LMFDB - Embedded newform 441.2.f.h.295.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(148,441)]

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([2, 0]))

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

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

chi := DirichletCharacter("441.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.52140272914$
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			295.6
Character	$\chi$	$=$	441.295
Dual form			441.2.f.h.148.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0341870 + 0.0592136i) q^{2} +(1.69514 - 0.355671i) q^{3} +(0.997662 + 1.72800i) q^{4} +(1.33190 + 2.30691i) q^{5} +(-0.0368912 + 0.112535i) q^{6} -0.273176 q^{8} +(2.74700 - 1.20582i) q^{9} +O(q^{10})$	\(q+(-0.0341870 + 0.0592136i) q^{2} +(1.69514 - 0.355671i) q^{3} +(0.997662 + 1.72800i) q^{4} +(1.33190 + 2.30691i) q^{5} +(-0.0368912 + 0.112535i) q^{6} -0.273176 q^{8} +(2.74700 - 1.20582i) q^{9} -0.182134 q^{10} +(0.799563 - 1.38488i) q^{11} +(2.30578 + 2.57437i) q^{12} +(-2.62690 - 4.54992i) q^{13} +(3.07825 + 3.43682i) q^{15} +(-1.98599 + 3.43983i) q^{16} -6.54721 q^{17} +(-0.0225104 + 0.203883i) q^{18} +1.90194 q^{19} +(-2.65756 + 4.60304i) q^{20} +(0.0546693 + 0.0946900i) q^{22} +(1.53419 + 2.65729i) q^{23} +(-0.463072 + 0.0971608i) q^{24} +(-1.04789 + 1.81500i) q^{25} +0.359223 q^{26} +(4.22767 - 3.02106i) q^{27} +(-3.19452 + 5.53306i) q^{29} +(-0.308743 + 0.0647797i) q^{30} +(-3.35961 - 5.81902i) q^{31} +(-0.408966 - 0.708350i) q^{32} +(0.862809 - 2.63195i) q^{33} +(0.223829 - 0.387684i) q^{34} +(4.82424 + 3.54381i) q^{36} +4.22955 q^{37} +(-0.0650215 + 0.112621i) q^{38} +(-6.07124 - 6.77845i) q^{39} +(-0.363842 - 0.630193i) q^{40} +(-3.69648 - 6.40249i) q^{41} +(5.63176 - 9.75450i) q^{43} +3.19078 q^{44} +(6.44044 + 4.73105i) q^{45} -0.209797 q^{46} +(-1.89959 + 3.29018i) q^{47} +(-2.14308 + 6.53735i) q^{48} +(-0.0716485 - 0.124099i) q^{50} +(-11.0984 + 2.32865i) q^{51} +(5.24152 - 9.07858i) q^{52} +8.89862 q^{53} +(0.0343569 + 0.353616i) q^{54} +4.25974 q^{55} +(3.22405 - 0.676463i) q^{57} +(-0.218422 - 0.378317i) q^{58} +(5.44639 + 9.43343i) q^{59} +(-2.86778 + 8.74801i) q^{60} +(-1.35693 + 2.35027i) q^{61} +0.459420 q^{62} -7.88802 q^{64} +(6.99751 - 12.1200i) q^{65} +(0.126351 + 0.141069i) q^{66} +(1.66267 + 2.87982i) q^{67} +(-6.53190 - 11.3136i) q^{68} +(3.54578 + 3.95881i) q^{69} -12.3890 q^{71} +(-0.750414 + 0.329402i) q^{72} +2.19863 q^{73} +(-0.144596 + 0.250447i) q^{74} +(-1.13078 + 3.44939i) q^{75} +(1.89749 + 3.28655i) q^{76} +(0.608933 - 0.127765i) q^{78} +(-0.406778 + 0.704560i) q^{79} -10.5805 q^{80} +(6.09198 - 6.62478i) q^{81} +0.505486 q^{82} +(-3.41842 + 5.92088i) q^{83} +(-8.72020 - 15.1038i) q^{85} +(0.385066 + 0.666954i) q^{86} +(-3.44720 + 10.5155i) q^{87} +(-0.218422 + 0.378317i) q^{88} +0.470572 q^{89} +(-0.500321 + 0.219621i) q^{90} +(-3.06120 + 5.30216i) q^{92} +(-7.76467 - 8.66914i) q^{93} +(-0.129882 - 0.224963i) q^{94} +(2.53318 + 4.38760i) q^{95} +(-0.945194 - 1.05529i) q^{96} +(2.57623 - 4.46216i) q^{97} +(0.526472 - 4.76840i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9} + 20 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} + 48 q^{32} - 4 q^{36} + 24 q^{37} + 32 q^{39} - 112 q^{44} - 48 q^{46} - 4 q^{50} - 56 q^{51} - 64 q^{53} - 12 q^{57} - 88 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} + 168 q^{72} + 68 q^{74} - 60 q^{78} + 12 q^{79} + 80 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 80 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9 + 20 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 + 48 * q^32 - 4 * q^36 + 24 * q^37 + 32 * q^39 - 112 * q^44 - 48 * q^46 - 4 * q^50 - 56 * q^51 - 64 * q^53 - 12 * q^57 - 88 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 + 168 * q^72 + 68 * q^74 - 60 * q^78 + 12 * q^79 + 80 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 80 * q^93 + 64 * q^95 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.0341870	+	0.0592136i	−0.0241739	+	0.0418703i	−0.877859	−	0.478919i	$-0.841029\pi$
$2$	−0.0341870	+	0.0592136i	−0.0241739	+	0.0418703i	0.853685	+	0.520789i	$0.174362\pi$
$3$	1.69514	−	0.355671i	0.978689	−	0.205347i
$3$	1.69514	−	0.355671i	0.978689	−	0.205347i
$4$	0.997662	+	1.72800i	0.498831	+	0.864001i
$5$	1.33190	+	2.30691i	0.595642	+	1.03168i	0.993456	+	0.114216i	$0.0364355\pi$
$5$	1.33190	+	2.30691i	0.595642	+	1.03168i	−0.397814	+	0.917466i	$0.630231\pi$
$6$	−0.0368912	+	0.112535i	−0.0150608	+	0.0459421i
$7$		0			0
$7$		0			0
$8$	−0.273176			−0.0965824
$9$	2.74700	−	1.20582i	0.915666	−	0.401941i
$10$	−0.182134			−0.0575958
$11$	0.799563	−	1.38488i	0.241077	−	0.417558i	−0.719944	−	0.694032i	$-0.755833\pi$
$11$	0.799563	−	1.38488i	0.241077	−	0.417558i	0.961021	+	0.276474i	$0.0891659\pi$
$12$	2.30578	+	2.57437i	0.665620	+	0.743155i
$13$	−2.62690	−	4.54992i	−0.728571	−	1.26192i	−0.957487	−	0.288476i	$-0.906852\pi$
$13$	−2.62690	−	4.54992i	−0.728571	−	1.26192i	0.228916	−	0.973446i	$-0.426482\pi$
$14$		0			0
$15$	3.07825	+	3.43682i	0.794801	+	0.887383i
$16$	−1.98599	+	3.43983i	−0.496496	+	0.859957i
$17$	−6.54721			−1.58793			−0.793966	−	0.607963i	$-0.791987\pi$
$17$	−6.54721			−1.58793			−0.793966	+	0.607963i	$0.791987\pi$
$18$	−0.0225104	+	0.203883i	−0.00530576	+	0.0480557i
$19$	1.90194			0.436334			0.218167	−	0.975911i	$-0.429992\pi$
$19$	1.90194			0.436334			0.218167	+	0.975911i	$0.429992\pi$
$20$	−2.65756	+	4.60304i	−0.594249	+	1.02927i
$21$		0			0
$22$	0.0546693	+	0.0946900i	0.0116555	+	0.0201880i
$23$	1.53419	+	2.65729i	0.319900	+	0.554083i	0.980467	−	0.196684i	$-0.0630173\pi$
$23$	1.53419	+	2.65729i	0.319900	+	0.554083i	−0.660567	+	0.750767i	$0.729684\pi$
$24$	−0.463072	+	0.0971608i	−0.0945242	+	0.0198329i
$25$	−1.04789	+	1.81500i	−0.209578	+	0.363000i
$26$	0.359223			0.0704495
$27$	4.22767	−	3.02106i	0.813615	−	0.581404i
$28$		0			0
$29$	−3.19452	+	5.53306i	−0.593207	+	1.02746i	0.400591	+	0.916257i	$0.368805\pi$
$29$	−3.19452	+	5.53306i	−0.593207	+	1.02746i	−0.993797	+	0.111207i	$0.964528\pi$
$30$	−0.308743	+	0.0647797i	−0.0563684	+	0.0118271i
$31$	−3.35961	−	5.81902i	−0.603405	−	1.04513i	−0.992301	−	0.123846i	$-0.960477\pi$
$31$	−3.35961	−	5.81902i	−0.603405	−	1.04513i	0.388897	−	0.921281i	$-0.372856\pi$
$32$	−0.408966	−	0.708350i	−0.0722957	−	0.125220i
$33$	0.862809	−	2.63195i	0.150196	−	0.458164i
$34$	0.223829	−	0.387684i	0.0383864	−	0.0664872i
$35$		0			0
$36$	4.82424	+	3.54381i	0.804040	+	0.590635i
$37$	4.22955			0.695333			0.347667	−	0.937618i	$-0.386974\pi$
$37$	4.22955			0.695333			0.347667	+	0.937618i	$0.386974\pi$
$38$	−0.0650215	+	0.112621i	−0.0105479	+	0.0182695i
$39$	−6.07124	−	6.77845i	−0.972176	−	1.08542i
$40$	−0.363842	−	0.630193i	−0.0575285	−	0.0996423i
$41$	−3.69648	−	6.40249i	−0.577293	−	0.999901i	−0.995788	−	0.0916820i	$-0.970776\pi$
$41$	−3.69648	−	6.40249i	−0.577293	−	0.999901i	0.418495	−	0.908219i	$-0.362558\pi$
$42$		0			0
$43$	5.63176	−	9.75450i	0.858836	−	1.48755i	−0.0142043	−	0.999899i	$-0.504522\pi$
$43$	5.63176	−	9.75450i	0.858836	−	1.48755i	0.873040	−	0.487648i	$-0.162145\pi$
$44$	3.19078			0.481028
$45$	6.44044	+	4.73105i	0.960084	+	0.705263i
$46$	−0.209797			−0.0309329
$47$	−1.89959	+	3.29018i	−0.277083	+	0.479922i	−0.970659	−	0.240462i	$-0.922701\pi$
$47$	−1.89959	+	3.29018i	−0.277083	+	0.479922i	0.693575	+	0.720384i	$0.256034\pi$
$48$	−2.14308	+	6.53735i	−0.309327	+	0.943585i
$49$		0			0
$50$	−0.0716485	−	0.124099i	−0.0101326	−	0.0175502i
$51$	−11.0984	+	2.32865i	−1.55409	+	0.326076i
$52$	5.24152	−	9.07858i	0.726868	−	1.25897i
$53$	8.89862			1.22232			0.611160	−	0.791507i	$-0.290703\pi$
$53$	8.89862			1.22232			0.611160	+	0.791507i	$0.290703\pi$
$54$	0.0343569	+	0.353616i	0.00467539	+	0.0481211i
$55$	4.25974			0.574383
$56$		0			0
$57$	3.22405	−	0.676463i	0.427036	−	0.0895997i
$58$	−0.218422	−	0.378317i	−0.0286802	−	0.0496755i
$59$	5.44639	+	9.43343i	0.709060	+	1.22813i	0.965206	+	0.261490i	$0.0842138\pi$
$59$	5.44639	+	9.43343i	0.709060	+	1.22813i	−0.256146	+	0.966638i	$0.582453\pi$
$60$	−2.86778	+	8.74801i	−0.370228	+	1.12936i
$61$	−1.35693	+	2.35027i	−0.173737	+	0.300922i	−0.939724	−	0.341935i	$-0.888918\pi$
$61$	−1.35693	+	2.35027i	−0.173737	+	0.300922i	0.765986	+	0.642857i	$0.222251\pi$
$62$	0.459420			0.0583465
$63$		0			0
$64$	−7.88802			−0.986002
$65$	6.99751	−	12.1200i	0.867935	−	1.50331i
$66$	0.126351	+	0.141069i	0.0155527	+	0.0173643i
$67$	1.66267	+	2.87982i	0.203127	+	0.351826i	0.949534	−	0.313663i	$-0.101556\pi$
$67$	1.66267	+	2.87982i	0.203127	+	0.351826i	−0.746407	+	0.665489i	$0.768223\pi$
$68$	−6.53190	−	11.3136i	−0.792110	−	1.37197i
$69$	3.54578	+	3.95881i	0.426862	+	0.476585i
$70$		0			0
$71$	−12.3890			−1.47031			−0.735154	−	0.677900i	$-0.762890\pi$
$71$	−12.3890			−1.47031			−0.735154	+	0.677900i	$0.762890\pi$
$72$	−0.750414	+	0.329402i	−0.0884372	+	0.0388204i
$73$	2.19863			0.257331			0.128665	−	0.991688i	$-0.458931\pi$
$73$	2.19863			0.257331			0.128665	+	0.991688i	$0.458931\pi$
$74$	−0.144596	+	0.250447i	−0.0168089	+	0.0291138i
$75$	−1.13078	+	3.44939i	−0.130571	+	0.398301i
$76$	1.89749	+	3.28655i	0.217657	+	0.376993i
$77$		0			0
$78$	0.608933	−	0.127765i	0.0689481	−	0.0144666i
$79$	−0.406778	+	0.704560i	−0.0457661	+	0.0792692i	−0.888001	−	0.459841i	$-0.847906\pi$
$79$	−0.406778	+	0.704560i	−0.0457661	+	0.0792692i	0.842235	+	0.539111i	$0.181240\pi$
$80$	−10.5805			−1.18294
$81$	6.09198	−	6.62478i	0.676887	−	0.736087i
$82$	0.505486			0.0558216
$83$	−3.41842	+	5.92088i	−0.375220	+	0.649901i	−0.990360	−	0.138517i	$-0.955766\pi$
$83$	−3.41842	+	5.92088i	−0.375220	+	0.649901i	0.615140	+	0.788418i	$0.289100\pi$
$84$		0			0
$85$	−8.72020	−	15.1038i	−0.945838	−	1.63824i
$86$	0.385066	+	0.666954i	0.0415227	+	0.0719195i
$87$	−3.44720	+	10.5155i	−0.369579	+	1.12738i
$88$	−0.218422	+	0.378317i	−0.0232838	+	0.0403288i
$89$	0.470572			0.0498805			0.0249403	−	0.999689i	$-0.492060\pi$
$89$	0.470572			0.0498805			0.0249403	+	0.999689i	$0.492060\pi$
$90$	−0.500321	+	0.219621i	−0.0527385	+	0.0231501i
$91$		0			0
$92$	−3.06120	+	5.30216i	−0.319152	+	0.552788i
$93$	−7.76467	−	8.66914i	−0.805159	−	0.898948i
$94$	−0.129882	−	0.224963i	−0.0133963	−	0.0232031i
$95$	2.53318	+	4.38760i	0.259899	+	0.450158i
$96$	−0.945194	−	1.05529i	−0.0964684	−	0.107706i
$97$	2.57623	−	4.46216i	0.261576	−	0.453064i	−0.705085	−	0.709123i	$-0.749091\pi$
$97$	2.57623	−	4.46216i	0.261576	−	0.453064i	0.966661	+	0.256059i	$0.0824243\pi$
$98$		0			0
$99$	0.526472	−	4.76840i	0.0529125	−	0.479243i
$100$	−4.18177			−0.418177
$101$	0.922440	−	1.59771i	0.0917862	−	0.158978i	−0.816477	−	0.577379i	$-0.804076\pi$
$101$	0.922440	−	1.59771i	0.0917862	−	0.158978i	0.908263	+	0.418400i	$0.137409\pi$
$102$	0.241534	−	0.736788i	0.0239155	−	0.0729529i
$103$	−2.58901	−	4.48430i	−0.255103	−	0.441851i	0.709821	−	0.704383i	$-0.248776\pi$
$103$	−2.58901	−	4.48430i	−0.255103	−	0.441851i	−0.964923	+	0.262531i	$0.915443\pi$
$104$	0.717607	+	1.24293i	0.0703671	+	0.121879i
$105$		0			0
$106$	−0.304217	+	0.526920i	−0.0295482	+	0.0511790i
$107$	−16.9489			−1.63851			−0.819256	−	0.573428i	$-0.805613\pi$
$107$	−16.9489			−1.63851			−0.819256	+	0.573428i	$0.805613\pi$
$108$	9.43819	+	4.29141i	0.908190	+	0.412942i
$109$	−8.49992			−0.814145			−0.407073	−	0.913396i	$-0.633450\pi$
$109$	−8.49992			−0.814145			−0.407073	+	0.913396i	$0.633450\pi$
$110$	−0.145628	+	0.252235i	−0.0138851	+	0.0240496i
$111$	7.16967	−	1.50433i	0.680515	−	0.142784i
$112$		0			0
$113$	−1.95196	−	3.38089i	−0.183625	−	0.318048i	0.759487	−	0.650522i	$-0.225450\pi$
$113$	−1.95196	−	3.38089i	−0.183625	−	0.318048i	−0.943112	+	0.332474i	$0.892116\pi$
$114$	−0.0701647	+	0.214034i	−0.00657152	+	0.0200461i
$115$	−4.08675	+	7.07847i	−0.381092	+	0.660070i
$116$	−12.7482			−1.18364
$117$	−12.7025	−	9.33105i	−1.17435	−	0.862656i
$118$	−0.744783			−0.0685628
$119$		0			0
$120$	−0.840905	−	0.938858i	−0.0767637	−	0.0857056i
$121$	4.22140	+	7.31167i	0.383763	+	0.664698i
$122$	−0.0927788	−	0.160698i	−0.00839980	−	0.0145489i
$123$	−8.54323	−	9.53838i	−0.770317	−	0.860047i
$124$	6.70352	−	11.6108i	0.601994	−	1.04268i
$125$	7.73623			0.691949
$126$		0			0
$127$	10.9533			0.971946			0.485973	−	0.873974i	$-0.338465\pi$
$127$	10.9533			0.971946			0.485973	+	0.873974i	$0.338465\pi$
$128$	1.08760	−	1.88378i	0.0961311	−	0.166504i
$129$	6.07724	−	18.5383i	0.535071	−	1.63221i
$130$	0.478448	+	0.828696i	0.0419626	+	0.0726814i
$131$	2.22671	+	3.85678i	0.194549	+	0.336968i	0.946752	−	0.321962i	$-0.104342\pi$
$131$	2.22671	+	3.85678i	0.194549	+	0.336968i	−0.752204	+	0.658931i	$0.771009\pi$
$132$	5.40881	−	1.13487i	0.470777	−	0.0987774i
$133$		0			0
$134$	−0.227366			−0.0196414
$135$	12.6001	+	5.72911i	1.08445	+	0.493083i
$136$	1.78854			0.153366
$137$	9.76800	−	16.9187i	0.834537	−	1.44546i	−0.0598699	−	0.998206i	$-0.519069\pi$
$137$	9.76800	−	16.9187i	0.834537	−	1.44546i	0.894407	−	0.447254i	$-0.147598\pi$
$138$	−0.355635	+	0.0746186i	−0.0302737	+	0.00635196i
$139$	−1.31540	−	2.27833i	−0.111570	−	0.193246i	0.804833	−	0.593501i	$-0.202255\pi$
$139$	−1.31540	−	2.27833i	−0.111570	−	0.193246i	−0.916404	+	0.400256i	$0.868921\pi$
$140$		0			0
$141$	−2.04984	+	6.25295i	−0.172628	+	0.526593i
$142$	0.423544	−	0.733599i	0.0355430	−	0.0615623i
$143$	−8.40149			−0.702568
$144$	−1.30767	+	11.8439i	−0.108973	+	0.986995i
$145$	−17.0190			−1.41335
$146$	−0.0751647	+	0.130189i	−0.00622067	+	0.0107745i
$147$		0			0
$148$	4.21966	+	7.30867i	0.346854	+	0.600769i
$149$	4.40640	+	7.63212i	0.360987	+	0.625247i	0.988124	−	0.153662i	$-0.0491066\pi$
$149$	4.40640	+	7.63212i	0.360987	+	0.625247i	−0.627137	+	0.778909i	$0.715773\pi$
$150$	−0.165593	−	0.184882i	−0.0135206	−	0.0150955i
$151$	−2.33211	+	4.03933i	−0.189784	+	0.328716i	−0.945178	−	0.326555i	$-0.894112\pi$
$151$	−2.33211	+	4.03933i	−0.189784	+	0.328716i	0.755394	+	0.655271i	$0.227446\pi$
$152$	−0.519564			−0.0421422
$153$	−17.9852	+	7.89478i	−1.45401	+	0.638255i
$154$		0			0
$155$	8.94931	−	15.5007i	0.718826	−	1.24504i
$156$	5.65612	−	17.2537i	0.452852	−	1.38140i
$157$	2.03647	+	3.52727i	0.162528	+	0.281506i	0.935775	−	0.352599i	$-0.114702\pi$
$157$	2.03647	+	3.52727i	0.162528	+	0.281506i	−0.773247	+	0.634105i	$0.781369\pi$
$158$	−0.0278130	−	0.0481736i	−0.00221269	−	0.00383249i
$159$	15.0844	−	3.16498i	1.19627	−	0.250999i
$160$	1.08940	−	1.88690i	0.0861246	−	0.149172i
$161$		0			0
$162$	0.184011	+	0.587210i	0.0144573	+	0.0461355i
$163$	−12.1222			−0.949487			−0.474744	−	0.880124i	$-0.657459\pi$
$163$	−12.1222			−0.949487			−0.474744	+	0.880124i	$0.657459\pi$
$164$	7.37568	−	12.7750i	0.575944	−	0.997564i
$165$	7.22085	−	1.51506i	0.562143	−	0.117948i
$166$	−0.233731	−	0.404834i	−0.0181410	−	0.0314212i
$167$	2.39951	+	4.15608i	0.185680	+	0.321607i	0.943805	−	0.330502i	$-0.107218\pi$
$167$	2.39951	+	4.15608i	0.185680	+	0.321607i	−0.758126	+	0.652109i	$0.773885\pi$
$168$		0			0
$169$	−7.30121	+	12.6461i	−0.561631	+	0.972774i
$170$	1.19247			0.0914582
$171$	5.22461	−	2.29340i	0.399536	−	0.175381i
$172$	22.4744			1.71366
$173$	−2.51585	+	4.35759i	−0.191277	+	0.331301i	−0.945674	−	0.325118i	$-0.894596\pi$
$173$	−2.51585	+	4.35759i	−0.191277	+	0.331301i	0.754397	+	0.656419i	$0.227929\pi$
$174$	−0.504812	−	0.563615i	−0.0382697	−	0.0427275i
$175$		0			0
$176$	3.17584	+	5.50072i	0.239388	+	0.414632i
$177$	12.5876	+	14.0539i	0.946141	+	1.05635i
$178$	−0.0160874	+	0.0278642i	−0.00120580	+	0.00208851i
$179$	−16.3979			−1.22564			−0.612819	−	0.790224i	$-0.709964\pi$
$179$	−16.3979			−1.22564			−0.612819	+	0.790224i	$0.709964\pi$
$180$	−1.74987	+	15.8491i	−0.130428	+	1.18132i
$181$	−14.4345			−1.07291			−0.536454	−	0.843930i	$-0.680237\pi$
$181$	−14.4345			−1.07291			−0.536454	+	0.843930i	$0.680237\pi$
$182$		0			0
$183$	−1.46426	+	4.46666i	−0.108242	+	0.330185i
$184$	−0.419103	−	0.725908i	−0.0308967	−	0.0535147i
$185$	5.63332	+	9.75719i	0.414170	+	0.717363i
$186$	0.778782	−	0.163402i	0.0571031	−	0.0119812i
$187$	−5.23491	+	9.06713i	−0.382814	+	0.663054i
$188$	−7.58059			−0.552871
$189$		0			0
$190$	−0.346407			−0.0251310
$191$	−1.42066	+	2.46065i	−0.102795	+	0.178046i	−0.912835	−	0.408328i	$-0.866112\pi$
$191$	−1.42066	+	2.46065i	−0.102795	+	0.178046i	0.810040	+	0.586374i	$0.199445\pi$
$192$	−13.3713	+	2.80554i	−0.964990	+	0.202472i
$193$	−4.41443	−	7.64601i	−0.317758	−	0.550372i	0.662262	−	0.749272i	$-0.269596\pi$
$193$	−4.41443	−	7.64601i	−0.317758	−	0.550372i	−0.980020	+	0.198900i	$0.936263\pi$
$194$	0.176147	+	0.305096i	0.0126466	+	0.0219046i
$195$	7.55102	−	23.0340i	0.540739	−	1.64950i
$196$		0			0
$197$	5.72354			0.407785			0.203893	−	0.978993i	$-0.434641\pi$
$197$	5.72354			0.407785			0.203893	+	0.978993i	$0.434641\pi$
$198$	0.264356	+	0.194192i	0.0187870	+	0.0138006i
$199$	−11.4150			−0.809191			−0.404596	−	0.914496i	$-0.632588\pi$
$199$	−11.4150			−0.809191			−0.404596	+	0.914496i	$0.632588\pi$
$200$	0.286259	−	0.495815i	0.0202416	−	0.0350594i
$201$	3.84272	+	4.29034i	0.271044	+	0.302617i
$202$	0.0630709	+	0.109242i	0.00443765	+	0.00768624i
$203$		0			0
$204$	−15.0964	−	16.8549i	−1.05696	−	1.18008i
$205$	9.84665	−	17.0549i	0.687720	−	1.19117i
$206$	0.354042			0.0246673
$207$	7.41863	+	5.44961i	0.515630	+	0.378774i
$208$	20.8679			1.44693
$209$	1.52072	−	2.63396i	0.105190	−	0.182195i
$210$		0			0
$211$	10.6919	+	18.5189i	0.736059	+	1.27489i	0.954257	+	0.298986i	$0.0966486\pi$
$211$	10.6919	+	18.5189i	0.736059	+	1.27489i	−0.218199	+	0.975904i	$0.570018\pi$
$212$	8.87782	+	15.3768i	0.609731	+	1.05609i
$213$	−21.0011	+	4.40642i	−1.43897	+	0.301923i
$214$	0.579432	−	1.00361i	0.0396091	−	0.0686050i
$215$	30.0037			2.04623
$216$	−1.15490	+	0.825283i	−0.0785809	+	0.0561534i
$217$		0			0
$218$	0.290587	−	0.503311i	0.0196810	−	0.0340885i
$219$	3.72699	−	0.781990i	0.251847	−	0.0528420i
$220$	4.24978	+	7.36084i	0.286520	+	0.496268i
$221$	17.1989	+	29.7893i	1.15692	+	2.00385i
$222$	−0.156033	+	0.475971i	−0.0104722	+	0.0319451i
$223$	−3.58387	+	6.20744i	−0.239994	+	0.415681i	−0.960712	−	0.277547i	$-0.910479\pi$
$223$	−3.58387	+	6.20744i	−0.239994	+	0.415681i	0.720719	+	0.693228i	$0.243812\pi$
$224$		0			0
$225$	−0.689984	+	6.24938i	−0.0459989	+	0.416625i
$226$	0.266926			0.0177557
$227$	6.89434	−	11.9413i	0.457593	−	0.792575i	−0.541240	−	0.840868i	$-0.682045\pi$
$227$	6.89434	−	11.9413i	0.457593	−	0.792575i	0.998833	+	0.0482933i	$0.0153782\pi$
$228$	4.38544	+	4.89628i	0.290433	+	0.324264i
$229$	13.1972	+	22.8581i	0.872092	+	1.51051i	0.859828	+	0.510584i	$0.170571\pi$
$229$	13.1972	+	22.8581i	0.872092	+	1.51051i	0.0122645	+	0.999925i	$0.496096\pi$
$230$	−0.279428	−	0.483983i	−0.0184249	−	0.0319129i
$231$		0			0
$232$	0.872666	−	1.51150i	0.0572933	−	0.0992349i
$233$	−12.6446			−0.828375			−0.414187	−	0.910192i	$-0.635934\pi$
$233$	−12.6446			−0.828375			−0.414187	+	0.910192i	$0.635934\pi$
$234$	0.986785	−	0.433160i	0.0645081	−	0.0283165i
$235$	−10.1202			−0.660170
$236$	−10.8673	+	18.8228i	−0.707403	+	1.22526i
$237$	−0.438954	+	1.33901i	−0.0285131	+	0.0869779i
$238$		0			0
$239$	7.71640	+	13.3652i	0.499133	+	0.864523i	0.999999	−	0.00100121i	$-0.000318696\pi$
$239$	7.71640	+	13.3652i	0.499133	+	0.864523i	−0.500867	+	0.865524i	$0.666985\pi$
$240$	−17.9354	+	3.76318i	−1.15773	+	0.242912i
$241$	−0.589942	+	1.02181i	−0.0380015	+	0.0658205i	−0.884401	−	0.466729i	$-0.845432\pi$
$241$	−0.589942	+	1.02181i	−0.0380015	+	0.0658205i	0.846399	+	0.532549i	$0.178766\pi$
$242$	−0.577267			−0.0371082
$243$	7.97052	−	13.3967i	0.511309	−	0.859397i
$244$	−5.41504			−0.346662
$245$		0			0
$246$	0.856869	−	0.179787i	0.0546320	−	0.0114628i
$247$	−4.99620	−	8.65367i	−0.317900	−	0.550620i
$248$	0.917767	+	1.58962i	0.0582783	+	0.100941i
$249$	−3.68882	+	11.2525i	−0.233769	+	0.713101i
$250$	−0.264478	+	0.458090i	−0.0167271	+	0.0289721i
$251$	5.54970			0.350294			0.175147	−	0.984542i	$-0.443960\pi$
$251$	5.54970			0.350294			0.175147	+	0.984542i	$0.443960\pi$
$252$		0			0
$253$	4.90672			0.308483
$254$	−0.374459	+	0.648583i	−0.0234957	+	0.0406957i
$255$	−20.1539	−	22.5016i	−1.26209	−	1.40910i
$256$	−7.81365	−	13.5336i	−0.488353	−	0.845853i
$257$	−4.91538	−	8.51369i	−0.306613	−	0.531069i	0.671006	−	0.741452i	$-0.265862\pi$
$257$	−4.91538	−	8.51369i	−0.306613	−	0.531069i	−0.977619	+	0.210382i	$0.932529\pi$
$258$	0.889957	+	0.993623i	0.0554063	+	0.0618603i
$259$		0			0
$260$	27.9246			1.73181
$261$	−2.10343	+	19.0513i	−0.130199	+	1.17925i
$262$	−0.304498			−0.0188120
$263$	−5.96612	+	10.3336i	−0.367887	+	0.637199i	−0.989235	−	0.146336i	$-0.953252\pi$
$263$	−5.96612	+	10.3336i	−0.367887	+	0.637199i	0.621348	+	0.783535i	$0.286585\pi$
$264$	−0.235699	+	0.718987i	−0.0145063	+	0.0442506i
$265$	11.8520	+	20.5283i	0.728065	+	1.26105i
$266$		0			0
$267$	0.797685	−	0.167369i	0.0488175	−	0.0102428i
$268$	−3.31756	+	5.74618i	−0.202652	+	0.351004i
$269$	29.9648			1.82699			0.913494	−	0.406853i	$-0.133374\pi$
$269$	29.9648			1.82699			0.913494	+	0.406853i	$0.133374\pi$
$270$	−0.770002	+	0.550239i	−0.0468608	+	0.0334865i
$271$	−7.09650			−0.431082			−0.215541	−	0.976495i	$-0.569151\pi$
$271$	−7.09650			−0.431082			−0.215541	+	0.976495i	$0.569151\pi$
$272$	13.0027	−	22.5213i	0.788402	−	1.36555i
$273$		0			0
$274$	0.667877	+	1.15680i	0.0403479	+	0.0698847i
$275$	1.67571	+	2.90242i	0.101049	+	0.175022i
$276$	−3.30334	+	10.0767i	−0.198838	+	0.606545i
$277$	4.91175	−	8.50741i	0.295119	−	0.511161i	−0.679894	−	0.733311i	$-0.737974\pi$
$277$	4.91175	−	8.50741i	0.295119	−	0.511161i	0.975013	+	0.222150i	$0.0713075\pi$
$278$	0.179878			0.0107883
$279$	−16.2456	−	11.9337i	−0.972596	−	0.714454i
$280$		0			0
$281$	11.9389	−	20.6787i	0.712213	−	1.23359i	−0.251812	−	0.967776i	$-0.581026\pi$
$281$	11.9389	−	20.6787i	0.712213	−	1.23359i	0.964025	−	0.265813i	$-0.0856403\pi$
$282$	−0.300181	−	0.335148i	−0.0178755	−	0.0199578i
$283$	1.50798	+	2.61189i	0.0896399	+	0.155261i	0.907359	−	0.420357i	$-0.138095\pi$
$283$	1.50798	+	2.61189i	0.0896399	+	0.155261i	−0.817719	+	0.575618i	$0.804762\pi$
$284$	−12.3601	−	21.4083i	−0.733435	−	1.27035i
$285$	5.85464	+	6.53661i	0.346799	+	0.387196i
$286$	0.287222	−	0.497483i	0.0169838	−	0.0294168i
$287$		0			0
$288$	−1.97757	−	1.45269i	−0.116530	−	0.0856008i
$289$	25.8659			1.52153
$290$	0.581830	−	1.00776i	0.0341662	−	0.0591776i
$291$	2.78001	−	8.48027i	0.162967	−	0.497123i
$292$	2.19350	+	3.79925i	0.128365	+	0.222334i
$293$	−8.52913	−	14.7729i	−0.498277	−	0.863041i	0.501721	−	0.865030i	$-0.332700\pi$
$293$	−8.52913	−	14.7729i	−0.498277	−	0.863041i	−0.999998	+	0.00198814i	$0.999367\pi$
$294$		0			0
$295$	−14.5081	+	25.1287i	−0.844692	+	1.46305i
$296$	−1.15541			−0.0671570
$297$	−0.803538	−	8.27036i	−0.0466260	−	0.479895i
$298$	−0.602567			−0.0349058
$299$	8.06031	−	13.9609i	0.466140	−	0.807378i
$300$	−7.08868	+	1.48733i	−0.409265	+	0.0858712i
$301$		0			0
$302$	−0.159456	−	0.276185i	−0.00917564	−	0.0158927i
$303$	0.995404	−	3.03643i	0.0571845	−	0.174438i
$304$	−3.77722	+	6.54234i	−0.216638	+	0.375229i
$305$	−7.22917			−0.413941
$306$	0.147380	−	1.33486i	0.00842518	−	0.0763091i
$307$	23.2178			1.32511			0.662554	−	0.749014i	$-0.269473\pi$
$307$	23.2178			1.32511			0.662554	+	0.749014i	$0.269473\pi$
$308$		0			0
$309$	−5.98367	−	6.68068i	−0.340399	−	0.380050i
$310$	0.611900	+	1.05984i	0.0347536	+	0.0601950i
$311$	−0.895467	−	1.55100i	−0.0507773	−	0.0879489i	0.839520	−	0.543329i	$-0.182837\pi$
$311$	−0.895467	−	1.55100i	−0.0507773	−	0.0879489i	−0.890297	+	0.455381i	$0.849503\pi$
$312$	1.65852	+	1.85171i	0.0938951	+	0.104832i
$313$	−2.30458	+	3.99166i	−0.130263	+	0.225622i	−0.923778	−	0.382929i	$-0.874915\pi$
$313$	−2.30458	+	3.99166i	−0.130263	+	0.225622i	0.793515	+	0.608551i	$0.208249\pi$
$314$	−0.278483			−0.0157157
$315$		0			0
$316$	−1.62331			−0.0913183
$317$	12.9421	−	22.4163i	0.726898	−	1.25902i	−0.231290	−	0.972885i	$-0.574295\pi$
$317$	12.9421	−	22.4163i	0.726898	−	1.25902i	0.958188	−	0.286140i	$-0.0923721\pi$
$318$	−0.328281	+	1.00140i	−0.0184091	+	0.0561559i
$319$	5.10843	+	8.84807i	0.286017	+	0.495397i
$320$	−10.5060	−	18.1970i	−0.587304	−	1.01724i
$321$	−28.7307	+	6.02823i	−1.60359	+	0.336463i
$322$		0			0
$323$	−12.4524			−0.692869
$324$	17.5254	+	3.91766i	0.973632	+	0.217648i
$325$	11.0108			0.610771
$326$	0.414423	−	0.717802i	0.0229528	−	0.0397554i
$327$	−14.4086	+	3.02317i	−0.796795	+	0.167182i
$328$	1.00979	+	1.74901i	0.0557563	+	0.0965728i
$329$		0			0
$330$	−0.157147	+	0.479368i	−0.00865065	+	0.0263884i
$331$	−0.0806617	+	0.139710i	−0.00443357	+	0.00767917i	−0.868234	−	0.496156i	$-0.834745\pi$
$331$	−0.0806617	+	0.139710i	−0.00443357	+	0.00767917i	0.863800	+	0.503835i	$0.168078\pi$
$332$	−13.6417			−0.748687
$333$	11.6186	−	5.10009i	0.636693	−	0.279483i
$334$	−0.328128			−0.0179544
$335$	−4.42899	+	7.67124i	−0.241982	+	0.419125i
$336$		0			0
$337$	4.52675	+	7.84057i	0.246588	+	0.427103i	0.962577	−	0.271009i	$-0.0873572\pi$
$337$	4.52675	+	7.84057i	0.246588	+	0.427103i	−0.715989	+	0.698112i	$0.754024\pi$
$338$	−0.499213	−	0.864662i	−0.0271536	−	0.0470314i
$339$	−4.51133	−	5.03683i	−0.245022	−	0.273563i
$340$	17.3996	−	30.1370i	0.943627	−	1.63441i
$341$	−10.7449			−0.581869
$342$	−0.0428134	+	0.387773i	−0.00231508	+	0.0209683i
$343$		0			0
$344$	−1.53846	+	2.66470i	−0.0829484	+	0.143671i
$345$	−4.41002	+	13.4525i	−0.237427	+	0.724260i
$346$	−0.172019	−	0.297945i	−0.00924779	−	0.0160176i
$347$	2.90984	+	5.03999i	0.156208	+	0.270561i	0.933498	−	0.358582i	$-0.116740\pi$
$347$	2.90984	+	5.03999i	0.156208	+	0.270561i	−0.777290	+	0.629142i	$0.783406\pi$
$348$	−21.6100	+	4.53416i	−1.15842	+	0.243056i
$349$	−13.6310	+	23.6095i	−0.729648	+	1.26379i	0.227384	+	0.973805i	$0.426983\pi$
$349$	−13.6310	+	23.6095i	−0.729648	+	1.26379i	−0.957032	+	0.289983i	$0.906350\pi$
$350$		0			0
$351$	−24.8513	−	11.2995i	−1.32646	−	0.603124i
$352$	−1.30798			−0.0697154
$353$	12.0948	−	20.9488i	0.643741	−	1.11499i	−0.340850	−	0.940118i	$-0.610715\pi$
$353$	12.0948	−	20.9488i	0.643741	−	1.11499i	0.984591	−	0.174874i	$-0.0559517\pi$
$354$	−1.26251	+	0.264898i	−0.0671017	+	0.0140791i
$355$	−16.5009	−	28.5804i	−0.875777	−	1.51689i
$356$	0.469472	+	0.813149i	0.0248820	+	0.0430968i
$357$		0			0
$358$	0.560595	−	0.970979i	0.0296284	−	0.0513179i
$359$	−21.0376			−1.11032			−0.555161	−	0.831743i	$-0.687343\pi$
$359$	−21.0376			−1.11032			−0.555161	+	0.831743i	$0.687343\pi$
$360$	−1.75938	−	1.29241i	−0.0927272	−	0.0681160i
$361$	−15.3826			−0.809612
$362$	0.493472	−	0.854719i	0.0259363	−	0.0449230i
$363$	9.75641	+	10.8929i	0.512079	+	0.571728i
$364$		0			0
$365$	2.92835	+	5.07205i	0.153277	+	0.265483i
$366$	−0.214428	−	0.239406i	−0.0112084	−	0.0125140i
$367$	−17.5190	+	30.3438i	−0.914485	+	1.58393i	−0.106831	+	0.994277i	$0.534070\pi$
$367$	−17.5190	+	30.3438i	−0.914485	+	1.58393i	−0.807654	+	0.589657i	$0.799263\pi$
$368$	−12.1875			−0.635317
$369$	−17.8745	−	13.1303i	−0.930509	−	0.683537i
$370$	−0.770345			−0.0400483
$371$		0			0
$372$	7.23377	−	22.0662i	0.375054	−	1.14408i
$373$	−0.564310	−	0.977414i	−0.0292189	−	0.0506086i	0.851046	−	0.525091i	$-0.175969\pi$
$373$	−0.564310	−	0.977414i	−0.0292189	−	0.0506086i	−0.880265	+	0.474482i	$0.842635\pi$
$374$	−0.357931	−	0.619955i	−0.0185082	−	0.0320571i
$375$	13.1140	−	2.75155i	0.677203	−	0.142089i
$376$	0.518922	−	0.898800i	0.0267614	−	0.0463521i
$377$	33.5667			1.72877
$378$		0			0
$379$	−21.9619			−1.12811			−0.564054	−	0.825738i	$-0.690759\pi$
$379$	−21.9619			−1.12811			−0.564054	+	0.825738i	$0.690759\pi$
$380$	−5.05452	+	8.75468i	−0.259291	+	0.449106i
$381$	18.5673	−	3.89576i	0.951233	−	0.199586i
$382$	−0.0971359	−	0.168244i	−0.00496991	−	0.00860813i
$383$	11.5200	+	19.9533i	0.588647	+	1.01957i	0.994410	+	0.105588i	$0.0336724\pi$
$383$	11.5200	+	19.9533i	0.588647	+	1.01957i	−0.405763	+	0.913978i	$0.632994\pi$
$384$	1.17363	−	3.58009i	0.0598915	−	0.182696i
$385$		0			0
$386$	0.603664			0.0307257
$387$	3.70823	−	33.5865i	0.188500	−	1.70730i
$388$	10.2808			0.521930
$389$	−7.88753	+	13.6616i	−0.399914	+	0.692671i	−0.993715	−	0.111941i	$-0.964293\pi$
$389$	−7.88753	+	13.6616i	−0.399914	+	0.692671i	0.593801	+	0.804612i	$0.297627\pi$
$390$	1.10578	+	1.23459i	0.0559933	+	0.0625157i
$391$	−10.0446	−	17.3978i	−0.507979	−	0.879846i
$392$		0			0
$393$	5.14633	+	5.74580i	0.259598	+	0.289837i
$394$	−0.195671	+	0.338912i	−0.00985774	+	0.0170741i
$395$	−2.16714			−0.109041
$396$	8.76505	−	3.84751i	0.440461	−	0.193345i
$397$	16.5055			0.828389			0.414195	−	0.910188i	$-0.364063\pi$
$397$	16.5055			0.828389			0.414195	+	0.910188i	$0.364063\pi$
$398$	0.390246	−	0.675926i	0.0195613	−	0.0338811i
$399$		0			0
$400$	−4.16220	−	7.20914i	−0.208110	−	0.360457i
$401$	−10.8300	−	18.7581i	−0.540823	−	0.936733i	−0.998857	−	0.0477986i	$-0.984779\pi$
$401$	−10.8300	−	18.7581i	−0.540823	−	0.936733i	0.458034	−	0.888935i	$-0.348554\pi$
$402$	−0.385417	+	0.0808675i	−0.0192229	+	0.00403330i
$403$	−17.6507	+	30.5720i	−0.879246	+	1.52290i
$404$	3.68113			0.183143
$405$	23.3967	+	5.23014i	1.16259	+	0.259888i
$406$		0			0
$407$	3.38179	−	5.85743i	0.167629	−	0.290342i
$408$	3.03183	−	0.636132i	0.150098	−	0.0314932i
$409$	15.2860	+	26.4762i	0.755846	+	1.30916i	0.944953	+	0.327207i	$0.106107\pi$
$409$	15.2860	+	26.4762i	0.755846	+	1.30916i	−0.189107	+	0.981956i	$0.560559\pi$
$410$	0.673255	+	1.16611i	0.0332497	+	0.0575901i
$411$	10.5407	−	32.1537i	0.519932	−	1.58603i
$412$	5.16592	−	8.94763i	0.254507	−	0.440818i
$413$		0			0
$414$	−0.576311	+	0.252978i	−0.0283242	+	0.0124332i
$415$	−18.2119			−0.893988
$416$	−2.14863	+	3.72153i	−0.105345	+	0.182463i
$417$	−3.04011	−	3.39424i	−0.148875	−	0.166217i
$418$	0.103978	+	0.180094i	0.00508571	+	0.00880871i
$419$	10.8081	+	18.7202i	0.528011	+	0.914542i	0.999467	+	0.0326524i	$0.0103954\pi$
$419$	10.8081	+	18.7202i	0.528011	+	0.914542i	−0.471456	+	0.881890i	$0.656271\pi$
$420$		0			0
$421$	13.6217	−	23.5935i	0.663881	−	1.14988i	−0.315706	−	0.948857i	$-0.602241\pi$
$421$	13.6217	−	23.5935i	0.663881	−	1.14988i	0.979587	−	0.201019i	$-0.0644252\pi$
$422$	−1.46209			−0.0711735
$423$	−1.25078	+	11.3287i	−0.0608152	+	0.550820i
$424$	−2.43089			−0.118055
$425$	6.86077	−	11.8832i	0.332796	−	0.576420i
$426$	0.457046	−	1.39419i	0.0221439	−	0.0675490i
$427$		0			0
$428$	−16.9093	−	29.2877i	−0.817341	−	1.41568i
$429$	−14.2417	+	2.98816i	−0.687596	+	0.144270i
$430$	−1.02574	+	1.77663i	−0.0494654	+	0.0856765i
$431$	8.19687			0.394829			0.197415	−	0.980320i	$-0.436745\pi$
$431$	8.19687			0.394829			0.197415	+	0.980320i	$0.436745\pi$
$432$	1.99586	+	20.5422i	0.0960258	+	0.988339i
$433$	3.41468			0.164099			0.0820494	−	0.996628i	$-0.473853\pi$
$433$	3.41468			0.164099			0.0820494	+	0.996628i	$0.473853\pi$
$434$		0			0
$435$	−28.8497	+	6.05318i	−1.38324	+	0.290228i
$436$	−8.48005	−	14.6879i	−0.406121	−	0.703422i
$437$	2.91793	+	5.05400i	0.139583	+	0.241765i
$438$	−0.0811102	+	0.247423i	−0.00387560	+	0.0118223i
$439$	−3.29416	+	5.70564i	−0.157221	+	0.272316i	−0.933866	−	0.357624i	$-0.883587\pi$
$439$	−3.29416	+	5.70564i	−0.157221	+	0.272316i	0.776644	+	0.629939i	$0.216920\pi$
$440$	−1.16366			−0.0554753
$441$		0			0
$442$	−2.35191			−0.111869
$443$	−14.3456	+	24.8473i	−0.681581	+	1.18053i	0.292917	+	0.956138i	$0.405374\pi$
$443$	−14.3456	+	24.8473i	−0.681581	+	1.18053i	−0.974498	+	0.224395i	$0.927959\pi$
$444$	9.75240	+	10.8884i	0.462828	+	0.516741i
$445$	0.626752	+	1.08557i	0.0297109	+	0.0514608i
$446$	−0.245043	−	0.424428i	−0.0116031	−	0.0200972i
$447$	10.1840	+	11.3703i	0.481686	+	0.537796i
$448$		0			0
$449$	0.457724			0.0216013			0.0108007	−	0.999942i	$-0.496562\pi$
$449$	0.457724			0.0216013			0.0108007	+	0.999942i	$0.496562\pi$
$450$	−0.346460	−	0.254504i	−0.0163323	−	0.0119974i
$451$	−11.8223			−0.556689
$452$	3.89479	−	6.74598i	0.183196	−	0.317304i
$453$	−2.51658	+	7.67669i	−0.118239	+	0.360683i
$454$	0.471393	+	0.816477i	0.0221236	+	0.0383192i
$455$		0			0
$456$	−0.880733	+	0.184794i	−0.0412441	+	0.00865376i
$457$	−10.1105	+	17.5119i	−0.472950	+	0.819173i	−0.999521	−	0.0309581i	$-0.990144\pi$
$457$	−10.1105	+	17.5119i	−0.472950	+	0.819173i	0.526571	+	0.850131i	$0.323477\pi$
$458$	−1.80468			−0.0843273
$459$	−27.6794	+	19.7795i	−1.29196	+	0.923230i
$460$	−16.3088			−0.760402
$461$	−12.1036	+	20.9640i	−0.563719	+	0.976390i	0.433449	+	0.901178i	$0.357297\pi$
$461$	−12.1036	+	20.9640i	−0.563719	+	0.976390i	−0.997168	+	0.0752117i	$0.976037\pi$
$462$		0			0
$463$	2.40242	+	4.16111i	0.111650	+	0.193383i	0.916436	−	0.400182i	$-0.131053\pi$
$463$	2.40242	+	4.16111i	0.111650	+	0.193383i	−0.804786	+	0.593565i	$0.797720\pi$
$464$	−12.6885	−	21.9772i	−0.589050	−	1.02026i
$465$	9.65720	−	29.4588i	0.447842	−	1.36612i
$466$	0.432281	−	0.748732i	0.0200250	−	0.0346843i
$467$	−27.2456			−1.26078			−0.630389	−	0.776279i	$-0.717105\pi$
$467$	−27.2456			−1.26078			−0.630389	+	0.776279i	$0.717105\pi$
$468$	3.45128	−	31.2592i	0.159535	−	1.44496i
$469$		0			0
$470$	0.345979	−	0.599254i	0.0159588	−	0.0276415i
$471$	4.70664	+	5.25490i	0.216871	+	0.242133i
$472$	−1.48783	−	2.57699i	−0.0684827	−	0.118616i
$473$	−9.00590	−	15.5987i	−0.414092	−	0.717228i
$474$	−0.0642809	−	0.0717687i	−0.00295252	−	0.00329644i
$475$	−1.99302	+	3.45202i	−0.0914462	+	0.158389i
$476$		0			0
$477$	24.4445	−	10.7302i	1.11924	−	0.491301i
$478$	−1.05520			−0.0482638
$479$	−10.2628	+	17.7756i	−0.468917	+	0.812188i	−0.999369	−	0.0355269i	$-0.988689\pi$
$479$	−10.2628	+	17.7756i	−0.468917	+	0.812188i	0.530452	+	0.847715i	$0.322022\pi$
$480$	1.17557	−	3.58602i	0.0536572	−	0.163679i
$481$	−11.1106	−	19.2441i	−0.506600	−	0.877457i
$482$	−0.0403366	−	0.0698651i	−0.00183728	−	0.00318227i
$483$		0			0
$484$	−8.42306	+	14.5892i	−0.382866	+	0.663144i
$485$	13.7251			0.623224
$486$	0.520777	+	0.929955i	0.0236229	+	0.0421836i
$487$	25.8449			1.17114			0.585571	−	0.810621i	$-0.300870\pi$
$487$	25.8449			1.17114			0.585571	+	0.810621i	$0.300870\pi$
$488$	0.370682	−	0.642039i	0.0167800	−	0.0290638i
$489$	−20.5489	+	4.31153i	−0.929253	+	0.194974i
$490$		0			0
$491$	−7.80775	−	13.5234i	−0.352359	−	0.610303i	0.634303	−	0.773084i	$-0.281287\pi$
$491$	−7.80775	−	13.5234i	−0.352359	−	0.610303i	−0.986662	+	0.162781i	$0.947954\pi$
$492$	7.95909	−	24.2788i	0.358824	−	1.09457i
$493$	20.9152	−	36.2261i	0.941971	−	1.63154i
$494$	0.683220			0.0307395
$495$	11.7015	−	5.13649i	0.525943	−	0.230868i
$496$	26.6886			1.19835
$497$		0			0
$498$	−0.540194	−	0.603119i	−0.0242067	−	0.0270264i
$499$	−10.6345	−	18.4195i	−0.476066	−	0.824571i	0.523558	−	0.851990i	$-0.324604\pi$
$499$	−10.6345	−	18.4195i	−0.476066	−	0.824571i	−0.999624	+	0.0274192i	$0.991271\pi$
$500$	7.71814	+	13.3682i	0.345166	+	0.597845i
$501$	5.54570	+	6.19170i	0.247764	+	0.276625i
$502$	−0.189728	+	0.328618i	−0.00846795	+	0.0146669i
$503$	−16.3298			−0.728110			−0.364055	−	0.931377i	$-0.618608\pi$
$503$	−16.3298			−0.728110			−0.364055	+	0.931377i	$0.618608\pi$
$504$		0			0
$505$	4.91437			0.218687
$506$	−0.167746	+	0.290544i	−0.00745722	+	0.0129163i
$507$	−7.87873	+	24.0337i	−0.349907	+	1.06737i
$508$	10.9277	+	18.9273i	0.484837	+	0.839762i
$509$	6.73089	+	11.6582i	0.298342	+	0.516743i	0.975757	−	0.218858i	$-0.0702332\pi$
$509$	6.73089	+	11.6582i	0.298342	+	0.516743i	−0.677415	+	0.735601i	$0.736900\pi$
$510$	2.02140	−	0.424126i	0.0895092	−	0.0187806i
$511$		0			0
$512$	5.41890			0.239484
$513$	8.04076	−	5.74587i	0.355008	−	0.253687i
$514$	0.672168			0.0296481
$515$	6.89659	−	11.9452i	0.303900	−	0.526370i
$516$	38.0972	−	7.99349i	1.67714	−	0.351894i
$517$	3.03768	+	5.26142i	0.133597	+	0.231397i
$518$		0			0
$519$	−2.71486	+	8.28153i	−0.119169	+	0.363519i
$520$	−1.91155	+	3.31091i	−0.0838272	+	0.145193i
$521$	−1.42619			−0.0624826			−0.0312413	−	0.999512i	$-0.509946\pi$
$521$	−1.42619			−0.0624826			−0.0312413	+	0.999512i	$0.509946\pi$
$522$	−1.05619	−	0.775859i	−0.0462281	−	0.0339584i
$523$	−7.71060			−0.337161			−0.168581	−	0.985688i	$-0.553918\pi$
$523$	−7.71060			−0.337161			−0.168581	+	0.985688i	$0.553918\pi$
$524$	−4.44301	+	7.69553i	−0.194094	+	0.336181i
$525$		0			0
$526$	−0.407928	−	0.706551i	−0.0177865	−	0.0308071i
$527$	21.9961	+	38.0984i	0.958165	+	1.65959i
$528$	7.33994	+	8.19494i	0.319430	+	0.356639i
$529$	6.79254	−	11.7650i	0.295328	−	0.511523i
$530$	−1.62074			−0.0704005
$531$	26.3363	+	19.3462i	1.14290	+	0.839554i
$532$		0			0
$533$	−19.4206	+	33.6374i	−0.841198	+	1.45700i
$534$	−0.0173599	+	0.0529556i	−0.000751238	+	0.00229161i
$535$	−22.5742	−	39.0996i	−0.975966	−	1.69042i
$536$	−0.454201	−	0.786699i	−0.0196185	−	0.0339802i
$537$	−27.7967	+	5.83226i	−1.19952	+	0.251680i
$538$	−1.02441	+	1.77432i	−0.0441653	+	0.0764966i
$539$		0			0
$540$	2.67078	+	27.4888i	0.114932	+	1.18293i
$541$	28.0456			1.20577			0.602886	−	0.797827i	$-0.294017\pi$
$541$	28.0456			1.20577			0.602886	+	0.797827i	$0.294017\pi$
$542$	0.242608	−	0.420209i	0.0104209	−	0.0180495i
$543$	−24.4685	+	5.13393i	−1.05004	+	0.220318i
$544$	2.67759	+	4.63771i	0.114801	+	0.198840i
$545$	−11.3210	−	19.6086i	−0.484939	−	0.839939i
$546$		0			0
$547$	17.7305	−	30.7101i	0.758101	−	1.31307i	−0.185717	−	0.982603i	$-0.559461\pi$
$547$	17.7305	−	30.7101i	0.758101	−	1.31307i	0.943818	−	0.330466i	$-0.107206\pi$
$548$	38.9807			1.66517
$549$	−0.893471	+	8.09242i	−0.0381324	+	0.345376i
$550$	−0.229150			−0.00977099
$551$	−6.07577	+	10.5235i	−0.258836	+	0.448318i
$552$	−0.968623	−	1.08145i	−0.0412273	−	0.0460297i
$553$		0			0
$554$	0.335836	+	0.581685i	0.0142683	+	0.0247134i
$555$	13.0196	+	14.5362i	0.552651	+	0.617027i
$556$	2.62464	−	4.54601i	0.111310	−	0.192794i
$557$	35.0419			1.48477			0.742386	−	0.669972i	$-0.233694\pi$
$557$	35.0419			1.48477			0.742386	+	0.669972i	$0.233694\pi$
$558$	1.26203	−	0.553980i	0.0534258	−	0.0234518i
$559$	−59.1763			−2.50289
$560$		0			0
$561$	−5.64899	+	17.2319i	−0.238500	+	0.727533i
$562$	0.816308	+	1.41389i	0.0344339	+	0.0596412i
$563$	−8.01311	−	13.8791i	−0.337712	−	0.584935i	0.646290	−	0.763092i	$-0.276320\pi$
$563$	−8.01311	−	13.8791i	−0.337712	−	0.584935i	−0.984002	+	0.178157i	$0.942986\pi$
$564$	−12.8502	+	2.69619i	−0.541089	+	0.113530i
$565$	5.19961	−	9.00599i	0.218749	−	0.378885i
$566$	−0.206213			−0.00866776
$567$		0			0
$568$	3.38439			0.142006
$569$	−0.185651	+	0.321557i	−0.00778290	+	0.0134804i	−0.869891	−	0.493245i	$-0.835811\pi$
$569$	−0.185651	+	0.321557i	−0.00778290	+	0.0134804i	0.862108	+	0.506725i	$0.169144\pi$
$570$	−0.587209	+	0.123207i	−0.0245955	+	0.00516057i
$571$	−14.6152	−	25.3142i	−0.611626	−	1.05937i	−0.990966	−	0.134110i	$-0.957182\pi$
$571$	−14.6152	−	25.3142i	−0.611626	−	1.05937i	0.379340	−	0.925257i	$-0.376151\pi$
$572$	−8.38185	−	14.5178i	−0.350463	−	0.607019i
$573$	−1.53303	+	4.67643i	−0.0640432	+	0.195361i
$574$		0			0
$575$	−6.43065			−0.268177
$576$	−21.6684	+	9.51155i	−0.902848	+	0.396315i
$577$	−15.0570			−0.626833			−0.313417	−	0.949616i	$-0.601474\pi$
$577$	−15.0570			−0.626833			−0.313417	+	0.949616i	$0.601474\pi$
$578$	−0.884279	+	1.53162i	−0.0367811	+	0.0637068i
$579$	−10.2025	−	11.3910i	−0.424003	−	0.473393i
$580$	−16.9793	−	29.4089i	−0.705025	−	1.22114i
$581$		0			0
$582$	0.407107	+	0.454529i	0.0168751	+	0.0188408i
$583$	7.11501	−	12.3236i	0.294674	−	0.510390i
$584$	−0.600615			−0.0248536
$585$	4.60751	−	41.7315i	0.190497	−	1.72538i
$586$	1.16634			0.0481811
$587$	−0.835901	+	1.44782i	−0.0345013	+	0.0597580i	−0.882760	−	0.469823i	$-0.844318\pi$
$587$	−0.835901	+	1.44782i	−0.0345013	+	0.0597580i	0.848259	+	0.529581i	$0.177651\pi$
$588$		0			0
$589$	−6.38977	−	11.0674i	−0.263286	−	0.456025i
$590$	−0.991973	−	1.71815i	−0.0408389	−	0.0707350i
$591$	9.70220	−	2.03570i	0.399095	−	0.0837374i
$592$	−8.39982	+	14.5489i	−0.345231	+	0.597957i
$593$	−10.8174			−0.444218			−0.222109	−	0.975022i	$-0.571294\pi$
$593$	−10.8174			−0.444218			−0.222109	+	0.975022i	$0.571294\pi$
$594$	0.517188	+	0.235158i	0.0212205	+	0.00964867i
$595$		0			0
$596$	−8.79221	+	15.2286i	−0.360143	+	0.623786i
$597$	−19.3501	+	4.06000i	−0.791947	+	0.166165i
$598$	0.551116	+	0.954560i	0.0225368	+	0.0390349i
$599$	−8.32007	−	14.4108i	−0.339949	−	0.588809i	0.644474	−	0.764626i	$-0.277076\pi$
$599$	−8.32007	−	14.4108i	−0.339949	−	0.588809i	−0.984423	+	0.175817i	$0.943743\pi$
$600$	0.308902	−	0.942290i	0.0126109	−	0.0384688i
$601$	12.9011	−	22.3453i	0.526246	−	0.911485i	−0.473286	−	0.880909i	$-0.656932\pi$
$601$	12.9011	−	22.3453i	0.526246	−	0.911485i	0.999532	−	0.0305765i	$-0.00973432\pi$
$602$		0			0
$603$	8.03989	+	5.90598i	0.327410	+	0.240510i
$604$	−9.30663			−0.378681
$605$	−11.2449	+	19.4768i	−0.457171	+	0.791843i
$606$	0.145768	+	0.162748i	0.00592142	+	0.00661118i
$607$	18.9025	+	32.7400i	0.767227	+	1.32888i	0.939061	+	0.343750i	$0.111697\pi$
$607$	18.9025	+	32.7400i	0.767227	+	1.32888i	−0.171834	+	0.985126i	$0.554969\pi$
$608$	−0.777828	−	1.34724i	−0.0315451	−	0.0546377i
$609$		0			0
$610$	0.247143	−	0.428065i	0.0100065	−	0.0173318i
$611$	19.9601			0.807499
$612$	−31.5853	−	23.2021i	−1.27676	−	0.937888i
$613$	−12.9544			−0.523222			−0.261611	−	0.965173i	$-0.584254\pi$
$613$	−12.9544			−0.523222			−0.261611	+	0.965173i	$0.584254\pi$
$614$	−0.793745	+	1.37481i	−0.0320330	+	0.0554827i
$615$	10.6255	−	32.4126i	0.428462	−	1.30700i
$616$		0			0
$617$	16.2202	+	28.0941i	0.652999	+	1.13103i	0.982391	+	0.186834i	$0.0598227\pi$
$617$	16.2202	+	28.0941i	0.652999	+	1.13103i	−0.329393	+	0.944193i	$0.606844\pi$
$618$	0.600151	−	0.125922i	0.0241416	−	0.00506534i
$619$	16.5987	−	28.7498i	0.667157	−	1.15555i	−0.311538	−	0.950234i	$-0.600844\pi$
$619$	16.5987	−	28.7498i	0.667157	−	1.15555i	0.978696	−	0.205317i	$-0.0658224\pi$
$620$	35.7136			1.43429
$621$	14.5139	+	6.59926i	0.582422	+	0.264819i
$622$	0.122453			0.00490993
$623$		0			0
$624$	35.3741	−	7.42212i	1.41610	−	0.297122i
$625$	15.5433	+	26.9218i	0.621732	+	1.07687i
$626$	−0.157574	−	0.272925i	−0.00629791	−	0.0109083i
$627$	1.64101	−	5.00581i	0.0655355	−	0.199913i
$628$	−4.06342	+	7.03804i	−0.162148	+	0.280848i
$629$	−27.6917			−1.10414
$630$		0			0
$631$	32.2773			1.28494			0.642470	−	0.766311i	$-0.277910\pi$
$631$	32.2773			1.28494			0.642470	+	0.766311i	$0.277910\pi$
$632$	0.111122	−	0.192469i	0.00442020	−	0.00765601i
$633$	24.7108	+	27.5893i	0.982167	+	1.09657i
$634$	0.884900	+	1.53269i	0.0351439	+	0.0608709i
$635$	14.5886	+	25.2682i	0.578931	+	1.00274i
$636$	20.5182	+	22.9083i	0.813601	+	0.908374i
$637$		0			0
$638$	−0.698568			−0.0276566
$639$	−34.0326	+	14.9390i	−1.34631	+	0.590977i
$640$	5.79428			0.229039
$641$	−21.5407	+	37.3096i	−0.850806	+	1.47364i	0.0296762	+	0.999560i	$0.490552\pi$
$641$	−21.5407	+	37.3096i	−0.850806	+	1.47364i	−0.880482	+	0.474079i	$0.842781\pi$
$642$	0.625265	−	1.90734i	0.0246772	−	0.0752766i
$643$	3.20088	+	5.54409i	0.126230	+	0.218638i	0.922213	−	0.386682i	$-0.126379\pi$
$643$	3.20088	+	5.54409i	0.126230	+	0.218638i	−0.795983	+	0.605319i	$0.793045\pi$
$644$		0			0
$645$	50.8604	−	10.6714i	2.00263	−	0.420187i
$646$	0.425709	−	0.737350i	0.0167493	−	0.0290107i
$647$	−3.88807			−0.152856			−0.0764278	−	0.997075i	$-0.524351\pi$
$647$	−3.88807			−0.152856			−0.0764278	+	0.997075i	$0.524351\pi$
$648$	−1.66418	+	1.80973i	−0.0653753	+	0.0710931i
$649$	17.4189			0.683753
$650$	−0.376427	+	0.651991i	−0.0147647	+	0.0255732i
$651$		0			0
$652$	−12.0939	−	20.9473i	−0.473634	−	0.820358i
$653$	−7.55174	−	13.0800i	−0.295522	−	0.511860i	0.679584	−	0.733598i	$-0.262160\pi$
$653$	−7.55174	−	13.0800i	−0.295522	−	0.511860i	−0.975106	+	0.221738i	$0.928827\pi$
$654$	0.313572	−	0.956536i	0.0122616	−	0.0374035i
$655$	−5.93150	+	10.2737i	−0.231763	+	0.401425i
$656$	29.3646			1.14650
$657$	6.03964	−	2.65116i	0.235629	−	0.103432i
$658$		0			0
$659$	−7.13002	+	12.3496i	−0.277746	+	0.481070i	−0.970824	−	0.239792i	$-0.922921\pi$
$659$	−7.13002	+	12.3496i	−0.277746	+	0.481070i	0.693078	+	0.720862i	$0.256254\pi$
$660$	9.82201	+	10.9661i	0.382321	+	0.426856i
$661$	−9.70965	−	16.8176i	−0.377662	−	0.654129i	0.613060	−	0.790036i	$-0.289938\pi$
$661$	−9.70965	−	16.8176i	−0.377662	−	0.654129i	−0.990722	+	0.135907i	$0.956605\pi$
$662$	−0.00551516	−	0.00955254i	−0.000214353	−	0.000371270i
$663$	39.7497	+	44.3799i	1.54375	+	1.72357i
$664$	0.933832	−	1.61744i	0.0362397	−	0.0627690i
$665$		0			0
$666$	−0.0952089	+	0.862333i	−0.00368927	+	0.0334147i
$667$	−19.6039			−0.759067
$668$	−4.78781	+	8.29273i	−0.185246	+	0.320855i
$669$	−3.86735	+	11.7972i	−0.149521	+	0.456105i
$670$	−0.302828	−	0.524513i	−0.0116993	−	0.0202637i
$671$	2.16991	+	3.75839i	0.0837683	+	0.145091i
$672$		0			0
$673$	−2.96563	+	5.13663i	−0.114317	+	0.198002i	−0.917506	−	0.397721i	$-0.869801\pi$
$673$	−2.96563	+	5.13663i	−0.114317	+	0.198002i	0.803190	+	0.595723i	$0.203135\pi$
$674$	−0.619024			−0.0238439
$675$	1.05310	+	10.8390i	0.0405339	+	0.417192i
$676$	−29.1366			−1.12064
$677$	18.4913	−	32.0278i	0.710678	−	1.23093i	−0.253925	−	0.967224i	$-0.581722\pi$
$677$	18.4913	−	32.0278i	0.710678	−	1.23093i	0.964603	−	0.263706i	$-0.0849449\pi$
$678$	0.452477	−	0.0949379i	0.0173773	−	0.00364607i
$679$		0			0
$680$	2.38215	+	4.12601i	0.0913513	+	0.158225i
$681$	7.43968	−	22.6944i	0.285089	−	0.869650i
$682$	0.367336	−	0.636244i	0.0140660	−	0.0243630i
$683$	13.1360			0.502635			0.251317	−	0.967905i	$-0.419136\pi$
$683$	13.1360			0.502635			0.251317	+	0.967905i	$0.419136\pi$
$684$	9.17540	+	6.74011i	0.350830	+	0.257714i
$685$	52.0398			1.98834
$686$		0			0
$687$	30.5010	+	34.0539i	1.16369	+	1.29924i
$688$	22.3692	+	38.7446i	0.852818	+	1.47712i
$689$	−23.3758	−	40.4881i	−0.890547	−	1.54247i
$690$	−0.645807	−	0.721034i	−0.0245855	−	0.0274493i
$691$	7.38292	−	12.7876i	0.280860	−	0.486463i	−0.690737	−	0.723106i	$-0.742714\pi$
$691$	7.38292	−	12.7876i	0.280860	−	0.486463i	0.971597	+	0.236643i	$0.0760472\pi$
$692$	−10.0399			−0.381659
$693$		0			0
$694$	−0.397915			−0.0151046
$695$	3.50394	−	6.06900i	0.132912	−	0.230210i
$696$	0.941693	−	2.87259i	0.0356948	−	0.108885i
$697$	24.2016	+	41.9184i	0.916702	+	1.58777i
$698$	−0.932003	−	1.61428i	−0.0352768	−	0.0611012i
$699$	−21.4344	+	4.49731i	−0.810722	+	0.170104i
$700$		0			0
$701$	−30.4627			−1.15056			−0.575281	−	0.817956i	$-0.695107\pi$
$701$	−30.4627			−1.15056			−0.575281	+	0.817956i	$0.695107\pi$
$702$	1.51868	−	1.08524i	0.0573187	−	0.0409596i
$703$	8.04433			0.303398
$704$	−6.30697	+	10.9240i	−0.237703	+	0.411713i
$705$	−17.1552	+	3.59946i	−0.646101	+	0.135564i
$706$	0.826969	+	1.43235i	0.0311234	+	0.0539073i
$707$		0			0
$708$	−11.7269	+	35.7724i	−0.440725	+	1.34441i
$709$	−7.05152	+	12.2136i	−0.264825	+	0.458691i	−0.967518	−	0.252803i	$-0.918648\pi$
$709$	−7.05152	+	12.2136i	−0.264825	+	0.458691i	0.702693	+	0.711494i	$0.251981\pi$
$710$	2.25646			0.0846836
$711$	−0.267843	+	2.42593i	−0.0100449	+	0.0909794i
$712$	−0.128549			−0.00481758
$713$	10.3086	−	17.8549i	0.386058	−	0.668673i
$714$		0			0
$715$	−11.1899	−	19.3815i	−0.418479	−	0.724827i
$716$	−16.3596	−	28.3356i	−0.611386	−	1.05895i
$717$	17.8340	+	19.9114i	0.666023	+	0.743604i
$718$	0.719212	−	1.24571i	0.0268408	−	0.0464896i
$719$	−14.9958			−0.559249			−0.279624	−	0.960109i	$-0.590210\pi$
$719$	−14.9958			−0.559249			−0.279624	+	0.960109i	$0.590210\pi$
$720$	−29.0646	+	12.7582i	−1.08317	+	0.475471i
$721$		0			0
$722$	0.525886	−	0.910861i	0.0195715	−	0.0338987i
$723$	−0.636606	+	1.94193i	−0.0236756	+	0.0722213i
$724$	−14.4008	−	24.9429i	−0.535200	−	0.926994i
$725$	−6.69501	−	11.5961i	−0.248646	−	0.430668i
$726$	−0.978549	+	0.205317i	−0.0363174	+	0.00762003i
$727$	13.0527	−	22.6080i	0.484099	−	0.838485i	−0.515734	−	0.856749i	$-0.672481\pi$
$727$	13.0527	−	22.6080i	0.484099	−	0.838485i	0.999833	+	0.0182642i	$0.00581399\pi$
$728$		0			0
$729$	8.74633	−	25.5441i	0.323938	−	0.946078i
$730$	−0.400446			−0.0148212
$731$	−36.8723	+	63.8648i	−1.36377	+	2.36212i
$732$	−9.17925	+	1.92597i	−0.339275	+	0.0711859i
$733$	14.1911	+	24.5796i	0.524159	+	0.907869i	0.999604	+	0.0281244i	$0.00895345\pi$
$733$	14.1911	+	24.5796i	0.524159	+	0.907869i	−0.475446	+	0.879745i	$0.657713\pi$
$734$	−1.19784	−	2.07473i	−0.0442132	−	0.0765796i
$735$		0			0
$736$	1.25486	−	2.17348i	0.0462548	−	0.0801156i
$737$	5.31763			0.195877
$738$	1.38857	−	0.609527i	0.0511139	−	0.0224370i
$739$	46.5865			1.71371			0.856857	−	0.515555i	$-0.172414\pi$
$739$	46.5865			1.71371			0.856857	+	0.515555i	$0.172414\pi$
$740$	−11.2403	+	19.4688i	−0.413202	+	0.715686i
$741$	−11.5471	−	12.8922i	−0.424194	−	0.473606i
$742$		0			0
$743$	−0.169513	−	0.293606i	−0.00621884	−	0.0107713i	0.862899	−	0.505376i	$-0.168646\pi$
$743$	−0.169513	−	0.293606i	−0.00621884	−	0.0107713i	−0.869118	+	0.494605i	$0.835313\pi$
$744$	2.12112	+	2.36820i	0.0777642	+	0.0868225i
$745$	−11.7377	+	20.3304i	−0.430038	+	0.744847i
$746$	0.0771683			0.00282533
$747$	−2.25086	+	20.3866i	−0.0823546	+	0.745908i
$748$	−20.8907			−0.763839
$749$		0			0
$750$	−0.285398	+	0.870593i	−0.0104213	+	0.0317896i
$751$	18.1831	+	31.4940i	0.663510	+	1.14923i	0.979687	+	0.200533i	$0.0642673\pi$
$751$	18.1831	+	31.4940i	0.663510	+	1.14923i	−0.316177	+	0.948700i	$0.602399\pi$
$752$	−7.54511	−	13.0685i	−0.275142	−	0.476560i
$753$	9.40752	−	1.97387i	0.342829	−	0.0719317i
$754$	−1.14754	+	1.98760i	−0.0417911	+	0.0723843i
$755$	−12.4245			−0.452174
$756$		0			0
$757$	−27.4703			−0.998424			−0.499212	−	0.866480i	$-0.666377\pi$
$757$	−27.4703			−0.998424			−0.499212	+	0.866480i	$0.666377\pi$
$758$	0.750812	−	1.30044i	0.0272707	−	0.0472343i
$759$	8.31757	−	1.74518i	0.301909	−	0.0633459i
$760$	−0.692005	−	1.19859i	−0.0251017	−	0.0434773i
$761$	16.5178	+	28.6097i	0.598771	+	1.03710i	0.993003	+	0.118091i	$0.0376774\pi$
$761$	16.5178	+	28.6097i	0.598771	+	1.03710i	−0.394232	+	0.919011i	$0.628989\pi$
$762$	−0.404079	+	1.23262i	−0.0146382	+	0.0446532i
$763$		0			0
$764$	−5.66934			−0.205110
$765$	−42.1669	−	30.9751i	−1.52455	−	1.11991i
$766$	−1.57534			−0.0569194
$767$	28.6143	−	49.5614i	1.03320	−	1.78956i
$768$	−18.0588	−	20.1623i	−0.651639	−	0.727546i
$769$	1.28876	+	2.23219i	0.0464738	+	0.0804949i	0.888327	−	0.459212i	$-0.151868\pi$
$769$	1.28876	+	2.23219i	0.0464738	+	0.0804949i	−0.841853	+	0.539707i	$0.818535\pi$
$770$		0			0
$771$	−11.3603	−	12.6836i	−0.409132	−	0.456790i
$772$	8.80822	−	15.2563i	0.317015	−	0.549086i
$773$	−6.72973			−0.242051			−0.121026	−	0.992649i	$-0.538618\pi$
$773$	−6.72973			−0.242051			−0.121026	+	0.992649i	$0.538618\pi$
$774$	1.86200	+	1.36780i	0.0669283	+	0.0491645i
$775$	14.0820			0.505842
$776$	−0.703765	+	1.21896i	−0.0252637	+	0.0437580i
$777$		0			0
$778$	−0.539302	−	0.934099i	−0.0193349	−	0.0334891i
$779$	−7.03047	−	12.1771i	−0.251893	−	0.436291i
$780$	47.3361	−	9.93197i	1.69491	−	0.355622i
$781$	−9.90581	+	17.1574i	−0.354458	+	0.613939i
$782$	1.37358			0.0491193
$783$	3.21039	+	33.0428i	0.114730	+	1.18085i
$784$		0			0
$785$	−5.42473	+	9.39590i	−0.193617	+	0.335354i
$786$	−0.516167	+	0.108301i	−0.0184111	+	0.00386297i
$787$	14.3341	+	24.8274i	0.510956	+	0.885003i	0.999919	+	0.0126980i	$0.00404201\pi$
$787$	14.3341	+	24.8274i	0.510956	+	0.885003i	−0.488963	+	0.872305i	$0.662625\pi$
$788$	5.71016	+	9.89029i	0.203416	+	0.352327i
$789$	−6.43804	+	19.6389i	−0.229200	+	0.699164i
$790$	0.0740881	−	0.128324i	0.00263594	−	0.00456558i
$791$		0			0
$792$	−0.143820	+	1.30261i	−0.00511041	+	0.0462864i
$793$	14.2581			0.506320
$794$	−0.564275	+	0.977352i	−0.0200254	+	0.0346849i
$795$	27.3922	+	30.5830i	0.971501	+	1.08467i
$796$	−11.3884	−	19.7252i	−0.403650	−	0.699142i
$797$	−11.4913	−	19.9035i	−0.407042	−	0.705017i	0.587515	−	0.809213i	$-0.300106\pi$
$797$	−11.4913	−	19.9035i	−0.407042	−	0.705017i	−0.994557	+	0.104196i	$0.966773\pi$
$798$		0			0
$799$	12.4370	−	21.5415i	0.439989	−	0.762084i
$800$	1.71421			0.0606064
$801$	1.29266	−	0.567426i	0.0456739	−	0.0200490i
$802$	1.48098			0.0522951
$803$	1.75795	−	3.04485i	0.0620366	−	0.107451i
$804$	−3.57998	+	10.9205i	−0.126256	+	0.385138i
$805$		0			0
$806$	−1.20685	−	2.09033i	−0.0425095	−	0.0736287i
$807$	50.7945	−	10.6576i	1.78805	−	0.375166i
$808$	−0.251989	+	0.436457i	−0.00886493	+	0.0153545i
$809$	−16.4779			−0.579332			−0.289666	−	0.957128i	$-0.593544\pi$
$809$	−16.4779			−0.579332			−0.289666	+	0.957128i	$0.593544\pi$
$810$	−1.10956	+	1.20660i	−0.0389859	+	0.0423955i
$811$	−40.4318			−1.41975			−0.709876	−	0.704326i	$-0.751249\pi$
$811$	−40.4318			−1.41975			−0.709876	+	0.704326i	$0.751249\pi$
$812$		0			0
$813$	−12.0296	+	2.52402i	−0.421895	+	0.0885212i
$814$	0.231227	+	0.400496i	0.00810449	+	0.0140374i
$815$	−16.1456	−	27.9649i	−0.565554	−	0.979569i
$816$	14.0312	−	42.8014i	0.491189	−	1.49835i
$817$	10.7113	−	18.5524i	0.374739	−	0.649068i
$818$	−2.09033			−0.0730868
$819$		0			0
$820$	39.2945			1.37222
$821$	14.0543	−	24.3428i	0.490499	−	0.849569i	−0.509441	−	0.860506i	$-0.670148\pi$
$821$	14.0543	−	24.3428i	0.490499	−	0.849569i	0.999940	+	0.0109361i	$0.00348114\pi$
$822$	1.54358	+	1.72339i	0.0538387	+	0.0601101i
$823$	−12.9529	−	22.4351i	−0.451510	−	0.782038i	0.546970	−	0.837152i	$-0.315781\pi$
$823$	−12.9529	−	22.4351i	−0.451510	−	0.782038i	−0.998480	+	0.0551142i	$0.982448\pi$
$824$	0.707256	+	1.22500i	0.0246384	+	0.0426750i
$825$	3.87287	+	4.32400i	0.134836	+	0.150542i
$826$		0			0
$827$	−17.7998			−0.618961			−0.309480	−	0.950906i	$-0.600155\pi$
$827$	−17.7998			−0.618961			−0.309480	+	0.950906i	$0.600155\pi$
$828$	−2.01565	+	18.2563i	−0.0700486	+	0.634449i
$829$	15.7069			0.545523			0.272761	−	0.962082i	$-0.412063\pi$
$829$	15.7069			0.545523			0.272761	+	0.962082i	$0.412063\pi$
$830$	0.622611	−	1.07839i	0.0216111	−	0.0374316i
$831$	5.30027	−	16.1682i	0.183864	−	0.560869i
$832$	20.7210	+	35.8899i	0.718373	+	1.24426i
$833$		0			0
$834$	0.304918	−	0.0639772i	0.0105584	−	0.00221535i
$835$	−6.39180	+	11.0709i	−0.221197	+	0.383125i
$836$	6.06866			0.209889
$837$	−31.7830	−	14.4513i	−1.09858	−	0.499509i
$838$	−1.47799			−0.0510563
$839$	3.69822	−	6.40550i	0.127677	−	0.221142i	−0.795099	−	0.606479i	$-0.792581\pi$
$839$	3.69822	−	6.40550i	0.127677	−	0.221142i	0.922776	+	0.385337i	$0.125915\pi$
$840$		0			0
$841$	−5.90986	−	10.2362i	−0.203788	−	0.352971i
$842$	0.931370	+	1.61318i	0.0320971	+	0.0555938i
$843$	12.8832	−	39.2996i	0.443722	−	1.35355i
$844$	−21.3338	+	36.9511i	−0.734338	+	1.27191i
$845$	−38.8978			−1.33812
$846$	−0.628052	−	0.461357i	−0.0215929	−	0.0158618i
$847$		0			0
$848$	−17.6725	+	30.6097i	−0.606878	+	1.05114i
$849$	3.48520	+	3.89118i	0.119612	+	0.133545i
$850$	0.469098	+	0.812501i	0.0160899	+	0.0278686i
$851$	6.48892	+	11.2391i	0.222437	+	0.385273i
$852$	−28.5663	−	31.8939i	−0.978667	−	1.09267i
$853$	26.5631	−	46.0086i	0.909503	−	1.57530i	0.0947464	−	0.995501i	$-0.469796\pi$
$853$	26.5631	−	46.0086i	0.909503	−	1.57530i	0.814756	−	0.579804i	$-0.196871\pi$
$854$		0			0
$855$	12.2493	+	8.99815i	0.418917	+	0.307730i
$856$	4.63004			0.158251
$857$	1.90765	−	3.30414i	0.0651640	−	0.112867i	−0.831603	−	0.555371i	$-0.812576\pi$
$857$	1.90765	−	3.30414i	0.0651640	−	0.112867i	0.896767	+	0.442504i	$0.145910\pi$
$858$	0.309941	−	0.945459i	0.0105812	−	0.0322774i
$859$	−19.4884	−	33.7549i	−0.664936	−	1.15170i	−0.979303	−	0.202401i	$-0.935126\pi$
$859$	−19.4884	−	33.7549i	−0.664936	−	1.15170i	0.314367	−	0.949301i	$-0.398208\pi$
$860$	29.9336	+	51.8464i	1.02073	+	1.76795i
$861$		0			0
$862$	−0.280226	+	0.485366i	−0.00954454	+	0.0165316i
$863$	26.6736			0.907978			0.453989	−	0.891007i	$-0.350000\pi$
$863$	26.6736			0.907978			0.453989	+	0.891007i	$0.350000\pi$
$864$	−3.86894	−	1.75915i	−0.131624	−	0.0598477i
$865$	−13.4034			−0.455730
$866$	−0.116737	+	0.202195i	−0.00396690	+	0.00687087i
$867$	43.8464	−	9.19976i	1.48910	−	0.312440i
$868$		0			0
$869$	0.650490	+	1.12668i	0.0220664	+	0.0382200i
$870$	0.627852	−	1.91523i	0.0212862	−	0.0649324i
$871$	8.73531	−	15.1300i	0.295985	−	0.512661i
$872$	2.32198			0.0786321
$873$	1.69632	−	15.3640i	0.0574117	−	0.519993i
$874$	−0.399020			−0.0134971
$875$		0			0
$876$	5.06956	+	5.66009i	0.171285	+	0.191237i
$877$	−12.0068	−	20.7963i	−0.405440	−	0.702242i	0.588933	−	0.808182i	$-0.299548\pi$
$877$	−12.0068	−	20.7963i	−0.405440	−	0.702242i	−0.994373	+	0.105940i	$0.966215\pi$
$878$	−0.225235	−	0.390118i	−0.00760130	−	0.0131658i
$879$	−19.7124	−	22.0085i	−0.664881	−	0.742330i
$880$	−8.45978	+	14.6528i	−0.285179	+	0.493945i
$881$	−4.67326			−0.157446			−0.0787231	−	0.996897i	$-0.525084\pi$
$881$	−4.67326			−0.157446			−0.0787231	+	0.996897i	$0.525084\pi$
$882$		0			0
$883$	−35.6948			−1.20122			−0.600612	−	0.799541i	$-0.705076\pi$
$883$	−35.6948			−1.20122			−0.600612	+	0.799541i	$0.705076\pi$
$884$	−34.3173	+	59.4393i	−1.15422	+	1.99916i
$885$	−15.6556	+	47.7567i	−0.526259	+	1.60532i
$886$	−0.980867	−	1.69891i	−0.0329529	−	0.0570761i
$887$	−14.5516	−	25.2041i	−0.488596	−	0.846272i	0.511318	−	0.859391i	$-0.329157\pi$
$887$	−14.5516	−	25.2041i	−0.488596	−	0.846272i	−0.999914	+	0.0131191i	$0.995824\pi$
$888$	−1.95858	+	0.410946i	−0.0657258	+	0.0137905i
$889$		0			0
$890$	−0.0857071			−0.00287291
$891$	−4.30363	−	13.7336i	−0.144177	−	0.460094i
$892$	−14.3020			−0.478865
$893$	−3.61290	+	6.25772i	−0.120901	+	0.209407i
$894$	−1.02143	+	0.214315i	−0.0341619	+	0.00716778i
$895$	−21.8403	−	37.8285i	−0.730041	−	1.26447i
$896$		0			0
$897$	8.69788	−	26.5324i	0.290414	−	0.885892i
$898$	−0.0156482	+	0.0271035i	−0.000522187	+	0.000904455i
$899$	42.9294			1.43177
$900$	−11.4873	+	5.04247i	−0.382910	+	0.168082i
$901$	−58.2611			−1.94096
$902$	0.404168	−	0.700040i	0.0134573	−	0.0233088i
$903$		0			0
$904$	0.533229	+	0.923579i	0.0177349	+	0.0307178i
$905$	−19.2252	−	33.2991i	−0.639069	−	1.10690i
$906$	−0.368530	−	0.411459i	−0.0122436	−	0.0136698i
$907$	20.6071	−	35.6925i	0.684247	−	1.18515i	−0.289426	−	0.957201i	$-0.593464\pi$
$907$	20.6071	−	35.6925i	0.684247	−	1.18515i	0.973673	−	0.227950i	$-0.0732024\pi$
$908$	27.5129			0.913047
$909$	0.607380	−	5.50121i	0.0201455	−	0.182464i
$910$		0			0
$911$	28.8619	−	49.9903i	0.956239	−	1.65625i	0.224731	−	0.974421i	$-0.427850\pi$
$911$	28.8619	−	49.9903i	0.956239	−	1.65625i	0.731508	−	0.681833i	$-0.238817\pi$
$912$	−4.07600	+	12.4336i	−0.134970	+	0.411718i
$913$	5.46649	+	9.46824i	0.180914	+	0.313353i
$914$	−0.691296	−	1.19736i	−0.0228660	−	0.0396051i
$915$	−12.2544	+	2.57120i	−0.405119	+	0.0850013i
$916$	−26.3326	+	45.6094i	−0.870054	+	1.50698i
$917$		0			0
$918$	−0.224942	−	2.31520i	−0.00742419	−	0.0764130i
$919$	−51.5598			−1.70080			−0.850400	−	0.526137i	$-0.823640\pi$
$919$	−51.5598			−1.70080			−0.850400	+	0.526137i	$0.823640\pi$
$920$	1.11640	−	1.93367i	0.0368068	−	0.0637512i
$921$	39.3573	−	8.25788i	1.29687	−	0.272106i
$922$	−0.827569	−	1.43339i	−0.0272545	−	0.0472062i
$923$	32.5447	+	56.3691i	1.07122	+	1.85541i
$924$		0			0
$925$	−4.43211	+	7.67664i	−0.145727	+	0.252406i
$926$	−0.328525			−0.0107960
$927$	−12.5193	−	9.19646i	−0.411187	−	0.302052i
$928$	5.22579			0.171545
$929$	25.1412	−	43.5458i	0.824856	−	1.42869i	−0.0771732	−	0.997018i	$-0.524589\pi$
$929$	25.1412	−	43.5458i	0.824856	−	1.42869i	0.902029	−	0.431675i	$-0.142077\pi$
$930$	1.41421	+	1.57895i	0.0463738	+	0.0517757i
$931$		0			0
$932$	−12.6150	−	21.8499i	−0.413219	−	0.715717i
$933$	−2.06959	−	2.31066i	−0.0677552	−	0.0756477i
$934$	0.931446	−	1.61331i	0.0304779	−	0.0527892i
$935$	−27.8894			−0.912081
$936$	3.47002	+	2.54902i	0.113421	+	0.0833174i
$937$	18.1400			0.592607			0.296303	−	0.955094i	$-0.404246\pi$
$937$	18.1400			0.592607			0.296303	+	0.955094i	$0.404246\pi$
$938$		0			0
$939$	−2.48688	+	7.58609i	−0.0811561	+	0.247563i
$940$	−10.0966	−	17.4877i	−0.329313	−	0.570387i
$941$	8.51660	+	14.7512i	0.277633	+	0.480875i	0.970796	−	0.239906i	$-0.0771166\pi$
$941$	8.51660	+	14.7512i	0.277633	+	0.480875i	−0.693163	+	0.720781i	$0.743783\pi$
$942$	−0.472067	+	0.0990482i	−0.0153808	+	0.00322716i
$943$	11.3422	−	19.6452i	0.369352	−	0.639737i
$944$	−43.2658			−1.40818
$945$		0			0
$946$	1.23154			0.0400408
$947$	−15.7530	+	27.2849i	−0.511903	+	0.886641i	0.488002	+	0.872842i	$0.337726\pi$
$947$	−15.7530	+	27.2849i	−0.511903	+	0.886641i	−0.999905	+	0.0137988i	$0.995608\pi$
$948$	−2.75174	+	0.577364i	−0.0893722	+	0.0187519i
$949$	−5.77559	−	10.0036i	−0.187484	−	0.324731i
$950$	−0.136271	−	0.236028i	−0.00442121	−	0.00765777i
$951$	13.9658	−	42.6019i	0.452871	−	1.38146i
$952$		0			0
$953$	16.0677			0.520485			0.260242	−	0.965543i	$-0.416197\pi$
$953$	16.0677			0.520485			0.260242	+	0.965543i	$0.416197\pi$
$954$	−0.200312	+	1.81428i	−0.00648533	+	0.0587394i
$955$	−7.56866			−0.244916
$956$	−15.3967	+	26.6679i	−0.497966	+	0.862502i
$957$	11.8065	+	13.1818i	0.381650	+	0.426107i
$958$	−0.701705	−	1.21539i	−0.0226711	−	0.0392674i
$959$		0			0
$960$	−24.2813	−	27.1097i	−0.783675	−	0.874962i
$961$	−7.07402	+	12.2526i	−0.228194	+	0.395244i
$962$	1.51935			0.0489859
$963$	−46.5586	+	20.4374i	−1.50033	+	0.658585i
$964$	−2.35425			−0.0758253
$965$	11.7591	−	20.3674i	0.378539	−	0.655649i
$966$		0			0
$967$	13.3049	+	23.0448i	0.427857	+	0.741069i	0.996682	−	0.0813886i	$-0.0259355\pi$
$967$	13.3049	+	23.0448i	0.427857	+	0.741069i	−0.568826	+	0.822458i	$0.692602\pi$
$968$	−1.15319	−	1.99738i	−0.0370648	−	0.0641981i
$969$	−21.1085	+	4.42895i	−0.678103	+	0.142278i
$970$	−0.469219	+	0.812711i	−0.0150657	+	0.0260946i
$971$	−56.5678			−1.81535			−0.907674	−	0.419676i	$-0.862144\pi$
$971$	−56.5678			−1.81535			−0.907674	+	0.419676i	$0.862144\pi$
$972$	31.1014	+	0.407712i	0.997577	+	0.0130774i
$973$		0			0
$974$	−0.883558	+	1.53037i	−0.0283110	+	0.0490361i
$975$	18.6649	−	3.91623i	0.597755	−	0.125420i
$976$	−5.38969	−	9.33522i	−0.172520	−	0.298813i
$977$	−26.8780	−	46.5541i	−0.859904	−	1.48940i	−0.872020	−	0.489471i	$-0.837190\pi$
$977$	−26.8780	−	46.5541i	−0.859904	−	1.48940i	0.0121160	−	0.999927i	$-0.496143\pi$
$978$	0.447204	−	1.36417i	0.0143000	−	0.0436214i
$979$	0.376252	−	0.651687i	0.0120251	−	0.0208280i
$980$		0			0
$981$	−23.3493	+	10.2494i	−0.745485	+	0.327238i
$982$	1.06769			0.0340715
$983$	−13.7051	+	23.7379i	−0.437125	+	0.757122i	−0.997466	−	0.0711394i	$-0.977336\pi$
$983$	−13.7051	+	23.7379i	−0.437125	+	0.757122i	0.560342	+	0.828262i	$0.310670\pi$
$984$	2.33381	+	2.60566i	0.0743990	+	0.0830654i
$985$	7.62316	+	13.2037i	0.242894	+	0.420705i
$986$	1.43005	+	2.47692i	0.0455421	+	0.0788813i
$987$		0			0
$988$	9.96904	−	17.2669i	0.317157	−	0.549333i
$989$	34.5607			1.09897
$990$	−0.0958885	+	0.868489i	−0.00304754	+	0.0276024i
$991$	−17.3374			−0.550740			−0.275370	−	0.961338i	$-0.588800\pi$
$991$	−17.3374			−0.550740			−0.275370	+	0.961338i	$0.588800\pi$
$992$	−2.74794	+	4.75957i	−0.0872471	+	0.151116i
$993$	−0.0870420	+	0.265517i	−0.00276220	+	0.00842594i
$994$		0			0
$995$	−15.2037	−	26.3335i	−0.481988	−	0.834828i
$996$	−23.1246	+	4.85196i	−0.732732	+	0.153740i
$997$	17.8319	−	30.8858i	0.564742	−	0.978162i	−0.432332	−	0.901715i	$-0.642309\pi$
$997$	17.8319	−	30.8858i	0.564742	−	0.978162i	0.997074	−	0.0764472i	$-0.0243576\pi$
$998$	1.45425			0.0460334
$999$	17.8811	−	12.7777i	0.565734	−	0.404270i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.f.h.295.6	yes	24
3.2	odd	2		1323.2.f.h.883.7		24
7.2	even	3		441.2.h.h.214.7		24
7.3	odd	6		441.2.g.h.79.6		24
7.4	even	3		441.2.g.h.79.5		24
7.5	odd	6		441.2.h.h.214.8		24
7.6	odd	2	inner	441.2.f.h.295.5	yes	24
9.2	odd	6		3969.2.a.bi.1.6		12
9.4	even	3	inner	441.2.f.h.148.6	yes	24
9.5	odd	6		1323.2.f.h.442.7		24
9.7	even	3		3969.2.a.bh.1.7		12
21.2	odd	6		1323.2.h.h.802.6		24
21.5	even	6		1323.2.h.h.802.5		24
21.11	odd	6		1323.2.g.h.667.8		24
21.17	even	6		1323.2.g.h.667.7		24
21.20	even	2		1323.2.f.h.883.8		24
63.4	even	3		441.2.h.h.373.7		24
63.5	even	6		1323.2.g.h.361.7		24
63.13	odd	6	inner	441.2.f.h.148.5	✓	24
63.20	even	6		3969.2.a.bi.1.5		12
63.23	odd	6		1323.2.g.h.361.8		24
63.31	odd	6		441.2.h.h.373.8		24
63.32	odd	6		1323.2.h.h.226.6		24
63.34	odd	6		3969.2.a.bh.1.8		12
63.40	odd	6		441.2.g.h.67.6		24
63.41	even	6		1323.2.f.h.442.8		24
63.58	even	3		441.2.g.h.67.5		24
63.59	even	6		1323.2.h.h.226.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.5	✓	24	63.13	odd	6	inner
441.2.f.h.148.6	yes	24	9.4	even	3	inner
441.2.f.h.295.5	yes	24	7.6	odd	2	inner
441.2.f.h.295.6	yes	24	1.1	even	1	trivial
441.2.g.h.67.5		24	63.58	even	3
441.2.g.h.67.6		24	63.40	odd	6
441.2.g.h.79.5		24	7.4	even	3
441.2.g.h.79.6		24	7.3	odd	6
441.2.h.h.214.7		24	7.2	even	3
441.2.h.h.214.8		24	7.5	odd	6
441.2.h.h.373.7		24	63.4	even	3
441.2.h.h.373.8		24	63.31	odd	6
1323.2.f.h.442.7		24	9.5	odd	6
1323.2.f.h.442.8		24	63.41	even	6
1323.2.f.h.883.7		24	3.2	odd	2
1323.2.f.h.883.8		24	21.20	even	2
1323.2.g.h.361.7		24	63.5	even	6
1323.2.g.h.361.8		24	63.23	odd	6
1323.2.g.h.667.7		24	21.17	even	6
1323.2.g.h.667.8		24	21.11	odd	6
1323.2.h.h.226.5		24	63.59	even	6
1323.2.h.h.226.6		24	63.32	odd	6
1323.2.h.h.802.5		24	21.5	even	6
1323.2.h.h.802.6		24	21.2	odd	6
3969.2.a.bh.1.7		12	9.7	even	3
3969.2.a.bh.1.8		12	63.34	odd	6
3969.2.a.bi.1.5		12	63.20	even	6
3969.2.a.bi.1.6		12	9.2	odd	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0341870 + 0.0592136i) q^{2} +(1.69514 - 0.355671i) q^{3} +(0.997662 + 1.72800i) q^{4} +(1.33190 + 2.30691i) q^{5} +(-0.0368912 + 0.112535i) q^{6} -0.273176 q^{8} +(2.74700 - 1.20582i) q^{9} +O(q^{10})\)	\(q+(-0.0341870 + 0.0592136i) q^{2} +(1.69514 - 0.355671i) q^{3} +(0.997662 + 1.72800i) q^{4} +(1.33190 + 2.30691i) q^{5} +(-0.0368912 + 0.112535i) q^{6} -0.273176 q^{8} +(2.74700 - 1.20582i) q^{9} -0.182134 q^{10} +(0.799563 - 1.38488i) q^{11} +(2.30578 + 2.57437i) q^{12} +(-2.62690 - 4.54992i) q^{13} +(3.07825 + 3.43682i) q^{15} +(-1.98599 + 3.43983i) q^{16} -6.54721 q^{17} +(-0.0225104 + 0.203883i) q^{18} +1.90194 q^{19} +(-2.65756 + 4.60304i) q^{20} +(0.0546693 + 0.0946900i) q^{22} +(1.53419 + 2.65729i) q^{23} +(-0.463072 + 0.0971608i) q^{24} +(-1.04789 + 1.81500i) q^{25} +0.359223 q^{26} +(4.22767 - 3.02106i) q^{27} +(-3.19452 + 5.53306i) q^{29} +(-0.308743 + 0.0647797i) q^{30} +(-3.35961 - 5.81902i) q^{31} +(-0.408966 - 0.708350i) q^{32} +(0.862809 - 2.63195i) q^{33} +(0.223829 - 0.387684i) q^{34} +(4.82424 + 3.54381i) q^{36} +4.22955 q^{37} +(-0.0650215 + 0.112621i) q^{38} +(-6.07124 - 6.77845i) q^{39} +(-0.363842 - 0.630193i) q^{40} +(-3.69648 - 6.40249i) q^{41} +(5.63176 - 9.75450i) q^{43} +3.19078 q^{44} +(6.44044 + 4.73105i) q^{45} -0.209797 q^{46} +(-1.89959 + 3.29018i) q^{47} +(-2.14308 + 6.53735i) q^{48} +(-0.0716485 - 0.124099i) q^{50} +(-11.0984 + 2.32865i) q^{51} +(5.24152 - 9.07858i) q^{52} +8.89862 q^{53} +(0.0343569 + 0.353616i) q^{54} +4.25974 q^{55} +(3.22405 - 0.676463i) q^{57} +(-0.218422 - 0.378317i) q^{58} +(5.44639 + 9.43343i) q^{59} +(-2.86778 + 8.74801i) q^{60} +(-1.35693 + 2.35027i) q^{61} +0.459420 q^{62} -7.88802 q^{64} +(6.99751 - 12.1200i) q^{65} +(0.126351 + 0.141069i) q^{66} +(1.66267 + 2.87982i) q^{67} +(-6.53190 - 11.3136i) q^{68} +(3.54578 + 3.95881i) q^{69} -12.3890 q^{71} +(-0.750414 + 0.329402i) q^{72} +2.19863 q^{73} +(-0.144596 + 0.250447i) q^{74} +(-1.13078 + 3.44939i) q^{75} +(1.89749 + 3.28655i) q^{76} +(0.608933 - 0.127765i) q^{78} +(-0.406778 + 0.704560i) q^{79} -10.5805 q^{80} +(6.09198 - 6.62478i) q^{81} +0.505486 q^{82} +(-3.41842 + 5.92088i) q^{83} +(-8.72020 - 15.1038i) q^{85} +(0.385066 + 0.666954i) q^{86} +(-3.44720 + 10.5155i) q^{87} +(-0.218422 + 0.378317i) q^{88} +0.470572 q^{89} +(-0.500321 + 0.219621i) q^{90} +(-3.06120 + 5.30216i) q^{92} +(-7.76467 - 8.66914i) q^{93} +(-0.129882 - 0.224963i) q^{94} +(2.53318 + 4.38760i) q^{95} +(-0.945194 - 1.05529i) q^{96} +(2.57623 - 4.46216i) q^{97} +(0.526472 - 4.76840i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9} + 20 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} + 48 q^{32} - 4 q^{36} + 24 q^{37} + 32 q^{39} - 112 q^{44} - 48 q^{46} - 4 q^{50} - 56 q^{51} - 64 q^{53} - 12 q^{57} - 88 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} + 168 q^{72} + 68 q^{74} - 60 q^{78} + 12 q^{79} + 80 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 80 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9 + 20 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 + 48 * q^32 - 4 * q^36 + 24 * q^37 + 32 * q^39 - 112 * q^44 - 48 * q^46 - 4 * q^50 - 56 * q^51 - 64 * q^53 - 12 * q^57 - 88 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 + 168 * q^72 + 68 * q^74 - 60 * q^78 + 12 * q^79 + 80 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 80 * q^93 + 64 * q^95 + 20 * q^99

Introduction

L-functions

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