LMFDB - Embedded newform 672.2.ch.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(11,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 12, 16]))

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

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

chi := DirichletCharacter("672.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.ch (of order $24$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$124$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	672.11
Dual form			672.2.ch.a.611.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40871 + 0.124645i) q^{2} +(0.277691 + 1.70965i) q^{3} +(1.96893 - 0.351176i) q^{4} +(-0.255599 - 1.94146i) q^{5} +(-0.604284 - 2.37378i) q^{6} +(2.57575 + 0.604593i) q^{7} +(-2.72988 + 0.740122i) q^{8} +(-2.84578 + 0.949506i) q^{9} +O(q^{10})$	\(q+(-1.40871 + 0.124645i) q^{2} +(0.277691 + 1.70965i) q^{3} +(1.96893 - 0.351176i) q^{4} +(-0.255599 - 1.94146i) q^{5} +(-0.604284 - 2.37378i) q^{6} +(2.57575 + 0.604593i) q^{7} +(-2.72988 + 0.740122i) q^{8} +(-2.84578 + 0.949506i) q^{9} +(0.602057 + 2.70310i) q^{10} +(1.79918 - 1.38056i) q^{11} +(1.14714 + 3.26865i) q^{12} +(-1.92877 - 4.65646i) q^{13} +(-3.70384 - 0.530643i) q^{14} +(3.24824 - 0.976110i) q^{15} +(3.75335 - 1.38288i) q^{16} +(1.19495 - 2.06972i) q^{17} +(3.89052 - 1.69229i) q^{18} +(4.99682 + 3.83419i) q^{19} +(-1.18505 - 3.73284i) q^{20} +(-0.318378 + 4.57150i) q^{21} +(-2.36245 + 2.16907i) q^{22} +(3.16226 + 0.847324i) q^{23} +(-2.02341 - 4.46159i) q^{24} +(1.12568 - 0.301625i) q^{25} +(3.29748 + 6.31919i) q^{26} +(-2.41357 - 4.60160i) q^{27} +(5.28378 + 0.285858i) q^{28} +(-2.48556 - 6.00067i) q^{29} +(-4.45416 + 1.77993i) q^{30} +(-9.01077 - 5.20237i) q^{31} +(-5.11501 + 2.41591i) q^{32} +(2.85989 + 2.69260i) q^{33} +(-1.42536 + 3.06458i) q^{34} +(0.515438 - 5.15525i) q^{35} +(-5.26968 + 2.86888i) q^{36} +(1.15771 - 0.152415i) q^{37} +(-7.51698 - 4.77844i) q^{38} +(7.42529 - 4.59057i) q^{39} +(2.13467 + 5.11078i) q^{40} +(4.27010 + 4.27010i) q^{41} +(-0.121311 - 6.47961i) q^{42} +(0.428652 - 1.03486i) q^{43} +(3.05764 - 3.35006i) q^{44} +(2.57081 + 5.28228i) q^{45} +(-4.56032 - 0.799476i) q^{46} +(7.29458 - 4.21153i) q^{47} +(3.40651 + 6.03288i) q^{48} +(6.26893 + 3.11456i) q^{49} +(-1.54816 + 0.565212i) q^{50} +(3.87032 + 1.46820i) q^{51} +(-5.43284 - 8.49089i) q^{52} +(2.31480 + 3.01671i) q^{53} +(3.97358 + 6.18148i) q^{54} +(-3.14018 - 3.14018i) q^{55} +(-7.47894 + 0.255903i) q^{56} +(-5.16754 + 9.60751i) q^{57} +(4.24939 + 8.14340i) q^{58} +(5.48396 + 7.14683i) q^{59} +(6.05276 - 3.06259i) q^{60} +(-0.554859 - 0.425758i) q^{61} +(13.3420 + 6.20549i) q^{62} +(-7.90406 + 0.725151i) q^{63} +(6.90444 - 4.04088i) q^{64} +(-8.54736 + 4.93482i) q^{65} +(-4.36437 - 3.43662i) q^{66} +(1.34586 + 0.177185i) q^{67} +(1.62594 - 4.49477i) q^{68} +(-0.570494 + 5.64163i) q^{69} +(-0.0835285 + 7.32650i) q^{70} +(5.88019 + 5.88019i) q^{71} +(7.06586 - 4.69826i) q^{72} +(2.96588 + 11.0688i) q^{73} +(-1.61188 + 0.359012i) q^{74} +(0.828262 + 1.84075i) q^{75} +(11.1849 + 5.79448i) q^{76} +(5.46892 - 2.46820i) q^{77} +(-9.88790 + 7.39230i) q^{78} +(4.45229 + 7.71159i) q^{79} +(-3.64417 - 6.93353i) q^{80} +(7.19688 - 5.40416i) q^{81} +(-6.54758 - 5.48309i) q^{82} +(-4.92540 - 11.8910i) q^{83} +(0.978541 + 9.11276i) q^{84} +(-4.32372 - 1.79094i) q^{85} +(-0.474857 + 1.51124i) q^{86} +(9.56881 - 5.91576i) q^{87} +(-3.88976 + 5.10038i) q^{88} +(8.46454 + 2.26807i) q^{89} +(-4.27993 - 7.12076i) q^{90} +(-2.15276 - 13.1600i) q^{91} +(6.52382 + 0.557810i) q^{92} +(6.39200 - 16.8499i) q^{93} +(-9.75101 + 6.84206i) q^{94} +(6.16677 - 10.6812i) q^{95} +(-5.55075 - 8.07398i) q^{96} -12.2775 q^{97} +(-9.21932 - 3.60612i) q^{98} +(-3.80922 + 5.63711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9}+O(q^{10}) $ 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9	$ 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} - 32 q^{13} - 32 q^{15} + 24 q^{16} - 4 q^{18} - 8 q^{19} - 8 q^{21} - 32 q^{22} - 44 q^{24} - 8 q^{25} - 16 q^{27} - 16 q^{28} - 36 q^{30} - 8 q^{33} + 64 q^{36} - 8 q^{37} - 4 q^{39} - 72 q^{40} - 68 q^{42} - 32 q^{43} - 4 q^{45} - 8 q^{46} - 16 q^{48} + 20 q^{51} + 16 q^{52} - 92 q^{54} - 32 q^{55} - 16 q^{57} + 24 q^{58} - 20 q^{60} - 8 q^{61} - 128 q^{64} - 20 q^{66} - 72 q^{67} - 16 q^{69} - 16 q^{70} - 4 q^{72} - 8 q^{73} + 16 q^{75} - 32 q^{76} + 136 q^{78} - 16 q^{79} - 48 q^{82} + 124 q^{84} + 48 q^{85} - 4 q^{87} - 8 q^{88} + 128 q^{90} - 64 q^{91} - 28 q^{93} - 64 q^{94} - 72 q^{96} - 64 q^{97} - 16 q^{99}+O(q^{100}) $ 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9 - 8 * q^10 - 4 * q^12 - 32 * q^13 - 32 * q^15 + 24 * q^16 - 4 * q^18 - 8 * q^19 - 8 * q^21 - 32 * q^22 - 44 * q^24 - 8 * q^25 - 16 * q^27 - 16 * q^28 - 36 * q^30 - 8 * q^33 + 64 * q^36 - 8 * q^37 - 4 * q^39 - 72 * q^40 - 68 * q^42 - 32 * q^43 - 4 * q^45 - 8 * q^46 - 16 * q^48 + 20 * q^51 + 16 * q^52 - 92 * q^54 - 32 * q^55 - 16 * q^57 + 24 * q^58 - 20 * q^60 - 8 * q^61 - 128 * q^64 - 20 * q^66 - 72 * q^67 - 16 * q^69 - 16 * q^70 - 4 * q^72 - 8 * q^73 + 16 * q^75 - 32 * q^76 + 136 * q^78 - 16 * q^79 - 48 * q^82 + 124 * q^84 + 48 * q^85 - 4 * q^87 - 8 * q^88 + 128 * q^90 - 64 * q^91 - 28 * q^93 - 64 * q^94 - 72 * q^96 - 64 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.40871	+	0.124645i	−0.996108	+	0.0881371i
$2$	−1.40871	+	0.124645i	−0.996108	+	0.0881371i
$3$	0.277691	+	1.70965i	0.160325	+	0.987064i
$3$	0.277691	+	1.70965i	0.160325	+	0.987064i
$4$	1.96893	−	0.351176i	0.984464	−	0.175588i
$5$	−0.255599	−	1.94146i	−0.114307	−	0.868249i	−0.948500	−	0.316776i	$-0.897400\pi$
$5$	−0.255599	−	1.94146i	−0.114307	−	0.868249i	0.834193	−	0.551472i	$-0.185934\pi$
$6$	−0.604284	−	2.37378i	−0.246698	−	0.969092i
$7$	2.57575	+	0.604593i	0.973540	+	0.228515i
$7$	2.57575	+	0.604593i	0.973540	+	0.228515i
$8$	−2.72988	+	0.740122i	−0.965157	+	0.261673i
$9$	−2.84578	+	0.949506i	−0.948592	+	0.316502i
$10$	0.602057	+	2.70310i	0.190387	+	0.854795i
$11$	1.79918	−	1.38056i	0.542474	−	0.416255i	−0.300841	−	0.953674i	$-0.597267\pi$
$11$	1.79918	−	1.38056i	0.542474	−	0.416255i	0.843315	+	0.537419i	$0.180601\pi$
$12$	1.14714	+	3.26865i	0.331151	+	0.943578i
$13$	−1.92877	−	4.65646i	−0.534944	−	1.29147i	−0.928214	−	0.372047i	$-0.878656\pi$
$13$	−1.92877	−	4.65646i	−0.534944	−	1.29147i	0.393270	−	0.919423i	$-0.371344\pi$
$14$	−3.70384	−	0.530643i	−0.989892	−	0.141820i
$15$	3.24824	−	0.976110i	0.838691	−	0.252030i
$16$	3.75335	−	1.38288i	0.938338	−	0.345720i
$17$	1.19495	−	2.06972i	0.289819	−	0.501981i	−0.683947	−	0.729531i	$-0.739738\pi$
$17$	1.19495	−	2.06972i	0.289819	−	0.501981i	0.973766	+	0.227550i	$0.0730716\pi$
$18$	3.89052	−	1.69229i	0.917005	−	0.398877i
$19$	4.99682	+	3.83419i	1.14635	+	0.879624i	0.994073	−	0.108714i	$-0.0346731\pi$
$19$	4.99682	+	3.83419i	1.14635	+	0.879624i	0.152276	+	0.988338i	$0.451340\pi$
$20$	−1.18505	−	3.73284i	−0.264986	−	0.834689i
$21$	−0.318378	+	4.57150i	−0.0694758	+	0.997584i
$22$	−2.36245	+	2.16907i	−0.503676	+	0.462447i
$23$	3.16226	+	0.847324i	0.659376	+	0.176679i	0.572965	−	0.819580i	$-0.305793\pi$
$23$	3.16226	+	0.847324i	0.659376	+	0.176679i	0.0864118	+	0.996260i	$0.472460\pi$
$24$	−2.02341	−	4.46159i	−0.413027	−	0.910719i
$25$	1.12568	−	0.301625i	0.225136	−	0.0603250i
$26$	3.29748	+	6.31919i	0.646689	+	1.23930i
$27$	−2.41357	−	4.60160i	−0.464491	−	0.885578i
$28$	5.28378	+	0.285858i	0.998540	+	0.0540221i
$29$	−2.48556	−	6.00067i	−0.461557	−	1.11430i	−0.967758	−	0.251882i	$-0.918951\pi$
$29$	−2.48556	−	6.00067i	−0.461557	−	1.11430i	0.506201	−	0.862416i	$-0.331049\pi$
$30$	−4.45416	+	1.77993i	−0.813214	+	0.324969i
$31$	−9.01077	−	5.20237i	−1.61838	−	0.934374i	−0.987339	−	0.158627i	$-0.949293\pi$
$31$	−9.01077	−	5.20237i	−1.61838	−	0.934374i	−0.631044	−	0.775747i	$-0.717373\pi$
$32$	−5.11501	+	2.41591i	−0.904215	+	0.427077i
$33$	2.85989	+	2.69260i	0.497843	+	0.468721i
$34$	−1.42536	+	3.06458i	−0.244448	+	0.525571i
$35$	0.515438	−	5.15525i	0.0871250	−	0.871396i
$36$	−5.26968	+	2.86888i	−0.878280	+	0.478146i
$37$	1.15771	−	0.152415i	0.190326	−	0.0250569i	−0.0347603	−	0.999396i	$-0.511067\pi$
$37$	1.15771	−	0.152415i	0.190326	−	0.0250569i	0.225087	+	0.974339i	$0.427733\pi$
$38$	−7.51698	−	4.77844i	−1.21942	−	0.775165i
$39$	7.42529	−	4.59057i	1.18900	−	0.735079i
$40$	2.13467	+	5.11078i	0.337521	+	0.808085i
$41$	4.27010	+	4.27010i	0.666878	+	0.666878i	0.956992	−	0.290114i	$-0.0936932\pi$
$41$	4.27010	+	4.27010i	0.666878	+	0.666878i	−0.290114	+	0.956992i	$0.593693\pi$
$42$	−0.121311	−	6.47961i	−0.0187187	−	0.999825i
$43$	0.428652	−	1.03486i	0.0653688	−	0.157814i	−0.887819	−	0.460192i	$-0.847780\pi$
$43$	0.428652	−	1.03486i	0.0653688	−	0.157814i	0.953188	+	0.302378i	$0.0977805\pi$
$44$	3.05764	−	3.35006i	0.460957	−	0.505040i
$45$	2.57081	+	5.28228i	0.383233	+	0.787435i
$46$	−4.56032	−	0.799476i	−0.672382	−	0.117876i
$47$	7.29458	−	4.21153i	1.06402	−	0.614315i	0.137482	−	0.990504i	$-0.456099\pi$
$47$	7.29458	−	4.21153i	1.06402	−	0.614315i	0.926543	+	0.376190i	$0.122766\pi$
$48$	3.40651	+	6.03288i	0.491687	+	0.870772i
$49$	6.26893	+	3.11456i	0.895562	+	0.444937i
$50$	−1.54816	+	0.565212i	−0.218943	+	0.0799330i
$51$	3.87032	+	1.46820i	0.541953	+	0.205590i
$52$	−5.43284	−	8.49089i	−0.753400	−	1.17748i
$53$	2.31480	+	3.01671i	0.317963	+	0.414377i	0.924803	−	0.380447i	$-0.124230\pi$
$53$	2.31480	+	3.01671i	0.317963	+	0.414377i	−0.606840	+	0.794824i	$0.707563\pi$
$54$	3.97358	+	6.18148i	0.540736	+	0.841193i
$55$	−3.14018	−	3.14018i	−0.423422	−	0.423422i
$56$	−7.47894	+	0.255903i	−0.999415	+	0.0341965i
$57$	−5.16754	+	9.60751i	−0.684458	+	1.27255i
$58$	4.24939	+	8.14340i	0.557972	+	1.06928i
$59$	5.48396	+	7.14683i	0.713950	+	0.930438i	0.999611	−	0.0278929i	$-0.00887972\pi$
$59$	5.48396	+	7.14683i	0.713950	+	0.930438i	−0.285661	+	0.958331i	$0.592213\pi$
$60$	6.05276	−	3.06259i	0.781407	−	0.395379i
$61$	−0.554859	−	0.425758i	−0.0710424	−	0.0545127i	0.572630	−	0.819814i	$-0.305923\pi$
$61$	−0.554859	−	0.425758i	−0.0710424	−	0.0545127i	−0.643672	+	0.765301i	$0.722590\pi$
$62$	13.3420	+	6.20549i	1.69444	+	0.788098i
$63$	−7.90406	+	0.725151i	−0.995818	+	0.0913605i
$64$	6.90444	−	4.04088i	0.863055	−	0.505110i
$65$	−8.54736	+	4.93482i	−1.06017	+	0.612089i
$66$	−4.36437	−	3.43662i	−0.537217	−	0.423018i
$67$	1.34586	+	0.177185i	0.164422	+	0.0216466i	0.212288	−	0.977207i	$-0.431909\pi$
$67$	1.34586	+	0.177185i	0.164422	+	0.0216466i	−0.0478654	+	0.998854i	$0.515242\pi$
$68$	1.62594	−	4.49477i	0.197174	−	0.545071i
$69$	−0.570494	+	5.64163i	−0.0686794	+	0.679173i
$70$	−0.0835285	+	7.32650i	−0.00998357	+	0.875684i
$71$	5.88019	+	5.88019i	0.697850	+	0.697850i	0.963946	−	0.266097i	$-0.0857341\pi$
$71$	5.88019	+	5.88019i	0.697850	+	0.697850i	−0.266097	+	0.963946i	$0.585734\pi$
$72$	7.06586	−	4.69826i	0.832720	−	0.553695i
$73$	2.96588	+	11.0688i	0.347130	+	1.29551i	0.890104	+	0.455757i	$0.150632\pi$
$73$	2.96588	+	11.0688i	0.347130	+	1.29551i	−0.542974	+	0.839750i	$0.682702\pi$
$74$	−1.61188	+	0.359012i	−0.187377	+	0.0417342i
$75$	0.828262	+	1.84075i	0.0956395	+	0.212552i
$76$	11.1849	+	5.79448i	1.28299	+	0.664673i
$77$	5.46892	−	2.46820i	0.623241	−	0.281278i
$78$	−9.88790	+	7.39230i	−1.11958	+	0.837013i
$79$	4.45229	+	7.71159i	0.500921	+	0.867621i	0.999999	+	0.00106415i	$0.000338728\pi$
$79$	4.45229	+	7.71159i	0.500921	+	0.867621i	−0.499078	+	0.866557i	$0.666328\pi$
$80$	−3.64417	−	6.93353i	−0.407430	−	0.775192i
$81$	7.19688	−	5.40416i	0.799653	−	0.600463i
$82$	−6.54758	−	5.48309i	−0.723060	−	0.605506i
$83$	−4.92540	−	11.8910i	−0.540633	−	1.30520i	−0.924277	−	0.381723i	$-0.875331\pi$
$83$	−4.92540	−	11.8910i	−0.540633	−	1.30520i	0.383644	−	0.923481i	$-0.374669\pi$
$84$	0.978541	+	9.11276i	0.106768	+	0.994284i
$85$	−4.32372	−	1.79094i	−0.468973	−	0.194255i
$86$	−0.474857	+	1.51124i	−0.0512051	+	0.162962i
$87$	9.56881	−	5.91576i	1.02588	−	0.634236i
$88$	−3.88976	+	5.10038i	−0.414650	+	0.543702i
$89$	8.46454	+	2.26807i	0.897240	+	0.240415i	0.677830	−	0.735218i	$-0.262920\pi$
$89$	8.46454	+	2.26807i	0.897240	+	0.240415i	0.219409	+	0.975633i	$0.429587\pi$
$90$	−4.27993	−	7.12076i	−0.451144	−	0.750594i
$91$	−2.15276	−	13.1600i	−0.225670	−	1.37954i
$92$	6.52382	+	0.557810i	0.680155	+	0.0581557i
$93$	6.39200	−	16.8499i	0.662820	−	1.74725i
$94$	−9.75101	+	6.84206i	−1.00574	+	0.705704i
$95$	6.16677	−	10.6812i	0.632697	−	1.09586i
$96$	−5.55075	−	8.07398i	−0.566521	−	0.824047i
$97$	−12.2775			−1.24660			−0.623298	−	0.781984i	$-0.714208\pi$
$97$	−12.2775			−1.24660			−0.623298	+	0.781984i	$0.714208\pi$
$98$	−9.21932	−	3.60612i	−0.931292	−	0.364273i
$99$	−3.80922	+	5.63711i	−0.382841	+	0.566550i
$100$	2.11046	−	0.989189i	0.211046	−	0.0989189i
$101$	2.48375	−	1.90585i	0.247142	−	0.189639i	−0.477761	−	0.878490i	$-0.658551\pi$
$101$	2.48375	−	1.90585i	0.247142	−	0.189639i	0.724903	+	0.688851i	$0.241885\pi$
$102$	−5.63516	−	1.58586i	−0.557964	−	0.157024i
$103$	−11.2972	−	3.02707i	−1.11315	−	0.298267i	−0.345039	−	0.938588i	$-0.612134\pi$
$103$	−11.2972	−	3.02707i	−1.11315	−	0.298267i	−0.768107	+	0.640322i	$0.778801\pi$
$104$	8.71165	+	11.2840i	0.854247	+	1.10649i
$105$	8.95678	−	0.550350i	0.874092	−	0.0537086i
$106$	−3.63691	−	3.96114i	−0.353247	−	0.384740i
$107$	−0.0731021	−	0.555266i	−0.00706705	−	0.0536796i	0.987548	−	0.157318i	$-0.0502848\pi$
$107$	−0.0731021	−	0.555266i	−0.00706705	−	0.0536796i	−0.994615	+	0.103639i	$0.966951\pi$
$108$	−6.36811	−	8.21262i	−0.612771	−	0.790260i
$109$	11.7454	+	1.54632i	1.12501	+	0.148110i	0.669989	−	0.742371i	$-0.266299\pi$
$109$	11.7454	+	1.54632i	1.12501	+	0.148110i	0.455020	+	0.890481i	$0.349632\pi$
$110$	4.81501	+	4.03220i	0.459093	+	0.384455i
$111$	0.582062	+	1.93695i	0.0552469	+	0.183847i
$112$	10.5038	−	1.29270i	0.992512	−	0.122149i
$113$	−13.4003			−1.26060			−0.630298	−	0.776353i	$-0.717067\pi$
$113$	−13.4003			−1.26060			−0.630298	+	0.776353i	$0.717067\pi$
$114$	6.08204	−	14.1783i	0.569635	−	1.32792i
$115$	0.836781	−	6.35598i	0.0780302	−	0.592698i
$116$	−7.00118	−	10.9420i	−0.650044	−	1.01594i
$117$	9.91018	+	11.4199i	0.916197	+	1.05577i
$118$	−8.61612	−	9.38426i	−0.793178	−	0.863891i
$119$	4.32924	−	4.60861i	0.396860	−	0.422471i
$120$	−8.14484	+	5.06875i	−0.743519	+	0.462711i
$121$	−1.51590	+	5.65742i	−0.137809	+	0.514311i
$122$	0.834704	+	0.530609i	0.0755705	+	0.0480391i
$123$	−6.11460	+	8.48613i	−0.551334	+	0.765169i
$124$	−19.5685	−	7.07872i	−1.75730	−	0.635688i
$125$	−4.62020	−	11.1542i	−0.413243	−	0.997658i
$126$	11.0441	−	2.00673i	0.983890	−	0.178773i
$127$			7.15326i			0.634749i	0.948300	+	0.317375i	$0.102801\pi$
$127$			7.15326i			0.634749i	−0.948300	+	0.317375i	$0.897199\pi$
$128$	−9.22268	+	6.55303i	−0.815177	+	0.579212i
$129$	1.88827	+	0.445472i	0.166253	+	0.0392216i
$130$	11.4256	−	8.01711i	1.00210	−	0.703147i
$131$	−9.54755	−	7.32609i	−0.834173	−	0.640084i	0.100759	−	0.994911i	$-0.467873\pi$
$131$	−9.54755	−	7.32609i	−0.834173	−	0.640084i	−0.934932	+	0.354827i	$0.884540\pi$
$132$	6.57649	+	4.29720i	0.572410	+	0.374023i
$133$	10.5524	+	12.8970i	0.915010	+	1.11831i
$134$	−1.91801	−	0.0818489i	−0.165690	−	0.00707067i
$135$	−8.31693	+	5.86201i	−0.715807	+	0.504522i
$136$	−1.73023	+	6.53449i	−0.148366	+	0.560328i
$137$	−15.1651	+	4.06349i	−1.29565	+	0.347167i	−0.839802	−	0.542892i	$-0.817329\pi$
$137$	−15.1651	+	4.06349i	−1.29565	+	0.347167i	−0.455844	+	0.890060i	$0.650662\pi$
$138$	0.100460	−	8.01853i	0.00855176	−	0.682583i
$139$	3.96030	−	9.56100i	0.335908	−	0.810954i	−0.662192	−	0.749334i	$-0.730374\pi$
$139$	3.96030	−	9.56100i	0.335908	−	0.810954i	0.998100	−	0.0616192i	$-0.0196264\pi$
$140$	−0.795542	−	10.3313i	−0.0672356	−	0.873156i
$141$	9.22586	+	11.3016i	0.776958	+	0.951771i
$142$	−9.01641	−	7.55054i	−0.756640	−	0.633627i
$143$	−9.89874	−	5.71504i	−0.827774	−	0.477916i
$144$	−9.36814	+	7.49920i	−0.780678	+	0.624933i
$145$	−11.0148	+	6.35939i	−0.914728	+	0.528119i
$146$	−5.55773	−	15.2231i	−0.459961	−	1.25987i
$147$	−3.58396	+	11.5825i	−0.295600	+	0.955312i
$148$	2.22592	−	0.706655i	0.182970	−	0.0580867i
$149$	−5.29078	+	0.696545i	−0.433438	+	0.0570632i	−0.344089	−	0.938937i	$-0.611812\pi$
$149$	−5.29078	+	0.696545i	−0.433438	+	0.0570632i	−0.0893492	+	0.996000i	$0.528479\pi$
$150$	−1.39622	−	2.48985i	−0.114001	−	0.203295i
$151$	−16.9048	+	4.52962i	−1.37569	+	0.368615i	−0.869554	−	0.493838i	$-0.835594\pi$
$151$	−16.9048	+	4.52962i	−1.37569	+	0.368615i	−0.506137	+	0.862453i	$0.668927\pi$
$152$	−16.4785	−	6.76862i	−1.33658	−	0.549007i
$153$	−1.43536	+	7.02458i	−0.116042	+	0.567903i
$154$	−7.39647	+	4.15865i	−0.596025	+	0.335114i
$155$	−7.79708	+	18.8238i	−0.626276	+	1.51196i
$156$	13.0078	−	11.6461i	1.04145	−	0.932433i
$157$	2.73863	−	20.8020i	0.218567	−	1.66018i	−0.432855	−	0.901463i	$-0.642494\pi$
$157$	2.73863	−	20.8020i	0.218567	−	1.66018i	0.651422	−	0.758716i	$-0.274173\pi$
$158$	−7.23319	−	10.3084i	−0.575442	−	0.820095i
$159$	−4.51471	+	4.79521i	−0.358040	+	0.380285i
$160$	5.99780	+	9.31311i	0.474168	+	0.736266i
$161$	7.63289	+	4.09437i	0.601556	+	0.322682i
$162$	−9.46471	+	8.50995i	−0.743618	+	0.668605i
$163$	4.84724	−	6.31705i	0.379666	−	0.494790i	−0.563961	−	0.825801i	$-0.690723\pi$
$163$	4.84724	−	6.31705i	0.379666	−	0.494790i	0.943627	+	0.331012i	$0.107390\pi$
$164$	9.90709	+	6.90797i	0.773613	+	0.539421i
$165$	4.49659	−	6.24059i	0.350059	−	0.485830i
$166$	8.42061	+	16.1370i	0.653566	+	1.25247i
$167$	−4.04871	−	4.04871i	−0.313298	−	0.313298i	0.532888	−	0.846186i	$-0.321107\pi$
$167$	−4.04871	−	4.04871i	−0.313298	−	0.313298i	−0.846186	+	0.532888i	$0.821107\pi$
$168$	−2.51434	−	12.7153i	−0.193985	−	0.981004i
$169$	−8.77008	+	8.77008i	−0.674622	+	0.674622i
$170$	6.31409	+	1.98399i	0.484269	+	0.152165i
$171$	−17.8604	−	6.16674i	−1.36582	−	0.471583i
$172$	0.480567	−	2.18809i	0.0366429	−	0.166840i
$173$	0.708618	+	0.543742i	0.0538753	+	0.0413399i	0.635348	−	0.772226i	$-0.280857\pi$
$173$	0.708618	+	0.543742i	0.0538753	+	0.0413399i	−0.581473	+	0.813566i	$0.697523\pi$
$174$	−12.7423	+	9.52629i	−0.965992	+	0.722186i
$175$	3.08182	−	0.0963312i	0.232964	−	0.00728195i
$176$	4.84381	−	7.66979i	0.365116	−	0.578132i
$177$	−10.6957	+	11.3602i	−0.803938	+	0.853887i
$178$	−12.2068	−	2.13999i	−0.914937	−	0.160399i
$179$	3.65978	+	0.481820i	0.273545	+	0.0360129i	0.266051	−	0.963959i	$-0.414281\pi$
$179$	3.65978	+	0.481820i	0.273545	+	0.0360129i	0.00749431	+	0.999972i	$0.497614\pi$
$180$	6.91675	+	9.49761i	0.515544	+	0.707910i
$181$	9.67018	+	4.00552i	0.718779	+	0.297728i	0.711932	−	0.702249i	$-0.247820\pi$
$181$	9.67018	+	4.00552i	0.718779	+	0.297728i	0.00684708	+	0.999977i	$0.497820\pi$
$182$	4.67293	+	18.2703i	0.346381	+	1.35428i
$183$	0.573816	−	1.06684i	0.0424177	−	0.0788632i
$184$	−9.25969	+	0.0273671i	−0.682634	+	0.00201753i
$185$	−0.591818	−	2.20869i	−0.0435113	−	0.162386i
$186$	−6.90423	+	24.5333i	−0.506243	+	1.79887i
$187$	−0.707437	−	5.37352i	−0.0517329	−	0.392950i
$188$	12.8835	−	10.8539i	0.939627	−	0.791601i
$189$	−3.43464	−	13.3118i	−0.249833	−	0.968289i
$190$	−7.35584	+	15.8153i	−0.533649	+	1.14736i
$191$	12.1342	+	21.0171i	0.878003	+	1.52075i	0.853529	+	0.521045i	$0.174458\pi$
$191$	12.1342	+	21.0171i	0.878003	+	1.52075i	0.0244738	+	0.999700i	$0.492209\pi$
$192$	8.82578	+	10.6820i	0.636946	+	0.770909i
$193$	8.48358	−	14.6940i	0.610662	−	1.05770i	−0.380467	−	0.924794i	$-0.624237\pi$
$193$	8.48358	−	14.6940i	0.610662	−	1.05770i	0.991129	−	0.132903i	$-0.0424298\pi$
$194$	17.2955	−	1.53033i	1.24174	−	0.109871i
$195$	−10.8103	−	13.2426i	−0.774143	−	0.948322i
$196$	13.4368	+	3.93083i	0.959774	+	0.280774i
$197$	−11.0886	−	4.59305i	−0.790030	−	0.327241i	−0.0490746	−	0.998795i	$-0.515627\pi$
$197$	−11.0886	−	4.59305i	−0.790030	−	0.327241i	−0.740956	+	0.671554i	$0.765627\pi$
$198$	4.66345	−	8.41585i	0.331417	−	0.598088i
$199$	3.52499	+	13.1554i	0.249880	+	0.932565i	0.970868	+	0.239617i	$0.0770218\pi$
$199$	3.52499	+	13.1554i	0.249880	+	0.932565i	−0.720988	+	0.692948i	$0.756312\pi$
$200$	−2.84972	+	1.65654i	−0.201506	+	0.117135i
$201$	0.0708081	+	2.35014i	0.00499442	+	0.165766i
$202$	−3.26133	+	2.99437i	−0.229466	+	0.210683i
$203$	−2.77421	−	16.9590i	−0.194711	−	1.19029i
$204$	8.13597	+	1.53162i	0.569632	+	0.107235i
$205$	7.19882	−	9.38168i	0.502787	−	0.655245i
$206$	16.2918	+	2.85613i	1.13510	+	0.198996i
$207$	−9.80362	+	0.591289i	−0.681398	+	0.0410974i
$208$	−13.6787	−	14.8101i	−0.948446	−	1.02689i
$209$	14.2835			0.988013
$210$	−12.5489	+	1.89170i	−0.865957	+	0.130540i
$211$	−12.4527	+	5.15807i	−0.857279	+	0.355096i	−0.767643	−	0.640878i	$-0.778570\pi$
$211$	−12.4527	+	5.15807i	−0.857279	+	0.355096i	−0.0896360	+	0.995975i	$0.528570\pi$
$212$	5.61708	+	5.12678i	0.385783	+	0.352109i
$213$	−8.42016	+	11.6859i	−0.576940	+	0.800705i
$214$	0.172191	+	0.773096i	0.0117707	+	0.0528478i
$215$	−2.11870	−	0.567704i	−0.144494	−	0.0387171i
$216$	9.99448	+	10.7755i	0.680038	+	0.733177i
$217$	−20.0641	−	18.8478i	−1.36204	−	1.27947i
$218$	−16.7387	−	0.714305i	−1.13369	−	0.0483788i
$219$	−18.1002	+	8.14431i	−1.22310	+	0.550342i
$220$	−7.28554	−	5.08003i	−0.491191	−	0.342495i
$221$	−11.9424	−	1.57224i	−0.803330	−	0.105760i
$222$	−1.06139	−	2.65605i	−0.0712356	−	0.178262i
$223$		−	17.8513i		−	1.19541i	−0.801715	−	0.597707i	$-0.796079\pi$
$223$		−	17.8513i		−	1.19541i	0.801715	−	0.597707i	$-0.203921\pi$
$224$	−14.6356	+	3.13028i	−0.977883	+	0.209151i
$225$	−2.91704	+	1.92720i	−0.194469	+	0.128480i
$226$	18.8772	−	1.67028i	1.25569	−	0.111105i
$227$	−1.02716	+	7.80205i	−0.0681749	+	0.517840i	0.922951	+	0.384917i	$0.125770\pi$
$227$	−1.02716	+	7.80205i	−0.0681749	+	0.517840i	−0.991126	+	0.132923i	$0.957564\pi$
$228$	−6.80058	+	20.7312i	−0.450379	+	1.37296i
$229$	−6.68569	+	0.880188i	−0.441803	+	0.0581644i	−0.348146	−	0.937440i	$-0.613189\pi$
$229$	−6.68569	+	0.880188i	−0.441803	+	0.0581644i	−0.0936563	+	0.995605i	$0.529855\pi$
$230$	−0.386542	+	9.05804i	−0.0254878	+	0.597269i
$231$	5.73842	+	8.66451i	0.377560	+	0.570083i
$232$	11.2265	+	14.5415i	0.737056	+	0.954695i
$233$	−6.45360	+	24.0852i	−0.422790	+	1.57787i	0.345913	+	0.938266i	$0.387569\pi$
$233$	−6.45360	+	24.0852i	−0.422790	+	1.57787i	−0.768703	+	0.639606i	$0.779098\pi$
$234$	−15.3840	−	14.8520i	−1.00568	−	0.970907i
$235$	−10.0410	−	13.0857i	−0.655004	−	0.853617i
$236$	13.3073	+	12.1458i	0.866232	+	0.790621i
$237$	−11.9477	+	9.75327i	−0.776088	+	0.633543i
$238$	−5.52420	+	7.03182i	−0.358081	+	0.455805i
$239$		−	7.84044i		−	0.507156i	−0.967315	−	0.253578i	$-0.918393\pi$
$239$		−	7.84044i		−	0.507156i	0.967315	−	0.253578i	$-0.0816074\pi$
$240$	10.8419	−	8.15561i	0.699843	−	0.526442i
$241$	−8.99942	−	5.19582i	−0.579703	−	0.334692i	0.181312	−	0.983426i	$-0.441966\pi$
$241$	−8.99942	−	5.19582i	−0.579703	−	0.334692i	−0.761016	+	0.648734i	$0.775299\pi$
$242$	1.43030	−	8.15861i	0.0919429	−	0.524455i
$243$	11.2377	+	10.8034i	0.720900	+	0.693040i
$244$	−1.24199	−	0.643433i	−0.0795104	−	0.0411916i
$245$	4.44447	−	12.9670i	0.283947	−	0.828430i
$246$	7.55594	−	12.7167i	0.481749	−	0.810784i
$247$	8.21606	−	30.6628i	0.522776	−	1.95102i
$248$	28.4487	+	7.53276i	1.80649	+	0.478330i
$249$	18.9616	−	11.7227i	1.20164	−	0.742896i
$250$	7.89883	+	15.1371i	0.499566	+	0.957353i
$251$	1.33879	−	3.23213i	0.0845038	−	0.204010i	−0.875979	−	0.482349i	$-0.839784\pi$
$251$	1.33879	−	3.23213i	0.0845038	−	0.204010i	0.960483	+	0.278339i	$0.0897837\pi$
$252$	−15.3079	+	4.20349i	−0.964305	+	0.264795i
$253$	6.85927	−	2.84120i	0.431238	−	0.178625i
$254$	−0.891616	−	10.0769i	−0.0559450	−	0.632279i
$255$	1.86122	−	7.88935i	0.116554	−	0.494050i
$256$	12.1753	−	10.3809i	0.760955	−	0.648805i
$257$	−20.5309	+	11.8535i	−1.28068	+	0.739404i	−0.976974	−	0.213361i	$-0.931559\pi$
$257$	−20.5309	+	11.8535i	−1.28068	+	0.739404i	−0.303711	+	0.952764i	$0.598226\pi$
$258$	−2.71555	−	0.392178i	−0.169063	−	0.0244159i
$259$	3.07412	+	0.307360i	0.191016	+	0.0190984i
$260$	−15.0961	+	12.7179i	−0.936222	+	0.788733i
$261$	12.7710	+	14.7165i	0.790507	+	0.910930i
$262$	14.3629	+	9.13029i	0.887342	+	0.564071i
$263$	17.1935	−	4.60698i	1.06020	−	0.284079i	0.313737	−	0.949510i	$-0.398419\pi$
$263$	17.1935	−	4.60698i	1.06020	−	0.284079i	0.746459	+	0.665432i	$0.231752\pi$
$264$	−9.79999	−	5.23378i	−0.603148	−	0.322117i
$265$	5.26518	−	5.26518i	0.323437	−	0.323437i
$266$	−16.4728	−	16.8528i	−1.01001	−	1.03331i
$267$	−1.52706	+	15.1012i	−0.0934548	+	0.924178i
$268$	2.71212	−	0.123768i	0.165669	−	0.00756033i
$269$	−0.0439789	+	0.334053i	−0.00268144	+	0.0203676i	−0.992733	−	0.120336i	$-0.961603\pi$
$269$	−0.0439789	+	0.334053i	−0.00268144	+	0.0203676i	0.990052	+	0.140703i	$0.0449363\pi$
$270$	10.9855	−	9.29453i	0.668555	−	0.565647i
$271$	−11.0751	−	19.1827i	−0.672767	−	1.16527i	−0.977116	−	0.212707i	$-0.931772\pi$
$271$	−11.0751	−	19.1827i	−0.672767	−	1.16527i	0.304349	−	0.952561i	$-0.401561\pi$
$272$	1.62290	−	9.42087i	0.0984028	−	0.571224i
$273$	21.9011	−	7.33486i	1.32551	−	0.443926i
$274$	20.8568	−	7.61453i	1.26001	−	0.460011i
$275$	1.60889	−	2.09675i	0.0970198	−	0.126439i
$276$	0.857948	+	11.3083i	0.0516424	+	0.680680i
$277$	−11.9479	+	9.16798i	−0.717883	+	0.550851i	−0.901833	−	0.432085i	$-0.857778\pi$
$277$	−11.9479	+	9.16798i	−0.717883	+	0.550851i	0.183950	+	0.982936i	$0.441111\pi$
$278$	−4.38718	+	13.9623i	−0.263126	+	0.837404i
$279$	30.5823	+	6.24900i	1.83092	+	0.374118i
$280$	2.40843	+	14.4547i	0.143931	+	0.863832i
$281$	2.67726	−	2.67726i	0.159712	−	0.159712i	−0.622727	−	0.782439i	$-0.713975\pi$
$281$	2.67726	−	2.67726i	0.159712	−	0.159712i	0.782439	+	0.622727i	$0.213975\pi$
$282$	−14.4053	−	14.7708i	−0.857821	−	0.879588i
$283$	2.89865	−	2.22421i	0.172307	−	0.132216i	−0.519008	−	0.854769i	$-0.673698\pi$
$283$	2.89865	−	2.22421i	0.172307	−	0.132216i	0.691315	+	0.722554i	$0.257032\pi$
$284$	13.6426	+	9.51268i	0.809542	+	0.564473i
$285$	19.9734	+	7.57693i	1.18312	+	0.448818i
$286$	14.6568	+	6.81701i	0.866675	+	0.403098i
$287$	8.41703	+	13.5804i	0.496842	+	0.801624i
$288$	12.2623	−	11.7319i	0.722560	−	0.691308i
$289$	5.64417	+	9.77599i	0.332010	+	0.575058i
$290$	14.7240	−	10.3315i	0.864622	−	0.606685i
$291$	−3.40936	−	20.9903i	−0.199861	−	1.23047i
$292$	9.72671	+	20.7521i	0.569213	+	1.21443i
$293$	−11.6309	−	4.81769i	−0.679486	−	0.281452i	0.0161258	−	0.999870i	$-0.494867\pi$
$293$	−11.6309	−	4.81769i	−0.679486	−	0.281452i	−0.695612	+	0.718417i	$0.744867\pi$
$294$	3.60506	−	16.7632i	0.210251	−	0.977647i
$295$	12.4736	−	12.4736i	0.726242	−	0.726242i
$296$	−3.04760	+	1.27292i	−0.177138	+	0.0739871i
$297$	−10.6952	−	4.94704i	−0.620601	−	0.287056i
$298$	7.36636	−	1.64070i	0.426722	−	0.0950430i
$299$	−2.15373	−	16.3592i	−0.124554	−	0.946078i
$300$	2.27722	+	3.33344i	0.131475	+	0.192456i
$301$	1.72977	−	2.40637i	0.0997021	−	0.138701i
$302$	23.2493	−	8.48801i	1.33785	−	0.488430i
$303$	3.94804	+	3.71709i	0.226809	+	0.213541i
$304$	24.0570	+	7.48106i	1.37977	+	0.429068i
$305$	−0.684773	+	1.18606i	−0.0392100	+	0.0679137i
$306$	1.14643	−	10.0745i	0.0655368	−	0.575921i
$307$	11.1660	−	4.62512i	0.637278	−	0.263969i	−0.0405637	−	0.999177i	$-0.512915\pi$
$307$	11.1660	−	4.62512i	0.637278	−	0.263969i	0.677842	+	0.735208i	$0.262915\pi$
$308$	9.90113	−	6.78027i	0.564169	−	0.386342i
$309$	2.03809	−	20.1548i	0.115943	−	1.14657i
$310$	8.63753	−	27.4892i	0.490579	−	1.56128i
$311$	8.40200	+	31.3567i	0.476434	+	1.77808i	0.615874	+	0.787845i	$0.288803\pi$
$311$	8.40200	+	31.3567i	0.476434	+	1.77808i	−0.139440	+	0.990231i	$0.544530\pi$
$312$	−16.8725	+	18.0273i	−0.955220	+	1.02060i
$313$	5.17583	−	19.3165i	0.292555	−	1.09183i	−0.650584	−	0.759434i	$-0.725476\pi$
$313$	5.17583	−	19.3165i	0.292555	−	1.09183i	0.943140	−	0.332397i	$-0.107857\pi$
$314$	−1.26508	+	29.6453i	−0.0713927	+	1.67298i
$315$	3.42812	+	15.1601i	0.193153	+	0.854175i
$316$	11.4744	+	13.6200i	0.645483	+	0.766186i
$317$	−12.8201	+	16.7075i	−0.720048	+	0.938385i	−0.999765	−	0.0216978i	$-0.993093\pi$
$317$	−12.8201	+	16.7075i	−0.720048	+	0.938385i	0.279717	+	0.960083i	$0.409760\pi$
$318$	5.76222	−	7.31779i	0.323129	−	0.410361i
$319$	−12.7563	−	7.36484i	−0.714215	−	0.412352i
$320$	−9.60999	−	12.3719i	−0.537215	−	0.691609i
$321$	0.929008	−	0.279171i	0.0518521	−	0.0155818i
$322$	−11.2629	−	4.81638i	−0.627655	−	0.268407i
$323$	13.9067	−	5.76034i	0.773788	−	0.320514i
$324$	12.2723	−	13.1678i	0.681795	−	0.731543i
$325$	−3.57568	−	4.65991i	−0.198343	−	0.258486i
$326$	−6.04097	+	9.50308i	−0.334579	+	0.526327i
$327$	0.617951	+	20.5100i	0.0341727	+	1.13420i
$328$	−14.8173	−	8.49645i	−0.818146	−	0.469138i
$329$	21.3353	−	6.43758i	1.17625	−	0.354915i
$330$	−5.55654	+	9.35166i	−0.305877	+	0.514792i
$331$	−19.5893	+	2.57897i	−1.07672	+	0.141753i	−0.647968	−	0.761668i	$-0.724381\pi$
$331$	−19.5893	+	2.57897i	−1.07672	+	0.141753i	−0.428755	+	0.903421i	$0.641048\pi$
$332$	−13.8736	−	21.6828i	−0.761412	−	1.19000i
$333$	−3.14986	+	1.53299i	−0.172611	+	0.0840075i
$334$	6.20810	+	5.19880i	0.339692	+	0.284466i
$335$		−	2.65822i		−	0.145234i
$336$	5.12686	+	17.5987i	0.279693	+	0.960089i
$337$			9.27464i			0.505222i	0.967568	+	0.252611i	$0.0812893\pi$
$337$			9.27464i			0.505222i	−0.967568	+	0.252611i	$0.918711\pi$
$338$	11.2614	−	13.4476i	0.612537	−	0.731455i
$339$	−3.72115	−	22.9098i	−0.202105	−	1.24429i
$340$	−9.14202	−	2.00785i	−0.495796	−	0.108891i
$341$	−23.3942	+	3.07991i	−1.26687	+	0.166786i
$342$	25.9288	+	6.46095i	1.40207	+	0.349368i
$343$	14.2641	+	11.8125i	0.770191	+	0.637813i
$344$	−0.404245	+	3.14229i	−0.0217955	+	0.169421i
$345$	11.0988	−	0.334400i	0.597542	−	0.0180035i
$346$	−1.06601	−	0.677649i	−0.0573092	−	0.0364307i
$347$	−7.79832	−	10.1630i	−0.418636	−	0.545577i	0.535663	−	0.844432i	$-0.320062\pi$
$347$	−7.79832	−	10.1630i	−0.418636	−	0.545577i	−0.954298	+	0.298855i	$0.903395\pi$
$348$	16.7628	−	15.0080i	0.898581	−	0.804516i
$349$	8.45746	−	3.50320i	0.452718	−	0.187522i	−0.144661	−	0.989481i	$-0.546209\pi$
$349$	8.45746	−	3.50320i	0.452718	−	0.187522i	0.597378	+	0.801960i	$0.296209\pi$
$350$	−4.32939	+	0.519836i	−0.231416	+	0.0277864i
$351$	−16.7719	+	20.1141i	−0.895220	+	1.07361i
$352$	−5.86753	+	11.4083i	−0.312740	+	0.608063i
$353$	−19.2604	−	11.1200i	−1.02513	−	0.591858i	−0.109543	−	0.993982i	$-0.534939\pi$
$353$	−19.2604	−	11.1200i	−1.02513	−	0.591858i	−0.915585	+	0.402124i	$0.868272\pi$
$354$	13.6511	−	17.3364i	0.725550	−	0.921421i
$355$	9.91320	−	12.9191i	0.526138	−	0.685676i
$356$	17.4626	+	1.49311i	0.925514	+	0.0791347i
$357$	9.08129	+	6.12169i	0.480633	+	0.323994i
$358$	−5.21563	−	0.222571i	−0.275655	−	0.0117633i
$359$	−3.52298	+	13.1480i	−0.185936	+	0.693922i	0.808492	+	0.588507i	$0.200284\pi$
$359$	−3.52298	+	13.1480i	−0.185936	+	0.693922i	−0.994428	+	0.105416i	$0.966383\pi$
$360$	−10.9275	−	12.5172i	−0.575931	−	0.659717i
$361$	5.34959	+	19.9650i	0.281558	+	1.05079i
$362$	−14.1217	−	4.43728i	−0.742223	−	0.233218i
$363$	−10.0931	−	1.02064i	−0.529752	−	0.0535696i
$364$	−8.86009	−	25.1550i	−0.464395	−	1.31848i
$365$	20.7316	−	8.58732i	1.08514	−	0.449481i
$366$	−0.675364	+	1.57439i	−0.0353019	+	0.0822948i
$367$	−17.2083	+	29.8056i	−0.898264	+	1.55584i	−0.0685520	+	0.997648i	$0.521838\pi$
$367$	−17.2083	+	29.8056i	−0.898264	+	1.55584i	−0.829712	+	0.558192i	$0.811495\pi$
$368$	13.0408	−	1.19272i	0.679799	−	0.0621750i
$369$	−16.2062	−	8.09727i	−0.843664	−	0.421527i
$370$	1.10900	+	3.03764i	0.0576543	+	0.157920i
$371$	4.13847	+	9.16980i	0.214858	+	0.476072i
$372$	6.66811	−	35.4209i	0.345725	−	1.83649i
$373$	2.28608	+	17.3645i	0.118369	+	0.899098i	0.942852	+	0.333212i	$0.108132\pi$
$373$	2.28608	+	17.3645i	0.118369	+	0.899098i	−0.824483	+	0.565886i	$0.808534\pi$
$374$	1.66635	+	7.48155i	0.0861651	+	0.386862i
$375$	17.7867	−	10.9963i	0.918499	−	0.567847i
$376$	−16.7963	+	16.8958i	−0.866201	+	0.871336i
$377$	−23.1478	+	23.1478i	−1.19217	+	1.19217i
$378$	6.49765	+	18.3243i	0.334203	+	0.942501i
$379$	18.6512	+	7.72558i	0.958048	+	0.396836i	0.806250	−	0.591575i	$-0.201494\pi$
$379$	18.6512	+	7.72558i	0.958048	+	0.396836i	0.151798	+	0.988412i	$0.451494\pi$
$380$	8.39095	−	23.1960i	0.430447	−	1.18993i
$381$	−12.2295	+	1.98640i	−0.626538	+	0.101766i
$382$	−19.7133	−	28.0946i	−1.00862	−	1.43744i
$383$	−4.52031	−	7.82940i	−0.230977	−	0.400064i	0.727119	−	0.686512i	$-0.240859\pi$
$383$	−4.52031	−	7.82940i	−0.230977	−	0.400064i	−0.958096	+	0.286448i	$0.907526\pi$
$384$	−13.7644	−	13.9478i	−0.702412	−	0.711770i
$385$	−6.18977	−	9.98683i	−0.315460	−	0.508976i
$386$	−10.1194	+	21.7570i	−0.515063	+	1.10740i
$387$	−0.237244	+	3.35198i	−0.0120598	+	0.170391i
$388$	−24.1736	+	4.31159i	−1.22723	+	0.218888i
$389$	−7.54876	+	5.79237i	−0.382738	+	0.293685i	−0.782155	−	0.623085i	$-0.785879\pi$
$389$	−7.54876	+	5.79237i	−0.382738	+	0.293685i	0.399417	+	0.916769i	$0.369213\pi$
$390$	16.8792	+	17.3075i	0.854712	+	0.876401i
$391$	5.53248	−	5.53248i	0.279789	−	0.279789i
$392$	−19.4186	−	3.86257i	−0.980785	−	0.195089i
$393$	9.87375	−	18.3573i	0.498065	−	0.926004i
$394$	16.1931	+	5.08814i	0.815798	+	0.256337i
$395$	13.8338	−	10.6150i	0.696052	−	0.534100i
$396$	−5.52046	+	12.4368i	−0.277413	+	0.624971i
$397$	−14.8789	+	19.3905i	−0.746749	+	0.973183i	0.253234	+	0.967405i	$0.418506\pi$
$397$	−14.8789	+	19.3905i	−0.746749	+	0.973183i	−0.999983	+	0.00577752i	$0.998161\pi$
$398$	−6.60544	−	18.0928i	−0.331101	−	0.906912i
$399$	−19.1189	+	21.6222i	−0.957142	+	1.08247i
$400$	3.80796	−	2.68878i	0.190398	−	0.134439i
$401$	−6.71153	−	11.6247i	−0.335158	−	0.580511i	0.648357	−	0.761336i	$-0.275456\pi$
$401$	−6.71153	−	11.6247i	−0.335158	−	0.580511i	−0.983515	+	0.180826i	$0.942123\pi$
$402$	−0.392680	−	3.30184i	−0.0195851	−	0.164681i
$403$	−6.84494	+	51.9925i	−0.340971	+	2.58993i
$404$	4.22103	−	4.62471i	0.210004	−	0.230088i
$405$	−12.3315	−	12.5912i	−0.612757	−	0.625660i
$406$	6.02190	+	23.5445i	0.298862	+	1.16849i
$407$	1.87251	−	1.87251i	0.0928171	−	0.0928171i
$408$	−11.6521	−	1.14351i	−0.576867	−	0.0566121i
$409$	21.4086	−	5.73640i	1.05858	−	0.283647i	0.312790	−	0.949822i	$-0.398736\pi$
$409$	21.4086	−	5.73640i	1.05858	−	0.283647i	0.745795	+	0.666175i	$0.232070\pi$
$410$	−8.97167	+	14.1134i	−0.443079	+	0.697010i
$411$	−11.1584	−	24.7986i	−0.550401	−	1.22323i
$412$	−23.3064	−	1.99278i	−1.14822	−	0.0981773i
$413$	9.80435	+	21.7240i	0.482441	+	1.06897i
$414$	13.7367	−	2.05492i	0.675124	−	0.100994i
$415$	−21.8270	+	12.6018i	−1.07144	+	0.618598i
$416$	21.1153	+	19.1581i	1.03526	+	0.939304i
$417$	17.4457	+	4.11570i	0.854318	+	0.201547i
$418$	−20.1214	+	1.78037i	−0.984168	+	0.0870806i
$419$	−18.9106	+	7.83303i	−0.923843	+	0.382668i	−0.793340	−	0.608779i	$-0.791659\pi$
$419$	−18.9106	+	7.83303i	−0.923843	+	0.382668i	−0.130504	+	0.991448i	$0.541659\pi$
$420$	17.4420	−	4.22901i	0.851082	−	0.206355i
$421$	8.51087	−	20.5471i	0.414794	−	1.00140i	−0.569038	−	0.822311i	$-0.692684\pi$
$421$	8.51087	−	20.5471i	0.414794	−	1.00140i	0.983832	−	0.179091i	$-0.0573157\pi$
$422$	16.8993	−	8.81839i	0.822645	−	0.429273i
$423$	−16.7599	+	18.9113i	−0.814893	+	0.919500i
$424$	−8.55186	−	6.52201i	−0.415315	−	0.316737i
$425$	0.720855	−	2.69027i	0.0349666	−	0.130497i
$426$	10.4050	−	17.5116i	0.504123	−	0.848439i
$427$	−1.17176	−	1.43211i	−0.0567057	−	0.0693046i
$428$	−0.338929	−	1.06761i	−0.0163827	−	0.0516047i
$429$	7.02190	−	18.5104i	0.339021	−	0.893688i
$430$	3.05540	+	0.535646i	0.147344	+	0.0258311i
$431$	20.5187	+	11.8465i	0.988351	+	0.570624i	0.904781	−	0.425877i	$-0.140035\pi$
$431$	20.5187	+	11.8465i	0.988351	+	0.570624i	0.0835697	+	0.996502i	$0.473368\pi$
$432$	−15.4224	−	13.9337i	−0.742012	−	0.670387i
$433$			12.6521i			0.608020i	0.952669	+	0.304010i	$0.0983255\pi$
$433$			12.6521i			0.608020i	−0.952669	+	0.304010i	$0.901674\pi$
$434$	30.6138	+	24.0503i	1.46951	+	1.15445i
$435$	−13.9310	−	17.0654i	−0.667941	−	0.818225i
$436$	23.6690	−	1.08014i	1.13354	−	0.0517292i
$437$	12.5524	+	16.3586i	0.600464	+	0.782540i
$438$	24.4827	−	13.7291i	1.16983	−	0.656000i
$439$	8.28923	−	30.9358i	0.395623	−	1.47649i	−0.425093	−	0.905150i	$-0.639759\pi$
$439$	8.28923	−	30.9358i	0.395623	−	1.47649i	0.820716	−	0.571336i	$-0.193575\pi$
$440$	10.8964	+	6.24818i	0.519466	+	0.297870i
$441$	−20.7973	−	2.91093i	−0.990346	−	0.138616i
$442$	17.0193	+	0.726280i	0.809525	+	0.0345456i
$443$	37.5250	−	4.94026i	1.78287	−	0.234719i	0.834304	−	0.551305i	$-0.185870\pi$
$443$	37.5250	−	4.94026i	1.78287	−	0.234719i	0.948564	+	0.316586i	$0.102536\pi$
$444$	1.82625	+	3.60931i	0.0866699	+	0.171290i
$445$	2.23985	−	17.0133i	0.106179	−	0.806508i
$446$	2.22507	+	25.1473i	0.105360	+	1.19076i
$447$	−2.66005	−	8.85194i	−0.125816	−	0.418682i
$448$	20.2272	−	6.23391i	0.955644	−	0.294525i
$449$			32.4222i			1.53010i	0.643973	+	0.765048i	$0.277285\pi$
$449$			32.4222i			1.53010i	−0.643973	+	0.765048i	$0.722715\pi$
$450$	3.86904	−	3.07845i	0.182388	−	0.145120i
$451$	13.5778	+	1.78756i	0.639356	+	0.0841728i
$452$	−26.3843	+	4.70588i	−1.24101	+	0.221346i
$453$	−12.4383	−	27.6433i	−0.584404	−	1.29880i
$454$	0.474485	−	11.1189i	0.0222687	−	0.521834i
$455$	−24.9994	+	7.54317i	−1.17199	+	0.353629i
$456$	6.99601	−	30.0519i	0.327618	−	1.40731i
$457$	6.21352	+	1.66491i	0.290656	+	0.0778811i	0.401201	−	0.915990i	$-0.368593\pi$
$457$	6.21352	+	1.66491i	0.290656	+	0.0778811i	−0.110545	+	0.993871i	$0.535260\pi$
$458$	9.30849	−	2.07326i	0.434957	−	0.0968773i
$459$	−12.4081	−	0.503290i	−0.579162	−	0.0234916i
$460$	−0.584511	−	12.8083i	−0.0272529	−	0.597191i
$461$	−21.0476	+	8.71819i	−0.980283	+	0.406046i	−0.814530	−	0.580121i	$-0.803005\pi$
$461$	−21.0476	+	8.71819i	−0.980283	+	0.406046i	−0.165752	+	0.986167i	$0.553005\pi$
$462$	−9.16376	−	11.4905i	−0.426337	−	0.534587i
$463$	17.5944			0.817682			0.408841	−	0.912606i	$-0.365933\pi$
$463$	17.5944			0.817682			0.408841	+	0.912606i	$0.365933\pi$
$464$	−17.6274	−	19.0854i	−0.818332	−	0.886017i
$465$	−34.3472	−	8.10304i	−1.59281	−	0.375769i
$466$	6.08917	−	34.7334i	0.282075	−	1.60900i
$467$	−19.8970	+	25.9302i	−0.920722	+	1.19991i	0.0587393	+	0.998273i	$0.481292\pi$
$467$	−19.8970	+	25.9302i	−0.920722	+	1.19991i	−0.979461	+	0.201634i	$0.935375\pi$
$468$	23.5228	+	19.0047i	1.08734	+	0.878490i
$469$	3.35946	+	1.27008i	0.155125	+	0.0586468i
$470$	15.7759	+	17.1824i	0.727690	+	0.792565i
$471$	36.3245	−	1.09443i	1.67374	−	0.0504288i
$472$	−20.2600	−	15.4512i	−0.932544	−	0.711197i
$473$	−0.657461	−	2.45368i	−0.0302301	−	0.112820i
$474$	15.6152	−	15.2287i	0.717229	−	0.699479i
$475$	6.78130	+	2.80891i	0.311147	+	0.128882i
$476$	6.90552	−	10.5944i	0.316514	−	0.485591i
$477$	−9.45180	−	6.38696i	−0.432768	−	0.292439i
$478$	0.977269	+	11.0449i	0.0446993	+	0.505182i
$479$	9.58796	−	16.6068i	0.438085	−	0.758786i	−0.559457	−	0.828860i	$-0.688990\pi$
$479$	9.58796	−	16.6068i	0.438085	−	0.758786i	0.997542	+	0.0700738i	$0.0223235\pi$
$480$	−14.2566	+	12.8403i	−0.650721	+	0.586076i
$481$	−2.94267	−	5.09686i	−0.134174	−	0.232397i
$482$	13.3252	+	6.19767i	0.606946	+	0.282296i
$483$	−4.88034	+	14.1865i	−0.222063	+	0.645508i
$484$	−0.997946	+	11.6714i	−0.0453612	+	0.530518i
$485$	3.13812	+	23.8364i	0.142495	+	1.08236i
$486$	−17.1773	−	13.8182i	−0.779177	−	0.626804i
$487$	5.52560	+	20.6218i	0.250389	+	0.934463i	0.970598	+	0.240706i	$0.0773791\pi$
$487$	5.52560	+	20.6218i	0.250389	+	0.934463i	−0.720209	+	0.693757i	$0.755954\pi$
$488$	1.82981	+	0.751603i	0.0828315	+	0.0340235i
$489$	12.1460	+	6.53288i	0.549259	+	0.295427i
$490$	−4.64470	+	18.8207i	−0.209826	+	0.850232i
$491$	−10.0761	−	4.17366i	−0.454728	−	0.188354i	0.143550	−	0.989643i	$-0.454148\pi$
$491$	−10.0761	−	4.17366i	−0.454728	−	0.188354i	−0.598278	+	0.801289i	$0.704148\pi$
$492$	−9.05906	+	18.8559i	−0.408414	+	0.850089i
$493$	−15.3899	−	2.02611i	−0.693124	−	0.0912515i
$494$	−7.75210	+	44.2190i	−0.348783	+	1.98951i
$495$	11.9179	+	5.95462i	0.535668	+	0.267640i
$496$	−41.0149	−	7.06549i	−1.84162	−	0.317250i
$497$	11.5907	+	18.7010i	0.519916	+	0.838854i
$498$	−25.2502	+	18.8774i	−1.13149	+	0.845915i
$499$	21.0902	+	16.1831i	0.944129	+	0.724456i	0.961331	−	0.275396i	$-0.0888091\pi$
$499$	21.0902	+	16.1831i	0.944129	+	0.724456i	−0.0172018	+	0.999852i	$0.505476\pi$
$500$	−13.0139	−	20.3392i	−0.582000	−	0.909597i
$501$	5.79756	−	8.04614i	0.259016	−	0.359475i
$502$	−1.48310	+	4.72001i	−0.0661941	+	0.210664i
$503$	9.80141	−	9.80141i	0.437023	−	0.437023i	−0.453986	−	0.891009i	$-0.649998\pi$
$503$	9.80141	−	9.80141i	0.437023	−	0.437023i	0.891009	+	0.453986i	$0.149998\pi$
$504$	21.0404	−	7.82954i	0.937214	−	0.348756i
$505$	−4.33498	−	4.33498i	−0.192904	−	0.192904i
$506$	−9.30857	+	4.85740i	−0.413817	+	0.215938i
$507$	−17.4291	−	12.5584i	−0.774054	−	0.557736i
$508$	2.51206	+	14.0842i	0.111454	+	0.624887i
$509$	12.5102	−	16.3036i	0.554503	−	0.722642i	−0.429046	−	0.903283i	$-0.641150\pi$
$509$	12.5102	−	16.3036i	0.554503	−	0.722642i	0.983549	+	0.180640i	$0.0578169\pi$
$510$	−1.63855	+	11.3458i	−0.0725563	+	0.502400i
$511$	0.947226	+	30.3036i	0.0419028	+	1.34055i
$512$	−15.8575	+	16.1412i	−0.700810	+	0.713348i
$513$	5.58327	−	32.2474i	0.246507	−	1.42376i
$514$	27.4447	−	19.2573i	1.21053	−	0.849402i
$515$	−2.98941	+	22.7068i	−0.131729	+	1.00058i
$516$	3.87431	+	0.213986i	0.170557	+	0.00942020i
$517$	7.31002	−	17.6479i	0.321494	−	0.776156i
$518$	−4.36885	−	0.0498087i	−0.191956	−	0.00218847i
$519$	−0.732829	+	1.36248i	−0.0321676	+	0.0598062i
$520$	19.6808	−	19.7975i	0.863062	−	0.868179i
$521$	−4.53248	+	1.21447i	−0.198571	+	0.0532070i	−0.356734	−	0.934206i	$-0.616110\pi$
$521$	−4.53248	+	1.21447i	−0.198571	+	0.0532070i	0.158162	+	0.987413i	$0.449443\pi$
$522$	−19.8250	−	19.1395i	−0.867717	−	0.837712i
$523$	−20.3292	+	2.67639i	−0.888932	+	0.117030i	−0.561141	−	0.827720i	$-0.689638\pi$
$523$	−20.3292	+	2.67639i	−0.888932	+	0.117030i	−0.327791	+	0.944750i	$0.606304\pi$
$524$	−21.3712	−	11.0717i	−0.933604	−	0.483668i
$525$	1.02049	+	5.24208i	0.0445377	+	0.228783i
$526$	−23.6464	+	8.63297i	−1.03103	+	0.376416i
$527$	−21.5349	+	12.4332i	−0.938076	+	0.541598i
$528$	14.4577	+	6.15137i	0.629191	+	0.267704i
$529$	−10.6367	−	6.14108i	−0.462464	−	0.267004i
$530$	−6.76083	+	8.07338i	−0.293672	+	0.350685i
$531$	−22.3921	−	15.1312i	−0.971733	−	0.656639i
$532$	25.3060	+	21.6874i	1.09716	+	0.940268i
$533$	11.6475	−	28.1196i	0.504510	−	1.21800i
$534$	0.268906	−	21.4635i	0.0116367	−	0.928818i
$535$	−1.05934	+	0.283850i	−0.0457994	+	0.0122719i
$536$	−3.80516	+	0.512404i	−0.164358	+	0.0221325i
$537$	0.192548	+	6.39073i	0.00830907	+	0.275780i
$538$	0.0203156	−	0.476066i	0.000875868	−	0.0205247i
$539$	15.5788	−	3.05100i	0.671026	−	0.131416i
$540$	−14.3168	+	14.4626i	−0.616098	+	0.622371i
$541$	−13.1239	−	10.0703i	−0.564240	−	0.432957i	0.286851	−	0.957975i	$-0.407392\pi$
$541$	−13.1239	−	10.0703i	−0.564240	−	0.432957i	−0.851091	+	0.525019i	$0.824058\pi$
$542$	17.9927	+	25.6424i	0.772852	+	1.10144i
$543$	−4.16270	+	17.6449i	−0.178638	+	0.757214i
$544$	−1.11194	+	13.4736i	−0.0476738	+	0.577674i
$545$		−	23.1986i		−	0.993719i
$546$	−29.9380	+	13.0625i	−1.28123	+	0.559025i
$547$	14.7814	+	35.6855i	0.632008	+	1.52580i	0.837094	+	0.547059i	$0.184253\pi$
$547$	14.7814	+	35.6855i	0.632008	+	1.52580i	−0.205085	+	0.978744i	$0.565747\pi$
$548$	−28.4321	+	13.3264i	−1.21456	+	0.569274i
$549$	1.98326	+	0.684770i	0.0846436	+	0.0292253i
$550$	−2.00511	+	3.15425i	−0.0854983	+	0.134498i
$551$	10.5879	−	39.5144i	0.451058	−	1.68337i
$552$	−2.61812	−	15.8232i	−0.111435	−	0.673480i
$553$	6.80559	+	22.5549i	0.289403	+	0.959132i
$554$	15.6885	−	14.4043i	0.666538	−	0.611979i
$555$	3.61174	−	1.62513i	0.153310	−	0.0689831i
$556$	4.43994	−	20.2157i	0.188295	−	0.857336i
$557$	1.55830	−	11.8365i	0.0660273	−	0.501527i	−0.926195	−	0.377046i	$-0.876940\pi$
$557$	1.55830	−	11.8365i	0.0660273	−	0.501527i	0.992222	−	0.124482i	$-0.0397268\pi$
$558$	−43.8605	−	4.99110i	−1.85676	−	0.211290i
$559$	−5.64554			−0.238781
$560$	−5.19448	−	20.0622i	−0.219507	−	0.847785i
$561$	8.99036	−	2.70164i	0.379573	−	0.114063i
$562$	−3.43777	+	4.10518i	−0.145014	+	0.173167i
$563$	−3.10536	−	0.408828i	−0.130875	−	0.0172300i	0.0648040	−	0.997898i	$-0.479358\pi$
$563$	−3.10536	−	0.408828i	−0.130875	−	0.0172300i	−0.195679	+	0.980668i	$0.562691\pi$
$564$	22.1339	+	19.0122i	0.932007	+	0.800559i
$565$	3.42510	+	26.0162i	0.144095	+	1.09451i
$566$	−3.80612	+	3.49457i	−0.159983	+	0.146888i
$567$	21.8046	−	9.56857i	0.915709	−	0.401842i
$568$	−20.4042	−	11.7001i	−0.856142	−	0.490926i
$569$	7.05055	+	1.88919i	0.295575	+	0.0791990i	0.403559	−	0.914954i	$-0.367773\pi$
$569$	7.05055	+	1.88919i	0.295575	+	0.0791990i	−0.107984	+	0.994153i	$0.534440\pi$
$570$	−29.0812	−	8.18411i	−1.21808	−	0.342795i
$571$	13.3756	−	10.2635i	0.559752	−	0.429513i	−0.289747	−	0.957103i	$-0.593571\pi$
$571$	13.3756	−	10.2635i	0.559752	−	0.429513i	0.849499	+	0.527591i	$0.176905\pi$
$572$	−21.4969	−	7.77629i	−0.898830	−	0.325143i
$573$	−32.5623	+	26.5815i	−1.36031	+	1.11046i
$574$	−13.5499	−	18.0817i	−0.565561	−	0.754715i
$575$	3.81526			0.159107
$576$	−15.8116	+	18.0553i	−0.658818	+	0.752302i
$577$	−9.71119	+	16.8203i	−0.404282	+	0.700237i	−0.994238	−	0.107199i	$-0.965812\pi$
$577$	−9.71119	+	16.8203i	−0.404282	+	0.700237i	0.589956	+	0.807436i	$0.299145\pi$
$578$	−9.16952	−	13.0680i	−0.381402	−	0.543558i
$579$	27.4773	+	10.4235i	1.14192	+	0.433187i
$580$	−19.4540	+	16.3893i	−0.807785	+	0.680529i
$581$	−5.49739	−	33.6060i	−0.228070	−	1.39421i
$582$	7.41913	+	29.1442i	0.307533	+	1.20807i
$583$	8.32952	+	2.23189i	0.344973	+	0.0924353i
$584$	−16.2888	−	28.0214i	−0.674034	−	1.15953i
$585$	19.6382	−	22.1592i	0.811940	−	0.916168i
$586$	16.9851	+	5.33699i	0.701648	+	0.220469i
$587$	−35.2056	−	14.5826i	−1.45309	−	0.601890i	−0.490158	−	0.871634i	$-0.663061\pi$
$587$	−35.2056	−	14.5826i	−1.45309	−	0.601890i	−0.962932	+	0.269744i	$0.913061\pi$
$588$	−2.98904	+	24.0638i	−0.123266	+	0.992374i
$589$	−25.0783	−	60.5444i	−1.03333	−	2.49469i
$590$	−16.0169	+	19.1265i	−0.659407	+	0.787425i
$591$	4.77328	−	20.2330i	0.196347	−	0.832276i
$592$	4.13452	−	2.17304i	0.169928	−	0.0893116i
$593$	−1.69805	−	2.94111i	−0.0697306	−	0.120777i	0.829052	−	0.559171i	$-0.188881\pi$
$593$	−1.69805	−	2.94111i	−0.0697306	−	0.120777i	−0.898783	+	0.438394i	$0.855547\pi$
$594$	15.6831	+	5.63584i	0.643486	+	0.231241i
$595$	−10.0540	−	7.22710i	−0.412174	−	0.296282i
$596$	−10.1726	+	3.22944i	−0.416684	+	0.132283i
$597$	−21.5123	+	9.67963i	−0.880439	+	0.396161i
$598$	5.07307	+	22.7769i	0.207453	+	0.931418i
$599$	5.96400	+	22.2579i	0.243682	+	0.909435i	0.974041	+	0.226371i	$0.0726862\pi$
$599$	5.96400	+	22.2579i	0.243682	+	0.909435i	−0.730359	+	0.683064i	$0.760647\pi$
$600$	−3.62344	−	4.41201i	−0.147926	−	0.180120i
$601$	11.1296	+	11.1296i	0.453988	+	0.453988i	0.896676	−	0.442688i	$-0.145975\pi$
$601$	11.1296	+	11.1296i	0.453988	+	0.453988i	−0.442688	+	0.896676i	$0.645975\pi$
$602$	−2.13680	+	3.60548i	−0.0870894	+	0.146949i
$603$	−3.99824	+	0.773669i	−0.162821	+	0.0315063i
$604$	−31.6936	+	14.8550i	−1.28959	+	0.604443i
$605$	11.3711	+	1.49704i	0.462302	+	0.0608632i
$606$	−6.02496	−	4.74420i	−0.244747	−	0.192720i
$607$	3.11629	−	1.79919i	0.126486	−	0.0730269i	−0.435422	−	0.900227i	$-0.643401\pi$
$607$	3.11629	−	1.79919i	0.126486	−	0.0730269i	0.561908	+	0.827200i	$0.310067\pi$
$608$	−34.8219	−	7.54006i	−1.41221	−	0.305790i
$609$	28.2234	−	9.45226i	1.14367	−	0.383025i
$610$	0.816810	−	1.75617i	0.0330717	−	0.0711052i
$611$	−33.6804	−	25.8439i	−1.36256	−	1.04553i
$612$	−0.359248	+	14.3349i	−0.0145217	+	0.579456i
$613$	−0.275540	−	0.359091i	−0.0111290	−	0.0145035i	0.787756	−	0.615988i	$-0.211243\pi$
$613$	−0.275540	−	0.359091i	−0.0111290	−	0.0145035i	−0.798885	+	0.601484i	$0.794576\pi$
$614$	−15.1532	+	7.90723i	−0.611533	+	0.319110i
$615$	18.0384	+	9.70222i	0.727379	+	0.391231i
$616$	−13.1027	+	10.7856i	−0.527922	+	0.434562i
$617$	15.1546	+	15.1546i	0.610101	+	0.610101i	0.942972	−	0.332871i	$-0.108017\pi$
$617$	15.1546	+	15.1546i	0.610101	+	0.610101i	−0.332871	+	0.942972i	$0.608017\pi$
$618$	−0.358896	+	28.6463i	−0.0144369	+	1.15232i
$619$	10.5681	+	13.7726i	0.424767	+	0.553567i	0.955889	−	0.293728i	$-0.0948961\pi$
$619$	10.5681	+	13.7726i	0.424767	+	0.553567i	−0.531122	+	0.847295i	$0.678229\pi$
$620$	−8.74140	+	39.8009i	−0.351063	+	1.59844i
$621$	−3.73327	−	16.5965i	−0.149811	−	0.665995i
$622$	−15.7444	−	43.1252i	−0.631294	−	1.72916i
$623$	20.4312	+	10.9596i	0.818561	+	0.439086i
$624$	21.5215	−	27.4983i	0.861550	−	1.10081i
$625$	−15.4282	+	8.90746i	−0.617127	+	0.356299i
$626$	−4.88355	+	27.8564i	−0.195186	+	1.11337i
$627$	3.96641	+	24.4198i	0.158403	+	0.975232i
$628$	−1.91300	−	41.9193i	−0.0763369	−	1.67276i
$629$	1.06795	−	2.57827i	0.0425821	−	0.102802i
$630$	−6.71885	−	20.9289i	−0.267686	−	0.833827i
$631$	−8.25051	−	8.25051i	−0.328448	−	0.328448i	0.523548	−	0.851996i	$-0.324608\pi$
$631$	−8.25051	−	8.25051i	−0.328448	−	0.328448i	−0.851996	+	0.523548i	$0.824608\pi$
$632$	−17.8617	−	17.7564i	−0.710500	−	0.706313i
$633$	−12.2765	−	19.8573i	−0.487946	−	0.789258i
$634$	15.9773	−	25.1339i	0.634539	−	0.998196i
$635$	13.8878	−	1.82836i	0.551120	−	0.0725564i
$636$	−7.20517	+	11.0269i	−0.285703	+	0.437244i
$637$	2.41148	−	35.1983i	0.0955463	−	1.39461i
$638$	18.8879	+	8.78493i	0.747779	+	0.347799i
$639$	−22.3170	−	11.1504i	−0.882845	−	0.441104i
$640$	15.0798	+	16.2305i	0.596081	+	0.641569i
$641$	19.6898	+	11.3679i	0.777701	+	0.449006i	0.835615	−	0.549316i	$-0.185112\pi$
$641$	19.6898	+	11.3679i	0.777701	+	0.449006i	−0.0579138	+	0.998322i	$0.518445\pi$
$642$	−1.27391	+	0.509067i	−0.0502770	+	0.0200913i
$643$	3.75320	+	9.06102i	0.148012	+	0.357332i	0.980445	−	0.196793i	$-0.0630529\pi$
$643$	3.75320	+	9.06102i	0.148012	+	0.357332i	−0.832433	+	0.554125i	$0.813053\pi$
$644$	16.4664	+	5.38103i	0.648869	+	0.212042i
$645$	0.382229	−	3.77987i	0.0150502	−	0.148832i
$646$	−18.8725	+	9.84804i	−0.742528	+	0.387466i
$647$	35.6893	−	9.56293i	1.40309	−	0.375958i	0.523638	−	0.851941i	$-0.324574\pi$
$647$	35.6893	−	9.56293i	1.40309	−	0.375958i	0.879454	+	0.475983i	$0.157908\pi$
$648$	−15.6468	+	20.0793i	−0.614666	+	0.788788i
$649$	19.7333	+	5.28752i	0.774599	+	0.207553i
$650$	5.61793	+	6.11878i	0.220353	+	0.239998i
$651$	26.6515	−	39.5365i	1.04455	−	1.54956i
$652$	7.32547	−	14.1401i	0.286888	−	0.553767i
$653$	23.6757	+	18.1670i	0.926502	+	0.710930i	0.957453	−	0.288591i	$-0.0931866\pi$
$653$	23.6757	+	18.1670i	0.926502	+	0.710930i	−0.0309502	+	0.999521i	$0.509853\pi$
$654$	−3.42697	−	28.8155i	−0.134005	−	1.12678i
$655$	−11.7830	+	20.4088i	−0.460400	+	0.797436i
$656$	21.9322	+	10.1221i	0.856310	+	0.395203i
$657$	−18.9501	−	28.6832i	−0.739315	−	1.11904i
$658$	−29.2528	+	11.7280i	−1.14039	+	0.457205i
$659$	15.7317	+	37.9796i	0.612819	+	1.47948i	0.859891	+	0.510478i	$0.170532\pi$
$659$	15.7317	+	37.9796i	0.612819	+	1.47948i	−0.247072	+	0.968997i	$0.579468\pi$
$660$	6.66192	−	13.8664i	0.259315	−	0.539748i
$661$	−31.9676	+	24.5296i	−1.24340	+	0.954091i	−0.999875	−	0.0158050i	$-0.994969\pi$
$661$	−31.9676	+	24.5296i	−1.24340	+	0.954091i	−0.243520	+	0.969896i	$0.578302\pi$
$662$	27.2741	−	6.07472i	1.06004	−	0.236101i
$663$	−0.628311	−	20.8538i	−0.0244016	−	0.809895i
$664$	22.2465	+	28.8155i	0.863332	+	1.11826i
$665$	22.3418	−	23.7836i	0.866377	−	0.922287i
$666$	4.24616	−	2.55216i	0.164536	−	0.0988941i
$667$	−2.77547	−	21.0818i	−0.107466	−	0.816289i
$668$	−9.39342	−	6.54980i	−0.363442	−	0.253419i
$669$	30.5194	−	4.95715i	1.17995	−	0.191655i
$670$	0.331333	+	3.74466i	0.0128005	+	0.144669i
$671$	−1.58608			−0.0612299
$672$	−9.41585	−	24.1525i	−0.363224	−	0.931702i
$673$	−42.6046			−1.64229			−0.821143	−	0.570722i	$-0.806663\pi$
$673$	−42.6046			−1.64229			−0.821143	+	0.570722i	$0.806663\pi$
$674$	−1.15603	−	13.0653i	−0.0445288	−	0.503256i
$675$	−4.10486	−	4.45193i	−0.157996	−	0.171355i
$676$	−14.1878	+	20.3475i	−0.545685	+	0.782596i
$677$	−0.994441	−	7.55353i	−0.0382195	−	0.290306i	−0.999871	−	0.0160332i	$-0.994896\pi$
$677$	−0.994441	−	7.55353i	−0.0382195	−	0.290306i	0.961652	−	0.274273i	$-0.0884371\pi$
$678$	8.09761	+	31.8094i	0.310987	+	1.22163i
$679$	−31.6238	−	7.42292i	−1.21361	−	0.284866i
$680$	13.1287	+	1.68897i	0.503464	+	0.0647690i
$681$	−13.6240	+	0.410481i	−0.522072	+	0.0157297i
$682$	32.5718	−	7.25467i	1.24724	−	0.277796i
$683$	7.72137	−	5.92482i	0.295450	−	0.226707i	−0.450390	−	0.892832i	$-0.648715\pi$
$683$	7.72137	−	5.92482i	0.295450	−	0.226707i	0.745840	+	0.666125i	$0.232048\pi$
$684$	−37.3315	−	5.86971i	−1.42740	−	0.224434i
$685$	11.7653	+	28.4040i	0.449529	+	1.08526i
$686$	−21.5664	−	14.8624i	−0.823409	−	0.567448i
$687$	−3.36136	−	11.1857i	−0.128244	−	0.426763i
$688$	0.177795	−	4.47696i	0.00677838	−	0.170682i
$689$	9.58248	−	16.5973i	0.365063	−	0.632308i
$690$	−15.5934	+	1.85449i	−0.593629	+	0.0705991i
$691$	19.8149	+	15.2045i	0.753795	+	0.578407i	0.912576	−	0.408906i	$-0.134090\pi$
$691$	19.8149	+	15.2045i	0.753795	+	0.578407i	−0.158781	+	0.987314i	$0.550756\pi$
$692$	1.58617	+	0.821738i	0.0602970	+	0.0312378i
$693$	−13.2197	+	12.2167i	−0.502176	+	0.464075i
$694$	12.2523	+	13.3447i	0.465092	+	0.506556i
$695$	−19.5746	−	5.24499i	−0.742506	−	0.198954i
$696$	−21.7433	+	23.2314i	−0.824176	+	0.880583i
$697$	13.9405	−	3.73535i	0.528034	−	0.141486i
$698$	−11.4775	+	5.98917i	−0.434428	+	0.226693i
$699$	−42.9692	−	4.34514i	−1.62525	−	0.164348i
$700$	6.03406	−	1.27193i	0.228066	−	0.0480745i
$701$	−2.82384	−	6.81736i	−0.106655	−	0.257488i	0.861538	−	0.507694i	$-0.169502\pi$
$701$	−2.82384	−	6.81736i	−0.106655	−	0.257488i	−0.968193	+	0.250206i	$0.919502\pi$
$702$	21.1197	−	30.4255i	0.797111	−	1.14833i
$703$	6.36926	+	3.67729i	0.240221	+	0.138692i
$704$	6.84366	−	16.8023i	0.257930	−	0.633260i
$705$	19.5836	−	20.8004i	0.737562	−	0.783387i
$706$	28.5184	+	13.2642i	1.07330	+	0.499203i
$707$	7.54977	−	3.40732i	0.283938	−	0.128146i
$708$	−17.0696	+	26.1235i	−0.641515	+	0.981783i
$709$	−19.2172	+	2.52999i	−0.721716	+	0.0950157i	−0.482431	−	0.875934i	$-0.660246\pi$
$709$	−19.2172	+	2.52999i	−0.721716	+	0.0950157i	−0.239285	+	0.970949i	$0.576913\pi$
$710$	−12.3545	+	19.4349i	−0.463657	+	0.729380i
$711$	−19.9924	−	17.7180i	−0.749774	−	0.664476i
$712$	−24.7858	+	0.0732545i	−0.928887	+	0.00274533i
$713$	−24.0863	−	24.0863i	−0.902039	−	0.902039i
$714$	−13.5559	−	7.49175i	−0.507318	−	0.280372i
$715$	−8.56544	+	20.6788i	−0.320329	+	0.773343i
$716$	7.37505	−	0.336562i	0.275619	−	0.0125779i
$717$	13.4044	−	2.17722i	0.500595	−	0.0813098i
$718$	3.32404	−	18.9608i	0.124052	−	0.707610i
$719$	29.2913	−	16.9113i	1.09238	−	0.630686i	0.158171	−	0.987412i	$-0.449440\pi$
$719$	29.2913	−	16.9113i	1.09238	−	0.630686i	0.934209	+	0.356725i	$0.116107\pi$
$720$	16.9539	+	16.2711i	0.631835	+	0.606388i
$721$	−27.2686	−	14.6272i	−1.01553	−	0.544745i
$722$	−10.0246	−	27.4580i	−0.373075	−	1.02188i
$723$	6.38395	−	16.8286i	0.237422	−	0.625864i
$724$	20.4465	+	4.49064i	0.759889	+	0.166893i
$725$	−4.60790	−	6.00513i	−0.171133	−	0.223025i
$726$	14.3455	+	0.179728i	0.532412	+	0.00667034i
$727$	21.4761	+	21.4761i	0.796505	+	0.796505i	0.982543	−	0.186037i	$-0.0595645\pi$
$727$	21.4761	+	21.4761i	0.796505	+	0.796505i	−0.186037	+	0.982543i	$0.559565\pi$
$728$	15.6167	+	34.3318i	0.578795	+	1.27242i
$729$	−15.3494	+	22.2125i	−0.568496	+	0.822686i
$730$	−28.1345	+	14.6811i	−1.04130	+	0.543373i
$731$	−1.62965	−	2.12380i	−0.0602747	−	0.0785515i
$732$	0.755153	−	2.30204i	0.0279113	−	0.0850860i
$733$	−17.2318	−	13.2224i	−0.636471	−	0.488381i	0.239404	−	0.970920i	$-0.423048\pi$
$733$	−17.2318	−	13.2224i	−0.636471	−	0.488381i	−0.875875	+	0.482539i	$0.839715\pi$
$734$	20.5263	−	44.1323i	0.757641	−	1.62895i
$735$	23.4031	+	3.99765i	0.863238	+	0.147455i
$736$	−18.2221	+	3.30567i	−0.671674	+	0.121849i
$737$	2.66606	−	1.53925i	0.0982055	−	0.0566990i
$738$	23.8392	+	9.38668i	0.877533	+	0.345528i
$739$	−9.96715	−	1.31220i	−0.366647	−	0.0482700i	−0.0550483	−	0.998484i	$-0.517531\pi$
$739$	−9.96715	−	1.31220i	−0.366647	−	0.0482700i	−0.311599	+	0.950214i	$0.600865\pi$
$740$	−1.94089	−	4.14093i	−0.0713485	−	0.152224i
$741$	54.7040	+	5.53178i	2.00960	+	0.203215i
$742$	−6.97286	−	12.4017i	−0.255982	−	0.455283i
$743$	−24.6163	−	24.6163i	−0.903084	−	0.903084i	0.0926173	−	0.995702i	$-0.470477\pi$
$743$	−24.6163	−	24.6163i	−0.903084	−	0.903084i	−0.995702	+	0.0926173i	$0.970477\pi$
$744$	−4.97840	+	50.7289i	−0.182517	+	1.85981i
$745$	2.70463	+	10.0938i	0.0990901	+	0.369809i
$746$	−5.38481	−	24.1766i	−0.197152	−	0.885166i
$747$	25.3071	+	29.1623i	0.925940	+	1.06699i
$748$	−3.27994	−	10.3316i	−0.119927	−	0.377762i
$749$	0.147417	−	1.47442i	0.00538651	−	0.0538741i
$750$	−23.6856	+	17.7076i	−0.864876	+	0.646591i
$751$	6.82153	+	11.8152i	0.248921	+	0.431144i	0.963227	−	0.268690i	$-0.0865907\pi$
$751$	6.82153	+	11.8152i	0.248921	+	0.431144i	−0.714306	+	0.699834i	$0.753257\pi$
$752$	21.5551	−	25.8949i	0.786033	−	0.944290i
$753$	5.89757	+	1.39133i	0.214919	+	0.0507028i
$754$	29.7233	−	35.4938i	1.08246	−	1.29261i
$755$	13.1149	+	31.6622i	0.477301	+	1.15231i
$756$	−11.4373	−	25.0037i	−0.415972	−	0.909378i
$757$	−6.28447	−	2.60311i	−0.228413	−	0.0946118i	0.265542	−	0.964099i	$-0.414449\pi$
$757$	−6.28447	−	2.60311i	−0.228413	−	0.0946118i	−0.493955	+	0.869488i	$0.664449\pi$
$758$	−27.2371	−	8.55833i	−0.989295	−	0.310852i
$759$	6.76220	+	10.9379i	0.245452	+	0.397022i
$760$	−8.92915	+	33.7224i	−0.323894	+	1.22324i
$761$	13.6120	+	3.64733i	0.493435	+	0.132216i	0.496952	−	0.867778i	$-0.334453\pi$
$761$	13.6120	+	3.64733i	0.493435	+	0.132216i	−0.00351641	+	0.999994i	$0.501119\pi$
$762$	16.9803	−	4.32260i	0.615131	−	0.156591i
$763$	29.3184	+	11.0841i	1.06140	+	0.401273i
$764$	31.2722	+	37.1199i	1.13139	+	1.34295i
$765$	14.0048	+	0.991222i	0.506346	+	0.0358377i
$766$	7.34370	+	10.4659i	0.265339	+	0.378149i
$767$	22.7016	−	39.3204i	0.819709	−	1.41978i
$768$	21.1286	+	17.9327i	0.762412	+	0.647092i
$769$	43.8227			1.58029			0.790143	−	0.612923i	$-0.210006\pi$
$769$	43.8227			1.58029			0.790143	+	0.612923i	$0.210006\pi$
$770$	9.96440	+	13.2970i	0.359092	+	0.479192i
$771$	−25.9666	−	31.8090i	−0.935165	−	1.14557i
$772$	11.5434	−	31.9107i	0.415455	−	1.14849i
$773$	−4.37658	+	3.35827i	−0.157415	+	0.120788i	−0.684466	−	0.729045i	$-0.739964\pi$
$773$	−4.37658	+	3.35827i	−0.157415	+	0.120788i	0.527051	+	0.849834i	$0.323298\pi$
$774$	−0.0835992	−	4.75154i	−0.00300491	−	0.170790i
$775$	−11.7124	−	3.13833i	−0.420722	−	0.112732i
$776$	33.5162	−	9.08689i	1.20316	−	0.326200i
$777$	0.328178	+	5.34100i	0.0117733	+	0.191607i
$778$	9.91203	−	9.10068i	0.355364	−	0.326275i
$779$	4.96453	+	37.7093i	0.177873	+	1.35108i
$780$	−25.9352	−	22.2774i	−0.928630	−	0.797658i
$781$	18.6975	+	2.46157i	0.669049	+	0.0880820i
$782$	−7.10406	+	8.48325i	−0.254041	+	0.303360i
$783$	−21.6136	+	25.9206i	−0.772408	+	0.926326i
$784$	27.8366	+	3.02082i	0.994163	+	0.107887i
$785$	−41.0863			−1.46643
$786$	−11.6211	+	27.0908i	−0.414511	+	0.966298i
$787$	1.44390	−	10.9675i	0.0514693	−	0.390948i	−0.946249	−	0.323438i	$-0.895161\pi$
$787$	1.44390	−	10.9675i	0.0514693	−	0.390948i	0.997719	−	0.0675101i	$-0.0215055\pi$
$788$	−23.4456	−	5.14933i	−0.835216	−	0.183437i
$789$	12.6508	+	28.1154i	0.450380	+	1.00094i
$790$	−18.1647	+	16.6778i	−0.646269	+	0.593369i
$791$	−34.5158	−	8.10174i	−1.22724	−	0.288065i
$792$	6.22655	−	18.2079i	0.221251	−	0.646989i
$793$	−0.912331	+	3.40487i	−0.0323978	+	0.120910i
$794$	18.5431	−	29.1702i	0.658070	−	1.03521i
$795$	10.4637	+	7.53949i	0.371108	+	0.267398i
$796$	11.5603	+	24.6642i	0.409745	+	0.874200i
$797$	14.6186	+	35.2924i	0.517817	+	1.25012i	0.939242	+	0.343257i	$0.111530\pi$
$797$	14.6186	+	35.2924i	0.517817	+	1.25012i	−0.421425	+	0.906863i	$0.638470\pi$
$798$	24.2379	−	32.8425i	0.858012	−	1.16261i
$799$		−	20.1303i		−	0.712160i
$800$	−5.02916	+	4.26236i	−0.177808	+	0.150697i
$801$	−26.2417	+	1.58273i	−0.927206	+	0.0559229i
$802$	10.9036	+	15.5393i	0.385018	+	0.548712i
$803$	20.6173	+	15.8202i	0.727570	+	0.558284i
$804$	0.964730	+	4.60239i	0.0340234	+	0.162314i
$805$	5.99812	−	15.8655i	0.211406	−	0.559185i
$806$	3.16195	−	74.0955i	0.111375	−	2.60990i
$807$	−0.583325	+	0.0175752i	−0.0205340	+	0.000618676i
$808$	−5.36976	+	7.04100i	−0.188908	+	0.247702i
$809$	−27.9252	+	7.48253i	−0.981797	+	0.263072i	−0.713801	−	0.700348i	$-0.753028\pi$
$809$	−27.9252	+	7.48253i	−0.981797	+	0.263072i	−0.267996	+	0.963420i	$0.586361\pi$
$810$	18.9409	+	16.2003i	0.665516	+	0.569219i
$811$	−10.3197	+	24.9138i	−0.362372	+	0.874843i	0.632580	+	0.774495i	$0.281996\pi$
$811$	−10.3197	+	24.9138i	−0.362372	+	0.874843i	−0.994952	+	0.100349i	$0.968004\pi$
$812$	−11.4178	−	32.4167i	−0.400686	−	1.13760i
$813$	29.7202	−	24.2614i	1.04233	−	0.850886i
$814$	−2.40443	+	2.87123i	−0.0842752	+	0.100636i
$815$	−13.5033	−	7.79612i	−0.472999	−	0.273086i
$816$	16.5570	+	0.158495i	0.579611	+	0.00554843i
$817$	6.10974	−	3.52746i	0.213753	−	0.123410i
$818$	−29.4434	+	10.7494i	−1.02947	+	0.375844i
$819$	18.6217	+	35.4063i	0.650696	+	1.23720i
$820$	10.8793	−	20.9999i	0.379923	−	0.733349i
$821$	−13.2186	+	1.74027i	−0.461333	+	0.0607357i	−0.357611	−	0.933871i	$-0.616409\pi$
$821$	−13.2186	+	1.74027i	−0.461333	+	0.0607357i	−0.103722	+	0.994606i	$0.533075\pi$
$822$	18.8099	+	33.5433i	0.656071	+	1.16996i
$823$	−26.4571	+	7.08915i	−0.922235	+	0.247112i	−0.688541	−	0.725198i	$-0.741748\pi$
$823$	−26.4571	+	7.08915i	−0.922235	+	0.247112i	−0.233695	+	0.972310i	$0.575082\pi$
$824$	33.0803	−	0.0977691i	1.15241	−	0.00340595i
$825$	4.03147	+	2.16839i	0.140358	+	0.0754935i
$826$	−16.5193	−	29.3807i	−0.574779	−	1.02229i
$827$	9.48114	−	22.8895i	0.329691	−	0.795946i	−0.668923	−	0.743331i	$-0.733245\pi$
$827$	9.48114	−	22.8895i	0.329691	−	0.795946i	0.998615	−	0.0526143i	$-0.0167554\pi$
$828$	−19.0950	+	4.60700i	−0.663596	+	0.160104i
$829$	−0.593608	+	4.50890i	−0.0206169	+	0.156601i	−0.998657	−	0.0518182i	$-0.983498\pi$
$829$	−0.593608	+	4.50890i	−0.0206169	+	0.156601i	0.978040	+	0.208419i	$0.0668317\pi$
$830$	29.1771	−	20.4729i	1.01275	−	0.710625i
$831$	−18.9918	−	17.8809i	−0.658820	−	0.620281i
$832$	−32.1333	−	24.3563i	−1.11402	−	0.844403i
$833$	13.9373	−	9.25319i	0.482901	−	0.320604i
$834$	−25.0889	−	3.62332i	−0.868757	−	0.125465i
$835$	−6.82557	+	8.89526i	−0.236209	+	0.307833i
$836$	28.1232	−	5.01604i	0.972663	−	0.173483i
$837$	−2.19113	+	54.0202i	−0.0757366	+	1.86721i
$838$	25.6632	−	13.3916i	0.886521	−	0.462604i
$839$	−36.1307	−	36.1307i	−1.24737	−	1.24737i	−0.956877	−	0.290492i	$-0.906181\pi$
$839$	−36.1307	−	36.1307i	−1.24737	−	1.24737i	−0.290492	−	0.956877i	$-0.593819\pi$
$840$	−24.0436	+	8.13150i	−0.829582	+	0.280563i
$841$	−9.32399	+	9.32399i	−0.321517	+	0.321517i
$842$	−9.42826	+	30.0057i	−0.324919	+	1.03406i
$843$	5.32061	+	3.83371i	0.183252	+	0.132040i
$844$	−22.7070	+	14.5290i	−0.781609	+	0.500108i
$845$	19.2684	+	14.7852i	0.662854	+	0.508625i
$846$	21.2526	−	28.7296i	0.730680	−	0.987744i
$847$	−7.32501	+	13.6556i	−0.251690	+	0.469211i
$848$	12.8600	+	8.12168i	0.441615	+	0.278899i
$849$	4.60755	+	4.33802i	0.158131	+	0.148881i
$850$	−0.680148	+	3.87966i	−0.0233289	+	0.133071i
$851$	3.79012	+	0.498979i	0.129924	+	0.0171048i
$852$	−12.4749	+	25.9657i	−0.427382	+	0.889569i
$853$	43.2967	+	17.9341i	1.48245	+	0.614051i	0.969659	−	0.244463i	$-0.0786115\pi$
$853$	43.2967	+	17.9341i	1.48245	+	0.614051i	0.512791	+	0.858513i	$0.328612\pi$
$854$	1.82918	+	1.87137i	0.0625933	+	0.0640370i
$855$	−7.40741	+	36.2516i	−0.253328	+	1.23978i
$856$	0.610524	+	1.46170i	0.0208673	+	0.0499599i
$857$	−10.9489	−	40.8620i	−0.374009	−	1.39582i	−0.854787	−	0.518978i	$-0.826313\pi$
$857$	−10.9489	−	40.8620i	−0.374009	−	1.39582i	0.480778	−	0.876842i	$-0.340354\pi$
$858$	−7.58461	+	26.9510i	−0.258934	+	0.920091i
$859$	1.45924	+	11.0840i	0.0497885	+	0.378181i	0.998140	+	0.0609604i	$0.0194163\pi$
$859$	1.45924	+	11.0840i	0.0497885	+	0.378181i	−0.948352	+	0.317221i	$0.897250\pi$
$860$	−4.37093	−	0.373730i	−0.149048	−	0.0127441i
$861$	−20.8803	+	18.1613i	−0.711599	+	0.618935i
$862$	−30.3815	−	14.1307i	−1.03480	−	0.481293i
$863$	18.2875	+	31.6748i	0.622512	+	1.07822i	0.989016	+	0.147807i	$0.0472213\pi$
$863$	18.2875	+	31.6748i	0.622512	+	1.07822i	−0.366504	+	0.930416i	$0.619445\pi$
$864$	23.4625	+	17.7063i	0.798210	+	0.602379i
$865$	0.874534	−	1.51474i	0.0297350	−	0.0515026i
$866$	−1.57701	−	17.8231i	−0.0535891	−	0.605653i
$867$	−15.1461	+	12.3642i	−0.514390	+	0.419911i
$868$	−46.1238	−	30.0640i	−1.56554	−	1.02044i
$869$	18.6568	+	7.72790i	0.632889	+	0.262151i
$870$	21.7519	+	22.3038i	0.737457	+	0.756170i
$871$	−1.77079	−	6.60867i	−0.0600009	−	0.223926i
$872$	−33.2081	+	4.47181i	−1.12457	+	0.151435i
$873$	34.9391	−	11.6576i	1.18251	−	0.394550i
$874$	−19.7217	−	21.4800i	−0.667098	−	0.726571i
$875$	−5.15674	−	31.5236i	−0.174330	−	1.06569i
$876$	−32.7778	+	22.3919i	−1.10746	+	0.756553i
$877$	14.0419	−	18.2997i	0.474160	−	0.617937i	−0.493638	−	0.869668i	$-0.664333\pi$
$877$	14.0419	−	18.2997i	0.474160	−	0.617937i	0.967797	+	0.251731i	$0.0809998\pi$
$878$	−7.82113	+	44.6128i	−0.263950	+	1.50561i
$879$	5.00674	−	21.2226i	0.168873	−	0.715821i
$880$	−16.1287	−	7.44370i	−0.543698	−	0.250927i
$881$	−15.5598			−0.524222			−0.262111	−	0.965038i	$-0.584419\pi$
$881$	−15.5598			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$882$	29.6602	+	1.50839i	0.998709	+	0.0507902i
$883$	2.93230	−	1.21460i	0.0986797	−	0.0408745i	−0.332797	−	0.942998i	$-0.607993\pi$
$883$	2.93230	−	1.21460i	0.0986797	−	0.0408745i	0.431477	+	0.902124i	$0.357993\pi$
$884$	−24.0658	+	1.09825i	−0.809420	+	0.0369380i
$885$	24.7893	+	17.8617i	0.833282	+	0.600413i
$886$	−52.2461	+	11.6367i	−1.75524	+	0.390942i
$887$	−17.0202	−	4.56055i	−0.571482	−	0.153128i	−0.0385061	−	0.999258i	$-0.512260\pi$
$887$	−17.0202	−	4.56055i	−0.571482	−	0.153128i	−0.532976	+	0.846130i	$0.678927\pi$
$888$	−3.02254	−	4.85683i	−0.101430	−	0.162985i
$889$	−4.32481	+	18.4250i	−0.145049	+	0.617954i
$890$	−1.03467	+	24.2460i	−0.0346823	+	0.812728i
$891$	5.48772	−	19.6588i	0.183845	−	0.658595i
$892$	−6.26897	−	35.1480i	−0.209901	−	1.17684i
$893$	52.5975	+	6.92460i	1.76011	+	0.231723i
$894$	4.85058	+	12.1383i	0.162228	+	0.405964i
$895$		−	7.22849i		−	0.241622i
$896$	−27.7172	+	11.3030i	−0.925966	+	0.377606i
$897$	27.3704	−	8.22493i	0.913871	−	0.274622i
$898$	−4.04125	−	45.6734i	−0.134858	−	1.52414i
$899$	−8.82092	+	67.0015i	−0.294194	+	2.23463i
$900$	−5.06664	+	4.81890i	−0.168888	+	0.160630i
$901$	9.00984	−	1.18617i	0.300161	−	0.0395170i
$902$	−19.3501	−	0.825743i	−0.644286	−	0.0274942i
$903$	4.59438	+	2.28906i	0.152891	+	0.0761751i
$904$	36.5812	−	9.91788i	1.21667	−	0.329864i
$905$	5.30489	−	19.7981i	0.176340	−	0.658111i
$906$	20.9676	+	37.3911i	0.696602	+	1.24223i
$907$	−0.915859	−	1.19357i	−0.0304106	−	0.0396319i	0.777901	−	0.628387i	$-0.216285\pi$
$907$	−0.915859	−	1.19357i	−0.0304106	−	0.0396319i	−0.808311	+	0.588756i	$0.799618\pi$
$908$	0.717494	+	15.7224i	0.0238109	+	0.521765i
$909$	−5.25858	+	7.78195i	−0.174416	+	0.258111i
$910$	34.2767	−	13.7422i	1.13626	−	0.455549i
$911$			14.7262i			0.487902i	0.969788	+	0.243951i	$0.0784436\pi$
$911$			14.7262i			0.487902i	−0.969788	+	0.243951i	$0.921556\pi$
$912$	−6.10954	+	43.2065i	−0.202307	+	1.43071i
$913$	−25.2779	−	14.5942i	−0.836577	−	0.482998i
$914$	−8.96057	−	1.57089i	−0.296389	−	0.0519604i
$915$	−2.21790	−	0.841360i	−0.0733215	−	0.0278145i
$916$	−12.8545	+	4.08088i	−0.424726	+	0.134836i
$917$	−20.1628	−	24.6425i	−0.665833	−	0.813768i
$918$	17.5422	−	0.837617i	0.578978	−	0.0276455i
$919$	5.63173	−	21.0179i	0.185774	−	0.693316i	−0.808690	−	0.588235i	$-0.799823\pi$
$919$	5.63173	−	21.0179i	0.185774	−	0.693316i	0.994464	−	0.105081i	$-0.0335103\pi$
$920$	2.41990	+	17.9704i	0.0797816	+	0.592465i
$921$	11.0080	+	17.8056i	0.362726	+	0.586714i
$922$	28.5632	−	14.9049i	0.940680	−	0.490866i
$923$	16.0393	−	38.7224i	0.527941	−	1.27456i
$924$	14.3413	+	15.0446i	0.471794	+	0.494931i
$925$	1.25724	−	0.520765i	0.0413377	−	0.0171226i
$926$	−24.7854	+	2.19305i	−0.814500	+	0.0720682i
$927$	35.0235	−	2.11239i	1.15032	−	0.0693798i
$928$	27.2108	+	24.6886i	0.893238	+	0.810444i
$929$	−34.2743	+	19.7883i	−1.12450	+	0.649233i	−0.942547	−	0.334074i	$-0.891577\pi$
$929$	−34.2743	+	19.7883i	−1.12450	+	0.649233i	−0.181957	+	0.983306i	$0.558243\pi$
$930$	49.3953	+	7.13363i	1.61973	+	0.233921i
$931$	19.3829	+	39.5992i	0.635250	+	1.29781i
$932$	−4.24853	+	49.6883i	−0.139165	+	1.62759i
$933$	−51.2757	+	23.0719i	−1.67869	+	0.755341i
$934$	24.7970	−	39.0082i	0.811382	−	1.27639i
$935$	−10.2517	+	2.74693i	−0.335265	+	0.0898341i
$936$	−35.5057	−	23.8401i	−1.16054	−	0.779236i
$937$	6.95961	−	6.95961i	0.227361	−	0.227361i	−0.584229	−	0.811589i	$-0.698603\pi$
$937$	6.95961	−	6.95961i	0.227361	−	0.227361i	0.811589	+	0.584229i	$0.198603\pi$
$938$	−4.89081	−	1.37043i	−0.159691	−	0.0447463i
$939$	34.4616	+	3.48483i	1.12461	+	0.113723i
$940$	−24.3654	−	22.2386i	−0.794713	−	0.725344i
$941$	−4.56286	+	34.6584i	−0.148745	+	1.12983i	0.740387	+	0.672180i	$0.234642\pi$
$941$	−4.56286	+	34.6584i	−0.148745	+	1.12983i	−0.889132	+	0.457650i	$0.848691\pi$
$942$	−51.0343	+	6.06940i	−1.66279	+	0.197752i
$943$	9.88501	+	17.1213i	0.321900	+	0.557547i
$944$	30.4664	+	19.2409i	0.991598	+	0.626238i
$945$	−24.9664	+	10.0707i	−0.812158	+	0.327600i
$946$	1.23201	+	3.37457i	0.0400561	+	0.109717i
$947$	15.3242	−	19.9709i	0.497970	−	0.648967i	−0.474976	−	0.879999i	$-0.657543\pi$
$947$	15.3242	−	19.9709i	0.497970	−	0.648967i	0.972946	+	0.231031i	$0.0742100\pi$
$948$	−20.0991	+	23.3992i	−0.652787	+	0.759972i
$949$	45.8210	−	35.1597i	1.48741	−	1.14133i
$950$	−9.90300	−	3.11168i	−0.321296	−	0.100956i
$951$	−32.1239	−	17.2783i	−1.04169	−	0.560287i
$952$	−8.40734	+	15.7851i	−0.272483	+	0.511598i
$953$	34.9184	−	34.9184i	1.13112	−	1.13112i	0.141128	−	0.989991i	$-0.454927\pi$
$953$	34.9184	−	34.9184i	1.13112	−	1.13112i	0.989991	−	0.141128i	$-0.0450728\pi$
$954$	14.1109	+	7.81926i	0.456859	+	0.253158i
$955$	37.7025	−	28.9301i	1.22002	−	0.936157i
$956$	−2.75338	−	15.4373i	−0.0890506	−	0.499277i
$957$	9.04897	−	23.8539i	0.292512	−	0.771086i
$958$	−11.4367	+	24.5893i	−0.369503	+	0.794444i
$959$	−41.5183	+	1.29777i	−1.34070	+	0.0419073i
$960$	18.4829	−	19.8652i	0.596533	−	0.641148i
$961$	38.6294	+	66.9080i	1.24611	+	2.15832i
$962$	4.78067	+	6.81320i	0.154135	+	0.219667i
$963$	0.735260	+	1.51075i	0.0236934	+	0.0486832i
$964$	−19.5438	−	7.06980i	−0.629465	−	0.227703i
$965$	−30.6963	−	12.7148i	−0.988147	−	0.409304i
$966$	5.10671	−	20.5930i	0.164306	−	0.662568i
$967$	15.1363	−	15.1363i	0.486750	−	0.486750i	−0.420529	−	0.907279i	$-0.638155\pi$
$967$	15.1363	−	15.1363i	0.486750	−	0.486750i	0.907279	+	0.420529i	$0.138155\pi$
$968$	−0.0489609	−	16.5660i	−0.00157366	−	0.532451i
$969$	13.7099	+	22.1759i	0.440425	+	0.712393i
$970$	−7.39179	−	33.1874i	−0.237336	−	1.06558i
$971$	4.30331	+	32.6869i	0.138100	+	1.04897i	0.910404	+	0.413720i	$0.135771\pi$
$971$	4.30331	+	32.6869i	0.138100	+	1.04897i	−0.772304	+	0.635253i	$0.780896\pi$
$972$	25.9201	+	17.3247i	0.831389	+	0.555691i
$973$	15.9812	−	22.2323i	0.512335	−	0.712736i
$974$	−10.3544	−	28.3614i	−0.331775	−	0.908758i
$975$	6.97387	−	7.40716i	0.223343	−	0.237219i
$976$	−2.67135	−	0.830715i	−0.0855079	−	0.0265905i
$977$	10.1767	−	17.6266i	0.325582	−	0.563925i	−0.656048	−	0.754719i	$-0.727773\pi$
$977$	10.1767	−	17.6266i	0.325582	−	0.563925i	0.981630	+	0.190794i	$0.0611063\pi$
$978$	−17.9244	−	7.68901i	−0.573160	−	0.245867i
$979$	18.3605	−	7.60515i	0.586803	−	0.243062i
$980$	4.19713	−	27.0918i	0.134072	−	0.865417i
$981$	−34.8931	+	6.75191i	−1.11405	+	0.215572i
$982$	14.7145	+	4.62354i	0.469559	+	0.147543i
$983$	−0.428698	−	1.59992i	−0.0136733	−	0.0510296i	0.958752	−	0.284244i	$-0.0917424\pi$
$983$	−0.428698	−	1.59992i	−0.0136733	−	0.0510296i	−0.972425	+	0.233214i	$0.925076\pi$
$984$	10.4113	−	27.6916i	0.331900	−	0.882777i
$985$	−6.08301	+	22.7021i	−0.193821	+	0.723349i
$986$	21.9324	+	0.935941i	0.698469	+	0.0298064i
$987$	16.9306	+	34.6881i	0.538906	+	1.10413i
$988$	5.40879	−	63.2580i	0.172077	−	2.01251i
$989$	2.23237	−	2.90928i	0.0709852	−	0.0925097i
$990$	−17.5310	−	6.90284i	−0.557173	−	0.219387i
$991$	−38.0382	−	21.9613i	−1.20832	−	0.697625i	−0.245930	−	0.969288i	$-0.579093\pi$
$991$	−38.0382	−	21.9613i	−1.20832	−	0.697625i	−0.962393	+	0.271663i	$0.912427\pi$
$992$	58.6587	+	4.84094i	1.86242	+	0.153700i
$993$	−9.84889	−	32.7745i	−0.312545	−	1.04007i
$994$	−18.6590	−	24.8995i	−0.591827	−	0.789765i
$995$	24.6398	−	10.2062i	0.781135	−	0.323557i
$996$	33.2173	−	29.7400i	1.05253	−	0.942349i
$997$	−15.1193	−	19.7038i	−0.478832	−	0.624026i	0.490007	−	0.871719i	$-0.336994\pi$
$997$	−15.1193	−	19.7038i	−0.478832	−	0.624026i	−0.968839	+	0.247693i	$0.920328\pi$
$998$	−31.7272	−	20.1685i	−1.00431	−	0.638423i
$999$	−3.49556	−	4.95945i	−0.110595	−	0.156910i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.ch.a.11.5	✓	992
3.2	odd	2	inner	672.2.ch.a.11.120	yes	992
7.2	even	3	inner	672.2.ch.a.107.88	yes	992
21.2	odd	6	inner	672.2.ch.a.107.37	yes	992
32.3	odd	8	inner	672.2.ch.a.515.37	yes	992
96.35	even	8	inner	672.2.ch.a.515.88	yes	992
224.163	odd	24	inner	672.2.ch.a.611.120	yes	992
672.611	even	24	inner	672.2.ch.a.611.5	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.ch.a.11.5	✓	992	1.1	even	1	trivial
672.2.ch.a.11.120	yes	992	3.2	odd	2	inner
672.2.ch.a.107.37	yes	992	21.2	odd	6	inner
672.2.ch.a.107.88	yes	992	7.2	even	3	inner
672.2.ch.a.515.37	yes	992	32.3	odd	8	inner
672.2.ch.a.515.88	yes	992	96.35	even	8	inner
672.2.ch.a.611.5	yes	992	672.611	even	24	inner
672.2.ch.a.611.120	yes	992	224.163	odd	24	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.ch (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40871 + 0.124645i) q^{2} +(0.277691 + 1.70965i) q^{3} +(1.96893 - 0.351176i) q^{4} +(-0.255599 - 1.94146i) q^{5} +(-0.604284 - 2.37378i) q^{6} +(2.57575 + 0.604593i) q^{7} +(-2.72988 + 0.740122i) q^{8} +(-2.84578 + 0.949506i) q^{9} +O(q^{10})\)	\(q+(-1.40871 + 0.124645i) q^{2} +(0.277691 + 1.70965i) q^{3} +(1.96893 - 0.351176i) q^{4} +(-0.255599 - 1.94146i) q^{5} +(-0.604284 - 2.37378i) q^{6} +(2.57575 + 0.604593i) q^{7} +(-2.72988 + 0.740122i) q^{8} +(-2.84578 + 0.949506i) q^{9} +(0.602057 + 2.70310i) q^{10} +(1.79918 - 1.38056i) q^{11} +(1.14714 + 3.26865i) q^{12} +(-1.92877 - 4.65646i) q^{13} +(-3.70384 - 0.530643i) q^{14} +(3.24824 - 0.976110i) q^{15} +(3.75335 - 1.38288i) q^{16} +(1.19495 - 2.06972i) q^{17} +(3.89052 - 1.69229i) q^{18} +(4.99682 + 3.83419i) q^{19} +(-1.18505 - 3.73284i) q^{20} +(-0.318378 + 4.57150i) q^{21} +(-2.36245 + 2.16907i) q^{22} +(3.16226 + 0.847324i) q^{23} +(-2.02341 - 4.46159i) q^{24} +(1.12568 - 0.301625i) q^{25} +(3.29748 + 6.31919i) q^{26} +(-2.41357 - 4.60160i) q^{27} +(5.28378 + 0.285858i) q^{28} +(-2.48556 - 6.00067i) q^{29} +(-4.45416 + 1.77993i) q^{30} +(-9.01077 - 5.20237i) q^{31} +(-5.11501 + 2.41591i) q^{32} +(2.85989 + 2.69260i) q^{33} +(-1.42536 + 3.06458i) q^{34} +(0.515438 - 5.15525i) q^{35} +(-5.26968 + 2.86888i) q^{36} +(1.15771 - 0.152415i) q^{37} +(-7.51698 - 4.77844i) q^{38} +(7.42529 - 4.59057i) q^{39} +(2.13467 + 5.11078i) q^{40} +(4.27010 + 4.27010i) q^{41} +(-0.121311 - 6.47961i) q^{42} +(0.428652 - 1.03486i) q^{43} +(3.05764 - 3.35006i) q^{44} +(2.57081 + 5.28228i) q^{45} +(-4.56032 - 0.799476i) q^{46} +(7.29458 - 4.21153i) q^{47} +(3.40651 + 6.03288i) q^{48} +(6.26893 + 3.11456i) q^{49} +(-1.54816 + 0.565212i) q^{50} +(3.87032 + 1.46820i) q^{51} +(-5.43284 - 8.49089i) q^{52} +(2.31480 + 3.01671i) q^{53} +(3.97358 + 6.18148i) q^{54} +(-3.14018 - 3.14018i) q^{55} +(-7.47894 + 0.255903i) q^{56} +(-5.16754 + 9.60751i) q^{57} +(4.24939 + 8.14340i) q^{58} +(5.48396 + 7.14683i) q^{59} +(6.05276 - 3.06259i) q^{60} +(-0.554859 - 0.425758i) q^{61} +(13.3420 + 6.20549i) q^{62} +(-7.90406 + 0.725151i) q^{63} +(6.90444 - 4.04088i) q^{64} +(-8.54736 + 4.93482i) q^{65} +(-4.36437 - 3.43662i) q^{66} +(1.34586 + 0.177185i) q^{67} +(1.62594 - 4.49477i) q^{68} +(-0.570494 + 5.64163i) q^{69} +(-0.0835285 + 7.32650i) q^{70} +(5.88019 + 5.88019i) q^{71} +(7.06586 - 4.69826i) q^{72} +(2.96588 + 11.0688i) q^{73} +(-1.61188 + 0.359012i) q^{74} +(0.828262 + 1.84075i) q^{75} +(11.1849 + 5.79448i) q^{76} +(5.46892 - 2.46820i) q^{77} +(-9.88790 + 7.39230i) q^{78} +(4.45229 + 7.71159i) q^{79} +(-3.64417 - 6.93353i) q^{80} +(7.19688 - 5.40416i) q^{81} +(-6.54758 - 5.48309i) q^{82} +(-4.92540 - 11.8910i) q^{83} +(0.978541 + 9.11276i) q^{84} +(-4.32372 - 1.79094i) q^{85} +(-0.474857 + 1.51124i) q^{86} +(9.56881 - 5.91576i) q^{87} +(-3.88976 + 5.10038i) q^{88} +(8.46454 + 2.26807i) q^{89} +(-4.27993 - 7.12076i) q^{90} +(-2.15276 - 13.1600i) q^{91} +(6.52382 + 0.557810i) q^{92} +(6.39200 - 16.8499i) q^{93} +(-9.75101 + 6.84206i) q^{94} +(6.16677 - 10.6812i) q^{95} +(-5.55075 - 8.07398i) q^{96} -12.2775 q^{97} +(-9.21932 - 3.60612i) q^{98} +(-3.80922 + 5.63711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9}+O(q^{10}) \) 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9	\( 992 q - 4 q^{3} - 8 q^{4} - 16 q^{6} - 16 q^{7} - 4 q^{9} - 8 q^{10} - 4 q^{12} - 32 q^{13} - 32 q^{15} + 24 q^{16} - 4 q^{18} - 8 q^{19} - 8 q^{21} - 32 q^{22} - 44 q^{24} - 8 q^{25} - 16 q^{27} - 16 q^{28} - 36 q^{30} - 8 q^{33} + 64 q^{36} - 8 q^{37} - 4 q^{39} - 72 q^{40} - 68 q^{42} - 32 q^{43} - 4 q^{45} - 8 q^{46} - 16 q^{48} + 20 q^{51} + 16 q^{52} - 92 q^{54} - 32 q^{55} - 16 q^{57} + 24 q^{58} - 20 q^{60} - 8 q^{61} - 128 q^{64} - 20 q^{66} - 72 q^{67} - 16 q^{69} - 16 q^{70} - 4 q^{72} - 8 q^{73} + 16 q^{75} - 32 q^{76} + 136 q^{78} - 16 q^{79} - 48 q^{82} + 124 q^{84} + 48 q^{85} - 4 q^{87} - 8 q^{88} + 128 q^{90} - 64 q^{91} - 28 q^{93} - 64 q^{94} - 72 q^{96} - 64 q^{97} - 16 q^{99}+O(q^{100}) \) 992 * q - 4 * q^3 - 8 * q^4 - 16 * q^6 - 16 * q^7 - 4 * q^9 - 8 * q^10 - 4 * q^12 - 32 * q^13 - 32 * q^15 + 24 * q^16 - 4 * q^18 - 8 * q^19 - 8 * q^21 - 32 * q^22 - 44 * q^24 - 8 * q^25 - 16 * q^27 - 16 * q^28 - 36 * q^30 - 8 * q^33 + 64 * q^36 - 8 * q^37 - 4 * q^39 - 72 * q^40 - 68 * q^42 - 32 * q^43 - 4 * q^45 - 8 * q^46 - 16 * q^48 + 20 * q^51 + 16 * q^52 - 92 * q^54 - 32 * q^55 - 16 * q^57 + 24 * q^58 - 20 * q^60 - 8 * q^61 - 128 * q^64 - 20 * q^66 - 72 * q^67 - 16 * q^69 - 16 * q^70 - 4 * q^72 - 8 * q^73 + 16 * q^75 - 32 * q^76 + 136 * q^78 - 16 * q^79 - 48 * q^82 + 124 * q^84 + 48 * q^85 - 4 * q^87 - 8 * q^88 + 128 * q^90 - 64 * q^91 - 28 * q^93 - 64 * q^94 - 72 * q^96 - 64 * q^97 - 16 * q^99

Introduction

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