LMFDB - Embedded newform 420.2.bn.a.89.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(89,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("420.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bn (of order $6$, degree $2$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.9
Character	$\chi$	$=$	420.89
Dual form			420.2.bn.a.269.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0216419 + 1.73192i) q^{3} +(-2.23530 + 0.0584556i) q^{5} +(-0.0973684 + 2.64396i) q^{7} +(-2.99906 + 0.0749640i) q^{9} +O(q^{10})$	\(q+(0.0216419 + 1.73192i) q^{3} +(-2.23530 + 0.0584556i) q^{5} +(-0.0973684 + 2.64396i) q^{7} +(-2.99906 + 0.0749640i) q^{9} +(2.62913 - 1.51793i) q^{11} -2.31738 q^{13} +(-0.149616 - 3.87009i) q^{15} +(-4.49684 + 2.59625i) q^{17} +(-5.58515 - 3.22459i) q^{19} +(-4.58122 - 0.111414i) q^{21} +(-2.43442 + 4.21654i) q^{23} +(4.99317 - 0.261332i) q^{25} +(-0.194737 - 5.19250i) q^{27} +3.48622i q^{29} +(1.16615 - 0.673279i) q^{31} +(2.68582 + 4.52058i) q^{33} +(0.0630937 - 5.91574i) q^{35} +(2.43579 + 1.40630i) q^{37} +(-0.0501525 - 4.01350i) q^{39} -1.06401 q^{41} +2.42063i q^{43} +(6.69944 - 0.342879i) q^{45} +(-3.30233 - 1.90660i) q^{47} +(-6.98104 - 0.514876i) q^{49} +(-4.59381 - 7.73196i) q^{51} +(3.52984 + 6.11386i) q^{53} +(-5.78817 + 3.54672i) q^{55} +(5.46384 - 9.74279i) q^{57} +(6.18029 + 10.7046i) q^{59} +(11.4447 + 6.60758i) q^{61} +(0.0938123 - 7.93670i) q^{63} +(5.18004 - 0.135464i) q^{65} +(3.72081 - 2.14821i) q^{67} +(-7.35538 - 4.12496i) q^{69} +7.08288i q^{71} +(0.0763237 + 0.132196i) q^{73} +(0.560667 + 8.64209i) q^{75} +(3.75734 + 7.09910i) q^{77} +(-3.04462 + 5.27344i) q^{79} +(8.98876 - 0.449644i) q^{81} -10.2758i q^{83} +(9.90003 - 6.06628i) q^{85} +(-6.03784 + 0.0754485i) q^{87} +(-7.10913 + 12.3134i) q^{89} +(0.225639 - 6.12705i) q^{91} +(1.19130 + 2.00511i) q^{93} +(12.6730 + 6.88145i) q^{95} -8.63266 q^{97} +(-7.77113 + 4.74945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 2 q^{15} + 12 q^{19} - 8 q^{21} + 6 q^{25} - 12 q^{31} + 24 q^{39} + 33 q^{45} - 44 q^{49} - 10 q^{51} - 24 q^{61} + 21 q^{75} - 28 q^{79} - 20 q^{81} - 4 q^{85} + 16 q^{91} - 28 q^{99}+O(q^{100}) $ 32 * q + 2 * q^15 + 12 * q^19 - 8 * q^21 + 6 * q^25 - 12 * q^31 + 24 * q^39 + 33 * q^45 - 44 * q^49 - 10 * q^51 - 24 * q^61 + 21 * q^75 - 28 * q^79 - 20 * q^81 - 4 * q^85 + 16 * q^91 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.0216419	+	1.73192i	0.0124950	+	0.999922i
$3$	0.0216419	+	1.73192i	0.0124950	+	0.999922i
$4$		0			0
$5$	−2.23530	+	0.0584556i	−0.999658	+	0.0261421i
$5$	−2.23530	+	0.0584556i	−0.999658	+	0.0261421i
$6$		0			0
$7$	−0.0973684	+	2.64396i	−0.0368018	+	0.999323i
$7$	−0.0973684	+	2.64396i	−0.0368018	+	0.999323i
$8$		0			0
$9$	−2.99906	+	0.0749640i	−0.999688	+	0.0249880i
$10$		0			0
$11$	2.62913	−	1.51793i	0.792712	−	0.457672i	−0.0482045	−	0.998837i	$-0.515350\pi$
$11$	2.62913	−	1.51793i	0.792712	−	0.457672i	0.840916	+	0.541165i	$0.182017\pi$
$12$		0			0
$13$	−2.31738			−0.642724			−0.321362	−	0.946956i	$-0.604141\pi$
$13$	−2.31738			−0.642724			−0.321362	+	0.946956i	$0.604141\pi$
$14$		0			0
$15$	−0.149616	−	3.87009i	−0.0386308	−	0.999254i
$16$		0			0
$17$	−4.49684	+	2.59625i	−1.09064	+	0.629683i	−0.933748	−	0.357932i	$-0.883482\pi$
$17$	−4.49684	+	2.59625i	−1.09064	+	0.629683i	−0.156896	+	0.987615i	$0.550149\pi$
$18$		0			0
$19$	−5.58515	−	3.22459i	−1.28132	−	0.739771i	−0.304231	−	0.952598i	$-0.598400\pi$
$19$	−5.58515	−	3.22459i	−1.28132	−	0.739771i	−0.977090	+	0.212827i	$0.931733\pi$
$20$		0			0
$21$	−4.58122	−	0.111414i	−0.999704	−	0.0243124i
$22$		0			0
$23$	−2.43442	+	4.21654i	−0.507612	+	0.879209i	0.492349	+	0.870398i	$0.336138\pi$
$23$	−2.43442	+	4.21654i	−0.507612	+	0.879209i	−0.999961	+	0.00881178i	$0.997195\pi$
$24$		0			0
$25$	4.99317	−	0.261332i	0.998633	−	0.0522664i
$26$		0			0
$27$	−0.194737	−	5.19250i	−0.0374771	−	0.999297i
$28$		0			0
$29$			3.48622i			0.647374i	0.946164	+	0.323687i	$0.104923\pi$
$29$			3.48622i			0.647374i	−0.946164	+	0.323687i	$0.895077\pi$
$30$		0			0
$31$	1.16615	−	0.673279i	0.209447	−	0.120924i	−0.391607	−	0.920132i	$-0.628081\pi$
$31$	1.16615	−	0.673279i	0.209447	−	0.120924i	0.601054	+	0.799208i	$0.294747\pi$
$32$		0			0
$33$	2.68582	+	4.52058i	0.467542	+	0.786931i
$34$		0			0
$35$	0.0630937	−	5.91574i	0.0106648	−	0.999943i
$36$		0			0
$37$	2.43579	+	1.40630i	0.400441	+	0.231195i	0.686674	−	0.726965i	$-0.259070\pi$
$37$	2.43579	+	1.40630i	0.400441	+	0.231195i	−0.286233	+	0.958160i	$0.592403\pi$
$38$		0			0
$39$	−0.0501525	−	4.01350i	−0.00803082	−	0.642674i
$40$		0			0
$41$	−1.06401			−0.166171			−0.0830853	−	0.996542i	$-0.526477\pi$
$41$	−1.06401			−0.166171			−0.0830853	+	0.996542i	$0.526477\pi$
$42$		0			0
$43$			2.42063i			0.369142i	0.982819	+	0.184571i	$0.0590896\pi$
$43$			2.42063i			0.369142i	−0.982819	+	0.184571i	$0.940910\pi$
$44$		0			0
$45$	6.69944	−	0.342879i	0.998693	−	0.0511134i
$46$		0			0
$47$	−3.30233	−	1.90660i	−0.481695	−	0.278106i	0.239428	−	0.970914i	$-0.423040\pi$
$47$	−3.30233	−	1.90660i	−0.481695	−	0.278106i	−0.721122	+	0.692808i	$0.756373\pi$
$48$		0			0
$49$	−6.98104	−	0.514876i	−0.997291	−	0.0735537i
$50$		0			0
$51$	−4.59381	−	7.73196i	−0.643262	−	1.08269i
$52$		0			0
$53$	3.52984	+	6.11386i	0.484861	+	0.839803i	0.999849	−	0.0173942i	$-0.00553703\pi$
$53$	3.52984	+	6.11386i	0.484861	+	0.839803i	−0.514988	+	0.857197i	$0.672204\pi$
$54$		0			0
$55$	−5.78817	+	3.54672i	−0.780476	+	0.478239i
$56$		0			0
$57$	5.46384	−	9.74279i	0.723703	−	1.29046i
$58$		0			0
$59$	6.18029	+	10.7046i	0.804605	+	1.39362i	0.916558	+	0.399903i	$0.130956\pi$
$59$	6.18029	+	10.7046i	0.804605	+	1.39362i	−0.111953	+	0.993714i	$0.535711\pi$
$60$		0			0
$61$	11.4447	+	6.60758i	1.46534	+	0.846014i	0.999250	−	0.0387246i	$-0.0123295\pi$
$61$	11.4447	+	6.60758i	1.46534	+	0.846014i	0.466088	+	0.884738i	$0.345663\pi$
$62$		0			0
$63$	0.0938123	−	7.93670i	0.0118192	−	0.999930i
$64$		0			0
$65$	5.18004	−	0.135464i	0.642505	−	0.0168022i
$66$		0			0
$67$	3.72081	−	2.14821i	0.454569	−	0.262446i	−0.255189	−	0.966891i	$-0.582138\pi$
$67$	3.72081	−	2.14821i	0.454569	−	0.262446i	0.709758	+	0.704446i	$0.248804\pi$
$68$		0			0
$69$	−7.35538	−	4.12496i	−0.885483	−	0.496586i
$70$		0			0
$71$			7.08288i			0.840583i	0.907389	+	0.420292i	$0.138072\pi$
$71$			7.08288i			0.840583i	−0.907389	+	0.420292i	$0.861928\pi$
$72$		0			0
$73$	0.0763237	+	0.132196i	0.00893301	+	0.0154724i	0.870457	−	0.492244i	$-0.163823\pi$
$73$	0.0763237	+	0.132196i	0.00893301	+	0.0154724i	−0.861524	+	0.507716i	$0.830490\pi$
$74$		0			0
$75$	0.560667	+	8.64209i	0.0647402	+	0.997902i
$76$		0			0
$77$	3.75734	+	7.09910i	0.428189	+	0.809018i
$78$		0			0
$79$	−3.04462	+	5.27344i	−0.342547	+	0.593309i	−0.984905	−	0.173096i	$-0.944623\pi$
$79$	−3.04462	+	5.27344i	−0.342547	+	0.593309i	0.642358	+	0.766405i	$0.277956\pi$
$80$		0			0
$81$	8.98876	−	0.449644i	0.998751	−	0.0499604i
$82$		0			0
$83$		−	10.2758i		−	1.12791i	−0.825804	−	0.563957i	$-0.809278\pi$
$83$		−	10.2758i		−	1.12791i	0.825804	−	0.563957i	$-0.190722\pi$
$84$		0			0
$85$	9.90003	−	6.06628i	1.07381	−	0.657980i
$86$		0			0
$87$	−6.03784	+	0.0754485i	−0.647324	+	0.00808893i
$88$		0			0
$89$	−7.10913	+	12.3134i	−0.753567	+	1.30522i	0.192517	+	0.981294i	$0.438335\pi$
$89$	−7.10913	+	12.3134i	−0.753567	+	1.30522i	−0.946084	+	0.323922i	$0.894998\pi$
$90$		0			0
$91$	0.225639	−	6.12705i	0.0236534	−	0.642289i
$92$		0			0
$93$	1.19130	+	2.00511i	0.123532	+	0.207920i
$94$		0			0
$95$	12.6730	+	6.88145i	1.30022	+	0.706022i
$96$		0			0
$97$	−8.63266			−0.876514			−0.438257	−	0.898850i	$-0.644404\pi$
$97$	−8.63266			−0.876514			−0.438257	+	0.898850i	$0.644404\pi$
$98$		0			0
$99$	−7.77113	+	4.74945i	−0.781028	+	0.477338i
$100$		0			0
$101$	8.23108	+	14.2566i	0.819023	+	1.41859i	0.906403	+	0.422414i	$0.138817\pi$
$101$	8.23108	+	14.2566i	0.819023	+	1.41859i	−0.0873801	+	0.996175i	$0.527849\pi$
$102$		0			0
$103$	3.30237	−	5.71987i	0.325392	−	0.563596i	−0.656199	−	0.754588i	$-0.727837\pi$
$103$	3.30237	−	5.71987i	0.325392	−	0.563596i	0.981592	+	0.190992i	$0.0611703\pi$
$104$		0			0
$105$	10.2469	−	0.0187551i	0.999998	−	0.00183031i
$106$		0			0
$107$	9.26659	−	16.0502i	0.895835	−	1.55163i	0.0630674	−	0.998009i	$-0.479912\pi$
$107$	9.26659	−	16.0502i	0.895835	−	1.55163i	0.832768	−	0.553623i	$-0.186755\pi$
$108$		0			0
$109$	−9.25130	−	16.0237i	−0.886114	−	1.53479i	−0.844432	−	0.535664i	$-0.820062\pi$
$109$	−9.25130	−	16.0237i	−0.886114	−	1.53479i	−0.0416824	−	0.999131i	$-0.513272\pi$
$110$		0			0
$111$	−2.38288	+	4.24901i	−0.226173	+	0.403299i
$112$		0			0
$113$	5.86968			0.552173			0.276087	−	0.961133i	$-0.410962\pi$
$113$	5.86968			0.552173			0.276087	+	0.961133i	$0.410962\pi$
$114$		0			0
$115$	5.19519	−	9.56755i	0.484454	−	0.892179i
$116$		0			0
$117$	6.94995	−	0.173720i	0.642524	−	0.0160604i
$118$		0			0
$119$	−6.42653	−	12.1423i	−0.589119	−	1.11308i
$120$		0			0
$121$	−0.891792	+	1.54463i	−0.0810720	+	0.140421i
$122$		0			0
$123$	−0.0230272	−	1.84278i	−0.00207630	−	0.166158i
$124$		0			0
$125$	−11.1460	+	0.876035i	−0.996926	+	0.0783550i
$126$		0			0
$127$			14.5896i			1.29462i	0.762226	+	0.647311i	$0.224106\pi$
$127$			14.5896i			1.29462i	−0.762226	+	0.647311i	$0.775894\pi$
$128$		0			0
$129$	−4.19232	+	0.0523870i	−0.369113	+	0.00461242i
$130$		0			0
$131$	10.0356	−	17.3822i	0.876817	−	1.51869i	0.0220016	−	0.999758i	$-0.492996\pi$
$131$	10.0356	−	17.3822i	0.876817	−	1.51869i	0.854815	−	0.518933i	$-0.173671\pi$
$132$		0			0
$133$	9.06949	−	14.4529i	0.786425	−	1.25323i
$134$		0			0
$135$	0.738827	+	11.5954i	0.0635881	+	0.997976i
$136$		0			0
$137$	2.33533	+	4.04491i	0.199521	+	0.345580i	0.948373	−	0.317157i	$-0.102728\pi$
$137$	2.33533	+	4.04491i	0.199521	+	0.345580i	−0.748852	+	0.662737i	$0.769395\pi$
$138$		0			0
$139$			5.51296i			0.467603i	0.972284	+	0.233801i	$0.0751166\pi$
$139$			5.51296i			0.467603i	−0.972284	+	0.233801i	$0.924883\pi$
$140$		0			0
$141$	3.23060	−	5.76062i	0.272066	−	0.485132i
$142$		0			0
$143$	−6.09268	+	3.51761i	−0.509495	+	0.294157i
$144$		0			0
$145$	−0.203789	−	7.79276i	−0.0169238	−	0.647153i
$146$		0			0
$147$	0.740639	−	12.1017i	0.0610869	−	0.998132i
$148$		0			0
$149$	12.6579	+	7.30806i	1.03698	+	0.598700i	0.918976	−	0.394313i	$-0.129018\pi$
$149$	12.6579	+	7.30806i	1.03698	+	0.598700i	0.118003	+	0.993013i	$0.462351\pi$
$150$		0			0
$151$	−4.48104	−	7.76139i	−0.364662	−	0.631613i	0.624060	−	0.781376i	$-0.285482\pi$
$151$	−4.48104	−	7.76139i	−0.364662	−	0.631613i	−0.988722	+	0.149764i	$0.952149\pi$
$152$		0			0
$153$	13.2917	−	8.12342i	1.07457	−	0.656740i
$154$		0			0
$155$	−2.56735	+	1.57315i	−0.206214	+	0.126358i
$156$		0			0
$157$	10.2703	+	17.7886i	0.819657	+	1.41969i	0.905935	+	0.423416i	$0.139169\pi$
$157$	10.2703	+	17.7886i	0.819657	+	1.41969i	−0.0862784	+	0.996271i	$0.527497\pi$
$158$		0			0
$159$	−10.5123	+	6.24570i	−0.833679	+	0.495316i
$160$		0			0
$161$	−10.9113	−	6.84707i	−0.859933	−	0.539624i
$162$		0			0
$163$	−17.3645	−	10.0254i	−1.36009	−	0.785250i	−0.370457	−	0.928850i	$-0.620799\pi$
$163$	−17.3645	−	10.0254i	−1.36009	−	0.785250i	−0.989636	+	0.143600i	$0.954132\pi$
$164$		0			0
$165$	−6.26788	−	9.94786i	−0.487954	−	0.774440i
$166$		0			0
$167$			12.2463i			0.947646i	0.880620	+	0.473823i	$0.157126\pi$
$167$			12.2463i			0.947646i	−0.880620	+	0.473823i	$0.842874\pi$
$168$		0			0
$169$	−7.62977			−0.586906
$170$		0			0
$171$	16.9919	+	9.25206i	1.29941	+	0.707522i
$172$		0			0
$173$	−18.9007	−	10.9123i	−1.43699	−	0.829647i	−0.439352	−	0.898315i	$-0.644792\pi$
$173$	−18.9007	−	10.9123i	−1.43699	−	0.829647i	−0.997640	+	0.0686676i	$0.978125\pi$
$174$		0			0
$175$	0.204775	+	13.2272i	0.0154795	+	0.999880i
$176$		0			0
$177$	−18.4057	+	10.9354i	−1.38345	+	0.821955i
$178$		0			0
$179$	1.11034	−	0.641056i	0.0829909	−	0.0479148i	−0.457930	−	0.888988i	$-0.651409\pi$
$179$	1.11034	−	0.641056i	0.0829909	−	0.0479148i	0.540921	+	0.841073i	$0.318076\pi$
$180$		0			0
$181$			14.5617i			1.08236i	0.840906	+	0.541182i	$0.182023\pi$
$181$			14.5617i			1.08236i	−0.840906	+	0.541182i	$0.817977\pi$
$182$		0			0
$183$	−11.1961	+	19.9642i	−0.827638	+	1.47579i
$184$		0			0
$185$	−5.52693	−	3.00113i	−0.406348	−	0.220647i
$186$		0			0
$187$	−7.88184	+	13.6518i	−0.576377	+	0.998315i
$188$		0			0
$189$	13.7477	−	0.00929051i	1.00000	−	0.000675785i
$190$		0			0
$191$	−20.7027	−	11.9527i	−1.49800	−	0.864869i	−0.498000	−	0.867177i	$-0.665932\pi$
$191$	−20.7027	−	11.9527i	−1.49800	−	0.864869i	−0.999997	+	0.00230818i	$0.999265\pi$
$192$		0			0
$193$	−7.30736	+	4.21891i	−0.525996	+	0.303684i	−0.739384	−	0.673284i	$-0.764883\pi$
$193$	−7.30736	+	4.21891i	−0.525996	+	0.303684i	0.213389	+	0.976967i	$0.431550\pi$
$194$		0			0
$195$	0.346718	+	8.96846i	0.0248290	+	0.642244i
$196$		0			0
$197$	−8.25869			−0.588408			−0.294204	−	0.955743i	$-0.595054\pi$
$197$	−8.25869			−0.588408			−0.294204	+	0.955743i	$0.595054\pi$
$198$		0			0
$199$	8.94051	−	5.16181i	0.633776	−	0.365911i	−0.148437	−	0.988922i	$-0.547424\pi$
$199$	8.94051	−	5.16181i	0.633776	−	0.365911i	0.782213	+	0.623011i	$0.214091\pi$
$200$		0			0
$201$	3.80104	+	6.39763i	0.268105	+	0.451254i
$202$		0			0
$203$	−9.21742	−	0.339448i	−0.646936	−	0.0238245i
$204$		0			0
$205$	2.37839	−	0.0621974i	0.166114	−	0.00434406i
$206$		0			0
$207$	6.98489	−	12.8282i	0.485484	−	0.891619i
$208$		0			0
$209$	−19.5788			−1.35429
$210$		0			0
$211$	−5.75694			−0.396324			−0.198162	−	0.980169i	$-0.563497\pi$
$211$	−5.75694			−0.396324			−0.198162	+	0.980169i	$0.563497\pi$
$212$		0			0
$213$	−12.2670	+	0.153287i	−0.840518	+	0.0105031i
$214$		0			0
$215$	−0.141499	−	5.41083i	−0.00965016	−	0.369016i
$216$		0			0
$217$	1.66657	+	3.14882i	0.113134	+	0.213756i
$218$		0			0
$219$	−0.227301	+	0.135047i	−0.0153596	+	0.00912564i
$220$		0			0
$221$	10.4209	−	6.01649i	0.700983	−	0.404713i
$222$		0			0
$223$	27.0927			1.81426			0.907129	−	0.420852i	$-0.138269\pi$
$223$	27.0927			1.81426			0.907129	+	0.420852i	$0.138269\pi$
$224$		0			0
$225$	−14.9552	+	1.15806i	−0.997015	+	0.0772040i
$226$		0			0
$227$	6.20333	−	3.58150i	0.411730	−	0.237712i	−0.279803	−	0.960057i	$-0.590269\pi$
$227$	6.20333	−	3.58150i	0.411730	−	0.237712i	0.691533	+	0.722345i	$0.256936\pi$
$228$		0			0
$229$	4.16615	+	2.40533i	0.275307	+	0.158949i	0.631297	−	0.775541i	$-0.282523\pi$
$229$	4.16615	+	2.40533i	0.275307	+	0.158949i	−0.355990	+	0.934490i	$0.615856\pi$
$230$		0			0
$231$	−12.2137	+	6.66104i	−0.803605	+	0.438264i
$232$		0			0
$233$	8.90616	−	15.4259i	0.583462	−	1.01059i	−0.411604	−	0.911363i	$-0.635031\pi$
$233$	8.90616	−	15.4259i	0.583462	−	1.01059i	0.995065	−	0.0992223i	$-0.0316355\pi$
$234$		0			0
$235$	7.49317	+	4.06879i	0.488800	+	0.265419i
$236$		0			0
$237$	−9.19905	−	5.15890i	−0.597542	−	0.335107i
$238$		0			0
$239$		−	13.7867i		−	0.891789i	−0.895086	−	0.445894i	$-0.852886\pi$
$239$		−	13.7867i		−	0.891789i	0.895086	−	0.445894i	$-0.147114\pi$
$240$		0			0
$241$	−11.7785	+	6.80032i	−0.758720	+	0.438047i	−0.828836	−	0.559492i	$-0.810996\pi$
$241$	−11.7785	+	6.80032i	−0.758720	+	0.438047i	0.0701158	+	0.997539i	$0.477663\pi$
$242$		0			0
$243$	0.973279	+	15.5580i	0.0624359	+	0.998049i
$244$		0			0
$245$	15.6348	+	0.742824i	0.998873	+	0.0474573i
$246$		0			0
$247$	12.9429	+	7.47258i	0.823536	+	0.475469i
$248$		0			0
$249$	17.7968	−	0.222388i	1.12783	−	0.0140933i
$250$		0			0
$251$	−7.89600			−0.498391			−0.249196	−	0.968453i	$-0.580166\pi$
$251$	−7.89600			−0.498391			−0.249196	+	0.968453i	$0.580166\pi$
$252$		0			0
$253$			14.7811i			0.929280i
$254$		0			0
$255$	10.7205	+	17.0147i	0.671346	+	1.06550i
$256$		0			0
$257$	−15.9997	−	9.23741i	−0.998032	−	0.576214i	−0.0903666	−	0.995909i	$-0.528804\pi$
$257$	−15.9997	−	9.23741i	−0.998032	−	0.576214i	−0.907665	+	0.419695i	$0.862137\pi$
$258$		0			0
$259$	−3.95538	+	6.30320i	−0.245775	+	0.391661i
$260$		0			0
$261$	−0.261341	−	10.4554i	−0.0161766	−	0.647172i
$262$		0			0
$263$	10.7794	+	18.6705i	0.664687	+	1.15127i	0.979370	+	0.202075i	$0.0647686\pi$
$263$	10.7794	+	18.6705i	0.664687	+	1.15127i	−0.314683	+	0.949197i	$0.601898\pi$
$264$		0			0
$265$	−8.24765	−	13.4600i	−0.506649	−	0.826841i
$266$		0			0
$267$	−21.4796	−	12.0459i	−1.31453	−	0.737199i
$268$		0			0
$269$	−7.98483	−	13.8301i	−0.486844	−	0.843238i	0.513042	−	0.858364i	$-0.328519\pi$
$269$	−7.98483	−	13.8301i	−0.486844	−	0.843238i	−0.999886	+	0.0151253i	$0.995185\pi$
$270$		0			0
$271$	−4.72410	−	2.72746i	−0.286968	−	0.165681i	0.349605	−	0.936897i	$-0.386316\pi$
$271$	−4.72410	−	2.72746i	−0.286968	−	0.165681i	−0.636574	+	0.771216i	$0.719649\pi$
$272$		0			0
$273$	10.6164	+	0.258187i	0.642534	+	0.0156262i
$274$		0			0
$275$	12.7310	−	8.26634i	0.767707	−	0.498479i
$276$		0			0
$277$	−6.72315	+	3.88162i	−0.403955	+	0.233224i	−0.688189	−	0.725531i	$-0.741594\pi$
$277$	−6.72315	+	3.88162i	−0.403955	+	0.233224i	0.284234	+	0.958755i	$0.408261\pi$
$278$		0			0
$279$	−3.44689	+	2.10662i	−0.206360	+	0.126120i
$280$		0			0
$281$			0.742571i			0.0442981i	0.999755	+	0.0221490i	$0.00705084\pi$
$281$			0.742571i			0.0442981i	−0.999755	+	0.0221490i	$0.992949\pi$
$282$		0			0
$283$	−4.79525	−	8.30562i	−0.285048	−	0.493718i	0.687573	−	0.726116i	$-0.258676\pi$
$283$	−4.79525	−	8.30562i	−0.285048	−	0.493718i	−0.972621	+	0.232398i	$0.925343\pi$
$284$		0			0
$285$	−11.6438	+	22.0975i	−0.689720	+	1.30894i
$286$		0			0
$287$	0.103601	−	2.81320i	0.00611538	−	0.166058i
$288$		0			0
$289$	4.98104	−	8.62741i	0.293002	−	0.507495i
$290$		0			0
$291$	−0.186827	−	14.9510i	−0.0109520	−	0.876445i
$292$		0			0
$293$		−	0.569685i		−	0.0332814i	−0.999862	−	0.0166407i	$-0.994703\pi$
$293$		−	0.569685i		−	0.0332814i	0.999862	−	0.0166407i	$-0.00529714\pi$
$294$		0			0
$295$	−14.4406	−	23.5667i	−0.840762	−	1.37211i
$296$		0			0
$297$	−8.39383	−	13.3562i	−0.487059	−	0.775003i
$298$		0			0
$299$	5.64147	−	9.77131i	0.326254	−	0.565089i
$300$		0			0
$301$	−6.40003	−	0.235692i	−0.368892	−	0.0135851i
$302$		0			0
$303$	−24.5132	+	14.5641i	−1.40824	+	0.836684i
$304$		0			0
$305$	−25.9685	−	14.1009i	−1.48695	−	0.807417i
$306$		0			0
$307$	9.46424			0.540153			0.270076	−	0.962839i	$-0.412951\pi$
$307$	9.46424			0.540153			0.270076	+	0.962839i	$0.412951\pi$
$308$		0			0
$309$	9.97781	+	5.59564i	0.567618	+	0.318325i
$310$		0			0
$311$	3.25858	+	5.64403i	0.184777	+	0.320044i	0.943501	−	0.331368i	$-0.107510\pi$
$311$	3.25858	+	5.64403i	0.184777	+	0.320044i	−0.758724	+	0.651412i	$0.774177\pi$
$312$		0			0
$313$	−11.0684	+	19.1711i	−0.625626	+	1.08362i	0.362794	+	0.931869i	$0.381823\pi$
$313$	−11.0684	+	19.1711i	−0.625626	+	1.08362i	−0.988420	+	0.151746i	$0.951510\pi$
$314$		0			0
$315$	0.254246	+	17.7464i	0.0143251	+	0.999897i
$316$		0			0
$317$	2.10782	−	3.65086i	0.118387	−	0.205053i	−0.800741	−	0.599010i	$-0.795561\pi$
$317$	2.10782	−	3.65086i	0.118387	−	0.205053i	0.919129	+	0.393957i	$0.128894\pi$
$318$		0			0
$319$	5.29183	+	9.16571i	0.296285	+	0.513181i
$320$		0			0
$321$	27.9981	+	15.7016i	1.56270	+	0.876378i
$322$		0			0
$323$	33.4874			1.86329
$324$		0			0
$325$	−11.5710	+	0.605605i	−0.641846	+	0.0335929i
$326$		0			0
$327$	27.5515	−	16.3693i	1.52360	−	0.905222i
$328$		0			0
$329$	5.36252	−	8.54559i	0.295645	−	0.471133i
$330$		0			0
$331$	12.0041	−	20.7918i	0.659807	−	1.14282i	−0.320858	−	0.947127i	$-0.603971\pi$
$331$	12.0041	−	20.7918i	0.659807	−	1.14282i	0.980665	−	0.195693i	$-0.0626955\pi$
$332$		0			0
$333$	−7.41051	−	4.03500i	−0.406093	−	0.221116i
$334$		0			0
$335$	−8.19156	+	5.01940i	−0.447553	+	0.274239i
$336$		0			0
$337$		−	9.42028i		−	0.513155i	−0.966524	−	0.256578i	$-0.917405\pi$
$337$		−	9.42028i		−	0.513155i	0.966524	−	0.256578i	$-0.0825949\pi$
$338$		0			0
$339$	0.127031	+	10.1658i	0.00689939	+	0.552130i
$340$		0			0
$341$	2.04398	−	3.54027i	0.110688	−	0.191716i
$342$		0			0
$343$	2.04104	−	18.4074i	0.110206	−	0.993909i
$344$		0			0
$345$	16.6826	+	8.79057i	0.898163	+	0.473268i
$346$		0			0
$347$	11.1961	+	19.3922i	0.601037	+	1.04103i	0.992664	+	0.120903i	$0.0385789\pi$
$347$	11.1961	+	19.3922i	0.601037	+	1.04103i	−0.391627	+	0.920124i	$0.628088\pi$
$348$		0			0
$349$			12.0663i			0.645895i	0.946417	+	0.322948i	$0.104674\pi$
$349$			12.0663i			0.645895i	−0.946417	+	0.322948i	$0.895326\pi$
$350$		0			0
$351$	0.451278	+	12.0330i	0.0240875	+	0.642273i
$352$		0			0
$353$	7.19515	−	4.15412i	0.382959	−	0.221102i	−0.296146	−	0.955143i	$-0.595701\pi$
$353$	7.19515	−	4.15412i	0.382959	−	0.221102i	0.679105	+	0.734041i	$0.262368\pi$
$354$		0			0
$355$	−0.414034	−	15.8324i	−0.0219747	−	0.840296i
$356$		0			0
$357$	20.8903	−	11.3930i	1.10563	−	0.602981i
$358$		0			0
$359$	−6.27295	−	3.62169i	−0.331074	−	0.191145i	0.325244	−	0.945630i	$-0.394554\pi$
$359$	−6.27295	−	3.62169i	−0.331074	−	0.191145i	−0.656318	+	0.754485i	$0.727887\pi$
$360$		0			0
$361$	11.2959	+	19.5651i	0.594522	+	1.02974i
$362$		0			0
$363$	−2.69447	−	1.51108i	−0.141423	−	0.0793111i
$364$		0			0
$365$	−0.178334	−	0.291038i	−0.00933444	−	0.0152336i
$366$		0			0
$367$	−0.624486	−	1.08164i	−0.0325979	−	0.0564612i	0.849266	−	0.527965i	$-0.177045\pi$
$367$	−0.624486	−	1.08164i	−0.0325979	−	0.0564612i	−0.881864	+	0.471504i	$0.843711\pi$
$368$		0			0
$369$	3.19104	−	0.0797625i	0.166119	−	0.00415227i
$370$		0			0
$371$	−16.5085	+	8.73745i	−0.857078	+	0.453626i
$372$		0			0
$373$	−26.7505	−	15.4444i	−1.38509	−	0.799682i	−0.392334	−	0.919823i	$-0.628332\pi$
$373$	−26.7505	−	15.4444i	−1.38509	−	0.799682i	−0.992757	+	0.120141i	$0.961665\pi$
$374$		0			0
$375$	−1.75844	−	19.2849i	−0.0908054	−	0.995869i
$376$		0			0
$377$		−	8.07888i		−	0.416083i
$378$		0			0
$379$	29.6463			1.52283			0.761413	−	0.648267i	$-0.224506\pi$
$379$	29.6463			1.52283			0.761413	+	0.648267i	$0.224506\pi$
$380$		0			0
$381$	−25.2680	+	0.315748i	−1.29452	+	0.0161763i
$382$		0			0
$383$	18.1740	+	10.4927i	0.928646	+	0.536154i	0.886383	−	0.462952i	$-0.153210\pi$
$383$	18.1740	+	10.4927i	0.928646	+	0.536154i	0.0422631	+	0.999107i	$0.486543\pi$
$384$		0			0
$385$	−8.81379	−	15.6490i	−0.449192	−	0.797548i
$386$		0			0
$387$	−0.181460	−	7.25961i	−0.00922412	−	0.369027i
$388$		0			0
$389$	−14.2540	+	8.22952i	−0.722704	+	0.417253i	−0.815747	−	0.578409i	$-0.803674\pi$
$389$	−14.2540	+	8.22952i	−0.722704	+	0.417253i	0.0930430	+	0.995662i	$0.470341\pi$
$390$		0			0
$391$		−	25.2815i		−	1.27854i
$392$		0			0
$393$	30.3217	+	17.0047i	1.52953	+	0.857772i
$394$		0			0
$395$	6.49740	−	11.9657i	0.326919	−	0.602061i
$396$		0			0
$397$	−2.04631	+	3.54432i	−0.102702	+	0.177884i	−0.912797	−	0.408414i	$-0.866082\pi$
$397$	−2.04631	+	3.54432i	−0.102702	+	0.177884i	0.810095	+	0.586298i	$0.199415\pi$
$398$		0			0
$399$	25.2275	+	15.3948i	1.26296	+	0.770704i
$400$		0			0
$401$	22.5314	+	13.0085i	1.12516	+	0.649613i	0.942714	−	0.333602i	$-0.108264\pi$
$401$	22.5314	+	13.0085i	1.12516	+	0.649613i	0.182449	+	0.983215i	$0.441598\pi$
$402$		0			0
$403$	−2.70241	+	1.56024i	−0.134617	+	0.0777210i
$404$		0			0
$405$	−20.0663	+	1.53053i	−0.997104	+	0.0760528i
$406$		0			0
$407$	8.53866			0.423246
$408$		0			0
$409$	30.5083	−	17.6140i	1.50854	−	0.870955i	0.508587	−	0.861010i	$-0.330168\pi$
$409$	30.5083	−	17.6140i	1.50854	−	0.870955i	0.999951	−	0.00994431i	$-0.00316542\pi$
$410$		0			0
$411$	−6.95490	+	4.13214i	−0.343060	+	0.203823i
$412$		0			0
$413$	−28.9042	+	15.2981i	−1.42228	+	0.752772i
$414$		0			0
$415$	0.600678	+	22.9695i	0.0294861	+	1.12753i
$416$		0			0
$417$	−9.54798	+	0.119311i	−0.467566	+	0.00584269i
$418$		0			0
$419$	40.3278			1.97014			0.985072	−	0.172146i	$-0.0550700\pi$
$419$	40.3278			1.97014			0.985072	+	0.172146i	$0.0550700\pi$
$420$		0			0
$421$	0.216416			0.0105475			0.00527375	−	0.999986i	$-0.498321\pi$
$421$	0.216416			0.0105475			0.00527375	+	0.999986i	$0.498321\pi$
$422$		0			0
$423$	10.0468	+	5.47046i	0.488493	+	0.265983i
$424$		0			0
$425$	−21.7750	+	14.1387i	−1.05624	+	0.685827i
$426$		0			0
$427$	−18.5845	+	29.6158i	−0.899367	+	1.43321i
$428$		0			0
$429$	−6.22406	−	10.4759i	−0.300500	−	0.505780i
$430$		0			0
$431$	−25.3179	+	14.6173i	−1.21952	+	0.704090i	−0.964815	−	0.262928i	$-0.915312\pi$
$431$	−25.3179	+	14.6173i	−1.21952	+	0.704090i	−0.254705	+	0.967019i	$0.581978\pi$
$432$		0			0
$433$	19.8669			0.954743			0.477371	−	0.878702i	$-0.341590\pi$
$433$	19.8669			0.954743			0.477371	+	0.878702i	$0.341590\pi$
$434$		0			0
$435$	13.4920	−	0.521596i	0.646891	−	0.0250086i
$436$		0			0
$437$	27.1932	−	15.7000i	1.30083	−	0.751033i
$438$		0			0
$439$	19.0134	+	10.9774i	0.907459	+	0.523921i	0.879613	−	0.475691i	$-0.157802\pi$
$439$	19.0134	+	10.9774i	0.907459	+	0.523921i	0.0278460	+	0.999612i	$0.491135\pi$
$440$		0			0
$441$	20.9752	+	1.02082i	0.998818	+	0.0486105i
$442$		0			0
$443$	4.36391	−	7.55852i	0.207336	−	0.359116i	−0.743539	−	0.668693i	$-0.766854\pi$
$443$	4.36391	−	7.55852i	0.207336	−	0.359116i	0.950874	+	0.309577i	$0.100187\pi$
$444$		0			0
$445$	15.1713	−	27.9397i	0.719188	−	1.32447i
$446$		0			0
$447$	−12.3830	+	22.0806i	−0.585696	+	1.04438i
$448$		0			0
$449$			1.03244i			0.0487238i	0.999703	+	0.0243619i	$0.00775540\pi$
$449$			1.03244i			0.0487238i	−0.999703	+	0.0243619i	$0.992245\pi$
$450$		0			0
$451$	−2.79742	+	1.61509i	−0.131725	+	0.0760517i
$452$		0			0
$453$	13.3451	−	7.92875i	0.627007	−	0.372525i
$454$		0			0
$455$	−0.146212	+	13.7090i	−0.00685452	+	0.642688i
$456$		0			0
$457$	27.2085	+	15.7088i	1.27276	+	0.734828i	0.975506	−	0.219971i	$-0.0705963\pi$
$457$	27.2085	+	15.7088i	1.27276	+	0.734828i	0.297253	+	0.954799i	$0.403930\pi$
$458$		0			0
$459$	14.3567	+	22.8443i	0.670115	+	1.06628i
$460$		0			0
$461$	3.22290			0.150105			0.0750526	−	0.997180i	$-0.476088\pi$
$461$	3.22290			0.150105			0.0750526	+	0.997180i	$0.476088\pi$
$462$		0			0
$463$			5.06917i			0.235584i	0.993038	+	0.117792i	$0.0375817\pi$
$463$			5.06917i			0.235584i	−0.993038	+	0.117792i	$0.962418\pi$
$464$		0			0
$465$	−2.78013	−	4.41238i	−0.128925	−	0.204619i
$466$		0			0
$467$	−7.81525	−	4.51214i	−0.361647	−	0.208797i	0.308156	−	0.951336i	$-0.400288\pi$
$467$	−7.81525	−	4.51214i	−0.361647	−	0.208797i	−0.669803	+	0.742539i	$0.733621\pi$
$468$		0			0
$469$	5.31749	+	10.0468i	0.245539	+	0.463920i
$470$		0			0
$471$	−30.5861	+	18.1722i	−1.40933	+	0.837332i
$472$		0			0
$473$	3.67433	+	6.36413i	0.168946	+	0.292623i
$474$		0			0
$475$	−28.7303	−	14.6413i	−1.31823	−	0.671790i
$476$		0			0
$477$	−11.0445	−	18.0712i	−0.505694	−	0.827425i
$478$		0			0
$479$	−1.26094	−	2.18401i	−0.0576137	−	0.0997899i	0.835780	−	0.549064i	$-0.185016\pi$
$479$	−1.26094	−	2.18401i	−0.0576137	−	0.0997899i	−0.893394	+	0.449275i	$0.851683\pi$
$480$		0			0
$481$	−5.64464	−	3.25893i	−0.257373	−	0.148594i
$482$		0			0
$483$	11.6224	−	19.0457i	0.528837	−	0.866608i
$484$		0			0
$485$	19.2966	−	0.504628i	0.876214	−	0.0229140i
$486$		0			0
$487$	−2.12791	+	1.22855i	−0.0964247	+	0.0556709i	−0.547437	−	0.836847i	$-0.684396\pi$
$487$	−2.12791	+	1.22855i	−0.0964247	+	0.0556709i	0.451012	+	0.892518i	$0.351063\pi$
$488$		0			0
$489$	16.9873	−	30.2908i	0.768194	−	1.36980i
$490$		0			0
$491$			14.3239i			0.646429i	0.946326	+	0.323215i	$0.104764\pi$
$491$			14.3239i			0.646429i	−0.946326	+	0.323215i	$0.895236\pi$
$492$		0			0
$493$	−9.05110	−	15.6770i	−0.407641	−	0.706055i
$494$		0			0
$495$	17.0932	−	11.0707i	0.768282	−	0.497592i
$496$		0			0
$497$	−18.7268	−	0.689649i	−0.840014	−	0.0309350i
$498$		0			0
$499$	−19.8770	+	34.4279i	−0.889816	+	1.54121i	−0.0497229	+	0.998763i	$0.515834\pi$
$499$	−19.8770	+	34.4279i	−0.889816	+	1.54121i	−0.840093	+	0.542443i	$0.817500\pi$
$500$		0			0
$501$	−21.2095	+	0.265033i	−0.947572	+	0.0118408i
$502$		0			0
$503$		−	10.6486i		−	0.474796i	−0.971412	−	0.237398i	$-0.923705\pi$
$503$		−	10.6486i		−	0.474796i	0.971412	−	0.237398i	$-0.0762946\pi$
$504$		0			0
$505$	−19.2323	−	31.3868i	−0.855828	−	1.39669i
$506$		0			0
$507$	−0.165123	−	13.2141i	−0.00733337	−	0.586860i
$508$		0			0
$509$	18.5593	−	32.1456i	0.822626	−	1.42483i	−0.0810950	−	0.996706i	$-0.525842\pi$
$509$	18.5593	−	32.1456i	0.822626	−	1.42483i	0.903721	−	0.428123i	$-0.140825\pi$
$510$		0			0
$511$	−0.356954	+	0.188925i	−0.0157907	+	0.00835755i
$512$		0			0
$513$	−15.6560	+	29.6288i	−0.691231	+	1.30815i
$514$		0			0
$515$	−7.04744	+	12.9787i	−0.310547	+	0.571910i
$516$		0			0
$517$	−11.5763			−0.509127
$518$		0			0
$519$	18.4901	−	32.9705i	0.811627	−	1.44725i
$520$		0			0
$521$	−8.12000	−	14.0642i	−0.355744	−	0.616166i	0.631501	−	0.775375i	$-0.282439\pi$
$521$	−8.12000	−	14.0642i	−0.355744	−	0.616166i	−0.987245	+	0.159209i	$0.949106\pi$
$522$		0			0
$523$	8.87476	−	15.3715i	0.388066	−	0.672150i	−0.604123	−	0.796891i	$-0.706477\pi$
$523$	8.87476	−	15.3715i	0.388066	−	0.672150i	0.992189	+	0.124741i	$0.0398099\pi$
$524$		0			0
$525$	−22.9039	+	0.640914i	−0.999609	+	0.0279718i
$526$		0			0
$527$	−3.49600	+	6.05525i	−0.152288	+	0.263771i
$528$		0			0
$529$	−0.352809	−	0.611082i	−0.0153395	−	0.0265688i
$530$		0			0
$531$	−19.3375	−	31.6404i	−0.839177	−	1.37308i
$532$		0			0
$533$	2.46571			0.106802
$534$		0			0
$535$	−19.7754	+	36.4188i	−0.854966	+	1.57452i
$536$		0			0
$537$	1.13429	+	1.90914i	0.0489480	+	0.0823857i
$538$		0			0
$539$	−19.1356	+	9.24304i	−0.824228	+	0.398126i
$540$		0			0
$541$	−0.167695	+	0.290456i	−0.00720976	+	0.0124877i	−0.869608	−	0.493743i	$-0.835628\pi$
$541$	−0.167695	+	0.290456i	−0.00720976	+	0.0124877i	0.862398	+	0.506231i	$0.168962\pi$
$542$		0			0
$543$	−25.2197	+	0.315144i	−1.08228	+	0.0135241i
$544$		0			0
$545$	21.6161	+	35.2771i	0.925934	+	1.51110i
$546$		0			0
$547$		−	11.7041i		−	0.500433i	−0.968190	−	0.250216i	$-0.919498\pi$
$547$		−	11.7041i		−	0.500433i	0.968190	−	0.250216i	$-0.0805018\pi$
$548$		0			0
$549$	−34.8186	−	18.9586i	−1.48602	−	0.809133i
$550$		0			0
$551$	11.2416	−	19.4710i	0.478909	−	0.829495i
$552$		0			0
$553$	−13.6463	−	8.56333i	−0.580300	−	0.364150i
$554$		0			0
$555$	5.07809	−	9.63713i	0.215553	−	0.409073i
$556$		0			0
$557$	−2.55833	−	4.43115i	−0.108400	−	0.187754i	0.806722	−	0.590931i	$-0.201239\pi$
$557$	−2.55833	−	4.43115i	−0.108400	−	0.187754i	−0.915122	+	0.403177i	$0.867906\pi$
$558$		0			0
$559$		−	5.60950i		−	0.237256i
$560$		0			0
$561$	−23.8143	−	13.3552i	−1.00544	−	0.563858i
$562$		0			0
$563$	−16.8089	+	9.70464i	−0.708412	+	0.409002i	−0.810473	−	0.585776i	$-0.800790\pi$
$563$	−16.8089	+	9.70464i	−0.708412	+	0.409002i	0.102061	+	0.994778i	$0.467456\pi$
$564$		0			0
$565$	−13.1205	+	0.343116i	−0.551984	+	0.0144350i
$566$		0			0
$567$	0.313618	+	23.8097i	0.0131707	+	0.999913i
$568$		0			0
$569$	20.1553	+	11.6367i	0.844954	+	0.487834i	0.858945	−	0.512068i	$-0.171120\pi$
$569$	20.1553	+	11.6367i	0.844954	+	0.487834i	−0.0139912	+	0.999902i	$0.504454\pi$
$570$		0			0
$571$	7.04462	+	12.2016i	0.294808	+	0.510623i	0.974940	−	0.222467i	$-0.0714109\pi$
$571$	7.04462	+	12.2016i	0.294808	+	0.510623i	−0.680132	+	0.733090i	$0.738078\pi$
$572$		0			0
$573$	20.2531	−	36.1141i	0.846084	−	1.50869i
$574$		0			0
$575$	−11.0535	+	21.6901i	−0.460965	+	0.904539i
$576$		0			0
$577$	11.0816	+	19.1938i	0.461332	+	0.799050i	0.999028	−	0.0440886i	$-0.0140384\pi$
$577$	11.0816	+	19.1938i	0.461332	+	0.799050i	−0.537696	+	0.843139i	$0.680705\pi$
$578$		0			0
$579$	−7.46494	−	12.5644i	−0.310232	−	0.522160i
$580$		0			0
$581$	27.1688	+	1.00054i	1.12715	+	0.0415093i
$582$		0			0
$583$	18.5608	+	10.7161i	0.768709	+	0.443815i
$584$		0			0
$585$	−15.5251	+	0.794580i	−0.641884	+	0.0328518i
$586$		0			0
$587$			11.5459i			0.476550i	0.971198	+	0.238275i	$0.0765819\pi$
$587$			11.5459i			0.476550i	−0.971198	+	0.238275i	$0.923418\pi$
$588$		0			0
$589$	−8.68418			−0.357825
$590$		0			0
$591$	−0.178734	−	14.3034i	−0.00735214	−	0.588362i
$592$		0			0
$593$	−18.5778	−	10.7259i	−0.762901	−	0.440461i	0.0674357	−	0.997724i	$-0.478518\pi$
$593$	−18.5778	−	10.7259i	−0.762901	−	0.440461i	−0.830336	+	0.557263i	$0.811852\pi$
$594$		0			0
$595$	15.0750	+	26.7660i	0.618016	+	1.09730i
$596$		0			0
$597$	9.13331	+	15.3725i	0.373801	+	0.629155i
$598$		0			0
$599$	−3.19001	+	1.84175i	−0.130340	+	0.0752519i	−0.563752	−	0.825944i	$-0.690643\pi$
$599$	−3.19001	+	1.84175i	−0.130340	+	0.0752519i	0.433412	+	0.901196i	$0.357309\pi$
$600$		0			0
$601$		−	8.20607i		−	0.334733i	−0.985895	−	0.167366i	$-0.946474\pi$
$601$		−	8.20607i		−	0.334733i	0.985895	−	0.167366i	$-0.0535263\pi$
$602$		0			0
$603$	−10.9979	+	6.72154i	−0.447869	+	0.273722i
$604$		0			0
$605$	1.90313	−	3.50484i	0.0773734	−	0.142492i
$606$		0			0
$607$	3.52607	−	6.10733i	0.143119	−	0.247889i	−0.785551	−	0.618797i	$-0.787620\pi$
$607$	3.52607	−	6.10733i	0.143119	−	0.247889i	0.928670	+	0.370908i	$0.120954\pi$
$608$		0			0
$609$	0.388412	−	15.9711i	0.0157392	−	0.647183i
$610$		0			0
$611$	7.65274	+	4.41831i	0.309597	+	0.178746i
$612$		0			0
$613$	−17.0882	+	9.86586i	−0.690185	+	0.398478i	−0.803681	−	0.595060i	$-0.797128\pi$
$613$	−17.0882	+	9.86586i	−0.690185	+	0.398478i	0.113496	+	0.993538i	$0.463795\pi$
$614$		0			0
$615$	0.159194	+	4.11782i	0.00641930	+	0.166047i
$616$		0			0
$617$	7.15802			0.288171			0.144086	−	0.989565i	$-0.453976\pi$
$617$	7.15802			0.288171			0.144086	+	0.989565i	$0.453976\pi$
$618$		0			0
$619$	−8.50675	+	4.91137i	−0.341915	+	0.197405i	−0.661119	−	0.750281i	$-0.729918\pi$
$619$	−8.50675	+	4.91137i	−0.341915	+	0.197405i	0.319204	+	0.947686i	$0.396585\pi$
$620$		0			0
$621$	22.3685	+	11.8196i	0.897616	+	0.474305i
$622$		0			0
$623$	−31.8639	−	19.9952i	−1.27660	−	0.801090i
$624$		0			0
$625$	24.8634	−	2.60975i	0.994536	−	0.104390i
$626$		0			0
$627$	−0.423722	−	33.9088i	−0.0169218	−	1.35419i
$628$		0			0
$629$	−14.6045			−0.582318
$630$		0			0
$631$	−13.2595			−0.527854			−0.263927	−	0.964543i	$-0.585018\pi$
$631$	−13.2595			−0.527854			−0.263927	+	0.964543i	$0.585018\pi$
$632$		0			0
$633$	−0.124591	−	9.97054i	−0.00495206	−	0.396293i
$634$		0			0
$635$	−0.852847	−	32.6123i	−0.0338442	−	1.29418i
$636$		0			0
$637$	16.1777	+	1.19316i	0.640983	+	0.0472748i
$638$		0			0
$639$	−0.530961	−	21.2420i	−0.0210045	−	0.840321i
$640$		0			0
$641$	−24.8302	+	14.3357i	−0.980734	+	0.566227i	−0.902492	−	0.430707i	$-0.858264\pi$
$641$	−24.8302	+	14.3357i	−0.980734	+	0.566227i	−0.0782423	+	0.996934i	$0.524931\pi$
$642$		0			0
$643$	38.1006			1.50254			0.751271	−	0.659994i	$-0.229441\pi$
$643$	38.1006			1.50254			0.751271	+	0.659994i	$0.229441\pi$
$644$		0			0
$645$	9.36804	−	0.362166i	0.368866	−	0.0142603i
$646$		0			0
$647$	−33.4126	+	19.2908i	−1.31359	+	0.758399i	−0.982688	−	0.185268i	$-0.940685\pi$
$647$	−33.4126	+	19.2908i	−1.31359	+	0.758399i	−0.330897	+	0.943667i	$0.607351\pi$
$648$		0			0
$649$	32.4975	+	18.7625i	1.27564	+	0.736491i
$650$		0			0
$651$	−5.41742	+	2.95451i	−0.212325	+	0.115796i
$652$		0			0
$653$	−21.2942	+	36.8826i	−0.833306	+	1.44333i	0.0620956	+	0.998070i	$0.480222\pi$
$653$	−21.2942	+	36.8826i	−0.833306	+	1.44333i	−0.895402	+	0.445259i	$0.853112\pi$
$654$		0			0
$655$	−21.4166	+	39.4412i	−0.836815	+	1.54109i
$656$		0			0
$657$	−0.238810	−	0.390744i	−0.00931685	−	0.0152444i
$658$		0			0
$659$			13.0441i			0.508128i	0.967187	+	0.254064i	$0.0817674\pi$
$659$			13.0441i			0.508128i	−0.967187	+	0.254064i	$0.918233\pi$
$660$		0			0
$661$	−12.9159	+	7.45701i	−0.502371	+	0.290044i	−0.729692	−	0.683776i	$-0.760337\pi$
$661$	−12.9159	+	7.45701i	−0.502371	+	0.290044i	0.227321	+	0.973820i	$0.427003\pi$
$662$		0			0
$663$	10.6456	+	17.9178i	0.413440	+	0.695871i
$664$		0			0
$665$	−19.4282	+	32.8369i	−0.753394	+	1.27336i
$666$		0			0
$667$	−14.6998	−	8.48692i	−0.569178	−	0.328615i
$668$		0			0
$669$	0.586337	+	46.9222i	0.0226691	+	1.81412i
$670$		0			0
$671$	40.1193			1.54879
$672$		0			0
$673$			51.0490i			1.96780i	0.178732	+	0.983898i	$0.442801\pi$
$673$			51.0490i			1.96780i	−0.178732	+	0.983898i	$0.557199\pi$
$674$		0			0
$675$	−2.32932	−	25.8761i	−0.0896556	−	0.995973i
$676$		0			0
$677$	0.281190	+	0.162345i	0.0108070	+	0.00623942i	0.505394	−	0.862889i	$-0.331347\pi$
$677$	0.281190	+	0.162345i	0.0108070	+	0.00623942i	−0.494587	+	0.869128i	$0.664681\pi$
$678$		0			0
$679$	0.840548	−	22.8244i	0.0322573	−	0.875920i
$680$		0			0
$681$	6.33710	+	10.6661i	0.242838	+	0.408727i
$682$		0			0
$683$	−14.8704	−	25.7563i	−0.569001	−	0.985538i	−0.996665	−	0.0816004i	$-0.973997\pi$
$683$	−14.8704	−	25.7563i	−0.569001	−	0.985538i	0.427665	−	0.903938i	$-0.359336\pi$
$684$		0			0
$685$	−5.45662	−	8.90509i	−0.208487	−	0.340246i
$686$		0			0
$687$	−4.07566	+	7.26748i	−0.155496	+	0.277272i
$688$		0			0
$689$	−8.17996	−	14.1681i	−0.311632	−	0.539762i
$690$		0			0
$691$	−25.2719	−	14.5907i	−0.961388	−	0.555058i	−0.0647879	−	0.997899i	$-0.520637\pi$
$691$	−25.2719	−	14.5907i	−0.961388	−	0.555058i	−0.896600	+	0.442842i	$0.853970\pi$
$692$		0			0
$693$	−11.8007	−	21.0090i	−0.448271	−	0.798066i
$694$		0			0
$695$	−0.322263	−	12.3231i	−0.0122241	−	0.467443i
$696$		0			0
$697$	4.78468	−	2.76244i	0.181233	−	0.104635i
$698$		0			0
$699$	26.9091	+	15.0909i	1.01780	+	0.570789i
$700$		0			0
$701$		−	4.22879i		−	0.159719i	−0.996806	−	0.0798596i	$-0.974553\pi$
$701$		−	4.22879i		−	0.159719i	0.996806	−	0.0798596i	$-0.0254472\pi$
$702$		0			0
$703$	−9.06949	−	15.7088i	−0.342062	−	0.592470i
$704$		0			0
$705$	−6.88464	+	13.0656i	−0.259291	+	0.492078i
$706$		0			0
$707$	−38.4954	+	20.3745i	−1.44777	+	0.766261i
$708$		0			0
$709$	13.9852	−	24.2230i	0.525225	−	0.909716i	−0.474344	−	0.880340i	$-0.657315\pi$
$709$	13.9852	−	24.2230i	0.525225	−	0.909716i	0.999568	−	0.0293760i	$-0.00935203\pi$
$710$		0			0
$711$	8.73570	−	16.0436i	0.327614	−	0.601683i
$712$		0			0
$713$			6.55617i			0.245531i
$714$		0			0
$715$	13.4134	−	8.21907i	0.501631	−	0.307376i
$716$		0			0
$717$	23.8774	−	0.298371i	0.891719	−	0.0111429i
$718$		0			0
$719$	2.81744	−	4.87995i	0.105073	−	0.181991i	−0.808695	−	0.588228i	$-0.799826\pi$
$719$	2.81744	−	4.87995i	0.105073	−	0.181991i	0.913768	+	0.406237i	$0.133159\pi$
$720$		0			0
$721$	14.8016	+	9.28827i	0.551239	+	0.345913i
$722$		0			0
$723$	−12.0325	−	20.2522i	−0.447493	−	0.753188i
$724$		0			0
$725$	0.911061	+	17.4073i	0.0338360	+	0.646490i
$726$		0			0
$727$	−36.1095			−1.33923			−0.669613	−	0.742710i	$-0.733540\pi$
$727$	−36.1095			−1.33923			−0.669613	+	0.742710i	$0.733540\pi$
$728$		0			0
$729$	−26.9242	+	2.02234i	−0.997191	+	0.0749016i
$730$		0			0
$731$	−6.28455	−	10.8852i	−0.232443	−	0.402602i
$732$		0			0
$733$	−2.99103	+	5.18062i	−0.110476	+	0.191351i	−0.915962	−	0.401264i	$-0.868571\pi$
$733$	−2.99103	+	5.18062i	−0.110476	+	0.191351i	0.805486	+	0.592615i	$0.201904\pi$
$734$		0			0
$735$	−0.948140	+	27.0943i	−0.0349727	+	0.999388i
$736$		0			0
$737$	6.52165	−	11.2958i	0.240228	−	0.416087i
$738$		0			0
$739$	−19.1257	−	33.1266i	−0.703549	−	1.21858i	−0.967213	−	0.253968i	$-0.918264\pi$
$739$	−19.1257	−	33.1266i	−0.703549	−	1.21858i	0.263663	−	0.964615i	$-0.415069\pi$
$740$		0			0
$741$	−12.6618	+	22.5777i	−0.465142	+	0.829413i
$742$		0			0
$743$	−3.60215			−0.132150			−0.0660750	−	0.997815i	$-0.521048\pi$
$743$	−3.60215			−0.132150			−0.0660750	+	0.997815i	$0.521048\pi$
$744$		0			0
$745$	−28.7215	−	15.5958i	−1.05228	−	0.571386i
$746$		0			0
$747$	0.770315	+	30.8178i	0.0281843	+	1.12756i
$748$		0			0
$749$	41.5338	+	26.0633i	1.51761	+	0.952331i
$750$		0			0
$751$	2.07691	−	3.59731i	0.0757874	−	0.131268i	−0.825641	−	0.564196i	$-0.809186\pi$
$751$	2.07691	−	3.59731i	0.0757874	−	0.131268i	0.901428	+	0.432928i	$0.142520\pi$
$752$		0			0
$753$	−0.170885	−	13.6752i	−0.00622738	−	0.498352i
$754$		0			0
$755$	10.4702	+	17.0871i	0.381049	+	0.621864i
$756$		0			0
$757$		−	15.4535i		−	0.561668i	−0.959756	−	0.280834i	$-0.909389\pi$
$757$		−	15.4535i		−	0.561668i	0.959756	−	0.280834i	$-0.0906110\pi$
$758$		0			0
$759$	−25.5996	+	0.319891i	−0.929207	+	0.0116113i
$760$		0			0
$761$	−14.2676	+	24.7122i	−0.517199	+	0.895816i	0.482601	+	0.875840i	$0.339692\pi$
$761$	−14.2676	+	24.7122i	−0.517199	+	0.895816i	−0.999800	+	0.0199755i	$0.993641\pi$
$762$		0			0
$763$	43.2669	−	22.8999i	1.56637	−	0.829031i
$764$		0			0
$765$	−29.2361	+	18.9353i	−1.05703	+	0.684607i
$766$		0			0
$767$	−14.3220	−	24.8065i	−0.517139	−	0.895711i
$768$		0			0
$769$			19.5067i			0.703431i	0.936107	+	0.351716i	$0.114402\pi$
$769$			19.5067i			0.703431i	−0.936107	+	0.351716i	$0.885598\pi$
$770$		0			0
$771$	15.6522	−	27.9100i	0.563699	−	1.00515i
$772$		0			0
$773$	18.2685	−	10.5473i	0.657074	−	0.379362i	−0.134087	−	0.990970i	$-0.542810\pi$
$773$	18.2685	−	10.5473i	0.657074	−	0.379362i	0.791161	+	0.611608i	$0.209477\pi$
$774$		0			0
$775$	5.64684	−	3.66654i	0.202841	−	0.131706i
$776$		0			0
$777$	−11.0022	−	6.71396i	−0.394702	−	0.240862i
$778$		0			0
$779$	5.94266	+	3.43100i	0.212918	+	0.122928i
$780$		0			0
$781$	10.7513	+	18.6218i	0.384712	+	0.666340i
$782$		0			0
$783$	18.1022	−	0.678895i	0.646920	−	0.0242617i
$784$		0			0
$785$	−23.9970	−	39.1626i	−0.856490	−	1.39777i
$786$		0			0
$787$	−2.60421	−	4.51062i	−0.0928301	−	0.160786i	0.815871	−	0.578234i	$-0.196258\pi$
$787$	−2.60421	−	4.51062i	−0.0928301	−	0.160786i	−0.908701	+	0.417448i	$0.862925\pi$
$788$		0			0
$789$	−32.1024	+	19.0731i	−1.14288	+	0.679021i
$790$		0			0
$791$	−0.571521	+	15.5192i	−0.0203210	+	0.551799i
$792$		0			0
$793$	−26.5216	−	15.3122i	−0.941808	−	0.543753i
$794$		0			0
$795$	23.1331	−	14.5755i	0.820446	−	0.516941i
$796$		0			0
$797$			41.1247i			1.45671i	0.685199	+	0.728356i	$0.259715\pi$
$797$			41.1247i			1.45671i	−0.685199	+	0.728356i	$0.740285\pi$
$798$		0			0
$799$	19.8001			0.700476
$800$		0			0
$801$	20.3977	−	37.4615i	0.720717	−	1.32364i
$802$		0			0
$803$	0.401329	+	0.231708i	0.0141626	+	0.00817679i
$804$		0			0
$805$	24.7904	+	14.6674i	0.873746	+	0.516960i
$806$		0			0
$807$	23.7798	−	14.1284i	0.837089	−	0.497342i
$808$		0			0
$809$	−8.18379	+	4.72491i	−0.287727	+	0.166119i	−0.636916	−	0.770933i	$-0.719790\pi$
$809$	−8.18379	+	4.72491i	−0.287727	+	0.166119i	0.349190	+	0.937052i	$0.386457\pi$
$810$		0			0
$811$		−	13.1110i		−	0.460388i	−0.973145	−	0.230194i	$-0.926064\pi$
$811$		−	13.1110i		−	0.460388i	0.973145	−	0.230194i	$-0.0739361\pi$
$812$		0			0
$813$	4.62149	−	8.24076i	0.162083	−	0.289016i
$814$		0			0
$815$	39.4010	+	21.3948i	1.38016	+	0.749426i
$816$		0			0
$817$	7.80552	−	13.5196i	0.273081	−	0.472989i
$818$		0			0
$819$	−0.217398	+	18.3923i	−0.00759651	+	0.642679i
$820$		0			0
$821$	24.7530	+	14.2911i	0.863885	+	0.498764i	0.865311	−	0.501235i	$-0.167121\pi$
$821$	24.7530	+	14.2911i	0.863885	+	0.498764i	−0.00142663	+	0.999999i	$0.500454\pi$
$822$		0			0
$823$	−21.4406	+	12.3787i	−0.747371	+	0.431495i	−0.824743	−	0.565508i	$-0.808680\pi$
$823$	−21.4406	+	12.3787i	−0.747371	+	0.431495i	0.0773725	+	0.997002i	$0.475347\pi$
$824$		0			0
$825$	14.5921	+	21.8701i	0.508033	+	0.761419i
$826$		0			0
$827$	35.9582			1.25039			0.625194	−	0.780470i	$-0.285020\pi$
$827$	35.9582			1.25039			0.625194	+	0.780470i	$0.285020\pi$
$828$		0			0
$829$	−12.8068	+	7.39399i	−0.444798	+	0.256804i	−0.705631	−	0.708580i	$-0.749336\pi$
$829$	−12.8068	+	7.39399i	−0.444798	+	0.256804i	0.260833	+	0.965384i	$0.416003\pi$
$830$		0			0
$831$	−6.86813	−	11.5599i	−0.238253	−	0.401010i
$832$		0			0
$833$	32.7294	−	15.8092i	1.13400	−	0.547757i
$834$		0			0
$835$	−0.715864	−	27.3742i	−0.0247735	−	0.947322i
$836$		0			0
$837$	−3.72309	−	5.92414i	−0.128689	−	0.204768i
$838$		0			0
$839$	−0.979006			−0.0337991			−0.0168995	−	0.999857i	$-0.505380\pi$
$839$	−0.979006			−0.0337991			−0.0168995	+	0.999857i	$0.505380\pi$
$840$		0			0
$841$	16.8463			0.580906
$842$		0			0
$843$	−1.28607	+	0.0160707i	−0.0442946	+	0.000553504i
$844$		0			0
$845$	17.0549	−	0.446003i	0.586705	−	0.0153430i
$846$		0			0
$847$	−3.99710	−	2.50826i	−0.137342	−	0.0861848i
$848$		0			0
$849$	14.2809	−	8.48472i	0.490118	−	0.291195i
$850$		0			0
$851$	−11.8595	+	6.84707i	−0.406537	+	0.234714i
$852$		0			0
$853$	31.6889			1.08501			0.542504	−	0.840053i	$-0.317476\pi$
$853$	31.6889			1.08501			0.542504	+	0.840053i	$0.317476\pi$
$854$		0			0
$855$	−38.5230	−	19.6879i	−1.31746	−	0.673311i
$856$		0			0
$857$	28.0280	−	16.1820i	0.957419	−	0.552766i	0.0620413	−	0.998074i	$-0.480239\pi$
$857$	28.0280	−	16.1820i	0.957419	−	0.552766i	0.895378	+	0.445307i	$0.146906\pi$
$858$		0			0
$859$	−41.2350	−	23.8070i	−1.40692	−	0.812285i	−0.411830	−	0.911261i	$-0.635110\pi$
$859$	−41.2350	−	23.8070i	−1.40692	−	0.812285i	−0.995090	+	0.0989753i	$0.968444\pi$
$860$		0			0
$861$	4.87447	+	0.118545i	0.166121	+	0.00404001i
$862$		0			0
$863$	−2.98476	+	5.16975i	−0.101602	+	0.175980i	−0.912345	−	0.409422i	$-0.865730\pi$
$863$	−2.98476	+	5.16975i	−0.101602	+	0.175980i	0.810743	+	0.585403i	$0.199064\pi$
$864$		0			0
$865$	42.8866	+	23.2875i	1.45819	+	0.791798i
$866$		0			0
$867$	15.0497	+	8.44002i	0.511116	+	0.286638i
$868$		0			0
$869$			18.4861i			0.627097i
$870$		0			0
$871$	−8.62251	+	4.97821i	−0.292163	+	0.168680i
$872$		0			0
$873$	25.8899	−	0.647139i	0.876240	−	0.0219023i
$874$		0			0
$875$	−1.23094	−	29.5548i	−0.0416132	−	0.999134i
$876$		0			0
$877$	−14.7945	−	8.54159i	−0.499574	−	0.288429i	0.228964	−	0.973435i	$-0.426466\pi$
$877$	−14.7945	−	8.54159i	−0.499574	−	0.288429i	−0.728537	+	0.685006i	$0.759800\pi$
$878$		0			0
$879$	0.986646	−	0.0123291i	0.0332788	−	0.000415850i
$880$		0			0
$881$	−13.7490			−0.463215			−0.231607	−	0.972809i	$-0.574399\pi$
$881$	−13.7490			−0.463215			−0.231607	+	0.972809i	$0.574399\pi$
$882$		0			0
$883$			29.4325i			0.990482i	0.868756	+	0.495241i	$0.164920\pi$
$883$			29.4325i			0.990482i	−0.868756	+	0.495241i	$0.835080\pi$
$884$		0			0
$885$	40.5030	−	25.5199i	1.36149	−	0.857841i
$886$		0			0
$887$	14.5904	+	8.42380i	0.489899	+	0.282843i	0.724533	−	0.689240i	$-0.242056\pi$
$887$	14.5904	+	8.42380i	0.489899	+	0.282843i	−0.234633	+	0.972084i	$0.575389\pi$
$888$		0			0
$889$	−38.5744	−	1.42057i	−1.29374	−	0.0476444i
$890$		0			0
$891$	22.9501	−	14.8265i	0.768856	−	0.496705i
$892$		0			0
$893$	12.2960	+	21.2973i	0.411470	+	0.712687i
$894$		0			0
$895$	−2.44448	+	1.49786i	−0.0817099	+	0.0500680i
$896$		0			0
$897$	17.0452	+	9.55907i	0.569122	+	0.319168i
$898$		0			0
$899$	2.34720	+	4.06546i	0.0782834	+	0.135591i
$900$		0			0
$901$	−31.7462	−	18.3287i	−1.05762	−	0.610617i
$902$		0			0
$903$	0.269690	−	11.0894i	0.00897473	−	0.369033i
$904$		0			0
$905$	−0.851214	−	32.5498i	−0.0282953	−	1.08199i
$906$		0			0
$907$	14.0050	−	8.08581i	0.465030	−	0.268485i	−0.249127	−	0.968471i	$-0.580144\pi$
$907$	14.0050	−	8.08581i	0.465030	−	0.268485i	0.714157	+	0.699986i	$0.246810\pi$
$908$		0			0
$909$	−25.7543	−	42.1395i	−0.854215	−	1.39768i
$910$		0			0
$911$		−	13.3127i		−	0.441071i	−0.975379	−	0.220535i	$-0.929220\pi$
$911$		−	13.3127i		−	0.441071i	0.975379	−	0.220535i	$-0.0707805\pi$
$912$		0			0
$913$	−15.5979	−	27.0164i	−0.516216	−	0.894111i
$914$		0			0
$915$	23.8596	−	45.2805i	0.788775	−	1.49693i
$916$		0			0
$917$	44.9807	+	28.2263i	1.48539	+	0.932113i
$918$		0			0
$919$	6.00415	−	10.3995i	0.198058	−	0.343047i	−0.749840	−	0.661619i	$-0.769870\pi$
$919$	6.00415	−	10.3995i	0.198058	−	0.343047i	0.947899	+	0.318571i	$0.103203\pi$
$920$		0			0
$921$	0.204824	+	16.3913i	0.00674919	+	0.540110i
$922$		0			0
$923$		−	16.4137i		−	0.540263i
$924$		0			0
$925$	12.5298	+	6.38535i	0.411978	+	0.209949i
$926$		0			0
$927$	−9.47523	+	17.4018i	−0.311208	+	0.571551i
$928$		0			0
$929$	−3.50004	+	6.06225i	−0.114833	+	0.198896i	−0.917713	−	0.397244i	$-0.869966\pi$
$929$	−3.50004	+	6.06225i	−0.114833	+	0.198896i	0.802880	+	0.596140i	$0.203300\pi$
$930$		0			0
$931$	37.3299	+	25.3866i	1.22344	+	0.832013i
$932$		0			0
$933$	−9.70446	+	5.76574i	−0.317710	+	0.188762i
$934$		0			0
$935$	16.8203	−	30.9765i	0.550082	−	1.01304i
$936$		0			0
$937$	20.7984			0.679456			0.339728	−	0.940524i	$-0.389665\pi$
$937$	20.7984			0.679456			0.339728	+	0.940524i	$0.389665\pi$
$938$		0			0
$939$	−33.4423	−	18.7547i	−1.09135	−	0.612037i
$940$		0			0
$941$	−14.5688	−	25.2339i	−0.474929	−	0.822600i	0.524659	−	0.851312i	$-0.324193\pi$
$941$	−14.5688	−	25.2339i	−0.474929	−	0.822600i	−0.999588	+	0.0287120i	$0.990859\pi$
$942$		0			0
$943$	2.59025	−	4.48644i	0.0843501	−	0.146099i
$944$		0			0
$945$	−30.7298	+	0.824399i	−0.999640	+	0.0268177i
$946$		0			0
$947$	7.98578	−	13.8318i	0.259503	−	0.449472i	−0.706606	−	0.707607i	$-0.749775\pi$
$947$	7.98578	−	13.8318i	0.259503	−	0.449472i	0.966109	+	0.258135i	$0.0831079\pi$
$948$		0			0
$949$	−0.176871	−	0.306349i	−0.00574146	−	0.00994451i
$950$		0			0
$951$	6.36860	+	3.57156i	0.206516	+	0.115816i
$952$		0			0
$953$	24.9487			0.808167			0.404084	−	0.914722i	$-0.367590\pi$
$953$	24.9487			0.808167			0.404084	+	0.914722i	$0.367590\pi$
$954$		0			0
$955$	46.9756	+	25.5078i	1.52009	+	0.825413i
$956$		0			0
$957$	−15.7597	+	9.36336i	−0.509439	+	0.302674i
$958$		0			0
$959$	−10.9220	+	5.78067i	−0.352689	+	0.186668i
$960$		0			0
$961$	−14.5934	+	25.2765i	−0.470755	+	0.815371i
$962$		0			0
$963$	−26.5879	+	48.8302i	−0.856783	+	1.57353i
$964$		0			0
$965$	16.0876	−	9.85770i	0.517877	−	0.317331i
$966$		0			0
$967$			7.93647i			0.255220i	0.991824	+	0.127610i	$0.0407305\pi$
$967$			7.93647i			0.255220i	−0.991824	+	0.127610i	$0.959269\pi$
$968$		0			0
$969$	0.724731	+	57.9973i	0.0232817	+	1.86314i
$970$		0			0
$971$	−17.5378	+	30.3763i	−0.562814	+	0.974822i	0.434436	+	0.900703i	$0.356948\pi$
$971$	−17.5378	+	30.3763i	−0.562814	+	0.974822i	−0.997249	+	0.0741192i	$0.976385\pi$
$972$		0			0
$973$	−14.5760	−	0.536788i	−0.467286	−	0.0172086i
$974$		0			0
$975$	−1.29928	−	20.0270i	−0.0416101	−	0.641376i
$976$		0			0
$977$	−1.56200	−	2.70546i	−0.0499728	−	0.0865554i	0.839957	−	0.542653i	$-0.182580\pi$
$977$	−1.56200	−	2.70546i	−0.0499728	−	0.0865554i	−0.889930	+	0.456098i	$0.849247\pi$
$978$		0			0
$979$			43.1646i			1.37955i
$980$		0			0
$981$	28.9464	+	47.3626i	0.924189	+	1.51217i
$982$		0			0
$983$	19.8301	−	11.4489i	0.632481	−	0.365163i	−0.149231	−	0.988802i	$-0.547680\pi$
$983$	19.8301	−	11.4489i	0.632481	−	0.365163i	0.781712	+	0.623639i	$0.214347\pi$
$984$		0			0
$985$	18.4607	−	0.482767i	0.588207	−	0.0153822i
$986$		0			0
$987$	14.9163	+	9.10249i	0.474791	+	0.289735i
$988$		0			0
$989$	−10.2067	−	5.89282i	−0.324553	−	0.187381i
$990$		0			0
$991$	−5.34209	−	9.25277i	−0.169697	−	0.293924i	0.768616	−	0.639710i	$-0.220946\pi$
$991$	−5.34209	−	9.25277i	−0.169697	−	0.293924i	−0.938313	+	0.345786i	$0.887612\pi$
$992$		0			0
$993$	36.2694	+	20.3402i	1.15098	+	0.645476i
$994$		0			0
$995$	−19.6830	+	12.0608i	−0.623994	+	0.382354i
$996$		0			0
$997$	−25.1937	−	43.6367i	−0.797892	−	1.38199i	−0.920986	−	0.389595i	$-0.872615\pi$
$997$	−25.1937	−	43.6367i	−0.797892	−	1.38199i	0.123094	−	0.992395i	$-0.460718\pi$
$998$		0			0
$999$	6.82789	−	12.9217i	0.216025	−	0.408824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bn.a.89.9	yes	32
3.2	odd	2	inner	420.2.bn.a.89.14	yes	32
5.2	odd	4		2100.2.bi.n.1601.16		32
5.3	odd	4		2100.2.bi.n.1601.1		32
5.4	even	2	inner	420.2.bn.a.89.8	yes	32
7.2	even	3		2940.2.f.a.1469.6		32
7.3	odd	6	inner	420.2.bn.a.269.3	yes	32
7.5	odd	6		2940.2.f.a.1469.27		32
15.2	even	4		2100.2.bi.n.1601.11		32
15.8	even	4		2100.2.bi.n.1601.6		32
15.14	odd	2	inner	420.2.bn.a.89.3	✓	32
21.2	odd	6		2940.2.f.a.1469.7		32
21.5	even	6		2940.2.f.a.1469.26		32
21.17	even	6	inner	420.2.bn.a.269.8	yes	32
35.3	even	12		2100.2.bi.n.101.6		32
35.9	even	6		2940.2.f.a.1469.28		32
35.17	even	12		2100.2.bi.n.101.11		32
35.19	odd	6		2940.2.f.a.1469.5		32
35.24	odd	6	inner	420.2.bn.a.269.14	yes	32
105.17	odd	12		2100.2.bi.n.101.16		32
105.38	odd	12		2100.2.bi.n.101.1		32
105.44	odd	6		2940.2.f.a.1469.25		32
105.59	even	6	inner	420.2.bn.a.269.9	yes	32
105.89	even	6		2940.2.f.a.1469.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bn.a.89.3	✓	32	15.14	odd	2	inner
420.2.bn.a.89.8	yes	32	5.4	even	2	inner
420.2.bn.a.89.9	yes	32	1.1	even	1	trivial
420.2.bn.a.89.14	yes	32	3.2	odd	2	inner
420.2.bn.a.269.3	yes	32	7.3	odd	6	inner
420.2.bn.a.269.8	yes	32	21.17	even	6	inner
420.2.bn.a.269.9	yes	32	105.59	even	6	inner
420.2.bn.a.269.14	yes	32	35.24	odd	6	inner
2100.2.bi.n.101.1		32	105.38	odd	12
2100.2.bi.n.101.6		32	35.3	even	12
2100.2.bi.n.101.11		32	35.17	even	12
2100.2.bi.n.101.16		32	105.17	odd	12
2100.2.bi.n.1601.1		32	5.3	odd	4
2100.2.bi.n.1601.6		32	15.8	even	4
2100.2.bi.n.1601.11		32	15.2	even	4
2100.2.bi.n.1601.16		32	5.2	odd	4
2940.2.f.a.1469.5		32	35.19	odd	6
2940.2.f.a.1469.6		32	7.2	even	3
2940.2.f.a.1469.7		32	21.2	odd	6
2940.2.f.a.1469.8		32	105.89	even	6
2940.2.f.a.1469.25		32	105.44	odd	6
2940.2.f.a.1469.26		32	21.5	even	6
2940.2.f.a.1469.27		32	7.5	odd	6
2940.2.f.a.1469.28		32	35.9	even	6

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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0216419 + 1.73192i) q^{3} +(-2.23530 + 0.0584556i) q^{5} +(-0.0973684 + 2.64396i) q^{7} +(-2.99906 + 0.0749640i) q^{9} +O(q^{10})\)	\(q+(0.0216419 + 1.73192i) q^{3} +(-2.23530 + 0.0584556i) q^{5} +(-0.0973684 + 2.64396i) q^{7} +(-2.99906 + 0.0749640i) q^{9} +(2.62913 - 1.51793i) q^{11} -2.31738 q^{13} +(-0.149616 - 3.87009i) q^{15} +(-4.49684 + 2.59625i) q^{17} +(-5.58515 - 3.22459i) q^{19} +(-4.58122 - 0.111414i) q^{21} +(-2.43442 + 4.21654i) q^{23} +(4.99317 - 0.261332i) q^{25} +(-0.194737 - 5.19250i) q^{27} +3.48622i q^{29} +(1.16615 - 0.673279i) q^{31} +(2.68582 + 4.52058i) q^{33} +(0.0630937 - 5.91574i) q^{35} +(2.43579 + 1.40630i) q^{37} +(-0.0501525 - 4.01350i) q^{39} -1.06401 q^{41} +2.42063i q^{43} +(6.69944 - 0.342879i) q^{45} +(-3.30233 - 1.90660i) q^{47} +(-6.98104 - 0.514876i) q^{49} +(-4.59381 - 7.73196i) q^{51} +(3.52984 + 6.11386i) q^{53} +(-5.78817 + 3.54672i) q^{55} +(5.46384 - 9.74279i) q^{57} +(6.18029 + 10.7046i) q^{59} +(11.4447 + 6.60758i) q^{61} +(0.0938123 - 7.93670i) q^{63} +(5.18004 - 0.135464i) q^{65} +(3.72081 - 2.14821i) q^{67} +(-7.35538 - 4.12496i) q^{69} +7.08288i q^{71} +(0.0763237 + 0.132196i) q^{73} +(0.560667 + 8.64209i) q^{75} +(3.75734 + 7.09910i) q^{77} +(-3.04462 + 5.27344i) q^{79} +(8.98876 - 0.449644i) q^{81} -10.2758i q^{83} +(9.90003 - 6.06628i) q^{85} +(-6.03784 + 0.0754485i) q^{87} +(-7.10913 + 12.3134i) q^{89} +(0.225639 - 6.12705i) q^{91} +(1.19130 + 2.00511i) q^{93} +(12.6730 + 6.88145i) q^{95} -8.63266 q^{97} +(-7.77113 + 4.74945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 2 q^{15} + 12 q^{19} - 8 q^{21} + 6 q^{25} - 12 q^{31} + 24 q^{39} + 33 q^{45} - 44 q^{49} - 10 q^{51} - 24 q^{61} + 21 q^{75} - 28 q^{79} - 20 q^{81} - 4 q^{85} + 16 q^{91} - 28 q^{99}+O(q^{100}) \) 32 * q + 2 * q^15 + 12 * q^19 - 8 * q^21 + 6 * q^25 - 12 * q^31 + 24 * q^39 + 33 * q^45 - 44 * q^49 - 10 * q^51 - 24 * q^61 + 21 * q^75 - 28 * q^79 - 20 * q^81 - 4 * q^85 + 16 * q^91 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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