LMFDB - Embedded newform 135.2.p.a.49.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,2,Mod(4,135)] 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("135.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([2, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.p (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.7
Character	$\chi$	$=$	135.49
Dual form			135.2.p.a.124.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.195467 - 0.232949i) q^{2} +(-1.57417 - 0.722492i) q^{3} +(0.331239 - 1.87855i) q^{4} +(-2.07799 + 0.825805i) q^{5} +(0.139394 + 0.507924i) q^{6} +(-3.36181 + 0.592777i) q^{7} +(-1.02906 + 0.594126i) q^{8} +(1.95601 + 2.27465i) q^{9} +(0.598549 + 0.322648i) q^{10} +(-2.75854 - 1.00403i) q^{11} +(-1.87866 + 2.71783i) q^{12} +(3.53380 - 4.21142i) q^{13} +(0.795210 + 0.667260i) q^{14} +(3.86774 + 0.201377i) q^{15} +(-3.24543 - 1.18124i) q^{16} +(-1.83496 - 1.05942i) q^{17} +(0.147541 - 0.900269i) q^{18} +(-2.20534 - 3.81976i) q^{19} +(0.863003 + 4.17714i) q^{20} +(5.72033 + 1.49575i) q^{21} +(0.305317 + 0.838853i) q^{22} +(4.56507 + 0.804944i) q^{23} +(2.04916 - 0.191769i) q^{24} +(3.63609 - 3.43203i) q^{25} -1.67179 q^{26} +(-1.43567 - 4.99388i) q^{27} +6.51167i q^{28} +(0.308828 - 0.259138i) q^{29} +(-0.709106 - 0.940348i) q^{30} +(-0.573021 + 3.24976i) q^{31} +(1.17202 + 3.22009i) q^{32} +(3.61701 + 3.57353i) q^{33} +(0.111885 + 0.634533i) q^{34} +(6.49629 - 4.00798i) q^{35} +(4.92094 - 2.92101i) q^{36} +(3.52072 + 2.03269i) q^{37} +(-0.458737 + 1.26037i) q^{38} +(-8.60551 + 4.07634i) q^{39} +(1.64774 - 2.08439i) q^{40} +(-3.73852 - 3.13699i) q^{41} +(-0.769703 - 1.62491i) q^{42} +(0.0361245 - 0.0992511i) q^{43} +(-2.79985 + 4.84948i) q^{44} +(-5.94299 - 3.11142i) q^{45} +(-0.704810 - 1.22077i) q^{46} +(-11.3497 + 2.00126i) q^{47} +(4.25542 + 4.20427i) q^{48} +(4.37252 - 1.59147i) q^{49} +(-1.51022 - 0.176174i) q^{50} +(2.12312 + 2.99344i) q^{51} +(-6.74082 - 8.03340i) q^{52} -11.5814i q^{53} +(-0.882691 + 1.31058i) q^{54} +(6.56135 - 0.191657i) q^{55} +(3.10730 - 2.60734i) q^{56} +(0.711828 + 7.60629i) q^{57} +(-0.120732 - 0.0212882i) q^{58} +(5.15923 - 1.87781i) q^{59} +(1.65944 - 7.19904i) q^{60} +(1.18992 + 6.74834i) q^{61} +(0.869034 - 0.501737i) q^{62} +(-7.92409 - 6.48745i) q^{63} +(-2.93269 + 5.07957i) q^{64} +(-3.86539 + 11.6695i) q^{65} +(0.125444 - 1.54108i) q^{66} +(-2.45463 + 2.92531i) q^{67} +(-2.59797 + 3.09614i) q^{68} +(-6.60462 - 4.56534i) q^{69} +(-2.20346 - 0.729873i) q^{70} +(6.75694 - 11.7034i) q^{71} +(-3.36427 - 1.17862i) q^{72} +(-6.69232 + 3.86382i) q^{73} +(-0.214673 - 1.21747i) q^{74} +(-8.20344 + 2.77554i) q^{75} +(-7.90610 + 2.87758i) q^{76} +(9.86885 + 1.74014i) q^{77} +(2.63167 + 1.20785i) q^{78} +(-1.80591 + 1.51534i) q^{79} +(7.71945 - 0.225486i) q^{80} +(-1.34805 + 8.89847i) q^{81} +1.48406i q^{82} +(-4.37992 - 5.21978i) q^{83} +(4.70463 - 10.2505i) q^{84} +(4.68790 + 0.686136i) q^{85} +(-0.0301816 + 0.0109852i) q^{86} +(-0.673373 + 0.184800i) q^{87} +(3.43521 - 0.605720i) q^{88} +(0.870723 + 1.50814i) q^{89} +(0.436858 + 1.99259i) q^{90} +(-9.38352 + 16.2527i) q^{91} +(3.02425 - 8.30907i) q^{92} +(3.24996 - 4.70167i) q^{93} +(2.68468 + 2.25271i) q^{94} +(7.73705 + 6.11625i) q^{95} +(0.481539 - 5.91574i) q^{96} +(-0.152119 + 0.417944i) q^{97} +(-1.22541 - 0.707493i) q^{98} +(-3.11193 - 8.23860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31}+ \cdots + 36 q^{99}+O(q^{100}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

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 $

$2$	−0.195467	−	0.232949i	−0.138216	−	0.164720i	0.692496	−	0.721422i	$-0.256511\pi$
$2$	−0.195467	−	0.232949i	−0.138216	−	0.164720i	−0.830712	+	0.556702i	$0.812067\pi$
$3$	−1.57417	−	0.722492i	−0.908846	−	0.417131i
$3$	−1.57417	−	0.722492i	−0.908846	−	0.417131i
$4$	0.331239	−	1.87855i	0.165619	−	0.939274i
$5$	−2.07799	+	0.825805i	−0.929306	+	0.369311i
$5$	−2.07799	+	0.825805i	−0.929306	+	0.369311i
$6$	0.139394	+	0.507924i	0.0569076	+	0.207359i
$7$	−3.36181	+	0.592777i	−1.27064	+	0.224049i	−0.768003	−	0.640446i	$-0.778749\pi$
$7$	−3.36181	+	0.592777i	−1.27064	+	0.224049i	−0.502641	+	0.864495i	$0.667638\pi$
$8$	−1.02906	+	0.594126i	−0.363826	+	0.210055i
$9$	1.95601	+	2.27465i	0.652003	+	0.758216i
$10$	0.598549	+	0.322648i	0.189278	+	0.102030i
$11$	−2.75854	−	1.00403i	−0.831732	−	0.302726i	−0.109162	−	0.994024i	$-0.534817\pi$
$11$	−2.75854	−	1.00403i	−0.831732	−	0.302726i	−0.722569	+	0.691298i	$0.757039\pi$
$12$	−1.87866	+	2.71783i	−0.542323	+	0.784571i
$13$	3.53380	−	4.21142i	0.980100	−	1.16804i	−0.00567819	−	0.999984i	$-0.501807\pi$
$13$	3.53380	−	4.21142i	0.980100	−	1.16804i	0.985778	−	0.168053i	$-0.0537481\pi$
$14$	0.795210	+	0.667260i	0.212529	+	0.178333i
$15$	3.86774	+	0.201377i	0.998647	+	0.0519954i
$16$	−3.24543	−	1.18124i	−0.811358	−	0.295310i
$17$	−1.83496	−	1.05942i	−0.445044	−	0.256946i	0.260691	−	0.965422i	$-0.416050\pi$
$17$	−1.83496	−	1.05942i	−0.445044	−	0.256946i	−0.705735	+	0.708476i	$0.749383\pi$
$18$	0.147541	−	0.900269i	0.0347757	−	0.212195i
$19$	−2.20534	−	3.81976i	−0.505940	−	0.876313i	−0.999976	−	0.00687212i	$-0.997813\pi$
$19$	−2.20534	−	3.81976i	−0.505940	−	0.876313i	0.494037	−	0.869441i	$-0.335521\pi$
$20$	0.863003	+	4.17714i	0.192973	+	0.934038i
$21$	5.72033	+	1.49575i	1.24828	+	0.326399i
$22$	0.305317	+	0.838853i	0.0650939	+	0.178844i
$23$	4.56507	+	0.804944i	0.951882	+	0.167843i	0.627964	−	0.778243i	$-0.283889\pi$
$23$	4.56507	+	0.804944i	0.951882	+	0.167843i	0.323918	+	0.946085i	$0.395000\pi$
$24$	2.04916	−	0.191769i	0.418283	−	0.0391446i
$25$	3.63609	−	3.43203i	0.727219	−	0.686406i
$26$	−1.67179			−0.327864
$27$	−1.43567	−	4.99388i	−0.276295	−	0.961073i
$28$			6.51167i			1.23059i
$29$	0.308828	−	0.259138i	0.0573480	−	0.0481207i	−0.613663	−	0.789568i	$-0.710305\pi$
$29$	0.308828	−	0.259138i	0.0573480	−	0.0481207i	0.671011	+	0.741447i	$0.265860\pi$
$30$	−0.709106	−	0.940348i	−0.129465	−	0.171683i
$31$	−0.573021	+	3.24976i	−0.102918	+	0.583674i	0.889114	+	0.457686i	$0.151321\pi$
$31$	−0.573021	+	3.24976i	−0.102918	+	0.583674i	−0.992032	+	0.125989i	$0.959790\pi$
$32$	1.17202	+	3.22009i	0.207186	+	0.569238i
$33$	3.61701	+	3.57353i	0.629640	+	0.622072i
$34$	0.111885	+	0.634533i	0.0191882	+	0.108821i
$35$	6.49629	−	4.00798i	1.09807	−	0.677473i
$36$	4.92094	−	2.92101i	0.820157	−	0.486834i
$37$	3.52072	+	2.03269i	0.578803	+	0.334172i	0.760658	−	0.649153i	$-0.224877\pi$
$37$	3.52072	+	2.03269i	0.578803	+	0.334172i	−0.181854	+	0.983325i	$0.558210\pi$
$38$	−0.458737	+	1.26037i	−0.0744169	+	0.204459i
$39$	−8.60551	+	4.07634i	−1.37798	+	0.652736i
$40$	1.64774	−	2.08439i	0.260530	−	0.329570i
$41$	−3.73852	−	3.13699i	−0.583859	−	0.489916i	0.302353	−	0.953196i	$-0.402228\pi$
$41$	−3.73852	−	3.13699i	−0.583859	−	0.489916i	−0.886212	+	0.463280i	$0.846672\pi$
$42$	−0.769703	−	1.62491i	−0.118768	−	0.250729i
$43$	0.0361245	−	0.0992511i	0.00550893	−	0.0151357i	−0.936908	−	0.349577i	$-0.886325\pi$
$43$	0.0361245	−	0.0992511i	0.00550893	−	0.0151357i	0.942417	+	0.334441i	$0.108548\pi$
$44$	−2.79985	+	4.84948i	−0.422093	+	0.731087i
$45$	−5.94299	−	3.11142i	−0.885928	−	0.463823i
$46$	−0.704810	−	1.22077i	−0.103919	−	0.179992i
$47$	−11.3497	+	2.00126i	−1.65552	+	0.291913i	−0.921837	−	0.387577i	$-0.873312\pi$
$47$	−11.3497	+	2.00126i	−1.65552	+	0.291913i	−0.733684	+	0.679490i	$0.762201\pi$
$48$	4.25542	+	4.20427i	0.614217	+	0.606834i
$49$	4.37252	−	1.59147i	0.624646	−	0.227352i
$50$	−1.51022	−	0.176174i	−0.213578	−	0.0249148i
$51$	2.12312	+	2.99344i	0.297296	+	0.419166i
$52$	−6.74082	−	8.03340i	−0.934784	−	1.11403i
$53$		−	11.5814i		−	1.59083i	−0.606068	−	0.795413i	$-0.707254\pi$
$53$		−	11.5814i		−	1.59083i	0.606068	−	0.795413i	$-0.292746\pi$
$54$	−0.882691	+	1.31058i	−0.120119	+	0.178347i
$55$	6.56135	−	0.191657i	0.884733	−	0.0258431i
$56$	3.10730	−	2.60734i	0.415231	−	0.348420i
$57$	0.711828	+	7.60629i	0.0942839	+	1.00748i
$58$	−0.120732	−	0.0212882i	−0.0158528	−	0.00279528i
$59$	5.15923	−	1.87781i	0.671674	−	0.244469i	0.0164056	−	0.999865i	$-0.494778\pi$
$59$	5.15923	−	1.87781i	0.671674	−	0.244469i	0.655269	+	0.755396i	$0.272555\pi$
$60$	1.65944	−	7.19904i	0.214233	−	0.929392i
$61$	1.18992	+	6.74834i	0.152353	+	0.864037i	0.961166	+	0.275971i	$0.0889993\pi$
$61$	1.18992	+	6.74834i	0.152353	+	0.864037i	−0.808813	+	0.588066i	$0.799890\pi$
$62$	0.869034	−	0.501737i	0.110367	−	0.0637207i
$63$	−7.92409	−	6.48745i	−0.998341	−	0.817342i
$64$	−2.93269	+	5.07957i	−0.366586	+	0.634946i
$65$	−3.86539	+	11.6695i	−0.479443	+	1.44743i
$66$	0.125444	−	1.54108i	0.0154411	−	0.189694i
$67$	−2.45463	+	2.92531i	−0.299881	+	0.357384i	−0.894852	−	0.446363i	$-0.852719\pi$
$67$	−2.45463	+	2.92531i	−0.299881	+	0.357384i	0.594971	+	0.803747i	$0.297163\pi$
$68$	−2.59797	+	3.09614i	−0.315051	+	0.375463i
$69$	−6.60462	−	4.56534i	−0.795102	−	0.549603i
$70$	−2.20346	−	0.729873i	−0.263364	−	0.0872365i
$71$	6.75694	−	11.7034i	0.801901	−	1.38893i	−0.116462	−	0.993195i	$-0.537155\pi$
$71$	6.75694	−	11.7034i	0.801901	−	1.38893i	0.918363	−	0.395738i	$-0.129511\pi$
$72$	−3.36427	−	1.17862i	−0.396483	−	0.138902i
$73$	−6.69232	+	3.86382i	−0.783277	+	0.452225i	−0.837591	−	0.546299i	$-0.816036\pi$
$73$	−6.69232	+	3.86382i	−0.783277	+	0.452225i	0.0543132	+	0.998524i	$0.482703\pi$
$74$	−0.214673	−	1.21747i	−0.0249552	−	0.141528i
$75$	−8.20344	+	2.77554i	−0.947251	+	0.320492i
$76$	−7.90610	+	2.87758i	−0.906891	+	0.330082i
$77$	9.86885	+	1.74014i	1.12466	+	0.198308i
$78$	2.63167	+	1.20785i	0.297978	+	0.136762i
$79$	−1.80591	+	1.51534i	−0.203181	+	0.170489i	−0.738701	−	0.674034i	$-0.764560\pi$
$79$	−1.80591	+	1.51534i	−0.203181	+	0.170489i	0.535520	+	0.844523i	$0.320116\pi$
$80$	7.71945	−	0.225486i	0.863061	−	0.0252100i
$81$	−1.34805	+	8.89847i	−0.149784	+	0.988719i
$82$			1.48406i			0.163887i
$83$	−4.37992	−	5.21978i	−0.480758	−	0.572946i	0.470084	−	0.882622i	$-0.344224\pi$
$83$	−4.37992	−	5.21978i	−0.480758	−	0.572946i	−0.950842	+	0.309676i	$0.899779\pi$
$84$	4.70463	−	10.2505i	0.513317	−	1.11842i
$85$	4.68790	+	0.686136i	0.508475	+	0.0744219i
$86$	−0.0301816	+	0.0109852i	−0.00325456	+	0.00118456i
$87$	−0.673373	+	0.184800i	−0.0721931	+	0.0198127i
$88$	3.43521	−	0.605720i	0.366195	−	0.0645700i
$89$	0.870723	+	1.50814i	0.0922964	+	0.159862i	0.908477	−	0.417935i	$-0.137246\pi$
$89$	0.870723	+	1.50814i	0.0922964	+	0.159862i	−0.816181	+	0.577797i	$0.803913\pi$
$90$	0.436858	+	1.99259i	0.0460489	+	0.210037i
$91$	−9.38352	+	16.2527i	−0.983660	+	1.70375i
$92$	3.02425	−	8.30907i	0.315300	−	0.866280i
$93$	3.24996	−	4.70167i	0.337005	−	0.487540i
$94$	2.68468	+	2.25271i	0.276904	+	0.232350i
$95$	7.73705	+	6.11625i	0.793805	+	0.627514i
$96$	0.481539	−	5.91574i	0.0491469	−	0.603773i
$97$	−0.152119	+	0.417944i	−0.0154454	+	0.0424358i	−0.947176	−	0.320715i	$-0.896077\pi$
$97$	−0.152119	+	0.417944i	−0.0154454	+	0.0424358i	0.931730	+	0.363151i	$0.118299\pi$
$98$	−1.22541	−	0.707493i	−0.123785	−	0.0714676i
$99$	−3.11193	−	8.23860i	−0.312760	−	0.828010i
$100$	−5.24282	−	7.96740i	−0.524282	−	0.796740i
$101$	−1.10822	−	6.28500i	−0.110272	−	0.625381i	−0.988983	−	0.148028i	$-0.952707\pi$
$101$	−1.10822	−	6.28500i	−0.110272	−	0.625381i	0.878712	−	0.477353i	$-0.158404\pi$
$102$	0.282319	−	1.07970i	0.0279537	−	0.106906i
$103$	−4.17454	−	11.4695i	−0.411330	−	1.13012i	−0.956484	−	0.291783i	$-0.905751\pi$
$103$	−4.17454	−	11.4695i	−0.411330	−	1.13012i	0.545155	−	0.838335i	$-0.316471\pi$
$104$	−1.13437	+	6.43330i	−0.111234	+	0.630837i
$105$	−13.1220	+	1.61572i	−1.28057	+	0.157678i
$106$	−2.69787	+	2.26378i	−0.262040	+	0.219878i
$107$			1.69143i			0.163517i	0.996652	+	0.0817585i	$0.0260536\pi$
$107$			1.69143i			0.163517i	−0.996652	+	0.0817585i	$0.973946\pi$
$108$	−9.85679	+	1.04281i	−0.948471	+	0.100345i
$109$	15.3531			1.47056			0.735279	−	0.677765i	$-0.237051\pi$
$109$	15.3531			1.47056			0.735279	+	0.677765i	$0.237051\pi$
$110$	−1.32718	−	1.49100i	−0.126541	−	0.142161i
$111$	−4.07361	−	5.74349i	−0.386650	−	0.545148i
$112$	11.6107	+	2.04729i	1.09711	+	0.193450i
$113$	5.36085	+	14.7288i	0.504307	+	1.38557i	0.887031	+	0.461709i	$0.152764\pi$
$113$	5.36085	+	14.7288i	0.504307	+	1.38557i	−0.382725	+	0.923862i	$0.625014\pi$
$114$	1.63273	−	1.65260i	0.152920	−	0.154780i
$115$	−10.1509	+	2.09719i	−0.946576	+	0.195564i
$116$	−0.384507	−	0.665985i	−0.0357005	−	0.0618352i
$117$	16.4916	−	0.199423i	1.52465	−	0.0184366i
$118$	−1.44589	−	0.834786i	−0.133105	−	0.0768483i
$119$	6.79679	+	2.47383i	0.623060	+	0.226775i
$120$	−4.09977	+	2.09070i	−0.374256	+	0.190854i
$121$	−1.82501	−	1.53136i	−0.165910	−	0.139215i
$122$	1.33943	−	1.59627i	0.121266	−	0.144519i
$123$	3.61861	+	7.63921i	0.326279	+	0.688804i
$124$	5.91503	+	2.15289i	0.531185	+	0.193336i
$125$	−4.72158	+	10.1344i	−0.422311	+	0.906451i
$126$	0.0376555	+	3.11399i	0.00335462	+	0.277416i
$127$	11.2018	−	6.46736i	0.993998	−	0.573885i	0.0875312	−	0.996162i	$-0.472102\pi$
$127$	11.2018	−	6.46736i	0.993998	−	0.573885i	0.906467	+	0.422277i	$0.138769\pi$
$128$	8.50591	−	1.49982i	0.751823	−	0.132567i
$129$	−0.128574	+	0.130138i	−0.0113203	+	0.0114580i
$130$	3.47396	−	1.38057i	0.304686	−	0.121084i
$131$	1.99841	−	11.3335i	0.174602	−	0.990215i	−0.764001	−	0.645215i	$-0.776768\pi$
$131$	1.99841	−	11.3335i	0.174602	−	0.990215i	0.938603	−	0.345000i	$-0.112121\pi$
$132$	7.91114	−	5.61103i	0.688577	−	0.488377i
$133$	9.67820	+	11.5340i	0.839206	+	1.00013i
$134$	1.16125			0.100316
$135$	7.10728	+	9.19166i	0.611698	+	0.791092i
$136$	2.51770			0.215891
$137$	7.83825	+	9.34126i	0.669667	+	0.798078i	0.988739	−	0.149653i	$-0.0478155\pi$
$137$	7.83825	+	9.34126i	0.669667	+	0.798078i	−0.319072	+	0.947731i	$0.603371\pi$
$138$	0.227495	+	2.43091i	0.0193656	+	0.206933i
$139$	−0.0420242	+	0.238331i	−0.00356445	+	0.0202150i	−0.986538	−	0.163532i	$-0.947711\pi$
$139$	−0.0420242	+	0.238331i	−0.00356445	+	0.0202150i	0.982974	+	0.183747i	$0.0588226\pi$
$140$	−5.37737	−	13.5312i	−0.454470	−	1.14359i
$141$	19.3122	+	5.04975i	1.62638	+	0.425265i
$142$	−4.04704	+	0.713602i	−0.339620	+	0.0598842i
$143$	−13.9765	+	8.06934i	−1.16877	+	0.674792i
$144$	−3.66119	−	9.69273i	−0.305099	−	0.807728i
$145$	−0.427745	+	0.793518i	−0.0355223	+	0.0658980i
$146$	2.20820	+	0.803719i	0.182752	+	0.0665163i
$147$	−8.03290	−	0.653875i	−0.662543	−	0.0539307i
$148$	4.98470	−	5.94054i	0.409740	−	0.488309i
$149$	−9.73479	−	8.16846i	−0.797505	−	0.669186i	0.150086	−	0.988673i	$-0.452045\pi$
$149$	−9.73479	−	8.16846i	−0.797505	−	0.669186i	−0.947591	+	0.319487i	$0.896489\pi$
$150$	2.25006	+	1.36845i	0.183717	+	0.111734i
$151$	4.13101	+	1.50356i	0.336177	+	0.122358i	0.504592	−	0.863358i	$-0.331643\pi$
$151$	4.13101	+	1.50356i	0.336177	+	0.122358i	−0.168416	+	0.985716i	$0.553865\pi$
$152$	4.53883	+	2.62050i	0.368148	+	0.212550i
$153$	−1.17940	−	6.24612i	−0.0953492	−	0.504969i
$154$	−1.52367	−	2.63908i	−0.122781	−	0.212663i
$155$	−1.49294	−	7.22618i	−0.119916	−	0.580421i
$156$	4.80712	+	17.5161i	0.384877	+	1.40241i
$157$	1.69008	+	4.64345i	0.134883	+	0.370587i	0.988684	−	0.150011i	$-0.0479310\pi$
$157$	1.69008	+	4.64345i	0.134883	+	0.370587i	−0.853802	+	0.520599i	$0.825709\pi$
$158$	0.705992	+	0.124486i	0.0561657	+	0.00990353i
$159$	−8.36746	+	18.2310i	−0.663583	+	1.44582i
$160$	−5.09461	−	5.72347i	−0.402765	−	0.452480i
$161$	−15.8240			−1.24711
$162$	2.33639	−	1.42533i	0.183564	−	0.111985i
$163$		−	0.134430i		−	0.0105294i	−0.999986	−	0.00526468i	$-0.998324\pi$
$163$		−	0.134430i		−	0.0105294i	0.999986	−	0.00526468i	$-0.00167581\pi$
$164$	−7.13134	+	5.98390i	−0.556864	+	0.467264i
$165$	−10.4671	−	4.43883i	−0.814866	−	0.345562i
$166$	−0.359811	+	2.04059i	−0.0279268	+	0.158381i
$167$	−5.22746	−	14.3623i	−0.404513	−	1.11139i	−0.960033	−	0.279887i	$-0.909703\pi$
$167$	−5.22746	−	14.3623i	−0.404513	−	1.11139i	0.555520	−	0.831503i	$-0.312519\pi$
$168$	−6.77520	+	1.85938i	−0.522718	+	0.143455i
$169$	−2.99088	−	16.9621i	−0.230068	−	1.30478i
$170$	−0.756497	−	1.22616i	−0.0580206	−	0.0940420i
$171$	4.37495	−	12.4879i	0.334561	−	0.954971i
$172$	−0.174482	−	0.100737i	−0.0133041	−	0.00768115i
$173$	5.17275	−	14.2120i	0.393277	−	1.08052i	−0.572218	−	0.820101i	$-0.693917\pi$
$173$	5.17275	−	14.2120i	0.393277	−	1.08052i	0.965496	−	0.260419i	$-0.0838607\pi$
$174$	0.174671	+	0.120739i	0.0132418	+	0.00915319i
$175$	−10.1894	+	13.6932i	−0.770248	+	1.03511i
$176$	7.76666	+	6.51700i	0.585434	+	0.491238i
$177$	−9.47819	−	0.771521i	−0.712424	−	0.0579911i
$178$	0.181121	−	0.497625i	0.0135756	−	0.0372985i
$179$	0.794987	−	1.37696i	0.0594201	−	0.102919i	−0.834785	−	0.550576i	$-0.814408\pi$
$179$	0.794987	−	1.37696i	0.0594201	−	0.102919i	0.894205	+	0.447657i	$0.147742\pi$
$180$	−7.81349	+	10.1336i	−0.582383	+	0.755311i
$181$	−10.8756	−	18.8371i	−0.808375	−	1.40015i	−0.913989	−	0.405740i	$-0.867014\pi$
$181$	−10.8756	−	18.8371i	−0.808375	−	1.40015i	0.105613	−	0.994407i	$-0.466319\pi$
$182$	5.62022	−	0.990997i	0.416599	−	0.0734576i
$183$	3.00250	−	11.4827i	0.221951	−	0.848828i
$184$	−5.17595	+	1.88389i	−0.381576	+	0.138882i
$185$	−8.99463	−	1.31648i	−0.661299	−	0.0967897i
$186$	−1.73051	+	0.161948i	−0.126887	+	0.0118746i
$187$	3.99814	+	4.76479i	0.292373	+	0.348436i
$188$			21.9838i			1.60333i
$189$	7.78671	+	15.9374i	0.566400	+	1.15928i
$190$	−0.0875677	−	2.99786i	−0.00635283	−	0.217488i
$191$	−6.03626	+	5.06502i	−0.436768	+	0.366492i	−0.834498	−	0.551010i	$-0.814242\pi$
$191$	−6.03626	+	5.06502i	−0.436768	+	0.366492i	0.397730	+	0.917502i	$0.369798\pi$
$192$	8.28650	−	5.87725i	0.598026	−	0.424154i
$193$	−17.5840	−	3.10054i	−1.26573	−	0.223182i	−0.499817	−	0.866131i	$-0.666599\pi$
$193$	−17.5840	−	3.10054i	−1.26573	−	0.223182i	−0.765909	+	0.642950i	$0.777710\pi$
$194$	0.127094	−	0.0462583i	0.00912480	−	0.00332115i
$195$	14.5159	−	15.5771i	1.03951	−	1.11550i
$196$	−1.54130	−	8.74114i	−0.110093	−	0.624367i
$197$	8.23989	−	4.75730i	0.587068	−	0.338944i	−0.176870	−	0.984234i	$-0.556597\pi$
$197$	8.23989	−	4.75730i	0.587068	−	0.338944i	0.763937	+	0.645291i	$0.223264\pi$
$198$	−1.31089	+	2.33529i	−0.0931610	+	0.165962i
$199$	−5.46922	+	9.47297i	−0.387703	+	0.671521i	−0.992140	−	0.125132i	$-0.960065\pi$
$199$	−5.46922	+	9.47297i	−0.387703	+	0.671521i	0.604437	+	0.796653i	$0.293398\pi$
$200$	−1.70269	+	5.69205i	−0.120398	+	0.402488i
$201$	5.97751	−	2.83148i	0.421621	−	0.199717i
$202$	−1.24746	+	1.48667i	−0.0877712	+	0.104602i
$203$	−0.884610	+	1.05424i	−0.0620875	+	0.0739930i
$204$	6.32659	−	2.99684i	0.442950	−	0.209820i
$205$	10.3592	+	3.43135i	0.723515	+	0.239656i
$206$	−1.85581	+	3.21435i	−0.129300	+	0.223955i
$207$	7.09835	+	11.9584i	0.493369	+	0.831166i
$208$	−16.4434	+	9.49360i	−1.14014	+	0.658263i
$209$	2.24838	+	12.7512i	0.155524	+	0.882018i
$210$	2.94130	+	2.74093i	0.202969	+	0.189142i
$211$	9.58727	−	3.48948i	0.660015	−	0.240226i	0.00977203	−	0.999952i	$-0.496889\pi$
$211$	9.58727	−	3.48948i	0.660015	−	0.240226i	0.650243	+	0.759727i	$0.274667\pi$
$212$	−21.7562	−	3.83620i	−1.49422	−	0.263471i
$213$	−19.0921	+	13.5412i	−1.30817	+	0.927829i
$214$	0.394017	−	0.330619i	0.0269344	−	0.0226007i
$215$	0.00689575	+	0.236075i	0.000470286	+	0.0161002i
$216$	4.44438	+	4.28601i	0.302402	+	0.291626i
$217$		−	11.2647i		−	0.764701i
$218$	−3.00102	−	3.57648i	−0.203255	−	0.242230i
$219$	13.3264	−	1.24714i	0.900516	−	0.0842740i
$220$	1.81334	−	12.3893i	0.122255	−	0.835287i
$221$	−10.9460	+	3.98403i	−0.736310	+	0.267995i
$222$	−0.541682	+	2.07160i	−0.0363553	+	0.139037i
$223$	22.5991	−	3.98483i	1.51335	−	0.266844i	0.645534	−	0.763732i	$-0.276635\pi$
$223$	22.5991	−	3.98483i	1.51335	−	0.266844i	0.867815	+	0.496888i	$0.165524\pi$
$224$	−5.84890	−	10.1306i	−0.390796	−	0.676879i
$225$	14.9189	+	1.55775i	0.994593	+	0.103850i
$226$	2.38319	−	4.12780i	0.158527	−	0.274577i
$227$	−2.44376	+	6.71417i	−0.162198	+	0.445635i	−0.993992	−	0.109448i	$-0.965092\pi$
$227$	−2.44376	+	6.71417i	−0.162198	+	0.445635i	0.831794	+	0.555084i	$0.187314\pi$
$228$	14.5246	+	1.18229i	0.961912	+	0.0782993i
$229$	−14.3264	−	12.0213i	−0.946713	−	0.794387i	0.0320278	−	0.999487i	$-0.489803\pi$
$229$	−14.3264	−	12.0213i	−0.946713	−	0.794387i	−0.978741	+	0.205100i	$0.934248\pi$
$230$	2.47270	+	1.95471i	0.163045	+	0.128890i
$231$	−14.2780	−	9.86945i	−0.939423	−	0.649362i
$232$	−0.163841	+	0.450150i	−0.0107567	+	0.0295538i
$233$	−21.3371	−	12.3190i	−1.39784	−	0.807043i	−0.403673	−	0.914903i	$-0.632267\pi$
$233$	−21.3371	−	12.3190i	−1.39784	−	0.807043i	−0.994166	+	0.107861i	$0.965600\pi$
$234$	−3.27003	−	3.80273i	−0.213768	−	0.248592i
$235$	21.9319	−	13.5312i	1.43068	−	0.882679i
$236$	−1.81861	−	10.3139i	−0.118382	−	0.671375i
$237$	3.93763	−	1.08064i	0.255776	−	0.0701952i
$238$	−0.752273	−	2.06685i	−0.0487626	−	0.133974i
$239$	−3.02299	+	17.1443i	−0.195541	+	1.10897i	0.716105	+	0.697993i	$0.245923\pi$
$239$	−3.02299	+	17.1443i	−0.195541	+	1.10897i	−0.911646	+	0.410977i	$0.865188\pi$
$240$	−12.3146	−	5.22229i	−0.794906	−	0.337098i
$241$	−5.58320	+	4.68486i	−0.359646	+	0.301778i	−0.804649	−	0.593750i	$-0.797647\pi$
$241$	−5.58320	+	4.68486i	−0.359646	+	0.301778i	0.445004	+	0.895529i	$0.353202\pi$
$242$			0.724464i			0.0465703i
$243$	8.55114	−	13.0337i	0.548556	−	0.836114i
$244$	13.0712			0.836800
$245$	−7.77181	+	6.91790i	−0.496523	+	0.441968i
$246$	1.07222	−	2.33616i	0.0683625	−	0.148948i
$247$	−23.8798	−	4.21066i	−1.51944	−	0.267918i
$248$	−1.34110	−	3.68463i	−0.0851597	−	0.233974i
$249$	3.12347	+	11.3813i	0.197942	+	0.721259i
$250$	3.28372	−	0.881061i	0.207680	−	0.0557232i
$251$	11.4223	+	19.7840i	0.720971	+	1.24876i	0.960611	+	0.277896i	$0.0896371\pi$
$251$	11.4223	+	19.7840i	0.720971	+	1.24876i	−0.239641	+	0.970862i	$0.577030\pi$
$252$	−14.8118	+	12.7369i	−0.933053	+	0.802348i
$253$	−11.7847	−	6.80392i	−0.740900	−	0.427759i
$254$	−3.69614	−	1.34529i	−0.231917	−	0.0844108i
$255$	−6.88382	−	4.46707i	−0.431082	−	0.279739i
$256$	6.97428	+	5.85212i	0.435892	+	0.365757i
$257$	0.945818	−	1.12718i	0.0589985	−	0.0703117i	−0.735738	−	0.677266i	$-0.763165\pi$
$257$	0.945818	−	1.12718i	0.0589985	−	0.0703117i	0.794737	+	0.606955i	$0.207609\pi$
$258$	0.0554476	+	0.00451341i	0.00345201	+	0.000280993i
$259$	−13.0409	−	4.74651i	−0.810324	−	0.294934i
$260$	20.6414	+	11.1267i	1.28012	+	0.690050i
$261$	1.19352	+	0.195600i	0.0738769	+	0.0121073i
$262$	−3.03075	+	1.74981i	−0.187241	+	0.108103i
$263$	21.2787	−	3.75201i	1.31210	−	0.231359i	0.526543	−	0.850148i	$-0.323488\pi$
$263$	21.2787	−	3.75201i	1.31210	−	0.231359i	0.785557	+	0.618790i	$0.212377\pi$
$264$	−5.84523	−	1.52841i	−0.359749	−	0.0940670i
$265$	9.56396	+	24.0660i	0.587510	+	1.47836i
$266$	0.795066	−	4.50905i	0.0487486	−	0.276467i
$267$	−0.281047	−	3.00315i	−0.0171998	−	0.183790i
$268$	4.68227	+	5.58012i	0.286015	+	0.340860i
$269$	13.3362			0.813125			0.406562	−	0.913623i	$-0.366727\pi$
$269$	13.3362			0.813125			0.406562	+	0.913623i	$0.366727\pi$
$270$	0.751943	−	3.45230i	0.0457618	−	0.210100i
$271$	19.7312			1.19859			0.599293	−	0.800530i	$-0.295448\pi$
$271$	19.7312			1.19859			0.599293	+	0.800530i	$0.295448\pi$
$272$	4.70382	+	5.60579i	0.285211	+	0.339901i
$273$	26.5137	−	18.8050i	1.60468	−	1.13813i
$274$	0.643914	−	3.65182i	0.0389003	−	0.220614i
$275$	−13.4762	+	5.81666i	−0.812643	+	0.350758i
$276$	−10.7639	+	10.8949i	−0.647912	+	0.655794i
$277$	26.1115	−	4.60416i	1.56889	−	0.276637i	0.679460	−	0.733712i	$-0.262214\pi$
$277$	26.1115	−	4.60416i	1.56889	−	0.276637i	0.889428	+	0.457075i	$0.151103\pi$
$278$	0.0637333	−	0.0367964i	0.00382247	−	0.00220690i
$279$	−8.51290	+	5.05314i	−0.509654	+	0.302524i
$280$	−4.30380	+	7.98405i	−0.257201	+	0.477138i
$281$	−6.13842	−	2.23420i	−0.366188	−	0.133281i	0.152371	−	0.988323i	$-0.451309\pi$
$281$	−6.13842	−	2.23420i	−0.366188	−	0.133281i	−0.518559	+	0.855042i	$0.673531\pi$
$282$	−2.59857	−	5.48581i	−0.154742	−	0.326675i
$283$	−4.12955	+	4.92140i	−0.245476	+	0.292547i	−0.874688	−	0.484687i	$-0.838933\pi$
$283$	−4.12955	+	4.92140i	−0.245476	+	0.292547i	0.629212	+	0.777234i	$0.283378\pi$
$284$	−19.7472	−	16.5698i	−1.17178	−	0.983239i
$285$	−7.76048	−	15.2180i	−0.459691	−	0.901434i
$286$	4.61169	+	1.67852i	0.272695	+	0.0992529i
$287$	14.4277	+	8.32986i	0.851642	+	0.491696i
$288$	−5.03210	+	8.96447i	−0.296520	+	0.528236i
$289$	−6.25528	−	10.8345i	−0.367957	−	0.637321i
$290$	0.268459	−	0.0554639i	0.0157645	−	0.00325695i
$291$	0.541422	−	0.548009i	0.0317387	−	0.0321248i
$292$	5.04161	+	13.8517i	0.295038	+	0.810609i
$293$	13.7780	+	2.42943i	0.804919	+	0.141929i	0.560945	−	0.827853i	$-0.310438\pi$
$293$	13.7780	+	2.42943i	0.804919	+	0.141929i	0.243974	+	0.969782i	$0.421549\pi$
$294$	1.41785	+	1.99906i	0.0826906	+	0.116588i
$295$	−9.17013	+	8.16258i	−0.533905	+	0.475244i
$296$	−4.83069			−0.280778
$297$	−1.05363	+	15.2173i	−0.0611379	+	0.882996i
$298$			3.86437i			0.223857i
$299$	19.5220	−	16.3809i	1.12899	−	0.947332i
$300$	2.49669	+	16.3299i	0.144147	+	0.942808i
$301$	−0.0626096	+	0.355077i	−0.00360876	+	0.0204663i
$302$	−0.457223	−	1.25621i	−0.0263102	−	0.0722868i
$303$	−2.79635	+	10.6943i	−0.160646	+	0.614373i
$304$	2.64522	+	15.0018i	0.151714	+	0.860413i
$305$	−8.04545	−	13.0404i	−0.460681	−	0.746689i
$306$	−1.22449	+	1.49565i	−0.0699995	+	0.0855007i
$307$	−13.7290	−	7.92646i	−0.783557	−	0.452387i	0.0541324	−	0.998534i	$-0.482761\pi$
$307$	−13.7290	−	7.92646i	−0.783557	−	0.452387i	−0.837689	+	0.546147i	$0.816094\pi$
$308$	6.53789	−	17.9627i	0.372531	−	1.02352i
$309$	−1.71517	+	21.0709i	−0.0975723	+	1.19868i
$310$	−1.39151	+	1.76026i	−0.0790324	+	0.0999759i
$311$	11.9922	+	10.0626i	0.680015	+	0.570600i	0.916011	−	0.401154i	$-0.131391\pi$
$311$	11.9922	+	10.0626i	0.680015	+	0.570600i	−0.235996	+	0.971754i	$0.575835\pi$
$312$	6.43369	−	9.30753i	0.364236	−	0.526935i
$313$	0.347220	−	0.953980i	0.0196261	−	0.0539221i	−0.929493	−	0.368840i	$-0.879755\pi$
$313$	0.347220	−	0.953980i	0.0196261	−	0.0539221i	0.949119	+	0.314918i	$0.101977\pi$
$314$	0.751330	−	1.30134i	0.0424000	−	0.0734390i
$315$	21.8236	+	6.93712i	1.22962	+	0.390862i
$316$	2.24845	+	3.89443i	0.126485	+	0.219079i
$317$	−11.3695	+	2.00474i	−0.638573	+	0.112598i	−0.483555	−	0.875314i	$-0.660655\pi$
$317$	−11.3695	+	2.00474i	−0.638573	+	0.112598i	−0.155018	+	0.987912i	$0.549544\pi$
$318$	5.88246	−	1.61438i	0.329872	−	0.0905300i
$319$	−1.11210	+	0.404770i	−0.0622655	+	0.0226628i
$320$	1.89937	−	12.9771i	0.106178	−	0.725444i
$321$	1.22205	−	2.66260i	0.0682080	−	0.148612i
$322$	3.09308	+	3.68619i	0.172370	+	0.205423i
$323$			9.34549i			0.519997i
$324$	16.2697	+	5.47990i	0.903871	+	0.304439i
$325$	−1.60449	−	27.4412i	−0.0890009	−	1.52216i
$326$	−0.0313152	+	0.0262766i	−0.00173439	+	0.00145533i
$327$	−24.1683	−	11.0925i	−1.33651	−	0.613415i
$328$	5.71092	+	1.00699i	0.315333	+	0.0556017i
$329$	36.9692	−	13.4557i	2.03818	−	0.741835i
$330$	1.01196	+	3.30595i	0.0557068	+	0.181987i
$331$	−0.601404	−	3.41073i	−0.0330562	−	0.187471i	0.963809	−	0.266595i	$-0.0858987\pi$
$331$	−0.601404	−	3.41073i	−0.0330562	−	0.187471i	−0.996865	+	0.0791244i	$0.974788\pi$
$332$	−11.2564	+	6.49889i	−0.617776	+	0.356673i
$333$	2.26291	+	11.9844i	0.124007	+	0.656739i
$334$	−2.32389	+	4.02509i	−0.127157	+	0.220243i
$335$	2.68496	−	8.10582i	0.146695	−	0.442868i
$336$	−16.7981	−	11.6114i	−0.916411	−	0.633456i
$337$	0.0975969	−	0.116311i	0.00531644	−	0.00633589i	−0.763380	−	0.645950i	$-0.776461\pi$
$337$	0.0975969	−	0.116311i	0.00531644	−	0.00633589i	0.768696	+	0.639614i	$0.220906\pi$
$338$	−3.36668	+	4.01226i	−0.183123	+	0.218238i
$339$	2.20258	−	27.0588i	0.119628	−	1.46963i
$340$	2.84176	−	8.57918i	0.154116	−	0.465271i
$341$	4.84355	−	8.38927i	0.262293	−	0.454305i
$342$	−3.76419	+	1.42183i	−0.203544	+	0.0768837i
$343$	6.93809	−	4.00571i	0.374622	−	0.216288i
$344$	0.0217936	+	0.123597i	0.00117503	+	0.00666392i
$345$	17.4944	+	4.03262i	0.941868	+	0.217109i
$346$	−4.32178	+	1.57300i	−0.232340	+	0.0845649i
$347$	−20.4648	−	3.60850i	−1.09861	−	0.193714i	−0.405178	−	0.914238i	$-0.632790\pi$
$347$	−20.4648	−	3.60850i	−1.09861	−	0.193714i	−0.693430	+	0.720524i	$0.743901\pi$
$348$	0.124109	+	1.32618i	0.00665294	+	0.0710905i
$349$	4.76037	−	3.99442i	0.254817	−	0.213816i	−0.506427	−	0.862283i	$-0.669034\pi$
$349$	4.76037	−	3.99442i	0.254817	−	0.213816i	0.761243	+	0.648467i	$0.224589\pi$
$350$	5.18151	−	0.302963i	0.276963	−	0.0161940i
$351$	−26.1047	−	11.6012i	−1.39337	−	0.619224i
$352$		−	10.0595i		−	0.536173i
$353$	3.85011	+	4.58839i	0.204921	+	0.244215i	0.858710	−	0.512461i	$-0.171266\pi$
$353$	3.85011	+	4.58839i	0.204921	+	0.244215i	−0.653789	+	0.756677i	$0.726822\pi$
$354$	1.67295	+	2.35874i	0.0889163	+	0.125366i
$355$	−4.37617	+	29.8994i	−0.232263	+	1.58689i
$356$	3.12152	−	1.13614i	0.165440	−	0.0602154i
$357$	−8.91196	−	8.80485i	−0.471671	−	0.466002i
$358$	−0.476154	+	0.0839588i	−0.0251655	+	0.00443736i
$359$	−0.255829	−	0.443109i	−0.0135022	−	0.0233864i	0.859195	−	0.511648i	$-0.170965\pi$
$359$	−0.255829	−	0.443109i	−0.0135022	−	0.0233864i	−0.872698	+	0.488261i	$0.837631\pi$
$360$	7.96424	−	0.329058i	0.419752	−	0.0173429i
$361$	−0.227046	+	0.393256i	−0.0119498	+	0.0206977i
$362$	−2.26225	+	6.21548i	−0.118901	+	0.326678i
$363$	1.76647	+	3.72918i	0.0927157	+	0.195731i
$364$	27.4234	+	23.0109i	1.43737	+	1.20610i
$365$	10.7158	−	13.5555i	0.560892	−	0.709529i
$366$	−3.26178	+	1.54507i	−0.170496	+	0.0807620i
$367$	−7.02326	+	19.2963i	−0.366611	+	1.00726i	0.610030	+	0.792378i	$0.291157\pi$
$367$	−7.02326	+	19.2963i	−0.366611	+	1.00726i	−0.976641	+	0.214878i	$0.931065\pi$
$368$	−13.8648	−	8.00483i	−0.722752	−	0.417281i
$369$	−0.177030	−	14.6398i	−0.00921581	−	0.762118i
$370$	1.45148	+	2.35262i	0.0754590	+	0.122307i
$371$	6.86518	+	38.9344i	0.356423	+	2.02137i
$372$	−7.75580	−	7.66258i	−0.402119	−	0.397286i
$373$	−4.29128	−	11.7902i	−0.222194	−	0.610472i	0.777640	−	0.628710i	$-0.216417\pi$
$373$	−4.29128	−	11.7902i	−0.222194	−	0.610472i	−0.999834	+	0.0182375i	$0.994195\pi$
$374$	0.328448	−	1.86272i	0.0169836	−	0.0963190i
$375$	14.7546	−	12.5420i	0.761925	−	0.647665i
$376$	10.4905	−	8.80254i	0.541004	−	0.453956i
$377$		−	2.21635i		−	0.114148i
$378$	2.19056	−	4.92915i	0.112670	−	0.253528i
$379$	−29.8914			−1.53542			−0.767710	−	0.640798i	$-0.778604\pi$
$379$	−29.8914			−1.53542			−0.767710	+	0.640798i	$0.778604\pi$
$380$	14.0525	−	12.5085i	0.720877	−	0.641672i
$381$	−22.3061	+	2.08750i	−1.14278	+	0.106946i
$382$	2.35978	+	0.416093i	0.120737	+	0.0212892i
$383$	7.45556	+	20.4840i	0.380961	+	1.04668i	0.970952	+	0.239273i	$0.0769089\pi$
$383$	7.45556	+	20.4840i	0.380961	+	1.04668i	−0.589991	+	0.807410i	$0.700869\pi$
$384$	−14.4733	−	3.78448i	−0.738589	−	0.193126i
$385$	−21.9444	+	4.53374i	−1.11839	+	0.231061i
$386$	2.71483	+	4.70223i	0.138181	+	0.239337i
$387$	0.296421	−	0.111966i	0.0150679	−	0.00569154i
$388$	0.734740	+	0.424202i	0.0373008	+	0.0215356i
$389$	−9.78677	−	3.56209i	−0.496209	−	0.180605i	0.0817791	−	0.996650i	$-0.473940\pi$
$389$	−9.78677	−	3.56209i	−0.496209	−	0.180605i	−0.577988	+	0.816045i	$0.696162\pi$
$390$	−6.46604	−	0.336660i	−0.327421	−	0.0170474i
$391$	−7.52395	−	6.31335i	−0.380503	−	0.319280i
$392$	−3.55403	+	4.23553i	−0.179506	+	0.213927i
$393$	−11.3342	+	16.3971i	−0.571736	+	0.827122i
$394$	−2.71883	−	0.989574i	−0.136973	−	0.0498540i
$395$	2.50129	−	4.64019i	0.125854	−	0.233473i
$396$	−16.5074	+	3.11696i	−0.829528	+	0.156633i
$397$	−18.9260	+	10.9269i	−0.949866	+	0.548406i	−0.893039	−	0.449978i	$-0.851432\pi$
$397$	−18.9260	+	10.9269i	−0.949866	+	0.548406i	−0.0568270	+	0.998384i	$0.518098\pi$
$398$	3.27577	−	0.577606i	0.164199	−	0.0289528i
$399$	−6.90186	−	25.1489i	−0.345525	−	1.25902i
$400$	−15.8547	+	6.84332i	−0.792737	+	0.342166i
$401$	−3.50040	+	19.8518i	−0.174802	+	0.991351i	0.763570	+	0.645725i	$0.223445\pi$
$401$	−3.50040	+	19.8518i	−0.174802	+	0.991351i	−0.938372	+	0.345626i	$0.887667\pi$
$402$	−1.82800	−	0.838992i	−0.0911722	−	0.0418451i
$403$	11.6612	+	13.8972i	0.580884	+	0.692271i
$404$	−12.1738			−0.605667
$405$	−4.54716	−	19.6042i	−0.225950	−	0.974139i
$406$	0.418495			0.0207696
$407$	−7.67118	−	9.14216i	−0.380246	−	0.453160i
$408$	−3.96329	−	1.81902i	−0.196212	−	0.0900550i
$409$	−2.34346	+	13.2904i	−0.115876	+	0.657168i	0.870436	+	0.492282i	$0.163837\pi$
$409$	−2.34346	+	13.2904i	−0.115876	+	0.657168i	−0.986313	+	0.164887i	$0.947274\pi$
$410$	−1.22555	−	3.08387i	−0.0605254	−	0.152301i
$411$	−5.58973	−	20.3678i	−0.275721	−	1.00467i
$412$	−22.9287	+	4.04295i	−1.12962	+	0.199182i
$413$	−16.2312	+	9.37109i	−0.798686	+	0.461121i
$414$	1.39820	−	3.99102i	0.0687178	−	0.196148i
$415$	13.4120	+	7.22970i	0.658367	+	0.354892i
$416$	17.7028	+	6.44331i	0.867953	+	0.315909i
$417$	0.238346	−	0.344811i	0.0116718	−	0.0168855i
$418$	2.53089	−	3.01619i	0.123790	−	0.147527i
$419$	1.56378	+	1.31217i	0.0763959	+	0.0641037i	0.680186	−	0.733040i	$-0.261899\pi$
$419$	1.56378	+	1.31217i	0.0763959	+	0.0641037i	−0.603790	+	0.797143i	$0.706343\pi$
$420$	−1.31130	+	25.1855i	−0.0639850	+	1.22892i
$421$	−2.58533	−	0.940984i	−0.126001	−	0.0458608i	0.278250	−	0.960509i	$-0.410246\pi$
$421$	−2.58533	−	0.940984i	−0.126001	−	0.0458608i	−0.404251	+	0.914648i	$0.632468\pi$
$422$	−2.68687	−	1.55126i	−0.130795	−	0.0755143i
$423$	−26.7522	−	21.9021i	−1.30074	−	1.06491i
$424$	6.88080	+	11.9179i	0.334161	+	0.578784i
$425$	−10.3080	+	2.44551i	−0.500013	+	0.118625i
$426$	6.88629	+	1.80063i	0.333642	+	0.0872406i
$427$	−8.00053	−	21.9813i	−0.387173	−	1.06375i
$428$	3.17744	+	0.560268i	0.153587	+	0.0270816i
$429$	27.8314	−	2.60458i	1.34371	−	0.125750i
$430$	0.0536454	−	0.0477512i	0.00258701	−	0.00230277i
$431$	20.0948			0.967932			0.483966	−	0.875087i	$-0.339196\pi$
$431$	20.0948			0.967932			0.483966	+	0.875087i	$0.339196\pi$
$432$	−1.23960	+	17.9032i	−0.0596403	+	0.861367i
$433$			11.8614i			0.570023i	0.958524	+	0.285011i	$0.0919974\pi$
$433$			11.8614i			0.570023i	−0.958524	+	0.285011i	$0.908003\pi$
$434$	−2.62411	+	2.20189i	−0.125961	+	0.105694i
$435$	1.24665	−	0.940087i	0.0597724	−	0.0450737i
$436$	5.08553	−	28.8415i	0.243553	−	1.38126i
$437$	−6.99283	−	19.2126i	−0.334512	−	0.919065i
$438$	−2.89540	−	2.86060i	−0.138347	−	0.136685i
$439$	6.50324	+	36.8817i	0.310383	+	1.76027i	0.597018	+	0.802228i	$0.296352\pi$
$439$	6.50324	+	36.8817i	0.310383	+	1.76027i	−0.286636	+	0.958040i	$0.592537\pi$
$440$	−6.63813	+	4.09549i	−0.316460	+	0.195245i
$441$	12.1727	+	6.83302i	0.579653	+	0.325382i
$442$	3.06766	+	1.77112i	0.145914	+	0.0842434i
$443$	5.07737	−	13.9500i	0.241233	−	0.662783i	−0.758702	−	0.651437i	$-0.774166\pi$
$443$	5.07737	−	13.9500i	0.241233	−	0.662783i	0.999936	−	0.0113453i	$-0.00361141\pi$
$444$	−12.1388	+	5.75000i	−0.576080	+	0.272883i
$445$	−3.05478	−	2.41485i	−0.144810	−	0.114475i
$446$	−5.34565	−	4.48553i	−0.253124	−	0.212396i
$447$	9.42255	+	19.8918i	0.445671	+	0.940852i
$448$	6.84809	−	18.8150i	0.323542	−	0.888924i
$449$	−8.86789	+	15.3596i	−0.418502	+	0.724866i	−0.995789	−	0.0916751i	$-0.970778\pi$
$449$	−8.86789	+	15.3596i	−0.418502	+	0.724866i	0.577287	+	0.816541i	$0.304111\pi$
$450$	−2.55328	−	3.77983i	−0.120363	−	0.178183i
$451$	7.16325	+	12.4071i	0.337304	+	0.584228i
$452$	29.4445	−	5.19186i	1.38495	−	0.244205i
$453$	−5.41659	−	5.35149i	−0.254494	−	0.251435i
$454$	2.04173	−	0.743130i	0.0958232	−	0.0348768i
$455$	6.07729	−	41.5220i	0.284908	−	1.94658i
$456$	−5.25160	−	7.40438i	−0.245929	−	0.346742i
$457$	−9.44358	−	11.2544i	−0.441752	−	0.526460i	0.498522	−	0.866877i	$-0.333876\pi$
$457$	−9.44358	−	11.2544i	−0.441752	−	0.526460i	−0.940275	+	0.340417i	$0.889432\pi$
$458$			5.68707i			0.265739i
$459$	−2.65619	+	10.6846i	−0.123980	+	0.498712i
$460$	0.577296	+	19.7636i	0.0269166	+	0.921483i
$461$	11.0104	−	9.23885i	0.512807	−	0.430296i	−0.349308	−	0.937008i	$-0.613583\pi$
$461$	11.0104	−	9.23885i	0.512807	−	0.430296i	0.862116	+	0.506711i	$0.169139\pi$
$462$	0.491802	+	5.25519i	0.0228807	+	0.244494i
$463$	8.00949	+	1.41229i	0.372232	+	0.0656346i	0.356635	−	0.934244i	$-0.383924\pi$
$463$	8.00949	+	1.41229i	0.372232	+	0.0656346i	0.0155973	+	0.999878i	$0.495035\pi$
$464$	−1.30838	+	0.476213i	−0.0607402	+	0.0221076i
$465$	−2.87073	+	12.4539i	−0.133127	+	0.577534i
$466$	1.30101	+	7.37840i	0.0602681	+	0.341798i
$467$	18.6732	−	10.7810i	0.864091	−	0.498883i	−0.00128884	−	0.999999i	$-0.500410\pi$
$467$	18.6732	−	10.7810i	0.864091	−	0.498883i	0.865380	+	0.501116i	$0.167077\pi$
$468$	5.08804	−	31.0464i	0.235195	−	1.43512i
$469$	6.51793	−	11.2894i	0.300970	−	0.521296i
$470$	−7.43904	−	2.46410i	−0.343137	−	0.113660i
$471$	0.694390	−	8.53063i	0.0319958	−	0.393071i
$472$	−4.19348	+	4.99759i	−0.193021	+	0.230033i
$473$	−0.199302	+	0.237518i	−0.00916390	+	0.0109211i
$474$	−1.02141	−	0.706035i	−0.0469149	−	0.0324293i
$475$	−21.1284	−	6.32021i	−0.969435	−	0.289991i
$476$	6.89856	−	11.9487i	0.316195	−	0.547666i
$477$	26.3436	−	22.6533i	1.20619	−	1.03722i
$478$	4.58463	−	2.64694i	0.209696	−	0.121068i
$479$	−6.11802	−	34.6970i	−0.279540	−	1.58535i	−0.724162	−	0.689630i	$-0.757773\pi$
$479$	−6.11802	−	34.6970i	−0.279540	−	1.58535i	0.444622	−	0.895718i	$-0.353338\pi$
$480$	3.88461	+	12.6905i	0.177308	+	0.579240i
$481$	21.0020	−	7.64412i	0.957610	−	0.348542i
$482$	2.18266	+	0.384863i	0.0994176	+	0.0175300i
$483$	24.9097	+	11.4327i	1.13343	+	0.520208i
$484$	−3.48125	+	2.92112i	−0.158239	+	0.132778i
$485$	−0.0290378	−	0.994104i	−0.00131854	−	0.0451399i
$486$	−4.70766	+	0.555690i	−0.213544	+	0.0252066i
$487$			21.9486i			0.994588i	0.867582	+	0.497294i	$0.165673\pi$
$487$			21.9486i			0.994588i	−0.867582	+	0.497294i	$0.834327\pi$
$488$	−5.23385	−	6.23746i	−0.236925	−	0.282357i
$489$	−0.0971245	+	0.211615i	−0.00439212	+	0.00956956i
$490$	3.13065	+	0.458212i	0.141428	+	0.0206999i
$491$	−19.2925	+	7.02190i	−0.870659	+	0.316894i	−0.738434	−	0.674326i	$-0.764434\pi$
$491$	−19.2925	+	7.02190i	−0.870659	+	0.316894i	−0.132225	+	0.991220i	$0.542212\pi$
$492$	15.5492	−	4.26733i	0.701014	−	0.192386i
$493$	−0.841223	+	0.148330i	−0.0378868	+	0.00668046i
$494$	3.68686	+	6.38582i	0.165879	+	0.287312i
$495$	13.2700	+	14.5499i	0.596443	+	0.653969i
$496$	5.69845	−	9.87000i	0.255868	−	0.443176i
$497$	−15.7780	+	43.3498i	−0.707742	+	1.94450i
$498$	2.04072	−	2.95227i	0.0914466	−	0.132295i
$499$	−19.5778	−	16.4277i	−0.876422	−	0.735405i	0.0890184	−	0.996030i	$-0.471627\pi$
$499$	−19.5778	−	16.4277i	−0.876422	−	0.735405i	−0.965440	+	0.260625i	$0.916071\pi$
$500$	17.4740	+	12.2266i	0.781463	+	0.546792i
$501$	−2.14777	+	26.3855i	−0.0959553	+	1.17882i
$502$	2.37598	−	6.52794i	0.106045	−	0.291356i
$503$	9.72392	+	5.61411i	0.433568	+	0.250321i	0.700866	−	0.713293i	$-0.252797\pi$
$503$	9.72392	+	5.61411i	0.433568	+	0.250321i	−0.267297	+	0.963614i	$0.586131\pi$
$504$	12.0087	+	1.96805i	0.534910	+	0.0876638i
$505$	7.49305	+	12.1450i	0.333436	+	0.540446i
$506$	0.718565	+	4.07518i	0.0319441	+	0.181164i
$507$	−7.54685	+	28.8621i	−0.335168	+	1.28181i
$508$	−8.43877	−	23.1853i	−0.374410	−	1.02868i
$509$	−5.09372	+	28.8879i	−0.225775	+	1.28043i	0.635423	+	0.772164i	$0.280826\pi$
$509$	−5.09372	+	28.8879i	−0.225775	+	1.28043i	−0.861198	+	0.508269i	$0.830285\pi$
$510$	0.304963	+	2.47674i	0.0135040	+	0.109672i
$511$	20.2079	−	16.9565i	0.893946	−	0.750110i
$512$		−	20.0428i		−	0.885775i
$513$	−15.9093	+	16.4971i	−0.702412	+	0.728366i
$514$	−0.447452			−0.0197362
$515$	18.1462	+	20.3861i	0.799616	+	0.898317i
$516$	0.201882	+	0.284639i	0.00888737	+	0.0125306i
$517$	33.3179	+	5.87484i	1.46532	+	0.258375i
$518$	1.44338	+	3.96565i	0.0634184	+	0.174241i
$519$	−18.4109	+	18.6348i	−0.808147	+	0.817979i
$520$	−2.95545	−	14.3051i	−0.129605	−	0.627321i
$521$	−4.09744	−	7.09698i	−0.179512	−	0.310924i	0.762201	−	0.647340i	$-0.224119\pi$
$521$	−4.09744	−	7.09698i	−0.179512	−	0.310924i	−0.941714	+	0.336416i	$0.890785\pi$
$522$	−0.187729	−	0.316262i	−0.00821667	−	0.0138424i
$523$	8.30466	+	4.79470i	0.363137	+	0.209657i	0.670456	−	0.741949i	$-0.266098\pi$
$523$	8.30466	+	4.79470i	0.363137	+	0.209657i	−0.307319	+	0.951607i	$0.599432\pi$
$524$	−20.6286	−	7.50821i	−0.901166	−	0.327998i
$525$	25.9331	−	14.1936i	1.13181	−	0.619462i
$526$	−5.03331	−	4.22345i	−0.219463	−	0.184151i
$527$	4.49432	−	5.35612i	0.195776	−	0.233316i
$528$	−7.51754	−	15.8702i	−0.327159	−	0.690662i
$529$	−1.42103	−	0.517213i	−0.0617840	−	0.0224875i
$530$	3.73671	−	6.93203i	0.162312	−	0.301108i
$531$	14.3628	+	8.06242i	0.623294	+	0.349879i
$532$	24.8730	−	14.3604i	1.07838	−	0.622604i
$533$	−26.4224	+	4.65898i	−1.14448	+	0.201803i
$534$	−0.644644	+	0.652487i	−0.0278965	+	0.0282359i
$535$	−1.39679	−	3.51478i	−0.0603886	−	0.151957i
$536$	0.787947	−	4.46867i	0.0340341	−	0.193017i
$537$	−2.24628	+	1.59319i	−0.0969343	+	0.0687513i
$538$	−2.60680	−	3.10666i	−0.112387	−	0.133938i
$539$	−13.6596			−0.588363
$540$	19.6212	−	10.3067i	0.844361	−	0.443531i
$541$	−5.81809			−0.250139			−0.125070	−	0.992148i	$-0.539915\pi$
$541$	−5.81809			−0.250139			−0.125070	+	0.992148i	$0.539915\pi$
$542$	−3.85681	−	4.59636i	−0.165664	−	0.197431i
$543$	3.51036	+	37.5102i	0.150644	+	1.60972i
$544$	1.26081	−	7.15041i	0.0540568	−	0.306571i
$545$	−31.9035	+	12.6786i	−1.36660	+	0.543093i
$546$	−9.56316	−	2.50057i	−0.409266	−	0.107015i
$547$	0.590106	−	0.104052i	0.0252311	−	0.00444893i	−0.161018	−	0.986951i	$-0.551478\pi$
$547$	0.590106	−	0.104052i	0.0252311	−	0.00444893i	0.186249	+	0.982502i	$0.440367\pi$
$548$	20.1443	−	11.6303i	0.860524	−	0.496824i
$549$	−13.0226	+	15.9065i	−0.555792	+	0.678871i
$550$	3.98913	+	2.00229i	0.170097	+	0.0853779i
$551$	−1.67091	−	0.608163i	−0.0711834	−	0.0259086i
$552$	9.50890	+	0.774022i	0.404726	+	0.0329445i
$553$	5.17287	−	6.16478i	0.219973	−	0.262153i
$554$	−6.17648	−	5.18268i	−0.262413	−	0.220191i
$555$	13.2079	+	8.57092i	0.560645	+	0.363815i
$556$	0.433796	+	0.157889i	0.0183971	+	0.00669598i
$557$	3.15552	+	1.82184i	0.133704	+	0.0771940i	0.565360	−	0.824844i	$-0.308737\pi$
$557$	3.15552	+	1.82184i	0.133704	+	0.0771940i	−0.431656	+	0.902038i	$0.642071\pi$
$558$	2.84111	+	0.995345i	0.120274	+	0.0421363i
$559$	−0.290331	−	0.502869i	−0.0122797	−	0.0212691i
$560$	−25.8177	+	5.33396i	−1.09099	+	0.225401i
$561$	−2.85121	−	10.3892i	−0.120378	−	0.438633i
$562$	0.679405	+	1.86665i	0.0286590	+	0.0787399i
$563$	0.769406	+	0.135667i	0.0324266	+	0.00571768i	0.189838	−	0.981815i	$-0.439204\pi$
$563$	0.769406	+	0.135667i	0.0324266	+	0.00571768i	−0.157411	+	0.987533i	$0.550315\pi$
$564$	15.8831	−	34.6062i	0.668801	−	1.45718i
$565$	−23.3029	−	26.1794i	−0.980362	−	1.10137i
$566$	1.95362			0.0821169
$567$	−0.742919	−	30.7140i	−0.0311997	−	1.28987i
$568$			16.0579i			0.673774i
$569$	−26.6979	+	22.4022i	−1.11923	+	0.939149i	−0.998566	−	0.0535433i	$-0.982948\pi$
$569$	−26.6979	+	22.4022i	−1.11923	+	0.939149i	−0.120669	+	0.992693i	$0.538504\pi$
$570$	−2.02809	+	4.78240i	−0.0849471	+	0.200313i
$571$	−2.28374	+	12.9518i	−0.0955717	+	0.542014i	0.898999	+	0.437951i	$0.144296\pi$
$571$	−2.28374	+	12.9518i	−0.0955717	+	0.542014i	−0.994571	+	0.104063i	$0.966816\pi$
$572$	10.5291	+	28.9284i	0.440243	+	1.20956i
$573$	13.1615	−	3.61204i	0.549830	−	0.150895i
$574$	−0.879719	−	4.98913i	−0.0367188	−	0.208242i
$575$	19.3616	−	12.7406i	0.807435	−	0.531319i
$576$	−17.2906	+	3.26485i	−0.720442	+	0.136035i
$577$	22.3145	+	12.8833i	0.928964	+	0.536338i	0.886484	−	0.462760i	$-0.153141\pi$
$577$	22.3145	+	12.8833i	0.928964	+	0.536338i	0.0424803	+	0.999097i	$0.486474\pi$
$578$	−1.30117	+	3.57494i	−0.0541216	+	0.148698i
$579$	25.4401	+	17.5851i	1.05725	+	0.730811i
$580$	1.34897	+	1.06638i	0.0560131	+	0.0442792i
$581$	17.8186	+	14.9516i	0.739241	+	0.620296i
$582$	−0.233488	−	0.0190058i	−0.00967839	−	0.000787818i
$583$	−11.6280	+	31.9477i	−0.481584	+	1.32314i
$584$	4.59118	−	7.95216i	0.189985	−	0.329063i
$585$	−34.1048	+	14.0333i	−1.41006	+	0.580205i
$586$	−2.12721	−	3.68444i	−0.0878743	−	0.152203i
$587$	−6.55502	+	1.15583i	−0.270555	+	0.0477061i	−0.307279	−	0.951619i	$-0.599419\pi$
$587$	−6.55502	+	1.15583i	−0.270555	+	0.0477061i	0.0367248	+	0.999325i	$0.488308\pi$
$588$	−3.88914	+	14.8736i	−0.160386	+	0.613377i
$589$	13.6770	−	4.97803i	0.563552	−	0.205116i
$590$	3.69392	+	0.540653i	0.152076	+	0.0222584i
$591$	−16.4081	+	1.53554i	−0.674938	+	0.0631635i
$592$	−9.02517	−	10.7558i	−0.370932	−	0.442060i
$593$		−	46.9838i		−	1.92939i	−0.263360	−	0.964697i	$-0.584831\pi$
$593$		−	46.9838i		−	1.92939i	0.263360	−	0.964697i	$-0.415169\pi$
$594$	3.75080	−	2.72904i	0.153897	−	0.111974i
$595$	−16.1666	+	0.472226i	−0.662764	+	0.0193594i
$596$	−18.5694	+	15.5816i	−0.760631	+	0.638246i
$597$	15.4536	−	10.9606i	0.632475	−	0.448587i
$598$	−7.63181	−	1.34569i	−0.312088	−	0.0550295i
$599$	30.7181	−	11.1805i	1.25511	−	0.456821i	0.372982	−	0.927839i	$-0.378335\pi$
$599$	30.7181	−	11.1805i	1.25511	−	0.456821i	0.882124	+	0.471018i	$0.156113\pi$
$600$	6.79277	−	7.73006i	0.277314	−	0.315578i
$601$	−4.40564	−	24.9856i	−0.179710	−	1.01918i	−0.932566	−	0.361000i	$-0.882436\pi$
$601$	−4.40564	−	24.9856i	−0.179710	−	1.01918i	0.752856	−	0.658185i	$-0.228676\pi$
$602$	0.0949528	−	0.0548210i	0.00386999	−	0.00223434i
$603$	−11.4553	+	0.138522i	−0.466497	+	0.00564105i
$604$	4.19287	−	7.26226i	0.170605	−	0.295497i
$605$	5.05696	+	1.67506i	0.205595	+	0.0681008i
$606$	3.03782	−	1.43898i	0.123403	−	0.0584547i
$607$	10.3912	−	12.3838i	0.421766	−	0.502641i	−0.512762	−	0.858531i	$-0.671378\pi$
$607$	10.3912	−	12.3838i	0.421766	−	0.502641i	0.934528	+	0.355890i	$0.115822\pi$
$608$	9.71529	−	11.5782i	0.394007	−	0.469559i
$609$	2.15420	−	1.02042i	0.0872927	−	0.0413496i
$610$	−1.46511	+	4.42314i	−0.0593207	+	0.179088i
$611$	−31.6794	+	54.8703i	−1.28161	+	2.21981i
$612$	−12.1243	+	0.146611i	−0.490096	+	0.00592641i
$613$	−35.6170	+	20.5635i	−1.43856	+	0.830551i	−0.997750	−	0.0670516i	$-0.978641\pi$
$613$	−35.6170	+	20.5635i	−1.43856	+	0.830551i	−0.440806	+	0.897602i	$0.645307\pi$
$614$	0.837116	+	4.74752i	0.0337832	+	0.191594i
$615$	−13.8279	−	12.8859i	−0.557596	−	0.519611i
$616$	−11.1895	+	4.07263i	−0.450836	+	0.164091i
$617$	41.3880	+	7.29783i	1.66622	+	0.293799i	0.925706	−	0.378243i	$-0.123472\pi$
$617$	41.3880	+	7.29783i	1.66622	+	0.293799i	0.740513	+	0.672042i	$0.234583\pi$
$618$	5.24370	−	3.71913i	0.210933	−	0.149605i
$619$	8.65367	−	7.26129i	0.347821	−	0.291856i	−0.452094	−	0.891970i	$-0.649323\pi$
$619$	8.65367	−	7.26129i	0.347821	−	0.291856i	0.799914	+	0.600114i	$0.204878\pi$
$620$	−14.0692	+	0.410963i	−0.565034	+	0.0165047i
$621$	−2.53414	−	23.9530i	−0.101692	−	0.961202i
$622$		−	4.76048i		−	0.190878i
$623$	−3.82119	−	4.55392i	−0.153093	−	0.182449i
$624$	32.7437	−	3.06429i	1.31080	−	0.122670i
$625$	1.44235	−	24.9584i	0.0576939	−	0.998334i
$626$	−0.290099	+	0.105587i	−0.0115947	+	0.00422011i
$627$	5.67331	−	21.6969i	0.226570	−	0.866493i
$628$	9.28275	−	1.63680i	0.370422	−	0.0653154i
$629$	−4.30693	−	7.45982i	−0.171728	−	0.297442i
$630$	−2.64979	−	6.43975i	−0.105570	−	0.256566i
$631$	22.9413	−	39.7354i	0.913278	−	1.58184i	0.103874	−	0.994590i	$-0.466876\pi$
$631$	22.9413	−	39.7354i	0.913278	−	1.58184i	0.809404	−	0.587253i	$-0.199791\pi$
$632$	0.958081	−	2.63231i	0.0381104	−	0.104708i
$633$	−17.6131	−	1.43370i	−0.700058	−	0.0569844i
$634$	2.68936	+	2.25664i	0.106808	+	0.0896227i
$635$	−17.9364	+	22.6896i	−0.711786	+	0.900409i
$636$	31.4763	+	21.7575i	1.24812	+	0.862741i
$637$	8.74927	−	24.0384i	0.346659	−	0.952437i
$638$	0.311669	+	0.179942i	0.0123391	+	0.00712398i
$639$	39.8377	−	7.52223i	1.57595	−	0.297575i
$640$	−16.4366	+	10.1408i	−0.649715	+	0.400852i
$641$	−3.68466	−	20.8967i	−0.145535	−	0.825372i	−0.966936	−	0.255020i	$-0.917918\pi$
$641$	−3.68466	−	20.8967i	−0.145535	−	0.825372i	0.821401	−	0.570352i	$-0.193193\pi$
$642$	−0.859119	+	0.235776i	−0.0339067	+	0.00930535i
$643$	5.47651	+	15.0466i	0.215972	+	0.593379i	0.999613	−	0.0278358i	$-0.00886157\pi$
$643$	5.47651	+	15.0466i	0.215972	+	0.593379i	−0.783640	+	0.621215i	$0.786639\pi$
$644$	−5.24153	+	29.7262i	−0.206545	+	1.17138i
$645$	0.159707	−	0.376603i	0.00628846	−	0.0148287i
$646$	2.17702	−	1.82674i	0.0856536	−	0.0718719i
$647$			14.3391i			0.563729i	0.959454	+	0.281864i	$0.0909528\pi$
$647$			14.3391i			0.563729i	−0.959454	+	0.281864i	$0.909047\pi$
$648$	−3.89959	−	9.95793i	−0.153190	−	0.391185i
$649$	−16.1173			−0.632660
$650$	−6.07877	+	5.73762i	−0.238429	+	0.225048i
$651$	−8.13869	+	17.7326i	−0.318981	+	0.694996i
$652$	−0.252533	−	0.0445283i	−0.00988995	−	0.00174386i
$653$	7.51262	+	20.6408i	0.293992	+	0.807735i	0.995473	+	0.0950471i	$0.0303002\pi$
$653$	7.51262	+	20.6408i	0.293992	+	0.807735i	−0.701481	+	0.712688i	$0.747478\pi$
$654$	2.14013	+	7.79819i	0.0836858	+	0.304933i
$655$	5.20661	+	25.2013i	0.203439	+	0.984695i
$656$	8.42758	+	14.5970i	0.329042	+	0.569917i
$657$	−21.8791	−	7.66503i	−0.853584	−	0.299041i
$658$	−10.3607	−	5.98177i	−0.403904	−	0.233194i
$659$	41.9142	+	15.2555i	1.63274	+	0.594270i	0.985749	−	0.168223i	$-0.0538030\pi$
$659$	41.9142	+	15.2555i	1.63274	+	0.594270i	0.646996	+	0.762494i	$0.276025\pi$
$660$	−11.8057	+	18.1927i	−0.459535	+	0.708151i
$661$	8.07733	+	6.77768i	0.314172	+	0.263621i	0.786214	−	0.617955i	$-0.212039\pi$
$661$	8.07733	+	6.77768i	0.314172	+	0.263621i	−0.472042	+	0.881576i	$0.656483\pi$
$662$	−0.676971	+	0.806782i	−0.0263112	+	0.0313565i
$663$	20.1093	+	1.63689i	0.780981	+	0.0635716i
$664$	7.60839	+	2.76923i	0.295263	+	0.107467i
$665$	−29.6361	−	15.9753i	−1.14924	−	0.619496i
$666$	2.34942	−	2.86969i	0.0910381	−	0.111198i
$667$	1.61841	−	0.934391i	0.0626652	−	0.0361798i
$668$	−28.7118	+	5.06267i	−1.11089	+	0.195881i
$669$	−38.4538	−	10.0549i	−1.48671	−	0.388744i
$670$	−2.41306	+	0.958963i	−0.0932247	+	0.0370480i
$671$	3.49309	−	19.8103i	0.134849	−	0.764768i
$672$	1.88788	+	20.1730i	0.0728264	+	0.778192i
$673$	−16.9132	−	20.1564i	−0.651957	−	0.776972i	0.334251	−	0.942484i	$-0.391517\pi$
$673$	−16.9132	−	20.1564i	−0.651957	−	0.776972i	−0.986208	+	0.165513i	$0.947072\pi$
$674$	−0.0461716			−0.00177846
$675$	−22.3594	−	13.2309i	−0.860613	−	0.509259i
$676$	−32.8548			−1.26365
$677$	−27.1278	−	32.3296i	−1.04260	−	1.24253i	−0.969471	−	0.245205i	$-0.921145\pi$
$677$	−27.1278	−	32.3296i	−1.04260	−	1.24253i	−0.0731331	−	0.997322i	$-0.523300\pi$
$678$	−6.73385	+	4.77602i	−0.258612	+	0.183422i
$679$	0.263647	−	1.49522i	0.0101179	−	0.0573812i
$680$	−5.23177	+	2.07913i	−0.200629	+	0.0797311i
$681$	8.69783	−	8.80364i	0.333301	−	0.337356i
$682$	−2.90102	+	0.511529i	−0.111086	+	0.0195875i
$683$	−16.0571	+	9.27055i	−0.614407	+	0.354728i	−0.774688	−	0.632343i	$-0.782093\pi$
$683$	−16.0571	+	9.27055i	−0.614407	+	0.354728i	0.160281	+	0.987071i	$0.448760\pi$
$684$	−22.0099	−	12.3550i	−0.841569	−	0.472406i
$685$	−24.0019	−	12.9382i	−0.917064	−	0.494343i
$686$	−2.28929	−	0.833234i	−0.0874056	−	0.0318130i
$687$	13.8669	+	29.2742i	0.529053	+	1.11688i
$688$	−0.234479	+	0.279441i	−0.00893942	+	0.0106536i
$689$	−48.7741	−	40.9263i	−1.85814	−	1.55917i
$690$	−2.48019	−	4.86354i	−0.0944192	−	0.185152i
$691$	−9.82430	−	3.57575i	−0.373734	−	0.136028i	0.148322	−	0.988939i	$-0.452613\pi$
$691$	−9.82430	−	3.57575i	−0.373734	−	0.136028i	−0.522056	+	0.852911i	$0.674835\pi$
$692$	−24.9846	−	14.4248i	−0.949770	−	0.548350i
$693$	15.3454	+	25.8519i	0.582922	+	0.982033i
$694$	3.15960	+	5.47259i	0.119937	+	0.207737i
$695$	−0.109489	−	0.529954i	−0.00415316	−	0.0201023i
$696$	0.583143	−	0.590238i	0.0221040	−	0.0223729i
$697$	3.53667	+	9.71691i	0.133961	+	0.368054i
$698$	−1.86099	−	0.328143i	−0.0704395	−	0.0124204i
$699$	24.6878	+	34.8080i	0.933778	+	1.31656i
$700$	22.3482	+	23.6770i	0.844684	+	0.894908i
$701$	−18.2363			−0.688774			−0.344387	−	0.938828i	$-0.611913\pi$
$701$	−18.2363			−0.688774			−0.344387	+	0.938828i	$0.611913\pi$
$702$	2.40014	+	8.34870i	0.0905873	+	0.315101i
$703$		−	17.9311i		−	0.676284i
$704$	13.1900	−	11.0677i	0.497116	−	0.417130i
$705$	−44.3007	+	5.45478i	−1.66846	+	0.205439i
$706$	0.316288	−	1.79376i	0.0119037	−	0.0675090i
$707$	7.45122	+	20.4721i	0.280232	+	0.769931i
$708$	−4.58888	+	17.5497i	−0.172461	+	0.659557i
$709$	−7.63846	−	43.3199i	−0.286869	−	1.62691i	−0.698534	−	0.715577i	$-0.746164\pi$
$709$	−7.63846	−	43.3199i	−0.286869	−	1.62691i	0.411665	−	0.911335i	$-0.364947\pi$
$710$	7.82042	−	4.82492i	0.293495	−	0.181076i
$711$	−6.97924	−	1.14379i	−0.261742	−	0.0428956i
$712$	−1.79204	−	1.03464i	−0.0671597	−	0.0387747i
$713$	−5.23175	+	14.3741i	−0.195931	+	0.538315i
$714$	−0.309082	+	3.79709i	−0.0115671	+	0.142102i
$715$	22.3794	−	28.3099i	0.836941	−	1.05873i
$716$	−2.32335	−	1.94952i	−0.0868277	−	0.0728571i
$717$	17.1453	−	24.8038i	0.640303	−	0.926316i
$718$	−0.0532155	+	0.146208i	−0.00198598	+	0.00545645i
$719$	21.3751	−	37.0227i	0.797155	−	1.38071i	−0.124307	−	0.992244i	$-0.539671\pi$
$719$	21.3751	−	37.0227i	0.797155	−	1.38071i	0.921462	−	0.388469i	$-0.126996\pi$
$720$	15.6122	+	17.1180i	0.581833	+	0.637950i
$721$	20.8328	+	36.0835i	0.775855	+	1.34382i
$722$	0.135988	−	0.0239784i	0.00506096	−	0.000892385i
$723$	12.1737	−	3.34094i	0.452744	−	0.124251i
$724$	−38.9887	+	14.1907i	−1.44900	+	0.527394i
$725$	0.233560	−	2.00216i	0.00867421	−	0.0743582i
$726$	0.523420	−	1.14043i	0.0194259	−	0.0423253i
$727$	−6.68922	−	7.97191i	−0.248090	−	0.295662i	0.627600	−	0.778536i	$-0.284037\pi$
$727$	−6.68922	−	7.97191i	−0.248090	−	0.295662i	−0.875690	+	0.482874i	$0.839593\pi$
$728$		−	22.3000i		−	0.826492i
$729$	−22.8777	+	14.3391i	−0.847322	+	0.531080i
$730$	−5.25233	+	0.153421i	−0.194398	+	0.00567836i
$731$	−0.171435	+	0.143851i	−0.00634076	+	0.00532053i
$732$	−20.5763	−	9.44387i	−0.760523	−	0.349055i
$733$	32.4643	+	5.72433i	1.19910	+	0.211433i	0.737308	−	0.675557i	$-0.236097\pi$
$733$	32.4643	+	5.72433i	1.19910	+	0.211433i	0.461788	+	0.886990i	$0.347208\pi$
$734$	5.86785	−	2.13572i	0.216586	−	0.0788310i
$735$	17.2323	−	5.27486i	0.635622	−	0.194566i
$736$	2.75835	+	15.6434i	0.101674	+	0.576622i
$737$	9.70829	−	5.60508i	0.357609	−	0.206466i
$738$	−3.37572	+	2.90284i	−0.124262	+	0.106855i
$739$	13.1005	−	22.6907i	0.481909	−	0.834690i	−0.517876	−	0.855456i	$-0.673277\pi$
$739$	13.1005	−	22.6907i	0.481909	−	0.834690i	0.999784	+	0.0207656i	$0.00661038\pi$
$740$	−5.45245	+	16.4608i	−0.200436	+	0.605110i
$741$	34.5487	+	23.8813i	1.26918	+	0.877301i
$742$	7.72780	−	9.20963i	0.283696	−	0.338096i
$743$	−10.4298	+	12.4297i	−0.382631	+	0.456002i	−0.922643	−	0.385655i	$-0.873975\pi$
$743$	−10.4298	+	12.4297i	−0.382631	+	0.456002i	0.540012	+	0.841658i	$0.318420\pi$
$744$	−0.551007	+	6.76916i	−0.0202009	+	0.248169i
$745$	26.9744	+	8.93495i	0.988264	+	0.327351i
$746$	−1.90770	+	3.30424i	−0.0698460	+	0.120977i
$747$	3.30601	−	20.1727i	0.120961	−	0.738081i
$748$	10.2752	−	5.93241i	0.375700	−	0.216910i
$749$	−1.00264	−	5.68627i	−0.0366358	−	0.207772i
$750$	−5.80568	−	0.985521i	−0.211993	−	0.0359861i
$751$	7.02136	−	2.55556i	0.256213	−	0.0932539i	−0.210720	−	0.977546i	$-0.567581\pi$
$751$	7.02136	−	2.55556i	0.256213	−	0.0932539i	0.466933	+	0.884292i	$0.345359\pi$
$752$	39.1986	+	6.91177i	1.42943	+	0.252046i
$753$	−3.68684	−	39.3959i	−0.134356	−	1.43567i
$754$	−0.516295	+	0.433223i	−0.0188023	+	0.0157770i
$755$	−9.82585	+	0.287014i	−0.357599	+	0.0104455i
$756$	32.5185	−	9.34862i	1.18269	−	0.340006i
$757$			25.7164i			0.934678i	0.884078	+	0.467339i	$0.154787\pi$
$757$			25.7164i			0.934678i	−0.884078	+	0.467339i	$0.845213\pi$
$758$	5.84279	+	6.96317i	0.212220	+	0.252914i
$759$	13.6354	+	19.2249i	0.494933	+	0.697820i
$760$	−11.5957	−	1.69718i	−0.420619	−	0.0615632i
$761$	19.3050	−	7.02645i	0.699807	−	0.254709i	0.0324783	−	0.999472i	$-0.489660\pi$
$761$	19.3050	−	7.02645i	0.699807	−	0.254709i	0.667328	+	0.744764i	$0.267438\pi$
$762$	4.84639	+	4.78814i	0.175566	+	0.173456i
$763$	−51.6141	+	9.10096i	−1.86856	+	0.329477i
$764$	7.51544	+	13.0171i	0.271899	+	0.470943i
$765$	7.60887	+	12.0054i	0.275099	+	0.434057i
$766$	3.31440	−	5.74070i	0.119754	−	0.207420i
$767$	10.3235	−	28.3635i	0.372758	−	1.02414i
$768$	−6.75058	−	14.2511i	−0.243591	−	0.514241i
$769$	−1.56802	−	1.31573i	−0.0565444	−	0.0474464i	0.614077	−	0.789246i	$-0.289528\pi$
$769$	−1.56802	−	1.31573i	−0.0565444	−	0.0474464i	−0.670622	+	0.741799i	$0.733973\pi$
$770$	5.34554	+	4.22572i	0.192640	+	0.152284i
$771$	−2.30326	+	1.09103i	−0.0829497	+	0.0392924i
$772$	−11.6490	+	32.0054i	−0.419257	+	1.15190i
$773$	20.3868	+	11.7703i	0.733262	+	0.423349i	0.819614	−	0.572916i	$-0.194188\pi$
$773$	20.3868	+	11.7703i	0.733262	+	0.423349i	−0.0863523	+	0.996265i	$0.527521\pi$
$774$	−0.0840229	−	0.0471653i	−0.00302014	−	0.00169532i
$775$	9.06972	+	13.7831i	0.325794	+	0.495102i
$776$	−0.0917721	−	0.520465i	−0.00329442	−	0.0186836i
$777$	17.0993	+	16.8938i	0.613434	+	0.606061i
$778$	1.08321	+	2.97609i	0.0388349	+	0.106698i
$779$	−3.73785	+	21.1984i	−0.133922	+	0.759512i
$780$	−24.4540	−	32.4286i	−0.875595	−	1.16113i
$781$	−30.3898	+	25.5001i	−1.08743	+	0.912464i
$782$			2.98675i			0.106806i
$783$	−1.73748	−	1.17021i	−0.0620924	−	0.0418201i
$784$	−16.0706			−0.573951
$785$	−7.34654	−	8.25337i	−0.262209	−	0.294575i
$786$	6.03514	−	0.564793i	0.215266	−	0.0201455i
$787$	−23.3076	−	4.10976i	−0.830826	−	0.146497i	−0.257970	−	0.966153i	$-0.583053\pi$
$787$	−23.3076	−	4.10976i	−0.830826	−	0.146497i	−0.572856	+	0.819656i	$0.694165\pi$
$788$	−6.20745	−	17.0548i	−0.221131	−	0.607553i
$789$	−36.2070	−	9.46740i	−1.28900	−	0.337048i
$790$	−1.56985	+	0.324332i	−0.0558526	+	0.0115392i
$791$	−26.7531	−	46.3377i	−0.951230	−	1.64758i
$792$	8.09711	+	6.62910i	0.287718	+	0.235555i
$793$	32.6250	+	18.8361i	1.15855	+	0.668888i
$794$	6.24481	+	2.27292i	0.221620	+	0.0806631i
$795$	2.33223	−	44.7938i	0.0827156	−	1.58867i
$796$	15.9838	+	13.4120i	0.566531	+	0.475376i
$797$	18.5974	−	22.1635i	0.658755	−	0.785073i	−0.328452	−	0.944521i	$-0.606527\pi$
$797$	18.5974	−	22.1635i	0.658755	−	0.785073i	0.987206	+	0.159448i	$0.0509713\pi$
$798$	−4.50932	+	6.52357i	−0.159628	+	0.230932i
$799$	22.9464	+	8.35181i	0.811785	+	0.295466i
$800$	15.3130	+	7.68616i	0.541397	+	0.271747i
$801$	−1.72734	+	4.93052i	−0.0610325	+	0.174211i
$802$	5.30866	−	3.06496i	0.187455	−	0.108227i
$803$	22.3404	−	3.93922i	0.788377	−	0.139012i
$804$	−3.33909	−	12.1669i	−0.117761	−	0.429095i
$805$	32.8822	−	13.0676i	1.15895	−	0.460571i
$806$	0.957968	−	5.43290i	0.0337430	−	0.191366i
$807$	−20.9935	−	9.63533i	−0.739005	−	0.339180i
$808$	4.87450	+	5.80920i	0.171484	+	0.204367i
$809$	50.0898			1.76106			0.880532	−	0.473986i	$-0.157185\pi$
$809$	50.0898			1.76106			0.880532	+	0.473986i	$0.157185\pi$
$810$	−3.67794	+	4.89122i	−0.129230	+	0.171860i
$811$	−22.3607			−0.785192			−0.392596	−	0.919711i	$-0.628423\pi$
$811$	−22.3607			−0.785192			−0.392596	+	0.919711i	$0.628423\pi$
$812$	1.68742	+	2.01099i	0.0592168	+	0.0705718i
$813$	−31.0603	−	14.2557i	−1.08933	−	0.499968i
$814$	−0.630190	+	3.57398i	−0.0220881	+	0.125268i
$815$	0.111013	+	0.279344i	0.00388861	+	0.00978499i
$816$	−3.35446	−	12.2229i	−0.117430	−	0.427888i
$817$	−0.458782	+	0.0808957i	−0.0160508	+	0.00283018i
$818$	3.55405	−	2.05193i	0.124264	−	0.0717441i
$819$	−55.3235	+	10.4463i	−1.93316	+	0.365023i
$820$	9.87732	−	18.3236i	0.344931	−	0.639887i
$821$	−12.3587	−	4.49819i	−0.431321	−	0.156988i	0.117230	−	0.993105i	$-0.462598\pi$
$821$	−12.3587	−	4.49819i	−0.431321	−	0.156988i	−0.548552	+	0.836117i	$0.684821\pi$
$822$	−3.65204	+	5.28335i	−0.127380	+	0.184278i
$823$	14.5049	−	17.2863i	0.505611	−	0.602563i	−0.451505	−	0.892268i	$-0.649113\pi$
$823$	14.5049	−	17.2863i	0.505611	−	0.602563i	0.957116	+	0.289705i	$0.0935573\pi$
$824$	11.1101	+	9.32250i	0.387040	+	0.324765i
$825$	25.4162	+	0.580025i	0.884880	+	0.0201939i
$826$	5.35565	+	1.94930i	0.186347	+	0.0678247i
$827$	−3.32717	−	1.92094i	−0.115697	−	0.0667978i	0.441035	−	0.897490i	$-0.354612\pi$
$827$	−3.32717	−	1.92094i	−0.115697	−	0.0667978i	−0.556732	+	0.830692i	$0.687945\pi$
$828$	24.8157	−	9.37350i	0.862404	−	0.325752i
$829$	22.2051	+	38.4603i	0.771214	+	1.33578i	0.936898	+	0.349602i	$0.113683\pi$
$829$	22.2051	+	38.4603i	0.771214	+	1.33578i	−0.165685	+	0.986179i	$0.552983\pi$
$830$	−0.937445	−	4.53746i	−0.0325392	−	0.157498i
$831$	−44.4304	−	11.6176i	−1.54127	−	0.403011i
$832$	11.0287	+	30.3010i	0.382350	+	1.05050i
$833$	−9.70943	−	1.71203i	−0.336412	−	0.0593185i
$834$	−0.126912	+	0.0118769i	−0.00439460	+	0.000411265i
$835$	22.7231	+	25.5279i	0.786365	+	0.883430i
$836$	24.6985			0.854214
$837$	17.0516	−	1.80399i	0.589389	−	0.0623551i
$838$		−	0.620768i		−	0.0214441i
$839$	−5.58926	+	4.68995i	−0.192963	+	0.161915i	−0.734150	−	0.678987i	$-0.762419\pi$
$839$	−5.58926	+	4.68995i	−0.192963	+	0.161915i	0.541188	+	0.840902i	$0.317975\pi$
$840$	12.5433	−	9.45877i	0.432785	−	0.326359i
$841$	−5.00757	+	28.3994i	−0.172675	+	0.979289i
$842$	0.286147	+	0.786181i	0.00986126	+	0.0270936i
$843$	8.04872	+	7.95198i	0.277213	+	0.273881i
$844$	−3.37948	−	19.1660i	−0.116327	−	0.659721i
$845$	20.2224	+	32.7772i	0.695672	+	1.12757i
$846$	0.127127	+	10.5130i	0.00437073	+	0.361446i
$847$	7.04308	+	4.06633i	0.242003	+	0.139721i
$848$	−13.6804	+	37.5866i	−0.469787	+	1.29073i
$849$	10.0563	−	4.76355i	0.345130	−	0.163485i
$850$	2.58456	+	1.92323i	0.0886497	+	0.0659661i
$851$	14.4361	+	12.1134i	0.494864	+	0.415240i
$852$	19.1138	+	40.3509i	0.654827	+	1.38240i
$853$	18.7864	−	51.6153i	0.643235	−	1.76727i	0.00191802	−	0.999998i	$-0.499389\pi$
$853$	18.7864	−	51.6153i	0.643235	−	1.76727i	0.641317	−	0.767276i	$-0.278388\pi$
$854$	−3.55667	+	6.16033i	−0.121707	+	0.210802i
$855$	1.22143	+	29.5625i	0.0417722	+	1.01102i
$856$	−1.00492	−	1.74058i	−0.0343476	−	0.0594917i
$857$	8.75197	−	1.54321i	0.298961	−	0.0527150i	−0.0221554	−	0.999755i	$-0.507053\pi$
$857$	8.75197	−	1.54321i	0.298961	−	0.0527150i	0.321117	+	0.947040i	$0.395942\pi$
$858$	−6.04686	−	5.97418i	−0.206436	−	0.203955i
$859$	4.71452	−	1.71594i	0.160857	−	0.0585473i	−0.260336	−	0.965518i	$-0.583833\pi$
$859$	4.71452	−	1.71594i	0.160857	−	0.0585473i	0.421194	+	0.906971i	$0.361611\pi$
$860$	0.445762	+	0.0652431i	0.0152003	+	0.00222477i
$861$	−16.6934	−	23.5365i	−0.568910	−	0.802123i
$862$	−3.92787	−	4.68106i	−0.133784	−	0.159437i
$863$			15.4472i			0.525828i	0.964819	+	0.262914i	$0.0846836\pi$
$863$			15.4472i			0.525828i	−0.964819	+	0.262914i	$0.915316\pi$
$864$	14.3981	−	10.4759i	0.489834	−	0.356398i
$865$	0.987421	+	33.8041i	0.0335733	+	1.14938i
$866$	2.76310	−	2.31851i	0.0938939	−	0.0787863i
$867$	2.01904	+	21.5746i	0.0685703	+	0.732713i
$868$	−21.1614	−	3.73132i	−0.718264	−	0.126649i
$869$	6.50312	−	2.36694i	0.220603	−	0.0802930i
$870$	−0.462672	−	0.106650i	−0.0156860	−	0.00361577i
$871$	3.64555	+	20.6749i	0.123525	+	0.700544i
$872$	−15.7992	+	9.12165i	−0.535027	+	0.308898i
$873$	−1.24822	+	0.471485i	−0.0422459	+	0.0159573i
$874$	−3.10869	+	5.38441i	−0.105153	+	0.182130i
$875$	9.86559	−	36.8689i	0.333518	−	1.24639i
$876$	2.07141	−	25.4474i	0.0699865	−	0.859789i
$877$	−7.74532	+	9.23051i	−0.261541	+	0.311692i	−0.880794	−	0.473499i	$-0.842991\pi$
$877$	−7.74532	+	9.23051i	−0.261541	+	0.311692i	0.619254	+	0.785191i	$0.287435\pi$
$878$	7.32037	−	8.72408i	0.247051	−	0.294423i
$879$	−19.9336	−	13.7788i	−0.672344	−	0.464748i
$880$	−21.5208	−	7.12853i	−0.725467	−	0.240303i
$881$	17.1975	−	29.7869i	0.579398	−	1.00355i	−0.416151	−	0.909296i	$-0.636621\pi$
$881$	17.1975	−	29.7869i	0.579398	−	1.00355i	0.995548	−	0.0942507i	$-0.0300455\pi$
$882$	−0.787623	−	4.17125i	−0.0265207	−	0.140453i
$883$	23.5099	−	13.5734i	0.791171	−	0.456783i	−0.0492038	−	0.998789i	$-0.515668\pi$
$883$	23.5099	−	13.5734i	0.791171	−	0.456783i	0.840375	+	0.542006i	$0.182335\pi$
$884$	3.85844	+	21.8823i	0.129773	+	0.735982i
$885$	20.3327	−	6.22392i	0.683477	−	0.209215i
$886$	−4.24208	+	1.54399i	−0.142516	+	0.0518714i
$887$	−48.5493	−	8.56056i	−1.63013	−	0.287435i	−0.717601	−	0.696454i	$-0.754760\pi$
$887$	−48.5493	−	8.56056i	−1.63013	−	0.287435i	−0.912526	+	0.409019i	$0.865871\pi$
$888$	7.60432	+	3.49014i	0.255184	+	0.117121i
$889$	−33.8246	+	28.3822i	−1.13444	+	0.951908i
$890$	0.0345739	+	1.18363i	0.00115892	+	0.0396754i
$891$	12.6530	−	23.1933i	0.423890	−	0.777005i
$892$		−	43.7735i		−	1.46564i
$893$	32.6742	+	38.9396i	1.09340	+	1.30306i
$894$	2.79198	−	6.08317i	0.0933777	−	0.203452i
$895$	−0.514877	+	3.51781i	−0.0172105	+	0.117587i
$896$	−27.7062	+	10.0842i	−0.925598	+	0.336890i
$897$	−42.5660	+	11.6818i	−1.42124	+	0.390044i
$898$	5.31139	−	0.936541i	0.177243	−	0.0312528i
$899$	0.665171	+	1.15211i	0.0221847	+	0.0384250i
$900$	7.86803	−	27.5099i	0.262268	−	0.916996i
$901$	−12.2695	+	21.2514i	−0.408756	+	0.707987i
$902$	1.49004	−	4.09385i	0.0496129	−	0.136310i
$903$	0.355098	−	0.513716i	0.0118169	−	0.0170954i
$904$	−14.2674	−	11.9718i	−0.474526	−	0.398175i
$905$	38.1551	+	30.1621i	1.26832	+	1.00262i
$906$	−0.187856	+	2.30783i	−0.00624111	+	0.0766724i
$907$	4.60719	−	12.6581i	0.152979	−	0.420307i	−0.839402	−	0.543511i	$-0.817095\pi$
$907$	4.60719	−	12.6581i	0.152979	−	0.420307i	0.992381	+	0.123204i	$0.0393170\pi$
$908$	11.8034	+	6.81471i	0.391711	+	0.226154i
$909$	12.1285	−	14.8143i	0.402277	−	0.491360i
$910$	−10.8604	+	6.70049i	−0.360019	+	0.222119i
$911$	−4.06209	−	23.0373i	−0.134583	−	0.763259i	−0.975149	−	0.221550i	$-0.928888\pi$
$911$	−4.06209	−	23.0373i	−0.134583	−	0.763259i	0.840566	−	0.541709i	$-0.182223\pi$
$912$	6.67467	−	25.5265i	0.221020	−	0.845268i
$913$	6.84138	+	18.7965i	0.226417	+	0.622075i
$914$	−0.775793	+	4.39974i	−0.0256609	+	0.145530i
$915$	3.24332	+	26.3405i	0.107221	+	0.870790i
$916$	−27.3279	+	22.9309i	−0.902941	+	0.757657i
$917$			39.2858i			1.29733i
$918$	3.00815	−	1.46972i	0.0992838	−	0.0485081i
$919$	6.93563			0.228785			0.114393	−	0.993436i	$-0.463508\pi$
$919$	6.93563			0.228785			0.114393	+	0.993436i	$0.463508\pi$
$920$	9.19984	−	8.18903i	0.303310	−	0.269984i
$921$	15.8850	+	22.3967i	0.523428	+	0.737996i
$922$	−4.30436	−	0.758974i	−0.141756	−	0.0249955i
$923$	−25.4101	−	69.8136i	−0.836383	−	2.29794i
$924$	−23.2697	+	23.5527i	−0.765515	+	0.774828i
$925$	19.7779	−	4.69217i	0.650294	−	0.154278i
$926$	−1.23660	−	2.14186i	−0.0406372	−	0.0703857i
$927$	17.9235	−	31.9300i	0.588686	−	1.04872i
$928$	1.19640	+	0.690742i	0.0392738	+	0.0226747i
$929$	−11.5336	−	4.19788i	−0.378404	−	0.137728i	0.145814	−	0.989312i	$-0.453420\pi$
$929$	−11.5336	−	4.19788i	−0.378404	−	0.137728i	−0.524218	+	0.851584i	$0.675642\pi$
$930$	3.46224	−	1.76559i	0.113531	−	0.0578959i
$931$	−15.7219	−	13.1922i	−0.515265	−	0.432358i
$932$	−30.2094	+	36.0022i	−0.989543	+	1.17929i
$933$	−11.6075	−	24.5046i	−0.380014	−	0.802243i
$934$	−6.16140	−	2.24257i	−0.201607	−	0.0733790i
$935$	−12.2429	−	6.59952i	−0.400385	−	0.215827i
$936$	−16.8523	+	10.0033i	−0.550836	+	0.326969i
$937$	−21.4835	+	12.4035i	−0.701836	+	0.405205i	−0.808031	−	0.589140i	$-0.799467\pi$
$937$	−21.4835	+	12.4035i	−0.701836	+	0.405205i	0.106195	+	0.994345i	$0.466133\pi$
$938$	−3.90389	+	0.688361i	−0.127466	+	0.0224758i
$939$	−1.23583	+	1.25086i	−0.0403297	+	0.0408203i
$940$	−18.1543	−	45.6822i	−0.592129	−	1.48999i
$941$	9.97338	−	56.5618i	0.325123	−	1.84386i	−0.183688	−	0.982985i	$-0.558804\pi$
$941$	9.97338	−	56.5618i	0.325123	−	1.84386i	0.508811	−	0.860878i	$-0.330085\pi$
$942$	−2.12293	+	1.50570i	−0.0691688	+	0.0490584i
$943$	−14.5415	−	17.3299i	−0.473537	−	0.564339i
$944$	−18.9621			−0.617162
$945$	−29.3419	−	26.6875i	−0.954493	−	0.868146i
$946$	0.0942865			0.00306552
$947$	2.64449	+	3.15158i	0.0859344	+	0.102413i	0.807298	−	0.590144i	$-0.200929\pi$
$947$	2.64449	+	3.15158i	0.0859344	+	0.102413i	−0.721364	+	0.692556i	$0.756484\pi$
$948$	−0.725742	−	7.75497i	−0.0235710	−	0.251870i
$949$	−7.37719	+	41.8381i	−0.239474	+	1.35812i
$950$	2.65761	+	6.15721i	0.0862243	+	0.199766i
$951$	19.3459	+	5.05855i	0.627333	+	0.164035i
$952$	−8.46404	+	1.49244i	−0.274321	+	0.0483702i
$953$	9.44189	−	5.45128i	0.305853	−	0.176584i	−0.339216	−	0.940708i	$-0.610162\pi$
$953$	9.44189	−	5.45128i	0.305853	−	0.176584i	0.645069	+	0.764124i	$0.276829\pi$
$954$	−10.4264	−	1.70873i	−0.337566	−	0.0553220i
$955$	8.36057	−	15.5098i	0.270542	−	0.501887i
$956$	31.2050	+	11.3577i	1.00924	+	0.367334i
$957$	2.04307	+	0.166305i	0.0660431	+	0.00537588i
$958$	−6.88676	+	8.20732i	−0.222501	+	0.265166i
$959$	−31.8880	−	26.7572i	−1.02972	−	0.864035i
$960$	−12.3658	+	19.0559i	−0.399105	+	0.615027i
$961$	18.8979	+	6.87826i	0.609609	+	0.221879i
$962$	−5.88589	−	3.39822i	−0.189769	−	0.109563i
$963$	−3.84741	+	3.30846i	−0.123981	+	0.106614i
$964$	6.95136	+	12.0401i	0.223888	+	0.387786i
$965$	39.0999	−	8.07808i	1.25867	−	0.260043i
$966$	−2.20578	−	8.03740i	−0.0709699	−	0.258599i
$967$	−12.2571	−	33.6762i	−0.394163	−	1.08295i	−0.965082	−	0.261947i	$-0.915635\pi$
$967$	−12.2571	−	33.6762i	−0.394163	−	1.08295i	0.570920	−	0.821006i	$-0.306587\pi$
$968$	2.78786	+	0.491574i	0.0896051	+	0.0157998i
$969$	6.75204	−	14.7114i	0.216907	−	0.472597i
$970$	−0.225899	+	0.201079i	−0.00725319	+	0.00645626i
$971$	28.9416			0.928779			0.464390	−	0.885631i	$-0.346274\pi$
$971$	28.9416			0.928779			0.464390	+	0.885631i	$0.346274\pi$
$972$	−21.6520	−	20.3810i	−0.694489	−	0.653721i
$973$		−	0.826134i		−	0.0264847i
$974$	5.11291	−	4.29024i	0.163828	−	0.137468i
$975$	−17.3003	+	44.3563i	−0.554054	+	1.42054i
$976$	4.10963	−	23.3069i	0.131546	−	0.746035i
$977$	−8.34110	−	22.9170i	−0.266855	−	0.733179i	−0.998664	−	0.0516691i	$-0.983546\pi$
$977$	−8.34110	−	22.9170i	−0.266855	−	0.733179i	0.731809	−	0.681510i	$-0.238676\pi$
$978$	0.0682801	−	0.0187388i	0.00218336	−	0.000599200i
$979$	−0.887716	−	5.03448i	−0.0283715	−	0.160903i
$980$	10.4213	+	16.8912i	0.332896	+	0.539570i
$981$	30.0308	+	34.9228i	0.958808	+	1.11500i
$982$	5.40679	+	3.12161i	0.172538	+	0.0996147i
$983$	0.899750	−	2.47204i	0.0286976	−	0.0788460i	−0.924517	−	0.381142i	$-0.875531\pi$
$983$	0.899750	−	2.47204i	0.0286976	−	0.0788460i	0.953214	+	0.302296i	$0.0977531\pi$
$984$	−8.26240	−	5.71126i	−0.263396	−	0.182068i
$985$	−13.1938	+	16.6902i	−0.420390	+	0.531793i
$986$	0.198985	+	0.166968i	0.00633696	+	0.00531734i
$987$	−67.9173	−	5.52844i	−2.16183	−	0.175972i
$988$	−15.8199	+	43.4647i	−0.503297	+	1.38280i
$989$	0.244802	−	0.424010i	0.00778426	−	0.0134827i
$990$	0.795524	−	5.93526i	0.0252834	−	0.188635i
$991$	9.51245	+	16.4761i	0.302173	+	0.523379i	0.976628	−	0.214937i	$-0.0689546\pi$
$991$	9.51245	+	16.4761i	0.302173	+	0.523379i	−0.674455	+	0.738316i	$0.735621\pi$
$992$	−11.1361	+	1.96360i	−0.353572	+	0.0623444i
$993$	−1.51752	+	5.80358i	−0.0481569	+	0.184171i
$994$	13.1824	−	4.79799i	0.418119	−	0.152183i
$995$	3.54217	−	24.2013i	0.112294	−	0.767232i
$996$	22.4149	−	2.09768i	0.710243	−	0.0664674i
$997$	10.8627	+	12.9456i	0.344025	+	0.409993i	0.910118	−	0.414348i	$-0.135990\pi$
$997$	10.8627	+	12.9456i	0.344025	+	0.409993i	−0.566094	+	0.824341i	$0.691546\pi$
$998$			7.77169i			0.246009i
$999$	5.09641	−	20.5003i	0.161243	−	0.648602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.p.a.49.7	✓	96
3.2	odd	2		405.2.p.a.199.10		96
5.2	odd	4		675.2.l.h.76.10		96
5.3	odd	4		675.2.l.h.76.7		96
5.4	even	2	inner	135.2.p.a.49.10	yes	96
15.14	odd	2		405.2.p.a.199.7		96
27.11	odd	18		405.2.p.a.289.7		96
27.16	even	9	inner	135.2.p.a.124.10	yes	96
135.43	odd	36		675.2.l.h.151.7		96
135.97	odd	36		675.2.l.h.151.10		96
135.119	odd	18		405.2.p.a.289.10		96
135.124	even	18	inner	135.2.p.a.124.7	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.7	✓	96	1.1	even	1	trivial
135.2.p.a.49.10	yes	96	5.4	even	2	inner
135.2.p.a.124.7	yes	96	135.124	even	18	inner
135.2.p.a.124.10	yes	96	27.16	even	9	inner
405.2.p.a.199.7		96	15.14	odd	2
405.2.p.a.199.10		96	3.2	odd	2
405.2.p.a.289.7		96	27.11	odd	18
405.2.p.a.289.10		96	135.119	odd	18
675.2.l.h.76.7		96	5.3	odd	4
675.2.l.h.76.10		96	5.2	odd	4
675.2.l.h.151.7		96	135.43	odd	36
675.2.l.h.151.10		96	135.97	odd	36

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.195467 - 0.232949i) q^{2} +(-1.57417 - 0.722492i) q^{3} +(0.331239 - 1.87855i) q^{4} +(-2.07799 + 0.825805i) q^{5} +(0.139394 + 0.507924i) q^{6} +(-3.36181 + 0.592777i) q^{7} +(-1.02906 + 0.594126i) q^{8} +(1.95601 + 2.27465i) q^{9} +(0.598549 + 0.322648i) q^{10} +(-2.75854 - 1.00403i) q^{11} +(-1.87866 + 2.71783i) q^{12} +(3.53380 - 4.21142i) q^{13} +(0.795210 + 0.667260i) q^{14} +(3.86774 + 0.201377i) q^{15} +(-3.24543 - 1.18124i) q^{16} +(-1.83496 - 1.05942i) q^{17} +(0.147541 - 0.900269i) q^{18} +(-2.20534 - 3.81976i) q^{19} +(0.863003 + 4.17714i) q^{20} +(5.72033 + 1.49575i) q^{21} +(0.305317 + 0.838853i) q^{22} +(4.56507 + 0.804944i) q^{23} +(2.04916 - 0.191769i) q^{24} +(3.63609 - 3.43203i) q^{25} -1.67179 q^{26} +(-1.43567 - 4.99388i) q^{27} +6.51167i q^{28} +(0.308828 - 0.259138i) q^{29} +(-0.709106 - 0.940348i) q^{30} +(-0.573021 + 3.24976i) q^{31} +(1.17202 + 3.22009i) q^{32} +(3.61701 + 3.57353i) q^{33} +(0.111885 + 0.634533i) q^{34} +(6.49629 - 4.00798i) q^{35} +(4.92094 - 2.92101i) q^{36} +(3.52072 + 2.03269i) q^{37} +(-0.458737 + 1.26037i) q^{38} +(-8.60551 + 4.07634i) q^{39} +(1.64774 - 2.08439i) q^{40} +(-3.73852 - 3.13699i) q^{41} +(-0.769703 - 1.62491i) q^{42} +(0.0361245 - 0.0992511i) q^{43} +(-2.79985 + 4.84948i) q^{44} +(-5.94299 - 3.11142i) q^{45} +(-0.704810 - 1.22077i) q^{46} +(-11.3497 + 2.00126i) q^{47} +(4.25542 + 4.20427i) q^{48} +(4.37252 - 1.59147i) q^{49} +(-1.51022 - 0.176174i) q^{50} +(2.12312 + 2.99344i) q^{51} +(-6.74082 - 8.03340i) q^{52} -11.5814i q^{53} +(-0.882691 + 1.31058i) q^{54} +(6.56135 - 0.191657i) q^{55} +(3.10730 - 2.60734i) q^{56} +(0.711828 + 7.60629i) q^{57} +(-0.120732 - 0.0212882i) q^{58} +(5.15923 - 1.87781i) q^{59} +(1.65944 - 7.19904i) q^{60} +(1.18992 + 6.74834i) q^{61} +(0.869034 - 0.501737i) q^{62} +(-7.92409 - 6.48745i) q^{63} +(-2.93269 + 5.07957i) q^{64} +(-3.86539 + 11.6695i) q^{65} +(0.125444 - 1.54108i) q^{66} +(-2.45463 + 2.92531i) q^{67} +(-2.59797 + 3.09614i) q^{68} +(-6.60462 - 4.56534i) q^{69} +(-2.20346 - 0.729873i) q^{70} +(6.75694 - 11.7034i) q^{71} +(-3.36427 - 1.17862i) q^{72} +(-6.69232 + 3.86382i) q^{73} +(-0.214673 - 1.21747i) q^{74} +(-8.20344 + 2.77554i) q^{75} +(-7.90610 + 2.87758i) q^{76} +(9.86885 + 1.74014i) q^{77} +(2.63167 + 1.20785i) q^{78} +(-1.80591 + 1.51534i) q^{79} +(7.71945 - 0.225486i) q^{80} +(-1.34805 + 8.89847i) q^{81} +1.48406i q^{82} +(-4.37992 - 5.21978i) q^{83} +(4.70463 - 10.2505i) q^{84} +(4.68790 + 0.686136i) q^{85} +(-0.0301816 + 0.0109852i) q^{86} +(-0.673373 + 0.184800i) q^{87} +(3.43521 - 0.605720i) q^{88} +(0.870723 + 1.50814i) q^{89} +(0.436858 + 1.99259i) q^{90} +(-9.38352 + 16.2527i) q^{91} +(3.02425 - 8.30907i) q^{92} +(3.24996 - 4.70167i) q^{93} +(2.68468 + 2.25271i) q^{94} +(7.73705 + 6.11625i) q^{95} +(0.481539 - 5.91574i) q^{96} +(-0.152119 + 0.417944i) q^{97} +(-1.22541 - 0.707493i) q^{98} +(-3.11193 - 8.23860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31}+ \cdots + 36 q^{99}+O(q^{100}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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