LMFDB - Embedded newform 740.2.i.a.121.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(121,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.121"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,0,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 24x^{12} + 204x^{10} + 727x^{8} + 1008x^{6} + 426x^{4} + 64x^{2} + 3 $ x^14 + 24x^12 + 204x^10 + 727x^8 + 1008x^6 + 426x^4 + 64x^2 + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.7
Root			$2.88103i$ of defining polynomial
Character	$\chi$	$=$	740.121
Dual form			740.2.i.a.581.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.64482 + 2.84891i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.43427 + 4.21628i) q^{7} +(-3.91088 + 6.77384i) q^{9} +3.55441 q^{11} +(-0.872967 - 1.51202i) q^{13} +(1.64482 - 2.84891i) q^{15} +(1.30594 - 2.26196i) q^{17} +(-3.36801 - 5.83357i) q^{19} +(-8.00788 + 13.8701i) q^{21} +2.56690 q^{23} +(-0.500000 + 0.866025i) q^{25} -15.8619 q^{27} -4.54281 q^{29} +3.31582 q^{31} +(5.84636 + 10.1262i) q^{33} +(2.43427 - 4.21628i) q^{35} +(-1.91177 - 5.77453i) q^{37} +(2.87175 - 4.97402i) q^{39} +(3.12285 + 5.40893i) q^{41} -2.10275 q^{43} +7.82175 q^{45} +7.60303 q^{47} +(-8.35134 + 14.4649i) q^{49} +8.59218 q^{51} +(3.92202 - 6.79315i) q^{53} +(-1.77720 - 3.07821i) q^{55} +(11.0796 - 19.1904i) q^{57} +(-6.62467 + 11.4743i) q^{59} +(0.837134 + 1.44996i) q^{61} -38.0805 q^{63} +(-0.872967 + 1.51202i) q^{65} +(-6.07691 - 10.5255i) q^{67} +(4.22209 + 7.31288i) q^{69} +(-2.18471 - 3.78403i) q^{71} -7.12131 q^{73} -3.28964 q^{75} +(8.65238 + 14.9864i) q^{77} +(4.37194 + 7.57243i) q^{79} +(-14.3573 - 24.8676i) q^{81} +(3.78494 - 6.55571i) q^{83} -2.61189 q^{85} +(-7.47211 - 12.9421i) q^{87} +(6.69509 - 11.5962i) q^{89} +(4.25007 - 7.36134i) q^{91} +(5.45394 + 9.44650i) q^{93} +(-3.36801 + 5.83357i) q^{95} -16.8732 q^{97} +(-13.9008 + 24.0770i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 7 q^{5} + 4 q^{7} - 13 q^{9} + 14 q^{11} + 4 q^{13} + q^{17} + 4 q^{19} - 3 q^{21} + 12 q^{23} - 7 q^{25} - 6 q^{27} - 4 q^{29} - 24 q^{31} + 13 q^{33} + 4 q^{35} + 10 q^{37} + 21 q^{39} + 5 q^{41}+ \cdots - 58 q^{99}+O(q^{100}) $ 14 * q - 7 * q^5 + 4 * q^7 - 13 * q^9 + 14 * q^11 + 4 * q^13 + q^17 + 4 * q^19 - 3 * q^21 + 12 * q^23 - 7 * q^25 - 6 * q^27 - 4 * q^29 - 24 * q^31 + 13 * q^33 + 4 * q^35 + 10 * q^37 + 21 * q^39 + 5 * q^41 - 6 * q^43 + 26 * q^45 - 16 * q^47 - 11 * q^49 + 26 * q^51 + 14 * q^53 - 7 * q^55 + 24 * q^57 - 16 * q^59 + 12 * q^61 - 98 * q^63 + 4 * q^65 + 21 * q^69 - 9 * q^71 - 40 * q^73 + 3 * q^77 + 3 * q^79 - 43 * q^81 + 5 * q^83 - 2 * q^85 + 31 * q^87 + 20 * q^89 - 2 * q^91 + 37 * q^93 + 4 * q^95 - 58 * q^97 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.64482	+	2.84891i	0.949638	+	1.64482i	0.746187	+	0.665737i	$0.231883\pi$
$3$	1.64482	+	2.84891i	0.949638	+	1.64482i	0.203452	+	0.979085i	$0.434784\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	2.43427	+	4.21628i	0.920068	+	1.59360i	0.799308	+	0.600922i	$0.205200\pi$
$7$	2.43427	+	4.21628i	0.920068	+	1.59360i	0.120760	+	0.992682i	$0.461467\pi$
$8$		0			0
$9$	−3.91088	+	6.77384i	−1.30363	+	2.25795i
$10$		0			0
$11$	3.55441			1.07169			0.535847	−	0.844315i	$-0.319992\pi$
$11$	3.55441			1.07169			0.535847	+	0.844315i	$0.319992\pi$
$12$		0			0
$13$	−0.872967	−	1.51202i	−0.242117	−	0.419360i	0.719200	−	0.694803i	$-0.244509\pi$
$13$	−0.872967	−	1.51202i	−0.242117	−	0.419360i	−0.961317	+	0.275444i	$0.911175\pi$
$14$		0			0
$15$	1.64482	−	2.84891i	0.424691	−	0.735587i
$16$		0			0
$17$	1.30594	−	2.26196i	0.316738	−	0.548606i	−0.663068	−	0.748560i	$-0.730746\pi$
$17$	1.30594	−	2.26196i	0.316738	−	0.548606i	0.979805	+	0.199954i	$0.0640791\pi$
$18$		0			0
$19$	−3.36801	−	5.83357i	−0.772675	−	1.33831i	−0.936092	−	0.351755i	$-0.885585\pi$
$19$	−3.36801	−	5.83357i	−0.772675	−	1.33831i	0.163417	−	0.986557i	$-0.447748\pi$
$20$		0			0
$21$	−8.00788	+	13.8701i	−1.74746	+	3.02669i
$22$		0			0
$23$	2.56690			0.535236			0.267618	−	0.963525i	$-0.413764\pi$
$23$	2.56690			0.535236			0.267618	+	0.963525i	$0.413764\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−15.8619			−3.05262
$28$		0			0
$29$	−4.54281			−0.843578			−0.421789	−	0.906694i	$-0.638598\pi$
$29$	−4.54281			−0.843578			−0.421789	+	0.906694i	$0.638598\pi$
$30$		0			0
$31$	3.31582			0.595540			0.297770	−	0.954638i	$-0.403757\pi$
$31$	3.31582			0.595540			0.297770	+	0.954638i	$0.403757\pi$
$32$		0			0
$33$	5.84636	+	10.1262i	1.01772	+	1.76275i
$34$		0			0
$35$	2.43427	−	4.21628i	0.411467	−	0.712681i
$36$		0			0
$37$	−1.91177	−	5.77453i	−0.314292	−	0.949326i
$37$	−1.91177	−	5.77453i	−0.314292	−	0.949326i
$38$		0			0
$39$	2.87175	−	4.97402i	0.459848	−	0.796480i
$40$		0			0
$41$	3.12285	+	5.40893i	0.487706	+	0.844732i	0.999900	−	0.0141376i	$-0.00450030\pi$
$41$	3.12285	+	5.40893i	0.487706	+	0.844732i	−0.512194	+	0.858870i	$0.671167\pi$
$42$		0			0
$43$	−2.10275			−0.320666			−0.160333	−	0.987063i	$-0.551257\pi$
$43$	−2.10275			−0.320666			−0.160333	+	0.987063i	$0.551257\pi$
$44$		0			0
$45$	7.82175			1.16600
$46$		0			0
$47$	7.60303			1.10902			0.554508	−	0.832178i	$-0.312906\pi$
$47$	7.60303			1.10902			0.554508	+	0.832178i	$0.312906\pi$
$48$		0			0
$49$	−8.35134	+	14.4649i	−1.19305	+	2.06642i
$50$		0			0
$51$	8.59218			1.20315
$52$		0			0
$53$	3.92202	−	6.79315i	0.538732	−	0.933110i	−0.460241	−	0.887794i	$-0.652237\pi$
$53$	3.92202	−	6.79315i	0.538732	−	0.933110i	0.998973	−	0.0453165i	$-0.0144296\pi$
$54$		0			0
$55$	−1.77720	−	3.07821i	−0.239638	−	0.415065i
$56$		0			0
$57$	11.0796	−	19.1904i	1.46752	−	2.54183i
$58$		0			0
$59$	−6.62467	+	11.4743i	−0.862458	+	1.49382i	0.00709131	+	0.999975i	$0.497743\pi$
$59$	−6.62467	+	11.4743i	−0.862458	+	1.49382i	−0.869549	+	0.493846i	$0.835591\pi$
$60$		0			0
$61$	0.837134	+	1.44996i	0.107184	+	0.185648i	0.914628	−	0.404296i	$-0.132483\pi$
$61$	0.837134	+	1.44996i	0.107184	+	0.185648i	−0.807444	+	0.589944i	$0.799150\pi$
$62$		0			0
$63$	−38.0805			−4.79770
$64$		0			0
$65$	−0.872967	+	1.51202i	−0.108278	+	0.187543i
$66$		0			0
$67$	−6.07691	−	10.5255i	−0.742412	−	1.28590i	−0.951394	−	0.307976i	$-0.900348\pi$
$67$	−6.07691	−	10.5255i	−0.742412	−	1.28590i	0.208982	−	0.977919i	$-0.432985\pi$
$68$		0			0
$69$	4.22209	+	7.31288i	0.508280	+	0.880367i
$70$		0			0
$71$	−2.18471	−	3.78403i	−0.259277	−	0.449082i	0.706771	−	0.707442i	$-0.250151\pi$
$71$	−2.18471	−	3.78403i	−0.259277	−	0.449082i	−0.966049	+	0.258361i	$0.916818\pi$
$72$		0			0
$73$	−7.12131			−0.833486			−0.416743	−	0.909024i	$-0.636828\pi$
$73$	−7.12131			−0.833486			−0.416743	+	0.909024i	$0.636828\pi$
$74$		0			0
$75$	−3.28964			−0.379855
$76$		0			0
$77$	8.65238	+	14.9864i	0.986031	+	1.70786i
$78$		0			0
$79$	4.37194	+	7.57243i	0.491882	+	0.851965i	0.999956	−	0.00934836i	$-0.00297572\pi$
$79$	4.37194	+	7.57243i	0.491882	+	0.851965i	−0.508074	+	0.861313i	$0.669642\pi$
$80$		0			0
$81$	−14.3573	−	24.8676i	−1.59525	−	2.76306i
$82$		0			0
$83$	3.78494	−	6.55571i	0.415451	−	0.719583i	−0.580024	−	0.814599i	$-0.696957\pi$
$83$	3.78494	−	6.55571i	0.415451	−	0.719583i	0.995476	+	0.0950163i	$0.0302903\pi$
$84$		0			0
$85$	−2.61189			−0.283299
$86$		0			0
$87$	−7.47211	−	12.9421i	−0.801094	−	1.38754i
$88$		0			0
$89$	6.69509	−	11.5962i	0.709678	−	1.22920i	−0.255298	−	0.966862i	$-0.582174\pi$
$89$	6.69509	−	11.5962i	0.709678	−	1.22920i	0.964976	−	0.262337i	$-0.0844931\pi$
$90$		0			0
$91$	4.25007	−	7.36134i	0.445529	−	0.771678i
$92$		0			0
$93$	5.45394	+	9.44650i	0.565547	+	0.979557i
$94$		0			0
$95$	−3.36801	+	5.83357i	−0.345551	+	0.598512i
$96$		0			0
$97$	−16.8732			−1.71322			−0.856608	−	0.515968i	$-0.827432\pi$
$97$	−16.8732			−1.71322			−0.856608	+	0.515968i	$0.827432\pi$
$98$		0			0
$99$	−13.9008	+	24.0770i	−1.39709	+	2.41983i
$100$		0			0
$101$	9.58060			0.953305			0.476653	−	0.879092i	$-0.341850\pi$
$101$	9.58060			0.953305			0.476653	+	0.879092i	$0.341850\pi$
$102$		0			0
$103$	16.2023			1.59646			0.798228	−	0.602355i	$-0.205771\pi$
$103$	16.2023			1.59646			0.798228	+	0.602355i	$0.205771\pi$
$104$		0			0
$105$	16.0158			1.56298
$106$		0			0
$107$	9.51814	+	16.4859i	0.920153	+	1.59375i	0.799176	+	0.601097i	$0.205269\pi$
$107$	9.51814	+	16.4859i	0.920153	+	1.59375i	0.120977	+	0.992655i	$0.461397\pi$
$108$		0			0
$109$	3.24214	−	5.61554i	0.310540	−	0.537872i	−0.667939	−	0.744216i	$-0.732823\pi$
$109$	3.24214	−	5.61554i	0.310540	−	0.537872i	0.978479	+	0.206344i	$0.0661567\pi$
$110$		0			0
$111$	13.3066	−	14.9445i	1.26301	−	1.41847i
$112$		0			0
$113$	−1.93722	+	3.35537i	−0.182239	+	0.315647i	−0.942643	−	0.333804i	$-0.891668\pi$
$113$	−1.93722	+	3.35537i	−0.182239	+	0.315647i	0.760404	+	0.649450i	$0.225001\pi$
$114$		0			0
$115$	−1.28345	−	2.22300i	−0.119682	−	0.207296i
$116$		0			0
$117$	13.6563			1.26252
$118$		0			0
$119$	12.7161			1.16568
$120$		0			0
$121$	1.63380			0.148528
$122$		0			0
$123$	−10.2730	+	17.7934i	−0.926289	+	1.60438i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	5.20320	−	9.01221i	0.461710	−	0.799705i	−0.537337	−	0.843368i	$-0.680570\pi$
$127$	5.20320	−	9.01221i	0.461710	−	0.799705i	0.999046	+	0.0436633i	$0.0139029\pi$
$128$		0			0
$129$	−3.45864	−	5.99054i	−0.304516	−	0.527438i
$130$		0			0
$131$	3.73853	−	6.47533i	0.326637	−	0.565752i	−0.655205	−	0.755451i	$-0.727418\pi$
$131$	3.73853	−	6.47533i	0.326637	−	0.565752i	0.981842	+	0.189699i	$0.0607512\pi$
$132$		0			0
$133$	16.3973	−	28.4010i	1.42183	−	2.46268i
$134$		0			0
$135$	7.93093	+	13.7368i	0.682586	+	1.18227i
$136$		0			0
$137$	6.86658			0.586652			0.293326	−	0.956013i	$-0.405238\pi$
$137$	6.86658			0.586652			0.293326	+	0.956013i	$0.405238\pi$
$138$		0			0
$139$	−0.493431	+	0.854648i	−0.0418523	+	0.0724903i	−0.886193	−	0.463317i	$-0.846659\pi$
$139$	−0.493431	+	0.854648i	−0.0418523	+	0.0724903i	0.844340	+	0.535807i	$0.179993\pi$
$140$		0			0
$141$	12.5056	+	21.6604i	1.05316	+	1.82413i
$142$		0			0
$143$	−3.10288	−	5.37434i	−0.259476	−	0.449425i
$144$		0			0
$145$	2.27140	+	3.93419i	0.188630	+	0.326716i
$146$		0			0
$147$	−54.9459			−4.53186
$148$		0			0
$149$	−1.63931			−0.134298			−0.0671488	−	0.997743i	$-0.521390\pi$
$149$	−1.63931			−0.134298			−0.0671488	+	0.997743i	$0.521390\pi$
$150$		0			0
$151$	−1.20805	−	2.09240i	−0.0983094	−	0.170277i	0.812676	−	0.582716i	$-0.198010\pi$
$151$	−1.20805	−	2.09240i	−0.0983094	−	0.170277i	−0.910985	+	0.412440i	$0.864677\pi$
$152$		0			0
$153$	10.2148	+	17.6925i	0.825815	+	1.43035i
$154$		0			0
$155$	−1.65791	−	2.87159i	−0.133167	−	0.230652i
$156$		0			0
$157$	7.32019	−	12.6789i	0.584215	−	1.01189i	−0.410758	−	0.911745i	$-0.634736\pi$
$157$	7.32019	−	12.6789i	0.584215	−	1.01189i	0.994973	−	0.100146i	$-0.0319309\pi$
$158$		0			0
$159$	25.8041			2.04640
$160$		0			0
$161$	6.24853	+	10.8228i	0.492453	+	0.852954i
$162$		0			0
$163$	−5.67518	+	9.82971i	−0.444515	+	0.769922i	−0.998018	−	0.0629247i	$-0.979957\pi$
$163$	−5.67518	+	9.82971i	−0.444515	+	0.769922i	0.553504	+	0.832847i	$0.313291\pi$
$164$		0			0
$165$	5.84636	−	10.1262i	0.455139	−	0.788324i
$166$		0			0
$167$	7.70599	+	13.3472i	0.596308	+	1.03283i	0.993361	+	0.115039i	$0.0366995\pi$
$167$	7.70599	+	13.3472i	0.596308	+	1.03283i	−0.397053	+	0.917796i	$0.629967\pi$
$168$		0			0
$169$	4.97586	−	8.61844i	0.382758	−	0.662957i
$170$		0			0
$171$	52.6875			4.02912
$172$		0			0
$173$	−5.57527	+	9.65665i	−0.423880	+	0.734182i	−0.996315	−	0.0857684i	$-0.972665\pi$
$173$	−5.57527	+	9.65665i	−0.423880	+	0.734182i	0.572435	+	0.819950i	$0.305999\pi$
$174$		0			0
$175$	−4.86854			−0.368027
$176$		0			0
$177$	−43.5856			−3.27609
$178$		0			0
$179$	−16.9010			−1.26324			−0.631622	−	0.775277i	$-0.717610\pi$
$179$	−16.9010			−1.26324			−0.631622	+	0.775277i	$0.717610\pi$
$180$		0			0
$181$	8.61498	+	14.9216i	0.640346	+	1.10911i	0.985355	+	0.170513i	$0.0545425\pi$
$181$	8.61498	+	14.9216i	0.640346	+	1.10911i	−0.345009	+	0.938599i	$0.612124\pi$
$182$		0			0
$183$	−2.75387	+	4.76985i	−0.203572	+	0.352597i
$184$		0			0
$185$	−4.04500	+	4.54290i	−0.297395	+	0.334001i
$186$		0			0
$187$	4.64185	−	8.03993i	0.339446	−	0.587938i
$188$		0			0
$189$	−38.6120	−	66.8780i	−2.80861	−	4.86466i
$190$		0			0
$191$	−7.82780			−0.566400			−0.283200	−	0.959061i	$-0.591396\pi$
$191$	−7.82780			−0.566400			−0.283200	+	0.959061i	$0.591396\pi$
$192$		0			0
$193$	0.0692318			0.00498341			0.00249171	−	0.999997i	$-0.499207\pi$
$193$	0.0692318			0.00498341			0.00249171	+	0.999997i	$0.499207\pi$
$194$		0			0
$195$	−5.74350			−0.411301
$196$		0			0
$197$	5.07727	−	8.79409i	0.361741	−	0.626553i	−0.626507	−	0.779416i	$-0.715516\pi$
$197$	5.07727	−	8.79409i	0.361741	−	0.626553i	0.988247	+	0.152863i	$0.0488493\pi$
$198$		0			0
$199$	−0.506833			−0.0359284			−0.0179642	−	0.999839i	$-0.505718\pi$
$199$	−0.506833			−0.0359284			−0.0179642	+	0.999839i	$0.505718\pi$
$200$		0			0
$201$	19.9909	−	34.6252i	1.41005	−	2.44227i
$202$		0			0
$203$	−11.0584	−	19.1537i	−0.776149	−	1.34433i
$204$		0			0
$205$	3.12285	−	5.40893i	0.218109	−	0.377776i
$206$		0			0
$207$	−10.0388	+	17.3878i	−0.697747	+	1.20853i
$208$		0			0
$209$	−11.9713	−	20.7349i	−0.828071	−	1.43426i
$210$		0			0
$211$	2.77262			0.190875			0.0954376	−	0.995435i	$-0.469575\pi$
$211$	2.77262			0.190875			0.0954376	+	0.995435i	$0.469575\pi$
$212$		0			0
$213$	7.18692	−	12.4481i	0.492439	−	0.852930i
$214$		0			0
$215$	1.05137	+	1.82103i	0.0717030	+	0.124193i
$216$		0			0
$217$	8.07161	+	13.9804i	0.547937	+	0.949054i
$218$		0			0
$219$	−11.7133	−	20.2880i	−0.791510	−	1.37094i
$220$		0			0
$221$	−4.56018			−0.306751
$222$		0			0
$223$	−9.09828			−0.609266			−0.304633	−	0.952470i	$-0.598534\pi$
$223$	−9.09828			−0.609266			−0.304633	+	0.952470i	$0.598534\pi$
$224$		0			0
$225$	−3.91088	−	6.77384i	−0.260725	−	0.451589i
$226$		0			0
$227$	−2.98215	−	5.16524i	−0.197933	−	0.342829i	0.749925	−	0.661522i	$-0.230089\pi$
$227$	−2.98215	−	5.16524i	−0.197933	−	0.342829i	−0.947858	+	0.318693i	$0.896756\pi$
$228$		0			0
$229$	−0.642125	−	1.11219i	−0.0424328	−	0.0734958i	0.844029	−	0.536298i	$-0.180178\pi$
$229$	−0.642125	−	1.11219i	−0.0424328	−	0.0734958i	−0.886462	+	0.462802i	$0.846844\pi$
$230$		0			0
$231$	−28.4633	+	49.2998i	−1.87275	+	3.24369i
$232$		0			0
$233$	9.34778			0.612394			0.306197	−	0.951968i	$-0.400943\pi$
$233$	9.34778			0.612394			0.306197	+	0.951968i	$0.400943\pi$
$234$		0			0
$235$	−3.80152	−	6.58442i	−0.247984	−	0.429520i
$236$		0			0
$237$	−14.3821	+	24.9106i	−0.934220	+	1.61812i
$238$		0			0
$239$	−0.214233	+	0.371062i	−0.0138576	+	0.0240020i	−0.872871	−	0.487951i	$-0.837744\pi$
$239$	−0.214233	+	0.371062i	−0.0138576	+	0.0240020i	0.859013	+	0.511953i	$0.171078\pi$
$240$		0			0
$241$	−5.39077	−	9.33708i	−0.347250	−	0.601454i	0.638510	−	0.769613i	$-0.279551\pi$
$241$	−5.39077	−	9.33708i	−0.347250	−	0.601454i	−0.985760	+	0.168159i	$0.946218\pi$
$242$		0			0
$243$	23.4376	−	40.5951i	1.50352	−	2.60418i
$244$		0			0
$245$	16.7027			1.06710
$246$		0			0
$247$	−5.88033	+	10.1850i	−0.374156	+	0.648058i
$248$		0			0
$249$	24.9022			1.57811
$250$		0			0
$251$	−9.08886			−0.573684			−0.286842	−	0.957978i	$-0.592605\pi$
$251$	−9.08886			−0.573684			−0.286842	+	0.957978i	$0.592605\pi$
$252$		0			0
$253$	9.12381			0.573609
$254$		0			0
$255$	−4.29609	−	7.44105i	−0.269032	−	0.465976i
$256$		0			0
$257$	−11.2310	+	19.4527i	−0.700571	+	1.21342i	0.267695	+	0.963504i	$0.413738\pi$
$257$	−11.2310	+	19.4527i	−0.700571	+	1.21342i	−0.968266	+	0.249921i	$0.919595\pi$
$258$		0			0
$259$	19.6933	−	22.1173i	1.22368	−	1.37430i
$260$		0			0
$261$	17.7664	−	30.7722i	1.09971	−	1.90475i
$262$		0			0
$263$	−12.4190	−	21.5104i	−0.765791	−	1.32639i	−0.939828	−	0.341649i	$-0.889015\pi$
$263$	−12.4190	−	21.5104i	−0.765791	−	1.32639i	0.174037	−	0.984739i	$-0.444319\pi$
$264$		0			0
$265$	−7.84405			−0.481856
$266$		0			0
$267$	44.0489			2.69575
$268$		0			0
$269$	2.82239			0.172084			0.0860422	−	0.996291i	$-0.472578\pi$
$269$	2.82239			0.172084			0.0860422	+	0.996291i	$0.472578\pi$
$270$		0			0
$271$	6.27217	−	10.8637i	0.381007	−	0.659924i	−0.610199	−	0.792248i	$-0.708911\pi$
$271$	6.27217	−	10.8637i	0.381007	−	0.659924i	0.991207	+	0.132324i	$0.0422439\pi$
$272$		0			0
$273$	27.9625			1.69236
$274$		0			0
$275$	−1.77720	+	3.07821i	−0.107169	+	0.185623i
$276$		0			0
$277$	3.20252	+	5.54692i	0.192421	+	0.333282i	0.946052	−	0.324015i	$-0.105033\pi$
$277$	3.20252	+	5.54692i	0.192421	+	0.333282i	−0.753631	+	0.657297i	$0.771700\pi$
$278$		0			0
$279$	−12.9678	+	22.4609i	−0.776361	+	1.34470i
$280$		0			0
$281$	−1.78255	+	3.08748i	−0.106338	+	0.184183i	−0.914284	−	0.405073i	$-0.867246\pi$
$281$	−1.78255	+	3.08748i	−0.106338	+	0.184183i	0.807946	+	0.589257i	$0.200579\pi$
$282$		0			0
$283$	−10.8012	−	18.7081i	−0.642062	−	1.11208i	−0.984972	−	0.172715i	$-0.944746\pi$
$283$	−10.8012	−	18.7081i	−0.642062	−	1.11208i	0.342910	−	0.939368i	$-0.388587\pi$
$284$		0			0
$285$	−22.1591			−1.31259
$286$		0			0
$287$	−15.2037	+	26.3336i	−0.897446	+	1.55442i
$288$		0			0
$289$	5.08902	+	8.81444i	0.299354	+	0.518497i
$290$		0			0
$291$	−27.7534	−	48.0704i	−1.62693	−	2.81793i
$292$		0			0
$293$	6.89039	+	11.9345i	0.402541	+	0.697222i	0.994032	−	0.109090i	$-0.0347937\pi$
$293$	6.89039	+	11.9345i	0.402541	+	0.697222i	−0.591491	+	0.806312i	$0.701460\pi$
$294$		0			0
$295$	13.2493			0.771406
$296$		0			0
$297$	−56.3795			−3.27147
$298$		0			0
$299$	−2.24082	−	3.88121i	−0.129590	−	0.224456i
$300$		0			0
$301$	−5.11865	−	8.86576i	−0.295034	−	0.511014i
$302$		0			0
$303$	15.7584	+	27.2943i	0.905295	+	1.56802i
$304$		0			0
$305$	0.837134	−	1.44996i	0.0479341	−	0.0830244i
$306$		0			0
$307$	−9.20952			−0.525615			−0.262808	−	0.964848i	$-0.584648\pi$
$307$	−9.20952			−0.525615			−0.262808	+	0.964848i	$0.584648\pi$
$308$		0			0
$309$	26.6498	+	46.1589i	1.51606	+	2.62589i
$310$		0			0
$311$	−14.4589	+	25.0436i	−0.819889	+	1.42009i	0.0858745	+	0.996306i	$0.472632\pi$
$311$	−14.4589	+	25.0436i	−0.819889	+	1.42009i	−0.905764	+	0.423784i	$0.860702\pi$
$312$		0			0
$313$	−3.75246	+	6.49946i	−0.212102	+	0.367371i	−0.952372	−	0.304938i	$-0.901364\pi$
$313$	−3.75246	+	6.49946i	−0.212102	+	0.367371i	0.740270	+	0.672309i	$0.234698\pi$
$314$		0			0
$315$	19.0403	+	32.9787i	1.07280	+	1.85814i
$316$		0			0
$317$	−4.26608	+	7.38907i	−0.239607	+	0.415012i	−0.960602	−	0.277929i	$-0.910352\pi$
$317$	−4.26608	+	7.38907i	−0.239607	+	0.415012i	0.720995	+	0.692941i	$0.243685\pi$
$318$		0			0
$319$	−16.1470			−0.904057
$320$		0			0
$321$	−31.3113	+	54.2327i	−1.74763	+	3.02698i
$322$		0			0
$323$	−17.5937			−0.978942
$324$		0			0
$325$	1.74593			0.0968470
$326$		0			0
$327$	21.3309			1.17960
$328$		0			0
$329$	18.5078	+	32.0565i	1.02037	+	1.76733i
$330$		0			0
$331$	−10.3508	+	17.9281i	−0.568933	+	0.985420i	0.427739	+	0.903902i	$0.359310\pi$
$331$	−10.3508	+	17.9281i	−0.568933	+	0.985420i	−0.996672	+	0.0815180i	$0.974023\pi$
$332$		0			0
$333$	46.5924	+	9.63347i	2.55325	+	0.527911i
$334$		0			0
$335$	−6.07691	+	10.5255i	−0.332017	+	0.575070i
$336$		0			0
$337$	−5.19264	−	8.99392i	−0.282861	−	0.489930i	0.689227	−	0.724546i	$-0.257950\pi$
$337$	−5.19264	−	8.99392i	−0.282861	−	0.489930i	−0.972088	+	0.234615i	$0.924617\pi$
$338$		0			0
$339$	−12.7456			−0.692243
$340$		0			0
$341$	11.7858			0.638236
$342$		0			0
$343$	−47.2379			−2.55061
$344$		0			0
$345$	4.22209	−	7.31288i	0.227310	−	0.393712i
$346$		0			0
$347$	6.81462			0.365828			0.182914	−	0.983129i	$-0.441447\pi$
$347$	6.81462			0.365828			0.182914	+	0.983129i	$0.441447\pi$
$348$		0			0
$349$	−0.228562	+	0.395881i	−0.0122346	+	0.0211910i	−0.872078	−	0.489367i	$-0.837228\pi$
$349$	−0.228562	+	0.395881i	−0.0122346	+	0.0211910i	0.859843	+	0.510558i	$0.170561\pi$
$350$		0			0
$351$	13.8469	+	23.9835i	0.739091	+	1.28014i
$352$		0			0
$353$	9.69143	−	16.7860i	0.515823	−	0.893431i	−0.484009	−	0.875063i	$-0.660820\pi$
$353$	9.69143	−	16.7860i	0.515823	−	0.893431i	0.999831	−	0.0183678i	$-0.00584697\pi$
$354$		0			0
$355$	−2.18471	+	3.78403i	−0.115952	+	0.200835i
$356$		0			0
$357$	20.9157	+	36.2270i	1.10698	+	1.91734i
$358$		0			0
$359$	−1.52846			−0.0806692			−0.0403346	−	0.999186i	$-0.512842\pi$
$359$	−1.52846			−0.0806692			−0.0403346	+	0.999186i	$0.512842\pi$
$360$		0			0
$361$	−13.1870	+	22.8406i	−0.694054	+	1.20214i
$362$		0			0
$363$	2.68731	+	4.65457i	0.141047	+	0.244301i
$364$		0			0
$365$	3.56065	+	6.16723i	0.186373	+	0.322808i
$366$		0			0
$367$	−0.127787	−	0.221334i	−0.00667043	−	0.0115535i	0.862671	−	0.505766i	$-0.168790\pi$
$367$	−0.127787	−	0.221334i	−0.00667043	−	0.0115535i	−0.869341	+	0.494212i	$0.835457\pi$
$368$		0			0
$369$	−48.8523			−2.54315
$370$		0			0
$371$	38.1891			1.98268
$372$		0			0
$373$	−7.37219	−	12.7690i	−0.381717	−	0.661154i	0.609590	−	0.792716i	$-0.291334\pi$
$373$	−7.37219	−	12.7690i	−0.381717	−	0.661154i	−0.991308	+	0.131563i	$0.958001\pi$
$374$		0			0
$375$	1.64482	+	2.84891i	0.0849382	+	0.147117i
$376$		0			0
$377$	3.96572	+	6.86883i	0.204245	+	0.353763i
$378$		0			0
$379$	14.3422	−	24.8413i	0.736707	−	1.27601i	−0.217263	−	0.976113i	$-0.569713\pi$
$379$	14.3422	−	24.8413i	0.736707	−	1.27601i	0.953970	−	0.299901i	$-0.0969537\pi$
$380$		0			0
$381$	34.2334			1.75383
$382$		0			0
$383$	−6.79382	−	11.7672i	−0.347148	−	0.601278i	0.638593	−	0.769544i	$-0.279517\pi$
$383$	−6.79382	−	11.7672i	−0.347148	−	0.601278i	−0.985742	+	0.168266i	$0.946183\pi$
$384$		0			0
$385$	8.65238	−	14.9864i	0.440966	−	0.763776i
$386$		0			0
$387$	8.22358	−	14.2437i	0.418028	−	0.724046i
$388$		0			0
$389$	−14.1622	−	24.5297i	−0.718053	−	1.24370i	−0.961770	−	0.273858i	$-0.911700\pi$
$389$	−14.1622	−	24.5297i	−0.718053	−	1.24370i	0.243718	−	0.969846i	$-0.421633\pi$
$390$		0			0
$391$	3.35223	−	5.80623i	0.169529	−	0.293634i
$392$		0			0
$393$	24.5969			1.24075
$394$		0			0
$395$	4.37194	−	7.57243i	0.219976	−	0.381010i
$396$		0			0
$397$	−26.4002			−1.32499			−0.662493	−	0.749068i	$-0.730502\pi$
$397$	−26.4002			−1.32499			−0.662493	+	0.749068i	$0.730502\pi$
$398$		0			0
$399$	107.883			5.40088
$400$		0			0
$401$	30.5823			1.52721			0.763604	−	0.645685i	$-0.223428\pi$
$401$	30.5823			1.52721			0.763604	+	0.645685i	$0.223428\pi$
$402$		0			0
$403$	−2.89460	−	5.01360i	−0.144191	−	0.249745i
$404$		0			0
$405$	−14.3573	+	24.8676i	−0.713420	+	1.23568i
$406$		0			0
$407$	−6.79519	−	20.5250i	−0.336825	−	1.01739i
$408$		0			0
$409$	−19.3399	+	33.4976i	−0.956294	+	1.65635i	−0.224917	+	0.974378i	$0.572211\pi$
$409$	−19.3399	+	33.4976i	−0.956294	+	1.65635i	−0.731378	+	0.681973i	$0.761122\pi$
$410$		0			0
$411$	11.2943	+	19.5623i	0.557107	+	0.964938i
$412$		0			0
$413$	−64.5049			−3.17408
$414$		0			0
$415$	−7.56988			−0.371591
$416$		0			0
$417$	−3.24643			−0.158978
$418$		0			0
$419$	−1.29640	+	2.24543i	−0.0633332	+	0.109696i	−0.895953	−	0.444148i	$-0.853506\pi$
$419$	−1.29640	+	2.24543i	−0.0633332	+	0.109696i	0.832620	+	0.553844i	$0.186840\pi$
$420$		0			0
$421$	−20.5837			−1.00319			−0.501594	−	0.865103i	$-0.667253\pi$
$421$	−20.5837			−1.00319			−0.501594	+	0.865103i	$0.667253\pi$
$422$		0			0
$423$	−29.7345	+	51.5017i	−1.44574	+	2.50410i
$424$		0			0
$425$	1.30594	+	2.26196i	0.0633476	+	0.109721i
$426$		0			0
$427$	−4.07562	+	7.05918i	−0.197233	+	0.341618i
$428$		0			0
$429$	10.2074	−	17.6797i	0.492816	−	0.853583i
$430$		0			0
$431$	0.943939	+	1.63495i	0.0454680	+	0.0787528i	0.887864	−	0.460106i	$-0.152189\pi$
$431$	0.943939	+	1.63495i	0.0454680	+	0.0787528i	−0.842396	+	0.538859i	$0.818855\pi$
$432$		0			0
$433$	−20.7559			−0.997467			−0.498733	−	0.866756i	$-0.666201\pi$
$433$	−20.7559			−0.997467			−0.498733	+	0.866756i	$0.666201\pi$
$434$		0			0
$435$	−7.47211	+	12.9421i	−0.358260	+	0.620525i
$436$		0			0
$437$	−8.64535	−	14.9742i	−0.413563	−	0.716313i
$438$		0			0
$439$	16.8391	+	29.1661i	0.803685	+	1.39202i	0.917175	+	0.398485i	$0.130464\pi$
$439$	16.8391	+	29.1661i	0.803685	+	1.39202i	−0.113490	+	0.993539i	$0.536203\pi$
$440$		0			0
$441$	−65.3221	−	113.141i	−3.11058	−	5.38768i
$442$		0			0
$443$	24.8309			1.17975			0.589877	−	0.807493i	$-0.299176\pi$
$443$	24.8309			1.17975			0.589877	+	0.807493i	$0.299176\pi$
$444$		0			0
$445$	−13.3902			−0.634756
$446$		0			0
$447$	−2.69637	−	4.67025i	−0.127534	−	0.220895i
$448$		0			0
$449$	8.92761	+	15.4631i	0.421320	+	0.729748i	0.996069	−	0.0885822i	$-0.0282336\pi$
$449$	8.92761	+	15.4631i	0.421320	+	0.729748i	−0.574749	+	0.818330i	$0.694900\pi$
$450$		0			0
$451$	11.0999	+	19.2255i	0.522672	+	0.905294i
$452$		0			0
$453$	3.97404	−	6.88324i	0.186717	−	0.323403i
$454$		0			0
$455$	−8.50015			−0.398493
$456$		0			0
$457$	−11.4312	−	19.7994i	−0.534729	−	0.926178i	−0.999176	−	0.0405773i	$-0.987080\pi$
$457$	−11.4312	−	19.7994i	−0.534729	−	0.926178i	0.464447	−	0.885601i	$-0.346253\pi$
$458$		0			0
$459$	−20.7147	+	35.8789i	−0.966879	+	1.67468i
$460$		0			0
$461$	2.71334	−	4.69963i	0.126373	−	0.218884i	−0.795896	−	0.605433i	$-0.793000\pi$
$461$	2.71334	−	4.69963i	0.126373	−	0.218884i	0.922269	+	0.386550i	$0.126333\pi$
$462$		0			0
$463$	−17.3081	−	29.9785i	−0.804374	−	1.39322i	−0.916713	−	0.399547i	$-0.869167\pi$
$463$	−17.3081	−	29.9785i	−0.804374	−	1.39322i	0.112338	−	0.993670i	$-0.464166\pi$
$464$		0			0
$465$	5.45394	−	9.44650i	0.252920	−	0.438071i
$466$		0			0
$467$	−2.39725			−0.110932			−0.0554658	−	0.998461i	$-0.517664\pi$
$467$	−2.39725			−0.110932			−0.0554658	+	0.998461i	$0.517664\pi$
$468$		0			0
$469$	29.5857	−	51.2439i	1.36614	−	2.36622i
$470$		0			0
$471$	48.1617			2.21917
$472$		0			0
$473$	−7.47401			−0.343655
$474$		0			0
$475$	6.73603			0.309070
$476$		0			0
$477$	30.6771	+	53.1343i	1.40461	+	2.43285i
$478$		0			0
$479$	−0.00205067	+	0.00355186i	−9.36975e−5	+	0.000162289i	−0.866072	−	0.499919i	$-0.833363\pi$
$479$	−0.00205067	+	0.00355186i	−9.36975e−5	+	0.000162289i	0.865979	+	0.500081i	$0.166696\pi$
$480$		0			0
$481$	−7.06231	+	7.93160i	−0.322013	+	0.361650i
$482$		0			0
$483$	−20.5554	+	35.6030i	−0.935304	+	1.61999i
$484$		0			0
$485$	8.43661	+	14.6126i	0.383087	+	0.663525i
$486$		0			0
$487$	14.8134			0.671258			0.335629	−	0.941994i	$-0.391051\pi$
$487$	14.8134			0.671258			0.335629	+	0.941994i	$0.391051\pi$
$488$		0			0
$489$	−37.3387			−1.68851
$490$		0			0
$491$	−40.4508			−1.82552			−0.912761	−	0.408495i	$-0.866054\pi$
$491$	−40.4508			−1.82552			−0.912761	+	0.408495i	$0.866054\pi$
$492$		0			0
$493$	−5.93265	+	10.2757i	−0.267193	+	0.462792i
$494$		0			0
$495$	27.8017			1.24959
$496$		0			0
$497$	10.6363	−	18.4227i	0.477105	−	0.826371i
$498$		0			0
$499$	−9.97119	−	17.2706i	−0.446372	−	0.773138i	0.551775	−	0.833993i	$-0.313951\pi$
$499$	−9.97119	−	17.2706i	−0.446372	−	0.773138i	−0.998147	+	0.0608547i	$0.980617\pi$
$500$		0			0
$501$	−25.3500	+	43.9074i	−1.13255	+	1.96164i
$502$		0			0
$503$	20.9777	−	36.3344i	0.935349	−	1.62007i	0.161339	−	0.986899i	$-0.448419\pi$
$503$	20.9777	−	36.3344i	0.935349	−	1.62007i	0.774010	−	0.633173i	$-0.218248\pi$
$504$		0			0
$505$	−4.79030	−	8.29704i	−0.213166	−	0.369214i
$506$		0			0
$507$	32.7376			1.45393
$508$		0			0
$509$	−11.4043	+	19.7529i	−0.505488	+	0.875530i	0.494492	+	0.869182i	$0.335354\pi$
$509$	−11.4043	+	19.7529i	−0.505488	+	0.875530i	−0.999980	+	0.00634819i	$0.997979\pi$
$510$		0			0
$511$	−17.3352	−	30.0254i	−0.766863	−	1.32825i
$512$		0			0
$513$	53.4229	+	92.5312i	2.35868	+	4.08535i
$514$		0			0
$515$	−8.10113	−	14.0316i	−0.356979	−	0.618305i
$516$		0			0
$517$	27.0243			1.18853
$518$		0			0
$519$	−36.6813			−1.61013
$520$		0			0
$521$	−1.18189	−	2.04710i	−0.0517797	−	0.0896851i	0.838974	−	0.544172i	$-0.183156\pi$
$521$	−1.18189	−	2.04710i	−0.0517797	−	0.0896851i	−0.890754	+	0.454487i	$0.849823\pi$
$522$		0			0
$523$	−14.8751	−	25.7645i	−0.650445	−	1.12660i	−0.983015	−	0.183525i	$-0.941249\pi$
$523$	−14.8751	−	25.7645i	−0.650445	−	1.12660i	0.332570	−	0.943078i	$-0.392084\pi$
$524$		0			0
$525$	−8.00788	−	13.8701i	−0.349493	−	0.605339i
$526$		0			0
$527$	4.33028	−	7.50027i	0.188630	−	0.326717i
$528$		0			0
$529$	−16.4110			−0.713523
$530$		0			0
$531$	−51.8165	−	89.7488i	−2.24864	−	3.89477i
$532$		0			0
$533$	5.45228	−	9.44363i	0.236164	−	0.409049i
$534$		0			0
$535$	9.51814	−	16.4859i	0.411505	−	0.712748i
$536$		0			0
$537$	−27.7992	−	48.1496i	−1.19962	−	2.07781i
$538$		0			0
$539$	−29.6841	+	51.4143i	−1.27858	+	2.21457i
$540$		0			0
$541$	−22.8393			−0.981938			−0.490969	−	0.871177i	$-0.663357\pi$
$541$	−22.8393			−0.981938			−0.490969	+	0.871177i	$0.663357\pi$
$542$		0			0
$543$	−28.3402	+	49.0867i	−1.21619	+	2.10651i
$544$		0			0
$545$	−6.48427			−0.277756
$546$		0			0
$547$	−0.638247			−0.0272895			−0.0136447	−	0.999907i	$-0.504343\pi$
$547$	−0.638247			−0.0272895			−0.0136447	+	0.999907i	$0.504343\pi$
$548$		0			0
$549$	−13.0957			−0.558911
$550$		0			0
$551$	15.3002	+	26.5008i	0.651812	+	1.12897i
$552$		0			0
$553$	−21.2850	+	36.8667i	−0.905130	+	1.56773i
$554$		0			0
$555$	−19.5956	−	4.05161i	−0.831789	−	0.171981i
$556$		0			0
$557$	−11.4810	+	19.8857i	−0.486467	+	0.842586i	−0.999879	−	0.0155565i	$-0.995048\pi$
$557$	−11.4810	+	19.8857i	−0.486467	+	0.842586i	0.513412	+	0.858142i	$0.328381\pi$
$558$		0			0
$559$	1.83563	+	3.17940i	0.0776388	+	0.134474i
$560$		0			0
$561$	30.5401			1.28940
$562$		0			0
$563$	4.79785			0.202205			0.101103	−	0.994876i	$-0.467763\pi$
$563$	4.79785			0.202205			0.101103	+	0.994876i	$0.467763\pi$
$564$		0			0
$565$	3.87445			0.162999
$566$		0			0
$567$	69.8991	−	121.069i	2.93548	−	5.08441i
$568$		0			0
$569$	20.7517			0.869958			0.434979	−	0.900441i	$-0.356756\pi$
$569$	20.7517			0.869958			0.434979	+	0.900441i	$0.356756\pi$
$570$		0			0
$571$	4.43806	−	7.68694i	0.185727	−	0.321688i	−0.758094	−	0.652145i	$-0.773869\pi$
$571$	4.43806	−	7.68694i	0.185727	−	0.321688i	0.943821	+	0.330457i	$0.107203\pi$
$572$		0			0
$573$	−12.8753	−	22.3007i	−0.537875	−	0.931626i
$574$		0			0
$575$	−1.28345	+	2.22300i	−0.0535236	+	0.0927055i
$576$		0			0
$577$	−14.0062	+	24.2594i	−0.583085	+	1.00993i	0.412026	+	0.911172i	$0.364821\pi$
$577$	−14.0062	+	24.2594i	−0.583085	+	1.00993i	−0.995111	+	0.0987610i	$0.968512\pi$
$578$		0			0
$579$	0.113874	+	0.197235i	0.00473244	+	0.00819683i
$580$		0			0
$581$	36.8543			1.52897
$582$		0			0
$583$	13.9405	−	24.1456i	0.577355	−	1.00001i
$584$		0			0
$585$	−6.82813	−	11.8267i	−0.282309	−	0.488973i
$586$		0			0
$587$	−0.338463	−	0.586235i	−0.0139699	−	0.0241965i	0.858956	−	0.512049i	$-0.171114\pi$
$587$	−0.338463	−	0.586235i	−0.0139699	−	0.0241965i	−0.872926	+	0.487853i	$0.837780\pi$
$588$		0			0
$589$	−11.1677	−	19.3431i	−0.460159	−	0.797018i
$590$		0			0
$591$	33.4048			1.37409
$592$		0			0
$593$	2.31917			0.0952368			0.0476184	−	0.998866i	$-0.484837\pi$
$593$	2.31917			0.0952368			0.0476184	+	0.998866i	$0.484837\pi$
$594$		0			0
$595$	−6.35804	−	11.0124i	−0.260654	−	0.451466i
$596$		0			0
$597$	−0.833649	−	1.44392i	−0.0341190	−	0.0590958i
$598$		0			0
$599$	2.95548	+	5.11905i	0.120758	+	0.209159i	0.920067	−	0.391762i	$-0.128134\pi$
$599$	2.95548	+	5.11905i	0.120758	+	0.209159i	−0.799309	+	0.600920i	$0.794801\pi$
$600$		0			0
$601$	−15.7141	+	27.2176i	−0.640991	+	1.11023i	0.344221	+	0.938889i	$0.388143\pi$
$601$	−15.7141	+	27.2176i	−0.640991	+	1.11023i	−0.985212	+	0.171341i	$0.945190\pi$
$602$		0			0
$603$	95.0641			3.87131
$604$		0			0
$605$	−0.816901	−	1.41491i	−0.0332118	−	0.0575245i
$606$		0			0
$607$	−21.0614	+	36.4795i	−0.854858	+	1.48066i	0.0219189	+	0.999760i	$0.493022\pi$
$607$	−21.0614	+	36.4795i	−0.854858	+	1.48066i	−0.876777	+	0.480898i	$0.840311\pi$
$608$		0			0
$609$	36.3783	−	63.0090i	1.47412	−	2.55325i
$610$		0			0
$611$	−6.63720	−	11.4960i	−0.268512	−	0.465077i
$612$		0			0
$613$	1.83191	−	3.17296i	0.0739901	−	0.128155i	−0.826657	−	0.562707i	$-0.809760\pi$
$613$	1.83191	−	3.17296i	0.0739901	−	0.128155i	0.900647	+	0.434552i	$0.143093\pi$
$614$		0			0
$615$	20.5461			0.828499
$616$		0			0
$617$	17.3993	−	30.1365i	0.700471	−	1.21325i	−0.267830	−	0.963466i	$-0.586307\pi$
$617$	17.3993	−	30.1365i	0.700471	−	1.21325i	0.968301	−	0.249786i	$-0.0803601\pi$
$618$		0			0
$619$	−9.38055			−0.377036			−0.188518	−	0.982070i	$-0.560368\pi$
$619$	−9.38055			−0.377036			−0.188518	+	0.982070i	$0.560368\pi$
$620$		0			0
$621$	−40.7158			−1.63387
$622$		0			0
$623$	65.1907			2.61181
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	39.3813	−	68.2103i	1.57274	−	2.72406i
$628$		0			0
$629$	−15.5584	−	3.21687i	−0.620354	−	0.128265i
$630$		0			0
$631$	17.9658	−	31.1177i	0.715208	−	1.23878i	−0.247671	−	0.968844i	$-0.579665\pi$
$631$	17.9658	−	31.1177i	0.715208	−	1.23878i	0.962879	−	0.269933i	$-0.0870015\pi$
$632$		0			0
$633$	4.56047	+	7.89896i	0.181262	+	0.313956i
$634$		0			0
$635$	−10.4064			−0.412966
$636$		0			0
$637$	29.1618			1.15543
$638$		0			0
$639$	34.1765			1.35200
$640$		0			0
$641$	−12.7002	+	21.9974i	−0.501627	+	0.868843i	0.498371	+	0.866964i	$0.333932\pi$
$641$	−12.7002	+	21.9974i	−0.501627	+	0.868843i	−0.999998	+	0.00187955i	$0.999402\pi$
$642$		0			0
$643$	−34.4802			−1.35977			−0.679884	−	0.733320i	$-0.737970\pi$
$643$	−34.4802			−1.35977			−0.679884	+	0.733320i	$0.737970\pi$
$644$		0			0
$645$	−3.45864	+	5.99054i	−0.136184	+	0.235877i
$646$		0			0
$647$	3.23312	+	5.59994i	0.127107	+	0.220156i	0.922555	−	0.385866i	$-0.126097\pi$
$647$	3.23312	+	5.59994i	0.127107	+	0.220156i	−0.795447	+	0.606023i	$0.792764\pi$
$648$		0			0
$649$	−23.5468	+	40.7842i	−0.924291	+	1.60092i
$650$		0			0
$651$	−26.5527	+	45.9907i	−1.04068	+	1.80252i
$652$		0			0
$653$	0.874062	+	1.51392i	0.0342047	+	0.0592443i	0.882621	−	0.470085i	$-0.155777\pi$
$653$	0.874062	+	1.51392i	0.0342047	+	0.0592443i	−0.848416	+	0.529330i	$0.822444\pi$
$654$		0			0
$655$	−7.47706			−0.292153
$656$		0			0
$657$	27.8506	−	48.2386i	1.08655	−	1.88197i
$658$		0			0
$659$	16.5148	+	28.6044i	0.643324	+	1.11427i	0.984686	+	0.174338i	$0.0557784\pi$
$659$	16.5148	+	28.6044i	0.643324	+	1.11427i	−0.341362	+	0.939932i	$0.610888\pi$
$660$		0			0
$661$	23.2194	+	40.2171i	0.903128	+	1.56426i	0.823410	+	0.567447i	$0.192069\pi$
$661$	23.2194	+	40.2171i	0.903128	+	1.56426i	0.0797181	+	0.996817i	$0.474598\pi$
$662$		0			0
$663$	−7.50069	−	12.9916i	−0.291303	−	0.504551i
$664$		0			0
$665$	−32.7946			−1.27172
$666$		0			0
$667$	−11.6609			−0.451513
$668$		0			0
$669$	−14.9650	−	25.9202i	−0.578582	−	1.00213i
$670$		0			0
$671$	2.97551	+	5.15374i	0.114868	+	0.198958i
$672$		0			0
$673$	21.8279	+	37.8071i	0.841404	+	1.45735i	0.888708	+	0.458474i	$0.151604\pi$
$673$	21.8279	+	37.8071i	0.841404	+	1.45735i	−0.0473036	+	0.998881i	$0.515063\pi$
$674$		0			0
$675$	7.93093	−	13.7368i	0.305262	−	0.528728i
$676$		0			0
$677$	−2.98129			−0.114580			−0.0572902	−	0.998358i	$-0.518246\pi$
$677$	−2.98129			−0.114580			−0.0572902	+	0.998358i	$0.518246\pi$
$678$		0			0
$679$	−41.0740	−	71.1422i	−1.57627	−	2.73019i
$680$		0			0
$681$	9.81022	−	16.9918i	0.375929	−	0.651127i
$682$		0			0
$683$	12.7990	−	22.1684i	0.489738	−	0.848252i	−0.510192	−	0.860061i	$-0.670426\pi$
$683$	12.7990	−	22.1684i	0.489738	−	0.848252i	0.999930	+	0.0118088i	$0.00375895\pi$
$684$		0			0
$685$	−3.43329	−	5.94664i	−0.131179	−	0.227209i
$686$		0			0
$687$	2.11236	−	3.65872i	0.0805917	−	0.139589i
$688$		0			0
$689$	−13.6952			−0.521745
$690$		0			0
$691$	11.8554	−	20.5341i	0.450999	−	0.781153i	−0.547449	−	0.836839i	$-0.684401\pi$
$691$	11.8554	−	20.5341i	0.450999	−	0.781153i	0.998448	+	0.0556855i	$0.0177344\pi$
$692$		0			0
$693$	−135.354			−5.14166
$694$		0			0
$695$	0.986863			0.0374338
$696$		0			0
$697$	16.3130			0.617900
$698$		0			0
$699$	15.3754	+	26.6310i	0.581553	+	1.00728i
$700$		0			0
$701$	−0.429472	+	0.743867i	−0.0162209	+	0.0280955i	−0.874022	−	0.485886i	$-0.838497\pi$
$701$	−0.429472	+	0.743867i	−0.0162209	+	0.0280955i	0.857801	+	0.513982i	$0.171830\pi$
$702$		0			0
$703$	−27.2472	+	30.6011i	−1.02765	+	1.15414i
$704$		0			0
$705$	12.5056	−	21.6604i	0.470989	−	0.815778i
$706$		0			0
$707$	23.3218	+	40.3945i	0.877105	+	1.51919i
$708$		0			0
$709$	−16.3732			−0.614907			−0.307453	−	0.951563i	$-0.599477\pi$
$709$	−16.3732			−0.614907			−0.307453	+	0.951563i	$0.599477\pi$
$710$		0			0
$711$	−68.3926			−2.56492
$712$		0			0
$713$	8.51139			0.318754
$714$		0			0
$715$	−3.10288	+	5.37434i	−0.116041	+	0.200989i
$716$		0			0
$717$	−1.40950			−0.0526386
$718$		0			0
$719$	−0.120587	+	0.208864i	−0.00449715	+	0.00778930i	−0.868265	−	0.496100i	$-0.834765\pi$
$719$	−0.120587	+	0.208864i	−0.00449715	+	0.00778930i	0.863768	+	0.503890i	$0.168098\pi$
$720$		0			0
$721$	39.4407	+	68.3133i	1.46885	+	2.54412i
$722$		0			0
$723$	17.7337	−	30.7157i	0.659523	−	1.14233i
$724$		0			0
$725$	2.27140	−	3.93419i	0.0843578	−	0.146112i
$726$		0			0
$727$	−18.1919	−	31.5094i	−0.674702	−	1.16862i	−0.976556	−	0.215263i	$-0.930939\pi$
$727$	−18.1919	−	31.5094i	−0.674702	−	1.16862i	0.301854	−	0.953354i	$-0.402394\pi$
$728$		0			0
$729$	68.0589			2.52070
$730$		0			0
$731$	−2.74607	+	4.75633i	−0.101567	+	0.175919i
$732$		0			0
$733$	20.9919	+	36.3590i	0.775354	+	1.34295i	0.934595	+	0.355712i	$0.115762\pi$
$733$	20.9919	+	36.3590i	0.775354	+	1.34295i	−0.159242	+	0.987240i	$0.550905\pi$
$734$		0			0
$735$	27.4729	+	47.5845i	1.01335	+	1.75518i
$736$		0			0
$737$	−21.5998	−	37.4119i	−0.795638	−	1.37809i
$738$		0			0
$739$	10.4791			0.385478			0.192739	−	0.981250i	$-0.438263\pi$
$739$	10.4791			0.385478			0.192739	+	0.981250i	$0.438263\pi$
$740$		0			0
$741$	−38.6884			−1.42125
$742$		0			0
$743$	−7.74726	−	13.4186i	−0.284219	−	0.492282i	0.688200	−	0.725521i	$-0.258401\pi$
$743$	−7.74726	−	13.4186i	−0.284219	−	0.492282i	−0.972420	+	0.233239i	$0.925068\pi$
$744$		0			0
$745$	0.819655	+	1.41968i	0.0300298	+	0.0520132i
$746$		0			0
$747$	29.6049	+	51.2772i	1.08319	+	1.87613i
$748$		0			0
$749$	−46.3394	+	80.2623i	−1.69321	+	2.93272i
$750$		0			0
$751$	−10.1532			−0.370494			−0.185247	−	0.982692i	$-0.559309\pi$
$751$	−10.1532			−0.370494			−0.185247	+	0.982692i	$0.559309\pi$
$752$		0			0
$753$	−14.9496	−	25.8934i	−0.544792	−	0.943607i
$754$		0			0
$755$	−1.20805	+	2.09240i	−0.0439653	+	0.0761501i
$756$		0			0
$757$	8.40157	−	14.5519i	0.305360	−	0.528899i	−0.671981	−	0.740568i	$-0.734556\pi$
$757$	8.40157	−	14.5519i	0.305360	−	0.528899i	0.977341	+	0.211669i	$0.0678898\pi$
$758$		0			0
$759$	15.0070	+	25.9929i	0.544721	+	0.943484i
$760$		0			0
$761$	7.09381	−	12.2868i	0.257150	−	0.445397i	−0.708327	−	0.705884i	$-0.750550\pi$
$761$	7.09381	−	12.2868i	0.257150	−	0.445397i	0.965477	+	0.260487i	$0.0838831\pi$
$762$		0			0
$763$	31.5689			1.14287
$764$		0			0
$765$	10.2148	−	17.6925i	0.369316	−	0.639674i
$766$		0			0
$767$	23.1325			0.835264
$768$		0			0
$769$	18.5419			0.668637			0.334318	−	0.942460i	$-0.391494\pi$
$769$	18.5419			0.668637			0.334318	+	0.942460i	$0.391494\pi$
$770$		0			0
$771$	−73.8920			−2.66116
$772$		0			0
$773$	−17.6858	−	30.6328i	−0.636115	−	1.10178i	−0.986278	−	0.165095i	$-0.947207\pi$
$773$	−17.6858	−	30.6328i	−0.636115	−	1.10178i	0.350162	−	0.936689i	$-0.386126\pi$
$774$		0			0
$775$	−1.65791	+	2.87159i	−0.0595540	+	0.103151i
$776$		0			0
$777$	95.4022	+	19.7254i	3.42253	+	0.707645i
$778$		0			0
$779$	21.0356	−	36.4347i	0.753677	−	1.30541i
$780$		0			0
$781$	−7.76535	−	13.4500i	−0.277866	−	0.481278i
$782$		0			0
$783$	72.0574			2.57512
$784$		0			0
$785$	−14.6404			−0.522538
$786$		0			0
$787$	7.21829			0.257304			0.128652	−	0.991690i	$-0.458935\pi$
$787$	7.21829			0.257304			0.128652	+	0.991690i	$0.458935\pi$
$788$		0			0
$789$	40.8542	−	70.7616i	1.45445	−	2.51918i
$790$		0			0
$791$	−18.8629			−0.670688
$792$		0			0
$793$	1.46158	−	2.53153i	0.0519022	−	0.0898973i
$794$		0			0
$795$	−12.9021	−	22.3470i	−0.457589	−	0.792567i
$796$		0			0
$797$	11.9780	−	20.7465i	0.424282	−	0.734879i	−0.572071	−	0.820204i	$-0.693860\pi$
$797$	11.9780	−	20.7465i	0.424282	−	0.734879i	0.996353	+	0.0853257i	$0.0271931\pi$
$798$		0			0
$799$	9.92913	−	17.1978i	0.351268	−	0.608413i
$800$		0			0
$801$	52.3674	+	90.7030i	1.85031	+	3.20483i
$802$		0			0
$803$	−25.3120			−0.893242
$804$		0			0
$805$	6.24853	−	10.8228i	0.220232	−	0.381452i
$806$		0			0
$807$	4.64233	+	8.04076i	0.163418	+	0.283048i
$808$		0			0
$809$	17.9360	+	31.0660i	0.630595	+	1.09222i	0.987430	+	0.158056i	$0.0505226\pi$
$809$	17.9360	+	31.0660i	0.630595	+	1.09222i	−0.356835	+	0.934167i	$0.616144\pi$
$810$		0			0
$811$	4.19024	+	7.25772i	0.147139	+	0.254853i	0.930169	−	0.367131i	$-0.119660\pi$
$811$	4.19024	+	7.25772i	0.147139	+	0.254853i	−0.783030	+	0.621984i	$0.786327\pi$
$812$		0			0
$813$	41.2664			1.44728
$814$		0			0
$815$	11.3504			0.397586
$816$		0			0
$817$	7.08208	+	12.2665i	0.247770	+	0.429151i
$818$		0			0
$819$	33.2430	+	57.5786i	1.16161	+	2.01196i
$820$		0			0
$821$	−14.1537	−	24.5149i	−0.493967	−	0.855576i	0.506009	−	0.862528i	$-0.331120\pi$
$821$	−14.1537	−	24.5149i	−0.493967	−	0.855576i	−0.999976	+	0.00695214i	$0.997787\pi$
$822$		0			0
$823$	13.6946	−	23.7198i	0.477365	−	0.826820i	−0.522299	−	0.852763i	$-0.674925\pi$
$823$	13.6946	−	23.7198i	0.477365	−	0.826820i	0.999663	+	0.0259426i	$0.00825870\pi$
$824$		0			0
$825$	−11.6927			−0.407089
$826$		0			0
$827$	4.87153	+	8.43775i	0.169400	+	0.293409i	0.938209	−	0.346069i	$-0.112484\pi$
$827$	4.87153	+	8.43775i	0.169400	+	0.293409i	−0.768809	+	0.639478i	$0.779150\pi$
$828$		0			0
$829$	−7.39100	+	12.8016i	−0.256700	+	0.444617i	−0.965356	−	0.260937i	$-0.915969\pi$
$829$	−7.39100	+	12.8016i	−0.256700	+	0.444617i	0.708656	+	0.705554i	$0.249302\pi$
$830$		0			0
$831$	−10.5351	+	18.2474i	−0.365460	+	0.632995i
$832$		0			0
$833$	21.8128	+	37.7808i	0.755767	+	1.30903i
$834$		0			0
$835$	7.70599	−	13.3472i	0.266677	−	0.461898i
$836$		0			0
$837$	−52.5951			−1.81795
$838$		0			0
$839$	−25.3013	+	43.8232i	−0.873500	+	1.51295i	−0.0151470	+	0.999885i	$0.504822\pi$
$839$	−25.3013	+	43.8232i	−0.873500	+	1.51295i	−0.858353	+	0.513060i	$0.828512\pi$
$840$		0			0
$841$	−8.36290			−0.288376
$842$		0			0
$843$	−11.7279			−0.403932
$844$		0			0
$845$	−9.95172			−0.342349
$846$		0			0
$847$	3.97712	+	6.88857i	0.136655	+	0.236694i
$848$		0			0
$849$	35.5319	−	61.5431i	1.21945	−	2.11215i
$850$		0			0
$851$	−4.90731	−	14.8226i	−0.168221	−	0.508113i
$852$		0			0
$853$	−1.99621	+	3.45754i	−0.0683490	+	0.118384i	−0.898175	−	0.439639i	$-0.855106\pi$
$853$	−1.99621	+	3.45754i	−0.0683490	+	0.118384i	0.829826	+	0.558023i	$0.188440\pi$
$854$		0			0
$855$	−26.3438	−	45.6287i	−0.900938	−	1.56047i
$856$		0			0
$857$	−41.7635			−1.42662			−0.713308	−	0.700851i	$-0.752804\pi$
$857$	−41.7635			−1.42662			−0.713308	+	0.700851i	$0.752804\pi$
$858$		0			0
$859$	−0.204229			−0.00696822			−0.00348411	−	0.999994i	$-0.501109\pi$
$859$	−0.204229			−0.00696822			−0.00348411	+	0.999994i	$0.501109\pi$
$860$		0			0
$861$	−100.029			−3.40900
$862$		0			0
$863$	6.10884	−	10.5808i	0.207947	−	0.360176i	−0.743120	−	0.669158i	$-0.766655\pi$
$863$	6.10884	−	10.5808i	0.207947	−	0.360176i	0.951068	+	0.308982i	$0.0999884\pi$
$864$		0			0
$865$	11.1505			0.379130
$866$		0			0
$867$	−16.7411	+	28.9964i	−0.568556	+	0.984769i
$868$		0			0
$869$	15.5397	+	26.9155i	0.527147	+	0.913046i
$870$		0			0
$871$	−10.6099	+	18.3768i	−0.359502	+	0.622675i
$872$		0			0
$873$	65.9891	−	114.296i	2.23339	−	3.86835i
$874$		0			0
$875$	2.43427	+	4.21628i	0.0822933	+	0.142536i
$876$		0			0
$877$	45.3539			1.53149			0.765746	−	0.643144i	$-0.222370\pi$
$877$	45.3539			1.53149			0.765746	+	0.643144i	$0.222370\pi$
$878$		0			0
$879$	−22.6669	+	39.2603i	−0.764537	+	1.32422i
$880$		0			0
$881$	−25.7108	−	44.5324i	−0.866219	−	1.50034i	−0.865832	−	0.500335i	$-0.833210\pi$
$881$	−25.7108	−	44.5324i	−0.866219	−	1.50034i	−0.000387265	−	1.00000i	$-0.500123\pi$
$882$		0			0
$883$	0.616145	+	1.06719i	0.0207349	+	0.0359140i	0.876207	−	0.481936i	$-0.160066\pi$
$883$	0.616145	+	1.06719i	0.0207349	+	0.0359140i	−0.855472	+	0.517849i	$0.826733\pi$
$884$		0			0
$885$	21.7928	+	37.7462i	0.732557	+	1.26883i
$886$		0			0
$887$	−3.78556			−0.127107			−0.0635533	−	0.997978i	$-0.520243\pi$
$887$	−3.78556			−0.127107			−0.0635533	+	0.997978i	$0.520243\pi$
$888$		0			0
$889$	50.6640			1.69922
$890$		0			0
$891$	−51.0316	−	88.3894i	−1.70962	−	2.96116i
$892$		0			0
$893$	−25.6071	−	44.3528i	−0.856909	−	1.48421i
$894$		0			0
$895$	8.45052	+	14.6367i	0.282470	+	0.489252i
$896$		0			0
$897$	7.37149	−	12.7678i	0.246127	−	0.426305i
$898$		0			0
$899$	−15.0632			−0.502384
$900$		0			0
$901$	−10.2439	−	17.7429i	−0.341273	−	0.591103i
$902$		0			0
$903$	16.8385	−	29.1652i	0.560351	−	0.970557i
$904$		0			0
$905$	8.61498	−	14.9216i	0.286372	−	0.496010i
$906$		0			0
$907$	2.46357	+	4.26703i	0.0818016	+	0.141685i	0.904024	−	0.427482i	$-0.140599\pi$
$907$	2.46357	+	4.26703i	0.0818016	+	0.141685i	−0.822222	+	0.569167i	$0.807266\pi$
$908$		0			0
$909$	−37.4685	+	64.8974i	−1.24275	+	2.15251i
$910$		0			0
$911$	−32.6800			−1.08274			−0.541368	−	0.840786i	$-0.682093\pi$
$911$	−32.6800			−1.08274			−0.541368	+	0.840786i	$0.682093\pi$
$912$		0			0
$913$	13.4532	−	23.3017i	0.445237	−	0.771172i
$914$		0			0
$915$	5.50774			0.182080
$916$		0			0
$917$	36.4024			1.20211
$918$		0			0
$919$	4.87789			0.160907			0.0804533	−	0.996758i	$-0.474363\pi$
$919$	4.87789			0.160907			0.0804533	+	0.996758i	$0.474363\pi$
$920$		0			0
$921$	−15.1480	−	26.2371i	−0.499144	−	0.864543i
$922$		0			0
$923$	−3.81436	+	6.60666i	−0.125551	+	0.217461i
$924$		0			0
$925$	5.95677	+	1.23162i	0.195857	+	0.0404956i
$926$		0			0
$927$	−63.3651	+	109.752i	−2.08118	+	3.60471i
$928$		0			0
$929$	−13.8306	−	23.9553i	−0.453768	−	0.785949i	0.544849	−	0.838534i	$-0.316587\pi$
$929$	−13.8306	−	23.9553i	−0.453768	−	0.785949i	−0.998616	+	0.0525854i	$0.983254\pi$
$930$		0			0
$931$	112.510			3.68736
$932$		0			0
$933$	−95.1293			−3.11439
$934$		0			0
$935$	−9.28371			−0.303610
$936$		0			0
$937$	10.3499	−	17.9265i	0.338116	−	0.585633i	−0.645963	−	0.763369i	$-0.723544\pi$
$937$	10.3499	−	17.9265i	0.338116	−	0.585633i	0.984078	+	0.177736i	$0.0568772\pi$
$938$		0			0
$939$	−24.6885			−0.805680
$940$		0			0
$941$	23.4228	−	40.5694i	0.763560	−	1.32253i	−0.177444	−	0.984131i	$-0.556783\pi$
$941$	23.4228	−	40.5694i	0.763560	−	1.32253i	0.941004	−	0.338394i	$-0.109884\pi$
$942$		0			0
$943$	8.01603	+	13.8842i	0.261038	+	0.452131i
$944$		0			0
$945$	−38.6120	+	66.8780i	−1.25605	+	2.17554i
$946$		0			0
$947$	29.2629	−	50.6847i	0.950915	−	1.64703i	0.207464	−	0.978243i	$-0.433479\pi$
$947$	29.2629	−	50.6847i	0.950915	−	1.64703i	0.743451	−	0.668790i	$-0.233188\pi$
$948$		0			0
$949$	6.21666	+	10.7676i	0.201801	+	0.349530i
$950$		0			0
$951$	−28.0678			−0.910160
$952$		0			0
$953$	−2.00531	+	3.47330i	−0.0649585	+	0.112511i	−0.896676	−	0.442688i	$-0.854025\pi$
$953$	−2.00531	+	3.47330i	−0.0649585	+	0.112511i	0.831717	+	0.555200i	$0.187358\pi$
$954$		0			0
$955$	3.91390	+	6.77907i	0.126651	+	0.219366i
$956$		0			0
$957$	−26.5589	−	46.0014i	−0.858528	−	1.48701i
$958$		0			0
$959$	16.7151	+	28.9514i	0.539759	+	0.934891i
$960$		0			0
$961$	−20.0053			−0.645332
$962$		0			0
$963$	−148.897			−4.79814
$964$		0			0
$965$	−0.0346159	−	0.0599565i	−0.00111433	−	0.00193007i
$966$		0			0
$967$	13.1913	+	22.8480i	0.424203	+	0.734741i	0.996346	−	0.0854130i	$-0.0272210\pi$
$967$	13.1913	+	22.8480i	0.424203	+	0.734741i	−0.572143	+	0.820154i	$0.693888\pi$
$968$		0			0
$969$	−28.9386	−	50.1231i	−0.929641	−	1.61019i
$970$		0			0
$971$	5.34730	−	9.26179i	0.171603	−	0.297225i	−0.767378	−	0.641196i	$-0.778439\pi$
$971$	5.34730	−	9.26179i	0.171603	−	0.297225i	0.938980	+	0.343971i	$0.111772\pi$
$972$		0			0
$973$	−4.80458			−0.154028
$974$		0			0
$975$	2.87175	+	4.97402i	0.0919696	+	0.159296i
$976$		0			0
$977$	21.2797	−	36.8575i	0.680798	−	1.17918i	−0.293940	−	0.955824i	$-0.594967\pi$
$977$	21.2797	−	36.8575i	0.680798	−	1.17918i	0.974738	−	0.223352i	$-0.0717000\pi$
$978$		0			0
$979$	23.7971	−	41.2178i	0.760558	−	1.31733i
$980$		0			0
$981$	25.3592	+	43.9234i	0.809657	+	1.40237i
$982$		0			0
$983$	23.1419	−	40.0829i	0.738112	−	1.27845i	−0.215232	−	0.976563i	$-0.569051\pi$
$983$	23.1419	−	40.0829i	0.738112	−	1.27845i	0.953344	−	0.301885i	$-0.0976158\pi$
$984$		0			0
$985$	−10.1545			−0.323551
$986$		0			0
$987$	−60.8842	+	105.455i	−1.93797	+	3.35665i
$988$		0			0
$989$	−5.39754			−0.171632
$990$		0			0
$991$	30.6194			0.972657			0.486329	−	0.873776i	$-0.338336\pi$
$991$	30.6194			0.972657			0.486329	+	0.873776i	$0.338336\pi$
$992$		0			0
$993$	−68.1010			−2.16112
$994$		0			0
$995$	0.253416	+	0.438930i	0.00803384	+	0.0139150i
$996$		0			0
$997$	−19.2317	+	33.3103i	−0.609075	+	1.05495i	0.382318	+	0.924031i	$0.375126\pi$
$997$	−19.2317	+	33.3103i	−0.609075	+	1.05495i	−0.991393	+	0.130918i	$0.958207\pi$
$998$		0			0
$999$	30.3242	+	91.5947i	0.959414	+	2.89793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.i.a.121.7	✓	14
37.26	even	3	inner	740.2.i.a.581.7	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.i.a.121.7	✓	14	1.1	even	1	trivial
740.2.i.a.581.7	yes	14	37.26	even	3	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.64482 + 2.84891i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.43427 + 4.21628i) q^{7} +(-3.91088 + 6.77384i) q^{9} +3.55441 q^{11} +(-0.872967 - 1.51202i) q^{13} +(1.64482 - 2.84891i) q^{15} +(1.30594 - 2.26196i) q^{17} +(-3.36801 - 5.83357i) q^{19} +(-8.00788 + 13.8701i) q^{21} +2.56690 q^{23} +(-0.500000 + 0.866025i) q^{25} -15.8619 q^{27} -4.54281 q^{29} +3.31582 q^{31} +(5.84636 + 10.1262i) q^{33} +(2.43427 - 4.21628i) q^{35} +(-1.91177 - 5.77453i) q^{37} +(2.87175 - 4.97402i) q^{39} +(3.12285 + 5.40893i) q^{41} -2.10275 q^{43} +7.82175 q^{45} +7.60303 q^{47} +(-8.35134 + 14.4649i) q^{49} +8.59218 q^{51} +(3.92202 - 6.79315i) q^{53} +(-1.77720 - 3.07821i) q^{55} +(11.0796 - 19.1904i) q^{57} +(-6.62467 + 11.4743i) q^{59} +(0.837134 + 1.44996i) q^{61} -38.0805 q^{63} +(-0.872967 + 1.51202i) q^{65} +(-6.07691 - 10.5255i) q^{67} +(4.22209 + 7.31288i) q^{69} +(-2.18471 - 3.78403i) q^{71} -7.12131 q^{73} -3.28964 q^{75} +(8.65238 + 14.9864i) q^{77} +(4.37194 + 7.57243i) q^{79} +(-14.3573 - 24.8676i) q^{81} +(3.78494 - 6.55571i) q^{83} -2.61189 q^{85} +(-7.47211 - 12.9421i) q^{87} +(6.69509 - 11.5962i) q^{89} +(4.25007 - 7.36134i) q^{91} +(5.45394 + 9.44650i) q^{93} +(-3.36801 + 5.83357i) q^{95} -16.8732 q^{97} +(-13.9008 + 24.0770i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 7 q^{5} + 4 q^{7} - 13 q^{9} + 14 q^{11} + 4 q^{13} + q^{17} + 4 q^{19} - 3 q^{21} + 12 q^{23} - 7 q^{25} - 6 q^{27} - 4 q^{29} - 24 q^{31} + 13 q^{33} + 4 q^{35} + 10 q^{37} + 21 q^{39} + 5 q^{41}+ \cdots - 58 q^{99}+O(q^{100}) \) 14 * q - 7 * q^5 + 4 * q^7 - 13 * q^9 + 14 * q^11 + 4 * q^13 + q^17 + 4 * q^19 - 3 * q^21 + 12 * q^23 - 7 * q^25 - 6 * q^27 - 4 * q^29 - 24 * q^31 + 13 * q^33 + 4 * q^35 + 10 * q^37 + 21 * q^39 + 5 * q^41 - 6 * q^43 + 26 * q^45 - 16 * q^47 - 11 * q^49 + 26 * q^51 + 14 * q^53 - 7 * q^55 + 24 * q^57 - 16 * q^59 + 12 * q^61 - 98 * q^63 + 4 * q^65 + 21 * q^69 - 9 * q^71 - 40 * q^73 + 3 * q^77 + 3 * q^79 - 43 * q^81 + 5 * q^83 - 2 * q^85 + 31 * q^87 + 20 * q^89 - 2 * q^91 + 37 * q^93 + 4 * q^95 - 58 * q^97 - 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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