LMFDB - Embedded newform 570.2.bf.a.29.18

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			29.18
Character	$\chi$	$=$	570.29
Dual form			570.2.bf.a.59.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(1.54873 - 0.775516i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.272408 - 2.21941i) q^{5} +(-1.39054 + 1.03267i) q^{6} +(1.48423 + 0.856923i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(1.79715 - 2.40214i) q^{9} +O(q^{10})$	\(q+(-0.984808 + 0.173648i) q^{2} +(1.54873 - 0.775516i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.272408 - 2.21941i) 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} +(0.117127 + 2.23300i) 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} +(-1.29930 - 3.64854i) 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} +(-4.85159 - 1.20917i) 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} +(1.91313 + 3.36748i) 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} +(2.30618 - 3.06070i) q^{35} +(0.867188 - 2.87193i) q^{36} -9.38078 q^{37} +(-1.70589 + 4.01123i) q^{38} +(6.24886 + 1.48880i) q^{39} +(0.873794 + 2.05827i) 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} +(-4.84177 - 4.64298i) 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} +(4.98785 + 0.348333i) 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} +(0.234926 + 0.553382i) q^{55} -1.71385 q^{56} +(0.846806 - 7.50219i) q^{57} +2.05559i q^{58} +(2.44329 + 13.8566i) q^{59} +(-2.46882 - 2.98411i) 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} +(6.06489 - 5.65612i) 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} +(-1.73966 + 3.41466i) 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} +(-8.45155 + 1.88980i) q^{75} +(0.983433 - 4.24651i) q^{76} -0.460781 q^{77} +(-6.41245 - 0.381074i) q^{78} +(3.38643 + 4.03579i) q^{79} +(-1.21793 - 1.87527i) 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} +(3.43584 - 0.180220i) 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} +(5.57446 + 3.73167i) q^{90} +(2.17397 + 5.97292i) q^{91} +(-0.653494 + 0.548347i) q^{92} +(0.488982 + 0.0290588i) 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} +(-0.0955274 + 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

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

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
$3$	1.54873	−	0.775516i	0.894161	−	0.447745i
$3$	1.54873	−	0.775516i	0.894161	−	0.447745i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	0.272408	−	2.21941i	0.121825	−	0.992552i
$5$	0.272408	−	2.21941i	0.121825	−	0.992552i
$6$	−1.39054	+	1.03267i	−0.567685	+	0.421585i
$7$	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
$9$	1.79715	−	2.40214i	0.599050	−	0.800712i
$10$	0.117127	+	2.23300i	0.0370389	+	0.706136i
$11$	−0.232838	+	0.134429i	−0.0702032	+	0.0405318i	−0.534691	−	0.845048i	$-0.679572\pi$
$11$	−0.232838	+	0.134429i	−0.0702032	+	0.0405318i	0.464488	+	0.885580i	$0.346239\pi$
$12$	1.19009	−	1.25844i	0.343550	−	0.363282i
$13$	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
$15$	−1.29930	−	3.64854i	−0.335479	−	0.942048i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.267187	+	1.51529i	0.0648023	+	0.367512i	0.999913	+	0.0131574i	$0.00418826\pi$
$17$	0.267187	+	1.51529i	0.0648023	+	0.367512i	−0.935111	+	0.354354i	$0.884701\pi$
$18$	−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	$-0.639459\pi$
$23$	−0.801629	+	0.291769i	−0.167151	+	0.0608381i	0.257089	+	0.966388i	$0.417237\pi$
$24$	−0.953484	+	1.44598i	−0.194629	+	0.295160i
$25$	−4.85159	−	1.20917i	−0.970318	−	0.241834i
$26$	−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	−0.933563	−	0.358413i	$-0.883318\pi$
$29$	0.356949	−	2.02436i	0.0662838	−	0.375914i	0.999847	−	0.0175008i	$-0.00557095\pi$
$30$	1.91313	+	3.36748i	0.349287	+	0.614816i
$31$	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
$33$	−0.256352	+	0.388764i	−0.0446251	+	0.0676751i
$34$	−0.526255	−	1.44587i	−0.0902520	−	0.247965i
$35$	2.30618	−	3.06070i	0.389816	−	0.517352i
$36$	0.867188	−	2.87193i	0.144531	−	0.478655i
$37$	−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	−0.478591	−	0.878038i	$-0.658852\pi$
$41$	1.94015	−	1.62798i	0.303001	−	0.254248i	0.781592	+	0.623790i	$0.214408\pi$
$42$	−2.94880	+	0.341140i	−0.455010	+	0.0526390i
$43$	−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
$45$	−4.84177	−	4.64298i	−0.721769	−	0.692134i
$46$	0.738785	−	0.426538i	0.108928	−	0.0628896i
$47$	1.42871	−	8.10262i	0.208399	−	1.18189i	−0.683602	−	0.729855i	$-0.739588\pi$
$47$	1.42871	−	8.10262i	0.208399	−	1.18189i	0.892001	−	0.452033i	$-0.149301\pi$
$48$	0.687906	−	1.58959i	0.0992907	−	0.229437i
$49$	−2.03137	−	3.51843i	−0.290195	−	0.502633i
$50$	4.98785	+	0.348333i	0.705389	+	0.0492617i
$51$	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	$-0.0407645\pi$
$53$	1.09162	+	2.99920i	0.149946	+	0.411972i	−0.841865	+	0.539688i	$0.818542\pi$
$54$	−0.0183905	+	5.19612i	−0.00250263	+	0.707102i
$55$	0.234926	+	0.553382i	0.0316775	+	0.0746181i
$56$	−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	0.554352	+	0.832283i	$0.312966\pi$
$59$	2.44329	+	13.8566i	0.318089	+	1.80397i	−0.236263	+	0.971689i	$0.575923\pi$
$60$	−2.46882	−	2.98411i	−0.318723	−	0.385247i
$61$	−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
$63$	4.72584	−	2.02531i	0.595399	−	0.255166i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	6.06489	−	5.65612i	0.752258	−	0.701555i
$66$	0.184949	−	0.427373i	0.0227656	−	0.0526059i
$67$	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
$69$	−1.01524	+	1.07355i	−0.122220	+	0.129240i
$70$	−1.73966	+	3.41466i	−0.207930	+	0.408130i
$71$	−2.24601	−	0.817480i	−0.266552	−	0.0970170i	0.205287	−	0.978702i	$-0.434187\pi$
$71$	−2.24601	−	0.817480i	−0.266552	−	0.0970170i	−0.471839	+	0.881685i	$0.656410\pi$
$72$	−0.355308	+	2.97889i	−0.0418735	+	0.351065i
$73$	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
$75$	−8.45155	+	1.88980i	−0.975901	+	0.218215i
$76$	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	0.922131	−	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
$81$	−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	−0.0926542	−	0.995698i	$-0.529535\pi$
$83$	7.43387	−	12.8758i	0.815973	−	1.41331i	0.908627	−	0.417608i	$-0.137132\pi$
$84$	2.84476	−	0.848011i	0.310389	−	0.0925256i
$85$	3.43584	−	0.180220i	0.372669	−	0.0195476i
$86$	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	0.999061	−	0.0433325i	$-0.0137975\pi$
$89$	10.6592	+	8.94412i	1.12987	+	0.948075i	0.130811	+	0.991407i	$0.458242\pi$
$90$	5.57446	+	3.73167i	0.587600	+	0.393353i
$91$	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
$95$	−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
$99$	−0.0955274	+	0.800896i	−0.00960087	+	0.0804931i
$100$	−4.97256	+	0.523090i	−0.497256	+	0.0523090i
$101$	−3.25434	+	3.87837i	−0.323819	+	0.385913i	−0.903254	−	0.429106i	$-0.858829\pi$
$101$	−3.25434	+	3.87837i	−0.323819	+	0.385913i	0.579435	+	0.815018i	$0.303273\pi$
$102$	−1.93633	−	1.83115i	−0.191725	−	0.181311i
$103$	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
$105$	1.19804	−	6.52869i	0.116917	−	0.637134i
$106$	−1.59584	−	2.76408i	−0.155002	−	0.268471i
$107$	−12.2975	−	7.09995i	−1.18884	−	0.686378i	−0.230799	−	0.973002i	$-0.574134\pi$
$107$	−12.2975	−	7.09995i	−1.18884	−	0.686378i	−0.958043	+	0.286623i	$0.907467\pi$
$108$	−0.884186	−	5.12037i	−0.0850808	−	0.492708i
$109$	−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
$111$	−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
$120$	2.94950	+	2.51007i	0.269251	+	0.229137i
$121$	−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
$125$	−4.00526	+	10.4383i	−0.358242	+	0.933629i
$126$	−4.30235	+	2.81518i	−0.383284	+	0.250796i
$127$	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
$129$	1.17324	+	10.1415i	0.103298	+	0.892907i
$130$	−4.99058	+	6.62335i	−0.437703	+	0.580906i
$131$	3.40772	−	0.600872i	0.297733	−	0.0524984i	−0.0227860	−	0.999740i	$-0.507254\pi$
$131$	3.40772	−	0.600872i	0.297733	−	0.0524984i	0.320519	+	0.947242i	$0.396143\pi$
$132$	−0.107927	+	0.452996i	−0.00939380	+	0.0394282i
$133$	6.65856	−	3.38699i	0.577370	−	0.293689i
$134$			2.26770i			0.195899i
$135$	−11.0993	−	3.43586i	−0.955277	−	0.295711i
$136$	−0.989036	−	1.17869i	−0.0848091	−	0.101072i
$137$	−18.9427	+	6.89459i	−1.61839	+	0.589045i	−0.983074	−	0.183209i	$-0.941351\pi$
$137$	−18.9427	+	6.89459i	−1.61839	+	0.589045i	−0.635314	+	0.772254i	$0.719129\pi$
$138$	0.813394	−	1.23353i	0.0692407	−	0.105005i
$139$	−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
$141$	−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
$145$	−4.39565	−	1.34367i	−0.365039	−	0.111586i
$146$	−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	0.878705	+	0.477366i	$0.158408\pi$
$149$	14.6019	+	17.4018i	1.19623	+	1.42561i	0.317528	+	0.948249i	$0.397147\pi$
$150$	7.99499	−	3.32869i	0.652788	−	0.271786i
$151$			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
$156$	6.38121	−	0.738226i	0.510905	−	0.0591054i
$157$	−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
$159$	4.01656	+	3.79839i	0.318534	+	0.301232i
$160$	1.52507	+	1.63529i	0.120567	+	0.129281i
$161$	−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	$-0.987965\pi$
$163$	−18.7191	+	10.8075i	−1.46619	+	0.846507i	−0.466907	+	0.884306i	$0.654632\pi$
$164$	1.26634	−	2.19337i	0.0988849	−	0.171274i
$165$	0.792995	+	0.674852i	0.0617346	+	0.0525372i
$166$	−5.08506	+	13.9711i	−0.394678	+	1.08437i
$167$	5.05375	+	13.8851i	0.391071	+	1.07446i	0.966513	+	0.256616i	$0.0826076\pi$
$167$	5.05375	+	13.8851i	0.391071	+	1.07446i	−0.575443	+	0.817842i	$0.695170\pi$
$168$	−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	$-0.677300\pi$
$173$	−9.66856	+	1.70483i	−0.735087	+	0.129616i	−0.206442	+	0.978459i	$0.566189\pi$
$174$	1.59414	+	3.18356i	0.120852	+	0.241345i
$175$	−6.16473	−	5.95213i	−0.466009	−	0.449939i
$176$	−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	0.832926	−	0.553385i	$-0.186664\pi$
$179$	−0.839976	−	1.45488i	−0.0627827	−	0.108743i	−0.895708	+	0.444642i	$0.853331\pi$
$180$	−6.13777	−	2.70699i	−0.457482	−	0.201767i
$181$	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
$183$	−1.40851	+	1.48941i	−0.104120	+	0.110101i
$184$	0.548347	−	0.653494i	0.0404247	−	0.0481762i
$185$	−2.55540	+	20.8198i	−0.187877	+	1.53070i
$186$	−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
$190$	8.43787	+	4.87877i	0.612147	+	0.353943i
$191$			4.72693i			0.342028i	0.985269	+	0.171014i	$0.0547044\pi$
$191$			4.72693i			0.342028i	−0.985269	+	0.171014i	$0.945296\pi$
$192$	0.102750	−	1.72900i	0.00741532	−	0.124780i
$193$	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
$195$	5.00649	−	13.4632i	0.358522	−	0.964123i
$196$	−3.11223	−	2.61147i	−0.222302	−	0.186534i
$197$	−3.15567	+	5.46578i	−0.224832	+	0.389421i	−0.956269	−	0.292488i	$-0.905517\pi$
$197$	−3.15567	+	5.46578i	−0.224832	+	0.389421i	0.731437	+	0.681909i	$0.238850\pi$
$198$	−0.0449980	−	0.805317i	−0.00319787	−	0.0572314i
$199$	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
$201$	−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
$205$	−3.08465	−	4.74947i	−0.215441	−	0.331718i
$206$	−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
$210$	−0.0461480	+	6.63754i	−0.00318451	+	0.458034i
$211$	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
$213$	−4.11243	+	0.475757i	−0.281779	+	0.0325984i
$214$	13.3435	+	4.85665i	0.912146	+	0.331994i
$215$	11.7437	+	5.98303i	0.800911	+	0.408039i
$216$	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
$220$	0.410026	+	0.439660i	0.0276440	+	0.0296419i
$221$	−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	$-0.328197\pi$
$223$	5.31883	+	1.93590i	0.356175	+	0.129637i	−0.157734	+	0.987482i	$0.550419\pi$
$224$	−1.61049	+	0.586170i	−0.107605	+	0.0391651i
$225$	−11.6236	+	9.48111i	−0.774908	+	0.632074i
$226$	−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	$0.515100\pi$
$230$	−0.745413	−	1.75586i	−0.0491511	−	0.115778i
$231$	−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	$-0.523508\pi$
$233$	−11.7741	−	4.28541i	−0.771345	−	0.280747i	−0.697559	+	0.716528i	$0.745730\pi$
$234$	−10.2267	+	4.38278i	−0.668541	+	0.286511i
$235$	−17.5939	−	5.37812i	−1.14770	−	0.350830i
$236$	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	−0.430301	−	0.902685i	$-0.641593\pi$
$239$	2.10709	−	1.21653i	0.136297	−	0.0786909i	0.566598	+	0.823994i	$0.308259\pi$
$240$	−3.34056	−	1.95976i	−0.215632	−	0.126502i
$241$	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
$243$	−10.6304	−	11.4015i	−0.681939	−	0.731409i
$244$	−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
$249$	1.52765	−	25.7063i	0.0968112	−	1.62907i
$250$	2.13183	−	10.9752i	0.134829	−	0.694133i
$251$	−7.49044	−	20.5798i	−0.472792	−	1.29899i	−0.915499	−	0.402320i	$-0.868204\pi$
$251$	−7.49044	−	20.5798i	−0.472792	−	1.29899i	0.442707	−	0.896666i	$-0.354018\pi$
$252$	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
$255$	5.18143	−	2.94366i	0.324474	−	0.184339i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−7.45354	−	1.31426i	−0.464939	−	0.0819813i	−0.0637288	−	0.997967i	$-0.520299\pi$
$257$	−7.45354	−	1.31426i	−0.464939	−	0.0819813i	−0.401210	+	0.915986i	$0.631410\pi$
$258$	−2.91647	−	9.78367i	−0.181571	−	0.609105i
$259$	−13.9233	−	8.03860i	−0.865150	−	0.499495i
$260$	3.76463	−	7.38933i	0.233472	−	0.458267i
$261$	−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	$-0.594720\pi$
$263$	9.68843	−	8.12956i	0.597414	−	0.501290i	0.890613	+	0.454761i	$0.150275\pi$
$264$	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	−0.355434	+	0.934701i	$0.615667\pi$
$269$	−21.9392	+	18.4092i	−1.33766	+	1.12243i	−0.982222	+	0.187725i	$0.939889\pi$
$270$	11.5273	+	1.45628i	0.701531	+	0.0886265i
$271$	−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
$273$	7.99899	+	7.56451i	0.484121	+	0.457825i
$274$	17.4577	−	10.0792i	1.05466	−	0.608908i
$275$	1.29218	−	0.370653i	0.0779214	−	0.0223512i
$276$	−0.586836	+	1.35604i	−0.0353234	+	0.0816239i
$277$	−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
$279$	0.779838	−	0.334209i	0.0466877	−	0.0200086i
$280$	−0.466866	+	3.80373i	−0.0279006	+	0.227317i
$281$	3.96398	−	1.44277i	0.236471	−	0.0860685i	−0.221066	−	0.975259i	$-0.570954\pi$
$281$	3.96398	−	1.44277i	0.236471	−	0.0860685i	0.457538	+	0.889190i	$0.348732\pi$
$282$	6.38065	+	12.7424i	0.379962	+	0.758797i
$283$	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
$285$	−16.4198	−	3.92307i	−0.972624	−	0.232383i
$286$	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
$290$	4.56220	+	0.559959i	0.267901	+	0.0328819i
$291$	−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	$-0.440168\pi$
$293$	19.3607	−	11.1779i	1.13106	−	0.653020i	0.944202	+	0.329366i	$0.106835\pi$
$294$	6.45806	+	2.79478i	0.376642	+	0.162995i
$295$	31.4190	−	1.64802i	1.82929	−	0.0959515i
$296$	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
$300$	−7.29551	+	4.66643i	−0.421206	+	0.269417i
$301$	−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	$-0.744217\pi$
$307$	−1.85340	+	1.55519i	−0.105779	+	0.0887592i	0.588364	+	0.808596i	$0.299772\pi$
$308$	−0.432992	+	0.157596i	−0.0246720	+	0.00897988i
$309$	13.7603	+	9.07354i	0.782794	+	0.516176i
$310$	−0.287072	+	0.563473i	−0.0163046	+	0.0320031i
$311$	23.3442	+	13.4778i	1.32373	+	0.764254i	0.984321	−	0.176386i	$-0.0564406\pi$
$311$	23.3442	+	13.4778i	1.32373	+	0.764254i	0.339406	+	0.940640i	$0.389774\pi$
$312$	−6.15607	+	1.83510i	−0.348519	+	0.103892i
$313$	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
$315$	−3.20765	−	11.0403i	−0.180731	−	0.622050i
$316$	4.56253	+	2.63418i	0.256662	+	0.148184i
$317$	−11.5302	+	13.7411i	−0.647600	+	0.771779i	−0.985550	−	0.169385i	$-0.945822\pi$
$317$	−11.5302	+	13.7411i	−0.647600	+	0.771779i	0.337950	+	0.941164i	$0.390266\pi$
$318$	−4.61512	−	3.04322i	−0.258803	−	0.170655i
$319$	0.189021	+	0.519331i	0.0105831	+	0.0290769i
$320$	−1.78586	−	1.34562i	−0.0998328	−	0.0752224i
$321$	−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
$325$	−10.9011	−	15.0013i	−0.604686	−	0.832121i
$326$	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
$330$	−0.898135	−	0.526898i	−0.0494407	−	0.0290048i
$331$	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
$333$	−16.8586	+	22.5339i	−0.923848	+	1.23485i
$334$	−7.38809	−	12.7965i	−0.404258	−	0.700196i
$335$	−4.84922	−	1.48232i	−0.264941	−	0.0809877i
$336$	2.38317	−	1.76984i	0.130012	−	0.0965525i
$337$	−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
$339$	5.73524	+	11.4535i	0.311496	+	0.622068i
$340$	3.16699	−	1.34448i	0.171754	−	0.0729145i
$341$	−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
$345$	2.10609	+	2.54568i	0.113388	+	0.137055i
$346$	9.22564	−	3.35786i	0.495973	−	0.180520i
$347$	−27.1609	−	9.88575i	−1.45807	−	0.530695i	−0.513239	−	0.858246i	$-0.671554\pi$
$347$	−27.1609	−	9.88575i	−1.45807	−	0.530695i	−0.944833	+	0.327551i	$0.893777\pi$
$348$	−2.12274	−	2.85837i	−0.113791	−	0.153225i
$349$	−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
$351$	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	0.939362	+	0.342927i	$0.111418\pi$
$353$	14.4043	+	24.9490i	0.766665	+	1.32790i	−0.172697	+	0.984975i	$0.555248\pi$
$354$	−17.7067	−	16.7450i	−0.941102	−	0.889985i
$355$	−2.42616	+	4.76213i	−0.128767	+	0.252748i
$356$	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	−0.382837	−	0.923816i	$-0.625053\pi$
$359$	−8.08336	+	1.42531i	−0.426623	+	0.0752252i	−0.0437858	+	0.999041i	$0.513942\pi$
$360$	6.51459	+	1.60005i	0.343349	+	0.0843300i
$361$	−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
$365$	13.6508	−	8.86580i	0.714515	−	0.464057i
$366$	1.12848	−	1.71137i	0.0589866	−	0.0894547i
$367$	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
$369$	−0.423890	−	7.58623i	−0.0220668	−	0.394923i
$370$	−1.09875	−	20.9473i	−0.0571211	−	1.08900i
$371$	−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	$-0.677173\pi$
$373$	9.09941	−	15.7606i	0.471149	−	0.816055i	0.999455	+	0.0329993i	$0.0105059\pi$
$374$	0.316899	+	0.265910i	0.0163865	+	0.0137499i
$375$	1.89198	+	19.2723i	0.0977013	+	0.995216i
$376$	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	$0.104753\pi$
$379$			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	0.906781	−	0.421601i	$-0.138532\pi$
$383$	6.53894	+	7.79281i	0.334124	+	0.398194i	−0.572657	+	0.819795i	$0.694087\pi$
$384$	0.199049	+	1.72058i	0.0101577	+	0.0878027i
$385$	−0.125520	+	1.02266i	−0.00639711	+	0.0521197i
$386$	−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	−0.400725	−	0.916198i	$-0.631242\pi$
$389$	−21.5108	−	3.79294i	−1.09064	−	0.192310i	−0.689917	+	0.723889i	$0.742353\pi$
$390$	−2.59256	+	14.1281i	−0.131280	+	0.715403i
$391$	−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
$395$	9.87959	−	6.41651i	0.497096	−	0.322850i
$396$	0.184156	+	0.785269i	0.00925420	+	0.0394612i
$397$	−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
$399$	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	0.999311	−	0.0371161i	$-0.0118171\pi$
$401$	0.952616	+	5.40255i	0.0475714	+	0.269791i	−0.951740	+	0.306907i	$0.900706\pi$
$402$	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
$405$	−19.8544	+	3.28648i	−0.986575	+	0.163306i
$406$	−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	0.784404	−	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
$411$	−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
$415$	−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	$-0.774237\pi$
$419$		−	26.6623i		−	1.30254i	0.758847	−	0.651269i	$-0.225763\pi$
$420$	−1.10715	−	6.54471i	−0.0540234	−	0.319349i
$421$	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
$423$	−16.8960	−	17.9936i	−0.821511	−	0.874877i
$424$	−2.44497	−	2.05157i	−0.118738	−	0.0996332i
$425$	0.535968	−	7.67464i	0.0259983	−	0.372275i
$426$	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
$430$	−12.6042	−	3.85287i	−0.607828	−	0.185802i
$431$	−24.3191	−	20.4062i	−1.17141	−	0.982930i	−0.171413	−	0.985199i	$-0.554833\pi$
$431$	−24.3191	−	20.4062i	−1.17141	−	0.982930i	−0.999997	+	0.00226871i	$0.999278\pi$
$432$	−2.58213	−	4.50917i	−0.124233	−	0.216947i
$433$	−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
$435$	−7.84973	+	1.32791i	−0.376366	+	0.0636686i
$436$			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
$441$	−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	$-0.324273\pi$
$443$	−4.69348	−	3.93830i	−0.222994	−	0.187114i	−0.747440	+	0.664330i	$0.768717\pi$
$444$	−11.1640	+	11.8052i	−0.529819	+	0.560250i
$445$	22.7543	−	21.2207i	1.07866	−	1.00596i
$446$	−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	−0.496188	−	0.868215i	$-0.665267\pi$
$449$	10.6754	−	18.4903i	0.503802	−	0.872611i	0.999990	−	0.00439613i	$-0.00139934\pi$
$450$	9.80065	−	11.3555i	0.462007	−	0.535303i
$451$	−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
$460$	1.03899	+	1.59975i	0.0484432	+	0.0745886i
$461$	−10.0255	+	27.5449i	−0.466935	+	1.28289i	0.453240	+	0.891388i	$0.350268\pi$
$461$	−10.0255	+	27.5449i	−0.466935	+	1.28289i	−0.920176	+	0.391506i	$0.871954\pi$
$462$	0.640733	−	0.475834i	0.0298096	−	0.0221378i
$463$	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
$465$	0.197696	−	1.07734i	0.00916794	−	0.0499603i
$466$	12.3393	+	2.17576i	0.571609	+	0.100790i
$467$	−16.4861	−	28.5548i	−0.762886	−	1.32136i	−0.941357	−	0.337413i	$-0.890448\pi$
$467$	−16.4861	−	28.5548i	−0.762886	−	1.32136i	0.178471	−	0.983945i	$-0.442885\pi$
$468$	9.31028	−	6.09204i	0.430368	−	0.281605i
$469$	2.49818	−	2.97722i	0.115355	−	0.137475i
$470$	18.2605	+	2.24127i	0.842293	+	0.103382i
$471$	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
$475$	−15.9483	+	14.8544i	−0.731757	+	0.681566i
$476$			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	−0.818756	−	0.574142i	$-0.805336\pi$
$479$	−12.2694	−	33.7099i	−0.560604	−	1.54025i	0.258152	−	0.966104i	$-0.416886\pi$
$480$	3.63012	+	1.34991i	0.165691	+	0.0616146i
$481$	−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
$485$	−13.4284	+	0.704358i	−0.609752	+	0.0319833i
$486$	12.4487	+	9.38238i	0.564686	+	0.425593i
$487$	−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
$489$	−20.6095	+	31.2549i	−0.931994	+	1.41339i
$490$	7.61871	−	4.94814i	0.344178	−	0.223534i
$491$	−5.68342	−	6.77324i	−0.256489	−	0.305672i	0.622399	−	0.782701i	$-0.286158\pi$
$491$	−5.68342	−	6.77324i	−0.256489	−	0.305672i	−0.878888	+	0.477028i	$0.841714\pi$
$492$	0.260233	−	4.37902i	0.0117322	−	0.197421i
$493$	3.16286			0.142448
$494$	−14.4091	+	7.32945i	−0.648297	+	0.329767i
$495$	1.75150	+	0.430185i	0.0787239	+	0.0193354i
$496$	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	−0.0539286	−	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
$501$	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	0.780819	+	0.624757i	$0.214802\pi$
$503$	−3.73623	+	21.1892i	−0.166590	+	0.944780i	−0.947410	+	0.320023i	$0.896309\pi$
$504$	−3.08004	+	4.11689i	−0.137196	+	0.183381i
$505$	7.72120	+	8.27923i	0.343589	+	0.368421i
$506$	−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	0.293920	−	0.955830i	$-0.405040\pi$
$509$	25.5723	−	9.30755i	1.13347	−	0.412550i	0.839552	+	0.543280i	$0.182818\pi$
$510$	−4.59156	+	3.79869i	−0.203317	+	0.168209i
$511$	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
$515$	19.5869	−	8.31520i	0.863103	−	0.366411i
$516$	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
$520$	−2.42429	+	7.93079i	−0.106312	+	0.347788i
$521$	10.2847	+	17.8136i	0.450580	+	0.780428i	0.998422	−	0.0561538i	$-0.0178837\pi$
$521$	10.2847	+	17.8136i	0.450580	+	0.780428i	−0.547842	+	0.836582i	$0.684550\pi$
$522$	4.93780	+	3.69420i	0.216122	+	0.161691i
$523$	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
$525$	−14.1635	−	4.43742i	−0.618145	−	0.193665i
$526$	−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
$530$	−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
$534$	−24.0583	−	1.42972i	−1.04111	−	0.0618700i
$535$	−19.1077	+	25.3591i	−0.826096	+	1.09637i
$536$	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
$540$	−11.6051	+	0.567542i	−0.499403	+	0.0244231i
$541$	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
$543$	25.3547	−	7.55812i	1.08807	−	0.324350i
$544$	−1.33252	−	0.769333i	−0.0571315	−	0.0329849i
$545$	33.2699	+	16.9500i	1.42512	+	0.726056i
$546$	−9.19103	−	6.06058i	−0.393340	−	0.259369i
$547$	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
$549$	−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
$555$	12.1885	+	34.2261i	0.517372	+	1.45282i
$556$	−17.9219	−	6.52302i	−0.760056	−	0.276638i
$557$	−16.6543	−	13.9746i	−0.705665	−	0.592123i	0.217714	−	0.976013i	$-0.430140\pi$
$557$	−16.6543	−	13.9746i	−0.705665	−	0.592123i	−0.923379	+	0.383889i	$0.874584\pi$
$558$	−0.709956	+	0.464549i	−0.0300548	+	0.0196659i
$559$	−18.9316	+	10.9302i	−0.800721	+	0.462296i
$560$	−0.200738	−	3.82702i	−0.00848274	−	0.161721i
$561$	−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	$-0.484531\pi$
$563$	−18.7954	−	10.8516i	−0.792134	−	0.457339i	−0.840713	+	0.541481i	$0.817864\pi$
$564$	−8.49640	−	11.4408i	−0.357763	−	0.481745i
$565$	16.4134	+	2.01456i	0.690518	+	0.0847533i
$566$	−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	$0.419199\pi$
$570$	16.8516	+	1.01220i	0.705835	+	0.0423965i
$571$	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
$575$	4.24197	−	0.446236i	0.176903	−	0.0186093i
$576$	−1.18174	−	2.75744i	−0.0492390	−	0.114894i
$577$	−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
$579$	6.35102	−	14.6757i	0.263939	−	0.609901i
$580$	−4.59012	+	0.240765i	−0.190594	+	0.00999724i
$581$	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
$585$	−2.68724	−	24.7336i	−0.111104	−	1.02261i
$586$	−17.1255	+	14.3700i	−0.707450	+	0.593621i
$587$	−3.47915	−	19.7312i	−0.143600	−	0.814395i	−0.968481	−	0.249089i	$-0.919869\pi$
$587$	−3.47915	−	19.7312i	−0.143600	−	0.814395i	0.824881	−	0.565307i	$-0.191242\pi$
$588$	−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	$-0.385207\pi$
$593$	29.8213	−	10.8541i	1.22462	−	0.445723i	0.871750	+	0.489951i	$0.162985\pi$
$594$	−0.694226	−	1.21232i	−0.0284845	−	0.0497423i
$595$	5.25403	+	2.67676i	0.215394	+	0.109737i
$596$	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	0.926950	+	0.375186i	$0.122421\pi$
$599$	−1.77242	+	10.0519i	−0.0724191	+	0.410709i	−0.999369	+	0.0355237i	$0.988690\pi$
$600$	6.37435	−	5.86239i	0.260232	−	0.239331i
$601$	−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
$603$	−4.65687	−	4.95939i	−0.189643	−	0.201962i
$604$	3.51735	+	9.66384i	0.143119	+	0.393216i
$605$	19.5154	+	14.7045i	0.793414	+	0.597825i
$606$	0.520207	−	8.75368i	0.0211320	−	0.355594i
$607$	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
$612$	4.58351	+	0.546701i	0.185277	+	0.0220991i
$613$	−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
$615$	−8.46059	−	4.96347i	−0.341164	−	0.200146i
$616$	0.399048	−	0.230390i	0.0160781	−	0.00928269i
$617$	−1.13238	+	6.42203i	−0.0455878	+	0.258541i	−0.999080	−	0.0428750i	$-0.986348\pi$
$617$	−1.13238	+	6.42203i	−0.0455878	+	0.258541i	0.953493	+	0.301416i	$0.0974594\pi$
$618$	−15.1268	−	6.54625i	−0.608490	−	0.263329i
$619$	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
$621$	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
$625$	22.0758	+	11.7328i	0.883032	+	0.469312i
$626$	−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
$630$	5.07605	+	10.3156i	0.202235	+	0.410982i
$631$	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
$633$	21.5425	−	15.9983i	0.856236	−	0.635876i
$634$	8.96889	−	15.5346i	0.356200	−	0.616957i
$635$	2.64330	−	2.46514i	0.104896	−	0.0978260i
$636$	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
$640$	1.99240	+	1.01506i	0.0787564	+	0.0401239i
$641$	−19.3301	−	7.03558i	−0.763493	−	0.277889i	−0.0692208	−	0.997601i	$-0.522051\pi$
$641$	−19.3301	−	7.03558i	−0.763493	−	0.277889i	−0.694272	+	0.719713i	$0.744274\pi$
$642$	24.4320	−	2.82648i	0.964254	−	0.111552i
$643$	−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
$645$	22.8277	+	0.158711i	0.898841	+	0.00624926i
$646$	−6.53396	−	1.51317i	−0.257075	−	0.0595351i
$647$	41.3515			1.62570			0.812848	−	0.582476i	$-0.197916\pi$
$647$	41.3515			1.62570			0.812848	+	0.582476i	$0.197916\pi$
$648$	6.51714	+	6.20700i	0.256018	+	0.243834i
$649$	−2.43161	−	2.89788i	−0.0954491	−	0.113752i
$650$	13.3405	+	12.8804i	0.523256	+	0.505211i
$651$	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	0.154973	−	0.987919i	$-0.450471\pi$
$653$	23.8430	−	41.2973i	0.933049	−	1.61609i	0.778076	−	0.628170i	$-0.216196\pi$
$654$	−8.26237	−	27.7172i	−0.323084	−	1.08383i
$655$	−0.405294	−	7.72681i	−0.0158361	−	0.301911i
$656$	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	0.0449886	−	0.998988i	$-0.485675\pi$
$659$	−23.9000	−	20.0544i	−0.931010	−	0.781210i	−0.975998	+	0.217777i	$0.930119\pi$
$660$	0.975985	+	0.362933i	0.0379902	+	0.0141272i
$661$	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
$663$	−0.586346	+	9.86662i	−0.0227718	+	0.383188i
$664$			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
$669$	9.73877	−	1.12665i	0.376523	−	0.0435590i
$670$	5.03295	+	0.617739i	0.194440	+	0.0238653i
$671$	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	0.834590	+	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
$675$	−10.6491	+	23.6980i	−0.409885	+	0.912137i
$676$	0.377460	+	0.653780i	0.0145177	+	0.0251454i
$677$	−1.73145	−	0.999652i	−0.0665450	−	0.0384197i	0.466358	−	0.884596i	$-0.345566\pi$
$677$	−1.73145	−	0.999652i	−0.0665450	−	0.0384197i	−0.532903	+	0.846176i	$0.678899\pi$
$678$	−7.63699	−	10.2836i	−0.293297	−	0.394938i
$679$	3.52500	−	9.68485i	0.135277	−	0.371671i
$680$	−2.88541	+	1.87399i	−0.110651	+	0.0718644i
$681$	−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
$690$	−2.51615	−	2.14128i	−0.0957880	−	0.0815172i
$691$	−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
$693$	−0.828092	+	1.10686i	−0.0314566	+	0.0420461i
$694$	28.4649	+	5.01913i	1.08051	+	0.190523i
$695$	−31.1883	+	29.0862i	−1.18304	+	1.10330i
$696$	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
$700$	−7.82870	−	3.48472i	−0.295897	−	0.131710i
$701$	11.8330	−	2.08649i	0.446928	−	0.0788055i	0.0543454	−	0.998522i	$-0.482693\pi$
$701$	11.8330	−	2.08649i	0.446928	−	0.0788055i	0.392583	+	0.919717i	$0.371582\pi$
$702$	−12.4395	+	14.7187i	−0.469499	+	0.555523i
$703$	−22.2936	+	34.2779i	−0.840818	+	1.29282i
$704$			0.268858i			0.0101330i
$705$	−31.4190	+	5.31506i	−1.18331	+	0.200177i
$706$	−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	0.107774	−	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
$711$	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
$715$	−0.651790	+	2.13225i	−0.0243756	+	0.0797418i
$716$	−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	0.500789	−	0.865570i	$-0.333043\pi$
$719$	−11.7605	−	14.0156i	−0.438592	−	0.522694i	−0.939381	+	0.342876i	$0.888599\pi$
$720$	−6.69346	−	0.444494i	−0.249451	−	0.0165653i
$721$			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
$726$	−2.17515	−	18.8020i	−0.0807275	−	0.697806i
$727$	−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
$729$	−25.3057	−	9.41390i	−0.937248	−	0.348663i
$730$	−11.9039	+	11.1015i	−0.440582	+	0.410887i
$731$	−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	$-0.818001\pi$
$733$	−21.4641	+	12.3923i	−0.792795	+	0.457721i	0.0481505	+	0.998840i	$0.484667\pi$
$734$	−3.00188	+	5.19941i	−0.110802	+	0.191914i
$735$	−10.1977	+	11.9830i	−0.376150	+	0.442000i
$736$	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	−0.977192	−	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
$741$	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	$-0.438846\pi$
$743$	19.2467	−	3.39371i	0.706093	−	0.124503i	0.515153	+	0.857098i	$0.327735\pi$
$744$	−0.438000	+	0.219325i	−0.0160579	+	0.00804085i
$745$	42.5996	−	27.6672i	1.56073	−	1.01365i
$746$	−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
$750$	−5.20983	−	18.6509i	−0.190236	−	0.681036i
$751$	−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
$753$	−27.5607	−	26.0637i	−1.00437	−	0.949813i
$754$	−4.90041	+	5.84008i	−0.178462	+	0.212683i
$755$	22.8245	+	2.80146i	0.830670	+	0.101955i
$756$	3.07543	−	8.35751i	0.111852	−	0.303960i
$757$	−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	$0.263861\pi$
$761$			40.6741i			1.47444i	−0.675655	+	0.737218i	$0.736139\pi$
$762$	−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
$765$	5.74180	−	8.57723i	0.207595	−	0.310111i
$766$	−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	−0.679669	−	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
$771$	−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	$-0.954198\pi$
$773$	−18.8113	+	22.4185i	−0.676596	+	0.806336i	0.313070	+	0.949730i	$0.398643\pi$
$774$	−12.1042	−	12.8905i	−0.435077	−	0.463341i
$775$	−1.01728	−	0.982196i	−0.0365417	−	0.0352815i
$776$	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
$780$	0.0998642	−	14.3636i	0.00357571	−	0.514300i
$781$	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
$785$	19.2181	+	9.79103i	0.685924	+	0.349457i
$786$	−4.11805	+	4.35458i	−0.146886	+	0.155323i
$787$	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
$789$	8.70019	−	20.1041i	0.309735	−	0.715724i
$790$	−8.61528	+	8.03460i	−0.306518	+	0.285858i
$791$	−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
$795$	9.52434	−	7.87969i	0.337794	−	0.279464i
$796$	−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
$800$	4.04482	−	2.93929i	0.143006	−	0.103920i
$801$	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
$805$	−0.955688	+	3.12642i	−0.0336836	+	0.110192i
$806$	−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	−0.531026	−	0.847356i	$-0.678193\pi$
$809$	−1.78358	+	1.02975i	−0.0627075	+	0.0362042i	0.468318	+	0.883560i	$0.344860\pi$
$810$	18.9821	−	6.68424i	0.666964	−	0.234860i
$811$	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
$813$	−16.1383	+	1.86700i	−0.565994	+	0.0654784i
$814$	−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
$819$	18.2547	+	5.51207i	0.637871	+	0.192607i
$820$	−4.52304	−	3.40803i	−0.157951	−	0.119014i
$821$	−7.02435	−	19.2992i	−0.245152	−	0.673548i	−0.999847	−	0.0174734i	$-0.994438\pi$
$821$	−7.02435	−	19.2992i	−0.245152	−	0.673548i	0.754696	−	0.656075i	$-0.227784\pi$
$822$	19.2208	−	29.1488i	0.670401	−	1.01668i
$823$	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
$825$	1.71379	−	1.57615i	0.0596667	−	0.0548744i
$826$	4.18742	−	23.7480i	0.145699	−	0.826300i
$827$	27.1327	+	4.78422i	0.943495	+	0.166364i	0.624176	−	0.781284i	$-0.285435\pi$
$827$	27.1327	+	4.78422i	0.943495	+	0.166364i	0.319319	+	0.947647i	$0.396546\pi$
$828$	0.142777	+	2.55524i	0.00496185	+	0.0888008i
$829$	−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
$831$	−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	−0.985938	−	0.167114i	$-0.946555\pi$
$839$	−28.7503	+	24.1243i	−0.992569	+	0.832864i	−0.00663147	+	0.999978i	$0.502111\pi$
$840$	2.22681	+	6.25303i	0.0768321	+	0.215750i
$841$	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
$845$	1.68573	−	0.0884217i	0.0579910	−	0.00304180i
$846$	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
$850$	0.804862	+	7.65111i	0.0276065	+	0.262431i
$851$	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	$-0.188640\pi$
$853$	52.5699	−	9.26950i	1.79996	−	0.317381i	0.970485	+	0.241162i	$0.0775287\pi$
$854$	2.02839			0.0694102
$855$	−28.4723	+	6.65803i	−0.973731	+	0.227700i
$856$	14.1999			0.485343
$857$	−16.7281	+	2.94961i	−0.571420	+	0.100757i	−0.451890	−	0.892074i	$-0.649250\pi$
$857$	−16.7281	+	2.94961i	−0.571420	+	0.100757i	−0.119530	+	0.992831i	$0.538139\pi$
$858$	1.54429	−	0.773290i	0.0527211	−	0.0263997i
$859$	−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
$861$	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	$-0.741894\pi$
$863$	−11.9136	+	6.87833i	−0.405544	+	0.234141i	0.283329	+	0.959023i	$0.408561\pi$
$864$	3.32591	+	3.99228i	0.113150	+	0.135820i
$865$	1.14992	+	21.9229i	0.0390986	+	0.745403i
$866$	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
$870$	7.49988	−	2.67083i	0.254270	−	0.0905497i
$871$	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	$-0.810293\pi$
$877$	−12.3939	+	10.3998i	−0.418514	+	0.351175i	0.409084	+	0.912497i	$0.365848\pi$
$878$	32.6574	−	11.8863i	1.10213	−	0.401143i
$879$	21.3159	−	32.3261i	0.718968	−	1.09033i
$880$	0.535671	+	0.272908i	0.0180575	+	0.00919972i
$881$	11.9255	+	6.88519i	0.401780	+	0.231968i	0.687252	−	0.726419i	$-0.258817\pi$
$881$	11.9255	+	6.88519i	0.401780	+	0.231968i	−0.285472	+	0.958387i	$0.592150\pi$
$882$	12.1692	−	0.679969i	0.409759	−	0.0228957i
$883$	−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
$885$	47.3816	−	26.9183i	1.59272	−	0.904849i
$886$	5.30605	+	3.06345i	0.178260	+	0.102919i
$887$	−31.9511	+	38.0778i	−1.07281	+	1.27853i	−0.114311	+	0.993445i	$0.536466\pi$
$887$	−31.9511	+	38.0778i	−1.07281	+	1.27853i	−0.958503	+	0.285084i	$0.907978\pi$
$888$	8.94442	−	13.5644i	0.300155	−	0.455193i
$889$	0.947492	+	2.60321i	0.0317779	+	0.0873089i
$890$	−18.7237	+	24.8495i	−0.627621	+	0.832959i
$891$	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
$895$	−3.45780	+	1.46793i	−0.115581	+	0.0490675i
$896$	−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
$900$	−7.67990	+	12.8848i	−0.255997	+	0.429495i
$901$	−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
$905$	9.98482	−	32.6642i	0.331907	−	1.08579i
$906$	−10.6200	−	14.3003i	−0.352826	−	0.475097i
$907$	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
$909$	3.46784	+	14.7874i	0.115021	+	0.490467i
$910$	−13.0829	+	5.55405i	−0.433694	+	0.184115i
$911$	−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
$915$	2.92193	+	3.53180i	0.0965960	+	0.116758i
$916$	−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	−0.844984	−	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
$921$	−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
$925$	45.5117	+	11.3430i	1.49641	+	0.372955i
$926$	−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	0.00643416	−	0.999979i	$-0.497952\pi$
$929$	10.8048	−	1.90517i	0.354493	−	0.0625067i	0.348059	+	0.937473i	$0.386841\pi$
$930$	−0.00761515	+	1.09530i	−0.000249711	+	0.0359163i
$931$	−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
$935$	−0.775766	+	0.503838i	−0.0253703	+	0.0164773i
$936$	−8.11096	+	7.61621i	−0.265115	+	0.248943i
$937$	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
$939$	32.9267	−	9.81528i	1.07452	−	0.320310i
$940$	−18.3722	+	0.963678i	−0.599236	+	0.0314317i
$941$	8.26369	−	46.8657i	0.269388	−	1.52778i	−0.486852	−	0.873484i	$-0.661855\pi$
$941$	8.26369	−	46.8657i	0.269388	−	1.52778i	0.756241	−	0.654294i	$-0.227034\pi$
$942$	−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
$945$	−13.5297	−	14.6109i	−0.440122	−	0.475292i
$946$	0.542003	+	1.48914i	0.0176220	+	0.0484161i
$947$	25.8684	−	21.7061i	0.840609	−	0.705354i	−0.117092	−	0.993121i	$-0.537357\pi$
$947$	25.8684	−	21.7061i	0.840609	−	0.705354i	0.957701	+	0.287767i	$0.0929128\pi$
$948$	9.10899	+	0.541322i	0.295846	+	0.0175813i
$949$			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	0.323850	−	0.946108i	$-0.395023\pi$
$953$	−20.5019	−	24.4332i	−0.664120	−	0.791468i	−0.987971	+	0.154640i	$0.950578\pi$
$954$	−9.50766	−	1.13403i	−0.307822	−	0.0367156i
$955$	10.4910	+	1.28765i	0.339481	+	0.0416675i
$956$	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
$960$	−3.80938	−	0.699038i	−0.122947	−	0.0225613i
$961$	−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
$965$	−11.2444	−	17.3132i	−0.361972	−	0.557332i
$966$	2.26431	−	1.13384i	0.0728530	−	0.0364806i
$967$	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
$969$	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	0.534239	+	0.845333i	$0.320598\pi$
$971$	10.0132	+	56.7878i	0.321340	+	1.82241i	−0.212900	+	0.977074i	$0.568291\pi$
$972$	−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
$975$	−28.5167	−	14.7790i	−0.913265	−	0.473306i
$976$	−0.591767	+	1.02497i	−0.0189420	+	0.0328085i
$977$	−18.5256	+	10.6957i	−0.592685	+	0.342187i	−0.766158	−	0.642652i	$-0.777834\pi$
$977$	−18.5256	+	10.6957i	−0.592685	+	0.342187i	0.173474	+	0.984839i	$0.444501\pi$
$978$	14.8691	−	34.3588i	0.475460	−	1.09867i
$979$	−3.68421	−	0.649625i	−0.117748	−	0.0207621i
$980$	−6.64373	+	6.19594i	−0.212226	+	0.197922i
$981$	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	$-0.986697\pi$
$983$	−6.48673	+	17.8222i	−0.206895	+	0.568439i	0.792232	+	0.610220i	$0.208919\pi$
$984$	0.504129	+	4.35768i	0.0160711	+	0.138918i
$985$	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
$990$	−1.79959	−	0.119506i	−0.0571947	−	0.00379814i
$991$	−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
$993$	24.0207	−	36.4281i	0.762275	−	1.15601i
$994$	3.13799	+	2.63308i	0.0995309	+	0.0835164i
$995$	−51.6910	−	15.8010i	−1.63872	−	0.500925i
$996$	−7.35655	−	24.6785i	−0.233101	−	0.781969i
$997$	−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
$999$	−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.29.18	yes	240
3.2	odd	2	inner	570.2.bf.a.29.34	yes	240
5.4	even	2	inner	570.2.bf.a.29.23	yes	240
15.14	odd	2	inner	570.2.bf.a.29.7	✓	240
19.2	odd	18	inner	570.2.bf.a.59.7	yes	240
57.2	even	18	inner	570.2.bf.a.59.23	yes	240
95.59	odd	18	inner	570.2.bf.a.59.34	yes	240
285.59	even	18	inner	570.2.bf.a.59.18	yes	240

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

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(1.54873 - 0.775516i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.272408 - 2.21941i) q^{5} +(-1.39054 + 1.03267i) q^{6} +(1.48423 + 0.856923i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(1.79715 - 2.40214i) q^{9} +O(q^{10})\)	\(q+(-0.984808 + 0.173648i) q^{2} +(1.54873 - 0.775516i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.272408 - 2.21941i) 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} +(0.117127 + 2.23300i) 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} +(-1.29930 - 3.64854i) 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} +(-4.85159 - 1.20917i) 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} +(1.91313 + 3.36748i) 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} +(2.30618 - 3.06070i) q^{35} +(0.867188 - 2.87193i) q^{36} -9.38078 q^{37} +(-1.70589 + 4.01123i) q^{38} +(6.24886 + 1.48880i) q^{39} +(0.873794 + 2.05827i) 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} +(-4.84177 - 4.64298i) 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} +(4.98785 + 0.348333i) 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} +(0.234926 + 0.553382i) q^{55} -1.71385 q^{56} +(0.846806 - 7.50219i) q^{57} +2.05559i q^{58} +(2.44329 + 13.8566i) q^{59} +(-2.46882 - 2.98411i) 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} +(6.06489 - 5.65612i) 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} +(-1.73966 + 3.41466i) 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} +(-8.45155 + 1.88980i) q^{75} +(0.983433 - 4.24651i) q^{76} -0.460781 q^{77} +(-6.41245 - 0.381074i) q^{78} +(3.38643 + 4.03579i) q^{79} +(-1.21793 - 1.87527i) 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} +(3.43584 - 0.180220i) 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} +(5.57446 + 3.73167i) q^{90} +(2.17397 + 5.97292i) q^{91} +(-0.653494 + 0.548347i) q^{92} +(0.488982 + 0.0290588i) 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} +(-0.0955274 + 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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