LMFDB - Embedded newform 273.2.g.a.272.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(272,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("273.272");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.g (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			272.8
Character	$\chi$	$=$	273.272
Dual form			273.2.g.a.272.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.77583 q^{2} +(1.65032 + 0.525794i) q^{3} +1.15356 q^{4} +3.85624i q^{5} +(-2.93067 - 0.933719i) q^{6} +(1.56982 - 2.12971i) q^{7} +1.50313 q^{8} +(2.44708 + 1.73545i) q^{9} +O(q^{10})$	\(q-1.77583 q^{2} +(1.65032 + 0.525794i) q^{3} +1.15356 q^{4} +3.85624i q^{5} +(-2.93067 - 0.933719i) q^{6} +(1.56982 - 2.12971i) q^{7} +1.50313 q^{8} +(2.44708 + 1.73545i) q^{9} -6.84801i q^{10} -2.15272 q^{11} +(1.90374 + 0.606535i) q^{12} +(-2.48064 + 2.61657i) q^{13} +(-2.78774 + 3.78199i) q^{14} +(-2.02759 + 6.36401i) q^{15} -4.97642 q^{16} -1.53264 q^{17} +(-4.34559 - 3.08186i) q^{18} +6.24228 q^{19} +4.44841i q^{20} +(3.71049 - 2.68928i) q^{21} +3.82286 q^{22} +0.929599i q^{23} +(2.48064 + 0.790336i) q^{24} -9.87058 q^{25} +(4.40518 - 4.64658i) q^{26} +(3.12597 + 4.15070i) q^{27} +(1.81089 - 2.45675i) q^{28} +2.00195i q^{29} +(3.60064 - 11.3014i) q^{30} +0.380929 q^{31} +5.83100 q^{32} +(-3.55267 - 1.13189i) q^{33} +2.72170 q^{34} +(8.21266 + 6.05362i) q^{35} +(2.82286 + 2.00195i) q^{36} +8.77233i q^{37} -11.0852 q^{38} +(-5.46961 + 3.01386i) q^{39} +5.79643i q^{40} -2.58097i q^{41} +(-6.58919 + 4.77570i) q^{42} +5.97642 q^{43} -2.48329 q^{44} +(-6.69231 + 9.43653i) q^{45} -1.65081i q^{46} -1.59247i q^{47} +(-8.21266 - 2.61657i) q^{48} +(-2.07131 - 6.68653i) q^{49} +17.5284 q^{50} +(-2.52934 - 0.805852i) q^{51} +(-2.86157 + 3.01837i) q^{52} -12.4975i q^{53} +(-5.55118 - 7.37093i) q^{54} -8.30140i q^{55} +(2.35965 - 3.20123i) q^{56} +(10.3017 + 3.28215i) q^{57} -3.55511i q^{58} +0.317196i q^{59} +(-2.33894 + 7.34128i) q^{60} -1.21307i q^{61} -0.676464 q^{62} +(7.53749 - 2.48722i) q^{63} -0.402008 q^{64} +(-10.0901 - 9.56593i) q^{65} +(6.30892 + 2.01003i) q^{66} -11.0772i q^{67} -1.76799 q^{68} +(-0.488777 + 1.53413i) q^{69} +(-14.5843 - 10.7502i) q^{70} -7.83765 q^{71} +(3.67828 + 2.60861i) q^{72} -1.37652 q^{73} -15.5781i q^{74} +(-16.2896 - 5.18989i) q^{75} +7.20085 q^{76} +(-3.37939 + 4.58466i) q^{77} +(9.71308 - 5.35210i) q^{78} +10.4262 q^{79} -19.1903i q^{80} +(2.97642 + 8.49358i) q^{81} +4.58336i q^{82} -7.59111i q^{83} +(4.28028 - 3.10225i) q^{84} -5.91022i q^{85} -10.6131 q^{86} +(-1.05261 + 3.30385i) q^{87} -3.23582 q^{88} +4.75381i q^{89} +(11.8844 - 16.7576i) q^{90} +(1.67836 + 9.39059i) q^{91} +1.07235i q^{92} +(0.628653 + 0.200290i) q^{93} +2.82794i q^{94} +24.0717i q^{95} +(9.62299 + 3.06590i) q^{96} +13.5813 q^{97} +(3.67828 + 11.8741i) q^{98} +(-5.26788 - 3.73594i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4}+O(q^{10}) $ 32 * q + 16 * q^4	$ 32 q + 16 q^{4} - 16 q^{16} - 16 q^{25} + 16 q^{30} - 32 q^{36} - 48 q^{42} + 48 q^{43} - 32 q^{49} - 16 q^{51} - 80 q^{64} + 32 q^{78} + 80 q^{79} - 48 q^{81} - 96 q^{88} + 32 q^{91}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^16 - 16 * q^25 + 16 * q^30 - 32 * q^36 - 48 * q^42 + 48 * q^43 - 32 * q^49 - 16 * q^51 - 80 * q^64 + 32 * q^78 + 80 * q^79 - 48 * q^81 - 96 * q^88 + 32 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.77583			−1.25570			−0.627850	−	0.778335i	$-0.716065\pi$
$2$	−1.77583			−1.25570			−0.627850	+	0.778335i	$0.716065\pi$
$3$	1.65032	+	0.525794i	0.952810	+	0.303567i
$3$	1.65032	+	0.525794i	0.952810	+	0.303567i
$4$	1.15356			0.576780
$5$			3.85624i			1.72456i	0.506430	+	0.862281i	$0.330965\pi$
$5$			3.85624i			1.72456i	−0.506430	+	0.862281i	$0.669035\pi$
$6$	−2.93067	−	0.933719i	−1.19644	−	0.381189i
$7$	1.56982	−	2.12971i	0.593338	−	0.804954i
$7$	1.56982	−	2.12971i	0.593338	−	0.804954i
$8$	1.50313			0.531436
$9$	2.44708	+	1.73545i	0.815694	+	0.578484i
$10$		−	6.84801i		−	2.16553i
$11$	−2.15272			−0.649070			−0.324535	−	0.945874i	$-0.605208\pi$
$11$	−2.15272			−0.649070			−0.324535	+	0.945874i	$0.605208\pi$
$12$	1.90374	+	0.606535i	0.549562	+	0.175092i
$13$	−2.48064	+	2.61657i	−0.688005	+	0.725706i
$13$	−2.48064	+	2.61657i	−0.688005	+	0.725706i
$14$	−2.78774	+	3.78199i	−0.745054	+	1.01078i
$15$	−2.02759	+	6.36401i	−0.523521	+	1.64318i
$16$	−4.97642			−1.24410
$17$	−1.53264			−0.371719			−0.185860	−	0.982576i	$-0.559507\pi$
$17$	−1.53264			−0.371719			−0.185860	+	0.982576i	$0.559507\pi$
$18$	−4.34559	−	3.08186i	−1.02427	−	0.726402i
$19$	6.24228			1.43208			0.716038	−	0.698061i	$-0.245954\pi$
$19$	6.24228			1.43208			0.716038	+	0.698061i	$0.245954\pi$
$20$			4.44841i			0.994694i
$21$	3.71049	−	2.68928i	0.809696	−	0.586850i
$22$	3.82286			0.815036
$23$			0.929599i			0.193835i	0.995292	+	0.0969174i	$0.0308983\pi$
$23$			0.929599i			0.193835i	−0.995292	+	0.0969174i	$0.969102\pi$
$24$	2.48064	+	0.790336i	0.506358	+	0.161327i
$25$	−9.87058			−1.97412
$26$	4.40518	−	4.64658i	0.863927	−	0.911268i
$27$	3.12597	+	4.15070i	0.601593	+	0.798803i
$28$	1.81089	−	2.45675i	0.342226	−	0.464282i
$29$			2.00195i			0.371753i	0.982573	+	0.185876i	$0.0595124\pi$
$29$			2.00195i			0.371753i	−0.982573	+	0.185876i	$0.940488\pi$
$30$	3.60064	−	11.3014i	0.657384	−	2.06334i
$31$	0.380929			0.0684169			0.0342084	−	0.999415i	$-0.489109\pi$
$31$	0.380929			0.0684169			0.0342084	+	0.999415i	$0.489109\pi$
$32$	5.83100			1.03078
$33$	−3.55267	−	1.13189i	−0.618440	−	0.197036i
$34$	2.72170			0.466768
$35$	8.21266	+	6.05362i	1.38819	+	1.02325i
$36$	2.82286	+	2.00195i	0.470476	+	0.333658i
$37$			8.77233i			1.44216i	0.692851	+	0.721081i	$0.256354\pi$
$37$			8.77233i			1.44216i	−0.692851	+	0.721081i	$0.743646\pi$
$38$	−11.0852			−1.79826
$39$	−5.46961	+	3.01386i	−0.875839	+	0.482604i
$40$			5.79643i			0.916495i
$41$		−	2.58097i		−	0.403080i	−0.979480	−	0.201540i	$-0.935405\pi$
$41$		−	2.58097i		−	0.403080i	0.979480	−	0.201540i	$-0.0645946\pi$
$42$	−6.58919	+	4.77570i	−1.01673	+	0.736907i
$43$	5.97642			0.911395			0.455698	−	0.890135i	$-0.349390\pi$
$43$	5.97642			0.911395			0.455698	+	0.890135i	$0.349390\pi$
$44$	−2.48329			−0.374371
$45$	−6.69231	+	9.43653i	−0.997631	+	1.40672i
$46$		−	1.65081i		−	0.243398i
$47$		−	1.59247i		−	0.232285i	−0.993233	−	0.116143i	$-0.962947\pi$
$47$		−	1.59247i		−	0.232285i	0.993233	−	0.116143i	$-0.0370529\pi$
$48$	−8.21266	−	2.61657i	−1.18540	−	0.377669i
$49$	−2.07131	−	6.68653i	−0.295901	−	0.955219i
$50$	17.5284			2.47890
$51$	−2.52934	−	0.805852i	−0.354178	−	0.112842i
$52$	−2.86157	+	3.01837i	−0.396828	+	0.418573i
$53$		−	12.4975i		−	1.71666i	−0.513097	−	0.858330i	$-0.671502\pi$
$53$		−	12.4975i		−	1.71666i	0.513097	−	0.858330i	$-0.328498\pi$
$54$	−5.55118	−	7.37093i	−0.755419	−	1.00306i
$55$		−	8.30140i		−	1.11936i
$56$	2.35965	−	3.20123i	0.315321	−	0.427782i
$57$	10.3017	+	3.28215i	1.36450	+	0.434731i
$58$		−	3.55511i		−	0.466809i
$59$			0.317196i			0.0412954i	0.999787	+	0.0206477i	$0.00657284\pi$
$59$			0.317196i			0.0412954i	−0.999787	+	0.0206477i	$0.993427\pi$
$60$	−2.33894	+	7.34128i	−0.301956	+	0.947755i
$61$		−	1.21307i		−	0.155318i	−0.996980	−	0.0776589i	$-0.975255\pi$
$61$		−	1.21307i		−	0.155318i	0.996980	−	0.0776589i	$-0.0247445\pi$
$62$	−0.676464			−0.0859110
$63$	7.53749	−	2.48722i	0.949635	−	0.313360i
$64$	−0.402008			−0.0502511
$65$	−10.0901	−	9.56593i	−1.25153	−	1.18651i
$66$	6.30892	+	2.01003i	0.776575	+	0.247418i
$67$		−	11.0772i		−	1.35330i	−0.736306	−	0.676649i	$-0.763432\pi$
$67$		−	11.0772i		−	1.35330i	0.736306	−	0.676649i	$-0.236568\pi$
$68$	−1.76799			−0.214401
$69$	−0.488777	+	1.53413i	−0.0588419	+	0.184688i
$70$	−14.5843	−	10.7502i	−1.74315	−	1.28489i
$71$	−7.83765			−0.930158			−0.465079	−	0.885269i	$-0.653974\pi$
$71$	−7.83765			−0.930158			−0.465079	+	0.885269i	$0.653974\pi$
$72$	3.67828	+	2.60861i	0.433489	+	0.307427i
$73$	−1.37652			−0.161109			−0.0805546	−	0.996750i	$-0.525669\pi$
$73$	−1.37652			−0.161109			−0.0805546	+	0.996750i	$0.525669\pi$
$74$		−	15.5781i		−	1.81092i
$75$	−16.2896	−	5.18989i	−1.88096	−	0.599277i
$76$	7.20085			0.825994
$77$	−3.37939	+	4.58466i	−0.385117	+	0.522471i
$78$	9.71308	−	5.35210i	1.09979	−	0.606006i
$79$	10.4262			1.17303			0.586517	−	0.809937i	$-0.300499\pi$
$79$	10.4262			1.17303			0.586517	+	0.809937i	$0.300499\pi$
$80$		−	19.1903i		−	2.14554i
$81$	2.97642	+	8.49358i	0.330713	+	0.943731i
$82$			4.58336i			0.506147i
$83$		−	7.59111i		−	0.833233i	−0.909082	−	0.416617i	$-0.863216\pi$
$83$		−	7.59111i		−	0.833233i	0.909082	−	0.416617i	$-0.136784\pi$
$84$	4.28028	−	3.10225i	0.467017	−	0.338484i
$85$		−	5.91022i		−	0.641054i
$86$	−10.6131			−1.14444
$87$	−1.05261	+	3.30385i	−0.112852	+	0.354210i
$88$	−3.23582			−0.344939
$89$			4.75381i			0.503903i	0.967740	+	0.251951i	$0.0810723\pi$
$89$			4.75381i			0.503903i	−0.967740	+	0.251951i	$0.918928\pi$
$90$	11.8844	−	16.7576i	1.25272	−	1.76641i
$91$	1.67836	+	9.39059i	0.175940	+	0.984401i
$92$			1.07235i			0.111800i
$93$	0.628653	+	0.200290i	0.0651883	+	0.0207691i
$94$			2.82794i			0.291680i
$95$			24.0717i			2.46971i
$96$	9.62299	+	3.06590i	0.982142	+	0.312912i
$97$	13.5813			1.37898			0.689488	−	0.724297i	$-0.257836\pi$
$97$	13.5813			1.37898			0.689488	+	0.724297i	$0.257836\pi$
$98$	3.67828	+	11.8741i	0.371562	+	1.19947i
$99$	−5.26788	−	3.73594i	−0.529442	−	0.375476i
$100$	−11.3863			−1.13863
$101$	9.88980			0.984072			0.492036	−	0.870575i	$-0.336253\pi$
$101$	9.88980			0.984072			0.492036	+	0.870575i	$0.336253\pi$
$102$	4.49166	+	1.43105i	0.444741	+	0.141695i
$103$		−	11.5929i		−	1.14228i	−0.820853	−	0.571139i	$-0.806502\pi$
$103$		−	11.5929i		−	1.14228i	0.820853	−	0.571139i	$-0.193498\pi$
$104$	−3.72872	+	3.93304i	−0.365631	+	0.385667i
$105$	10.3705	+	14.3085i	1.01206	+	1.39637i
$106$			22.1934i			2.15561i
$107$		−	16.2003i		−	1.56614i	−0.621931	−	0.783072i	$-0.713652\pi$
$107$		−	16.2003i		−	1.56614i	0.621931	−	0.783072i	$-0.286348\pi$
$108$	3.60599	+	4.78809i	0.346987	+	0.460734i
$109$		−	6.56430i		−	0.628746i	−0.949300	−	0.314373i	$-0.898206\pi$
$109$		−	6.56430i		−	0.628746i	0.949300	−	0.314373i	$-0.101794\pi$
$110$			14.7419i			1.40558i
$111$	−4.61244	+	14.4771i	−0.437793	+	1.37411i
$112$	−7.81210	+	10.5983i	−0.738174	+	1.00145i
$113$		−	5.47285i		−	0.514842i	−0.966299	−	0.257421i	$-0.917127\pi$
$113$		−	5.47285i		−	0.514842i	0.966299	−	0.257421i	$-0.0828728\pi$
$114$	−18.2941	−	5.82853i	−1.71340	−	0.545892i
$115$	−3.58476			−0.334280
$116$			2.30937i			0.214420i
$117$	−10.6113	+	2.09794i	−0.981011	+	0.193954i
$118$		−	0.563286i		−	0.0518547i
$119$	−2.40597	+	3.26407i	−0.220555	+	0.299217i
$120$	−3.04772	+	9.56593i	−0.278218	+	0.873246i
$121$	−6.36580			−0.578709
$122$			2.15420i			0.195032i
$123$	1.35706	−	4.25941i	0.122362	−	0.384058i
$124$	0.439425			0.0394615
$125$		−	18.7821i		−	1.67993i
$126$	−13.3853	+	4.41686i	−1.19246	+	0.393485i
$127$	−12.8470			−1.13999			−0.569994	−	0.821649i	$-0.693054\pi$
$127$	−12.8470			−1.13999			−0.569994	+	0.821649i	$0.693054\pi$
$128$	−10.9481			−0.967685
$129$	9.86298	+	3.14236i	0.868387	+	0.276670i
$130$	17.9183	+	16.9874i	1.57154	+	1.48990i
$131$	8.53887			0.746045			0.373022	−	0.927822i	$-0.378322\pi$
$131$	8.53887			0.746045			0.373022	+	0.927822i	$0.378322\pi$
$132$	−4.09822	−	1.30570i	−0.356704	−	0.113647i
$133$	9.79928	−	13.2942i	0.849705	−	1.15276i
$134$			19.6712i			1.69933i
$135$	−16.0061	+	12.0545i	−1.37759	+	1.03748i
$136$	−2.30375			−0.197545
$137$	9.50928			0.812433			0.406216	−	0.913777i	$-0.366848\pi$
$137$	9.50928			0.812433			0.406216	+	0.913777i	$0.366848\pi$
$138$	0.867984	−	2.72435i	0.0738877	−	0.231912i
$139$			19.9808i			1.69475i	0.530999	+	0.847373i	$0.321817\pi$
$139$			19.9808i			1.69475i	−0.530999	+	0.847373i	$0.678183\pi$
$140$	9.47381	+	6.98322i	0.800683	+	0.590189i
$141$	0.837309	−	2.62807i	0.0705141	−	0.221324i
$142$	13.9183			1.16800
$143$	5.34012	−	5.63274i	0.446563	−	0.471034i
$144$	−12.1777	−	8.63633i	−1.01481	−	0.719694i
$145$	−7.71999			−0.641111
$146$	2.44446			0.202305
$147$	0.0974286	−	12.1240i	0.00803578	−	0.999968i
$148$			10.1194i			0.831811i
$149$	14.1034			1.15540			0.577699	−	0.816250i	$-0.303951\pi$
$149$	14.1034			1.15540			0.577699	+	0.816250i	$0.303951\pi$
$150$	28.9275	+	9.21635i	2.36192	+	0.752512i
$151$			12.4243i			1.01108i	0.862805	+	0.505538i	$0.168706\pi$
$151$			12.4243i			1.01108i	−0.862805	+	0.505538i	$0.831294\pi$
$152$	9.38295			0.761058
$153$	−3.75049	−	2.65982i	−0.303209	−	0.215034i
$154$	6.00121	−	8.14157i	0.483592	−	0.656066i
$155$			1.46895i			0.117989i
$156$	−6.30953	+	3.47667i	−0.505167	+	0.278357i
$157$			4.98516i			0.397859i	0.980014	+	0.198929i	$0.0637465\pi$
$157$			4.98516i			0.397859i	−0.980014	+	0.198929i	$0.936254\pi$
$158$	−18.5150			−1.47298
$159$	6.57110	−	20.6248i	0.521122	−	1.63565i
$160$			22.4857i			1.77765i
$161$	1.97977	+	1.45931i	0.156028	+	0.115010i
$162$	−5.28560	−	15.0831i	−0.415276	−	1.18504i
$163$		−	13.7248i		−	1.07501i	−0.843262	−	0.537503i	$-0.819368\pi$
$163$		−	13.7248i		−	1.07501i	0.843262	−	0.537503i	$-0.180632\pi$
$164$		−	2.97731i		−	0.232489i
$165$	4.36483	−	13.6999i	0.339801	−	1.06654i
$166$			13.4805i			1.04629i
$167$			18.2018i			1.40849i	0.709955	+	0.704247i	$0.248715\pi$
$167$			18.2018i			1.40849i	−0.709955	+	0.704247i	$0.751285\pi$
$168$	5.57735	−	4.04234i	0.430302	−	0.311874i
$169$	−0.692878	−	12.9815i	−0.0532983	−	0.998579i
$170$			10.4955i			0.804970i
$171$	15.2754	+	10.8332i	1.16814	+	0.828433i
$172$	6.89416			0.525675
$173$	18.5426			1.40977			0.704885	−	0.709321i	$-0.250998\pi$
$173$	18.5426			1.40977			0.704885	+	0.709321i	$0.250998\pi$
$174$	1.86926	−	5.86706i	0.141708	−	0.444781i
$175$	−15.4951	+	21.0215i	−1.17132	+	1.58907i
$176$	10.7128			0.807510
$177$	−0.166780	+	0.523474i	−0.0125359	+	0.0393467i
$178$		−	8.44194i		−	0.632750i
$179$			2.62413i			0.196136i	0.995180	+	0.0980682i	$0.0312663\pi$
$179$			2.62413i			0.196136i	−0.995180	+	0.0980682i	$0.968734\pi$
$180$	−7.71999	+	10.8856i	−0.575414	+	0.811366i
$181$			8.52459i			0.633628i	0.948488	+	0.316814i	$0.102613\pi$
$181$			8.52459i			0.633628i	−0.948488	+	0.316814i	$0.897387\pi$
$182$	−2.98048	−	16.6761i	−0.220928	−	1.23611i
$183$	0.637825	−	2.00195i	0.0471494	−	0.147988i
$184$			1.39731i			0.103011i
$185$	−33.8282			−2.48710
$186$	−1.11638	−	0.355681i	−0.0818569	−	0.0260798i
$187$	3.29934			0.241272
$188$		−	1.83701i		−	0.133977i
$189$	13.7470	−	0.141524i	0.999947	−	0.0102944i
$190$		−	42.7472i		−	3.10121i
$191$			17.9767i			1.30075i	0.759614	+	0.650374i	$0.225388\pi$
$191$			17.9767i			1.30075i	−0.759614	+	0.650374i	$0.774612\pi$
$192$	−0.663441	−	0.211374i	−0.0478797	−	0.0152546i
$193$		−	10.1194i		−	0.728411i	−0.931319	−	0.364206i	$-0.881340\pi$
$193$		−	10.1194i		−	0.728411i	0.931319	−	0.364206i	$-0.118660\pi$
$194$	−24.1181			−1.73158
$195$	−11.6222	−	21.0921i	−0.832281	−	1.51044i
$196$	−2.38938	−	7.71332i	−0.170670	−	0.550951i
$197$	−10.7483			−0.765783			−0.382892	−	0.923793i	$-0.625072\pi$
$197$	−10.7483			−0.765783			−0.382892	+	0.923793i	$0.625072\pi$
$198$	9.35485	+	6.63438i	0.664820	+	0.471485i
$199$		−	12.3215i		−	0.873446i	−0.899596	−	0.436723i	$-0.856139\pi$
$199$		−	12.3215i		−	0.873446i	0.899596	−	0.436723i	$-0.143861\pi$
$200$	−14.8368			−1.04912
$201$	5.82433	−	18.2809i	0.410817	−	1.28944i
$202$	−17.5626			−1.23570
$203$	4.26356	+	3.14271i	0.299244	+	0.220575i
$204$	−2.91774	−	0.929599i	−0.204283	−	0.0650850i
$205$	9.95284			0.695136
$206$			20.5869i			1.43436i
$207$	−1.61327	+	2.27481i	−0.112130	+	0.158110i
$208$	12.3447	−	13.0211i	0.855950	−	0.902854i
$209$	−13.4379			−0.929517
$210$	−18.4163	−	25.4095i	−1.27084	−	1.75342i
$211$	−0.468012			−0.0322192			−0.0161096	−	0.999870i	$-0.505128\pi$
$211$	−0.468012			−0.0322192			−0.0161096	+	0.999870i	$0.505128\pi$
$212$		−	14.4166i		−	0.990136i
$213$	−12.9346	−	4.12099i	−0.886264	−	0.282365i
$214$			28.7690i			1.96661i
$215$			23.0465i			1.57176i
$216$	4.69873	+	6.23904i	0.319708	+	0.424513i
$217$	0.597992	−	0.811267i	0.0405943	−	0.0550724i
$218$			11.6571i			0.789516i
$219$	−2.27169	−	0.723764i	−0.153506	−	0.0489074i
$220$		−	9.57618i		−	0.645626i
$221$	3.80192	−	4.01026i	0.255745	−	0.269759i
$222$	8.19089	−	25.7088i	0.549736	−	1.72546i
$223$	−18.8650			−1.26330			−0.631649	−	0.775255i	$-0.717621\pi$
$223$	−18.8650			−1.26330			−0.631649	+	0.775255i	$0.717621\pi$
$224$	9.15364	−	12.4183i	0.611604	−	0.829734i
$225$	−24.1541	−	17.1299i	−1.61027	−	1.14199i
$226$			9.71884i			0.646487i
$227$		−	21.9835i		−	1.45910i	−0.683928	−	0.729549i	$-0.739730\pi$
$227$		−	21.9835i		−	1.45910i	0.683928	−	0.729549i	$-0.260270\pi$
$228$	11.8837	+	3.78616i	0.787015	+	0.250745i
$229$	−22.3429			−1.47646			−0.738231	−	0.674548i	$-0.764339\pi$
$229$	−22.3429			−1.47646			−0.738231	+	0.674548i	$0.764339\pi$
$230$	6.36591			0.419756
$231$	−7.98765	+	5.78928i	−0.525549	+	0.380907i
$232$			3.00919i			0.197563i
$233$		−	18.9063i		−	1.23859i	−0.785158	−	0.619296i	$-0.787418\pi$
$233$		−	18.9063i		−	1.23859i	0.785158	−	0.619296i	$-0.212582\pi$
$234$	18.8437	−	3.72557i	1.23185	−	0.243548i
$235$	6.14093			0.400590
$236$			0.365905i			0.0238184i
$237$	17.2064	+	5.48201i	1.11768	+	0.356095i
$238$	4.27259	−	5.79643i	0.276951	−	0.375726i
$239$	8.42148			0.544740			0.272370	−	0.962193i	$-0.412193\pi$
$239$	8.42148			0.544740			0.272370	+	0.962193i	$0.412193\pi$
$240$	10.0901	−	31.6700i	0.651314	−	2.04429i
$241$	1.44070			0.0928035			0.0464017	−	0.998923i	$-0.485225\pi$
$241$	1.44070			0.0928035			0.0464017	+	0.998923i	$0.485225\pi$
$242$	11.3046			0.726684
$243$	0.446158	+	15.5821i	0.0286210	+	0.999590i
$244$		−	1.39935i		−	0.0895842i
$245$	25.7849	−	7.98745i	1.64733	−	0.510299i
$246$	−2.40990	+	7.56398i	−0.153650	+	0.482262i
$247$	−15.4848	+	16.3334i	−0.985276	+	1.03927i
$248$	0.572586			0.0363592
$249$	3.99136	−	12.5277i	0.252942	−	0.793913i
$250$			33.3538i			2.10948i
$251$	−17.3854			−1.09736			−0.548678	−	0.836034i	$-0.684869\pi$
$251$	−17.3854			−1.09736			−0.548678	+	0.836034i	$0.684869\pi$
$252$	8.69495	−	2.86915i	0.547731	−	0.180740i
$253$		−	2.00117i		−	0.125812i
$254$	22.8141			1.43148
$255$	3.10756	−	9.75373i	0.194603	−	0.610802i
$256$	20.2460			1.26537
$257$	−12.5261			−0.781354			−0.390677	−	0.920528i	$-0.627759\pi$
$257$	−12.5261			−0.781354			−0.390677	+	0.920528i	$0.627759\pi$
$258$	−17.5149	−	5.58029i	−1.09043	−	0.347414i
$259$	18.6825	+	13.7710i	1.16087	+	0.855689i
$260$	−11.6396	−	11.0349i	−0.721855	−	0.684354i
$261$	−3.47428	+	4.89893i	−0.215053	+	0.303236i
$262$	−15.1636			−0.936807
$263$		−	7.42123i		−	0.457613i	−0.973472	−	0.228806i	$-0.926518\pi$
$263$		−	7.42123i		−	0.457613i	0.973472	−	0.228806i	$-0.0734823\pi$
$264$	−5.34012	−	1.70137i	−0.328662	−	0.104712i
$265$	48.1933			2.96049
$266$	−17.4018	+	23.6082i	−1.06697	+	1.44751i
$267$	−2.49952	+	7.84529i	−0.152968	+	0.480124i
$268$		−	12.7782i		−	0.780555i
$269$	−12.7197			−0.775535			−0.387768	−	0.921757i	$-0.626754\pi$
$269$	−12.7197			−0.775535			−0.387768	+	0.921757i	$0.626754\pi$
$270$	28.4241	−	21.4067i	1.72983	−	1.30277i
$271$	8.93682			0.542873			0.271436	−	0.962456i	$-0.412501\pi$
$271$	8.93682			0.542873			0.271436	+	0.962456i	$0.412501\pi$
$272$	7.62705			0.462458
$273$	−2.16768	+	16.3799i	−0.131194	+	0.991357i
$274$	−16.8868			−1.02017
$275$	21.2486			1.28134
$276$	−0.563835	+	1.76971i	−0.0339389	+	0.106524i
$277$	−23.9074			−1.43645			−0.718227	−	0.695809i	$-0.755046\pi$
$277$	−23.9074			−1.43645			−0.718227	+	0.695809i	$0.755046\pi$
$278$		−	35.4824i		−	2.12809i
$279$	0.932165	+	0.661084i	0.0558072	+	0.0395780i
$280$	12.3447	+	9.09937i	0.737736	+	0.543791i
$281$	−28.5987			−1.70606			−0.853029	−	0.521864i	$-0.825237\pi$
$281$	−28.5987			−1.70606			−0.853029	+	0.521864i	$0.825237\pi$
$282$	−1.48692	+	4.66700i	−0.0885445	+	0.277916i
$283$			5.71378i			0.339649i	0.985474	+	0.169825i	$0.0543201\pi$
$283$			5.71378i			0.339649i	−0.985474	+	0.169825i	$0.945680\pi$
$284$	−9.04121			−0.536497
$285$	−12.6568	+	39.7259i	−0.749722	+	2.35316i
$286$	−9.48312	+	10.0028i	−0.560749	+	0.591477i
$287$	−5.49671	−	4.05167i	−0.324461	−	0.239162i
$288$	14.2689	+	10.1194i	0.840805	+	0.596292i
$289$	−14.6510			−0.861825
$290$	13.7094			0.805042
$291$	22.4135	+	7.14098i	1.31390	+	0.418612i
$292$	−1.58790			−0.0929246
$293$			7.06162i			0.412544i	0.978495	+	0.206272i	$0.0661332\pi$
$293$			7.06162i			0.412544i	−0.978495	+	0.206272i	$0.933867\pi$
$294$	−0.173016	+	21.5301i	−0.0100905	+	1.25566i
$295$	−1.22319			−0.0712166
$296$			13.1859i			0.766417i
$297$	−6.72933	−	8.93530i	−0.390476	−	0.518479i
$298$	−25.0452			−1.45083
$299$	−2.43236	−	2.30600i	−0.140667	−	0.133359i
$300$	−18.7910	−	5.98686i	−1.08490	−	0.345651i
$301$	9.38193	−	12.7280i	0.540765	−	0.733631i
$302$		−	22.0634i		−	1.26961i
$303$	16.3213	+	5.19999i	0.937633	+	0.298732i
$304$	−31.0642			−1.78165
$305$	4.67789			0.267855
$306$	6.66022	+	4.72338i	0.380740	+	0.270018i
$307$	16.2290			0.926238			0.463119	−	0.886296i	$-0.346730\pi$
$307$	16.2290			0.926238			0.463119	+	0.886296i	$0.346730\pi$
$308$	−3.89833	+	5.28869i	−0.222128	+	0.301351i
$309$	6.09545	−	19.1319i	0.346758	−	1.08837i
$310$		−	2.60861i		−	0.148159i
$311$	12.2685			0.695684			0.347842	−	0.937553i	$-0.386915\pi$
$311$	12.2685			0.695684			0.347842	+	0.937553i	$0.386915\pi$
$312$	−8.22153	+	4.53022i	−0.465452	+	0.256473i
$313$			15.2073i			0.859565i	0.902932	+	0.429783i	$0.141410\pi$
$313$			15.2073i			0.859565i	−0.902932	+	0.429783i	$0.858590\pi$
$314$		−	8.85278i		−	0.499591i
$315$	9.59130	+	29.0664i	0.540408	+	1.63770i
$316$	12.0272			0.676583
$317$	22.8754			1.28481			0.642404	−	0.766366i	$-0.277937\pi$
$317$	22.8754			1.28481			0.642404	+	0.766366i	$0.277937\pi$
$318$	−11.6691	+	36.6260i	−0.654372	+	2.05389i
$319$		−	4.30963i		−	0.241293i
$320$		−	1.55024i		−	0.0866611i
$321$	8.51802	−	26.7356i	0.475430	−	1.49224i
$322$	−3.51574	−	2.59148i	−0.195924	−	0.144417i
$323$	−9.56716			−0.532331
$324$	3.43348	+	9.79786i	0.190749	+	0.544326i
$325$	24.4853	−	25.8271i	1.35820	−	1.43263i
$326$			24.3728i			1.34988i
$327$	3.45147	−	10.8332i	0.190867	−	0.599076i
$328$		−	3.87953i		−	0.214211i
$329$	−3.39149	−	2.49989i	−0.186979	−	0.137823i
$330$	−7.75118	+	24.3287i	−0.426688	+	1.33925i
$331$			1.39731i			0.0768030i	0.999262	+	0.0384015i	$0.0122266\pi$
$331$			1.39731i			0.0768030i	−0.999262	+	0.0384015i	$0.987773\pi$
$332$		−	8.75681i		−	0.480593i
$333$	−15.2239	+	21.4666i	−0.834267	+	1.17636i
$334$		−	32.3232i		−	1.76865i
$335$	42.7164			2.33385
$336$	−18.4650	+	13.3830i	−1.00735	+	0.730103i
$337$	−18.3737			−1.00088			−0.500439	−	0.865772i	$-0.666828\pi$
$337$	−18.3737			−1.00088			−0.500439	+	0.865772i	$0.666828\pi$
$338$	1.23043	+	23.0529i	0.0669267	+	1.25391i
$339$	2.87759	−	9.03193i	0.156289	−	0.490547i
$340$		−	6.81780i		−	0.369747i
$341$	−0.820034			−0.0444073
$342$	−27.1264	−	19.2378i	−1.46683	−	1.04026i
$343$	−17.4919	−	6.08540i	−0.944476	−	0.328581i
$344$	8.98333			0.484349
$345$	−5.91598	−	1.88484i	−0.318506	−	0.101477i
$346$	−32.9285			−1.77025
$347$			17.8948i			0.960645i	0.877092	+	0.480323i	$0.159480\pi$
$347$			17.8948i			0.960645i	−0.877092	+	0.480323i	$0.840520\pi$
$348$	−1.21425	+	3.81119i	−0.0650908	+	0.204301i
$349$	8.89980			0.476395			0.238198	−	0.971217i	$-0.423443\pi$
$349$	8.89980			0.476395			0.238198	+	0.971217i	$0.423443\pi$
$350$	27.5166	−	37.3305i	1.47082	−	1.99540i
$351$	−18.6150	−	2.11707i	−0.993595	−	0.113001i
$352$	−12.5525			−0.669051
$353$		−	5.96822i		−	0.317656i	−0.987306	−	0.158828i	$-0.949228\pi$
$353$		−	5.96822i		−	0.317656i	0.987306	−	0.158828i	$-0.0507716\pi$
$354$	0.296172	−	0.929599i	0.0157414	−	0.0494076i
$355$		−	30.2239i		−	1.60412i
$356$			5.48381i			0.290641i
$357$	−5.68684	+	4.12170i	−0.300980	+	0.218144i
$358$		−	4.65999i		−	0.246288i
$359$	−21.6718			−1.14379			−0.571897	−	0.820325i	$-0.693792\pi$
$359$	−21.6718			−1.14379			−0.571897	+	0.820325i	$0.693792\pi$
$360$	−10.0594	+	14.1843i	−0.530178	+	0.747580i
$361$	19.9660			1.05084
$362$		−	15.1382i		−	0.795646i
$363$	−10.5056	−	3.34710i	−0.551400	−	0.175677i
$364$	1.93610	+	10.8326i	0.101479	+	0.567783i
$365$		−	5.30818i		−	0.277843i
$366$	−1.13267	+	3.55511i	−0.0592054	+	0.185829i
$367$			18.0639i			0.942926i	0.881886	+	0.471463i	$0.156274\pi$
$367$			18.0639i			0.942926i	−0.881886	+	0.471463i	$0.843726\pi$
$368$		−	4.62608i		−	0.241151i
$369$	4.47915	−	6.31584i	0.233175	−	0.328790i
$370$	60.0730			3.12305
$371$	−26.6160	−	19.6188i	−1.38183	−	1.01856i
$372$	0.725190	+	0.231047i	0.0375993	+	0.0119792i
$373$	2.04910			0.106098			0.0530492	−	0.998592i	$-0.483106\pi$
$373$	2.04910			0.106098			0.0530492	+	0.998592i	$0.483106\pi$
$374$	−5.85906			−0.302965
$375$	9.87553	−	30.9964i	0.509970	−	1.60065i
$376$		−	2.39368i		−	0.123445i
$377$	−5.23824	−	4.96611i	−0.269783	−	0.255768i
$378$	−24.4123	+	0.251322i	−1.25563	+	0.0129266i
$379$			20.5036i			1.05320i	0.850113	+	0.526600i	$0.176534\pi$
$379$			20.5036i			1.05320i	−0.850113	+	0.526600i	$0.823466\pi$
$380$			27.7682i			1.42448i
$381$	−21.2016	−	6.75487i	−1.08619	−	0.346063i
$382$		−	31.9235i		−	1.63335i
$383$			0.212299i			0.0108480i	0.999985	+	0.00542398i	$0.00172651\pi$
$383$			0.212299i			0.0108480i	−0.999985	+	0.00542398i	$0.998273\pi$
$384$	−18.0678	−	5.75644i	−0.922020	−	0.293757i
$385$	−17.6796	−	13.0317i	−0.901034	−	0.664159i
$386$			17.9703i			0.914666i
$387$	14.6248	+	10.3718i	0.743420	+	0.527227i
$388$	15.6669			0.795367
$389$			14.5121i			0.735795i	0.929866	+	0.367898i	$0.119922\pi$
$389$			14.5121i			0.735795i	−0.929866	+	0.367898i	$0.880078\pi$
$390$	20.6390	+	37.4560i	1.04509	+	1.89666i
$391$		−	1.42474i		−	0.0720522i
$392$	−3.11344	−	10.0507i	−0.157252	−	0.507638i
$393$	14.0918	+	4.48968i	0.710839	+	0.226475i
$394$	19.0871			0.961594
$395$			40.2057i			2.02297i
$396$	−6.07682	−	4.30963i	−0.305372	−	0.216567i
$397$	6.62889			0.332695			0.166347	−	0.986067i	$-0.446803\pi$
$397$	6.62889			0.332695			0.166347	+	0.986067i	$0.446803\pi$
$398$			21.8808i			1.09679i
$399$	23.1619	−	16.7873i	1.15955	−	0.840414i
$400$	49.1202			2.45601
$401$	2.85574			0.142609			0.0713045	−	0.997455i	$-0.477284\pi$
$401$	2.85574			0.142609			0.0713045	+	0.997455i	$0.477284\pi$
$402$	−10.3430	+	32.4637i	−0.515862	+	1.61914i
$403$	−0.944947	+	0.996728i	−0.0470711	+	0.0496505i
$404$	11.4085			0.567593
$405$	−32.7533	+	11.4778i	−1.62752	+	0.570336i
$406$	−7.57135	−	5.58090i	−0.375760	−	0.276976i
$407$		−	18.8844i		−	0.936063i
$408$	−3.80192	−	1.21130i	−0.188223	−	0.0599683i
$409$	−12.8195			−0.633883			−0.316941	−	0.948445i	$-0.602656\pi$
$409$	−12.8195			−0.633883			−0.316941	+	0.948445i	$0.602656\pi$
$410$	−17.6745			−0.872882
$411$	15.6933	+	4.99992i	0.774094	+	0.246628i
$412$		−	13.3731i		−	0.658843i
$413$	0.675535	+	0.497942i	0.0332409	+	0.0245021i
$414$	2.86490	−	4.03966i	0.140802	−	0.198538i
$415$	29.2732			1.43696
$416$	−14.4646	+	15.2572i	−0.709185	+	0.748047i
$417$	−10.5058	+	32.9745i	−0.514469	+	1.61477i
$418$	23.8633			1.16719
$419$	−17.5604			−0.857882			−0.428941	−	0.903333i	$-0.641113\pi$
$419$	−17.5604			−0.857882			−0.428941	+	0.903333i	$0.641113\pi$
$420$	11.9630	+	16.5058i	0.583736	+	0.805399i
$421$			12.4356i			0.606074i	0.952979	+	0.303037i	$0.0980006\pi$
$421$			12.4356i			0.606074i	−0.952979	+	0.303037i	$0.901999\pi$
$422$	0.831107			0.0404577
$423$	2.76365	−	3.89689i	0.134373	−	0.189473i
$424$		−	18.7853i		−	0.912296i
$425$	15.1280			0.733818
$426$	22.9696	+	7.31816i	1.11288	+	0.354566i
$427$	−2.58348	−	1.90431i	−0.125024	−	0.0921559i
$428$		−	18.6881i		−	0.903321i
$429$	11.7745	−	6.48800i	0.568480	−	0.313244i
$430$		−	40.9266i		−	1.97366i
$431$	−3.20508			−0.154383			−0.0771916	−	0.997016i	$-0.524595\pi$
$431$	−3.20508			−0.154383			−0.0771916	+	0.997016i	$0.524595\pi$
$432$	−15.5561	−	20.6556i	−0.748444	−	0.993795i
$433$		−	22.9625i		−	1.10351i	−0.834007	−	0.551754i	$-0.813959\pi$
$433$		−	22.9625i		−	1.10351i	0.834007	−	0.551754i	$-0.186041\pi$
$434$	−1.06193	+	1.44067i	−0.0509742	+	0.0691544i
$435$	−12.7404	−	4.05912i	−0.610857	−	0.194620i
$436$		−	7.57232i		−	0.362648i
$437$			5.80282i			0.277586i
$438$	4.03412	+	1.28528i	0.192758	+	0.0614130i
$439$			28.2320i			1.34744i	0.738987	+	0.673719i	$0.235304\pi$
$439$			28.2320i			1.34744i	−0.738987	+	0.673719i	$0.764696\pi$
$440$		−	12.4781i		−	0.594869i
$441$	6.53549	−	19.9571i	0.311214	−	0.950340i
$442$	−6.75155	+	7.12152i	−0.321139	+	0.338736i
$443$		−	36.9658i		−	1.75630i	−0.478387	−	0.878149i	$-0.658778\pi$
$443$		−	36.9658i		−	1.75630i	0.478387	−	0.878149i	$-0.341222\pi$
$444$	−5.32073	+	16.7002i	−0.252510	+	0.792558i
$445$	−18.3318			−0.869012
$446$	33.5011			1.58632
$447$	23.2751	+	7.41549i	1.10087	+	0.350741i
$448$	−0.631083	+	0.856160i	−0.0298158	+	0.0404498i
$449$	−4.66488			−0.220149			−0.110075	−	0.993923i	$-0.535109\pi$
$449$	−4.66488			−0.220149			−0.110075	+	0.993923i	$0.535109\pi$
$450$	42.8935	+	30.4198i	2.02202	+	1.43400i
$451$			5.55611i			0.261627i
$452$		−	6.31327i		−	0.296951i
$453$	−6.53262	+	20.5040i	−0.306929	+	0.963363i
$454$			39.0389i			1.83219i
$455$	−36.2123	+	6.47218i	−1.69766	+	0.303420i
$456$	15.4848	+	4.93350i	0.725143	+	0.231032i
$457$			0.907579i			0.0424548i	0.999775	+	0.0212274i	$0.00675739\pi$
$457$			0.907579i			0.0424548i	−0.999775	+	0.0212274i	$0.993243\pi$
$458$	39.6772			1.85399
$459$	−4.79098	−	6.36153i	−0.223624	−	0.296931i
$460$	−4.13524			−0.192806
$461$		−	11.2351i		−	0.523269i	−0.965167	−	0.261634i	$-0.915739\pi$
$461$		−	11.2351i		−	0.523269i	0.965167	−	0.261634i	$-0.0842614\pi$
$462$	14.1847	−	10.2808i	0.659931	−	0.478304i
$463$			10.6766i			0.496185i	0.968736	+	0.248093i	$0.0798037\pi$
$463$			10.6766i			0.496185i	−0.968736	+	0.248093i	$0.920196\pi$
$464$		−	9.96254i		−	0.462499i
$465$	−0.772367	+	2.42424i	−0.0358176	+	0.112421i
$466$			33.5743i			1.55530i
$467$	−2.87161			−0.132882			−0.0664412	−	0.997790i	$-0.521164\pi$
$467$	−2.87161			−0.132882			−0.0664412	+	0.997790i	$0.521164\pi$
$468$	−12.2407	+	2.42010i	−0.565828	+	0.111869i
$469$	−23.5912	−	17.3893i	−1.08934	−	0.802962i
$470$	−10.9052			−0.503021
$471$	−2.62117	+	8.22708i	−0.120777	+	0.379084i
$472$			0.476787i			0.0219459i
$473$	−12.8656			−0.591559
$474$	−30.5557	−	9.73509i	−1.40347	−	0.447148i
$475$	−61.6149			−2.82709
$476$	−2.77544	+	3.76531i	−0.127212	+	0.172582i
$477$	21.6888	−	30.5824i	0.993060	−	1.40027i
$478$	−14.9551			−0.684030
$479$			21.8317i			0.997517i	0.866741	+	0.498759i	$0.166211\pi$
$479$			21.8317i			0.997517i	−0.866741	+	0.498759i	$0.833789\pi$
$480$	−11.8229	+	37.1086i	−0.539637	+	1.69377i
$481$	−22.9534	−	21.7610i	−1.04659	−	0.992215i
$482$	−2.55843			−0.116533
$483$	2.49996	+	3.44927i	0.113752	+	0.156947i
$484$	−7.34333			−0.333788
$485$			52.3729i			2.37813i
$486$	−0.792299	−	27.6711i	−0.0359394	−	1.25518i
$487$		−	23.7663i		−	1.07695i	−0.842640	−	0.538477i	$-0.819000\pi$
$487$		−	23.7663i		−	1.07695i	0.842640	−	0.538477i	$-0.181000\pi$
$488$		−	1.82340i		−	0.0825415i
$489$	7.21639	−	22.6502i	0.326336	−	1.02428i
$490$	−45.7895	+	14.1843i	−2.06856	+	0.640783i
$491$		−	23.2249i		−	1.04813i	−0.851679	−	0.524063i	$-0.824415\pi$
$491$		−	23.2249i		−	1.04813i	0.851679	−	0.524063i	$-0.175585\pi$
$492$	1.56545	−	4.91349i	0.0705759	−	0.221517i
$493$		−	3.06826i		−	0.138188i
$494$	27.4984	−	29.0052i	1.23721	−	1.30501i
$495$	14.4067	−	20.3142i	0.647532	−	0.913056i
$496$	−1.89566			−0.0851178
$497$	−12.3037	+	16.6919i	−0.551898	+	0.748734i
$498$	−7.08797	+	22.2471i	−0.317619	+	0.996916i
$499$		−	7.16045i		−	0.320546i	−0.987073	−	0.160273i	$-0.948763\pi$
$499$		−	7.16045i		−	0.320546i	0.987073	−	0.160273i	$-0.0512374\pi$
$500$		−	21.6663i		−	0.968948i
$501$	−9.57037	+	30.0386i	−0.427573	+	1.34203i
$502$	30.8734			1.37795
$503$	−31.9509			−1.42462			−0.712311	−	0.701864i	$-0.752351\pi$
$503$	−31.9509			−1.42462			−0.712311	+	0.701864i	$0.752351\pi$
$504$	11.3298	−	3.73861i	0.504670	−	0.166531i
$505$			38.1374i			1.69709i
$506$			3.55373i			0.157982i
$507$	5.68214	−	21.7879i	0.252353	−	0.967635i
$508$	−14.8198			−0.657522
$509$			43.7079i			1.93732i	0.248396	+	0.968659i	$0.420097\pi$
$509$			43.7079i			1.93732i	−0.248396	+	0.968659i	$0.579903\pi$
$510$	−5.51848	+	17.3209i	−0.244363	+	0.766984i
$511$	−2.16089	+	2.93158i	−0.0955921	+	0.129685i
$512$	−14.0571			−0.621242
$513$	19.5132	+	25.9098i	0.861527	+	1.14395i
$514$	22.2441			0.981146
$515$	44.7048			1.96993
$516$	11.3775	+	3.62491i	0.500868	+	0.159578i
$517$			3.42813i			0.150769i
$518$	−33.1769	−	24.4549i	−1.45771	−	1.07449i
$519$	30.6012	+	9.74960i	1.34324	+	0.427960i
$520$	−15.1668	−	14.3788i	−0.665106	−	0.630553i
$521$	42.5293			1.86324			0.931621	−	0.363432i	$-0.118395\pi$
$521$	42.5293			1.86324			0.931621	+	0.363432i	$0.118395\pi$
$522$	6.16973	−	8.69966i	0.270042	−	0.380774i
$523$			23.0490i			1.00786i	0.863744	+	0.503932i	$0.168114\pi$
$523$			23.0490i			1.00786i	−0.863744	+	0.503932i	$0.831886\pi$
$524$	9.85011			0.430304
$525$	−36.6247	+	26.5448i	−1.59843	+	1.15851i
$526$			13.1788i			0.574624i
$527$	−0.583827			−0.0254319
$528$	17.6796	+	5.63274i	0.769404	+	0.245134i
$529$	22.1358			0.962428
$530$	−85.5829			−3.71748
$531$	−0.550479	+	0.776205i	−0.0238887	+	0.0336844i
$532$	11.3041	−	15.3357i	0.490093	−	0.664887i
$533$	6.75329	+	6.40245i	0.292517	+	0.277321i
$534$	4.43872	−	13.9319i	0.192082	−	0.602891i
$535$	62.4723			2.70091
$536$		−	16.6505i		−	0.719191i
$537$	−1.37975	+	4.33064i	−0.0595406	+	0.186881i
$538$	22.5880			0.973839
$539$	4.45894	+	14.3942i	0.192060	+	0.620003i
$540$	−18.4640	+	13.9056i	−0.794565	+	0.598401i
$541$		−	41.8007i		−	1.79715i	−0.438818	−	0.898576i	$-0.644603\pi$
$541$		−	41.8007i		−	1.79715i	0.438818	−	0.898576i	$-0.355397\pi$
$542$	−15.8702			−0.681685
$543$	−4.48218	+	14.0683i	−0.192349	+	0.603727i
$544$	−8.93682			−0.383163
$545$	25.3135			1.08431
$546$	3.84943	−	29.0879i	0.164740	−	1.24485i
$547$	2.09183			0.0894401			0.0447201	−	0.999000i	$-0.485760\pi$
$547$	2.09183			0.0894401			0.0447201	+	0.999000i	$0.485760\pi$
$548$	10.9695			0.468595
$549$	2.10522	−	2.96848i	0.0898488	−	0.126692i
$550$	−37.7338			−1.60898
$551$			12.4967i			0.532378i
$552$	−0.734696	+	2.30600i	−0.0312707	+	0.0981498i
$553$	16.3672	−	22.2047i	0.696005	−	0.944238i
$554$	42.4553			1.80375
$555$	−55.8272	−	17.7867i	−2.36973	−	0.755001i
$556$			23.0490i			0.977496i
$557$	−3.24052			−0.137305			−0.0686527	−	0.997641i	$-0.521870\pi$
$557$	−3.24052			−0.137305			−0.0686527	+	0.997641i	$0.521870\pi$
$558$	−1.65536	−	1.17397i	−0.0700771	−	0.0496981i
$559$	−14.8253	+	15.6377i	−0.627045	+	0.661405i
$560$	−40.8696	−	30.1253i	−1.72706	−	1.27303i
$561$	5.44495	+	1.73477i	0.229886	+	0.0732422i
$562$	50.7864			2.14229
$563$	9.66654			0.407396			0.203698	−	0.979034i	$-0.434704\pi$
$563$	9.66654			0.407396			0.203698	+	0.979034i	$0.434704\pi$
$564$	0.965887	−	3.03164i	0.0406712	−	0.127655i
$565$	21.1046			0.887878
$566$		−	10.1467i		−	0.426497i
$567$	22.7613	+	6.99453i	0.955885	+	0.293743i
$568$	−11.7810			−0.494320
$569$			24.1545i			1.01261i	0.862354	+	0.506306i	$0.168989\pi$
$569$			24.1545i			1.01261i	−0.862354	+	0.506306i	$0.831011\pi$
$570$	22.4762	−	70.5464i	0.941425	−	2.95486i
$571$	36.2794			1.51824			0.759122	−	0.650948i	$-0.225629\pi$
$571$	36.2794			1.51824			0.759122	+	0.650948i	$0.225629\pi$
$572$	6.16015	−	6.49771i	0.257569	−	0.271683i
$573$	−9.45203	+	29.6672i	−0.394864	+	1.23937i
$574$	9.76121	+	7.19506i	0.407425	+	0.300316i
$575$		−	9.17569i		−	0.382653i
$576$	−0.983748	−	0.697666i	−0.0409895	−	0.0290694i
$577$	−36.8942			−1.53593			−0.767963	−	0.640494i	$-0.778730\pi$
$577$	−36.8942			−1.53593			−0.767963	+	0.640494i	$0.778730\pi$
$578$	26.0177			1.08219
$579$	5.32073	−	16.7002i	0.221122	−	0.694038i
$580$	−8.90548			−0.369780
$581$	−16.1669	−	11.9167i	−0.670714	−	0.494389i
$582$	−39.8025	−	12.6812i	−1.64987	−	0.525651i
$583$			26.9036i			1.11423i
$584$	−2.06908			−0.0856193
$585$	−8.09015	−	40.9195i	−0.334486	−	1.69181i
$586$		−	12.5402i		−	0.518031i
$587$			18.2831i			0.754623i	0.926086	+	0.377312i	$0.123151\pi$
$587$			18.2831i			0.754623i	−0.926086	+	0.377312i	$0.876849\pi$
$588$	0.112390	−	13.9857i	0.00463488	−	0.576762i
$589$	2.37786			0.0979782
$590$	2.17216			0.0894266
$591$	−17.7381	−	5.65138i	−0.729646	−	0.232467i
$592$		−	43.6548i		−	1.79420i
$593$		−	27.6045i		−	1.13358i	−0.823862	−	0.566790i	$-0.808185\pi$
$593$		−	27.6045i		−	1.13358i	0.823862	−	0.566790i	$-0.191815\pi$
$594$	11.9501	+	15.8675i	0.490320	+	0.651053i
$595$	−12.5870	−	9.27801i	−0.516018	−	0.380361i
$596$	16.2692			0.666410
$597$	6.47855	−	20.3343i	0.265150	−	0.832228i
$598$	4.31945	+	4.09505i	0.176636	+	0.167459i
$599$			35.6396i			1.45619i	0.685474	+	0.728097i	$0.259595\pi$
$599$			35.6396i			1.45619i	−0.685474	+	0.728097i	$0.740405\pi$
$600$	−24.4853	−	7.80108i	−0.999610	−	0.318478i
$601$		−	0.0864987i		−	0.00352836i	−0.999998	−	0.00176418i	$-0.999438\pi$
$601$		−	0.0864987i		−	0.00352836i	0.999998	−	0.00176418i	$-0.000561556\pi$
$602$	−16.6607	+	22.6028i	−0.679038	+	0.921220i
$603$	19.2240	−	27.1069i	0.782860	−	1.10388i
$604$			14.3322i			0.583169i
$605$		−	24.5480i		−	0.998020i
$606$	−28.9838	−	9.23429i	−1.17739	−	0.375117i
$607$			3.06826i			0.124537i	0.998059	+	0.0622685i	$0.0198335\pi$
$607$			3.06826i			0.124537i	−0.998059	+	0.0622685i	$0.980166\pi$
$608$	36.3987			1.47616
$609$	5.38381	+	7.42821i	0.218163	+	0.301006i
$610$	−8.30712			−0.336346
$611$	4.16680	+	3.95033i	0.168571	+	0.159813i
$612$	−4.32642	−	3.06826i	−0.174885	−	0.124027i
$613$			0.868652i			0.0350845i	0.999846	+	0.0175423i	$0.00558416\pi$
$613$			0.868652i			0.0350845i	−0.999846	+	0.0175423i	$0.994416\pi$
$614$	−28.8199			−1.16308
$615$	16.4253	+	5.23314i	0.662333	+	0.211021i
$616$	−5.07966	+	6.89134i	−0.204665	+	0.277660i
$617$	−9.75955			−0.392905			−0.196452	−	0.980513i	$-0.562942\pi$
$617$	−9.75955			−0.392905			−0.196452	+	0.980513i	$0.562942\pi$
$618$	−10.8245	+	33.9749i	−0.435424	+	1.36667i
$619$	−13.9868			−0.562177			−0.281088	−	0.959682i	$-0.590695\pi$
$619$	−13.9868			−0.562177			−0.281088	+	0.959682i	$0.590695\pi$
$620$			1.69453i			0.0680539i
$621$	−3.85849	+	2.90590i	−0.154836	+	0.116610i
$622$	−21.7868			−0.873570
$623$	10.1242	+	7.46264i	0.405618	+	0.298985i
$624$	27.2191	−	14.9982i	1.08963	−	0.600410i
$625$	23.0755			0.923020
$626$		−	27.0055i		−	1.07936i
$627$	−22.1767	−	7.06555i	−0.885653	−	0.282171i
$628$			5.75068i			0.229477i
$629$		−	13.4448i		−	0.536080i
$630$	−17.0325	−	51.6168i	−0.678590	−	2.05646i
$631$		−	14.8392i		−	0.590739i	−0.955383	−	0.295369i	$-0.904557\pi$
$631$		−	14.8392i		−	0.590739i	0.955383	−	0.295369i	$-0.0954427\pi$
$632$	15.6719			0.623393
$633$	−0.772367	−	0.246078i	−0.0306988	−	0.00978070i
$634$	−40.6227			−1.61333
$635$		−	49.5411i		−	1.96598i
$636$	7.58016	−	23.7919i	0.300573	−	0.943412i
$637$	22.6339	+	11.1671i	0.896789	+	0.442458i
$638$			7.65317i			0.302992i
$639$	−19.1794	−	13.6019i	−0.758724	−	0.538081i
$640$		−	42.2185i		−	1.66883i
$641$		−	32.2579i		−	1.27411i	−0.770819	−	0.637055i	$-0.780152\pi$
$641$		−	32.2579i		−	1.27411i	0.770819	−	0.637055i	$-0.219848\pi$
$642$	−15.1265	+	47.4778i	−0.596997	+	1.87380i
$643$	7.82119			0.308438			0.154219	−	0.988037i	$-0.450714\pi$
$643$	7.82119			0.308438			0.154219	+	0.988037i	$0.450714\pi$
$644$	2.28379	+	1.68340i	0.0899939	+	0.0663352i
$645$	−12.1177	+	38.0340i	−0.477134	+	1.49759i
$646$	16.9896			0.668447
$647$	−9.06322			−0.356312			−0.178156	−	0.984002i	$-0.557013\pi$
$647$	−9.06322			−0.356312			−0.178156	+	0.984002i	$0.557013\pi$
$648$	4.47394	+	12.7670i	0.175753	+	0.501533i
$649$		−	0.682835i		−	0.0268036i
$650$	−43.4817	+	45.8644i	−1.70549	+	1.79895i
$651$	1.41343	−	1.02443i	0.0553968	−	0.0401504i
$652$		−	15.8323i		−	0.620042i
$653$		−	1.94202i		−	0.0759972i	−0.999278	−	0.0379986i	$-0.987902\pi$
$653$		−	1.94202i		−	0.0759972i	0.999278	−	0.0379986i	$-0.0120982\pi$
$654$	−6.12921	+	19.2378i	−0.239671	+	0.752259i
$655$			32.9279i			1.28660i
$656$			12.8440i			0.501473i
$657$	−3.36845	−	2.38888i	−0.131416	−	0.0931990i
$658$	6.02269	+	4.43937i	0.234789	+	0.173065i
$659$		−	9.73060i		−	0.379050i	−0.981876	−	0.189525i	$-0.939305\pi$
$659$		−	9.73060i		−	0.379050i	0.981876	−	0.189525i	$-0.0606949\pi$
$660$	5.03509	−	15.8037i	0.195991	−	0.615159i
$661$	7.16383			0.278641			0.139320	−	0.990247i	$-0.455508\pi$
$661$	7.16383			0.278641			0.139320	+	0.990247i	$0.455508\pi$
$662$		−	2.48138i		−	0.0964414i
$663$	8.38294	−	4.61916i	0.325566	−	0.179393i
$664$		−	11.4104i		−	0.442810i
$665$	51.2657	+	37.7884i	1.98800	+	1.46537i
$666$	27.0351	−	38.1210i	1.04759	−	1.47716i
$667$	−1.86101			−0.0720586
$668$			20.9968i			0.812392i
$669$	−31.1333	−	9.91913i	−1.20368	−	0.383496i
$670$	−75.8569			−2.93061
$671$			2.61140i			0.100812i
$672$	21.6359	−	15.6812i	0.834622	−	0.604916i
$673$	0.515173			0.0198585			0.00992924	−	0.999951i	$-0.496839\pi$
$673$	0.515173			0.0198585			0.00992924	+	0.999951i	$0.496839\pi$
$674$	32.6285			1.25680
$675$	−30.8551	−	40.9698i	−1.18761	−	1.57693i
$676$	−0.799277	−	14.9750i	−0.0307414	−	0.575961i
$677$	21.0474			0.808918			0.404459	−	0.914556i	$-0.367460\pi$
$677$	21.0474			0.808918			0.404459	+	0.914556i	$0.367460\pi$
$678$	−5.11010	+	16.0391i	−0.196252	+	0.615980i
$679$	21.3203	−	28.9243i	0.818199	−	1.11001i
$680$		−	8.88383i		−	0.340679i
$681$	11.5588	−	36.2798i	0.442934	−	1.39024i
$682$	1.45624			0.0557622
$683$	5.91920			0.226492			0.113246	−	0.993567i	$-0.463875\pi$
$683$	5.91920			0.226492			0.113246	+	0.993567i	$0.463875\pi$
$684$	17.6211	+	12.4967i	0.673758	+	0.477824i
$685$			36.6701i			1.40109i
$686$	31.0627	+	10.8066i	1.18598	+	0.412599i
$687$	−36.8729	−	11.7478i	−1.40679	−	0.448205i
$688$	−29.7412			−1.13387
$689$	32.7005	+	31.0017i	1.24579	+	1.18107i
$690$	10.5058	+	3.34715i	0.399947	+	0.127424i
$691$	−29.8504			−1.13556			−0.567782	−	0.823179i	$-0.692198\pi$
$691$	−29.8504			−1.13556			−0.567782	+	0.823179i	$0.692198\pi$
$692$	21.3901			0.813128
$693$	−16.2261	+	5.35428i	−0.616379	+	0.203392i
$694$		−	31.7781i		−	1.20628i
$695$	−77.0506			−2.92269
$696$	−1.58221	+	4.96611i	−0.0599736	+	0.188240i
$697$			3.95569i			0.149833i
$698$	−15.8045			−0.598209
$699$	9.94081	−	31.2013i	0.375996	−	1.18014i
$700$	−17.8745	+	24.2495i	−0.675593	+	0.916546i
$701$			18.9891i			0.717209i	0.933490	+	0.358604i	$0.116747\pi$
$701$			18.9891i			0.717209i	−0.933490	+	0.358604i	$0.883253\pi$
$702$	33.0570	+	3.75955i	1.24766	+	0.141895i
$703$			54.7593i			2.06529i
$704$	0.865412			0.0326164
$705$	10.1345	+	3.22886i	0.381686	+	0.121606i
$706$			10.5985i			0.398881i
$707$	15.5252	−	21.0624i	0.583887	−	0.792132i
$708$	−0.192391	+	0.603859i	−0.00723049	+	0.0226944i
$709$			6.20265i			0.232945i	0.993194	+	0.116473i	$0.0371587\pi$
$709$			6.20265i			0.232945i	−0.993194	+	0.116473i	$0.962841\pi$
$710$			53.6723i			2.01429i
$711$	25.5136	+	18.0941i	0.956837	+	0.678581i
$712$			7.14559i			0.267792i
$713$			0.354111i			0.0132616i
$714$	10.0988	−	7.31943i	0.377940	−	0.273923i
$715$	21.7212	+	20.5928i	0.812327	+	0.770126i
$716$			3.02709i			0.113128i
$717$	13.8981	+	4.42796i	0.519034	+	0.165365i
$718$	38.4854			1.43626
$719$	−4.85732			−0.181147			−0.0905737	−	0.995890i	$-0.528870\pi$
$719$	−4.85732			−0.181147			−0.0905737	+	0.995890i	$0.528870\pi$
$720$	33.3038	−	46.9601i	1.24116	−	1.75010i
$721$	−24.6894	−	18.1987i	−0.919481	−	0.677756i
$722$	−35.4562			−1.31954
$723$	2.37761	+	0.757510i	0.0884241	+	0.0281721i
$724$			9.83363i			0.365464i
$725$		−	19.7604i		−	0.733883i
$726$	18.6561	+	5.94386i	0.692392	+	0.220597i
$727$		−	35.5187i		−	1.31732i	−0.752443	−	0.658658i	$-0.771125\pi$
$727$		−	35.5187i		−	1.31732i	0.752443	−	0.658658i	$-0.228875\pi$
$728$	2.52280	+	14.1153i	0.0935011	+	0.523146i
$729$	−7.45665	+	25.9499i	−0.276172	+	0.961108i
$730$			9.42641i			0.348887i
$731$	−9.15969			−0.338783
$732$	0.735770	−	2.30937i	0.0271948	−	0.0853568i
$733$	9.20075			0.339838			0.169919	−	0.985458i	$-0.445649\pi$
$733$	9.20075			0.339838			0.169919	+	0.985458i	$0.445649\pi$
$734$		−	32.0783i		−	1.18403i
$735$	46.7529	+	0.375708i	1.72451	+	0.0138582i
$736$			5.42049i			0.199802i
$737$			23.8461i			0.878384i
$738$	−7.95419	+	11.2158i	−0.292798	+	0.412861i
$739$			3.49892i			0.128710i	0.997927	+	0.0643548i	$0.0204990\pi$
$739$			3.49892i			0.128710i	−0.997927	+	0.0643548i	$0.979501\pi$
$740$	−39.0229			−1.43451
$741$	−34.1428	+	18.8134i	−1.25427	+	0.691126i
$742$	47.2654	+	34.8397i	1.73517	+	1.27900i
$743$	24.3352			0.892771			0.446385	−	0.894841i	$-0.352711\pi$
$743$	24.3352			0.892771			0.446385	+	0.894841i	$0.352711\pi$
$744$	0.944947	+	0.301062i	0.0346434	+	0.0110375i
$745$			54.3862i			1.99255i
$746$	−3.63885			−0.133228
$747$	13.1740	−	18.5761i	0.482012	−	0.679663i
$748$	3.80599			0.139161
$749$	−34.5019	−	25.4316i	−1.26067	−	0.929252i
$750$	−17.5372	+	55.0443i	−0.640369	+	2.00993i
$751$	−28.0466			−1.02344			−0.511718	−	0.859154i	$-0.670991\pi$
$751$	−28.0466			−1.02344			−0.511718	+	0.859154i	$0.670991\pi$
$752$			7.92478i			0.288987i
$753$	−28.6914	−	9.14112i	−1.04557	−	0.333121i
$754$	9.30221	+	8.81895i	0.338766	+	0.321167i
$755$	−47.9111			−1.74366
$756$	15.8580	−	0.163257i	0.576750	−	0.00593759i
$757$	−10.6053			−0.385457			−0.192728	−	0.981252i	$-0.561734\pi$
$757$	−10.6053			−0.385457			−0.192728	+	0.981252i	$0.561734\pi$
$758$		−	36.4109i		−	1.32250i
$759$	1.05220	−	3.30256i	0.0381925	−	0.119875i
$760$			36.1829i			1.31249i
$761$		−	34.9160i		−	1.26570i	−0.774274	−	0.632851i	$-0.781885\pi$
$761$		−	34.9160i		−	1.26570i	0.774274	−	0.632851i	$-0.218115\pi$
$762$	37.6504	+	11.9955i	1.36393	+	0.434551i
$763$	−13.9800	−	10.3048i	−0.506111	−	0.373059i
$764$			20.7372i			0.750246i
$765$	10.2569	−	14.4628i	0.370839	−	0.522903i
$766$		−	0.377006i		−	0.0136218i
$767$	−0.829967	−	0.786849i	−0.0299684	−	0.0284115i
$768$	33.4122	+	10.6452i	1.20566	+	0.384125i
$769$	7.03547			0.253706			0.126853	−	0.991922i	$-0.459512\pi$
$769$	7.03547			0.253706			0.126853	+	0.991922i	$0.459512\pi$
$770$	31.3958	+	23.1421i	1.13143	+	0.833984i
$771$	−20.6719	−	6.58612i	−0.744482	−	0.237193i
$772$		−	11.6734i		−	0.420134i
$773$			18.1313i			0.652137i	0.945346	+	0.326068i	$0.105724\pi$
$773$			18.1313i			0.652137i	−0.945346	+	0.326068i	$0.894276\pi$
$774$	−25.9711	−	18.4185i	−0.933511	−	0.662039i
$775$	−3.75999			−0.135063
$776$	20.4145			0.732838
$777$	23.5913	+	32.5496i	0.846333	+	1.16771i
$778$		−	25.7711i		−	0.923937i
$779$		−	16.1111i		−	0.577241i
$780$	−13.4069	−	24.3311i	−0.480044	−	0.871191i
$781$	16.8723			0.603737
$782$			2.53009i			0.0904759i
$783$	−8.30949	+	6.25803i	−0.296957	+	0.223644i
$784$	10.3077	+	33.2750i	0.368132	+	1.18839i
$785$	−19.2240			−0.686133
$786$	−25.0246	−	7.97290i	−0.892600	−	0.284384i
$787$	0.232857			0.00830046			0.00415023	−	0.999991i	$-0.498679\pi$
$787$	0.232857			0.00830046			0.00415023	+	0.999991i	$0.498679\pi$
$788$	−12.3988			−0.441689
$789$	3.90204	−	12.2474i	0.138916	−	0.436018i
$790$		−	71.3984i		−	2.54024i
$791$	−11.6556	−	8.59141i	−0.414424	−	0.305475i
$792$	−7.91831	−	5.61560i	−0.281365	−	0.199542i
$793$	3.17408	+	3.00919i	0.112715	+	0.106859i
$794$	−11.7718			−0.417764
$795$	79.5341	+	25.3397i	2.82078	+	0.898707i
$796$		−	14.2136i		−	0.503787i
$797$	27.1612			0.962099			0.481050	−	0.876693i	$-0.340256\pi$
$797$	27.1612			0.962099			0.481050	+	0.876693i	$0.340256\pi$
$798$	−41.1316	+	29.8113i	−1.45604	+	1.05531i
$799$			2.44067i			0.0863449i
$800$	−57.5554			−2.03489
$801$	−8.25000	+	11.6330i	−0.291500	+	0.411030i
$802$	−5.07131			−0.179074
$803$	2.96326			0.104571
$804$	6.71872	−	21.0881i	0.236951	−	0.743721i
$805$	−5.62744	+	7.63448i	−0.198341	+	0.269080i
$806$	1.67806	−	1.77002i	0.0591072	−	0.0623461i
$807$	−20.9916	−	6.68795i	−0.738938	−	0.235427i
$808$	14.8656			0.522972
$809$		−	11.5523i		−	0.406158i	−0.979162	−	0.203079i	$-0.934905\pi$
$809$		−	11.5523i		−	0.406158i	0.979162	−	0.203079i	$-0.0650948\pi$
$810$	58.1642	−	20.3826i	2.04368	−	0.716170i
$811$	3.05094			0.107133			0.0535666	−	0.998564i	$-0.482941\pi$
$811$	3.05094			0.107133			0.0535666	+	0.998564i	$0.482941\pi$
$812$	4.91828	+	3.62530i	0.172598	+	0.127223i
$813$	14.7486	+	4.69892i	0.517255	+	0.164798i
$814$			33.5354i			1.17541i
$815$	52.9259			1.85391
$816$	12.5870	+	4.01026i	0.440635	+	0.140387i
$817$	37.3065			1.30519
$818$	22.7652			0.795966
$819$	−12.1898	+	25.8923i	−0.425946	+	0.904748i
$820$	11.4812			0.400941
$821$	4.53082			0.158127			0.0790633	−	0.996870i	$-0.474807\pi$
$821$	4.53082			0.158127			0.0790633	+	0.996870i	$0.474807\pi$
$822$	−27.8686	−	8.87899i	−0.972029	−	0.309690i
$823$	2.84700			0.0992402			0.0496201	−	0.998768i	$-0.484199\pi$
$823$	2.84700			0.0992402			0.0496201	+	0.998768i	$0.484199\pi$
$824$		−	17.4256i		−	0.607048i
$825$	35.0669	+	11.1724i	1.22087	+	0.388972i
$826$	−1.19963	−	0.884260i	−0.0417406	−	0.0307673i
$827$	18.4956			0.643155			0.321577	−	0.946883i	$-0.395787\pi$
$827$	18.4956			0.643155			0.321577	+	0.946883i	$0.395787\pi$
$828$	−1.86101	+	2.62413i	−0.0646746	+	0.0911947i
$829$		−	20.5116i		−	0.712397i	−0.934410	−	0.356198i	$-0.884073\pi$
$829$		−	20.5116i		−	0.712397i	0.934410	−	0.356198i	$-0.115927\pi$
$830$	−51.9841			−1.80439
$831$	−39.4547	−	12.5703i	−1.36867	−	0.436060i
$832$	0.997237	−	1.05188i	0.0345730	−	0.0364675i
$833$	3.17456	+	10.2480i	0.109992	+	0.355073i
$834$	18.6564	−	58.5571i	0.646018	−	2.02767i
$835$	−70.1903			−2.42904
$836$	−15.5014			−0.536127
$837$	1.19077	+	1.58112i	0.0411591	+	0.0546516i
$838$	31.1842			1.07724
$839$			18.3131i			0.632240i	0.948719	+	0.316120i	$0.102380\pi$
$839$			18.3131i			0.632240i	−0.948719	+	0.316120i	$0.897620\pi$
$840$	15.5882	+	21.5076i	0.537845	+	0.742082i
$841$	24.9922			0.861800
$842$		−	22.0835i		−	0.761046i
$843$	−47.1969	−	15.0370i	−1.62555	−	0.517903i
$844$	−0.539880			−0.0185834
$845$	50.0599	−	2.67190i	1.72211	−	0.0919163i
$846$	−4.90776	+	6.92021i	−0.168732	+	0.237922i
$847$	−9.99318	+	13.5573i	−0.343370	+	0.465834i
$848$			62.1927i			2.13571i
$849$	−3.00427	+	9.42954i	−0.103106	+	0.323621i
$850$	−26.8648			−0.921454
$851$	−8.15475			−0.279541
$852$	−14.9208	−	4.75381i	−0.511180	−	0.162863i
$853$	−11.1608			−0.382140			−0.191070	−	0.981576i	$-0.561196\pi$
$853$	−11.1608			−0.382140			−0.191070	+	0.981576i	$0.561196\pi$
$854$	4.58782	+	3.38172i	0.156992	+	0.115720i
$855$	−41.7753	+	58.9055i	−1.42868	+	2.01452i
$856$		−	24.3512i		−	0.832306i
$857$	−4.23109			−0.144531			−0.0722656	−	0.997385i	$-0.523023\pi$
$857$	−4.23109			−0.144531			−0.0722656	+	0.997385i	$0.523023\pi$
$858$	−20.9095	+	11.5216i	−0.713840	+	0.393340i
$859$		−	19.7691i		−	0.674512i	−0.941413	−	0.337256i	$-0.890501\pi$
$859$		−	19.7691i		−	0.674512i	0.941413	−	0.337256i	$-0.109499\pi$
$860$			26.5855i			0.906560i
$861$	−6.94096	−	9.57667i	−0.236547	−	0.326372i
$862$	5.69167			0.193859
$863$	16.1539			0.549886			0.274943	−	0.961461i	$-0.411341\pi$
$863$	16.1539			0.549886			0.274943	+	0.961461i	$0.411341\pi$
$864$	18.2275	+	24.2027i	0.620113	+	0.823394i
$865$			71.5049i			2.43124i
$866$			40.7775i			1.38567i
$867$	−24.1788	−	7.70341i	−0.821155	−	0.261622i
$868$	0.689820	−	0.935846i	0.0234140	−	0.0317647i
$869$	−22.4446			−0.761380
$870$	22.6248	+	7.20830i	0.767052	+	0.244384i
$871$	28.9843	+	27.4786i	0.982096	+	0.931075i
$872$		−	9.86699i		−	0.334139i
$873$	33.2347	+	23.5698i	1.12482	+	0.797715i
$874$		−	10.3048i		−	0.348565i
$875$	−40.0004	−	29.4846i	−1.35226	−	0.996763i
$876$	−2.62053	−	0.834906i	−0.0885395	−	0.0282089i
$877$			48.1564i			1.62613i	0.582176	+	0.813063i	$0.302202\pi$
$877$			48.1564i			1.62613i	−0.582176	+	0.813063i	$0.697798\pi$
$878$		−	50.1351i		−	1.69198i
$879$	−3.71296	+	11.6539i	−0.125235	+	0.393076i
$880$			41.3113i			1.39260i
$881$	−47.5515			−1.60205			−0.801026	−	0.598630i	$-0.795712\pi$
$881$	−47.5515			−1.60205			−0.801026	+	0.598630i	$0.795712\pi$
$882$	−11.6059	+	35.4404i	−0.390791	+	1.19334i
$883$	−33.1794			−1.11658			−0.558288	−	0.829647i	$-0.688541\pi$
$883$	−33.1794			−1.11658			−0.558288	+	0.829647i	$0.688541\pi$
$884$	4.38575	−	4.62608i	0.147509	−	0.155592i
$885$	−2.01864	−	0.643143i	−0.0678559	−	0.0216190i
$886$			65.6449i			2.20538i
$887$	−13.4740			−0.452413			−0.226207	−	0.974079i	$-0.572632\pi$
$887$	−13.4740			−0.452413			−0.226207	+	0.974079i	$0.572632\pi$
$888$	−6.93309	+	21.7610i	−0.232659	+	0.730250i
$889$	−20.1675	+	27.3604i	−0.676397	+	0.917637i
$890$	32.5542			1.09122
$891$	−6.40740	−	18.2843i	−0.214656	−	0.612547i
$892$	−21.7620			−0.728645
$893$		−	9.94061i		−	0.332650i
$894$	−41.3325	−	13.1686i	−1.38237	−	0.440425i
$895$	−10.1193			−0.338250
$896$	−17.1866	+	23.3163i	−0.574164	+	0.778941i
$897$	−2.80168	−	5.08455i	−0.0935455	−	0.169768i
$898$	8.28401			0.276441
$899$			0.762600i			0.0254341i
$900$	−27.8633	−	19.7604i	−0.928775	−	0.658680i
$901$			19.1541i			0.638116i
$902$		−	9.86668i		−	0.328525i
$903$	22.1755	−	16.0723i	0.737953	−	0.534852i
$904$		−	8.22640i		−	0.273606i
$905$	−32.8729			−1.09273
$906$	11.6008	−	36.4116i	0.385411	−	1.20969i
$907$	17.5006			0.581098			0.290549	−	0.956860i	$-0.406162\pi$
$907$	17.5006			0.581098			0.290549	+	0.956860i	$0.406162\pi$
$908$		−	25.3593i		−	0.841579i
$909$	24.2011	+	17.1633i	0.802701	+	0.569269i
$910$	64.3069	−	11.4935i	2.13175	−	0.381005i
$911$		−	14.1604i		−	0.469154i	−0.972098	−	0.234577i	$-0.924630\pi$
$911$		−	14.1604i		−	0.469154i	0.972098	−	0.234577i	$-0.0753704\pi$
$912$	−51.2657	−	16.3334i	−1.69758	−	0.540852i
$913$			16.3415i			0.540826i
$914$		−	1.61170i		−	0.0533104i
$915$	7.71999	+	2.45961i	0.255215	+	0.0813120i
$916$	−25.7739			−0.851594
$917$	13.4045	−	18.1853i	0.442656	−	0.600531i
$918$	8.50795	+	11.2970i	0.280804	+	0.372856i
$919$	25.6311			0.845491			0.422745	−	0.906249i	$-0.361066\pi$
$919$	25.6311			0.845491			0.422745	+	0.906249i	$0.361066\pi$
$920$	−5.38835			−0.177649
$921$	26.7830	+	8.53311i	0.882529	+	0.281176i
$922$			19.9515i			0.657068i
$923$	19.4424	−	20.5078i	0.639953	−	0.675021i
$924$	−9.21424	+	6.67828i	−0.303126	+	0.219699i
$925$		−	86.5880i		−	2.84700i
$926$		−	18.9599i		−	0.623060i
$927$	20.1188	−	28.3687i	0.660789	−	0.931749i
$928$			11.6734i			0.383197i
$929$			23.2588i			0.763097i	0.924349	+	0.381548i	$0.124609\pi$
$929$			23.2588i			0.763097i	−0.924349	+	0.381548i	$0.875391\pi$
$930$	1.37159	−	4.30502i	0.0449762	−	0.141167i
$931$	−12.9297	−	41.7392i	−0.423753	−	1.36795i
$932$		−	21.8096i		−	0.714396i
$933$	20.2469	+	6.45071i	0.662854	+	0.211187i
$934$	5.09949			0.166860
$935$			12.7231i			0.416088i
$936$	−15.9501	+	3.15347i	−0.521345	+	0.103074i
$937$			24.9405i			0.814771i	0.913256	+	0.407386i	$0.133560\pi$
$937$			24.9405i			0.814771i	−0.913256	+	0.407386i	$0.866440\pi$
$938$	41.8939	+	30.8803i	1.36789	+	1.00828i
$939$	−7.99589	+	25.0968i	−0.260936	+	0.819003i
$940$	7.08394			0.231053
$941$			5.04058i			0.164318i	0.996619	+	0.0821590i	$0.0261815\pi$
$941$			5.04058i			0.164318i	−0.996619	+	0.0821590i	$0.973818\pi$
$942$	4.65474	−	14.6099i	0.151659	−	0.476016i
$943$	2.39927			0.0781309
$944$		−	1.57850i		−	0.0513759i
$945$	0.545751	+	53.0117i	0.0177533	+	1.72447i
$946$	22.8470			0.742820
$947$	0.541268			0.0175889			0.00879443	−	0.999961i	$-0.497201\pi$
$947$	0.541268			0.0175889			0.00879443	+	0.999961i	$0.497201\pi$
$948$	19.8487	+	6.32383i	0.644655	+	0.205388i
$949$	3.41464	−	3.60175i	0.110844	−	0.116918i
$950$	109.417			3.54997
$951$	37.7516	+	12.0277i	1.22418	+	0.390026i
$952$	−3.61649	+	4.90632i	−0.117211	+	0.159015i
$953$			6.38689i			0.206892i	0.994635	+	0.103446i	$0.0329868\pi$
$953$			6.38689i			0.206892i	−0.994635	+	0.103446i	$0.967013\pi$
$954$	−38.5155	+	54.3090i	−1.24698	+	1.75832i
$955$	−69.3224			−2.24322
$956$	9.71469			0.314195
$957$	2.26598	−	7.11226i	0.0732487	−	0.229907i
$958$		−	38.7694i		−	1.25258i
$959$	14.9279	−	20.2520i	0.482047	−	0.653971i
$960$	0.815107	−	2.55839i	0.0263075	−	0.0825716i
$961$	−30.8549			−0.995319
$962$	40.7613	+	38.6437i	1.31420	+	1.24592i
$963$	28.1149	−	39.6435i	0.905988	−	1.27749i
$964$	1.66193			0.0535272
$965$	39.0229			1.25619
$966$	−4.43949	−	6.12531i	−0.142838	−	0.197078i
$967$		−	37.2263i		−	1.19712i	−0.801079	−	0.598558i	$-0.795741\pi$
$967$		−	37.2263i		−	1.19712i	0.801079	−	0.598558i	$-0.204259\pi$
$968$	−9.56861			−0.307547
$969$	−15.7888	−	5.03035i	−0.507210	−	0.161598i
$970$		−	93.0052i		−	2.98622i
$971$	−17.7958			−0.571093			−0.285546	−	0.958365i	$-0.592175\pi$
$971$	−17.7958			−0.571093			−0.285546	+	0.958365i	$0.592175\pi$
$972$	0.514670	+	17.9749i	0.0165081	+	0.576544i
$973$	42.5532	+	31.3663i	1.36419	+	1.00556i
$974$			42.2049i			1.35233i
$975$	53.9882	−	29.7486i	1.72901	−	0.952717i
$976$			6.03675i			0.193232i
$977$	−45.9697			−1.47070			−0.735350	−	0.677687i	$-0.762982\pi$
$977$	−45.9697			−1.47070			−0.735350	+	0.677687i	$0.762982\pi$
$978$	−12.8151	+	40.2228i	−0.409780	+	1.28618i
$979$		−	10.2336i		−	0.327068i
$980$	29.7444	−	9.21401i	0.950150	−	0.294331i
$981$	11.3920	−	16.0634i	0.363719	−	0.512864i
$982$			41.2435i			1.31613i
$983$		−	42.4391i		−	1.35360i	−0.736169	−	0.676798i	$-0.763367\pi$
$983$		−	42.4391i		−	1.35360i	0.736169	−	0.676798i	$-0.236633\pi$
$984$	2.03983	−	6.40245i	0.0650275	−	0.204103i
$985$		−	41.4480i		−	1.32064i
$986$			5.44871i			0.173522i
$987$	−4.28259	−	5.90883i	−0.136316	−	0.188080i
$988$	−17.8627	+	18.8415i	−0.568288	+	0.599429i
$989$			5.55567i			0.176660i
$990$	−25.5838	+	36.0745i	−0.813106	+	1.14652i
$991$	55.3125			1.75706			0.878530	−	0.477687i	$-0.158525\pi$
$991$	55.3125			1.75706			0.878530	+	0.477687i	$0.158525\pi$
$992$	2.22120			0.0705231
$993$	−0.734696	+	2.30600i	−0.0233149	+	0.0731786i
$994$	21.8493	−	29.6419i	0.693017	−	0.940185i
$995$	47.5146			1.50631
$996$	4.60428	−	14.4515i	0.145892	−	0.457913i
$997$		−	40.4840i		−	1.28214i	−0.767481	−	0.641071i	$-0.778490\pi$
$997$		−	40.4840i		−	1.28214i	0.767481	−	0.641071i	$-0.221510\pi$
$998$			12.7157i			0.402509i
$999$	−36.4113	+	27.4220i	−1.15200	+	0.867594i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.g.a.272.8	yes	32
3.2	odd	2	inner	273.2.g.a.272.26	yes	32
7.6	odd	2	inner	273.2.g.a.272.5	✓	32
13.12	even	2	inner	273.2.g.a.272.28	yes	32
21.20	even	2	inner	273.2.g.a.272.27	yes	32
39.38	odd	2	inner	273.2.g.a.272.6	yes	32
91.90	odd	2	inner	273.2.g.a.272.25	yes	32
273.272	even	2	inner	273.2.g.a.272.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.g.a.272.5	✓	32	7.6	odd	2	inner
273.2.g.a.272.6	yes	32	39.38	odd	2	inner
273.2.g.a.272.7	yes	32	273.272	even	2	inner
273.2.g.a.272.8	yes	32	1.1	even	1	trivial
273.2.g.a.272.25	yes	32	91.90	odd	2	inner
273.2.g.a.272.26	yes	32	3.2	odd	2	inner
273.2.g.a.272.27	yes	32	21.20	even	2	inner
273.2.g.a.272.28	yes	32	13.12	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.77583 q^{2} +(1.65032 + 0.525794i) q^{3} +1.15356 q^{4} +3.85624i q^{5} +(-2.93067 - 0.933719i) q^{6} +(1.56982 - 2.12971i) q^{7} +1.50313 q^{8} +(2.44708 + 1.73545i) q^{9} +O(q^{10})\)	\(q-1.77583 q^{2} +(1.65032 + 0.525794i) q^{3} +1.15356 q^{4} +3.85624i q^{5} +(-2.93067 - 0.933719i) q^{6} +(1.56982 - 2.12971i) q^{7} +1.50313 q^{8} +(2.44708 + 1.73545i) q^{9} -6.84801i q^{10} -2.15272 q^{11} +(1.90374 + 0.606535i) q^{12} +(-2.48064 + 2.61657i) q^{13} +(-2.78774 + 3.78199i) q^{14} +(-2.02759 + 6.36401i) q^{15} -4.97642 q^{16} -1.53264 q^{17} +(-4.34559 - 3.08186i) q^{18} +6.24228 q^{19} +4.44841i q^{20} +(3.71049 - 2.68928i) q^{21} +3.82286 q^{22} +0.929599i q^{23} +(2.48064 + 0.790336i) q^{24} -9.87058 q^{25} +(4.40518 - 4.64658i) q^{26} +(3.12597 + 4.15070i) q^{27} +(1.81089 - 2.45675i) q^{28} +2.00195i q^{29} +(3.60064 - 11.3014i) q^{30} +0.380929 q^{31} +5.83100 q^{32} +(-3.55267 - 1.13189i) q^{33} +2.72170 q^{34} +(8.21266 + 6.05362i) q^{35} +(2.82286 + 2.00195i) q^{36} +8.77233i q^{37} -11.0852 q^{38} +(-5.46961 + 3.01386i) q^{39} +5.79643i q^{40} -2.58097i q^{41} +(-6.58919 + 4.77570i) q^{42} +5.97642 q^{43} -2.48329 q^{44} +(-6.69231 + 9.43653i) q^{45} -1.65081i q^{46} -1.59247i q^{47} +(-8.21266 - 2.61657i) q^{48} +(-2.07131 - 6.68653i) q^{49} +17.5284 q^{50} +(-2.52934 - 0.805852i) q^{51} +(-2.86157 + 3.01837i) q^{52} -12.4975i q^{53} +(-5.55118 - 7.37093i) q^{54} -8.30140i q^{55} +(2.35965 - 3.20123i) q^{56} +(10.3017 + 3.28215i) q^{57} -3.55511i q^{58} +0.317196i q^{59} +(-2.33894 + 7.34128i) q^{60} -1.21307i q^{61} -0.676464 q^{62} +(7.53749 - 2.48722i) q^{63} -0.402008 q^{64} +(-10.0901 - 9.56593i) q^{65} +(6.30892 + 2.01003i) q^{66} -11.0772i q^{67} -1.76799 q^{68} +(-0.488777 + 1.53413i) q^{69} +(-14.5843 - 10.7502i) q^{70} -7.83765 q^{71} +(3.67828 + 2.60861i) q^{72} -1.37652 q^{73} -15.5781i q^{74} +(-16.2896 - 5.18989i) q^{75} +7.20085 q^{76} +(-3.37939 + 4.58466i) q^{77} +(9.71308 - 5.35210i) q^{78} +10.4262 q^{79} -19.1903i q^{80} +(2.97642 + 8.49358i) q^{81} +4.58336i q^{82} -7.59111i q^{83} +(4.28028 - 3.10225i) q^{84} -5.91022i q^{85} -10.6131 q^{86} +(-1.05261 + 3.30385i) q^{87} -3.23582 q^{88} +4.75381i q^{89} +(11.8844 - 16.7576i) q^{90} +(1.67836 + 9.39059i) q^{91} +1.07235i q^{92} +(0.628653 + 0.200290i) q^{93} +2.82794i q^{94} +24.0717i q^{95} +(9.62299 + 3.06590i) q^{96} +13.5813 q^{97} +(3.67828 + 11.8741i) q^{98} +(-5.26788 - 3.73594i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4}+O(q^{10}) \) 32 * q + 16 * q^4	\( 32 q + 16 q^{4} - 16 q^{16} - 16 q^{25} + 16 q^{30} - 32 q^{36} - 48 q^{42} + 48 q^{43} - 32 q^{49} - 16 q^{51} - 80 q^{64} + 32 q^{78} + 80 q^{79} - 48 q^{81} - 96 q^{88} + 32 q^{91}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^16 - 16 * q^25 + 16 * q^30 - 32 * q^36 - 48 * q^42 + 48 * q^43 - 32 * q^49 - 16 * q^51 - 80 * q^64 + 32 * q^78 + 80 * q^79 - 48 * q^81 - 96 * q^88 + 32 * q^91

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