LMFDB - Embedded newform 77.2.n.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(17,77)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(77, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 27]))

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

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

chi := DirichletCharacter("77.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.n (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:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	77.17
Dual form			77.2.n.a.68.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.386517 + 0.348022i) q^{2} +(0.460952 + 1.03532i) q^{3} +(-0.180780 - 1.72001i) q^{4} +(0.678628 + 3.19269i) q^{5} +(-0.182146 + 0.560588i) q^{6} +(-1.97073 - 1.76528i) q^{7} +(1.14015 - 1.56929i) q^{8} +(1.14799 - 1.27497i) q^{9} +O(q^{10})$	\(q+(0.386517 + 0.348022i) q^{2} +(0.460952 + 1.03532i) q^{3} +(-0.180780 - 1.72001i) q^{4} +(0.678628 + 3.19269i) q^{5} +(-0.182146 + 0.560588i) q^{6} +(-1.97073 - 1.76528i) q^{7} +(1.14015 - 1.56929i) q^{8} +(1.14799 - 1.27497i) q^{9} +(-0.848825 + 1.47021i) q^{10} +(-2.68346 + 1.94911i) q^{11} +(1.69742 - 0.980007i) q^{12} +(-0.467677 - 1.43936i) q^{13} +(-0.147363 - 1.36817i) q^{14} +(-2.99263 + 2.17427i) q^{15} +(-2.39655 + 0.509402i) q^{16} +(-1.68086 - 1.86679i) q^{17} +(0.887437 - 0.0932734i) q^{18} +(0.167684 - 1.59541i) q^{19} +(5.36879 - 1.74442i) q^{20} +(0.919214 - 2.85404i) q^{21} +(-1.71554 - 0.180539i) q^{22} +(-1.98346 - 3.43545i) q^{23} +(2.15026 + 0.457052i) q^{24} +(-5.16504 + 2.29962i) q^{25} +(0.320164 - 0.719100i) q^{26} +(5.08265 + 1.65145i) q^{27} +(-2.68004 + 3.70880i) q^{28} +(4.95563 + 6.82084i) q^{29} +(-1.91340 - 0.201106i) q^{30} +(-1.98422 + 9.33500i) q^{31} +(-4.46333 - 2.57690i) q^{32} +(-3.25489 - 1.87978i) q^{33} -1.30652i q^{34} +(4.29862 - 7.48991i) q^{35} +(-2.40050 - 1.74407i) q^{36} +(6.07381 + 2.70423i) q^{37} +(0.620051 - 0.558296i) q^{38} +(1.27462 - 1.14767i) q^{39} +(5.78399 + 2.57520i) q^{40} +(3.25998 + 2.36851i) q^{41} +(1.34856 - 0.783228i) q^{42} -5.21386i q^{43} +(3.83761 + 4.26322i) q^{44} +(4.84966 + 2.79995i) q^{45} +(0.428971 - 2.01815i) q^{46} +(0.345400 + 0.0363030i) q^{47} +(-1.63209 - 2.24637i) q^{48} +(0.767543 + 6.95779i) q^{49} +(-2.79669 - 0.908701i) q^{50} +(1.15792 - 2.60072i) q^{51} +(-2.39117 + 1.06462i) q^{52} +(-3.34833 - 0.711709i) q^{53} +(1.38979 + 2.40719i) q^{54} +(-8.04399 - 7.24476i) q^{55} +(-5.01717 + 1.07994i) q^{56} +(1.72905 - 0.561802i) q^{57} +(-0.458364 + 4.36104i) q^{58} +(-0.669977 + 0.0704175i) q^{59} +(4.28078 + 4.75429i) q^{60} +(-7.31980 + 1.55587i) q^{61} +(-4.01572 + 2.91759i) q^{62} +(-4.51307 + 0.486096i) q^{63} +(0.685905 + 2.11100i) q^{64} +(4.27807 - 2.46994i) q^{65} +(-0.603866 - 1.85934i) q^{66} +(4.14200 - 7.17416i) q^{67} +(-2.90703 + 3.22858i) q^{68} +(2.64250 - 3.63709i) q^{69} +(4.26814 - 1.39896i) q^{70} +(0.797453 - 2.45431i) q^{71} +(-0.691912 - 3.25519i) q^{72} +(-1.24013 - 11.7990i) q^{73} +(1.40650 + 3.15905i) q^{74} +(-4.76167 - 4.28742i) q^{75} -2.77444 q^{76} +(8.72911 + 0.895908i) q^{77} +0.892075 q^{78} +(-8.76150 - 7.88889i) q^{79} +(-3.25273 - 7.30576i) q^{80} +(0.0950812 + 0.904637i) q^{81} +(0.435744 + 2.05001i) q^{82} +(-4.17113 + 12.8374i) q^{83} +(-5.07515 - 1.06510i) q^{84} +(4.81940 - 6.63334i) q^{85} +(1.81454 - 2.01525i) q^{86} +(-4.77741 + 8.27472i) q^{87} +(-0.000847655 + 6.43340i) q^{88} +(6.53328 - 3.77199i) q^{89} +(0.900033 + 2.77002i) q^{90} +(-1.61922 + 3.66218i) q^{91} +(-5.55045 + 4.03264i) q^{92} +(-10.5793 + 2.24870i) q^{93} +(0.120869 + 0.134238i) q^{94} +(5.20746 - 0.547326i) q^{95} +(0.610527 - 5.80878i) q^{96} +(-4.04522 + 1.31437i) q^{97} +(-2.12479 + 2.95643i) q^{98} +(-0.595529 + 5.65890i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9}+O(q^{10}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9	$ 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26} - 40 q^{28} - 40 q^{29} + 25 q^{30} + 9 q^{31} + 42 q^{33} + 5 q^{35} - 38 q^{36} - q^{37} + 33 q^{38} - 45 q^{39} + 75 q^{40} + 64 q^{42} + 30 q^{44} - 84 q^{45} - 20 q^{46} + 3 q^{47} + 59 q^{49} + 30 q^{50} + 55 q^{51} - 15 q^{52} - 3 q^{53} - 8 q^{56} + 60 q^{57} + 46 q^{58} - 3 q^{59} - 15 q^{60} - 30 q^{61} - 40 q^{63} + 12 q^{64} - 93 q^{66} + 44 q^{67} - 75 q^{68} - 27 q^{70} + 20 q^{71} - 60 q^{72} - 60 q^{73} + 45 q^{74} - 57 q^{75} + 92 q^{78} - 70 q^{79} - 75 q^{80} - 29 q^{81} - 129 q^{82} - 125 q^{84} + 10 q^{85} - 62 q^{86} + 19 q^{88} + 6 q^{89} - 12 q^{91} + 30 q^{92} - 92 q^{93} + 105 q^{94} + 30 q^{95} + 75 q^{96} - 12 q^{99}+O(q^{100}) $ 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	0.386517	+	0.348022i	0.273309	+	0.246088i	0.794375	−	0.607428i	$-0.207799\pi$
$2$	0.386517	+	0.348022i	0.273309	+	0.246088i	−0.521066	+	0.853517i	$0.674465\pi$
$3$	0.460952	+	1.03532i	0.266131	+	0.597739i	0.996339	−	0.0854847i	$-0.0272439\pi$
$3$	0.460952	+	1.03532i	0.266131	+	0.597739i	−0.730209	+	0.683224i	$0.760577\pi$
$4$	−0.180780	−	1.72001i	−0.0903902	−	0.860006i
$5$	0.678628	+	3.19269i	0.303492	+	1.42782i	0.820407	+	0.571780i	$0.193747\pi$
$5$	0.678628	+	3.19269i	0.303492	+	1.42782i	−0.516915	+	0.856037i	$0.672920\pi$
$6$	−0.182146	+	0.560588i	−0.0743609	+	0.228859i
$7$	−1.97073	−	1.76528i	−0.744865	−	0.667215i
$7$	−1.97073	−	1.76528i	−0.744865	−	0.667215i
$8$	1.14015	−	1.56929i	0.403105	−	0.554826i
$9$	1.14799	−	1.27497i	0.382664	−	0.424991i
$10$	−0.848825	+	1.47021i	−0.268422	+	0.464921i
$11$	−2.68346	+	1.94911i	−0.809094	+	0.587679i
$11$	−2.68346	+	1.94911i	−0.809094	+	0.587679i
$12$	1.69742	−	0.980007i	0.490004	−	0.282904i
$13$	−0.467677	−	1.43936i	−0.129710	−	0.399207i	0.865020	−	0.501738i	$-0.167306\pi$
$13$	−0.467677	−	1.43936i	−0.129710	−	0.399207i	−0.994730	+	0.102531i	$0.967306\pi$
$14$	−0.147363	−	1.36817i	−0.0393845	−	0.365659i
$15$	−2.99263	+	2.17427i	−0.772694	+	0.561395i
$16$	−2.39655	+	0.509402i	−0.599138	+	0.127351i
$17$	−1.68086	−	1.86679i	−0.407669	−	0.452763i	0.503990	−	0.863710i	$-0.331865\pi$
$17$	−1.68086	−	1.86679i	−0.407669	−	0.452763i	−0.911659	+	0.410947i	$0.865198\pi$
$18$	0.887437	−	0.0932734i	0.209171	−	0.0219847i
$19$	0.167684	−	1.59541i	0.0384695	−	0.366012i	−0.958304	−	0.285750i	$-0.907757\pi$
$19$	0.167684	−	1.59541i	0.0384695	−	0.366012i	0.996774	−	0.0802627i	$-0.0255759\pi$
$20$	5.36879	−	1.74442i	1.20050	−	0.390065i
$21$	0.919214	−	2.85404i	0.200589	−	0.622802i
$22$	−1.71554	−	0.180539i	−0.365754	−	0.0384910i
$23$	−1.98346	−	3.43545i	−0.413580	−	0.716342i	0.581698	−	0.813405i	$-0.302389\pi$
$23$	−1.98346	−	3.43545i	−0.413580	−	0.716342i	−0.995278	+	0.0970630i	$0.969055\pi$
$24$	2.15026	+	0.457052i	0.438920	+	0.0932953i
$25$	−5.16504	+	2.29962i	−1.03301	+	0.459924i
$26$	0.320164	−	0.719100i	0.0627893	−	0.141027i
$27$	5.08265	+	1.65145i	0.978156	+	0.317822i
$28$	−2.68004	+	3.70880i	−0.506480	+	0.700898i
$29$	4.95563	+	6.82084i	0.920238	+	1.26660i	0.963548	+	0.267537i	$0.0862098\pi$
$29$	4.95563	+	6.82084i	0.920238	+	1.26660i	−0.0433097	+	0.999062i	$0.513790\pi$
$30$	−1.91340	−	0.201106i	−0.349337	−	0.0367168i
$31$	−1.98422	+	9.33500i	−0.356376	+	1.67662i	0.325809	+	0.945436i	$0.394363\pi$
$31$	−1.98422	+	9.33500i	−0.356376	+	1.67662i	−0.682185	+	0.731180i	$0.738970\pi$
$32$	−4.46333	−	2.57690i	−0.789012	−	0.455536i
$33$	−3.25489	−	1.87978i	−0.566604	−	0.327228i
$34$		−	1.30652i		−	0.224067i
$35$	4.29862	−	7.48991i	0.726600	−	1.26603i
$36$	−2.40050	−	1.74407i	−0.400084	−	0.290678i
$37$	6.07381	+	2.70423i	0.998528	+	0.444573i	0.839886	−	0.542763i	$-0.182622\pi$
$37$	6.07381	+	2.70423i	0.998528	+	0.444573i	0.158642	+	0.987336i	$0.449288\pi$
$38$	0.620051	−	0.558296i	0.100585	−	0.0905676i
$39$	1.27462	−	1.14767i	0.204102	−	0.183774i
$40$	5.78399	+	2.57520i	0.914529	+	0.407175i
$41$	3.25998	+	2.36851i	0.509123	+	0.369900i	0.812491	−	0.582974i	$-0.198111\pi$
$41$	3.25998	+	2.36851i	0.509123	+	0.369900i	−0.303368	+	0.952874i	$0.598111\pi$
$42$	1.34856	−	0.783228i	0.208087	−	0.120855i
$43$		−	5.21386i		−	0.795106i	−0.917579	−	0.397553i	$-0.869859\pi$
$43$		−	5.21386i		−	0.795106i	0.917579	−	0.397553i	$-0.130141\pi$
$44$	3.83761	+	4.26322i	0.578541	+	0.642705i
$45$	4.84966	+	2.79995i	0.722945	+	0.417392i
$46$	0.428971	−	2.01815i	0.0632483	−	0.297560i
$47$	0.345400	+	0.0363030i	0.0503818	+	0.00529534i	0.129686	−	0.991555i	$-0.458603\pi$
$47$	0.345400	+	0.0363030i	0.0503818	+	0.00529534i	−0.0793040	+	0.996850i	$0.525270\pi$
$48$	−1.63209	−	2.24637i	−0.235571	−	0.324236i
$49$	0.767543	+	6.95779i	0.109649	+	0.993970i
$50$	−2.79669	−	0.908701i	−0.395512	−	0.128510i
$51$	1.15792	−	2.60072i	0.162141	−	0.364174i
$52$	−2.39117	+	1.06462i	−0.331596	+	0.147636i
$53$	−3.34833	−	0.711709i	−0.459928	−	0.0977607i	−0.0278800	−	0.999611i	$-0.508876\pi$
$53$	−3.34833	−	0.711709i	−0.459928	−	0.0977607i	−0.432048	+	0.901851i	$0.642209\pi$
$54$	1.38979	+	2.40719i	0.189126	+	0.327576i
$55$	−8.04399	−	7.24476i	−1.08465	−	0.976883i
$56$	−5.01717	+	1.07994i	−0.670447	+	0.144313i
$57$	1.72905	−	0.561802i	0.229018	−	0.0744124i
$58$	−0.458364	+	4.36104i	−0.0601861	+	0.572633i
$59$	−0.669977	+	0.0704175i	−0.0872236	+	0.00916757i	−0.148040	−	0.988981i	$-0.547296\pi$
$59$	−0.669977	+	0.0704175i	−0.0872236	+	0.00916757i	0.0608161	+	0.998149i	$0.480630\pi$
$60$	4.28078	+	4.75429i	0.552647	+	0.613776i
$61$	−7.31980	+	1.55587i	−0.937204	+	0.199209i	−0.651102	−	0.758990i	$-0.725693\pi$
$61$	−7.31980	+	1.55587i	−0.937204	+	0.199209i	−0.286102	+	0.958199i	$0.592360\pi$
$62$	−4.01572	+	2.91759i	−0.509996	+	0.370534i
$63$	−4.51307	+	0.486096i	−0.568593	+	0.0612423i
$64$	0.685905	+	2.11100i	0.0857381	+	0.263875i
$65$	4.27807	−	2.46994i	0.530629	−	0.306359i
$66$	−0.603866	−	1.85934i	−0.0743307	−	0.228869i
$67$	4.14200	−	7.17416i	0.506026	−	0.876463i	−0.493950	−	0.869490i	$-0.664447\pi$
$67$	4.14200	−	7.17416i	0.506026	−	0.876463i	0.999976	−	0.00697221i	$-0.00221934\pi$
$68$	−2.90703	+	3.22858i	−0.352529	+	0.391523i
$69$	2.64250	−	3.63709i	0.318119	−	0.437854i
$70$	4.26814	−	1.39896i	0.510140	−	0.167208i
$71$	0.797453	−	2.45431i	0.0946402	−	0.291273i	−0.892520	−	0.451009i	$-0.851064\pi$
$71$	0.797453	−	2.45431i	0.0946402	−	0.291273i	0.987160	+	0.159736i	$0.0510643\pi$
$72$	−0.691912	−	3.25519i	−0.0815426	−	0.383628i
$73$	−1.24013	−	11.7990i	−0.145146	−	1.38097i	−0.788327	−	0.615256i	$-0.789053\pi$
$73$	−1.24013	−	11.7990i	−0.145146	−	1.38097i	0.643181	−	0.765714i	$-0.277614\pi$
$74$	1.40650	+	3.15905i	0.163502	+	0.367232i
$75$	−4.76167	−	4.28742i	−0.549830	−	0.495069i
$76$	−2.77444			−0.318250
$77$	8.72911	+	0.895908i	0.994774	+	0.102098i
$78$	0.892075			0.101008
$79$	−8.76150	−	7.88889i	−0.985745	−	0.887569i	0.00791781	−	0.999969i	$-0.497480\pi$
$79$	−8.76150	−	7.88889i	−0.985745	−	0.887569i	−0.993663	+	0.112400i	$0.964146\pi$
$80$	−3.25273	−	7.30576i	−0.363667	−	0.816809i
$81$	0.0950812	+	0.904637i	0.0105646	+	0.100515i
$82$	0.435744	+	2.05001i	0.0481199	+	0.226386i
$83$	−4.17113	+	12.8374i	−0.457841	+	1.40909i	0.409927	+	0.912119i	$0.365554\pi$
$83$	−4.17113	+	12.8374i	−0.457841	+	1.40909i	−0.867767	+	0.496971i	$0.834446\pi$
$84$	−5.07515	−	1.06510i	−0.553744	−	0.116212i
$85$	4.81940	−	6.63334i	0.522738	−	0.719487i
$86$	1.81454	−	2.01525i	0.195667	−	0.217310i
$87$	−4.77741	+	8.27472i	−0.512192	+	0.887143i
$88$	−0.000847655		6.43340i	−9.03604e−5		0.685803i
$89$	6.53328	−	3.77199i	0.692526	−	0.399830i	−0.112032	−	0.993705i	$-0.535736\pi$
$89$	6.53328	−	3.77199i	0.692526	−	0.399830i	0.804558	+	0.593874i	$0.202402\pi$
$90$	0.900033	+	2.77002i	0.0948718	+	0.291985i
$91$	−1.61922	+	3.66218i	−0.169740	+	0.383900i
$92$	−5.55045	+	4.03264i	−0.578674	+	0.420431i
$93$	−10.5793	+	2.24870i	−1.09702	+	0.233179i
$94$	0.120869	+	0.134238i	0.0124667	+	0.0138456i
$95$	5.20746	−	0.547326i	0.534274	−	0.0561544i
$96$	0.610527	−	5.80878i	0.0623116	−	0.592856i
$97$	−4.04522	+	1.31437i	−0.410730	+	0.133454i	−0.507092	−	0.861892i	$-0.669279\pi$
$97$	−4.04522	+	1.31437i	−0.410730	+	0.133454i	0.0963618	+	0.995346i	$0.469279\pi$
$98$	−2.12479	+	2.95643i	−0.214637	+	0.298644i
$99$	−0.595529	+	5.65890i	−0.0598529	+	0.568741i
$100$	4.88911	+	8.46819i	0.488911	+	0.846819i
$101$	5.52306	+	1.17396i	0.549565	+	0.116814i	0.474322	−	0.880352i	$-0.342693\pi$
$101$	5.52306	+	1.17396i	0.549565	+	0.116814i	0.0752433	+	0.997165i	$0.476027\pi$
$102$	1.35266	−	0.602244i	0.133934	−	0.0596311i
$103$	−0.175308	+	0.393748i	−0.0172736	+	0.0387971i	−0.921976	−	0.387246i	$-0.873426\pi$
$103$	−0.175308	+	0.393748i	−0.0172736	+	0.0387971i	0.904703	+	0.426043i	$0.140093\pi$
$104$	−2.79199	−	0.907174i	−0.273778	−	0.0889557i
$105$	9.73587	+	0.997941i	0.950124	+	0.0973890i
$106$	−1.04650	−	1.44038i	−0.101645	−	0.139902i
$107$	−3.58824	−	0.377140i	−0.346889	−	0.0364595i	−0.0705178	−	0.997511i	$-0.522465\pi$
$107$	−3.58824	−	0.377140i	−0.346889	−	0.0364595i	−0.276371	+	0.961051i	$0.589132\pi$
$108$	1.92167	−	9.04076i	0.184913	−	0.869947i
$109$	10.2082	+	5.89369i	0.977766	+	0.564513i	0.901595	−	0.432582i	$-0.142397\pi$
$109$	10.2082	+	5.89369i	0.977766	+	0.564513i	0.0761707	+	0.997095i	$0.475731\pi$
$110$	−0.587807	−	5.59970i	−0.0560452	−	0.533911i
$111$			7.53483i			0.715174i
$112$	5.62219	+	3.22670i	0.531247	+	0.304894i
$113$	0.308036	+	0.223801i	0.0289776	+	0.0210535i	0.602180	−	0.798361i	$-0.294299\pi$
$113$	0.308036	+	0.223801i	0.0289776	+	0.0210535i	−0.573202	+	0.819414i	$0.694299\pi$
$114$	0.863826	+	0.384600i	0.0809047	+	0.0360211i
$115$	9.62233	−	8.66398i	0.897286	−	0.807920i
$116$	10.8360	−	9.75682i	1.00610	−	0.905898i
$117$	−2.37204	−	1.05610i	−0.219295	−	0.0976364i
$118$	−0.283465	−	0.205949i	−0.0260950	−	0.0189591i
$119$	0.0171142	+	6.64614i	0.00156886	+	0.609250i
$120$			7.17529i			0.655012i
$121$	3.40194	−	10.4607i	0.309268	−	0.950975i
$122$	−3.37070	−	1.94608i	−0.305169	−	0.176189i
$123$	−0.949464	+	4.46688i	−0.0856103	+	0.402765i
$124$	16.4150	+	1.72529i	1.47411	+	0.154935i
$125$	−1.25441	−	1.72655i	−0.112198	−	0.154427i
$126$	−1.91355	−	1.38276i	−0.170473	−	0.123186i
$127$	5.93404	+	1.92809i	0.526561	+	0.171090i	0.560221	−	0.828343i	$-0.310716\pi$
$127$	5.93404	+	1.92809i	0.526561	+	0.171090i	−0.0336599	+	0.999433i	$0.510716\pi$
$128$	−4.66204	+	10.4711i	−0.412070	+	0.925525i
$129$	5.39799	−	2.40334i	0.475266	−	0.211602i
$130$	2.51314	+	0.534184i	0.220417	+	0.0468511i
$131$	−8.00359	−	13.8626i	−0.699277	−	1.21118i	−0.968718	−	0.248166i	$-0.920172\pi$
$131$	−8.00359	−	13.8626i	−0.699277	−	1.21118i	0.269441	−	0.963017i	$-0.413161\pi$
$132$	−2.64483	+	5.93827i	−0.230203	+	0.516860i
$133$	−3.14681	+	2.84811i	−0.272863	+	0.246963i
$134$	4.09772	−	1.33143i	0.353989	−	0.115018i
$135$	−1.82335	+	17.3481i	−0.156929	+	1.49308i
$136$	−4.84596	+	0.509331i	−0.415538	+	0.0436748i
$137$	−6.10457	−	6.77982i	−0.521549	−	0.579239i	0.423612	−	0.905844i	$-0.360762\pi$
$137$	−6.10457	−	6.77982i	−0.521549	−	0.579239i	−0.945161	+	0.326605i	$0.894095\pi$
$138$	2.28716	−	0.486150i	0.194696	−	0.0413838i
$139$	6.79273	−	4.93521i	0.576152	−	0.418599i	−0.261183	−	0.965289i	$-0.584113\pi$
$139$	6.79273	−	4.93521i	0.576152	−	0.418599i	0.837335	+	0.546691i	$0.184113\pi$
$140$	−13.6598	−	6.03965i	−1.15447	−	0.510443i
$141$	0.121628	+	0.374332i	0.0102429	+	0.0315244i
$142$	1.16238	−	0.671101i	0.0975449	−	0.0563176i
$143$	4.06047	+	2.95092i	0.339554	+	0.246768i
$144$	−2.10174	+	3.64033i	−0.175145	+	0.303361i
$145$	−18.4138	+	20.4506i	−1.52919	+	1.69833i
$146$	3.62698	−	4.99211i	0.300171	−	0.413150i
$147$	−6.84971	+	4.00186i	−0.564954	+	0.330068i
$148$	3.55329	−	10.9359i	0.292078	−	0.898925i
$149$	0.273116	+	1.28491i	0.0223745	+	0.105264i	0.987918	−	0.154979i	$-0.0495309\pi$
$149$	0.273116	+	1.28491i	0.0223745	+	0.105264i	−0.965543	+	0.260242i	$0.916198\pi$
$150$	−0.348350	−	3.31433i	−0.0284426	−	0.270614i
$151$	5.76516	+	12.9488i	0.469162	+	1.05376i	0.980882	+	0.194603i	$0.0623419\pi$
$151$	5.76516	+	12.9488i	0.469162	+	1.05376i	−0.511720	+	0.859152i	$0.670991\pi$
$152$	−2.31247	−	2.08216i	−0.187566	−	0.168885i
$153$	−4.30972			−0.348420
$154$	3.06216	+	3.38420i	0.246756	+	0.272707i
$155$	−31.1504			−2.50206
$156$	−2.20443	−	1.98488i	−0.176496	−	0.158917i
$157$	−6.24883	−	14.0351i	−0.498711	−	1.12012i	−0.971087	−	0.238727i	$-0.923270\pi$
$157$	−6.24883	−	14.0351i	−0.498711	−	1.12012i	0.472376	−	0.881397i	$-0.343397\pi$
$158$	−0.640966	−	6.09838i	−0.0509925	−	0.485161i
$159$	−0.806575	−	3.79464i	−0.0639656	−	0.300934i
$160$	5.19832	−	15.9988i	0.410964	−	1.26482i
$161$	−2.15569	+	10.2717i	−0.169892	+	0.809525i
$162$	−0.278083	+	0.382748i	−0.0218482	+	0.0300715i
$163$	9.40117	−	10.4411i	0.736356	−	0.817806i	−0.252356	−	0.967634i	$-0.581205\pi$
$163$	9.40117	−	10.4411i	0.736356	−	0.817806i	0.988712	+	0.149828i	$0.0478720\pi$
$164$	3.48453	−	6.03538i	0.272096	−	0.471284i
$165$	3.79271	−	11.6675i	0.295262	−	0.908317i
$166$	−6.07991	+	3.51024i	−0.471893	+	0.272447i
$167$	2.59583	+	7.98916i	0.200872	+	0.618220i	0.999858	+	0.0168699i	$0.00537011\pi$
$167$	2.59583	+	7.98916i	0.200872	+	0.618220i	−0.798986	+	0.601350i	$0.794630\pi$
$168$	−3.43075	−	4.69655i	−0.264688	−	0.362346i
$169$	8.66418	−	6.29489i	0.666475	−	0.484223i
$170$	4.17133	−	0.886643i	0.319926	−	0.0680024i
$171$	−1.84161	−	2.04531i	−0.140831	−	0.156409i
$172$	−8.96790	+	0.942564i	−0.683796	+	0.0718699i
$173$	−2.43026	+	23.1223i	−0.184769	+	1.75796i	0.372878	+	0.927881i	$0.378371\pi$
$173$	−2.43026	+	23.1223i	−0.184769	+	1.75796i	−0.557647	+	0.830078i	$0.688296\pi$
$174$	−4.72633	+	1.53568i	−0.358303	+	0.116420i
$175$	14.2384	+	4.58583i	1.07632	+	0.346656i
$176$	5.43817	−	6.03810i	0.409918	−	0.455139i
$177$	−0.381732	−	0.661179i	−0.0286927	−	0.0496972i
$178$	3.83796	+	0.815783i	0.287667	+	0.0611456i
$179$	10.3762	−	4.61980i	0.775557	−	0.345300i	0.0195031	−	0.999810i	$-0.493792\pi$
$179$	10.3762	−	4.61980i	0.775557	−	0.345300i	0.756054	+	0.654510i	$0.227125\pi$
$180$	3.93923	−	8.84765i	0.293613	−	0.659465i
$181$	−18.1294	−	5.89061i	−1.34755	−	0.437846i	−0.455683	−	0.890142i	$-0.650605\pi$
$181$	−18.1294	−	5.89061i	−1.34755	−	0.437846i	−0.891868	+	0.452297i	$0.850605\pi$
$182$	−1.90037	+	0.851971i	−0.140865	+	0.0631523i
$183$	−4.98489	−	6.86111i	−0.368494	−	0.507188i
$184$	−7.65266	−	0.804327i	−0.564161	−	0.0592957i
$185$	−4.51194	+	21.2270i	−0.331724	+	1.56064i
$186$	−4.87168	−	2.81266i	−0.357209	−	0.206234i
$187$	8.14911	+	1.73327i	0.595922	+	0.126749i
$188$		−	0.600655i		−	0.0438073i
$189$	−7.10123	−	12.2269i	−0.516539	−	0.889375i
$190$	2.20325	+	1.60076i	0.159841	+	0.116131i
$191$	3.10709	+	1.38336i	0.224821	+	0.100097i	0.516056	−	0.856555i	$-0.327400\pi$
$191$	3.10709	+	1.38336i	0.224821	+	0.100097i	−0.291235	+	0.956651i	$0.594066\pi$
$192$	−1.86938	+	1.68320i	−0.134911	+	0.121474i
$193$	−6.79316	+	6.11659i	−0.488982	+	0.440282i	−0.876372	−	0.481634i	$-0.840043\pi$
$193$	−6.79316	+	6.11659i	−0.488982	+	0.440282i	0.387390	+	0.921916i	$0.373377\pi$
$194$	−2.02098	−	0.899797i	−0.145098	−	0.0646016i
$195$	4.52915	+	3.29062i	0.324339	+	0.235646i
$196$	11.8287	−	2.57801i	0.844909	−	0.184144i
$197$			3.18338i			0.226806i	0.993549	+	0.113403i	$0.0361752\pi$
$197$			3.18338i			0.226806i	−0.993549	+	0.113403i	$0.963825\pi$
$198$	−2.19960	+	1.98001i	−0.156319	+	0.140713i
$199$	2.10661	+	1.21625i	0.149333	+	0.0862176i	0.572805	−	0.819692i	$-0.305855\pi$
$199$	2.10661	+	1.21625i	0.149333	+	0.0862176i	−0.423472	+	0.905909i	$0.639189\pi$
$200$	−2.28017	+	10.7273i	−0.161232	+	0.758537i
$201$	9.33678	+	0.981335i	0.658565	+	0.0692180i
$202$	1.72619	+	2.37590i	0.121455	+	0.167168i
$203$	2.27452	−	22.1901i	0.159640	−	1.55744i
$204$	−4.68260	−	1.52147i	−0.327848	−	0.106524i
$205$	−5.34963	+	12.0155i	−0.373634	+	0.839196i
$206$	−0.204792	+	0.0911794i	−0.0142686	+	0.00635277i
$207$	−6.65711	−	1.41501i	−0.462701	−	0.0983501i
$208$	1.85403	+	3.21127i	0.128554	+	0.222661i
$209$	2.65966	+	4.60806i	0.183972	+	0.318746i
$210$	3.41578	+	3.77402i	0.235711	+	0.260432i
$211$	5.67364	−	1.84348i	0.390590	−	0.126910i	−0.107137	−	0.994244i	$-0.534168\pi$
$211$	5.67364	−	1.84348i	0.390590	−	0.126910i	0.497727	+	0.867334i	$0.334168\pi$
$212$	−0.618835	+	5.88782i	−0.0425018	+	0.404377i
$213$	2.90857	−	0.305703i	0.199292	−	0.0209464i
$214$	−1.25567	−	1.39456i	−0.0858355	−	0.0953300i
$215$	16.6463	−	3.53827i	1.13527	−	0.241308i
$216$	8.38659	−	6.09322i	0.570635	−	0.414591i
$217$	20.3893	−	14.8940i	1.38411	−	1.01107i
$218$	1.89450	+	5.83068i	0.128312	+	0.394903i
$219$	11.6441	−	6.72270i	0.786832	−	0.454278i
$220$	−11.0069	+	15.1455i	−0.742083	+	1.02111i
$221$	−1.90088	+	3.29243i	−0.127867	+	0.221473i
$222$	−2.62228	+	2.91234i	−0.175996	+	0.195463i
$223$	−0.721212	+	0.992663i	−0.0482959	+	0.0664736i	−0.832482	−	0.554052i	$-0.813081\pi$
$223$	−0.721212	+	0.992663i	−0.0482959	+	0.0664736i	0.784186	+	0.620526i	$0.213081\pi$
$224$	4.24704	+	12.9574i	0.283767	+	0.865754i
$225$	−2.99746	+	9.22523i	−0.199831	+	0.615015i
$226$	0.0411736	+	0.193706i	0.00273882	+	0.0128852i
$227$	−0.0929676	−	0.884527i	−0.00617047	−	0.0587081i	0.991003	−	0.133837i	$-0.0427299\pi$
$227$	−0.0929676	−	0.884527i	−0.00617047	−	0.0587081i	−0.997174	+	0.0751289i	$0.976063\pi$
$228$	−1.27888	−	2.87242i	−0.0846961	−	0.190231i
$229$	−19.6258	−	17.6712i	−1.29691	−	1.16774i	−0.975303	−	0.220871i	$-0.929110\pi$
$229$	−19.6258	−	17.6712i	−1.29691	−	1.16774i	−0.321608	−	0.946873i	$-0.604223\pi$
$230$	6.73445			0.444056
$231$	3.09615	+	9.45035i	0.203712	+	0.621787i
$232$	16.3540			1.07369
$233$	−15.2132	−	13.6980i	−0.996651	−	0.897389i	−0.00192959	−	0.999998i	$-0.500614\pi$
$233$	−15.2132	−	13.6980i	−0.996651	−	0.897389i	−0.994722	+	0.102609i	$0.967281\pi$
$234$	−0.549288	−	1.23372i	−0.0359081	−	0.0806509i
$235$	0.118494	+	1.12739i	0.00772969	+	0.0735431i
$236$	0.242238	+	1.13964i	0.0157683	+	0.0741841i
$237$	4.12885	−	12.7073i	0.268198	−	0.825428i
$238$	−2.30638	+	2.57480i	−0.149501	+	0.166900i
$239$	−8.11554	+	11.1701i	−0.524951	+	0.722533i	−0.986350	−	0.164660i	$-0.947347\pi$
$239$	−8.11554	+	11.1701i	−0.524951	+	0.722533i	0.461400	+	0.887192i	$0.347347\pi$
$240$	6.06441	−	6.73521i	0.391456	−	0.434756i
$241$	−12.2594	+	21.2339i	−0.789697	+	1.36780i	0.136455	+	0.990646i	$0.456429\pi$
$241$	−12.2594	+	21.2339i	−0.789697	+	1.36780i	−0.926152	+	0.377150i	$0.876904\pi$
$242$	4.95547	−	2.85930i	0.318550	−	0.183803i
$243$	12.9919	−	7.50088i	0.833431	−	0.481182i
$244$	3.99939	+	12.3089i	0.256035	+	0.787994i
$245$	−21.6932	+	7.17228i	−1.38593	+	0.458220i
$246$	−1.92155	+	1.39609i	−0.122514	+	0.0890115i
$247$	−2.37480	+	0.504779i	−0.151105	+	0.0321183i
$248$	12.3870	+	13.7571i	0.786573	+	0.873578i
$249$	−15.2135	+	1.59900i	−0.964114	+	0.101332i
$250$	0.116025	−	1.10390i	0.00733807	−	0.0698171i
$251$	−13.8245	+	4.49184i	−0.872592	+	0.283522i	−0.710878	−	0.703315i	$-0.751702\pi$
$251$	−13.8245	+	4.49184i	−0.872592	+	0.283522i	−0.161714	+	0.986838i	$0.551702\pi$
$252$	1.65196	+	7.67465i	0.104064	+	0.483458i
$253$	12.0186	+	5.35293i	0.755604	+	0.336536i
$254$	1.62259	+	2.81041i	0.101811	+	0.176341i
$255$	9.08911	+	1.93195i	0.569182	+	0.120983i
$256$	−1.39066	+	0.619162i	−0.0869162	+	0.0386976i
$257$	7.40361	−	16.6288i	0.461824	−	1.03727i	−0.521139	−	0.853472i	$-0.674493\pi$
$257$	7.40361	−	16.6288i	0.461824	−	1.03727i	0.982963	−	0.183802i	$-0.0588407\pi$
$258$	2.92283	+	0.949685i	0.181967	+	0.0591248i
$259$	−7.19609	−	16.0513i	−0.447143	−	0.997380i
$260$	−5.02172	−	6.91180i	−0.311434	−	0.428652i
$261$	14.3854	+	1.51197i	0.890435	+	0.0935885i
$262$	1.73097	−	8.14356i	0.106940	−	0.503111i
$263$	2.90941	+	1.67975i	0.179402	+	0.103578i	0.587012	−	0.809578i	$-0.300304\pi$
$263$	2.90941	+	1.67975i	0.179402	+	0.103578i	−0.407610	+	0.913156i	$0.633638\pi$
$264$	−6.66099	+	2.96461i	−0.409955	+	0.182459i
$265$		−	11.1732i		−	0.686363i
$266$	−2.20750	+	0.00568447i	−0.135351	+	0.000348537i
$267$	6.91673	+	5.02530i	0.423297	+	0.307543i
$268$	−13.0884	−	5.82734i	−0.799503	−	0.355961i
$269$	2.10757	−	1.89767i	0.128501	−	0.115703i	−0.602375	−	0.798214i	$-0.705779\pi$
$269$	2.10757	−	1.89767i	0.128501	−	0.115703i	0.730876	+	0.682511i	$0.239112\pi$
$270$	−6.74226	+	6.07076i	−0.410321	+	0.369454i
$271$	9.76081	+	4.34579i	0.592927	+	0.263988i	0.681187	−	0.732109i	$-0.261464\pi$
$271$	9.76081	+	4.34579i	0.592927	+	0.263988i	−0.0882602	+	0.996097i	$0.528131\pi$
$272$	4.97922	+	3.61762i	0.301910	+	0.219350i
$273$	−4.53789	+	0.0116854i	−0.274645	+	0.000707230i
$274$		−	4.74504i		−	0.286658i
$275$	9.37797	−	16.2382i	0.565513	−	0.979199i
$276$	−6.73354	−	3.88761i	−0.405311	−	0.234007i
$277$	−0.0596936	+	0.280837i	−0.00358664	+	0.0168738i	−0.979905	−	0.199467i	$-0.936079\pi$
$277$	−0.0596936	+	0.280837i	−0.00358664	+	0.0168738i	0.976318	+	0.216341i	$0.0694123\pi$
$278$	4.34306	+	0.456474i	0.260480	+	0.0273775i
$279$	9.62402	+	13.2463i	0.576175	+	0.793037i
$280$	−6.85272	−	15.2854i	−0.409528	−	0.913477i
$281$	6.34392	+	2.06126i	0.378446	+	0.122965i	0.492062	−	0.870560i	$-0.336243\pi$
$281$	6.34392	+	2.06126i	0.378446	+	0.122965i	−0.113616	+	0.993525i	$0.536243\pi$
$282$	−0.0832644	+	0.187015i	−0.00495832	+	0.0111366i
$283$	8.73063	−	3.88713i	0.518982	−	0.231066i	−0.130492	−	0.991449i	$-0.541656\pi$
$283$	8.73063	−	3.88713i	0.518982	−	0.231066i	0.649474	+	0.760384i	$0.274989\pi$
$284$	−4.36560	−	0.927937i	−0.259051	−	0.0550629i
$285$	2.96704	+	5.13907i	0.175752	+	0.304412i
$286$	0.542457	+	2.55371i	0.0320761	+	0.151004i
$287$	−2.24343	−	10.4225i	−0.132426	−	0.615220i
$288$	−8.40934	+	2.73236i	−0.495525	+	0.161006i
$289$	1.11739	−	10.6312i	0.0657287	−	0.625367i
$290$	−14.2345	+	1.49611i	−0.835880	+	0.0878546i
$291$	−3.22544	−	3.58221i	−0.189079	−	0.209993i
$292$	−20.0702	+	4.26606i	−1.17452	+	0.249652i
$293$	22.7817	−	16.5519i	1.33092	−	0.966973i	0.331198	−	0.943561i	$-0.392547\pi$
$293$	22.7817	−	16.5519i	1.33092	−	0.966973i	0.999726	−	0.0234116i	$-0.00745284\pi$
$294$	−4.04026	−	0.837060i	−0.235633	−	0.0488183i
$295$	−0.679487	−	2.09125i	−0.0395613	−	0.121757i
$296$	11.1688	−	6.44830i	0.649172	−	0.374800i
$297$	−16.8580	+	5.47503i	−0.978198	+	0.317693i
$298$	−0.341612	+	0.591689i	−0.0197891	+	0.0342756i
$299$	−4.01724	+	4.46160i	−0.232323	+	0.258021i
$300$	−6.51360	+	8.96520i	−0.376063	+	0.517606i
$301$	−9.20395	+	10.2751i	−0.530507	+	0.592247i
$302$	−2.27812	+	7.01132i	−0.131091	+	0.403456i
$303$	1.33044	+	6.25925i	0.0764320	+	0.359584i
$304$	0.410842	+	3.90890i	0.0235634	+	0.224191i
$305$	−9.93484	−	22.3140i	−0.568867	−	1.27770i
$306$	−1.66578	−	1.49988i	−0.0952264	−	0.0857423i
$307$	−11.4173			−0.651620			−0.325810	−	0.945435i	$-0.605637\pi$
$307$	−11.4173			−0.651620			−0.325810	+	0.945435i	$0.605637\pi$
$308$	−0.0370799	−	15.1761i	−0.00211283	−	0.864740i
$309$	−0.488462			−0.0277876
$310$	−12.0401	−	10.8410i	−0.683834	−	0.615727i
$311$	2.80934	+	6.30989i	0.159303	+	0.357801i	0.975509	−	0.219961i	$-0.0705929\pi$
$311$	2.80934	+	6.30989i	0.159303	+	0.357801i	−0.816205	+	0.577762i	$0.803926\pi$
$312$	−0.347764	−	3.30876i	−0.0196883	−	0.187321i
$313$	5.54962	+	26.1089i	0.313683	+	1.47576i	0.798951	+	0.601396i	$0.205389\pi$
$313$	5.54962	+	26.1089i	0.313683	+	1.47576i	−0.485268	+	0.874365i	$0.661278\pi$
$314$	2.46924	−	7.59954i	0.139347	−	0.428867i
$315$	−4.61465	−	14.0790i	−0.260006	−	0.793260i
$316$	−11.9851	+	16.4960i	−0.674213	+	0.927974i
$317$	1.71627	−	1.90611i	0.0963952	−	0.107058i	−0.693017	−	0.720921i	$-0.743719\pi$
$317$	1.71627	−	1.90611i	0.0963952	−	0.107058i	0.789412	+	0.613864i	$0.210386\pi$
$318$	1.00886	−	1.74740i	0.0565741	−	0.0979892i
$319$	−26.5928	−	8.64441i	−1.48891	−	0.483994i
$320$	−6.27430	+	3.62247i	−0.350744	+	0.202502i
$321$	−1.26355	−	3.88881i	−0.0705245	−	0.217052i
$322$	−4.40799	+	3.21997i	−0.245648	+	0.179442i
$323$	−3.26015	+	2.36864i	−0.181400	+	0.131795i
$324$	1.53880	−	0.327081i	0.0854887	−	0.0181712i
$325$	5.72556	+	6.35888i	0.317597	+	0.352727i
$326$	7.26743	−	0.763837i	0.402505	−	0.0423050i
$327$	−1.39635	+	13.2854i	−0.0772183	+	0.734683i
$328$	7.43375	−	2.41537i	0.410460	−	0.133367i
$329$	−0.616605	−	0.681273i	−0.0339945	−	0.0375598i
$330$	5.52651	−	3.18976i	0.304224	−	0.175590i
$331$	12.7236	+	22.0380i	0.699355	+	1.21132i	0.968690	+	0.248272i	$0.0798625\pi$
$331$	12.7236	+	22.0380i	0.699355	+	1.21132i	−0.269336	+	0.963046i	$0.586804\pi$
$332$	22.8345	+	4.85363i	1.25321	+	0.266378i
$333$	10.4205	−	4.63951i	0.571040	−	0.254243i
$334$	−1.77707	+	3.99135i	−0.0972367	+	0.218397i
$335$	25.7158	+	8.35556i	1.40500	+	0.456513i
$336$	−0.749090	+	7.30809i	−0.0408662	+	0.398689i
$337$	−10.2286	−	14.0785i	−0.557188	−	0.766904i	0.433777	−	0.901020i	$-0.357180\pi$
$337$	−10.2286	−	14.0785i	−0.557188	−	0.766904i	−0.990966	+	0.134116i	$0.957180\pi$
$338$	5.53961	+	0.582237i	0.301315	+	0.0316695i
$339$	−0.0897151	+	0.422076i	−0.00487265	+	0.0229240i
$340$	−12.2807	−	7.09025i	−0.666013	−	0.384523i
$341$	−12.8704	−	28.9176i	−0.696970	−	1.56597i
$342$		−	1.43147i		−	0.0774049i
$343$	10.7699	−	15.0669i	0.581518	−	0.813534i
$344$	−8.18204	−	5.94460i	−0.441146	−	0.320511i
$345$	13.4054	+	5.96846i	0.721721	+	0.321331i
$346$	−8.98641	+	8.09140i	−0.483112	+	0.434996i
$347$	−15.4366	+	13.8992i	−0.828681	+	0.746148i	−0.969815	−	0.243843i	$-0.921592\pi$
$347$	−15.4366	+	13.8992i	−0.828681	+	0.746148i	0.141134	+	0.989991i	$0.454925\pi$
$348$	15.0963	+	6.72129i	0.809245	+	0.360299i
$349$	−16.0483	−	11.6598i	−0.859044	−	0.624132i	0.0685804	−	0.997646i	$-0.478153\pi$
$349$	−16.0483	−	11.6598i	−0.859044	−	0.624132i	−0.927625	+	0.373513i	$0.878153\pi$
$350$	3.90741	+	6.72776i	0.208860	+	0.359614i
$351$		−	8.08812i		−	0.431712i
$352$	16.9998	−	1.78449i	0.906094	−	0.0951136i
$353$	−22.7842	−	13.1545i	−1.21268	−	0.700142i	−0.249338	−	0.968416i	$-0.580213\pi$
$353$	−22.7842	−	13.1545i	−1.21268	−	0.700142i	−0.963342	+	0.268275i	$0.913546\pi$
$354$	0.0825586	−	0.388408i	0.00438794	−	0.0206436i
$355$	8.37703	+	0.880461i	0.444607	+	0.0467300i
$356$	−7.66895	−	10.5554i	−0.406454	−	0.559436i
$357$	−6.87296	+	3.08127i	−0.363755	+	0.163078i
$358$	5.61839	+	1.82552i	0.296941	+	0.0964820i
$359$	−13.2936	+	29.8579i	−0.701609	+	1.57584i	0.111525	+	0.993762i	$0.464427\pi$
$359$	−13.2936	+	29.8579i	−0.701609	+	1.57584i	−0.813133	+	0.582077i	$0.802240\pi$
$360$	9.92328	−	4.41813i	0.523003	−	0.232856i
$361$	16.0676	+	3.41527i	0.845662	+	0.179751i
$362$	−4.95728	−	8.58626i	−0.260549	−	0.451284i
$363$	12.3983	−	1.29981i	0.650741	−	0.0682223i
$364$	6.59171	+	2.12302i	0.345499	+	0.111277i
$365$	36.8291	−	11.9665i	1.92772	−	0.626355i
$366$	0.461070	−	4.38679i	0.0241005	−	0.229301i
$367$	−7.17340	+	0.753955i	−0.374448	+	0.0393561i	−0.289884	−	0.957062i	$-0.593617\pi$
$367$	−7.17340	+	0.753955i	−0.374448	+	0.0393561i	−0.0845647	+	0.996418i	$0.526950\pi$
$368$	6.50349	+	7.22286i	0.339018	+	0.376518i
$369$	6.76222	−	1.43735i	0.352027	−	0.0748257i
$370$	−9.13139	+	6.63434i	−0.474718	+	0.344903i
$371$	5.34228	+	7.31333i	0.277357	+	0.379689i
$372$	5.78032	+	17.7900i	0.299695	+	0.922368i
$373$	−29.5645	+	17.0691i	−1.53079	+	0.883804i	−0.531469	+	0.847078i	$0.678360\pi$
$373$	−29.5645	+	17.0691i	−1.53079	+	0.883804i	−0.999325	+	0.0367265i	$0.988307\pi$
$374$	2.54656	+	3.50601i	0.131679	+	0.181291i
$375$	1.20930	−	2.09457i	0.0624480	−	0.108163i
$376$	0.450779	−	0.500640i	0.0232471	−	0.0258186i
$377$	7.50003	−	10.3229i	0.386271	−	0.531657i
$378$	1.51047	−	7.19728i	0.0776902	−	0.370188i
$379$	−2.05337	+	6.31963i	−0.105475	+	0.324618i	−0.989842	−	0.142175i	$-0.954590\pi$
$379$	−2.05337	+	6.31963i	−0.105475	+	0.324618i	0.884367	+	0.466792i	$0.154590\pi$
$380$	−1.88281	−	8.85794i	−0.0965862	−	0.454403i
$381$	0.739130	+	7.03236i	0.0378668	+	0.360278i
$382$	0.719502	+	1.61603i	0.0368129	+	0.0826832i
$383$	16.0123	+	14.4176i	0.818192	+	0.736703i	0.967713	−	0.252055i	$-0.0811065\pi$
$383$	16.0123	+	14.4176i	0.818192	+	0.736703i	−0.149521	+	0.988759i	$0.547773\pi$
$384$	−12.9899			−0.662887
$385$	3.06346	+	28.4774i	0.156128	+	1.45134i
$386$	−4.75438			−0.241991
$387$	−6.64754	−	5.98547i	−0.337913	−	0.304258i
$388$	2.99203	+	6.72021i	0.151897	+	0.341167i
$389$	2.00908	+	19.1152i	0.101865	+	0.969177i	0.919407	+	0.393308i	$0.128670\pi$
$389$	2.00908	+	19.1152i	0.101865	+	0.969177i	−0.817542	+	0.575869i	$0.804664\pi$
$390$	0.605388	+	2.84812i	0.0306550	+	0.144220i
$391$	−3.07934	+	9.47723i	−0.155729	+	0.479284i
$392$	11.7939	+	6.72845i	0.595681	+	0.339838i
$393$	10.6629	−	14.6762i	0.537873	−	0.740318i
$394$	−1.10788	+	1.23043i	−0.0558144	+	0.0619882i
$395$	19.2410	−	33.3264i	0.968120	−	1.67683i
$396$	9.84104	+	0.00129664i	0.494531	+	6.51586e-5i
$397$	3.07639	−	1.77615i	0.154400	−	0.0891426i	−0.420810	−	0.907149i	$-0.638254\pi$
$397$	3.07639	−	1.77615i	0.154400	−	0.0891426i	0.575209	+	0.818006i	$0.304921\pi$
$398$	0.390958	+	1.20325i	0.0195970	+	0.0603132i
$399$	−4.39922	−	1.94510i	−0.220237	−	0.0973769i
$400$	11.2068	−	8.14224i	0.560342	−	0.407112i
$401$	9.18799	−	1.95297i	0.458826	−	0.0975265i	0.0273008	−	0.999627i	$-0.491309\pi$
$401$	9.18799	−	1.95297i	0.458826	−	0.0975265i	0.431526	+	0.902101i	$0.357975\pi$
$402$	3.26730	+	3.62870i	0.162958	+	0.180983i
$403$	14.3644	−	1.50976i	0.715543	−	0.0752066i
$404$	1.02077	−	9.71195i	0.0507851	−	0.483188i
$405$	−2.82371	+	0.917478i	−0.140311	+	0.0455898i
$406$	8.60179	−	7.78529i	0.426900	−	0.386377i
$407$	−21.5697	+	4.58181i	−1.06917	+	0.227112i
$408$	−2.76108	−	4.78232i	−0.136694	−	0.236760i
$409$	1.11987	+	0.238035i	0.0553738	+	0.0117701i	0.235515	−	0.971871i	$-0.424322\pi$
$409$	1.11987	+	0.238035i	0.0553738	+	0.0117701i	−0.180141	+	0.983641i	$0.557656\pi$
$410$	−6.24936	+	2.78240i	−0.308634	+	0.137413i
$411$	4.20533	−	9.44533i	0.207434	−	0.465904i
$412$	0.708943	+	0.230350i	0.0349271	+	0.0113485i
$413$	1.44465	+	1.04393i	0.0710866	+	0.0513683i
$414$	−2.08063	−	2.86374i	−0.102258	−	0.140745i
$415$	−43.8166	−	4.60531i	−2.15087	−	0.226066i
$416$	−1.62170	+	7.62950i	−0.0795104	+	0.374067i
$417$	8.24061	+	4.75772i	0.403545	+	0.232987i
$418$	−0.575702	+	2.70671i	−0.0281585	+	0.132390i
$419$			12.6920i			0.620044i	0.950729	+	0.310022i	$0.100336\pi$
$419$			12.6920i			0.620044i	−0.950729	+	0.310022i	$0.899664\pi$
$420$	−0.0435861	−	16.9262i	−0.00212678	−	0.825915i
$421$	−23.2174	−	16.8685i	−1.13155	−	0.822118i	−0.145630	−	0.989339i	$-0.546521\pi$
$421$	−23.2174	−	16.8685i	−1.13155	−	0.822118i	−0.985919	+	0.167221i	$0.946521\pi$
$422$	2.83453	+	1.26201i	0.137983	+	0.0614339i
$423$	0.442802	−	0.398701i	0.0215298	−	0.0193855i
$424$	−4.93448	+	4.44302i	−0.239639	+	0.215772i
$425$	12.9746	+	5.77668i	0.629362	+	0.280210i
$426$	1.23060	+	0.894086i	0.0596229	+	0.0433186i
$427$	17.1719	+	9.85532i	0.831006	+	0.476932i
$428$			6.24000i			0.301622i
$429$	−1.18345	+	5.56410i	−0.0571376	+	0.268637i
$430$	7.66547	+	4.42566i	0.369662	+	0.213424i
$431$	0.458840	−	2.15867i	0.0221015	−	0.103980i	−0.965714	−	0.259608i	$-0.916407\pi$
$431$	0.458840	−	2.15867i	0.0221015	−	0.103980i	0.987816	+	0.155628i	$0.0497401\pi$
$432$	−13.0221	−	1.36867i	−0.626525	−	0.0658504i
$433$	−7.15901	−	9.85353i	−0.344040	−	0.473530i	0.601576	−	0.798816i	$-0.294540\pi$
$433$	−7.15901	−	9.85353i	−0.344040	−	0.473530i	−0.945616	+	0.325285i	$0.894540\pi$
$434$	13.0643	+	1.33911i	0.627105	+	0.0642791i
$435$	−29.6607	−	9.63736i	−1.42212	−	0.462076i
$436$	8.29178	−	18.6236i	0.397104	−	0.891910i
$437$	−5.81356	+	2.58836i	−0.278100	+	0.123818i
$438$	6.84027	+	1.45394i	0.326841	+	0.0694722i
$439$	−6.30209	−	10.9155i	−0.300782	−	0.520970i	0.675531	−	0.737332i	$-0.263914\pi$
$439$	−6.30209	−	10.9155i	−0.300782	−	0.520970i	−0.976313	+	0.216361i	$0.930581\pi$
$440$	−20.5405	+	4.36318i	−0.979228	+	0.208007i
$441$	9.75213	+	7.00889i	0.464387	+	0.333757i
$442$	−1.88056	+	0.611031i	−0.0894491	+	0.0290638i
$443$	−3.74705	+	35.6508i	−0.178028	+	1.69382i	0.432347	+	0.901707i	$0.357686\pi$
$443$	−3.74705	+	35.6508i	−0.178028	+	1.69382i	−0.610375	+	0.792113i	$0.708981\pi$
$444$	12.9600	−	1.36215i	0.615054	−	0.0646448i
$445$	16.4765	+	18.2990i	0.781060	+	0.867455i
$446$	−0.624229	+	0.132684i	−0.0295581	+	0.00628277i
$447$	−1.20439	+	0.875042i	−0.0569658	+	0.0413881i
$448$	2.37478	−	5.37102i	0.112198	−	0.253757i
$449$	−1.34204	−	4.13038i	−0.0633349	−	0.194925i	0.914382	−	0.404852i	$-0.132677\pi$
$449$	−1.34204	−	4.13038i	−0.0633349	−	0.194925i	−0.977717	+	0.209928i	$0.932677\pi$
$450$	−4.36915	+	2.52253i	−0.205964	+	0.118913i
$451$	−13.3645	−	0.00176089i	−0.629311	−	8.29171e-5i
$452$	0.329254	−	0.570285i	0.0154868	−	0.0268239i
$453$	−10.7486	+	11.9375i	−0.505013	+	0.560873i
$454$	0.271901	−	0.374240i	0.0127610	−	0.0175639i
$455$	−12.7911	−	2.68442i	−0.599654	−	0.125847i
$456$	1.08975	−	3.35391i	0.0510323	−	0.157061i
$457$	−0.0351205	−	0.165229i	−0.00164287	−	0.00772909i	0.977319	−	0.211775i	$-0.0679243\pi$
$457$	−0.0351205	−	0.165229i	−0.00164287	−	0.00772909i	−0.978961	+	0.204046i	$0.934591\pi$
$458$	−1.43577	−	13.6604i	−0.0670891	−	0.638310i
$459$	−5.46032	−	12.2641i	−0.254866	−	0.572439i
$460$	−16.6417	−	14.9842i	−0.775922	−	0.698643i
$461$	2.70208			0.125848			0.0629242	−	0.998018i	$-0.479957\pi$
$461$	2.70208			0.125848			0.0629242	+	0.998018i	$0.479957\pi$
$462$	−2.09221	+	4.73025i	−0.0973384	+	0.220071i
$463$	27.6343			1.28428			0.642138	−	0.766589i	$-0.278048\pi$
$463$	27.6343			1.28428			0.642138	+	0.766589i	$0.278048\pi$
$464$	−15.3510	−	13.8221i	−0.712651	−	0.641674i
$465$	−14.3588	−	32.2504i	−0.665874	−	1.49558i
$466$	−1.11296	−	10.5891i	−0.0515567	−	0.490529i
$467$	0.658405	+	3.09755i	0.0304673	+	0.143338i	0.990752	−	0.135684i	$-0.0433232\pi$
$467$	0.658405	+	3.09755i	0.0304673	+	0.143338i	−0.960285	+	0.279022i	$0.909990\pi$
$468$	−1.38768	+	4.27085i	−0.0641457	+	0.197420i
$469$	−20.8272	+	6.82651i	−0.961710	+	0.315219i
$470$	−0.346557	+	0.476995i	−0.0159855	+	0.0220022i
$471$	11.6504	−	12.9390i	0.536820	−	0.596199i
$472$	−0.653371	+	1.13167i	−0.0300739	+	0.0520894i
$473$	10.1624	+	13.9912i	0.467267	+	0.643316i
$474$	6.01829	−	3.47466i	0.276429	−	0.159596i
$475$	2.80275	+	8.62597i	0.128599	+	0.395787i
$476$	11.4283	−	1.23093i	0.523817	−	0.0564195i
$477$	−4.75126	+	3.45199i	−0.217545	+	0.158056i
$478$	−7.02423	+	1.49305i	−0.321281	+	0.0682903i
$479$	−26.7953	−	29.7592i	−1.22431	−	1.35973i	−0.912230	−	0.409678i	$-0.865641\pi$
$479$	−26.7953	−	29.7592i	−1.22431	−	1.35973i	−0.312080	−	0.950056i	$-0.601026\pi$
$480$	18.9600	−	1.99277i	0.865400	−	0.0909572i
$481$	1.05179	−	10.0071i	0.0479575	−	0.456285i
$482$	−12.1283	+	3.94073i	−0.552430	+	0.179495i
$483$	−11.6281	+	2.50295i	−0.529099	+	0.113888i
$484$	−18.6076	−	3.96029i	−0.845799	−	0.180013i
$485$	−6.94159	−	12.0232i	−0.315201	−	0.545944i
$486$	7.63207	+	1.62225i	0.346198	+	0.0735866i
$487$	13.1830	−	5.86945i	0.597379	−	0.265970i	−0.0856926	−	0.996322i	$-0.527310\pi$
$487$	13.1830	−	5.86945i	0.597379	−	0.265970i	0.683072	+	0.730351i	$0.260644\pi$
$488$	−5.90408	+	13.2608i	−0.267265	+	0.600287i
$489$	15.1433	+	4.92035i	0.684802	+	0.222506i
$490$	−10.8809	−	4.77750i	−0.491550	−	0.215826i
$491$	15.4413	+	21.2531i	0.696855	+	0.959139i	0.999981	+	0.00618844i	$0.00196985\pi$
$491$	15.4413	+	21.2531i	0.696855	+	0.959139i	−0.303126	+	0.952951i	$0.598030\pi$
$492$	7.85472	+	0.825564i	0.354118	+	0.0372193i
$493$	4.40333	−	20.7160i	0.198316	−	0.933003i
$494$	−1.09357	−	0.631375i	−0.0492022	−	0.0284069i
$495$	−18.4713	+	1.93895i	−0.830223	+	0.0871494i
$496$		−	23.3826i		−	1.04991i
$497$	−5.90411	+	3.42904i	−0.264836	+	0.153814i
$498$	−6.43675	−	4.67657i	−0.288438	−	0.209562i
$499$	30.0488	+	13.3786i	1.34517	+	0.598908i	0.947834	−	0.318765i	$-0.103268\pi$
$499$	30.0488	+	13.3786i	1.34517	+	0.598908i	0.397336	+	0.917673i	$0.369935\pi$
$500$	−2.74291	+	2.46973i	−0.122667	+	0.110450i
$501$	−7.07474	+	6.37012i	−0.316076	+	0.284596i
$502$	−6.90665	−	3.07504i	−0.308259	−	0.137246i
$503$	−6.95818	−	5.05541i	−0.310250	−	0.225410i	0.421754	−	0.906710i	$-0.361415\pi$
$503$	−6.95818	−	5.05541i	−0.310250	−	0.225410i	−0.732004	+	0.681301i	$0.761415\pi$
$504$	−4.38277	+	7.63652i	−0.195224	+	0.340158i
$505$			18.4301i			0.820130i
$506$	2.78247	+	6.25174i	0.123696	+	0.277924i
$507$	10.5110	+	6.06851i	0.466809	+	0.269512i
$508$	2.24357	−	10.5552i	0.0995424	−	0.468310i
$509$	−17.6146	−	1.85137i	−0.780755	−	0.0820607i	−0.294239	−	0.955732i	$-0.595066\pi$
$509$	−17.6146	−	1.85137i	−0.780755	−	0.0820607i	−0.486517	+	0.873671i	$0.661733\pi$
$510$	2.84074	+	3.90994i	0.125790	+	0.173135i
$511$	−18.3847	+	25.4418i	−0.813289	+	1.12548i
$512$	21.0491	+	6.83928i	0.930249	+	0.302256i
$513$	3.48703	−	7.83199i	0.153956	−	0.345791i
$514$	8.64879	−	3.85069i	0.381482	−	0.169847i
$515$	−1.37609	−	0.292496i	−0.0606376	−	0.0128889i
$516$	−5.10962	−	8.85012i	−0.224939	−	0.389605i
$517$	−0.997627	+	0.575805i	−0.0438756	+	0.0253239i
$518$	2.80479	−	8.70850i	0.123235	−	0.382630i
$519$	−25.0591	+	8.14221i	−1.09997	+	0.357403i
$520$	1.00160	−	9.52962i	0.0439232	−	0.417901i
$521$	2.96731	−	0.311877i	0.130000	−	0.0136636i	−0.0393049	−	0.999227i	$-0.512514\pi$
$521$	2.96731	−	0.311877i	0.130000	−	0.0136636i	0.169305	+	0.985564i	$0.445848\pi$
$522$	5.03401	+	5.59084i	0.220333	+	0.244704i
$523$	8.17896	−	1.73849i	0.357641	−	0.0760189i	−0.0255873	−	0.999673i	$-0.508146\pi$
$523$	8.17896	−	1.73849i	0.357641	−	0.0760189i	0.383228	+	0.923654i	$0.374812\pi$
$524$	−22.3970	+	16.2724i	−0.978416	+	0.710861i
$525$	1.81543	+	16.8550i	0.0792319	+	0.735614i
$526$	0.539949	+	1.66179i	0.0235429	+	0.0724575i
$527$	20.7617	−	11.9868i	0.904392	−	0.522151i
$528$	8.75807	+	2.84695i	0.381146	+	0.123897i
$529$	3.63177	−	6.29041i	0.157903	−	0.273496i
$530$	3.88851	−	4.31862i	0.168906	−	0.187589i
$531$	−0.679348	+	0.935042i	−0.0294812	+	0.0405774i
$532$	5.46767	+	4.89767i	0.237053	+	0.212341i
$533$	1.88453	−	5.79999i	0.0816281	−	0.251225i
$534$	0.924522	+	4.34953i	0.0400080	+	0.188223i
$535$	−1.23099	−	11.7121i	−0.0532204	−	0.506359i
$536$	−6.53579	−	14.6796i	−0.282303	−	0.634063i
$537$	9.56590	+	8.61317i	0.412799	+	0.371686i
$538$	1.47504			0.0635936
$539$	−15.6212	−	17.1750i	−0.672852	−	0.739778i
$540$	30.1685			1.29824
$541$	18.7525	+	16.8848i	0.806231	+	0.725934i	0.965246	−	0.261342i	$-0.0841651\pi$
$541$	18.7525	+	16.8848i	0.806231	+	0.725934i	−0.159015	+	0.987276i	$0.550832\pi$
$542$	2.26029	+	5.07670i	0.0970878	+	0.218063i
$543$	−2.25816	−	21.4850i	−0.0969070	−	0.922008i
$544$	2.69171	+	12.6635i	0.115406	+	0.542943i
$545$	−11.8892	+	36.5912i	−0.509277	+	1.56739i
$546$	−1.75804	−	1.57477i	−0.0752371	−	0.0673938i
$547$	12.9242	−	17.7887i	0.552600	−	0.760588i	−0.437762	−	0.899091i	$-0.644229\pi$
$547$	12.9242	−	17.7887i	0.552600	−	0.760588i	0.990362	+	0.138503i	$0.0442289\pi$
$548$	−10.5578	+	11.7256i	−0.451006	+	0.500892i
$549$	−6.41937	+	11.1187i	−0.273972	+	0.474533i
$550$	9.27598	−	3.01260i	0.395529	−	0.128458i
$551$	11.7130	−	6.76252i	0.498992	−	0.288093i
$552$	−2.69478	−	8.29367i	−0.114697	−	0.353002i
$553$	3.34040	+	31.0134i	0.142048	+	1.31882i
$554$	−0.120810	+	0.0877735i	−0.00513272	+	0.00372914i
$555$	−24.0564	+	5.11335i	−1.02114	+	0.217049i
$556$	−9.71660	−	10.7914i	−0.412076	−	0.457656i
$557$	20.9817	−	2.20526i	0.889023	−	0.0934401i	0.351005	−	0.936374i	$-0.385840\pi$
$557$	20.9817	−	2.20526i	0.889023	−	0.0934401i	0.538018	+	0.842933i	$0.319173\pi$
$558$	−0.890159	+	8.46930i	−0.0376834	+	0.358534i
$559$	−7.50464	+	2.43840i	−0.317412	+	0.103134i
$560$	−6.48649	+	20.1397i	−0.274104	+	0.851056i
$561$	1.96187	+	9.23585i	0.0828302	+	0.389938i
$562$	1.73467	+	3.00453i	0.0731726	+	0.126739i
$563$	20.8858	+	4.43941i	0.880231	+	0.187099i	0.625792	−	0.779990i	$-0.284776\pi$
$563$	20.8858	+	4.43941i	0.880231	+	0.187099i	0.254439	+	0.967089i	$0.418109\pi$
$564$	0.621867	−	0.276873i	0.0261853	−	0.0116585i
$565$	−0.505487	+	1.13534i	−0.0212660	+	0.0477643i
$566$	4.72734	+	1.53601i	0.198705	+	0.0645632i
$567$	1.40956	−	1.95064i	0.0591961	−	0.0819192i
$568$	−2.94229	−	4.04972i	−0.123456	−	0.169922i
$569$	0.696980	+	0.0732555i	0.0292189	+	0.00307103i	0.119127	−	0.992879i	$-0.461991\pi$
$569$	0.696980	+	0.0732555i	0.0292189	+	0.00307103i	−0.0899077	+	0.995950i	$0.528657\pi$
$570$	−0.641694	+	3.01893i	−0.0268776	+	0.126449i
$571$	0.315440	+	0.182119i	0.0132007	+	0.00762146i	0.506586	−	0.862190i	$-0.330907\pi$
$571$	0.315440	+	0.182119i	0.0132007	+	0.00762146i	−0.493385	+	0.869811i	$0.664241\pi$
$572$	4.34156	−	7.51752i	0.181530	−	0.314323i
$573$			3.85448i			0.161023i
$574$	2.76012	−	4.80923i	0.115205	−	0.200734i
$575$	18.1449	+	13.1830i	0.756694	+	0.549771i
$576$	3.47888	+	1.54890i	0.144953	+	0.0645374i
$577$	15.2131	−	13.6979i	0.633329	−	0.570252i	−0.288677	−	0.957426i	$-0.593215\pi$
$577$	15.2131	−	13.6979i	0.633329	−	0.570252i	0.922007	+	0.387174i	$0.126549\pi$
$578$	4.13179	−	3.72028i	0.171860	−	0.154743i
$579$	−9.46391	−	4.21361i	−0.393307	−	0.175111i
$580$	38.5042	+	27.9749i	1.59880	+	1.16160i
$581$	30.8818	−	17.9358i	1.28119	−	0.744104i
$582$		−	2.50711i		−	0.103923i
$583$	10.3723	−	4.61641i	0.429577	−	0.191192i
$584$	−19.9300	−	11.5066i	−0.824707	−	0.476145i
$585$	1.76207	−	8.28989i	0.0728527	−	0.342745i
$586$	14.5660	+	1.53094i	0.601714	+	0.0632427i
$587$	−26.4039	−	36.3419i	−1.08981	−	1.49999i	−0.848245	−	0.529604i	$-0.822340\pi$
$587$	−26.4039	−	36.3419i	−1.08981	−	1.49999i	−0.241562	−	0.970385i	$-0.577660\pi$
$588$	8.12153	+	11.0581i	0.334926	+	0.456029i
$589$	14.5604	+	4.73097i	0.599953	+	0.194936i
$590$	0.465165	−	1.04478i	0.0191506	−	0.0430129i
$591$	−3.29580	+	1.46738i	−0.135571	+	0.0603601i
$592$	−15.9337	−	3.38682i	−0.654872	−	0.139197i
$593$	−5.16565	−	8.94718i	−0.212128	−	0.367416i	0.740252	−	0.672329i	$-0.234706\pi$
$593$	−5.16565	−	8.94718i	−0.212128	−	0.367416i	−0.952380	+	0.304913i	$0.901373\pi$
$594$	−8.42132	−	3.75074i	−0.345531	−	0.153895i
$595$	−21.2075	+	4.56490i	−0.869421	+	0.187142i
$596$	2.16068	−	0.702048i	0.0885050	−	0.0287570i
$597$	−0.288157	+	2.74163i	−0.0117935	+	0.112208i
$598$	−3.10547	+	0.326398i	−0.126992	+	0.0133474i
$599$	−7.01122	−	7.78675i	−0.286471	−	0.318158i	0.582683	−	0.812699i	$-0.302003\pi$
$599$	−7.01122	−	7.78675i	−0.286471	−	0.318158i	−0.869154	+	0.494541i	$0.835336\pi$
$600$	−12.1572	+	2.58410i	−0.496316	+	0.105495i
$601$	−5.20538	+	3.78193i	−0.212332	+	0.154268i	−0.688868	−	0.724887i	$-0.741892\pi$
$601$	−5.20538	+	3.78193i	−0.212332	+	0.154268i	0.476536	+	0.879155i	$0.341892\pi$
$602$	−7.13344	+	0.768332i	−0.290737	+	0.0313149i
$603$	−4.39188	−	13.5168i	−0.178851	−	0.550447i
$604$	21.2298	−	12.2570i	0.863828	−	0.498731i
$605$	35.7066	+	3.76242i	1.45168	+	0.152964i
$606$	−1.66411	+	2.88233i	−0.0676000	+	0.117087i
$607$	24.7661	−	27.5056i	1.00523	−	1.11642i	0.0120346	−	0.999928i	$-0.496169\pi$
$607$	24.7661	−	27.5056i	1.00523	−	1.11642i	0.993192	−	0.116490i	$-0.0371642\pi$
$608$	−4.85965	+	6.68873i	−0.197085	+	0.271264i
$609$	24.0222	−	7.87374i	0.973429	−	0.319060i
$610$	3.92577	−	12.0823i	0.158950	−	0.489198i
$611$	−0.109283	−	0.514134i	−0.00442110	−	0.0207996i
$612$	0.779114	+	7.41277i	0.0314938	+	0.299644i
$613$	16.6874	+	37.4806i	0.673998	+	1.51383i	0.848515	+	0.529171i	$0.177497\pi$
$613$	16.6874	+	37.4806i	0.673998	+	1.51383i	−0.174517	+	0.984654i	$0.555836\pi$
$614$	−4.41298	−	3.97347i	−0.178094	−	0.160356i
$615$	−14.9057			−0.601056
$616$	11.3585	−	12.6770i	0.457645	−	0.510771i
$617$	−22.6748			−0.912852			−0.456426	−	0.889761i	$-0.650871\pi$
$617$	−22.6748			−0.912852			−0.456426	+	0.889761i	$0.650871\pi$
$618$	−0.188799	−	0.169995i	−0.00759460	−	0.00683821i
$619$	7.13232	+	16.0194i	0.286672	+	0.643876i	0.998275	−	0.0587055i	$-0.0186973\pi$
$619$	7.13232	+	16.0194i	0.286672	+	0.643876i	−0.711603	+	0.702581i	$0.752031\pi$
$620$	5.63137	+	53.5790i	0.226161	+	2.15178i
$621$	−4.40774	−	20.7368i	−0.176877	−	0.832139i
$622$	−1.11012	+	3.41659i	−0.0445117	+	0.136993i
$623$	−19.5340	−	4.09953i	−0.782611	−	0.164244i
$624$	−2.47006	+	3.39974i	−0.0988814	+	0.136099i
$625$	−14.2547	+	15.8315i	−0.570188	+	0.633258i
$626$	−6.94144	+	12.0229i	−0.277436	+	0.480533i
$627$	−3.54482	+	4.87768i	−0.141567	+	0.194796i
$628$	−23.0109	+	13.2853i	−0.918234	+	0.530143i
$629$	−5.16101	−	15.8840i	−0.205783	−	0.633335i
$630$	3.11615	−	7.04777i	0.124150	−	0.280790i
$631$	−25.5281	+	18.5473i	−1.01626	+	0.738355i	−0.965513	−	0.260356i	$-0.916160\pi$
$631$	−25.5281	+	18.5473i	−1.01626	+	0.738355i	−0.0507462	+	0.998712i	$0.516160\pi$
$632$	−22.3694	+	4.75475i	−0.889805	+	0.189134i
$633$	4.52386	+	5.02425i	0.179807	+	0.199696i
$634$	1.32673	−	0.139445i	0.0526913	−	0.00553808i
$635$	−2.12878	+	20.2540i	−0.0844782	+	0.803757i
$636$	−6.38100	+	2.07331i	−0.253023	+	0.0822123i
$637$	9.65582	−	4.35877i	0.382578	−	0.172701i
$638$	−7.27014	−	12.5961i	−0.287828	−	0.498684i
$639$	−2.21371	−	3.83426i	−0.0875729	−	0.151681i
$640$	−36.5949	−	7.77848i	−1.44654	−	0.307471i
$641$	−22.3684	+	9.95907i	−0.883501	+	0.393360i	−0.797772	−	0.602959i	$-0.793988\pi$
$641$	−22.3684	+	9.95907i	−0.883501	+	0.393360i	−0.0857282	+	0.996319i	$0.527322\pi$
$642$	0.865005	−	1.94283i	0.0341390	−	0.0766775i
$643$	−1.51386	−	0.491883i	−0.0597008	−	0.0193980i	0.279014	−	0.960287i	$-0.409992\pi$
$643$	−1.51386	−	0.491883i	−0.0597008	−	0.0193980i	−0.338715	+	0.940889i	$0.609992\pi$
$644$	18.0572	+	1.85089i	0.711553	+	0.0729352i
$645$	11.3364	+	15.6032i	0.446369	+	0.614374i
$646$	−2.08444	−	0.219084i	−0.0820112	−	0.00861973i
$647$	−2.72425	+	12.8166i	−0.107101	+	0.503871i	0.891596	+	0.452833i	$0.149587\pi$
$647$	−2.72425	+	12.8166i	−0.107101	+	0.503871i	−0.998697	+	0.0510387i	$0.983747\pi$
$648$	1.52804	+	0.882215i	0.0600271	+	0.0346567i
$649$	1.66061	−	1.49482i	0.0651846	−	0.0586769i
$650$			4.45043i			0.174560i
$651$	24.8185	+	14.2439i	0.972714	+	0.558262i
$652$	−19.6583	−	14.2826i	−0.769877	−	0.559349i
$653$	−39.3416	−	17.5160i	−1.53956	−	0.685454i	−0.550751	−	0.834670i	$-0.685659\pi$
$653$	−39.3416	−	17.5160i	−1.53956	−	0.685454i	−0.988805	+	0.149215i	$0.952325\pi$
$654$	−5.16331	+	4.64907i	−0.201902	+	0.181793i
$655$	38.8277	−	34.9606i	1.51712	−	1.36602i
$656$	−9.01923	−	4.01562i	−0.352142	−	0.156784i
$657$	−16.4671	−	11.9640i	−0.642442	−	0.466761i
$658$	−0.00123066	−	0.477916i	−4.79763e−5	−	0.0186311i
$659$		−	6.50970i		−	0.253582i	−0.991929	−	0.126791i	$-0.959532\pi$
$659$		−	6.50970i		−	0.253582i	0.991929	−	0.126791i	$-0.0404677\pi$
$660$	−20.7540	−	4.41425i	−0.807847	−	0.171824i
$661$	−10.7563	−	6.21018i	−0.418373	−	0.241548i	0.276008	−	0.961155i	$-0.410988\pi$
$661$	−10.7563	−	6.21018i	−0.418373	−	0.241548i	−0.694381	+	0.719607i	$0.744322\pi$
$662$	−2.75179	+	12.9462i	−0.106951	+	0.503167i
$663$	−4.28491	−	0.450363i	−0.166412	−	0.0174906i
$664$	15.3898	+	21.1823i	0.597242	+	0.822033i
$665$	−11.2287	−	8.11401i	−0.435429	−	0.314648i
$666$	5.64235	+	1.83331i	0.218637	+	0.0710394i
$667$	13.6034	−	30.5537i	0.526726	−	1.18304i
$668$	13.2722	−	5.90915i	0.513515	−	0.228632i
$669$	−1.36016	−	0.289111i	−0.0525869	−	0.0111777i
$670$	7.03167	+	12.1792i	0.271657	+	0.470524i
$671$	16.6098	−	18.4422i	0.641216	−	0.711953i
$672$	−11.4573	+	10.3698i	−0.441976	+	0.400022i
$673$	−22.7582	+	7.39460i	−0.877265	+	0.285041i	−0.712821	−	0.701346i	$-0.752583\pi$
$673$	−22.7582	+	7.39460i	−0.877265	+	0.285041i	−0.164444	+	0.986386i	$0.552583\pi$
$674$	0.946080	−	9.00135i	0.0364417	−	0.346719i
$675$	−30.0498	+	3.15836i	−1.15662	+	0.121565i
$676$	−12.3936	−	13.7645i	−0.476677	−	0.529403i
$677$	9.63877	−	2.04878i	0.370448	−	0.0787411i	−0.0189261	−	0.999821i	$-0.506025\pi$
$677$	9.63877	−	2.04878i	0.370448	−	0.0787411i	0.389374	+	0.921080i	$0.372691\pi$
$678$	−0.181568	+	0.131917i	−0.00697308	+	0.00506624i
$679$	10.2923	+	4.55069i	0.394981	+	0.174640i
$680$	−4.91475	−	15.1260i	−0.188472	−	0.580057i
$681$	0.872911	−	0.503975i	0.0334500	−	0.0193124i
$682$	5.08932	−	15.6563i	0.194880	−	0.599511i
$683$	−4.31582	+	7.47523i	−0.165140	+	0.286032i	−0.936705	−	0.350119i	$-0.886141\pi$
$683$	−4.31582	+	7.47523i	−0.165140	+	0.286032i	0.771565	+	0.636151i	$0.219474\pi$
$684$	−3.18503	+	3.53734i	−0.121783	+	0.135253i
$685$	17.5031	−	24.0910i	0.668761	−	0.920470i
$686$	9.40633	−	2.07545i	0.359135	−	0.0792411i
$687$	9.24867	−	28.4645i	0.352859	−	1.08599i
$688$	2.65595	+	12.4953i	0.101257	+	0.476378i
$689$	0.541529	+	5.15231i	0.0206306	+	0.196287i
$690$	3.10426	+	6.97227i	0.118177	+	0.265430i
$691$	4.16452	+	3.74975i	0.158426	+	0.142647i	0.744531	−	0.667588i	$-0.232673\pi$
$691$	4.16452	+	3.74975i	0.158426	+	0.142647i	−0.586106	+	0.810235i	$0.699340\pi$
$692$	40.2100			1.52856
$693$	11.1632	−	10.1009i	0.424055	−	0.383701i
$694$	−10.8037			−0.410104
$695$	20.3663	+	18.3379i	0.772539	+	0.695598i
$696$	7.53842	+	16.9316i	0.285743	+	0.641789i
$697$	−1.05807	−	10.0668i	−0.0400772	−	0.381309i
$698$	−2.14509	−	10.0918i	−0.0811928	−	0.381982i
$699$	7.16923	−	22.0646i	0.271165	−	0.834561i
$700$	5.31365	−	25.3192i	0.200837	−	0.956975i
$701$	9.17773	−	12.6321i	0.346638	−	0.477107i	−0.599727	−	0.800204i	$-0.704724\pi$
$701$	9.17773	−	12.6321i	0.346638	−	0.477107i	0.946366	+	0.323098i	$0.104724\pi$
$702$	2.81484	−	3.12620i	0.106239	−	0.117991i
$703$	5.33285	−	9.23676i	0.201132	−	0.348371i
$704$	−5.95517	−	4.32788i	−0.224444	−	0.163113i
$705$	−1.11259	+	0.642353i	−0.0419025	+	0.0241924i
$706$	−4.22845	−	13.0138i	−0.159140	−	0.489782i
$707$	−8.81207	−	12.0633i	−0.331412	−	0.453688i
$708$	−1.06822	+	0.776111i	−0.0401463	+	0.0291680i
$709$	30.4657	−	6.47568i	1.14416	−	0.243199i	0.403437	−	0.915007i	$-0.367815\pi$
$709$	30.4657	−	6.47568i	1.14416	−	0.243199i	0.740725	+	0.671808i	$0.234482\pi$
$710$	2.93145	+	3.25570i	0.110015	+	0.122184i
$711$	−20.1162	+	2.11430i	−0.754418	+	0.0792925i
$712$	1.52961	−	14.5532i	0.0573244	−	0.545405i
$713$	36.0056	−	11.6989i	1.34842	−	0.438128i
$714$	−3.72886	−	1.20097i	−0.139549	−	0.0449453i
$715$	−6.66584	+	14.9664i	−0.249288	+	0.559712i
$716$	−9.82193	−	17.0121i	−0.367063	−	0.635771i
$717$	−15.3054	−	3.25327i	−0.571592	−	0.121496i
$718$	−15.5294	+	6.91413i	−0.579552	+	0.258033i
$719$	−9.97726	+	22.4093i	−0.372089	+	0.835725i	0.626332	+	0.779556i	$0.284555\pi$
$719$	−9.97726	+	22.4093i	−0.372089	+	0.835725i	−0.998421	+	0.0561693i	$0.982111\pi$
$720$	−13.0488	−	4.23980i	−0.486298	−	0.158008i
$721$	1.04056	−	0.466502i	0.0387525	−	0.0173734i
$722$	5.02181	+	6.91193i	0.186892	+	0.257235i
$723$	−27.6348	−	2.90453i	−1.02775	−	0.108021i
$724$	−6.85447	+	32.2477i	−0.254744	+	1.19848i
$725$	−41.2814	−	23.8338i	−1.53315	−	0.885166i
$726$	5.24451	+	3.81247i	0.194642	+	0.141494i
$727$			15.0031i			0.556433i	0.960518	+	0.278217i	$0.0897433\pi$
$727$			15.0031i			0.556433i	−0.960518	+	0.278217i	$0.910257\pi$
$728$	3.90084	+	6.71646i	0.144575	+	0.248928i
$729$	15.9621	+	11.5972i	0.591190	+	0.429524i
$730$	18.3997	+	8.19206i	0.681002	+	0.303202i
$731$	−9.73318	+	8.76379i	−0.359995	+	0.324141i
$732$	−10.9000	+	9.81442i	−0.402876	+	0.362751i
$733$	25.1246	+	11.1862i	0.927998	+	0.413171i	0.814366	−	0.580351i	$-0.197085\pi$
$733$	25.1246	+	11.1862i	0.927998	+	0.413171i	0.113632	+	0.993523i	$0.463751\pi$
$734$	−3.03504	−	2.20508i	−0.112025	−	0.0813911i
$735$	−17.4251	−	19.1533i	−0.642735	−	0.706478i
$736$			20.4447i			0.753603i
$737$	2.86831	+	27.3248i	0.105656	+	1.00652i
$738$	3.11394	+	1.79784i	0.114626	+	0.0661793i
$739$	−2.12909	+	10.0166i	−0.0783199	+	0.368466i	−0.999801	−	0.0199576i	$-0.993647\pi$
$739$	−2.12909	+	10.0166i	−0.0783199	+	0.368466i	0.921481	+	0.388423i	$0.126980\pi$
$740$	37.3263	+	3.92315i	1.37214	+	0.144218i
$741$	−1.61727	−	2.22598i	−0.0594120	−	0.0817736i
$742$	−0.480317	+	4.68596i	−0.0176330	+	0.172027i
$743$	−34.0749	−	11.0716i	−1.25009	−	0.406178i	−0.392135	−	0.919908i	$-0.628263\pi$
$743$	−34.0749	−	11.0716i	−1.25009	−	0.406178i	−0.857952	+	0.513730i	$0.828263\pi$
$744$	−8.53316	+	19.1658i	−0.312841	+	0.702652i
$745$	−3.91698	+	1.74395i	−0.143507	+	0.0638934i
$746$	−17.3676	−	3.69160i	−0.635874	−	0.135159i
$747$	11.5789	+	20.0553i	0.423651	+	0.733786i
$748$	1.50804	−	14.3299i	0.0551395	−	0.523953i
$749$	6.40570	+	7.07751i	0.234059	+	0.258607i
$750$	1.19637	−	0.388724i	0.0436853	−	0.0141942i
$751$	−0.739216	+	7.03317i	−0.0269744	+	0.256644i	0.972721	+	0.231977i	$0.0745193\pi$
$751$	−0.739216	+	7.03317i	−0.0269744	+	0.256644i	−0.999696	+	0.0246673i	$0.992147\pi$
$752$	−0.846262	+	0.0889457i	−0.0308600	+	0.00324352i
$753$	−11.0229	−	12.2421i	−0.401696	−	0.446128i
$754$	6.49148	−	1.37981i	0.236406	−	0.0502496i
$755$	−37.4290	+	27.1938i	−1.36218	+	0.989684i
$756$	−19.7466	+	14.4246i	−0.718177	+	0.524617i
$757$	−0.619668	−	1.90714i	−0.0225222	−	0.0693163i	0.939164	−	0.343470i	$-0.111602\pi$
$757$	−0.619668	−	1.90714i	−0.0225222	−	0.0693163i	−0.961686	+	0.274154i	$0.911602\pi$
$758$	−2.99303	+	1.72803i	−0.108712	+	0.0627648i
$759$	−0.00196459	+	14.9105i	−7.13099e−5	+	0.541217i
$760$	5.07838	−	8.79602i	0.184212	−	0.319065i
$761$	−31.9197	+	35.4505i	−1.15709	+	1.28508i	−0.205172	+	0.978726i	$0.565775\pi$
$761$	−31.9197	+	35.4505i	−1.15709	+	1.28508i	−0.951918	+	0.306352i	$0.900891\pi$
$762$	−2.16173	+	2.97536i	−0.0783111	+	0.107786i
$763$	−9.71350	−	29.6352i	−0.351652	−	1.07287i
$764$	1.81770	−	5.59431i	0.0657621	−	0.202395i
$765$	−2.92470	−	13.7596i	−0.105743	−	0.497480i
$766$	1.17142	+	11.1453i	0.0423250	+	0.402695i
$767$	0.414689	+	0.931408i	0.0149736	+	0.0336312i
$768$	−1.28205	−	1.15437i	−0.0462622	−	0.0416546i
$769$	36.1480			1.30353			0.651766	−	0.758420i	$-0.274029\pi$
$769$	36.1480			1.30353			0.651766	+	0.758420i	$0.274029\pi$
$770$	−8.72666	+	12.0731i	−0.314487	+	0.435086i
$771$	20.6287			0.742925
$772$	11.7487	+	10.5785i	0.422844	+	0.380730i
$773$	−2.79444	−	6.27641i	−0.100509	−	0.225747i	0.856291	−	0.516494i	$-0.172763\pi$
$773$	−2.79444	−	6.27641i	−0.100509	−	0.225747i	−0.956800	+	0.290747i	$0.906096\pi$
$774$	−0.486314	−	4.62697i	−0.0174802	−	0.166313i
$775$	−11.2184	−	52.7786i	−0.402978	−	1.89586i
$776$	−2.54954	+	7.84669i	−0.0915233	+	0.281680i
$777$	13.3011	−	14.8491i	0.477175	−	0.532708i
$778$	−5.87595	+	8.08755i	−0.210663	+	0.289953i
$779$	4.32540	−	4.80384i	0.154974	−	0.172116i
$780$	4.84112	−	8.38507i	0.173340	−	0.300234i
$781$	2.64378	+	8.14037i	0.0946019	+	0.291285i
$782$	−4.48850	+	2.59144i	−0.160508	+	0.0926696i
$783$	13.9234	+	42.8519i	0.497583	+	1.53140i
$784$	−5.38377	−	16.2837i	−0.192278	−	0.581561i
$785$	40.5692	−	29.4752i	1.44798	−	1.05202i
$786$	9.22905	−	1.96169i	0.329189	−	0.0699713i
$787$	20.1686	+	22.3995i	0.718934	+	0.798457i	0.986269	−	0.165147i	$-0.0528097\pi$
$787$	20.1686	+	22.3995i	0.718934	+	0.798457i	−0.267335	+	0.963604i	$0.586143\pi$
$788$	5.47545	−	0.575493i	0.195055	−	0.0205011i
$789$	−0.397971	+	3.78644i	−0.0141681	+	0.134801i
$790$	19.0353	−	6.18494i	0.677245	−	0.220050i
$791$	−0.211983	−	0.984823i	−0.00753724	−	0.0350163i
$792$	8.20144	+	7.38657i	0.291426	+	0.262470i
$793$	5.66276	+	9.80819i	0.201091	+	0.348299i
$794$	1.80722	+	0.384136i	0.0641357	+	0.0136325i
$795$	11.5678	−	5.15030i	0.410266	−	0.182662i
$796$	1.71113	−	3.84326i	0.0606493	−	0.136221i
$797$	−15.3794	−	4.99707i	−0.544767	−	0.177005i	0.0236890	−	0.999719i	$-0.492459\pi$
$797$	−15.3794	−	4.99707i	−0.544767	−	0.177005i	−0.568456	+	0.822714i	$0.692459\pi$
$798$	−1.02344	−	2.28284i	−0.0362293	−	0.0808117i
$799$	−0.512801	−	0.705809i	−0.0181416	−	0.0249697i
$800$	28.9791	+	3.04583i	1.02457	+	0.107686i
$801$	2.69096	−	12.6600i	0.0950804	−	0.447318i
$802$	4.23099	+	2.44276i	0.149401	+	0.0862570i
$803$	26.3254	+	29.2451i	0.929003	+	1.03204i
$804$		−	16.2368i		−	0.572626i
$805$	−34.2574	+	0.0882150i	−1.20741	+	0.00310917i
$806$	6.07753	+	4.41558i	0.214072	+	0.155532i
$807$	2.93617	+	1.30727i	0.103358	+	0.0460180i
$808$	8.13941	−	7.32876i	0.286344	−	0.257825i
$809$	40.6264	−	36.5802i	1.42835	−	1.28609i	0.529168	−	0.848517i	$-0.322504\pi$
$809$	40.6264	−	36.5802i	1.42835	−	1.28609i	0.899182	−	0.437575i	$-0.144162\pi$
$810$	−1.41071	−	0.628090i	−0.0495674	−	0.0220688i
$811$	−6.01647	−	4.37122i	−0.211267	−	0.153494i	0.477120	−	0.878838i	$-0.341681\pi$
$811$	−6.01647	−	4.37122i	−0.211267	−	0.153494i	−0.688387	+	0.725344i	$0.741681\pi$
$812$	−38.5785	+	0.0993421i	−1.35384	+	0.00348622i
$813$			12.1087i			0.424671i
$814$	−9.93162	−	5.73577i	−0.348103	−	0.201039i
$815$	39.7150	+	22.9295i	1.39116	+	0.803184i
$816$	−1.45019	+	6.82261i	−0.0507668	+	0.238839i
$817$	−8.31825	−	0.874284i	−0.291019	−	0.0305873i
$818$	0.350006	+	0.481742i	0.0122377	+	0.0168437i
$819$	2.81033	+	6.26861i	0.0982008	+	0.219043i
$820$	21.6338	+	7.02926i	0.755486	+	0.245472i
$821$	8.79614	−	19.7565i	0.306988	−	0.689505i	−0.692503	−	0.721415i	$-0.743492\pi$
$821$	8.79614	−	19.7565i	0.306988	−	0.689505i	0.999491	+	0.0319095i	$0.0101588\pi$
$822$	4.91261	−	2.18724i	0.171347	−	0.0762886i
$823$	−24.8764	−	5.28764i	−0.867137	−	0.184316i	−0.247197	−	0.968965i	$-0.579510\pi$
$823$	−24.8764	−	5.28764i	−0.867137	−	0.184316i	−0.619940	+	0.784649i	$0.712843\pi$
$824$	0.418025	+	0.724041i	0.0145626	+	0.0252232i
$825$	21.1344	+	2.22413i	0.735806	+	0.0774343i
$826$	0.195073	+	0.906265i	0.00678746	+	0.0315330i
$827$	−27.6468	+	8.98300i	−0.961374	+	0.312369i	−0.747329	−	0.664454i	$-0.768664\pi$
$827$	−27.6468	+	8.98300i	−0.961374	+	0.312369i	−0.214045	+	0.976824i	$0.568664\pi$
$828$	−1.23036	+	11.7061i	−0.0427580	+	0.406815i
$829$	44.8185	−	4.71061i	1.55661	−	0.163606i	0.713233	−	0.700927i	$-0.247230\pi$
$829$	44.8185	−	4.71061i	1.55661	−	0.163606i	0.843378	+	0.537321i	$0.180564\pi$
$830$	−15.3331	−	17.0292i	−0.532220	−	0.591090i
$831$	−0.318270	+	0.0676504i	−0.0110407	+	0.00234677i
$832$	2.71771	−	1.97453i	0.0942196	−	0.0684546i
$833$	11.6986	−	13.1279i	0.405332	−	0.454856i
$834$	1.52935	+	4.70685i	0.0529570	+	0.162985i
$835$	−23.7453	+	13.7094i	−0.821741	+	0.474432i
$836$	7.44510	−	5.40769i	0.257494	−	0.187029i
$837$	−25.5014	+	44.1697i	−0.881456	+	1.52673i
$838$	−4.41709	+	4.90567i	−0.152586	+	0.169464i
$839$	28.9525	−	39.8497i	0.999552	−	1.37577i	0.0739529	−	0.997262i	$-0.476439\pi$
$839$	28.9525	−	39.8497i	0.999552	−	1.37577i	0.925600	−	0.378504i	$-0.123561\pi$
$840$	12.6664	−	14.1406i	0.437033	−	0.487896i
$841$	−13.0041	+	40.0225i	−0.448418	+	1.38009i
$842$	−3.10335	−	14.6001i	−0.106949	−	0.503154i
$843$	0.790184	+	7.51809i	0.0272154	+	0.258937i
$844$	−4.19649	−	9.42546i	−0.144449	−	0.324438i
$845$	25.9774	+	23.3902i	0.893651	+	0.804647i
$846$	0.309907			0.0106548
$847$	−25.1705	+	14.6099i	−0.864867	+	0.502001i
$848$	8.38698			0.288010
$849$	8.04880	+	7.24717i	0.276234	+	0.248722i
$850$	3.00451	+	6.74824i	0.103054	+	0.231463i
$851$	−2.75689	−	26.2300i	−0.0945049	−	0.899154i
$852$	−1.05162	−	4.94751i	−0.0360281	−	0.169499i
$853$	−4.33029	+	13.3273i	−0.148266	+	0.456317i	−0.997417	−	0.0718343i	$-0.977115\pi$
$853$	−4.33029	+	13.3273i	−0.148266	+	0.456317i	0.849150	+	0.528152i	$0.177115\pi$
$854$	3.20736	+	9.78544i	0.109754	+	0.334851i
$855$	5.28029	−	7.26769i	0.180582	−	0.248550i
$856$	−4.68299	+	5.20098i	−0.160061	+	0.177766i
$857$	−25.4620	+	44.1015i	−0.869765	+	1.50648i	−0.00752798	+	0.999972i	$0.502396\pi$
$857$	−25.4620	+	44.1015i	−0.869765	+	1.50648i	−0.862237	+	0.506505i	$0.830937\pi$
$858$	−2.39385	+	1.73875i	−0.0817247	+	0.0593600i
$859$	2.76956	−	1.59901i	0.0944962	−	0.0545574i	−0.452007	−	0.892014i	$-0.649292\pi$
$859$	2.76956	−	1.59901i	0.0944962	−	0.0545574i	0.546503	+	0.837457i	$0.315959\pi$
$860$	−9.09519	−	27.9921i	−0.310143	−	0.954523i
$861$	9.75644	−	7.12693i	0.332499	−	0.242885i
$862$	0.928614	−	0.674678i	0.0316287	−	0.0229796i
$863$	5.90451	−	1.25504i	0.200992	−	0.0427222i	−0.106315	−	0.994332i	$-0.533905\pi$
$863$	5.90451	−	1.25504i	0.200992	−	0.0427222i	0.307307	+	0.951610i	$0.400572\pi$
$864$	−18.4299	−	20.4684i	−0.626997	−	0.696351i
$865$	−75.4718	+	7.93241i	−2.56612	+	0.269710i
$866$	0.662162	−	6.30005i	0.0225012	−	0.214084i
$867$	11.5217	−	3.74364i	0.391299	−	0.127141i
$868$	−29.3039	−	32.3772i	−0.994640	−	1.09895i
$869$	38.8874	+	4.09242i	1.31917	+	0.138826i
$870$	−8.11038	−	14.0476i	−0.274968	−	0.476258i
$871$	−12.2633	−	2.60665i	−0.415527	−	0.0883230i
$872$	20.8878	−	9.29983i	0.707349	−	0.314932i
$873$	−2.96809	+	6.66643i	−0.100455	+	0.225625i
$874$	−3.14785	−	1.02280i	−0.106477	−	0.0345966i
$875$	−0.575746	+	5.61696i	−0.0194638	+	0.189888i
$876$	−13.6681	−	18.8126i	−0.461803	−	0.635618i
$877$	9.02019	+	0.948060i	0.304590	+	0.0320137i	0.255591	−	0.966785i	$-0.417730\pi$
$877$	9.02019	+	0.948060i	0.304590	+	0.0320137i	0.0489995	+	0.998799i	$0.484397\pi$
$878$	1.36298	−	6.41231i	0.0459983	−	0.216405i
$879$	27.6377	+	15.9567i	0.932198	+	0.538205i
$880$	22.9683	+	13.2648i	0.774262	+	0.447156i
$881$			13.7246i			0.462395i	0.972907	+	0.231198i	$0.0742644\pi$
$881$			13.7246i			0.462395i	−0.972907	+	0.231198i	$0.925736\pi$
$882$	1.33012	+	6.10301i	0.0447876	+	0.205499i
$883$	22.1076	+	16.0621i	0.743980	+	0.540533i	0.893955	−	0.448157i	$-0.147919\pi$
$883$	22.1076	+	16.0621i	0.743980	+	0.540533i	−0.149975	+	0.988690i	$0.547919\pi$
$884$	6.00665	+	2.67433i	0.202026	+	0.0899476i
$885$	1.85189	−	1.66745i	0.0622505	−	0.0560506i
$886$	−13.8555	+	12.4756i	−0.465486	+	0.419126i
$887$	−51.6206	−	22.9830i	−1.73325	−	0.771693i	−0.995300	−	0.0968395i	$-0.969127\pi$
$887$	−51.6206	−	22.9830i	−1.73325	−	0.771693i	−0.737951	−	0.674854i	$-0.764207\pi$
$888$	11.8243	+	8.59085i	0.396797	+	0.288290i
$889$	−8.29076	−	14.2750i	−0.278063	−	0.478768i
$890$			12.8070i			0.429293i
$891$	−2.01838	−	2.24224i	−0.0676184	−	0.0751177i
$892$	1.83777	+	1.06104i	0.0615332	+	0.0355262i
$893$	0.115836	−	0.544968i	0.00387632	−	0.0182367i
$894$	−0.770052	−	0.0809357i	−0.0257544	−	0.00270689i
$895$	21.7912	+	29.9930i	0.728400	+	1.00256i
$896$	27.6721	−	12.4059i	0.924460	−	0.414452i
$897$	−6.47092	−	2.10253i	−0.216058	−	0.0702014i
$898$	0.918740	−	2.06352i	0.0306587	−	0.0688606i
$899$	−73.5056	+	32.7268i	−2.45155	+	1.09150i
$900$	16.4094	+	3.48792i	0.546979	+	0.116264i
$901$	4.29947	+	7.44690i	0.143236	+	0.248092i
$902$	−5.16501	−	4.65182i	−0.171976	−	0.154889i
$903$	−14.8806	−	4.79266i	−0.495194	−	0.159490i
$904$	0.702416	−	0.228229i	0.0233620	−	0.00759078i
$905$	6.50378	−	61.8793i	0.216193	−	2.05694i
$906$	−8.30903	+	0.873314i	−0.276049	+	0.0290139i
$907$	9.32842	+	10.3603i	0.309745	+	0.344007i	0.877838	−	0.478958i	$-0.158985\pi$
$907$	9.32842	+	10.3603i	0.309745	+	0.344007i	−0.568093	+	0.822964i	$0.692319\pi$
$908$	−1.50459	+	0.319810i	−0.0499316	+	0.0106133i
$909$	7.83720	−	5.69406i	0.259943	−	0.188860i
$910$	−4.00973	−	5.48914i	−0.132921	−	0.181963i
$911$	−8.30921	−	25.5731i	−0.275296	−	0.847275i	−0.989141	−	0.146971i	$-0.953048\pi$
$911$	−8.30921	−	25.5731i	−0.275296	−	0.847275i	0.713845	−	0.700304i	$-0.246952\pi$
$912$	−3.85757	+	2.22717i	−0.127737	+	0.0737489i
$913$	−13.8285	−	42.5787i	−0.457655	−	1.40915i
$914$	0.0439286	−	0.0760866i	0.00145303	−	0.00251672i
$915$	18.5226	−	20.5714i	0.612337	−	0.680069i
$916$	−26.8466	+	36.9512i	−0.887038	+	1.22090i
$917$	−8.69857	+	41.4481i	−0.287252	+	1.36874i
$918$	2.15766	−	6.64059i	0.0712134	−	0.219172i
$919$	−5.73182	−	26.9661i	−0.189075	−	0.889529i	−0.965719	−	0.259589i	$-0.916413\pi$
$919$	−5.73182	−	26.9661i	−0.189075	−	0.889529i	0.776644	−	0.629940i	$-0.216921\pi$
$920$	−2.62534	−	24.9784i	−0.0865549	−	0.823515i
$921$	−5.26283	−	11.8205i	−0.173416	−	0.389499i
$922$	1.04440	+	0.940383i	0.0343955	+	0.0309699i
$923$	−3.90559			−0.128554
$924$	15.6950	−	7.03385i	0.516327	−	0.231397i
$925$	−37.5902			−1.23596
$926$	10.6811	+	9.61734i	0.351004	+	0.316046i
$927$	0.300766	+	0.675532i	0.00987846	+	0.0221874i
$928$	−4.54196	−	43.2138i	−0.149097	−	1.41856i
$929$	−0.842850	−	3.96530i	−0.0276530	−	0.130097i	0.962156	−	0.272500i	$-0.0878505\pi$
$929$	−0.842850	−	3.96530i	−0.0276530	−	0.130097i	−0.989809	+	0.142403i	$0.954517\pi$
$930$	5.67392	−	17.4625i	0.186055	−	0.572619i
$931$	11.2292	−	0.0578325i	0.368024	−	0.00189538i
$932$	−20.8105	+	28.6432i	−0.681672	+	0.938241i
$933$	−5.23775	+	5.81711i	−0.171476	+	0.190444i
$934$	−0.823530	+	1.42640i	−0.0269467	+	0.0466731i
$935$	−0.00358302	+	27.1939i	−0.000117177	+	0.889335i
$936$	−4.36181	+	2.51829i	−0.142570	+	0.0823129i
$937$	6.81525	+	20.9752i	0.222644	+	0.685229i	0.998522	+	0.0543457i	$0.0173073\pi$
$937$	6.81525	+	20.9752i	0.222644	+	0.685229i	−0.775878	+	0.630883i	$0.782693\pi$
$938$	−10.4258	−	4.60975i	−0.340416	−	0.150514i
$939$	−24.4728	+	17.7805i	−0.798640	+	0.580246i
$940$	1.91771	−	0.407621i	0.0625487	−	0.0132951i
$941$	10.9567	+	12.1687i	0.357179	+	0.396687i	0.894776	−	0.446514i	$-0.147335\pi$
$941$	10.9567	+	12.1687i	0.357179	+	0.396687i	−0.537598	+	0.843201i	$0.680668\pi$
$942$	9.00612	−	0.946582i	0.293435	−	0.0308413i
$943$	1.67088	−	15.8974i	0.0544113	−	0.517689i
$944$	1.56976	−	0.510047i	0.0510914	−	0.0166006i
$945$	34.2176	−	30.9696i	1.11310	−	1.00744i
$946$	−0.941304	+	8.94457i	−0.0306044	+	0.290813i
$947$	0.0560179	+	0.0970258i	0.00182034	+	0.00315291i	0.866934	−	0.498423i	$-0.166087\pi$
$947$	0.0560179	+	0.0970258i	0.00182034	+	0.00315291i	−0.865114	+	0.501576i	$0.832754\pi$
$948$	−22.6031	−	4.80444i	−0.734115	−	0.156041i
$949$	−16.4031	+	7.30312i	−0.532466	+	0.237069i
$950$	−1.91871	+	4.30950i	−0.0622513	+	0.139819i
$951$	2.76454	+	0.898253i	0.0896463	+	0.0291279i
$952$	10.4492	+	7.55075i	0.338660	+	0.244721i
$953$	−11.3810	−	15.6646i	−0.368666	−	0.507425i	0.583872	−	0.811846i	$-0.301537\pi$
$953$	−11.3810	−	15.6646i	−0.368666	−	0.507425i	−0.952538	+	0.304421i	$0.901537\pi$
$954$	−3.03781	−	0.319287i	−0.0983528	−	0.0103373i
$955$	−2.30810	+	10.8588i	−0.0746885	+	0.351382i
$956$	20.6798	+	11.9395i	0.668832	+	0.386151i
$957$	−3.30833	−	31.5166i	−0.106943	−	1.01879i
$958$		−	20.8278i		−	0.672916i
$959$	0.0621556	+	24.1375i	0.00200711	+	0.779440i
$960$	−6.64254	−	4.82609i	−0.214387	−	0.155761i
$961$	−54.8852	−	24.4365i	−1.77049	−	0.788273i
$962$	3.88923	−	3.50188i	0.125394	−	0.112905i
$963$	−4.60012	+	4.14196i	−0.148237	+	0.133473i
$964$	38.7388	+	17.2476i	1.24769	+	0.555509i
$965$	−24.1384	−	17.5376i	−0.777043	−	0.564555i
$966$	−5.36556	−	3.07941i	−0.172634	−	0.0990784i
$967$		−	46.1717i		−	1.48478i	−0.669967	−	0.742391i	$-0.733692\pi$
$967$		−	46.1717i		−	1.48478i	0.669967	−	0.742391i	$-0.266308\pi$
$968$	−12.5371	−	17.2654i	−0.402959	−	0.554932i
$969$	−3.95506	−	2.28345i	−0.127055	−	0.0733551i
$970$	1.50128	−	7.06299i	0.0482033	−	0.226779i
$971$	−42.8625	−	4.50503i	−1.37552	−	0.144573i	−0.612257	−	0.790659i	$-0.709738\pi$
$971$	−42.8625	−	4.50503i	−1.37552	−	0.144573i	−0.763265	+	0.646085i	$0.776405\pi$
$972$	−15.2503	−	20.9902i	−0.489153	−	0.673261i
$973$	−22.0987	−	2.26514i	−0.708451	−	0.0726172i
$974$	7.13816	+	2.31933i	0.228721	+	0.0743161i
$975$	−3.94423	+	8.85889i	−0.126317	+	0.283712i
$976$	16.7497	−	7.45744i	0.536145	−	0.238707i
$977$	12.2504	+	2.60390i	0.391925	+	0.0833062i	0.399659	−	0.916664i	$-0.369129\pi$
$977$	12.2504	+	2.60390i	0.391925	+	0.0833062i	−0.00773418	+	0.999970i	$0.502462\pi$
$978$	4.14075	+	7.17198i	0.132406	+	0.229335i
$979$	−10.1798	+	22.8561i	−0.325347	+	0.730483i
$980$	16.2581	+	36.0160i	0.519347	+	1.15049i
$981$	19.2332	−	6.24924i	0.614069	−	0.199523i
$982$	−1.42822	+	13.5886i	−0.0455763	+	0.433629i
$983$	26.4588	−	2.78093i	0.843903	−	0.0886978i	0.327298	−	0.944921i	$-0.393862\pi$
$983$	26.4588	−	2.78093i	0.843903	−	0.0886978i	0.516606	+	0.856223i	$0.327195\pi$
$984$	5.92727	+	6.58290i	0.188954	+	0.209855i
$985$	−10.1636	+	2.16033i	−0.323838	+	0.0688339i
$986$	8.91159	−	6.47465i	0.283803	−	0.206195i
$987$	0.421107	−	0.952414i	0.0134040	−	0.0303157i
$988$	1.29754	+	3.99342i	0.0412803	+	0.127048i
$989$	−17.9120	+	10.3415i	−0.569568	+	0.328840i
$990$	−7.81427	−	5.67897i	−0.248354	−	0.180490i
$991$	−5.18947	+	8.98842i	−0.164849	+	0.285527i	−0.936602	−	0.350396i	$-0.886047\pi$
$991$	−5.18947	+	8.98842i	−0.164849	+	0.285527i	0.771753	+	0.635923i	$0.219380\pi$
$992$	32.9116	−	36.5520i	1.04494	−	1.16053i
$993$	−16.9513	+	23.3314i	−0.537933	+	0.740401i
$994$	−3.47542	−	0.729375i	−0.110234	−	0.0231344i
$995$	−2.45351	+	7.55113i	−0.0777815	+	0.239387i
$996$	5.50059	+	25.8782i	0.174293	+	0.819984i
$997$	4.96018	+	47.1930i	0.157091	+	1.49462i	0.734749	+	0.678339i	$0.237300\pi$
$997$	4.96018	+	47.1930i	0.157091	+	1.49462i	−0.577659	+	0.816279i	$0.696033\pi$
$998$	6.95834	+	15.6287i	0.220262	+	0.494718i
$999$	26.4051	+	23.7753i	0.835421	+	0.752216i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.n.a.17.5	✓	48
3.2	odd	2		693.2.cg.a.325.2		48
7.2	even	3		539.2.s.d.215.5		48
7.3	odd	6		539.2.m.a.391.3		48
7.4	even	3		539.2.m.a.391.4		48
7.5	odd	6	inner	77.2.n.a.61.5	yes	48
7.6	odd	2		539.2.s.d.325.5		48
11.2	odd	10	inner	77.2.n.a.24.5	yes	48
11.3	even	5		847.2.i.b.241.15		48
11.4	even	5		847.2.r.a.360.2		48
11.5	even	5		847.2.r.d.766.2		48
11.6	odd	10		847.2.r.a.766.5		48
11.7	odd	10		847.2.r.d.360.5		48
11.8	odd	10		847.2.i.b.241.10		48
11.9	even	5		847.2.r.c.717.2		48
11.10	odd	2		847.2.r.c.94.2		48
21.5	even	6		693.2.cg.a.523.2		48
33.2	even	10		693.2.cg.a.640.2		48
77.2	odd	30		539.2.s.d.68.5		48
77.5	odd	30		847.2.r.d.40.5		48
77.13	even	10		539.2.s.d.178.5		48
77.19	even	30		847.2.i.b.362.15		48
77.24	even	30		539.2.m.a.244.4		48
77.26	odd	30		847.2.r.a.481.5		48
77.40	even	30		847.2.r.d.481.2		48
77.46	odd	30		539.2.m.a.244.3		48
77.47	odd	30		847.2.i.b.362.10		48
77.54	even	6		847.2.r.c.215.2		48
77.61	even	30		847.2.r.a.40.2		48
77.68	even	30	inner	77.2.n.a.68.5	yes	48
77.75	odd	30		847.2.r.c.838.2		48
231.68	odd	30		693.2.cg.a.145.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.n.a.17.5	✓	48	1.1	even	1	trivial
77.2.n.a.24.5	yes	48	11.2	odd	10	inner
77.2.n.a.61.5	yes	48	7.5	odd	6	inner
77.2.n.a.68.5	yes	48	77.68	even	30	inner
539.2.m.a.244.3		48	77.46	odd	30
539.2.m.a.244.4		48	77.24	even	30
539.2.m.a.391.3		48	7.3	odd	6
539.2.m.a.391.4		48	7.4	even	3
539.2.s.d.68.5		48	77.2	odd	30
539.2.s.d.178.5		48	77.13	even	10
539.2.s.d.215.5		48	7.2	even	3
539.2.s.d.325.5		48	7.6	odd	2
693.2.cg.a.145.2		48	231.68	odd	30
693.2.cg.a.325.2		48	3.2	odd	2
693.2.cg.a.523.2		48	21.5	even	6
693.2.cg.a.640.2		48	33.2	even	10
847.2.i.b.241.10		48	11.8	odd	10
847.2.i.b.241.15		48	11.3	even	5
847.2.i.b.362.10		48	77.47	odd	30
847.2.i.b.362.15		48	77.19	even	30
847.2.r.a.40.2		48	77.61	even	30
847.2.r.a.360.2		48	11.4	even	5
847.2.r.a.481.5		48	77.26	odd	30
847.2.r.a.766.5		48	11.6	odd	10
847.2.r.c.94.2		48	11.10	odd	2
847.2.r.c.215.2		48	77.54	even	6
847.2.r.c.717.2		48	11.9	even	5
847.2.r.c.838.2		48	77.75	odd	30
847.2.r.d.40.5		48	77.5	odd	30
847.2.r.d.360.5		48	11.7	odd	10
847.2.r.d.481.2		48	77.40	even	30
847.2.r.d.766.2		48	11.5	even	5

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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.n (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.386517 + 0.348022i) q^{2} +(0.460952 + 1.03532i) q^{3} +(-0.180780 - 1.72001i) q^{4} +(0.678628 + 3.19269i) q^{5} +(-0.182146 + 0.560588i) q^{6} +(-1.97073 - 1.76528i) q^{7} +(1.14015 - 1.56929i) q^{8} +(1.14799 - 1.27497i) q^{9} +O(q^{10})\)	\(q+(0.386517 + 0.348022i) q^{2} +(0.460952 + 1.03532i) q^{3} +(-0.180780 - 1.72001i) q^{4} +(0.678628 + 3.19269i) q^{5} +(-0.182146 + 0.560588i) q^{6} +(-1.97073 - 1.76528i) q^{7} +(1.14015 - 1.56929i) q^{8} +(1.14799 - 1.27497i) q^{9} +(-0.848825 + 1.47021i) q^{10} +(-2.68346 + 1.94911i) q^{11} +(1.69742 - 0.980007i) q^{12} +(-0.467677 - 1.43936i) q^{13} +(-0.147363 - 1.36817i) q^{14} +(-2.99263 + 2.17427i) q^{15} +(-2.39655 + 0.509402i) q^{16} +(-1.68086 - 1.86679i) q^{17} +(0.887437 - 0.0932734i) q^{18} +(0.167684 - 1.59541i) q^{19} +(5.36879 - 1.74442i) q^{20} +(0.919214 - 2.85404i) q^{21} +(-1.71554 - 0.180539i) q^{22} +(-1.98346 - 3.43545i) q^{23} +(2.15026 + 0.457052i) q^{24} +(-5.16504 + 2.29962i) q^{25} +(0.320164 - 0.719100i) q^{26} +(5.08265 + 1.65145i) q^{27} +(-2.68004 + 3.70880i) q^{28} +(4.95563 + 6.82084i) q^{29} +(-1.91340 - 0.201106i) q^{30} +(-1.98422 + 9.33500i) q^{31} +(-4.46333 - 2.57690i) q^{32} +(-3.25489 - 1.87978i) q^{33} -1.30652i q^{34} +(4.29862 - 7.48991i) q^{35} +(-2.40050 - 1.74407i) q^{36} +(6.07381 + 2.70423i) q^{37} +(0.620051 - 0.558296i) q^{38} +(1.27462 - 1.14767i) q^{39} +(5.78399 + 2.57520i) q^{40} +(3.25998 + 2.36851i) q^{41} +(1.34856 - 0.783228i) q^{42} -5.21386i q^{43} +(3.83761 + 4.26322i) q^{44} +(4.84966 + 2.79995i) q^{45} +(0.428971 - 2.01815i) q^{46} +(0.345400 + 0.0363030i) q^{47} +(-1.63209 - 2.24637i) q^{48} +(0.767543 + 6.95779i) q^{49} +(-2.79669 - 0.908701i) q^{50} +(1.15792 - 2.60072i) q^{51} +(-2.39117 + 1.06462i) q^{52} +(-3.34833 - 0.711709i) q^{53} +(1.38979 + 2.40719i) q^{54} +(-8.04399 - 7.24476i) q^{55} +(-5.01717 + 1.07994i) q^{56} +(1.72905 - 0.561802i) q^{57} +(-0.458364 + 4.36104i) q^{58} +(-0.669977 + 0.0704175i) q^{59} +(4.28078 + 4.75429i) q^{60} +(-7.31980 + 1.55587i) q^{61} +(-4.01572 + 2.91759i) q^{62} +(-4.51307 + 0.486096i) q^{63} +(0.685905 + 2.11100i) q^{64} +(4.27807 - 2.46994i) q^{65} +(-0.603866 - 1.85934i) q^{66} +(4.14200 - 7.17416i) q^{67} +(-2.90703 + 3.22858i) q^{68} +(2.64250 - 3.63709i) q^{69} +(4.26814 - 1.39896i) q^{70} +(0.797453 - 2.45431i) q^{71} +(-0.691912 - 3.25519i) q^{72} +(-1.24013 - 11.7990i) q^{73} +(1.40650 + 3.15905i) q^{74} +(-4.76167 - 4.28742i) q^{75} -2.77444 q^{76} +(8.72911 + 0.895908i) q^{77} +0.892075 q^{78} +(-8.76150 - 7.88889i) q^{79} +(-3.25273 - 7.30576i) q^{80} +(0.0950812 + 0.904637i) q^{81} +(0.435744 + 2.05001i) q^{82} +(-4.17113 + 12.8374i) q^{83} +(-5.07515 - 1.06510i) q^{84} +(4.81940 - 6.63334i) q^{85} +(1.81454 - 2.01525i) q^{86} +(-4.77741 + 8.27472i) q^{87} +(-0.000847655 + 6.43340i) q^{88} +(6.53328 - 3.77199i) q^{89} +(0.900033 + 2.77002i) q^{90} +(-1.61922 + 3.66218i) q^{91} +(-5.55045 + 4.03264i) q^{92} +(-10.5793 + 2.24870i) q^{93} +(0.120869 + 0.134238i) q^{94} +(5.20746 - 0.547326i) q^{95} +(0.610527 - 5.80878i) q^{96} +(-4.04522 + 1.31437i) q^{97} +(-2.12479 + 2.95643i) q^{98} +(-0.595529 + 5.65890i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9}+O(q^{10}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9	\( 48 q - 5 q^{2} - 9 q^{3} - 9 q^{4} - 15 q^{5} - 5 q^{7} - 11 q^{9} - q^{11} - 12 q^{12} - 8 q^{14} - 27 q^{16} + 15 q^{17} + 20 q^{18} - 15 q^{19} - 76 q^{22} + 10 q^{23} + 75 q^{24} + q^{25} + 27 q^{26} - 40 q^{28} - 40 q^{29} + 25 q^{30} + 9 q^{31} + 42 q^{33} + 5 q^{35} - 38 q^{36} - q^{37} + 33 q^{38} - 45 q^{39} + 75 q^{40} + 64 q^{42} + 30 q^{44} - 84 q^{45} - 20 q^{46} + 3 q^{47} + 59 q^{49} + 30 q^{50} + 55 q^{51} - 15 q^{52} - 3 q^{53} - 8 q^{56} + 60 q^{57} + 46 q^{58} - 3 q^{59} - 15 q^{60} - 30 q^{61} - 40 q^{63} + 12 q^{64} - 93 q^{66} + 44 q^{67} - 75 q^{68} - 27 q^{70} + 20 q^{71} - 60 q^{72} - 60 q^{73} + 45 q^{74} - 57 q^{75} + 92 q^{78} - 70 q^{79} - 75 q^{80} - 29 q^{81} - 129 q^{82} - 125 q^{84} + 10 q^{85} - 62 q^{86} + 19 q^{88} + 6 q^{89} - 12 q^{91} + 30 q^{92} - 92 q^{93} + 105 q^{94} + 30 q^{95} + 75 q^{96} - 12 q^{99}+O(q^{100}) \) 48 * q - 5 * q^2 - 9 * q^3 - 9 * q^4 - 15 * q^5 - 5 * q^7 - 11 * q^9 - q^11 - 12 * q^12 - 8 * q^14 - 27 * q^16 + 15 * q^17 + 20 * q^18 - 15 * q^19 - 76 * q^22 + 10 * q^23 + 75 * q^24 + q^25 + 27 * q^26 - 40 * q^28 - 40 * q^29 + 25 * q^30 + 9 * q^31 + 42 * q^33 + 5 * q^35 - 38 * q^36 - q^37 + 33 * q^38 - 45 * q^39 + 75 * q^40 + 64 * q^42 + 30 * q^44 - 84 * q^45 - 20 * q^46 + 3 * q^47 + 59 * q^49 + 30 * q^50 + 55 * q^51 - 15 * q^52 - 3 * q^53 - 8 * q^56 + 60 * q^57 + 46 * q^58 - 3 * q^59 - 15 * q^60 - 30 * q^61 - 40 * q^63 + 12 * q^64 - 93 * q^66 + 44 * q^67 - 75 * q^68 - 27 * q^70 + 20 * q^71 - 60 * q^72 - 60 * q^73 + 45 * q^74 - 57 * q^75 + 92 * q^78 - 70 * q^79 - 75 * q^80 - 29 * q^81 - 129 * q^82 - 125 * q^84 + 10 * q^85 - 62 * q^86 + 19 * q^88 + 6 * q^89 - 12 * q^91 + 30 * q^92 - 92 * q^93 + 105 * q^94 + 30 * q^95 + 75 * q^96 - 12 * q^99

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