LMFDB - Embedded newform 729.2.g.c.595.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

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

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

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			595.4
Character	$\chi$	$=$	729.595
Dual form			729.2.g.c.136.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.368322 + 0.0872939i) q^{2} +(-1.65922 + 0.833294i) q^{4} +(0.765743 + 1.02857i) q^{5} +(-1.59613 + 1.04979i) q^{7} +(1.11832 - 0.938383i) q^{8} +(-0.371828 - 0.312001i) q^{10} +(-4.84662 - 0.566489i) q^{11} +(-0.986538 - 3.29527i) q^{13} +(0.496250 - 0.525994i) q^{14} +(1.88752 - 2.53538i) q^{16} +(0.0728119 - 0.412937i) q^{17} +(-0.626542 - 3.55329i) q^{19} +(-2.12764 - 1.06854i) q^{20} +(1.83457 - 0.214430i) q^{22} +(5.60929 + 3.68929i) q^{23} +(0.962419 - 3.21470i) q^{25} +(0.651020 + 1.12760i) q^{26} +(1.77356 - 3.07189i) q^{28} +(3.44661 + 3.65320i) q^{29} +(0.385862 - 6.62500i) q^{31} +(-1.63034 + 3.77955i) q^{32} +(0.00922864 + 0.158450i) q^{34} +(-2.30201 - 0.837864i) q^{35} +(0.465059 - 0.169268i) q^{37} +(0.540950 + 1.25406i) q^{38} +(1.82154 + 0.431713i) q^{40} +(-5.90634 - 1.39983i) q^{41} +(-4.59446 - 10.6512i) q^{43} +(8.51368 - 3.09873i) q^{44} +(-2.38808 - 0.869188i) q^{46} +(-0.352677 - 6.05524i) q^{47} +(-1.32699 + 3.07630i) q^{49} +(-0.0738560 + 1.26806i) q^{50} +(4.38281 + 4.64551i) q^{52} +(2.95007 - 5.10967i) q^{53} +(-3.12859 - 5.41888i) q^{55} +(-0.799881 + 2.67179i) q^{56} +(-1.58836 - 1.04468i) q^{58} +(-5.59693 + 0.654187i) q^{59} +(-2.48606 - 1.24855i) q^{61} +(0.436200 + 2.47381i) q^{62} +(-0.827191 + 4.69124i) q^{64} +(2.63398 - 3.53805i) q^{65} +(4.96592 - 5.26357i) q^{67} +(0.223286 + 0.745828i) q^{68} +(0.921022 + 0.107652i) q^{70} +(-11.9949 - 10.0649i) q^{71} +(-5.04326 + 4.23179i) q^{73} +(-0.156515 + 0.102942i) q^{74} +(4.00051 + 5.37362i) q^{76} +(8.33054 - 4.18375i) q^{77} +(3.71934 - 0.881500i) q^{79} +4.05318 q^{80} +2.29763 q^{82} +(-4.72027 + 1.11872i) q^{83} +(0.480490 - 0.241311i) q^{85} +(2.62202 + 3.52198i) q^{86} +(-5.95166 + 3.91447i) q^{88} +(-7.97723 + 6.69369i) q^{89} +(5.03399 + 4.22402i) q^{91} +(-12.3813 - 1.44717i) q^{92} +(0.658484 + 2.19949i) q^{94} +(3.17505 - 3.36535i) q^{95} +(-1.29193 + 1.73537i) q^{97} +(0.220216 - 1.24891i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) $ 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{25}{27}\right)$

Coefficient data

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

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

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

$2$	−0.368322	+	0.0872939i	−0.260443	+	0.0617261i	−0.358763	−	0.933429i	$-0.616801\pi$
$2$	−0.368322	+	0.0872939i	−0.260443	+	0.0617261i	0.0983199	+	0.995155i	$0.468653\pi$
$3$		0			0
$3$		0			0
$4$	−1.65922	+	0.833294i	−0.829612	+	0.416647i
$5$	0.765743	+	1.02857i	0.342451	+	0.459991i	0.939668	−	0.342088i	$-0.111134\pi$
$5$	0.765743	+	1.02857i	0.342451	+	0.459991i	−0.597217	+	0.802080i	$0.703727\pi$
$6$		0			0
$7$	−1.59613	+	1.04979i	−0.603281	+	0.396784i	−0.814086	−	0.580744i	$-0.802762\pi$
$7$	−1.59613	+	1.04979i	−0.603281	+	0.396784i	0.210805	+	0.977528i	$0.432391\pi$
$8$	1.11832	−	0.938383i	0.395386	−	0.331768i
$9$		0			0
$10$	−0.371828	−	0.312001i	−0.117582	−	0.0986633i
$11$	−4.84662	−	0.566489i	−1.46131	−	0.170803i	−0.652016	−	0.758205i	$-0.726077\pi$
$11$	−4.84662	−	0.566489i	−1.46131	−	0.170803i	−0.809295	+	0.587402i	$0.800151\pi$
$12$		0			0
$13$	−0.986538	−	3.29527i	−0.273616	−	0.913942i	−0.978783	−	0.204900i	$-0.934313\pi$
$13$	−0.986538	−	3.29527i	−0.273616	−	0.913942i	0.705167	−	0.709042i	$-0.250872\pi$
$14$	0.496250	−	0.525994i	0.132628	−	0.140578i
$15$		0			0
$16$	1.88752	−	2.53538i	0.471881	−	0.633846i
$17$	0.0728119	−	0.412937i	0.0176595	−	0.100152i	−0.974704	−	0.223499i	$-0.928252\pi$
$17$	0.0728119	−	0.412937i	0.0176595	−	0.100152i	0.992364	+	0.123348i	$0.0393630\pi$
$18$		0			0
$19$	−0.626542	−	3.55329i	−0.143739	−	0.815182i	−0.968371	−	0.249513i	$-0.919729\pi$
$19$	−0.626542	−	3.55329i	−0.143739	−	0.815182i	0.824633	−	0.565668i	$-0.191382\pi$
$20$	−2.12764	−	1.06854i	−0.475755	−	0.238933i
$21$		0			0
$22$	1.83457	−	0.214430i	0.391131	−	0.0457167i
$23$	5.60929	+	3.68929i	1.16962	+	0.769269i	0.977258	−	0.212055i	$-0.0680156\pi$
$23$	5.60929	+	3.68929i	1.16962	+	0.769269i	0.192360	+	0.981325i	$0.438386\pi$
$24$		0			0
$25$	0.962419	−	3.21470i	0.192484	−	0.642941i
$26$	0.651020	+	1.12760i	0.127675	+	0.221140i
$27$		0			0
$28$	1.77356	−	3.07189i	0.335170	−	0.580532i
$29$	3.44661	+	3.65320i	0.640020	+	0.678382i	0.963455	−	0.267869i	$-0.0863193\pi$
$29$	3.44661	+	3.65320i	0.640020	+	0.678382i	−0.323435	+	0.946250i	$0.604838\pi$
$30$		0			0
$31$	0.385862	−	6.62500i	0.0693029	−	1.18988i	−0.767011	−	0.641634i	$-0.778257\pi$
$31$	0.385862	−	6.62500i	0.0693029	−	1.18988i	0.836314	−	0.548251i	$-0.184706\pi$
$32$	−1.63034	+	3.77955i	−0.288206	+	0.668136i
$33$		0			0
$34$	0.00922864	+	0.158450i	0.00158270	+	0.0271739i
$35$	−2.30201	−	0.837864i	−0.389111	−	0.141625i
$36$		0			0
$37$	0.465059	−	0.169268i	0.0764552	−	0.0278274i	−0.303509	−	0.952828i	$-0.598158\pi$
$37$	0.465059	−	0.169268i	0.0764552	−	0.0278274i	0.379965	+	0.925001i	$0.375936\pi$
$38$	0.540950	+	1.25406i	0.0877536	+	0.203436i
$39$		0			0
$40$	1.82154	+	0.431713i	0.288011	+	0.0682598i
$41$	−5.90634	−	1.39983i	−0.922415	−	0.218616i	−0.258142	−	0.966107i	$-0.583110\pi$
$41$	−5.90634	−	1.39983i	−0.922415	−	0.218616i	−0.664272	+	0.747491i	$0.731258\pi$
$42$		0			0
$43$	−4.59446	−	10.6512i	−0.700649	−	1.62429i	−0.778745	−	0.627340i	$-0.784144\pi$
$43$	−4.59446	−	10.6512i	−0.700649	−	1.62429i	0.0780967	−	0.996946i	$-0.475116\pi$
$44$	8.51368	−	3.09873i	1.28349	−	0.467151i
$45$		0			0
$46$	−2.38808	−	0.869188i	−0.352102	−	0.128155i
$47$	−0.352677	−	6.05524i	−0.0514433	−	0.883247i	−0.921036	−	0.389477i	$-0.872656\pi$
$47$	−0.352677	−	6.05524i	−0.0514433	−	0.883247i	0.869593	−	0.493770i	$-0.164381\pi$
$48$		0			0
$49$	−1.32699	+	3.07630i	−0.189569	+	0.439471i
$50$	−0.0738560	+	1.26806i	−0.0104448	+	0.179331i
$51$		0			0
$52$	4.38281	+	4.64551i	0.607787	+	0.644216i
$53$	2.95007	−	5.10967i	0.405223	−	0.701867i	−0.589124	−	0.808043i	$-0.700527\pi$
$53$	2.95007	−	5.10967i	0.405223	−	0.701867i	0.994347	+	0.106175i	$0.0338605\pi$
$54$		0			0
$55$	−3.12859	−	5.41888i	−0.421859	−	0.730682i
$56$	−0.799881	+	2.67179i	−0.106889	+	0.357033i
$57$		0			0
$58$	−1.58836	−	1.04468i	−0.208562	−	0.137174i
$59$	−5.59693	+	0.654187i	−0.728658	+	0.0851680i	−0.472330	−	0.881422i	$-0.656587\pi$
$59$	−5.59693	+	0.654187i	−0.728658	+	0.0851680i	−0.256328	+	0.966590i	$0.582513\pi$
$60$		0			0
$61$	−2.48606	−	1.24855i	−0.318307	−	0.159860i	0.282471	−	0.959276i	$-0.408846\pi$
$61$	−2.48606	−	1.24855i	−0.318307	−	0.159860i	−0.600778	+	0.799416i	$0.705142\pi$
$62$	0.436200	+	2.47381i	0.0553975	+	0.314175i
$63$		0			0
$64$	−0.827191	+	4.69124i	−0.103399	+	0.586404i
$65$	2.63398	−	3.53805i	0.326705	−	0.438841i
$66$		0			0
$67$	4.96592	−	5.26357i	0.606684	−	0.643048i	−0.349111	−	0.937081i	$-0.613516\pi$
$67$	4.96592	−	5.26357i	0.606684	−	0.643048i	0.955795	+	0.294034i	$0.0949978\pi$
$68$	0.223286	+	0.745828i	0.0270774	+	0.0904450i
$69$		0			0
$70$	0.921022	+	0.107652i	0.110083	+	0.0128669i
$71$	−11.9949	−	10.0649i	−1.42353	−	1.19448i	−0.949418	−	0.314015i	$-0.898326\pi$
$71$	−11.9949	−	10.0649i	−1.42353	−	1.19448i	−0.474109	−	0.880466i	$-0.657230\pi$
$72$		0			0
$73$	−5.04326	+	4.23179i	−0.590268	+	0.495294i	−0.888301	−	0.459262i	$-0.848114\pi$
$73$	−5.04326	+	4.23179i	−0.590268	+	0.495294i	0.298033	+	0.954556i	$0.403670\pi$
$74$	−0.156515	+	0.102942i	−0.0181945	+	0.0119667i
$75$		0			0
$76$	4.00051	+	5.37362i	0.458890	+	0.616396i
$77$	8.33054	−	4.18375i	0.949353	−	0.476783i
$78$		0			0
$79$	3.71934	−	0.881500i	0.418459	−	0.0991765i	−0.0159920	−	0.999872i	$-0.505091\pi$
$79$	3.71934	−	0.881500i	0.418459	−	0.0991765i	0.434451	+	0.900696i	$0.356942\pi$
$80$	4.05318			0.453160
$81$		0			0
$82$	2.29763			0.253731
$83$	−4.72027	+	1.11872i	−0.518117	+	0.122796i	−0.481351	−	0.876528i	$-0.659854\pi$
$83$	−4.72027	+	1.11872i	−0.518117	+	0.122796i	−0.0367659	+	0.999324i	$0.511706\pi$
$84$		0			0
$85$	0.480490	−	0.241311i	0.0521165	−	0.0261739i
$86$	2.62202	+	3.52198i	0.282740	+	0.379785i
$87$		0			0
$88$	−5.95166	+	3.91447i	−0.634449	+	0.417284i
$89$	−7.97723	+	6.69369i	−0.845585	+	0.709530i	−0.958813	−	0.284039i	$-0.908325\pi$
$89$	−7.97723	+	6.69369i	−0.845585	+	0.709530i	0.113228	+	0.993569i	$0.463881\pi$
$90$		0			0
$91$	5.03399	+	4.22402i	0.527705	+	0.442797i
$92$	−12.3813	−	1.44717i	−1.29084	−	0.150878i
$93$		0			0
$94$	0.658484	+	2.19949i	0.0679174	+	0.226860i
$95$	3.17505	−	3.36535i	0.325753	−	0.345278i
$96$		0			0
$97$	−1.29193	+	1.73537i	−0.131176	+	0.176200i	−0.862858	−	0.505446i	$-0.831328\pi$
$97$	−1.29193	+	1.73537i	−0.131176	+	0.176200i	0.731682	+	0.681646i	$0.238735\pi$
$98$	0.220216	−	1.24891i	0.0222452	−	0.126159i
$99$		0			0
$100$	1.08192	+	6.13589i	0.108192	+	0.613589i
$101$	14.5862	+	7.32547i	1.45138	+	0.728911i	0.987593	−	0.157035i	$-0.0501936\pi$
$101$	14.5862	+	7.32547i	1.45138	+	0.728911i	0.463788	+	0.885946i	$0.346490\pi$
$102$		0			0
$103$	−17.9458	+	2.09756i	−1.76825	+	0.206679i	−0.937025	−	0.349262i	$-0.886432\pi$
$103$	−17.9458	+	2.09756i	−1.76825	+	0.206679i	−0.831222	+	0.555940i	$0.812358\pi$
$104$	−4.19549	−	2.75941i	−0.411401	−	0.270583i
$105$		0			0
$106$	−0.640532	+	2.13953i	−0.0622140	+	0.207809i
$107$	8.06607	+	13.9708i	0.779777	+	1.35061i	0.932070	+	0.362277i	$0.118001\pi$
$107$	8.06607	+	13.9708i	0.779777	+	1.35061i	−0.152294	+	0.988335i	$0.548666\pi$
$108$		0			0
$109$	4.04171	−	7.00045i	0.387126	−	0.670521i	−0.604936	−	0.796274i	$-0.706801\pi$
$109$	4.04171	−	7.00045i	0.387126	−	0.670521i	0.992062	+	0.125753i	$0.0401347\pi$
$110$	1.62536	+	1.72279i	0.154972	+	0.164261i
$111$		0			0
$112$	−0.351109	+	6.02832i	−0.0331767	+	0.569622i
$113$	−0.681557	+	1.58003i	−0.0641154	+	0.148636i	−0.947261	−	0.320462i	$-0.896162\pi$
$113$	−0.681557	+	1.58003i	−0.0641154	+	0.148636i	0.883146	+	0.469098i	$0.155421\pi$
$114$		0			0
$115$	0.500579	+	8.59460i	0.0466792	+	0.801451i
$116$	−8.76289	−	3.18943i	−0.813614	−	0.296131i
$117$		0			0
$118$	2.00437	−	0.729529i	0.184517	−	0.0671586i
$119$	0.317280	+	0.735538i	0.0290850	+	0.0674267i
$120$		0			0
$121$	12.4653	+	2.95434i	1.13321	+	0.268576i
$122$	1.02466	+	0.242849i	0.0927684	+	0.0219865i
$123$		0			0
$124$	4.88034	+	11.3139i	0.438267	+	1.01602i
$125$	10.0684	−	3.66460i	0.900546	−	0.327772i
$126$		0			0
$127$	−4.79894	−	1.74667i	−0.425837	−	0.154992i	0.120206	−	0.992749i	$-0.461644\pi$
$127$	−4.79894	−	1.74667i	−0.425837	−	0.154992i	−0.546044	+	0.837757i	$0.683867\pi$
$128$	−0.583513	−	10.0185i	−0.0515758	−	0.885522i
$129$		0			0
$130$	−0.661303	+	1.53307i	−0.0580001	+	0.134459i
$131$	0.677467	−	11.6317i	0.0591905	−	1.01626i	−0.829720	−	0.558181i	$-0.811500\pi$
$131$	0.677467	−	11.6317i	0.0591905	−	1.01626i	0.888910	−	0.458082i	$-0.151463\pi$
$132$		0			0
$133$	4.73026	+	5.01379i	0.410166	+	0.434750i
$134$	−1.36958	+	2.37218i	−0.118314	+	0.204925i
$135$		0			0
$136$	−0.306066	−	0.530121i	−0.0262449	−	0.0454575i
$137$	−1.42070	+	4.74547i	−0.121379	+	0.405433i	−0.996985	−	0.0775920i	$-0.975277\pi$
$137$	−1.42070	+	4.74547i	−0.121379	+	0.405433i	0.875606	+	0.483025i	$0.160462\pi$
$138$		0			0
$139$	−14.0604	−	9.24768i	−1.19259	−	0.784378i	−0.211395	−	0.977401i	$-0.567801\pi$
$139$	−14.0604	−	9.24768i	−1.19259	−	0.784378i	−0.981194	+	0.193022i	$0.938171\pi$
$140$	4.51775	−	0.528049i	0.381819	−	0.0446283i
$141$		0			0
$142$	5.29657	+	2.66004i	0.444478	+	0.223225i
$143$	2.91464	+	16.5298i	0.243735	+	1.38229i
$144$		0			0
$145$	−1.11835	+	6.34250i	−0.0928742	+	0.526716i
$146$	1.48813	−	1.99891i	0.123159	−	0.165431i
$147$		0			0
$148$	−0.630588	+	0.668384i	−0.0518340	+	0.0549408i
$149$	−4.99831	−	16.6955i	−0.409477	−	1.36775i	−0.875603	−	0.483031i	$-0.839536\pi$
$149$	−4.99831	−	16.6955i	−0.409477	−	1.36775i	0.466126	−	0.884718i	$-0.345649\pi$
$150$		0			0
$151$	−6.41195	−	0.749449i	−0.521797	−	0.0609893i	−0.148882	−	0.988855i	$-0.547568\pi$
$151$	−6.41195	−	0.749449i	−0.521797	−	0.0609893i	−0.372915	+	0.927866i	$0.621642\pi$
$152$	−4.03503	−	3.38579i	−0.327284	−	0.274624i
$153$		0			0
$154$	−2.70310	+	2.26817i	−0.217822	+	0.182775i
$155$	7.10976	−	4.67616i	0.571070	−	0.375598i
$156$		0			0
$157$	7.62652	+	10.2442i	0.608662	+	0.817576i	0.994472	−	0.105003i	$-0.0334852\pi$
$157$	7.62652	+	10.2442i	0.608662	+	0.817576i	−0.385809	+	0.922578i	$0.626078\pi$
$158$	−1.29297	+	0.649352i	−0.102863	+	0.0516596i
$159$		0			0
$160$	−5.13596	+	1.21724i	−0.406033	+	0.0962316i
$161$	−12.8261			−1.01084
$162$		0			0
$163$	−0.599869			−0.0469853			−0.0234927	−	0.999724i	$-0.507479\pi$
$163$	−0.599869			−0.0469853			−0.0234927	+	0.999724i	$0.507479\pi$
$164$	10.9664	−	2.59909i	0.856332	−	0.202954i
$165$		0			0
$166$	1.64092	−	0.824101i	0.127360	−	0.0639626i
$167$	−1.81203	−	2.43398i	−0.140219	−	0.188347i	0.726466	−	0.687202i	$-0.241161\pi$
$167$	−1.81203	−	2.43398i	−0.140219	−	0.188347i	−0.866685	+	0.498855i	$0.833754\pi$
$168$		0			0
$169$	0.975825	−	0.641810i	0.0750635	−	0.0493700i
$170$	−0.155910	+	0.130824i	−0.0119578	+	0.0100337i
$171$		0			0
$172$	16.4988	+	13.8441i	1.25802	+	1.05560i
$173$	9.59030	+	1.12094i	0.729137	+	0.0852239i	0.472558	−	0.881300i	$-0.343331\pi$
$173$	9.59030	+	1.12094i	0.729137	+	0.0852239i	0.256579	+	0.966523i	$0.417405\pi$
$174$		0			0
$175$	1.83862	+	6.14143i	0.138987	+	0.464248i
$176$	−10.5844	+	11.2188i	−0.797828	+	0.845648i
$177$		0			0
$178$	2.35387	−	3.16180i	0.176430	−	0.236987i
$179$	−4.48229	+	25.4203i	−0.335022	+	1.90001i	0.0919897	+	0.995760i	$0.470677\pi$
$179$	−4.48229	+	25.4203i	−0.335022	+	1.90001i	−0.427012	+	0.904246i	$0.640434\pi$
$180$		0			0
$181$	0.154861	+	0.878259i	0.0115107	+	0.0652805i	0.990022	−	0.140913i	$-0.0450036\pi$
$181$	0.154861	+	0.878259i	0.0115107	+	0.0652805i	−0.978511	+	0.206193i	$0.933893\pi$
$182$	−2.22286	−	1.11636i	−0.164769	−	0.0827502i
$183$		0			0
$184$	9.73495	−	1.13785i	0.717670	−	0.0838836i
$185$	0.530220	+	0.348731i	0.0389825	+	0.0256392i
$186$		0			0
$187$	−0.586815	+	1.96010i	−0.0429122	+	0.143337i
$188$	5.63096	+	9.75311i	0.410680	+	0.711319i
$189$		0			0
$190$	−0.875665	+	1.51670i	−0.0635274	+	0.110033i
$191$	5.54100	+	5.87312i	0.400933	+	0.424964i	0.896113	−	0.443826i	$-0.146379\pi$
$191$	5.54100	+	5.87312i	0.400933	+	0.424964i	−0.495180	+	0.868790i	$0.664898\pi$
$192$		0			0
$193$	−0.0113262	+	0.194463i	−0.000815278	+	0.0139978i	−0.998691	−	0.0511445i	$-0.983713\pi$
$193$	−0.0113262	+	0.194463i	−0.000815278	+	0.0139978i	0.997876	+	0.0651423i	$0.0207501\pi$
$194$	0.324360	−	0.751952i	0.0232877	−	0.0539870i
$195$		0			0
$196$	−0.361694	−	6.21004i	−0.0258353	−	0.443574i
$197$	−10.8405	−	3.94561i	−0.772351	−	0.281113i	−0.0743718	−	0.997231i	$-0.523695\pi$
$197$	−10.8405	−	3.94561i	−0.772351	−	0.281113i	−0.697980	+	0.716118i	$0.745917\pi$
$198$		0			0
$199$	−1.65236	+	0.601410i	−0.117133	+	0.0426328i	−0.399922	−	0.916549i	$-0.630963\pi$
$199$	−1.65236	+	0.601410i	−0.117133	+	0.0426328i	0.282789	+	0.959182i	$0.408740\pi$
$200$	−1.94033	−	4.49819i	−0.137202	−	0.318070i
$201$		0			0
$202$	−6.01188	−	1.42484i	−0.422995	−	0.100252i
$203$	−9.33634	−	2.21275i	−0.655283	−	0.155305i
$204$		0			0
$205$	−3.08291	−	7.14700i	−0.215320	−	0.499168i
$206$	6.42671	−	2.33913i	0.447770	−	0.162975i
$207$		0			0
$208$	−10.2169	−	3.71864i	−0.708413	−	0.257841i
$209$	1.02371	+	17.5764i	0.0708114	+	1.21578i
$210$		0			0
$211$	−1.41664	+	3.28414i	−0.0975255	+	0.226090i	−0.959994	−	0.280022i	$-0.909658\pi$
$211$	−1.41664	+	3.28414i	−0.0975255	+	0.226090i	0.862468	+	0.506111i	$0.168918\pi$
$212$	−0.636971	+	10.9364i	−0.0437473	+	0.751113i
$213$		0			0
$214$	−4.19048	−	4.44165i	−0.286455	−	0.303625i
$215$	7.43730	−	12.8818i	0.507220	−	0.878530i
$216$		0			0
$217$	6.33898	+	10.9794i	0.430318	+	0.745333i
$218$	−0.877554	+	2.93123i	−0.0594354	+	0.198528i
$219$		0			0
$220$	9.70656	+	6.38411i	0.654416	+	0.430416i
$221$	−1.43257	+	0.167443i	−0.0963649	+	0.0112634i
$222$		0			0
$223$	−5.86322	−	2.94462i	−0.392630	−	0.197186i	0.241521	−	0.970396i	$-0.422354\pi$
$223$	−5.86322	−	2.94462i	−0.392630	−	0.197186i	−0.634151	+	0.773209i	$0.718650\pi$
$224$	−1.36551	−	7.74417i	−0.0912368	−	0.517429i
$225$		0			0
$226$	0.113106	−	0.641454i	0.00752367	−	0.0426689i
$227$	−4.85385	+	6.51985i	−0.322161	+	0.432738i	−0.933471	−	0.358654i	$-0.883236\pi$
$227$	−4.85385	+	6.51985i	−0.322161	+	0.432738i	0.611309	+	0.791392i	$0.290643\pi$
$228$		0			0
$229$	−5.37657	+	5.69883i	−0.355294	+	0.376589i	−0.880226	−	0.474555i	$-0.842609\pi$
$229$	−5.37657	+	5.69883i	−0.355294	+	0.376589i	0.524932	+	0.851144i	$0.324091\pi$
$230$	−0.934630	−	3.12188i	−0.0616277	−	0.205851i
$231$		0			0
$232$	7.28252	+	0.851204i	0.478121	+	0.0558843i
$233$	−19.7955	−	16.6104i	−1.29685	−	1.08818i	−0.990681	−	0.136205i	$-0.956509\pi$
$233$	−19.7955	−	16.6104i	−1.29685	−	1.08818i	−0.306166	−	0.951978i	$-0.599046\pi$
$234$		0			0
$235$	5.95818	−	4.99951i	0.388669	−	0.326132i
$236$	8.74144	−	5.74933i	0.569019	−	0.374250i
$237$		0			0
$238$	−0.181069	−	0.243218i	−0.0117370	−	0.0157655i
$239$	0.156903	−	0.0787995i	0.0101492	−	0.00509711i	−0.443717	−	0.896167i	$-0.646341\pi$
$239$	0.156903	−	0.0787995i	0.0101492	−	0.00509711i	0.453867	+	0.891070i	$0.350044\pi$
$240$		0			0
$241$	18.8079	−	4.45756i	1.21152	−	0.287137i	0.425286	−	0.905059i	$-0.360174\pi$
$241$	18.8079	−	4.45756i	1.21152	−	0.287137i	0.786239	+	0.617922i	$0.212025\pi$
$242$	−4.84915			−0.311715
$243$		0			0
$244$	5.16534			0.330677
$245$	−4.18033	+	0.990756i	−0.267071	+	0.0632971i
$246$		0			0
$247$	−11.0909	+	5.57008i	−0.705700	+	0.354416i
$248$	−5.78527	−	7.77096i	−0.367365	−	0.493457i
$249$		0			0
$250$	−3.38852	+	2.22866i	−0.214309	+	0.140953i
$251$	18.5138	−	15.5349i	1.16858	−	0.980554i	0.168592	−	0.985686i	$-0.446078\pi$
$251$	18.5138	−	15.5349i	1.16858	−	0.980554i	0.999987	+	0.00513137i	$0.00163337\pi$
$252$		0			0
$253$	−25.0962	−	21.0582i	−1.57778	−	1.32392i
$254$	1.92003	+	0.224419i	0.120473	+	0.0140813i
$255$		0			0
$256$	−1.64296	−	5.48786i	−0.102685	−	0.342991i
$257$	9.39588	−	9.95905i	0.586099	−	0.621228i	−0.364667	−	0.931138i	$-0.618817\pi$
$257$	9.39588	−	9.95905i	0.586099	−	0.621228i	0.950766	+	0.309909i	$0.100299\pi$
$258$		0			0
$259$	−0.564600	+	0.758389i	−0.0350825	+	0.0471240i
$260$	−1.42213	+	8.06530i	−0.0881968	+	0.500189i
$261$		0			0
$262$	0.765846	+	4.34333i	0.0473141	+	0.268332i
$263$	−12.9775	−	6.51756i	−0.800229	−	0.401890i	0.00118561	−	0.999999i	$-0.499623\pi$
$263$	−12.9775	−	6.51756i	−0.800229	−	0.401890i	−0.801415	+	0.598109i	$0.795919\pi$
$264$		0			0
$265$	7.51466	−	0.878338i	0.461622	−	0.0539559i
$266$	−2.17993	−	1.43376i	−0.133660	−	0.0879097i
$267$		0			0
$268$	−3.85348	+	12.8715i	−0.235389	+	0.786253i
$269$	0.0908847	+	0.157417i	0.00554134	+	0.00959788i	0.868783	−	0.495193i	$-0.164903\pi$
$269$	0.0908847	+	0.157417i	0.00554134	+	0.00959788i	−0.863241	+	0.504791i	$0.831569\pi$
$270$		0			0
$271$	−10.1446	+	17.5709i	−0.616239	+	1.06736i	0.373927	+	0.927458i	$0.378011\pi$
$271$	−10.1446	+	17.5709i	−0.616239	+	1.06736i	−0.990166	+	0.139899i	$0.955322\pi$
$272$	−0.909519	−	0.964034i	−0.0551477	−	0.0584531i
$273$		0			0
$274$	0.109025	−	1.87188i	0.00658642	−	0.113084i
$275$	−6.48557	+	15.0352i	−0.391095	+	0.906660i
$276$		0			0
$277$	0.647666	+	11.1200i	0.0389144	+	0.668135i	0.960211	+	0.279275i	$0.0900941\pi$
$277$	0.647666	+	11.1200i	0.0389144	+	0.668135i	−0.921297	+	0.388860i	$0.872869\pi$
$278$	5.98603	+	2.17874i	0.359018	+	0.130672i
$279$		0			0
$280$	−3.36063	+	1.22317i	−0.200836	+	0.0730983i
$281$	0.793419	+	1.83935i	0.0473314	+	0.109727i	0.940241	−	0.340509i	$-0.110599\pi$
$281$	0.793419	+	1.83935i	0.0473314	+	0.109727i	−0.892910	+	0.450235i	$0.851340\pi$
$282$		0			0
$283$	2.22602	+	0.527576i	0.132323	+	0.0313611i	0.296244	−	0.955112i	$-0.404266\pi$
$283$	2.22602	+	0.527576i	0.132323	+	0.0313611i	−0.163921	+	0.986474i	$0.552414\pi$
$284$	28.2891	+	6.70465i	1.67865	+	0.397848i
$285$		0			0
$286$	−2.51647	−	5.83384i	−0.148802	−	0.344962i
$287$	10.8968	−	3.96612i	0.643219	−	0.234112i
$288$		0			0
$289$	15.8096	+	5.75421i	0.929974	+	0.338483i
$290$	−0.141747	−	2.43371i	−0.00832369	−	0.142912i
$291$		0			0
$292$	4.84157	−	11.2240i	0.283331	−	0.656836i
$293$	−0.291717	+	5.00859i	−0.0170423	+	0.292605i	0.979008	+	0.203819i	$0.0653356\pi$
$293$	−0.291717	+	5.00859i	−0.0170423	+	0.292605i	−0.996051	+	0.0887854i	$0.971701\pi$
$294$		0			0
$295$	−4.95869	−	5.25591i	−0.288706	−	0.306011i
$296$	0.361248	−	0.625699i	0.0209971	−	0.0363680i
$297$		0			0
$298$	3.29840	+	5.71300i	0.191071	+	0.330945i
$299$	6.62340	−	22.1237i	0.383041	−	1.27945i
$300$		0			0
$301$	18.5149	+	12.1774i	1.06718	+	0.701895i
$302$	2.42708	−	0.283685i	0.139663	−	0.0163243i
$303$		0			0
$304$	−10.1916	−	5.11840i	−0.584527	−	0.293561i
$305$	−0.619464	−	3.51316i	−0.0354704	−	0.201163i
$306$		0			0
$307$	3.72532	−	21.1273i	0.212615	−	1.20580i	−0.672382	−	0.740204i	$-0.734729\pi$
$307$	3.72532	−	21.1273i	0.212615	−	1.20580i	0.884997	−	0.465596i	$-0.154160\pi$
$308$	−10.3359	+	13.8836i	−0.588945	+	0.791090i
$309$		0			0
$310$	−2.21048	+	2.34297i	−0.125547	+	0.133072i
$311$	3.45316	+	11.5344i	0.195811	+	0.654053i	0.998348	+	0.0574516i	$0.0182975\pi$
$311$	3.45316	+	11.5344i	0.195811	+	0.654053i	−0.802538	+	0.596601i	$0.796517\pi$
$312$		0			0
$313$	−9.24856	−	1.08100i	−0.522760	−	0.0611018i	−0.149379	−	0.988780i	$-0.547727\pi$
$313$	−9.24856	−	1.08100i	−0.522760	−	0.0611018i	−0.373381	+	0.927678i	$0.621801\pi$
$314$	−3.70327	−	3.10741i	−0.208988	−	0.175361i
$315$		0			0
$316$	−5.43668	+	4.56191i	−0.305837	+	0.256628i
$317$	−13.6839	+	9.00003i	−0.768563	+	0.505492i	−0.872216	−	0.489122i	$-0.837317\pi$
$317$	−13.6839	+	9.00003i	−0.768563	+	0.505492i	0.103652	+	0.994614i	$0.466947\pi$
$318$		0			0
$319$	−14.6349	−	19.6581i	−0.819399	−	1.10064i
$320$	−5.45869	+	2.74146i	−0.305150	+	0.153252i
$321$		0			0
$322$	4.72415	−	1.11964i	0.263267	−	0.0623953i
$323$	−1.51290			−0.0841803
$324$		0			0
$325$	−11.5428			−0.640277
$326$	0.220945	−	0.0523649i	0.0122370	−	0.00290022i
$327$		0			0
$328$	−7.91875	+	3.97695i	−0.437240	+	0.219590i
$329$	6.91966	+	9.29471i	0.381493	+	0.512434i
$330$		0			0
$331$	4.28517	−	2.81840i	0.235534	−	0.154913i	−0.426255	−	0.904603i	$-0.640167\pi$
$331$	4.28517	−	2.81840i	0.235534	−	0.154913i	0.661790	+	0.749689i	$0.269797\pi$
$332$	6.89976	−	5.78959i	0.378673	−	0.317745i
$333$		0			0
$334$	0.879884	+	0.738310i	0.0481451	+	0.0403985i
$335$	9.21658	+	1.07726i	0.503556	+	0.0588572i
$336$		0			0
$337$	−3.59205	−	11.9983i	−0.195671	−	0.653588i	−0.998363	−	0.0571939i	$-0.981785\pi$
$337$	−3.59205	−	11.9983i	−0.195671	−	0.653588i	0.802692	−	0.596394i	$-0.203401\pi$
$338$	−0.303392	+	0.321576i	−0.0165023	+	0.0174914i
$339$		0			0
$340$	−0.596158	+	0.800779i	−0.0323312	+	0.0434283i
$341$	−5.62311	+	31.8903i	−0.304509	+	1.72695i
$342$		0			0
$343$	−3.43362	−	19.4730i	−0.185398	−	1.05144i
$344$	−15.1329	−	7.60005i	−0.815914	−	0.409767i
$345$		0			0
$346$	−3.63017	+	0.424306i	−0.195159	+	0.0228108i
$347$	11.7607	+	7.73512i	0.631346	+	0.415243i	0.824449	−	0.565936i	$-0.191485\pi$
$347$	11.7607	+	7.73512i	0.631346	+	0.415243i	−0.193103	+	0.981178i	$0.561855\pi$
$348$		0			0
$349$	4.41633	−	14.7516i	0.236401	−	0.789633i	−0.754648	−	0.656130i	$-0.772192\pi$
$349$	4.41633	−	14.7516i	0.236401	−	0.789633i	0.991048	−	0.133503i	$-0.0426226\pi$
$350$	−1.21331	−	2.10152i	−0.0648544	−	0.112331i
$351$		0			0
$352$	10.0427	−	17.3945i	0.535278	−	0.927129i
$353$	−23.0484	−	24.4299i	−1.22674	−	1.30027i	−0.939556	−	0.342395i	$-0.888762\pi$
$353$	−23.0484	−	24.4299i	−1.22674	−	1.30027i	−0.287186	−	0.957875i	$-0.592720\pi$
$354$		0			0
$355$	1.16747	−	20.0447i	0.0619628	−	1.06386i
$356$	7.65820	−	17.7537i	0.405884	−	0.940945i
$357$		0			0
$358$	−0.568114	−	9.75415i	−0.0300258	−	0.515523i
$359$	11.6368	+	4.23546i	0.614168	+	0.223539i	0.630326	−	0.776330i	$-0.282921\pi$
$359$	11.6368	+	4.23546i	0.614168	+	0.223539i	−0.0161577	+	0.999869i	$0.505143\pi$
$360$		0			0
$361$	5.62081	−	2.04581i	0.295832	−	0.107674i
$362$	−0.133705	−	0.309964i	−0.00702739	−	0.0162913i
$363$		0			0
$364$	−11.8724	−	2.81380i	−0.622281	−	0.147483i
$365$	−8.21454	−	1.94688i	−0.429969	−	0.101904i
$366$		0			0
$367$	11.3665	+	26.3505i	0.593327	+	1.37549i	0.905047	+	0.425312i	$0.139836\pi$
$367$	11.3665	+	26.3505i	0.593327	+	1.37549i	−0.311720	+	0.950174i	$0.600905\pi$
$368$	19.9414	−	7.25809i	1.03952	−	0.378354i
$369$		0			0
$370$	−0.225734	−	0.0821603i	−0.0117353	−	0.00427131i
$371$	0.655393	+	11.2527i	0.0340263	+	0.584209i
$372$		0			0
$373$	7.52047	−	17.4344i	0.389395	−	0.902720i	−0.604924	−	0.796283i	$-0.706797\pi$
$373$	7.52047	−	17.4344i	0.389395	−	0.902720i	0.994319	−	0.106437i	$-0.0339441\pi$
$374$	0.0450322	−	0.773173i	0.00232856	−	0.0399798i
$375$		0			0
$376$	−6.07654	−	6.44075i	−0.313373	−	0.332156i
$377$	8.63804	−	14.9615i	0.444882	−	0.770557i
$378$		0			0
$379$	−9.40390	−	16.2880i	−0.483046	−	0.836660i	0.516764	−	0.856128i	$-0.327136\pi$
$379$	−9.40390	−	16.2880i	−0.483046	−	0.836660i	−0.999810	+	0.0194673i	$0.993803\pi$
$380$	−2.46379	+	8.22963i	−0.126390	+	0.422171i
$381$		0			0
$382$	−2.55356	−	1.67950i	−0.130651	−	0.0859308i
$383$	−6.61584	+	0.773280i	−0.338053	+	0.0395128i	−0.283426	−	0.958994i	$-0.591471\pi$
$383$	−6.61584	+	0.773280i	−0.338053	+	0.0395128i	−0.0546272	+	0.998507i	$0.517397\pi$
$384$		0			0
$385$	10.6823	+	5.36488i	0.544423	+	0.273419i
$386$	−0.0128038	−	0.0726138i	−0.000651695	−	0.00369595i
$387$		0			0
$388$	0.697536	−	3.95592i	0.0354120	−	0.200832i
$389$	0.522322	−	0.701600i	0.0264828	−	0.0355725i	−0.788685	−	0.614798i	$-0.789238\pi$
$389$	0.522322	−	0.701600i	0.0264828	−	0.0355725i	0.815167	+	0.579225i	$0.196645\pi$
$390$		0			0
$391$	1.93186	−	2.04766i	0.0976986	−	0.103554i
$392$	1.40275	+	4.68551i	0.0708496	+	0.236654i
$393$		0			0
$394$	4.33721	+	0.506947i	0.218505	+	0.0255396i
$395$	3.75475	+	3.15061i	0.188922	+	0.158524i
$396$		0			0
$397$	26.1379	−	21.9323i	1.31182	−	1.10075i	0.323854	−	0.946107i	$-0.395021\pi$
$397$	26.1379	−	21.9323i	1.31182	−	1.10075i	0.987970	−	0.154644i	$-0.0494231\pi$
$398$	0.556101	−	0.365753i	0.0278748	−	0.0183336i
$399$		0			0
$400$	−6.33392	−	8.50793i	−0.316696	−	0.425397i
$401$	−3.75292	+	1.88479i	−0.187412	+	0.0941218i	−0.540031	−	0.841645i	$-0.681587\pi$
$401$	−3.75292	+	1.88479i	−0.187412	+	0.0941218i	0.352619	+	0.935767i	$0.385291\pi$
$402$		0			0
$403$	−22.2118	+	5.26429i	−1.10645	+	0.262233i
$404$	−30.3060			−1.50778
$405$		0			0
$406$	3.63194			0.180250
$407$	−2.34985	+	0.556926i	−0.116478	+	0.0276058i
$408$		0			0
$409$	19.3745	−	9.73022i	0.958006	−	0.481129i	0.100124	−	0.994975i	$-0.468076\pi$
$409$	19.3745	−	9.73022i	0.958006	−	0.481129i	0.857882	+	0.513846i	$0.171780\pi$
$410$	1.75939	+	2.36328i	0.0868903	+	0.116714i
$411$		0			0
$412$	28.0282	−	18.4344i	1.38085	−	0.908198i
$413$	8.24668	−	6.91978i	0.405792	−	0.340500i
$414$		0			0
$415$	−4.76520	−	3.99848i	−0.233915	−	0.196278i
$416$	14.0630	+	1.64373i	0.689496	+	0.0805905i
$417$		0			0
$418$	−1.91137	−	6.38441i	−0.0934880	−	0.312272i
$419$	2.87237	−	3.04453i	0.140324	−	0.148735i	−0.653400	−	0.757013i	$-0.726658\pi$
$419$	2.87237	−	3.04453i	0.140324	−	0.148735i	0.793724	+	0.608278i	$0.208139\pi$
$420$		0			0
$421$	2.96790	−	3.98658i	0.144647	−	0.194294i	−0.723895	−	0.689910i	$-0.757650\pi$
$421$	2.96790	−	3.98658i	0.144647	−	0.194294i	0.868542	+	0.495616i	$0.165058\pi$
$422$	0.235094	−	1.33328i	0.0114442	−	0.0649033i
$423$		0			0
$424$	−1.49570	−	8.48255i	−0.0726377	−	0.411949i
$425$	−1.25739	−	0.631487i	−0.0609925	−	0.0306316i
$426$		0			0
$427$	5.27879	−	0.617002i	0.255459	−	0.0298588i
$428$	−25.0252	−	16.4594i	−1.20964	−	0.795593i
$429$		0			0
$430$	−1.61482	+	5.39387i	−0.0778735	+	0.260116i
$431$	−13.2418	−	22.9355i	−0.637837	−	1.10477i	−0.985907	−	0.167297i	$-0.946496\pi$
$431$	−13.2418	−	22.9355i	−0.637837	−	1.10477i	0.348070	−	0.937469i	$-0.386837\pi$
$432$		0			0
$433$	−10.6919	+	18.5189i	−0.513820	+	0.889962i	0.486052	+	0.873930i	$0.338437\pi$
$433$	−10.6919	+	18.5189i	−0.513820	+	0.889962i	−0.999871	+	0.0160319i	$0.994897\pi$
$434$	−3.29322	−	3.49061i	−0.158080	−	0.167555i
$435$		0			0
$436$	−0.872675	+	14.9832i	−0.0417935	+	0.717567i
$437$	9.59467	−	22.2429i	0.458975	−	1.06402i
$438$		0			0
$439$	−1.87864	−	32.2549i	−0.0896624	−	1.53944i	−0.680557	−	0.732696i	$-0.738262\pi$
$439$	−1.87864	−	32.2549i	−0.0896624	−	1.53944i	0.590894	−	0.806749i	$-0.298775\pi$
$440$	−8.58376	−	3.12423i	−0.409215	−	0.148942i
$441$		0			0
$442$	0.513029	−	0.186727i	0.0244023	−	0.00888171i
$443$	−12.8789	−	29.8566i	−0.611894	−	1.41853i	−0.889098	−	0.457718i	$-0.848667\pi$
$443$	−12.8789	−	29.8566i	−0.611894	−	1.41853i	0.277204	−	0.960811i	$-0.410592\pi$
$444$		0			0
$445$	−12.9935	−	3.07950i	−0.615949	−	0.145983i
$446$	2.41660	+	0.572744i	0.114429	+	0.0271202i
$447$		0			0
$448$	−3.60452	−	8.35621i	−0.170297	−	0.394794i
$449$	15.0197	−	5.46673i	0.708825	−	0.257991i	0.0376508	−	0.999291i	$-0.488013\pi$
$449$	15.0197	−	5.46673i	0.708825	−	0.257991i	0.671174	+	0.741300i	$0.265790\pi$
$450$		0			0
$451$	27.8328	+	10.1303i	1.31059	+	0.477017i
$452$	−0.185770	−	3.18955i	−0.00873790	−	0.150024i
$453$		0			0
$454$	1.21864	−	2.82512i	0.0571934	−	0.132589i
$455$	−0.489962	+	8.41233i	−0.0229698	+	0.394376i
$456$		0			0
$457$	−13.2384	−	14.0319i	−0.619268	−	0.656386i	0.339490	−	0.940610i	$-0.389746\pi$
$457$	−13.2384	−	14.0319i	−0.619268	−	0.656386i	−0.958758	+	0.284224i	$0.908264\pi$
$458$	1.48283	−	2.56834i	0.0692883	−	0.120011i
$459$		0			0
$460$	−7.99240	−	13.8432i	−0.372648	−	0.645445i
$461$	−4.25033	+	14.1971i	−0.197957	+	0.661224i	0.800154	+	0.599795i	$0.204751\pi$
$461$	−4.25033	+	14.1971i	−0.197957	+	0.661224i	−0.998111	+	0.0614293i	$0.980434\pi$
$462$		0			0
$463$	−2.31382	−	1.52182i	−0.107532	−	0.0707252i	0.494604	−	0.869119i	$-0.335313\pi$
$463$	−2.31382	−	1.52182i	−0.107532	−	0.0707252i	−0.602136	+	0.798393i	$0.705684\pi$
$464$	15.7678	−	1.84299i	0.732003	−	0.0855589i
$465$		0			0
$466$	8.74110	+	4.38995i	0.404924	+	0.203360i
$467$	3.42252	+	19.4101i	0.158375	+	0.898191i	0.955635	+	0.294554i	$0.0951712\pi$
$467$	3.42252	+	19.4101i	0.158375	+	0.898191i	−0.797259	+	0.603637i	$0.793718\pi$
$468$		0			0
$469$	−2.40061	+	13.6145i	−0.110850	+	0.628661i
$470$	−1.75810	+	2.36154i	−0.0810952	+	0.108930i
$471$		0			0
$472$	−5.64529	+	5.98366i	−0.259845	+	0.275420i
$473$	16.2338	+	54.2248i	0.746433	+	2.49326i
$474$		0			0
$475$	−12.0258	−	1.40561i	−0.551781	−	0.0644939i
$476$	−1.13936	−	0.956036i	−0.0522224	−	0.0438198i
$477$		0			0
$478$	−0.0509120	+	0.0427202i	−0.00232866	+	0.00195398i
$479$	−15.5739	+	10.2431i	−0.711588	+	0.468019i	−0.852986	−	0.521934i	$-0.825211\pi$
$479$	−15.5739	+	10.2431i	−0.711588	+	0.468019i	0.141398	+	0.989953i	$0.454840\pi$
$480$		0			0
$481$	−1.01658	−	1.36550i	−0.0463521	−	0.0622616i
$482$	−6.53825	+	3.28363i	−0.297809	+	0.149565i
$483$		0			0
$484$	−23.1446	+	5.48537i	−1.05203	+	0.249335i
$485$	−2.77424			−0.125972
$486$		0			0
$487$	−5.34343			−0.242134			−0.121067	−	0.992644i	$-0.538632\pi$
$487$	−5.34343			−0.242134			−0.121067	+	0.992644i	$0.538632\pi$
$488$	−3.95183	+	0.936600i	−0.178891	+	0.0423979i
$489$		0			0
$490$	1.45322	−	0.729834i	0.0656497	−	0.0329705i
$491$	2.21017	+	2.96877i	0.0997434	+	0.133979i	0.849193	−	0.528083i	$-0.177089\pi$
$491$	2.21017	+	2.96877i	0.0997434	+	0.133979i	−0.749449	+	0.662062i	$0.769682\pi$
$492$		0			0
$493$	1.75949	−	1.15724i	0.0792436	−	0.0521193i
$494$	3.59880	−	3.01975i	0.161918	−	0.135865i
$495$		0			0
$496$	−16.0686	−	13.4832i	−0.721501	−	0.605411i
$497$	29.7114	+	3.47276i	1.33274	+	0.155775i
$498$		0			0
$499$	8.01629	+	26.7763i	0.358858	+	1.19867i	0.926785	+	0.375592i	$0.122560\pi$
$499$	8.01629	+	26.7763i	0.358858	+	1.19867i	−0.567927	+	0.823079i	$0.692254\pi$
$500$	−13.6521	+	14.4703i	−0.610539	+	0.647134i
$501$		0			0
$502$	−5.46293	+	7.33798i	−0.243822	+	0.327510i
$503$	−1.72317	+	9.77258i	−0.0768323	+	0.435738i	0.921990	+	0.387214i	$0.126563\pi$
$503$	−1.72317	+	9.77258i	−0.0768323	+	0.435738i	−0.998822	+	0.0485234i	$0.984548\pi$
$504$		0			0
$505$	3.63452	+	20.6124i	0.161734	+	0.917239i
$506$	11.0817	+	5.56544i	0.492642	+	0.247414i
$507$		0			0
$508$	9.41802	−	1.10081i	0.417857	−	0.0488405i
$509$	0.0236368	+	0.0155462i	0.00104768	+	0.000689072i	0.550033	−	0.835143i	$-0.314615\pi$
$509$	0.0236368	+	0.0155462i	0.00104768	+	0.000689072i	−0.548985	+	0.835832i	$0.684986\pi$
$510$		0			0
$511$	3.60719	−	12.0489i	0.159573	−	0.533011i
$512$	11.1197	+	19.2599i	0.491426	+	0.851176i
$513$		0			0
$514$	−2.59134	+	4.48834i	−0.114299	+	0.197972i
$515$	−15.8993	−	16.8523i	−0.700608	−	0.742601i
$516$		0			0
$517$	−1.72093	+	29.5472i	−0.0756864	+	1.29949i
$518$	0.141752	−	0.328617i	0.00622821	−	0.0144386i
$519$		0			0
$520$	−0.374409	−	6.42836i	−0.0164189	−	0.281902i
$521$	−2.11604	−	0.770177i	−0.0927056	−	0.0337421i	0.295251	−	0.955420i	$-0.404597\pi$
$521$	−2.11604	−	0.770177i	−0.0927056	−	0.0337421i	−0.387957	+	0.921678i	$0.626819\pi$
$522$		0			0
$523$	−11.5433	+	4.20142i	−0.504753	+	0.183715i	−0.581831	−	0.813310i	$-0.697663\pi$
$523$	−11.5433	+	4.20142i	−0.504753	+	0.183715i	0.0770775	+	0.997025i	$0.475441\pi$
$524$	8.56852	+	19.8641i	0.374317	+	0.867765i
$525$		0			0
$526$	5.34885	+	1.26770i	0.233221	+	0.0552744i
$527$	−2.70761	−	0.641715i	−0.117945	−	0.0279535i
$528$		0			0
$529$	8.74344	+	20.2696i	0.380149	+	0.881285i
$530$	−2.69114	+	0.979495i	−0.116896	+	0.0425465i
$531$		0			0
$532$	−12.0265	−	4.37730i	−0.521416	−	0.189780i
$533$	1.21402	+	20.8439i	0.0525851	+	0.902851i
$534$		0			0
$535$	−8.19348	+	18.9946i	−0.354235	+	0.821209i
$536$	0.614252	−	10.5463i	0.0265316	−	0.455531i
$537$		0			0
$538$	−0.0472163	−	0.0500464i	−0.00203564	−	0.00215765i
$539$	8.17409	−	14.1579i	0.352083	−	0.609826i
$540$		0			0
$541$	19.8474	+	34.3766i	0.853304	+	1.47797i	0.878209	+	0.478277i	$0.158738\pi$
$541$	19.8474	+	34.3766i	0.853304	+	1.47797i	−0.0249047	+	0.999690i	$0.507928\pi$
$542$	2.20263	−	7.35731i	0.0946113	−	0.316024i
$543$		0			0
$544$	1.44201	+	0.948422i	0.0618255	+	0.0406633i
$545$	10.2954	−	1.20336i	0.441005	−	0.0515461i
$546$		0			0
$547$	7.26795	+	3.65010i	0.310755	+	0.156067i	0.597341	−	0.801988i	$-0.296224\pi$
$547$	7.26795	+	3.65010i	0.310755	+	0.156067i	−0.286586	+	0.958055i	$0.592520\pi$
$548$	−1.59711	−	9.05767i	−0.0682252	−	0.386924i
$549$		0			0
$550$	1.07629	−	6.10396i	0.0458933	−	0.260274i
$551$	10.8214	−	14.5357i	0.461009	−	0.619242i
$552$		0			0
$553$	−5.01117	+	5.31153i	−0.213097	+	0.225869i
$554$	−1.20926	−	4.03920i	−0.0513764	−	0.171609i
$555$		0			0
$556$	31.0354	+	3.62752i	1.31620	+	0.153841i
$557$	−16.2629	−	13.6462i	−0.689081	−	0.578207i	0.229563	−	0.973294i	$-0.426270\pi$
$557$	−16.2629	−	13.6462i	−0.689081	−	0.578207i	−0.918644	+	0.395086i	$0.870715\pi$
$558$		0			0
$559$	−30.5658	+	25.6477i	−1.29279	+	1.08478i
$560$	−6.46942	+	4.25500i	−0.273383	+	0.179807i
$561$		0			0
$562$	−0.452798	−	0.608213i	−0.0191001	−	0.0256559i
$563$	−40.3740	+	20.2766i	−1.70156	+	0.854556i	−0.713469	+	0.700686i	$0.752877\pi$
$563$	−40.3740	+	20.2766i	−1.70156	+	0.854556i	−0.988091	+	0.153869i	$0.950827\pi$
$564$		0			0
$565$	−2.14707	+	0.508864i	−0.0903278	+	0.0214081i
$566$	−0.865945			−0.0363984
$567$		0			0
$568$	−22.8588			−0.959134
$569$	5.58216	−	1.32300i	0.234017	−	0.0554629i	−0.111934	−	0.993716i	$-0.535705\pi$
$569$	5.58216	−	1.32300i	0.234017	−	0.0554629i	0.345951	+	0.938253i	$0.387556\pi$
$570$		0			0
$571$	38.7524	−	19.4622i	1.62174	−	0.814467i	0.622237	−	0.782829i	$-0.286224\pi$
$571$	38.7524	−	19.4622i	1.62174	−	0.814467i	0.999499	−	0.0316376i	$-0.0100722\pi$
$572$	−18.6102	−	24.9978i	−0.778132	−	1.04521i
$573$		0			0
$574$	−3.66732	+	2.41203i	−0.153071	+	0.100676i
$575$	17.2584	−	14.4816i	0.719727	−	0.603923i
$576$		0			0
$577$	10.1857	+	8.54680i	0.424035	+	0.355808i	0.829696	−	0.558216i	$-0.188514\pi$
$577$	10.1857	+	8.54680i	0.424035	+	0.355808i	−0.405660	+	0.914024i	$0.632958\pi$
$578$	−6.32531	−	0.739323i	−0.263098	−	0.0307518i
$579$		0			0
$580$	−3.42957	−	11.4555i	−0.142405	−	0.475666i
$581$	6.35974	−	6.74093i	0.263847	−	0.279661i
$582$		0			0
$583$	−17.1924	+	23.0935i	−0.712038	+	0.956433i
$584$	−1.66894	+	9.46501i	−0.0690611	+	0.391665i
$585$		0			0
$586$	−0.329773	−	1.87024i	−0.0136228	−	0.0772588i
$587$	11.0537	+	5.55138i	0.456235	+	0.229130i	0.662048	−	0.749461i	$-0.269687\pi$
$587$	11.0537	+	5.55138i	0.456235	+	0.229130i	−0.205813	+	0.978591i	$0.565984\pi$
$588$		0			0
$589$	−23.7823	+	2.77976i	−0.979934	+	0.114538i
$590$	2.28520	+	1.50300i	0.0940803	+	0.0618776i
$591$		0			0
$592$	0.448652	−	1.49860i	0.0184395	−	0.0615921i
$593$	0.572367	+	0.991369i	0.0235043	+	0.0407106i	0.877538	−	0.479507i	$-0.159184\pi$
$593$	0.572367	+	0.991369i	0.0235043	+	0.0407106i	−0.854034	+	0.520217i	$0.825851\pi$
$594$		0			0
$595$	−0.513599	+	0.889579i	−0.0210555	+	0.0364692i
$596$	22.2056	+	23.5365i	0.909576	+	0.964094i
$597$		0			0
$598$	−0.508280	+	8.72683i	−0.0207851	+	0.356867i
$599$	0.960870	−	2.22755i	0.0392601	−	0.0910151i	−0.897458	−	0.441101i	$-0.854588\pi$
$599$	0.960870	−	2.22755i	0.0392601	−	0.0910151i	0.936718	+	0.350085i	$0.113847\pi$
$600$		0			0
$601$	2.28082	+	39.1601i	0.0930364	+	1.59737i	0.645449	+	0.763803i	$0.276670\pi$
$601$	2.28082	+	39.1601i	0.0930364	+	1.59737i	−0.552413	+	0.833571i	$0.686293\pi$
$602$	−7.88244	−	2.86897i	−0.321264	−	0.116931i
$603$		0			0
$604$	11.2634	−	4.09953i	0.458300	−	0.166808i
$605$	6.50650	+	15.0838i	0.264527	+	0.613242i
$606$		0			0
$607$	−6.89165	−	1.63335i	−0.279724	−	0.0662957i	0.0883594	−	0.996089i	$-0.471838\pi$
$607$	−6.89165	−	1.63335i	−0.279724	−	0.0662957i	−0.368083	+	0.929793i	$0.619986\pi$
$608$	14.4513	+	3.42503i	0.586079	+	0.138903i
$609$		0			0
$610$	0.534839	+	1.23990i	0.0216550	+	0.0502020i
$611$	−19.6057	+	7.13588i	−0.793161	+	0.288687i
$612$		0			0
$613$	19.4482	+	7.07855i	0.785503	+	0.285900i	0.703466	−	0.710729i	$-0.251635\pi$
$613$	19.4482	+	7.07855i	0.785503	+	0.285900i	0.0820378	+	0.996629i	$0.473857\pi$
$614$	0.472171	+	8.10686i	0.0190553	+	0.327166i
$615$		0			0
$616$	5.39026	−	12.4960i	0.217180	−	0.503479i
$617$	1.38614	−	23.7991i	0.0558038	−	0.958114i	−0.847954	−	0.530070i	$-0.822166\pi$
$617$	1.38614	−	23.7991i	0.0558038	−	0.958114i	0.903758	−	0.428044i	$-0.140797\pi$
$618$		0			0
$619$	0.456777	+	0.484155i	0.0183594	+	0.0194598i	0.736488	−	0.676450i	$-0.236483\pi$
$619$	0.456777	+	0.484155i	0.0183594	+	0.0194598i	−0.718129	+	0.695910i	$0.755001\pi$
$620$	−7.90007	+	13.6833i	−0.317274	+	0.549535i
$621$		0			0
$622$	−2.27875	−	3.94691i	−0.0913696	−	0.158257i
$623$	5.70572	−	19.0584i	0.228595	−	0.763560i
$624$		0			0
$625$	−2.53901	−	1.66993i	−0.101560	−	0.0667973i
$626$	3.50081	−	0.409186i	0.139921	−	0.0163544i
$627$		0			0
$628$	−21.1905	−	10.6423i	−0.845594	−	0.424673i
$629$	−0.0360350	−	0.204365i	−0.00143681	−	0.00814855i
$630$		0			0
$631$	4.06193	−	23.0363i	0.161703	−	0.917062i	−0.790696	−	0.612209i	$-0.790281\pi$
$631$	4.06193	−	23.0363i	0.161703	−	0.917062i	0.952399	−	0.304854i	$-0.0986076\pi$
$632$	3.33223	−	4.47597i	0.132549	−	0.178044i
$633$		0			0
$634$	4.25442	−	4.50943i	0.168965	−	0.179092i
$635$	−1.87818	−	6.27356i	−0.0745334	−	0.248959i
$636$		0			0
$637$	11.4463	+	1.33789i	0.453521	+	0.0530090i
$638$	7.10640	+	5.96298i	0.281345	+	0.236077i
$639$		0			0
$640$	9.85797	−	8.27182i	0.389670	−	0.326972i
$641$	−5.94994	+	3.91334i	−0.235009	+	0.154568i	−0.661551	−	0.749900i	$-0.730102\pi$
$641$	−5.94994	+	3.91334i	−0.235009	+	0.154568i	0.426543	+	0.904467i	$0.359731\pi$
$642$		0			0
$643$	9.24097	+	12.4128i	0.364428	+	0.489512i	0.946083	−	0.323924i	$-0.105002\pi$
$643$	9.24097	+	12.4128i	0.364428	+	0.489512i	−0.581655	+	0.813436i	$0.697595\pi$
$644$	21.2815	−	10.6879i	0.838607	−	0.421164i
$645$		0			0
$646$	0.557236	−	0.132067i	0.0219242	−	0.00519612i
$647$	−15.3916			−0.605107			−0.302554	−	0.953132i	$-0.597839\pi$
$647$	−15.3916			−0.605107			−0.302554	+	0.953132i	$0.597839\pi$
$648$		0			0
$649$	27.4968			1.07934
$650$	4.25145	−	1.00761i	0.166756	−	0.0395218i
$651$		0			0
$652$	0.995317	−	0.499867i	0.0389796	−	0.0195763i
$653$	−0.735567	−	0.988038i	−0.0287850	−	0.0386649i	0.787498	−	0.616318i	$-0.211376\pi$
$653$	−0.735567	−	0.988038i	−0.0287850	−	0.0386649i	−0.816283	+	0.577653i	$0.803969\pi$
$654$		0			0
$655$	12.4828	−	8.21004i	0.487742	−	0.320793i
$656$	−14.6975	+	12.3326i	−0.573839	+	0.481508i
$657$		0			0
$658$	−3.36003	−	2.81940i	−0.130988	−	0.109912i
$659$	−6.85544	−	0.801287i	−0.267050	−	0.0312137i	−0.0184860	−	0.999829i	$-0.505885\pi$
$659$	−6.85544	−	0.801287i	−0.267050	−	0.0312137i	−0.248564	+	0.968615i	$0.579959\pi$
$660$		0			0
$661$	10.3084	+	34.4323i	0.400948	+	1.33926i	0.885557	+	0.464530i	$0.153777\pi$
$661$	10.3084	+	34.4323i	0.400948	+	1.33926i	−0.484609	+	0.874731i	$0.661038\pi$
$662$	−1.33229	+	1.41215i	−0.0517811	+	0.0548847i
$663$		0			0
$664$	−4.22898	+	5.68051i	−0.164116	+	0.220447i
$665$	−1.53487	+	8.70469i	−0.0595198	+	0.337553i
$666$		0			0
$667$	5.85536	+	33.2074i	0.226720	+	1.28579i
$668$	5.03480	+	2.52857i	0.194802	+	0.0978333i
$669$		0			0
$670$	−3.48871	+	0.407771i	−0.134781	+	0.0157536i
$671$	11.3417	+	7.45955i	0.437841	+	0.287973i
$672$		0			0
$673$	−2.49492	+	8.33360i	−0.0961719	+	0.321237i	−0.992515	−	0.122125i	$-0.961029\pi$
$673$	−2.49492	+	8.33360i	−0.0961719	+	0.321237i	0.896343	+	0.443362i	$0.146214\pi$
$674$	2.37041	+	4.10567i	0.0913047	+	0.158144i
$675$		0			0
$676$	−1.08430	+	1.87806i	−0.0417037	+	0.0722329i
$677$	0.396082	+	0.419823i	0.0152227	+	0.0161351i	0.734940	−	0.678132i	$-0.237210\pi$
$677$	0.396082	+	0.419823i	0.0152227	+	0.0161351i	−0.719718	+	0.694267i	$0.755729\pi$
$678$		0			0
$679$	0.240320	−	4.12614i	0.00922264	−	0.158347i
$680$	0.310900	−	0.720747i	0.0119225	−	0.0276394i
$681$		0			0
$682$	−0.712709	−	12.2367i	−0.0272910	−	0.468569i
$683$	33.8572	+	12.3230i	1.29551	+	0.471528i	0.895532	−	0.444997i	$-0.146795\pi$
$683$	33.8572	+	12.3230i	1.29551	+	0.471528i	0.399979	+	0.916524i	$0.369017\pi$
$684$		0			0
$685$	−5.96895	+	2.17252i	−0.228062	+	0.0830078i
$686$	2.96455	+	6.87260i	0.113187	+	0.262397i
$687$		0			0
$688$	−35.6769	−	8.45559i	−1.36017	−	0.322366i
$689$	−19.7481	−	4.68038i	−0.752342	−	0.178308i
$690$		0			0
$691$	−5.81367	−	13.4776i	−0.221163	−	0.512712i	0.771123	−	0.636686i	$-0.219695\pi$
$691$	−5.81367	−	13.4776i	−0.221163	−	0.512712i	−0.992285	+	0.123974i	$0.960436\pi$
$692$	−16.8465	+	6.13164i	−0.640409	+	0.233090i
$693$		0			0
$694$	−5.00694	−	1.82238i	−0.190061	−	0.0691765i
$695$	−1.25477	−	21.5435i	−0.0475960	−	0.817192i
$696$		0			0
$697$	−1.00809	+	2.33702i	−0.0381842	+	0.0885209i
$698$	−0.338909	+	5.81884i	−0.0128279	+	0.220246i
$699$		0			0
$700$	−8.16830	−	8.65790i	−0.308733	−	0.327238i
$701$	−15.3027	+	26.5051i	−0.577976	+	1.00108i	0.417735	+	0.908569i	$0.362824\pi$
$701$	−15.3027	+	26.5051i	−0.577976	+	1.00108i	−0.995711	+	0.0925152i	$0.970509\pi$
$702$		0			0
$703$	−0.892837	−	1.54644i	−0.0336740	−	0.0583250i
$704$	6.66661	−	22.2680i	0.251257	−	0.839258i
$705$		0			0
$706$	10.6218	+	6.98607i	0.399757	+	0.262924i
$707$	−30.9717	+	3.62007i	−1.16481	+	0.136147i
$708$		0			0
$709$	41.1962	+	20.6895i	1.54715	+	0.777010i	0.998265	−	0.0588852i	$-0.0187546\pi$
$709$	41.1962	+	20.6895i	1.54715	+	0.777010i	0.548889	+	0.835895i	$0.315051\pi$
$710$	1.31977	+	7.48480i	0.0495302	+	0.280900i
$711$		0			0
$712$	−2.63986	+	14.9714i	−0.0989329	+	0.561077i
$713$	26.6059	−	35.7380i	0.996400	−	1.33840i
$714$		0			0
$715$	−14.7702	+	15.6555i	−0.552373	+	0.585482i
$716$	−13.7455	−	45.9131i	−0.513693	−	1.71585i
$717$		0			0
$718$	−4.65583	−	0.544188i	−0.173754	−	0.0203089i
$719$	15.5899	+	13.0815i	0.581404	+	0.487856i	0.885408	−	0.464815i	$-0.153879\pi$
$719$	15.5899	+	13.0815i	0.581404	+	0.487856i	−0.304004	+	0.952671i	$0.598324\pi$
$720$		0			0
$721$	26.4418	−	22.1873i	0.984743	−	0.826298i
$722$	−1.89168	+	1.24418i	−0.0704011	+	0.0463035i
$723$		0			0
$724$	−0.988797	−	1.32819i	−0.0367484	−	0.0493616i
$725$	15.0610	−	7.56393i	0.559353	−	0.280917i
$726$		0			0
$727$	−23.6498	+	5.60511i	−0.877123	+	0.207882i	−0.644425	−	0.764667i	$-0.722903\pi$
$727$	−23.6498	+	5.60511i	−0.877123	+	0.207882i	−0.232698	+	0.972549i	$0.574755\pi$
$728$	9.59336			0.355554
$729$		0			0
$730$	3.19555			0.118272
$731$	−4.73278	+	1.12169i	−0.175048	+	0.0414872i
$732$		0			0
$733$	−35.6503	+	17.9042i	−1.31677	+	0.661308i	−0.961847	−	0.273587i	$-0.911790\pi$
$733$	−35.6503	+	17.9042i	−1.31677	+	0.661308i	−0.354925	+	0.934895i	$0.615494\pi$
$734$	−6.48677	−	8.71325i	−0.239431	−	0.321612i
$735$		0			0
$736$	−23.0889	+	15.1858i	−0.851067	+	0.559756i
$737$	−27.0497	+	22.6974i	−0.996389	+	0.836069i
$738$		0			0
$739$	6.20932	+	5.21024i	0.228413	+	0.191662i	0.749811	−	0.661652i	$-0.230145\pi$
$739$	6.20932	+	5.21024i	0.228413	+	0.191662i	−0.521397	+	0.853314i	$0.674589\pi$
$740$	−1.17035	−	0.136794i	−0.0430229	−	0.00502866i
$741$		0			0
$742$	−1.22368	−	4.08739i	−0.0449229	−	0.150053i
$743$	17.0239	−	18.0443i	0.624546	−	0.661980i	−0.335429	−	0.942066i	$-0.608881\pi$
$743$	17.0239	−	18.0443i	0.624546	−	0.661980i	0.959975	+	0.280085i	$0.0903627\pi$
$744$		0			0
$745$	13.3451	−	17.9256i	0.488927	−	0.656743i
$746$	−1.24804	+	7.07796i	−0.0456938	+	0.259143i
$747$		0			0
$748$	−0.659681	−	3.74124i	−0.0241203	−	0.136793i
$749$	−27.5410	−	13.8316i	−1.00633	−	0.505396i
$750$		0			0
$751$	31.4482	−	3.67576i	1.14756	−	0.134130i	0.479018	−	0.877805i	$-0.340993\pi$
$751$	31.4482	−	3.67576i	1.14756	−	0.134130i	0.668542	+	0.743675i	$0.266919\pi$
$752$	−16.0180	−	10.5352i	−0.584118	−	0.384180i
$753$		0			0
$754$	−1.87553	+	6.26470i	−0.0683027	+	0.228147i
$755$	−4.13904	−	7.16903i	−0.150635	−	0.260908i
$756$		0			0
$757$	−7.21394	+	12.4949i	−0.262195	+	0.454135i	−0.966825	−	0.255440i	$-0.917780\pi$
$757$	−7.21394	+	12.4949i	−0.262195	+	0.454135i	0.704630	+	0.709575i	$0.251113\pi$
$758$	4.88551	+	5.17834i	0.177450	+	0.188086i
$759$		0			0
$760$	0.392733	−	6.74296i	0.0142459	−	0.244593i
$761$	8.84381	−	20.5023i	0.320588	−	0.743207i	−0.679368	−	0.733798i	$-0.737746\pi$
$761$	8.84381	−	20.5023i	0.320588	−	0.743207i	0.999956	−	0.00940855i	$-0.00299488\pi$
$762$		0			0
$763$	0.897914	+	15.4166i	0.0325067	+	0.558118i
$764$	−14.0878	−	5.12754i	−0.509679	−	0.185508i
$765$		0			0
$766$	2.36925	−	0.862338i	0.0856046	−	0.0311575i
$767$	7.67730	+	17.7980i	0.277211	+	0.642648i
$768$		0			0
$769$	26.5460	+	6.29151i	0.957272	+	0.226878i	0.679423	−	0.733747i	$-0.262230\pi$
$769$	26.5460	+	6.29151i	0.957272	+	0.226878i	0.277849	+	0.960625i	$0.410378\pi$
$770$	−4.40286	−	1.04350i	−0.158668	−	0.0376050i
$771$		0			0
$772$	−0.143252	−	0.332097i	−0.00515577	−	0.0119524i
$773$	7.11832	−	2.59086i	0.256028	−	0.0931867i	−0.210817	−	0.977525i	$-0.567613\pi$
$773$	7.11832	−	2.59086i	0.256028	−	0.0931867i	0.466846	+	0.884339i	$0.345390\pi$
$774$		0			0
$775$	−20.9260	−	7.61646i	−0.751686	−	0.273591i
$776$	0.183643	+	3.15303i	0.00659239	+	0.113187i
$777$		0			0
$778$	−0.131137	+	0.304010i	−0.00470150	+	0.0108993i
$779$	−1.27343	+	21.8640i	−0.0456255	+	0.783359i
$780$		0			0
$781$	52.4329	+	55.5756i	1.87620	+	1.98865i
$782$	−0.532800	+	0.922836i	−0.0190529	+	0.0330006i
$783$		0			0
$784$	5.29489	+	9.17101i	0.189103	+	0.327536i
$785$	−4.69693	+	15.6888i	−0.167641	+	0.559959i
$786$		0			0
$787$	6.69226	+	4.40157i	0.238553	+	0.156899i	0.663157	−	0.748480i	$-0.269216\pi$
$787$	6.69226	+	4.40157i	0.238553	+	0.156899i	−0.424604	+	0.905379i	$0.639587\pi$
$788$	21.2746	−	2.48665i	0.757877	−	0.0885831i
$789$		0			0
$790$	−1.65798	−	0.832671i	−0.0589884	−	0.0296251i
$791$	−0.570845	−	3.23742i	−0.0202969	−	0.115109i
$792$		0			0
$793$	−1.66170	+	9.42396i	−0.0590087	+	0.334655i
$794$	−7.71261	+	10.3598i	−0.273710	+	0.367657i
$795$		0			0
$796$	2.24049	−	2.37478i	0.0794119	−	0.0841717i
$797$	−3.92017	−	13.0943i	−0.138860	−	0.463823i	0.860065	−	0.510184i	$-0.170423\pi$
$797$	−3.92017	−	13.0943i	−0.138860	−	0.463823i	−0.998925	+	0.0463609i	$0.985238\pi$
$798$		0			0
$799$	−2.52611	−	0.295260i	−0.0893673	−	0.0104455i
$800$	10.5811	+	8.87856i	0.374097	+	0.313905i
$801$		0			0
$802$	1.21775	−	1.02182i	0.0430003	−	0.0360816i
$803$	26.8400	−	17.6530i	0.947164	−	0.622959i
$804$		0			0
$805$	−9.82153	−	13.1926i	−0.346164	−	0.464978i
$806$	7.72155	−	3.87791i	0.271980	−	0.136593i
$807$		0			0
$808$	23.1861	−	5.49522i	0.815686	−	0.193321i
$809$	6.31109			0.221886			0.110943	−	0.993827i	$-0.464613\pi$
$809$	6.31109			0.221886			0.110943	+	0.993827i	$0.464613\pi$
$810$		0			0
$811$	−29.8809			−1.04926			−0.524631	−	0.851330i	$-0.675797\pi$
$811$	−29.8809			−1.04926			−0.524631	+	0.851330i	$0.675797\pi$
$812$	17.3350	−	4.10846i	0.608338	−	0.144179i
$813$		0			0
$814$	0.816886	−	0.410256i	0.0286318	−	0.0143795i
$815$	−0.459345	−	0.617008i	−0.0160902	−	0.0216128i
$816$		0			0
$817$	−34.9681	+	22.9989i	−1.22338	+	0.804628i
$818$	−6.28665	+	5.27513i	−0.219808	+	0.184440i
$819$		0			0
$820$	11.0708	+	9.28950i	0.386609	+	0.324403i
$821$	−31.5538	−	3.68811i	−1.10124	−	0.128716i	−0.453997	−	0.891003i	$-0.650002\pi$
$821$	−31.5538	−	3.68811i	−1.10124	−	0.128716i	−0.647239	+	0.762287i	$0.724076\pi$
$822$		0			0
$823$	−7.37926	−	24.6485i	−0.257225	−	0.859191i	−0.984879	−	0.173246i	$-0.944574\pi$
$823$	−7.37926	−	24.6485i	−0.257225	−	0.859191i	0.727654	−	0.685945i	$-0.240611\pi$
$824$	−18.1008	+	19.1857i	−0.630571	+	0.668367i
$825$		0			0
$826$	−2.43338	+	3.26859i	−0.0846680	+	0.113729i
$827$	3.15225	−	17.8773i	0.109615	−	0.621655i	−0.879662	−	0.475600i	$-0.842231\pi$
$827$	3.15225	−	17.8773i	0.109615	−	0.621655i	0.989276	−	0.146056i	$-0.0466578\pi$
$828$		0			0
$829$	−4.93669	−	27.9974i	−0.171458	−	0.972389i	−0.942153	−	0.335184i	$-0.891202\pi$
$829$	−4.93669	−	27.9974i	−0.171458	−	0.972389i	0.770694	−	0.637205i	$-0.219910\pi$
$830$	2.10417	+	1.05675i	0.0730368	+	0.0366805i
$831$		0			0
$832$	16.2749	−	1.90227i	0.564231	−	0.0659492i
$833$	1.17370	+	0.771952i	0.0406662	+	0.0267466i
$834$		0			0
$835$	1.11597	−	3.72761i	0.0386199	−	0.128999i
$836$	−16.3449	−	28.3101i	−0.565299	−	0.979127i
$837$		0			0
$838$	−0.792187	+	1.37211i	−0.0273656	+	0.0473987i
$839$	20.4897	+	21.7178i	0.707384	+	0.749783i	0.977013	−	0.213181i	$-0.0683824\pi$
$839$	20.4897	+	21.7178i	0.707384	+	0.749783i	−0.269629	+	0.962964i	$0.586901\pi$
$840$		0			0
$841$	0.219498	−	3.76863i	0.00756889	−	0.129953i
$842$	−0.745138	+	1.72742i	−0.0256792	+	0.0595310i
$843$		0			0
$844$	−0.386131	−	6.62961i	−0.0132912	−	0.228200i
$845$	1.40738	+	0.512244i	0.0484153	+	0.0176217i
$846$		0			0
$847$	−22.9977	+	8.37050i	−0.790212	+	0.287614i
$848$	−7.38665	−	17.1242i	−0.253659	−	0.588047i
$849$		0			0
$850$	0.518250	+	0.122828i	0.0177758	+	0.00421295i
$851$	3.23313	+	0.766265i	0.110830	+	0.0262672i
$852$		0			0
$853$	−2.02174	−	4.68693i	−0.0692232	−	0.160477i	0.880092	−	0.474803i	$-0.157481\pi$
$853$	−2.02174	−	4.68693i	−0.0692232	−	0.160477i	−0.949315	+	0.314326i	$0.898222\pi$
$854$	−1.89043	+	0.688062i	−0.0646893	+	0.0235450i
$855$		0			0
$856$	22.1305	+	8.05483i	0.756403	+	0.275308i
$857$	−0.828039	−	14.2169i	−0.0282853	−	0.485640i	−0.982470	−	0.186421i	$-0.940311\pi$
$857$	−0.828039	−	14.2169i	−0.0282853	−	0.485640i	0.954185	−	0.299218i	$-0.0967259\pi$
$858$		0			0
$859$	−16.6241	+	38.5390i	−0.567207	+	1.31493i	0.357380	+	0.933959i	$0.383670\pi$
$859$	−16.6241	+	38.5390i	−0.567207	+	1.31493i	−0.924586	+	0.380973i	$0.875589\pi$
$860$	−1.60584	+	27.5712i	−0.0547587	+	0.940171i
$861$		0			0
$862$	6.87939	+	7.29173i	0.234313	+	0.248357i
$863$	12.5420	−	21.7234i	0.426934	−	0.739472i	−0.569665	−	0.821877i	$-0.692927\pi$
$863$	12.5420	−	21.7234i	0.426934	−	0.739472i	0.996599	+	0.0824054i	$0.0262602\pi$
$864$		0			0
$865$	6.19073	+	10.7227i	0.210491	+	0.364582i
$866$	2.32147	−	7.75426i	0.0788868	−	0.263500i
$867$		0			0
$868$	−19.6669	−	12.9351i	−0.667538	−	0.439047i
$869$	−18.5256	+	2.16533i	−0.628438	+	0.0734539i
$870$		0			0
$871$	−22.2439	−	11.1713i	−0.753707	−	0.378526i
$872$	−2.04917	−	11.6214i	−0.0693936	−	0.393551i
$873$		0			0
$874$	−1.59225	+	9.03012i	−0.0538588	+	0.305448i
$875$	−12.2234	+	16.4189i	−0.413228	+	0.555061i
$876$		0			0
$877$	21.8720	−	23.1830i	0.738565	−	0.782833i	−0.243796	−	0.969827i	$-0.578393\pi$
$877$	21.8720	−	23.1830i	0.738565	−	0.782833i	0.982361	+	0.186993i	$0.0598742\pi$
$878$	3.50760	+	11.7162i	0.118376	+	0.395403i
$879$		0			0
$880$	−19.6443	−	2.29608i	−0.662208	−	0.0774010i
$881$	−4.45428	−	3.73758i	−0.150068	−	0.125922i	0.564662	−	0.825322i	$-0.309006\pi$
$881$	−4.45428	−	3.73758i	−0.150068	−	0.125922i	−0.714731	+	0.699400i	$0.753451\pi$
$882$		0			0
$883$	−0.930865	+	0.781089i	−0.0313261	+	0.0262857i	−0.658316	−	0.752741i	$-0.728731\pi$
$883$	−0.930865	+	0.781089i	−0.0313261	+	0.0262857i	0.626990	+	0.779027i	$0.284287\pi$
$884$	2.23742	−	1.47158i	0.0752526	−	0.0494944i
$885$		0			0
$886$	7.34987	+	9.87258i	0.246924	+	0.331676i
$887$	2.32758	−	1.16896i	0.0781525	−	0.0392497i	−0.409294	−	0.912403i	$-0.634225\pi$
$887$	2.32758	−	1.16896i	0.0781525	−	0.0392497i	0.487446	+	0.873153i	$0.337929\pi$
$888$		0			0
$889$	9.49339	−	2.24997i	0.318398	−	0.0754617i
$890$	5.05459			0.169430
$891$		0			0
$892$	12.1821			0.407888
$893$	−21.2951	+	5.04702i	−0.712612	+	0.168892i
$894$		0			0
$895$	−29.5789	+	14.8551i	−0.988715	+	0.496551i
$896$	11.4487	+	15.3783i	0.382476	+	0.513754i
$897$		0			0
$898$	−5.05488	+	3.32465i	−0.168684	+	0.110945i
$899$	25.5323	−	21.4242i	0.851551	−	0.714536i
$900$		0			0
$901$	−1.89517	−	1.59024i	−0.0631373	−	0.0529785i
$902$	−11.1357	−	1.30158i	−0.370779	−	0.0433379i
$903$		0			0
$904$	0.720470	+	2.40654i	0.0239625	+	0.0800402i
$905$	−0.784769	+	0.831807i	−0.0260866	+	0.0276502i
$906$		0			0
$907$	8.02886	−	10.7846i	0.266594	−	0.358098i	−0.648587	−	0.761140i	$-0.724640\pi$
$907$	8.02886	−	10.7846i	0.266594	−	0.358098i	0.915181	+	0.403042i	$0.132047\pi$
$908$	2.62067	−	14.8626i	0.0869701	−	0.493232i
$909$		0			0
$910$	−0.553881	−	3.14122i	−0.0183610	−	0.104130i
$911$	25.1915	+	12.6516i	0.834631	+	0.419167i	0.814172	−	0.580623i	$-0.197191\pi$
$911$	25.1915	+	12.6516i	0.834631	+	0.419167i	0.0204586	+	0.999791i	$0.493487\pi$
$912$		0			0
$913$	23.5111	−	2.74805i	0.778104	−	0.0909473i
$914$	6.10091	+	4.01263i	0.201800	+	0.132726i
$915$		0			0
$916$	4.17213	−	13.9359i	0.137851	−	0.460455i
$917$	11.1295	+	19.2768i	0.367528	+	0.636578i
$918$		0			0
$919$	13.5339	−	23.4413i	0.446441	−	0.773258i	−0.551710	−	0.834036i	$-0.686025\pi$
$919$	13.5339	−	23.4413i	0.446441	−	0.773258i	0.998151	+	0.0607774i	$0.0193580\pi$
$920$	8.62483	+	9.14179i	0.284352	+	0.301396i
$921$		0			0
$922$	0.326170	−	5.60012i	0.0107418	−	0.184430i
$923$	−21.3331	+	49.4556i	−0.702186	+	1.62785i
$924$		0			0
$925$	−0.0965636	−	1.65793i	−0.00317499	−	0.0545125i
$926$	0.985077	+	0.358539i	0.0323716	+	0.0117823i
$927$		0			0
$928$	−19.4266	+	7.07070i	−0.637709	+	0.232107i
$929$	19.0596	+	44.1852i	0.625326	+	1.44967i	0.876344	+	0.481686i	$0.159976\pi$
$929$	19.0596	+	44.1852i	0.625326	+	1.44967i	−0.251018	+	0.967983i	$0.580765\pi$
$930$		0			0
$931$	11.7624	+	2.78774i	0.385497	+	0.0913646i
$932$	46.6865	+	11.0649i	1.52927	+	0.362443i
$933$		0			0
$934$	−2.95497	−	6.85039i	−0.0966895	−	0.224152i
$935$	−2.46545	+	0.897352i	−0.0806290	+	0.0293465i
$936$		0			0
$937$	−48.7239	−	17.7340i	−1.59174	−	0.579346i	−0.614026	−	0.789286i	$-0.710451\pi$
$937$	−48.7239	−	17.7340i	−1.59174	−	0.579346i	−0.977714	+	0.209940i	$0.932673\pi$
$938$	−0.304269	−	5.22409i	−0.00993472	−	0.170573i
$939$		0			0
$940$	−5.71990	+	13.2602i	−0.186563	+	0.432501i
$941$	2.63290	−	45.2051i	0.0858300	−	1.47364i	−0.630666	−	0.776054i	$-0.717218\pi$
$941$	2.63290	−	45.2051i	0.0858300	−	1.47364i	0.716496	−	0.697591i	$-0.245745\pi$
$942$		0			0
$943$	−27.9660	−	29.6422i	−0.910697	−	0.965283i
$944$	−8.90573	+	15.4252i	−0.289857	+	0.502047i
$945$		0			0
$946$	−10.7128	−	18.5551i	−0.348302	−	0.603277i
$947$	−6.02556	+	20.1268i	−0.195804	+	0.654032i	0.802545	+	0.596592i	$0.203479\pi$
$947$	−6.02556	+	20.1268i	−0.195804	+	0.654032i	−0.998349	+	0.0574398i	$0.981706\pi$
$948$		0			0
$949$	18.9202	+	12.4440i	0.614177	+	0.403951i
$950$	4.55206	−	0.532059i	0.147688	−	0.0172623i
$951$		0			0
$952$	1.04504	+	0.524838i	0.0338699	+	0.0170101i
$953$	−1.52233	−	8.63357i	−0.0493132	−	0.279669i	0.950173	−	0.311723i	$-0.100906\pi$
$953$	−1.52233	−	8.63357i	−0.0493132	−	0.279669i	−0.999486	+	0.0320543i	$0.989795\pi$
$954$		0			0
$955$	−1.79794	+	10.1966i	−0.0581800	+	0.329955i
$956$	−0.194674	+	0.261492i	−0.00629619	+	0.00845726i
$957$		0			0
$958$	4.84204	−	5.13226i	0.156439	−	0.165816i
$959$	−2.71413	−	9.06584i	−0.0876440	−	0.292751i
$960$		0			0
$961$	−12.9513	−	1.51379i	−0.417785	−	0.0488320i
$962$	0.493629	+	0.414204i	0.0159152	+	0.0133545i
$963$		0			0
$964$	−27.4921	+	23.0686i	−0.885461	+	0.742990i
$965$	−0.208693	+	0.137259i	−0.00671805	+	0.00441853i
$966$		0			0
$967$	−13.5181	−	18.1580i	−0.434713	−	0.583921i	0.529745	−	0.848157i	$-0.322288\pi$
$967$	−13.5181	−	18.1580i	−0.434713	−	0.583921i	−0.964458	+	0.264236i	$0.914880\pi$
$968$	16.7125	−	8.39335i	0.537161	−	0.269773i
$969$		0			0
$970$	1.02181	−	0.242174i	0.0328084	−	0.00777574i
$971$	13.1781			0.422905			0.211453	−	0.977388i	$-0.432181\pi$
$971$	13.1781			0.422905			0.211453	+	0.977388i	$0.432181\pi$
$972$		0			0
$973$	32.1504			1.03070
$974$	1.96810	−	0.466448i	0.0630620	−	0.0149460i
$975$		0			0
$976$	−7.85804	+	3.94646i	−0.251530	+	0.126323i
$977$	23.7247	+	31.8677i	0.759019	+	1.01954i	0.998813	+	0.0487157i	$0.0155128\pi$
$977$	23.7247	+	31.8677i	0.759019	+	1.01954i	−0.239794	+	0.970824i	$0.577080\pi$
$978$		0			0
$979$	42.4545	−	27.9228i	1.35685	−	0.892415i
$980$	6.11051	−	5.12733i	0.195193	−	0.163786i
$981$		0			0
$982$	−1.07321	−	0.900528i	−0.0342474	−	0.0287370i
$983$	−58.2683	−	6.81058i	−1.85847	−	0.217224i	−0.888234	−	0.459390i	$-0.848068\pi$
$983$	−58.2683	−	6.81058i	−1.85847	−	0.217224i	−0.970235	+	0.242167i	$0.922142\pi$
$984$		0			0
$985$	−4.24268	−	14.1715i	−0.135183	−	0.451542i
$986$	−0.547040	+	0.579828i	−0.0174213	+	0.0184655i
$987$		0			0
$988$	13.7608	−	18.4840i	0.437791	−	0.588055i
$989$	13.5235	−	76.6957i	0.430023	−	2.43878i
$990$		0			0
$991$	3.30423	+	18.7392i	0.104962	+	0.595270i	0.991235	+	0.132108i	$0.0421744\pi$
$991$	3.30423	+	18.7392i	0.104962	+	0.595270i	−0.886273	+	0.463163i	$0.846714\pi$
$992$	24.4104	+	12.2594i	0.775032	+	0.389236i
$993$		0			0
$994$	−11.2465	+	1.31453i	−0.356717	+	0.0416943i
$995$	−1.88388	−	1.23905i	−0.0597229	−	0.0392804i
$996$		0			0
$997$	1.63245	−	5.45275i	0.0517001	−	0.172690i	−0.928240	−	0.371981i	$-0.878679\pi$
$997$	1.63245	−	5.45275i	0.0517001	−	0.172690i	0.979940	+	0.199291i	$0.0638638\pi$
$998$	−5.28998	−	9.16251i	−0.167451	−	0.290034i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.c.595.4		144
3.2	odd	2		729.2.g.b.595.5		144
9.2	odd	6		243.2.g.a.199.4		144
9.4	even	3		729.2.g.d.352.5		144
9.5	odd	6		729.2.g.a.352.4		144
9.7	even	3		81.2.g.a.22.5	✓	144
81.4	even	27		6561.2.a.c.1.34		72
81.11	odd	54		729.2.g.a.379.4		144
81.16	even	27	inner	729.2.g.c.136.4		144
81.38	odd	54		243.2.g.a.127.4		144
81.43	even	27		81.2.g.a.70.5	yes	144
81.65	odd	54		729.2.g.b.136.5		144
81.70	even	27		729.2.g.d.379.5		144
81.77	odd	54		6561.2.a.d.1.39		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.22.5	✓	144	9.7	even	3
81.2.g.a.70.5	yes	144	81.43	even	27
243.2.g.a.127.4		144	81.38	odd	54
243.2.g.a.199.4		144	9.2	odd	6
729.2.g.a.352.4		144	9.5	odd	6
729.2.g.a.379.4		144	81.11	odd	54
729.2.g.b.136.5		144	81.65	odd	54
729.2.g.b.595.5		144	3.2	odd	2
729.2.g.c.136.4		144	81.16	even	27	inner
729.2.g.c.595.4		144	1.1	even	1	trivial
729.2.g.d.352.5		144	9.4	even	3
729.2.g.d.379.5		144	81.70	even	27
6561.2.a.c.1.34		72	81.4	even	27
6561.2.a.d.1.39		72	81.77	odd	54

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.368322 + 0.0872939i) q^{2} +(-1.65922 + 0.833294i) q^{4} +(0.765743 + 1.02857i) q^{5} +(-1.59613 + 1.04979i) q^{7} +(1.11832 - 0.938383i) q^{8} +(-0.371828 - 0.312001i) q^{10} +(-4.84662 - 0.566489i) q^{11} +(-0.986538 - 3.29527i) q^{13} +(0.496250 - 0.525994i) q^{14} +(1.88752 - 2.53538i) q^{16} +(0.0728119 - 0.412937i) q^{17} +(-0.626542 - 3.55329i) q^{19} +(-2.12764 - 1.06854i) q^{20} +(1.83457 - 0.214430i) q^{22} +(5.60929 + 3.68929i) q^{23} +(0.962419 - 3.21470i) q^{25} +(0.651020 + 1.12760i) q^{26} +(1.77356 - 3.07189i) q^{28} +(3.44661 + 3.65320i) q^{29} +(0.385862 - 6.62500i) q^{31} +(-1.63034 + 3.77955i) q^{32} +(0.00922864 + 0.158450i) q^{34} +(-2.30201 - 0.837864i) q^{35} +(0.465059 - 0.169268i) q^{37} +(0.540950 + 1.25406i) q^{38} +(1.82154 + 0.431713i) q^{40} +(-5.90634 - 1.39983i) q^{41} +(-4.59446 - 10.6512i) q^{43} +(8.51368 - 3.09873i) q^{44} +(-2.38808 - 0.869188i) q^{46} +(-0.352677 - 6.05524i) q^{47} +(-1.32699 + 3.07630i) q^{49} +(-0.0738560 + 1.26806i) q^{50} +(4.38281 + 4.64551i) q^{52} +(2.95007 - 5.10967i) q^{53} +(-3.12859 - 5.41888i) q^{55} +(-0.799881 + 2.67179i) q^{56} +(-1.58836 - 1.04468i) q^{58} +(-5.59693 + 0.654187i) q^{59} +(-2.48606 - 1.24855i) q^{61} +(0.436200 + 2.47381i) q^{62} +(-0.827191 + 4.69124i) q^{64} +(2.63398 - 3.53805i) q^{65} +(4.96592 - 5.26357i) q^{67} +(0.223286 + 0.745828i) q^{68} +(0.921022 + 0.107652i) q^{70} +(-11.9949 - 10.0649i) q^{71} +(-5.04326 + 4.23179i) q^{73} +(-0.156515 + 0.102942i) q^{74} +(4.00051 + 5.37362i) q^{76} +(8.33054 - 4.18375i) q^{77} +(3.71934 - 0.881500i) q^{79} +4.05318 q^{80} +2.29763 q^{82} +(-4.72027 + 1.11872i) q^{83} +(0.480490 - 0.241311i) q^{85} +(2.62202 + 3.52198i) q^{86} +(-5.95166 + 3.91447i) q^{88} +(-7.97723 + 6.69369i) q^{89} +(5.03399 + 4.22402i) q^{91} +(-12.3813 - 1.44717i) q^{92} +(0.658484 + 2.19949i) q^{94} +(3.17505 - 3.36535i) q^{95} +(-1.29193 + 1.73537i) q^{97} +(0.220216 - 1.24891i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28}+ \cdots + 81 q^{98}+O(q^{100}) \) 144 * q + 9 * q^2 + 9 * q^4 + 9 * q^5 + 9 * q^7 - 18 * q^8 - 18 * q^10 + 9 * q^11 + 9 * q^13 + 9 * q^14 + 9 * q^16 - 18 * q^17 - 18 * q^19 - 63 * q^20 + 9 * q^22 + 36 * q^23 + 9 * q^25 + 45 * q^26 - 9 * q^28 - 45 * q^29 + 9 * q^31 + 63 * q^32 + 9 * q^34 + 9 * q^35 - 18 * q^37 - 9 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 + 54 * q^44 - 18 * q^46 + 63 * q^47 + 9 * q^49 - 225 * q^50 + 27 * q^52 + 45 * q^53 - 9 * q^55 + 99 * q^56 + 9 * q^58 - 117 * q^59 + 9 * q^61 + 81 * q^62 - 18 * q^64 + 81 * q^65 + 36 * q^67 - 18 * q^68 + 63 * q^70 - 90 * q^71 - 18 * q^73 + 81 * q^74 + 90 * q^76 + 81 * q^77 + 63 * q^79 - 288 * q^80 - 36 * q^82 + 45 * q^83 + 63 * q^85 + 81 * q^86 + 90 * q^88 - 81 * q^89 - 18 * q^91 - 63 * q^92 + 63 * q^94 + 153 * q^95 + 36 * q^97 + 81 * q^98

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