LMFDB - Embedded newform 675.2.l.h.151.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(76,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.76"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([14, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.l (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			151.7
Character	$\chi$	$=$	675.151
Dual form			675.2.l.h.76.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.232949 - 0.195467i) q^{2} +(0.722492 + 1.57417i) q^{3} +(-0.331239 - 1.87855i) q^{4} +(0.139394 - 0.507924i) q^{6} +(0.592777 - 3.36181i) q^{7} +(-0.594126 + 1.02906i) q^{8} +(-1.95601 + 2.27465i) q^{9} +(-2.75854 + 1.00403i) q^{11} +(2.71783 - 1.87866i) q^{12} +(4.21142 - 3.53380i) q^{13} +(-0.795210 + 0.667260i) q^{14} +(-3.24543 + 1.18124i) q^{16} +(-1.05942 - 1.83496i) q^{17} +(0.900269 - 0.147541i) q^{18} +(2.20534 - 3.81976i) q^{19} +(5.72033 - 1.49575i) q^{21} +(0.838853 + 0.305317i) q^{22} +(-0.804944 - 4.56507i) q^{23} +(-2.04916 - 0.191769i) q^{24} -1.67179 q^{26} +(-4.99388 - 1.43567i) q^{27} -6.51167 q^{28} +(-0.308828 - 0.259138i) q^{29} +(-0.573021 - 3.24976i) q^{31} +(3.22009 + 1.17202i) q^{32} +(-3.57353 - 3.61701i) q^{33} +(-0.111885 + 0.634533i) q^{34} +(4.92094 + 2.92101i) q^{36} +(2.03269 + 3.52072i) q^{37} +(-1.26037 + 0.458737i) q^{38} +(8.60551 + 4.07634i) q^{39} +(-3.73852 + 3.13699i) q^{41} +(-1.62491 - 0.769703i) q^{42} +(0.0992511 - 0.0361245i) q^{43} +(2.79985 + 4.84948i) q^{44} +(-0.704810 + 1.22077i) q^{46} +(2.00126 - 11.3497i) q^{47} +(-4.20427 - 4.25542i) q^{48} +(-4.37252 - 1.59147i) q^{49} +(2.12312 - 2.99344i) q^{51} +(-8.03340 - 6.74082i) q^{52} +11.5814 q^{53} +(0.882691 + 1.31058i) q^{54} +(3.10730 + 2.60734i) q^{56} +(7.60629 + 0.711828i) q^{57} +(0.0212882 + 0.120732i) q^{58} +(-5.15923 - 1.87781i) q^{59} +(1.18992 - 6.74834i) q^{61} +(-0.501737 + 0.869034i) q^{62} +(6.48745 + 7.92409i) q^{63} +(2.93269 + 5.07957i) q^{64} +(0.125444 + 1.54108i) q^{66} +(2.92531 - 2.45463i) q^{67} +(-3.09614 + 2.59797i) q^{68} +(6.60462 - 4.56534i) q^{69} +(6.75694 + 11.7034i) q^{71} +(-1.17862 - 3.36427i) q^{72} +(-3.86382 + 6.69232i) q^{73} +(0.214673 - 1.21747i) q^{74} +(-7.90610 - 2.87758i) q^{76} +(1.74014 + 9.86885i) q^{77} +(-1.20785 - 2.63167i) q^{78} +(1.80591 + 1.51534i) q^{79} +(-1.34805 - 8.89847i) q^{81} +1.48406 q^{82} +(5.21978 + 4.37992i) q^{83} +(-4.70463 - 10.2505i) q^{84} +(-0.0301816 - 0.0109852i) q^{86} +(0.184800 - 0.673373i) q^{87} +(0.605720 - 3.43521i) q^{88} +(-0.870723 + 1.50814i) q^{89} +(-9.38352 - 16.2527i) q^{91} +(-8.30907 + 3.02425i) q^{92} +(4.70167 - 3.24996i) q^{93} +(-2.68468 + 2.25271i) q^{94} +(0.481539 + 5.91574i) q^{96} +(0.417944 - 0.152119i) q^{97} +(0.707493 + 1.22541i) q^{98} +(3.11193 - 8.23860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{4} - 6 q^{6} + 18 q^{9} - 6 q^{11} + 18 q^{14} - 24 q^{16} + 6 q^{19} + 24 q^{21} + 30 q^{24} + 48 q^{26} + 30 q^{29} - 30 q^{31} + 24 q^{34} + 54 q^{36} + 6 q^{39} - 12 q^{41} - 78 q^{44}+ \cdots - 36 q^{99}+O(q^{100}) $ 96 * q + 12 * q^4 - 6 * q^6 + 18 * q^9 - 6 * q^11 + 18 * q^14 - 24 * q^16 + 6 * q^19 + 24 * q^21 + 30 * q^24 + 48 * q^26 + 30 * q^29 - 30 * q^31 + 24 * q^34 + 54 * q^36 + 6 * q^39 - 12 * q^41 - 78 * q^44 - 6 * q^46 + 30 * q^49 - 90 * q^51 - 108 * q^54 - 96 * q^56 - 66 * q^59 + 6 * q^61 - 150 * q^66 - 24 * q^69 - 90 * q^71 - 66 * q^74 + 12 * q^76 - 24 * q^79 - 54 * q^81 - 198 * q^84 + 18 * q^86 - 96 * q^89 - 6 * q^91 - 24 * q^94 + 42 * q^96 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.232949	−	0.195467i	−0.164720	−	0.138216i	0.556702	−	0.830712i	$-0.312067\pi$
$2$	−0.232949	−	0.195467i	−0.164720	−	0.138216i	−0.721422	+	0.692496i	$0.756511\pi$
$3$	0.722492	+	1.57417i	0.417131	+	0.908846i
$3$	0.722492	+	1.57417i	0.417131	+	0.908846i
$4$	−0.331239	−	1.87855i	−0.165619	−	0.939274i
$5$		0			0
$5$		0			0
$6$	0.139394	−	0.507924i	0.0569076	−	0.207359i
$7$	0.592777	−	3.36181i	0.224049	−	1.27064i	−0.640446	−	0.768003i	$-0.721251\pi$
$7$	0.592777	−	3.36181i	0.224049	−	1.27064i	0.864495	−	0.502641i	$-0.167638\pi$
$8$	−0.594126	+	1.02906i	−0.210055	+	0.363826i
$9$	−1.95601	+	2.27465i	−0.652003	+	0.758216i
$10$		0			0
$11$	−2.75854	+	1.00403i	−0.831732	+	0.302726i	−0.722569	−	0.691298i	$-0.757039\pi$
$11$	−2.75854	+	1.00403i	−0.831732	+	0.302726i	−0.109162	+	0.994024i	$0.534817\pi$
$12$	2.71783	−	1.87866i	0.784571	−	0.542323i
$13$	4.21142	−	3.53380i	1.16804	−	0.980100i	0.168053	−	0.985778i	$-0.446252\pi$
$13$	4.21142	−	3.53380i	1.16804	−	0.980100i	0.999984	+	0.00567819i	$0.00180744\pi$
$14$	−0.795210	+	0.667260i	−0.212529	+	0.178333i
$15$		0			0
$16$	−3.24543	+	1.18124i	−0.811358	+	0.295310i
$17$	−1.05942	−	1.83496i	−0.256946	−	0.445044i	0.708476	−	0.705735i	$-0.249383\pi$
$17$	−1.05942	−	1.83496i	−0.256946	−	0.445044i	−0.965422	+	0.260691i	$0.916050\pi$
$18$	0.900269	−	0.147541i	0.212195	−	0.0347757i
$19$	2.20534	−	3.81976i	0.505940	−	0.876313i	−0.494037	−	0.869441i	$-0.664479\pi$
$19$	2.20534	−	3.81976i	0.505940	−	0.876313i	0.999976	−	0.00687212i	$-0.00218748\pi$
$20$		0			0
$21$	5.72033	−	1.49575i	1.24828	−	0.326399i
$22$	0.838853	+	0.305317i	0.178844	+	0.0650939i
$23$	−0.804944	−	4.56507i	−0.167843	−	0.951882i	−0.946085	−	0.323918i	$-0.895000\pi$
$23$	−0.804944	−	4.56507i	−0.167843	−	0.951882i	0.778243	−	0.627964i	$-0.216111\pi$
$24$	−2.04916	−	0.191769i	−0.418283	−	0.0391446i
$25$		0			0
$26$	−1.67179			−0.327864
$27$	−4.99388	−	1.43567i	−0.961073	−	0.276295i
$28$	−6.51167			−1.23059
$29$	−0.308828	−	0.259138i	−0.0573480	−	0.0481207i	0.613663	−	0.789568i	$-0.289695\pi$
$29$	−0.308828	−	0.259138i	−0.0573480	−	0.0481207i	−0.671011	+	0.741447i	$0.734140\pi$
$30$		0			0
$31$	−0.573021	−	3.24976i	−0.102918	−	0.583674i	−0.992032	−	0.125989i	$-0.959790\pi$
$31$	−0.573021	−	3.24976i	−0.102918	−	0.583674i	0.889114	−	0.457686i	$-0.151321\pi$
$32$	3.22009	+	1.17202i	0.569238	+	0.207186i
$33$	−3.57353	−	3.61701i	−0.622072	−	0.629640i
$34$	−0.111885	+	0.634533i	−0.0191882	+	0.108821i
$35$		0			0
$36$	4.92094	+	2.92101i	0.820157	+	0.486834i
$37$	2.03269	+	3.52072i	0.334172	+	0.578803i	0.983325	−	0.181854i	$-0.0582100\pi$
$37$	2.03269	+	3.52072i	0.334172	+	0.578803i	−0.649153	+	0.760658i	$0.724877\pi$
$38$	−1.26037	+	0.458737i	−0.204459	+	0.0744169i
$39$	8.60551	+	4.07634i	1.37798	+	0.652736i
$40$		0			0
$41$	−3.73852	+	3.13699i	−0.583859	+	0.489916i	−0.886212	−	0.463280i	$-0.846672\pi$
$41$	−3.73852	+	3.13699i	−0.583859	+	0.489916i	0.302353	+	0.953196i	$0.402228\pi$
$42$	−1.62491	−	0.769703i	−0.250729	−	0.118768i
$43$	0.0992511	−	0.0361245i	0.0151357	−	0.00550893i	−0.334441	−	0.942417i	$-0.608548\pi$
$43$	0.0992511	−	0.0361245i	0.0151357	−	0.00550893i	0.349577	+	0.936908i	$0.386325\pi$
$44$	2.79985	+	4.84948i	0.422093	+	0.731087i
$45$		0			0
$46$	−0.704810	+	1.22077i	−0.103919	+	0.179992i
$47$	2.00126	−	11.3497i	0.291913	−	1.65552i	−0.387577	−	0.921837i	$-0.626688\pi$
$47$	2.00126	−	11.3497i	0.291913	−	1.65552i	0.679490	−	0.733684i	$-0.262201\pi$
$48$	−4.20427	−	4.25542i	−0.606834	−	0.614217i
$49$	−4.37252	−	1.59147i	−0.624646	−	0.227352i
$50$		0			0
$51$	2.12312	−	2.99344i	0.297296	−	0.419166i
$52$	−8.03340	−	6.74082i	−1.11403	−	0.934784i
$53$	11.5814			1.59083			0.795413	−	0.606068i	$-0.207254\pi$
$53$	11.5814			1.59083			0.795413	+	0.606068i	$0.207254\pi$
$54$	0.882691	+	1.31058i	0.120119	+	0.178347i
$55$		0			0
$56$	3.10730	+	2.60734i	0.415231	+	0.348420i
$57$	7.60629	+	0.711828i	1.00748	+	0.0942839i
$58$	0.0212882	+	0.120732i	0.00279528	+	0.0158528i
$59$	−5.15923	−	1.87781i	−0.671674	−	0.244469i	−0.0164056	−	0.999865i	$-0.505222\pi$
$59$	−5.15923	−	1.87781i	−0.671674	−	0.244469i	−0.655269	+	0.755396i	$0.727445\pi$
$60$		0			0
$61$	1.18992	−	6.74834i	0.152353	−	0.864037i	−0.808813	−	0.588066i	$-0.799890\pi$
$61$	1.18992	−	6.74834i	0.152353	−	0.864037i	0.961166	−	0.275971i	$-0.0889993\pi$
$62$	−0.501737	+	0.869034i	−0.0637207	+	0.110367i
$63$	6.48745	+	7.92409i	0.817342	+	0.998341i
$64$	2.93269	+	5.07957i	0.366586	+	0.634946i
$65$		0			0
$66$	0.125444	+	1.54108i	0.0154411	+	0.189694i
$67$	2.92531	−	2.45463i	0.357384	−	0.299881i	−0.446363	−	0.894852i	$-0.647281\pi$
$67$	2.92531	−	2.45463i	0.357384	−	0.299881i	0.803747	+	0.594971i	$0.202837\pi$
$68$	−3.09614	+	2.59797i	−0.375463	+	0.315051i
$69$	6.60462	−	4.56534i	0.795102	−	0.549603i
$70$		0			0
$71$	6.75694	+	11.7034i	0.801901	+	1.38893i	0.918363	+	0.395738i	$0.129511\pi$
$71$	6.75694	+	11.7034i	0.801901	+	1.38893i	−0.116462	+	0.993195i	$0.537155\pi$
$72$	−1.17862	−	3.36427i	−0.138902	−	0.396483i
$73$	−3.86382	+	6.69232i	−0.452225	+	0.783277i	−0.998524	−	0.0543132i	$-0.982703\pi$
$73$	−3.86382	+	6.69232i	−0.452225	+	0.783277i	0.546299	+	0.837591i	$0.316036\pi$
$74$	0.214673	−	1.21747i	0.0249552	−	0.141528i
$75$		0			0
$76$	−7.90610	−	2.87758i	−0.906891	−	0.330082i
$77$	1.74014	+	9.86885i	0.198308	+	1.12466i
$78$	−1.20785	−	2.63167i	−0.136762	−	0.297978i
$79$	1.80591	+	1.51534i	0.203181	+	0.170489i	0.738701	−	0.674034i	$-0.235440\pi$
$79$	1.80591	+	1.51534i	0.203181	+	0.170489i	−0.535520	+	0.844523i	$0.679884\pi$
$80$		0			0
$81$	−1.34805	−	8.89847i	−0.149784	−	0.988719i
$82$	1.48406			0.163887
$83$	5.21978	+	4.37992i	0.572946	+	0.480758i	0.882622	−	0.470084i	$-0.155776\pi$
$83$	5.21978	+	4.37992i	0.572946	+	0.480758i	−0.309676	+	0.950842i	$0.600221\pi$
$84$	−4.70463	−	10.2505i	−0.513317	−	1.11842i
$85$		0			0
$86$	−0.0301816	−	0.0109852i	−0.00325456	−	0.00118456i
$87$	0.184800	−	0.673373i	0.0198127	−	0.0721931i
$88$	0.605720	−	3.43521i	0.0645700	−	0.366195i
$89$	−0.870723	+	1.50814i	−0.0922964	+	0.159862i	−0.908477	−	0.417935i	$-0.862754\pi$
$89$	−0.870723	+	1.50814i	−0.0922964	+	0.159862i	0.816181	+	0.577797i	$0.196087\pi$
$90$		0			0
$91$	−9.38352	−	16.2527i	−0.983660	−	1.70375i
$92$	−8.30907	+	3.02425i	−0.866280	+	0.315300i
$93$	4.70167	−	3.24996i	0.487540	−	0.337005i
$94$	−2.68468	+	2.25271i	−0.276904	+	0.232350i
$95$		0			0
$96$	0.481539	+	5.91574i	0.0491469	+	0.603773i
$97$	0.417944	−	0.152119i	0.0424358	−	0.0154454i	−0.320715	−	0.947176i	$-0.603923\pi$
$97$	0.417944	−	0.152119i	0.0424358	−	0.0154454i	0.363151	+	0.931730i	$0.381701\pi$
$98$	0.707493	+	1.22541i	0.0714676	+	0.123785i
$99$	3.11193	−	8.23860i	0.312760	−	0.828010i
$100$		0			0
$101$	−1.10822	+	6.28500i	−0.110272	+	0.625381i	0.878712	+	0.477353i	$0.158404\pi$
$101$	−1.10822	+	6.28500i	−0.110272	+	0.625381i	−0.988983	+	0.148028i	$0.952707\pi$
$102$	−1.07970	+	0.282319i	−0.106906	+	0.0279537i
$103$	11.4695	+	4.17454i	1.13012	+	0.411330i	0.838335	−	0.545155i	$-0.183529\pi$
$103$	11.4695	+	4.17454i	1.13012	+	0.411330i	0.291783	+	0.956484i	$0.405751\pi$
$104$	1.13437	+	6.43330i	0.111234	+	0.630837i
$105$		0			0
$106$	−2.69787	−	2.26378i	−0.262040	−	0.219878i
$107$	1.69143			0.163517			0.0817585	−	0.996652i	$-0.473946\pi$
$107$	1.69143			0.163517			0.0817585	+	0.996652i	$0.473946\pi$
$108$	−1.04281	+	9.85679i	−0.100345	+	0.948471i
$109$	−15.3531			−1.47056			−0.735279	−	0.677765i	$-0.762949\pi$
$109$	−15.3531			−1.47056			−0.735279	+	0.677765i	$0.762949\pi$
$110$		0			0
$111$	−4.07361	+	5.74349i	−0.386650	+	0.545148i
$112$	2.04729	+	11.6107i	0.193450	+	1.09711i
$113$	−14.7288	−	5.36085i	−1.38557	−	0.504307i	−0.461709	−	0.887031i	$-0.652764\pi$
$113$	−14.7288	−	5.36085i	−1.38557	−	0.504307i	−0.923862	+	0.382725i	$0.874986\pi$
$114$	−1.63273	−	1.65260i	−0.152920	−	0.154780i
$115$		0			0
$116$	−0.384507	+	0.665985i	−0.0357005	+	0.0618352i
$117$	−0.199423	+	16.4916i	−0.0184366	+	1.52465i
$118$	0.834786	+	1.44589i	0.0768483	+	0.133105i
$119$	−6.79679	+	2.47383i	−0.623060	+	0.226775i
$120$		0			0
$121$	−1.82501	+	1.53136i	−0.165910	+	0.139215i
$122$	−1.59627	+	1.33943i	−0.144519	+	0.121266i
$123$	−7.63921	−	3.61861i	−0.688804	−	0.326279i
$124$	−5.91503	+	2.15289i	−0.531185	+	0.193336i
$125$		0			0
$126$	0.0376555	−	3.11399i	0.00335462	−	0.277416i
$127$	−6.46736	+	11.2018i	−0.573885	+	0.993998i	0.422277	+	0.906467i	$0.361231\pi$
$127$	−6.46736	+	11.2018i	−0.573885	+	0.993998i	−0.996162	+	0.0875312i	$0.972102\pi$
$128$	1.49982	−	8.50591i	0.132567	−	0.751823i
$129$	0.128574	+	0.130138i	0.0113203	+	0.0114580i
$130$		0			0
$131$	1.99841	+	11.3335i	0.174602	+	0.990215i	0.938603	+	0.345000i	$0.112121\pi$
$131$	1.99841	+	11.3335i	0.174602	+	0.990215i	−0.764001	+	0.645215i	$0.776768\pi$
$132$	−5.61103	+	7.91114i	−0.488377	+	0.688577i
$133$	−11.5340	−	9.67820i	−1.00013	−	0.839206i
$134$	−1.16125			−0.100316
$135$		0			0
$136$	2.51770			0.215891
$137$	9.34126	+	7.83825i	0.798078	+	0.669667i	0.947731	−	0.319072i	$-0.103371\pi$
$137$	9.34126	+	7.83825i	0.798078	+	0.669667i	−0.149653	+	0.988739i	$0.547816\pi$
$138$	−2.43091	−	0.227495i	−0.206933	−	0.0193656i
$139$	0.0420242	+	0.238331i	0.00356445	+	0.0202150i	0.986538	−	0.163532i	$-0.0522886\pi$
$139$	0.0420242	+	0.238331i	0.00356445	+	0.0202150i	−0.982974	+	0.183747i	$0.941177\pi$
$140$		0			0
$141$	19.3122	−	5.04975i	1.62638	−	0.425265i
$142$	0.713602	−	4.04704i	0.0598842	−	0.339620i
$143$	−8.06934	+	13.9765i	−0.674792	+	1.16877i
$144$	3.66119	−	9.69273i	0.305099	−	0.807728i
$145$		0			0
$146$	2.20820	−	0.803719i	0.182752	−	0.0665163i
$147$	−0.653875	−	8.03290i	−0.0539307	−	0.662543i
$148$	5.94054	−	4.98470i	0.488309	−	0.409740i
$149$	9.73479	−	8.16846i	0.797505	−	0.669186i	−0.150086	−	0.988673i	$-0.547955\pi$
$149$	9.73479	−	8.16846i	0.797505	−	0.669186i	0.947591	+	0.319487i	$0.103511\pi$
$150$		0			0
$151$	4.13101	−	1.50356i	0.336177	−	0.122358i	−0.168416	−	0.985716i	$-0.553865\pi$
$151$	4.13101	−	1.50356i	0.336177	−	0.122358i	0.504592	+	0.863358i	$0.331643\pi$
$152$	2.62050	+	4.53883i	0.212550	+	0.368148i
$153$	6.24612	+	1.17940i	0.504969	+	0.0953492i
$154$	1.52367	−	2.63908i	0.122781	−	0.212663i
$155$		0			0
$156$	4.80712	−	17.5161i	0.384877	−	1.40241i
$157$	4.64345	+	1.69008i	0.370587	+	0.134883i	0.520599	−	0.853802i	$-0.325709\pi$
$157$	4.64345	+	1.69008i	0.370587	+	0.134883i	−0.150011	+	0.988684i	$0.547931\pi$
$158$	−0.124486	−	0.705992i	−0.00990353	−	0.0561657i
$159$	8.36746	+	18.2310i	0.663583	+	1.44582i
$160$		0			0
$161$	−15.8240			−1.24711
$162$	−1.42533	+	2.33639i	−0.111985	+	0.183564i
$163$	0.134430			0.0105294			0.00526468	−	0.999986i	$-0.498324\pi$
$163$	0.134430			0.0105294			0.00526468	+	0.999986i	$0.498324\pi$
$164$	7.13134	+	5.98390i	0.556864	+	0.467264i
$165$		0			0
$166$	−0.359811	−	2.04059i	−0.0279268	−	0.158381i
$167$	−14.3623	−	5.22746i	−1.11139	−	0.404513i	−0.279887	−	0.960033i	$-0.590297\pi$
$167$	−14.3623	−	5.22746i	−1.11139	−	0.404513i	−0.831503	+	0.555520i	$0.812519\pi$
$168$	−1.85938	+	6.77520i	−0.143455	+	0.522718i
$169$	2.99088	−	16.9621i	0.230068	−	1.30478i
$170$		0			0
$171$	4.37495	+	12.4879i	0.334561	+	0.954971i
$172$	−0.100737	−	0.174482i	−0.00768115	−	0.0133041i
$173$	14.2120	−	5.17275i	1.08052	−	0.393277i	0.260419	−	0.965496i	$-0.416139\pi$
$173$	14.2120	−	5.17275i	1.08052	−	0.393277i	0.820101	+	0.572218i	$0.193917\pi$
$174$	−0.174671	+	0.120739i	−0.0132418	+	0.00915319i
$175$		0			0
$176$	7.76666	−	6.51700i	0.585434	−	0.491238i
$177$	−0.771521	−	9.47819i	−0.0579911	−	0.712424i
$178$	0.497625	−	0.181121i	0.0372985	−	0.0135756i
$179$	−0.794987	−	1.37696i	−0.0594201	−	0.102919i	0.834785	−	0.550576i	$-0.185592\pi$
$179$	−0.794987	−	1.37696i	−0.0594201	−	0.102919i	−0.894205	+	0.447657i	$0.852258\pi$
$180$		0			0
$181$	−10.8756	+	18.8371i	−0.808375	+	1.40015i	0.105613	+	0.994407i	$0.466319\pi$
$181$	−10.8756	+	18.8371i	−0.808375	+	1.40015i	−0.913989	+	0.405740i	$0.867014\pi$
$182$	−0.990997	+	5.62022i	−0.0734576	+	0.416599i
$183$	11.4827	−	3.00250i	0.848828	−	0.221951i
$184$	5.17595	+	1.88389i	0.381576	+	0.138882i
$185$		0			0
$186$	−1.73051	−	0.161948i	−0.126887	−	0.0118746i
$187$	4.76479	+	3.99814i	0.348436	+	0.292373i
$188$	−21.9838			−1.60333
$189$	−7.78671	+	15.9374i	−0.566400	+	1.15928i
$190$		0			0
$191$	−6.03626	−	5.06502i	−0.436768	−	0.366492i	0.397730	−	0.917502i	$-0.369798\pi$
$191$	−6.03626	−	5.06502i	−0.436768	−	0.366492i	−0.834498	+	0.551010i	$0.814242\pi$
$192$	−5.87725	+	8.28650i	−0.424154	+	0.598026i
$193$	3.10054	+	17.5840i	0.223182	+	1.26573i	0.866131	+	0.499817i	$0.166599\pi$
$193$	3.10054	+	17.5840i	0.223182	+	1.26573i	−0.642950	+	0.765909i	$0.722290\pi$
$194$	−0.127094	−	0.0462583i	−0.00912480	−	0.00332115i
$195$		0			0
$196$	−1.54130	+	8.74114i	−0.110093	+	0.624367i
$197$	−4.75730	+	8.23989i	−0.338944	+	0.587068i	−0.984234	−	0.176870i	$-0.943403\pi$
$197$	−4.75730	+	8.23989i	−0.338944	+	0.587068i	0.645291	+	0.763937i	$0.276736\pi$
$198$	−2.33529	+	1.31089i	−0.165962	+	0.0931610i
$199$	5.46922	+	9.47297i	0.387703	+	0.671521i	0.992140	−	0.125132i	$-0.0399353\pi$
$199$	5.46922	+	9.47297i	0.387703	+	0.671521i	−0.604437	+	0.796653i	$0.706602\pi$
$200$		0			0
$201$	5.97751	+	2.83148i	0.421621	+	0.199717i
$202$	1.48667	−	1.24746i	0.104602	−	0.0877712i
$203$	−1.05424	+	0.884610i	−0.0739930	+	0.0620875i
$204$	−6.32659	−	2.99684i	−0.442950	−	0.209820i
$205$		0			0
$206$	−1.85581	−	3.21435i	−0.129300	−	0.223955i
$207$	11.9584	+	7.09835i	0.831166	+	0.493369i
$208$	−9.49360	+	16.4434i	−0.658263	+	1.14014i
$209$	−2.24838	+	12.7512i	−0.155524	+	0.882018i
$210$		0			0
$211$	9.58727	+	3.48948i	0.660015	+	0.240226i	0.650243	−	0.759727i	$-0.274667\pi$
$211$	9.58727	+	3.48948i	0.660015	+	0.240226i	0.00977203	+	0.999952i	$0.496889\pi$
$212$	−3.83620	−	21.7562i	−0.263471	−	1.49422i
$213$	−13.5412	+	19.0921i	−0.927829	+	1.30817i
$214$	−0.394017	−	0.330619i	−0.0269344	−	0.0226007i
$215$		0			0
$216$	4.44438	−	4.28601i	0.302402	−	0.291626i
$217$	−11.2647			−0.764701
$218$	3.57648	+	3.00102i	0.242230	+	0.203255i
$219$	−13.3264	−	1.24714i	−0.900516	−	0.0842740i
$220$		0			0
$221$	−10.9460	−	3.98403i	−0.736310	−	0.267995i
$222$	2.07160	−	0.541682i	0.139037	−	0.0363553i
$223$	3.98483	−	22.5991i	0.266844	−	1.51335i	−0.496888	−	0.867815i	$-0.665524\pi$
$223$	3.98483	−	22.5991i	0.266844	−	1.51335i	0.763732	−	0.645534i	$-0.223365\pi$
$224$	5.84890	−	10.1306i	0.390796	−	0.676879i
$225$		0			0
$226$	2.38319	+	4.12780i	0.158527	+	0.274577i
$227$	6.71417	−	2.44376i	0.445635	−	0.162198i	−0.109448	−	0.993992i	$-0.534908\pi$
$227$	6.71417	−	2.44376i	0.445635	−	0.162198i	0.555084	+	0.831794i	$0.312686\pi$
$228$	−1.18229	−	14.5246i	−0.0782993	−	0.961912i
$229$	14.3264	−	12.0213i	0.946713	−	0.794387i	−0.0320278	−	0.999487i	$-0.510197\pi$
$229$	14.3264	−	12.0213i	0.946713	−	0.794387i	0.978741	+	0.205100i	$0.0657521\pi$
$230$		0			0
$231$	−14.2780	+	9.86945i	−0.939423	+	0.649362i
$232$	0.450150	−	0.163841i	0.0295538	−	0.0107567i
$233$	12.3190	+	21.3371i	0.807043	+	1.39784i	0.914903	+	0.403673i	$0.132267\pi$
$233$	12.3190	+	21.3371i	0.807043	+	1.39784i	−0.107861	+	0.994166i	$0.534400\pi$
$234$	3.27003	−	3.80273i	0.213768	−	0.248592i
$235$		0			0
$236$	−1.81861	+	10.3139i	−0.118382	+	0.671375i
$237$	−1.08064	+	3.93763i	−0.0701952	+	0.255776i
$238$	2.06685	+	0.752273i	0.133974	+	0.0487626i
$239$	3.02299	+	17.1443i	0.195541	+	1.10897i	0.911646	+	0.410977i	$0.134812\pi$
$239$	3.02299	+	17.1443i	0.195541	+	1.10897i	−0.716105	+	0.697993i	$0.754077\pi$
$240$		0			0
$241$	−5.58320	−	4.68486i	−0.359646	−	0.301778i	0.445004	−	0.895529i	$-0.353202\pi$
$241$	−5.58320	−	4.68486i	−0.359646	−	0.301778i	−0.804649	+	0.593750i	$0.797647\pi$
$242$	0.724464			0.0465703
$243$	13.0337	−	8.55114i	0.836114	−	0.548556i
$244$	−13.0712			−0.836800
$245$		0			0
$246$	1.07222	+	2.33616i	0.0683625	+	0.148948i
$247$	−4.21066	−	23.8798i	−0.267918	−	1.51944i
$248$	3.68463	+	1.34110i	0.233974	+	0.0851597i
$249$	−3.12347	+	11.3813i	−0.197942	+	0.721259i
$250$		0			0
$251$	11.4223	−	19.7840i	0.720971	−	1.24876i	−0.239641	−	0.970862i	$-0.577030\pi$
$251$	11.4223	−	19.7840i	0.720971	−	1.24876i	0.960611	−	0.277896i	$-0.0896371\pi$
$252$	12.7369	−	14.8118i	0.802348	−	0.933053i
$253$	6.80392	+	11.7847i	0.427759	+	0.740900i
$254$	3.69614	−	1.34529i	0.231917	−	0.0844108i
$255$		0			0
$256$	6.97428	−	5.85212i	0.435892	−	0.365757i
$257$	−1.12718	+	0.945818i	−0.0703117	+	0.0589985i	−0.677266	−	0.735738i	$-0.736835\pi$
$257$	−1.12718	+	0.945818i	−0.0703117	+	0.0589985i	0.606955	+	0.794737i	$0.292391\pi$
$258$	−0.00451341	−	0.0554476i	−0.000280993	−	0.00345201i
$259$	13.0409	−	4.74651i	0.810324	−	0.294934i
$260$		0			0
$261$	1.19352	−	0.195600i	0.0738769	−	0.0121073i
$262$	1.74981	−	3.03075i	0.108103	−	0.187241i
$263$	3.75201	−	21.2787i	0.231359	−	1.31210i	−0.618790	−	0.785557i	$-0.712377\pi$
$263$	3.75201	−	21.2787i	0.231359	−	1.31210i	0.850148	−	0.526543i	$-0.176512\pi$
$264$	5.84523	−	1.52841i	0.359749	−	0.0940670i
$265$		0			0
$266$	0.795066	+	4.50905i	0.0487486	+	0.276467i
$267$	−3.00315	−	0.281047i	−0.183790	−	0.0171998i
$268$	−5.58012	−	4.68227i	−0.340860	−	0.286015i
$269$	−13.3362			−0.813125			−0.406562	−	0.913623i	$-0.633273\pi$
$269$	−13.3362			−0.813125			−0.406562	+	0.913623i	$0.633273\pi$
$270$		0			0
$271$	19.7312			1.19859			0.599293	−	0.800530i	$-0.295448\pi$
$271$	19.7312			1.19859			0.599293	+	0.800530i	$0.295448\pi$
$272$	5.60579	+	4.70382i	0.339901	+	0.285211i
$273$	18.8050	−	26.5137i	1.13813	−	1.60468i
$274$	−0.643914	−	3.65182i	−0.0389003	−	0.220614i
$275$		0			0
$276$	−10.7639	−	10.8949i	−0.647912	−	0.655794i
$277$	−4.60416	+	26.1115i	−0.276637	+	1.56889i	0.457075	+	0.889428i	$0.348897\pi$
$277$	−4.60416	+	26.1115i	−0.276637	+	1.56889i	−0.733712	+	0.679460i	$0.762214\pi$
$278$	0.0367964	−	0.0637333i	0.00220690	−	0.00382247i
$279$	8.51290	+	5.05314i	0.509654	+	0.302524i
$280$		0			0
$281$	−6.13842	+	2.23420i	−0.366188	+	0.133281i	−0.518559	−	0.855042i	$-0.673531\pi$
$281$	−6.13842	+	2.23420i	−0.366188	+	0.133281i	0.152371	+	0.988323i	$0.451309\pi$
$282$	−5.48581	−	2.59857i	−0.326675	−	0.154742i
$283$	−4.92140	+	4.12955i	−0.292547	+	0.245476i	−0.777234	−	0.629212i	$-0.783378\pi$
$283$	−4.92140	+	4.12955i	−0.292547	+	0.245476i	0.484687	+	0.874688i	$0.338933\pi$
$284$	19.7472	−	16.5698i	1.17178	−	0.983239i
$285$		0			0
$286$	4.61169	−	1.67852i	0.272695	−	0.0992529i
$287$	8.32986	+	14.4277i	0.491696	+	0.851642i
$288$	−8.96447	+	5.03210i	−0.528236	+	0.296520i
$289$	6.25528	−	10.8345i	0.367957	−	0.637321i
$290$		0			0
$291$	0.541422	+	0.548009i	0.0317387	+	0.0321248i
$292$	13.8517	+	5.04161i	0.810609	+	0.295038i
$293$	−2.42943	−	13.7780i	−0.141929	−	0.804919i	−0.969782	−	0.243974i	$-0.921549\pi$
$293$	−2.42943	−	13.7780i	−0.141929	−	0.804919i	0.827853	−	0.560945i	$-0.189562\pi$
$294$	−1.41785	+	1.99906i	−0.0826906	+	0.116588i
$295$		0			0
$296$	−4.83069			−0.280778
$297$	15.2173	−	1.05363i	0.882996	−	0.0611379i
$298$	−3.86437			−0.223857
$299$	−19.5220	−	16.3809i	−1.12899	−	0.947332i
$300$		0			0
$301$	−0.0626096	−	0.355077i	−0.00360876	−	0.0204663i
$302$	−1.25621	−	0.457223i	−0.0722868	−	0.0263102i
$303$	−10.6943	+	2.79635i	−0.614373	+	0.160646i
$304$	−2.64522	+	15.0018i	−0.151714	+	0.860413i
$305$		0			0
$306$	−1.22449	−	1.49565i	−0.0699995	−	0.0855007i
$307$	−7.92646	−	13.7290i	−0.452387	−	0.783557i	0.546147	−	0.837689i	$-0.316094\pi$
$307$	−7.92646	−	13.7290i	−0.452387	−	0.783557i	−0.998534	+	0.0541324i	$0.982761\pi$
$308$	17.9627	−	6.53789i	1.02352	−	0.372531i
$309$	1.71517	+	21.0709i	0.0975723	+	1.19868i
$310$		0			0
$311$	11.9922	−	10.0626i	0.680015	−	0.570600i	−0.235996	−	0.971754i	$-0.575835\pi$
$311$	11.9922	−	10.0626i	0.680015	−	0.570600i	0.916011	+	0.401154i	$0.131391\pi$
$312$	−9.30753	+	6.43369i	−0.526935	+	0.364236i
$313$	0.953980	−	0.347220i	0.0539221	−	0.0196261i	−0.314918	−	0.949119i	$-0.601977\pi$
$313$	0.953980	−	0.347220i	0.0539221	−	0.0196261i	0.368840	+	0.929493i	$0.379755\pi$
$314$	−0.751330	−	1.30134i	−0.0424000	−	0.0734390i
$315$		0			0
$316$	2.24845	−	3.89443i	0.126485	−	0.219079i
$317$	2.00474	−	11.3695i	0.112598	−	0.638573i	−0.875314	−	0.483555i	$-0.839345\pi$
$317$	2.00474	−	11.3695i	0.112598	−	0.638573i	0.987912	−	0.155018i	$-0.0495436\pi$
$318$	1.61438	−	5.88246i	0.0905300	−	0.329872i
$319$	1.11210	+	0.404770i	0.0622655	+	0.0226628i
$320$		0			0
$321$	1.22205	+	2.66260i	0.0682080	+	0.148612i
$322$	3.68619	+	3.09308i	0.205423	+	0.172370i
$323$	−9.34549			−0.519997
$324$	−16.2697	+	5.47990i	−0.903871	+	0.304439i
$325$		0			0
$326$	−0.0313152	−	0.0262766i	−0.00173439	−	0.00145533i
$327$	−11.0925	−	24.1683i	−0.613415	−	1.33651i
$328$	−1.00699	−	5.71092i	−0.0556017	−	0.315333i
$329$	−36.9692	−	13.4557i	−2.03818	−	0.741835i
$330$		0			0
$331$	−0.601404	+	3.41073i	−0.0330562	+	0.187471i	−0.996865	−	0.0791244i	$-0.974788\pi$
$331$	−0.601404	+	3.41073i	−0.0330562	+	0.187471i	0.963809	+	0.266595i	$0.0858987\pi$
$332$	6.49889	−	11.2564i	0.356673	−	0.617776i
$333$	−11.9844	−	2.26291i	−0.656739	−	0.124007i
$334$	2.32389	+	4.02509i	0.127157	+	0.220243i
$335$		0			0
$336$	−16.7981	+	11.6114i	−0.916411	+	0.633456i
$337$	−0.116311	+	0.0975969i	−0.00633589	+	0.00531644i	−0.645950	−	0.763380i	$-0.723539\pi$
$337$	−0.116311	+	0.0975969i	−0.00633589	+	0.00531644i	0.639614	+	0.768696i	$0.279094\pi$
$338$	−4.01226	+	3.36668i	−0.218238	+	0.183123i
$339$	−2.20258	−	27.0588i	−0.119628	−	1.46963i
$340$		0			0
$341$	4.84355	+	8.38927i	0.262293	+	0.454305i
$342$	1.42183	−	3.76419i	0.0768837	−	0.203544i
$343$	4.00571	−	6.93809i	0.216288	−	0.374622i
$344$	−0.0217936	+	0.123597i	−0.00117503	+	0.00666392i
$345$		0			0
$346$	−4.32178	−	1.57300i	−0.232340	−	0.0845649i
$347$	−3.60850	−	20.4648i	−0.193714	−	1.09861i	−0.914238	−	0.405178i	$-0.867210\pi$
$347$	−3.60850	−	20.4648i	−0.193714	−	1.09861i	0.720524	−	0.693430i	$-0.243901\pi$
$348$	−1.32618	−	0.124109i	−0.0710905	−	0.00665294i
$349$	−4.76037	−	3.99442i	−0.254817	−	0.213816i	0.506427	−	0.862283i	$-0.330966\pi$
$349$	−4.76037	−	3.99442i	−0.254817	−	0.213816i	−0.761243	+	0.648467i	$0.775411\pi$
$350$		0			0
$351$	−26.1047	+	11.6012i	−1.39337	+	0.619224i
$352$	−10.0595			−0.536173
$353$	−4.58839	−	3.85011i	−0.244215	−	0.204921i	0.512461	−	0.858710i	$-0.328734\pi$
$353$	−4.58839	−	3.85011i	−0.244215	−	0.204921i	−0.756677	+	0.653789i	$0.773178\pi$
$354$	−1.67295	+	2.35874i	−0.0889163	+	0.125366i
$355$		0			0
$356$	3.12152	+	1.13614i	0.165440	+	0.0602154i
$357$	−8.80485	−	8.91196i	−0.466002	−	0.471671i
$358$	−0.0839588	+	0.476154i	−0.00443736	+	0.0251655i
$359$	0.255829	−	0.443109i	0.0135022	−	0.0233864i	−0.859195	−	0.511648i	$-0.829035\pi$
$359$	0.255829	−	0.443109i	0.0135022	−	0.0233864i	0.872698	+	0.488261i	$0.162369\pi$
$360$		0			0
$361$	−0.227046	−	0.393256i	−0.0119498	−	0.0206977i
$362$	6.21548	−	2.26225i	0.326678	−	0.118901i
$363$	−3.72918	−	1.76647i	−0.195731	−	0.0927157i
$364$	−27.4234	+	23.0109i	−1.43737	+	1.20610i
$365$		0			0
$366$	−3.26178	−	1.54507i	−0.170496	−	0.0807620i
$367$	19.2963	−	7.02326i	1.00726	−	0.366611i	0.214878	−	0.976641i	$-0.431065\pi$
$367$	19.2963	−	7.02326i	1.00726	−	0.366611i	0.792378	+	0.610030i	$0.208843\pi$
$368$	8.00483	+	13.8648i	0.417281	+	0.722752i
$369$	0.177030	−	14.6398i	0.00921581	−	0.762118i
$370$		0			0
$371$	6.86518	−	38.9344i	0.356423	−	2.02137i
$372$	−7.66258	−	7.75580i	−0.397286	−	0.402119i
$373$	11.7902	+	4.29128i	0.610472	+	0.222194i	0.628710	−	0.777640i	$-0.283583\pi$
$373$	11.7902	+	4.29128i	0.610472	+	0.222194i	−0.0182375	+	0.999834i	$0.505805\pi$
$374$	−0.328448	−	1.86272i	−0.0169836	−	0.0963190i
$375$		0			0
$376$	10.4905	+	8.80254i	0.541004	+	0.453956i
$377$	−2.21635			−0.114148
$378$	4.92915	−	2.19056i	0.253528	−	0.112670i
$379$	29.8914			1.53542			0.767710	−	0.640798i	$-0.221396\pi$
$379$	29.8914			1.53542			0.767710	+	0.640798i	$0.221396\pi$
$380$		0			0
$381$	−22.3061	−	2.08750i	−1.14278	−	0.106946i
$382$	0.416093	+	2.35978i	0.0212892	+	0.120737i
$383$	−20.4840	−	7.45556i	−1.04668	−	0.380961i	−0.239273	−	0.970952i	$-0.576909\pi$
$383$	−20.4840	−	7.45556i	−1.04668	−	0.380961i	−0.807410	+	0.589991i	$0.799131\pi$
$384$	14.4733	−	3.78448i	0.738589	−	0.193126i
$385$		0			0
$386$	2.71483	−	4.70223i	0.138181	−	0.239337i
$387$	−0.111966	+	0.296421i	−0.00569154	+	0.0150679i
$388$	−0.424202	−	0.734740i	−0.0215356	−	0.0373008i
$389$	9.78677	−	3.56209i	0.496209	−	0.180605i	−0.0817791	−	0.996650i	$-0.526060\pi$
$389$	9.78677	−	3.56209i	0.496209	−	0.180605i	0.577988	+	0.816045i	$0.303838\pi$
$390$		0			0
$391$	−7.52395	+	6.31335i	−0.380503	+	0.319280i
$392$	4.23553	−	3.55403i	0.213927	−	0.179506i
$393$	−16.3971	+	11.3342i	−0.827122	+	0.571736i
$394$	2.71883	−	0.989574i	0.136973	−	0.0498540i
$395$		0			0
$396$	−16.5074	−	3.11696i	−0.829528	−	0.156633i
$397$	10.9269	−	18.9260i	0.548406	−	0.949866i	−0.449978	−	0.893039i	$-0.648568\pi$
$397$	10.9269	−	18.9260i	0.548406	−	0.949866i	0.998384	−	0.0568270i	$-0.0180983\pi$
$398$	0.577606	−	3.27577i	0.0289528	−	0.164199i
$399$	6.90186	−	25.1489i	0.345525	−	1.25902i
$400$		0			0
$401$	−3.50040	−	19.8518i	−0.174802	−	0.991351i	−0.938372	−	0.345626i	$-0.887667\pi$
$401$	−3.50040	−	19.8518i	−0.174802	−	0.991351i	0.763570	−	0.645725i	$-0.223445\pi$
$402$	−0.838992	−	1.82800i	−0.0418451	−	0.0911722i
$403$	−13.8972	−	11.6612i	−0.692271	−	0.580884i
$404$	12.1738			0.605667
$405$		0			0
$406$	0.418495			0.0207696
$407$	−9.14216	−	7.67118i	−0.453160	−	0.380246i
$408$	1.81902	+	3.96329i	0.0900550	+	0.196212i
$409$	2.34346	+	13.2904i	0.115876	+	0.657168i	0.986313	+	0.164887i	$0.0527258\pi$
$409$	2.34346	+	13.2904i	0.115876	+	0.657168i	−0.870436	+	0.492282i	$0.836163\pi$
$410$		0			0
$411$	−5.58973	+	20.3678i	−0.275721	+	1.00467i
$412$	4.04295	−	22.9287i	0.199182	−	1.12962i
$413$	−9.37109	+	16.2312i	−0.461121	+	0.798686i
$414$	−1.39820	−	3.99102i	−0.0687178	−	0.196148i
$415$		0			0
$416$	17.7028	−	6.44331i	0.867953	−	0.315909i
$417$	−0.344811	+	0.238346i	−0.0168855	+	0.0116718i
$418$	3.01619	−	2.53089i	0.147527	−	0.123790i
$419$	−1.56378	+	1.31217i	−0.0763959	+	0.0641037i	−0.680186	−	0.733040i	$-0.738101\pi$
$419$	−1.56378	+	1.31217i	−0.0763959	+	0.0641037i	0.603790	+	0.797143i	$0.293657\pi$
$420$		0			0
$421$	−2.58533	+	0.940984i	−0.126001	+	0.0458608i	−0.404251	−	0.914648i	$-0.632468\pi$
$421$	−2.58533	+	0.940984i	−0.126001	+	0.0458608i	0.278250	+	0.960509i	$0.410246\pi$
$422$	−1.55126	−	2.68687i	−0.0755143	−	0.130795i
$423$	21.9021	+	26.7522i	1.06491	+	1.30074i
$424$	−6.88080	+	11.9179i	−0.334161	+	0.578784i
$425$		0			0
$426$	6.88629	−	1.80063i	0.333642	−	0.0872406i
$427$	−21.9813	−	8.00053i	−1.06375	−	0.387173i
$428$	−0.560268	−	3.17744i	−0.0270816	−	0.153587i
$429$	−27.8314	−	2.60458i	−1.34371	−	0.125750i
$430$		0			0
$431$	20.0948			0.967932			0.483966	−	0.875087i	$-0.339196\pi$
$431$	20.0948			0.967932			0.483966	+	0.875087i	$0.339196\pi$
$432$	17.9032	−	1.23960i	0.861367	−	0.0596403i
$433$	−11.8614			−0.570023			−0.285011	−	0.958524i	$-0.591997\pi$
$433$	−11.8614			−0.570023			−0.285011	+	0.958524i	$0.591997\pi$
$434$	2.62411	+	2.20189i	0.125961	+	0.105694i
$435$		0			0
$436$	5.08553	+	28.8415i	0.243553	+	1.38126i
$437$	−19.2126	−	6.99283i	−0.919065	−	0.334512i
$438$	2.86060	+	2.89540i	0.136685	+	0.138347i
$439$	−6.50324	+	36.8817i	−0.310383	+	1.76027i	0.286636	+	0.958040i	$0.407463\pi$
$439$	−6.50324	+	36.8817i	−0.310383	+	1.76027i	−0.597018	+	0.802228i	$0.703648\pi$
$440$		0			0
$441$	12.1727	−	6.83302i	0.579653	−	0.325382i
$442$	1.77112	+	3.06766i	0.0842434	+	0.145914i
$443$	13.9500	−	5.07737i	0.662783	−	0.241233i	0.0113453	−	0.999936i	$-0.496389\pi$
$443$	13.9500	−	5.07737i	0.662783	−	0.241233i	0.651437	+	0.758702i	$0.274166\pi$
$444$	12.1388	+	5.75000i	0.576080	+	0.272883i
$445$		0			0
$446$	−5.34565	+	4.48553i	−0.253124	+	0.212396i
$447$	19.8918	+	9.42255i	0.940852	+	0.445671i
$448$	18.8150	−	6.84809i	0.888924	−	0.323542i
$449$	8.86789	+	15.3596i	0.418502	+	0.724866i	0.995789	−	0.0916751i	$-0.0292221\pi$
$449$	8.86789	+	15.3596i	0.418502	+	0.724866i	−0.577287	+	0.816541i	$0.695889\pi$
$450$		0			0
$451$	7.16325	−	12.4071i	0.337304	−	0.584228i
$452$	−5.19186	+	29.4445i	−0.244205	+	1.38495i
$453$	5.35149	+	5.41659i	0.251435	+	0.254494i
$454$	−2.04173	−	0.743130i	−0.0958232	−	0.0348768i
$455$		0			0
$456$	−5.25160	+	7.40438i	−0.245929	+	0.346742i
$457$	−11.2544	−	9.44358i	−0.526460	−	0.441752i	0.340417	−	0.940275i	$-0.389432\pi$
$457$	−11.2544	−	9.44358i	−0.526460	−	0.441752i	−0.866877	+	0.498522i	$0.833876\pi$
$458$	−5.68707			−0.265739
$459$	2.65619	+	10.6846i	0.123980	+	0.498712i
$460$		0			0
$461$	11.0104	+	9.23885i	0.512807	+	0.430296i	0.862116	−	0.506711i	$-0.169139\pi$
$461$	11.0104	+	9.23885i	0.512807	+	0.430296i	−0.349308	+	0.937008i	$0.613583\pi$
$462$	5.25519	+	0.491802i	0.244494	+	0.0228807i
$463$	−1.41229	−	8.00949i	−0.0656346	−	0.372232i	−0.999878	−	0.0155973i	$-0.995035\pi$
$463$	−1.41229	−	8.00949i	−0.0656346	−	0.372232i	0.934244	−	0.356635i	$-0.116076\pi$
$464$	1.30838	+	0.476213i	0.0607402	+	0.0221076i
$465$		0			0
$466$	1.30101	−	7.37840i	0.0602681	−	0.341798i
$467$	−10.7810	+	18.6732i	−0.498883	+	0.864091i	−0.999999	−	0.00128884i	$-0.999590\pi$
$467$	−10.7810	+	18.6732i	−0.498883	+	0.864091i	0.501116	+	0.865380i	$0.332923\pi$
$468$	31.0464	−	5.08804i	1.43512	−	0.235195i
$469$	−6.51793	−	11.2894i	−0.300970	−	0.521296i
$470$		0			0
$471$	0.694390	+	8.53063i	0.0319958	+	0.393071i
$472$	4.99759	−	4.19348i	0.230033	−	0.193021i
$473$	−0.237518	+	0.199302i	−0.0109211	+	0.00916390i
$474$	1.02141	−	0.706035i	0.0469149	−	0.0324293i
$475$		0			0
$476$	6.89856	+	11.9487i	0.316195	+	0.547666i
$477$	−22.6533	+	26.3436i	−1.03722	+	1.20619i
$478$	2.64694	−	4.58463i	0.121068	−	0.209696i
$479$	6.11802	−	34.6970i	0.279540	−	1.58535i	−0.444622	−	0.895718i	$-0.646662\pi$
$479$	6.11802	−	34.6970i	0.279540	−	1.58535i	0.724162	−	0.689630i	$-0.242227\pi$
$480$		0			0
$481$	21.0020	+	7.64412i	0.957610	+	0.348542i
$482$	0.384863	+	2.18266i	0.0175300	+	0.0994176i
$483$	−11.4327	−	24.9097i	−0.520208	−	1.13343i
$484$	3.48125	+	2.92112i	0.158239	+	0.132778i
$485$		0			0
$486$	−4.70766	−	0.555690i	−0.213544	−	0.0252066i
$487$	21.9486			0.994588			0.497294	−	0.867582i	$-0.334327\pi$
$487$	21.9486			0.994588			0.497294	+	0.867582i	$0.334327\pi$
$488$	6.23746	+	5.23385i	0.282357	+	0.236925i
$489$	0.0971245	+	0.211615i	0.00439212	+	0.00956956i
$490$		0			0
$491$	−19.2925	−	7.02190i	−0.870659	−	0.316894i	−0.132225	−	0.991220i	$-0.542212\pi$
$491$	−19.2925	−	7.02190i	−0.870659	−	0.316894i	−0.738434	+	0.674326i	$0.764434\pi$
$492$	−4.26733	+	15.5492i	−0.192386	+	0.701014i
$493$	−0.148330	+	0.841223i	−0.00668046	+	0.0378868i
$494$	−3.68686	+	6.38582i	−0.165879	+	0.287312i
$495$		0			0
$496$	5.69845	+	9.87000i	0.255868	+	0.443176i
$497$	43.3498	−	15.7780i	1.94450	−	0.707742i
$498$	2.95227	−	2.04072i	0.132295	−	0.0914466i
$499$	19.5778	−	16.4277i	0.876422	−	0.735405i	−0.0890184	−	0.996030i	$-0.528373\pi$
$499$	19.5778	−	16.4277i	0.876422	−	0.735405i	0.965440	+	0.260625i	$0.0839285\pi$
$500$		0			0
$501$	−2.14777	−	26.3855i	−0.0959553	−	1.17882i
$502$	−6.52794	+	2.37598i	−0.291356	+	0.106045i
$503$	−5.61411	−	9.72392i	−0.250321	−	0.433568i	0.713293	−	0.700866i	$-0.247203\pi$
$503$	−5.61411	−	9.72392i	−0.250321	−	0.433568i	−0.963614	+	0.267297i	$0.913869\pi$
$504$	−12.0087	+	1.96805i	−0.534910	+	0.0876638i
$505$		0			0
$506$	0.718565	−	4.07518i	0.0319441	−	0.181164i
$507$	28.8621	−	7.54685i	1.28181	−	0.335168i
$508$	23.1853	+	8.43877i	1.02868	+	0.374410i
$509$	5.09372	+	28.8879i	0.225775	+	1.28043i	0.861198	+	0.508269i	$0.169715\pi$
$509$	5.09372	+	28.8879i	0.225775	+	1.28043i	−0.635423	+	0.772164i	$0.719174\pi$
$510$		0			0
$511$	20.2079	+	16.9565i	0.893946	+	0.750110i
$512$	−20.0428			−0.885775
$513$	−16.4971	+	15.9093i	−0.728366	+	0.702412i
$514$	0.447452			0.0197362
$515$		0			0
$516$	0.201882	−	0.284639i	0.00888737	−	0.0125306i
$517$	5.87484	+	33.3179i	0.258375	+	1.46532i
$518$	−3.96565	−	1.44338i	−0.174241	−	0.0634184i
$519$	18.4109	+	18.6348i	0.808147	+	0.817979i
$520$		0			0
$521$	−4.09744	+	7.09698i	−0.179512	+	0.310924i	−0.941714	−	0.336416i	$-0.890785\pi$
$521$	−4.09744	+	7.09698i	−0.179512	+	0.310924i	0.762201	+	0.647340i	$0.224119\pi$
$522$	−0.316262	−	0.187729i	−0.0138424	−	0.00821667i
$523$	−4.79470	−	8.30466i	−0.209657	−	0.363137i	0.741949	−	0.670456i	$-0.233902\pi$
$523$	−4.79470	−	8.30466i	−0.209657	−	0.363137i	−0.951607	+	0.307319i	$0.900568\pi$
$524$	20.6286	−	7.50821i	0.901166	−	0.327998i
$525$		0			0
$526$	−5.03331	+	4.22345i	−0.219463	+	0.184151i
$527$	−5.35612	+	4.49432i	−0.233316	+	0.195776i
$528$	15.8702	+	7.51754i	0.690662	+	0.327159i
$529$	1.42103	−	0.517213i	0.0617840	−	0.0224875i
$530$		0			0
$531$	14.3628	−	8.06242i	0.623294	−	0.349879i
$532$	−14.3604	+	24.8730i	−0.622604	+	1.07838i
$533$	−4.65898	+	26.4224i	−0.201803	+	1.14448i
$534$	0.644644	+	0.652487i	0.0278965	+	0.0282359i
$535$		0			0
$536$	0.787947	+	4.46867i	0.0340341	+	0.193017i
$537$	1.59319	−	2.24628i	0.0687513	−	0.0969343i
$538$	3.10666	+	2.60680i	0.133938	+	0.112387i
$539$	13.6596			0.588363
$540$		0			0
$541$	−5.81809			−0.250139			−0.125070	−	0.992148i	$-0.539915\pi$
$541$	−5.81809			−0.250139			−0.125070	+	0.992148i	$0.539915\pi$
$542$	−4.59636	−	3.85681i	−0.197431	−	0.165664i
$543$	−37.5102	−	3.51036i	−1.60972	−	0.150644i
$544$	−1.26081	−	7.15041i	−0.0540568	−	0.306571i
$545$		0			0
$546$	−9.56316	+	2.50057i	−0.409266	+	0.107015i
$547$	−0.104052	+	0.590106i	−0.00444893	+	0.0252311i	−0.986951	−	0.161018i	$-0.948522\pi$
$547$	−0.104052	+	0.590106i	−0.00444893	+	0.0252311i	0.982502	+	0.186249i	$0.0596333\pi$
$548$	11.6303	−	20.1443i	0.496824	−	0.860524i
$549$	13.0226	+	15.9065i	0.555792	+	0.678871i
$550$		0			0
$551$	−1.67091	+	0.608163i	−0.0711834	+	0.0259086i
$552$	0.774022	+	9.50890i	0.0329445	+	0.404726i
$553$	6.16478	−	5.17287i	0.262153	−	0.219973i
$554$	6.17648	−	5.18268i	0.262413	−	0.220191i
$555$		0			0
$556$	0.433796	−	0.157889i	0.0183971	−	0.00669598i
$557$	1.82184	+	3.15552i	0.0771940	+	0.133704i	0.902038	−	0.431656i	$-0.142071\pi$
$557$	1.82184	+	3.15552i	0.0771940	+	0.133704i	−0.824844	+	0.565360i	$0.808737\pi$
$558$	−0.995345	−	2.84111i	−0.0421363	−	0.120274i
$559$	0.290331	−	0.502869i	0.0122797	−	0.0212691i
$560$		0			0
$561$	−2.85121	+	10.3892i	−0.120378	+	0.438633i
$562$	1.86665	+	0.679405i	0.0787399	+	0.0286590i
$563$	−0.135667	−	0.769406i	−0.00571768	−	0.0324266i	0.981815	−	0.189838i	$-0.0607963\pi$
$563$	−0.135667	−	0.769406i	−0.00571768	−	0.0324266i	−0.987533	+	0.157411i	$0.949685\pi$
$564$	−15.8831	−	34.6062i	−0.668801	−	1.45718i
$565$		0			0
$566$	1.95362			0.0821169
$567$	−30.7140	−	0.742919i	−1.28987	−	0.0311997i
$568$	−16.0579			−0.673774
$569$	26.6979	+	22.4022i	1.11923	+	0.939149i	0.998566	−	0.0535433i	$-0.0170515\pi$
$569$	26.6979	+	22.4022i	1.11923	+	0.939149i	0.120669	+	0.992693i	$0.461496\pi$
$570$		0			0
$571$	−2.28374	−	12.9518i	−0.0955717	−	0.542014i	−0.994571	−	0.104063i	$-0.966816\pi$
$571$	−2.28374	−	12.9518i	−0.0955717	−	0.542014i	0.898999	−	0.437951i	$-0.144296\pi$
$572$	28.9284	+	10.5291i	1.20956	+	0.440243i
$573$	3.61204	−	13.1615i	0.150895	−	0.549830i
$574$	0.879719	−	4.98913i	0.0367188	−	0.208242i
$575$		0			0
$576$	−17.2906	−	3.26485i	−0.720442	−	0.136035i
$577$	12.8833	+	22.3145i	0.536338	+	0.928964i	0.999097	+	0.0424803i	$0.0135260\pi$
$577$	12.8833	+	22.3145i	0.536338	+	0.928964i	−0.462760	+	0.886484i	$0.653141\pi$
$578$	−3.57494	+	1.30117i	−0.148698	+	0.0541216i
$579$	−25.4401	+	17.5851i	−1.05725	+	0.730811i
$580$		0			0
$581$	17.8186	−	14.9516i	0.739241	−	0.620296i
$582$	−0.0190058	−	0.233488i	−0.000787818	−	0.00967839i
$583$	−31.9477	+	11.6280i	−1.32314	+	0.481584i
$584$	−4.59118	−	7.95216i	−0.189985	−	0.329063i
$585$		0			0
$586$	−2.12721	+	3.68444i	−0.0878743	+	0.152203i
$587$	1.15583	−	6.55502i	0.0477061	−	0.270555i	−0.951619	−	0.307279i	$-0.900581\pi$
$587$	1.15583	−	6.55502i	0.0477061	−	0.270555i	0.999325	+	0.0367248i	$0.0116925\pi$
$588$	−14.8736	+	3.88914i	−0.613377	+	0.160386i
$589$	−13.6770	−	4.97803i	−0.563552	−	0.205116i
$590$		0			0
$591$	−16.4081	−	1.53554i	−0.674938	−	0.0631635i
$592$	−10.7558	−	9.02517i	−0.442060	−	0.370932i
$593$	46.9838			1.92939			0.964697	−	0.263360i	$-0.0848309\pi$
$593$	46.9838			1.92939			0.964697	+	0.263360i	$0.0848309\pi$
$594$	−3.75080	−	2.72904i	−0.153897	−	0.111974i
$595$		0			0
$596$	−18.5694	−	15.5816i	−0.760631	−	0.638246i
$597$	−10.9606	+	15.4536i	−0.448587	+	0.632475i
$598$	1.34569	+	7.63181i	0.0550295	+	0.312088i
$599$	−30.7181	−	11.1805i	−1.25511	−	0.456821i	−0.372982	−	0.927839i	$-0.621665\pi$
$599$	−30.7181	−	11.1805i	−1.25511	−	0.456821i	−0.882124	+	0.471018i	$0.843887\pi$
$600$		0			0
$601$	−4.40564	+	24.9856i	−0.179710	+	1.01918i	0.752856	+	0.658185i	$0.228676\pi$
$601$	−4.40564	+	24.9856i	−0.179710	+	1.01918i	−0.932566	+	0.361000i	$0.882436\pi$
$602$	−0.0548210	+	0.0949528i	−0.00223434	+	0.00386999i
$603$	−0.138522	+	11.4553i	−0.00564105	+	0.466497i
$604$	−4.19287	−	7.26226i	−0.170605	−	0.295497i
$605$		0			0
$606$	3.03782	+	1.43898i	0.123403	+	0.0584547i
$607$	−12.3838	+	10.3912i	−0.502641	+	0.421766i	−0.858531	−	0.512762i	$-0.828622\pi$
$607$	−12.3838	+	10.3912i	−0.502641	+	0.421766i	0.355890	+	0.934528i	$0.384178\pi$
$608$	11.5782	−	9.71529i	0.469559	−	0.394007i
$609$	−2.15420	−	1.02042i	−0.0872927	−	0.0413496i
$610$		0			0
$611$	−31.6794	−	54.8703i	−1.28161	−	2.21981i
$612$	0.146611	−	12.1243i	0.00592641	−	0.490096i
$613$	−20.5635	+	35.6170i	−0.830551	+	1.43856i	0.0670516	+	0.997750i	$0.478641\pi$
$613$	−20.5635	+	35.6170i	−0.830551	+	1.43856i	−0.897602	+	0.440806i	$0.854693\pi$
$614$	−0.837116	+	4.74752i	−0.0337832	+	0.191594i
$615$		0			0
$616$	−11.1895	−	4.07263i	−0.450836	−	0.164091i
$617$	7.29783	+	41.3880i	0.293799	+	1.66622i	0.672042	+	0.740513i	$0.265417\pi$
$617$	7.29783	+	41.3880i	0.293799	+	1.66622i	−0.378243	+	0.925706i	$0.623472\pi$
$618$	3.71913	−	5.24370i	0.149605	−	0.210933i
$619$	−8.65367	−	7.26129i	−0.347821	−	0.291856i	0.452094	−	0.891970i	$-0.350677\pi$
$619$	−8.65367	−	7.26129i	−0.347821	−	0.291856i	−0.799914	+	0.600114i	$0.795122\pi$
$620$		0			0
$621$	−2.53414	+	23.9530i	−0.101692	+	0.961202i
$622$	−4.76048			−0.190878
$623$	4.55392	+	3.82119i	0.182449	+	0.153093i
$624$	−32.7437	−	3.06429i	−1.31080	−	0.122670i
$625$		0			0
$626$	−0.290099	−	0.105587i	−0.0115947	−	0.00422011i
$627$	−21.6969	+	5.67331i	−0.866493	+	0.226570i
$628$	1.63680	−	9.28275i	0.0653154	−	0.370422i
$629$	4.30693	−	7.45982i	0.171728	−	0.297442i
$630$		0			0
$631$	22.9413	+	39.7354i	0.913278	+	1.58184i	0.809404	+	0.587253i	$0.199791\pi$
$631$	22.9413	+	39.7354i	0.913278	+	1.58184i	0.103874	+	0.994590i	$0.466876\pi$
$632$	−2.63231	+	0.958081i	−0.104708	+	0.0381104i
$633$	1.43370	+	17.6131i	0.0569844	+	0.700058i
$634$	−2.68936	+	2.25664i	−0.106808	+	0.0896227i
$635$		0			0
$636$	31.4763	−	21.7575i	1.24812	−	0.862741i
$637$	−24.0384	+	8.74927i	−0.952437	+	0.346659i
$638$	−0.179942	−	0.311669i	−0.00712398	−	0.0123391i
$639$	−39.8377	−	7.52223i	−1.57595	−	0.297575i
$640$		0			0
$641$	−3.68466	+	20.8967i	−0.145535	+	0.825372i	0.821401	+	0.570352i	$0.193193\pi$
$641$	−3.68466	+	20.8967i	−0.145535	+	0.825372i	−0.966936	+	0.255020i	$0.917918\pi$
$642$	0.235776	−	0.859119i	0.00930535	−	0.0339067i
$643$	−15.0466	−	5.47651i	−0.593379	−	0.215972i	0.0278358	−	0.999613i	$-0.491138\pi$
$643$	−15.0466	−	5.47651i	−0.593379	−	0.215972i	−0.621215	+	0.783640i	$0.713361\pi$
$644$	5.24153	+	29.7262i	0.206545	+	1.17138i
$645$		0			0
$646$	2.17702	+	1.82674i	0.0856536	+	0.0718719i
$647$	14.3391			0.563729			0.281864	−	0.959454i	$-0.409047\pi$
$647$	14.3391			0.563729			0.281864	+	0.959454i	$0.409047\pi$
$648$	9.95793	+	3.89959i	0.391185	+	0.153190i
$649$	16.1173			0.632660
$650$		0			0
$651$	−8.13869	−	17.7326i	−0.318981	−	0.694996i
$652$	−0.0445283	−	0.252533i	−0.00174386	−	0.00988995i
$653$	−20.6408	−	7.51262i	−0.807735	−	0.293992i	−0.0950471	−	0.995473i	$-0.530300\pi$
$653$	−20.6408	−	7.51262i	−0.807735	−	0.293992i	−0.712688	+	0.701481i	$0.752522\pi$
$654$	−2.14013	+	7.79819i	−0.0836858	+	0.304933i
$655$		0			0
$656$	8.42758	−	14.5970i	0.329042	−	0.569917i
$657$	−7.66503	−	21.8791i	−0.299041	−	0.853584i
$658$	5.98177	+	10.3607i	0.233194	+	0.403904i
$659$	−41.9142	+	15.2555i	−1.63274	+	0.594270i	−0.985749	−	0.168223i	$-0.946197\pi$
$659$	−41.9142	+	15.2555i	−1.63274	+	0.594270i	−0.646996	+	0.762494i	$0.723975\pi$
$660$		0			0
$661$	8.07733	−	6.77768i	0.314172	−	0.263621i	−0.472042	−	0.881576i	$-0.656483\pi$
$661$	8.07733	−	6.77768i	0.314172	−	0.263621i	0.786214	+	0.617955i	$0.212039\pi$
$662$	0.806782	−	0.676971i	0.0313565	−	0.0263112i
$663$	−1.63689	−	20.1093i	−0.0635716	−	0.780981i
$664$	−7.60839	+	2.76923i	−0.295263	+	0.107467i
$665$		0			0
$666$	2.34942	+	2.86969i	0.0910381	+	0.111198i
$667$	−0.934391	+	1.61841i	−0.0361798	+	0.0626652i
$668$	−5.06267	+	28.7118i	−0.195881	+	1.11089i
$669$	38.4538	−	10.0549i	1.48671	−	0.388744i
$670$		0			0
$671$	3.49309	+	19.8103i	0.134849	+	0.764768i
$672$	20.1730	+	1.88788i	0.778192	+	0.0728264i
$673$	20.1564	+	16.9132i	0.776972	+	0.651957i	0.942484	−	0.334251i	$-0.108483\pi$
$673$	20.1564	+	16.9132i	0.776972	+	0.651957i	−0.165513	+	0.986208i	$0.552928\pi$
$674$	0.0461716			0.00177846
$675$		0			0
$676$	−32.8548			−1.26365
$677$	−32.3296	−	27.1278i	−1.24253	−	1.04260i	−0.997322	−	0.0731331i	$-0.976700\pi$
$677$	−32.3296	−	27.1278i	−1.24253	−	1.04260i	−0.245205	−	0.969471i	$-0.578855\pi$
$678$	−4.77602	+	6.73385i	−0.183422	+	0.258612i
$679$	−0.263647	−	1.49522i	−0.0101179	−	0.0573812i
$680$		0			0
$681$	8.69783	+	8.80364i	0.333301	+	0.337356i
$682$	0.511529	−	2.90102i	0.0195875	−	0.111086i
$683$	−9.27055	+	16.0571i	−0.354728	+	0.614407i	−0.987071	−	0.160281i	$-0.948760\pi$
$683$	−9.27055	+	16.0571i	−0.354728	+	0.614407i	0.632343	+	0.774688i	$0.282093\pi$
$684$	22.0099	−	12.3550i	0.841569	−	0.472406i
$685$		0			0
$686$	−2.28929	+	0.833234i	−0.0874056	+	0.0318130i
$687$	29.2742	+	13.8669i	1.11688	+	0.529053i
$688$	−0.279441	+	0.234479i	−0.0106536	+	0.00893942i
$689$	48.7741	−	40.9263i	1.85814	−	1.55917i
$690$		0			0
$691$	−9.82430	+	3.57575i	−0.373734	+	0.136028i	−0.522056	−	0.852911i	$-0.674835\pi$
$691$	−9.82430	+	3.57575i	−0.373734	+	0.136028i	0.148322	+	0.988939i	$0.452613\pi$
$692$	−14.4248	−	24.9846i	−0.548350	−	0.949770i
$693$	−25.8519	−	15.3454i	−0.982033	−	0.582922i
$694$	−3.15960	+	5.47259i	−0.119937	+	0.207737i
$695$		0			0
$696$	0.583143	+	0.590238i	0.0221040	+	0.0223729i
$697$	9.71691	+	3.53667i	0.368054	+	0.133961i
$698$	0.328143	+	1.86099i	0.0124204	+	0.0704395i
$699$	−24.6878	+	34.8080i	−0.933778	+	1.31656i
$700$		0			0
$701$	−18.2363			−0.688774			−0.344387	−	0.938828i	$-0.611913\pi$
$701$	−18.2363			−0.688774			−0.344387	+	0.938828i	$0.611913\pi$
$702$	8.34870	+	2.40014i	0.315101	+	0.0905873i
$703$	17.9311			0.676284
$704$	−13.1900	−	11.0677i	−0.497116	−	0.417130i
$705$		0			0
$706$	0.316288	+	1.79376i	0.0119037	+	0.0675090i
$707$	20.4721	+	7.45122i	0.769931	+	0.280232i
$708$	−17.5497	+	4.58888i	−0.659557	+	0.172461i
$709$	7.63846	−	43.3199i	0.286869	−	1.62691i	−0.411665	−	0.911335i	$-0.635053\pi$
$709$	7.63846	−	43.3199i	0.286869	−	1.62691i	0.698534	−	0.715577i	$-0.253836\pi$
$710$		0			0
$711$	−6.97924	+	1.14379i	−0.261742	+	0.0428956i
$712$	−1.03464	−	1.79204i	−0.0387747	−	0.0671597i
$713$	−14.3741	+	5.23175i	−0.538315	+	0.195931i
$714$	0.309082	+	3.79709i	0.0115671	+	0.142102i
$715$		0			0
$716$	−2.32335	+	1.94952i	−0.0868277	+	0.0728571i
$717$	−24.8038	+	17.1453i	−0.926316	+	0.640303i
$718$	−0.146208	+	0.0532155i	−0.00545645	+	0.00198598i
$719$	−21.3751	−	37.0227i	−0.797155	−	1.38071i	−0.921462	−	0.388469i	$-0.873004\pi$
$719$	−21.3751	−	37.0227i	−0.797155	−	1.38071i	0.124307	−	0.992244i	$-0.460329\pi$
$720$		0			0
$721$	20.8328	−	36.0835i	0.775855	−	1.34382i
$722$	−0.0239784	+	0.135988i	−0.000892385	+	0.00506096i
$723$	3.34094	−	12.1737i	0.124251	−	0.452744i
$724$	38.9887	+	14.1907i	1.44900	+	0.527394i
$725$		0			0
$726$	0.523420	+	1.14043i	0.0194259	+	0.0423253i
$727$	−7.97191	−	6.68922i	−0.295662	−	0.248090i	0.482874	−	0.875690i	$-0.339593\pi$
$727$	−7.97191	−	6.68922i	−0.295662	−	0.248090i	−0.778536	+	0.627600i	$0.784037\pi$
$728$	22.3000			0.826492
$729$	22.8777	+	14.3391i	0.847322	+	0.531080i
$730$		0			0
$731$	−0.171435	−	0.143851i	−0.00634076	−	0.00532053i
$732$	−9.44387	−	20.5763i	−0.349055	−	0.760523i
$733$	−5.72433	−	32.4643i	−0.211433	−	1.19910i	−0.886990	−	0.461788i	$-0.847208\pi$
$733$	−5.72433	−	32.4643i	−0.211433	−	1.19910i	0.675557	−	0.737308i	$-0.263903\pi$
$734$	−5.86785	−	2.13572i	−0.216586	−	0.0788310i
$735$		0			0
$736$	2.75835	−	15.6434i	0.101674	−	0.576622i
$737$	−5.60508	+	9.70829i	−0.206466	+	0.357609i
$738$	−2.90284	+	3.37572i	−0.106855	+	0.124262i
$739$	−13.1005	−	22.6907i	−0.481909	−	0.834690i	0.517876	−	0.855456i	$-0.326723\pi$
$739$	−13.1005	−	22.6907i	−0.481909	−	0.834690i	−0.999784	+	0.0207656i	$0.993390\pi$
$740$		0			0
$741$	34.5487	−	23.8813i	1.26918	−	0.877301i
$742$	−9.20963	+	7.72780i	−0.338096	+	0.283696i
$743$	−12.4297	+	10.4298i	−0.456002	+	0.382631i	−0.841658	−	0.540012i	$-0.818420\pi$
$743$	−12.4297	+	10.4298i	−0.456002	+	0.382631i	0.385655	+	0.922643i	$0.373975\pi$
$744$	0.551007	+	6.76916i	0.0202009	+	0.248169i
$745$		0			0
$746$	−1.90770	−	3.30424i	−0.0698460	−	0.120977i
$747$	−20.1727	+	3.30601i	−0.738081	+	0.120961i
$748$	5.93241	−	10.2752i	0.216910	−	0.375700i
$749$	1.00264	−	5.68627i	0.0366358	−	0.207772i
$750$		0			0
$751$	7.02136	+	2.55556i	0.256213	+	0.0932539i	0.466933	−	0.884292i	$-0.345359\pi$
$751$	7.02136	+	2.55556i	0.256213	+	0.0932539i	−0.210720	+	0.977546i	$0.567581\pi$
$752$	6.91177	+	39.1986i	0.252046	+	1.42943i
$753$	39.3959	+	3.68684i	1.43567	+	0.134356i
$754$	0.516295	+	0.433223i	0.0188023	+	0.0157770i
$755$		0			0
$756$	32.5185	+	9.34862i	1.18269	+	0.340006i
$757$	25.7164			0.934678			0.467339	−	0.884078i	$-0.345213\pi$
$757$	25.7164			0.934678			0.467339	+	0.884078i	$0.345213\pi$
$758$	−6.96317	−	5.84279i	−0.252914	−	0.212220i
$759$	−13.6354	+	19.2249i	−0.494933	+	0.697820i
$760$		0			0
$761$	19.3050	+	7.02645i	0.699807	+	0.254709i	0.667328	−	0.744764i	$-0.267438\pi$
$761$	19.3050	+	7.02645i	0.699807	+	0.254709i	0.0324783	+	0.999472i	$0.489660\pi$
$762$	4.78814	+	4.84639i	0.173456	+	0.175566i
$763$	−9.10096	+	51.6141i	−0.329477	+	1.86856i
$764$	−7.51544	+	13.0171i	−0.271899	+	0.470943i
$765$		0			0
$766$	3.31440	+	5.74070i	0.119754	+	0.207420i
$767$	−28.3635	+	10.3235i	−1.02414	+	0.372758i
$768$	14.2511	+	6.75058i	0.514241	+	0.243591i
$769$	1.56802	−	1.31573i	0.0565444	−	0.0474464i	−0.614077	−	0.789246i	$-0.710472\pi$
$769$	1.56802	−	1.31573i	0.0565444	−	0.0474464i	0.670622	+	0.741799i	$0.266027\pi$
$770$		0			0
$771$	−2.30326	−	1.09103i	−0.0829497	−	0.0392924i
$772$	32.0054	−	11.6490i	1.15190	−	0.419257i
$773$	−11.7703	−	20.3868i	−0.423349	−	0.733262i	0.572916	−	0.819614i	$-0.305812\pi$
$773$	−11.7703	−	20.3868i	−0.423349	−	0.733262i	−0.996265	+	0.0863523i	$0.972479\pi$
$774$	0.0840229	−	0.0471653i	0.00302014	−	0.00169532i
$775$		0			0
$776$	−0.0917721	+	0.520465i	−0.00329442	+	0.0186836i
$777$	16.8938	+	17.0993i	0.606061	+	0.613434i
$778$	−2.97609	−	1.08321i	−0.106698	−	0.0388349i
$779$	3.73785	+	21.1984i	0.133922	+	0.759512i
$780$		0			0
$781$	−30.3898	−	25.5001i	−1.08743	−	0.912464i
$782$	2.98675			0.106806
$783$	1.17021	+	1.73748i	0.0418201	+	0.0620924i
$784$	16.0706			0.573951
$785$		0			0
$786$	6.03514	+	0.564793i	0.215266	+	0.0201455i
$787$	−4.10976	−	23.3076i	−0.146497	−	0.830826i	−0.966153	−	0.257970i	$-0.916947\pi$
$787$	−4.10976	−	23.3076i	−0.146497	−	0.830826i	0.819656	−	0.572856i	$-0.194165\pi$
$788$	17.0548	+	6.20745i	0.607553	+	0.221131i
$789$	36.2070	−	9.46740i	1.28900	−	0.337048i
$790$		0			0
$791$	−26.7531	+	46.3377i	−0.951230	+	1.64758i
$792$	6.62910	+	8.09711i	0.235555	+	0.287718i
$793$	−18.8361	−	32.6250i	−0.668888	−	1.15855i
$794$	−6.24481	+	2.27292i	−0.221620	+	0.0806631i
$795$		0			0
$796$	15.9838	−	13.4120i	0.566531	−	0.475376i
$797$	−22.1635	+	18.5974i	−0.785073	+	0.658755i	−0.944521	−	0.328452i	$-0.893473\pi$
$797$	−22.1635	+	18.5974i	−0.785073	+	0.658755i	0.159448	+	0.987206i	$0.449029\pi$
$798$	−6.52357	+	4.50932i	−0.230932	+	0.159628i
$799$	−22.9464	+	8.35181i	−0.811785	+	0.295466i
$800$		0			0
$801$	−1.72734	−	4.93052i	−0.0610325	−	0.174211i
$802$	−3.06496	+	5.30866i	−0.108227	+	0.187455i
$803$	3.93922	−	22.3404i	0.139012	−	0.788377i
$804$	3.33909	−	12.1669i	0.117761	−	0.429095i
$805$		0			0
$806$	0.957968	+	5.43290i	0.0337430	+	0.191366i
$807$	−9.63533	−	20.9935i	−0.339180	−	0.739005i
$808$	−5.80920	−	4.87450i	−0.204367	−	0.171484i
$809$	−50.0898			−1.76106			−0.880532	−	0.473986i	$-0.842815\pi$
$809$	−50.0898			−1.76106			−0.880532	+	0.473986i	$0.842815\pi$
$810$		0			0
$811$	−22.3607			−0.785192			−0.392596	−	0.919711i	$-0.628423\pi$
$811$	−22.3607			−0.785192			−0.392596	+	0.919711i	$0.628423\pi$
$812$	2.01099	+	1.68742i	0.0705718	+	0.0592168i
$813$	14.2557	+	31.0603i	0.499968	+	1.08933i
$814$	0.630190	+	3.57398i	0.0220881	+	0.125268i
$815$		0			0
$816$	−3.35446	+	12.2229i	−0.117430	+	0.427888i
$817$	0.0808957	−	0.458782i	0.00283018	−	0.0160508i
$818$	2.05193	−	3.55405i	0.0717441	−	0.124264i
$819$	55.3235	+	10.4463i	1.93316	+	0.365023i
$820$		0			0
$821$	−12.3587	+	4.49819i	−0.431321	+	0.156988i	−0.548552	−	0.836117i	$-0.684821\pi$
$821$	−12.3587	+	4.49819i	−0.431321	+	0.156988i	0.117230	+	0.993105i	$0.462598\pi$
$822$	5.28335	−	3.65204i	0.184278	−	0.127380i
$823$	17.2863	−	14.5049i	0.602563	−	0.505611i	−0.289705	−	0.957116i	$-0.593557\pi$
$823$	17.2863	−	14.5049i	0.602563	−	0.505611i	0.892268	+	0.451505i	$0.149113\pi$
$824$	−11.1101	+	9.32250i	−0.387040	+	0.324765i
$825$		0			0
$826$	5.35565	−	1.94930i	0.186347	−	0.0678247i
$827$	−1.92094	−	3.32717i	−0.0667978	−	0.115697i	0.830692	−	0.556732i	$-0.187945\pi$
$827$	−1.92094	−	3.32717i	−0.0667978	−	0.115697i	−0.897490	+	0.441035i	$0.854612\pi$
$828$	9.37350	−	24.8157i	0.325752	−	0.862404i
$829$	−22.2051	+	38.4603i	−0.771214	+	1.33578i	0.165685	+	0.986179i	$0.447017\pi$
$829$	−22.2051	+	38.4603i	−0.771214	+	1.33578i	−0.936898	+	0.349602i	$0.886317\pi$
$830$		0			0
$831$	−44.4304	+	11.6176i	−1.54127	+	0.403011i
$832$	30.3010	+	11.0287i	1.05050	+	0.382350i
$833$	1.71203	+	9.70943i	0.0593185	+	0.336412i
$834$	0.126912	+	0.0118769i	0.00439460	+	0.000411265i
$835$		0			0
$836$	24.6985			0.854214
$837$	−1.80399	+	17.0516i	−0.0623551	+	0.589389i
$838$	0.620768			0.0214441
$839$	5.58926	+	4.68995i	0.192963	+	0.161915i	0.734150	−	0.678987i	$-0.237581\pi$
$839$	5.58926	+	4.68995i	0.192963	+	0.161915i	−0.541188	+	0.840902i	$0.682025\pi$
$840$		0			0
$841$	−5.00757	−	28.3994i	−0.172675	−	0.979289i
$842$	0.786181	+	0.286147i	0.0270936	+	0.00986126i
$843$	−7.95198	−	8.04872i	−0.273881	−	0.277213i
$844$	3.37948	−	19.1660i	0.116327	−	0.659721i
$845$		0			0
$846$	0.127127	−	10.5130i	0.00437073	−	0.361446i
$847$	4.06633	+	7.04308i	0.139721	+	0.242003i
$848$	−37.5866	+	13.6804i	−1.29073	+	0.469787i
$849$	−10.0563	−	4.76355i	−0.345130	−	0.163485i
$850$		0			0
$851$	14.4361	−	12.1134i	0.494864	−	0.415240i
$852$	40.3509	+	19.1138i	1.38240	+	0.654827i
$853$	51.6153	−	18.7864i	1.76727	−	0.643235i	0.767276	−	0.641317i	$-0.221612\pi$
$853$	51.6153	−	18.7864i	1.76727	−	0.643235i	0.999998	−	0.00191802i	$-0.000610526\pi$
$854$	3.55667	+	6.16033i	0.121707	+	0.210802i
$855$		0			0
$856$	−1.00492	+	1.74058i	−0.0343476	+	0.0594917i
$857$	−1.54321	+	8.75197i	−0.0527150	+	0.298961i	−0.999755	−	0.0221554i	$-0.992947\pi$
$857$	−1.54321	+	8.75197i	−0.0527150	+	0.298961i	0.947040	+	0.321117i	$0.104058\pi$
$858$	5.97418	+	6.04686i	0.203955	+	0.206436i
$859$	−4.71452	−	1.71594i	−0.160857	−	0.0585473i	0.260336	−	0.965518i	$-0.416167\pi$
$859$	−4.71452	−	1.71594i	−0.160857	−	0.0585473i	−0.421194	+	0.906971i	$0.638389\pi$
$860$		0			0
$861$	−16.6934	+	23.5365i	−0.568910	+	0.802123i
$862$	−4.68106	−	3.92787i	−0.159437	−	0.133784i
$863$	−15.4472			−0.525828			−0.262914	−	0.964819i	$-0.584684\pi$
$863$	−15.4472			−0.525828			−0.262914	+	0.964819i	$0.584684\pi$
$864$	−14.3981	−	10.4759i	−0.489834	−	0.356398i
$865$		0			0
$866$	2.76310	+	2.31851i	0.0938939	+	0.0787863i
$867$	21.5746	+	2.01904i	0.732713	+	0.0685703i
$868$	3.73132	+	21.1614i	0.126649	+	0.718264i
$869$	−6.50312	−	2.36694i	−0.220603	−	0.0802930i
$870$		0			0
$871$	3.64555	−	20.6749i	0.123525	−	0.700544i
$872$	9.12165	−	15.7992i	0.308898	−	0.535027i
$873$	−0.471485	+	1.24822i	−0.0159573	+	0.0422459i
$874$	3.10869	+	5.38441i	0.105153	+	0.182130i
$875$		0			0
$876$	2.07141	+	25.4474i	0.0699865	+	0.859789i
$877$	9.23051	−	7.74532i	0.311692	−	0.261541i	−0.473499	−	0.880794i	$-0.657009\pi$
$877$	9.23051	−	7.74532i	0.311692	−	0.261541i	0.785191	+	0.619254i	$0.212565\pi$
$878$	8.72408	−	7.32037i	0.294423	−	0.247051i
$879$	19.9336	−	13.7788i	0.672344	−	0.464748i
$880$		0			0
$881$	17.1975	+	29.7869i	0.579398	+	1.00355i	0.995548	+	0.0942507i	$0.0300455\pi$
$881$	17.1975	+	29.7869i	0.579398	+	1.00355i	−0.416151	+	0.909296i	$0.636621\pi$
$882$	−4.17125	−	0.787623i	−0.140453	−	0.0265207i
$883$	13.5734	−	23.5099i	0.456783	−	0.791171i	−0.542006	−	0.840375i	$-0.682335\pi$
$883$	13.5734	−	23.5099i	0.456783	−	0.791171i	0.998789	+	0.0492038i	$0.0156684\pi$
$884$	−3.85844	+	21.8823i	−0.129773	+	0.735982i
$885$		0			0
$886$	−4.24208	−	1.54399i	−0.142516	−	0.0518714i
$887$	−8.56056	−	48.5493i	−0.287435	−	1.63013i	−0.696454	−	0.717601i	$-0.745240\pi$
$887$	−8.56056	−	48.5493i	−0.287435	−	1.63013i	0.409019	−	0.912526i	$-0.365871\pi$
$888$	−3.49014	−	7.60432i	−0.117121	−	0.255184i
$889$	33.8246	+	28.3822i	1.13444	+	0.951908i
$890$		0			0
$891$	12.6530	+	23.1933i	0.423890	+	0.777005i
$892$	−43.7735			−1.46564
$893$	−38.9396	−	32.6742i	−1.30306	−	1.09340i
$894$	−2.79198	−	6.08317i	−0.0933777	−	0.203452i
$895$		0			0
$896$	−27.7062	−	10.0842i	−0.925598	−	0.336890i
$897$	11.6818	−	42.5660i	0.390044	−	1.42124i
$898$	0.936541	−	5.31139i	0.0312528	−	0.177243i
$899$	−0.665171	+	1.15211i	−0.0221847	+	0.0384250i
$900$		0			0
$901$	−12.2695	−	21.2514i	−0.408756	−	0.707987i
$902$	−4.09385	+	1.49004i	−0.136310	+	0.0496129i
$903$	0.513716	−	0.355098i	0.0170954	−	0.0118169i
$904$	14.2674	−	11.9718i	0.474526	−	0.398175i
$905$		0			0
$906$	−0.187856	−	2.30783i	−0.00624111	−	0.0766724i
$907$	−12.6581	+	4.60719i	−0.420307	+	0.152979i	−0.543511	−	0.839402i	$-0.682905\pi$
$907$	−12.6581	+	4.60719i	−0.420307	+	0.152979i	0.123204	+	0.992381i	$0.460683\pi$
$908$	−6.81471	−	11.8034i	−0.226154	−	0.391711i
$909$	−12.1285	−	14.8143i	−0.402277	−	0.491360i
$910$		0			0
$911$	−4.06209	+	23.0373i	−0.134583	+	0.763259i	0.840566	+	0.541709i	$0.182223\pi$
$911$	−4.06209	+	23.0373i	−0.134583	+	0.763259i	−0.975149	+	0.221550i	$0.928888\pi$
$912$	−25.5265	+	6.67467i	−0.845268	+	0.221020i
$913$	−18.7965	−	6.84138i	−0.622075	−	0.226417i
$914$	0.775793	+	4.39974i	0.0256609	+	0.145530i
$915$		0			0
$916$	−27.3279	−	22.9309i	−0.902941	−	0.757657i
$917$	39.2858			1.29733
$918$	1.46972	−	3.00815i	0.0485081	−	0.0992838i
$919$	−6.93563			−0.228785			−0.114393	−	0.993436i	$-0.536492\pi$
$919$	−6.93563			−0.228785			−0.114393	+	0.993436i	$0.536492\pi$
$920$		0			0
$921$	15.8850	−	22.3967i	0.523428	−	0.737996i
$922$	−0.758974	−	4.30436i	−0.0249955	−	0.141756i
$923$	69.8136	+	25.4101i	2.29794	+	0.836383i
$924$	23.2697	+	23.5527i	0.765515	+	0.774828i
$925$		0			0
$926$	−1.23660	+	2.14186i	−0.0406372	+	0.0703857i
$927$	−31.9300	+	17.9235i	−1.04872	+	0.588686i
$928$	−0.690742	−	1.19640i	−0.0226747	−	0.0392738i
$929$	11.5336	−	4.19788i	0.378404	−	0.137728i	−0.145814	−	0.989312i	$-0.546580\pi$
$929$	11.5336	−	4.19788i	0.378404	−	0.137728i	0.524218	+	0.851584i	$0.324358\pi$
$930$		0			0
$931$	−15.7219	+	13.1922i	−0.515265	+	0.432358i
$932$	36.0022	−	30.2094i	1.17929	−	0.989543i
$933$	24.5046	+	11.6075i	0.802243	+	0.380014i
$934$	6.16140	−	2.24257i	0.201607	−	0.0733790i
$935$		0			0
$936$	−16.8523	−	10.0033i	−0.550836	−	0.326969i
$937$	12.4035	−	21.4835i	0.405205	−	0.701836i	−0.589140	−	0.808031i	$-0.700533\pi$
$937$	12.4035	−	21.4835i	0.405205	−	0.701836i	0.994345	+	0.106195i	$0.0338668\pi$
$938$	−0.688361	+	3.90389i	−0.0224758	+	0.127466i
$939$	1.23583	+	1.25086i	0.0403297	+	0.0408203i
$940$		0			0
$941$	9.97338	+	56.5618i	0.325123	+	1.84386i	0.508811	+	0.860878i	$0.330085\pi$
$941$	9.97338	+	56.5618i	0.325123	+	1.84386i	−0.183688	+	0.982985i	$0.558804\pi$
$942$	1.50570	−	2.12293i	0.0490584	−	0.0691688i
$943$	17.3299	+	14.5415i	0.564339	+	0.473537i
$944$	18.9621			0.617162
$945$		0			0
$946$	0.0942865			0.00306552
$947$	3.15158	+	2.64449i	0.102413	+	0.0859344i	0.692556	−	0.721364i	$-0.256484\pi$
$947$	3.15158	+	2.64449i	0.102413	+	0.0859344i	−0.590144	+	0.807298i	$0.700929\pi$
$948$	7.75497	+	0.725742i	0.251870	+	0.0235710i
$949$	7.37719	+	41.8381i	0.239474	+	1.35812i
$950$		0			0
$951$	19.3459	−	5.05855i	0.627333	−	0.164035i
$952$	1.49244	−	8.46404i	0.0483702	−	0.274321i
$953$	5.45128	−	9.44189i	0.176584	−	0.305853i	−0.764124	−	0.645069i	$-0.776829\pi$
$953$	5.45128	−	9.44189i	0.176584	−	0.305853i	0.940708	+	0.339216i	$0.110162\pi$
$954$	10.4264	−	1.70873i	0.337566	−	0.0553220i
$955$		0			0
$956$	31.2050	−	11.3577i	1.00924	−	0.367334i
$957$	0.166305	+	2.04307i	0.00537588	+	0.0660431i
$958$	−8.20732	+	6.88676i	−0.265166	+	0.222501i
$959$	31.8880	−	26.7572i	1.02972	−	0.864035i
$960$		0			0
$961$	18.8979	−	6.87826i	0.609609	−	0.221879i
$962$	−3.39822	−	5.88589i	−0.109563	−	0.189769i
$963$	−3.30846	+	3.84741i	−0.106614	+	0.123981i
$964$	−6.95136	+	12.0401i	−0.223888	+	0.387786i
$965$		0			0
$966$	−2.20578	+	8.03740i	−0.0709699	+	0.258599i
$967$	−33.6762	−	12.2571i	−1.08295	−	0.394163i	−0.261947	−	0.965082i	$-0.584365\pi$
$967$	−33.6762	−	12.2571i	−1.08295	−	0.394163i	−0.821006	+	0.570920i	$0.806587\pi$
$968$	−0.491574	−	2.78786i	−0.0157998	−	0.0896051i
$969$	−6.75204	−	14.7114i	−0.216907	−	0.472597i
$970$		0			0
$971$	28.9416			0.928779			0.464390	−	0.885631i	$-0.346274\pi$
$971$	28.9416			0.928779			0.464390	+	0.885631i	$0.346274\pi$
$972$	−20.3810	−	21.6520i	−0.653721	−	0.694489i
$973$	0.826134			0.0264847
$974$	−5.11291	−	4.29024i	−0.163828	−	0.137468i
$975$		0			0
$976$	4.10963	+	23.3069i	0.131546	+	0.746035i
$977$	−22.9170	−	8.34110i	−0.733179	−	0.266855i	−0.0516691	−	0.998664i	$-0.516454\pi$
$977$	−22.9170	−	8.34110i	−0.733179	−	0.266855i	−0.681510	+	0.731809i	$0.738676\pi$
$978$	0.0187388	−	0.0682801i	0.000599200	−	0.00218336i
$979$	0.887716	−	5.03448i	0.0283715	−	0.160903i
$980$		0			0
$981$	30.0308	−	34.9228i	0.958808	−	1.11500i
$982$	3.12161	+	5.40679i	0.0996147	+	0.172538i
$983$	2.47204	−	0.899750i	0.0788460	−	0.0286976i	−0.302296	−	0.953214i	$-0.597753\pi$
$983$	2.47204	−	0.899750i	0.0788460	−	0.0286976i	0.381142	+	0.924517i	$0.375531\pi$
$984$	8.26240	−	5.71126i	0.263396	−	0.182068i
$985$		0			0
$986$	0.198985	−	0.166968i	0.00633696	−	0.00531734i
$987$	−5.52844	−	67.9173i	−0.175972	−	2.16183i
$988$	−43.4647	+	15.8199i	−1.38280	+	0.503297i
$989$	−0.244802	−	0.424010i	−0.00778426	−	0.0134827i
$990$		0			0
$991$	9.51245	−	16.4761i	0.302173	−	0.523379i	−0.674455	−	0.738316i	$-0.735621\pi$
$991$	9.51245	−	16.4761i	0.302173	−	0.523379i	0.976628	+	0.214937i	$0.0689546\pi$
$992$	1.96360	−	11.1361i	0.0623444	−	0.353572i
$993$	−5.80358	+	1.51752i	−0.184171	+	0.0481569i
$994$	−13.1824	−	4.79799i	−0.418119	−	0.152183i
$995$		0			0
$996$	22.4149	+	2.09768i	0.710243	+	0.0664674i
$997$	12.9456	+	10.8627i	0.409993	+	0.344025i	0.824341	−	0.566094i	$-0.191546\pi$
$997$	12.9456	+	10.8627i	0.409993	+	0.344025i	−0.414348	+	0.910118i	$0.635990\pi$
$998$	−7.77169			−0.246009
$999$	−5.09641	−	20.5003i	−0.161243	−	0.648602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.l.h.151.7		96
5.2	odd	4		135.2.p.a.124.10	yes	96
5.3	odd	4		135.2.p.a.124.7	yes	96
5.4	even	2	inner	675.2.l.h.151.10		96
15.2	even	4		405.2.p.a.289.7		96
15.8	even	4		405.2.p.a.289.10		96
27.22	even	9	inner	675.2.l.h.76.7		96
135.22	odd	36		135.2.p.a.49.7	✓	96
135.32	even	36		405.2.p.a.199.10		96
135.49	even	18	inner	675.2.l.h.76.10		96
135.103	odd	36		135.2.p.a.49.10	yes	96
135.113	even	36		405.2.p.a.199.7		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.7	✓	96	135.22	odd	36
135.2.p.a.49.10	yes	96	135.103	odd	36
135.2.p.a.124.7	yes	96	5.3	odd	4
135.2.p.a.124.10	yes	96	5.2	odd	4
405.2.p.a.199.7		96	135.113	even	36
405.2.p.a.199.10		96	135.32	even	36
405.2.p.a.289.7		96	15.2	even	4
405.2.p.a.289.10		96	15.8	even	4
675.2.l.h.76.7		96	27.22	even	9	inner
675.2.l.h.76.10		96	135.49	even	18	inner
675.2.l.h.151.7		96	1.1	even	1	trivial
675.2.l.h.151.10		96	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.232949 - 0.195467i) q^{2} +(0.722492 + 1.57417i) q^{3} +(-0.331239 - 1.87855i) q^{4} +(0.139394 - 0.507924i) q^{6} +(0.592777 - 3.36181i) q^{7} +(-0.594126 + 1.02906i) q^{8} +(-1.95601 + 2.27465i) q^{9} +(-2.75854 + 1.00403i) q^{11} +(2.71783 - 1.87866i) q^{12} +(4.21142 - 3.53380i) q^{13} +(-0.795210 + 0.667260i) q^{14} +(-3.24543 + 1.18124i) q^{16} +(-1.05942 - 1.83496i) q^{17} +(0.900269 - 0.147541i) q^{18} +(2.20534 - 3.81976i) q^{19} +(5.72033 - 1.49575i) q^{21} +(0.838853 + 0.305317i) q^{22} +(-0.804944 - 4.56507i) q^{23} +(-2.04916 - 0.191769i) q^{24} -1.67179 q^{26} +(-4.99388 - 1.43567i) q^{27} -6.51167 q^{28} +(-0.308828 - 0.259138i) q^{29} +(-0.573021 - 3.24976i) q^{31} +(3.22009 + 1.17202i) q^{32} +(-3.57353 - 3.61701i) q^{33} +(-0.111885 + 0.634533i) q^{34} +(4.92094 + 2.92101i) q^{36} +(2.03269 + 3.52072i) q^{37} +(-1.26037 + 0.458737i) q^{38} +(8.60551 + 4.07634i) q^{39} +(-3.73852 + 3.13699i) q^{41} +(-1.62491 - 0.769703i) q^{42} +(0.0992511 - 0.0361245i) q^{43} +(2.79985 + 4.84948i) q^{44} +(-0.704810 + 1.22077i) q^{46} +(2.00126 - 11.3497i) q^{47} +(-4.20427 - 4.25542i) q^{48} +(-4.37252 - 1.59147i) q^{49} +(2.12312 - 2.99344i) q^{51} +(-8.03340 - 6.74082i) q^{52} +11.5814 q^{53} +(0.882691 + 1.31058i) q^{54} +(3.10730 + 2.60734i) q^{56} +(7.60629 + 0.711828i) q^{57} +(0.0212882 + 0.120732i) q^{58} +(-5.15923 - 1.87781i) q^{59} +(1.18992 - 6.74834i) q^{61} +(-0.501737 + 0.869034i) q^{62} +(6.48745 + 7.92409i) q^{63} +(2.93269 + 5.07957i) q^{64} +(0.125444 + 1.54108i) q^{66} +(2.92531 - 2.45463i) q^{67} +(-3.09614 + 2.59797i) q^{68} +(6.60462 - 4.56534i) q^{69} +(6.75694 + 11.7034i) q^{71} +(-1.17862 - 3.36427i) q^{72} +(-3.86382 + 6.69232i) q^{73} +(0.214673 - 1.21747i) q^{74} +(-7.90610 - 2.87758i) q^{76} +(1.74014 + 9.86885i) q^{77} +(-1.20785 - 2.63167i) q^{78} +(1.80591 + 1.51534i) q^{79} +(-1.34805 - 8.89847i) q^{81} +1.48406 q^{82} +(5.21978 + 4.37992i) q^{83} +(-4.70463 - 10.2505i) q^{84} +(-0.0301816 - 0.0109852i) q^{86} +(0.184800 - 0.673373i) q^{87} +(0.605720 - 3.43521i) q^{88} +(-0.870723 + 1.50814i) q^{89} +(-9.38352 - 16.2527i) q^{91} +(-8.30907 + 3.02425i) q^{92} +(4.70167 - 3.24996i) q^{93} +(-2.68468 + 2.25271i) q^{94} +(0.481539 + 5.91574i) q^{96} +(0.417944 - 0.152119i) q^{97} +(0.707493 + 1.22541i) q^{98} +(3.11193 - 8.23860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{4} - 6 q^{6} + 18 q^{9} - 6 q^{11} + 18 q^{14} - 24 q^{16} + 6 q^{19} + 24 q^{21} + 30 q^{24} + 48 q^{26} + 30 q^{29} - 30 q^{31} + 24 q^{34} + 54 q^{36} + 6 q^{39} - 12 q^{41} - 78 q^{44}+ \cdots - 36 q^{99}+O(q^{100}) \) 96 * q + 12 * q^4 - 6 * q^6 + 18 * q^9 - 6 * q^11 + 18 * q^14 - 24 * q^16 + 6 * q^19 + 24 * q^21 + 30 * q^24 + 48 * q^26 + 30 * q^29 - 30 * q^31 + 24 * q^34 + 54 * q^36 + 6 * q^39 - 12 * q^41 - 78 * q^44 - 6 * q^46 + 30 * q^49 - 90 * q^51 - 108 * q^54 - 96 * q^56 - 66 * q^59 + 6 * q^61 - 150 * q^66 - 24 * q^69 - 90 * q^71 - 66 * q^74 + 12 * q^76 - 24 * q^79 - 54 * q^81 - 198 * q^84 + 18 * q^86 - 96 * q^89 - 6 * q^91 - 24 * q^94 + 42 * q^96 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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