LMFDB - Embedded newform 357.2.bf.a.29.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(29,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 0, 13])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.29"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bf (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$36$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			29.7
Character	$\chi$	$=$	357.29
Dual form			357.2.bf.a.197.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.98193 + 0.820944i) q^{2} +(1.72218 - 0.184679i) q^{3} +(1.83990 - 1.83990i) q^{4} +(-0.0197905 + 0.0994937i) q^{5} +(-3.26163 + 1.77983i) q^{6} +(-0.980785 + 0.195090i) q^{7} +(-0.494214 + 1.19314i) q^{8} +(2.93179 - 0.636101i) q^{9} +(-0.0424552 - 0.213437i) q^{10} +(-0.557010 - 0.372182i) q^{11} +(2.82884 - 3.50842i) q^{12} +(3.89622 + 3.89622i) q^{13} +(1.78369 - 1.19183i) q^{14} +(-0.0157083 + 0.175001i) q^{15} +2.43357i q^{16} +(2.16970 + 3.50606i) q^{17} +(-5.28840 + 3.66754i) q^{18} +(-2.49251 - 6.01745i) q^{19} +(0.146646 + 0.219471i) q^{20} +(-1.65306 + 0.517111i) q^{21} +(1.40950 + 0.280366i) q^{22} +(5.17029 - 7.73789i) q^{23} +(-0.630775 + 2.14606i) q^{24} +(4.60989 + 1.90948i) q^{25} +(-10.9206 - 4.52347i) q^{26} +(4.93158 - 1.63692i) q^{27} +(-1.44560 + 2.16349i) q^{28} +(-2.02841 - 0.403476i) q^{29} +(-0.112533 - 0.359735i) q^{30} +(4.75542 + 7.11698i) q^{31} +(-2.98625 - 7.20946i) q^{32} +(-1.02800 - 0.538095i) q^{33} +(-7.17846 - 5.16757i) q^{34} -0.101443i q^{35} +(4.22382 - 6.56455i) q^{36} +(-4.00502 + 2.67607i) q^{37} +(9.87997 + 9.87997i) q^{38} +(7.42952 + 5.99042i) q^{39} +(-0.108929 - 0.0727839i) q^{40} +(2.13583 + 10.7375i) q^{41} +(2.85173 - 2.38195i) q^{42} +(0.489747 - 1.18235i) q^{43} +(-1.70962 + 0.340064i) q^{44} +(0.00526647 + 0.304283i) q^{45} +(-3.89480 + 19.5805i) q^{46} +(-1.36863 + 1.36863i) q^{47} +(0.449431 + 4.19105i) q^{48} +(0.923880 - 0.382683i) q^{49} -10.7041 q^{50} +(4.38410 + 5.63735i) q^{51} +14.3373 q^{52} +(-0.780086 + 0.323122i) q^{53} +(-8.43024 + 7.29282i) q^{54} +(0.0480533 - 0.0480533i) q^{55} +(0.251948 - 1.26663i) q^{56} +(-5.40384 - 9.90280i) q^{57} +(4.35141 - 0.865548i) q^{58} +(0.238614 - 0.576065i) q^{59} +(0.293081 + 0.350885i) q^{60} +(-2.02246 - 10.1676i) q^{61} +(-15.2676 - 10.2015i) q^{62} +(-2.75136 + 1.19584i) q^{63} +(8.39552 + 8.39552i) q^{64} +(-0.464757 + 0.310541i) q^{65} +(2.47918 + 0.222535i) q^{66} -4.86548i q^{67} +(10.4428 + 2.45876i) q^{68} +(7.47512 - 14.2809i) q^{69} +(0.0832789 + 0.201053i) q^{70} +(2.60774 + 3.90275i) q^{71} +(-0.689973 + 3.81239i) q^{72} +(-7.26060 - 1.44422i) q^{73} +(5.74077 - 8.59167i) q^{74} +(8.29169 + 2.43711i) q^{75} +(-15.6574 - 6.48553i) q^{76} +(0.618916 + 0.256364i) q^{77} +(-19.6426 - 5.77340i) q^{78} +(-4.28505 + 6.41304i) q^{79} +(-0.242125 - 0.0481617i) q^{80} +(8.19075 - 3.72983i) q^{81} +(-13.0480 - 19.5277i) q^{82} +(-4.50149 - 10.8675i) q^{83} +(-2.09002 + 3.99288i) q^{84} +(-0.391770 + 0.146484i) q^{85} +2.74540i q^{86} +(-3.56780 - 0.320251i) q^{87} +(0.719346 - 0.480652i) q^{88} +(-2.65581 - 2.65581i) q^{89} +(-0.260237 - 0.598745i) q^{90} +(-4.58146 - 3.06124i) q^{91} +(-4.72411 - 23.7497i) q^{92} +(9.50403 + 11.3785i) q^{93} +(1.58896 - 3.83609i) q^{94} +(0.648026 - 0.128900i) q^{95} +(-6.47430 - 11.8645i) q^{96} +(1.74146 - 8.75492i) q^{97} +(-1.51691 + 1.51691i) q^{98} +(-1.86978 - 0.736844i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 48 q^{12} - 48 q^{24} - 64 q^{25} - 64 q^{31} - 224 q^{34} + 16 q^{39} + 64 q^{40} - 64 q^{43} + 64 q^{45} + 32 q^{51} + 128 q^{52} + 112 q^{54} - 32 q^{57} + 32 q^{58} - 144 q^{60} + 32 q^{61}+ \cdots + 304 q^{96}+O(q^{100}) $ 288 * q - 48 * q^12 - 48 * q^24 - 64 * q^25 - 64 * q^31 - 224 * q^34 + 16 * q^39 + 64 * q^40 - 64 * q^43 + 64 * q^45 + 32 * q^51 + 128 * q^52 + 112 * q^54 - 32 * q^57 + 32 * q^58 - 144 * q^60 + 32 * q^61 + 64 * q^64 - 192 * q^66 - 32 * q^70 - 208 * q^72 - 128 * q^76 - 208 * q^78 - 64 * q^79 - 112 * q^81 - 256 * q^82 + 32 * q^85 + 32 * q^88 + 240 * q^90 - 96 * q^91 + 64 * q^93 + 304 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$1$	$e\left(\frac{13}{16}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.98193	+	0.820944i	−1.40144	+	0.580495i	−0.950125	−	0.311871i	$-0.899044\pi$
$2$	−1.98193	+	0.820944i	−1.40144	+	0.580495i	−0.451314	+	0.892365i	$0.649044\pi$
$3$	1.72218	−	0.184679i	0.994299	−	0.106625i
$3$	1.72218	−	0.184679i	0.994299	−	0.106625i
$4$	1.83990	−	1.83990i	0.919948	−	0.919948i
$5$	−0.0197905	+	0.0994937i	−0.00885059	+	0.0444949i	−0.984958	−	0.172793i	$-0.944721\pi$
$5$	−0.0197905	+	0.0994937i	−0.00885059	+	0.0444949i	0.976108	+	0.217288i	$0.0697209\pi$
$6$	−3.26163	+	1.77983i	−1.33155	+	0.726614i
$7$	−0.980785	+	0.195090i	−0.370702	+	0.0737372i
$7$	−0.980785	+	0.195090i	−0.370702	+	0.0737372i
$8$	−0.494214	+	1.19314i	−0.174731	+	0.421838i
$9$	2.93179	−	0.636101i	0.977262	−	0.212034i
$10$	−0.0424552	−	0.213437i	−0.0134255	−	0.0674946i
$11$	−0.557010	−	0.372182i	−0.167945	−	0.112217i	0.468757	−	0.883327i	$-0.344702\pi$
$11$	−0.557010	−	0.372182i	−0.167945	−	0.112217i	−0.636702	+	0.771110i	$0.719702\pi$
$12$	2.82884	−	3.50842i	0.816615	−	1.01279i
$13$	3.89622	+	3.89622i	1.08062	+	1.08062i	0.996452	+	0.0841638i	$0.0268219\pi$
$13$	3.89622	+	3.89622i	1.08062	+	1.08062i	0.0841638	+	0.996452i	$0.473178\pi$
$14$	1.78369	−	1.19183i	0.476712	−	0.318529i
$15$	−0.0157083	+	0.175001i	−0.00405588	+	0.0451850i
$16$			2.43357i			0.608394i
$17$	2.16970	+	3.50606i	0.526228	+	0.850343i
$17$	2.16970	+	3.50606i	0.526228	+	0.850343i
$18$	−5.28840	+	3.66754i	−1.24649	+	0.864448i
$19$	−2.49251	−	6.01745i	−0.571821	−	1.38050i	−0.900003	−	0.435883i	$-0.856436\pi$
$19$	−2.49251	−	6.01745i	−0.571821	−	1.38050i	0.328182	−	0.944614i	$-0.393564\pi$
$20$	0.146646	+	0.219471i	0.0327909	+	0.0490751i
$21$	−1.65306	+	0.517111i	−0.360727	+	0.112843i
$22$	1.40950	+	0.280366i	0.300506	+	0.0597743i
$23$	5.17029	−	7.73789i	1.07808	−	1.61346i	0.337724	−	0.941245i	$-0.390343\pi$
$23$	5.17029	−	7.73789i	1.07808	−	1.61346i	0.740356	−	0.672216i	$-0.234657\pi$
$24$	−0.630775	+	2.14606i	−0.128756	+	0.438064i
$25$	4.60989	+	1.90948i	0.921978	+	0.381896i
$26$	−10.9206	−	4.52347i	−2.14171	−	0.887125i
$27$	4.93158	−	1.63692i	0.949083	−	0.315025i
$28$	−1.44560	+	2.16349i	−0.273192	+	0.408861i
$29$	−2.02841	−	0.403476i	−0.376666	−	0.0749236i	0.00312656	−	0.999995i	$-0.499005\pi$
$29$	−2.02841	−	0.403476i	−0.376666	−	0.0749236i	−0.379793	+	0.925071i	$0.624005\pi$
$30$	−0.112533	−	0.359735i	−0.0205456	−	0.0656783i
$31$	4.75542	+	7.11698i	0.854098	+	1.27825i	0.958897	+	0.283755i	$0.0915802\pi$
$31$	4.75542	+	7.11698i	0.854098	+	1.27825i	−0.104799	+	0.994493i	$0.533420\pi$
$32$	−2.98625	−	7.20946i	−0.527900	−	1.27446i
$33$	−1.02800	−	0.538095i	−0.178953	−	0.0936703i
$34$	−7.17846	−	5.16757i	−1.23110	−	0.886231i
$35$		−	0.101443i		−	0.0171470i
$36$	4.22382	−	6.56455i	0.703971	−	1.09409i
$37$	−4.00502	+	2.67607i	−0.658420	+	0.439942i	−0.839378	−	0.543548i	$-0.817080\pi$
$37$	−4.00502	+	2.67607i	−0.658420	+	0.439942i	0.180957	+	0.983491i	$0.442080\pi$
$38$	9.87997	+	9.87997i	1.60274	+	1.60274i
$39$	7.42952	+	5.99042i	1.18968	+	0.959235i
$40$	−0.108929	−	0.0727839i	−0.0172232	−	0.0115081i
$41$	2.13583	+	10.7375i	0.333560	+	1.67692i	0.675627	+	0.737244i	$0.263873\pi$
$41$	2.13583	+	10.7375i	0.333560	+	1.67692i	−0.342067	+	0.939676i	$0.611127\pi$
$42$	2.85173	−	2.38195i	0.440031	−	0.367542i
$43$	0.489747	−	1.18235i	0.0746858	−	0.180307i	−0.882127	−	0.471011i	$-0.843889\pi$
$43$	0.489747	−	1.18235i	0.0746858	−	0.180307i	0.956813	+	0.290703i	$0.0938893\pi$
$44$	−1.70962	+	0.340064i	−0.257735	+	0.0512666i
$45$	0.00526647	+	0.304283i	0.000785079	+	0.0453598i
$46$	−3.89480	+	19.5805i	−0.574257	+	2.88699i
$47$	−1.36863	+	1.36863i	−0.199635	+	0.199635i	−0.799843	−	0.600209i	$-0.795084\pi$
$47$	−1.36863	+	1.36863i	−0.199635	+	0.199635i	0.600209	+	0.799843i	$0.295084\pi$
$48$	0.449431	+	4.19105i	0.0648698	+	0.604925i
$49$	0.923880	−	0.382683i	0.131983	−	0.0546691i
$50$	−10.7041			−1.51378
$51$	4.38410	+	5.63735i	0.613896	+	0.789387i
$52$	14.3373			1.98822
$53$	−0.780086	+	0.323122i	−0.107153	+	0.0443843i	−0.435616	−	0.900133i	$-0.643469\pi$
$53$	−0.780086	+	0.323122i	−0.107153	+	0.0443843i	0.328463	+	0.944517i	$0.393469\pi$
$54$	−8.43024	+	7.29282i	−1.14721	+	0.992427i
$55$	0.0480533	−	0.0480533i	0.00647950	−	0.00647950i
$56$	0.251948	−	1.26663i	0.0336680	−	0.169260i
$57$	−5.40384	−	9.90280i	−0.715756	−	1.31166i
$58$	4.35141	−	0.865548i	0.571368	−	0.113652i
$59$	0.238614	−	0.576065i	0.0310649	−	0.0749973i	−0.907586	−	0.419867i	$-0.862077\pi$
$59$	0.238614	−	0.576065i	0.0310649	−	0.0749973i	0.938651	+	0.344869i	$0.112077\pi$
$60$	0.293081	+	0.350885i	0.0378366	+	0.0452990i
$61$	−2.02246	−	10.1676i	−0.258950	−	1.30183i	−0.863130	−	0.504982i	$-0.831499\pi$
$61$	−2.02246	−	10.1676i	−0.258950	−	1.30183i	0.604180	−	0.796848i	$-0.293501\pi$
$62$	−15.2676	−	10.2015i	−1.93898	−	1.29559i
$63$	−2.75136	+	1.19584i	−0.346638	+	0.150662i
$64$	8.39552	+	8.39552i	1.04944	+	1.04944i
$65$	−0.464757	+	0.310541i	−0.0576460	+	0.0385178i
$66$	2.47918	+	0.222535i	0.305166	+	0.0273922i
$67$		−	4.86548i		−	0.594413i	−0.954813	−	0.297207i	$-0.903945\pi$
$67$		−	4.86548i		−	0.594413i	0.954813	−	0.297207i	$-0.0960550\pi$
$68$	10.4428	+	2.45876i	1.26637	+	0.298169i
$69$	7.47512	−	14.2809i	0.899899	−	1.71921i
$70$	0.0832789	+	0.201053i	0.00995373	+	0.0240304i
$71$	2.60774	+	3.90275i	0.309481	+	0.463172i	0.953308	−	0.302000i	$-0.0976542\pi$
$71$	2.60774	+	3.90275i	0.309481	+	0.463172i	−0.643827	+	0.765171i	$0.722654\pi$
$72$	−0.689973	+	3.81239i	−0.0813141	+	0.449295i
$73$	−7.26060	−	1.44422i	−0.849789	−	0.169034i	−0.249062	−	0.968488i	$-0.580122\pi$
$73$	−7.26060	−	1.44422i	−0.849789	−	0.169034i	−0.600727	+	0.799454i	$0.705122\pi$
$74$	5.74077	−	8.59167i	0.667351	−	0.998762i
$75$	8.29169	+	2.43711i	0.957442	+	0.281413i
$76$	−15.6574	−	6.48553i	−1.79603	−	0.743941i
$77$	0.618916	+	0.256364i	0.0705321	+	0.0292153i
$78$	−19.6426	−	5.77340i	−2.22409	−	0.653708i
$79$	−4.28505	+	6.41304i	−0.482106	+	0.721523i	−0.990181	−	0.139790i	$-0.955357\pi$
$79$	−4.28505	+	6.41304i	−0.482106	+	0.721523i	0.508075	+	0.861313i	$0.330357\pi$
$80$	−0.242125	−	0.0481617i	−0.0270704	−	0.00538464i
$81$	8.19075	−	3.72983i	0.910083	−	0.414425i
$82$	−13.0480	−	19.5277i	−1.44091	−	2.15647i
$83$	−4.50149	−	10.8675i	−0.494102	−	1.19287i	−0.952615	−	0.304180i	$-0.901618\pi$
$83$	−4.50149	−	10.8675i	−0.494102	−	1.19287i	0.458512	−	0.888688i	$-0.348382\pi$
$84$	−2.09002	+	3.99288i	−0.228040	+	0.435659i
$85$	−0.391770	+	0.146484i	−0.0424934	+	0.0158884i
$86$			2.74540i			0.296044i
$87$	−3.56780	−	0.320251i	−0.382508	−	0.0343345i
$88$	0.719346	−	0.480652i	0.0766826	−	0.0512376i
$89$	−2.65581	−	2.65581i	−0.281515	−	0.281515i	0.552198	−	0.833713i	$-0.313789\pi$
$89$	−2.65581	−	2.65581i	−0.281515	−	0.281515i	−0.833713	+	0.552198i	$0.813789\pi$
$90$	−0.260237	−	0.598745i	−0.0274314	−	0.0631133i
$91$	−4.58146	−	3.06124i	−0.480268	−	0.320905i
$92$	−4.72411	−	23.7497i	−0.492523	−	2.47608i
$93$	9.50403	+	11.3785i	0.985522	+	1.17989i
$94$	1.58896	−	3.83609i	0.163889	−	0.395663i
$95$	0.648026	−	0.128900i	0.0664861	−	0.0132249i
$96$	−6.47430	−	11.8645i	−0.660780	−	1.21091i
$97$	1.74146	−	8.75492i	0.176819	−	0.888927i	−0.785886	−	0.618372i	$-0.787793\pi$
$97$	1.74146	−	8.75492i	0.176819	−	0.888927i	0.962704	−	0.270556i	$-0.0872074\pi$
$98$	−1.51691	+	1.51691i	−0.153231	+	0.153231i
$99$	−1.86978	−	0.736844i	−0.187920	−	0.0740556i
$100$	11.9950	−	4.96848i	1.19950	−	0.496848i
$101$	−8.45834			−0.841636			−0.420818	−	0.907145i	$-0.638257\pi$
$101$	−8.45834			−0.841636			−0.420818	+	0.907145i	$0.638257\pi$
$102$	−13.3169	−	7.57375i	−1.31857	−	0.749913i
$103$	−13.1695			−1.29763			−0.648815	−	0.760946i	$-0.724735\pi$
$103$	−13.1695			−1.29763			−0.648815	+	0.760946i	$0.724735\pi$
$104$	−6.57428	+	2.72316i	−0.644661	+	0.267027i
$105$	−0.0187344	−	0.174703i	−0.00182829	−	0.0170492i
$106$	1.28081	−	1.28081i	0.124404	−	0.124404i
$107$	−0.327791	+	1.64792i	−0.0316887	+	0.159310i	−0.993390	−	0.114791i	$-0.963380\pi$
$107$	−0.327791	+	1.64792i	−0.0316887	+	0.159310i	0.961701	+	0.274101i	$0.0883802\pi$
$108$	6.06184	−	12.0854i	0.583300	−	1.16291i
$109$	−11.5512	+	2.29767i	−1.10640	+	0.220077i	−0.714296	−	0.699844i	$-0.753253\pi$
$109$	−11.5512	+	2.29767i	−1.10640	+	0.220077i	−0.392105	+	0.919921i	$0.628253\pi$
$110$	−0.0557893	+	0.134687i	−0.00531931	+	0.0128419i
$111$	−6.40313	+	5.34830i	−0.607758	+	0.507638i
$112$	−0.474767	−	2.38681i	−0.0448612	−	0.225533i
$113$	−0.685561	−	0.458077i	−0.0644921	−	0.0430923i	0.522906	−	0.852390i	$-0.324848\pi$
$113$	−0.685561	−	0.458077i	−0.0644921	−	0.0430923i	−0.587398	+	0.809298i	$0.699848\pi$
$114$	18.8397	+	15.1904i	1.76450	+	1.42271i
$115$	0.667548	+	0.667548i	0.0622491	+	0.0622491i
$116$	−4.47442	+	2.98971i	−0.415440	+	0.277588i
$117$	13.9013	+	8.94449i	1.28517	+	0.826918i
$118$			1.33761i			0.123137i
$119$	−2.81200	−	3.01540i	−0.257776	−	0.276421i
$120$	−0.201036	−	0.105230i	−0.0183520	−	0.00960613i
$121$	−4.03778	−	9.74806i	−0.367071	−	0.886187i
$122$	12.3554	+	18.4912i	1.11861	+	1.67411i
$123$	5.66127	+	18.0975i	0.510460	+	1.63179i
$124$	21.8440	+	4.34504i	1.96165	+	0.390196i
$125$	−0.563006	+	0.842598i	−0.0503568	+	0.0753643i
$126$	4.47128	−	4.62879i	0.398334	−	0.412365i
$127$	−7.18398	−	2.97570i	−0.637475	−	0.264051i	0.0404504	−	0.999182i	$-0.487121\pi$
$127$	−7.18398	−	2.97570i	−0.637475	−	0.264051i	−0.677925	+	0.735131i	$0.737121\pi$
$128$	−9.11269	−	3.77460i	−0.805456	−	0.333631i
$129$	0.625075	−	2.12667i	0.0550348	−	0.187243i
$130$	0.666181	−	0.997010i	0.0584279	−	0.0874435i
$131$	8.71466	+	1.73345i	0.761403	+	0.151453i	0.560495	−	0.828158i	$-0.310611\pi$
$131$	8.71466	+	1.73345i	0.761403	+	0.151453i	0.200908	+	0.979610i	$0.435611\pi$
$132$	−2.88146	+	0.901382i	−0.250799	+	0.0784552i
$133$	3.61856	+	5.41556i	0.313769	+	0.469589i
$134$	3.99429	+	9.64306i	0.345054	+	0.833033i
$135$	0.0652646	+	0.523057i	0.00561708	+	0.0450175i
$136$	−5.25550	+	0.856004i	−0.450655	+	0.0734017i
$137$		−	14.2970i		−	1.22148i	−0.791832	−	0.610738i	$-0.790873\pi$
$137$		−	14.2970i		−	1.22148i	0.791832	−	0.610738i	$-0.209127\pi$
$138$	−3.09142	+	34.4404i	−0.263159	+	2.93176i
$139$	0.307838	−	0.205691i	0.0261105	−	0.0174465i	−0.542447	−	0.840090i	$-0.682502\pi$
$139$	0.307838	−	0.205691i	0.0261105	−	0.0174465i	0.568557	+	0.822644i	$0.307502\pi$
$140$	−0.186644	−	0.186644i	−0.0157743	−	0.0157743i
$141$	−2.10426	+	2.60978i	−0.177211	+	0.219783i
$142$	−8.37230	−	5.59419i	−0.702588	−	0.469454i
$143$	−0.720129	−	3.62033i	−0.0602202	−	0.302747i
$144$	1.54800	+	7.13472i	0.129000	+	0.594560i
$145$	0.0802866	−	0.193829i	0.00666744	−	0.0160966i
$146$	15.5756	−	3.09819i	1.28905	−	0.256408i
$147$	1.52041	−	0.829670i	0.125401	−	0.0684300i
$148$	−2.44513	+	12.2925i	−0.200988	+	1.01044i
$149$	−15.3068	+	15.3068i	−1.25398	+	1.25398i	−0.300057	+	0.953921i	$0.597006\pi$
$149$	−15.3068	+	15.3068i	−1.25398	+	1.25398i	−0.953921	+	0.300057i	$0.902994\pi$
$150$	−18.4343	+	1.97682i	−1.50515	+	0.161407i
$151$	1.10038	−	0.455791i	0.0895475	−	0.0370918i	−0.337460	−	0.941340i	$-0.609568\pi$
$151$	1.10038	−	0.455791i	0.0895475	−	0.0370918i	0.427008	+	0.904248i	$0.359568\pi$
$152$	8.41148			0.682261
$153$	8.59129	+	8.89886i	0.694565	+	0.719430i
$154$	−1.43711			−0.115806
$155$	−0.802207	+	0.332285i	−0.0644348	+	0.0266898i
$156$	24.6913	−	2.64780i	1.97689	−	0.211994i
$157$	13.7956	−	13.7956i	1.10101	−	1.10101i	0.106719	−	0.994289i	$-0.465965\pi$
$157$	13.7956	−	13.7956i	1.10101	−	1.10101i	0.994289	−	0.106719i	$-0.0340345\pi$
$158$	3.22795	−	16.2280i	0.256802	−	1.29103i
$159$	−1.28377	+	0.700540i	−0.101810	+	0.0555564i
$160$	0.776395	−	0.154434i	0.0613794	−	0.0122091i
$161$	−3.56136	+	8.59788i	−0.280674	+	0.677608i
$162$	−13.1715	+	14.1164i	−1.03485	+	1.10909i
$163$	−2.01416	−	10.1259i	−0.157761	−	0.793119i	−0.975920	−	0.218127i	$-0.930005\pi$
$163$	−2.01416	−	10.1259i	−0.157761	−	0.793119i	0.818159	−	0.574992i	$-0.194995\pi$
$164$	23.6856	+	15.8262i	1.84954	+	1.23582i
$165$	0.0738818	−	0.0916307i	0.00575169	−	0.00713344i
$166$	17.8433	+	17.8433i	1.38491	+	1.38491i
$167$	11.7142	−	7.82717i	0.906471	−	0.605685i	−0.0125377	−	0.999921i	$-0.503991\pi$
$167$	11.7142	−	7.82717i	0.906471	−	0.605685i	0.919009	+	0.394237i	$0.128991\pi$
$168$	0.199979	−	2.22789i	0.0154287	−	0.171885i
$169$			17.3610i			1.33546i
$170$	0.656206	−	0.611943i	0.0503287	−	0.0469339i
$171$	−11.1352	−	16.0564i	−0.851531	−	1.22786i
$172$	−1.27433	−	3.07649i	−0.0971664	−	0.234581i
$173$	6.93650	+	10.3812i	0.527372	+	0.789268i	0.995537	−	0.0943729i	$-0.0300846\pi$
$173$	6.93650	+	10.3812i	0.527372	+	0.789268i	−0.468165	+	0.883641i	$0.655085\pi$
$174$	7.33404	−	2.29424i	0.555992	−	0.173926i
$175$	−4.89383	−	0.973444i	−0.369939	−	0.0735854i
$176$	0.905733	−	1.35552i	0.0682722	−	0.102177i
$177$	0.304548	−	1.03615i	0.0228912	−	0.0778820i
$178$	7.44390	+	3.08336i	0.557944	+	0.231108i
$179$	−12.6750	−	5.25018i	−0.947377	−	0.392417i	−0.145133	−	0.989412i	$-0.546361\pi$
$179$	−12.6750	−	5.25018i	−0.947377	−	0.392417i	−0.802244	+	0.596996i	$0.796361\pi$
$180$	0.569539	+	0.550159i	0.0424509	+	0.0410065i
$181$	−7.10801	+	10.6379i	−0.528334	+	0.790708i	−0.995629	−	0.0933935i	$-0.970229\pi$
$181$	−7.10801	+	10.6379i	−0.528334	+	0.790708i	0.467295	+	0.884101i	$0.345229\pi$
$182$	11.5933	+	2.30604i	0.859350	+	0.170935i
$183$	−5.36079	−	17.1369i	−0.396281	−	1.26680i
$184$	6.67713	+	9.99303i	0.492245	+	0.736696i
$185$	−0.186990	−	0.451434i	−0.0137478	−	0.0331901i
$186$	−28.1774	−	14.7491i	−2.06607	−	1.08146i
$187$	0.0963492	−	2.76043i	0.00704575	−	0.201863i
$188$			5.03627i			0.367307i
$189$	−4.51747	+	2.56757i	−0.328598	+	0.186763i
$190$	−1.17852	+	0.787465i	−0.0854992	+	0.0571287i
$191$	7.13994	+	7.13994i	0.516628	+	0.516628i	0.916549	−	0.399922i	$-0.130963\pi$
$191$	7.13994	+	7.13994i	0.516628	+	0.516628i	−0.399922	+	0.916549i	$0.630963\pi$
$192$	16.0090	+	12.9081i	1.15535	+	0.931561i
$193$	−1.58216	−	1.05716i	−0.113886	−	0.0760962i	0.497323	−	0.867566i	$-0.334316\pi$
$193$	−1.58216	−	1.05716i	−0.113886	−	0.0760962i	−0.611209	+	0.791469i	$0.709316\pi$
$194$	3.73583	+	18.7813i	0.268217	+	1.34842i
$195$	−0.743043	+	0.620637i	−0.0532104	+	0.0444447i
$196$	0.995745	−	2.40394i	0.0711246	−	0.171710i
$197$	−6.38849	+	1.27075i	−0.455161	+	0.0905372i	−0.417346	−	0.908748i	$-0.637040\pi$
$197$	−6.38849	+	1.27075i	−0.455161	+	0.0905372i	−0.0378149	+	0.999285i	$0.512040\pi$
$198$	4.31069	−	0.0746085i	0.306347	−	0.00530220i
$199$	−2.44475	+	12.2906i	−0.173304	+	0.871258i	0.792078	+	0.610419i	$0.208999\pi$
$199$	−2.44475	+	12.2906i	−0.173304	+	0.871258i	−0.965382	+	0.260839i	$0.916001\pi$
$200$	−4.55654	+	4.55654i	−0.322196	+	0.322196i
$201$	−0.898554	−	8.37922i	−0.0633791	−	0.591025i
$202$	16.7639	−	6.94382i	1.17950	−	0.488565i
$203$	2.06815			0.145156
$204$	18.4384	+	2.30586i	1.29095	+	0.161442i
$205$	−1.11058			−0.0775666
$206$	26.1011	−	10.8114i	1.81855	−	0.753268i
$207$	10.2361	−	25.9747i	0.711459	−	1.80536i
$208$	−9.48173	+	9.48173i	−0.657440	+	0.657440i
$209$	−0.851235	+	4.27945i	−0.0588812	+	0.296016i
$210$	0.180551	+	0.330869i	0.0124592	+	0.0228321i
$211$	15.7696	−	3.13676i	1.08562	−	0.215944i	0.380323	−	0.924854i	$-0.375813\pi$
$211$	15.7696	−	3.13676i	1.08562	−	0.215944i	0.705299	+	0.708910i	$0.250813\pi$
$212$	−0.840766	+	2.02979i	−0.0577441	+	0.139406i
$213$	5.21174	+	6.23964i	0.357103	+	0.427533i
$214$	−0.703187	−	3.53516i	−0.0480688	−	0.241658i
$215$	0.107944	+	0.0721262i	0.00736175	+	0.00491896i
$216$	−0.484184	+	6.69304i	−0.0329446	+	0.455404i
$217$	−6.05250	−	6.05250i	−0.410870	−	0.410870i
$218$	21.0074	−	14.0367i	1.42280	−	0.950684i
$219$	−12.7708	−	1.14632i	−0.862968	−	0.0774614i
$220$		−	0.176826i		−	0.0119216i
$221$	−5.20675	+	22.1139i	−0.350244	+	1.48755i
$222$	8.29992	−	15.8566i	0.557054	−	1.06422i
$223$	4.62551	+	11.1670i	0.309747	+	0.747795i	0.999713	+	0.0239534i	$0.00762534\pi$
$223$	4.62551	+	11.1670i	0.309747	+	0.747795i	−0.689966	+	0.723842i	$0.742375\pi$
$224$	4.33537	+	6.48834i	0.289669	+	0.433520i
$225$	14.7298	+	2.66583i	0.981989	+	0.177722i
$226$	1.73479	+	0.345071i	0.115397	+	0.0229538i
$227$	−9.81528	+	14.6896i	−0.651463	+	0.974983i	0.347836	+	0.937555i	$0.386917\pi$
$227$	−9.81528	+	14.6896i	−0.651463	+	0.974983i	−0.999299	+	0.0374281i	$0.988083\pi$
$228$	−28.1626	−	8.27762i	−1.86512	−	0.548199i
$229$	−6.63834	−	2.74969i	−0.438674	−	0.181705i	0.152406	−	0.988318i	$-0.451298\pi$
$229$	−6.63834	−	2.74969i	−0.438674	−	0.181705i	−0.591079	+	0.806613i	$0.701298\pi$
$230$	−1.87105	−	0.775016i	−0.123374	−	0.0511030i
$231$	1.11323	+	0.327202i	0.0732450	+	0.0215283i
$232$	1.48387	−	2.22077i	0.0974209	−	0.145801i
$233$	−28.3272	−	5.63463i	−1.85578	−	0.369137i	−0.864684	−	0.502316i	$-0.832481\pi$
$233$	−28.3272	−	5.63463i	−1.85578	−	0.369137i	−0.991092	+	0.133179i	$0.957481\pi$
$234$	−34.8943	−	6.31522i	−2.28111	−	0.412839i
$235$	−0.109084	−	0.163256i	−0.00711585	−	0.0106496i
$236$	−0.620875	−	1.49893i	−0.0404155	−	0.0975717i
$237$	−6.19526	+	11.8357i	−0.402426	+	0.768814i
$238$	8.04867	+	3.66783i	0.521718	+	0.237750i
$239$			20.0413i			1.29637i	0.761484	+	0.648184i	$0.224471\pi$
$239$			20.0413i			1.29637i	−0.761484	+	0.648184i	$0.775529\pi$
$240$	−0.425877	−	0.0382274i	−0.0274902	−	0.00246757i
$241$	5.87676	−	3.92673i	0.378555	−	0.252943i	−0.351706	−	0.936111i	$-0.614398\pi$
$241$	5.87676	−	3.92673i	0.378555	−	0.252943i	0.730261	+	0.683168i	$0.239398\pi$
$242$	16.0052	+	16.0052i	1.02885	+	1.02885i
$243$	13.4171	−	7.93609i	0.860707	−	0.509100i
$244$	−22.4285	−	14.9862i	−1.43584	−	0.959395i
$245$	0.0197905	+	0.0994937i	0.00126437	+	0.00635642i
$246$	−26.0773	−	31.2204i	−1.66263	−	1.99054i
$247$	13.7339	−	33.1566i	0.873869	−	2.10971i
$248$	−10.8417	+	2.15655i	−0.688451	+	0.136941i
$249$	−9.75937	−	17.8845i	−0.618475	−	1.13338i
$250$	0.424115	−	2.13217i	0.0268234	−	0.134850i
$251$	6.56901	−	6.56901i	0.414632	−	0.414632i	−0.468716	−	0.883349i	$-0.655283\pi$
$251$	6.56901	−	6.56901i	0.414632	−	0.414632i	0.883349	+	0.468716i	$0.155283\pi$
$252$	−2.86199	+	7.26244i	−0.180288	+	0.457491i
$253$	−5.75980	+	2.38579i	−0.362116	+	0.149993i
$254$	16.6810			1.04666
$255$	−0.647644	+	0.324624i	−0.0405570	+	0.0203287i
$256$	−2.58664			−0.161665
$257$	−6.66838	+	2.76213i	−0.415962	+	0.172297i	−0.580842	−	0.814017i	$-0.697276\pi$
$257$	−6.66838	+	2.76213i	−0.415962	+	0.172297i	0.164880	+	0.986314i	$0.447276\pi$
$258$	0.507019	+	4.72807i	0.0315657	+	0.294357i
$259$	3.40599	−	3.40599i	0.211638	−	0.211638i
$260$	−0.283742	+	1.42647i	−0.0175969	+	0.0884657i
$261$	−6.20352	+	0.107369i	−0.383988	+	0.00664600i
$262$	−18.6949	+	3.71865i	−1.15498	+	0.229739i
$263$	−2.42094	+	5.84467i	−0.149282	+	0.360398i	−0.980776	−	0.195135i	$-0.937486\pi$
$263$	−2.42094	+	5.84467i	−0.149282	+	0.360398i	0.831495	+	0.555532i	$0.187486\pi$
$264$	1.15007	−	0.960616i	0.0707822	−	0.0591218i
$265$	−0.0167103	−	0.0840084i	−0.00102651	−	0.00516059i
$266$	−11.6176	−	7.76265i	−0.712322	−	0.475958i
$267$	−5.06424	−	4.08330i	−0.309927	−	0.249894i
$268$	−8.95198	−	8.95198i	−0.546829	−	0.546829i
$269$	12.6175	−	8.43075i	0.769303	−	0.514032i	−0.107894	−	0.994162i	$-0.534411\pi$
$269$	12.6175	−	8.43075i	0.769303	−	0.514032i	0.877197	+	0.480131i	$0.159411\pi$
$270$	−0.558750	−	0.983084i	−0.0340044	−	0.0598286i
$271$			8.54847i			0.519283i	0.965705	+	0.259641i	$0.0836043\pi$
$271$			8.54847i			0.519283i	−0.965705	+	0.259641i	$0.916396\pi$
$272$	−8.53225	+	5.28011i	−0.517343	+	0.320154i
$273$	−8.45544	−	4.42589i	−0.511747	−	0.267867i
$274$	11.7370	+	28.3357i	0.709061	+	1.71182i
$275$	−1.85708	−	2.77932i	−0.111986	−	0.167599i
$276$	−12.5218	−	40.0288i	−0.753726	−	2.40945i
$277$	22.0628	+	4.38857i	1.32563	+	0.263683i	0.806611	−	0.591082i	$-0.201299\pi$
$277$	22.0628	+	4.38857i	1.32563	+	0.263683i	0.519015	+	0.854765i	$0.326299\pi$
$278$	−0.441254	+	0.660383i	−0.0264646	+	0.0396071i
$279$	18.4690	+	17.8406i	1.10571	+	1.06809i
$280$	0.121035	+	0.0501344i	0.00723324	+	0.00299611i
$281$	−29.0119	−	12.0171i	−1.73071	−	0.716882i	−0.999393	−	0.0348387i	$-0.988908\pi$
$281$	−29.0119	−	12.0171i	−1.73071	−	0.716882i	−0.731312	−	0.682043i	$-0.761092\pi$
$282$	2.02803	−	6.89988i	0.120767	−	0.410882i
$283$	−8.97649	+	13.4343i	−0.533597	+	0.798584i	−0.996118	−	0.0880238i	$-0.971945\pi$
$283$	−8.97649	+	13.4343i	−0.533597	+	0.798584i	0.462521	+	0.886608i	$0.346945\pi$
$284$	11.9786	+	2.38270i	0.710801	+	0.141387i
$285$	1.09221	−	0.341666i	0.0646970	−	0.0202386i
$286$	4.39934	+	6.58407i	0.260138	+	0.389324i
$287$	−4.18957	−	10.1145i	−0.247303	−	0.597042i
$288$	−13.3410	−	19.2370i	−0.786126	−	1.13355i
$289$	−7.58484	+	15.2141i	−0.446167	+	0.894950i
$290$			0.450067i			0.0264288i
$291$	1.38225	−	15.3991i	0.0810290	−	0.902713i
$292$	−16.0160	+	10.7015i	−0.937264	+	0.626260i
$293$	−10.9849	−	10.9849i	−0.641744	−	0.641744i	0.309240	−	0.950984i	$-0.399925\pi$
$293$	−10.9849	−	10.9849i	−0.641744	−	0.641744i	−0.950984	+	0.309240i	$0.899925\pi$
$294$	−2.33224	+	2.89252i	−0.136019	+	0.168695i
$295$	0.0525925	+	0.0351412i	0.00306205	+	0.00204600i
$296$	−1.21358	−	6.10108i	−0.0705379	−	0.354618i
$297$	−3.35617	−	0.923666i	−0.194745	−	0.0535965i
$298$	17.7710	−	42.9029i	1.02945	−	2.48530i
$299$	50.2930	−	10.0039i	2.90852	−	0.578541i
$300$	19.7399	−	10.7718i	1.13968	−	0.621911i
$301$	−0.249671	+	1.25518i	−0.0143908	+	0.0723474i
$302$	−1.80670	+	1.80670i	−0.103964	+	0.103964i
$303$	−14.5668	+	1.56208i	−0.836838	+	0.0897392i
$304$	14.6439	−	6.06571i	0.839886	−	0.347892i
$305$	1.05164			0.0602167
$306$	−24.3328	−	10.5840i	−1.39102	−	0.605046i
$307$	10.8705			0.620410			0.310205	−	0.950670i	$-0.399602\pi$
$307$	10.8705			0.620410			0.310205	+	0.950670i	$0.399602\pi$
$308$	1.61042	−	0.667060i	0.0917624	−	0.0380092i
$309$	−22.6802	+	2.43214i	−1.29023	+	0.138360i
$310$	1.31713	−	1.31713i	0.0748081	−	0.0748081i
$311$	−1.69936	+	8.54325i	−0.0963618	+	0.484443i	0.902223	+	0.431269i	$0.141934\pi$
$311$	−1.69936	+	8.54325i	−0.0963618	+	0.484443i	−0.998585	+	0.0531745i	$0.983066\pi$
$312$	−10.8192	+	5.90389i	−0.612515	+	0.334242i
$313$	20.2877	−	4.03547i	1.14673	−	0.228098i	0.415083	−	0.909784i	$-0.363753\pi$
$313$	20.2877	−	4.03547i	1.14673	−	0.228098i	0.731646	+	0.681685i	$0.238753\pi$
$314$	−16.0165	+	38.6673i	−0.903866	+	2.18212i
$315$	−0.0645279	−	0.297409i	−0.00363574	−	0.0167571i
$316$	3.91527	+	19.6834i	0.220251	+	1.10728i
$317$	−13.5030	−	9.02238i	−0.758401	−	0.506748i	0.115228	−	0.993339i	$-0.463240\pi$
$317$	−13.5030	−	9.02238i	−0.758401	−	0.506748i	−0.873630	+	0.486591i	$0.838240\pi$
$318$	1.96925	−	2.44233i	0.110430	−	0.136959i
$319$	0.979678	+	0.979678i	0.0548515	+	0.0548515i
$320$	−1.00145	+	0.669149i	−0.0559829	+	0.0374066i
$321$	−0.260178	+	2.89854i	−0.0145217	+	0.161781i
$322$		−	19.9641i		−	1.11256i
$323$	15.6895	−	21.7949i	0.872989	−	1.21270i
$324$	8.20764	−	21.9326i	0.455980	−	1.21848i
$325$	10.5214	+	25.4009i	0.583621	+	1.40899i
$326$	12.3047	+	18.4153i	0.681494	+	1.01993i
$327$	−19.4688	+	6.09025i	−1.07663	+	0.336792i
$328$	−13.8669	−	2.75830i	−0.765671	−	0.152301i
$329$	1.07532	−	1.60934i	0.0592845	−	0.0887255i
$330$	−0.0712051	+	0.242259i	−0.00391971	+	0.0133359i
$331$	−18.2595	−	7.56333i	−1.00363	−	0.415718i	−0.180504	−	0.983574i	$-0.557773\pi$
$331$	−18.2595	−	7.56333i	−1.00363	−	0.415718i	−0.823128	+	0.567856i	$0.807773\pi$
$332$	−28.2774	−	11.7129i	−1.55193	−	0.642829i
$333$	−10.0396	+	10.3933i	−0.550167	+	0.569547i
$334$	−16.7911	+	25.1296i	−0.918767	+	1.37503i
$335$	0.484085	+	0.0962904i	0.0264484	+	0.00526091i
$336$	−1.25843	−	4.02284i	−0.0686529	−	0.219464i
$337$	0.0824970	+	0.123465i	0.00449390	+	0.00672559i	0.833710	−	0.552203i	$-0.186213\pi$
$337$	0.0824970	+	0.123465i	0.00449390	+	0.00672559i	−0.829216	+	0.558928i	$0.811213\pi$
$338$	−14.2524	−	34.4083i	−0.775228	−	1.87157i
$339$	−1.26525	−	0.662281i	−0.0687192	−	0.0359701i
$340$	−0.451300	+	0.990332i	−0.0244752	+	0.0537083i
$341$		−	5.73411i		−	0.310520i
$342$	35.2506	+	22.6813i	1.90614	+	1.22647i
$343$	−0.831470	+	0.555570i	−0.0448951	+	0.0299980i
$344$	1.16867	+	1.16867i	0.0630105	+	0.0630105i
$345$	1.27292	+	1.02635i	0.0685316	+	0.0552570i
$346$	−22.2701	−	14.8804i	−1.19725	−	0.799974i
$347$	−3.33115	−	16.7468i	−0.178825	−	0.899015i	−0.961125	−	0.276113i	$-0.910953\pi$
$347$	−3.33115	−	16.7468i	−0.178825	−	0.899015i	0.782300	−	0.622902i	$-0.214047\pi$
$348$	−7.15361	+	5.97515i	−0.383473	+	0.320301i
$349$	−2.42801	+	5.86174i	−0.129968	+	0.313772i	−0.975446	−	0.220240i	$-0.929316\pi$
$349$	−2.42801	+	5.86174i	−0.129968	+	0.313772i	0.845477	+	0.534011i	$0.179316\pi$
$350$	10.4984	−	2.08826i	0.561163	−	0.111622i
$351$	25.5923	+	12.8367i	1.36602	+	0.685173i
$352$	−1.01986	+	5.12717i	−0.0543586	+	0.273279i
$353$	6.43976	−	6.43976i	0.342754	−	0.342754i	−0.514648	−	0.857402i	$-0.672077\pi$
$353$	6.43976	−	6.43976i	0.342754	−	0.342754i	0.857402	+	0.514648i	$0.172077\pi$
$354$	0.247029	+	2.30360i	0.0131295	+	0.122435i
$355$	−0.439908	+	0.182216i	−0.0233479	+	0.00967101i
$356$	−9.77282			−0.517959
$357$	−5.39965	−	4.67373i	−0.285780	−	0.247360i
$358$	29.4312			1.55549
$359$	6.81964	−	2.82479i	0.359927	−	0.149087i	−0.195389	−	0.980726i	$-0.562597\pi$
$359$	6.81964	−	2.82479i	0.359927	−	0.149087i	0.555317	+	0.831639i	$0.312597\pi$
$360$	−0.365654	−	0.144097i	−0.0192717	−	0.00759459i
$361$	−16.5621	+	16.5621i	−0.871688	+	0.871688i
$362$	5.35449	−	26.9189i	0.281426	−	1.41482i
$363$	−8.75403	−	16.0422i	−0.459468	−	0.841996i
$364$	−14.0618	+	2.79706i	−0.737038	+	0.146606i
$365$	0.287382	−	0.693802i	0.0150423	−	0.0363152i
$366$	24.6932	+	29.5633i	1.29073	+	1.54530i
$367$	−0.513862	−	2.58336i	−0.0268234	−	0.134850i	0.965053	−	0.262054i	$-0.0843998\pi$
$367$	−0.513862	−	2.58336i	−0.0268234	−	0.134850i	−0.991877	+	0.127204i	$0.959400\pi$
$368$	18.8307	+	12.5823i	0.981619	+	0.655897i
$369$	13.0919	+	30.1215i	0.681539	+	1.56806i
$370$	0.741204	+	0.741204i	0.0385334	+	0.0385334i
$371$	0.702059	−	0.469101i	0.0364491	−	0.0243545i
$372$	38.4217	+	3.44879i	1.99207	+	0.178812i
$373$			19.7377i			1.02198i	0.859587	+	0.510989i	$0.170721\pi$
$373$			19.7377i			1.02198i	−0.859587	+	0.510989i	$0.829279\pi$
$374$	2.07520	+	5.55008i	0.107306	+	0.286988i
$375$	−0.813986	+	1.55508i	−0.0420340	+	0.0803040i
$376$	−0.956566	−	2.30935i	−0.0493311	−	0.119096i
$377$	−6.33110	−	9.47516i	−0.326068	−	0.487995i
$378$	6.84550	−	8.79735i	0.352095	−	0.452487i
$379$	−11.6495	−	2.31724i	−0.598396	−	0.119028i	−0.113407	−	0.993549i	$-0.536176\pi$
$379$	−11.6495	−	2.31724i	−0.598396	−	0.119028i	−0.484989	+	0.874520i	$0.661176\pi$
$380$	0.955138	−	1.42946i	0.0489975	−	0.0733300i
$381$	−12.9216	−	3.79795i	−0.661995	−	0.194575i
$382$	−20.0124	−	8.28939i	−1.02392	−	0.424122i
$383$	7.18632	+	2.97667i	0.367204	+	0.152101i	0.558653	−	0.829402i	$-0.311319\pi$
$383$	7.18632	+	2.97667i	0.367204	+	0.152101i	−0.191449	+	0.981503i	$0.561319\pi$
$384$	−16.3908	−	4.81760i	−0.836437	−	0.245847i
$385$	−0.0377552	+	0.0565047i	−0.00192418	+	0.00287974i
$386$	4.00360	+	0.796365i	0.203778	+	0.0405339i
$387$	0.683737	−	3.77794i	0.0347563	−	0.192044i
$388$	−12.9040	−	19.3123i	−0.655103	−	0.980431i
$389$	9.00765	+	21.7464i	0.456706	+	1.10259i	0.969723	+	0.244207i	$0.0785278\pi$
$389$	9.00765	+	21.7464i	0.456706	+	1.10259i	−0.513017	+	0.858378i	$0.671472\pi$
$390$	0.963154	−	1.84006i	0.0487712	−	0.0931749i
$391$	38.3474	+	1.33847i	1.93931	+	0.0676892i
$392$			1.29144i			0.0652277i
$393$	15.3283	+	1.37590i	0.773211	+	0.0694047i
$394$	11.6183	−	7.76313i	0.585324	−	0.391101i
$395$	−0.553253	−	0.553253i	−0.0278372	−	0.0278372i
$396$	−4.79592	+	2.08449i	−0.241004	+	0.104749i
$397$	15.6261	+	10.4410i	0.784251	+	0.524020i	0.882033	−	0.471188i	$-0.156175\pi$
$397$	15.6261	+	10.4410i	0.784251	+	0.524020i	−0.0977816	+	0.995208i	$0.531175\pi$
$398$	−5.24456	−	26.3662i	−0.262886	−	1.32162i
$399$	7.23195	+	8.65828i	0.362050	+	0.433456i
$400$	−4.64686	+	11.2185i	−0.232343	+	0.560926i
$401$	−0.784324	+	0.156012i	−0.0391673	+	0.00779085i	−0.214635	−	0.976694i	$-0.568856\pi$
$401$	−0.784324	+	0.156012i	−0.0391673	+	0.00779085i	0.175468	+	0.984485i	$0.443856\pi$
$402$	8.65974	+	15.8694i	0.431909	+	0.791493i
$403$	−9.20118	+	46.2574i	−0.458343	+	2.30425i
$404$	−15.5625	+	15.5625i	−0.774261	+	0.774261i
$405$	0.208995	+	0.888743i	0.0103850	+	0.0441620i
$406$	−4.09893	+	1.69783i	−0.203427	+	0.0842621i
$407$	3.22682			0.159947
$408$	−8.89281	+	2.44477i	−0.440260	+	0.121034i
$409$	31.0016			1.53293			0.766466	−	0.642284i	$-0.222013\pi$
$409$	31.0016			1.53293			0.766466	+	0.642284i	$0.222013\pi$
$410$	2.20110	−	0.911727i	0.108705	−	0.0450270i
$411$	−2.64037	−	24.6220i	−0.130240	−	1.21451i
$412$	−24.2305	+	24.2305i	−1.19375	+	1.19375i
$413$	−0.121644	+	0.611547i	−0.00598573	+	0.0300923i
$414$	1.03645	+	59.8833i	0.0509387	+	2.94310i
$415$	1.17034	−	0.232795i	0.0574497	−	0.0114274i
$416$	16.4545	−	39.7247i	0.806748	−	1.94766i
$417$	0.492165	−	0.411087i	0.0241014	−	0.0201310i
$418$	−1.82609	−	9.18039i	−0.0893172	−	0.449028i
$419$	−10.0855	−	6.73893i	−0.492710	−	0.329218i	0.284269	−	0.958744i	$-0.408249\pi$
$419$	−10.0855	−	6.73893i	−0.492710	−	0.329218i	−0.776979	+	0.629526i	$0.783249\pi$
$420$	−0.355904	−	0.286965i	−0.0173663	−	0.0140025i
$421$	3.48866	+	3.48866i	0.170027	+	0.170027i	0.786991	−	0.616964i	$-0.211638\pi$
$421$	3.48866	+	3.48866i	0.170027	+	0.170027i	−0.616964	+	0.786991i	$0.711638\pi$
$422$	−28.6791	+	19.1628i	−1.39608	+	0.932829i
$423$	−3.14194	+	4.88311i	−0.152766	+	0.237425i
$424$		−	1.09044i		−	0.0529565i
$425$	3.30732	+	20.3055i	0.160429	+	0.984962i
$426$	−15.4517	−	8.08800i	−0.748638	−	0.391865i
$427$	3.96721	+	9.57768i	0.191987	+	0.463497i
$428$	2.42889	+	3.63510i	0.117405	+	0.175709i
$429$	−1.90879	−	6.10186i	−0.0921573	−	0.294601i
$430$	−0.273150	−	0.0543329i	−0.0131725	−	0.00262017i
$431$	−2.58295	+	3.86566i	−0.124416	+	0.186202i	−0.888449	−	0.458975i	$-0.848217\pi$
$431$	−2.58295	+	3.86566i	−0.124416	+	0.186202i	0.764033	+	0.645178i	$0.223217\pi$
$432$	3.98357	+	12.0014i	0.191659	+	0.577416i
$433$	8.80414	+	3.64679i	0.423100	+	0.175254i	0.584066	−	0.811706i	$-0.301461\pi$
$433$	8.80414	+	3.64679i	0.423100	+	0.175254i	−0.160966	+	0.986960i	$0.551461\pi$
$434$	16.9644	+	7.02689i	0.814317	+	0.337301i
$435$	0.102472	−	0.348635i	0.00491313	−	0.0167158i
$436$	−17.0255	+	25.4804i	−0.815372	+	1.22029i
$437$	−59.4493	−	11.8252i	−2.84385	−	0.565676i
$438$	26.2518	−	8.21213i	1.25436	−	0.392391i
$439$	−5.48822	−	8.21370i	−0.261939	−	0.392019i	0.677067	−	0.735922i	$-0.263251\pi$
$439$	−5.48822	−	8.21370i	−0.261939	−	0.392019i	−0.939005	+	0.343903i	$0.888251\pi$
$440$	0.0335856	+	0.0810827i	0.00160113	+	0.00386547i
$441$	2.46519	−	1.70963i	0.117390	−	0.0814108i
$442$	−7.83488	−	48.1028i	−0.372667	−	2.28802i
$443$		−	29.3796i		−	1.39587i	−0.716162	−	0.697934i	$-0.754103\pi$
$443$		−	29.3796i		−	1.39587i	0.716162	−	0.697934i	$-0.245897\pi$
$444$	−1.94077	+	21.6214i	−0.0921051	+	1.02611i
$445$	0.316796	−	0.211676i	0.0150176	−	0.0100344i
$446$	−18.3349	−	18.3349i	−0.868182	−	0.868182i
$447$	−23.5341	+	29.1878i	−1.11312	+	1.38053i
$448$	−9.87208	−	6.59632i	−0.466412	−	0.311647i
$449$	4.35484	+	21.8933i	0.205518	+	1.03321i	0.936462	+	0.350770i	$0.114080\pi$
$449$	4.35484	+	21.8933i	0.205518	+	1.03321i	−0.730944	+	0.682437i	$0.760920\pi$
$450$	−31.3820	+	6.80887i	−1.47936	+	0.320973i
$451$	2.80664	−	6.77582i	0.132159	−	0.319061i
$452$	−2.10417	+	0.418546i	−0.0989721	+	0.0196868i
$453$	1.81087	−	0.988171i	0.0850821	−	0.0464283i
$454$	7.39389	−	37.1716i	0.347013	−	1.74455i
$455$	0.395243	−	0.395243i	0.0185293	−	0.0185293i
$456$	14.4861	−	1.55343i	0.678371	−	0.0727459i
$457$	−23.7237	+	9.82667i	−1.10975	+	0.459672i	−0.860851	−	0.508858i	$-0.830068\pi$
$457$	−23.7237	+	9.82667i	−1.10975	+	0.459672i	−0.248897	+	0.968530i	$0.580068\pi$
$458$	15.4141			0.720253
$459$	16.4392	+	13.7388i	0.767314	+	0.641271i
$460$	2.45644			0.114532
$461$	20.7903	−	8.61160i	0.968299	−	0.401082i	0.158220	−	0.987404i	$-0.449424\pi$
$461$	20.7903	−	8.61160i	0.968299	−	0.401082i	0.810078	+	0.586321i	$0.199424\pi$
$462$	−2.47496	+	0.265405i	−0.115145	+	0.0123477i
$463$	21.6126	−	21.6126i	1.00442	−	1.00442i	0.00443267	−	0.999990i	$-0.498589\pi$
$463$	21.6126	−	21.6126i	1.00442	−	1.00442i	0.999990	−	0.00443267i	$-0.00141097\pi$
$464$	0.981889	−	4.93629i	0.0455830	−	0.229161i
$465$	−1.32018	+	0.720405i	−0.0612217	+	0.0334080i
$466$	60.7683	−	12.0876i	2.81504	−	0.559946i
$467$	−3.42590	+	8.27087i	−0.158532	+	0.382730i	−0.983109	−	0.183019i	$-0.941413\pi$
$467$	−3.42590	+	8.27087i	−0.158532	+	0.382730i	0.824577	+	0.565749i	$0.191413\pi$
$468$	42.0338	−	9.11996i	1.94301	−	0.421570i
$469$	0.949208	+	4.77199i	0.0438304	+	0.220350i
$470$	0.350221	+	0.234010i	0.0161545	+	0.0107941i
$471$	21.2107	−	26.3062i	0.977337	−	1.21213i
$472$	0.569398	+	0.569398i	0.0262087	+	0.0262087i
$473$	−0.712845	+	0.476308i	−0.0327767	+	0.0219007i
$474$	2.56212	−	28.5436i	0.117682	−	1.31105i
$475$		−	32.4992i		−	1.49116i
$476$	−10.7218	−	0.374231i	−0.491434	−	0.0171529i
$477$	−2.08151	+	1.44354i	−0.0953057	+	0.0660951i
$478$	−16.4528	−	39.7206i	−0.752534	−	1.81678i
$479$	−12.8218	−	19.1892i	−0.585843	−	0.876776i	0.413589	−	0.910464i	$-0.364275\pi$
$479$	−12.8218	−	19.1892i	−0.585843	−	0.876776i	−0.999432	+	0.0336873i	$0.989275\pi$
$480$	1.30857	−	0.409348i	0.0597277	−	0.0186841i
$481$	−26.0309	−	5.17787i	−1.18691	−	0.236091i
$482$	−8.42373	+	12.6070i	−0.383690	+	0.574233i
$483$	−4.54544	+	15.4648i	−0.206825	+	0.703672i
$484$	−25.3645	−	10.5063i	−1.15293	−	0.477560i
$485$	0.836594	+	0.346529i	0.0379878	+	0.0157351i
$486$	−20.0767	+	26.7435i	−0.910698	+	1.21311i
$487$	−1.08616	+	1.62555i	−0.0492184	+	0.0736606i	−0.855263	−	0.518195i	$-0.826604\pi$
$487$	−1.08616	+	1.62555i	−0.0492184	+	0.0736606i	0.806044	+	0.591855i	$0.201604\pi$
$488$	13.1309	+	2.61190i	0.594407	+	0.118235i
$489$	−5.33878	−	17.0666i	−0.241428	−	0.771777i
$490$	−0.120902	−	0.180943i	−0.00546180	−	0.00817417i
$491$	−7.54096	−	18.2055i	−0.340319	−	0.821602i	−0.997683	−	0.0680294i	$-0.978329\pi$
$491$	−7.54096	−	18.2055i	−0.340319	−	0.821602i	0.657365	−	0.753573i	$-0.271671\pi$
$492$	43.7136	+	22.8813i	1.97076	+	1.03157i
$493$	−2.98642	−	7.98714i	−0.134502	−	0.359723i
$494$			76.9890i			3.46390i
$495$	0.110315	−	0.171449i	0.00495830	−	0.00770605i
$496$	−17.3197	+	11.5727i	−0.777678	+	0.519628i
$497$	−3.31902	−	3.31902i	−0.148878	−	0.148878i
$498$	34.0246	+	27.4340i	1.52468	+	1.22935i
$499$	−14.3384	−	9.58060i	−0.641874	−	0.428886i	0.191579	−	0.981477i	$-0.438639\pi$
$499$	−14.3384	−	9.58060i	−0.641874	−	0.428886i	−0.833453	+	0.552591i	$0.813639\pi$
$500$	0.514421	+	2.58617i	0.0230056	+	0.115657i
$501$	18.7284	−	15.6431i	0.836723	−	0.698884i
$502$	−7.62655	+	18.4121i	−0.340390	+	0.821773i
$503$	−4.88901	+	0.972485i	−0.217990	+	0.0433610i	−0.302877	−	0.953030i	$-0.597947\pi$
$503$	−4.88901	+	0.972485i	−0.217990	+	0.0433610i	0.0848868	+	0.996391i	$0.472947\pi$
$504$	−0.0670461	−	3.87375i	−0.00298647	−	0.172550i
$505$	0.167395	−	0.841551i	0.00744897	−	0.0374485i
$506$	9.45695	−	9.45695i	0.420413	−	0.420413i
$507$	3.20622	+	29.8987i	0.142393	+	1.32785i
$508$	−18.6928	+	7.74279i	−0.829357	+	0.343531i
$509$	−0.419679			−0.0186020			−0.00930098	−	0.999957i	$-0.502961\pi$
$509$	−0.419679			−0.0186020			−0.00930098	+	0.999957i	$0.502961\pi$
$510$	1.01709	−	1.17506i	0.0450375	−	0.0520326i
$511$	7.40284			0.327482
$512$	23.3519	−	9.67268i	1.03202	−	0.427476i
$513$	−22.1421	−	25.5955i	−0.977598	−	1.13007i
$514$	10.9487	−	10.9487i	0.482928	−	0.482928i
$515$	0.260632	−	1.31028i	0.0114848	−	0.0577380i
$516$	−2.76278	−	5.06293i	−0.121625	−	0.222883i
$517$	1.27172	−	0.252960i	0.0559301	−	0.0111252i
$518$	−3.95431	+	9.54656i	−0.173743	+	0.419452i
$519$	13.8631	+	16.5972i	0.608521	+	0.728538i
$520$	−0.140828	−	0.707992i	−0.00617573	−	0.0310475i
$521$	20.7223	+	13.8462i	0.907860	+	0.606613i	0.919401	−	0.393321i	$-0.128674\pi$
$521$	20.7223	+	13.8462i	0.907860	+	0.606613i	−0.0115413	+	0.999933i	$0.503674\pi$
$522$	12.2068	−	5.30554i	0.534278	−	0.232217i
$523$	−19.9866	−	19.9866i	−0.873955	−	0.873955i	0.118946	−	0.992901i	$-0.462048\pi$
$523$	−19.9866	−	19.9866i	−0.873955	−	0.873955i	−0.992901	+	0.118946i	$0.962048\pi$
$524$	19.2234	−	12.8447i	0.839780	−	0.561123i
$525$	−8.60782	−	0.772652i	−0.375676	−	0.0337213i
$526$		−	13.5712i		−	0.591732i
$527$	−14.6347	+	32.1144i	−0.637499	+	1.39893i
$528$	1.30949	−	2.50172i	0.0569884	−	0.108874i
$529$	−24.3413	−	58.7650i	−1.05832	−	2.55500i
$530$	0.102085	+	0.152781i	0.00443428	+	0.00663637i
$531$	0.333129	−	1.84068i	0.0144566	−	0.0798788i
$532$	16.6219	+	3.30629i	0.720649	+	0.143346i
$533$	−33.5141	+	50.1573i	−1.45166	+	2.17256i
$534$	13.3891	+	3.93536i	0.579405	+	0.170300i
$535$	−0.157470	−	0.0652262i	−0.00680802	−	0.00281998i
$536$	5.80519	+	2.40459i	0.250746	+	0.103862i
$537$	−22.7983	−	6.70091i	−0.983818	−	0.289166i
$538$	−18.0859	+	27.0674i	−0.779738	+	1.16696i
$539$	−0.657038	−	0.130693i	−0.0283006	−	0.00562935i
$540$	1.08245	+	0.842290i	0.0465812	+	0.0362464i
$541$	23.8575	+	35.7053i	1.02571	+	1.53509i	0.832570	+	0.553920i	$0.186869\pi$
$541$	23.8575	+	35.7053i	1.02571	+	1.53509i	0.193145	+	0.981170i	$0.438131\pi$
$542$	−7.01781	−	16.9425i	−0.301441	−	0.727743i
$543$	−10.2766	+	19.6330i	−0.441013	+	0.842534i
$544$	18.7975	−	26.1123i	0.805936	−	1.11956i
$545$		−	1.19474i		−	0.0511770i
$546$	20.3915	+	1.83038i	0.872677	+	0.0783329i
$547$	−0.221339	+	0.147894i	−0.00946376	+	0.00632348i	−0.560293	−	0.828294i	$-0.689312\pi$
$547$	−0.221339	+	0.147894i	−0.00946376	+	0.00632348i	0.550829	+	0.834618i	$0.314312\pi$
$548$	−26.3050	−	26.3050i	−1.12370	−	1.12370i
$549$	−12.3971	−	28.5228i	−0.529094	−	1.21732i
$550$	5.96227	+	3.98386i	0.254232	+	0.169872i
$551$	2.62794	+	13.2115i	0.111954	+	0.562830i
$552$	13.3447	+	15.9766i	0.567989	+	0.680011i
$553$	2.95160	−	7.12578i	0.125515	−	0.303019i
$554$	−47.3298	+	9.41448i	−2.01085	+	0.399983i
$555$	−0.405401	−	0.742917i	−0.0172083	−	0.0315351i
$556$	0.187940	−	0.944840i	0.00797045	−	0.0400701i
$557$	12.8379	−	12.8379i	0.543958	−	0.543958i	−0.380729	−	0.924687i	$-0.624327\pi$
$557$	12.8379	−	12.8379i	0.543958	−	0.543958i	0.924687	+	0.380729i	$0.124327\pi$
$558$	−51.2504	−	20.1968i	−2.16960	−	0.854998i
$559$	6.51487	−	2.69855i	0.275550	−	0.114136i
$560$	0.246869			0.0104321
$561$	−0.343864	−	4.77174i	−0.0145180	−	0.201463i
$562$	67.3650			2.84162
$563$	26.4216	−	10.9442i	1.11354	−	0.461242i	0.251382	−	0.967888i	$-0.419115\pi$
$563$	26.4216	−	10.9442i	1.11354	−	0.461242i	0.862154	+	0.506646i	$0.169115\pi$
$564$	0.930095	+	8.67334i	0.0391641	+	0.365214i
$565$	0.0591433	−	0.0591433i	0.00248818	−	0.00248818i
$566$	6.76203	−	33.9950i	0.284229	−	1.42892i
$567$	−7.30571	+	5.25610i	−0.306811	+	0.220735i
$568$	−5.94530	+	1.18259i	−0.249459	+	0.0496205i
$569$	−10.4206	+	25.1575i	−0.436853	+	1.05466i	0.540176	+	0.841552i	$0.318358\pi$
$569$	−10.4206	+	25.1575i	−0.436853	+	1.05466i	−0.977029	+	0.213105i	$0.931642\pi$
$570$	−1.88420	+	1.57380i	−0.0789204	+	0.0659194i
$571$	−0.759178	−	3.81665i	−0.0317706	−	0.159722i	0.961643	−	0.274303i	$-0.0884472\pi$
$571$	−0.759178	−	3.81665i	−0.0317706	−	0.159722i	−0.993414	+	0.114582i	$0.963447\pi$
$572$	−7.98600	−	5.33607i	−0.333911	−	0.223112i
$573$	13.6148	+	10.9776i	0.568768	+	0.458597i
$574$	16.6069	+	16.6069i	0.693159	+	0.693159i
$575$	38.6098	−	25.7982i	1.61014	−	1.07586i
$576$	29.9543	+	19.2735i	1.24809	+	0.803061i
$577$		−	16.4659i		−	0.685483i	−0.939430	−	0.342742i	$-0.888644\pi$
$577$		−	16.4659i		−	0.685483i	0.939430	−	0.342742i	$-0.111356\pi$
$578$	2.54270	−	36.3801i	0.105762	−	1.51321i
$579$	−2.91999	−	1.52843i	−0.121351	−	0.0635194i
$580$	−0.208906	−	0.504344i	−0.00867436	−	0.0209418i
$581$	6.53514	+	9.78053i	0.271123	+	0.405765i
$582$	9.90229	+	31.6548i	0.410463	+	1.31213i
$583$	0.554776	+	0.110352i	0.0229765	+	0.00457030i
$584$	5.31144	−	7.94914i	0.219789	−	0.328938i
$585$	−1.16503	+	1.20607i	−0.0481682	+	0.0498649i
$586$	30.7893	+	12.7533i	1.27189	+	0.526835i
$587$	29.2009	+	12.0954i	1.20525	+	0.499230i	0.892691	−	0.450669i	$-0.148814\pi$
$587$	29.2009	+	12.0954i	1.20525	+	0.499230i	0.312557	+	0.949899i	$0.398814\pi$
$588$	1.27089	−	4.32391i	0.0524106	−	0.178315i
$589$	30.9732	−	46.3546i	1.27623	−	1.91001i
$590$	−0.133084	−	0.0264720i	−0.00547897	−	0.00108984i
$591$	−10.7674	+	3.36828i	−0.442913	+	0.138552i
$592$	−6.51240	−	9.74650i	−0.267658	−	0.400579i
$593$	−3.70681	−	8.94903i	−0.152220	−	0.367493i	0.829313	−	0.558785i	$-0.188732\pi$
$593$	−3.70681	−	8.94903i	−0.152220	−	0.367493i	−0.981533	+	0.191292i	$0.938732\pi$
$594$	7.40999	−	0.924584i	0.304035	−	0.0379362i
$595$	0.355664	−	0.220100i	0.0145808	−	0.00902322i
$596$			56.3257i			2.30719i
$597$	−1.94048	+	21.6181i	−0.0794184	+	0.884770i
$598$	−91.4648	+	61.1148i	−3.74027	+	2.49917i
$599$	−12.7855	−	12.7855i	−0.522400	−	0.522400i	0.395896	−	0.918295i	$-0.370434\pi$
$599$	−12.7855	−	12.7855i	−0.522400	−	0.522400i	−0.918295	+	0.395896i	$0.870434\pi$
$600$	−7.00567	+	8.68867i	−0.286005	+	0.354713i
$601$	−4.69103	−	3.13444i	−0.191351	−	0.127857i	0.456204	−	0.889875i	$-0.349209\pi$
$601$	−4.69103	−	3.13444i	−0.191351	−	0.127857i	−0.647555	+	0.762018i	$0.724209\pi$
$602$	−0.535601	−	2.69265i	−0.0218295	−	0.109744i
$603$	−3.09494	−	14.2646i	−0.126036	−	0.580898i
$604$	1.18597	−	2.86319i	0.0482565	−	0.116502i
$605$	1.04978	−	0.208814i	0.0426796	−	0.00848950i
$606$	27.5879	−	15.0544i	1.12068	−	0.611544i
$607$	5.56640	−	27.9842i	0.225933	−	1.13584i	−0.686661	−	0.726978i	$-0.740924\pi$
$607$	5.56640	−	27.9842i	0.225933	−	1.13584i	0.912595	−	0.408866i	$-0.134076\pi$
$608$	−35.9393	+	35.9393i	−1.45753	+	1.45753i
$609$	3.56172	−	0.381945i	0.144328	−	0.0154772i
$610$	−2.08428	+	0.863336i	−0.0843899	+	0.0349555i
$611$	−10.6649			−0.431457
$612$	32.1801	+	0.565896i	1.30080	+	0.0228750i
$613$	3.55808			0.143709			0.0718547	−	0.997415i	$-0.477108\pi$
$613$	3.55808			0.143709			0.0718547	+	0.997415i	$0.477108\pi$
$614$	−21.5445	+	8.92403i	−0.869466	+	0.360145i
$615$	−1.91262	+	0.205102i	−0.0771244	+	0.00827052i
$616$	−0.611754	+	0.611754i	−0.0246483	+	0.0246483i
$617$	−3.66790	+	18.4398i	−0.147664	+	0.742357i	0.834004	+	0.551759i	$0.186043\pi$
$617$	−3.66790	+	18.4398i	−0.147664	+	0.742357i	−0.981668	+	0.190599i	$0.938957\pi$
$618$	42.9541	−	23.4395i	1.72787	−	0.942876i
$619$	−17.6251	+	3.50585i	−0.708412	+	0.140912i	−0.536129	−	0.844136i	$-0.680114\pi$
$619$	−17.6251	+	3.50585i	−0.708412	+	0.140912i	−0.172282	+	0.985048i	$0.555114\pi$
$620$	−0.864608	+	2.08735i	−0.0347235	+	0.0838299i
$621$	12.8314	−	46.6234i	0.514906	−	1.87093i
$622$	−3.64551	−	18.3272i	−0.146172	−	0.734855i
$623$	3.12290	+	2.08665i	0.125116	+	0.0836001i
$624$	−14.5781	+	18.0803i	−0.583592	+	0.723791i
$625$	17.5686	+	17.5686i	0.702744	+	0.702744i
$626$	−36.8960	+	24.6531i	−1.47466	+	0.985336i
$627$	−0.675651	+	7.52717i	−0.0269829	+	0.300606i
$628$		−	50.7649i		−	2.02574i
$629$	−18.0721	−	8.23556i	−0.720582	−	0.328373i
$630$	0.372046	+	0.536471i	0.0148227	+	0.0213735i
$631$	−10.9182	−	26.3589i	−0.434647	−	1.04933i	−0.977770	−	0.209678i	$-0.932758\pi$
$631$	−10.9182	−	26.3589i	−0.434647	−	1.04933i	0.543123	−	0.839653i	$-0.317242\pi$
$632$	−5.53390	−	8.28207i	−0.220127	−	0.329443i
$633$	26.5787	−	8.31438i	1.05641	−	0.330467i
$634$	34.1688	+	6.79660i	1.35702	+	0.269927i
$635$	0.438238	−	0.655869i	0.0173909	−	0.0260274i
$636$	−1.07309	+	3.65093i	−0.0425507	+	0.144769i
$637$	5.09065	+	2.10862i	0.201699	+	0.0835464i
$638$	−2.74592	−	1.13740i	−0.108712	−	0.0450300i
$639$	10.1279	+	9.78326i	0.400653	+	0.387020i
$640$	0.555894	−	0.831954i	0.0219736	−	0.0328859i
$641$	5.72965	+	1.13970i	0.226308	+	0.0450154i	0.306941	−	0.951728i	$-0.400694\pi$
$641$	5.72965	+	1.13970i	0.226308	+	0.0450154i	−0.0806338	+	0.996744i	$0.525694\pi$
$642$	−1.86388	−	5.95830i	−0.0735616	−	0.235155i
$643$	13.3683	+	20.0071i	0.527194	+	0.789002i	0.995520	−	0.0945542i	$-0.0301426\pi$
$643$	13.3683	+	20.0071i	0.527194	+	0.789002i	−0.468326	+	0.883556i	$0.655143\pi$
$644$	9.26668	+	22.3717i	0.365158	+	0.881570i
$645$	0.199220	+	0.104279i	0.00784426	+	0.00410598i
$646$	−13.2032	+	56.0763i	−0.519473	+	2.20629i
$647$			7.58199i			0.298079i	0.988831	+	0.149039i	$0.0476181\pi$
$647$			7.58199i			0.298079i	−0.988831	+	0.149039i	$0.952382\pi$
$648$	0.402216	+	11.6160i	0.0158005	+	0.456320i
$649$	−0.347311	+	0.232066i	−0.0136332	+	0.00910939i
$650$	−41.7054	−	41.7054i	−1.63582	−	1.63582i
$651$	−11.5412	−	9.30570i	−0.452337	−	0.364719i
$652$	−22.3364	−	14.9247i	−0.874761	−	0.584497i
$653$	3.18274	+	16.0007i	0.124550	+	0.626156i	0.991749	+	0.128194i	$0.0409181\pi$
$653$	3.18274	+	16.0007i	0.124550	+	0.626156i	−0.867199	+	0.497962i	$0.834082\pi$
$654$	33.5861	−	28.0533i	1.31332	−	1.09697i
$655$	−0.344935	+	0.832747i	−0.0134777	+	0.0325381i
$656$	−26.1306	+	5.19769i	−1.02023	+	0.202936i
$657$	−22.2052	+	0.384323i	−0.866307	+	0.0149939i
$658$	−0.810046	+	4.07238i	−0.0315789	+	0.158758i
$659$	−0.451881	+	0.451881i	−0.0176028	+	0.0176028i	−0.715853	−	0.698251i	$-0.753962\pi$
$659$	−0.451881	+	0.451881i	−0.0176028	+	0.0176028i	0.698251	+	0.715853i	$0.253962\pi$
$660$	−0.0326562	−	0.304526i	−0.00127114	−	0.0118537i
$661$	−25.7954	+	10.6848i	−1.00333	+	0.415591i	−0.823015	−	0.568019i	$-0.807710\pi$
$661$	−25.7954	+	10.6848i	−1.00333	+	0.415591i	−0.180310	+	0.983610i	$0.557710\pi$
$662$	42.3981			1.64785
$663$	−4.88295	+	39.0457i	−0.189638	+	1.51641i
$664$	15.1912			0.589532
$665$	−0.610427	+	0.252847i	−0.0236714	+	0.00980500i
$666$	11.3655	−	28.8407i	0.440406	−	1.11755i
$667$	−13.6095	+	13.6095i	−0.526963	+	0.526963i
$668$	7.15171	−	35.9541i	0.276708	−	1.39111i
$669$	10.0282	+	18.3772i	0.387714	+	0.710505i
$670$	−1.03847	+	0.206565i	−0.0401197	+	0.00798030i
$671$	−2.65767	+	6.41619i	−0.102598	+	0.247694i
$672$	8.66454	+	10.3734i	0.334242	+	0.400163i
$673$	7.34797	+	36.9407i	0.283243	+	1.42396i	0.816176	+	0.577803i	$0.196090\pi$
$673$	7.34797	+	36.9407i	0.283243	+	1.42396i	−0.532933	+	0.846157i	$0.678910\pi$
$674$	−0.264862	−	0.176975i	−0.0102021	−	0.00681682i
$675$	25.8597	+	1.87073i	0.995341	+	0.0720044i
$676$	31.9424	+	31.9424i	1.22855	+	1.22855i
$677$	20.7667	−	13.8759i	0.798130	−	0.533294i	−0.0883337	−	0.996091i	$-0.528154\pi$
$677$	20.7667	−	13.8759i	0.798130	−	0.533294i	0.886464	+	0.462797i	$0.153154\pi$
$678$	3.05134	+	0.273894i	0.117186	+	0.0105188i
$679$			8.92644i			0.342565i
$680$	0.0188421	−	0.539829i	0.000722560	−	0.0207015i
$681$	−14.1908	+	27.1108i	−0.543792	+	1.03889i
$682$	4.70738	+	11.3646i	0.180255	+	0.435174i
$683$	−9.93345	−	14.8665i	−0.380093	−	0.568849i	0.591263	−	0.806479i	$-0.298630\pi$
$683$	−9.93345	−	14.8665i	−0.380093	−	0.568849i	−0.971356	+	0.237630i	$0.923630\pi$
$684$	−50.0298	−	9.05446i	−1.91294	−	0.346206i
$685$	1.42246	+	0.282945i	0.0543495	+	0.0108108i
$686$	1.19183	−	1.78369i	0.0455041	−	0.0681017i
$687$	−11.9402	−	3.50949i	−0.455547	−	0.133895i
$688$	2.87735	+	1.19184i	0.109698	+	0.0454383i
$689$	−4.29834	−	1.78043i	−0.163754	−	0.0678290i
$690$	−3.36542	−	0.989169i	−0.128119	−	0.0376570i
$691$	−4.27230	+	6.39394i	−0.162526	+	0.243237i	−0.903790	−	0.427976i	$-0.859227\pi$
$691$	−4.27230	+	6.39394i	−0.162526	+	0.243237i	0.741264	+	0.671214i	$0.234227\pi$
$692$	31.8628	+	6.33790i	1.21124	+	0.240931i
$693$	1.97760	+	0.357910i	0.0751230	+	0.0135959i
$694$	20.3503	+	30.4564i	0.772486	+	1.15611i
$695$	0.0143727	+	0.0346987i	0.000545186	+	0.00131620i
$696$	2.14536	−	4.09860i	0.0813195	−	0.155357i
$697$	−33.0123	+	30.7855i	−1.25043	+	1.16608i
$698$		−	13.6108i		−	0.515177i
$699$	−49.8250	−	4.47238i	−1.88456	−	0.169161i
$700$	−10.7952	+	7.21311i	−0.408020	+	0.272630i
$701$	20.4987	+	20.4987i	0.774227	+	0.774227i	0.978842	−	0.204616i	$-0.0655945\pi$
$701$	20.4987	+	20.4987i	0.774227	+	0.774227i	−0.204616	+	0.978842i	$0.565594\pi$
$702$	−61.2604	−	4.43167i	−2.31213	−	0.167263i
$703$	26.0856	+	17.4299i	0.983838	+	0.657380i
$704$	−1.55172	−	7.80105i	−0.0584828	−	0.294013i
$705$	−0.218012	−	0.261009i	−0.00821080	−	0.00983019i
$706$	−7.47649	+	18.0499i	−0.281382	+	0.679315i
$707$	8.29581	−	1.65014i	0.311996	−	0.0620599i
$708$	−1.34608	−	2.46675i	−0.0505887	−	0.0927062i
$709$	−5.42531	+	27.2749i	−0.203752	+	1.02433i	0.734561	+	0.678542i	$0.237388\pi$
$709$	−5.42531	+	27.2749i	−0.203752	+	1.02433i	−0.938313	+	0.345787i	$0.887612\pi$
$710$	0.722279	−	0.722279i	0.0271066	−	0.0271066i
$711$	−8.48352	+	21.5274i	−0.318157	+	0.807340i
$712$	4.48128	−	1.85621i	0.167943	−	0.0695643i
$713$	79.6573			2.98319
$714$	14.5386	+	4.83022i	0.544094	+	0.180767i
$715$	0.374452			0.0140037
$716$	−32.9806	+	13.6610i	−1.23254	+	0.510535i
$717$	3.70123	+	34.5147i	0.138225	+	1.28898i
$718$	−11.1971	+	11.1971i	−0.417872	+	0.417872i
$719$	−1.12242	+	5.64281i	−0.0418594	+	0.210441i	−0.996054	−	0.0887437i	$-0.971715\pi$
$719$	−1.12242	+	5.64281i	−0.0418594	+	0.210441i	0.954195	+	0.299185i	$0.0967148\pi$
$720$	−0.740495	+	0.0128164i	−0.0275966	+	0.000477637i
$721$	12.9165	−	2.56924i	0.481034	−	0.0956837i
$722$	19.2284	−	46.4215i	0.715607	−	1.72763i
$723$	9.39564	−	7.84783i	0.349427	−	0.291864i
$724$	6.49461	+	32.6506i	0.241370	+	1.21345i
$725$	−8.58032	−	5.73319i	−0.318665	−	0.212925i
$726$	30.5196	+	24.6080i	1.13269	+	0.913287i
$727$	−3.75952	−	3.75952i	−0.139433	−	0.139433i	0.633945	−	0.773378i	$-0.281434\pi$
$727$	−3.75952	−	3.75952i	−0.139433	−	0.139433i	−0.773378	+	0.633945i	$0.781434\pi$
$728$	5.91670	−	3.95341i	0.219287	−	0.146523i
$729$	21.6410	−	16.1452i	0.801518	−	0.597971i
$730$			1.61099i			0.0596255i
$731$	5.20800	−	0.848268i	0.192625	−	0.0313743i
$732$	−41.3935	−	21.6669i	−1.52995	−	0.800830i
$733$	−9.49378	−	22.9200i	−0.350661	−	0.846570i	−0.996539	−	0.0831293i	$-0.973509\pi$
$733$	−9.49378	−	22.9200i	−0.350661	−	0.846570i	0.645878	−	0.763441i	$-0.276491\pi$
$734$	3.13923	+	4.69819i	0.115871	+	0.173413i
$735$	0.0524572	+	0.167691i	0.00193491	+	0.00618537i
$736$	−71.2257	−	14.1677i	−2.62542	−	0.522228i
$737$	−1.81085	+	2.71012i	−0.0667033	+	0.0998286i
$738$	−50.6754	−	48.9511i	−1.86539	−	1.80192i
$739$	−11.0915	−	4.59424i	−0.408006	−	0.169002i	0.169234	−	0.985576i	$-0.445871\pi$
$739$	−11.0915	−	4.59424i	−0.408006	−	0.169002i	−0.577241	+	0.816574i	$0.695871\pi$
$740$	−1.17464	−	0.486550i	−0.0431804	−	0.0178859i
$741$	17.5289	−	59.6380i	0.643941	−	2.19086i
$742$	−1.00633	+	1.50608i	−0.0369435	+	0.0552898i
$743$	−44.9012	−	8.93141i	−1.64727	−	0.327662i	−0.717710	−	0.696342i	$-0.754810\pi$
$743$	−44.9012	−	8.93141i	−1.64727	−	0.327662i	−0.929556	+	0.368680i	$0.879810\pi$
$744$	−18.2731	+	5.71621i	−0.669925	+	0.209567i
$745$	−1.22000	−	1.82585i	−0.0446972	−	0.0668941i
$746$	−16.2035	−	39.1188i	−0.593253	−	1.43224i
$747$	−20.1103	−	28.9979i	−0.735796	−	1.06098i
$748$	−4.90163	−	5.25618i	−0.179221	−	0.192185i
$749$		−	1.68020i		−	0.0613932i
$750$	0.336633	−	3.75030i	0.0122921	−	0.136942i
$751$	9.05003	−	6.04704i	0.330240	−	0.220659i	−0.379385	−	0.925239i	$-0.623864\pi$
$751$	9.05003	−	6.04704i	0.330240	−	0.220659i	0.709625	+	0.704579i	$0.248864\pi$
$752$	−3.33066	−	3.33066i	−0.121457	−	0.121457i
$753$	10.0998	−	12.5262i	0.368058	−	0.456479i
$754$	20.3264	+	13.5817i	0.740243	+	0.494615i
$755$	0.0235713	+	0.118501i	0.000857848	+	0.00431269i
$756$	−3.58762	+	13.0358i	−0.130481	+	0.474106i
$757$	5.07486	−	12.2518i	0.184449	−	0.445299i	−0.804425	−	0.594054i	$-0.797527\pi$
$757$	5.07486	−	12.2518i	0.184449	−	0.445299i	0.988874	+	0.148755i	$0.0475266\pi$
$758$	24.9909	−	4.97100i	0.907711	−	0.180555i
$759$	−9.47880	+	5.17247i	−0.344059	+	0.187749i
$760$	−0.166467	+	0.836889i	−0.00603841	+	0.0303571i
$761$	19.6037	−	19.6037i	0.710634	−	0.710634i	−0.256034	−	0.966668i	$-0.582416\pi$
$761$	19.6037	−	19.6037i	0.710634	−	0.710634i	0.966668	+	0.256034i	$0.0824159\pi$
$762$	28.7277	−	3.08065i	1.04070	−	0.111600i
$763$	10.8810	−	4.50704i	0.393917	−	0.163166i
$764$	26.2735			0.950542
$765$	−1.05541	+	0.678666i	−0.0381583	+	0.0245372i
$766$	−16.6865			−0.602907
$767$	3.17416	−	1.31478i	0.114612	−	0.0474740i
$768$	−4.45465	+	0.477699i	−0.160743	+	0.0172375i
$769$	27.6770	−	27.6770i	0.998058	−	0.998058i	−0.00193986	−	0.999998i	$-0.500617\pi$
$769$	27.6770	−	27.6770i	0.998058	−	0.998058i	0.999998	+	0.00193986i	$0.000617477\pi$
$770$	0.0284412	−	0.142983i	0.00102495	−	0.00515276i
$771$	−10.9740	+	5.98839i	−0.395220	+	0.215667i
$772$	−4.85607	+	0.965933i	−0.174774	+	0.0347647i
$773$	15.4469	−	37.2921i	0.555586	−	1.34130i	−0.357644	−	0.933858i	$-0.616420\pi$
$773$	15.4469	−	37.2921i	0.555586	−	1.34130i	0.913230	−	0.407445i	$-0.133580\pi$
$774$	1.74635	+	8.04893i	0.0627714	+	0.289313i
$775$	8.33222	+	41.8889i	0.299302	+	1.50469i
$776$	9.58516	+	6.40460i	0.344087	+	0.229912i
$777$	5.23669	−	6.49473i	0.187865	−	0.232997i
$778$	−35.7051	−	35.7051i	−1.28009	−	1.28009i
$779$	59.2890	−	39.6156i	2.12425	−	1.41938i
$780$	−0.225215	+	2.50903i	−0.00806398	+	0.0898377i
$781$		−	3.14443i		−	0.112516i
$782$	−77.1008	+	28.8283i	−2.75712	+	1.03090i
$783$	−10.6637	+	1.33057i	−0.381091	+	0.0475508i
$784$	0.931289	+	2.24833i	0.0332603	+	0.0802975i
$785$	1.09955	+	1.64560i	0.0392447	+	0.0587338i
$786$	−31.5092	+	9.85675i	−1.12390	+	0.351579i
$787$	35.2230	+	7.00628i	1.25556	+	0.249747i	0.777671	−	0.628672i	$-0.216401\pi$
$787$	35.2230	+	7.00628i	1.25556	+	0.249747i	0.477892	+	0.878419i	$0.341401\pi$
$788$	−9.41611	+	14.0922i	−0.335435	+	0.502014i
$789$	−3.08990	+	10.5126i	−0.110003	+	0.374260i
$790$	1.55070	+	0.642321i	0.0551714	+	0.0228528i
$791$	0.761754	+	0.315529i	0.0270849	+	0.0112189i
$792$	1.80323	−	1.86675i	0.0640749	−	0.0663319i
$793$	31.7353	−	47.4952i	1.12695	−	1.68660i
$794$	−39.5414	−	7.86527i	−1.40327	−	0.279128i
$795$	−0.0442927	−	0.141591i	−0.00157090	−	0.00502172i
$796$	18.1154	+	27.1116i	0.642082	+	0.960943i
$797$	0.533280	+	1.28745i	0.0188897	+	0.0456039i	0.933043	−	0.359765i	$-0.117143\pi$
$797$	0.533280	+	1.28745i	0.0188897	+	0.0456039i	−0.914153	+	0.405369i	$0.867143\pi$
$798$	−21.4412	−	11.2231i	−0.759010	−	0.397294i
$799$	−7.76799	−	1.82898i	−0.274812	−	0.0647046i
$800$		−	38.9370i		−	1.37663i
$801$	−9.47563	−	6.09690i	−0.334805	−	0.215423i
$802$	1.42640	−	0.953090i	0.0503680	−	0.0336548i
$803$	3.50671	+	3.50671i	0.123749	+	0.123749i
$804$	−17.0701	−	13.7637i	−0.602018	−	0.485407i
$805$	−0.784953	−	0.524489i	−0.0276660	−	0.0184858i
$806$	−19.7386	−	99.2328i	−0.695264	−	3.49533i
$807$	20.1726	−	16.8494i	0.710109	−	0.593128i
$808$	4.18022	−	10.0920i	0.147060	−	0.355034i
$809$	−25.4975	+	5.07177i	−0.896445	+	0.178314i	−0.621749	−	0.783217i	$-0.713577\pi$
$809$	−25.4975	+	5.07177i	−0.896445	+	0.178314i	−0.274697	+	0.961531i	$0.588577\pi$
$810$	−1.14382	−	1.58986i	−0.0401898	−	0.0558618i
$811$	−1.22572	+	6.16211i	−0.0430409	+	0.216381i	−0.996320	−	0.0857092i	$-0.972684\pi$
$811$	−1.22572	+	6.16211i	−0.0430409	+	0.216381i	0.953279	+	0.302090i	$0.0976844\pi$
$812$	3.80518	−	3.80518i	0.133536	−	0.133536i
$813$	1.57873	+	14.7220i	0.0553684	+	0.516322i
$814$	−6.39533	+	2.64903i	−0.224156	+	0.0928486i
$815$	1.04732			0.0366861
$816$	−13.7189	+	10.6690i	−0.480258	+	0.373490i
$817$	−8.33546			−0.291621
$818$	−61.4432	+	25.4506i	−2.14831	+	0.889859i
$819$	−15.3791	−	6.06062i	−0.537391	−	0.211775i
$820$	−2.04336	+	2.04336i	−0.0713573	+	0.0713573i
$821$	8.29940	−	41.7239i	0.289651	−	1.45617i	−0.512312	−	0.858800i	$-0.671211\pi$
$821$	8.29940	−	41.7239i	0.289651	−	1.45617i	0.801963	−	0.597374i	$-0.203789\pi$
$822$	25.4463	+	46.6316i	0.887541	+	1.62646i
$823$	−45.4389	+	9.03835i	−1.58390	+	0.315057i	−0.907036	−	0.421052i	$-0.861661\pi$
$823$	−45.4389	+	9.03835i	−1.58390	+	0.315057i	−0.676863	+	0.736109i	$0.736661\pi$
$824$	6.50855	−	15.7130i	0.226736	−	0.547390i
$825$	−3.71150	−	4.44351i	−0.129218	−	0.154703i
$826$	−0.260955	−	1.31191i	−0.00907978	−	0.0456472i
$827$	29.0263	+	19.3948i	1.00934	+	0.674422i	0.946200	−	0.323582i	$-0.104887\pi$
$827$	29.0263	+	19.3948i	1.00934	+	0.674422i	0.0631438	+	0.998004i	$0.479887\pi$
$828$	−28.9573	−	66.6241i	−1.00634	−	2.31535i
$829$	−39.0392	−	39.0392i	−1.35589	−	1.35589i	−0.878921	−	0.476967i	$-0.841736\pi$
$829$	−39.0392	−	39.0392i	−1.35589	−	1.35589i	−0.476967	−	0.878921i	$-0.658264\pi$
$830$	−2.12842	+	1.42217i	−0.0738786	+	0.0493641i
$831$	38.8065	+	3.48334i	1.34618	+	0.120836i
$832$			65.4215i			2.26808i
$833$	3.34625	+	2.40887i	0.115941	+	0.0834623i
$834$	−0.637958	+	1.21879i	−0.0220907	+	0.0422031i
$835$	0.546924	+	1.32039i	0.0189271	+	0.0456940i
$836$	6.30756	+	9.43993i	0.218151	+	0.326487i
$837$	35.1017	+	27.3137i	1.21329	+	0.944101i
$838$	25.5211	+	5.07646i	0.881612	+	0.175363i
$839$	−21.0616	+	31.5210i	−0.727128	+	1.08822i	0.265152	+	0.964207i	$0.414578\pi$
$839$	−21.0616	+	31.5210i	−0.727128	+	1.08822i	−0.992280	+	0.124018i	$0.960422\pi$
$840$	0.217703	+	0.0639876i	0.00751146	+	0.00220778i
$841$	−22.8408	−	9.46099i	−0.787615	−	0.326241i
$842$	−9.77829	−	4.05030i	−0.336982	−	0.139583i
$843$	−52.1830	−	15.3377i	−1.79728	−	0.528259i
$844$	23.2431	−	34.7857i	0.800059	−	1.19737i
$845$	−1.72731	−	0.343583i	−0.0594212	−	0.0118196i
$846$	2.21835	−	12.2574i	0.0762686	−	0.421416i
$847$	5.86194	+	8.77302i	0.201419	+	0.301445i
$848$	−0.786342	−	1.89840i	−0.0270031	−	0.0651912i
$849$	−12.9781	+	24.7940i	−0.445406	+	0.850927i
$850$	−23.2246	−	37.5291i	−0.796596	−	1.28724i
$851$			44.8264i			1.53663i
$852$	21.0694	+	1.89122i	0.721824	+	0.0647921i
$853$	4.39922	−	2.93946i	0.150626	−	0.100645i	−0.477973	−	0.878374i	$-0.658628\pi$
$853$	4.39922	−	2.93946i	0.150626	−	0.100645i	0.628600	+	0.777729i	$0.283628\pi$
$854$	−15.7255	−	15.7255i	−0.538115	−	0.538115i
$855$	1.81788	−	0.790119i	0.0621702	−	0.0270215i
$856$	−1.80419	−	1.20552i	−0.0616660	−	0.0412039i
$857$	11.1108	+	55.8579i	0.379539	+	1.90807i	0.417269	+	0.908783i	$0.362987\pi$
$857$	11.1108	+	55.8579i	0.379539	+	1.90807i	−0.0377302	+	0.999288i	$0.512013\pi$
$858$	8.79238	+	10.5265i	0.300167	+	0.359368i
$859$	−3.44262	+	8.31121i	−0.117461	+	0.283575i	−0.971665	−	0.236362i	$-0.924045\pi$
$859$	−3.44262	+	8.31121i	−0.117461	+	0.283575i	0.854204	+	0.519937i	$0.174045\pi$
$860$	0.331311	−	0.0659019i	0.0112976	−	0.00224724i
$861$	−9.08313	−	16.6453i	−0.309552	−	0.567269i
$862$	1.94575	−	9.78194i	0.0662725	−	0.333174i
$863$	28.2323	−	28.2323i	0.961038	−	0.961038i	−0.0382312	−	0.999269i	$-0.512172\pi$
$863$	28.2323	−	28.2323i	0.961038	−	0.961038i	0.999269	+	0.0382312i	$0.0121724\pi$
$864$	−26.5283	−	30.6658i	−0.902510	−	1.04327i
$865$	−1.17014	+	0.484688i	−0.0397860	+	0.0164799i
$866$	−20.4430			−0.694682
$867$	−10.2527	+	27.6022i	−0.348200	+	0.937420i
$868$	−22.2719			−0.755959
$869$	4.77363	−	1.97730i	0.161934	−	0.0670755i
$870$	0.0831181	+	0.775095i	0.00281797	+	0.0262782i
$871$	18.9570	−	18.9570i	0.642332	−	0.642332i
$872$	2.96731	−	14.9177i	0.100486	−	0.505176i
$873$	−0.463422	−	26.7753i	−0.0156845	−	0.906207i
$874$	127.532	−	25.3678i	4.31385	−	0.858078i
$875$	0.387805	−	0.936245i	0.0131102	−	0.0316509i
$876$	−25.6060	+	21.3878i	−0.865146	+	0.722625i
$877$	−1.27179	−	6.39374i	−0.0429454	−	0.215901i	0.953354	−	0.301856i	$-0.0976060\pi$
$877$	−1.27179	−	6.39374i	−0.0429454	−	0.215901i	−0.996299	+	0.0859545i	$0.972606\pi$
$878$	17.6203	+	11.7735i	0.594655	+	0.397336i
$879$	−20.9466	−	16.8892i	−0.706511	−	0.569660i
$880$	0.116941	+	0.116941i	0.00394209	+	0.00394209i
$881$	−24.3806	+	16.2906i	−0.821402	+	0.548843i	−0.893765	−	0.448535i	$-0.851946\pi$
$881$	−24.3806	+	16.2906i	−0.821402	+	0.548843i	0.0723632	+	0.997378i	$0.476946\pi$
$882$	−3.48234	+	5.41215i	−0.117256	+	0.182237i
$883$			3.29128i			0.110760i	0.998465	+	0.0553801i	$0.0176371\pi$
$883$			3.29128i			0.110760i	−0.998465	+	0.0553801i	$0.982363\pi$
$884$	31.1075	+	50.2673i	1.04626	+	1.69067i
$885$	0.0970635	+	0.0508066i	0.00326275	+	0.00170785i
$886$	24.1190	+	58.2285i	0.810294	+	1.95622i
$887$	−24.7102	−	36.9815i	−0.829688	−	1.24172i	−0.967906	−	0.251314i	$-0.919137\pi$
$887$	−24.7102	−	36.9815i	−0.829688	−	1.24172i	0.138218	−	0.990402i	$-0.455863\pi$
$888$	−3.21674	−	10.2830i	−0.107947	−	0.345075i
$889$	7.62647	+	1.51700i	0.255784	+	0.0508785i
$890$	−0.454094	+	0.679600i	−0.0152213	+	0.0227802i
$891$	−5.95050	−	0.970900i	−0.199349	−	0.0325264i
$892$	29.0565	+	12.0356i	0.972884	+	0.402982i
$893$	11.6470	+	4.82433i	0.389751	+	0.161440i
$894$	22.6815	−	77.1684i	0.758582	−	2.58090i
$895$	0.773205	−	1.15718i	0.0258454	−	0.0386804i
$896$	9.67398	+	1.92427i	0.323185	+	0.0642855i
$897$	84.7660	−	26.5166i	2.83025	−	0.885363i
$898$	−26.6041	−	39.8159i	−0.887792	−	1.32867i
$899$	−6.77441	−	16.3549i	−0.225939	−	0.545465i
$900$	32.0062	−	22.1965i	1.06687	−	0.739884i
$901$	−2.82543	−	2.03395i	−0.0941288	−	0.0677606i
$902$			15.7333i			0.523862i
$903$	−0.198172	+	2.20775i	−0.00659473	+	0.0734694i
$904$	0.885362	−	0.591580i	0.0294467	−	0.0196757i
$905$	−0.917731	−	0.917731i	−0.0305064	−	0.0305064i
$906$	−2.77779	+	3.44511i	−0.0922859	+	0.114456i
$907$	−9.44235	−	6.30918i	−0.313528	−	0.209493i	0.388842	−	0.921304i	$-0.372875\pi$
$907$	−9.44235	−	6.30918i	−0.313528	−	0.209493i	−0.702371	+	0.711811i	$0.747875\pi$
$908$	8.96825	+	45.0865i	0.297622	+	1.49625i
$909$	−24.7980	+	5.38036i	−0.822499	+	0.178455i
$910$	−0.458873	+	1.10782i	−0.0152115	+	0.0367238i
$911$	−19.7762	+	3.93372i	−0.655213	+	0.130330i	−0.511492	−	0.859288i	$-0.670907\pi$
$911$	−19.7762	+	3.93372i	−0.655213	+	0.130330i	−0.143721	+	0.989618i	$0.545907\pi$
$912$	24.0992	−	13.1507i	0.798004	−	0.435462i
$913$	−1.53733	+	7.72870i	−0.0508784	+	0.255783i
$914$	38.9516	−	38.9516i	1.28840	−	1.28840i
$915$	1.81111	−	0.194216i	0.0598734	−	0.00642059i
$916$	−17.2730	+	7.15471i	−0.570716	+	0.236398i
$917$	−8.88539			−0.293421
$918$	−43.8601	−	13.7337i	−1.44760	−	0.453280i
$919$	1.27881			0.0421842			0.0210921	−	0.999778i	$-0.493286\pi$
$919$	1.27881			0.0421842			0.0210921	+	0.999778i	$0.493286\pi$
$920$	−1.12639	+	0.466565i	−0.0371359	+	0.0153822i
$921$	18.7208	−	2.00755i	0.616873	−	0.0661510i
$922$	−34.1352	+	34.1352i	−1.12418	+	1.12418i
$923$	−5.04567	+	25.3663i	−0.166080	+	0.834941i
$924$	2.65024	−	1.44621i	0.0871866	−	0.0475767i
$925$	−23.5726	+	4.68888i	−0.775061	+	0.154169i
$926$	−25.0920	+	60.5775i	−0.824574	+	1.99070i
$927$	−38.6102	+	8.37715i	−1.26813	+	0.275142i
$928$	3.14851	+	15.8286i	0.103355	+	0.519600i
$929$	−12.3743	−	8.26823i	−0.405987	−	0.271272i	0.335766	−	0.941946i	$-0.391005\pi$
$929$	−12.3743	−	8.26823i	−0.405987	−	0.271272i	−0.741752	+	0.670674i	$0.766005\pi$
$930$	2.02509	−	2.51158i	0.0664053	−	0.0823581i
$931$	−4.60556	−	4.60556i	−0.150941	−	0.150941i
$932$	−62.4862	+	41.7520i	−2.04680	+	1.36763i
$933$	−1.34883	+	15.0268i	−0.0441588	+	0.491956i
$934$		−	19.2048i		−	0.628399i
$935$	0.272738	+	0.0642165i	0.00891950	+	0.00210010i
$936$	−17.5422	+	12.1656i	−0.573384	+	0.397646i
$937$	−7.72113	−	18.6405i	−0.252238	−	0.608957i	0.746146	−	0.665783i	$-0.231902\pi$
$937$	−7.72113	−	18.6405i	−0.252238	−	0.608957i	−0.998384	+	0.0568253i	$0.981902\pi$
$938$	−5.79880	−	8.67852i	−0.189338	−	0.283364i
$939$	34.1937	−	10.6965i	1.11587	−	0.349068i
$940$	−0.501077	−	0.0996703i	−0.0163433	−	0.00325089i
$941$	−10.7955	+	16.1565i	−0.351922	+	0.526688i	−0.964625	−	0.263625i	$-0.915082\pi$
$941$	−10.7955	+	16.1565i	−0.351922	+	0.526688i	0.612703	+	0.790313i	$0.290082\pi$
$942$	−20.4423	+	69.5499i	−0.666045	+	2.26606i
$943$	94.1286	+	38.9893i	3.06525	+	1.26967i
$944$	1.40190	+	0.580685i	0.0456279	+	0.0188997i
$945$	−0.166054	−	0.500274i	−0.00540173	−	0.0162739i
$946$	1.02179	−	1.52922i	0.0332212	−	0.0497191i
$947$	−5.89708	−	1.17300i	−0.191629	−	0.0381174i	0.0983425	−	0.995153i	$-0.468646\pi$
$947$	−5.89708	−	1.17300i	−0.191629	−	0.0381174i	−0.289972	+	0.957035i	$0.593646\pi$
$948$	10.3779	+	33.1752i	0.337059	+	1.07748i
$949$	−22.6619	−	33.9159i	−0.735635	−	1.10096i
$950$	26.6800	+	64.4112i	0.865613	+	2.08978i
$951$	−24.9207	−	13.0444i	−0.808110	−	0.422994i
$952$	4.98752	−	1.86485i	0.161646	−	0.0604402i
$953$			17.1170i			0.554474i	0.960802	+	0.277237i	$0.0894187\pi$
$953$			17.1170i			0.554474i	−0.960802	+	0.277237i	$0.910581\pi$
$954$	2.94034	−	4.56980i	0.0951972	−	0.147953i
$955$	−0.851681	+	0.569075i	−0.0275598	+	0.0184148i
$956$	36.8740	+	36.8740i	1.19259	+	1.19259i
$957$	1.86811	+	1.50625i	0.0603873	+	0.0486902i
$958$	41.1652	+	27.5057i	1.32999	+	0.888669i
$959$	2.78921	+	14.0223i	0.0900683	+	0.452804i
$960$	−1.60110	+	1.33734i	−0.0516753	+	0.0431625i
$961$	−16.1743	+	39.0482i	−0.521751	+	1.25962i
$962$	55.8423	−	11.1077i	1.80043	−	0.358127i
$963$	0.0872287	+	5.03985i	0.00281091	+	0.162407i
$964$	3.58786	−	18.0374i	0.115557	−	0.580946i
$965$	0.136493	−	0.136493i	0.00439385	−	0.00439385i
$966$	−3.68696	−	34.3817i	−0.118626	−	1.10621i
$967$	−30.5189	+	12.6413i	−0.981421	+	0.406518i	−0.814952	−	0.579529i	$-0.803237\pi$
$967$	−30.5189	+	12.6413i	−0.981421	+	0.406518i	−0.166469	+	0.986047i	$0.553237\pi$
$968$	13.6263			0.437966
$969$	22.9951	−	40.4322i	0.738708	−	1.29887i
$970$	−1.94255			−0.0623717
$971$	21.7544	−	9.01095i	0.698130	−	0.289175i	−0.00525249	−	0.999986i	$-0.501672\pi$
$971$	21.7544	−	9.01095i	0.698130	−	0.289175i	0.703383	+	0.710811i	$0.251672\pi$
$972$	10.0845	−	39.2877i	0.323460	−	1.26015i
$973$	−0.261795	+	0.261795i	−0.00839275	+	0.00839275i
$974$	0.818206	−	4.11340i	0.0262170	−	0.131802i
$975$	22.8107	+	41.8017i	0.730527	+	1.33873i
$976$	24.7436	−	4.92182i	0.792025	−	0.157544i
$977$	13.3630	−	32.2611i	0.427520	−	1.03212i	−0.552552	−	0.833478i	$-0.686346\pi$
$977$	13.3630	−	32.2611i	0.427520	−	1.03212i	0.980071	−	0.198645i	$-0.0636541\pi$
$978$	24.5918	+	29.4420i	0.786359	+	0.941450i
$979$	0.490867	+	2.46776i	0.0156882	+	0.0788698i
$980$	0.219471	+	0.146646i	0.00701073	+	0.00468442i
$981$	−32.4040	+	14.0840i	−1.03458	+	0.449667i
$982$	29.8914	+	29.8914i	0.953871	+	0.953871i
$983$	−28.4246	+	18.9927i	−0.906605	+	0.605774i	−0.919047	−	0.394149i	$-0.871040\pi$
$983$	−28.4246	+	18.9927i	−0.906605	+	0.605774i	0.0124419	+	0.999923i	$0.496040\pi$
$984$	−24.3906	−	2.18934i	−0.777545	−	0.0697938i
$985$		−	0.660763i		−	0.0210537i
$986$	12.4759	+	13.3783i	0.397313	+	0.426052i
$987$	1.55469	−	2.97015i	0.0494862	−	0.0945410i
$988$	−35.7358	−	86.2738i	−1.13691	−	2.74474i
$989$	−6.61679	−	9.90272i	−0.210402	−	0.314888i
$990$	−0.0778876	+	0.430362i	−0.00247543	+	0.0136778i
$991$	14.3202	+	2.84846i	0.454895	+	0.0904842i	0.417219	−	0.908806i	$-0.363005\pi$
$991$	14.3202	+	2.84846i	0.454895	+	0.0904842i	0.0376754	+	0.999290i	$0.488005\pi$
$992$	37.1087	−	55.5371i	1.17820	−	1.76330i
$993$	−32.8429	−	9.65323i	−1.04224	−	0.306336i
$994$	9.30280	+	3.85335i	0.295067	+	0.122221i
$995$	−1.17445	−	0.486475i	−0.0372327	−	0.0154223i
$996$	−50.8619	−	14.9494i	−1.61162	−	0.473690i
$997$	6.20485	−	9.28622i	0.196510	−	0.294097i	−0.720108	−	0.693862i	$-0.755908\pi$
$997$	6.20485	−	9.28622i	0.196510	−	0.294097i	0.916618	+	0.399764i	$0.130908\pi$
$998$	36.2828	+	7.21710i	1.14851	+	0.228453i
$999$	−15.3706	+	19.7531i	−0.486303	+	0.624961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bf.a.29.7	✓	288
3.2	odd	2	inner	357.2.bf.a.29.30	yes	288
17.10	odd	16	inner	357.2.bf.a.197.30	yes	288
51.44	even	16	inner	357.2.bf.a.197.7	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bf.a.29.7	✓	288	1.1	even	1	trivial
357.2.bf.a.29.30	yes	288	3.2	odd	2	inner
357.2.bf.a.197.7	yes	288	51.44	even	16	inner
357.2.bf.a.197.30	yes	288	17.10	odd	16	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bf (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98193 + 0.820944i) q^{2} +(1.72218 - 0.184679i) q^{3} +(1.83990 - 1.83990i) q^{4} +(-0.0197905 + 0.0994937i) q^{5} +(-3.26163 + 1.77983i) q^{6} +(-0.980785 + 0.195090i) q^{7} +(-0.494214 + 1.19314i) q^{8} +(2.93179 - 0.636101i) q^{9} +(-0.0424552 - 0.213437i) q^{10} +(-0.557010 - 0.372182i) q^{11} +(2.82884 - 3.50842i) q^{12} +(3.89622 + 3.89622i) q^{13} +(1.78369 - 1.19183i) q^{14} +(-0.0157083 + 0.175001i) q^{15} +2.43357i q^{16} +(2.16970 + 3.50606i) q^{17} +(-5.28840 + 3.66754i) q^{18} +(-2.49251 - 6.01745i) q^{19} +(0.146646 + 0.219471i) q^{20} +(-1.65306 + 0.517111i) q^{21} +(1.40950 + 0.280366i) q^{22} +(5.17029 - 7.73789i) q^{23} +(-0.630775 + 2.14606i) q^{24} +(4.60989 + 1.90948i) q^{25} +(-10.9206 - 4.52347i) q^{26} +(4.93158 - 1.63692i) q^{27} +(-1.44560 + 2.16349i) q^{28} +(-2.02841 - 0.403476i) q^{29} +(-0.112533 - 0.359735i) q^{30} +(4.75542 + 7.11698i) q^{31} +(-2.98625 - 7.20946i) q^{32} +(-1.02800 - 0.538095i) q^{33} +(-7.17846 - 5.16757i) q^{34} -0.101443i q^{35} +(4.22382 - 6.56455i) q^{36} +(-4.00502 + 2.67607i) q^{37} +(9.87997 + 9.87997i) q^{38} +(7.42952 + 5.99042i) q^{39} +(-0.108929 - 0.0727839i) q^{40} +(2.13583 + 10.7375i) q^{41} +(2.85173 - 2.38195i) q^{42} +(0.489747 - 1.18235i) q^{43} +(-1.70962 + 0.340064i) q^{44} +(0.00526647 + 0.304283i) q^{45} +(-3.89480 + 19.5805i) q^{46} +(-1.36863 + 1.36863i) q^{47} +(0.449431 + 4.19105i) q^{48} +(0.923880 - 0.382683i) q^{49} -10.7041 q^{50} +(4.38410 + 5.63735i) q^{51} +14.3373 q^{52} +(-0.780086 + 0.323122i) q^{53} +(-8.43024 + 7.29282i) q^{54} +(0.0480533 - 0.0480533i) q^{55} +(0.251948 - 1.26663i) q^{56} +(-5.40384 - 9.90280i) q^{57} +(4.35141 - 0.865548i) q^{58} +(0.238614 - 0.576065i) q^{59} +(0.293081 + 0.350885i) q^{60} +(-2.02246 - 10.1676i) q^{61} +(-15.2676 - 10.2015i) q^{62} +(-2.75136 + 1.19584i) q^{63} +(8.39552 + 8.39552i) q^{64} +(-0.464757 + 0.310541i) q^{65} +(2.47918 + 0.222535i) q^{66} -4.86548i q^{67} +(10.4428 + 2.45876i) q^{68} +(7.47512 - 14.2809i) q^{69} +(0.0832789 + 0.201053i) q^{70} +(2.60774 + 3.90275i) q^{71} +(-0.689973 + 3.81239i) q^{72} +(-7.26060 - 1.44422i) q^{73} +(5.74077 - 8.59167i) q^{74} +(8.29169 + 2.43711i) q^{75} +(-15.6574 - 6.48553i) q^{76} +(0.618916 + 0.256364i) q^{77} +(-19.6426 - 5.77340i) q^{78} +(-4.28505 + 6.41304i) q^{79} +(-0.242125 - 0.0481617i) q^{80} +(8.19075 - 3.72983i) q^{81} +(-13.0480 - 19.5277i) q^{82} +(-4.50149 - 10.8675i) q^{83} +(-2.09002 + 3.99288i) q^{84} +(-0.391770 + 0.146484i) q^{85} +2.74540i q^{86} +(-3.56780 - 0.320251i) q^{87} +(0.719346 - 0.480652i) q^{88} +(-2.65581 - 2.65581i) q^{89} +(-0.260237 - 0.598745i) q^{90} +(-4.58146 - 3.06124i) q^{91} +(-4.72411 - 23.7497i) q^{92} +(9.50403 + 11.3785i) q^{93} +(1.58896 - 3.83609i) q^{94} +(0.648026 - 0.128900i) q^{95} +(-6.47430 - 11.8645i) q^{96} +(1.74146 - 8.75492i) q^{97} +(-1.51691 + 1.51691i) q^{98} +(-1.86978 - 0.736844i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 48 q^{12} - 48 q^{24} - 64 q^{25} - 64 q^{31} - 224 q^{34} + 16 q^{39} + 64 q^{40} - 64 q^{43} + 64 q^{45} + 32 q^{51} + 128 q^{52} + 112 q^{54} - 32 q^{57} + 32 q^{58} - 144 q^{60} + 32 q^{61}+ \cdots + 304 q^{96}+O(q^{100}) \) 288 * q - 48 * q^12 - 48 * q^24 - 64 * q^25 - 64 * q^31 - 224 * q^34 + 16 * q^39 + 64 * q^40 - 64 * q^43 + 64 * q^45 + 32 * q^51 + 128 * q^52 + 112 * q^54 - 32 * q^57 + 32 * q^58 - 144 * q^60 + 32 * q^61 + 64 * q^64 - 192 * q^66 - 32 * q^70 - 208 * q^72 - 128 * q^76 - 208 * q^78 - 64 * q^79 - 112 * q^81 - 256 * q^82 + 32 * q^85 + 32 * q^88 + 240 * q^90 - 96 * q^91 + 64 * q^93 + 304 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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