LMFDB - Embedded newform 666.2.bj.c.469.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(289,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("666.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bj (of order $18$, degree $6$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			469.2
Root			$0.642788 + 0.766044i$ of defining polynomial
Character	$\chi$	$=$	666.469
Dual form			666.2.bj.c.595.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 + 0.766044i) q^{2} +(-0.173648 + 0.984808i) q^{4} +(-0.273629 - 0.751790i) q^{5} +(-0.138449 + 0.0503913i) q^{7} +(-0.866025 + 0.500000i) q^{8} +O(q^{10})$	\(q+(0.642788 + 0.766044i) q^{2} +(-0.173648 + 0.984808i) q^{4} +(-0.273629 - 0.751790i) q^{5} +(-0.138449 + 0.0503913i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.400019 - 0.692853i) q^{10} +(2.40570 + 4.16679i) q^{11} +(1.91858 + 0.338298i) q^{13} +(-0.127595 - 0.0736672i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(3.43779 - 0.606175i) q^{17} +(-4.33625 + 5.16775i) q^{19} +(0.787884 - 0.138925i) q^{20} +(-1.64560 + 4.52124i) q^{22} +(3.61610 + 2.08776i) q^{23} +(3.33991 - 2.80251i) q^{25} +(0.974090 + 1.68717i) q^{26} +(-0.0255844 - 0.145096i) q^{28} +(-2.63134 + 1.51921i) q^{29} +8.13740i q^{31} +(-0.342020 - 0.939693i) q^{32} +(2.67412 + 2.24386i) q^{34} +(0.0757674 + 0.0902961i) q^{35} +(6.08227 + 0.0772535i) q^{37} -6.74601 q^{38} +(0.612865 + 0.514255i) q^{40} +(-0.676822 + 3.83845i) q^{41} -8.10852i q^{43} +(-4.52124 + 1.64560i) q^{44} +(0.725070 + 4.11208i) q^{46} +(4.16911 - 7.22111i) q^{47} +(-5.34568 + 4.48556i) q^{49} +(4.29370 + 0.757095i) q^{50} +(-0.666317 + 1.83069i) q^{52} +(-10.2327 - 3.72440i) q^{53} +(2.47428 - 2.94874i) q^{55} +(0.0947047 - 0.112865i) q^{56} +(-2.85517 - 1.03920i) q^{58} +(2.96569 - 8.14816i) q^{59} +(-0.346344 - 0.0610698i) q^{61} +(-6.23361 + 5.23062i) q^{62} +(0.500000 - 0.866025i) q^{64} +(-0.270651 - 1.53494i) q^{65} +(-2.25471 + 0.820647i) q^{67} +3.49082i q^{68} +(-0.0204685 + 0.116082i) q^{70} +(-5.34953 - 4.48879i) q^{71} +1.13399 q^{73} +(3.85043 + 4.70895i) q^{74} +(-4.33625 - 5.16775i) q^{76} +(-0.543037 - 0.455662i) q^{77} +(0.646510 + 1.77627i) q^{79} +0.800038i q^{80} +(-3.37547 + 1.94883i) q^{82} +(1.71997 + 9.75442i) q^{83} +(-1.39639 - 2.41863i) q^{85} +(6.21149 - 5.21206i) q^{86} +(-4.16679 - 2.40570i) q^{88} +(3.45924 - 9.50418i) q^{89} +(-0.282673 + 0.0498429i) q^{91} +(-2.68397 + 3.19863i) q^{92} +(8.21154 - 1.44792i) q^{94} +(5.07158 + 1.84591i) q^{95} +(5.08812 + 2.93763i) q^{97} +(-6.87228 - 1.21177i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{7}+O(q^{10}) $ 12 * q - 12 * q^7	$ 12 q - 12 q^{7} + 6 q^{10} + 6 q^{11} + 6 q^{13} + 18 q^{14} - 18 q^{19} - 18 q^{25} - 12 q^{26} - 6 q^{28} - 18 q^{29} + 12 q^{34} - 18 q^{35} + 30 q^{37} + 24 q^{38} + 12 q^{40} - 24 q^{41} - 6 q^{44} + 30 q^{46} - 6 q^{47} + 12 q^{49} + 36 q^{50} - 12 q^{52} + 12 q^{53} - 18 q^{55} + 6 q^{58} - 36 q^{61} + 6 q^{64} - 36 q^{65} - 30 q^{67} - 12 q^{70} - 12 q^{71} + 48 q^{74} - 18 q^{76} - 12 q^{77} + 6 q^{79} + 48 q^{83} + 18 q^{85} + 36 q^{86} - 36 q^{88} + 18 q^{89} - 6 q^{91} - 18 q^{92} + 36 q^{97} - 36 q^{98}+O(q^{100}) $ 12 * q - 12 * q^7 + 6 * q^10 + 6 * q^11 + 6 * q^13 + 18 * q^14 - 18 * q^19 - 18 * q^25 - 12 * q^26 - 6 * q^28 - 18 * q^29 + 12 * q^34 - 18 * q^35 + 30 * q^37 + 24 * q^38 + 12 * q^40 - 24 * q^41 - 6 * q^44 + 30 * q^46 - 6 * q^47 + 12 * q^49 + 36 * q^50 - 12 * q^52 + 12 * q^53 - 18 * q^55 + 6 * q^58 - 36 * q^61 + 6 * q^64 - 36 * q^65 - 30 * q^67 - 12 * q^70 - 12 * q^71 + 48 * q^74 - 18 * q^76 - 12 * q^77 + 6 * q^79 + 48 * q^83 + 18 * q^85 + 36 * q^86 - 36 * q^88 + 18 * q^89 - 6 * q^91 - 18 * q^92 + 36 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{5}{18}\right)$

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 $

$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$3$		0			0
$3$		0			0
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	−0.273629	−	0.751790i	−0.122371	−	0.336211i	0.863349	−	0.504608i	$-0.168363\pi$
$5$	−0.273629	−	0.751790i	−0.122371	−	0.336211i	−0.985719	+	0.168397i	$0.946141\pi$
$6$		0			0
$7$	−0.138449	+	0.0503913i	−0.0523288	+	0.0190461i	−0.368052	−	0.929805i	$-0.619975\pi$
$7$	−0.138449	+	0.0503913i	−0.0523288	+	0.0190461i	0.315723	+	0.948851i	$0.397753\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$		0			0
$10$	0.400019	−	0.692853i	0.126497	−	0.219099i
$11$	2.40570	+	4.16679i	0.725346	+	1.25634i	0.958832	+	0.283975i	$0.0916533\pi$
$11$	2.40570	+	4.16679i	0.725346	+	1.25634i	−0.233486	+	0.972360i	$0.575013\pi$
$12$		0			0
$13$	1.91858	+	0.338298i	0.532119	+	0.0938270i	0.433251	−	0.901274i	$-0.357367\pi$
$13$	1.91858	+	0.338298i	0.532119	+	0.0938270i	0.0988686	+	0.995100i	$0.468478\pi$
$14$	−0.127595	−	0.0736672i	−0.0341013	−	0.0196884i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	3.43779	−	0.606175i	0.833786	−	0.147019i	0.259572	−	0.965724i	$-0.416419\pi$
$17$	3.43779	−	0.606175i	0.833786	−	0.147019i	0.574214	+	0.818705i	$0.305308\pi$
$18$		0			0
$19$	−4.33625	+	5.16775i	−0.994805	+	1.18556i	−0.0121861	+	0.999926i	$0.503879\pi$
$19$	−4.33625	+	5.16775i	−0.994805	+	1.18556i	−0.982619	+	0.185636i	$0.940565\pi$
$20$	0.787884	−	0.138925i	0.176176	−	0.0310646i
$21$		0			0
$22$	−1.64560	+	4.52124i	−0.350842	+	0.963931i
$23$	3.61610	+	2.08776i	0.754009	+	0.435327i	0.827141	−	0.561995i	$-0.189966\pi$
$23$	3.61610	+	2.08776i	0.754009	+	0.435327i	−0.0731316	+	0.997322i	$0.523299\pi$
$24$		0			0
$25$	3.33991	−	2.80251i	0.667981	−	0.560503i
$26$	0.974090	+	1.68717i	0.191035	+	0.330882i
$27$		0			0
$28$	−0.0255844	−	0.145096i	−0.00483499	−	0.0274206i
$29$	−2.63134	+	1.51921i	−0.488628	+	0.282109i	−0.724005	−	0.689795i	$-0.757701\pi$
$29$	−2.63134	+	1.51921i	−0.488628	+	0.282109i	0.235377	+	0.971904i	$0.424367\pi$
$30$		0			0
$31$			8.13740i			1.46152i	0.682634	+	0.730760i	$0.260834\pi$
$31$			8.13740i			1.46152i	−0.682634	+	0.730760i	$0.739166\pi$
$32$	−0.342020	−	0.939693i	−0.0604612	−	0.166116i
$33$		0			0
$34$	2.67412	+	2.24386i	0.458609	+	0.384818i
$35$	0.0757674	+	0.0902961i	0.0128070	+	0.0152628i
$36$		0			0
$37$	6.08227	+	0.0772535i	0.999919	+	0.0127004i
$37$	6.08227	+	0.0772535i	0.999919	+	0.0127004i
$38$	−6.74601			−1.09435
$39$		0			0
$40$	0.612865	+	0.514255i	0.0969024	+	0.0813108i
$41$	−0.676822	+	3.83845i	−0.105702	+	0.599465i	0.885236	+	0.465142i	$0.153997\pi$
$41$	−0.676822	+	3.83845i	−0.105702	+	0.599465i	−0.990938	+	0.134322i	$0.957114\pi$
$42$		0			0
$43$		−	8.10852i		−	1.23654i	−0.785966	−	0.618269i	$-0.787834\pi$
$43$		−	8.10852i		−	1.23654i	0.785966	−	0.618269i	$-0.212166\pi$
$44$	−4.52124	+	1.64560i	−0.681602	+	0.248083i
$45$		0			0
$46$	0.725070	+	4.11208i	0.106906	+	0.606293i
$47$	4.16911	−	7.22111i	0.608127	−	1.05331i	−0.383422	−	0.923573i	$-0.625254\pi$
$47$	4.16911	−	7.22111i	0.608127	−	1.05331i	0.991549	−	0.129734i	$-0.0414122\pi$
$48$		0			0
$49$	−5.34568	+	4.48556i	−0.763669	+	0.640794i
$50$	4.29370	+	0.757095i	0.607221	+	0.107069i
$51$		0			0
$52$	−0.666317	+	1.83069i	−0.0924015	+	0.253871i
$53$	−10.2327	−	3.72440i	−1.40557	−	0.511586i	−0.475744	−	0.879584i	$-0.657821\pi$
$53$	−10.2327	−	3.72440i	−1.40557	−	0.511586i	−0.929827	+	0.367998i	$0.880043\pi$
$54$		0			0
$55$	2.47428	−	2.94874i	0.333632	−	0.397607i
$56$	0.0947047	−	0.112865i	0.0126555	−	0.0150822i
$57$		0			0
$58$	−2.85517	−	1.03920i	−0.374902	−	0.136453i
$59$	2.96569	−	8.14816i	0.386100	−	1.06080i	−0.582642	−	0.812729i	$-0.697981\pi$
$59$	2.96569	−	8.14816i	0.386100	−	1.06080i	0.968742	−	0.248072i	$-0.0797968\pi$
$60$		0			0
$61$	−0.346344	−	0.0610698i	−0.0443448	−	0.00781919i	0.151432	−	0.988468i	$-0.451612\pi$
$61$	−0.346344	−	0.0610698i	−0.0443448	−	0.00781919i	−0.195777	+	0.980649i	$0.562723\pi$
$62$	−6.23361	+	5.23062i	−0.791670	+	0.664290i
$63$		0			0
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−0.270651	−	1.53494i	−0.0335702	−	0.190386i
$66$		0			0
$67$	−2.25471	+	0.820647i	−0.275457	+	0.100258i	−0.476055	−	0.879416i	$-0.657934\pi$
$67$	−2.25471	+	0.820647i	−0.275457	+	0.100258i	0.200598	+	0.979674i	$0.435711\pi$
$68$			3.49082i			0.423324i
$69$		0			0
$70$	−0.0204685	+	0.116082i	−0.00244645	+	0.0138745i
$71$	−5.34953	−	4.48879i	−0.634873	−	0.532721i	0.267566	−	0.963539i	$-0.413781\pi$
$71$	−5.34953	−	4.48879i	−0.634873	−	0.532721i	−0.902439	+	0.430818i	$0.858225\pi$
$72$		0			0
$73$	1.13399			0.132724			0.0663618	−	0.997796i	$-0.478861\pi$
$73$	1.13399			0.132724			0.0663618	+	0.997796i	$0.478861\pi$
$74$	3.85043	+	4.70895i	0.447603	+	0.547404i
$75$		0			0
$76$	−4.33625	−	5.16775i	−0.497402	−	0.592781i
$77$	−0.543037	−	0.455662i	−0.0618848	−	0.0519275i
$78$		0			0
$79$	0.646510	+	1.77627i	0.0727380	+	0.199846i	0.970734	−	0.240158i	$-0.0771992\pi$
$79$	0.646510	+	1.77627i	0.0727380	+	0.199846i	−0.897996	+	0.440004i	$0.854977\pi$
$80$			0.800038i			0.0894470i
$81$		0			0
$82$	−3.37547	+	1.94883i	−0.372759	+	0.215212i
$83$	1.71997	+	9.75442i	0.188791	+	1.07069i	0.920987	+	0.389593i	$0.127384\pi$
$83$	1.71997	+	9.75442i	0.188791	+	1.07069i	−0.732196	+	0.681094i	$0.761505\pi$
$84$		0			0
$85$	−1.39639	−	2.41863i	−0.151460	−	0.262337i
$86$	6.21149	−	5.21206i	0.669802	−	0.562031i
$87$		0			0
$88$	−4.16679	−	2.40570i	−0.444182	−	0.256448i
$89$	3.45924	−	9.50418i	0.366679	−	1.00744i	−0.609937	−	0.792450i	$-0.708805\pi$
$89$	3.45924	−	9.50418i	0.366679	−	1.00744i	0.976616	−	0.214992i	$-0.0689724\pi$
$90$		0			0
$91$	−0.282673	+	0.0498429i	−0.0296322	+	0.00522496i
$92$	−2.68397	+	3.19863i	−0.279823	+	0.333480i
$93$		0			0
$94$	8.21154	−	1.44792i	0.846956	−	0.149341i
$95$	5.07158	+	1.84591i	0.520333	+	0.189386i
$96$		0			0
$97$	5.08812	+	2.93763i	0.516620	+	0.298271i	0.735551	−	0.677470i	$-0.236923\pi$
$97$	5.08812	+	2.93763i	0.516620	+	0.298271i	−0.218930	+	0.975740i	$0.570257\pi$
$98$	−6.87228	−	1.21177i	−0.694205	−	0.122407i
$99$		0			0
$100$	2.17997	+	3.77582i	0.217997	+	0.377582i
$101$	8.50866	−	14.7374i	0.846643	−	1.46643i	−0.0375439	−	0.999295i	$-0.511953\pi$
$101$	8.50866	−	14.7374i	0.846643	−	1.46643i	0.884187	−	0.467134i	$-0.154713\pi$
$102$		0			0
$103$	11.0391	−	6.37342i	1.08771	−	0.627992i	0.154747	−	0.987954i	$-0.450544\pi$
$103$	11.0391	−	6.37342i	1.08771	−	0.627992i	0.932967	+	0.359962i	$0.117210\pi$
$104$	−1.83069	+	0.666317i	−0.179514	+	0.0653377i
$105$		0			0
$106$	−3.72440	−	10.2327i	−0.361746	−	0.993889i
$107$	−2.47252	+	14.0223i	−0.239027	+	1.35559i	0.594937	+	0.803773i	$0.297177\pi$
$107$	−2.47252	+	14.0223i	−0.239027	+	1.35559i	−0.833964	+	0.551819i	$0.813934\pi$
$108$		0			0
$109$	−12.7198	−	15.1589i	−1.21834	−	1.45196i	−0.853664	−	0.520823i	$-0.825625\pi$
$109$	−12.7198	−	15.1589i	−1.21834	−	1.45196i	−0.364674	−	0.931135i	$-0.618819\pi$
$110$	3.84930			0.367017
$111$		0			0
$112$	0.147334			0.0139218
$113$	−5.46470	−	6.51257i	−0.514075	−	0.612651i	0.445094	−	0.895484i	$-0.353170\pi$
$113$	−5.46470	−	6.51257i	−0.514075	−	0.612651i	−0.959169	+	0.282833i	$0.908726\pi$
$114$		0			0
$115$	0.580084	−	3.28982i	0.0540931	−	0.306777i
$116$	−1.03920	−	2.85517i	−0.0964871	−	0.265096i
$117$		0			0
$118$	8.14816	−	2.96569i	0.750099	−	0.273014i
$119$	−0.445413	+	0.257159i	−0.0408309	+	0.0235737i
$120$		0			0
$121$	−6.07478	+	10.5218i	−0.552252	+	0.956529i
$122$	−0.175844	−	0.304570i	−0.0159201	−	0.0275745i
$123$		0			0
$124$	−8.01378	−	1.41305i	−0.719659	−	0.126895i
$125$	−6.48506	−	3.74415i	−0.580042	−	0.334887i
$126$		0			0
$127$	−5.19901	−	1.89229i	−0.461338	−	0.167913i	0.100887	−	0.994898i	$-0.467832\pi$
$127$	−5.19901	−	1.89229i	−0.461338	−	0.167913i	−0.562224	+	0.826985i	$0.690054\pi$
$128$	0.984808	−	0.173648i	0.0870455	−	0.0153485i
$129$		0			0
$130$	1.00186	−	1.19397i	0.0878690	−	0.104718i
$131$	−0.810446	+	0.142903i	−0.0708090	+	0.0124855i	−0.208940	−	0.977928i	$-0.567001\pi$
$131$	−0.810446	+	0.142903i	−0.0708090	+	0.0124855i	0.138131	+	0.990414i	$0.455890\pi$
$132$		0			0
$133$	0.339941	−	0.933979i	0.0294766	−	0.0809863i
$134$	−2.07795	−	1.19971i	−0.179508	−	0.103639i
$135$		0			0
$136$	−2.67412	+	2.24386i	−0.229304	+	0.192409i
$137$	3.37116	+	5.83902i	0.288018	+	0.498861i	0.973336	−	0.229382i	$-0.0736705\pi$
$137$	3.37116	+	5.83902i	0.288018	+	0.498861i	−0.685319	+	0.728243i	$0.740337\pi$
$138$		0			0
$139$	−2.08444	−	11.8214i	−0.176800	−	1.00268i	−0.936046	−	0.351878i	$-0.885543\pi$
$139$	−2.08444	−	11.8214i	−0.176800	−	1.00268i	0.759246	−	0.650804i	$-0.225568\pi$
$140$	−0.102081	+	0.0589366i	−0.00862743	+	0.00498105i
$141$		0			0
$142$		−	6.98332i		−	0.586027i
$143$	3.20592	+	8.80818i	0.268092	+	0.736577i
$144$		0			0
$145$	1.86213	+	1.56252i	0.154642	+	0.129760i
$146$	0.728915	+	0.868687i	0.0603254	+	0.0718930i
$147$		0			0
$148$	−1.13226	+	5.97645i	−0.0930708	+	0.491261i
$149$	9.21354			0.754803			0.377401	−	0.926050i	$-0.376818\pi$
$149$	9.21354			0.754803			0.377401	+	0.926050i	$0.376818\pi$
$150$		0			0
$151$	9.02729	+	7.57480i	0.734631	+	0.616428i	0.931390	−	0.364023i	$-0.118597\pi$
$151$	9.02729	+	7.57480i	0.734631	+	0.616428i	−0.196759	+	0.980452i	$0.563042\pi$
$152$	1.17143	−	6.64352i	0.0950157	−	0.538861i
$153$		0			0
$154$		−	0.708885i		−	0.0571235i
$155$	6.11762	−	2.22663i	0.491379	−	0.178847i
$156$		0			0
$157$	−3.01657	−	17.1078i	−0.240749	−	1.36535i	−0.830162	−	0.557522i	$-0.811752\pi$
$157$	−3.01657	−	17.1078i	−0.240749	−	1.36535i	0.589414	−	0.807831i	$-0.299359\pi$
$158$	−0.945134	+	1.63702i	−0.0751908	+	0.130234i
$159$		0			0
$160$	−0.612865	+	0.514255i	−0.0484512	+	0.0406554i
$161$	−0.605851	−	0.106828i	−0.0477477	−	0.00841921i
$162$		0			0
$163$	0.773358	−	2.12478i	0.0605741	−	0.166426i	−0.905714	−	0.423889i	$-0.860665\pi$
$163$	0.773358	−	2.12478i	0.0605741	−	0.166426i	0.966288	+	0.257464i	$0.0828867\pi$
$164$	−3.66260	−	1.33308i	−0.286001	−	0.104096i
$165$		0			0
$166$	−6.36675	+	7.58759i	−0.494155	+	0.588912i
$167$	10.2563	−	12.2230i	0.793658	−	0.945845i	−0.205805	−	0.978593i	$-0.565981\pi$
$167$	10.2563	−	12.2230i	0.793658	−	0.945845i	0.999464	+	0.0327478i	$0.0104258\pi$
$168$		0			0
$169$	−8.64949	−	3.14816i	−0.665345	−	0.242166i
$170$	0.955190	−	2.62436i	0.0732598	−	0.201280i
$171$		0			0
$172$	7.98534	+	1.40803i	0.608876	+	0.107361i
$173$	2.35572	−	1.97668i	0.179102	−	0.150284i	−0.548829	−	0.835934i	$-0.684926\pi$
$173$	2.35572	−	1.97668i	0.179102	−	0.150284i	0.727931	+	0.685650i	$0.240482\pi$
$174$		0			0
$175$	−0.321185	+	0.556308i	−0.0242793	+	0.0420529i
$176$	−0.835490	−	4.73830i	−0.0629775	−	0.357163i
$177$		0			0
$178$	9.50418	−	3.45924i	0.712368	−	0.259281i
$179$			10.4466i			0.780819i	0.920641	+	0.390410i	$0.127667\pi$
$179$			10.4466i			0.780819i	−0.920641	+	0.390410i	$0.872333\pi$
$180$		0			0
$181$	1.56392	−	8.86942i	0.116245	−	0.659259i	−0.869881	−	0.493262i	$-0.835805\pi$
$181$	1.56392	−	8.86942i	0.116245	−	0.659259i	0.986126	−	0.165997i	$-0.0530843\pi$
$182$	−0.219881	−	0.184502i	−0.0162986	−	0.0136762i
$183$		0			0
$184$	−4.17551			−0.307823
$185$	−1.60621	−	4.59373i	−0.118091	−	0.337738i
$186$		0			0
$187$	10.7961	+	12.8663i	0.789488	+	0.940875i
$188$	6.38745	+	5.35970i	0.465852	+	0.390897i
$189$		0			0
$190$	1.84591	+	5.07158i	0.133916	+	0.367931i
$191$			1.00551i			0.0727558i	0.999338	+	0.0363779i	$0.0115820\pi$
$191$			1.00551i			0.0727558i	−0.999338	+	0.0363779i	$0.988418\pi$
$192$		0			0
$193$	−9.52217	+	5.49763i	−0.685421	+	0.395728i	−0.801894	−	0.597466i	$-0.796174\pi$
$193$	−9.52217	+	5.49763i	−0.685421	+	0.395728i	0.116473	+	0.993194i	$0.462841\pi$
$194$	1.02023	+	5.78600i	0.0732481	+	0.415410i
$195$		0			0
$196$	−3.48915	−	6.04338i	−0.249225	−	0.431670i
$197$	−19.8444	+	16.6514i	−1.41386	+	1.18637i	−0.459319	+	0.888271i	$0.651906\pi$
$197$	−19.8444	+	16.6514i	−1.41386	+	1.18637i	−0.954537	+	0.298094i	$0.903649\pi$
$198$		0			0
$199$	−13.4873	−	7.78692i	−0.956092	−	0.552000i	−0.0611237	−	0.998130i	$-0.519468\pi$
$199$	−13.4873	−	7.78692i	−0.956092	−	0.552000i	−0.894968	+	0.446130i	$0.852802\pi$
$200$	−1.49119	+	4.09700i	−0.105443	+	0.289702i
$201$		0			0
$202$	16.7588	−	2.95503i	1.17914	−	0.207915i
$203$	0.287752	−	0.342929i	0.0201962	−	0.0240689i
$204$		0			0
$205$	3.07090	−	0.541483i	0.214481	−	0.0378188i
$206$	11.9781	+	4.35968i	0.834555	+	0.303753i
$207$		0			0
$208$	−1.68717	−	0.974090i	−0.116984	−	0.0675410i
$209$	−31.9646	−	5.63623i	−2.21104	−	0.389866i
$210$		0			0
$211$	11.5871	+	20.0694i	0.797688	+	1.38164i	0.921118	+	0.389283i	$0.127277\pi$
$211$	11.5871	+	20.0694i	0.797688	+	1.38164i	−0.123430	+	0.992353i	$0.539390\pi$
$212$	5.44471	−	9.43052i	0.373944	−	0.647691i
$213$		0			0
$214$	−12.3310	+	7.11933i	−0.842933	+	0.486667i
$215$	−6.09591	+	2.21873i	−0.415737	+	0.151316i
$216$		0			0
$217$	−0.410055	−	1.12662i	−0.0278363	−	0.0764797i
$218$	3.43624	−	19.4879i	0.232732	−	1.31989i
$219$		0			0
$220$	2.47428	+	2.94874i	0.166816	+	0.198804i
$221$	6.80075			0.457468
$222$		0			0
$223$	9.91195			0.663754			0.331877	−	0.943323i	$-0.392318\pi$
$223$	9.91195			0.663754			0.331877	+	0.943323i	$0.392318\pi$
$224$	0.0947047	+	0.112865i	0.00632773	+	0.00754109i
$225$		0			0
$226$	1.47628	−	8.37240i	0.0982007	−	0.556924i
$227$	0.684171	+	1.87974i	0.0454100	+	0.124763i	0.960325	−	0.278884i	$-0.0899646\pi$
$227$	0.684171	+	1.87974i	0.0454100	+	0.124763i	−0.914915	+	0.403647i	$0.867742\pi$
$228$		0			0
$229$	8.40320	−	3.05851i	0.555299	−	0.202112i	−0.0491004	−	0.998794i	$-0.515635\pi$
$229$	8.40320	−	3.05851i	0.555299	−	0.202112i	0.604399	+	0.796682i	$0.293413\pi$
$230$	2.89302	−	1.67028i	0.190760	−	0.110135i
$231$		0			0
$232$	1.51921	−	2.63134i	0.0997407	−	0.172756i
$233$	−10.8675	−	18.8230i	−0.711952	−	1.23314i	−0.964123	−	0.265455i	$-0.914478\pi$
$233$	−10.8675	−	18.8230i	−0.711952	−	1.23314i	0.252171	−	0.967683i	$-0.418855\pi$
$234$		0			0
$235$	−6.56955	−	1.15839i	−0.428550	−	0.0755649i
$236$	7.50939	+	4.33555i	0.488820	+	0.282220i
$237$		0			0
$238$	−0.483301	−	0.175907i	−0.0313278	−	0.0114024i
$239$	7.79702	−	1.37482i	0.504347	−	0.0889300i	0.0843148	−	0.996439i	$-0.473130\pi$
$239$	7.79702	−	1.37482i	0.504347	−	0.0889300i	0.420032	+	0.907509i	$0.362019\pi$
$240$		0			0
$241$	19.1413	−	22.8117i	1.23300	−	1.46943i	0.399665	−	0.916661i	$-0.369127\pi$
$241$	19.1413	−	22.8117i	1.23300	−	1.46943i	0.833334	−	0.552769i	$-0.186429\pi$
$242$	−11.9650	+	2.10975i	−0.769137	+	0.135620i
$243$		0			0
$244$	0.120284	−	0.330478i	0.00770040	−	0.0211567i
$245$	4.83493	+	2.79145i	0.308893	+	0.178339i
$246$		0			0
$247$	−10.0677	+	8.44780i	−0.640592	+	0.537521i
$248$	−4.06870	−	7.04720i	−0.258363	−	0.447498i
$249$		0			0
$250$	−1.30033	−	7.37454i	−0.0822402	−	0.466407i
$251$	−19.7765	+	11.4180i	−1.24828	+	0.720695i	−0.970766	−	0.240026i	$-0.922844\pi$
$251$	−19.7765	+	11.4180i	−1.24828	+	0.720695i	−0.277514	+	0.960721i	$0.589511\pi$
$252$		0			0
$253$			20.0901i			1.26305i
$254$	−1.89229	−	5.19901i	−0.118733	−	0.326215i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	10.5496	+	12.5726i	0.658068	+	0.784255i	0.987107	−	0.160062i	$-0.0511693\pi$
$257$	10.5496	+	12.5726i	0.658068	+	0.784255i	−0.329039	+	0.944316i	$0.606725\pi$
$258$		0			0
$259$	−0.845978	+	0.295798i	−0.0525665	+	0.0183800i
$260$	1.55862			0.0966614
$261$		0			0
$262$	−0.630415	−	0.528981i	−0.0389472	−	0.0326806i
$263$	−0.270840	+	1.53601i	−0.0167007	+	0.0947145i	−0.992019	−	0.126090i	$-0.959757\pi$
$263$	−0.270840	+	1.53601i	−0.0167007	+	0.0947145i	0.975318	+	0.220805i	$0.0708683\pi$
$264$		0			0
$265$			8.71195i			0.535171i
$266$	0.933979	−	0.339941i	0.0572659	−	0.0208431i
$267$		0			0
$268$	−0.416654	−	2.36296i	−0.0254512	−	0.144341i
$269$	1.64927	−	2.85662i	0.100558	−	0.174171i	−0.811357	−	0.584551i	$-0.801271\pi$
$269$	1.64927	−	2.85662i	0.100558	−	0.174171i	0.911915	+	0.410380i	$0.134604\pi$
$270$		0			0
$271$	2.76033	−	2.31620i	0.167678	−	0.140699i	−0.555087	−	0.831792i	$-0.687315\pi$
$271$	2.76033	−	2.31620i	0.167678	−	0.140699i	0.722766	+	0.691093i	$0.242871\pi$
$272$	−3.43779	−	0.606175i	−0.208447	−	0.0367547i
$273$		0			0
$274$	−2.30601	+	6.33571i	−0.139311	+	0.382754i
$275$	19.7123	+	7.17469i	1.18870	+	0.432650i
$276$		0			0
$277$	−10.0841	+	12.0177i	−0.605894	+	0.722076i	−0.978577	−	0.205883i	$-0.933993\pi$
$277$	−10.0841	+	12.0177i	−0.605894	+	0.722076i	0.372683	+	0.927959i	$0.378438\pi$
$278$	7.71590	−	9.19545i	0.462769	−	0.551506i
$279$		0			0
$280$	−0.110765	−	0.0403150i	−0.00661945	−	0.00240928i
$281$	1.74041	−	4.78173i	0.103824	−	0.285254i	−0.876894	−	0.480684i	$-0.840388\pi$
$281$	1.74041	−	4.78173i	0.103824	−	0.285254i	0.980718	+	0.195431i	$0.0626105\pi$
$282$		0			0
$283$	−9.02521	−	1.59139i	−0.536493	−	0.0945982i	−0.101164	−	0.994870i	$-0.532257\pi$
$283$	−9.02521	−	1.59139i	−0.536493	−	0.0945982i	−0.435329	+	0.900272i	$0.643368\pi$
$284$	5.34953	−	4.48879i	0.317436	−	0.266361i
$285$		0			0
$286$	−4.68673	+	8.11766i	−0.277132	+	0.480007i
$287$	−0.0997192	−	0.565536i	−0.00588624	−	0.0333825i
$288$		0			0
$289$	−4.52384	+	1.64654i	−0.266108	+	0.0968554i
$290$			2.43084i			0.142744i
$291$		0			0
$292$	−0.196915	+	1.11676i	−0.0115236	+	0.0653536i
$293$	19.3966	+	16.2757i	1.13316	+	0.950838i	0.999194	−	0.0401477i	$-0.0127829\pi$
$293$	19.3966	+	16.2757i	1.13316	+	0.950838i	0.133970	+	0.990985i	$0.457227\pi$
$294$		0			0
$295$	−6.93721			−0.403900
$296$	−5.30603	+	2.97423i	−0.308407	+	0.172874i
$297$		0			0
$298$	5.92235	+	7.05798i	0.343073	+	0.408858i
$299$	6.23150	+	5.22885i	0.360377	+	0.302392i
$300$		0			0
$301$	0.408599	+	1.12262i	0.0235513	+	0.0647066i
$302$			11.7843i			0.678110i
$303$		0			0
$304$	5.84222	−	3.37301i	0.335074	−	0.193455i
$305$	0.0488582	+	0.277089i	0.00279761	+	0.0158660i
$306$		0			0
$307$	4.35284	+	7.53934i	0.248430	+	0.430293i	0.963090	−	0.269178i	$-0.0867521\pi$
$307$	4.35284	+	7.53934i	0.248430	+	0.430293i	−0.714661	+	0.699471i	$0.753419\pi$
$308$	0.543037	−	0.455662i	0.0309424	−	0.0259638i
$309$		0			0
$310$	5.63803	+	3.25512i	0.320218	+	0.184878i
$311$	−1.98686	+	5.45885i	−0.112664	+	0.309543i	−0.983191	−	0.182578i	$-0.941556\pi$
$311$	−1.98686	+	5.45885i	−0.112664	+	0.309543i	0.870527	+	0.492121i	$0.163778\pi$
$312$		0			0
$313$	−7.74595	+	1.36582i	−0.437827	+	0.0772007i	−0.388217	−	0.921568i	$-0.626909\pi$
$313$	−7.74595	+	1.36582i	−0.437827	+	0.0772007i	−0.0496099	+	0.998769i	$0.515798\pi$
$314$	11.1663	−	13.3075i	0.630153	−	0.750987i
$315$		0			0
$316$	−1.86155	+	0.328242i	−0.104720	+	0.0184650i
$317$	−5.26133	−	1.91497i	−0.295506	−	0.107555i	0.190013	−	0.981782i	$-0.439147\pi$
$317$	−5.26133	−	1.91497i	−0.295506	−	0.107555i	−0.485519	+	0.874226i	$0.661369\pi$
$318$		0			0
$319$	−12.6604	−	7.30950i	−0.708848	−	0.409253i
$320$	−0.787884	−	0.138925i	−0.0440440	−	0.00776615i
$321$		0			0
$322$	−0.307598	−	0.532776i	−0.0171418	−	0.0296905i
$323$	−11.7746	+	20.3941i	−0.655154	+	1.13476i
$324$		0			0
$325$	7.35597	−	4.24697i	0.408036	−	0.235580i
$326$	2.12478	−	0.773358i	0.117681	−	0.0428323i
$327$		0			0
$328$	−1.33308	−	3.66260i	−0.0736070	−	0.202234i
$329$	−0.213328	+	1.20984i	−0.0117612	+	0.0667008i
$330$		0			0
$331$	−11.6926	−	13.9348i	−0.642686	−	0.765923i	0.342106	−	0.939661i	$-0.388860\pi$
$331$	−11.6926	−	13.9348i	−0.642686	−	0.765923i	−0.984792	+	0.173738i	$0.944415\pi$
$332$	−9.90490			−0.543602
$333$		0			0
$334$	15.9560			0.873074
$335$	1.23391	+	1.47052i	0.0674156	+	0.0803428i
$336$		0			0
$337$	−5.73735	+	32.5381i	−0.312533	+	1.77246i	0.273198	+	0.961958i	$0.411919\pi$
$337$	−5.73735	+	32.5381i	−0.312533	+	1.77246i	−0.585731	+	0.810505i	$0.699193\pi$
$338$	−3.14816	−	8.64949i	−0.171237	−	0.470470i
$339$		0			0
$340$	2.62436	−	0.955190i	0.142326	−	0.0518025i
$341$	−33.9069	+	19.5761i	−1.83616	+	1.06011i
$342$		0			0
$343$	1.02974	−	1.78357i	0.0556008	−	0.0963035i
$344$	4.05426	+	7.02219i	0.218591	+	0.378611i
$345$		0			0
$346$	3.02845	+	0.533998i	0.162811	+	0.0287079i
$347$	−27.9743	−	16.1510i	−1.50174	−	0.867029i	−0.999998	−	0.00201032i	$-0.999360\pi$
$347$	−27.9743	−	16.1510i	−1.50174	−	0.867029i	−0.501740	−	0.865018i	$-0.667307\pi$
$348$		0			0
$349$	−2.14851	−	0.781994i	−0.115007	−	0.0418592i	0.283876	−	0.958861i	$-0.408380\pi$
$349$	−2.14851	−	0.781994i	−0.115007	−	0.0418592i	−0.398883	+	0.917002i	$0.630602\pi$
$350$	−0.632610	+	0.111546i	−0.0338144	+	0.00596240i
$351$		0			0
$352$	3.09271	−	3.68574i	0.164842	−	0.196451i
$353$	−6.32439	+	1.11516i	−0.336613	+	0.0593540i	−0.339400	−	0.940642i	$-0.610224\pi$
$353$	−6.32439	+	1.11516i	−0.336613	+	0.0593540i	0.00278690	+	0.999996i	$0.499113\pi$
$354$		0			0
$355$	−1.91084	+	5.24999i	−0.101417	+	0.278640i
$356$	8.75910	+	5.05707i	0.464231	+	0.268024i
$357$		0			0
$358$	−8.00260	+	6.71498i	−0.422950	+	0.354898i
$359$	−3.66122	−	6.34142i	−0.193232	−	0.334687i	0.753088	−	0.657920i	$-0.228564\pi$
$359$	−3.66122	−	6.34142i	−0.193232	−	0.334687i	−0.946319	+	0.323233i	$0.895230\pi$
$360$		0			0
$361$	−4.60318	−	26.1060i	−0.242273	−	1.37400i
$362$	7.79964	−	4.50312i	0.409940	−	0.236679i
$363$		0			0
$364$		−	0.287034i		−	0.0150447i
$365$	−0.310293	−	0.852522i	−0.0162415	−	0.0446231i
$366$		0			0
$367$	24.1722	+	20.2829i	1.26178	+	1.05876i	0.995490	+	0.0948646i	$0.0302418\pi$
$367$	24.1722	+	20.2829i	1.26178	+	1.05876i	0.266288	+	0.963893i	$0.414203\pi$
$368$	−2.68397	−	3.19863i	−0.139912	−	0.166740i
$369$		0			0
$370$	2.48655	−	4.18322i	0.129270	−	0.217475i
$371$	1.60439			0.0832956
$372$		0			0
$373$	−6.41137	−	5.37977i	−0.331968	−	0.278554i	0.461533	−	0.887123i	$-0.347300\pi$
$373$	−6.41137	−	5.37977i	−0.331968	−	0.278554i	−0.793501	+	0.608569i	$0.791744\pi$
$374$	−2.91655	+	16.5406i	−0.150811	+	0.855292i
$375$		0			0
$376$			8.33822i			0.430011i
$377$	−5.56239	+	2.02454i	−0.286478	+	0.104269i
$378$		0			0
$379$	4.89452	+	27.7582i	0.251415	+	1.42584i	0.805111	+	0.593124i	$0.202106\pi$
$379$	4.89452	+	27.7582i	0.251415	+	1.42584i	−0.553696	+	0.832719i	$0.686783\pi$
$380$	−2.69853	+	4.67400i	−0.138432	+	0.239771i
$381$		0			0
$382$	−0.770262	+	0.646327i	−0.0394100	+	0.0330689i
$383$	8.95650	+	1.57927i	0.457656	+	0.0806970i	0.397723	−	0.917505i	$-0.369800\pi$
$383$	8.95650	+	1.57927i	0.457656	+	0.0806970i	0.0599323	+	0.998202i	$0.480912\pi$
$384$		0			0
$385$	−0.193971	+	0.532932i	−0.00988570	+	0.0271607i
$386$	−10.3322	−	3.76060i	−0.525893	−	0.191409i
$387$		0			0
$388$	−3.77654	+	4.50071i	−0.191725	+	0.228489i
$389$	1.28903	−	1.53620i	0.0653563	−	0.0778886i	−0.732376	−	0.680901i	$-0.761589\pi$
$389$	1.28903	−	1.53620i	0.0653563	−	0.0778886i	0.797732	+	0.603012i	$0.206033\pi$
$390$		0			0
$391$	13.6969	+	4.98528i	0.692684	+	0.252116i
$392$	2.38672	−	6.55745i	0.120547	−	0.331201i
$393$		0			0
$394$	−25.5115	−	4.49836i	−1.28525	−	0.226624i
$395$	1.15848	−	0.972079i	0.0582894	−	0.0489106i
$396$		0			0
$397$	−9.53782	+	16.5200i	−0.478690	+	0.829115i	−0.999701	−	0.0244346i	$-0.992221\pi$
$397$	−9.53782	+	16.5200i	−0.478690	+	0.829115i	0.521012	+	0.853550i	$0.325555\pi$
$398$	−2.70437	−	15.3372i	−0.135558	−	0.768786i
$399$		0			0
$400$	−4.09700	+	1.49119i	−0.204850	+	0.0745593i
$401$		−	24.7444i		−	1.23568i	−0.786305	−	0.617839i	$-0.788008\pi$
$401$		−	24.7444i		−	1.23568i	0.786305	−	0.617839i	$-0.211992\pi$
$402$		0			0
$403$	−2.75287	+	15.6123i	−0.137130	+	0.777703i
$404$	13.0360	+	10.9385i	0.648566	+	0.544212i
$405$		0			0
$406$	0.447662			0.0222171
$407$	14.3102	+	25.5294i	0.709331	+	1.26545i
$408$		0			0
$409$	−15.8423	−	18.8801i	−0.783350	−	0.933560i	0.215729	−	0.976453i	$-0.430787\pi$
$409$	−15.8423	−	18.8801i	−0.783350	−	0.933560i	−0.999080	+	0.0428927i	$0.986343\pi$
$410$	2.38874	+	2.00439i	0.117971	+	0.0989898i
$411$		0			0
$412$	4.35968	+	11.9781i	0.214786	+	0.590120i
$413$			1.27755i			0.0628642i
$414$		0			0
$415$	6.86264	−	3.96215i	0.336874	−	0.194494i
$416$	−0.338298	−	1.91858i	−0.0165864	−	0.0940663i
$417$		0			0
$418$	−16.2289	−	28.1092i	−0.793780	−	1.37487i
$419$	14.0011	−	11.7483i	0.683997	−	0.573942i	−0.233174	−	0.972435i	$-0.574911\pi$
$419$	14.0011	−	11.7483i	0.683997	−	0.573942i	0.917171	+	0.398493i	$0.130467\pi$
$420$		0			0
$421$	32.5605	+	18.7988i	1.58690	+	0.916198i	0.993814	+	0.111060i	$0.0354245\pi$
$421$	32.5605	+	18.7988i	1.58690	+	0.916198i	0.593087	+	0.805138i	$0.297909\pi$
$422$	−7.92603	+	21.7766i	−0.385833	+	1.06007i
$423$		0			0
$424$	10.7240	−	1.89093i	0.520803	−	0.0918316i
$425$	9.78308	−	11.6590i	0.474549	−	0.565545i
$426$		0			0
$427$	0.0510284	−	0.00899769i	0.00246944	−	0.000435429i
$428$	−13.3800	−	4.86991i	−0.646745	−	0.235396i
$429$		0			0
$430$	−5.61802	−	3.24356i	−0.270925	−	0.156419i
$431$	36.3170	+	6.40367i	1.74933	+	0.308454i	0.954463	−	0.298330i	$-0.0964295\pi$
$431$	36.3170	+	6.40367i	1.74933	+	0.308454i	0.794867	+	0.606784i	$0.207541\pi$
$432$		0			0
$433$	−5.44689	−	9.43429i	−0.261761	−	0.453383i	0.704949	−	0.709258i	$-0.250970\pi$
$433$	−5.44689	−	9.43429i	−0.261761	−	0.453383i	−0.966710	+	0.255875i	$0.917637\pi$
$434$	0.599460	−	1.03829i	0.0287750	−	0.0498398i
$435$		0			0
$436$	17.1374	−	9.89427i	0.820731	−	0.473849i
$437$	−26.4693	+	9.63404i	−1.26620	+	0.460859i
$438$		0			0
$439$	6.39195	+	17.5617i	0.305071	+	0.838176i	0.993599	+	0.112966i	$0.0360351\pi$
$439$	6.39195	+	17.5617i	0.305071	+	0.838176i	−0.688528	+	0.725210i	$0.741743\pi$
$440$	−0.668424	+	3.79082i	−0.0318659	+	0.180720i
$441$		0			0
$442$	4.37144	+	5.20968i	0.207928	+	0.247799i
$443$	−18.1659			−0.863090			−0.431545	−	0.902092i	$-0.642031\pi$
$443$	−18.1659			−0.863090			−0.431545	+	0.902092i	$0.642031\pi$
$444$		0			0
$445$	−8.09170			−0.383583
$446$	6.37128	+	7.59300i	0.301689	+	0.359539i
$447$		0			0
$448$	−0.0255844	+	0.145096i	−0.00120875	+	0.00685515i
$449$	5.32504	+	14.6304i	0.251304	+	0.690453i	0.999632	+	0.0271236i	$0.00863478\pi$
$449$	5.32504	+	14.6304i	0.251304	+	0.690453i	−0.748328	+	0.663329i	$0.769143\pi$
$450$		0			0
$451$	−17.6222	+	6.41397i	−0.829799	+	0.302022i
$452$	7.36257	−	4.25078i	0.346306	−	0.199940i
$453$		0			0
$454$	−1.00019	+	1.73238i	−0.0469413	+	0.0813047i
$455$	0.114819	+	0.198872i	0.00538280	+	0.00932328i
$456$		0			0
$457$	−10.8568	−	1.91434i	−0.507858	−	0.0895491i	−0.0861526	−	0.996282i	$-0.527457\pi$
$457$	−10.8568	−	1.91434i	−0.507858	−	0.0895491i	−0.421705	+	0.906733i	$0.638568\pi$
$458$	7.74443	+	4.47125i	0.361873	+	0.208928i
$459$		0			0
$460$	3.13911	+	1.14254i	0.146362	+	0.0532713i
$461$	21.0232	−	3.70696i	0.979148	−	0.172650i	0.338903	−	0.940821i	$-0.389944\pi$
$461$	21.0232	−	3.70696i	0.979148	−	0.172650i	0.640245	+	0.768171i	$0.278833\pi$
$462$		0			0
$463$	21.3348	−	25.4258i	0.991512	−	1.18164i	0.00815253	−	0.999967i	$-0.497405\pi$
$463$	21.3348	−	25.4258i	0.991512	−	1.18164i	0.983359	−	0.181671i	$-0.0581506\pi$
$464$	2.99225	−	0.527614i	0.138912	−	0.0244939i
$465$		0			0
$466$	7.43379	−	20.4242i	0.344364	−	0.946132i
$467$	−12.8279	−	7.40621i	−0.593606	−	0.342719i	0.172916	−	0.984937i	$-0.444681\pi$
$467$	−12.8279	−	7.40621i	−0.593606	−	0.342719i	−0.766522	+	0.642218i	$0.778014\pi$
$468$		0			0
$469$	0.270809	−	0.227236i	0.0125048	−	0.0104928i
$470$	−3.33545	−	5.77716i	−0.153853	−	0.266481i
$471$		0			0
$472$	1.50572	+	8.53936i	0.0693064	+	0.393056i
$473$	33.7865	−	19.5067i	1.55351	−	0.896917i
$474$		0			0
$475$			29.4122i			1.34952i
$476$	−0.175907	−	0.483301i	−0.00806269	−	0.0221521i
$477$		0			0
$478$	6.06500	+	5.08914i	0.277407	+	0.232772i
$479$	−5.78865	−	6.89864i	−0.264490	−	0.315207i	0.617412	−	0.786640i	$-0.288181\pi$
$479$	−5.78865	−	6.89864i	−0.264490	−	0.315207i	−0.881902	+	0.471433i	$0.843737\pi$
$480$		0			0
$481$	11.6432	+	2.20584i	0.530885	+	0.100578i
$482$	29.7786			1.35638
$483$		0			0
$484$	−9.30710	−	7.80958i	−0.423050	−	0.354981i
$485$	0.816221	−	4.62902i	0.0370627	−	0.210193i
$486$		0			0
$487$			3.39198i			0.153705i	0.997042	+	0.0768525i	$0.0244871\pi$
$487$			3.39198i			0.153705i	−0.997042	+	0.0768525i	$0.975513\pi$
$488$	0.330478	−	0.120284i	0.0149600	−	0.00544500i
$489$		0			0
$490$	0.969460	+	5.49808i	0.0437958	+	0.248378i
$491$	−10.3671	+	17.9564i	−0.467862	+	0.810361i	−0.999326	−	0.0367202i	$-0.988309\pi$
$491$	−10.3671	+	17.9564i	−0.467862	+	0.810361i	0.531463	+	0.847081i	$0.321642\pi$
$492$		0			0
$493$	−8.12509	+	6.81776i	−0.365935	+	0.307056i
$494$	−12.9428	−	2.28216i	−0.582323	−	0.102679i
$495$		0			0
$496$	2.78316	−	7.64666i	0.124967	−	0.343345i
$497$	0.966834	+	0.351899i	0.0433684	+	0.0157848i
$498$		0			0
$499$	15.8653	−	18.9076i	0.710229	−	0.846418i	−0.283413	−	0.958998i	$-0.591467\pi$
$499$	15.8653	−	18.9076i	0.710229	−	0.846418i	0.993643	+	0.112579i	$0.0359113\pi$
$500$	4.81339	−	5.73638i	0.215261	−	0.256539i
$501$		0			0
$502$	−21.4587	−	7.81034i	−0.957751	−	0.348593i
$503$	5.69356	−	15.6429i	0.253863	−	0.697484i	−0.745651	−	0.666336i	$-0.767862\pi$
$503$	5.69356	−	15.6429i	0.253863	−	0.697484i	0.999515	−	0.0311477i	$-0.00991621\pi$
$504$		0			0
$505$	−13.4077	−	2.36413i	−0.596633	−	0.105203i
$506$	−15.3899	+	12.9136i	−0.684163	+	0.574081i
$507$		0			0
$508$	2.76634	−	4.79144i	0.122736	−	0.212586i
$509$	−4.36442	−	24.7519i	−0.193450	−	1.09711i	−0.914609	−	0.404339i	$-0.867502\pi$
$509$	−4.36442	−	24.7519i	−0.193450	−	1.09711i	0.721160	−	0.692769i	$-0.243609\pi$
$510$		0			0
$511$	−0.157000	+	0.0571433i	−0.00694527	+	0.00252787i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−2.84997	+	16.1630i	−0.125707	+	0.712918i
$515$	−7.81209	−	6.55513i	−0.344242	−	0.288853i
$516$		0			0
$517$	40.1185			1.76441
$518$	−0.770379	−	0.457921i	−0.0338485	−	0.0201199i
$519$		0			0
$520$	1.00186	+	1.19397i	0.0439345	+	0.0523591i
$521$	22.0872	+	18.5334i	0.967659	+	0.811962i	0.982182	−	0.187932i	$-0.0601786\pi$
$521$	22.0872	+	18.5334i	0.967659	+	0.811962i	−0.0145232	+	0.999895i	$0.504623\pi$
$522$		0			0
$523$	1.23619	+	3.39641i	0.0540548	+	0.148514i	0.963781	−	0.266693i	$-0.0859311\pi$
$523$	1.23619	+	3.39641i	0.0540548	+	0.148514i	−0.909727	+	0.415208i	$0.863709\pi$
$524$		−	0.822948i		−	0.0359507i
$525$		0			0
$526$	−1.35075	+	0.779853i	−0.0588953	+	0.0340032i
$527$	4.93269	+	27.9747i	0.214871	+	1.21860i
$528$		0			0
$529$	−2.78255	−	4.81951i	−0.120980	−	0.209544i
$530$	−6.67374	+	5.59994i	−0.289889	+	0.243246i
$531$		0			0
$532$	0.860760	+	0.496960i	0.0373187	+	0.0215459i
$533$	−2.59708	+	7.13541i	−0.112492	+	0.309069i
$534$		0			0
$535$	11.2184	−	1.97811i	0.485014	−	0.0855211i
$536$	1.54231	−	1.83806i	0.0666178	−	0.0793920i
$537$		0			0
$538$	3.24843	−	0.572786i	0.140050	−	0.0246946i
$539$	−31.5505	−	11.4834i	−1.35898	−	0.494627i
$540$		0			0
$541$	−9.89184	−	5.71106i	−0.425284	−	0.245538i	0.272052	−	0.962283i	$-0.412298\pi$
$541$	−9.89184	−	5.71106i	−0.425284	−	0.245538i	−0.697335	+	0.716745i	$0.745631\pi$
$542$	3.54862	+	0.625717i	0.152426	+	0.0268768i
$543$		0			0
$544$	−1.74541	−	3.02314i	−0.0748339	−	0.129616i
$545$	−7.91579	+	13.7106i	−0.339075	+	0.587295i
$546$		0			0
$547$	28.9864	−	16.7353i	1.23937	−	0.715550i	0.270404	−	0.962747i	$-0.412843\pi$
$547$	28.9864	−	16.7353i	1.23937	−	0.715550i	0.968965	+	0.247197i	$0.0795094\pi$
$548$	−6.33571	+	2.30601i	−0.270648	+	0.0985078i
$549$		0			0
$550$	7.17469	+	19.7123i	0.305930	+	0.840536i
$551$	3.55929	−	20.1858i	0.151631	−	0.859942i
$552$		0			0
$553$	−0.179017	−	0.213345i	−0.00761259	−	0.00907234i
$554$	−15.6880			−0.666521
$555$		0			0
$556$	12.0038			0.509075
$557$	−12.5025	−	14.8999i	−0.529747	−	0.631328i	0.433109	−	0.901341i	$-0.357416\pi$
$557$	−12.5025	−	14.8999i	−0.529747	−	0.631328i	−0.962857	+	0.270013i	$0.912972\pi$
$558$		0			0
$559$	2.74310	−	15.5569i	0.116021	−	0.657986i
$560$	−0.0403150	−	0.110765i	−0.00170362	−	0.00468066i
$561$		0			0
$562$	4.78173	−	1.74041i	0.201705	−	0.0734146i
$563$	−16.3919	+	9.46387i	−0.690837	+	0.398855i	−0.803925	−	0.594730i	$-0.797259\pi$
$563$	−16.3919	+	9.46387i	−0.690837	+	0.398855i	0.113089	+	0.993585i	$0.463926\pi$
$564$		0			0
$565$	−3.40079	+	5.89033i	−0.143072	+	0.247808i
$566$	−4.58222	−	7.93663i	−0.192605	−	0.333602i
$567$		0			0
$568$	6.87722	+	1.21264i	0.288562	+	0.0508813i
$569$	−6.71294	−	3.87572i	−0.281421	−	0.162479i	0.352645	−	0.935757i	$-0.385282\pi$
$569$	−6.71294	−	3.87572i	−0.281421	−	0.162479i	−0.634067	+	0.773278i	$0.718616\pi$
$570$		0			0
$571$	−4.66196	−	1.69681i	−0.195097	−	0.0710094i	0.242624	−	0.970120i	$-0.421992\pi$
$571$	−4.66196	−	1.69681i	−0.195097	−	0.0710094i	−0.437721	+	0.899111i	$0.644214\pi$
$572$	−9.23107	+	1.62769i	−0.385970	+	0.0680570i
$573$		0			0
$574$	0.369127	−	0.439909i	0.0154071	−	0.0183614i
$575$	17.9284	−	3.16126i	0.747666	−	0.131834i
$576$		0			0
$577$	7.21587	−	19.8254i	0.300401	−	0.825344i	−0.694030	−	0.719946i	$-0.744166\pi$
$577$	7.21587	−	19.8254i	0.300401	−	0.825344i	0.994430	−	0.105397i	$-0.0336114\pi$
$578$	−4.16919	−	2.40708i	−0.173415	−	0.100121i
$579$		0			0
$580$	−1.86213	+	1.56252i	−0.0773209	+	0.0648800i
$581$	−0.729667	−	1.26382i	−0.0302717	−	0.0524321i
$582$		0			0
$583$	−9.09801	−	51.5974i	−0.376801	−	2.13694i
$584$	−0.982064	+	0.566995i	−0.0406381	+	0.0234624i
$585$		0			0
$586$			25.3205i			1.04598i
$587$	0.000238503	0	0.000655281i	9.84406e−6	0	2.70463e-5i	0.939698	−	0.342007i	$-0.111107\pi$
$587$	0.000238503	0	0.000655281i	9.84406e−6	0	2.70463e-5i	−0.939688	+	0.342034i	$0.888884\pi$
$588$		0			0
$589$	−42.0520	−	35.2858i	−1.73272	−	1.45393i
$590$	−4.45915	−	5.31421i	−0.183580	−	0.218783i
$591$		0			0
$592$	−5.68904	−	2.15285i	−0.233818	−	0.0884818i
$593$	8.38840			0.344470			0.172235	−	0.985056i	$-0.444901\pi$
$593$	8.38840			0.344470			0.172235	+	0.985056i	$0.444901\pi$
$594$		0			0
$595$	0.315207	+	0.264490i	0.0129222	+	0.0108431i
$596$	−1.59992	+	9.07357i	−0.0655351	+	0.371668i
$597$		0			0
$598$			8.13465i			0.332651i
$599$	24.7128	−	8.99471i	1.00974	−	0.367514i	0.216405	−	0.976304i	$-0.430567\pi$
$599$	24.7128	−	8.99471i	1.00974	−	0.367514i	0.793332	+	0.608790i	$0.208345\pi$
$600$		0			0
$601$	7.49727	+	42.5191i	0.305820	+	1.73439i	0.619620	+	0.784902i	$0.287287\pi$
$601$	7.49727	+	42.5191i	0.305820	+	1.73439i	−0.313800	+	0.949489i	$0.601602\pi$
$602$	−0.597332	+	1.03461i	−0.0243454	+	0.0421676i
$603$		0			0
$604$	−9.02729	+	7.57480i	−0.367315	+	0.308214i
$605$	9.57243	+	1.68788i	0.389175	+	0.0686220i
$606$		0			0
$607$	11.6866	−	32.1087i	0.474345	−	1.30325i	−0.439885	−	0.898054i	$-0.644981\pi$
$607$	11.6866	−	32.1087i	0.474345	−	1.30325i	0.914229	−	0.405197i	$-0.132797\pi$
$608$	6.33918	+	2.30727i	0.257088	+	0.0935722i
$609$		0			0
$610$	−0.180857	+	0.215537i	−0.00732267	+	0.00872682i
$611$	10.4417	−	12.4439i	0.422425	−	0.503426i
$612$		0			0
$613$	−38.7066	−	14.0880i	−1.56334	−	0.569011i	−0.591844	−	0.806052i	$-0.701600\pi$
$613$	−38.7066	−	14.0880i	−1.56334	−	0.569011i	−0.971499	+	0.237042i	$0.923822\pi$
$614$	−2.97752	+	8.18067i	−0.120163	+	0.330145i
$615$		0			0
$616$	0.698115	+	0.123097i	0.0281279	+	0.00495970i
$617$	24.5087	−	20.5652i	0.986681	−	0.827924i	0.00159734	−	0.999999i	$-0.499492\pi$
$617$	24.5087	−	20.5652i	0.986681	−	0.827924i	0.985084	+	0.172075i	$0.0550471\pi$
$618$		0			0
$619$	−3.10000	+	5.36936i	−0.124600	+	0.215813i	−0.921576	−	0.388197i	$-0.873098\pi$
$619$	−3.10000	+	5.36936i	−0.124600	+	0.215813i	0.796977	+	0.604010i	$0.206431\pi$
$620$	1.13049	+	6.41133i	0.0454016	+	0.257485i
$621$		0			0
$622$	−5.45885	+	1.98686i	−0.218880	+	0.0796657i
$623$			1.49016i			0.0597020i
$624$		0			0
$625$	2.74516	−	15.5686i	0.109807	−	0.622744i
$626$	−6.02528	−	5.05581i	−0.240819	−	0.202071i
$627$		0			0
$628$	17.3717			0.693208
$629$	20.9564	−	3.42134i	0.835586	−	0.136418i
$630$		0			0
$631$	−23.4724	−	27.9733i	−0.934421	−	1.11360i	−0.993326	−	0.115336i	$-0.963205\pi$
$631$	−23.4724	−	27.9733i	−0.934421	−	1.11360i	0.0589052	−	0.998264i	$-0.481239\pi$
$632$	−1.44803	−	1.21504i	−0.0575995	−	0.0483317i
$633$		0			0
$634$	−1.91497	−	5.26133i	−0.0760531	−	0.208954i
$635$			4.42635i			0.175654i
$636$		0			0
$637$	−11.7736	+	6.79748i	−0.466487	+	0.269326i
$638$	−2.53856	−	14.3969i	−0.100503	−	0.569979i
$639$		0			0
$640$	−0.400019	−	0.692853i	−0.0158121	−	0.0273874i
$641$	15.2619	−	12.8063i	0.602810	−	0.505817i	−0.289538	−	0.957167i	$-0.593502\pi$
$641$	15.2619	−	12.8063i	0.602810	−	0.505817i	0.892347	+	0.451349i	$0.149057\pi$
$642$		0			0
$643$	−28.9945	−	16.7400i	−1.14343	−	0.660161i	−0.196155	−	0.980573i	$-0.562845\pi$
$643$	−28.9945	−	16.7400i	−1.14343	−	0.660161i	−0.947278	+	0.320412i	$0.896179\pi$
$644$	0.210410	−	0.578096i	0.00829130	−	0.0227802i
$645$		0			0
$646$	−23.1914	+	4.08926i	−0.912452	+	0.160890i
$647$	7.67494	−	9.14664i	0.301733	−	0.359592i	−0.593779	−	0.804628i	$-0.702365\pi$
$647$	7.67494	−	9.14664i	0.301733	−	0.359592i	0.895513	+	0.445036i	$0.146809\pi$
$648$		0			0
$649$	41.0863	−	7.24462i	1.61278	−	0.284376i
$650$	7.98170	+	2.90510i	0.313068	+	0.113947i
$651$		0			0
$652$	1.95821	+	1.13057i	0.0766895	+	0.0442767i
$653$	−13.4694	−	2.37501i	−0.527097	−	0.0929414i	−0.0962338	−	0.995359i	$-0.530680\pi$
$653$	−13.4694	−	2.37501i	−0.527097	−	0.0929414i	−0.430863	+	0.902417i	$0.641791\pi$
$654$		0			0
$655$	0.329195	+	0.570182i	0.0128627	+	0.0222789i
$656$	1.94883	−	3.37547i	0.0760891	−	0.131790i
$657$		0			0
$658$	−1.06392	+	0.614253i	−0.0414758	+	0.0239461i
$659$	−31.2934	+	11.3899i	−1.21902	+	0.443686i	−0.869822	−	0.493365i	$-0.835767\pi$
$659$	−31.2934	+	11.3899i	−1.21902	+	0.443686i	−0.349194	+	0.937051i	$0.613544\pi$
$660$		0			0
$661$	−1.38912	−	3.81658i	−0.0540305	−	0.148448i	0.909741	−	0.415175i	$-0.136280\pi$
$661$	−1.38912	−	3.81658i	−0.0540305	−	0.148448i	−0.963772	+	0.266728i	$0.914058\pi$
$662$	3.15875	−	17.9142i	0.122768	−	0.696254i
$663$		0			0
$664$	−6.36675	−	7.58759i	−0.247078	−	0.294456i
$665$	−0.795174			−0.0308355
$666$		0			0
$667$	−12.6869			−0.491240
$668$	10.2563	+	12.2230i	0.396829	+	0.472923i
$669$		0			0
$670$	−0.333339	+	1.89046i	−0.0128780	+	0.0730348i
$671$	−0.578735	−	1.59006i	−0.0223418	−	0.0613836i
$672$		0			0
$673$	17.0237	−	6.19612i	0.656216	−	0.238843i	0.00761402	−	0.999971i	$-0.497576\pi$
$673$	17.0237	−	6.19612i	0.656216	−	0.238843i	0.648602	+	0.761128i	$0.275354\pi$
$674$	−28.6135	+	16.5200i	−1.10215	+	0.636328i
$675$		0			0
$676$	4.60230	−	7.97141i	0.177011	−	0.306593i
$677$	10.1473	+	17.5756i	0.389991	+	0.675484i	0.992448	−	0.122667i	$-0.0391448\pi$
$677$	10.1473	+	17.5756i	0.389991	+	0.675484i	−0.602457	+	0.798151i	$0.705811\pi$
$678$		0			0
$679$	−0.852477	−	0.150315i	−0.0327150	−	0.00576855i
$680$	2.41863	+	1.39639i	0.0927501	+	0.0535493i
$681$		0			0
$682$	−36.7911	−	13.3909i	−1.40880	−	0.512763i
$683$	23.3553	−	4.11816i	0.893665	−	0.157577i	0.292087	−	0.956392i	$-0.405650\pi$
$683$	23.3553	−	4.11816i	0.893665	−	0.157577i	0.601577	+	0.798814i	$0.294539\pi$
$684$		0			0
$685$	3.46727	−	4.13213i	0.132477	−	0.157881i
$686$	2.02820	−	0.357626i	0.0774369	−	0.0136542i
$687$		0			0
$688$	−2.77328	+	7.61952i	−0.105730	+	0.290491i
$689$	−18.3723	−	10.6073i	−0.699931	−	0.404105i
$690$		0			0
$691$	−2.69427	+	2.26076i	−0.102495	+	0.0860034i	−0.692595	−	0.721327i	$-0.743533\pi$
$691$	−2.69427	+	2.26076i	−0.102495	+	0.0860034i	0.590100	+	0.807330i	$0.299088\pi$
$692$	1.53759	+	2.66318i	0.0584502	+	0.101239i
$693$		0			0
$694$	−5.60917	−	31.8112i	−0.212921	−	1.20754i
$695$	−8.31688	+	4.80175i	−0.315477	+	0.182141i
$696$		0			0
$697$			13.6060i			0.515366i
$698$	−0.781994	−	2.14851i	−0.0295989	−	0.0813224i
$699$		0			0
$700$	−0.492083	−	0.412907i	−0.0185990	−	0.0156064i
$701$	−12.2023	−	14.5422i	−0.460876	−	0.549251i	0.484688	−	0.874687i	$-0.338933\pi$
$701$	−12.2023	−	14.5422i	−0.460876	−	0.549251i	−0.945564	+	0.325436i	$0.894489\pi$
$702$		0			0
$703$	−26.7735	+	31.0966i	−1.00978	+	1.17283i
$704$	4.81140			0.181336
$705$		0			0
$706$	−4.91950	−	4.12795i	−0.185148	−	0.155357i
$707$	−0.435377	+	2.46915i	−0.0163740	+	0.0928618i
$708$		0			0
$709$			13.0236i			0.489113i	0.969635	+	0.244556i	$0.0786423\pi$
$709$			13.0236i			0.489113i	−0.969635	+	0.244556i	$0.921358\pi$
$710$	−5.24999	+	1.91084i	−0.197029	+	0.0717125i
$711$		0			0
$712$	1.75630	+	9.96048i	0.0658202	+	0.373285i
$713$	−16.9889	+	29.4257i	−0.636240	+	1.10200i
$714$		0			0
$715$	5.74467	−	4.82035i	0.214838	−	0.180271i
$716$	−10.2879	−	1.81404i	−0.384478	−	0.0677939i
$717$		0			0
$718$	2.50442	−	6.88084i	0.0934642	−	0.256791i
$719$	−23.6018	−	8.59034i	−0.880197	−	0.320366i	−0.137908	−	0.990445i	$-0.544038\pi$
$719$	−23.6018	−	8.59034i	−0.880197	−	0.320366i	−0.742289	+	0.670079i	$0.766260\pi$
$720$		0			0
$721$	−1.20719	+	1.43867i	−0.0449580	+	0.0535789i
$722$	17.0394	−	20.3068i	0.634143	−	0.755742i
$723$		0			0
$724$	8.46310	+	3.08032i	0.314529	+	0.114479i
$725$	−4.53084	+	12.4484i	−0.168271	+	0.462321i
$726$		0			0
$727$	−19.0823	−	3.36472i	−0.707723	−	0.124791i	−0.191811	−	0.981432i	$-0.561436\pi$
$727$	−19.0823	−	3.36472i	−0.707723	−	0.124791i	−0.515913	+	0.856641i	$0.672547\pi$
$728$	0.219881	−	0.184502i	0.00814932	−	0.00683810i
$729$		0			0
$730$	0.453618	−	0.785689i	0.0167891	−	0.0290796i
$731$	−4.91518	−	27.8754i	−0.181795	−	1.03101i
$732$		0			0
$733$	10.1457	−	3.69274i	0.374741	−	0.136395i	−0.147781	−	0.989020i	$-0.547213\pi$
$733$	10.1457	−	3.69274i	0.374741	−	0.136395i	0.522523	+	0.852625i	$0.324991\pi$
$734$			31.5546i			1.16470i
$735$		0			0
$736$	0.725070	−	4.11208i	0.0267264	−	0.151573i
$737$	−8.84362	−	7.42068i	−0.325759	−	0.273344i
$738$		0			0
$739$	−28.0429			−1.03157			−0.515787	−	0.856717i	$-0.672500\pi$
$739$	−28.0429			−1.03157			−0.515787	+	0.856717i	$0.672500\pi$
$740$	4.80286	−	0.784114i	0.176556	−	0.0288246i
$741$		0			0
$742$	1.03128	+	1.22903i	0.0378595	+	0.0451192i
$743$	−13.7013	−	11.4967i	−0.502651	−	0.421774i	0.355883	−	0.934530i	$-0.384180\pi$
$743$	−13.7013	−	11.4967i	−0.502651	−	0.421774i	−0.858534	+	0.512756i	$0.828625\pi$
$744$		0			0
$745$	−2.52109	−	6.92665i	−0.0923657	−	0.253773i
$746$		−	8.36944i		−	0.306427i
$747$		0			0
$748$	−14.5455	+	8.39787i	−0.531837	+	0.307056i
$749$	−0.364287	−	2.06597i	−0.0133108	−	0.0754891i
$750$		0			0
$751$	1.32138	+	2.28870i	0.0482179	+	0.0835159i	0.889127	−	0.457660i	$-0.151312\pi$
$751$	1.32138	+	2.28870i	0.0482179	+	0.0835159i	−0.840909	+	0.541176i	$0.817979\pi$
$752$	−6.38745	+	5.35970i	−0.232926	+	0.195448i
$753$		0			0
$754$	−5.12632	−	2.95969i	−0.186690	−	0.107785i
$755$	3.22453	−	8.85931i	0.117353	−	0.322423i
$756$		0			0
$757$	47.2794	−	8.33663i	1.71840	−	0.303000i	0.774337	−	0.632773i	$-0.218083\pi$
$757$	47.2794	−	8.33663i	1.71840	−	0.303000i	0.944060	+	0.329773i	$0.106972\pi$
$758$	−18.1179	+	21.5920i	−0.658071	+	0.784258i
$759$		0			0
$760$	−5.31507	+	0.937191i	−0.192798	+	0.0339955i
$761$	−3.02398	−	1.10064i	−0.109619	−	0.0398981i	0.286628	−	0.958042i	$-0.407466\pi$
$761$	−3.02398	−	1.10064i	−0.109619	−	0.0398981i	−0.396247	+	0.918144i	$0.629688\pi$
$762$		0			0
$763$	2.52492	+	1.45777i	0.0914084	+	0.0527747i
$764$	−0.990230	−	0.174604i	−0.0358253	−	0.00631696i
$765$		0			0
$766$	4.54733	+	7.87621i	0.164302	+	0.284579i
$767$	8.44643	−	14.6296i	0.304983	−	0.528246i
$768$		0			0
$769$	17.4613	−	10.0813i	0.629671	−	0.363541i	−0.150954	−	0.988541i	$-0.548234\pi$
$769$	17.4613	−	10.0813i	0.629671	−	0.363541i	0.780625	+	0.625000i	$0.214901\pi$
$770$	−0.532932	+	0.193971i	−0.0192055	+	0.00699025i
$771$		0			0
$772$	−3.76060	−	10.3322i	−0.135347	−	0.371863i
$773$	3.61493	−	20.5013i	0.130020	−	0.737380i	−0.848179	−	0.529710i	$-0.822301\pi$
$773$	3.61493	−	20.5013i	0.130020	−	0.737380i	0.978199	−	0.207670i	$-0.0665881\pi$
$774$		0			0
$775$	22.8052	+	27.1782i	0.819187	+	0.976269i
$776$	−5.87526			−0.210909
$777$		0			0
$778$	2.00537			0.0718960
$779$	−16.9013	−	20.1421i	−0.605550	−	0.721667i
$780$		0			0
$781$	5.83450	−	33.0891i	0.208775	−	1.18402i
$782$	4.98528	+	13.6969i	0.178273	+	0.489801i
$783$		0			0
$784$	6.55745	−	2.38672i	0.234195	−	0.0852399i
$785$	−12.0361	+	6.94903i	−0.429586	+	0.248021i
$786$		0			0
$787$	4.71795	−	8.17173i	0.168177	−	0.291291i	−0.769602	−	0.638524i	$-0.779545\pi$
$787$	4.71795	−	8.17173i	0.168177	−	0.291291i	0.937779	+	0.347233i	$0.112879\pi$
$788$	−12.9525	−	22.4344i	−0.461414	−	0.799193i
$789$		0			0
$790$	1.48931	+	0.262606i	0.0529873	+	0.00934310i
$791$	1.08476	+	0.626286i	0.0385696	+	0.0222682i
$792$		0			0
$793$	−0.643830	−	0.234335i	−0.0228631	−	0.00832148i
$794$	−18.7858	+	3.31245i	−0.666685	+	0.117555i
$795$		0			0
$796$	10.0107	−	11.9302i	0.354819	−	0.422856i
$797$	44.0733	−	7.77131i	1.56116	−	0.275274i	0.674701	−	0.738091i	$-0.264272\pi$
$797$	44.0733	−	7.77131i	1.56116	−	0.275274i	0.886454	+	0.462817i	$0.153161\pi$
$798$		0			0
$799$	9.95526	−	27.3519i	0.352192	−	0.967639i
$800$	−3.77582	−	2.17997i	−0.133495	−	0.0770736i
$801$		0			0
$802$	18.9553	−	15.9054i	0.669336	−	0.561640i
$803$	2.72804	+	4.72510i	0.0962704	+	0.166745i
$804$		0			0
$805$	0.0854663	+	0.484704i	0.00301229	+	0.0170836i
$806$	−13.7292	+	7.92656i	−0.483591	+	0.279201i
$807$		0			0
$808$			17.0173i			0.598667i
$809$	7.22920	+	19.8621i	0.254165	+	0.698313i	0.999500	+	0.0316227i	$0.0100675\pi$
$809$	7.22920	+	19.8621i	0.254165	+	0.698313i	−0.745335	+	0.666691i	$0.767710\pi$
$810$		0			0
$811$	5.83069	+	4.89253i	0.204743	+	0.171800i	0.739394	−	0.673273i	$-0.235112\pi$
$811$	5.83069	+	4.89253i	0.204743	+	0.171800i	−0.534651	+	0.845073i	$0.679557\pi$
$812$	0.287752	+	0.342929i	0.0100981	+	0.0120345i
$813$		0			0
$814$	−10.3582	+	27.3723i	−0.363056	+	0.959397i
$815$	−1.80900			−0.0633666
$816$		0			0
$817$	41.9028	+	35.1606i	1.46599	+	1.23011i
$818$	4.27977	−	24.2718i	0.149639	−	0.848643i
$819$		0			0
$820$			3.11828i			0.108895i
$821$	5.77582	−	2.10223i	0.201577	−	0.0733682i	−0.239258	−	0.970956i	$-0.576904\pi$
$821$	5.77582	−	2.10223i	0.201577	−	0.0733682i	0.440836	+	0.897588i	$0.354682\pi$
$822$		0			0
$823$	4.84392	+	27.4712i	0.168848	+	0.957587i	0.945007	+	0.327050i	$0.106054\pi$
$823$	4.84392	+	27.4712i	0.168848	+	0.957587i	−0.776159	+	0.630538i	$0.782834\pi$
$824$	−6.37342	+	11.0391i	−0.222029	+	0.384565i
$825$		0			0
$826$	−0.978661	+	0.821194i	−0.0340520	+	0.0285730i
$827$	24.0641	+	4.24315i	0.836791	+	0.147549i	0.575593	−	0.817736i	$-0.304771\pi$
$827$	24.0641	+	4.24315i	0.836791	+	0.147549i	0.261198	+	0.965285i	$0.415882\pi$
$828$		0			0
$829$	16.1603	−	44.4002i	0.561272	−	1.54208i	−0.256503	−	0.966543i	$-0.582570\pi$
$829$	16.1603	−	44.4002i	0.561272	−	1.54208i	0.817775	−	0.575538i	$-0.195207\pi$
$830$	7.44640	+	2.71027i	0.258468	+	0.0940748i
$831$		0			0
$832$	1.25227	−	1.49239i	0.0434145	−	0.0517394i
$833$	−15.6583	+	18.6608i	−0.542528	+	0.646559i
$834$		0			0
$835$	−11.9956	−	4.36603i	−0.415124	−	0.151093i
$836$	11.1012	−	30.5003i	0.383943	−	1.05488i
$837$		0			0
$838$	17.9994	+	3.17378i	0.621780	+	0.109637i
$839$	36.0502	−	30.2497i	1.24459	−	1.04434i	0.247441	−	0.968903i	$-0.420410\pi$
$839$	36.0502	−	30.2497i	1.24459	−	1.04434i	0.997151	−	0.0754333i	$-0.0240340\pi$
$840$		0			0
$841$	−9.88403	+	17.1196i	−0.340829	+	0.590333i
$842$	6.52876	+	37.0264i	0.224996	+	1.27601i
$843$		0			0
$844$	−21.7766	+	7.92603i	−0.749582	+	0.272825i
$845$			7.36403i			0.253330i
$846$		0			0
$847$	0.310838	−	1.76285i	0.0106805	−	0.0605723i
$848$	8.34178	+	6.99959i	0.286458	+	0.240367i
$849$		0			0
$850$	15.2198			0.522034
$851$	21.8328	+	12.9777i	0.748419	+	0.444868i
$852$		0			0
$853$	17.8441	+	21.2658i	0.610971	+	0.728127i	0.979490	−	0.201493i	$-0.0645794\pi$
$853$	17.8441	+	21.2658i	0.610971	+	0.728127i	−0.368519	+	0.929620i	$0.620135\pi$
$854$	0.0396931	+	0.0333064i	0.00135827	+	0.00113972i
$855$		0			0
$856$	−4.86991	−	13.3800i	−0.166450	−	0.457318i
$857$		−	23.8545i		−	0.814853i	−0.913238	−	0.407426i	$-0.866426\pi$
$857$		−	23.8545i		−	0.814853i	0.913238	−	0.407426i	$-0.133574\pi$
$858$		0			0
$859$	−38.3629	+	22.1488i	−1.30893	+	0.755708i	−0.981917	−	0.189313i	$-0.939374\pi$
$859$	−38.3629	+	22.1488i	−1.30893	+	0.755708i	−0.327008	+	0.945021i	$0.606041\pi$
$860$	−1.12648	−	6.38857i	−0.0384126	−	0.217849i
$861$		0			0
$862$	18.4386	+	31.9367i	0.628023	+	1.08777i
$863$	−33.1007	+	27.7748i	−1.12676	+	0.945465i	−0.998926	−	0.0463308i	$-0.985247\pi$
$863$	−33.1007	+	27.7748i	−1.12676	+	0.945465i	−0.127835	+	0.991795i	$0.540803\pi$
$864$		0			0
$865$	−2.13064	−	1.23013i	−0.0724440	−	0.0418256i
$866$	3.72589	−	10.2368i	0.126611	−	0.347861i
$867$		0			0
$868$	1.18071	−	0.208190i	0.0400758	−	0.00706644i
$869$	−5.84605	+	6.96705i	−0.198314	+	0.236341i
$870$		0			0
$871$	−4.60347	+	0.811716i	−0.155983	+	0.0275040i
$872$	18.5951	+	6.76808i	0.629711	+	0.229196i
$873$		0			0
$874$	−24.3943	−	14.0840i	−0.825148	−	0.476399i
$875$	1.08652	+	0.191584i	0.0367312	+	0.00647671i
$876$		0			0
$877$	20.2553	+	35.0832i	0.683972	+	1.18467i	0.973759	+	0.227583i	$0.0730823\pi$
$877$	20.2553	+	35.0832i	0.683972	+	1.18467i	−0.289787	+	0.957091i	$0.593584\pi$
$878$	−9.34440	+	16.1850i	−0.315358	+	0.546217i
$879$		0			0
$880$	−3.33359	+	1.92465i	−0.112375	+	0.0648800i
$881$	22.9486	−	8.35260i	0.773157	−	0.281406i	0.0748407	−	0.997196i	$-0.476155\pi$
$881$	22.9486	−	8.35260i	0.773157	−	0.281406i	0.698316	+	0.715789i	$0.253933\pi$
$882$		0			0
$883$	8.25110	+	22.6697i	0.277671	+	0.762896i	0.997625	+	0.0688742i	$0.0219407\pi$
$883$	8.25110	+	22.6697i	0.277671	+	0.762896i	−0.719954	+	0.694022i	$0.755837\pi$
$884$	−1.18094	+	6.69743i	−0.0397192	+	0.225259i
$885$		0			0
$886$	−11.6768	−	13.9159i	−0.392291	−	0.467514i
$887$	4.81523			0.161679			0.0808397	−	0.996727i	$-0.474240\pi$
$887$	4.81523			0.161679			0.0808397	+	0.996727i	$0.474240\pi$
$888$		0			0
$889$	0.815153			0.0273394
$890$	−5.20124	−	6.19860i	−0.174346	−	0.207777i
$891$		0			0
$892$	−1.72119	+	9.76137i	−0.0576298	+	0.326835i
$893$	19.2385	+	52.8574i	0.643793	+	1.76881i
$894$		0			0
$895$	7.85369	−	2.85851i	0.262520	−	0.0955494i
$896$	−0.127595	+	0.0736672i	−0.00426266	+	0.00246105i
$897$		0			0
$898$	−7.78469	+	13.4835i	−0.259778	+	0.449949i
$899$	−12.3624	−	21.4123i	−0.412309	−	0.714139i
$900$		0			0
$901$	−37.4355	−	6.60089i	−1.24716	−	0.219908i
$902$	−16.2408	−	9.37660i	−0.540758	−	0.312207i
$903$		0			0
$904$	7.98885	+	2.90770i	0.265705	+	0.0967088i
$905$	−7.09587	+	1.25119i	−0.235875	+	0.0415911i
$906$		0			0
$907$	−3.00851	+	3.58540i	−0.0998959	+	0.119051i	−0.813676	−	0.581318i	$-0.802537\pi$
$907$	−3.00851	+	3.58540i	−0.0998959	+	0.119051i	0.713780	+	0.700370i	$0.246982\pi$
$908$	−1.96999	+	0.347363i	−0.0653765	+	0.0115276i
$909$		0			0
$910$	−0.0785409	+	0.215789i	−0.00260360	+	0.00715334i
$911$	7.63660	+	4.40899i	0.253012	+	0.146077i	0.621143	−	0.783698i	$-0.286669\pi$
$911$	7.63660	+	4.40899i	0.253012	+	0.146077i	−0.368131	+	0.929774i	$0.620002\pi$
$912$		0			0
$913$	−36.5069	+	30.6330i	−1.20820	+	1.01380i
$914$	−5.51212	−	9.54728i	−0.182325	−	0.315796i
$915$		0			0
$916$	1.55285	+	8.80664i	0.0513075	+	0.290980i
$917$	0.105004	−	0.0606243i	0.00346755	−	0.00200199i
$918$		0			0
$919$			8.95913i			0.295535i	0.989022	+	0.147767i	$0.0472087\pi$
$919$			8.95913i			0.295535i	−0.989022	+	0.147767i	$0.952791\pi$
$920$	1.14254	+	3.13911i	0.0376685	+	0.103493i
$921$		0			0
$922$	16.3531	+	13.7219i	0.538562	+	0.451907i
$923$	−8.74497	−	10.4218i	−0.287844	−	0.343039i
$924$		0			0
$925$	20.5307	−	16.7876i	0.675046	−	0.551974i
$926$	33.1910			1.09073
$927$		0			0
$928$	2.32756	+	1.95305i	0.0764058	+	0.0641121i
$929$	−6.26803	+	35.5478i	−0.205647	+	1.16628i	0.690770	+	0.723074i	$0.257271\pi$
$929$	−6.26803	+	35.5478i	−0.205647	+	1.16628i	−0.896418	+	0.443210i	$0.853840\pi$
$930$		0			0
$931$		−	47.0756i		−	1.54284i
$932$	20.4242	−	7.43379i	0.669016	−	0.243502i
$933$		0			0
$934$	−2.57215	−	14.5874i	−0.0841633	−	0.477314i
$935$	6.71861	−	11.6370i	0.219722	−	0.380570i
$936$		0			0
$937$	−5.84891	+	4.90782i	−0.191076	+	0.160331i	−0.733307	−	0.679898i	$-0.762024\pi$
$937$	−5.84891	+	4.90782i	−0.191076	+	0.160331i	0.542231	+	0.840229i	$0.317580\pi$
$938$	0.348145	+	0.0613874i	0.0113674	+	0.00200437i
$939$		0			0
$940$	2.28158	−	6.26859i	0.0744169	−	0.204459i
$941$	−42.2064	−	15.3619i	−1.37589	−	0.500782i	−0.454959	−	0.890512i	$-0.650346\pi$
$941$	−42.2064	−	15.3619i	−1.37589	−	0.500782i	−0.920929	+	0.389730i	$0.872568\pi$
$942$		0			0
$943$	−10.4612	+	12.4672i	−0.340664	+	0.405987i
$944$	−5.57367	+	6.64244i	−0.181408	+	0.216193i
$945$		0			0
$946$	36.6605	+	13.3433i	1.19194	+	0.433830i
$947$	−2.43767	+	6.69744i	−0.0792136	+	0.217638i	−0.972977	−	0.230900i	$-0.925833\pi$
$947$	−2.43767	+	6.69744i	−0.0792136	+	0.217638i	0.893764	+	0.448538i	$0.148055\pi$
$948$		0			0
$949$	2.17565	+	0.383626i	0.0706247	+	0.0124530i
$950$	−22.5311	+	18.9058i	−0.731004	+	0.613385i
$951$		0			0
$952$	0.257159	−	0.445413i	0.00833457	−	0.0144359i
$953$	−1.91509	−	10.8610i	−0.0620358	−	0.351823i	−0.999987	−	0.00505584i	$-0.998391\pi$
$953$	−1.91509	−	10.8610i	−0.0620358	−	0.351823i	0.937951	−	0.346767i	$-0.112720\pi$
$954$		0			0
$955$	0.755929	−	0.275136i	0.0244613	−	0.00890318i
$956$			7.91730i			0.256064i
$957$		0			0
$958$	1.56380	−	8.86872i	0.0505239	−	0.286535i
$959$	−0.760970	−	0.638530i	−0.0245730	−	0.0206192i
$960$		0			0
$961$	−35.2173			−1.13604
$962$	5.79434	+	10.3371i	0.186817	+	0.333281i
$963$		0			0
$964$	19.1413	+	22.8117i	0.616499	+	0.734715i
$965$	6.73861	+	5.65436i	0.216923	+	0.182020i
$966$		0			0
$967$	9.23888	+	25.3836i	0.297102	+	0.816282i	0.994981	+	0.100066i	$0.0319053\pi$
$967$	9.23888	+	25.3836i	0.297102	+	0.816282i	−0.697879	+	0.716216i	$0.745872\pi$
$968$		−	12.1496i		−	0.390501i
$969$		0			0
$970$	4.07069	−	2.35021i	0.130702	−	0.0754608i
$971$	8.75426	+	49.6479i	0.280937	+	1.59328i	0.719446	+	0.694548i	$0.244396\pi$
$971$	8.75426	+	49.6479i	0.280937	+	1.59328i	−0.438509	+	0.898727i	$0.644493\pi$
$972$		0			0
$973$	0.884287	+	1.53163i	0.0283489	+	0.0491018i
$974$	−2.59840	+	2.18032i	−0.0832582	+	0.0698620i
$975$		0			0
$976$	0.304570	+	0.175844i	0.00974905	+	0.00562862i
$977$	−6.82658	+	18.7559i	−0.218402	+	0.600054i	−0.999710	−	0.0240919i	$-0.992331\pi$
$977$	−6.82658	+	18.7559i	−0.218402	+	0.600054i	0.781308	+	0.624146i	$0.214553\pi$
$978$		0			0
$979$	47.9238	−	8.45027i	1.53165	−	0.270072i
$980$	−3.58862	+	4.27675i	−0.114634	+	0.136616i
$981$		0			0
$982$	−20.4193	+	3.60047i	−0.651605	+	0.114896i
$983$	−10.0028	−	3.64071i	−0.319039	−	0.116121i	0.177537	−	0.984114i	$-0.443187\pi$
$983$	−10.0028	−	3.64071i	−0.319039	−	0.116121i	−0.496576	+	0.867994i	$0.665409\pi$
$984$		0			0
$985$	17.9484	+	10.3625i	0.571883	+	0.330177i
$986$	−10.4454	−	1.84181i	−0.332650	−	0.0586551i
$987$		0			0
$988$	−6.57122	−	11.3817i	−0.209058	−	0.362100i
$989$	16.9286	−	29.3212i	0.538299	−	0.932361i
$990$		0			0
$991$	−28.8161	+	16.6370i	−0.915375	+	0.528492i	−0.882156	−	0.470956i	$-0.843909\pi$
$991$	−28.8161	+	16.6370i	−0.915375	+	0.528492i	−0.0332181	+	0.999448i	$0.510576\pi$
$992$	7.64666	−	2.78316i	0.242782	−	0.0883653i
$993$		0			0
$994$	0.351899	+	0.966834i	0.0111616	+	0.0306661i
$995$	−2.16360	+	12.2704i	−0.0685906	+	0.388997i
$996$		0			0
$997$	8.80737	+	10.4962i	0.278932	+	0.332418i	0.887262	−	0.461266i	$-0.152605\pi$
$997$	8.80737	+	10.4962i	0.278932	+	0.332418i	−0.608330	+	0.793684i	$0.708160\pi$
$998$	24.6821			0.781297
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bj.c.469.2		12
3.2	odd	2		74.2.h.a.25.1	yes	12
12.11	even	2		592.2.bq.b.321.2		12
37.3	even	18	inner	666.2.bj.c.595.2		12
111.59	even	36		2738.2.a.r.1.1		6
111.77	odd	18		74.2.h.a.3.1	✓	12
111.89	even	36		2738.2.a.s.1.2		6
444.299	even	18		592.2.bq.b.225.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.3.1	✓	12	111.77	odd	18
74.2.h.a.25.1	yes	12	3.2	odd	2
592.2.bq.b.225.2		12	444.299	even	18
592.2.bq.b.321.2		12	12.11	even	2
666.2.bj.c.469.2		12	1.1	even	1	trivial
666.2.bj.c.595.2		12	37.3	even	18	inner
2738.2.a.r.1.1		6	111.59	even	36
2738.2.a.s.1.2		6	111.89	even	36

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 + 0.766044i) q^{2} +(-0.173648 + 0.984808i) q^{4} +(-0.273629 - 0.751790i) q^{5} +(-0.138449 + 0.0503913i) q^{7} +(-0.866025 + 0.500000i) q^{8} +O(q^{10})\)	\(q+(0.642788 + 0.766044i) q^{2} +(-0.173648 + 0.984808i) q^{4} +(-0.273629 - 0.751790i) q^{5} +(-0.138449 + 0.0503913i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.400019 - 0.692853i) q^{10} +(2.40570 + 4.16679i) q^{11} +(1.91858 + 0.338298i) q^{13} +(-0.127595 - 0.0736672i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(3.43779 - 0.606175i) q^{17} +(-4.33625 + 5.16775i) q^{19} +(0.787884 - 0.138925i) q^{20} +(-1.64560 + 4.52124i) q^{22} +(3.61610 + 2.08776i) q^{23} +(3.33991 - 2.80251i) q^{25} +(0.974090 + 1.68717i) q^{26} +(-0.0255844 - 0.145096i) q^{28} +(-2.63134 + 1.51921i) q^{29} +8.13740i q^{31} +(-0.342020 - 0.939693i) q^{32} +(2.67412 + 2.24386i) q^{34} +(0.0757674 + 0.0902961i) q^{35} +(6.08227 + 0.0772535i) q^{37} -6.74601 q^{38} +(0.612865 + 0.514255i) q^{40} +(-0.676822 + 3.83845i) q^{41} -8.10852i q^{43} +(-4.52124 + 1.64560i) q^{44} +(0.725070 + 4.11208i) q^{46} +(4.16911 - 7.22111i) q^{47} +(-5.34568 + 4.48556i) q^{49} +(4.29370 + 0.757095i) q^{50} +(-0.666317 + 1.83069i) q^{52} +(-10.2327 - 3.72440i) q^{53} +(2.47428 - 2.94874i) q^{55} +(0.0947047 - 0.112865i) q^{56} +(-2.85517 - 1.03920i) q^{58} +(2.96569 - 8.14816i) q^{59} +(-0.346344 - 0.0610698i) q^{61} +(-6.23361 + 5.23062i) q^{62} +(0.500000 - 0.866025i) q^{64} +(-0.270651 - 1.53494i) q^{65} +(-2.25471 + 0.820647i) q^{67} +3.49082i q^{68} +(-0.0204685 + 0.116082i) q^{70} +(-5.34953 - 4.48879i) q^{71} +1.13399 q^{73} +(3.85043 + 4.70895i) q^{74} +(-4.33625 - 5.16775i) q^{76} +(-0.543037 - 0.455662i) q^{77} +(0.646510 + 1.77627i) q^{79} +0.800038i q^{80} +(-3.37547 + 1.94883i) q^{82} +(1.71997 + 9.75442i) q^{83} +(-1.39639 - 2.41863i) q^{85} +(6.21149 - 5.21206i) q^{86} +(-4.16679 - 2.40570i) q^{88} +(3.45924 - 9.50418i) q^{89} +(-0.282673 + 0.0498429i) q^{91} +(-2.68397 + 3.19863i) q^{92} +(8.21154 - 1.44792i) q^{94} +(5.07158 + 1.84591i) q^{95} +(5.08812 + 2.93763i) q^{97} +(-6.87228 - 1.21177i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{7}+O(q^{10}) \) 12 * q - 12 * q^7	\( 12 q - 12 q^{7} + 6 q^{10} + 6 q^{11} + 6 q^{13} + 18 q^{14} - 18 q^{19} - 18 q^{25} - 12 q^{26} - 6 q^{28} - 18 q^{29} + 12 q^{34} - 18 q^{35} + 30 q^{37} + 24 q^{38} + 12 q^{40} - 24 q^{41} - 6 q^{44} + 30 q^{46} - 6 q^{47} + 12 q^{49} + 36 q^{50} - 12 q^{52} + 12 q^{53} - 18 q^{55} + 6 q^{58} - 36 q^{61} + 6 q^{64} - 36 q^{65} - 30 q^{67} - 12 q^{70} - 12 q^{71} + 48 q^{74} - 18 q^{76} - 12 q^{77} + 6 q^{79} + 48 q^{83} + 18 q^{85} + 36 q^{86} - 36 q^{88} + 18 q^{89} - 6 q^{91} - 18 q^{92} + 36 q^{97} - 36 q^{98}+O(q^{100}) \) 12 * q - 12 * q^7 + 6 * q^10 + 6 * q^11 + 6 * q^13 + 18 * q^14 - 18 * q^19 - 18 * q^25 - 12 * q^26 - 6 * q^28 - 18 * q^29 + 12 * q^34 - 18 * q^35 + 30 * q^37 + 24 * q^38 + 12 * q^40 - 24 * q^41 - 6 * q^44 + 30 * q^46 - 6 * q^47 + 12 * q^49 + 36 * q^50 - 12 * q^52 + 12 * q^53 - 18 * q^55 + 6 * q^58 - 36 * q^61 + 6 * q^64 - 36 * q^65 - 30 * q^67 - 12 * q^70 - 12 * q^71 + 48 * q^74 - 18 * q^76 - 12 * q^77 + 6 * q^79 + 48 * q^83 + 18 * q^85 + 36 * q^86 - 36 * q^88 + 18 * q^89 - 6 * q^91 - 18 * q^92 + 36 * q^97 - 36 * q^98

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