LMFDB - Embedded newform 288.2.bc.a.205.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [288,2,Mod(13,288)]

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([0, 21, 8]))

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

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

chi := DirichletCharacter("288.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 288 = 2^{5} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	288.bc (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			205.32
Character	$\chi$	$=$	288.205
Dual form			288.2.bc.a.229.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.830777 - 1.14447i) q^{2} +(-1.55972 - 0.753177i) q^{3} +(-0.619620 - 1.90160i) q^{4} +(-1.83769 - 1.41011i) q^{5} +(-2.15777 + 1.15933i) q^{6} +(0.454899 + 1.69771i) q^{7} +(-2.69109 - 0.870667i) q^{8} +(1.86545 + 2.34949i) q^{9} +O(q^{10})$	\(q+(0.830777 - 1.14447i) q^{2} +(-1.55972 - 0.753177i) q^{3} +(-0.619620 - 1.90160i) q^{4} +(-1.83769 - 1.41011i) q^{5} +(-2.15777 + 1.15933i) q^{6} +(0.454899 + 1.69771i) q^{7} +(-2.69109 - 0.870667i) q^{8} +(1.86545 + 2.34949i) q^{9} +(-3.14054 + 0.931695i) q^{10} +(-4.25482 - 0.560157i) q^{11} +(-0.465806 + 3.43264i) q^{12} +(-0.303048 - 2.30188i) q^{13} +(2.32089 + 0.889796i) q^{14} +(1.80422 + 3.58349i) q^{15} +(-3.23214 + 2.35653i) q^{16} -1.85832i q^{17} +(4.23869 - 0.183047i) q^{18} +(2.22188 + 0.920333i) q^{19} +(-1.54279 + 4.36828i) q^{20} +(0.569158 - 2.99056i) q^{21} +(-4.17588 + 4.40414i) q^{22} +(-1.01925 + 3.80389i) q^{23} +(3.54157 + 3.38486i) q^{24} +(0.0946054 + 0.353072i) q^{25} +(-2.88619 - 1.56552i) q^{26} +(-1.13999 - 5.06956i) q^{27} +(2.94649 - 1.91697i) q^{28} +(-3.06112 - 3.98933i) q^{29} +(5.60009 + 0.912201i) q^{30} +(-3.53119 - 6.11620i) q^{31} +(0.0117927 + 5.65684i) q^{32} +(6.21442 + 4.07832i) q^{33} +(-2.12679 - 1.54385i) q^{34} +(1.55799 - 3.76132i) q^{35} +(3.31191 - 5.00312i) q^{36} +(3.25157 - 1.34684i) q^{37} +(2.89918 - 1.77828i) q^{38} +(-1.26105 + 3.81853i) q^{39} +(3.71765 + 5.39475i) q^{40} +(3.20240 - 11.9515i) q^{41} +(-2.94976 - 3.13587i) q^{42} +(-2.39632 - 0.315482i) q^{43} +(1.57118 + 8.43803i) q^{44} +(-0.115079 - 6.94813i) q^{45} +(3.50667 + 4.32669i) q^{46} +(-5.58096 - 3.22217i) q^{47} +(6.81612 - 1.24116i) q^{48} +(3.38691 - 1.95543i) q^{49} +(0.482676 + 0.185051i) q^{50} +(-1.39964 + 2.89845i) q^{51} +(-4.18947 + 2.00256i) q^{52} +(-3.40394 - 8.21784i) q^{53} +(-6.74903 - 2.90698i) q^{54} +(7.02916 + 7.02916i) q^{55} +(0.253964 - 4.96473i) q^{56} +(-2.77234 - 3.10893i) q^{57} +(-7.10878 + 0.189116i) q^{58} +(11.8297 + 9.07722i) q^{59} +(5.69641 - 5.65130i) q^{60} +(8.00680 + 10.4347i) q^{61} +(-9.93343 - 1.03986i) q^{62} +(-3.14015 + 4.23576i) q^{63} +(6.48388 + 4.68608i) q^{64} +(-2.68899 + 4.65747i) q^{65} +(9.83030 - 3.72404i) q^{66} +(-5.13255 + 0.675713i) q^{67} +(-3.53377 + 1.15145i) q^{68} +(4.45475 - 5.16533i) q^{69} +(-3.01037 - 4.90789i) q^{70} +(0.786895 - 0.786895i) q^{71} +(-2.97446 - 7.94686i) q^{72} +(6.89191 + 6.89191i) q^{73} +(1.15991 - 4.84024i) q^{74} +(0.118368 - 0.621948i) q^{75} +(0.373381 - 4.79538i) q^{76} +(-0.984528 - 7.47824i) q^{77} +(3.32254 + 4.61558i) q^{78} +(-7.90822 - 4.56581i) q^{79} +(9.26266 + 0.227094i) q^{80} +(-2.04021 + 8.76570i) q^{81} +(-11.0177 - 13.5941i) q^{82} +(2.78023 - 2.13335i) q^{83} +(-6.03951 + 0.770702i) q^{84} +(-2.62043 + 3.41501i) q^{85} +(-2.35187 + 2.48042i) q^{86} +(1.76982 + 8.52780i) q^{87} +(10.9624 + 5.21196i) q^{88} +(3.68687 - 3.68687i) q^{89} +(-8.04753 - 5.64064i) q^{90} +(3.77005 - 1.56161i) q^{91} +(7.86502 - 0.418765i) q^{92} +(0.901082 + 12.1992i) q^{93} +(-8.32420 + 3.71033i) q^{94} +(-2.78536 - 4.82439i) q^{95} +(4.24221 - 8.83197i) q^{96} +(-4.33284 + 7.50470i) q^{97} +(0.575832 - 5.50074i) q^{98} +(-6.62105 - 11.0416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) $ 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.830777	−	1.14447i	0.587448	−	0.809262i
$2$	0.830777	−	1.14447i	0.587448	−	0.809262i
$3$	−1.55972	−	0.753177i	−0.900504	−	0.434847i
$3$	−1.55972	−	0.753177i	−0.900504	−	0.434847i
$4$	−0.619620	−	1.90160i	−0.309810	−	0.950799i
$5$	−1.83769	−	1.41011i	−0.821841	−	0.630621i	0.109819	−	0.993952i	$-0.464973\pi$
$5$	−1.83769	−	1.41011i	−0.821841	−	0.630621i	−0.931660	+	0.363331i	$0.881640\pi$
$6$	−2.15777	+	1.15933i	−0.880905	+	0.473294i
$7$	0.454899	+	1.69771i	0.171936	+	0.641672i	0.997053	+	0.0767115i	$0.0244420\pi$
$7$	0.454899	+	1.69771i	0.171936	+	0.641672i	−0.825118	+	0.564961i	$0.808891\pi$
$8$	−2.69109	−	0.870667i	−0.951442	−	0.307827i
$9$	1.86545	+	2.34949i	0.621816	+	0.783163i
$10$	−3.14054	+	0.931695i	−0.993126	+	0.294628i
$11$	−4.25482	−	0.560157i	−1.28288	−	0.168894i	−0.541910	−	0.840437i	$-0.682298\pi$
$11$	−4.25482	−	0.560157i	−1.28288	−	0.168894i	−0.740966	+	0.671543i	$0.765632\pi$
$12$	−0.465806	+	3.43264i	−0.134467	+	0.990918i
$13$	−0.303048	−	2.30188i	−0.0840503	−	0.638425i	−0.980676	−	0.195637i	$-0.937323\pi$
$13$	−0.303048	−	2.30188i	−0.0840503	−	0.638425i	0.896626	−	0.442788i	$-0.146011\pi$
$14$	2.32089	+	0.889796i	0.620284	+	0.237808i
$15$	1.80422	+	3.58349i	0.465848	+	0.925252i
$16$	−3.23214	+	2.35653i	−0.808036	+	0.589134i
$17$		−	1.85832i		−	0.450708i	−0.974277	−	0.225354i	$-0.927646\pi$
$17$		−	1.85832i		−	0.450708i	0.974277	−	0.225354i	$-0.0723539\pi$
$18$	4.23869	−	0.183047i	0.999069	−	0.0431445i
$19$	2.22188	+	0.920333i	0.509734	+	0.211139i	0.622701	−	0.782460i	$-0.286035\pi$
$19$	2.22188	+	0.920333i	0.509734	+	0.211139i	−0.112967	+	0.993599i	$0.536035\pi$
$20$	−1.54279	+	4.36828i	−0.344979	+	0.976778i
$21$	0.569158	−	2.99056i	0.124201	−	0.652594i
$22$	−4.17588	+	4.40414i	−0.890302	+	0.938966i
$23$	−1.01925	+	3.80389i	−0.212528	+	0.793167i	0.774494	+	0.632582i	$0.218005\pi$
$23$	−1.01925	+	3.80389i	−0.212528	+	0.793167i	−0.987022	+	0.160585i	$0.948662\pi$
$24$	3.54157	+	3.38486i	0.722920	+	0.690932i
$25$	0.0946054	+	0.353072i	0.0189211	+	0.0706145i
$26$	−2.88619	−	1.56552i	−0.566029	−	0.307023i
$27$	−1.13999	−	5.06956i	−0.219392	−	0.975637i
$28$	2.94649	−	1.91697i	0.556834	−	0.362272i
$29$	−3.06112	−	3.98933i	−0.568436	−	0.740800i	0.417361	−	0.908741i	$-0.362955\pi$
$29$	−3.06112	−	3.98933i	−0.568436	−	0.740800i	−0.985797	+	0.167940i	$0.946288\pi$
$30$	5.60009	+	0.912201i	1.02243	+	0.166544i
$31$	−3.53119	−	6.11620i	−0.634220	−	1.09850i	−0.986680	−	0.162674i	$-0.947988\pi$
$31$	−3.53119	−	6.11620i	−0.634220	−	1.09850i	0.352460	−	0.935827i	$-0.385345\pi$
$32$	0.0117927	+	5.65684i	0.00208468	+	0.999998i
$33$	6.21442	+	4.07832i	1.08179	+	0.709944i
$34$	−2.12679	−	1.54385i	−0.364741	−	0.264767i
$35$	1.55799	−	3.76132i	0.263348	−	0.635779i
$36$	3.31191	−	5.00312i	0.551986	−	0.833854i
$37$	3.25157	−	1.34684i	0.534554	−	0.221420i	−0.0990423	−	0.995083i	$-0.531578\pi$
$37$	3.25157	−	1.34684i	0.534554	−	0.221420i	0.633597	+	0.773664i	$0.281578\pi$
$38$	2.89918	−	1.77828i	0.470309	−	0.288476i
$39$	−1.26105	+	3.81853i	−0.201930	+	0.611454i
$40$	3.71765	+	5.39475i	0.587812	+	0.852984i
$41$	3.20240	−	11.9515i	0.500131	−	1.86651i	0.000976646	−	1.00000i	$-0.499689\pi$
$41$	3.20240	−	11.9515i	0.500131	−	1.86651i	0.499154	−	0.866513i	$-0.333644\pi$
$42$	−2.94976	−	3.13587i	−0.455158	−	0.483876i
$43$	−2.39632	−	0.315482i	−0.365435	−	0.0481105i	−0.0544273	−	0.998518i	$-0.517333\pi$
$43$	−2.39632	−	0.315482i	−0.365435	−	0.0481105i	−0.311008	+	0.950407i	$0.600667\pi$
$44$	1.57118	+	8.43803i	0.236864	+	1.27208i
$45$	−0.115079	−	6.94813i	−0.0171549	−	1.03577i
$46$	3.50667	+	4.32669i	0.517030	+	0.637935i
$47$	−5.58096	−	3.22217i	−0.814066	−	0.470001i	0.0342998	−	0.999412i	$-0.489080\pi$
$47$	−5.58096	−	3.22217i	−0.814066	−	0.470001i	−0.848366	+	0.529410i	$0.822413\pi$
$48$	6.81612	−	1.24116i	0.983823	−	0.179146i
$49$	3.38691	−	1.95543i	0.483844	−	0.279347i
$50$	0.482676	+	0.185051i	0.0682607	+	0.0261702i
$51$	−1.39964	+	2.89845i	−0.195989	+	0.405865i
$52$	−4.18947	+	2.00256i	−0.580974	+	0.277705i
$53$	−3.40394	−	8.21784i	−0.467567	−	1.12881i	−0.965222	−	0.261432i	$-0.915805\pi$
$53$	−3.40394	−	8.21784i	−0.467567	−	1.12881i	0.497655	−	0.867375i	$-0.334195\pi$
$54$	−6.74903	−	2.90698i	−0.918427	−	0.395590i
$55$	7.02916	+	7.02916i	0.947812	+	0.947812i
$56$	0.253964	−	4.96473i	0.0339374	−	0.663441i
$57$	−2.77234	−	3.10893i	−0.367205	−	0.411788i
$58$	−7.10878	+	0.189116i	−0.933428	+	0.0248321i
$59$	11.8297	+	9.07722i	1.54009	+	1.18175i	0.916522	+	0.399985i	$0.130985\pi$
$59$	11.8297	+	9.07722i	1.54009	+	1.18175i	0.623569	+	0.781768i	$0.285682\pi$
$60$	5.69641	−	5.65130i	0.735404	−	0.729580i
$61$	8.00680	+	10.4347i	1.02517	+	1.33602i	0.940567	+	0.339608i	$0.110294\pi$
$61$	8.00680	+	10.4347i	1.02517	+	1.33602i	0.0845990	+	0.996415i	$0.473039\pi$
$62$	−9.93343	−	1.03986i	−1.26155	−	0.132062i
$63$	−3.14015	+	4.23576i	−0.395622	+	0.533656i
$64$	6.48388	+	4.68608i	0.810485	+	0.585760i
$65$	−2.68899	+	4.65747i	−0.333528	+	0.577688i
$66$	9.83030	−	3.72404i	1.21003	−	0.458398i
$67$	−5.13255	+	0.675713i	−0.627041	+	0.0825515i	−0.437348	−	0.899292i	$-0.644082\pi$
$67$	−5.13255	+	0.675713i	−0.627041	+	0.0825515i	−0.189692	+	0.981844i	$0.560749\pi$
$68$	−3.53377	+	1.15145i	−0.428533	+	0.139634i
$69$	4.45475	−	5.16533i	0.536289	−	0.621833i
$70$	−3.01037	−	4.90789i	−0.359808	−	0.586605i
$71$	0.786895	−	0.786895i	0.0933873	−	0.0933873i	−0.658870	−	0.752257i	$-0.728965\pi$
$71$	0.786895	−	0.786895i	0.0933873	−	0.0933873i	0.752257	+	0.658870i	$0.228965\pi$
$72$	−2.97446	−	7.94686i	−0.350543	−	0.936547i
$73$	6.89191	+	6.89191i	0.806637	+	0.806637i	0.984123	−	0.177486i	$-0.0567966\pi$
$73$	6.89191	+	6.89191i	0.806637	+	0.806637i	−0.177486	+	0.984123i	$0.556797\pi$
$74$	1.15991	−	4.84024i	0.134836	−	0.562667i
$75$	0.118368	−	0.621948i	0.0136680	−	0.0718164i
$76$	0.373381	−	4.79538i	0.0428298	−	0.550068i
$77$	−0.984528	−	7.47824i	−0.112197	−	0.852224i
$78$	3.32254	+	4.61558i	0.376203	+	0.522611i
$79$	−7.90822	−	4.56581i	−0.889745	−	0.513694i	−0.0158857	−	0.999874i	$-0.505057\pi$
$79$	−7.90822	−	4.56581i	−0.889745	−	0.513694i	−0.873859	+	0.486180i	$0.838390\pi$
$80$	9.26266	+	0.227094i	1.03560	+	0.0253898i
$81$	−2.04021	+	8.76570i	−0.226689	+	0.973967i
$82$	−11.0177	−	13.5941i	−1.21670	−	1.50122i
$83$	2.78023	−	2.13335i	0.305170	−	0.234165i	−0.444811	−	0.895624i	$-0.646729\pi$
$83$	2.78023	−	2.13335i	0.305170	−	0.234165i	0.749981	+	0.661459i	$0.230062\pi$
$84$	−6.03951	+	0.770702i	−0.658964	+	0.0840905i
$85$	−2.62043	+	3.41501i	−0.284226	+	0.370410i
$86$	−2.35187	+	2.48042i	−0.253608	+	0.267471i
$87$	1.76982	+	8.52780i	0.189744	+	0.914277i
$88$	10.9624	+	5.21196i	1.16859	+	0.555596i
$89$	3.68687	−	3.68687i	0.390808	−	0.390808i	−0.484168	−	0.874975i	$-0.660877\pi$
$89$	3.68687	−	3.68687i	0.390808	−	0.390808i	0.874975	+	0.484168i	$0.160877\pi$
$90$	−8.04753	−	5.64064i	−0.848284	−	0.594576i
$91$	3.77005	−	1.56161i	0.395209	−	0.163701i
$92$	7.86502	−	0.418765i	0.819985	−	0.0436593i
$93$	0.901082	+	12.1992i	0.0934378	+	1.26499i
$94$	−8.32420	+	3.71033i	−0.858576	+	0.382692i
$95$	−2.78536	−	4.82439i	−0.285772	−	0.494972i
$96$	4.24221	−	8.83197i	0.432969	−	0.901409i
$97$	−4.33284	+	7.50470i	−0.439933	+	0.761987i	−0.997684	−	0.0680218i	$-0.978331\pi$
$97$	−4.33284	+	7.50470i	−0.439933	+	0.761987i	0.557750	+	0.830009i	$0.311665\pi$
$98$	0.575832	−	5.50074i	0.0581679	−	0.555659i
$99$	−6.62105	−	11.0416i	−0.665441	−	1.10972i
$100$	0.612782	−	0.398672i	0.0612782	−	0.0398672i
$101$	−1.11753	+	8.48846i	−0.111198	+	0.844633i	0.841402	+	0.540409i	$0.181731\pi$
$101$	−1.11753	+	8.48846i	−0.111198	+	0.844633i	−0.952600	+	0.304224i	$0.901603\pi$
$102$	2.15440	+	4.00981i	0.213317	+	0.397031i
$103$	5.15005	+	1.37995i	0.507449	+	0.135971i	0.503455	−	0.864021i	$-0.332062\pi$
$103$	5.15005	+	1.37995i	0.507449	+	0.135971i	0.00399421	+	0.999992i	$0.498729\pi$
$104$	−1.18864	+	6.45840i	−0.116556	+	0.633298i
$105$	−5.26296	+	4.69316i	−0.513613	+	0.458005i
$106$	−12.2330	−	2.93149i	−1.18817	−	0.284731i
$107$	−2.80668	−	6.77594i	−0.271332	−	0.655055i	0.728208	−	0.685356i	$-0.240353\pi$
$107$	−2.80668	−	6.77594i	−0.271332	−	0.655055i	−0.999541	+	0.0303013i	$0.990353\pi$
$108$	−8.93389	+	5.30901i	−0.859664	+	0.510859i
$109$	−16.4296	−	6.80536i	−1.57367	−	0.651835i	−0.586275	−	0.810112i	$-0.699406\pi$
$109$	−16.4296	−	6.80536i	−1.57367	−	0.651835i	−0.987395	+	0.158277i	$0.949406\pi$
$110$	13.8843	−	2.20499i	1.32382	−	0.210238i
$111$	−6.08594	−	0.348309i	−0.577652	−	0.0330600i
$112$	−5.47100	−	4.41524i	−0.516961	−	0.417201i
$113$	−7.30520	+	4.21766i	−0.687216	+	0.396764i	−0.802568	−	0.596561i	$-0.796534\pi$
$113$	−7.30520	+	4.21766i	−0.687216	+	0.396764i	0.115353	+	0.993325i	$0.463200\pi$
$114$	−5.86127	+	0.590026i	−0.548958	+	0.0552610i
$115$	7.23698	−	5.55313i	0.674852	−	0.517832i
$116$	−5.68937	+	8.29289i	−0.528245	+	0.769975i
$117$	4.84291	−	5.00604i	0.447728	−	0.462808i
$118$	20.2164	−	5.99754i	1.86107	−	0.552119i
$119$	3.15487	−	0.845346i	0.289207	−	0.0774927i
$120$	−1.73529	−	11.2143i	−0.158410	−	1.02372i
$121$	7.16449	+	1.91972i	0.651318	+	0.174520i
$122$	18.5940	−	0.494660i	1.68342	−	0.0447844i
$123$	−13.9964	+	16.2290i	−1.26202	+	1.46332i
$124$	−9.44255	+	10.5046i	−0.847966	+	0.943342i
$125$	−4.10815	+	9.91795i	−0.367444	+	0.887088i
$126$	2.23893	+	7.11278i	0.199460	+	0.633657i
$127$	−6.45329			−0.572637			−0.286318	−	0.958135i	$-0.592431\pi$
$127$	−6.45329			−0.572637			−0.286318	+	0.958135i	$0.592431\pi$
$128$	10.7497	−	3.52752i	0.950151	−	0.311791i
$129$	3.49997	+	2.29692i	0.308155	+	0.202232i
$130$	3.09638	+	6.94679i	0.271570	+	0.609274i
$131$	13.9681	−	1.83894i	1.22040	−	0.160669i	0.507324	−	0.861755i	$-0.330635\pi$
$131$	13.9681	−	1.83894i	1.22040	−	0.160669i	0.713076	+	0.701087i	$0.247301\pi$
$132$	3.90474	−	14.3443i	0.339864	−	1.24851i
$133$	−0.551723	+	4.19076i	−0.0478405	+	0.363385i
$134$	−3.49067	+	6.43541i	−0.301548	+	0.555935i
$135$	−5.05368	+	10.9238i	−0.434952	+	0.940172i
$136$	−1.61797	+	5.00089i	−0.138740	+	0.428823i
$137$	15.6302	−	4.18811i	1.33538	−	0.357814i	0.480662	−	0.876906i	$-0.340396\pi$
$137$	15.6302	−	4.18811i	1.33538	−	0.357814i	0.854718	+	0.519092i	$0.173730\pi$
$138$	−2.21066	−	9.38956i	−0.188184	−	0.799293i
$139$	13.4223	−	17.4923i	1.13846	−	1.48367i	0.288007	−	0.957628i	$-0.407007\pi$
$139$	13.4223	−	17.4923i	1.13846	−	1.48367i	0.850456	−	0.526046i	$-0.176326\pi$
$140$	−8.11787	−	0.632080i	−0.686085	−	0.0534205i
$141$	6.27786	+	9.22912i	0.528691	+	0.777232i
$142$	−0.246843	−	1.55431i	−0.0207146	−	0.130435i
$143$			9.96381i			0.833216i
$144$	−11.5660	−	3.19789i	−0.963837	−	0.266491i
$145$			11.6477i			0.967288i
$146$	13.6132	−	2.16194i	1.12664	−	0.178923i
$147$	−6.75541	+	0.498984i	−0.557177	+	0.0411555i
$148$	−4.57589	−	5.34864i	−0.376136	−	0.439655i
$149$	−6.93266	+	9.03482i	−0.567946	+	0.740161i	−0.985721	−	0.168389i	$-0.946143\pi$
$149$	−6.93266	+	9.03482i	−0.567946	+	0.740161i	0.417775	+	0.908551i	$0.362810\pi$
$150$	−0.613463	−	0.652169i	−0.0500891	−	0.0532494i
$151$	14.1741	−	3.79793i	1.15347	−	0.309071i	0.369115	−	0.929384i	$-0.379661\pi$
$151$	14.1741	−	3.79793i	1.15347	−	0.309071i	0.784355	+	0.620313i	$0.212994\pi$
$152$	−5.17797	−	4.41121i	−0.419989	−	0.357797i
$153$	4.36610	−	3.46659i	0.352978	−	0.280258i
$154$	−9.37654	−	5.08598i	−0.755583	−	0.409840i
$155$	−2.13528	+	16.2191i	−0.171510	+	1.30275i
$156$	8.04267	+	0.0319744i	0.643929	+	0.00256000i
$157$	−1.68402	+	0.221706i	−0.134400	+	0.0176941i	−0.197426	−	0.980318i	$-0.563258\pi$
$157$	−1.68402	+	0.221706i	−0.134400	+	0.0176941i	0.0630262	+	0.998012i	$0.479925\pi$
$158$	−11.7954	+	5.25755i	−0.938392	+	0.418268i
$159$	−0.880298	+	15.3813i	−0.0698121	+	1.21982i
$160$	7.95510	−	10.4122i	0.628906	−	0.823154i
$161$	−6.92155			−0.545494
$162$	8.33712	+	9.61730i	0.655026	+	0.755606i
$163$	−3.09378	+	7.46904i	−0.242323	+	0.585020i	−0.997513	−	0.0704864i	$-0.977545\pi$
$163$	−3.09378	+	7.46904i	−0.242323	+	0.585020i	0.755189	+	0.655507i	$0.227545\pi$
$164$	−24.7112	+	1.31572i	−1.92962	+	0.102741i
$165$	−5.66931	−	16.2577i	−0.441355	−	1.26566i
$166$	−0.131798	−	4.95423i	−0.0102295	−	0.384523i
$167$	−20.5475	−	5.50569i	−1.59001	−	0.426043i	−0.648007	−	0.761634i	$-0.724397\pi$
$167$	−20.5475	−	5.50569i	−1.59001	−	0.426043i	−0.942008	+	0.335591i	$0.891064\pi$
$168$	−4.13544	+	7.55231i	−0.319056	+	0.582673i
$169$	7.35024	−	1.96949i	0.565403	−	0.151499i
$170$	1.73138	+	5.83612i	0.132791	+	0.447610i
$171$	1.98249	+	6.93712i	0.151605	+	0.530495i
$172$	0.884889	+	4.75231i	0.0674721	+	0.362361i
$173$	−4.37183	+	3.35462i	−0.332384	+	0.255047i	−0.761447	−	0.648227i	$-0.775511\pi$
$173$	−4.37183	+	3.35462i	−0.332384	+	0.255047i	0.429063	+	0.903275i	$0.358844\pi$
$174$	11.2301	+	5.05920i	0.851354	+	0.383537i
$175$	−0.556377	+	0.321224i	−0.0420581	+	0.0242823i
$176$	15.0722	−	8.21611i	1.13611	−	0.619313i
$177$	−11.6142	−	23.0677i	−0.872977	−	1.73388i
$178$	−1.15654	−	7.28248i	−0.0866867	−	0.545845i
$179$	20.4046	+	8.45184i	1.52511	+	0.631721i	0.978607	−	0.205738i	$-0.0659594\pi$
$179$	20.4046	+	8.45184i	1.52511	+	0.631721i	0.546501	+	0.837458i	$0.315959\pi$
$180$	−13.1412	+	4.52403i	−0.979490	+	0.337201i
$181$	−7.15352	−	17.2701i	−0.531717	−	1.28368i	−0.930385	−	0.366583i	$-0.880528\pi$
$181$	−7.15352	−	17.2701i	−0.531717	−	1.28368i	0.398669	−	0.917095i	$-0.369472\pi$
$182$	1.34486	−	5.61205i	0.0996877	−	0.415993i
$183$	−4.62921	−	22.3057i	−0.342201	−	1.64888i
$184$	6.05481	−	9.34918i	0.446367	−	0.689230i
$185$	−7.87458	−	2.10999i	−0.578951	−	0.155129i
$186$	14.7102	+	9.10352i	1.07860	+	0.667502i
$187$	−1.04095	+	7.90679i	−0.0761218	+	0.578202i
$188$	−2.66919	+	12.6092i	−0.194671	+	0.919624i
$189$	8.08803	−	4.24151i	0.588318	−	0.308524i
$190$	−7.83538	−	0.820228i	−0.568438	−	0.0595056i
$191$	−7.49890	+	12.9885i	−0.542601	+	0.939813i	0.456152	+	0.889902i	$0.349227\pi$
$191$	−7.49890	+	12.9885i	−0.542601	+	0.939813i	−0.998754	+	0.0499114i	$0.984106\pi$
$192$	−6.58359	−	12.1925i	−0.475129	−	0.879916i
$193$	−0.624997	−	1.08253i	−0.0449883	−	0.0779220i	0.842654	−	0.538455i	$-0.180992\pi$
$193$	−0.624997	−	1.08253i	−0.0449883	−	0.0779220i	−0.887643	+	0.460533i	$0.847658\pi$
$194$	4.98928	+	11.1935i	0.358209	+	0.803649i
$195$	7.70197	−	5.23906i	0.551550	−	0.375177i
$196$	−5.81704	−	5.22891i	−0.415503	−	0.373494i
$197$	0.313242	−	0.129749i	0.0223176	−	0.00924423i	−0.371497	−	0.928434i	$-0.621155\pi$
$197$	0.313242	−	0.129749i	0.0223176	−	0.00924423i	0.393814	+	0.919190i	$0.371155\pi$
$198$	−18.1374	−	1.59550i	−1.28897	−	0.113387i
$199$	4.29098	−	4.29098i	0.304179	−	0.304179i	−0.538467	−	0.842646i	$-0.680996\pi$
$199$	4.29098	−	4.29098i	0.304179	−	0.304179i	0.842646	+	0.538467i	$0.180996\pi$
$200$	0.0528170	−	1.03252i	0.00373473	−	0.0730100i
$201$	8.51427	+	2.81180i	0.600550	+	0.198329i
$202$	8.78637	+	8.33099i	0.618207	+	0.586167i
$203$	5.38021	−	7.01162i	0.377617	−	0.492120i
$204$	6.37893	+	0.865616i	0.446615	+	0.0606052i
$205$	−22.7380	+	17.4475i	−1.58809	+	1.21858i
$206$	5.85785	−	4.74764i	0.408136	−	0.330784i
$207$	−10.8386	+	4.70125i	−0.753333	+	0.326759i
$208$	6.40394	+	6.72585i	0.444034	+	0.466354i
$209$	−8.93816	−	5.16045i	−0.618265	−	0.356956i
$210$	0.998827	+	9.92227i	0.0689256	+	0.684701i
$211$	−1.02001	−	7.74778i	−0.0702207	−	0.533379i	−0.990013	−	0.140974i	$-0.954977\pi$
$211$	−1.02001	−	7.74778i	−0.0702207	−	0.533379i	0.919793	−	0.392405i	$-0.128357\pi$
$212$	−13.5179	+	11.5649i	−0.928411	+	0.794278i
$213$	−1.82001	+	0.634664i	−0.124705	+	0.0434865i
$214$	−10.0866	−	2.41713i	−0.689504	−	0.165231i
$215$	3.95884	+	3.95884i	0.269990	+	0.269990i
$216$	−1.34608	+	14.6352i	−0.0915888	+	0.995797i
$217$	8.77716	−	8.77716i	0.595833	−	0.595833i
$218$	−21.4378	+	13.1494i	−1.45195	+	0.890592i
$219$	−5.55861	−	15.9403i	−0.375616	−	1.07714i
$220$	9.01122	−	17.7220i	0.607536	−	1.19482i
$221$	−4.27761	+	0.563159i	−0.287743	+	0.0378821i
$222$	−5.45469	+	6.67581i	−0.366095	+	0.448051i
$223$	8.01763	−	13.8869i	0.536900	−	0.929938i	−0.462169	−	0.886792i	$-0.652929\pi$
$223$	8.01763	−	13.8869i	0.536900	−	0.929938i	0.999069	−	0.0431461i	$-0.0137381\pi$
$224$	−9.59828	+	2.59331i	−0.641312	+	0.173273i
$225$	−0.653058	+	0.880913i	−0.0435372	+	0.0587275i
$226$	−1.24201	+	11.8645i	−0.0826172	+	0.789216i
$227$	−14.3169	−	18.6581i	−0.950243	−	1.23838i	−0.971118	−	0.238599i	$-0.923312\pi$
$227$	−14.3169	−	18.6581i	−0.950243	−	1.23838i	0.0208752	−	0.999782i	$-0.493355\pi$
$228$	−4.19414	+	7.19822i	−0.277764	+	0.476714i
$229$	−5.90651	−	4.53223i	−0.390313	−	0.299498i	0.394899	−	0.918725i	$-0.370780\pi$
$229$	−5.90651	−	4.53223i	−0.390313	−	0.299498i	−0.785212	+	0.619227i	$0.787446\pi$
$230$	−0.343072	−	12.8959i	−0.0226215	−	0.850332i
$231$	−4.09685	+	12.4055i	−0.269553	+	0.816220i
$232$	4.76436	+	13.4008i	0.312796	+	0.879809i
$233$	5.74620	+	5.74620i	0.376446	+	0.376446i	0.869818	−	0.493372i	$-0.164236\pi$
$233$	5.74620	+	5.74620i	0.376446	+	0.376446i	−0.493372	+	0.869818i	$0.664236\pi$
$234$	−1.70588	−	9.70147i	−0.111517	−	0.634205i
$235$	5.71247	+	13.7911i	0.372640	+	0.899633i
$236$	9.93132	−	28.1197i	0.646474	−	1.83044i
$237$	8.89574	+	13.0777i	0.577840	+	0.849487i
$238$	1.65352	−	4.31295i	0.107182	−	0.279567i
$239$	6.52718	−	3.76847i	0.422208	−	0.243762i	−0.273814	−	0.961783i	$-0.588285\pi$
$239$	6.52718	−	3.76847i	0.422208	−	0.243762i	0.696021	+	0.718021i	$0.254952\pi$
$240$	−14.2761	−	7.33063i	−0.921519	−	0.473190i
$241$	13.4698	+	7.77681i	0.867668	+	0.500948i	0.866573	−	0.499051i	$-0.166318\pi$
$241$	13.4698	+	7.77681i	0.867668	+	0.500948i	0.00109546	+	0.999999i	$0.499651\pi$
$242$	8.14916	−	6.60468i	0.523848	−	0.424565i
$243$	9.78428	−	12.1354i	0.627662	−	0.778486i
$244$	14.8814	−	21.6912i	0.952682	−	1.38864i
$245$	−8.98147	−	1.18243i	−0.573805	−	0.0755429i
$246$	6.94570	+	29.5012i	0.442842	+	1.88093i
$247$	1.44516	−	5.39340i	0.0919531	−	0.343174i
$248$	4.17756	+	19.5337i	0.265275	+	1.24039i
$249$	−5.94317	+	1.23342i	−0.376633	+	0.0781646i
$250$	7.93783	+	12.9413i	0.502033	+	0.818477i
$251$	4.10085	−	1.69863i	0.258843	−	0.107216i	−0.249488	−	0.968378i	$-0.580262\pi$
$251$	4.10085	−	1.69863i	0.258843	−	0.107216i	0.508332	+	0.861161i	$0.330262\pi$
$252$	10.0004	+	3.34674i	0.629967	+	0.210825i
$253$	6.46750	−	15.6139i	0.406608	−	0.981639i
$254$	−5.36124	+	7.38559i	−0.336394	+	0.463413i
$255$	6.65925	−	3.35281i	0.417018	−	0.209961i
$256$	4.89349	−	15.2333i	0.305843	−	0.952082i
$257$	−10.8708	−	18.8289i	−0.678105	−	1.17451i	−0.975551	−	0.219773i	$-0.929468\pi$
$257$	−10.8708	−	18.8289i	−0.678105	−	1.17451i	0.297446	−	0.954738i	$-0.403865\pi$
$258$	5.53645	−	2.09739i	0.344684	−	0.130578i
$259$	3.76568	+	4.90752i	0.233988	+	0.304939i
$260$	10.5228	+	2.22752i	0.652595	+	0.138145i
$261$	3.66253	−	14.6340i	0.226705	−	0.905820i
$262$	9.49978	−	17.5138i	0.586898	−	1.08201i
$263$	5.44235	+	20.3111i	0.335590	+	1.25244i	0.903228	+	0.429160i	$0.141190\pi$
$263$	5.44235	+	20.3111i	0.335590	+	1.25244i	−0.567638	+	0.823278i	$0.692143\pi$
$264$	−13.1727	−	16.3858i	−0.810722	−	1.00848i
$265$	−5.33267	+	19.9018i	−0.327583	+	1.22256i
$266$	4.33783	+	4.11301i	0.265970	+	0.252185i
$267$	−8.52736	+	2.97362i	−0.521866	+	0.181982i
$268$	4.46516	+	9.34135i	0.272753	+	0.570614i
$269$	25.8978	+	10.7272i	1.57902	+	0.654051i	0.988258	−	0.152796i	$-0.0488276\pi$
$269$	25.8978	+	10.7272i	1.57902	+	0.654051i	0.590761	+	0.806847i	$0.298828\pi$
$270$	8.30348	+	14.8590i	0.505334	+	0.904292i
$271$		−	23.6586i		−	1.43716i	−0.695446	−	0.718578i	$-0.744793\pi$
$271$		−	23.6586i		−	1.43716i	0.695446	−	0.718578i	$-0.255207\pi$
$272$	4.37919	+	6.00634i	0.265527	+	0.364188i
$273$	−7.05639	−	0.403849i	−0.427072	−	0.0244420i
$274$	8.19207	−	21.3677i	0.494901	−	1.29087i
$275$	−0.204753	−	1.55525i	−0.0123471	−	0.0937852i
$276$	−12.5826	−	5.27060i	−0.757385	−	0.317253i
$277$	−4.03808	−	0.531624i	−0.242625	−	0.0319422i	0.00823300	−	0.999966i	$-0.497379\pi$
$277$	−4.03808	−	0.531624i	−0.242625	−	0.0319422i	−0.250858	+	0.968024i	$0.580713\pi$
$278$	−8.86843	−	29.8936i	−0.531893	−	1.79290i
$279$	7.78269	−	19.7059i	0.465938	−	1.17976i
$280$	−7.46753	+	8.76554i	−0.446271	+	0.523841i
$281$	3.88392	+	14.4950i	0.231695	+	0.864699i	0.979611	+	0.200905i	$0.0643882\pi$
$281$	3.88392	+	14.4950i	0.231695	+	0.864699i	−0.747915	+	0.663794i	$0.768945\pi$
$282$	15.7780	+	0.482521i	0.939563	+	0.0287337i
$283$	−6.90282	−	5.29672i	−0.410330	−	0.314857i	0.382888	−	0.923795i	$-0.374929\pi$
$283$	−6.90282	−	5.29672i	−0.410330	−	0.314857i	−0.793218	+	0.608937i	$0.791596\pi$
$284$	−1.98393	−	1.00878i	−0.117725	−	0.0598602i
$285$	0.710763	+	9.62256i	0.0421020	+	0.569991i
$286$	11.4033	+	8.27770i	0.674290	+	0.489471i
$287$	21.7469			1.28368
$288$	−13.2687	+	10.5803i	−0.781865	+	0.623447i
$289$	13.5467			0.796862
$290$	13.3304	+	9.67663i	0.782789	+	0.568231i
$291$	12.4104	−	8.44183i	0.727510	−	0.494869i
$292$	8.83527	−	17.3760i	0.517045	−	1.01685i
$293$	7.03681	+	5.39954i	0.411095	+	0.315444i	0.793522	−	0.608541i	$-0.208245\pi$
$293$	7.03681	+	5.39954i	0.411095	+	0.315444i	−0.382427	+	0.923986i	$0.624912\pi$
$294$	−5.04117	+	8.14591i	−0.294007	+	0.475079i
$295$	−8.93940	−	33.3623i	−0.520472	−	1.94243i
$296$	−9.92289	+	0.793439i	−0.576757	+	0.0461177i
$297$	2.01071	+	22.2086i	0.116673	+	1.28867i
$298$	4.58058	+	15.4401i	0.265346	+	0.894423i
$299$	9.06497	+	1.19343i	0.524241	+	0.0690176i
$300$	−1.25604	+	0.160283i	−0.0725174	+	0.00925395i
$301$	−0.554488	−	4.21176i	−0.0319602	−	0.242762i
$302$	7.42887	−	19.3770i	0.427483	−	1.11502i
$303$	8.13634	−	12.3979i	0.467421	−	0.712242i
$304$	−9.35023	+	2.26129i	−0.536272	+	0.129694i
$305$		−	30.4662i		−	1.74449i
$306$	−0.340159	−	7.87683i	−0.0194456	−	0.450288i
$307$	−21.6584	−	8.97121i	−1.23611	−	0.512014i	−0.333614	−	0.942710i	$-0.608268\pi$
$307$	−21.6584	−	8.97121i	−1.23611	−	0.512014i	−0.902497	+	0.430696i	$0.858268\pi$
$308$	−13.6106	+	6.50584i	−0.775534	+	0.370705i
$309$	−6.99328	−	6.03123i	−0.397834	−	0.343105i
$310$	16.7883	+	15.9182i	0.953510	+	0.904092i
$311$	−2.12062	+	7.91425i	−0.120249	+	0.448776i	−0.999626	−	0.0273506i	$-0.991293\pi$
$311$	−2.12062	+	7.91425i	−0.120249	+	0.448776i	0.879377	+	0.476127i	$0.157960\pi$
$312$	6.71826	−	9.17803i	0.380347	−	0.519604i
$313$	−3.00966	−	11.2322i	−0.170116	−	0.634882i	−0.997332	−	0.0729977i	$-0.976743\pi$
$313$	−3.00966	−	11.2322i	−0.170116	−	0.634882i	0.827216	−	0.561884i	$-0.189923\pi$
$314$	−1.14531	+	2.11150i	−0.0646337	+	0.119159i
$315$	11.7435	−	3.35606i	0.661673	−	0.189093i
$316$	−3.78225	+	17.8673i	−0.212768	+	1.00512i
$317$	−2.53499	−	3.30366i	−0.142379	−	0.185552i	0.716720	−	0.697361i	$-0.245642\pi$
$317$	−2.53499	−	3.30366i	−0.142379	−	0.185552i	−0.859100	+	0.511808i	$0.828976\pi$
$318$	16.8721	+	13.7859i	0.946140	+	0.773075i
$319$	10.7899	+	18.6886i	0.604116	+	1.04636i
$320$	−5.30749	−	17.7546i	−0.296698	−	0.992510i
$321$	−0.725840	+	12.6825i	−0.0405125	+	0.707868i
$322$	−5.75026	+	7.92150i	−0.320449	+	0.441448i
$323$	1.71027	−	4.12896i	0.0951620	−	0.229741i
$324$	17.9330	−	1.55176i	0.996277	−	0.0862087i
$325$	0.784059	−	0.324768i	0.0434917	−	0.0180149i
$326$	5.97785	+	9.74584i	0.331082	+	0.539772i
$327$	20.4999	+	22.9888i	1.13365	+	1.27129i
$328$	−19.0237	+	29.3743i	−1.05041	+	1.62193i
$329$	2.93152	−	10.9406i	0.161620	−	0.603174i
$330$	−23.3164	−	7.01818i	−1.28353	−	0.386338i
$331$	−18.8304	−	2.47907i	−1.03501	−	0.136262i	−0.406173	−	0.913796i	$-0.633137\pi$
$331$	−18.8304	−	2.47907i	−1.03501	−	0.136262i	−0.628840	+	0.777534i	$0.716470\pi$
$332$	−5.77946	−	3.96502i	−0.317189	−	0.217609i
$333$	9.23002	+	5.12706i	0.505802	+	0.280961i
$334$	−23.3715	+	18.9420i	−1.27883	+	1.03646i
$335$	10.3849	+	5.99571i	0.567386	+	0.327581i
$336$	5.20776	+	11.0072i	0.284107	+	0.600490i
$337$	−25.9301	+	14.9707i	−1.41250	+	0.815508i	−0.995624	−	0.0934545i	$-0.970209\pi$
$337$	−25.9301	+	14.9707i	−1.41250	+	0.815508i	−0.416878	+	0.908963i	$0.636876\pi$
$338$	3.85239	−	10.0483i	0.209542	−	0.546557i
$339$	14.5707	−	1.07625i	0.791372	−	0.0584541i
$340$	8.11765	+	2.86700i	0.440242	+	0.155485i
$341$	11.5985	+	28.0013i	0.628095	+	1.51636i
$342$	9.58633	+	3.49430i	0.518369	+	0.188950i
$343$	13.5601	+	13.5601i	0.732176	+	0.732176i
$344$	6.17402	+	2.93538i	0.332881	+	0.158265i
$345$	−15.4702	+	3.21060i	−0.832885	+	0.172853i
$346$	0.207248	+	7.79037i	0.0111417	+	0.418813i
$347$	6.79457	+	5.21366i	0.364752	+	0.279884i	0.774834	−	0.632165i	$-0.217833\pi$
$347$	6.79457	+	5.21366i	0.364752	+	0.279884i	−0.410082	+	0.912048i	$0.634500\pi$
$348$	15.1198	−	8.64948i	0.810508	−	0.463661i
$349$	5.31013	+	6.92030i	0.284245	+	0.370435i	0.913552	−	0.406721i	$-0.133328\pi$
$349$	5.31013	+	6.92030i	0.284245	+	0.370435i	−0.629308	+	0.777156i	$0.716661\pi$
$350$	−0.0945936	+	0.903622i	−0.00505624	+	0.0483006i
$351$	−11.3240	+	4.16044i	−0.604431	+	0.222068i
$352$	3.11854	−	24.0754i	0.166219	−	1.28322i
$353$	0.687258	−	1.19037i	0.0365790	−	0.0633567i	−0.847156	−	0.531344i	$-0.821687\pi$
$353$	0.687258	−	1.19037i	0.0365790	−	0.0633567i	0.883735	+	0.467987i	$0.155021\pi$
$354$	−36.0491	−	5.87205i	−1.91599	−	0.312096i
$355$	−2.55568	+	0.336462i	−0.135641	+	0.0178575i
$356$	−9.29541	−	4.72649i	−0.492656	−	0.250503i
$357$	−5.55741	−	1.05768i	−0.294129	−	0.0559782i
$358$	26.6245	−	16.3308i	1.40715	−	0.863109i
$359$	5.66910	−	5.66910i	0.299204	−	0.299204i	−0.541498	−	0.840702i	$-0.682143\pi$
$359$	5.66910	−	5.66910i	0.299204	−	0.299204i	0.840702	+	0.541498i	$0.182143\pi$
$360$	−5.73982	+	18.7982i	−0.302515	+	0.990752i
$361$	−9.34529	−	9.34529i	−0.491857	−	0.491857i
$362$	−25.7081	−	6.16063i	−1.35119	−	0.323796i
$363$	−9.72871	−	8.39036i	−0.510625	−	0.440380i
$364$	−5.30554	−	6.20151i	−0.278086	−	0.325048i
$365$	−2.94685	−	22.3836i	−0.154245	−	1.17161i
$366$	−29.3740	−	13.2331i	−1.53541	−	0.691703i
$367$	−30.7867	−	17.7747i	−1.60705	−	0.927832i	−0.990025	−	0.140890i	$-0.955004\pi$
$367$	−30.7867	−	17.7747i	−1.60705	−	0.927832i	−0.617027	−	0.786942i	$-0.711663\pi$
$368$	−5.66965	−	14.6966i	−0.295551	−	0.766115i
$369$	34.0539	−	14.7709i	1.77277	−	0.768944i
$370$	−8.95683	+	7.25929i	−0.465644	+	0.377392i
$371$	12.4030	−	9.51717i	0.643933	−	0.494107i
$372$	22.6396	−	9.27233i	1.17381	−	0.480748i
$373$	−14.1600	+	18.4537i	−0.733178	+	0.955496i	−0.999966	−	0.00825904i	$-0.997371\pi$
$373$	−14.1600	+	18.4537i	−0.733178	+	0.955496i	0.266788	+	0.963755i	$0.414038\pi$
$374$	8.18429	+	7.76012i	0.423199	+	0.401266i
$375$	13.8775	−	12.3751i	0.716633	−	0.639045i
$376$	12.2134	+	13.5303i	0.629858	+	0.697771i
$377$	−8.25528	+	8.25528i	−0.425169	+	0.425169i
$378$	1.86507	−	12.7803i	0.0959290	−	0.657345i
$379$	−5.76133	+	2.38642i	−0.295939	+	0.122582i	−0.525713	−	0.850662i	$-0.676201\pi$
$379$	−5.76133	+	2.38642i	−0.295939	+	0.122582i	0.229774	+	0.973244i	$0.426201\pi$
$380$	−7.44818	+	8.28592i	−0.382083	+	0.425059i
$381$	10.0653	+	4.86047i	0.515662	+	0.249009i
$382$	8.63500	+	19.3728i	0.441805	+	0.991198i
$383$	−14.3541	−	24.8620i	−0.733458	−	1.27039i	−0.955396	−	0.295326i	$-0.904572\pi$
$383$	−14.3541	−	24.8620i	−0.733458	−	1.27039i	0.221938	−	0.975061i	$-0.428762\pi$
$384$	−19.4234	−	2.59451i	−0.991196	−	0.132401i
$385$	−8.73588	+	15.1310i	−0.445222	+	0.771147i
$386$	−1.75815	−	0.184048i	−0.0894876	−	0.00936780i
$387$	−3.72899	−	6.21864i	−0.189555	−	0.316111i
$388$	16.9556	+	3.58926i	0.860792	+	0.182217i
$389$	−0.287817	+	2.18619i	−0.0145929	+	0.110844i	−0.997191	−	0.0749000i	$-0.976136\pi$
$389$	−0.287817	+	2.18619i	−0.0145929	+	0.110844i	0.982598	+	0.185744i	$0.0594696\pi$
$390$	0.402678	−	13.1672i	0.0203904	−	0.666745i
$391$	7.06884	+	1.89409i	0.357487	+	0.0957882i
$392$	−10.8170	+	2.31337i	−0.546340	+	0.116843i
$393$	−23.1714	−	7.65224i	−1.16884	−	0.386004i
$394$	0.111740	−	0.466288i	0.00562939	−	0.0234913i
$395$	8.09458	+	19.5420i	0.407282	+	0.983267i
$396$	−16.8941	+	19.4322i	−0.848961	+	0.976503i
$397$	6.18835	+	2.56330i	0.310584	+	0.128648i	0.532531	−	0.846411i	$-0.321241\pi$
$397$	6.18835	+	2.56330i	0.310584	+	0.128648i	−0.221947	+	0.975059i	$0.571241\pi$
$398$	−1.34605	−	8.47573i	−0.0674712	−	0.424850i
$399$	4.01692	−	6.12086i	0.201097	−	0.306426i
$400$	−1.13781	−	0.918239i	−0.0568903	−	0.0459119i
$401$	−2.39063	+	1.38023i	−0.119382	+	0.0689254i	−0.558502	−	0.829503i	$-0.688624\pi$
$401$	−2.39063	+	1.38023i	−0.119382	+	0.0689254i	0.439120	+	0.898429i	$0.355290\pi$
$402$	10.2915	−	7.40834i	0.513292	−	0.369494i
$403$	−13.0086	+	9.98185i	−0.648005	+	0.497231i
$404$	16.8341	−	3.13453i	0.837526	−	0.155949i
$405$	16.1099	−	13.2318i	0.800507	−	0.657491i
$406$	−3.55484	−	11.9826i	−0.176424	−	0.594685i
$407$	−14.5893	+	3.90918i	−0.723163	+	0.193771i
$408$	6.29014	−	6.58136i	0.311408	−	0.325826i
$409$	−12.1909	−	3.26654i	−0.602801	−	0.161520i	−0.0555039	−	0.998458i	$-0.517677\pi$
$409$	−12.1909	−	3.26654i	−0.602801	−	0.161520i	−0.547297	+	0.836938i	$0.684343\pi$
$410$	1.07790	+	40.5179i	0.0532338	+	2.00104i
$411$	−27.5331	−	5.24006i	−1.35811	−	0.258473i
$412$	−0.566961	−	10.6484i	−0.0279322	−	0.524607i
$413$	−10.0291	+	24.2125i	−0.493502	+	1.19142i
$414$	−3.62400	+	16.3101i	−0.178110	+	0.801598i
$415$	−8.11747			−0.398471
$416$	13.0178	−	1.74144i	0.638249	−	0.0853810i
$417$	−34.1098	+	17.1737i	−1.67036	+	0.840998i
$418$	−13.3316	+	5.94227i	−0.652069	+	0.290646i
$419$	−1.70659	+	0.224677i	−0.0833725	+	0.0109762i	−0.172097	−	0.985080i	$-0.555054\pi$
$419$	−1.70659	+	0.224677i	−0.0833725	+	0.0109762i	0.0887245	+	0.996056i	$0.471721\pi$
$420$	12.1855	+	7.10006i	0.594593	+	0.346448i
$421$	4.47164	−	33.9655i	0.217934	−	1.65537i	−0.436832	−	0.899543i	$-0.643899\pi$
$421$	4.47164	−	33.9655i	0.217934	−	1.65537i	0.654766	−	0.755832i	$-0.272767\pi$
$422$	−9.71450	−	5.26930i	−0.472895	−	0.256506i
$423$	−2.84054	−	19.1232i	−0.138112	−	0.929801i
$424$	2.00530	+	25.0786i	0.0973858	+	1.21793i
$425$	0.656120	−	0.175807i	0.0318265	−	0.00852789i
$426$	−0.785666	+	2.61021i	−0.0380656	+	0.126465i
$427$	−14.0727	+	18.3399i	−0.681026	+	0.887530i
$428$	−11.1460	+	9.53569i	−0.538763	+	0.460925i
$429$	7.50451	−	15.5407i	0.362321	−	0.750314i
$430$	7.81967	−	1.24186i	0.377098	−	0.0598877i
$431$		−	6.06871i		−	0.292319i	−0.989261	−	0.146160i	$-0.953309\pi$
$431$		−	6.06871i		−	0.292319i	0.989261	−	0.146160i	$-0.0466913\pi$
$432$	15.6312	+	13.6991i	0.752057	+	0.659098i
$433$			22.3463i			1.07390i	0.843615	+	0.536948i	$0.180423\pi$
$433$			22.3463i			1.07390i	−0.843615	+	0.536948i	$0.819577\pi$
$434$	−2.75333	−	17.3371i	−0.132164	−	0.832205i
$435$	8.77277	−	18.1671i	0.420622	−	0.871047i
$436$	−2.76095	+	35.4592i	−0.132226	+	1.69819i
$437$	−5.76550	+	7.51375i	−0.275801	+	0.359431i
$438$	−22.8611	−	6.88114i	−1.09235	−	0.328794i
$439$	3.99922	−	1.07159i	0.190872	−	0.0511440i	−0.162117	−	0.986772i	$-0.551832\pi$
$439$	3.99922	−	1.07159i	0.190872	−	0.0511440i	0.352989	+	0.935628i	$0.385165\pi$
$440$	−12.7960	−	25.0361i	−0.610026	−	1.19355i
$441$	10.9124	+	4.30975i	0.519637	+	0.205226i
$442$	−2.90922	+	5.36346i	−0.138378	+	0.255114i
$443$	−2.96177	+	22.4968i	−0.140718	+	1.06886i	0.764715	+	0.644368i	$0.222880\pi$
$443$	−2.96177	+	22.4968i	−0.140718	+	1.06886i	−0.905433	+	0.424489i	$0.860454\pi$
$444$	3.10863	+	11.7888i	0.147529	+	0.559473i
$445$	−11.9742	+	1.57644i	−0.567633	+	0.0747304i
$446$	−9.23231	−	20.7129i	−0.437163	−	0.980783i
$447$	17.6178	−	8.87026i	0.833294	−	0.419549i
$448$	−5.00607	+	13.1394i	−0.236514	+	0.620779i
$449$	−30.9160			−1.45901			−0.729507	−	0.683973i	$-0.760251\pi$
$449$	−30.9160			−1.45901			−0.729507	+	0.683973i	$0.760251\pi$
$450$	0.465632	+	1.47925i	0.0219501	+	0.0697324i
$451$	−20.3203	+	49.0576i	−0.956847	+	2.31003i
$452$	12.5467	+	11.2782i	0.590149	+	0.530482i
$453$	−24.9681	−	4.75188i	−1.17310	−	0.223263i
$454$	−33.2477	+	0.884494i	−1.56039	+	0.0415114i
$455$	−9.13023	−	2.44644i	−0.428032	−	0.114691i
$456$	4.75375	+	10.7802i	0.222615	+	0.504828i
$457$	14.5332	−	3.89417i	0.679836	−	0.182161i	0.0976544	−	0.995220i	$-0.468866\pi$
$457$	14.5332	−	3.89417i	0.679836	−	0.182161i	0.582181	+	0.813059i	$0.302199\pi$
$458$	−10.0940	+	2.99455i	−0.471661	+	0.139926i
$459$	−9.42084	+	2.11847i	−0.439727	+	0.0988817i
$460$	−15.0440	−	10.3210i	−0.701430	−	0.481219i
$461$	4.99081	−	3.82958i	0.232445	−	0.178361i	−0.485971	−	0.873975i	$-0.661534\pi$
$461$	4.99081	−	3.82958i	0.232445	−	0.178361i	0.718416	+	0.695614i	$0.244867\pi$
$462$	10.7941	+	14.9949i	0.502188	+	0.697626i
$463$	34.3974	−	19.8593i	1.59858	−	0.922941i	0.606819	−	0.794840i	$-0.292445\pi$
$463$	34.3974	−	19.8593i	1.59858	−	0.922941i	0.991761	−	0.128101i	$-0.0408882\pi$
$464$	19.2950	+	5.68045i	0.895747	+	0.263708i
$465$	15.5463	−	23.6889i	0.720940	−	1.09855i
$466$	11.3502	−	1.80254i	0.525786	−	0.0835011i
$467$	−25.1605	−	10.4218i	−1.16429	−	0.482265i	−0.284989	−	0.958531i	$-0.591990\pi$
$467$	−25.1605	−	10.4218i	−1.16429	−	0.482265i	−0.879301	+	0.476266i	$0.841990\pi$
$468$	−12.5202	−	6.10743i	−0.578748	−	0.282316i
$469$	−3.48195	−	8.40617i	−0.160782	−	0.388161i
$470$	20.5293	+	4.91960i	0.946946	+	0.226924i
$471$	2.79359	+	0.922569i	0.128722	+	0.0425097i
$472$	−23.9314	−	34.7273i	−1.10153	−	1.59845i
$473$	10.0192	+	2.68463i	0.460682	+	0.123439i
$474$	22.3574	+	0.683733i	1.02691	+	0.0314049i
$475$	−0.114742	+	0.871553i	−0.00526473	+	0.0399896i
$476$	−3.56233	−	5.47551i	−0.163279	−	0.250969i
$477$	12.9579	−	23.3275i	0.593300	−	1.06809i
$478$	1.10973	−	10.6009i	0.0507579	−	0.484874i
$479$	5.20509	−	9.01548i	0.237827	−	0.411928i	−0.722264	−	0.691618i	$-0.756898\pi$
$479$	5.20509	−	9.01548i	0.237827	−	0.411928i	0.960090	+	0.279690i	$0.0902317\pi$
$480$	−20.2499	+	10.2485i	−0.924279	+	0.467776i
$481$	−4.08564	−	7.07654i	−0.186289	−	0.322663i
$482$	20.0907	−	8.95501i	0.915108	−	0.407890i
$483$	10.7957	+	5.21315i	0.491220	+	0.237207i
$484$	−0.788728	−	14.8135i	−0.0358513	−	0.673340i
$485$	18.5449	−	7.68155i	0.842080	−	0.348801i
$486$	−5.76005	−	21.2796i	−0.261281	−	0.965263i
$487$	−2.62552	+	2.62552i	−0.118974	+	0.118974i	−0.764087	−	0.645113i	$-0.776810\pi$
$487$	−2.62552	+	2.62552i	−0.118974	+	0.118974i	0.645113	+	0.764087i	$0.276810\pi$
$488$	−12.4619	−	35.0518i	−0.564122	−	1.58672i
$489$	10.4509	−	9.31944i	0.472608	−	0.421440i
$490$	−8.81486	+	9.29668i	−0.398215	+	0.419981i
$491$	−10.7896	+	14.0613i	−0.486928	+	0.634577i	−0.970607	−	0.240668i	$-0.922633\pi$
$491$	−10.7896	+	14.0613i	−0.486928	+	0.634577i	0.483680	+	0.875245i	$0.339300\pi$
$492$	39.5336	+	16.5598i	1.78231	+	0.746572i
$493$	−7.41344	+	5.68853i	−0.333885	+	0.256199i
$494$	−4.97197	−	6.13465i	−0.223700	−	0.276011i
$495$	−3.40240	+	29.6275i	−0.152927	+	1.33166i
$496$	25.8263	+	11.4470i	1.15964	+	0.513988i
$497$	1.69387	+	0.977958i	0.0759806	+	0.0438674i
$498$	−3.52584	+	7.82647i	−0.157997	+	0.350713i
$499$	2.87974	+	21.8738i	0.128915	+	0.979206i	0.926578	+	0.376102i	$0.122736\pi$
$499$	2.87974	+	21.8738i	0.128915	+	0.979206i	−0.797663	+	0.603103i	$0.793931\pi$
$500$	21.4054	+	1.66669i	0.957280	+	0.0745364i
$501$	27.9016	+	24.0633i	1.24655	+	1.07507i
$502$	1.46286	−	6.10447i	0.0652908	−	0.272456i
$503$	−11.3945	−	11.3945i	−0.508054	−	0.508054i	0.405875	−	0.913929i	$-0.366967\pi$
$503$	−11.3945	−	11.3945i	−0.508054	−	0.508054i	−0.913929	+	0.405875i	$0.866967\pi$
$504$	12.1383	−	8.66477i	0.540685	−	0.385959i
$505$	14.0233	−	14.0233i	0.624031	−	0.624031i
$506$	−12.4966	−	20.3735i	−0.555542	−	0.905714i
$507$	−12.9477	−	2.46418i	−0.575027	−	0.109438i
$508$	3.99859	+	12.2716i	0.177409	+	0.544462i
$509$	35.6378	−	4.69180i	1.57962	−	0.207960i	0.710908	−	0.703285i	$-0.248284\pi$
$509$	35.6378	−	4.69180i	1.57962	−	0.207960i	0.868708	+	0.495325i	$0.164951\pi$
$510$	1.69516	−	10.4067i	0.0750629	−	0.460819i
$511$	−8.56531	+	14.8355i	−0.378907	+	0.656286i
$512$	−13.3687	−	18.2559i	−0.590817	−	0.806806i
$513$	2.13275	−	12.3131i	0.0941633	−	0.543638i
$514$	−30.5803	−	3.20123i	−1.34884	−	0.141200i
$515$	−7.51832	−	9.79807i	−0.331297	−	0.431754i
$516$	2.19916	−	8.07875i	0.0968124	−	0.355647i
$517$	21.9410	+	16.8359i	0.964965	+	0.740444i
$518$	8.74495	−	0.232643i	0.384231	−	0.0102218i
$519$	9.34546	−	1.93951i	0.410220	−	0.0851350i
$520$	11.2914	−	10.1924i	0.495161	−	0.446968i
$521$	−8.86700	−	8.86700i	−0.388470	−	0.388470i	0.485671	−	0.874142i	$-0.338575\pi$
$521$	−8.86700	−	8.86700i	−0.388470	−	0.388470i	−0.874142	+	0.485671i	$0.838575\pi$
$522$	−13.7054	−	16.3492i	−0.599868	−	0.715586i
$523$	6.58354	+	15.8941i	0.287878	+	0.695000i	0.999975	−	0.00708176i	$-0.00225421\pi$
$523$	6.58354	+	15.8941i	0.287878	+	0.695000i	−0.712097	+	0.702081i	$0.752254\pi$
$524$	−12.1518	−	25.4223i	−0.530856	−	1.11058i
$525$	1.10973	−	0.0819694i	0.0484326	−	0.00357744i
$526$	27.7669	+	10.6454i	1.21069	+	0.464162i
$527$	−11.3658	+	6.56206i	−0.495103	+	0.285848i
$528$	−29.6966	+	1.46279i	−1.29238	+	0.0636599i
$529$	6.48785	+	3.74576i	0.282080	+	0.162859i
$530$	18.3467	+	22.6370i	0.796932	+	0.983290i
$531$	0.740789	+	44.7268i	0.0321475	+	1.94098i
$532$	8.31099	−	1.54752i	0.360327	−	0.0670935i
$533$	−28.4814	−	3.74964i	−1.23367	−	0.162415i
$534$	−3.68111	+	12.2297i	−0.159297	+	0.529231i
$535$	−4.39700	+	16.4098i	−0.190099	+	0.709459i
$536$	14.4004	+	2.65034i	0.622005	+	0.114477i
$537$	−25.4596	−	28.5508i	−1.09866	−	1.23206i
$538$	33.7923	−	20.7273i	1.45689	−	0.893619i
$539$	−15.5060	+	6.42280i	−0.667891	+	0.276650i
$540$	23.9040	+	2.84146i	1.02867	+	0.122277i
$541$	−7.03001	+	16.9719i	−0.302244	+	0.729681i	0.697668	+	0.716421i	$0.254221\pi$
$541$	−7.03001	+	16.9719i	−0.302244	+	0.729681i	−0.999912	+	0.0132601i	$0.995779\pi$
$542$	−27.0765	−	19.6550i	−1.16304	−	0.844254i
$543$	−1.84998	+	32.3244i	−0.0793902	+	1.38717i
$544$	10.5122	−	0.0219146i	0.450707	−	0.000939581i
$545$	20.5962	+	35.6737i	0.882245	+	1.52809i
$546$	−6.32447	+	7.74031i	−0.270662	+	0.331255i
$547$	−0.688805	−	0.897668i	−0.0294512	−	0.0383815i	0.778396	−	0.627774i	$-0.216034\pi$
$547$	−0.688805	−	0.897668i	−0.0294512	−	0.0383815i	−0.807847	+	0.589393i	$0.799367\pi$
$548$	−17.6489	−	27.1274i	−0.753923	−	1.15882i
$549$	−9.57987	+	38.2772i	−0.408859	+	1.63363i
$550$	−1.95004	−	1.05773i	−0.0831500	−	0.0451019i
$551$	−3.12993	−	11.6811i	−0.133340	−	0.497630i
$552$	−16.4854	+	10.0217i	−0.701665	+	0.426554i
$553$	4.15397	−	15.5028i	0.176645	−	0.659247i
$554$	−3.96317	+	4.17980i	−0.168379	+	0.177583i
$555$	10.6929	+	9.22194i	0.453890	+	0.391450i
$556$	−41.5799	−	14.6852i	−1.76338	−	0.622792i
$557$	22.7424	+	9.42021i	0.963626	+	0.399147i	0.808336	−	0.588722i	$-0.200369\pi$
$557$	22.7424	+	9.42021i	0.963626	+	0.399147i	0.155290	+	0.987869i	$0.450369\pi$
$558$	−16.0872	−	25.2783i	−0.681024	−	1.07012i
$559$			5.61164i			0.237347i
$560$	3.82803	+	15.8286i	0.161764	+	0.668879i
$561$	7.57881	−	11.5484i	0.319977	−	0.487572i
$562$	19.8157	+	7.59707i	0.835877	+	0.320463i
$563$	1.37291	+	10.4283i	0.0578615	+	0.439501i	0.995715	+	0.0924711i	$0.0294766\pi$
$563$	1.37291	+	10.4283i	0.0578615	+	0.439501i	−0.937854	+	0.347030i	$0.887190\pi$
$564$	13.6602	−	17.6565i	0.575198	−	0.743473i
$565$	19.3721	+	2.55038i	0.814990	+	0.107295i
$566$	−11.7966	+	3.49967i	−0.495850	+	0.147102i
$567$	−15.8097	+	0.523841i	−0.663944	+	0.0219992i
$568$	−2.80273	+	1.43248i	−0.117600	+	0.0601055i
$569$	6.74726	+	25.1811i	0.282860	+	1.05565i	0.950389	+	0.311064i	$0.100685\pi$
$569$	6.74726	+	25.1811i	0.282860	+	1.05565i	−0.667529	+	0.744584i	$0.732648\pi$
$570$	11.6032	+	7.18075i	0.486005	+	0.300769i
$571$	−1.21106	−	0.929276i	−0.0506811	−	0.0388890i	0.583110	−	0.812393i	$-0.301836\pi$
$571$	−1.21106	−	0.929276i	−0.0506811	−	0.0388890i	−0.633791	+	0.773504i	$0.718502\pi$
$572$	18.9472	−	6.17377i	0.792220	−	0.258138i
$573$	21.4788	−	14.6104i	0.897290	−	0.610357i
$574$	18.0668	−	24.8887i	0.754095	−	1.03883i
$575$	−1.43948			−0.0600303
$576$	1.08545	+	23.9754i	0.0452272	+	0.998977i
$577$	−7.93730			−0.330434			−0.165217	−	0.986257i	$-0.552832\pi$
$577$	−7.93730			−0.330434			−0.165217	+	0.986257i	$0.552832\pi$
$578$	11.2542	−	15.5037i	0.468115	−	0.644870i
$579$	0.159486	+	2.15917i	0.00662800	+	0.0897321i
$580$	22.1492	−	7.21714i	0.919696	−	0.299675i
$581$	4.88652	+	3.74956i	0.202727	+	0.155558i
$582$	0.648845	−	21.2166i	0.0268955	−	0.879456i
$583$	9.87986	+	36.8721i	0.409182	+	1.52709i
$584$	−12.5462	−	24.5473i	−0.519164	−	1.01577i
$585$	−15.9589	+	2.37051i	−0.659817	+	0.0980086i
$586$	12.0256	−	3.56761i	0.496774	−	0.147377i
$587$	35.8443	+	4.71899i	1.47945	+	0.194774i	0.826633	−	0.562741i	$-0.190253\pi$
$587$	35.8443	+	4.71899i	1.47945	+	0.194774i	0.652819	+	0.757514i	$0.273586\pi$
$588$	5.13465	+	12.5369i	0.211750	+	0.517013i
$589$	−2.21694	−	16.8393i	−0.0913474	−	0.693852i
$590$	−45.6087	−	17.4857i	−1.87768	−	0.719877i
$591$	−0.586293	−	0.0335546i	−0.0241169	−	0.00138025i
$592$	−7.33564	+	12.0156i	−0.301493	+	0.493839i
$593$		−	3.46481i		−	0.142283i	−0.997466	−	0.0711414i	$-0.977336\pi$
$593$		−	3.46481i		−	0.142283i	0.997466	−	0.0711414i	$-0.0226641\pi$
$594$	27.0875	+	16.1492i	1.11141	+	0.662610i
$595$	−6.98972	−	2.89524i	−0.286551	−	0.118693i
$596$	21.4762	+	7.58497i	0.879699	+	0.310693i
$597$	−9.92458	+	3.46085i	−0.406186	+	0.141643i
$598$	8.89681	−	9.38311i	0.363818	−	0.383704i
$599$	−3.63671	+	13.5724i	−0.148592	+	0.554552i	0.850977	+	0.525202i	$0.176010\pi$
$599$	−3.63671	+	13.5724i	−0.148592	+	0.554552i	−0.999569	+	0.0293500i	$0.990656\pi$
$600$	−0.860048	+	1.57066i	−0.0351113	+	0.0641218i
$601$	4.39361	+	16.3972i	0.179219	+	0.668854i	0.995794	+	0.0916156i	$0.0292031\pi$
$601$	4.39361	+	16.3972i	0.179219	+	0.668854i	−0.816576	+	0.577239i	$0.804130\pi$
$602$	−5.28088	−	2.86443i	−0.215233	−	0.116746i
$603$	−11.1621	−	10.7984i	−0.454555	−	0.439743i
$604$	−16.0047	−	24.6001i	−0.651221	−	1.00096i
$605$	−10.4591	−	13.6306i	−0.425224	−	0.554162i
$606$	−7.42955	−	19.6117i	−0.301805	−	0.796671i
$607$	11.5502	+	20.0056i	0.468809	+	0.812001i	0.999364	−	0.0356492i	$-0.0113499\pi$
$607$	11.5502	+	20.0056i	0.468809	+	0.812001i	−0.530555	+	0.847650i	$0.678017\pi$
$608$	−5.17998	+	12.5797i	−0.210076	+	0.510173i
$609$	−13.6726	+	6.88392i	−0.554042	+	0.278950i
$610$	−34.8676	−	25.3106i	−1.41175	−	1.02480i
$611$	−5.72573	+	13.8231i	−0.231638	+	0.559224i
$612$	−9.29738	−	6.15459i	−0.375825	−	0.248784i
$613$	31.7359	−	13.1454i	1.28180	−	0.530940i	0.365270	−	0.930902i	$-0.380977\pi$
$613$	31.7359	−	13.1454i	1.28180	−	0.530940i	0.916532	+	0.399962i	$0.130977\pi$
$614$	−28.2606	+	17.3343i	−1.14050	+	0.699556i
$615$	48.6059	−	10.0874i	1.95998	−	0.406764i
$616$	−3.86160	+	20.9818i	−0.155588	+	0.845379i
$617$	2.69022	−	10.0400i	0.108304	−	0.404196i	−0.890395	−	0.455189i	$-0.849572\pi$
$617$	2.69022	−	10.0400i	0.108304	−	0.404196i	0.998699	+	0.0509925i	$0.0162384\pi$
$618$	−12.7124	+	2.99299i	−0.511368	+	0.120396i
$619$	−14.1656	−	1.86494i	−0.569364	−	0.0749582i	−0.159653	−	0.987173i	$-0.551037\pi$
$619$	−14.1656	−	1.86494i	−0.569364	−	0.0749582i	−0.409712	+	0.912215i	$0.634371\pi$
$620$	32.1652	−	5.98921i	1.29178	−	0.240532i
$621$	20.4460	+	0.830734i	0.820470	+	0.0333362i
$622$	7.29586	+	9.00196i	0.292537	+	0.360946i
$623$	7.93638	+	4.58207i	0.317964	+	0.183577i
$624$	−4.92260	−	15.3137i	−0.197062	−	0.613040i
$625$	23.1177	−	13.3470i	0.924708	−	0.533881i
$626$	−15.3553	−	5.88699i	−0.613720	−	0.235291i
$627$	10.0543	+	14.7809i	0.401530	+	0.590291i
$628$	1.46505	+	3.06496i	0.0584618	+	0.122305i
$629$	−2.50286	−	6.04244i	−0.0997956	−	0.240928i
$630$	5.91534	−	16.2282i	0.235673	−	0.646549i
$631$	−13.2206	−	13.2206i	−0.526306	−	0.526306i	0.393163	−	0.919469i	$-0.371381\pi$
$631$	−13.2206	−	13.2206i	−0.526306	−	0.526306i	−0.919469	+	0.393163i	$0.871381\pi$
$632$	17.3064	+	19.1724i	0.688412	+	0.762638i
$633$	−4.24452	+	12.8526i	−0.168704	+	0.510846i
$634$	−5.88696	+	0.156612i	−0.233801	+	0.00621984i
$635$	11.8592	+	9.09985i	0.470616	+	0.361117i
$636$	29.7945	−	7.85659i	1.18143	−	0.311534i
$637$	−5.52756	−	7.20365i	−0.219010	−	0.285419i
$638$	30.3525	+	3.17738i	1.20167	+	0.125794i
$639$	3.31671	+	0.380890i	0.131207	+	0.0150678i
$640$	−24.7289	−	8.67582i	−0.977495	−	0.342942i
$641$	24.8380	−	43.0207i	0.981042	−	1.69921i	0.322687	−	0.946506i	$-0.395414\pi$
$641$	24.8380	−	43.0207i	0.981042	−	1.69921i	0.658354	−	0.752708i	$-0.271253\pi$
$642$	13.9117	+	11.3670i	0.549051	+	0.448620i
$643$	12.8341	−	1.68965i	0.506129	−	0.0666331i	0.126862	−	0.991920i	$-0.459510\pi$
$643$	12.8341	−	1.68965i	0.506129	−	0.0666331i	0.379267	+	0.925287i	$0.376176\pi$
$644$	4.28873	+	13.1620i	0.169000	+	0.518655i
$645$	−3.19297	−	9.15638i	−0.125723	−	0.360532i
$646$	−3.30461	−	5.38759i	−0.130018	−	0.211972i
$647$	−2.03731	+	2.03731i	−0.0800948	+	0.0800948i	−0.746019	−	0.665924i	$-0.768037\pi$
$647$	−2.03731	+	2.03731i	−0.0800948	+	0.0800948i	0.665924	+	0.746019i	$0.268037\pi$
$648$	13.1224	−	21.8129i	0.515495	−	0.856892i
$649$	−45.2484	−	45.2484i	−1.77615	−	1.77615i
$650$	0.279691	−	1.16714i	0.0109704	−	0.0457790i
$651$	−20.3007	+	7.07915i	−0.795646	+	0.277454i
$652$	16.1201	+	1.25515i	0.631311	+	0.0491556i
$653$	3.71856	+	28.2453i	0.145519	+	1.10532i	0.895880	+	0.444295i	$0.146546\pi$
$653$	3.71856	+	28.2453i	0.145519	+	1.10532i	−0.750362	+	0.661027i	$0.770121\pi$
$654$	43.3409	−	4.36292i	1.69476	−	0.170604i
$655$	−28.2622	−	16.3172i	−1.10430	−	0.637566i
$656$	17.8135	+	46.1756i	0.695502	+	1.80285i
$657$	−3.33597	+	29.0490i	−0.130149	+	1.13331i
$658$	−10.0857	−	12.4442i	−0.393182	−	0.485126i
$659$	4.14294	−	3.17899i	0.161386	−	0.123836i	−0.524911	−	0.851157i	$-0.675902\pi$
$659$	4.14294	−	3.17899i	0.161386	−	0.123836i	0.686297	+	0.727321i	$0.259235\pi$
$660$	−27.4028	+	20.8544i	−1.06665	+	0.811755i
$661$	11.2302	−	14.6355i	0.436806	−	0.569256i	−0.522135	−	0.852863i	$-0.674864\pi$
$661$	11.2302	−	14.6355i	0.436806	−	0.569256i	0.958941	+	0.283607i	$0.0915310\pi$
$662$	−18.4811	+	19.4913i	−0.718288	+	0.757550i
$663$	7.09604	+	2.34343i	0.275587	+	0.0910114i
$664$	−9.33928	+	3.32037i	−0.362434	+	0.128855i
$665$	6.92333	−	6.92333i	0.268475	−	0.268475i
$666$	13.5358	−	6.30404i	0.524504	−	0.244277i
$667$	18.2950	−	7.57806i	0.708387	−	0.293423i
$668$	2.26205	+	42.4845i	0.0875212	+	1.64378i
$669$	−22.9646	+	15.6210i	−0.887862	+	0.603944i
$670$	15.4894	−	6.90407i	0.598409	−	0.266728i
$671$	−28.2224	−	48.8827i	−1.08951	−	1.88709i
$672$	16.9239	+	3.18437i	0.652852	+	0.122840i
$673$	25.3190	−	43.8538i	0.975976	−	1.69044i	0.299299	−	0.954159i	$-0.403247\pi$
$673$	25.3190	−	43.8538i	0.975976	−	1.69044i	0.676677	−	0.736280i	$-0.263419\pi$
$674$	−4.40856	+	42.1135i	−0.169811	+	1.62215i
$675$	1.68207	−	0.882108i	0.0647429	−	0.0339523i
$676$	−8.29954	−	12.7569i	−0.319213	−	0.490649i
$677$	−4.63871	+	35.2345i	−0.178280	+	1.35417i	0.635095	+	0.772434i	$0.280961\pi$
$677$	−4.63871	+	35.2345i	−0.178280	+	1.35417i	−0.813375	+	0.581739i	$0.802372\pi$
$678$	10.8733	−	17.5699i	0.417585	−	0.674766i
$679$	−14.7118	−	3.94201i	−0.564586	−	0.151280i
$680$	10.0251	−	6.90857i	0.384447	−	0.264932i
$681$	8.27743	+	39.8845i	0.317192	+	1.52838i
$682$	41.6824	+	9.98868i	1.59610	+	0.382486i
$683$	−8.93273	−	21.5655i	−0.341801	−	0.825182i	−0.997534	−	0.0701882i	$-0.977640\pi$
$683$	−8.93273	−	21.5655i	−0.341801	−	0.825182i	0.655732	−	0.754993i	$-0.272360\pi$
$684$	11.9632	−	8.06827i	0.457425	−	0.308498i
$685$	−34.6292	−	14.3439i	−1.32312	−	0.548052i
$686$	26.7845	−	4.25370i	1.02264	−	0.162407i
$687$	5.79893	+	11.5177i	0.221243	+	0.439426i
$688$	8.48869	−	4.62733i	0.323628	−	0.176415i
$689$	−17.8849	+	10.3258i	−0.681360	+	0.393383i
$690$	−9.17781	+	20.3724i	−0.349393	+	0.775564i
$691$	18.4151	−	14.1304i	0.700545	−	0.537547i	−0.195943	−	0.980615i	$-0.562777\pi$
$691$	18.4151	−	14.1304i	0.700545	−	0.537547i	0.896488	+	0.443068i	$0.146110\pi$
$692$	9.08802	+	6.23487i	0.345475	+	0.237014i
$693$	15.7335	−	16.2634i	0.597664	−	0.617796i
$694$	11.6116	−	3.44479i	0.440772	−	0.130762i
$695$	−49.3321	+	13.2185i	−1.87127	+	0.501406i
$696$	2.66215	−	24.4900i	0.100908	−	0.928290i
$697$	−22.2097	−	5.95107i	−0.841252	−	0.225413i
$698$	12.3316	−	0.328059i	0.466758	−	0.0124172i
$699$	−4.63455	−	13.2904i	−0.175295	−	0.502688i
$700$	0.955581	+	0.858967i	0.0361176	+	0.0324659i
$701$	7.72776	−	18.6565i	0.291873	−	0.704645i	−0.708126	−	0.706087i	$-0.750459\pi$
$701$	7.72776	−	18.6565i	0.291873	−	0.704645i	0.999999	+	0.00144185i	$0.000458956\pi$
$702$	−4.64623	+	16.4164i	−0.175361	+	0.619597i
$703$	8.46414			0.319231
$704$	−24.9628	−	23.5704i	−0.940820	−	0.888342i
$705$	1.47731	−	25.8128i	0.0556387	−	0.972165i
$706$	−0.791379	−	1.77547i	−0.0297839	−	0.0668208i
$707$	−14.9193	+	1.96416i	−0.561097	+	0.0738698i
$708$	−36.6692	+	36.3788i	−1.37811	+	1.36720i
$709$	−0.363175	+	2.75859i	−0.0136393	+	0.103601i	−0.996910	−	0.0785475i	$-0.974972\pi$
$709$	−0.363175	+	2.75859i	−0.0136393	+	0.103601i	0.983271	+	0.182148i	$0.0583051\pi$
$710$	−1.73813	+	3.20442i	−0.0652309	+	0.120260i
$711$	−4.02505	−	27.0976i	−0.150951	−	1.01624i
$712$	−13.1317	+	6.71165i	−0.492132	+	0.251530i
$713$	26.8645	−	7.19833i	1.00608	−	0.269579i
$714$	−5.82745	+	5.48159i	−0.218087	+	0.205144i
$715$	14.0501	−	18.3104i	0.525443	−	0.684771i
$716$	3.42893	−	44.0382i	0.128145	−	1.64578i
$717$	−13.0189	+	0.961630i	−0.486199	+	0.0359127i
$718$	−1.77835	−	11.1979i	−0.0663676	−	0.417901i
$719$			21.4415i			0.799633i	0.916595	+	0.399816i	$0.130926\pi$
$719$			21.4415i			0.799633i	−0.916595	+	0.399816i	$0.869074\pi$
$720$	16.7455	+	22.1862i	0.624066	+	0.826829i
$721$			9.37100i			0.348994i
$722$	−18.4592	+	2.93155i	−0.686982	+	0.109101i
$723$	−15.1518	−	22.2748i	−0.563503	−	0.828409i
$724$	−28.4083	+	24.3040i	−1.05579	+	0.903252i
$725$	1.11892	−	1.45821i	0.0415558	−	0.0541566i
$726$	−17.6849	+	4.16369i	−0.656348	+	0.154529i
$727$	8.94901	−	2.39788i	0.331900	−	0.0889325i	−0.0890205	−	0.996030i	$-0.528374\pi$
$727$	8.94901	−	2.39788i	0.331900	−	0.0889325i	0.420921	+	0.907097i	$0.361707\pi$
$728$	−11.5052	+	0.919957i	−0.426410	+	0.0340959i
$729$	−24.4008	+	11.5585i	−0.903734	+	0.428094i
$730$	−28.0655	−	15.2232i	−1.03875	−	0.563435i
$731$	−0.586265	+	4.45312i	−0.0216838	+	0.164705i
$732$	−39.5481	+	22.6239i	−1.46174	+	0.836205i
$733$	−19.0409	+	2.50679i	−0.703293	+	0.0925902i	−0.473687	−	0.880693i	$-0.657077\pi$
$733$	−19.0409	+	2.50679i	−0.703293	+	0.0925902i	−0.229606	+	0.973284i	$0.573744\pi$
$734$	−45.9195	+	20.4676i	−1.69492	+	0.755473i
$735$	13.1180	+	8.60890i	0.483865	+	0.317544i
$736$	−21.5300	−	5.72088i	−0.793608	−	0.210874i
$737$	22.2166			0.818357
$738$	11.3863	−	51.2450i	0.419135	−	1.88635i
$739$	1.58086	−	3.81654i	0.0581529	−	0.140394i	−0.892132	−	0.451774i	$-0.850791\pi$
$739$	1.58086	−	3.81654i	0.0581529	−	0.140394i	0.950285	+	0.311380i	$0.100791\pi$
$740$	0.866901	+	16.2817i	0.0318679	+	0.598526i
$741$	−6.31622	+	7.32373i	−0.232032	+	0.269044i
$742$	−0.587970	−	22.1015i	−0.0215851	−	0.811373i
$743$	1.95375	+	0.523506i	0.0716762	+	0.0192056i	0.294479	−	0.955658i	$-0.404854\pi$
$743$	1.95375	+	0.523506i	0.0716762	+	0.0192056i	−0.222803	+	0.974864i	$0.571521\pi$
$744$	8.19651	−	33.6135i	0.300499	−	1.23233i
$745$	25.4802	−	6.82740i	0.933522	−	0.250136i
$746$	9.35587	+	31.5366i	0.342543	+	1.15464i
$747$	10.1987	+	2.55248i	0.373150	+	0.0933904i
$748$	15.6805	−	2.91974i	0.573337	−	0.106756i
$749$	10.2268	−	7.84729i	0.373679	−	0.286734i
$750$	−2.63374	−	26.1633i	−0.0961704	−	0.955349i
$751$	13.0403	−	7.52882i	0.475847	−	0.274730i	−0.242837	−	0.970067i	$-0.578078\pi$
$751$	13.0403	−	7.52882i	0.475847	−	0.274730i	0.718684	+	0.695337i	$0.244745\pi$
$752$	25.6316	−	2.73722i	0.934688	−	0.0998160i
$753$	−7.67554	−	0.439284i	−0.279712	−	0.0160084i
$754$	2.58962	+	16.3062i	0.0943084	+	0.593837i
$755$	−31.4031	−	13.0076i	−1.14287	−	0.473394i
$756$	−13.0771	−	12.7521i	−0.475611	−	0.463788i
$757$	10.9898	+	26.5317i	0.399430	+	0.964310i	0.987801	+	0.155719i	$0.0497694\pi$
$757$	10.9898	+	26.5317i	0.399430	+	0.964310i	−0.588371	+	0.808591i	$0.700231\pi$
$758$	−2.05519	+	8.57624i	−0.0746479	+	0.311503i
$759$	−21.8475	+	19.4822i	−0.793015	+	0.707158i
$760$	3.29521	+	15.4080i	0.119530	+	0.558905i
$761$	23.6362	+	6.33331i	0.856813	+	0.229582i	0.660377	−	0.750934i	$-0.270397\pi$
$761$	23.6362	+	6.33331i	0.856813	+	0.229582i	0.196436	+	0.980517i	$0.437063\pi$
$762$	13.9247	−	7.48148i	0.504438	−	0.271025i
$763$	4.07969	−	30.9883i	0.147695	−	1.12185i
$764$	29.3453	+	6.21197i	1.06168	+	0.224741i
$765$	−12.9118	+	0.213853i	−0.466828	+	0.00773187i
$766$	−40.3788	−	4.22696i	−1.45894	−	0.152726i
$767$	17.3097	−	29.9812i	0.625016	−	1.08256i
$768$	−19.1059	+	20.0740i	−0.689423	+	0.724359i
$769$	−1.81707	−	3.14725i	−0.0655252	−	0.113493i	0.831402	−	0.555672i	$-0.187539\pi$
$769$	−1.81707	−	3.14725i	−0.0655252	−	0.113493i	−0.896927	+	0.442179i	$0.854206\pi$
$770$	10.0594	+	22.5684i	0.362515	+	0.813310i
$771$	2.77400	+	37.5554i	0.0999032	+	1.35252i
$772$	−1.67127	+	1.85925i	−0.0601503	+	0.0669158i
$773$	−3.52157	+	1.45868i	−0.126662	+	0.0524652i	−0.445114	−	0.895474i	$-0.646837\pi$
$773$	−3.52157	+	1.45868i	−0.126662	+	0.0524652i	0.318452	+	0.947939i	$0.396837\pi$
$774$	−10.2150	−	0.898590i	−0.367171	−	0.0322991i
$775$	1.82539	−	1.82539i	0.0655699	−	0.0655699i
$776$	18.1941	−	16.4233i	0.653131	−	0.589563i
$777$	−2.17716	−	10.4906i	−0.0781052	−	0.376348i
$778$	2.26291	+	2.14563i	0.0811294	+	0.0769247i
$779$	18.1147	−	23.6076i	0.649027	−	0.845829i
$780$	−14.7349	−	11.3998i	−0.527593	−	0.408179i
$781$	−3.78888	+	2.90731i	−0.135577	+	0.104032i
$782$	8.04036	−	6.51650i	0.287523	−	0.233030i
$783$	−16.7345	+	20.0663i	−0.598042	+	0.717113i
$784$	−6.33893	+	14.3016i	−0.226390	+	0.510772i
$785$	3.40735	+	1.96723i	0.121613	+	0.0702135i
$786$	−28.0080	+	20.1616i	−0.999012	+	0.719142i
$787$	2.12471	+	16.1388i	0.0757378	+	0.575286i	0.986671	+	0.162731i	$0.0520302\pi$
$787$	2.12471	+	16.1388i	0.0757378	+	0.575286i	−0.910933	+	0.412555i	$0.864636\pi$
$788$	−0.440821	−	0.515265i	−0.0157036	−	0.0183555i
$789$	6.80934	−	35.7787i	0.242419	−	1.27376i
$790$	29.0900	+	6.97108i	1.03498	+	0.248020i
$791$	−10.4835	−	10.4835i	−0.372749	−	0.372749i
$792$	8.20428	+	35.4786i	0.291526	+	1.26068i
$793$	21.5929	−	21.5929i	0.766785	−	0.766785i
$794$	8.07475	−	4.95285i	0.286562	−	0.175770i
$795$	23.3071	−	27.0248i	0.826616	−	0.958470i
$796$	−10.8185	−	5.50093i	−0.383451	−	0.194975i
$797$	−14.9904	+	1.97352i	−0.530986	+	0.0699056i	−0.391252	−	0.920283i	$-0.627958\pi$
$797$	−14.9904	+	1.97352i	−0.530986	+	0.0699056i	−0.139734	+	0.990189i	$0.544625\pi$
$798$	−3.66797	−	9.68230i	−0.129845	−	0.342750i
$799$	−5.98781	+	10.3712i	−0.211833	+	0.366906i
$800$	−1.99616	+	0.539332i	−0.0705749	+	0.0190683i
$801$	15.5399	+	1.78460i	0.549077	+	0.0630557i
$802$	−0.406448	+	3.88266i	−0.0143522	+	0.137102i
$803$	−25.4632	−	33.1843i	−0.898578	−	1.17105i
$804$	0.0712942	−	17.9329i	0.00251435	−	0.632446i
$805$	12.7197	+	9.76015i	0.448310	+	0.344000i
$806$	0.616678	+	23.1806i	0.0217216	+	0.816503i
$807$	−32.3138	−	36.2371i	−1.13750	−	1.27561i
$808$	10.3980	−	21.8702i	0.365800	−	0.769390i
$809$	−31.8739	−	31.8739i	−1.12063	−	1.12063i	−0.991647	−	0.128980i	$-0.958830\pi$
$809$	−31.8739	−	31.8739i	−1.12063	−	1.12063i	−0.128980	−	0.991647i	$-0.541170\pi$
$810$	−1.75962	−	29.4299i	−0.0618266	−	1.03406i
$811$	−7.59731	−	18.3415i	−0.266778	−	0.644058i	0.732550	−	0.680713i	$-0.238330\pi$
$811$	−7.59731	−	18.3415i	−0.266778	−	0.644058i	−0.999328	+	0.0366546i	$0.988330\pi$
$812$	−16.6670	−	5.88645i	−0.584896	−	0.206574i
$813$	−17.8191	+	36.9007i	−0.624943	+	1.29417i
$814$	−7.64648	+	19.9446i	−0.268009	+	0.699058i
$815$	16.2176	−	9.36323i	0.568077	−	0.327980i
$816$	−2.30646	−	12.6665i	−0.0807423	−	0.443417i
$817$	−5.03399	−	2.90637i	−0.176117	−	0.101681i
$818$	−13.8664	+	11.2383i	−0.484826	+	0.392939i
$819$	10.7018	+	5.94460i	0.373952	+	0.207721i
$820$	47.2670	+	32.4277i	1.65063	+	1.13242i
$821$	−10.9855	−	1.44626i	−0.383396	−	0.0504750i	−0.0636347	−	0.997973i	$-0.520269\pi$
$821$	−10.9855	−	1.44626i	−0.383396	−	0.0504750i	−0.319761	+	0.947498i	$0.603603\pi$
$822$	−28.8710	+	27.1575i	−1.00699	+	0.947227i
$823$	−4.92417	+	18.3772i	−0.171646	+	0.640590i	0.825453	+	0.564471i	$0.190920\pi$
$823$	−4.92417	+	18.3772i	−0.171646	+	0.640590i	−0.997099	+	0.0761196i	$0.975747\pi$
$824$	−12.6577	−	8.19754i	−0.440953	−	0.285575i
$825$	−0.852023	+	2.57997i	−0.0296636	+	0.0898230i
$826$	19.3785	+	31.5932i	0.674263	+	1.09927i
$827$	9.16153	−	3.79483i	0.318578	−	0.131959i	−0.217664	−	0.976024i	$-0.569844\pi$
$827$	9.16153	−	3.79483i	0.318578	−	0.131959i	0.536241	+	0.844065i	$0.319844\pi$
$828$	15.6557	+	17.6976i	0.544072	+	0.615034i
$829$	−1.43211	+	3.45742i	−0.0497393	+	0.120081i	−0.946796	−	0.321834i	$-0.895701\pi$
$829$	−1.43211	+	3.45742i	−0.0497393	+	0.120081i	0.897057	+	0.441915i	$0.145701\pi$
$830$	−6.74381	+	9.29020i	−0.234081	+	0.322468i
$831$	5.89787	+	3.87057i	0.204595	+	0.134269i
$832$	8.82184	−	16.3452i	0.305842	−	0.566667i
$833$	−3.63381	−	6.29395i	−0.125904	−	0.218072i
$834$	−8.68288	+	53.3050i	−0.300663	+	1.84580i
$835$	29.9964	+	39.0921i	1.03807	+	1.35284i
$836$	−4.27483	+	20.1943i	−0.147848	+	0.698434i
$837$	−26.9809	+	24.8740i	−0.932595	+	0.859771i
$838$	−1.16066	+	2.13980i	−0.0400944	+	0.0739181i
$839$	−3.19848	−	11.9369i	−0.110424	−	0.412107i	0.888480	−	0.458915i	$-0.151762\pi$
$839$	−3.19848	−	11.9369i	−0.110424	−	0.412107i	−0.998904	+	0.0468078i	$0.985095\pi$
$840$	18.2493	−	8.04740i	0.629659	−	0.277662i
$841$	0.961452	−	3.58819i	0.0331535	−	0.123731i
$842$	−35.1575	−	33.3354i	−1.21161	−	1.14881i
$843$	4.85947	−	25.5334i	0.167369	−	0.879417i
$844$	−14.1011	+	6.74034i	−0.485381	+	0.232012i
$845$	−16.2847	−	6.74534i	−0.560210	−	0.232047i
$846$	−24.2458	−	12.6362i	−0.833586	−	0.434441i
$847$			13.0365i			0.447939i
$848$	30.3677	+	18.5397i	1.04283	+	0.636657i
$849$	6.77709	+	13.4604i	0.232589	+	0.461961i
$850$	0.343884	−	0.896966i	0.0117951	−	0.0307657i
$851$	1.80909	+	13.7414i	0.0620147	+	0.471049i
$852$	2.33459	+	3.06767i	0.0799817	+	0.105097i
$853$	45.3255	+	5.96722i	1.55192	+	0.204314i	0.857205	−	0.514975i	$-0.172199\pi$
$853$	45.3255	+	5.96722i	1.55192	+	0.204314i	0.694712	+	0.719288i	$0.255532\pi$
$854$	9.29818	+	31.3422i	0.318177	+	1.07251i
$855$	6.13890	−	15.5438i	0.209946	−	0.531588i
$856$	1.65345	+	20.6783i	0.0565136	+	0.706770i
$857$	6.43751	+	24.0251i	0.219901	+	0.820682i	0.984383	+	0.176037i	$0.0563279\pi$
$857$	6.43751	+	24.0251i	0.219901	+	0.820682i	−0.764482	+	0.644645i	$0.777005\pi$
$858$	−11.5513	−	21.4996i	−0.394356	−	0.733983i
$859$	42.7839	+	32.8292i	1.45977	+	1.12012i	0.968471	+	0.249127i	$0.0801436\pi$
$859$	42.7839	+	32.8292i	1.45977	+	1.12012i	0.491297	+	0.870992i	$0.336523\pi$
$860$	5.07514	−	9.98108i	0.173061	−	0.340352i
$861$	−33.9191	−	16.3793i	−1.15596	−	0.558204i
$862$	−6.94545	−	5.04174i	−0.236563	−	0.171722i
$863$	1.48658			0.0506037			0.0253019	−	0.999680i	$-0.491945\pi$
$863$	1.48658			0.0506037			0.0253019	+	0.999680i	$0.491945\pi$
$864$	28.6642	−	6.50855i	0.975177	−	0.221425i
$865$	12.7645			0.434005
$866$	25.5747	+	18.5648i	0.869064	+	0.630858i
$867$	−21.1290	−	10.2030i	−0.717578	−	0.346513i
$868$	−22.1291	−	11.2521i	−0.751112	−	0.381922i
$869$	31.0905	+	23.8565i	1.05467	+	0.809278i
$870$	−13.5035	−	25.1330i	−0.457811	−	0.852088i
$871$	3.11081	+	11.6097i	0.105406	+	0.393380i
$872$	38.2882	+	32.6185i	1.29660	+	1.10460i
$873$	−25.7149	+	3.81967i	−0.870318	+	0.129276i
$874$	3.80941	+	12.8407i	0.128855	+	0.434343i
$875$	−18.7065	−	2.46276i	−0.632397	−	0.0832566i
$876$	−26.8677	+	20.4472i	−0.907777	+	0.690845i
$877$	−3.55920	−	27.0348i	−0.120186	−	0.912900i	−0.940216	−	0.340579i	$-0.889377\pi$
$877$	−3.55920	−	27.0348i	−0.120186	−	0.912900i	0.820030	−	0.572320i	$-0.193957\pi$
$878$	2.09606	−	5.46723i	0.0707385	−	0.184510i
$879$	−6.90865	−	13.7217i	−0.233023	−	0.462822i
$880$	−39.2837	−	6.15479i	−1.32425	−	0.207478i
$881$			16.3864i			0.552073i	0.961147	+	0.276036i	$0.0890211\pi$
$881$			16.3864i			0.552073i	−0.961147	+	0.276036i	$0.910979\pi$
$882$	13.9981	−	8.90843i	0.471341	−	0.299963i
$883$	−35.6527	−	14.7678i	−1.19981	−	0.496977i	−0.308872	−	0.951104i	$-0.599951\pi$
$883$	−35.6527	−	14.7678i	−1.19981	−	0.496977i	−0.890937	+	0.454127i	$0.849951\pi$
$884$	3.72140	+	7.78535i	0.125164	+	0.261850i
$885$	−11.1848	+	58.7687i	−0.375972	+	1.97549i
$886$	23.2864	+	22.0795i	0.782321	+	0.741775i
$887$	−0.241937	+	0.902923i	−0.00812347	+	0.0303172i	−0.969869	−	0.243629i	$-0.921662\pi$
$887$	−0.241937	+	0.902923i	−0.00812347	+	0.0303172i	0.961745	+	0.273946i	$0.0883289\pi$
$888$	16.0745	+	6.23616i	0.539426	+	0.209272i
$889$	−2.93559	−	10.9558i	−0.0984566	−	0.367445i
$890$	−8.14373	+	15.0138i	−0.272979	+	0.503264i
$891$	13.5909	−	36.1536i	0.455311	−	1.21119i
$892$	−31.3752	−	6.64167i	−1.05052	−	0.222380i
$893$	−9.43475	−	12.2956i	−0.315722	−	0.411457i
$894$	4.48474	−	27.5323i	0.149992	−	0.920817i
$895$	−25.5793	−	44.3046i	−0.855021	−	1.48094i
$896$	10.8787	+	16.6452i	0.363433	+	0.556077i
$897$	−13.2399	−	8.68894i	−0.442069	−	0.290115i
$898$	−25.6843	+	35.3824i	−0.857095	+	1.18073i
$899$	−13.5901	+	32.8095i	−0.453257	+	1.09426i
$900$	2.07979	+	0.696023i	0.0693263	+	0.0232008i
$901$	−15.2714	+	6.32560i	−0.508763	+	0.210736i
$902$	39.2633	+	64.0119i	1.30732	+	2.13136i
$903$	−2.30735	+	6.98679i	−0.0767839	+	0.232506i
$904$	23.3311	−	4.98969i	0.775981	−	0.165955i
$905$	−11.2068	+	41.8244i	−0.372527	+	1.39029i
$906$	−26.1813	+	24.6274i	−0.869815	+	0.818192i
$907$	14.1169	+	1.85852i	0.468742	+	0.0617111i	0.361198	−	0.932489i	$-0.382368\pi$
$907$	14.1169	+	1.85852i	0.468742	+	0.0617111i	0.107544	+	0.994200i	$0.465701\pi$
$908$	−26.6092	+	38.7858i	−0.883056	+	1.28715i
$909$	−22.0282	+	13.2092i	−0.730631	+	0.438120i
$910$	−10.3851	+	8.41682i	−0.344261	+	0.279015i
$911$	12.0229	+	6.94141i	0.398336	+	0.229979i	0.685766	−	0.727822i	$-0.259468\pi$
$911$	12.0229	+	6.94141i	0.398336	+	0.229979i	−0.287430	+	0.957802i	$0.592801\pi$
$912$	16.2869	+	3.51540i	0.539313	+	0.116407i
$913$	−13.0244	+	7.51964i	−0.431044	+	0.248864i
$914$	7.61712	−	19.8680i	0.251952	−	0.657176i
$915$	−22.9464	+	47.5187i	−0.758586	+	1.57092i
$916$	−4.95868	+	14.0401i	−0.163839	+	0.463897i
$917$	9.47605	+	22.8772i	0.312927	+	0.755472i
$918$	−5.40210	+	12.5418i	−0.178296	+	0.413942i
$919$	26.8207	+	26.8207i	0.884735	+	0.884735i	0.994011	−	0.109277i	$-0.0348534\pi$
$919$	26.8207	+	26.8207i	0.884735	+	0.884735i	−0.109277	+	0.994011i	$0.534853\pi$
$920$	−24.3103	+	8.64295i	−0.801486	+	0.284950i
$921$	27.0241	+	30.3052i	0.890476	+	0.998590i
$922$	−0.236591	−	8.89335i	−0.00779171	−	0.292887i
$923$	−2.04980	−	1.57287i	−0.0674700	−	0.0517716i
$924$	26.1287	+	0.103877i	0.859571	+	0.00341731i
$925$	0.783149	+	1.02062i	0.0257498	+	0.0335578i
$926$	5.84814	−	55.8654i	0.192182	−	1.83585i
$927$	6.36497	+	14.6742i	0.209053	+	0.481964i
$928$	22.5309	−	17.3633i	0.739614	−	0.569979i
$929$	13.2213	−	22.9000i	0.433777	−	0.751323i	−0.563418	−	0.826172i	$-0.690514\pi$
$929$	13.2213	−	22.9000i	0.433777	−	0.751323i	0.997195	+	0.0748486i	$0.0238473\pi$
$930$	−14.1958	−	37.4724i	−0.465498	−	1.22877i
$931$	9.32495	−	1.22765i	0.305613	−	0.0402347i
$932$	7.36650	−	14.4874i	0.241298	−	0.474551i
$933$	9.26840	−	10.7468i	0.303434	−	0.351835i
$934$	−32.8303	+	20.1372i	−1.07424	+	0.658911i
$935$	13.0624	−	13.0624i	0.427186	−	0.427186i
$936$	−17.3913	+	9.25511i	−0.568452	+	0.302513i
$937$	−6.06603	−	6.06603i	−0.198169	−	0.198169i	0.601046	−	0.799215i	$-0.294751\pi$
$937$	−6.06603	−	6.06603i	−0.198169	−	0.198169i	−0.799215	+	0.601046i	$0.794751\pi$
$938$	−12.5133	−	2.99867i	−0.408575	−	0.0979100i
$939$	−3.76561	+	19.7859i	−0.122886	+	0.645688i
$940$	22.6856	−	19.4081i	0.739922	−	0.633021i
$941$	−1.47034	−	11.1683i	−0.0479316	−	0.364077i	−0.998555	−	0.0537312i	$-0.982889\pi$
$941$	−1.47034	−	11.1683i	−0.0479316	−	0.364077i	0.950624	−	0.310346i	$-0.100445\pi$
$942$	3.37670	−	2.43073i	0.110019	−	0.0791973i
$943$	42.1982	+	24.3632i	1.37416	+	0.793374i
$944$	−59.6259	−	1.46186i	−1.94066	−	0.0475793i
$945$	−20.8443	−	3.61044i	−0.678066	−	0.117447i
$946$	11.3962	−	9.23631i	0.370522	−	0.300298i
$947$	30.3374	−	23.2787i	0.985832	−	0.756456i	0.0159107	−	0.999873i	$-0.494935\pi$
$947$	30.3374	−	23.2787i	0.985832	−	0.756456i	0.969922	+	0.243418i	$0.0782686\pi$
$948$	19.3565	−	25.0193i	0.628670	−	0.812589i
$949$	13.7757	−	17.9529i	0.447179	−	0.582776i
$950$	0.902140	+	0.855385i	0.0292693	+	0.0277523i
$951$	1.46563	+	7.06209i	0.0475263	+	0.229004i
$952$	−9.22605	−	0.471946i	−0.299018	−	0.0152959i
$953$	21.1060	−	21.1060i	0.683689	−	0.683689i	−0.277140	−	0.960829i	$-0.589387\pi$
$953$	21.1060	−	21.1060i	0.683689	−	0.683689i	0.960829	+	0.277140i	$0.0893867\pi$
$954$	−15.9325	−	34.2098i	−0.515834	−	1.10758i
$955$	32.0959	−	13.2945i	1.03860	−	0.430201i
$956$	−11.2105	−	10.0770i	−0.362573	−	0.325915i
$957$	−2.75334	−	37.2756i	−0.0890027	−	1.20495i
$958$	−5.99367	−	13.4469i	−0.193647	−	0.434450i
$959$	14.2203	+	24.6303i	0.459199	+	0.795355i
$960$	−5.09414	+	31.6896i	−0.164413	+	1.02278i
$961$	−9.43857	+	16.3481i	−0.304470	+	0.527357i
$962$	−11.4931	−	1.20313i	−0.370554	−	0.0387906i
$963$	10.6843	−	19.2344i	0.344296	−	0.619821i
$964$	6.44218	−	30.4329i	0.207489	−	0.980176i
$965$	−0.377931	+	2.87067i	−0.0121660	+	0.0924101i
$966$	14.9351	−	8.02435i	0.480528	−	0.258179i
$967$	−22.6691	−	6.07416i	−0.728988	−	0.195332i	−0.124810	−	0.992181i	$-0.539832\pi$
$967$	−22.6691	−	6.07416i	−0.728988	−	0.195332i	−0.604179	+	0.796849i	$0.706499\pi$
$968$	−17.6088	−	11.4040i	−0.565969	−	0.366539i
$969$	−5.77738	+	5.15188i	−0.185596	+	0.165502i
$970$	6.61537	−	27.6057i	0.212407	−	0.886366i
$971$	1.72920	+	4.17465i	0.0554926	+	0.133971i	0.949194	−	0.314691i	$-0.101901\pi$
$971$	1.72920	+	4.17465i	0.0554926	+	0.133971i	−0.893702	+	0.448662i	$0.851901\pi$
$972$	−29.1392	−	11.0864i	−0.934639	−	0.355597i
$973$	35.8025	+	14.8299i	1.14777	+	0.475424i
$974$	0.823607	+	5.18605i	0.0263901	+	0.166172i
$975$	−1.46752	−	0.0839886i	−0.0469982	−	0.00268979i
$976$	−50.4688	−	14.8580i	−1.61547	−	0.475594i
$977$	−17.3350	+	10.0084i	−0.554597	+	0.320197i	−0.750974	−	0.660332i	$-0.770416\pi$
$977$	−17.3350	+	10.0084i	−0.554597	+	0.320197i	0.196377	+	0.980528i	$0.437082\pi$
$978$	−1.98342	−	19.7031i	−0.0634228	−	0.630037i
$979$	−17.7522	+	13.6217i	−0.567362	+	0.435353i
$980$	3.31659	+	17.8118i	0.105945	+	0.568977i
$981$	−14.6594	−	51.2962i	−0.468040	−	1.63776i
$982$	7.12896	+	24.0302i	0.227494	+	0.766833i
$983$	36.5166	−	9.78459i	1.16470	−	0.312080i	0.375857	−	0.926678i	$-0.377348\pi$
$983$	36.5166	−	9.78459i	1.16470	−	0.312080i	0.788841	+	0.614598i	$0.210682\pi$
$984$	51.7957	−	31.4875i	1.65119	−	1.00378i
$985$	−0.758603	−	0.203267i	−0.0241711	−	0.00647662i
$986$	0.351437	+	13.2104i	0.0111920	+	0.420704i
$987$	−12.8125	+	14.8563i	−0.407828	+	0.472880i
$988$	−11.1515	+	0.593751i	−0.354777	+	0.0188897i
$989$	3.64251	−	8.79379i	0.115825	−	0.279626i
$990$	31.0811	+	28.5078i	0.987822	+	0.906036i
$991$	−52.8446			−1.67866			−0.839332	−	0.543619i	$-0.817054\pi$
$991$	−52.8446			−1.67866			−0.839332	+	0.543619i	$0.817054\pi$
$992$	34.5567	−	20.0475i	1.09718	−	0.636509i
$993$	27.5030	+	18.0493i	0.872780	+	0.572777i
$994$	2.52647	−	1.12612i	0.0801349	−	0.0357184i
$995$	−13.9362	+	1.83474i	−0.441809	+	0.0581652i
$996$	6.02797	+	10.5373i	0.191004	+	0.333886i
$997$	7.96815	−	60.5241i	0.252354	−	1.91682i	−0.127627	−	0.991822i	$-0.540736\pi$
$997$	7.96815	−	60.5241i	0.252354	−	1.91682i	0.379981	−	0.924994i	$-0.375931\pi$
$998$	27.4263	+	14.8765i	0.868165	+	0.470906i
$999$	−10.5347	−	14.9486i	−0.333302	−	0.472953i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	288.2.bc.a.205.32	yes	368
3.2	odd	2		864.2.bk.a.397.15		368
9.4	even	3	inner	288.2.bc.a.13.30	✓	368
9.5	odd	6		864.2.bk.a.685.17		368
32.5	even	8	inner	288.2.bc.a.133.30	yes	368
96.5	odd	8		864.2.bk.a.613.17		368
288.5	odd	24		864.2.bk.a.37.15		368
288.229	even	24	inner	288.2.bc.a.229.32	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bc.a.13.30	✓	368	9.4	even	3	inner
288.2.bc.a.133.30	yes	368	32.5	even	8	inner
288.2.bc.a.205.32	yes	368	1.1	even	1	trivial
288.2.bc.a.229.32	yes	368	288.229	even	24	inner
864.2.bk.a.37.15		368	288.5	odd	24
864.2.bk.a.397.15		368	3.2	odd	2
864.2.bk.a.613.17		368	96.5	odd	8
864.2.bk.a.685.17		368	9.5	odd	6

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.bc (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.830777 - 1.14447i) q^{2} +(-1.55972 - 0.753177i) q^{3} +(-0.619620 - 1.90160i) q^{4} +(-1.83769 - 1.41011i) q^{5} +(-2.15777 + 1.15933i) q^{6} +(0.454899 + 1.69771i) q^{7} +(-2.69109 - 0.870667i) q^{8} +(1.86545 + 2.34949i) q^{9} +O(q^{10})\)	\(q+(0.830777 - 1.14447i) q^{2} +(-1.55972 - 0.753177i) q^{3} +(-0.619620 - 1.90160i) q^{4} +(-1.83769 - 1.41011i) q^{5} +(-2.15777 + 1.15933i) q^{6} +(0.454899 + 1.69771i) q^{7} +(-2.69109 - 0.870667i) q^{8} +(1.86545 + 2.34949i) q^{9} +(-3.14054 + 0.931695i) q^{10} +(-4.25482 - 0.560157i) q^{11} +(-0.465806 + 3.43264i) q^{12} +(-0.303048 - 2.30188i) q^{13} +(2.32089 + 0.889796i) q^{14} +(1.80422 + 3.58349i) q^{15} +(-3.23214 + 2.35653i) q^{16} -1.85832i q^{17} +(4.23869 - 0.183047i) q^{18} +(2.22188 + 0.920333i) q^{19} +(-1.54279 + 4.36828i) q^{20} +(0.569158 - 2.99056i) q^{21} +(-4.17588 + 4.40414i) q^{22} +(-1.01925 + 3.80389i) q^{23} +(3.54157 + 3.38486i) q^{24} +(0.0946054 + 0.353072i) q^{25} +(-2.88619 - 1.56552i) q^{26} +(-1.13999 - 5.06956i) q^{27} +(2.94649 - 1.91697i) q^{28} +(-3.06112 - 3.98933i) q^{29} +(5.60009 + 0.912201i) q^{30} +(-3.53119 - 6.11620i) q^{31} +(0.0117927 + 5.65684i) q^{32} +(6.21442 + 4.07832i) q^{33} +(-2.12679 - 1.54385i) q^{34} +(1.55799 - 3.76132i) q^{35} +(3.31191 - 5.00312i) q^{36} +(3.25157 - 1.34684i) q^{37} +(2.89918 - 1.77828i) q^{38} +(-1.26105 + 3.81853i) q^{39} +(3.71765 + 5.39475i) q^{40} +(3.20240 - 11.9515i) q^{41} +(-2.94976 - 3.13587i) q^{42} +(-2.39632 - 0.315482i) q^{43} +(1.57118 + 8.43803i) q^{44} +(-0.115079 - 6.94813i) q^{45} +(3.50667 + 4.32669i) q^{46} +(-5.58096 - 3.22217i) q^{47} +(6.81612 - 1.24116i) q^{48} +(3.38691 - 1.95543i) q^{49} +(0.482676 + 0.185051i) q^{50} +(-1.39964 + 2.89845i) q^{51} +(-4.18947 + 2.00256i) q^{52} +(-3.40394 - 8.21784i) q^{53} +(-6.74903 - 2.90698i) q^{54} +(7.02916 + 7.02916i) q^{55} +(0.253964 - 4.96473i) q^{56} +(-2.77234 - 3.10893i) q^{57} +(-7.10878 + 0.189116i) q^{58} +(11.8297 + 9.07722i) q^{59} +(5.69641 - 5.65130i) q^{60} +(8.00680 + 10.4347i) q^{61} +(-9.93343 - 1.03986i) q^{62} +(-3.14015 + 4.23576i) q^{63} +(6.48388 + 4.68608i) q^{64} +(-2.68899 + 4.65747i) q^{65} +(9.83030 - 3.72404i) q^{66} +(-5.13255 + 0.675713i) q^{67} +(-3.53377 + 1.15145i) q^{68} +(4.45475 - 5.16533i) q^{69} +(-3.01037 - 4.90789i) q^{70} +(0.786895 - 0.786895i) q^{71} +(-2.97446 - 7.94686i) q^{72} +(6.89191 + 6.89191i) q^{73} +(1.15991 - 4.84024i) q^{74} +(0.118368 - 0.621948i) q^{75} +(0.373381 - 4.79538i) q^{76} +(-0.984528 - 7.47824i) q^{77} +(3.32254 + 4.61558i) q^{78} +(-7.90822 - 4.56581i) q^{79} +(9.26266 + 0.227094i) q^{80} +(-2.04021 + 8.76570i) q^{81} +(-11.0177 - 13.5941i) q^{82} +(2.78023 - 2.13335i) q^{83} +(-6.03951 + 0.770702i) q^{84} +(-2.62043 + 3.41501i) q^{85} +(-2.35187 + 2.48042i) q^{86} +(1.76982 + 8.52780i) q^{87} +(10.9624 + 5.21196i) q^{88} +(3.68687 - 3.68687i) q^{89} +(-8.04753 - 5.64064i) q^{90} +(3.77005 - 1.56161i) q^{91} +(7.86502 - 0.418765i) q^{92} +(0.901082 + 12.1992i) q^{93} +(-8.32420 + 3.71033i) q^{94} +(-2.78536 - 4.82439i) q^{95} +(4.24221 - 8.83197i) q^{96} +(-4.33284 + 7.50470i) q^{97} +(0.575832 - 5.50074i) q^{98} +(-6.62105 - 11.0416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9}+O(q^{10}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9	\( 368 q - 4 q^{2} - 8 q^{3} - 4 q^{4} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 16 q^{8} - 8 q^{9} - 16 q^{10} - 4 q^{11} - 8 q^{12} - 4 q^{13} - 4 q^{14} - 4 q^{16} - 8 q^{18} - 16 q^{19} - 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{23} - 48 q^{24} - 4 q^{25} - 16 q^{26} - 32 q^{27} - 16 q^{28} - 4 q^{29} + 24 q^{30} - 8 q^{31} - 4 q^{32} - 16 q^{33} + 4 q^{34} - 16 q^{35} + 20 q^{36} - 16 q^{37} - 60 q^{38} - 32 q^{39} - 4 q^{40} - 4 q^{41} - 88 q^{42} - 4 q^{43} - 104 q^{44} - 8 q^{45} - 16 q^{46} - 60 q^{48} + 48 q^{50} + 16 q^{51} - 4 q^{52} - 16 q^{53} - 52 q^{54} - 16 q^{55} - 84 q^{56} - 8 q^{57} - 40 q^{58} - 4 q^{59} - 52 q^{60} - 4 q^{61} - 24 q^{62} - 16 q^{63} - 16 q^{64} - 8 q^{65} + 64 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{69} - 4 q^{70} - 16 q^{71} - 68 q^{72} - 16 q^{73} - 4 q^{74} - 28 q^{75} + 20 q^{76} - 4 q^{77} - 72 q^{78} + 48 q^{80} - 16 q^{82} + 36 q^{83} + 200 q^{84} + 16 q^{85} + 100 q^{86} - 64 q^{87} - 4 q^{88} - 16 q^{89} + 4 q^{90} - 16 q^{91} - 80 q^{92} + 4 q^{93} - 20 q^{94} - 136 q^{95} + 28 q^{96} - 8 q^{97} + 104 q^{98} - 72 q^{99}+O(q^{100}) \) 368 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 - 4 * q^5 - 8 * q^6 - 4 * q^7 - 16 * q^8 - 8 * q^9 - 16 * q^10 - 4 * q^11 - 8 * q^12 - 4 * q^13 - 4 * q^14 - 4 * q^16 - 8 * q^18 - 16 * q^19 - 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^23 - 48 * q^24 - 4 * q^25 - 16 * q^26 - 32 * q^27 - 16 * q^28 - 4 * q^29 + 24 * q^30 - 8 * q^31 - 4 * q^32 - 16 * q^33 + 4 * q^34 - 16 * q^35 + 20 * q^36 - 16 * q^37 - 60 * q^38 - 32 * q^39 - 4 * q^40 - 4 * q^41 - 88 * q^42 - 4 * q^43 - 104 * q^44 - 8 * q^45 - 16 * q^46 - 60 * q^48 + 48 * q^50 + 16 * q^51 - 4 * q^52 - 16 * q^53 - 52 * q^54 - 16 * q^55 - 84 * q^56 - 8 * q^57 - 40 * q^58 - 4 * q^59 - 52 * q^60 - 4 * q^61 - 24 * q^62 - 16 * q^63 - 16 * q^64 - 8 * q^65 + 64 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^69 - 4 * q^70 - 16 * q^71 - 68 * q^72 - 16 * q^73 - 4 * q^74 - 28 * q^75 + 20 * q^76 - 4 * q^77 - 72 * q^78 + 48 * q^80 - 16 * q^82 + 36 * q^83 + 200 * q^84 + 16 * q^85 + 100 * q^86 - 64 * q^87 - 4 * q^88 - 16 * q^89 + 4 * q^90 - 16 * q^91 - 80 * q^92 + 4 * q^93 - 20 * q^94 - 136 * q^95 + 28 * q^96 - 8 * q^97 + 104 * q^98 - 72 * q^99

Introduction

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