LMFDB - Embedded newform 680.2.co.a.419.94

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(99,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 8, 8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.99"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.co (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:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$104$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			419.94
Character	$\chi$	$=$	680.419
Dual form			680.2.co.a.99.94

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.35478 + 0.405659i) q^{2} +(3.02940 - 0.602586i) q^{3} +(1.67088 + 1.09916i) q^{4} +(0.0803191 - 2.23462i) q^{5} +(4.34863 + 0.412531i) q^{6} +(-3.84724 + 2.57064i) q^{7} +(1.81780 + 2.16693i) q^{8} +(6.04253 - 2.50290i) q^{9} +(1.01531 - 2.99485i) q^{10} +(2.30746 + 0.458983i) q^{11} +(5.72411 + 2.32295i) q^{12} +(-0.474407 + 0.474407i) q^{13} +(-6.25499 + 1.92200i) q^{14} +(-1.10323 - 6.81798i) q^{15} +(1.58369 + 3.67314i) q^{16} +(-3.71414 + 1.79030i) q^{17} +(9.20166 - 0.939681i) q^{18} +(-6.53598 - 2.70729i) q^{19} +(2.59042 - 3.64551i) q^{20} +(-10.1058 + 10.1058i) q^{21} +(2.93992 + 1.55787i) q^{22} +(1.31540 - 6.61299i) q^{23} +(6.81261 + 5.46914i) q^{24} +(-4.98710 - 0.358966i) q^{25} +(-0.835166 + 0.450272i) q^{26} +(9.09245 - 6.07538i) q^{27} +(-9.25383 + 0.0665044i) q^{28} +(4.89597 + 3.27138i) q^{29} +(1.27113 - 9.68443i) q^{30} +(-0.996655 - 5.01052i) q^{31} +(0.655518 + 5.61875i) q^{32} +7.26681 q^{33} +(-5.75811 + 0.918803i) q^{34} +(5.43542 + 8.80361i) q^{35} +(12.8474 + 2.45967i) q^{36} +(1.03900 + 5.22343i) q^{37} +(-7.75660 - 6.31917i) q^{38} +(-1.15130 + 1.72304i) q^{39} +(4.98829 - 3.88805i) q^{40} +(-3.57941 + 2.39169i) q^{41} +(-17.7907 + 9.59168i) q^{42} +(-0.819076 - 1.97742i) q^{43} +(3.35100 + 3.30318i) q^{44} +(-5.10771 - 13.7038i) q^{45} +(4.46471 - 8.42556i) q^{46} +(-1.24163 + 1.24163i) q^{47} +(7.01101 + 10.1731i) q^{48} +(5.51427 - 13.3126i) q^{49} +(-6.61082 - 2.50938i) q^{50} +(-10.1728 + 7.66164i) q^{51} +(-1.31413 + 0.271228i) q^{52} +(-2.20958 - 0.915237i) q^{53} +(14.7828 - 4.54240i) q^{54} +(1.21099 - 5.11945i) q^{55} +(-12.5639 - 3.66380i) q^{56} +(-21.4315 - 4.26299i) q^{57} +(5.30591 + 6.41811i) q^{58} +(0.257860 + 0.622529i) q^{59} +(5.65068 - 12.6047i) q^{60} +(-3.33081 + 2.22558i) q^{61} +(0.682311 - 7.19248i) q^{62} +(-16.8130 + 25.1625i) q^{63} +(-1.39121 + 7.87810i) q^{64} +(1.02202 + 1.09823i) q^{65} +(9.84496 + 2.94785i) q^{66} -0.662256 q^{67} +(-8.17371 - 1.09105i) q^{68} -20.8260i q^{69} +(3.79255 + 14.1319i) q^{70} +(2.50239 - 0.497757i) q^{71} +(16.4077 + 8.54401i) q^{72} +(-0.683178 + 1.02245i) q^{73} +(-0.711304 + 7.49810i) q^{74} +(-15.3242 + 1.91770i) q^{75} +(-7.94509 - 11.7077i) q^{76} +(-10.0572 + 4.16585i) q^{77} +(-2.25873 + 1.86731i) q^{78} +(0.742184 - 3.73121i) q^{79} +(8.33528 - 3.24393i) q^{80} +(10.0095 - 10.0095i) q^{81} +(-5.81954 + 1.78820i) q^{82} +(5.07078 + 2.10039i) q^{83} +(-27.9935 + 5.77770i) q^{84} +(3.70234 + 8.44350i) q^{85} +(-0.307511 - 3.01125i) q^{86} +(16.8031 + 6.96009i) q^{87} +(3.19992 + 5.83446i) q^{88} +(5.59049 + 5.59049i) q^{89} +(-1.36077 - 20.6377i) q^{90} +(0.605626 - 3.04469i) q^{91} +(9.46662 - 9.60367i) q^{92} +(-6.03854 - 14.5783i) q^{93} +(-2.18582 + 1.17846i) q^{94} +(-6.57474 + 14.3880i) q^{95} +(5.37160 + 16.6264i) q^{96} +(11.5356 + 7.70783i) q^{97} +(12.8710 - 15.7988i) q^{98} +(15.0917 - 3.00193i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 16 q^{4} - 16 q^{6} - 32 q^{9} - 8 q^{10} - 32 q^{11} - 16 q^{14} - 32 q^{19} - 8 q^{20} - 32 q^{24} - 16 q^{25} - 48 q^{26} + 56 q^{30} + 48 q^{34} - 32 q^{35} + 48 q^{36} - 72 q^{40} - 32 q^{41}+ \cdots - 128 q^{99}+O(q^{100}) $ 832 * q - 16 * q^4 - 16 * q^6 - 32 * q^9 - 8 * q^10 - 32 * q^11 - 16 * q^14 - 32 * q^19 - 8 * q^20 - 32 * q^24 - 16 * q^25 - 48 * q^26 + 56 * q^30 + 48 * q^34 - 32 * q^35 + 48 * q^36 - 72 * q^40 - 32 * q^41 - 48 * q^44 - 32 * q^46 - 32 * q^49 - 32 * q^51 + 32 * q^54 - 16 * q^56 - 32 * q^59 - 112 * q^60 - 16 * q^64 - 96 * q^65 - 48 * q^66 - 80 * q^70 - 16 * q^74 - 16 * q^75 - 16 * q^76 - 104 * q^80 - 32 * q^81 - 192 * q^86 - 32 * q^89 + 72 * q^90 - 32 * q^91 - 16 * q^94 + 288 * q^96 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$e\left(\frac{7}{16}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.35478	+	0.405659i	0.957977	+	0.286844i
$2$	1.35478	+	0.405659i	0.957977	+	0.286844i
$3$	3.02940	−	0.602586i	1.74903	−	0.347903i	0.786189	−	0.617986i	$-0.212051\pi$
$3$	3.02940	−	0.602586i	1.74903	−	0.347903i	0.962837	+	0.270083i	$0.0870510\pi$
$4$	1.67088	+	1.09916i	0.835441	+	0.549581i
$5$	0.0803191	−	2.23462i	0.0359198	−	0.999355i
$5$	0.0803191	−	2.23462i	0.0359198	−	0.999355i
$6$	4.34863	+	0.412531i	1.77532	+	0.168415i
$7$	−3.84724	+	2.57064i	−1.45412	+	0.971612i	−0.457522	+	0.889198i	$0.651263\pi$
$7$	−3.84724	+	2.57064i	−1.45412	+	0.971612i	−0.996598	+	0.0824138i	$0.973737\pi$
$8$	1.81780	+	2.16693i	0.642689	+	0.766127i
$9$	6.04253	−	2.50290i	2.01418	−	0.834300i
$10$	1.01531	−	2.99485i	0.321070	−	0.947056i
$11$	2.30746	+	0.458983i	0.695726	+	0.138389i	0.530270	−	0.847829i	$-0.322090\pi$
$11$	2.30746	+	0.458983i	0.695726	+	0.138389i	0.165456	+	0.986217i	$0.447090\pi$
$12$	5.72411	+	2.32295i	1.65241	+	0.670579i
$13$	−0.474407	+	0.474407i	−0.131577	+	0.131577i	−0.769828	−	0.638251i	$-0.779658\pi$
$13$	−0.474407	+	0.474407i	−0.131577	+	0.131577i	0.638251	+	0.769828i	$0.279658\pi$
$14$	−6.25499	+	1.92200i	−1.67172	+	0.513676i
$15$	−1.10323	−	6.81798i	−0.284854	−	1.76039i
$16$	1.58369	+	3.67314i	0.395922	+	0.918284i
$17$	−3.71414	+	1.79030i	−0.900810	+	0.434213i
$17$	−3.71414	+	1.79030i	−0.900810	+	0.434213i
$18$	9.20166	−	0.939681i	2.16885	−	0.221485i
$19$	−6.53598	−	2.70729i	−1.49946	−	0.621095i	−0.526106	−	0.850419i	$-0.676348\pi$
$19$	−6.53598	−	2.70729i	−1.49946	−	0.621095i	−0.973350	+	0.229324i	$0.926348\pi$
$20$	2.59042	−	3.64551i	0.579235	−	0.815161i
$21$	−10.1058	+	10.1058i	−2.20527	+	2.20527i
$22$	2.93992	+	1.55787i	0.626794	+	0.332138i
$23$	1.31540	−	6.61299i	0.274281	−	1.37890i	−0.560424	−	0.828206i	$-0.689362\pi$
$23$	1.31540	−	6.61299i	0.274281	−	1.37890i	0.834705	−	0.550697i	$-0.185638\pi$
$24$	6.81261	+	5.46914i	1.39062	+	1.11638i
$25$	−4.98710	−	0.358966i	−0.997420	−	0.0717933i
$26$	−0.835166	+	0.450272i	−0.163790	+	0.0883055i
$27$	9.09245	−	6.07538i	1.74984	−	1.16921i
$28$	−9.25383	+	0.0665044i	−1.74881	+	0.0125681i
$29$	4.89597	+	3.27138i	0.909158	+	0.607480i	0.919768	−	0.392464i	$-0.128377\pi$
$29$	4.89597	+	3.27138i	0.909158	+	0.607480i	−0.0106093	+	0.999944i	$0.503377\pi$
$30$	1.27113	−	9.68443i	0.232076	−	1.76813i
$31$	−0.996655	−	5.01052i	−0.179005	−	0.899917i	−0.960982	−	0.276610i	$-0.910789\pi$
$31$	−0.996655	−	5.01052i	−0.179005	−	0.899917i	0.781978	−	0.623306i	$-0.214211\pi$
$32$	0.655518	+	5.61875i	0.115880	+	0.993263i
$33$	7.26681			1.26499
$34$	−5.75811	+	0.918803i	−0.987507	+	0.157573i
$35$	5.43542	+	8.80361i	0.918753	+	1.48808i
$36$	12.8474	+	2.45967i	2.14124	+	0.409945i
$37$	1.03900	+	5.22343i	0.170811	+	0.858727i	0.967215	+	0.253961i	$0.0817334\pi$
$37$	1.03900	+	5.22343i	0.170811	+	0.858727i	−0.796403	+	0.604766i	$0.793267\pi$
$38$	−7.75660	−	6.31917i	−1.25829	−	1.02511i
$39$	−1.15130	+	1.72304i	−0.184355	+	0.275907i
$40$	4.98829	−	3.88805i	0.788718	−	0.614755i
$41$	−3.57941	+	2.39169i	−0.559010	+	0.373519i	−0.802744	−	0.596323i	$-0.796628\pi$
$41$	−3.57941	+	2.39169i	−0.559010	+	0.373519i	0.243734	+	0.969842i	$0.421628\pi$
$42$	−17.7907	+	9.59168i	−2.74517	+	1.48003i
$43$	−0.819076	−	1.97742i	−0.124908	−	0.301554i	0.849039	−	0.528330i	$-0.177182\pi$
$43$	−0.819076	−	1.97742i	−0.124908	−	0.301554i	−0.973947	+	0.226776i	$0.927182\pi$
$44$	3.35100	+	3.30318i	0.505182	+	0.497973i
$45$	−5.10771	−	13.7038i	−0.761413	−	2.04285i
$46$	4.46471	−	8.42556i	0.658285	−	1.24228i
$47$	−1.24163	+	1.24163i	−0.181110	+	0.181110i	−0.791840	−	0.610729i	$-0.790876\pi$
$47$	−1.24163	+	1.24163i	−0.181110	+	0.181110i	0.610729	+	0.791840i	$0.290876\pi$
$48$	7.01101	+	10.1731i	1.01195	+	1.46836i
$49$	5.51427	−	13.3126i	0.787752	−	1.90180i
$50$	−6.61082	−	2.50938i	−0.934912	−	0.354880i
$51$	−10.1728	+	7.66164i	−1.42448	+	1.07284i
$52$	−1.31413	+	0.271228i	−0.182237	+	0.0376126i
$53$	−2.20958	−	0.915237i	−0.303509	−	0.125717i	0.225731	−	0.974190i	$-0.427523\pi$
$53$	−2.20958	−	0.915237i	−0.303509	−	0.125717i	−0.529240	+	0.848472i	$0.677523\pi$
$54$	14.7828	−	4.54240i	2.01169	−	0.618142i
$55$	1.21099	−	5.11945i	0.163290	−	0.690306i
$56$	−12.5639	−	3.66380i	−1.67893	−	0.489596i
$57$	−21.4315	−	4.26299i	−2.83867	−	0.564646i
$58$	5.30591	+	6.41811i	0.696701	+	0.842739i
$59$	0.257860	+	0.622529i	0.0335705	+	0.0810463i	0.939776	−	0.341792i	$-0.111034\pi$
$59$	0.257860	+	0.622529i	0.0335705	+	0.0810463i	−0.906205	+	0.422838i	$0.861034\pi$
$60$	5.65068	−	12.6047i	0.729500	−	1.62726i
$61$	−3.33081	+	2.22558i	−0.426467	+	0.284956i	−0.750224	−	0.661184i	$-0.770054\pi$
$61$	−3.33081	+	2.22558i	−0.426467	+	0.284956i	0.323756	+	0.946140i	$0.395054\pi$
$62$	0.682311	−	7.19248i	0.0866536	−	0.913446i
$63$	−16.8130	+	25.1625i	−2.11824	+	3.17017i
$64$	−1.39121	+	7.87810i	−0.173901	+	0.984763i
$65$	1.02202	+	1.09823i	0.126766	+	0.136218i
$66$	9.84496	+	2.94785i	1.21183	+	0.362855i
$67$	−0.662256			−0.0809074			−0.0404537	−	0.999181i	$-0.512880\pi$
$67$	−0.662256			−0.0809074			−0.0404537	+	0.999181i	$0.512880\pi$
$68$	−8.17371	−	1.09105i	−0.991209	−	0.132309i
$69$		−	20.8260i		−	2.50716i
$70$	3.79255	+	14.1319i	0.453297	+	1.68909i
$71$	2.50239	−	0.497757i	0.296979	−	0.0590729i	−0.0443517	−	0.999016i	$-0.514122\pi$
$71$	2.50239	−	0.497757i	0.296979	−	0.0590729i	0.341331	+	0.939943i	$0.389122\pi$
$72$	16.4077	+	8.54401i	1.93367	+	1.00692i
$73$	−0.683178	+	1.02245i	−0.0799600	+	0.119669i	−0.869294	−	0.494296i	$-0.835426\pi$
$73$	−0.683178	+	1.02245i	−0.0799600	+	0.119669i	0.789334	+	0.613964i	$0.210426\pi$
$74$	−0.711304	+	7.49810i	−0.0826874	+	0.871637i
$75$	−15.3242	+	1.91770i	−1.76949	+	0.221437i
$76$	−7.94509	−	11.7077i	−0.911365	−	1.34296i
$77$	−10.0572	+	4.16585i	−1.14613	+	0.474742i
$78$	−2.25873	+	1.86731i	−0.255751	+	0.211432i
$79$	0.742184	−	3.73121i	0.0835022	−	0.419794i	−0.916311	−	0.400467i	$-0.868848\pi$
$79$	0.742184	−	3.73121i	0.0835022	−	0.419794i	0.999813	−	0.0193266i	$-0.00615225\pi$
$80$	8.33528	−	3.24393i	0.931913	−	0.362682i
$81$	10.0095	−	10.0095i	1.11217	−	1.11217i
$82$	−5.81954	+	1.78820i	−0.642661	+	0.197474i
$83$	5.07078	+	2.10039i	0.556590	+	0.230547i	0.643204	−	0.765695i	$-0.277605\pi$
$83$	5.07078	+	2.10039i	0.556590	+	0.230547i	−0.0866138	+	0.996242i	$0.527605\pi$
$84$	−27.9935	+	5.77770i	−3.05434	+	0.630398i
$85$	3.70234	+	8.44350i	0.401575	+	0.915826i
$86$	−0.307511	−	3.01125i	−0.0331598	−	0.324711i
$87$	16.8031	+	6.96009i	1.80149	+	0.746200i
$88$	3.19992	+	5.83446i	0.341112	+	0.621955i
$89$	5.59049	+	5.59049i	0.592591	+	0.592591i	0.938330	−	0.345740i	$-0.112372\pi$
$89$	5.59049	+	5.59049i	0.592591	+	0.592591i	−0.345740	+	0.938330i	$0.612372\pi$
$90$	−1.36077	−	20.6377i	−0.143437	−	2.17541i
$91$	0.605626	−	3.04469i	0.0634869	−	0.319170i
$92$	9.46662	−	9.60367i	0.986964	−	1.00125i
$93$	−6.03854	−	14.5783i	−0.626167	−	1.51170i
$94$	−2.18582	+	1.17846i	−0.225450	+	0.121549i
$95$	−6.57474	+	14.3880i	−0.674554	+	1.47618i
$96$	5.37160	+	16.6264i	0.548237	+	1.69693i
$97$	11.5356	+	7.70783i	1.17126	+	0.782612i	0.980014	−	0.198930i	$-0.0637467\pi$
$97$	11.5356	+	7.70783i	1.17126	+	0.782612i	0.191247	+	0.981542i	$0.438747\pi$
$98$	12.8710	−	15.7988i	1.30017	−	1.59592i
$99$	15.0917	−	3.00193i	1.51677	−	0.301705i
$100$	−7.93829	−	6.08141i	−0.793829	−	0.608141i
$101$	9.64388			0.959602			0.479801	−	0.877377i	$-0.340709\pi$
$101$	9.64388			0.959602			0.479801	+	0.877377i	$0.340709\pi$
$102$	−16.8900	+	6.25318i	−1.67236	+	0.619157i
$103$	−8.39042			−0.826733			−0.413367	−	0.910565i	$-0.635647\pi$
$103$	−8.39042			−0.826733			−0.413367	+	0.910565i	$0.635647\pi$
$104$	−1.89038	−	0.165632i	−0.185367	−	0.0162416i
$105$	21.7710	+	23.3944i	2.12463	+	2.28306i
$106$	−2.62223	−	2.13628i	−0.254693	−	0.207494i
$107$	2.87140	−	4.29736i	0.277589	−	0.415441i	−0.666310	−	0.745675i	$-0.732127\pi$
$107$	2.87140	−	4.29736i	0.277589	−	0.415441i	0.943899	+	0.330233i	$0.107127\pi$
$108$	21.8702	−	0.157174i	2.10446	−	0.0151241i
$109$	8.15843	+	12.2099i	0.781436	+	1.16950i	0.981826	+	0.189785i	$0.0607790\pi$
$109$	8.15843	+	12.2099i	0.781436	+	1.16950i	−0.200390	+	0.979716i	$0.564221\pi$
$110$	3.71738	−	6.44450i	0.354438	−	0.614459i
$111$	6.29513	+	15.1978i	0.597507	+	1.44251i
$112$	−15.5352	−	10.0603i	−1.46793	−	0.950612i
$113$	−2.15817	+	10.8499i	−0.203024	+	1.02067i	0.736043	+	0.676935i	$0.236692\pi$
$113$	−2.15817	+	10.8499i	−0.203024	+	1.02067i	−0.939067	+	0.343735i	$0.888308\pi$
$114$	−27.3057	−	14.4693i	−2.55741	−	1.35517i
$115$	−14.6719	−	3.47059i	−1.36816	−	0.323634i
$116$	4.58481	+	10.8475i	0.425689	+	1.00717i
$117$	−1.67923	+	4.05401i	−0.155245	+	0.374794i
$118$	0.0968101	+	0.947995i	0.00891209	+	0.0872701i
$119$	9.68694	−	16.4355i	0.888000	−	1.50664i
$120$	12.7687	−	14.7844i	1.16561	−	1.34962i
$121$	−5.04896	−	2.09135i	−0.458996	−	0.190122i
$122$	−5.41536	+	1.66400i	−0.490284	+	0.150652i
$123$	−9.40229	+	9.40229i	−0.847776	+	0.847776i
$124$	3.84208	−	9.46747i	0.345029	−	0.850204i
$125$	−1.20271	+	11.1155i	−0.107574	+	0.994197i
$126$	−32.9854	+	27.2694i	−2.93857	+	2.42935i
$127$	−1.16418	−	2.81058i	−0.103304	−	0.249399i	0.863773	−	0.503881i	$-0.168095\pi$
$127$	−1.16418	−	2.81058i	−0.103304	−	0.249399i	−0.967078	+	0.254482i	$0.918095\pi$
$128$	−5.08061	+	10.1088i	−0.449067	+	0.893498i
$129$	−3.67288	−	5.49685i	−0.323379	−	0.483971i
$130$	0.939108	+	1.90245i	0.0823652	+	0.166856i
$131$	−2.06466	+	3.08997i	−0.180390	+	0.269972i	−0.910634	−	0.413214i	$-0.864406\pi$
$131$	−2.06466	+	3.08997i	−0.180390	+	0.269972i	0.730244	+	0.683186i	$0.239406\pi$
$132$	12.1420	+	7.98739i	1.05682	+	0.695213i
$133$	32.1050	−	6.38607i	2.78385	−	0.553743i
$134$	−0.897213	−	0.268650i	−0.0775074	−	0.0232078i
$135$	−12.8459	−	20.8062i	−1.10560	−	1.79071i
$136$	−10.6310	−	4.79388i	−0.911603	−	0.411071i
$137$		−	18.1100i		−	1.54724i	−0.633647	−	0.773622i	$-0.718443\pi$
$137$		−	18.1100i		−	1.54724i	0.633647	−	0.773622i	$-0.281557\pi$
$138$	8.44827	−	28.2148i	0.719165	−	2.40180i
$139$	−3.76434	−	18.9246i	−0.319287	−	1.60516i	−0.723383	−	0.690447i	$-0.757414\pi$
$139$	−3.76434	−	18.9246i	−0.319287	−	1.60516i	0.404096	−	0.914717i	$-0.367586\pi$
$140$	−0.594648	+	20.6842i	−0.0502569	+	1.74813i
$141$	−3.01321	+	4.50959i	−0.253758	+	0.379776i
$142$	3.59212	+	0.340765i	0.301444	+	0.0285964i
$143$	−1.31242	+	0.876931i	−0.109750	+	0.0733327i
$144$	18.7630	+	18.2312i	1.56358	+	1.51927i
$145$	7.70355	−	10.6779i	0.639745	−	0.886751i
$146$	−1.34032	+	1.10806i	−0.110926	+	0.0917037i
$147$	8.68294	−	43.6521i	0.716157	−	3.60036i
$148$	−4.00534	+	9.86977i	−0.329237	+	0.811290i
$149$	−12.0584	−	12.0584i	−0.987865	−	0.987865i	0.0120627	−	0.999927i	$-0.496160\pi$
$149$	−12.0584	−	12.0584i	−0.987865	−	0.987865i	−0.999927	+	0.0120627i	$0.996160\pi$
$150$	−21.5390	−	3.61834i	−1.75865	−	0.295437i
$151$	12.5641	+	5.20422i	1.02245	+	0.423514i	0.829983	−	0.557789i	$-0.188350\pi$
$151$	12.5641	+	5.20422i	1.02245	+	0.423514i	0.192470	+	0.981303i	$0.438350\pi$
$152$	−6.01458	−	19.0843i	−0.487846	−	1.54794i
$153$	−17.9618	+	20.1141i	−1.45213	+	1.62613i
$154$	−15.3153	+	1.56401i	−1.23414	+	0.126032i
$155$	−11.2767	+	1.82471i	−0.905766	+	0.146564i
$156$	−3.81758	+	1.61353i	−0.305651	+	0.129186i
$157$	−3.51971	−	3.51971i	−0.280903	−	0.280903i	0.552566	−	0.833469i	$-0.313649\pi$
$157$	−3.51971	−	3.51971i	−0.280903	−	0.280903i	−0.833469	+	0.552566i	$0.813649\pi$
$158$	2.51910	−	4.75391i	0.200409	−	0.378201i
$159$	−7.24521	−	1.44116i	−0.574582	−	0.114292i
$160$	12.6084	−	1.01354i	0.996785	−	0.0801276i
$161$	11.9390	+	28.8232i	0.940921	+	2.27159i
$162$	17.6211	−	9.50026i	1.38445	−	0.746411i
$163$	−6.27516	+	4.19293i	−0.491509	+	0.328416i	−0.776503	−	0.630114i	$-0.783008\pi$
$163$	−6.27516	+	4.19293i	−0.491509	+	0.328416i	0.284994	+	0.958529i	$0.408008\pi$
$164$	−8.60962	+	0.0618746i	−0.672299	+	0.00483160i
$165$	0.583664	−	16.2386i	0.0454382	−	1.26417i
$166$	6.01777	+	4.90258i	0.467070	+	0.380514i
$167$	6.97603	−	1.38762i	0.539822	−	0.107377i	0.0823535	−	0.996603i	$-0.473756\pi$
$167$	6.97603	−	1.38762i	0.539822	−	0.107377i	0.457468	+	0.889226i	$0.348756\pi$
$168$	−40.2690	−	3.52829i	−3.10682	−	0.272214i
$169$			12.5499i			0.965375i
$170$	1.59069	+	12.9410i	0.122001	+	0.992530i
$171$	−46.2699			−3.53835
$172$	0.804929	−	4.20434i	0.0613753	−	0.320578i
$173$	0.767815	+	3.86007i	0.0583759	+	0.293475i	0.998934	−	0.0461568i	$-0.0146974\pi$
$173$	0.767815	+	3.86007i	0.0583759	+	0.293475i	−0.940558	+	0.339632i	$0.889697\pi$
$174$	19.9412	+	16.2458i	1.51174	+	1.23159i
$175$	20.1093	−	11.4390i	1.52012	−	0.864709i
$176$	1.96840	+	9.20251i	0.148374	+	0.693665i
$177$	1.15629	+	1.73051i	0.0869120	+	0.130073i
$178$	5.30608	+	9.84174i	0.397707	+	0.737670i
$179$	−0.0746106	+	0.0309047i	−0.00557666	+	0.00230993i	−0.385470	−	0.922720i	$-0.625961\pi$
$179$	−0.0746106	+	0.0309047i	−0.00557666	+	0.00230993i	0.379893	+	0.925030i	$0.375961\pi$
$180$	6.52834	−	28.5117i	0.486593	−	2.12513i
$181$	3.90988	−	19.6563i	0.290619	−	1.46104i	−0.509121	−	0.860695i	$-0.670030\pi$
$181$	3.90988	−	19.6563i	0.290619	−	1.46104i	0.799741	−	0.600346i	$-0.204970\pi$
$182$	2.05560	−	3.87922i	0.152371	−	0.287547i
$183$	−8.74928	+	8.74928i	−0.646765	+	0.646765i
$184$	16.7210	−	9.17069i	1.23269	−	0.676072i
$185$	11.7559	−	1.90224i	0.864308	−	0.139856i
$186$	−2.26709	−	22.2001i	−0.166231	−	1.62779i
$187$	−9.39195	+	2.42634i	−0.686807	+	0.177431i
$188$	−3.43937	+	0.709866i	−0.250842	+	0.0517723i
$189$	−19.3632	+	46.7469i	−1.40847	+	3.40034i
$190$	−14.7440	+	16.8255i	−1.06964	+	1.22065i
$191$	7.64238	−	7.64238i	0.552983	−	0.552983i	−0.374317	−	0.927301i	$-0.622123\pi$
$191$	7.64238	−	7.64238i	0.552983	−	0.552983i	0.927301	+	0.374317i	$0.122123\pi$
$192$	0.532699	+	24.7043i	0.0384442	+	1.78288i
$193$	26.3626	+	5.24384i	1.89762	+	0.377460i	0.998218	−	0.0596648i	$-0.0190032\pi$
$193$	26.3626	+	5.24384i	1.89762	+	0.377460i	0.899401	+	0.437125i	$0.144003\pi$
$194$	12.5015	+	15.1220i	0.897554	+	1.08569i
$195$	3.75788	+	2.71111i	0.269107	+	0.194147i
$196$	23.8464	−	16.1827i	1.70331	−	1.15591i
$197$	2.39931	+	3.59083i	0.170944	+	0.255836i	0.907043	−	0.421038i	$-0.138334\pi$
$197$	2.39931	+	3.59083i	0.170944	+	0.255836i	−0.736099	+	0.676874i	$0.763334\pi$
$198$	21.6638	+	2.05512i	1.53958	+	0.146051i
$199$	13.0589	+	8.72570i	0.925723	+	0.618548i	0.924389	−	0.381451i	$-0.124575\pi$
$199$	13.0589	+	8.72570i	0.925723	+	0.618548i	0.00133382	+	0.999999i	$0.499575\pi$
$200$	−8.28769	−	11.4592i	−0.586028	−	0.810291i
$201$	−2.00624	+	0.399066i	−0.141509	+	0.0281479i
$202$	13.0654	+	3.91213i	0.919277	+	0.275256i
$203$	−27.2455			−1.91226
$204$	−25.4189	+	1.62014i	−1.77968	+	0.113432i
$205$	5.05703	+	8.19074i	0.353198	+	0.572066i
$206$	−11.3672	−	3.40365i	−0.791991	−	0.237144i
$207$	−8.60326	−	43.2515i	−0.597968	−	3.00619i
$208$	−2.49387	−	0.991247i	−0.172919	−	0.0687306i
$209$	−13.8389	−	9.24687i	−0.957258	−	0.639620i
$210$	20.0049	+	40.5259i	1.38047	+	2.79656i
$211$	10.8875	−	7.27478i	0.749525	−	0.500817i	−0.121175	−	0.992631i	$-0.538666\pi$
$211$	10.8875	−	7.27478i	0.749525	−	0.500817i	0.870700	+	0.491815i	$0.163666\pi$
$212$	−2.68595	−	3.95793i	−0.184472	−	0.271832i
$213$	7.28082	−	3.01581i	0.498873	−	0.206640i
$214$	5.63339	−	4.65718i	0.385091	−	0.318359i
$215$	−4.48459	+	1.67150i	−0.305846	+	0.113996i
$216$	29.6932	+	8.65892i	2.02037	+	0.589165i
$217$	16.7146	+	16.7146i	1.13466	+	1.13466i
$218$	6.09983	+	19.8514i	0.413133	+	1.34451i
$219$	−1.45351	+	3.50908i	−0.0982191	+	0.237122i
$220$	7.65052	−	7.22292i	0.515798	−	0.486969i
$221$	0.912679	−	2.61134i	0.0613934	−	0.175658i
$222$	2.36342	+	23.1434i	0.158623	+	1.55328i
$223$	−8.19765	−	3.39558i	−0.548955	−	0.227385i	0.0909273	−	0.995858i	$-0.471017\pi$
$223$	−8.19765	−	3.39558i	−0.548955	−	0.227385i	−0.639882	+	0.768473i	$0.721017\pi$
$224$	−16.9657	−	19.9316i	−1.13357	−	1.33173i
$225$	−31.0332	+	10.3131i	−2.06888	+	0.687543i
$226$	−7.32520	+	13.8237i	−0.487265	+	0.919542i
$227$	−15.6337	−	3.10973i	−1.03764	−	0.206400i	−0.353262	−	0.935525i	$-0.614927\pi$
$227$	−15.6337	−	3.10973i	−1.03764	−	0.206400i	−0.684381	+	0.729125i	$0.739927\pi$
$228$	−31.1238	−	30.6796i	−2.06122	−	2.03181i
$229$	−11.5640	+	4.78996i	−0.764170	+	0.316530i	−0.730509	−	0.682904i	$-0.760717\pi$
$229$	−11.5640	+	4.78996i	−0.764170	+	0.316530i	−0.0336619	+	0.999433i	$0.510717\pi$
$230$	−18.4694	−	10.6537i	−1.21783	−	0.702483i
$231$	−27.9572	+	18.6804i	−1.83945	+	1.22908i
$232$	1.81102	+	16.5560i	0.118899	+	1.08695i
$233$	8.30073	+	5.54637i	0.543799	+	0.363355i	0.796925	−	0.604078i	$-0.206459\pi$
$233$	8.30073	+	5.54637i	0.543799	+	0.363355i	−0.253126	+	0.967433i	$0.581459\pi$
$234$	−3.91954	+	4.81112i	−0.256228	+	0.314513i
$235$	2.67485	+	2.87431i	0.174488	+	0.187499i
$236$	−0.253406	+	1.32360i	−0.0164953	+	0.0861591i
$237$		−	11.7506i		−	0.763282i
$238$	19.7909	−	18.3369i	1.28285	−	1.18860i
$239$		−	14.8681i		−	0.961737i	−0.876793	−	0.480868i	$-0.840322\pi$
$239$		−	14.8681i		−	0.961737i	0.876793	−	0.480868i	$-0.159678\pi$
$240$	23.2962	−	14.8499i	1.50376	−	0.958556i
$241$	0.111847	+	0.562292i	0.00720469	+	0.0362204i	0.984220	−	0.176947i	$-0.0566221\pi$
$241$	0.111847	+	0.562292i	0.00720469	+	0.0362204i	−0.977016	+	0.213167i	$0.931622\pi$
$242$	−5.99187	−	4.88148i	−0.385172	−	0.313793i
$243$	6.06506	−	9.07700i	0.389074	−	0.582290i
$244$	−8.01167	+	0.0575773i	−0.512894	+	0.00368601i
$245$	−29.3058	−	13.3916i	−1.87228	−	0.855556i
$246$	−16.5522	+	8.92395i	−1.05533	+	0.568970i
$247$	4.38507	−	1.81635i	0.279015	−	0.115572i
$248$	9.04576	−	11.2678i	0.574406	−	0.715507i
$249$	16.6271	+	3.30734i	1.05370	+	0.209594i
$250$	−6.13851	+	14.5712i	−0.388233	+	0.921561i
$251$	6.76542	−	6.76542i	0.427029	−	0.427029i	−0.460586	−	0.887615i	$-0.652361\pi$
$251$	6.76542	−	6.76542i	0.427029	−	0.427029i	0.887615	+	0.460586i	$0.152361\pi$
$252$	−55.7502	+	23.5633i	−3.51193	+	1.48435i
$253$	6.07049	−	14.6555i	0.381649	−	0.921381i
$254$	−0.437077	−	4.28000i	−0.0274246	−	0.268551i
$255$	16.3038	+	23.3478i	1.02098	+	1.46209i
$256$	−10.9839	+	11.6342i	−0.686491	+	0.727139i
$257$	11.5256	−	27.8252i	0.718946	−	1.73569i	0.0426152	−	0.999092i	$-0.486431\pi$
$257$	11.5256	−	27.8252i	0.718946	−	1.73569i	0.676331	−	0.736598i	$-0.263569\pi$
$258$	−2.74611	−	8.93699i	−0.170965	−	0.556392i
$259$	−17.4249	−	17.4249i	−1.08273	−	1.08273i
$260$	0.500543	+	2.95837i	0.0310424	+	0.183470i
$261$	37.7720	+	7.51332i	2.33803	+	0.465063i
$262$	−4.05064	+	3.34870i	−0.250249	+	0.206884i
$263$	−1.74904	−	4.22255i	−0.107850	−	0.260374i	0.860736	−	0.509052i	$-0.170004\pi$
$263$	−1.74904	−	4.22255i	−0.107850	−	0.260374i	−0.968586	+	0.248678i	$0.920004\pi$
$264$	13.2096	+	15.7467i	0.812995	+	0.969142i
$265$	−2.22268	+	4.86406i	−0.136538	+	0.298797i
$266$	46.0859	+	4.37191i	2.82571	+	0.268059i
$267$	20.3046	+	13.5671i	1.24262	+	0.830293i
$268$	−1.10655	−	0.727926i	−0.0675933	−	0.0444651i
$269$	2.06052	+	10.3590i	0.125632	+	0.631596i	0.991369	+	0.131097i	$0.0418501\pi$
$269$	2.06052	+	10.3590i	0.125632	+	0.631596i	−0.865737	+	0.500499i	$0.833150\pi$
$270$	−8.96321	−	33.3989i	−0.545483	−	2.03260i
$271$	−21.4104			−1.30059			−0.650296	−	0.759681i	$-0.725355\pi$
$271$	−21.4104			−1.30059			−0.650296	+	0.759681i	$0.725355\pi$
$272$	−12.4581	−	10.8072i	−0.755382	−	0.655285i
$273$		−	9.58853i		−	0.580324i
$274$	7.34650	−	24.5352i	0.443818	−	1.48222i
$275$	−11.3428	−	3.11729i	−0.683995	−	0.187980i
$276$	22.8912	−	34.7979i	1.37789	−	2.09458i
$277$	8.62180	+	5.76090i	0.518034	+	0.346139i	0.786942	−	0.617027i	$-0.211663\pi$
$277$	8.62180	+	5.76090i	0.518034	+	0.346139i	−0.268908	+	0.963166i	$0.586663\pi$
$278$	2.57707	−	27.1658i	0.154562	−	1.62930i
$279$	−18.5632	−	27.7817i	−1.11135	−	1.66325i
$280$	−9.19635	+	27.7814i	−0.549587	+	1.66026i
$281$	−26.5442	+	10.9950i	−1.58349	+	0.655905i	−0.988962	−	0.148168i	$-0.952662\pi$
$281$	−26.5442	+	10.9950i	−1.58349	+	0.655905i	−0.594531	+	0.804072i	$0.702662\pi$
$282$	−5.91161	+	4.88719i	−0.352031	+	0.291028i
$283$	2.50060	−	12.5713i	0.148645	−	0.747289i	−0.832501	−	0.554023i	$-0.813092\pi$
$283$	2.50060	−	12.5713i	0.148645	−	0.747289i	0.981146	−	0.193266i	$-0.0619080\pi$
$284$	4.72832	+	1.91884i	0.280574	+	0.113862i
$285$	−11.2475	+	47.5489i	−0.666246	+	2.81656i
$286$	−2.13378	+	0.655658i	−0.126173	+	0.0387698i
$287$	7.62269	−	18.4028i	0.449953	−	1.08628i
$288$	18.0241	+	32.3108i	1.06208	+	1.90393i
$289$	10.5896	−	13.2989i	0.622919	−	0.782286i
$290$	14.7682	−	11.3412i	0.867220	−	0.665980i
$291$	39.5906	+	16.3989i	2.32084	+	0.961323i
$292$	−2.26535	+	0.957467i	−0.132569	+	0.0560315i
$293$	−15.0394	−	15.0394i	−0.878613	−	0.878613i	0.114778	−	0.993391i	$-0.463384\pi$
$293$	−15.0394	−	15.0394i	−0.878613	−	0.878613i	−0.993391	+	0.114778i	$0.963384\pi$
$294$	29.4714	−	55.6169i	1.71881	−	3.24364i
$295$	1.41183	−	0.526219i	0.0821999	−	0.0306377i
$296$	−9.43013	+	11.7466i	−0.548115	+	0.682758i
$297$	23.7690	−	9.84543i	1.37922	−	0.571290i
$298$	−11.4450	−	21.2282i	−0.662989	−	1.22972i
$299$	2.51321	+	3.76128i	0.145343	+	0.217521i
$300$	−27.7128	−	13.6396i	−1.60000	−	0.787480i
$301$	8.23444	+	5.50207i	0.474625	+	0.317134i
$302$	14.9105	+	12.1473i	0.858004	+	0.699001i
$303$	29.2152	−	5.81126i	1.67837	−	0.333848i
$304$	−0.406716	−	28.2950i	−0.0233268	−	1.62283i
$305$	4.70581	+	7.62188i	0.269454	+	0.436427i
$306$	−32.4939	+	19.9639i	−1.85755	+	1.14126i
$307$			26.9859i			1.54017i	0.637943	+	0.770083i	$0.279785\pi$
$307$			26.9859i			1.54017i	−0.637943	+	0.770083i	$0.720215\pi$
$308$	−21.3834	−	4.09389i	−1.21843	−	0.233271i
$309$	−25.4180	+	5.05595i	−1.44598	+	0.287623i
$310$	−16.0177	−	2.10240i	−0.909744	−	0.119409i
$311$	−8.78046	+	13.1409i	−0.497894	+	0.745151i	−0.992270	−	0.124097i	$-0.960397\pi$
$311$	−8.78046	+	13.1409i	−0.497894	+	0.745151i	0.494376	+	0.869248i	$0.335397\pi$
$312$	−5.82655	+	0.637353i	−0.329863	+	0.0360830i
$313$	−16.3030	−	24.3992i	−0.921501	−	1.37912i	−0.925343	−	0.379131i	$-0.876223\pi$
$313$	−16.3030	−	24.3992i	−0.921501	−	1.37912i	0.00384177	−	0.999993i	$-0.498777\pi$
$314$	−3.34065	−	6.19625i	−0.188524	−	0.349675i
$315$	54.8783	+	39.5918i	3.09204	+	2.23075i
$316$	5.34130	−	5.41863i	0.300472	−	0.304822i
$317$	12.7689	+	2.53989i	0.717171	+	0.142654i	0.540169	−	0.841556i	$-0.318360\pi$
$317$	12.7689	+	2.53989i	0.717171	+	0.142654i	0.177002	+	0.984211i	$0.443360\pi$
$318$	−9.23107	−	4.89155i	−0.517653	−	0.274304i
$319$	9.79575	+	9.79575i	0.548457	+	0.548457i
$320$	17.4929	+	3.74159i	0.977881	+	0.209161i
$321$	6.10911	−	14.7487i	0.340977	−	0.823192i
$322$	4.48232	+	43.8923i	0.249790	+	2.44602i
$323$	29.1224	−	1.64614i	1.62041	−	0.0915938i
$324$	27.7267	−	5.72263i	1.54037	−	0.317924i
$325$	2.53621	−	2.19562i	0.140684	−	0.121791i
$326$	−10.2024	+	3.13494i	−0.565058	+	0.173628i
$327$	32.0727	+	32.0727i	1.77362	+	1.77362i
$328$	−11.6893	−	3.40875i	−0.645433	−	0.188216i
$329$	1.58506	−	7.96864i	0.0873873	−	0.439326i
$330$	7.37807	−	21.7630i	0.406149	−	1.19802i
$331$	3.67576	+	8.87408i	0.202038	+	0.487763i	0.992128	−	0.125228i	$-0.0399661\pi$
$331$	3.67576	+	8.87408i	0.202038	+	0.487763i	−0.790090	+	0.612991i	$0.789966\pi$
$332$	6.16401	+	9.08310i	0.338294	+	0.498500i
$333$	19.3519	+	28.9622i	1.06048	+	1.58712i
$334$	10.0139	+	0.949966i	0.547937	+	0.0519798i
$335$	−0.0531918	+	1.47989i	−0.00290618	+	0.0808552i
$336$	−53.1245	−	21.1155i	−2.89818	−	1.15195i
$337$	1.51971	+	7.64009i	0.0827838	+	0.416182i	0.999848	+	0.0174423i	$0.00555234\pi$
$337$	1.51971	+	7.64009i	0.0827838	+	0.416182i	−0.917064	+	0.398740i	$0.869448\pi$
$338$	−5.09097	+	17.0024i	−0.276912	+	0.924807i
$339$			34.1691i			1.85581i
$340$	−3.09459	+	18.1776i	−0.167828	+	0.985816i
$341$		−	12.0190i		−	0.650868i
$342$	−62.6858	−	18.7698i	−3.38966	−	1.01496i
$343$	6.68845	+	33.6251i	0.361143	+	1.81559i
$344$	2.79603	−	5.36945i	0.150752	−	0.289501i
$345$	−46.5384	−	1.67273i	−2.50554	−	0.0900568i
$346$	−0.525647	+	5.54103i	−0.0282590	+	0.297888i
$347$	−7.66148	−	11.4662i	−0.411290	−	0.615538i	0.566767	−	0.823878i	$-0.308194\pi$
$347$	−7.66148	−	11.4662i	−0.411290	−	0.615538i	−0.978057	+	0.208340i	$0.933194\pi$
$348$	20.4258	+	30.0988i	1.09494	+	1.61347i
$349$	−1.56644	−	3.78172i	−0.0838496	−	0.202431i	0.876394	−	0.481595i	$-0.159943\pi$
$349$	−1.56644	−	3.78172i	−0.0838496	−	0.202431i	−0.960243	+	0.279165i	$0.909943\pi$
$350$	31.8842	−	7.33987i	1.70428	−	0.392333i
$351$	−1.43132	+	7.19572i	−0.0763981	+	0.384079i
$352$	−1.06633	+	13.2659i	−0.0568353	+	0.707076i
$353$	−5.12718	−	5.12718i	−0.272892	−	0.272892i	0.557371	−	0.830263i	$-0.311810\pi$
$353$	−5.12718	−	5.12718i	−0.272892	−	0.272892i	−0.830263	+	0.557371i	$0.811810\pi$
$354$	0.864525	+	2.81352i	0.0459490	+	0.149537i
$355$	−0.911310	−	5.63189i	−0.0483673	−	0.298910i
$356$	3.19620	+	15.4859i	0.169398	+	0.820751i
$357$	19.4419	−	55.6268i	1.02897	−	2.94408i
$358$	−0.113618	+	0.0116028i	−0.00600490	+	0.000613226i
$359$	−0.508478	+	1.22757i	−0.0268364	+	0.0647889i	−0.936730	−	0.350054i	$-0.886163\pi$
$359$	−0.508478	+	1.22757i	−0.0268364	+	0.0647889i	0.909893	+	0.414843i	$0.136163\pi$
$360$	20.4105	−	35.9789i	1.07573	−	1.89625i
$361$	21.9545	+	21.9545i	1.15550	+	1.15550i
$362$	13.2708	−	25.0440i	0.697497	−	1.31628i
$363$	−16.5555	−	3.29310i	−0.868941	−	0.172843i
$364$	4.35853	−	4.42163i	0.228449	−	0.231757i
$365$	2.22992	+	1.60877i	0.116719	+	0.0842068i
$366$	−15.4026	+	8.30416i	−0.805107	+	0.434065i
$367$	4.29723	+	6.43125i	0.224313	+	0.335709i	0.926507	−	0.376277i	$-0.122796\pi$
$367$	4.29723	+	6.43125i	0.224313	+	0.335709i	−0.702194	+	0.711986i	$0.747796\pi$
$368$	26.3736	−	5.64126i	1.37482	−	0.294071i
$369$	−15.6426	+	23.4108i	−0.814320	+	1.21872i
$370$	16.6983	+	2.19174i	0.868104	+	0.113943i
$371$	10.8535	−	2.15890i	0.563487	−	0.112084i
$372$	5.93424	−	30.9960i	0.307676	−	1.60707i
$373$		−	24.3172i		−	1.25910i	−0.776960	−	0.629549i	$-0.783240\pi$
$373$		−	24.3172i		−	1.25910i	0.776960	−	0.629549i	$-0.216760\pi$
$374$	−13.7083	−	0.522768i	−0.708841	−	0.0270317i
$375$	3.05451	+	34.3980i	0.157734	+	1.77630i
$376$	−4.94757	−	0.433497i	−0.255151	−	0.0223559i
$377$	−3.87465	+	0.770715i	−0.199554	+	0.0396938i
$378$	−45.1963	+	55.4771i	−2.32464	+	2.85343i
$379$	21.8652	+	14.6099i	1.12314	+	0.750459i	0.971279	−	0.237943i	$-0.0764732\pi$
$379$	21.8652	+	14.6099i	1.12314	+	0.750459i	0.151862	+	0.988402i	$0.451473\pi$
$380$	−26.8004	+	16.8140i	−1.37483	+	0.862538i
$381$	−5.22040	−	7.81287i	−0.267449	−	0.400266i
$382$	13.4540	−	7.25358i	0.688365	−	0.371125i
$383$	−12.7732	+	5.29085i	−0.652682	+	0.270350i	−0.684355	−	0.729149i	$-0.739916\pi$
$383$	−12.7732	+	5.29085i	−0.652682	+	0.270350i	0.0316735	+	0.999498i	$0.489916\pi$
$384$	−9.29982	+	33.6851i	−0.474580	+	1.71898i
$385$	8.50132	+	22.8088i	0.433267	+	1.16244i
$386$	33.5884	+	17.7985i	1.70960	+	0.905919i
$387$	−9.89859	−	9.89859i	−0.503174	−	0.503174i
$388$	10.8024	+	25.5583i	0.548411	+	1.29753i
$389$	28.1359	+	11.6543i	1.42655	+	0.590895i	0.956496	−	0.291745i	$-0.0942360\pi$
$389$	28.1359	+	11.6543i	1.42655	+	0.590895i	0.470050	+	0.882640i	$0.344236\pi$
$390$	3.99133	+	5.19739i	0.202109	+	0.263180i
$391$	6.95366	+	26.9165i	0.351662	+	1.36123i
$392$	38.8714	−	12.2506i	1.96330	−	0.618749i
$393$	−4.39270	+	10.6049i	−0.221582	+	0.534947i
$394$	1.79390	+	5.83810i	0.0903755	+	0.294119i
$395$	−8.27825	−	1.95819i	−0.416524	−	0.0985273i
$396$	28.5161	+	11.5724i	1.43299	+	0.581533i
$397$	−5.81201	+	29.2189i	−0.291696	+	1.46646i	0.505547	+	0.862799i	$0.331291\pi$
$397$	−5.81201	+	29.2189i	−0.291696	+	1.46646i	−0.797244	+	0.603658i	$0.793709\pi$
$398$	14.1524	+	17.1189i	0.709394	+	0.858094i
$399$	93.4107	−	38.6920i	4.67638	−	1.93702i
$400$	−6.57948	−	18.8868i	−0.328974	−	0.944339i
$401$	−0.979570	−	1.46603i	−0.0489174	−	0.0732100i	0.806205	−	0.591637i	$-0.201518\pi$
$401$	−0.979570	−	1.46603i	−0.0489174	−	0.0732100i	−0.855122	+	0.518427i	$0.826518\pi$
$402$	−2.87991	−	0.273201i	−0.143637	−	0.0136260i
$403$	2.84985	+	1.90421i	0.141961	+	0.0948553i
$404$	16.1138	+	10.6002i	0.801691	+	0.527379i
$405$	−21.5635	−	23.1714i	−1.07150	−	1.15140i
$406$	−36.9118	−	11.0524i	−1.83190	−	0.548521i
$407$			12.5298i			0.621077i
$408$	−35.0944	−	8.11648i	−1.73743	−	0.401825i
$409$	20.4889			1.01311			0.506554	−	0.862208i	$-0.330919\pi$
$409$	20.4889			1.01311			0.506554	+	0.862208i	$0.330919\pi$
$410$	3.52853	+	13.1481i	0.174262	+	0.649339i
$411$	−10.9128	−	54.8626i	−0.538291	−	2.70617i
$412$	−14.0194	−	9.22243i	−0.690686	−	0.454356i
$413$	−2.59235	−	1.73215i	−0.127561	−	0.0852336i
$414$	5.88980	−	62.0865i	0.289468	−	3.05138i
$415$	5.10086	−	11.1626i	0.250391	−	0.547950i
$416$	−2.97655	−	2.35459i	−0.145938	−	0.115443i
$417$	−22.8074	−	55.0619i	−1.11688	−	2.69639i
$418$	−14.9977	−	18.1414i	−0.733560	−	0.887325i
$419$	−21.0452	−	4.18615i	−1.02812	−	0.204507i	−0.347916	−	0.937526i	$-0.613111\pi$
$419$	−21.0452	−	4.18615i	−1.02812	−	0.204507i	−0.680208	+	0.733019i	$0.738111\pi$
$420$	10.6626	+	63.0191i	0.520280	+	3.07502i
$421$	6.24485	+	6.24485i	0.304355	+	0.304355i	0.842715	−	0.538360i	$-0.180956\pi$
$421$	6.24485	+	6.24485i	0.304355	+	0.304355i	−0.538360	+	0.842715i	$0.680956\pi$
$422$	17.7013	−	5.43915i	0.861684	−	0.264774i
$423$	−4.39492	+	10.6103i	−0.213688	+	0.515889i
$424$	−2.03331	−	6.45172i	−0.0987462	−	0.313323i
$425$	19.1654	−	7.59517i	0.929659	−	0.368420i
$426$	11.0873	−	1.13225i	0.537183	−	0.0548576i
$427$	7.09327	−	17.1247i	0.343267	−	0.828721i
$428$	9.52126	−	4.02424i	0.460228	−	0.194519i
$429$	−3.44742	+	3.44742i	−0.166443	+	0.166443i
$430$	−6.75371	+	0.445312i	−0.325693	+	0.0214748i
$431$	7.66662	+	1.52499i	0.369288	+	0.0734560i	0.376246	−	0.926520i	$-0.377215\pi$
$431$	7.66662	+	1.52499i	0.369288	+	0.0734560i	−0.00695775	+	0.999976i	$0.502215\pi$
$432$	36.7153	+	23.7763i	1.76647	+	1.14394i
$433$	15.6913	−	6.49954i	0.754075	−	0.312348i	0.0276718	−	0.999617i	$-0.491191\pi$
$433$	15.6913	−	6.49954i	0.754075	−	0.312348i	0.726403	+	0.687269i	$0.241191\pi$
$434$	15.8643	+	29.4252i	0.761510	+	1.41245i
$435$	16.9028	−	36.9897i	0.810428	−	1.77352i
$436$	0.211064	+	29.3688i	0.0101081	+	1.40651i
$437$	−26.5007	+	39.6611i	−1.26770	+	1.89725i
$438$	−3.39268	+	4.16442i	−0.162109	+	0.198984i
$439$	−0.593019	−	2.98131i	−0.0283033	−	0.142290i	0.964050	−	0.265721i	$-0.0856101\pi$
$439$	−0.593019	−	2.98131i	−0.0283033	−	0.142290i	−0.992353	+	0.123431i	$0.960610\pi$
$440$	13.2948	−	6.68200i	0.633807	−	0.318552i
$441$		−	94.2436i		−	4.48779i
$442$	2.29580	−	3.16757i	0.109200	−	0.150666i
$443$		−	36.5984i		−	1.73884i	−0.494071	−	0.869422i	$-0.664492\pi$
$443$		−	36.5984i		−	1.73884i	0.494071	−	0.869422i	$-0.335508\pi$
$444$	−6.18640	+	32.3131i	−0.293594	+	1.53351i
$445$	12.9417	−	12.0436i	0.613494	−	0.570923i
$446$	−9.72860	−	7.92572i	−0.460662	−	0.375294i
$447$	−43.7961	−	29.2636i	−2.07148	−	1.38412i
$448$	−14.8995	−	33.8853i	−0.703934	−	1.60093i
$449$	−26.0335	+	17.3951i	−1.22860	+	0.820923i	−0.988705	−	0.149876i	$-0.952113\pi$
$449$	−26.0335	+	17.3951i	−1.22860	+	0.820923i	−0.239894	+	0.970799i	$0.577113\pi$
$450$	−46.2269	+	1.38320i	−2.17916	+	0.0652045i
$451$	−9.35710	+	3.87584i	−0.440609	+	0.182506i
$452$	−15.5318	+	15.7567i	−0.730554	+	0.741131i
$453$	41.1977	+	8.19474i	1.93564	+	0.385022i
$454$	−19.9188	−	10.5549i	−0.934833	−	0.495368i
$455$	−6.75509	−	1.59789i	−0.316684	−	0.0749104i
$456$	−29.7205	−	54.1899i	−1.39179	−	2.53767i
$457$	−1.92714	−	0.798247i	−0.0901477	−	0.0373404i	0.337154	−	0.941450i	$-0.390536\pi$
$457$	−1.92714	−	0.798247i	−0.0901477	−	0.0373404i	−0.427302	+	0.904109i	$0.640536\pi$
$458$	−17.6098	+	1.79833i	−0.822853	+	0.0840304i
$459$	−22.8938	+	38.8430i	−1.06859	+	1.81304i
$460$	−20.7003	−	21.9257i	−0.965155	−	1.02229i
$461$	−2.11083	+	5.09600i	−0.0983113	+	0.237344i	−0.965382	−	0.260841i	$-0.916000\pi$
$461$	−2.11083	+	5.09600i	−0.0983113	+	0.237344i	0.867070	+	0.498185i	$0.166000\pi$
$462$	−45.4538	+	13.9668i	−2.11470	+	0.649795i
$463$	−12.5310	−	12.5310i	−0.582367	−	0.582367i	0.353186	−	0.935553i	$-0.385098\pi$
$463$	−12.5310	−	12.5310i	−0.582367	−	0.582367i	−0.935553	+	0.353186i	$0.885098\pi$
$464$	−4.26253	+	23.1644i	−0.197883	+	1.07538i
$465$	−33.0621	+	12.3230i	−1.53322	+	0.571463i
$466$	8.99577	+	10.8814i	0.416721	+	0.504072i
$467$	−10.0201	+	4.15047i	−0.463676	+	0.192061i	−0.602277	−	0.798287i	$-0.705740\pi$
$467$	−10.0201	+	4.15047i	−0.463676	+	0.192061i	0.138601	+	0.990348i	$0.455740\pi$
$468$	−7.26180	+	4.92803i	−0.335677	+	0.227798i
$469$	2.54786	−	1.70242i	0.117649	−	0.0786106i
$470$	2.45786	+	4.97914i	0.113373	+	0.229671i
$471$	−12.7835	−	8.54169i	−0.589035	−	0.393580i
$472$	−0.880241	+	1.69040i	−0.0405164	+	0.0778069i
$473$	−0.982383	−	4.93877i	−0.0451700	−	0.227085i
$474$	4.76673	−	15.9195i	0.218943	−	0.731207i
$475$	31.6237	+	15.8477i	1.45100	+	0.727143i
$476$	34.2509	−	16.8142i	1.56989	−	0.770677i
$477$	−15.6422			−0.716207
$478$	6.03137	−	20.1431i	0.275869	−	0.921322i
$479$	−33.4364	+	6.65092i	−1.52775	+	0.303888i	−0.886240	−	0.463227i	$-0.846692\pi$
$479$	−33.4364	+	6.65092i	−1.52775	+	0.303888i	−0.641509	+	0.767115i	$0.721692\pi$
$480$	37.5853	−	10.6681i	1.71553	−	0.486930i
$481$	−2.97094	−	1.98512i	−0.135463	−	0.0905137i
$482$	−0.0765705	+	0.807156i	−0.00348769	+	0.0367649i
$483$	53.5363	+	80.1228i	2.43599	+	3.64571i
$484$	−6.13748	−	9.04401i	−0.278976	−	0.411091i
$485$	18.1506	−	25.1586i	0.824178	−	1.14239i
$486$	11.8990	−	9.83703i	0.539750	−	0.446217i
$487$	−1.81761	−	0.361545i	−0.0823638	−	0.0163832i	0.153736	−	0.988112i	$-0.450869\pi$
$487$	−1.81761	−	0.361545i	−0.0823638	−	0.0163832i	−0.236100	+	0.971729i	$0.575869\pi$
$488$	−10.8774	−	3.17200i	−0.492398	−	0.143590i
$489$	−16.4834	+	16.4834i	−0.745405	+	0.745405i
$490$	−34.2706	−	30.0309i	−1.54819	−	1.35666i
$491$	−4.80286	+	11.5951i	−0.216750	+	0.523281i	−0.994432	−	0.105376i	$-0.966395\pi$
$491$	−4.80286	+	11.5951i	−0.216750	+	0.523281i	0.777682	+	0.628658i	$0.216395\pi$
$492$	−26.0447	+	5.37548i	−1.17419	+	0.242345i
$493$	−24.0411	−	3.38508i	−1.08275	−	0.152456i
$494$	6.67764	−	0.681927i	0.300441	−	0.0306813i
$495$	−5.49603	−	33.9654i	−0.247028	−	1.52663i
$496$	16.8259	−	11.5960i	0.755507	−	0.520674i
$497$	−8.34775	+	8.34775i	−0.374448	+	0.374448i
$498$	21.1845	+	11.2257i	0.949299	+	0.503034i
$499$	−6.39294	+	32.1395i	−0.286187	+	1.43876i	0.523564	+	0.851987i	$0.324602\pi$
$499$	−6.39294	+	32.1395i	−0.286187	+	1.43876i	−0.809751	+	0.586774i	$0.800398\pi$
$500$	−14.2273	+	17.2506i	−0.636263	+	0.771472i
$501$	20.2971	−	8.40732i	0.906806	−	0.375611i
$502$	11.9101	−	6.42123i	0.531575	−	0.286594i
$503$	16.8664	+	25.2424i	0.752036	+	1.12550i	0.988107	+	0.153766i	$0.0491400\pi$
$503$	16.8664	+	25.2424i	0.752036	+	1.12550i	−0.236072	+	0.971736i	$0.575860\pi$
$504$	−85.0881	+	9.30760i	−3.79013	+	0.414593i
$505$	0.774588	−	21.5505i	0.0344687	−	0.958983i
$506$	14.1693	−	17.3924i	0.629904	−	0.773189i
$507$	7.56238	+	38.0186i	0.335857	+	1.68847i
$508$	1.14407	−	5.97578i	0.0507601	−	0.265132i
$509$	5.68733			0.252087			0.126043	−	0.992025i	$-0.459772\pi$
$509$	5.68733			0.252087			0.126043	+	0.992025i	$0.459772\pi$
$510$	12.6169	+	38.2450i	0.558687	+	1.69352i
$511$		−	5.68981i		−	0.251703i
$512$	−19.6003	+	11.3062i	−0.866218	+	0.499666i
$513$	−75.8759	+	15.0926i	−3.35000	+	0.666357i
$514$	26.9022	−	33.0217i	1.18661	−	1.45653i
$515$	−0.673912	+	18.7495i	−0.0296961	+	0.826199i
$516$	−0.0950200	−	13.2217i	−0.00418302	−	0.582052i
$517$	−3.43490	+	2.29513i	−0.151067	+	0.100940i
$518$	−16.5384	−	30.6755i	−0.726655	−	1.34780i
$519$	4.65204	+	11.2310i	0.204202	+	0.492987i
$520$	−0.521959	+	4.21100i	−0.0228894	+	0.184664i
$521$	5.48013	+	1.09007i	0.240089	+	0.0477567i	0.313668	−	0.949533i	$-0.398442\pi$
$521$	5.48013	+	1.09007i	0.240089	+	0.0477567i	−0.0735790	+	0.997289i	$0.523442\pi$
$522$	48.1251	+	25.5015i	2.10638	+	1.11617i
$523$	−14.3521	−	14.3521i	−0.627573	−	0.627573i	0.319884	−	0.947457i	$-0.396356\pi$
$523$	−14.3521	−	14.3521i	−0.627573	−	0.627573i	−0.947457	+	0.319884i	$0.896356\pi$
$524$	−6.84617	+	2.89359i	−0.299076	+	0.126407i
$525$	54.0263	−	46.7710i	2.35790	−	2.04125i
$526$	−0.656654	−	6.43016i	−0.0286315	−	0.280368i
$527$	12.6721	+	16.8255i	0.552004	+	0.732928i
$528$	11.5084	+	26.6920i	0.500838	+	1.16162i
$529$	−20.7521	−	8.59579i	−0.902264	−	0.373730i
$530$	−4.98441	+	5.68811i	−0.216509	+	0.247076i
$531$	3.11625	+	3.11625i	0.135234	+	0.135234i
$532$	60.6629	+	24.6181i	2.63007	+	1.06733i
$533$	0.563465	−	2.83273i	0.0244064	−	0.122699i
$534$	22.0047	+	26.6172i	0.952238	+	1.15184i
$535$	−9.37236	−	6.76167i	−0.405202	−	0.292332i
$536$	−1.20385	−	1.43506i	−0.0519983	−	0.0619853i
$537$	−0.207403	+	0.138582i	−0.00895010	+	0.00598026i
$538$	−1.41064	+	14.8700i	−0.0608169	+	0.641092i
$539$	18.8342	−	28.1874i	0.811247	−	1.21412i
$540$	1.40537	−	48.8844i	0.0604776	−	2.10365i
$541$	−1.32194	−	6.64586i	−0.0568348	−	0.285728i	0.941907	−	0.335873i	$-0.109031\pi$
$541$	−1.32194	−	6.64586i	−0.0568348	−	0.285728i	−0.998742	+	0.0501457i	$0.984031\pi$
$542$	−29.0065	−	8.68534i	−1.24594	−	0.373067i
$543$		−	61.9029i		−	2.65651i
$544$	−12.4939	−	19.6952i	−0.535674	−	0.844425i
$545$	27.9399	−	17.2503i	1.19682	−	0.738923i
$546$	3.88967	−	12.9904i	0.166463	−	0.555937i
$547$	0.517804	−	0.102998i	0.0221397	−	0.00440386i	−0.184008	−	0.982925i	$-0.558907\pi$
$547$	0.517804	−	0.102998i	0.0221397	−	0.00440386i	0.206148	+	0.978521i	$0.433907\pi$
$548$	19.9058	−	30.2597i	0.850335	−	1.29263i
$549$	−14.5562	+	21.7848i	−0.621242	+	0.929754i
$550$	−14.1025	−	8.82456i	−0.601331	−	0.376281i
$551$	−23.1434	−	34.6365i	−0.985940	−	1.47556i
$552$	45.1287	−	37.8576i	1.92080	−	1.61133i
$553$	6.73626	+	16.2628i	0.286455	+	0.691563i
$554$	9.34372	+	11.3023i	0.396977	+	0.480189i
$555$	34.4670	−	12.8466i	1.46304	−	0.545307i
$556$	14.5114	−	35.7584i	0.615422	−	1.51649i
$557$	−7.07083	+	7.07083i	−0.299601	+	0.299601i	−0.840857	−	0.541257i	$-0.817949\pi$
$557$	−7.07083	+	7.07083i	−0.299601	+	0.299601i	0.541257	+	0.840857i	$0.317949\pi$
$558$	−13.8792	−	45.1686i	−0.587552	−	1.91214i
$559$	1.32668	+	0.549528i	0.0561125	+	0.0232426i
$560$	−23.7288	+	33.9072i	−1.00273	+	1.43284i
$561$	−26.9899	+	13.0098i	−1.13952	+	0.549274i
$562$	−40.4219	+	4.12791i	−1.70509	+	0.174126i
$563$	−5.01599	+	12.1097i	−0.211399	+	0.510362i	−0.993639	−	0.112615i	$-0.964077\pi$
$563$	−5.01599	+	12.1097i	−0.211399	+	0.510362i	0.782240	+	0.622978i	$0.214077\pi$
$564$	−9.99149	+	4.22299i	−0.420717	+	0.177820i
$565$	24.0720	+	5.69416i	1.01272	+	0.239555i
$566$	8.48745	−	16.0171i	0.356754	−	0.673248i
$567$	−12.7781	+	64.2397i	−0.536629	+	2.69782i
$568$	5.62746	+	4.51770i	0.236123	+	0.189558i
$569$	5.02147	+	12.1229i	0.210511	+	0.508219i	0.993502	−	0.113814i	$-0.0363069\pi$
$569$	5.02147	+	12.1229i	0.210511	+	0.508219i	−0.782991	+	0.622033i	$0.786307\pi$
$570$	−34.5266	+	59.8559i	−1.44616	+	2.50709i
$571$	6.28432	+	9.40515i	0.262991	+	0.393593i	0.939340	−	0.342988i	$-0.111439\pi$
$571$	6.28432	+	9.40515i	0.262991	+	0.393593i	−0.676349	+	0.736581i	$0.736439\pi$
$572$	−3.15679	+	0.0226868i	−0.131992	+	0.000948584i
$573$	18.5467	−	27.7570i	0.774798	−	1.15957i
$574$	17.7924	−	21.8396i	0.742639	−	0.911567i
$575$	−8.93389	+	32.5074i	−0.372569	+	1.35565i
$576$	11.3117	+	51.0858i	0.471320	+	2.12857i
$577$	35.4243			1.47473			0.737366	−	0.675493i	$-0.236069\pi$
$577$	35.4243			1.47473			0.737366	+	0.675493i	$0.236069\pi$
$578$	19.7415	−	13.7213i	0.821136	−	0.570732i
$579$	83.0227			3.45031
$580$	24.6084	−	9.37406i	1.02181	−	0.389237i
$581$	−24.9079	+	4.95448i	−1.03335	+	0.205546i
$582$	46.9843	+	38.2773i	1.94756	+	1.58665i
$583$	−4.67844	−	3.12603i	−0.193761	−	0.129467i
$584$	−3.45746	+	0.378204i	−0.143071	+	0.0156502i
$585$	8.92432	+	4.07806i	0.368975	+	0.168607i
$586$	−14.2743	−	26.4761i	−0.589666	−	1.09372i
$587$	3.42440	+	8.26724i	0.141340	+	0.341226i	0.978659	−	0.205489i	$-0.0658784\pi$
$587$	3.42440	+	8.26724i	0.141340	+	0.341226i	−0.837319	+	0.546714i	$0.815878\pi$
$588$	62.4888	−	63.3935i	2.57700	−	2.61430i
$589$	−7.05083	+	35.4469i	−0.290524	+	1.46056i
$590$	2.12619	−	0.140192i	0.0875339	−	0.00577162i
$591$	9.43227	+	9.43227i	0.387992	+	0.387992i
$592$	−17.5409	+	12.0887i	−0.720927	+	0.496843i
$593$	−20.4753	−	8.48116i	−0.840821	−	0.348280i	−0.0796440	−	0.996823i	$-0.525378\pi$
$593$	−20.4753	−	8.48116i	−0.840821	−	0.348280i	−0.761177	+	0.648544i	$0.775378\pi$
$594$	36.1957	−	3.69634i	1.48513	−	0.151663i
$595$	−35.9490	−	22.9668i	−1.47377	−	0.941546i
$596$	−6.89405	−	33.4023i	−0.282391	−	1.36821i
$597$	44.8187	+	18.5645i	1.83431	+	0.759796i
$598$	1.87906	+	6.11523i	0.0768404	+	0.250070i
$599$	−9.05146	+	9.05146i	−0.369832	+	0.369832i	−0.867416	−	0.497584i	$-0.834221\pi$
$599$	−9.05146	+	9.05146i	−0.369832	+	0.369832i	0.497584	+	0.867416i	$0.334221\pi$
$600$	−32.0119	−	29.7206i	−1.30688	−	1.21334i
$601$	−4.90373	+	24.6527i	−0.200027	+	1.00561i	0.742084	+	0.670306i	$0.233837\pi$
$601$	−4.90373	+	24.6527i	−0.200027	+	1.00561i	−0.942112	+	0.335299i	$0.891163\pi$
$602$	8.92392	+	10.7945i	0.363712	+	0.439951i
$603$	−4.00170	+	1.65756i	−0.162962	+	0.0675010i
$604$	15.2729	+	22.5056i	0.621443	+	0.915740i
$605$	−5.07890	+	11.1146i	−0.206487	+	0.451871i
$606$	41.9377	+	3.97840i	1.70360	+	0.161611i
$607$	20.8307	−	31.1753i	0.845492	−	1.26537i	−0.116747	−	0.993162i	$-0.537247\pi$
$607$	20.8307	−	31.1753i	0.845492	−	1.26537i	0.962239	−	0.272207i	$-0.0877534\pi$
$608$	10.9271	−	38.4987i	0.443153	−	1.56133i
$609$	−82.5377	+	16.4178i	−3.34459	+	0.665281i
$610$	3.28347	+	12.2350i	0.132944	+	0.495379i
$611$		−	1.17808i		−	0.0476599i
$612$	−52.1207	+	13.8653i	−2.10686	+	0.560471i
$613$	−18.2924			−0.738821			−0.369411	−	0.929266i	$-0.620440\pi$
$613$	−18.2924			−0.738821			−0.369411	+	0.929266i	$0.620440\pi$
$614$	−10.9471	+	36.5601i	−0.441788	+	1.47544i
$615$	20.2554	+	21.7658i	0.816777	+	0.877681i
$616$	−27.3092	−	14.2207i	−1.10032	−	0.572969i
$617$	10.0381	−	15.0231i	0.404119	−	0.604806i	−0.572469	−	0.819926i	$-0.694014\pi$
$617$	10.0381	−	15.0231i	0.404119	−	0.604806i	0.976588	+	0.215120i	$0.0690143\pi$
$618$	−36.4869	−	3.46131i	−1.46772	−	0.139234i
$619$	−17.1673	+	11.4709i	−0.690014	+	0.461053i	−0.850493	−	0.525987i	$-0.823696\pi$
$619$	−17.1673	+	11.4709i	−0.690014	+	0.461053i	0.160479	+	0.987039i	$0.448696\pi$
$620$	−20.8477	−	9.34603i	−0.837262	−	0.375345i
$621$	−28.2162	−	68.1198i	−1.13228	−	2.73355i
$622$	−17.2264	+	14.2412i	−0.690714	+	0.571020i
$623$	−35.8791	−	7.13680i	−1.43747	−	0.285930i
$624$	−8.15226	−	1.50011i	−0.326352	−	0.0600527i
$625$	24.7423	+	3.58040i	0.989691	+	0.143216i
$626$	−12.1893	−	39.6691i	−0.487183	−	1.58550i
$627$	−47.4957	−	19.6734i	−1.89680	−	0.785679i
$628$	−2.01229	−	9.74975i	−0.0802991	−	0.389057i
$629$	−13.2105	−	17.5404i	−0.526739	−	0.699381i
$630$	58.2874	+	75.9002i	2.32223	+	3.02394i
$631$	−3.60818	+	8.71092i	−0.143639	+	0.346776i	−0.979283	−	0.202496i	$-0.935095\pi$
$631$	−3.60818	+	8.71092i	−0.143639	+	0.346776i	0.835644	+	0.549272i	$0.185095\pi$
$632$	9.43443	−	5.17433i	0.375282	−	0.205824i
$633$	28.5989	−	28.5989i	1.13670	−	1.13670i
$634$	16.2687	+	8.62081i	0.646114	+	0.342376i
$635$	−6.37411	+	2.37577i	−0.252949	+	0.0942794i
$636$	−10.5218	−	10.3717i	−0.417217	−	0.411263i
$637$	3.69959	+	8.93160i	0.146583	+	0.353883i
$638$	9.29740	+	17.2449i	0.368087	+	0.682731i
$639$	13.8750	−	9.27095i	0.548885	−	0.366753i
$640$	22.1813	+	12.1652i	0.876791	+	0.480872i
$641$	−13.4708	+	20.1605i	−0.532064	+	0.796290i	−0.995979	−	0.0895896i	$-0.971444\pi$
$641$	−13.4708	+	20.1605i	−0.532064	+	0.796290i	0.463915	+	0.885880i	$0.346444\pi$
$642$	14.2595	−	17.5031i	0.562776	−	0.690792i
$643$	3.81347	+	19.1716i	0.150388	+	0.756054i	0.980200	+	0.198010i	$0.0634479\pi$
$643$	3.81347	+	19.1716i	0.150388	+	0.756054i	−0.829812	+	0.558044i	$0.811552\pi$
$644$	−11.7327	+	61.2830i	−0.462335	+	2.41489i
$645$	−12.5784	+	7.76600i	−0.495274	+	0.305786i
$646$	40.1223	+	9.58359i	1.57859	+	0.377061i
$647$	−31.9601			−1.25648			−0.628241	−	0.778018i	$-0.716225\pi$
$647$	−31.9601			−1.25648			−0.628241	+	0.778018i	$0.716225\pi$
$648$	39.8851	+	3.49466i	1.56684	+	0.137283i
$649$	0.309272	+	1.55482i	0.0121400	+	0.0610318i
$650$	4.32669	−	1.94575i	0.169707	−	0.0763187i
$651$	60.7074	+	40.5634i	2.37931	+	1.58980i
$652$	−15.0938	+	0.108474i	−0.591117	+	0.00424817i
$653$	−32.2102	+	21.5222i	−1.26048	+	0.842228i	−0.992624	−	0.121230i	$-0.961316\pi$
$653$	−32.2102	+	21.5222i	−1.26048	+	0.842228i	−0.267859	+	0.963458i	$0.586316\pi$
$654$	30.4410	+	56.4622i	1.19034	+	2.20785i
$655$	6.73910	+	4.86191i	0.263319	+	0.189971i
$656$	−14.4537	−	9.35998i	−0.564321	−	0.365446i
$657$	−1.56904	+	7.88811i	−0.0612142	+	0.307744i
$658$	5.37997	−	10.1528i	0.209733	−	0.395797i
$659$	−13.6422	+	13.6422i	−0.531424	+	0.531424i	−0.920996	−	0.389572i	$-0.872623\pi$
$659$	−13.6422	+	13.6422i	−0.531424	+	0.531424i	0.389572	+	0.920996i	$0.372623\pi$
$660$	18.8241	−	26.4912i	0.732726	−	1.03117i
$661$	−19.3537	−	8.01657i	−0.752772	−	0.311808i	−0.0269000	−	0.999638i	$-0.508564\pi$
$661$	−19.3537	−	8.01657i	−0.752772	−	0.311808i	−0.725872	+	0.687830i	$0.758564\pi$
$662$	1.38002	+	13.5136i	0.0536359	+	0.525220i
$663$	1.19131	−	8.46078i	0.0462668	−	0.328590i
$664$	4.66626	+	14.8061i	0.181086	+	0.574589i
$665$	−11.6918	−	72.2555i	−0.453390	−	2.80195i
$666$	14.4689	+	47.0879i	0.560659	+	1.82462i
$667$	28.0738	−	28.0738i	1.08702	−	1.08702i
$668$	13.1813	+	5.34924i	0.510001	+	0.206968i
$669$	−26.8801	−	5.34679i	−1.03924	−	0.206719i
$670$	−0.672395	+	1.98336i	−0.0259769	+	0.0766238i
$671$	−8.70723	+	3.60665i	−0.336139	+	0.139233i
$672$	−63.4065	−	50.1574i	−2.44596	−	1.93486i
$673$	33.9787	−	22.7038i	1.30978	−	0.875169i	0.312578	−	0.949892i	$-0.398807\pi$
$673$	33.9787	−	22.7038i	1.30978	−	0.875169i	0.997204	+	0.0747236i	$0.0238074\pi$
$674$	−1.04039	+	10.9672i	−0.0400745	+	0.422439i
$675$	−47.5258	+	27.0346i	−1.82927	+	1.04056i
$676$	−13.7943	+	20.9694i	−0.530551	+	0.806514i
$677$	32.5951	−	6.48358i	1.25273	−	0.249184i	0.476243	−	0.879314i	$-0.341998\pi$
$677$	32.5951	−	6.48358i	1.25273	−	0.249184i	0.776490	+	0.630130i	$0.216998\pi$
$678$	−13.8610	+	46.2918i	−0.532329	+	1.77782i
$679$	−64.1942			−2.46355
$680$	−11.5664	+	23.3713i	−0.443551	+	0.896249i
$681$	−49.2345			−1.88667
$682$	4.87563	−	16.2832i	0.186698	−	0.623516i
$683$	40.1356	−	7.98347i	1.53575	−	0.305479i	0.646503	−	0.762912i	$-0.276231\pi$
$683$	40.1356	−	7.98347i	1.53575	−	0.305479i	0.889244	+	0.457433i	$0.151231\pi$
$684$	−77.3116	−	50.8581i	−2.95608	−	1.94461i
$685$	−40.4691	−	1.45458i	−1.54625	−	0.0555767i
$686$	−4.57892	+	48.2680i	−0.174824	+	1.84288i
$687$	−32.1456	+	21.4790i	−1.22643	+	0.819476i
$688$	5.96619	−	6.14020i	0.227459	−	0.234093i
$689$	1.48243	−	0.614044i	0.0564762	−	0.0233932i
$690$	−62.3709	−	21.1449i	−2.37442	−	0.804973i
$691$	−43.5640	−	8.66542i	−1.65725	−	0.329648i	−0.724255	−	0.689532i	$-0.757816\pi$
$691$	−43.5640	−	8.66542i	−1.65725	−	0.329648i	−0.932997	+	0.359884i	$0.882816\pi$
$692$	−2.95991	+	7.29366i	−0.112519	+	0.277264i
$693$	−50.3445	+	50.3445i	−1.91243	+	1.91243i
$694$	−5.72828	−	18.6422i	−0.217442	−	0.707648i
$695$	−42.5917	+	6.89188i	−1.61560	+	0.261424i
$696$	15.4627	+	49.0634i	0.586112	+	1.85974i
$697$	9.01258	−	15.2913i	0.341376	−	0.579199i
$698$	−0.588099	−	5.75886i	−0.0222599	−	0.217976i
$699$	28.4884	+	11.8003i	1.07753	+	0.446328i
$700$	46.1737	+	2.99015i	1.74520	+	0.113017i
$701$	−24.9507	+	24.9507i	−0.942374	+	0.942374i	−0.998428	−	0.0560536i	$-0.982148\pi$
$701$	−24.9507	+	24.9507i	−0.942374	+	0.942374i	0.0560536	+	0.998428i	$0.482148\pi$
$702$	−4.85814	+	9.16802i	−0.183359	+	0.346025i
$703$	7.35043	−	36.9531i	0.277227	−	1.39371i
$704$	−6.82608	+	17.5399i	−0.257268	+	0.661059i
$705$	9.83522	+	7.09560i	0.370416	+	0.267236i
$706$	−4.86633	−	9.02610i	−0.183147	−	0.339702i
$707$	−37.1023	+	24.7910i	−1.39538	+	0.932361i
$708$	0.0299140	+	4.16242i	0.00112424	+	0.156433i
$709$	−40.1803	−	26.8476i	−1.50900	−	1.00828i	−0.987952	−	0.154758i	$-0.950540\pi$
$709$	−40.1803	−	26.8476i	−1.50900	−	1.00828i	−0.521051	−	0.853525i	$-0.674460\pi$
$710$	1.05000	−	7.99968i	0.0394057	−	0.300223i
$711$	−4.85418	−	24.4036i	−0.182046	−	0.915206i
$712$	−1.95183	+	22.2766i	−0.0731481	+	0.834851i
$713$	−34.4455			−1.29000
$714$	48.9051	−	67.4756i	1.83023	−	2.52521i
$715$	1.85420	+	3.00320i	0.0693432	+	0.112313i
$716$	−0.158635	−	0.0303709i	−0.00592846	−	0.00113502i
$717$	−8.95930	−	45.0414i	−0.334591	−	1.68210i
$718$	−1.18685	+	1.45683i	−0.0442930	+	0.0543684i
$719$	11.4596	−	17.1506i	0.427373	−	0.639609i	−0.553821	−	0.832636i	$-0.686831\pi$
$719$	11.4596	−	17.1506i	0.427373	−	0.639609i	0.981193	+	0.193027i	$0.0618307\pi$
$720$	42.2470	−	40.4639i	1.57445	−	1.50800i
$721$	32.2800	−	21.5688i	1.20217	−	0.803264i
$722$	20.8376	+	38.6497i	0.775496	+	1.43839i
$723$	0.677658	+	1.63601i	0.0252024	+	0.0608439i
$724$	28.1384	−	28.5457i	1.04575	−	1.06089i
$725$	−23.2424	−	18.0722i	−0.863199	−	0.671184i
$726$	−21.0933	−	11.1773i	−0.782846	−	0.414830i
$727$	11.6539	−	11.6539i	0.432220	−	0.432220i	−0.457163	−	0.889383i	$-0.651134\pi$
$727$	11.6539	−	11.6539i	0.432220	−	0.432220i	0.889383	+	0.457163i	$0.151134\pi$
$728$	7.69855	−	4.22228i	0.285327	−	0.156488i
$729$	−3.34745	+	8.08147i	−0.123980	+	0.299314i
$730$	2.36844	+	3.08412i	0.0876601	+	0.114148i
$731$	6.58235	+	5.87803i	0.243457	+	0.217407i
$732$	−24.2359	+	5.00214i	−0.895783	+	0.184884i
$733$	−18.1974	−	7.53760i	−0.672136	−	0.278408i	0.0203994	−	0.999792i	$-0.493506\pi$
$733$	−18.1974	−	7.53760i	−0.672136	−	0.278408i	−0.692535	+	0.721384i	$0.743506\pi$
$734$	3.21292	+	10.4562i	0.118591	+	0.385944i
$735$	−96.8486	−	22.9092i	−3.57232	−	0.845019i
$736$	38.0190	+	3.05599i	1.40140	+	0.112645i
$737$	−1.52813	−	0.303964i	−0.0562894	−	0.0111967i
$738$	−30.6891	+	25.3710i	−1.12968	+	0.933919i
$739$	−14.7461	−	35.6002i	−0.542443	−	1.30957i	−0.922994	−	0.384814i	$-0.874266\pi$
$739$	−14.7461	−	35.6002i	−0.542443	−	1.30957i	0.380551	−	0.924760i	$-0.375734\pi$
$740$	21.7335	+	9.74316i	0.798940	+	0.358166i
$741$	12.1896	−	8.14485i	0.447797	−	0.299209i
$742$	15.5800	+	1.47799i	0.571958	+	0.0542585i
$743$	−9.70475	+	14.5242i	−0.356033	+	0.532841i	−0.965647	−	0.259858i	$-0.916324\pi$
$743$	−9.70475	+	14.5242i	−0.356033	+	0.532841i	0.609614	+	0.792698i	$0.291324\pi$
$744$	20.6134	−	39.5856i	0.755725	−	1.45128i
$745$	−27.9146	+	25.9775i	−1.02271	+	0.951743i
$746$	9.86451	−	32.9446i	0.361165	−	1.20619i
$747$	35.8974			1.31342
$748$	−18.3598	−	6.26915i	−0.671300	−	0.229223i
$749$			23.9143i			0.873811i
$750$	−9.81564	+	47.8409i	−0.358416	+	1.74690i
$751$	39.1835	−	7.79408i	1.42983	−	0.284410i	0.581354	−	0.813650i	$-0.302523\pi$
$751$	39.1835	−	7.79408i	1.42983	−	0.284410i	0.848472	+	0.529240i	$0.177523\pi$
$752$	−6.52704	−	2.59432i	−0.238017	−	0.0946051i
$753$	16.4184	−	24.5719i	0.598321	−	0.895451i
$754$	−5.56196	−	0.527632i	−0.202555	−	0.0192152i
$755$	12.6386	−	27.6581i	0.459967	−	1.00658i
$756$	−83.7360	+	56.8253i	−3.04545	+	2.06671i
$757$	−11.2462	+	4.65834i	−0.408751	+	0.169310i	−0.577578	−	0.816335i	$-0.696002\pi$
$757$	−11.2462	+	4.65834i	−0.408751	+	0.169310i	0.168827	+	0.985646i	$0.446002\pi$
$758$	23.6960	+	28.6630i	0.860679	+	1.04109i
$759$	9.55880	−	48.0553i	0.346962	−	1.74430i
$760$	−43.1294	+	11.9075i	−1.56447	+	0.431930i
$761$	24.8892	−	24.8892i	0.902231	−	0.902231i	−0.0933975	−	0.995629i	$-0.529773\pi$
$761$	24.8892	−	24.8892i	0.902231	−	0.902231i	0.995629	+	0.0933975i	$0.0297727\pi$
$762$	−3.90315	−	12.7025i	−0.141396	−	0.460162i
$763$	−62.7749	−	26.0022i	−2.27260	−	0.941343i
$764$	21.1697	−	4.36930i	0.765893	−	0.158076i
$765$	43.5048	+	41.7535i	1.57292	+	1.50960i
$766$	−19.4513	+	1.98638i	−0.702803	+	0.0717708i
$767$	−0.417662	−	0.173001i	−0.0150809	−	0.00624672i
$768$	−26.2639	+	41.8634i	−0.947717	+	1.51062i
$769$	5.65391	+	5.65391i	0.203885	+	0.203885i	0.801662	−	0.597777i	$-0.203949\pi$
$769$	5.65391	+	5.65391i	0.203885	+	0.203885i	−0.597777	+	0.801662i	$0.703949\pi$
$770$	2.26487	+	34.3496i	0.0816202	+	1.23787i
$771$	18.1486	−	91.2390i	0.653604	−	3.28589i
$772$	38.2849	+	37.7385i	1.37790	+	1.35824i
$773$	15.4563	+	37.3149i	0.555925	+	1.34212i	0.912967	+	0.408034i	$0.133785\pi$
$773$	15.4563	+	37.3149i	0.555925	+	1.34212i	−0.357042	+	0.934089i	$0.616215\pi$
$774$	−9.39500	−	17.4259i	−0.337696	−	0.626361i
$775$	3.17181	+	25.3457i	0.113935	+	0.910446i
$776$	4.26701	+	39.0081i	0.153177	+	1.40031i
$777$	−63.2870	−	42.2870i	−2.27041	−	1.51704i
$778$	33.3904	+	27.2026i	1.19710	+	0.975260i
$779$	29.8700	−	5.94150i	1.07020	−	0.212876i
$780$	3.29902	+	8.66046i	0.118124	+	0.310094i
$781$	6.00264			0.214791
$782$	−1.49821	+	39.2869i	−0.0535758	+	1.40490i
$783$	64.3912			2.30115
$784$	57.6319	−	0.828408i	2.05828	−	0.0295860i
$785$	−8.14793	+	7.58253i	−0.290812	+	0.270632i
$786$	−10.2531	+	12.5854i	−0.365717	+	0.448907i
$787$	9.12912	−	13.6627i	0.325418	−	0.487022i	−0.632303	−	0.774721i	$-0.717890\pi$
$787$	9.12912	−	13.6627i	0.325418	−	0.487022i	0.957721	+	0.287699i	$0.0928902\pi$
$788$	0.0620720	+	8.63708i	0.00221122	+	0.307683i
$789$	−7.84300	−	11.7379i	−0.279218	−	0.417879i
$790$	−10.4209	−	6.01107i	−0.370758	−	0.213864i
$791$	−19.5881	−	47.2899i	−0.696474	−	1.68144i
$792$	33.9387	+	27.2458i	1.20596	+	0.968139i
$793$	0.524331	−	2.63599i	0.0186195	−	0.0936068i
$794$	−19.7269	+	37.2277i	−0.700083	+	1.32116i
$795$	−3.80238	+	16.0746i	−0.134857	+	0.570106i
$796$	12.2290	+	28.9335i	0.433445	+	1.02552i
$797$	−16.2731	+	39.2868i	−0.576424	+	1.39161i	0.319578	+	0.947560i	$0.396459\pi$
$797$	−16.2731	+	39.2868i	−0.576424	+	1.39161i	−0.896002	+	0.444050i	$0.853541\pi$
$798$	142.247	−	14.5264i	5.03549	−	0.514229i
$799$	2.38869	−	6.83448i	0.0845058	−	0.241787i
$800$	−1.25219	−	28.2565i	−0.0442716	−	0.999020i
$801$	47.7732	+	19.7883i	1.68798	+	0.699185i
$802$	−0.732397	−	2.38352i	−0.0258619	−	0.0841652i
$803$	−2.04569	+	2.04569i	−0.0721910	+	0.0721910i
$804$	−3.79083	−	1.53839i	−0.133692	−	0.0542548i
$805$	65.3679	−	24.3640i	2.30392	−	0.858719i
$806$	3.08847	+	3.73585i	0.108787	+	0.131590i
$807$	12.4843	+	30.1398i	0.439469	+	1.06097i
$808$	17.5306	+	20.8977i	0.616726	+	0.735177i
$809$	−7.20992	−	10.7904i	−0.253487	−	0.379371i	0.682800	−	0.730605i	$-0.260762\pi$
$809$	−7.20992	−	10.7904i	−0.253487	−	0.379371i	−0.936287	+	0.351235i	$0.885762\pi$
$810$	−19.8142	−	40.1397i	−0.696200	−	1.41036i
$811$	0.282462	−	0.422734i	0.00991857	−	0.0148442i	−0.826477	−	0.562970i	$-0.809659\pi$
$811$	0.282462	−	0.422734i	0.00991857	−	0.0148442i	0.836396	+	0.548126i	$0.184659\pi$
$812$	−45.5240	−	29.9472i	−1.59758	−	1.05094i
$813$	−64.8608	+	12.9016i	−2.27477	+	0.452480i
$814$	−5.08281	+	16.9751i	−0.178152	+	0.594978i
$815$	8.86561	+	14.3594i	0.310549	+	0.502988i
$816$	−44.2528	−	25.2324i	−1.54916	−	0.883312i
$817$			15.1419i			0.529747i
$818$	27.7580	+	8.31149i	0.970535	+	0.290604i
$819$	−3.96103	−	19.9135i	−0.138410	−	0.695832i
$820$	−0.553251	+	19.2443i	−0.0193204	+	0.672038i
$821$	−11.8178	+	17.6866i	−0.412444	+	0.617267i	−0.978289	−	0.207245i	$-0.933550\pi$
$821$	−11.8178	+	17.6866i	−0.412444	+	0.617267i	0.565845	+	0.824512i	$0.308550\pi$
$822$	7.47095	−	78.7539i	0.260579	−	2.74686i
$823$	30.9347	−	20.6699i	1.07832	−	0.720507i	0.116221	−	0.993223i	$-0.462922\pi$
$823$	30.9347	−	20.6699i	1.07832	−	0.720507i	0.962095	+	0.272716i	$0.0879220\pi$
$824$	−15.2521	−	18.1815i	−0.531332	−	0.633382i
$825$	−36.2403	−	2.60854i	−1.26173	−	0.0908177i
$826$	−2.80941	−	3.39830i	−0.0977519	−	0.118242i
$827$	−8.42546	+	42.3576i	−0.292982	+	1.47292i	0.501249	+	0.865303i	$0.332874\pi$
$827$	−8.42546	+	42.3576i	−0.292982	+	1.47292i	−0.794231	+	0.607616i	$0.792126\pi$
$828$	33.1654	−	81.7245i	1.15258	−	2.84012i
$829$	25.1539	+	25.1539i	0.873632	+	0.873632i	0.992866	−	0.119234i	$-0.0380439\pi$
$829$	25.1539	+	25.1539i	0.873632	+	0.873632i	−0.119234	+	0.992866i	$0.538044\pi$
$830$	11.4388	−	13.0537i	0.397045	−	0.453100i
$831$	29.5904	+	12.2567i	1.02648	+	0.425181i
$832$	−3.07743	−	4.39743i	−0.106691	−	0.152453i
$833$	3.35290	+	59.3171i	0.116171	+	2.05521i
$834$	−8.56274	−	83.8491i	−0.296503	−	2.90346i
$835$	−2.54050	−	15.7003i	−0.0879176	−	0.543330i
$836$	−12.9594	−	30.6616i	−0.448210	−	1.06045i
$837$	−39.5029	−	39.5029i	−1.36542	−	1.36542i
$838$	−26.8135	−	14.2085i	−0.926259	−	0.490824i
$839$	32.7696	+	6.51827i	1.13133	+	0.225036i	0.725039	−	0.688707i	$-0.241822\pi$
$839$	32.7696	+	6.51827i	1.13133	+	0.225036i	0.406292	+	0.913743i	$0.366822\pi$
$840$	−11.1188	+	89.7026i	−0.383634	+	3.09503i
$841$	2.17074	+	5.24064i	0.0748532	+	0.180712i
$842$	5.92715	+	10.9937i	0.204263	+	0.378868i
$843$	−73.7876	+	49.3033i	−2.54138	+	1.69810i
$844$	26.1878	−	0.188204i	0.901423	−	0.00647824i
$845$	28.0443	+	1.00800i	0.964752	+	0.0346761i
$846$	−10.2583	+	12.5918i	−0.352688	+	0.432915i
$847$	24.8007	−	4.93316i	0.852161	−	0.169505i
$848$	−0.137496	−	9.56553i	−0.00472163	−	0.328481i
$849$		−	39.5905i		−	1.35874i
$850$	29.0461	−	2.51520i	0.996272	−	0.0862705i
$851$	35.9092			1.23095
$852$	15.4802	+	2.96372i	0.530345	+	0.101536i
$853$	−4.54863	−	22.8675i	−0.155742	−	0.782969i	−0.977137	−	0.212609i	$-0.931804\pi$
$853$	−4.54863	−	22.8675i	−0.155742	−	0.782969i	0.821395	−	0.570360i	$-0.193196\pi$
$854$	16.5566	−	20.3228i	0.566556	−	0.695432i
$855$	−3.71636	+	103.396i	−0.127097	+	3.53607i
$856$	14.5317	−	1.58959i	0.496684	−	0.0543312i
$857$	14.7329	+	22.0493i	0.503265	+	0.753189i	0.992927	−	0.118723i	$-0.0378800\pi$
$857$	14.7329	+	22.0493i	0.503265	+	0.753189i	−0.489663	+	0.871912i	$0.662880\pi$
$858$	−6.06900	+	3.27204i	−0.207192	+	0.111706i
$859$	−25.9168	+	10.7351i	−0.884270	+	0.366277i	−0.778151	−	0.628077i	$-0.783842\pi$
$859$	−25.9168	+	10.7351i	−0.884270	+	0.366277i	−0.106119	+	0.994353i	$0.533842\pi$
$860$	−9.33047	−	2.13640i	−0.318166	−	0.0728507i
$861$	12.0029	−	60.3428i	0.409059	−	2.05648i
$862$	9.76800	+	5.17606i	0.332699	+	0.176297i
$863$	−18.4466	+	18.4466i	−0.627928	+	0.627928i	−0.947546	−	0.319618i	$-0.896445\pi$
$863$	−18.4466	+	18.4466i	−0.627928	+	0.627928i	0.319618	+	0.947546i	$0.396445\pi$
$864$	40.0963	+	47.1056i	1.36410	+	1.60257i
$865$	8.68747	−	1.40574i	0.295383	−	0.0477966i
$866$	23.8949	−	2.44017i	0.811982	−	0.0829202i
$867$	24.0665	−	46.6688i	0.817342	−	1.58496i
$868$	9.55610	+	46.3003i	0.324355	+	1.57153i
$869$	3.42512	−	8.26898i	0.116189	−	0.280506i
$870$	37.9049	−	43.2563i	1.28510	−	1.46653i
$871$	0.314179	−	0.314179i	0.0106455	−	0.0106455i
$872$	−11.6278	+	39.8740i	−0.393766	+	1.35030i
$873$	88.9961	+	17.7024i	3.01206	+	0.599136i
$874$	−51.9917	+	42.9820i	−1.75864	+	1.45389i
$875$	−23.9468	−	45.8556i	−0.809548	−	1.55020i
$876$	−6.28569	+	4.26562i	−0.212374	+	0.144122i
$877$	−13.3258	−	19.9435i	−0.449980	−	0.673443i	0.535247	−	0.844696i	$-0.320219\pi$
$877$	−13.3258	−	19.9435i	−0.449980	−	0.673443i	−0.985227	+	0.171253i	$0.945219\pi$
$878$	0.405982	−	4.27959i	0.0137012	−	0.144429i
$879$	−54.6231	−	36.4980i	−1.84239	−	1.23105i
$880$	20.7223	−	3.65950i	0.698547	−	0.123362i
$881$	−44.7081	+	8.89300i	−1.50625	+	0.299613i	−0.878101	−	0.478476i	$-0.841189\pi$
$881$	−44.7081	+	8.89300i	−1.50625	+	0.299613i	−0.628154	+	0.778089i	$0.716189\pi$
$882$	38.2308	−	127.680i	1.28730	−	4.29920i
$883$	−27.6490			−0.930462			−0.465231	−	0.885189i	$-0.654029\pi$
$883$	−27.6490			−0.930462			−0.465231	+	0.885189i	$0.654029\pi$
$884$	4.39527	−	3.36007i	0.147829	−	0.113011i
$885$	3.95991	−	2.44488i	0.133111	−	0.0821837i
$886$	14.8465	−	49.5830i	0.498777	−	1.66577i
$887$	−5.71744	−	28.7435i	−0.191973	−	0.965113i	−0.949848	−	0.312713i	$-0.898762\pi$
$887$	−5.71744	−	28.7435i	−0.191973	−	0.965113i	0.757875	−	0.652400i	$-0.226238\pi$
$888$	−21.4893	+	41.2677i	−0.721134	+	1.38485i
$889$	11.7039	+	7.82030i	0.392536	+	0.262284i
$890$	22.4188	−	11.0666i	0.751479	−	0.370954i
$891$	27.6907	−	18.5023i	0.927673	−	0.619852i
$892$	−9.96501	−	14.6841i	−0.333653	−	0.491661i
$893$	11.4767	−	4.75382i	0.384054	−	0.159080i
$894$	−47.4632	−	57.4121i	−1.58741	−	1.92015i
$895$	0.0630678	+	0.169209i	0.00210813	+	0.00565603i
$896$	−6.43972	−	51.9513i	−0.215136	−	1.73557i
$897$	9.88002	+	9.88002i	0.329884	+	0.329884i
$898$	−42.3263	+	13.0058i	−1.41245	+	0.434009i
$899$	11.5117	−	27.7918i	0.383938	−	0.926908i
$900$	−63.1885	−	16.8784i	−2.10628	−	0.562614i
$901$	9.84522	−	0.556501i	0.327992	−	0.0185397i
$902$	−14.2491	+	1.45513i	−0.474444	+	0.0484506i
$903$	28.2609	+	11.7060i	0.940464	+	0.389553i
$904$	−27.4341	+	15.0463i	−0.912444	+	0.500431i
$905$	−43.6104	−	10.3159i	−1.44966	−	0.342912i
$906$	52.4898	+	27.8143i	1.74386	+	0.924069i
$907$	−17.4275	−	3.46654i	−0.578669	−	0.115104i	−0.102927	−	0.994689i	$-0.532821\pi$
$907$	−17.4275	−	3.46654i	−0.578669	−	0.115104i	−0.475743	+	0.879584i	$0.657821\pi$
$908$	−22.7039	−	22.3799i	−0.753456	−	0.742703i
$909$	58.2735	−	24.1377i	1.93281	−	0.800596i
$910$	−8.50349	−	4.90507i	−0.281888	−	0.162601i
$911$	18.7799	−	12.5483i	0.622205	−	0.415744i	−0.204114	−	0.978947i	$-0.565431\pi$
$911$	18.7799	−	12.5483i	0.622205	−	0.415744i	0.826318	+	0.563203i	$0.190431\pi$
$912$	−18.2823	−	85.4720i	−0.605387	−	2.83026i
$913$	10.7366	+	7.17396i	0.355329	+	0.237424i
$914$	−2.28704	−	1.86321i	−0.0756486	−	0.0616296i
$915$	18.8486	+	20.2541i	0.623116	+	0.669579i
$916$	−24.5870	−	4.70723i	−0.812378	−	0.155531i
$917$		−	17.1954i		−	0.567841i
$918$	−46.7732	+	43.3369i	−1.54375	+	1.43033i
$919$		−	7.45779i		−	0.246010i	−0.992406	−	0.123005i	$-0.960747\pi$
$919$		−	7.45779i		−	0.246010i	0.992406	−	0.123005i	$-0.0392531\pi$
$920$	−19.1500	−	38.1019i	−0.631358	−	1.25618i
$921$	16.2613	+	81.7512i	0.535829	+	2.69379i
$922$	−4.92696	+	6.04770i	−0.162261	+	0.199171i
$923$	−0.951013	+	1.42329i	−0.0313030	+	0.0468482i
$924$	−67.2459	+	0.483275i	−2.21223	+	0.0158986i
$925$	−3.30658	−	26.4227i	−0.108720	−	0.868774i
$926$	−11.8935	−	22.0602i	−0.390846	−	0.724943i
$927$	−50.6994	+	21.0004i	−1.66519	+	0.689743i
$928$	−15.1717	+	29.6536i	−0.498034	+	0.973428i
$929$	43.8254	+	8.71741i	1.43786	+	0.286009i	0.851635	−	0.524136i	$-0.175612\pi$
$929$	43.8254	+	8.71741i	1.43786	+	0.286009i	0.586230	+	0.810145i	$0.300612\pi$
$930$	−49.7909	+	3.28301i	−1.63271	+	0.107654i
$931$	−72.0822	+	72.0822i	−2.36240	+	2.36240i
$932$	7.77319	+	18.3912i	0.254619	+	0.602423i
$933$	−18.6810	+	45.1000i	−0.611590	+	1.47651i
$934$	−15.2588	+	1.55824i	−0.499283	+	0.0509872i
$935$	4.66760	+	21.1824i	0.152647	+	0.692737i
$936$	−11.8373	+	3.73061i	−0.386913	+	0.121939i
$937$	−12.2093	+	29.4759i	−0.398862	+	0.962937i	0.589075	+	0.808078i	$0.299492\pi$
$937$	−12.2093	+	29.4759i	−0.398862	+	0.962937i	−0.987937	+	0.154859i	$0.950508\pi$
$938$	4.14240	−	1.27286i	0.135254	−	0.0415602i
$939$	−64.0910	−	64.0910i	−2.09153	−	2.09153i
$940$	1.31004	+	7.74272i	0.0427287	+	0.252540i
$941$	−53.0362	−	10.5495i	−1.72893	−	0.343905i	−0.772310	−	0.635246i	$-0.780899\pi$
$941$	−53.0362	−	10.5495i	−1.72893	−	0.343905i	−0.956619	+	0.291341i	$0.905899\pi$
$942$	−13.8539	−	16.7579i	−0.451386	−	0.546002i
$943$	11.1078	+	26.8166i	0.361720	+	0.873270i
$944$	−1.87826	+	1.93305i	−0.0611322	+	0.0629153i
$945$	102.907	+	47.0242i	3.34755	+	1.52970i
$946$	0.672541	−	7.08949i	0.0218662	−	0.230499i
$947$	3.39667	+	2.26958i	0.110377	+	0.0737515i	0.609534	−	0.792760i	$-0.291357\pi$
$947$	3.39667	+	2.26958i	0.110377	+	0.0737515i	−0.499157	+	0.866512i	$0.666357\pi$
$948$	12.9158	−	19.6338i	0.419485	−	0.637677i
$949$	−0.160952	−	0.809161i	−0.00522473	−	0.0262665i
$950$	36.4146	+	34.2987i	1.18144	+	1.11280i
$951$	40.2126			1.30398
$952$	53.2235	−	8.88539i	1.72498	−	0.287977i
$953$			12.3069i			0.398660i	0.979932	+	0.199330i	$0.0638766\pi$
$953$			12.3069i			0.398660i	−0.979932	+	0.199330i	$0.936123\pi$
$954$	−21.1918	−	6.34539i	−0.686110	−	0.205440i
$955$	−16.4640	−	17.6917i	−0.532763	−	0.572489i
$956$	16.3424	−	24.8428i	0.528552	−	0.803474i
$957$	35.5781	+	23.7725i	1.15008	+	0.768456i
$958$	−47.9972	−	4.55323i	−1.55072	−	0.147108i
$959$	46.5544	+	69.6736i	1.50332	+	2.24988i
$960$	55.2476	+	0.793844i	1.78311	+	0.0256212i
$961$	4.52824	−	1.87566i	0.146072	−	0.0605052i
$962$	−3.21970	−	3.89460i	−0.103807	−	0.125567i
$963$	6.59470	−	33.1538i	0.212511	−	1.06837i
$964$	−0.431167	+	1.06246i	−0.0138869	+	0.0342196i
$965$	13.8354	−	58.4893i	0.445378	−	1.88284i
$966$	40.0277	+	130.267i	1.28787	+	4.19126i
$967$	22.2182	−	53.6396i	0.714491	−	1.72493i	0.0260278	−	0.999661i	$-0.491714\pi$
$967$	22.2182	−	53.6396i	0.714491	−	1.72493i	0.688463	−	0.725272i	$-0.258286\pi$
$968$	−4.64618	−	14.7424i	−0.149334	−	0.473839i
$969$	87.2315	−	22.5356i	2.80228	−	0.723947i
$970$	34.7960	−	26.7215i	1.11723	−	0.857977i
$971$	18.4211	+	7.63026i	0.591160	+	0.244867i	0.658150	−	0.752887i	$-0.271339\pi$
$971$	18.4211	+	7.63026i	0.591160	+	0.244867i	−0.0669895	+	0.997754i	$0.521339\pi$
$972$	20.1111	−	8.50012i	0.645063	−	0.272641i
$973$	63.1307	+	63.1307i	2.02388	+	2.02388i
$974$	−2.31581	−	1.22715i	−0.0742032	−	0.0393203i
$975$	6.36015	−	8.17969i	0.203688	−	0.261960i
$976$	−13.4498	−	8.70991i	−0.430519	−	0.278797i
$977$	−18.1960	+	7.53703i	−0.582141	+	0.241131i	−0.654266	−	0.756265i	$-0.727022\pi$
$977$	−18.1960	+	7.53703i	−0.582141	+	0.241131i	0.0721243	+	0.997396i	$0.477022\pi$
$978$	−29.0181	+	15.6448i	−0.927896	+	0.500266i
$979$	10.3339	+	15.4658i	0.330273	+	0.494289i
$980$	−34.2470	−	54.5875i	−1.09398	−	1.74373i
$981$	79.8579	+	53.3593i	2.54967	+	1.70363i
$982$	−11.2105	+	13.7606i	−0.357742	+	0.439118i
$983$	−22.6886	+	4.51305i	−0.723655	+	0.143944i	−0.543157	−	0.839631i	$-0.682771\pi$
$983$	−22.6886	+	4.51305i	−0.723655	+	0.143944i	−0.180498	+	0.983575i	$0.557771\pi$
$984$	−37.4656	−	3.28267i	−1.19436	−	0.104648i
$985$	8.21686	−	5.07316i	0.261811	−	0.161644i
$986$	−31.1973	−	14.3385i	−0.993523	−	0.456632i
$987$		−	25.0954i		−	0.798794i
$988$	9.32340	+	1.78498i	0.296617	+	0.0567879i
$989$	−14.1541	+	2.81542i	−0.450074	+	0.0895253i
$990$	6.33245	−	48.2453i	0.201258	−	1.53334i
$991$	−20.1923	+	30.2199i	−0.641429	+	0.959967i	0.358224	+	0.933636i	$0.383382\pi$
$991$	−20.1923	+	30.2199i	−0.641429	+	0.959967i	−0.999653	+	0.0263313i	$0.991618\pi$
$992$	27.4995	−	8.88444i	0.873111	−	0.282081i
$993$	16.4828	+	24.6682i	0.523065	+	0.782821i
$994$	−14.6957	+	7.92307i	−0.466121	+	0.251304i
$995$	20.5475	−	28.4810i	0.651401	−	0.902907i
$996$	24.1466	+	23.8020i	0.765115	+	0.754196i
$997$	−28.0244	−	5.57440i	−0.887542	−	0.176543i	−0.269793	−	0.962918i	$-0.586955\pi$
$997$	−28.0244	−	5.57440i	−0.887542	−	0.176543i	−0.617749	+	0.786375i	$0.711955\pi$
$998$	−21.6987	+	40.9487i	−0.686861	+	1.29621i
$999$	41.1814	+	41.1814i	1.30292	+	1.30292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.co.a.419.94	yes	832
5.4	even	2	inner	680.2.co.a.419.11	yes	832
8.3	odd	2	inner	680.2.co.a.419.16	yes	832
17.14	odd	16	inner	680.2.co.a.99.89	yes	832
40.19	odd	2	inner	680.2.co.a.419.89	yes	832
85.14	odd	16	inner	680.2.co.a.99.16	yes	832
136.99	even	16	inner	680.2.co.a.99.11	✓	832
680.99	even	16	inner	680.2.co.a.99.94	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.co.a.99.11	✓	832	136.99	even	16	inner
680.2.co.a.99.16	yes	832	85.14	odd	16	inner
680.2.co.a.99.89	yes	832	17.14	odd	16	inner
680.2.co.a.99.94	yes	832	680.99	even	16	inner
680.2.co.a.419.11	yes	832	5.4	even	2	inner
680.2.co.a.419.16	yes	832	8.3	odd	2	inner
680.2.co.a.419.89	yes	832	40.19	odd	2	inner
680.2.co.a.419.94	yes	832	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.co (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35478 + 0.405659i) q^{2} +(3.02940 - 0.602586i) q^{3} +(1.67088 + 1.09916i) q^{4} +(0.0803191 - 2.23462i) q^{5} +(4.34863 + 0.412531i) q^{6} +(-3.84724 + 2.57064i) q^{7} +(1.81780 + 2.16693i) q^{8} +(6.04253 - 2.50290i) q^{9} +(1.01531 - 2.99485i) q^{10} +(2.30746 + 0.458983i) q^{11} +(5.72411 + 2.32295i) q^{12} +(-0.474407 + 0.474407i) q^{13} +(-6.25499 + 1.92200i) q^{14} +(-1.10323 - 6.81798i) q^{15} +(1.58369 + 3.67314i) q^{16} +(-3.71414 + 1.79030i) q^{17} +(9.20166 - 0.939681i) q^{18} +(-6.53598 - 2.70729i) q^{19} +(2.59042 - 3.64551i) q^{20} +(-10.1058 + 10.1058i) q^{21} +(2.93992 + 1.55787i) q^{22} +(1.31540 - 6.61299i) q^{23} +(6.81261 + 5.46914i) q^{24} +(-4.98710 - 0.358966i) q^{25} +(-0.835166 + 0.450272i) q^{26} +(9.09245 - 6.07538i) q^{27} +(-9.25383 + 0.0665044i) q^{28} +(4.89597 + 3.27138i) q^{29} +(1.27113 - 9.68443i) q^{30} +(-0.996655 - 5.01052i) q^{31} +(0.655518 + 5.61875i) q^{32} +7.26681 q^{33} +(-5.75811 + 0.918803i) q^{34} +(5.43542 + 8.80361i) q^{35} +(12.8474 + 2.45967i) q^{36} +(1.03900 + 5.22343i) q^{37} +(-7.75660 - 6.31917i) q^{38} +(-1.15130 + 1.72304i) q^{39} +(4.98829 - 3.88805i) q^{40} +(-3.57941 + 2.39169i) q^{41} +(-17.7907 + 9.59168i) q^{42} +(-0.819076 - 1.97742i) q^{43} +(3.35100 + 3.30318i) q^{44} +(-5.10771 - 13.7038i) q^{45} +(4.46471 - 8.42556i) q^{46} +(-1.24163 + 1.24163i) q^{47} +(7.01101 + 10.1731i) q^{48} +(5.51427 - 13.3126i) q^{49} +(-6.61082 - 2.50938i) q^{50} +(-10.1728 + 7.66164i) q^{51} +(-1.31413 + 0.271228i) q^{52} +(-2.20958 - 0.915237i) q^{53} +(14.7828 - 4.54240i) q^{54} +(1.21099 - 5.11945i) q^{55} +(-12.5639 - 3.66380i) q^{56} +(-21.4315 - 4.26299i) q^{57} +(5.30591 + 6.41811i) q^{58} +(0.257860 + 0.622529i) q^{59} +(5.65068 - 12.6047i) q^{60} +(-3.33081 + 2.22558i) q^{61} +(0.682311 - 7.19248i) q^{62} +(-16.8130 + 25.1625i) q^{63} +(-1.39121 + 7.87810i) q^{64} +(1.02202 + 1.09823i) q^{65} +(9.84496 + 2.94785i) q^{66} -0.662256 q^{67} +(-8.17371 - 1.09105i) q^{68} -20.8260i q^{69} +(3.79255 + 14.1319i) q^{70} +(2.50239 - 0.497757i) q^{71} +(16.4077 + 8.54401i) q^{72} +(-0.683178 + 1.02245i) q^{73} +(-0.711304 + 7.49810i) q^{74} +(-15.3242 + 1.91770i) q^{75} +(-7.94509 - 11.7077i) q^{76} +(-10.0572 + 4.16585i) q^{77} +(-2.25873 + 1.86731i) q^{78} +(0.742184 - 3.73121i) q^{79} +(8.33528 - 3.24393i) q^{80} +(10.0095 - 10.0095i) q^{81} +(-5.81954 + 1.78820i) q^{82} +(5.07078 + 2.10039i) q^{83} +(-27.9935 + 5.77770i) q^{84} +(3.70234 + 8.44350i) q^{85} +(-0.307511 - 3.01125i) q^{86} +(16.8031 + 6.96009i) q^{87} +(3.19992 + 5.83446i) q^{88} +(5.59049 + 5.59049i) q^{89} +(-1.36077 - 20.6377i) q^{90} +(0.605626 - 3.04469i) q^{91} +(9.46662 - 9.60367i) q^{92} +(-6.03854 - 14.5783i) q^{93} +(-2.18582 + 1.17846i) q^{94} +(-6.57474 + 14.3880i) q^{95} +(5.37160 + 16.6264i) q^{96} +(11.5356 + 7.70783i) q^{97} +(12.8710 - 15.7988i) q^{98} +(15.0917 - 3.00193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 16 q^{4} - 16 q^{6} - 32 q^{9} - 8 q^{10} - 32 q^{11} - 16 q^{14} - 32 q^{19} - 8 q^{20} - 32 q^{24} - 16 q^{25} - 48 q^{26} + 56 q^{30} + 48 q^{34} - 32 q^{35} + 48 q^{36} - 72 q^{40} - 32 q^{41}+ \cdots - 128 q^{99}+O(q^{100}) \) 832 * q - 16 * q^4 - 16 * q^6 - 32 * q^9 - 8 * q^10 - 32 * q^11 - 16 * q^14 - 32 * q^19 - 8 * q^20 - 32 * q^24 - 16 * q^25 - 48 * q^26 + 56 * q^30 + 48 * q^34 - 32 * q^35 + 48 * q^36 - 72 * q^40 - 32 * q^41 - 48 * q^44 - 32 * q^46 - 32 * q^49 - 32 * q^51 + 32 * q^54 - 16 * q^56 - 32 * q^59 - 112 * q^60 - 16 * q^64 - 96 * q^65 - 48 * q^66 - 80 * q^70 - 16 * q^74 - 16 * q^75 - 16 * q^76 - 104 * q^80 - 32 * q^81 - 192 * q^86 - 32 * q^89 + 72 * q^90 - 32 * q^91 - 16 * q^94 + 288 * q^96 - 128 * q^99

Introduction

L-functions

Modular forms

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Database

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