LMFDB - Embedded newform 441.2.h.h.373.7

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			373.7
Character	$\chi$	$=$	441.373
Dual form			441.2.h.h.214.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0683740 q^{2} +(-0.539550 - 1.64587i) q^{3} -1.99532 q^{4} +(1.33190 + 2.30691i) q^{5} +(-0.0368912 - 0.112535i) q^{6} -0.273176 q^{8} +(-2.41777 + 1.77606i) q^{9} +O(q^{10})$	\(q+0.0683740 q^{2} +(-0.539550 - 1.64587i) q^{3} -1.99532 q^{4} +(1.33190 + 2.30691i) q^{5} +(-0.0368912 - 0.112535i) q^{6} -0.273176 q^{8} +(-2.41777 + 1.77606i) q^{9} +(0.0910670 + 0.157733i) q^{10} +(0.799563 - 1.38488i) q^{11} +(1.07658 + 3.28404i) q^{12} +(-2.62690 + 4.54992i) q^{13} +(3.07825 - 3.43682i) q^{15} +3.97197 q^{16} +(3.27360 + 5.67005i) q^{17} +(-0.165313 + 0.121436i) q^{18} +(-0.950968 + 1.64713i) q^{19} +(-2.65756 - 4.60304i) q^{20} +(0.0546693 - 0.0946900i) q^{22} +(1.53419 + 2.65729i) q^{23} +(0.147392 + 0.449612i) q^{24} +(-1.04789 + 1.81500i) q^{25} +(-0.179612 + 0.311096i) q^{26} +(4.22767 + 3.02106i) q^{27} +(-3.19452 - 5.53306i) q^{29} +(0.210472 - 0.234989i) q^{30} +6.71923 q^{31} +0.817932 q^{32} +(-2.71074 - 0.568763i) q^{33} +(0.223829 + 0.387684i) q^{34} +(4.82424 - 3.54381i) q^{36} +(-2.11477 + 3.66290i) q^{37} +(-0.0650215 + 0.112621i) q^{38} +(8.90592 + 1.86862i) q^{39} +(-0.363842 - 0.630193i) q^{40} +(-3.69648 + 6.40249i) q^{41} +(5.63176 + 9.75450i) q^{43} +(-1.59539 + 2.76329i) q^{44} +(-7.31743 - 3.21206i) q^{45} +(0.104898 + 0.181689i) q^{46} +3.79918 q^{47} +(-2.14308 - 6.53735i) q^{48} +(-0.0716485 + 0.124099i) q^{50} +(7.56589 - 8.44720i) q^{51} +(5.24152 - 9.07858i) q^{52} +(-4.44931 - 7.70643i) q^{53} +(0.289062 + 0.206562i) q^{54} +4.25974 q^{55} +(3.22405 + 0.676463i) q^{57} +(-0.218422 - 0.378317i) q^{58} -10.8928 q^{59} +(-6.14211 + 6.85757i) q^{60} +2.71386 q^{61} +0.459420 q^{62} -7.88802 q^{64} -13.9950 q^{65} +(-0.185344 - 0.0388886i) q^{66} -3.32533 q^{67} +(-6.53190 - 11.3136i) q^{68} +(3.54578 - 3.95881i) q^{69} -12.3890 q^{71} +(0.660478 - 0.485177i) q^{72} +(-1.09932 - 1.90407i) q^{73} +(-0.144596 + 0.250447i) q^{74} +(3.55265 + 0.745409i) q^{75} +(1.89749 - 3.28655i) q^{76} +(0.608933 + 0.127765i) q^{78} +0.813556 q^{79} +(5.29025 + 9.16298i) q^{80} +(2.69124 - 8.58820i) q^{81} +(-0.252743 + 0.437764i) q^{82} +(-3.41842 - 5.92088i) q^{83} +(-8.72020 + 15.1038i) q^{85} +(0.385066 + 0.666954i) q^{86} +(-7.38310 + 8.24312i) q^{87} +(-0.218422 + 0.378317i) q^{88} +(-0.235286 + 0.407527i) q^{89} +(-0.500321 - 0.219621i) q^{90} +(-3.06120 - 5.30216i) q^{92} +(-3.62536 - 11.0590i) q^{93} +0.259765 q^{94} -5.06636 q^{95} +(-0.441315 - 1.34621i) q^{96} +(2.57623 + 4.46216i) q^{97} +(0.526472 + 4.76840i) 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.0683740			0.0483477			0.0241739	−	0.999708i	$-0.492304\pi$
$2$	0.0683740			0.0483477			0.0241739	+	0.999708i	$0.492304\pi$
$3$	−0.539550	−	1.64587i	−0.311509	−	0.950243i
$3$	−0.539550	−	1.64587i	−0.311509	−	0.950243i
$4$	−1.99532			−0.997662
$5$	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
$9$	−2.41777	+	1.77606i	−0.805924	+	0.592019i
$10$	0.0910670	+	0.157733i	0.0287979	+	0.0498794i
$11$	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	$0.0891659\pi$
$12$	1.07658	+	3.28404i	0.310781	+	0.948022i
$13$	−2.62690	+	4.54992i	−0.728571	+	1.26192i	0.228916	+	0.973446i	$0.426482\pi$
$13$	−2.62690	+	4.54992i	−0.728571	+	1.26192i	−0.957487	+	0.288476i	$0.906852\pi$
$14$		0			0
$15$	3.07825	−	3.43682i	0.794801	−	0.887383i
$16$	3.97197			0.992993
$17$	3.27360	+	5.67005i	0.793966	+	1.37519i	0.923494	+	0.383613i	$0.125320\pi$
$17$	3.27360	+	5.67005i	0.793966	+	1.37519i	−0.129528	+	0.991576i	$0.541346\pi$
$18$	−0.165313	+	0.121436i	−0.0389646	+	0.0286228i
$19$	−0.950968	+	1.64713i	−0.218167	+	0.377877i	−0.954248	−	0.299017i	$-0.903341\pi$
$19$	−0.950968	+	1.64713i	−0.218167	+	0.377877i	0.736081	+	0.676894i	$0.236674\pi$
$20$	−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	$0.729684\pi$
$24$	0.147392	+	0.449612i	0.0300863	+	0.0917768i
$25$	−1.04789	+	1.81500i	−0.209578	+	0.363000i
$26$	−0.179612	+	0.311096i	−0.0352247	+	0.0610110i
$27$	4.22767	+	3.02106i	0.813615	+	0.581404i
$28$		0			0
$29$	−3.19452	−	5.53306i	−0.593207	−	1.02746i	−0.993797	−	0.111207i	$-0.964528\pi$
$29$	−3.19452	−	5.53306i	−0.593207	−	1.02746i	0.400591	−	0.916257i	$-0.368805\pi$
$30$	0.210472	−	0.234989i	0.0384268	−	0.0429029i
$31$	6.71923			1.20681			0.603405	−	0.797435i	$-0.293810\pi$
$31$	6.71923			1.20681			0.603405	+	0.797435i	$0.293810\pi$
$32$	0.817932			0.144591
$33$	−2.71074	−	0.568763i	−0.471880	−	0.0990088i
$34$	0.223829	+	0.387684i	0.0383864	+	0.0664872i
$35$		0			0
$36$	4.82424	−	3.54381i	0.804040	−	0.590635i
$37$	−2.11477	+	3.66290i	−0.347667	+	0.602176i	−0.985835	−	0.167721i	$-0.946359\pi$
$37$	−2.11477	+	3.66290i	−0.347667	+	0.602176i	0.638168	+	0.769897i	$0.279693\pi$
$38$	−0.0650215	+	0.112621i	−0.0105479	+	0.0182695i
$39$	8.90592	+	1.86862i	1.42609	+	0.299219i
$40$	−0.363842	−	0.630193i	−0.0575285	−	0.0996423i
$41$	−3.69648	+	6.40249i	−0.577293	+	0.999901i	0.418495	+	0.908219i	$0.362558\pi$
$41$	−3.69648	+	6.40249i	−0.577293	+	0.999901i	−0.995788	+	0.0916820i	$0.970776\pi$
$42$		0			0
$43$	5.63176	+	9.75450i	0.858836	+	1.48755i	0.873040	+	0.487648i	$0.162145\pi$
$43$	5.63176	+	9.75450i	0.858836	+	1.48755i	−0.0142043	+	0.999899i	$0.504522\pi$
$44$	−1.59539	+	2.76329i	−0.240514	+	0.416582i
$45$	−7.31743	−	3.21206i	−1.09082	−	0.478826i
$46$	0.104898	+	0.181689i	0.0154664	+	0.0267887i
$47$	3.79918			0.554167			0.277083	−	0.960846i	$-0.410632\pi$
$47$	3.79918			0.554167			0.277083	+	0.960846i	$0.410632\pi$
$48$	−2.14308	−	6.53735i	−0.309327	−	0.943585i
$49$		0			0
$50$	−0.0716485	+	0.124099i	−0.0101326	+	0.0175502i
$51$	7.56589	−	8.44720i	1.05944	−	1.18284i
$52$	5.24152	−	9.07858i	0.726868	−	1.25897i
$53$	−4.44931	−	7.70643i	−0.611160	−	1.05856i	−0.991045	−	0.133527i	$-0.957370\pi$
$53$	−4.44931	−	7.70643i	−0.611160	−	1.05856i	0.379885	−	0.925034i	$-0.375963\pi$
$54$	0.289062	+	0.206562i	0.0393364	+	0.0281096i
$55$	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
$59$	−10.8928			−1.41812			−0.709060	−	0.705148i	$-0.750880\pi$
$59$	−10.8928			−1.41812			−0.709060	+	0.705148i	$0.750880\pi$
$60$	−6.14211	+	6.85757i	−0.792943	+	0.885309i
$61$	2.71386			0.347475			0.173737	−	0.984792i	$-0.444416\pi$
$61$	2.71386			0.347475			0.173737	+	0.984792i	$0.444416\pi$
$62$	0.459420			0.0583465
$63$		0			0
$64$	−7.88802			−0.986002
$65$	−13.9950			−1.73587
$66$	−0.185344	−	0.0388886i	−0.0228143	−	0.00478685i
$67$	−3.32533			−0.406254			−0.203127	−	0.979152i	$-0.565110\pi$
$67$	−3.32533			−0.406254			−0.203127	+	0.979152i	$0.565110\pi$
$68$	−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	$0.762890\pi$
$72$	0.660478	−	0.485177i	0.0778381	−	0.0571786i
$73$	−1.09932	−	1.90407i	−0.128665	−	0.222855i	0.794494	−	0.607271i	$-0.207736\pi$
$73$	−1.09932	−	1.90407i	−0.128665	−	0.222855i	−0.923160	+	0.384417i	$0.874403\pi$
$74$	−0.144596	+	0.250447i	−0.0168089	+	0.0291138i
$75$	3.55265	+	0.745409i	0.410224	+	0.0860724i
$76$	1.89749	−	3.28655i	0.217657	−	0.376993i
$77$		0			0
$78$	0.608933	+	0.127765i	0.0689481	+	0.0144666i
$79$	0.813556			0.0915322			0.0457661	−	0.998952i	$-0.485427\pi$
$79$	0.813556			0.0915322			0.0457661	+	0.998952i	$0.485427\pi$
$80$	5.29025	+	9.16298i	0.591468	+	1.02445i
$81$	2.69124	−	8.58820i	0.299027	−	0.954245i
$82$	−0.252743	+	0.437764i	−0.0279108	+	0.0483429i
$83$	−3.41842	−	5.92088i	−0.375220	−	0.649901i	0.615140	−	0.788418i	$-0.289100\pi$
$83$	−3.41842	−	5.92088i	−0.375220	−	0.649901i	−0.990360	+	0.138517i	$0.955766\pi$
$84$		0			0
$85$	−8.72020	+	15.1038i	−0.945838	+	1.63824i
$86$	0.385066	+	0.666954i	0.0415227	+	0.0719195i
$87$	−7.38310	+	8.24312i	−0.791551	+	0.883755i
$88$	−0.218422	+	0.378317i	−0.0232838	+	0.0403288i
$89$	−0.235286	+	0.407527i	−0.0249403	+	0.0431978i	−0.878226	−	0.478246i	$-0.841273\pi$
$89$	−0.235286	+	0.407527i	−0.0249403	+	0.0431978i	0.853286	+	0.521443i	$0.174606\pi$
$90$	−0.500321	−	0.219621i	−0.0527385	−	0.0231501i
$91$		0			0
$92$	−3.06120	−	5.30216i	−0.319152	−	0.552788i
$93$	−3.62536	−	11.0590i	−0.375932	−	1.14676i
$94$	0.259765			0.0267927
$95$	−5.06636			−0.519798
$96$	−0.441315	−	1.34621i	−0.0450415	−	0.137397i
$97$	2.57623	+	4.46216i	0.261576	+	0.453064i	0.966661	−	0.256059i	$-0.0824243\pi$
$97$	2.57623	+	4.46216i	0.261576	+	0.453064i	−0.705085	+	0.709123i	$0.749091\pi$
$98$		0			0
$99$	0.526472	+	4.76840i	0.0529125	+	0.479243i
$100$	2.09088	−	3.62152i	0.209088	−	0.362152i
$101$	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	$0.137409\pi$
$102$	0.517310	−	0.577569i	0.0512213	−	0.0571878i
$103$	−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
$107$	8.47445	−	14.6782i	0.819256	−	1.41899i	−0.0869755	−	0.996210i	$-0.527720\pi$
$107$	8.47445	−	14.6782i	0.819256	−	1.41899i	0.906231	−	0.422782i	$-0.138946\pi$
$108$	−8.43557	−	6.02801i	−0.811713	−	0.580045i
$109$	4.24996	+	7.36115i	0.407073	+	0.705070i	0.994560	−	0.104163i	$-0.0332163\pi$
$109$	4.24996	+	7.36115i	0.407073	+	0.705070i	−0.587488	+	0.809233i	$0.699883\pi$
$110$	0.291255			0.0277701
$111$	7.16967	+	1.50433i	0.680515	+	0.142784i
$112$		0			0
$113$	−1.95196	+	3.38089i	−0.183625	+	0.318048i	−0.943112	−	0.332474i	$-0.892116\pi$
$113$	−1.95196	+	3.38089i	−0.183625	+	0.318048i	0.759487	+	0.650522i	$0.225450\pi$
$114$	0.220441	+	0.0462525i	0.0206462	+	0.00433194i
$115$	−4.08675	+	7.07847i	−0.381092	+	0.660070i
$116$	6.37410	+	11.0403i	0.591820	+	1.02506i
$117$	−1.72968	−	15.6662i	−0.159909	−	1.44834i
$118$	−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
$122$	0.185558			0.0167996
$123$	12.5321	+	2.62946i	1.12998	+	0.237090i
$124$	−13.4070			−1.20399
$125$	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	$0.338465\pi$
$128$	−2.17520			−0.192262
$129$	13.0160	−	14.5322i	1.14600	−	1.27949i
$130$	−0.956896			−0.0839253
$131$	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
$135$	−1.33852	+	13.7766i	−0.115201	+	1.18570i
$136$	−0.894271	−	1.54892i	−0.0766831	−	0.132819i
$137$	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	$-0.147598\pi$
$138$	0.242439	−	0.270680i	0.0206378	−	0.0230418i
$139$	−1.31540	+	2.27833i	−0.111570	+	0.193246i	−0.916404	−	0.400256i	$-0.868921\pi$
$139$	−1.31540	+	2.27833i	−0.111570	+	0.193246i	0.804833	+	0.593501i	$0.202255\pi$
$140$		0			0
$141$	−2.04984	−	6.25295i	−0.172628	−	0.526593i
$142$	−0.847087			−0.0710860
$143$	4.20075	+	7.27590i	0.351284	+	0.608442i
$144$	−9.60332	+	7.05445i	−0.800277	+	0.587871i
$145$	8.50952	−	14.7389i	0.706677	−	1.22400i
$146$	−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	$0.715773\pi$
$150$	0.242908	+	0.0509666i	0.0198334	+	0.00416140i
$151$	−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	$0.227446\pi$
$152$	0.259782	−	0.449956i	0.0210711	−	0.0364962i
$153$	−17.9852	−	7.89478i	−1.45401	−	0.638255i
$154$		0			0
$155$	8.94931	+	15.5007i	0.718826	+	1.24504i
$156$	−17.7702	−	3.72851i	−1.42276	−	0.298520i
$157$	−4.07294			−0.325056			−0.162528	−	0.986704i	$-0.551965\pi$
$157$	−4.07294			−0.325056			−0.162528	+	0.986704i	$0.551965\pi$
$158$	0.0556261			0.00442537
$159$	−10.2832	+	11.4810i	−0.815507	+	0.910502i
$160$	1.08940	+	1.88690i	0.0861246	+	0.149172i
$161$		0			0
$162$	0.184011	−	0.587210i	0.0144573	−	0.0461355i
$163$	6.06112	−	10.4982i	0.474744	−	0.822280i	−0.524838	−	0.851202i	$-0.675874\pi$
$163$	6.06112	−	10.4982i	0.474744	−	0.822280i	0.999582	+	0.0289220i	$0.00920745\pi$
$164$	7.37568	−	12.7750i	0.575944	−	0.997564i
$165$	−2.29834	−	7.01097i	−0.178926	−	0.545804i
$166$	−0.233731	−	0.404834i	−0.0181410	−	0.0314212i
$167$	2.39951	−	4.15608i	0.185680	−	0.321607i	−0.758126	−	0.652109i	$-0.773885\pi$
$167$	2.39951	−	4.15608i	0.185680	−	0.321607i	0.943805	+	0.330502i	$0.107218\pi$
$168$		0			0
$169$	−7.30121	−	12.6461i	−0.561631	−	0.972774i
$170$	−0.596235	+	1.03271i	−0.0457291	+	0.0792051i
$171$	−0.626165	−	5.67135i	−0.0478840	−	0.433699i
$172$	−11.2372	−	19.4634i	−0.856828	−	1.48407i
$173$	5.03171			0.382554			0.191277	−	0.981536i	$-0.438737\pi$
$173$	5.03171			0.382554			0.191277	+	0.981536i	$0.438737\pi$
$174$	−0.504812	+	0.563615i	−0.0382697	+	0.0427275i
$175$		0			0
$176$	3.17584	−	5.50072i	0.239388	−	0.414632i
$177$	5.87720	+	17.9281i	0.441758	+	1.34756i
$178$	−0.0160874	+	0.0278642i	−0.00120580	+	0.00208851i
$179$	8.19896	+	14.2010i	0.612819	+	1.06143i	0.990763	+	0.135605i	$0.0432977\pi$
$179$	8.19896	+	14.2010i	0.612819	+	1.06143i	−0.377944	+	0.925828i	$0.623369\pi$
$180$	14.6006	+	6.40911i	1.08827	+	0.477707i
$181$	−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
$185$	−11.2666			−0.828339
$186$	−0.247880	−	0.756146i	−0.0181755	−	0.0554433i
$187$	10.4698			0.765629
$188$	−7.58059			−0.552871
$189$		0			0
$190$	−0.346407			−0.0251310
$191$	2.84131			0.205590			0.102795	−	0.994703i	$-0.467221\pi$
$191$	2.84131			0.205590			0.102795	+	0.994703i	$0.467221\pi$
$192$	4.25598	+	12.9826i	0.307149	+	0.936942i
$193$	8.82886			0.635515			0.317758	−	0.948172i	$-0.397070\pi$
$193$	8.82886			0.635515			0.317758	+	0.948172i	$0.397070\pi$
$194$	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	$0.434641\pi$
$198$	0.0359970	+	0.326035i	0.00255820	+	0.0231703i
$199$	5.70752	+	9.88572i	0.404596	+	0.700780i	0.994274	−	0.106858i	$-0.0340789\pi$
$199$	5.70752	+	9.88572i	0.404596	+	0.700780i	−0.589679	+	0.807638i	$0.700746\pi$
$200$	0.286259	−	0.495815i	0.0202416	−	0.0350594i
$201$	1.79418	+	5.47306i	0.126552	+	0.386040i
$202$	0.0630709	−	0.109242i	0.00443765	−	0.00768624i
$203$		0			0
$204$	−15.0964	+	16.8549i	−1.05696	+	1.18008i
$205$	−19.6933			−1.37544
$206$	−0.177021	−	0.306609i	−0.0123336	−	0.0213625i
$207$	−8.42881	−	3.69992i	−0.585843	−	0.257162i
$208$	−10.4340	+	18.0722i	−0.723466	+	1.25308i
$209$	1.52072	+	2.63396i	0.105190	+	0.182195i
$210$		0			0
$211$	10.6919	−	18.5189i	0.736059	−	1.27489i	−0.218199	−	0.975904i	$-0.570018\pi$
$211$	10.6919	−	18.5189i	0.736059	−	1.27489i	0.954257	−	0.298986i	$-0.0966486\pi$
$212$	8.87782	+	15.3768i	0.609731	+	1.05609i
$213$	6.68450	+	20.3907i	0.458014	+	1.39715i
$214$	0.579432	−	1.00361i	0.0396091	−	0.0686050i
$215$	−15.0018	+	25.9840i	−1.02312	+	1.77209i
$216$	−1.15490	−	0.825283i	−0.0785809	−	0.0561534i
$217$		0			0
$218$	0.290587	+	0.503311i	0.0196810	+	0.0340885i
$219$	−2.54072	+	2.83668i	−0.171686	+	0.191685i
$220$	−8.49956			−0.573041
$221$	−34.3977			−2.31384
$222$	0.490219	+	0.102857i	0.0329014	+	0.00690330i
$223$	−3.58387	−	6.20744i	−0.239994	−	0.415681i	0.720719	−	0.693228i	$-0.243812\pi$
$223$	−3.58387	−	6.20744i	−0.239994	−	0.415681i	−0.960712	+	0.277547i	$0.910479\pi$
$224$		0			0
$225$	−0.689984	−	6.24938i	−0.0459989	−	0.416625i
$226$	−0.133463	+	0.231165i	−0.00887784	+	0.0153769i
$227$	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	$0.0153782\pi$
$228$	−6.43302	−	1.34976i	−0.426037	−	0.0893903i
$229$	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
$233$	6.32230	−	10.9505i	0.414187	−	0.717394i	−0.581155	−	0.813793i	$-0.697399\pi$
$233$	6.32230	−	10.9505i	0.414187	−	0.717394i	0.995343	+	0.0963989i	$0.0307324\pi$
$234$	−0.118265	−	1.07116i	−0.00773124	−	0.0700240i
$235$	5.06010	+	8.76436i	0.330085	+	0.571724i
$236$	21.7346			1.41481
$237$	−0.438954	−	1.33901i	−0.0285131	−	0.0869779i
$238$		0			0
$239$	7.71640	−	13.3652i	0.499133	−	0.864523i	−0.500867	−	0.865524i	$-0.666985\pi$
$239$	7.71640	−	13.3652i	0.499133	−	0.864523i	0.999999	+	0.00100121i	$0.000318696\pi$
$240$	12.2267	−	13.6510i	0.789231	−	0.881165i
$241$	−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	$0.178766\pi$
$242$	0.288634	+	0.499928i	0.0185541	+	0.0321366i
$243$	−15.5871	+	0.204333i	−0.999914	+	0.0131080i
$244$	−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
$248$	−1.83553			−0.116557
$249$	−7.90059	+	8.82089i	−0.500679	+	0.559001i
$250$	0.528957			0.0334542
$251$	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
$254$	0.748919			0.0469913
$255$	29.5639	+	6.20304i	1.85136	+	0.388449i
$256$	15.6273			0.976707
$257$	−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
$261$	17.5506	+	7.70404i	1.08636	+	0.476868i
$262$	0.152249	+	0.263703i	0.00940598	+	0.0162916i
$263$	−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	$0.286585\pi$
$264$	0.740511	+	0.155372i	0.0455753	+	0.00956251i
$265$	11.8520	−	20.5283i	0.728065	−	1.26105i
$266$		0			0
$267$	0.797685	+	0.167369i	0.0488175	+	0.0102428i
$268$	6.63512			0.405304
$269$	−14.9824	−	25.9503i	−0.913494	−	1.58222i	−0.809092	−	0.587682i	$-0.800041\pi$
$269$	−14.9824	−	25.9503i	−0.913494	−	1.58222i	−0.104401	−	0.994535i	$-0.533293\pi$
$270$	−0.0915197	+	0.941960i	−0.00556971	+	0.0573259i
$271$	3.54825	−	6.14575i	0.215541	−	0.373328i	−0.737899	−	0.674911i	$-0.764182\pi$
$271$	3.54825	−	6.14575i	0.215541	−	0.373328i	0.953440	+	0.301584i	$0.0975152\pi$
$272$	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
$276$	−7.07499	+	7.89912i	−0.425864	+	0.475471i
$277$	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	$0.0713075\pi$
$278$	−0.0899388	+	0.155779i	−0.00539417	+	0.00934298i
$279$	−16.2456	+	11.9337i	−0.972596	+	0.714454i
$280$		0			0
$281$	11.9389	+	20.6787i	0.712213	+	1.23359i	0.964025	+	0.265813i	$0.0856403\pi$
$281$	11.9389	+	20.6787i	0.712213	+	1.23359i	−0.251812	+	0.967776i	$0.581026\pi$
$282$	−0.140156	−	0.427539i	−0.00834617	−	0.0254596i
$283$	−3.01595			−0.179280			−0.0896399	−	0.995974i	$-0.528572\pi$
$283$	−3.01595			−0.179280			−0.0896399	+	0.995974i	$0.528572\pi$
$284$	24.7201			1.46687
$285$	2.73356	+	8.33857i	0.161922	+	0.493934i
$286$	0.287222	+	0.497483i	0.0169838	+	0.0294168i
$287$		0			0
$288$	−1.97757	+	1.45269i	−0.116530	+	0.0856008i
$289$	−12.9330	+	22.4006i	−0.760763	+	1.31768i
$290$	0.581830	−	1.00776i	0.0341662	−	0.0591776i
$291$	5.95413	−	6.64770i	0.349037	−	0.389695i
$292$	2.19350	+	3.79925i	0.128365	+	0.222334i
$293$	−8.52913	+	14.7729i	−0.498277	+	0.863041i	−0.999998	−	0.00198814i	$-0.999367\pi$
$293$	−8.52913	+	14.7729i	−0.498277	+	0.863041i	0.501721	+	0.865030i	$0.332700\pi$
$294$		0			0
$295$	−14.5081	−	25.1287i	−0.844692	−	1.46305i
$296$	0.577706	−	1.00062i	0.0335785	−	0.0581596i
$297$	7.56411	−	3.43930i	0.438914	−	0.199568i
$298$	0.301283	+	0.521838i	0.0174529	+	0.0302293i
$299$	−16.1206			−0.932280
$300$	−7.08868	−	1.48733i	−0.409265	−	0.0858712i
$301$		0			0
$302$	−0.159456	+	0.276185i	−0.00917564	+	0.0158927i
$303$	−3.12733	−	0.656170i	−0.179660	−	0.0376960i
$304$	−3.77722	+	6.54234i	−0.216638	+	0.375229i
$305$	3.61458	+	6.26064i	0.206970	+	0.358483i
$306$	−1.22972	−	0.539797i	−0.0702982	−	0.0308582i
$307$	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
$311$	1.79093			0.101555			0.0507773	−	0.998710i	$-0.483830\pi$
$311$	1.79093			0.101555			0.0507773	+	0.998710i	$0.483830\pi$
$312$	−2.43289	−	0.510463i	−0.137735	−	0.0288993i
$313$	4.60917			0.260526			0.130263	−	0.991480i	$-0.458418\pi$
$313$	4.60917			0.260526			0.130263	+	0.991480i	$0.458418\pi$
$314$	−0.278483			−0.0157157
$315$		0			0
$316$	−1.62331			−0.0913183
$317$	−25.8841			−1.45380			−0.726898	−	0.686745i	$-0.759039\pi$
$317$	−25.8841			−1.45380			−0.726898	+	0.686745i	$0.759039\pi$
$318$	−0.703100	+	0.785001i	−0.0394279	+	0.0440207i
$319$	−10.2169			−0.572035
$320$	−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
$324$	−5.36990	+	17.1363i	−0.298328	+	0.952014i
$325$	−5.50541	−	9.53566i	−0.305385	−	0.528943i
$326$	0.414423	−	0.717802i	0.0229528	−	0.0397554i
$327$	9.82242	−	10.9666i	0.543181	−	0.606454i
$328$	1.00979	−	1.74901i	0.0557563	−	0.0965728i
$329$		0			0
$330$	−0.157147	−	0.479368i	−0.00865065	−	0.0263884i
$331$	0.161323			0.00886714			0.00443357	−	0.999990i	$-0.498589\pi$
$331$	0.161323			0.00886714			0.00443357	+	0.999990i	$0.498589\pi$
$332$	6.82086	+	11.8141i	0.374343	+	0.648382i
$333$	−1.39247	−	12.6120i	−0.0763070	−	0.691134i
$334$	0.164064	−	0.284168i	0.00897719	−	0.0155490i
$335$	−4.42899	−	7.67124i	−0.241982	−	0.419125i
$336$		0			0
$337$	4.52675	−	7.84057i	0.246588	−	0.427103i	−0.715989	−	0.698112i	$-0.754024\pi$
$337$	4.52675	−	7.84057i	0.246588	−	0.427103i	0.962577	+	0.271009i	$0.0873572\pi$
$338$	−0.499213	−	0.864662i	−0.0271536	−	0.0470314i
$339$	6.61769	+	1.38851i	0.359423	+	0.0754135i
$340$	17.3996	−	30.1370i	0.943627	−	1.63441i
$341$	5.37245	−	9.30535i	0.290934	−	0.503913i
$342$	−0.0428134	−	0.387773i	−0.00231508	−	0.0209683i
$343$		0			0
$344$	−1.53846	−	2.66470i	−0.0829484	−	0.143671i
$345$	13.8552	+	2.90708i	0.745941	+	0.156512i
$346$	0.344038			0.0184956
$347$	−5.81968			−0.312417			−0.156208	−	0.987724i	$-0.549927\pi$
$347$	−5.81968			−0.312417			−0.156208	+	0.987724i	$0.549927\pi$
$348$	14.7317	−	16.4477i	0.789701	−	0.881689i
$349$	−13.6310	−	23.6095i	−0.729648	−	1.26379i	−0.957032	−	0.289983i	$-0.906350\pi$
$349$	−13.6310	−	23.6095i	−0.729648	−	1.26379i	0.227384	−	0.973805i	$-0.426983\pi$
$350$		0			0
$351$	−24.8513	+	11.2995i	−1.32646	+	0.603124i
$352$	0.653988	−	1.13274i	0.0348577	−	0.0603753i
$353$	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	$-0.0559517\pi$
$354$	0.401848	+	1.22582i	0.0213580	+	0.0651514i
$355$	−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
$359$	10.5188	−	18.2191i	0.555161	−	0.961567i	−0.442730	−	0.896655i	$-0.645990\pi$
$359$	10.5188	−	18.2191i	0.555161	−	0.961567i	0.997891	−	0.0649124i	$-0.0206768\pi$
$360$	1.99895	+	0.877459i	0.105354	+	0.0462461i
$361$	7.69132	+	13.3218i	0.404806	+	0.701145i
$362$	−0.986944			−0.0518726
$363$	9.75641	−	10.8929i	0.512079	−	0.571728i
$364$		0			0
$365$	2.92835	−	5.07205i	0.153277	−	0.265483i
$366$	−0.100118	−	0.305404i	−0.00523323	−	0.0159637i
$367$	−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	$0.799263\pi$
$368$	6.09375	+	10.5547i	0.317659	+	0.550201i
$369$	−2.43395	−	22.0449i	−0.126706	−	1.14761i
$370$	−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	$0.842635\pi$
$374$	0.715863			0.0370164
$375$	−4.17408	−	12.7328i	−0.215549	−	0.657520i
$376$	−1.03784			−0.0535227
$377$	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	$0.690759\pi$
$380$	10.1090			0.518583
$381$	−5.90984	−	18.0277i	−0.302770	−	0.923585i
$382$	0.194272			0.00993981
$383$	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
$387$	−30.9409	−	13.5818i	−1.57281	−	0.690403i
$388$	−5.14042	−	8.90346i	−0.260965	−	0.452005i
$389$	−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	$0.297627\pi$
$390$	0.516293	+	1.57493i	0.0261435	+	0.0797494i
$391$	−10.0446	+	17.3978i	−0.507979	+	0.879846i
$392$		0			0
$393$	5.14633	−	5.74580i	0.259598	−	0.289837i
$394$	0.391341			0.0197155
$395$	1.08357	+	1.87680i	0.0545204	+	0.0944321i
$396$	−1.05048	−	9.51452i	−0.0527888	−	0.478122i
$397$	−8.25277	+	14.2942i	−0.414195	+	0.717406i	−0.995344	−	0.0963911i	$-0.969270\pi$
$397$	−8.25277	+	14.2942i	−0.414195	+	0.717406i	0.581149	+	0.813797i	$0.302603\pi$
$398$	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	$-0.348554\pi$
$402$	0.122675	+	0.374215i	0.00611849	+	0.0186641i
$403$	−17.6507	+	30.5720i	−0.879246	+	1.52290i
$404$	−1.84057	+	3.18796i	−0.0915716	+	0.158607i
$405$	23.3967	−	5.23014i	1.16259	−	0.259888i
$406$		0			0
$407$	3.38179	+	5.85743i	0.167629	+	0.290342i
$408$	−2.06682	+	2.30757i	−0.102323	+	0.114242i
$409$	−30.5721			−1.51169			−0.755846	−	0.654750i	$-0.772774\pi$
$409$	−30.5721			−1.51169			−0.755846	+	0.654750i	$0.772774\pi$
$410$	−1.34651			−0.0664993
$411$	−33.1163	−	6.94839i	−1.63350	−	0.342739i
$412$	5.16592	+	8.94763i	0.254507	+	0.440818i
$413$		0			0
$414$	−0.576311	−	0.252978i	−0.0283242	−	0.0124332i
$415$	9.10596	−	15.7720i	0.446994	−	0.774216i
$416$	−2.14863	+	3.72153i	−0.105345	+	0.182463i
$417$	4.45956	+	0.935695i	0.218385	+	0.0458212i
$418$	0.103978	+	0.180094i	0.00508571	+	0.00880871i
$419$	10.8081	−	18.7202i	0.528011	−	0.914542i	−0.471456	−	0.881890i	$-0.656271\pi$
$419$	10.8081	−	18.7202i	0.528011	−	0.914542i	0.999467	−	0.0326524i	$-0.0103954\pi$
$420$		0			0
$421$	13.6217	+	23.5935i	0.663881	+	1.14988i	0.979587	+	0.201019i	$0.0644252\pi$
$421$	13.6217	+	23.5935i	0.663881	+	1.14988i	−0.315706	+	0.948857i	$0.602241\pi$
$422$	0.731046	−	1.26621i	0.0355867	−	0.0616380i
$423$	−9.18554	+	6.74755i	−0.446616	+	0.328077i
$424$	1.21545	+	2.10521i	0.0590273	+	0.102238i
$425$	−13.7215			−0.665592
$426$	0.457046	+	1.39419i	0.0221439	+	0.0675490i
$427$		0			0
$428$	−16.9093	+	29.2877i	−0.817341	+	1.41568i
$429$	9.70868	−	10.8396i	0.468739	−	0.523340i
$430$	−1.02574	+	1.77663i	−0.0494654	+	0.0856765i
$431$	−4.09843	−	7.09869i	−0.197415	−	0.341932i	0.750275	−	0.661126i	$-0.229921\pi$
$431$	−4.09843	−	7.09869i	−0.197415	−	0.341932i	−0.947689	+	0.319194i	$0.896588\pi$
$432$	16.7922	+	11.9996i	0.807914	+	0.577330i
$433$	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
$437$	−5.83585			−0.279167
$438$	−0.173719	+	0.193955i	−0.00830062	+	0.00926752i
$439$	6.58831			0.314443			0.157221	−	0.987563i	$-0.449746\pi$
$439$	6.58831			0.314443			0.157221	+	0.987563i	$0.449746\pi$
$440$	−1.16366			−0.0554753
$441$		0			0
$442$	−2.35191			−0.111869
$443$	28.6912			1.36316			0.681581	−	0.731743i	$-0.261293\pi$
$443$	28.6912			1.36316			0.681581	+	0.731743i	$0.261293\pi$
$444$	−14.3058	−	3.00162i	−0.678925	−	0.142451i
$445$	−1.25350			−0.0594218
$446$	−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	$0.496562\pi$
$450$	−0.0471770	−	0.427295i	−0.00222394	−	0.0201429i
$451$	5.91114	+	10.2384i	0.278345	+	0.482107i
$452$	3.89479	−	6.74598i	0.183196	−	0.317304i
$453$	7.90650	+	1.65893i	0.371480	+	0.0779431i
$454$	0.471393	−	0.816477i	0.0221236	−	0.0383192i
$455$		0			0
$456$	−0.880733	−	0.184794i	−0.0412441	−	0.00865376i
$457$	20.2210			0.945900			0.472950	−	0.881089i	$-0.343189\pi$
$457$	20.2210			0.945900			0.472950	+	0.881089i	$0.343189\pi$
$458$	0.902342	+	1.56290i	0.0421637	+	0.0730296i
$459$	−3.28988	+	33.8608i	−0.153558	+	1.58049i
$460$	8.15440	−	14.1238i	0.380201	−	0.658527i
$461$	−12.1036	−	20.9640i	−0.563719	−	0.976390i	−0.997168	−	0.0752117i	$-0.976037\pi$
$461$	−12.1036	−	20.9640i	−0.563719	−	0.976390i	0.433449	−	0.901178i	$-0.357297\pi$
$462$		0			0
$463$	2.40242	−	4.16111i	0.111650	−	0.193383i	−0.804786	−	0.593565i	$-0.797720\pi$
$463$	2.40242	−	4.16111i	0.111650	−	0.193383i	0.916436	+	0.400182i	$0.131053\pi$
$464$	−12.6885	−	21.9772i	−0.589050	−	1.02026i
$465$	20.6835	−	23.0928i	0.959173	−	1.07090i
$466$	0.432281	−	0.748732i	0.0200250	−	0.0346843i
$467$	13.6228	−	23.5954i	0.630389	−	1.09187i	−0.357083	−	0.934073i	$-0.616229\pi$
$467$	13.6228	−	23.5954i	0.630389	−	1.09187i	0.987472	−	0.157793i	$-0.0504379\pi$
$468$	3.45128	+	31.2592i	0.159535	+	1.44496i
$469$		0			0
$470$	0.345979	+	0.599254i	0.0159588	+	0.0276415i
$471$	2.19755	+	6.70352i	0.101258	+	0.308882i
$472$	2.97565			0.136965
$473$	18.0118			0.828184
$474$	−0.0300130	−	0.0915532i	−0.00137854	−	0.00420518i
$475$	−1.99302	−	3.45202i	−0.0914462	−	0.158389i
$476$		0			0
$477$	24.4445	+	10.7302i	1.11924	+	0.491301i
$478$	0.527601	−	0.913832i	0.0241319	−	0.0417977i
$479$	−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	$0.322022\pi$
$480$	2.51780	−	2.81108i	0.114921	−	0.128308i
$481$	−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
$485$	−6.86254	+	11.8863i	−0.311612	+	0.539727i
$486$	−1.06575	+	0.0139711i	−0.0483435	+	0.000633742i
$487$	−12.9224	−	22.3823i	−0.585571	−	1.01424i	−0.994804	−	0.101809i	$-0.967537\pi$
$487$	−12.9224	−	22.3823i	−0.585571	−	1.01424i	0.409233	−	0.912430i	$-0.365796\pi$
$488$	−0.741363			−0.0335599
$489$	−20.5489	−	4.31153i	−0.929253	−	0.194974i
$490$		0			0
$491$	−7.80775	+	13.5234i	−0.352359	+	0.610303i	−0.986662	−	0.162781i	$-0.947954\pi$
$491$	−7.80775	+	13.5234i	−0.352359	+	0.610303i	0.634303	+	0.773084i	$0.281287\pi$
$492$	−25.0056	−	5.24663i	−1.12734	−	0.236536i
$493$	20.9152	−	36.2261i	0.941971	−	1.63154i
$494$	−0.341610	−	0.591686i	−0.0153698	−	0.0266212i
$495$	−10.2991	+	7.56554i	−0.462909	+	0.340046i
$496$	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	$0.991271\pi$
$500$	−15.4363			−0.690332
$501$	−8.13502	−	1.70687i	−0.363446	−	0.0762574i
$502$	0.379455			0.0169359
$503$	−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
$506$	0.335492			0.0149144
$507$	−16.8744	+	18.8400i	−0.749418	+	0.836714i
$508$	−21.8553			−0.969674
$509$	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
$513$	−8.99645	+	4.09056i	−0.397203	+	0.180603i
$514$	−0.336084	−	0.582115i	−0.0148240	−	0.0256760i
$515$	6.89659	−	11.9452i	0.303900	−	0.526370i
$516$	−25.9712	+	28.9964i	−1.14332	+	1.27650i
$517$	3.03768	−	5.26142i	0.133597	−	0.231397i
$518$		0			0
$519$	−2.71486	−	8.28153i	−0.119169	−	0.363519i
$520$	3.82311			0.167654
$521$	0.713095	+	1.23512i	0.0312413	+	0.0541115i	0.881223	−	0.472700i	$-0.156721\pi$
$521$	0.713095	+	1.23512i	0.0312413	+	0.0541115i	−0.849982	+	0.526812i	$0.823387\pi$
$522$	1.20001	+	0.526756i	0.0525229	+	0.0230555i
$523$	3.85530	−	6.67758i	0.168581	−	0.291990i	−0.769340	−	0.638839i	$-0.779415\pi$
$523$	3.85530	−	6.67758i	0.168581	−	0.291990i	0.937921	+	0.346849i	$0.112748\pi$
$524$	−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
$528$	−10.7670	−	2.25911i	−0.468573	−	0.0983151i
$529$	6.79254	−	11.7650i	0.295328	−	0.511523i
$530$	0.810371	−	1.40360i	0.0352003	−	0.0609686i
$531$	26.3363	−	19.3462i	1.14290	−	0.839554i
$532$		0			0
$533$	−19.4206	−	33.6374i	−0.841198	−	1.45700i
$534$	0.0545409	+	0.0114437i	0.00236021	+	0.000495215i
$535$	45.1483			1.95193
$536$	0.908402			0.0392370
$537$	18.9493	−	21.1566i	0.817721	−	0.912973i
$538$	−1.02441	−	1.77432i	−0.0441653	−	0.0764966i
$539$		0			0
$540$	2.67078	−	27.4888i	0.114932	−	1.18293i
$541$	−14.0228	+	24.2882i	−0.602886	+	1.04423i	0.389495	+	0.921028i	$0.372649\pi$
$541$	−14.0228	+	24.2882i	−0.602886	+	1.04423i	−0.992382	+	0.123201i	$0.960684\pi$
$542$	0.242608	−	0.420209i	0.0104209	−	0.0180495i
$543$	7.78813	+	23.7573i	0.334221	+	1.01952i
$544$	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	0.943818	+	0.330466i	$0.107206\pi$
$547$	17.7305	+	30.7101i	0.758101	+	1.31307i	−0.185717	+	0.982603i	$0.559461\pi$
$548$	−19.4903	+	33.7583i	−0.832586	+	1.44208i
$549$	−6.56150	+	4.81998i	−0.280038	+	0.205712i
$550$	0.114575	+	0.198450i	0.00488550	+	0.00846193i
$551$	12.1515			0.517673
$552$	−0.968623	+	1.08145i	−0.0412273	+	0.0460297i
$553$		0			0
$554$	0.335836	−	0.581685i	0.0142683	−	0.0247134i
$555$	6.07891	+	18.5434i	0.258035	+	0.787124i
$556$	2.62464	−	4.54601i	0.111310	−	0.192794i
$557$	−17.5209	−	30.3472i	−0.742386	−	1.28585i	−0.951406	−	0.307940i	$-0.900361\pi$
$557$	−17.5209	−	30.3472i	−0.742386	−	1.28585i	0.209019	−	0.977911i	$-0.432973\pi$
$558$	−1.11077	+	0.815957i	−0.0470228	+	0.0345422i
$559$	−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
$563$	16.0262			0.675425			0.337712	−	0.941249i	$-0.390347\pi$
$563$	16.0262			0.675425			0.337712	+	0.941249i	$0.390347\pi$
$564$	4.09011	+	12.4767i	0.172225	+	0.525362i
$565$	−10.3992			−0.437499
$566$	−0.206213			−0.00866776
$567$		0			0
$568$	3.38439			0.142006
$569$	0.371302			0.0155658			0.00778290	−	0.999970i	$-0.497523\pi$
$569$	0.371302			0.0155658			0.00778290	+	0.999970i	$0.497523\pi$
$570$	0.186904	+	0.570141i	0.00782855	+	0.0238806i
$571$	29.2304			1.22325			0.611626	−	0.791147i	$-0.290516\pi$
$571$	29.2304			1.22325			0.611626	+	0.791147i	$0.290516\pi$
$572$	−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
$576$	19.0714	−	14.0096i	0.794643	−	0.583732i
$577$	7.52852	+	13.0398i	0.313417	+	0.542853i	0.979100	−	0.203381i	$-0.0651930\pi$
$577$	7.52852	+	13.0398i	0.313417	+	0.542853i	−0.665683	+	0.746235i	$0.731860\pi$
$578$	−0.884279	+	1.53162i	−0.0367811	+	0.0637068i
$579$	−4.76361	−	14.5311i	−0.197969	−	0.603894i
$580$	−16.9793	+	29.4089i	−0.705025	+	1.22114i
$581$		0			0
$582$	0.407107	−	0.454529i	0.0168751	−	0.0188408i
$583$	−14.2300			−0.589347
$584$	0.300307	+	0.520148i	0.0124268	+	0.0215239i
$585$	33.8368	−	24.8560i	1.39898	−	1.02767i
$586$	−0.583171	+	1.01008i	−0.0240906	+	0.0417261i
$587$	−0.835901	−	1.44782i	−0.0345013	−	0.0597580i	0.848259	−	0.529581i	$-0.177651\pi$
$587$	−0.835901	−	1.44782i	−0.0345013	−	0.0597580i	−0.882760	+	0.469823i	$0.844318\pi$
$588$		0			0
$589$	−6.38977	+	11.0674i	−0.263286	+	0.456025i
$590$	−0.991973	−	1.71815i	−0.0408389	−	0.0707350i
$591$	−3.08814	−	9.42020i	−0.127029	−	0.387495i
$592$	−8.39982	+	14.5489i	−0.345231	+	0.597957i
$593$	5.40871	−	9.36816i	0.222109	−	0.384704i	−0.733339	−	0.679863i	$-0.762039\pi$
$593$	5.40871	−	9.36816i	0.222109	−	0.384704i	0.955448	+	0.295159i	$0.0953726\pi$
$594$	0.517188	−	0.235158i	0.0212205	−	0.00964867i
$595$		0			0
$596$	−8.79221	−	15.2286i	−0.360143	−	0.623786i
$597$	13.1911	−	14.7277i	0.539876	−	0.602764i
$598$	−1.10223			−0.0450736
$599$	16.6401			0.679898			0.339949	−	0.940444i	$-0.389590\pi$
$599$	16.6401			0.679898			0.339949	+	0.940444i	$0.389590\pi$
$600$	−0.970498	−	0.203628i	−0.0396204	−	0.00831308i
$601$	12.9011	+	22.3453i	0.526246	+	0.911485i	0.999532	+	0.0305765i	$0.00973432\pi$
$601$	12.9011	+	22.3453i	0.526246	+	0.911485i	−0.473286	+	0.880909i	$0.656932\pi$
$602$		0			0
$603$	8.03989	−	5.90598i	0.327410	−	0.240510i
$604$	4.65332	−	8.05978i	0.189341	−	0.327948i
$605$	−11.2449	+	19.4768i	−0.457171	+	0.791843i
$606$	−0.213828	−	0.0448649i	−0.00868616	−	0.00182251i
$607$	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
$611$	−9.98005	+	17.2860i	−0.403750	+	0.699315i
$612$	35.8862	+	15.7526i	1.45062	+	0.636763i
$613$	6.47719	+	11.2188i	0.261611	+	0.453124i	0.966670	−	0.256025i	$-0.0824129\pi$
$613$	6.47719	+	11.2188i	0.261611	+	0.453124i	−0.705059	+	0.709149i	$0.749080\pi$
$614$	1.58749			0.0640659
$615$	10.6255	+	32.4126i	0.428462	+	1.30700i
$616$		0			0
$617$	16.2202	−	28.0941i	0.652999	−	1.13103i	−0.329393	−	0.944193i	$-0.606844\pi$
$617$	16.2202	−	28.0941i	0.652999	−	1.13103i	0.982391	−	0.186834i	$-0.0598227\pi$
$618$	−0.409127	+	0.456784i	−0.0164575	+	0.0183746i
$619$	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	$-0.0658224\pi$
$620$	−17.8568	−	30.9289i	−0.717146	−	1.24213i
$621$	−1.54181	+	15.8690i	−0.0618708	+	0.636802i
$622$	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
$626$	0.315147			0.0125958
$627$	3.51465	−	3.92406i	0.140362	−	0.156712i
$628$	8.12683			0.324296
$629$	−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	$0.277910\pi$
$632$	−0.222244			−0.00884040
$633$	−36.2484	−	7.60557i	−1.44075	−	0.302294i
$634$	−1.76980			−0.0702877
$635$	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
$639$	29.9538	−	22.0036i	1.18496	−	0.870450i
$640$	−2.89714	−	5.01799i	−0.114519	−	0.198353i
$641$	−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	$0.842781\pi$
$642$	−1.96444	−	0.412174i	−0.0775301	−	0.0162672i
$643$	3.20088	−	5.54409i	0.126230	−	0.218638i	−0.795983	−	0.605319i	$-0.793045\pi$
$643$	3.20088	−	5.54409i	0.126230	−	0.218638i	0.922213	+	0.386682i	$0.126379\pi$
$644$		0			0
$645$	50.8604	+	10.6714i	2.00263	+	0.420187i
$646$	−0.851419			−0.0334986
$647$	1.94403	+	3.36716i	0.0764278	+	0.132377i	0.901706	−	0.432349i	$-0.142315\pi$
$647$	1.94403	+	3.36716i	0.0764278	+	0.132377i	−0.825278	+	0.564726i	$0.808982\pi$
$648$	−0.735183	+	2.34609i	−0.0288807	+	0.0921632i
$649$	−8.70947	+	15.0852i	−0.341877	+	0.592148i
$650$	−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	$0.928827\pi$
$654$	0.671598	−	0.749829i	0.0262616	−	0.0293206i
$655$	−5.93150	+	10.2737i	−0.231763	+	0.401425i
$656$	−14.6823	+	25.4305i	−0.573248	+	0.992895i
$657$	6.03964	+	2.65116i	0.235629	+	0.103432i
$658$		0			0
$659$	−7.13002	−	12.3496i	−0.277746	−	0.481070i	0.693078	−	0.720862i	$-0.256254\pi$
$659$	−7.13002	−	12.3496i	−0.277746	−	0.481070i	−0.970824	+	0.239792i	$0.922921\pi$
$660$	4.58594	+	13.9892i	0.178507	+	0.544528i
$661$	19.4193			0.755323			0.377662	−	0.925944i	$-0.376728\pi$
$661$	19.4193			0.755323			0.377662	+	0.925944i	$0.376728\pi$
$662$	0.0110303			0.000428706
$663$	18.5593	+	56.6142i	0.720783	+	2.19871i
$664$	0.933832	+	1.61744i	0.0362397	+	0.0627690i
$665$		0			0
$666$	−0.0952089	−	0.862333i	−0.00368927	−	0.0334147i
$667$	9.80197	−	16.9775i	0.379534	−	0.657372i
$668$	−4.78781	+	8.29273i	−0.185246	+	0.320855i
$669$	−8.28297	+	9.24781i	−0.320238	+	0.357541i
$670$	−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	0.803190	−	0.595723i	$-0.203135\pi$
$673$	−2.96563	−	5.13663i	−0.114317	−	0.198002i	−0.917506	+	0.397721i	$0.869801\pi$
$674$	0.309512	−	0.536091i	0.0119220	−	0.0206494i
$675$	−9.91337	+	4.50747i	−0.381566	+	0.173493i
$676$	14.5683	+	25.2330i	0.560318	+	0.970500i
$677$	−36.9826			−1.42136			−0.710678	−	0.703518i	$-0.751612\pi$
$677$	−36.9826			−1.42136			−0.710678	+	0.703518i	$0.751612\pi$
$678$	0.452477	+	0.0949379i	0.0173773	+	0.00364607i
$679$		0			0
$680$	2.38215	−	4.12601i	0.0913513	−	0.158225i
$681$	−23.3737	−	4.90423i	−0.895683	−	0.187930i
$682$	0.367336	−	0.636244i	0.0140660	−	0.0243630i
$683$	−6.56800	−	11.3761i	−0.251317	−	0.435294i	0.712571	−	0.701600i	$-0.247530\pi$
$683$	−6.56800	−	11.3761i	−0.251317	−	0.435294i	−0.963889	+	0.266305i	$0.914197\pi$
$684$	1.24940	+	11.3162i	0.0477721	+	0.432685i
$685$	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
$689$	46.7516			1.78109
$690$	0.947338	+	0.198768i	0.0360645	+	0.00756699i
$691$	−14.7658			−0.561719			−0.280860	−	0.959749i	$-0.590620\pi$
$691$	−14.7658			−0.561719			−0.280860	+	0.959749i	$0.590620\pi$
$692$	−10.0399			−0.381659
$693$		0			0
$694$	−0.397915			−0.0151046
$695$	−7.00788			−0.265824
$696$	2.01689	−	2.25182i	0.0764499	−	0.0853552i
$697$	−48.4032			−1.83340
$698$	−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	$0.695107\pi$
$702$	−1.69918	+	0.772594i	−0.0641314	+	0.0291597i
$703$	−4.02217	−	6.96660i	−0.151699	−	0.262750i
$704$	−6.30697	+	10.9240i	−0.237703	+	0.411713i
$705$	11.6948	−	13.0571i	0.440452	−	0.491758i
$706$	0.826969	−	1.43235i	0.0311234	−	0.0539073i
$707$		0			0
$708$	−11.7269	−	35.7724i	−0.440725	−	1.34441i
$709$	14.1030			0.529650			0.264825	−	0.964296i	$-0.414686\pi$
$709$	14.1030			0.529650			0.264825	+	0.964296i	$0.414686\pi$
$710$	−1.12823	−	1.95415i	−0.0423418	−	0.0733381i
$711$	−1.96699	+	1.44492i	−0.0737680	+	0.0541888i
$712$	0.0642745	−	0.111327i	0.00240879	−	0.00417215i
$713$	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
$717$	−26.1608	−	5.48900i	−0.976992	−	0.204990i
$718$	0.719212	−	1.24571i	0.0268408	−	0.0464896i
$719$	7.49790	−	12.9867i	0.279624	−	0.484324i	−0.691667	−	0.722217i	$-0.743123\pi$
$719$	7.49790	−	12.9867i	0.279624	−	0.484324i	0.971291	+	0.237893i	$0.0764567\pi$
$720$	−29.0646	−	12.7582i	−1.08317	−	0.475471i
$721$		0			0
$722$	0.525886	+	0.910861i	0.0195715	+	0.0338987i
$723$	2.00007	+	0.419650i	0.0743833	+	0.0156069i
$724$	28.8015			1.07040
$725$	13.3900			0.497293
$726$	0.667084	−	0.744790i	0.0247578	−	0.0276417i
$727$	13.0527	+	22.6080i	0.484099	+	0.838485i	0.999833	−	0.0182642i	$-0.00581399\pi$
$727$	13.0527	+	22.6080i	0.484099	+	0.838485i	−0.515734	+	0.856749i	$0.672481\pi$
$728$		0			0
$729$	8.74633	+	25.5441i	0.323938	+	0.946078i
$730$	0.200223	−	0.346796i	0.00741059	−	0.0128355i
$731$	−36.8723	+	63.8648i	−1.36377	+	2.36212i
$732$	2.92168	+	8.91245i	0.107989	+	0.329414i
$733$	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
$737$	−2.65881	+	4.60520i	−0.0979386	+	0.169635i
$738$	−0.166419	−	1.50730i	−0.00612595	−	0.0554844i
$739$	−23.2933	−	40.3451i	−0.856857	−	1.48412i	−0.874912	−	0.484282i	$-0.839081\pi$
$739$	−23.2933	−	40.3451i	−0.856857	−	1.48412i	0.0180552	−	0.999837i	$-0.494253\pi$
$740$	22.4806			0.826403
$741$	−11.5471	+	12.8922i	−0.424194	+	0.473606i
$742$		0			0
$743$	−0.169513	+	0.293606i	−0.00621884	+	0.0107713i	−0.869118	−	0.494605i	$-0.835313\pi$
$743$	−0.169513	+	0.293606i	−0.00621884	+	0.0107713i	0.862899	+	0.505376i	$0.168646\pi$
$744$	0.990362	+	3.02105i	0.0363084	+	0.110757i
$745$	−11.7377	+	20.3304i	−0.430038	+	0.744847i
$746$	−0.0385841	−	0.0668297i	−0.00141267	−	0.00244681i
$747$	18.7808	+	8.24402i	0.687153	+	0.301633i
$748$	−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	$0.602399\pi$
$752$	15.0902			0.550284
$753$	−2.99434	−	9.13408i	−0.109120	−	0.332864i
$754$	2.29509			0.0835822
$755$	−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	$0.666377\pi$
$758$	−1.50162			−0.0545415
$759$	−2.64742	−	8.07582i	−0.0960952	−	0.293134i
$760$	1.38401			0.0502033
$761$	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
$765$	−5.74181	−	52.0052i	−0.207596	−	1.88025i
$766$	0.787671	+	1.36429i	0.0284597	+	0.0492937i
$767$	28.6143	−	49.5614i	1.03320	−	1.78956i
$768$	−8.43171	−	25.7205i	−0.304253	−	0.928109i
$769$	1.28876	−	2.23219i	0.0464738	−	0.0804949i	−0.841853	−	0.539707i	$-0.818535\pi$
$769$	1.28876	−	2.23219i	0.0464738	−	0.0804949i	0.888327	+	0.459212i	$0.151868\pi$
$770$		0			0
$771$	−11.3603	+	12.6836i	−0.409132	+	0.456790i
$772$	−17.6164			−0.634030
$773$	3.36486	+	5.82811i	0.121026	+	0.209623i	0.920172	−	0.391513i	$-0.128048\pi$
$773$	3.36486	+	5.82811i	0.121026	+	0.209623i	−0.799147	+	0.601136i	$0.794715\pi$
$774$	−2.11555	−	0.928643i	−0.0760419	−	0.0333794i
$775$	−7.04102	+	12.1954i	−0.252921	+	0.438072i
$776$	−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
$780$	−15.0667	−	45.9603i	−0.539475	−	1.64564i
$781$	−9.90581	+	17.1574i	−0.354458	+	0.613939i
$782$	−0.686792	+	1.18956i	−0.0245596	+	0.0425385i
$783$	3.21039	−	33.0428i	0.114730	−	1.18085i
$784$		0			0
$785$	−5.42473	−	9.39590i	−0.193617	−	0.335354i
$786$	0.351875	−	0.392863i	0.0125510	−	0.0140130i
$787$	−28.6683			−1.02191			−0.510956	−	0.859607i	$-0.670709\pi$
$787$	−28.6683			−1.02191			−0.510956	+	0.859607i	$0.670709\pi$
$788$	−11.4203			−0.406832
$789$	20.2268	+	4.24395i	0.720094	+	0.151089i
$790$	0.0740881	+	0.128324i	0.00263594	+	0.00456558i
$791$		0			0
$792$	−0.143820	−	1.30261i	−0.00511041	−	0.0462864i
$793$	−7.12905	+	12.3479i	−0.253160	+	0.438486i
$794$	−0.564275	+	0.977352i	−0.0200254	+	0.0346849i
$795$	−40.1817	−	8.43085i	−1.42510	−	0.299011i
$796$	−11.3884	−	19.7252i	−0.403650	−	0.699142i
$797$	−11.4913	+	19.9035i	−0.407042	+	0.705017i	−0.994557	−	0.104196i	$-0.966773\pi$
$797$	−11.4913	+	19.9035i	−0.407042	+	0.705017i	0.587515	+	0.809213i	$0.300106\pi$
$798$		0			0
$799$	12.4370	+	21.5415i	0.439989	+	0.762084i
$800$	−0.857104	+	1.48455i	−0.0303032	+	0.0524867i
$801$	−0.154924	−	1.40319i	−0.00547397	−	0.0495792i
$802$	−0.740489	−	1.28256i	−0.0261476	−	0.0452889i
$803$	−3.51589			−0.124073
$804$	−3.57998	−	10.9205i	−0.126256	−	0.385138i
$805$		0			0
$806$	−1.20685	+	2.09033i	−0.0425095	+	0.0736287i
$807$	−34.6270	+	38.6606i	−1.21893	+	1.36092i
$808$	−0.251989	+	0.436457i	−0.00886493	+	0.0153545i
$809$	8.23894	+	14.2703i	0.289666	+	0.501716i	0.973730	−	0.227706i	$-0.0731225\pi$
$809$	8.23894	+	14.2703i	0.289666	+	0.501716i	−0.684064	+	0.729422i	$0.739789\pi$
$810$	1.59972	−	0.357605i	0.0562085	−	0.0125650i
$811$	−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
$815$	32.2911			1.13111
$816$	30.0515	−	33.5520i	1.05201	−	1.17456i
$817$	−21.4225			−0.749479
$818$	−2.09033			−0.0730868
$819$		0			0
$820$	39.2945			1.37222
$821$	−28.1086			−0.980998			−0.490499	−	0.871442i	$-0.663186\pi$
$821$	−28.1086			−0.980998			−0.490499	+	0.871442i	$0.663186\pi$
$822$	−2.26429	−	0.475089i	−0.0789762	−	0.0165706i
$823$	25.9058			0.903019			0.451510	−	0.892266i	$-0.350886\pi$
$823$	25.9058			0.903019			0.451510	+	0.892266i	$0.350886\pi$
$824$	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	$0.600155\pi$
$828$	16.8182	+	7.38254i	0.584474	+	0.256561i
$829$	−7.85344	−	13.6026i	−0.272761	−	0.472436i	0.696807	−	0.717259i	$-0.254604\pi$
$829$	−7.85344	−	13.6026i	−0.272761	−	0.472436i	−0.969568	+	0.244823i	$0.921270\pi$
$830$	0.622611	−	1.07839i	0.0216111	−	0.0374316i
$831$	−16.6522	−	3.49393i	−0.577659	−	0.121203i
$832$	20.7210	−	35.8899i	0.718373	−	1.24426i
$833$		0			0
$834$	0.304918	+	0.0639772i	0.0105584	+	0.00221535i
$835$	12.7836			0.442395
$836$	−3.03433	−	5.25561i	−0.104944	−	0.181769i
$837$	28.4067	+	20.2992i	0.981878	+	0.701644i
$838$	0.738994	−	1.27998i	0.0255281	−	0.0442160i
$839$	3.69822	+	6.40550i	0.127677	+	0.221142i	0.922776	−	0.385337i	$-0.125915\pi$
$839$	3.69822	+	6.40550i	0.127677	+	0.221142i	−0.795099	+	0.606479i	$0.792581\pi$
$840$		0			0
$841$	−5.90986	+	10.2362i	−0.203788	+	0.352971i
$842$	0.931370	+	1.61318i	0.0320971	+	0.0555938i
$843$	27.5929	−	30.8070i	0.950349	−	1.06105i
$844$	−21.3338	+	36.9511i	−0.734338	+	1.27191i
$845$	19.4489	−	33.6865i	0.669062	−	1.15885i
$846$	−0.628052	+	0.461357i	−0.0215929	+	0.0158618i
$847$		0			0
$848$	−17.6725	−	30.6097i	−0.606878	−	1.05114i
$849$	1.62726	+	4.96386i	0.0558473	+	0.170359i
$850$	−0.938196			−0.0321798
$851$	−12.9778			−0.444874
$852$	−13.3378	−	40.6861i	−0.456944	−	1.39388i
$853$	26.5631	+	46.0086i	0.909503	+	1.57530i	0.814756	+	0.579804i	$0.196871\pi$
$853$	26.5631	+	46.0086i	0.909503	+	1.57530i	0.0947464	+	0.995501i	$0.469796\pi$
$854$		0			0
$855$	12.2493	−	8.99815i	0.418917	−	0.307730i
$856$	−2.31502	+	4.00973i	−0.0791257	+	0.137050i
$857$	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	$0.145910\pi$
$858$	0.663821	−	0.741146i	0.0226625	−	0.0253023i
$859$	−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
$863$	−13.3368	+	23.1000i	−0.453989	+	0.786332i	−0.998629	−	0.0523375i	$-0.983333\pi$
$863$	−13.3368	+	23.1000i	−0.453989	+	0.786332i	0.544640	+	0.838670i	$0.316666\pi$
$864$	3.45794	+	2.47103i	0.117642	+	0.0840660i
$865$	6.70171	+	11.6077i	0.227865	+	0.394674i
$866$	0.233475			0.00793380
$867$	43.8464	+	9.19976i	1.48910	+	0.312440i
$868$		0			0
$869$	0.650490	−	1.12668i	0.0220664	−	0.0382200i
$870$	−1.97257	−	0.413880i	−0.0668762	−	0.0140318i
$871$	8.73531	−	15.1300i	0.295985	−	0.512661i
$872$	−1.16099	−	2.01089i	−0.0393160	−	0.0680974i
$873$	−14.1538	−	6.21295i	−0.479033	−	0.210277i
$874$	−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	$0.966215\pi$
$878$	0.450469			0.0152026
$879$	28.9161	+	6.06713i	0.975317	+	0.204639i
$880$	16.9196			0.570358
$881$	−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	$0.705076\pi$
$884$	68.6346			2.30843
$885$	−33.5307	+	37.4365i	−1.12712	+	1.25842i
$886$	1.96173			0.0659058
$887$	−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
$891$	−9.74185	−	10.5939i	−0.326364	−	0.354908i
$892$	7.15098	+	12.3859i	0.239433	+	0.414710i
$893$	−3.61290	+	6.25772i	−0.120901	+	0.209407i
$894$	0.696320	−	0.777431i	0.0232884	−	0.0260012i
$895$	−21.8403	+	37.8285i	−0.730041	+	1.26447i
$896$		0			0
$897$	8.69788	+	26.5324i	0.290414	+	0.885892i
$898$	0.0312964			0.00104437
$899$	−21.4647	−	37.1779i	−0.715887	−	1.23995i
$900$	1.37674	+	12.4695i	0.0458914	+	0.415651i
$901$	29.1306	−	50.4556i	0.970480	−	1.68092i
$902$	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
$906$	0.540599	+	0.113427i	0.0179602	+	0.00376837i
$907$	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	$-0.0732024\pi$
$908$	−13.7564	+	23.8269i	−0.456524	+	0.790722i
$909$	0.607380	+	5.50121i	0.0201455	+	0.182464i
$910$		0			0
$911$	28.8619	+	49.9903i	0.956239	+	1.65625i	0.731508	+	0.681833i	$0.238817\pi$
$911$	28.8619	+	49.9903i	0.956239	+	1.65625i	0.224731	+	0.974421i	$0.427850\pi$
$912$	12.8058	+	2.68689i	0.424043	+	0.0889719i
$913$	−10.9330			−0.361829
$914$	1.38259			0.0457321
$915$	8.35395	−	9.32706i	0.276173	−	0.308343i
$916$	−26.3326	−	45.6094i	−0.870054	−	1.50698i
$917$		0			0
$918$	−0.224942	+	2.31520i	−0.00742419	+	0.0764130i
$919$	25.7799	−	44.6521i	0.850400	−	1.47294i	−0.0304476	−	0.999536i	$-0.509693\pi$
$919$	25.7799	−	44.6521i	0.850400	−	1.47294i	0.880848	−	0.473400i	$-0.156973\pi$
$920$	1.11640	−	1.93367i	0.0368068	−	0.0637512i
$921$	−12.5271	−	38.2134i	−0.412783	−	1.25917i
$922$	−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
$926$	0.164263	−	0.284511i	0.00539801	−	0.00934962i
$927$	14.2240	+	6.24378i	0.467178	+	0.205073i
$928$	−2.61290	−	4.52567i	−0.0857725	−	0.148562i
$929$	−50.2824			−1.64971			−0.824856	−	0.565343i	$-0.808744\pi$
$929$	−50.2824			−1.64971			−0.824856	+	0.565343i	$0.808744\pi$
$930$	1.41421	−	1.57895i	0.0463738	−	0.0517757i
$931$		0			0
$932$	−12.6150	+	21.8499i	−0.413219	+	0.715717i
$933$	−0.966299	−	2.94764i	−0.0316352	−	0.0965016i
$934$	0.931446	−	1.61331i	0.0304779	−	0.0527892i
$935$	13.9447	+	24.1529i	0.456040	+	0.789885i
$936$	0.472508	+	4.27963i	0.0154444	+	0.139884i
$937$	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
$941$	−17.0332			−0.555267			−0.277633	−	0.960687i	$-0.589550\pi$
$941$	−17.0332			−0.555267			−0.277633	+	0.960687i	$0.589550\pi$
$942$	0.150255	+	0.458346i	0.00489559	+	0.0149337i
$943$	−22.6844			−0.738704
$944$	−43.2658			−1.40818
$945$		0			0
$946$	1.23154			0.0400408
$947$	31.5059			1.02381			0.511903	−	0.859044i	$-0.328941\pi$
$947$	31.5059			1.02381			0.511903	+	0.859044i	$0.328941\pi$
$948$	0.875856	+	2.67175i	0.0284465	+	0.0867746i
$949$	11.5512			0.374967
$950$	−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	$0.416197\pi$
$954$	1.67137	+	0.733664i	0.0541125	+	0.0237533i
$955$	3.78433	+	6.55465i	0.122458	+	0.212104i
$956$	−15.3967	+	26.6679i	−0.497966	+	0.862502i
$957$	5.51251	+	16.8156i	0.178194	+	0.543572i
$958$	−0.701705	+	1.21539i	−0.0226711	+	0.0392674i
$959$		0			0
$960$	−24.2813	+	27.1097i	−0.783675	+	0.874962i
$961$	14.1480			0.456388
$962$	−0.759676	−	1.31580i	−0.0244929	−	0.0424230i
$963$	5.58000	+	50.5396i	0.179813	+	1.62862i
$964$	1.17713	−	2.03884i	0.0379126	−	0.0656666i
$965$	11.7591	+	20.3674i	0.378539	+	0.655649i
$966$		0			0
$967$	13.3049	−	23.0448i	0.427857	−	0.741069i	−0.568826	−	0.822458i	$-0.692602\pi$
$967$	13.3049	−	23.0448i	0.427857	−	0.741069i	0.996682	+	0.0813886i	$0.0259355\pi$
$968$	−1.15319	−	1.99738i	−0.0370648	−	0.0641981i
$969$	6.71868	+	20.4950i	0.215835	+	0.658394i
$970$	−0.469219	+	0.812711i	−0.0150657	+	0.0260946i
$971$	28.2839	−	48.9892i	0.907674	−	1.57214i	0.0903867	−	0.995907i	$-0.471190\pi$
$971$	28.2839	−	48.9892i	0.907674	−	1.57214i	0.817287	−	0.576231i	$-0.195477\pi$
$972$	31.1014	−	0.407712i	0.997577	−	0.0130774i
$973$		0			0
$974$	−0.883558	−	1.53037i	−0.0283110	−	0.0490361i
$975$	−12.7240	+	14.2062i	−0.407494	+	0.454961i
$976$	10.7794			0.345040
$977$	53.7560			1.71981			0.859904	−	0.510456i	$-0.170523\pi$
$977$	53.7560			1.71981			0.859904	+	0.510456i	$0.170523\pi$
$978$	−1.40501	−	0.294796i	−0.0449272	−	0.00942654i
$979$	0.376252	+	0.651687i	0.0120251	+	0.0208280i
$980$		0			0
$981$	−23.3493	−	10.2494i	−0.745485	−	0.327238i
$982$	−0.533847	+	0.924650i	−0.0170357	+	0.0295068i
$983$	−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	$0.310670\pi$
$984$	−3.42347	−	0.718306i	−0.109136	−	0.0228988i
$985$	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
$989$	−17.2804	+	29.9305i	−0.549483	+	0.951733i
$990$	−0.704189	+	0.517286i	−0.0223806	+	0.0164404i
$991$	8.66869	+	15.0146i	0.275370	+	0.476955i	0.970228	−	0.242192i	$-0.0778663\pi$
$991$	8.66869	+	15.0146i	0.275370	+	0.476955i	−0.694858	+	0.719147i	$0.744533\pi$
$992$	5.49587			0.174494
$993$	−0.0870420	−	0.265517i	−0.00276220	−	0.00842594i
$994$		0			0
$995$	−15.2037	+	26.3335i	−0.481988	+	0.834828i
$996$	15.7642	−	17.6005i	0.499509	−	0.557694i
$997$	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	$-0.0243576\pi$
$998$	−0.727124	−	1.25942i	−0.0230167	−	0.0398661i
$999$	−20.0064	+	9.09664i	−0.632975	+	0.287805i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.5	✓	24	7.5	odd	6
441.2.f.h.148.6	yes	24	7.2	even	3
441.2.f.h.295.5	yes	24	63.61	odd	6
441.2.f.h.295.6	yes	24	63.16	even	3
441.2.g.h.67.5		24	7.4	even	3
441.2.g.h.67.6		24	7.3	odd	6
441.2.g.h.79.5		24	9.7	even	3
441.2.g.h.79.6		24	63.34	odd	6
441.2.h.h.214.7		24	63.25	even	3	inner
441.2.h.h.214.8		24	63.52	odd	6	inner
441.2.h.h.373.7		24	1.1	even	1	trivial
441.2.h.h.373.8		24	7.6	odd	2	inner
1323.2.f.h.442.7		24	21.2	odd	6
1323.2.f.h.442.8		24	21.5	even	6
1323.2.f.h.883.7		24	63.2	odd	6
1323.2.f.h.883.8		24	63.47	even	6
1323.2.g.h.361.7		24	21.17	even	6
1323.2.g.h.361.8		24	21.11	odd	6
1323.2.g.h.667.7		24	63.20	even	6
1323.2.g.h.667.8		24	9.2	odd	6
1323.2.h.h.226.5		24	21.20	even	2
1323.2.h.h.226.6		24	3.2	odd	2
1323.2.h.h.802.5		24	63.38	even	6
1323.2.h.h.802.6		24	63.11	odd	6
3969.2.a.bh.1.7		12	63.58	even	3
3969.2.a.bh.1.8		12	63.40	odd	6
3969.2.a.bi.1.5		12	63.5	even	6
3969.2.a.bi.1.6		12	63.23	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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.0683740 q^{2} +(-0.539550 - 1.64587i) q^{3} -1.99532 q^{4} +(1.33190 + 2.30691i) q^{5} +(-0.0368912 - 0.112535i) q^{6} -0.273176 q^{8} +(-2.41777 + 1.77606i) q^{9} +O(q^{10})\)	\(q+0.0683740 q^{2} +(-0.539550 - 1.64587i) q^{3} -1.99532 q^{4} +(1.33190 + 2.30691i) q^{5} +(-0.0368912 - 0.112535i) q^{6} -0.273176 q^{8} +(-2.41777 + 1.77606i) q^{9} +(0.0910670 + 0.157733i) q^{10} +(0.799563 - 1.38488i) q^{11} +(1.07658 + 3.28404i) q^{12} +(-2.62690 + 4.54992i) q^{13} +(3.07825 - 3.43682i) q^{15} +3.97197 q^{16} +(3.27360 + 5.67005i) q^{17} +(-0.165313 + 0.121436i) q^{18} +(-0.950968 + 1.64713i) q^{19} +(-2.65756 - 4.60304i) q^{20} +(0.0546693 - 0.0946900i) q^{22} +(1.53419 + 2.65729i) q^{23} +(0.147392 + 0.449612i) q^{24} +(-1.04789 + 1.81500i) q^{25} +(-0.179612 + 0.311096i) q^{26} +(4.22767 + 3.02106i) q^{27} +(-3.19452 - 5.53306i) q^{29} +(0.210472 - 0.234989i) q^{30} +6.71923 q^{31} +0.817932 q^{32} +(-2.71074 - 0.568763i) q^{33} +(0.223829 + 0.387684i) q^{34} +(4.82424 - 3.54381i) q^{36} +(-2.11477 + 3.66290i) q^{37} +(-0.0650215 + 0.112621i) q^{38} +(8.90592 + 1.86862i) q^{39} +(-0.363842 - 0.630193i) q^{40} +(-3.69648 + 6.40249i) q^{41} +(5.63176 + 9.75450i) q^{43} +(-1.59539 + 2.76329i) q^{44} +(-7.31743 - 3.21206i) q^{45} +(0.104898 + 0.181689i) q^{46} +3.79918 q^{47} +(-2.14308 - 6.53735i) q^{48} +(-0.0716485 + 0.124099i) q^{50} +(7.56589 - 8.44720i) q^{51} +(5.24152 - 9.07858i) q^{52} +(-4.44931 - 7.70643i) q^{53} +(0.289062 + 0.206562i) q^{54} +4.25974 q^{55} +(3.22405 + 0.676463i) q^{57} +(-0.218422 - 0.378317i) q^{58} -10.8928 q^{59} +(-6.14211 + 6.85757i) q^{60} +2.71386 q^{61} +0.459420 q^{62} -7.88802 q^{64} -13.9950 q^{65} +(-0.185344 - 0.0388886i) q^{66} -3.32533 q^{67} +(-6.53190 - 11.3136i) q^{68} +(3.54578 - 3.95881i) q^{69} -12.3890 q^{71} +(0.660478 - 0.485177i) q^{72} +(-1.09932 - 1.90407i) q^{73} +(-0.144596 + 0.250447i) q^{74} +(3.55265 + 0.745409i) q^{75} +(1.89749 - 3.28655i) q^{76} +(0.608933 + 0.127765i) q^{78} +0.813556 q^{79} +(5.29025 + 9.16298i) q^{80} +(2.69124 - 8.58820i) q^{81} +(-0.252743 + 0.437764i) q^{82} +(-3.41842 - 5.92088i) q^{83} +(-8.72020 + 15.1038i) q^{85} +(0.385066 + 0.666954i) q^{86} +(-7.38310 + 8.24312i) q^{87} +(-0.218422 + 0.378317i) q^{88} +(-0.235286 + 0.407527i) q^{89} +(-0.500321 - 0.219621i) q^{90} +(-3.06120 - 5.30216i) q^{92} +(-3.62536 - 11.0590i) q^{93} +0.259765 q^{94} -5.06636 q^{95} +(-0.441315 - 1.34621i) q^{96} +(2.57623 + 4.46216i) q^{97} +(0.526472 + 4.76840i) 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