LMFDB - Embedded newform 570.2.bf.a.59.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(29,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 17]))

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

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

chi := DirichletCharacter("570.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bf (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.23
Character	$\chi$	$=$	570.59
Dual form			570.2.bf.a.29.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(-1.54873 - 0.775516i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.21793 + 1.87527i) q^{5} +(-1.39054 - 1.03267i) q^{6} +(-1.48423 + 0.856923i) q^{7} +(0.866025 + 0.500000i) q^{8} +(1.79715 + 2.40214i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(-1.54873 - 0.775516i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.21793 + 1.87527i) q^{5} +(-1.39054 - 1.03267i) q^{6} +(-1.48423 + 0.856923i) q^{7} +(0.866025 + 0.500000i) q^{8} +(1.79715 + 2.40214i) q^{9} +(0.873794 + 2.05827i) q^{10} +(-0.232838 - 0.134429i) q^{11} +(-1.19009 - 1.25844i) q^{12} +(-2.84108 + 2.38395i) q^{13} +(-1.61049 + 0.586170i) q^{14} +(-0.431953 - 3.84882i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.267187 + 1.51529i) q^{17} +(1.35272 + 2.67771i) q^{18} +(2.37652 + 3.65406i) q^{19} +(0.503104 + 2.17874i) q^{20} +(2.96324 - 0.176097i) q^{21} +(-0.205957 - 0.172818i) q^{22} +(0.801629 + 0.291769i) q^{23} +(-0.953484 - 1.44598i) q^{24} +(-2.03327 + 4.56791i) q^{25} +(-3.21188 + 1.85438i) q^{26} +(-0.920408 - 5.11399i) q^{27} +(-1.68781 + 0.297606i) q^{28} +(0.356949 + 2.02436i) q^{29} +(0.242950 - 3.86536i) q^{30} +(0.244922 - 0.141406i) q^{31} +(0.642788 + 0.766044i) q^{32} +(0.256352 + 0.388764i) q^{33} +(-0.526255 + 1.44587i) q^{34} +(-3.41466 - 1.73966i) q^{35} +(0.867188 + 2.87193i) q^{36} +9.38078 q^{37} +(1.70589 + 4.01123i) q^{38} +(6.24886 - 1.48880i) q^{39} +(0.117127 + 2.23300i) q^{40} +(1.94015 + 1.62798i) q^{41} +(2.94880 + 0.341140i) q^{42} +(2.01595 + 5.53877i) q^{43} +(-0.172818 - 0.205957i) q^{44} +(-2.31584 + 6.29578i) q^{45} +(0.738785 + 0.426538i) q^{46} +(-1.42871 - 8.10262i) q^{47} +(-0.687906 - 1.58959i) q^{48} +(-2.03137 + 3.51843i) q^{49} +(-2.79559 + 4.14544i) q^{50} +(1.58893 - 2.13957i) q^{51} +(-3.48510 + 1.26847i) q^{52} +(-1.09162 + 2.99920i) q^{53} +(-0.0183905 - 5.19612i) q^{54} +(-0.0314906 - 0.600359i) q^{55} -1.71385 q^{56} +(-0.846806 - 7.50219i) q^{57} +2.05559i q^{58} +(2.44329 - 13.8566i) q^{59} +(0.910471 - 3.76444i) q^{60} +(-1.11216 - 0.404792i) q^{61} +(0.265756 - 0.0967274i) q^{62} +(-4.72584 - 2.02531i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-7.93079 - 2.42429i) q^{65} +(0.184949 + 0.427373i) q^{66} +(-0.393781 - 2.23324i) q^{67} +(-0.769333 + 1.33252i) q^{68} +(-1.01524 - 1.07355i) q^{69} +(-3.06070 - 2.30618i) q^{70} +(-2.24601 + 0.817480i) q^{71} +(0.355308 + 2.97889i) q^{72} +(-4.67909 + 5.57633i) q^{73} +(9.23826 + 1.62895i) q^{74} +(6.69148 - 5.49764i) q^{75} +(0.983433 + 4.24651i) q^{76} +0.460781 q^{77} +(6.41245 - 0.381074i) q^{78} +(3.38643 - 4.03579i) q^{79} +(-0.272408 + 2.21941i) q^{80} +(-2.54051 + 8.63399i) q^{81} +(1.62798 + 1.94015i) q^{82} +(-7.43387 - 12.8758i) q^{83} +(2.84476 + 0.848011i) q^{84} +(-3.16699 + 1.34448i) q^{85} +(1.02352 + 5.80469i) q^{86} +(1.01710 - 3.41201i) q^{87} +(-0.134429 - 0.232838i) q^{88} +(10.6592 - 8.94412i) q^{89} +(-3.37391 + 5.79799i) q^{90} +(2.17397 - 5.97292i) q^{91} +(0.653494 + 0.548347i) q^{92} +(-0.488982 + 0.0290588i) q^{93} -8.22761i q^{94} +(-3.95791 + 8.90702i) q^{95} +(-0.401426 - 1.68489i) q^{96} +(1.04425 - 5.92225i) q^{97} +(-2.61147 + 3.11223i) q^{98} +(-0.0955274 - 0.800896i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) $ 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{18}\right)$	$-1$

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 $

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	−1.54873	−	0.775516i	−0.894161	−	0.447745i
$3$	−1.54873	−	0.775516i	−0.894161	−	0.447745i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	1.21793	+	1.87527i	0.544677	+	0.838646i
$5$	1.21793	+	1.87527i	0.544677	+	0.838646i
$6$	−1.39054	−	1.03267i	−0.567685	−	0.421585i
$7$	−1.48423	+	0.856923i	−0.560988	+	0.323887i	−0.753542	−	0.657400i	$-0.771656\pi$
$7$	−1.48423	+	0.856923i	−0.560988	+	0.323887i	0.192554	+	0.981286i	$0.438323\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	1.79715	+	2.40214i	0.599050	+	0.800712i
$10$	0.873794	+	2.05827i	0.276318	+	0.650883i
$11$	−0.232838	−	0.134429i	−0.0702032	−	0.0405318i	0.464488	−	0.885580i	$-0.346239\pi$
$11$	−0.232838	−	0.134429i	−0.0702032	−	0.0405318i	−0.534691	+	0.845048i	$0.679572\pi$
$12$	−1.19009	−	1.25844i	−0.343550	−	0.363282i
$13$	−2.84108	+	2.38395i	−0.787973	+	0.661188i	−0.945243	−	0.326368i	$-0.894175\pi$
$13$	−2.84108	+	2.38395i	−0.787973	+	0.661188i	0.157270	+	0.987556i	$0.449731\pi$
$14$	−1.61049	+	0.586170i	−0.430421	+	0.156661i
$15$	−0.431953	−	3.84882i	−0.111530	−	0.993761i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−0.267187	+	1.51529i	−0.0648023	+	0.367512i	0.935111	+	0.354354i	$0.115299\pi$
$17$	−0.267187	+	1.51529i	−0.0648023	+	0.367512i	−0.999913	+	0.0131574i	$0.995812\pi$
$18$	1.35272	+	2.67771i	0.318839	+	0.631143i
$19$	2.37652	+	3.65406i	0.545210	+	0.838299i
$19$	2.37652	+	3.65406i	0.545210	+	0.838299i
$20$	0.503104	+	2.17874i	0.112497	+	0.487180i
$21$	2.96324	−	0.176097i	0.646632	−	0.0384275i
$22$	−0.205957	−	0.172818i	−0.0439102	−	0.0368450i
$23$	0.801629	+	0.291769i	0.167151	+	0.0608381i	0.424240	−	0.905550i	$-0.360541\pi$
$23$	0.801629	+	0.291769i	0.167151	+	0.0608381i	−0.257089	+	0.966388i	$0.582763\pi$
$24$	−0.953484	−	1.44598i	−0.194629	−	0.295160i
$25$	−2.03327	+	4.56791i	−0.406654	+	0.913582i
$26$	−3.21188	+	1.85438i	−0.629902	+	0.363674i
$27$	−0.920408	−	5.11399i	−0.177133	−	0.984187i
$28$	−1.68781	+	0.297606i	−0.318966	+	0.0562423i
$29$	0.356949	+	2.02436i	0.0662838	+	0.375914i	0.999847	+	0.0175008i	$0.00557095\pi$
$29$	0.356949	+	2.02436i	0.0662838	+	0.375914i	−0.933563	+	0.358413i	$0.883318\pi$
$30$	0.242950	−	3.86536i	0.0443564	−	0.705714i
$31$	0.244922	−	0.141406i	0.0439893	−	0.0253973i	−0.477844	−	0.878445i	$-0.658582\pi$
$31$	0.244922	−	0.141406i	0.0439893	−	0.0253973i	0.521833	+	0.853047i	$0.325248\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	0.256352	+	0.388764i	0.0446251	+	0.0676751i
$34$	−0.526255	+	1.44587i	−0.0902520	+	0.247965i
$35$	−3.41466	−	1.73966i	−0.577183	−	0.294057i
$36$	0.867188	+	2.87193i	0.144531	+	0.478655i
$37$	9.38078			1.54219			0.771095	−	0.636720i	$-0.219709\pi$
$37$	9.38078			1.54219			0.771095	+	0.636720i	$0.219709\pi$
$38$	1.70589	+	4.01123i	0.276732	+	0.650707i
$39$	6.24886	−	1.48880i	1.00062	−	0.238398i
$40$	0.117127	+	2.23300i	0.0185195	+	0.353068i
$41$	1.94015	+	1.62798i	0.303001	+	0.254248i	0.781592	−	0.623790i	$-0.214408\pi$
$41$	1.94015	+	1.62798i	0.303001	+	0.254248i	−0.478591	+	0.878038i	$0.658852\pi$
$42$	2.94880	+	0.341140i	0.455010	+	0.0526390i
$43$	2.01595	+	5.53877i	0.307429	+	0.844654i	0.993156	+	0.116796i	$0.0372622\pi$
$43$	2.01595	+	5.53877i	0.307429	+	0.844654i	−0.685727	+	0.727859i	$0.740516\pi$
$44$	−0.172818	−	0.205957i	−0.0260534	−	0.0310492i
$45$	−2.31584	+	6.29578i	−0.345226	+	0.938520i
$46$	0.738785	+	0.426538i	0.108928	+	0.0628896i
$47$	−1.42871	−	8.10262i	−0.208399	−	1.18189i	−0.892001	−	0.452033i	$-0.850699\pi$
$47$	−1.42871	−	8.10262i	−0.208399	−	1.18189i	0.683602	−	0.729855i	$-0.260412\pi$
$48$	−0.687906	−	1.58959i	−0.0992907	−	0.229437i
$49$	−2.03137	+	3.51843i	−0.290195	+	0.502633i
$50$	−2.79559	+	4.14544i	−0.395356	+	0.586254i
$51$	1.58893	−	2.13957i	0.222495	−	0.299600i
$52$	−3.48510	+	1.26847i	−0.483296	+	0.175905i
$53$	−1.09162	+	2.99920i	−0.149946	+	0.411972i	−0.991811	−	0.127716i	$-0.959235\pi$
$53$	−1.09162	+	2.99920i	−0.149946	+	0.411972i	0.841865	+	0.539688i	$0.181458\pi$
$54$	−0.0183905	−	5.19612i	−0.00250263	−	0.707102i
$55$	−0.0314906	−	0.600359i	−0.00424619	−	0.0809524i
$56$	−1.71385			−0.229022
$57$	−0.846806	−	7.50219i	−0.112162	−	0.993690i
$58$			2.05559i			0.269912i
$59$	2.44329	−	13.8566i	0.318089	−	1.80397i	−0.236263	−	0.971689i	$-0.575923\pi$
$59$	2.44329	−	13.8566i	0.318089	−	1.80397i	0.554352	−	0.832283i	$-0.312966\pi$
$60$	0.910471	−	3.76444i	0.117541	−	0.485988i
$61$	−1.11216	−	0.404792i	−0.142397	−	0.0518284i	0.269838	−	0.962906i	$-0.413030\pi$
$61$	−1.11216	−	0.404792i	−0.142397	−	0.0518284i	−0.412236	+	0.911077i	$0.635252\pi$
$62$	0.265756	−	0.0967274i	0.0337511	−	0.0122844i
$63$	−4.72584	−	2.02531i	−0.595399	−	0.255166i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−7.93079	−	2.42429i	−0.983693	−	0.300697i
$66$	0.184949	+	0.427373i	0.0227656	+	0.0526059i
$67$	−0.393781	−	2.23324i	−0.0481080	−	0.272834i	0.951260	−	0.308391i	$-0.0997906\pi$
$67$	−0.393781	−	2.23324i	−0.0481080	−	0.272834i	−0.999368	+	0.0355570i	$0.988679\pi$
$68$	−0.769333	+	1.33252i	−0.0932953	+	0.161592i
$69$	−1.01524	−	1.07355i	−0.122220	−	0.129240i
$70$	−3.06070	−	2.30618i	−0.365823	−	0.275642i
$71$	−2.24601	+	0.817480i	−0.266552	+	0.0970170i	−0.471839	−	0.881685i	$-0.656410\pi$
$71$	−2.24601	+	0.817480i	−0.266552	+	0.0970170i	0.205287	+	0.978702i	$0.434187\pi$
$72$	0.355308	+	2.97889i	0.0418735	+	0.351065i
$73$	−4.67909	+	5.57633i	−0.547646	+	0.652660i	−0.966884	−	0.255217i	$-0.917853\pi$
$73$	−4.67909	+	5.57633i	−0.547646	+	0.652660i	0.419237	+	0.907877i	$0.362298\pi$
$74$	9.23826	+	1.62895i	1.07393	+	0.189362i
$75$	6.69148	−	5.49764i	0.772666	−	0.634813i
$76$	0.983433	+	4.24651i	0.112807	+	0.487108i
$77$	0.460781			0.0525108
$78$	6.41245	−	0.381074i	0.726067	−	0.0431481i
$79$	3.38643	−	4.03579i	0.381004	−	0.454062i	−0.541127	−	0.840941i	$-0.682002\pi$
$79$	3.38643	−	4.03579i	0.381004	−	0.454062i	0.922131	+	0.386878i	$0.126447\pi$
$80$	−0.272408	+	2.21941i	−0.0304562	+	0.248138i
$81$	−2.54051	+	8.63399i	−0.282279	+	0.959332i
$82$	1.62798	+	1.94015i	0.179780	+	0.214254i
$83$	−7.43387	−	12.8758i	−0.815973	−	1.41331i	−0.908627	−	0.417608i	$-0.862868\pi$
$83$	−7.43387	−	12.8758i	−0.815973	−	1.41331i	0.0926542	−	0.995698i	$-0.470465\pi$
$84$	2.84476	+	0.848011i	0.310389	+	0.0925256i
$85$	−3.16699	+	1.34448i	−0.343509	+	0.145829i
$86$	1.02352	+	5.80469i	0.110369	+	0.625936i
$87$	1.01710	−	3.41201i	0.109045	−	0.365806i
$88$	−0.134429	−	0.232838i	−0.0143302	−	0.0248206i
$89$	10.6592	−	8.94412i	1.12987	−	0.948075i	0.130811	−	0.991407i	$-0.458242\pi$
$89$	10.6592	−	8.94412i	1.12987	−	0.948075i	0.999061	+	0.0433325i	$0.0137975\pi$
$90$	−3.37391	+	5.79799i	−0.355641	+	0.611162i
$91$	2.17397	−	5.97292i	0.227893	−	0.626132i
$92$	0.653494	+	0.548347i	0.0681315	+	0.0571691i
$93$	−0.488982	+	0.0290588i	−0.0507051	+	0.00301326i
$94$		−	8.22761i		−	0.848613i
$95$	−3.95791	+	8.90702i	−0.406073	+	0.913841i
$96$	−0.401426	−	1.68489i	−0.0409704	−	0.171963i
$97$	1.04425	−	5.92225i	0.106028	−	0.601314i	−0.884777	−	0.466015i	$-0.845689\pi$
$97$	1.04425	−	5.92225i	0.106028	−	0.601314i	0.990805	−	0.135299i	$-0.0431995\pi$
$98$	−2.61147	+	3.11223i	−0.263799	+	0.314383i
$99$	−0.0955274	−	0.800896i	−0.00960087	−	0.0804931i
$100$	−3.47297	+	3.59701i	−0.347297	+	0.359701i
$101$	−3.25434	−	3.87837i	−0.323819	−	0.385913i	0.579435	−	0.815018i	$-0.303273\pi$
$101$	−3.25434	−	3.87837i	−0.323819	−	0.385913i	−0.903254	+	0.429106i	$0.858829\pi$
$102$	1.93633	−	1.83115i	0.191725	−	0.181311i
$103$	−4.75810	+	8.24127i	−0.468829	+	0.812036i	−0.999365	−	0.0356262i	$-0.988657\pi$
$103$	−4.75810	+	8.24127i	−0.468829	+	0.812036i	0.530536	+	0.847663i	$0.321991\pi$
$104$	−3.65242	+	0.644020i	−0.358149	+	0.0631513i
$105$	3.93926	+	5.34240i	0.384433	+	0.521365i
$106$	−1.59584	+	2.76408i	−0.155002	+	0.268471i
$107$	12.2975	−	7.09995i	1.18884	−	0.686378i	0.230799	−	0.973002i	$-0.425866\pi$
$107$	12.2975	−	7.09995i	1.18884	−	0.686378i	0.958043	+	0.286623i	$0.0925328\pi$
$108$	0.884186	−	5.12037i	0.0850808	−	0.492708i
$109$	−5.71119	−	15.6914i	−0.547033	−	1.50296i	−0.837697	−	0.546136i	$-0.816098\pi$
$109$	−5.71119	−	15.6914i	−0.547033	−	1.50296i	0.290664	−	0.956825i	$-0.406124\pi$
$110$	0.0732390	−	0.596706i	0.00698307	−	0.0568937i
$111$	−14.5283	−	7.27495i	−1.37897	−	0.690507i
$112$	−1.68781	−	0.297606i	−0.159483	−	0.0281212i
$113$			7.39539i			0.695699i	0.937550	+	0.347850i	$0.113088\pi$
$113$			7.39539i			0.695699i	−0.937550	+	0.347850i	$0.886912\pi$
$114$	0.468802	−	7.53527i	0.0439073	−	0.705742i
$115$	0.429186	+	1.85863i	0.0400218	+	0.173318i
$116$	−0.356949	+	2.02436i	−0.0331419	+	0.187957i
$117$	−10.8324	−	2.54035i	−1.00146	−	0.234855i
$118$	4.81234	−	13.2218i	0.443011	−	1.21716i
$119$	−0.901920	−	2.47800i	−0.0826789	−	0.227158i
$120$	1.55033	−	3.54915i	0.141525	−	0.323992i
$121$	−5.46386	−	9.46368i	−0.496714	−	0.860334i
$122$	−1.02497	−	0.591767i	−0.0927964	−	0.0535761i
$123$	−1.74225	−	4.02593i	−0.157094	−	0.363006i
$124$	0.278515	−	0.0491098i	0.0250114	−	0.00441019i
$125$	−11.0425	+	1.75048i	−0.987667	+	0.156568i
$126$	−4.30235	−	2.81518i	−0.383284	−	0.250796i
$127$	−1.23824	+	1.03901i	−0.109876	+	0.0921972i	−0.696071	−	0.717973i	$-0.745070\pi$
$127$	−1.23824	+	1.03901i	−0.109876	+	0.0921972i	0.586194	+	0.810170i	$0.300626\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	1.17324	−	10.1415i	0.103298	−	0.892907i
$130$	−7.38933	−	3.76463i	−0.648087	−	0.330180i
$131$	3.40772	+	0.600872i	0.297733	+	0.0524984i	0.320519	−	0.947242i	$-0.396143\pi$
$131$	3.40772	+	0.600872i	0.297733	+	0.0524984i	−0.0227860	+	0.999740i	$0.507254\pi$
$132$	0.107927	+	0.452996i	0.00939380	+	0.0394282i
$133$	−6.65856	−	3.38699i	−0.577370	−	0.293689i
$134$		−	2.26770i		−	0.195899i
$135$	8.46911	−	7.95451i	0.728905	−	0.684615i
$136$	−0.989036	+	1.17869i	−0.0848091	+	0.101072i
$137$	18.9427	+	6.89459i	1.61839	+	0.589045i	0.983074	−	0.183209i	$-0.0586486\pi$
$137$	18.9427	+	6.89459i	1.61839	+	0.589045i	0.635314	+	0.772254i	$0.280871\pi$
$138$	−0.813394	−	1.23353i	−0.0692407	−	0.105005i
$139$	−14.6100	+	12.2593i	−1.23921	+	1.03982i	−0.241621	+	0.970371i	$0.577679\pi$
$139$	−14.6100	+	12.2593i	−1.23921	+	1.03982i	−0.997586	+	0.0694469i	$0.977877\pi$
$140$	−2.61373	−	2.80263i	−0.220901	−	0.236866i
$141$	−4.07102	+	13.6568i	−0.342842	+	1.15011i
$142$	−2.35384	+	0.415045i	−0.197530	+	0.0348298i
$143$	0.981981	−	0.173150i	0.0821174	−	0.0144795i
$144$	−0.167367	+	2.99533i	−0.0139473	+	0.249611i
$145$	−3.36148	+	3.13491i	−0.279155	+	0.260340i
$146$	−5.57633	+	4.67909i	−0.461500	+	0.387244i
$147$	5.87464	−	3.87375i	0.484532	−	0.319501i
$148$	8.81505	+	3.20841i	0.724592	+	0.263730i
$149$	14.6019	−	17.4018i	1.19623	−	1.42561i	0.317528	−	0.948249i	$-0.397147\pi$
$149$	14.6019	−	17.4018i	1.19623	−	1.42561i	0.878705	−	0.477366i	$-0.158408\pi$
$150$	7.54448	−	4.25215i	0.616004	−	0.347187i
$151$		−	10.2840i		−	0.836904i	−0.908239	−	0.418452i	$-0.862573\pi$
$151$		−	10.2840i		−	0.836904i	0.908239	−	0.418452i	$-0.137427\pi$
$152$	0.231093	+	4.35277i	0.0187441	+	0.353056i
$153$	−4.12011	+	2.08138i	−0.333091	+	0.168270i
$154$	0.453780	+	0.0800137i	0.0365667	+	0.00644769i
$155$	0.563473	+	0.287072i	0.0452593	+	0.0230582i
$156$	6.38121	+	0.738226i	0.510905	+	0.0591054i
$157$	3.29903	+	9.06402i	0.263292	+	0.723388i	0.998940	+	0.0460245i	$0.0146552\pi$
$157$	3.29903	+	9.06402i	0.263292	+	0.723388i	−0.735649	+	0.677363i	$0.763123\pi$
$158$	4.03579	−	3.38643i	0.321071	−	0.269410i
$159$	4.01656	−	3.79839i	0.318534	−	0.301232i
$160$	−0.653667	+	2.13839i	−0.0516769	+	0.169055i
$161$	−1.43983	+	0.253881i	−0.113474	+	0.0200086i
$162$	−4.00119	+	8.06167i	−0.314364	+	0.633384i
$163$	18.7191	+	10.8075i	1.46619	+	0.846507i	0.999285	−	0.0377994i	$-0.0120348\pi$
$163$	18.7191	+	10.8075i	1.46619	+	0.846507i	0.466907	+	0.884306i	$0.345368\pi$
$164$	1.26634	+	2.19337i	0.0988849	+	0.171274i
$165$	−0.416818	+	0.954217i	−0.0324492	+	0.0742857i
$166$	−5.08506	−	13.9711i	−0.394678	−	1.08437i
$167$	−5.05375	+	13.8851i	−0.391071	+	1.07446i	0.575443	+	0.817842i	$0.304830\pi$
$167$	−5.05375	+	13.8851i	−0.391071	+	1.07446i	−0.966513	+	0.256616i	$0.917392\pi$
$168$	2.65429	+	1.32912i	0.204783	+	0.102544i
$169$	0.131090	−	0.743451i	0.0100839	−	0.0571885i
$170$	−3.35235	+	0.774109i	−0.257113	+	0.0593715i
$171$	−4.50660	+	12.2756i	−0.344628	+	0.938739i
$172$			5.89424i			0.449431i
$173$	9.66856	+	1.70483i	0.735087	+	0.129616i	0.528645	−	0.848843i	$-0.322700\pi$
$173$	9.66856	+	1.70483i	0.735087	+	0.129616i	0.206442	+	0.978459i	$0.433811\pi$
$174$	1.59414	−	3.18356i	0.120852	−	0.241345i
$175$	−0.896497	−	8.52221i	−0.0677688	−	0.644218i
$176$	−0.0919547	−	0.252644i	−0.00693135	−	0.0190437i
$177$	−14.5300	+	19.5653i	−1.09214	+	1.47062i
$178$	12.0504	−	6.95729i	0.903214	−	0.521471i
$179$	−0.839976	+	1.45488i	−0.0627827	+	0.108743i	−0.895708	−	0.444642i	$-0.853331\pi$
$179$	−0.839976	+	1.45488i	−0.0627827	+	0.108743i	0.832926	+	0.553385i	$0.186664\pi$
$180$	−4.32946	+	5.12403i	−0.322699	+	0.381923i
$181$	15.0430	−	2.65249i	1.11814	−	0.197158i	0.416116	−	0.909311i	$-0.363391\pi$
$181$	15.0430	−	2.65249i	1.11814	−	0.197158i	0.702024	+	0.712153i	$0.252280\pi$
$182$	3.17812	−	5.50467i	0.235578	−	0.408034i
$183$	1.40851	+	1.48941i	0.104120	+	0.110101i
$184$	0.548347	+	0.653494i	0.0404247	+	0.0481762i
$185$	11.4252	+	17.5915i	0.839995	+	1.29335i
$186$	−0.486599	−	0.0562935i	−0.0356792	−	0.00412764i
$187$	0.265910	−	0.316899i	0.0194453	−	0.0231740i
$188$	1.42871	−	8.10262i	0.104199	−	0.590944i
$189$	5.74839	+	6.80164i	0.418134	+	0.494746i
$190$	−5.44447	+	8.08442i	−0.394983	+	0.586505i
$191$		−	4.72693i		−	0.342028i	−0.985269	−	0.171014i	$-0.945296\pi$
$191$		−	4.72693i		−	0.342028i	0.985269	−	0.171014i	$-0.0547044\pi$
$192$	−0.102750	−	1.72900i	−0.00741532	−	0.124780i
$193$	−7.07242	−	5.93447i	−0.509084	−	0.427172i	0.351723	−	0.936104i	$-0.385596\pi$
$193$	−7.07242	−	5.93447i	−0.509084	−	0.427172i	−0.860807	+	0.508932i	$0.830040\pi$
$194$	2.05678	−	5.65095i	0.147668	−	0.405714i
$195$	10.4026	+	9.90504i	0.744945	+	0.709315i
$196$	−3.11223	+	2.61147i	−0.222302	+	0.186534i
$197$	3.15567	+	5.46578i	0.224832	+	0.389421i	0.956269	−	0.292488i	$-0.0944833\pi$
$197$	3.15567	+	5.46578i	0.224832	+	0.389421i	−0.731437	+	0.681909i	$0.761150\pi$
$198$	0.0449980	−	0.805317i	0.00319787	−	0.0572314i
$199$	4.19757	+	23.8056i	0.297558	+	1.68754i	0.656620	+	0.754221i	$0.271985\pi$
$199$	4.19757	+	23.8056i	0.297558	+	1.68754i	−0.359062	+	0.933314i	$0.616903\pi$
$200$	−4.04482	+	2.93929i	−0.286012	+	0.207839i
$201$	−1.12206	+	3.76408i	−0.0791437	+	0.265498i
$202$	−2.53143	−	4.38456i	−0.178111	−	0.308497i
$203$	−2.26452	−	2.69874i	−0.158938	−	0.189415i
$204$	2.22489	−	1.46709i	0.155773	−	0.102717i
$205$	−0.689925	+	5.62108i	−0.0481864	+	0.392593i
$206$	−6.11689	+	7.28983i	−0.426184	+	0.507907i
$207$	0.739778	+	2.44997i	0.0514181	+	0.170285i
$208$	−3.70876			−0.257156
$209$	−0.0621312	−	1.17028i	−0.00429770	−	0.0809496i
$210$	2.95172	+	5.94528i	0.203688	+	0.410264i
$211$	15.2568	+	2.69019i	1.05032	+	0.185200i	0.672059	−	0.740497i	$-0.265410\pi$
$211$	15.2568	+	2.69019i	1.05032	+	0.185200i	0.378264	+	0.925698i	$0.376521\pi$
$212$	−2.05157	+	2.44497i	−0.140903	+	0.167921i
$213$	4.11243	+	0.475757i	0.281779	+	0.0325984i
$214$	13.3435	−	4.85665i	0.912146	−	0.331994i
$215$	−7.93139	+	10.5263i	−0.540917	+	0.717888i
$216$	1.75990	−	4.88905i	0.119746	−	0.332657i
$217$	−0.242348	+	0.419759i	−0.0164517	+	0.0284951i
$218$	−2.89965	−	16.4447i	−0.196389	−	1.11378i
$219$	11.5712	−	5.00753i	0.781909	−	0.338377i
$220$	0.175743	−	0.574923i	0.0118486	−	0.0387613i
$221$	−2.85327	−	4.94202i	−0.191932	−	0.332436i
$222$	−13.0443	−	9.68724i	−0.875477	−	0.650165i
$223$	−5.31883	+	1.93590i	−0.356175	+	0.129637i	−0.513909	−	0.857844i	$-0.671803\pi$
$223$	−5.31883	+	1.93590i	−0.356175	+	0.129637i	0.157734	+	0.987482i	$0.449581\pi$
$224$	−1.61049	−	0.586170i	−0.107605	−	0.0391651i
$225$	−14.6268	+	3.32502i	−0.975122	+	0.221668i
$226$	−1.28420	+	7.28303i	−0.0854234	+	0.484460i
$227$		−	13.8007i		−	0.915983i	−0.888956	−	0.457992i	$-0.848569\pi$
$227$		−	13.8007i		−	0.915983i	0.888956	−	0.457992i	$-0.151431\pi$
$228$	1.77016	−	7.33938i	0.117232	−	0.486062i
$229$	−1.43517			−0.0948389			−0.0474194	−	0.998875i	$-0.515100\pi$
$229$	−1.43517			−0.0948389			−0.0474194	+	0.998875i	$0.515100\pi$
$230$	0.0999185	+	1.90492i	0.00658843	+	0.125607i
$231$	−0.713626	−	0.357343i	−0.0469532	−	0.0235114i
$232$	−0.703052	+	1.93162i	−0.0461576	+	0.126817i
$233$	11.7741	−	4.28541i	0.771345	−	0.280747i	0.0737860	−	0.997274i	$-0.476492\pi$
$233$	11.7741	−	4.28541i	0.771345	−	0.280747i	0.697559	+	0.716528i	$0.254270\pi$
$234$	−10.2267	−	4.38278i	−0.668541	−	0.286511i
$235$	13.4545	−	12.5477i	0.877676	−	0.818520i
$236$	7.03517	−	12.1853i	0.457950	−	0.793193i
$237$	−8.37451	+	3.62413i	−0.543983	+	0.235413i
$238$	−0.457917	−	2.59698i	−0.0296823	−	0.168337i
$239$	2.10709	+	1.21653i	0.136297	+	0.0786909i	0.566598	−	0.823994i	$-0.308259\pi$
$239$	2.10709	+	1.21653i	0.136297	+	0.0786909i	−0.430301	+	0.902685i	$0.641593\pi$
$240$	2.14308	−	3.22602i	0.138335	−	0.208239i
$241$	8.71138	+	10.3818i	0.561150	+	0.668752i	0.969789	−	0.243944i	$-0.0784412\pi$
$241$	8.71138	+	10.3818i	0.561150	+	0.668752i	−0.408640	+	0.912696i	$0.633997\pi$
$242$	−3.73750	−	10.2687i	−0.240256	−	0.660097i
$243$	10.6304	−	11.4015i	0.681939	−	0.731409i
$244$	−0.906639	−	0.760761i	−0.0580416	−	0.0487027i
$245$	−9.07207	+	0.475857i	−0.579593	+	0.0304014i
$246$	−1.01669	−	4.26730i	−0.0648217	−	0.272073i
$247$	−15.4630	−	4.71598i	−0.983884	−	0.300071i
$248$	0.282812			0.0179586
$249$	1.52765	+	25.7063i	0.0968112	+	1.62907i
$250$	−11.1787	−	0.193613i	−0.707001	−	0.0122452i
$251$	−7.49044	+	20.5798i	−0.472792	+	1.29899i	0.442707	+	0.896666i	$0.354018\pi$
$251$	−7.49044	+	20.5798i	−0.472792	+	1.29899i	−0.915499	+	0.402320i	$0.868204\pi$
$252$	−3.74813	−	3.51950i	−0.236110	−	0.221708i
$253$	−0.147427	−	0.175697i	−0.00926867	−	0.0110460i
$254$	−1.39985	+	0.808206i	−0.0878346	+	0.0507113i
$255$	5.94749	+	0.373819i	0.372446	+	0.0234094i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	7.45354	−	1.31426i	0.464939	−	0.0819813i	0.0637288	−	0.997967i	$-0.479701\pi$
$257$	7.45354	−	1.31426i	0.464939	−	0.0819813i	0.401210	+	0.915986i	$0.368590\pi$
$258$	2.91647	−	9.78367i	0.181571	−	0.609105i
$259$	−13.9233	+	8.03860i	−0.865150	+	0.499495i
$260$	−6.62335	−	4.99058i	−0.410762	−	0.309503i
$261$	−4.22129	+	4.49551i	−0.261291	+	0.278265i
$262$	3.25160	+	1.18349i	0.200885	+	0.0731161i
$263$	−9.68843	−	8.12956i	−0.597414	−	0.501290i	0.293199	−	0.956051i	$-0.405280\pi$
$263$	−9.68843	−	8.12956i	−0.597414	−	0.501290i	−0.890613	+	0.454761i	$0.849725\pi$
$264$	0.0276250	+	0.464855i	0.00170020	+	0.0286099i
$265$	−6.95383	+	1.60575i	−0.427170	+	0.0986403i
$266$	−5.96926	−	4.49178i	−0.365999	−	0.275409i
$267$	−23.4445	+	5.58568i	−1.43478	+	0.341838i
$268$	0.393781	−	2.23324i	0.0240540	−	0.136417i
$269$	−21.9392	−	18.4092i	−1.33766	−	1.12243i	−0.982222	−	0.187725i	$-0.939889\pi$
$269$	−21.9392	−	18.4092i	−1.33766	−	1.12243i	−0.355434	−	0.934701i	$-0.615667\pi$
$270$	9.72173	−	6.36302i	0.591645	−	0.387241i
$271$	−8.81392	+	3.20800i	−0.535407	+	0.194872i	−0.595551	−	0.803317i	$-0.703066\pi$
$271$	−8.81392	+	3.20800i	−0.535407	+	0.194872i	0.0601437	+	0.998190i	$0.480844\pi$
$272$	−1.17869	+	0.989036i	−0.0714684	+	0.0599691i
$273$	−7.99899	+	7.56451i	−0.484121	+	0.457825i
$274$	17.4577	+	10.0792i	1.05466	+	0.608908i
$275$	1.08748	−	0.790251i	0.0655776	−	0.0476539i
$276$	−0.586836	−	1.35604i	−0.0353234	−	0.0816239i
$277$	3.47035	+	2.00361i	0.208513	+	0.120385i	0.600620	−	0.799534i	$-0.294920\pi$
$277$	3.47035	+	2.00361i	0.208513	+	0.120385i	−0.392107	+	0.919920i	$0.628254\pi$
$278$	−16.5169	+	9.53602i	−0.990616	+	0.571932i
$279$	0.779838	+	0.334209i	0.0466877	+	0.0200086i
$280$	−2.08735	−	3.21392i	−0.124743	−	0.192069i
$281$	3.96398	+	1.44277i	0.236471	+	0.0860685i	0.457538	−	0.889190i	$-0.348732\pi$
$281$	3.96398	+	1.44277i	0.236471	+	0.0860685i	−0.221066	+	0.975259i	$0.570954\pi$
$282$	−6.38065	+	12.7424i	−0.379962	+	0.758797i
$283$	−7.69224	−	1.35635i	−0.457256	−	0.0806266i	−0.0597241	−	0.998215i	$-0.519022\pi$
$283$	−7.69224	−	1.35635i	−0.457256	−	0.0806266i	−0.397532	+	0.917588i	$0.630133\pi$
$284$	−2.39015			−0.141829
$285$	13.0373	−	10.7252i	0.772262	−	0.635304i
$286$	0.997129			0.0589615
$287$	−4.27469	−	0.753744i	−0.252327	−	0.0444921i
$288$	−0.684958	+	2.92076i	−0.0403615	+	0.172107i
$289$	13.7501	+	5.00461i	0.808827	+	0.294389i
$290$	−3.85478	+	2.50357i	−0.226360	+	0.147015i
$291$	−6.21007	+	8.36215i	−0.364041	+	0.490198i
$292$	−6.30412	+	3.63969i	−0.368921	+	0.212997i
$293$	−19.3607	−	11.1779i	−1.13106	−	0.653020i	−0.186862	−	0.982386i	$-0.559832\pi$
$293$	−19.3607	−	11.1779i	−1.13106	−	0.653020i	−0.944202	+	0.329366i	$0.893165\pi$
$294$	6.45806	−	2.79478i	0.376642	−	0.162995i
$295$	28.9606	−	12.2946i	1.68615	−	0.715818i
$296$	8.12399	+	4.69039i	0.472197	+	0.272623i
$297$	−0.473162	+	1.31446i	−0.0274556	+	0.0762726i
$298$	17.4018	−	14.6019i	1.00806	−	0.845864i
$299$	−2.97305	+	1.08210i	−0.171936	+	0.0625796i
$300$	8.16824	−	2.87747i	0.471594	−	0.166131i
$301$	−7.73844	−	6.49332i	−0.446036	−	0.374269i
$302$	1.78581	−	10.1278i	0.102762	−	0.582790i
$303$	2.03237	+	8.53036i	0.116756	+	0.490057i
$304$	−0.528268	+	4.32677i	−0.0302982	+	0.248157i
$305$	−0.595441	−	2.57861i	−0.0340948	−	0.147651i
$306$	−4.41894	+	1.33431i	−0.252614	+	0.0762776i
$307$	1.85340	+	1.55519i	0.105779	+	0.0887592i	0.694143	−	0.719837i	$-0.255783\pi$
$307$	1.85340	+	1.55519i	0.105779	+	0.0887592i	−0.588364	+	0.808596i	$0.700228\pi$
$308$	0.432992	+	0.157596i	0.0246720	+	0.00897988i
$309$	13.7603	−	9.07354i	0.782794	−	0.516176i
$310$	0.505064	+	0.380557i	0.0286857	+	0.0216142i
$311$	23.3442	−	13.4778i	1.32373	−	0.764254i	0.339406	−	0.940640i	$-0.389774\pi$
$311$	23.3442	−	13.4778i	1.32373	−	0.764254i	0.984321	+	0.176386i	$0.0564406\pi$
$312$	6.15607	+	1.83510i	0.348519	+	0.103892i
$313$	−19.5355	+	3.44464i	−1.10421	+	0.194702i	−0.695899	−	0.718139i	$-0.744994\pi$
$313$	−19.5355	+	3.44464i	−1.10421	+	0.194702i	−0.408313	+	0.912842i	$0.633883\pi$
$314$	1.67496	+	9.49919i	0.0945237	+	0.536070i
$315$	−1.95775	−	11.3289i	−0.110307	−	0.638312i
$316$	4.56253	−	2.63418i	0.256662	−	0.148184i
$317$	11.5302	+	13.7411i	0.647600	+	0.771779i	0.985550	−	0.169385i	$-0.0541780\pi$
$317$	11.5302	+	13.7411i	0.647600	+	0.771779i	−0.337950	+	0.941164i	$0.609734\pi$
$318$	4.61512	−	3.04322i	0.258803	−	0.170655i
$319$	0.189021	−	0.519331i	0.0105831	−	0.0290769i
$320$	−1.01506	+	1.99240i	−0.0567438	+	0.111378i
$321$	−24.5516	+	1.45904i	−1.37034	+	0.0814354i
$322$	−1.46204			−0.0814764
$323$	−6.17194	+	2.62480i	−0.343416	+	0.146048i
$324$	−5.34030	+	7.24439i	−0.296683	+	0.402466i
$325$	−5.11297	−	17.8250i	−0.283617	−	0.988753i
$326$	16.5580	+	13.8938i	0.917064	+	0.769508i
$327$	−3.32380	+	28.7309i	−0.183807	+	1.58882i
$328$	0.866230	+	2.37995i	0.0478296	+	0.131411i
$329$	9.06386	+	10.8019i	0.499707	+	0.595527i
$330$	−0.576183	+	0.867341i	−0.0317178	+	0.0477455i
$331$	21.8174	+	12.5963i	1.19919	+	0.692355i	0.960376	−	0.278709i	$-0.0899064\pi$
$331$	21.8174	+	12.5963i	1.19919	+	0.692355i	0.238819	+	0.971064i	$0.423240\pi$
$332$	−2.58176	−	14.6419i	−0.141692	−	0.803576i
$333$	16.8586	+	22.5339i	0.923848	+	1.23485i
$334$	−7.38809	+	12.7965i	−0.404258	+	0.700196i
$335$	3.70834	−	3.45839i	0.202608	−	0.188952i
$336$	2.38317	+	1.76984i	0.130012	+	0.0965525i
$337$	0.194977	−	0.0709657i	0.0106211	−	0.00386575i	−0.336704	−	0.941610i	$-0.609312\pi$
$337$	0.194977	−	0.0709657i	0.0106211	−	0.00386575i	0.347325	+	0.937745i	$0.387090\pi$
$338$	0.258198	−	0.709392i	0.0140441	−	0.0385859i
$339$	5.73524	−	11.4535i	0.311496	−	0.622068i
$340$	−3.43584	+	0.180220i	−0.186335	+	0.00977380i
$341$	−0.0760361			−0.00411759
$342$	−6.56977	+	11.3066i	−0.355252	+	0.611388i
$343$		−	18.9598i		−	1.02373i
$344$	−1.02352	+	5.80469i	−0.0551847	+	0.312968i
$345$	0.776701	−	3.21136i	0.0418162	−	0.172894i
$346$	9.22564	+	3.35786i	0.495973	+	0.180520i
$347$	27.1609	−	9.88575i	1.45807	−	0.530695i	0.513239	−	0.858246i	$-0.328446\pi$
$347$	27.1609	−	9.88575i	1.45807	−	0.530695i	0.944833	+	0.327551i	$0.106223\pi$
$348$	2.12274	−	2.85837i	0.113791	−	0.153225i
$349$	−10.8248	−	18.7491i	−0.579438	−	1.00362i	−0.995544	−	0.0942999i	$-0.969939\pi$
$349$	−10.8248	−	18.7491i	−0.579438	−	1.00362i	0.416106	−	0.909316i	$-0.363395\pi$
$350$	0.596989	−	8.54841i	0.0319104	−	0.456932i
$351$	14.8064	+	12.3350i	0.790308	+	0.658395i
$352$	−0.0466866	−	0.264773i	−0.00248841	−	0.0141125i
$353$	−14.4043	+	24.9490i	−0.766665	+	1.32790i	0.172697	+	0.984975i	$0.444752\pi$
$353$	−14.4043	+	24.9490i	−0.766665	+	1.32790i	−0.939362	+	0.342927i	$0.888582\pi$
$354$	−17.7067	+	16.7450i	−0.941102	+	0.889985i
$355$	−4.26848	−	3.21623i	−0.226548	−	0.170700i
$356$	13.0754	−	4.75907i	0.692996	−	0.252230i
$357$	−0.524900	+	4.53722i	−0.0277807	+	0.240135i
$358$	−1.07985	+	1.28692i	−0.0570719	+	0.0680157i
$359$	−8.08336	−	1.42531i	−0.426623	−	0.0752252i	−0.0437858	−	0.999041i	$-0.513942\pi$
$359$	−8.08336	−	1.42531i	−0.426623	−	0.0752252i	−0.382837	+	0.923816i	$0.625053\pi$
$360$	−5.15347	+	4.29439i	−0.271612	+	0.226334i
$361$	−7.70433	+	17.3679i	−0.405491	+	0.914099i
$362$	15.2751			0.802841
$363$	1.12282	+	18.8940i	0.0589327	+	0.991679i
$364$	4.08572	−	4.86917i	0.214150	−	0.255214i
$365$	−16.1559	−	1.98296i	−0.845641	−	0.103793i
$366$	1.12848	+	1.71137i	0.0589866	+	0.0894547i
$367$	−3.85915	−	4.59915i	−0.201446	−	0.240074i	0.655858	−	0.754884i	$-0.272307\pi$
$367$	−3.85915	−	4.59915i	−0.201446	−	0.240074i	−0.857304	+	0.514810i	$0.827862\pi$
$368$	0.426538	+	0.738785i	0.0222348	+	0.0385119i
$369$	−0.423890	+	7.58623i	−0.0220668	+	0.394923i
$370$	8.19687	+	19.3082i	0.426135	+	1.00378i
$371$	−0.949865	−	5.38695i	−0.0493145	−	0.279677i
$372$	−0.469431	−	0.139935i	−0.0243389	−	0.00725531i
$373$	−9.09941	−	15.7606i	−0.471149	−	0.816055i	0.528306	−	0.849054i	$-0.322827\pi$
$373$	−9.09941	−	15.7606i	−0.471149	−	0.816055i	−0.999455	+	0.0329993i	$0.989494\pi$
$374$	0.316899	−	0.265910i	0.0163865	−	0.0137499i
$375$	18.4593	+	5.85257i	0.953236	+	0.302226i
$376$	2.81401	−	7.73143i	0.145121	−	0.398718i
$377$	−5.84008	−	4.90041i	−0.300779	−	0.252384i
$378$	4.47997	+	7.69650i	0.230425	+	0.395865i
$379$		−	12.5834i		−	0.646365i	−0.946337	−	0.323182i	$-0.895247\pi$
$379$		−	12.5834i		−	0.646365i	0.946337	−	0.323182i	$-0.104753\pi$
$380$	−6.76560	+	7.01617i	−0.347068	+	0.359922i
$381$	2.72348	−	0.648870i	0.139528	−	0.0332426i
$382$	0.820822	−	4.65511i	0.0419969	−	0.238176i
$383$	−6.53894	+	7.79281i	−0.334124	+	0.398194i	−0.906781	−	0.421601i	$-0.861468\pi$
$383$	−6.53894	+	7.79281i	−0.334124	+	0.398194i	0.572657	+	0.819795i	$0.305913\pi$
$384$	0.199049	−	1.72058i	0.0101577	−	0.0878027i
$385$	0.561201	+	0.864088i	0.0286014	+	0.0440380i
$386$	−5.93447	−	7.07242i	−0.302056	−	0.359977i
$387$	−9.68192	+	14.7966i	−0.492160	+	0.752152i
$388$	3.00681	−	5.20794i	0.152647	−	0.264393i
$389$	−21.5108	+	3.79294i	−1.09064	+	0.192310i	−0.689917	−	0.723889i	$-0.742353\pi$
$389$	−21.5108	+	3.79294i	−1.09064	+	0.192310i	−0.400725	+	0.916198i	$0.631242\pi$
$390$	8.52456	+	11.5610i	0.431658	+	0.585412i
$391$	−0.656300	+	1.13674i	−0.0331905	+	0.0574876i
$392$	−3.51843	+	2.03137i	−0.177707	+	0.102599i
$393$	−4.81166	−	3.57333i	−0.242716	−	0.180251i
$394$	2.15861	+	5.93072i	0.108749	+	0.298785i
$395$	11.6927	+	1.43514i	0.588321	+	0.0722099i
$396$	0.184156	−	0.785269i	0.00925420	−	0.0394612i
$397$	18.4723	+	3.25716i	0.927096	+	0.163472i	0.616757	−	0.787154i	$-0.288446\pi$
$397$	18.4723	+	3.25716i	0.927096	+	0.163472i	0.310339	+	0.950626i	$0.399557\pi$
$398$			24.1729i			1.21168i
$399$	7.68566	+	10.4094i	0.384764	+	0.521120i
$400$	−4.49377	+	2.19226i	−0.224689	+	0.109613i
$401$	0.952616	−	5.40255i	0.0475714	−	0.269791i	−0.951740	−	0.306907i	$-0.900706\pi$
$401$	0.952616	−	5.40255i	0.0475714	−	0.269791i	0.999311	+	0.0371161i	$0.0118171\pi$
$402$	−1.75864	+	3.51206i	−0.0877128	+	0.175165i
$403$	−0.358739	+	0.985627i	−0.0178701	+	0.0490976i
$404$	−1.73160	−	4.75753i	−0.0861503	−	0.236696i
$405$	−19.2852	+	5.75149i	−0.958291	+	0.285794i
$406$	−1.76148	−	3.05097i	−0.0874208	−	0.151417i
$407$	−2.18420	−	1.26105i	−0.108267	−	0.0625078i
$408$	2.44584	−	1.05846i	0.121087	−	0.0524015i
$409$	26.4803	−	4.66918i	1.30936	−	0.230876i	0.524960	−	0.851127i	$-0.324080\pi$
$409$	26.4803	−	4.66918i	1.30936	−	0.230876i	0.784404	+	0.620250i	$0.212969\pi$
$410$	−1.65553	+	5.41588i	−0.0817610	+	0.267471i
$411$	−23.9904	−	25.3683i	−1.18336	−	1.25133i
$412$	−7.28983	+	6.11689i	−0.359144	+	0.301358i
$413$	8.24761	+	22.6601i	0.405838	+	1.11503i
$414$	0.303105	+	2.54122i	0.0148968	+	0.124894i
$415$	15.0917	−	29.6224i	0.740822	−	1.45411i
$416$	−3.65242	−	0.644020i	−0.179075	−	0.0315757i
$417$	32.1343	−	7.65602i	1.57362	−	0.374917i
$418$	0.142029	−	1.16329i	0.00694686	−	0.0568981i
$419$			26.6623i			1.30254i	0.758847	+	0.651269i	$0.225763\pi$
$419$			26.6623i			1.30254i	−0.758847	+	0.651269i	$0.774237\pi$
$420$	1.87449	+	6.36752i	0.0914656	+	0.310703i
$421$	18.3324	−	21.8477i	0.893466	−	1.06479i	−0.104066	−	0.994570i	$-0.533185\pi$
$421$	18.3324	−	21.8477i	0.893466	−	1.06479i	0.997532	−	0.0702204i	$-0.0223703\pi$
$422$	14.5579	+	5.29864i	0.708667	+	0.257934i
$423$	16.8960	−	17.9936i	0.821511	−	0.874877i
$424$	−2.44497	+	2.05157i	−0.118738	+	0.0996332i
$425$	−6.37845	−	4.30148i	−0.309400	−	0.208653i
$426$	3.96734	+	1.18265i	0.192218	+	0.0572994i
$427$	1.99758	−	0.352227i	0.0966696	−	0.0170455i
$428$	13.9842	−	2.46579i	0.675951	−	0.119188i
$429$	−1.65511	−	0.493379i	−0.0799093	−	0.0238206i
$430$	−9.63877	+	8.98911i	−0.464823	+	0.433493i
$431$	−24.3191	+	20.4062i	−1.17141	+	0.982930i	−0.999997	−	0.00226871i	$-0.999278\pi$
$431$	−24.3191	+	20.4062i	−1.17141	+	0.982930i	−0.171413	+	0.985199i	$0.554833\pi$
$432$	2.58213	−	4.50917i	0.124233	−	0.216947i
$433$	23.5039	+	8.55473i	1.12953	+	0.411114i	0.838121	−	0.545485i	$-0.183655\pi$
$433$	23.5039	+	8.55473i	1.12953	+	0.411114i	0.291407	+	0.956599i	$0.405877\pi$
$434$	−0.311557	+	0.371299i	−0.0149552	+	0.0178229i
$435$	7.63721	−	2.24826i	0.366176	−	0.107796i
$436$		−	16.6984i		−	0.799709i
$437$	0.838943	+	3.62260i	0.0401321	+	0.173292i
$438$	12.2650	−	2.92213i	0.586042	−	0.139625i
$439$	−34.2253	−	6.03484i	−1.63348	−	0.288027i	−0.719716	−	0.694268i	$-0.755728\pi$
$439$	−34.2253	−	6.03484i	−1.63348	−	0.288027i	−0.913766	+	0.406241i	$0.866839\pi$
$440$	0.272908	−	0.535671i	0.0130104	−	0.0255371i
$441$	−12.1024	+	1.44352i	−0.576305	+	0.0687392i
$442$	−1.95175	−	5.36240i	−0.0928355	−	0.255063i
$443$	4.69348	−	3.93830i	0.222994	−	0.187114i	−0.524446	−	0.851444i	$-0.675727\pi$
$443$	4.69348	−	3.93830i	0.222994	−	0.187114i	0.747440	+	0.664330i	$0.231283\pi$
$444$	−11.1640	−	11.8052i	−0.529819	−	0.560250i
$445$	29.7548	+	9.09550i	1.41051	+	0.431168i
$446$	−5.57419	+	0.982880i	−0.263946	+	0.0465407i
$447$	−36.1098	+	15.6268i	−1.70794	+	0.739123i
$448$	−1.48423	−	0.856923i	−0.0701235	−	0.0404858i
$449$	10.6754	+	18.4903i	0.503802	+	0.872611i	0.999990	+	0.00439613i	$0.00139934\pi$
$449$	10.6754	+	18.4903i	0.503802	+	0.872611i	−0.496188	+	0.868215i	$0.665267\pi$
$450$	−14.9820	+	0.734582i	−0.706258	+	0.0346285i
$451$	−0.232893	−	0.639867i	−0.0109665	−	0.0301302i
$452$	−2.52937	+	6.94939i	−0.118972	+	0.326872i
$453$	−7.97545	+	15.9272i	−0.374719	+	0.748327i
$454$	2.39646	−	13.5910i	0.112472	−	0.637858i
$455$	13.8486	−	3.19785i	0.649232	−	0.149918i
$456$	3.01774	−	6.92049i	0.141319	−	0.324082i
$457$		−	25.3271i		−	1.18475i	−0.805661	−	0.592377i	$-0.798190\pi$
$457$		−	25.3271i		−	1.18475i	0.805661	−	0.592377i	$-0.201810\pi$
$458$	−1.41337	−	0.249215i	−0.0660424	−	0.0116451i
$459$	7.99509	−	0.0282968i	0.373179	−	0.00132078i
$460$	−0.232385	+	1.89333i	−0.0108350	+	0.0882769i
$461$	−10.0255	−	27.5449i	−0.466935	−	1.28289i	−0.920176	−	0.391506i	$-0.871954\pi$
$461$	−10.0255	−	27.5449i	−0.466935	−	1.28289i	0.453240	−	0.891388i	$-0.350268\pi$
$462$	−0.640733	−	0.475834i	−0.0298096	−	0.0221378i
$463$	−10.1011	+	5.83185i	−0.469436	+	0.271029i	−0.716004	−	0.698097i	$-0.754031\pi$
$463$	−10.1011	+	5.83185i	−0.469436	+	0.271029i	0.246568	+	0.969126i	$0.420697\pi$
$464$	−1.02779	+	1.78019i	−0.0477141	+	0.0826433i
$465$	−0.650041	−	0.881581i	−0.0301449	−	0.0408823i
$466$	12.3393	−	2.17576i	0.571609	−	0.100790i
$467$	16.4861	−	28.5548i	0.762886	−	1.32136i	−0.178471	−	0.983945i	$-0.557115\pi$
$467$	16.4861	−	28.5548i	0.762886	−	1.32136i	0.941357	−	0.337413i	$-0.109552\pi$
$468$	−9.31028	−	6.09204i	−0.430368	−	0.281605i
$469$	2.49818	+	2.97722i	0.115355	+	0.137475i
$470$	15.4290	−	10.0207i	0.711686	−	0.462220i
$471$	1.91997	−	16.5962i	0.0884677	−	0.764713i
$472$	9.04423	−	10.7785i	0.416295	−	0.496121i
$473$	0.275182	−	1.56064i	0.0126529	−	0.0717581i
$474$	−8.87660	+	2.11486i	−0.407716	+	0.0971386i
$475$	−21.5235	+	3.42602i	−0.987567	+	0.157196i
$476$		−	2.63704i		−	0.120868i
$477$	−9.16629	+	2.76779i	−0.419696	+	0.126728i
$478$	1.86383	+	1.56394i	0.0852498	+	0.0715331i
$479$	−12.2694	+	33.7099i	−0.560604	+	1.54025i	0.258152	+	0.966104i	$0.416886\pi$
$479$	−12.2694	+	33.7099i	−0.560604	+	1.54025i	−0.818756	+	0.574142i	$0.805336\pi$
$480$	2.67071	−	2.80487i	0.121901	−	0.128024i
$481$	−26.6515	+	22.3633i	−1.21520	+	1.01968i
$482$	6.77625	+	11.7368i	0.308650	+	0.534597i
$483$	2.42680	+	0.723418i	0.110423	+	0.0329166i
$484$	−1.89758	−	10.7617i	−0.0862535	−	0.489168i
$485$	12.3776	−	5.25466i	0.562040	−	0.238602i
$486$	12.4487	−	9.38238i	0.564686	−	0.425593i
$487$	5.11325	+	8.85641i	0.231704	+	0.401322i	0.958310	−	0.285732i	$-0.0922368\pi$
$487$	5.11325	+	8.85641i	0.231704	+	0.401322i	−0.726606	+	0.687054i	$0.758903\pi$
$488$	−0.760761	−	0.906639i	−0.0344380	−	0.0410416i
$489$	−20.6095	−	31.2549i	−0.931994	−	1.41339i
$490$	−9.01688	−	1.10672i	−0.407341	−	0.0499966i
$491$	−5.68342	+	6.77324i	−0.256489	+	0.305672i	−0.878888	−	0.477028i	$-0.841714\pi$
$491$	−5.68342	+	6.77324i	−0.256489	+	0.305672i	0.622399	+	0.782701i	$0.286158\pi$
$492$	−0.260233	−	4.37902i	−0.0117322	−	0.197421i
$493$	−3.16286			−0.142448
$494$	−14.4091	−	7.32945i	−0.648297	−	0.329767i
$495$	1.38555	−	1.15458i	0.0622758	−	0.0518944i
$496$	0.278515	+	0.0491098i	0.0125057	+	0.00220509i
$497$	2.63308	−	3.13799i	0.118110	−	0.140758i
$498$	−2.95941	+	25.5811i	−0.132614	+	1.14631i
$499$	−16.4654	+	5.99292i	−0.737093	+	0.268280i	−0.683164	−	0.730265i	$-0.739397\pi$
$499$	−16.4654	+	5.99292i	−0.737093	+	0.268280i	−0.0539286	+	0.998545i	$0.517174\pi$
$500$	−10.9752	−	2.13183i	−0.490826	−	0.0953382i
$501$	18.5950	−	17.5850i	0.830763	−	0.785639i
$502$	−10.9503	+	18.9665i	−0.488735	+	0.846515i
$503$	3.73623	+	21.1892i	0.166590	+	0.944780i	0.947410	+	0.320023i	$0.103691\pi$
$503$	3.73623	+	21.1892i	0.166590	+	0.944780i	−0.780819	+	0.624757i	$0.785198\pi$
$504$	−3.08004	−	4.11689i	−0.137196	−	0.183381i
$505$	3.30942	−	10.8264i	0.147267	−	0.481767i
$506$	−0.114678	−	0.198628i	−0.00509806	−	0.00883010i
$507$	−0.779582	+	1.04974i	−0.0346225	+	0.0466208i
$508$	−1.51893	+	0.552845i	−0.0673916	+	0.0245285i
$509$	25.5723	+	9.30755i	1.13347	+	0.412550i	0.839552	−	0.543280i	$-0.182818\pi$
$509$	25.5723	+	9.30755i	1.13347	+	0.412550i	0.293920	+	0.955830i	$0.405040\pi$
$510$	5.79222	+	1.40091i	0.256484	+	0.0620334i
$511$	2.16639	−	12.2862i	0.0958354	−	0.543509i
$512$			1.00000i			0.0441942i
$513$	16.4995	−	15.5167i	0.728469	−	0.685079i
$514$	7.56853			0.333833
$515$	−21.2497	+	1.11461i	−0.936372	+	0.0491155i
$516$	4.57108	−	9.12860i	0.201230	−	0.401864i
$517$	−0.756568	+	2.07865i	−0.0332738	+	0.0914191i
$518$	−15.1076	+	5.49873i	−0.663791	+	0.241600i
$519$	−13.6519	−	10.1385i	−0.599252	−	0.445029i
$520$	−5.65612	−	6.06489i	−0.248037	−	0.265963i
$521$	10.2847	−	17.8136i	0.450580	−	0.780428i	−0.547842	−	0.836582i	$-0.684550\pi$
$521$	10.2847	−	17.8136i	0.450580	−	0.780428i	0.998422	+	0.0561538i	$0.0178837\pi$
$522$	−4.93780	+	3.69420i	−0.216122	+	0.161691i
$523$	−3.11314	−	17.6555i	−0.136128	−	0.772021i	−0.974067	−	0.226258i	$-0.927351\pi$
$523$	−3.11314	−	17.6555i	−0.136128	−	0.772021i	0.837939	−	0.545763i	$-0.183760\pi$
$524$	2.99669	+	1.73014i	0.130911	+	0.0755816i
$525$	−5.22068	+	13.8939i	−0.227849	+	0.606378i
$526$	−8.12956	−	9.68843i	−0.354466	−	0.422436i
$527$	0.148831	+	0.408910i	0.00648319	+	0.0178124i
$528$	−0.0535159	+	0.462590i	−0.00232898	+	0.0201316i
$529$	−17.0615	−	14.3163i	−0.741806	−	0.622449i
$530$	−7.12702	+	0.373833i	−0.309578	+	0.0162383i
$531$	37.6763	−	19.0332i	1.63501	−	0.825971i
$532$	−5.09858	−	5.46009i	−0.221051	−	0.236725i
$533$	−9.39314			−0.406862
$534$	−24.0583	+	1.42972i	−1.04111	+	0.0618700i
$535$	28.2918	+	14.4138i	1.22316	+	0.623163i
$536$	0.775598	−	2.13094i	0.0335007	−	0.0920425i
$537$	2.42918	−	1.60181i	0.104827	−	0.0691231i
$538$	−18.4092	−	21.9392i	−0.793675	−	0.945865i
$539$	0.945956	−	0.546148i	0.0407452	−	0.0235243i
$540$	10.6790	−	4.57819i	0.459549	−	0.197014i
$541$	2.60101	+	14.7510i	0.111826	+	0.634196i	0.988273	+	0.152698i	$0.0487962\pi$
$541$	2.60101	+	14.7510i	0.111826	+	0.634196i	−0.876447	+	0.481498i	$0.840093\pi$
$542$	−9.23708	+	1.62875i	−0.396767	+	0.0699607i
$543$	−25.3547	−	7.55812i	−1.08807	−	0.324350i
$544$	−1.33252	+	0.769333i	−0.0571315	+	0.0329849i
$545$	22.4697	−	29.8211i	0.962496	−	1.27739i
$546$	−9.19103	+	6.06058i	−0.393340	+	0.259369i
$547$	−33.9042	−	12.3401i	−1.44964	−	0.527626i	−0.507149	−	0.861858i	$-0.669301\pi$
$547$	−33.9042	−	12.3401i	−1.44964	−	0.527626i	−0.942491	+	0.334233i	$0.891523\pi$
$548$	15.4423	+	12.9576i	0.659661	+	0.553521i
$549$	−1.02635	−	3.39903i	−0.0438034	−	0.145067i
$550$	1.20819	−	0.589406i	0.0515172	−	0.0251324i
$551$	−6.54883	+	6.11523i	−0.278990	+	0.260518i
$552$	−0.342447	−	1.43734i	−0.0145755	−	0.0611772i
$553$	−1.56790	+	8.89198i	−0.0666737	+	0.378125i
$554$	3.06970	+	2.57579i	0.130419	+	0.109435i
$555$	−4.05205	−	36.1049i	−0.172000	−	1.53257i
$556$	−17.9219	+	6.52302i	−0.760056	+	0.276638i
$557$	16.6543	−	13.9746i	0.705665	−	0.592123i	−0.217714	−	0.976013i	$-0.569860\pi$
$557$	16.6543	−	13.9746i	0.705665	−	0.592123i	0.923379	+	0.383889i	$0.125416\pi$
$558$	0.709956	+	0.464549i	0.0300548	+	0.0196659i
$559$	−18.9316	−	10.9302i	−0.800721	−	0.462296i
$560$	−1.49755	−	3.52756i	−0.0632830	−	0.149067i
$561$	−0.657584	+	0.284575i	−0.0277632	+	0.0120147i
$562$	3.65322	+	2.10919i	0.154102	+	0.0889708i
$563$	18.7954	−	10.8516i	0.792134	−	0.457339i	−0.0485795	−	0.998819i	$-0.515469\pi$
$563$	18.7954	−	10.8516i	0.792134	−	0.457339i	0.840713	+	0.541481i	$0.182136\pi$
$564$	−8.49640	+	11.4408i	−0.357763	+	0.481745i
$565$	−13.8683	+	9.00710i	−0.583446	+	0.378931i
$566$	−7.33985	−	2.67149i	−0.308517	−	0.112291i
$567$	−3.62795	−	14.9919i	−0.152360	−	0.629600i
$568$	−2.35384	−	0.415045i	−0.0987649	−	0.0174149i
$569$	11.9807			0.502255			0.251128	−	0.967954i	$-0.419199\pi$
$569$	11.9807			0.502255			0.251128	+	0.967954i	$0.419199\pi$
$570$	14.7016	−	8.29833i	0.615783	−	0.347579i
$571$	11.2374			0.470273			0.235136	−	0.971962i	$-0.424446\pi$
$571$	11.2374			0.470273			0.235136	+	0.971962i	$0.424446\pi$
$572$	0.981981	+	0.173150i	0.0410587	+	0.00723975i
$573$	−3.66581	+	7.32075i	−0.153141	+	0.305829i
$574$	−4.07887	−	1.48459i	−0.170249	−	0.0619654i
$575$	−2.96271	+	3.06852i	−0.123553	+	0.127966i
$576$	−1.18174	+	2.75744i	−0.0492390	+	0.114894i
$577$	38.2042	−	22.0572i	1.59046	−	0.918254i	0.597236	−	0.802065i	$-0.296265\pi$
$577$	38.2042	−	22.0572i	1.59046	−	0.918254i	0.993227	−	0.116189i	$-0.0370679\pi$
$578$	12.6721	+	7.31625i	0.527091	+	0.304316i
$579$	6.35102	+	14.6757i	0.263939	+	0.609901i
$580$	−4.23096	+	1.79616i	−0.175681	+	0.0745815i
$581$	22.0672	+	12.7405i	0.915502	+	0.528565i
$582$	−7.56780	+	7.15674i	−0.313695	+	0.296657i
$583$	0.657349	−	0.551581i	0.0272246	−	0.0228442i
$584$	−6.84038	+	2.48969i	−0.283057	+	0.103024i
$585$	−8.42932	−	23.4076i	−0.348509	−	0.967787i
$586$	−17.1255	−	14.3700i	−0.707450	−	0.593621i
$587$	3.47915	−	19.7312i	0.143600	−	0.814395i	−0.824881	−	0.565307i	$-0.808758\pi$
$587$	3.47915	−	19.7312i	0.143600	−	0.814395i	0.968481	−	0.249089i	$-0.0801310\pi$
$588$	6.84526	−	1.63089i	0.282294	−	0.0672567i
$589$	1.09877	+	0.558907i	0.0452739	+	0.0230294i
$590$	30.6555	−	7.07884i	1.26207	−	0.291431i
$591$	−0.648488	−	10.9123i	−0.0266752	−	0.448872i
$592$	7.18609	+	6.02985i	0.295347	+	0.247825i
$593$	−29.8213	−	10.8541i	−1.22462	−	0.445723i	−0.352865	−	0.935674i	$-0.614793\pi$
$593$	−29.8213	−	10.8541i	−1.22462	−	0.445723i	−0.871750	+	0.489951i	$0.837015\pi$
$594$	−0.694226	+	1.21232i	−0.0284845	+	0.0497423i
$595$	3.54845	−	4.70939i	0.145472	−	0.193066i
$596$	19.6731	−	11.3582i	0.805840	−	0.465252i
$597$	11.9607	−	40.1238i	0.489520	−	1.64216i
$598$	−3.11579	+	0.549398i	−0.127414	+	0.0224665i
$599$	−1.77242	−	10.0519i	−0.0724191	−	0.410709i	−0.999369	−	0.0355237i	$-0.988690\pi$
$599$	−1.77242	−	10.0519i	−0.0724191	−	0.410709i	0.926950	−	0.375186i	$-0.122421\pi$
$600$	8.54382	−	1.41535i	0.348800	−	0.0577815i
$601$	−37.4289	+	21.6096i	−1.52676	+	0.881473i	−0.527260	+	0.849704i	$0.676781\pi$
$601$	−37.4289	+	21.6096i	−1.52676	+	0.881473i	−0.999495	+	0.0317688i	$0.989886\pi$
$602$	−6.49332	−	7.73844i	−0.264648	−	0.315395i
$603$	4.65687	−	4.95939i	0.189643	−	0.201962i
$604$	3.51735	−	9.66384i	0.143119	−	0.393216i
$605$	11.0923	−	21.7723i	0.450967	−	0.885172i
$606$	0.520207	+	8.75368i	0.0211320	+	0.355594i
$607$	−27.5373			−1.11770			−0.558852	−	0.829267i	$-0.688758\pi$
$607$	−27.5373			−1.11770			−0.558852	+	0.829267i	$0.688758\pi$
$608$	−1.27158	+	4.16930i	−0.0515693	+	0.169088i
$609$	1.41421	+	5.93580i	0.0573067	+	0.240531i
$610$	−0.138624	−	2.64283i	−0.00561273	−	0.107005i
$611$	23.3753	+	19.6142i	0.945663	+	0.793505i
$612$	−4.58351	+	0.546701i	−0.185277	+	0.0220991i
$613$	4.44877	+	12.2229i	0.179684	+	0.493678i	0.996535	−	0.0831701i	$-0.0265045\pi$
$613$	4.44877	+	12.2229i	0.179684	+	0.493678i	−0.816851	+	0.576849i	$0.804282\pi$
$614$	1.55519	+	1.85340i	0.0627622	+	0.0747971i
$615$	5.42775	−	8.17051i	0.218868	−	0.329467i
$616$	0.399048	+	0.230390i	0.0160781	+	0.00928269i
$617$	1.13238	+	6.42203i	0.0455878	+	0.258541i	0.999080	−	0.0428750i	$-0.0136517\pi$
$617$	1.13238	+	6.42203i	0.0455878	+	0.258541i	−0.953493	+	0.301416i	$0.902541\pi$
$618$	15.1268	−	6.54625i	0.608490	−	0.263329i
$619$	18.5495	−	32.1286i	0.745565	−	1.29136i	−0.204365	−	0.978895i	$-0.565513\pi$
$619$	18.5495	−	32.1286i	0.745565	−	1.29136i	0.949930	−	0.312462i	$-0.101154\pi$
$620$	0.431307	+	0.462479i	0.0173217	+	0.0185736i
$621$	0.754278	−	4.36807i	0.0302681	−	0.175284i
$622$	25.3299	−	9.21934i	1.01564	−	0.369662i
$623$	−8.15631	+	22.4093i	−0.326776	+	0.897809i
$624$	5.74388	+	2.87621i	0.229939	+	0.115140i
$625$	−16.7316	−	18.5756i	−0.669265	−	0.743024i
$626$	−19.8369			−0.792841
$627$	−0.811343	+	1.86063i	−0.0324019	+	0.0743063i
$628$			9.64573i			0.384907i
$629$	−2.50642	+	14.2146i	−0.0999374	+	0.566773i
$630$	0.0392410	−	11.4968i	0.00156340	−	0.458042i
$631$	19.1152	+	6.95736i	0.760963	+	0.276968i	0.693211	−	0.720734i	$-0.256195\pi$
$631$	19.1152	+	6.95736i	0.760963	+	0.276968i	0.0677517	+	0.997702i	$0.478417\pi$
$632$	4.95064	−	1.80188i	0.196926	−	0.0716751i
$633$	−21.5425	−	15.9983i	−0.856236	−	0.635876i
$634$	8.96889	+	15.5346i	0.356200	+	0.616957i
$635$	−3.45652	−	1.05659i	−0.137168	−	0.0419297i
$636$	5.07346	−	2.19558i	0.201176	−	0.0870603i
$637$	−2.61648	−	14.8388i	−0.103669	−	0.587934i
$638$	0.276330	−	0.478618i	0.0109400	−	0.0189487i
$639$	−6.00011	−	3.92608i	−0.237361	−	0.155313i
$640$	−1.34562	+	1.78586i	−0.0531903	+	0.0705925i
$641$	−19.3301	+	7.03558i	−0.763493	+	0.277889i	−0.694272	−	0.719713i	$-0.744274\pi$
$641$	−19.3301	+	7.03558i	−0.763493	+	0.277889i	−0.0692208	+	0.997601i	$0.522051\pi$
$642$	−24.4320	−	2.82648i	−0.964254	−	0.111552i
$643$	23.4283	−	27.9207i	0.923921	−	1.10109i	−0.0706987	−	0.997498i	$-0.522523\pi$
$643$	23.4283	−	27.9207i	0.923921	−	1.10109i	0.994620	−	0.103589i	$-0.0330327\pi$
$644$	−1.43983	−	0.253881i	−0.0567372	−	0.0100043i
$645$	20.4469	−	10.1515i	0.805097	−	0.399715i
$646$	−6.53396	+	1.51317i	−0.257075	+	0.0595351i
$647$	−41.3515			−1.62570			−0.812848	−	0.582476i	$-0.802084\pi$
$647$	−41.3515			−1.62570			−0.812848	+	0.582476i	$0.802084\pi$
$648$	−6.51714	+	6.20700i	−0.256018	+	0.243834i
$649$	−2.43161	+	2.89788i	−0.0954491	+	0.113752i
$650$	−1.94002	−	18.4421i	−0.0760938	−	0.723357i
$651$	0.700863	−	0.462150i	0.0274690	−	0.0181131i
$652$	13.8938	+	16.5580i	0.544124	+	0.648462i
$653$	−23.8430	−	41.2973i	−0.933049	−	1.61609i	−0.778076	−	0.628170i	$-0.783804\pi$
$653$	−23.8430	−	41.2973i	−0.933049	−	1.61609i	−0.154973	−	0.987919i	$-0.549529\pi$
$654$	−8.26237	+	27.7172i	−0.323084	+	1.08383i
$655$	3.02358	+	7.12221i	0.118141	+	0.278288i
$656$	0.439797	+	2.49421i	0.0171712	+	0.0973826i
$657$	−21.8041	−	1.21833i	−0.850660	−	0.0475316i
$658$	7.05043	+	12.2117i	0.274854	+	0.476062i
$659$	−23.9000	+	20.0544i	−0.931010	+	0.781210i	−0.975998	−	0.217777i	$-0.930119\pi$
$659$	−23.9000	+	20.0544i	−0.931010	+	0.781210i	0.0449886	+	0.998988i	$0.485675\pi$
$660$	−0.718042	+	0.754111i	−0.0279497	+	0.0293537i
$661$	6.43367	−	17.6764i	0.250241	−	0.687531i	−0.749435	−	0.662078i	$-0.769675\pi$
$661$	6.43367	−	17.6764i	0.250241	−	0.687531i	0.999676	−	0.0254533i	$-0.00810291\pi$
$662$	19.2987	+	16.1935i	0.750064	+	0.629378i
$663$	0.586346	+	9.86662i	0.0227718	+	0.383188i
$664$		−	14.8677i		−	0.576980i
$665$	−1.75816	−	16.6117i	−0.0681787	−	0.644175i
$666$	12.6896	+	25.1190i	0.491710	+	0.973343i
$667$	−0.304505	+	1.72693i	−0.0117905	+	0.0668670i
$668$	−9.49794	+	11.3192i	−0.367486	+	0.437953i
$669$	9.73877	+	1.12665i	0.376523	+	0.0435590i
$670$	4.25254	−	2.76191i	0.164290	−	0.106702i
$671$	0.204536	+	0.243757i	0.00789604	+	0.00941013i
$672$	2.03963	+	2.15678i	0.0786805	+	0.0831996i
$673$	−23.2018	+	40.1867i	−0.894364	+	1.54908i	−0.0597736	+	0.998212i	$0.519038\pi$
$673$	−23.2018	+	40.1867i	−0.894364	+	1.54908i	−0.834590	+	0.550871i	$0.814295\pi$
$674$	0.204338	−	0.0360302i	0.00787079	−	0.00138783i
$675$	25.2317	+	6.19378i	0.971167	+	0.238399i
$676$	0.377460	−	0.653780i	0.0145177	−	0.0251454i
$677$	1.73145	−	0.999652i	0.0665450	−	0.0384197i	−0.466358	−	0.884596i	$-0.654434\pi$
$677$	1.73145	−	0.999652i	0.0665450	−	0.0384197i	0.532903	+	0.846176i	$0.321101\pi$
$678$	7.63699	−	10.2836i	0.293297	−	0.394938i
$679$	3.52500	+	9.68485i	0.135277	+	0.371671i
$680$	−3.41494	−	0.419145i	−0.130957	−	0.0160735i
$681$	−10.7027	+	21.3736i	−0.410127	+	0.819037i
$682$	−0.0748810	−	0.0132035i	−0.00286734	−	0.000505590i
$683$		−	24.0620i		−	0.920707i	−0.887736	−	0.460354i	$-0.847723\pi$
$683$		−	24.0620i		−	0.920707i	0.887736	−	0.460354i	$-0.152277\pi$
$684$	−8.43332	+	9.99395i	−0.322456	+	0.382128i
$685$	10.1418	+	43.9199i	0.387498	+	1.67809i
$686$	3.29234	−	18.6718i	0.125702	−	0.712892i
$687$	2.22270	+	1.11300i	0.0848013	+	0.0424636i
$688$	−2.01595	+	5.53877i	−0.0768573	+	0.211164i
$689$	−4.04856	−	11.1233i	−0.154238	−	0.423765i
$690$	1.32255	−	3.02770i	0.0503485	−	0.115262i
$691$	−9.19334	−	15.9233i	−0.349731	−	0.605752i	0.636470	−	0.771301i	$-0.280394\pi$
$691$	−9.19334	−	15.9233i	−0.349731	−	0.605752i	−0.986202	+	0.165549i	$0.947060\pi$
$692$	8.50239	+	4.90886i	0.323212	+	0.186607i
$693$	0.828092	+	1.10686i	0.0314566	+	0.0420461i
$694$	28.4649	−	5.01913i	1.08051	−	0.190523i
$695$	−40.7835	−	12.4668i	−1.54701	−	0.472891i
$696$	2.58684	−	2.44634i	0.0980540	−	0.0927281i
$697$	−2.98525	+	2.50492i	−0.113074	+	0.0948806i
$698$	−7.40460	−	20.3440i	−0.280268	−	0.770030i
$699$	−21.5583	−	2.49403i	−0.815409	−	0.0943327i
$700$	2.07234	−	8.31488i	0.0783269	−	0.314273i
$701$	11.8330	+	2.08649i	0.446928	+	0.0788055i	0.392583	−	0.919717i	$-0.371582\pi$
$701$	11.8330	+	2.08649i	0.446928	+	0.0788055i	0.0543454	+	0.998522i	$0.482693\pi$
$702$	12.4395	+	14.7187i	0.469499	+	0.555523i
$703$	22.2936	+	34.2779i	0.840818	+	1.29282i
$704$		−	0.268858i		−	0.0101330i
$705$	−30.5684	+	8.99880i	−1.15127	+	0.338914i
$706$	−18.5178	+	22.0687i	−0.696928	+	0.830566i
$707$	8.15368	+	2.96770i	0.306651	+	0.111612i
$708$	−20.3455	+	13.4158i	−0.764629	+	0.504198i
$709$	−22.7018	+	19.0490i	−0.852583	+	0.715402i	−0.960357	−	0.278774i	$-0.910072\pi$
$709$	−22.7018	+	19.0490i	−0.852583	+	0.715402i	0.107774	+	0.994175i	$0.465628\pi$
$710$	−3.64514	−	3.90859i	−0.136800	−	0.146687i
$711$	15.7805	+	0.881751i	0.591813	+	0.0330683i
$712$	13.7032	−	2.41624i	0.513549	−	0.0905525i
$713$	0.237595	−	0.0418944i	0.00889799	−	0.00156896i
$714$	−1.30481	+	4.37714i	−0.0488311	+	0.163810i
$715$	1.52069	+	1.63059i	0.0568706	+	0.0609807i
$716$	−1.28692	+	1.07985i	−0.0480944	+	0.0403560i
$717$	−2.31989	−	3.51817i	−0.0866378	−	0.131388i
$718$	−7.71305	−	2.80732i	−0.287848	−	0.104768i
$719$	−11.7605	+	14.0156i	−0.438592	+	0.522694i	−0.939381	−	0.342876i	$-0.888599\pi$
$719$	−11.7605	+	14.0156i	−0.438592	+	0.522694i	0.500789	+	0.865570i	$0.333043\pi$
$720$	−5.82089	+	3.33425i	−0.216932	+	0.124260i
$721$		−	16.3093i		−	0.607390i
$722$	−10.6032	+	15.7662i	−0.394610	+	0.586756i
$723$	−5.44033	−	22.8345i	−0.202328	−	0.849224i
$724$	15.0430	+	2.65249i	0.559070	+	0.0985791i
$725$	−9.97286	−	2.48556i	−0.370383	−	0.0923113i
$726$	−2.17515	+	18.8020i	−0.0807275	+	0.697806i
$727$	6.91987	+	19.0122i	0.256644	+	0.705123i	0.999369	+	0.0355262i	$0.0113107\pi$
$727$	6.91987	+	19.0122i	0.256644	+	0.705123i	−0.742725	+	0.669597i	$0.766467\pi$
$728$	4.86917	−	4.08572i	0.180463	−	0.151427i
$729$	−25.3057	+	9.41390i	−0.937248	+	0.348663i
$730$	−15.5662	−	4.75829i	−0.576129	−	0.176112i
$731$	−8.93148	+	1.57486i	−0.330343	+	0.0582483i
$732$	0.814160	+	1.88133i	0.0300922	+	0.0695359i
$733$	21.4641	+	12.3923i	0.792795	+	0.457721i	0.840946	−	0.541120i	$-0.181999\pi$
$733$	21.4641	+	12.3923i	0.792795	+	0.457721i	−0.0481505	+	0.998840i	$0.515333\pi$
$734$	−3.00188	−	5.19941i	−0.110802	−	0.191914i
$735$	14.4193	+	6.29856i	0.531862	+	0.232326i
$736$	0.291769	+	0.801629i	0.0107548	+	0.0295484i
$737$	−0.208525	+	0.572919i	−0.00768113	+	0.0211037i
$738$	−1.73478	+	7.39737i	−0.0638583	+	0.272301i
$739$	−3.57648	+	20.2832i	−0.131563	+	0.746131i	0.845629	+	0.533772i	$0.179226\pi$
$739$	−3.57648	+	20.2832i	−0.131563	+	0.746131i	−0.977192	+	0.212359i	$0.931885\pi$
$740$	4.71951	+	20.4382i	0.173492	+	0.751324i
$741$	20.2907	+	19.2956i	0.745396	+	0.708841i
$742$		−	5.47005i		−	0.200812i
$743$	−19.2467	−	3.39371i	−0.706093	−	0.124503i	−0.190941	−	0.981602i	$-0.561154\pi$
$743$	−19.2467	−	3.39371i	−0.706093	−	0.124503i	−0.515153	+	0.857098i	$0.672265\pi$
$744$	−0.438000	−	0.219325i	−0.0160579	−	0.00804085i
$745$	50.4173	+	6.18816i	1.84715	+	0.226717i
$746$	−6.22436	−	17.1013i	−0.227890	−	0.626123i
$747$	17.5697	−	40.9970i	0.642843	−	1.50000i
$748$	0.358259	−	0.206841i	0.0130993	−	0.00756286i
$749$	−12.1682	+	21.0760i	−0.444617	+	0.770100i
$750$	17.1626	+	8.96909i	0.626690	+	0.327505i
$751$	−0.904984	+	0.159573i	−0.0330233	+	0.00582291i	−0.190135	−	0.981758i	$-0.560893\pi$
$751$	−0.904984	+	0.159573i	−0.0330233	+	0.00582291i	0.157112	+	0.987581i	$0.449782\pi$
$752$	4.11381	−	7.12532i	0.150015	−	0.259834i
$753$	27.5607	−	26.0637i	1.00437	−	0.949813i
$754$	−4.90041	−	5.84008i	−0.178462	−	0.212683i
$755$	19.2854	−	12.5253i	0.701866	−	0.455842i
$756$	3.07543	+	8.35751i	0.111852	+	0.303960i
$757$	22.7389	−	27.0992i	0.826459	−	0.984936i	−0.173541	−	0.984827i	$-0.555521\pi$
$757$	22.7389	−	27.0992i	0.826459	−	0.984936i	1.00000		0.000109327i	$-3.48000e-5\pi$
$758$	2.18508	−	12.3922i	0.0793657	−	0.450105i
$759$	0.0920696	+	0.386440i	0.00334191	+	0.0140269i
$760$	−7.88116	+	5.73475i	−0.285880	+	0.208021i
$761$		−	40.6741i		−	1.47444i	−0.675655	−	0.737218i	$-0.736139\pi$
$761$		−	40.6741i		−	1.47444i	0.675655	−	0.737218i	$-0.263861\pi$
$762$	2.79478	−	0.166086i	0.101244	−	0.00601665i
$763$	21.9230	+	18.3956i	0.793668	+	0.665966i
$764$	1.61670	−	4.44186i	0.0584903	−	0.160701i
$765$	−8.92118	−	5.19132i	−0.322546	−	0.187693i
$766$	−7.79281	+	6.53894i	−0.281566	+	0.236262i
$767$	26.0918	+	45.1922i	0.942119	+	1.63180i
$768$	0.494800	−	1.65987i	0.0178546	−	0.0598955i
$769$	5.82040	+	33.0091i	0.209889	+	1.19034i	0.889558	+	0.456822i	$0.151012\pi$
$769$	5.82040	+	33.0091i	0.209889	+	1.19034i	−0.679669	+	0.733519i	$0.737877\pi$
$770$	0.402628	+	0.948412i	0.0145097	+	0.0341784i
$771$	−12.5628	−	3.74491i	−0.452437	−	0.134869i
$772$	−4.61620	−	7.99549i	−0.166141	−	0.287764i
$773$	18.8113	+	22.4185i	0.676596	+	0.806336i	0.989666	−	0.143394i	$-0.0458017\pi$
$773$	18.8113	+	22.4185i	0.676596	+	0.806336i	−0.313070	+	0.949730i	$0.601357\pi$
$774$	−12.1042	+	12.8905i	−0.435077	+	0.463341i
$775$	0.147936	+	1.40630i	0.00531402	+	0.0505158i
$776$	3.86548	−	4.60669i	0.138762	−	0.165371i
$777$	27.7975	−	1.65193i	0.997230	−	0.0592626i
$778$	−21.8427			−0.783097
$779$	−1.33794	+	10.9584i	−0.0479366	+	0.392624i
$780$	6.38752	+	12.8656i	0.228710	+	0.460662i
$781$	0.632848	+	0.111588i	0.0226451	+	0.00399294i
$782$	−0.843723	+	1.00551i	−0.0301715	+	0.0359569i
$783$	10.0240	−	3.68867i	0.358229	−	0.131822i
$784$	−3.81772	+	1.38954i	−0.136347	+	0.0496263i
$785$	−12.9795	+	17.2260i	−0.463257	+	0.614821i
$786$	−4.11805	−	4.35458i	−0.146886	−	0.155323i
$787$	−17.4744	+	30.2665i	−0.622894	+	1.07888i	0.366050	+	0.930595i	$0.380710\pi$
$787$	−17.4744	+	30.2665i	−0.622894	+	1.07888i	−0.988944	+	0.148289i	$0.952623\pi$
$788$	1.09595	+	6.21546i	0.0390417	+	0.221416i
$789$	8.70019	+	20.1041i	0.309735	+	0.715724i
$790$	11.2658	+	3.44375i	0.400820	+	0.122523i
$791$	−6.33728	−	10.9765i	−0.225328	−	0.390279i
$792$	0.317719	−	0.741360i	0.0112897	−	0.0263431i
$793$	4.12473	−	1.50128i	0.146473	−	0.0533120i
$794$	17.6260	+	6.41535i	0.625524	+	0.227672i
$795$	12.0149	+	2.90593i	0.426125	+	0.103063i
$796$	−4.19757	+	23.8056i	−0.148779	+	0.843768i
$797$		−	37.8264i		−	1.33988i	−0.742415	−	0.669941i	$-0.766320\pi$
$797$		−	37.8264i		−	1.33988i	0.742415	−	0.669941i	$-0.233680\pi$
$798$	5.76133	+	11.5858i	0.203949	+	0.410134i
$799$	12.6595			0.447863
$800$	−4.80618	+	1.37862i	−0.169924	+	0.0487416i
$801$	40.6411	+	9.53090i	1.43598	+	0.336758i
$802$	1.87629	−	5.15506i	0.0662540	−	0.182031i
$803$	1.83909	−	0.669373i	0.0649000	−	0.0236217i
$804$	−2.34178	+	3.15332i	−0.0825882	+	0.111209i
$805$	−2.22971	−	2.39086i	−0.0785870	−	0.0842667i
$806$	−0.524441	+	0.908358i	−0.0184726	+	0.0319956i
$807$	19.7013	+	45.5251i	0.693520	+	1.60256i
$808$	−0.879156	−	4.98594i	−0.0309286	−	0.175405i
$809$	−1.78358	−	1.02975i	−0.0627075	−	0.0362042i	0.468318	−	0.883560i	$-0.344860\pi$
$809$	−1.78358	−	1.02975i	−0.0627075	−	0.0362042i	−0.531026	+	0.847356i	$0.678193\pi$
$810$	−19.9910	+	2.31526i	−0.702412	+	0.0813500i
$811$	11.1896	+	13.3353i	0.392921	+	0.468265i	0.925848	−	0.377896i	$-0.123352\pi$
$811$	11.1896	+	13.3353i	0.392921	+	0.468265i	−0.532927	+	0.846161i	$0.678908\pi$
$812$	−1.20492	−	3.31050i	−0.0422845	−	0.116176i
$813$	16.1383	+	1.86700i	0.565994	+	0.0654784i
$814$	−1.93204	−	1.62117i	−0.0677178	−	0.0568220i
$815$	2.53170	+	48.2661i	0.0886817	+	1.69069i
$816$	2.59248	−	0.617661i	0.0907551	−	0.0216225i
$817$	−15.4481	+	20.5294i	−0.540460	+	0.718232i
$818$	26.8888			0.940143
$819$	18.2547	−	5.51207i	0.637871	−	0.192607i
$820$	−2.57084	+	5.04612i	−0.0897776	+	0.176218i
$821$	−7.02435	+	19.2992i	−0.245152	+	0.673548i	0.754696	+	0.656075i	$0.227784\pi$
$821$	−7.02435	+	19.2992i	−0.245152	+	0.673548i	−0.999847	+	0.0174734i	$0.994438\pi$
$822$	−19.2208	−	29.1488i	−0.670401	−	1.01668i
$823$	−22.1939	−	26.4497i	−0.773632	−	0.921978i	0.224995	−	0.974360i	$-0.427763\pi$
$823$	−22.1939	−	26.4497i	−0.773632	−	0.921978i	−0.998627	+	0.0523814i	$0.983319\pi$
$824$	−8.24127	+	4.75810i	−0.287098	+	0.165756i
$825$	−2.29707	+	0.380528i	−0.0799737	+	0.0132483i
$826$	4.18742	+	23.7480i	0.145699	+	0.826300i
$827$	−27.1327	+	4.78422i	−0.943495	+	0.166364i	−0.624176	−	0.781284i	$-0.714565\pi$
$827$	−27.1327	+	4.78422i	−0.943495	+	0.166364i	−0.319319	+	0.947647i	$0.603454\pi$
$828$	−0.142777	+	2.55524i	−0.00496185	+	0.0888008i
$829$	−29.9117	+	17.2695i	−1.03888	+	0.599796i	−0.919515	−	0.393055i	$-0.871418\pi$
$829$	−29.9117	+	17.2695i	−1.03888	+	0.599796i	−0.119362	+	0.992851i	$0.538085\pi$
$830$	20.0063	−	26.5518i	0.694429	−	0.921625i
$831$	−3.82081	−	5.79437i	−0.132543	−	0.201004i
$832$	−3.48510	−	1.26847i	−0.120824	−	0.0439763i
$833$	−4.78869	−	4.01819i	−0.165918	−	0.139222i
$834$	32.9756	−	1.95965i	1.14185	−	0.0678570i
$835$	−32.1934	+	7.43395i	−1.11410	+	0.257263i
$836$	0.341874	−	1.12095i	0.0118239	−	0.0387688i
$837$	−0.948576	−	1.12238i	−0.0327876	−	0.0387951i
$838$	−4.62986	+	26.2572i	−0.159936	+	0.907041i
$839$	−28.7503	−	24.1243i	−0.992569	−	0.832864i	−0.00663147	−	0.999978i	$-0.502111\pi$
$839$	−28.7503	−	24.1243i	−0.992569	−	0.832864i	−0.985938	+	0.167114i	$0.946555\pi$
$840$	0.740301	+	6.59629i	0.0255428	+	0.227594i
$841$	23.2805	−	8.47340i	0.802775	−	0.292186i
$842$	21.8477	−	18.3324i	0.752921	−	0.631776i
$843$	−5.02025	−	5.30860i	−0.172907	−	0.182838i
$844$	13.4166	+	7.74609i	0.461819	+	0.266632i
$845$	1.55383	−	0.659644i	0.0534534	−	0.0226925i
$846$	19.7638	−	14.7862i	0.679495	−	0.508361i
$847$	16.2193	+	9.36421i	0.557301	+	0.321758i
$848$	−2.76408	+	1.59584i	−0.0949188	+	0.0548014i
$849$	10.8613	+	8.06608i	0.372761	+	0.276827i
$850$	−5.53460	−	5.34374i	−0.189835	−	0.183289i
$851$	7.51990	+	2.73702i	0.257779	+	0.0938239i
$852$	3.70171	+	1.85360i	0.126818	+	0.0635033i
$853$	−52.5699	−	9.26950i	−1.79996	−	0.317381i	−0.829475	−	0.558544i	$-0.811360\pi$
$853$	−52.5699	−	9.26950i	−1.79996	−	0.317381i	−0.970485	+	0.241162i	$0.922471\pi$
$854$	2.02839			0.0694102
$855$	−28.5088	+	6.49980i	−0.974981	+	0.222288i
$856$	14.1999			0.485343
$857$	16.7281	+	2.94961i	0.571420	+	0.100757i	0.451890	−	0.892074i	$-0.350750\pi$
$857$	16.7281	+	2.94961i	0.571420	+	0.100757i	0.119530	+	0.992831i	$0.461861\pi$
$858$	−1.54429	−	0.773290i	−0.0527211	−	0.0263997i
$859$	−2.01853	−	0.734683i	−0.0688712	−	0.0250671i	0.307355	−	0.951595i	$-0.400556\pi$
$859$	−2.01853	−	0.734683i	−0.0688712	−	0.0250671i	−0.376226	+	0.926528i	$0.622778\pi$
$860$	−11.0533	+	7.17879i	−0.376914	+	0.244795i
$861$	6.03582	+	4.48244i	0.205700	+	0.152761i
$862$	−27.4932	+	15.8732i	−0.936421	+	0.540643i
$863$	11.9136	+	6.87833i	0.405544	+	0.234141i	0.688873	−	0.724882i	$-0.258106\pi$
$863$	11.9136	+	6.87833i	0.405544	+	0.234141i	−0.283329	+	0.959023i	$0.591439\pi$
$864$	3.32591	−	3.99228i	0.113150	−	0.135820i
$865$	8.57866	+	20.2075i	0.291683	+	0.687077i
$866$	21.6613	+	12.5062i	0.736082	+	0.424977i
$867$	−17.4140	−	18.4142i	−0.591411	−	0.625379i
$868$	−0.371299	+	0.311557i	−0.0126027	+	0.0105749i
$869$	−1.33102	+	0.484450i	−0.0451516	+	0.0164339i
$870$	7.91159	−	0.887917i	0.268228	−	0.0301032i
$871$	6.44270	+	5.40607i	0.218303	+	0.183178i
$872$	2.89965	−	16.4447i	0.0981945	−	0.556889i
$873$	16.1027	−	8.13473i	0.544995	−	0.275319i
$874$	0.197140	+	3.71324i	0.00666836	+	0.125602i
$875$	14.8896	−	12.0607i	0.503359	−	0.407725i
$876$	12.5860	−	0.747953i	0.425243	−	0.0252710i
$877$	12.3939	+	10.3998i	0.418514	+	0.351175i	0.827597	−	0.561322i	$-0.189707\pi$
$877$	12.3939	+	10.3998i	0.418514	+	0.351175i	−0.409084	+	0.912497i	$0.634152\pi$
$878$	−32.6574	−	11.8863i	−1.10213	−	0.401143i
$879$	21.3159	+	32.3261i	0.718968	+	1.09033i
$880$	0.361780	−	0.480143i	0.0121956	−	0.0161856i
$881$	11.9255	−	6.88519i	0.401780	−	0.231968i	−0.285472	−	0.958387i	$-0.592150\pi$
$881$	11.9255	−	6.88519i	0.401780	−	0.231968i	0.687252	+	0.726419i	$0.258817\pi$
$882$	−12.1692	−	0.679969i	−0.409759	−	0.0228957i
$883$	39.1996	−	6.91195i	1.31917	−	0.232605i	0.530639	−	0.847598i	$-0.321952\pi$
$883$	39.1996	−	6.91195i	1.31917	−	0.232605i	0.788533	+	0.614993i	$0.210841\pi$
$884$	−0.990932	−	5.61985i	−0.0333286	−	0.189016i
$885$	−54.3868	−	3.41838i	−1.82819	−	0.114908i
$886$	5.30605	−	3.06345i	0.178260	−	0.102919i
$887$	31.9511	+	38.0778i	1.07281	+	1.27853i	0.958503	+	0.285084i	$0.0920215\pi$
$887$	31.9511	+	38.0778i	1.07281	+	1.27853i	0.114311	+	0.993445i	$0.463534\pi$
$888$	−8.94442	−	13.5644i	−0.300155	−	0.455193i
$889$	0.947492	−	2.60321i	0.0317779	−	0.0873089i
$890$	27.7234	+	14.1242i	0.929289	+	0.473444i
$891$	1.75218	−	1.66880i	0.0587004	−	0.0559069i
$892$	−5.66018			−0.189517
$893$	26.2121	−	24.4766i	0.877155	−	0.819078i
$894$	−38.2748	+	9.11900i	−1.28010	+	0.304985i
$895$	−3.75133	+	0.196768i	−0.125393	+	0.00657724i
$896$	−1.31288	−	1.10164i	−0.0438603	−	0.0368032i
$897$	5.44365	+	0.629763i	0.181758	+	0.0210272i
$898$	7.30239	+	20.0632i	0.243684	+	0.669516i
$899$	0.373681	+	0.445336i	0.0124630	+	0.0148528i
$900$	−14.8820	−	1.87818i	−0.496065	−	0.0626058i
$901$	−4.25299	−	2.45547i	−0.141688	−	0.0818035i
$902$	−0.118243	−	0.670588i	−0.00393705	−	0.0223281i
$903$	6.94910	+	16.0577i	0.231252	+	0.534367i
$904$	−3.69769	+	6.40459i	−0.122983	+	0.213014i
$905$	23.2956	+	24.9792i	0.774371	+	0.830336i
$906$	−10.6200	+	14.3003i	−0.352826	+	0.475097i
$907$	−12.5986	+	4.58552i	−0.418330	+	0.152260i	−0.542605	−	0.839988i	$-0.682562\pi$
$907$	−12.5986	+	4.58552i	−0.418330	+	0.152260i	0.124275	+	0.992248i	$0.460340\pi$
$908$	4.72011	−	12.9684i	0.156642	−	0.430371i
$909$	3.46784	−	14.7874i	0.115021	−	0.490467i
$910$	14.1935	−	0.744491i	0.470510	−	0.0246796i
$911$	−55.0860			−1.82508			−0.912541	−	0.408986i	$-0.865883\pi$
$911$	−55.0860			−1.82508			−0.912541	+	0.408986i	$0.865883\pi$
$912$	4.17363	−	6.29133i	0.138203	−	0.208327i
$913$			3.99730i			0.132291i
$914$	4.39801	−	24.9424i	0.145473	−	0.825020i
$915$	−1.07757	+	4.45535i	−0.0356235	+	0.147289i
$916$	−1.34862	−	0.490858i	−0.0445597	−	0.0162184i
$917$	−5.57275	+	2.02832i	−0.184028	+	0.0669809i
$918$	7.87854	+	1.36047i	0.260031	+	0.0449021i
$919$	1.23232	+	2.13444i	0.0406504	+	0.0704085i	0.885635	−	0.464382i	$-0.153724\pi$
$919$	1.23232	+	2.13444i	0.0406504	+	0.0704085i	−0.844984	+	0.534791i	$0.820390\pi$
$920$	−0.557627	+	1.82421i	−0.0183844	+	0.0601424i
$921$	−1.66435	−	3.84591i	−0.0548422	−	0.126727i
$922$	−5.09009	−	28.8674i	−0.167633	−	0.950696i
$923$	4.43225	−	7.67688i	0.145889	−	0.252688i
$924$	−0.548371	−	0.579867i	−0.0180401	−	0.0190762i
$925$	−19.0737	+	42.8505i	−0.627138	+	1.40892i
$926$	−10.9603	+	3.98922i	−0.360177	+	0.131094i
$927$	−28.3477	+	3.38119i	−0.931059	+	0.111053i
$928$	−1.32131	+	1.57467i	−0.0433740	+	0.0516911i
$929$	10.8048	+	1.90517i	0.354493	+	0.0625067i	0.348059	−	0.937473i	$-0.386841\pi$
$929$	10.8048	+	1.90517i	0.354493	+	0.0625067i	0.00643416	+	0.999979i	$0.497952\pi$
$930$	−0.487080	−	0.981066i	−0.0159720	−	0.0321704i
$931$	−17.6841	+	0.938869i	−0.579574	+	0.0307702i
$932$	12.5297			0.410424
$933$	−46.6061	+	2.76967i	−1.52582	+	0.0906750i
$934$	21.1941	−	25.2582i	0.693493	−	0.826473i
$935$	0.918132	+	0.112690i	0.0300261	+	0.00368537i
$936$	−8.11096	−	7.61621i	−0.265115	−	0.248943i
$937$	−8.57663	−	10.2212i	−0.280186	−	0.333913i	0.607536	−	0.794292i	$-0.292158\pi$
$937$	−8.57663	−	10.2212i	−0.280186	−	0.333913i	−0.887722	+	0.460379i	$0.847714\pi$
$938$	1.94324	+	3.36579i	0.0634491	+	0.109897i
$939$	32.9267	+	9.81528i	1.07452	+	0.320310i
$940$	16.9347	−	7.18924i	0.552348	−	0.234487i
$941$	8.26369	+	46.8657i	0.269388	+	1.52778i	0.756241	+	0.654294i	$0.227034\pi$
$941$	8.26369	+	46.8657i	0.269388	+	1.52778i	−0.486852	+	0.873484i	$0.661855\pi$
$942$	4.77271	−	16.0107i	0.155503	−	0.521656i
$943$	1.08029	+	1.87111i	0.0351790	+	0.0609318i
$944$	10.7785	−	9.04423i	0.350810	−	0.294365i
$945$	−5.75373	+	19.0637i	−0.187169	+	0.620143i
$946$	0.542003	−	1.48914i	0.0176220	−	0.0484161i
$947$	−25.8684	−	21.7061i	−0.840609	−	0.705354i	0.117092	−	0.993121i	$-0.462643\pi$
$947$	−25.8684	−	21.7061i	−0.840609	−	0.705354i	−0.957701	+	0.287767i	$0.907087\pi$
$948$	−9.10899	+	0.541322i	−0.295846	+	0.0175813i
$949$		−	26.9975i		−	0.876375i
$950$	−21.7915	−	0.363554i	−0.707008	−	0.0117953i
$951$	−7.20070	−	30.2232i	−0.233499	−	0.980055i
$952$	0.457917	−	2.59698i	0.0148412	−	0.0841684i
$953$	20.5019	−	24.4332i	0.664120	−	0.791468i	−0.323850	−	0.946108i	$-0.604977\pi$
$953$	20.5019	−	24.4332i	0.664120	−	0.791468i	0.987971	+	0.154640i	$0.0494219\pi$
$954$	−9.50766	+	1.13403i	−0.307822	+	0.0367156i
$955$	8.86426	−	5.75709i	0.286841	−	0.186295i
$956$	1.56394	+	1.86383i	0.0505815	+	0.0602807i
$957$	−0.695493	+	0.657716i	−0.0224821	+	0.0212609i
$958$	−17.9367	+	31.0672i	−0.579508	+	1.00374i
$959$	−34.0236	+	5.99928i	−1.09868	+	0.193727i
$960$	3.11720	−	2.29849i	0.100607	−	0.0741835i
$961$	−15.4600	+	26.7775i	−0.498710	+	0.863791i
$962$	−30.1299	+	17.3955i	−0.971429	+	0.560855i
$963$	39.1554	+	16.7805i	1.26177	+	0.540745i
$964$	4.63523	+	12.7352i	0.149291	+	0.410173i
$965$	2.51498	−	20.4905i	0.0809600	−	0.659612i
$966$	2.26431	+	1.13384i	0.0728530	+	0.0364806i
$967$	−16.5601	−	2.91999i	−0.532537	−	0.0939006i	−0.0990878	−	0.995079i	$-0.531592\pi$
$967$	−16.5601	−	2.91999i	−0.532537	−	0.0939006i	−0.433449	+	0.901178i	$0.642704\pi$
$968$		−	10.9277i		−	0.351230i
$969$	11.5943	+	0.721329i	0.372461	+	0.0231724i
$970$	13.1021	−	3.02547i	0.420682	−	0.0971421i
$971$	10.0132	−	56.7878i	0.321340	−	1.82241i	−0.212900	−	0.977074i	$-0.568291\pi$
$971$	10.0132	−	56.7878i	0.321340	−	1.82241i	0.534239	−	0.845333i	$-0.320598\pi$
$972$	13.8888	−	7.07814i	0.445485	−	0.227031i
$973$	11.1795	−	30.7153i	0.358397	−	0.984687i
$974$	3.49767	+	9.60977i	0.112073	+	0.307917i
$975$	−5.90495	+	31.5714i	−0.189110	+	1.01109i
$976$	−0.591767	−	1.02497i	−0.0189420	−	0.0328085i
$977$	18.5256	+	10.6957i	0.592685	+	0.342187i	0.766158	−	0.642652i	$-0.222166\pi$
$977$	18.5256	+	10.6957i	0.592685	+	0.342187i	−0.173474	+	0.984839i	$0.555499\pi$
$978$	−14.8691	−	34.3588i	−0.475460	−	1.09867i
$979$	−3.68421	+	0.649625i	−0.117748	+	0.0207621i
$980$	−8.68771	−	2.65567i	−0.277519	−	0.0848323i
$981$	27.4289	−	41.9188i	0.875739	−	1.33836i
$982$	−6.77324	+	5.68342i	−0.216143	+	0.181365i
$983$	6.48673	+	17.8222i	0.206895	+	0.568439i	0.999127	−	0.0417814i	$-0.0133033\pi$
$983$	6.48673	+	17.8222i	0.206895	+	0.568439i	−0.792232	+	0.610220i	$0.791081\pi$
$984$	0.504129	−	4.35768i	0.0160711	−	0.138918i
$985$	−6.40641	+	12.5747i	−0.204125	+	0.400663i
$986$	−3.11481	−	0.549225i	−0.0991958	−	0.0174909i
$987$	−5.66046	−	23.7584i	−0.180174	−	0.756239i
$988$	−12.9175	−	9.72021i	−0.410959	−	0.309241i
$989$			5.02823i			0.159888i
$990$	1.56499	−	0.896440i	0.0497387	−	0.0284907i
$991$	−22.7938	+	27.1646i	−0.724070	+	0.862913i	−0.995019	−	0.0996809i	$-0.968218\pi$
$991$	−22.7938	+	27.1646i	−0.724070	+	0.862913i	0.270950	+	0.962593i	$0.412662\pi$
$992$	0.265756	+	0.0967274i	0.00843777	+	0.00307110i
$993$	−24.0207	−	36.4281i	−0.762275	−	1.15601i
$994$	3.13799	−	2.63308i	0.0995309	−	0.0835164i
$995$	−39.5296	+	36.8653i	−1.25317	+	1.16871i
$996$	−7.35655	+	24.6785i	−0.233101	+	0.781969i
$997$	17.0051	−	2.99846i	0.538557	−	0.0949622i	0.102248	−	0.994759i	$-0.467396\pi$
$997$	17.0051	−	2.99846i	0.538557	−	0.0949622i	0.436309	+	0.899797i	$0.356285\pi$
$998$	−17.2559	+	3.04268i	−0.546226	+	0.0963144i
$999$	−8.63414	−	47.9732i	−0.273172	−	1.51780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bf.a.59.23	yes	240
3.2	odd	2	inner	570.2.bf.a.59.7	yes	240
5.4	even	2	inner	570.2.bf.a.59.18	yes	240
15.14	odd	2	inner	570.2.bf.a.59.34	yes	240
19.10	odd	18	inner	570.2.bf.a.29.34	yes	240
57.29	even	18	inner	570.2.bf.a.29.18	yes	240
95.29	odd	18	inner	570.2.bf.a.29.7	✓	240
285.29	even	18	inner	570.2.bf.a.29.23	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.29.7	✓	240	95.29	odd	18	inner
570.2.bf.a.29.18	yes	240	57.29	even	18	inner
570.2.bf.a.29.23	yes	240	285.29	even	18	inner
570.2.bf.a.29.34	yes	240	19.10	odd	18	inner
570.2.bf.a.59.7	yes	240	3.2	odd	2	inner
570.2.bf.a.59.18	yes	240	5.4	even	2	inner
570.2.bf.a.59.23	yes	240	1.1	even	1	trivial
570.2.bf.a.59.34	yes	240	15.14	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(-1.54873 - 0.775516i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.21793 + 1.87527i) q^{5} +(-1.39054 - 1.03267i) q^{6} +(-1.48423 + 0.856923i) q^{7} +(0.866025 + 0.500000i) q^{8} +(1.79715 + 2.40214i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(-1.54873 - 0.775516i) q^{3} +(0.939693 + 0.342020i) q^{4} +(1.21793 + 1.87527i) q^{5} +(-1.39054 - 1.03267i) q^{6} +(-1.48423 + 0.856923i) q^{7} +(0.866025 + 0.500000i) q^{8} +(1.79715 + 2.40214i) q^{9} +(0.873794 + 2.05827i) q^{10} +(-0.232838 - 0.134429i) q^{11} +(-1.19009 - 1.25844i) q^{12} +(-2.84108 + 2.38395i) q^{13} +(-1.61049 + 0.586170i) q^{14} +(-0.431953 - 3.84882i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.267187 + 1.51529i) q^{17} +(1.35272 + 2.67771i) q^{18} +(2.37652 + 3.65406i) q^{19} +(0.503104 + 2.17874i) q^{20} +(2.96324 - 0.176097i) q^{21} +(-0.205957 - 0.172818i) q^{22} +(0.801629 + 0.291769i) q^{23} +(-0.953484 - 1.44598i) q^{24} +(-2.03327 + 4.56791i) q^{25} +(-3.21188 + 1.85438i) q^{26} +(-0.920408 - 5.11399i) q^{27} +(-1.68781 + 0.297606i) q^{28} +(0.356949 + 2.02436i) q^{29} +(0.242950 - 3.86536i) q^{30} +(0.244922 - 0.141406i) q^{31} +(0.642788 + 0.766044i) q^{32} +(0.256352 + 0.388764i) q^{33} +(-0.526255 + 1.44587i) q^{34} +(-3.41466 - 1.73966i) q^{35} +(0.867188 + 2.87193i) q^{36} +9.38078 q^{37} +(1.70589 + 4.01123i) q^{38} +(6.24886 - 1.48880i) q^{39} +(0.117127 + 2.23300i) q^{40} +(1.94015 + 1.62798i) q^{41} +(2.94880 + 0.341140i) q^{42} +(2.01595 + 5.53877i) q^{43} +(-0.172818 - 0.205957i) q^{44} +(-2.31584 + 6.29578i) q^{45} +(0.738785 + 0.426538i) q^{46} +(-1.42871 - 8.10262i) q^{47} +(-0.687906 - 1.58959i) q^{48} +(-2.03137 + 3.51843i) q^{49} +(-2.79559 + 4.14544i) q^{50} +(1.58893 - 2.13957i) q^{51} +(-3.48510 + 1.26847i) q^{52} +(-1.09162 + 2.99920i) q^{53} +(-0.0183905 - 5.19612i) q^{54} +(-0.0314906 - 0.600359i) q^{55} -1.71385 q^{56} +(-0.846806 - 7.50219i) q^{57} +2.05559i q^{58} +(2.44329 - 13.8566i) q^{59} +(0.910471 - 3.76444i) q^{60} +(-1.11216 - 0.404792i) q^{61} +(0.265756 - 0.0967274i) q^{62} +(-4.72584 - 2.02531i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-7.93079 - 2.42429i) q^{65} +(0.184949 + 0.427373i) q^{66} +(-0.393781 - 2.23324i) q^{67} +(-0.769333 + 1.33252i) q^{68} +(-1.01524 - 1.07355i) q^{69} +(-3.06070 - 2.30618i) q^{70} +(-2.24601 + 0.817480i) q^{71} +(0.355308 + 2.97889i) q^{72} +(-4.67909 + 5.57633i) q^{73} +(9.23826 + 1.62895i) q^{74} +(6.69148 - 5.49764i) q^{75} +(0.983433 + 4.24651i) q^{76} +0.460781 q^{77} +(6.41245 - 0.381074i) q^{78} +(3.38643 - 4.03579i) q^{79} +(-0.272408 + 2.21941i) q^{80} +(-2.54051 + 8.63399i) q^{81} +(1.62798 + 1.94015i) q^{82} +(-7.43387 - 12.8758i) q^{83} +(2.84476 + 0.848011i) q^{84} +(-3.16699 + 1.34448i) q^{85} +(1.02352 + 5.80469i) q^{86} +(1.01710 - 3.41201i) q^{87} +(-0.134429 - 0.232838i) q^{88} +(10.6592 - 8.94412i) q^{89} +(-3.37391 + 5.79799i) q^{90} +(2.17397 - 5.97292i) q^{91} +(0.653494 + 0.548347i) q^{92} +(-0.488982 + 0.0290588i) q^{93} -8.22761i q^{94} +(-3.95791 + 8.90702i) q^{95} +(-0.401426 - 1.68489i) q^{96} +(1.04425 - 5.92225i) q^{97} +(-2.61147 + 3.11223i) q^{98} +(-0.0955274 - 0.800896i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) \) 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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