LMFDB - Embedded newform 666.2.bj.c.595.2

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			595.2
Root			$0.642788 - 0.766044i$ of defining polynomial
Character	$\chi$	$=$	666.595
Dual form			666.2.bj.c.469.2

$q$-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 $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{13}{18}\right)$

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	−0.985719	−	0.168397i	$-0.946141\pi$
$5$	−0.273629	+	0.751790i	−0.122371	+	0.336211i	0.863349	+	0.504608i	$0.168363\pi$
$6$		0			0
$7$	−0.138449	−	0.0503913i	−0.0523288	−	0.0190461i	0.315723	−	0.948851i	$-0.397753\pi$
$7$	−0.138449	−	0.0503913i	−0.0523288	−	0.0190461i	−0.368052	+	0.929805i	$0.619975\pi$
$8$	−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	−0.233486	−	0.972360i	$-0.575013\pi$
$11$	2.40570	−	4.16679i	0.725346	−	1.25634i	0.958832	−	0.283975i	$-0.0916533\pi$
$12$		0			0
$13$	1.91858	−	0.338298i	0.532119	−	0.0938270i	0.0988686	−	0.995100i	$-0.468478\pi$
$13$	1.91858	−	0.338298i	0.532119	−	0.0938270i	0.433251	+	0.901274i	$0.357367\pi$
$14$	−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	0.574214	−	0.818705i	$-0.305308\pi$
$17$	3.43779	+	0.606175i	0.833786	+	0.147019i	0.259572	+	0.965724i	$0.416419\pi$
$18$		0			0
$19$	−4.33625	−	5.16775i	−0.994805	−	1.18556i	−0.982619	−	0.185636i	$-0.940565\pi$
$19$	−4.33625	−	5.16775i	−0.994805	−	1.18556i	−0.0121861	−	0.999926i	$-0.503879\pi$
$20$	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	−0.0731316	−	0.997322i	$-0.523299\pi$
$23$	3.61610	−	2.08776i	0.754009	−	0.435327i	0.827141	+	0.561995i	$0.189966\pi$
$24$		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	0.235377	−	0.971904i	$-0.424367\pi$
$29$	−2.63134	−	1.51921i	−0.488628	−	0.282109i	−0.724005	+	0.689795i	$0.757701\pi$
$30$		0			0
$31$		−	8.13740i		−	1.46152i	−0.682634	−	0.730760i	$-0.739166\pi$
$31$		−	8.13740i		−	1.46152i	0.682634	−	0.730760i	$-0.260834\pi$
$32$	−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	−0.990938	−	0.134322i	$-0.957114\pi$
$41$	−0.676822	−	3.83845i	−0.105702	−	0.599465i	0.885236	−	0.465142i	$-0.153997\pi$
$42$		0			0
$43$			8.10852i			1.23654i	0.785966	+	0.618269i	$0.212166\pi$
$43$			8.10852i			1.23654i	−0.785966	+	0.618269i	$0.787834\pi$
$44$	−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	0.991549	+	0.129734i	$0.0414122\pi$
$47$	4.16911	+	7.22111i	0.608127	+	1.05331i	−0.383422	+	0.923573i	$0.625254\pi$
$48$		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	−0.929827	−	0.367998i	$-0.880043\pi$
$53$	−10.2327	+	3.72440i	−1.40557	+	0.511586i	−0.475744	+	0.879584i	$0.657821\pi$
$54$		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	0.968742	+	0.248072i	$0.0797968\pi$
$59$	2.96569	+	8.14816i	0.386100	+	1.06080i	−0.582642	+	0.812729i	$0.697981\pi$
$60$		0			0
$61$	−0.346344	+	0.0610698i	−0.0443448	+	0.00781919i	−0.195777	−	0.980649i	$-0.562723\pi$
$61$	−0.346344	+	0.0610698i	−0.0443448	+	0.00781919i	0.151432	+	0.988468i	$0.451612\pi$
$62$	−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	0.200598	−	0.979674i	$-0.435711\pi$
$67$	−2.25471	−	0.820647i	−0.275457	−	0.100258i	−0.476055	+	0.879416i	$0.657934\pi$
$68$		−	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	−0.902439	−	0.430818i	$-0.858225\pi$
$71$	−5.34953	+	4.48879i	−0.634873	+	0.532721i	0.267566	+	0.963539i	$0.413781\pi$
$72$		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	−0.897996	−	0.440004i	$-0.854977\pi$
$79$	0.646510	−	1.77627i	0.0727380	−	0.199846i	0.970734	+	0.240158i	$0.0771992\pi$
$80$		−	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	−0.732196	−	0.681094i	$-0.761505\pi$
$83$	1.71997	−	9.75442i	0.188791	−	1.07069i	0.920987	−	0.389593i	$-0.127384\pi$
$84$		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	0.976616	+	0.214992i	$0.0689724\pi$
$89$	3.45924	+	9.50418i	0.366679	+	1.00744i	−0.609937	+	0.792450i	$0.708805\pi$
$90$		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	−0.218930	−	0.975740i	$-0.570257\pi$
$97$	5.08812	−	2.93763i	0.516620	−	0.298271i	0.735551	+	0.677470i	$0.236923\pi$
$98$	−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	0.884187	+	0.467134i	$0.154713\pi$
$101$	8.50866	+	14.7374i	0.846643	+	1.46643i	−0.0375439	+	0.999295i	$0.511953\pi$
$102$		0			0
$103$	11.0391	+	6.37342i	1.08771	+	0.627992i	0.932967	−	0.359962i	$-0.117210\pi$
$103$	11.0391	+	6.37342i	1.08771	+	0.627992i	0.154747	+	0.987954i	$0.450544\pi$
$104$	−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	−0.833964	−	0.551819i	$-0.813934\pi$
$107$	−2.47252	−	14.0223i	−0.239027	−	1.35559i	0.594937	−	0.803773i	$-0.297177\pi$
$108$		0			0
$109$	−12.7198	+	15.1589i	−1.21834	+	1.45196i	−0.364674	+	0.931135i	$0.618819\pi$
$109$	−12.7198	+	15.1589i	−1.21834	+	1.45196i	−0.853664	+	0.520823i	$0.825625\pi$
$110$	3.84930			0.367017
$111$		0			0
$112$	0.147334			0.0139218
$113$	−5.46470	+	6.51257i	−0.514075	+	0.612651i	−0.959169	−	0.282833i	$-0.908726\pi$
$113$	−5.46470	+	6.51257i	−0.514075	+	0.612651i	0.445094	+	0.895484i	$0.353170\pi$
$114$		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	−0.562224	−	0.826985i	$-0.690054\pi$
$127$	−5.19901	+	1.89229i	−0.461338	+	0.167913i	0.100887	+	0.994898i	$0.467832\pi$
$128$	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	0.138131	−	0.990414i	$-0.455890\pi$
$131$	−0.810446	−	0.142903i	−0.0708090	−	0.0124855i	−0.208940	+	0.977928i	$0.567001\pi$
$132$		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	−0.685319	−	0.728243i	$-0.740337\pi$
$137$	3.37116	−	5.83902i	0.288018	−	0.498861i	0.973336	+	0.229382i	$0.0736705\pi$
$138$		0			0
$139$	−2.08444	+	11.8214i	−0.176800	+	1.00268i	0.759246	+	0.650804i	$0.225568\pi$
$139$	−2.08444	+	11.8214i	−0.176800	+	1.00268i	−0.936046	+	0.351878i	$0.885543\pi$
$140$	−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	−0.196759	−	0.980452i	$-0.563042\pi$
$151$	9.02729	−	7.57480i	0.734631	−	0.616428i	0.931390	+	0.364023i	$0.118597\pi$
$152$	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	0.589414	+	0.807831i	$0.299359\pi$
$157$	−3.01657	+	17.1078i	−0.240749	+	1.36535i	−0.830162	+	0.557522i	$0.811752\pi$
$158$	−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	0.966288	−	0.257464i	$-0.0828867\pi$
$163$	0.773358	+	2.12478i	0.0605741	+	0.166426i	−0.905714	+	0.423889i	$0.860665\pi$
$164$	−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	0.999464	−	0.0327478i	$-0.0104258\pi$
$167$	10.2563	+	12.2230i	0.793658	+	0.945845i	−0.205805	+	0.978593i	$0.565981\pi$
$168$		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	0.727931	−	0.685650i	$-0.240482\pi$
$173$	2.35572	+	1.97668i	0.179102	+	0.150284i	−0.548829	+	0.835934i	$0.684926\pi$
$174$		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	$-0.872333\pi$
$179$		−	10.4466i		−	0.780819i	0.920641	−	0.390410i	$-0.127667\pi$
$180$		0			0
$181$	1.56392	+	8.86942i	0.116245	+	0.659259i	0.986126	+	0.165997i	$0.0530843\pi$
$181$	1.56392	+	8.86942i	0.116245	+	0.659259i	−0.869881	+	0.493262i	$0.835805\pi$
$182$	−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	$-0.988418\pi$
$191$		−	1.00551i		−	0.0727558i	0.999338	−	0.0363779i	$-0.0115820\pi$
$192$		0			0
$193$	−9.52217	−	5.49763i	−0.685421	−	0.395728i	0.116473	−	0.993194i	$-0.462841\pi$
$193$	−9.52217	−	5.49763i	−0.685421	−	0.395728i	−0.801894	+	0.597466i	$0.796174\pi$
$194$	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	−0.954537	−	0.298094i	$-0.903649\pi$
$197$	−19.8444	−	16.6514i	−1.41386	−	1.18637i	−0.459319	−	0.888271i	$-0.651906\pi$
$198$		0			0
$199$	−13.4873	+	7.78692i	−0.956092	+	0.552000i	−0.894968	−	0.446130i	$-0.852802\pi$
$199$	−13.4873	+	7.78692i	−0.956092	+	0.552000i	−0.0611237	+	0.998130i	$0.519468\pi$
$200$	−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	−0.123430	−	0.992353i	$-0.539390\pi$
$211$	11.5871	−	20.0694i	0.797688	−	1.38164i	0.921118	−	0.389283i	$-0.127277\pi$
$212$	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	−0.914915	−	0.403647i	$-0.867742\pi$
$227$	0.684171	−	1.87974i	0.0454100	−	0.124763i	0.960325	+	0.278884i	$0.0899646\pi$
$228$		0			0
$229$	8.40320	+	3.05851i	0.555299	+	0.202112i	0.604399	−	0.796682i	$-0.293413\pi$
$229$	8.40320	+	3.05851i	0.555299	+	0.202112i	−0.0491004	+	0.998794i	$0.515635\pi$
$230$	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	0.252171	+	0.967683i	$0.418855\pi$
$233$	−10.8675	+	18.8230i	−0.711952	+	1.23314i	−0.964123	+	0.265455i	$0.914478\pi$
$234$		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	0.420032	−	0.907509i	$-0.362019\pi$
$239$	7.79702	+	1.37482i	0.504347	+	0.0889300i	0.0843148	+	0.996439i	$0.473130\pi$
$240$		0			0
$241$	19.1413	+	22.8117i	1.23300	+	1.46943i	0.833334	+	0.552769i	$0.186429\pi$
$241$	19.1413	+	22.8117i	1.23300	+	1.46943i	0.399665	+	0.916661i	$0.369127\pi$
$242$	−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	−0.277514	−	0.960721i	$-0.589511\pi$
$251$	−19.7765	−	11.4180i	−1.24828	−	0.720695i	−0.970766	+	0.240026i	$0.922844\pi$
$252$		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	−0.329039	−	0.944316i	$-0.606725\pi$
$257$	10.5496	−	12.5726i	0.658068	−	0.784255i	0.987107	+	0.160062i	$0.0511693\pi$
$258$		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	0.975318	−	0.220805i	$-0.0708683\pi$
$263$	−0.270840	−	1.53601i	−0.0167007	−	0.0947145i	−0.992019	+	0.126090i	$0.959757\pi$
$264$		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	0.911915	−	0.410380i	$-0.134604\pi$
$269$	1.64927	+	2.85662i	0.100558	+	0.174171i	−0.811357	+	0.584551i	$0.801271\pi$
$270$		0			0
$271$	2.76033	+	2.31620i	0.167678	+	0.140699i	0.722766	−	0.691093i	$-0.242871\pi$
$271$	2.76033	+	2.31620i	0.167678	+	0.140699i	−0.555087	+	0.831792i	$0.687315\pi$
$272$	−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	0.372683	−	0.927959i	$-0.378438\pi$
$277$	−10.0841	−	12.0177i	−0.605894	−	0.722076i	−0.978577	+	0.205883i	$0.933993\pi$
$278$	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	0.980718	−	0.195431i	$-0.0626105\pi$
$281$	1.74041	+	4.78173i	0.103824	+	0.285254i	−0.876894	+	0.480684i	$0.840388\pi$
$282$		0			0
$283$	−9.02521	+	1.59139i	−0.536493	+	0.0945982i	−0.435329	−	0.900272i	$-0.643368\pi$
$283$	−9.02521	+	1.59139i	−0.536493	+	0.0945982i	−0.101164	+	0.994870i	$0.532257\pi$
$284$	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	0.133970	−	0.990985i	$-0.457227\pi$
$293$	19.3966	−	16.2757i	1.13316	−	0.950838i	0.999194	+	0.0401477i	$0.0127829\pi$
$294$		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	−0.714661	−	0.699471i	$-0.753419\pi$
$307$	4.35284	−	7.53934i	0.248430	−	0.430293i	0.963090	+	0.269178i	$0.0867521\pi$
$308$	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	0.870527	−	0.492121i	$-0.163778\pi$
$311$	−1.98686	−	5.45885i	−0.112664	−	0.309543i	−0.983191	+	0.182578i	$0.941556\pi$
$312$		0			0
$313$	−7.74595	−	1.36582i	−0.437827	−	0.0772007i	−0.0496099	−	0.998769i	$-0.515798\pi$
$313$	−7.74595	−	1.36582i	−0.437827	−	0.0772007i	−0.388217	+	0.921568i	$0.626909\pi$
$314$	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	−0.485519	−	0.874226i	$-0.661369\pi$
$317$	−5.26133	+	1.91497i	−0.295506	+	0.107555i	0.190013	+	0.981782i	$0.439147\pi$
$318$		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	−0.984792	−	0.173738i	$-0.944415\pi$
$331$	−11.6926	+	13.9348i	−0.642686	+	0.765923i	0.342106	+	0.939661i	$0.388860\pi$
$332$	−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	−0.585731	−	0.810505i	$-0.699193\pi$
$337$	−5.73735	−	32.5381i	−0.312533	−	1.77246i	0.273198	−	0.961958i	$-0.411919\pi$
$338$	−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	−0.501740	+	0.865018i	$0.667307\pi$
$347$	−27.9743	+	16.1510i	−1.50174	+	0.867029i	−0.999998	+	0.00201032i	$0.999360\pi$
$348$		0			0
$349$	−2.14851	+	0.781994i	−0.115007	+	0.0418592i	−0.398883	−	0.917002i	$-0.630602\pi$
$349$	−2.14851	+	0.781994i	−0.115007	+	0.0418592i	0.283876	+	0.958861i	$0.408380\pi$
$350$	−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	0.00278690	−	0.999996i	$-0.499113\pi$
$353$	−6.32439	−	1.11516i	−0.336613	−	0.0593540i	−0.339400	+	0.940642i	$0.610224\pi$
$354$		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	−0.946319	−	0.323233i	$-0.895230\pi$
$359$	−3.66122	+	6.34142i	−0.193232	+	0.334687i	0.753088	+	0.657920i	$0.228564\pi$
$360$		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	0.266288	−	0.963893i	$-0.414203\pi$
$367$	24.1722	−	20.2829i	1.26178	−	1.05876i	0.995490	−	0.0948646i	$-0.0302418\pi$
$368$	−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	−0.793501	−	0.608569i	$-0.791744\pi$
$373$	−6.41137	+	5.37977i	−0.331968	+	0.278554i	0.461533	+	0.887123i	$0.347300\pi$
$374$	−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	−0.553696	−	0.832719i	$-0.686783\pi$
$379$	4.89452	−	27.7582i	0.251415	−	1.42584i	0.805111	−	0.593124i	$-0.202106\pi$
$380$	−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	0.0599323	−	0.998202i	$-0.480912\pi$
$383$	8.95650	−	1.57927i	0.457656	−	0.0806970i	0.397723	+	0.917505i	$0.369800\pi$
$384$		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	0.797732	−	0.603012i	$-0.206033\pi$
$389$	1.28903	+	1.53620i	0.0653563	+	0.0778886i	−0.732376	+	0.680901i	$0.761589\pi$
$390$		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	0.521012	−	0.853550i	$-0.325555\pi$
$397$	−9.53782	−	16.5200i	−0.478690	−	0.829115i	−0.999701	+	0.0244346i	$0.992221\pi$
$398$	−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	$0.211992\pi$
$401$			24.7444i			1.23568i	−0.786305	+	0.617839i	$0.788008\pi$
$402$		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	−0.999080	−	0.0428927i	$-0.986343\pi$
$409$	−15.8423	+	18.8801i	−0.783350	+	0.933560i	0.215729	+	0.976453i	$0.430787\pi$
$410$	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	0.917171	−	0.398493i	$-0.130467\pi$
$419$	14.0011	+	11.7483i	0.683997	+	0.573942i	−0.233174	+	0.972435i	$0.574911\pi$
$420$		0			0
$421$	32.5605	−	18.7988i	1.58690	−	0.916198i	0.593087	−	0.805138i	$-0.297909\pi$
$421$	32.5605	−	18.7988i	1.58690	−	0.916198i	0.993814	−	0.111060i	$-0.0354245\pi$
$422$	−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	0.794867	−	0.606784i	$-0.207541\pi$
$431$	36.3170	−	6.40367i	1.74933	−	0.308454i	0.954463	+	0.298330i	$0.0964295\pi$
$432$		0			0
$433$	−5.44689	+	9.43429i	−0.261761	+	0.453383i	−0.966710	−	0.255875i	$-0.917637\pi$
$433$	−5.44689	+	9.43429i	−0.261761	+	0.453383i	0.704949	+	0.709258i	$0.250970\pi$
$434$	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	−0.688528	−	0.725210i	$-0.741743\pi$
$439$	6.39195	−	17.5617i	0.305071	−	0.838176i	0.993599	−	0.112966i	$-0.0360351\pi$
$440$	−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	−0.748328	−	0.663329i	$-0.769143\pi$
$449$	5.32504	−	14.6304i	0.251304	−	0.690453i	0.999632	−	0.0271236i	$-0.00863478\pi$
$450$		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	−0.421705	−	0.906733i	$-0.638568\pi$
$457$	−10.8568	+	1.91434i	−0.507858	+	0.0895491i	−0.0861526	+	0.996282i	$0.527457\pi$
$458$	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	0.640245	−	0.768171i	$-0.278833\pi$
$461$	21.0232	+	3.70696i	0.979148	+	0.172650i	0.338903	+	0.940821i	$0.389944\pi$
$462$		0			0
$463$	21.3348	+	25.4258i	0.991512	+	1.18164i	0.983359	+	0.181671i	$0.0581506\pi$
$463$	21.3348	+	25.4258i	0.991512	+	1.18164i	0.00815253	+	0.999967i	$0.497405\pi$
$464$	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	−0.766522	−	0.642218i	$-0.778014\pi$
$467$	−12.8279	+	7.40621i	−0.593606	+	0.342719i	0.172916	+	0.984937i	$0.444681\pi$
$468$		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	−0.881902	−	0.471433i	$-0.843737\pi$
$479$	−5.78865	+	6.89864i	−0.264490	+	0.315207i	0.617412	+	0.786640i	$0.288181\pi$
$480$		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	$-0.975513\pi$
$487$		−	3.39198i		−	0.153705i	0.997042	−	0.0768525i	$-0.0244871\pi$
$488$	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	0.531463	−	0.847081i	$-0.321642\pi$
$491$	−10.3671	−	17.9564i	−0.467862	−	0.810361i	−0.999326	+	0.0367202i	$0.988309\pi$
$492$		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	0.993643	−	0.112579i	$-0.0359113\pi$
$499$	15.8653	+	18.9076i	0.710229	+	0.846418i	−0.283413	+	0.958998i	$0.591467\pi$
$500$	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	0.999515	+	0.0311477i	$0.00991621\pi$
$503$	5.69356	+	15.6429i	0.253863	+	0.697484i	−0.745651	+	0.666336i	$0.767862\pi$
$504$		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	0.721160	+	0.692769i	$0.243609\pi$
$509$	−4.36442	+	24.7519i	−0.193450	+	1.09711i	−0.914609	+	0.404339i	$0.867502\pi$
$510$		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	−0.0145232	−	0.999895i	$-0.504623\pi$
$521$	22.0872	−	18.5334i	0.967659	−	0.811962i	0.982182	+	0.187932i	$0.0601786\pi$
$522$		0			0
$523$	1.23619	−	3.39641i	0.0540548	−	0.148514i	−0.909727	−	0.415208i	$-0.863709\pi$
$523$	1.23619	−	3.39641i	0.0540548	−	0.148514i	0.963781	+	0.266693i	$0.0859311\pi$
$524$			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	−0.697335	−	0.716745i	$-0.745631\pi$
$541$	−9.89184	+	5.71106i	−0.425284	+	0.245538i	0.272052	+	0.962283i	$0.412298\pi$
$542$	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	0.968965	−	0.247197i	$-0.0795094\pi$
$547$	28.9864	+	16.7353i	1.23937	+	0.715550i	0.270404	+	0.962747i	$0.412843\pi$
$548$	−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	−0.962857	−	0.270013i	$-0.912972\pi$
$557$	−12.5025	+	14.8999i	−0.529747	+	0.631328i	0.433109	+	0.901341i	$0.357416\pi$
$558$		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	0.113089	−	0.993585i	$-0.463926\pi$
$563$	−16.3919	−	9.46387i	−0.690837	−	0.398855i	−0.803925	+	0.594730i	$0.797259\pi$
$564$		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	−0.634067	−	0.773278i	$-0.718616\pi$
$569$	−6.71294	+	3.87572i	−0.281421	+	0.162479i	0.352645	+	0.935757i	$0.385282\pi$
$570$		0			0
$571$	−4.66196	+	1.69681i	−0.195097	+	0.0710094i	−0.437721	−	0.899111i	$-0.644214\pi$
$571$	−4.66196	+	1.69681i	−0.195097	+	0.0710094i	0.242624	+	0.970120i	$0.421992\pi$
$572$	−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	0.994430	+	0.105397i	$0.0336114\pi$
$577$	7.21587	+	19.8254i	0.300401	+	0.825344i	−0.694030	+	0.719946i	$0.744166\pi$
$578$	−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	−0.939688	−	0.342034i	$-0.888884\pi$
$587$	0.000238503	0	0.000655281i	9.84406e−6	0	2.70463e-5i	0.939698	+	0.342007i	$0.111107\pi$
$588$		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	0.793332	−	0.608790i	$-0.208345\pi$
$599$	24.7128	+	8.99471i	1.00974	+	0.367514i	0.216405	+	0.976304i	$0.430567\pi$
$600$		0			0
$601$	7.49727	−	42.5191i	0.305820	−	1.73439i	−0.313800	−	0.949489i	$-0.601602\pi$
$601$	7.49727	−	42.5191i	0.305820	−	1.73439i	0.619620	−	0.784902i	$-0.287287\pi$
$602$	−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	0.914229	+	0.405197i	$0.132797\pi$
$607$	11.6866	+	32.1087i	0.474345	+	1.30325i	−0.439885	+	0.898054i	$0.644981\pi$
$608$	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	−0.971499	−	0.237042i	$-0.923822\pi$
$613$	−38.7066	+	14.0880i	−1.56334	+	0.569011i	−0.591844	+	0.806052i	$0.701600\pi$
$614$	−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	0.985084	−	0.172075i	$-0.0550471\pi$
$617$	24.5087	+	20.5652i	0.986681	+	0.827924i	0.00159734	+	0.999999i	$0.499492\pi$
$618$		0			0
$619$	−3.10000	−	5.36936i	−0.124600	−	0.215813i	0.796977	−	0.604010i	$-0.206431\pi$
$619$	−3.10000	−	5.36936i	−0.124600	−	0.215813i	−0.921576	+	0.388197i	$0.873098\pi$
$620$	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	0.0589052	+	0.998264i	$0.481239\pi$
$631$	−23.4724	+	27.9733i	−0.934421	+	1.11360i	−0.993326	+	0.115336i	$0.963205\pi$
$632$	−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	0.892347	−	0.451349i	$-0.149057\pi$
$641$	15.2619	+	12.8063i	0.602810	+	0.505817i	−0.289538	+	0.957167i	$0.593502\pi$
$642$		0			0
$643$	−28.9945	+	16.7400i	−1.14343	+	0.660161i	−0.947278	−	0.320412i	$-0.896179\pi$
$643$	−28.9945	+	16.7400i	−1.14343	+	0.660161i	−0.196155	+	0.980573i	$0.562845\pi$
$644$	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	0.895513	−	0.445036i	$-0.146809\pi$
$647$	7.67494	+	9.14664i	0.301733	+	0.359592i	−0.593779	+	0.804628i	$0.702365\pi$
$648$		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	−0.430863	−	0.902417i	$-0.641791\pi$
$653$	−13.4694	+	2.37501i	−0.527097	+	0.0929414i	−0.0962338	+	0.995359i	$0.530680\pi$
$654$		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	−0.349194	−	0.937051i	$-0.613544\pi$
$659$	−31.2934	−	11.3899i	−1.21902	−	0.443686i	−0.869822	+	0.493365i	$0.835767\pi$
$660$		0			0
$661$	−1.38912	+	3.81658i	−0.0540305	+	0.148448i	−0.963772	−	0.266728i	$-0.914058\pi$
$661$	−1.38912	+	3.81658i	−0.0540305	+	0.148448i	0.909741	+	0.415175i	$0.136280\pi$
$662$	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	0.648602	−	0.761128i	$-0.275354\pi$
$673$	17.0237	+	6.19612i	0.656216	+	0.238843i	0.00761402	+	0.999971i	$0.497576\pi$
$674$	−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	−0.602457	−	0.798151i	$-0.705811\pi$
$677$	10.1473	−	17.5756i	0.389991	−	0.675484i	0.992448	+	0.122667i	$0.0391448\pi$
$678$		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	0.601577	−	0.798814i	$-0.294539\pi$
$683$	23.3553	+	4.11816i	0.893665	+	0.157577i	0.292087	+	0.956392i	$0.405650\pi$
$684$		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	0.590100	−	0.807330i	$-0.299088\pi$
$691$	−2.69427	−	2.26076i	−0.102495	−	0.0860034i	−0.692595	+	0.721327i	$0.743533\pi$
$692$	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	−0.945564	−	0.325436i	$-0.894489\pi$
$701$	−12.2023	+	14.5422i	−0.460876	+	0.549251i	0.484688	+	0.874687i	$0.338933\pi$
$702$		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	$-0.921358\pi$
$709$		−	13.0236i		−	0.489113i	0.969635	−	0.244556i	$-0.0786423\pi$
$710$	−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	−0.742289	−	0.670079i	$-0.766260\pi$
$719$	−23.6018	+	8.59034i	−0.880197	+	0.320366i	−0.137908	+	0.990445i	$0.544038\pi$
$720$		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	−0.515913	−	0.856641i	$-0.672547\pi$
$727$	−19.0823	+	3.36472i	−0.707723	+	0.124791i	−0.191811	+	0.981432i	$0.561436\pi$
$728$	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	0.522523	−	0.852625i	$-0.324991\pi$
$733$	10.1457	+	3.69274i	0.374741	+	0.136395i	−0.147781	+	0.989020i	$0.547213\pi$
$734$		−	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	−0.858534	−	0.512756i	$-0.828625\pi$
$743$	−13.7013	+	11.4967i	−0.502651	+	0.421774i	0.355883	+	0.934530i	$0.384180\pi$
$744$		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	−0.840909	−	0.541176i	$-0.817979\pi$
$751$	1.32138	−	2.28870i	0.0482179	−	0.0835159i	0.889127	+	0.457660i	$0.151312\pi$
$752$	−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	0.944060	−	0.329773i	$-0.106972\pi$
$757$	47.2794	+	8.33663i	1.71840	+	0.303000i	0.774337	+	0.632773i	$0.218083\pi$
$758$	−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	−0.396247	−	0.918144i	$-0.629688\pi$
$761$	−3.02398	+	1.10064i	−0.109619	+	0.0398981i	0.286628	+	0.958042i	$0.407466\pi$
$762$		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	0.780625	−	0.625000i	$-0.214901\pi$
$769$	17.4613	+	10.0813i	0.629671	+	0.363541i	−0.150954	+	0.988541i	$0.548234\pi$
$770$	−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	0.978199	+	0.207670i	$0.0665881\pi$
$773$	3.61493	+	20.5013i	0.130020	+	0.737380i	−0.848179	+	0.529710i	$0.822301\pi$
$774$		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
$781$

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

Introduction

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