LMFDB - Embedded newform 552.2.q.b.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			73.1
Character	$\chi$	$=$	552.73
Dual form			552.2.q.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 + 0.281733i) q^{3} +(-2.59066 - 1.66492i) q^{5} +(0.565805 + 3.93526i) q^{7} +(0.841254 - 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.959493 + 0.281733i) q^{3} +(-2.59066 - 1.66492i) q^{5} +(0.565805 + 3.93526i) q^{7} +(0.841254 - 0.540641i) q^{9} +(0.839370 - 1.83796i) q^{11} +(0.139030 - 0.966976i) q^{13} +(2.95479 + 0.867604i) q^{15} +(-1.72867 - 1.99499i) q^{17} +(5.61953 - 6.48528i) q^{19} +(-1.65158 - 3.61645i) q^{21} +(1.39964 - 4.58705i) q^{23} +(1.86251 + 4.07833i) q^{25} +(-0.654861 + 0.755750i) q^{27} +(-3.80500 - 4.39120i) q^{29} +(-7.40293 - 2.17370i) q^{31} +(-0.287555 + 1.99999i) q^{33} +(5.08608 - 11.1370i) q^{35} +(2.96128 - 1.90310i) q^{37} +(0.139030 + 0.966976i) q^{39} +(-1.82716 - 1.17424i) q^{41} +(1.70043 - 0.499291i) q^{43} -3.07953 q^{45} +12.2205 q^{47} +(-8.44967 + 2.48105i) q^{49} +(2.22070 + 1.42716i) q^{51} +(0.691719 + 4.81101i) q^{53} +(-5.23459 + 3.36407i) q^{55} +(-3.56478 + 7.80578i) q^{57} +(1.34920 - 9.38386i) q^{59} +(-4.20390 - 1.23438i) q^{61} +(2.60355 + 3.00465i) q^{63} +(-1.97012 + 2.27364i) q^{65} +(3.35000 + 7.33547i) q^{67} +(-0.0506231 + 4.79556i) q^{69} +(4.28200 + 9.37627i) q^{71} +(10.4998 - 12.1174i) q^{73} +(-2.93607 - 3.38840i) q^{75} +(7.70778 + 2.26321i) q^{77} +(-1.14938 + 7.99412i) q^{79} +(0.415415 - 0.909632i) q^{81} +(1.37415 - 0.883115i) q^{83} +(1.15690 + 8.04644i) q^{85} +(4.88802 + 3.14134i) q^{87} +(-6.72270 + 1.97396i) q^{89} +3.88397 q^{91} +7.71546 q^{93} +(-25.3558 + 7.44513i) q^{95} +(-7.33989 - 4.71706i) q^{97} +(-0.287555 - 1.99999i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 3 * q^9	$ 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43} - 22 q^{45} + 22 q^{47} + 19 q^{49} + 17 q^{51} + 25 q^{53} + 10 q^{55} + 24 q^{57} + 7 q^{59} + 8 q^{61} - 28 q^{65} - 23 q^{67} - q^{69} + 5 q^{71} + 34 q^{73} - 23 q^{75} + 62 q^{77} + 20 q^{79} - 3 q^{81} + 29 q^{83} - 46 q^{85} + 10 q^{87} - 67 q^{89} - 118 q^{91} - 26 q^{93} - 99 q^{95} - 41 q^{97} + 9 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{2}{11}\right)$	$1$	$1$	$1$

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
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$3$	−0.959493	+	0.281733i	−0.553964	+	0.162658i
$4$		0			0
$5$	−2.59066	−	1.66492i	−1.15858	−	0.744574i	−0.187251	−	0.982312i	$-0.559958\pi$
$5$	−2.59066	−	1.66492i	−1.15858	−	0.744574i	−0.971329	+	0.237738i	$0.923594\pi$
$6$		0			0
$7$	0.565805	+	3.93526i	0.213854	+	1.48739i	0.760124	+	0.649778i	$0.225138\pi$
$7$	0.565805	+	3.93526i	0.213854	+	1.48739i	−0.546270	+	0.837609i	$0.683953\pi$
$8$		0			0
$9$	0.841254	−	0.540641i	0.280418	−	0.180214i
$10$		0			0
$11$	0.839370	−	1.83796i	0.253080	−	0.554167i	−0.739864	−	0.672757i	$-0.765110\pi$
$11$	0.839370	−	1.83796i	0.253080	−	0.554167i	0.992943	+	0.118590i	$0.0378373\pi$
$12$		0			0
$13$	0.139030	−	0.966976i	0.0385600	−	0.268191i	−0.961416	−	0.275098i	$-0.911290\pi$
$13$	0.139030	−	0.966976i	0.0385600	−	0.268191i	0.999976	+	0.00690731i	$0.00219868\pi$
$14$		0			0
$15$	2.95479	+	0.867604i	0.762923	+	0.224014i
$16$		0			0
$17$	−1.72867	−	1.99499i	−0.419264	−	0.483856i	0.506349	−	0.862329i	$-0.330995\pi$
$17$	−1.72867	−	1.99499i	−0.419264	−	0.483856i	−0.925612	+	0.378473i	$0.876449\pi$
$18$		0			0
$19$	5.61953	−	6.48528i	1.28921	−	1.48783i	0.511369	−	0.859361i	$-0.329138\pi$
$19$	5.61953	−	6.48528i	1.28921	−	1.48783i	0.777839	−	0.628464i	$-0.216316\pi$
$20$		0			0
$21$	−1.65158	−	3.61645i	−0.360403	−	0.789173i
$22$		0			0
$23$	1.39964	−	4.58705i	0.291845	−	0.956466i
$23$	1.39964	−	4.58705i	0.291845	−	0.956466i
$24$		0			0
$25$	1.86251	+	4.07833i	0.372503	+	0.815667i
$26$		0			0
$27$	−0.654861	+	0.755750i	−0.126028	+	0.145444i
$28$		0			0
$29$	−3.80500	−	4.39120i	−0.706571	−	0.815426i	0.283054	−	0.959104i	$-0.408653\pi$
$29$	−3.80500	−	4.39120i	−0.706571	−	0.815426i	−0.989624	+	0.143678i	$0.954107\pi$
$30$		0			0
$31$	−7.40293	−	2.17370i	−1.32961	−	0.390407i	−0.461656	−	0.887059i	$-0.652744\pi$
$31$	−7.40293	−	2.17370i	−1.32961	−	0.390407i	−0.867950	+	0.496652i	$0.834563\pi$
$32$		0			0
$33$	−0.287555	+	1.99999i	−0.0500570	+	0.348154i
$34$		0			0
$35$	5.08608	−	11.1370i	0.859704	−	1.88249i
$36$		0			0
$37$	2.96128	−	1.90310i	0.486831	−	0.312867i	−0.274099	−	0.961702i	$-0.588380\pi$
$37$	2.96128	−	1.90310i	0.486831	−	0.312867i	0.760930	+	0.648834i	$0.224743\pi$
$38$		0			0
$39$	0.139030	+	0.966976i	0.0222627	+	0.154840i
$40$		0			0
$41$	−1.82716	−	1.17424i	−0.285354	−	0.183386i	0.390132	−	0.920759i	$-0.372430\pi$
$41$	−1.82716	−	1.17424i	−0.285354	−	0.183386i	−0.675485	+	0.737373i	$0.736066\pi$
$42$		0			0
$43$	1.70043	−	0.499291i	0.259313	−	0.0761412i	−0.149492	−	0.988763i	$-0.547764\pi$
$43$	1.70043	−	0.499291i	0.259313	−	0.0761412i	0.408805	+	0.912622i	$0.365946\pi$
$44$		0			0
$45$	−3.07953			−0.459069
$46$		0			0
$47$	12.2205			1.78254			0.891269	−	0.453474i	$-0.149816\pi$
$47$	12.2205			1.78254			0.891269	+	0.453474i	$0.149816\pi$
$48$		0			0
$49$	−8.44967	+	2.48105i	−1.20710	+	0.354435i
$50$		0			0
$51$	2.22070	+	1.42716i	0.310960	+	0.199842i
$52$		0			0
$53$	0.691719	+	4.81101i	0.0950149	+	0.660843i	0.980550	+	0.196270i	$0.0628830\pi$
$53$	0.691719	+	4.81101i	0.0950149	+	0.660843i	−0.885535	+	0.464573i	$0.846208\pi$
$54$		0			0
$55$	−5.23459	+	3.36407i	−0.705832	+	0.453610i
$56$		0			0
$57$	−3.56478	+	7.80578i	−0.472167	+	1.03390i
$58$		0			0
$59$	1.34920	−	9.38386i	0.175650	−	1.22167i	−0.691036	−	0.722821i	$-0.742845\pi$
$59$	1.34920	−	9.38386i	0.175650	−	1.22167i	0.866686	−	0.498854i	$-0.166246\pi$
$60$		0			0
$61$	−4.20390	−	1.23438i	−0.538255	−	0.158046i	0.00129578	−	0.999999i	$-0.499588\pi$
$61$	−4.20390	−	1.23438i	−0.538255	−	0.158046i	−0.539550	+	0.841953i	$0.681406\pi$
$62$		0			0
$63$	2.60355	+	3.00465i	0.328016	+	0.378551i
$64$		0			0
$65$	−1.97012	+	2.27364i	−0.244363	+	0.282010i
$66$		0			0
$67$	3.35000	+	7.33547i	0.409267	+	0.896170i	0.996246	+	0.0865678i	$0.0275899\pi$
$67$	3.35000	+	7.33547i	0.409267	+	0.896170i	−0.586979	+	0.809602i	$0.699683\pi$
$68$		0			0
$69$	−0.0506231	+	4.79556i	−0.00609430	+	0.577318i
$70$		0			0
$71$	4.28200	+	9.37627i	0.508180	+	1.11276i	0.973723	+	0.227734i	$0.0731316\pi$
$71$	4.28200	+	9.37627i	0.508180	+	1.11276i	−0.465543	+	0.885025i	$0.654141\pi$
$72$		0			0
$73$	10.4998	−	12.1174i	1.22891	−	1.41823i	0.353089	−	0.935590i	$-0.385131\pi$
$73$	10.4998	−	12.1174i	1.22891	−	1.41823i	0.875817	−	0.482643i	$-0.160323\pi$
$74$		0			0
$75$	−2.93607	−	3.38840i	−0.339028	−	0.391259i
$76$		0			0
$77$	7.70778	+	2.26321i	0.878383	+	0.257917i
$78$		0			0
$79$	−1.14938	+	7.99412i	−0.129315	+	0.899409i	0.817109	+	0.576483i	$0.195575\pi$
$79$	−1.14938	+	7.99412i	−0.129315	+	0.899409i	−0.946424	+	0.322925i	$0.895334\pi$
$80$		0			0
$81$	0.415415	−	0.909632i	0.0461572	−	0.101070i
$82$		0			0
$83$	1.37415	−	0.883115i	0.150833	−	0.0969345i	−0.463047	−	0.886334i	$-0.653244\pi$
$83$	1.37415	−	0.883115i	0.150833	−	0.0969345i	0.613880	+	0.789399i	$0.289608\pi$
$84$		0			0
$85$	1.15690	+	8.04644i	0.125484	+	0.872759i
$86$		0			0
$87$	4.88802	+	3.14134i	0.524050	+	0.336787i
$88$		0			0
$89$	−6.72270	+	1.97396i	−0.712605	+	0.209240i	−0.617890	−	0.786265i	$-0.712012\pi$
$89$	−6.72270	+	1.97396i	−0.712605	+	0.209240i	−0.0947150	+	0.995504i	$0.530194\pi$
$90$		0			0
$91$	3.88397			0.407150
$92$		0			0
$93$	7.71546			0.800056
$94$		0			0
$95$	−25.3558	+	7.44513i	−2.60145	+	0.763854i
$96$		0			0
$97$	−7.33989	−	4.71706i	−0.745253	−	0.478945i	0.112085	−	0.993699i	$-0.464247\pi$
$97$	−7.33989	−	4.71706i	−0.745253	−	0.478945i	−0.857338	+	0.514754i	$0.827883\pi$
$98$		0			0
$99$	−0.287555	−	1.99999i	−0.0289004	−	0.201007i
$100$		0			0
$101$	2.90775	−	1.86870i	0.289332	−	0.185942i	−0.387921	−	0.921693i	$-0.626807\pi$
$101$	2.90775	−	1.86870i	0.289332	−	0.185942i	0.677253	+	0.735750i	$0.263170\pi$
$102$		0			0
$103$	−0.890282	+	1.94945i	−0.0877221	+	0.192085i	−0.948409	−	0.317051i	$-0.897307\pi$
$103$	−0.890282	+	1.94945i	−0.0877221	+	0.192085i	0.860686	+	0.509135i	$0.170035\pi$
$104$		0			0
$105$	−1.74241	+	12.1187i	−0.170042	+	1.18267i
$106$		0			0
$107$	−9.78522	−	2.87320i	−0.945973	−	0.277763i	−0.227864	−	0.973693i	$-0.573174\pi$
$107$	−9.78522	−	2.87320i	−0.945973	−	0.277763i	−0.718109	+	0.695930i	$0.754992\pi$
$108$		0			0
$109$	−11.5949	−	13.3812i	−1.11059	−	1.28169i	−0.955889	−	0.293727i	$-0.905104\pi$
$109$	−11.5949	−	13.3812i	−1.11059	−	1.28169i	−0.154700	−	0.987962i	$-0.549441\pi$
$110$		0			0
$111$	−2.30516	+	2.66030i	−0.218796	+	0.252504i
$112$		0			0
$113$	−7.79594	−	17.0707i	−0.733381	−	1.60588i	−0.794146	−	0.607727i	$-0.792081\pi$
$113$	−7.79594	−	17.0707i	−0.733381	−	1.60588i	0.0607652	−	0.998152i	$-0.480646\pi$
$114$		0			0
$115$	−11.2631	+	9.55322i	−1.05029	+	0.890842i
$116$		0			0
$117$	−0.405827	−	0.888638i	−0.0375187	−	0.0821546i
$118$		0			0
$119$	6.87271	−	7.93153i	0.630020	−	0.727082i
$120$		0			0
$121$	4.52990	+	5.22778i	0.411809	+	0.475253i
$122$		0			0
$123$	2.08397	+	0.611908i	0.187905	+	0.0551739i
$124$		0			0
$125$	−0.226363	+	1.57439i	−0.0202465	+	0.140818i
$126$		0			0
$127$	−7.79199	+	17.0621i	−0.691428	+	1.51402i	0.158637	+	0.987337i	$0.449290\pi$
$127$	−7.79199	+	17.0621i	−0.691428	+	1.51402i	−0.850065	+	0.526678i	$0.823437\pi$
$128$		0			0
$129$	−1.49088	+	0.958132i	−0.131265	+	0.0843588i
$130$		0			0
$131$	0.0465460	+	0.323734i	0.00406674	+	0.0282848i	0.991754	−	0.128158i	$-0.0409064\pi$
$131$	0.0465460	+	0.323734i	0.00406674	+	0.0282848i	−0.987687	+	0.156443i	$0.949997\pi$
$132$		0			0
$133$	28.7008	+	18.4449i	2.48868	+	1.59937i
$134$		0			0
$135$	2.95479	−	0.867604i	0.254308	−	0.0746714i
$136$		0			0
$137$	−7.22638			−0.617392			−0.308696	−	0.951161i	$-0.599893\pi$
$137$	−7.22638			−0.617392			−0.308696	+	0.951161i	$0.599893\pi$
$138$		0			0
$139$	−3.41127			−0.289340			−0.144670	−	0.989480i	$-0.546212\pi$
$139$	−3.41127			−0.289340			−0.144670	+	0.989480i	$0.546212\pi$
$140$		0			0
$141$	−11.7255	+	3.44290i	−0.987461	+	0.289945i
$142$		0			0
$143$	−1.66057	−	1.06718i	−0.138864	−	0.0892424i
$144$		0			0
$145$	2.54648	+	17.7112i	0.211474	+	1.47083i
$146$		0			0
$147$	7.40841	−	4.76109i	0.611035	−	0.392688i
$148$		0			0
$149$	−3.96628	+	8.68493i	−0.324930	+	0.711497i	−0.999647	−	0.0265795i	$-0.991538\pi$
$149$	−3.96628	+	8.68493i	−0.324930	+	0.711497i	0.674717	+	0.738077i	$0.264266\pi$
$150$		0			0
$151$	3.40181	−	23.6601i	0.276835	−	1.92543i	−0.0916333	−	0.995793i	$-0.529209\pi$
$151$	3.40181	−	23.6601i	0.276835	−	1.92543i	0.368469	−	0.929640i	$-0.379882\pi$
$152$		0			0
$153$	−2.53282	−	0.743703i	−0.204766	−	0.0601248i
$154$		0			0
$155$	15.5595	+	17.9566i	1.24977	+	1.44231i
$156$		0			0
$157$	0.716976	−	0.827434i	0.0572209	−	0.0660364i	−0.726418	−	0.687254i	$-0.758816\pi$
$157$	0.716976	−	0.827434i	0.0572209	−	0.0660364i	0.783638	+	0.621217i	$0.213362\pi$
$158$		0			0
$159$	−2.01912	−	4.42125i	−0.160126	−	0.350628i
$160$		0			0
$161$	18.8431	+	2.91257i	1.48505	+	0.229542i
$162$		0			0
$163$	5.36166	+	11.7404i	0.419958	+	0.919579i	0.994851	+	0.101351i	$0.0323164\pi$
$163$	5.36166	+	11.7404i	0.419958	+	0.919579i	−0.574893	+	0.818229i	$0.694956\pi$
$164$		0			0
$165$	4.07478	−	4.70255i	0.317221	−	0.366093i
$166$		0			0
$167$	−8.84095	−	10.2030i	−0.684133	−	0.789531i	0.302385	−	0.953186i	$-0.402217\pi$
$167$	−8.84095	−	10.2030i	−0.684133	−	0.789531i	−0.986518	+	0.163654i	$0.947672\pi$
$168$		0			0
$169$	11.5577	+	3.39365i	0.889053	+	0.261050i
$170$		0			0
$171$	1.22124	−	8.49391i	0.0933905	−	0.649546i
$172$		0			0
$173$	1.63464	−	3.57936i	0.124279	−	0.272134i	−0.837258	−	0.546808i	$-0.815843\pi$
$173$	1.63464	−	3.57936i	0.124279	−	0.272134i	0.961537	+	0.274674i	$0.0885700\pi$
$174$		0			0
$175$	−14.9955	+	9.63701i	−1.13355	+	0.728489i
$176$		0			0
$177$	1.34920	+	9.38386i	0.101412	+	0.705334i
$178$		0			0
$179$	−0.623512	−	0.400707i	−0.0466035	−	0.0299502i	0.517132	−	0.855906i	$-0.327000\pi$
$179$	−0.623512	−	0.400707i	−0.0466035	−	0.0299502i	−0.563735	+	0.825956i	$0.690636\pi$
$180$		0			0
$181$	1.18430	−	0.347741i	0.0880282	−	0.0258474i	−0.237422	−	0.971407i	$-0.576302\pi$
$181$	1.18430	−	0.347741i	0.0880282	−	0.0258474i	0.325450	+	0.945559i	$0.394484\pi$
$182$		0			0
$183$	4.38138			0.323881
$184$		0			0
$185$	−10.8402			−0.796985
$186$		0			0
$187$	−5.11771	+	1.50270i	−0.374244	+	0.109888i
$188$		0			0
$189$	−3.34459	−	2.14944i	−0.243283	−	0.156349i
$190$		0			0
$191$	3.20014	+	22.2575i	0.231554	+	1.61050i	0.691383	+	0.722488i	$0.257002\pi$
$191$	3.20014	+	22.2575i	0.231554	+	1.61050i	−0.459829	+	0.888008i	$0.652089\pi$
$192$		0			0
$193$	5.70575	−	3.66686i	0.410709	−	0.263946i	−0.318931	−	0.947778i	$-0.603324\pi$
$193$	5.70575	−	3.66686i	0.410709	−	0.263946i	0.729640	+	0.683831i	$0.239688\pi$
$194$		0			0
$195$	1.24976	−	2.73659i	0.0894969	−	0.195971i
$196$		0			0
$197$	−0.0712014	+	0.495216i	−0.00507289	+	0.0352827i	−0.992201	−	0.124651i	$-0.960219\pi$
$197$	−0.0712014	+	0.495216i	−0.00507289	+	0.0352827i	0.987128	+	0.159934i	$0.0511280\pi$
$198$		0			0
$199$	10.1862	+	2.99095i	0.722084	+	0.212023i	0.622068	−	0.782963i	$-0.286293\pi$
$199$	10.1862	+	2.99095i	0.722084	+	0.212023i	0.100015	+	0.994986i	$0.468111\pi$
$200$		0			0
$201$	−5.28094	−	6.09453i	−0.372489	−	0.429875i
$202$		0			0
$203$	15.1276	−	17.4582i	1.06175	−	1.22533i
$204$		0			0
$205$	2.77853	+	6.08414i	0.194061	+	0.424935i
$206$		0			0
$207$	−1.30249	−	4.61557i	−0.0905296	−	0.320804i
$208$		0			0
$209$	−7.20285	−	15.7720i	−0.498231	−	1.09097i
$210$		0			0
$211$	13.3261	−	15.3792i	0.917408	−	1.05875i	−0.0806674	−	0.996741i	$-0.525705\pi$
$211$	13.3261	−	15.3792i	0.917408	−	1.05875i	0.998076	−	0.0620047i	$-0.0197494\pi$
$212$		0			0
$213$	−6.75015	−	7.79009i	−0.462513	−	0.533768i
$214$		0			0
$215$	−5.23652	−	1.53758i	−0.357128	−	0.104862i
$216$		0			0
$217$	4.36544	−	30.3623i	0.296346	−	2.06113i
$218$		0			0
$219$	−6.66060	+	14.5847i	−0.450082	+	0.985541i
$220$		0			0
$221$	−2.16944	+	1.39422i	−0.145933	+	0.0937852i
$222$		0			0
$223$	−0.419647	−	2.91871i	−0.0281017	−	0.195451i	0.970935	−	0.239345i	$-0.0769328\pi$
$223$	−0.419647	−	2.91871i	−0.0281017	−	0.195451i	−0.999036	+	0.0438938i	$0.986024\pi$
$224$		0			0
$225$	3.77176	+	2.42396i	0.251451	+	0.161597i
$226$		0			0
$227$	−10.2490	+	3.00937i	−0.680249	+	0.199739i	−0.603562	−	0.797316i	$-0.706252\pi$
$227$	−10.2490	+	3.00937i	−0.680249	+	0.199739i	−0.0766869	+	0.997055i	$0.524434\pi$
$228$		0			0
$229$	−20.8987			−1.38103			−0.690514	−	0.723319i	$-0.742615\pi$
$229$	−20.8987			−1.38103			−0.690514	+	0.723319i	$0.742615\pi$
$230$		0			0
$231$	−8.03318			−0.528545
$232$		0			0
$233$	11.9086	−	3.49667i	0.780156	−	0.229075i	0.132679	−	0.991159i	$-0.457642\pi$
$233$	11.9086	−	3.49667i	0.780156	−	0.229075i	0.647477	+	0.762085i	$0.275824\pi$
$234$		0			0
$235$	−31.6591	−	20.3461i	−2.06521	−	1.32723i
$236$		0			0
$237$	−1.14938	−	7.99412i	−0.0746603	−	0.519274i
$238$		0			0
$239$	5.06707	−	3.25641i	0.327762	−	0.210640i	−0.366402	−	0.930457i	$-0.619411\pi$
$239$	5.06707	−	3.25641i	0.327762	−	0.210640i	0.694164	+	0.719817i	$0.255774\pi$
$240$		0			0
$241$	0.0317452	−	0.0695123i	0.00204489	−	0.00447768i	−0.908607	−	0.417653i	$-0.862853\pi$
$241$	0.0317452	−	0.0695123i	0.00204489	−	0.00447768i	0.910652	+	0.413175i	$0.135580\pi$
$242$		0			0
$243$	−0.142315	+	0.989821i	−0.00912950	+	0.0634971i
$244$		0			0
$245$	26.0210	+	7.64046i	1.66242	+	0.488131i
$246$		0			0
$247$	−5.48983	−	6.33560i	−0.349309	−	0.403125i
$248$		0			0
$249$	−1.06969	+	1.23449i	−0.0677888	+	0.0782324i
$250$		0			0
$251$	−0.959906	−	2.10190i	−0.0605887	−	0.132671i	0.876916	−	0.480644i	$-0.159597\pi$
$251$	−0.959906	−	2.10190i	−0.0605887	−	0.132671i	−0.937504	+	0.347974i	$0.886870\pi$
$252$		0			0
$253$	−7.25601	−	6.42272i	−0.456182	−	0.403793i
$254$		0			0
$255$	−3.37698	−	7.39457i	−0.211475	−	0.463066i
$256$		0			0
$257$	−8.21755	+	9.48356i	−0.512597	+	0.591568i	−0.951762	−	0.306838i	$-0.900729\pi$
$257$	−8.21755	+	9.48356i	−0.512597	+	0.591568i	0.439165	+	0.898406i	$0.355274\pi$
$258$		0			0
$259$	9.16468	+	10.5766i	0.569465	+	0.657198i
$260$		0			0
$261$	−5.57503	−	1.63698i	−0.345086	−	0.101326i
$262$		0			0
$263$	−3.40569	+	23.6871i	−0.210004	+	1.46061i	0.563132	+	0.826367i	$0.309596\pi$
$263$	−3.40569	+	23.6871i	−0.210004	+	1.46061i	−0.773136	+	0.634240i	$0.781313\pi$
$264$		0			0
$265$	6.21793	−	13.6154i	0.381964	−	0.836385i
$266$		0			0
$267$	5.89425	−	3.78801i	0.360722	−	0.231822i
$268$		0			0
$269$	−3.23037	−	22.4677i	−0.196959	−	1.36988i	−0.813045	−	0.582201i	$-0.802192\pi$
$269$	−3.23037	−	22.4677i	−0.196959	−	1.36988i	0.616086	−	0.787679i	$-0.288717\pi$
$270$		0			0
$271$	−7.06760	−	4.54207i	−0.429326	−	0.275911i	0.308080	−	0.951360i	$-0.400313\pi$
$271$	−7.06760	−	4.54207i	−0.429326	−	0.275911i	−0.737407	+	0.675449i	$0.763950\pi$
$272$		0			0
$273$	−3.72664	+	1.09424i	−0.225546	+	0.0662264i
$274$		0			0
$275$	9.05917			0.546288
$276$		0			0
$277$	15.5494			0.934270			0.467135	−	0.884186i	$-0.345286\pi$
$277$	15.5494			0.934270			0.467135	+	0.884186i	$0.345286\pi$
$278$		0			0
$279$	−7.40293	+	2.17370i	−0.443202	+	0.130136i
$280$		0			0
$281$	3.10183	+	1.99343i	0.185040	+	0.118918i	0.629881	−	0.776692i	$-0.283104\pi$
$281$	3.10183	+	1.99343i	0.185040	+	0.118918i	−0.444841	+	0.895609i	$0.646740\pi$
$282$		0			0
$283$	−4.08434	−	28.4072i	−0.242789	−	1.68863i	−0.637995	−	0.770041i	$-0.720236\pi$
$283$	−4.08434	−	28.4072i	−0.242789	−	1.68863i	0.395206	−	0.918593i	$-0.370673\pi$
$284$		0			0
$285$	22.2312	−	14.2871i	1.31686	−	0.846294i
$286$		0			0
$287$	3.58713	−	7.85473i	0.211742	−	0.463650i
$288$		0			0
$289$	1.42766	−	9.92962i	0.0839802	−	0.584095i
$290$		0			0
$291$	8.37152	+	2.45810i	0.490747	+	0.144096i
$292$		0			0
$293$	14.3867	+	16.6031i	0.840480	+	0.969965i	0.999851	−	0.0172535i	$-0.00549224\pi$
$293$	14.3867	+	16.6031i	0.840480	+	0.969965i	−0.159372	+	0.987219i	$0.550947\pi$
$294$		0			0
$295$	−19.1187	+	22.0641i	−1.11313	+	1.28462i
$296$		0			0
$297$	0.839370	+	1.83796i	0.0487052	+	0.106649i
$298$		0			0
$299$	−4.24098	−	1.99116i	−0.245262	−	0.115152i
$300$		0			0
$301$	2.92695	+	6.40912i	0.168707	+	0.369416i
$302$		0			0
$303$	−2.26349	+	2.61221i	−0.130034	+	0.150067i
$304$		0			0
$305$	8.83576	+	10.1970i	0.505934	+	0.583879i
$306$		0			0
$307$	6.22561	+	1.82801i	0.355315	+	0.104330i	0.454518	−	0.890737i	$-0.349811\pi$
$307$	6.22561	+	1.82801i	0.355315	+	0.104330i	−0.0992038	+	0.995067i	$0.531630\pi$
$308$		0			0
$309$	0.304997	−	2.12130i	0.0173507	−	0.120677i
$310$		0			0
$311$	0.541799	−	1.18637i	0.0307226	−	0.0672731i	−0.893649	−	0.448767i	$-0.851863\pi$
$311$	0.541799	−	1.18637i	0.0307226	−	0.0672731i	0.924371	+	0.381494i	$0.124590\pi$
$312$		0			0
$313$	15.9663	−	10.2609i	0.902466	−	0.579980i	−0.00505440	−	0.999987i	$-0.501609\pi$
$313$	15.9663	−	10.2609i	0.902466	−	0.579980i	0.907521	+	0.420007i	$0.137973\pi$
$314$		0			0
$315$	−1.74241	−	12.1187i	−0.0981738	−	0.682814i
$316$		0			0
$317$	−13.4923	−	8.67097i	−0.757803	−	0.487010i	0.103797	−	0.994599i	$-0.466901\pi$
$317$	−13.4923	−	8.67097i	−0.757803	−	0.487010i	−0.861600	+	0.507588i	$0.830537\pi$
$318$		0			0
$319$	−11.2647	+	3.30761i	−0.630701	+	0.185190i
$320$		0			0
$321$	10.1983			0.569215
$322$		0			0
$323$	−22.6524			−1.26041
$324$		0			0
$325$	4.20260	−	1.23399i	0.233118	−	0.0684497i
$326$		0			0
$327$	14.8951	+	9.57253i	0.823703	+	0.529362i
$328$		0			0
$329$	6.91440	+	48.0907i	0.381203	+	2.65133i
$330$		0			0
$331$	−0.914062	+	0.587432i	−0.0502414	+	0.0322882i	−0.565520	−	0.824734i	$-0.691325\pi$
$331$	−0.914062	+	0.587432i	−0.0502414	+	0.0322882i	0.515279	+	0.857022i	$0.327688\pi$
$332$		0			0
$333$	1.46229	−	3.20197i	0.0801331	−	0.175467i
$334$		0			0
$335$	3.53424	−	24.5812i	0.193096	−	1.34302i
$336$		0			0
$337$	31.7746	+	9.32986i	1.73087	+	0.508230i	0.987087	−	0.160188i	$-0.0512099\pi$
$337$	31.7746	+	9.32986i	1.73087	+	0.508230i	0.743786	+	0.668418i	$0.233028\pi$
$338$		0			0
$339$	12.2895	+	14.1829i	0.667476	+	0.770308i
$340$		0			0
$341$	−10.2090	+	11.7818i	−0.552847	+	0.638019i
$342$		0			0
$343$	−2.98339	−	6.53271i	−0.161088	−	0.352733i
$344$		0			0
$345$	8.11537	−	12.3394i	0.436917	−	0.664332i
$346$		0			0
$347$	6.77853	+	14.8429i	0.363890	+	0.796809i	0.999689	+	0.0249536i	$0.00794381\pi$
$347$	6.77853	+	14.8429i	0.363890	+	0.796809i	−0.635798	+	0.771855i	$0.719329\pi$
$348$		0			0
$349$	−8.01557	+	9.25046i	−0.429064	+	0.495166i	−0.928577	−	0.371141i	$-0.878967\pi$
$349$	−8.01557	+	9.25046i	−0.429064	+	0.495166i	0.499513	+	0.866306i	$0.333512\pi$
$350$		0			0
$351$	0.639747	+	0.738307i	0.0341471	+	0.0394079i
$352$		0			0
$353$	32.2202	+	9.46070i	1.71491	+	0.503542i	0.983884	−	0.178810i	$-0.0572246\pi$
$353$	32.2202	+	9.46070i	1.71491	+	0.503542i	0.731024	+	0.682352i	$0.239043\pi$
$354$		0			0
$355$	4.51751	−	31.4200i	0.239764	−	1.66760i
$356$		0			0
$357$	−4.35975	+	9.54651i	−0.230742	+	0.505255i
$358$		0			0
$359$	−22.8274	+	14.6703i	−1.20478	+	0.774267i	−0.979778	−	0.200090i	$-0.935877\pi$
$359$	−22.8274	+	14.6703i	−1.20478	+	0.774267i	−0.225006	+	0.974357i	$0.572240\pi$
$360$		0			0
$361$	−7.77579	−	54.0818i	−0.409252	−	2.84641i
$362$		0			0
$363$	−5.81924	−	3.73980i	−0.305431	−	0.196289i
$364$		0			0
$365$	−47.3759	+	13.9108i	−2.47977	+	0.728125i
$366$		0			0
$367$	22.1343			1.15540			0.577701	−	0.816249i	$-0.303950\pi$
$367$	22.1343			1.15540			0.577701	+	0.816249i	$0.303950\pi$
$368$		0			0
$369$	−2.17195			−0.113067
$370$		0			0
$371$	−18.5412	+	5.44418i	−0.962610	+	0.282648i
$372$		0			0
$373$	−1.59491	−	1.02498i	−0.0825811	−	0.0530717i	0.498699	−	0.866775i	$-0.333811\pi$
$373$	−1.59491	−	1.02498i	−0.0825811	−	0.0530717i	−0.581280	+	0.813704i	$0.697448\pi$
$374$		0			0
$375$	−0.226363	−	1.57439i	−0.0116893	−	0.0813012i
$376$		0			0
$377$	−4.77520	+	3.06884i	−0.245935	+	0.158053i
$378$		0			0
$379$	−4.85137	+	10.6230i	−0.249198	+	0.545668i	−0.992350	−	0.123455i	$-0.960603\pi$
$379$	−4.85137	+	10.6230i	−0.249198	+	0.545668i	0.743152	+	0.669122i	$0.233330\pi$
$380$		0			0
$381$	2.66942	−	18.5662i	0.136758	−	0.951176i
$382$		0			0
$383$	22.9393	+	6.73559i	1.17214	+	0.344172i	0.809140	−	0.587616i	$-0.199933\pi$
$383$	22.9393	+	6.73559i	1.17214	+	0.344172i	0.363003	+	0.931788i	$0.381751\pi$
$384$		0			0
$385$	−16.2002	−	18.6960i	−0.825640	−	0.952839i
$386$		0			0
$387$	1.16055	−	1.33935i	0.0589943	−	0.0680831i
$388$		0			0
$389$	−11.6365	−	25.4804i	−0.589994	−	1.29191i	−0.935446	−	0.353471i	$-0.885001\pi$
$389$	−11.6365	−	25.4804i	−0.589994	−	1.29191i	0.345451	−	0.938437i	$-0.387726\pi$
$390$		0			0
$391$	−11.5706	+	5.13722i	−0.585152	+	0.259800i
$392$		0			0
$393$	−0.135867	−	0.297507i	−0.00685359	−	0.0150073i
$394$		0			0
$395$	16.2872	−	18.7965i	0.819499	−	0.945752i
$396$		0			0
$397$	−17.2001	−	19.8499i	−0.863246	−	0.996239i	−0.999984	−	0.00563192i	$-0.998207\pi$
$397$	−17.2001	−	19.8499i	−0.863246	−	0.996239i	0.136738	−	0.990607i	$-0.456338\pi$
$398$		0			0
$399$	−32.7347	−	9.61179i	−1.63879	−	0.481191i
$400$		0			0
$401$	0.420665	−	2.92579i	0.0210070	−	0.146107i	−0.976618	−	0.214980i	$-0.931031\pi$
$401$	0.420665	−	2.92579i	0.0210070	−	0.146107i	0.997625	+	0.0688732i	$0.0219404\pi$
$402$		0			0
$403$	−3.13114	+	6.85625i	−0.155973	+	0.341534i
$404$		0			0
$405$	−2.59066	+	1.66492i	−0.128731	+	0.0827305i
$406$		0			0
$407$	−1.01222	−	7.04012i	−0.0501737	−	0.348966i
$408$		0			0
$409$	13.5717	+	8.72202i	0.671079	+	0.431276i	0.831314	−	0.555803i	$-0.187589\pi$
$409$	13.5717	+	8.72202i	0.671079	+	0.431276i	−0.160235	+	0.987079i	$0.551225\pi$
$410$		0			0
$411$	6.93366	−	2.03591i	0.342012	−	0.100424i
$412$		0			0
$413$	37.6913			1.85467
$414$		0			0
$415$	−5.03029			−0.246927
$416$		0			0
$417$	3.27309	−	0.961066i	0.160284	−	0.0470636i
$418$		0			0
$419$	−7.88437	−	5.06697i	−0.385176	−	0.247538i	0.333695	−	0.942681i	$-0.391705\pi$
$419$	−7.88437	−	5.06697i	−0.385176	−	0.247538i	−0.718871	+	0.695143i	$0.755341\pi$
$420$		0			0
$421$	3.51250	+	24.4300i	0.171189	+	1.19064i	0.876378	+	0.481625i	$0.159953\pi$
$421$	3.51250	+	24.4300i	0.171189	+	1.19064i	−0.705189	+	0.709020i	$0.749138\pi$
$422$		0			0
$423$	10.2805	−	6.60688i	0.499856	−	0.321238i
$424$		0			0
$425$	4.91657	−	10.7658i	0.238488	−	0.522217i
$426$		0			0
$427$	2.47900	−	17.2419i	0.119967	−	0.834392i
$428$		0			0
$429$	1.89397	+	0.556119i	0.0914415	+	0.0268497i
$430$		0			0
$431$	23.2206	+	26.7980i	1.11850	+	1.29081i	0.952450	+	0.304694i	$0.0985541\pi$
$431$	23.2206	+	26.7980i	1.11850	+	1.29081i	0.166045	+	0.986118i	$0.446900\pi$
$432$		0			0
$433$	−21.9307	+	25.3094i	−1.05392	+	1.21629i	−0.0782807	+	0.996931i	$0.524943\pi$
$433$	−21.9307	+	25.3094i	−1.05392	+	1.21629i	−0.975644	+	0.219362i	$0.929602\pi$
$434$		0			0
$435$	−7.43314	−	16.2763i	−0.356392	−	0.780389i
$436$		0			0
$437$	−21.8830	−	34.8541i	−1.04680	−	1.66730i
$438$		0			0
$439$	7.08746	+	15.5194i	0.338266	+	0.740700i	0.999959	−	0.00907560i	$-0.00288889\pi$
$439$	7.08746	+	15.5194i	0.338266	+	0.740700i	−0.661693	+	0.749775i	$0.730162\pi$
$440$		0			0
$441$	−5.76696	+	6.65543i	−0.274617	+	0.316925i
$442$		0			0
$443$	12.7007	+	14.6574i	0.603427	+	0.696392i	0.972472	−	0.233020i	$-0.0748607\pi$
$443$	12.7007	+	14.6574i	0.603427	+	0.696392i	−0.369045	+	0.929411i	$0.620315\pi$
$444$		0			0
$445$	20.7027	+	6.07887i	0.981404	+	0.288166i
$446$		0			0
$447$	1.35879	−	9.45056i	0.0642683	−	0.446996i
$448$		0			0
$449$	−14.9497	+	32.7352i	−0.705519	+	1.54487i	0.127630	+	0.991822i	$0.459263\pi$
$449$	−14.9497	+	32.7352i	−0.705519	+	1.54487i	−0.833149	+	0.553049i	$0.813464\pi$
$450$		0			0
$451$	−3.69188	+	2.37262i	−0.173844	+	0.111723i
$452$		0			0
$453$	3.40181	+	23.6601i	0.159831	+	1.11165i
$454$		0			0
$455$	−10.0621	−	6.46649i	−0.471716	−	0.303154i
$456$		0			0
$457$	−13.2564	+	3.89244i	−0.620109	+	0.182080i	−0.576672	−	0.816976i	$-0.695649\pi$
$457$	−13.2564	+	3.89244i	−0.620109	+	0.182080i	−0.0434370	+	0.999056i	$0.513831\pi$
$458$		0			0
$459$	2.63975			0.123213
$460$		0			0
$461$	−9.75109			−0.454153			−0.227077	−	0.973877i	$-0.572917\pi$
$461$	−9.75109			−0.454153			−0.227077	+	0.973877i	$0.572917\pi$
$462$		0			0
$463$	22.1455	−	6.50250i	1.02919	−	0.302197i	0.276807	−	0.960926i	$-0.410724\pi$
$463$	22.1455	−	6.50250i	1.02919	−	0.302197i	0.752380	+	0.658729i	$0.228906\pi$
$464$		0			0
$465$	−19.9882	−	12.8456i	−0.926929	−	0.595701i
$466$		0			0
$467$	−1.00187	−	6.96816i	−0.0463610	−	0.322448i	−0.999783	−	0.0208096i	$-0.993376\pi$
$467$	−1.00187	−	6.96816i	−0.0463610	−	0.322448i	0.953422	−	0.301638i	$-0.0975335\pi$
$468$		0			0
$469$	−26.9715	+	17.3335i	−1.24543	+	0.800389i
$470$		0			0
$471$	−0.454818	+	0.995913i	−0.0209569	+	0.0458892i
$472$		0			0
$473$	0.509610	−	3.54442i	0.0234319	−	0.162972i
$474$		0			0
$475$	36.9156	+	10.8394i	1.69380	+	0.497345i
$476$		0			0
$477$	3.18294	+	3.67331i	0.145737	+	0.168189i
$478$		0			0
$479$	−16.4277	+	18.9585i	−0.750600	+	0.866238i	−0.994626	−	0.103530i	$-0.966986\pi$
$479$	−16.4277	+	18.9585i	−0.750600	+	0.866238i	0.244027	+	0.969769i	$0.421532\pi$
$480$		0			0
$481$	−1.42854	−	3.12807i	−0.0651359	−	0.142628i
$482$		0			0
$483$	−18.9004	+	2.51414i	−0.859999	+	0.114397i
$484$		0			0
$485$	11.1617	+	24.4406i	0.506825	+	1.10979i
$486$		0			0
$487$	5.19952	−	6.00056i	0.235613	−	0.271911i	−0.625614	−	0.780133i	$-0.715151\pi$
$487$	5.19952	−	6.00056i	0.235613	−	0.271911i	0.861226	+	0.508222i	$0.169697\pi$
$488$		0			0
$489$	−8.45213	−	9.75428i	−0.382219	−	0.441104i
$490$		0			0
$491$	29.0114	+	8.51853i	1.30927	+	0.384436i	0.860609	−	0.509267i	$-0.170083\pi$
$491$	29.0114	+	8.51853i	1.30927	+	0.384436i	0.448659	+	0.893703i	$0.351902\pi$
$492$		0			0
$493$	−2.18282	+	15.1819i	−0.0983094	+	0.683757i
$494$		0			0
$495$	−2.58486	+	5.66006i	−0.116181	+	0.254401i
$496$		0			0
$497$	−34.4753	+	22.1559i	−1.54643	+	0.993829i
$498$		0			0
$499$	0.981946	+	6.82958i	0.0439579	+	0.305734i	0.999925	+	0.0122597i	$0.00390247\pi$
$499$	0.981946	+	6.82958i	0.0439579	+	0.305734i	−0.955967	+	0.293474i	$0.905188\pi$
$500$		0			0
$501$	11.3573	+	7.29892i	0.507409	+	0.326092i
$502$		0			0
$503$	7.76444	−	2.27985i	0.346199	−	0.101653i	−0.104010	−	0.994576i	$-0.533167\pi$
$503$	7.76444	−	2.27985i	0.346199	−	0.101653i	0.450210	+	0.892923i	$0.351349\pi$
$504$		0			0
$505$	−10.6442			−0.473662
$506$		0			0
$507$	−12.0456			−0.534965
$508$		0			0
$509$	41.5515	−	12.2006i	1.84174	−	0.540783i	0.841739	−	0.539884i	$-0.181532\pi$
$509$	41.5515	−	12.2006i	1.84174	−	0.540783i	1.00000		0.000898802i	$-0.000286098\pi$
$510$		0			0
$511$	53.6259	+	34.4633i	2.37227	+	1.52456i
$512$		0			0
$513$	1.22124	+	8.49391i	0.0539191	+	0.375015i
$514$		0			0
$515$	5.55209	−	3.56811i	0.244654	−	0.157230i
$516$		0			0
$517$	10.2575	−	22.4608i	0.451124	−	0.987824i
$518$		0			0
$519$	−0.560002	+	3.89490i	−0.0245814	+	0.170967i
$520$		0			0
$521$	−23.7768	−	6.98150i	−1.04168	−	0.305865i	−0.284230	−	0.958756i	$-0.591738\pi$
$521$	−23.7768	−	6.98150i	−1.04168	−	0.305865i	−0.757452	+	0.652891i	$0.773556\pi$
$522$		0			0
$523$	−7.17391	−	8.27913i	−0.313693	−	0.362021i	0.576906	−	0.816811i	$-0.304260\pi$
$523$	−7.17391	−	8.27913i	−0.313693	−	0.362021i	−0.890599	+	0.454790i	$0.849714\pi$
$524$		0			0
$525$	11.6730	−	13.4714i	0.509451	−	0.587938i
$526$		0			0
$527$	8.46071	+	18.5264i	0.368554	+	0.807021i
$528$		0			0
$529$	−19.0820	−	12.8404i	−0.829653	−	0.558279i
$530$		0			0
$531$	−3.93828	−	8.62364i	−0.170907	−	0.374234i
$532$		0			0
$533$	−1.38949	+	1.60356i	−0.0601857	+	0.0694580i
$534$		0			0
$535$	20.5666	+	23.7351i	0.889171	+	1.02616i
$536$		0			0
$537$	0.711148	+	0.208812i	0.0306883	+	0.00901090i
$538$		0			0
$539$	−2.53232	+	17.6127i	−0.109075	+	0.758633i
$540$		0			0
$541$	−10.3277	+	22.6145i	−0.444022	+	0.972272i	0.546821	+	0.837250i	$0.315838\pi$
$541$	−10.3277	+	22.6145i	−0.444022	+	0.972272i	−0.990843	+	0.135022i	$0.956889\pi$
$542$		0			0
$543$	−1.03836	+	0.667310i	−0.0445601	+	0.0286370i
$544$		0			0
$545$	7.75983	+	53.9708i	0.332395	+	2.31186i
$546$		0			0
$547$	0.578133	+	0.371543i	0.0247192	+	0.0158860i	0.552942	−	0.833220i	$-0.313505\pi$
$547$	0.578133	+	0.371543i	0.0247192	+	0.0158860i	−0.528223	+	0.849106i	$0.677141\pi$
$548$		0			0
$549$	−4.20390	+	1.23438i	−0.179418	+	0.0526819i
$550$		0			0
$551$	−49.8605			−2.12413
$552$		0			0
$553$	−32.1092			−1.36542
$554$		0			0
$555$	10.4011	−	3.05403i	0.441501	−	0.129636i
$556$		0			0
$557$	−8.51090	−	5.46963i	−0.360619	−	0.231755i	0.347767	−	0.937581i	$-0.386940\pi$
$557$	−8.51090	−	5.46963i	−0.360619	−	0.231755i	−0.708386	+	0.705825i	$0.750576\pi$
$558$		0			0
$559$	−0.246392	−	1.71369i	−0.0104213	−	0.0724814i
$560$		0			0
$561$	4.48705	−	2.88365i	0.189443	−	0.121748i
$562$		0			0
$563$	7.02482	−	15.3822i	0.296061	−	0.648282i	−0.701889	−	0.712286i	$-0.747660\pi$
$563$	7.02482	−	15.3822i	0.296061	−	0.648282i	0.997950	+	0.0640039i	$0.0203870\pi$
$564$		0			0
$565$	−8.22472	+	57.2042i	−0.346016	+	2.40660i
$566$		0			0
$567$	3.81468	+	1.12009i	0.160202	+	0.0470394i
$568$		0			0
$569$	7.88445	+	9.09914i	0.330533	+	0.381456i	0.896553	−	0.442936i	$-0.146063\pi$
$569$	7.88445	+	9.09914i	0.330533	+	0.381456i	−0.566020	+	0.824391i	$0.691518\pi$
$570$		0			0
$571$	−16.8867	+	19.4883i	−0.706687	+	0.815560i	−0.989640	−	0.143574i	$-0.954141\pi$
$571$	−16.8867	+	19.4883i	−0.706687	+	0.815560i	0.282953	+	0.959134i	$0.408686\pi$
$572$		0			0
$573$	−9.34118	−	20.4543i	−0.390233	−	0.854492i
$574$		0			0
$575$	21.3144	−	2.83524i	0.888870	−	0.118238i
$576$		0			0
$577$	−5.48927	−	12.0198i	−0.228521	−	0.500392i	0.760286	−	0.649588i	$-0.225059\pi$
$577$	−5.48927	−	12.0198i	−0.228521	−	0.500392i	−0.988808	+	0.149196i	$0.952331\pi$
$578$		0			0
$579$	−4.44155	+	5.12582i	−0.184585	+	0.213022i
$580$		0			0
$581$	4.25279	+	4.90798i	0.176435	+	0.203617i
$582$		0			0
$583$	9.42307	+	2.76686i	0.390264	+	0.114592i
$584$		0			0
$585$	−0.428148	+	2.97783i	−0.0177017	+	0.123118i
$586$		0			0
$587$	−17.2465	+	37.7646i	−0.711839	+	1.55871i	0.113161	+	0.993577i	$0.463902\pi$
$587$	−17.2465	+	37.7646i	−0.711839	+	1.55871i	−0.825000	+	0.565133i	$0.808825\pi$
$588$		0			0
$589$	−55.6980	+	35.7949i	−2.29500	+	1.47490i
$590$		0			0
$591$	−0.0712014	−	0.495216i	−0.00292883	−	0.0203705i
$592$		0			0
$593$	9.19857	+	5.91156i	0.377740	+	0.242759i	0.715709	−	0.698398i	$-0.246104\pi$
$593$	9.19857	+	5.91156i	0.377740	+	0.242759i	−0.337969	+	0.941157i	$0.609740\pi$
$594$		0			0
$595$	−31.0102	+	9.10543i	−1.27130	+	0.373286i
$596$		0			0
$597$	−10.6163			−0.434495
$598$		0			0
$599$	−11.4352			−0.467232			−0.233616	−	0.972329i	$-0.575056\pi$
$599$	−11.4352			−0.467232			−0.233616	+	0.972329i	$0.575056\pi$
$600$		0			0
$601$	−8.45197	+	2.48172i	−0.344763	+	0.101232i	−0.449530	−	0.893265i	$-0.648408\pi$
$601$	−8.45197	+	2.48172i	−0.344763	+	0.101232i	0.104767	+	0.994497i	$0.466590\pi$
$602$		0			0
$603$	6.78405	+	4.35984i	0.276268	+	0.177547i
$604$		0			0
$605$	−3.03161	−	21.0853i	−0.123253	−	0.857241i
$606$		0			0
$607$	28.7543	−	18.4793i	1.16710	−	0.750050i	0.194130	−	0.980976i	$-0.437812\pi$
$607$	28.7543	−	18.4793i	1.16710	−	0.750050i	0.972971	+	0.230925i	$0.0741754\pi$
$608$		0			0
$609$	−9.59631	+	21.0130i	−0.388862	+	0.851489i
$610$		0			0
$611$	1.69901	−	11.8169i	0.0687348	−	0.478061i
$612$		0			0
$613$	12.0864	+	3.54890i	0.488167	+	0.143339i	0.516547	−	0.856259i	$-0.327217\pi$
$613$	12.0864	+	3.54890i	0.488167	+	0.143339i	−0.0283809	+	0.999597i	$0.509035\pi$
$614$		0			0
$615$	−4.38008	−	5.05488i	−0.176622	−	0.203833i
$616$		0			0
$617$	16.3628	−	18.8837i	0.658741	−	0.760227i	−0.323830	−	0.946115i	$-0.604971\pi$
$617$	16.3628	−	18.8837i	0.658741	−	0.760227i	0.982571	+	0.185888i	$0.0595161\pi$
$618$		0			0
$619$	−15.3463	−	33.6038i	−0.616822	−	1.35065i	−0.917809	−	0.397023i	$-0.870043\pi$
$619$	−15.3463	−	33.6038i	−0.616822	−	1.35065i	0.300987	−	0.953628i	$-0.402684\pi$
$620$		0			0
$621$	2.55009	+	4.06165i	0.102332	+	0.162989i
$622$		0			0
$623$	−11.5718	−	25.3387i	−0.463614	−	1.01517i
$624$		0			0
$625$	17.8880	−	20.6439i	0.715520	−	0.825754i
$626$		0			0
$627$	11.3546	+	13.1039i	0.453458	+	0.523319i
$628$		0			0
$629$	−8.91572	−	2.61789i	−0.355493	−	0.104382i
$630$		0			0
$631$	6.88059	−	47.8555i	0.273912	−	1.90510i	−0.132110	−	0.991235i	$-0.542175\pi$
$631$	6.88059	−	47.8555i	0.273912	−	1.90510i	0.406022	−	0.913863i	$-0.366916\pi$
$632$		0			0
$633$	−8.45351	+	18.5106i	−0.335997	+	0.735731i
$634$		0			0
$635$	48.5934	−	31.2291i	1.92837	−	1.23929i
$636$		0			0
$637$	1.22435	+	8.51557i	0.0485107	+	0.337399i
$638$		0			0
$639$	8.67144	+	5.57280i	0.343037	+	0.220456i
$640$		0			0
$641$	30.7285	−	9.02269i	1.21370	−	0.356375i	0.388625	−	0.921396i	$-0.372950\pi$
$641$	30.7285	−	9.02269i	1.21370	−	0.356375i	0.825076	+	0.565021i	$0.191132\pi$
$642$		0			0
$643$	21.9873			0.867095			0.433547	−	0.901131i	$-0.357262\pi$
$643$	21.9873			0.867095			0.433547	+	0.901131i	$0.357262\pi$
$644$		0			0
$645$	5.45759			0.214892
$646$		0			0
$647$	−22.1222	+	6.49568i	−0.869715	+	0.255371i	−0.685994	−	0.727607i	$-0.740632\pi$
$647$	−22.1222	+	6.49568i	−0.869715	+	0.255371i	−0.183721	+	0.982978i	$0.558814\pi$
$648$		0			0
$649$	−16.1147	−	10.3563i	−0.632558	−	0.406520i
$650$		0			0
$651$	4.36544	+	30.3623i	0.171095	+	1.18999i
$652$		0			0
$653$	−5.02464	+	3.22914i	−0.196629	+	0.126366i	−0.635251	−	0.772306i	$-0.719103\pi$
$653$	−5.02464	+	3.22914i	−0.196629	+	0.126366i	0.438621	+	0.898672i	$0.355467\pi$
$654$		0			0
$655$	0.418407	−	0.916183i	0.0163485	−	0.0357982i
$656$		0			0
$657$	2.28182	−	15.8704i	0.0890223	−	0.619163i
$658$		0			0
$659$	−12.5615	−	3.68840i	−0.489328	−	0.143680i	0.0277555	−	0.999615i	$-0.491164\pi$
$659$	−12.5615	−	3.68840i	−0.489328	−	0.143680i	−0.517083	+	0.855935i	$0.672982\pi$
$660$		0			0
$661$	−6.17668	−	7.12827i	−0.240245	−	0.277257i	0.622804	−	0.782378i	$-0.285993\pi$
$661$	−6.17668	−	7.12827i	−0.240245	−	0.277257i	−0.863049	+	0.505121i	$0.831448\pi$
$662$		0			0
$663$	1.68877	−	1.94894i	0.0655864	−	0.0756907i
$664$		0			0
$665$	−43.6449	−	95.5690i	−1.69248	−	3.70601i
$666$		0			0
$667$	−25.4683	+	11.3076i	−0.986136	+	0.437833i
$668$		0			0
$669$	1.22494	+	2.68226i	0.0473591	+	0.103702i
$670$		0			0
$671$	−5.79737	+	6.69052i	−0.223805	+	0.258285i
$672$		0			0
$673$	15.6444	+	18.0546i	0.603049	+	0.695955i	0.972396	−	0.233336i	$-0.0749642\pi$
$673$	15.6444	+	18.0546i	0.603049	+	0.695955i	−0.369347	+	0.929291i	$0.620419\pi$
$674$		0			0
$675$	−4.30189	−	1.26315i	−0.165580	−	0.0486186i
$676$		0			0
$677$	1.71066	−	11.8979i	0.0657461	−	0.457274i	−0.930180	−	0.367103i	$-0.880350\pi$
$677$	1.71066	−	11.8979i	0.0657461	−	0.457274i	0.995926	−	0.0901711i	$-0.0287414\pi$
$678$		0			0
$679$	14.4099	−	31.5533i	0.553001	−	1.21090i
$680$		0			0
$681$	8.98599	−	5.77494i	0.344344	−	0.221296i
$682$		0			0
$683$	2.75102	+	19.1337i	0.105265	+	0.732132i	0.972275	+	0.233841i	$0.0751296\pi$
$683$	2.75102	+	19.1337i	0.105265	+	0.732132i	−0.867010	+	0.498291i	$0.833961\pi$
$684$		0			0
$685$	18.7211	+	12.0313i	0.715298	+	0.459694i
$686$		0			0
$687$	20.0522	−	5.88785i	0.765039	−	0.224636i
$688$		0			0
$689$	4.74830			0.180896
$690$		0			0
$691$	23.6699			0.900446			0.450223	−	0.892916i	$-0.351345\pi$
$691$	23.6699			0.900446			0.450223	+	0.892916i	$0.351345\pi$
$692$		0			0
$693$	7.70778	−	2.26321i	0.292794	−	0.0859722i
$694$		0			0
$695$	8.83745	+	5.67949i	0.335224	+	0.215435i
$696$		0			0
$697$	0.815947	+	5.67503i	0.0309062	+	0.214957i
$698$		0			0
$699$	−10.4411	+	6.71006i	−0.394917	+	0.253798i
$700$		0			0
$701$	15.9567	−	34.9404i	0.602677	−	1.31968i	−0.324794	−	0.945785i	$-0.605295\pi$
$701$	15.9567	−	34.9404i	0.602677	−	1.31968i	0.927471	−	0.373894i	$-0.121978\pi$
$702$		0			0
$703$	4.29886	−	29.8992i	0.162134	−	1.12767i
$704$		0			0
$705$	36.1089	+	10.6025i	1.35994	+	0.399314i
$706$		0			0
$707$	8.99902	+	10.3854i	0.338443	+	0.390584i
$708$		0			0
$709$	14.7718	−	17.0475i	0.554765	−	0.640233i	−0.407221	−	0.913330i	$-0.633502\pi$
$709$	14.7718	−	17.0475i	0.554765	−	0.640233i	0.961987	+	0.273096i	$0.0880477\pi$
$710$		0			0
$711$	3.35503	+	7.34648i	0.125823	+	0.275515i
$712$		0			0
$713$	−20.3323	+	30.9152i	−0.761450	+	1.15778i
$714$		0			0
$715$	2.52521	+	5.52943i	0.0944374	+	0.206789i
$716$		0			0
$717$	−3.94438	+	4.55206i	−0.147306	+	0.170000i
$718$		0			0
$719$	−7.62652	−	8.80148i	−0.284421	−	0.328240i	0.595503	−	0.803353i	$-0.296953\pi$
$719$	−7.62652	−	8.80148i	−0.284421	−	0.328240i	−0.879925	+	0.475113i	$0.842407\pi$
$720$		0			0
$721$	−8.17530	−	2.40048i	−0.304464	−	0.0893987i
$722$		0			0
$723$	−0.0108754	+	0.0756402i	−0.000404461	+	0.00281309i
$724$		0			0
$725$	10.8219	−	23.6967i	0.401917	−	0.880075i
$726$		0			0
$727$	−10.4150	+	6.69328i	−0.386269	+	0.248240i	−0.719335	−	0.694663i	$-0.755553\pi$
$727$	−10.4150	+	6.69328i	−0.386269	+	0.248240i	0.333066	+	0.942904i	$0.391917\pi$
$728$		0			0
$729$	−0.142315	−	0.989821i	−0.00527092	−	0.0366601i
$730$		0			0
$731$	−3.93556	−	2.52923i	−0.145562	−	0.0935469i
$732$		0			0
$733$	−13.1069	+	3.84853i	−0.484114	+	0.142149i	−0.514677	−	0.857384i	$-0.672088\pi$
$733$	−13.1069	+	3.84853i	−0.484114	+	0.142149i	0.0305630	+	0.999533i	$0.490270\pi$
$734$		0			0
$735$	−27.1195			−1.00032
$736$		0			0
$737$	16.2942			0.600205
$738$		0			0
$739$	−25.9329	+	7.61458i	−0.953956	+	0.280107i	−0.721433	−	0.692484i	$-0.756516\pi$
$739$	−25.9329	+	7.61458i	−0.953956	+	0.280107i	−0.232523	+	0.972591i	$0.574698\pi$
$740$		0			0
$741$	7.05240	+	4.53230i	0.259076	+	0.166498i
$742$		0			0
$743$	0.641562	+	4.46216i	0.0235366	+	0.163701i	0.998200	−	0.0599770i	$-0.0191027\pi$
$743$	0.641562	+	4.46216i	0.0235366	+	0.163701i	−0.974663	+	0.223678i	$0.928194\pi$
$744$		0			0
$745$	24.7350	−	15.8962i	0.906220	−	0.582392i
$746$		0			0
$747$	0.678564	−	1.48585i	0.0248274	−	0.0543643i
$748$		0			0
$749$	5.77026	−	40.1330i	0.210841	−	1.46643i
$750$		0			0
$751$	−4.02305	−	1.18127i	−0.146803	−	0.0431053i	0.207505	−	0.978234i	$-0.433466\pi$
$751$	−4.02305	−	1.18127i	−0.146803	−	0.0431053i	−0.354308	+	0.935129i	$0.615284\pi$
$752$		0			0
$753$	1.51320	+	1.74632i	0.0551440	+	0.0636395i
$754$		0			0
$755$	−48.2051	+	55.6317i	−1.75436	+	2.02464i
$756$		0			0
$757$	6.97975	+	15.2835i	0.253683	+	0.555489i	0.993034	−	0.117832i	$-0.0375944\pi$
$757$	6.97975	+	15.2835i	0.253683	+	0.555489i	−0.739350	+	0.673321i	$0.764867\pi$
$758$		0			0
$759$	8.77158	+	4.11830i	0.318388	+	0.149485i
$760$		0			0
$761$	−6.50274	−	14.2390i	−0.235724	−	0.516164i	0.754390	−	0.656426i	$-0.227933\pi$
$761$	−6.50274	−	14.2390i	−0.235724	−	0.516164i	−0.990114	+	0.140262i	$0.955205\pi$
$762$		0			0
$763$	46.0981	−	53.2000i	1.66886	−	1.92597i
$764$		0			0
$765$	5.32348	+	6.14363i	0.192471	+	0.222123i
$766$		0			0
$767$	−8.88639	−	2.60928i	−0.320869	−	0.0942156i
$768$		0			0
$769$	−2.65173	+	18.4432i	−0.0956239	+	0.665078i	0.884478	+	0.466582i	$0.154515\pi$
$769$	−2.65173	+	18.4432i	−0.0956239	+	0.665078i	−0.980102	+	0.198496i	$0.936394\pi$
$770$		0			0
$771$	5.21285	−	11.4146i	0.187736	−	0.411085i
$772$		0			0
$773$	−30.5736	+	19.6485i	−1.09966	+	0.706706i	−0.959015	−	0.283355i	$-0.908553\pi$
$773$	−30.5736	+	19.6485i	−1.09966	+	0.706706i	−0.140640	+	0.990061i	$0.544916\pi$
$774$		0			0
$775$	−4.92299	−	34.2402i	−0.176839	−	1.22994i
$776$		0			0
$777$	−11.7732	−	7.56619i	−0.422362	−	0.271435i
$778$		0			0
$779$	−17.8830	+	5.25094i	−0.640727	+	0.188134i
$780$		0			0
$781$	20.8274			0.745264
$782$		0			0
$783$	5.81040			0.207647
$784$		0			0
$785$	−3.23505	+	0.949898i	−0.115464	+	0.0339033i
$786$		0			0
$787$	28.7436	+	18.4724i	1.02460	+	0.658469i	0.941131	−	0.338041i	$-0.109764\pi$
$787$	28.7436	+	18.4724i	1.02460	+	0.658469i	0.0834671	+	0.996511i	$0.473401\pi$
$788$		0			0
$789$	−3.40569	−	23.6871i	−0.121246	−	0.843282i
$790$		0			0
$791$	62.7668	−	40.3377i	2.23173	−	1.43425i
$792$		0			0
$793$	−1.77808	+	3.89346i	−0.0631416	+	0.138261i
$794$		0			0
$795$	−2.13017	+	14.8156i	−0.0755493	+	0.525457i
$796$		0			0
$797$	28.0517	+	8.23672i	0.993642	+	0.291760i	0.737845	−	0.674971i	$-0.235844\pi$
$797$	28.0517	+	8.23672i	0.993642	+	0.291760i	0.255798	+	0.966730i	$0.417662\pi$
$798$		0			0
$799$	−21.1251	−	24.3797i	−0.747353	−	0.862492i
$800$		0			0
$801$	−4.58829	+	5.29517i	−0.162119	+	0.187096i
$802$		0			0
$803$	−13.4581	−	29.4692i	−0.474927	−	1.03995i
$804$		0			0
$805$	−43.9671	−	38.9178i	−1.54964	−	1.37167i
$806$		0			0
$807$	9.42940	+	20.6475i	0.331930	+	0.726826i
$808$		0			0
$809$	8.31136	−	9.59183i	0.292212	−	0.337231i	−0.590594	−	0.806969i	$-0.701106\pi$
$809$	8.31136	−	9.59183i	0.292212	−	0.337231i	0.882806	+	0.469739i	$0.155652\pi$
$810$		0			0
$811$	31.2783	+	36.0971i	1.09833	+	1.26754i	0.960860	+	0.277033i	$0.0893511\pi$
$811$	31.2783	+	36.0971i	1.09833	+	1.26754i	0.137468	+	0.990506i	$0.456103\pi$
$812$		0			0
$813$	8.06096	+	2.36691i	0.282710	+	0.0830112i
$814$		0			0
$815$	5.65655	−	39.3422i	0.198140	−	1.37810i
$816$		0			0
$817$	6.31756	−	13.8335i	0.221024	−	0.483974i
$818$		0			0
$819$	3.26740	−	2.09983i	0.114172	−	0.0733740i
$820$		0			0
$821$	0.471010	+	3.27594i	0.0164384	+	0.114331i	0.996388	−	0.0849117i	$-0.0270608\pi$
$821$	0.471010	+	3.27594i	0.0164384	+	0.114331i	−0.979950	+	0.199243i	$0.936152\pi$
$822$		0			0
$823$	−41.0448	−	26.3779i	−1.43073	−	0.919476i	−0.999854	−	0.0170663i	$-0.994567\pi$
$823$	−41.0448	−	26.3779i	−1.43073	−	0.919476i	−0.430879	−	0.902410i	$-0.641796\pi$
$824$		0			0
$825$	−8.69221	+	2.55226i	−0.302624	+	0.0888584i
$826$		0			0
$827$	−54.4776			−1.89437			−0.947185	−	0.320686i	$-0.896086\pi$
$827$	−54.4776			−1.89437			−0.947185	+	0.320686i	$0.896086\pi$
$828$		0			0
$829$	4.61846			0.160406			0.0802029	−	0.996779i	$-0.474443\pi$
$829$	4.61846			0.160406			0.0802029	+	0.996779i	$0.474443\pi$
$830$		0			0
$831$	−14.9195	+	4.38076i	−0.517552	+	0.151967i
$832$		0			0
$833$	19.5563	+	12.5681i	0.677587	+	0.435459i
$834$		0			0
$835$	5.91676	+	41.1520i	0.204758	+	1.42412i
$836$		0			0
$837$	6.49066	−	4.17129i	0.224350	−	0.144181i
$838$		0			0
$839$	10.8015	−	23.6520i	0.372909	−	0.816557i	−0.626404	−	0.779499i	$-0.715474\pi$
$839$	10.8015	−	23.6520i	0.372909	−	0.816557i	0.999313	−	0.0370586i	$-0.0117988\pi$
$840$		0			0
$841$	−0.677517	+	4.71224i	−0.0233627	+	0.162491i
$842$		0			0
$843$	−3.53780	−	1.03879i	−0.121848	−	0.0357779i
$844$		0			0
$845$	−24.2920	−	28.0344i	−0.835669	−	0.964413i
$846$		0			0
$847$	−18.0096	+	20.7842i	−0.618818	+	0.714154i
$848$		0			0
$849$	11.9221	+	26.1058i	0.409167	+	0.895950i
$850$		0			0
$851$	−4.58488	−	16.2472i	−0.157168	−	0.556946i
$852$		0			0
$853$	20.1195	+	44.0556i	0.688880	+	1.50844i	0.852953	+	0.521988i	$0.174809\pi$
$853$	20.1195	+	44.0556i	0.688880	+	1.50844i	−0.164073	+	0.986448i	$0.552463\pi$
$854$		0			0
$855$	−17.3055	+	19.9716i	−0.591835	+	0.683015i
$856$		0			0
$857$	3.91645	+	4.51983i	0.133783	+	0.154394i	0.818688	−	0.574238i	$-0.194702\pi$
$857$	3.91645	+	4.51983i	0.133783	+	0.154394i	−0.684905	+	0.728633i	$0.740156\pi$
$858$		0			0
$859$	−12.3126	−	3.61531i	−0.420101	−	0.123353i	0.0648483	−	0.997895i	$-0.479344\pi$
$859$	−12.3126	−	3.61531i	−0.420101	−	0.123353i	−0.484949	+	0.874542i	$0.661162\pi$
$860$		0			0
$861$	−1.22890	+	8.54717i	−0.0418807	+	0.291287i
$862$		0			0
$863$	14.9500	−	32.7359i	0.508904	−	1.11434i	−0.464568	−	0.885537i	$-0.653790\pi$
$863$	14.9500	−	32.7359i	0.508904	−	1.11434i	0.973472	−	0.228807i	$-0.0734824\pi$
$864$		0			0
$865$	−10.1941	+	6.55138i	−0.346611	+	0.222754i
$866$		0			0
$867$	1.42766	+	9.92962i	0.0484860	+	0.337227i
$868$		0			0
$869$	13.7281	+	8.82255i	0.465696	+	0.299284i
$870$		0			0
$871$	7.55898	−	2.21952i	0.256126	−	0.0752054i
$872$		0			0
$873$	−8.72494			−0.295295
$874$		0			0
$875$	−6.32371			−0.213780
$876$		0			0
$877$	−29.8313	+	8.75927i	−1.00733	+	0.295780i	−0.743462	−	0.668778i	$-0.766818\pi$
$877$	−29.8313	+	8.75927i	−1.00733	+	0.295780i	−0.263871	+	0.964558i	$0.584999\pi$
$878$		0			0
$879$	−18.4816	−	11.8774i	−0.623368	−	0.400614i
$880$		0			0
$881$	7.31549	+	50.8803i	0.246465	+	1.71420i	0.618333	+	0.785916i	$0.287808\pi$
$881$	7.31549	+	50.8803i	0.246465	+	1.71420i	−0.371868	+	0.928286i	$0.621283\pi$
$882$		0			0
$883$	15.8152	−	10.1638i	0.532225	−	0.342040i	−0.246766	−	0.969075i	$-0.579368\pi$
$883$	15.8152	−	10.1638i	0.532225	−	0.342040i	0.778991	+	0.627035i	$0.215732\pi$
$884$		0			0
$885$	12.1281	−	26.5567i	0.407680	−	0.892695i
$886$		0			0
$887$	4.21512	−	29.3168i	0.141530	−	0.984362i	−0.788016	−	0.615655i	$-0.788891\pi$
$887$	4.21512	−	29.3168i	0.141530	−	0.984362i	0.929546	−	0.368707i	$-0.120199\pi$
$888$		0			0
$889$	−71.5525	−	21.0097i	−2.39979	−	0.704643i
$890$		0			0
$891$	−1.32318	−	1.52704i	−0.0443283	−	0.0511576i
$892$		0			0
$893$	68.6733	−	79.2532i	2.29806	−	2.65211i
$894$		0			0
$895$	0.948166	+	2.07619i	0.0316937	+	0.0693995i
$896$		0			0
$897$	4.63016	+	0.715680i	0.154597	+	0.0238958i
$898$		0			0
$899$	18.6230	+	40.7787i	0.621112	+	1.36005i
$900$		0			0
$901$	8.40216	−	9.69661i	0.279917	−	0.323041i
$902$		0			0
$903$	−4.61405	−	5.32489i	−0.153546	−	0.177201i
$904$		0			0
$905$	−3.64708	−	1.07088i	−0.121233	−	0.0355972i
$906$		0			0
$907$	−7.28972	+	50.7011i	−0.242051	+	1.68350i	0.399744	+	0.916627i	$0.369099\pi$
$907$	−7.28972	+	50.7011i	−0.242051	+	1.68350i	−0.641795	+	0.766876i	$0.721810\pi$
$908$		0			0
$909$	1.43586	−	3.14409i	0.0476245	−	0.104283i
$910$		0			0
$911$	28.9955	−	18.6343i	0.960663	−	0.617380i	0.0364814	−	0.999334i	$-0.488385\pi$
$911$	28.9955	−	18.6343i	0.960663	−	0.617380i	0.924181	+	0.381954i	$0.124749\pi$
$912$		0			0
$913$	−0.469710	−	3.26691i	−0.0155451	−	0.108119i
$914$		0			0
$915$	−11.3507	−	7.29464i	−0.375242	−	0.241153i
$916$		0			0
$917$	−1.24764	+	0.366341i	−0.0412008	+	0.0120976i
$918$		0			0
$919$	51.6009			1.70216			0.851079	−	0.525038i	$-0.175949\pi$
$919$	51.6009			1.70216			0.851079	+	0.525038i	$0.175949\pi$
$920$		0			0
$921$	−6.48844			−0.213801
$922$		0			0
$923$	9.66196	−	2.83701i	0.318027	−	0.0933813i
$924$		0			0
$925$	13.2769	+	8.53253i	0.436541	+	0.280548i
$926$		0			0
$927$	0.304997	+	2.12130i	0.0100174	+	0.0696727i
$928$		0			0
$929$	6.43258	−	4.13397i	0.211046	−	0.135631i	−0.430848	−	0.902425i	$-0.641785\pi$
$929$	6.43258	−	4.13397i	0.211046	−	0.135631i	0.641894	+	0.766794i	$0.278149\pi$
$930$		0			0
$931$	−31.3929	+	68.7408i	−1.02886	+	2.25289i
$932$		0			0
$933$	−0.185612	+	1.29096i	−0.00607666	+	0.0422641i
$934$		0			0
$935$	15.7601	+	4.62759i	0.515412	+	0.151339i
$936$		0			0
$937$	6.46845	+	7.46499i	0.211315	+	0.243871i	0.851506	−	0.524346i	$-0.175690\pi$
$937$	6.46845	+	7.46499i	0.211315	+	0.243871i	−0.640190	+	0.768216i	$0.721145\pi$
$938$		0			0
$939$	−12.4287	+	14.3435i	−0.405595	+	0.468081i
$940$		0			0
$941$	4.68073	+	10.2494i	0.152587	+	0.334120i	0.970453	−	0.241289i	$-0.0775702\pi$
$941$	4.68073	+	10.2494i	0.152587	+	0.334120i	−0.817866	+	0.575409i	$0.804843\pi$
$942$		0			0
$943$	−7.94367	+	6.73774i	−0.258681	+	0.219411i
$944$		0			0
$945$	5.08608	+	11.1370i	0.165450	+	0.362285i
$946$		0			0
$947$	14.1332	−	16.3105i	0.459266	−	0.530021i	−0.478129	−	0.878290i	$-0.658685\pi$
$947$	14.1332	−	16.3105i	0.459266	−	0.530021i	0.937395	+	0.348268i	$0.113230\pi$
$948$		0			0
$949$	−10.2574	−	11.8377i	−0.332971	−	0.384269i
$950$		0			0
$951$	15.3887	+	4.51852i	0.499012	+	0.146523i
$952$		0			0
$953$	3.56313	−	24.7821i	0.115421	−	0.802771i	−0.847075	−	0.531474i	$-0.821638\pi$
$953$	3.56313	−	24.7821i	0.115421	−	0.802771i	0.962496	−	0.271297i	$-0.0874526\pi$
$954$		0			0
$955$	28.7664	−	62.9897i	0.930860	−	2.03830i
$956$		0			0
$957$	9.87652	−	6.34725i	0.319263	−	0.205178i
$958$		0			0
$959$	−4.08872	−	28.4377i	−0.132032	−	0.918301i
$960$		0			0
$961$	23.9996	+	15.4236i	0.774179	+	0.497535i
$962$		0			0
$963$	−9.78522	+	2.87320i	−0.315324	+	0.0925876i
$964$		0			0
$965$	−20.8867			−0.672367
$966$		0			0
$967$	39.6982			1.27661			0.638303	−	0.769785i	$-0.279637\pi$
$967$	39.6982			1.27661			0.638303	+	0.769785i	$0.279637\pi$
$968$		0			0
$969$	21.7348	−	6.38191i	0.698222	−	0.205016i
$970$		0			0
$971$	−23.3491	−	15.0056i	−0.749309	−	0.481552i	0.109411	−	0.993997i	$-0.465104\pi$
$971$	−23.3491	−	15.0056i	−0.749309	−	0.481552i	−0.858720	+	0.512445i	$0.828740\pi$
$972$		0			0
$973$	−1.93011	−	13.4242i	−0.0618766	−	0.430361i
$974$		0			0
$975$	−3.68471	+	2.36802i	−0.118005	+	0.0758373i
$976$		0			0
$977$	−21.8044	+	47.7451i	−0.697586	+	1.52750i	0.145288	+	0.989389i	$0.453589\pi$
$977$	−21.8044	+	47.7451i	−0.697586	+	1.52750i	−0.842874	+	0.538111i	$0.819138\pi$
$978$		0			0
$979$	−2.01476	+	14.0130i	−0.0643920	+	0.447856i
$980$		0			0
$981$	−16.9887	−	4.98833i	−0.542407	−	0.159265i
$982$		0			0
$983$	−9.28122	−	10.7111i	−0.296025	−	0.341631i	0.588180	−	0.808730i	$-0.299845\pi$
$983$	−9.28122	−	10.7111i	−0.296025	−	0.341631i	−0.884205	+	0.467099i	$0.845299\pi$
$984$		0			0
$985$	1.00895	−	1.16440i	0.0321480	−	0.0371007i
$986$		0			0
$987$	−20.1830	−	44.1947i	−0.642433	−	1.40673i
$988$		0			0
$989$	0.0897150	−	8.49878i	0.00285277	−	0.270245i
$990$		0			0
$991$	−19.4072	−	42.4959i	−0.616492	−	1.34993i	−0.918044	−	0.396479i	$-0.870232\pi$
$991$	−19.4072	−	42.4959i	−0.616492	−	1.34993i	0.301552	−	0.953450i	$-0.402495\pi$
$992$		0			0
$993$	0.711538	−	0.821158i	0.0225800	−	0.0260587i
$994$		0			0
$995$	−21.4095	−	24.7078i	−0.678725	−	0.783291i
$996$		0			0
$997$	2.44013	+	0.716486i	0.0772796	+	0.0226914i	0.320144	−	0.947369i	$-0.396269\pi$
$997$	2.44013	+	0.716486i	0.0772796	+	0.0226914i	−0.242864	+	0.970060i	$0.578087\pi$
$998$		0			0
$999$	−0.500959	+	3.48425i	−0.0158496	+	0.110237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.b.73.1	✓	30
23.6	even	11	inner	552.2.q.b.121.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.b.73.1	✓	30	1.1	even	1	trivial
552.2.q.b.121.1	yes	30	23.6	even	11	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{3} +(-2.59066 - 1.66492i) q^{5} +(0.565805 + 3.93526i) q^{7} +(0.841254 - 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.959493 + 0.281733i) q^{3} +(-2.59066 - 1.66492i) q^{5} +(0.565805 + 3.93526i) q^{7} +(0.841254 - 0.540641i) q^{9} +(0.839370 - 1.83796i) q^{11} +(0.139030 - 0.966976i) q^{13} +(2.95479 + 0.867604i) q^{15} +(-1.72867 - 1.99499i) q^{17} +(5.61953 - 6.48528i) q^{19} +(-1.65158 - 3.61645i) q^{21} +(1.39964 - 4.58705i) q^{23} +(1.86251 + 4.07833i) q^{25} +(-0.654861 + 0.755750i) q^{27} +(-3.80500 - 4.39120i) q^{29} +(-7.40293 - 2.17370i) q^{31} +(-0.287555 + 1.99999i) q^{33} +(5.08608 - 11.1370i) q^{35} +(2.96128 - 1.90310i) q^{37} +(0.139030 + 0.966976i) q^{39} +(-1.82716 - 1.17424i) q^{41} +(1.70043 - 0.499291i) q^{43} -3.07953 q^{45} +12.2205 q^{47} +(-8.44967 + 2.48105i) q^{49} +(2.22070 + 1.42716i) q^{51} +(0.691719 + 4.81101i) q^{53} +(-5.23459 + 3.36407i) q^{55} +(-3.56478 + 7.80578i) q^{57} +(1.34920 - 9.38386i) q^{59} +(-4.20390 - 1.23438i) q^{61} +(2.60355 + 3.00465i) q^{63} +(-1.97012 + 2.27364i) q^{65} +(3.35000 + 7.33547i) q^{67} +(-0.0506231 + 4.79556i) q^{69} +(4.28200 + 9.37627i) q^{71} +(10.4998 - 12.1174i) q^{73} +(-2.93607 - 3.38840i) q^{75} +(7.70778 + 2.26321i) q^{77} +(-1.14938 + 7.99412i) q^{79} +(0.415415 - 0.909632i) q^{81} +(1.37415 - 0.883115i) q^{83} +(1.15690 + 8.04644i) q^{85} +(4.88802 + 3.14134i) q^{87} +(-6.72270 + 1.97396i) q^{89} +3.88397 q^{91} +7.71546 q^{93} +(-25.3558 + 7.44513i) q^{95} +(-7.33989 - 4.71706i) q^{97} +(-0.287555 - 1.99999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 3 * q^9	\( 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43} - 22 q^{45} + 22 q^{47} + 19 q^{49} + 17 q^{51} + 25 q^{53} + 10 q^{55} + 24 q^{57} + 7 q^{59} + 8 q^{61} - 28 q^{65} - 23 q^{67} - q^{69} + 5 q^{71} + 34 q^{73} - 23 q^{75} + 62 q^{77} + 20 q^{79} - 3 q^{81} + 29 q^{83} - 46 q^{85} + 10 q^{87} - 67 q^{89} - 118 q^{91} - 26 q^{93} - 99 q^{95} - 41 q^{97} + 9 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * q^97 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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