LMFDB - Embedded newform 693.2.cb.a.74.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(74,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 20, 9]))

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

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

chi := DirichletCharacter("693.74");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.cb (of order $30$, degree $8$, 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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$736$
Relative dimension:	$92$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			74.9
Character	$\chi$	$=$	693.74
Dual form			693.2.cb.a.590.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.88049 + 1.36625i) q^{2} +(-1.33953 + 1.09803i) q^{3} +(1.05155 - 3.23634i) q^{4} +(-1.66986 - 3.75057i) q^{5} +(1.01877 - 3.89497i) q^{6} +(-2.00709 + 1.72383i) q^{7} +(1.00767 + 3.10129i) q^{8} +(0.588658 - 2.94168i) q^{9} +O(q^{10})$	\(q+(-1.88049 + 1.36625i) q^{2} +(-1.33953 + 1.09803i) q^{3} +(1.05155 - 3.23634i) q^{4} +(-1.66986 - 3.75057i) q^{5} +(1.01877 - 3.89497i) q^{6} +(-2.00709 + 1.72383i) q^{7} +(1.00767 + 3.10129i) q^{8} +(0.588658 - 2.94168i) q^{9} +(8.26440 + 4.77145i) q^{10} +(-1.63501 - 2.88561i) q^{11} +(2.14502 + 5.48979i) q^{12} +(0.131828 - 0.296091i) q^{13} +(1.41912 - 5.98384i) q^{14} +(6.35507 + 3.19043i) q^{15} +(-0.626072 - 0.454868i) q^{16} +(5.38425 - 2.39722i) q^{17} +(2.91212 + 6.33605i) q^{18} +(-4.06761 - 3.66250i) q^{19} +(-13.8941 + 1.46033i) q^{20} +(0.795735 - 4.51296i) q^{21} +(7.01709 + 3.19252i) q^{22} +(-0.686751 - 0.396496i) q^{23} +(-4.75511 - 3.04780i) q^{24} +(-7.93271 + 8.81017i) q^{25} +(0.156634 + 0.736907i) q^{26} +(2.44153 + 4.58682i) q^{27} +(3.46833 + 8.30832i) q^{28} +(1.08039 + 1.19990i) q^{29} +(-16.3096 + 2.68308i) q^{30} +(-4.35625 + 3.16500i) q^{31} -4.72299 q^{32} +(5.35862 + 2.07006i) q^{33} +(-6.84980 + 11.8642i) q^{34} +(9.81692 + 4.64919i) q^{35} +(-8.90127 - 4.99842i) q^{36} +(-2.51287 + 0.534127i) q^{37} +(12.6530 + 1.32988i) q^{38} +(0.148530 + 0.541373i) q^{39} +(9.94894 - 8.95807i) q^{40} +(2.77444 - 3.08133i) q^{41} +(4.66948 + 9.57374i) q^{42} +(4.77204 + 2.75514i) q^{43} +(-11.0581 + 2.25707i) q^{44} +(-12.0160 + 2.70440i) q^{45} +(1.83314 - 0.192671i) q^{46} +(-2.82547 + 0.918052i) q^{47} +(1.33810 - 0.0781389i) q^{48} +(1.05683 - 6.91976i) q^{49} +(2.88044 - 27.4055i) q^{50} +(-4.58012 + 9.12321i) q^{51} +(-0.819627 - 0.737996i) q^{52} +(-11.2450 + 1.18190i) q^{53} +(-10.8580 - 5.28971i) q^{54} +(-8.09246 + 10.9508i) q^{55} +(-7.36857 - 4.48752i) q^{56} +(9.47021 + 0.439644i) q^{57} +(-3.67102 - 0.780300i) q^{58} +(-8.73221 - 2.83727i) q^{59} +(17.0080 - 17.2123i) q^{60} +(2.38304 - 3.27997i) q^{61} +(3.86768 - 11.9035i) q^{62} +(3.88946 + 6.91897i) q^{63} +(10.1337 - 7.36254i) q^{64} -1.33065 q^{65} +(-12.9051 + 3.42852i) q^{66} +14.1606 q^{67} +(-2.09641 - 19.9461i) q^{68} +(1.35529 - 0.222957i) q^{69} +(-24.8126 + 4.66966i) q^{70} +(-7.93658 + 10.9238i) q^{71} +(9.71617 - 1.13864i) q^{72} +(3.08363 - 2.77652i) q^{73} +(3.99567 - 4.43764i) q^{74} +(0.952238 - 20.5118i) q^{75} +(-16.1304 + 9.31288i) q^{76} +(8.25591 + 2.97321i) q^{77} +(-1.01896 - 0.815117i) q^{78} +(0.217957 + 0.299992i) q^{79} +(-0.660562 + 3.10770i) q^{80} +(-8.30696 - 3.46329i) q^{81} +(-1.00742 + 9.58500i) q^{82} +(5.91611 - 2.63402i) q^{83} +(-13.7687 - 7.32087i) q^{84} +(-17.9819 - 16.1910i) q^{85} +(-12.7380 + 1.33882i) q^{86} +(-2.76473 - 0.420989i) q^{87} +(7.30156 - 7.97837i) q^{88} +(-7.11120 + 4.10565i) q^{89} +(18.9010 - 21.5025i) q^{90} +(0.245819 + 0.821532i) q^{91} +(-2.00535 + 1.80562i) q^{92} +(2.36004 - 9.02289i) q^{93} +(4.05898 - 5.58670i) q^{94} +(-6.94411 + 21.3718i) q^{95} +(6.32656 - 5.18598i) q^{96} +(-0.360829 - 3.43306i) q^{97} +(7.46679 + 14.4564i) q^{98} +(-9.45101 + 3.11103i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 736 q - 3 q^{3} - 182 q^{4} - 9 q^{5} - 20 q^{6} - 5 q^{7} - 9 q^{9}+O(q^{10}) $ 736 * q - 3 * q^3 - 182 * q^4 - 9 * q^5 - 20 * q^6 - 5 * q^7 - 9 * q^9	$ 736 q - 3 q^{3} - 182 q^{4} - 9 q^{5} - 20 q^{6} - 5 q^{7} - 9 q^{9} - 18 q^{11} + 20 q^{12} - 10 q^{13} - 9 q^{14} - 24 q^{15} - 158 q^{16} - 5 q^{18} - 10 q^{19} - 36 q^{20} - 4 q^{22} - 42 q^{23} + 35 q^{24} - 73 q^{25} - 24 q^{26} - 21 q^{27} - 20 q^{28} - 30 q^{29} - 35 q^{30} - 6 q^{31} + 40 q^{33} - 20 q^{34} + 75 q^{35} + 36 q^{36} - 6 q^{37} - 15 q^{38} - 45 q^{39} + 45 q^{40} - 30 q^{41} - 71 q^{42} + 39 q^{44} + 36 q^{45} + 10 q^{46} - 52 q^{48} - 3 q^{49} - 105 q^{50} + 75 q^{51} + 5 q^{52} - 36 q^{53} - 30 q^{55} + 30 q^{56} - 60 q^{57} + 29 q^{58} + 121 q^{60} - 10 q^{61} - 105 q^{63} - 148 q^{64} - 25 q^{66} - 16 q^{67} - 15 q^{68} + 105 q^{69} - 33 q^{70} - 125 q^{72} - 10 q^{73} - 15 q^{74} + 19 q^{75} - 15 q^{77} + 48 q^{78} - 10 q^{79} + 108 q^{80} + 59 q^{81} - 10 q^{82} - 30 q^{83} - 100 q^{84} - 10 q^{85} - 33 q^{86} + 8 q^{88} + 30 q^{89} - 180 q^{90} + 16 q^{91} + 72 q^{92} - 2 q^{93} - 10 q^{94} + 45 q^{96} - 6 q^{97} - 10 q^{99}+O(q^{100}) $ 736 * q - 3 * q^3 - 182 * q^4 - 9 * q^5 - 20 * q^6 - 5 * q^7 - 9 * q^9 - 18 * q^11 + 20 * q^12 - 10 * q^13 - 9 * q^14 - 24 * q^15 - 158 * q^16 - 5 * q^18 - 10 * q^19 - 36 * q^20 - 4 * q^22 - 42 * q^23 + 35 * q^24 - 73 * q^25 - 24 * q^26 - 21 * q^27 - 20 * q^28 - 30 * q^29 - 35 * q^30 - 6 * q^31 + 40 * q^33 - 20 * q^34 + 75 * q^35 + 36 * q^36 - 6 * q^37 - 15 * q^38 - 45 * q^39 + 45 * q^40 - 30 * q^41 - 71 * q^42 + 39 * q^44 + 36 * q^45 + 10 * q^46 - 52 * q^48 - 3 * q^49 - 105 * q^50 + 75 * q^51 + 5 * q^52 - 36 * q^53 - 30 * q^55 + 30 * q^56 - 60 * q^57 + 29 * q^58 + 121 * q^60 - 10 * q^61 - 105 * q^63 - 148 * q^64 - 25 * q^66 - 16 * q^67 - 15 * q^68 + 105 * q^69 - 33 * q^70 - 125 * q^72 - 10 * q^73 - 15 * q^74 + 19 * q^75 - 15 * q^77 + 48 * q^78 - 10 * q^79 + 108 * q^80 + 59 * q^81 - 10 * q^82 - 30 * q^83 - 100 * q^84 - 10 * q^85 - 33 * q^86 + 8 * q^88 + 30 * q^89 - 180 * q^90 + 16 * q^91 + 72 * q^92 - 2 * q^93 - 10 * q^94 + 45 * q^96 - 6 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−1.88049	+	1.36625i	−1.32971	+	0.966088i	−0.329950	+	0.943998i	$0.607032\pi$
$2$	−1.88049	+	1.36625i	−1.32971	+	0.966088i	−0.999756	+	0.0220895i	$0.992968\pi$
$3$	−1.33953	+	1.09803i	−0.773376	+	0.633948i
$3$	−1.33953	+	1.09803i	−0.773376	+	0.633948i
$4$	1.05155	−	3.23634i	0.525775	−	1.61817i
$5$	−1.66986	−	3.75057i	−0.746786	−	1.67731i	−0.735642	−	0.677370i	$-0.763120\pi$
$5$	−1.66986	−	3.75057i	−0.746786	−	1.67731i	−0.0111433	−	0.999938i	$-0.503547\pi$
$6$	1.01877	−	3.89497i	0.415912	−	1.59011i
$7$	−2.00709	+	1.72383i	−0.758609	+	0.651546i
$7$	−2.00709	+	1.72383i	−0.758609	+	0.651546i
$8$	1.00767	+	3.10129i	0.356265	+	1.09647i
$9$	0.588658	−	2.94168i	0.196219	−	0.980560i
$10$	8.26440	+	4.77145i	2.61343	+	1.50887i
$11$	−1.63501	−	2.88561i	−0.492973	−	0.870044i
$11$	−1.63501	−	2.88561i	−0.492973	−	0.870044i
$12$	2.14502	+	5.48979i	0.619214	+	1.58477i
$13$	0.131828	−	0.296091i	0.0365626	−	0.0821209i	−0.894341	−	0.447386i	$-0.852355\pi$
$13$	0.131828	−	0.296091i	0.0365626	−	0.0821209i	0.930904	+	0.365265i	$0.119022\pi$
$14$	1.41912	−	5.98384i	0.379277	−	1.59925i
$15$	6.35507	+	3.19043i	1.64087	+	0.823766i
$16$	−0.626072	−	0.454868i	−0.156518	−	0.113717i
$17$	5.38425	−	2.39722i	1.30587	−	0.581412i	0.368464	−	0.929642i	$-0.379884\pi$
$17$	5.38425	−	2.39722i	1.30587	−	0.581412i	0.937409	+	0.348230i	$0.113217\pi$
$18$	2.91212	+	6.33605i	0.686393	+	1.49342i
$19$	−4.06761	−	3.66250i	−0.933175	−	0.840234i	0.0542171	−	0.998529i	$-0.482734\pi$
$19$	−4.06761	−	3.66250i	−0.933175	−	0.840234i	−0.987392	+	0.158295i	$0.949400\pi$
$20$	−13.8941	+	1.46033i	−3.10681	+	0.326539i
$21$	0.795735	−	4.51296i	0.173644	−	0.984809i
$22$	7.01709	+	3.19252i	1.49605	+	0.680648i
$23$	−0.686751	−	0.396496i	−0.143197	−	0.0826751i	0.426690	−	0.904398i	$-0.359680\pi$
$23$	−0.686751	−	0.396496i	−0.143197	−	0.0826751i	−0.569887	+	0.821723i	$0.693013\pi$
$24$	−4.75511	−	3.04780i	−0.970632	−	0.622130i
$25$	−7.93271	+	8.81017i	−1.58654	+	1.76203i
$26$	0.156634	+	0.736907i	0.0307185	+	0.144519i
$27$	2.44153	+	4.58682i	0.469873	+	0.882734i
$28$	3.46833	+	8.30832i	0.655453	+	1.57012i
$29$	1.08039	+	1.19990i	0.200623	+	0.222815i	0.835058	−	0.550161i	$-0.185434\pi$
$29$	1.08039	+	1.19990i	0.200623	+	0.222815i	−0.634435	+	0.772976i	$0.718767\pi$
$30$	−16.3096	+	2.68308i	−2.97771	+	0.489861i
$31$	−4.35625	+	3.16500i	−0.782405	+	0.568450i	−0.905700	−	0.423920i	$-0.860654\pi$
$31$	−4.35625	+	3.16500i	−0.782405	+	0.568450i	0.123295	+	0.992370i	$0.460654\pi$
$32$	−4.72299			−0.834914
$33$	5.35862	+	2.07006i	0.932817	+	0.360352i
$34$	−6.84980	+	11.8642i	−1.17473	+	2.03469i
$35$	9.81692	+	4.64919i	1.65936	+	0.785857i
$36$	−8.90127	−	4.99842i	−1.48354	−	0.833070i
$37$	−2.51287	+	0.534127i	−0.413114	+	0.0878100i	−0.409780	−	0.912184i	$-0.634394\pi$
$37$	−2.51287	+	0.534127i	−0.413114	+	0.0878100i	−0.00333375	+	0.999994i	$0.501061\pi$
$38$	12.6530	+	1.32988i	2.05259	+	0.215736i
$39$	0.148530	+	0.541373i	0.0237838	+	0.0866891i
$40$	9.94894	−	8.95807i	1.57307	−	1.41639i
$41$	2.77444	−	3.08133i	0.433295	−	0.481223i	−0.486467	−	0.873699i	$-0.661715\pi$
$41$	2.77444	−	3.08133i	0.433295	−	0.481223i	0.919762	+	0.392476i	$0.128381\pi$
$42$	4.66948	+	9.57374i	0.720517	+	1.47726i
$43$	4.77204	+	2.75514i	0.727730	+	0.420155i	0.817591	−	0.575799i	$-0.195309\pi$
$43$	4.77204	+	2.75514i	0.727730	+	0.420155i	−0.0898614	+	0.995954i	$0.528642\pi$
$44$	−11.0581	+	2.25707i	−1.66707	+	0.340266i
$45$	−12.0160	+	2.70440i	−1.79124	+	0.403148i
$46$	1.83314	−	0.192671i	0.270282	−	0.0284078i
$47$	−2.82547	+	0.918052i	−0.412138	+	0.133912i	−0.507745	−	0.861508i	$-0.669521\pi$
$47$	−2.82547	+	0.918052i	−0.412138	+	0.133912i	0.0956073	+	0.995419i	$0.469521\pi$
$48$	1.33810	−	0.0781389i	0.193138	−	0.0112784i
$49$	1.05683	−	6.91976i	0.150976	−	0.988537i
$50$	2.88044	−	27.4055i	0.407355	−	3.87573i
$51$	−4.58012	+	9.12321i	−0.641345	+	1.27751i
$52$	−0.819627	−	0.737996i	−0.113662	−	0.102342i
$53$	−11.2450	+	1.18190i	−1.54462	+	0.162347i	−0.838169	−	0.545411i	$-0.816374\pi$
$53$	−11.2450	+	1.18190i	−1.54462	+	0.162347i	−0.706456	+	0.707757i	$0.749707\pi$
$54$	−10.8580	−	5.28971i	−1.47759	−	0.719838i
$55$	−8.09246	+	10.9508i	−1.09119	+	1.47660i
$56$	−7.36857	−	4.48752i	−0.984667	−	0.599670i
$57$	9.47021	+	0.439644i	1.25436	+	0.0582323i
$58$	−3.67102	−	0.780300i	−0.482029	−	0.102458i
$59$	−8.73221	−	2.83727i	−1.13684	−	0.369381i	−0.320667	−	0.947192i	$-0.603907\pi$
$59$	−8.73221	−	2.83727i	−1.13684	−	0.369381i	−0.816171	+	0.577811i	$0.803907\pi$
$60$	17.0080	−	17.2123i	2.19572	−	2.22209i
$61$	2.38304	−	3.27997i	0.305117	−	0.419957i	−0.628734	−	0.777621i	$-0.716426\pi$
$61$	2.38304	−	3.27997i	0.305117	−	0.419957i	0.933851	+	0.357663i	$0.116426\pi$
$62$	3.86768	−	11.9035i	0.491195	−	1.51174i
$63$	3.88946	+	6.91897i	0.490026	+	0.871708i
$64$	10.1337	−	7.36254i	1.26671	−	0.920317i
$65$	−1.33065			−0.165047
$66$	−12.9051	+	3.42852i	−1.58850	+	0.422021i
$67$	14.1606			1.72999			0.864996	−	0.501779i	$-0.167321\pi$
$67$	14.1606			1.72999			0.864996	+	0.501779i	$0.167321\pi$
$68$	−2.09641	−	19.9461i	−0.254228	−	2.41881i
$69$	1.35529	−	0.222957i	0.163157	−	0.0268409i
$70$	−24.8126	+	4.66966i	−2.96567	+	0.558131i
$71$	−7.93658	+	10.9238i	−0.941899	+	1.29641i	0.0131343	+	0.999914i	$0.495819\pi$
$71$	−7.93658	+	10.9238i	−0.941899	+	1.29641i	−0.955033	+	0.296499i	$0.904181\pi$
$72$	9.71617	−	1.13864i	1.14506	−	0.134190i
$73$	3.08363	−	2.77652i	0.360912	−	0.324967i	−0.468647	−	0.883385i	$-0.655258\pi$
$73$	3.08363	−	2.77652i	0.360912	−	0.324967i	0.829559	+	0.558419i	$0.188592\pi$
$74$	3.99567	−	4.43764i	0.464487	−	0.515866i
$75$	0.952238	−	20.5118i	0.109955	−	2.36850i
$76$	−16.1304	+	9.31288i	−1.85028	+	1.06826i
$77$	8.25591	+	2.97321i	0.940848	+	0.338829i
$78$	−1.01896	−	0.815117i	−0.115375	−	0.0922938i
$79$	0.217957	+	0.299992i	0.0245221	+	0.0337518i	0.821102	−	0.570781i	$-0.193360\pi$
$79$	0.217957	+	0.299992i	0.0245221	+	0.0337518i	−0.796580	+	0.604533i	$0.793360\pi$
$80$	−0.660562	+	3.10770i	−0.0738531	+	0.347451i
$81$	−8.30696	−	3.46329i	−0.922996	−	0.384810i
$82$	−1.00742	+	9.58500i	−0.111251	+	1.05849i
$83$	5.91611	−	2.63402i	0.649377	−	0.289121i	−0.0554916	−	0.998459i	$-0.517673\pi$
$83$	5.91611	−	2.63402i	0.649377	−	0.289121i	0.704869	+	0.709338i	$0.251006\pi$
$84$	−13.7687	−	7.32087i	−1.50229	−	0.798773i
$85$	−17.9819	−	16.1910i	−1.95041	−	1.75616i
$86$	−12.7380	+	1.33882i	−1.37357	+	0.144368i
$87$	−2.76473	−	0.420989i	−0.296410	−	0.0451347i
$88$	7.30156	−	7.97837i	0.778349	−	0.850497i
$89$	−7.11120	+	4.10565i	−0.753786	+	0.435198i	−0.827060	−	0.562113i	$-0.809988\pi$
$89$	−7.11120	+	4.10565i	−0.753786	+	0.435198i	0.0732744	+	0.997312i	$0.476655\pi$
$90$	18.9010	−	21.5025i	1.99234	−	2.26656i
$91$	0.245819	+	0.821532i	0.0257688	+	0.0861199i
$92$	−2.00535	+	1.80562i	−0.209072	+	0.188249i
$93$	2.36004	−	9.02289i	0.244725	−	0.935630i
$94$	4.05898	−	5.58670i	0.418651	−	0.576224i
$95$	−6.94411	+	21.3718i	−0.712450	+	2.19270i
$96$	6.32656	−	5.18598i	0.645702	−	0.529292i
$97$	−0.360829	−	3.43306i	−0.0366366	−	0.348574i	−0.997449	−	0.0713763i	$-0.977261\pi$
$97$	−0.360829	−	3.43306i	−0.0366366	−	0.348574i	0.960813	−	0.277198i	$-0.0894058\pi$
$98$	7.46679	+	14.4564i	0.754260	+	1.46032i
$99$	−9.45101	+	3.11103i	−0.949862	+	0.312670i
$100$	20.1711	+	34.9373i	2.01711	+	3.49373i
$101$	7.09360	+	3.15828i	0.705840	+	0.314260i	0.728080	−	0.685493i	$-0.240413\pi$
$101$	7.09360	+	3.15828i	0.705840	+	0.314260i	−0.0222398	+	0.999753i	$0.507080\pi$
$102$	−3.85177	−	23.4137i	−0.381382	−	2.31830i
$103$	10.3841	+	11.5327i	1.02318	+	1.13635i	0.990587	+	0.136885i	$0.0437092\pi$
$103$	10.3841	+	11.5327i	1.02318	+	1.13635i	0.0325909	+	0.999469i	$0.489624\pi$
$104$	1.05110	+	0.110475i	0.103069	+	0.0108330i
$105$	−18.2550	+	4.55156i	−1.78150	+	0.444187i
$106$	19.5314	−	17.5861i	1.89706	−	1.70812i
$107$	−11.4440	+	12.7098i	−1.10633	+	1.22871i	−0.135035	+	0.990841i	$0.543115\pi$
$107$	−11.4440	+	12.7098i	−1.10633	+	1.22871i	−0.971298	+	0.237866i	$0.923552\pi$
$108$	17.4119	−	3.07835i	1.67546	−	0.296214i
$109$	0.529299	+	0.305591i	0.0506977	+	0.0292703i	0.525135	−	0.851019i	$-0.324015\pi$
$109$	0.529299	+	0.305591i	0.0506977	+	0.0292703i	−0.474437	+	0.880290i	$0.657348\pi$
$110$	0.256206	−	31.6492i	0.0244282	−	3.01763i
$111$	2.77957	−	3.47469i	0.263825	−	0.329803i
$112$	2.04070	−	0.166279i	0.192828	−	0.0157119i
$113$	4.93792	+	4.44613i	0.464521	+	0.418256i	0.867871	−	0.496789i	$-0.165488\pi$
$113$	4.93792	+	4.44613i	0.464521	+	0.418256i	−0.403350	+	0.915046i	$0.632154\pi$
$114$	−18.4093	+	12.1120i	−1.72419	+	1.13439i
$115$	−0.340307	+	3.23780i	−0.0317338	+	0.301927i
$116$	5.01935	−	2.23476i	0.466035	−	0.207492i
$117$	−0.793404	−	0.562093i	−0.0733502	−	0.0519656i
$118$	20.2973	−	6.59498i	1.86851	−	0.607117i
$119$	−6.67428	+	14.0930i	−0.611831	+	1.29190i
$120$	−3.49063	+	22.9238i	−0.318650	+	2.09265i
$121$	−5.65350	+	9.43599i	−0.513955	+	0.857817i
$122$			9.42379i			0.853190i
$123$	−0.333042	+	7.17394i	−0.0300294	+	0.646853i
$124$	5.66219	+	17.4264i	0.508480	+	1.56494i
$125$	26.7669	+	8.69708i	2.39410	+	0.777891i
$126$	−16.7672	−	7.69704i	−1.49374	−	0.685707i
$127$	−12.3970	+	17.0630i	−1.10005	+	1.51409i	−0.264737	+	0.964321i	$0.585285\pi$
$127$	−12.3970	+	17.0630i	−1.10005	+	1.51409i	−0.835315	+	0.549771i	$0.814715\pi$
$128$	−6.07817	+	18.7067i	−0.537239	+	1.65345i
$129$	−9.41750	+	1.54927i	−0.829165	+	0.136405i
$130$	2.50227	−	1.81800i	0.219463	−	0.159449i
$131$	3.34564	−	5.79482i	0.292310	−	0.506296i	−0.682045	−	0.731310i	$-0.738909\pi$
$131$	3.34564	−	5.79482i	0.292310	−	0.506296i	0.974356	+	0.225014i	$0.0722427\pi$
$132$	12.3343	−	15.1655i	1.07356	−	1.31999i
$133$	14.4776	+	0.339099i	1.25537	+	0.0294036i
$134$	−26.6288	+	19.3470i	−2.30038	+	1.67132i
$135$	13.1262	−	16.8165i	1.12972	−	1.44733i
$136$	12.8600	+	14.2825i	1.10274	+	1.22471i
$137$	−12.0952	−	1.27126i	−1.03336	−	0.108611i	−0.427367	−	0.904078i	$-0.640559\pi$
$137$	−12.0952	−	1.27126i	−1.03336	−	0.108611i	−0.605997	+	0.795467i	$0.707226\pi$
$138$	−2.24398	+	2.27093i	−0.191020	+	0.193315i
$139$	−0.796420	−	3.74686i	−0.0675514	−	0.317804i	0.931379	−	0.364052i	$-0.118607\pi$
$139$	−0.796420	−	3.74686i	−0.0675514	−	0.317804i	−0.998930	+	0.0462476i	$0.985274\pi$
$140$	25.3693	−	26.8820i	2.14410	−	2.27194i
$141$	2.77674	−	4.33221i	0.233844	−	0.364838i
$142$		−	31.3854i		−	2.63380i
$143$	−1.06994	+	0.103706i	−0.0894733	+	0.00867234i
$144$	−1.70662	+	1.57394i	−0.142218	+	0.131162i
$145$	2.69619	−	6.05575i	0.223907	−	0.502902i
$146$	−2.00531	+	9.43424i	−0.165961	+	0.780783i
$147$	6.18245	+	10.4296i	0.509920	+	0.860222i
$148$	−0.913794	+	8.69417i	−0.0751134	+	0.714656i
$149$	2.47953	−	1.10396i	0.203131	−	0.0904398i	−0.302650	−	0.953102i	$-0.597871\pi$
$149$	2.47953	−	1.10396i	0.203131	−	0.0904398i	0.505781	+	0.862662i	$0.331205\pi$
$150$	26.2337	+	39.8732i	2.14197	+	3.25564i
$151$	15.1458	+	13.6373i	1.23255	+	1.10979i	0.990208	+	0.139600i	$0.0445818\pi$
$151$	15.1458	+	13.6373i	1.23255	+	1.10979i	0.242340	+	0.970191i	$0.422085\pi$
$152$	7.25965	−	16.3054i	0.588835	−	1.32255i
$153$	−3.88238	−	17.2499i	−0.313872	−	1.39457i
$154$	−19.5873	+	5.68858i	−1.57839	+	0.458398i
$155$	19.1449	+	11.0533i	1.53776	+	0.887823i
$156$	1.90825	+	0.0885886i	0.152783	+	0.00709276i
$157$	2.77064	+	8.52715i	0.221121	+	0.680540i	0.998662	+	0.0517084i	$0.0164666\pi$
$157$	2.77064	+	8.52715i	0.221121	+	0.680540i	−0.777541	+	0.628832i	$0.783533\pi$
$158$	−0.819732	−	0.266347i	−0.0652144	−	0.0211894i
$159$	13.7653	−	13.9306i	1.09166	−	1.10477i
$160$	7.88674	+	17.7139i	0.623502	+	1.40041i
$161$	2.06186	−	0.388037i	0.162498	−	0.0305816i
$162$	20.3529	−	4.83675i	1.59907	−	0.380011i
$163$	−14.9658	−	6.66318i	−1.17221	−	0.521901i	−0.274111	−	0.961698i	$-0.588384\pi$
$163$	−14.9658	−	6.66318i	−1.17221	−	0.521901i	−0.898097	+	0.439797i	$0.855050\pi$
$164$	−7.05476	−	12.2192i	−0.550884	−	0.954160i
$165$	−1.18424	−	23.5546i	−0.0921933	−	1.83373i
$166$	−7.52643	+	13.0362i	−0.584164	+	1.01180i
$167$	−0.673125	−	0.299695i	−0.0520880	−	0.0231911i	0.380527	−	0.924770i	$-0.375742\pi$
$167$	−0.673125	−	0.299695i	−0.0520880	−	0.0231911i	−0.432615	+	0.901579i	$0.642409\pi$
$168$	14.7978	−	2.07977i	1.14168	−	0.160458i
$169$	8.62841	+	9.58282i	0.663724	+	0.737140i
$170$	55.9358	+	5.87909i	4.29008	+	0.450906i
$171$	−13.1683	+	9.80966i	−1.00701	+	0.750164i
$172$	13.9346	−	12.5468i	1.06250	−	0.956683i
$173$	1.09126	+	3.35855i	0.0829670	+	0.255346i	0.983931	−	0.178547i	$-0.0571396\pi$
$173$	1.09126	+	3.35855i	0.0829670	+	0.255346i	−0.900964	+	0.433893i	$0.857140\pi$
$174$	5.77422	−	2.98566i	0.437743	−	0.226343i
$175$	0.734464	−	31.3575i	0.0555203	−	2.37040i
$176$	−0.288940	+	2.55031i	−0.0217797	+	0.192237i
$177$	14.8124	−	5.78764i	1.11337	−	0.435026i
$178$	7.76316	−	17.4363i	0.581874	−	1.30691i
$179$	−0.657591	+	3.09372i	−0.0491506	+	0.231236i	−0.995866	−	0.0908364i	$-0.971046\pi$
$179$	−0.657591	+	3.09372i	−0.0491506	+	0.231236i	0.946715	+	0.322072i	$0.104379\pi$
$180$	−3.88305	+	41.7316i	−0.289426	+	3.11049i
$181$	−4.66930	−	3.39245i	−0.347067	−	0.252159i	0.400571	−	0.916266i	$-0.368812\pi$
$181$	−4.66930	−	3.39245i	−0.347067	−	0.252159i	−0.747637	+	0.664107i	$0.768812\pi$
$182$	−1.58468	−	1.20903i	−0.117464	−	0.0896192i
$183$	0.409367	+	7.01026i	0.0302613	+	0.518213i
$184$	0.537630	−	2.52935i	0.0396346	−	0.186466i
$185$	6.19944	+	8.53280i	0.455792	+	0.627344i
$186$	7.88953	+	20.1918i	0.578489	+	1.48054i
$187$	−15.7207	−	11.6174i	−1.14961	−	0.849547i
$188$			10.1096i			0.737316i
$189$	−12.8073	−	4.99739i	−0.931592	−	0.363507i
$190$	−16.1410	−	49.6768i	−1.17099	−	3.60393i
$191$	6.95893	+	2.26109i	0.503530	+	0.163607i	0.549758	−	0.835324i	$-0.314720\pi$
$191$	6.95893	+	2.26109i	0.503530	+	0.163607i	−0.0462277	+	0.998931i	$0.514720\pi$
$192$	−5.49001	+	20.9894i	−0.396208	+	1.51478i
$193$	−1.39454	+	1.91942i	−0.100381	+	0.138163i	−0.856253	−	0.516557i	$-0.827213\pi$
$193$	−1.39454	+	1.91942i	−0.100381	+	0.138163i	0.755872	+	0.654720i	$0.227213\pi$
$194$	5.36897	+	5.96284i	0.385469	+	0.428107i
$195$	1.78244	−	1.46109i	0.127643	−	0.104631i
$196$	−21.2834	−	10.6967i	−1.52024	−	0.764053i
$197$	13.6877			0.975205			0.487603	−	0.873066i	$-0.337872\pi$
$197$	13.6877			0.975205			0.487603	+	0.873066i	$0.337872\pi$
$198$	13.5220	−	18.7627i	0.960970	−	1.33341i
$199$	3.16981	−	5.49028i	0.224702	−	0.389195i	−0.731528	−	0.681811i	$-0.761192\pi$
$199$	3.16981	−	5.49028i	0.224702	−	0.389195i	0.956230	+	0.292616i	$0.0945258\pi$
$200$	−35.3164	−	15.7239i	−2.49725	−	1.11185i
$201$	−18.9685	+	15.5488i	−1.33793	+	1.09672i
$202$	−17.6544	+	3.75257i	−1.24216	+	0.264030i
$203$	−4.23686	−	0.545892i	−0.297369	−	0.0383141i
$204$	24.7096	+	24.4163i	1.73002	+	1.70948i
$205$	−16.1897	−	5.26035i	−1.13074	−	0.367399i
$206$	−35.2839	−	7.49982i	−2.45834	−	0.522537i
$207$	−1.57063	+	1.78680i	−0.109166	+	0.124191i
$208$	−0.217217	+	0.125410i	−0.0150613	+	0.00869562i
$209$	−3.91796	+	17.7258i	−0.271011	+	1.22612i
$210$	28.1096	−	33.5001i	1.93975	−	2.31173i
$211$	−1.59992	+	3.59347i	−0.110143	+	0.247385i	−0.960204	−	0.279299i	$-0.909898\pi$
$211$	−1.59992	+	3.59347i	−0.110143	+	0.247385i	0.850062	+	0.526683i	$0.176565\pi$
$212$	−7.99969	+	37.6356i	−0.549421	+	2.58482i
$213$	−1.36337	−	23.3473i	−0.0934168	−	1.59973i
$214$	4.15541	−	39.5361i	0.284058	−	2.70263i
$215$	2.36470	−	22.4986i	0.161271	−	1.53439i
$216$	−11.7648	+	12.1939i	−0.800493	+	0.829689i
$217$	3.28747	−	13.8619i	0.223168	−	0.941004i
$218$	−1.41286	+	0.148497i	−0.0956907	+	0.0100575i
$219$	−1.08191	+	7.10514i	−0.0731086	+	0.480121i
$220$	26.9308	+	37.7053i	1.81568	+	2.54209i
$221$		−	1.91025i		−	0.128497i
$222$	−0.479638	+	10.3317i	−0.0321912	+	0.693419i
$223$	5.91682	+	1.25766i	0.396219	+	0.0842190i	0.401712	−	0.915766i	$-0.368415\pi$
$223$	5.91682	+	1.25766i	0.396219	+	0.0842190i	−0.00549301	+	0.999985i	$0.501748\pi$
$224$	9.47947	−	8.14162i	0.633374	−	0.543985i
$225$	21.2470	+	28.5217i	1.41647	+	1.90145i
$226$	−15.3602	−	1.61443i	−1.02175	−	0.107390i
$227$	−4.23264	+	0.899675i	−0.280930	+	0.0597135i	−0.346222	−	0.938153i	$-0.612536\pi$
$227$	−4.23264	+	0.899675i	−0.280930	+	0.0597135i	0.0652917	+	0.997866i	$0.479202\pi$
$228$	11.3812	−	30.1865i	0.753741	−	1.99915i
$229$	−1.45900	−	13.8814i	−0.0964133	−	0.917311i	−0.930652	−	0.365907i	$-0.880759\pi$
$229$	−1.45900	−	13.8814i	−0.0964133	−	0.917311i	0.834238	−	0.551404i	$-0.185908\pi$
$230$	−3.78372	−	6.55360i	−0.249491	−	0.432132i
$231$	−14.3237	+	5.08254i	−0.942429	+	0.334407i
$232$	−2.63254	+	4.55970i	−0.172835	+	0.299359i
$233$	−7.35008	−	3.27247i	−0.481520	−	0.214386i	0.151597	−	0.988442i	$-0.451558\pi$
$233$	−7.35008	−	3.27247i	−0.481520	−	0.214386i	−0.633117	+	0.774056i	$0.718225\pi$
$234$	2.25995	−	0.0269818i	0.147738	−	0.00176386i
$235$	8.16137	+	9.06412i	0.532389	+	0.591278i
$236$	−18.3647	+	25.2769i	−1.19544	+	1.64538i
$237$	−0.621360	−	0.162524i	−0.0403617	−	0.0105571i
$238$	−6.70367	−	35.6204i	−0.434534	−	2.30893i
$239$	2.91255	−	3.23472i	0.188397	−	0.209236i	−0.641545	−	0.767085i	$-0.721706\pi$
$239$	2.91255	−	3.23472i	0.188397	−	0.209236i	0.829943	+	0.557849i	$0.188373\pi$
$240$	−2.52751	−	4.88816i	−0.163150	−	0.315529i
$241$	−5.91243	+	3.41354i	−0.380853	+	0.219886i	−0.678189	−	0.734887i	$-0.737235\pi$
$241$	−5.91243	+	3.41354i	−0.380853	+	0.219886i	0.297336	+	0.954773i	$0.403902\pi$
$242$	−2.26062	−	25.4684i	−0.145318	−	1.63717i
$243$	14.9302	−	4.48213i	0.957772	−	0.287529i
$244$	−8.10922	−	11.1614i	−0.519139	−	0.714534i
$245$	−27.7179	+	7.59132i	−1.77083	+	0.484992i
$246$	−9.17515	−	13.9455i	−0.584986	−	0.889135i
$247$	−1.62066	+	0.721564i	−0.103120	+	0.0459120i
$248$	−14.2052	−	10.3207i	−0.902033	−	0.655365i
$249$	−5.03254	+	10.0244i	−0.318924	+	0.635271i
$250$	−62.2172	+	20.2156i	−3.93496	+	1.27855i
$251$	−11.4463	−	15.7544i	−0.722482	−	0.994411i	−0.999438	−	0.0335288i	$-0.989325\pi$
$251$	−11.4463	−	15.7544i	−0.722482	−	0.994411i	0.276956	−	0.960883i	$-0.410675\pi$
$252$	26.4821	−	5.31196i	1.66821	−	0.334622i
$253$	−0.0212900	+	2.62997i	−0.00133849	+	0.165345i
$254$		−	49.0241i		−	3.07604i
$255$	41.8655	+	1.94356i	2.62172	+	0.121710i
$256$	−6.38673	−	19.6563i	−0.399171	−	1.22852i
$257$	−11.7880	+	10.6139i	−0.735314	+	0.662080i	−0.949162	−	0.314787i	$-0.898067\pi$
$257$	−11.7880	+	10.6139i	−0.735314	+	0.662080i	0.213848	+	0.976867i	$0.431400\pi$
$258$	15.5928	−	15.7801i	0.970766	−	0.982425i
$259$	4.12282	−	5.40380i	0.256180	−	0.335776i
$260$	−1.39924	+	4.30643i	−0.0867774	+	0.267073i
$261$	4.16569	−	2.47183i	0.257850	−	0.153003i
$262$	1.62576	+	15.4681i	0.100440	+	0.955622i
$263$	0.844801	+	1.46324i	0.0520926	+	0.0902271i	0.890896	−	0.454208i	$-0.150078\pi$
$263$	0.844801	+	1.46324i	0.0520926	+	0.0902271i	−0.838803	+	0.544435i	$0.816744\pi$
$264$	−1.02014	+	18.7046i	−0.0627852	+	1.15119i
$265$	23.2105	+	40.2017i	1.42581	+	2.46957i
$266$	−27.6882	+	19.1424i	−1.69767	+	1.17370i
$267$	5.01750	−	13.3079i	0.307066	−	0.814433i
$268$	14.8906	−	45.8285i	0.909586	−	2.79942i
$269$	−0.157277	−	0.353251i	−0.00958937	−	0.0215381i	0.908687	−	0.417477i	$-0.137086\pi$
$269$	−0.157277	−	0.353251i	−0.00958937	−	0.0215381i	−0.918277	+	0.395939i	$0.870419\pi$
$270$	−1.70801	+	49.5570i	−0.103946	+	3.01594i
$271$	6.13674	+	28.8711i	0.372781	+	1.75380i	0.619776	+	0.784778i	$0.287223\pi$
$271$	6.13674	+	28.8711i	0.372781	+	1.75380i	−0.246996	+	0.969017i	$0.579443\pi$
$272$	−4.46135	−	0.948290i	−0.270509	−	0.0574985i
$273$	−1.23135	−	0.830546i	−0.0745245	−	0.0502669i
$274$	24.4818	−	14.1346i	1.47900	−	0.853900i
$275$	38.3928	+	8.48603i	2.31517	+	0.511727i
$276$	0.703586	−	4.62061i	0.0423509	−	0.278128i
$277$	−0.549746	+	1.23475i	−0.0330310	+	0.0741889i	−0.929308	−	0.369307i	$-0.879595\pi$
$277$	−0.549746	+	1.23475i	−0.0330310	+	0.0741889i	0.896277	+	0.443496i	$0.146262\pi$
$278$	6.61682	+	5.95781i	0.396851	+	0.357326i
$279$	6.74607	+	14.6778i	0.403877	+	0.878736i
$280$	−4.52627	+	35.1299i	−0.270496	+	2.09941i
$281$	−5.92554	+	2.63822i	−0.353488	+	0.157383i	−0.575796	−	0.817593i	$-0.695308\pi$
$281$	−5.92554	+	2.63822i	−0.353488	+	0.157383i	0.222308	+	0.974977i	$0.428641\pi$
$282$	0.697265	+	11.9404i	0.0415215	+	0.711041i
$283$	7.36514	−	2.39308i	0.437812	−	0.142254i	−0.0818140	−	0.996648i	$-0.526071\pi$
$283$	7.36514	−	2.39308i	0.437812	−	0.142254i	0.519626	+	0.854394i	$0.326071\pi$
$284$	27.0073	+	37.1724i	1.60259	+	2.20577i
$285$	−14.1650	−	36.2529i	−0.839064	−	2.14743i
$286$	1.87033	−	1.65683i	0.110595	−	0.0979707i
$287$	−0.256876	+	10.9672i	−0.0151629	+	0.647372i
$288$	−2.78023	+	13.8935i	−0.163826	+	0.818683i
$289$	11.8683	−	13.1810i	0.698133	−	0.775355i
$290$	3.20353	+	15.0714i	0.188118	+	0.885026i
$291$	4.25294	+	4.20247i	0.249312	+	0.246353i
$292$	−5.74315	−	12.8993i	−0.336093	−	0.754876i
$293$	12.9455	−	2.75165i	0.756283	−	0.160753i	0.186395	−	0.982475i	$-0.440320\pi$
$293$	12.9455	−	2.75165i	0.756283	−	0.160753i	0.569889	+	0.821722i	$0.306986\pi$
$294$	−25.8756	−	11.1660i	−1.50909	−	0.651214i
$295$	3.94022	+	37.4887i	0.229408	+	2.18268i
$296$	−4.18863	−	7.25492i	−0.243459	−	0.421683i
$297$	9.24386	−	14.5448i	0.536383	−	0.843975i
$298$	−3.15444	+	5.46365i	−0.182732	+	0.316501i
$299$	−0.207932	+	0.151072i	−0.0120250	+	0.00873669i
$300$	−65.3818	−	24.6510i	−3.77482	−	1.42322i
$301$	−14.3273	+	2.69636i	−0.825813	+	0.155416i
$302$	−47.1136	−	4.95184i	−2.71108	−	0.284946i
$303$	−12.9699	+	3.55840i	−0.745104	+	0.204425i
$304$	0.880668	+	4.14322i	0.0505098	+	0.237630i
$305$	−16.2811	−	3.46066i	−0.932255	−	0.198157i
$306$	30.8685	+	27.1339i	1.76463	+	1.55114i
$307$		−	8.69851i		−	0.496450i	−0.968702	−	0.248225i	$-0.920153\pi$
$307$		−	8.69851i		−	0.496450i	0.968702	−	0.248225i	$-0.0798473\pi$
$308$	18.3038	−	23.5924i	1.04296	−	1.34430i
$309$	−26.5731	−	4.04631i	−1.51169	−	0.230187i
$310$	−51.1034	+	5.37118i	−2.90248	+	0.305063i
$311$	14.3756	−	4.67092i	0.815166	−	0.264864i	0.128382	−	0.991725i	$-0.459022\pi$
$311$	14.3756	−	4.67092i	0.815166	−	0.264864i	0.686784	+	0.726861i	$0.259022\pi$
$312$	−1.52929	+	1.00616i	−0.0865788	+	0.0569625i
$313$	−5.92951	−	4.30804i	−0.335155	−	0.243505i	0.407460	−	0.913223i	$-0.366415\pi$
$313$	−5.92951	−	4.30804i	−0.335155	−	0.243505i	−0.742615	+	0.669719i	$0.766415\pi$
$314$	−16.8604	−	12.2498i	−0.951488	−	0.691296i
$315$	19.4552	−	26.1414i	1.09618	−	1.47290i
$316$	1.20007	−	0.389926i	0.0675092	−	0.0219351i
$317$	16.7779	+	23.0928i	0.942341	+	1.29702i	0.954846	+	0.297100i	$0.0960194\pi$
$317$	16.7779	+	23.0928i	0.942341	+	1.29702i	−0.0125051	+	0.999922i	$0.503981\pi$
$318$	−6.85268	+	45.0031i	−0.384279	+	2.52365i
$319$	1.69598	−	5.07942i	0.0949569	−	0.284393i
$320$	−44.5356	−	25.7126i	−2.48962	−	1.43738i
$321$	1.37373	−	29.5910i	0.0766742	−	1.65161i
$322$	−3.34715	+	3.54673i	−0.186529	+	0.197651i
$323$	−30.6809	−	9.96882i	−1.70713	−	0.554680i
$324$	−19.9436	+	23.2423i	−1.10798	+	1.29124i
$325$	1.56286	+	3.51024i	0.0866918	+	0.194713i
$326$	37.2465	−	7.91699i	2.06289	−	0.438482i
$327$	−1.04456	+	0.171840i	−0.0577642	+	0.00950275i
$328$	12.3518	+	5.49938i	0.682015	+	0.303653i
$329$	4.08842	−	6.71324i	0.225402	−	0.370113i
$330$	34.4086	+	42.6762i	1.89413	+	2.34925i
$331$	−0.753693			−0.0414267			−0.0207134	−	0.999785i	$-0.506594\pi$
$331$	−0.753693			−0.0414267			−0.0207134	+	0.999785i	$0.506594\pi$
$332$	−2.30350	−	21.9163i	−0.126421	−	1.20281i
$333$	0.0920088	+	7.70648i	0.00504205	+	0.422313i
$334$	1.67526	−	0.356088i	0.0916663	−	0.0194843i
$335$	−23.6463	−	53.1104i	−1.29193	−	2.90173i
$336$	−2.55099	+	2.46348i	−0.139168	+	0.134394i
$337$	−2.38272	−	11.2098i	−0.129795	−	0.610639i	−0.994173	−	0.107796i	$-0.965621\pi$
$337$	−2.38272	−	11.2098i	−0.129795	−	0.610639i	0.864378	−	0.502843i	$-0.167713\pi$
$338$	−29.3182	−	6.23177i	−1.59470	−	0.338964i
$339$	−11.4965	−	0.533710i	−0.624402	−	0.0289872i
$340$	−71.3084	+	41.1700i	−3.86724	+	2.23275i
$341$	16.2554	+	7.39564i	0.880282	+	0.400496i
$342$	11.3604	−	36.4382i	0.614300	−	1.97035i
$343$	9.80732	+	15.7104i	0.529545	+	0.848282i
$344$	−3.73584	+	17.5757i	−0.201423	+	0.947621i
$345$	−3.09936	−	4.71079i	−0.166864	−	0.253620i
$346$	−6.64074	−	4.82478i	−0.357009	−	0.259382i
$347$	−20.5694	−	14.9446i	−1.10422	−	0.802266i	−0.122480	−	0.992471i	$-0.539085\pi$
$347$	−20.5694	−	14.9446i	−1.10422	−	0.802266i	−0.981744	+	0.190205i	$0.939085\pi$
$348$	−4.26972	+	8.50492i	−0.228881	+	0.455911i
$349$	3.60752	−	16.9720i	0.193106	−	0.908493i	−0.769722	−	0.638379i	$-0.779605\pi$
$349$	3.60752	−	16.9720i	0.193106	−	0.908493i	0.962828	−	0.270114i	$-0.0870614\pi$
$350$	41.4611	+	59.9708i	2.21619	+	3.20557i
$351$	1.67998	−	0.118243i	0.0896707	−	0.00631135i
$352$	7.72212	+	13.6287i	0.411590	+	0.726412i
$353$	−7.81036	+	4.50931i	−0.415703	+	0.240007i	−0.693237	−	0.720709i	$-0.743816\pi$
$353$	−7.81036	+	4.50931i	−0.415703	+	0.240007i	0.277534	+	0.960716i	$0.410483\pi$
$354$	−19.9472	+	31.1211i	−1.06018	+	1.65407i
$355$	54.2234	+	11.5255i	2.87788	+	0.611712i
$356$	5.80950	+	27.3316i	0.307903	+	1.44857i
$357$	−6.53413	−	26.2065i	−0.345823	−	1.38699i
$358$	−2.99022	−	6.71614i	−0.158038	−	0.354959i
$359$	14.3214	−	3.04410i	0.755854	−	0.160662i	0.186161	−	0.982519i	$-0.440395\pi$
$359$	14.3214	−	3.04410i	0.755854	−	0.160662i	0.569693	+	0.821858i	$0.307062\pi$
$360$	−20.4952	−	34.5398i	−1.08019	−	1.82041i
$361$	1.14557	+	10.8993i	0.0602930	+	0.573649i
$362$	13.4155			0.705104
$363$	−2.78799	−	18.8475i	−0.146332	−	0.989236i
$364$	2.91725	+	0.0683286i	0.152905	+	0.00358139i
$365$	−15.5628	−	6.92900i	−0.814593	−	0.362680i
$366$	−10.3476	−	12.6234i	−0.540878	−	0.659836i
$367$	−25.1727	+	5.35063i	−1.31401	+	0.279301i	−0.811033	−	0.585001i	$-0.801094\pi$
$367$	−25.1727	+	5.35063i	−1.31401	+	0.279301i	−0.502974	+	0.864302i	$0.667761\pi$
$368$	0.249602	+	0.560616i	0.0130114	+	0.0292241i
$369$	−7.43109	−	9.97537i	−0.386847	−	0.519297i
$370$	−23.3159	−	7.57581i	−1.21214	−	0.393848i
$371$	20.5324	−	21.7567i	1.06599	−	1.12955i
$372$	−26.7194	−	17.1259i	−1.38534	−	0.887937i
$373$	0.381254	+	0.220117i	0.0197406	+	0.0113972i	0.509838	−	0.860271i	$-0.329705\pi$
$373$	0.381254	+	0.220117i	0.0197406	+	0.0113972i	−0.490097	+	0.871668i	$0.663039\pi$
$374$	45.4350	+	0.367804i	2.34939	+	0.0190187i
$375$	−45.4046	+	17.7409i	−2.34468	+	0.916135i
$376$	−5.69429	−	7.83751i	−0.293660	−	0.404189i
$377$	0.497705	−	0.161714i	0.0256331	−	0.00832869i
$378$	30.9116	−	8.10045i	1.58992	−	0.416642i
$379$	−11.9767	−	8.70155i	−0.615199	−	0.446968i	0.236042	−	0.971743i	$-0.424150\pi$
$379$	−11.9767	−	8.70155i	−0.615199	−	0.446968i	−0.851241	+	0.524774i	$0.824150\pi$
$380$	61.8642	+	44.9470i	3.17357	+	2.30573i
$381$	−2.12959	−	36.4685i	−0.109102	−	1.86834i
$382$	−16.1754	+	5.25571i	−0.827606	+	0.268905i
$383$	−17.0011	+	1.78689i	−0.868715	+	0.0913056i	−0.528389	−	0.849002i	$-0.677204\pi$
$383$	−17.0011	+	1.78689i	−0.868715	+	0.0913056i	−0.340325	+	0.940308i	$0.610537\pi$
$384$	−12.3986	−	31.7321i	−0.632715	−	1.61932i
$385$	−2.63497	−	35.9293i	−0.134291	−	1.83112i
$386$		−	5.51473i		−	0.280692i
$387$	10.9138	−	12.4160i	0.554782	−	0.631140i
$388$	−11.4900	−	2.44227i	−0.583315	−	0.123987i
$389$	3.09906	+	14.5799i	0.157129	+	0.739232i	0.984189	+	0.177119i	$0.0566779\pi$
$389$	3.09906	+	14.5799i	0.157129	+	0.739232i	−0.827061	+	0.562113i	$0.809989\pi$
$390$	−1.35563	+	5.18283i	−0.0686449	+	0.262443i
$391$	−4.64813	−	0.488538i	−0.235066	−	0.0247064i
$392$	22.5251	−	3.69529i	1.13769	−	0.186640i
$393$	1.88132	+	11.4359i	0.0948999	+	0.576866i
$394$	−25.7395	+	18.7008i	−1.29674	+	0.942134i
$395$	0.761185	−	1.31841i	0.0382994	−	0.0663365i
$396$	0.130137	+	33.8581i	0.00653962	+	1.70143i
$397$	3.13968	+	5.43808i	0.157576	+	0.272930i	0.933994	−	0.357289i	$-0.116299\pi$
$397$	3.13968	+	5.43808i	0.157576	+	0.272930i	−0.776418	+	0.630218i	$0.782965\pi$
$398$	1.54032	+	14.6552i	0.0772093	+	0.734597i
$399$	−19.7654	+	15.4426i	−0.989510	+	0.773097i
$400$	8.97392	−	1.90747i	0.448696	−	0.0953733i
$401$	3.39683	+	7.62941i	0.169630	+	0.380995i	0.978278	−	0.207298i	$-0.0664670\pi$
$401$	3.39683	+	7.62941i	0.169630	+	0.380995i	−0.808648	+	0.588293i	$0.799800\pi$
$402$	14.4264	−	55.1550i	0.719525	−	2.75088i
$403$	0.362852	+	1.70708i	0.0180749	+	0.0850358i
$404$	17.6805	−	19.6362i	0.879639	−	0.976938i
$405$	0.882168	+	36.9391i	0.0438353	+	1.83552i
$406$	8.71318	−	4.76208i	0.432428	−	0.236338i
$407$	5.64985	+	6.37787i	0.280053	+	0.316139i
$408$	−32.9090	−	5.01108i	−1.62924	−	0.248086i
$409$	−1.37728	−	1.89566i	−0.0681020	−	0.0937344i	0.773607	−	0.633665i	$-0.218450\pi$
$409$	−1.37728	−	1.89566i	−0.0681020	−	0.0937344i	−0.841709	+	0.539931i	$0.818450\pi$
$410$	37.6315	−	12.2272i	1.85849	−	0.603859i
$411$	17.5977	−	11.5780i	0.868032	−	0.571102i
$412$	48.2433	−	21.4793i	2.37677	−	1.05821i
$413$	22.4173	−	9.35818i	1.10308	−	0.460486i
$414$	0.512318	−	5.50593i	0.0251790	−	0.270602i
$415$	−19.7582	−	17.7903i	−0.969891	−	0.873294i
$416$	−0.622623	+	1.39844i	−0.0305266	+	0.0685639i
$417$	5.18099	+	4.14452i	0.253714	+	0.202958i
$418$	−16.8502	−	38.6860i	−0.824171	−	1.89220i
$419$	4.64959	−	2.68444i	0.227147	−	0.131144i	−0.382108	−	0.924118i	$-0.624802\pi$
$419$	4.64959	−	2.68444i	0.227147	−	0.131144i	0.609255	+	0.792974i	$0.291468\pi$
$420$	−4.46561	+	63.8654i	−0.217900	+	3.11631i
$421$	−30.9022	−	6.56846i	−1.50608	−	0.320127i	−0.620348	−	0.784326i	$-0.713009\pi$
$421$	−30.9022	−	6.56846i	−1.50608	−	0.320127i	−0.885731	+	0.464199i	$0.846342\pi$
$422$	−1.90097	−	8.94337i	−0.0925378	−	0.435356i
$423$	1.03738	+	8.85205i	0.0504390	+	0.430402i
$424$	−14.9967	−	33.6831i	−0.728304	−	1.63580i
$425$	−21.5918	+	66.4527i	−1.04736	+	3.22343i
$426$	34.4621	+	42.0416i	1.66970	+	2.03692i
$427$	0.871130	+	10.6912i	0.0421569	+	0.517381i
$428$	29.0994	+	50.4017i	1.40657	+	2.43626i
$429$	1.31935	−	1.31375i	0.0636986	−	0.0634284i
$430$	26.2920	+	45.5391i	1.26791	+	2.19609i
$431$	−2.64376	−	25.1537i	−0.127345	−	1.21161i	−0.852389	−	0.522908i	$-0.824847\pi$
$431$	−2.64376	−	25.1537i	−0.127345	−	1.21161i	0.725044	−	0.688703i	$-0.241819\pi$
$432$	0.557824	−	3.98226i	0.0268383	−	0.191596i
$433$	2.89297	−	8.90366i	0.139027	−	0.427882i	−0.857167	−	0.515038i	$-0.827778\pi$
$433$	2.89297	−	8.90366i	0.139027	−	0.427882i	0.996195	+	0.0871557i	$0.0277778\pi$
$434$	12.7568	+	30.5586i	0.612345	+	1.46686i
$435$	3.03777	+	11.0723i	0.145650	+	0.530877i
$436$	1.54558	−	1.39165i	0.0740199	−	0.0666478i
$437$	1.34127	+	4.12802i	0.0641618	+	0.197470i
$438$	−7.67292	−	14.8393i	−0.366626	−	0.709049i
$439$		−	29.6449i		−	1.41487i	−0.706777	−	0.707437i	$-0.749851\pi$
$439$		−	29.6449i		−	1.41487i	0.706777	−	0.707437i	$-0.250149\pi$
$440$	−42.1161	−	14.0623i	−2.00781	−	0.670393i
$441$	−19.7336	−	7.18224i	−0.939696	−	0.342012i
$442$	2.60989	+	3.59221i	0.124140	+	0.170864i
$443$	33.3837	−	10.8470i	1.58611	−	0.515358i	0.622487	−	0.782630i	$-0.286122\pi$
$443$	33.3837	−	10.8470i	1.58611	−	0.515358i	0.963621	+	0.267272i	$0.0861223\pi$
$444$	−8.32241	−	12.6494i	−0.394964	−	0.600316i
$445$	27.2733	+	19.8152i	1.29288	+	0.939331i
$446$	−12.8448	+	5.71887i	−0.608218	+	0.270796i
$447$	−2.10921	+	4.20138i	−0.0997624	+	0.198718i
$448$	−7.64745	+	32.2460i	−0.361308	+	1.52348i
$449$	−6.38182	−	8.78383i	−0.301177	−	0.414534i	0.631427	−	0.775435i	$-0.282469\pi$
$449$	−6.38182	−	8.78383i	−0.301177	−	0.414534i	−0.932604	+	0.360901i	$0.882469\pi$
$450$	−78.9227	−	24.6058i	−3.72045	−	1.15993i
$451$	−13.4278	−	2.96796i	−0.632288	−	0.139756i
$452$	19.5816	−	11.3055i	0.921043	−	0.531764i
$453$	−35.2624	−	1.63702i	−1.65677	−	0.0769139i
$454$	6.73024	−	7.47469i	0.315866	−	0.350805i
$455$	2.67073	−	2.29381i	0.125206	−	0.107535i
$456$	8.17938	+	29.8129i	0.383034	+	1.39612i
$457$	−15.8624	+	21.8327i	−0.742012	+	1.02129i	0.256489	+	0.966547i	$0.417434\pi$
$457$	−15.8624	+	21.8327i	−0.742012	+	1.02129i	−0.998500	+	0.0547443i	$0.982566\pi$
$458$	21.7092	+	24.1105i	1.01440	+	1.12661i
$459$	24.1414	+	18.8437i	1.12683	+	0.879549i
$460$	10.1208	+	4.50606i	0.471884	+	0.210096i
$461$	−2.70326	+	4.68218i	−0.125903	+	0.218071i	−0.922086	−	0.386986i	$-0.873516\pi$
$461$	−2.70326	+	4.68218i	−0.125903	+	0.218071i	0.796182	+	0.605057i	$0.206850\pi$
$462$	19.9915	−	29.1274i	0.930087	−	1.35513i
$463$	−20.2307	−	35.0407i	−0.940203	−	1.62848i	−0.765083	−	0.643931i	$-0.777302\pi$
$463$	−20.2307	−	35.0407i	−0.940203	−	1.62848i	−0.175119	−	0.984547i	$-0.556031\pi$
$464$	−0.130608	−	1.24266i	−0.00606335	−	0.0576889i
$465$	−37.7820	+	6.21548i	−1.75210	+	0.288236i
$466$	18.2928	−	3.88825i	0.847396	−	0.180120i
$467$	6.77736	+	0.712329i	0.313619	+	0.0329626i	0.260030	−	0.965600i	$-0.416267\pi$
$467$	6.77736	+	0.712329i	0.313619	+	0.0329626i	0.0535884	+	0.998563i	$0.482934\pi$
$468$	−2.65343	+	1.97665i	−0.122655	+	0.0913709i
$469$	−28.4216	+	24.4104i	−1.31239	+	1.12717i
$470$	−27.7313	−	5.89446i	−1.27915	−	0.271891i
$471$	−13.0744	−	8.38009i	−0.602437	−	0.386134i
$472$		−	29.9401i		−	1.37811i
$473$	0.147939	−	18.2749i	0.00680222	−	0.840282i
$474$	1.39051	−	0.543312i	0.0638682	−	0.0249551i
$475$	64.5345	−	6.78284i	2.96104	−	0.311218i
$476$	38.5913	+	36.4197i	1.76883	+	1.66929i
$477$	−3.14271	+	33.7750i	−0.143895	+	1.54645i
$478$	−1.05757	+	10.0621i	−0.0483722	+	0.460231i
$479$	1.66681	−	15.8587i	0.0761587	−	0.724602i	−0.888102	−	0.459646i	$-0.847976\pi$
$479$	1.66681	−	15.8587i	0.0761587	−	0.724602i	0.964261	−	0.264955i	$-0.0853572\pi$
$480$	−30.0149	−	15.0684i	−1.36999	−	0.687773i
$481$	−0.173117	+	0.814453i	−0.00789347	+	0.0371358i
$482$	6.45448	−	14.4970i	0.293994	−	0.660320i
$483$	−2.33584	+	2.78377i	−0.106284	+	0.126666i
$484$	24.5931	+	28.2191i	1.11787	+	1.28268i
$485$	−12.2734	+	7.08606i	−0.557307	+	0.321761i
$486$	−21.9523	+	28.8270i	−0.995777	+	1.30762i
$487$	7.81788	+	1.66174i	0.354262	+	0.0753007i	0.381605	−	0.924325i	$-0.375371\pi$
$487$	7.81788	+	1.66174i	0.354262	+	0.0753007i	−0.0273432	+	0.999626i	$0.508705\pi$
$488$	12.5735	+	4.08536i	0.569174	+	0.184936i
$489$	27.3634	−	7.50735i	1.23742	−	0.339494i
$490$	41.7514	−	52.1450i	1.88614	−	2.35567i
$491$	−4.75955	+	1.01167i	−0.214795	+	0.0456562i	−0.314052	−	0.949406i	$-0.601687\pi$
$491$	−4.75955	+	1.01167i	−0.214795	+	0.0456562i	0.0992570	+	0.995062i	$0.468353\pi$
$492$	22.8671	+	8.62160i	1.03093	+	0.388692i
$493$	8.69351	+	3.87060i	0.391536	+	0.174323i
$494$	2.06179	−	3.57113i	0.0927644	−	0.160673i
$495$	27.4500	+	30.2517i	1.23379	+	1.35971i
$496$	4.16698			0.187103
$497$	−2.90125	−	35.6063i	−0.130139	−	1.59716i
$498$	−4.23225	−	25.7265i	−0.189652	−	1.15283i
$499$	−0.404092	−	0.448789i	−0.0180896	−	0.0200906i	0.734032	−	0.679115i	$-0.237636\pi$
$499$	−0.404092	−	0.448789i	−0.0180896	−	0.0200906i	−0.752122	+	0.659024i	$0.770969\pi$
$500$	56.2934	−	77.4812i	2.51752	−	3.46507i
$501$	1.23074	−	0.337663i	0.0549855	−	0.0150857i
$502$	43.0492	+	13.9875i	1.92138	+	0.624294i
$503$	8.58429	+	26.4197i	0.382755	+	1.17800i	0.938096	+	0.346375i	$0.112587\pi$
$503$	8.58429	+	26.4197i	0.382755	+	1.17800i	−0.555342	+	0.831622i	$0.687413\pi$
$504$	−17.5384	+	19.0344i	−0.781223	+	0.847858i
$505$		−	31.8790i		−	1.41860i
$506$	−3.55317	−	4.97471i	−0.157958	−	0.221153i
$507$	−22.0802	−	3.36218i	−0.980616	−	0.149319i
$508$	42.1855	+	58.0633i	1.87168	+	2.57614i
$509$	7.65861	−	36.0309i	0.339462	−	1.59704i	−0.395190	−	0.918599i	$-0.629321\pi$
$509$	7.65861	−	36.0309i	0.339462	−	1.59704i	0.734652	−	0.678444i	$-0.237345\pi$
$510$	−81.3829	+	53.5440i	−3.60370	+	2.37097i
$511$	−1.40290	+	10.8884i	−0.0620606	+	0.481674i
$512$	7.04004	+	5.11489i	0.311129	+	0.226048i
$513$	6.86801	−	27.5995i	0.303230	−	1.21855i
$514$	7.66581	−	36.0648i	0.338124	−	1.59075i
$515$	25.9143	−	58.2045i	1.14192	−	2.56480i
$516$	−4.88902	+	32.1073i	−0.215227	+	1.41345i
$517$	7.26881	+	6.65219i	0.319682	+	0.292563i
$518$	−0.369946	+	15.7946i	−0.0162545	+	0.693975i
$519$	−5.14957	−	3.30063i	−0.226041	−	0.144882i
$520$	−1.34085	−	4.12672i	−0.0588003	−	0.180969i
$521$	24.8661	−	22.3895i	1.08940	−	0.980902i	0.0895155	−	0.995985i	$-0.471468\pi$
$521$	24.8661	−	22.3895i	1.08940	−	0.980902i	0.999886	+	0.0150837i	$0.00480147\pi$
$522$	−4.45637	+	10.3396i	−0.195050	+	0.452554i
$523$	7.63858	+	0.802848i	0.334012	+	0.0351061i	0.270050	−	0.962846i	$-0.412960\pi$
$523$	7.63858	+	0.802848i	0.334012	+	0.0351061i	0.0639619	+	0.997952i	$0.479626\pi$
$524$	−15.2359	−	16.9212i	−0.665583	−	0.739205i
$525$	33.4476	+	42.8106i	1.45977	+	1.86841i
$526$	−3.58779	−	1.59739i	−0.156435	−	0.0696494i
$527$	−15.8679	+	27.4840i	−0.691217	+	1.19722i
$528$	−2.41328	−	3.73348i	−0.105025	−	0.162479i
$529$	−11.1856	−	19.3740i	−0.486330	−	0.842348i
$530$	−98.5729	−	43.8875i	−4.28173	−	1.90635i
$531$	−13.4866	+	24.0172i	−0.585270	+	1.04226i
$532$	16.3213	−	46.4978i	0.707620	−	2.01594i
$533$	−0.546605	−	1.22769i	−0.0236761	−	0.0531774i
$534$	8.74668	+	31.8806i	0.378506	+	1.37961i
$535$	66.7791	+	21.6979i	2.88711	+	0.938080i
$536$	14.2692	+	43.9161i	0.616335	+	1.89689i
$537$	−2.51614	−	4.86617i	−0.108579	−	0.209991i
$538$	0.778389	+	0.449403i	0.0335587	+	0.0193751i
$539$	−21.6957	+	8.26425i	−0.934499	+	0.355966i
$540$	−40.6211	−	60.1642i	−1.74805	−	2.58905i
$541$	−11.1812	+	25.1134i	−0.480718	+	1.07971i	0.496608	+	0.867975i	$0.334579\pi$
$541$	−11.1812	+	25.1134i	−0.480718	+	1.07971i	−0.977327	+	0.211737i	$0.932088\pi$
$542$	−50.9854	−	45.9074i	−2.19001	−	1.97189i
$543$	9.97966	−	0.582767i	0.428268	−	0.0250089i
$544$	−25.4297	+	11.3221i	−1.09029	+	0.485429i
$545$	0.262285	−	2.49547i	0.0112350	−	0.106894i
$546$	3.45027	−	0.120502i	0.147658	−	0.00515700i
$547$	5.80915	−	27.3299i	0.248381	−	1.16854i	−0.660284	−	0.751016i	$-0.729564\pi$
$547$	5.80915	−	27.3299i	0.248381	−	1.16854i	0.908665	−	0.417526i	$-0.137103\pi$
$548$	−16.8329	+	37.8074i	−0.719068	+	1.61505i
$549$	−8.24583	−	8.94092i	−0.351924	−	0.381589i
$550$	−83.7912	+	36.4964i	−3.57287	+	1.55621i
$551$		−	8.83764i		−	0.376496i
$552$	2.05713	+	3.97846i	0.0875574	+	0.169335i
$553$	−0.954596	−	0.226392i	−0.0405935	−	0.00962715i
$554$	−0.653191	−	3.07302i	−0.0277514	−	0.130560i
$555$	−17.6736	−	4.62273i	−0.750202	−	0.196224i
$556$	−12.9636	−	1.36253i	−0.549778	−	0.0577840i
$557$	21.5416	+	23.9244i	0.912748	+	1.01371i	0.999847	+	0.0175099i	$0.00557385\pi$
$557$	21.5416	+	23.9244i	0.912748	+	1.01371i	−0.0870985	+	0.996200i	$0.527759\pi$
$558$	−32.7395	−	18.3845i	−1.38597	−	0.778280i
$559$	1.44486	−	1.04975i	0.0611112	−	0.0443999i
$560$	−4.03133	−	7.37613i	−0.170355	−	0.311699i
$561$	33.8146	−	1.70008i	1.42765	−	0.0717773i
$562$	7.53843	−	13.0569i	0.317989	−	0.550774i
$563$	−26.0394	+	18.9187i	−1.09743	+	0.797329i	−0.980638	−	0.195828i	$-0.937261\pi$
$563$	−26.0394	+	18.9187i	−1.09743	+	0.797329i	−0.116791	+	0.993157i	$0.537261\pi$
$564$	−11.1006	−	13.5420i	−0.467420	−	0.570222i
$565$	8.42987	−	25.9445i	0.354647	−	1.09149i
$566$	−10.5805	+	14.5628i	−0.444731	+	0.612120i
$567$	22.6430	−	7.36864i	0.950915	−	0.309454i
$568$	−41.8752	−	13.6061i	−1.75704	−	0.570898i
$569$	2.01615	+	6.20507i	0.0845214	+	0.260130i	0.984381	−	0.176049i	$-0.0563316\pi$
$569$	2.01615	+	6.20507i	0.0845214	+	0.260130i	−0.899860	+	0.436179i	$0.856332\pi$
$570$	76.1678	+	48.8200i	3.19032	+	2.04485i
$571$			11.5785i			0.484545i	0.970208	+	0.242273i	$0.0778928\pi$
$571$			11.5785i			0.484545i	−0.970208	+	0.242273i	$0.922107\pi$
$572$	−0.789472	+	3.57175i	−0.0330095	+	0.149343i
$573$	−11.8044	+	4.61232i	−0.493136	+	0.192683i
$574$	−14.5009	−	20.9746i	−0.605256	−	0.875463i
$575$	8.94100	−	2.90511i	0.372865	−	0.121151i
$576$	−15.6930	−	34.1440i	−0.653874	−	1.42267i
$577$	−9.62609	+	4.28581i	−0.400739	+	0.178421i	−0.597202	−	0.802091i	$-0.703721\pi$
$577$	−9.62609	+	4.28581i	−0.400739	+	0.178421i	0.196463	+	0.980511i	$0.437054\pi$
$578$	−4.30947	+	41.0018i	−0.179250	+	1.70545i
$579$	−0.239558	−	4.10235i	−0.00995571	−	0.170488i
$580$	−16.7633	−	15.0937i	−0.696057	−	0.626732i
$581$	−7.33357	+	15.4851i	−0.304248	+	0.642429i
$582$	−13.7393	−	2.09209i	−0.569510	−	0.0867200i
$583$	21.7962	+	30.5164i	0.902707	+	1.26386i
$584$	11.7181	+	6.76543i	0.484897	+	0.279955i
$585$	−0.783297	+	3.91434i	−0.0323853	+	0.161838i
$586$	−20.5844	+	22.8613i	−0.850333	+	0.944390i
$587$	−15.2553	+	13.7360i	−0.629655	+	0.566944i	−0.920946	−	0.389691i	$-0.872582\pi$
$587$	−15.2553	+	13.7360i	−0.629655	+	0.566944i	0.291291	+	0.956635i	$0.405915\pi$
$588$	40.2550	−	9.04122i	1.66009	−	0.372854i
$589$	29.3113	+	3.08074i	1.20775	+	0.126940i
$590$	−58.6286	−	65.1137i	−2.41370	−	2.68069i
$591$	−18.3350	+	15.0295i	−0.754200	+	0.618230i
$592$	1.81620	+	0.808623i	0.0746453	+	0.0332342i
$593$	16.9766	+	29.4043i	0.697146	+	1.20749i	0.969452	+	0.245281i	$0.0788802\pi$
$593$	16.9766	+	29.4043i	0.697146	+	1.20749i	−0.272306	+	0.962211i	$0.587786\pi$
$594$	2.48892	+	39.9808i	0.102122	+	1.64043i
$595$	64.0019	+	1.49907i	2.62382	+	0.0614559i
$596$	−0.965431	−	9.18546i	−0.0395456	−	0.376251i
$597$	1.78244	+	10.8349i	0.0729506	+	0.443444i
$598$	0.184612	−	0.568177i	0.00754934	−	0.0232345i
$599$	6.97087	−	9.59458i	0.284822	−	0.392024i	−0.642502	−	0.766284i	$-0.722103\pi$
$599$	6.97087	−	9.59458i	0.284822	−	0.392024i	0.927324	+	0.374260i	$0.122103\pi$
$600$	64.5726	−	17.7160i	2.63616	−	0.723251i
$601$	−23.4961	+	21.1560i	−0.958428	+	0.862972i	−0.990639	−	0.136509i	$-0.956412\pi$
$601$	−23.4961	+	21.1560i	−0.958428	+	0.862972i	0.0322110	+	0.999481i	$0.489745\pi$
$602$	23.2584	−	24.6452i	0.947943	−	1.00446i
$603$	8.33575	−	41.6559i	0.339458	−	1.69636i
$604$	60.0616	−	34.6766i	2.44387	−	1.41097i
$605$	44.8310	+	5.44707i	1.82264	+	0.221455i
$606$	19.5281	−	24.4118i	0.793277	−	0.991661i
$607$	12.3506	−	1.29810i	0.501293	−	0.0526881i	0.149492	−	0.988763i	$-0.452236\pi$
$607$	12.3506	−	1.29810i	0.501293	−	0.0526881i	0.351801	+	0.936075i	$0.385569\pi$
$608$	19.2113	+	17.2979i	0.779121	+	0.701523i
$609$	6.27478	−	3.92096i	0.254267	−	0.158885i
$610$	35.3446	−	15.7364i	1.43106	−	0.637150i
$611$	−0.100650	+	0.957623i	−0.00407187	+	0.0387413i
$612$	−59.9090	−	5.57443i	−2.42168	−	0.225333i
$613$	5.69551	−	26.7953i	0.230039	−	1.08225i	−0.699815	−	0.714324i	$-0.746734\pi$
$613$	5.69551	−	26.7953i	0.230039	−	1.08225i	0.929855	−	0.367927i	$-0.119932\pi$
$614$	11.8844	+	16.3574i	0.479614	+	0.660133i
$615$	27.4625	−	10.7304i	1.10740	−	0.432692i
$616$	−0.901570	+	28.6000i	−0.0363253	+	1.15233i
$617$	−33.8139	+	19.5225i	−1.36130	+	0.785946i	−0.989797	−	0.142487i	$-0.954490\pi$
$617$	−33.8139	+	19.5225i	−1.36130	+	0.785946i	−0.371501	+	0.928432i	$0.621157\pi$
$618$	55.4987	−	28.6966i	2.23248	−	1.15434i
$619$	16.0794	−	17.8580i	0.646287	−	0.717775i	−0.327598	−	0.944817i	$-0.606239\pi$
$619$	16.0794	−	17.8580i	0.646287	−	0.717775i	0.973885	+	0.227043i	$0.0729057\pi$
$620$	55.9041	−	50.3363i	2.24516	−	2.02155i
$621$	0.141932	−	4.11806i	0.00569552	−	0.165252i
$622$	−20.6515	+	28.4244i	−0.828050	+	1.13971i
$623$	7.19539	−	20.4989i	0.288277	−	0.821272i
$624$	0.153263	−	0.406500i	0.00613544	−	0.0162730i
$625$	−5.88190	−	55.9626i	−0.235276	−	2.23850i
$626$	17.0362			0.680905
$627$	−14.2152	−	28.0462i	−0.567701	−	1.12006i
$628$	30.5102			1.21749
$629$	−12.2495	+	8.89979i	−0.488420	+	0.354858i
$630$	−0.869486	+	75.7395i	−0.0346412	+	3.01753i
$631$	0.652065	−	2.00685i	0.0259583	−	0.0798914i	−0.937238	−	0.348690i	$-0.886627\pi$
$631$	0.652065	−	2.00685i	0.0259583	−	0.0798914i	0.963196	+	0.268799i	$0.0866266\pi$
$632$	−0.710734	+	0.978242i	−0.0282715	+	0.0389124i
$633$	−1.80261	−	6.57030i	−0.0716473	−	0.261146i
$634$	−63.1013	−	20.5029i	−2.50607	−	0.814273i
$635$	84.6971	+	18.0029i	3.36110	+	0.714424i
$636$	−30.6092	−	59.1977i	−1.21373	−	2.34734i
$637$	−1.90956	−	1.22514i	−0.0756595	−	0.0485418i
$638$	3.75051	+	11.8689i	0.148484	+	0.469896i
$639$	27.4623	+	29.7773i	1.08639	+	1.17797i
$640$	80.3105	−	8.44098i	3.17455	−	0.333659i
$641$	13.8810	+	12.4985i	0.548265	+	0.493660i	0.896074	−	0.443905i	$-0.146407\pi$
$641$	13.8810	+	12.4985i	0.548265	+	0.493660i	−0.347808	+	0.937566i	$0.613074\pi$
$642$	37.8456	+	57.5224i	1.49365	+	2.27023i
$643$	0.932191	−	8.86920i	0.0367620	−	0.349767i	−0.960644	−	0.277783i	$-0.910400\pi$
$643$	0.932191	−	8.86920i	0.0367620	−	0.349767i	0.997406	−	0.0719839i	$-0.0229330\pi$
$644$	0.912333	−	7.08093i	0.0359510	−	0.279028i
$645$	21.5366	+	32.7340i	0.848002	+	1.28890i
$646$	71.3150	−	23.1716i	2.80585	−	0.911676i
$647$	−43.6146	+	4.58408i	−1.71467	+	0.180219i	−0.910311	−	0.413926i	$-0.864157\pi$
$647$	−43.6146	+	4.58408i	−1.71467	+	0.180219i	−0.804358	+	0.594145i	$0.797491\pi$
$648$	2.36998	−	29.2521i	0.0931018	−	1.14913i
$649$	6.08998	+	29.8367i	0.239053	+	1.17119i
$650$	−7.73482	−	4.46570i	−0.303384	−	0.175159i
$651$	10.8171	+	22.1781i	0.423955	+	0.869227i
$652$	−37.3016	+	41.4276i	−1.46084	+	1.62243i
$653$	−30.1444	+	27.1421i	−1.17964	+	1.06215i	−0.182765	+	0.983157i	$0.558505\pi$
$653$	−30.1444	+	27.1421i	−1.17964	+	1.06215i	−0.996875	+	0.0789956i	$0.974829\pi$
$654$	1.72950	−	1.75028i	0.0676289	−	0.0684412i
$655$	−27.3207	−	2.87152i	−1.06751	−	0.112200i
$656$	−3.13860	+	0.667130i	−0.122542	+	0.0260471i
$657$	−6.35242	−	10.7055i	−0.247831	−	0.417661i
$658$	1.48377	+	18.2100i	0.0578436	+	0.709899i
$659$	−16.9951	+	29.4364i	−0.662035	+	1.14668i	0.318046	+	0.948075i	$0.396973\pi$
$659$	−16.9951	+	29.4364i	−0.662035	+	1.14668i	−0.980080	+	0.198602i	$0.936360\pi$
$660$	−77.4761	−	20.9363i	−3.01575	−	0.814943i
$661$	−42.0828			−1.63683			−0.818416	−	0.574627i	$-0.805147\pi$
$661$	−42.0828			−1.63683			−0.818416	+	0.574627i	$0.805147\pi$
$662$	1.41731	−	1.02974i	0.0550854	−	0.0400219i
$663$	2.09751	+	2.55883i	0.0814607	+	0.0993768i
$664$	14.1303	+	15.6933i	0.548363	+	0.609019i
$665$	−22.9038	−	54.8655i	−0.888171	−	2.12759i
$666$	−10.7020	−	14.3662i	−0.414696	−	0.556681i
$667$	−0.266206	−	1.25240i	−0.0103075	−	0.0484931i
$668$	−1.67774	+	1.86332i	−0.0649136	+	0.0720939i
$669$	−9.30668	+	4.81218i	−0.359817	+	0.186050i
$670$	117.029	+	67.5666i	4.52122	+	2.61033i
$671$	−13.3610	−	1.51375i	−0.515796	−	0.0584375i
$672$	−3.75825	+	21.3146i	−0.144978	+	0.822230i
$673$	−46.4079	+	4.87767i	−1.78889	+	0.188020i	−0.940145	−	0.340775i	$-0.889310\pi$
$673$	−46.4079	+	4.87767i	−1.78889	+	0.188020i	−0.848749	+	0.528796i	$0.822644\pi$
$674$	19.7962	+	17.8246i	0.762520	+	0.686576i
$675$	−59.7786	−	14.8756i	−2.30088	−	0.572563i
$676$	40.0864	−	17.8476i	1.54179	−	0.686447i
$677$	10.6664	+	7.74958i	0.409942	+	0.297841i	0.773578	−	0.633701i	$-0.218465\pi$
$677$	10.6664	+	7.74958i	0.409942	+	0.297841i	−0.363636	+	0.931541i	$0.618465\pi$
$678$	22.3481	−	14.7035i	0.858275	−	0.564683i
$679$	6.64222	+	6.26846i	0.254905	+	0.240561i
$680$	32.0931	−	72.0823i	1.23071	−	2.76423i
$681$	4.68186	−	5.85270i	0.179409	−	0.224276i
$682$	−40.6725	+	8.30167i	−1.55743	+	0.317887i
$683$	−34.1444	−	19.7133i	−1.30650	−	0.754308i	−0.324990	−	0.945717i	$-0.605361\pi$
$683$	−34.1444	−	19.7133i	−1.30650	−	0.754308i	−0.981510	+	0.191409i	$0.938694\pi$
$684$	17.9002	+	52.9325i	0.684432	+	2.02393i
$685$	15.4294	+	47.4868i	0.589527	+	1.81438i
$686$	−39.9069	−	16.1439i	−1.52365	−	0.616378i
$687$	17.1966	+	16.9925i	0.656091	+	0.648305i
$688$	−1.73442	−	3.89557i	−0.0661241	−	0.148517i
$689$	−1.13246	+	3.48537i	−0.0431434	+	0.132782i
$690$	12.2644	+	4.62407i	0.466899	+	0.176035i
$691$	−19.7033	+	14.3153i	−0.749548	+	0.544579i	−0.895687	−	0.444686i	$-0.853315\pi$
$691$	−19.7033	+	14.3153i	−0.749548	+	0.544579i	0.146139	+	0.989264i	$0.453315\pi$
$692$	12.0169			0.456815
$693$	13.6062	−	22.5360i	0.516855	−	0.856073i
$694$	59.0986			2.24335
$695$	−12.7230	+	9.24377i	−0.482610	+	0.350636i
$696$	−1.48033	−	8.99845i	−0.0561117	−	0.341085i
$697$	7.55166	−	23.2416i	0.286039	−	0.880339i
$698$	16.4042	+	36.8445i	0.620910	+	1.39459i
$699$	13.4389	−	3.68706i	0.508306	−	0.139457i
$700$	−100.711	−	35.3509i	−3.80652	−	1.33614i
$701$	0.0931267	+	0.286615i	0.00351735	+	0.0108253i	0.952800	−	0.303599i	$-0.0981884\pi$
$701$	0.0931267	+	0.286615i	0.00351735	+	0.0108253i	−0.949282	+	0.314425i	$0.898188\pi$
$702$	−2.99763	+	2.51764i	−0.113138	+	0.0950220i
$703$	12.1776	+	7.03076i	0.459288	+	0.265170i
$704$	−37.8140	−	17.2040i	−1.42517	−	0.648401i
$705$	−20.8851	−	3.18019i	−0.786577	−	0.119773i
$706$	8.52642	−	19.1507i	0.320896	−	0.720744i
$707$	−19.6818	+	5.88920i	−0.740212	+	0.221486i
$708$	−3.15476	−	54.0240i	−0.118563	−	2.03035i
$709$	29.3377	+	21.3151i	1.10180	+	0.800504i	0.981353	−	0.192215i	$-0.0615672\pi$
$709$	29.3377	+	21.3151i	1.10180	+	0.800504i	0.120447	+	0.992720i	$0.461567\pi$
$710$	−117.713	+	52.4093i	−4.41770	+	1.96689i
$711$	1.01078	−	0.464567i	0.0379074	−	0.0174226i
$712$	−19.8986	−	17.9167i	−0.745730	−	0.671458i
$713$	4.24656	−	0.446332i	0.159035	−	0.0167153i
$714$	48.0921	+	40.3537i	1.79980	+	1.51020i
$715$	2.17562	+	3.83973i	0.0813635	+	0.143598i
$716$	9.32084	+	5.38139i	0.348336	+	0.201112i
$717$	−0.349621	+	7.53105i	−0.0130568	+	0.281252i
$718$	−22.7722	+	25.2911i	−0.849850	+	0.943854i
$719$	−7.32452	−	34.4591i	−0.273158	−	1.28511i	−0.874072	−	0.485796i	$-0.838530\pi$
$719$	−7.32452	−	34.4591i	−0.273158	−	1.28511i	0.600914	−	0.799314i	$-0.294803\pi$
$720$	8.75301	+	3.77254i	0.326205	+	0.140594i
$721$	−40.7223	−	5.24682i	−1.51658	−	0.195402i
$722$	−17.0455	−	18.9309i	−0.634368	−	0.704537i
$723$	4.17168	−	11.0646i	0.155146	−	0.411495i
$724$	−15.8891	+	11.5441i	−0.590514	+	0.429034i
$725$	−19.1417			−0.710905
$726$	30.9932	+	31.6333i	1.15027	+	1.17402i
$727$	−17.9958	+	31.1696i	−0.667427	+	1.15602i	0.311195	+	0.950346i	$0.399271\pi$
$727$	−17.9958	+	31.1696i	−0.667427	+	1.15602i	−0.978621	+	0.205671i	$0.934062\pi$
$728$	−2.30010	+	1.59019i	−0.0852475	+	0.0589363i
$729$	−15.0779	+	22.3977i	−0.558439	+	0.829546i
$730$	38.7324	−	8.23283i	1.43355	−	0.304711i
$731$	32.2986	+	3.39471i	1.19461	+	0.125558i
$732$	23.1180	+	6.04679i	0.854467	+	0.223496i
$733$	−8.41185	+	7.57406i	−0.310699	+	0.279754i	−0.809696	−	0.586849i	$-0.800368\pi$
$733$	−8.41185	+	7.57406i	−0.310699	+	0.279754i	0.498998	+	0.866603i	$0.333702\pi$
$734$	40.0267	−	44.4542i	1.47741	−	1.64083i
$735$	28.7933	−	40.6038i	1.06206	−	1.49769i
$736$	3.24352	+	1.87264i	0.119558	+	0.0690266i
$737$	−23.1527	−	40.8620i	−0.852839	−	1.50517i
$738$	27.6030	+	8.60581i	1.01608	+	0.316784i
$739$	−47.9343	+	5.03810i	−1.76329	+	0.185329i	−0.930014	−	0.367524i	$-0.880205\pi$
$739$	−47.9343	+	5.03810i	−1.76329	+	0.185329i	−0.833278	+	0.552854i	$0.813539\pi$
$740$	34.1340	−	11.0908i	1.25479	−	0.407707i
$741$	1.37862	−	2.74609i	0.0506447	−	0.100880i
$742$	−8.88580	+	68.9657i	−0.326208	+	2.53181i
$743$	−4.29200	+	40.8356i	−0.157458	+	1.49811i	0.575479	+	0.817817i	$0.304816\pi$
$743$	−4.29200	+	40.8356i	−0.157458	+	1.49811i	−0.732937	+	0.680297i	$0.761851\pi$
$744$	30.3607	−	1.77293i	1.11308	−	0.0649986i
$745$	−8.28095	−	7.45620i	−0.303391	−	0.273174i
$746$	−1.01768	+	0.106962i	−0.0372599	+	0.00391617i
$747$	−4.26588	−	18.9538i	−0.156080	−	0.693484i
$748$	−54.1289	+	38.6614i	−1.97915	+	1.41360i
$749$	1.05956	−	45.2373i	0.0387156	−	1.65293i
$750$	61.1442	−	95.3957i	2.23267	−	3.48336i
$751$	10.2420	+	2.17701i	0.373737	+	0.0794403i	0.390951	−	0.920412i	$-0.372146\pi$
$751$	10.2420	+	2.17701i	0.373737	+	0.0794403i	−0.0172136	+	0.999852i	$0.505480\pi$
$752$	2.18654	+	0.710451i	0.0797350	+	0.0259075i
$753$	32.6314	+	8.53513i	1.18916	+	0.311037i
$754$	−0.714985	+	0.984092i	−0.0260382	+	0.0358385i
$755$	25.8565	−	79.5780i	0.941013	−	2.89614i
$756$	−29.6407	+	36.1936i	−1.07802	+	1.31635i
$757$	17.0484	−	12.3864i	0.619633	−	0.450190i	−0.233160	−	0.972438i	$-0.574907\pi$
$757$	17.0484	−	12.3864i	0.619633	−	0.450190i	0.852793	+	0.522248i	$0.174907\pi$
$758$	34.4105			1.24985
$759$	−2.85927	−	3.54629i	−0.103785	−	0.128722i
$760$	−73.2774			−2.65805
$761$	3.58658	+	34.1240i	0.130013	+	1.23700i	0.843810	+	0.536642i	$0.180308\pi$
$761$	3.58658	+	34.1240i	0.130013	+	1.23700i	−0.713796	+	0.700353i	$0.753026\pi$
$762$	53.8299	+	65.6690i	1.95005	+	2.37894i
$763$	−1.58914	+	0.299072i	−0.0575307	+	0.0108271i
$764$	14.6353	−	20.1438i	0.529487	−	0.728777i
$765$	−58.2140	+	43.3661i	−2.10473	+	1.56790i
$766$	29.5290	−	26.5880i	1.06693	−	0.960664i
$767$	−1.99124	+	2.21150i	−0.0718996	+	0.0798526i
$768$	30.1385	+	19.3173i	1.08753	+	0.697055i
$769$	32.0044	−	18.4777i	1.15411	−	0.666325i	0.204223	−	0.978924i	$-0.434533\pi$
$769$	32.0044	−	18.4777i	1.15411	−	0.666325i	0.949885	+	0.312600i	$0.101200\pi$
$770$	54.0436	+	63.9645i	1.94759	+	2.30512i
$771$	4.13587	−	27.1612i	0.148950	−	0.978187i
$772$	4.74545	+	6.53156i	0.170793	+	0.235076i
$773$	−0.582603	+	2.74093i	−0.0209548	+	0.0985845i	−0.987382	−	0.158355i	$-0.949381\pi$
$773$	−0.582603	+	2.74093i	−0.0209548	+	0.0985845i	0.966427	+	0.256940i	$0.0827142\pi$
$774$	−3.55995	+	38.2592i	−0.127960	+	1.37520i
$775$	6.67268	−	63.4863i	0.239690	−	2.28050i
$776$	10.2833	−	4.57842i	0.369149	−	0.164356i
$777$	0.410914	+	11.7655i	0.0147415	+	0.422086i
$778$	−25.7477	−	23.1833i	−0.923098	−	0.831161i
$779$	−22.5707	+	2.37228i	−0.808680	+	0.0849957i
$780$	−2.85427	−	7.30498i	−0.102199	−	0.261560i
$781$	44.4981	+	5.04145i	1.59227	+	0.180397i
$782$	9.40822	−	5.43184i	0.336437	−	0.194242i
$783$	−2.86590	+	7.88514i	−0.102419	+	0.281792i
$784$	−3.80923	+	3.85155i	−0.136044	+	0.137555i
$785$	27.3551	−	24.6307i	0.976346	−	0.879106i
$786$	−19.1622	−	18.9348i	−0.683493	−	0.675381i
$787$	7.09772	−	9.76917i	0.253006	−	0.348233i	−0.663555	−	0.748127i	$-0.730953\pi$
$787$	7.09772	−	9.76917i	0.253006	−	0.348233i	0.916561	+	0.399894i	$0.130953\pi$
$788$	14.3933	−	44.2979i	0.512739	−	1.57805i
$789$	−2.73831	−	1.03243i	−0.0974865	−	0.0367554i
$790$	0.369886	+	3.51923i	0.0131600	+	0.125209i
$791$	−17.5752	−	0.411652i	−0.624903	−	0.0146367i
$792$	−19.1717	−	26.1754i	−0.681236	−	0.930102i
$793$	−0.657019	−	1.13799i	−0.0233314	−	0.0404112i
$794$	−13.3339	−	5.93665i	−0.473204	−	0.210684i
$795$	−75.2338	−	28.3654i	−2.66827	−	1.00602i
$796$	−14.4352	−	16.0319i	−0.511641	−	0.568235i
$797$	−30.7206	−	3.22887i	−1.08818	−	0.114372i	−0.456591	−	0.889676i	$-0.650930\pi$
$797$	−30.7206	−	3.22887i	−1.08818	−	0.114372i	−0.631588	+	0.775304i	$0.717597\pi$
$798$	16.0702	−	56.0443i	0.568877	−	1.98395i
$799$	−13.0123	+	11.7163i	−0.460341	+	0.414493i
$800$	37.4661	−	41.6103i	1.32463	−	1.47115i
$801$	7.89145	+	23.3357i	0.278831	+	0.824527i
$802$	−16.8114	−	9.70608i	−0.593632	−	0.342734i
$803$	−13.0537	−	4.35855i	−0.460656	−	0.153810i
$804$	30.3747	+	77.7387i	1.07123	+	2.74163i
$805$	−4.89839	−	7.08520i	−0.172646	−	0.249721i
$806$	−3.01465	−	2.71440i	−0.106186	−	0.0956107i
$807$	0.598557	+	0.300493i	0.0210702	+	0.0105779i
$808$	−2.64671	+	25.1818i	−0.0931111	+	0.885893i
$809$	22.6000	−	10.0622i	0.794574	−	0.353767i	0.0310263	−	0.999519i	$-0.490122\pi$
$809$	22.6000	−	10.0622i	0.794574	−	0.353767i	0.763548	+	0.645751i	$0.223456\pi$
$810$	−52.1271	−	68.2583i	−1.83156	−	2.39835i
$811$	−45.8166	+	14.8867i	−1.60884	+	0.522743i	−0.969271	−	0.245994i	$-0.920886\pi$
$811$	−45.8166	+	14.8867i	−1.60884	+	0.522743i	−0.639566	+	0.768737i	$0.720886\pi$
$812$	−6.22196	+	13.1379i	−0.218348	+	0.461049i
$813$	−39.9217	−	31.9353i	−1.40011	−	1.12002i
$814$	−19.3383	−	4.27438i	−0.677806	−	0.149817i
$815$			67.2568i			2.35590i
$816$	7.01735	−	3.62844i	0.245656	−	0.127021i
$817$	−9.32014	−	28.6844i	−0.326070	−	1.00354i
$818$	5.17991	+	1.68305i	0.181111	+	0.0588466i
$819$	2.56139	−	0.239519i	0.0895021	−	0.00836947i
$820$	−34.0486	+	46.8638i	−1.18903	+	1.63656i
$821$	−10.1265	+	31.1661i	−0.353416	+	1.08770i	0.603506	+	0.797358i	$0.293770\pi$
$821$	−10.1265	+	31.1661i	−0.353416	+	1.08770i	−0.956922	+	0.290345i	$0.906230\pi$
$822$	−17.2738	+	45.8153i	−0.602493	+	1.59799i
$823$	−4.06920	+	2.95645i	−0.141844	+	0.103055i	−0.656444	−	0.754375i	$-0.727940\pi$
$823$	−4.06920	+	2.95645i	−0.141844	+	0.103055i	0.514601	+	0.857430i	$0.327940\pi$
$824$	−25.3026	+	43.8253i	−0.881457	+	1.52673i
$825$	−60.7460	+	30.7892i	−2.11491	+	1.07194i
$826$	−29.3698	+	48.2257i	−1.02191	+	1.67799i
$827$	10.6362	−	7.72762i	0.369856	−	0.268716i	−0.387296	−	0.921956i	$-0.626591\pi$
$827$	10.6362	−	7.72762i	0.369856	−	0.268716i	0.757151	+	0.653240i	$0.226591\pi$
$828$	4.13110	+	6.96199i	0.143566	+	0.241946i
$829$	32.7706	+	36.3954i	1.13817	+	1.26406i	0.959980	+	0.280069i	$0.0903572\pi$
$829$	32.7706	+	36.3954i	1.13817	+	1.26406i	0.178189	+	0.983996i	$0.442976\pi$
$830$	61.4612	+	6.45983i	2.13335	+	0.224224i
$831$	−0.619393	−	2.25762i	−0.0214865	−	0.0783158i
$832$	−0.844079	−	3.97108i	−0.0292632	−	0.137672i
$833$	−10.8980	−	39.7912i	−0.377592	−	1.37868i
$834$	−15.4053	−	0.715172i	−0.533441	−	0.0247644i
$835$			3.02506i			0.104686i
$836$	53.2466	+	31.3194i	1.84157	+	1.08320i
$837$	−25.1532	−	12.2539i	−0.869421	−	0.423556i
$838$	−5.07587	+	11.4006i	−0.175343	+	0.393827i
$839$	−7.30130	+	34.3499i	−0.252069	+	1.18589i	0.651904	+	0.758301i	$0.273970\pi$
$839$	−7.30130	+	34.3499i	−0.252069	+	1.18589i	−0.903973	+	0.427589i	$0.859363\pi$
$840$	−32.5107	−	52.0274i	−1.12172	−	1.79512i
$841$	2.75882	−	26.2484i	0.0951317	−	0.905118i
$842$	67.0853	−	29.8683i	2.31191	−	1.02933i
$843$	5.04057	−	10.0404i	0.173606	−	0.345809i
$844$	9.94729	+	8.95658i	0.342400	+	0.308298i
$845$	21.5328	−	48.3635i	0.740751	−	1.66375i
$846$	−14.0449	−	15.2289i	−0.482875	−	0.523579i
$847$	−4.91893	−	28.6846i	−0.169016	−	0.985613i
$848$	7.57782	+	4.37505i	0.260223	+	0.150240i
$849$	−7.23812	+	11.2927i	−0.248412	+	0.387566i
$850$	−50.1882	−	154.463i	−1.72144	−	5.29805i
$851$	1.93750	+	0.629531i	0.0664165	+	0.0215800i
$852$	−76.9933	−	20.1385i	−2.63775	−	0.689933i
$853$	−22.0203	−	49.4583i	−0.753960	−	1.69342i	−0.719976	−	0.693999i	$-0.755847\pi$
$853$	−22.0203	−	49.4583i	−0.753960	−	1.69342i	−0.0339837	−	0.999422i	$-0.510819\pi$
$854$	−16.2450	−	18.9144i	−0.555892	−	0.647238i
$855$	58.7812	+	33.0080i	2.01027	+	1.12885i
$856$	−50.9487	−	22.6838i	−1.74139	−	0.775316i
$857$	−13.6068	−	23.5677i	−0.464800	−	0.805056i	0.534393	−	0.845236i	$-0.320540\pi$
$857$	−13.6068	−	23.5677i	−0.464800	−	0.805056i	−0.999192	+	0.0401798i	$0.987207\pi$
$858$	−0.686099	+	4.27305i	−0.0234230	+	0.145880i
$859$	6.24537	−	10.8173i	0.213089	−	0.369082i	−0.739590	−	0.673057i	$-0.764981\pi$
$859$	6.24537	−	10.8173i	0.213089	−	0.369082i	0.952680	+	0.303976i	$0.0983141\pi$
$860$	−70.3265	−	31.3114i	−2.39811	−	1.06771i
$861$	−11.6982	−	14.9729i	−0.398673	−	0.510274i
$862$	39.3379	+	43.6892i	1.33985	+	1.48806i
$863$	−15.2079	−	1.59841i	−0.517683	−	0.0544107i	−0.157915	−	0.987453i	$-0.550477\pi$
$863$	−15.2079	−	1.59841i	−0.517683	−	0.0544107i	−0.359768	+	0.933042i	$0.617144\pi$
$864$	−11.5313	−	21.6635i	−0.392303	−	0.737007i
$865$	10.7743	−	9.70118i	0.366336	−	0.329850i
$866$	6.72446	+	20.6958i	0.228506	+	0.703271i
$867$	−1.42466	+	30.6880i	−0.0483839	+	1.04222i
$868$	−41.4047	−	25.2158i	−1.40537	−	0.855880i
$869$	0.509300	−	1.11943i	0.0172768	−	0.0379741i
$870$	−20.8401	−	16.6710i	−0.706546	−	0.565200i
$871$	1.86677	−	4.19283i	0.0632530	−	0.142069i
$872$	−0.414367	+	1.94945i	−0.0140322	+	0.0660165i
$873$	−10.3114	−	0.959455i	−0.348987	−	0.0324726i
$874$	−8.16217	−	5.93016i	−0.276089	−	0.200591i
$875$	−68.7158	+	28.6856i	−2.32302	+	0.969752i
$876$	21.8570	+	10.9728i	0.738478	+	0.370738i
$877$	−7.37235	+	34.6842i	−0.248947	+	1.17120i	0.659009	+	0.752135i	$0.270976\pi$
$877$	−7.37235	+	34.6842i	−0.248947	+	1.17120i	−0.907956	+	0.419067i	$0.862357\pi$
$878$	40.5025	+	55.7469i	1.36689	+	1.88137i
$879$	−14.3194	+	17.9004i	−0.482982	+	0.603767i
$880$	10.0476	−	3.17499i	0.338706	−	0.107029i
$881$			37.0844i			1.24940i	0.780863	+	0.624702i	$0.214780\pi$
$881$			37.0844i			1.24940i	−0.780863	+	0.624702i	$0.785220\pi$
$882$	46.9216	−	13.4550i	1.57993	−	0.453054i
$883$	0.969812	+	2.98478i	0.0326368	+	0.100446i	0.966048	−	0.258363i	$-0.0831831\pi$
$883$	0.969812	+	2.98478i	0.0326368	+	0.100446i	−0.933411	+	0.358809i	$0.883183\pi$
$884$	−6.18222	−	2.00873i	−0.207931	−	0.0675607i
$885$	−46.4417	−	45.8906i	−1.56112	−	1.54259i
$886$	−47.9579	+	66.0084i	−1.61118	+	2.21759i
$887$	−12.1762	−	13.5230i	−0.408836	−	0.454058i	0.503199	−	0.864170i	$-0.332156\pi$
$887$	−12.1762	−	13.5230i	−0.408836	−	0.454058i	−0.912035	+	0.410112i	$0.865490\pi$
$888$	13.5769	+	5.11891i	0.455611	+	0.171779i
$889$	−4.53176	−	55.6171i	−0.151990	−	1.86534i
$890$	−78.3597			−2.62662
$891$	3.58824	+	29.6332i	0.120210	+	0.992748i
$892$	10.2920	−	17.8263i	0.344603	−	0.596870i
$893$	14.8553	+	6.61400i	0.497113	+	0.221329i
$894$	−1.77380	−	10.7824i	−0.0593248	−	0.360616i
$895$	12.7013	−	2.69975i	0.424558	−	0.0902426i
$896$	−20.0477	−	48.0237i	−0.669745	−	1.60436i
$897$	0.112649	−	0.430680i	0.00376125	−	0.0143800i
$898$	24.0019	+	7.79869i	0.800953	+	0.260246i
$899$	−8.50411	−	1.80760i	−0.283628	−	0.0602870i
$900$	114.648	−	38.7706i	3.82161	−	1.29235i
$901$	−57.7128	+	33.3205i	−1.92269	+	1.11007i
$902$	29.3057	−	12.7645i	0.975774	−	0.425012i
$903$	16.2311	−	19.3437i	0.540138	−	0.643717i
$904$	−8.81292	+	19.7942i	−0.293113	+	0.658344i
$905$	−4.92653	+	23.1775i	−0.163763	+	0.770446i
$906$	68.5472	−	45.0991i	2.27733	−	1.49832i
$907$	−4.85817	+	46.2224i	−0.161313	+	1.53479i	0.551941	+	0.833883i	$0.313887\pi$
$907$	−4.85817	+	46.2224i	−0.161313	+	1.53479i	−0.713254	+	0.700906i	$0.752779\pi$
$908$	−1.53918	+	14.6443i	−0.0510794	+	0.485988i
$909$	13.4663	−	19.0080i	0.446650	−	0.630454i
$910$	−1.88835	+	7.96238i	−0.0625983	+	0.263950i
$911$	−30.2148	+	3.17570i	−1.00106	+	0.105216i	−0.590855	−	0.806778i	$-0.701209\pi$
$911$	−30.2148	+	3.17570i	−1.00106	+	0.105216i	−0.410205	+	0.911993i	$0.634543\pi$
$912$	−5.72906	−	4.58295i	−0.189708	−	0.151756i
$913$	−17.2736	−	12.7649i	−0.571674	−	0.422458i
$914$		−	62.7282i		−	2.07487i
$915$	25.6089	−	13.2415i	0.846604	−	0.437752i
$916$	−46.4592	−	9.87521i	−1.53506	−	0.326286i
$917$	3.27427	+	17.3980i	0.108126	+	0.574534i
$918$	−71.1430	−	2.45199i	−2.34807	−	0.0809277i
$919$	49.1451	+	5.16536i	1.62115	+	0.170390i	0.871139	−	0.491037i	$-0.163382\pi$
$919$	49.1451	+	5.16536i	1.62115	+	0.170390i	0.750010	+	0.661427i	$0.230049\pi$
$920$	−10.3843	+	2.20725i	−0.342360	+	0.0727708i
$921$	9.55123	+	11.6519i	0.314724	+	0.383942i
$922$	−1.31361	−	12.4981i	−0.0432613	−	0.411604i
$923$	2.18817	+	3.79001i	0.0720244	+	0.124750i
$924$	1.38675	+	51.7008i	0.0456207	+	1.70083i
$925$	15.2281	−	26.3759i	0.500698	−	0.867235i
$926$	85.9182	+	38.2532i	2.82345	+	1.25708i
$927$	40.0383	−	23.7579i	1.31503	−	0.780312i
$928$	−5.10267	−	5.66709i	−0.167503	−	0.186031i
$929$	−18.2406	+	25.1060i	−0.598454	+	0.823701i	−0.995566	−	0.0940695i	$-0.970012\pi$
$929$	−18.2406	+	25.1060i	−0.598454	+	0.823701i	0.397112	+	0.917770i	$0.370012\pi$
$930$	62.5566	−	63.3079i	2.05131	−	2.07595i
$931$	−29.6424	+	24.2763i	−0.971490	+	0.795623i
$932$	−18.3198	+	20.3462i	−0.600085	+	0.666462i
$933$	−14.1277	+	22.0417i	−0.462520	+	0.721612i
$934$	−13.7180	+	7.92007i	−0.448865	+	0.259153i
$935$	−17.3203	+	78.3613i	−0.566436	+	2.56269i
$936$	0.943724	−	3.02698i	0.0308466	−	0.0989399i
$937$	−7.97594	−	10.9779i	−0.260562	−	0.358633i	0.658613	−	0.752482i	$-0.271143\pi$
$937$	−7.97594	−	10.9779i	−0.260562	−	0.358633i	−0.919175	+	0.393848i	$0.871143\pi$
$938$	20.0956	−	84.7347i	0.656146	−	2.76668i
$939$	12.6731	−	0.740050i	0.413570	−	0.0241506i
$940$	37.9167	−	16.8816i	1.23671	−	0.550617i
$941$	−2.31807	−	1.68418i	−0.0755669	−	0.0549025i	0.549360	−	0.835585i	$-0.314871\pi$
$941$	−2.31807	−	1.68418i	−0.0755669	−	0.0549025i	−0.624927	+	0.780683i	$0.714871\pi$
$942$	36.0356	−	2.10431i	1.17410	−	0.0685622i
$943$	−3.12709	+	1.01605i	−0.101832	+	0.0330872i
$944$	4.17642	+	5.74834i	0.135931	+	0.187093i
$945$	2.64330	+	56.3796i	0.0859866	+	1.83403i
$946$	24.6900	+	34.5679i	0.802741	+	1.12390i
$947$			17.9099i			0.581992i	0.956724	+	0.290996i	$0.0939866\pi$
$947$			17.9099i			0.581992i	−0.956724	+	0.290996i	$0.906013\pi$
$948$	−1.17937	+	1.84003i	−0.0383043	+	0.0597614i
$949$	−0.415592	−	1.27906i	−0.0134907	−	0.0415201i
$950$	−112.089	+	100.926i	−3.63665	+	3.27446i
$951$	−47.8311	−	12.5108i	−1.55103	−	0.405689i
$952$	−50.4318	−	6.49782i	−1.63450	−	0.210596i
$953$	3.02478	−	9.30933i	0.0979824	−	0.301559i	−0.890037	−	0.455888i	$-0.849322\pi$
$953$	3.02478	−	9.30933i	0.0979824	−	0.301559i	0.988019	+	0.154329i	$0.0493217\pi$
$954$	−40.2355	−	67.8073i	−1.30267	−	2.19534i
$955$	−3.14006	−	29.8757i	−0.101610	−	0.966755i
$956$	−7.40594	−	12.8275i	−0.239525	−	0.414870i
$957$	3.30555	+	8.66626i	0.106853	+	0.280140i
$958$	18.5326	+	32.0994i	0.598760	+	1.03708i
$959$	26.4676	−	18.2985i	0.854684	−	0.590891i
$960$	87.8898	−	14.4587i	2.83663	−	0.466652i
$961$	−0.619861	+	1.90774i	−0.0199955	+	0.0615399i
$962$	−0.787205	−	1.76809i	−0.0253805	−	0.0570055i
$963$	30.6517	+	41.1463i	0.987737	+	1.32592i
$964$	4.83016	+	22.7241i	0.155569	+	0.731895i
$965$	9.52760	+	2.02515i	0.306704	+	0.0651920i
$966$	0.589179	−	8.42621i	0.0189565	−	0.271109i
$967$	6.54105	−	3.77648i	0.210346	−	0.121443i	−0.391126	−	0.920337i	$-0.627914\pi$
$967$	6.54105	−	3.77648i	0.210346	−	0.121443i	0.601472	+	0.798894i	$0.294581\pi$
$968$	−34.9606	−	8.02478i	−1.12368	−	0.257926i
$969$	52.0439	−	20.3350i	1.67189	−	0.653256i
$970$	13.3986	−	30.0938i	0.430205	−	0.966255i
$971$	6.79131	+	6.11492i	0.217943	+	0.196237i	0.770869	−	0.636993i	$-0.219822\pi$
$971$	6.79131	+	6.11492i	0.217943	+	0.196237i	−0.552926	+	0.833230i	$0.686489\pi$
$972$	1.19414	−	53.0323i	0.0383021	−	1.70101i
$973$	8.05743	+	6.14740i	0.258309	+	0.197077i
$974$	−16.9718	+	7.55633i	−0.543812	+	0.242121i
$975$	−5.94784	−	2.98599i	−0.190483	−	0.0956281i
$976$	−2.98391	+	0.969531i	−0.0955127	+	0.0310339i
$977$	5.87946	+	8.09238i	0.188100	+	0.258898i	0.892644	−	0.450763i	$-0.148848\pi$
$977$	5.87946	+	8.09238i	0.188100	+	0.258898i	−0.704543	+	0.709661i	$0.748848\pi$
$978$	−41.1996	+	51.5028i	−1.31742	+	1.64688i
$979$	23.4742	+	13.8074i	0.750238	+	0.441286i
$980$	−4.57862	+	97.6870i	−0.146259	+	3.12050i
$981$	1.21053	−	1.37714i	0.0386492	−	0.0439687i
$982$	7.56807	−	8.40519i	0.241507	−	0.268221i
$983$	−0.608585	−	2.86317i	−0.0194108	−	0.0913208i	0.967376	−	0.253345i	$-0.0815309\pi$
$983$	−0.608585	−	2.86317i	−0.0194108	−	0.0913208i	−0.986787	+	0.162025i	$0.948198\pi$
$984$	−22.5841	+	6.19610i	−0.719953	+	0.197525i
$985$	−22.8565	−	51.3366i	−0.728269	−	1.63572i
$986$	−21.6363	+	4.59893i	−0.689039	+	0.146460i
$987$	1.89480	+	13.4818i	0.0603122	+	0.429129i
$988$	0.631021	+	6.00377i	0.0200755	+	0.191005i
$989$	−2.18480	−	3.78419i	−0.0694727	−	0.120330i
$990$	−92.9510	−	19.3842i	−2.95418	−	0.616072i
$991$	4.03862	−	6.99510i	0.128291	−	0.222207i	−0.794724	−	0.606972i	$-0.792384\pi$
$991$	4.03862	−	6.99510i	0.128291	−	0.222207i	0.923015	+	0.384765i	$0.125718\pi$
$992$	20.5745	−	14.9482i	0.653241	−	0.474607i
$993$	1.00959	−	0.827578i	0.0320384	−	0.0262624i
$994$	54.1030	+	62.9934i	1.71604	+	1.99803i
$995$	−25.8848	−	2.72061i	−0.820605	−	0.0862490i
$996$	27.1504	+	26.8282i	0.860293	+	0.850083i
$997$	1.74274	+	8.19895i	0.0551932	+	0.259663i	0.997089	−	0.0762403i	$-0.0242916\pi$
$997$	1.74274	+	8.19895i	0.0551932	+	0.259663i	−0.941896	+	0.335904i	$0.890958\pi$
$998$	1.37305	+	0.291851i	0.0434631	+	0.00923837i
$999$	−8.58520	−	10.2220i	−0.271624	−	0.323410i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.cb.a.74.9	✓	736
7.2	even	3		693.2.cx.a.569.84	yes	736
9.5	odd	6		693.2.cx.a.536.84	yes	736
11.7	odd	10	inner	693.2.cb.a.326.84	yes	736
63.23	odd	6	inner	693.2.cb.a.338.84	yes	736
77.51	odd	30		693.2.cx.a.128.84	yes	736
99.95	even	30		693.2.cx.a.95.84	yes	736
693.590	even	30	inner	693.2.cb.a.590.9	yes	736

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.cb.a.74.9	✓	736	1.1	even	1	trivial
693.2.cb.a.326.84	yes	736	11.7	odd	10	inner
693.2.cb.a.338.84	yes	736	63.23	odd	6	inner
693.2.cb.a.590.9	yes	736	693.590	even	30	inner
693.2.cx.a.95.84	yes	736	99.95	even	30
693.2.cx.a.128.84	yes	736	77.51	odd	30
693.2.cx.a.536.84	yes	736	9.5	odd	6
693.2.cx.a.569.84	yes	736	7.2	even	3

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.cb (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.88049 + 1.36625i) q^{2} +(-1.33953 + 1.09803i) q^{3} +(1.05155 - 3.23634i) q^{4} +(-1.66986 - 3.75057i) q^{5} +(1.01877 - 3.89497i) q^{6} +(-2.00709 + 1.72383i) q^{7} +(1.00767 + 3.10129i) q^{8} +(0.588658 - 2.94168i) q^{9} +O(q^{10})\)	\(q+(-1.88049 + 1.36625i) q^{2} +(-1.33953 + 1.09803i) q^{3} +(1.05155 - 3.23634i) q^{4} +(-1.66986 - 3.75057i) q^{5} +(1.01877 - 3.89497i) q^{6} +(-2.00709 + 1.72383i) q^{7} +(1.00767 + 3.10129i) q^{8} +(0.588658 - 2.94168i) q^{9} +(8.26440 + 4.77145i) q^{10} +(-1.63501 - 2.88561i) q^{11} +(2.14502 + 5.48979i) q^{12} +(0.131828 - 0.296091i) q^{13} +(1.41912 - 5.98384i) q^{14} +(6.35507 + 3.19043i) q^{15} +(-0.626072 - 0.454868i) q^{16} +(5.38425 - 2.39722i) q^{17} +(2.91212 + 6.33605i) q^{18} +(-4.06761 - 3.66250i) q^{19} +(-13.8941 + 1.46033i) q^{20} +(0.795735 - 4.51296i) q^{21} +(7.01709 + 3.19252i) q^{22} +(-0.686751 - 0.396496i) q^{23} +(-4.75511 - 3.04780i) q^{24} +(-7.93271 + 8.81017i) q^{25} +(0.156634 + 0.736907i) q^{26} +(2.44153 + 4.58682i) q^{27} +(3.46833 + 8.30832i) q^{28} +(1.08039 + 1.19990i) q^{29} +(-16.3096 + 2.68308i) q^{30} +(-4.35625 + 3.16500i) q^{31} -4.72299 q^{32} +(5.35862 + 2.07006i) q^{33} +(-6.84980 + 11.8642i) q^{34} +(9.81692 + 4.64919i) q^{35} +(-8.90127 - 4.99842i) q^{36} +(-2.51287 + 0.534127i) q^{37} +(12.6530 + 1.32988i) q^{38} +(0.148530 + 0.541373i) q^{39} +(9.94894 - 8.95807i) q^{40} +(2.77444 - 3.08133i) q^{41} +(4.66948 + 9.57374i) q^{42} +(4.77204 + 2.75514i) q^{43} +(-11.0581 + 2.25707i) q^{44} +(-12.0160 + 2.70440i) q^{45} +(1.83314 - 0.192671i) q^{46} +(-2.82547 + 0.918052i) q^{47} +(1.33810 - 0.0781389i) q^{48} +(1.05683 - 6.91976i) q^{49} +(2.88044 - 27.4055i) q^{50} +(-4.58012 + 9.12321i) q^{51} +(-0.819627 - 0.737996i) q^{52} +(-11.2450 + 1.18190i) q^{53} +(-10.8580 - 5.28971i) q^{54} +(-8.09246 + 10.9508i) q^{55} +(-7.36857 - 4.48752i) q^{56} +(9.47021 + 0.439644i) q^{57} +(-3.67102 - 0.780300i) q^{58} +(-8.73221 - 2.83727i) q^{59} +(17.0080 - 17.2123i) q^{60} +(2.38304 - 3.27997i) q^{61} +(3.86768 - 11.9035i) q^{62} +(3.88946 + 6.91897i) q^{63} +(10.1337 - 7.36254i) q^{64} -1.33065 q^{65} +(-12.9051 + 3.42852i) q^{66} +14.1606 q^{67} +(-2.09641 - 19.9461i) q^{68} +(1.35529 - 0.222957i) q^{69} +(-24.8126 + 4.66966i) q^{70} +(-7.93658 + 10.9238i) q^{71} +(9.71617 - 1.13864i) q^{72} +(3.08363 - 2.77652i) q^{73} +(3.99567 - 4.43764i) q^{74} +(0.952238 - 20.5118i) q^{75} +(-16.1304 + 9.31288i) q^{76} +(8.25591 + 2.97321i) q^{77} +(-1.01896 - 0.815117i) q^{78} +(0.217957 + 0.299992i) q^{79} +(-0.660562 + 3.10770i) q^{80} +(-8.30696 - 3.46329i) q^{81} +(-1.00742 + 9.58500i) q^{82} +(5.91611 - 2.63402i) q^{83} +(-13.7687 - 7.32087i) q^{84} +(-17.9819 - 16.1910i) q^{85} +(-12.7380 + 1.33882i) q^{86} +(-2.76473 - 0.420989i) q^{87} +(7.30156 - 7.97837i) q^{88} +(-7.11120 + 4.10565i) q^{89} +(18.9010 - 21.5025i) q^{90} +(0.245819 + 0.821532i) q^{91} +(-2.00535 + 1.80562i) q^{92} +(2.36004 - 9.02289i) q^{93} +(4.05898 - 5.58670i) q^{94} +(-6.94411 + 21.3718i) q^{95} +(6.32656 - 5.18598i) q^{96} +(-0.360829 - 3.43306i) q^{97} +(7.46679 + 14.4564i) q^{98} +(-9.45101 + 3.11103i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 736 q - 3 q^{3} - 182 q^{4} - 9 q^{5} - 20 q^{6} - 5 q^{7} - 9 q^{9}+O(q^{10}) \) 736 * q - 3 * q^3 - 182 * q^4 - 9 * q^5 - 20 * q^6 - 5 * q^7 - 9 * q^9	\( 736 q - 3 q^{3} - 182 q^{4} - 9 q^{5} - 20 q^{6} - 5 q^{7} - 9 q^{9} - 18 q^{11} + 20 q^{12} - 10 q^{13} - 9 q^{14} - 24 q^{15} - 158 q^{16} - 5 q^{18} - 10 q^{19} - 36 q^{20} - 4 q^{22} - 42 q^{23} + 35 q^{24} - 73 q^{25} - 24 q^{26} - 21 q^{27} - 20 q^{28} - 30 q^{29} - 35 q^{30} - 6 q^{31} + 40 q^{33} - 20 q^{34} + 75 q^{35} + 36 q^{36} - 6 q^{37} - 15 q^{38} - 45 q^{39} + 45 q^{40} - 30 q^{41} - 71 q^{42} + 39 q^{44} + 36 q^{45} + 10 q^{46} - 52 q^{48} - 3 q^{49} - 105 q^{50} + 75 q^{51} + 5 q^{52} - 36 q^{53} - 30 q^{55} + 30 q^{56} - 60 q^{57} + 29 q^{58} + 121 q^{60} - 10 q^{61} - 105 q^{63} - 148 q^{64} - 25 q^{66} - 16 q^{67} - 15 q^{68} + 105 q^{69} - 33 q^{70} - 125 q^{72} - 10 q^{73} - 15 q^{74} + 19 q^{75} - 15 q^{77} + 48 q^{78} - 10 q^{79} + 108 q^{80} + 59 q^{81} - 10 q^{82} - 30 q^{83} - 100 q^{84} - 10 q^{85} - 33 q^{86} + 8 q^{88} + 30 q^{89} - 180 q^{90} + 16 q^{91} + 72 q^{92} - 2 q^{93} - 10 q^{94} + 45 q^{96} - 6 q^{97} - 10 q^{99}+O(q^{100}) \) 736 * q - 3 * q^3 - 182 * q^4 - 9 * q^5 - 20 * q^6 - 5 * q^7 - 9 * q^9 - 18 * q^11 + 20 * q^12 - 10 * q^13 - 9 * q^14 - 24 * q^15 - 158 * q^16 - 5 * q^18 - 10 * q^19 - 36 * q^20 - 4 * q^22 - 42 * q^23 + 35 * q^24 - 73 * q^25 - 24 * q^26 - 21 * q^27 - 20 * q^28 - 30 * q^29 - 35 * q^30 - 6 * q^31 + 40 * q^33 - 20 * q^34 + 75 * q^35 + 36 * q^36 - 6 * q^37 - 15 * q^38 - 45 * q^39 + 45 * q^40 - 30 * q^41 - 71 * q^42 + 39 * q^44 + 36 * q^45 + 10 * q^46 - 52 * q^48 - 3 * q^49 - 105 * q^50 + 75 * q^51 + 5 * q^52 - 36 * q^53 - 30 * q^55 + 30 * q^56 - 60 * q^57 + 29 * q^58 + 121 * q^60 - 10 * q^61 - 105 * q^63 - 148 * q^64 - 25 * q^66 - 16 * q^67 - 15 * q^68 + 105 * q^69 - 33 * q^70 - 125 * q^72 - 10 * q^73 - 15 * q^74 + 19 * q^75 - 15 * q^77 + 48 * q^78 - 10 * q^79 + 108 * q^80 + 59 * q^81 - 10 * q^82 - 30 * q^83 - 100 * q^84 - 10 * q^85 - 33 * q^86 + 8 * q^88 + 30 * q^89 - 180 * q^90 + 16 * q^91 + 72 * q^92 - 2 * q^93 - 10 * q^94 + 45 * q^96 - 6 * q^97 - 10 * q^99

Introduction

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