LMFDB - Embedded newform 273.2.r.b.269.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(68,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 2]))

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

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

chi := DirichletCharacter("273.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.r (of order $6$, degree $2$, 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:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.31
Character	$\chi$	$=$	273.269
Dual form			273.2.r.b.68.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.60090i q^{2} +(0.206727 + 1.71967i) q^{3} -4.76468 q^{4} +(1.54658 + 2.67876i) q^{5} +(-4.47269 + 0.537676i) q^{6} +(1.09877 - 2.40680i) q^{7} -7.19066i q^{8} +(-2.91453 + 0.711004i) q^{9} +O(q^{10})$	\(q+2.60090i q^{2} +(0.206727 + 1.71967i) q^{3} -4.76468 q^{4} +(1.54658 + 2.67876i) q^{5} +(-4.47269 + 0.537676i) q^{6} +(1.09877 - 2.40680i) q^{7} -7.19066i q^{8} +(-2.91453 + 0.711004i) q^{9} +(-6.96719 + 4.02251i) q^{10} +(-2.83459 + 1.63655i) q^{11} +(-0.984988 - 8.19368i) q^{12} +(3.57248 - 0.487210i) q^{13} +(6.25985 + 2.85780i) q^{14} +(-4.28686 + 3.21338i) q^{15} +9.17282 q^{16} +3.84439 q^{17} +(-1.84925 - 7.58040i) q^{18} +(2.16087 + 1.24758i) q^{19} +(-7.36897 - 12.7634i) q^{20} +(4.36605 + 1.39198i) q^{21} +(-4.25650 - 7.37248i) q^{22} -3.41565i q^{23} +(12.3656 - 1.48650i) q^{24} +(-2.28384 + 3.95572i) q^{25} +(1.26718 + 9.29167i) q^{26} +(-1.82520 - 4.86504i) q^{27} +(-5.23531 + 11.4676i) q^{28} +(3.85237 + 2.22417i) q^{29} +(-8.35769 - 11.1497i) q^{30} +(-5.89349 - 3.40261i) q^{31} +9.47627i q^{32} +(-3.40031 - 4.53623i) q^{33} +9.99886i q^{34} +(8.14659 - 0.778966i) q^{35} +(13.8868 - 3.38771i) q^{36} +1.96384 q^{37} +(-3.24483 + 5.62021i) q^{38} +(1.57637 + 6.04277i) q^{39} +(19.2620 - 11.1209i) q^{40} +(-4.81925 + 8.34719i) q^{41} +(-3.62039 + 11.3557i) q^{42} +(3.70565 + 6.41837i) q^{43} +(13.5059 - 7.79764i) q^{44} +(-6.41217 - 6.70769i) q^{45} +8.88377 q^{46} +(-1.63297 - 2.82838i) q^{47} +(1.89627 + 15.7742i) q^{48} +(-4.58539 - 5.28906i) q^{49} +(-10.2884 - 5.94003i) q^{50} +(0.794738 + 6.61107i) q^{51} +(-17.0217 + 2.32140i) q^{52} +(-3.67124 - 2.11959i) q^{53} +(12.6535 - 4.74717i) q^{54} +(-8.76785 - 5.06212i) q^{55} +(-17.3065 - 7.90091i) q^{56} +(-1.69871 + 3.97389i) q^{57} +(-5.78483 + 10.0196i) q^{58} +2.39655 q^{59} +(20.4255 - 15.3107i) q^{60} +(-8.03139 - 4.63693i) q^{61} +(8.84984 - 15.3284i) q^{62} +(-1.49116 + 7.79592i) q^{63} -6.30118 q^{64} +(6.83026 + 8.81631i) q^{65} +(11.7983 - 8.84387i) q^{66} +(4.88111 + 8.45433i) q^{67} -18.3173 q^{68} +(5.87379 - 0.706107i) q^{69} +(2.02601 + 21.1885i) q^{70} +(3.88678 - 2.24403i) q^{71} +(5.11259 + 20.9574i) q^{72} +(3.06234 + 1.76804i) q^{73} +5.10776i q^{74} +(-7.27467 - 3.10969i) q^{75} +(-10.2959 - 5.94432i) q^{76} +(0.824280 + 8.62049i) q^{77} +(-15.7166 + 4.09998i) q^{78} +(-3.24801 - 5.62572i) q^{79} +(14.1865 + 24.5718i) q^{80} +(7.98895 - 4.14448i) q^{81} +(-21.7102 - 12.5344i) q^{82} -3.84139 q^{83} +(-20.8028 - 6.63233i) q^{84} +(5.94566 + 10.2982i) q^{85} +(-16.6935 + 9.63802i) q^{86} +(-3.02844 + 7.08460i) q^{87} +(11.7679 + 20.3825i) q^{88} +7.17132 q^{89} +(17.4460 - 16.6774i) q^{90} +(2.75273 - 9.13359i) q^{91} +16.2745i q^{92} +(4.63302 - 10.8383i) q^{93} +(7.35633 - 4.24718i) q^{94} +7.71794i q^{95} +(-16.2960 + 1.95900i) q^{96} +(10.4630 - 6.04083i) q^{97} +(13.7563 - 11.9261i) q^{98} +(7.09789 - 6.78517i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9}+O(q^{10}) $ 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9	$ 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{12} + 12 q^{13} - 9 q^{15} + 32 q^{16} + 2 q^{18} - 36 q^{19} + 10 q^{21} + 10 q^{22} - 18 q^{24} - 24 q^{25} - 14 q^{28} + 8 q^{30} - 24 q^{31} - 45 q^{33} + 33 q^{39} + 90 q^{40} + 3 q^{42} - 20 q^{43} - 6 q^{48} - 6 q^{49} - 10 q^{51} - 48 q^{52} - 18 q^{55} + 4 q^{57} + 30 q^{58} + 55 q^{60} - 18 q^{61} + 31 q^{63} - 84 q^{64} + 75 q^{66} + 44 q^{67} + 33 q^{69} + 20 q^{70} + 17 q^{72} + 84 q^{73} - 18 q^{76} - 71 q^{78} + 20 q^{79} + 16 q^{81} - 18 q^{82} - 135 q^{84} - 2 q^{85} - 46 q^{88} - 10 q^{91} - 56 q^{93} + 36 q^{94} + 30 q^{96} - 24 q^{97} + 22 q^{99}+O(q^{100}) $ 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^12 + 12 * q^13 - 9 * q^15 + 32 * q^16 + 2 * q^18 - 36 * q^19 + 10 * q^21 + 10 * q^22 - 18 * q^24 - 24 * q^25 - 14 * q^28 + 8 * q^30 - 24 * q^31 - 45 * q^33 + 33 * q^39 + 90 * q^40 + 3 * q^42 - 20 * q^43 - 6 * q^48 - 6 * q^49 - 10 * q^51 - 48 * q^52 - 18 * q^55 + 4 * q^57 + 30 * q^58 + 55 * q^60 - 18 * q^61 + 31 * q^63 - 84 * q^64 + 75 * q^66 + 44 * q^67 + 33 * q^69 + 20 * q^70 + 17 * q^72 + 84 * q^73 - 18 * q^76 - 71 * q^78 + 20 * q^79 + 16 * q^81 - 18 * q^82 - 135 * q^84 - 2 * q^85 - 46 * q^88 - 10 * q^91 - 56 * q^93 + 36 * q^94 + 30 * q^96 - 24 * q^97 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$			2.60090i			1.83911i	0.392957	+	0.919557i	$0.371452\pi$
$2$			2.60090i			1.83911i	−0.392957	+	0.919557i	$0.628548\pi$
$3$	0.206727	+	1.71967i	0.119354	+	0.992852i
$3$	0.206727	+	1.71967i	0.119354	+	0.992852i
$4$	−4.76468			−2.38234
$5$	1.54658	+	2.67876i	0.691653	+	1.19798i	0.971296	+	0.237874i	$0.0764505\pi$
$5$	1.54658	+	2.67876i	0.691653	+	1.19798i	−0.279643	+	0.960104i	$0.590216\pi$
$6$	−4.47269	+	0.537676i	−1.82597	+	0.219505i
$7$	1.09877	−	2.40680i	0.415298	−	0.909686i
$7$	1.09877	−	2.40680i	0.415298	−	0.909686i
$8$		−	7.19066i		−	2.54228i
$9$	−2.91453	+	0.711004i	−0.971509	+	0.237001i
$10$	−6.96719	+	4.02251i	−2.20322	+	1.27203i
$11$	−2.83459	+	1.63655i	−0.854660	+	0.493438i	−0.862220	−	0.506533i	$-0.830927\pi$
$11$	−2.83459	+	1.63655i	−0.854660	+	0.493438i	0.00756034	+	0.999971i	$0.497593\pi$
$12$	−0.984988	−	8.19368i	−0.284341	−	2.36531i
$13$	3.57248	−	0.487210i	0.990828	−	0.135128i
$13$	3.57248	−	0.487210i	0.990828	−	0.135128i
$14$	6.25985	+	2.85780i	1.67302	+	0.763780i
$15$	−4.28686	+	3.21338i	−1.10686	+	0.829692i
$16$	9.17282			2.29320
$17$	3.84439			0.932400			0.466200	−	0.884679i	$-0.345623\pi$
$17$	3.84439			0.932400			0.466200	+	0.884679i	$0.345623\pi$
$18$	−1.84925	−	7.58040i	−0.435873	−	1.78672i
$19$	2.16087	+	1.24758i	0.495738	+	0.286214i	0.726952	−	0.686689i	$-0.240936\pi$
$19$	2.16087	+	1.24758i	0.495738	+	0.286214i	−0.231214	+	0.972903i	$0.574270\pi$
$20$	−7.36897	−	12.7634i	−1.64775	−	2.85399i
$21$	4.36605	+	1.39198i	0.952750	+	0.303754i
$22$	−4.25650	−	7.37248i	−0.907489	−	1.57182i
$23$		−	3.41565i		−	0.712212i	−0.934445	−	0.356106i	$-0.884104\pi$
$23$		−	3.41565i		−	0.712212i	0.934445	−	0.356106i	$-0.115896\pi$
$24$	12.3656	−	1.48650i	2.52411	−	0.303431i
$25$	−2.28384	+	3.95572i	−0.456768	+	0.791145i
$26$	1.26718	+	9.29167i	0.248515	+	1.82225i
$27$	−1.82520	−	4.86504i	−0.351261	−	0.936278i
$28$	−5.23531	+	11.4676i	−0.989380	+	2.16718i
$29$	3.85237	+	2.22417i	0.715367	+	0.413017i	0.813045	−	0.582201i	$-0.197808\pi$
$29$	3.85237	+	2.22417i	0.715367	+	0.413017i	−0.0976782	+	0.995218i	$0.531142\pi$
$30$	−8.35769	−	11.1497i	−1.52590	−	2.03565i
$31$	−5.89349	−	3.40261i	−1.05850	−	0.611126i	−0.133484	−	0.991051i	$-0.542617\pi$
$31$	−5.89349	−	3.40261i	−1.05850	−	0.611126i	−0.925017	+	0.379925i	$0.875950\pi$
$32$			9.47627i			1.67518i
$33$	−3.40031	−	4.53623i	−0.591918	−	0.789657i
$34$			9.99886i			1.71479i
$35$	8.14659	−	0.778966i	1.37703	−	0.131669i
$36$	13.8868	−	3.38771i	2.31447	−	0.564618i
$37$	1.96384			0.322854			0.161427	−	0.986885i	$-0.448390\pi$
$37$	1.96384			0.322854			0.161427	+	0.986885i	$0.448390\pi$
$38$	−3.24483	+	5.62021i	−0.526381	+	0.911718i
$39$	1.57637	+	6.04277i	0.252421	+	0.967618i
$40$	19.2620	−	11.1209i	3.04560	−	1.75838i
$41$	−4.81925	+	8.34719i	−0.752641	+	1.30361i	0.193898	+	0.981022i	$0.437887\pi$
$41$	−4.81925	+	8.34719i	−0.752641	+	1.30361i	−0.946539	+	0.322590i	$0.895446\pi$
$42$	−3.62039	+	11.3557i	−0.558639	+	1.75222i
$43$	3.70565	+	6.41837i	0.565106	+	0.978793i	0.997040	+	0.0768874i	$0.0244982\pi$
$43$	3.70565	+	6.41837i	0.565106	+	0.978793i	−0.431933	+	0.901905i	$0.642168\pi$
$44$	13.5059	−	7.79764i	2.03609	−	1.17554i
$45$	−6.41217	−	6.70769i	−0.955870	−	0.999924i
$46$	8.88377			1.30984
$47$	−1.63297	−	2.82838i	−0.238192	−	0.412561i	0.722003	−	0.691890i	$-0.243222\pi$
$47$	−1.63297	−	2.82838i	−0.238192	−	0.412561i	−0.960196	+	0.279328i	$0.909888\pi$
$48$	1.89627	+	15.7742i	0.273703	+	2.27681i
$49$	−4.58539	−	5.28906i	−0.655056	−	0.755580i
$50$	−10.2884	−	5.94003i	−1.45501	−	0.840048i
$51$	0.794738	+	6.61107i	0.111286	+	0.925735i
$52$	−17.0217	+	2.32140i	−2.36049	+	0.321920i
$53$	−3.67124	−	2.11959i	−0.504283	−	0.291148i	0.226197	−	0.974082i	$-0.427371\pi$
$53$	−3.67124	−	2.11959i	−0.504283	−	0.291148i	−0.730481	+	0.682933i	$0.760704\pi$
$54$	12.6535	−	4.74717i	1.72192	−	0.646008i
$55$	−8.76785	−	5.06212i	−1.18226	−	0.682576i
$56$	−17.3065	−	7.90091i	−2.31268	−	1.05580i
$57$	−1.69871	+	3.97389i	−0.225000	+	0.526355i
$58$	−5.78483	+	10.0196i	−0.759586	+	1.31564i
$59$	2.39655			0.312004			0.156002	−	0.987757i	$-0.450139\pi$
$59$	2.39655			0.312004			0.156002	+	0.987757i	$0.450139\pi$
$60$	20.4255	−	15.3107i	2.63692	−	1.97661i
$61$	−8.03139	−	4.63693i	−1.02831	−	0.593698i	−0.111813	−	0.993729i	$-0.535666\pi$
$61$	−8.03139	−	4.63693i	−1.02831	−	0.593698i	−0.916501	+	0.400032i	$0.868999\pi$
$62$	8.84984	−	15.3284i	1.12393	−	1.94671i
$63$	−1.49116	+	7.79592i	−0.187869	+	0.982194i
$64$	−6.30118			−0.787648
$65$	6.83026	+	8.81631i	0.847189	+	1.09353i
$66$	11.7983	−	8.84387i	1.45227	−	1.08860i
$67$	4.88111	+	8.45433i	0.596322	+	1.03286i	0.993359	+	0.115058i	$0.0367053\pi$
$67$	4.88111	+	8.45433i	0.596322	+	1.03286i	−0.397036	+	0.917803i	$0.629961\pi$
$68$	−18.3173			−2.22129
$69$	5.87379	−	0.706107i	0.707121	−	0.0850053i
$70$	2.02601	+	21.1885i	0.242155	+	2.53251i
$71$	3.88678	−	2.24403i	0.461275	−	0.266317i	−0.251305	−	0.967908i	$-0.580860\pi$
$71$	3.88678	−	2.24403i	0.461275	−	0.266317i	0.712580	+	0.701590i	$0.247526\pi$
$72$	5.11259	+	20.9574i	0.602524	+	2.46985i
$73$	3.06234	+	1.76804i	0.358420	+	0.206934i	0.668388	−	0.743813i	$-0.266985\pi$
$73$	3.06234	+	1.76804i	0.358420	+	0.206934i	−0.309967	+	0.950747i	$0.600318\pi$
$74$			5.10776i			0.593765i
$75$	−7.27467	−	3.10969i	−0.840006	−	0.359076i
$76$	−10.2959	−	5.94432i	−1.18102	−	0.681860i
$77$	0.824280	+	8.62049i	0.0939354	+	0.982396i
$78$	−15.7166	+	4.09998i	−1.77956	+	0.464231i
$79$	−3.24801	−	5.62572i	−0.365430	−	0.632943i	0.623415	−	0.781891i	$-0.285745\pi$
$79$	−3.24801	−	5.62572i	−0.365430	−	0.632943i	−0.988845	+	0.148948i	$0.952411\pi$
$80$	14.1865	+	24.5718i	1.58610	+	2.74721i
$81$	7.98895	−	4.14448i	0.887661	−	0.460498i
$82$	−21.7102	−	12.5344i	−2.39749	−	1.38419i
$83$	−3.84139			−0.421647			−0.210824	−	0.977524i	$-0.567615\pi$
$83$	−3.84139			−0.421647			−0.210824	+	0.977524i	$0.567615\pi$
$84$	−20.8028	−	6.63233i	−2.26978	−	0.723646i
$85$	5.94566	+	10.2982i	0.644897	+	1.11700i
$86$	−16.6935	+	9.63802i	−1.80011	+	1.03929i
$87$	−3.02844	+	7.08460i	−0.324683	+	0.759548i
$88$	11.7679	+	20.3825i	1.25446	+	2.17279i
$89$	7.17132			0.760159			0.380079	−	0.924954i	$-0.375897\pi$
$89$	7.17132			0.760159			0.380079	+	0.924954i	$0.375897\pi$
$90$	17.4460	−	16.6774i	1.83897	−	1.75795i
$91$	2.75273	−	9.13359i	0.288565	−	0.957460i
$92$			16.2745i			1.69673i
$93$	4.63302	−	10.8383i	0.480422	−	1.12388i
$94$	7.35633	−	4.24718i	0.758748	−	0.438063i
$95$			7.71794i			0.791844i
$96$	−16.2960	+	1.95900i	−1.66321	+	0.199940i
$97$	10.4630	−	6.04083i	1.06236	−	0.613353i	0.136275	−	0.990671i	$-0.456487\pi$
$97$	10.4630	−	6.04083i	1.06236	−	0.613353i	0.926084	+	0.377318i	$0.123154\pi$
$98$	13.7563	−	11.9261i	1.38960	−	1.20472i
$99$	7.09789	−	6.78517i	0.713365	−	0.681936i
$100$	10.8818	−	18.8478i	1.08818	−	1.88478i
$101$	1.01198	+	1.75279i	0.100695	+	0.174409i	0.911971	−	0.410254i	$-0.134560\pi$
$101$	1.01198	+	1.75279i	0.100695	+	0.174409i	−0.811276	+	0.584663i	$0.801227\pi$
$102$	−17.1947	+	2.06703i	−1.70253	+	0.204667i
$103$	−2.67408	+	1.54388i	−0.263485	+	0.152123i	−0.625923	−	0.779885i	$-0.715278\pi$
$103$	−2.67408	+	1.54388i	−0.263485	+	0.152123i	0.362438	+	0.932008i	$0.381944\pi$
$104$	−3.50336	−	25.6885i	−0.343533	−	2.51896i
$105$	3.02368	+	13.8484i	0.295081	+	1.35147i
$106$	5.51284	−	9.54853i	0.535455	−	0.927435i
$107$		−	9.03028i		−	0.872990i	−0.899707	−	0.436495i	$-0.856220\pi$
$107$		−	9.03028i		−	0.872990i	0.899707	−	0.436495i	$-0.143780\pi$
$108$	8.69651	+	23.1804i	0.836822	+	2.23053i
$109$	7.11124	−	12.3170i	0.681133	−	1.17976i	−0.293502	−	0.955958i	$-0.594821\pi$
$109$	7.11124	−	12.3170i	0.681133	−	1.17976i	0.974635	−	0.223799i	$-0.0718458\pi$
$110$	13.1661	−	22.8043i	1.25534	−	2.17430i
$111$	0.405980	+	3.37716i	0.0385339	+	0.320546i
$112$	10.0789	−	22.0772i	0.952362	−	2.08609i
$113$	−7.81695	+	4.51312i	−0.735357	+	0.424558i	−0.820379	−	0.571821i	$-0.806237\pi$
$113$	−7.81695	+	4.51312i	−0.735357	+	0.424558i	0.0850218	+	0.996379i	$0.472904\pi$
$114$	−10.3357	−	4.41819i	−0.968027	−	0.413801i
$115$	9.14971	−	5.28259i	0.853215	−	0.492604i
$116$	−18.3553	−	10.5974i	−1.70425	−	0.983947i
$117$	−10.0657	+	3.96004i	−0.930573	+	0.366106i
$118$			6.23319i			0.573812i
$119$	4.22411	−	9.25267i	0.387224	−	0.848191i
$120$	23.1063	+	30.8254i	2.10931	+	2.81396i
$121$	−0.143411	+	0.248395i	−0.0130374	+	0.0225814i
$122$	12.0602	−	20.8888i	1.09188	−	1.89119i
$123$	−15.3507	−	6.56193i	−1.38412	−	0.591670i
$124$	28.0806	+	16.2123i	2.52171	+	1.45591i
$125$	1.33725			0.119607
$126$	−20.2764	−	3.87836i	−1.80637	−	0.345512i
$127$	8.47423	−	14.6778i	0.751967	−	1.30244i	−0.194902	−	0.980823i	$-0.562439\pi$
$127$	8.47423	−	14.6778i	0.751967	−	1.30244i	0.946868	−	0.321622i	$-0.104228\pi$
$128$			2.56378i			0.226608i
$129$	−10.2714	+	7.69935i	−0.904349	+	0.677890i
$130$	−22.9303	+	17.7648i	−2.01112	+	1.55808i
$131$	−4.00613	−	6.93882i	−0.350017	−	0.606247i	0.636235	−	0.771495i	$-0.280491\pi$
$131$	−4.00613	−	6.93882i	−0.350017	−	0.606247i	−0.986252	+	0.165248i	$0.947158\pi$
$132$	16.2014	+	21.6137i	1.41015	+	1.88123i
$133$	5.37699	−	3.82998i	0.466244	−	0.332101i
$134$	−21.9889	+	12.6953i	−1.89955	+	1.09670i
$135$	10.2095	−	12.4135i	0.878690	−	1.06838i
$136$		−	27.6437i		−	2.37042i
$137$			19.6525i			1.67902i	0.543340	+	0.839512i	$0.317159\pi$
$137$			19.6525i			1.67902i	−0.543340	+	0.839512i	$0.682841\pi$
$138$	1.83651	+	15.2771i	0.156334	+	1.30048i
$139$	10.6633	−	6.15648i	0.904452	−	0.522186i	0.0258103	−	0.999667i	$-0.491783\pi$
$139$	10.6633	−	6.15648i	0.904452	−	0.522186i	0.878642	+	0.477481i	$0.158450\pi$
$140$	−38.8159	+	3.71153i	−3.28054	+	0.313681i
$141$	4.52630	−	3.39286i	0.381183	−	0.285731i
$142$	5.83650	+	10.1091i	0.489788	+	0.848338i
$143$	−9.32917	+	7.22758i	−0.780144	+	0.604401i
$144$	−26.7344	+	6.52191i	−2.22787	+	0.543493i
$145$			13.7594i			1.14266i
$146$	−4.59851	+	7.96485i	−0.380575	+	0.659176i
$147$	8.14752	−	8.97875i	0.671996	−	0.740555i
$148$	−9.35709			−0.769148
$149$	5.98319	+	3.45440i	0.490162	+	0.282995i	0.724642	−	0.689126i	$-0.242005\pi$
$149$	5.98319	+	3.45440i	0.490162	+	0.282995i	−0.234480	+	0.972121i	$0.575339\pi$
$150$	8.08800	−	18.9207i	0.660382	−	1.54487i
$151$	−8.07245	+	13.9819i	−0.656927	+	1.13783i	0.324480	+	0.945892i	$0.394811\pi$
$151$	−8.07245	+	13.9819i	−0.656927	+	1.13783i	−0.981407	+	0.191938i	$0.938523\pi$
$152$	8.97092	−	15.5381i	0.727637	−	1.26030i
$153$	−11.2046	+	2.73337i	−0.905836	+	0.220980i
$154$	−22.4210	+	2.14387i	−1.80674	+	0.172758i
$155$		−	21.0497i		−	1.69075i
$156$	−7.51089	−	28.7919i	−0.601353	−	2.30519i
$157$	0.0700969	+	0.0404705i	0.00559434	+	0.00322989i	0.502795	−	0.864406i	$-0.332305\pi$
$157$	0.0700969	+	0.0404705i	0.00559434	+	0.00322989i	−0.497200	+	0.867636i	$0.665639\pi$
$158$	14.6319	−	8.44775i	1.16405	−	0.672067i
$159$	2.88605	−	6.75150i	0.228879	−	0.535428i
$160$	−25.3846	+	14.6558i	−2.00683	+	1.15865i
$161$	−8.22080	−	3.75303i	−0.647889	−	0.295780i
$162$	10.7794	+	20.7784i	0.846909	+	1.63251i
$163$	2.43617	−	4.21957i	0.190816	−	0.330503i	−0.754705	−	0.656064i	$-0.772220\pi$
$163$	2.43617	−	4.21957i	0.190816	−	0.330503i	0.945521	+	0.325562i	$0.105553\pi$
$164$	22.9622	−	39.7717i	1.79305	−	3.10565i
$165$	6.89262	−	16.1243i	0.536590	−	1.25527i
$166$		−	9.99106i		−	0.775457i
$167$	9.25269	−	16.0261i	0.715995	−	1.24014i	−0.246580	−	0.969122i	$-0.579307\pi$
$167$	9.25269	−	16.0261i	0.715995	−	1.24014i	0.962575	−	0.271016i	$-0.0873598\pi$
$168$	10.0092	−	31.3948i	0.772229	−	2.42216i
$169$	12.5253	−	3.48110i	0.963481	−	0.267777i
$170$	−26.7846	+	15.4641i	−2.05428	+	1.18604i
$171$	−7.18495	−	2.09972i	−0.549447	−	0.160569i
$172$	−17.6562	−	30.5815i	−1.34628	−	2.33182i
$173$	1.55570	−	2.69454i	0.118277	−	0.204862i	−0.800808	−	0.598921i	$-0.795596\pi$
$173$	1.55570	−	2.69454i	0.118277	−	0.204862i	0.919085	+	0.394059i	$0.128929\pi$
$174$	−18.4263	−	7.87667i	−1.39690	−	0.597129i
$175$	7.01122	+	9.84319i	0.529998	+	0.744075i
$176$	−26.0011	+	15.0118i	−1.95991	+	1.13155i
$177$	0.495432	+	4.12128i	0.0372389	+	0.309774i
$178$			18.6519i			1.39802i
$179$	−4.47021	+	2.58088i	−0.334119	+	0.192904i	−0.657669	−	0.753307i	$-0.728457\pi$
$179$	−4.47021	+	2.58088i	−0.334119	+	0.192904i	0.323549	+	0.946211i	$0.395124\pi$
$180$	30.5519	+	31.9600i	2.27721	+	2.38216i
$181$			6.02673i			0.447963i	0.974593	+	0.223982i	$0.0719056\pi$
$181$			6.02673i			0.447963i	−0.974593	+	0.223982i	$0.928094\pi$
$182$	23.7556	+	7.15958i	1.76088	+	0.530704i
$183$	6.31368	−	14.7699i	0.466720	−	1.09182i
$184$	−24.5608			−1.81064
$185$	3.03725	+	5.26067i	0.223303	+	0.386772i
$186$	28.1892	+	12.0500i	2.06694	+	0.883550i
$187$	−10.8972	+	6.29153i	−0.796885	+	0.460082i
$188$	7.78056	+	13.4763i	0.567456	+	0.982862i
$189$	−13.7147	−	0.952678i	−0.997596	−	0.0692971i
$190$	−20.0736			−1.45629
$191$	−9.84111	−	5.68177i	−0.712078	−	0.411118i	0.0997520	−	0.995012i	$-0.468195\pi$
$191$	−9.84111	−	5.68177i	−0.712078	−	0.411118i	−0.811830	+	0.583894i	$0.801528\pi$
$192$	−1.30262	−	10.8360i	−0.0940088	−	0.782018i
$193$	−3.90115	−	6.75699i	−0.280811	−	0.486379i	0.690774	−	0.723071i	$-0.257270\pi$
$193$	−3.90115	−	6.75699i	−0.280811	−	0.486379i	−0.971585	+	0.236692i	$0.923937\pi$
$194$	15.7116	+	27.2133i	1.12803	+	1.95380i
$195$	−13.7491	+	13.5684i	−0.984597	+	0.971650i
$196$	21.8479	+	25.2007i	1.56057	+	1.80005i
$197$	19.0087	+	10.9747i	1.35431	+	0.781912i	0.988850	−	0.148914i	$-0.0475779\pi$
$197$	19.0087	+	10.9747i	1.35431	+	0.781912i	0.365461	+	0.930826i	$0.380911\pi$
$198$	17.6476	+	18.4609i	1.25416	+	1.31196i
$199$		−	22.5699i		−	1.59994i	−0.600042	−	0.799969i	$-0.704849\pi$
$199$		−	22.5699i		−	1.59994i	0.600042	−	0.799969i	$-0.295151\pi$
$200$	28.4442	+	16.4223i	2.01131	+	1.16123i
$201$	−13.5296	+	10.1416i	−0.954304	+	0.715336i
$202$	−4.55884	+	2.63205i	−0.320759	+	0.185190i
$203$	9.58601	−	6.82803i	0.672806	−	0.479234i
$204$	−3.78667	−	31.4996i	−0.265120	−	2.20542i
$205$	−29.8135			−2.08226
$206$	−4.01548	−	6.95501i	−0.279772	−	0.484579i
$207$	2.42854	+	9.95501i	0.168795	+	0.691921i
$208$	32.7697	−	4.46909i	2.27217	−	0.309876i
$209$	−8.16690			−0.564917
$210$	−36.0183	+	7.86430i	−2.48550	+	0.542688i
$211$	−5.55596	+	9.62320i	−0.382488	+	0.662488i	−0.991417	−	0.130736i	$-0.958266\pi$
$211$	−5.55596	+	9.62320i	−0.382488	+	0.662488i	0.608929	+	0.793224i	$0.291599\pi$
$212$	17.4923	+	10.0992i	1.20137	+	0.693614i
$213$	4.66249	+	6.22007i	0.319469	+	0.426192i
$214$	23.4869			1.60553
$215$	−11.4622	+	19.8531i	−0.781715	+	1.35397i
$216$	−34.9828	+	13.1244i	−2.38028	+	0.893003i
$217$	−14.6650	+	10.4458i	−0.995526	+	0.709105i
$218$	32.0353	+	18.4956i	2.16971	+	1.25268i
$219$	−2.40738	+	5.63172i	−0.162676	+	0.380556i
$220$	41.7760	+	24.1194i	2.81654	+	1.62613i
$221$	13.7340	−	1.87302i	0.923849	−	0.125993i
$222$	−8.78367	+	1.05591i	−0.589521	+	0.0708682i
$223$	−11.7188	−	6.76583i	−0.784747	−	0.453074i	0.0533631	−	0.998575i	$-0.483006\pi$
$223$	−11.7188	−	6.76583i	−0.784747	−	0.453074i	−0.838110	+	0.545501i	$0.816339\pi$
$224$	22.8075	+	10.4123i	1.52389	+	0.695699i
$225$	3.84377	−	13.1529i	0.256252	−	0.876859i
$226$	−11.7382	−	20.3311i	−0.780811	−	1.35241i
$227$	−14.6386			−0.971601			−0.485800	−	0.874070i	$-0.661472\pi$
$227$	−14.6386			−0.971601			−0.485800	+	0.874070i	$0.661472\pi$
$228$	8.09383	−	18.9343i	0.536027	−	1.25396i
$229$	−4.05914	+	2.34354i	−0.268235	+	0.154866i	−0.628085	−	0.778144i	$-0.716161\pi$
$229$	−4.05914	+	2.34354i	−0.268235	+	0.154866i	0.359850	+	0.933010i	$0.382828\pi$
$230$	13.7395	+	23.7975i	0.905955	+	1.56916i
$231$	−14.6540	+	3.19958i	−0.964162	+	0.210517i
$232$	15.9932	−	27.7011i	1.05001	−	1.81866i
$233$	7.23622	−	4.17783i	0.474061	−	0.273699i	−0.243877	−	0.969806i	$-0.578419\pi$
$233$	7.23622	−	4.17783i	0.474061	−	0.273699i	0.717938	+	0.696107i	$0.245086\pi$
$234$	−10.2997	−	26.1799i	−0.673310	−	1.71143i
$235$	5.05103	−	8.74865i	0.329493	−	0.570699i
$236$	−11.4188			−0.743301
$237$	9.00293	−	6.74849i	0.584803	−	0.438362i
$238$	24.0653	+	10.9865i	1.55992	+	0.712148i
$239$		−	2.23895i		−	0.144826i	−0.997375	−	0.0724128i	$-0.976930\pi$
$239$		−	2.23895i		−	0.144826i	0.997375	−	0.0724128i	$-0.0230699\pi$
$240$	−39.3226	+	29.4758i	−2.53826	+	1.90265i
$241$			3.88159i			0.250035i	0.992155	+	0.125018i	$0.0398988\pi$
$241$			3.88159i			0.250035i	−0.992155	+	0.125018i	$0.960101\pi$
$242$	−0.646051	−	0.372998i	−0.0415297	−	0.0239772i
$243$	8.77867	+	12.8816i	0.563152	+	0.826353i
$244$	38.2670	+	22.0935i	2.44979	+	1.41439i
$245$	7.07645	−	20.4631i	0.452098	−	1.30734i
$246$	17.0669	−	39.9256i	1.08815	−	2.54556i
$247$	8.32751	+	3.40416i	0.529867	+	0.216601i
$248$	−24.4670	+	42.3781i	−1.55365	+	2.69101i
$249$	−0.794118	−	6.60592i	−0.0503252	−	0.418633i
$250$			3.47805i			0.219971i
$251$	−12.9969	−	22.5112i	−0.820354	−	1.42089i	−0.905419	−	0.424520i	$-0.860443\pi$
$251$	−12.9969	−	22.5112i	−0.820354	−	1.42089i	0.0850647	−	0.996375i	$-0.472890\pi$
$252$	7.10491	−	37.1451i	0.447567	−	2.33992i
$253$	5.58988	+	9.68196i	0.351433	+	0.608700i
$254$	38.1755	+	22.0406i	2.39534	+	1.38295i
$255$	−16.4804	+	12.3535i	−1.03204	+	0.773605i
$256$	−19.2705			−1.20441
$257$	−13.0423			−0.813558			−0.406779	−	0.913527i	$-0.633348\pi$
$257$	−13.0423			−0.813558			−0.406779	+	0.913527i	$0.633348\pi$
$258$	−20.0252	−	26.7150i	−1.24672	−	1.66320i
$259$	2.15782	−	4.72659i	0.134081	−	0.293696i
$260$	−32.5440	−	42.0069i	−2.01829	−	2.60516i
$261$	−12.8092	−	3.74334i	−0.792871	−	0.231707i
$262$	18.0472	−	10.4195i	1.11496	−	0.643721i
$263$	−24.0966	+	13.9122i	−1.48586	+	0.857862i	−0.999870	−	0.0161014i	$-0.994875\pi$
$263$	−24.0966	+	13.9122i	−1.48586	+	0.857862i	−0.485991	+	0.873964i	$0.661541\pi$
$264$	−32.6185	+	24.4505i	−2.00753	+	1.50482i
$265$		−	13.1125i		−	0.805494i
$266$	9.96140	+	13.9850i	0.610772	+	0.857476i
$267$	1.48251	+	12.3323i	0.0907279	+	0.754725i
$268$	−23.2569	−	40.2822i	−1.42064	−	2.46063i
$269$	13.4574			0.820511			0.410255	−	0.911971i	$-0.365440\pi$
$269$	13.4574			0.820511			0.410255	+	0.911971i	$0.365440\pi$
$270$	32.2862	+	26.5538i	1.96488	+	1.61601i
$271$			17.8056i			1.08162i	0.841146	+	0.540808i	$0.181881\pi$
$271$			17.8056i			1.08162i	−0.841146	+	0.540808i	$0.818119\pi$
$272$	35.2638			2.13818
$273$	16.2758	+	2.84563i	0.985058	+	0.172225i
$274$	−51.1141			−3.08792
$275$		−	14.9505i		−	0.901546i
$276$	−27.9867	+	3.36437i	−1.68460	+	0.202512i
$277$	11.5595			0.694545			0.347273	−	0.937764i	$-0.387108\pi$
$277$	11.5595			0.694545			0.347273	+	0.937764i	$0.387108\pi$
$278$	16.0124	+	27.7343i	0.960359	+	1.66339i
$279$	19.5960	+	5.72670i	1.17318	+	0.342849i
$280$	−5.60128	−	58.5793i	−0.334740	−	3.50078i
$281$			4.47214i			0.266786i	0.991063	+	0.133393i	$0.0425872\pi$
$281$			4.47214i			0.266786i	−0.991063	+	0.133393i	$0.957413\pi$
$282$	8.82450	+	11.7725i	0.525491	+	0.701039i
$283$	−3.65503	+	2.11023i	−0.217269	+	0.125440i	−0.604685	−	0.796465i	$-0.706701\pi$
$283$	−3.65503	+	2.11023i	−0.217269	+	0.125440i	0.387416	+	0.921905i	$0.373368\pi$
$284$	−18.5192	+	10.6921i	−1.09891	+	0.634459i
$285$	−13.2723	+	1.59551i	−0.786184	+	0.0945097i
$286$	−18.7982	−	24.2642i	−1.11156	−	1.43477i
$287$	14.7948	+	20.7707i	0.873307	+	1.22605i
$288$	−6.73766	−	27.6188i	−0.397021	−	1.62746i
$289$	−2.22070			−0.130630
$290$	−35.7869			−2.10148
$291$	12.5512	+	16.7441i	0.735765	+	0.981559i
$292$	−14.5911	−	8.42417i	−0.853879	−	0.492987i
$293$	−12.7485	−	22.0810i	−0.744773	−	1.28998i	−0.950301	−	0.311333i	$-0.899225\pi$
$293$	−12.7485	−	22.0810i	−0.744773	−	1.28998i	0.205528	−	0.978651i	$-0.434109\pi$
$294$	23.3528	+	21.1909i	1.36196	+	1.23588i
$295$	3.70647	+	6.41979i	0.215799	+	0.373774i
$296$		−	14.1213i		−	0.820786i
$297$	13.1356	+	10.8033i	0.762204	+	0.626874i
$298$	−8.98454	+	15.5617i	−0.520460	+	0.901464i
$299$	−1.66414	−	12.2024i	−0.0962397	−	0.705680i
$300$	34.6615	+	14.8167i	2.00118	+	0.855442i
$301$	19.5194	−	1.86642i	1.12508	−	0.107579i
$302$	−36.3655	−	20.9956i	−2.09260	−	1.20816i
$303$	−2.80502	+	2.10261i	−0.161144	+	0.120792i
$304$	19.8213	+	11.4438i	1.13683	+	0.656348i
$305$		−	28.6856i		−	1.64253i
$306$	−7.10923	−	29.1420i	−0.406408	−	1.66593i
$307$			15.3847i			0.878050i	0.898475	+	0.439025i	$0.144676\pi$
$307$			15.3847i			0.878050i	−0.898475	+	0.439025i	$0.855324\pi$
$308$	−3.92743	−	41.0739i	−0.223786	−	2.34040i
$309$	−3.20777	−	4.27937i	−0.182484	−	0.243445i
$310$	54.7481			3.10948
$311$	−0.112724	+	0.195243i	−0.00639198	+	0.0110712i	−0.869204	−	0.494454i	$-0.835368\pi$
$311$	−0.112724	+	0.195243i	−0.00639198	+	0.0110712i	0.862812	+	0.505525i	$0.168701\pi$
$312$	43.4515	−	11.3351i	2.45996	−	0.641725i
$313$	9.06754	−	5.23514i	0.512527	−	0.295908i	−0.221345	−	0.975196i	$-0.571045\pi$
$313$	9.06754	−	5.23514i	0.512527	−	0.295908i	0.733872	+	0.679288i	$0.237711\pi$
$314$	−0.105260	+	0.182315i	−0.00594014	+	0.0102886i
$315$	−23.1896	+	8.06258i	−1.30659	+	0.454275i
$316$	15.4757	+	26.8048i	0.870578	+	1.50789i
$317$	−29.2482	+	16.8864i	−1.64274	+	0.948437i	−0.662887	+	0.748720i	$0.730669\pi$
$317$	−29.2482	+	16.8864i	−1.64274	+	0.948437i	−0.979854	+	0.199717i	$0.935998\pi$
$318$	17.5600	+	7.50633i	0.984714	+	0.420934i
$319$	−14.5598			−0.815194
$320$	−9.74531	−	16.8794i	−0.544779	−	0.943585i
$321$	15.5291	−	1.86680i	0.866750	−	0.104195i
$322$	9.76125	−	21.3815i	0.543973	−	1.19154i
$323$	8.30722	+	4.79618i	0.462226	+	0.266866i
$324$	−38.0648	+	19.7471i	−2.11471	+	1.09706i
$325$	−6.23170	+	15.2445i	−0.345673	+	0.845610i
$326$	10.9747	+	6.33624i	0.607832	+	0.350932i
$327$	22.6513	+	9.68272i	1.25262	+	0.535456i
$328$	60.0218	+	34.6536i	3.31415	+	1.91342i
$329$	−8.60161	+	0.822474i	−0.474222	+	0.0453445i
$330$	41.9376	+	17.9270i	2.30859	+	0.986850i
$331$	8.95942	−	15.5182i	0.492454	−	0.852956i	−0.507508	−	0.861647i	$-0.669433\pi$
$331$	8.95942	−	15.5182i	0.492454	−	0.852956i	0.999962	+	0.00869133i	$0.00276657\pi$
$332$	18.3030			1.00451
$333$	−5.72368	+	1.39630i	−0.313656	+	0.0765169i
$334$	41.6823	+	24.0653i	2.28076	+	1.31680i
$335$	−15.0981	+	26.1506i	−0.824896	+	1.42876i
$336$	40.0490	+	12.7684i	2.18485	+	0.696571i
$337$	−30.2006			−1.64513			−0.822565	−	0.568671i	$-0.807458\pi$
$337$	−30.2006			−1.64513			−0.822565	+	0.568671i	$0.807458\pi$
$338$	9.05399	+	32.5769i	0.492472	+	1.77195i
$339$	−9.37705	−	12.5096i	−0.509291	−	0.679428i
$340$	−28.3292	−	49.0676i	−1.53637	−	2.66106i
$341$	22.2741			1.20621
$342$	5.46115	−	18.6873i	0.295305	−	1.01050i
$343$	−17.7680	+	5.22464i	−0.959384	+	0.282104i
$344$	46.1523	−	26.6461i	2.48837	−	1.43666i
$345$	10.9758	+	14.6424i	0.590917	+	0.788322i
$346$	7.00824	+	4.04621i	0.376765	+	0.217525i
$347$		−	5.16299i		−	0.277164i	−0.990351	−	0.138582i	$-0.955746\pi$
$347$		−	5.16299i		−	0.277164i	0.990351	−	0.138582i	$-0.0442544\pi$
$348$	14.4296	−	33.7558i	0.773505	−	1.80950i
$349$	−8.34798	−	4.81971i	−0.446857	−	0.257993i	0.259645	−	0.965704i	$-0.416394\pi$
$349$	−8.34798	−	4.81971i	−0.446857	−	0.257993i	−0.706502	+	0.707711i	$0.749728\pi$
$350$	−25.6012	+	18.2355i	−1.36844	+	0.974728i
$351$	−8.89081	−	16.4910i	−0.474556	−	0.880225i
$352$	−15.5084	−	26.8613i	−0.826599	−	1.43171i
$353$	−7.17135	−	12.4211i	−0.381692	−	0.661110i	0.609612	−	0.792700i	$-0.291325\pi$
$353$	−7.17135	−	12.4211i	−0.381692	−	0.661110i	−0.991304	+	0.131589i	$0.957992\pi$
$354$	−10.7190	+	1.28857i	−0.569710	+	0.0684866i
$355$	12.0224	+	6.94116i	0.638085	+	0.368399i
$356$	−34.1691			−1.81096
$357$	16.7848	+	5.35130i	0.888345	+	0.283221i
$358$	−6.71261	−	11.6266i	−0.354772	−	0.614484i
$359$	12.1885	−	7.03703i	0.643284	−	0.371400i	−0.142595	−	0.989781i	$-0.545544\pi$
$359$	12.1885	−	7.03703i	0.643284	−	0.371400i	0.785878	+	0.618381i	$0.212211\pi$
$360$	−48.2327	+	46.1077i	−2.54209	+	2.43009i
$361$	−6.38709	−	11.0628i	−0.336163	−	0.582251i
$362$	−15.6749			−0.823856
$363$	−0.456805	−	0.195270i	−0.0239760	−	0.0102490i
$364$	−13.1159	+	43.5186i	−0.687459	+	2.28100i
$365$			10.9377i			0.572506i
$366$	38.4151	+	16.4212i	2.00799	+	0.858352i
$367$	0.839387	−	0.484620i	0.0438156	−	0.0252970i	−0.477932	−	0.878397i	$-0.658614\pi$
$367$	0.839387	−	0.484620i	0.0438156	−	0.0252970i	0.521748	+	0.853100i	$0.325280\pi$
$368$		−	31.3311i		−	1.63325i
$369$	8.11096	−	27.7546i	0.422240	−	1.44485i
$370$	−13.6825	+	7.89958i	−0.711318	+	0.410680i
$371$	−9.13530	+	6.50699i	−0.474281	+	0.337826i
$372$	−22.0748	+	51.6409i	−1.14453	+	2.67745i
$373$	9.08827	−	15.7413i	0.470573	−	0.815056i	−0.528861	−	0.848708i	$-0.677381\pi$
$373$	9.08827	−	15.7413i	0.470573	−	0.815056i	0.999434	+	0.0336529i	$0.0107141\pi$
$374$	−16.3636	−	28.3426i	−0.846143	−	1.46556i
$375$	0.276446	+	2.29963i	0.0142756	+	0.118752i
$376$	−20.3379	+	11.7421i	−1.04885	+	0.605552i
$377$	14.8462	+	6.06888i	0.764616	+	0.312563i
$378$	2.47782	−	35.6705i	0.127445	−	1.83469i
$379$	0.418571	−	0.724986i	0.0215005	−	0.0372400i	−0.855075	−	0.518504i	$-0.826489\pi$
$379$	0.418571	−	0.724986i	0.0215005	−	0.0372400i	0.876575	+	0.481264i	$0.159822\pi$
$380$		−	36.7735i		−	1.88644i
$381$	26.9928	+	11.5386i	1.38288	+	0.591140i
$382$	14.7777	−	25.5957i	0.756094	−	1.30959i
$383$	−2.59736	+	4.49876i	−0.132719	+	0.229876i	−0.924724	−	0.380639i	$-0.875704\pi$
$383$	−2.59736	+	4.49876i	−0.132719	+	0.229876i	0.792005	+	0.610515i	$0.209037\pi$
$384$	−4.40886	+	0.530003i	−0.224989	+	0.0270466i
$385$	−21.8174	+	15.5403i	−1.11192	+	0.792009i
$386$	17.5743	−	10.1465i	0.894506	−	0.516443i
$387$	−15.3637	−	16.0718i	−0.780981	−	0.816975i
$388$	−49.8529	+	28.7826i	−2.53090	+	1.46122i
$389$	−23.1078	−	13.3413i	−1.17161	−	0.676430i	−0.217553	−	0.976049i	$-0.569807\pi$
$389$	−23.1078	−	13.3413i	−1.17161	−	0.676430i	−0.954059	+	0.299618i	$0.903141\pi$
$390$	−35.2899	−	35.7602i	−1.78698	−	1.81079i
$391$		−	13.1311i		−	0.664067i
$392$	−38.0318	+	32.9720i	−1.92090	+	1.66534i
$393$	11.1043	−	8.32366i	0.560138	−	0.419873i
$394$	−28.5440	+	49.4396i	−1.43803	+	2.49073i
$395$	10.0466	−	17.4013i	0.505501	−	0.875554i
$396$	−33.8192	+	32.3292i	−1.69948	+	1.62460i
$397$	−21.0859	−	12.1739i	−1.05827	−	0.610993i	−0.133317	−	0.991073i	$-0.542563\pi$
$397$	−21.0859	−	12.1739i	−1.05827	−	0.610993i	−0.924953	+	0.380081i	$0.875896\pi$
$398$	58.7020			2.94247
$399$	7.69787	+	8.45488i	0.385376	+	0.423273i
$400$	−20.9492	+	36.2851i	−1.04746	+	1.81426i
$401$		−	11.0038i		−	0.549503i	−0.961515	−	0.274752i	$-0.911404\pi$
$401$		−	11.0038i		−	0.549503i	0.961515	−	0.274752i	$-0.0885956\pi$
$402$	−26.3774	−	35.1891i	−1.31558	−	1.75507i
$403$	−22.7122	−	9.28439i	−1.13137	−	0.462488i
$404$	−4.82174	−	8.35150i	−0.239890	−	0.415502i
$405$	23.4576	+	14.9907i	1.16562	+	0.744893i
$406$	17.7590	+	24.9322i	0.881366	+	1.23737i
$407$	−5.56669	+	3.21393i	−0.275931	+	0.159309i
$408$	47.5380	−	5.71469i	2.35348	−	0.282919i
$409$			21.6415i			1.07011i	0.844819	+	0.535053i	$0.179708\pi$
$409$			21.6415i			1.07011i	−0.844819	+	0.535053i	$0.820292\pi$
$410$		−	77.5419i		−	3.82952i
$411$	−33.7958	+	4.06270i	−1.66702	+	0.200398i
$412$	12.7411	−	7.35609i	0.627710	−	0.362409i
$413$	2.63327	−	5.76802i	0.129575	−	0.283826i
$414$	−25.8920	+	6.31640i	−1.27252	+	0.310434i
$415$	−5.94102	−	10.2902i	−0.291633	−	0.505124i
$416$	4.61693	+	33.8538i	0.226364	+	1.65982i
$417$	12.7915	+	17.0647i	0.626403	+	0.835662i
$418$		−	21.2413i		−	1.03895i
$419$	−6.04832	+	10.4760i	−0.295480	+	0.511786i	−0.975096	−	0.221782i	$-0.928813\pi$
$419$	−6.04832	+	10.4760i	−0.295480	+	0.511786i	0.679617	+	0.733567i	$0.262146\pi$
$420$	−14.4069	−	65.9833i	−0.702984	−	3.21965i
$421$	38.8227			1.89210			0.946052	−	0.324016i	$-0.105033\pi$
$421$	38.8227			1.89210			0.946052	+	0.324016i	$0.105033\pi$
$422$	−25.0290	−	14.4505i	−1.21839	−	0.703439i
$423$	6.77031	+	7.08234i	0.329184	+	0.344355i
$424$	−15.2412	+	26.3986i	−0.740181	+	1.28203i
$425$	−8.77995	+	15.2073i	−0.425890	+	0.737664i
$426$	−16.1778	+	12.1267i	−0.783816	+	0.587540i
$427$	−19.9849	+	14.2350i	−0.967135	+	0.688882i
$428$			43.0264i			2.07976i
$429$	−14.3576	−	14.5489i	−0.693194	−	0.702430i
$430$	−51.6359	−	29.8120i	−2.49010	−	1.43766i
$431$	−6.13958	+	3.54469i	−0.295733	+	0.170742i	−0.640524	−	0.767938i	$-0.721283\pi$
$431$	−6.13958	+	3.54469i	−0.295733	+	0.170742i	0.344791	+	0.938679i	$0.387950\pi$
$432$	−16.7423	−	44.6261i	−0.805512	−	2.14708i
$433$	−7.29369	+	4.21101i	−0.350512	+	0.202368i	−0.664911	−	0.746923i	$-0.731530\pi$
$433$	−7.29369	+	4.21101i	−0.350512	+	0.202368i	0.314399	+	0.949291i	$0.398197\pi$
$434$	−27.1684	−	38.1422i	−1.30412	−	1.83089i
$435$	−23.6617	+	2.84444i	−1.13449	+	0.136381i
$436$	−33.8828	+	58.6867i	−1.62269	+	2.81058i
$437$	4.26130	−	7.38078i	0.203845	−	0.353071i
$438$	−14.6475	−	6.26137i	−0.699887	−	0.299180i
$439$		−	13.3222i		−	0.635835i	−0.948118	−	0.317918i	$-0.897016\pi$
$439$		−	13.3222i		−	0.635835i	0.948118	−	0.317918i	$-0.102984\pi$
$440$	−36.4000	+	63.0466i	−1.73530	+	3.00563i
$441$	17.1248	+	12.1549i	0.815466	+	0.578804i
$442$	4.87155	+	35.7207i	0.231716	+	1.69906i
$443$	−4.72951	+	2.73058i	−0.224706	+	0.129734i	−0.608127	−	0.793839i	$-0.708079\pi$
$443$	−4.72951	+	2.73058i	−0.224706	+	0.129734i	0.383421	+	0.923573i	$0.374746\pi$
$444$	−1.93436	−	16.0911i	−0.0918008	−	0.763650i
$445$	11.0910	+	19.2103i	0.525766	+	0.910653i
$446$	17.5973	−	30.4793i	0.833254	−	1.44324i
$447$	−4.70353	+	11.0032i	−0.222469	+	0.520435i
$448$	−6.92358	+	15.1657i	−0.327108	+	0.716512i
$449$	−24.2926	+	14.0254i	−1.14644	+	0.661897i	−0.948017	−	0.318219i	$-0.896915\pi$
$449$	−24.2926	+	14.0254i	−1.14644	+	0.661897i	−0.198423	+	0.980117i	$0.563582\pi$
$450$	34.2093	+	9.99727i	1.61264	+	0.471276i
$451$		−	31.5478i		−	1.48553i
$452$	37.2453	−	21.5036i	1.75187	−	1.01144i
$453$	−25.7130	−	10.9915i	−1.20810	−	0.516426i
$454$		−	38.0736i		−	1.78688i
$455$	28.7240	−	6.75194i	1.34660	−	0.316536i
$456$	28.5749	+	12.2149i	1.33814	+	0.572014i
$457$	10.2671			0.480275			0.240138	−	0.970739i	$-0.422807\pi$
$457$	10.2671			0.480275			0.240138	+	0.970739i	$0.422807\pi$
$458$	−6.09532	−	10.5574i	−0.284816	−	0.493315i
$459$	−7.01679	−	18.7031i	−0.327516	−	0.872986i
$460$	−43.5954	+	25.1698i	−2.03265	+	1.17355i
$461$	−6.69370	−	11.5938i	−0.311756	−	0.539978i	0.666986	−	0.745070i	$-0.267584\pi$
$461$	−6.69370	−	11.5938i	−0.311756	−	0.539978i	−0.978743	+	0.205092i	$0.934251\pi$
$462$	−8.32178	−	38.1136i	−0.387164	−	1.77320i
$463$	28.5865			1.32853			0.664264	−	0.747498i	$-0.268745\pi$
$463$	28.5865			1.32853			0.664264	+	0.747498i	$0.268745\pi$
$464$	35.3371	+	20.4019i	1.64048	+	0.947133i
$465$	36.1985	−	4.35153i	1.67866	−	0.201797i
$466$	10.8661	+	18.8207i	0.503364	+	0.871851i
$467$	−16.4521	−	28.4959i	−0.761312	−	1.31863i	−0.942174	−	0.335123i	$-0.891222\pi$
$467$	−16.4521	−	28.4959i	−0.761312	−	1.31863i	0.180862	−	0.983508i	$-0.442111\pi$
$468$	47.9598	−	18.8683i	2.21694	−	0.872188i
$469$	25.7111	−	2.45846i	1.18723	−	0.113521i
$470$	22.7544	+	13.1372i	1.04958	+	0.605975i
$471$	−0.0551049	+	0.128910i	−0.00253910	+	0.00593985i
$472$		−	17.2328i		−	0.793203i
$473$	−21.0080	−	12.1290i	−0.965948	−	0.557690i
$474$	17.5522	+	23.4157i	0.806197	+	1.07552i
$475$	−9.87016	+	5.69854i	−0.452874	+	0.261467i
$476$	−20.1265	+	44.0860i	−0.922498	+	2.02068i
$477$	12.2070	+	3.56734i	0.558919	+	0.163337i
$478$	5.82329			0.266351
$479$	7.99625	+	13.8499i	0.365358	+	0.632818i	0.988834	−	0.149024i	$-0.0476133\pi$
$479$	7.99625	+	13.8499i	0.365358	+	0.632818i	−0.623476	+	0.781843i	$0.714280\pi$
$480$	−30.4509	−	40.6235i	−1.38989	−	1.85420i
$481$	7.01580	−	0.956805i	0.319893	−	0.0436266i
$482$	−10.0956			−0.459843
$483$	4.75451	−	14.9129i	0.216338	−	0.678561i
$484$	0.683308	−	1.18352i	0.0310594	−	0.0537965i
$485$	32.3639	+	18.6853i	1.46957	+	0.848455i
$486$	−33.5037	+	22.8324i	−1.51976	+	1.03570i
$487$	20.5163			0.929681			0.464841	−	0.885394i	$-0.346112\pi$
$487$	20.5163			0.929681			0.464841	+	0.885394i	$0.346112\pi$
$488$	−33.3425	+	57.7510i	−1.50935	+	2.61426i
$489$	7.75990	+	3.31711i	0.350915	+	0.150005i
$490$	53.2226	+	18.4051i	2.40435	+	0.831459i
$491$	15.6262	+	9.02180i	0.705201	+	0.407148i	0.809282	−	0.587421i	$-0.199857\pi$
$491$	15.6262	+	9.02180i	0.705201	+	0.407148i	−0.104081	+	0.994569i	$0.533190\pi$
$492$	73.1411	+	31.2655i	3.29745	+	1.40956i
$493$	14.8100	+	8.55055i	0.667008	+	0.385097i
$494$	−8.85387	+	21.6590i	−0.398355	+	0.974485i
$495$	29.1533	+	8.51971i	1.31034	+	0.382933i
$496$	−54.0599	−	31.2115i	−2.42736	−	1.40144i
$497$	−1.13025	−	11.8204i	−0.0506986	−	0.530217i
$498$	17.1813	−	2.06542i	0.769914	−	0.0925538i
$499$	16.6851	+	28.8994i	0.746926	+	1.29371i	0.949290	+	0.314403i	$0.101804\pi$
$499$	16.6851	+	28.8994i	0.746926	+	1.29371i	−0.202364	+	0.979310i	$0.564862\pi$
$500$	−6.37157			−0.284945
$501$	29.4724	+	12.5985i	1.31673	+	0.562861i
$502$	58.5494	−	33.8035i	2.61319	−	1.50872i
$503$	5.73038	+	9.92530i	0.255505	+	0.442547i	0.965033	−	0.262130i	$-0.0844250\pi$
$503$	5.73038	+	9.92530i	0.255505	+	0.442547i	−0.709528	+	0.704678i	$0.751092\pi$
$504$	56.0578	+	10.7224i	2.49701	+	0.477615i
$505$	−3.13021	+	5.42168i	−0.139292	+	0.241262i
$506$	−25.1818	+	14.5387i	−1.11947	+	0.646325i
$507$	8.57565	+	20.8197i	0.380858	+	0.924634i
$508$	−40.3770	+	69.9350i	−1.79144	+	3.10287i
$509$	−32.7895			−1.45337			−0.726684	−	0.686971i	$-0.758940\pi$
$509$	−32.7895			−1.45337			−0.726684	+	0.686971i	$0.758940\pi$
$510$	−32.1302	−	42.8637i	−1.42275	−	1.89804i
$511$	7.62016	−	5.42777i	0.337096	−	0.240111i
$512$		−	44.9931i		−	1.98843i
$513$	2.12550	−	12.7898i	0.0938430	−	0.564684i
$514$		−	33.9218i		−	1.49623i
$515$	−8.27137	−	4.77548i	−0.364480	−	0.210433i
$516$	48.9401	−	36.6849i	2.15447	−	1.61496i
$517$	9.25757	+	5.34486i	0.407147	+	0.235067i
$518$	12.2934	+	5.61228i	0.540140	+	0.246589i
$519$	4.95533	+	2.11825i	0.217515	+	0.0929807i
$520$	63.3951	−	49.1140i	2.78006	−	2.15379i
$521$	17.0863	−	29.5943i	0.748564	−	1.29655i	−0.199946	−	0.979807i	$-0.564077\pi$
$521$	17.0863	−	29.5943i	0.748564	−	1.29655i	0.948511	−	0.316745i	$-0.102590\pi$
$522$	9.73606	−	33.3155i	0.426136	−	1.45818i
$523$		−	33.9467i		−	1.48438i	−0.670187	−	0.742192i	$-0.733786\pi$
$523$		−	33.9467i		−	1.48438i	0.670187	−	0.742192i	$-0.266214\pi$
$524$	19.0879	+	33.0612i	0.833859	+	1.44429i
$525$	−15.4776	+	14.0918i	−0.675499	+	0.615018i
$526$	−36.1842	−	62.6729i	−1.57771	−	2.73267i
$527$	−22.6568	−	13.0809i	−0.986948	−	0.569814i
$528$	−31.1904	−	41.6100i	−1.35739	−	1.81084i
$529$	11.3333			0.492753
$530$	34.1043			1.48140
$531$	−6.98482	+	1.70396i	−0.303115	+	0.0739455i
$532$	−25.6196	+	18.2486i	−1.11075	+	0.791179i
$533$	−13.1499	+	32.1682i	−0.569583	+	1.39336i
$534$	−32.0751	+	3.85585i	−1.38802	+	0.166859i
$535$	24.1900	−	13.9661i	1.04582	−	0.603806i
$536$	60.7922	−	35.0984i	2.62582	−	1.51602i
$537$	−5.36237	−	7.15375i	−0.231403	−	0.308707i
$538$			35.0013i			1.50901i
$539$	21.6535	+	7.48809i	0.932682	+	0.322535i
$540$	−48.6448	+	59.1462i	−2.09334	+	2.54525i
$541$	6.13878	+	10.6327i	0.263927	+	0.457135i	0.967282	−	0.253704i	$-0.0816489\pi$
$541$	6.13878	+	10.6327i	0.263927	+	0.457135i	−0.703355	+	0.710839i	$0.748316\pi$
$542$	−46.3107			−1.98921
$543$	−10.3640	+	1.24589i	−0.444761	+	0.0534661i
$544$			36.4304i			1.56194i
$545$	43.9925			1.88443
$546$	−7.40120	+	42.3318i	−0.316742	+	1.81163i
$547$	−39.3727			−1.68345			−0.841727	−	0.539903i	$-0.818461\pi$
$547$	−39.3727			−1.68345			−0.841727	+	0.539903i	$0.818461\pi$
$548$		−	93.6378i		−	4.00001i
$549$	26.7046	+	7.80410i	1.13972	+	0.333071i
$550$	38.8846			1.65805
$551$	5.54965	+	9.61227i	0.236423	+	0.409497i
$552$	−5.07737	−	42.2364i	−0.216107	−	1.79770i
$553$	−17.1088	+	1.63592i	−0.727541	+	0.0695665i
$554$			30.0652i			1.27735i
$555$	−8.41873	+	6.31059i	−0.357355	+	0.267869i
$556$	−50.8074	+	29.3337i	−2.15471	+	1.24402i
$557$	−15.8259	+	9.13707i	−0.670563	+	0.387150i	−0.796290	−	0.604915i	$-0.793207\pi$
$557$	−15.8259	+	9.13707i	−0.670563	+	0.387150i	0.125727	+	0.992065i	$0.459874\pi$
$558$	−14.8946	+	50.9672i	−0.630537	+	2.15762i
$559$	16.3655	+	21.1241i	0.692185	+	0.893454i
$560$	74.7272	−	7.14531i	3.15780	−	0.301945i
$561$	−13.0721	−	17.4390i	−0.551905	−	0.736277i
$562$	−11.6316			−0.490649
$563$	−22.6051			−0.952689			−0.476345	−	0.879259i	$-0.658039\pi$
$563$	−22.6051			−0.952689			−0.476345	+	0.879259i	$0.658039\pi$
$564$	−21.5664	+	16.1659i	−0.908108	+	0.680708i
$565$	−24.1791	−	13.9598i	−1.01722	−	0.587294i
$566$	−5.48851	−	9.50637i	−0.230699	−	0.399583i
$567$	−1.19690	−	23.7817i	−0.0502652	−	0.998736i
$568$	−16.1361	−	27.9485i	−0.677054	−	1.17269i
$569$		−	4.95360i		−	0.207666i	−0.994595	−	0.103833i	$-0.966889\pi$
$569$		−	4.95360i		−	0.207666i	0.994595	−	0.103833i	$-0.0331107\pi$
$570$	−4.14975	−	34.5200i	−0.173814	−	1.44588i
$571$	14.5385	−	25.1815i	0.608419	−	1.05381i	−0.383082	−	0.923714i	$-0.625137\pi$
$571$	14.5385	−	25.1815i	0.608419	−	1.05381i	0.991501	−	0.130098i	$-0.0415293\pi$
$572$	44.4505	−	34.4371i	1.85857	−	1.43989i
$573$	7.73634	−	18.0980i	0.323190	−	0.756056i
$574$	−54.0224	+	38.4797i	−2.25485	+	1.60611i
$575$	13.5114	+	7.80079i	0.563463	+	0.325316i
$576$	18.3650	−	4.48017i	0.765207	−	0.186674i
$577$	−18.5775	−	10.7257i	−0.773393	−	0.446518i	0.0606909	−	0.998157i	$-0.480670\pi$
$577$	−18.5775	−	10.7257i	−0.773393	−	0.446518i	−0.834084	+	0.551638i	$0.814003\pi$
$578$		−	5.77582i		−	0.240243i
$579$	10.8133	−	8.10554i	0.449386	−	0.336855i
$580$		−	65.5593i		−	2.72220i
$581$	−4.22082	+	9.24546i	−0.175109	+	0.383566i
$582$	−43.5498	+	32.6445i	−1.80520	+	1.35316i
$583$	13.8753			0.574655
$584$	12.7134	−	22.0203i	0.526084	−	0.911205i
$585$	−26.1754	−	20.8390i	−1.08222	−	0.861588i
$586$	57.4304	−	33.1575i	2.37243	−	1.36972i
$587$	−22.9823	+	39.8064i	−0.948579	+	1.64299i	−0.200158	+	0.979764i	$0.564145\pi$
$587$	−22.9823	+	39.8064i	−0.948579	+	1.64299i	−0.748421	+	0.663224i	$0.769188\pi$
$588$	−38.8203	+	42.7809i	−1.60092	+	1.76425i
$589$	−8.49005	−	14.7052i	−0.349826	−	0.605917i
$590$	−16.6972	+	9.64015i	−0.687414	+	0.396879i
$591$	−14.9432	+	34.9574i	−0.614681	+	1.43795i
$592$	18.0140			0.740370
$593$	−5.11847	−	8.86545i	−0.210190	−	0.364060i	0.741584	−	0.670860i	$-0.234075\pi$
$593$	−5.11847	−	8.86545i	−0.210190	−	0.364060i	−0.951774	+	0.306800i	$0.900742\pi$
$594$	−28.0984	+	34.1643i	−1.15289	+	1.40178i
$595$	31.3186	−	2.99465i	1.28394	−	0.122769i
$596$	−28.5080	−	16.4591i	−1.16773	−	0.674191i
$597$	38.8128	−	4.66581i	1.58850	−	0.190959i
$598$	31.7371	−	4.32826i	1.29783	−	0.176996i
$599$	26.9857	+	15.5802i	1.10261	+	0.636590i	0.936904	−	0.349586i	$-0.113678\pi$
$599$	26.9857	+	15.5802i	1.10261	+	0.636590i	0.165701	+	0.986176i	$0.447011\pi$
$600$	−22.3607	+	52.3096i	−0.912873	+	2.13553i
$601$	−7.77985	−	4.49170i	−0.317347	−	0.183220i	0.332863	−	0.942975i	$-0.391985\pi$
$601$	−7.77985	−	4.49170i	−0.317347	−	0.183220i	−0.650209	+	0.759755i	$0.725319\pi$
$602$	4.85438	+	50.7681i	0.197850	+	2.06915i
$603$	−20.2372	−	21.1699i	−0.824122	−	0.862105i
$604$	38.4626	−	66.6193i	1.56502	−	2.71070i
$605$	−0.887188			−0.0360693
$606$	−5.46869	−	7.29558i	−0.222150	−	0.296363i
$607$	28.8701	+	16.6682i	1.17180	+	0.676540i	0.954104	−	0.299476i	$-0.0968119\pi$
$607$	28.8701	+	16.6682i	1.17180	+	0.676540i	0.217698	+	0.976016i	$0.430145\pi$
$608$	−11.8224	+	20.4770i	−0.479461	+	0.830452i
$609$	13.7236	+	15.0732i	0.556110	+	0.610798i
$610$	74.6083			3.02080
$611$	−7.21175	−	9.30874i	−0.291756	−	0.376591i
$612$	53.3862	−	13.0237i	2.15801	−	0.526450i
$613$	17.3720	+	30.0892i	0.701649	+	1.21529i	0.967887	+	0.251385i	$0.0808859\pi$
$613$	17.3720	+	30.0892i	0.701649	+	1.21529i	−0.266238	+	0.963907i	$0.585781\pi$
$614$	−40.0140			−1.61483
$615$	−6.16325	−	51.2694i	−0.248526	−	2.06738i
$616$	61.9870	−	5.92711i	2.49753	−	0.238810i
$617$	26.8450	−	15.4989i	1.08074	−	0.623964i	0.149642	−	0.988740i	$-0.452188\pi$
$617$	26.8450	−	15.4989i	1.08074	−	0.623964i	0.931095	+	0.364776i	$0.118855\pi$
$618$	11.1302	−	8.34308i	0.447723	−	0.335608i
$619$	3.26509	+	1.88510i	0.131235	+	0.0757686i	0.564180	−	0.825652i	$-0.309192\pi$
$619$	3.26509	+	1.88510i	0.131235	+	0.0757686i	−0.432945	+	0.901420i	$0.642526\pi$
$620$			100.295i			4.02794i
$621$	−16.6173	+	6.23426i	−0.666829	+	0.250172i
$622$	−0.507808	−	0.293183i	−0.0203613	−	0.0117556i
$623$	7.87966	−	17.2600i	0.315692	−	0.691505i
$624$	14.4597	+	55.4292i	0.578853	+	2.21894i
$625$	13.4874	+	23.3608i	0.539494	+	0.934432i
$626$	13.6161	+	23.5838i	0.544208	+	0.942596i
$627$	−1.68832	−	14.0444i	−0.0674250	−	0.560878i
$628$	−0.333989	−	0.192829i	−0.0133276	−	0.00769471i
$629$	7.54978			0.301029
$630$	−20.9700	−	60.3139i	−0.835463	−	2.40296i
$631$	0.379300	+	0.656968i	0.0150997	+	0.0261535i	0.873477	−	0.486866i	$-0.161860\pi$
$631$	0.379300	+	0.656968i	0.0150997	+	0.0261535i	−0.858377	+	0.513020i	$0.828527\pi$
$632$	−40.4526	+	23.3553i	−1.60912	+	0.929025i
$633$	−17.6973	−	7.56503i	−0.703404	−	0.300683i
$634$	−43.9199	−	76.0715i	−1.74428	−	3.02119i
$635$	52.4244			2.08040
$636$	−13.7511	+	32.1687i	−0.545267	+	1.27557i
$637$	−18.9581	−	16.6610i	−0.751148	−	0.660134i
$638$		−	37.8687i		−	1.49923i
$639$	−9.73260	+	9.30381i	−0.385016	+	0.368053i
$640$	−6.86776	+	3.96510i	−0.271472	+	0.156734i
$641$			4.11691i			0.162608i	0.996689	+	0.0813040i	$0.0259085\pi$
$641$			4.11691i			0.162608i	−0.996689	+	0.0813040i	$0.974092\pi$
$642$	4.85537	+	40.3896i	0.191626	+	1.59405i
$643$	1.02787	−	0.593443i	0.0405354	−	0.0234031i	−0.479595	−	0.877490i	$-0.659217\pi$
$643$	1.02787	−	0.593443i	0.0405354	−	0.0234031i	0.520131	+	0.854087i	$0.325883\pi$
$644$	39.1695	+	17.8820i	1.54349	+	0.704649i
$645$	−36.5103	−	15.6070i	−1.43759	−	0.614525i
$646$	−12.4744	+	21.6063i	−0.490798	+	0.850087i
$647$	3.48671	+	6.03916i	0.137077	+	0.237424i	0.926389	−	0.376568i	$-0.122896\pi$
$647$	3.48671	+	6.03916i	0.137077	+	0.237424i	−0.789312	+	0.613992i	$0.789563\pi$
$648$	−29.8016	−	57.4458i	−1.17072	−	2.25668i
$649$	−6.79323	+	3.92208i	−0.266658	+	0.153955i
$650$	−39.6493	−	16.2080i	−1.55517	−	0.635731i
$651$	−20.9949	−	23.0596i	−0.822856	−	0.903775i
$652$	−11.6076	+	20.1049i	−0.454588	+	0.787370i
$653$		−	2.74846i		−	0.107555i	−0.998553	−	0.0537777i	$-0.982874\pi$
$653$		−	2.74846i		−	0.107555i	0.998553	−	0.0537777i	$-0.0171262\pi$
$654$	−25.1838	+	58.9138i	−0.984764	+	2.30371i
$655$	12.3916	−	21.4629i	0.484181	−	0.838625i
$656$	−44.2061	+	76.5672i	−1.72596	+	2.98945i
$657$	−10.1824	−	2.97568i	−0.397252	−	0.116092i
$658$	−2.13917	−	22.3719i	−0.0833937	−	0.872148i
$659$	26.4438	−	15.2673i	1.03010	−	0.594731i	0.113090	−	0.993585i	$-0.463925\pi$
$659$	26.4438	−	15.2673i	1.03010	−	0.594731i	0.917015	+	0.398853i	$0.130592\pi$
$660$	−32.8411	+	76.8270i	−1.27834	+	2.99049i
$661$	−20.9223	+	12.0795i	−0.813784	+	0.469839i	−0.848268	−	0.529567i	$-0.822355\pi$
$661$	−20.9223	+	12.0795i	−0.813784	+	0.469839i	0.0344841	+	0.999405i	$0.489021\pi$
$662$	40.3612	+	23.3026i	1.56868	+	0.905679i
$663$	6.06017	+	23.2307i	0.235357	+	0.902207i
$664$			27.6221i			1.07195i
$665$	18.5756	+	8.48028i	0.720329	+	0.328851i
$666$	−3.63164	−	14.8867i	−0.140723	−	0.576849i
$667$	7.59697	−	13.1583i	0.294156	−	0.509493i
$668$	−44.0861	+	76.3594i	−1.70574	+	2.95443i
$669$	9.21241	−	21.5511i	0.356173	−	0.833213i
$670$	−68.0152	−	39.2686i	−2.62766	−	1.51708i
$671$	30.3542			1.17181
$672$	−13.1908	+	41.3739i	−0.508844	+	1.59603i
$673$	−18.1149	+	31.3760i	−0.698279	+	1.20946i	0.270783	+	0.962640i	$0.412717\pi$
$673$	−18.1149	+	31.3760i	−0.698279	+	1.20946i	−0.969063	+	0.246815i	$0.920616\pi$
$674$		−	78.5486i		−	3.02558i
$675$	23.4132	+	3.89097i	0.901176	+	0.149763i
$676$	−59.6788	+	16.5863i	−2.29534	+	0.637935i
$677$	−2.63877	−	4.57048i	−0.101416	−	0.175658i	0.810852	−	0.585251i	$-0.199004\pi$
$677$	−2.63877	−	4.57048i	−0.101416	−	0.175658i	−0.912268	+	0.409593i	$0.865671\pi$
$678$	32.5362	−	24.3888i	1.24954	−	0.936645i
$679$	−3.04258	−	31.8199i	−0.116763	−	1.22114i
$680$	74.0507	−	42.7532i	2.83972	−	1.63951i
$681$	−3.02620	−	25.1736i	−0.115964	−	0.964656i
$682$			57.9328i			2.21836i
$683$			33.6552i			1.28778i	0.765117	+	0.643891i	$0.222681\pi$
$683$			33.6552i			1.28778i	−0.765117	+	0.643891i	$0.777319\pi$
$684$	34.2340	+	10.0045i	1.30897	+	0.382531i
$685$	−52.6443	+	30.3942i	−2.01143	+	1.16130i
$686$	−13.5888	−	46.2129i	−0.518822	−	1.76442i
$687$	−4.86925	−	6.49590i	−0.185774	−	0.247834i
$688$	33.9912	+	58.8746i	1.29590	+	2.24457i
$689$	−14.1481	−	5.78354i	−0.539000	−	0.220335i
$690$	−38.0835	+	28.5470i	−1.44981	+	1.08676i
$691$			23.7842i			0.904795i	0.891816	+	0.452397i	$0.149431\pi$
$691$			23.7842i			0.904795i	−0.891816	+	0.452397i	$0.850569\pi$
$692$	−7.41239	+	12.8386i	−0.281777	+	0.488052i
$693$	−8.53159	−	24.5386i	−0.324088	−	0.932144i
$694$	13.4284			0.509736
$695$	32.9835	+	19.0430i	1.25113	+	0.722343i
$696$	50.9429	+	21.7765i	1.93099	+	0.825436i
$697$	−18.5271	+	32.0898i	−0.701763	+	1.21549i
$698$	12.5356	−	21.7123i	0.474479	−	0.821821i
$699$	8.68042	+	11.5802i	0.328323	+	0.438005i
$700$	−33.4062	−	46.8997i	−1.26264	−	1.77264i
$701$			16.8828i			0.637656i	0.947813	+	0.318828i	$0.103289\pi$
$701$			16.8828i			0.637656i	−0.947813	+	0.318828i	$0.896711\pi$
$702$	42.8915	−	23.1241i	1.61883	−	0.872763i
$703$	4.24362	+	2.45005i	0.160051	+	0.0924055i
$704$	17.8613	−	10.3122i	0.673171	−	0.388656i
$705$	16.0890	+	6.87753i	0.605946	+	0.259023i
$706$	32.3061	−	18.6520i	1.21586	−	0.701976i
$707$	5.33056	−	0.509701i	0.200476	−	0.0191693i
$708$	−2.36057	−	19.6366i	−0.0887158	−	0.737987i
$709$	5.66732	−	9.81608i	0.212841	−	0.368651i	−0.739762	−	0.672869i	$-0.765062\pi$
$709$	5.66732	−	9.81608i	0.212841	−	0.368651i	0.952602	+	0.304218i	$0.0983952\pi$
$710$	−18.0533	+	31.2692i	−0.677527	+	1.17351i
$711$	13.4663	+	14.0870i	0.505027	+	0.528303i
$712$		−	51.5665i		−	1.93254i
$713$	−11.6221	+	20.1301i	−0.435252	+	0.753878i
$714$	−13.9182	+	43.6555i	−0.520875	+	1.63377i
$715$	−33.7893	−	13.8125i	−1.26365	−	0.516560i
$716$	21.2991	−	12.2971i	0.795986	−	0.459563i
$717$	3.85026	−	0.462851i	0.143790	−	0.0172855i
$718$	18.3026	+	31.7010i	0.683047	+	1.18307i
$719$	−1.24951	+	2.16422i	−0.0465989	+	0.0807116i	−0.888384	−	0.459101i	$-0.848172\pi$
$719$	−1.24951	+	2.16422i	−0.0465989	+	0.0807116i	0.841785	+	0.539813i	$0.181505\pi$
$720$	−58.8177	−	61.5285i	−2.19200	−	2.29303i
$721$	0.777605	+	8.13235i	0.0289595	+	0.302865i
$722$	28.7731	−	16.6122i	1.07083	−	0.618241i
$723$	−6.67506	+	0.802430i	−0.248248	+	0.0298427i
$724$		−	28.7154i		−	1.06720i
$725$	−17.5964	+	10.1593i	−0.653513	+	0.377306i
$726$	0.507877	−	1.18810i	0.0188491	−	0.0440946i
$727$			36.3744i			1.34905i	0.738252	+	0.674525i	$0.235652\pi$
$727$			36.3744i			1.34905i	−0.738252	+	0.674525i	$0.764348\pi$
$728$	−65.6765	−	19.7940i	−2.43413	−	0.733613i
$729$	−20.3373	+	17.7594i	−0.753232	+	0.657755i
$730$	−28.4479			−1.05290
$731$	14.2459	+	24.6747i	0.526905	+	0.912627i
$732$	−30.0827	+	70.3739i	−1.11189	+	2.60110i
$733$	29.3079	−	16.9209i	1.08251	−	0.624990i	0.150940	−	0.988543i	$-0.451770\pi$
$733$	29.3079	−	16.9209i	1.08251	−	0.624990i	0.931573	+	0.363553i	$0.118437\pi$
$734$	1.26045	+	2.18316i	0.0465240	+	0.0805819i
$735$	36.6527	+	7.93887i	1.35196	+	0.292830i
$736$	32.3676			1.19309
$737$	−27.6719	−	15.9764i	−1.01931	−	0.588497i
$738$	72.1870	+	21.0958i	2.65724	+	0.776547i
$739$	−3.22766	−	5.59048i	−0.118732	−	0.205649i	0.800534	−	0.599288i	$-0.204549\pi$
$739$	−3.22766	−	5.59048i	−0.118732	−	0.205649i	−0.919265	+	0.393639i	$0.871216\pi$
$740$	−14.4715	−	25.0654i	−0.531984	−	0.921423i
$741$	−4.13251	+	15.0243i	−0.151811	+	0.551931i
$742$	−16.9240	−	23.7600i	−0.621301	−	0.872257i
$743$	−15.8456	−	9.14848i	−0.581320	−	0.335625i	0.180338	−	0.983605i	$-0.442281\pi$
$743$	−15.8456	−	9.14848i	−0.581320	−	0.335625i	−0.761658	+	0.647979i	$0.775614\pi$
$744$	−77.9342	−	33.3144i	−2.85721	−	1.22137i
$745$			21.3700i			0.782938i
$746$	40.9416	+	23.6377i	1.49898	+	0.865437i
$747$	11.1958	−	2.73124i	0.409634	−	0.0999309i
$748$	51.9219	−	29.9771i	1.89845	−	1.09607i
$749$	−21.7341	−	9.92224i	−0.794147	−	0.362551i
$750$	−5.98110	+	0.719007i	−0.218399	+	0.0262544i
$751$	−45.6216			−1.66476			−0.832378	−	0.554208i	$-0.813021\pi$
$751$	−45.6216			−1.66476			−0.832378	+	0.554208i	$0.813021\pi$
$752$	−14.9789	−	25.9442i	−0.546224	−	0.946088i
$753$	36.0250	−	27.0040i	1.31283	−	0.984079i
$754$	−15.7845	+	38.6134i	−0.574839	+	1.40622i
$755$	−49.9389			−1.81746
$756$	65.3461	+	4.53921i	2.37661	+	0.165089i
$757$	−14.7785	+	25.5971i	−0.537134	+	0.930344i	0.461922	+	0.886920i	$0.347160\pi$
$757$	−14.7785	+	25.5971i	−0.537134	+	0.930344i	−0.999057	+	0.0434237i	$0.986173\pi$
$758$	1.88562	+	1.08866i	0.0684887	+	0.0395420i
$759$	−15.4942	+	11.6143i	−0.562404	+	0.421571i
$760$	55.4971			2.01309
$761$	15.9767	−	27.6725i	0.579155	−	1.00313i	−0.416422	−	0.909172i	$-0.636716\pi$
$761$	15.9767	−	27.6725i	0.579155	−	1.00313i	0.995577	−	0.0939540i	$-0.0299507\pi$
$762$	−30.0107	+	70.2056i	−1.08717	+	2.54328i
$763$	−21.8310	−	30.6490i	−0.790335	−	1.10957i
$764$	46.8898	+	27.0718i	1.69641	+	0.979424i
$765$	−24.6508	−	25.7870i	−0.891253	−	0.932330i
$766$	−11.7008	−	6.75547i	−0.422768	−	0.244085i
$767$	8.56164	−	1.16762i	0.309143	−	0.0421605i
$768$	−3.98373	−	33.1389i	−0.143751	−	1.19580i
$769$	−35.7363	−	20.6324i	−1.28868	−	0.744022i	−0.310264	−	0.950650i	$-0.600418\pi$
$769$	−35.7363	−	20.6324i	−1.28868	−	0.744022i	−0.978420	+	0.206628i	$0.933751\pi$
$770$	−40.4189	−	56.7449i	−1.45660	−	2.04494i
$771$	−2.69620	−	22

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.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.60090i q^{2} +(0.206727 + 1.71967i) q^{3} -4.76468 q^{4} +(1.54658 + 2.67876i) q^{5} +(-4.47269 + 0.537676i) q^{6} +(1.09877 - 2.40680i) q^{7} -7.19066i q^{8} +(-2.91453 + 0.711004i) q^{9} +O(q^{10})\)	\(q+2.60090i q^{2} +(0.206727 + 1.71967i) q^{3} -4.76468 q^{4} +(1.54658 + 2.67876i) q^{5} +(-4.47269 + 0.537676i) q^{6} +(1.09877 - 2.40680i) q^{7} -7.19066i q^{8} +(-2.91453 + 0.711004i) q^{9} +(-6.96719 + 4.02251i) q^{10} +(-2.83459 + 1.63655i) q^{11} +(-0.984988 - 8.19368i) q^{12} +(3.57248 - 0.487210i) q^{13} +(6.25985 + 2.85780i) q^{14} +(-4.28686 + 3.21338i) q^{15} +9.17282 q^{16} +3.84439 q^{17} +(-1.84925 - 7.58040i) q^{18} +(2.16087 + 1.24758i) q^{19} +(-7.36897 - 12.7634i) q^{20} +(4.36605 + 1.39198i) q^{21} +(-4.25650 - 7.37248i) q^{22} -3.41565i q^{23} +(12.3656 - 1.48650i) q^{24} +(-2.28384 + 3.95572i) q^{25} +(1.26718 + 9.29167i) q^{26} +(-1.82520 - 4.86504i) q^{27} +(-5.23531 + 11.4676i) q^{28} +(3.85237 + 2.22417i) q^{29} +(-8.35769 - 11.1497i) q^{30} +(-5.89349 - 3.40261i) q^{31} +9.47627i q^{32} +(-3.40031 - 4.53623i) q^{33} +9.99886i q^{34} +(8.14659 - 0.778966i) q^{35} +(13.8868 - 3.38771i) q^{36} +1.96384 q^{37} +(-3.24483 + 5.62021i) q^{38} +(1.57637 + 6.04277i) q^{39} +(19.2620 - 11.1209i) q^{40} +(-4.81925 + 8.34719i) q^{41} +(-3.62039 + 11.3557i) q^{42} +(3.70565 + 6.41837i) q^{43} +(13.5059 - 7.79764i) q^{44} +(-6.41217 - 6.70769i) q^{45} +8.88377 q^{46} +(-1.63297 - 2.82838i) q^{47} +(1.89627 + 15.7742i) q^{48} +(-4.58539 - 5.28906i) q^{49} +(-10.2884 - 5.94003i) q^{50} +(0.794738 + 6.61107i) q^{51} +(-17.0217 + 2.32140i) q^{52} +(-3.67124 - 2.11959i) q^{53} +(12.6535 - 4.74717i) q^{54} +(-8.76785 - 5.06212i) q^{55} +(-17.3065 - 7.90091i) q^{56} +(-1.69871 + 3.97389i) q^{57} +(-5.78483 + 10.0196i) q^{58} +2.39655 q^{59} +(20.4255 - 15.3107i) q^{60} +(-8.03139 - 4.63693i) q^{61} +(8.84984 - 15.3284i) q^{62} +(-1.49116 + 7.79592i) q^{63} -6.30118 q^{64} +(6.83026 + 8.81631i) q^{65} +(11.7983 - 8.84387i) q^{66} +(4.88111 + 8.45433i) q^{67} -18.3173 q^{68} +(5.87379 - 0.706107i) q^{69} +(2.02601 + 21.1885i) q^{70} +(3.88678 - 2.24403i) q^{71} +(5.11259 + 20.9574i) q^{72} +(3.06234 + 1.76804i) q^{73} +5.10776i q^{74} +(-7.27467 - 3.10969i) q^{75} +(-10.2959 - 5.94432i) q^{76} +(0.824280 + 8.62049i) q^{77} +(-15.7166 + 4.09998i) q^{78} +(-3.24801 - 5.62572i) q^{79} +(14.1865 + 24.5718i) q^{80} +(7.98895 - 4.14448i) q^{81} +(-21.7102 - 12.5344i) q^{82} -3.84139 q^{83} +(-20.8028 - 6.63233i) q^{84} +(5.94566 + 10.2982i) q^{85} +(-16.6935 + 9.63802i) q^{86} +(-3.02844 + 7.08460i) q^{87} +(11.7679 + 20.3825i) q^{88} +7.17132 q^{89} +(17.4460 - 16.6774i) q^{90} +(2.75273 - 9.13359i) q^{91} +16.2745i q^{92} +(4.63302 - 10.8383i) q^{93} +(7.35633 - 4.24718i) q^{94} +7.71794i q^{95} +(-16.2960 + 1.95900i) q^{96} +(10.4630 - 6.04083i) q^{97} +(13.7563 - 11.9261i) q^{98} +(7.09789 - 6.78517i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9}+O(q^{10}) \) 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9	\( 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{12} + 12 q^{13} - 9 q^{15} + 32 q^{16} + 2 q^{18} - 36 q^{19} + 10 q^{21} + 10 q^{22} - 18 q^{24} - 24 q^{25} - 14 q^{28} + 8 q^{30} - 24 q^{31} - 45 q^{33} + 33 q^{39} + 90 q^{40} + 3 q^{42} - 20 q^{43} - 6 q^{48} - 6 q^{49} - 10 q^{51} - 48 q^{52} - 18 q^{55} + 4 q^{57} + 30 q^{58} + 55 q^{60} - 18 q^{61} + 31 q^{63} - 84 q^{64} + 75 q^{66} + 44 q^{67} + 33 q^{69} + 20 q^{70} + 17 q^{72} + 84 q^{73} - 18 q^{76} - 71 q^{78} + 20 q^{79} + 16 q^{81} - 18 q^{82} - 135 q^{84} - 2 q^{85} - 46 q^{88} - 10 q^{91} - 56 q^{93} + 36 q^{94} + 30 q^{96} - 24 q^{97} + 22 q^{99}+O(q^{100}) \) 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^12 + 12 * q^13 - 9 * q^15 + 32 * q^16 + 2 * q^18 - 36 * q^19 + 10 * q^21 + 10 * q^22 - 18 * q^24 - 24 * q^25 - 14 * q^28 + 8 * q^30 - 24 * q^31 - 45 * q^33 + 33 * q^39 + 90 * q^40 + 3 * q^42 - 20 * q^43 - 6 * q^48 - 6 * q^49 - 10 * q^51 - 48 * q^52 - 18 * q^55 + 4 * q^57 + 30 * q^58 + 55 * q^60 - 18 * q^61 + 31 * q^63 - 84 * q^64 + 75 * q^66 + 44 * q^67 + 33 * q^69 + 20 * q^70 + 17 * q^72 + 84 * q^73 - 18 * q^76 - 71 * q^78 + 20 * q^79 + 16 * q^81 - 18 * q^82 - 135 * q^84 - 2 * q^85 - 46 * q^88 - 10 * q^91 - 56 * q^93 + 36 * q^94 + 30 * q^96 - 24 * q^97 + 22 * q^99

Introduction

L-functions

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