LMFDB - Embedded newform 273.2.e.a.209.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(209,273)]

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, 0]))

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

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

chi := DirichletCharacter("273.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.e (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			209.4
Character	$\chi$	$=$	273.209
Dual form			273.2.e.a.209.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37766i q^{2} +(1.58497 - 0.698482i) q^{3} -3.65324 q^{4} +1.30604 q^{5} +(-1.66075 - 3.76851i) q^{6} +(-0.0678621 - 2.64488i) q^{7} +3.93085i q^{8} +(2.02425 - 2.21414i) q^{9} +O(q^{10})$	\(q-2.37766i q^{2} +(1.58497 - 0.698482i) q^{3} -3.65324 q^{4} +1.30604 q^{5} +(-1.66075 - 3.76851i) q^{6} +(-0.0678621 - 2.64488i) q^{7} +3.93085i q^{8} +(2.02425 - 2.21414i) q^{9} -3.10530i q^{10} +5.27205i q^{11} +(-5.79027 + 2.55173i) q^{12} +1.00000i q^{13} +(-6.28861 + 0.161353i) q^{14} +(2.07003 - 0.912243i) q^{15} +2.03971 q^{16} -0.801293 q^{17} +(-5.26447 - 4.81296i) q^{18} -1.71006i q^{19} -4.77127 q^{20} +(-1.95496 - 4.14465i) q^{21} +12.5351 q^{22} +2.35494i q^{23} +(2.74562 + 6.23026i) q^{24} -3.29427 q^{25} +2.37766 q^{26} +(1.66183 - 4.92324i) q^{27} +(0.247917 + 9.66240i) q^{28} +6.71855i q^{29} +(-2.16900 - 4.92181i) q^{30} -0.0594188i q^{31} +3.01197i q^{32} +(3.68243 + 8.35603i) q^{33} +1.90520i q^{34} +(-0.0886304 - 3.45431i) q^{35} +(-7.39507 + 8.08880i) q^{36} +6.59192 q^{37} -4.06592 q^{38} +(0.698482 + 1.58497i) q^{39} +5.13383i q^{40} +11.0219 q^{41} +(-9.85455 + 4.64822i) q^{42} -4.90826 q^{43} -19.2601i q^{44} +(2.64374 - 2.89175i) q^{45} +5.59924 q^{46} +5.84623 q^{47} +(3.23287 - 1.42470i) q^{48} +(-6.99079 + 0.358974i) q^{49} +7.83264i q^{50} +(-1.27002 + 0.559689i) q^{51} -3.65324i q^{52} -6.42005i q^{53} +(-11.7058 - 3.95125i) q^{54} +6.88549i q^{55} +(10.3966 - 0.266756i) q^{56} +(-1.19444 - 2.71038i) q^{57} +15.9744 q^{58} -10.7167 q^{59} +(-7.56231 + 3.33265i) q^{60} -11.0415i q^{61} -0.141278 q^{62} +(-5.99351 - 5.20363i) q^{63} +11.2408 q^{64} +1.30604i q^{65} +(19.8678 - 8.75555i) q^{66} +9.44978 q^{67} +2.92732 q^{68} +(1.64488 + 3.73250i) q^{69} +(-8.21316 + 0.210733i) q^{70} +2.37782i q^{71} +(8.70345 + 7.95700i) q^{72} -1.43970i q^{73} -15.6733i q^{74} +(-5.22131 + 2.30099i) q^{75} +6.24725i q^{76} +(13.9439 - 0.357772i) q^{77} +(3.76851 - 1.66075i) q^{78} -15.2242 q^{79} +2.66393 q^{80} +(-0.804857 - 8.96394i) q^{81} -26.2062i q^{82} -0.698538 q^{83} +(7.14195 + 15.1414i) q^{84} -1.04652 q^{85} +11.6701i q^{86} +(4.69278 + 10.6487i) q^{87} -20.7236 q^{88} -7.59165 q^{89} +(-6.87559 - 6.28590i) q^{90} +(2.64488 - 0.0678621i) q^{91} -8.60317i q^{92} +(-0.0415030 - 0.0941770i) q^{93} -13.9003i q^{94} -2.23339i q^{95} +(2.10381 + 4.77388i) q^{96} +14.3029i q^{97} +(0.853518 + 16.6217i) q^{98} +(11.6731 + 10.6719i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9	$ 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9} - 12 q^{15} + 16 q^{16} - 20 q^{18} - 4 q^{21} - 16 q^{22} - 28 q^{28} + 16 q^{30} + 24 q^{36} + 24 q^{37} + 32 q^{43} - 24 q^{46} - 24 q^{49} - 8 q^{51} + 32 q^{57} + 24 q^{58} - 28 q^{60} + 8 q^{63} + 48 q^{64} - 32 q^{67} - 8 q^{70} + 64 q^{72} + 20 q^{78} - 32 q^{79} + 32 q^{81} - 48 q^{84} - 16 q^{85} + 64 q^{88} + 4 q^{91} - 52 q^{93} + 20 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9 - 12 * q^15 + 16 * q^16 - 20 * q^18 - 4 * q^21 - 16 * q^22 - 28 * q^28 + 16 * q^30 + 24 * q^36 + 24 * q^37 + 32 * q^43 - 24 * q^46 - 24 * q^49 - 8 * q^51 + 32 * q^57 + 24 * q^58 - 28 * q^60 + 8 * q^63 + 48 * q^64 - 32 * q^67 - 8 * q^70 + 64 * q^72 + 20 * q^78 - 32 * q^79 + 32 * q^81 - 48 * q^84 - 16 * q^85 + 64 * q^88 + 4 * q^91 - 52 * q^93 + 20 * q^99

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 $

$2$		−	2.37766i		−	1.68126i	−0.541613	−	0.840628i	$-0.682186\pi$
$2$		−	2.37766i		−	1.68126i	0.541613	−	0.840628i	$-0.317814\pi$
$3$	1.58497	−	0.698482i	0.915082	−	0.403269i
$3$	1.58497	−	0.698482i	0.915082	−	0.403269i
$4$	−3.65324			−1.82662
$5$	1.30604			0.584077			0.292039	−	0.956407i	$-0.405666\pi$
$5$	1.30604			0.584077			0.292039	+	0.956407i	$0.405666\pi$
$6$	−1.66075	−	3.76851i	−0.677998	−	1.53849i
$7$	−0.0678621	−	2.64488i	−0.0256495	−	0.999671i
$7$	−0.0678621	−	2.64488i	−0.0256495	−	0.999671i
$8$			3.93085i			1.38976i
$9$	2.02425	−	2.21414i	0.674749	−	0.738048i
$10$		−	3.10530i		−	0.981983i
$11$			5.27205i			1.58958i	0.606883	+	0.794791i	$0.292420\pi$
$11$			5.27205i			1.58958i	−0.606883	+	0.794791i	$0.707580\pi$
$12$	−5.79027	+	2.55173i	−1.67151	+	0.736620i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−6.28861	+	0.161353i	−1.68070	+	0.0431233i
$15$	2.07003	−	0.912243i	0.534478	−	0.235540i
$16$	2.03971			0.509926
$17$	−0.801293			−0.194342			−0.0971711	−	0.995268i	$-0.530979\pi$
$17$	−0.801293			−0.194342			−0.0971711	+	0.995268i	$0.530979\pi$
$18$	−5.26447	−	4.81296i	−1.24085	−	1.13443i
$19$		−	1.71006i		−	0.392314i	−0.980573	−	0.196157i	$-0.937154\pi$
$19$		−	1.71006i		−	0.392314i	0.980573	−	0.196157i	$-0.0628462\pi$
$20$	−4.77127			−1.06689
$21$	−1.95496	−	4.14465i	−0.426607	−	0.904437i
$22$	12.5351			2.67250
$23$			2.35494i			0.491039i	0.969392	+	0.245520i	$0.0789585\pi$
$23$			2.35494i			0.491039i	−0.969392	+	0.245520i	$0.921041\pi$
$24$	2.74562	+	6.23026i	0.560448	+	1.27175i
$25$	−3.29427			−0.658854
$26$	2.37766			0.466297
$27$	1.66183	−	4.92324i	0.319819	−	0.947479i
$28$	0.247917	+	9.66240i	0.0468519	+	1.82602i
$29$			6.71855i			1.24760i	0.781583	+	0.623802i	$0.214413\pi$
$29$			6.71855i			1.24760i	−0.781583	+	0.623802i	$0.785587\pi$
$30$	−2.16900	−	4.92181i	−0.396003	−	0.898595i
$31$		−	0.0594188i		−	0.0106719i	−0.999986	−	0.00533597i	$-0.998301\pi$
$31$		−	0.0594188i		−	0.0106719i	0.999986	−	0.00533597i	$-0.00169850\pi$
$32$			3.01197i			0.532447i
$33$	3.68243	+	8.35603i	0.641029	+	1.45460i
$34$			1.90520i			0.326739i
$35$	−0.0886304	−	3.45431i	−0.0149813	−	0.583885i
$36$	−7.39507	+	8.08880i	−1.23251	+	1.34813i
$37$	6.59192			1.08371			0.541853	−	0.840473i	$-0.317723\pi$
$37$	6.59192			1.08371			0.541853	+	0.840473i	$0.317723\pi$
$38$	−4.06592			−0.659580
$39$	0.698482	+	1.58497i	0.111847	+	0.253798i
$40$			5.13383i			0.811729i
$41$	11.0219			1.72133			0.860665	−	0.509172i	$-0.170048\pi$
$41$	11.0219			1.72133			0.860665	+	0.509172i	$0.170048\pi$
$42$	−9.85455	+	4.64822i	−1.52059	+	0.717236i
$43$	−4.90826			−0.748503			−0.374251	−	0.927327i	$-0.622100\pi$
$43$	−4.90826			−0.748503			−0.374251	+	0.927327i	$0.622100\pi$
$44$		−	19.2601i		−	2.90357i
$45$	2.64374	−	2.89175i	0.394105	−	0.431077i
$46$	5.59924			0.825562
$47$	5.84623			0.852760			0.426380	−	0.904544i	$-0.359789\pi$
$47$	5.84623			0.852760			0.426380	+	0.904544i	$0.359789\pi$
$48$	3.23287	−	1.42470i	0.466624	−	0.205637i
$49$	−6.99079	+	0.358974i	−0.998684	+	0.0512821i
$50$			7.83264i			1.10770i
$51$	−1.27002	+	0.559689i	−0.177839	+	0.0783721i
$52$		−	3.65324i		−	0.506614i
$53$		−	6.42005i		−	0.881862i	−0.897541	−	0.440931i	$-0.854648\pi$
$53$		−	6.42005i		−	0.881862i	0.897541	−	0.440931i	$-0.145352\pi$
$54$	−11.7058	−	3.95125i	−1.59295	−	0.537697i
$55$			6.88549i			0.928439i
$56$	10.3966	−	0.266756i	1.38931	−	0.0356467i
$57$	−1.19444	−	2.71038i	−0.158208	−	0.358999i
$58$	15.9744			2.09754
$59$	−10.7167			−1.39520			−0.697601	−	0.716487i	$-0.745749\pi$
$59$	−10.7167			−1.39520			−0.697601	+	0.716487i	$0.745749\pi$
$60$	−7.56231	+	3.33265i	−0.976290	+	0.430243i
$61$		−	11.0415i		−	1.41372i	−0.707354	−	0.706859i	$-0.750111\pi$
$61$		−	11.0415i		−	1.41372i	0.707354	−	0.706859i	$-0.249889\pi$
$62$	−0.141278			−0.0179423
$63$	−5.99351	−	5.20363i	−0.755112	−	0.655596i
$64$	11.2408			1.40511
$65$			1.30604i			0.161994i
$66$	19.8678	−	8.75555i	2.44555	−	1.07773i
$67$	9.44978			1.15447			0.577237	−	0.816576i	$-0.304131\pi$
$67$	9.44978			1.15447			0.577237	+	0.816576i	$0.304131\pi$
$68$	2.92732			0.354990
$69$	1.64488	+	3.73250i	0.198021	+	0.449341i
$70$	−8.21316	+	0.210733i	−0.981660	+	0.0251874i
$71$			2.37782i			0.282195i	0.989996	+	0.141098i	$0.0450632\pi$
$71$			2.37782i			0.282195i	−0.989996	+	0.141098i	$0.954937\pi$
$72$	8.70345	+	7.95700i	1.02571	+	0.937741i
$73$		−	1.43970i		−	0.168505i	−0.996444	−	0.0842523i	$-0.973150\pi$
$73$		−	1.43970i		−	0.168505i	0.996444	−	0.0842523i	$-0.0268502\pi$
$74$		−	15.6733i		−	1.82199i
$75$	−5.22131	+	2.30099i	−0.602905	+	0.265695i
$76$			6.24725i			0.716609i
$77$	13.9439	−	0.357772i	1.58906	−	0.0407720i
$78$	3.76851	−	1.66075i	0.426699	−	0.188043i
$79$	−15.2242			−1.71286			−0.856430	−	0.516263i	$-0.827323\pi$
$79$	−15.2242			−1.71286			−0.856430	+	0.516263i	$0.827323\pi$
$80$	2.66393			0.297836
$81$	−0.804857	−	8.96394i	−0.0894285	−	0.995993i
$82$		−	26.2062i		−	2.89400i
$83$	−0.698538			−0.0766745			−0.0383373	−	0.999265i	$-0.512206\pi$
$83$	−0.698538			−0.0766745			−0.0383373	+	0.999265i	$0.512206\pi$
$84$	7.14195	+	15.1414i	0.779251	+	1.65206i
$85$	−1.04652			−0.113511
$86$			11.6701i			1.25842i
$87$	4.69278	+	10.6487i	0.503119	+	1.14166i
$88$	−20.7236			−2.20914
$89$	−7.59165			−0.804713			−0.402357	−	0.915483i	$-0.631809\pi$
$89$	−7.59165			−0.804713			−0.402357	+	0.915483i	$0.631809\pi$
$90$	−6.87559	−	6.28590i	−0.724750	−	0.662592i
$91$	2.64488	−	0.0678621i	0.277259	−	0.00711388i
$92$		−	8.60317i		−	0.896943i
$93$	−0.0415030	−	0.0941770i	−0.00430366	−	0.00976570i
$94$		−	13.9003i		−	1.43371i
$95$		−	2.23339i		−	0.229141i
$96$	2.10381	+	4.77388i	0.214719	+	0.487232i
$97$			14.3029i			1.45224i	0.687570	+	0.726118i	$0.258678\pi$
$97$			14.3029i			1.45224i	−0.687570	+	0.726118i	$0.741322\pi$
$98$	0.853518	+	16.6217i	0.0862183	+	1.67904i
$99$	11.6731	+	10.6719i	1.17319	+	1.07257i
$100$	12.0348			1.20348
$101$	5.97760			0.594794			0.297397	−	0.954754i	$-0.403882\pi$
$101$	5.97760			0.594794			0.297397	+	0.954754i	$0.403882\pi$
$102$	1.33075	+	3.01968i	0.131764	+	0.298993i
$103$			17.9566i			1.76932i	0.466239	+	0.884659i	$0.345609\pi$
$103$			17.9566i			1.76932i	−0.466239	+	0.884659i	$0.654391\pi$
$104$	−3.93085			−0.385451
$105$	−2.55325	−	5.41306i	−0.249172	−	0.528261i
$106$	−15.2647			−1.48264
$107$		−	8.49082i		−	0.820839i	−0.911897	−	0.410419i	$-0.865382\pi$
$107$		−	8.49082i		−	0.820839i	0.911897	−	0.410419i	$-0.134618\pi$
$108$	−6.07106	+	17.9858i	−0.584188	+	1.73069i
$109$	4.48445			0.429533			0.214766	−	0.976665i	$-0.431101\pi$
$109$	4.48445			0.429533			0.214766	+	0.976665i	$0.431101\pi$
$110$	16.3713			1.56094
$111$	10.4480	−	4.60434i	0.991679	−	0.437025i
$112$	−0.138419	−	5.39478i	−0.0130793	−	0.509759i
$113$			11.8249i			1.11239i	0.831052	+	0.556195i	$0.187739\pi$
$113$			11.8249i			1.11239i	−0.831052	+	0.556195i	$0.812261\pi$
$114$	−6.44436	+	2.83997i	−0.603569	+	0.265988i
$115$			3.07564i			0.286805i
$116$		−	24.5445i		−	2.27890i
$117$	2.21414	+	2.02425i	0.204698	+	0.187142i
$118$			25.4807i			2.34569i
$119$	0.0543775	+	2.11933i	0.00498477	+	0.194278i
$120$	3.58588	+	8.13695i	0.327345	+	0.742798i
$121$	−16.7945			−1.52677
$122$	−26.2529			−2.37682
$123$	17.4693	−	7.69859i	1.57516	−	0.694158i
$124$			0.217072i			0.0194936i
$125$	−10.8326			−0.968899
$126$	−12.3724	+	14.2505i	−1.10222	+	1.26954i
$127$	0.900158			0.0798761			0.0399380	−	0.999202i	$-0.487284\pi$
$127$	0.900158			0.0798761			0.0399380	+	0.999202i	$0.487284\pi$
$128$		−	20.7029i		−	1.82990i
$129$	−7.77943	+	3.42833i	−0.684941	+	0.301848i
$130$	3.10530			0.272353
$131$	−20.8735			−1.82373			−0.911864	−	0.410491i	$-0.865357\pi$
$131$	−20.8735			−1.82373			−0.911864	+	0.410491i	$0.865357\pi$
$132$	−13.4528	−	30.5266i	−1.17092	−	2.65700i
$133$	−4.52289	+	0.116048i	−0.392185	+	0.0100626i
$134$		−	22.4683i		−	1.94097i
$135$	2.17040	−	6.42993i	0.186799	−	0.553401i
$136$		−	3.14976i		−	0.270090i
$137$			3.48336i			0.297604i	0.988867	+	0.148802i	$0.0475416\pi$
$137$			3.48336i			0.297604i	−0.988867	+	0.148802i	$0.952458\pi$
$138$	8.87461	−	3.91097i	0.755457	−	0.332923i
$139$		−	16.9530i		−	1.43794i	−0.695042	−	0.718969i	$-0.744614\pi$
$139$		−	16.9530i		−	1.43794i	0.695042	−	0.718969i	$-0.255386\pi$
$140$	0.323788	+	12.6194i	0.0273651	+	1.06654i
$141$	9.26608	−	4.08348i	0.780345	−	0.343891i
$142$	5.65364			0.474443
$143$	−5.27205			−0.440871
$144$	4.12887	−	4.51620i	0.344072	−	0.376350i
$145$			8.77467i			0.728696i
$146$	−3.42312			−0.283299
$147$	−10.8294	+	5.45190i	−0.893197	+	0.449665i
$148$	−24.0819			−1.97952
$149$		−	5.95646i		−	0.487972i	−0.969779	−	0.243986i	$-0.921545\pi$
$149$		−	5.95646i		−	0.487972i	0.969779	−	0.243986i	$-0.0784551\pi$
$150$	5.47096	+	12.4145i	0.446702	+	1.01364i
$151$	2.73667			0.222707			0.111353	−	0.993781i	$-0.464481\pi$
$151$	2.73667			0.222707			0.111353	+	0.993781i	$0.464481\pi$
$152$	6.72197			0.545223
$153$	−1.62201	+	1.77418i	−0.131132	+	0.143434i
$154$	−0.850660	−	33.1539i	−0.0685481	−	2.67162i
$155$		−	0.0776032i		−	0.00623324i
$156$	−2.55173	−	5.79027i	−0.204302	−	0.463593i
$157$			6.42503i			0.512773i	0.966574	+	0.256386i	$0.0825320\pi$
$157$			6.42503i			0.512773i	−0.966574	+	0.256386i	$0.917468\pi$
$158$			36.1980i			2.87976i
$159$	−4.48429	−	10.1756i	−0.355627	−	0.806975i
$160$			3.93375i			0.310990i
$161$	6.22854	−	0.159811i	0.490877	−	0.0125949i
$162$	−21.3132	+	1.91367i	−1.67452	+	0.150352i
$163$	−15.5138			−1.21513			−0.607567	−	0.794268i	$-0.707855\pi$
$163$	−15.5138			−1.21513			−0.607567	+	0.794268i	$0.707855\pi$
$164$	−40.2656			−3.14422
$165$	4.80939	+	10.9133i	0.374410	+	0.849597i
$166$			1.66088i			0.128909i
$167$	−8.77114			−0.678731			−0.339366	−	0.940655i	$-0.610212\pi$
$167$	−8.77114			−0.678731			−0.339366	+	0.940655i	$0.610212\pi$
$168$	16.2920	−	7.68465i	1.25695	−	0.592883i
$169$	−1.00000			−0.0769231
$170$			2.48826i			0.190841i
$171$	−3.78631	−	3.46157i	−0.289546	−	0.264713i
$172$	17.9311			1.36723
$173$	11.1707			0.849296			0.424648	−	0.905359i	$-0.360398\pi$
$173$	11.1707			0.849296			0.424648	+	0.905359i	$0.360398\pi$
$174$	25.3189	−	11.1578i	1.91942	−	0.845873i
$175$	0.223556	+	8.71295i	0.0168993	+	0.658637i
$176$			10.7534i			0.810570i
$177$	−16.9857	+	7.48545i	−1.27672	+	0.562641i
$178$			18.0503i			1.35293i
$179$			11.9012i			0.889537i	0.895646	+	0.444768i	$0.146714\pi$
$179$			11.9012i			0.889537i	−0.895646	+	0.444768i	$0.853286\pi$
$180$	−9.65822	+	10.5643i	−0.719881	+	0.787414i
$181$		−	6.53948i		−	0.486075i	−0.970017	−	0.243038i	$-0.921856\pi$
$181$		−	6.53948i		−	0.486075i	0.970017	−	0.243038i	$-0.0781439\pi$
$182$	−0.161353	−	6.28861i	−0.0119603	−	0.466143i
$183$	−7.71229	−	17.5004i	−0.570109	−	1.29367i
$184$	−9.25691			−0.682428
$185$	8.60929			0.632968
$186$	−0.223920	+	0.0986798i	−0.0164186	+	0.00723555i
$187$		−	4.22446i		−	0.308923i
$188$	−21.3577			−1.55767
$189$	−13.1342	−	4.06123i	−0.955370	−	0.295411i
$190$	−5.31024			−0.385245
$191$			17.2471i			1.24796i	0.781440	+	0.623980i	$0.214485\pi$
$191$			17.2471i			1.24796i	−0.781440	+	0.623980i	$0.785515\pi$
$192$	17.8164	−	7.85153i	1.28579	−	0.566635i
$193$	23.3740			1.68250			0.841250	−	0.540646i	$-0.181820\pi$
$193$	23.3740			1.68250			0.841250	+	0.540646i	$0.181820\pi$
$194$	34.0073			2.44158
$195$	0.912243	+	2.07003i	0.0653270	+	0.148238i
$196$	25.5391	−	1.31142i	1.82422	−	0.0936730i
$197$			7.54621i			0.537645i	0.963190	+	0.268823i	$0.0866346\pi$
$197$			7.54621i			0.537645i	−0.963190	+	0.268823i	$0.913365\pi$
$198$	25.3742	−	27.7545i	1.80326	−	1.97243i
$199$		−	10.6700i		−	0.756376i	−0.925729	−	0.378188i	$-0.876547\pi$
$199$		−	10.6700i		−	0.756376i	0.925729	−	0.378188i	$-0.123453\pi$
$200$		−	12.9493i		−	0.915651i
$201$	14.9776	−	6.60050i	1.05644	−	0.465564i
$202$		−	14.2127i		−	1.00000i
$203$	17.7698	−	0.455935i	1.24719	−	0.0320004i
$204$	4.63971	−	2.04468i	0.324845	−	0.143156i
$205$	14.3950			1.00539
$206$	42.6946			2.97468
$207$	5.21417	+	4.76698i	0.362410	+	0.331328i
$208$			2.03971i			0.141428i
$209$	9.01550			0.623615
$210$	−12.8704	+	6.07075i	−0.888142	+	0.418921i
$211$	−15.2247			−1.04811			−0.524054	−	0.851685i	$-0.675581\pi$
$211$	−15.2247			−1.04811			−0.524054	+	0.851685i	$0.675581\pi$
$212$			23.4540i			1.61083i
$213$	1.66086	+	3.76877i	0.113801	+	0.258232i
$214$	−20.1882			−1.38004
$215$	−6.41036			−0.437183
$216$	19.3525	+	6.53238i	1.31677	+	0.444472i
$217$	−0.157156	+	0.00403229i	−0.0106684	+	0.000273730i
$218$		−	10.6625i		−	0.722155i
$219$	−1.00561	−	2.28188i	−0.0679526	−	0.154195i
$220$		−	25.1544i		−	1.69591i
$221$		−	0.801293i		−	0.0539008i
$222$	−10.9475	−	24.8417i	−0.734750	−	1.66727i
$223$		−	19.0534i		−	1.27591i	−0.770073	−	0.637956i	$-0.779780\pi$
$223$		−	19.0534i		−	1.27591i	0.770073	−	0.637956i	$-0.220220\pi$
$224$	7.96631	−	0.204399i	0.532271	−	0.0136570i
$225$	−6.66841	+	7.29398i	−0.444561	+	0.486266i
$226$	28.1155			1.87021
$227$	−26.1181			−1.73352			−0.866759	−	0.498727i	$-0.833801\pi$
$227$	−26.1181			−1.73352			−0.866759	+	0.498727i	$0.833801\pi$
$228$	4.36359	+	9.90169i	0.288986	+	0.655756i
$229$			12.0895i			0.798898i	0.916756	+	0.399449i	$0.130798\pi$
$229$			12.0895i			0.798898i	−0.916756	+	0.399449i	$0.869202\pi$
$230$	7.31280			0.482192
$231$	21.8508	−	10.3066i	1.43768	−	0.678128i
$232$	−26.4096			−1.73387
$233$		−	12.8920i		−	0.844584i	−0.906460	−	0.422292i	$-0.861226\pi$
$233$		−	12.8920i		−	0.844584i	0.906460	−	0.422292i	$-0.138774\pi$
$234$	4.81296	−	5.26447i	0.314633	−	0.344149i
$235$	7.63538			0.498078
$236$	39.1509			2.54851
$237$	−24.1299	+	10.6339i	−1.56741	+	0.690743i
$238$	5.03902	−	0.129291i	0.326631	−	0.00838068i
$239$			14.9488i			0.966960i	0.875355	+	0.483480i	$0.160627\pi$
$239$			14.9488i			0.966960i	−0.875355	+	0.483480i	$0.839373\pi$
$240$	4.22224	−	1.86071i	0.272545	−	0.120108i
$241$		−	12.8418i		−	0.827216i	−0.910455	−	0.413608i	$-0.864268\pi$
$241$		−	12.8418i		−	0.827216i	0.910455	−	0.413608i	$-0.135732\pi$
$242$			39.9315i			2.56690i
$243$	−7.53682	−	13.6454i	−0.483487	−	0.875351i
$244$			40.3373i			2.58233i
$245$	−9.13022	+	0.468834i	−0.583309	+	0.0299527i
$246$	−18.3046	−	41.5361i	−1.16706	−	2.64824i
$247$	1.71006			0.108808
$248$	0.233566			0.0148315
$249$	−1.10716	+	0.487916i	−0.0701634	+	0.0309204i
$250$			25.7562i			1.62897i
$251$	−1.01030			−0.0637695			−0.0318848	−	0.999492i	$-0.510151\pi$
$251$	−1.01030			−0.0637695			−0.0318848	+	0.999492i	$0.510151\pi$
$252$	21.8958	+	19.0101i	1.37930	+	1.19753i
$253$	−12.4154			−0.780547
$254$		−	2.14026i		−	0.134292i
$255$	−1.65870	+	0.730974i	−0.103872	+	0.0457754i
$256$	−26.7427			−1.67142
$257$	−26.1478			−1.63105			−0.815527	−	0.578720i	$-0.803553\pi$
$257$	−26.1478			−1.63105			−0.815527	+	0.578720i	$0.803553\pi$
$258$	8.15139	+	18.4968i	0.507483	+	1.15156i
$259$	−0.447342	−	17.4349i	−0.0277965	−	1.08335i
$260$		−	4.77127i		−	0.295902i
$261$	14.8758	+	13.6000i	0.920791	+	0.841819i
$262$			49.6301i			3.06616i
$263$		−	3.56322i		−	0.219717i	−0.993947	−	0.109859i	$-0.964960\pi$
$263$		−	3.56322i		−	0.219717i	0.993947	−	0.109859i	$-0.0350398\pi$
$264$	−32.8463	+	14.4751i	−2.02155	+	0.890879i
$265$		−	8.38482i		−	0.515075i
$266$	0.275922	+	10.7539i	0.0169179	+	0.659363i
$267$	−12.0325	+	5.30263i	−0.736379	+	0.324516i
$268$	−34.5224			−2.10879
$269$	21.6665			1.32103			0.660514	−	0.750814i	$-0.270339\pi$
$269$	21.6665			1.32103			0.660514	+	0.750814i	$0.270339\pi$
$270$	−15.2882	−	5.16047i	−0.930408	−	0.314056i
$271$		−	5.64273i		−	0.342772i	−0.985204	−	0.171386i	$-0.945176\pi$
$271$		−	5.64273i		−	0.342772i	0.985204	−	0.171386i	$-0.0548245\pi$
$272$	−1.63440			−0.0991002
$273$	4.14465	−	1.95496i	0.250846	−	0.118320i
$274$	8.28223			0.500348
$275$		−	17.3676i		−	1.04730i
$276$	−6.00916	−	13.6358i	−0.361709	−	0.820776i
$277$	14.8371			0.891472			0.445736	−	0.895164i	$-0.352942\pi$
$277$	14.8371			0.891472			0.445736	+	0.895164i	$0.352942\pi$
$278$	−40.3085			−2.41754
$279$	−0.131562	−	0.120278i	−0.00787640	−	0.00720088i
$280$	13.5784	−	0.348392i	0.811462	−	0.0208204i
$281$		−	20.4548i		−	1.22023i	−0.792313	−	0.610115i	$-0.791123\pi$
$281$		−	20.4548i		−	1.22023i	0.792313	−	0.610115i	$-0.208877\pi$
$282$	−9.70912	−	22.0316i	−0.578170	−	1.31196i
$283$		−	17.8012i		−	1.05817i	−0.848569	−	0.529084i	$-0.822536\pi$
$283$		−	17.8012i		−	1.05817i	0.848569	−	0.529084i	$-0.177464\pi$
$284$		−	8.68676i		−	0.515464i
$285$	−1.55999	−	3.53986i	−0.0924056	−	0.209683i
$286$			12.5351i			0.741217i
$287$	−0.747969	−	29.1516i	−0.0441512	−	1.72076i
$288$	6.66894	+	6.09697i	0.392971	+	0.359268i
$289$	−16.3579			−0.962231
$290$	20.8631			1.22513
$291$	9.99030	+	22.6696i	0.585642	+	1.32892i
$292$			5.25959i			0.307794i
$293$	13.9111			0.812697			0.406348	−	0.913718i	$-0.366802\pi$
$293$	13.9111			0.812697			0.406348	+	0.913718i	$0.366802\pi$
$294$	12.9627	+	25.7487i	0.756003	+	1.50169i
$295$	−13.9965			−0.814905
$296$			25.9118i			1.50609i
$297$	25.9556	+	8.76123i	1.50610	+	0.508378i
$298$	−14.1624			−0.820406
$299$	−2.35494			−0.136190
$300$	19.0747	−	8.40607i	1.10128	−	0.485325i
$301$	0.333085	+	12.9818i	0.0191987	+	0.748256i
$302$		−	6.50685i		−	0.374427i
$303$	9.47431	−	4.17525i	0.544285	−	0.239862i
$304$		−	3.48801i		−	0.200051i
$305$		−	14.4206i		−	0.825721i
$306$	4.21838	+	3.85659i	0.241149	+	0.220467i
$307$		−	21.4056i		−	1.22168i	−0.791752	−	0.610842i	$-0.790831\pi$
$307$		−	21.4056i		−	1.22168i	0.791752	−	0.610842i	$-0.209169\pi$
$308$	−50.9406	+	1.30703i	−2.90261	+	0.0744750i
$309$	12.5424	+	28.4607i	0.713511	+	1.61907i
$310$	−0.184514			−0.0104797
$311$	−6.98339			−0.395992			−0.197996	−	0.980203i	$-0.563443\pi$
$311$	−6.98339			−0.395992			−0.197996	+	0.980203i	$0.563443\pi$
$312$	−6.23026	+	2.74562i	−0.352719	+	0.155440i
$313$		−	2.38679i		−	0.134909i	−0.997722	−	0.0674547i	$-0.978512\pi$
$313$		−	2.38679i		−	0.134909i	0.997722	−	0.0674547i	$-0.0214878\pi$
$314$	15.2765			0.862102
$315$	−7.82774	−	6.79613i	−0.441043	−	0.382919i
$316$	55.6179			3.12875
$317$			8.07054i			0.453287i	0.973978	+	0.226643i	$0.0727751\pi$
$317$			8.07054i			0.453287i	−0.973978	+	0.226643i	$0.927225\pi$
$318$	−24.1940	+	10.6621i	−1.35673	+	0.597900i
$319$	−35.4205			−1.98317
$320$	14.6809			0.820690
$321$	−5.93068	−	13.4577i	−0.331019	−	0.751134i
$322$	−0.379976	−	14.8093i	−0.0211752	−	0.825291i
$323$			1.37026i			0.0762431i
$324$	2.94034	+	32.7475i	0.163352	+	1.81930i
$325$		−	3.29427i		−	0.182733i
$326$			36.8865i			2.04295i
$327$	7.10771	−	3.13231i	0.393057	−	0.173217i
$328$			43.3253i			2.39224i
$329$	−0.396737	−	15.4626i	−0.0218728	−	0.852479i
$330$	25.9480	−	11.4351i	1.42839	−	0.629480i
$331$	0.989255			0.0543744			0.0271872	−	0.999630i	$-0.491345\pi$
$331$	0.989255			0.0543744			0.0271872	+	0.999630i	$0.491345\pi$
$332$	2.55193			0.140055
$333$	13.3437	−	14.5955i	0.731229	−	0.799826i
$334$			20.8548i			1.14112i
$335$	12.3418			0.674302
$336$	−3.98755	−	8.45387i	−0.217538	−	0.461196i
$337$	14.3737			0.782984			0.391492	−	0.920181i	$-0.371959\pi$
$337$	14.3737			0.782984			0.391492	+	0.920181i	$0.371959\pi$
$338$			2.37766i			0.129327i
$339$	8.25946	+	18.7420i	0.448592	+	1.01793i
$340$	3.82319			0.207341
$341$	0.313259			0.0169639
$342$	−8.23043	+	9.00254i	−0.445051	+	0.486801i
$343$	1.42385	+	18.4654i	0.0768809	+	0.997040i
$344$		−	19.2936i		−	1.04024i
$345$	2.14828	+	4.87479i	0.115659	+	0.262450i
$346$		−	26.5602i		−	1.42788i
$347$		−	21.3809i		−	1.14779i	−0.818929	−	0.573895i	$-0.805432\pi$
$347$		−	21.3809i		−	1.14779i	0.818929	−	0.573895i	$-0.194568\pi$
$348$	−17.1439	−	38.9022i	−0.919009	−	2.08538i
$349$			20.1489i			1.07855i	0.842131	+	0.539274i	$0.181301\pi$
$349$			20.1489i			1.07855i	−0.842131	+	0.539274i	$0.818699\pi$
$350$	20.7164	−	0.531540i	1.10734	−	0.0284120i
$351$	4.92324	+	1.66183i	0.262783	+	0.0887017i
$352$	−15.8793			−0.846368
$353$	−5.59804			−0.297954			−0.148977	−	0.988841i	$-0.547598\pi$
$353$	−5.59804			−0.297954			−0.148977	+	0.988841i	$0.547598\pi$
$354$	17.7978	+	40.3861i	0.945944	+	2.14650i
$355$			3.10552i			0.164824i
$356$	27.7342			1.46991
$357$	1.56650	+	3.32108i	0.0829078	+	0.175770i
$358$	28.2969			1.49554
$359$		−	11.9080i		−	0.628482i	−0.949343	−	0.314241i	$-0.898250\pi$
$359$		−	11.9080i		−	0.628482i	0.949343	−	0.314241i	$-0.101750\pi$
$360$	11.3670	+	10.3921i	0.599095	+	0.547713i
$361$	16.0757			0.846090
$362$	−15.5486			−0.817217
$363$	−26.6187	+	11.7307i	−1.39712	+	0.615700i
$364$	−9.66240	+	0.247917i	−0.506447	+	0.0129944i
$365$		−	1.88030i		−	0.0984197i
$366$	−41.6100	+	18.3372i	−2.17499	+	0.958499i
$367$			2.77210i			0.144702i	0.997379	+	0.0723511i	$0.0230502\pi$
$367$			2.77210i			0.144702i	−0.997379	+	0.0723511i	$0.976950\pi$
$368$			4.80339i			0.250394i
$369$	22.3110	−	24.4040i	1.16146	−	1.27042i
$370$		−	20.4699i		−	1.06418i
$371$	−16.9803	+	0.435678i	−0.881572	+	0.0226193i
$372$	0.151621	+	0.344051i	0.00786116	+	0.0178382i
$373$	−17.6790			−0.915384			−0.457692	−	0.889111i	$-0.651324\pi$
$373$	−17.6790			−0.915384			−0.457692	+	0.889111i	$0.651324\pi$
$374$	−10.0443			−0.519379
$375$	−17.1693	+	7.56639i	−0.886621	+	0.390727i
$376$			22.9806i			1.18513i
$377$	−6.71855			−0.346023
$378$	−9.65620	+	31.2285i	−0.496662	+	1.60622i
$379$	9.10040			0.467456			0.233728	−	0.972302i	$-0.424907\pi$
$379$	9.10040			0.467456			0.233728	+	0.972302i	$0.424907\pi$
$380$			8.15914i			0.418555i
$381$	1.42672	−	0.628744i	0.0730931	−	0.0322115i
$382$	41.0078			2.09814
$383$	12.3375			0.630419			0.315209	−	0.949022i	$-0.397925\pi$
$383$	12.3375			0.630419			0.315209	+	0.949022i	$0.397925\pi$
$384$	−14.4606	−	32.8134i	−0.737940	−	1.67450i
$385$	18.2113	−	0.467264i	0.928133	−	0.0238140i
$386$		−	55.5754i		−	2.82872i
$387$	−9.93552	+	10.8676i	−0.505051	+	0.552431i
$388$		−	52.2519i		−	2.65269i
$389$			1.00846i			0.0511308i	0.999673	+	0.0255654i	$0.00813861\pi$
$389$			1.00846i			0.0511308i	−0.999673	+	0.0255654i	$0.991861\pi$
$390$	4.92181	−	2.16900i	0.249225	−	0.109832i
$391$		−	1.88700i		−	0.0954296i
$392$	−1.41107	−	27.4797i	−0.0712700	−	1.38794i
$393$	−33.0839	+	14.5798i	−1.66886	+	0.735453i
$394$	17.9423			0.903920
$395$	−19.8834			−1.00044
$396$	−42.6446	−	38.9871i	−2.14297	−	1.95918i
$397$			7.16645i			0.359674i	0.983696	+	0.179837i	$0.0575570\pi$
$397$			7.16645i			0.359674i	−0.983696	+	0.179837i	$0.942443\pi$
$398$	−25.3696			−1.27166
$399$	−7.08758	+	3.34309i	−0.354823	+	0.167364i
$400$	−6.71934			−0.335967
$401$			11.7059i			0.584567i	0.956332	+	0.292284i	$0.0944151\pi$
$401$			11.7059i			0.584567i	−0.956332	+	0.292284i	$0.905585\pi$
$402$	−15.6937	−	35.6116i	−0.782732	−	1.77614i
$403$	0.0594188			0.00295986
$404$	−21.8376			−1.08646
$405$	−1.05117	−	11.7072i	−0.0522332	−	0.581737i
$406$	−1.08406	−	42.2504i	−0.0538008	−	2.09685i
$407$			34.7530i			1.72264i
$408$	−2.20005	−	4.99227i	−0.108919	−	0.247154i
$409$		−	33.0347i		−	1.63346i	−0.577020	−	0.816730i	$-0.695784\pi$
$409$		−	33.0347i		−	1.63346i	0.577020	−	0.816730i	$-0.304216\pi$
$410$		−	34.2263i		−	1.69032i
$411$	2.43307	+	5.52102i	0.120014	+	0.272332i
$412$		−	65.5999i		−	3.23188i
$413$	0.727261	+	28.3445i	0.0357862	+	1.39474i
$414$	11.3342	−	12.3975i	0.557047	−	0.609304i
$415$	−0.912316			−0.0447838
$416$	−3.01197			−0.147674
$417$	−11.8414	−	26.8700i	−0.579876	−	1.31583i
$418$		−	21.4357i		−	1.04846i
$419$	6.62409			0.323608			0.161804	−	0.986823i	$-0.448269\pi$
$419$	6.62409			0.323608			0.161804	+	0.986823i	$0.448269\pi$
$420$	9.32764	+	19.7752i	0.455142	+	0.964933i
$421$	29.5920			1.44222			0.721112	−	0.692818i	$-0.243631\pi$
$421$	29.5920			1.44222			0.721112	+	0.692818i	$0.243631\pi$
$422$			36.1990i			1.76214i
$423$	11.8342	−	12.9444i	0.575399	−	0.629377i
$424$	25.2362			1.22558
$425$	2.63968			0.128043
$426$	8.96083	−	3.94896i	0.434154	−	0.191328i
$427$	−29.2034	+	0.749300i	−1.41325	+	0.0362611i
$428$			31.0190i			1.49936i
$429$	−8.35603	+	3.68243i	−0.403433	+	0.177789i
$430$			15.2416i			0.735017i
$431$		−	20.8160i		−	1.00267i	−0.865253	−	0.501335i	$-0.832842\pi$
$431$		−	20.8160i		−	1.00267i	0.865253	−	0.501335i	$-0.167158\pi$
$432$	3.38964	−	10.0420i	0.163084	−	0.483145i
$433$			0.784792i			0.0377147i	0.999822	+	0.0188573i	$0.00600283\pi$
$433$			0.784792i			0.0377147i	−0.999822	+	0.0188573i	$0.993997\pi$
$434$	0.00958739	+	0.373662i	0.000460210	+	0.0179364i
$435$	6.12895	+	13.9076i	0.293860	+	0.666817i
$436$	−16.3828			−0.784594
$437$	4.02708			0.192641
$438$	−5.42553	+	2.39099i	−0.259242	+	0.114246i
$439$			23.6486i			1.12869i	0.825540	+	0.564343i	$0.190871\pi$
$439$			23.6486i			1.12869i	−0.825540	+	0.564343i	$0.809129\pi$
$440$	−27.0658			−1.29031
$441$	−13.3563	+	16.2053i	−0.636012	+	0.771679i
$442$	−1.90520			−0.0906211
$443$		−	11.7837i		−	0.559859i	−0.960021	−	0.279930i	$-0.909689\pi$
$443$		−	11.7837i		−	0.559859i	0.960021	−	0.279930i	$-0.0903111\pi$
$444$	−38.1691	+	16.8208i	−1.81142	+	0.798279i
$445$	−9.91497			−0.470015
$446$	−45.3025			−2.14514
$447$	−4.16048	−	9.44079i	−0.196784	−	0.446534i
$448$	−0.762828	−	29.7307i	−0.0360402	−	1.40464i
$449$		−	13.3714i		−	0.631035i	−0.948920	−	0.315517i	$-0.897822\pi$
$449$		−	13.3714i		−	0.631035i	0.948920	−	0.315517i	$-0.102178\pi$
$450$	17.3426	+	15.8552i	0.817537	+	0.747421i
$451$			58.1079i			2.73620i
$452$		−	43.1992i		−	2.03192i
$453$	4.33753	−	1.91151i	0.203795	−	0.0898106i
$454$			62.0998i			2.91449i
$455$	3.45431	−	0.0886304i	0.161941	−	0.00415506i
$456$	10.6541	−	4.69517i	0.498924	−	0.219872i
$457$	33.8545			1.58365			0.791824	−	0.610750i	$-0.209132\pi$
$457$	33.8545			1.58365			0.791824	+	0.610750i	$0.209132\pi$
$458$	28.7447			1.34315
$459$	−1.33161	+	3.94496i	−0.0621542	+	0.184135i
$460$		−	11.2361i		−	0.523884i
$461$	−8.88641			−0.413881			−0.206941	−	0.978354i	$-0.566351\pi$
$461$	−8.88641			−0.413881			−0.206941	+	0.978354i	$0.566351\pi$
$462$	−24.5057	−	51.9537i	−1.14011	−	2.41710i
$463$	−11.2494			−0.522803			−0.261401	−	0.965230i	$-0.584185\pi$
$463$	−11.2494			−0.522803			−0.261401	+	0.965230i	$0.584185\pi$
$464$			13.7039i			0.636186i
$465$	−0.0542044	−	0.122999i	−0.00251367	−	0.00570392i
$466$	−30.6528			−1.41996
$467$	−1.60871			−0.0744423			−0.0372212	−	0.999307i	$-0.511851\pi$
$467$	−1.60871			−0.0744423			−0.0372212	+	0.999307i	$0.511851\pi$
$468$	−8.08880	−	7.39507i	−0.373905	−	0.341837i
$469$	−0.641282	−	24.9935i	−0.0296117	−	1.15409i
$470$		−	18.1543i		−	0.837396i
$471$	4.48776	+	10.1835i	0.206785	+	0.469229i
$472$		−	42.1259i		−	1.93900i
$473$		−	25.8766i		−	1.18981i
$474$	25.2836	+	57.3727i	1.16132	+	2.63521i
$475$			5.63339i			0.258477i
$476$	−0.198654	−	7.74241i	−0.00910530	−	0.354873i
$477$	−14.2149	−	12.9958i	−0.650856	−	0.595035i
$478$	35.5432			1.62571
$479$	28.2154			1.28920			0.644598	−	0.764522i	$-0.277025\pi$
$479$	28.2154			1.28920			0.644598	+	0.764522i	$0.277025\pi$
$480$	2.74765	+	6.23486i	0.125412	+	0.284581i
$481$			6.59192i			0.300566i
$482$	−30.5335			−1.39076
$483$	9.76041	−	4.60382i	0.444114	−	0.209481i
$484$	61.3544			2.78884
$485$			18.6801i			0.848218i
$486$	−32.4440	+	17.9200i	−1.47169	+	0.812866i
$487$	−3.13667			−0.142136			−0.0710680	−	0.997471i	$-0.522641\pi$
$487$	−3.13667			−0.142136			−0.0710680	+	0.997471i	$0.522641\pi$
$488$	43.4024			1.96474
$489$	−24.5889	+	10.8361i	−1.11195	+	0.490026i
$490$	1.11472	+	21.7085i	0.0503581	+	0.980691i
$491$		−	13.8904i		−	0.626865i	−0.949611	−	0.313432i	$-0.898521\pi$
$491$		−	13.8904i		−	0.626865i	0.949611	−	0.313432i	$-0.101479\pi$
$492$	−63.8198	+	28.1248i	−2.87722	+	1.26797i
$493$		−	5.38353i		−	0.242462i
$494$		−	4.06592i		−	0.182935i
$495$	15.2454	+	13.9379i	0.685232	+	0.626463i
$496$		−	0.121197i		−	0.00544190i
$497$	6.28905	−	0.161364i	0.282103	−	0.00723816i
$498$	1.16010	+	2.63245i	0.0519852	+	0.117963i
$499$	17.7660			0.795314			0.397657	−	0.917534i	$-0.369823\pi$
$499$	17.7660			0.795314			0.397657	+	0.917534i	$0.369823\pi$
$500$	39.5742			1.76981
$501$	−13.9020	+	6.12649i	−0.621095	+	0.273711i
$502$			2.40214i			0.107213i
$503$	32.3589			1.44281			0.721407	−	0.692512i	$-0.243496\pi$
$503$	32.3589			1.44281			0.721407	+	0.692512i	$0.243496\pi$
$504$	20.4547	−	23.5596i	0.911124	−	1.04943i
$505$	7.80696			0.347405
$506$			29.5194i			1.31230i
$507$	−1.58497	+	0.698482i	−0.0703909	+	0.0310207i
$508$	−3.28850			−0.145903
$509$	−21.0344			−0.932334			−0.466167	−	0.884697i	$-0.654365\pi$
$509$	−21.0344			−0.932334			−0.466167	+	0.884697i	$0.654365\pi$
$510$	1.73800	+	3.94381i	0.0769601	+	0.174635i
$511$	−3.80784	+	0.0977014i	−0.168449	+	0.00432205i
$512$			22.1791i			0.980186i
$513$	−8.41902	−	2.84182i	−0.371709	−	0.125469i
$514$			62.1704i			2.74222i
$515$			23.4520i			1.03342i
$516$	28.4202	−	12.5245i	1.25113	−	0.551362i
$517$			30.8216i			1.35553i
$518$	−41.4541	+	1.06363i	−1.82139	+	0.0467330i
$519$	17.7053	−	7.80256i	0.777175	−	0.342494i
$520$	−5.13383			−0.225133
$521$	18.8906			0.827614			0.413807	−	0.910365i	$-0.364199\pi$
$521$	18.8906			0.827614			0.413807	+	0.910365i	$0.364199\pi$
$522$	32.3361	−	35.3696i	1.41531	−	1.54808i
$523$		−	5.64594i		−	0.246880i	−0.992352	−	0.123440i	$-0.960607\pi$
$523$		−	5.64594i		−	0.246880i	0.992352	−	0.123440i	$-0.0393926\pi$
$524$	76.2561			3.33126
$525$	6.44017	+	13.6536i	0.281072	+	0.595892i
$526$	−8.47210			−0.369401
$527$			0.0476119i			0.00207401i
$528$	7.51108	+	17.0438i	0.326878	+	0.741738i
$529$	17.4543			0.758881
$530$	−19.9362			−0.865973
$531$	−21.6933	+	23.7284i	−0.941410	+	1.02973i
$532$	16.5232	−	0.423952i	0.716373	−	0.0183806i
$533$			11.0219i			0.477411i
$534$	12.6078	+	28.6092i	0.545594	+	1.23804i
$535$		−	11.0893i		−	0.479433i
$536$			37.1456i			1.60445i
$537$	8.31277	+	18.8630i	0.358722	+	0.813999i
$538$		−	51.5154i		−	2.22098i
$539$	−1.89253	−	36.8558i	−0.0815171	−	1.58749i
$540$	−7.92902	+	23.4901i	−0.341211	+	1.01085i
$541$	17.4067			0.748372			0.374186	−	0.927354i	$-0.377922\pi$
$541$	17.4067			0.748372			0.374186	+	0.927354i	$0.377922\pi$
$542$	−13.4165			−0.576287
$543$	−4.56771	−	10.3649i	−0.196019	−	0.444799i
$544$		−	2.41347i		−	0.103477i
$545$	5.85686			0.250880
$546$	−4.64822	−	9.85455i	−0.198926	−	0.421736i
$547$	8.17213			0.349415			0.174707	−	0.984620i	$-0.444102\pi$
$547$	8.17213			0.349415			0.174707	+	0.984620i	$0.444102\pi$
$548$		−	12.7256i		−	0.543609i
$549$	−24.4475	−	22.3507i	−1.04339	−	0.953905i
$550$	−41.2941			−1.76078
$551$	11.4891			0.489452
$552$	−14.6719	+	6.46578i	−0.624477	+	0.275202i
$553$	1.03315	+	40.2663i	0.0439340	+	1.71230i
$554$		−	35.2774i		−	1.49879i
$555$	13.6454	−	6.01343i	0.579217	−	0.255256i
$556$			61.9336i			2.62657i
$557$			12.1045i			0.512882i	0.966560	+	0.256441i	$0.0825500\pi$
$557$			12.1045i			0.512882i	−0.966560	+	0.256441i	$0.917450\pi$
$558$	−0.285980	+	0.312809i	−0.0121065	+	0.0132422i
$559$		−	4.90826i		−	0.207597i
$560$	−0.180780	−	7.04578i	−0.00763935	−	0.297738i
$561$	−2.95071	−	6.69563i	−0.124579	−	0.282690i
$562$	−48.6344			−2.05152
$563$	−26.8237			−1.13048			−0.565242	−	0.824925i	$-0.691217\pi$
$563$	−26.8237			−1.13048			−0.565242	+	0.824925i	$0.691217\pi$
$564$	−33.8513	+	14.9180i	−1.42540	+	0.628160i
$565$			15.4437i			0.649722i
$566$	−42.3250			−1.77905
$567$	−23.6539	+	2.73706i	−0.993372	+	0.114946i
$568$	−9.34684			−0.392185
$569$			31.7789i			1.33224i	0.745845	+	0.666120i	$0.232046\pi$
$569$			31.7789i			1.33224i	−0.745845	+	0.666120i	$0.767954\pi$
$570$	−8.41656	+	3.70911i	−0.352531	+	0.155357i
$571$	−39.8161			−1.66625			−0.833127	−	0.553082i	$-0.813452\pi$
$571$	−39.8161			−1.66625			−0.833127	+	0.553082i	$0.813452\pi$
$572$	19.2601			0.805305
$573$	12.0468	+	27.3362i	0.503263	+	1.14198i
$574$	−69.3124	+	1.77841i	−2.89304	+	0.0742295i
$575$		−	7.75781i		−	0.323523i
$576$	22.7542	−	24.8888i	0.948093	−	1.03703i
$577$			36.3628i			1.51380i	0.653530	+	0.756901i	$0.273287\pi$
$577$			36.3628i			1.51380i	−0.653530	+	0.756901i	$0.726713\pi$
$578$			38.8935i			1.61776i
$579$	37.0471	−	16.3264i	1.53963	−	0.678500i
$580$		−	32.0560i		−	1.33105i
$581$	0.0474043	+	1.84755i	0.00196666	+	0.0766493i
$582$	53.9005	−	23.7535i	2.23425	−	0.984614i
$583$	33.8468			1.40179
$584$	5.65925			0.234182
$585$	2.89175	+	2.64374i	0.119559	+	0.109305i
$586$		−	33.0759i		−	1.36635i
$587$	10.3902			0.428851			0.214426	−	0.976740i	$-0.431212\pi$
$587$	10.3902			0.428851			0.214426	+	0.976740i	$0.431212\pi$
$588$	39.5626	−	19.9171i	1.63153	−	0.821369i
$589$	−0.101610			−0.00418675
$590$			33.2787i			1.37006i
$591$	5.27089	+	11.9605i	0.216816	+	0.491989i
$592$	13.4456			0.552610
$593$	−6.17427			−0.253547			−0.126773	−	0.991932i	$-0.540462\pi$
$593$	−6.17427			−0.253547			−0.126773	+	0.991932i	$0.540462\pi$
$594$	20.8312	−	61.7134i	0.854714	−	2.53213i
$595$	0.0710189	+	2.76791i	0.00291149	+	0.113473i
$596$			21.7604i			0.891340i
$597$	−7.45280	−	16.9116i	−0.305023	−	0.692146i
$598$			5.59924i			0.228970i
$599$			15.6452i			0.639244i	0.947545	+	0.319622i	$0.103556\pi$
$599$			15.6452i			0.639244i	−0.947545	+	0.319622i	$0.896444\pi$
$600$	−9.04483	−	20.5242i	−0.369254	−	0.837896i
$601$			40.1236i			1.63668i	0.574736	+	0.818339i	$0.305105\pi$
$601$			40.1236i			1.63668i	−0.574736	+	0.818339i	$0.694895\pi$
$602$	30.8662	−	0.791961i	1.25801	−	0.0322779i
$603$	19.1287	−	20.9232i	0.778980	−	0.852057i
$604$	−9.99771			−0.406801
$605$	−21.9342			−0.891753
$606$	−9.92730	−	22.5266i	−0.403269	−	0.915082i
$607$			6.91437i			0.280646i	0.990106	+	0.140323i	$0.0448140\pi$
$607$			6.91437i			0.280646i	−0.990106	+	0.140323i	$0.955186\pi$
$608$	5.15064			0.208886
$609$	27.8460	−	13.1345i	1.12838	−	0.532237i
$610$	−34.2872			−1.38825
$611$			5.84623i			0.236513i
$612$	5.92562	−	6.48150i	0.239529	−	0.261999i
$613$	−3.98925			−0.161124			−0.0805622	−	0.996750i	$-0.525672\pi$
$613$	−3.98925			−0.161124			−0.0805622	+	0.996750i	$0.525672\pi$
$614$	−50.8952			−2.05396
$615$	22.8156	−	10.0546i	0.920013	−	0.405442i
$616$	1.40635	+	54.8115i	0.0566634	+	2.20842i
$617$		−	2.94791i		−	0.118678i	−0.998238	−	0.0593391i	$-0.981101\pi$
$617$		−	2.94791i		−	0.118678i	0.998238	−	0.0593391i	$-0.0188993\pi$
$618$	67.6696	−	29.8214i	2.72207	−	1.19959i
$619$		−	26.3053i		−	1.05730i	−0.848841	−	0.528649i	$-0.822699\pi$
$619$		−	26.3053i		−	1.05730i	0.848841	−	0.528649i	$-0.177301\pi$
$620$			0.283503i			0.0113858i
$621$	11.5939	+	3.91350i	0.465249	+	0.157043i
$622$			16.6041i			0.665763i
$623$	0.515186	+	20.0790i	0.0206405	+	0.804449i
$624$	1.42470	+	3.23287i	0.0570336	+	0.129418i
$625$	2.32356			0.0929426
$626$	−5.67497			−0.226817
$627$	14.2893	−	6.29716i	0.570659	−	0.251484i
$628$		−	23.4722i		−	0.936642i
$629$	−5.28206			−0.210610
$630$	−16.1589	+	18.6117i	−0.643784	+	0.741507i
$631$	24.0536			0.957558			0.478779	−	0.877935i	$-0.341080\pi$
$631$	24.0536			0.957558			0.478779	+	0.877935i	$0.341080\pi$
$632$		−	59.8441i		−	2.38047i
$633$	−24.1306	+	10.6341i	−0.959105	+	0.422669i
$634$	19.1890			0.762091
$635$	1.17564			0.0466538
$636$	16.3822	+	37.1739i	0.649597	+	1.47404i
$637$	−0.358974	−	6.99079i	−0.0142231	−	0.276985i
$638$			84.2178i			3.33421i
$639$	5.26483	+	4.81329i	0.208274	+	0.190411i
$640$		−	27.0387i		−	1.06880i
$641$		−	23.0473i		−	0.910313i	−0.890411	−	0.455156i	$-0.849583\pi$
$641$		−	23.0473i		−	0.910313i	0.890411	−	0.455156i	$-0.150417\pi$
$642$	−31.9977	+	14.1011i	−1.26285	+	0.556527i
$643$		−	24.7695i		−	0.976814i	−0.872616	−	0.488407i	$-0.837578\pi$
$643$		−	24.7695i		−	0.976814i	0.872616	−	0.488407i	$-0.162422\pi$
$644$	−22.7544	+	0.583830i	−0.896648	+	0.0230061i
$645$	−10.1602	+	4.47752i	−0.400058	+	0.176302i
$646$	3.25800			0.128184
$647$	38.5439			1.51532			0.757659	−	0.652650i	$-0.226343\pi$
$647$	38.5439			1.51532			0.757659	+	0.652650i	$0.226343\pi$
$648$	35.2359	−	3.16377i	1.38420	−	0.124285i
$649$		−	56.4992i		−	2.21779i
$650$	−7.83264			−0.307221
$651$	−0.246270	+	0.116162i	−0.00965210	+	0.00455273i
$652$	56.6757			2.21959
$653$		−	11.3301i		−	0.443380i	−0.975117	−	0.221690i	$-0.928843\pi$
$653$		−	11.3301i		−	0.443380i	0.975117	−	0.221690i	$-0.0711573\pi$
$654$	−7.44755	−	16.8997i	−0.291222	−	0.660830i
$655$	−27.2616			−1.06520
$656$	22.4814			0.877751
$657$	−3.18771	−	2.91431i	−0.124364	−	0.113698i
$658$	−36.7647	+	0.943305i	−1.43324	+	0.0367739i
$659$			43.9153i			1.71070i	0.518052	+	0.855349i	$0.326657\pi$
$659$			43.9153i			1.71070i	−0.518052	+	0.855349i	$0.673343\pi$
$660$	−17.5699	−	39.8689i	−0.683906	−	1.55189i
$661$		−	22.8566i		−	0.889019i	−0.895774	−	0.444510i	$-0.853378\pi$
$661$		−	22.8566i		−	0.889019i	0.895774	−	0.444510i	$-0.146622\pi$
$662$		−	2.35211i		−	0.0914173i
$663$	−0.559689	−	1.27002i	−0.0217365	−	0.0493236i
$664$		−	2.74585i		−	0.106559i
$665$	−5.90706	+	0.151563i	−0.229066	+	0.00587736i
$666$	−34.7030	−	31.7267i	−1.34471	−	1.22938i
$667$	−15.8218			−0.612622
$668$	32.0431			1.23979
$669$	−13.3085	−	30.1991i	−0.514536	−	1.16756i
$670$		−	29.3444i		−	1.13367i
$671$	58.2113			2.24722
$672$	12.4836	−	5.88829i	0.481564	−	0.227146i
$673$	−43.6869			−1.68400			−0.842002	−	0.539474i	$-0.818623\pi$
$673$	−43.6869			−1.68400			−0.842002	+	0.539474i	$0.818623\pi$
$674$		−	34.1757i		−	1.31640i
$675$	−5.47450	+	16.2185i	−0.210714	+	0.624250i
$676$	3.65324			0.140509
$677$	1.75811			0.0675696			0.0337848	−	0.999429i	$-0.489244\pi$
$677$	1.75811			0.0675696			0.0337848	+	0.999429i	$0.489244\pi$
$678$	44.5621	−	19.6382i	1.71140	−	0.754199i
$679$	37.8294	−	0.970623i	1.45176	−	0.0372491i
$680$		−	4.11370i		−	0.157753i
$681$	−41.3963	+	18.2430i	−1.58631	+	0.699074i
$682$		−	0.744822i		−	0.0285207i
$683$			19.7054i			0.754008i	0.926212	+	0.377004i	$0.123046\pi$
$683$			19.7054i			0.754008i	−0.926212	+	0.377004i	$0.876954\pi$
$684$	13.8323	+	12.6460i	0.528892	+	0.483531i
$685$			4.54940i			0.173823i
$686$	43.9045	−	3.38544i	1.67628	−	0.129257i
$687$	8.44431	+	19.1615i	0.322170	+	0.731056i
$688$	−10.0114			−0.381681
$689$	6.42005			0.244584
$690$	11.5906	−	5.10786i	0.441245	−	0.194453i
$691$		−	16.9590i		−	0.645149i	−0.946544	−	0.322575i	$-0.895452\pi$
$691$		−	16.9590i		−	0.645149i	0.946544	−	0.322575i	$-0.104548\pi$
$692$	−40.8095			−1.55134
$693$	27.4338	−	31.5981i	1.04212	−	1.20031i
$694$	−50.8365			−1.92973
$695$		−	22.1413i		−	0.839867i
$696$	−41.8583	+	18.4466i	−1.58664	+	0.699217i
$697$	−8.83176			−0.334527
$698$	47.9072			1.81331
$699$	−9.00484	−	20.4334i	−0.340594	−	0.772863i
$700$	−0.816705	−	31.8305i	−0.0308686	−	1.20308i
$701$			12.4182i			0.469029i	0.972113	+	0.234514i	$0.0753500\pi$
$701$			12.4182i			0.469029i	−0.972113	+	0.234514i	$0.924650\pi$
$702$	3.95125	−	11.7058i	0.149130	−	0.441806i
$703$		−	11.2726i		−	0.425153i
$704$			59.2623i			2.23353i
$705$	12.1018	−	5.33318i	0.455782	−	0.200859i
$706$			13.3102i			0.500937i
$707$	−0.405653	−	15.8100i	−0.0152561	−	0.594598i
$708$	62.0529	−	27.3462i	2.33209	−	1.02773i
$709$	−40.6691			−1.52736			−0.763679	−	0.645596i	$-0.776609\pi$
$709$	−40.6691			−1.52736			−0.763679	+	0.645596i	$0.776609\pi$
$710$	7.38385			0.277111
$711$	−30.8176	+	33.7086i	−1.15575	+	1.26417i
$712$		−	29.8416i		−	1.11836i
$713$	0.139928			0.00524034
$714$	7.89638	−	3.72459i	0.295515	−	0.139389i
$715$	−6.88549			−0.257503
$716$		−	43.4780i		−	1.62485i
$717$	10.4415	+	23.6934i	0.389945	+	0.884847i
$718$	−28.3132			−1.05664
$719$	−45.8031			−1.70817			−0.854084	−	0.520136i	$-0.825881\pi$
$719$	−45.8031			−1.70817			−0.854084	+	0.520136i	$0.825881\pi$
$720$	5.39245	−	5.89832i	0.200965	−	0.219817i
$721$	47.4931	−	1.21857i	1.76874	−	0.0453821i
$722$		−	38.2225i		−	1.42249i
$723$	−8.96979	−	20.3539i	−0.333590	−	0.756970i
$724$			23.8903i			0.887876i
$725$		−	22.1327i		−	0.821988i
$726$	27.8915	+	63.2902i	1.03515	+	2.34892i
$727$			45.2897i			1.67970i	0.542816	+	0.839851i	$0.317358\pi$
$727$			45.2897i			1.67970i	−0.542816	+	0.839851i	$0.682642\pi$
$728$	0.266756	+	10.3966i	0.00988662	+	0.385324i
$729$	−21.4767	−	16.3631i	−0.795432	−	0.606043i
$730$	−4.47072			−0.165469
$731$	3.93296			0.145466
$732$	28.1749	+	63.9333i	1.04137	+	2.36304i
$733$		−	35.0859i		−	1.29593i	−0.761672	−	0.647963i	$-0.775621\pi$
$733$		−	35.0859i		−	1.29593i	0.761672	−	0.647963i	$-0.224379\pi$
$734$	6.59109			0.243282
$735$	−14.1436	+	7.12038i	−0.521696	+	0.262639i
$736$	−7.09302			−0.261452
$737$			49.8197i			1.83513i
$738$	−58.0244	−	53.0479i	−2.13591	−	1.95272i
$739$	27.5255			1.01254			0.506271	−	0.862374i	$-0.331023\pi$
$739$	27.5255			1.01254			0.506271	+	0.862374i	$0.331023\pi$
$740$	−31.4518			−1.15619
$741$	2.71038	−	1.19444i	0.0995684	−	0.0438790i
$742$	1.03589	+	40.3732i	0.0380288	+	1.48215i
$743$			13.0242i			0.477810i	0.971043	+	0.238905i	$0.0767884\pi$
$743$			13.0242i			0.477810i	−0.971043	+	0.238905i	$0.923212\pi$
$744$	0.370195	−	0.163142i	0.0135720	−	0.00598107i
$745$		−	7.77935i		−	0.285013i
$746$			42.0346i			1.53899i
$747$	−1.41401	+	1.54666i	−0.0517360	+	0.0565894i
$748$			15.4330i			0.564285i
$749$	−22.4572	+	0.576205i	−0.820568	+	0.0210541i
$750$	17.9903	+	40.8228i	0.656911	+	1.49064i
$751$	27.1767			0.991691			0.495846	−	0.868411i	$-0.334858\pi$
$751$	27.1767			0.991691			0.495846	+	0.868411i	$0.334858\pi$
$752$	11.9246			0.434845
$753$	−1.60129	+	0.705676i	−0.0583543	+	0.0257163i
$754$			15.9744i			0.581753i
$755$	3.57418			0.130078
$756$	47.9823	+	14.8367i	1.74510	+	0.539604i
$757$	31.6636			1.15083			0.575417	−	0.817860i	$-0.304840\pi$
$757$	31.6636			1.15083			0.575417	+	0.817860i	$0.304840\pi$
$758$		−	21.6376i		−	0.785913i
$759$	−19.6779	+	8.67191i	−0.714264	+	0.314770i
$760$	8.77913			0.318452
$761$	−17.1558			−0.621898			−0.310949	−	0.950427i	$-0.600647\pi$
$761$	−17.1558			−0.621898			−0.310949	+	0.950427i	$0.600647\pi$
$762$	−1.49494	−	3.39225i	−0.0541558	−	0.122888i
$763$	−0.304325	−	11.8608i	−0.0110173	−	0.429391i
$764$		−	63.0080i		−	2.27955i
$765$	−2.11841	+	2.31714i	−0.0765913	+	0.0837764i
$766$		−	29.3344i		−	1.05990i
$767$		−	10.7167i		−	0.386959i
$768$	−42.3863	+	18.6793i	−1.52948	+	0.674031i
$769$		−	23.9313i		−	0.862986i	−0.902116	−	0.431493i	$-0.857987\pi$
$769$		−	23.9313i		−	0.862986i	0.902116	−	0.431493i	$-0.142013\pi$
$770$	−1.11099	−	43.3002i	−0.0400374	−	1.56043i
$771$	−41.4434	+	18.2637i	−1.49255	+	0.657753i
$772$	−85.3911			−3.07329
$773$	34.5517			1.24274			0.621368	−	0.783519i	$-0.286577\pi$
$773$	34.5517			1.24274			0.621368	+	0.783519i	$0.286577\pi$
$774$	25.8394	+	23.6233i	0.928777	+	0.849120i
$775$			0.195742i			0.00703125i
$776$	−56.2224			−2.01827
$777$	−12.8870	−	27.3212i	−0.462317	−	0.980143i
$778$	2.39776			0.0859640
$779$		−	18.8480i		−	0.675301i
$780$	−3.33265	−	7.56231i	−0.119328	−	0.270774i
$781$	−12.5360			−0.448573
$782$	−4.48663			−0.160442
$783$	33.0771	+	11.1651i	1.18208	+	0.399007i
$784$	−14.2592	+	0.732202i	−0.509256	+	0.0261501i
$785$			8.39131i			0.299499i
$786$	34.6657	+	78.6621i	1.23648	+	2.80578i
$787$		−	37.7756i		−	1.34655i	−0.739391	−	0.673277i	$-0.764886\pi$
$787$		−	37.7756i		−	1.34655i	0.739391	−	0.673277i	$-0.235114\pi$
$788$		−	27.5682i		−	0.982075i
$789$	−2.48884	−	5.64759i	−0.0886052	−	0.201059i
$790$			47.2759i			1.68200i
$791$	31.2754	−	0.802461i	1.11202	−	0.0285322i
$792$	−41.9497	+	45.8850i	−1.49062	+	1.63045i
$793$	11.0415			0.392095
$794$	17.0393			0.604704
$795$	−5.85664	−	13.2897i	−0.207714	−	0.471336i
$796$			38.9801i			1.38161i
$797$	−17.5665			−0.622239			−0.311119	−	0.950371i	$-0.600704\pi$
$797$	−17.5665			−0.622239			−0.311119	+	0.950371i	$0.600704\pi$
$798$	7.94872	+	16.8518i	0.281382	+	0.596548i
$799$	−4.68454			−0.165727
$800$		−	9.92225i		−	0.350805i
$801$	−15.3674	+	16.8090i	−0.542979	+	0.593917i
$802$	27.8327			0.982807
$803$	7.59019			0.267852
$804$	−54.7168	+	24.1132i	−1.92971	+	0.850409i
$805$	8.13469	−	0.208719i	0.286710	−	0.00735639i
$806$		−	0.141278i		−	0.00497629i
$807$	34.3406	−	15.1336i	1.20885	−	0.532729i
$808$			23.4970i			0.826623i
$809$			4.95280i			0.174131i	0.996203	+	0.0870656i	$0.0277490\pi$
$809$			4.95280i			0.174131i	−0.996203	+	0.0870656i	$0.972251\pi$
$810$	−27.8358	+	2.49932i	−0.978049	+	0.0878173i
$811$			20.6467i			0.725004i	0.931983	+	0.362502i	$0.118077\pi$
$811$			20.6467i			0.725004i	−0.931983	+	0.362502i	$0.881923\pi$
$812$	−64.9173	+	1.66564i	−2.27815	+	0.0584526i
$813$	−3.94135	−	8.94355i	−0.138229	−	0.313664i
$814$	82.6305			2.89620
$815$	−20.2616			−0.709732
$816$	−2.59048	+	1.14160i	−0.0906848	+	0.0399640i
$817$			8.39340i			0.293648i
$818$	−78.5451			−2.74627
$819$	5.20363	−	5.99351i	0.181830	−	0.209430i
$820$	−52.5884			−1.83647
$821$		−	13.4087i		−	0.467966i	−0.972241	−	0.233983i	$-0.924824\pi$
$821$		−	13.4087i		−	0.467966i	0.972241	−	0.233983i	$-0.0751760\pi$
$822$	13.1271	−	5.78499i	0.457859	−	0.201775i
$823$	4.81544			0.167856			0.0839279	−	0.996472i	$-0.473253\pi$
$823$	4.81544			0.167856			0.0839279	+	0.996472i	$0.473253\pi$
$824$	−70.5847			−2.45893
$825$	−12.1309	−	27.5270i	−0.422345	−	0.958368i
$826$	67.3935	−	1.72918i	2.34492	−	0.0601657i
$827$			27.6726i			0.962272i	0.876646	+	0.481136i	$0.159776\pi$
$827$			27.6726i			0.962272i	−0.876646	+	0.481136i	$0.840224\pi$
$828$	−19.0487	−	17.4149i	−0.661986	−	0.605211i
$829$		−	47.4183i		−	1.64691i	−0.567385	−	0.823453i	$-0.692045\pi$
$829$		−	47.4183i		−	1.64691i	0.567385	−	0.823453i	$-0.307955\pi$
$830$			2.16917i			0.0752931i
$831$	23.5163	−	10.3634i	0.815770	−	0.359503i
$832$			11.2408i			0.389706i
$833$	5.60167	−	0.287644i	0.194086	−	0.00996627i
$834$	−63.8877	+	28.1548i	−2.21225	+	0.974920i
$835$	−11.4554			−0.396431
$836$	−32.9358			−1.13911
$837$	−0.292534	−	0.0987438i	−0.0101114	−	0.00341308i
$838$		−	15.7498i		−	0.544068i
$839$	−13.9589			−0.481915			−0.240958	−	0.970536i	$-0.577461\pi$
$839$	−13.9589			−0.481915			−0.240958	+	0.970536i	$0.577461\pi$
$840$	21.2779	−	10.0364i	0.734158	−	0.346290i
$841$	−16.1389			−0.556514
$842$		−	70.3595i		−	2.42475i
$843$	−14.2873	−	32.4202i	−0.492081	−	1.11661i
$844$	55.6194			1.91450
$845$	−1.30604			−0.0449290
$846$	−30.7773	−	28.1377i	−1.05814	−	0.967392i
$847$	1.13971	+	44.4195i	0.0391609	+	1.52627i
$848$		−	13.0950i		−	0.449685i
$849$	−12.4338	−	28.2143i	−0.426726	−	0.968311i
$850$		−	6.27624i		−	0.215273i
$851$			15.5236i			0.532142i
$852$	−6.06754	−	13.7682i	−0.207871	−	0.471692i
$853$		−	12.9150i		−	0.442202i	−0.975251	−	0.221101i	$-0.929035\pi$
$853$		−	12.9150i		−	0.442202i	0.975251	−	0.221101i	$-0.0709651\pi$
$854$	1.78158	+	69.4357i	0.0609643	+	2.37604i
$855$	−4.94505	−	4.52094i	−0.169117	−	0.154613i
$856$	33.3761			1.14077
$857$	−6.20273			−0.211881			−0.105941	−	0.994372i	$-0.533785\pi$
$857$	−6.20273			−0.211881			−0.105941	+	0.994372i	$0.533785\pi$
$858$	8.75555	+	19.8678i	0.298910	+	0.678274i
$859$			8.24498i			0.281315i	0.990058	+	0.140657i	$0.0449216\pi$
$859$			8.24498i			0.281315i	−0.990058	+	0.140657i	$0.955078\pi$
$860$	23.4186			0.798568
$861$	−21.5474	−	45.6819i	−0.734332	−	1.55683i
$862$	−49.4932			−1.68574
$863$			11.6422i			0.396305i	0.980171	+	0.198153i	$0.0634942\pi$
$863$			11.6422i			0.396305i	−0.980171	+	0.198153i	$0.936506\pi$
$864$	14.8287	+	5.00537i	0.504482	+	0.170286i
$865$	14.5894			0.496054
$866$	1.86596			0.0634080
$867$	−25.9268	+	11.4257i	−0.880520	+	0.388038i
$868$	0.574128	−	0.0147309i	0.0194872	−	0.000500001i
$869$		−	80.2629i		−	2.72273i
$870$	33.0674	−	14.5725i	1.12109	−	0.494055i
$871$			9.44978i			0.320194i
$872$			17.6277i			0.596949i
$873$	31.6686	+	28.9525i	1.07182	+	0.979895i
$874$		−	9.57501i		−	0.323879i
$875$	0.735124	+	28.6510i	0.0248517	+	0.968580i
$876$	3.67373	+	8.33628i	0.124124	+	0.281657i
$877$	−4.32934			−0.146191			−0.0730956	−	0.997325i	$-0.523288\pi$
$877$	−4.32934			−0.146191			−0.0730956	+	0.997325i	$0.523288\pi$
$878$	56.2283			1.89761
$879$	22.0487	−	9.71667i	0.743684	−	0.327735i
$880$			14.0444i			0.473435i
$881$	−45.9169			−1.54698			−0.773490	−	0.633808i	$-0.781491\pi$
$881$	−45.9169			−1.54698			−0.773490	+	0.633808i	$0.781491\pi$
$882$	38.5305	+	31.7566i	1.29739	+	1.06930i
$883$	3.98052			0.133955			0.0669776	−	0.997754i	$-0.478664\pi$
$883$	3.98052			0.133955			0.0669776	+	0.997754i	$0.478664\pi$
$884$			2.92732i			0.0984564i
$885$	−22.1839	+	9.77627i	−0.745705	+	0.328626i
$886$	−28.0175			−0.941267
$887$	20.2330			0.679357			0.339679	−	0.940542i	$-0.389682\pi$
$887$	20.2330			0.679357			0.339679	+	0.940542i	$0.389682\pi$
$888$	18.0989	+	41.0694i	0.607361	+	1.37820i
$889$	−0.0610866	−	2.38081i	−0.00204878	−	0.0798498i
$890$			23.5744i			0.790215i
$891$	47.2583	−	4.24325i	1.58321	−	0.142154i
$892$			69.6069i			2.33061i
$893$		−	9.99738i		−	0.334549i
$894$	−22.4469	+	9.89218i	−0.750738	+	0.330844i
$895$			15.5434i			0.519558i
$896$	−54.7567	+	1.40494i	−1.82929	+	0.0469359i
$897$	−3.73250	+	1.64488i	−0.124625	+	0.0549211i
$898$	−31.7925			−1.06093
$899$	0.399208			0.0133143
$900$	24.3613	−	26.6467i	0.812045	−	0.888224i
$901$			5.14434i			0.171383i
$902$	138.161			4.60025
$903$	9.59545	+	20.3430i	0.319317	+	0.676973i
$904$	−46.4818			−1.54596
$905$		−	8.54079i		−	0.283905i
$906$	−4.54491	−	10.3131i	−0.150995	−	0.342631i
$907$	−13.1754			−0.437481			−0.218741	−	0.975783i	$-0.570195\pi$
$907$	−13.1754			−0.437481			−0.218741	+	0.975783i	$0.570195\pi$
$908$	95.4157			3.16648
$909$	12.1001	−	13.2353i	0.401336	−	0.438986i
$910$	−0.210733	−	8.21316i	−0.00698571	−	0.272264i
$911$		−	25.5221i		−	0.845586i	−0.906226	−	0.422793i	$-0.861050\pi$
$911$		−	25.5221i		−	0.845586i	0.906226	−	0.422793i	$-0.138950\pi$
$912$	−2.43631	−	5.52839i	−0.0806744	−	0.183063i
$913$		−	3.68273i		−	0.121880i
$914$		−	80.4944i		−	2.66252i
$915$	−10.0725	−	22.8562i	−0.332987	−	0.755602i
$916$		−	44.1660i		−	1.45928i
$917$	1.41652	+	55.2080i	0.0467777	+	1.82313i
$918$	9.37976	+	3.16611i	0.309578	+	0.104497i
$919$	24.8561			0.819926			0.409963	−	0.912102i	$-0.365542\pi$
$919$	24.8561			0.819926			0.409963	+	0.912102i	$0.365542\pi$
$920$	−12.0899			−0.398591
$921$	−14.9515	−	33.9273i	−0.492667	−	1.11794i
$922$			21.1288i			0.695840i
$923$	−2.37782			−0.0782669
$924$	−79.8263	+	37.6527i	−2.62609	+	1.23868i
$925$	−21.7156			−0.714004
$926$			26.7471i			0.878965i
$927$	39.7585	+	36.3486i	1.30584	+	1.19384i
$928$	−20.2361			−0.664282
$929$	−44.7158			−1.46708			−0.733538	−	0.679648i	$-0.762133\pi$
$929$	−44.7158			−1.46708			−0.733538	+	0.679648i	$0.762133\pi$
$930$	−0.292448	+	0.128879i	−0.00958975	+	0.00422612i
$931$	0.613866	+	11.9546i	0.0201187	+	0.391798i
$932$			47.0977i			1.54274i
$933$	−11.0684	+	4.87777i	−0.362365	+	0.159691i
$934$			3.82496i			0.125157i
$935$		−	5.51729i		−	0.180435i
$936$	−7.95700	+	8.70345i	−0.260083	+	0.284481i
$937$		−	16.9933i		−	0.555146i	−0.960704	−	0.277573i	$-0.910470\pi$
$937$		−	16.9933i		−	0.555146i	0.960704	−	0.277573i	$-0.0895301\pi$
$938$	−59.4260	+	1.52475i	−1.94033	+	0.0497848i
$939$	−1.66713	−	3.78299i	−0.0544048	−	0.123453i
$940$	−27.8939			−0.909800
$941$	0.151960			0.00495374			0.00247687	−	0.999997i	$-0.499212\pi$
$941$	0.151960			0.00495374			0.00247687	+	0.999997i	$0.499212\pi$
$942$	24.2128	−	10.6704i	0.788894	−	0.347659i
$943$			25.9559i			0.845240i
$944$	−21.8590			−0.711450
$945$	−17.1537	−	5.30411i	−0.558010	−	0.172543i
$946$	−61.5256			−2.00037
$947$			40.0680i			1.30203i	0.759063	+	0.651017i	$0.225657\pi$
$947$			40.0680i			1.30203i	−0.759063	+	0.651017i	$0.774343\pi$
$948$	88.1525	−	38.8481i	2.86306	−	1.26173i
$949$	1.43970			0.0467348
$950$	13.3942			0.434567
$951$	5.63712	+	12.7915i	0.182796	+	0.414794i
$952$	−8.33074	+	0.213749i	−0.270001	+	0.00692766i
$953$		−	29.9201i		−	0.969206i	−0.874734	−	0.484603i	$-0.838964\pi$
$953$		−	29.9201i		−	0.969206i	0.874734	−	0.484603i	$-0.161036\pi$
$954$	−30.8994	+	33.7981i	−1.00041	+	1.09426i
$955$			22.5254i			0.728905i
$956$		−	54.6118i		−	1.76627i
$957$	−56.1404	+	24.7406i	−1.81476	+	0.799750i
$958$		−	67.0866i		−	2.16747i
$959$	9.21308	−	0.236388i	0.297506	−	0.00763338i
$960$	23.2688	−	10.2544i	0.750998	−	0.330959i
$961$	30.9965			0.999886
$962$	15.6733			0.505328
$963$	−18.7999	−	17.1875i	−0.605818	−	0.553860i
$964$			46.9144i			1.51101i
$965$	30.5274			0.982710
$966$	−10.9463	−	23.2069i	−0.352191	−	0.746669i
$967$	−51.8928			−1.66876			−0.834379	−	0.551191i	$-0.814174\pi$
$967$	−51.8928			−1.66876			−0.834379	+	0.551191i	$0.814174\pi$
$968$		−	66.0166i		−	2.12185i
$969$	0.957099	+	2.17181i	0.0307465	+	0.0697687i
$970$	44.4148			1.42607
$971$	22.7141			0.728929			0.364464	−	0.931217i	$-0.381252\pi$
$971$	22.7141			0.728929			0.364464	+	0.931217i	$0.381252\pi$
$972$	27.5339	+	49.8499i	0.883149	+	1.59894i
$973$	−44.8388	+	1.15047i	−1.43747	+	0.0368824i
$974$			7.45791i			0.238967i
$975$	−2.30099	−	5.22131i	−0.0736906	−	0.167216i
$976$		−	22.5214i		−	0.720893i
$977$			10.6566i			0.340935i	0.985363	+	0.170468i	$0.0545278\pi$
$977$			10.6566i			0.340935i	−0.985363	+	0.170468i	$0.945472\pi$
$978$	25.7645	+	58.4639i	0.823859	+	1.86947i
$979$		−	40.0236i		−	1.27916i
$980$	33.3549	−	1.71276i	1.06548	−	0.0547122i
$981$	9.07764	−	9.92922i	0.289827	−	0.317016i
$982$	−33.0266			−1.05392
$983$	37.1111			1.18366			0.591829	−	0.806063i	$-0.298406\pi$
$983$	37.1111			1.18366			0.591829	+	0.806063i	$0.298406\pi$
$984$	30.2620	+	68.6693i	0.964716	+	2.18910i
$985$			9.85562i			0.314026i
$986$	−12.8002			−0.407641
$987$	−11.4291	−	24.2306i	−0.363794	−	0.771268i
$988$	−6.24725			−0.198752
$989$		−	11.5587i		−	0.367544i
$990$	33.1396	−	36.2484i	1.05324	−	1.15205i
$991$	−30.8059			−0.978583			−0.489292	−	0.872120i	$-0.662745\pi$
$991$	−30.8059			−0.978583			−0.489292	+	0.872120i	$0.662745\pi$
$992$	0.178968			0.00568224
$993$	1.56794	−	0.690977i	0.0497570	−	0.0219275i
$994$	−0.383668	−	14.9532i	−0.0121692	−	0.474287i
$995$		−	13.9354i		−	0.441782i
$996$	4.04473	−	1.78248i	0.128162	−	0.0564800i
$997$		−	30.2312i		−	0.957433i	−0.877970	−	0.478716i	$-0.841102\pi$
$997$		−	30.2312i		−	0.957433i	0.877970	−	0.478716i	$-0.158898\pi$
$998$		−	42.2413i		−	1.33713i
$999$	10.9546	−	32.4537i	0.346589	−	1.02679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.e.a.209.4	yes	32
3.2	odd	2	inner	273.2.e.a.209.29	yes	32
7.6	odd	2	inner	273.2.e.a.209.3	✓	32
21.20	even	2	inner	273.2.e.a.209.30	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.e.a.209.3	✓	32	7.6	odd	2	inner
273.2.e.a.209.4	yes	32	1.1	even	1	trivial
273.2.e.a.209.29	yes	32	3.2	odd	2	inner
273.2.e.a.209.30	yes	32	21.20	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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.37766i q^{2} +(1.58497 - 0.698482i) q^{3} -3.65324 q^{4} +1.30604 q^{5} +(-1.66075 - 3.76851i) q^{6} +(-0.0678621 - 2.64488i) q^{7} +3.93085i q^{8} +(2.02425 - 2.21414i) q^{9} +O(q^{10})\)	\(q-2.37766i q^{2} +(1.58497 - 0.698482i) q^{3} -3.65324 q^{4} +1.30604 q^{5} +(-1.66075 - 3.76851i) q^{6} +(-0.0678621 - 2.64488i) q^{7} +3.93085i q^{8} +(2.02425 - 2.21414i) q^{9} -3.10530i q^{10} +5.27205i q^{11} +(-5.79027 + 2.55173i) q^{12} +1.00000i q^{13} +(-6.28861 + 0.161353i) q^{14} +(2.07003 - 0.912243i) q^{15} +2.03971 q^{16} -0.801293 q^{17} +(-5.26447 - 4.81296i) q^{18} -1.71006i q^{19} -4.77127 q^{20} +(-1.95496 - 4.14465i) q^{21} +12.5351 q^{22} +2.35494i q^{23} +(2.74562 + 6.23026i) q^{24} -3.29427 q^{25} +2.37766 q^{26} +(1.66183 - 4.92324i) q^{27} +(0.247917 + 9.66240i) q^{28} +6.71855i q^{29} +(-2.16900 - 4.92181i) q^{30} -0.0594188i q^{31} +3.01197i q^{32} +(3.68243 + 8.35603i) q^{33} +1.90520i q^{34} +(-0.0886304 - 3.45431i) q^{35} +(-7.39507 + 8.08880i) q^{36} +6.59192 q^{37} -4.06592 q^{38} +(0.698482 + 1.58497i) q^{39} +5.13383i q^{40} +11.0219 q^{41} +(-9.85455 + 4.64822i) q^{42} -4.90826 q^{43} -19.2601i q^{44} +(2.64374 - 2.89175i) q^{45} +5.59924 q^{46} +5.84623 q^{47} +(3.23287 - 1.42470i) q^{48} +(-6.99079 + 0.358974i) q^{49} +7.83264i q^{50} +(-1.27002 + 0.559689i) q^{51} -3.65324i q^{52} -6.42005i q^{53} +(-11.7058 - 3.95125i) q^{54} +6.88549i q^{55} +(10.3966 - 0.266756i) q^{56} +(-1.19444 - 2.71038i) q^{57} +15.9744 q^{58} -10.7167 q^{59} +(-7.56231 + 3.33265i) q^{60} -11.0415i q^{61} -0.141278 q^{62} +(-5.99351 - 5.20363i) q^{63} +11.2408 q^{64} +1.30604i q^{65} +(19.8678 - 8.75555i) q^{66} +9.44978 q^{67} +2.92732 q^{68} +(1.64488 + 3.73250i) q^{69} +(-8.21316 + 0.210733i) q^{70} +2.37782i q^{71} +(8.70345 + 7.95700i) q^{72} -1.43970i q^{73} -15.6733i q^{74} +(-5.22131 + 2.30099i) q^{75} +6.24725i q^{76} +(13.9439 - 0.357772i) q^{77} +(3.76851 - 1.66075i) q^{78} -15.2242 q^{79} +2.66393 q^{80} +(-0.804857 - 8.96394i) q^{81} -26.2062i q^{82} -0.698538 q^{83} +(7.14195 + 15.1414i) q^{84} -1.04652 q^{85} +11.6701i q^{86} +(4.69278 + 10.6487i) q^{87} -20.7236 q^{88} -7.59165 q^{89} +(-6.87559 - 6.28590i) q^{90} +(2.64488 - 0.0678621i) q^{91} -8.60317i q^{92} +(-0.0415030 - 0.0941770i) q^{93} -13.9003i q^{94} -2.23339i q^{95} +(2.10381 + 4.77388i) q^{96} +14.3029i q^{97} +(0.853518 + 16.6217i) q^{98} +(11.6731 + 10.6719i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9	\( 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9} - 12 q^{15} + 16 q^{16} - 20 q^{18} - 4 q^{21} - 16 q^{22} - 28 q^{28} + 16 q^{30} + 24 q^{36} + 24 q^{37} + 32 q^{43} - 24 q^{46} - 24 q^{49} - 8 q^{51} + 32 q^{57} + 24 q^{58} - 28 q^{60} + 8 q^{63} + 48 q^{64} - 32 q^{67} - 8 q^{70} + 64 q^{72} + 20 q^{78} - 32 q^{79} + 32 q^{81} - 48 q^{84} - 16 q^{85} + 64 q^{88} + 4 q^{91} - 52 q^{93} + 20 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9 - 12 * q^15 + 16 * q^16 - 20 * q^18 - 4 * q^21 - 16 * q^22 - 28 * q^28 + 16 * q^30 + 24 * q^36 + 24 * q^37 + 32 * q^43 - 24 * q^46 - 24 * q^49 - 8 * q^51 + 32 * q^57 + 24 * q^58 - 28 * q^60 + 8 * q^63 + 48 * q^64 - 32 * q^67 - 8 * q^70 + 64 * q^72 + 20 * q^78 - 32 * q^79 + 32 * q^81 - 48 * q^84 - 16 * q^85 + 64 * q^88 + 4 * q^91 - 52 * q^93 + 20 * q^99

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