LMFDB - Embedded newform 784.2.x.o.373.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			373.1
Character	$\chi$	$=$	784.373
Dual form			784.2.x.o.557.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40462 + 0.164410i) q^{2} +(0.839165 + 0.224854i) q^{3} +(1.94594 - 0.461868i) q^{4} +(3.16320 - 0.847576i) q^{5} +(-1.21568 - 0.177868i) q^{6} +(-2.65738 + 0.968682i) q^{8} +(-1.94444 - 1.12262i) q^{9} +(-4.30375 + 1.71059i) q^{10} +(-0.769121 + 2.87040i) q^{11} +(1.73682 + 0.0499683i) q^{12} +(3.63293 - 3.63293i) q^{13} +2.84503 q^{15} +(3.57336 - 1.79753i) q^{16} +(1.81856 + 3.14984i) q^{17} +(2.91577 + 1.25718i) q^{18} +(0.429496 + 1.60290i) q^{19} +(5.76392 - 3.11031i) q^{20} +(0.608405 - 4.15828i) q^{22} +(5.33698 + 3.08131i) q^{23} +(-2.44779 + 0.215363i) q^{24} +(4.95730 - 2.86210i) q^{25} +(-4.50561 + 5.70019i) q^{26} +(-3.22221 - 3.22221i) q^{27} +(5.10266 - 5.10266i) q^{29} +(-3.99619 + 0.467750i) q^{30} +(1.00761 + 1.74523i) q^{31} +(-4.72369 + 3.11235i) q^{32} +(-1.29084 + 2.23580i) q^{33} +(-3.07226 - 4.12535i) q^{34} +(-4.30226 - 1.28648i) q^{36} +(-5.57162 + 1.49291i) q^{37} +(-0.866812 - 2.18086i) q^{38} +(3.86550 - 2.23175i) q^{39} +(-7.58478 + 5.31646i) q^{40} -3.71244i q^{41} +(-2.91640 - 2.91640i) q^{43} +(-0.170919 + 5.94085i) q^{44} +(-7.10214 - 1.90301i) q^{45} +(-8.00305 - 3.45063i) q^{46} +(5.06565 - 8.77396i) q^{47} +(3.40282 - 0.704944i) q^{48} +(-6.49259 + 4.83520i) q^{50} +(0.817820 + 3.05215i) q^{51} +(5.39152 - 8.74739i) q^{52} +(-0.986836 + 3.68292i) q^{53} +(5.05576 + 3.99624i) q^{54} +9.73153i q^{55} +1.44167i q^{57} +(-6.32839 + 8.00624i) q^{58} +(-0.977963 + 3.64981i) q^{59} +(5.53625 - 1.31403i) q^{60} +(-1.75433 - 6.54724i) q^{61} +(-1.70224 - 2.28573i) q^{62} +(6.12331 - 5.14831i) q^{64} +(8.41248 - 14.5708i) q^{65} +(1.44556 - 3.35269i) q^{66} +(5.88390 + 1.57659i) q^{67} +(4.99362 + 5.28946i) q^{68} +(3.78577 + 3.78577i) q^{69} +9.55168i q^{71} +(6.25456 + 1.09969i) q^{72} +(-0.990000 + 0.571577i) q^{73} +(7.58058 - 3.01301i) q^{74} +(4.80355 - 1.28711i) q^{75} +(1.57610 + 2.92078i) q^{76} +(-5.06266 + 3.77030i) q^{78} +(0.120696 - 0.209052i) q^{79} +(9.77969 - 8.71464i) q^{80} +(1.38842 + 2.40481i) q^{81} +(0.610362 + 5.21459i) q^{82} +(0.459183 - 0.459183i) q^{83} +(8.42219 + 8.42219i) q^{85} +(4.57593 + 3.61696i) q^{86} +(5.42932 - 3.13462i) q^{87} +(-0.736657 - 8.37277i) q^{88} +(3.76823 + 2.17559i) q^{89} +(10.2887 + 1.50536i) q^{90} +(11.8086 + 3.53106i) q^{92} +(0.453128 + 1.69110i) q^{93} +(-5.67281 + 13.1570i) q^{94} +(2.71716 + 4.70626i) q^{95} +(-4.66378 + 1.54964i) q^{96} -6.80176 q^{97} +(4.71788 - 4.71788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27}+ \cdots - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.40462	+	0.164410i	−0.993219	+	0.116255i
$2$	−1.40462	+	0.164410i	−0.993219	+	0.116255i
$3$	0.839165	+	0.224854i	0.484492	+	0.129819i	0.492794	−	0.870146i	$-0.335976\pi$
$3$	0.839165	+	0.224854i	0.484492	+	0.129819i	−0.00830125	+	0.999966i	$0.502642\pi$
$4$	1.94594	−	0.461868i	0.972969	−	0.230934i
$5$	3.16320	−	0.847576i	1.41462	−	0.379048i	0.531051	−	0.847340i	$-0.321797\pi$
$5$	3.16320	−	0.847576i	1.41462	−	0.379048i	0.883574	+	0.468292i	$0.155131\pi$
$6$	−1.21568	−	0.177868i	−0.496299	−	0.0726143i
$7$		0			0
$7$		0			0
$8$	−2.65738	+	0.968682i	−0.939525	+	0.342481i
$9$	−1.94444	−	1.12262i	−0.648146	−	0.374207i
$10$	−4.30375	+	1.71059i	−1.36097	+	0.540935i
$11$	−0.769121	+	2.87040i	−0.231899	+	0.865458i	0.747624	+	0.664123i	$0.231195\pi$
$11$	−0.769121	+	2.87040i	−0.231899	+	0.865458i	−0.979522	+	0.201335i	$0.935472\pi$
$12$	1.73682	+	0.0499683i	0.501376	+	0.0144246i
$13$	3.63293	−	3.63293i	1.00759	−	1.00759i	0.00762179	−	0.999971i	$-0.497574\pi$
$13$	3.63293	−	3.63293i	1.00759	−	1.00759i	0.999971	−	0.00762179i	$-0.00242611\pi$
$14$		0			0
$15$	2.84503			0.734583
$16$	3.57336	−	1.79753i	0.893339	−	0.449383i
$17$	1.81856	+	3.14984i	0.441066	+	0.763948i	0.997769	−	0.0667634i	$-0.0212673\pi$
$17$	1.81856	+	3.14984i	0.441066	+	0.763948i	−0.556703	+	0.830711i	$0.687934\pi$
$18$	2.91577	+	1.25718i	0.687254	+	0.296319i
$19$	0.429496	+	1.60290i	0.0985331	+	0.367730i	0.997531	−	0.0702216i	$-0.0223706\pi$
$19$	0.429496	+	1.60290i	0.0985331	+	0.367730i	−0.898998	+	0.437952i	$0.855704\pi$
$20$	5.76392	−	3.11031i	1.28885	−	0.695486i
$21$		0			0
$22$	0.608405	−	4.15828i	0.129712	−	0.886549i
$23$	5.33698	+	3.08131i	1.11284	+	0.642497i	0.939563	−	0.342377i	$-0.111232\pi$
$23$	5.33698	+	3.08131i	1.11284	+	0.642497i	0.173275	+	0.984874i	$0.444565\pi$
$24$	−2.44779	+	0.215363i	−0.499653	+	0.0439608i
$25$	4.95730	−	2.86210i	0.991461	−	0.572420i
$26$	−4.50561	+	5.70019i	−0.883623	+	1.11790i
$27$	−3.22221	−	3.22221i	−0.620115	−	0.620115i
$28$		0			0
$29$	5.10266	−	5.10266i	0.947539	−	0.947539i	−0.0511514	−	0.998691i	$-0.516289\pi$
$29$	5.10266	−	5.10266i	0.947539	−	0.947539i	0.998691	+	0.0511514i	$0.0162891\pi$
$30$	−3.99619	+	0.467750i	−0.729602	+	0.0853990i
$31$	1.00761	+	1.74523i	0.180972	+	0.313452i	0.942212	−	0.335018i	$-0.108742\pi$
$31$	1.00761	+	1.74523i	0.180972	+	0.313452i	−0.761240	+	0.648470i	$0.775409\pi$
$32$	−4.72369	+	3.11235i	−0.835039	+	0.550191i
$33$	−1.29084	+	2.23580i	−0.224706	+	0.389203i
$34$	−3.07226	−	4.12535i	−0.526888	−	0.707492i
$35$		0			0
$36$	−4.30226	−	1.28648i	−0.717043	−	0.214413i
$37$	−5.57162	+	1.49291i	−0.915969	+	0.245433i	−0.685861	−	0.727732i	$-0.740574\pi$
$37$	−5.57162	+	1.49291i	−0.915969	+	0.245433i	−0.230107	+	0.973165i	$0.573908\pi$
$38$	−0.866812	−	2.18086i	−0.140616	−	0.353782i
$39$	3.86550	−	2.23175i	0.618976	−	0.357366i
$40$	−7.58478	+	5.31646i	−1.19926	+	0.840606i
$41$		−	3.71244i		−	0.579786i	−0.957059	−	0.289893i	$-0.906380\pi$
$41$		−	3.71244i		−	0.579786i	0.957059	−	0.289893i	$-0.0936198\pi$
$42$		0			0
$43$	−2.91640	−	2.91640i	−0.444747	−	0.444747i	0.448857	−	0.893604i	$-0.351831\pi$
$43$	−2.91640	−	2.91640i	−0.444747	−	0.444747i	−0.893604	+	0.448857i	$0.851831\pi$
$44$	−0.170919	+	5.94085i	−0.0257669	+	0.895617i
$45$	−7.10214	−	1.90301i	−1.05872	−	0.283685i
$46$	−8.00305	−	3.45063i	−1.17999	−	0.508767i
$47$	5.06565	−	8.77396i	0.738900	−	1.27981i	−0.214090	−	0.976814i	$-0.568679\pi$
$47$	5.06565	−	8.77396i	0.738900	−	1.27981i	0.952991	−	0.302999i	$-0.0979880\pi$
$48$	3.40282	−	0.704944i	0.491155	−	0.101750i
$49$		0			0
$50$	−6.49259	+	4.83520i	−0.918191	+	0.683801i
$51$	0.817820	+	3.05215i	0.114518	+	0.427386i
$52$	5.39152	−	8.74739i	0.747670	−	1.21304i
$53$	−0.986836	+	3.68292i	−0.135552	+	0.505888i	0.864443	+	0.502731i	$0.167672\pi$
$53$	−0.986836	+	3.68292i	−0.135552	+	0.505888i	−0.999995	+	0.00315690i	$0.998995\pi$
$54$	5.05576	+	3.99624i	0.688002	+	0.543819i
$55$			9.73153i			1.31220i
$56$		0			0
$57$			1.44167i			0.190954i
$58$	−6.32839	+	8.00624i	−0.830958	+	1.05127i
$59$	−0.977963	+	3.64981i	−0.127320	+	0.475164i	−0.999912	−	0.0132857i	$-0.995771\pi$
$59$	−0.977963	+	3.64981i	−0.127320	+	0.475164i	0.872592	+	0.488450i	$0.162438\pi$
$60$	5.53625	−	1.31403i	0.714727	−	0.169640i
$61$	−1.75433	−	6.54724i	−0.224619	−	0.838288i	−0.982557	−	0.185962i	$-0.940460\pi$
$61$	−1.75433	−	6.54724i	−0.224619	−	0.838288i	0.757938	−	0.652326i	$-0.226207\pi$
$62$	−1.70224	−	2.28573i	−0.216185	−	0.290288i
$63$		0			0
$64$	6.12331	−	5.14831i	0.765414	−	0.643538i
$65$	8.41248	−	14.5708i	1.04344	−	1.80729i
$66$	1.44556	−	3.35269i	0.177936	−	0.412687i
$67$	5.88390	+	1.57659i	0.718833	+	0.192611i	0.599651	−	0.800262i	$-0.295306\pi$
$67$	5.88390	+	1.57659i	0.718833	+	0.192611i	0.119182	+	0.992872i	$0.461973\pi$
$68$	4.99362	+	5.28946i	0.605565	+	0.641441i
$69$	3.78577	+	3.78577i	0.455753	+	0.455753i
$70$		0			0
$71$			9.55168i			1.13358i	0.823864	+	0.566788i	$0.191814\pi$
$71$			9.55168i			1.13358i	−0.823864	+	0.566788i	$0.808186\pi$
$72$	6.25456	+	1.09969i	0.737108	+	0.129599i
$73$	−0.990000	+	0.571577i	−0.115871	+	0.0668980i	−0.556815	−	0.830636i	$-0.687977\pi$
$73$	−0.990000	+	0.571577i	−0.115871	+	0.0668980i	0.440945	+	0.897534i	$0.354644\pi$
$74$	7.58058	−	3.01301i	0.881225	−	0.350255i
$75$	4.80355	−	1.28711i	0.554666	−	0.148622i
$76$	1.57610	+	2.92078i	0.180791	+	0.335036i
$77$		0			0
$78$	−5.06266	+	3.77030i	−0.573233	+	0.426902i
$79$	0.120696	−	0.209052i	0.0135794	−	0.0235202i	−0.859156	−	0.511714i	$-0.829011\pi$
$79$	0.120696	−	0.209052i	0.0135794	−	0.0235202i	0.872735	+	0.488194i	$0.162344\pi$
$80$	9.77969	−	8.71464i	1.09340	−	0.974326i
$81$	1.38842	+	2.40481i	0.154269	+	0.267201i
$82$	0.610362	+	5.21459i	0.0674032	+	0.575855i
$83$	0.459183	−	0.459183i	0.0504018	−	0.0504018i	−0.681457	−	0.731858i	$-0.738653\pi$
$83$	0.459183	−	0.459183i	0.0504018	−	0.0504018i	0.731858	+	0.681457i	$0.238653\pi$
$84$		0			0
$85$	8.42219	+	8.42219i	0.913515	+	0.913515i
$86$	4.57593	+	3.61696i	0.493435	+	0.390027i
$87$	5.42932	−	3.13462i	0.582085	−	0.336067i
$88$	−0.736657	−	8.37277i	−0.0785279	−	0.892540i
$89$	3.76823	+	2.17559i	0.399432	+	0.230612i	0.686239	−	0.727376i	$-0.259261\pi$
$89$	3.76823	+	2.17559i	0.399432	+	0.230612i	−0.286807	+	0.957988i	$0.592594\pi$
$90$	10.2887	+	1.50536i	1.08453	+	0.158679i
$91$		0			0
$92$	11.8086	+	3.53106i	1.23113	+	0.368138i
$93$	0.453128	+	1.69110i	0.0469872	+	0.175359i
$94$	−5.67281	+	13.1570i	−0.585105	+	1.35704i
$95$	2.71716	+	4.70626i	0.278775	+	0.482852i
$96$	−4.66378	+	1.54964i	−0.475995	+	0.158159i
$97$	−6.80176			−0.690614			−0.345307	−	0.938490i	$-0.612225\pi$
$97$	−6.80176			−0.690614			−0.345307	+	0.938490i	$0.612225\pi$
$98$		0			0
$99$	4.71788	−	4.71788i	0.474165	−	0.474165i
$100$	8.32470	−	7.85909i	0.832470	−	0.785909i
$101$	0.824407	−	3.07673i	0.0820316	−	0.306146i	−0.912704	−	0.408621i	$-0.866010\pi$
$101$	0.824407	−	3.07673i	0.0820316	−	0.306146i	0.994736	+	0.102475i	$0.0326763\pi$
$102$	−1.65053	−	4.15266i	−0.163427	−	0.411175i
$103$	−3.25557	−	1.87960i	−0.320781	−	0.185203i	0.330960	−	0.943645i	$-0.392628\pi$
$103$	−3.25557	−	1.87960i	−0.320781	−	0.185203i	−0.651741	+	0.758442i	$0.725961\pi$
$104$	−6.13491	+	13.1732i	−0.601577	+	1.29174i
$105$		0			0
$106$	0.780626	−	5.33537i	0.0758211	−	0.518217i
$107$	−0.366346	+	0.0981620i	−0.0354160	+	0.00948968i	−0.276484	−	0.961019i	$-0.589169\pi$
$107$	−0.366346	+	0.0981620i	−0.0354160	+	0.00948968i	0.241068	+	0.970508i	$0.422502\pi$
$108$	−7.75847	−	4.78200i	−0.746559	−	0.460148i
$109$	−9.65655	−	2.58746i	−0.924929	−	0.247834i	−0.235238	−	0.971938i	$-0.575587\pi$
$109$	−9.65655	−	2.58746i	−0.924929	−	0.247834i	−0.689691	+	0.724104i	$0.742254\pi$
$110$	−1.59996	−	13.6691i	−0.152550	−	1.30330i
$111$	−5.01120			−0.475642
$112$		0			0
$113$	2.62015			0.246483			0.123242	−	0.992377i	$-0.460671\pi$
$113$	2.62015			0.246483			0.123242	+	0.992377i	$0.460671\pi$
$114$	−0.237025	−	2.02501i	−0.0221994	−	0.189659i
$115$	19.4936	+	5.22328i	1.81778	+	0.487074i
$116$	7.57271	−	12.2862i	0.703108	−	1.14075i
$117$	−11.1424	+	2.98560i	−1.03012	+	0.276018i
$118$	0.773607	−	5.28739i	0.0712163	−	0.486744i
$119$		0			0
$120$	−7.56031	+	2.75592i	−0.690159	+	0.251580i
$121$	1.87863	+	1.08463i	0.170785	+	0.0986027i
$122$	3.54060	+	8.90799i	0.320551	+	0.806491i
$123$	0.834757	−	3.11535i	0.0752675	−	0.280902i
$124$	2.76680	+	2.93072i	0.248466	+	0.263187i
$125$	1.67697	−	1.67697i	0.149993	−	0.149993i
$126$		0			0
$127$	−12.8840			−1.14327			−0.571635	−	0.820508i	$-0.693691\pi$
$127$	−12.8840			−1.14327			−0.571635	+	0.820508i	$0.693691\pi$
$128$	−7.75452	+	8.23817i	−0.685409	+	0.728158i
$129$	−1.79158	−	3.10311i	−0.157740	−	0.273213i
$130$	−9.42079	+	21.8497i	−0.826258	+	1.91634i
$131$	−2.40496	−	8.97544i	−0.210122	−	0.784188i	−0.987827	−	0.155557i	$-0.950283\pi$
$131$	−2.40496	−	8.97544i	−0.210122	−	0.784188i	0.777704	−	0.628630i	$-0.216384\pi$
$132$	−1.47925	+	4.94693i	−0.128752	+	0.430575i
$133$		0			0
$134$	−8.52388	−	1.24714i	−0.736351	−	0.107737i
$135$	−12.9236	−	7.46143i	−1.11228	−	0.642177i
$136$	−7.88379	−	6.60871i	−0.676030	−	0.566692i
$137$	−10.2211	+	5.90118i	−0.873251	+	0.504172i	−0.868427	−	0.495817i	$-0.834869\pi$
$137$	−10.2211	+	5.90118i	−0.873251	+	0.504172i	−0.00482362	+	0.999988i	$0.501535\pi$
$138$	−5.94000	−	4.69516i	−0.505646	−	0.399679i
$139$	−8.15708	−	8.15708i	−0.691874	−	0.691874i	0.270770	−	0.962644i	$-0.412722\pi$
$139$	−8.15708	−	8.15708i	−0.691874	−	0.691874i	−0.962644	+	0.270770i	$0.912722\pi$
$140$		0			0
$141$	6.22377	−	6.22377i	0.524136	−	0.524136i
$142$	−1.57039	−	13.4165i	−0.131784	−	1.12589i
$143$	7.63379	+	13.2221i	0.638370	+	1.10569i
$144$	−8.96611	−	0.516338i	−0.747176	−	0.0430282i
$145$	11.8158	−	20.4656i	0.981250	−	1.69958i
$146$	1.29660	−	0.965616i	0.107308	−	0.0799149i
$147$		0			0
$148$	−10.1525	+	5.47846i	−0.834531	+	0.450327i
$149$	11.3488	−	3.04089i	0.929727	−	0.249119i	0.237989	−	0.971268i	$-0.423512\pi$
$149$	11.3488	−	3.04089i	0.929727	−	0.249119i	0.691738	+	0.722148i	$0.256845\pi$
$150$	−6.53557	+	2.59765i	−0.533627	+	0.212097i
$151$	−16.9805	+	9.80371i	−1.38186	+	0.797815i	−0.992379	−	0.123222i	$-0.960677\pi$
$151$	−16.9805	+	9.80371i	−1.38186	+	0.797815i	−0.389476	+	0.921036i	$0.627344\pi$
$152$	−2.69403	−	3.84347i	−0.218515	−	0.311746i
$153$		−	8.16622i		−	0.660199i
$154$		0			0
$155$	4.66647	+	4.66647i	0.374820	+	0.374820i
$156$	6.49126	−	6.12820i	0.519717	−	0.490649i
$157$	−5.22347	−	1.39962i	−0.416878	−	0.111702i	0.0442821	−	0.999019i	$-0.485900\pi$
$157$	−5.22347	−	1.39962i	−0.416878	−	0.111702i	−0.461160	+	0.887317i	$0.652567\pi$
$158$	−0.135163	+	0.313484i	−0.0107530	+	0.0249394i
$159$	−1.65624	+	2.86869i	−0.131348	+	0.227502i
$160$	−12.3040	+	13.8487i	−0.972718	+	1.09483i
$161$		0			0
$162$	−2.34558	−	3.14959i	−0.184286	−	0.247455i
$163$	2.91941	+	10.8954i	0.228666	+	0.853394i	0.980902	+	0.194500i	$0.0623085\pi$
$163$	2.91941	+	10.8954i	0.228666	+	0.853394i	−0.752236	+	0.658893i	$0.771025\pi$
$164$	−1.71466	−	7.22419i	−0.133892	−	0.564114i
$165$	−2.18817	+	8.16636i	−0.170349	+	0.635750i
$166$	−0.569485	+	0.720473i	−0.0442006	+	0.0559195i
$167$			21.8111i			1.68779i	0.536508	+	0.843895i	$0.319743\pi$
$167$			21.8111i			1.68779i	−0.536508	+	0.843895i	$0.680257\pi$
$168$		0			0
$169$		−	13.3963i		−	1.03049i
$170$	−13.2147	−	10.4453i	−1.01352	−	0.801120i
$171$	0.964322	−	3.59890i	0.0737435	−	0.275215i
$172$	−7.02213	−	4.32815i	−0.535432	−	0.330018i
$173$	5.87840	+	21.9385i	0.446927	+	1.66795i	0.710799	+	0.703396i	$0.248334\pi$
$173$	5.87840	+	21.9385i	0.446927	+	1.66795i	−0.263872	+	0.964558i	$0.585000\pi$
$174$	−7.11080	+	5.29560i	−0.539068	+	0.401458i
$175$		0			0
$176$	2.41129	+	11.6395i	0.181758	+	0.877359i
$177$	−1.64135	+	2.84289i	−0.123371	+	0.213685i
$178$	−5.65064	−	2.43635i	−0.423533	−	0.182612i
$179$	20.7936	+	5.57162i	1.55418	+	0.416443i	0.930817	−	0.365486i	$-0.119097\pi$
$179$	20.7936	+	5.57162i	1.55418	+	0.416443i	0.623368	+	0.781929i	$0.285764\pi$
$180$	−14.6993	−	0.422899i	−1.09562	−	0.0315210i
$181$	11.8484	+	11.8484i	0.880684	+	0.880684i	0.993604	−	0.112920i	$-0.0360205\pi$
$181$	11.8484	+	11.8484i	0.880684	+	0.880684i	−0.112920	+	0.993604i	$0.536020\pi$
$182$		0			0
$183$		−	5.88869i		−	0.435304i
$184$	−17.1672	−	3.01836i	−1.26558	−	0.222517i
$185$	−16.3588	+	9.44474i	−1.20272	+	0.694391i
$186$	−0.914508	−	2.30086i	−0.0670550	−	0.168707i
$187$	−10.4400	+	2.79739i	−0.763448	+	0.204565i
$188$	5.80503	−	19.4132i	0.423375	−	1.41586i
$189$		0			0
$190$	−4.59034	−	6.16380i	−0.333018	−	0.447169i
$191$	−3.94400	+	6.83120i	−0.285377	+	0.494288i	−0.972701	−	0.232063i	$-0.925452\pi$
$191$	−3.94400	+	6.83120i	−0.285377	+	0.494288i	0.687323	+	0.726352i	$0.258786\pi$
$192$	6.29609	−	2.94343i	0.454381	−	0.212424i
$193$	−12.4404	−	21.5474i	−0.895478	−	1.55101i	−0.833212	−	0.552954i	$-0.813500\pi$
$193$	−12.4404	−	21.5474i	−0.895478	−	1.55101i	−0.0622664	−	0.998060i	$-0.519833\pi$
$194$	9.55392	−	1.11828i	0.685931	−	0.0802875i
$195$	10.3358	−	10.3358i	0.740160	−	0.740160i
$196$		0			0
$197$	−7.75408	−	7.75408i	−0.552455	−	0.552455i	0.374694	−	0.927149i	$-0.377748\pi$
$197$	−7.75408	−	7.75408i	−0.552455	−	0.552455i	−0.927149	+	0.374694i	$0.877748\pi$
$198$	−5.85118	+	7.40251i	−0.415825	+	0.526074i
$199$	9.91354	−	5.72359i	0.702753	−	0.405734i	−0.105619	−	0.994407i	$-0.533682\pi$
$199$	9.91354	−	5.72359i	0.702753	−	0.405734i	0.808372	+	0.588672i	$0.200349\pi$
$200$	−10.4010	+	12.4077i	−0.735459	+	0.877359i
$201$	4.58307	+	2.64603i	0.323264	+	0.186637i
$202$	−0.652139	+	4.45719i	−0.0458843	+	0.313607i
$203$		0			0
$204$	3.00112	+	5.56157i	0.210120	+	0.389387i
$205$	−3.14658	−	11.7432i	−0.219767	−	0.820180i
$206$	4.88188	+	2.10489i	0.340137	+	0.146655i
$207$	−6.91828	−	11.9828i	−0.480854	−	0.832863i
$208$	6.45144	−	19.5120i	0.447327	−	1.35292i
$209$	−4.93130			−0.341105
$210$		0			0
$211$	−8.69524	+	8.69524i	−0.598605	+	0.598605i	−0.939941	−	0.341336i	$-0.889120\pi$
$211$	−8.69524	+	8.69524i	−0.598605	+	0.598605i	0.341336	+	0.939941i	$0.389120\pi$
$212$	−0.219300	+	7.62253i	−0.0150616	+	0.523518i
$213$	−2.14773	+	8.01544i	−0.147160	+	0.549209i
$214$	0.498439	−	0.198112i	0.0340726	−	0.0135426i
$215$	−11.6970	−	6.75328i	−0.797730	−	0.460570i
$216$	11.6839	+	5.44134i	0.794991	+	0.370236i
$217$		0			0
$218$	13.9892	+	2.04679i	0.947470	+	0.138626i
$219$	−0.959295	+	0.257042i	−0.0648231	+	0.0173693i
$220$	4.49468	+	18.9370i	0.303031	+	1.27673i
$221$	18.0498	+	4.83644i	1.21416	+	0.325334i
$222$	7.03885	−	0.823889i	0.472417	−	0.0552958i
$223$	−21.9483			−1.46976			−0.734882	−	0.678195i	$-0.762762\pi$
$223$	−21.9483			−1.46976			−0.734882	+	0.678195i	$0.762762\pi$
$224$		0			0
$225$	−12.8522			−0.856814
$226$	−3.68033	+	0.430779i	−0.244812	+	0.0286550i
$227$	−23.8284	−	6.38481i	−1.58155	−	0.423774i	−0.642143	−	0.766585i	$-0.721955\pi$
$227$	−23.8284	−	6.38481i	−1.58155	−	0.423774i	−0.939405	+	0.342810i	$0.888621\pi$
$228$	0.665862	+	2.80541i	0.0440978	+	0.185793i
$229$	−9.19018	+	2.46250i	−0.607304	+	0.162727i	−0.549350	−	0.835592i	$-0.685125\pi$
$229$	−9.19018	+	2.46250i	−0.607304	+	0.162727i	−0.0579547	+	0.998319i	$0.518458\pi$
$230$	−28.2399	−	4.13182i	−1.86208	−	0.272444i
$231$		0			0
$232$	−8.61684	+	18.5025i	−0.565723	+	1.21475i
$233$	−19.2584	−	11.1188i	−1.26166	−	0.728418i	−0.288262	−	0.957552i	$-0.593077\pi$
$233$	−19.2584	−	11.1188i	−1.26166	−	0.728418i	−0.973395	+	0.229133i	$0.926411\pi$
$234$	15.1600	−	6.02556i	0.991042	−	0.393903i
$235$	8.58704	−	32.0473i	0.560157	−	2.09053i
$236$	−0.217329	+	7.55399i	−0.0141469	+	0.491723i
$237$	0.148290	−	0.148290i	0.00963250	−	0.00963250i
$238$		0			0
$239$	14.9579			0.967548			0.483774	−	0.875193i	$-0.339266\pi$
$239$	14.9579			0.967548			0.483774	+	0.875193i	$0.339266\pi$
$240$	10.1663	−	5.11403i	0.656231	−	0.330109i
$241$	−12.1750	−	21.0877i	−0.784262	−	1.35838i	−0.929439	−	0.368975i	$-0.879709\pi$
$241$	−12.1750	−	21.0877i	−0.784262	−	1.35838i	0.145178	−	0.989406i	$-0.453625\pi$
$242$	−2.81710	−	1.21463i	−0.181090	−	0.0780795i
$243$	4.16262	+	15.5351i	0.267032	+	0.996577i
$244$	−6.43777	−	11.9303i	−0.412136	−	0.763757i
$245$		0			0
$246$	−0.660325	+	4.51315i	−0.0421008	+	0.287748i
$247$	7.38355	+	4.26289i	0.469804	+	0.271241i
$248$	−4.36816	−	3.66168i	−0.277378	−	0.232517i
$249$	0.488579	−	0.282081i	0.0309624	−	0.0178762i
$250$	−2.07981	+	2.63123i	−0.131539	+	0.166414i
$251$	3.50509	+	3.50509i	0.221239	+	0.221239i	0.809020	−	0.587781i	$-0.199998\pi$
$251$	3.50509	+	3.50509i	0.221239	+	0.221239i	−0.587781	+	0.809020i	$0.699998\pi$
$252$		0			0
$253$	−12.9494	+	12.9494i	−0.814120	+	0.814120i
$254$	18.0972	−	2.11825i	1.13552	−	0.132911i
$255$	5.17385	+	8.96137i	0.323999	+	0.561183i
$256$	9.53776	−	12.8464i	0.596110	−	0.802903i
$257$	3.24853	−	5.62661i	0.202638	−	0.350978i	−0.746740	−	0.665116i	$-0.768382\pi$
$257$	3.24853	−	5.62661i	0.202638	−	0.350978i	0.949377	+	0.314138i	$0.101715\pi$
$258$	3.02668	+	4.06415i	0.188433	+	0.253023i
$259$		0			0
$260$	9.64038	−	32.2394i	0.597871	−	1.99940i
$261$	−15.6501	+	4.19344i	−0.968719	+	0.259568i
$262$	4.85372	+	12.2117i	0.299864	+	0.754442i
$263$	−21.4222	+	12.3681i	−1.32095	+	0.762650i	−0.983880	−	0.178829i	$-0.942769\pi$
$263$	−21.4222	+	12.3681i	−1.32095	+	0.762650i	−0.337069	+	0.941480i	$0.609436\pi$
$264$	1.26447	−	7.19178i	0.0778228	−	0.442623i
$265$			12.4862i			0.767023i
$266$		0			0
$267$	2.67298	+	2.67298i	0.163584	+	0.163584i
$268$	12.1779	+	0.350358i	0.743883	+	0.0214015i
$269$	−1.44745	−	0.387844i	−0.0882528	−	0.0236473i	0.214422	−	0.976741i	$-0.431213\pi$
$269$	−1.44745	−	0.387844i	−0.0882528	−	0.0236473i	−0.302675	+	0.953094i	$0.597880\pi$
$270$	19.3795	+	8.35574i	1.17940	+	0.508514i
$271$	−3.68123	+	6.37608i	−0.223619	+	0.387320i	−0.955904	−	0.293679i	$-0.905120\pi$
$271$	−3.68123	+	6.37608i	−0.223619	+	0.387320i	0.732285	+	0.680998i	$0.238454\pi$
$272$	12.1603	+	7.98658i	0.737327	+	0.484257i
$273$		0			0
$274$	13.3866	−	9.96939i	0.808717	−	0.602273i
$275$	4.40260	+	16.4307i	0.265487	+	0.990811i
$276$	9.11539	+	5.61835i	0.548682	+	0.338185i
$277$	−1.17214	+	4.37447i	−0.0704268	+	0.262836i	−0.992157	−	0.124994i	$-0.960109\pi$
$277$	−1.17214	+	4.37447i	−0.0704268	+	0.262836i	0.921731	+	0.387831i	$0.126775\pi$
$278$	12.7987	+	10.1165i	0.767617	+	0.606749i
$279$		−	4.52464i		−	0.270883i
$280$		0			0
$281$			9.72875i			0.580369i	0.956971	+	0.290184i	$0.0937166\pi$
$281$			9.72875i			0.580369i	−0.956971	+	0.290184i	$0.906283\pi$
$282$	−7.71881	+	9.76531i	−0.459649	+	0.581516i
$283$	−1.04114	+	3.88559i	−0.0618893	+	0.230974i	−0.989942	−	0.141475i	$-0.954815\pi$
$283$	−1.04114	+	3.88559i	−0.0618893	+	0.230974i	0.928052	+	0.372450i	$0.121482\pi$
$284$	4.41161	+	18.5870i	0.261781	+	1.10293i
$285$	1.22193	+	4.56029i	0.0723807	+	0.270128i
$286$	−12.8965	−	17.3170i	−0.762583	−	1.02398i
$287$		0			0
$288$	12.6789	−	0.748855i	0.747112	−	0.0441267i
$289$	1.88568	−	3.26609i	0.110922	−	0.192123i
$290$	−13.2320	+	30.6891i	−0.777012	+	1.80213i
$291$	−5.70780	−	1.52940i	−0.334597	−	0.0896551i
$292$	−1.66249	+	1.56950i	−0.0972896	+	0.0918481i
$293$	−1.88131	−	1.88131i	−0.109908	−	0.109908i	0.650014	−	0.759922i	$-0.274763\pi$
$293$	−1.88131	−	1.88131i	−0.109908	−	0.109908i	−0.759922	+	0.650014i	$0.774763\pi$
$294$		0			0
$295$			12.3740i			0.720440i
$296$	13.3597	−	9.36435i	0.776519	−	0.544292i
$297$	11.7273	−	6.77077i	0.680488	−	0.392880i
$298$	−15.4408	+	6.13715i	−0.894461	+	0.355516i
$299$	30.5830	−	8.19470i	1.76866	−	0.473912i
$300$	8.75295	−	4.72324i	0.505352	−	0.272696i
$301$		0			0
$302$	22.2394	−	16.5623i	1.27974	−	0.953053i
$303$	1.38363	−	2.39651i	0.0794874	−	0.137676i
$304$	4.41601	+	4.95570i	0.253275	+	0.284229i
$305$	−11.0986	−	19.2233i	−0.635502	−	1.10072i
$306$	1.34260	+	11.4705i	0.0767516	+	0.655723i
$307$	−3.98977	+	3.98977i	−0.227708	+	0.227708i	−0.811735	−	0.584026i	$-0.801476\pi$
$307$	−3.98977	+	3.98977i	−0.227708	+	0.227708i	0.584026	+	0.811735i	$0.301476\pi$
$308$		0			0
$309$	−2.30933	−	2.30933i	−0.131373	−	0.131373i
$310$	−7.32185	−	5.78743i	−0.415853	−	0.328704i
$311$	0.699829	−	0.404047i	0.0396837	−	0.0229114i	−0.480027	−	0.877254i	$-0.659373\pi$
$311$	0.699829	−	0.404047i	0.0396837	−	0.0229114i	0.519711	+	0.854342i	$0.326040\pi$
$312$	−8.11025	+	9.67505i	−0.459152	+	0.547742i
$313$	−20.1745	−	11.6478i	−1.14033	−	0.658371i	−0.193819	−	0.981037i	$-0.562087\pi$
$313$	−20.1745	−	11.6478i	−1.14033	−	0.658371i	−0.946513	+	0.322666i	$0.895421\pi$
$314$	7.56712	+	1.10716i	0.427037	+	0.0624805i
$315$		0			0
$316$	0.138313	−	0.462549i	0.00778073	−	0.0260204i
$317$	−0.808194	−	3.01622i	−0.0453927	−	0.169408i	0.939508	−	0.342526i	$-0.111282\pi$
$317$	−0.808194	−	3.01622i	−0.0453927	−	0.169408i	−0.984901	+	0.173118i	$0.944616\pi$
$318$	1.85475	−	4.30173i	0.104009	−	0.241229i
$319$	10.7221	+	18.5712i	0.600322	+	1.03979i
$320$	15.0057	−	21.4751i	0.838842	−	1.20049i
$321$	−0.329497			−0.0183907
$322$		0			0
$323$	−4.26781	+	4.26781i	−0.237467	+	0.237467i
$324$	3.81248	+	4.03835i	0.211805	+	0.224353i
$325$	7.61172	−	28.4073i	0.422222	−	1.57575i
$326$	−5.89199	−	14.8240i	−0.326327	−	0.821023i
$327$	−7.52164	−	4.34262i	−0.415948	−	0.240147i
$328$	3.59618	+	9.86537i	0.198566	+	0.544724i
$329$		0			0
$330$	1.73093	−	11.8304i	0.0952845	−	0.651244i
$331$	15.2162	−	4.07718i	0.836360	−	0.224102i	0.184874	−	0.982762i	$-0.440812\pi$
$331$	15.2162	−	4.07718i	0.836360	−	0.224102i	0.651486	+	0.758660i	$0.274146\pi$
$332$	0.681460	−	1.10562i	0.0374000	−	0.0606789i
$333$	12.5096	+	3.35195i	0.685524	+	0.183686i
$334$	−3.58595	−	30.6363i	−0.196214	−	1.67635i
$335$	19.9482			1.08989
$336$		0			0
$337$	−5.36065			−0.292013			−0.146007	−	0.989284i	$-0.546642\pi$
$337$	−5.36065			−0.292013			−0.146007	+	0.989284i	$0.546642\pi$
$338$	2.20248	+	18.8168i	0.119799	+	1.02350i
$339$	2.19874	+	0.589151i	0.119419	+	0.0319983i
$340$	20.2790	+	12.4991i	1.09978	+	0.677861i
$341$	−5.78447	+	1.54994i	−0.313247	+	0.0839341i
$342$	−0.762816	+	5.21364i	−0.0412484	+	0.281922i
$343$		0			0
$344$	10.5750	+	4.92491i	0.570168	+	0.265534i
$345$	15.1838	+	8.76640i	0.817471	+	0.471967i
$346$	−11.8639	−	29.8489i	−0.637805	−	1.60469i
$347$	−4.29752	+	16.0386i	−0.230703	+	0.860995i	0.749336	+	0.662190i	$0.230373\pi$
$347$	−4.29752	+	16.0386i	−0.230703	+	0.860995i	−0.980039	+	0.198805i	$0.936294\pi$
$348$	9.11735	−	8.60741i	0.488741	−	0.461406i
$349$	22.2799	−	22.2799i	1.19262	−	1.19262i	0.216286	−	0.976330i	$-0.430606\pi$
$349$	22.2799	−	22.2799i	1.19262	−	1.19262i	0.976330	−	0.216286i	$-0.0693943\pi$
$350$		0			0
$351$	−23.4121			−1.24965
$352$	−5.30060	−	15.9527i	−0.282523	−	0.850280i
$353$	6.84373	+	11.8537i	0.364255	+	0.630908i	0.988656	−	0.150196i	$-0.0479904\pi$
$353$	6.84373	+	11.8537i	0.364255	+	0.630908i	−0.624401	+	0.781104i	$0.714657\pi$
$354$	1.83807	−	4.26305i	0.0976926	−	0.226579i
$355$	8.09577	+	30.2138i	0.429679	+	1.60358i
$356$	8.33758	+	2.49314i	0.441891	+	0.132136i
$357$		0			0
$358$	−30.1232	−	4.40737i	−1.59206	−	0.232937i
$359$	−5.47529	−	3.16116i	−0.288974	−	0.166840i	0.348505	−	0.937307i	$-0.386690\pi$
$359$	−5.47529	−	3.16116i	−0.288974	−	0.166840i	−0.637479	+	0.770467i	$0.720023\pi$
$360$	20.7165	−	1.82269i	1.09185	−	0.0960642i
$361$	14.0697	−	8.12312i	0.740508	−	0.427533i
$362$	−18.5905	−	14.6945i	−0.977096	−	0.772328i
$363$	1.33260	+	1.33260i	0.0699434	+	0.0699434i
$364$		0			0
$365$	−2.64711	+	2.64711i	−0.138556	+	0.138556i
$366$	0.968157	+	8.27139i	0.0506064	+	0.432353i
$367$	−18.6164	−	32.2445i	−0.971768	−	1.68315i	−0.690213	−	0.723606i	$-0.742483\pi$
$367$	−18.6164	−	32.2445i	−0.971768	−	1.68315i	−0.281555	−	0.959545i	$-0.590850\pi$
$368$	24.6097	+	1.41722i	1.28287	+	0.0738775i
$369$	−4.16767	+	7.21861i	−0.216960	+	0.375786i
$370$	21.4251	−	15.9559i	1.11384	−	0.829505i
$371$		0			0
$372$	1.66282	+	3.08149i	0.0862134	+	0.159768i
$373$	−4.17538	+	1.11879i	−0.216193	+	0.0579287i	−0.365290	−	0.930894i	$-0.619030\pi$
$373$	−4.17538	+	1.11879i	−0.216193	+	0.0579287i	0.149097	+	0.988823i	$0.452363\pi$
$374$	14.2043	−	5.64571i	0.734489	−	0.291933i
$375$	1.78433	−	1.03019i	0.0921426	−	0.0531985i
$376$	−4.96217	+	28.2227i	−0.255904	+	1.45548i
$377$		−	37.0752i		−	1.90947i
$378$		0			0
$379$	−11.5118	−	11.5118i	−0.591323	−	0.591323i	0.346666	−	0.937989i	$-0.387314\pi$
$379$	−11.5118	−	11.5118i	−0.591323	−	0.591323i	−0.937989	+	0.346666i	$0.887314\pi$
$380$	7.46109	+	7.90312i	0.382746	+	0.405422i
$381$	−10.8118	−	2.89701i	−0.553906	−	0.148419i
$382$	4.41672	−	10.2437i	0.225979	−	0.524113i
$383$	−9.86334	+	17.0838i	−0.503993	+	0.872942i	0.495996	+	0.868325i	$0.334803\pi$
$383$	−9.86334	+	17.0838i	−0.503993	+	0.872942i	−0.999989	+	0.00461719i	$0.998530\pi$
$384$	−8.35971	+	5.16955i	−0.426605	+	0.263808i
$385$		0			0
$386$	21.0167	+	28.2206i	1.06972	+	1.43639i
$387$	2.39674	+	8.94477i	0.121833	+	0.454688i
$388$	−13.2358	+	3.14151i	−0.671947	+	0.159486i
$389$	−1.53689	+	5.73576i	−0.0779236	+	0.290815i	−0.993880	−	0.110462i	$-0.964767\pi$
$389$	−1.53689	+	5.73576i	−0.0779236	+	0.290815i	0.915957	+	0.401277i	$0.131434\pi$
$390$	−12.8186	+	16.2172i	−0.649094	+	0.821189i
$391$			22.4142i			1.13353i
$392$		0			0
$393$		−	8.07264i		−	0.407211i
$394$	12.1664	+	9.61672i	0.612935	+	0.484483i
$395$	0.204599	−	0.763573i	0.0102945	−	0.0384195i
$396$	7.00167	−	11.3597i	0.351847	−	0.570848i
$397$	6.61855	+	24.7008i	0.332175	+	1.23970i	0.906899	+	0.421348i	$0.138443\pi$
$397$	6.61855	+	24.7008i	0.332175	+	1.23970i	−0.574724	+	0.818348i	$0.694890\pi$
$398$	−12.9838	+	9.66937i	−0.650819	+	0.484682i
$399$		0			0
$400$	12.5695	−	19.1382i	0.628475	−	0.956911i
$401$	−1.80147	+	3.12023i	−0.0899610	+	0.155817i	−0.907494	−	0.420064i	$-0.862008\pi$
$401$	−1.80147	+	3.12023i	−0.0899610	+	0.155817i	0.817533	+	0.575881i	$0.195341\pi$
$402$	−6.87252	−	2.96318i	−0.342770	−	0.147790i
$403$	10.0008	+	2.67972i	0.498177	+	0.133486i
$404$	0.183205	−	6.36790i	0.00911476	−	0.316815i
$405$	6.43010	+	6.43010i	0.319514	+	0.319514i
$406$		0			0
$407$		−	17.1410i		−	0.849648i
$408$	−5.12981	−	7.31850i	−0.253964	−	0.362320i
$409$	13.2778	−	7.66595i	0.656546	−	0.379057i	−0.134414	−	0.990925i	$-0.542915\pi$
$409$	13.2778	−	7.66595i	0.656546	−	0.379057i	0.790959	+	0.611869i	$0.209582\pi$
$410$	6.35046	+	15.9774i	0.313627	+	0.789070i
$411$	−9.90413	+	2.65380i	−0.488535	+	0.130902i
$412$	−7.20327	−	2.15395i	−0.354880	−	0.106118i
$413$		0			0
$414$	11.6877	+	15.6939i	0.574418	+	0.771314i
$415$	1.06329	−	1.84168i	0.0521950	−	0.0904044i
$416$	−5.85388	+	28.4678i	−0.287010	+	1.39575i
$417$	−5.01099	−	8.67929i	−0.245389	−	0.425027i
$418$	6.92662	−	0.810753i	0.338792	−	0.0396552i
$419$	17.2949	−	17.2949i	0.844910	−	0.844910i	−0.144583	−	0.989493i	$-0.546184\pi$
$419$	17.2949	−	17.2949i	0.844910	−	0.844910i	0.989493	+	0.144583i	$0.0461841\pi$
$420$		0			0
$421$	18.2430	+	18.2430i	0.889111	+	0.889111i	0.994438	−	0.105327i	$-0.0335888\pi$
$421$	18.2430	+	18.2430i	0.889111	+	0.889111i	−0.105327	+	0.994438i	$0.533589\pi$
$422$	10.7840	−	13.6431i	0.524955	−	0.664137i
$423$	−19.6997	+	11.3736i	−0.957830	+	0.553003i
$424$	−0.945183	−	10.7428i	−0.0459021	−	0.521719i
$425$	18.0303	+	10.4098i	0.874598	+	0.504950i
$426$	1.69894	−	11.6118i	0.0823138	−	0.562593i
$427$		0			0
$428$	−0.667549	+	0.360221i	−0.0322672	+	0.0174119i
$429$	3.43297	+	12.8120i	0.165745	+	0.618571i
$430$	17.5402	+	7.56271i	0.845865	+	0.364707i
$431$	−16.8098	−	29.1154i	−0.809698	−	1.40244i	−0.913073	−	0.407796i	$-0.866297\pi$
$431$	−16.8098	−	29.1154i	−0.809698	−	1.40244i	0.103375	−	0.994642i	$-0.467036\pi$
$432$	−17.3062	−	5.72209i	−0.832643	−	0.275304i
$433$	−26.5511			−1.27596			−0.637982	−	0.770051i	$-0.720231\pi$
$433$	−26.5511			−1.27596			−0.637982	+	0.770051i	$0.720231\pi$
$434$		0			0
$435$	14.5172	−	14.5172i	0.696046	−	0.696046i
$436$	−19.9861	−	0.575001i	−0.957161	−	0.0275375i
$437$	−2.64682	+	9.87805i	−0.126614	+	0.472531i
$438$	1.30519	−	0.518765i	0.0623643	−	0.0247876i
$439$	−16.9833	−	9.80529i	−0.810567	−	0.467981i	0.0365859	−	0.999331i	$-0.488352\pi$
$439$	−16.9833	−	9.80529i	−0.810567	−	0.467981i	−0.847153	+	0.531350i	$0.821685\pi$
$440$	−9.42675	−	25.8603i	−0.449403	−	1.23284i
$441$		0			0
$442$	−26.1484	−	3.82581i	−1.24375	−	0.181975i
$443$	−6.58948	+	1.76565i	−0.313076	+	0.0838883i	−0.411935	−	0.911213i	$-0.635147\pi$
$443$	−6.58948	+	1.76565i	−0.313076	+	0.0838883i	0.0988599	+	0.995101i	$0.468480\pi$
$444$	−9.75148	+	2.31451i	−0.462785	+	0.109842i
$445$	13.7636	+	3.68795i	0.652459	+	0.174826i
$446$	30.8291	−	3.60850i	1.45980	−	0.170868i
$447$	10.2072			0.482786
$448$		0			0
$449$	6.32412			0.298454			0.149227	−	0.988803i	$-0.452322\pi$
$449$	6.32412			0.298454			0.149227	+	0.988803i	$0.452322\pi$
$450$	18.0525	−	2.11303i	0.851005	−	0.0996091i
$451$	10.6562	+	2.85532i	0.501781	+	0.134452i
$452$	5.09866	−	1.21016i	0.239821	−	0.0569213i
$453$	−16.4539	+	4.40880i	−0.773070	+	0.207144i
$454$	34.5197	+	5.05063i	1.62009	+	0.237038i
$455$		0			0
$456$	−1.39652	−	3.83107i	−0.0653981	−	0.179406i
$457$	34.2066	+	19.7492i	1.60012	+	0.923829i	0.991462	+	0.130396i	$0.0416248\pi$
$457$	34.2066	+	19.7492i	1.60012	+	0.923829i	0.608657	+	0.793433i	$0.291709\pi$
$458$	12.5039	−	4.96985i	0.584269	−	0.232226i
$459$	4.28966	−	16.0092i	0.200224	−	0.747248i
$460$	40.3457	+	1.16075i	1.88113	+	0.0541202i
$461$	1.26773	−	1.26773i	0.0590440	−	0.0590440i	−0.676968	−	0.736012i	$-0.736707\pi$
$461$	1.26773	−	1.26773i	0.0590440	−	0.0590440i	0.736012	+	0.676968i	$0.236707\pi$
$462$		0			0
$463$	−14.4427			−0.671208			−0.335604	−	0.942003i	$-0.608940\pi$
$463$	−14.4427			−0.671208			−0.335604	+	0.942003i	$0.608940\pi$
$464$	9.06142	−	27.4058i	0.420666	−	1.27228i
$465$	2.86667	+	4.96521i	0.132939	+	0.230256i
$466$	28.8788	+	12.4515i	1.33778	+	0.576805i
$467$	4.49607	+	16.7796i	0.208053	+	0.776465i	0.988497	+	0.151240i	$0.0483265\pi$
$467$	4.49607	+	16.7796i	0.208053	+	0.776465i	−0.780444	+	0.625226i	$0.785007\pi$
$468$	−20.3035	+	10.9561i	−0.938528	+	0.506446i
$469$		0			0
$470$	−6.79269	+	46.4262i	−0.313323	+	2.14148i
$471$	−4.06864	−	2.34903i	−0.187473	−	0.108238i
$472$	−0.936684	−	10.6463i	−0.0431144	−	0.490033i
$473$	10.6143	−	6.12817i	0.488046	−	0.281773i
$474$	−0.183912	+	0.232673i	−0.00844736	+	0.0106870i
$475$	6.71680	+	6.71680i	0.308188	+	0.308188i
$476$		0			0
$477$	6.05337	−	6.05337i	0.277165	−	0.277165i
$478$	−21.0103	+	2.45923i	−0.960988	+	0.112483i
$479$	−2.39344	−	4.14556i	−0.109359	−	0.189416i	0.806152	−	0.591709i	$-0.201547\pi$
$479$	−2.39344	−	4.14556i	−0.109359	−	0.189416i	−0.915511	+	0.402293i	$0.868213\pi$
$480$	−13.4390	+	8.85472i	−0.613405	+	0.404161i
$481$	−14.8177	+	25.6649i	−0.675627	+	1.17022i
$482$	20.5684	+	27.6187i	0.936863	+	1.25800i
$483$		0			0
$484$	4.15666	+	1.24294i	0.188939	+	0.0564974i
$485$	−21.5153	+	5.76501i	−0.976960	+	0.261776i
$486$	−8.40104	−	21.1366i	−0.381079	−	0.958776i
$487$	23.2700	−	13.4349i	1.05446	−	0.608795i	0.130568	−	0.991439i	$-0.458320\pi$
$487$	23.2700	−	13.4349i	1.05446	−	0.608795i	0.923896	+	0.382644i	$0.124987\pi$
$488$	11.0041	+	15.6991i	0.498132	+	0.710665i
$489$			9.79948i			0.443148i
$490$		0			0
$491$	−11.7576	−	11.7576i	−0.530611	−	0.530611i	0.390143	−	0.920754i	$-0.372426\pi$
$491$	−11.7576	−	11.7576i	−0.530611	−	0.530611i	−0.920754	+	0.390143i	$0.872426\pi$
$492$	0.185504	−	6.44784i	0.00836319	−	0.290691i
$493$	25.3520	+	6.79306i	1.14180	+	0.305944i
$494$	−11.0720	−	4.77384i	−0.498151	−	0.214785i
$495$	10.9248	−	18.9223i	0.491034	−	0.850496i
$496$	6.73764	+	4.42511i	0.302529	+	0.198693i
$497$		0			0
$498$	−0.639893	+	0.476545i	−0.0286743	+	0.0213545i
$499$	−5.10099	−	19.0371i	−0.228352	−	0.852220i	−0.981034	−	0.193836i	$-0.937907\pi$
$499$	−5.10099	−	19.0371i	−0.228352	−	0.852220i	0.752682	−	0.658384i	$-0.228760\pi$
$500$	2.48875	−	4.03783i	0.111300	−	0.180577i
$501$	−4.90430	+	18.3031i	−0.219108	+	0.817721i
$502$	−5.49961	−	4.34707i	−0.245460	−	0.194019i
$503$		−	23.6387i		−	1.05400i	−0.849866	−	0.526999i	$-0.823317\pi$
$503$		−	23.6387i		−	1.05400i	0.849866	−	0.526999i	$-0.176683\pi$
$504$		0			0
$505$		−	10.4311i		−	0.464176i
$506$	16.0600	−	20.3180i	0.713954	−	0.903245i
$507$	3.01221	−	11.2417i	0.133777	−	0.499263i
$508$	−25.0715	+	5.95070i	−1.11237	+	0.264020i
$509$	−8.81005	−	32.8795i	−0.390498	−	1.45736i	−0.829314	−	0.558783i	$-0.811269\pi$
$509$	−8.81005	−	32.8795i	−0.390498	−	1.45736i	0.438816	−	0.898577i	$-0.355398\pi$
$510$	−8.74065	−	11.7367i	−0.387043	−	0.519711i
$511$		0			0
$512$	−11.2849	+	19.6125i	−0.498726	+	0.866760i
$513$	3.78096	−	6.54881i	0.166933	−	0.289137i
$514$	−3.63789	+	8.43737i	−0.160460	+	0.372156i
$515$	−11.8911	−	3.18622i	−0.523985	−	0.140401i
$516$	−4.91953	−	5.21098i	−0.216570	−	0.229401i
$517$	21.2887	+	21.2887i	0.936274	+	0.936274i
$518$		0			0
$519$			19.7318i			0.866131i
$520$	−8.24063	+	46.8693i	−0.361376	+	2.05535i
$521$	−15.2768	+	8.82007i	−0.669289	+	0.386414i	−0.795807	−	0.605550i	$-0.792953\pi$
$521$	−15.2768	+	8.82007i	−0.669289	+	0.386414i	0.126518	+	0.991964i	$0.459620\pi$
$522$	21.2931	−	8.46325i	0.931975	−	0.370426i
$523$	13.8896	−	3.72172i	0.607352	−	0.162739i	0.0579803	−	0.998318i	$-0.481534\pi$
$523$	13.8896	−	3.72172i	0.607352	−	0.162739i	0.549371	+	0.835578i	$0.314867\pi$
$524$	−8.82537	−	16.3549i	−0.385538	−	0.714466i
$525$		0			0
$526$	28.0567	−	20.8946i	1.22333	−	0.911046i
$527$	−3.66479	+	6.34760i	−0.159641	+	0.276506i
$528$	−0.593708	+	10.3096i	−0.0258378	+	0.448669i
$529$	7.48891	+	12.9712i	0.325605	+	0.563964i
$530$	−2.05286	−	17.5385i	−0.0891704	−	0.761822i
$531$	5.99894	−	5.99894i	0.260332	−	0.260332i
$532$		0			0
$533$	−13.4870	−	13.4870i	−0.584189	−	0.584189i
$534$	−4.19400	−	3.31507i	−0.181492	−	0.143457i
$535$	−1.07562	+	0.621012i	−0.0465033	+	0.0268487i
$536$	−17.1630	+	1.51004i	−0.741327	+	0.0652238i
$537$	16.1964	+	9.35102i	0.698928	+	0.403526i
$538$	2.09689	+	0.306800i	0.0904035	+	0.0132271i
$539$		0			0
$540$	−28.5947	−	8.55050i	−1.23052	−	0.367955i
$541$	7.69386	+	28.7139i	0.330785	+	1.23451i	0.908367	+	0.418173i	$0.137330\pi$
$541$	7.69386	+	28.7139i	0.330785	+	1.23451i	−0.577582	+	0.816332i	$0.696004\pi$
$542$	4.12246	−	9.56123i	0.177075	−	0.410690i
$543$	7.27860	+	12.6069i	0.312355	+	0.541014i
$544$	−18.3937	−	9.21887i	−0.788624	−	0.395256i
$545$	−32.7386			−1.40237
$546$		0			0
$547$	27.6503	−	27.6503i	1.18224	−	1.18224i	0.203076	−	0.979163i	$-0.434906\pi$
$547$	27.6503	−	27.6503i	1.18224	−	1.18224i	0.979163	−	0.203076i	$-0.0650940\pi$
$548$	−17.1641	+	16.2041i	−0.733216	+	0.692207i
$549$	−3.93889	+	14.7001i	−0.168108	+	0.627387i
$550$	−8.88538	−	22.3552i	−0.378874	−	0.953229i
$551$	10.3706	+	5.98748i	0.441803	+	0.255075i
$552$	−13.7274	−	6.39301i	−0.584277	−	0.272105i
$553$		0			0
$554$	0.927205	−	6.33720i	0.0393932	−	0.269242i
$555$	−15.8514	+	4.24737i	−0.672855	+	0.180291i
$556$	−19.6407	−	12.1057i	−0.832950	−	0.513396i
$557$	−6.35511	−	1.70285i	−0.269275	−	0.0721519i	0.121655	−	0.992572i	$-0.461180\pi$
$557$	−6.35511	−	1.70285i	−0.269275	−	0.0721519i	−0.390930	+	0.920421i	$0.627846\pi$
$558$	0.743895	+	6.35542i	0.0314916	+	0.269047i
$559$	−21.1901			−0.896247
$560$		0			0
$561$	−9.38988			−0.396441
$562$	−1.59950	−	13.6652i	−0.0674709	−	0.576433i
$563$	−25.7157	−	6.89049i	−1.08379	−	0.290399i	−0.327640	−	0.944803i	$-0.606253\pi$
$563$	−25.7157	−	6.89049i	−1.08379	−	0.290399i	−0.756146	+	0.654403i	$0.772920\pi$
$564$	9.23652	−	14.9856i	0.388928	−	0.631009i
$565$	8.28807	−	2.22078i	0.348682	−	0.0934289i
$566$	0.823582	−	5.62896i	0.0346178	−	0.236603i
$567$		0			0
$568$	−9.25253	−	25.3824i	−0.388228	−	1.06502i
$569$	−2.20198	−	1.27132i	−0.0923119	−	0.0532963i	0.453133	−	0.891443i	$-0.350306\pi$
$569$	−2.20198	−	1.27132i	−0.0923119	−	0.0532963i	−0.545445	+	0.838146i	$0.683639\pi$
$570$	−2.46610	−	6.20460i	−0.103294	−	0.259882i
$571$	−10.3843	+	38.7549i	−0.434571	+	1.62184i	0.307521	+	0.951541i	$0.400501\pi$
$571$	−10.3843	+	38.7549i	−0.434571	+	1.62184i	−0.742091	+	0.670299i	$0.766166\pi$
$572$	20.9618	+	22.2036i	0.876455	+	0.928380i
$573$	−4.84569	+	4.84569i	−0.202431	+	0.202431i
$574$		0			0
$575$	35.2760			1.47111
$576$	−17.6860	+	3.13639i	−0.736916	+	0.130683i
$577$	17.3756	+	30.0953i	0.723354	+	1.25289i	0.959648	+	0.281204i	$0.0907337\pi$
$577$	17.3756	+	30.0953i	0.723354	+	1.25289i	−0.236294	+	0.971682i	$0.575933\pi$
$578$	−2.11169	+	4.89765i	−0.0878348	+	0.203715i
$579$	−5.59453	−	20.8791i	−0.232501	−	0.867705i
$580$	13.5405	−	45.2821i	0.562237	−	1.88024i
$581$		0			0
$582$	8.26877	+	1.20982i	0.342751	+	0.0501485i
$583$	−9.81246	−	5.66523i	−0.406391	−	0.234630i
$584$	2.07713	−	2.47789i	0.0859521	−	0.102536i
$585$	−32.7151	+	18.8881i	−1.35260	+	0.780925i
$586$	2.95185	+	2.33323i	0.121940	+	0.0963850i
$587$	−20.1643	−	20.1643i	−0.832268	−	0.832268i	0.155559	−	0.987827i	$-0.450282\pi$
$587$	−20.1643	−	20.1643i	−0.832268	−	0.832268i	−0.987827	+	0.155559i	$0.950282\pi$
$588$		0			0
$589$	−2.36466	+	2.36466i	−0.0974341	+	0.0974341i
$590$	−2.03440	−	17.3808i	−0.0837548	−	0.715555i
$591$	−4.76342	−	8.25049i	−0.195941	−	0.339380i
$592$	−17.2258	+	15.3499i	−0.707977	+	0.630876i
$593$	4.20461	−	7.28261i	0.172663	−	0.299061i	−0.766687	−	0.642021i	$-0.778096\pi$
$593$	4.20461	−	7.28261i	0.172663	−	0.299061i	0.939350	+	0.342960i	$0.111430\pi$
$594$	−15.3593	+	11.4385i	−0.630199	+	0.469326i
$595$		0			0
$596$	20.6795	−	11.1590i	0.847065	−	0.457091i
$597$	9.60607	−	2.57394i	0.393150	−	0.105344i
$598$	−41.6104	+	16.5386i	−1.70157	+	0.676314i
$599$	−3.08368	+	1.78037i	−0.125996	+	0.0727438i	−0.561673	−	0.827359i	$-0.689842\pi$
$599$	−3.08368	+	1.78037i	−0.125996	+	0.0727438i	0.435677	+	0.900103i	$0.356509\pi$
$600$	−11.5181	+	8.07344i	−0.470223	+	0.329597i
$601$			45.3712i			1.85073i	0.379076	+	0.925365i	$0.376242\pi$
$601$			45.3712i			1.85073i	−0.379076	+	0.925365i	$0.623758\pi$
$602$		0			0
$603$	−9.67096	−	9.67096i	−0.393832	−	0.393832i
$604$	−28.5150	+	26.9202i	−1.16026	+	1.09537i
$605$	6.86180	+	1.83861i	0.278972	+	0.0747502i
$606$	−1.54947	+	3.59368i	−0.0629428	+	0.145983i
$607$	−2.45090	+	4.24508i	−0.0994789	+	0.172302i	−0.911469	−	0.411369i	$-0.865051\pi$
$607$	−2.45090	+	4.24508i	−0.0994789	+	0.172302i	0.811990	+	0.583671i	$0.198384\pi$
$608$	−7.01759	−	6.23486i	−0.284601	−	0.252857i
$609$		0			0
$610$	18.7498	+	25.1768i	0.759158	+	1.01938i
$611$	−13.4720	−	50.2783i	−0.545020	−	2.03404i
$612$	−3.77171	−	15.8910i	−0.152462	−	0.642354i
$613$	−2.06747	+	7.71591i	−0.0835045	+	0.311643i	−0.995027	−	0.0996077i	$-0.968241\pi$
$613$	−2.06747	+	7.71591i	−0.0835045	+	0.311643i	0.911522	+	0.411251i	$0.134908\pi$
$614$	4.94817	−	6.26008i	0.199692	−	0.252636i
$615$		−	10.5620i		−	0.425901i
$616$		0			0
$617$			40.2966i			1.62228i	0.584852	+	0.811140i	$0.301153\pi$
$617$			40.2966i			1.62228i	−0.584852	+	0.811140i	$0.698847\pi$
$618$	3.62341	+	2.86406i	0.145755	+	0.115209i
$619$	−5.20932	+	19.4415i	−0.209380	+	0.781418i	0.778689	+	0.627410i	$0.215885\pi$
$619$	−5.20932	+	19.4415i	−0.209380	+	0.781418i	−0.988070	+	0.154008i	$0.950782\pi$
$620$	11.2360	+	6.92538i	0.451247	+	0.278130i
$621$	−7.26826	−	27.1255i	−0.291665	−	1.08851i
$622$	−0.916568	+	0.682592i	−0.0367510	+	0.0273695i
$623$		0			0
$624$	9.80118	−	14.9232i	0.392361	−	0.597406i
$625$	−10.4273	+	18.0606i	−0.417091	+	0.722422i
$626$	30.2526	+	13.0439i	1.20914	+	0.521337i
$627$	−4.13817	−	1.10882i	−0.165263	−	0.0442820i
$628$	−10.8110	−	0.311032i	−0.431405	−	0.0124115i
$629$	−14.8348	−	14.8348i	−0.591500	−	0.591500i
$630$		0			0
$631$			15.2886i			0.608631i	0.952571	+	0.304315i	$0.0984277\pi$
$631$			15.2886i			0.608631i	−0.952571	+	0.304315i	$0.901572\pi$
$632$	−0.118231	+	0.672447i	−0.00470297	+	0.0267485i
$633$	−9.25190	+	5.34159i	−0.367730	+	0.212309i
$634$	1.63110	+	4.10378i	0.0647794	+	0.162982i
$635$	−40.7546	+	10.9202i	−1.61730	+	0.433354i
$636$	−1.89798	+	6.34725i	−0.0752599	+	0.251685i
$637$		0			0
$638$	−18.1138	−	24.3228i	−0.717133	−	0.962948i
$639$	10.7229	−	18.5726i	0.424192	−	0.734722i
$640$	−17.5466	+	32.6315i	−0.693591	+	1.28987i
$641$	6.18366	+	10.7104i	0.244240	+	0.423036i	0.961918	−	0.273340i	$-0.0881283\pi$
$641$	6.18366	+	10.7104i	0.244240	+	0.423036i	−0.717678	+	0.696375i	$0.754795\pi$
$642$	0.462819	−	0.0541725i	0.0182660	−	0.00213802i
$643$	29.2082	−	29.2082i	1.15186	−	1.15186i	0.165677	−	0.986180i	$-0.447019\pi$
$643$	29.2082	−	29.2082i	1.15186	−	1.15186i	0.986180	−	0.165677i	$-0.0529809\pi$
$644$		0			0
$645$	−8.29724	−	8.29724i	−0.326703	−	0.326703i
$646$	5.29300	−	6.69634i	0.208250	−	0.263464i
$647$	12.4455	−	7.18540i	0.489282	−	0.282487i	−0.234994	−	0.971997i	$-0.575507\pi$
$647$	12.4455	−	7.18540i	0.489282	−	0.282487i	0.724277	+	0.689509i	$0.242174\pi$
$648$	−6.01905	−	5.04556i	−0.236451	−	0.198208i
$649$	−9.72423	−	5.61429i	−0.381710	−	0.220380i
$650$	−6.02117	+	41.1531i	−0.236170	+	1.61416i
$651$		0			0
$652$	10.7132	+	19.8534i	0.419563	+	0.777519i
$653$	3.79601	+	14.1669i	0.148549	+	0.554393i	0.999572	+	0.0292641i	$0.00931639\pi$
$653$	3.79601	+	14.1669i	0.148549	+	0.554393i	−0.851022	+	0.525129i	$0.824017\pi$
$654$	11.2790	+	4.86312i	0.441046	+	0.190163i
$655$	−15.2147	−	26.3527i	−0.594489	−	1.02968i
$656$	−6.67324	−	13.2659i	−0.260546	−	0.517946i
$657$	2.56666			0.100135
$658$		0			0
$659$	−30.0445	+	30.0445i	−1.17037	+	1.17037i	−0.188248	+	0.982122i	$0.560281\pi$
$659$	−30.0445	+	30.0445i	−1.17037	+	1.17037i	−0.982122	+	0.188248i	$0.939719\pi$
$660$	−0.486268	+	16.9019i	−0.0189279	+	0.657905i
$661$	0.717370	−	2.67726i	0.0279025	−	0.104133i	−0.950570	−	0.310509i	$-0.899500\pi$
$661$	0.717370	−	2.67726i	0.0279025	−	0.104133i	0.978473	+	0.206376i	$0.0661670\pi$
$662$	−20.7028	+	8.22860i	−0.804636	+	0.319814i
$663$	14.0593	+	8.11714i	0.546018	+	0.315244i
$664$	−0.775420	+	1.66502i	−0.0300921	+	0.0646154i
$665$		0			0
$666$	−18.1224	−	2.65152i	−0.702230	−	0.102744i
$667$	42.9556	−	11.5099i	1.66325	−	0.445666i
$668$	10.0738	+	42.4430i	0.389768	+	1.64217i
$669$	−18.4182	−	4.93515i	−0.712089	−	0.190804i
$670$	−28.0197	+	3.27968i	−1.08250	+	0.126705i
$671$	20.1425			0.777592
$672$		0			0
$673$	−4.79538			−0.184848			−0.0924242	−	0.995720i	$-0.529462\pi$
$673$	−4.79538			−0.184848			−0.0924242	+	0.995720i	$0.529462\pi$
$674$	7.52969	−	0.881342i	0.290033	−	0.0339480i
$675$	−25.1958	−	6.75119i	−0.969786	−	0.259854i
$676$	−6.18733	−	26.0684i	−0.237974	−	1.00263i
$677$	48.0358	−	12.8711i	1.84616	−	0.494678i	0.846855	−	0.531824i	$-0.178493\pi$
$677$	48.0358	−	12.8711i	1.84616	−	0.494678i	0.999310	+	0.0371454i	$0.0118265\pi$
$678$	−3.18527	−	0.466042i	−0.122330	−	0.0178982i
$679$		0			0
$680$	−30.5394	−	14.2225i	−1.17113	−	0.545409i
$681$	−18.5603	−	10.7158i	−0.711234	−	0.410631i
$682$	7.87018	−	3.12811i	0.301365	−	0.119782i
$683$	−1.06566	+	3.97711i	−0.0407764	+	0.152180i	−0.983312	−	0.181925i	$-0.941767\pi$
$683$	−1.06566	+	3.97711i	−0.0407764	+	0.152180i	0.942536	+	0.334105i	$0.108434\pi$
$684$	0.214297	−	7.44863i	0.00819386	−	0.284805i
$685$	−27.3298	+	27.3298i	−1.04422	+	1.04422i
$686$		0			0
$687$	−8.26579			−0.315360
$688$	−15.6637	−	5.17902i	−0.597172	−	0.197448i
$689$	9.79469	+	16.9649i	0.373148	+	0.646311i
$690$	−22.7689	−	9.81713i	−0.866797	−	0.373732i
$691$	−9.19198	−	34.3049i	−0.349679	−	1.30502i	−0.887049	−	0.461674i	$-0.847249\pi$
$691$	−9.19198	−	34.3049i	−0.349679	−	1.30502i	0.537370	−	0.843347i	$-0.319418\pi$
$692$	21.5717	+	39.9759i	0.820033	+	1.51966i
$693$		0			0
$694$	3.39951	−	23.2347i	0.129043	−	0.881977i
$695$	−32.7162	−	18.8887i	−1.24100	−	0.716489i
$696$	−11.3913	+	13.5892i	−0.431787	+	0.515096i
$697$	11.6936	−	6.75130i	0.442927	−	0.255724i
$698$	−27.6319	+	34.9579i	−1.04588	+	1.32318i
$699$	−13.6608	−	13.6608i	−0.516701	−	0.516701i
$700$		0			0
$701$	15.7687	−	15.7687i	0.595575	−	0.595575i	−0.343557	−	0.939132i	$-0.611632\pi$
$701$	15.7687	−	15.7687i	0.595575	−	0.595575i	0.939132	+	0.343557i	$0.111632\pi$
$702$	32.8853	−	3.84918i	1.24117	−	0.145278i
$703$	−4.78597	−	8.28955i	−0.180506	−	0.312646i
$704$	10.0681	+	21.5360i	0.379457	+	0.811669i
$705$	14.4119	−	24.9621i	0.542783	−	0.940129i
$706$	−11.5617	−	15.5248i	−0.435131	−	0.584283i
$707$		0			0
$708$	−1.88092	+	6.29018i	−0.0706892	+	0.236400i
$709$	11.1596	−	2.99021i	0.419108	−	0.112300i	−0.0431009	−	0.999071i	$-0.513724\pi$
$709$	11.1596	−	2.99021i	0.419108	−	0.112300i	0.462209	+	0.886771i	$0.347057\pi$
$710$	−16.3390	−	41.1081i	−0.613190	−	1.54276i
$711$	−0.469373	+	0.270993i	−0.0176029	+	0.0101630i
$712$	−12.1211	−	2.13115i	−0.454256	−	0.0798681i
$713$			12.4190i			0.465095i
$714$		0			0
$715$	35.3539	+	35.3539i	1.32216	+	1.32216i
$716$	43.0364	+	1.23816i	1.60834	+	0.0462721i
$717$	12.5522	+	3.36335i	0.468770	+	0.125607i
$718$	8.21044	+	3.54005i	0.306411	+	0.132113i
$719$	14.4263	−	24.9871i	0.538011	−	0.931863i	−0.461000	−	0.887400i	$-0.652509\pi$
$719$	14.4263	−	24.9871i	0.538011	−	0.931863i	0.999011	−	0.0444624i	$-0.0141575\pi$
$720$	−28.7992	+	5.96618i	−1.07328	+	0.222347i
$721$		0			0
$722$	−18.4271	+	13.7231i	−0.685784	+	0.510722i
$723$	−5.47519	−	20.4337i	−0.203625	−	0.759938i
$724$	28.5286	+	17.5839i	1.06026	+	0.653499i
$725$	10.6911	−	39.8997i	0.397057	−	1.48184i
$726$	−2.09090	−	1.65271i	−0.0776005	−	0.0613379i
$727$		−	19.1342i		−	0.709648i	−0.934933	−	0.354824i	$-0.884541\pi$
$727$		−	19.1342i		−	0.709648i	0.934933	−	0.354824i	$-0.115459\pi$
$728$		0			0
$729$			5.64199i			0.208963i
$730$	3.28298	−	4.15340i	0.121509	−	0.153724i
$731$	3.88254	−	14.4898i	0.143601	−	0.535926i
$732$	−2.71979	−	11.4590i	−0.100526	−	0.423538i
$733$	2.99140	+	11.1641i	0.110490	+	0.412354i	0.998910	−	0.0466772i	$-0.0148632\pi$
$733$	2.99140	+	11.1641i	0.110490	+	0.412354i	−0.888420	+	0.459031i	$0.848197\pi$
$734$	31.4504	+	42.2308i	1.16085	+	1.55877i
$735$		0			0
$736$	−34.8004	+	2.05541i	−1.28276	+	0.0757636i
$737$	−9.05087	+	15.6766i	−0.333393	+	0.577453i
$738$	4.66720	−	10.8246i	0.171802	−	0.398461i
$739$	8.01230	+	2.14689i	0.294737	+	0.0789746i	0.403158	−	0.915130i	$-0.367913\pi$
$739$	8.01230	+	2.14689i	0.294737	+	0.0789746i	−0.108420	+	0.994105i	$0.534579\pi$
$740$	−27.4710	+	25.9345i	−1.00985	+	0.953371i
$741$	5.23749	+	5.23749i	0.192404	+	0.192404i
$742$		0			0
$743$		−	9.24326i		−	0.339102i	−0.985521	−	0.169551i	$-0.945768\pi$
$743$		−	9.24326i		−	0.339102i	0.985521	−	0.169551i	$-0.0542318\pi$
$744$	−2.84227	−	4.05495i	−0.104203	−	0.148662i
$745$	33.3210	−	19.2379i	1.22079	−	0.704821i
$746$	5.68090	−	2.25795i	0.207993	−	0.0826695i
$747$	−1.40834	+	0.377363i	−0.0515284	+	0.0138070i
$748$	−19.0236	+	10.2654i	−0.695570	+	0.375341i
$749$		0			0
$750$	−2.33695	+	1.74038i	−0.0853332	+	0.0635499i
$751$	10.3379	−	17.9057i	0.377234	−	0.653388i	−0.613425	−	0.789753i	$-0.710209\pi$
$751$	10.3379	−	17.9057i	0.377234	−	0.653388i	0.990659	+	0.136365i	$0.0435421\pi$
$752$	2.32989	−	40.4581i	0.0849624	−	1.47536i
$753$	2.15322	+	3.72949i	0.0784677	+	0.135910i
$754$	6.09551	+	52.0767i	0.221986	+	1.89652i
$755$	−45.4034	+	45.4034i	−1.65240	+	1.65240i
$756$		0			0
$757$	19.3612	+	19.3612i	0.703694	+	0.703694i	0.965201	−	0.261508i	$-0.0842197\pi$
$757$	19.3612	+	19.3612i	0.703694	+	0.703694i	−0.261508	+	0.965201i	$0.584220\pi$
$758$	18.0624	+	14.2771i	0.656057	+	0.518569i
$759$	−13.7784	+	7.95495i	−0.500123	+	0.288746i
$760$	−11.7794	−	9.87424i	−0.427283	−	0.358176i
$761$	−15.2778	−	8.82065i	−0.553821	−	0.319748i	0.196841	−	0.980435i	$-0.436932\pi$
$761$	−15.2778	−	8.82065i	−0.553821	−	0.319748i	−0.750662	+	0.660687i	$0.770265\pi$
$762$	15.6628	+	2.29165i	0.567404	+	0.0830178i
$763$		0			0
$764$	−4.51966	+	15.1147i	−0.163516	+	0.546831i
$765$	−6.92149	−	25.8313i	−0.250247	−	0.933934i
$766$	11.0455	−	25.6180i	0.399092	−	0.925615i
$767$	9.70662	+	16.8124i	0.350486	+	0.607059i
$768$	10.8923	−	8.63570i	0.393043	−	0.311614i
$769$	33.4127			1.20489			0.602447	−	0.798159i	$-0.294193\pi$
$769$	33.4127			1.20489			0.602447	+	0.798159i	$0.294193\pi$
$770$		0			0
$771$	3.99122	−	3.99122i	0.143740	−	0.143740i
$772$	−34.1603	−	36.1841i	−1.22945	−	1.30229i
$773$	3.46760	−	12.9412i	0.124721	−	0.465464i	−0.875109	−	0.483926i	$-0.839210\pi$
$773$	3.46760	−	12.9412i	0.124721	−	0.465464i	0.999830	+	0.0184619i	$0.00587695\pi$
$774$	−4.83713	−	12.1700i	−0.173867	−	0.437441i
$775$	9.99003	+	5.76774i	0.358852	+	0.207183i
$776$	18.0748	−	6.58874i	0.648849	−	0.236522i
$777$		0			0
$778$	1.21574	−	8.30927i	0.0435865	−	0.297902i
$779$	5.95068	−	1.59448i	0.213205	−	0.0571281i
$780$	15.3390	−	24.8865i	0.549225	−	0.891081i
$781$	−27.4171	−	7.34640i	−0.981062	−	0.262875i
$782$	−3.68511	−	31.4835i	−0.131779	−	1.12585i
$783$	−32.8837			−1.17517
$784$		0			0
$785$	−17.7091			−0.632066
$786$	1.32722	+	11.3390i	0.0473404	+	0.404450i
$787$	−9.30456	−	2.49315i	−0.331672	−	0.0888712i	0.0891401	−	0.996019i	$-0.471588\pi$
$787$	−9.30456	−	2.49315i	−0.331672	−	0.0888712i	−0.420812	+	0.907148i	$0.638255\pi$
$788$	−18.6703	−	11.5076i	−0.665102	−	0.409941i
$789$	−20.7578	+	5.56203i	−0.738997	+	0.198014i
$790$	−0.161846	+	1.10617i	−0.00575821	+	0.0393558i
$791$		0			0
$792$	−7.96706	+	17.1073i	−0.283097	+	0.607882i
$793$	−30.1590	−	17.4123i	−1.07098	−	0.618329i
$794$	−13.3576	−	33.6071i	−0.474044	−	1.19267i
$795$	−2.80758	+	10.4780i	−0.0995744	+	0.371617i
$796$	16.6476	−	15.7165i	0.590059	−	0.557056i
$797$	−3.47475	+	3.47475i	−0.123082	+	0.123082i	−0.765965	−	0.642883i	$-0.777738\pi$
$797$	−3.47475	+	3.47475i	−0.123082	+	0.123082i	0.642883	+	0.765965i	$0.277738\pi$
$798$		0			0
$799$	36.8487			1.30361
$800$	−14.5089	+	28.9486i	−0.512967	+	1.02349i
$801$	−4.88472	−	8.46059i	−0.172593	−	0.298940i
$802$	2.01739	−	4.67893i	0.0712365	−	0.165219i
$803$	−0.879223	−	3.28131i	−0.0310271	−	0.115795i
$804$	10.1405	+	3.03225i	0.357627	+	0.106939i
$805$		0			0
$806$	−14.4880	−	2.11976i	−0.510318	−	0.0746654i
$807$	−1.12744	−	0.650930i	−0.0396879	−	0.0229138i
$808$	0.789610	+	8.97462i	0.0277784	+	0.315726i
$809$	38.9261	−	22.4740i	1.36857	−	0.790144i	0.377824	−	0.925877i	$-0.376672\pi$
$809$	38.9261	−	22.4740i	1.36857	−	0.790144i	0.990745	+	0.135734i	$0.0433391\pi$
$810$	−10.0891	−	7.97471i	−0.354493	−	0.280203i
$811$	23.3543	+	23.3543i	0.820080	+	0.820080i	0.986119	−	0.166039i	$-0.0530978\pi$
$811$	23.3543	+	23.3543i	0.820080	+	0.820080i	−0.166039	+	0.986119i	$0.553098\pi$
$812$		0			0
$813$	−4.52285	+	4.52285i	−0.158623	+	0.158623i
$814$	2.81815	+	24.0767i	0.0987760	+	0.843887i
$815$	18.4694	+	31.9899i	0.646953	+	1.12056i
$816$	8.40869	+	9.43635i	0.294363	+	0.330338i
$817$	3.42212	−	5.92728i	0.119725	−	0.207369i
$818$	−17.3900	+	12.9508i	−0.608026	+	0.452813i
$819$		0			0
$820$	−11.5468	−	21.3982i	−0.403233	−	0.747259i
$821$	31.0690	−	8.32491i	1.08432	−	0.290541i	0.327953	−	0.944694i	$-0.393641\pi$
$821$	31.0690	−	8.32491i	1.08432	−	0.290541i	0.756362	+	0.654153i	$0.226975\pi$
$822$	13.4753	−	5.35593i	0.470004	−	0.186810i
$823$	5.60251	−	3.23461i	0.195291	−	0.112751i	−0.399166	−	0.916879i	$-0.630700\pi$
$823$	5.60251	−	3.23461i	0.195291	−	0.112751i	0.594457	+	0.804127i	$0.297367\pi$
$824$	10.4720	+	1.84121i	0.364810	+	0.0641415i
$825$			14.7781i			0.514506i
$826$		0			0
$827$	0.313180	+	0.313180i	0.0108903	+	0.0108903i	0.712531	−	0.701641i	$-0.247549\pi$
$827$	0.313180	+	0.313180i	0.0108903	+	0.0108903i	−0.701641	+	0.712531i	$0.747549\pi$
$828$	−18.9970	−	20.1225i	−0.660192	−	0.699305i
$829$	27.5710	+	7.38763i	0.957581	+	0.256583i	0.703576	−	0.710620i	$-0.251585\pi$
$829$	27.5710	+	7.38763i	0.957581	+	0.256583i	0.254005	+	0.967203i	$0.418252\pi$
$830$	−1.19074	+	2.76168i	−0.0413311	+	0.0958593i
$831$	−1.96723	+	3.40735i	−0.0682425	+	0.118200i
$832$	3.54213	−	40.9490i	0.122801	−	1.41965i
$833$		0			0
$834$	8.46552	+	11.3673i	0.293137	+	0.393617i
$835$	18.4865	+	68.9927i	0.639753	+	2.38759i
$836$	−9.59600	+	2.27761i	−0.331885	+	0.0787727i
$837$	2.37677	−	8.87022i	0.0821531	−	0.306600i
$838$	−21.4493	+	27.1362i	−0.740955	+	0.937406i
$839$			49.1079i			1.69539i	0.530482	+	0.847696i	$0.322011\pi$
$839$			49.1079i			1.69539i	−0.530482	+	0.847696i	$0.677989\pi$
$840$		0			0
$841$		−	23.0742i		−	0.795662i
$842$	−28.6239	−	22.6253i	−0.986446	−	0.779718i
$843$	−2.18755	+	8.16403i	−0.0753431	+	0.281184i
$844$	−12.9044	+	20.9365i	−0.444186	+	0.720662i
$845$	−11.3544	−	42.3752i	−0.390603	−	1.45775i
$846$	25.8007	−	19.2145i	0.887046	−	0.660606i
$847$		0			0
$848$	3.09385	+	14.9343i	0.106243	+	0.512845i
$849$	−1.74738	+	3.02655i	−0.0599698	+	0.103871i
$850$	−27.0373	−	11.6575i	−0.927371	−	0.399849i
$851$	−34.3357	−	9.20023i	−1.17701	−	0.315380i
$852$	−0.477281	+	16.5895i	−0.0163514	+	0.568348i
$853$	−4.33966	−	4.33966i	−0.148587	−	0.148587i	0.628899	−	0.777487i	$-0.283506\pi$
$853$	−4.33966	−	4.33966i	−0.148587	−	0.148587i	−0.777487	+	0.628899i	$0.783506\pi$
$854$		0			0
$855$		−	12.2014i		−	0.417278i
$856$	0.878431	−	0.615726i	0.0300242	−	0.0210451i
$857$	14.0065	−	8.08667i	0.478454	−	0.276235i	−0.241318	−	0.970446i	$-0.577580\pi$
$857$	14.0065	−	8.08667i	0.478454	−	0.276235i	0.719772	+	0.694211i	$0.244246\pi$
$858$	−6.92846	−	17.4317i	−0.236534	−	0.595107i
$859$	43.0148	−	11.5258i	1.46765	−	0.393254i	0.565522	−	0.824733i	$-0.308675\pi$
$859$	43.0148	−	11.5258i	1.46765	−	0.393254i	0.902123	+	0.431479i	$0.142008\pi$
$860$	−25.8808	−	7.73899i	−0.882528	−	0.263897i
$861$		0			0
$862$	28.3983	+	38.1325i	0.967249	+	1.29880i
$863$	−2.85176	+	4.93940i	−0.0970752	+	0.168139i	−0.910473	−	0.413569i	$-0.864282\pi$
$863$	−2.85176	+	4.93940i	−0.0970752	+	0.168139i	0.813398	+	0.581708i	$0.197615\pi$
$864$	25.2494	+	5.19208i	0.859002	+	0.176638i
$865$	37.1891	+	64.4134i	1.26447	+	2.19012i
$866$	37.2943	−	4.36526i	1.26731	−	0.148338i
$867$	2.31679	−	2.31679i	0.0786822	−	0.0786822i
$868$		0			0
$869$	0.507233	+	0.507233i	0.0172067	+	0.0172067i
$870$	−18.0044	+	22.7780i	−0.610407	+	0.772245i
$871$	27.1034	−	15.6482i	0.918364	−	0.530218i
$872$	28.1675	−	2.47825i	0.953872	−	0.0839241i
$873$	13.2256	+	7.63580i	0.447619	+	0.258433i
$874$	2.09374	−	14.3101i	0.0708217	−	0.484047i
$875$		0			0
$876$	−1.74801	+	0.943255i	−0.0590598	+	0.0318696i
$877$	4.09303	+	15.2754i	0.138212	+	0.515814i	0.999964	+	0.00848425i	$0.00270065\pi$
$877$	4.09303	+	15.2754i	0.138212	+	0.515814i	−0.861752	+	0.507330i	$0.830633\pi$
$878$	25.4672	+	10.9805i	0.859476	+	0.370575i
$879$	−1.15571	−	2.00176i	−0.0389813	−	0.0675175i
$880$	17.4927	+	34.7742i	0.589680	+	1.17224i
$881$	−20.6047			−0.694190			−0.347095	−	0.937830i	$-0.612832\pi$
$881$	−20.6047			−0.694190			−0.347095	+	0.937830i	$0.612832\pi$
$882$		0			0
$883$	3.92964	−	3.92964i	0.132243	−	0.132243i	−0.637887	−	0.770130i	$-0.720191\pi$
$883$	3.92964	−	3.92964i	0.132243	−	0.132243i	0.770130	+	0.637887i	$0.220191\pi$
$884$	37.3577	+	1.07478i	1.25647	+	0.0361488i
$885$	−2.78233	+	10.3838i	−0.0935270	+	0.349048i
$886$	8.96545	−	3.56344i	0.301200	−	0.119716i
$887$	16.0874	+	9.28808i	0.540163	+	0.311863i	0.745145	−	0.666903i	$-0.232380\pi$
$887$	16.0874	+	9.28808i	0.540163	+	0.311863i	−0.204982	+	0.978766i	$0.565714\pi$
$888$	13.3166	−	4.85425i	0.446877	−	0.162898i
$889$		0			0
$890$	−19.9391	−	2.91732i	−0.668359	−	0.0977887i
$891$	−7.97063	+	2.13573i	−0.267026	+	0.0715495i
$892$	−42.7100	+	10.1372i	−1.43004	+	0.339418i
$893$	16.2394	+	4.35135i	0.543432	+	0.145612i
$894$	−14.3373	+	1.67817i	−0.479512	+	0.0561264i
$895$	70.4965			2.35644
$896$		0			0
$897$	27.5068			0.918426
$898$	−8.88301	+	1.03975i	−0.296430	+	0.0346968i
$899$	14.0468	+	3.76382i	0.468486	+	0.125530i
$900$	−25.0096	+	5.93602i	−0.833654	+	0.197867i
$901$	−13.3952	+	3.58924i	−0.446260	+	0.119575i
$902$	−15.4374	−	2.25867i	−0.514009	−	0.0752055i
$903$		0			0
$904$	−6.96274	+	2.53810i	−0.231577	+	0.0844158i
$905$	47.5212	+	27.4364i	1.57966	+	0.912016i
$906$	22.3867	−	8.89788i	0.743747	−	0.295612i
$907$	7.38295	−	27.5535i	0.245147	−	0.914900i	−0.728163	−	0.685404i	$-0.759626\pi$
$907$	7.38295	−	27.5535i	0.245147	−	0.914900i	0.973310	−	0.229496i	$-0.0737078\pi$
$908$	−49.3176	−	1.41887i	−1.63666	−	0.0470868i
$909$	−5.05701	+	5.05701i	−0.167730	+	0.167730i
$910$		0			0
$911$	40.6520			1.34686			0.673431	−	0.739250i	$-0.264820\pi$
$911$	40.6520			1.34686			0.673431	+	0.739250i	$0.264820\pi$
$912$	2.59145	+	5.15161i	0.0858116	+	0.170587i
$913$	0.964870	+	1.67120i	0.0319325	+	0.0553088i
$914$	−51.2944	−	22.1163i	−1.69667	−	0.731543i
$915$	−4.99111	−	18.6271i	−0.165001	−	0.615792i
$916$	−16.7462	+	9.03653i	−0.553310	+	0.298575i
$917$		0			0
$918$	−3.39329	+	23.1922i	−0.111995	+	0.765458i
$919$	23.3547	+	13.4838i	0.770400	+	0.444790i	0.833017	−	0.553247i	$-0.186611\pi$
$919$	23.3547	+	13.4838i	0.770400	+	0.444790i	−0.0626175	+	0.998038i	$0.519945\pi$
$920$	−56.8615	+	5.00282i	−1.87467	+	0.164938i
$921$	−4.24519	+	2.45096i	−0.139884	+	0.0807619i
$922$	−1.57225	+	1.98911i	−0.0517794	+	0.0655078i
$923$	34.7005	+	34.7005i	1.14218	+	1.14218i
$924$		0			0
$925$	−23.3473	+	23.3473i	−0.767656	+	0.767656i
$926$	20.2865	−	2.37451i	0.666657	−	0.0780314i
$927$	4.22017	+	7.30954i	0.138608	+	0.240077i
$928$	−8.22212	+	39.9846i	−0.269904	+	1.31256i
$929$	7.81601	−	13.5377i	0.256435	−	0.444159i	−0.708849	−	0.705360i	$-0.750785\pi$
$929$	7.81601	−	13.5377i	0.256435	−	0.444159i	0.965284	+	0.261201i	$0.0841187\pi$
$930$	−4.84292	−	6.50295i	−0.158806	−	0.213240i
$931$		0			0
$932$	−42.6110	−	12.7417i	−1.39577	−	0.417369i
$933$	0.678124	−	0.181703i	0.0222008	−	0.00594868i
$934$	−9.07401	−	22.8298i	−0.296911	−	0.747013i
$935$	−30.6527	+	17.6974i	−1.00245	+	0.578766i
$936$	26.7175	−	18.7273i	0.873288	−	0.612121i
$937$		−	47.9244i		−	1.56562i	−0.622260	−	0.782811i	$-0.713785\pi$
$937$		−	47.9244i		−	1.56562i	0.622260	−	0.782811i	$-0.286215\pi$
$938$		0			0
$939$	−14.3107	−	14.3107i	−0.467013	−	0.467013i
$940$	1.90826	−	66.3281i	0.0622406	−	2.16338i
$941$	10.4101	+	2.78937i	0.339359	+	0.0909309i	0.424474	−	0.905440i	$-0.360459\pi$
$941$	10.4101	+	2.78937i	0.339359	+	0.0909309i	−0.0851151	+	0.996371i	$0.527126\pi$
$942$	6.10112	+	2.63058i	0.198785	+	0.0857090i
$943$	11.4392	−	19.8132i	0.372511	−	0.645208i
$944$	3.06604	+	14.8000i	0.0997910	+	0.481698i
$945$		0			0
$946$	−13.9016	+	10.3529i	−0.451979	+	0.336601i
$947$	−7.18339	−	26.8088i	−0.233429	−	0.871168i	−0.978851	−	0.204575i	$-0.934419\pi$
$947$	−7.18339	−	26.8088i	−0.233429	−	0.871168i	0.745422	−	0.666593i	$-0.232248\pi$
$948$	0.220074	−	0.357055i	0.00714766	−	0.0115966i
$949$	−1.52010	+	5.67309i	−0.0493446	+	0.184156i
$950$	−10.5389	−	8.33028i	−0.341927	−	0.270270i
$951$		−	2.71283i		−	0.0879696i
$952$		0			0
$953$		−	3.58597i		−	0.116161i	−0.998312	−	0.0580805i	$-0.981502\pi$
$953$		−	3.58597i		−	0.116161i	0.998312	−	0.0580805i	$-0.0184980\pi$
$954$	−7.50747	+	9.49794i	−0.243063	+	0.307507i
$955$	−6.68567	+	24.9513i	−0.216343	+	0.807404i
$956$	29.1072	−	6.90859i	0.941395	−	0.223440i
$957$	4.82181	+	17.9952i	0.155867	+	0.581703i
$958$	4.04346	+	5.42945i	0.130638	+	0.175418i
$959$		0			0
$960$	17.4210	−	14.6471i	0.562260	−	0.472732i
$961$	13.4695	−	23.3298i	0.434499	−	0.752574i
$962$	16.5937	−	38.4857i	0.535001	−	1.24083i
$963$	0.822535	+	0.220398i	0.0265058	+	0.00710221i
$964$	−33.4316	−	35.4122i	−1.07676	−	1.14055i
$965$	−57.6144	−	57.6144i	−1.85467	−	1.85467i
$966$		0			0
$967$		−	51.9947i		−	1.67204i	−0.548703	−	0.836018i	$-0.684878\pi$
$967$		−	51.9947i		−	1.67204i	0.548703	−	0.836018i	$-0.315122\pi$
$968$	−6.04290	−	1.06247i	−0.194226	−	0.0341492i
$969$	−4.54103	+	2.62177i	−0.145879	+	0.0842233i
$970$	29.2731	−	11.6350i	0.939903	−	0.373577i
$971$	−47.9206	+	12.8403i	−1.53785	+	0.412064i	−0.925569	−	0.378579i	$-0.876413\pi$
$971$	−47.9206	+	12.8403i	−1.53785	+	0.412064i	−0.612277	+	0.790644i	$0.709746\pi$
$972$	15.2754	+	28.3078i	0.489958	+	0.907973i
$973$		0			0
$974$	−30.4768	+	22.6968i	−0.976538	+	0.727254i
$975$	12.7750	−	22.1269i	0.409127	−	0.708629i
$976$	−18.0377	−	20.2422i	−0.577373	−	0.647936i
$977$	−2.83541	−	4.91108i	−0.0907129	−	0.157119i	0.817098	−	0.576498i	$-0.195581\pi$
$977$	−2.83541	−	4.91108i	−0.0907129	−	0.157119i	−0.907811	+	0.419379i	$0.862248\pi$
$978$	−1.61113	−	13.7646i	−0.0515182	−	0.440143i
$979$	−9.14303	+	9.14303i	−0.292213	+	0.292213i
$980$		0			0
$981$	15.8718	+	15.8718i	0.506748	+	0.506748i
$982$	18.4480	+	14.5819i	0.588699	+	0.465327i
$983$	−40.4834	+	23.3731i	−1.29122	+	0.745486i	−0.978870	−	0.204482i	$-0.934449\pi$
$983$	−40.4834	+	23.3731i	−1.29122	+	0.745486i	−0.312349	+	0.949968i	$0.601116\pi$
$984$	0.799523	+	9.08729i	0.0254879	+	0.289692i
$985$	−31.0998	−	17.9555i	−0.990923	−	0.572110i
$986$	−36.7269	−	5.37357i	−1.16962	−	0.171129i
$987$		0			0
$988$	16.3368	+	4.88511i	0.519744	+	0.155416i
$989$	−6.57845	−	24.5511i	−0.209182	−	0.780679i
$990$	−12.2342	+	28.3749i	−0.388830	+	0.901814i
$991$	−7.20690	−	12.4827i	−0.228935	−	0.396527i	0.728558	−	0.684984i	$-0.240191\pi$
$991$	−7.20690	−	12.4827i	−0.228935	−	0.396527i	−0.957493	+	0.288457i	$0.906858\pi$
$992$	−10.1914	−	5.10788i	−0.323577	−	0.162175i
$993$	13.6857			0.434303
$994$		0			0
$995$	26.5073	−	26.5073i	0.840339	−	0.840339i
$996$	0.820461	−	0.774572i	0.0259973	−	0.0245432i
$997$	−14.7190	+	54.9322i	−0.466156	+	1.73972i	0.186871	+	0.982384i	$0.440165\pi$
$997$	−14.7190	+	54.9322i	−0.466156	+	1.73972i	−0.653027	+	0.757334i	$0.726501\pi$
$998$	10.2949	+	25.9014i	0.325878	+	0.819894i
$999$	22.7634	+	13.1425i	0.720203	+	0.415809i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.o.373.1		48
7.2	even	3		784.2.m.k.197.8		24
7.3	odd	6		112.2.w.c.53.9	yes	48
7.4	even	3	inner	784.2.x.o.165.9		48
7.5	odd	6		784.2.m.j.197.8		24
7.6	odd	2		112.2.w.c.37.1	✓	48
16.13	even	4	inner	784.2.x.o.765.9		48
28.3	even	6		448.2.ba.c.305.5		48
28.27	even	2		448.2.ba.c.177.8		48
56.3	even	6		896.2.ba.e.865.8		48
56.13	odd	2		896.2.ba.f.737.8		48
56.27	even	2		896.2.ba.e.737.5		48
56.45	odd	6		896.2.ba.f.865.5		48
112.3	even	12		448.2.ba.c.81.8		48
112.13	odd	4		112.2.w.c.93.9	yes	48
112.27	even	4		896.2.ba.e.289.8		48
112.45	odd	12		112.2.w.c.109.1	yes	48
112.59	even	12		896.2.ba.e.417.5		48
112.61	odd	12		784.2.m.j.589.8		24
112.69	odd	4		896.2.ba.f.289.5		48
112.83	even	4		448.2.ba.c.401.5		48
112.93	even	12		784.2.m.k.589.8		24
112.101	odd	12		896.2.ba.f.417.8		48
112.109	even	12	inner	784.2.x.o.557.1		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.1	✓	48	7.6	odd	2
112.2.w.c.53.9	yes	48	7.3	odd	6
112.2.w.c.93.9	yes	48	112.13	odd	4
112.2.w.c.109.1	yes	48	112.45	odd	12
448.2.ba.c.81.8		48	112.3	even	12
448.2.ba.c.177.8		48	28.27	even	2
448.2.ba.c.305.5		48	28.3	even	6
448.2.ba.c.401.5		48	112.83	even	4
784.2.m.j.197.8		24	7.5	odd	6
784.2.m.j.589.8		24	112.61	odd	12
784.2.m.k.197.8		24	7.2	even	3
784.2.m.k.589.8		24	112.93	even	12
784.2.x.o.165.9		48	7.4	even	3	inner
784.2.x.o.373.1		48	1.1	even	1	trivial
784.2.x.o.557.1		48	112.109	even	12	inner
784.2.x.o.765.9		48	16.13	even	4	inner
896.2.ba.e.289.8		48	112.27	even	4
896.2.ba.e.417.5		48	112.59	even	12
896.2.ba.e.737.5		48	56.27	even	2
896.2.ba.e.865.8		48	56.3	even	6
896.2.ba.f.289.5		48	112.69	odd	4
896.2.ba.f.417.8		48	112.101	odd	12
896.2.ba.f.737.8		48	56.13	odd	2
896.2.ba.f.865.5		48	56.45	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40462 + 0.164410i) q^{2} +(0.839165 + 0.224854i) q^{3} +(1.94594 - 0.461868i) q^{4} +(3.16320 - 0.847576i) q^{5} +(-1.21568 - 0.177868i) q^{6} +(-2.65738 + 0.968682i) q^{8} +(-1.94444 - 1.12262i) q^{9} +(-4.30375 + 1.71059i) q^{10} +(-0.769121 + 2.87040i) q^{11} +(1.73682 + 0.0499683i) q^{12} +(3.63293 - 3.63293i) q^{13} +2.84503 q^{15} +(3.57336 - 1.79753i) q^{16} +(1.81856 + 3.14984i) q^{17} +(2.91577 + 1.25718i) q^{18} +(0.429496 + 1.60290i) q^{19} +(5.76392 - 3.11031i) q^{20} +(0.608405 - 4.15828i) q^{22} +(5.33698 + 3.08131i) q^{23} +(-2.44779 + 0.215363i) q^{24} +(4.95730 - 2.86210i) q^{25} +(-4.50561 + 5.70019i) q^{26} +(-3.22221 - 3.22221i) q^{27} +(5.10266 - 5.10266i) q^{29} +(-3.99619 + 0.467750i) q^{30} +(1.00761 + 1.74523i) q^{31} +(-4.72369 + 3.11235i) q^{32} +(-1.29084 + 2.23580i) q^{33} +(-3.07226 - 4.12535i) q^{34} +(-4.30226 - 1.28648i) q^{36} +(-5.57162 + 1.49291i) q^{37} +(-0.866812 - 2.18086i) q^{38} +(3.86550 - 2.23175i) q^{39} +(-7.58478 + 5.31646i) q^{40} -3.71244i q^{41} +(-2.91640 - 2.91640i) q^{43} +(-0.170919 + 5.94085i) q^{44} +(-7.10214 - 1.90301i) q^{45} +(-8.00305 - 3.45063i) q^{46} +(5.06565 - 8.77396i) q^{47} +(3.40282 - 0.704944i) q^{48} +(-6.49259 + 4.83520i) q^{50} +(0.817820 + 3.05215i) q^{51} +(5.39152 - 8.74739i) q^{52} +(-0.986836 + 3.68292i) q^{53} +(5.05576 + 3.99624i) q^{54} +9.73153i q^{55} +1.44167i q^{57} +(-6.32839 + 8.00624i) q^{58} +(-0.977963 + 3.64981i) q^{59} +(5.53625 - 1.31403i) q^{60} +(-1.75433 - 6.54724i) q^{61} +(-1.70224 - 2.28573i) q^{62} +(6.12331 - 5.14831i) q^{64} +(8.41248 - 14.5708i) q^{65} +(1.44556 - 3.35269i) q^{66} +(5.88390 + 1.57659i) q^{67} +(4.99362 + 5.28946i) q^{68} +(3.78577 + 3.78577i) q^{69} +9.55168i q^{71} +(6.25456 + 1.09969i) q^{72} +(-0.990000 + 0.571577i) q^{73} +(7.58058 - 3.01301i) q^{74} +(4.80355 - 1.28711i) q^{75} +(1.57610 + 2.92078i) q^{76} +(-5.06266 + 3.77030i) q^{78} +(0.120696 - 0.209052i) q^{79} +(9.77969 - 8.71464i) q^{80} +(1.38842 + 2.40481i) q^{81} +(0.610362 + 5.21459i) q^{82} +(0.459183 - 0.459183i) q^{83} +(8.42219 + 8.42219i) q^{85} +(4.57593 + 3.61696i) q^{86} +(5.42932 - 3.13462i) q^{87} +(-0.736657 - 8.37277i) q^{88} +(3.76823 + 2.17559i) q^{89} +(10.2887 + 1.50536i) q^{90} +(11.8086 + 3.53106i) q^{92} +(0.453128 + 1.69110i) q^{93} +(-5.67281 + 13.1570i) q^{94} +(2.71716 + 4.70626i) q^{95} +(-4.66378 + 1.54964i) q^{96} -6.80176 q^{97} +(4.71788 - 4.71788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27}+ \cdots - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

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