LMFDB - Embedded newform 570.2.bf.a.29.34

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			29.34
Character	$\chi$	$=$	570.29
Dual form			570.2.bf.a.59.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 - 0.173648i) q^{2} +(1.03267 - 1.39054i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-0.272408 + 2.21941i) q^{5} +(0.775516 - 1.54873i) q^{6} +(1.48423 + 0.856923i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.867188 - 2.87193i) q^{9} +O(q^{10})$	\(q+(0.984808 - 0.173648i) q^{2} +(1.03267 - 1.39054i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-0.272408 + 2.21941i) q^{5} +(0.775516 - 1.54873i) q^{6} +(1.48423 + 0.856923i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.867188 - 2.87193i) q^{9} +(0.117127 + 2.23300i) q^{10} +(0.232838 - 0.134429i) q^{11} +(0.494800 - 1.65987i) q^{12} +(2.84108 + 2.38395i) q^{13} +(1.61049 + 0.586170i) q^{14} +(2.80487 + 2.67071i) 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} +(2.72431 - 1.17897i) q^{21} +(0.205957 - 0.172818i) q^{22} +(0.801629 - 0.291769i) q^{23} +(0.199049 - 1.72058i) q^{24} +(-4.85159 - 1.20917i) q^{25} +(3.21188 + 1.85438i) q^{26} +(-4.88905 - 1.75990i) q^{27} +(1.68781 + 0.297606i) q^{28} +(-0.356949 + 2.02436i) q^{29} +(3.22602 + 2.14308i) q^{30} +(0.244922 + 0.141406i) q^{31} +(0.642788 - 0.766044i) q^{32} +(0.0535159 - 0.462590i) q^{33} +(-0.526255 - 1.44587i) q^{34} +(-2.30618 + 3.06070i) q^{35} +(-1.79715 - 2.40214i) q^{36} -9.38078 q^{37} +(1.70589 - 4.01123i) q^{38} +(6.24886 - 1.48880i) q^{39} +(0.873794 + 2.05827i) q^{40} +(-1.94015 + 1.62798i) q^{41} +(2.47819 - 1.63413i) q^{42} +(-2.01595 + 5.53877i) q^{43} +(0.172818 - 0.205957i) q^{44} +(6.61023 - 1.14231i) q^{45} +(0.738785 - 0.426538i) q^{46} +(-1.42871 + 8.10262i) q^{47} +(-0.102750 - 1.72900i) q^{48} +(-2.03137 - 3.51843i) q^{49} +(-4.98785 - 0.348333i) q^{50} +(-2.38298 - 1.19326i) q^{51} +(3.48510 + 1.26847i) q^{52} +(-1.09162 - 2.99920i) q^{53} +(-5.12037 - 0.884186i) q^{54} +(0.234926 + 0.553382i) q^{55} +1.71385 q^{56} +(-2.62695 - 7.07807i) q^{57} +2.05559i q^{58} +(-2.44329 - 13.8566i) q^{59} +(3.54915 + 1.55033i) q^{60} +(-1.11216 + 0.404792i) q^{61} +(0.265756 + 0.0967274i) q^{62} +(1.17391 - 5.00573i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-6.06489 + 5.65612i) q^{65} +(-0.0276250 - 0.464855i) q^{66} +(0.393781 - 2.23324i) q^{67} +(-0.769333 - 1.33252i) q^{68} +(0.422102 - 1.41600i) q^{69} +(-1.73966 + 3.41466i) q^{70} +(2.24601 + 0.817480i) q^{71} +(-2.18697 - 2.05357i) 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} +(5.89540 - 2.55128i) q^{78} +(3.38643 + 4.03579i) q^{79} +(1.21793 + 1.87527i) q^{80} +(-7.49597 + 4.98101i) q^{81} +(-1.62798 + 1.94015i) q^{82} +(-7.43387 + 12.8758i) q^{83} +(2.15678 - 2.03963i) q^{84} +(3.43584 - 0.180220i) q^{85} +(-1.02352 + 5.80469i) q^{86} +(2.44634 + 2.58684i) q^{87} +(0.134429 - 0.232838i) q^{88} +(-10.6592 - 8.94412i) q^{89} +(6.31144 - 2.27281i) q^{90} +(2.17397 + 5.97292i) q^{91} +(0.653494 - 0.548347i) q^{92} +(0.449554 - 0.194548i) q^{93} +8.22761i q^{94} +(7.46249 + 6.26987i) q^{95} +(-0.401426 - 1.68489i) q^{96} +(-1.04425 - 5.92225i) q^{97} +(-2.61147 - 3.11223i) q^{98} +(-0.587984 - 0.552118i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$	$-1$

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
$3$	1.03267	−	1.39054i	0.596212	−	0.802827i
$3$	1.03267	−	1.39054i	0.596212	−	0.802827i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	−0.272408	+	2.21941i	−0.121825	+	0.992552i
$5$	−0.272408	+	2.21941i	−0.121825	+	0.992552i
$6$	0.775516	−	1.54873i	0.316603	−	0.632268i
$7$	1.48423	+	0.856923i	0.560988	+	0.323887i	0.753542	−	0.657400i	$-0.228344\pi$
$7$	1.48423	+	0.856923i	0.560988	+	0.323887i	−0.192554	+	0.981286i	$0.561677\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−0.867188	−	2.87193i	−0.289063	−	0.957310i
$10$	0.117127	+	2.23300i	0.0370389	+	0.706136i
$11$	0.232838	−	0.134429i	0.0702032	−	0.0405318i	−0.464488	−	0.885580i	$-0.653761\pi$
$11$	0.232838	−	0.134429i	0.0702032	−	0.0405318i	0.534691	+	0.845048i	$0.320428\pi$
$12$	0.494800	−	1.65987i	0.142836	−	0.479164i
$13$	2.84108	+	2.38395i	0.787973	+	0.661188i	0.945243	−	0.326368i	$-0.105825\pi$
$13$	2.84108	+	2.38395i	0.787973	+	0.661188i	−0.157270	+	0.987556i	$0.550269\pi$
$14$	1.61049	+	0.586170i	0.430421	+	0.156661i
$15$	2.80487	+	2.67071i	0.724214	+	0.689575i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−0.267187	−	1.51529i	−0.0648023	−	0.367512i	−0.999913	−	0.0131574i	$-0.995812\pi$
$17$	−0.267187	−	1.51529i	−0.0648023	−	0.367512i	0.935111	−	0.354354i	$-0.115299\pi$
$18$	−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
$21$	2.72431	−	1.17897i	0.594493	−	0.257271i
$22$	0.205957	−	0.172818i	0.0439102	−	0.0368450i
$23$	0.801629	−	0.291769i	0.167151	−	0.0608381i	−0.257089	−	0.966388i	$-0.582763\pi$
$23$	0.801629	−	0.291769i	0.167151	−	0.0608381i	0.424240	+	0.905550i	$0.360541\pi$
$24$	0.199049	−	1.72058i	0.0406307	−	0.351211i
$25$	−4.85159	−	1.20917i	−0.970318	−	0.241834i
$26$	3.21188	+	1.85438i	0.629902	+	0.363674i
$27$	−4.88905	−	1.75990i	−0.940897	−	0.338692i
$28$	1.68781	+	0.297606i	0.318966	+	0.0562423i
$29$	−0.356949	+	2.02436i	−0.0662838	+	0.375914i	0.933563	+	0.358413i	$0.116682\pi$
$29$	−0.356949	+	2.02436i	−0.0662838	+	0.375914i	−0.999847	+	0.0175008i	$0.994429\pi$
$30$	3.22602	+	2.14308i	0.588988	+	0.391271i
$31$	0.244922	+	0.141406i	0.0439893	+	0.0253973i	0.521833	−	0.853047i	$-0.325248\pi$
$31$	0.244922	+	0.141406i	0.0439893	+	0.0253973i	−0.477844	+	0.878445i	$0.658582\pi$
$32$	0.642788	−	0.766044i	0.113630	−	0.135419i
$33$	0.0535159	−	0.462590i	0.00931592	−	0.0805266i
$34$	−0.526255	−	1.44587i	−0.0902520	−	0.247965i
$35$	−2.30618	+	3.06070i	−0.389816	+	0.517352i
$36$	−1.79715	−	2.40214i	−0.299525	−	0.400356i
$37$	−9.38078			−1.54219			−0.771095	−	0.636720i	$-0.780291\pi$
$37$	−9.38078			−1.54219			−0.771095	+	0.636720i	$0.780291\pi$
$38$	1.70589	−	4.01123i	0.276732	−	0.650707i
$39$	6.24886	−	1.48880i	1.00062	−	0.238398i
$40$	0.873794	+	2.05827i	0.138159	+	0.325441i
$41$	−1.94015	+	1.62798i	−0.303001	+	0.254248i	−0.781592	−	0.623790i	$-0.785592\pi$
$41$	−1.94015	+	1.62798i	−0.303001	+	0.254248i	0.478591	+	0.878038i	$0.341148\pi$
$42$	2.47819	−	1.63413i	0.382394	−	0.252151i
$43$	−2.01595	+	5.53877i	−0.307429	+	0.844654i	0.685727	+	0.727859i	$0.259484\pi$
$43$	−2.01595	+	5.53877i	−0.307429	+	0.844654i	−0.993156	+	0.116796i	$0.962738\pi$
$44$	0.172818	−	0.205957i	0.0260534	−	0.0310492i
$45$	6.61023	−	1.14231i	0.985395	−	0.170286i
$46$	0.738785	−	0.426538i	0.108928	−	0.0628896i
$47$	−1.42871	+	8.10262i	−0.208399	+	1.18189i	0.683602	+	0.729855i	$0.260412\pi$
$47$	−1.42871	+	8.10262i	−0.208399	+	1.18189i	−0.892001	+	0.452033i	$0.850699\pi$
$48$	−0.102750	−	1.72900i	−0.0148306	−	0.249560i
$49$	−2.03137	−	3.51843i	−0.290195	−	0.502633i
$50$	−4.98785	−	0.348333i	−0.705389	−	0.0492617i
$51$	−2.38298	−	1.19326i	−0.333684	−	0.167090i
$52$	3.48510	+	1.26847i	0.483296	+	0.175905i
$53$	−1.09162	−	2.99920i	−0.149946	−	0.411972i	0.841865	−	0.539688i	$-0.181458\pi$
$53$	−1.09162	−	2.99920i	−0.149946	−	0.411972i	−0.991811	+	0.127716i	$0.959235\pi$
$54$	−5.12037	−	0.884186i	−0.696794	−	0.120322i
$55$	0.234926	+	0.553382i	0.0316775	+	0.0746181i
$56$	1.71385			0.229022
$57$	−2.62695	−	7.07807i	−0.347948	−	0.937514i
$58$			2.05559i			0.269912i
$59$	−2.44329	−	13.8566i	−0.318089	−	1.80397i	−0.554352	−	0.832283i	$-0.687034\pi$
$59$	−2.44329	−	13.8566i	−0.318089	−	1.80397i	0.236263	−	0.971689i	$-0.424077\pi$
$60$	3.54915	+	1.55033i	0.458194	+	0.200146i
$61$	−1.11216	+	0.404792i	−0.142397	+	0.0518284i	−0.412236	−	0.911077i	$-0.635252\pi$
$61$	−1.11216	+	0.404792i	−0.142397	+	0.0518284i	0.269838	+	0.962906i	$0.413030\pi$
$62$	0.265756	+	0.0967274i	0.0337511	+	0.0122844i
$63$	1.17391	−	5.00573i	0.147899	−	0.630663i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	−6.06489	+	5.65612i	−0.752258	+	0.701555i
$66$	−0.0276250	−	0.464855i	−0.00340041	−	0.0572197i
$67$	0.393781	−	2.23324i	0.0481080	−	0.272834i	−0.951260	−	0.308391i	$-0.900209\pi$
$67$	0.393781	−	2.23324i	0.0481080	−	0.272834i	0.999368	+	0.0355570i	$0.0113205\pi$
$68$	−0.769333	−	1.33252i	−0.0932953	−	0.161592i
$69$	0.422102	−	1.41600i	0.0508151	−	0.170466i
$70$	−1.73966	+	3.41466i	−0.207930	+	0.408130i
$71$	2.24601	+	0.817480i	0.266552	+	0.0970170i	0.471839	−	0.881685i	$-0.343590\pi$
$71$	2.24601	+	0.817480i	0.266552	+	0.0970170i	−0.205287	+	0.978702i	$0.565813\pi$
$72$	−2.18697	−	2.05357i	−0.257737	−	0.242016i
$73$	4.67909	+	5.57633i	0.547646	+	0.652660i	0.966884	−	0.255217i	$-0.0821469\pi$
$73$	4.67909	+	5.57633i	0.547646	+	0.652660i	−0.419237	+	0.907877i	$0.637702\pi$
$74$	−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
$78$	5.89540	−	2.55128i	0.667522	−	0.288876i
$79$	3.38643	+	4.03579i	0.381004	+	0.454062i	0.922131	−	0.386878i	$-0.126447\pi$
$79$	3.38643	+	4.03579i	0.381004	+	0.454062i	−0.541127	+	0.840941i	$0.682002\pi$
$80$	1.21793	+	1.87527i	0.136169	+	0.209662i
$81$	−7.49597	+	4.98101i	−0.832885	+	0.553446i
$82$	−1.62798	+	1.94015i	−0.179780	+	0.214254i
$83$	−7.43387	+	12.8758i	−0.815973	+	1.41331i	0.0926542	+	0.995698i	$0.470465\pi$
$83$	−7.43387	+	12.8758i	−0.815973	+	1.41331i	−0.908627	+	0.417608i	$0.862868\pi$
$84$	2.15678	−	2.03963i	0.235324	−	0.222542i
$85$	3.43584	−	0.180220i	0.372669	−	0.0195476i
$86$	−1.02352	+	5.80469i	−0.110369	+	0.625936i
$87$	2.44634	+	2.58684i	0.262275	+	0.277339i
$88$	0.134429	−	0.232838i	0.0143302	−	0.0248206i
$89$	−10.6592	−	8.94412i	−1.12987	−	0.948075i	−0.130811	−	0.991407i	$-0.541758\pi$
$89$	−10.6592	−	8.94412i	−1.12987	−	0.948075i	−0.999061	+	0.0433325i	$0.986203\pi$
$90$	6.31144	−	2.27281i	0.665285	−	0.239575i
$91$	2.17397	+	5.97292i	0.227893	+	0.626132i
$92$	0.653494	−	0.548347i	0.0681315	−	0.0571691i
$93$	0.449554	−	0.194548i	0.0466166	−	0.0201737i
$94$			8.22761i			0.848613i
$95$	7.46249	+	6.26987i	0.765635	+	0.643275i
$96$	−0.401426	−	1.68489i	−0.0409704	−	0.171963i
$97$	−1.04425	−	5.92225i	−0.106028	−	0.601314i	−0.990805	−	0.135299i	$-0.956801\pi$
$97$	−1.04425	−	5.92225i	−0.106028	−	0.601314i	0.884777	−	0.466015i	$-0.154311\pi$
$98$	−2.61147	−	3.11223i	−0.263799	−	0.314383i
$99$	−0.587984	−	0.552118i	−0.0590947	−	0.0554900i
$100$	−4.97256	+	0.523090i	−0.497256	+	0.0523090i
$101$	3.25434	−	3.87837i	0.323819	−	0.385913i	−0.579435	−	0.815018i	$-0.696727\pi$
$101$	3.25434	−	3.87837i	0.323819	−	0.385913i	0.903254	+	0.429106i	$0.141171\pi$
$102$	−2.55399	−	0.761332i	−0.252883	−	0.0753831i
$103$	4.75810	+	8.24127i	0.468829	+	0.812036i	0.999365	−	0.0356262i	$-0.0113426\pi$
$103$	4.75810	+	8.24127i	0.468829	+	0.812036i	−0.530536	+	0.847663i	$0.678009\pi$
$104$	3.65242	+	0.644020i	0.358149	+	0.0631513i
$105$	1.87449	+	6.36752i	0.182931	+	0.621407i
$106$	−1.59584	−	2.76408i	−0.155002	−	0.268471i
$107$	12.2975	+	7.09995i	1.18884	+	0.686378i	0.958043	−	0.286623i	$-0.0925328\pi$
$107$	12.2975	+	7.09995i	1.18884	+	0.686378i	0.230799	+	0.973002i	$0.425866\pi$
$108$	−5.19612	+	0.0183905i	−0.499997	+	0.00176963i
$109$	−5.71119	+	15.6914i	−0.547033	+	1.50296i	0.290664	+	0.956825i	$0.406124\pi$
$109$	−5.71119	+	15.6914i	−0.547033	+	1.50296i	−0.837697	+	0.546136i	$0.816098\pi$
$110$	0.327451	+	0.504181i	0.0312212	+	0.0480717i
$111$	−9.68724	+	13.0443i	−0.919472	+	1.23811i
$112$	1.68781	−	0.297606i	0.159483	−	0.0281212i
$113$		−	7.39539i		−	0.695699i	−0.937550	−	0.347850i	$-0.886912\pi$
$113$		−	7.39539i		−	0.695699i	0.937550	−	0.347850i	$-0.113088\pi$
$114$	−3.81614	−	6.51438i	−0.357414	−	0.610127i
$115$	0.429186	+	1.85863i	0.0400218	+	0.173318i
$116$	0.356949	+	2.02436i	0.0331419	+	0.187957i
$117$	4.38278	−	10.2267i	0.405188	−	0.945459i
$118$	−4.81234	−	13.2218i	−0.443011	−	1.21716i
$119$	0.901920	−	2.47800i	0.0826789	−	0.227158i
$120$	3.76444	+	0.910471i	0.343645	+	0.0831142i
$121$	−5.46386	+	9.46368i	−0.496714	+	0.860334i
$122$	−1.02497	+	0.591767i	−0.0927964	+	0.0535761i
$123$	0.260233	+	4.37902i	0.0234644	+	0.394843i
$124$	0.278515	+	0.0491098i	0.0250114	+	0.00441019i
$125$	4.00526	−	10.4383i	0.358242	−	0.933629i
$126$	0.286842	−	5.13353i	0.0255539	−	0.457331i
$127$	1.23824	+	1.03901i	0.109876	+	0.0921972i	0.696071	−	0.717973i	$-0.254930\pi$
$127$	1.23824	+	1.03901i	0.109876	+	0.0921972i	−0.586194	+	0.810170i	$0.699374\pi$
$128$	0.342020	−	0.939693i	0.0302306	−	0.0830579i
$129$	5.62006	+	8.52297i	0.494819	+	0.750405i
$130$	−4.99058	+	6.62335i	−0.437703	+	0.580906i
$131$	−3.40772	+	0.600872i	−0.297733	+	0.0524984i	−0.320519	−	0.947242i	$-0.603857\pi$
$131$	−3.40772	+	0.600872i	−0.297733	+	0.0524984i	0.0227860	+	0.999740i	$0.492746\pi$
$132$	−0.107927	−	0.452996i	−0.00939380	−	0.0394282i
$133$	6.65856	−	3.38699i	0.577370	−	0.293689i
$134$		−	2.26770i		−	0.195899i
$135$	5.23775	−	10.3714i	0.450794	−	0.892628i
$136$	−0.989036	−	1.17869i	−0.0848091	−	0.101072i
$137$	18.9427	−	6.89459i	1.61839	−	0.589045i	0.635314	−	0.772254i	$-0.280871\pi$
$137$	18.9427	−	6.89459i	1.61839	−	0.589045i	0.983074	+	0.183209i	$0.0586486\pi$
$138$	0.169804	−	1.46778i	0.0144547	−	0.124946i
$139$	−14.6100	−	12.2593i	−1.23921	−	1.03982i	−0.997586	−	0.0694469i	$-0.977877\pi$
$139$	−14.6100	−	12.2593i	−1.23921	−	1.03982i	−0.241621	−	0.970371i	$-0.577679\pi$
$140$	−1.12028	+	3.66488i	−0.0946813	+	0.309738i
$141$	9.79161	+	10.3540i	0.824602	+	0.871964i
$142$	2.35384	+	0.415045i	0.197530	+	0.0348298i
$143$	0.981981	+	0.173150i	0.0821174	+	0.0144795i
$144$	−2.51035	−	1.64261i	−0.209196	−	0.136884i
$145$	−4.39565	−	1.34367i	−0.365039	−	0.111586i
$146$	5.57633	+	4.67909i	0.461500	+	0.387244i
$147$	−6.99023	−	0.808683i	−0.576545	−	0.0666990i
$148$	−8.81505	+	3.20841i	−0.724592	+	0.263730i
$149$	−14.6019	−	17.4018i	−1.19623	−	1.42561i	−0.878705	−	0.477366i	$-0.841592\pi$
$149$	−14.6019	−	17.4018i	−1.19623	−	1.42561i	−0.317528	−	0.948249i	$-0.602853\pi$
$150$	−5.63517	+	6.57608i	−0.460110	+	0.536935i
$151$			10.2840i			0.836904i	0.908239	+	0.418452i	$0.137427\pi$
$151$			10.2840i			0.836904i	−0.908239	+	0.418452i	$0.862573\pi$
$152$	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
$155$	−0.380557	+	0.505064i	−0.0305671	+	0.0405677i
$156$	5.36281	−	3.53625i	0.429368	−	0.283126i
$157$	−3.29903	+	9.06402i	−0.263292	+	0.723388i	0.735649	+	0.677363i	$0.236877\pi$
$157$	−3.29903	+	9.06402i	−0.263292	+	0.723388i	−0.998940	+	0.0460245i	$0.985345\pi$
$158$	4.03579	+	3.38643i	0.321071	+	0.269410i
$159$	−5.29778	−	1.57924i	−0.420142	−	0.125242i
$160$	1.52507	+	1.63529i	0.120567	+	0.129281i
$161$	1.43983	+	0.253881i	0.113474	+	0.0200086i
$162$	−6.51714	+	6.20700i	−0.512035	+	0.487668i
$163$	−18.7191	+	10.8075i	−1.46619	+	0.846507i	−0.999285	−	0.0377994i	$-0.987965\pi$
$163$	−18.7191	+	10.8075i	−1.46619	+	0.846507i	−0.466907	+	0.884306i	$0.654632\pi$
$164$	−1.26634	+	2.19337i	−0.0988849	+	0.171274i
$165$	1.01210	+	0.244787i	0.0787919	+	0.0190567i
$166$	−5.08506	+	13.9711i	−0.394678	+	1.08437i
$167$	−5.05375	−	13.8851i	−0.391071	−	1.07446i	−0.966513	−	0.256616i	$-0.917392\pi$
$167$	−5.05375	−	13.8851i	−0.391071	−	1.07446i	0.575443	−	0.817842i	$-0.304830\pi$
$168$	1.76984	−	2.38317i	0.136546	−	0.183865i
$169$	0.131090	+	0.743451i	0.0100839	+	0.0571885i
$170$	3.35235	−	0.774109i	0.257113	−	0.0593715i
$171$	−12.5551	−	3.65643i	−0.960112	−	0.279614i
$172$			5.89424i			0.449431i
$173$	9.66856	−	1.70483i	0.735087	−	0.129616i	0.206442	−	0.978459i	$-0.433811\pi$
$173$	9.66856	−	1.70483i	0.735087	−	0.129616i	0.528645	+	0.848843i	$0.322700\pi$
$174$	2.85837	+	2.12274i	0.216693	+	0.160925i
$175$	−6.16473	−	5.95213i	−0.466009	−	0.449939i
$176$	0.0919547	−	0.252644i	0.00693135	−	0.0190437i
$177$	−21.7912	−	10.9118i	−1.63793	−	0.820179i
$178$	−12.0504	−	6.95729i	−0.903214	−	0.521471i
$179$	0.839976	+	1.45488i	0.0627827	+	0.108743i	0.895708	−	0.444642i	$-0.146669\pi$
$179$	0.839976	+	1.45488i	0.0627827	+	0.108743i	−0.832926	+	0.553385i	$0.813336\pi$
$180$	5.82089	−	3.33425i	0.433863	−	0.248521i
$181$	15.0430	+	2.65249i	1.11814	+	0.197158i	0.702024	−	0.712153i	$-0.252280\pi$
$181$	15.0430	+	2.65249i	1.11814	+	0.197158i	0.416116	+	0.909311i	$0.363391\pi$
$182$	3.17812	+	5.50467i	0.235578	+	0.408034i
$183$	−0.585612	+	1.96451i	−0.0432897	+	0.145221i
$184$	0.548347	−	0.653494i	0.0404247	−	0.0481762i
$185$	2.55540	−	20.8198i	0.187877	−	1.53070i
$186$	0.408941	−	0.269657i	0.0299850	−	0.0197722i
$187$	−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
$190$	8.43787	+	4.87877i	0.612147	+	0.353943i
$191$		−	4.72693i		−	0.342028i	−0.985269	−	0.171014i	$-0.945296\pi$
$191$		−	4.72693i		−	0.342028i	0.985269	−	0.171014i	$-0.0547044\pi$
$192$	−0.687906	−	1.58959i	−0.0496453	−	0.114719i
$193$	7.07242	−	5.93447i	0.509084	−	0.427172i	−0.351723	−	0.936104i	$-0.614404\pi$
$193$	7.07242	−	5.93447i	0.509084	−	0.427172i	0.860807	+	0.508932i	$0.169960\pi$
$194$	−2.05678	−	5.65095i	−0.147668	−	0.405714i
$195$	1.60201	+	14.2744i	0.114722	+	1.02221i
$196$	−3.11223	−	2.61147i	−0.222302	−	0.186534i
$197$	3.15567	−	5.46578i	0.224832	−	0.389421i	−0.731437	−	0.681909i	$-0.761150\pi$
$197$	3.15567	−	5.46578i	0.224832	−	0.389421i	0.956269	+	0.292488i	$0.0944833\pi$
$198$	−0.674926	−	0.441628i	−0.0479649	−	0.0313851i
$199$	4.19757	−	23.8056i	0.297558	−	1.68754i	−0.359062	−	0.933314i	$-0.616903\pi$
$199$	4.19757	−	23.8056i	0.297558	−	1.68754i	0.656620	−	0.754221i	$-0.271985\pi$
$200$	−4.80618	+	1.37862i	−0.339849	+	0.0974831i
$201$	−2.69876	−	2.85377i	−0.190356	−	0.201289i
$202$	2.53143	−	4.38456i	0.178111	−	0.308497i
$203$	−2.26452	+	2.69874i	−0.158938	+	0.189415i
$204$	−2.64739	−	0.306270i	−0.185354	−	0.0214432i
$205$	−3.08465	−	4.74947i	−0.215441	−	0.331718i
$206$	6.11689	+	7.28983i	0.426184	+	0.507907i
$207$	−1.53310	−	2.04920i	−0.106558	−	0.142430i
$208$	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	0.378264	−	0.925698i	$-0.376521\pi$
$211$	15.2568	−	2.69019i	1.05032	−	0.185200i	0.672059	+	0.740497i	$0.265410\pi$
$212$	−2.05157	−	2.44497i	−0.140903	−	0.167921i
$213$	3.45612	−	2.27897i	0.236809	−	0.156153i
$214$	13.3435	+	4.85665i	0.912146	+	0.331994i
$215$	−11.7437	−	5.98303i	−0.800911	−	0.408039i
$216$	−5.11399	+	0.920408i	−0.347963	+	0.0626258i
$217$	0.242348	+	0.419759i	0.0164517	+	0.0284951i
$218$	−2.89965	+	16.4447i	−0.196389	+	1.11378i
$219$	12.5860	−	0.747953i	0.850486	−	0.0505420i
$220$	0.410026	+	0.439660i	0.0276440	+	0.0296419i
$221$	2.85327	−	4.94202i	0.191932	−	0.332436i
$222$	−7.27495	+	14.5283i	−0.488262	+	0.975077i
$223$	5.31883	+	1.93590i	0.356175	+	0.129637i	0.513909	−	0.857844i	$-0.328197\pi$
$223$	5.31883	+	1.93590i	0.356175	+	0.129637i	−0.157734	+	0.987482i	$0.550419\pi$
$224$	1.61049	−	0.586170i	0.107605	−	0.0391651i
$225$	0.734582	+	14.9820i	0.0489721	+	0.998800i
$226$	−1.28420	−	7.28303i	−0.0854234	−	0.484460i
$227$			13.8007i			0.915983i	0.888956	+	0.457992i	$0.151431\pi$
$227$			13.8007i			0.915983i	−0.888956	+	0.457992i	$0.848569\pi$
$228$	−4.88937	−	5.75274i	−0.323807	−	0.380985i
$229$	−1.43517			−0.0948389			−0.0474194	−	0.998875i	$-0.515100\pi$
$229$	−1.43517			−0.0948389			−0.0474194	+	0.998875i	$0.515100\pi$
$230$	0.745413	+	1.75586i	0.0491511	+	0.115778i
$231$	0.475834	−	0.640733i	0.0313076	−	0.0421571i
$232$	0.703052	+	1.93162i	0.0461576	+	0.126817i
$233$	11.7741	+	4.28541i	0.771345	+	0.280747i	0.697559	−	0.716528i	$-0.254270\pi$
$233$	11.7741	+	4.28541i	0.771345	+	0.280747i	0.0737860	+	0.997274i	$0.476492\pi$
$234$	2.54035	−	10.8324i	0.166068	−	0.708136i
$235$	−17.5939	−	5.37812i	−1.14770	−	0.350830i
$236$	−7.03517	−	12.1853i	−0.457950	−	0.793193i
$237$	9.10899	−	0.541322i	0.591692	−	0.0351626i
$238$	0.457917	−	2.59698i	0.0296823	−	0.168337i
$239$	−2.10709	+	1.21653i	−0.136297	+	0.0786909i	−0.566598	−	0.823994i	$-0.691741\pi$
$239$	−2.10709	+	1.21653i	−0.136297	+	0.0786909i	0.430301	+	0.902685i	$0.358407\pi$
$240$	3.86536	+	0.242950i	0.249508	+	0.0156823i
$241$	8.71138	−	10.3818i	0.561150	−	0.668752i	−0.408640	−	0.912696i	$-0.633997\pi$
$241$	8.71138	−	10.3818i	0.561150	−	0.668752i	0.969789	+	0.243944i	$0.0784412\pi$
$242$	−3.73750	+	10.2687i	−0.240256	+	0.660097i
$243$	−0.814576	+	15.5672i	−0.0522551	+	0.998634i
$244$	−0.906639	+	0.760761i	−0.0580416	+	0.0487027i
$245$	8.36220	−	3.54999i	0.534242	−	0.226801i
$246$	1.01669	+	4.26730i	0.0648217	+	0.272073i
$247$	15.4630	−	4.71598i	0.983884	−	0.300071i
$248$	0.282812			0.0179586
$249$	10.2276	+	23.6336i	0.648148	+	1.49772i
$250$	2.13183	−	10.9752i	0.134829	−	0.694133i
$251$	7.49044	+	20.5798i	0.472792	+	1.29899i	0.915499	+	0.402320i	$0.131796\pi$
$251$	7.49044	+	20.5798i	0.472792	+	1.29899i	−0.442707	+	0.896666i	$0.645982\pi$
$252$	−0.608944	−	5.10535i	−0.0383599	−	0.321607i
$253$	0.147427	−	0.175697i	0.00926867	−	0.0110460i
$254$	1.39985	+	0.808206i	0.0878346	+	0.0507113i
$255$	3.29748	−	4.96377i	0.206496	−	0.310843i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	7.45354	+	1.31426i	0.464939	+	0.0819813i	0.401210	−	0.915986i	$-0.368590\pi$
$257$	7.45354	+	1.31426i	0.464939	+	0.0819813i	0.0637288	+	0.997967i	$0.479701\pi$
$258$	7.01468	+	7.41757i	0.436715	+	0.461798i
$259$	−13.9233	−	8.03860i	−0.865150	−	0.499495i
$260$	−3.76463	+	7.38933i	−0.233472	+	0.458267i
$261$	6.12336	−	0.730367i	0.379026	−	0.0452086i
$262$	−3.25160	+	1.18349i	−0.200885	+	0.0731161i
$263$	−9.68843	+	8.12956i	−0.597414	+	0.501290i	−0.890613	−	0.454761i	$-0.849725\pi$
$263$	−9.68843	+	8.12956i	−0.597414	+	0.501290i	0.293199	+	0.956051i	$0.405280\pi$
$264$	−0.184949	−	0.427373i	−0.0113828	−	0.0263030i
$265$	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	0.355434	−	0.934701i	$-0.384333\pi$
$269$	21.9392	−	18.4092i	1.33766	−	1.12243i	0.982222	−	0.187725i	$-0.0601114\pi$
$270$	3.35720	−	11.1234i	0.204313	−	0.676946i
$271$	−8.81392	−	3.20800i	−0.535407	−	0.194872i	0.0601437	−	0.998190i	$-0.480844\pi$
$271$	−8.81392	−	3.20800i	−0.535407	−	0.194872i	−0.595551	+	0.803317i	$0.703066\pi$
$272$	−1.17869	−	0.989036i	−0.0714684	−	0.0599691i
$273$	10.5506	+	3.14507i	0.638549	+	0.190348i
$274$	17.4577	−	10.0792i	1.05466	−	0.608908i
$275$	−1.29218	+	0.370653i	−0.0779214	+	0.0223512i
$276$	−0.0876533	−	1.47497i	−0.00527611	−	0.0887827i
$277$	−3.47035	+	2.00361i	−0.208513	+	0.120385i	−0.600620	−	0.799534i	$-0.705080\pi$
$277$	−3.47035	+	2.00361i	−0.208513	+	0.120385i	0.392107	+	0.919920i	$0.371746\pi$
$278$	−16.5169	−	9.53602i	−0.990616	−	0.571932i
$279$	0.193714	−	0.826025i	0.0115974	−	0.0494528i
$280$	−0.466866	+	3.80373i	−0.0279006	+	0.227317i
$281$	−3.96398	+	1.44277i	−0.236471	+	0.0860685i	−0.457538	−	0.889190i	$-0.651268\pi$
$281$	−3.96398	+	1.44277i	−0.236471	+	0.0860685i	0.221066	+	0.975259i	$0.429046\pi$
$282$	11.4408	+	8.49640i	0.681290	+	0.505953i
$283$	7.69224	−	1.35635i	0.457256	−	0.0806266i	0.0597241	−	0.998215i	$-0.480978\pi$
$283$	7.69224	−	1.35635i	0.457256	−	0.0806266i	0.397532	+	0.917588i	$0.369867\pi$
$284$	2.39015			0.141829
$285$	16.4248	−	3.90217i	0.972919	−	0.231145i
$286$	0.997129			0.0589615
$287$	−4.27469	+	0.753744i	−0.252327	+	0.0444921i
$288$	−2.75744	−	1.18174i	−0.162484	−	0.0696345i
$289$	13.7501	−	5.00461i	0.808827	−	0.294389i
$290$	−4.56220	−	0.559959i	−0.267901	−	0.0328819i
$291$	−9.31348	−	4.66365i	−0.545966	−	0.273388i
$292$	6.30412	+	3.63969i	0.368921	+	0.212997i
$293$	−19.3607	+	11.1779i	−1.13106	+	0.653020i	−0.944202	−	0.329366i	$-0.893165\pi$
$293$	−19.3607	+	11.1779i	−1.13106	+	0.653020i	−0.186862	+	0.982386i	$0.559832\pi$
$294$	−7.02446	+	0.417444i	−0.409675	+	0.0243458i
$295$	31.4190	−	1.64802i	1.82929	−	0.0959515i
$296$	−8.12399	+	4.69039i	−0.472197	+	0.272623i
$297$	−1.37493	+	0.247459i	−0.0797818	+	0.0143590i
$298$	−17.4018	−	14.6019i	−1.00806	−	0.845864i
$299$	2.97305	+	1.08210i	0.171936	+	0.0625796i
$300$	−4.40764	+	7.45471i	−0.254475	+	0.430398i
$301$	−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
$306$	−3.69609	+	2.76521i	−0.211291	+	0.158077i
$307$	−1.85340	+	1.55519i	−0.105779	+	0.0887592i	−0.694143	−	0.719837i	$-0.744217\pi$
$307$	−1.85340	+	1.55519i	−0.105779	+	0.0887592i	0.588364	+	0.808596i	$0.299772\pi$
$308$	0.432992	−	0.157596i	0.0246720	−	0.00897988i
$309$	16.3733	+	1.89419i	0.931446	+	0.107757i
$310$	−0.287072	+	0.563473i	−0.0163046	+	0.0320031i
$311$	−23.3442	−	13.4778i	−1.32373	−	0.764254i	−0.339406	−	0.940640i	$-0.610226\pi$
$311$	−23.3442	−	13.4778i	−1.32373	−	0.764254i	−0.984321	+	0.176386i	$0.943559\pi$
$312$	4.66727	−	4.41376i	0.264232	−	0.249880i
$313$	19.5355	+	3.44464i	1.10421	+	0.194702i	0.695899	−	0.718139i	$-0.255006\pi$
$313$	19.5355	+	3.44464i	1.10421	+	0.194702i	0.408313	+	0.912842i	$0.366117\pi$
$314$	−1.67496	+	9.49919i	−0.0945237	+	0.536070i
$315$	10.7900	+	3.96900i	0.607948	+	0.223628i
$316$	4.56253	+	2.63418i	0.256662	+	0.148184i
$317$	11.5302	−	13.7411i	0.647600	−	0.771779i	−0.337950	−	0.941164i	$-0.609734\pi$
$317$	11.5302	−	13.7411i	0.647600	−	0.771779i	0.985550	+	0.169385i	$0.0541780\pi$
$318$	−5.49153	−	0.635302i	−0.307950	−	0.0356259i
$319$	0.189021	+	0.519331i	0.0105831	+	0.0290769i
$320$	1.78586	+	1.34562i	0.0998328	+	0.0752224i
$321$	22.5720	−	9.76820i	1.25984	−	0.545208i
$322$	1.46204			0.0814764
$323$	−6.17194	−	2.62480i	−0.343416	−	0.146048i
$324$	−5.34030	+	7.24439i	−0.296683	+	0.402466i
$325$	−10.9011	−	15.0013i	−0.604686	−	0.832121i
$326$	−16.5580	+	13.8938i	−0.917064	+	0.769508i
$327$	15.9217	+	24.1456i	0.880470	+	1.33526i
$328$	−0.866230	+	2.37995i	−0.0478296	+	0.131411i
$329$	−9.06386	+	10.8019i	−0.499707	+	0.595527i
$330$	1.03923	+	0.0653189i	0.0572078	+	0.00359569i
$331$	21.8174	−	12.5963i	1.19919	−	0.692355i	0.238819	−	0.971064i	$-0.423240\pi$
$331$	21.8174	−	12.5963i	1.19919	−	0.692355i	0.960376	+	0.278709i	$0.0899064\pi$
$332$	−2.58176	+	14.6419i	−0.141692	+	0.803576i
$333$	8.13490	+	26.9409i	0.445790	+	1.47635i
$334$	−7.38809	−	12.7965i	−0.404258	−	0.700196i
$335$	4.84922	+	1.48232i	0.264941	+	0.0809877i
$336$	1.32912	−	2.65429i	0.0725092	−	0.144803i
$337$	−0.194977	−	0.0709657i	−0.0106211	−	0.00386575i	0.336704	−	0.941610i	$-0.390688\pi$
$337$	−0.194977	−	0.0709657i	−0.0106211	−	0.00386575i	−0.347325	+	0.937745i	$0.612910\pi$
$338$	0.258198	+	0.709392i	0.0140441	+	0.0385859i
$339$	−10.2836	−	7.63699i	−0.558526	−	0.414784i
$340$	3.16699	−	1.34448i	0.171754	−	0.0729145i
$341$	0.0760361			0.00411759
$342$	−12.9993	−	1.42071i	−0.702921	−	0.0768233i
$343$		−	18.9598i		−	1.02373i
$344$	1.02352	+	5.80469i	0.0551847	+	0.312968i
$345$	3.02770	+	1.32255i	0.163006	+	0.0712036i
$346$	9.22564	−	3.35786i	0.495973	−	0.180520i
$347$	27.1609	+	9.88575i	1.45807	+	0.530695i	0.944833	−	0.327551i	$-0.106223\pi$
$347$	27.1609	+	9.88575i	1.45807	+	0.530695i	0.513239	+	0.858246i	$0.328446\pi$
$348$	3.18356	+	1.59414i	0.170657	+	0.0854550i
$349$	−10.8248	+	18.7491i	−0.579438	+	1.00362i	0.416106	+	0.909316i	$0.363395\pi$
$349$	−10.8248	+	18.7491i	−0.579438	+	1.00362i	−0.995544	+	0.0942999i	$0.969939\pi$
$350$	−7.10465	−	4.79121i	−0.379759	−	0.256101i
$351$	−9.69466	−	16.6552i	−0.517462	−	0.888990i
$352$	0.0466866	−	0.264773i	0.00248841	−	0.0141125i
$353$	−14.4043	−	24.9490i	−0.766665	−	1.32790i	−0.939362	−	0.342927i	$-0.888582\pi$
$353$	−14.4043	−	24.9490i	−0.766665	−	1.32790i	0.172697	−	0.984975i	$-0.444752\pi$
$354$	−23.3549	−	6.96200i	−1.24130	−	0.370026i
$355$	−2.42616	+	4.76213i	−0.128767	+	0.252748i
$356$	−13.0754	−	4.75907i	−0.692996	−	0.252230i
$357$	−2.51437	−	3.81311i	−0.133075	−	0.201811i
$358$	1.07985	+	1.28692i	0.0570719	+	0.0680157i
$359$	8.08336	−	1.42531i	0.426623	−	0.0752252i	0.0437858	−	0.999041i	$-0.486058\pi$
$359$	8.08336	−	1.42531i	0.426623	−	0.0752252i	0.382837	+	0.923816i	$0.374947\pi$
$360$	5.15347	−	4.29439i	0.271612	−	0.226334i
$361$	−7.70433	−	17.3679i	−0.405491	−	0.914099i
$362$	15.2751			0.802841
$363$	7.51724	+	17.3705i	0.394553	+	0.911717i
$364$	4.08572	+	4.86917i	0.214150	+	0.255214i
$365$	−13.6508	+	8.86580i	−0.714515	+	0.464057i
$366$	−0.235581	+	2.03636i	−0.0123140	+	0.106442i
$367$	3.85915	−	4.59915i	0.201446	−	0.240074i	−0.655858	−	0.754884i	$-0.727693\pi$
$367$	3.85915	−	4.59915i	0.201446	−	0.240074i	0.857304	+	0.514810i	$0.172138\pi$
$368$	0.426538	−	0.738785i	0.0222348	−	0.0385119i
$369$	6.35792	+	4.16021i	0.330980	+	0.216572i
$370$	−1.09875	−	20.9473i	−0.0571211	−	1.08900i
$371$	0.949865	−	5.38695i	0.0493145	−	0.279677i
$372$	0.355903	−	0.336572i	0.0184527	−	0.0174504i
$373$	9.09941	−	15.7606i	0.471149	−	0.816055i	−0.528306	−	0.849054i	$-0.677173\pi$
$373$	9.09941	−	15.7606i	0.471149	−	0.816055i	0.999455	+	0.0329993i	$0.0105059\pi$
$374$	−0.316899	−	0.265910i	−0.0163865	−	0.0137499i
$375$	−10.3787	−	16.3488i	−0.535955	−	0.844247i
$376$	2.81401	+	7.73143i	0.145121	+	0.398718i
$377$	−5.84008	+	4.90041i	−0.300779	+	0.252384i
$378$	−6.84215	−	5.70010i	−0.351922	−	0.293182i
$379$			12.5834i			0.646365i	0.946337	+	0.323182i	$0.104753\pi$
$379$			12.5834i			0.646365i	−0.946337	+	0.323182i	$0.895247\pi$
$380$	9.15687	+	3.33943i	0.469737	+	0.171309i
$381$	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	0.572657	−	0.819795i	$-0.305913\pi$
$383$	−6.53894	−	7.79281i	−0.334124	−	0.398194i	−0.906781	+	0.421601i	$0.861468\pi$
$384$	−0.953484	−	1.44598i	−0.0486573	−	0.0737900i
$385$	−0.125520	+	1.02266i	−0.00639711	+	0.0521197i
$386$	5.93447	−	7.07242i	0.302056	−	0.359977i
$387$	17.6552	+	0.986503i	0.897463	+	0.0501468i
$388$	−3.00681	−	5.20794i	−0.152647	−	0.264393i
$389$	21.5108	+	3.79294i	1.09064	+	0.192310i	0.689917	−	0.723889i	$-0.257647\pi$
$389$	21.5108	+	3.79294i	1.09064	+	0.192310i	0.400725	+	0.916198i	$0.368758\pi$
$390$	4.05639	+	13.7793i	0.205403	+	0.697743i
$391$	−0.656300	−	1.13674i	−0.0331905	−	0.0574876i
$392$	−3.51843	−	2.03137i	−0.177707	−	0.102599i
$393$	−2.68351	+	5.35906i	−0.135365	+	0.270329i
$394$	2.15861	−	5.93072i	0.108749	−	0.298785i
$395$	−9.87959	+	6.41651i	−0.497096	+	0.322850i
$396$	−0.741360	−	0.317719i	−0.0372547	−	0.0159660i
$397$	−18.4723	+	3.25716i	−0.927096	+	0.163472i	−0.616757	−	0.787154i	$-0.711554\pi$
$397$	−18.4723	+	3.25716i	−0.927096	+	0.163472i	−0.310339	+	0.950626i	$0.600443\pi$
$398$		−	24.1729i		−	1.21168i
$399$	2.16635	−	12.7566i	0.108453	−	0.638630i
$400$	−4.49377	+	2.19226i	−0.224689	+	0.109613i
$401$	−0.952616	−	5.40255i	−0.0475714	−	0.269791i	0.951740	−	0.306907i	$-0.0992940\pi$
$401$	−0.952616	−	5.40255i	−0.0475714	−	0.269791i	−0.999311	+	0.0371161i	$0.988183\pi$
$402$	−3.15332	−	2.34178i	−0.157273	−	0.116797i
$403$	0.358739	+	0.985627i	0.0178701	+	0.0490976i
$404$	1.73160	−	4.75753i	0.0861503	−	0.236696i
$405$	−9.01295	−	17.9935i	−0.447857	−	0.894105i
$406$	−1.76148	+	3.05097i	−0.0874208	+	0.151417i
$407$	−2.18420	+	1.26105i	−0.108267	+	0.0625078i
$408$	−2.66035	+	0.158097i	−0.131707	+	0.00782699i
$409$	26.4803	+	4.66918i	1.30936	+	0.230876i	0.784404	−	0.620250i	$-0.212969\pi$
$409$	26.4803	+	4.66918i	1.30936	+	0.230876i	0.524960	+	0.851127i	$0.324080\pi$
$410$	−3.86252	−	4.14167i	−0.190756	−	0.204543i
$411$	9.97440	−	33.4604i	0.492001	−	1.65048i
$412$	7.28983	+	6.11689i	0.359144	+	0.301358i
$413$	8.24761	−	22.6601i	0.405838	−	1.11503i
$414$	−1.86565	−	1.75185i	−0.0916919	−	0.0860988i
$415$	−26.5518	−	20.0063i	−1.30337	−	0.982071i
$416$	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	$0.774237\pi$
$420$	3.93926	+	5.34240i	0.192216	+	0.260682i
$421$	18.3324	+	21.8477i	0.893466	+	1.06479i	0.997532	+	0.0702204i	$0.0223703\pi$
$421$	18.3324	+	21.8477i	0.893466	+	1.06479i	−0.104066	+	0.994570i	$0.533185\pi$
$422$	14.5579	−	5.29864i	0.708667	−	0.257934i
$423$	24.5091	−	2.92334i	1.19167	−	0.142138i
$424$	−2.44497	−	2.05157i	−0.118738	−	0.0996332i
$425$	−0.535968	+	7.67464i	−0.0259983	+	0.372275i
$426$	3.00787	−	2.84450i	0.145732	−	0.137816i
$427$	−1.99758	−	0.352227i	−0.0966696	−	0.0170455i
$428$	13.9842	+	2.46579i	0.675951	+	0.119188i
$429$	1.25483	−	1.18667i	0.0605839	−	0.0572932i
$430$	−12.6042	−	3.85287i	−0.607828	−	0.185802i
$431$	24.3191	+	20.4062i	1.17141	+	0.982930i	0.999997	−	0.00226871i	$-0.000722153\pi$
$431$	24.3191	+	20.4062i	1.17141	+	0.982930i	0.171413	+	0.985199i	$0.445167\pi$
$432$	−4.87647	+	1.79446i	−0.234619	+	0.0863360i
$433$	−23.5039	+	8.55473i	−1.12953	+	0.411114i	−0.838121	−	0.545485i	$-0.816345\pi$
$433$	−23.5039	+	8.55473i	−1.12953	+	0.411114i	−0.291407	+	0.956599i	$0.594123\pi$
$434$	0.311557	+	0.371299i	0.0149552	+	0.0178229i
$435$	−6.40768	+	4.72475i	−0.307225	+	0.226534i
$436$			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	−0.913766	−	0.406241i	$-0.866839\pi$
$439$	−34.2253	+	6.03484i	−1.63348	+	0.288027i	−0.719716	+	0.694268i	$0.755728\pi$
$440$	0.480143	+	0.361780i	0.0228899	+	0.0172472i
$441$	−8.34310	+	8.88508i	−0.397291	+	0.423099i
$442$	1.95175	−	5.36240i	0.0928355	−	0.255063i
$443$	4.69348	+	3.93830i	0.222994	+	0.187114i	0.747440	−	0.664330i	$-0.231283\pi$
$443$	4.69348	+	3.93830i	0.222994	+	0.187114i	−0.524446	+	0.851444i	$0.675727\pi$
$444$	−4.64161	+	15.5709i	−0.220281	+	0.738961i
$445$	22.7543	−	21.2207i	1.07866	−	1.00596i
$446$	5.57419	+	0.982880i	0.263946	+	0.0465407i
$447$	−39.2768	+	2.33411i	−1.85773	+	0.110400i
$448$	1.48423	−	0.856923i	0.0701235	−	0.0404858i
$449$	−10.6754	+	18.4903i	−0.503802	+	0.872611i	0.496188	+	0.868215i	$0.334733\pi$
$449$	−10.6754	+	18.4903i	−0.503802	+	0.872611i	−0.999990	+	0.00439613i	$0.998601\pi$
$450$	3.32502	+	14.6268i	0.156743	+	0.689516i
$451$	−0.232893	+	0.639867i	−0.0109665	+	0.0301302i
$452$	−2.52937	−	6.94939i	−0.118972	−	0.326872i
$453$	14.3003	+	10.6200i	0.671889	+	0.498972i
$454$	2.39646	+	13.5910i	0.112472	+	0.637858i
$455$	−13.8486	+	3.19785i	−0.649232	+	0.149918i
$456$	−5.81404	−	4.81631i	−0.272268	−	0.225545i
$457$		−	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
$459$	−1.36047	+	7.87854i	−0.0635011	+	0.367739i
$460$	1.03899	+	1.59975i	0.0484432	+	0.0745886i
$461$	10.0255	−	27.5449i	0.466935	−	1.28289i	−0.453240	−	0.891388i	$-0.649732\pi$
$461$	10.0255	−	27.5449i	0.466935	−	1.28289i	0.920176	−	0.391506i	$-0.128046\pi$
$462$	0.357343	−	0.713626i	0.0166251	−	0.0332009i
$463$	10.1011	+	5.83185i	0.469436	+	0.271029i	0.716004	−	0.698097i	$-0.245969\pi$
$463$	10.1011	+	5.83185i	0.469436	+	0.271029i	−0.246568	+	0.969126i	$0.579303\pi$
$464$	1.02779	+	1.78019i	0.0477141	+	0.0826433i
$465$	0.309320	+	1.05074i	0.0143444	+	0.0487270i
$466$	12.3393	+	2.17576i	0.571609	+	0.100790i
$467$	16.4861	+	28.5548i	0.762886	+	1.32136i	0.941357	+	0.337413i	$0.109552\pi$
$467$	16.4861	+	28.5548i	0.762886	+	1.32136i	−0.178471	+	0.983945i	$0.557115\pi$
$468$	0.620726	−	11.1090i	0.0286931	−	0.513512i
$469$	2.49818	−	2.97722i	0.115355	−	0.137475i
$470$	−18.2605	−	2.24127i	−0.842293	−	0.103382i
$471$	9.19705	+	13.9476i	0.423778	+	0.642670i
$472$	−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
$475$	−15.9483	+	14.8544i	−0.731757	+	0.681566i
$476$		−	2.63704i		−	0.120868i
$477$	−7.66686	+	5.73593i	−0.351041	+	0.262630i
$478$	−1.86383	+	1.56394i	−0.0852498	+	0.0715331i
$479$	12.2694	+	33.7099i	0.560604	+	1.54025i	0.818756	+	0.574142i	$0.194664\pi$
$479$	12.2694	+	33.7099i	0.560604	+	1.54025i	−0.258152	+	0.966104i	$0.583114\pi$
$480$	3.84882	−	0.431953i	0.175674	−	0.0197159i
$481$	−26.6515	−	22.3633i	−1.21520	−	1.01968i
$482$	6.77625	−	11.7368i	0.308650	−	0.534597i
$483$	1.83990	−	1.73996i	0.0837183	−	0.0791710i
$484$	−1.89758	+	10.7617i	−0.0862535	+	0.489168i
$485$	13.4284	−	0.704358i	0.609752	−	0.0319833i
$486$	1.90101	+	15.4721i	0.0862315	+	0.701829i
$487$	−5.11325	+	8.85641i	−0.231704	+	0.401322i	−0.958310	−	0.285732i	$-0.907763\pi$
$487$	−5.11325	+	8.85641i	−0.231704	+	0.401322i	0.726606	+	0.687054i	$0.241097\pi$
$488$	−0.760761	+	0.906639i	−0.0344380	+	0.0410416i
$489$	−4.30244	+	37.1902i	−0.194563	+	1.68180i
$490$	7.61871	−	4.94814i	0.344178	−	0.223534i
$491$	5.68342	+	6.77324i	0.256489	+	0.305672i	0.878888	−	0.477028i	$-0.158286\pi$
$491$	5.68342	+	6.77324i	0.256489	+	0.305672i	−0.622399	+	0.782701i	$0.713842\pi$
$492$	1.74225	+	4.02593i	0.0785468	+	0.181503i
$493$	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
$498$	14.1761	+	21.4985i	0.635248	+	0.963371i
$499$	−16.4654	−	5.99292i	−0.737093	−	0.268280i	−0.0539286	−	0.998545i	$-0.517174\pi$
$499$	−16.4654	−	5.99292i	−0.737093	−	0.268280i	−0.683164	+	0.730265i	$0.739397\pi$
$500$	0.193613	−	11.1787i	0.00865863	−	0.499925i
$501$	−24.5265	−	7.31125i	−1.09577	−	0.326643i
$502$	10.9503	+	18.9665i	0.488735	+	0.846515i
$503$	3.73623	−	21.1892i	0.166590	−	0.944780i	−0.780819	−	0.624757i	$-0.785198\pi$
$503$	3.73623	−	21.1892i	0.166590	−	0.944780i	0.947410	−	0.320023i	$-0.103691\pi$
$504$	−1.48623	−	4.92205i	−0.0662018	−	0.219245i
$505$	7.72120	+	8.27923i	0.343589	+	0.368421i
$506$	0.114678	−	0.198628i	0.00509806	−	0.00883010i
$507$	1.16917	+	0.585452i	0.0519246	+	0.0260009i
$508$	1.51893	+	0.552845i	0.0673916	+	0.0245285i
$509$	−25.5723	+	9.30755i	−1.13347	+	0.412550i	−0.839552	−	0.543280i	$-0.817182\pi$
$509$	−25.5723	+	9.30755i	−1.13347	+	0.412550i	−0.293920	+	0.955830i	$0.594960\pi$
$510$	2.38544	−	5.46096i	0.105629	−	0.241815i
$511$	2.16639	+	12.2862i	0.0958354	+	0.543509i
$512$		−	1.00000i		−	0.0441942i
$513$	−18.0497	+	13.6825i	−0.796912	+	0.604095i
$514$	7.56853			0.333833
$515$	−19.5869	+	8.31520i	−0.863103	+	0.366411i
$516$	8.19615	+	6.08680i	0.360816	+	0.267956i
$517$	0.756568	+	2.07865i	0.0332738	+	0.0914191i
$518$	−15.1076	−	5.49873i	−0.663791	−	0.241600i
$519$	7.61380	−	15.2050i	0.334209	−	0.667427i
$520$	−2.42429	+	7.93079i	−0.106312	+	0.347788i
$521$	−10.2847	−	17.8136i	−0.450580	−	0.780428i	0.547842	−	0.836582i	$-0.315450\pi$
$521$	−10.2847	−	17.8136i	−0.450580	−	0.780428i	−0.998422	+	0.0561538i	$0.982116\pi$
$522$	5.90350	−	1.78258i	0.258389	−	0.0780215i
$523$	3.11314	−	17.6555i	0.136128	−	0.772021i	−0.837939	−	0.545763i	$-0.816240\pi$
$523$	3.11314	−	17.6555i	0.136128	−	0.772021i	0.974067	−	0.226258i	$-0.0726492\pi$
$524$	−2.99669	+	1.73014i	−0.130911	+	0.0755816i
$525$	−14.6428	+	2.42570i	−0.639064	+	0.105866i
$526$	−8.12956	+	9.68843i	−0.354466	+	0.422436i
$527$	0.148831	−	0.408910i	0.00648319	−	0.0178124i
$528$	−0.256352	−	0.388764i	−0.0111563	−	0.0169188i
$529$	−17.0615	+	14.3163i	−0.741806	+	0.622449i
$530$	6.56935	−	2.78887i	0.285354	−	0.121141i
$531$	−37.6763	+	19.0332i	−1.63501	+	0.825971i
$532$	5.09858	−	5.46009i	0.221051	−	0.236725i
$533$	−9.39314			−0.406862
$534$	−22.1184	+	9.57192i	−0.957158	+	0.414218i
$535$	−19.1077	+	25.3591i	−0.826096	+	1.09637i
$536$	−0.775598	−	2.13094i	−0.0335007	−	0.0920425i
$537$	2.89048	+	0.334393i	0.124734	+	0.0144301i
$538$	18.4092	−	21.9392i	0.793675	−	0.945865i
$539$	−0.945956	−	0.546148i	−0.0407452	−	0.0235243i
$540$	1.37465	−	11.5373i	0.0591555	−	0.496488i
$541$	2.60101	−	14.7510i	0.111826	−	0.634196i	−0.876447	−	0.481498i	$-0.840093\pi$
$541$	2.60101	−	14.7510i	0.111826	−	0.634196i	0.988273	−	0.152698i	$-0.0487962\pi$
$542$	−9.23708	−	1.62875i	−0.396767	−	0.0699607i
$543$	19.2229	−	18.1788i	0.824932	−	0.780125i
$544$	−1.33252	−	0.769333i	−0.0571315	−	0.0329849i
$545$	−33.2699	−	16.9500i	−1.42512	−	0.726056i
$546$	10.9364	+	1.26521i	0.468035	+	0.0541458i
$547$	33.9042	−	12.3401i	1.44964	−	0.527626i	0.507149	−	0.861858i	$-0.330699\pi$
$547$	33.9042	−	12.3401i	1.44964	−	0.527626i	0.942491	+	0.334233i	$0.108477\pi$
$548$	15.4423	−	12.9576i	0.659661	−	0.553521i
$549$	2.12699	+	2.84301i	0.0907775	+	0.121337i
$550$	−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
$555$	−26.3118	−	25.0534i	−1.11688	−	1.06346i
$556$	−17.9219	−	6.52302i	−0.760056	−	0.276638i
$557$	16.6543	+	13.9746i	0.705665	+	0.592123i	0.923379	−	0.383889i	$-0.125416\pi$
$557$	16.6543	+	13.9746i	0.705665	+	0.592123i	−0.217714	+	0.976013i	$0.569860\pi$
$558$	0.0473335	−	0.847114i	0.00200379	−	0.0358612i
$559$	−18.9316	+	10.9302i	−0.800721	+	0.462296i
$560$	0.200738	+	3.82702i	0.00848274	+	0.161721i
$561$	−0.715257	+	0.0425057i	−0.0301982	+	0.00179459i
$562$	−3.65322	+	2.10919i	−0.154102	+	0.0889708i
$563$	18.7954	+	10.8516i	0.792134	+	0.457339i	0.840713	−	0.541481i	$-0.182136\pi$
$563$	18.7954	+	10.8516i	0.792134	+	0.457339i	−0.0485795	+	0.998819i	$0.515469\pi$
$564$	12.7424	+	6.38065i	0.536551	+	0.268674i
$565$	16.4134	+	2.01456i	0.690518	+	0.0847533i
$566$	7.33985	−	2.67149i	0.308517	−	0.112291i
$567$	−15.3941	+	0.969517i	−0.646492	+	0.0407159i
$568$	2.35384	−	0.415045i	0.0987649	−	0.0174149i
$569$	−11.9807			−0.502255			−0.251128	−	0.967954i	$-0.580801\pi$
$569$	−11.9807			−0.502255			−0.251128	+	0.967954i	$0.580801\pi$
$570$	15.4976	−	6.69502i	0.649125	−	0.280423i
$571$	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
$573$	−6.57297	−	4.88135i	−0.274590	−	0.203921i
$574$	−4.07887	+	1.48459i	−0.170249	+	0.0619654i
$575$	−4.24197	+	0.446236i	−0.176903	+	0.0186093i
$576$	−2.92076	−	0.684958i	−0.121698	−	0.0285399i
$577$	−38.2042	−	22.0572i	−1.59046	−	0.918254i	−0.993227	−	0.116189i	$-0.962932\pi$
$577$	−38.2042	−	22.0572i	−1.59046	−	0.918254i	−0.597236	−	0.802065i	$-0.703735\pi$
$578$	12.6721	−	7.31625i	0.527091	−	0.304316i
$579$	−0.948625	−	15.9628i	−0.0394235	−	0.663392i
$580$	−4.59012	+	0.240765i	−0.190594	+	0.00999724i
$581$	−22.0672	+	12.7405i	−0.915502	+	0.528565i
$582$	−9.98182	−	2.97553i	−0.413760	−	0.123340i
$583$	−0.657349	−	0.551581i	−0.0272246	−	0.0228442i
$584$	6.84038	+	2.48969i	0.283057	+	0.103024i
$585$	21.5034	+	12.5130i	0.889055	+	0.517350i
$586$	−17.1255	+	14.3700i	−0.707450	+	0.593621i
$587$	3.47915	+	19.7312i	0.143600	+	0.814395i	0.968481	+	0.249089i	$0.0801310\pi$
$587$	3.47915	+	19.7312i	0.143600	+	0.814395i	−0.824881	+	0.565307i	$0.808758\pi$
$588$	−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
$591$	−4.34161	−	10.0324i	−0.178590	−	0.412679i
$592$	−7.18609	+	6.02985i	−0.295347	+	0.247825i
$593$	−29.8213	+	10.8541i	−1.22462	+	0.445723i	−0.871750	−	0.489951i	$-0.837015\pi$
$593$	−29.8213	+	10.8541i	−1.22462	+	0.445723i	−0.352865	+	0.935674i	$0.614793\pi$
$594$	−1.31108	+	0.482454i	−0.0537941	+	0.0197953i
$595$	5.25403	+	2.67676i	0.215394	+	0.109737i
$596$	−19.6731	−	11.3582i	−0.805840	−	0.465252i
$597$	−28.7679	−	30.4202i	−1.17739	−	1.24502i
$598$	3.11579	+	0.549398i	0.127414	+	0.0224665i
$599$	1.77242	−	10.0519i	0.0724191	−	0.410709i	−0.926950	−	0.375186i	$-0.877579\pi$
$599$	1.77242	−	10.0519i	0.0724191	−	0.410709i	0.999369	−	0.0355237i	$-0.0113099\pi$
$600$	−3.04618	+	8.10684i	−0.124360	+	0.330960i
$601$	−37.4289	−	21.6096i	−1.52676	−	0.881473i	−0.999495	−	0.0317688i	$-0.989886\pi$
$601$	−37.4289	−	21.6096i	−1.52676	−	0.881473i	−0.527260	−	0.849704i	$-0.676781\pi$
$602$	−6.49332	+	7.73844i	−0.264648	+	0.315395i
$603$	−6.75521	+	0.805732i	−0.275093	+	0.0328119i
$604$	3.51735	+	9.66384i	0.143119	+	0.393216i
$605$	−19.5154	−	14.7045i	−0.793414	−	0.597825i
$606$	−3.48277	−	8.04785i	−0.141478	−	0.326922i
$607$	27.5373			1.11770			0.558852	−	0.829267i	$-0.311242\pi$
$607$	27.5373			1.11770			0.558852	+	0.829267i	$0.311242\pi$
$608$	−1.27158	−	4.16930i	−0.0515693	−	0.169088i
$609$	1.41421	+	5.93580i	0.0573067	+	0.240531i
$610$	−1.03416	−	2.43603i	−0.0418721	−	0.0986321i
$611$	−23.3753	+	19.6142i	−0.945663	+	0.793505i
$612$	−3.15976	+	3.36502i	−0.127726	+	0.136023i
$613$	−4.44877	+	12.2229i	−0.179684	+	0.493678i	−0.996535	−	0.0831701i	$-0.973496\pi$
$613$	−4.44877	+	12.2229i	−0.179684	+	0.493678i	0.816851	+	0.576849i	$0.195718\pi$
$614$	−1.55519	+	1.85340i	−0.0627622	+	0.0747971i
$615$	−9.78974	−	0.615316i	−0.394760	−	0.0248119i
$616$	0.399048	−	0.230390i	0.0160781	−	0.00928269i
$617$	1.13238	−	6.42203i	0.0455878	−	0.258541i	−0.953493	−	0.301416i	$-0.902541\pi$
$617$	1.13238	−	6.42203i	0.0455878	−	0.258541i	0.999080	+	0.0428750i	$0.0136517\pi$
$618$	16.4535	−	0.977786i	0.661857	−	0.0393323i
$619$	18.5495	+	32.1286i	0.745565	+	1.29136i	0.949930	+	0.312462i	$0.101154\pi$
$619$	18.5495	+	32.1286i	0.745565	+	1.29136i	−0.204365	+	0.978895i	$0.565513\pi$
$620$	−0.184865	+	0.604763i	−0.00742434	+	0.0242879i
$621$	−4.43268	+	0.0156885i	−0.177878	+	0.000629557i
$622$	−25.3299	−	9.21934i	−1.01564	−	0.369662i
$623$	−8.15631	−	22.4093i	−0.326776	−	0.897809i
$624$	3.82993	−	5.15717i	0.153320	−	0.206452i
$625$	22.0758	+	11.7328i	0.883032	+	0.469312i
$626$	19.8369			0.792841
$627$	−1.56315	−	1.29490i	−0.0624262	−	0.0517134i
$628$			9.64573i			0.384907i
$629$	2.50642	+	14.2146i	0.0999374	+	0.566773i
$630$	11.3153	+	2.03504i	0.450812	+	0.0810778i
$631$	19.1152	−	6.95736i	0.760963	−	0.276968i	0.0677517	−	0.997702i	$-0.478417\pi$
$631$	19.1152	−	6.95736i	0.760963	−	0.276968i	0.693211	+	0.720734i	$0.256195\pi$
$632$	4.95064	+	1.80188i	0.196926	+	0.0716751i
$633$	12.0144	−	23.9933i	0.477531	−	0.953647i
$634$	8.96889	−	15.5346i	0.356200	−	0.616957i
$635$	−2.64330	+	2.46514i	−0.104896	+	0.0978260i
$636$	−5.51842	+	0.327944i	−0.218820	+	0.0130038i
$637$	2.61648	−	14.8388i	0.103669	−	0.587934i
$638$	0.276330	+	0.478618i	0.0109400	+	0.0189487i
$639$	0.400034	−	7.15929i	0.0158251	−	0.283217i
$640$	1.99240	+	1.01506i	0.0787564	+	0.0401239i
$641$	19.3301	+	7.03558i	0.763493	+	0.277889i	0.694272	−	0.719713i	$-0.255726\pi$
$641$	19.3301	+	7.03558i	0.763493	+	0.277889i	0.0692208	+	0.997601i	$0.477949\pi$
$642$	20.5328	−	13.5394i	0.810366	−	0.534357i
$643$	−23.4283	−	27.9207i	−0.923921	−	1.10109i	−0.994620	−	0.103589i	$-0.966967\pi$
$643$	−23.4283	−	27.9207i	−0.923921	−	1.10109i	0.0706987	−	0.997498i	$-0.477477\pi$
$644$	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	$0.802084\pi$
$648$	−4.00119	+	8.06167i	−0.157182	+	0.316692i
$649$	−2.43161	−	2.89788i	−0.0954491	−	0.113752i
$650$	−13.3405	−	12.8804i	−0.523256	−	0.505211i
$651$	0.833956	+	0.0964783i	0.0326853	+	0.00378128i
$652$	−13.8938	+	16.5580i	−0.544124	+	0.648462i
$653$	−23.8430	+	41.2973i	−0.933049	+	1.61609i	−0.154973	+	0.987919i	$0.549529\pi$
$653$	−23.8430	+	41.2973i	−0.933049	+	1.61609i	−0.778076	+	0.628170i	$0.783804\pi$
$654$	19.8726	+	21.0140i	0.777081	+	0.821714i
$655$	−0.405294	−	7.72681i	−0.0158361	−	0.301911i
$656$	−0.439797	+	2.49421i	−0.0171712	+	0.0973826i
$657$	11.9572	−	18.2738i	0.466493	−	0.712927i
$658$	−7.05043	+	12.2117i	−0.274854	+	0.476062i
$659$	23.9000	+	20.0544i	0.931010	+	0.781210i	0.975998	−	0.217777i	$-0.0698807\pi$
$659$	23.9000	+	20.0544i	0.931010	+	0.781210i	−0.0449886	+	0.998988i	$0.514325\pi$
$660$	1.03478	−	0.116134i	0.0402789	−	0.00452051i
$661$	6.43367	+	17.6764i	0.250241	+	0.687531i	0.999676	+	0.0254533i	$0.00810291\pi$
$661$	6.43367	+	17.6764i	0.250241	+	0.687531i	−0.749435	+	0.662078i	$0.769675\pi$
$662$	19.2987	−	16.1935i	0.750064	−	0.629378i
$663$	−3.92557	−	9.07105i	−0.152456	−	0.352290i
$664$			14.8677i			0.576980i
$665$	5.70329	+	15.7007i	0.221164	+	0.608848i
$666$	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
$669$	8.18453	−	5.39689i	0.316432	−	0.208656i
$670$	5.03295	+	0.617739i	0.194440	+	0.0238653i
$671$	−0.204536	+	0.243757i	−0.00789604	+	0.00941013i
$672$	0.848011	−	2.84476i	0.0327127	−	0.109739i
$673$	23.2018	+	40.1867i	0.894364	+	1.54908i	0.834590	+	0.550871i	$0.185705\pi$
$673$	23.2018	+	40.1867i	0.894364	+	1.54908i	0.0597736	+	0.998212i	$0.480962\pi$
$674$	−0.204338	−	0.0360302i	−0.00787079	−	0.00138783i
$675$	21.5916	+	14.4500i	0.831062	+	0.556180i
$676$	0.377460	+	0.653780i	0.0145177	+	0.0251454i
$677$	1.73145	+	0.999652i	0.0665450	+	0.0384197i	0.532903	−	0.846176i	$-0.321101\pi$
$677$	1.73145	+	0.999652i	0.0665450	+	0.0384197i	−0.466358	+	0.884596i	$0.654434\pi$
$678$	−11.4535	−	5.73524i	−0.439868	−	0.220261i
$679$	3.52500	−	9.68485i	0.135277	−	0.371671i
$680$	2.88541	−	1.87399i	0.110651	−	0.0718644i
$681$	19.1904	+	14.2515i	0.735376	+	0.546120i
$682$	0.0748810	−	0.0132035i	0.00286734	−	0.000505590i
$683$			24.0620i			0.920707i	0.887736	+	0.460354i	$0.152277\pi$
$683$			24.0620i			0.920707i	−0.887736	+	0.460354i	$0.847723\pi$
$684$	−13.0485	+	0.858175i	−0.498922	+	0.0328132i
$685$	10.1418	+	43.9199i	0.387498	+	1.67809i
$686$	−3.29234	−	18.6718i	−0.125702	−	0.712892i
$687$	−1.48206	+	1.99566i	−0.0565441	+	0.0761392i
$688$	2.01595	+	5.53877i	0.0768573	+	0.211164i
$689$	4.04856	−	11.1233i	0.154238	−	0.423765i
$690$	3.21136	+	0.776701i	0.122254	+	0.0295685i
$691$	−9.19334	+	15.9233i	−0.349731	+	0.605752i	−0.986202	−	0.165549i	$-0.947060\pi$
$691$	−9.19334	+	15.9233i	−0.349731	+	0.605752i	0.636470	+	0.771301i	$0.280394\pi$
$692$	8.50239	−	4.90886i	0.323212	−	0.186607i
$693$	−0.399584	−	1.32333i	−0.0151789	−	0.0502692i
$694$	28.4649	+	5.01913i	1.08051	+	0.190523i
$695$	31.1883	−	29.0862i	1.18304	−	1.10330i
$696$	3.41201	+	1.01710i	0.129332	+	0.0385532i
$697$	2.98525	+	2.50492i	0.113074	+	0.0948806i
$698$	−7.40460	+	20.3440i	−0.280268	+	0.770030i
$699$	18.1177	−	11.9469i	0.685276	−	0.451872i
$700$	−7.82870	−	3.48472i	−0.295897	−	0.131710i
$701$	−11.8330	+	2.08649i	−0.446928	+	0.0788055i	−0.392583	−	0.919717i	$-0.628418\pi$
$701$	−11.8330	+	2.08649i	−0.446928	+	0.0788055i	−0.0543454	+	0.998522i	$0.517307\pi$
$702$	−12.4395	−	14.7187i	−0.469499	−	0.555523i
$703$	−22.2936	+	34.2779i	−0.840818	+	1.29282i
$704$		−	0.268858i		−	0.0101330i
$705$	−25.6471	+	18.9111i	−0.965926	+	0.712233i
$706$	−18.5178	−	22.0687i	−0.696928	−	0.830566i
$707$	8.15368	−	2.96770i	0.306651	−	0.111612i
$708$	−24.2091	−	2.80069i	−0.909832	−	0.105256i
$709$	−22.7018	−	19.0490i	−0.852583	−	0.715402i	0.107774	−	0.994175i	$-0.465628\pi$
$709$	−22.7018	−	19.0490i	−0.852583	−	0.715402i	−0.960357	+	0.278774i	$0.910072\pi$
$710$	−1.56236	+	5.11108i	−0.0586344	+	0.191815i
$711$	8.65385	−	13.2254i	0.324545	−	0.495991i
$712$	−13.7032	−	2.41624i	−0.513549	−	0.0905525i
$713$	0.237595	+	0.0418944i	0.00889799	+	0.00156896i
$714$	−3.13831	−	3.31857i	−0.117448	−	0.124194i
$715$	−0.651790	+	2.13225i	−0.0243756	+	0.0797418i
$716$	1.28692	+	1.07985i	0.0480944	+	0.0403560i
$717$	−0.484299	+	4.18627i	−0.0180865	+	0.156339i
$718$	7.71305	−	2.80732i	0.287848	−	0.104768i
$719$	11.7605	+	14.0156i	0.438592	+	0.522694i	0.939381	−	0.342876i	$-0.111401\pi$
$719$	11.7605	+	14.0156i	0.438592	+	0.522694i	−0.500789	+	0.865570i	$0.666957\pi$
$720$	4.32946	−	5.12403i	0.161350	−	0.190962i
$721$			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
$725$	4.17957	−	9.38974i	0.155225	−	0.348726i
$726$	10.4194	+	15.8013i	0.386700	+	0.586441i
$727$	−6.91987	+	19.0122i	−0.256644	+	0.705123i	0.742725	+	0.669597i	$0.233533\pi$
$727$	−6.91987	+	19.0122i	−0.256644	+	0.705123i	−0.999369	+	0.0355262i	$0.988689\pi$
$728$	4.86917	+	4.08572i	0.180463	+	0.151427i
$729$	20.8055	+	17.2084i	0.770575	+	0.637349i
$730$	−11.9039	+	11.1015i	−0.440582	+	0.410887i
$731$	8.93148	+	1.57486i	0.330343	+	0.0582483i
$732$	0.121608	+	2.04633i	0.00449475	+	0.0756345i
$733$	−21.4641	+	12.3923i	−0.792795	+	0.457721i	−0.840946	−	0.541120i	$-0.818001\pi$
$733$	−21.4641	+	12.3923i	−0.792795	+	0.457721i	0.0481505	+	0.998840i	$0.484667\pi$
$734$	3.00188	−	5.19941i	0.110802	−	0.191914i
$735$	3.69900	−	15.2939i	0.136440	−	0.564125i
$736$	0.291769	−	0.801629i	0.0107548	−	0.0295484i
$737$	−0.208525	−	0.572919i	−0.00768113	−	0.0211037i
$738$	6.98375	+	2.99297i	0.257075	+	0.110173i
$739$	−3.57648	−	20.2832i	−0.131563	−	0.746131i	−0.977192	−	0.212359i	$-0.931885\pi$
$739$	−3.57648	−	20.2832i	−0.131563	−	0.746131i	0.845629	−	0.533772i	$-0.179226\pi$
$740$	−4.71951	−	20.4382i	−0.173492	−	0.751324i
$741$	9.41037	−	26.3719i	0.345699	−	0.968795i
$742$		−	5.47005i		−	0.200812i
$743$	−19.2467	+	3.39371i	−0.706093	+	0.124503i	−0.515153	−	0.857098i	$-0.672265\pi$
$743$	−19.2467	+	3.39371i	−0.706093	+	0.124503i	−0.190941	+	0.981602i	$0.561154\pi$
$744$	0.292051	−	0.393260i	0.0107071	−	0.0144176i
$745$	42.5996	−	27.6672i	1.56073	−	1.01365i
$746$	6.22436	−	17.1013i	0.227890	−	0.626123i
$747$	43.4251	+	10.1838i	1.58884	+	0.372605i
$748$	−0.358259	−	0.206841i	−0.0130993	−	0.00756286i
$749$	12.1682	+	21.0760i	0.444617	+	0.770100i
$750$	−13.0600	−	14.2981i	−0.476883	−	0.522095i
$751$	−0.904984	−	0.159573i	−0.0330233	−	0.00582291i	0.157112	−	0.987581i	$-0.449782\pi$
$751$	−0.904984	−	0.159573i	−0.0330233	−	0.00582291i	−0.190135	+	0.981758i	$0.560893\pi$
$752$	4.11381	+	7.12532i	0.150015	+	0.259834i
$753$	36.3522	+	10.8364i	1.32475	+	0.394901i
$754$	−4.90041	+	5.84008i	−0.178462	+	0.212683i
$755$	−22.8245	−	2.80146i	−0.830670	−	0.101955i
$756$	−7.72802	−	4.42538i	−0.281065	−	0.160950i
$757$	−22.7389	−	27.0992i	−0.826459	−	0.984936i	−1.00000		0.000109327i	$-0.999965\pi$
$757$	−22.7389	−	27.0992i	−0.826459	−	0.984936i	0.173541	−	0.984827i	$-0.444479\pi$
$758$	2.18508	+	12.3922i	0.0793657	+	0.450105i
$759$	−0.0920696	−	0.386440i	−0.00334191	−	0.0140269i
$760$	9.59764	+	1.69862i	0.348143	+	0.0616155i
$761$		−	40.6741i		−	1.47444i	−0.675655	−	0.737218i	$-0.736139\pi$
$761$		−	40.6741i		−	1.47444i	0.675655	−	0.737218i	$-0.263861\pi$
$762$	2.56943	−	1.11194i	0.0930805	−	0.0402813i
$763$	−21.9230	+	18.3956i	−0.793668	+	0.665966i
$764$	−1.61670	−	4.44186i	−0.0584903	−	0.160701i
$765$	−3.49710	−	9.71121i	−0.126438	−	0.351109i
$766$	−7.79281	−	6.53894i	−0.281566	−	0.236262i
$767$	26.0918	−	45.1922i	0.942119	−	1.63180i
$768$	−1.19009	−	1.25844i	−0.0429437	−	0.0454102i
$769$	5.82040	−	33.0091i	0.209889	−	1.19034i	−0.679669	−	0.733519i	$-0.737877\pi$
$769$	5.82040	−	33.0091i	0.209889	−	1.19034i	0.889558	−	0.456822i	$-0.151012\pi$
$770$	0.0539700	+	1.02892i	0.00194495	+	0.0370798i
$771$	9.52457	−	9.00723i	0.343019	−	0.324388i
$772$	4.61620	−	7.99549i	0.166141	−	0.287764i
$773$	18.8113	−	22.4185i	0.676596	−	0.806336i	−0.313070	−	0.949730i	$-0.601357\pi$
$773$	18.8113	−	22.4185i	0.676596	−	0.806336i	0.989666	+	0.143394i	$0.0458017\pi$
$774$	17.5582	−	2.09427i	0.631118	−	0.0752770i
$775$	−1.01728	−	0.982196i	−0.0365417	−	0.0352815i
$776$	−3.86548	−	4.60669i	−0.138762	−	0.165371i
$777$	−25.5561	+	11.0596i	−0.916820	+	0.396761i
$778$	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
$783$	5.30780	−	9.26899i	0.189685	−	0.331247i
$784$	−3.81772	−	1.38954i	−0.136347	−	0.0496263i
$785$	−19.2181	−	9.79103i	−0.685924	−	0.349457i
$786$	−1.71215	+	5.74363i	−0.0610703	+	0.204868i
$787$	17.4744	+	30.2665i	0.622894	+	1.07888i	0.988944	+	0.148289i	$0.0473767\pi$
$787$	17.4744	+	30.2665i	0.622894	+	1.07888i	−0.366050	+	0.930595i	$0.619290\pi$
$788$	1.09595	−	6.21546i	0.0390417	−	0.221416i
$789$	1.29951	+	21.8673i	0.0462638	+	0.778496i
$790$	−8.61528	+	8.03460i	−0.306518	+	0.285858i
$791$	6.33728	−	10.9765i	0.225328	−	0.390279i
$792$	−0.785269	−	0.184156i	−0.0279033	−	0.00654371i
$793$	−4.12473	−	1.50128i	−0.146473	−	0.0533120i
$794$	−17.6260	+	6.41535i	−0.625524	+	0.227672i
$795$	4.94815	−	11.3278i	0.175493	−	0.401755i
$796$	−4.19757	−	23.8056i	−0.148779	−	0.843768i
$797$			37.8264i			1.33988i	0.742415	+	0.669941i	$0.233680\pi$
$797$			37.8264i			1.33988i	−0.742415	+	0.669941i	$0.766320\pi$
$798$	−0.0817253	−	12.9390i	−0.00289305	−	0.458036i
$799$	12.6595			0.447863
$800$	−4.04482	+	2.93929i	−0.143006	+	0.103920i
$801$	−16.4434	+	38.3687i	−0.580998	+	1.35569i
$802$	−1.87629	−	5.15506i	−0.0662540	−	0.182031i
$803$	1.83909	+	0.669373i	0.0649000	+	0.0236217i
$804$	−3.51206	−	1.75864i	−0.123861	−	0.0620223i
$805$	−0.955688	+	3.12642i	−0.0336836	+	0.110192i
$806$	0.524441	+	0.908358i	0.0184726	+	0.0319956i
$807$	−2.94271	−	49.5178i	−0.103588	−	1.74311i
$808$	0.879156	−	4.98594i	0.0309286	−	0.175405i
$809$	1.78358	−	1.02975i	0.0627075	−	0.0362042i	−0.468318	−	0.883560i	$-0.655140\pi$
$809$	1.78358	−	1.02975i	0.0627075	−	0.0362042i	0.531026	+	0.847356i	$0.321807\pi$
$810$	−12.0006	−	16.1551i	−0.421657	−	0.567631i
$811$	11.1896	−	13.3353i	0.392921	−	0.468265i	−0.532927	−	0.846161i	$-0.678908\pi$
$811$	11.1896	−	13.3353i	0.392921	−	0.468265i	0.925848	+	0.377896i	$0.123352\pi$
$812$	−1.20492	+	3.31050i	−0.0422845	+	0.116176i
$813$	−13.5627	+	8.94328i	−0.475665	+	0.313654i
$814$	−1.93204	+	1.62117i	−0.0677178	+	0.0568220i
$815$	−18.8870	−	44.4894i	−0.661583	−	1.55840i
$816$	−2.59248	+	0.617661i	−0.0907551	+	0.0216225i
$817$	15.4481	+	20.5294i	0.540460	+	0.718232i
$818$	26.8888			0.940143
$819$	15.2686	−	11.4231i	0.533527	−	0.399156i
$820$	−4.52304	−	3.40803i	−0.157951	−	0.119014i
$821$	7.02435	+	19.2992i	0.245152	+	0.673548i	0.999847	+	0.0174734i	$0.00556225\pi$
$821$	7.02435	+	19.2992i	0.245152	+	0.673548i	−0.754696	+	0.656075i	$0.772216\pi$
$822$	4.01252	−	34.6841i	0.139953	−	1.20975i
$823$	22.1939	−	26.4497i	0.773632	−	0.921978i	−0.224995	−	0.974360i	$-0.572237\pi$
$823$	22.1939	−	26.4497i	0.773632	−	0.921978i	0.998627	+	0.0523814i	$0.0166812\pi$
$824$	8.24127	+	4.75810i	0.287098	+	0.165756i
$825$	−0.818988	+	2.17959i	−0.0285135	+	0.0758834i
$826$	4.18742	−	23.7480i	0.145699	−	0.826300i
$827$	−27.1327	−	4.78422i	−0.943495	−	0.166364i	−0.319319	−	0.947647i	$-0.603454\pi$
$827$	−27.1327	−	4.78422i	−0.943495	−	0.166364i	−0.624176	+	0.781284i	$0.714565\pi$
$828$	−2.14152	−	1.40127i	−0.0744228	−	0.0486975i
$829$	−29.9117	−	17.2695i	−1.03888	−	0.599796i	−0.119362	−	0.992851i	$-0.538085\pi$
$829$	−29.9117	−	17.2695i	−1.03888	−	0.599796i	−0.919515	+	0.393055i	$0.871418\pi$
$830$	−29.6224	−	15.0917i	−1.02821	−	0.523841i
$831$	−0.797632	+	6.89471i	−0.0276696	+	0.239175i
$832$	3.48510	−	1.26847i	0.120824	−	0.0439763i
$833$	−4.78869	+	4.01819i	−0.165918	+	0.139222i
$834$	−30.3167	+	13.1198i	−1.04978	+	0.454301i
$835$	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	$-0.497889\pi$
$839$	28.7503	−	24.1243i	0.992569	−	0.832864i	0.985938	+	0.167114i	$0.0534447\pi$
$840$	4.80711	+	4.57719i	0.165861	+	0.157928i
$841$	23.2805	+	8.47340i	0.802775	+	0.292186i
$842$	21.8477	+	18.3324i	0.752921	+	0.631776i
$843$	−2.08725	+	7.00197i	−0.0718888	+	0.241161i
$844$	13.4166	−	7.74609i	0.461819	−	0.266632i
$845$	−1.68573	+	0.0884217i	−0.0579910	+	0.00304180i
$846$	23.6291	−	7.13489i	0.812386	−	0.245303i
$847$	−16.2193	+	9.36421i	−0.557301	+	0.321758i
$848$	−2.76408	−	1.59584i	−0.0949188	−	0.0548014i
$849$	6.05748	−	12.0970i	0.207892	−	0.415168i
$850$	0.804862	+	7.65111i	0.0276065	+	0.262431i
$851$	−7.51990	+	2.73702i	−0.257779	+	0.0938239i
$852$	2.46824	−	3.32359i	0.0845604	−	0.113864i
$853$	52.5699	−	9.26950i	1.79996	−	0.317381i	0.829475	−	0.558544i	$-0.188640\pi$
$853$	52.5699	−	9.26950i	1.79996	−	0.317381i	0.970485	+	0.241162i	$0.0775287\pi$
$854$	−2.02839			−0.0694102
$855$	11.5352	−	26.8689i	0.394497	−	0.918897i
$856$	14.1999			0.485343
$857$	16.7281	−	2.94961i	0.571420	−	0.100757i	0.119530	−	0.992831i	$-0.461861\pi$
$857$	16.7281	−	2.94961i	0.571420	−	0.100757i	0.451890	+	0.892074i	$0.350750\pi$
$858$	1.02970	−	1.38655i	0.0351535	−	0.0473359i
$859$	−2.01853	+	0.734683i	−0.0688712	+	0.0250671i	−0.376226	−	0.926528i	$-0.622778\pi$
$859$	−2.01853	+	0.734683i	−0.0688712	+	0.0250671i	0.307355	+	0.951595i	$0.400556\pi$
$860$	−13.0817	−	1.60564i	−0.446084	−	0.0547518i
$861$	−3.36624	+	6.72249i	−0.114721	+	0.229102i
$862$	27.4932	+	15.8732i	0.936421	+	0.540643i
$863$	11.9136	−	6.87833i	0.405544	−	0.234141i	−0.283329	−	0.959023i	$-0.591439\pi$
$863$	11.9136	−	6.87833i	0.405544	−	0.234141i	0.688873	+	0.724882i	$0.258106\pi$
$864$	−4.49078	+	2.61399i	−0.152779	+	0.0889296i
$865$	1.14992	+	21.9229i	0.0390986	+	0.745403i
$866$	−21.6613	+	12.5062i	−0.736082	+	0.424977i
$867$	7.24016	−	24.2881i	0.245889	−	0.824866i
$868$	0.371299	+	0.311557i	0.0126027	+	0.0105749i
$869$	1.33102	+	0.484450i	0.0451516	+	0.0164339i
$870$	−5.48988	+	5.76565i	−0.186124	+	0.195474i
$871$	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
$876$	11.5712	−	5.00753i	0.390955	−	0.169189i
$877$	−12.3939	+	10.3998i	−0.418514	+	0.351175i	−0.827597	−	0.561322i	$-0.810293\pi$
$877$	−12.3939	+	10.3998i	−0.418514	+	0.351175i	0.409084	+	0.912497i	$0.365848\pi$
$878$	−32.6574	+	11.8863i	−1.10213	+	0.401143i
$879$	−4.44990	+	38.4649i	−0.150092	+	1.29739i
$880$	0.535671	+	0.272908i	0.0180575	+	0.00919972i
$881$	−11.9255	−	6.88519i	−0.401780	−	0.231968i	0.285472	−	0.958387i	$-0.407850\pi$
$881$	−11.9255	−	6.88519i	−0.401780	−	0.231968i	−0.687252	+	0.726419i	$0.741183\pi$
$882$	−6.67348	+	10.1989i	−0.224708	+	0.343413i
$883$	−39.1996	−	6.91195i	−1.31917	−	0.232605i	−0.530639	−	0.847598i	$-0.678048\pi$
$883$	−39.1996	−	6.91195i	−1.31917	−	0.232605i	−0.788533	+	0.614993i	$0.789159\pi$
$884$	0.990932	−	5.61985i	0.0333286	−	0.189016i
$885$	30.1538	−	45.3912i	1.01361	−	1.52581i
$886$	5.30605	+	3.06345i	0.178260	+	0.102919i
$887$	31.9511	−	38.0778i	1.07281	−	1.27853i	0.114311	−	0.993445i	$-0.463534\pi$
$887$	31.9511	−	38.0778i	1.07281	−	1.27853i	0.958503	−	0.285084i	$-0.0920215\pi$
$888$	−1.86724	+	16.1403i	−0.0626603	+	0.541634i
$889$	0.947492	+	2.60321i	0.0317779	+	0.0873089i
$890$	18.7237	−	24.8495i	0.627621	−	0.832959i
$891$	−1.07575	+	2.16744i	−0.0360390	+	0.0726120i
$892$	5.66018			0.189517
$893$	26.2121	+	24.4766i	0.877155	+	0.819078i
$894$	−38.2748	+	9.11900i	−1.28010	+	0.304985i
$895$	−3.45780	+	1.46793i	−0.115581	+	0.0490675i
$896$	1.31288	−	1.10164i	0.0438603	−	0.0368032i
$897$	4.57488	−	3.01669i	0.152751	−	0.100724i
$898$	−7.30239	+	20.0632i	−0.243684	+	0.669516i
$899$	−0.373681	+	0.445336i	−0.0124630	+	0.0148528i
$900$	5.81443	+	13.8272i	0.193814	+	0.460908i
$901$	−4.25299	+	2.45547i	−0.141688	+	0.0818035i
$902$	−0.118243	+	0.670588i	−0.00393705	+	0.0223281i
$903$	1.03796	+	17.4660i	0.0345411	+	0.581233i
$904$	−3.69769	−	6.40459i	−0.122983	−	0.213014i
$905$	−9.98482	+	32.6642i	−0.331907	+	1.08579i
$906$	15.9272	+	7.97545i	0.529147	+	0.264966i
$907$	12.5986	+	4.58552i	0.418330	+	0.152260i	0.542605	−	0.839988i	$-0.317438\pi$
$907$	12.5986	+	4.58552i	0.418330	+	0.152260i	−0.124275	+	0.992248i	$0.539660\pi$
$908$	4.72011	+	12.9684i	0.156642	+	0.430371i
$909$	−13.9605	−	5.98296i	−0.463042	−	0.198442i
$910$	−13.0829	+	5.55405i	−0.433694	+	0.184115i
$911$	55.0860			1.82508			0.912541	−	0.408986i	$-0.134117\pi$
$911$	55.0860			1.82508			0.912541	+	0.408986i	$0.134117\pi$
$912$	−6.56206	−	3.73355i	−0.217292	−	0.123630i
$913$			3.99730i			0.132291i
$914$	−4.39801	−	24.9424i	−0.145473	−	0.825020i
$915$	−4.20054	−	1.83487i	−0.138866	−	0.0606588i
$916$	−1.34862	+	0.490858i	−0.0445597	+	0.0162184i
$917$	−5.57275	−	2.02832i	−0.184028	−	0.0669809i
$918$	0.0282968	+	7.99509i	0.000933934	+	0.263877i
$919$	1.23232	−	2.13444i	0.0406504	−	0.0704085i	−0.844984	−	0.534791i	$-0.820390\pi$
$919$	1.23232	−	2.13444i	0.0406504	−	0.0704085i	0.885635	+	0.464382i	$0.153724\pi$
$920$	1.30100	+	1.39502i	0.0428927	+	0.0459926i
$921$	0.248597	+	4.18322i	0.00819154	+	0.137842i
$922$	5.09009	−	28.8674i	0.167633	−	0.950696i
$923$	4.43225	+	7.67688i	0.145889	+	0.252688i
$924$	0.227994	−	0.764837i	0.00750046	−	0.0251613i
$925$	45.5117	+	11.3430i	1.49641	+	0.372955i
$926$	10.9603	+	3.98922i	0.360177	+	0.131094i
$927$	19.5422	−	20.8117i	0.641849	−	0.683545i
$928$	1.32131	+	1.57467i	0.0433740	+	0.0516911i
$929$	−10.8048	+	1.90517i	−0.354493	+	0.0625067i	−0.348059	−	0.937473i	$-0.613159\pi$
$929$	−10.8048	+	1.90517i	−0.354493	+	0.0625067i	−0.00643416	+	0.999979i	$0.502048\pi$
$930$	0.487080	+	0.981066i	0.0159720	+	0.0321704i
$931$	−17.6841	−	0.938869i	−0.579574	−	0.0307702i
$932$	12.5297			0.410424
$933$	−42.8482	+	18.5429i	−1.40279	+	0.607067i
$934$	21.1941	+	25.2582i	0.693493	+	0.826473i
$935$	0.775766	−	0.503838i	0.0253703	−	0.0164773i
$936$	−1.31775	−	11.0480i	−0.0430722	−	0.361114i
$937$	8.57663	−	10.2212i	0.280186	−	0.333913i	−0.607536	−	0.794292i	$-0.707842\pi$
$937$	8.57663	−	10.2212i	0.280186	−	0.333913i	0.887722	+	0.460379i	$0.152286\pi$
$938$	1.94324	−	3.36579i	0.0634491	−	0.109897i
$939$	24.9636	−	23.6077i	0.814657	−	0.770408i
$940$	−18.3722	+	0.963678i	−0.599236	+	0.0314317i
$941$	−8.26369	+	46.8657i	−0.269388	+	1.52778i	0.486852	+	0.873484i	$0.338145\pi$
$941$	−8.26369	+	46.8657i	−0.269388	+	1.52778i	−0.756241	+	0.654294i	$0.772966\pi$
$942$	11.4793	+	12.1386i	0.374016	+	0.395498i
$943$	−1.08029	+	1.87111i	−0.0351790	+	0.0609318i
$944$	−10.7785	−	9.04423i	−0.350810	−	0.294365i
$945$	16.6615	−	10.9052i	0.542000	−	0.354747i
$946$	0.542003	+	1.48914i	0.0176220	+	0.0484161i
$947$	−25.8684	+	21.7061i	−0.840609	+	0.705354i	−0.957701	−	0.287767i	$-0.907087\pi$
$947$	−25.8684	+	21.7061i	−0.840609	+	0.705354i	0.117092	+	0.993121i	$0.462643\pi$
$948$	8.37451	−	3.62413i	0.271991	−	0.117706i
$949$			26.9975i			0.876375i
$950$	−13.1265	+	17.3981i	−0.425881	+	0.564469i
$951$	−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	0.987971	−	0.154640i	$-0.0494219\pi$
$953$	20.5019	+	24.4332i	0.664120	+	0.791468i	−0.323850	+	0.946108i	$0.604977\pi$
$954$	−6.55435	+	6.98012i	−0.212205	+	0.225990i
$955$	10.4910	+	1.28765i	0.339481	+	0.0416675i
$956$	−1.56394	+	1.86383i	−0.0505815	+	0.0602807i
$957$	0.917345	+	0.273456i	0.0296536	+	0.00883959i
$958$	17.9367	+	31.0672i	0.579508	+	1.00374i
$959$	34.0236	+	5.99928i	1.09868	+	0.193727i
$960$	3.71534	−	1.09373i	0.119912	−	0.0353000i
$961$	−15.4600	−	26.7775i	−0.498710	−	0.863791i
$962$	−30.1299	−	17.3955i	−0.971429	−	0.560855i
$963$	9.72634	−	41.4745i	0.313427	−	1.33650i
$964$	4.63523	−	12.7352i	0.149291	−	0.410173i
$965$	11.2444	+	17.3132i	0.361972	+	0.557332i
$966$	1.50980	−	2.03302i	0.0485772	−	0.0654114i
$967$	16.5601	−	2.91999i	0.532537	−	0.0939006i	0.0990878	−	0.995079i	$-0.468408\pi$
$967$	16.5601	−	2.91999i	0.532537	−	0.0939006i	0.433449	+	0.901178i	$0.357296\pi$
$968$			10.9277i			0.351230i
$969$	−10.0234	+	5.87176i	−0.322000	+	0.188628i
$970$	13.1021	−	3.02547i	0.420682	−	0.0971421i
$971$	−10.0132	−	56.7878i	−0.321340	−	1.82241i	−0.534239	−	0.845333i	$-0.679402\pi$
$971$	−10.0132	−	56.7878i	−0.321340	−	1.82241i	0.212900	−	0.977074i	$-0.431709\pi$
$972$	4.55883	+	14.9069i	0.146225	+	0.478141i
$973$	−11.1795	−	30.7153i	−0.358397	−	0.984687i
$974$	−3.49767	+	9.60977i	−0.112073	+	0.307917i
$975$	−32.1171	−	0.332927i	−1.02857	−	0.0106622i
$976$	−0.591767	+	1.02497i	−0.0189420	+	0.0328085i
$977$	18.5256	−	10.6957i	0.592685	−	0.342187i	−0.173474	−	0.984839i	$-0.555499\pi$
$977$	18.5256	−	10.6957i	0.592685	−	0.342187i	0.766158	+	0.642652i	$0.222166\pi$
$978$	2.22093	+	37.3723i	0.0710175	+	1.19503i
$979$	−3.68421	−	0.649625i	−0.117748	−	0.0207621i
$980$	6.64373	−	6.19594i	0.212226	−	0.197922i
$981$	50.0172	+	2.79477i	1.59693	+	0.0892302i
$982$	6.77324	+	5.68342i	0.216143	+	0.181365i
$983$	6.48673	−	17.8222i	0.206895	−	0.568439i	−0.792232	−	0.610220i	$-0.791081\pi$
$983$	6.48673	−	17.8222i	0.206895	−	0.568439i	0.999127	+	0.0417814i	$0.0133033\pi$
$984$	2.41488	+	3.66222i	0.0769835	+	0.116747i
$985$	11.2712	+	8.49266i	0.359130	+	0.270599i
$986$	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
$990$	1.16401	−	1.37764i	0.0369947	−	0.0437842i
$991$	−22.7938	−	27.1646i	−0.724070	−	0.862913i	0.270950	−	0.962593i	$-0.412662\pi$
$991$	−22.7938	−	27.1646i	−0.724070	−	0.862913i	−0.995019	+	0.0996809i	$0.968218\pi$
$992$	0.265756	−	0.0967274i	0.00843777	−	0.00307110i
$993$	5.01457	−	43.3458i	0.159132	−	1.37554i
$994$	3.13799	+	2.63308i	0.0995309	+	0.0835164i
$995$	51.6910	+	15.8010i	1.63872	+	0.500925i
$996$	17.6940	+	18.7102i	0.560654	+	0.592856i
$997$	−17.0051	−	2.99846i	−0.538557	−	0.0949622i	−0.102248	−	0.994759i	$-0.532604\pi$
$997$	−17.0051	−	2.99846i	−0.538557	−	0.0949622i	−0.436309	+	0.899797i	$0.643715\pi$
$998$	−17.2559	−	3.04268i	−0.546226	−	0.0963144i
$999$	45.8630	+	16.5092i	1.45104	+	0.522328i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.29.7	✓	240	5.4	even	2	inner
570.2.bf.a.29.18	yes	240	3.2	odd	2	inner
570.2.bf.a.29.23	yes	240	15.14	odd	2	inner
570.2.bf.a.29.34	yes	240	1.1	even	1	trivial
570.2.bf.a.59.7	yes	240	57.2	even	18	inner
570.2.bf.a.59.18	yes	240	95.59	odd	18	inner
570.2.bf.a.59.23	yes	240	19.2	odd	18	inner
570.2.bf.a.59.34	yes	240	285.59	even	18	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)

\(f(q)\)	\(=\)	\(q+(0.984808 - 0.173648i) q^{2} +(1.03267 - 1.39054i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-0.272408 + 2.21941i) q^{5} +(0.775516 - 1.54873i) q^{6} +(1.48423 + 0.856923i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.867188 - 2.87193i) q^{9} +O(q^{10})\)	\(q+(0.984808 - 0.173648i) q^{2} +(1.03267 - 1.39054i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-0.272408 + 2.21941i) q^{5} +(0.775516 - 1.54873i) q^{6} +(1.48423 + 0.856923i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-0.867188 - 2.87193i) q^{9} +(0.117127 + 2.23300i) q^{10} +(0.232838 - 0.134429i) q^{11} +(0.494800 - 1.65987i) q^{12} +(2.84108 + 2.38395i) q^{13} +(1.61049 + 0.586170i) q^{14} +(2.80487 + 2.67071i) 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} +(2.72431 - 1.17897i) q^{21} +(0.205957 - 0.172818i) q^{22} +(0.801629 - 0.291769i) q^{23} +(0.199049 - 1.72058i) q^{24} +(-4.85159 - 1.20917i) q^{25} +(3.21188 + 1.85438i) q^{26} +(-4.88905 - 1.75990i) q^{27} +(1.68781 + 0.297606i) q^{28} +(-0.356949 + 2.02436i) q^{29} +(3.22602 + 2.14308i) q^{30} +(0.244922 + 0.141406i) q^{31} +(0.642788 - 0.766044i) q^{32} +(0.0535159 - 0.462590i) q^{33} +(-0.526255 - 1.44587i) q^{34} +(-2.30618 + 3.06070i) q^{35} +(-1.79715 - 2.40214i) q^{36} -9.38078 q^{37} +(1.70589 - 4.01123i) q^{38} +(6.24886 - 1.48880i) q^{39} +(0.873794 + 2.05827i) q^{40} +(-1.94015 + 1.62798i) q^{41} +(2.47819 - 1.63413i) q^{42} +(-2.01595 + 5.53877i) q^{43} +(0.172818 - 0.205957i) q^{44} +(6.61023 - 1.14231i) q^{45} +(0.738785 - 0.426538i) q^{46} +(-1.42871 + 8.10262i) q^{47} +(-0.102750 - 1.72900i) q^{48} +(-2.03137 - 3.51843i) q^{49} +(-4.98785 - 0.348333i) q^{50} +(-2.38298 - 1.19326i) q^{51} +(3.48510 + 1.26847i) q^{52} +(-1.09162 - 2.99920i) q^{53} +(-5.12037 - 0.884186i) q^{54} +(0.234926 + 0.553382i) q^{55} +1.71385 q^{56} +(-2.62695 - 7.07807i) q^{57} +2.05559i q^{58} +(-2.44329 - 13.8566i) q^{59} +(3.54915 + 1.55033i) q^{60} +(-1.11216 + 0.404792i) q^{61} +(0.265756 + 0.0967274i) q^{62} +(1.17391 - 5.00573i) q^{63} +(0.500000 - 0.866025i) q^{64} +(-6.06489 + 5.65612i) q^{65} +(-0.0276250 - 0.464855i) q^{66} +(0.393781 - 2.23324i) q^{67} +(-0.769333 - 1.33252i) q^{68} +(0.422102 - 1.41600i) q^{69} +(-1.73966 + 3.41466i) q^{70} +(2.24601 + 0.817480i) q^{71} +(-2.18697 - 2.05357i) 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} +(5.89540 - 2.55128i) q^{78} +(3.38643 + 4.03579i) q^{79} +(1.21793 + 1.87527i) q^{80} +(-7.49597 + 4.98101i) q^{81} +(-1.62798 + 1.94015i) q^{82} +(-7.43387 + 12.8758i) q^{83} +(2.15678 - 2.03963i) q^{84} +(3.43584 - 0.180220i) q^{85} +(-1.02352 + 5.80469i) q^{86} +(2.44634 + 2.58684i) q^{87} +(0.134429 - 0.232838i) q^{88} +(-10.6592 - 8.94412i) q^{89} +(6.31144 - 2.27281i) q^{90} +(2.17397 + 5.97292i) q^{91} +(0.653494 - 0.548347i) q^{92} +(0.449554 - 0.194548i) q^{93} +8.22761i q^{94} +(7.46249 + 6.26987i) q^{95} +(-0.401426 - 1.68489i) q^{96} +(-1.04425 - 5.92225i) q^{97} +(-2.61147 - 3.11223i) q^{98} +(-0.587984 - 0.552118i) 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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