LMFDB - Embedded newform 76.3.j.a.41.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [76,3,Mod(13,76)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(76, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("76.13"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	76.j (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.07085000914$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 93 x^{16} + 3429 x^{14} + 64261 x^{12} + 647217 x^{10} + 3386277 x^{8} + 8232133 x^{6} + \cdots + 69312 $ x^18 + 93x^16 + 3429x^14 + 64261x^12 + 647217x^10 + 3386277x^8 + 8232133x^6 + 8319228x^4 + 2467872x^2 + 69312
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.1
Root			$-3.09175i$ of defining polynomial
Character	$\chi$	$=$	76.41
Dual form			76.3.j.a.13.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.617749 - 1.69725i) q^{3} +(0.757040 - 4.29338i) q^{5} +(-2.41011 - 4.17443i) q^{7} +(4.39535 - 3.68814i) q^{9} +(0.0945208 - 0.163715i) q^{11} +(1.39295 - 3.82710i) q^{13} +(-7.75461 + 1.36735i) q^{15} +(13.1145 + 11.0044i) q^{17} +(-8.88753 + 16.7932i) q^{19} +(-5.59622 + 6.66931i) q^{21} +(2.45173 + 13.9044i) q^{23} +(5.63227 + 2.04998i) q^{25} +(-23.0527 - 13.3095i) q^{27} +(18.3700 + 21.8925i) q^{29} +(-5.92457 + 3.42055i) q^{31} +(-0.336255 - 0.0592909i) q^{33} +(-19.7470 + 7.18732i) q^{35} -31.9736i q^{37} -7.35605 q^{39} +(19.4006 + 53.3028i) q^{41} +(7.16167 - 40.6158i) q^{43} +(-12.5071 - 21.6630i) q^{45} +(44.9103 - 37.6842i) q^{47} +(12.8827 - 22.3136i) q^{49} +(10.5757 - 29.0566i) q^{51} +(-5.32437 + 0.938830i) q^{53} +(-0.631335 - 0.529753i) q^{55} +(33.9926 + 4.71039i) q^{57} +(-36.3323 + 43.2991i) q^{59} +(-15.7238 - 89.1742i) q^{61} +(-25.9892 - 9.45928i) q^{63} +(-15.3767 - 8.87775i) q^{65} +(5.04936 + 6.01760i) q^{67} +(22.0848 - 12.7506i) q^{69} +(23.9368 + 4.22071i) q^{71} +(-111.851 + 40.7104i) q^{73} -10.8258i q^{75} -0.911222 q^{77} +(47.8267 + 131.403i) q^{79} +(0.618357 - 3.50688i) q^{81} +(52.0220 + 90.1047i) q^{83} +(57.1743 - 47.9749i) q^{85} +(25.8090 - 44.7025i) q^{87} +(-52.7400 + 144.902i) q^{89} +(-19.3332 + 3.40896i) q^{91} +(9.46544 + 7.94245i) q^{93} +(65.3715 + 50.8707i) q^{95} +(-52.4375 + 62.4925i) q^{97} +(-0.188351 - 1.06819i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9} - 15 q^{11} + 51 q^{13} + 21 q^{15} - 45 q^{17} + 30 q^{19} - 63 q^{21} + 48 q^{23} - 54 q^{25} - 198 q^{27} - 39 q^{29} - 108 q^{31} - 105 q^{33} + 51 q^{35} + 48 q^{39}+ \cdots - 267 q^{99}+O(q^{100}) $ 18 * q - 6 * q^3 + 9 * q^7 + 6 * q^9 - 15 * q^11 + 51 * q^13 + 21 * q^15 - 45 * q^17 + 30 * q^19 - 63 * q^21 + 48 * q^23 - 54 * q^25 - 198 * q^27 - 39 * q^29 - 108 * q^31 - 105 * q^33 + 51 * q^35 + 48 * q^39 + 54 * q^41 + 75 * q^43 + 288 * q^45 + 339 * q^47 - 24 * q^49 + 360 * q^51 + 69 * q^53 - 51 * q^55 + 510 * q^57 - 483 * q^59 - 36 * q^61 - 267 * q^63 - 585 * q^65 - 87 * q^67 - 351 * q^69 - 234 * q^71 - 132 * q^73 + 108 * q^77 + 363 * q^79 + 258 * q^81 + 279 * q^83 + 666 * q^85 + 600 * q^89 + 270 * q^91 - 456 * q^93 - 39 * q^95 - 801 * q^97 - 267 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$

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
$3$	−0.617749	−	1.69725i	−0.205916	−	0.565751i	0.793147	−	0.609031i	$-0.208441\pi$
$3$	−0.617749	−	1.69725i	−0.205916	−	0.565751i	−0.999063	+	0.0432802i	$0.986219\pi$
$4$		0			0
$5$	0.757040	−	4.29338i	0.151408	−	0.858677i	−0.810589	−	0.585616i	$-0.800853\pi$
$5$	0.757040	−	4.29338i	0.151408	−	0.858677i	0.961997	−	0.273061i	$-0.0880361\pi$
$6$		0			0
$7$	−2.41011	−	4.17443i	−0.344301	−	0.596347i	0.640925	−	0.767603i	$-0.278551\pi$
$7$	−2.41011	−	4.17443i	−0.344301	−	0.596347i	−0.985227	+	0.171256i	$0.945218\pi$
$8$		0			0
$9$	4.39535	−	3.68814i	0.488372	−	0.409793i
$10$		0			0
$11$	0.0945208	−	0.163715i	0.00859280	−	0.0148832i	−0.861697	−	0.507423i	$-0.830598\pi$
$11$	0.0945208	−	0.163715i	0.00859280	−	0.0148832i	0.870290	+	0.492540i	$0.163931\pi$
$12$		0			0
$13$	1.39295	−	3.82710i	0.107150	−	0.294393i	−0.874517	−	0.484994i	$-0.838822\pi$
$13$	1.39295	−	3.82710i	0.107150	−	0.294393i	0.981667	+	0.190602i	$0.0610439\pi$
$14$		0			0
$15$	−7.75461	+	1.36735i	−0.516974	+	0.0911565i
$16$		0			0
$17$	13.1145	+	11.0044i	0.771443	+	0.647317i	0.941078	−	0.338190i	$-0.109814\pi$
$17$	13.1145	+	11.0044i	0.771443	+	0.647317i	−0.169635	+	0.985507i	$0.554259\pi$
$18$		0			0
$19$	−8.88753	+	16.7932i	−0.467765	+	0.883853i
$19$	−8.88753	+	16.7932i	−0.467765	+	0.883853i
$20$		0			0
$21$	−5.59622	+	6.66931i	−0.266487	+	0.317586i
$22$		0			0
$23$	2.45173	+	13.9044i	0.106597	+	0.604541i	0.990571	+	0.137004i	$0.0437473\pi$
$23$	2.45173	+	13.9044i	0.106597	+	0.604541i	−0.883974	+	0.467537i	$0.845142\pi$
$24$		0			0
$25$	5.63227	+	2.04998i	0.225291	+	0.0819992i
$26$		0			0
$27$	−23.0527	−	13.3095i	−0.853803	−	0.492943i
$28$		0			0
$29$	18.3700	+	21.8925i	0.633447	+	0.754913i	0.983320	−	0.181884i	$-0.0582196\pi$
$29$	18.3700	+	21.8925i	0.633447	+	0.754913i	−0.349873	+	0.936797i	$0.613775\pi$
$30$		0			0
$31$	−5.92457	+	3.42055i	−0.191115	+	0.110340i	−0.592505	−	0.805567i	$-0.701861\pi$
$31$	−5.92457	+	3.42055i	−0.191115	+	0.110340i	0.401389	+	0.915908i	$0.368527\pi$
$32$		0			0
$33$	−0.336255	−	0.0592909i	−0.0101896	−	0.00179669i
$34$		0			0
$35$	−19.7470	+	7.18732i	−0.564200	+	0.205352i
$36$		0			0
$37$		−	31.9736i		−	0.864152i	−0.901837	−	0.432076i	$-0.857781\pi$
$37$		−	31.9736i		−	0.864152i	0.901837	−	0.432076i	$-0.142219\pi$
$38$		0			0
$39$	−7.35605			−0.188617
$40$		0			0
$41$	19.4006	+	53.3028i	0.473186	+	1.30007i	0.915178	+	0.403049i	$0.132050\pi$
$41$	19.4006	+	53.3028i	0.473186	+	1.30007i	−0.441993	+	0.897019i	$0.645728\pi$
$42$		0			0
$43$	7.16167	−	40.6158i	0.166550	−	0.944554i	−0.780901	−	0.624655i	$-0.785240\pi$
$43$	7.16167	−	40.6158i	0.166550	−	0.944554i	0.947451	−	0.319899i	$-0.103649\pi$
$44$		0			0
$45$	−12.5071	−	21.6630i	−0.277936	−	0.481400i
$46$		0			0
$47$	44.9103	−	37.6842i	0.955538	−	0.801791i	−0.0246837	−	0.999695i	$-0.507858\pi$
$47$	44.9103	−	37.6842i	0.955538	−	0.801791i	0.980221	+	0.197904i	$0.0634134\pi$
$48$		0			0
$49$	12.8827	−	22.3136i	0.262913	−	0.455379i
$50$		0			0
$51$	10.5757	−	29.0566i	0.207367	−	0.569737i
$52$		0			0
$53$	−5.32437	+	0.938830i	−0.100460	+	0.0177138i	−0.223652	−	0.974669i	$-0.571798\pi$
$53$	−5.32437	+	0.938830i	−0.100460	+	0.0177138i	0.123192	+	0.992383i	$0.460687\pi$
$54$		0			0
$55$	−0.631335	−	0.529753i	−0.0114788	−	0.00963187i
$56$		0			0
$57$	33.9926	+	4.71039i	0.596361	+	0.0826385i
$58$		0			0
$59$	−36.3323	+	43.2991i	−0.615801	+	0.733883i	−0.980342	−	0.197304i	$-0.936781\pi$
$59$	−36.3323	+	43.2991i	−0.615801	+	0.733883i	0.364541	+	0.931187i	$0.381226\pi$
$60$		0			0
$61$	−15.7238	−	89.1742i	−0.257767	−	1.46187i	−0.788868	−	0.614563i	$-0.789332\pi$
$61$	−15.7238	−	89.1742i	−0.257767	−	1.46187i	0.531100	−	0.847309i	$-0.321779\pi$
$62$		0			0
$63$	−25.9892	−	9.45928i	−0.412526	−	0.150147i
$64$		0			0
$65$	−15.3767	−	8.87775i	−0.236565	−	0.136581i
$66$		0			0
$67$	5.04936	+	6.01760i	0.0753637	+	0.0898149i	0.802409	−	0.596775i	$-0.203551\pi$
$67$	5.04936	+	6.01760i	0.0753637	+	0.0898149i	−0.727045	+	0.686590i	$0.759107\pi$
$68$		0			0
$69$	22.0848	−	12.7506i	0.320069	−	0.184792i
$70$		0			0
$71$	23.9368	+	4.22071i	0.337138	+	0.0594466i	0.339655	−	0.940550i	$-0.389690\pi$
$71$	23.9368	+	4.22071i	0.337138	+	0.0594466i	−0.00251622	+	0.999997i	$0.500801\pi$
$72$		0			0
$73$	−111.851	+	40.7104i	−1.53220	+	0.557677i	−0.964160	−	0.265322i	$-0.914522\pi$
$73$	−111.851	+	40.7104i	−1.53220	+	0.557677i	−0.568044	+	0.822998i	$0.692300\pi$
$74$		0			0
$75$		−	10.8258i		−	0.144343i
$76$		0			0
$77$	−0.911222			−0.0118340
$78$		0			0
$79$	47.8267	+	131.403i	0.605401	+	1.66333i	0.740146	+	0.672446i	$0.234756\pi$
$79$	47.8267	+	131.403i	0.605401	+	1.66333i	−0.134745	+	0.990880i	$0.543022\pi$
$80$		0			0
$81$	0.618357	−	3.50688i	0.00763404	−	0.0432948i
$82$		0			0
$83$	52.0220	+	90.1047i	0.626770	+	1.08560i	0.988196	+	0.153197i	$0.0489570\pi$
$83$	52.0220	+	90.1047i	0.626770	+	1.08560i	−0.361425	+	0.932401i	$0.617710\pi$
$84$		0			0
$85$	57.1743	−	47.9749i	0.672639	−	0.564411i
$86$		0			0
$87$	25.8090	−	44.7025i	0.296655	−	0.513822i
$88$		0			0
$89$	−52.7400	+	144.902i	−0.592584	+	1.62811i	0.173108	+	0.984903i	$0.444619\pi$
$89$	−52.7400	+	144.902i	−0.592584	+	1.62811i	−0.765692	+	0.643208i	$0.777603\pi$
$90$		0			0
$91$	−19.3332	+	3.40896i	−0.212452	+	0.0374611i
$92$		0			0
$93$	9.46544	+	7.94245i	0.101779	+	0.0854027i
$94$		0			0
$95$	65.3715	+	50.8707i	0.688121	+	0.535481i
$96$		0			0
$97$	−52.4375	+	62.4925i	−0.540592	+	0.644253i	−0.965320	−	0.261068i	$-0.915925\pi$
$97$	−52.4375	+	62.4925i	−0.540592	+	0.644253i	0.424728	+	0.905321i	$0.360370\pi$
$98$		0			0
$99$	−0.188351	−	1.06819i	−0.00190253	−	0.0107898i
$100$		0			0
$101$	−110.337	−	40.1595i	−1.09245	−	0.397619i	−0.267922	−	0.963441i	$-0.586337\pi$
$101$	−110.337	−	40.1595i	−1.09245	−	0.397619i	−0.824528	+	0.565822i	$0.808559\pi$
$102$		0			0
$103$	−134.487	−	77.6462i	−1.30570	−	0.753846i	−0.324325	−	0.945946i	$-0.605137\pi$
$103$	−134.487	−	77.6462i	−1.30570	−	0.753846i	−0.981376	+	0.192099i	$0.938470\pi$
$104$		0			0
$105$	24.3974	+	29.0756i	0.232356	+	0.276911i
$106$		0			0
$107$	138.583	−	80.0108i	1.29517	−	0.747765i	0.315601	−	0.948892i	$-0.397794\pi$
$107$	138.583	−	80.0108i	1.29517	−	0.747765i	0.979565	+	0.201127i	$0.0644604\pi$
$108$		0			0
$109$	−105.342	−	18.5747i	−0.966443	−	0.170410i	−0.331914	−	0.943310i	$-0.607695\pi$
$109$	−105.342	−	18.5747i	−0.966443	−	0.170410i	−0.634528	+	0.772900i	$0.718806\pi$
$110$		0			0
$111$	−54.2673	+	19.7517i	−0.488894	+	0.177943i
$112$		0			0
$113$			54.9633i			0.486401i	0.969976	+	0.243201i	$0.0781973\pi$
$113$			54.9633i			0.486401i	−0.969976	+	0.243201i	$0.921803\pi$
$114$		0			0
$115$	61.5531			0.535245
$116$		0			0
$117$	−7.99237	−	21.9589i	−0.0683109	−	0.187683i
$118$		0			0
$119$	14.3297	−	81.2675i	0.120417	−	0.682920i
$120$		0			0
$121$	60.4821	+	104.758i	0.499852	+	0.865770i
$122$		0			0
$123$	78.4835	−	65.8555i	0.638077	−	0.535410i
$124$		0			0
$125$	67.5604	−	117.018i	0.540483	−	0.936145i
$126$		0			0
$127$	57.6206	−	158.311i	0.453705	−	1.24655i	−0.476392	−	0.879233i	$-0.658056\pi$
$127$	57.6206	−	158.311i	0.453705	−	1.24655i	0.930098	−	0.367312i	$-0.119722\pi$
$128$		0			0
$129$	−73.3594	+	12.9352i	−0.568677	+	0.100273i
$130$		0			0
$131$	26.6313	+	22.3463i	0.203292	+	0.170582i	0.738750	−	0.673980i	$-0.235416\pi$
$131$	26.6313	+	22.3463i	0.203292	+	0.170582i	−0.535458	+	0.844562i	$0.679861\pi$
$132$		0			0
$133$	91.5220	−	3.37306i	0.688135	−	0.0253613i
$134$		0			0
$135$	−74.5945	+	88.8982i	−0.552552	+	0.658505i
$136$		0			0
$137$	−28.3002	−	160.498i	−0.206571	−	1.17152i	−0.894949	−	0.446169i	$-0.852788\pi$
$137$	−28.3002	−	160.498i	−0.206571	−	1.17152i	0.688378	−	0.725352i	$-0.258323\pi$
$138$		0			0
$139$	24.9206	+	9.07036i	0.179285	+	0.0652544i	0.430103	−	0.902780i	$-0.358477\pi$
$139$	24.9206	+	9.07036i	0.179285	+	0.0652544i	−0.250818	+	0.968034i	$0.580700\pi$
$140$		0			0
$141$	−91.7028	−	52.9447i	−0.650375	−	0.375494i
$142$		0			0
$143$	−0.494891	−	0.589788i	−0.00346077	−	0.00412439i
$144$		0			0
$145$	107.900	−	62.2959i	0.744135	−	0.429627i
$146$		0			0
$147$	−45.8301	−	8.08107i	−0.311769	−	0.0549733i
$148$		0			0
$149$	−147.677	+	53.7500i	−0.991121	+	0.360739i	−0.786154	−	0.618030i	$-0.787931\pi$
$149$	−147.677	+	53.7500i	−0.991121	+	0.360739i	−0.204967	+	0.978769i	$0.565709\pi$
$150$		0			0
$151$			26.7672i			0.177267i	0.996064	+	0.0886333i	$0.0282499\pi$
$151$			26.7672i			0.177267i	−0.996064	+	0.0886333i	$0.971750\pi$
$152$		0			0
$153$	98.2287			0.642017
$154$		0			0
$155$	10.2006	+	28.0260i	0.0658104	+	0.180813i
$156$		0			0
$157$	35.9951	−	204.138i	0.229268	−	1.30024i	−0.625087	−	0.780555i	$-0.714937\pi$
$157$	35.9951	−	204.138i	0.229268	−	1.30024i	0.854355	−	0.519689i	$-0.173952\pi$
$158$		0			0
$159$	4.88255	+	8.45683i	0.0307079	+	0.0531876i
$160$		0			0
$161$	52.1342	−	43.7458i	0.323815	−	0.271713i
$162$		0			0
$163$	−78.8734	+	136.613i	−0.483886	+	0.838115i	−0.999829	−	0.0185078i	$-0.994108\pi$
$163$	−78.8734	+	136.613i	−0.483886	+	0.838115i	0.515943	+	0.856623i	$0.327442\pi$
$164$		0			0
$165$	−0.509117	+	1.39879i	−0.00308556	+	0.00847750i
$166$		0			0
$167$	11.7322	−	2.06870i	0.0702526	−	0.0123874i	−0.138411	−	0.990375i	$-0.544200\pi$
$167$	11.7322	−	2.06870i	0.0702526	−	0.0123874i	0.208664	+	0.977987i	$0.433088\pi$
$168$		0			0
$169$	116.755	+	97.9692i	0.690859	+	0.579699i
$170$		0			0
$171$	22.8718	+	106.590i	0.133753	+	0.623336i
$172$		0			0
$173$	−86.5340	+	103.127i	−0.500197	+	0.596111i	−0.955780	−	0.294082i	$-0.904986\pi$
$173$	−86.5340	+	103.127i	−0.500197	+	0.596111i	0.455584	+	0.890193i	$0.349431\pi$
$174$		0			0
$175$	−5.01689	−	28.4522i	−0.0286680	−	0.162584i
$176$		0			0
$177$	95.9337	+	34.9170i	0.541998	+	0.197271i
$178$		0			0
$179$	−278.151	−	160.591i	−1.55392	−	0.897154i	−0.997817	−	0.0660376i	$-0.978964\pi$
$179$	−278.151	−	160.591i	−1.55392	−	0.897154i	−0.556099	−	0.831116i	$-0.687702\pi$
$180$		0			0
$181$	47.0632	+	56.0877i	0.260017	+	0.309877i	0.880221	−	0.474564i	$-0.157394\pi$
$181$	47.0632	+	56.0877i	0.260017	+	0.309877i	−0.620203	+	0.784441i	$0.712950\pi$
$182$		0			0
$183$	−141.638	+	81.7745i	−0.773976	+	0.446855i
$184$		0			0
$185$	−137.275	−	24.2053i	−0.742027	−	0.130839i
$186$		0			0
$187$	3.04118	−	1.10690i	0.0162630	−	0.00591924i
$188$		0			0
$189$			128.309i			0.678884i
$190$		0			0
$191$	133.689			0.699940			0.349970	−	0.936761i	$-0.386192\pi$
$191$	133.689			0.699940			0.349970	+	0.936761i	$0.386192\pi$
$192$		0			0
$193$	73.5478	+	202.071i	0.381077	+	1.04700i	0.970904	+	0.239470i	$0.0769736\pi$
$193$	73.5478	+	202.071i	0.381077	+	1.04700i	−0.589827	+	0.807529i	$0.700804\pi$
$194$		0			0
$195$	−5.56882	+	31.5824i	−0.0285581	+	0.161961i
$196$		0			0
$197$	62.1141	+	107.585i	0.315300	+	0.546115i	0.979501	−	0.201438i	$-0.0645616\pi$
$197$	62.1141	+	107.585i	0.315300	+	0.546115i	−0.664201	+	0.747554i	$0.731228\pi$
$198$		0			0
$199$	−212.314	+	178.153i	−1.06691	+	0.895240i	−0.994769	−	0.102155i	$-0.967426\pi$
$199$	−212.314	+	178.153i	−1.06691	+	0.895240i	−0.0721368	+	0.997395i	$0.522982\pi$
$200$		0			0
$201$	7.09414	−	12.2874i	0.0352942	−	0.0611314i
$202$		0			0
$203$	47.1150	−	129.447i	0.232094	−	0.637672i
$204$		0			0
$205$	243.536	−	42.9420i	1.18798	−	0.209473i
$206$		0			0
$207$	62.0577	+	52.0726i	0.299795	+	0.251558i
$208$		0			0
$209$	1.90924	+	3.04233i	0.00913512	+	0.0145566i
$210$		0			0
$211$	−160.725	+	191.544i	−0.761729	+	0.907793i	−0.997956	−	0.0639050i	$-0.979645\pi$
$211$	−160.725	+	191.544i	−0.761729	+	0.907793i	0.236227	+	0.971698i	$0.424089\pi$
$212$		0			0
$213$	−7.62335	−	43.2342i	−0.0357904	−	0.202977i
$214$		0			0
$215$	−168.958	−	61.4956i	−0.785850	−	0.286026i
$216$		0			0
$217$	28.5577	+	16.4878i	0.131602	+	0.0759807i
$218$		0			0
$219$	138.192	+	164.690i	0.631012	+	0.752010i
$220$		0			0
$221$	60.3829	−	34.8621i	0.273226	−	0.157747i
$222$		0			0
$223$	109.691	+	19.3415i	0.491887	+	0.0867330i	0.414090	−	0.910236i	$-0.364100\pi$
$223$	109.691	+	19.3415i	0.491887	+	0.0867330i	0.0777978	+	0.996969i	$0.475211\pi$
$224$		0			0
$225$	32.3164	−	11.7622i	0.143629	−	0.0522765i
$226$		0			0
$227$		−	345.131i		−	1.52040i	−0.649689	−	0.760200i	$-0.725101\pi$
$227$		−	345.131i		−	1.52040i	0.649689	−	0.760200i	$-0.274899\pi$
$228$		0			0
$229$	−138.138			−0.603225			−0.301612	−	0.953431i	$-0.597525\pi$
$229$	−138.138			−0.603225			−0.301612	+	0.953431i	$0.597525\pi$
$230$		0			0
$231$	0.562906	+	1.54657i	0.00243682	+	0.00669512i
$232$		0			0
$233$	−16.3333	+	92.6309i	−0.0701002	+	0.397558i	0.929488	+	0.368853i	$0.120249\pi$
$233$	−16.3333	+	92.6309i	−0.0701002	+	0.397558i	−0.999588	+	0.0287048i	$0.990862\pi$
$234$		0			0
$235$	−127.794	−	221.345i	−0.543804	−	0.941896i
$236$		0			0
$237$	193.479	−	162.348i	0.816366	−	0.685012i
$238$		0			0
$239$	106.213	−	183.966i	0.444404	−	0.769731i	−0.553606	−	0.832779i	$-0.686749\pi$
$239$	106.213	−	183.966i	0.444404	−	0.769731i	0.998011	+	0.0630478i	$0.0200821\pi$
$240$		0			0
$241$	10.3102	−	28.3272i	0.0427811	−	0.117540i	−0.916462	−	0.400121i	$-0.868968\pi$
$241$	10.3102	−	28.3272i	0.0427811	−	0.117540i	0.959244	+	0.282581i	$0.0911904\pi$
$242$		0			0
$243$	−242.265	+	42.7178i	−0.996975	+	0.175794i
$244$		0			0
$245$	−86.0480	−	72.2028i	−0.351216	−	0.294705i
$246$		0			0
$247$	51.8894	+	57.4057i	0.210079	+	0.232412i
$248$		0			0
$249$	120.794	−	143.956i	0.485116	−	0.578138i
$250$		0			0
$251$	0.289957	+	1.64443i	0.00115521	+	0.00655150i	0.985380	−	0.170371i	$-0.0544968\pi$
$251$	0.289957	+	1.64443i	0.00115521	+	0.00655150i	−0.984225	+	0.176923i	$0.943386\pi$
$252$		0			0
$253$	2.50810	+	0.912874i	0.00991344	+	0.00360820i
$254$		0			0
$255$	−116.745	−	67.4027i	−0.457823	−	0.264324i
$256$		0			0
$257$	−231.634	−	276.051i	−0.901299	−	1.07413i	−0.996898	−	0.0787067i	$-0.974921\pi$
$257$	−231.634	−	276.051i	−0.901299	−	1.07413i	0.0955985	−	0.995420i	$-0.469523\pi$
$258$		0			0
$259$	−133.472	+	77.0599i	−0.515335	+	0.297529i
$260$		0			0
$261$	161.485	+	28.4742i	0.618716	+	0.109096i
$262$		0			0
$263$	126.255	−	45.9530i	0.480056	−	0.174726i	−0.0906463	−	0.995883i	$-0.528893\pi$
$263$	126.255	−	45.9530i	0.480056	−	0.174726i	0.570702	+	0.821157i	$0.306671\pi$
$264$		0			0
$265$			23.5703i			0.0889445i
$266$		0			0
$267$	278.515			1.04313
$268$		0			0
$269$	−18.1149	−	49.7703i	−0.0673417	−	0.185020i	0.901457	−	0.432869i	$-0.142499\pi$
$269$	−18.1149	−	49.7703i	−0.0673417	−	0.185020i	−0.968799	+	0.247849i	$0.920276\pi$
$270$		0			0
$271$	25.0084	−	141.830i	0.0922819	−	0.523357i	−0.903264	−	0.429084i	$-0.858836\pi$
$271$	25.0084	−	141.830i	0.0922819	−	0.523357i	0.995546	−	0.0942727i	$-0.0300525\pi$
$272$		0			0
$273$	17.7289	+	30.7073i	0.0649410	+	0.112481i
$274$		0			0
$275$	0.867979	−	0.728321i	0.00315629	−	0.00264844i
$276$		0			0
$277$	−36.9790	+	64.0496i	−0.133498	+	0.231226i	−0.925023	−	0.379912i	$-0.875954\pi$
$277$	−36.9790	+	64.0496i	−0.133498	+	0.231226i	0.791524	+	0.611137i	$0.209288\pi$
$278$		0			0
$279$	−13.4251	+	36.8852i	−0.0481187	+	0.132205i
$280$		0			0
$281$	−62.2447	+	10.9754i	−0.221511	+	0.0390584i	−0.283302	−	0.959031i	$-0.591430\pi$
$281$	−62.2447	+	10.9754i	−0.221511	+	0.0390584i	0.0617909	+	0.998089i	$0.480319\pi$
$282$		0			0
$283$	−74.5778	−	62.5782i	−0.263526	−	0.221125i	0.501445	−	0.865190i	$-0.332802\pi$
$283$	−74.5778	−	62.5782i	−0.263526	−	0.221125i	−0.764971	+	0.644065i	$0.777247\pi$
$284$		0			0
$285$	45.9572	−	142.377i	0.161253	−	0.499569i
$286$		0			0
$287$	175.751	−	209.452i	0.612373	−	0.729798i
$288$		0			0
$289$	0.709798	+	4.02546i	0.00245605	+	0.0139289i
$290$		0			0
$291$	138.459	+	50.3949i	0.475803	+	0.173178i
$292$		0			0
$293$	337.975	+	195.130i	1.15350	+	0.665972i	0.949737	−	0.313048i	$-0.101350\pi$
$293$	337.975	+	195.130i	1.15350	+	0.665972i	0.203761	+	0.979021i	$0.434684\pi$
$294$		0			0
$295$	158.395	+	188.767i	0.536931	+	0.639890i
$296$		0			0
$297$	−4.35791	+	2.51604i	−0.0146731	+	0.00847153i
$298$		0			0
$299$	56.6289	+	9.98520i	0.189394	+	0.0333953i
$300$		0			0
$301$	−186.808	+	67.9927i	−0.620626	+	0.225889i
$302$		0			0
$303$			212.079i			0.699930i
$304$		0			0
$305$	−394.763			−1.29430
$306$		0			0
$307$	−16.9626	−	46.6044i	−0.0552528	−	0.151806i	0.908996	−	0.416805i	$-0.136850\pi$
$307$	−16.9626	−	46.6044i	−0.0552528	−	0.151806i	−0.964248	+	0.265000i	$0.914628\pi$
$308$		0			0
$309$	−48.7058	+	276.224i	−0.157624	+	0.893930i
$310$		0			0
$311$	−106.770	−	184.932i	−0.343313	−	0.594636i	0.641732	−	0.766929i	$-0.278216\pi$
$311$	−106.770	−	184.932i	−0.343313	−	0.594636i	−0.985046	+	0.172292i	$0.944883\pi$
$312$		0			0
$313$	148.248	−	124.395i	0.473635	−	0.397427i	−0.374484	−	0.927234i	$-0.622180\pi$
$313$	148.248	−	124.395i	0.473635	−	0.397427i	0.848118	+	0.529807i	$0.177736\pi$
$314$		0			0
$315$	−60.2871	+	104.420i	−0.191388	+	0.331493i
$316$		0			0
$317$	−204.114	+	560.798i	−0.643892	+	1.76908i	−0.00475166	+	0.999989i	$0.501513\pi$
$317$	−204.114	+	560.798i	−0.643892	+	1.76908i	−0.639140	+	0.769090i	$0.720710\pi$
$318$		0			0
$319$	5.32047	−	0.938142i	0.0166786	−	0.00294088i
$320$		0			0
$321$	−221.408	−	185.783i	−0.689744	−	0.578764i
$322$		0			0
$323$	−301.355	+	122.433i	−0.932987	+	0.379050i
$324$		0			0
$325$	15.6910	−	18.6998i	0.0482799	−	0.0575378i
$326$		0			0
$327$	33.5492	+	190.267i	0.102597	+	0.581856i
$328$		0			0
$329$	−265.549	−	96.6518i	−0.807139	−	0.293775i
$330$		0			0
$331$	479.438	+	276.804i	1.44845	+	0.836265i	0.998390	−	0.0567306i	$-0.0180676\pi$
$331$	479.438	+	276.804i	1.44845	+	0.836265i	0.450065	+	0.892996i	$0.351401\pi$
$332$		0			0
$333$	−117.923	−	140.535i	−0.354123	−	0.422028i
$334$		0			0
$335$	29.6584	−	17.1233i	0.0885326	−	0.0511143i
$336$		0			0
$337$	60.2142	+	10.6174i	0.178677	+	0.0315056i	0.262271	−	0.964994i	$-0.415529\pi$
$337$	60.2142	+	10.6174i	0.178677	+	0.0315056i	−0.0835936	+	0.996500i	$0.526640\pi$
$338$		0			0
$339$	93.2866	−	33.9535i	0.275182	−	0.100158i
$340$		0			0
$341$			1.29325i			0.00379253i
$342$		0			0
$343$	−360.386			−1.05069
$344$		0			0
$345$	−38.0244	−	104.471i	−0.110216	−	0.302815i
$346$		0			0
$347$	−34.8091	+	197.412i	−0.100315	+	0.568912i	0.892674	+	0.450703i	$0.148826\pi$
$347$	−34.8091	+	197.412i	−0.100315	+	0.568912i	−0.992989	+	0.118209i	$0.962285\pi$
$348$		0			0
$349$	127.380	+	220.629i	0.364986	+	0.632173i	0.988774	−	0.149420i	$-0.0477406\pi$
$349$	127.380	+	220.629i	0.364986	+	0.632173i	−0.623788	+	0.781593i	$0.714407\pi$
$350$		0			0
$351$	−83.0480	+	69.6856i	−0.236604	+	0.198534i
$352$		0			0
$353$	48.6888	−	84.3315i	0.137929	−	0.238899i	−0.788784	−	0.614671i	$-0.789289\pi$
$353$	48.6888	−	84.3315i	0.137929	−	0.238899i	0.926712	+	0.375771i	$0.122622\pi$
$354$		0			0
$355$	36.2422	−	99.5747i	0.102091	−	0.280492i
$356$		0			0
$357$	−146.784	+	25.8819i	−0.411158	+	0.0724983i
$358$		0			0
$359$	435.611	+	365.521i	1.21340	+	1.01817i	0.999143	+	0.0413888i	$0.0131782\pi$
$359$	435.611	+	365.521i	1.21340	+	1.01817i	0.214259	+	0.976777i	$0.431266\pi$
$360$		0			0
$361$	−203.023	−	298.500i	−0.562392	−	0.826871i
$362$		0			0
$363$	140.438	−	167.368i	0.386882	−	0.461068i
$364$		0			0
$365$	90.1098	+	511.038i	0.246876	+	1.40010i
$366$		0			0
$367$	403.610	+	146.902i	1.09975	+	0.400278i	0.827226	−	0.561870i	$-0.189918\pi$
$367$	403.610	+	146.902i	1.09975	+	0.400278i	0.272529	+	0.962148i	$0.412140\pi$
$368$		0			0
$369$	281.860	+	162.732i	0.763849	+	0.441009i
$370$		0			0
$371$	16.7514	+	19.9635i	0.0451520	+	0.0538101i
$372$		0			0
$373$	168.596	−	97.3387i	0.451999	−	0.260962i	−0.256675	−	0.966498i	$-0.582627\pi$
$373$	168.596	−	97.3387i	0.451999	−	0.260962i	0.708674	+	0.705536i	$0.249294\pi$
$374$		0			0
$375$	−240.344	−	42.3792i	−0.640919	−	0.113011i
$376$		0			0
$377$	109.373	−	39.8086i	0.290115	−	0.105593i
$378$		0			0
$379$		−	296.888i		−	0.783345i	−0.920105	−	0.391672i	$-0.871897\pi$
$379$		−	296.888i		−	0.783345i	0.920105	−	0.391672i	$-0.128103\pi$
$380$		0			0
$381$	−304.289			−0.798659
$382$		0			0
$383$	−86.3957	−	237.370i	−0.225576	−	0.619766i	0.774339	−	0.632771i	$-0.218083\pi$
$383$	−86.3957	−	237.370i	−0.225576	−	0.619766i	−0.999915	+	0.0130049i	$0.995860\pi$
$384$		0			0
$385$	−0.689831	+	3.91222i	−0.00179177	+	0.0101616i
$386$		0			0
$387$	−118.319	−	204.934i	−0.305733	−	0.529545i
$388$		0			0
$389$	−218.384	+	183.246i	−0.561398	+	0.471069i	−0.878779	−	0.477229i	$-0.841641\pi$
$389$	−218.384	+	183.246i	−0.561398	+	0.471069i	0.317381	+	0.948298i	$0.397197\pi$
$390$		0			0
$391$	−120.857	+	209.330i	−0.309096	+	0.535371i
$392$		0			0
$393$	21.4758	−	59.0044i	0.0546459	−	0.150138i
$394$		0			0
$395$	600.369	−	105.861i	1.51992	−	0.268003i
$396$		0			0
$397$	−515.532	−	432.583i	−1.29857	−	1.08963i	−0.990390	−	0.138300i	$-0.955836\pi$
$397$	−515.532	−	432.583i	−1.29857	−	1.08963i	−0.308178	−	0.951329i	$-0.599719\pi$
$398$		0			0
$399$	−62.2626	−	153.252i	−0.156047	−	0.384091i
$400$		0			0
$401$	349.553	−	416.581i	0.871703	−	1.03886i	−0.127193	−	0.991878i	$-0.540597\pi$
$401$	349.553	−	416.581i	0.871703	−	1.03886i	0.998896	−	0.0469775i	$-0.0149589\pi$
$402$		0			0
$403$	4.83817	+	27.4386i	0.0120054	+	0.0680859i
$404$		0			0
$405$	−14.5883	−	5.30969i	−0.0360204	−	0.0131103i
$406$		0			0
$407$	−5.23455	−	3.02217i	−0.0128613	−	0.00742548i
$408$		0			0
$409$	−388.659	−	463.185i	−0.950266	−	1.13248i	−0.991074	−	0.133316i	$-0.957438\pi$
$409$	−388.659	−	463.185i	−0.950266	−	1.13248i	0.0408077	−	0.999167i	$-0.487007\pi$
$410$		0			0
$411$	−254.924	+	147.180i	−0.620253	+	0.358103i
$412$		0			0
$413$	268.314	+	47.3110i	0.649670	+	0.114554i
$414$		0			0
$415$	426.237	−	155.137i	1.02708	−	0.373825i
$416$		0			0
$417$		−	47.8997i		−	0.114867i
$418$		0			0
$419$	66.8368			0.159515			0.0797575	−	0.996814i	$-0.474585\pi$
$419$	66.8368			0.159515			0.0797575	+	0.996814i	$0.474585\pi$
$420$		0			0
$421$	−70.5506	−	193.836i	−0.167579	−	0.460419i	0.827268	−	0.561807i	$-0.189894\pi$
$421$	−70.5506	−	193.836i	−0.167579	−	0.460419i	−0.994847	+	0.101389i	$0.967671\pi$
$422$		0			0
$423$	58.4119	−	331.271i	0.138090	−	0.783145i
$424$		0			0
$425$	51.3058	+	88.8643i	0.120720	+	0.209092i
$426$		0			0
$427$	−334.355	+	280.558i	−0.783034	+	0.657043i
$428$		0			0
$429$	−0.695300	+	1.20429i	−0.00162075	+	0.00280721i
$430$		0			0
$431$	89.0241	−	244.592i	0.206552	−	0.567498i	−0.792552	−	0.609804i	$-0.791248\pi$
$431$	89.0241	−	244.592i	0.206552	−	0.567498i	0.999105	+	0.0423058i	$0.0134704\pi$
$432$		0			0
$433$	−207.053	+	36.5090i	−0.478182	+	0.0843164i	−0.407544	−	0.913186i	$-0.633615\pi$
$433$	−207.053	+	36.5090i	−0.478182	+	0.0843164i	−0.0706382	+	0.997502i	$0.522504\pi$
$434$		0			0
$435$	−172.387	−	144.650i	−0.396291	−	0.332528i
$436$		0			0
$437$	−255.290	−	82.4038i	−0.584187	−	0.188567i
$438$		0			0
$439$	312.137	−	371.990i	0.711018	−	0.847359i	−0.282707	−	0.959206i	$-0.591232\pi$
$439$	312.137	−	371.990i	0.711018	−	0.847359i	0.993725	+	0.111848i	$0.0356768\pi$
$440$		0			0
$441$	−25.6713	−	145.589i	−0.0582116	−	0.330135i
$442$		0			0
$443$	381.133	+	138.721i	0.860346	+	0.313140i	0.734251	−	0.678878i	$-0.237533\pi$
$443$	381.133	+	138.721i	0.860346	+	0.313140i	0.126095	+	0.992018i	$0.459756\pi$
$444$		0			0
$445$	582.193	+	336.129i	1.30830	+	0.755347i
$446$		0			0
$447$	182.455	+	217.441i	0.408176	+	0.486445i
$448$		0			0
$449$	8.43341	−	4.86903i	0.0187826	−	0.0108442i	−0.490579	−	0.871397i	$-0.663215\pi$
$449$	8.43341	−	4.86903i	0.0187826	−	0.0108442i	0.509362	+	0.860552i	$0.329881\pi$
$450$		0			0
$451$	10.5602	+	1.86205i	0.0234151	+	0.00412872i
$452$		0			0
$453$	45.4308	−	16.5354i	0.100289	−	0.0365021i
$454$		0			0
$455$			85.5854i			0.188100i
$456$		0			0
$457$	233.468			0.510871			0.255435	−	0.966826i	$-0.417781\pi$
$457$	233.468			0.510871			0.255435	+	0.966826i	$0.417781\pi$
$458$		0			0
$459$	−155.862	−	428.228i	−0.339569	−	0.932959i
$460$		0			0
$461$	−121.198	+	687.346i	−0.262902	+	1.49099i	0.512043	+	0.858960i	$0.328889\pi$
$461$	−121.198	+	687.346i	−0.262902	+	1.49099i	−0.774944	+	0.632030i	$0.782222\pi$
$462$		0			0
$463$	−380.012	−	658.199i	−0.820759	−	1.42160i	−0.905117	−	0.425162i	$-0.860217\pi$
$463$	−380.012	−	658.199i	−0.820759	−	1.42160i	0.0843581	−	0.996436i	$-0.473116\pi$
$464$		0			0
$465$	41.2657	−	34.6260i	0.0887434	−	0.0744646i
$466$		0			0
$467$	−197.668	+	342.370i	−0.423271	+	0.733127i	−0.996257	−	0.0864380i	$-0.972452\pi$
$467$	−197.668	+	342.370i	−0.423271	+	0.733127i	0.572986	+	0.819565i	$0.305785\pi$
$468$		0			0
$469$	12.9505	−	35.5813i	0.0276131	−	0.0758663i
$470$		0			0
$471$	−368.710	+	65.0135i	−0.782824	+	0.138033i
$472$		0			0
$473$	−5.97249	−	5.01151i	−0.0126268	−	0.0105952i
$474$		0			0
$475$	−84.4828	+	76.3647i	−0.177858	+	0.160768i
$476$		0			0
$477$	−19.9399	+	23.7635i	−0.0418028	+	0.0498186i
$478$		0			0
$479$	69.4029	+	393.603i	0.144891	+	0.821719i	0.967454	+	0.253045i	$0.0814322\pi$
$479$	69.4029	+	393.603i	0.144891	+	0.821719i	−0.822563	+	0.568674i	$0.807457\pi$
$480$		0			0
$481$	−122.366	−	44.5377i	−0.254400	−	0.0925940i
$482$		0			0
$483$	−106.453	−	61.4609i	−0.220400	−	0.127248i
$484$		0			0
$485$	228.607	+	272.443i	0.471355	+	0.561739i
$486$		0			0
$487$	−833.507	+	481.226i	−1.71151	+	0.988143i	−0.778989	+	0.627038i	$0.784267\pi$
$487$	−833.507	+	481.226i	−1.71151	+	0.988143i	−0.932525	+	0.361105i	$0.882400\pi$
$488$		0			0
$489$	280.590	+	49.4756i	0.573804	+	0.101177i
$490$		0			0
$491$	881.263	−	320.754i	1.79483	−	0.653266i	0.795984	−	0.605318i	$-0.206954\pi$
$491$	881.263	−	320.754i	1.79483	−	0.653266i	0.998850	−	0.0479482i	$-0.0152682\pi$
$492$		0			0
$493$			489.260i			0.992414i
$494$		0			0
$495$	−4.72874			−0.00955301
$496$		0			0
$497$	−40.0713	−	110.095i	−0.0806264	−	0.221519i
$498$		0			0
$499$	−53.2720	+	302.121i	−0.106758	+	0.605452i	0.883746	+	0.467966i	$0.155013\pi$
$499$	−53.2720	+	302.121i	−0.106758	+	0.605452i	−0.990504	+	0.137486i	$0.956098\pi$
$500$		0			0
$501$	−10.7587	−	18.6345i	−0.0214744	−	0.0371947i
$502$		0			0
$503$	−705.700	+	592.153i	−1.40298	+	1.17724i	−0.443226	+	0.896410i	$0.646166\pi$
$503$	−705.700	+	592.153i	−1.40298	+	1.17724i	−0.959757	+	0.280832i	$0.909390\pi$
$504$		0			0
$505$	−255.950	+	443.318i	−0.506832	+	0.877858i
$506$		0			0
$507$	94.1530	−	258.683i	0.185706	−	0.510223i
$508$		0			0
$509$	751.063	−	132.433i	1.47557	−	0.260182i	0.622762	−	0.782412i	$-0.286011\pi$
$509$	751.063	−	132.433i	1.47557	−	0.260182i	0.852805	+	0.522229i	$0.174900\pi$
$510$		0			0
$511$	439.516	+	368.797i	0.860109	+	0.721717i
$512$		0			0
$513$	428.390	−	268.840i	0.835069	−	0.524055i
$514$		0			0
$515$	−435.177	+	518.624i	−0.845004	+	1.00704i
$516$		0			0
$517$	−1.92451	−	10.9144i	−0.00372245	−	0.0211111i
$518$		0			0
$519$	228.489	+	83.1633i	0.440249	+	0.160237i
$520$		0			0
$521$	−37.4959	−	21.6483i	−0.0719691	−	0.0415514i	0.463584	−	0.886053i	$-0.346563\pi$
$521$	−37.4959	−	21.6483i	−0.0719691	−	0.0415514i	−0.535553	+	0.844502i	$0.679897\pi$
$522$		0			0
$523$	−511.250	−	609.284i	−0.977533	−	1.16498i	−0.986291	−	0.165017i	$-0.947232\pi$
$523$	−511.250	−	609.284i	−0.977533	−	1.16498i	0.00875793	−	0.999962i	$-0.497212\pi$
$524$		0			0
$525$	−45.1914	+	26.0913i	−0.0860788	+	0.0496976i
$526$		0			0
$527$	−115.339	−	20.3374i	−0.218860	−	0.0385909i
$528$		0			0
$529$	309.775	−	112.749i	0.585586	−	0.213136i
$530$		0			0
$531$			324.313i			0.610759i
$532$		0			0
$533$	231.019			0.433432
$534$		0			0
$535$	−238.605	−	655.561i	−0.445990	−	1.22535i
$536$		0			0
$537$	−100.735	+	571.297i	−0.187589	+	1.06387i
$538$		0			0
$539$	−2.43537	−	4.21819i	−0.00451832	−	0.00782596i
$540$		0			0
$541$	−407.967	+	342.325i	−0.754097	+	0.632763i	−0.936583	−	0.350446i	$-0.886030\pi$
$541$	−407.967	+	342.325i	−0.754097	+	0.632763i	0.182486	+	0.983209i	$0.441586\pi$
$542$		0			0
$543$	66.1217	−	114.526i	0.121771	−	0.210914i
$544$		0			0
$545$	−159.496	+	438.213i	−0.292654	+	0.804061i
$546$		0			0
$547$	6.49765	−	1.14571i	0.0118787	−	0.00209454i	−0.167706	−	0.985837i	$-0.553636\pi$
$547$	6.49765	−	1.14571i	0.0118787	−	0.00209454i	0.179584	+	0.983743i	$0.442525\pi$
$548$		0			0
$549$	−397.998	−	333.960i	−0.724952	−	0.608307i
$550$		0			0
$551$	−530.909	+	113.921i	−0.963536	+	0.206752i
$552$		0			0
$553$	433.264	−	516.344i	0.783480	−	0.933715i
$554$		0			0
$555$	43.7190	+	247.943i	0.0787731	+	0.446744i
$556$		0			0
$557$	−158.030	−	57.5181i	−0.283716	−	0.103264i	0.196242	−	0.980555i	$-0.437126\pi$
$557$	−158.030	−	57.5181i	−0.283716	−	0.103264i	−0.479958	+	0.877291i	$0.659348\pi$
$558$		0			0
$559$	−145.465	−	83.9844i	−0.260224	−	0.150240i
$560$		0			0
$561$	−3.75737	−	4.47786i	−0.00669763	−	0.00798192i
$562$		0			0
$563$	−692.075	+	399.570i	−1.22926	+	0.709715i	−0.966876	−	0.255248i	$-0.917843\pi$
$563$	−692.075	+	399.570i	−1.22926	+	0.709715i	−0.262387	+	0.964963i	$0.584510\pi$
$564$		0			0
$565$	235.979	+	41.6094i	0.417661	+	0.0736450i
$566$		0			0
$567$	−16.1295	+	5.87067i	−0.0284471	+	0.0103539i
$568$		0			0
$569$		−	799.192i		−	1.40456i	−0.711903	−	0.702278i	$-0.752166\pi$
$569$		−	799.192i		−	1.40456i	0.711903	−	0.702278i	$-0.247834\pi$
$570$		0			0
$571$	761.851			1.33424			0.667120	−	0.744950i	$-0.267527\pi$
$571$	761.851			1.33424			0.667120	+	0.744950i	$0.267527\pi$
$572$		0			0
$573$	−82.5860	−	226.903i	−0.144129	−	0.395991i
$574$		0			0
$575$	−14.6950	+	83.3396i	−0.0255565	+	0.144938i
$576$		0			0
$577$	88.2589	+	152.869i	0.152962	+	0.264937i	0.932315	−	0.361647i	$-0.117786\pi$
$577$	88.2589	+	152.869i	0.152962	+	0.264937i	−0.779353	+	0.626585i	$0.784452\pi$
$578$		0			0
$579$	297.531	−	249.658i	0.513871	−	0.431189i
$580$		0			0
$581$	250.757	−	434.324i	0.431596	−	0.747546i
$582$		0			0
$583$	−0.349563	+	0.960417i	−0.000599594	+	0.00164737i
$584$		0			0
$585$	−100.328	+	17.6906i	−0.171502	+	0.0302404i
$586$		0			0
$587$	260.508	+	218.592i	0.443796	+	0.372389i	0.837128	−	0.547007i	$-0.184233\pi$
$587$	260.508	+	218.592i	0.443796	+	0.372389i	−0.393332	+	0.919397i	$0.628678\pi$
$588$		0			0
$589$	−4.78722	−	129.893i	−0.00812771	−	0.220531i
$590$		0			0
$591$	144.227	−	171.884i	0.244040	−	0.290835i
$592$		0			0
$593$	29.4003	+	166.737i	0.0495789	+	0.281176i	0.999511	−	0.0312817i	$-0.00995889\pi$
$593$	29.4003	+	166.737i	0.0495789	+	0.281176i	−0.949932	+	0.312458i	$0.898848\pi$
$594$		0			0
$595$	−338.064	−	123.045i	−0.568176	−	0.206799i
$596$		0			0
$597$	433.527	+	250.297i	0.726176	+	0.419258i
$598$		0			0
$599$	−27.9949	−	33.3630i	−0.0467361	−	0.0556979i	0.742170	−	0.670212i	$-0.233797\pi$
$599$	−27.9949	−	33.3630i	−0.0467361	−	0.0556979i	−0.788906	+	0.614514i	$0.789352\pi$
$600$		0			0
$601$	829.079	−	478.669i	1.37950	−	0.796454i	0.387400	−	0.921912i	$-0.373373\pi$
$601$	829.079	−	478.669i	1.37950	−	0.796454i	0.992099	+	0.125458i	$0.0400400\pi$
$602$		0			0
$603$	44.3875	+	7.82671i	0.0736110	+	0.0129796i
$604$		0			0
$605$	495.554	−	180.367i	0.819098	−	0.298127i
$606$		0			0
$607$			383.700i			0.632124i	0.948738	+	0.316062i	$0.102361\pi$
$607$			383.700i			0.632124i	−0.948738	+	0.316062i	$0.897639\pi$
$608$		0			0
$609$	−248.810			−0.408555
$610$		0			0
$611$	−81.6635	−	224.369i	−0.133655	−	0.367215i
$612$		0			0
$613$	92.6661	−	525.535i	0.151168	−	0.857317i	−0.811038	−	0.584994i	$-0.801097\pi$
$613$	92.6661	−	525.535i	0.151168	−	0.857317i	0.962206	−	0.272323i	$-0.0877920\pi$
$614$		0			0
$615$	−223.328	−	386.815i	−0.363135	−	0.628967i
$616$		0			0
$617$	−522.562	+	438.481i	−0.846940	+	0.710667i	−0.959113	−	0.283022i	$-0.908663\pi$
$617$	−522.562	+	438.481i	−0.846940	+	0.710667i	0.112174	+	0.993689i	$0.464219\pi$
$618$		0			0
$619$	−90.2029	+	156.236i	−0.145724	+	0.252401i	−0.929643	−	0.368462i	$-0.879884\pi$
$619$	−90.2029	+	156.236i	−0.145724	+	0.252401i	0.783919	+	0.620863i	$0.213218\pi$
$620$		0			0
$621$	128.542	−	353.166i	0.206992	−	0.568705i
$622$		0			0
$623$	731.992	−	129.070i	1.17495	−	0.207175i
$624$		0			0
$625$	−336.471	−	282.333i	−0.538353	−	0.451732i
$626$		0			0
$627$	3.98416	−	5.11985i	0.00635433	−	0.00816564i
$628$		0			0
$629$	351.850	−	419.319i	0.559380	−	0.666644i
$630$		0			0
$631$	−104.292	−	591.469i	−0.165280	−	0.937351i	−0.948775	−	0.315953i	$-0.897676\pi$
$631$	−104.292	−	591.469i	−0.165280	−	0.937351i	0.783495	−	0.621399i	$-0.213435\pi$
$632$		0			0
$633$	424.386	+	154.464i	0.670437	+	0.244019i
$634$		0			0
$635$	−636.070	−	367.235i	−1.00169	−	0.578323i
$636$		0			0
$637$	−67.4513	−	80.3854i	−0.105889	−	0.126194i
$638$		0			0
$639$	120.777	−	69.7308i	0.189010	−	0.109125i
$640$		0			0
$641$	−762.921	−	134.524i	−1.19020	−	0.209865i	−0.456744	−	0.889598i	$-0.650985\pi$
$641$	−762.921	−	134.524i	−1.19020	−	0.209865i	−0.733460	+	0.679733i	$0.762096\pi$
$642$		0			0
$643$	101.877	−	37.0801i	0.158440	−	0.0576674i	−0.261583	−	0.965181i	$-0.584244\pi$
$643$	101.877	−	37.0801i	0.158440	−	0.0576674i	0.420023	+	0.907514i	$0.362022\pi$
$644$		0			0
$645$			324.753i			0.503492i
$646$		0			0
$647$	−230.970			−0.356986			−0.178493	−	0.983941i	$-0.557122\pi$
$647$	−230.970			−0.356986			−0.178493	+	0.983941i	$0.557122\pi$
$648$		0			0
$649$	3.65455	+	10.0408i	0.00563105	+	0.0154712i
$650$		0			0
$651$	10.3425	−	58.6550i	0.0158870	−	0.0900998i
$652$		0			0
$653$	341.320	+	591.183i	0.522695	+	0.905334i	0.999651	+	0.0264072i	$0.00840665\pi$
$653$	341.320	+	591.183i	0.522695	+	0.905334i	−0.476956	+	0.878927i	$0.658260\pi$
$654$		0			0
$655$	116.102	−	97.4213i	0.177255	−	0.148735i
$656$		0			0
$657$	−341.478	+	591.458i	−0.519754	+	0.900240i
$658$		0			0
$659$	212.474	−	583.768i	0.322419	−	0.885839i	−0.667551	−	0.744564i	$-0.732657\pi$
$659$	212.474	−	583.768i	0.322419	−	0.885839i	0.989970	−	0.141275i	$-0.0451203\pi$
$660$		0			0
$661$	−1006.10	+	177.403i	−1.52209	+	0.268386i	−0.871255	−	0.490831i	$-0.836693\pi$
$661$	−1006.10	+	177.403i	−1.52209	+	0.268386i	−0.650838	+	0.759217i	$0.725582\pi$
$662$		0			0
$663$	−96.4712	−	80.9489i	−0.145507	−	0.122095i
$664$		0			0
$665$	54.8039	−	395.493i	0.0824120	−	0.594726i
$666$		0			0
$667$	−259.364	+	309.098i	−0.388852	+	0.463416i
$668$		0			0
$669$	−34.9341	−	198.121i	−0.0522184	−	0.296145i
$670$		0			0
$671$	−16.0854	−	5.85459i	−0.0239722	−	0.00872518i
$672$		0			0
$673$	753.056	+	434.777i	1.11895	+	0.646028i	0.941134	−	0.338035i	$-0.109762\pi$
$673$	753.056	+	434.777i	1.11895	+	0.646028i	0.177820	+	0.984063i	$0.443095\pi$
$674$		0			0
$675$	−102.555	−	122.220i	−0.151933	−	0.181067i
$676$		0			0
$677$	523.041	−	301.978i	0.772587	−	0.446053i	−0.0612099	−	0.998125i	$-0.519496\pi$
$677$	523.041	−	301.978i	0.772587	−	0.446053i	0.833797	+	0.552072i	$0.186163\pi$
$678$		0			0
$679$	387.251	+	68.2828i	0.570325	+	0.100564i
$680$		0			0
$681$	−585.774	+	213.204i	−0.860167	+	0.313075i
$682$		0			0
$683$		−	192.200i		−	0.281406i	−0.990052	−	0.140703i	$-0.955064\pi$
$683$		−	192.200i		−	0.281406i	0.990052	−	0.140703i	$-0.0449363\pi$
$684$		0			0
$685$	−710.506			−1.03724
$686$		0			0
$687$	85.3349	+	234.456i	0.124214	+	0.341275i
$688$		0			0
$689$	−3.82359	+	21.6847i	−0.00554948	+	0.0314727i
$690$		0			0
$691$	119.347	+	206.715i	0.172716	+	0.299154i	0.939369	−	0.342909i	$-0.111412\pi$
$691$	119.347	+	206.715i	0.172716	+	0.299154i	−0.766652	+	0.642063i	$0.778079\pi$
$692$		0			0
$693$	−4.00514	+	3.36071i	−0.00577942	+	0.00484951i
$694$		0			0
$695$	57.8084	−	100.127i	0.0831776	−	0.144068i
$696$		0			0
$697$	−332.135	+	912.533i	−0.476520	+	1.30923i
$698$		0			0
$699$	167.308	−	29.5009i	0.239353	−	0.0422044i
$700$		0			0
$701$	13.1679	+	11.0492i	0.0187845	+	0.0157621i	0.652132	−	0.758106i	$-0.273875\pi$
$701$	13.1679	+	11.0492i	0.0187845	+	0.0157621i	−0.633347	+	0.773868i	$0.718319\pi$
$702$		0			0
$703$	536.939	+	284.167i	0.763783	+	0.404220i
$704$		0			0
$705$	−296.734	+	353.634i	−0.420900	+	0.501609i
$706$		0			0
$707$	98.2820	+	557.385i	0.139013	+	0.788380i
$708$		0			0
$709$	89.6670	+	32.6361i	0.126470	+	0.0460312i	0.404480	−	0.914547i	$-0.367453\pi$
$709$	89.6670	+	32.6361i	0.126470	+	0.0460312i	−0.278010	+	0.960578i	$0.589675\pi$
$710$		0			0
$711$	694.847	+	401.170i	0.977281	+	0.564233i
$712$		0			0
$713$	−62.0863	−	73.9916i	−0.0870776	−	0.103775i
$714$		0			0
$715$	−2.90684	+	1.67826i	−0.00406551	+	0.00234722i
$716$		0			0
$717$	−377.849	−	66.6249i	−0.526986	−	0.0929218i
$718$		0			0
$719$	−458.305	+	166.809i	−0.637420	+	0.232002i	−0.640458	−	0.767994i	$-0.721255\pi$
$719$	−458.305	+	166.809i	−0.637420	+	0.232002i	0.00303783	+	0.999995i	$0.499033\pi$
$720$		0			0
$721$			748.543i			1.03820i
$722$		0			0
$723$	−54.4475			−0.0753077
$724$		0			0
$725$	58.5856	+	160.962i	0.0808077	+	0.222017i
$726$		0			0
$727$	−1.77453	+	10.0639i	−0.00244090	+	0.0138430i	−0.986004	−	0.166722i	$-0.946682\pi$
$727$	−1.77453	+	10.0639i	−0.00244090	+	0.0138430i	0.983563	+	0.180565i	$0.0577927\pi$
$728$		0			0
$729$	206.137	+	357.041i	0.282767	+	0.489768i
$730$		0			0
$731$	540.875	−	453.848i	0.739910	−	0.620859i
$732$		0			0
$733$	251.354	−	435.357i	0.342911	−	0.593939i	−0.642061	−	0.766653i	$-0.721920\pi$
$733$	251.354	−	435.357i	0.342911	−	0.593939i	0.984972	+	0.172714i	$0.0552538\pi$
$734$		0			0
$735$	−69.3903	+	190.648i	−0.0944086	+	0.259385i
$736$		0			0
$737$	1.46244	−	0.257868i	0.00198431	−	0.000349888i
$738$		0			0
$739$	−172.968	−	145.138i	−0.234057	−	0.196397i	0.518214	−	0.855251i	$-0.326597\pi$
$739$	−172.968	−	145.138i	−0.234057	−	0.196397i	−0.752271	+	0.658854i	$0.771042\pi$
$740$		0			0
$741$	65.3772	−	123.532i	0.0882283	−	0.166709i
$742$		0			0
$743$	22.9359	−	27.3339i	0.0308693	−	0.0367886i	−0.750389	−	0.660997i	$-0.770134\pi$
$743$	22.9359	−	27.3339i	0.0308693	−	0.0367886i	0.781258	+	0.624208i	$0.214578\pi$
$744$		0			0
$745$	118.972	+	674.725i	0.159694	+	0.905671i
$746$		0			0
$747$	560.973	+	204.178i	0.750968	+	0.273330i
$748$		0			0
$749$	−667.999	−	385.670i	−0.891855	−	0.514913i
$750$		0			0
$751$	662.322	+	789.325i	0.881920	+	1.05103i	0.998326	+	0.0578298i	$0.0184181\pi$
$751$	662.322	+	789.325i	0.881920	+	1.05103i	−0.116406	+	0.993202i	$0.537137\pi$
$752$		0			0
$753$	2.61189	−	1.50797i	0.00346864	−	0.00200262i
$754$		0			0
$755$	114.922	+	20.2639i	0.152215	+	0.0268396i
$756$		0			0
$757$	−1300.99	+	473.521i	−1.71861	+	0.625524i	−0.997718	−	0.0675215i	$-0.978491\pi$
$757$	−1300.99	+	473.521i	−1.71861	+	0.625524i	−0.720894	+	0.693045i	$0.756269\pi$
$758$		0			0
$759$		−	4.82081i		−	0.00635152i
$760$		0			0
$761$	−723.684			−0.950965			−0.475483	−	0.879725i	$-0.657727\pi$
$761$	−723.684			−0.950965			−0.475483	+	0.879725i	$0.657727\pi$
$762$		0			0
$763$	176.348	+	484.511i	0.231124	+	0.635008i
$764$		0			0
$765$	74.3630	−	421.733i	0.0972065	−	0.551286i
$766$		0			0
$767$	115.101	+	199.361i	0.150067	+	0.259923i
$768$		0			0
$769$	726.061	−	609.238i	0.944163	−	0.792247i	−0.0341420	−	0.999417i	$-0.510870\pi$
$769$	726.061	−	609.238i	0.944163	−	0.792247i	0.978305	+	0.207170i	$0.0664254\pi$
$770$		0			0
$771$	−325.436	+	563.671i	−0.422095	+	0.731091i
$772$		0			0
$773$	−190.354	+	522.993i	−0.246253	+	0.676575i	0.753562	+	0.657376i	$0.228334\pi$
$773$	−190.354	+	522.993i	−0.246253	+	0.676575i	−0.999816	+	0.0191990i	$0.993888\pi$
$774$		0			0
$775$	−40.3809	+	7.12024i	−0.0521044	+	0.00918740i
$776$		0			0
$777$	213.242	+	178.931i	0.274443	+	0.230285i
$778$		0			0
$779$	−1067.55	−	147.932i	−1.37041	−	0.189899i
$780$		0			0
$781$	2.95352	−	3.51987i	0.00378172	−	0.00450687i
$782$		0			0
$783$	−132.100	−	749.175i	−0.168710	−	0.956801i
$784$		0			0
$785$	−849.194	−	309.082i	−1.08178	−	0.393734i
$786$		0			0
$787$	−296.622	−	171.255i	−0.376902	−	0.217604i	0.299568	−	0.954075i	$-0.403158\pi$
$787$	−296.622	−	171.255i	−0.376902	−	0.217604i	−0.676469	+	0.736471i	$0.736491\pi$
$788$		0			0
$789$	−155.987	−	185.899i	−0.197703	−	0.235613i
$790$		0			0
$791$	229.441	−	132.468i	0.290064	−	0.167469i
$792$		0			0
$793$	−363.182	−	64.0387i	−0.457984	−	0.0807550i
$794$		0			0
$795$	40.0047	−	14.5605i	0.0503204	−	0.0183151i
$796$		0			0
$797$		−	1411.17i		−	1.77060i	−0.465019	−	0.885301i	$-0.653952\pi$
$797$		−	1411.17i		−	1.77060i	0.465019	−	0.885301i	$-0.346048\pi$
$798$		0			0
$799$	1003.67			1.25616
$800$		0			0
$801$	302.607	+	831.407i	0.377787	+	1.03796i
$802$		0			0
$803$	−3.90734	+	22.1596i	−0.00486593	+	0.0275960i
$804$		0			0
$805$	−148.350	−	256.949i	−0.184285	−	0.319192i
$806$		0			0
$807$	−73.2823	+	61.4911i	−0.0908083	+	0.0761972i
$808$		0			0
$809$	703.686	−	1218.82i	0.869822	−	1.50658i	0.00764386	−	0.999971i	$-0.497567\pi$
$809$	703.686	−	1218.82i	0.869822	−	1.50658i	0.862178	−	0.506605i	$-0.169100\pi$
$810$		0			0
$811$	172.417	−	473.711i	0.212598	−	0.584108i	−0.786857	−	0.617136i	$-0.788293\pi$
$811$	172.417	−	473.711i	0.212598	−	0.584108i	0.999454	+	0.0330281i	$0.0105151\pi$
$812$		0			0
$813$	−256.170	+	45.1696i	−0.315092	+	0.0555592i
$814$		0			0
$815$	526.821	+	442.055i	0.646406	+	0.542399i
$816$		0			0
$817$	618.420	+	481.242i	0.756941	+	0.589035i
$818$		0			0
$819$	−72.4033	+	86.2869i	−0.0884045	+	0.105356i
$820$		0			0
$821$	−210.354	−	1192.98i	−0.256216	−	1.45308i	−0.792931	−	0.609312i	$-0.791446\pi$
$821$	−210.354	−	1192.98i	−0.256216	−	1.45308i	0.536714	−	0.843764i	$-0.319665\pi$
$822$		0			0
$823$	−385.490	−	140.307i	−0.468396	−	0.170482i	0.0970294	−	0.995282i	$-0.469066\pi$
$823$	−385.490	−	140.307i	−0.468396	−	0.170482i	−0.565426	+	0.824799i	$0.691288\pi$
$824$		0			0
$825$	−1.77234	−	1.02326i	−0.00214829	−	0.00124031i
$826$		0			0
$827$	−283.443	−	337.795i	−0.342737	−	0.408458i	0.566950	−	0.823752i	$-0.308123\pi$
$827$	−283.443	−	337.795i	−0.342737	−	0.408458i	−0.909687	+	0.415294i	$0.863679\pi$
$828$		0			0
$829$	134.275	−	77.5237i	0.161972	−	0.0935147i	−0.416823	−	0.908988i	$-0.636856\pi$
$829$	134.275	−	77.5237i	0.161972	−	0.0935147i	0.578795	+	0.815473i	$0.303523\pi$
$830$		0			0
$831$	131.552	+	23.1962i	0.158306	+	0.0279136i
$832$		0			0
$833$	414.499	−	150.865i	0.497597	−	0.181111i
$834$		0			0
$835$		−	51.9369i		−	0.0621999i
$836$		0			0
$837$	182.103			0.217566
$838$		0			0
$839$	250.499	+	688.241i	0.298569	+	0.820311i	0.994740	+	0.102435i	$0.0326633\pi$
$839$	250.499	+	688.241i	0.298569	+	0.820311i	−0.696171	+	0.717876i	$0.745115\pi$
$840$		0			0
$841$	4.21334	−	23.8950i	0.00500991	−	0.0284126i
$842$		0			0
$843$	57.0796	+	98.8648i	0.0677101	+	0.117277i
$844$		0			0
$845$	509.007	−	427.108i	0.602376	−	0.505453i
$846$		0			0
$847$	291.537	−	504.957i	0.344200	−	0.596171i
$848$		0			0
$849$	−60.1406	+	165.235i	−0.0708370	+	0.194623i
$850$		0			0
$851$	444.575	−	78.3906i	0.522415	−	0.0921158i
$852$		0			0
$853$	−226.059	−	189.686i	−0.265016	−	0.222375i	0.500590	−	0.865685i	$-0.333116\pi$
$853$	−226.059	−	189.686i	−0.265016	−	0.222375i	−0.765606	+	0.643309i	$0.777561\pi$
$854$		0			0
$855$	474.949	−	17.5043i	0.555496	−	0.0204729i
$856$		0			0
$857$	24.3399	−	29.0071i	0.0284013	−	0.0338473i	−0.751657	−	0.659554i	$-0.770745\pi$
$857$	24.3399	−	29.0071i	0.0284013	−	0.0338473i	0.780058	+	0.625707i	$0.215189\pi$
$858$		0			0
$859$	29.0571	+	164.791i	0.0338266	+	0.191840i	0.997039	−	0.0769024i	$-0.0245030\pi$
$859$	29.0571	+	164.791i	0.0338266	+	0.191840i	−0.963212	+	0.268743i	$0.913392\pi$
$860$		0			0
$861$	−464.063	−	168.905i	−0.538981	−	0.196173i
$862$		0			0
$863$	−1171.31	−	676.254i	−1.35725	−	0.783608i	−0.367997	−	0.929827i	$-0.619956\pi$
$863$	−1171.31	−	676.254i	−1.35725	−	0.783608i	−0.989252	+	0.146219i	$0.953290\pi$
$864$		0			0
$865$	377.255	+	449.595i	0.436133	+	0.519763i
$866$		0			0
$867$	6.39375	−	3.69143i	0.00737456	−	0.00425771i
$868$		0			0
$869$	26.0332	+	4.59035i	0.0299576	+	0.00528234i
$870$		0			0
$871$	30.0635	−	10.9422i	0.0345161	−	0.0125628i
$872$		0			0
$873$			468.073i			0.536166i
$874$		0			0
$875$	−651.312			−0.744356
$876$		0			0
$877$	−171.809	−	472.041i	−0.195905	−	0.538245i	0.802378	−	0.596816i	$-0.203568\pi$
$877$	−171.809	−	472.041i	−0.195905	−	0.538245i	−0.998283	+	0.0585713i	$0.981346\pi$
$878$		0			0
$879$	122.401	−	694.170i	0.139250	−	0.789727i
$880$		0			0
$881$	−170.295	−	294.960i	−0.193297	−	0.334801i	0.753044	−	0.657971i	$-0.228585\pi$
$881$	−170.295	−	294.960i	−0.193297	−	0.334801i	−0.946341	+	0.323170i	$0.895252\pi$
$882$		0			0
$883$	1203.63	−	1009.96i	1.36311	−	1.14379i	0.388102	−	0.921616i	$-0.373131\pi$
$883$	1203.63	−	1009.96i	1.36311	−	1.14379i	0.975008	−	0.222169i	$-0.0713137\pi$
$884$		0			0
$885$	222.538	−	385.447i	0.251455	−	0.435533i
$886$		0			0
$887$	−26.4753	+	72.7402i	−0.0298481	+	0.0820070i	−0.953722	−	0.300691i	$-0.902783\pi$
$887$	−26.4753	+	72.7402i	−0.0298481	+	0.0820070i	0.923874	+	0.382698i	$0.125005\pi$
$888$		0			0
$889$	−799.731	+	141.014i	−0.899585	+	0.158621i
$890$		0			0
$891$	−0.515680	−	0.432707i	−0.000578766	−	0.000485642i
$892$		0			0
$893$	233.697	+	1089.11i	0.261699	+	1.21960i
$894$		0			0
$895$	−900.048	+	1072.64i	−1.00564	+	1.19848i
$896$		0			0
$897$	−18.0350	−	102.282i	−0.0201059	−	0.114027i
$898$		0			0
$899$	−183.719	−	66.8681i	−0.204359	−	0.0743805i
$900$		0			0
$901$	−80.1578	−	46.2792i	−0.0889654	−	0.0513642i
$902$		0			0
$903$	230.801	+	275.058i	0.255594	+	0.304605i
$904$		0			0
$905$	276.435	−	159.600i	0.305453	−	0.176353i
$906$		0			0
$907$	1554.83	+	274.159i	1.71426	+	0.302270i	0.942639	−	0.333813i	$-0.108335\pi$
$907$	1554.83	+	274.159i	1.71426	+	0.302270i	0.771620	+	0.636083i	$0.219447\pi$
$908$		0			0
$909$	−633.085	+	230.424i	−0.696464	+	0.253492i
$910$		0			0
$911$		−	1736.18i		−	1.90580i	−0.303290	−	0.952898i	$-0.598085\pi$
$911$		−	1736.18i		−	1.90580i	0.303290	−	0.952898i	$-0.401915\pi$
$912$		0			0
$913$	19.6686			0.0215428
$914$		0			0
$915$	243.864	+	670.012i	0.266518	+	0.732253i
$916$		0			0
$917$	29.0988	−	165.028i	0.0317326	−	0.179965i
$918$		0			0
$919$	−621.707	−	1076.83i	−0.676503	−	1.17174i	−0.976027	−	0.217649i	$-0.930161\pi$
$919$	−621.707	−	1076.83i	−0.676503	−	1.17174i	0.299524	−	0.954089i	$-0.403172\pi$
$920$		0			0
$921$	−68.6207	+	57.5796i	−0.0745067	+	0.0625186i
$922$		0			0
$923$	49.4959	−	85.7295i	0.0536251	−	0.0928814i
$924$		0			0
$925$	65.5453	−	180.084i	0.0708597	−	0.194686i
$926$		0			0
$927$	−877.488	+	154.725i	−0.946589	+	0.166909i
$928$		0			0
$929$	437.894	+	367.436i	0.471360	+	0.395518i	0.847291	−	0.531130i	$-0.178232\pi$
$929$	437.894	+	367.436i	0.471360	+	0.395518i	−0.375930	+	0.926648i	$0.622677\pi$
$930$		0			0
$931$	260.221	+	414.655i	0.279507	+	0.445387i
$932$		0			0
$933$	−247.919	+	295.458i	−0.265722	+	0.316675i
$934$		0			0
$935$	−2.45005	−	13.8949i	−0.00262037	−	0.0148609i
$936$		0			0
$937$	76.0200	+	27.6690i	0.0811313	+	0.0295294i	0.382267	−	0.924052i	$-0.375143\pi$
$937$	76.0200	+	27.6690i	0.0811313	+	0.0295294i	−0.301136	+	0.953581i	$0.597366\pi$
$938$		0			0
$939$	−302.709	−	174.769i	−0.322374	−	0.186122i
$940$		0			0
$941$	617.870	+	736.349i	0.656610	+	0.782518i	0.986895	−	0.161364i	$-0.0515892\pi$
$941$	617.870	+	736.349i	0.656610	+	0.782518i	−0.330285	+	0.943881i	$0.607145\pi$
$942$		0			0
$943$	−693.580	+	400.438i	−0.735503	+	0.424643i
$944$		0			0
$945$	550.880	+	97.1351i	0.582942	+	0.102788i
$946$		0			0
$947$	−1623.43	+	590.881i	−1.71429	+	0.623951i	−0.997321	−	0.0731531i	$-0.976694\pi$
$947$	−1623.43	+	590.881i	−1.71429	+	0.623951i	−0.716970	+	0.697104i	$0.754472\pi$
$948$		0			0
$949$			484.773i			0.510825i
$950$		0			0
$951$	1077.91			1.13345
$952$		0			0
$953$	520.185	+	1429.20i	0.545840	+	1.49968i	0.839277	+	0.543704i	$0.182979\pi$
$953$	520.185	+	1429.20i	0.545840	+	1.49968i	−0.293437	+	0.955978i	$0.594799\pi$
$954$		0			0
$955$	101.208	−	573.976i	0.105976	−	0.601022i
$956$		0			0
$957$	−4.87898	−	8.45063i	−0.00509820	−	0.00883034i
$958$		0			0
$959$	−601.783	+	504.956i	−0.627511	+	0.526544i
$960$		0			0
$961$	−457.100	+	791.720i	−0.475650	+	0.823850i
$962$		0			0
$963$	314.029	−	862.788i	0.326095	−	0.895938i
$964$		0			0
$965$	923.247	−	162.793i	0.956732	−	0.168698i
$966$		0			0
$967$	347.163	+	291.304i	0.359010	+	0.301245i	0.804396	−	0.594093i	$-0.202489\pi$
$967$	347.163	+	291.304i	0.359010	+	0.301245i	−0.445386	+	0.895339i	$0.646934\pi$
$968$		0			0
$969$	393.961	+	435.842i	0.406565	+	0.449786i
$970$		0			0
$971$	−566.677	+	675.340i	−0.583602	+	0.695510i	−0.974363	−	0.224983i	$-0.927767\pi$
$971$	−566.677	+	675.340i	−0.583602	+	0.695510i	0.390761	+	0.920492i	$0.372212\pi$
$972$		0			0
$973$	−22.1978	−	125.890i	−0.0228138	−	0.129383i
$974$		0			0
$975$	−41.4313	−	15.0798i	−0.0424937	−	0.0154664i
$976$		0			0
$977$	−1269.34	−	732.855i	−1.29922	−	0.750108i	−0.318954	−	0.947770i	$-0.603332\pi$
$977$	−1269.34	−	732.855i	−1.29922	−	0.750108i	−0.980270	+	0.197662i	$0.936665\pi$
$978$		0			0
$979$	18.7376	+	22.3305i	0.0191395	+	0.0228095i
$980$		0			0
$981$	−531.522	+	306.874i	−0.541817	+	0.312818i
$982$		0			0
$983$	−1852.95	−	326.724i	−1.88499	−	0.332375i	−0.892142	−	0.451754i	$-0.850798\pi$
$983$	−1852.95	−	326.724i	−1.88499	−	0.332375i	−0.992849	+	0.119380i	$0.961909\pi$
$984$		0			0
$985$	508.925	−	185.234i	0.516675	−	0.188054i
$986$		0			0
$987$			510.410i			0.517132i
$988$		0			0
$989$	582.299			0.588775
$990$		0			0
$991$	179.003	+	491.807i	0.180629	+	0.496274i	0.996653	−	0.0817435i	$-0.0260488\pi$
$991$	179.003	+	491.807i	0.180629	+	0.496274i	−0.816024	+	0.578017i	$0.803827\pi$
$992$		0			0
$993$	173.633	−	984.723i	0.174857	−	0.991664i
$994$		0			0
$995$	604.148	+	1046.42i	0.607184	+	1.05167i
$996$		0			0
$997$	512.180	−	429.770i	0.513721	−	0.431063i	−0.348715	−	0.937229i	$-0.613382\pi$
$997$	512.180	−	429.770i	0.513721	−	0.431063i	0.862436	+	0.506165i	$0.168937\pi$
$998$		0			0
$999$	−425.552	+	737.077i	−0.425978	+	0.737815i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.j.a.41.1	yes	18
4.3	odd	2		304.3.z.b.193.3		18
19.5	even	9		1444.3.c.c.721.11		18
19.13	odd	18	inner	76.3.j.a.13.1	✓	18
19.14	odd	18		1444.3.c.c.721.8		18
76.51	even	18		304.3.z.b.241.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.j.a.13.1	✓	18	19.13	odd	18	inner
76.3.j.a.41.1	yes	18	1.1	even	1	trivial
304.3.z.b.193.3		18	4.3	odd	2
304.3.z.b.241.3		18	76.51	even	18
1444.3.c.c.721.8		18	19.14	odd	18
1444.3.c.c.721.11		18	19.5	even	9

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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.617749 - 1.69725i) q^{3} +(0.757040 - 4.29338i) q^{5} +(-2.41011 - 4.17443i) q^{7} +(4.39535 - 3.68814i) q^{9} +(0.0945208 - 0.163715i) q^{11} +(1.39295 - 3.82710i) q^{13} +(-7.75461 + 1.36735i) q^{15} +(13.1145 + 11.0044i) q^{17} +(-8.88753 + 16.7932i) q^{19} +(-5.59622 + 6.66931i) q^{21} +(2.45173 + 13.9044i) q^{23} +(5.63227 + 2.04998i) q^{25} +(-23.0527 - 13.3095i) q^{27} +(18.3700 + 21.8925i) q^{29} +(-5.92457 + 3.42055i) q^{31} +(-0.336255 - 0.0592909i) q^{33} +(-19.7470 + 7.18732i) q^{35} -31.9736i q^{37} -7.35605 q^{39} +(19.4006 + 53.3028i) q^{41} +(7.16167 - 40.6158i) q^{43} +(-12.5071 - 21.6630i) q^{45} +(44.9103 - 37.6842i) q^{47} +(12.8827 - 22.3136i) q^{49} +(10.5757 - 29.0566i) q^{51} +(-5.32437 + 0.938830i) q^{53} +(-0.631335 - 0.529753i) q^{55} +(33.9926 + 4.71039i) q^{57} +(-36.3323 + 43.2991i) q^{59} +(-15.7238 - 89.1742i) q^{61} +(-25.9892 - 9.45928i) q^{63} +(-15.3767 - 8.87775i) q^{65} +(5.04936 + 6.01760i) q^{67} +(22.0848 - 12.7506i) q^{69} +(23.9368 + 4.22071i) q^{71} +(-111.851 + 40.7104i) q^{73} -10.8258i q^{75} -0.911222 q^{77} +(47.8267 + 131.403i) q^{79} +(0.618357 - 3.50688i) q^{81} +(52.0220 + 90.1047i) q^{83} +(57.1743 - 47.9749i) q^{85} +(25.8090 - 44.7025i) q^{87} +(-52.7400 + 144.902i) q^{89} +(-19.3332 + 3.40896i) q^{91} +(9.46544 + 7.94245i) q^{93} +(65.3715 + 50.8707i) q^{95} +(-52.4375 + 62.4925i) q^{97} +(-0.188351 - 1.06819i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{3} + 9 q^{7} + 6 q^{9} - 15 q^{11} + 51 q^{13} + 21 q^{15} - 45 q^{17} + 30 q^{19} - 63 q^{21} + 48 q^{23} - 54 q^{25} - 198 q^{27} - 39 q^{29} - 108 q^{31} - 105 q^{33} + 51 q^{35} + 48 q^{39}+ \cdots - 267 q^{99}+O(q^{100}) \) 18 * q - 6 * q^3 + 9 * q^7 + 6 * q^9 - 15 * q^11 + 51 * q^13 + 21 * q^15 - 45 * q^17 + 30 * q^19 - 63 * q^21 + 48 * q^23 - 54 * q^25 - 198 * q^27 - 39 * q^29 - 108 * q^31 - 105 * q^33 + 51 * q^35 + 48 * q^39 + 54 * q^41 + 75 * q^43 + 288 * q^45 + 339 * q^47 - 24 * q^49 + 360 * q^51 + 69 * q^53 - 51 * q^55 + 510 * q^57 - 483 * q^59 - 36 * q^61 - 267 * q^63 - 585 * q^65 - 87 * q^67 - 351 * q^69 - 234 * q^71 - 132 * q^73 + 108 * q^77 + 363 * q^79 + 258 * q^81 + 279 * q^83 + 666 * q^85 + 600 * q^89 + 270 * q^91 - 456 * q^93 - 39 * q^95 - 801 * q^97 - 267 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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