LMFDB - Embedded newform 441.2.h.h.214.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(214,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 4]))

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

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

chi := DirichletCharacter("441.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.h (of order $3$, degree $2$, not 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			214.3
Character	$\chi$	$=$	441.214
Dual form			441.2.h.h.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.72661 q^{2} +(-1.70981 + 0.276691i) q^{3} +0.981184 q^{4} +(-1.75616 + 3.04175i) q^{5} +(2.95217 - 0.477737i) q^{6} +1.75910 q^{8} +(2.84688 - 0.946176i) q^{9} +O(q^{10})$	\(q-1.72661 q^{2} +(-1.70981 + 0.276691i) q^{3} +0.981184 q^{4} +(-1.75616 + 3.04175i) q^{5} +(2.95217 - 0.477737i) q^{6} +1.75910 q^{8} +(2.84688 - 0.946176i) q^{9} +(3.03220 - 5.25192i) q^{10} +(3.04532 + 5.27465i) q^{11} +(-1.67764 + 0.271484i) q^{12} +(0.560139 + 0.970190i) q^{13} +(2.16106 - 5.68672i) q^{15} -4.99965 q^{16} +(-0.601978 + 1.04266i) q^{17} +(-4.91546 + 1.63368i) q^{18} +(1.10269 + 1.90991i) q^{19} +(-1.72311 + 2.98452i) q^{20} +(-5.25808 - 9.10727i) q^{22} +(0.636695 - 1.10279i) q^{23} +(-3.00772 + 0.486726i) q^{24} +(-3.66817 - 6.35345i) q^{25} +(-0.967143 - 1.67514i) q^{26} +(-4.60583 + 2.40548i) q^{27} +(-3.10262 + 5.37390i) q^{29} +(-3.73132 + 9.81875i) q^{30} -0.188404 q^{31} +5.11425 q^{32} +(-6.66636 - 8.17602i) q^{33} +(1.03938 - 1.80026i) q^{34} +(2.79332 - 0.928373i) q^{36} +(-1.78835 - 3.09752i) q^{37} +(-1.90391 - 3.29767i) q^{38} +(-1.22617 - 1.50385i) q^{39} +(-3.08925 + 5.35074i) q^{40} +(1.68320 + 2.91538i) q^{41} +(-1.90276 + 3.29567i) q^{43} +(2.98802 + 5.17540i) q^{44} +(-2.12154 + 10.3211i) q^{45} +(-1.09932 + 1.90408i) q^{46} -5.72070 q^{47} +(8.54843 - 1.38336i) q^{48} +(6.33349 + 10.9699i) q^{50} +(0.740773 - 1.94930i) q^{51} +(0.549600 + 0.951935i) q^{52} +(4.16913 - 7.22115i) q^{53} +(7.95247 - 4.15334i) q^{54} -21.3922 q^{55} +(-2.41384 - 2.96047i) q^{57} +(5.35702 - 9.27862i) q^{58} -11.2685 q^{59} +(2.12040 - 5.57972i) q^{60} +12.0022 q^{61} +0.325300 q^{62} +1.16898 q^{64} -3.93477 q^{65} +(11.5102 + 14.1168i) q^{66} -7.91303 q^{67} +(-0.590651 + 1.02304i) q^{68} +(-0.783494 + 2.06172i) q^{69} -12.2052 q^{71} +(5.00795 - 1.66442i) q^{72} +(2.65737 - 4.60269i) q^{73} +(3.08779 + 5.34820i) q^{74} +(8.02980 + 9.84823i) q^{75} +(1.08194 + 1.87397i) q^{76} +(2.11712 + 2.59657i) q^{78} +9.21711 q^{79} +(8.78016 - 15.2077i) q^{80} +(7.20950 - 5.38731i) q^{81} +(-2.90623 - 5.03373i) q^{82} +(0.624950 - 1.08245i) q^{83} +(-2.11433 - 3.66213i) q^{85} +(3.28532 - 5.69034i) q^{86} +(3.81798 - 10.0468i) q^{87} +(5.35702 + 9.27862i) q^{88} +(-2.77066 - 4.79892i) q^{89} +(3.66308 - 17.8206i) q^{90} +(0.624715 - 1.08204i) q^{92} +(0.322134 - 0.0521295i) q^{93} +9.87741 q^{94} -7.74596 q^{95} +(-8.74438 + 1.41506i) q^{96} +(8.24277 - 14.2769i) q^{97} +(13.6604 + 12.1349i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9	$ 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9} + 20 q^{11} + 4 q^{15} + 24 q^{16} - 32 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} - 84 q^{30} - 96 q^{32} - 4 q^{36} - 12 q^{37} + 8 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} + 64 q^{51} + 32 q^{53} - 12 q^{57} + 32 q^{60} + 96 q^{64} - 120 q^{65} + 24 q^{67} - 112 q^{71} + 68 q^{74} - 60 q^{78} - 24 q^{79} - 40 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 32 q^{93} - 128 q^{95} + 20 q^{99}+O(q^{100}) $ 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9 + 20 * q^11 + 4 * q^15 + 24 * q^16 - 32 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 - 84 * q^30 - 96 * q^32 - 4 * q^36 - 12 * q^37 + 8 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 + 64 * q^51 + 32 * q^53 - 12 * q^57 + 32 * q^60 + 96 * q^64 - 120 * q^65 + 24 * q^67 - 112 * q^71 + 68 * q^74 - 60 * q^78 - 24 * q^79 - 40 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 32 * q^93 - 128 * q^95 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.72661			−1.22090			−0.610449	−	0.792056i	$-0.709011\pi$
$2$	−1.72661			−1.22090			−0.610449	+	0.792056i	$0.709011\pi$
$3$	−1.70981	+	0.276691i	−0.987158	+	0.159747i
$3$	−1.70981	+	0.276691i	−0.987158	+	0.159747i
$4$	0.981184			0.490592
$5$	−1.75616	+	3.04175i	−0.785377	+	1.36031i	0.143397	+	0.989665i	$0.454197\pi$
$5$	−1.75616	+	3.04175i	−0.785377	+	1.36031i	−0.928774	+	0.370647i	$0.879136\pi$
$6$	2.95217	−	0.477737i	1.20522	−	0.195035i
$7$		0			0
$7$		0			0
$8$	1.75910			0.621935
$9$	2.84688	−	0.946176i	0.948962	−	0.315392i
$10$	3.03220	−	5.25192i	0.958865	−	1.66080i
$11$	3.04532	+	5.27465i	0.918199	+	1.59037i	0.802150	+	0.597123i	$0.203690\pi$
$11$	3.04532	+	5.27465i	0.918199	+	1.59037i	0.116049	+	0.993244i	$0.462977\pi$
$12$	−1.67764	+	0.271484i	−0.484292	+	0.0783708i
$13$	0.560139	+	0.970190i	0.155355	+	0.269082i	0.933188	−	0.359388i	$-0.117015\pi$
$13$	0.560139	+	0.970190i	0.155355	+	0.269082i	−0.777833	+	0.628471i	$0.783681\pi$
$14$		0			0
$15$	2.16106	−	5.68672i	0.557984	−	1.46831i
$16$	−4.99965			−1.24991
$17$	−0.601978	+	1.04266i	−0.146001	+	0.252881i	−0.929746	−	0.368202i	$-0.879974\pi$
$17$	−0.601978	+	1.04266i	−0.146001	+	0.252881i	0.783745	+	0.621083i	$0.213307\pi$
$18$	−4.91546	+	1.63368i	−1.15859	+	0.385061i
$19$	1.10269	+	1.90991i	0.252974	+	0.438163i	0.964343	−	0.264655i	$-0.0852581\pi$
$19$	1.10269	+	1.90991i	0.252974	+	0.438163i	−0.711370	+	0.702818i	$0.751925\pi$
$20$	−1.72311	+	2.98452i	−0.385300	+	0.667359i
$21$		0			0
$22$	−5.25808	−	9.10727i	−1.12103	−	1.94168i
$23$	0.636695	−	1.10279i	0.132760	−	0.229947i	−0.791980	−	0.610548i	$-0.790949\pi$
$23$	0.636695	−	1.10279i	0.132760	−	0.229947i	0.924740	+	0.380601i	$0.124283\pi$
$24$	−3.00772	+	0.486726i	−0.613948	+	0.0993525i
$25$	−3.66817	−	6.35345i	−0.733633	−	1.27069i
$26$	−0.967143	−	1.67514i	−0.189672	−	0.328522i
$27$	−4.60583	+	2.40548i	−0.886392	+	0.462936i
$28$		0			0
$29$	−3.10262	+	5.37390i	−0.576142	+	0.997907i	0.419774	+	0.907628i	$0.362109\pi$
$29$	−3.10262	+	5.37390i	−0.576142	+	0.997907i	−0.995917	+	0.0902789i	$0.971224\pi$
$30$	−3.73132	+	9.81875i	−0.681242	+	1.79265i
$31$	−0.188404			−0.0338383			−0.0169192	−	0.999857i	$-0.505386\pi$
$31$	−0.188404			−0.0338383			−0.0169192	+	0.999857i	$0.505386\pi$
$32$	5.11425			0.904079
$33$	−6.66636	−	8.17602i	−1.16046	−	1.42326i
$34$	1.03938	−	1.80026i	0.178252	−	0.308742i
$35$		0			0
$36$	2.79332	−	0.928373i	0.465553	−	0.154729i
$37$	−1.78835	−	3.09752i	−0.294003	−	0.509228i	0.680749	−	0.732516i	$-0.261654\pi$
$37$	−1.78835	−	3.09752i	−0.294003	−	0.509228i	−0.974753	+	0.223288i	$0.928321\pi$
$38$	−1.90391	−	3.29767i	−0.308855	−	0.534953i
$39$	−1.22617	−	1.50385i	−0.196345	−	0.240809i
$40$	−3.08925	+	5.35074i	−0.488453	+	0.846026i
$41$	1.68320	+	2.91538i	0.262871	+	0.455307i	0.967004	−	0.254762i	$-0.0819972\pi$
$41$	1.68320	+	2.91538i	0.262871	+	0.455307i	−0.704132	+	0.710069i	$0.748664\pi$
$42$		0			0
$43$	−1.90276	+	3.29567i	−0.290168	+	0.502585i	−0.973849	−	0.227195i	$-0.927044\pi$
$43$	−1.90276	+	3.29567i	−0.290168	+	0.502585i	0.683681	+	0.729781i	$0.260378\pi$
$44$	2.98802	+	5.17540i	0.450461	+	0.780221i
$45$	−2.12154	+	10.3211i	−0.316261	+	1.53859i
$46$	−1.09932	+	1.90408i	−0.162086	+	0.280742i
$47$	−5.72070			−0.834449			−0.417225	−	0.908803i	$-0.636997\pi$
$47$	−5.72070			−0.834449			−0.417225	+	0.908803i	$0.636997\pi$
$48$	8.54843	−	1.38336i	1.23386	−	0.199670i
$49$		0			0
$50$	6.33349	+	10.9699i	0.895691	+	1.55138i
$51$	0.740773	−	1.94930i	0.103729	−	0.272957i
$52$	0.549600	+	0.951935i	0.0762158	+	0.132010i
$53$	4.16913	−	7.22115i	0.572675	−	0.991901i	−0.423615	−	0.905842i	$-0.639239\pi$
$53$	4.16913	−	7.22115i	0.572675	−	0.991901i	0.996290	−	0.0860593i	$-0.0274275\pi$
$54$	7.95247	−	4.15334i	1.08219	−	0.565197i
$55$	−21.3922			−2.88453
$56$		0			0
$57$	−2.41384	−	2.96047i	−0.319720	−	0.392124i
$58$	5.35702	−	9.27862i	0.703411	−	1.21834i
$59$	−11.2685			−1.46704			−0.733519	−	0.679669i	$-0.762123\pi$
$59$	−11.2685			−1.46704			−0.733519	+	0.679669i	$0.762123\pi$
$60$	2.12040	−	5.57972i	0.273743	−	0.720339i
$61$	12.0022			1.53672			0.768361	−	0.640017i	$-0.221073\pi$
$61$	12.0022			1.53672			0.768361	+	0.640017i	$0.221073\pi$
$62$	0.325300			0.0413131
$63$		0			0
$64$	1.16898			0.146123
$65$	−3.93477			−0.488048
$66$	11.5102	+	14.1168i	1.41681	+	1.73766i
$67$	−7.91303			−0.966731			−0.483366	−	0.875419i	$-0.660586\pi$
$67$	−7.91303			−0.966731			−0.483366	+	0.875419i	$0.660586\pi$
$68$	−0.590651	+	1.02304i	−0.0716270	+	0.124062i
$69$	−0.783494	+	2.06172i	−0.0943217	+	0.248202i
$70$		0			0
$71$	−12.2052			−1.44850			−0.724248	−	0.689540i	$-0.757813\pi$
$71$	−12.2052			−1.44850			−0.724248	+	0.689540i	$0.757813\pi$
$72$	5.00795	−	1.66442i	0.590192	−	0.196153i
$73$	2.65737	−	4.60269i	0.311021	−	0.538704i	−0.667563	−	0.744554i	$-0.732662\pi$
$73$	2.65737	−	4.60269i	0.311021	−	0.538704i	0.978584	+	0.205849i	$0.0659957\pi$
$74$	3.08779	+	5.34820i	0.358948	+	0.621716i
$75$	8.02980	+	9.84823i	0.927201	+	1.13718i
$76$	1.08194	+	1.87397i	0.124107	+	0.214959i
$77$		0			0
$78$	2.11712	+	2.59657i	0.239717	+	0.294003i
$79$	9.21711			1.03701			0.518503	−	0.855076i	$-0.326490\pi$
$79$	9.21711			1.03701			0.518503	+	0.855076i	$0.326490\pi$
$80$	8.78016	−	15.2077i	0.981651	−	1.70027i
$81$	7.20950	−	5.38731i	0.801056	−	0.598589i
$82$	−2.90623	−	5.03373i	−0.320939	−	0.555883i
$83$	0.624950	−	1.08245i	0.0685972	−	0.118814i	−0.829687	−	0.558229i	$-0.811481\pi$
$83$	0.624950	−	1.08245i	0.0685972	−	0.118814i	0.898284	+	0.439415i	$0.144814\pi$
$84$		0			0
$85$	−2.11433	−	3.66213i	−0.229332	−	0.397214i
$86$	3.28532	−	5.69034i	0.354265	−	0.613605i
$87$	3.81798	−	10.0468i	0.409330	−	1.07713i
$88$	5.35702	+	9.27862i	0.571060	+	0.989105i
$89$	−2.77066	−	4.79892i	−0.293689	−	0.508684i	0.680990	−	0.732293i	$-0.261550\pi$
$89$	−2.77066	−	4.79892i	−0.293689	−	0.508684i	−0.974679	+	0.223608i	$0.928216\pi$
$90$	3.66308	−	17.8206i	0.386122	−	1.87846i
$91$		0			0
$92$	0.624715	−	1.08204i	0.0651310	−	0.112810i
$93$	0.322134	−	0.0521295i	0.0334038	−	0.00540558i
$94$	9.87741			1.01878
$95$	−7.74596			−0.794718
$96$	−8.74438	+	1.41506i	−0.892469	+	0.144424i
$97$	8.24277	−	14.2769i	0.836926	−	1.44960i	−0.0555261	−	0.998457i	$-0.517684\pi$
$97$	8.24277	−	14.2769i	0.836926	−	1.44960i	0.892452	−	0.451142i	$-0.148983\pi$
$98$		0			0
$99$	13.6604	+	12.1349i	1.37292	+	1.21960i
$100$	−3.59915	−	6.23391i	−0.359915	−	0.623391i
$101$	6.48192	+	11.2270i	0.644975	+	1.11713i	0.984307	+	0.176463i	$0.0564657\pi$
$101$	6.48192	+	11.2270i	0.644975	+	1.11713i	−0.339332	+	0.940667i	$0.610201\pi$
$102$	−1.27903	+	3.36569i	−0.126643	+	0.333253i
$103$	−1.35091	+	2.33984i	−0.133109	+	0.230552i	−0.924873	−	0.380275i	$-0.875829\pi$
$103$	−1.35091	+	2.33984i	−0.133109	+	0.230552i	0.791765	+	0.610826i	$0.209163\pi$
$104$	0.985340	+	1.70666i	0.0966205	+	0.167352i
$105$		0			0
$106$	−7.19847	+	12.4681i	−0.699177	+	1.21101i
$107$	0.0892402	+	0.154569i	0.00862718	+	0.0149427i	0.870307	−	0.492510i	$-0.163921\pi$
$107$	0.0892402	+	0.154569i	0.00862718	+	0.0149427i	−0.861680	+	0.507453i	$0.830587\pi$
$108$	−4.51917	+	2.36022i	−0.434857	+	0.227113i
$109$	−4.67927	+	8.10473i	−0.448192	+	0.776292i	−0.998268	−	0.0588226i	$-0.981265\pi$
$109$	−4.67927	+	8.10473i	−0.448192	+	0.776292i	0.550076	+	0.835115i	$0.314599\pi$
$110$	36.9360			3.52171
$111$	3.91479	+	4.80134i	0.371575	+	0.455723i
$112$		0			0
$113$	4.21019	+	7.29226i	0.396061	+	0.685998i	0.993236	−	0.116113i	$-0.0370434\pi$
$113$	4.21019	+	7.29226i	0.396061	+	0.685998i	−0.597175	+	0.802111i	$0.703710\pi$
$114$	4.16775	+	5.11159i	0.390346	+	0.478744i
$115$	2.23627	+	3.87333i	0.208533	+	0.361190i
$116$	−3.04424	+	5.27278i	−0.282651	+	0.489565i
$117$	2.51262	+	2.23203i	0.232292	+	0.206351i
$118$	19.4564			1.79110
$119$		0			0
$120$	3.80152	−	10.0035i	0.347030	−	0.913190i
$121$	−13.0479	+	22.5997i	−1.18618	+	2.05452i
$122$	−20.7231			−1.87618
$123$	−3.68460	−	4.51902i	−0.332230	−	0.407467i
$124$	−0.184859			−0.0166008
$125$	8.20593			0.733960
$126$		0			0
$127$	−9.92438			−0.880647			−0.440323	−	0.897839i	$-0.645136\pi$
$127$	−9.92438			−0.880647			−0.440323	+	0.897839i	$0.645136\pi$
$128$	−12.2469			−1.08248
$129$	2.34147	−	6.16144i	0.206155	−	0.542485i
$130$	6.79381			0.595857
$131$	7.62335	−	13.2040i	0.666055	−	1.15364i	−0.312943	−	0.949772i	$-0.601315\pi$
$131$	7.62335	−	13.2040i	0.666055	−	1.15364i	0.978998	−	0.203870i	$-0.0653519\pi$
$132$	−6.54093	−	8.02219i	−0.569314	−	0.698242i
$133$		0			0
$134$	13.6627			1.18028
$135$	0.771665	−	18.2342i	0.0664144	−	1.56935i
$136$	−1.05894	+	1.83413i	−0.0908032	+	0.157276i
$137$	−3.07350	−	5.32346i	−0.262587	−	0.454814i	0.704342	−	0.709861i	$-0.251242\pi$
$137$	−3.07350	−	5.32346i	−0.262587	−	0.454814i	−0.966929	+	0.255047i	$0.917909\pi$
$138$	1.35279	−	3.55979i	0.115157	−	0.303030i
$139$	0.438687	+	0.759829i	0.0372090	+	0.0644478i	0.884030	−	0.467430i	$-0.154820\pi$
$139$	0.438687	+	0.759829i	0.0372090	+	0.0644478i	−0.846821	+	0.531878i	$0.821487\pi$
$140$		0			0
$141$	9.78129	−	1.58286i	0.823733	−	0.133301i
$142$	21.0737			1.76847
$143$	−3.41161	+	5.90908i	−0.285293	+	0.494142i
$144$	−14.2334	+	4.73054i	−1.18612	+	0.394212i
$145$	−10.8974	−	18.8748i	−0.904977	−	1.56747i
$146$	−4.58824	+	7.94706i	−0.379725	+	0.657703i
$147$		0			0
$148$	−1.75470	−	3.03923i	−0.144236	−	0.249823i
$149$	−2.88776	+	5.00175i	−0.236575	+	0.409760i	−0.959729	−	0.280927i	$-0.909358\pi$
$149$	−2.88776	+	5.00175i	−0.236575	+	0.409760i	0.723154	+	0.690686i	$0.242692\pi$
$150$	−13.8643	−	17.0041i	−1.13202	−	1.38838i
$151$	1.01321	+	1.75494i	0.0824541	+	0.142815i	0.904304	−	0.426890i	$-0.140391\pi$
$151$	1.01321	+	1.75494i	0.0824541	+	0.142815i	−0.821849	+	0.569705i	$0.807058\pi$
$152$	1.93973	+	3.35972i	0.157333	+	0.272509i
$153$	−0.727226	+	3.53790i	−0.0587927	+	0.286022i
$154$		0			0
$155$	0.330866	−	0.573077i	0.0265758	−	0.0460307i
$156$	−1.20310	−	1.47556i	−0.0963252	−	0.118139i
$157$	−3.04756			−0.243222			−0.121611	−	0.992578i	$-0.538806\pi$
$157$	−3.04756			−0.243222			−0.121611	+	0.992578i	$0.538806\pi$
$158$	−15.9144			−1.26608
$159$	−5.13039	+	13.5003i	−0.406867	+	1.07065i
$160$	−8.98141	+	15.5563i	−0.710043	+	1.22983i
$161$		0			0
$162$	−12.4480	+	9.30178i	−0.978008	+	0.730817i
$163$	2.69445	+	4.66693i	0.211046	+	0.365542i	0.952042	−	0.305967i	$-0.0989797\pi$
$163$	2.69445	+	4.66693i	0.211046	+	0.365542i	−0.740996	+	0.671509i	$0.765646\pi$
$164$	1.65153	+	2.86053i	0.128963	+	0.223370i
$165$	36.5766	−	5.91903i	2.84748	−	0.460796i
$166$	−1.07905	+	1.86896i	−0.0837502	+	0.145060i
$167$	−8.30480	−	14.3843i	−0.642645	−	1.11309i	−0.984840	−	0.173464i	$-0.944504\pi$
$167$	−8.30480	−	14.3843i	−0.642645	−	1.11309i	0.342196	−	0.939629i	$-0.388829\pi$
$168$		0			0
$169$	5.87249	−	10.1714i	0.451730	−	0.782419i
$170$	3.65063	+	6.32308i	0.279991	+	0.484958i
$171$	4.94633	+	4.39396i	0.378255	+	0.336014i
$172$	−1.86696	+	3.23366i	−0.142354	+	0.246564i
$173$	−17.6503			−1.34193			−0.670965	−	0.741489i	$-0.734120\pi$
$173$	−17.6503			−1.34193			−0.670965	+	0.741489i	$0.734120\pi$
$174$	−6.59216	+	17.3469i	−0.499750	+	1.31507i
$175$		0			0
$176$	−15.2255	−	26.3714i	−1.14767	−	1.98782i
$177$	19.2670	−	3.11790i	1.44820	−	0.234355i
$178$	4.78384	+	8.28586i	0.358564	+	0.621051i
$179$	−1.31422	+	2.27630i	−0.0982294	+	0.170138i	−0.910952	−	0.412513i	$-0.864651\pi$
$179$	−1.31422	+	2.27630i	−0.0982294	+	0.170138i	0.812722	+	0.582651i	$0.197985\pi$
$180$	−2.08162	+	10.1269i	−0.155155	+	0.754818i
$181$	3.97391			0.295378			0.147689	−	0.989034i	$-0.452816\pi$
$181$	3.97391			0.295378			0.147689	+	0.989034i	$0.452816\pi$
$182$		0			0
$183$	−20.5214	+	3.32089i	−1.51699	+	0.245487i
$184$	1.12001	−	1.93991i	0.0825681	−	0.143012i
$185$	12.5625			0.923613
$186$	−0.556200	+	0.0900074i	−0.0407826	+	0.00659966i
$187$	−7.33286			−0.536232
$188$	−5.61306			−0.409374
$189$		0			0
$190$	13.3743			0.970270
$191$	−18.2059			−1.31733			−0.658666	−	0.752435i	$-0.728879\pi$
$191$	−18.2059			−1.31733			−0.658666	+	0.752435i	$0.728879\pi$
$192$	−1.99873	+	0.323446i	−0.144246	+	0.0233427i
$193$	−0.202385			−0.0145680			−0.00728401	−	0.999973i	$-0.502319\pi$
$193$	−0.202385			−0.0145680			−0.00728401	+	0.999973i	$0.502319\pi$
$194$	−14.2321	+	24.6506i	−1.02180	+	1.76981i
$195$	6.72770	−	1.08871i	0.481780	−	0.0779644i
$196$		0			0
$197$	−1.63136			−0.116229			−0.0581147	−	0.998310i	$-0.518509\pi$
$197$	−1.63136			−0.116229			−0.0581147	+	0.998310i	$0.518509\pi$
$198$	−23.5862	−	20.9523i	−1.67620	−	1.48901i
$199$	−3.14605	+	5.44912i	−0.223018	+	0.386278i	−0.955723	−	0.294268i	$-0.904924\pi$
$199$	−3.14605	+	5.44912i	−0.223018	+	0.386278i	0.732705	+	0.680546i	$0.238257\pi$
$200$	−6.45266	−	11.1763i	−0.456272	−	0.790287i
$201$	13.5298	−	2.18946i	0.954316	−	0.154433i
$202$	−11.1918	−	19.3847i	−0.787449	−	1.36390i
$203$		0			0
$204$	0.726835	−	1.91263i	0.0508886	−	0.133911i
$205$	−11.8238			−0.825812
$206$	2.33249	−	4.04000i	0.162512	−	0.281480i
$207$	0.769166	−	3.74193i	0.0534607	−	0.260082i
$208$	−2.80050	−	4.85061i	−0.194180	−	0.336329i
$209$	−6.71607	+	11.6326i	−0.464560	+	0.804642i
$210$		0			0
$211$	8.14368	+	14.1053i	0.560634	+	0.971046i	0.997441	+	0.0714912i	$0.0227758\pi$
$211$	8.14368	+	14.1053i	0.560634	+	0.971046i	−0.436807	+	0.899555i	$0.643891\pi$
$212$	4.09069	−	7.08528i	0.280950	−	0.486619i
$213$	20.8686	−	3.37708i	1.42989	−	0.231393i
$214$	−0.154083	−	0.266880i	−0.0105329	−	0.0182435i
$215$	−6.68308	−	11.5754i	−0.455782	−	0.789438i
$216$	−8.10210	+	4.23148i	−0.551278	+	0.287916i
$217$		0			0
$218$	8.07927	−	13.9937i	0.547197	−	0.947773i
$219$	−3.27006	+	8.60499i	−0.220970	+	0.581471i
$220$	−20.9897			−1.41513
$221$	−1.34877			−0.0907278
$222$	−6.75932	−	8.29004i	−0.453656	−	0.556391i
$223$	−9.98472	+	17.2940i	−0.668626	+	1.15809i	0.309662	+	0.950847i	$0.399784\pi$
$223$	−9.98472	+	17.2940i	−0.668626	+	1.15809i	−0.978288	+	0.207248i	$0.933549\pi$
$224$		0			0
$225$	−16.4543	−	14.6168i	−1.09695	−	0.974454i
$226$	−7.26936	−	12.5909i	−0.483551	−	0.837534i
$227$	−1.80642	−	3.12880i	−0.119896	−	0.207666i	0.799830	−	0.600226i	$-0.204923\pi$
$227$	−1.80642	−	3.12880i	−0.119896	−	0.207666i	−0.919726	+	0.392560i	$0.871589\pi$
$228$	−2.36842	−	2.90477i	−0.156852	−	0.192373i
$229$	−6.85733	+	11.8772i	−0.453145	+	0.784870i	−0.998579	−	0.0532835i	$-0.983031\pi$
$229$	−6.85733	+	11.8772i	−0.453145	+	0.784870i	0.545435	+	0.838153i	$0.316365\pi$
$230$	−3.86117	−	6.68774i	−0.254598	−	0.440976i
$231$		0			0
$232$	−5.45781	+	9.45321i	−0.358323	+	0.620634i
$233$	12.6271	+	21.8707i	0.827227	+	1.43280i	0.900205	+	0.435466i	$0.143417\pi$
$233$	12.6271	+	21.8707i	0.827227	+	1.43280i	−0.0729776	+	0.997334i	$0.523250\pi$
$234$	−4.33832	−	3.85384i	−0.283605	−	0.251934i
$235$	10.0464	−	17.4009i	0.655357	−	1.13511i
$236$	−11.0565			−0.719717
$237$	−15.7595	+	2.55029i	−1.02369	+	0.165659i
$238$		0			0
$239$	−4.49495	−	7.78549i	−0.290754	−	0.503601i	0.683234	−	0.730200i	$-0.260573\pi$
$239$	−4.49495	−	7.78549i	−0.290754	−	0.503601i	−0.973988	+	0.226598i	$0.927240\pi$
$240$	−10.8046	+	28.4316i	−0.697431	+	1.83525i
$241$	−4.62862	−	8.01701i	−0.298156	−	0.516421i	0.677558	−	0.735469i	$-0.263038\pi$
$241$	−4.62862	−	8.01701i	−0.298156	−	0.516421i	−0.975714	+	0.219048i	$0.929705\pi$
$242$	22.5287	−	39.0209i	1.44820	−	2.50836i
$243$	−10.8362	+	11.2061i	−0.695146	+	0.718869i
$244$	11.7763			0.753903
$245$		0			0
$246$	6.36188	+	7.80259i	0.405619	+	0.497475i
$247$	−1.23532	+	2.13963i	−0.0786013	+	0.136141i
$248$	−0.331421			−0.0210452
$249$	−0.769042	+	2.02369i	−0.0487361	+	0.128246i
$250$	−14.1684			−0.896091
$251$	20.6517			1.30353			0.651763	−	0.758422i	$-0.274030\pi$
$251$	20.6517			1.30353			0.651763	+	0.758422i	$0.274030\pi$
$252$		0			0
$253$	7.75576			0.487600
$254$	17.1355			1.07518
$255$	4.62838	+	5.67653i	0.289841	+	0.355478i
$256$	18.8076			1.17548
$257$	1.22289	−	2.11811i	0.0762819	−	0.132124i	−0.825361	−	0.564605i	$-0.809028\pi$
$257$	1.22289	−	2.11811i	0.0762819	−	0.132124i	0.901643	+	0.432481i	$0.142362\pi$
$258$	−4.04280	+	10.6384i	−0.251694	+	0.662318i
$259$		0			0
$260$	−3.86073			−0.239432
$261$	−3.74815	+	18.2345i	−0.232005	+	1.12869i
$262$	−13.1626	+	22.7982i	−0.813186	+	1.40848i
$263$	12.2814	+	21.2720i	0.757302	+	1.31169i	0.944222	+	0.329311i	$0.106816\pi$
$263$	12.2814	+	21.2720i	0.757302	+	1.31169i	−0.186919	+	0.982375i	$0.559850\pi$
$264$	−11.7268	−	14.3824i	−0.721733	−	0.885177i
$265$	14.6433	+	25.3629i	0.899531	+	1.55803i
$266$		0			0
$267$	6.06510	+	7.43861i	0.371178	+	0.455236i
$268$	−7.76415			−0.474271
$269$	14.7851	−	25.6086i	0.901466	−	1.56139i	0.0758746	−	0.997117i	$-0.475825\pi$
$269$	14.7851	−	25.6086i	0.901466	−	1.56139i	0.825592	−	0.564268i	$-0.190842\pi$
$270$	−1.33237	+	31.4833i	−0.0810852	+	1.91601i
$271$	12.3958	+	21.4701i	0.752989	+	1.30421i	0.946368	+	0.323090i	$0.104722\pi$
$271$	12.3958	+	21.4701i	0.752989	+	1.30421i	−0.193380	+	0.981124i	$0.561945\pi$
$272$	3.00968	−	5.21291i	0.182488	−	0.316079i
$273$		0			0
$274$	5.30674	+	9.19154i	0.320592	+	0.555281i
$275$	22.3415	−	38.6966i	1.34724	−	2.33349i
$276$	−0.768752	+	2.02293i	−0.0462735	+	0.121766i
$277$	−0.939249	−	1.62683i	−0.0564340	−	0.0977466i	0.836428	−	0.548076i	$-0.184640\pi$
$277$	−0.939249	−	1.62683i	−0.0564340	−	0.0977466i	−0.892862	+	0.450330i	$0.851306\pi$
$278$	−0.757442	−	1.31193i	−0.0454284	−	0.0786842i
$279$	−0.536364	+	0.178263i	−0.0321113	+	0.0106723i
$280$		0			0
$281$	6.03965	−	10.4610i	0.360295	−	0.624049i	−0.627714	−	0.778444i	$-0.716009\pi$
$281$	6.03965	−	10.4610i	0.360295	−	0.624049i	0.988009	+	0.154395i	$0.0493427\pi$
$282$	−16.8885	+	2.73299i	−1.00569	+	0.162747i
$283$	−27.9719			−1.66276			−0.831378	−	0.555708i	$-0.812447\pi$
$283$	−27.9719			−1.66276			−0.831378	+	0.555708i	$0.812447\pi$
$284$	−11.9756			−0.710620
$285$	13.2441	−	2.14323i	0.784513	−	0.126954i
$286$	5.89052	−	10.2027i	0.348314	−	0.603297i
$287$		0			0
$288$	14.5597	−	4.83897i	0.857937	−	0.285139i
$289$	7.77524	+	13.4671i	0.457367	+	0.792183i
$290$	18.8155	+	32.5894i	1.10488	+	1.91372i
$291$	−10.1433	+	26.6914i	−0.594609	+	1.56468i
$292$	2.60736	−	4.51609i	0.152584	−	0.264284i
$293$	−4.41163	−	7.64117i	−0.257730	−	0.446402i	0.707903	−	0.706309i	$-0.249641\pi$
$293$	−4.41163	−	7.64117i	−0.257730	−	0.446402i	−0.965634	+	0.259908i	$0.916308\pi$
$294$		0			0
$295$	19.7893	−	34.2761i	1.15218	−	1.99563i
$296$	−3.14589	−	5.44883i	−0.182851	−	0.316707i
$297$	−26.7143	−	16.9687i	−1.55012	−	0.984621i
$298$	4.98604	−	8.63608i	0.288834	−	0.500275i
$299$	1.42655			0.0824996
$300$	7.87871	+	9.66293i	0.454878	+	0.557889i
$301$		0			0
$302$	−1.74942	−	3.03009i	−0.100668	−	0.174362i
$303$	−14.1893	−	17.4026i	−0.815151	−	0.999751i
$304$	−5.51304	−	9.54887i	−0.316195	−	0.547665i
$305$	−21.0777	+	36.5076i	−1.20691	+	2.09042i
$306$	1.25564	−	6.10857i	0.0717799	−	0.349204i
$307$	1.05532			0.0602304			0.0301152	−	0.999546i	$-0.490413\pi$
$307$	1.05532			0.0602304			0.0301152	+	0.999546i	$0.490413\pi$
$308$		0			0
$309$	1.66238	−	4.37446i	0.0945696	−	0.248855i
$310$	−0.571277	+	0.989481i	−0.0324464	+	0.0561988i
$311$	3.07215			0.174206			0.0871029	−	0.996199i	$-0.472239\pi$
$311$	3.07215			0.174206			0.0871029	+	0.996199i	$0.472239\pi$
$312$	−2.15696	−	2.64542i	−0.122114	−	0.149768i
$313$	28.1621			1.59181			0.795907	−	0.605419i	$-0.206994\pi$
$313$	28.1621			1.59181			0.795907	+	0.605419i	$0.206994\pi$
$314$	5.26196			0.296949
$315$		0			0
$316$	9.04368			0.508747
$317$	12.8465			0.721530			0.360765	−	0.932657i	$-0.382516\pi$
$317$	12.8465			0.721530			0.360765	+	0.932657i	$0.382516\pi$
$318$	8.85819	−	23.3098i	0.496743	−	1.30715i
$319$	−37.7939			−2.11605
$320$	−2.05291	+	3.55575i	−0.114761	+	0.198772i
$321$	−0.195351	−	0.239591i	−0.0109034	−	0.0133726i
$322$		0			0
$323$	−2.65517			−0.147738
$324$	7.07385	−	5.28594i	0.392992	−	0.293663i
$325$	4.10937	−	7.11763i	0.227947	−	0.394815i
$326$	−4.65227	−	8.05797i	−0.257665	−	0.446290i
$327$	5.75814	−	15.1522i	0.318426	−	0.837920i
$328$	2.96091	+	5.12845i	0.163489	+	0.283171i
$329$		0			0
$330$	−63.1535	+	10.2199i	−3.47649	+	0.562585i
$331$	−21.5560			−1.18483			−0.592413	−	0.805634i	$-0.701825\pi$
$331$	−21.5560			−1.18483			−0.592413	+	0.805634i	$0.701825\pi$
$332$	0.613191	−	1.06208i	0.0336532	−	0.0582891i
$333$	−8.02202	−	7.12617i	−0.439604	−	0.390512i
$334$	14.3392	+	24.8361i	0.784604	+	1.35897i
$335$	13.8965	−	24.0695i	0.759248	−	1.31506i
$336$		0			0
$337$	6.30340	+	10.9178i	0.343368	+	0.594731i	0.985056	−	0.172235i	$-0.0550989\pi$
$337$	6.30340	+	10.9178i	0.343368	+	0.594731i	−0.641688	+	0.766966i	$0.721766\pi$
$338$	−10.1395	+	17.5621i	−0.551516	+	0.955254i
$339$	−9.21632	−	11.3034i	−0.500562	−	0.613919i
$340$	−2.07455	−	3.59323i	−0.112508	−	0.194870i
$341$	−0.573750	−	0.993764i	−0.0310703	−	0.0538153i
$342$	−8.54039	−	7.58665i	−0.461811	−	0.410239i
$343$		0			0
$344$	−3.34714	+	5.79741i	−0.180466	+	0.312575i
$345$	−4.89531	−	6.00390i	−0.263554	−	0.323239i
$346$	30.4752			1.63836
$347$	23.1366			1.24204			0.621020	−	0.783795i	$-0.286719\pi$
$347$	23.1366			1.24204			0.621020	+	0.783795i	$0.286719\pi$
$348$	3.74614	−	9.85776i	0.200814	−	0.528431i
$349$	8.24346	−	14.2781i	0.441262	−	0.764289i	−0.556521	−	0.830833i	$-0.687864\pi$
$349$	8.24346	−	14.2781i	0.441262	−	0.764289i	0.997783	+	0.0665448i	$0.0211975\pi$
$350$		0			0
$351$	−4.91368	−	3.12112i	−0.262273	−	0.166593i
$352$	15.5745	+	26.9759i	0.830124	+	1.43782i
$353$	12.2438	+	21.2068i	0.651669	+	1.12872i	0.982718	+	0.185110i	$0.0592642\pi$
$353$	12.2438	+	21.2068i	0.651669	+	1.12872i	−0.331049	+	0.943614i	$0.607402\pi$
$354$	−33.2666	+	5.38339i	−1.76810	+	0.286124i
$355$	21.4343	−	37.1253i	1.13761	−	1.97041i
$356$	−2.71852	−	4.70862i	−0.144081	−	0.249556i
$357$		0			0
$358$	2.26915	−	3.93028i	0.119928	−	0.207722i
$359$	−10.2389	−	17.7342i	−0.540386	−	0.935977i	−0.998882	−	0.0472797i	$-0.984945\pi$
$359$	−10.2389	−	17.7342i	−0.540386	−	0.935977i	0.458495	−	0.888697i	$-0.348389\pi$
$360$	−3.73200	+	18.1559i	−0.196694	+	0.956900i
$361$	7.06816	−	12.2424i	0.372009	−	0.644338i
$362$	−6.86139			−0.360627
$363$	16.0564	−	42.2514i	0.842740	−	2.21762i
$364$		0			0
$365$	9.33349	+	16.1661i	0.488537	+	0.846172i
$366$	35.4325	−	5.73388i	1.85209	−	0.299715i
$367$	−11.1269	−	19.2724i	−0.580821	−	1.00601i	−0.995382	−	0.0959900i	$-0.969398\pi$
$367$	−11.1269	−	19.2724i	−0.580821	−	1.00601i	0.414561	−	0.910021i	$-0.363935\pi$
$368$	−3.18325	+	5.51355i	−0.165938	+	0.287414i
$369$	7.55034	+	6.70716i	0.393055	+	0.349161i
$370$	−21.6905			−1.12764
$371$		0			0
$372$	0.316073	−	0.0511487i	0.0163876	−	0.00265194i
$373$	16.2684	−	28.1777i	0.842347	−	1.45899i	−0.0455576	−	0.998962i	$-0.514506\pi$
$373$	16.2684	−	28.1777i	0.842347	−	1.45899i	0.887905	−	0.460027i	$-0.152160\pi$
$374$	12.6610			0.654685
$375$	−14.0306	+	2.27050i	−0.724535	+	0.117248i
$376$	−10.0633			−0.518973
$377$	−6.95160			−0.358026
$378$		0			0
$379$	1.54440			0.0793306			0.0396653	−	0.999213i	$-0.487371\pi$
$379$	1.54440			0.0793306			0.0396653	+	0.999213i	$0.487371\pi$
$380$	−7.60021			−0.389883
$381$	16.9688	−	2.74598i	0.869337	−	0.140681i
$382$	31.4345			1.60833
$383$	−15.8147	+	27.3919i	−0.808093	+	1.39966i	0.106090	+	0.994357i	$0.466167\pi$
$383$	−15.8147	+	27.3919i	−0.808093	+	1.39966i	−0.914183	+	0.405302i	$0.867166\pi$
$384$	20.9398	−	3.38859i	1.06858	−	0.172923i
$385$		0			0
$386$	0.349441			0.0177861
$387$	−2.29865	+	11.1827i	−0.116847	+	0.568451i
$388$	8.08767	−	14.0083i	0.410589	−	0.711162i
$389$	2.62313	+	4.54340i	0.132998	+	0.230359i	0.924831	−	0.380378i	$-0.124206\pi$
$389$	2.62313	+	4.54340i	0.132998	+	0.230359i	−0.791833	+	0.610738i	$0.790873\pi$
$390$	−11.6161	+	1.87978i	−0.588205	+	0.0951866i
$391$	0.766552	+	1.32771i	0.0387662	+	0.0671451i
$392$		0			0
$393$	−9.38103	+	24.6857i	−0.473210	+	1.24523i
$394$	2.81672			0.141904
$395$	−16.1867	+	28.0362i	−0.814440	+	1.41065i
$396$	13.4034	+	11.9066i	0.673546	+	0.598328i
$397$	−0.0138175	−	0.0239325i	−0.000693478	−	0.00120114i	0.865678	−	0.500600i	$-0.166887\pi$
$397$	−0.0138175	−	0.0239325i	−0.000693478	−	0.00120114i	−0.866372	+	0.499399i	$0.833554\pi$
$398$	5.43201	−	9.40851i	0.272282	−	0.471606i
$399$		0			0
$400$	18.3395	+	31.7650i	0.916977	+	1.58825i
$401$	−6.06885	+	10.5115i	−0.303064	+	0.524922i	−0.976828	−	0.214024i	$-0.931343\pi$
$401$	−6.06885	+	10.5115i	−0.303064	+	0.524922i	0.673765	+	0.738946i	$0.264676\pi$
$402$	−23.3606	+	3.78035i	−1.16512	+	0.188547i
$403$	−0.105532	−	0.182787i	−0.00525694	−	0.00910529i
$404$	6.35996	+	11.0158i	0.316420	+	0.548055i
$405$	3.72583	+	31.3905i	0.185138	+	1.55980i
$406$		0			0
$407$	10.8922	−	18.8659i	0.539907	−	0.935146i
$408$	1.30309	−	3.42902i	0.0645127	−	0.169762i
$409$	31.3453			1.54993			0.774963	−	0.632007i	$-0.217769\pi$
$409$	31.3453			1.54993			0.774963	+	0.632007i	$0.217769\pi$
$410$	20.4152			1.00823
$411$	6.72805	+	8.25168i	0.331870	+	0.407025i
$412$	−1.32549	+	2.29582i	−0.0653022	+	0.113107i
$413$		0			0
$414$	−1.32805	+	6.46086i	−0.0652701	+	0.317534i
$415$	2.19502	+	3.80189i	0.107749	+	0.186627i
$416$	2.86469	+	4.96179i	0.140453	+	0.243272i
$417$	−0.960308	−	1.17778i	−0.0470265	−	0.0576762i
$418$	11.5960	−	20.0849i	0.567181	−	0.982385i
$419$	7.44319	+	12.8920i	0.363623	+	0.629814i	0.988554	−	0.150866i	$-0.0482061\pi$
$419$	7.44319	+	12.8920i	0.363623	+	0.629814i	−0.624931	+	0.780680i	$0.714873\pi$
$420$		0			0
$421$	−4.54213	+	7.86721i	−0.221370	+	0.383424i	−0.955224	−	0.295883i	$-0.904386\pi$
$421$	−4.54213	+	7.86721i	−0.221370	+	0.383424i	0.733854	+	0.679307i	$0.237720\pi$
$422$	−14.0610	−	24.3543i	−0.684477	−	1.18555i
$423$	−16.2862	+	5.41278i	−0.791860	+	0.263179i
$424$	7.33392	−	12.7027i	0.356166	−	0.616898i
$425$	8.83262			0.428445
$426$	−36.0320	+	5.83089i	−1.74575	+	0.282508i
$427$		0			0
$428$	0.0875611	+	0.151660i	0.00423243	+	0.00733078i
$429$	4.19821	−	11.0473i	0.202691	−	0.533371i
$430$	11.5391	+	19.9863i	0.556463	+	0.963823i
$431$	8.31776	−	14.4068i	0.400652	−	0.693950i	−0.593152	−	0.805090i	$-0.702117\pi$
$431$	8.31776	−	14.4068i	0.400652	−	0.693950i	0.993805	+	0.111140i	$0.0354502\pi$
$432$	23.0275	−	12.0266i	1.10791	−	0.578629i
$433$	19.7423			0.948756			0.474378	−	0.880321i	$-0.342673\pi$
$433$	19.7423			0.948756			0.474378	+	0.880321i	$0.342673\pi$
$434$		0			0
$435$	23.8549	+	29.2571i	1.14375	+	1.40277i
$436$	−4.59122	+	7.95223i	−0.219880	+	0.380843i
$437$	2.80830			0.134339
$438$	5.64612	−	14.8575i	0.269782	−	0.709917i
$439$	−6.73514			−0.321451			−0.160725	−	0.986999i	$-0.551383\pi$
$439$	−6.73514			−0.321451			−0.160725	+	0.986999i	$0.551383\pi$
$440$	−37.6310			−1.79399
$441$		0			0
$442$	2.32879			0.110769
$443$	28.6403			1.36074			0.680372	−	0.732867i	$-0.261818\pi$
$443$	28.6403			1.36074			0.680372	+	0.732867i	$0.261818\pi$
$444$	3.84113	+	4.71100i	0.182292	+	0.223574i
$445$	19.4628			0.922626
$446$	17.2397	−	29.8601i	0.816324	−	1.41392i
$447$	3.55358	−	9.35105i	0.168079	−	0.442290i
$448$		0			0
$449$	−6.66872			−0.314716			−0.157358	−	0.987542i	$-0.550298\pi$
$449$	−6.66872			−0.314716			−0.157358	+	0.987542i	$0.550298\pi$
$450$	28.4102	+	25.2375i	1.33927	+	1.18971i
$451$	−10.2518	+	17.7566i	−0.482736	+	0.836124i
$452$	4.13097	+	7.15505i	0.194305	+	0.336545i
$453$	−2.21797	−	2.72026i	−0.104210	−	0.127809i
$454$	3.11898	+	5.40223i	0.146381	+	0.253539i
$455$		0			0
$456$	−4.24617	−	5.20776i	−0.198845	−	0.243876i
$457$	−28.6573			−1.34053			−0.670266	−	0.742121i	$-0.733820\pi$
$457$	−28.6573			−1.34053			−0.670266	+	0.742121i	$0.733820\pi$
$458$	11.8399	−	20.5074i	0.553244	−	0.958246i
$459$	0.264513	−	6.25034i	0.0123464	−	0.291741i
$460$	2.19419	+	3.80045i	0.102305	+	0.177197i
$461$	−10.0087	+	17.3355i	−0.466150	+	0.807395i	−0.999253	−	0.0386554i	$-0.987693\pi$
$461$	−10.0087	+	17.3355i	−0.466150	+	0.807395i	0.533103	+	0.846050i	$0.321026\pi$
$462$		0			0
$463$	−4.95789	−	8.58731i	−0.230413	−	0.399086i	0.727517	−	0.686090i	$-0.240674\pi$
$463$	−4.95789	−	8.58731i	−0.230413	−	0.399086i	−0.957930	+	0.287003i	$0.907341\pi$
$464$	15.5120	−	26.8676i	0.720127	−	1.24730i
$465$	−0.407153	+	1.07140i	−0.0188813	+	0.0496850i
$466$	−21.8020	−	37.7623i	−1.00996	−	1.74930i
$467$	8.04035	+	13.9263i	0.372063	+	0.644432i	0.989883	−	0.141888i	$-0.0453172\pi$
$467$	8.04035	+	13.9263i	0.372063	+	0.644432i	−0.617820	+	0.786320i	$0.711984\pi$
$468$	2.46535	+	2.19003i	0.113961	+	0.101234i
$469$		0			0
$470$	−17.3463	+	30.0446i	−0.800124	+	1.38586i
$471$	5.21075	−	0.843232i	0.240099	−	0.0388541i
$472$	−19.8225			−0.912402
$473$	−23.1780			−1.06573
$474$	27.2105	−	4.40335i	1.24982	−	0.202253i
$475$	8.08967	−	14.0117i	0.371180	−	0.642902i
$476$		0			0
$477$	5.03657	−	24.5025i	0.230609	−	1.12189i
$478$	7.76103	+	13.4425i	0.354981	+	0.614846i
$479$	−4.10128	−	7.10362i	−0.187392	−	0.324573i	0.756988	−	0.653429i	$-0.226670\pi$
$479$	−4.10128	−	7.10362i	−0.187392	−	0.324573i	−0.944380	+	0.328856i	$0.893337\pi$
$480$	11.0522	−	29.0833i	0.504462	−	1.32746i
$481$	2.00345	−	3.47008i	0.0913496	−	0.158222i
$482$	7.99183	+	13.8423i	0.364018	+	0.630497i
$483$		0			0
$484$	−12.8024	+	22.1745i	−0.581929	+	1.00793i
$485$	28.9512	+	50.1449i	1.31460	+	2.27696i
$486$	18.7100	−	19.3485i	0.848702	−	0.877666i
$487$	−1.36840	+	2.37014i	−0.0620081	+	0.107401i	−0.895363	−	0.445337i	$-0.853084\pi$
$487$	−1.36840	+	2.37014i	−0.0620081	+	0.107401i	0.833355	+	0.552738i	$0.186417\pi$
$488$	21.1130			0.955741
$489$	−5.89829	−	7.23402i	−0.266730	−	0.327134i
$490$		0			0
$491$	9.85482	+	17.0690i	0.444742	+	0.770315i	0.998034	−	0.0626719i	$-0.0199622\pi$
$491$	9.85482	+	17.0690i	0.444742	+	0.770315i	−0.553293	+	0.832987i	$0.686629\pi$
$492$	−3.61528	−	4.43399i	−0.162989	−	0.199900i
$493$	−3.73542	−	6.46993i	−0.168235	−	0.291391i
$494$	2.13291	−	3.69431i	0.0959642	−	0.166215i
$495$	−60.9012	+	20.2408i	−2.73731	+	0.909756i
$496$	0.941952			0.0422949
$497$		0			0
$498$	1.32784	−	3.49413i	0.0595018	−	0.156576i
$499$	16.5480	−	28.6619i	0.740789	−	1.28309i	−0.211347	−	0.977411i	$-0.567785\pi$
$499$	16.5480	−	28.6619i	0.740789	−	1.28309i	0.952136	−	0.305674i	$-0.0988817\pi$
$500$	8.05153			0.360075
$501$	18.1796	+	22.2966i	0.812205	+	0.996138i
$502$	−35.6575			−1.59147
$503$	−12.1860			−0.543346			−0.271673	−	0.962390i	$-0.587577\pi$
$503$	−12.1860			−0.543346			−0.271673	+	0.962390i	$0.587577\pi$
$504$		0			0
$505$	−45.5331			−2.02619
$506$	−13.3912			−0.595310
$507$	−7.22648	+	19.0161i	−0.320939	+	0.844534i
$508$	−9.73765			−0.432038
$509$	6.81965	−	11.8120i	0.302276	−	0.523557i	−0.674375	−	0.738389i	$-0.735587\pi$
$509$	6.81965	−	11.8120i	0.302276	−	0.523557i	0.976651	+	0.214832i	$0.0689204\pi$
$510$	−7.99142	−	9.80116i	−0.353866	−	0.434002i
$511$		0			0
$512$	−7.97968			−0.352656
$513$	−9.67304	−	6.14422i	−0.427075	−	0.271274i
$514$	−2.11146	+	3.65715i	−0.0931325	+	0.161310i
$515$	−4.74481	−	8.21826i	−0.209081	−	0.362140i
$516$	2.29741	−	6.04551i	0.101138	−	0.266139i
$517$	−17.4214	−	30.1747i	−0.766190	−	1.32708i
$518$		0			0
$519$	30.1787	−	4.88368i	1.32470	−	0.214370i
$520$	−6.92164			−0.303534
$521$	−17.7745	+	30.7863i	−0.778714	+	1.34877i	0.153969	+	0.988076i	$0.450794\pi$
$521$	−17.7745	+	30.7863i	−0.778714	+	1.34877i	−0.932683	+	0.360697i	$0.882539\pi$
$522$	6.47160	−	31.4839i	0.283254	−	1.37801i
$523$	13.3593	+	23.1391i	0.584163	+	1.01180i	0.994979	+	0.100082i	$0.0319105\pi$
$523$	13.3593	+	23.1391i	0.584163	+	1.01180i	−0.410816	+	0.911718i	$0.634756\pi$
$524$	7.47991	−	12.9556i	0.326761	−	0.565967i
$525$		0			0
$526$	−21.2052	−	36.7284i	−0.924589	−	1.60143i
$527$	0.113415	−	0.196440i	0.00494043	−	0.00855708i
$528$	33.3294	+	40.8772i	1.45048	+	1.77895i
$529$	10.6892	+	18.5143i	0.464750	+	0.804970i
$530$	−25.2833	−	43.7919i	−1.09824	−	1.90220i
$531$	−32.0802	+	10.6620i	−1.39216	+	0.462692i
$532$		0			0
$533$	−1.88565	+	3.26604i	−0.0816766	+	0.141468i
$534$	−10.4721	−	12.8436i	−0.453171	−	0.555796i
$535$	−0.626879			−0.0271023
$536$	−13.9198			−0.601244
$537$	1.61723	−	4.25566i	0.0697888	−	0.183645i
$538$	−25.5282	+	44.2161i	−1.10060	+	1.90629i
$539$		0			0
$540$	0.757146	−	17.8911i	0.0325824	−	0.769910i
$541$	−18.7927	−	32.5500i	−0.807963	−	1.39943i	−0.914272	−	0.405100i	$-0.867237\pi$
$541$	−18.7927	−	32.5500i	−0.807963	−	1.39943i	0.106309	−	0.994333i	$-0.466097\pi$
$542$	−21.4026	−	37.0705i	−0.919322	−	1.59231i
$543$	−6.79462	+	1.09954i	−0.291585	+	0.0471859i
$544$	−3.07866	+	5.33240i	−0.131997	+	0.228625i
$545$	−16.4350	−	28.4663i	−0.704000	−	1.21936i
$546$		0			0
$547$	−9.13381	+	15.8202i	−0.390533	+	0.676424i	−0.992520	−	0.122082i	$-0.961043\pi$
$547$	−9.13381	+	15.8202i	−0.390533	+	0.676424i	0.601986	+	0.798506i	$0.294376\pi$
$548$	−3.01567	−	5.22329i	−0.128823	−	0.223128i
$549$	34.1688	−	11.3562i	1.45829	−	0.484669i
$550$	−38.5750	+	66.8139i	−1.64485	+	2.84896i
$551$	−13.6849			−0.582995
$552$	−1.37824	+	3.62677i	−0.0586619	+	0.154366i
$553$		0			0
$554$	1.62172	+	2.80890i	0.0689002	+	0.119339i
$555$	−21.4794	+	3.47592i	−0.911752	+	0.147545i
$556$	0.430433	+	0.745532i	0.0182544	+	0.0316176i
$557$	1.94636	−	3.37119i	0.0824698	−	0.142842i	−0.821840	−	0.569718i	$-0.807053\pi$
$557$	1.94636	−	3.37119i	0.0824698	−	0.142842i	0.904310	+	0.426876i	$0.140386\pi$
$558$	0.926091	−	0.307791i	0.0392046	−	0.0130298i
$559$	−4.26324			−0.180316
$560$		0			0
$561$	12.5378	−	2.02893i	0.529346	−	0.0856617i
$562$	−10.4281	+	18.0620i	−0.439884	+	0.761901i
$563$	3.32855			0.140282			0.0701409	−	0.997537i	$-0.477655\pi$
$563$	3.32855			0.140282			0.0701409	+	0.997537i	$0.477655\pi$
$564$	9.59725	−	1.55308i	0.404117	−	0.0653965i
$565$	−29.5750			−1.24423
$566$	48.2965			2.03006
$567$		0			0
$568$	−21.4702			−0.900870
$569$	−36.6244			−1.53538			−0.767688	−	0.640824i	$-0.778593\pi$
$569$	−36.6244			−1.53538			−0.767688	+	0.640824i	$0.778593\pi$
$570$	−22.8674	+	3.70053i	−0.957810	+	0.154998i
$571$	−22.5824			−0.945044			−0.472522	−	0.881319i	$-0.656656\pi$
$571$	−22.5824			−0.945044			−0.472522	+	0.881319i	$0.656656\pi$
$572$	−3.34742	+	5.79789i	−0.139962	+	0.242422i
$573$	31.1286	−	5.03740i	1.30042	−	0.210441i
$574$		0			0
$575$	−9.34201			−0.389589
$576$	3.32795	−	1.10606i	0.138665	−	0.0460859i
$577$	−11.2725	+	19.5245i	−0.469279	+	0.812815i	−0.999383	−	0.0351177i	$-0.988819\pi$
$577$	−11.2725	+	19.5245i	−0.469279	+	0.812815i	0.530104	+	0.847932i	$0.322153\pi$
$578$	−13.4248	−	23.2525i	−0.558399	−	0.967175i
$579$	0.346040	−	0.0559981i	0.0143809	−	0.00232720i
$580$	−10.6923	−	18.5197i	−0.443975	−	0.768987i
$581$		0			0
$582$	17.5135	−	46.0857i	0.725957	−	1.91031i
$583$	50.7854			2.10332
$584$	4.67457	−	8.09659i	0.193435	−	0.335039i
$585$	−11.2018	+	3.72298i	−0.463139	+	0.153926i
$586$	7.61717	+	13.1933i	0.314662	+	0.545011i
$587$	−12.1198	+	20.9921i	−0.500237	+	0.866436i	0.499763	+	0.866162i	$0.333421\pi$
$587$	−12.1198	+	20.9921i	−0.500237	+	0.866436i	−1.00000		0.000273884i	$0.999913\pi$
$588$		0			0
$589$	−0.207750	−	0.359834i	−0.00856020	−	0.0148267i
$590$	−34.1684	+	59.1814i	−1.40669	+	2.43646i
$591$	2.78931	−	0.451381i	0.114737	−	0.0185673i
$592$	8.94112	+	15.4865i	0.367478	+	0.636490i
$593$	22.8663	+	39.6056i	0.939007	+	1.62641i	0.767328	+	0.641255i	$0.221586\pi$
$593$	22.8663	+	39.6056i	0.939007	+	1.62641i	0.171680	+	0.985153i	$0.445081\pi$
$594$	46.1252	+	29.2983i	1.89254	+	1.20212i
$595$		0			0
$596$	−2.83343	+	4.90764i	−0.116062	+	0.201025i
$597$	3.87142	−	10.1874i	0.158447	−	0.416944i
$598$	−2.46310			−0.100724
$599$	−30.1668			−1.23258			−0.616290	−	0.787519i	$-0.711365\pi$
$599$	−30.1668			−1.23258			−0.616290	+	0.787519i	$0.711365\pi$
$600$	14.1252	+	17.3240i	0.576659	+	0.707249i
$601$	7.36933	−	12.7641i	0.300601	−	0.520657i	−0.675671	−	0.737203i	$-0.736146\pi$
$601$	7.36933	−	12.7641i	0.300601	−	0.520657i	0.976272	+	0.216547i	$0.0694794\pi$
$602$		0			0
$603$	−22.5275	+	7.48712i	−0.917391	+	0.304899i
$604$	0.994149	+	1.72192i	0.0404513	+	0.0700638i
$605$	−45.8285	−	79.3772i	−1.86319	−	3.22714i
$606$	24.4993	+	30.0474i	0.995217	+	1.22059i
$607$	3.03918	−	5.26401i	0.123356	−	0.213660i	−0.797733	−	0.603011i	$-0.793967\pi$
$607$	3.03918	−	5.26401i	0.123356	−	0.213660i	0.921089	+	0.389351i	$0.127301\pi$
$608$	5.63941	+	9.76774i	0.228708	+	0.396134i
$609$		0			0
$610$	36.3930	−	63.0345i	1.47351	−	2.55219i
$611$	−3.20439	−	5.55016i	−0.129636	−	0.224535i
$612$	−0.713543	+	3.47133i	−0.0288432	+	0.140320i
$613$	−5.88668	+	10.1960i	−0.237761	+	0.411814i	−0.960071	−	0.279755i	$-0.909747\pi$
$613$	−5.88668	+	10.1960i	−0.237761	+	0.411814i	0.722311	+	0.691569i	$0.243080\pi$
$614$	−1.82213			−0.0735352
$615$	20.2165	−	3.27154i	0.815207	−	0.131921i
$616$		0			0
$617$	−16.0319	−	27.7680i	−0.645418	−	1.11790i	−0.984205	−	0.177034i	$-0.943350\pi$
$617$	−16.0319	−	27.7680i	−0.645418	−	1.11790i	0.338786	−	0.940863i	$-0.389984\pi$
$618$	−2.87029	+	7.55300i	−0.115460	+	0.303826i
$619$	6.27588	+	10.8701i	0.252249	+	0.436908i	0.964145	−	0.265377i	$-0.0854965\pi$
$619$	6.27588	+	10.8701i	0.252249	+	0.436908i	−0.711896	+	0.702285i	$0.752163\pi$
$620$	0.324641	−	0.562294i	0.0130379	−	0.0225823i
$621$	−0.279767	+	6.61081i	−0.0112267	+	0.265283i
$622$	−5.30441			−0.212688
$623$		0			0
$624$	6.13043	+	7.51873i	0.245414	+	0.300990i
$625$	3.92995	−	6.80687i	0.157198	−	0.272275i
$626$	−48.6249			−1.94344
$627$	8.26456	−	21.7477i	0.330055	−	0.868521i
$628$	−2.99022			−0.119323
$629$	4.30619			0.171699
$630$		0			0
$631$	33.4642			1.33219			0.666095	−	0.745867i	$-0.267964\pi$
$631$	33.4642			1.33219			0.666095	+	0.745867i	$0.267964\pi$
$632$	16.2138			0.644950
$633$	−17.8269	−	21.8640i	−0.708556	−	0.869016i
$634$	−22.1809			−0.880915
$635$	17.4288	−	30.1875i	0.691639	−	1.19795i
$636$	−5.03386	+	13.2463i	−0.199606	+	0.525251i
$637$		0			0
$638$	65.2553			2.58348
$639$	−34.7469	+	11.5483i	−1.37457	+	0.456844i
$640$	21.5074	−	37.2519i	0.850155	−	1.47251i
$641$	9.49183	+	16.4403i	0.374905	+	0.649354i	0.990313	−	0.138855i	$-0.0443421\pi$
$641$	9.49183	+	16.4403i	0.374905	+	0.649354i	−0.615408	+	0.788209i	$0.711009\pi$
$642$	0.337296	+	0.413680i	0.0133120	+	0.0163266i
$643$	4.81347	+	8.33718i	0.189825	+	0.328786i	0.945192	−	0.326516i	$-0.105875\pi$
$643$	4.81347	+	8.33718i	0.189825	+	0.328786i	−0.755367	+	0.655302i	$0.772541\pi$
$644$		0			0
$645$	14.6296	+	17.9426i	0.576039	+	0.706490i
$646$	4.58445			0.180373
$647$	3.90607	−	6.76551i	0.153564	−	0.265980i	−0.778972	−	0.627059i	$-0.784258\pi$
$647$	3.90607	−	6.76551i	0.153564	−	0.265980i	0.932535	+	0.361079i	$0.117592\pi$
$648$	12.6822	−	9.47680i	0.498205	−	0.372284i
$649$	−34.3163	−	59.4375i	−1.34703	−	2.33313i
$650$	−7.09528	+	12.2894i	−0.278300	+	0.482029i
$651$		0			0
$652$	2.64376	+	4.57912i	0.103537	+	0.179332i
$653$	−15.8714	+	27.4901i	−0.621097	+	1.07577i	0.368185	+	0.929753i	$0.379979\pi$
$653$	−15.8714	+	27.4901i	−0.621097	+	1.07577i	−0.989282	+	0.146019i	$0.953354\pi$
$654$	−9.94207	+	26.1620i	−0.388766	+	1.02302i
$655$	26.7756	+	46.3767i	1.04621	+	1.81209i
$656$	−8.41540	−	14.5759i	−0.328566	−	0.569093i
$657$	3.21026	−	15.6177i	0.125244	−	0.609303i
$658$		0			0
$659$	3.10685	−	5.38122i	0.121026	−	0.209623i	−0.799147	−	0.601136i	$-0.794715\pi$
$659$	3.10685	−	5.38122i	0.121026	−	0.209623i	0.920172	+	0.391513i	$0.128048\pi$
$660$	35.8884	−	5.80766i	1.39695	−	0.226063i
$661$	27.5263			1.07065			0.535324	−	0.844647i	$-0.320190\pi$
$661$	27.5263			1.07065			0.535324	+	0.844647i	$0.320190\pi$
$662$	37.2189			1.44655
$663$	2.30613	−	0.373191i	0.0895627	−	0.0144935i
$664$	1.09935	−	1.90413i	0.0426630	−	0.0738945i
$665$		0			0
$666$	13.8509	+	12.3041i	0.536712	+	0.476775i
$667$	3.95084	+	6.84306i	0.152977	+	0.264964i
$668$	−8.14854	−	14.1137i	−0.315276	−	0.546075i
$669$	12.2868	−	32.3322i	0.475037	−	1.25003i
$670$	−23.9939	+	41.5586i	−0.926965	+	1.60555i
$671$	36.5505	+	63.3073i	1.41102	+	2.44395i
$672$		0			0
$673$	−8.10894	+	14.0451i	−0.312577	+	0.541399i	−0.978919	−	0.204247i	$-0.934526\pi$
$673$	−8.10894	+	14.0451i	−0.312577	+	0.541399i	0.666343	+	0.745646i	$0.267859\pi$
$674$	−10.8835	−	18.8508i	−0.419217	−	0.726106i
$675$	32.1781	+	20.4392i	1.23853	+	0.786704i
$676$	5.76199	−	9.98006i	0.221615	−	0.383849i
$677$	−20.5090			−0.788225			−0.394112	−	0.919062i	$-0.628948\pi$
$677$	−20.5090			−0.788225			−0.394112	+	0.919062i	$0.628948\pi$
$678$	15.9130	+	19.5167i	0.611135	+	0.749532i
$679$		0			0
$680$	−3.71932	−	6.44205i	−0.142629	−	0.247041i
$681$	3.95433	+	4.84983i	0.151530	+	0.185846i
$682$	0.990642	+	1.71584i	0.0379337	+	0.0657030i
$683$	0.0561542	−	0.0972618i	0.00214868	−	0.00372162i	−0.864949	−	0.501860i	$-0.832649\pi$
$683$	0.0561542	−	0.0972618i	0.00214868	−	0.00372162i	0.867098	+	0.498138i	$0.165983\pi$
$684$	4.85326	+	4.31128i	0.185569	+	0.164846i
$685$	21.5902			0.824918
$686$		0			0
$687$	8.43839	−	22.2052i	0.321945	−	0.847179i
$688$	9.51311	−	16.4772i	0.362684	−	0.628187i
$689$	9.34118			0.355871
$690$	8.45229	+	10.3664i	0.321773	+	0.394642i
$691$	18.8670			0.717735			0.358868	−	0.933388i	$-0.383163\pi$
$691$	18.8670			0.717735			0.358868	+	0.933388i	$0.383163\pi$
$692$	−17.3182			−0.658340
$693$		0			0
$694$	−39.9480			−1.51640
$695$	−3.08161			−0.116892
$696$	6.71620	−	17.6733i	0.254577	−	0.669905i
$697$	−4.05299			−0.153518
$698$	−14.2332	+	24.6527i	−0.538736	+	0.933118i
$699$	−27.6413	−	33.9010i	−1.04549	−	1.28225i
$700$		0			0
$701$	−3.16006			−0.119354			−0.0596770	−	0.998218i	$-0.519007\pi$
$701$	−3.16006			−0.119354			−0.0596770	+	0.998218i	$0.519007\pi$
$702$	8.48402	+	5.38896i	0.320209	+	0.203393i
$703$	3.94398	−	6.83118i	0.148750	−	0.257643i
$704$	3.55992	+	6.16596i	0.134170	+	0.232388i
$705$	−12.3628	+	32.5320i	−0.465610	+	1.22523i
$706$	−21.1402	−	36.6159i	−0.795622	−	1.37806i
$707$		0			0
$708$	18.9045	−	3.05923i	0.710475	−	0.114973i
$709$	−21.5211			−0.808243			−0.404121	−	0.914705i	$-0.632423\pi$
$709$	−21.5211			−0.808243			−0.404121	+	0.914705i	$0.632423\pi$
$710$	−37.0087	+	64.1009i	−1.38891	+	2.40567i
$711$	26.2400	−	8.72100i	0.984079	−	0.327063i
$712$	−4.87385	−	8.44176i	−0.182655	−	0.316368i
$713$	−0.119956	+	0.207769i	−0.00449237	+	0.00778102i
$714$		0			0
$715$	−11.9826	−	20.7545i	−0.448125	−	0.776175i
$716$	−1.28949	+	2.23347i	−0.0481906	+	0.0834685i
$717$	9.83968	+	12.0680i	0.367469	+	0.450687i
$718$	17.6785	+	30.6201i	0.659757	+	1.14273i
$719$	9.41508	+	16.3074i	0.351123	+	0.608163i	0.986447	−	0.164083i	$-0.0524665\pi$
$719$	9.41508	+	16.3074i	0.351123	+	0.608163i	−0.635323	+	0.772246i	$0.719133\pi$
$720$	10.6070	−	51.6021i	0.395298	−	1.92310i
$721$		0			0
$722$	−12.2040	+	21.1379i	−0.454185	+	0.786671i
$723$	10.1323	+	12.4268i	0.376824	+	0.462159i
$724$	3.89914			0.144910
$725$	45.5237			1.69071
$726$	−27.7231	+	72.9517i	−1.02890	+	2.70749i
$727$	−19.5426	+	33.8489i	−0.724797	+	1.25538i	0.234261	+	0.972174i	$0.424733\pi$
$727$	−19.5426	+	33.8489i	−0.724797	+	1.25538i	−0.959058	+	0.283211i	$0.908600\pi$
$728$		0			0
$729$	15.4273	−	22.1585i	0.571381	−	0.820685i
$730$	−16.1153	−	27.9125i	−0.596454	−	1.03309i
$731$	−2.29084	−	3.96784i	−0.0847296	−	0.146756i
$732$	−20.1353	+	3.25841i	−0.744222	+	0.120434i
$733$	−9.29924	+	16.1068i	−0.343475	+	0.594917i	−0.985076	−	0.172123i	$-0.944937\pi$
$733$	−9.29924	+	16.1068i	−0.343475	+	0.594917i	0.641600	+	0.767039i	$0.278271\pi$
$734$	19.2119	+	33.2759i	0.709123	+	1.22824i
$735$		0			0
$736$	3.25621	−	5.63993i	0.120026	−	0.207890i
$737$	−24.0977	−	41.7385i	−0.887651	−	1.53746i
$738$	−13.0365	−	11.5807i	−0.479880	−	0.426290i
$739$	−2.75068	+	4.76432i	−0.101185	+	0.175258i	−0.912173	−	0.409805i	$-0.865597\pi$
$739$	−2.75068	+	4.76432i	−0.101185	+	0.175258i	0.810988	+	0.585063i	$0.198930\pi$
$740$	12.3261			0.453117
$741$	1.52014	−	4.00016i	0.0558436	−	0.146949i
$742$		0			0
$743$	10.2326	+	17.7234i	0.375399	+	0.650210i	0.990387	−	0.138327i	$-0.0441725\pi$
$743$	10.2326	+	17.7234i	0.375399	+	0.650210i	−0.614988	+	0.788537i	$0.710839\pi$
$744$	0.566666	−	0.0917010i	0.0207750	−	0.00336192i
$745$	−10.1427	−	17.5677i	−0.371601	−	0.643631i
$746$	−28.0892	+	48.6520i	−1.02842	+	1.78128i
$747$	0.754977	−	3.67291i	0.0276232	−	0.134385i
$748$	−7.19489			−0.263071
$749$		0			0
$750$	24.2253	−	3.92027i	0.884583	−	0.143148i
$751$	−19.0230	+	32.9488i	−0.694159	+	1.20232i	0.276305	+	0.961070i	$0.410890\pi$
$751$	−19.0230	+	32.9488i	−0.694159	+	1.20232i	−0.970463	+	0.241248i	$0.922443\pi$
$752$	28.6015			1.04299
$753$	−35.3105	+	5.71414i	−1.28679	+	0.208235i
$754$	12.0027			0.437113
$755$	−7.11744			−0.259030
$756$		0			0
$757$	−51.0780			−1.85646			−0.928230	−	0.372006i	$-0.878670\pi$
$757$	−51.0780			−1.85646			−0.928230	+	0.372006i	$0.878670\pi$
$758$	−2.66658			−0.0968546
$759$	−13.2609	+	2.14595i	−0.481338	+	0.0778929i
$760$	−13.6259			−0.494263
$761$	20.0375	−	34.7059i	0.726357	−	1.25809i	−0.232055	−	0.972703i	$-0.574545\pi$
$761$	20.0375	−	34.7059i	0.726357	−	1.25809i	0.958413	−	0.285385i	$-0.0921216\pi$
$762$	−29.2985	+	4.74124i	−1.06137	+	0.171757i
$763$		0			0
$764$	−17.8633			−0.646273
$765$	−9.48429	−	8.42514i	−0.342905	−	0.304612i
$766$	27.3058	−	47.2951i	0.986599	−	1.70884i
$767$	−6.31195	−	10.9326i	−0.227911	−	0.394754i
$768$	−32.1574	+	5.20389i	−1.16038	+	0.187779i
$769$	22.4828	+	38.9414i	0.810751	+	1.40426i	0.912339	+	0.409436i	$0.134274\pi$
$769$	22.4828	+	38.9414i	0.810751	+	1.40426i	−0.101587	+	0.994827i	$0.532392\pi$
$770$		0			0
$771$	−1.50485	+	3.95993i	−0.0541958	+	0.142613i
$772$	−0.198577			−0.00714695
$773$	12.1781	−	21.0930i	0.438014	−	0.758663i	−0.559522	−	0.828816i	$-0.689015\pi$
$773$	12.1781	−	21.0930i	0.438014	−	0.758663i	0.997536	+	0.0701524i	$0.0223485\pi$
$774$	3.96887	−	19.3082i	0.142658	−	0.694020i
$775$	0.691096	+	1.19701i	0.0248249	+	0.0429980i
$776$	14.4998	−	25.1145i	0.520514	−	0.901556i
$777$		0			0
$778$	−4.52913	−	7.84468i	−0.162377	−	0.281245i
$779$	−3.71208	+	6.42951i	−0.132999	+	0.230361i
$780$	6.60111	−	1.06823i	0.236358	−	0.0382487i
$781$	−37.1689	−	64.3784i	−1.33001	−	2.30364i
$782$	−1.32354	−	2.29243i	−0.0473296	−	0.0819773i
$783$	1.36331	−	32.2145i	0.0487207	−	1.15125i
$784$		0			0
$785$	5.35200	−	9.26993i	0.191021	−	0.330858i
$786$	16.1974	−	42.6225i	0.577742	−	1.52030i
$787$	41.5233			1.48015			0.740073	−	0.672526i	$-0.234791\pi$
$787$	41.5233			1.48015			0.740073	+	0.672526i	$0.234791\pi$
$788$	−1.60066			−0.0570212
$789$	−26.8846	−	32.9728i	−0.957115	−	1.17386i
$790$	27.9481	−	48.4075i	0.994349	−	1.72226i
$791$		0			0
$792$	24.0300	+	21.3465i	0.853869	+	0.758515i
$793$	6.72289	+	11.6444i	0.238737	+	0.413504i
$794$	0.0238574	+	0.0413222i	0.000846666	+	0.00146647i
$795$	−32.0549	−	39.3141i	−1.13687	−	1.39433i
$796$	−3.08686	+	5.34659i	−0.109411	+	0.189505i
$797$	−17.3018	−	29.9676i	−0.612861	−	1.06151i	−0.990756	−	0.135657i	$-0.956685\pi$
$797$	−17.3018	−	29.9676i	−0.612861	−	1.06151i	0.377895	−	0.925848i	$-0.376648\pi$
$798$		0			0
$799$	3.44373	−	5.96472i	0.121831	−	0.211017i
$800$	−18.7599	−	32.4931i	−0.663263	−	1.14880i
$801$	−12.4284	−	11.0404i	−0.439134	−	0.390095i
$802$	10.4785	−	18.1494i	0.370010	−	0.640876i
$803$	32.3701			1.14232
$804$	13.2752	−	2.14827i	0.468180	−	0.0757635i
$805$		0			0
$806$	0.182213	+	0.315603i	0.00641819	+	0.0111166i
$807$	−18.1941	+	47.8767i	−0.640462	+	1.68534i
$808$	11.4023	+	19.7494i	0.401133	+	0.694782i
$809$	5.62597	−	9.74446i	0.197799	−	0.342597i	−0.750016	−	0.661420i	$-0.769954\pi$
$809$	5.62597	−	9.74446i	0.197799	−	0.342597i	0.947814	+	0.318823i	$0.103287\pi$
$810$	−6.43306	−	54.1991i	−0.226035	−	1.90436i
$811$	−29.6803			−1.04222			−0.521108	−	0.853491i	$-0.674481\pi$
$811$	−29.6803			−1.04222			−0.521108	+	0.853491i	$0.674481\pi$
$812$		0			0
$813$	−27.1349	−	33.2799i	−0.951664	−	1.16718i
$814$	−18.8066	+	32.5740i	−0.659171	+	1.14172i
$815$	−18.9275			−0.663002
$816$	−3.70360	+	9.74583i	−0.129652	+	0.341172i
$817$	−8.39258			−0.293619
$818$	−54.1211			−1.89230
$819$		0			0
$820$	−11.6014			−0.405137
$821$	34.6431			1.20905			0.604526	−	0.796585i	$-0.293362\pi$
$821$	34.6431			1.20905			0.604526	+	0.796585i	$0.293362\pi$
$822$	−11.6167	−	14.2474i	−0.405179	−	0.496937i
$823$	36.3870			1.26837			0.634186	−	0.773180i	$-0.281335\pi$
$823$	36.3870			1.26837			0.634186	+	0.773180i	$0.281335\pi$
$824$	−2.37638	+	4.11601i	−0.0827851	+	0.143388i
$825$	−27.4927	+	72.3454i	−0.957171	+	2.51874i
$826$		0			0
$827$	−24.3576			−0.846997			−0.423498	−	0.905897i	$-0.639198\pi$
$827$	−24.3576			−0.846997			−0.423498	+	0.905897i	$0.639198\pi$
$828$	0.754693	−	3.67153i	0.0262274	−	0.127594i
$829$	−19.5851	+	33.9224i	−0.680219	+	1.17817i	0.294694	+	0.955592i	$0.404782\pi$
$829$	−19.5851	+	33.9224i	−0.680219	+	1.17817i	−0.974914	+	0.222583i	$0.928551\pi$
$830$	−3.78994	−	6.56438i	−0.131551	−	0.227853i
$831$	2.05606	+	2.52168i	0.0713240	+	0.0874761i
$832$	0.654792	+	1.13413i	0.0227008	+	0.0393190i
$833$		0			0
$834$	1.65808	+	2.03357i	0.0574146	+	0.0704167i
$835$	58.3381			2.01887
$836$	−6.58970	+	11.4137i	−0.227910	+	0.394751i
$837$	0.867755	−	0.453202i	0.0299940	−	0.0156650i
$838$	−12.8515	−	22.2594i	−0.443947	−	0.768939i
$839$	−17.1739	+	29.7460i	−0.592907	+	1.02695i	0.400931	+	0.916108i	$0.368687\pi$
$839$	−17.1739	+	29.7460i	−0.592907	+	1.02695i	−0.993839	+	0.110838i	$0.964647\pi$
$840$		0			0
$841$	−4.75250	−	8.23157i	−0.163879	−	0.283847i
$842$	7.84250	−	13.5836i	0.270270	−	0.468122i
$843$	−7.43218	+	19.5574i	−0.255978	+	0.673591i
$844$	7.99045	+	13.8399i	0.275043	+	0.476388i
$845$	20.6260	+	35.7253i	0.709556	+	1.22899i
$846$	28.1199	−	9.34577i	0.966781	−	0.321314i
$847$		0			0
$848$	−20.8442	+	36.1032i	−0.715793	+	1.23979i
$849$	47.8265	−	7.73956i	1.64140	−	0.265621i
$850$	−15.2505			−0.523088
$851$	−4.55454			−0.156127
$852$	20.4760	−	3.31353i	0.701495	−	0.113520i
$853$	−16.3371	+	28.2967i	−0.559373	+	0.968862i	0.438176	+	0.898889i	$0.355625\pi$
$853$	−16.3371	+	28.2967i	−0.559373	+	0.968862i	−0.997549	+	0.0699730i	$0.977709\pi$
$854$		0			0
$855$	−22.0518	+	7.32904i	−0.754157	+	0.250648i
$856$	0.156982	+	0.271901i	0.00536555	+	0.00929340i
$857$	28.8340	+	49.9419i	0.984950	+	1.70598i	0.642159	+	0.766571i	$0.278039\pi$
$857$	28.8340	+	49.9419i	0.984950	+	1.70598i	0.342791	+	0.939412i	$0.388628\pi$
$858$	−7.24867	+	19.0745i	−0.247465	+	0.651191i
$859$	−14.9884	+	25.9607i	−0.511397	+	0.885766i	0.488515	+	0.872555i	$0.337539\pi$
$859$	−14.9884	+	25.9607i	−0.511397	+	0.885766i	−0.999913	+	0.0132108i	$0.995795\pi$
$860$	−6.55733	−	11.3576i	−0.223603	−	0.387292i
$861$		0			0
$862$	−14.3615	+	24.8749i	−0.489156	+	0.847243i
$863$	11.5888	+	20.0724i	0.394487	+	0.683272i	0.993036	−	0.117815i	$-0.0375889\pi$
$863$	11.5888	+	20.0724i	0.394487	+	0.683272i	−0.598548	+	0.801087i	$0.704256\pi$
$864$	−23.5553	+	12.3022i	−0.801369	+	0.418531i
$865$	30.9967	−	53.6879i	1.05392	−	1.82544i
$866$	−34.0873			−1.15833
$867$	−17.0204	−	20.8748i	−0.578043	−	0.708947i
$868$		0			0
$869$	28.0690	+	48.6170i	0.952177	+	1.64922i
$870$	−41.1881	−	50.5156i	−1.39641	−	1.71264i
$871$	−4.43240	−	7.67715i	−0.150186	−	0.260130i
$872$	−8.23129	+	14.2570i	−0.278747	+	0.482803i
$873$	9.95776	−	48.4438i	0.337019	−	1.63957i
$874$	−4.84884			−0.164014
$875$		0			0
$876$	−3.20853	+	8.44308i	−0.108406	+	0.285265i
$877$	0.369978	−	0.640820i	0.0124933	−	0.0216390i	−0.859711	−	0.510780i	$-0.829357\pi$
$877$	0.369978	−	0.640820i	0.0124933	−	0.0216390i	0.872204	+	0.489141i	$0.162690\pi$
$878$	11.6290			0.392458
$879$	9.65728	+	11.8443i	0.325732	+	0.399497i
$880$	106.954			3.60540
$881$	−18.0285			−0.607395			−0.303697	−	0.952769i	$-0.598221\pi$
$881$	−18.0285			−0.607395			−0.303697	+	0.952769i	$0.598221\pi$
$882$		0			0
$883$	43.0928			1.45019			0.725095	−	0.688649i	$-0.241796\pi$
$883$	43.0928			1.45019			0.725095	+	0.688649i	$0.241796\pi$
$884$	−1.32339			−0.0445104
$885$	−24.3520	+	64.0810i	−0.818584	+	2.15406i
$886$	−49.4507			−1.66133
$887$	15.4763	−	26.8058i	0.519645	−	0.900051i	−0.480094	−	0.877217i	$-0.659398\pi$
$887$	15.4763	−	26.8058i	0.519645	−	0.900051i	0.999739	−	0.0228344i	$-0.00726904\pi$
$888$	6.88650	+	8.44602i	0.231096	+	0.283430i
$889$		0			0
$890$	−33.6047			−1.12643
$891$	50.3714	+	21.6215i	1.68751	+	0.724349i
$892$	−9.79685	+	16.9686i	−0.328023	+	0.568152i
$893$	−6.30813	−	10.9260i	−0.211094	−	0.365625i
$894$	−6.13565	+	16.1456i	−0.205207	+	0.539991i
$895$	−4.61595	−	7.99506i	−0.154294	−	0.267245i
$896$		0			0
$897$	−2.43913	+	0.394713i	−0.0814401	+	0.0131791i
$898$	11.5143			0.384236
$899$	0.584545	−	1.01246i	0.0194957	−	0.0337675i
$900$	−16.1447	−	14.3418i	−0.538157	−	0.478059i
$901$	5.01945	+	8.69395i	0.167222	+	0.289637i
$902$	17.7008	−	30.6587i	0.589372	−	1.02082i
$903$		0			0
$904$	7.40614	+	12.8278i	0.246324	+	0.426646i
$905$	−6.97880	+	12.0876i	−0.231983	+	0.401807i
$906$	3.82958	+	4.69683i	0.127229	+	0.156042i
$907$	21.4042	+	37.0731i	0.710714	+	1.23099i	0.964590	+	0.263755i	$0.0849611\pi$
$907$	21.4042	+	37.0731i	0.710714	+	1.23099i	−0.253876	+	0.967237i	$0.581706\pi$
$908$	−1.77243	−	3.06993i	−0.0588200	−	0.101879i
$909$	29.0760	+	25.8290i	0.964391	+	0.856694i
$910$		0			0
$911$	3.04869	−	5.28049i	0.101008	−	0.174950i	−0.811092	−	0.584918i	$-0.801127\pi$
$911$	3.04869	−	5.28049i	0.101008	−	0.174950i	0.912100	+	0.409968i	$0.134460\pi$
$912$	12.0683	+	14.8013i	0.399622	+	0.490121i
$913$	7.61269			0.251943
$914$	49.4800			1.63665
$915$	25.9375	−	68.2530i	0.857467	−	2.25638i
$916$	−6.72830	+	11.6538i	−0.222309	+	0.385051i
$917$		0			0
$918$	−0.456710	+	10.7919i	−0.0150737	+	0.356186i
$919$	−12.4307	−	21.5305i	−0.410050	−	0.710227i	0.584845	−	0.811145i	$-0.301155\pi$
$919$	−12.4307	−	21.5305i	−0.410050	−	0.710227i	−0.994895	+	0.100918i	$0.967822\pi$
$920$	3.93382	+	6.81357i	0.129694	+	0.224637i
$921$	−1.80440	+	0.291998i	−0.0594569	+	0.00962165i
$922$	17.2811	−	29.9317i	0.569121	−	0.985747i
$923$	−6.83664	−	11.8414i	−0.225031	−	0.389764i
$924$		0			0
$925$	−13.1199	+	22.7244i	−0.431381	+	0.747174i
$926$	8.56034	+	14.8269i	0.281310	+	0.487244i
$927$	−1.63198	+	7.93946i	−0.0536012	+	0.260766i
$928$	−15.8676	+	27.4834i	−0.520878	+	0.902188i
$929$	−41.8402			−1.37273			−0.686366	−	0.727256i	$-0.740795\pi$
$929$	−41.8402			−1.37273			−0.686366	+	0.727256i	$0.740795\pi$
$930$	0.702994	−	1.84989i	0.0230521	−	0.0606603i
$931$		0			0
$932$	12.3895	+	21.4592i	0.405831	+	0.702920i
$933$	−5.25279	+	0.850036i	−0.171969	+	0.0278289i
$934$	−13.8826	−	24.0453i	−0.454251	−	0.786786i
$935$	12.8776	−	22.3047i	0.421144	−	0.729443i
$936$	4.41995	+	3.92636i	0.144471	+	0.128337i
$937$	−29.2537			−0.955676			−0.477838	−	0.878448i	$-0.658579\pi$
$937$	−29.2537			−0.955676			−0.477838	+	0.878448i	$0.658579\pi$
$938$		0			0
$939$	−48.1517	+	7.79218i	−1.57137	+	0.254288i
$940$	9.85740	−	17.0735i	0.321513	−	0.556877i
$941$	−3.35737			−0.109447			−0.0547236	−	0.998502i	$-0.517428\pi$
$941$	−3.35737			−0.109447			−0.0547236	+	0.998502i	$0.517428\pi$
$942$	−8.99693	+	1.45593i	−0.293136	+	0.0474369i
$943$	4.28673			0.139595
$944$	56.3387			1.83367
$945$		0			0
$946$	40.0194			1.30114
$947$	5.26601			0.171122			0.0855612	−	0.996333i	$-0.472732\pi$
$947$	5.26601			0.171122			0.0855612	+	0.996333i	$0.472732\pi$
$948$	−15.4630	+	2.50230i	−0.502214	+	0.0812710i
$949$	5.95398			0.193274
$950$	−13.9677	+	24.1928i	−0.453173	+	0.784918i
$951$	−21.9650	+	3.55450i	−0.712264	+	0.115263i
$952$		0			0
$953$	56.2520			1.82218			0.911090	−	0.412208i	$-0.135242\pi$
$953$	56.2520			1.82218			0.911090	+	0.412208i	$0.135242\pi$
$954$	−8.69619	+	42.3063i	−0.281549	+	1.36972i
$955$	31.9724	−	55.3778i	1.03460	−	1.79198i
$956$	−4.41038	−	7.63900i	−0.142642	−	0.247063i
$957$	64.6203	−	10.4572i	2.08888	−	0.338034i
$958$	7.08131	+	12.2652i	0.228787	+	0.396270i
$959$		0			0
$960$	2.52624	−	6.64767i	0.0815341	−	0.214553i
$961$	−30.9645			−0.998855
$962$	−3.45918	+	5.99148i	−0.111528	+	0.193173i
$963$	0.400306	+	0.355602i	0.0128997	+	0.0114591i
$964$	−4.54153	−	7.86616i	−0.146273	−	0.253352i
$965$	0.355420	−	0.615606i	0.0114414	−	0.0198171i
$966$		0			0
$967$	−6.88641	−	11.9276i	−0.221452	−	0.383566i	0.733797	−	0.679369i	$-0.237746\pi$
$967$	−6.88641	−	11.9276i	−0.221452	−	0.383566i	−0.955249	+	0.295803i	$0.904413\pi$
$968$	−22.9526	+	39.7551i	−0.737725	+	1.27778i
$969$	4.53983	−	0.734661i	0.145840	−	0.0236007i
$970$	−49.9874	−	86.5807i	−1.60500	−	2.77994i
$971$	−25.6627	−	44.4491i	−0.823555	−	1.42644i	−0.903019	−	0.429602i	$-0.858654\pi$
$971$	−25.6627	−	44.4491i	−0.823555	−	1.42644i	0.0794635	−	0.996838i	$-0.474679\pi$
$972$	−10.6324	+	10.9952i	−0.341033	+	0.352671i
$973$		0			0
$974$	2.36269	−	4.09230i	0.0757055	−	0.131126i
$975$	−5.05685	+	13.3068i	−0.161949	+	0.426159i
$976$	−60.0066			−1.92077
$977$	17.6850			0.565794			0.282897	−	0.959150i	$-0.408704\pi$
$977$	17.6850			0.565794			0.282897	+	0.959150i	$0.408704\pi$
$978$	10.1841	+	12.4903i	0.325650	+	0.399397i
$979$	16.8751	−	29.2285i	0.539329	−	0.934146i
$980$		0			0
$981$	−5.65284	+	27.5006i	−0.180481	+	0.878027i
$982$	−17.0154	−	29.4716i	−0.542984	−	0.940476i
$983$	−8.00207	−	13.8600i	−0.255226	−	0.442065i	0.709731	−	0.704473i	$-0.248817\pi$
$983$	−8.00207	−	13.8600i	−0.255226	−	0.442065i	−0.964957	+	0.262408i	$0.915483\pi$
$984$	−6.48158	−	7.94940i	−0.206625	−	0.253418i
$985$	2.86492	−	4.96218i	0.0912839	−	0.158108i
$986$	6.44961	+	11.1711i	0.205397	+	0.355759i
$987$		0			0
$988$	−1.21207	+	2.09937i	−0.0385612	+	0.0667899i
$989$	2.42295	+	4.19667i	0.0770454	+	0.133446i
$990$	105.153	−	34.9480i	3.34197	−	1.11072i
$991$	5.43319	−	9.41055i	0.172591	−	0.298936i	−0.766734	−	0.641965i	$-0.778120\pi$
$991$	5.43319	−	9.41055i	0.172591	−	0.298936i	0.939325	+	0.343029i	$0.111453\pi$
$992$	−0.963543			−0.0305925
$993$	36.8567	−	5.96435i	1.16961	−	0.189273i
$994$		0			0
$995$	−11.0499	−	19.1390i	−0.350306	−	0.606748i
$996$	−0.754572	+	1.98561i	−0.0239095	+	0.0629166i
$997$	20.5187	+	35.5395i	0.649835	+	1.12555i	0.983162	+	0.182736i	$0.0584954\pi$
$997$	20.5187	+	35.5395i	0.649835	+	1.12555i	−0.333327	+	0.942811i	$0.608171\pi$
$998$	−28.5719	+	49.4880i	−0.904428	+	1.56652i
$999$	15.6879	+	9.96477i	0.496342	+	0.315271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.h.h.214.3		24
3.2	odd	2		1323.2.h.h.802.9		24
7.2	even	3		441.2.g.h.79.10		24
7.3	odd	6		441.2.f.h.295.9	yes	24
7.4	even	3		441.2.f.h.295.10	yes	24
7.5	odd	6		441.2.g.h.79.9		24
7.6	odd	2	inner	441.2.h.h.214.4		24
9.4	even	3		441.2.g.h.67.10		24
9.5	odd	6		1323.2.g.h.361.3		24
21.2	odd	6		1323.2.g.h.667.3		24
21.5	even	6		1323.2.g.h.667.4		24
21.11	odd	6		1323.2.f.h.883.4		24
21.17	even	6		1323.2.f.h.883.3		24
21.20	even	2		1323.2.h.h.802.10		24
63.4	even	3		441.2.f.h.148.10	yes	24
63.5	even	6		1323.2.h.h.226.10		24
63.11	odd	6		3969.2.a.bi.1.9		12
63.13	odd	6		441.2.g.h.67.9		24
63.23	odd	6		1323.2.h.h.226.9		24
63.25	even	3		3969.2.a.bh.1.4		12
63.31	odd	6		441.2.f.h.148.9	✓	24
63.32	odd	6		1323.2.f.h.442.4		24
63.38	even	6		3969.2.a.bi.1.10		12
63.40	odd	6	inner	441.2.h.h.373.4		24
63.41	even	6		1323.2.g.h.361.4		24
63.52	odd	6		3969.2.a.bh.1.3		12
63.58	even	3	inner	441.2.h.h.373.3		24
63.59	even	6		1323.2.f.h.442.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.9	✓	24	63.31	odd	6
441.2.f.h.148.10	yes	24	63.4	even	3
441.2.f.h.295.9	yes	24	7.3	odd	6
441.2.f.h.295.10	yes	24	7.4	even	3
441.2.g.h.67.9		24	63.13	odd	6
441.2.g.h.67.10		24	9.4	even	3
441.2.g.h.79.9		24	7.5	odd	6
441.2.g.h.79.10		24	7.2	even	3
441.2.h.h.214.3		24	1.1	even	1	trivial
441.2.h.h.214.4		24	7.6	odd	2	inner
441.2.h.h.373.3		24	63.58	even	3	inner
441.2.h.h.373.4		24	63.40	odd	6	inner
1323.2.f.h.442.3		24	63.59	even	6
1323.2.f.h.442.4		24	63.32	odd	6
1323.2.f.h.883.3		24	21.17	even	6
1323.2.f.h.883.4		24	21.11	odd	6
1323.2.g.h.361.3		24	9.5	odd	6
1323.2.g.h.361.4		24	63.41	even	6
1323.2.g.h.667.3		24	21.2	odd	6
1323.2.g.h.667.4		24	21.5	even	6
1323.2.h.h.226.9		24	63.23	odd	6
1323.2.h.h.226.10		24	63.5	even	6
1323.2.h.h.802.9		24	3.2	odd	2
1323.2.h.h.802.10		24	21.20	even	2
3969.2.a.bh.1.3		12	63.52	odd	6
3969.2.a.bh.1.4		12	63.25	even	3
3969.2.a.bi.1.9		12	63.11	odd	6
3969.2.a.bi.1.10		12	63.38	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.72661 q^{2} +(-1.70981 + 0.276691i) q^{3} +0.981184 q^{4} +(-1.75616 + 3.04175i) q^{5} +(2.95217 - 0.477737i) q^{6} +1.75910 q^{8} +(2.84688 - 0.946176i) q^{9} +O(q^{10})\)	\(q-1.72661 q^{2} +(-1.70981 + 0.276691i) q^{3} +0.981184 q^{4} +(-1.75616 + 3.04175i) q^{5} +(2.95217 - 0.477737i) q^{6} +1.75910 q^{8} +(2.84688 - 0.946176i) q^{9} +(3.03220 - 5.25192i) q^{10} +(3.04532 + 5.27465i) q^{11} +(-1.67764 + 0.271484i) q^{12} +(0.560139 + 0.970190i) q^{13} +(2.16106 - 5.68672i) q^{15} -4.99965 q^{16} +(-0.601978 + 1.04266i) q^{17} +(-4.91546 + 1.63368i) q^{18} +(1.10269 + 1.90991i) q^{19} +(-1.72311 + 2.98452i) q^{20} +(-5.25808 - 9.10727i) q^{22} +(0.636695 - 1.10279i) q^{23} +(-3.00772 + 0.486726i) q^{24} +(-3.66817 - 6.35345i) q^{25} +(-0.967143 - 1.67514i) q^{26} +(-4.60583 + 2.40548i) q^{27} +(-3.10262 + 5.37390i) q^{29} +(-3.73132 + 9.81875i) q^{30} -0.188404 q^{31} +5.11425 q^{32} +(-6.66636 - 8.17602i) q^{33} +(1.03938 - 1.80026i) q^{34} +(2.79332 - 0.928373i) q^{36} +(-1.78835 - 3.09752i) q^{37} +(-1.90391 - 3.29767i) q^{38} +(-1.22617 - 1.50385i) q^{39} +(-3.08925 + 5.35074i) q^{40} +(1.68320 + 2.91538i) q^{41} +(-1.90276 + 3.29567i) q^{43} +(2.98802 + 5.17540i) q^{44} +(-2.12154 + 10.3211i) q^{45} +(-1.09932 + 1.90408i) q^{46} -5.72070 q^{47} +(8.54843 - 1.38336i) q^{48} +(6.33349 + 10.9699i) q^{50} +(0.740773 - 1.94930i) q^{51} +(0.549600 + 0.951935i) q^{52} +(4.16913 - 7.22115i) q^{53} +(7.95247 - 4.15334i) q^{54} -21.3922 q^{55} +(-2.41384 - 2.96047i) q^{57} +(5.35702 - 9.27862i) q^{58} -11.2685 q^{59} +(2.12040 - 5.57972i) q^{60} +12.0022 q^{61} +0.325300 q^{62} +1.16898 q^{64} -3.93477 q^{65} +(11.5102 + 14.1168i) q^{66} -7.91303 q^{67} +(-0.590651 + 1.02304i) q^{68} +(-0.783494 + 2.06172i) q^{69} -12.2052 q^{71} +(5.00795 - 1.66442i) q^{72} +(2.65737 - 4.60269i) q^{73} +(3.08779 + 5.34820i) q^{74} +(8.02980 + 9.84823i) q^{75} +(1.08194 + 1.87397i) q^{76} +(2.11712 + 2.59657i) q^{78} +9.21711 q^{79} +(8.78016 - 15.2077i) q^{80} +(7.20950 - 5.38731i) q^{81} +(-2.90623 - 5.03373i) q^{82} +(0.624950 - 1.08245i) q^{83} +(-2.11433 - 3.66213i) q^{85} +(3.28532 - 5.69034i) q^{86} +(3.81798 - 10.0468i) q^{87} +(5.35702 + 9.27862i) q^{88} +(-2.77066 - 4.79892i) q^{89} +(3.66308 - 17.8206i) q^{90} +(0.624715 - 1.08204i) q^{92} +(0.322134 - 0.0521295i) q^{93} +9.87741 q^{94} -7.74596 q^{95} +(-8.74438 + 1.41506i) q^{96} +(8.24277 - 14.2769i) q^{97} +(13.6604 + 12.1349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9	\( 24 q - 8 q^{2} + 24 q^{4} - 24 q^{8} - 4 q^{9} + 20 q^{11} + 4 q^{15} + 24 q^{16} - 32 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} - 84 q^{30} - 96 q^{32} - 4 q^{36} - 12 q^{37} + 8 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} + 64 q^{51} + 32 q^{53} - 12 q^{57} + 32 q^{60} + 96 q^{64} - 120 q^{65} + 24 q^{67} - 112 q^{71} + 68 q^{74} - 60 q^{78} - 24 q^{79} - 40 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 32 q^{93} - 128 q^{95} + 20 q^{99}+O(q^{100}) \) 24 * q - 8 * q^2 + 24 * q^4 - 24 * q^8 - 4 * q^9 + 20 * q^11 + 4 * q^15 + 24 * q^16 - 32 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 - 84 * q^30 - 96 * q^32 - 4 * q^36 - 12 * q^37 + 8 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 + 64 * q^51 + 32 * q^53 - 12 * q^57 + 32 * q^60 + 96 * q^64 - 120 * q^65 + 24 * q^67 - 112 * q^71 + 68 * q^74 - 60 * q^78 - 24 * q^79 - 40 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 32 * q^93 - 128 * q^95 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more