LMFDB - Embedded newform 288.2.bf.a.11.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(11,288)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(288, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 15, 4]))

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

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

chi := DirichletCharacter("288.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bf (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:	$2.29969157821$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			11.38
Character	$\chi$	$=$	288.11
Dual form			288.2.bf.a.131.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17233 - 0.790981i) q^{2} +(1.73154 + 0.0420726i) q^{3} +(0.748697 - 1.85458i) q^{4} +(-0.0883963 - 0.671437i) q^{5} +(2.06321 - 1.32029i) q^{6} +(-0.0557412 - 0.208029i) q^{7} +(-0.589218 - 2.76637i) q^{8} +(2.99646 + 0.145701i) q^{9} +O(q^{10})$	\(q+(1.17233 - 0.790981i) q^{2} +(1.73154 + 0.0420726i) q^{3} +(0.748697 - 1.85458i) q^{4} +(-0.0883963 - 0.671437i) q^{5} +(2.06321 - 1.32029i) q^{6} +(-0.0557412 - 0.208029i) q^{7} +(-0.589218 - 2.76637i) q^{8} +(2.99646 + 0.145701i) q^{9} +(-0.634723 - 0.717223i) q^{10} +(-4.50341 + 3.45559i) q^{11} +(1.37443 - 3.17977i) q^{12} +(-3.30781 + 4.31082i) q^{13} +(-0.229894 - 0.199788i) q^{14} +(-0.124813 - 1.16634i) q^{15} +(-2.87891 - 2.77703i) q^{16} -0.0148356 q^{17} +(3.62807 - 2.19933i) q^{18} +(3.86908 - 1.60262i) q^{19} +(-1.31141 - 0.338765i) q^{20} +(-0.0877658 - 0.362556i) q^{21} +(-2.54616 + 7.61319i) q^{22} +(0.419209 + 0.112327i) q^{23} +(-0.903866 - 4.81488i) q^{24} +(4.38662 - 1.17539i) q^{25} +(-0.468052 + 7.67011i) q^{26} +(5.18236 + 0.378356i) q^{27} +(-0.427539 - 0.0523744i) q^{28} +(0.271469 + 0.0357395i) q^{29} +(-1.06887 - 1.26860i) q^{30} +(-4.43423 + 2.56010i) q^{31} +(-5.57160 - 0.978425i) q^{32} +(-7.94322 + 5.79402i) q^{33} +(-0.0173922 + 0.0117347i) q^{34} +(-0.134751 + 0.0558157i) q^{35} +(2.51365 - 5.44808i) q^{36} +(1.74098 - 4.20310i) q^{37} +(3.26817 - 4.93916i) q^{38} +(-5.90897 + 7.32519i) q^{39} +(-1.80536 + 0.640160i) q^{40} +(-0.470501 + 1.75593i) q^{41} +(-0.389665 - 0.355612i) q^{42} +(4.11098 + 5.35753i) q^{43} +(3.03696 + 10.9391i) q^{44} +(-0.167047 - 2.02481i) q^{45} +(0.580298 - 0.199903i) q^{46} +(-10.1840 - 5.87973i) q^{47} +(-4.86810 - 4.92966i) q^{48} +(6.02201 - 3.47681i) q^{49} +(4.21283 - 4.84767i) q^{50} +(-0.0256885 - 0.000624174i) q^{51} +(5.51820 + 9.36209i) q^{52} +(-0.483863 + 1.16815i) q^{53} +(6.37469 - 3.65559i) q^{54} +(2.71829 + 2.71829i) q^{55} +(-0.542642 + 0.276775i) q^{56} +(6.76688 - 2.61222i) q^{57} +(0.346519 - 0.172828i) q^{58} +(-8.49106 + 1.11787i) q^{59} +(-2.25651 - 0.641760i) q^{60} +(1.26680 - 9.62227i) q^{61} +(-3.17337 + 6.50867i) q^{62} +(-0.136716 - 0.631472i) q^{63} +(-7.30564 + 3.26000i) q^{64} +(3.18684 + 1.83992i) q^{65} +(-4.72908 + 13.0754i) q^{66} +(-8.50990 + 11.0903i) q^{67} +(-0.0111074 + 0.0275138i) q^{68} +(0.721151 + 0.212135i) q^{69} +(-0.113823 + 0.172020i) q^{70} +(-6.64660 - 6.64660i) q^{71} +(-1.36251 - 8.37518i) q^{72} +(5.76433 - 5.76433i) q^{73} +(-1.28358 - 6.30449i) q^{74} +(7.64505 - 1.85068i) q^{75} +(-0.0754224 - 8.37537i) q^{76} +(0.969888 + 0.744221i) q^{77} +(-1.13315 + 13.2614i) q^{78} +(-1.89962 + 3.29024i) q^{79} +(-1.61012 + 2.17848i) q^{80} +(8.95754 + 0.873174i) q^{81} +(0.837330 + 2.43068i) q^{82} +(-2.39015 - 0.314669i) q^{83} +(-0.738097 - 0.108676i) q^{84} +(0.00131141 + 0.00996118i) q^{85} +(9.05711 + 3.02907i) q^{86} +(0.468555 + 0.0733058i) q^{87} +(12.2129 + 10.4220i) q^{88} +(2.45783 - 2.45783i) q^{89} +(-1.79742 - 2.24161i) q^{90} +(1.08116 + 0.447830i) q^{91} +(0.522179 - 0.693356i) q^{92} +(-7.78576 + 4.24636i) q^{93} +(-16.5897 + 1.16239i) q^{94} +(-1.41807 - 2.45617i) q^{95} +(-9.60628 - 1.92859i) q^{96} +(-4.10794 + 7.11516i) q^{97} +(4.30967 - 8.83925i) q^{98} +(-13.9978 + 9.69838i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	$ 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) $ 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/288\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	1.17233	−	0.790981i	0.828960	−	0.559308i
$2$	1.17233	−	0.790981i	0.828960	−	0.559308i
$3$	1.73154	+	0.0420726i	0.999705	+	0.0242907i
$3$	1.73154	+	0.0420726i	0.999705	+	0.0242907i
$4$	0.748697	−	1.85458i	0.374348	−	0.927288i
$5$	−0.0883963	−	0.671437i	−0.0395320	−	0.300276i	−0.999777	−	0.0211169i	$-0.993278\pi$
$5$	−0.0883963	−	0.671437i	−0.0395320	−	0.300276i	0.960245	−	0.279159i	$-0.0900556\pi$
$6$	2.06321	−	1.32029i	0.842301	−	0.539007i
$7$	−0.0557412	−	0.208029i	−0.0210682	−	0.0786276i	0.954591	−	0.297918i	$-0.0962923\pi$
$7$	−0.0557412	−	0.208029i	−0.0210682	−	0.0786276i	−0.975660	+	0.219291i	$0.929626\pi$
$8$	−0.589218	−	2.76637i	−0.208320	−	0.978061i
$9$	2.99646	+	0.145701i	0.998820	+	0.0485670i
$10$	−0.634723	−	0.717223i	−0.200717	−	0.226806i
$11$	−4.50341	+	3.45559i	−1.35783	+	1.04190i	−0.363950	+	0.931418i	$0.618572\pi$
$11$	−4.50341	+	3.45559i	−1.35783	+	1.04190i	−0.993878	+	0.110480i	$0.964761\pi$
$12$	1.37443	−	3.17977i	0.396762	−	0.917921i
$13$	−3.30781	+	4.31082i	−0.917422	+	1.19561i	0.0628641	+	0.998022i	$0.479977\pi$
$13$	−3.30781	+	4.31082i	−0.917422	+	1.19561i	−0.980286	+	0.197585i	$0.936690\pi$
$14$	−0.229894	−	0.199788i	−0.0614417	−	0.0533955i
$15$	−0.124813	−	1.16634i	−0.0322265	−	0.301147i
$16$	−2.87891	−	2.77703i	−0.719726	−	0.694258i
$17$	−0.0148356			−0.00359817			−0.00179908	−	0.999998i	$-0.500573\pi$
$17$	−0.0148356			−0.00359817			−0.00179908	+	0.999998i	$0.500573\pi$
$18$	3.62807	−	2.19933i	0.855145	−	0.518388i
$19$	3.86908	−	1.60262i	0.887627	−	0.367667i	0.108177	−	0.994132i	$-0.465499\pi$
$19$	3.86908	−	1.60262i	0.887627	−	0.367667i	0.779450	+	0.626465i	$0.215499\pi$
$20$	−1.31141	−	0.338765i	−0.293241	−	0.0757501i
$21$	−0.0877658	−	0.362556i	−0.0191521	−	0.0791161i
$22$	−2.54616	+	7.61319i	−0.542843	+	1.62314i
$23$	0.419209	+	0.112327i	0.0874111	+	0.0234217i	0.302259	−	0.953226i	$-0.402259\pi$
$23$	0.419209	+	0.112327i	0.0874111	+	0.0234217i	−0.214848	+	0.976647i	$0.568926\pi$
$24$	−0.903866	−	4.81488i	−0.184501	−	0.982832i
$25$	4.38662	−	1.17539i	0.877323	−	0.235078i
$26$	−0.468052	+	7.67011i	−0.0917926	+	1.50423i
$27$	5.18236	+	0.378356i	0.997345	+	0.0728146i
$28$	−0.427539	−	0.0523744i	−0.0807973	−	0.00989783i
$29$	0.271469	+	0.0357395i	0.0504105	+	0.00663667i	0.155689	−	0.987806i	$-0.450240\pi$
$29$	0.271469	+	0.0357395i	0.0504105	+	0.00663667i	−0.105279	+	0.994443i	$0.533573\pi$
$30$	−1.06887	−	1.26860i	−0.195149	−	0.231614i
$31$	−4.43423	+	2.56010i	−0.796411	+	0.459808i	−0.842215	−	0.539142i	$-0.818749\pi$
$31$	−4.43423	+	2.56010i	−0.796411	+	0.459808i	0.0458035	+	0.998950i	$0.485415\pi$
$32$	−5.57160	−	0.978425i	−0.984928	−	0.172963i
$33$	−7.94322	+	5.79402i	−1.38274	+	1.00861i
$34$	−0.0173922	+	0.0117347i	−0.00298274	+	0.00201248i
$35$	−0.134751	+	0.0558157i	−0.0227771	+	0.00943457i
$36$	2.51365	−	5.44808i	0.418942	−	0.908013i
$37$	1.74098	−	4.20310i	0.286216	−	0.690985i	−0.713740	−	0.700411i	$-0.753000\pi$
$37$	1.74098	−	4.20310i	0.286216	−	0.690985i	0.999956	+	0.00942527i	$0.00300020\pi$
$38$	3.26817	−	4.93916i	0.530168	−	0.801238i
$39$	−5.90897	+	7.32519i	−0.946193	+	1.17297i
$40$	−1.80536	+	0.640160i	−0.285453	+	0.101218i
$41$	−0.470501	+	1.75593i	−0.0734799	+	0.274231i	−0.992884	−	0.119083i	$-0.962005\pi$
$41$	−0.470501	+	1.75593i	−0.0734799	+	0.274231i	0.919404	+	0.393313i	$0.128671\pi$
$42$	−0.389665	−	0.355612i	−0.0601266	−	0.0548722i
$43$	4.11098	+	5.35753i	0.626918	+	0.817016i	0.993555	−	0.113348i	$-0.0361576\pi$
$43$	4.11098	+	5.35753i	0.626918	+	0.817016i	−0.366637	+	0.930364i	$0.619491\pi$
$44$	3.03696	+	10.9391i	0.457839	+	1.64913i
$45$	−0.167047	−	2.02481i	−0.0249019	−	0.301841i
$46$	0.580298	−	0.199903i	0.0855602	−	0.0294741i
$47$	−10.1840	−	5.87973i	−1.48549	−	0.857647i	−0.485624	−	0.874168i	$-0.661408\pi$
$47$	−10.1840	−	5.87973i	−1.48549	−	0.857647i	−0.999864	+	0.0165209i	$0.994741\pi$
$48$	−4.86810	−	4.92966i	−0.702650	−	0.711536i
$49$	6.02201	−	3.47681i	0.860287	−	0.496687i
$50$	4.21283	−	4.84767i	0.595784	−	0.685564i
$51$	−0.0256885		0.000624174i	−0.00359711		8.74018e-5i
$52$	5.51820	+	9.36209i	0.765237	+	1.29829i
$53$	−0.483863	+	1.16815i	−0.0664638	+	0.160458i	−0.953621	−	0.301009i	$-0.902677\pi$
$53$	−0.483863	+	1.16815i	−0.0664638	+	0.160458i	0.887158	+	0.461467i	$0.152677\pi$
$54$	6.37469	−	3.65559i	0.867485	−	0.497463i
$55$	2.71829	+	2.71829i	0.366535	+	0.366535i
$56$	−0.542642	+	0.276775i	−0.0725136	+	0.0369857i
$57$	6.76688	−	2.61222i	0.896296	−	0.345998i
$58$	0.346519	−	0.172828i	0.0455002	−	0.0226935i
$59$	−8.49106	+	1.11787i	−1.10544	+	0.145534i	−0.661081	−	0.750314i	$-0.729902\pi$
$59$	−8.49106	+	1.11787i	−1.10544	+	0.145534i	−0.444360	+	0.895848i	$0.646569\pi$
$60$	−2.25651	−	0.641760i	−0.291314	−	0.0828508i
$61$	1.26680	−	9.62227i	0.162197	−	1.23201i	−0.695757	−	0.718278i	$-0.744931\pi$
$61$	1.26680	−	9.62227i	0.162197	−	1.23201i	0.857953	−	0.513728i	$-0.171736\pi$
$62$	−3.17337	+	6.50867i	−0.403018	+	0.826602i
$63$	−0.136716	−	0.631472i	−0.0172246	−	0.0795580i
$64$	−7.30564	+	3.26000i	−0.913205	+	0.407499i
$65$	3.18684	+	1.83992i	0.395279	+	0.228215i
$66$	−4.72908	+	13.0754i	−0.582110	+	1.60947i
$67$	−8.50990	+	11.0903i	−1.03965	+	1.35490i	−0.106942	+	0.994265i	$0.534106\pi$
$67$	−8.50990	+	11.0903i	−1.03965	+	1.35490i	−0.932708	+	0.360633i	$0.882561\pi$
$68$	−0.0111074	+	0.0275138i	−0.00134697	+	0.00333654i
$69$	0.721151	+	0.212135i	0.0868163	+	0.0255381i
$70$	−0.113823	+	0.172020i	−0.0136044	+	0.0205603i
$71$	−6.64660	−	6.64660i	−0.788806	−	0.788806i	0.192493	−	0.981298i	$-0.438343\pi$
$71$	−6.64660	−	6.64660i	−0.788806	−	0.788806i	−0.981298	+	0.192493i	$0.938343\pi$
$72$	−1.36251	−	8.37518i	−0.160573	−	0.987024i
$73$	5.76433	−	5.76433i	0.674664	−	0.674664i	−0.284123	−	0.958788i	$-0.591703\pi$
$73$	5.76433	−	5.76433i	0.674664	−	0.674664i	0.958788	+	0.284123i	$0.0917026\pi$
$74$	−1.28358	−	6.30449i	−0.149213	−	0.732882i
$75$	7.64505	−	1.85068i	0.882774	−	0.213698i
$76$	−0.0754224	−	8.37537i	−0.00865154	−	0.960721i
$77$	0.969888	+	0.744221i	0.110529	+	0.0848119i
$78$	−1.13315	+	13.2614i	−0.128304	+	1.50156i
$79$	−1.89962	+	3.29024i	−0.213724	+	0.370181i	−0.952877	−	0.303357i	$-0.901893\pi$
$79$	−1.89962	+	3.29024i	−0.213724	+	0.370181i	0.739153	+	0.673538i	$0.235226\pi$
$80$	−1.61012	+	2.17848i	−0.180016	+	0.243562i
$81$	8.95754	+	0.873174i	0.995282	+	0.0970193i
$82$	0.837330	+	2.43068i	0.0924676	+	0.268424i
$83$	−2.39015	−	0.314669i	−0.262353	−	0.0345394i	−0.00179787	−	0.999998i	$-0.500572\pi$
$83$	−2.39015	−	0.314669i	−0.262353	−	0.0345394i	−0.260555	+	0.965459i	$0.583906\pi$
$84$	−0.738097	−	0.108676i	−0.0805330	−	0.0118575i
$85$	0.00131141	+	0.00996118i	0.000142243	+	0.00108044i
$86$	9.05711	+	3.02907i	0.976653	+	0.326633i
$87$	0.468555	+	0.0733058i	0.0502344	+	0.00785921i
$88$	12.2129	+	10.4220i	1.30190	+	1.11099i
$89$	2.45783	−	2.45783i	0.260529	−	0.260529i	−0.564740	−	0.825269i	$-0.691023\pi$
$89$	2.45783	−	2.45783i	0.260529	−	0.260529i	0.825269	+	0.564740i	$0.191023\pi$
$90$	−1.79742	−	2.24161i	−0.189465	−	0.236286i
$91$	1.08116	+	0.447830i	0.113336	+	0.0469454i
$92$	0.522179	−	0.693356i	0.0544409	−	0.0722873i
$93$	−7.78576	+	4.24636i	−0.807345	+	0.440327i
$94$	−16.5897	+	1.16239i	−1.71110	+	0.119891i
$95$	−1.41807	−	2.45617i	−0.145491	−	0.251998i
$96$	−9.60628	−	1.92859i	−0.980436	−	0.196836i
$97$	−4.10794	+	7.11516i	−0.417098	+	0.722435i	−0.995646	−	0.0932134i	$-0.970286\pi$
$97$	−4.10794	+	7.11516i	−0.417098	+	0.722435i	0.578548	+	0.815648i	$0.303619\pi$
$98$	4.30967	−	8.83925i	0.435342	−	0.892899i
$99$	−13.9978	+	9.69838i	−1.40683	+	0.974723i
$100$	1.10440	−	9.01532i	0.110440	−	0.901532i
$101$	−0.600080	+	0.460457i	−0.0597102	+	0.0458172i	−0.638185	−	0.769883i	$-0.720315\pi$
$101$	−0.600080	+	0.460457i	−0.0597102	+	0.0458172i	0.578475	+	0.815700i	$0.303648\pi$
$102$	−0.0306090	+	0.0195874i	−0.00303074	+	0.00193944i
$103$	17.2779	+	4.62961i	1.70245	+	0.456169i	0.973554	−	0.228459i	$-0.0733685\pi$
$103$	17.2779	+	4.62961i	1.70245	+	0.456169i	0.728893	+	0.684628i	$0.240035\pi$
$104$	13.8744	+	6.61062i	1.36049	+	0.648225i
$105$	−0.235675	+	0.0909778i	−0.0229995	+	0.00887852i
$106$	0.356739	+	1.75218i	0.0346495	+	0.170187i
$107$	7.67127	+	3.17755i	0.741610	+	0.307185i	0.721313	−	0.692609i	$-0.243539\pi$
$107$	7.67127	+	3.17755i	0.741610	+	0.307185i	0.0202969	+	0.999794i	$0.493539\pi$
$108$	4.58171	−	9.32781i	0.440875	−	0.897569i
$109$	3.88254	+	9.37329i	0.371880	+	0.897798i	0.993432	+	0.114425i	$0.0365025\pi$
$109$	3.88254	+	9.37329i	0.371880	+	0.897798i	−0.621552	+	0.783373i	$0.713497\pi$
$110$	5.33684	+	1.03661i	0.508848	+	0.0988366i
$111$	3.19141	−	7.20459i	0.302916	−	0.683829i
$112$	−0.417229	+	0.753691i	−0.0394245	+	0.0712171i
$113$	−9.74325	−	16.8758i	−0.916568	−	1.58754i	−0.804589	−	0.593832i	$-0.797615\pi$
$113$	−9.74325	−	16.8758i	−0.916568	−	1.58754i	−0.111979	−	0.993711i	$-0.535719\pi$
$114$	5.86677	−	8.41486i	0.549474	−	0.788124i
$115$	0.0383637	−	0.291401i	0.00357744	−	0.0271733i
$116$	0.269530	−	0.476701i	0.0250252	−	0.0442606i
$117$	−10.5398	+	12.4353i	−0.974406	+	1.14964i
$118$	−9.07007	+	8.02677i	−0.834968	+	0.738924i
$119$	0.000826956		0.00308624i	7.58069e−5		0.000282915i
$120$	−3.15299	+	1.03251i	−0.287827	+	0.0942545i
$121$	5.49260	−	20.4986i	0.499327	−	1.86351i
$122$	−6.12594	−	12.2825i	−0.554616	−	1.11200i
$123$	−0.888568	+	3.02067i	−0.0801195	+	0.272365i
$124$	1.42801	+	10.1404i	0.128239	+	0.910631i
$125$	−2.47279	−	5.96983i	−0.221173	−	0.533958i
$126$	−0.659759	−	0.632151i	−0.0587760	−	0.0563165i
$127$		−	14.8387i		−	1.31672i	−0.752704	−	0.658359i	$-0.771251\pi$
$127$		−	14.8387i		−	1.31672i	0.752704	−	0.658359i	$-0.228749\pi$
$128$	−5.98600	+	9.60041i	−0.529093	+	0.848564i
$129$	6.89291	+	9.44973i	0.606887	+	0.832003i
$130$	5.19137	−	0.363742i	0.455313	−	0.0319023i
$131$	−4.18185	−	3.20885i	−0.365370	−	0.280358i	0.409717	−	0.912213i	$-0.365627\pi$
$131$	−4.18185	−	3.20885i	−0.365370	−	0.280358i	−0.775087	+	0.631854i	$0.782294\pi$
$132$	4.79838	+	19.0693i	0.417645	+	1.65977i
$133$	−0.549059	−	0.715548i	−0.0476095	−	0.0620459i
$134$	−1.20414	+	19.7326i	−0.104022	+	1.70464i
$135$	−0.204059	−	3.51307i	−0.0175626	−	0.302357i
$136$	0.00874142	+	0.0410409i	0.000749571	+	0.00351923i
$137$	13.3449	−	3.57577i	1.14014	−	0.305498i	0.361130	−	0.932516i	$-0.382391\pi$
$137$	13.3449	−	3.57577i	1.14014	−	0.305498i	0.779005	+	0.627017i	$0.215724\pi$
$138$	1.01322	−	0.321725i	0.0862509	−	0.0273871i
$139$	−1.29513	+	0.170507i	−0.109852	+	0.0144622i	−0.185252	−	0.982691i	$-0.559310\pi$
$139$	−1.29513	+	0.170507i	−0.109852	+	0.0144622i	0.0753999	+	0.997153i	$0.475977\pi$
$140$	0.00262679	+	0.291695i	0.000222004	+	0.0246527i
$141$	−17.3866	−	10.6095i	−1.46422	−	0.893477i
$142$	−13.0493	−	2.53464i	−1.09507	−	0.212703i
$143$		−	30.8438i		−	2.57929i
$144$	−8.22191	−	8.74072i	−0.685159	−	0.728393i
$145$		−	0.185433i		−	0.0153994i
$146$	2.19820	−	11.3172i	0.181924	−	0.936615i
$147$	10.5736	−	5.76687i	0.872098	−	0.475643i
$148$	−6.49150	−	6.37563i	−0.533598	−	0.524074i
$149$	17.1826	−	2.26213i	1.40765	−	0.185321i	0.611896	−	0.790938i	$-0.290407\pi$
$149$	17.1826	−	2.26213i	1.40765	−	0.185321i	0.795756	+	0.605617i	$0.207074\pi$
$150$	7.49864	−	8.21669i	0.612261	−	0.670890i
$151$	−0.547737	+	0.146766i	−0.0445742	+	0.0119436i	−0.281037	−	0.959697i	$-0.590678\pi$
$151$	−0.547737	+	0.146766i	−0.0445742	+	0.0119436i	0.236463	+	0.971640i	$0.424012\pi$
$152$	−6.71318	−	9.75901i	−0.544511	−	0.791560i
$153$	−0.0444543	−	0.00216156i	−0.00359392	−	0.000174752i
$154$	1.72569	+	0.105307i	0.139060	+	0.00848585i
$155$	2.11092	+	2.75100i	0.169553	+	0.220966i
$156$	9.16110	+	16.4430i	0.733475	+	1.31649i
$157$	−9.06471	−	6.95559i	−0.723442	−	0.555117i	0.180083	−	0.983651i	$-0.442363\pi$
$157$	−9.06471	−	6.95559i	−0.723442	−	0.555117i	−0.903525	+	0.428535i	$0.859030\pi$
$158$	0.375543	+	5.35980i	0.0298766	+	0.426403i
$159$	−0.886976	+	2.00234i	−0.0703418	+	0.158796i
$160$	−0.164442	+	3.82746i	−0.0130003	+	0.302588i
$161$		−	0.0934688i		−	0.00736637i
$162$	11.1918	−	6.06160i	0.879313	−	0.476245i
$163$	−8.68977	−	20.9790i	−0.680635	−	1.64320i	−0.762843	−	0.646584i	$-0.776197\pi$
$163$	−8.68977	−	20.9790i	−0.680635	−	1.64320i	0.0822078	−	0.996615i	$-0.473803\pi$
$164$	2.90425	+	2.18724i	0.226784	+	0.170795i
$165$	4.59247	+	4.82120i	0.357523	+	0.375330i
$166$	−3.05093	+	1.52167i	−0.236798	+	0.118104i
$167$	−3.77990	+	14.1068i	−0.292498	+	1.09162i	0.650687	+	0.759346i	$0.274481\pi$
$167$	−3.77990	+	14.1068i	−0.292498	+	1.09162i	−0.943184	+	0.332270i	$0.892186\pi$
$168$	−0.951251	+	0.456417i	−0.0733906	+	0.0352134i
$169$	−4.27693	−	15.9617i	−0.328995	−	1.22783i
$170$	0.00941652	+	0.0106405i	0.000722214	+	0.000816085i
$171$	11.8270	−	4.23847i	0.904436	−	0.324124i
$172$	13.0138	−	3.61295i	0.992295	−	0.275485i
$173$	−2.39785	+	18.2135i	−0.182305	+	1.38475i	0.618482	+	0.785799i	$0.287748\pi$
$173$	−2.39785	+	18.2135i	−0.182305	+	1.38475i	−0.800788	+	0.598948i	$0.795585\pi$
$174$	0.607283	−	0.284680i	0.0460380	−	0.0215815i
$175$	−0.489030	−	0.847026i	−0.0369672	−	0.0640291i
$176$	22.5612	+	2.55780i	1.70061	+	0.192801i
$177$	−14.7496	+	1.57839i	−1.10865	+	0.118639i
$178$	0.937281	−	4.82548i	0.0702521	−	0.361685i
$179$	5.10861	+	12.3333i	0.381836	+	0.921833i	0.991611	+	0.129258i	$0.0412596\pi$
$179$	5.10861	+	12.3333i	0.381836	+	0.921833i	−0.609775	+	0.792574i	$0.708740\pi$
$180$	−3.88024	−	1.20617i	−0.289216	−	0.0899026i
$181$	0.783773	+	0.324649i	0.0582574	+	0.0241310i	0.411622	−	0.911355i	$-0.364962\pi$
$181$	0.783773	+	0.324649i	0.0582574	+	0.0241310i	−0.353364	+	0.935486i	$0.614962\pi$
$182$	1.62169	−	0.330173i	0.120208	−	0.0244740i
$183$	2.59834	−	16.6080i	0.192075	−	1.22770i
$184$	0.0637320	−	1.22587i	0.00469839	−	0.0903725i
$185$	−2.97601	−	0.797420i	−0.218801	−	0.0586275i
$186$	−5.76865	+	11.1365i	−0.422978	+	0.816569i
$187$	0.0668109	−	0.0512658i	0.00488569	−	0.00374892i
$188$	−18.5291	+	14.4849i	−1.35138	+	1.05642i
$189$	−0.210162	−	1.09917i	−0.0152870	−	0.0799529i
$190$	−3.60523	−	1.75777i	−0.261551	−	0.127522i
$191$	−2.87740	+	4.98380i	−0.208201	+	0.360615i	−0.951148	−	0.308736i	$-0.900094\pi$
$191$	−2.87740	+	4.98380i	−0.208201	+	0.360615i	0.742947	+	0.669350i	$0.233428\pi$
$192$	−12.7872	+	5.33744i	−0.922834	+	0.385197i
$193$	−4.13279	−	7.15820i	−0.297485	−	0.515259i	0.678075	−	0.734993i	$-0.262814\pi$
$193$	−4.13279	−	7.15820i	−0.297485	−	0.515259i	−0.975560	+	0.219734i	$0.929481\pi$
$194$	0.812114	+	11.5906i	0.0583064	+	0.832156i
$195$	5.44074	+	3.31998i	0.389619	+	0.237749i
$196$	−1.93935	−	13.7714i	−0.138525	−	0.983668i
$197$	24.2901	+	10.0613i	1.73060	+	0.716838i	0.999399	+	0.0346754i	$0.0110397\pi$
$197$	24.2901	+	10.0613i	1.73060	+	0.716838i	0.731201	+	0.682162i	$0.238960\pi$
$198$	−8.73871	+	22.4416i	−0.621033	+	1.59486i
$199$	0.714900	−	0.714900i	0.0506779	−	0.0506779i	−0.681314	−	0.731992i	$-0.738591\pi$
$199$	0.714900	−	0.714900i	0.0506779	−	0.0506779i	0.731992	+	0.681314i	$0.238591\pi$
$200$	−5.83624	−	11.4425i	−0.412685	−	0.809104i
$201$	−15.2018	+	18.8453i	−1.07225	+	1.32924i
$202$	−0.339276	+	1.01446i	−0.0238714	+	0.0713770i
$203$	−0.00769713	−	0.0584655i	−0.000540233	−	0.00410348i
$204$	−0.0203905	+	0.0471739i	−0.00142762	+	0.00330283i
$205$	1.22059	+	0.160694i	0.0852496	+	0.0112233i
$206$	23.9173	−	8.23912i	1.66640	−	0.574047i
$207$	1.23978	+	0.397661i	0.0861704	+	0.0276394i
$208$	21.4942	−	3.22456i	1.49035	−	0.223583i
$209$	−11.8860	+	20.5872i	−0.822173	+	1.42405i
$210$	−0.204326	+	0.293070i	−0.0140999	+	0.0202238i
$211$	0.458068	+	0.351488i	0.0315347	+	0.0241974i	0.624409	−	0.781098i	$-0.285340\pi$
$211$	0.458068	+	0.351488i	0.0315347	+	0.0241974i	−0.592874	+	0.805295i	$0.702007\pi$
$212$	1.80416	+	1.77195i	0.123910	+	0.121698i
$213$	−11.2292	−	11.7885i	−0.769413	−	0.807734i
$214$	11.5066	−	2.34271i	0.786576	−	0.160145i
$215$	3.23385	−	3.23385i	0.220547	−	0.220547i
$216$	−2.00687	−	14.5593i	−0.136550	−	0.990633i
$217$	0.779745	+	0.779745i	0.0529326	+	0.0529326i
$218$	11.9657	+	7.91753i	0.810419	+	0.536243i
$219$	10.2237	−	9.73865i	0.690853	−	0.658077i
$220$	7.07646	−	3.00610i	0.477095	−	0.202671i
$221$	0.0490734	−	0.0639537i	0.00330104	−	0.00430199i
$222$	−1.95732	−	10.9705i	−0.131367	−	0.736290i
$223$	13.9104	+	8.03118i	0.931510	+	0.537807i	0.887289	−	0.461214i	$-0.152586\pi$
$223$	13.9104	+	8.03118i	0.931510	+	0.537807i	0.0442211	+	0.999022i	$0.485919\pi$
$224$	0.107027	+	1.21359i	0.00715102	+	0.0810865i
$225$	13.3156	−	2.88288i	0.887705	−	0.192192i
$226$	−24.7707	−	12.0772i	−1.64772	−	0.803365i
$227$	0.289351	−	2.19784i	0.0192049	−	0.145876i	−0.979156	−	0.203110i	$-0.934895\pi$
$227$	0.289351	−	2.19784i	0.0192049	−	0.145876i	0.998361	+	0.0572347i	$0.0182283\pi$
$228$	0.221777	−	14.5055i	0.0146876	−	0.960648i
$229$	−17.4568	+	2.29823i	−1.15358	+	0.151871i	−0.682953	−	0.730462i	$-0.739305\pi$
$229$	−17.4568	+	2.29823i	−1.15358	+	0.151871i	−0.470625	+	0.882334i	$0.655971\pi$
$230$	−0.185518	−	0.371962i	−0.0122327	−	0.0245265i
$231$	1.64809	+	1.32945i	0.108436	+	0.0874716i
$232$	−0.0610854	−	0.772042i	−0.00401045	−	0.0506871i
$233$	−0.891379	−	0.891379i	−0.0583962	−	0.0583962i	0.677306	−	0.735702i	$-0.263147\pi$
$233$	−0.891379	−	0.891379i	−0.0583962	−	0.0583962i	−0.735702	+	0.677306i	$0.763147\pi$
$234$	−2.52004	+	22.9150i	−0.164740	+	1.49800i
$235$	−3.04764	+	7.35765i	−0.198806	+	0.479960i
$236$	−4.28406	+	16.5843i	−0.278868	+	1.07954i
$237$	−3.42770	+	5.61726i	−0.222653	+	0.364880i
$238$	0.00341062	+	0.00296397i	0.000221078	+	0.000192126i
$239$	14.3675	−	8.29506i	0.929354	−	0.536563i	0.0427467	−	0.999086i	$-0.486389\pi$
$239$	14.3675	−	8.29506i	0.929354	−	0.536563i	0.886607	+	0.462523i	$0.153056\pi$
$240$	−2.87963	+	3.70439i	−0.185880	+	0.239117i
$241$	6.98248	+	4.03134i	0.449781	+	0.259681i	0.707738	−	0.706475i	$-0.249716\pi$
$241$	6.98248	+	4.03134i	0.449781	+	0.259681i	−0.257957	+	0.966156i	$0.583049\pi$
$242$	−9.77493	−	28.3756i	−0.628357	−	1.82406i
$243$	15.4736	+	1.88880i	0.992632	+	0.121167i
$244$	−16.8968	−	9.55354i	−1.08171	−	0.611602i
$245$	−2.86678	−	3.73606i	−0.183152	−	0.238688i
$246$	1.34760	+	4.24405i	0.0859201	+	0.270591i
$247$	−5.88954	+	21.9801i	−0.374743	+	1.39856i
$248$	9.69493	+	10.7583i	0.615629	+	0.683151i
$249$	−4.12540	−	0.645422i	−0.261437	−	0.0409020i
$250$	−7.62094	−	5.04266i	−0.481990	−	0.318926i
$251$	2.85834	−	6.90064i	0.180417	−	0.435565i	−0.807636	−	0.589682i	$-0.799253\pi$
$251$	2.85834	−	6.90064i	0.180417	−	0.435565i	0.988053	+	0.154117i	$0.0492533\pi$
$252$	−1.27347	−	0.219231i	−0.0802212	−	0.0138102i
$253$	−2.27602	+	0.942759i	−0.143092	+	0.0592708i
$254$	−11.7371	−	17.3957i	−0.736451	−	1.09151i
$255$	0.00185167	+	0.0173034i	0.000115956	+	0.00108358i
$256$	0.576196	+	15.9896i	0.0360123	+	0.999351i
$257$	−6.91963	+	3.99505i	−0.431635	+	0.249204i	−0.700043	−	0.714101i	$-0.746836\pi$
$257$	−6.91963	+	3.99505i	−0.431635	+	0.249204i	0.268408	+	0.963305i	$0.413502\pi$
$258$	15.5553	+	5.62600i	0.968431	+	0.350260i
$259$	−0.971411	−	0.127889i	−0.0603606	−	0.00794662i
$260$	5.79826	−	4.53270i	0.359593	−	0.281106i
$261$	0.808238	+	0.146645i	0.0500287	+	0.00907712i
$262$	−7.44064	−	0.454049i	−0.459684	−	0.0280513i
$263$	25.6114	−	6.86256i	1.57927	−	0.423164i	0.640569	−	0.767900i	$-0.278698\pi$
$263$	25.6114	−	6.86256i	1.57927	−	0.423164i	0.938700	+	0.344736i	$0.112032\pi$
$264$	20.7087	+	18.5600i	1.27453	+	1.14229i
$265$	0.827111	+	0.221624i	0.0508090	+	0.0136142i
$266$	−1.20966	−	0.404560i	−0.0741691	−	0.0248052i
$267$	4.35924	−	4.15242i	0.266781	−	0.254124i
$268$	14.1965	+	24.0855i	0.867189	+	1.47126i
$269$	−15.4360	+	6.39378i	−0.941147	+	0.389836i	−0.799896	−	0.600138i	$-0.795112\pi$
$269$	−15.4360	+	6.39378i	−0.941147	+	0.389836i	−0.141250	+	0.989974i	$0.545112\pi$
$270$	−3.01800	−	3.95706i	−0.183670	−	0.240819i
$271$	6.40082			0.388822			0.194411	−	0.980920i	$-0.437720\pi$
$271$	6.40082			0.388822			0.194411	+	0.980920i	$0.437720\pi$
$272$	0.0427104	+	0.0411990i	0.00258970	+	0.00249806i
$273$	1.85323	+	0.820923i	0.112162	+	0.0496845i
$274$	12.8163	−	14.7476i	0.774258	−	0.890933i
$275$	−15.6931	+	20.4516i	−0.946327	+	1.23328i
$276$	0.933344	−	1.17860i	0.0561807	−	0.0709436i
$277$	−23.0844	+	17.7133i	−1.38701	+	1.06429i	−0.397844	+	0.917453i	$0.630242\pi$
$277$	−23.0844	+	17.7133i	−1.38701	+	1.06429i	−0.989161	+	0.146834i	$0.953092\pi$
$278$	−1.38345	+	1.22431i	−0.0829737	+	0.0734295i
$279$	−13.6600	+	7.02518i	−0.817803	+	0.420586i
$280$	0.233805	+	0.339884i	0.0139725	+	0.0203120i
$281$	4.13455	+	15.4304i	0.246647	+	0.920498i	0.972549	+	0.232700i	$0.0747560\pi$
$281$	4.13455	+	15.4304i	0.246647	+	0.920498i	−0.725902	+	0.687798i	$0.758577\pi$
$282$	−28.7747	+	1.31474i	−1.71351	+	0.0782919i
$283$	−1.03921	−	7.89357i	−0.0617745	−	0.469224i	−0.994173	−	0.107793i	$-0.965622\pi$
$283$	−1.03921	−	7.89357i	−0.0617745	−	0.469224i	0.932399	−	0.361431i	$-0.117712\pi$
$284$	−17.3029	+	7.35033i	−1.02674	+	0.436162i
$285$	−2.35211	−	4.31262i	−0.139327	−	0.255458i
$286$	−24.3969	−	36.1590i	−1.44262	−	2.13813i
$287$	0.391511			0.0231102
$288$	−16.5525	−	3.74360i	−0.975366	−	0.220594i
$289$	−16.9998			−0.999987
$290$	−0.146674	−	0.217388i	−0.00861301	−	0.0127655i
$291$	−7.41241	+	12.1473i	−0.434523	+	0.712090i
$292$	−6.37466	−	15.0061i	−0.373049	−	0.878168i
$293$	3.42320	+	26.0018i	0.199985	+	1.51904i	0.737247	+	0.675624i	$0.236126\pi$
$293$	3.42320	+	26.0018i	0.199985	+	1.51904i	−0.537261	+	0.843416i	$0.680541\pi$
$294$	7.83425	−	15.1242i	0.456903	−	0.882061i
$295$	1.50116	+	5.60239i	0.0874007	+	0.326184i
$296$	−12.6532	−	2.33966i	−0.735450	−	0.135990i
$297$	−24.6457	+	16.2042i	−1.43009	+	0.940263i
$298$	18.3543	−	16.2431i	1.06324	−	0.940936i
$299$	−1.87088	+	1.43558i	−0.108196	+	0.0830217i
$300$	2.29160	−	15.5639i	0.132306	−	0.898584i
$301$	0.885371	−	1.15384i	0.0510319	−	0.0665061i
$302$	−0.526037	+	0.605307i	−0.0302700	+	0.0348315i
$303$	−1.05843	+	0.772053i	−0.0608055	+	0.0443533i
$304$	−15.5892	−	6.13074i	−0.894104	−	0.351622i
$305$	−6.57273			−0.376353
$306$	−0.0538247	+	0.0326285i	−0.00307696	+	0.00186525i
$307$	−19.3223	+	8.00354i	−1.10278	+	0.456786i	−0.858445	−	0.512905i	$-0.828569\pi$
$307$	−19.3223	+	8.00354i	−1.10278	+	0.456786i	−0.244334	+	0.969691i	$0.578569\pi$
$308$	2.10637	−	1.24153i	0.120021	−	0.0707430i
$309$	29.7227	+	8.74329i	1.69086	+	0.497388i
$310$	4.65068	+	1.55537i	0.264141	+	0.0883393i
$311$	−24.2485	−	6.49736i	−1.37500	−	0.368431i	−0.505701	−	0.862709i	$-0.668766\pi$
$311$	−24.2485	−	6.49736i	−1.37500	−	0.368431i	−0.869304	+	0.494277i	$0.835433\pi$
$312$	23.7459	+	12.0303i	1.34435	+	0.681081i
$313$	11.2697	−	3.01970i	0.636999	−	0.170683i	0.0741554	−	0.997247i	$-0.476374\pi$
$313$	11.2697	−	3.01970i	0.636999	−	0.170683i	0.562844	+	0.826563i	$0.309707\pi$
$314$	−16.1285	−	0.984210i	−0.910186	−	0.0555422i
$315$	−0.411908	+	0.147616i	−0.0232084	+	0.00831723i
$316$	4.67976	+	5.98639i	0.263257	+	0.336761i
$317$	15.6526	+	2.06070i	0.879135	+	0.115740i	0.556564	−	0.830805i	$-0.312119\pi$
$317$	15.6526	+	2.06070i	0.879135	+	0.115740i	0.322571	+	0.946545i	$0.395453\pi$
$318$	0.543989	+	3.04898i	0.0305054	+	0.170978i
$319$	−1.34604	+	0.777134i	−0.0753635	+	0.0435112i
$320$	2.83467	+	4.61711i	0.158463	+	0.258104i
$321$	13.1494	+	5.82480i	0.733930	+	0.325108i
$322$	−0.0739321	−	0.109576i	−0.00412007	−	0.00610643i
$323$	−0.0574001	+	0.0237759i	−0.00319383	+	0.00132293i
$324$	8.32585	−	15.9587i	0.462547	−	0.886595i
$325$	−9.44320	+	22.7979i	−0.523814	+	1.26460i
$326$	−26.7812	−	17.7207i	−1.48327	−	0.981461i
$327$	6.32842	+	16.3936i	0.349962	+	0.906566i
$328$	5.13479	+	0.266953i	0.283522	+	0.0147400i
$329$	−0.655486	+	2.44631i	−0.0361381	+	0.134869i
$330$	9.19735	+	2.01946i	0.506297	+	0.111168i
$331$	9.17055	+	11.9513i	0.504059	+	0.656903i	0.974199	−	0.225689i	$-0.0724633\pi$
$331$	9.17055	+	11.9513i	0.504059	+	0.656903i	−0.470140	+	0.882592i	$0.655797\pi$
$332$	−2.37308	+	4.19712i	−0.130240	+	0.230347i
$333$	5.82918	−	12.3408i	0.319437	−	0.676269i
$334$	6.72693	+	19.5276i	0.368081	+	1.06850i
$335$	8.19869	+	4.73352i	0.447942	+	0.258620i
$336$	−0.754159	+	1.28749i	−0.0411427	+	0.0702384i
$337$	8.56862	−	4.94710i	0.466763	−	0.269485i	−0.248121	−	0.968729i	$-0.579813\pi$
$337$	8.56862	−	4.94710i	0.466763	−	0.269485i	0.714883	+	0.699244i	$0.246480\pi$
$338$	−17.6394	−	15.3294i	−0.959457	−	0.833809i
$339$	−16.1608	−	29.6311i	−0.877735	−	1.60934i
$340$	0.0194556	+	0.00502579i	0.00105513	+	0.000272562i
$341$	11.1225	−	26.8521i	0.602316	−	1.45412i
$342$	10.5126	−	14.3238i	0.568456	−	0.774544i
$343$	−2.12497	−	2.12497i	−0.114737	−	0.114737i
$344$	12.3987	−	14.5293i	0.668491	−	0.783365i
$345$	0.0786883	−	0.502959i	0.00423644	−	0.0270784i
$346$	11.5955	+	23.2488i	0.623377	+	1.24986i
$347$	3.76455	−	0.495613i	0.202092	−	0.0266059i	−0.0288006	−	0.999585i	$-0.509169\pi$
$347$	3.76455	−	0.495613i	0.202092	−	0.0266059i	0.230892	+	0.972979i	$0.425835\pi$
$348$	0.486757	−	0.814088i	0.0260929	−	0.0436397i
$349$	0.609483	−	4.62949i	0.0326249	−	0.247811i	−0.967359	−	0.253408i	$-0.918448\pi$
$349$	0.609483	−	4.62949i	0.0326249	−	0.247811i	0.999984	+	0.00559751i	$0.00178175\pi$
$350$	−1.24328	−	0.606176i	−0.0664564	−	0.0324015i
$351$	−18.7733	+	21.0887i	−1.00204	+	1.12563i
$352$	28.4722	−	14.8469i	1.51757	−	0.791342i
$353$	10.8753	+	6.27887i	0.578835	+	0.334191i	0.760670	−	0.649138i	$-0.224870\pi$
$353$	10.8753	+	6.27887i	0.578835	+	0.334191i	−0.181835	+	0.983329i	$0.558204\pi$
$354$	−16.0429	+	13.5171i	−0.852671	+	0.718425i
$355$	−3.87523	+	5.05030i	−0.205676	+	0.268042i
$356$	−2.71806	−	6.39840i	−0.144057	−	0.339115i
$357$	0.00130206	+	0.00537874i	6.89123e−5	+	0.000284673i
$358$	15.7444	+	10.4178i	0.832115	+	0.550598i
$359$	9.17704	+	9.17704i	0.484346	+	0.484346i	0.906516	−	0.422171i	$-0.138732\pi$
$359$	9.17704	+	9.17704i	0.484346	+	0.484346i	−0.422171	+	0.906516i	$0.638732\pi$
$360$	−5.50296	+	1.65517i	−0.290032	+	0.0872352i
$361$	−1.03369	+	1.03369i	−0.0544046	+	0.0544046i
$362$	1.17563	−	0.239355i	0.0617897	−	0.0125802i
$363$	10.3731	−	35.2631i	0.544446	−	1.85083i
$364$	1.63999	−	1.66980i	0.0859591	−	0.0875213i
$365$	−4.37993	−	3.36084i	−0.229256	−	0.175914i
$366$	−10.0906	−	21.5253i	−0.527442	−	1.12514i
$367$	−13.9731	+	24.2020i	−0.729387	+	1.26334i	0.227755	+	0.973718i	$0.426861\pi$
$367$	−13.9731	+	24.2020i	−0.729387	+	1.26334i	−0.957142	+	0.289618i	$0.906472\pi$
$368$	−0.894928	−	1.48753i	−0.0466513	−	0.0775430i
$369$	−1.66568	+	5.19303i	−0.0867117	+	0.270338i
$370$	−4.11960	+	1.41913i	−0.214168	+	0.0737773i
$371$	0.269980	+	0.0355436i	0.0140167	+	0.00184533i
$372$	2.04603	+	17.6185i	0.106082	+	0.913478i
$373$	0.404073	+	3.06924i	0.0209221	+	0.158919i	0.998717	−	0.0506467i	$-0.0161283\pi$
$373$	0.404073	+	3.06924i	0.0209221	+	0.158919i	−0.977795	+	0.209566i	$0.932795\pi$
$374$	0.0377738	−	0.112946i	0.00195324	−	0.00584032i
$375$	−4.03056	−	10.4410i	−0.208137	−	0.539173i
$376$	−10.2649	+	31.6372i	−0.529374	+	1.63156i
$377$	−1.05203	+	1.05203i	−0.0541825	+	0.0541825i
$378$	−1.11580	−	1.12235i	−0.0573907	−	0.0577276i
$379$	−1.15861	−	0.479912i	−0.0595138	−	0.0246514i	0.352728	−	0.935726i	$-0.385254\pi$
$379$	−1.15861	−	0.479912i	−0.0595138	−	0.0246514i	−0.412242	+	0.911074i	$0.635254\pi$
$380$	−5.61687	+	0.790994i	−0.288139	+	0.0405771i
$381$	0.624302	−	25.6937i	0.0319839	−	1.31633i
$382$	0.568843	+	8.11860i	0.0291046	+	0.415384i
$383$	−9.06305	−	15.6977i	−0.463100	−	0.802113i	0.536013	−	0.844210i	$-0.319930\pi$
$383$	−9.06305	−	15.6977i	−0.463100	−	0.802113i	−0.999114	+	0.0420964i	$0.986596\pi$
$384$	−10.7689	+	16.3716i	−0.549549	+	0.835462i
$385$	0.413963	−	0.717005i	0.0210975	−	0.0365419i
$386$	−10.5070	−	5.12279i	−0.534791	−	0.260743i
$387$	11.5378	+	16.6526i	0.586498	+	0.846499i
$388$	10.1200	+	12.9456i	0.513765	+	0.657212i
$389$	21.8498	−	16.7660i	1.10783	−	0.850068i	0.118098	−	0.993002i	$-0.462320\pi$
$389$	21.8498	−	16.7660i	1.10783	−	0.850068i	0.989732	+	0.142934i	$0.0456536\pi$
$390$	9.00436	−	0.411419i	0.455954	−	0.0208330i
$391$	−0.00621922	−	0.00166644i	−0.000314520	−	8.42753e-5i
$392$	−13.1664	−	14.6105i	−0.665005	−	0.737943i
$393$	−7.10604	−	5.73219i	−0.358452	−	0.289151i
$394$	36.4342	−	7.41791i	1.83553	−	0.373709i
$395$	2.37711	+	0.984631i	0.119605	+	0.0495421i
$396$	7.50629	+	33.2211i	0.377205	+	1.66942i
$397$	8.77052	+	21.1739i	0.440180	+	1.06269i	0.975885	+	0.218283i	$0.0700457\pi$
$397$	8.77052	+	21.1739i	0.440180	+	1.06269i	−0.535705	+	0.844405i	$0.679954\pi$
$398$	0.272623	−	1.40357i	0.0136654	−	0.0703545i
$399$	−0.920613	−	1.26210i	−0.0460883	−	0.0631840i
$400$	−15.8927	−	8.79793i	−0.794637	−	0.439897i
$401$	−8.33898	−	14.4435i	−0.416429	−	0.721275i	0.579149	−	0.815222i	$-0.303385\pi$
$401$	−8.33898	−	14.4435i	−0.416429	−	0.721275i	−0.995577	+	0.0939465i	$0.970052\pi$
$402$	−2.91523	+	34.1172i	−0.145398	+	1.70161i
$403$	3.63144	−	27.5835i	0.180895	−	1.37403i
$404$	0.404675	+	1.45764i	0.0201334	+	0.0725201i
$405$	−0.205533	−	6.09161i	−0.0102130	−	0.302694i
$406$	−0.0552687	−	0.0624524i	−0.00274294	−	0.00309946i
$407$	6.68383	+	24.9444i	0.331305	+	1.23645i
$408$	0.0134094	+	0.0714317i	0.000663865	+	0.00353639i
$409$	1.84560	−	6.88786i	0.0912589	−	0.340583i	−0.905167	−	0.425056i	$-0.860254\pi$
$409$	1.84560	−	6.88786i	0.0912589	−	0.340583i	0.996426	+	0.0844737i	$0.0269209\pi$
$410$	1.55803	−	0.777078i	0.0769458	−	0.0383771i
$411$	23.2577	−	5.63012i	1.14722	−	0.277713i
$412$	21.5219	−	28.5771i	1.06031	−	1.40789i
$413$	0.705851	+	1.70407i	0.0347327	+	0.0838520i
$414$	1.76796	−	0.514451i	0.0868907	−	0.0252839i
$415$			1.63265i			0.0801437i
$416$	22.6476	−	20.7817i	1.11039	−	1.01891i
$417$	−2.24974	+	0.240750i	−0.110170	+	0.0117896i
$418$	2.34979	+	33.5365i	0.114932	+	1.64033i
$419$	5.67603	+	4.35537i	0.277292	+	0.212774i	0.738039	−	0.674758i	$-0.235752\pi$
$419$	5.67603	+	4.35537i	0.277292	+	0.212774i	−0.460747	+	0.887531i	$0.652419\pi$
$420$	−0.00772400	+	0.505192i	−0.000376892	+	0.0246509i
$421$	−13.1087	−	17.0836i	−0.638878	−	0.832602i	0.355915	−	0.934518i	$-0.384169\pi$
$421$	−13.1087	−	17.0836i	−0.638878	−	0.832602i	−0.994793	+	0.101916i	$0.967503\pi$
$422$	0.815026	+	0.0497353i	0.0396748	+	0.00242107i
$423$	−29.6592	−	19.1022i	−1.44208	−	0.928780i
$424$	3.51664	+	0.650252i	0.170783	+	0.0315790i
$425$	−0.0650782	+	0.0174376i	−0.00315676	+	0.000845850i
$426$	−22.4888	−	4.93786i	−1.08958	−	0.239240i
$427$	−2.07232	+	0.272827i	−0.100287	+	0.0132030i
$428$	11.6365	−	11.8479i	0.562470	−	0.572692i
$429$	1.29768	−	53.4073i	0.0626526	−	2.57853i
$430$	1.23321	−	6.34904i	0.0594707	−	0.306178i
$431$		−	16.5026i		−	0.794901i	−0.917624	−	0.397451i	$-0.869895\pi$
$431$		−	16.5026i		−	0.794901i	0.917624	−	0.397451i	$-0.130105\pi$
$432$	−13.8688	−	15.4808i	−0.667264	−	0.744821i
$433$			30.5881i			1.46997i	0.678084	+	0.734985i	$0.262811\pi$
$433$			30.5881i			1.46997i	−0.678084	+	0.734985i	$0.737189\pi$
$434$	1.53088	+	0.297352i	0.0734846	+	0.0142733i
$435$	0.00780167	−	0.321085i	0.000374062	−	0.0153949i
$436$	20.2903	−	0.182720i	0.971730	−	0.00875068i
$437$	1.80197	−	0.237233i	0.0861998	−	0.0113484i
$438$	4.28241	−	19.5036i	0.204622	−	0.931919i
$439$	14.2147	−	3.80882i	0.678431	−	0.181785i	0.0968811	−	0.995296i	$-0.469113\pi$
$439$	14.2147	−	3.80882i	0.678431	−	0.181785i	0.581549	+	0.813511i	$0.302447\pi$
$440$	5.91815	−	9.12148i	0.282136	−	0.434850i
$441$	18.5513	−	9.54070i	0.883394	−	0.454319i
$442$	0.00694385	−	0.113791i	0.000330285	−	0.00541248i
$443$	−5.95453	−	7.76010i	−0.282908	−	0.368693i	0.630184	−	0.776446i	$-0.282979\pi$
$443$	−5.95453	−	7.76010i	−0.282908	−	0.368693i	−0.913093	+	0.407752i	$0.866313\pi$
$444$	−10.9721	−	11.3128i	−0.520711	−	0.536880i
$445$	−1.86754	−	1.43301i	−0.0885299	−	0.0679314i
$446$	22.6600	−	1.58771i	1.07298	−	0.0751804i
$447$	29.8475	−	3.19405i	1.41174	−	0.151074i
$448$	1.08540	+	1.33807i	0.0512803	+	0.0632179i
$449$		−	2.78748i		−	0.131549i	−0.997835	−	0.0657747i	$-0.979048\pi$
$449$		−	2.78748i		−	0.131549i	0.997835	−	0.0657747i	$-0.0209519\pi$
$450$	13.3299	−	13.9120i	0.628377	−	0.655820i
$451$	−3.94892	−	9.53354i	−0.185947	−	0.448917i
$452$	−38.5922	+	5.43474i	−1.81522	+	0.255629i
$453$	−0.954603	+	0.231086i	−0.0448512	+	0.0108574i
$454$	−1.39924	−	2.80545i	−0.0656694	−	0.131666i
$455$	0.205119	−	0.765516i	0.00961614	−	0.0358879i
$456$	−11.2136	−	17.1806i	−0.525123	−	0.804553i
$457$	1.60232	+	5.97994i	0.0749534	+	0.279730i	0.993223	−	0.116226i	$-0.0370798\pi$
$457$	1.60232	+	5.97994i	0.0749534	+	0.279730i	−0.918269	+	0.395956i	$0.870413\pi$
$458$	−18.6472	+	16.5023i	−0.871326	+	0.771101i
$459$	−0.0768835	−	0.00561315i	−0.00358862	−	0.000261999i
$460$	−0.511703	−	0.289320i	−0.0238583	−	0.0134896i
$461$	4.18625	−	31.7978i	0.194973	−	1.48097i	−0.561790	−	0.827280i	$-0.689887\pi$
$461$	4.18625	−	31.7978i	0.194973	−	1.48097i	0.756763	−	0.653689i	$-0.226780\pi$
$462$	2.98367	+	0.254947i	0.138813	+	0.0118612i
$463$	11.9666	+	20.7268i	0.556137	+	0.963257i	0.997814	+	0.0660830i	$0.0210502\pi$
$463$	11.9666	+	20.7268i	0.556137	+	0.963257i	−0.441677	+	0.897174i	$0.645616\pi$
$464$	−0.682283	−	0.856768i	−0.0316742	−	0.0397745i
$465$	3.53940	+	4.85228i	0.164136	+	0.225019i
$466$	−1.75005	−	0.339923i	−0.0810696	−	0.0157466i
$467$	11.5307	+	27.8376i	0.533578	+	1.28817i	0.929139	+	0.369731i	$0.120550\pi$
$467$	11.5307	+	27.8376i	0.533578	+	1.28817i	−0.395561	+	0.918440i	$0.629450\pi$
$468$	15.1710	+	28.8571i	0.701280	+	1.33392i
$469$	2.78146	+	1.15212i	0.128436	+	0.0531999i
$470$	2.24694	+	11.0362i	0.103644	+	0.509062i
$471$	−15.4033	−	12.4253i	−0.709745	−	0.572526i
$472$	8.09553	+	22.8308i	0.372627	+	1.05087i
$473$	−37.0268	−	9.92130i	−1.70249	−	0.456182i
$474$	0.424767	+	9.29651i	0.0195102	+	0.427003i
$475$	15.0884	−	11.5778i	0.692305	−	0.531224i
$476$	0.00634281		0.000777006i	0.000290722		3.56140e-5i
$477$	−1.62008	+	3.42981i	−0.0741783	+	0.157040i
$478$	10.2821	−	21.0889i	0.470293	−	0.964584i
$479$	−0.187642	+	0.325005i	−0.00857356	+	0.0148498i	−0.870280	−	0.492557i	$-0.836062\pi$
$479$	−0.187642	+	0.325005i	−0.00857356	+	0.0148498i	0.861707	+	0.507407i	$0.169396\pi$
$480$	−0.445770	+	6.62049i	−0.0203465	+	0.302183i
$481$	12.3600	+	21.4081i	0.563567	+	0.976126i
$482$	11.3745	−	0.796970i	0.518092	−	0.0363010i
$483$	0.00393248	−	0.161845i	0.000178934	−	0.00736420i
$484$	−33.9040	−	25.5337i	−1.54109	−	1.16062i
$485$	5.14051	+	2.12927i	0.233418	+	0.0966850i
$486$	19.6341	−	10.0250i	0.890622	−	0.454745i
$487$	23.4958	−	23.4958i	1.06470	−	1.06470i	0.0669402	−	0.997757i	$-0.478676\pi$
$487$	23.4958	−	23.4958i	1.06470	−	1.06470i	0.997757	−	0.0669402i	$-0.0213237\pi$
$488$	−27.3652	+	2.16519i	−1.23877	+	0.0980134i
$489$	−14.1640	−	36.6915i	−0.640520	−	1.65925i
$490$	−6.31596	−	2.11231i	−0.285326	−	0.0954245i
$491$	−3.56902	−	27.1094i	−0.161068	−	1.22343i	−0.860769	−	0.508996i	$-0.830017\pi$
$491$	−3.56902	−	27.1094i	−0.161068	−	1.22343i	0.699701	−	0.714436i	$-0.253316\pi$
$492$	4.93680	+	3.90949i	0.222568	+	0.176253i
$493$	−0.00402741		0.000530218i	−0.000181385		2.38798e-5i
$494$	10.4814	+	30.4263i	0.471579	+	1.36895i
$495$	7.74920	+	8.54131i	0.348300	+	0.383903i
$496$	19.8752	+	4.94370i	0.892424	+	0.221979i
$497$	−1.01220	+	1.75317i	−0.0454032	+	0.0786406i
$498$	−5.34683	+	2.50647i	−0.239597	+	0.112318i
$499$	−23.1493	−	17.7631i	−1.03631	−	0.795185i	−0.0571640	−	0.998365i	$-0.518206\pi$
$499$	−23.1493	−	17.7631i	−1.03631	−	0.795185i	−0.979141	+	0.203180i	$0.934872\pi$
$500$	−12.9229	+	0.116374i	−0.577929	+	0.00520439i
$501$	−7.13856	+	24.2674i	−0.318927	+	1.08419i
$502$	−2.10737	−	10.3507i	−0.0940567	−	0.461974i
$503$	−25.8068	+	25.8068i	−1.15067	+	1.15067i	−0.164251	+	0.986419i	$0.552521\pi$
$503$	−25.8068	+	25.8068i	−1.15067	+	1.15067i	−0.986419	+	0.164251i	$0.947479\pi$
$504$	−1.66633	+	0.750283i	−0.0742243	+	0.0334203i
$505$	0.362213	+	0.362213i	0.0161183	+	0.0161183i
$506$	−1.92254	+	2.90551i	−0.0854671	+	0.129166i
$507$	−6.73413	−	27.8183i	−0.299073	−	1.23546i
$508$	−27.5194	−	11.1097i	−1.22098	−	0.492911i
$509$	−3.53290	+	4.60417i	−0.156593	+	0.204076i	−0.865061	−	0.501667i	$-0.832720\pi$
$509$	−3.53290	+	4.60417i	−0.156593	+	0.204076i	0.708468	+	0.705743i	$0.249387\pi$
$510$	0.0158574	+	0.0188205i	0.000702177	+	0.000833388i
$511$	−1.52046	−	0.877838i	−0.0672612	−	0.0388333i
$512$	13.3230	+	18.2893i	0.588798	+	0.808280i
$513$	20.6573	−	6.84148i	0.912042	−	0.302059i
$514$	−4.95205	+	10.1568i	−0.218426	+	0.447997i
$515$	1.58118	−	12.0103i	0.0696753	−	0.529237i
$516$	22.6860	−	5.70845i	0.998694	−	0.251300i
$517$	66.1806	−	8.71284i	2.91062	−	0.383190i
$518$	−1.23997	+	0.618441i	−0.0544811	+	0.0271727i
$519$	−4.91827	+	31.4365i	−0.215888	+	1.37991i
$520$	3.21217	−	9.90012i	0.140863	−	0.434149i
$521$	20.3324	+	20.3324i	0.890777	+	0.890777i	0.994596	−	0.103819i	$-0.0331064\pi$
$521$	20.3324	+	20.3324i	0.890777	+	0.890777i	−0.103819	+	0.994596i	$0.533106\pi$
$522$	1.06351	−	0.467385i	0.0465487	−	0.0204569i
$523$	−14.0229	+	33.8544i	−0.613181	+	1.48035i	0.246307	+	0.969192i	$0.420783\pi$
$523$	−14.0229	+	33.8544i	−0.613181	+	1.48035i	−0.859487	+	0.511157i	$0.829217\pi$
$524$	−9.08200	+	5.35311i	−0.396749	+	0.233852i
$525$	−0.811139	−	1.48723i	−0.0354010	−	0.0649082i
$526$	24.5968	−	28.3033i	1.07247	−	1.23408i
$527$	0.0657846	−	0.0379807i	0.00286562	−	0.00165447i
$528$	38.9579	+	5.37813i	1.69543	+	0.234053i
$529$	−19.7555	−	11.4058i	−0.858933	−	0.495905i
$530$	1.14494	−	0.394414i	0.0497332	−	0.0171322i
$531$	−25.6060	+	2.11249i	−1.11121	+	0.0916744i
$532$	−1.73812	+	0.482544i	−0.0753569	+	0.0209209i
$533$	−6.01319	−	7.83654i	−0.260460	−	0.339438i
$534$	1.82596	−	8.31607i	0.0790170	−	0.359872i
$535$	1.45541	−	5.43166i	0.0629228	−	0.234831i
$536$	35.6941	+	17.0069i	1.54175	+	0.734588i
$537$	8.32687	+	21.5705i	0.359331	+	0.930836i
$538$	−13.0386	+	19.7051i	−0.562134	+	0.849549i
$539$	−15.1052	+	36.4671i	−0.650625	+	1.57075i
$540$	−6.66804	−	2.25178i	−0.286947	−	0.0969013i
$541$	27.4696	−	11.3783i	1.18101	−	0.489191i	0.296193	−	0.955128i	$-0.404283\pi$
$541$	27.4696	−	11.3783i	1.18101	−	0.489191i	0.884818	+	0.465937i	$0.154283\pi$
$542$	7.50385	−	5.06293i	0.322318	−	0.217472i
$543$	1.34348	+	0.595119i	0.0576540	+	0.0255390i
$544$	0.0826581	+	0.0145155i	0.00354394	+	0.000622349i
$545$	5.95037	−	3.43545i	0.254886	−	0.147158i
$546$	2.82192	−	0.503478i	0.120767	−	0.0215469i
$547$	−13.0199	−	1.71410i	−0.556689	−	0.0732895i	−0.153068	−	0.988216i	$-0.548915\pi$
$547$	−13.0199	−	1.71410i	−0.556689	−	0.0732895i	−0.403621	+	0.914926i	$0.632249\pi$
$548$	3.35979	−	27.4264i	0.143523	−	1.17160i
$549$	5.19788	−	28.6482i	0.221840	−	1.22267i
$550$	−2.22055	+	36.3889i	−0.0946847	+	1.55163i
$551$	1.10761	−	0.296783i	0.0471858	−	0.0126434i
$552$	0.161930	−	2.11997i	0.00689221	−	0.0902317i
$553$	0.790353	+	0.211774i	0.0336092	+	0.00900556i
$554$	−13.0516	+	39.0250i	−0.554507	+	1.65801i
$555$	−5.11953	−	1.50597i	−0.217312	−	0.0639250i
$556$	−0.653442	+	2.52958i	−0.0277121	+	0.107278i
$557$	−7.13067	+	2.95362i	−0.302136	+	0.125149i	−0.528601	−	0.848870i	$-0.677283\pi$
$557$	−7.13067	+	2.95362i	−0.302136	+	0.125149i	0.226465	+	0.974019i	$0.427283\pi$
$558$	−10.4572	+	19.0406i	−0.442688	+	0.806053i
$559$	−36.6937			−1.55198
$560$	0.542937	+	0.213520i	0.0229433	+	0.00902285i
$561$	0.117843	−	0.0859578i	0.00497532	−	0.00362914i
$562$	17.0522	+	14.8191i	0.719303	+	0.625104i
$563$	22.3260	−	29.0958i	0.940929	−	1.22624i	−0.0330156	−	0.999455i	$-0.510511\pi$
$563$	22.3260	−	29.0958i	0.940929	−	1.22624i	0.973944	−	0.226787i	$-0.0728222\pi$
$564$	−32.6933	+	24.3015i	−1.37664	+	1.02328i
$565$	−10.4698	+	8.03374i	−0.440467	+	0.337982i
$566$	−7.46195	−	8.43184i	−0.313649	−	0.354417i
$567$	−0.317659	−	1.91210i	−0.0133404	−	0.0803007i
$568$	−14.4707	+	22.3033i	−0.607176	+	0.935824i
$569$	−0.708785	−	2.64522i	−0.0297138	−	0.110893i	0.949476	−	0.313839i	$-0.101615\pi$
$569$	−0.708785	−	2.64522i	−0.0297138	−	0.110893i	−0.979190	+	0.202946i	$0.934949\pi$
$570$	−6.16865	−	3.19533i	−0.258376	−	0.133837i
$571$	−4.98129	−	37.8367i	−0.208461	−	1.58342i	−0.701023	−	0.713139i	$-0.747273\pi$
$571$	−4.98129	−	37.8367i	−0.208461	−	1.58342i	0.492562	−	0.870277i	$-0.336060\pi$
$572$	−57.2022	−	23.0927i	−2.39174	−	0.965553i
$573$	−5.19201	+	8.50858i	−0.216899	+	0.355451i
$574$	0.458979	−	0.309678i	0.0191574	−	0.0129257i
$575$	1.97094			0.0821937
$576$	−22.3661	+	8.70401i	−0.931919	+	0.362667i
$577$	−33.6046			−1.39898			−0.699489	−	0.714643i	$-0.746589\pi$
$577$	−33.6046			−1.39898			−0.699489	+	0.714643i	$0.746589\pi$
$578$	−19.9293	+	13.4465i	−0.828949	+	0.559301i
$579$	−6.85493	−	12.5686i	−0.284881	−	0.522333i
$580$	−0.343900	−	0.138833i	−0.0142797	−	0.00576474i
$581$	0.0677695	+	0.514761i	0.00281155	+	0.0213559i
$582$	0.918561	+	20.1037i	0.0380756	+	0.833326i
$583$	−1.85761	−	6.93269i	−0.0769343	−	0.287123i
$584$	−19.3428	−	12.5498i	−0.800409	−	0.519316i
$585$	9.28117	+	5.97759i	0.383729	+	0.247143i
$586$	24.5800	+	27.7749i	1.01539	+	1.14737i
$587$	−31.6921	+	24.3182i	−1.30807	+	1.00372i	−0.309470	+	0.950909i	$0.600152\pi$
$587$	−31.6921	+	24.3182i	−1.30807	+	1.00372i	−0.998605	+	0.0528114i	$0.983182\pi$
$588$	−2.77866	−	23.9272i	−0.114590	−	0.986742i
$589$	−13.0535	+	17.0116i	−0.537860	+	0.700952i
$590$	6.19123	+	5.38044i	0.254889	+	0.221509i
$591$	41.6360	+	18.4435i	1.71268	+	0.758664i
$592$	−16.6843	+	7.26557i	−0.685719	+	0.298613i
$593$	−33.6668			−1.38253			−0.691265	−	0.722601i	$-0.742946\pi$
$593$	−33.6668			−1.38253			−0.691265	+	0.722601i	$0.742946\pi$
$594$	−16.0756	+	38.4909i	−0.659590	+	1.57930i
$595$	0.00199912		0.000828061i	8.19557e−5		3.39472e-5i
$596$	8.66926	−	33.5601i	0.355107	−	1.37467i
$597$	1.26796	−	1.20780i	0.0518940	−	0.0494320i
$598$	−1.05777	+	3.16280i	−0.0432554	+	0.129337i
$599$	25.5424	+	6.84407i	1.04363	+	0.279641i	0.739619	−	0.673026i	$-0.235006\pi$
$599$	25.5424	+	6.84407i	1.04363	+	0.279641i	0.304016	+	0.952667i	$0.401672\pi$
$600$	−9.62427	−	20.0586i	−0.392909	−	0.818889i
$601$	−43.5605	+	11.6720i	−1.77687	+	0.476111i	−0.990007	−	0.141018i	$-0.954962\pi$
$601$	−43.5605	+	11.6720i	−1.77687	+	0.476111i	−0.786862	+	0.617129i	$0.788296\pi$
$602$	0.125279	−	2.05299i	0.00510600	−	0.0836734i
$603$	−27.1154	+	31.9918i	−1.10423	+	1.30281i
$604$	−0.137901	+	1.12570i	−0.00561111	+	0.0458042i
$605$	−14.2491	−	1.87593i	−0.579307	−	0.0762672i
$606$	−0.630151	+	1.74230i	−0.0255981	+	0.0707761i
$607$	−22.1830	+	12.8074i	−0.900380	+	0.519835i	−0.877323	−	0.479899i	$-0.840673\pi$
$607$	−22.1830	+	12.8074i	−0.900380	+	0.519835i	−0.0230566	+	0.999734i	$0.507340\pi$
$608$	−23.1250	+	5.14357i	−0.937842	+	0.208599i
$609$	−0.0108681	−	0.101559i	−0.000440397	−	0.00411539i
$610$	−7.70538	+	5.19890i	−0.311982	+	0.210497i
$611$	59.0332	−	24.4523i	2.38823	−	0.989236i
$612$	−0.0372916	+	0.0808256i	−0.00150742	+	0.00326718i
$613$	−0.393125	+	0.949089i	−0.0158782	+	0.0383333i	−0.931620	−	0.363434i	$-0.881604\pi$
$613$	−0.393125	+	0.949089i	−0.0158782	+	0.0383333i	0.915742	+	0.401768i	$0.131604\pi$
$614$	−16.3213	+	24.6663i	−0.658675	+	0.995451i
$615$	2.10674	+	0.329601i	0.0849518	+	0.0132908i
$616$	1.48732	−	3.12158i	0.0599257	−	0.125772i
$617$	−1.95430	+	7.29355i	−0.0786772	+	0.293627i	−0.994042	−	0.108998i	$-0.965236\pi$
$617$	−1.95430	+	7.29355i	−0.0786772	+	0.293627i	0.915365	+	0.402626i	$0.131902\pi$
$618$	41.7604	−	13.2601i	1.67985	−	0.533399i
$619$	2.98955	+	3.89606i	0.120160	+	0.156596i	0.849560	−	0.527492i	$-0.176867\pi$
$619$	2.98955	+	3.89606i	0.120160	+	0.156596i	−0.729400	+	0.684087i	$0.760201\pi$
$620$	6.68238	−	1.85519i	0.268371	−	0.0745063i
$621$	2.12999	+	0.740727i	0.0854736	+	0.0297244i
$622$	−33.5664	+	11.5631i	−1.34589	+	0.463637i
$623$	−0.648302	−	0.374298i	−0.0259737	−	0.0149959i
$624$	37.3537	−	4.67914i	1.49534	−	0.187315i
$625$	15.8749	−	9.16537i	0.634995	−	0.366615i
$626$	10.8232	−	12.4542i	0.432582	−	0.497769i
$627$	−21.4473	+	35.1475i	−0.856522	+	1.40365i
$628$	−19.6864	+	11.6036i	−0.785573	+	0.463032i
$629$	−0.0258285	+	0.0623556i	−0.00102985	+	0.00248628i
$630$	−0.366129	+	0.498866i	−0.0145869	+	0.0198753i
$631$	23.6010	+	23.6010i	0.939541	+	0.939541i	0.998274	−	0.0587323i	$-0.0187058\pi$
$631$	23.6010	+	23.6010i	0.939541	+	0.939541i	−0.0587323	+	0.998274i	$0.518706\pi$
$632$	10.2213	+	3.31639i	0.406583	+	0.131919i
$633$	0.778375	+	0.627888i	0.0309376	+	0.0249563i
$634$	19.9799	−	9.96507i	0.793502	−	0.395763i
$635$	−9.96322	+	1.31168i	−0.395378	+	0.0520526i
$636$	3.04942	+	3.14411i	0.120917	+	0.124672i
$637$	−4.93176	+	37.4604i	−0.195403	+	1.48424i
$638$	−0.963294	+	1.97574i	−0.0381372	+	0.0782204i
$639$	−18.9478	−	20.8847i	−0.749565	−	0.826185i
$640$	6.97521	+	3.17058i	0.275719	+	0.125328i
$641$	−28.2977	−	16.3377i	−1.11769	−	0.645300i	−0.176882	−	0.984232i	$-0.556601\pi$
$641$	−28.2977	−	16.3377i	−1.11769	−	0.645300i	−0.940811	+	0.338932i	$0.889934\pi$
$642$	20.0227	−	3.57239i	0.790234	−	0.140991i
$643$	−8.11552	+	10.5764i	−0.320045	+	0.417091i	−0.925476	−	0.378807i	$-0.876334\pi$
$643$	−8.11552	+	10.5764i	−0.320045	+	0.417091i	0.605431	+	0.795898i	$0.293001\pi$
$644$	−0.173345	−	0.0699798i	−0.00683075	−	0.00275759i
$645$	5.73559	−	5.46348i	0.225839	−	0.215124i
$646$	−0.0484854	+	0.0732756i	−0.00190763	+	0.00288299i
$647$	−11.4323	−	11.4323i	−0.449448	−	0.449448i	0.445723	−	0.895171i	$-0.352947\pi$
$647$	−11.4323	−	11.4323i	−0.449448	−	0.449448i	−0.895171	+	0.445723i	$0.852947\pi$
$648$	−2.86242	−	25.2944i	−0.112447	−	0.993658i
$649$	34.3758	−	34.3758i	1.34937	−	1.34937i
$650$	6.96220	+	34.1960i	0.273080	+	1.34128i
$651$	1.31735	+	1.38297i	0.0516312	+	0.0542027i
$652$	−45.4131	+	0.408956i	−1.77851	+	0.0160160i
$653$	32.7578	+	25.1359i	1.28191	+	0.983645i	0.999705	+	0.0242915i	$0.00773300\pi$
$653$	32.7578	+	25.1359i	1.28191	+	0.983645i	0.282207	+	0.959354i	$0.408934\pi$
$654$	20.3860	+	14.2129i	0.797155	+	0.555770i
$655$	−1.78488	+	3.09150i	−0.0697410	+	0.120795i
$656$	6.23081	−	3.74857i	0.243272	−	0.146357i
$657$	18.1125	−	16.4327i	0.706635	−	0.641102i
$658$	1.16654	+	3.38635i	0.0454765	+	0.132014i
$659$	−0.227175	−	0.0299082i	−0.00884949	−	0.00116506i	0.126100	−	0.992018i	$-0.459754\pi$
$659$	−0.227175	−	0.0299082i	−0.00884949	−	0.00116506i	−0.134950	+	0.990852i	$0.543087\pi$
$660$	12.3796	−	4.90746i	0.481877	−	0.191023i
$661$	−5.06243	−	38.4530i	−0.196906	−	1.49565i	−0.749392	−	0.662126i	$-0.769654\pi$
$661$	−5.06243	−	38.4530i	−0.196906	−	1.49565i	0.552486	−	0.833522i	$-0.313679\pi$
$662$	20.2041	+	6.75708i	0.785256	+	0.262621i
$663$	0.0876633	−	0.108674i	0.00340456	−	0.00422054i
$664$	0.537827	+	6.79746i	0.0208718	+	0.263793i
$665$	−0.431910	+	0.431910i	−0.0167488	+	0.0167488i
$666$	−2.92762	−	19.0782i	−0.113443	−	0.739264i
$667$	0.109788	+	0.0454755i	0.00425099	+	0.00176082i
$668$	23.3321	+	17.5718i	0.902746	+	0.679874i
$669$	23.7485	+	14.4916i	0.918171	+	0.560276i
$670$	13.3557	−	0.935787i	0.515974	−	0.0361526i
$671$	27.5457	+	47.7105i	1.06339	+	1.84184i
$672$	0.134262	+	2.10589i	0.00517926	+	0.0812363i
$673$	−2.41000	+	4.17424i	−0.0928986	+	0.160905i	−0.908730	−	0.417385i	$-0.862947\pi$
$673$	−2.41000	+	4.17424i	−0.0928986	+	0.160905i	0.815831	+	0.578290i	$0.196280\pi$
$674$	6.13216	−	12.5772i	0.236202	−	0.484457i
$675$	23.1777	−	4.43159i	0.892111	−	0.170572i
$676$	−32.8044	−	4.01860i	−1.26171	−	0.154562i
$677$	−7.79586	+	5.98197i	−0.299619	+	0.229906i	−0.747619	−	0.664128i	$-0.768803\pi$
$677$	−7.79586	+	5.98197i	−0.299619	+	0.229906i	0.448000	+	0.894034i	$0.352136\pi$
$678$	−42.3834	−	21.9544i	−1.62772	−	0.843152i
$679$	1.70914	+	0.457963i	0.0655908	+	0.0175750i
$680$	0.0267836	−	0.00949717i	0.00102711	−	0.000364200i
$681$	0.593491	−	3.79347i	0.0227426	−	0.145366i
$682$	−8.20030	−	40.2771i	−0.314006	−	1.54229i
$683$	−22.2635	−	9.22185i	−0.851890	−	0.352864i	−0.0863595	−	0.996264i	$-0.527523\pi$
$683$	−22.2635	−	9.22185i	−0.851890	−	0.352864i	−0.765530	+	0.643400i	$0.777523\pi$
$684$	0.994300	−	25.1075i	0.0380180	−	0.960008i
$685$	−3.58054	−	8.64420i	−0.136806	−	0.330278i
$686$	−4.17196	−	0.810344i	−0.159286	−	0.0309391i
$687$	−30.3238	+	3.24502i	−1.15693	+	0.123805i
$688$	3.04291	−	26.8401i	0.116010	−	1.02327i
$689$	−3.43516	−	5.94987i	−0.130869	−	0.226672i
$690$	−0.305583	−	0.651873i	−0.0116333	−	0.0248164i
$691$	4.05827	−	30.8256i	0.154384	−	1.17266i	−0.722295	−	0.691585i	$-0.756913\pi$
$691$	4.05827	−	30.8256i	0.154384	−	1.17266i	0.876679	−	0.481076i	$-0.159754\pi$
$692$	31.9831	+	18.0834i	1.21581	+	0.687428i
$693$	2.79780	+	2.37134i	0.106279	+	0.0900798i
$694$	4.02126	−	3.55871i	0.152645	−	0.135087i
$695$	0.228970	+	0.854527i	0.00868532	+	0.0324140i
$696$	−0.0732900	−	1.33939i	−0.00277805	−	0.0507695i
$697$	0.00698017	−	0.0260504i	0.000264393	−	0.000986728i
$698$	−2.94732	−	5.90936i	−0.111558	−	0.223672i
$699$	−1.50596	−	1.58096i	−0.0569605	−	0.0597974i
$700$	−1.93701	+	0.272779i	−0.0732121	+	0.0103101i
$701$	17.9882	+	43.4273i	0.679404	+	1.64023i	0.765104	+	0.643906i	$0.222687\pi$
$701$	17.9882	+	43.4273i	0.679404	+	1.64023i	−0.0856997	+	0.996321i	$0.527313\pi$
$702$	−5.32765	+	39.5722i	−0.201079	+	1.49355i
$703$		−	19.0522i		−	0.718569i
$704$	21.6351	−	39.9264i	0.815403	−	1.50478i
$705$	−5.58667	+	12.6118i	−0.210406	+	0.474990i
$706$	17.7159	−	1.24129i	0.666747	−	0.0467167i
$707$	0.129238	+	0.0991675i	0.00486048	+	0.00372958i
$708$	−8.11576	+	28.5361i	−0.305009	+	1.07245i
$709$	−25.0771	−	32.6811i	−0.941791	−	1.22737i	−0.973691	−	0.227874i	$-0.926822\pi$
$709$	−25.0771	−	32.6811i	−0.941791	−	1.22737i	0.0319000	−	0.999491i	$-0.489844\pi$
$710$	−0.548342	+	8.98584i	−0.0205789	+	0.337233i
$711$	−6.17153	+	9.58230i	−0.231450	+	0.359364i
$712$	−8.24747	−	5.35108i	−0.309087	−	0.200540i
$713$	−2.14644	+	0.575136i	−0.0803847	+	0.0215390i
$714$	0.00578092	+	0.00527573i	0.000216346	+	0.000197439i
$715$	−20.7097	+	2.72648i	−0.774498	+	0.101965i
$716$	26.6978	−	0.240421i	0.997744	−	0.00898494i
$717$	25.2268	−	13.7587i	0.942113	−	0.513830i
$718$	18.0174	+	3.49962i	0.672402	+	0.130605i
$719$		−	17.9058i		−	0.667773i	−0.942613	−	0.333886i	$-0.891640\pi$
$719$		−	17.9058i		−	0.667773i	0.942613	−	0.333886i	$-0.108360\pi$
$720$	−5.14206	+	6.29314i	−0.191633	+	0.234531i
$721$		−	3.85237i		−	0.143470i
$722$	−0.394191	+	2.02944i	−0.0146703	+	0.0755281i
$723$	11.9208	+	7.27419i	0.443341	+	0.270530i
$724$	1.18890	−	1.21050i	0.0441850	−	0.0449880i
$725$	1.23284	−	0.162306i	0.0457864	−	0.00602790i
$726$	−15.7318	−	49.5448i	−0.583864	−	1.83878i
$727$	39.6198	−	10.6161i	1.46942	−	0.393729i	0.566686	−	0.823934i	$-0.308225\pi$
$727$	39.6198	−	10.6161i	1.46942	−	0.393729i	0.902732	+	0.430204i	$0.141558\pi$
$728$	0.601828	−	3.25476i	0.0223052	−	0.120629i
$729$	26.7137	+	3.92155i	0.989396	+	0.145243i
$730$	−7.79307	−	0.475556i	−0.288434	−	0.0176011i
$731$	−0.0609889	−	0.0794823i	−0.00225576	−	0.00293976i
$732$	−28.8555	−	17.2532i	−1.06653	−	0.637697i
$733$	18.3166	+	14.0548i	0.676539	+	0.519126i	0.888921	−	0.458060i	$-0.151456\pi$
$733$	18.3166	+	14.0548i	0.676539	+	0.519126i	−0.212383	+	0.977187i	$0.568122\pi$
$734$	2.76239	+	39.4251i	0.101962	+	1.45521i
$735$	−4.80676	−	6.58975i	−0.177300	−	0.243067i
$736$	−2.22576	−	1.03600i	−0.0820425	−	0.0381876i
$737$		−	79.3509i		−	2.92293i
$738$	2.15487	+	7.40545i	0.0793220	+	0.272598i
$739$	−8.19677	−	19.7888i	−0.301523	−	0.727941i	−0.999925	−	0.0122357i	$-0.996105\pi$
$739$	−8.19677	−	19.7888i	−0.301523	−	0.727941i	0.698402	−	0.715706i	$-0.253895\pi$
$740$	−3.70701	+	4.92222i	−0.136272	+	0.180944i
$741$	−11.1227	+	37.8116i	−0.408604	+	1.38904i
$742$	0.344619	−	0.171881i	0.0126514	−	0.00630994i
$743$	2.76434	−	10.3167i	0.101414	−	0.378482i	−0.896500	−	0.443044i	$-0.853899\pi$
$743$	2.76434	−	10.3167i	0.101414	−	0.378482i	0.997914	+	0.0645625i	$0.0205652\pi$
$744$	16.3345	+	19.0363i	0.598853	+	0.697904i
$745$	−3.03776	−	11.3371i	−0.111295	−	0.415358i
$746$	2.90142	+	3.27853i	0.106228	+	0.120036i
$747$	−7.11614	−	1.29114i	−0.260366	−	0.0472404i
$748$	−0.0450552	−	0.162288i	−0.00164738	−	0.00593385i
$749$	0.233416	−	1.77297i	0.00852882	−	0.0647828i
$750$	−12.9838	−	9.05220i	−0.474101	−	0.330540i
$751$	−0.984092	−	1.70450i	−0.0359100	−	0.0621980i	0.847512	−	0.530777i	$-0.178100\pi$
$751$	−0.984092	−	1.70450i	−0.0359100	−	0.0621980i	−0.883422	+	0.468579i	$0.844766\pi$
$752$	12.9906	+	45.2084i	0.473717	+	1.64858i
$753$	5.23966	−	11.8285i	0.190944	−	0.431054i
$754$	−0.401188	+	2.06547i	−0.0146104	+	0.0752199i
$755$	0.146962	+	0.354797i	0.00534849	+	0.0129124i
$756$	−2.19584	−	0.433185i	−0.0798621	−	0.0157548i
$757$	−4.06977	−	1.68576i	−0.147918	−	0.0612698i	0.307496	−	0.951549i	$-0.400509\pi$
$757$	−4.06977	−	1.68576i	−0.147918	−	0.0612698i	−0.455414	+	0.890280i	$0.650509\pi$
$758$	−1.73787	+	0.353825i	−0.0631222	+	0.0128515i
$759$	−3.98069	+	1.53667i	−0.144490	+	0.0557775i
$760$	−5.95914	+	5.37014i	−0.216161	+	0.194795i
$761$	−4.44416	−	1.19081i	−0.161101	−	0.0431668i	0.177367	−	0.984145i	$-0.443242\pi$
$761$	−4.44416	−	1.19081i	−0.161101	−	0.0431668i	−0.338468	+	0.940978i	$0.609909\pi$
$762$	−19.5914	−	30.6152i	−0.709721	−	1.10907i
$763$	1.73350	−	1.33016i	0.0627568	−	0.0481550i
$764$	7.08853	+	9.06770i	0.256454	+	0.328058i
$765$	0.00247825	+	0.0300394i	8.96012e−5	+	0.00108608i
$766$	−23.0414	−	11.2341i	−0.832520	−	0.405904i
$767$	23.2679	−	40.3011i	0.840154	−	1.45519i
$768$	0.324981	+	27.7109i	0.0117267	+	0.999931i
$769$	8.62649	+	14.9415i	0.311079	+	0.538805i	0.978596	−	0.205789i	$-0.0659762\pi$
$769$	8.62649	+	14.9415i	0.311079	+	0.538805i	−0.667517	+	0.744595i	$0.732643\pi$
$770$	−0.0818379	−	1.16800i	−0.00294923	−	0.0420918i
$771$	−12.1497	+	6.62646i	−0.437561	+	0.238646i
$772$	−16.3696	+	2.30525i	−0.589156	+	0.0829678i
$773$	−17.1447	−	7.10157i	−0.616652	−	0.255426i	0.0524178	−	0.998625i	$-0.483307\pi$
$773$	−17.1447	−	7.10157i	−0.616652	−	0.255426i	−0.669070	+	0.743200i	$0.733307\pi$
$774$	26.6979	+	10.3961i	0.959637	+	0.373680i
$775$	−16.4421	+	16.4421i	−0.590619	+	0.590619i
$776$	22.1037	+	7.17171i	0.793475	+	0.257449i
$777$	−1.67666	−	0.262314i	−0.0601497	−	0.00941047i
$778$	12.3536	−	36.9380i	0.442897	−	1.32429i
$779$	0.993696	+	7.54787i	0.0356029	+	0.270431i
$780$	10.2306	−	7.60460i	0.366315	−	0.272288i
$781$	52.9002	+	6.96445i	1.89292	+	0.249207i
$782$	−0.00860908	+	0.00296568i	−0.000307860	+	0.000106053i
$783$	1.39333	+	0.287927i	0.0497934	+	0.0102897i
$784$	−26.9920	−	6.71390i	−0.964000	−	0.239782i
$785$	−3.86895	+	6.70123i	−0.138089	+	0.239177i
$786$	−12.8647	−	1.09925i	−0.458867	−	0.0392090i
$787$	21.2521	+	16.3073i	0.757554	+	0.581292i	0.913675	−	0.406446i	$-0.133232\pi$
$787$	21.2521	+	16.3073i	0.757554	+	0.581292i	−0.156121	+	0.987738i	$0.549899\pi$
$788$	36.8454	−	37.5150i	1.31256	−	1.33642i
$789$	44.6359	−	10.8053i	1.58908	−	0.384677i
$790$	3.56557	−	0.725940i	0.126857	−	0.0258278i
$791$	−2.96756	+	2.96756i	−0.105514	+	0.105514i
$792$	35.0771	+	33.0086i	1.24641	+	1.17291i
$793$	37.2896	+	37.2896i	1.32419	+	1.32419i
$794$	27.0301	+	17.8854i	0.959262	+	0.634730i
$795$	1.42285	+	0.418549i	0.0504633	+	0.0148444i
$796$	−0.790593	−	1.86108i	−0.0280218	−	0.0659642i
$797$	11.8786	−	15.4805i	0.420762	−	0.548347i	−0.534091	−	0.845427i	$-0.679346\pi$
$797$	11.8786	−	15.4805i	0.420762	−	0.548347i	0.954853	+	0.297080i	$0.0960127\pi$
$798$	−2.07756	−	0.751405i	−0.0735447	−	0.0265994i
$799$	0.151086	+	0.0872295i	0.00534503	+	0.00308596i
$800$	−25.5905	+	2.25682i	−0.904760	+	0.0797908i
$801$	7.72290	−	7.00668i	0.272875	−	0.247569i
$802$	−21.2006	−	10.3366i	−0.748618	−	0.364996i
$803$	−6.03999	+	45.8783i	−0.213147	+	1.61901i
$804$	23.5685	+	42.3024i	0.831196	+	1.49189i
$805$	−0.0627584	+	0.00826230i	−0.00221194	+	0.000291208i
$806$	−17.5608	−	35.2093i	−0.618554	−	1.24019i
$807$	−26.9970	+	10.4217i	−0.950338	+	0.366860i
$808$	1.62738	+	1.38873i	0.0572509	+	0.0488555i
$809$	−0.0988201	−	0.0988201i	−0.00347433	−	0.00347433i	0.705367	−	0.708842i	$-0.250782\pi$
$809$	−0.0988201	−	0.0988201i	−0.00347433	−	0.00347433i	−0.708842	+	0.705367i	$0.750782\pi$
$810$	−5.05930	−	6.97878i	−0.177766	−	0.245209i
$811$	9.29653	−	22.4438i	0.326445	−	0.788109i	−0.672405	−	0.740183i	$-0.734739\pi$
$811$	9.29653	−	22.4438i	0.326445	−	0.788109i	0.998851	−	0.0479260i	$-0.0152612\pi$
$812$	−0.114192	−	0.0294981i	−0.00400734	−	0.00103518i
$813$	11.0833	+	0.269300i	0.388708	+	0.00944475i
$814$	27.5662	+	23.9562i	0.966194	+	0.839663i
$815$	−13.3179	+	7.68909i	−0.466506	+	0.269337i
$816$	0.0722213	+	0.0731346i	0.00252825	+	0.00256022i
$817$	24.4918	+	14.1403i	0.856859	+	0.494708i
$818$	−3.28453	−	9.53465i	−0.114841	−	0.333371i
$819$	3.17440	+	1.49943i	0.110922	+	0.0523943i
$820$	1.21187	−	2.14336i	0.0423203	−	0.0748495i
$821$	−32.0606	−	41.7822i	−1.11892	−	1.45821i	−0.872218	−	0.489117i	$-0.837319\pi$
$821$	−32.0606	−	41.7822i	−1.11892	−	1.45821i	−0.246704	−	0.969091i	$-0.579348\pi$
$822$	22.8123	−	24.9968i	0.795671	−	0.871863i
$823$	7.43890	−	27.7624i	0.259304	−	0.967735i	−0.706341	−	0.707871i	$-0.749656\pi$
$823$	7.43890	−	27.7624i	0.259304	−	0.967735i	0.965645	−	0.259864i	$-0.0836777\pi$
$824$	2.62675	−	50.5251i	0.0915073	−	1.76013i
$825$	−28.0336	+	34.7525i	−0.976005	+	1.20993i
$826$	2.17538	+	1.43942i	0.0756911	+	0.0500837i
$827$	−11.6589	+	28.1470i	−0.405419	+	0.978767i	0.580909	+	0.813969i	$0.302697\pi$
$827$	−11.6589	+	28.1470i	−0.405419	+	0.978767i	−0.986327	+	0.164798i	$0.947303\pi$
$828$	1.66571	−	2.00153i	0.0578874	−	0.0695580i
$829$	−22.6347	+	9.37559i	−0.786135	+	0.325628i	−0.739388	−	0.673279i	$-0.764885\pi$
$829$	−22.6347	+	9.37559i	−0.786135	+	0.325628i	−0.0467464	+	0.998907i	$0.514885\pi$
$830$	1.29140	+	1.91400i	0.0448250	+	0.0664359i
$831$	−40.7168	+	29.7000i	−1.41245	+	1.03028i
$832$	10.1124	−	42.2768i	0.350585	−	1.46568i
$833$	−0.0893403	+	0.0515806i	−0.00309546	+	0.00178716i
$834$	−2.44701	+	2.06174i	−0.0847329	+	0.0713924i
$835$	9.80594	+	1.29098i	0.339349	+	0.0446761i
$836$	29.2815	+	37.4571i	1.01272	+	1.29548i
$837$	−23.9484	+	11.5897i	−0.827778	+	0.400597i
$838$	10.0992	+	0.616281i	0.348870	+	0.0212891i
$839$	7.24339	−	1.94086i	0.250070	−	0.0670059i	−0.131607	−	0.991302i	$-0.542014\pi$
$839$	7.24339	−	1.94086i	0.250070	−	0.0670059i	0.381676	+	0.924296i	$0.375347\pi$
$840$	0.390543	+	0.598359i	0.0134750	+	0.0206454i
$841$	−27.9394	−	7.48635i	−0.963429	−	0.258150i
$842$	−28.8804	−	9.65879i	−0.995286	−	0.332864i
$843$	6.50995	+	26.8922i	0.224214	+	0.926218i
$844$	0.994816	−	0.586364i	0.0342430	−	0.0201835i
$845$	−10.3392	+	4.28265i	−0.355680	+	0.147328i
$846$	−49.8798	+	1.06591i	−1.71490	+	0.0366466i
$847$	−4.57048			−0.157043
$848$	4.63699	−	2.01929i	0.159235	−	0.0693427i
$849$	−1.46733	−	13.7117i	−0.0503585	−	0.470586i
$850$	−0.0625000	+	0.0719182i	−0.00214373	+	0.00246677i
$851$	1.20195	−	1.56642i	0.0412025	−	0.0536961i
$852$	−30.2699	+	11.9994i	−1.03703	+	0.411093i
$853$	−32.5584	+	24.9830i	−1.11478	+	0.855401i	−0.990591	−	0.136858i	$-0.956300\pi$
$853$	−32.5584	+	24.9830i	−1.11478	+	0.855401i	−0.124189	+	0.992259i	$0.539633\pi$
$854$	−2.21364	+	1.95901i	−0.0757492	+	0.0670360i
$855$	−3.89133	−	7.56644i	−0.133081	−	0.258767i
$856$	4.27022	−	23.0939i	0.145953	−	0.789332i
$857$	7.74621	+	28.9093i	0.264606	+	0.987522i	0.962491	+	0.271313i	$0.0874577\pi$
$857$	7.74621	+	28.9093i	0.264606	+	0.987522i	−0.697886	+	0.716209i	$0.745876\pi$
$858$	−40.7229	−	63.6372i	−1.39026	−	2.17254i
$859$	2.74932	+	20.8832i	0.0938057	+	0.712525i	0.972127	+	0.234455i	$0.0753304\pi$
$859$	2.74932	+	20.8832i	0.0938057	+	0.712525i	−0.878321	+	0.478071i	$0.841336\pi$
$860$	−3.57624	−	8.41859i	−0.121949	−	0.287071i
$861$	0.677917	+	0.0164719i	0.0231034	+	0.000561361i
$862$	−13.0532	−	19.3464i	−0.444595	−	0.658941i
$863$	−33.8067			−1.15079			−0.575397	−	0.817874i	$-0.695152\pi$
$863$	−33.8067			−1.15079			−0.575397	+	0.817874i	$0.695152\pi$
$864$	−28.5038	−	7.17860i	−0.969720	−	0.244221i
$865$	12.4412			0.423013
$866$	24.1946	+	35.8592i	0.822166	+	1.21855i
$867$	−29.4358	−	0.715226i	−0.999692	−	0.0242903i
$868$	2.02989	−	0.862304i	0.0688990	−	0.0292685i
$869$	−2.81494	−	21.3816i	−0.0954904	−	0.725321i
$870$	−0.244826	−	0.382588i	−0.00830039	−	0.0129709i
$871$	−19.6593	−	73.3693i	−0.666129	−	2.48603i
$872$	23.6423	−	16.2635i	0.800631	−	0.550751i
$873$	−13.3460	+	20.7218i	−0.451692	+	0.701325i
$874$	1.92485	−	1.70344i	0.0651089	−	0.0576196i
$875$	−1.10406	+	0.847177i	−0.0373241	+	0.0286398i
$876$	−10.4066	−	26.2519i	−0.351607	−	0.886970i
$877$	−0.785283	+	1.02340i	−0.0265171	+	0.0345578i	−0.806424	−	0.591338i	$-0.798600\pi$
$877$	−0.785283	+	1.02340i	−0.0265171	+	0.0345578i	0.779907	+	0.625896i	$0.215267\pi$
$878$	13.6516	−	15.7087i	0.460718	−	0.530144i
$879$	4.83344	+	45.1671i	0.163028	+	1.52345i
$880$	−0.276925	−	15.3745i	−0.00933514	−	0.518274i
$881$	29.1795			0.983083			0.491541	−	0.870854i	$-0.336434\pi$
$881$	29.1795			0.983083			0.491541	+	0.870854i	$0.336434\pi$
$882$	14.2016	−	25.8585i	0.478194	−	0.870702i
$883$	31.0060	−	12.8431i	1.04344	−	0.432205i	0.205891	−	0.978575i	$-0.433991\pi$
$883$	31.0060	−	12.8431i	1.04344	−	0.432205i	0.837544	+	0.546370i	$0.183991\pi$
$884$	−0.0818660	−	0.138892i	−0.00275345	−	0.00467146i
$885$	2.36360	+	9.76392i	0.0794517	+	0.328211i
$886$	−13.1188	−	4.38744i	−0.440733	−	0.147399i
$887$	23.9620	+	6.42059i	0.804564	+	0.215582i	0.637587	−	0.770378i	$-0.279933\pi$
$887$	23.9620	+	6.42059i	0.804564	+	0.215582i	0.166977	+	0.985961i	$0.446599\pi$
$888$	−21.8110	−	4.58357i	−0.731930	−	0.153814i
$889$	−3.08687	+	0.827125i	−0.103530	+	0.0277409i
$890$	−3.32285	−	0.202770i	−0.111382	−	0.00679687i
$891$	−43.3568	+	27.0213i	−1.45251	+	0.905248i
$892$	25.3091	−	19.7850i	0.847412	−	0.662451i
$893$	−48.8256	−	6.42802i	−1.63389	−	0.215105i
$894$	32.4646	−	27.3533i	1.08578	−	0.914831i
$895$	7.82943	−	4.52033i	0.261709	−	0.151098i
$896$	2.33083	+	0.710124i	0.0778676	+	0.0237236i
$897$	−3.29991	+	2.40705i	−0.110181	+	0.0803690i
$898$	−2.20485	−	3.26784i	−0.0735767	−	0.109049i
$899$	−1.29525	+	0.536511i	−0.0431991	+	0.0178936i
$900$	4.62282	−	26.8531i	0.154094	−	0.895105i
$901$	0.00717842	−	0.0173302i	0.000239148	−	0.000577354i
$902$	−12.1703	−	8.05289i	−0.405226	−	0.268132i
$903$	1.58160	−	1.96067i	0.0526323	−	0.0652469i
$904$	−40.9439	+	36.8970i	−1.36177	+	1.22718i
$905$	0.148699	−	0.554952i	0.00494292	−	0.0184472i
$906$	−0.936321	+	1.02598i	−0.0311072	+	0.0340859i
$907$	15.0625	+	19.6298i	0.500141	+	0.651797i	0.973396	−	0.229129i	$-0.0735877\pi$
$907$	15.0625	+	19.6298i	0.500141	+	0.651797i	−0.473255	+	0.880926i	$0.656921\pi$
$908$	−3.85942	−	2.18214i	−0.128079	−	0.0724168i
$909$	−1.86520	+	1.29231i	−0.0618649	+	0.0428632i
$910$	−0.365042	−	1.05968i	−0.0121010	−	0.0351280i
$911$	44.1489	+	25.4894i	1.46272	+	0.844501i	0.999136	−	0.0415531i	$-0.0132306\pi$
$911$	44.1489	+	25.4894i	1.46272	+	0.844501i	0.463582	+	0.886054i	$0.346564\pi$
$912$	−26.7354	−	11.2715i	−0.885299	−	0.373237i
$913$	11.8512	−	6.84229i	0.392217	−	0.226447i
$914$	6.60847	+	5.74304i	0.218589	+	0.189963i
$915$	−11.3809	−	0.276532i	−0.376242	−	0.00914187i
$916$	−8.80761	+	34.0956i	−0.291012	+	1.12655i
$917$	−0.434432	+	1.04881i	−0.0143462	+	0.0346348i
$918$	−0.0945725	+	0.0542330i	−0.00312136	+	0.00178996i
$919$	−3.55656	−	3.55656i	−0.117320	−	0.117320i	0.646009	−	0.763330i	$-0.276437\pi$
$919$	−3.55656	−	3.55656i	−0.117320	−	0.117320i	−0.763330	+	0.646009i	$0.776437\pi$
$920$	−0.828730	+	0.0655706i	−0.0273224	+	0.00216180i
$921$	−33.7940	+	13.0455i	−1.11355	+	0.429864i
$922$	−20.2438	−	40.5886i	−0.666693	−	1.33671i
$923$	50.6380	−	6.66662i	1.66677	−	0.219434i
$924$	3.69949	−	2.06115i	0.121704	−	0.0678067i
$925$	2.69673	−	20.4837i	0.0886680	−	0.673500i
$926$	30.4233	+	14.8332i	0.999772	+	0.487449i
$927$	51.0981	+	16.3899i	1.67828	+	0.538314i
$928$	−1.47755	−	0.464738i	−0.0485028	−	0.0152558i
$929$	−21.8929	−	12.6399i	−0.718284	−	0.414701i	0.0958368	−	0.995397i	$-0.469447\pi$
$929$	−21.8929	−	12.6399i	−0.718284	−	0.414701i	−0.814121	+	0.580696i	$0.802781\pi$
$930$	7.98739	+	2.88886i	0.261917	+	0.0947294i
$931$	17.7276	−	23.1030i	0.580998	−	0.757172i
$932$	−2.32050	+	0.985758i	−0.0760106	+	0.0322896i
$933$	−41.7138	−	12.2706i	−1.36565	−	0.401723i
$934$	35.5368	+	23.5142i	1.16280	+	0.769407i
$935$	−0.0403276	−	0.0403276i	−0.00131885	−	0.00131885i
$936$	40.6108	+	21.8300i	1.32741	+	0.713535i
$937$	8.79433	−	8.79433i	0.287298	−	0.287298i	−0.548713	−	0.836011i	$-0.684882\pi$
$937$	8.79433	−	8.79433i	0.287298	−	0.287298i	0.836011	+	0.548713i	$0.184882\pi$
$938$	4.17208	−	0.849424i	0.136223	−	0.0277347i
$939$	19.6409	−	4.75458i	0.640957	−	0.155160i
$940$	11.3636	+	11.1607i	0.370639	+	0.364023i
$941$	9.59558	+	7.36295i	0.312807	+	0.240025i	0.753218	−	0.657771i	$-0.228501\pi$
$941$	9.59558	+	7.36295i	0.312807	+	0.240025i	−0.440411	+	0.897796i	$0.645167\pi$
$942$	−27.8858	−	2.38277i	−0.908568	−	0.0776348i
$943$	−0.394476	+	0.683253i	−0.0128459	+	0.0222498i
$944$	27.5493	+	20.3617i	0.896654	+	0.662717i
$945$	−0.719446	+	0.238273i	−0.0234036	+	0.00775103i
$946$	−51.2551	+	17.6565i	−1.66645	+	0.574063i
$947$	−2.26421	−	0.298089i	−0.0735769	−	0.00968658i	0.0936479	−	0.995605i	$-0.470147\pi$
$947$	−2.26421	−	0.298089i	−0.0735769	−	0.00968658i	−0.167225	+	0.985919i	$0.553481\pi$
$948$	7.85133	+	10.5626i	0.254999	+	0.343056i
$949$	5.78170	+	43.9163i	0.187682	+	1.42559i
$950$	8.53077	−	25.5076i	0.276775	−	0.827576i
$951$	27.0163	+	4.22672i	0.876064	+	0.137061i
$952$	0.00805043	−	0.00410614i	0.000260916	−	0.000133081i
$953$	18.6869	−	18.6869i	0.605327	−	0.605327i	−0.336394	−	0.941721i	$-0.609207\pi$
$953$	18.6869	−	18.6869i	0.605327	−	0.605327i	0.941721	+	0.336394i	$0.109207\pi$
$954$	0.813660	+	5.30231i	0.0263432	+	0.171669i
$955$	3.60065	+	1.49144i	0.116514	+	0.0482619i
$956$	−4.62694	−	32.8560i	−0.149646	−	1.06264i
$957$	−2.36341	+	1.28901i	−0.0763982	+	0.0416677i
$958$	0.0370956	+	0.529433i	0.00119850	+	0.0171052i
$959$	−1.48773	−	2.57682i	−0.0480412	−	0.0832098i
$960$	4.71409	+	8.11397i	0.152147	+	0.261877i
$961$	−2.39173	+	4.14260i	−0.0771527	+	0.133632i
$962$	31.4234	+	15.3208i	1.01313	+	0.493962i
$963$	22.5237	+	10.6391i	0.725816	+	0.342840i
$964$	12.7042	−	9.93129i	0.409174	−	0.319865i
$965$	−4.44096	+	3.40767i	−0.142959	+	0.109697i
$966$	−0.123406	−	0.192846i	−0.00397053	−	0.00620470i
$967$	−6.09250	−	1.63248i	−0.195922	−	0.0524971i	0.159524	−	0.987194i	$-0.449004\pi$
$967$	−6.09250	−	1.63248i	−0.195922	−	0.0524971i	−0.355445	+	0.934697i	$0.615671\pi$
$968$	−59.9433	−	3.11640i	−1.92665	−	0.100165i
$969$	−0.100391	+	0.0387540i	−0.00322502	+	0.00124496i
$970$	7.71056	−	1.56985i	0.247571	−	0.0504048i
$971$	−28.7852	−	11.9232i	−0.923760	−	0.382634i	−0.130452	−	0.991455i	$-0.541643\pi$
$971$	−28.7852	−	11.9232i	−0.923760	−	0.382634i	−0.793308	+	0.608821i	$0.791643\pi$
$972$	15.0880	−	27.2828i	0.483947	−	0.875097i
$973$	0.107663	+	0.259921i	0.00345151	+	0.00833267i
$974$	8.96001	−	46.1295i	0.287097	−	1.47809i
$975$	−17.3104	+	39.0782i	−0.554378	+	1.25150i
$976$	−30.3683	+	24.1837i	−0.972067	+	0.774101i
$977$	19.4991	+	33.7734i	0.623831	+	1.08051i	0.988766	+	0.149474i	$0.0477579\pi$
$977$	19.4991	+	33.7734i	0.623831	+	1.08051i	−0.364935	+	0.931033i	$0.618909\pi$
$978$	−45.6272	−	31.8109i	−1.45900	−	1.01720i
$979$	−2.57537	+	19.5619i	−0.0823091	+	0.625200i
$980$	−9.07516	+	2.51949i	−0.289895	+	0.0804820i
$981$	10.2682	+	28.6524i	0.327838	+	0.914800i
$982$	−25.6271	−	28.9581i	−0.817794	−	0.924089i
$983$	−5.13194	−	19.1527i	−0.163684	−	0.610875i	−0.998204	−	0.0598990i	$-0.980922\pi$
$983$	−5.13194	−	19.1527i	−0.163684	−	0.610875i	0.834521	−	0.550976i	$-0.185745\pi$
$984$	8.87987	+	0.678275i	0.283080	+	0.0216226i
$985$	4.60837	−	17.1987i	0.146835	−	0.547995i
$986$	−0.00514083	+	0.00256402i	−0.000163717	+	8.16549e-5i
$987$	−1.23792	+	4.20830i	−0.0394035	+	0.133952i
$988$	36.3542	+	27.3790i	1.15658	+	0.871043i
$989$	1.12156	+	2.70769i	0.0356637	+	0.0860997i
$990$	15.8406	+	3.88373i	0.503447	+	0.123433i
$991$		−	18.4586i		−	0.586356i	−0.956058	−	0.293178i	$-0.905287\pi$
$991$		−	18.4586i		−	0.586356i	0.956058	−	0.293178i	$-0.0947129\pi$
$992$	27.2106	−	9.92530i	0.863938	−	0.315129i
$993$	15.3764	+	21.0800i	0.487954	+	0.668953i
$994$	0.200105	+	2.85592i	0.00634694	+	0.0905843i
$995$	−0.543205	−	0.416816i	−0.0172207	−	0.0132139i
$996$	−4.28566	+	7.16765i	−0.135796	+	0.227116i
$997$	−26.0134	−	33.9014i	−0.823854	−	1.07367i	−0.996067	−	0.0886072i	$-0.971758\pi$
$997$	−26.0134	−	33.9014i	−0.823854	−	1.07367i	0.172213	−	0.985060i	$-0.444908\pi$
$998$	−41.1888	−	2.51346i	−1.30381	−	0.0795622i
$999$	10.6127	−	21.1233i	0.335770	−	0.668311i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bf.a.11.38	✓	368
3.2	odd	2		864.2.bn.a.683.9		368
9.4	even	3		864.2.bn.a.395.24		368
9.5	odd	6	inner	288.2.bf.a.203.23	yes	368
32.3	odd	8	inner	288.2.bf.a.227.23	yes	368
96.35	even	8		864.2.bn.a.35.24		368
288.67	odd	24		864.2.bn.a.611.9		368
288.131	even	24	inner	288.2.bf.a.131.38	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.38	✓	368	1.1	even	1	trivial
288.2.bf.a.131.38	yes	368	288.131	even	24	inner
288.2.bf.a.203.23	yes	368	9.5	odd	6	inner
288.2.bf.a.227.23	yes	368	32.3	odd	8	inner
864.2.bn.a.35.24		368	96.35	even	8
864.2.bn.a.395.24		368	9.4	even	3
864.2.bn.a.611.9		368	288.67	odd	24
864.2.bn.a.683.9		368	3.2	odd	2

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:	\( N \)	\(=\)	\( 288 = 2^{5} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	288.bf (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17233 - 0.790981i) q^{2} +(1.73154 + 0.0420726i) q^{3} +(0.748697 - 1.85458i) q^{4} +(-0.0883963 - 0.671437i) q^{5} +(2.06321 - 1.32029i) q^{6} +(-0.0557412 - 0.208029i) q^{7} +(-0.589218 - 2.76637i) q^{8} +(2.99646 + 0.145701i) q^{9} +O(q^{10})\)	\(q+(1.17233 - 0.790981i) q^{2} +(1.73154 + 0.0420726i) q^{3} +(0.748697 - 1.85458i) q^{4} +(-0.0883963 - 0.671437i) q^{5} +(2.06321 - 1.32029i) q^{6} +(-0.0557412 - 0.208029i) q^{7} +(-0.589218 - 2.76637i) q^{8} +(2.99646 + 0.145701i) q^{9} +(-0.634723 - 0.717223i) q^{10} +(-4.50341 + 3.45559i) q^{11} +(1.37443 - 3.17977i) q^{12} +(-3.30781 + 4.31082i) q^{13} +(-0.229894 - 0.199788i) q^{14} +(-0.124813 - 1.16634i) q^{15} +(-2.87891 - 2.77703i) q^{16} -0.0148356 q^{17} +(3.62807 - 2.19933i) q^{18} +(3.86908 - 1.60262i) q^{19} +(-1.31141 - 0.338765i) q^{20} +(-0.0877658 - 0.362556i) q^{21} +(-2.54616 + 7.61319i) q^{22} +(0.419209 + 0.112327i) q^{23} +(-0.903866 - 4.81488i) q^{24} +(4.38662 - 1.17539i) q^{25} +(-0.468052 + 7.67011i) q^{26} +(5.18236 + 0.378356i) q^{27} +(-0.427539 - 0.0523744i) q^{28} +(0.271469 + 0.0357395i) q^{29} +(-1.06887 - 1.26860i) q^{30} +(-4.43423 + 2.56010i) q^{31} +(-5.57160 - 0.978425i) q^{32} +(-7.94322 + 5.79402i) q^{33} +(-0.0173922 + 0.0117347i) q^{34} +(-0.134751 + 0.0558157i) q^{35} +(2.51365 - 5.44808i) q^{36} +(1.74098 - 4.20310i) q^{37} +(3.26817 - 4.93916i) q^{38} +(-5.90897 + 7.32519i) q^{39} +(-1.80536 + 0.640160i) q^{40} +(-0.470501 + 1.75593i) q^{41} +(-0.389665 - 0.355612i) q^{42} +(4.11098 + 5.35753i) q^{43} +(3.03696 + 10.9391i) q^{44} +(-0.167047 - 2.02481i) q^{45} +(0.580298 - 0.199903i) q^{46} +(-10.1840 - 5.87973i) q^{47} +(-4.86810 - 4.92966i) q^{48} +(6.02201 - 3.47681i) q^{49} +(4.21283 - 4.84767i) q^{50} +(-0.0256885 - 0.000624174i) q^{51} +(5.51820 + 9.36209i) q^{52} +(-0.483863 + 1.16815i) q^{53} +(6.37469 - 3.65559i) q^{54} +(2.71829 + 2.71829i) q^{55} +(-0.542642 + 0.276775i) q^{56} +(6.76688 - 2.61222i) q^{57} +(0.346519 - 0.172828i) q^{58} +(-8.49106 + 1.11787i) q^{59} +(-2.25651 - 0.641760i) q^{60} +(1.26680 - 9.62227i) q^{61} +(-3.17337 + 6.50867i) q^{62} +(-0.136716 - 0.631472i) q^{63} +(-7.30564 + 3.26000i) q^{64} +(3.18684 + 1.83992i) q^{65} +(-4.72908 + 13.0754i) q^{66} +(-8.50990 + 11.0903i) q^{67} +(-0.0111074 + 0.0275138i) q^{68} +(0.721151 + 0.212135i) q^{69} +(-0.113823 + 0.172020i) q^{70} +(-6.64660 - 6.64660i) q^{71} +(-1.36251 - 8.37518i) q^{72} +(5.76433 - 5.76433i) q^{73} +(-1.28358 - 6.30449i) q^{74} +(7.64505 - 1.85068i) q^{75} +(-0.0754224 - 8.37537i) q^{76} +(0.969888 + 0.744221i) q^{77} +(-1.13315 + 13.2614i) q^{78} +(-1.89962 + 3.29024i) q^{79} +(-1.61012 + 2.17848i) q^{80} +(8.95754 + 0.873174i) q^{81} +(0.837330 + 2.43068i) q^{82} +(-2.39015 - 0.314669i) q^{83} +(-0.738097 - 0.108676i) q^{84} +(0.00131141 + 0.00996118i) q^{85} +(9.05711 + 3.02907i) q^{86} +(0.468555 + 0.0733058i) q^{87} +(12.2129 + 10.4220i) q^{88} +(2.45783 - 2.45783i) q^{89} +(-1.79742 - 2.24161i) q^{90} +(1.08116 + 0.447830i) q^{91} +(0.522179 - 0.693356i) q^{92} +(-7.78576 + 4.24636i) q^{93} +(-16.5897 + 1.16239i) q^{94} +(-1.41807 - 2.45617i) q^{95} +(-9.60628 - 1.92859i) q^{96} +(-4.10794 + 7.11516i) q^{97} +(4.30967 - 8.83925i) q^{98} +(-13.9978 + 9.69838i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9	\( 368 q - 12 q^{2} - 8 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{6} - 4 q^{7} - 8 q^{9} - 16 q^{10} - 12 q^{11} - 8 q^{12} - 4 q^{13} - 12 q^{14} - 16 q^{15} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 12 q^{20} - 8 q^{21} - 4 q^{22} - 12 q^{23} + 32 q^{24} - 4 q^{25} + 16 q^{27} - 16 q^{28} - 12 q^{29} - 56 q^{30} - 12 q^{32} - 16 q^{33} - 12 q^{34} - 60 q^{36} - 16 q^{37} - 12 q^{38} + 16 q^{39} - 4 q^{40} - 12 q^{41} - 8 q^{42} - 4 q^{43} - 8 q^{45} - 16 q^{46} - 24 q^{47} - 60 q^{48} - 168 q^{50} - 32 q^{51} - 4 q^{52} - 52 q^{54} - 16 q^{55} - 12 q^{56} - 8 q^{57} + 32 q^{58} - 12 q^{59} - 20 q^{60} - 4 q^{61} - 16 q^{64} - 24 q^{65} - 80 q^{66} - 4 q^{67} - 60 q^{68} - 8 q^{69} - 4 q^{70} + 52 q^{72} - 16 q^{73} - 12 q^{74} - 28 q^{75} - 28 q^{76} - 12 q^{77} + 80 q^{78} - 8 q^{79} - 16 q^{82} - 132 q^{83} - 104 q^{84} - 24 q^{85} - 12 q^{86} - 64 q^{87} - 4 q^{88} + 124 q^{90} - 16 q^{91} + 216 q^{92} - 20 q^{93} - 20 q^{94} + 92 q^{96} - 8 q^{97} - 72 q^{99}+O(q^{100}) \) 368 * q - 12 * q^2 - 8 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^6 - 4 * q^7 - 8 * q^9 - 16 * q^10 - 12 * q^11 - 8 * q^12 - 4 * q^13 - 12 * q^14 - 16 * q^15 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 12 * q^20 - 8 * q^21 - 4 * q^22 - 12 * q^23 + 32 * q^24 - 4 * q^25 + 16 * q^27 - 16 * q^28 - 12 * q^29 - 56 * q^30 - 12 * q^32 - 16 * q^33 - 12 * q^34 - 60 * q^36 - 16 * q^37 - 12 * q^38 + 16 * q^39 - 4 * q^40 - 12 * q^41 - 8 * q^42 - 4 * q^43 - 8 * q^45 - 16 * q^46 - 24 * q^47 - 60 * q^48 - 168 * q^50 - 32 * q^51 - 4 * q^52 - 52 * q^54 - 16 * q^55 - 12 * q^56 - 8 * q^57 + 32 * q^58 - 12 * q^59 - 20 * q^60 - 4 * q^61 - 16 * q^64 - 24 * q^65 - 80 * q^66 - 4 * q^67 - 60 * q^68 - 8 * q^69 - 4 * q^70 + 52 * q^72 - 16 * q^73 - 12 * q^74 - 28 * q^75 - 28 * q^76 - 12 * q^77 + 80 * q^78 - 8 * q^79 - 16 * q^82 - 132 * q^83 - 104 * q^84 - 24 * q^85 - 12 * q^86 - 64 * q^87 - 4 * q^88 + 124 * q^90 - 16 * q^91 + 216 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^96 - 8 * q^97 - 72 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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