0.322246i) q^{15} +(2.29329 - 3.27732i) q^{16} +(-3.39107 - 1.95784i) q^{17} +(-2.63265 - 3.32703i) q^{18} +(-4.86040 - 2.80615i) q^{19} +(4.24303 - 6.66249i) q^{20} +(2.07430 + 4.01889i) q^{21} +(-0.202975 - 0.211997i) q^{22} -1.56206 q^{23} +(-4.84437 + 0.729461i) q^{24} +(5.29901 - 9.17816i) q^{25} +(3.35326 + 3.50231i) q^{26} +(-0.732164 + 5.14431i) q^{27} +(5.21734 + 0.226985i) q^{28} +7.63843i q^{29} +(-9.49460 + 1.85491i) q^{30} +(-5.45799 - 1.10016i) q^{31} +(-2.04822 + 5.27303i) q^{32} +(-0.0169334 + 0.359062i) q^{33} +(5.31649 + 1.54917i) q^{34} +10.3125 q^{35} +(4.73507 + 3.68499i) q^{36} +(-3.79678 + 6.57622i) q^{37} +(7.62008 + 2.22041i) q^{38} +(0.279749 - 5.93191i) q^{39} +(-3.58824 + 10.5787i) q^{40} +(-4.66304 + 2.69221i) q^{41} +(-4.20070 - 4.82311i) q^{42} +(0.114409 + 0.0660539i) q^{43} +(0.350101 + 0.222963i) q^{44} +(9.65786 + 6.86352i) q^{45} +(2.14574 - 0.525234i) q^{46} +12.5078 q^{47} +(6.40923 - 2.63092i) q^{48} +(-0.0909767 - 0.157576i) q^{49} +(-4.19293 + 14.3894i) q^{50} +(-3.11062 - 6.02674i) q^{51} +(-5.78386 - 3.68347i) q^{52} +(-1.04024 + 0.600584i) q^{53} +(-0.724005 - 7.31272i) q^{54} +(0.709834 + 0.409823i) q^{55} +(-7.24317 + 1.44250i) q^{56} +(-4.45843 - 8.63807i) q^{57} +(-2.56838 - 10.4926i) q^{58} +(-1.23031 + 2.13097i) q^{59} +(12.4186 - 5.74053i) q^{60} +0.154002 q^{61} +(7.86734 - 0.323981i) q^{62} +(-0.737209 + 7.79865i) q^{63} +(1.04053 - 7.93204i) q^{64} +(-11.7269 - 6.77050i) q^{65} +(-0.0974721 - 0.498923i) q^{66} +(4.26005 - 2.45954i) q^{67} +(-7.82395 - 0.340388i) q^{68} +(-2.27676 - 1.46166i) q^{69} +(-14.1659 + 3.46753i) q^{70} +(-4.14969 - 7.18748i) q^{71} +(-7.74342 - 3.46978i) q^{72} +(7.27086 + 12.5935i) q^{73} +(3.00427 - 10.3101i) q^{74} +(16.3117 - 8.41909i) q^{75} +(-11.2140 - 0.487876i) q^{76} +0.541903i q^{77} +(1.61029 + 8.24248i) q^{78} +(3.59507 + 2.07561i) q^{79} +(1.37199 - 15.7380i) q^{80} +(-5.88082 + 6.81293i) q^{81} +(5.50019 - 5.26610i) q^{82} +(4.05426 + 7.02219i) q^{83} +(7.39208 + 5.21284i) q^{84} -15.4647 q^{85} +(-0.179369 - 0.0522662i) q^{86} +(-7.14747 + 11.1333i) q^{87} +(-0.555889 - 0.188555i) q^{88} -7.41534i q^{89} +(-15.5744 - 6.18073i) q^{90} -8.95254i q^{91} +(-2.77090 + 1.44299i) q^{92} +(-6.92578 - 6.71070i) q^{93} +(-17.1814 + 4.20568i) q^{94} -22.1654 q^{95} +(-7.91946 + 5.76906i) q^{96} +1.34931 q^{97} +(0.177955 + 0.185866i) q^{98} +(-0.360665 + 0.507502i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 12 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 4 q^{16} - 2 q^{18} - 14 q^{21} - 6 q^{22} - 4 q^{24} + 48 q^{25} + 6 q^{28} - 48 q^{30} + 4 q^{33} + 28 q^{34} + 2 q^{36} - 8 q^{37} + 36 q^{40} - 4 q^{42}+ \cdots + 48 q^{96}+O(q^{100}) $ 120 * q - 12 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 4 * q^16 - 2 * q^18 - 14 * q^21 - 6 * q^22 - 4 * q^24 + 48 * q^25 + 6 * q^28 - 48 * q^30 + 4 * q^33 + 28 * q^34 + 2 * q^36 - 8 * q^37 + 36 * q^40 - 4 * q^42 - 34 * q^45 - 48 * q^46 + 10 * q^48 + 60 * q^49 + 8 * q^52 - 84 * q^54 - 14 * q^57 - 28 * q^58 - 60 * q^60 - 64 * q^61 + 84 * q^64 - 132 * q^66 - 4 * q^69 - 120 * q^70 + 44 * q^72 + 28 * q^76 + 20 * q^78 - 2 * q^81 + 48 * q^82 - 8 * q^84 + 8 * q^85 - 10 * q^88 + 24 * q^90 - 78 * q^93 - 88 * q^94 + 48 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/372\mathbb{Z}\right)^\times$.

$n$	$125$	$187$	$313$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.37366	+	0.336245i	−0.971324	+	0.237761i
$2$	−1.37366	+	0.336245i	−0.971324	+	0.237761i
$3$	1.45754	+	0.935726i	0.841510	+	0.540241i
$3$	1.45754	+	0.935726i	0.841510	+	0.540241i
$4$	1.77388	−	0.923772i	0.886939	−	0.461886i
$5$	3.42031	−	1.97472i	1.52961	−	0.883120i	0.530231	−	0.847853i	$-0.322105\pi$
$5$	3.42031	−	1.97472i	1.52961	−	0.883120i	0.999378	−	0.0352669i	$-0.0112281\pi$
$6$	−2.31679	−	0.795278i	−0.945827	−	0.324671i
$7$	2.26131	+	1.30557i	0.854696	+	0.493459i	0.862232	−	0.506513i	$-0.169066\pi$
$7$	2.26131	+	1.30557i	0.854696	+	0.493459i	−0.00753664	+	0.999972i	$0.502399\pi$
$8$	−2.12609	+	1.86541i	−0.751687	+	0.659520i
$9$	1.24884	+	2.72771i	0.416278	+	0.909237i
$10$	−4.03435	+	3.86265i	−1.27577	+	1.22148i
$11$	0.103767	+	0.179731i	0.0312871	+	0.0541908i	0.881245	−	0.472660i	$-0.156706\pi$
$11$	0.103767	+	0.179731i	0.0312871	+	0.0541908i	−0.849958	+	0.526851i	$0.823373\pi$
$12$	3.44989	+	0.313431i	0.995898	+	0.0904798i
$13$	−1.71430	−	2.96925i	−0.475461	−	0.823522i	0.524144	−	0.851629i	$-0.324385\pi$
$13$	−1.71430	−	2.96925i	−0.475461	−	0.823522i	−0.999605	+	0.0281076i	$0.991052\pi$
$14$	−3.54526	−	1.03305i	−0.947512	−	0.276095i
$15$	6.83302	+	0.322246i	1.76428	+	0.0832035i
$16$	2.29329	−	3.27732i	0.573323	−	0.819329i
$17$	−3.39107	−	1.95784i	−0.822456	−	0.474845i	0.0288065	−	0.999585i	$-0.490829\pi$
$17$	−3.39107	−	1.95784i	−0.822456	−	0.474845i	−0.851263	+	0.524740i	$0.824163\pi$
$18$	−2.63265	−	3.32703i	−0.620522	−	0.784189i
$19$	−4.86040	−	2.80615i	−1.11505	−	0.643775i	−0.174919	−	0.984583i	$-0.555966\pi$
$19$	−4.86040	−	2.80615i	−1.11505	−	0.643775i	−0.940133	+	0.340808i	$0.889300\pi$
$20$	4.24303	−	6.66249i	0.948770	−	1.48978i
$21$	2.07430	+	4.01889i	0.452648	+	0.876993i
$22$	−0.202975	−	0.211997i	−0.0432743	−	0.0451980i
$23$	−1.56206			−0.325712			−0.162856	−	0.986650i	$-0.552071\pi$
$23$	−1.56206			−0.325712			−0.162856	+	0.986650i	$0.552071\pi$
$24$	−4.84437	+	0.729461i	−0.988852	+	0.148901i
$25$	5.29901	−	9.17816i	1.05980	−	1.83563i
$26$	3.35326	+	3.50231i	0.657627	+	0.686860i
$27$	−0.732164	+	5.14431i	−0.140905	+	0.990023i
$28$	5.21734	+	0.226985i	0.985985	+	0.0428962i
$29$			7.63843i			1.41842i	0.704997	+	0.709210i	$0.250948\pi$
$29$			7.63843i			1.41842i	−0.704997	+	0.709210i	$0.749052\pi$
$30$	−9.49460	+	1.85491i	−1.73347	+	0.338659i
$31$	−5.45799	−	1.10016i	−0.980284	−	0.197594i
$31$	−5.45799	−	1.10016i	−0.980284	−	0.197594i
$32$	−2.04822	+	5.27303i	−0.362078	+	0.932148i
$33$	−0.0169334	+	0.359062i	−0.00294772	+	0.0625047i
$34$	5.31649	+	1.54917i	0.911771	+	0.265680i
$35$	10.3125			1.74313
$36$	4.73507	+	3.68499i	0.789178	+	0.614165i
$37$	−3.79678	+	6.57622i	−0.624187	+	1.08112i	0.364510	+	0.931199i	$0.381236\pi$
$37$	−3.79678	+	6.57622i	−0.624187	+	1.08112i	−0.988697	+	0.149925i	$0.952097\pi$
$38$	7.62008	+	2.22041i	1.23614	+	0.360198i
$39$	0.279749	−	5.93191i	0.0447957	−	0.949865i
$40$	−3.58824	+	10.5787i	−0.567351	+	1.67264i
$41$	−4.66304	+	2.69221i	−0.728245	+	0.420452i	−0.817780	−	0.575531i	$-0.804795\pi$
$41$	−4.66304	+	2.69221i	−0.728245	+	0.420452i	0.0895350	+	0.995984i	$0.471462\pi$
$42$	−4.20070	−	4.82311i	−0.648183	−	0.744222i
$43$	0.114409	+	0.0660539i	0.0174472	+	0.0100731i	0.508698	−	0.860945i	$-0.330127\pi$
$43$	0.114409	+	0.0660539i	0.0174472	+	0.0100731i	−0.491251	+	0.871018i	$0.663460\pi$
$44$	0.350101	+	0.222963i	0.0527797	+	0.0336129i
$45$	9.65786	+	6.86352i	1.43971	+	1.02315i
$46$	2.14574	−	0.525234i	0.316372	−	0.0774416i
$47$	12.5078			1.82445			0.912225	−	0.409690i	$-0.134363\pi$
$47$	12.5078			1.82445			0.912225	+	0.409690i	$0.134363\pi$
$48$	6.40923	−	2.63092i	0.925093	−	0.379741i
$49$	−0.0909767	−	0.157576i	−0.0129967	−	0.0225109i
$50$	−4.19293	+	14.3894i	−0.592969	+	2.03497i
$51$	−3.11062	−	6.02674i	−0.435574	−	0.843912i
$52$	−5.78386	−	3.68347i	−0.802078	−	0.510805i
$53$	−1.04024	+	0.600584i	−0.142888	+	0.0824966i	−0.569740	−	0.821825i	$-0.692956\pi$
$53$	−1.04024	+	0.600584i	−0.142888	+	0.0824966i	0.426852	+	0.904322i	$0.359623\pi$
$54$	−0.724005	−	7.31272i	−0.0985246	−	0.995135i
$55$	0.709834	+	0.409823i	0.0957140	+	0.0552605i
$56$	−7.24317	+	1.44250i	−0.967910	+	0.192763i
$57$	−4.45843	−	8.63807i	−0.590533	−	1.14414i
$58$	−2.56838	−	10.4926i	−0.337245	−	1.37775i
$59$	−1.23031	+	2.13097i	−0.160173	+	0.277428i	−0.934931	−	0.354830i	$-0.884539\pi$
$59$	−1.23031	+	2.13097i	−0.160173	+	0.277428i	0.774758	+	0.632258i	$0.217872\pi$
$60$	12.4186	−	5.74053i	1.60324	−	0.741099i
$61$	0.154002			0.0197180			0.00985898	−	0.999951i	$-0.496862\pi$
$61$	0.154002			0.0197180			0.00985898	+	0.999951i	$0.496862\pi$
$62$	7.86734	−	0.323981i	0.999153	−	0.0411456i
$63$	−0.737209	+	7.79865i	−0.0928796	+	0.982538i
$64$	1.04053	−	7.93204i	0.130066	−	0.991505i
$65$	−11.7269	−	6.77050i	−1.45454	−	0.839778i
$66$	−0.0974721	−	0.498923i	−0.0119980	−	0.0614131i
$67$	4.26005	−	2.45954i	0.520448	−	0.300481i	−0.216670	−	0.976245i	$-0.569519\pi$
$67$	4.26005	−	2.45954i	0.520448	−	0.300481i	0.737118	+	0.675764i	$0.236186\pi$
$68$	−7.82395	−	0.340388i	−0.948793	−	0.0412781i
$69$	−2.27676	−	1.46166i	−0.274090	−	0.175963i
$70$	−14.1659	+	3.46753i	−1.69315	+	0.414449i
$71$	−4.14969	−	7.18748i	−0.492478	−	0.852997i	0.507484	−	0.861661i	$-0.330576\pi$
$71$	−4.14969	−	7.18748i	−0.492478	−	0.852997i	−0.999962	+	0.00866383i	$0.997242\pi$
$72$	−7.74342	−	3.46978i	−0.912571	−	0.408917i
$73$	7.27086	+	12.5935i	0.850989	+	1.47396i	0.880317	+	0.474387i	$0.157330\pi$
$73$	7.27086	+	12.5935i	0.850989	+	1.47396i	−0.0293272	+	0.999570i	$0.509336\pi$
$74$	3.00427	−	10.3101i	0.349239	−	1.19853i
$75$	16.3117	−	8.41909i	1.88352	−	0.972153i
$76$	−11.2140	−	0.487876i	−1.28633	−	0.0559632i
$77$			0.541903i			0.0617555i
$78$	1.61029	+	8.24248i	0.182330	+	0.933277i
$79$	3.59507	+	2.07561i	0.404477	+	0.233525i	0.688414	−	0.725318i	$-0.258307\pi$
$79$	3.59507	+	2.07561i	0.404477	+	0.233525i	−0.283937	+	0.958843i	$0.591641\pi$
$80$	1.37199	−	15.7380i	0.153394	−	1.75957i
$81$	−5.88082	+	6.81293i	−0.653424	+	0.756992i
$82$	5.50019	−	5.26610i	0.607394	−	0.581543i
$83$	4.05426	+	7.02219i	0.445013	+	0.770786i	0.998053	−	0.0623691i	$-0.0198656\pi$
$83$	4.05426	+	7.02219i	0.445013	+	0.770786i	−0.553040	+	0.833155i	$0.686532\pi$
$84$	7.39208	+	5.21284i	0.806542	+	0.568768i
$85$	−15.4647			−1.67738
$86$	−0.179369	−	0.0522662i	−0.0193419	−	0.00563601i
$87$	−7.14747	+	11.1333i	−0.766289	+	1.19362i
$88$	−0.555889	−	0.188555i	−0.0592580	−	0.0201000i
$89$		−	7.41534i		−	0.786024i	−0.919533	−	0.393012i	$-0.871433\pi$
$89$		−	7.41534i		−	0.786024i	0.919533	−	0.393012i	$-0.128567\pi$
$90$	−15.5744	−	6.18073i	−1.64169	−	0.651506i
$91$		−	8.95254i		−	0.938481i
$92$	−2.77090	+	1.44299i	−0.288887	+	0.150442i
$93$	−6.92578	−	6.71070i	−0.718170	−	0.695867i
$94$	−17.1814	+	4.20568i	−1.77213	+	0.433783i
$95$	−22.1654			−2.27412
$96$	−7.91946	+	5.76906i	−0.808277	+	0.588803i
$97$	1.34931			0.137002			0.0685008	−	0.997651i	$-0.478178\pi$
$97$	1.34931			0.137002			0.0685008	+	0.997651i	$0.478178\pi$
$98$	0.177955	+	0.185866i	0.0179762	+	0.0187753i
$99$	−0.360665	+	0.507502i	−0.0362482	+	0.0510058i
$100$	0.921282	−	21.1760i	0.0921282	−	2.11760i
$101$			3.09100i			0.307566i	0.988105	+	0.153783i	$0.0491457\pi$
$101$			3.09100i			0.307566i	−0.988105	+	0.153783i	$0.950854\pi$
$102$	6.29939	+	7.23275i	0.623733	+	0.716149i
$103$	−6.00461	+	3.46676i	−0.591652	+	0.341590i	−0.765750	−	0.643138i	$-0.777632\pi$
$103$	−6.00461	+	3.46676i	−0.591652	+	0.341590i	0.174099	+	0.984728i	$0.444299\pi$
$104$	9.18361	+	3.11504i	0.900527	+	0.305455i
$105$	15.0309	+	9.64969i	1.46686	+	0.941713i
$106$	1.22700	−	1.17477i	0.119176	−	0.114104i
$107$	7.20284	−	12.4757i	0.696324	−	1.20607i	−0.273408	−	0.961898i	$-0.588151\pi$
$107$	7.20284	−	12.4757i	0.696324	−	1.20607i	0.969732	−	0.244171i	$-0.0785159\pi$
$108$	3.45340	+	9.80174i	0.332303	+	0.943173i
$109$	−5.14668			−0.492962			−0.246481	−	0.969148i	$-0.579274\pi$
$109$	−5.14668			−0.492962			−0.246481	+	0.969148i	$0.579274\pi$
$110$	−1.11287	−	0.324279i	−0.106108	−	0.0309188i
$111$	−11.6875	+	6.03235i	−1.10933	+	0.572565i
$112$	9.46462	−	4.41699i	0.894322	−	0.417366i
$113$	−6.32002	+	3.64886i	−0.594537	+	0.343256i	−0.766890	−	0.641779i	$-0.778197\pi$
$113$	−6.32002	+	3.64886i	−0.594537	+	0.343256i	0.172352	+	0.985035i	$0.444863\pi$
$114$	9.02887	+	10.3666i	0.845631	+	0.970925i
$115$	−5.34273	+	3.08462i	−0.498212	+	0.287643i
$116$	7.05616	+	13.5496i	0.655148	+	1.25805i
$117$	5.95838	−	8.38421i	0.550853	−	0.775121i
$118$	0.973505	−	3.34091i	0.0896184	−	0.307555i
$119$	−5.11219	−	8.85457i	−0.468633	−	0.811697i
$120$	−15.1288	+	12.0612i	−1.38106	+	1.10104i
$121$	5.47846	−	9.48898i	0.498042	−	0.862634i
$122$	−0.211547	+	0.0517825i	−0.0191525	+	0.00468816i
$123$	−9.31573	−	0.439330i	−0.839971	−	0.0396131i
$124$	−10.6981	+	3.09039i	−0.960718	+	0.277525i
$125$		−	22.1090i		−	1.97749i
$126$	−1.60958	−	10.9606i	−0.143393	−	0.976445i
$127$	−10.7362	−	6.19857i	−0.952688	−	0.550035i	−0.0587729	−	0.998271i	$-0.518719\pi$
$127$	−10.7362	−	6.19857i	−0.952688	−	0.550035i	−0.893915	+	0.448237i	$0.852052\pi$
$128$	1.23778	+	11.2458i	0.109405	+	0.993997i
$129$	0.104947	+	0.203331i	0.00924005	+	0.0179023i
$130$	18.3852	+	5.35727i	1.61249	+	0.469863i
$131$	−2.00451	+	3.47191i	−0.175135	+	0.303342i	−0.940208	−	0.340601i	$-0.889369\pi$
$131$	−2.00451	+	3.47191i	−0.175135	+	0.303342i	0.765073	+	0.643943i	$0.222703\pi$
$132$	0.301654	+	0.652575i	0.0262556	+	0.0567994i
$133$	−7.32725	−	12.6912i	−0.635353	−	1.10046i
$134$	−5.02485	+	4.81099i	−0.434081	+	0.415607i
$135$	7.65433	+	19.0410i	0.658780	+	1.63878i
$136$	10.8619	−	2.16319i	0.931400	−	0.185492i
$137$	16.6428	−	9.60871i	1.42189	−	0.820928i	0.425428	−	0.904992i	$-0.360124\pi$
$137$	16.6428	−	9.60871i	1.42189	−	0.820928i	0.996460	+	0.0840645i	$0.0267902\pi$
$138$	3.61897	+	1.24227i	0.308067	+	0.105749i
$139$			1.32937i			0.112756i	0.998409	+	0.0563780i	$0.0179552\pi$
$139$			1.32937i			0.112756i	−0.998409	+	0.0563780i	$0.982045\pi$
$140$	18.2932	−	9.52641i	1.54605	−	0.805129i
$141$	18.2306	+	11.7039i	1.53529	+	0.985643i
$142$	8.11702	+	8.47784i	0.681165	+	0.711444i
$143$	0.355777	−	0.616223i	0.0297515	−	0.0515312i
$144$	11.8035	+	2.16261i	0.983627	+	0.180217i
$145$	15.0837	+	26.1258i	1.25264	+	2.16963i
$146$	−14.2222	−	14.8544i	−1.17704	−	1.22936i
$147$	0.0148461	−	0.314803i	0.00122449	−	0.0259645i
$148$	−0.660106	+	15.1728i	−0.0542604	+	1.24719i
$149$	−17.4403	−	10.0691i	−1.42876	−	0.824896i	−0.431738	−	0.901999i	$-0.642100\pi$
$149$	−17.4403	−	10.0691i	−1.42876	−	0.824896i	−0.997023	+	0.0771031i	$0.975433\pi$
$150$	−19.5759	+	17.0497i	−1.59837	+	1.39210i
$151$			6.32563i			0.514772i	0.966309	+	0.257386i	$0.0828612\pi$
$151$			6.32563i			0.514772i	−0.966309	+	0.257386i	$0.917139\pi$
$152$	15.5683	−	3.10048i	1.26275	−	0.251482i
$153$	1.10552	−	11.6949i	0.0893762	−	0.945476i
$154$	−0.182212	−	0.744389i	−0.0146831	−	0.0599846i
$155$	−20.8405	+	7.01511i	−1.67395	+	0.563467i
$156$	−4.98349	−	10.7809i	−0.398998	−	0.863163i
$157$	22.4951			1.79531			0.897653	−	0.440703i	$-0.145271\pi$
$157$	22.4951			1.79531			0.897653	+	0.440703i	$0.145271\pi$
$158$	−5.63631	−	1.64236i	−0.448401	−	0.130659i
$159$	−2.07818	−	0.0980069i	−0.164810	−	0.00777245i
$160$	3.40718	+	22.0800i	0.269362	+	1.74558i
$161$	−3.53230	−	2.03938i	−0.278385	−	0.160725i
$162$	5.78743	−	11.3360i	0.454703	−	0.890643i
$163$			16.3193i			1.27823i	0.769112	+	0.639113i	$0.220699\pi$
$163$			16.3193i			1.27823i	−0.769112	+	0.639113i	$0.779301\pi$
$164$	−5.78468	+	9.08324i	−0.451708	+	0.709282i
$165$	0.651128	+	1.26154i	0.0506903	+	0.0982109i
$166$	−7.93035	−	8.28287i	−0.615515	−	0.642876i
$167$	8.27206	−	14.3276i	0.640111	−	1.10871i	−0.345296	−	0.938494i	$-0.612221\pi$
$167$	8.27206	−	14.3276i	0.640111	−	1.10871i	0.985408	−	0.170212i	$-0.0544452\pi$
$168$	−11.9070	−	4.67512i	−0.918644	−	0.360693i
$169$	0.622370	−	1.07798i	0.0478746	−	0.0829212i
$170$	21.2432	−	5.19993i	1.62928	−	0.398816i
$171$	1.58454	−	16.7622i	0.121172	−	1.28184i
$172$	0.263966	+	0.0114841i	0.0201272	+	0.000875654i
$173$	−4.53164	+	2.61634i	−0.344534	+	0.198917i	−0.662275	−	0.749261i	$-0.730409\pi$
$173$	−4.53164	+	2.61634i	−0.344534	+	0.198917i	0.317741	+	0.948178i	$0.397076\pi$
$174$	6.07467	−	17.6967i	0.460520	−	1.34158i
$175$	23.9654	−	13.8365i	1.81162	−	1.04594i
$176$	0.827003	+	0.0720956i	0.0623377	+	0.00543441i
$177$	−3.78723	+	1.95473i	−0.284665	+	0.146926i
$178$	2.49337	+	10.1861i	0.186886	+	0.763484i
$179$	−4.26889	+	7.39393i	−0.319072	+	0.552648i	−0.980295	−	0.197541i	$-0.936704\pi$
$179$	−4.26889	+	7.39393i	−0.319072	+	0.552648i	0.661223	+	0.750189i	$0.270038\pi$
$180$	23.4722	+	3.25340i	1.74951	+	0.242494i
$181$	−8.16415	−	14.1407i	−0.606837	−	1.05107i	−0.991758	−	0.128123i	$-0.959105\pi$
$181$	−8.16415	−	14.1407i	−0.606837	−	1.05107i	0.384922	−	0.922949i	$-0.374228\pi$
$182$	3.01024	+	12.2977i	0.223134	+	0.911569i
$183$	0.224464	+	0.144104i	0.0165929	+	0.0106525i
$184$	3.32108	−	2.91387i	0.244833	−	0.214814i
$185$			29.9903i			2.20493i
$186$	11.7701	+	6.88946i	0.863026	+	0.505159i
$187$		−	0.812639i		−	0.0594261i
$188$	22.1873	−	11.5543i	1.61818	−	0.842687i
$189$	−8.37191	+	10.6770i	−0.608967	+	0.776638i
$190$	30.4477	−	7.45301i	2.20891	−	0.540698i
$191$	2.18511	+	3.78472i	0.158109	+	0.273853i	0.934187	−	0.356785i	$-0.116127\pi$
$191$	2.18511	+	3.78472i	0.158109	+	0.273853i	−0.776078	+	0.630637i	$0.782794\pi$
$192$	8.93882	−	10.5876i	0.645104	−	0.764095i
$193$	8.35283	−	14.4675i	0.601250	−	1.04140i	−0.391382	−	0.920228i	$-0.628003\pi$
$193$	8.35283	−	14.4675i	0.601250	−	1.04140i	0.992632	−	0.121167i	$-0.0386638\pi$
$194$	−1.85349	+	0.453698i	−0.133073	+	0.0325736i
$195$	−10.7570	−	20.8414i	−0.770325	−	1.49248i
$196$	−0.306946	−	0.195480i	−0.0219247	−	0.0139628i
$197$	−9.40039	+	5.42732i	−0.669750	+	0.386681i	−0.795982	−	0.605320i	$-0.793045\pi$
$197$	−9.40039	+	5.42732i	−0.669750	+	0.386681i	0.126232	+	0.992001i	$0.459712\pi$
$198$	0.324785	−	0.818406i	0.0230815	−	0.0581616i
$199$	−14.6129	+	8.43677i	−1.03588	+	0.598067i	−0.918664	−	0.395039i	$-0.870731\pi$
$199$	−14.6129	+	8.43677i	−1.03588	+	0.598067i	−0.117218	+	0.993106i	$0.537398\pi$
$200$	5.85480	+	29.3984i	0.413997	+	2.07878i
$201$	8.51065	+	0.401363i	0.600295	+	0.0283099i
$202$	−1.03933	−	4.24599i	−0.0731273	−	0.298747i
$203$	−9.97250	+	17.2729i	−0.699932	+	1.21232i
$204$	−11.0852	−	7.81720i	−0.776119	−	0.547313i
$205$	−10.6327	+	18.4164i	−0.742620	+	1.28626i
$206$	7.08261	−	6.78117i	0.493469	−	0.472467i
$207$	−1.95076	−	4.26085i	−0.135587	−	0.296149i
$208$	−13.6626	−	1.19106i	−0.947328	−	0.0825851i
$209$		−	1.16475i		−	0.0805674i
$210$	−23.8920	−	8.20132i	−1.64870	−	0.565945i
$211$	3.26296	+	1.88387i	0.224632	+	0.129691i	0.608093	−	0.793866i	$-0.291935\pi$
$211$	3.26296	+	1.88387i	0.224632	+	0.129691i	−0.383461	+	0.923557i	$0.625268\pi$
$212$	−1.29046	+	2.02631i	−0.0886292	+	0.139168i
$213$	0.677172	−	14.3590i	0.0463990	−	0.983863i
$214$	−5.69936	+	19.5592i	−0.389600	+	1.33704i
$215$	0.521751			0.0355831
$216$	−8.03958	−	12.3031i	−0.547024	−	0.837117i
$217$	−10.9059	−	9.61358i	−0.740340	−	0.652613i
$218$	7.06978	−	1.73054i	0.478826	−	0.117207i
$219$	−1.18650	+	25.1590i	−0.0801763	+	1.70009i
$220$	1.63774	+	0.0712515i	0.110417	+	0.00480377i
$221$			13.4253i			0.903081i
$222$	14.0263	−	12.2162i	0.941383	−	0.819901i
$223$	19.9649	+	11.5267i	1.33695	+	0.771887i	0.986354	−	0.164640i	$-0.0526464\pi$
$223$	19.9649	+	11.5267i	1.33695	+	0.771887i	0.350594	+	0.936528i	$0.385980\pi$
$224$	−11.5160	+	9.24987i	−0.769443	+	0.618033i
$225$	31.6530	+	2.99217i	2.11020	+	0.199478i
$226$	7.45464	−	7.13737i	0.495875	−	0.474771i
$227$	1.63294	+	2.82833i	0.108382	+	0.187723i	0.915115	−	0.403193i	$-0.132100\pi$
$227$	1.63294	+	2.82833i	0.108382	+	0.187723i	−0.806733	+	0.590916i	$0.798766\pi$
$228$	−15.8883	−	11.2043i	−1.05223	−	0.742024i
$229$	−11.2661	+	19.5134i	−0.744483	+	1.28948i	0.205953	+	0.978562i	$0.433971\pi$
$229$	−11.2661	+	19.5134i	−0.744483	+	1.28948i	−0.950436	+	0.310920i	$0.899363\pi$
$230$	6.30190	−	6.03369i	0.415535	−	0.397850i
$231$	−0.507072	+	0.789844i	−0.0333629	+	0.0519679i
$232$	−14.2488	−	16.2400i	−0.935477	−	1.06621i
$233$		−	13.6684i		−	0.895448i	−0.894172	−	0.447724i	$-0.852235\pi$
$233$		−	13.6684i		−	0.895448i	0.894172	−	0.447724i	$-0.147765\pi$
$234$	−5.36564	+	13.5205i	−0.350763	+	0.883864i
$235$	42.7805	−	24.6994i	2.79069	−	1.61121i
$236$	−0.213901	+	4.91660i	−0.0139238	+	0.320044i
$237$	3.29774	+	6.38928i	0.214211	+	0.415028i
$238$	9.99970	+	10.4442i	0.648184	+	0.676997i
$239$	3.28285	+	5.68607i	0.212350	+	0.367801i	0.952450	−	0.304696i	$-0.0985549\pi$
$239$	3.28285	+	5.68607i	0.212350	+	0.367801i	−0.740099	+	0.672497i	$0.765222\pi$
$240$	16.7262	−	21.6550i	1.07967	−	1.39782i
$241$	7.65184	−	13.2534i	0.492898	−	0.853725i	−0.507068	−	0.861906i	$-0.669271\pi$
$241$	7.65184	−	13.2534i	0.492898	−	0.853725i	0.999967	+	0.00818079i	$0.00260406\pi$
$242$	−4.33492	+	14.8767i	−0.278659	+	0.956312i
$243$	−14.9465	+	4.42727i	−0.958822	+	0.284009i
$244$	0.273181	−	0.142263i	0.0174886	−	0.00910745i
$245$	−0.622337	−	0.359306i	−0.0397597	−	0.0229552i
$246$	12.9444	−	2.52888i	0.825302	−	0.161235i
$247$			19.2423i			1.22436i
$248$	13.6564	−	7.84233i	0.867184	−	0.497988i
$249$	−0.661599	+	14.0288i	−0.0419271	+	0.889039i
$250$	7.43404	+	30.3703i	0.470170	+	1.92078i
$251$	9.82770	−	17.0221i	0.620319	−	1.07442i	−0.369108	−	0.929387i	$-0.620337\pi$
$251$	9.82770	−	17.0221i	0.620319	−	1.07442i	0.989426	−	0.145037i	$-0.0463300\pi$
$252$	5.89645	+	14.5149i	0.371442	+	0.914351i
$253$	−0.162091	−	0.280750i	−0.0101906	−	0.0176506i
$254$	16.8322	+	4.90472i	1.05614	+	0.307750i
$255$	−22.5404	−	14.4707i	−1.41153	−	0.906191i
$256$	−5.48163	−	15.0317i	−0.342602	−	0.939481i
$257$	13.3298	−	7.69598i	0.831492	−	0.480062i	−0.0228711	−	0.999738i	$-0.507281\pi$
$257$	13.3298	−	7.69598i	0.831492	−	0.480062i	0.854363	+	0.519676i	$0.173947\pi$
$258$	−0.212530	−	0.244020i	−0.0132316	−	0.0151920i
$259$	−17.1714	+	9.91393i	−1.06698	+	0.616022i
$260$	−27.0564	−	1.17711i	−1.67797	−	0.0730016i
$261$	−20.8354	+	9.53914i	−1.28968	+	0.590458i
$262$	1.58610	−	5.44322i	0.0979894	−	0.336283i
$263$	−13.5866			−0.837783			−0.418891	−	0.908036i	$-0.637581\pi$
$263$	−13.5866			−0.837783			−0.418891	+	0.908036i	$0.637581\pi$
$264$	−0.633794	−	0.794986i	−0.0390073	−	0.0489280i
$265$	−2.37197	+	4.10837i	−0.145709	+	0.252375i
$266$	14.3325	+	14.9696i	0.878781	+	0.917845i
$267$	6.93872	−	10.8081i	0.424643	−	0.661447i
$268$	5.28476	−	8.29825i	0.322818	−	0.506896i
$269$	11.8869	−	6.86288i	0.724754	−	0.418437i	−0.0917457	−	0.995782i	$-0.529245\pi$
$269$	11.8869	−	6.86288i	0.724754	−	0.418437i	0.816500	+	0.577345i	$0.195911\pi$
$270$	−16.9169	−	23.5820i	−1.02953	−	1.43516i
$271$			1.75353i			0.106519i	0.998581	+	0.0532597i	$0.0169611\pi$
$271$			1.75353i			0.106519i	−0.998581	+	0.0532597i	$0.983039\pi$
$272$	−14.1932	+	6.62374i	−0.860588	+	0.401623i
$273$	8.37712	−	13.0487i	0.507006	−	0.789741i
$274$	−19.6306	+	18.7951i	−1.18593	+	1.13546i
$275$	2.19946			0.132632
$276$	−5.38894	−	0.489598i	−0.324376	−	0.0294703i
$277$	−15.1715			−0.911567			−0.455783	−	0.890091i	$-0.650641\pi$
$277$	−15.1715			−0.911567			−0.455783	+	0.890091i	$0.650641\pi$
$278$	−0.446995	−	1.82610i	−0.0268090	−	0.109522i
$279$	−3.81522	−	16.2617i	−0.228411	−	0.973565i
$280$	−21.9254	+	19.2370i	−1.31029	+	1.14963i
$281$			8.60821i			0.513523i	0.966475	+	0.256761i	$0.0826555\pi$
$281$			8.60821i			0.513523i	−0.966475	+	0.256761i	$0.917345\pi$
$282$	−28.9780	−	9.94718i	−1.72561	−	0.592346i
$283$		−	10.2357i		−	0.608451i	−0.952600	−	0.304225i	$-0.901602\pi$
$283$		−	10.2357i		−	0.608451i	0.952600	−	0.304225i	$-0.0983976\pi$
$284$	−14.0006	−	8.91635i	−0.830786	−	0.529088i
$285$	−32.3069	−	20.7407i	−1.91370	−	1.22858i
$286$	−0.281514	+	0.966109i	−0.0166463	+	0.0571272i
$287$	−14.0595			−0.829904
$288$	−16.9412	+	0.998188i	−0.998269	+	0.0588188i
$289$	−0.833745	−	1.44409i	−0.0490438	−	0.0849464i
$290$	−29.5046	−	30.8161i	−1.73257	−	1.80958i
$291$	1.96667	+	1.26258i	0.115288	+	0.0740139i
$292$	24.5311	+	15.6227i	1.43558	+	0.914250i
$293$	−19.7156	−	11.3828i	−1.15180	−	0.664991i	−0.202473	−	0.979288i	$-0.564898\pi$
$293$	−19.7156	−	11.3828i	−1.15180	−	0.664991i	−0.949325	+	0.314297i	$0.898231\pi$
$294$	0.0854573	+	0.437424i	0.00498397	+	0.0255111i
$295$			9.71808i			0.565808i
$296$	−4.19501	−	21.0642i	−0.243830	−	1.22433i
$297$	−1.00056	+	0.402220i	−0.0580586	+	0.0233392i
$298$	27.3427	+	7.96736i	1.58392	+	0.461537i
$299$	2.67783	+	4.63815i	0.154863	+	0.268231i
$300$	21.1577	−	30.0028i	1.22154	−	1.73221i
$301$	0.172476	+	0.298737i	0.00994135	+	0.0172189i
$302$	−2.12696	−	8.68926i	−0.122393	−	0.500011i
$303$	−2.89233	+	4.50526i	−0.166160	+	0.258820i
$304$	−20.3430	+	9.49374i	−1.16675	+	0.544503i
$305$	0.526735	−	0.304111i	0.0301608	−	0.0174133i
$306$	2.41374	+	16.4365i	0.137984	+	0.939613i
$307$	−16.0339	−	9.25716i	−0.915101	−	0.528334i	−0.0330325	−	0.999454i	$-0.510516\pi$
$307$	−16.0339	−	9.25716i	−0.915101	−	0.528334i	−0.882069	+	0.471120i	$0.843850\pi$
$308$	0.500594	+	0.961270i	0.0285240	+	0.0547734i
$309$	−11.9959	−	0.565727i	−0.682422	−	0.0321831i
$310$	26.2690	−	16.6439i	1.49198	−	0.945309i
$311$	10.2620			0.581904			0.290952	−	0.956738i	$-0.406028\pi$
$311$	10.2620			0.581904			0.290952	+	0.956738i	$0.406028\pi$
$312$	10.4706	+	13.1336i	0.592783	+	0.743545i
$313$	1.01466	−	1.75745i	0.0573522	−	0.0993369i	−0.835924	−	0.548845i	$-0.815068\pi$
$313$	1.01466	−	1.75745i	0.0573522	−	0.0993369i	0.893276	+	0.449509i	$0.148401\pi$
$314$	−30.9006	+	7.56387i	−1.74382	+	0.426854i
$315$	12.8786	+	28.1296i	0.725629	+	1.58492i
$316$	8.29461	+	0.360865i	0.466608	+	0.0203002i
$317$	8.17576	+	4.72028i	0.459196	+	0.265117i	0.711706	−	0.702477i	$-0.247923\pi$
$317$	8.17576	+	4.72028i	0.459196	+	0.265117i	−0.252510	+	0.967594i	$0.581256\pi$
$318$	2.88766	−	0.564148i	0.161932	−	0.0316358i
$319$	−1.37286	+	0.792620i	−0.0768653	+	0.0443782i
$320$	−12.1046	−	29.1848i	−0.676668	−	1.63148i
$321$	22.1722	−	11.4439i	1.23753	−	0.638736i
$322$	5.53791	+	1.61369i	0.308616	+	0.0899274i
$323$	10.9880	+	19.0317i	0.611387	+	1.05895i
$324$	−4.13827	+	17.5178i	−0.229904	+	0.973213i
$325$	−36.3363			−2.01558
$326$	−5.48728	−	22.4172i	−0.303913	−	1.24157i
$327$	−7.50148	−	4.81588i	−0.414833	−	0.266319i
$328$	4.89199	−	14.4223i	0.270115	−	0.796341i
$329$	28.2840	+	16.3298i	1.55935	+	0.900291i
$330$	−1.31862	−	1.51399i	−0.0725874	−	0.0833424i
$331$	−11.4961	+	6.63730i	−0.631885	+	0.364819i	−0.781482	−	0.623928i	$-0.785536\pi$
$331$	−11.4961	+	6.63730i	−0.631885	+	0.364819i	0.149597	+	0.988747i	$0.452202\pi$
$332$	13.6787	+	8.71130i	0.750715	+	0.478095i
$333$	−22.6796	−	2.14391i	−1.24283	−	0.117486i
$334$	−6.54540	+	22.4627i	−0.358148	+	1.22911i
$335$	9.71380	−	16.8248i	0.530722	−	0.919237i
$336$	17.9281	+	2.41835i	0.978060	+	0.131932i
$337$	16.9738			0.924623			0.462311	−	0.886718i	$-0.347020\pi$
$337$	16.9738			0.924623			0.462311	+	0.886718i	$0.347020\pi$
$338$	−0.492460	+	1.69004i	−0.0267863	+	0.0919261i
$339$	−12.6260	−	0.595443i	−0.685750	−	0.0323400i
$340$	−27.4325	+	14.2858i	−1.48774	+	0.774759i
$341$	−0.368630	−	1.09513i	−0.0199624	−	0.0593045i
$342$	3.45959	+	23.5583i	0.187073	+	1.27389i
$343$		−	18.7531i		−	1.01257i
$344$	−0.366461	+	0.0729820i	−0.0197582	+	0.00393493i
$345$	−10.6736	−	0.503367i	−0.574647	−	0.0271004i
$346$	5.34520	−	5.11771i	0.287360	−	0.275130i
$347$	17.2853	−	29.9390i	0.927922	−	1.60721i	0.141128	−	0.989991i	$-0.454927\pi$
$347$	17.2853	−	29.9390i	0.927922	−	1.60721i	0.786793	−	0.617216i	$-0.211740\pi$
$348$	−2.39412	+	26.3518i	−0.128338	+	1.41260i
$349$	14.5272			0.777621			0.388810	−	0.921318i	$-0.372886\pi$
$349$	14.5272			0.777621			0.388810	+	0.921318i	$0.372886\pi$
$350$	−28.2679	+	27.0648i	−1.51098	+	1.44668i
$351$	16.5299	−	6.64490i	0.882300	−	0.354679i
$352$	−1.16026	+	0.179041i	−0.0618422	+	0.00954291i
$353$	2.94141	+	1.69822i	0.156555	+	0.0903873i	0.576231	−	0.817287i	$-0.304523\pi$
$353$	2.94141	+	1.69822i	0.156555	+	0.0903873i	−0.419676	+	0.907674i	$0.637856\pi$
$354$	4.54509	−	3.95856i	0.241569	−	0.210395i
$355$	−28.3865	−	16.3889i	−1.50660	−	0.869835i
$356$	−6.85008	−	13.1539i	−0.363053	−	0.697156i
$357$	0.834237	−	17.6895i	0.0441525	−	0.936226i
$358$	3.37782	−	11.5921i	0.178524	−	0.612663i
$359$	13.3436	+	23.1118i	0.704248	+	1.21979i	0.966962	+	0.254920i	$0.0820491\pi$
$359$	13.3436	+	23.1118i	0.704248	+	1.21979i	−0.262714	+	0.964874i	$0.584618\pi$
$360$	−33.3367	+	3.42335i	−1.75700	+	0.180426i
$361$	6.24897	+	10.8235i	0.328893	+	0.569660i
$362$	15.9695	+	16.6794i	0.839339	+	0.876649i
$363$	16.8642	−	8.70421i	0.885138	−	0.456853i
$364$	−8.27010	−	15.8807i	−0.433471	−	0.832376i
$365$	49.7372	+	28.7158i	2.60336	+	1.50305i
$366$	−0.356791	−	0.122475i	−0.0186498	−	0.00640185i
$367$	24.6665	−	14.2412i	1.28758	−	0.743387i	0.309361	−	0.950945i	$-0.399885\pi$
$367$	24.6665	−	14.2412i	1.28758	−	0.743387i	0.978223	+	0.207558i	$0.0665517\pi$
$368$	−3.58226	+	5.11937i	−0.186738	+	0.266865i
$369$	−13.1669	−	9.35731i	−0.685443	−	0.487122i
$370$	−10.0841	−	41.1964i	−0.524246	−	2.14170i
$371$	−3.13642			−0.162835
$372$	−18.4847	−	5.50613i	−0.958385	−	0.285479i
$373$	13.9489			0.722249			0.361124	−	0.932518i	$-0.382393\pi$
$373$	13.9489			0.722249			0.361124	+	0.932518i	$0.382393\pi$
$374$	0.273246	+	1.11629i	0.0141292	+	0.0577220i
$375$	20.6880	−	32.2247i	1.06832	−	1.66408i
$376$	−26.5927	+	23.3321i	−1.37141	+	1.20326i
$377$	22.6804	−	13.0945i	1.16810	−	0.674403i
$378$	7.91006	−	17.4816i	0.406849	−	0.899155i
$379$	−10.1809	−	5.87792i	−0.522955	−	0.301928i	0.215188	−	0.976573i	$-0.430964\pi$
$379$	−10.1809	−	5.87792i	−0.522955	−	0.301928i	−0.738143	+	0.674644i	$0.764297\pi$
$380$	−39.3188	+	20.4758i	−2.01701	+	1.05039i
$381$	−9.84832	−	19.0808i	−0.504545	−	0.977541i
$382$	−4.27419	−	4.46418i	−0.218686	−	0.228407i
$383$	8.97682	+	15.5483i	0.458694	+	0.794481i	0.998892	−	0.0470564i	$-0.0149840\pi$
$383$	8.97682	+	15.5483i	0.458694	+	0.794481i	−0.540198	+	0.841538i	$0.681651\pi$
$384$	−8.71887	+	17.5494i	−0.444933	+	0.895564i
$385$	1.07010	+	1.85347i	0.0545376	+	0.0944618i
$386$	−6.60931	+	22.6821i	−0.336405	+	1.15449i
$387$	−0.0372983	+	0.394565i	−0.00189598	+	0.0200568i
$388$	2.39351	−	1.24645i	0.121512	−	0.0632791i
$389$	−14.7547	−	8.51860i	−0.748091	−	0.431910i	0.0769129	−	0.997038i	$-0.475494\pi$
$389$	−14.7547	−	8.51860i	−0.748091	−	0.431910i	−0.825004	+	0.565127i	$0.808827\pi$
$390$	21.7843	+	25.0120i	1.10309	+	1.26653i
$391$	5.29706	+	3.05826i	0.267884	+	0.154663i
$392$	0.487368	+	0.165313i	0.0246158	+	0.00834958i
$393$	−6.17040	+	3.18477i	−0.311255	+	0.160650i
$394$	11.0880	−	10.6161i	0.558607	−	0.534832i
$395$	16.3950			0.824921
$396$	−0.170960	+	1.23342i	−0.00859104	+	0.0619816i
$397$	−9.59407	+	16.6174i	−0.481512	+	0.834004i	−0.999775	−	0.0212177i	$-0.993246\pi$
$397$	−9.59407	+	16.6174i	−0.481512	+	0.834004i	0.518263	+	0.855222i	$0.326579\pi$
$398$	17.2364	−	16.5028i	0.863980	−	0.827209i
$399$	1.19570	−	25.3542i	0.0598601	−	1.26930i
$400$	−17.9276	−	38.4147i	−0.896378	−	1.92074i
$401$			21.4586i			1.07159i	0.844347	+	0.535797i	$0.179989\pi$
$401$			21.4586i			1.07159i	−0.844347	+	0.535797i	$0.820011\pi$
$402$	−11.8257	+	2.31033i	−0.589812	+	0.115229i
$403$	6.08998	+	18.0921i	0.303363	+	0.901233i
$404$	2.85538	+	5.48307i	0.142061	+	0.272793i
$405$	−6.66063	+	34.9153i	−0.330969	+	1.73495i
$406$	7.89090	−	27.0802i	0.391619	−	1.34397i
$407$	−1.57593			−0.0781160
$408$	17.8558	+	7.01082i	0.883992	+	0.347088i
$409$	−5.88083	+	10.1859i	−0.290788	+	0.503660i	−0.973996	−	0.226564i	$-0.927251\pi$
$409$	−5.88083	+	10.1859i	−0.290788	+	0.503660i	0.683208	+	0.730224i	$0.260584\pi$
$410$	8.41329	−	28.8730i	0.415503	−	1.42594i
$411$	33.2486	+	1.56801i	1.64003	+	0.0773441i
$412$	−7.44895	+	11.6965i	−0.366984	+	0.576246i
$413$	−5.56425	+	3.21252i	−0.273799	+	0.158078i
$414$	4.11236	+	5.19702i	0.202112	+	0.255420i
$415$	27.7337	+	16.0120i	1.36139	+	0.786000i
$416$	19.1682	−	2.95786i	0.939798	−	0.145021i
$417$	−1.24393	+	1.93761i	−0.0609154	+	0.0948852i
$418$	0.391641	+	1.59997i	0.0191558	+	0.0782570i
$419$	−0.826543			−0.0403793			−0.0201896	−	0.999796i	$-0.506427\pi$
$419$	−0.826543			−0.0403793			−0.0201896	+	0.999796i	$0.506427\pi$
$420$	35.5771	+	3.23226i	1.73598	+	0.157718i
$421$	3.90144	+	6.75750i	0.190145	+	0.329340i	0.945298	−	0.326208i	$-0.105771\pi$
$421$	3.90144	+	6.75750i	0.190145	+	0.329340i	−0.755153	+	0.655548i	$0.772438\pi$
$422$	−5.11564	−	1.49064i	−0.249026	−	0.0725634i
$423$	15.6202	+	34.1177i	0.759479	+	1.65886i
$424$	1.09132	−	3.21737i	0.0529991	−	0.156249i
$425$	−35.9387	+	20.7492i	−1.74328	+	1.00648i
$426$	3.89794	+	19.9521i	0.188856	+	0.966681i
$427$	0.348247	+	0.201061i	0.0168529	+	0.00973000i
$428$	1.25228	−	28.7841i	0.0605312	−	1.39133i
$429$	1.09517	−	0.565260i	0.0528755	−	0.0272910i
$430$	−0.716708	+	0.175436i	−0.0345627	+	0.00846028i
$431$	2.78276	−	4.81989i	0.134041	−	0.232166i	−0.791190	−	0.611571i	$-0.790538\pi$
$431$	2.78276	−	4.81989i	0.134041	−	0.232166i	0.925231	+	0.379405i	$0.123871\pi$
$432$	15.1805	+	14.1969i	0.730371	+	0.683051i
$433$	9.56018			0.459433			0.229716	−	0.973258i	$-0.426220\pi$
$433$	9.56018			0.459433			0.229716	+	0.973258i	$0.426220\pi$
$434$	18.2135	+	9.53874i	0.874276	+	0.457874i
$435$	−2.46145	+	52.1936i	−0.118018	+	2.50249i
$436$	−9.12958	+	4.75435i	−0.437228	+	0.227692i
$437$	7.59223	+	4.38338i	0.363186	+	0.209685i
$438$	−6.82974	−	34.9589i	−0.326338	−	1.67040i
$439$	21.9459	−	12.6705i	1.04742	−	0.604728i	0.125494	−	0.992094i	$-0.459948\pi$
$439$	21.9459	−	12.6705i	1.04742	−	0.604728i	0.921926	+	0.387366i	$0.126615\pi$
$440$	−2.27366	+	0.452807i	−0.108392	+	0.0215867i
$441$	0.316208	−	0.444945i	0.0150575	−	0.0211879i
$442$	−4.51418	−	18.4417i	−0.214717	−	0.877184i
$443$	6.16615	+	10.6801i	0.292963	+	0.507426i	0.974509	−	0.224349i	$-0.0720255\pi$
$443$	6.16615	+	10.6801i	0.292963	+	0.507426i	−0.681546	+	0.731775i	$0.738692\pi$
$444$	−15.1597	+	21.4972i	−0.719447	+	1.02021i
$445$	−14.6432	−	25.3628i	−0.694154	−	1.20231i
$446$	−31.3008	−	9.12071i	−1.48213	−	0.431878i
$447$	−15.9979	−	30.9954i	−0.756674	−	1.46603i
$448$	12.7088	−	16.5783i	0.600434	−	0.783253i
$449$		−	26.5483i		−	1.25289i	−0.779465	−	0.626446i	$-0.784509\pi$
$449$		−	26.5483i		−	1.25289i	0.779465	−	0.626446i	$-0.215491\pi$
$450$	−44.4865	+	6.53293i	−2.09711	+	0.307965i
$451$	−0.967744	−	0.558727i	−0.0455693	−	0.0263094i
$452$	−7.84023	+	12.3109i	−0.368773	+	0.579056i
$453$	−5.91905	+	9.21985i	−0.278101	+	0.433186i
$454$	−3.19412	−	3.33610i	−0.149907	−	0.156571i
$455$	−17.6787	−	30.6204i	−0.828791	−	1.43551i
$456$	25.5925	+	10.0486i	1.19848	+	0.470567i
$457$	−11.3089			−0.529008			−0.264504	−	0.964385i	$-0.585208\pi$
$457$	−11.3089			−0.529008			−0.264504	+	0.964385i	$0.585208\pi$
$458$	8.91446	−	30.5929i	0.416545	−	1.42951i
$459$	12.5545	−	16.0113i	0.585996	−	0.747343i
$460$	−6.62786	+	10.4072i	−0.309026	+	0.485239i
$461$			3.46910i			0.161572i	0.996731	+	0.0807860i	$0.0257430\pi$
$461$			3.46910i			0.161572i	−0.996731	+	0.0807860i	$0.974257\pi$
$462$	0.430963	−	1.25548i	0.0200502	−	0.0584101i
$463$		−	17.4348i		−	0.810266i	−0.914258	−	0.405133i	$-0.867225\pi$
$463$		−	17.4348i		−	0.810266i	0.914258	−	0.405133i	$-0.132775\pi$
$464$	25.0336	+	17.5171i	1.16215	+	0.813213i
$465$	−36.9401	−	9.27621i	−1.71305	−	0.430174i
$466$	4.59593	+	18.7757i	0.212903	+	0.869769i
$467$	24.2213			1.12083			0.560413	−	0.828213i	$-0.310642\pi$
$467$	24.2213			1.12083			0.560413	+	0.828213i	$0.310642\pi$
$468$	2.82435	−	20.3768i	0.130556	−	0.941916i
$469$	12.8444			0.593100
$470$	−50.4608	+	48.3132i	−2.32758	+	2.22852i
$471$	32.7875	+	21.0493i	1.51077	+	0.969899i
$472$	−1.35935	−	6.82566i	−0.0625694	−	0.314176i
$473$			0.0274170i			0.00126064i
$474$	−6.67834	−	7.66785i	−0.306746	−	0.352196i
$475$	−51.5106	+	29.7397i	−2.36347	+	1.36455i
$476$	−17.2480	−	10.9844i	−0.790561	−	0.503471i
$477$	−2.93731	−	2.08745i	−0.134490	−	0.0955778i
$478$	−6.42143	−	6.70688i	−0.293710	−	0.306766i
$479$	−4.12563	+	7.14581i	−0.188505	+	0.326500i	−0.944752	−	0.327786i	$-0.893698\pi$
$479$	−4.12563	+	7.14581i	−0.188505	+	0.326500i	0.756247	+	0.654286i	$0.227031\pi$
$480$	−15.6947	+	35.3707i	−0.716364	+	1.61444i
$481$	26.0353			1.18711
$482$	−6.05464	+	20.7785i	−0.275781	+	0.946436i
$483$	−3.24017	−	6.27774i	−0.147433	−	0.285647i
$484$	0.952482	−	21.8931i	0.0432946	−	0.995143i
$485$	4.61505	−	2.66450i	0.209559	−	0.120989i
$486$	19.0428	−	11.1073i	0.863800	−	0.503835i
$487$	−11.8489	+	6.84094i	−0.536923	+	0.309993i	−0.743831	−	0.668368i	$-0.766993\pi$
$487$	−11.8489	+	6.84094i	−0.536923	+	0.309993i	0.206908	+	0.978360i	$0.433660\pi$
$488$	−0.327423	+	0.287277i	−0.0148217	+	0.0130044i
$489$	−15.2704	+	23.7860i	−0.690551	+	1.07564i
$490$	0.975694	+	0.284307i	0.0440774	+	0.0128437i
$491$	−8.58572	−	14.8709i	−0.387468	−	0.671114i	0.604640	−	0.796499i	$-0.293317\pi$
$491$	−8.58572	−	14.8709i	−0.387468	−	0.671114i	−0.992108	+	0.125384i	$0.959984\pi$
$492$	−16.9308	+	7.82629i	−0.763300	+	0.352836i
$493$	14.9548	−	25.9025i	0.673530	−	1.16659i
$494$	−6.47013	−	26.4324i	−0.291105	−	1.18925i
$495$	−0.231413	+	2.44802i	−0.0104012	+	0.110030i
$496$	−16.1223	+	15.3646i	−0.723914	+	0.689890i
$497$		−	21.6709i		−	0.972071i
$498$	−3.80830	−	19.4932i	−0.170654	−	0.873513i
$499$	−24.9843	−	14.4247i	−1.11845	−	0.645737i	−0.177445	−	0.984131i	$-0.556783\pi$
$499$	−24.9843	−	14.4247i	−1.11845	−	0.645737i	−0.941005	+	0.338393i	$0.890117\pi$
$500$	−20.4237	−	39.2187i	−0.913375	−	1.75391i
$501$	25.4636	−	13.1427i	1.13763	−	0.587172i
$502$	−7.77632	+	26.6870i	−0.347074	+	1.19110i
$503$	−20.0784	+	34.7769i	−0.895254	+	1.55062i	−0.0617635	+	0.998091i	$0.519672\pi$
$503$	−20.0784	+	34.7769i	−0.895254	+	1.55062i	−0.833490	+	0.552534i	$0.813661\pi$
$504$	−12.9803	−	17.9558i	−0.578187	−	0.799816i
$505$	6.10386	+	10.5722i	0.271618	+	0.470456i
$506$	0.317058	+	0.331152i	0.0140950	+	0.0147215i
$507$	1.91582	−	0.988824i	0.0850844	−	0.0439152i
$508$	−24.7709	−	1.07768i	−1.09903	−	0.0478143i
$509$	−11.1221	+	6.42137i	−0.492980	+	0.284622i	−0.725810	−	0.687895i	$-0.758535\pi$
$509$	−11.1221	+	6.42137i	−0.492980	+	0.284622i	0.232830	+	0.972517i	$0.425201\pi$
$510$	35.8285	+	12.2987i	1.58651	+	0.544597i
$511$			37.9704i			1.67971i
$512$	12.5842	+	18.8053i	0.556149	+	0.831083i
$513$	17.9943	−	22.9488i	0.794469	−	1.01322i
$514$	−15.7229	+	15.0537i	−0.693508	+	0.663992i
$515$	−13.6918	+	23.7148i	−0.603331	+	1.04500i
$516$	0.373995	+	0.263738i	0.0164642	+	0.0116104i
$517$	1.29790	+	2.24803i	0.0570817	+	0.0988684i
$518$	20.2542	−	19.3922i	0.889918	−	0.852043i
$519$	−9.05322	−	0.426951i	−0.397392	−	0.0187411i
$520$	37.5621	−	7.48063i	1.64721	−	0.328047i
$521$	8.48268	+	4.89748i	0.371633	+	0.214562i	0.674172	−	0.738575i	$-0.264501\pi$
$521$	8.48268	+	4.89748i	0.371633	+	0.214562i	−0.302539	+	0.953137i	$0.597834\pi$
$522$	25.4133	−	20.1093i	1.11231	−	0.880162i
$523$			26.4240i			1.15544i	0.816235	+	0.577721i	$0.196058\pi$
$523$			26.4240i			1.15544i	−0.816235	+	0.577721i	$0.803942\pi$
$524$	−0.348502	+	8.01045i	−0.0152244	+	0.349938i
$525$	47.8777	+	2.25791i	2.08955	+	0.0985435i
$526$	18.6633	−	4.56841i	0.813758	−	0.199192i
$527$	16.3545	+	14.4166i	0.712414	+	0.627996i
$528$	1.13793	+	0.878930i	0.0495219	+	0.0382505i
$529$	−20.5600			−0.893912
$530$	1.87686	−	6.44106i	0.0815255	−	0.279782i
$531$	−7.34912	−	0.694715i	−0.318924	−	0.0301481i
$532$	−24.7214	−	15.7439i	−1.07181	−	0.682584i
$533$	15.9877	+	9.23049i	0.692503	+	0.399817i
$534$	−5.89726	+	17.1798i	−0.255199	+	0.743443i
$535$		−	56.8942i		−	2.45975i
$536$	−4.46922	+	13.1759i	−0.193041	+	0.569114i
$537$	−13.1408	+	6.78243i	−0.567065	+	0.292683i
$538$	−14.0209	+	13.4242i	−0.604483	+	0.578756i
$539$	0.0188808	−	0.0327026i	0.000813256	−	0.00140860i
$540$	31.1673	+	26.7055i	1.34123	+	1.14922i
$541$	4.50911	−	7.81002i	0.193862	−	0.335779i	−0.752665	−	0.658404i	$-0.771232\pi$
$541$	4.50911	−	7.81002i	0.193862	−	0.335779i	0.946527	+	0.322625i	$0.104565\pi$
$542$	−0.589616	−	2.40875i	−0.0253262	−	0.103465i
$543$	1.33227	−	28.2501i	0.0571734	−	1.21233i
$544$	17.2694	−	13.8711i	0.740419	−	0.594720i
$545$	−17.6032	+	10.1632i	−0.754039	+	0.435345i
$546$	−7.11976	+	20.7412i	−0.304697	+	0.887641i
$547$	12.4420	−	7.18337i	0.531980	−	0.307139i	−0.209842	−	0.977735i	$-0.567295\pi$
$547$	12.4420	−	7.18337i	0.531980	−	0.307139i	0.741822	+	0.670596i	$0.233962\pi$
$548$	20.6460	−	32.4188i	0.881954	−	1.38486i
$549$	0.192323	+	0.420074i	0.00820816	+	0.0179283i
$550$	−3.02131	+	0.739557i	−0.128829	+	0.0315348i
$551$	21.4346	−	37.1258i	0.913144	−	1.58161i
$552$	7.56719	−	1.13946i	0.322081	−	0.0484987i
$553$	5.41971	+	9.38722i	0.230470	+	0.399185i
$554$	20.8405	−	5.10134i	0.885427	−	0.216735i
$555$	−28.0627	+	43.7120i	−1.19119	+	1.85547i
$556$	1.22804	+	2.35815i	0.0520804	+	0.100008i
$557$		−	2.78690i		−	0.118085i	−0.998255	−	0.0590423i	$-0.981195\pi$
$557$		−	2.78690i		−	0.118085i	0.998255	−	0.0590423i	$-0.0188047\pi$
$558$	10.7087	+	21.0552i	0.453337	+	0.891339i
$559$		−	0.452944i		−	0.0191575i
$560$	23.6496	−	33.7974i	0.999379	−	1.42820i
$561$	0.760407	−	1.18445i	0.0321044	−	0.0500076i
$562$	−2.89447	−	11.8247i	−0.122096	−	0.498797i
$563$	−5.77934	−	10.0101i	−0.243570	−	0.421876i	0.718158	−	0.695880i	$-0.244985\pi$
$563$	−5.77934	−	10.0101i	−0.243570	−	0.421876i	−0.961729	+	0.274004i	$0.911652\pi$
$564$	43.1506	+	3.92033i	1.81697	+	0.165076i
$565$	−14.4109	+	24.9605i	−0.606273	+	1.05010i
$566$	3.44171	+	14.0604i	0.144666	+	0.591002i
$567$	−22.1931	+	7.72834i	−0.932023	+	0.324560i
$568$	22.2302	+	7.54038i	0.932758	+	0.316387i
$569$	23.0044	−	13.2816i	0.964394	−	0.556793i	0.0668711	−	0.997762i	$-0.478698\pi$
$569$	23.0044	−	13.2816i	0.964394	−	0.556793i	0.897522	+	0.440969i	$0.145365\pi$
$570$	51.3527	+	17.6277i	2.15093	+	0.738342i
$571$	6.87059	−	3.96674i	0.287525	−	0.166003i	−0.349300	−	0.937011i	$-0.613581\pi$
$571$	6.87059	−	3.96674i	0.287525	−	0.166003i	0.636825	+	0.771008i	$0.280247\pi$
$572$	0.0618551	−	1.42176i	0.00258629	−	0.0594468i
$573$	−0.356579	+	7.56103i	−0.0148963	+	0.315867i
$574$	19.3129	−	4.72742i	0.806105	−	0.197319i
$575$	−8.27737	+	14.3368i	−0.345190	+	0.597887i
$576$	22.9358	−	7.06756i	0.955657	−	0.294481i
$577$	19.6286	−	33.9977i	0.817150	−	1.41534i	−0.0906243	−	0.995885i	$-0.528886\pi$
$577$	19.6286	−	33.9977i	0.817150	−	1.41534i	0.907774	−	0.419460i	$-0.137780\pi$
$578$	1.63085	+	1.70334i	0.0678343	+	0.0708497i
$579$	25.7122	−	13.2710i	1.06856	−	0.551525i
$580$	50.8910	+	32.4101i	2.11313	+	1.34575i
$581$			21.1725i			0.878383i
$582$	−3.12607	−	1.07308i	−0.129580	−	0.0444804i
$583$	−0.215887	−	0.124642i	−0.00894111	−	0.00516215i
$584$	−38.9505	−	13.2118i	−1.61178	−	0.546709i
$585$	3.82307	−	40.4427i	0.158064	−	1.67210i
$586$	30.9099	+	9.00683i	1.27688	+	0.372069i
$587$	−46.7434			−1.92930			−0.964652	−	0.263525i	$-0.915115\pi$
$587$	−46.7434			−1.92930			−0.964652	+	0.263525i	$0.915115\pi$
$588$	−0.264471	−	0.572136i	−0.0109066	−	0.0235945i
$589$	23.4408	+	20.6631i	0.965861	+	0.851410i
$590$	−3.26765	−	13.3493i	−0.134527	−	0.549583i
$591$	−18.7799	−	0.885662i	−0.772502	−	0.0364313i
$592$	12.8452	+	27.5245i	0.527936	+	1.13125i
$593$			33.9827i			1.39550i	0.716340	+	0.697751i	$0.245816\pi$
$593$			33.9827i			1.39550i	−0.716340	+	0.697751i	$0.754184\pi$
$594$	1.23919	−	0.888948i	0.0508446	−	0.0364740i
$595$	−34.9705	−	20.1902i	−1.43365	−	0.827719i
$596$	−40.2385	−	1.75061i	−1.64823	−	0.0717079i
$597$	−29.1934	−	1.37676i	−1.19481	−	0.0563471i
$598$	−5.23798	−	5.47082i	−0.214197	−	0.223719i
$599$	3.14601	+	5.44904i	0.128542	+	0.222642i	0.923112	−	0.384531i	$-0.125637\pi$
$599$	3.14601	+	5.44904i	0.128542	+	0.222642i	−0.794570	+	0.607173i	$0.792304\pi$
$600$	−18.9752	+	48.3278i	−0.774661	+	1.97297i
$601$	0.0599165	−	0.103778i	0.00244404	−	0.00423321i	−0.864801	−	0.502115i	$-0.832555\pi$
$601$	0.0599165	−	0.103778i	0.00244404	−	0.00423321i	0.867245	+	0.497882i	$0.165889\pi$
$602$	−0.337372	−	0.352369i	−0.0137503	−	0.0143615i
$603$	12.0290	+	8.54863i	0.489860	+	0.348127i
$604$	5.84344	+	11.2209i	0.237766	+	0.456572i
$605$		−	43.2737i		−	1.75932i
$606$	2.45821	−	7.16122i	0.0998579	−	0.290905i
$607$	3.75868	−	2.17008i	0.152560	−	0.0880807i	−0.421777	−	0.906700i	$-0.638593\pi$
$607$	3.75868	−	2.17008i	0.152560	−	0.0880807i	0.574337	+	0.818619i	$0.305260\pi$
$608$	24.7521	−	19.8814i	1.00383	−	0.806297i
$609$	−30.6980	+	15.8444i	−1.24394	+	0.642046i
$610$	−0.621299	+	0.594857i	−0.0251557	+	0.0240850i
$611$	−21.4421	−	37.1388i	−0.867454	−	1.50247i
$612$	−8.84234	−	21.7666i	−0.357431	−	0.879861i
$613$	−0.674030	+	1.16745i	−0.0272238	+	0.0471531i	−0.879316	−	0.476238i	$-0.842000\pi$
$613$	−0.674030	+	1.16745i	−0.0272238	+	0.0471531i	0.852093	+	0.523391i	$0.175333\pi$
$614$	25.1377	+	7.32488i	1.01448	+	0.295608i
$615$	−32.7302	+	16.8933i	−1.31981	+	0.681203i
$616$	−1.01087	−	1.15213i	−0.0407290	−	0.0464208i
$617$	−14.4949	−	8.36865i	−0.583544	−	0.336909i	0.178997	−	0.983850i	$-0.442715\pi$
$617$	−14.4949	−	8.36865i	−0.583544	−	0.336909i	−0.762540	+	0.646940i	$0.776048\pi$
$618$	16.6685	−	3.25644i	0.670505	−	0.130993i
$619$			15.8050i			0.635256i	0.948215	+	0.317628i	$0.102886\pi$
$619$			15.8050i			0.635256i	−0.948215	+	0.317628i	$0.897114\pi$
$620$	−30.4882	+	31.6958i	−1.22444	+	1.27294i
$621$	1.14368	−	8.03572i	0.0458944	−	0.322462i
$622$	−14.0965	+	3.45054i	−0.565217	+	0.138354i
$623$	9.68124	−	16.7684i	0.387871	−	0.671812i
$624$	−18.7992	−	14.5204i	−0.752570	−	0.581282i
$625$	−17.1640	−	29.7289i	−0.686560	−	1.18916i
$626$	−0.802869	+	2.75531i	−0.0320891	+	0.110124i
$627$	1.08989	−	1.69767i	0.0435258	−	0.0677983i
$628$	39.9036	−	20.7804i	1.59233	−	0.829227i
$629$	25.7503	−	14.8670i	1.02673	−	0.592785i
$630$	−27.1493	−	34.3101i	−1.08165	−	1.36695i
$631$	−11.5518	+	6.66943i	−0.459870	+	0.265506i	−0.711989	−	0.702190i	$-0.752206\pi$
$631$	−11.5518	+	6.66943i	−0.459870	+	0.265506i	0.252120	+	0.967696i	$0.418872\pi$
$632$	−11.5153	+	2.29331i	−0.458054	+	0.0912231i
$633$	2.99311	+	5.79906i	0.118965	+	0.230492i
$634$	−12.8179	−	3.73499i	−0.509063	−	0.148336i
$635$	−48.9617			−1.94299
$636$	−3.77697	+	1.74591i	−0.149766	+	0.0692297i
$637$	−0.311922	+	0.540265i	−0.0123588	+	0.0214061i
$638$	1.61933	−	1.55041i	0.0641097	−	0.0613812i
$639$	14.4231	−	20.2952i	0.570569	−	0.802864i
$640$	26.4408	+	36.0198i	1.04517	+	1.42381i
$641$	−8.90301	+	5.14016i	−0.351648	+	0.203024i	−0.665411	−	0.746477i	$-0.731744\pi$
$641$	−8.90301	+	5.14016i	−0.351648	+	0.203024i	0.313763	+	0.949501i	$0.398410\pi$
$642$	−26.6091	+	23.1753i	−1.05018	+	0.914657i
$643$		−	2.24083i		−	0.0883697i	−0.999023	−	0.0441849i	$-0.985931\pi$
$643$		−	2.24083i		−	0.0883697i	0.999023	−	0.0441849i	$-0.0140691\pi$
$644$	−8.14980	−	0.354565i	−0.321147	−	0.0139718i
$645$	0.760472	+	0.488216i	0.0299436	+	0.0192235i
$646$	−21.4931	−	22.4485i	−0.845633	−	0.883223i
$647$	26.1082			1.02642			0.513210	−	0.858263i	$-0.328456\pi$
$647$	26.1082			1.02642			0.513210	+	0.858263i	$0.328456\pi$
$648$	−0.205706	−	25.4550i	−0.00808091	−	0.999967i
$649$	−0.510666			−0.0200454
$650$	49.9137	−	12.2179i	1.95778	−	0.479226i
$651$	−6.90008	−	24.2171i	−0.270435	−	0.949142i
$652$	15.0753	+	28.9485i	0.590395	+	1.13371i
$653$			32.7751i			1.28259i	0.767296	+	0.641293i	$0.221602\pi$
$653$			32.7751i			1.28259i	−0.767296	+	0.641293i	$0.778398\pi$
$654$	11.9238	+	4.09304i	0.466257	+	0.160051i
$655$			15.8333i			0.618659i
$656$	−1.87049	+	21.4563i	−0.0730304	+	0.837727i
$657$	−25.2713	+	35.5600i	−0.985928	+	1.38733i
$658$	−44.3434	−	12.9212i	−1.72869	−	0.503721i
$659$	38.0025			1.48037			0.740185	−	0.672404i	$-0.234738\pi$
$659$	38.0025			1.48037			0.740185	+	0.672404i	$0.234738\pi$
$660$	2.32040	+	1.63633i	0.0903214	+	0.0636940i
$661$	−8.45454	−	14.6437i	−0.328843	−	0.569574i	0.653439	−	0.756979i	$-0.273326\pi$
$661$	−8.45454	−	14.6437i	−0.328843	−	0.569574i	−0.982283	+	0.187405i	$0.939992\pi$
$662$	13.5600	−	12.9829i	0.527025	−	0.504595i
$663$	−12.5624	+	19.5678i	−0.487882	+	0.759952i
$664$	−21.7190	−	7.36698i	−0.842859	−	0.285894i
$665$	−50.1229	−	28.9385i	−1.94368	−	1.12219i
$666$	31.8749	−	4.68089i	1.23513	−	0.181381i
$667$		−	11.9317i		−	0.461996i
$668$	1.43818	−	33.0570i	0.0556447	−	1.27901i
$669$	18.3137	+	35.4823i	0.708050	+	1.37183i
$670$	−7.68620	+	26.3777i	−0.296944	+	1.01906i
$671$	0.0159804	+	0.0276789i	0.000616917	+	0.00106853i
$672$	−25.4403	+	2.70625i	−0.981381	+	0.104396i
$673$	10.4297	+	18.0648i	0.402036	+	0.696347i	0.993972	−	0.109639i	$-0.0349694\pi$
$673$	10.4297	+	18.0648i	0.402036	+	0.696347i	−0.591936	+	0.805985i	$0.701636\pi$
$674$	−23.3162	+	5.70736i	−0.898108	+	0.219839i
$675$	43.3356	+	33.9797i	1.66799	+	1.30788i
$676$	0.108205	−	2.48713i	0.00416172	−	0.0956587i
$677$	12.7648	−	7.36976i	0.490591	−	0.283243i	−0.234228	−	0.972182i	$-0.575256\pi$
$677$	12.7648	−	7.36976i	0.490591	−	0.283243i	0.724820	+	0.688939i	$0.241923\pi$
$678$	17.5440	−	3.42749i	0.673775	−	0.131632i
$679$	3.05121	+	1.76162i	0.117095	+	0.0676046i
$680$	32.8794	−	28.8479i	1.26087	−	1.10627i
$681$	−0.266473	+	5.65039i	−0.0102113	+	0.216523i
$682$	0.874603	+	1.38038i	0.0334903	+	0.0528576i
$683$	−31.9631			−1.22304			−0.611518	−	0.791231i	$-0.709441\pi$
$683$	−31.9631			−1.22304			−0.611518	+	0.791231i	$0.709441\pi$
$684$	−12.6737	−	31.1978i	−0.484589	−	1.19288i
$685$	37.9490	−	65.7295i	1.44996	−	2.51140i
$686$	6.30563	+	25.7603i	0.240750	+	0.983534i
$687$	−34.6799	+	17.8996i	−1.32312	+	0.682912i
$688$	0.478852	−	0.223473i	0.0182561	−	0.00851983i
$689$	3.56657	+	2.05916i	0.135875	+	0.0784477i
$690$	14.8311	−	2.89749i	0.564611	−	0.110305i
$691$	9.86252	−	5.69413i	0.375188	−	0.216615i	−0.300535	−	0.953771i	$-0.597165\pi$
$691$	9.86252	−	5.69413i	0.375188	−	0.216615i	0.675722	+	0.737156i	$0.263832\pi$
$692$	−5.62168	+	8.82728i	−0.213704	+	0.335563i
$693$	−1.47815	+	0.676747i	−0.0561504	+	0.0257075i
$694$	−13.6772	+	46.9380i	−0.519181	+	1.78174i
$695$	2.62513	+	4.54687i	0.0995770	+	0.172472i
$696$	−5.57194	−	37.0033i	−0.211204	−	1.40261i
$697$	21.0836			0.798599
$698$	−19.9554	+	4.88468i	−0.755321	+	0.184888i
$699$	12.7899	−	19.9222i	0.483758	−	0.753528i
$700$	29.7301	−	46.6828i	1.12369	−	1.76444i
$701$	−25.8765	−	14.9398i	−0.977342	−	0.564269i	−0.0758752	−	0.997117i	$-0.524175\pi$
$701$	−25.8765	−	14.9398i	−0.977342	−	0.564269i	−0.901467	+	0.432849i	$0.857508\pi$
$702$	−20.4721	+	14.6859i	−0.772670	+	0.554284i
$703$	36.9077	−	21.3087i	1.39200	−	0.803673i
$704$	1.53360	−	0.636073i	0.0577999	−	0.0239729i
$705$	85.4661	+	4.03059i	3.21884	+	0.151801i
$706$	−4.61151	−	1.34375i	−0.173557	−	0.0505726i
$707$	−4.03552	+	6.98973i	−0.151771	+	0.262876i
$708$	−4.91236	+	6.96598i	−0.184618	+	0.261798i
$709$	−45.4639			−1.70743			−0.853717	−	0.520737i	$-0.825657\pi$
$709$	−45.4639			−1.70743			−0.853717	+	0.520737i	$0.825657\pi$
$710$	44.5040	+	12.9680i	1.67021	+	0.486681i
$711$	−1.17203	+	12.3984i	−0.0439544	+	0.464977i
$712$	13.8326	+	15.7657i	0.518399	+	0.590844i
$713$	8.52571	+	1.71851i	0.319290	+	0.0643587i
$714$	4.80204	+	24.5798i	0.179712	+	0.919876i
$715$		−	2.81023i		−	0.105097i
$716$	−0.742186	+	17.0594i	−0.0277368	+	0.637540i
$717$	−0.535716	+	11.3595i	−0.0200067	+	0.424229i
$718$	−26.1008	−	27.2610i	−0.974072	−	1.01737i
$719$	−13.7548	+	23.8239i	−0.512966	+	0.888483i	0.486921	+	0.873446i	$0.338120\pi$
$719$	−13.7548	+	23.8239i	−0.512966	+	0.888483i	−0.999887	+	0.0150372i	$0.995213\pi$
$720$	44.6422	−	15.9118i	1.66372	−	0.592999i
$721$	−18.1044			−0.674243
$722$	−12.2233	−	12.7667i	−0.454905	−	0.475126i
$723$	23.5544	−	12.1573i	0.875997	−	0.452134i
$724$	−27.5450	−	17.5421i	−1.02370	−	0.651948i
$725$	70.1067	+	40.4761i	2.60370	+	1.50325i
$726$	−20.2388	+	17.6271i	−0.751134	+	0.654203i
$727$	32.1309	+	18.5508i	1.19167	+	0.688010i	0.958685	−	0.284471i	$-0.0918178\pi$
$727$	32.1309	+	18.5508i	1.19167	+	0.688010i	0.232984	+	0.972481i	$0.425151\pi$
$728$	16.7001	+	19.0339i	0.618947	+	0.705444i
$729$	−25.9279	−	7.53296i	−0.960292	−	0.278998i
$730$	−77.9774	−	22.7218i	−2.88607	−	0.840972i
$731$	−0.258646	−	0.447988i	−0.00956636	−	0.0165694i
$732$	0.531291	+	0.0482691i	0.0196371	+	0.00178408i
$733$	−1.33480	−	2.31194i	−0.0493018	−	0.0853933i	0.840321	−	0.542089i	$-0.182366\pi$
$733$	−1.33480	−	2.31194i	−0.0493018	−	0.0853933i	−0.889623	+	0.456695i	$0.849033\pi$
$734$	−29.0949	+	27.8566i	−1.07391	+	1.02821i
$735$	−0.570868	−	1.10604i	−0.0210568	−	0.0407969i
$736$	3.19944	−	8.23678i	0.117933	−	0.303612i
$737$	0.884110	+	0.510441i	0.0325666	+	0.0188023i
$738$	21.2332	+	8.42643i	0.781606	+	0.310181i
$739$	−0.860757	+	0.496958i	−0.0316635	+	0.0182809i	−0.515748	−	0.856740i	$-0.672486\pi$
$739$	−0.860757	+	0.496958i	−0.0316635	+	0.0182809i	0.484085	+	0.875021i	$0.339153\pi$
$740$	27.7042	+	53.1991i	1.01843	+	1.95564i
$741$	−18.0055	+	28.0464i	−0.661449	+	1.03031i
$742$	4.30837	−	1.05460i	0.158165	−	0.0387157i
$743$	−50.8770			−1.86650			−0.933249	−	0.359231i	$-0.883039\pi$
$743$	−50.8770			−1.86650			−0.933249	+	0.359231i	$0.883039\pi$
$744$	27.2430	+	1.34817i	0.998778	+	0.0494263i
$745$	−79.5348			−2.91393
$746$	−19.1611	+	4.69026i	−0.701537	+	0.171723i
$747$	−14.0914	+	19.8284i	−0.515578	+	0.725484i
$748$	−0.750693	−	1.44152i	−0.0274481	−	0.0527073i
$749$	32.5757	−	18.8076i	1.19029	−	0.687215i
$750$	−17.5828	+	51.2220i	−0.642034	+	1.87036i
$751$	33.6978	+	19.4555i	1.22965	+	0.709940i	0.966957	−	0.254939i	$-0.0820555\pi$
$751$	33.6978	+	19.4555i	1.22965	+	0.709940i	0.262695	+	0.964879i	$0.415389\pi$
$752$	28.6840	−	40.9920i	1.04600	−	1.49483i
$753$	30.2522	−	15.6143i	1.10245	−	0.569016i
$754$	−26.7522	+	25.6136i	−0.974257	+	0.932792i
$755$	12.4913	+	21.6356i	0.454606	+	0.787400i
$756$	−4.98763	+	26.6734i	−0.181398	+	0.970104i
$757$	3.37956	+	5.85356i	0.122832	+	0.212751i	0.920883	−	0.389838i	$-0.127469\pi$
$757$	3.37956	+	5.85356i	0.122832	+	0.212751i	−0.798051	+	0.602589i	$0.794136\pi$
$758$	15.9614	+	4.65100i	0.579746	+	0.168932i
$759$	0.0264510	−	0.560876i	0.000960109	−	0.0203585i
$760$	47.1257	−	41.3475i	1.70943	−	1.49983i
$761$	4.28604	+	2.47455i	0.155369	+	0.0897023i	0.575669	−	0.817683i	$-0.304742\pi$
$761$	4.28604	+	2.47455i	0.155369	+	0.0897023i	−0.420300	+	0.907385i	$0.638075\pi$
$762$	19.9441	+	22.8991i	0.722498	+	0.829548i
$763$	−11.6382	−	6.71934i	−0.421333	−	0.243257i
$764$	7.37233	+	4.69509i	0.266722	+	0.169862i
$765$	−19.3129	−	42.1832i	−0.698258	−	1.52514i
$766$	−17.5591	−	18.3397i	−0.634437	−	0.662639i
$767$	8.43649			0.304624
$768$	6.07586	−	27.0386i	0.219244	−	0.975670i
$769$	−14.7527	+	25.5525i	−0.531997	+	0.921447i	0.467305	+	0.884096i	$0.345225\pi$
$769$	−14.7527	+	25.5525i	−0.531997	+	0.921447i	−0.999302	+	0.0373504i	$0.988108\pi$
$770$	−2.09318	−	2.18623i	−0.0754330	−	0.0787861i
$771$	26.6301	+	1.25588i	0.959059	+	0.0452293i
$772$	1.45222	−	33.3798i	0.0522665	−	1.20136i
$773$		−	7.73134i		−	0.278077i	−0.990287	−	0.139039i	$-0.955599\pi$
$773$		−	7.73134i		−	0.278077i	0.990287	−	0.139039i	$-0.0444012\pi$
$774$	−0.0814351	−	0.554539i	−0.00292713	−	0.0199325i
$775$	−39.0194	+	44.2645i	−1.40162	+	1.59003i
$776$	−2.86875	+	2.51701i	−0.102982	+	0.0903553i
$777$	−34.3047	−	1.61781i	−1.23068	−	0.0580387i
$778$	23.1322	+	6.74048i	0.829330	+	0.241658i
$779$	30.2190			1.08271
$780$	−38.3343	−	27.0331i	−1.37259	−	0.967939i
$781$	0.861207	−	1.49165i	0.0308164	−	0.0533756i
$782$	−8.30468	−	2.41990i	−0.296975	−	0.0865353i
$783$	−39.2945	−	5.59258i	−1.40427	−	0.199863i
$784$	−0.725064	−	0.0632088i	−0.0258951	−	0.00225746i
$785$	76.9403	−	44.4215i	2.74612	−	1.58547i
$786$	7.40516	−	6.44955i	0.264133	−	0.230048i
$787$	10.7691	+	6.21757i	0.383878	+	0.221632i	0.679504	−	0.733671i	$-0.262195\pi$
$787$	10.7691	+	6.21757i	0.383878	+	0.221632i	−0.295626	+	0.955304i	$0.595528\pi$
$788$	−11.6616	+	18.3112i	−0.415426	+	0.652310i
$789$	−19.8029	−	12.7133i	−0.705003	−	0.452605i
$790$	−22.5211	+	5.51273i	−0.801266	+	0.196134i
$791$	−19.0554			−0.677531
$792$	−0.179890	−	1.75178i	−0.00639212	−	0.0622468i
$793$	−0.264006	−	0.457271i	−0.00937511	−	0.0162382i
$794$	7.59146	−	26.0526i	0.269411	−	0.924573i
$795$	−7.30154	+	3.76859i	−0.258959	+	0.133658i
$796$	−18.1279	+	28.4648i	−0.642526	+	1.00891i
$797$	−41.0026	+	23.6729i	−1.45239	+	0.838537i	−0.998617	−	0.0525812i	$-0.983255\pi$
$797$	−41.0026	+	23.6729i	−1.45239	+	0.838537i	−0.453772	+	0.891118i	$0.649922\pi$
$798$	6.88272	+	35.2300i	0.243646	+	1.24713i
$799$	−42.4149	−	24.4882i	−1.50053	−	0.866331i
$800$	37.5431	+	46.7407i	1.32735	+	1.65253i
$801$	20.2269	−	9.26054i	0.714682	−	0.327205i
$802$	−7.21536	−	29.4769i	−0.254783	−	1.04086i
$803$	−1.50896	+	2.61359i	−0.0532499	+	0.0922316i
$804$	15.4676	−	7.14993i	0.545501	−	0.252158i
$805$	−16.1088			−0.567759
$806$	−14.4489	−	22.8047i	−0.508942	−	0.803261i
$807$	23.7473	+	1.11993i	0.835945	+	0.0394232i
$808$	−5.76598	−	6.57176i	−0.202846	−	0.231194i
$809$	−12.0541	−	6.95941i	−0.423798	−	0.244680i	0.272903	−	0.962042i	$-0.412016\pi$
$809$	−12.0541	−	6.95941i	−0.423798	−	0.244680i	−0.696701	+	0.717362i	$0.745350\pi$
$810$	−2.59065	−	50.2013i	−0.0910262	−	1.76389i
$811$	15.0353	−	8.68061i	0.527959	−	0.304817i	−0.212226	−	0.977221i	$-0.568071\pi$
$811$	15.0353	−	8.68061i	0.527959	−	0.304817i	0.740185	+	0.672403i	$0.234738\pi$
$812$	−1.73381	+	39.8523i	−0.0608449	+	1.39854i
$813$	−1.64082	+	2.55584i	−0.0575462	+	0.0896371i
$814$	2.16479	−	0.529899i	0.0758759	−	0.0185729i
$815$	32.2260	+	55.8171i	1.12883	+	1.95519i
$816$	−26.8851	−	3.62657i	−0.941167	−	0.126955i
$817$	−0.370715	−	0.642097i	−0.0129697	−	0.0224641i
$818$	4.65330	−	15.9693i	0.162699	−	0.558355i
$819$	24.4199	−	11.1802i	0.853302	−	0.390669i
$820$	−1.84859	+	42.4906i	−0.0645557	+	1.48384i
$821$			43.8618i			1.53079i	0.643563	+	0.765393i	$0.277455\pi$
$821$			43.8618i			1.53079i	−0.643563	+	0.765393i	$0.722545\pi$
$822$	−46.1995	+	9.02577i	−1.61139	+	0.314810i
$823$	−46.0561	−	26.5905i	−1.60542	−	0.926887i	−0.990378	−	0.138389i	$-0.955807\pi$
$823$	−46.0561	−	26.5905i	−1.60542	−	0.926887i	−0.615038	−	0.788498i	$-0.710859\pi$
$824$	6.29943	−	18.5717i	0.219451	−	0.646975i
$825$	3.20580	+	2.05809i	0.111612	+	0.0716535i
$826$	6.56318	−	6.28385i	0.228362	−	0.218643i
$827$	−5.54499	−	9.60421i	−0.192818	−	0.333971i	0.753365	−	0.657603i	$-0.228429\pi$
$827$	−5.54499	−	9.60421i	−0.192818	−	0.333971i	−0.946183	+	0.323632i	$0.895096\pi$
$828$	−7.39645	−	5.75617i	−0.257045	−	0.200041i
$829$	28.9104			1.00410			0.502050	−	0.864839i	$-0.332579\pi$
$829$	28.9104			1.00410			0.502050	+	0.864839i	$0.332579\pi$
$830$	−43.4806	−	12.6698i	−1.50923	−	0.439775i
$831$	−22.1130	−	14.1964i	−0.767093	−	0.492466i
$832$	−25.3360	+	10.5083i	−0.878367	+	0.364309i
$833$			0.712470i			0.0246856i
$834$	1.05722	−	3.07988i	0.0366086	−	0.106648i
$835$		−	65.3399i		−	2.26118i
$836$	−1.07596	−	2.06612i	−0.0372129	−	0.0714584i
$837$	9.65569	−	27.2721i	0.333749	−	0.942662i
$838$	1.13539	−	0.277921i	0.0392213	−	0.00960062i
$839$	−49.0946			−1.69493			−0.847467	−	0.530848i	$-0.821874\pi$
$839$	−49.0946			−1.69493			−0.847467	+	0.530848i	$0.821874\pi$
$840$	−49.9576	+	7.52258i	−1.72370	+	0.259554i
$841$	−29.3456			−1.01192
$842$	−7.63143	−	7.97066i	−0.262996	−	0.274687i
$843$	−8.05492	+	12.5468i	−0.277426	+	0.432135i
$844$	7.52837	+	0.327529i	0.259137	+	0.0112740i
$845$		−	4.91602i		−	0.169116i
$846$	−32.9287	−	41.6138i	−1.13211	−	1.43071i
$847$	24.7770	−	14.3050i	0.851349	−	0.491527i
$848$	−0.417274	+	4.78652i	−0.0143292	+	0.164370i
$849$	9.57783	−	14.9190i	0.328710	−	0.512017i
$850$	42.3907	−	40.5865i	1.45399	−	1.39211i
$851$	5.93080	−	10.2724i	0.203305	−	0.352135i
$852$	−12.0632	−	26.0967i	−0.413279	−	0.894058i
$853$	11.4826			0.393158			0.196579	−	0.980488i	$-0.437017\pi$
$853$	11.4826			0.393158			0.196579	+	0.980488i	$0.437017\pi$
$854$	−0.545979	−	0.159092i	−0.0186830	−	0.00544403i
$855$	−27.6810	−	60.4609i	−0.946669	−	2.06772i
$856$	7.95831	+	39.9606i	0.272009	+	1.36583i
$857$	−23.1206	+	13.3487i	−0.789783	+	0.455982i	−0.839886	−	0.542762i	$-0.817378\pi$
$857$	−23.1206	+	13.3487i	−0.789783	+	0.455982i	0.0501030	+	0.998744i	$0.484045\pi$
$858$	−1.31433	+	1.14472i	−0.0448705	+	0.0390801i
$859$	−17.6320	+	10.1799i	−0.601597	+	0.347332i	−0.769670	−	0.638442i	$-0.779579\pi$
$859$	−17.6320	+	10.1799i	−0.601597	+	0.347332i	0.168073	+	0.985775i	$0.446246\pi$
$860$	0.925523	−	0.481979i	0.0315601	−	0.0164353i
$861$	−20.4922	−	13.1558i	−0.698372	−	0.448348i
$862$	−2.20191	+	7.55657i	−0.0749972	+	0.257378i
$863$	2.40752	+	4.16994i	0.0819529	+	0.141947i	0.904089	−	0.427345i	$-0.140551\pi$
$863$	2.40752	+	4.16994i	0.0819529	+	0.141947i	−0.822136	+	0.569291i	$0.807218\pi$
$864$	−25.6264	−	14.3974i	−0.871830	−	0.489809i
$865$	−10.3331	+	17.8974i	−0.351335	+	0.608530i
$866$	−13.1324	+	3.21456i	−0.446258	+	0.109235i
$867$	0.136055	−	2.88497i	0.00462068	−	0.0979787i
$868$	−28.2265	−	6.97878i	−0.958069	−	0.236875i
$869$			0.861525i			0.0292252i
$870$	−14.1686	−	72.5238i	−0.480361	−	2.45879i
$871$	−14.6060	−	8.43277i	−0.494905	−	0.285734i
$872$	10.9423	−	9.60064i	0.370553	−	0.325119i
$873$	1.68506	+	3.68053i	0.0570308	+	0.124567i
$874$	−11.9030	−	3.46842i	−0.402626	−	0.117321i
$875$	28.8649	−	49.9954i	0.975810	−	1.69015i
$876$	21.1365	+	45.7251i	0.714136	+	1.54491i
$877$	20.6798	+	35.8185i	0.698309	+	1.20951i	0.969053	+	0.246855i	$0.0793970\pi$
$877$	20.6798	+	35.8185i	0.698309	+	1.20951i	−0.270744	+	0.962651i	$0.587270\pi$
$878$	−25.8858	+	24.7841i	−0.873603	+	0.836422i
$879$	−18.0851	−	35.0393i	−0.609994	−	1.18185i
$880$	2.97098	−	1.38651i	0.100152	−	0.0467392i
$881$	−3.74458	+	2.16194i	−0.126158	+	0.0728375i	−0.561751	−	0.827306i	$-0.689872\pi$
$881$	−3.74458	+	2.16194i	−0.126158	+	0.0728375i	0.435593	+	0.900144i	$0.356539\pi$
$882$	−0.284751	+	0.717526i	−0.00958807	+	0.0241604i
$883$			31.3586i			1.05530i	0.849461	+	0.527651i	$0.176927\pi$
$883$			31.3586i			1.05530i	−0.849461	+	0.527651i	$0.823073\pi$
$884$	12.4019	+	23.8148i	0.417120	+	0.800978i
$885$	−9.09346	+	14.1645i	−0.305673	+	0.476134i
$886$	−12.0613	−	12.5975i	−0.405208	−	0.423220i
$887$	−15.2611	+	26.4330i	−0.512418	+	0.887533i	0.487479	+	0.873135i	$0.337917\pi$
$887$	−15.2611	+	26.4330i	−0.512418	+	0.887533i	−0.999896	+	0.0143985i	$0.995417\pi$
$888$	13.5959	−	34.6272i	0.456249	−	1.16201i
$889$	−16.1853	−	28.0338i	−0.542839	−	0.940224i
$890$	28.6428	+	29.9161i	0.960111	+	1.00279i
$891$	−1.83473	−	0.350003i	−0.0614657	−	0.0117255i
$892$	46.0634	+	2.00403i	1.54232	+	0.0670999i
$893$	−60.7929	−	35.0988i	−2.03436	−	1.17454i
$894$	32.3977	+	37.1980i	1.08354	+	1.24409i
$895$			33.7194i			1.12711i
$896$	−11.8832	+	27.0463i	−0.396989	+	0.903552i
$897$	−0.436985	+	9.26599i	−0.0145905	+	0.309382i
$898$	8.92673	+	36.4683i	0.297889	+	1.21696i
$899$	8.40347	−	41.6905i	0.280271	−	1.39045i
$900$	58.9126	−	23.9324i	1.96375	−	0.797746i
$901$	4.70339			0.156692
$902$	1.51722	+	0.442102i	0.0505179	+	0.0147204i
$903$	−0.0281457	+	0.596811i	−0.000936629	+	0.0198606i
$904$	6.63033	−	19.5472i	0.220521	−	0.650131i
$905$	−55.8479	−	32.2438i	−1.85645	−	1.07182i
$906$	5.03063	−	14.6552i	0.167132	−	0.486886i
$907$		−	16.6955i		−	0.554364i	−0.960817	−	0.277182i	$-0.910599\pi$
$907$		−	16.6955i		−	0.554364i	0.960817	−	0.277182i	$-0.0894005\pi$
$908$	5.50937	+	3.50866i	0.182835	+	0.116439i
$909$	−8.43137	+	3.86016i	−0.279651	+	0.128033i
$910$	34.5805	+	36.1177i	1.14633	+	1.19729i
$911$	14.9874	−	25.9589i	0.496554	−	0.860057i	−0.503438	−	0.864031i	$-0.667932\pi$
$911$	14.9874	−	25.9589i	0.496554	−	0.860057i	0.999992	+	0.00397470i	$0.00126519\pi$
$912$	−38.5342	−	5.19793i	−1.27599	−	0.172121i
$913$	−0.841402	+	1.45735i	−0.0278463	+	0.0482313i
$914$	15.5346	−	3.80256i	0.513838	−	0.125778i
$915$	1.05230	+	0.0496266i	0.0347880	+	0.00164060i
$916$	−1.95871	+	45.0217i	−0.0647176	+	1.48756i
$917$	−9.06563	+	5.23404i	−0.299374	+	0.172843i
$918$	−11.8620	+	26.2154i	−0.391503	+	0.865239i
$919$	11.7495	−	6.78358i	0.387580	−	0.223770i	−0.293531	−	0.955950i	$-0.594830\pi$
$919$	11.7495	−	6.78358i	0.387580	−	0.223770i	0.681111	+	0.732180i	$0.261497\pi$
$920$	5.60505	−	16.5245i	0.184793	−	0.544798i
$921$	−14.7078	−	28.4960i	−0.484639	−	0.938974i
$922$	−1.16647	−	4.76536i	−0.0384155	−	0.156939i
$923$	−14.2276	+	24.6430i	−0.468308	+	0.811133i
$924$	−0.169849	+	1.86951i	−0.00558763	+	0.0615022i
$925$	40.2384	+	69.6949i	1.32303	+	2.29156i
$926$	5.86238	+	23.9495i	0.192650	+	0.787031i
$927$	−16.9551	−	12.0494i	−0.556879	−	0.395755i
$928$	−40.2776	−	15.6452i	−1.32218	−	0.513578i
$929$			28.5186i			0.935666i	0.883817	+	0.467833i	$0.154965\pi$
$929$			28.5186i			0.935666i	−0.883817	+	0.467833i	$0.845035\pi$
$930$	53.8621	+	0.321448i	1.76621	+	0.0105407i
$931$			1.02118i			0.0334678i
$932$	−12.6265	−	24.2461i	−0.413595	−	0.794208i
$933$	14.9572	+	9.60241i	0.489678	+	0.314369i
$934$	−33.2717	+	8.14427i	−1.08868	+	0.266489i
$935$	−1.60473	−	2.77948i	−0.0524804	−	0.0908987i
$936$	2.97189	+	28.9404i	0.0971392	+	0.945947i
$937$	24.2221	−	41.9539i	0.791301	−	1.37057i	−0.133861	−	0.991000i	$-0.542738\pi$
$937$	24.2221	−	41.9539i	0.791301	−	1.37057i	0.925162	−	0.379573i	$-0.123929\pi$
$938$	−17.6438	+	4.31887i	−0.576092	+	0.141016i
$939$	3.12340	−	1.61210i	0.101928	−	0.0526090i
$940$	53.0709	−	83.3331i	1.73098	−	2.71803i
$941$	15.1143	−	8.72622i	0.492711	−	0.284467i	−0.232988	−	0.972480i	$-0.574850\pi$
$941$	15.1143	−	8.72622i	0.492711	−	0.284467i	0.725698	+	0.688013i	$0.241517\pi$
$942$	−52.1166	−	17.8899i	−1.69805	−	0.582884i
$943$	7.28395	−	4.20539i	0.237198	−	0.136946i
$944$	4.16238	+	8.91905i	0.135474	+	0.290290i
$945$	−7.55045	+	53.0508i	−0.245616	+	1.72574i
$946$	−0.00921883	−	0.0376616i	−0.000299730	−	0.00122448i
$947$	−11.8017	+	20.4411i	−0.383503	+	0.664247i	−0.991560	−	0.129647i	$-0.958616\pi$
$947$	−11.8017	+	20.4411i	−0.383503	+	0.664247i	0.608057	+	0.793893i	$0.291949\pi$
$948$	11.7520	+	8.28745i	0.381688	+	0.269164i
$949$	24.9288	−	43.1780i	0.809224	−	1.40162i
$950$	60.7582	−	58.1723i	1.97126	−	1.88736i
$951$	7.49960	+	14.5302i	0.243191	+	0.471176i
$952$	27.3863	+	9.28932i	0.887596	+	0.301068i
$953$		−	11.4941i		−	0.372329i	−0.982519	−	0.186165i	$-0.940394\pi$
$953$		−	11.4941i		−	0.372329i	0.982519	−	0.186165i	$-0.0596058\pi$
$954$	4.73676	+	1.87979i	0.153358	+	0.0608604i
$955$	14.9475	+	8.62994i	0.483689	+	0.279258i
$956$	11.0760	+	7.05379i	0.358224	+	0.228136i
$957$	−2.74267	−	0.129344i	−0.0886579	−	0.00418111i
$958$	3.26447	−	11.2031i	0.105470	−	0.361957i
$959$	50.1794			1.62038
$960$	9.66602	−	53.8645i	0.311970	−	1.73847i
$961$	28.5793	+	12.0093i	0.921913	+	0.387396i
$962$	−35.7636	+	8.75422i	−1.15306	+	0.282247i
$963$	43.0252	+	4.06719i	1.38647	+	0.131063i
$964$	1.33034	−	30.5784i	0.0428475	−	0.984865i
$965$		−	65.9779i		−	2.12390i
$966$	6.56175	+	7.53398i	0.211121	+	0.242402i
$967$	34.4429	+	19.8856i	1.10761	+	0.639478i	0.938209	−	0.346069i	$-0.112484\pi$
$967$	34.4429	+	19.8856i	1.10761	+	0.639478i	0.169400	+	0.985547i	$0.445817\pi$
$968$	6.05307	+	30.3940i	0.194553	+	0.976900i
$969$	−1.79308	+	38.0212i	−0.0576021	+	1.22142i
$970$	−5.44359	+	5.21191i	−0.174783	+	0.167344i
$971$	−19.7790	−	34.2582i	−0.634737	−	1.09940i	−0.986571	−	0.163335i	$-0.947775\pi$
$971$	−19.7790	−	34.2582i	−0.634737	−	1.09940i	0.351834	−	0.936063i	$-0.385558\pi$
$972$	−22.4236	+	21.6606i	−0.719237	+	0.694765i
$973$	−1.73559	+	3.00613i	−0.0556404	+	0.0963720i
$974$	13.9761	−	13.3812i	0.447822	−	0.428763i
$975$	−52.9616	−	34.0008i	−1.69613	−	1.08890i
$976$	0.353172	−	0.504714i	0.0113048	−	0.0161555i
$977$			48.9599i			1.56637i	0.621791	+	0.783183i	$0.286405\pi$
$977$			48.9599i			1.56637i	−0.621791	+	0.783183i	$0.713595\pi$
$978$	12.9784	−	37.8085i	0.415003	−	1.20898i
$979$	1.33276	−	0.769471i	0.0425953	−	0.0245924i
$980$	−1.43587	−	0.0624688i	−0.0458671	−	0.00199549i
$981$	−6.42735	−	14.0386i	−0.205210	−	0.448220i
$982$	16.7941	+	17.5406i	0.535922	+	0.559744i
$983$	22.0725	+	38.2307i	0.704004	+	1.21937i	0.967050	+	0.254588i	$0.0819399\pi$
$983$	22.0725	+	38.2307i	0.704004	+	1.21937i	−0.263045	+	0.964784i	$0.584727\pi$
$984$	20.6256	−	16.4436i	0.657521	−	0.524201i
$985$	−21.4348	+	37.1262i	−0.682971	+	1.18294i
$986$	−11.8332	+	40.6096i	−0.376847	+	1.29327i
$987$	25.9449	+	50.2674i	0.825834	+	1.60003i
$988$	17.7755	+	34.1335i	0.565514	+	1.08593i
$989$	−0.178713	−	0.103180i	−0.00568275	−	0.00328094i
$990$	−0.505253	−	3.44056i	−0.0160580	−	0.109348i
$991$		−	29.5417i		−	0.938424i	−0.883086	−	0.469212i	$-0.844538\pi$
$991$		−	29.5417i		−	0.938424i	0.883086	−	0.469212i	$-0.155462\pi$
$992$	16.9803	−	26.5268i	0.539126	−	0.842225i
$993$	−22.9667	−	1.08311i	−0.728828	−	0.0343716i
$994$	7.28671	+	29.7684i	0.231121	+	0.944195i
$995$	−33.3205	+	57.7128i	−1.05633	+	1.82962i
$996$	11.7858	+	25.4965i	0.373448	+	0.807889i
$997$	21.9127	+	37.9540i	0.693983	+	1.20201i	0.970522	+	0.241012i	$0.0774792\pi$
$997$	21.9127	+	37.9540i	0.693983	+	1.20201i	−0.276539	+	0.961003i	$0.589187\pi$
$998$	39.1701	+	11.4138i	1.23991	+	0.361296i
$999$	−31.0503	−	24.3467i	−0.982387	−	0.770296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	372.2.p.a.191.6	yes	120
3.2	odd	2	inner	372.2.p.a.191.55	yes	120
4.3	odd	2	inner	372.2.p.a.191.56	yes	120
12.11	even	2	inner	372.2.p.a.191.5	✓	120
31.25	even	3	inner	372.2.p.a.335.6	yes	120
93.56	odd	6	inner	372.2.p.a.335.55	yes	120
124.87	odd	6	inner	372.2.p.a.335.56	yes	120
372.335	even	6	inner	372.2.p.a.335.5	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
372.2.p.a.191.5	✓	120	12.11	even	2	inner
372.2.p.a.191.6	yes	120	1.1	even	1	trivial
372.2.p.a.191.55	yes	120	3.2	odd	2	inner
372.2.p.a.191.56	yes	120	4.3	odd	2	inner
372.2.p.a.335.5	yes	120	372.335	even	6	inner
372.2.p.a.335.6	yes	120	31.25	even	3	inner
372.2.p.a.335.55	yes	120	93.56	odd	6	inner
372.2.p.a.335.56	yes	120	124.87	odd	6	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 372 = 2^{2} \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	372.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37366 + 0.336245i) q^{2} +(1.45754 + 0.935726i) q^{3} +(1.77388 - 0.923772i) q^{4} +(3.42031 - 1.97472i) q^{5} +(-2.31679 - 0.795278i) q^{6} +(2.26131 + 1.30557i) q^{7} +(-2.12609 + 1.86541i) q^{8} +(1.24884 + 2.72771i) q^{9} +(-4.03435 + 3.86265i) q^{10} +(0.103767 + 0.179731i) q^{11} +(3.44989 + 0.313431i) q^{12} +(-1.71430 - 2.96925i) q^{13} +(-3.54526 - 1.03305i) q^{14} +(6.83302 + 0.322246i) q^{15} +(2.29329 - 3.27732i) q^{16} +(-3.39107 - 1.95784i) q^{17} +(-2.63265 - 3.32703i) q^{18} +(-4.86040 - 2.80615i) q^{19} +(4.24303 - 6.66249i) q^{20} +(2.07430 + 4.01889i) q^{21} +(-0.202975 - 0.211997i) q^{22} -1.56206 q^{23} +(-4.84437 + 0.729461i) q^{24} +(5.29901 - 9.17816i) q^{25} +(3.35326 + 3.50231i) q^{26} +(-0.732164 + 5.14431i) q^{27} +(5.21734 + 0.226985i) q^{28} +7.63843i q^{29} +(-9.49460 + 1.85491i) q^{30} +(-5.45799 - 1.10016i) q^{31} +(-2.04822 + 5.27303i) q^{32} +(-0.0169334 + 0.359062i) q^{33} +(5.31649 + 1.54917i) q^{34} +10.3125 q^{35} +(4.73507 + 3.68499i) q^{36} +(-3.79678 + 6.57622i) q^{37} +(7.62008 + 2.22041i) q^{38} +(0.279749 - 5.93191i) q^{39} +(-3.58824 + 10.5787i) q^{40} +(-4.66304 + 2.69221i) q^{41} +(-4.20070 - 4.82311i) q^{42} +(0.114409 + 0.0660539i) q^{43} +(0.350101 + 0.222963i) q^{44} +(9.65786 + 6.86352i) q^{45} +(2.14574 - 0.525234i) q^{46} +12.5078 q^{47} +(6.40923 - 2.63092i) q^{48} +(-0.0909767 - 0.157576i) q^{49} +(-4.19293 + 14.3894i) q^{50} +(-3.11062 - 6.02674i) q^{51} +(-5.78386 - 3.68347i) q^{52} +(-1.04024 + 0.600584i) q^{53} +(-0.724005 - 7.31272i) q^{54} +(0.709834 + 0.409823i) q^{55} +(-7.24317 + 1.44250i) q^{56} +(-4.45843 - 8.63807i) q^{57} +(-2.56838 - 10.4926i) q^{58} +(-1.23031 + 2.13097i) q^{59} +(12.4186 - 5.74053i) q^{60} +0.154002 q^{61} +(7.86734 - 0.323981i) q^{62} +(-0.737209 + 7.79865i) q^{63} +(1.04053 - 7.93204i) q^{64} +(-11.7269 - 6.77050i) q^{65} +(-0.0974721 - 0.498923i) q^{66} +(4.26005 - 2.45954i) q^{67} +(-7.82395 - 0.340388i) q^{68} +(-2.27676 - 1.46166i) q^{69} +(-14.1659 + 3.46753i) q^{70} +(-4.14969 - 7.18748i) q^{71} +(-7.74342 - 3.46978i) q^{72} +(7.27086 + 12.5935i) q^{73} +(3.00427 - 10.3101i) q^{74} +(16.3117 - 8.41909i) q^{75} +(-11.2140 - 0.487876i) q^{76} +0.541903i q^{77} +(1.61029 + 8.24248i) q^{78} +(3.59507 + 2.07561i) q^{79} +(1.37199 - 15.7380i) q^{80} +(-5.88082 + 6.81293i) q^{81} +(5.50019 - 5.26610i) q^{82} +(4.05426 + 7.02219i) q^{83} +(7.39208 + 5.21284i) q^{84} -15.4647 q^{85} +(-0.179369 - 0.0522662i) q^{86} +(-7.14747 + 11.1333i) q^{87} +(-0.555889 - 0.188555i) q^{88} -7.41534i q^{89} +(-15.5744 - 6.18073i) q^{90} -8.95254i q^{91} +(-2.77090 + 1.44299i) q^{92} +(-6.92578 - 6.71070i) q^{93} +(-17.1814 + 4.20568i) q^{94} -22.1654 q^{95} +(-7.91946 + 5.76906i) q^{96} +1.34931 q^{97} +(0.177955 + 0.185866i) q^{98} +(-0.360665 + 0.507502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{4} - 2 q^{9} + 4 q^{10} - 4 q^{12} - 4 q^{16} - 2 q^{18} - 14 q^{21} - 6 q^{22} - 4 q^{24} + 48 q^{25} + 6 q^{28} - 48 q^{30} + 4 q^{33} + 28 q^{34} + 2 q^{36} - 8 q^{37} + 36 q^{40} - 4 q^{42}+ \cdots + 48 q^{96}+O(q^{100}) \) 120 * q - 12 * q^4 - 2 * q^9 + 4 * q^10 - 4 * q^12 - 4 * q^16 - 2 * q^18 - 14 * q^21 - 6 * q^22 - 4 * q^24 + 48 * q^25 + 6 * q^28 - 48 * q^30 + 4 * q^33 + 28 * q^34 + 2 * q^36 - 8 * q^37 + 36 * q^40 - 4 * q^42 - 34 * q^45 - 48 * q^46 + 10 * q^48 + 60 * q^49 + 8 * q^52 - 84 * q^54 - 14 * q^57 - 28 * q^58 - 60 * q^60 - 64 * q^61 + 84 * q^64 - 132 * q^66 - 4 * q^69 - 120 * q^70 + 44 * q^72 + 28 * q^76 + 20 * q^78 - 2 * q^81 + 48 * q^82 - 8 * q^84 + 8 * q^85 - 10 * q^88 + 24 * q^90 - 78 * q^93 - 88 * q^94 + 48 * q^96

Introduction

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