LMFDB - Embedded newform 546.2.bw.a.527.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(11,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 7]))

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

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

chi := DirichletCharacter("546.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bw (of order $12$, degree $4$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			527.38
Character	$\chi$	$=$	546.527
Dual form			546.2.bw.a.431.38

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(1.72806 - 0.117493i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.12449 + 4.19664i) q^{5} +(1.69959 + 0.333765i) q^{6} +(-2.63306 + 0.258797i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.97239 - 0.406071i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(1.72806 - 0.117493i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.12449 + 4.19664i) q^{5} +(1.69959 + 0.333765i) q^{6} +(-2.63306 + 0.258797i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.97239 - 0.406071i) q^{9} +4.34468i q^{10} +(-1.35259 - 1.35259i) q^{11} +(1.55529 + 0.762278i) q^{12} +(-0.217387 - 3.59899i) q^{13} +(-2.61033 - 0.431508i) q^{14} +(2.43626 + 7.11992i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.351682 - 0.609132i) q^{17} +(2.97621 + 0.377077i) q^{18} +(-2.51491 - 2.51491i) q^{19} +(-1.12449 + 4.19664i) q^{20} +(-4.51969 + 0.756585i) q^{21} +(-0.956425 - 1.65658i) q^{22} +(0.914210 + 1.58346i) q^{23} +(1.30500 + 1.13884i) q^{24} +(-12.0172 + 6.93811i) q^{25} +(0.721508 - 3.53262i) q^{26} +(5.08876 - 1.05095i) q^{27} +(-2.40970 - 1.09241i) q^{28} +(6.59692 + 3.80874i) q^{29} +(0.510470 + 7.50787i) q^{30} +(1.94735 - 7.26761i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-2.49628 - 2.17844i) q^{33} +(0.497354 - 0.497354i) q^{34} +(-4.04692 - 10.7590i) q^{35} +(2.77720 + 1.13453i) q^{36} +(1.43162 + 0.383602i) q^{37} +(-1.77831 - 3.08012i) q^{38} +(-0.798516 - 6.19374i) q^{39} +(-2.17234 + 3.76260i) q^{40} +(-0.735223 - 2.74389i) q^{41} +(-4.56150 - 0.438977i) q^{42} +(3.30528 - 1.90831i) q^{43} +(-0.495082 - 1.84767i) q^{44} +(5.04654 + 12.0174i) q^{45} +(0.473230 + 1.76612i) q^{46} +(-0.438948 + 0.117616i) q^{47} +(0.965783 + 1.43780i) q^{48} +(6.86605 - 1.36286i) q^{49} +(-13.4034 + 3.59143i) q^{50} +(0.536160 - 1.09394i) q^{51} +(1.61123 - 3.22551i) q^{52} +(6.96361 - 4.02044i) q^{53} +(5.18737 + 0.301928i) q^{54} +(4.15536 - 7.19729i) q^{55} +(-2.04485 - 1.67886i) q^{56} +(-4.64140 - 4.05043i) q^{57} +(5.38637 + 5.38637i) q^{58} +(-6.58533 + 1.76453i) q^{59} +(-1.45010 + 7.38416i) q^{60} +10.3019 q^{61} +(3.76199 - 6.51596i) q^{62} +(-7.72140 + 1.83846i) q^{63} +1.00000i q^{64} +(14.8592 - 4.95931i) q^{65} +(-1.84740 - 2.75029i) q^{66} +(1.89378 + 1.89378i) q^{67} +(0.609132 - 0.351682i) q^{68} +(1.76586 + 2.62890i) q^{69} +(-1.12439 - 11.4398i) q^{70} +(-12.7586 - 3.41866i) q^{71} +(2.38893 + 1.81466i) q^{72} +(-13.7090 - 3.67331i) q^{73} +(1.28356 + 0.741062i) q^{74} +(-19.9512 + 13.4014i) q^{75} +(-0.920521 - 3.43543i) q^{76} +(3.91150 + 3.21141i) q^{77} +(0.831750 - 6.18936i) q^{78} +(-0.155398 + 0.269158i) q^{79} +(-3.07215 + 3.07215i) q^{80} +(8.67021 - 2.41400i) q^{81} -2.84068i q^{82} +(0.970732 - 0.970732i) q^{83} +(-4.29246 - 1.60462i) q^{84} +(2.95177 + 0.790923i) q^{85} +(3.68656 - 0.987812i) q^{86} +(11.8474 + 5.80663i) q^{87} -1.91285i q^{88} +(-3.19161 + 11.9113i) q^{89} +(1.76425 + 12.9141i) q^{90} +(1.50380 + 9.42012i) q^{91} +1.82842i q^{92} +(2.51125 - 12.7877i) q^{93} -0.454432 q^{94} +(7.72618 - 13.3821i) q^{95} +(0.560745 + 1.63877i) q^{96} +(-2.18315 + 8.14762i) q^{97} +(6.98483 + 0.460643i) q^{98} +(-4.56967 - 3.47117i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 12 q^{7}+O(q^{10}) $ 152 * q + 12 * q^7	$ 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	1.72806	−	0.117493i	0.997697	−	0.0678347i
$3$	1.72806	−	0.117493i	0.997697	−	0.0678347i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	1.12449	+	4.19664i	0.502885	+	1.87679i	0.480408	+	0.877045i	$0.340489\pi$
$5$	1.12449	+	4.19664i	0.502885	+	1.87679i	0.0224773	+	0.999747i	$0.492845\pi$
$6$	1.69959	+	0.333765i	0.693854	+	0.136259i
$7$	−2.63306	+	0.258797i	−0.995205	+	0.0978162i
$7$	−2.63306	+	0.258797i	−0.995205	+	0.0978162i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.97239	−	0.406071i	0.990797	−	0.135357i
$10$			4.34468i			1.37391i
$11$	−1.35259	−	1.35259i	−0.407821	−	0.407821i	0.473157	−	0.880978i	$-0.343114\pi$
$11$	−1.35259	−	1.35259i	−0.407821	−	0.407821i	−0.880978	+	0.473157i	$0.843114\pi$
$12$	1.55529	+	0.762278i	0.448974	+	0.220051i
$13$	−0.217387	−	3.59899i	−0.0602924	−	0.998181i
$13$	−0.217387	−	3.59899i	−0.0602924	−	0.998181i
$14$	−2.61033	−	0.431508i	−0.697639	−	0.115325i
$15$	2.43626	+	7.11992i	0.629038	+	1.83836i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.351682	−	0.609132i	0.0852955	−	0.147736i	−0.820222	−	0.572046i	$-0.806150\pi$
$17$	0.351682	−	0.609132i	0.0852955	−	0.147736i	0.905517	+	0.424310i	$0.139483\pi$
$18$	2.97621	+	0.377077i	0.701499	+	0.0888779i
$19$	−2.51491	−	2.51491i	−0.576960	−	0.576960i	0.357105	−	0.934064i	$-0.383764\pi$
$19$	−2.51491	−	2.51491i	−0.576960	−	0.576960i	−0.934064	+	0.357105i	$0.883764\pi$
$20$	−1.12449	+	4.19664i	−0.251443	+	0.938396i
$21$	−4.51969	+	0.756585i	−0.986277	+	0.165100i
$22$	−0.956425	−	1.65658i	−0.203910	−	0.353183i
$23$	0.914210	+	1.58346i	0.190626	+	0.330174i	0.945458	−	0.325744i	$-0.105615\pi$
$23$	0.914210	+	1.58346i	0.190626	+	0.330174i	−0.754832	+	0.655918i	$0.772282\pi$
$24$	1.30500	+	1.13884i	0.266383	+	0.232465i
$25$	−12.0172	+	6.93811i	−2.40343	+	1.38762i
$26$	0.721508	−	3.53262i	0.141499	−	0.692804i
$27$	5.08876	−	1.05095i	0.979333	−	0.202256i
$28$	−2.40970	−	1.09241i	−0.455390	−	0.206445i
$29$	6.59692	+	3.80874i	1.22502	+	0.707265i	0.965984	−	0.258604i	$-0.0832623\pi$
$29$	6.59692	+	3.80874i	1.22502	+	0.707265i	0.259035	+	0.965868i	$0.416596\pi$
$30$	0.510470	+	7.50787i	0.0931987	+	1.37074i
$31$	1.94735	−	7.26761i	0.349754	−	1.30530i	−0.537204	−	0.843452i	$-0.680519\pi$
$31$	1.94735	−	7.26761i	0.349754	−	1.30530i	0.886959	−	0.461849i	$-0.152814\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−2.49628	−	2.17844i	−0.434546	−	0.379217i
$34$	0.497354	−	0.497354i	0.0852955	−	0.0852955i
$35$	−4.04692	−	10.7590i	−0.684054	−	1.81860i
$36$	2.77720	+	1.13453i	0.462867	+	0.189088i
$37$	1.43162	+	0.383602i	0.235357	+	0.0630638i	0.374570	−	0.927199i	$-0.377790\pi$
$37$	1.43162	+	0.383602i	0.235357	+	0.0630638i	−0.139212	+	0.990263i	$0.544457\pi$
$38$	−1.77831	−	3.08012i	−0.288480	−	0.499662i
$39$	−0.798516	−	6.19374i	−0.127865	−	0.991792i
$40$	−2.17234	+	3.76260i	−0.343477	+	0.594919i
$41$	−0.735223	−	2.74389i	−0.114822	−	0.428523i	0.884451	−	0.466633i	$-0.154533\pi$
$41$	−0.735223	−	2.74389i	−0.114822	−	0.428523i	−0.999274	+	0.0381096i	$0.987866\pi$
$42$	−4.56150	−	0.438977i	−0.703855	−	0.0677356i
$43$	3.30528	−	1.90831i	0.504051	−	0.291014i	−0.226334	−	0.974050i	$-0.572674\pi$
$43$	3.30528	−	1.90831i	0.504051	−	0.291014i	0.730385	+	0.683036i	$0.239341\pi$
$44$	−0.495082	−	1.84767i	−0.0746364	−	0.278547i
$45$	5.04654	+	12.0174i	0.752294	+	1.79145i
$46$	0.473230	+	1.76612i	0.0697740	+	0.260400i
$47$	−0.438948	+	0.117616i	−0.0640271	+	0.0171560i	−0.290690	−	0.956817i	$-0.593885\pi$
$47$	−0.438948	+	0.117616i	−0.0640271	+	0.0171560i	0.226663	+	0.973973i	$0.427218\pi$
$48$	0.965783	+	1.43780i	0.139399	+	0.207528i
$49$	6.86605	−	1.36286i	0.980864	−	0.194694i
$50$	−13.4034	+	3.59143i	−1.89553	+	0.507905i
$51$	0.536160	−	1.09394i	0.0750774	−	0.153182i
$52$	1.61123	−	3.22551i	0.223438	−	0.447298i
$53$	6.96361	−	4.02044i	0.956526	−	0.552250i	0.0614236	−	0.998112i	$-0.480436\pi$
$53$	6.96361	−	4.02044i	0.956526	−	0.552250i	0.895102	+	0.445862i	$0.147103\pi$
$54$	5.18737	+	0.301928i	0.705912	+	0.0410871i
$55$	4.15536	−	7.19729i	0.560308	−	0.970482i
$56$	−2.04485	−	1.67886i	−0.273255	−	0.224347i
$57$	−4.64140	−	4.05043i	−0.614769	−	0.536493i
$58$	5.38637	+	5.38637i	0.707265	+	0.707265i
$59$	−6.58533	+	1.76453i	−0.857336	+	0.229723i	−0.660604	−	0.750735i	$-0.729700\pi$
$59$	−6.58533	+	1.76453i	−0.857336	+	0.229723i	−0.196732	+	0.980457i	$0.563033\pi$
$60$	−1.45010	+	7.38416i	−0.187207	+	0.953291i
$61$	10.3019			1.31903			0.659513	−	0.751693i	$-0.270762\pi$
$61$	10.3019			1.31903			0.659513	+	0.751693i	$0.270762\pi$
$62$	3.76199	−	6.51596i	0.477773	−	0.827528i
$63$	−7.72140	+	1.83846i	−0.972805	+	0.231624i
$64$			1.00000i			0.125000i
$65$	14.8592	−	4.95931i	1.84306	−	0.615127i
$66$	−1.84740	−	2.75029i	−0.227399	−	0.338537i
$67$	1.89378	+	1.89378i	0.231362	+	0.231362i	0.813261	−	0.581899i	$-0.197690\pi$
$67$	1.89378	+	1.89378i	0.231362	+	0.231362i	−0.581899	+	0.813261i	$0.697690\pi$
$68$	0.609132	−	0.351682i	0.0738681	−	0.0426478i
$69$	1.76586	+	2.62890i	0.212584	+	0.316482i
$70$	−1.12439	−	11.4398i	−0.134390	−	1.36732i
$71$	−12.7586	−	3.41866i	−1.51417	−	0.405720i	−0.596351	−	0.802724i	$-0.703383\pi$
$71$	−12.7586	−	3.41866i	−1.51417	−	0.405720i	−0.917817	+	0.397004i	$0.870050\pi$
$72$	2.38893	+	1.81466i	0.281538	+	0.213860i
$73$	−13.7090	−	3.67331i	−1.60451	−	0.429928i	−0.658112	−	0.752920i	$-0.728645\pi$
$73$	−13.7090	−	3.67331i	−1.60451	−	0.429928i	−0.946402	+	0.322991i	$0.895312\pi$
$74$	1.28356	+	0.741062i	0.149211	+	0.0861468i
$75$	−19.9512	+	13.4014i	−2.30377	+	1.54746i
$76$	−0.920521	−	3.43543i	−0.105591	−	0.394071i
$77$	3.91150	+	3.21141i	0.445757	+	0.365974i
$78$	0.831750	−	6.18936i	0.0941771	−	0.700807i
$79$	−0.155398	+	0.269158i	−0.0174837	+	0.0302826i	−0.874635	−	0.484782i	$-0.838899\pi$
$79$	−0.155398	+	0.269158i	−0.0174837	+	0.0302826i	0.857151	+	0.515065i	$0.172232\pi$
$80$	−3.07215	+	3.07215i	−0.343477	+	0.343477i
$81$	8.67021	−	2.41400i	0.963357	−	0.268223i
$82$		−	2.84068i		−	0.313701i
$83$	0.970732	−	0.970732i	0.106552	−	0.106552i	−0.651821	−	0.758373i	$-0.725995\pi$
$83$	0.970732	−	0.970732i	0.106552	−	0.106552i	0.758373	+	0.651821i	$0.225995\pi$
$84$	−4.29246	−	1.60462i	−0.468345	−	0.175079i
$85$	2.95177	+	0.790923i	0.320164	+	0.0857877i
$86$	3.68656	−	0.987812i	0.397532	−	0.106518i
$87$	11.8474	+	5.80663i	1.27017	+	0.622537i
$88$		−	1.91285i		−	0.203910i
$89$	−3.19161	+	11.9113i	−0.338310	+	1.26259i	0.561925	+	0.827188i	$0.310061\pi$
$89$	−3.19161	+	11.9113i	−0.338310	+	1.26259i	−0.900235	+	0.435403i	$0.856606\pi$
$90$	1.76425	+	12.9141i	0.185968	+	1.36126i
$91$	1.50380	+	9.42012i	0.157641	+	0.987496i
$92$			1.82842i			0.190626i
$93$	2.51125	−	12.7877i	0.260404	−	1.32602i
$94$	−0.454432			−0.0468711
$95$	7.72618	−	13.3821i	0.792690	−	1.37298i
$96$	0.560745	+	1.63877i	0.0572308	+	0.167256i
$97$	−2.18315	+	8.14762i	−0.221665	+	0.827266i	0.762048	+	0.647521i	$0.224194\pi$
$97$	−2.18315	+	8.14762i	−0.221665	+	0.827266i	−0.983713	+	0.179745i	$0.942473\pi$
$98$	6.98483	+	0.460643i	0.705574	+	0.0465320i
$99$	−4.56967	−	3.47117i	−0.459269	−	0.348866i
$100$	−13.8762			−1.38762
$101$	−16.0093			−1.59299			−0.796493	−	0.604647i	$-0.793314\pi$
$101$	−16.0093			−1.59299			−0.796493	+	0.604647i	$0.793314\pi$
$102$	0.801023	−	0.917894i	0.0793130	−	0.0908850i
$103$	−0.487403	−	0.281403i	−0.0480253	−	0.0277274i	0.475795	−	0.879556i	$-0.342160\pi$
$103$	−0.487403	−	0.281403i	−0.0480253	−	0.0277274i	−0.523820	+	0.851829i	$0.675494\pi$
$104$	2.39116	−	2.69859i	0.234472	−	0.264618i
$105$	−8.25743	−	18.1167i	−0.805843	−	1.76801i
$106$	7.76690	−	2.08113i	0.754388	−	0.202138i
$107$	−9.00024	+	5.19629i	−0.870086	+	0.502345i	−0.867377	−	0.497652i	$-0.834196\pi$
$107$	−9.00024	+	5.19629i	−0.870086	+	0.502345i	−0.00270934	+	0.999996i	$0.500862\pi$
$108$	4.93247	+	1.63423i	0.474627	+	0.157254i
$109$	−2.17796	+	8.12825i	−0.208611	+	0.778546i	0.779708	+	0.626143i	$0.215368\pi$
$109$	−2.17796	+	8.12825i	−0.208611	+	0.778546i	−0.988319	+	0.152402i	$0.951299\pi$
$110$	5.87656	−	5.87656i	0.560308	−	0.560308i
$111$	2.51900	+	0.494682i	0.239093	+	0.0469531i
$112$	−1.54066	−	2.15090i	−0.145578	−	0.203241i
$113$	−12.1496	+	7.01456i	−1.14294	+	0.659874i	−0.947156	−	0.320774i	$-0.896057\pi$
$113$	−12.1496	+	7.01456i	−1.14294	+	0.659874i	−0.195780	+	0.980648i	$0.562724\pi$
$114$	−3.43492	−	5.11370i	−0.321710	−	0.478942i
$115$	−5.61718	+	5.61718i	−0.523805	+	0.523805i
$116$	3.80874	+	6.59692i	0.353632	+	0.612509i
$117$	−2.10761	−	10.6093i	−0.194848	−	0.980833i
$118$	−6.81763			−0.627614
$119$	−0.768361	+	1.69490i	−0.0704355	+	0.155371i
$120$	−3.31185	+	6.75724i	−0.302330	+	0.616849i
$121$		−	7.34101i		−	0.667364i
$122$	9.95090	+	2.66633i	0.900912	+	0.241399i
$123$	−1.59290	−	4.65522i	−0.143627	−	0.419747i
$124$	5.32026	−	5.32026i	0.477773	−	0.477773i
$125$	−27.2691	−	27.2691i	−2.43902	−	2.43902i
$126$	−7.93413	−	0.222633i	−0.706829	−	0.0198337i
$127$	9.30962	+	5.37491i	0.826095	+	0.476946i	0.852514	−	0.522705i	$-0.175077\pi$
$127$	9.30962	+	5.37491i	0.826095	+	0.476946i	−0.0264185	+	0.999651i	$0.508410\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	5.48752	−	3.68602i	0.483149	−	0.324536i
$130$	15.6365	−	0.944478i	1.37141	−	0.0828362i
$131$	−16.3398	−	9.43381i	−1.42762	−	0.824235i	−0.430685	−	0.902502i	$-0.641728\pi$
$131$	−16.3398	−	9.43381i	−1.42762	−	0.824235i	−0.996932	+	0.0782669i	$0.975061\pi$
$132$	−1.07262	−	3.13472i	−0.0933596	−	0.272842i
$133$	7.27277	+	5.97107i	0.630629	+	0.517757i
$134$	1.33911	+	2.31940i	0.115681	+	0.200366i
$135$	10.1327	+	20.1739i	0.872084	+	1.73629i
$136$	0.679398	−	0.182044i	0.0582579	−	0.0156102i
$137$	0.822183	−	0.220303i	0.0702438	−	0.0188218i	−0.223526	−	0.974698i	$-0.571757\pi$
$137$	0.822183	−	0.220303i	0.0702438	−	0.0188218i	0.293770	+	0.955876i	$0.405090\pi$
$138$	1.02528	+	2.99636i	0.0872774	+	0.255067i
$139$	−5.07478	−	8.78979i	−0.430438	−	0.745540i	0.566473	−	0.824080i	$-0.308307\pi$
$139$	−5.07478	−	8.78979i	−0.430438	−	0.745540i	−0.996911	+	0.0785402i	$0.974974\pi$
$140$	1.87476	−	11.3410i	0.158446	−	0.958491i
$141$	−0.744709	+	0.254820i	−0.0627158	+	0.0214598i
$142$	−11.4390	−	6.60434i	−0.959944	−	0.554224i
$143$	−4.57392	+	5.16199i	−0.382490	+	0.431667i
$144$	1.83786	+	2.37113i	0.153155	+	0.197594i
$145$	−8.56573	+	31.9678i	−0.711346	+	2.65478i
$146$	−12.2911	−	7.09629i	−1.01722	−	0.587293i
$147$	11.7048	−	3.16182i	0.965398	−	0.260782i
$148$	1.04802	+	1.04802i	0.0861468	+	0.0861468i
$149$	14.7603	−	14.7603i	1.20921	−	1.20921i	0.237931	−	0.971282i	$-0.423531\pi$
$149$	14.7603	−	14.7603i	1.20921	−	1.20921i	0.971282	−	0.237931i	$-0.0764691\pi$
$150$	−22.7399	+	7.78102i	−1.85671	+	0.635318i
$151$	4.44000	+	1.18969i	0.361322	+	0.0968159i	0.434913	−	0.900473i	$-0.356779\pi$
$151$	4.44000	+	1.18969i	0.361322	+	0.0968159i	−0.0735909	+	0.997289i	$0.523446\pi$
$152$		−	3.55662i		−	0.288480i
$153$	0.797987	−	1.95339i	0.0645134	−	0.157922i
$154$	2.94704	+	4.11435i	0.237480	+	0.331544i
$155$	32.6893			2.62567
$156$	2.40533	−	5.76319i	0.192581	−	0.461425i
$157$	5.46618	+	9.46769i	0.436248	+	0.755604i	0.997397	−	0.0721111i	$-0.0229736\pi$
$157$	5.46618	+	9.46769i	0.436248	+	0.755604i	−0.561148	+	0.827715i	$0.689640\pi$
$158$	−0.219766	+	0.219766i	−0.0174837	+	0.0174837i
$159$	11.5612	−	7.76575i	0.916860	−	0.615864i
$160$	−3.76260	+	2.17234i	−0.297460	+	0.171738i
$161$	−2.81697	−	3.93275i	−0.222008	−	0.309944i
$162$	8.99957	−	0.0877318i	0.707073	−	0.00689286i
$163$	6.59866	−	6.59866i	0.516847	−	0.516847i	−0.399769	−	0.916616i	$-0.630910\pi$
$163$	6.59866	−	6.59866i	0.516847	−	0.516847i	0.916616	+	0.399769i	$0.130910\pi$
$164$	0.735223	−	2.74389i	0.0574112	−	0.214262i
$165$	6.33508	−	12.9256i	0.493185	−	1.00625i
$166$	1.18890	−	0.686411i	0.0922765	−	0.0532759i
$167$	9.37699	−	2.51256i	0.725614	−	0.194428i	0.122939	−	0.992414i	$-0.460768\pi$
$167$	9.37699	−	2.51256i	0.725614	−	0.194428i	0.602675	+	0.797987i	$0.294102\pi$
$168$	−3.73089	−	2.66092i	−0.287844	−	0.205294i
$169$	−12.9055	+	1.56475i	−0.992730	+	0.120365i
$170$	2.64648	+	1.52795i	0.202976	+	0.117188i
$171$	−8.49653	−	6.45406i	−0.649746	−	0.493555i
$172$	3.81661			0.291014
$173$	5.30084			0.403015			0.201508	−	0.979487i	$-0.435416\pi$
$173$	5.30084			0.403015			0.201508	+	0.979487i	$0.435416\pi$
$174$	9.94083	+	8.67511i	0.753613	+	0.657658i
$175$	29.8464	−	21.3785i	2.25617	−	1.61606i
$176$	0.495082	−	1.84767i	0.0373182	−	0.139273i
$177$	−11.1725	+	3.82295i	−0.839778	+	0.287351i
$178$	−6.16573	+	10.6793i	−0.462141	+	0.800451i
$179$	−12.2235			−0.913630			−0.456815	−	0.889562i	$-0.651010\pi$
$179$	−12.2235			−0.913630			−0.456815	+	0.889562i	$0.651010\pi$
$180$	−1.63828	+	12.9307i	−0.122110	+	0.963795i
$181$			0.772809i			0.0574424i	0.999587	+	0.0287212i	$0.00914351\pi$
$181$			0.772809i			0.0574424i	−0.999587	+	0.0287212i	$0.990856\pi$
$182$	−0.985542	+	9.48835i	−0.0730532	+	0.703323i
$183$	17.8024	−	1.21041i	1.31599	−	0.0894758i
$184$	−0.473230	+	1.76612i	−0.0348870	+	0.130200i
$185$			6.43935i			0.473431i
$186$	5.73537	−	11.7020i	0.420538	−	0.858031i
$187$	−1.29959	+	0.348223i	−0.0950352	+	0.0254646i
$188$	−0.438948	−	0.117616i	−0.0320136	−	0.00857801i
$189$	−13.1271	+	4.08418i	−0.954852	+	0.297080i
$190$	10.9265	−	10.9265i	0.792690	−	0.792690i
$191$			12.6770i			0.917274i	0.888624	+	0.458637i	$0.151662\pi$
$191$			12.6770i			0.917274i	−0.888624	+	0.458637i	$0.848338\pi$
$192$	0.117493	+	1.72806i	0.00847934	+	0.124712i
$193$	−1.42433	+	1.42433i	−0.102525	+	0.102525i	−0.756509	−	0.653983i	$-0.773097\pi$
$193$	−1.42433	+	1.42433i	−0.102525	+	0.102525i	0.653983	+	0.756509i	$0.273097\pi$
$194$	−4.21752	+	7.30496i	−0.302800	+	0.524465i
$195$	25.0949	−	10.3158i	1.79709	−	0.738733i
$196$	6.62760	+	2.25275i	0.473400	+	0.160911i
$197$	1.77065	+	6.60816i	0.126154	+	0.470812i	0.999878	−	0.0156093i	$-0.00496879\pi$
$197$	1.77065	+	6.60816i	0.126154	+	0.470812i	−0.873725	+	0.486421i	$0.838302\pi$
$198$	−3.51555	−	4.53561i	−0.249840	−	0.322332i
$199$	−17.7513	−	10.2487i	−1.25836	−	0.726513i	−0.285602	−	0.958348i	$-0.592194\pi$
$199$	−17.7513	−	10.2487i	−1.25836	−	0.726513i	−0.972755	+	0.231835i	$0.925527\pi$
$200$	−13.4034	−	3.59143i	−0.947763	−	0.253952i
$201$	3.49508	+	3.05007i	0.246524	+	0.215135i
$202$	−15.4638	−	4.14352i	−1.08803	−	0.291537i
$203$	−18.3558	−	8.32138i	−1.28833	−	0.584046i
$204$	1.01130	−	0.679298i	0.0708049	−	0.0475603i
$205$	10.6884	−	6.17092i	0.746507	−	0.430996i
$206$	−0.397963	−	0.397963i	−0.0277274	−	0.0277274i
$207$	3.36039	+	4.33542i	0.233563	+	0.301333i
$208$	3.00812	−	1.98776i	0.208576	−	0.137826i
$209$			6.80328i			0.470593i
$210$	−3.28712	−	19.6366i	−0.226833	−	1.35505i
$211$	−6.47471	+	11.2145i	−0.445737	+	0.772040i	−0.998103	−	0.0615620i	$-0.980392\pi$
$211$	−6.47471	+	11.2145i	−0.445737	+	0.772040i	0.552366	+	0.833602i	$0.313725\pi$
$212$	8.04089			0.552250
$213$	−22.4493	−	4.40860i	−1.53820	−	0.302072i
$214$	−10.0385	+	2.68980i	−0.686215	+	0.183871i
$215$	11.7252	+	11.7252i	0.799652	+	0.799652i
$216$	4.34143	+	2.85516i	0.295397	+	0.194269i
$217$	−3.24666	+	19.6401i	−0.220398	+	1.33325i
$218$	−4.20749	+	7.28759i	−0.284967	+	0.493578i
$219$	−24.1215	−	4.73699i	−1.62998	−	0.320096i
$220$	7.19729	−	4.15536i	0.485241	−	0.280154i
$221$	−2.26871	−	1.13328i	−0.152610	−	0.0762330i
$222$	2.30514	+	1.12979i	0.154711	+	0.0758267i
$223$	−11.0922	+	2.97214i	−0.742788	+	0.199029i	−0.610317	−	0.792157i	$-0.708958\pi$
$223$	−11.0922	+	2.97214i	−0.742788	+	0.199029i	−0.132471	+	0.991187i	$0.542291\pi$
$224$	−0.931466	−	2.47636i	−0.0622362	−	0.165459i
$225$	−32.9023	+	25.5026i	−2.19349	+	1.70017i
$226$	−13.5511	+	3.63100i	−0.901405	+	0.241531i
$227$	−1.90921	−	7.12528i	−0.126719	−	0.472922i	0.873176	−	0.487405i	$-0.162056\pi$
$227$	−1.90921	−	7.12528i	−0.126719	−	0.472922i	−0.999895	+	0.0144831i	$0.995390\pi$
$228$	−1.99436	−	5.82848i	−0.132079	−	0.386001i
$229$	3.77001	+	14.0699i	0.249129	+	0.929762i	0.971263	+	0.238009i	$0.0764948\pi$
$229$	3.77001	+	14.0699i	0.249129	+	0.929762i	−0.722134	+	0.691753i	$0.756839\pi$
$230$	−6.87962	+	3.97195i	−0.453628	+	0.261903i
$231$	7.13663	+	5.08993i	0.469556	+	0.334893i
$232$	1.97155	+	7.35791i	0.129438	+	0.483071i
$233$	11.3337	−	19.6305i	0.742493	−	1.28603i	−0.208865	−	0.977945i	$-0.566977\pi$
$233$	11.3337	−	19.6305i	0.742493	−	1.28603i	0.951357	−	0.308090i	$-0.0996899\pi$
$234$	0.710107	−	10.7933i	0.0464211	−	0.705581i
$235$	−0.987180	−	1.70985i	−0.0643965	−	0.111538i
$236$	−6.58533	−	1.76453i	−0.428668	−	0.114861i
$237$	−0.236913	+	0.483379i	−0.0153892	+	0.0313989i
$238$	−1.18085	+	1.43828i	−0.0765432	+	0.0932298i
$239$	3.33310	−	3.33310i	0.215600	−	0.215600i	−0.591041	−	0.806641i	$-0.701283\pi$
$239$	3.33310	−	3.33310i	0.215600	−	0.215600i	0.806641	+	0.591041i	$0.201283\pi$
$240$	−4.94791	+	5.66982i	−0.319386	+	0.365985i
$241$	−2.72052	−	10.1531i	−0.175244	−	0.654019i	−0.996510	−	0.0834739i	$-0.973398\pi$
$241$	−2.72052	−	10.1531i	−0.175244	−	0.654019i	0.821266	−	0.570546i	$-0.193268\pi$
$242$	1.89999	−	7.09087i	0.122136	−	0.455818i
$243$	14.6990	−	5.19024i	0.942943	−	0.332954i
$244$	8.92173	+	5.15096i	0.571155	+	0.329757i
$245$	13.4402	+	27.2818i	0.858662	+	1.74297i
$246$	−0.333761	−	4.90887i	−0.0212798	−	0.312978i
$247$	−8.50443	+	9.59785i	−0.541124	+	0.610697i
$248$	6.51596	−	3.76199i	0.413764	−	0.238887i
$249$	1.56343	−	1.79154i	0.0990784	−	0.113534i
$250$	−19.2822	−	33.3977i	−1.21951	−	2.11225i
$251$	−4.52381	−	7.83547i	−0.285540	−	0.494570i	0.687200	−	0.726468i	$-0.258840\pi$
$251$	−4.52381	−	7.83547i	−0.285540	−	0.494570i	−0.972740	+	0.231898i	$0.925506\pi$
$252$	−7.60616	−	2.26855i	−0.479143	−	0.142905i
$253$	0.905218	−	3.37832i	0.0569105	−	0.212393i
$254$	7.60127	+	7.60127i	0.476946	+	0.476946i
$255$	5.19376	+	1.01995i	0.325246	+	0.0638718i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.86346	+	11.8879i	0.428131	+	0.741544i	0.996707	−	0.0810865i	$-0.0258390\pi$
$257$	6.86346	+	11.8879i	0.428131	+	0.741544i	−0.568576	+	0.822630i	$0.692506\pi$
$258$	6.25454	−	2.14014i	0.389391	−	0.133240i
$259$	−3.86883	−	0.639549i	−0.240397	−	0.0397396i
$260$	15.3481	+	3.13472i	0.951849	+	0.194407i
$261$	21.1553	+	8.64223i	1.30948	+	0.534941i
$262$	−13.3414	−	13.3414i	−0.824235	−	0.824235i
$263$			22.3462i			1.37793i	0.724796	+	0.688963i	$0.241934\pi$
$263$			22.3462i			1.37793i	−0.724796	+	0.688963i	$0.758066\pi$
$264$	−0.224747	−	3.30552i	−0.0138322	−	0.203441i
$265$	24.7028	+	24.7028i	1.51748	+	1.51748i
$266$	5.47953	+	7.64994i	0.335972	+	0.469048i
$267$	−4.11581	+	20.9584i	−0.251884	+	1.28263i
$268$	0.693173	+	2.58696i	0.0423423	+	0.158023i
$269$	−23.1251	−	13.3513i	−1.40996	−	0.814041i	−0.414576	−	0.910014i	$-0.636070\pi$
$269$	−23.1251	−	13.3513i	−1.40996	−	0.814041i	−0.995384	+	0.0959735i	$0.969404\pi$
$270$	4.56604	+	22.1090i	0.277881	+	1.34551i
$271$	21.5953	+	5.78645i	1.31182	+	0.351502i	0.845909	−	0.533328i	$-0.179059\pi$
$271$	21.5953	+	5.78645i	1.31182	+	0.351502i	0.465914	+	0.884830i	$0.345725\pi$
$272$	0.703365			0.0426478
$273$	3.70546	+	16.1018i	0.224265	+	0.974528i
$274$	0.851187			0.0514221
$275$	25.6387	+	6.86986i	1.54607	+	0.414268i
$276$	0.214827	+	3.15962i	0.0129311	+	0.190187i
$277$	−18.1674	−	10.4889i	−1.09157	−	0.630219i	−0.157577	−	0.987507i	$-0.550368\pi$
$277$	−18.1674	−	10.4889i	−1.09157	−	0.630219i	−0.933995	+	0.357287i	$0.883702\pi$
$278$	−2.62690	−	9.80373i	−0.157551	−	0.587989i
$279$	2.83712	−	22.3929i	0.169854	−	1.34063i
$280$	4.74616	−	10.4694i	0.283637	−	0.625664i
$281$	7.69733	+	7.69733i	0.459184	+	0.459184i	0.898388	−	0.439203i	$-0.144739\pi$
$281$	7.69733	+	7.69733i	0.459184	+	0.459184i	−0.439203	+	0.898388i	$0.644739\pi$
$282$	−0.785286	+	0.0533927i	−0.0467631	+	0.00317949i
$283$		−	13.9199i		−	0.827453i	−0.910401	−	0.413726i	$-0.864227\pi$
$283$		−	13.9199i		−	0.827453i	0.910401	−	0.413726i	$-0.135773\pi$
$284$	−9.33994	−	9.33994i	−0.554224	−	0.554224i
$285$	11.7790	−	24.0329i	0.697728	−	1.42359i
$286$	−5.75409	+	3.80228i	−0.340246	+	0.224834i
$287$	2.64600	+	7.03456i	0.156188	+	0.415237i
$288$	1.16155	+	2.76601i	0.0684447	+	0.162989i
$289$	8.25264	+	14.2940i	0.485449	+	0.840823i
$290$	−16.5477	+	28.6615i	−0.971716	+	1.68306i
$291$	−2.81532	+	14.3361i	−0.165037	+	0.840397i
$292$	−10.0357	−	10.0357i	−0.587293	−	0.587293i
$293$	−3.30757	+	12.3440i	−0.193230	+	0.721145i	0.799488	+	0.600682i	$0.205104\pi$
$293$	−3.30757	+	12.3440i	−0.193230	+	0.721145i	−0.992718	+	0.120462i	$0.961562\pi$
$294$	12.1243	−	0.0246502i	0.707105	−	0.00143763i
$295$	−14.8102	−	25.6520i	−0.862283	−	1.49352i
$296$	0.741062	+	1.28356i	0.0430734	+	0.0746053i
$297$	−8.30451	−	5.46150i	−0.481876	−	0.316908i
$298$	18.0776	−	10.4371i	1.04721	−	0.604606i
$299$	5.50012	−	3.63446i	0.318080	−	0.210186i
$300$	−23.9790	+	1.63036i	−1.38443	+	0.0941290i
$301$	−8.20915	+	5.88009i	−0.473168	+	0.338923i
$302$	3.98079	+	2.29831i	0.229069	+	0.132253i
$303$	−27.6651	+	1.88099i	−1.58932	+	0.108060i
$304$	0.920521	−	3.43543i	0.0527955	−	0.197035i
$305$	11.5844	+	43.2334i	0.663319	+	2.47554i
$306$	1.27637	−	1.68029i	0.0729652	−	0.0960559i
$307$	14.4885	−	14.4885i	0.826902	−	0.826902i	−0.160185	−	0.987087i	$-0.551209\pi$
$307$	14.4885	−	14.4885i	0.826902	−	0.826902i	0.987087	+	0.160185i	$0.0512092\pi$
$308$	1.78175	+	4.73691i	0.101525	+	0.269910i
$309$	−0.875326	−	0.429014i	−0.0497956	−	0.0244058i
$310$	31.5754	+	8.46061i	1.79336	+	0.480530i
$311$	13.5468	+	23.4638i	0.768170	+	1.33051i	0.938554	+	0.345132i	$0.112166\pi$
$311$	13.5468	+	23.4638i	0.768170	+	1.33051i	−0.170384	+	0.985378i	$0.554501\pi$
$312$	3.81500	−	4.94427i	0.215982	−	0.279914i
$313$	0.0972614	−	0.168462i	0.00549754	−	0.00952202i	−0.863264	−	0.504753i	$-0.831583\pi$
$313$	0.0972614	−	0.168462i	0.00549754	−	0.00952202i	0.868761	+	0.495231i	$0.164917\pi$
$314$	2.82950	+	10.5598i	0.159678	+	0.595926i
$315$	−16.3979	−	30.3366i	−0.923919	−	1.70927i
$316$	−0.269158	+	0.155398i	−0.0151413	+	0.00874184i
$317$	2.25773	+	8.42596i	0.126807	+	0.473249i	0.999898	−	0.0143085i	$-0.00455468\pi$
$317$	2.25773	+	8.42596i	0.126807	+	0.473249i	−0.873091	+	0.487557i	$0.837888\pi$
$318$	13.1772	−	4.50889i	0.738938	−	0.252846i
$319$	−3.77127	−	14.0746i	−0.211151	−	0.788025i
$320$	−4.19664	+	1.12449i	−0.234599	+	0.0628606i
$321$	−14.9424	+	10.0370i	−0.834006	+	0.560209i
$322$	−1.70311	−	4.52783i	−0.0949107	−	0.252326i
$323$	−2.41636	+	0.647462i	−0.134450	+	0.0360258i
$324$	8.71563	+	2.24452i	0.484201	+	0.124695i
$325$	27.5826	+	41.7414i	1.53001	+	2.31540i
$326$	8.08167	−	4.66596i	0.447602	−	0.258423i
$327$	−2.80863	+	14.3020i	−0.155318	+	0.790903i
$328$	1.42034	−	2.46010i	0.0784252	−	0.135836i
$329$	1.12534	−	0.423288i	0.0620419	−	0.0233366i
$330$	9.46460	−	10.8455i	0.521009	−	0.597026i
$331$	20.3694	+	20.3694i	1.11961	+	1.11961i	0.991799	+	0.127807i	$0.0407937\pi$
$331$	20.3694	+	20.3694i	1.11961	+	1.11961i	0.127807	+	0.991799i	$0.459206\pi$
$332$	1.32604	−	0.355313i	0.0727762	−	0.0195003i
$333$	4.41111	+	0.558875i	0.241727	+	0.0306262i
$334$	9.70778			0.531186
$335$	−5.81799	+	10.0770i	−0.317871	+	0.550568i
$336$	−2.91507	−	3.53587i	−0.159030	−	0.192898i
$337$		−	1.00336i		−	0.0546566i	−0.999627	−	0.0273283i	$-0.991300\pi$
$337$		−	1.00336i		−	0.0546566i	0.999627	−	0.0273283i	$-0.00869995\pi$
$338$	−12.8707	−	1.82875i	−0.700075	−	0.0994710i
$339$	−20.1710	+	13.5491i	−1.09554	+	0.735885i
$340$	2.16084	+	2.16084i	0.117188	+	0.117188i
$341$	−12.4641	+	7.19612i	−0.674966	+	0.389692i
$342$	−6.53658	−	8.43321i	−0.353458	−	0.456016i
$343$	−17.7260	+	5.36541i	−0.957116	+	0.289705i
$344$	3.68656	+	0.987812i	0.198766	+	0.0532592i
$345$	−9.04686	+	10.3668i	−0.487066	+	0.558131i
$346$	5.12022	+	1.37196i	0.275265	+	0.0737569i
$347$	20.9701	+	12.1071i	1.12574	+	0.649944i	0.942859	−	0.333192i	$-0.108126\pi$
$347$	20.9701	+	12.1071i	1.12574	+	0.649944i	0.182877	+	0.983136i	$0.441459\pi$
$348$	7.35682	+	10.9524i	0.394367	+	0.587110i
$349$	−1.03946	−	3.87933i	−0.0556411	−	0.207656i	0.932509	−	0.361147i	$-0.117615\pi$
$349$	−1.03946	−	3.87933i	−0.0556411	−	0.207656i	−0.988150	+	0.153492i	$0.950948\pi$
$350$	34.3625	−	12.9252i	1.83676	−	0.690882i
$351$	−4.88860	−	18.0860i	−0.260934	−	0.965357i
$352$	0.956425	−	1.65658i	0.0509776	−	0.0882958i
$353$	−9.93251	+	9.93251i	−0.528654	+	0.528654i	−0.920171	−	0.391517i	$-0.871950\pi$
$353$	−9.93251	+	9.93251i	−0.528654	+	0.528654i	0.391517	+	0.920171i	$0.371950\pi$
$354$	−11.7813	+	0.801025i	−0.626168	+	0.0425740i
$355$		−	57.3874i		−	3.04581i
$356$	−8.71965	+	8.71965i	−0.462141	+	0.462141i
$357$	−1.12864	+	3.01916i	−0.0597337	+	0.159791i
$358$	−11.8070	−	3.16368i	−0.624021	−	0.167206i
$359$	14.7324	−	3.94752i	0.777544	−	0.208342i	0.151843	−	0.988405i	$-0.451479\pi$
$359$	14.7324	−	3.94752i	0.777544	−	0.208342i	0.625702	+	0.780062i	$0.284813\pi$
$360$	−4.92916	+	12.0660i	−0.259789	+	0.635936i
$361$		−	6.35046i		−	0.334234i
$362$	−0.200018	+	0.746476i	−0.0105127	+	0.0392339i
$363$	−0.862519	−	12.6857i	−0.0452705	−	0.665827i
$364$	−3.40773	+	8.90996i	−0.178613	+	0.467009i
$365$		−	61.6622i		−	3.22755i
$366$	17.5090	+	3.43843i	0.915212	+	0.179729i
$367$	19.0750			0.995707			0.497853	−	0.867261i	$-0.334122\pi$
$367$	19.0750			0.995707			0.497853	+	0.867261i	$0.334122\pi$
$368$	−0.914210	+	1.58346i	−0.0476565	+	0.0825435i
$369$	−3.29958	−	7.85735i	−0.171769	−	0.409038i
$370$	−1.66663	+	6.21994i	−0.0866438	+	0.323359i
$371$	−17.2952	+	12.3882i	−0.897920	+	0.643166i
$372$	8.56864	−	9.81883i	0.444263	−	0.509083i
$373$	−20.6207			−1.06770			−0.533851	−	0.845579i	$-0.679256\pi$
$373$	−20.6207			−1.06770			−0.533851	+	0.845579i	$0.679256\pi$
$374$	−1.34543			−0.0695706
$375$	−50.3266	−	43.9187i	−2.59885	−	2.26795i
$376$	−0.393550	−	0.227216i	−0.0202958	−	0.0117178i
$377$	12.2735	−	24.5702i	0.632119	−	1.26543i
$378$	−13.7368	+	0.547483i	−0.706546	+	0.0281595i
$379$	28.8905	−	7.74120i	1.48401	−	0.397639i	0.576299	−	0.817239i	$-0.304496\pi$
$379$	28.8905	−	7.74120i	1.48401	−	0.397639i	0.907709	+	0.419600i	$0.137830\pi$
$380$	13.3821	−	7.72618i	0.686489	−	0.396345i
$381$	16.7191	+	8.19436i	0.856546	+	0.419810i
$382$	−3.28104	+	12.2450i	−0.167873	+	0.626510i
$383$	19.2054	−	19.2054i	0.981351	−	0.981351i	−0.0184784	−	0.999829i	$-0.505882\pi$
$383$	19.2054	−	19.2054i	0.981351	−	0.981351i	0.999829	+	0.0184784i	$0.00588218\pi$
$384$	−0.333765	+	1.69959i	−0.0170324	+	0.0867318i
$385$	−9.07868	+	20.0263i	−0.462692	+	1.02064i
$386$	−1.74444	+	1.00715i	−0.0887895	+	0.0512627i
$387$	9.04968	−	7.01441i	0.460021	−	0.356562i
$388$	−5.96447	+	5.96447i	−0.302800	+	0.302800i
$389$	3.66874	+	6.35444i	0.186012	+	0.322183i	0.943917	−	0.330182i	$-0.107110\pi$
$389$	3.66874	+	6.35444i	0.186012	+	0.322183i	−0.757905	+	0.652365i	$0.773777\pi$
$390$	26.9098	−	3.46929i	1.36263	−	0.175675i
$391$	1.28605			0.0650382
$392$	5.81872	+	3.89134i	0.293890	+	0.196542i
$393$	−29.3446	−	14.3824i	−1.48024	−	0.725495i
$394$			6.84127i			0.344658i
$395$	−1.30430	−	0.349486i	−0.0656264	−	0.0175846i
$396$	−2.22186	−	5.29096i	−0.111653	−	0.265881i
$397$	−3.98862	+	3.98862i	−0.200183	+	0.200183i	−0.800078	−	0.599895i	$-0.795209\pi$
$397$	−3.98862	+	3.98862i	−0.200183	+	0.200183i	0.599895	+	0.800078i	$0.295209\pi$
$398$	−14.4939	−	14.4939i	−0.726513	−	0.726513i
$399$	13.2694	+	9.46387i	0.664298	+	0.473786i
$400$	−12.0172	−	6.93811i	−0.600858	−	0.346905i
$401$	3.99356	−	14.9042i	0.199429	−	0.744278i	−0.791647	−	0.610979i	$-0.790776\pi$
$401$	3.99356	−	14.9042i	0.199429	−	0.744278i	0.991076	−	0.133300i	$-0.0425573\pi$
$402$	2.58657	+	3.85073i	0.129006	+	0.192057i
$403$	−26.5794	−	5.42861i	−1.32401	−	0.270418i
$404$	−13.8645	−	8.00466i	−0.689783	−	0.398247i
$405$	19.8802	+	33.6712i	0.987856	+	1.67314i
$406$	−15.5766	−	12.7887i	−0.773055	−	0.634691i
$407$	−1.41754	−	2.45525i	−0.0702649	−	0.121702i
$408$	1.15265	−	0.394408i	0.0570648	−	0.0195261i
$409$	−0.0271377	+	0.00727153i	−0.00134187	+	0.000359554i	−0.259490	−	0.965746i	$-0.583554\pi$
$409$	−0.0271377	+	0.00727153i	−0.00134187	+	0.000359554i	0.258148	+	0.966105i	$0.416888\pi$
$410$	11.9213	−	3.19430i	0.588751	−	0.157755i
$411$	1.39490	−	0.477299i	0.0688053	−	0.0235434i
$412$	−0.281403	−	0.487403i	−0.0138637	−	0.0240126i
$413$	16.8829	−	6.35039i	0.830754	−	0.312482i
$414$	2.12379	+	5.05743i	0.104379	+	0.248559i
$415$	5.16538	+	2.98224i	0.253559	+	0.146392i
$416$	3.42010	−	1.14147i	0.167684	−	0.0559651i
$417$	−9.80228	−	14.5930i	−0.480020	−	0.714624i
$418$	−1.76082	+	6.57146i	−0.0861244	+	0.321421i
$419$	9.40071	+	5.42750i	0.459255	+	0.265151i	0.711731	−	0.702452i	$-0.247912\pi$
$419$	9.40071	+	5.42750i	0.459255	+	0.265151i	−0.252476	+	0.967603i	$0.581245\pi$
$420$	1.90721	−	19.8183i	0.0930624	−	0.967032i
$421$	15.2184	+	15.2184i	0.741700	+	0.741700i	0.972905	−	0.231205i	$-0.0742668\pi$
$421$	15.2184	+	15.2184i	0.741700	+	0.741700i	−0.231205	+	0.972905i	$0.574267\pi$
$422$	−9.15662	+	9.15662i	−0.445737	+	0.445737i
$423$	−1.25696	+	0.527844i	−0.0611157	+	0.0256646i
$424$	7.76690	+	2.08113i	0.377194	+	0.101069i
$425$			9.76005i			0.473432i
$426$	−20.5433	−	10.0687i	−0.995328	−	0.487830i
$427$	−27.1256	+	2.66611i	−1.31270	+	0.129022i
$428$	−10.3926			−0.502345
$429$	−7.29751	+	9.45764i	−0.352327	+	0.456619i
$430$	8.29097	+	14.3604i	0.399826	+	0.692519i
$431$	17.0428	−	17.0428i	0.820924	−	0.820924i	−0.165316	−	0.986241i	$-0.552864\pi$
$431$	17.0428	−	17.0428i	0.820924	−	0.820924i	0.986241	+	0.165316i	$0.0528645\pi$
$432$	3.45453	+	3.88152i	0.166206	+	0.186750i
$433$	−2.73877	+	1.58123i	−0.131617	+	0.0759891i	−0.564363	−	0.825527i	$-0.690878\pi$
$433$	−2.73877	+	1.58123i	−0.131617	+	0.0759891i	0.432746	+	0.901516i	$0.357545\pi$
$434$	−8.21925	+	18.1305i	−0.394537	+	0.870294i
$435$	−11.0461	+	56.2487i	−0.529621	+	2.69692i
$436$	−5.95029	+	5.95029i	−0.284967	+	0.284967i
$437$	1.68310	−	6.28141i	0.0805136	−	0.300481i
$438$	−22.0736	−	10.8187i	−1.05472	−	0.516937i
$439$	−14.7347	+	8.50708i	−0.703249	+	0.406021i	−0.808556	−	0.588419i	$-0.799751\pi$
$439$	−14.7347	+	8.50708i	−0.703249	+	0.406021i	0.105307	+	0.994440i	$0.466417\pi$
$440$	8.02753	−	2.15097i	0.382698	−	0.102543i
$441$	19.8552	−	6.83905i	0.945484	−	0.325669i
$442$	−1.89809	−	1.68185i	−0.0902830	−	0.0799977i
$443$	4.31236	+	2.48974i	0.204886	+	0.118291i	0.598933	−	0.800799i	$-0.295592\pi$
$443$	4.31236	+	2.48974i	0.204886	+	0.118291i	−0.394046	+	0.919091i	$0.628925\pi$
$444$	1.93418	+	1.68791i	0.0917921	+	0.0801046i
$445$	−53.5762			−2.53975
$446$	−11.4835			−0.543759
$447$	23.7725	−	27.2410i	1.12440	−	1.28845i
$448$	−0.258797	−	2.63306i	−0.0122270	−	0.124401i
$449$	−8.91938	+	33.2876i	−0.420932	+	1.57094i	0.351718	+	0.936106i	$0.385598\pi$
$449$	−8.91938	+	33.2876i	−0.420932	+	1.57094i	−0.772650	+	0.634832i	$0.781069\pi$
$450$	−38.3818	+	16.1179i	−1.80933	+	0.759803i
$451$	−2.71690	+	4.70580i	−0.127934	+	0.221588i
$452$	−14.0291			−0.659874
$453$	7.81237	+	1.53419i	0.367057	+	0.0720827i
$454$		−	7.37664i		−	0.346203i
$455$	−37.8418	+	16.9037i	−1.77405	+	0.792458i
$456$	−0.417879	−	6.14606i	−0.0195690	−	0.287815i
$457$	−0.510419	+	1.90491i	−0.0238764	+	0.0891079i	−0.976836	−	0.213990i	$-0.931354\pi$
$457$	−0.510419	+	1.90491i	−0.0238764	+	0.0891079i	0.952960	+	0.303098i	$0.0980208\pi$
$458$			14.5662i			0.680633i
$459$	1.14946	−	3.46933i	0.0536522	−	0.161934i
$460$	−7.67322	+	2.05603i	−0.357766	+	0.0958630i
$461$	13.1727	+	3.52962i	0.613515	+	0.164391i	0.552178	−	0.833726i	$-0.313797\pi$
$461$	13.1727	+	3.52962i	0.613515	+	0.164391i	0.0613369	+	0.998117i	$0.480464\pi$
$462$	5.57608	+	6.76359i	0.259423	+	0.314671i
$463$	5.51839	−	5.51839i	0.256461	−	0.256461i	−0.567152	−	0.823613i	$-0.691955\pi$
$463$	5.51839	−	5.51839i	0.256461	−	0.256461i	0.823613	+	0.567152i	$0.191955\pi$
$464$			7.61747i			0.353632i
$465$	56.4891	−	3.84077i	2.61962	−	0.178111i
$466$	16.0282	−	16.0282i	0.742493	−	0.742493i
$467$	−7.36371	+	12.7543i	−0.340752	+	0.590200i	−0.984573	−	0.174977i	$-0.944015\pi$
$467$	−7.36371	+	12.7543i	−0.340752	+	0.590200i	0.643821	+	0.765177i	$0.277348\pi$
$468$	3.47943	−	10.2418i	0.160837	−	0.473425i
$469$	−5.47656	−	4.49635i	−0.252884	−	0.207622i
$470$	−0.511002	−	1.90709i	−0.0235708	−	0.0879673i
$471$	10.5583	+	15.7185i	0.486500	+	0.724271i
$472$	−5.90424	−	3.40882i	−0.271765	−	0.156903i
$473$	−7.05184	−	1.88953i	−0.324244	−	0.0868809i
$474$	−0.353949	+	0.405591i	−0.0162574	+	0.0186294i
$475$	47.6708	+	12.7734i	2.18729	+	0.586082i
$476$	−1.51287	+	1.08364i	−0.0693422	+	0.0496687i
$477$	19.0660	−	14.7780i	0.872972	−	0.676640i
$478$	4.08220	−	2.35686i	0.186715	−	0.107800i
$479$	−12.1470	−	12.1470i	−0.555009	−	0.555009i	0.372874	−	0.927882i	$-0.378373\pi$
$479$	−12.1470	−	12.1470i	−0.555009	−	0.555009i	−0.927882	+	0.372874i	$0.878373\pi$
$480$	−6.24677	+	4.19601i	−0.285125	+	0.191521i
$481$	1.06936	−	5.23579i	0.0487588	−	0.238731i
$482$		−	10.5113i		−	0.478775i
$483$	−5.32997	−	6.46506i	−0.242522	−	0.294170i
$484$	3.67050	−	6.35750i	0.166841	−	0.288977i
$485$	−36.6475			−1.66408
$486$	15.5415	−	1.20899i	0.704977	−	0.0548411i
$487$	12.6766	−	3.39668i	0.574431	−	0.153918i	0.0401029	−	0.999196i	$-0.487231\pi$
$487$	12.6766	−	3.39668i	0.574431	−	0.153918i	0.534328	+	0.845277i	$0.320565\pi$
$488$	7.28456	+	7.28456i	0.329757	+	0.329757i
$489$	10.6276	−	12.1782i	0.480596	−	0.550716i
$490$	5.92118	+	29.8308i	0.267492	+	1.34762i
$491$	3.28493	−	5.68966i	0.148247	−	0.256771i	−0.782333	−	0.622861i	$-0.785970\pi$
$491$	3.28493	−	5.68966i	0.148247	−	0.256771i	0.930579	+	0.366090i	$0.119304\pi$
$492$	0.948121	−	4.82799i	0.0427446	−	0.217663i
$493$	4.64004	−	2.67893i	0.208977	−	0.120653i
$494$	−10.6988	+	7.06970i	−0.481360	+	0.318081i
$495$	9.42873	−	23.0805i	0.423790	−	1.03739i
$496$	7.26761	−	1.94735i	0.326325	−	0.0874386i
$497$	34.4789	+	5.69965i	1.54659	+	0.255664i
$498$	1.97384	−	1.32585i	0.0884500	−	0.0594127i
$499$	−33.9764	+	9.10395i	−1.52099	+	0.407549i	−0.920069	−	0.391757i	$-0.871867\pi$
$499$	−33.9764	+	9.10395i	−1.52099	+	0.407549i	−0.600925	+	0.799306i	$0.705201\pi$
$500$	−9.98118	−	37.2503i	−0.446372	−	1.66588i
$501$	15.9088	−	5.44359i	0.710753	−	0.243202i
$502$	−2.34170	−	8.73933i	−0.104515	−	0.390055i
$503$	−16.1705	+	9.33603i	−0.721006	+	0.416273i	−0.815123	−	0.579288i	$-0.803331\pi$
$503$	−16.1705	+	9.33603i	−0.721006	+	0.416273i	0.0941167	+	0.995561i	$0.469997\pi$
$504$	−6.75984	−	4.15987i	−0.301107	−	0.185295i
$505$	−18.0022	−	67.1853i	−0.801089	−	2.98971i
$506$	1.74875	−	3.02892i	0.0777413	−	0.134652i
$507$	−22.1176	+	4.22029i	−0.982278	+	0.187430i
$508$	5.37491	+	9.30962i	0.238473	+	0.413048i
$509$	−27.2472	−	7.30085i	−1.20771	−	0.323605i	−0.401846	−	0.915707i	$-0.631631\pi$
$509$	−27.2472	−	7.30085i	−1.20771	−	0.323605i	−0.805863	+	0.592103i	$0.798298\pi$
$510$	4.75280	+	2.32944i	0.210458	+	0.103149i
$511$	37.0472	+	6.12421i	1.63887	+	0.270919i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−15.4408	−	10.1547i	−0.681729	−	0.448342i
$514$	3.55279	+	13.2592i	0.156707	+	0.584837i
$515$	0.632866	−	2.36189i	0.0278874	−	0.104077i
$516$	6.59534	−	0.448426i	0.290344	−	0.0197408i
$517$	0.752801	+	0.434630i	0.0331082	+	0.0191150i
$518$	−3.57147	−	1.61908i	−0.156922	−	0.0711384i
$519$	9.16017	−	0.622813i	0.402087	−	0.0273384i
$520$	14.0138	+	7.00029i	0.614546	+	0.306983i
$521$	26.7604	−	15.4501i	1.17239	−	0.676881i	0.218151	−	0.975915i	$-0.429998\pi$
$521$	26.7604	−	15.4501i	1.17239	−	0.676881i	0.954243	+	0.299034i	$0.0966643\pi$
$522$	18.1976	+	13.8231i	0.796489	+	0.605022i
$523$	13.0710	+	22.6396i	0.571553	+	0.989958i	0.996407	+	0.0846966i	$0.0269921\pi$
$523$	13.0710	+	22.6396i	0.571553	+	0.989958i	−0.424854	+	0.905262i	$0.639675\pi$
$524$	−9.43381	−	16.3398i	−0.412118	−	0.713809i
$525$	49.0645	−	40.4501i	2.14135	−	1.76539i
$526$	−5.78363	+	21.5848i	−0.252178	+	0.941141i
$527$	−3.74208	−	3.74208i	−0.163008	−	0.163008i
$528$	0.638443	−	3.25106i	0.0277847	−	0.141484i
$529$	9.82844	−	17.0234i	0.427323	−	0.740146i
$530$	17.4675	+	30.2546i	0.758741	+	1.31418i
$531$	−18.8576	+	7.91899i	−0.818352	+	0.343655i
$532$	3.31287	+	8.80748i	0.143631	+	0.381853i
$533$	−9.71540	+	3.24255i	−0.420821	+	0.140450i
$534$	−9.40000	+	19.1790i	−0.406778	+	0.829956i
$535$	−31.9276	−	31.9276i	−1.38035	−	1.38035i
$536$			2.67821i			0.115681i
$537$	−21.1230	+	1.43618i	−0.911526	+	0.0619759i
$538$	−18.8815	−	18.8815i	−0.814041	−	0.814041i
$539$	−11.1303	−	7.44355i	−0.479417	−	0.320616i
$540$	−1.31178	+	22.5375i	−0.0564499	+	0.969858i
$541$	−2.24375	−	8.37380i	−0.0964665	−	0.360018i	0.900771	−	0.434294i	$-0.143002\pi$
$541$	−2.24375	−	8.37380i	−0.0964665	−	0.360018i	−0.997238	+	0.0742761i	$0.976335\pi$
$542$	19.3618	+	11.1786i	0.831663	+	0.480161i
$543$	0.0907998	+	1.33546i	0.00389659	+	0.0573101i
$544$	0.679398	+	0.182044i	0.0291290	+	0.00780508i
$545$	−36.5604			−1.56608
$546$	−0.588261	+	16.5122i	−0.0251752	+	0.706658i
$547$	−34.8587			−1.49045			−0.745225	−	0.666813i	$-0.767658\pi$
$547$	−34.8587			−1.49045			−0.745225	+	0.666813i	$0.767658\pi$
$548$	0.822183	+	0.220303i	0.0351219	+	0.00941089i
$549$	30.6213	−	4.18331i	1.30689	−	0.178539i
$550$	22.9870	+	13.2716i	0.980169	+	0.565901i
$551$	−7.01204	−	26.1693i	−0.298723	−	1.11485i
$552$	−0.610263	+	3.10756i	−0.0259745	+	0.132267i
$553$	0.339516	−	0.748926i	0.0144377	−	0.0318476i
$554$	−14.8336	−	14.8336i	−0.630219	−	0.630219i
$555$	0.756581	+	11.1276i	0.0321151	+	0.472340i
$556$		−	10.1496i		−	0.430438i
$557$	17.3299	+	17.3299i	0.734289	+	0.734289i	0.971466	−	0.237177i	$-0.0762221\pi$
$557$	17.3299	+	17.3299i	0.734289	+	0.734289i	−0.237177	+	0.971466i	$0.576222\pi$
$558$	8.53617	−	20.8956i	0.361365	−	0.884582i
$559$	−7.58650	−	11.4808i	−0.320875	−	0.485588i
$560$	7.29410	−	8.88423i	0.308232	−	0.375427i
$561$	−2.20485	+	0.754443i	−0.0930889	+	0.0318526i
$562$	5.44284	+	9.42727i	0.229592	+	0.397665i
$563$	22.5671	−	39.0874i	0.951090	−	1.64734i	0.208019	−	0.978125i	$-0.433298\pi$
$563$	22.5671	−	39.0874i	0.951090	−	1.64734i	0.743072	−	0.669212i	$-0.233368\pi$
$564$	−0.772348	−	0.151674i	−0.0325217	−	0.00638662i
$565$	−43.0996	−	43.0996i	−1.81321	−	1.81321i
$566$	3.60274	−	13.4456i	0.151434	−	0.565161i
$567$	−22.2045	+	8.60005i	−0.932501	+	0.361168i
$568$	−6.60434	−	11.4390i	−0.277112	−	0.479972i
$569$	−19.2515	−	33.3446i	−0.807065	−	1.39788i	−0.914888	−	0.403708i	$-0.867721\pi$
$569$	−19.2515	−	33.3446i	−0.807065	−	1.39788i	0.107823	−	0.994170i	$-0.465612\pi$
$570$	17.5978	−	20.1654i	0.737092	−	0.844636i
$571$	7.09334	−	4.09534i	0.296847	−	0.171385i	−0.344179	−	0.938904i	$-0.611843\pi$
$571$	7.09334	−	4.09534i	0.296847	−	0.171385i	0.641026	+	0.767519i	$0.278509\pi$
$572$	−6.54213	+	2.18346i	−0.273540	+	0.0912949i
$573$	1.48946	+	21.9066i	0.0622231	+	0.915161i
$574$	0.735161	+	7.47970i	0.0306850	+	0.312196i
$575$	−21.9724	−	12.6858i	−0.916313	−	0.529034i
$576$	0.406071	+	2.97239i	0.0169196	+	0.123850i
$577$	3.58621	−	13.3839i	0.149296	−	0.557180i	−0.850231	−	0.526411i	$-0.823537\pi$
$577$	3.58621	−	13.3839i	0.149296	−	0.557180i	0.999527	−	0.0307697i	$-0.00979584\pi$
$578$	4.27188	+	15.9429i	0.177687	+	0.663136i
$579$	−2.29398	+	2.62867i	−0.0953344	+	0.109244i
$580$	−23.4020	+	23.4020i	−0.971716	+	0.971716i
$581$	−2.30478	+	2.80722i	−0.0956183	+	0.116463i
$582$	−6.42985	+	13.1189i	−0.266526	+	0.543798i
$583$	−14.8569	−	3.98090i	−0.615310	−	0.164872i
$584$	−7.09629	−	12.2911i	−0.293647	−	0.508611i
$585$	42.1535	−	20.7749i	1.74283	−	0.858936i
$586$	−6.38973	+	11.0673i	−0.263957	+	0.457187i
$587$	3.18558	+	11.8888i	0.131483	+	0.490701i	0.999988	−	0.00497976i	$-0.00158511\pi$
$587$	3.18558	+	11.8888i	0.131483	+	0.490701i	−0.868505	+	0.495681i	$0.834918\pi$
$588$	11.7176	+	3.11420i	0.483225	+	0.128427i
$589$	−23.1748	+	13.3800i	−0.954901	+	0.551312i
$590$	−7.66632	−	28.6111i	−0.315618	−	1.17790i
$591$	3.83621	+	11.2113i	0.157800	+	0.461170i
$592$	0.383602	+	1.43162i	0.0157660	+	0.0588393i
$593$	12.9309	−	3.46484i	0.531010	−	0.142284i	0.0166555	−	0.999861i	$-0.494698\pi$
$593$	12.9309	−	3.46484i	0.531010	−	0.142284i	0.514355	+	0.857578i	$0.328031\pi$
$594$	−6.60800	−	7.42477i	−0.271129	−	0.304642i
$595$	−7.97688	−	1.31864i	−0.327020	−	0.0540591i
$596$	20.1630	−	5.40265i	0.825908	−	0.221301i
$597$	−31.8795	−	15.6248i	−1.30474	−	0.639479i
$598$	6.25337	−	2.08708i	0.255719	−	0.0853472i
$599$	−0.589433	+	0.340309i	−0.0240836	+	0.0139047i	−0.511993	−	0.858989i	$-0.671093\pi$
$599$	−0.589433	+	0.340309i	−0.0240836	+	0.0139047i	0.487910	+	0.872894i	$0.337759\pi$
$600$	−23.5839	−	4.63140i	−0.962807	−	0.189076i
$601$	−1.74839	+	3.02830i	−0.0713184	+	0.123527i	−0.899479	−	0.436963i	$-0.856054\pi$
$601$	−1.74839	+	3.02830i	−0.0713184	+	0.123527i	0.828161	+	0.560490i	$0.189387\pi$
$602$	−9.45131	+	3.55504i	−0.385207	+	0.144893i
$603$	6.39807	+	4.86005i	0.260550	+	0.197917i
$604$	3.25030	+	3.25030i	0.132253	+	0.132253i
$605$	30.8075	−	8.25486i	1.25250	−	0.335608i
$606$	−27.2093	−	5.34336i	−1.10530	−	0.217059i
$607$	26.1270			1.06046			0.530231	−	0.847853i	$-0.322105\pi$
$607$	26.1270			1.06046			0.530231	+	0.847853i	$0.322105\pi$
$608$	1.77831	−	3.08012i	0.0721200	−	0.124915i
$609$	−32.6977	−	12.2232i	−1.32498	−	0.495308i
$610$			44.7585i			1.81222i
$611$	0.518720	+	1.55420i	0.0209851	+	0.0628762i
$612$	1.66777	−	1.29269i	0.0674156	−	0.0522538i
$613$	28.5138	+	28.5138i	1.15166	+	1.15166i	0.986219	+	0.165442i	$0.0529052\pi$
$613$	28.5138	+	28.5138i	1.15166	+	1.15166i	0.165442	+	0.986219i	$0.447095\pi$
$614$	17.7447	−	10.2449i	0.716118	−	0.413451i
$615$	17.7451	−	11.9195i	0.715551	−	0.480642i
$616$	0.495040	+	5.03665i	0.0199457	+	0.202933i
$617$	−12.8924	−	3.45450i	−0.519028	−	0.139073i	−0.0102110	−	0.999948i	$-0.503250\pi$
$617$	−12.8924	−	3.45450i	−0.519028	−	0.139073i	−0.508817	+	0.860875i	$0.669917\pi$
$618$	−0.734463	−	0.640947i	−0.0295444	−	0.0257827i
$619$	−20.6664	−	5.53754i	−0.830651	−	0.222572i	−0.181654	−	0.983363i	$-0.558145\pi$
$619$	−20.6664	−	5.53754i	−0.830651	−	0.222572i	−0.648998	+	0.760790i	$0.724812\pi$
$620$	28.3097	+	16.3446i	1.13695	+	0.656417i
$621$	6.31634	+	7.09705i	0.253466	+	0.284795i
$622$	7.01235	+	26.1705i	0.281170	+	1.04934i
$623$	5.32112	−	32.1891i	0.213186	−	1.28963i
$624$	4.96468	−	3.78840i	0.198746	−	0.151658i
$625$	49.0842	−	85.0163i	1.96337	−	3.40065i
$626$	0.137548	−	0.137548i	0.00549754	−	0.00549754i
$627$	0.799339	+	11.7565i	0.0319225	+	0.469509i
$628$			10.9324i			0.436248i
$629$	0.737141	−	0.737141i	0.0293917	−	0.0293917i
$630$	−7.98750	−	33.5470i	−0.318230	−	1.33654i
$631$	7.73214	+	2.07182i	0.307812	+	0.0824779i	0.409418	−	0.912347i	$-0.365732\pi$
$631$	7.73214	+	2.07182i	0.307812	+	0.0824779i	−0.101607	+	0.994825i	$0.532398\pi$
$632$	−0.300206	+	0.0804401i	−0.0119416	+	0.00319973i
$633$	−9.87106	+	20.1401i	−0.392340	+	0.800498i
$634$			8.72319i			0.346442i
$635$	−12.0880	+	45.1131i	−0.479698	+	1.79026i
$636$	13.8951	−	0.944750i	0.550978	−	0.0374618i
$637$	−6.39751	−	24.4146i	−0.253479	−	0.967341i
$638$		−	14.5711i		−	0.576874i
$639$	−39.3118	−	4.98069i	−1.55515	−	0.197033i
$640$	−4.34468			−0.171738
$641$	−6.45150	+	11.1743i	−0.254819	+	0.441360i	−0.964846	−	0.262815i	$-0.915349\pi$
$641$	−6.45150	+	11.1743i	−0.254819	+	0.441360i	0.710027	+	0.704174i	$0.248683\pi$
$642$	−17.0310	+	5.82759i	−0.672162	+	0.229997i
$643$	−9.32124	+	34.7873i	−0.367594	+	1.37188i	0.496277	+	0.868164i	$0.334700\pi$
$643$	−9.32124	+	34.7873i	−0.367594	+	1.37188i	−0.863870	+	0.503714i	$0.831966\pi$
$644$	−0.473190	−	4.81435i	−0.0186463	−	0.189712i
$645$	21.6395	+	18.8842i	0.852054	+	0.743566i
$646$	−2.50160			−0.0984242
$647$	2.75300			0.108231			0.0541157	−	0.998535i	$-0.482766\pi$
$647$	2.75300			0.108231			0.0541157	+	0.998535i	$0.482766\pi$
$648$	7.83772	+	4.42381i	0.307895	+	0.173784i
$649$	11.2939	+	6.52055i	0.443325	+	0.255954i
$650$	15.8393	+	47.4580i	0.621267	+	1.86146i
$651$	−3.30285	+	34.3207i	−0.129449	+	1.34513i
$652$	9.01393	−	2.41528i	0.353013	−	0.0945895i
$653$	−6.75178	+	3.89814i	−0.264218	+	0.152546i	−0.626257	−	0.779617i	$-0.715414\pi$
$653$	−6.75178	+	3.89814i	−0.264218	+	0.152546i	0.362039	+	0.932163i	$0.382081\pi$
$654$	−6.41456	+	13.0878i	−0.250829	+	0.511772i
$655$	21.2163	−	79.1805i	0.828991	−	3.09384i
$656$	2.00867	−	2.00867i	0.0784252	−	0.0784252i
$657$	−42.2401	−	5.35169i	−1.64794	−	0.208789i
$658$	1.19655	−	0.117606i	0.0466463	−	0.00458475i
$659$	−30.1598	+	17.4128i	−1.17486	+	0.678306i	−0.954820	−	0.297185i	$-0.903952\pi$
$659$	−30.1598	+	17.4128i	−1.17486	+	0.678306i	−0.220040	+	0.975491i	$0.570619\pi$
$660$	11.9491	−	8.02634i	0.465119	−	0.312425i
$661$	−24.9621	+	24.9621i	−0.970914	+	0.970914i	−0.999589	−	0.0286743i	$-0.990871\pi$
$661$	−24.9621	+	24.9621i	−0.970914	+	0.970914i	0.0286743	+	0.999589i	$0.490871\pi$
$662$	14.4034	+	24.9474i	0.559803	+	0.969607i
$663$	−4.05363	−	1.69183i	−0.157430	−	0.0657051i
$664$	1.37282			0.0532759
$665$	−16.8803	+	37.2355i	−0.654589	+	1.44393i
$666$	4.11616	+	1.68151i	0.159498	+	0.0651572i
$667$			13.9279i			0.539292i
$668$	9.37699	+	2.51256i	0.362807	+	0.0972138i
$669$	−18.8188	+	6.43930i	−0.727576	+	0.248958i
$670$	−8.22788	+	8.22788i	−0.317871	+	0.317871i
$671$	−13.9343	−	13.9343i	−0.537926	−	0.537926i
$672$	−1.90059	−	4.16986i	−0.0733167	−	0.160856i
$673$	22.7367	+	13.1271i	0.876437	+	0.506011i	0.869482	−	0.493965i	$-0.164453\pi$
$673$	22.7367	+	13.1271i	0.876437	+	0.506011i	0.00695514	+	0.999976i	$0.497786\pi$
$674$	0.259689	−	0.969173i	0.0100028	−	0.0373311i
$675$	−53.8608	+	47.9358i	−2.07310	+	1.84505i
$676$	−11.9589	−	5.09763i	−0.459956	−	0.196063i
$677$	28.1917	+	16.2765i	1.08349	+	0.625555i	0.931837	−	0.362878i	$-0.118206\pi$
$677$	28.1917	+	16.2765i	1.08349	+	0.625555i	0.151657	+	0.988433i	$0.451539\pi$
$678$	−22.9905	+	7.86675i	−0.882944	+	0.302121i
$679$	3.63979	−	22.0182i	0.139682	−	0.844981i
$680$	1.52795	+	2.64648i	0.0585941	+	0.101488i
$681$	−4.13641	−	12.0886i	−0.158508	−	0.463236i
$682$	−13.9018	+	3.72499i	−0.532329	+	0.142637i
$683$	−14.9363	+	4.00216i	−0.571520	+	0.153138i	−0.532994	−	0.846119i	$-0.678933\pi$
$683$	−14.9363	+	4.00216i	−0.571520	+	0.153138i	−0.0385265	+	0.999258i	$0.512266\pi$
$684$	−4.13118	−	9.83765i	−0.157959	−	0.376152i
$685$	1.84907	+	3.20268i	0.0706492	+	0.122368i
$686$	−18.5107	+	0.594751i	−0.706742	+	0.0227077i
$687$	8.16791	+	23.8706i	0.311625	+	0.910721i
$688$	3.30528	+	1.90831i	0.126013	+	0.0727535i
$689$	−15.9833	−	24.1880i	−0.608917	−	0.921489i
$690$	−11.4217	+	7.67208i	−0.434817	+	0.292071i
$691$	3.08383	−	11.5090i	0.117314	−	0.437824i	−0.882135	−	0.470996i	$-0.843894\pi$
$691$	3.08383	−	11.5090i	0.117314	−	0.437824i	0.999450	+	0.0331728i	$0.0105612\pi$
$692$	4.59066	+	2.65042i	0.174511	+	0.100754i
$693$	12.9306	+	7.95721i	0.491191	+	0.302269i
$694$	17.1221	+	17.1221i	0.649944	+	0.649944i
$695$	31.1810	−	31.1810i	1.18276	−	1.18276i
$696$	4.27146	+	12.4833i	0.161909	+	0.473178i
$697$	−1.92995	−	0.517130i	−0.0731022	−	0.0195877i
$698$		−	4.01617i		−	0.152014i
$699$	17.2788	−	35.2543i	0.653544	−	1.33344i
$700$	36.5370	−	3.59113i	1.38097	−	0.135732i
$701$	20.9371			0.790783			0.395392	−	0.918513i	$-0.370609\pi$
$701$	20.9371			0.790783			0.395392	+	0.918513i	$0.370609\pi$
$702$	−0.0410345	−	18.7349i	−0.00154875	−	0.707105i
$703$	−2.63568	−	4.56513i	−0.0994065	−	0.172177i
$704$	1.35259	−	1.35259i	0.0509776	−	0.0509776i
$705$	−1.90680	−	2.83873i	−0.0718144	−	0.106913i
$706$	−12.1648	+	7.02334i	−0.457828	+	0.264327i
$707$	42.1536	−	4.14317i	1.58535	−	0.155820i
$708$	−11.5872	−	2.27549i	−0.435472	−	0.0855181i
$709$	−21.3623	+	21.3623i	−0.802276	+	0.802276i	−0.983451	−	0.181175i	$-0.942010\pi$
$709$	−21.3623	+	21.3623i	−0.802276	+	0.802276i	0.181175	+	0.983451i	$0.442010\pi$
$710$	14.8530	−	55.4320i	0.557422	−	2.08033i
$711$	−0.352607	+	0.863145i	−0.0132238	+	0.0323704i
$712$	−10.6793	+	6.16573i	−0.400226	+	0.231070i
$713$	13.2882	−	3.56058i	0.497649	−	0.133345i
$714$	−1.87159	+	2.62418i	−0.0700427	+	0.0982073i
$715$	−26.8063	−	13.3905i	−1.00250	−	0.500776i
$716$	−10.5859	−	6.11177i	−0.395613	−	0.228408i
$717$	5.36819	−	6.15142i	0.200479	−	0.229729i
$718$	15.2521			0.569202
$719$	−21.9643			−0.819131			−0.409565	−	0.912281i	$-0.634320\pi$
$719$	−21.9643			−0.819131			−0.409565	+	0.912281i	$0.634320\pi$
$720$	−7.88412	+	10.3791i	−0.293824	+	0.386808i
$721$	1.35619	+	0.614812i	0.0505072	+	0.0228968i
$722$	1.64362	−	6.13407i	0.0611692	−	0.228286i
$723$	−5.89414	−	17.2256i	−0.219206	−	0.640625i
$724$	−0.386405	+	0.669272i	−0.0143606	+	0.0248733i
$725$	−105.702			−3.92566
$726$	2.45017	−	12.4767i	0.0909345	−	0.463054i
$727$			46.5924i			1.72802i	0.503477	+	0.864009i	$0.332054\pi$
$727$			46.5924i			1.72802i	−0.503477	+	0.864009i	$0.667946\pi$
$728$	−5.59768	+	7.72438i	−0.207464	+	0.286284i
$729$	24.7910	−	10.6961i	0.918185	−	0.396151i
$730$	15.9593	−	59.5611i	0.590682	−	2.20445i
$731$		−	2.68447i		−	0.0992887i
$732$	16.0225	+	7.85294i	0.592209	+	0.290253i
$733$	−8.03756	+	2.15366i	−0.296874	+	0.0795472i	−0.404182	−	0.914679i	$-0.632444\pi$
$733$	−8.03756	+	2.15366i	−0.296874	+	0.0795472i	0.107308	+	0.994226i	$0.465777\pi$
$734$	18.4250	+	4.93697i	0.680080	+	0.182227i
$735$	26.4309	+	45.5655i	0.974918	+	1.68071i
$736$	−1.29289	+	1.29289i	−0.0476565	+	0.0476565i
$737$		−	5.12302i		−	0.188709i
$738$	−1.15352	−	8.44362i	−0.0424616	−	0.310814i
$739$	−1.79379	+	1.79379i	−0.0659858	+	0.0659858i	−0.739330	−	0.673344i	$-0.764857\pi$
$739$	−1.79379	+	1.79379i	−0.0659858	+	0.0659858i	0.673344	+	0.739330i	$0.264857\pi$
$740$	−3.21968	+	5.57664i	−0.118358	+	0.205002i
$741$	−13.5685	+	17.5849i	−0.498451	+	0.645997i
$742$	−19.9121	+	7.48981i	−0.730998	+	0.274960i
$743$	−0.458051	−	1.70947i	−0.0168043	−	0.0627143i	0.957015	−	0.290040i	$-0.0936685\pi$
$743$	−0.458051	−	1.70947i	−0.0168043	−	0.0627143i	−0.973819	+	0.227325i	$0.927002\pi$
$744$	10.8180	−	7.26653i	0.396606	−	0.266404i
$745$	78.5415	+	45.3459i	2.87754	+	1.66135i
$746$	−19.9181	−	5.33704i	−0.729254	−	0.195403i
$747$	2.49121	−	3.27958i	0.0911486	−	0.119994i
$748$	−1.29959	−	0.348223i	−0.0475176	−	0.0127323i
$749$	22.3534	−	16.0114i	0.816776	−	0.585044i
$750$	−37.2447	−	55.4477i	−1.35999	−	2.02466i
$751$	1.63978	−	0.946727i	0.0598364	−	0.0345466i	−0.469783	−	0.882782i	$-0.655668\pi$
$751$	1.63978	−	0.946727i	0.0598364	−	0.0345466i	0.529620	+	0.848235i	$0.322335\pi$
$752$	−0.321332	−	0.321332i	−0.0117178	−	0.0117178i
$753$	−8.73803	−	13.0086i	−0.318432	−	0.474061i
$754$	18.2146	−	20.5564i	0.663335	−	0.748621i
$755$			19.9708i			0.726813i
$756$	−13.4104	−	3.02652i	−0.487733	−	0.110074i
$757$	15.1635	−	26.2640i	0.551128	−	0.954581i	−0.447066	−	0.894501i	$-0.647531\pi$
$757$	15.1635	−	26.2640i	0.551128	−	0.954581i	0.998194	−	0.0600801i	$-0.0191356\pi$
$758$	29.9097			1.08637
$759$	1.16734	−	5.94430i	0.0423718	−	0.215764i
$760$	14.9258	−	3.99937i	0.541417	−	0.145072i
$761$	−11.8216	−	11.8216i	−0.428532	−	0.428532i	0.459596	−	0.888128i	$-0.347994\pi$
$761$	−11.8216	−	11.8216i	−0.428532	−	0.428532i	−0.888128	+	0.459596i	$0.847994\pi$
$762$	14.0286	+	12.2424i	0.508201	+	0.443494i
$763$	3.63114	−	21.9659i	0.131456	−	0.795218i
$764$	−6.33849	+	10.9786i	−0.229319	+	0.397191i
$765$	9.09497	+	1.15231i	0.328829	+	0.0416617i
$766$	23.5217	−	13.5803i	0.849875	−	0.490675i
$767$	7.78211	+	23.3169i	0.280996	+	0.841926i
$768$	−0.762278	+	1.55529i	−0.0275064	+	0.0561217i
$769$	6.14055	−	1.64536i	0.221434	−	0.0593331i	−0.146396	−	0.989226i	$-0.546767\pi$
$769$	6.14055	−	1.64536i	0.221434	−	0.0593331i	0.367830	+	0.929893i	$0.380101\pi$
$770$	−13.9525	+	16.9942i	−0.502814	+	0.612428i
$771$	13.2572	+	19.7365i	0.477447	+	0.710794i
$772$	−1.94567	+	0.521340i	−0.0700261	+	0.0187634i
$773$	−0.849915	−	3.17193i	−0.0305693	−	0.114086i	0.948955	−	0.315410i	$-0.102142\pi$
$773$	−0.849915	−	3.17193i	−0.0305693	−	0.114086i	−0.979525	+	0.201324i	$0.935476\pi$
$774$	10.5568	−	4.43317i	0.379456	−	0.159347i
$775$	27.0219	+	100.847i	0.970654	+	3.62253i
$776$	−7.30496	+	4.21752i	−0.262233	+	0.151400i
$777$	−6.76072	−	0.650618i	−0.242539	−	0.0233408i
$778$	1.89908	+	7.08746i	0.0680853	+	0.254098i
$779$	−5.05161	+	8.74965i	−0.180993	+	0.313489i
$780$	26.8908	+	3.61368i	0.962844	+	0.129391i
$781$	12.6331	+	21.8812i	0.452048	+	0.782970i
$782$	1.24223	+	0.332853i	0.0444219	+	0.0119028i
$783$	37.5730	+	12.4487i	1.34275	+	0.444880i
$784$	4.61329	+	5.26474i	0.164761	+	0.188027i
$785$	−33.5858	+	33.5858i	−1.19873	+	1.19873i
$786$	−24.6223	−	21.4873i	−0.878249	−	0.766425i
$787$	4.80131	+	17.9187i	0.171148	+	0.638733i	0.997176	+	0.0751038i	$0.0239288\pi$
$787$	4.80131	+	17.9187i	0.171148	+	0.638733i	−0.826028	+	0.563630i	$0.809405\pi$
$788$	−1.77065	+	6.60816i	−0.0630768	+	0.235406i
$789$	2.62553	+	38.6156i	0.0934713	+	1.37475i
$790$	−1.16940	−	0.675155i	−0.0416055	−	0.0240209i
$791$	30.1752	−	21.6141i	1.07291	−	0.768507i
$792$	−0.776752	−	5.68573i	−0.0276007	−	0.202034i
$793$	−2.23951	−	37.0765i	−0.0795273	−	1.31663i
$794$	−4.88504	+	2.82038i	−0.173363	+	0.100091i
$795$	45.5904	+	39.7856i	1.61692	+	1.41105i
$796$	−10.2487	−	17.7513i	−0.363257	−	0.629179i
$797$	−8.29031	−	14.3592i	−0.293658	−	0.508631i	0.681014	−	0.732271i	$-0.261539\pi$
$797$	−8.29031	−	14.3592i	−0.293658	−	0.508631i	−0.974672	+	0.223640i	$0.928206\pi$
$798$	10.3678	+	12.5758i	0.367015	+	0.445177i
$799$	−0.0827267	+	0.308740i	−0.00292666	+	0.0109225i
$800$	−9.81197	−	9.81197i	−0.346905	−	0.346905i
$801$	−4.64990	+	36.7010i	−0.164296	+	1.29676i
$802$	7.71496	−	13.3627i	0.272425	−	0.471854i
$803$	13.5741	+	23.5111i	0.479021	+	0.829688i
$804$	1.50179	+	4.38897i	0.0529642	+	0.154787i
$805$	13.3367	−	16.2441i	0.470057	−	0.572530i
$806$	−24.2687	−	12.1229i	−0.854829	−	0.427011i
$807$	−41.5302	−	20.3548i	−1.46193	−	0.716522i
$808$	−11.3203	−	11.3203i	−0.398247	−	0.398247i
$809$		−	48.7489i		−	1.71392i	−0.515383	−	0.856960i	$-0.672350\pi$
$809$		−	48.7489i		−	1.71392i	0.515383	−	0.856960i	$-0.327650\pi$
$810$	10.4881	+	37.6693i	0.368513	+	1.32356i
$811$	−8.20253	−	8.20253i	−0.288030	−	0.288030i	0.548271	−	0.836301i	$-0.315286\pi$
$811$	−8.20253	−	8.20253i	−0.288030	−	0.288030i	−0.836301	+	0.548271i	$0.815286\pi$
$812$	−11.7359	−	16.3844i	−0.411850	−	0.574981i
$813$	37.9979	+	7.46204i	1.33265	+	0.261705i
$814$	−0.733773	−	2.73848i	−0.0257187	−	0.0959836i
$815$	35.1123	+	20.2721i	1.22993	+	0.710100i
$816$	1.21546	−	0.0826406i	0.0425495	−	0.00289300i
$817$	−13.1117	−	3.51327i	−0.458720	−	0.122914i
$818$	−0.0280950			−0.000982319
$819$	8.29513	+	27.3896i	0.289855	+	0.957070i
$820$	12.3418			0.430996
$821$	4.53552	+	1.21529i	0.158291	+	0.0424139i	0.337094	−	0.941471i	$-0.390556\pi$
$821$	4.53552	+	1.21529i	0.158291	+	0.0424139i	−0.178803	+	0.983885i	$0.557223\pi$
$822$	1.47090	−	0.100009i	0.0513036	−	0.00348820i
$823$	−7.77851	−	4.49092i	−0.271142	−	0.156544i	0.358265	−	0.933620i	$-0.383369\pi$
$823$	−7.77851	−	4.49092i	−0.271142	−	0.156544i	−0.629406	+	0.777076i	$0.716702\pi$
$824$	−0.145665	−	0.543628i	−0.00507447	−	0.0189382i
$825$	45.1124	+	8.85917i	1.57061	+	0.308437i
$826$	17.9513	−	1.76438i	0.624604	−	0.0613908i
$827$	6.72026	+	6.72026i	0.233686	+	0.233686i	0.814229	−	0.580543i	$-0.197160\pi$
$827$	6.72026	+	6.72026i	0.233686	+	0.233686i	−0.580543	+	0.814229i	$0.697160\pi$
$828$	0.742469	+	5.43478i	0.0258026	+	0.188872i
$829$		−	48.0277i		−	1.66807i	−0.551712	−	0.834035i	$-0.686025\pi$
$829$		−	48.0277i		−	1.66807i	0.551712	−	0.834035i	$-0.313975\pi$
$830$	4.21752	+	4.21752i	0.146392	+	0.146392i
$831$	−32.6267	−	15.9910i	−1.13181	−	0.554721i
$832$	3.59899	−	0.217387i	0.124773	−	0.00753655i
$833$	1.58451	−	4.66162i	0.0548999	−	0.161516i
$834$	−5.69132	−	16.6328i	−0.197074	−	0.575947i
$835$	21.0886	+	36.5265i	0.729800	+	1.26405i
$836$	−3.40164	+	5.89181i	−0.117648	+	0.203773i
$837$	2.27170	−	39.0297i	0.0785214	−	1.34906i
$838$	7.67565	+	7.67565i	0.265151	+	0.265151i
$839$	−4.99773	+	18.6518i	−0.172541	+	0.643931i	0.824417	+	0.565983i	$0.191503\pi$
$839$	−4.99773	+	18.6518i	−0.172541	+	0.643931i	−0.996957	+	0.0779477i	$0.975163\pi$
$840$	6.97157	−	18.6493i	0.240542	−	0.643463i
$841$	14.5129	+	25.1372i	0.500446	+	0.866798i
$842$	10.7610	+	18.6387i	0.370850	+	0.642331i
$843$	14.2058	+	12.3971i	0.489275	+	0.426978i
$844$	−11.2145	+	6.47471i	−0.386020	+	0.222869i
$845$	−21.0787	−	52.4001i	−0.725130	−	1.80262i
$846$	−1.35075	+	0.184532i	−0.0464397	+	0.00634433i
$847$	1.89983	+	19.3293i	0.0652790	+	0.664164i
$848$	6.96361	+	4.02044i	0.239131	+	0.138063i
$849$	−1.63550	−	24.0545i	−0.0561300	−	0.825547i
$850$	−2.52609	+	9.42748i	−0.0866440	+	0.323360i
$851$	0.701386	+	2.61761i	0.0240432	+	0.0897305i
$852$	−17.2374	−	15.0426i	−0.590543	−	0.515351i
$853$	9.76140	−	9.76140i	0.334224	−	0.334224i	−0.519964	−	0.854188i	$-0.674055\pi$
$853$	9.76140	−	9.76140i	0.334224	−	0.334224i	0.854188	+	0.519964i	$0.174055\pi$
$854$	−26.8914	−	4.44536i	−0.920204	−	0.152117i
$855$	17.5311	−	42.9143i	0.599552	−	1.46764i
$856$	−10.0385	−	2.68980i	−0.343108	−	0.0919354i
$857$	16.4315	+	28.4602i	0.561289	+	0.972182i	0.997384	+	0.0722810i	$0.0230279\pi$
$857$	16.4315	+	28.4602i	0.561289	+	0.972182i	−0.436095	+	0.899901i	$0.643639\pi$
$858$	−9.49667	+	7.24664i	−0.324211	+	0.247396i
$859$	−6.35388	+	11.0052i	−0.216792	+	0.375494i	−0.953825	−	0.300362i	$-0.902893\pi$
$859$	−6.35388	+	11.0052i	−0.216792	+	0.375494i	0.737034	+	0.675856i	$0.236226\pi$
$860$	4.29172	+	16.0169i	0.146347	+	0.546173i
$861$	5.39896	+	11.8453i	0.183996	+	0.403685i
$862$	20.8731	−	12.0511i	0.710941	−	0.410462i
$863$	−2.29597	−	8.56869i	−0.0781559	−	0.291682i	0.915775	−	0.401693i	$-0.131578\pi$
$863$	−2.29597	−	8.56869i	−0.0781559	−	0.291682i	−0.993930	+	0.110011i	$0.964911\pi$
$864$	2.33221	+	4.64336i	0.0793434	+	0.157970i
$865$	5.96071	+	22.2457i	0.202670	+	0.756376i
$866$	−3.05470	+	0.818505i	−0.103803	+	0.0278139i
$867$	15.9405	+	23.7313i	0.541368	+	0.805956i
$868$	−12.6317	+	15.3855i	−0.428748	+	0.522216i
$869$	0.574250	−	0.153870i	0.0194801	−	0.00521967i
$870$	−25.2280	+	51.4731i	−0.855308	+	1.74510i
$871$	6.40402	−	7.22739i	0.216992	−	0.244891i
$872$	−7.28759	+	4.20749i	−0.246789	+	0.142484i
$873$	−3.18066	+	25.1044i	−0.107649	+	0.849656i
$874$	3.25150	−	5.63176i	0.109984	−	0.190497i
$875$	78.8584	+	64.7441i	2.66590	+	2.18875i
$876$	−18.5214	−	16.1631i	−0.625779	−	0.546101i
$877$	2.76520	+	2.76520i	0.0933743	+	0.0933743i	0.752251	−	0.658877i	$-0.228968\pi$
$877$	2.76520	+	2.76520i	0.0933743	+	0.0933743i	−0.658877	+	0.752251i	$0.728968\pi$
$878$	−16.4344	+	4.40359i	−0.554635	+	0.148614i
$879$	−4.26534	+	21.7198i	−0.143866	+	0.732591i
$880$	8.31071			0.280154
$881$	−3.11388	+	5.39339i	−0.104909	+	0.181708i	−0.913701	−	0.406387i	$-0.866789\pi$
$881$	−3.11388	+	5.39339i	−0.104909	+	0.181708i	0.808792	+	0.588095i	$0.200122\pi$
$882$	20.9487	−	1.46712i	0.705379	−	0.0494006i
$883$			21.8076i			0.733883i	0.930244	+	0.366942i	$0.119595\pi$
$883$			21.8076i			0.733883i	−0.930244	+	0.366942i	$0.880405\pi$
$884$	−1.39812	−	2.11581i	−0.0470239	−	0.0711624i
$885$	−28.6069	−	42.5882i	−0.961609	−	1.43159i
$886$	3.52102	+	3.52102i	0.118291	+	0.118291i
$887$	−3.25715	+	1.88052i	−0.109365	+	0.0631416i	−0.553685	−	0.832726i	$-0.686779\pi$
$887$	−3.25715	+	1.88052i	−0.109365	+	0.0631416i	0.444320	+	0.895868i	$0.353445\pi$
$888$	1.43141	+	2.13100i	0.0480350	+	0.0715116i
$889$	−25.9038	−	11.7432i	−0.868787	−	0.393854i
$890$	−51.7506	−	13.8665i	−1.73468	−	0.464807i
$891$	−14.9924	−	8.46208i	−0.502264	−	0.283490i
$892$	−11.0922	−	2.97214i	−0.371394	−	0.0995147i
$893$	1.39971	+	0.808121i	0.0468394	+	0.0270427i
$894$	30.0130	−	20.1600i	1.00378	−	0.674251i
$895$	−13.7452	−	51.2977i	−0.459451	−	1.71469i
$896$	0.431508	−	2.61033i	0.0144157	−	0.0872049i
$897$	9.07751	−	6.92679i	0.303089	−	0.231279i
$898$	−17.2309	+	29.8448i	−0.575003	+	0.995935i
$899$	40.5269	−	40.5269i	1.35165	−	1.35165i
$900$	−41.2455	+	5.63473i	−1.37485	+	0.187824i
$901$		−	5.65568i		−	0.188418i
$902$	−3.84227	+	3.84227i	−0.127934	+	0.127934i
$903$	−13.4950	+	11.1257i	−0.449087	+	0.370239i
$904$	−13.5511	−	3.63100i	−0.450702	−	0.120765i
$905$	−3.24320	+	0.869012i	−0.107808	+	0.0288869i
$906$	7.14909	+	3.50391i	0.237513	+	0.116409i
$907$			39.7380i			1.31948i	0.751495	+	0.659739i	$0.229333\pi$
$907$			39.7380i			1.31948i	−0.751495	+	0.659739i	$0.770667\pi$
$908$	1.90921	−	7.12528i	0.0633595	−	0.236461i
$909$	−47.5859	+	6.50092i	−1.57833	+	0.215622i
$910$	−40.9274	+	6.53354i	−1.35673	+	0.216585i
$911$			32.9753i			1.09252i	0.837616	+	0.546260i	$0.183949\pi$
$911$			32.9753i			1.09252i	−0.837616	+	0.546260i	$0.816051\pi$
$912$	1.18708	−	6.04479i	0.0393080	−	0.200163i
$913$	−2.62600			−0.0869080
$914$	−0.986054	+	1.70790i	−0.0326158	+	0.0564922i
$915$	25.0981	+	73.3489i	0.829718	+	2.42484i
$916$	−3.77001	+	14.0699i	−0.124565	+	0.464881i
$917$	45.4653	+	20.6111i	1.50139	+	0.680639i
$918$	2.00822	−	3.05361i	0.0662812	−	0.100784i
$919$	−9.72717			−0.320870			−0.160435	−	0.987046i	$-0.551290\pi$
$919$	−9.72717			−0.320870			−0.160435	+	0.987046i	$0.551290\pi$
$920$	−7.94390			−0.261903
$921$	23.3347	−	26.7393i	0.768904	−	0.881090i
$922$	11.8103	+	6.81870i	0.388953	+	0.224562i
$923$	−9.53016	+	46.6613i	−0.313689	+	1.53587i
$924$	3.63553	+	7.97632i	0.119600	+	0.262402i
$925$	−19.8655	+	5.32295i	−0.653174	+	0.175017i
$926$	6.75861	−	3.90209i	0.222102	−	0.128231i
$927$	−1.56302	−	0.638518i	−0.0513364	−	0.0209717i
$928$	−1.97155	+	7.35791i	−0.0647192	+	0.241535i
$929$	−8.51157	+	8.51157i	−0.279255	+	0.279255i	−0.832812	−	0.553556i	$-0.813270\pi$
$929$	−8.51157	+	8.51157i	−0.279255	+	0.279255i	0.553556	+	0.832812i	$0.313270\pi$
$930$	55.5583	+	10.9106i	1.82183	+	0.357771i
$931$	−20.6950	−	13.8400i	−0.678250	−	0.453589i
$932$	19.6305	−	11.3337i	0.643017	−	0.371246i
$933$	26.1666	+	38.9552i	0.856655	+	1.27534i
$934$	−10.4139	+	10.4139i	−0.340752	+	0.340752i
$935$	−2.92273	−	5.06232i	−0.0955835	−	0.165556i
$936$	6.01163	−	8.99224i	0.196496	−	0.293920i
$937$	−14.9299			−0.487737			−0.243869	−	0.969808i	$-0.578417\pi$
$937$	−14.9299			−0.487737			−0.243869	+	0.969808i	$0.578417\pi$
$938$	−4.12621	−	5.76057i	−0.134725	−	0.188089i
$939$	0.148281	−	0.302540i	0.00483896	−	0.00987301i
$940$		−	1.97436i		−	0.0643965i
$941$	−46.3899	−	12.4301i	−1.51227	−	0.405211i	−0.595079	−	0.803667i	$-0.702879\pi$
$941$	−46.3899	−	12.4301i	−1.51227	−	0.405211i	−0.917187	+	0.398456i	$0.869546\pi$
$942$	6.13026	+	17.9156i	0.199735	+	0.583722i
$943$	3.67268	−	3.67268i	0.119599	−	0.119599i
$944$	−4.82079	−	4.82079i	−0.156903	−	0.156903i
$945$	−31.9010	−	50.4969i	−1.03774	−	1.64266i
$946$	−6.32251	−	3.65030i	−0.205562	−	0.118681i
$947$	−3.56628	+	13.3095i	−0.115888	+	0.432502i	−0.999352	−	0.0359985i	$-0.988539\pi$
$947$	−3.56628	+	13.3095i	−0.115888	+	0.432502i	0.883463	+	0.468500i	$0.155206\pi$
$948$	−0.446863	+	0.300162i	−0.0145134	+	0.00974881i
$949$	−10.2401	+	50.1370i	−0.332406	+	1.62752i
$950$	42.7405	+	24.6762i	1.38668	+	0.800602i
$951$	4.89149	+	14.2953i	0.158617	+	0.463557i
$952$	−1.74179	+	0.655160i	−0.0564516	+	0.0212339i
$953$	−0.835017	−	1.44629i	−0.0270489	−	0.0468500i	0.852184	−	0.523242i	$-0.175278\pi$
$953$	−0.835017	−	1.44629i	−0.0270489	−	0.0468500i	−0.879233	+	0.476392i	$0.841944\pi$
$954$	22.2412	−	9.33986i	0.720084	−	0.302389i
$955$	−53.2007	+	14.2551i	−1.72153	+	0.461283i
$956$	4.55310	−	1.22000i	0.147258	−	0.0394576i
$957$	−8.17066	−	23.8786i	−0.264120	−	0.771887i
$958$	−8.58920	−	14.8769i	−0.277504	−	0.480652i
$959$	−2.10785	+	0.792851i	−0.0680659	+	0.0256025i
$960$	−7.11992	+	2.43626i	−0.229795	+	0.0786298i
$961$	−22.1792	−	12.8052i	−0.715458	−	0.413070i
$962$	2.38805	−	4.78061i	0.0769938	−	0.154133i
$963$	−24.6422	+	19.1001i	−0.794083	+	0.615494i
$964$	2.72052	−	10.1531i	0.0876220	−	0.327010i
$965$	−7.57902	−	4.37575i	−0.243977	−	0.140860i
$966$	−3.47507	−	7.62427i	−0.111809	−	0.245307i
$967$	17.1848	+	17.1848i	0.552625	+	0.552625i	0.927198	−	0.374573i	$-0.122211\pi$
$967$	17.1848	+	17.1848i	0.552625	+	0.552625i	−0.374573	+	0.927198i	$0.622211\pi$
$968$	5.19088	−	5.19088i	0.166841	−	0.166841i
$969$	−4.09955	+	1.40276i	−0.131696	+	0.0450632i
$970$	−35.3988	−	9.48508i	−1.13659	−	0.304547i
$971$		−	58.4967i		−	1.87725i	−0.344941	−	0.938624i	$-0.612101\pi$
$971$		−	58.4967i		−	1.87725i	0.344941	−	0.938624i	$-0.387899\pi$
$972$	15.3249	+	2.85464i	0.491545	+	0.0915626i
$973$	15.6370	+	21.8307i	0.501299	+	0.699861i
$974$	13.1238			0.420513
$975$	52.5687	+	68.8909i	1.68355	+	2.20628i
$976$	5.15096	+	8.92173i	0.164878	+	0.285578i
$977$	26.9776	−	26.9776i	0.863088	−	0.863088i	−0.128607	−	0.991696i	$-0.541051\pi$
$977$	26.9776	−	26.9776i	0.863088	−	0.863088i	0.991696	+	0.128607i	$0.0410507\pi$
$978$	13.4174	−	9.01260i	0.429041	−	0.288191i
$979$	20.4280	−	11.7941i	0.652881	−	0.376941i
$980$	−2.00135	+	30.3468i	−0.0639307	+	0.969394i
$981$	−3.17310	+	25.0448i	−0.101309	+	0.799617i
$982$	4.64559	−	4.64559i	0.148247	−	0.148247i
$983$	5.83696	−	21.7838i	0.186170	−	0.694796i	−0.808207	−	0.588899i	$-0.799562\pi$
$983$	5.83696	−	21.7838i	0.186170	−	0.694796i	0.994377	−	0.105898i	$-0.0337716\pi$
$984$	2.16539	−	4.41809i	0.0690301	−	0.140844i
$985$	−25.7410	+	14.8616i	−0.820175	+	0.473528i
$986$	5.17530	−	1.38672i	0.164815	−	0.0441621i
$987$	1.89492	−	0.863687i	0.0603160	−	0.0274915i
$988$	−12.1640	+	4.05977i	−0.386988	+	0.129158i
$989$	6.04345	+	3.48918i	0.192170	+	0.110950i
$990$	15.0811	−	19.8537i	0.479310	−	0.630993i
$991$	−20.2315			−0.642675			−0.321338	−	0.946965i	$-0.604132\pi$
$991$	−20.2315			−0.642675			−0.321338	+	0.946965i	$0.604132\pi$
$992$	7.52398			0.238887
$993$	37.5929	+	32.8064i	1.19298	+	1.04108i
$994$	31.8289	+	14.4292i	1.00955	+	0.457668i
$995$	23.0491	−	86.0204i	0.730705	−	2.72703i
$996$	2.24974	−	0.769803i	0.0712857	−	0.0243922i
$997$	21.6297	−	37.4637i	0.685018	−	1.18649i	−0.288413	−	0.957506i	$-0.593128\pi$
$997$	21.6297	−	37.4637i	0.685018	−	1.18649i	0.973431	−	0.228980i	$-0.0735391\pi$
$998$	−35.1750			−1.11344
$999$	7.68833	+	0.447494i	0.243248	+	0.0141581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.527.38	yes	152
3.2	odd	2	inner	546.2.bw.a.527.19	yes	152
7.4	even	3		546.2.ch.a.137.7	yes	152
13.2	odd	12		546.2.ch.a.275.26	yes	152
21.11	odd	6		546.2.ch.a.137.26	yes	152
39.2	even	12		546.2.ch.a.275.7	yes	152
91.67	odd	12	inner	546.2.bw.a.431.19	✓	152
273.158	even	12	inner	546.2.bw.a.431.38	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.19	✓	152	91.67	odd	12	inner
546.2.bw.a.431.38	yes	152	273.158	even	12	inner
546.2.bw.a.527.19	yes	152	3.2	odd	2	inner
546.2.bw.a.527.38	yes	152	1.1	even	1	trivial
546.2.ch.a.137.7	yes	152	7.4	even	3
546.2.ch.a.137.26	yes	152	21.11	odd	6
546.2.ch.a.275.7	yes	152	39.2	even	12
546.2.ch.a.275.26	yes	152	13.2	odd	12

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(1.72806 - 0.117493i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.12449 + 4.19664i) q^{5} +(1.69959 + 0.333765i) q^{6} +(-2.63306 + 0.258797i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.97239 - 0.406071i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(1.72806 - 0.117493i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.12449 + 4.19664i) q^{5} +(1.69959 + 0.333765i) q^{6} +(-2.63306 + 0.258797i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.97239 - 0.406071i) q^{9} +4.34468i q^{10} +(-1.35259 - 1.35259i) q^{11} +(1.55529 + 0.762278i) q^{12} +(-0.217387 - 3.59899i) q^{13} +(-2.61033 - 0.431508i) q^{14} +(2.43626 + 7.11992i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.351682 - 0.609132i) q^{17} +(2.97621 + 0.377077i) q^{18} +(-2.51491 - 2.51491i) q^{19} +(-1.12449 + 4.19664i) q^{20} +(-4.51969 + 0.756585i) q^{21} +(-0.956425 - 1.65658i) q^{22} +(0.914210 + 1.58346i) q^{23} +(1.30500 + 1.13884i) q^{24} +(-12.0172 + 6.93811i) q^{25} +(0.721508 - 3.53262i) q^{26} +(5.08876 - 1.05095i) q^{27} +(-2.40970 - 1.09241i) q^{28} +(6.59692 + 3.80874i) q^{29} +(0.510470 + 7.50787i) q^{30} +(1.94735 - 7.26761i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-2.49628 - 2.17844i) q^{33} +(0.497354 - 0.497354i) q^{34} +(-4.04692 - 10.7590i) q^{35} +(2.77720 + 1.13453i) q^{36} +(1.43162 + 0.383602i) q^{37} +(-1.77831 - 3.08012i) q^{38} +(-0.798516 - 6.19374i) q^{39} +(-2.17234 + 3.76260i) q^{40} +(-0.735223 - 2.74389i) q^{41} +(-4.56150 - 0.438977i) q^{42} +(3.30528 - 1.90831i) q^{43} +(-0.495082 - 1.84767i) q^{44} +(5.04654 + 12.0174i) q^{45} +(0.473230 + 1.76612i) q^{46} +(-0.438948 + 0.117616i) q^{47} +(0.965783 + 1.43780i) q^{48} +(6.86605 - 1.36286i) q^{49} +(-13.4034 + 3.59143i) q^{50} +(0.536160 - 1.09394i) q^{51} +(1.61123 - 3.22551i) q^{52} +(6.96361 - 4.02044i) q^{53} +(5.18737 + 0.301928i) q^{54} +(4.15536 - 7.19729i) q^{55} +(-2.04485 - 1.67886i) q^{56} +(-4.64140 - 4.05043i) q^{57} +(5.38637 + 5.38637i) q^{58} +(-6.58533 + 1.76453i) q^{59} +(-1.45010 + 7.38416i) q^{60} +10.3019 q^{61} +(3.76199 - 6.51596i) q^{62} +(-7.72140 + 1.83846i) q^{63} +1.00000i q^{64} +(14.8592 - 4.95931i) q^{65} +(-1.84740 - 2.75029i) q^{66} +(1.89378 + 1.89378i) q^{67} +(0.609132 - 0.351682i) q^{68} +(1.76586 + 2.62890i) q^{69} +(-1.12439 - 11.4398i) q^{70} +(-12.7586 - 3.41866i) q^{71} +(2.38893 + 1.81466i) q^{72} +(-13.7090 - 3.67331i) q^{73} +(1.28356 + 0.741062i) q^{74} +(-19.9512 + 13.4014i) q^{75} +(-0.920521 - 3.43543i) q^{76} +(3.91150 + 3.21141i) q^{77} +(0.831750 - 6.18936i) q^{78} +(-0.155398 + 0.269158i) q^{79} +(-3.07215 + 3.07215i) q^{80} +(8.67021 - 2.41400i) q^{81} -2.84068i q^{82} +(0.970732 - 0.970732i) q^{83} +(-4.29246 - 1.60462i) q^{84} +(2.95177 + 0.790923i) q^{85} +(3.68656 - 0.987812i) q^{86} +(11.8474 + 5.80663i) q^{87} -1.91285i q^{88} +(-3.19161 + 11.9113i) q^{89} +(1.76425 + 12.9141i) q^{90} +(1.50380 + 9.42012i) q^{91} +1.82842i q^{92} +(2.51125 - 12.7877i) q^{93} -0.454432 q^{94} +(7.72618 - 13.3821i) q^{95} +(0.560745 + 1.63877i) q^{96} +(-2.18315 + 8.14762i) q^{97} +(6.98483 + 0.460643i) q^{98} +(-4.56967 - 3.47117i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 12 q^{7}+O(q^{10}) \) 152 * q + 12 * q^7	\( 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Introduction

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