LMFDB - Embedded newform 680.2.co.a.99.94

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)

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);

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")

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			99.94
Character	$\chi$	$=$	680.99
Dual form			680.2.co.a.419.94

$q$-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 $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$e\left(\frac{9}{16}\right)$	$-1$	$-1$

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	0.962837	−	0.270083i	$-0.0870510\pi$
$3$	3.02940	+	0.602586i	1.74903	+	0.347903i	0.786189	+	0.617986i	$0.212051\pi$
$4$	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	−0.996598	−	0.0824138i	$-0.973737\pi$
$7$	−3.84724	−	2.57064i	−1.45412	−	0.971612i	−0.457522	−	0.889198i	$-0.651263\pi$
$8$	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	0.165456	−	0.986217i	$-0.447090\pi$
$11$	2.30746	−	0.458983i	0.695726	−	0.138389i	0.530270	+	0.847829i	$0.322090\pi$
$12$	5.72411	−	2.32295i	1.65241	−	0.670579i
$13$	−0.474407	−	0.474407i	−0.131577	−	0.131577i	0.638251	−	0.769828i	$-0.279658\pi$
$13$	−0.474407	−	0.474407i	−0.131577	−	0.131577i	−0.769828	+	0.638251i	$0.779658\pi$
$14$	−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	−0.973350	−	0.229324i	$-0.926348\pi$
$19$	−6.53598	+	2.70729i	−1.49946	+	0.621095i	−0.526106	+	0.850419i	$0.676348\pi$
$20$	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	0.834705	+	0.550697i	$0.185638\pi$
$23$	1.31540	+	6.61299i	0.274281	+	1.37890i	−0.560424	+	0.828206i	$0.689362\pi$
$24$	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	−0.0106093	−	0.999944i	$-0.503377\pi$
$29$	4.89597	−	3.27138i	0.909158	−	0.607480i	0.919768	+	0.392464i	$0.128377\pi$
$30$	1.27113	+	9.68443i	0.232076	+	1.76813i
$31$	−0.996655	+	5.01052i	−0.179005	+	0.899917i	0.781978	+	0.623306i	$0.214211\pi$
$31$	−0.996655	+	5.01052i	−0.179005	+	0.899917i	−0.960982	+	0.276610i	$0.910789\pi$
$32$	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	−0.796403	−	0.604766i	$-0.793267\pi$
$37$	1.03900	−	5.22343i	0.170811	−	0.858727i	0.967215	−	0.253961i	$-0.0817334\pi$
$38$	−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	0.243734	−	0.969842i	$-0.421628\pi$
$41$	−3.57941	−	2.39169i	−0.559010	−	0.373519i	−0.802744	+	0.596323i	$0.796628\pi$
$42$	−17.7907	−	9.59168i	−2.74517	−	1.48003i
$43$	−0.819076	+	1.97742i	−0.124908	+	0.301554i	−0.973947	−	0.226776i	$-0.927182\pi$
$43$	−0.819076	+	1.97742i	−0.124908	+	0.301554i	0.849039	+	0.528330i	$0.177182\pi$
$44$	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	0.610729	−	0.791840i	$-0.290876\pi$
$47$	−1.24163	−	1.24163i	−0.181110	−	0.181110i	−0.791840	+	0.610729i	$0.790876\pi$
$48$	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	−0.529240	−	0.848472i	$-0.677523\pi$
$53$	−2.20958	+	0.915237i	−0.303509	+	0.125717i	0.225731	+	0.974190i	$0.427523\pi$
$54$	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	−0.906205	−	0.422838i	$-0.861034\pi$
$59$	0.257860	−	0.622529i	0.0335705	−	0.0810463i	0.939776	+	0.341792i	$0.111034\pi$
$60$	5.65068	+	12.6047i	0.729500	+	1.62726i
$61$	−3.33081	−	2.22558i	−0.426467	−	0.284956i	0.323756	−	0.946140i	$-0.395054\pi$
$61$	−3.33081	−	2.22558i	−0.426467	−	0.284956i	−0.750224	+	0.661184i	$0.770054\pi$
$62$	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	0.341331	−	0.939943i	$-0.389122\pi$
$71$	2.50239	+	0.497757i	0.296979	+	0.0590729i	−0.0443517	+	0.999016i	$0.514122\pi$
$72$	16.4077	−	8.54401i	1.93367	−	1.00692i
$73$	−0.683178	−	1.02245i	−0.0799600	−	0.119669i	0.789334	−	0.613964i	$-0.210426\pi$
$73$	−0.683178	−	1.02245i	−0.0799600	−	0.119669i	−0.869294	+	0.494296i	$0.835426\pi$
$74$	−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	0.999813	+	0.0193266i	$0.00615225\pi$
$79$	0.742184	+	3.73121i	0.0835022	+	0.419794i	−0.916311	+	0.400467i	$0.868848\pi$
$80$	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	−0.0866138	−	0.996242i	$-0.527605\pi$
$83$	5.07078	−	2.10039i	0.556590	−	0.230547i	0.643204	+	0.765695i	$0.277605\pi$
$84$	−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	−0.345740	−	0.938330i	$-0.612372\pi$
$89$	5.59049	−	5.59049i	0.592591	−	0.592591i	0.938330	+	0.345740i	$0.112372\pi$
$90$	−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	0.191247	−	0.981542i	$-0.438747\pi$
$97$	11.5356	−	7.70783i	1.17126	−	0.782612i	0.980014	+	0.198930i	$0.0637467\pi$
$98$	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	0.943899	−	0.330233i	$-0.107127\pi$
$107$	2.87140	+	4.29736i	0.277589	+	0.415441i	−0.666310	+	0.745675i	$0.732127\pi$
$108$	21.8702	+	0.157174i	2.10446	+	0.0151241i
$109$	8.15843	−	12.2099i	0.781436	−	1.16950i	−0.200390	−	0.979716i	$-0.564221\pi$
$109$	8.15843	−	12.2099i	0.781436	−	1.16950i	0.981826	−	0.189785i	$-0.0607790\pi$
$110$	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	−0.939067	−	0.343735i	$-0.888308\pi$
$113$	−2.15817	−	10.8499i	−0.203024	−	1.02067i	0.736043	−	0.676935i	$-0.236692\pi$
$114$	−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	−0.967078	−	0.254482i	$-0.918095\pi$
$127$	−1.16418	+	2.81058i	−0.103304	+	0.249399i	0.863773	+	0.503881i	$0.168095\pi$
$128$	−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	0.730244	−	0.683186i	$-0.239406\pi$
$131$	−2.06466	−	3.08997i	−0.180390	−	0.269972i	−0.910634	+	0.413214i	$0.864406\pi$
$132$	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	$0.281557\pi$
$137$			18.1100i			1.54724i	−0.633647	+	0.773622i	$0.718443\pi$
$138$	8.44827	+	28.2148i	0.719165	+	2.40180i
$139$	−3.76434	+	18.9246i	−0.319287	+	1.60516i	0.404096	+	0.914717i	$0.367586\pi$
$139$	−3.76434	+	18.9246i	−0.319287	+	1.60516i	−0.723383	+	0.690447i	$0.757414\pi$
$140$	−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	−0.999927	−	0.0120627i	$-0.996160\pi$
$149$	−12.0584	+	12.0584i	−0.987865	+	0.987865i	0.0120627	+	0.999927i	$0.496160\pi$
$150$	−21.5390	+	3.61834i	−1.75865	+	0.295437i
$151$	12.5641	−	5.20422i	1.02245	−	0.423514i	0.192470	−	0.981303i	$-0.438350\pi$
$151$	12.5641	−	5.20422i	1.02245	−	0.423514i	0.829983	+	0.557789i	$0.188350\pi$
$152$	−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	−0.833469	−	0.552566i	$-0.813649\pi$
$157$	−3.51971	+	3.51971i	−0.280903	+	0.280903i	0.552566	+	0.833469i	$0.313649\pi$
$158$	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	0.284994	−	0.958529i	$-0.408008\pi$
$163$	−6.27516	−	4.19293i	−0.491509	−	0.328416i	−0.776503	+	0.630114i	$0.783008\pi$
$164$	−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	0.457468	−	0.889226i	$-0.348756\pi$
$167$	6.97603	+	1.38762i	0.539822	+	0.107377i	0.0823535	+	0.996603i	$0.473756\pi$
$168$	−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	−0.940558	−	0.339632i	$-0.889697\pi$
$173$	0.767815	−	3.86007i	0.0583759	−	0.293475i	0.998934	+	0.0461568i	$0.0146974\pi$
$174$	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	0.379893	−	0.925030i	$-0.375961\pi$
$179$	−0.0746106	−	0.0309047i	−0.00557666	−	0.00230993i	−0.385470	+	0.922720i	$0.625961\pi$
$180$	6.52834	+	28.5117i	0.486593	+	2.12513i
$181$	3.90988	+	19.6563i	0.290619	+	1.46104i	0.799741	+	0.600346i	$0.204970\pi$
$181$	3.90988	+	19.6563i	0.290619	+	1.46104i	−0.509121	+	0.860695i	$0.670030\pi$
$182$	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	0.927301	−	0.374317i	$-0.122123\pi$
$191$	7.64238	+	7.64238i	0.552983	+	0.552983i	−0.374317	+	0.927301i	$0.622123\pi$
$192$	0.532699	−	24.7043i	0.0384442	−	1.78288i
$193$	26.3626	−	5.24384i	1.89762	−	0.377460i	0.899401	−	0.437125i	$-0.144003\pi$
$193$	26.3626	−	5.24384i	1.89762	−	0.377460i	0.998218	+	0.0596648i	$0.0190032\pi$
$194$	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	−0.736099	−	0.676874i	$-0.763334\pi$
$197$	2.39931	−	3.59083i	0.170944	−	0.255836i	0.907043	+	0.421038i	$0.138334\pi$
$198$	21.6638	−	2.05512i	1.53958	−	0.146051i
$199$	13.0589	−	8.72570i	0.925723	−	0.618548i	0.00133382	−	0.999999i	$-0.499575\pi$
$199$	13.0589	−	8.72570i	0.925723	−	0.618548i	0.924389	+	0.381451i	$0.124575\pi$
$200$	−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	0.870700	−	0.491815i	$-0.163666\pi$
$211$	10.8875	+	7.27478i	0.749525	+	0.500817i	−0.121175	+	0.992631i	$0.538666\pi$
$212$	−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	−0.639882	−	0.768473i	$-0.721017\pi$
$223$	−8.19765	+	3.39558i	−0.548955	+	0.227385i	0.0909273	+	0.995858i	$0.471017\pi$
$224$	−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	−0.684381	−	0.729125i	$-0.739927\pi$
$227$	−15.6337	+	3.10973i	−1.03764	+	0.206400i	−0.353262	+	0.935525i	$0.614927\pi$
$228$	−31.1238	+	30.6796i	−2.06122	+	2.03181i
$229$	−11.5640	−	4.78996i	−0.764170	−	0.316530i	−0.0336619	−	0.999433i	$-0.510717\pi$
$229$	−11.5640	−	4.78996i	−0.764170	−	0.316530i	−0.730509	+	0.682904i	$0.760717\pi$
$230$	−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	−0.253126	−	0.967433i	$-0.581459\pi$
$233$	8.30073	−	5.54637i	0.543799	−	0.363355i	0.796925	+	0.604078i	$0.206459\pi$
$234$	−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	$0.159678\pi$
$239$			14.8681i			0.961737i	−0.876793	+	0.480868i	$0.840322\pi$
$240$	23.2962	+	14.8499i	1.50376	+	0.958556i
$241$	0.111847	−	0.562292i	0.00720469	−	0.0362204i	−0.977016	−	0.213167i	$-0.931622\pi$
$241$	0.111847	−	0.562292i	0.00720469	−	0.0362204i	0.984220	+	0.176947i	$0.0566221\pi$
$242$	−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	0.887615	−	0.460586i	$-0.152361\pi$
$251$	6.76542	+	6.76542i	0.427029	+	0.427029i	−0.460586	+	0.887615i	$0.652361\pi$
$252$	−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	0.676331	+	0.736598i	$0.263569\pi$
$257$	11.5256	+	27.8252i	0.718946	+	1.73569i	0.0426152	+	0.999092i	$0.486431\pi$
$258$	−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	−0.968586	−	0.248678i	$-0.920004\pi$
$263$	−1.74904	+	4.22255i	−0.107850	+	0.260374i	0.860736	+	0.509052i	$0.170004\pi$
$264$	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	−0.865737	−	0.500499i	$-0.833150\pi$
$269$	2.06052	−	10.3590i	0.125632	−	0.631596i	0.991369	−	0.131097i	$-0.0418501\pi$
$270$	−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	−0.268908	−	0.963166i	$-0.586663\pi$
$277$	8.62180	−	5.76090i	0.518034	−	0.346139i	0.786942	+	0.617027i	$0.211663\pi$
$278$	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	−0.594531	−	0.804072i	$-0.702662\pi$
$281$	−26.5442	−	10.9950i	−1.58349	−	0.655905i	−0.988962	+	0.148168i	$0.952662\pi$
$282$	−5.91161	−	4.88719i	−0.352031	−	0.291028i
$283$	2.50060	+	12.5713i	0.148645	+	0.747289i	0.981146	+	0.193266i	$0.0619080\pi$
$283$	2.50060	+	12.5713i	0.148645	+	0.747289i	−0.832501	+	0.554023i	$0.813092\pi$
$284$	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	−0.993391	−	0.114778i	$-0.963384\pi$
$293$	−15.0394	+	15.0394i	−0.878613	+	0.878613i	0.114778	+	0.993391i	$0.463384\pi$
$294$	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	$-0.720215\pi$
$307$		−	26.9859i		−	1.54017i	0.637943	−	0.770083i	$-0.279785\pi$
$308$	−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	0.494376	−	0.869248i	$-0.335397\pi$
$311$	−8.78046	−	13.1409i	−0.497894	−	0.745151i	−0.992270	+	0.124097i	$0.960397\pi$
$312$	−5.82655	−	0.637353i	−0.329863	−	0.0360830i
$313$	−16.3030	+	24.3992i	−0.921501	+	1.37912i	0.00384177	+	0.999993i	$0.498777\pi$
$313$	−16.3030	+	24.3992i	−0.921501	+	1.37912i	−0.925343	+	0.379131i	$0.876223\pi$
$314$	−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	0.177002	−	0.984211i	$-0.443360\pi$
$317$	12.7689	−	2.53989i	0.717171	−	0.142654i	0.540169	+	0.841556i	$0.318360\pi$
$318$	−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	−0.790090	−	0.612991i	$-0.789966\pi$
$331$	3.67576	−	8.87408i	0.202038	−	0.487763i	0.992128	+	0.125228i	$0.0399661\pi$
$332$	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	−0.917064	−	0.398740i	$-0.869448\pi$
$337$	1.51971	−	7.64009i	0.0827838	−	0.416182i	0.999848	−	0.0174423i	$-0.00555234\pi$
$338$	−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	−0.978057	−	0.208340i	$-0.933194\pi$
$347$	−7.66148	+	11.4662i	−0.411290	+	0.615538i	0.566767	+	0.823878i	$0.308194\pi$
$348$	20.4258	−	30.0988i	1.09494	−	1.61347i
$349$	−1.56644	+	3.78172i	−0.0838496	+	0.202431i	−0.960243	−	0.279165i	$-0.909943\pi$
$349$	−1.56644	+	3.78172i	−0.0838496	+	0.202431i	0.876394	+	0.481595i	$0.159943\pi$
$350$	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	−0.830263	−	0.557371i	$-0.811810\pi$
$353$	−5.12718	+	5.12718i	−0.272892	+	0.272892i	0.557371	+	0.830263i	$0.311810\pi$
$354$	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	0.909893	−	0.414843i	$-0.136163\pi$
$359$	−0.508478	−	1.22757i	−0.0268364	−	0.0647889i	−0.936730	+	0.350054i	$0.886163\pi$
$360$	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	−0.702194	−	0.711986i	$-0.747796\pi$
$367$	4.29723	−	6.43125i	0.224313	−	0.335709i	0.926507	+	0.376277i	$0.122796\pi$
$368$	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	$0.216760\pi$
$373$			24.3172i			1.25910i	−0.776960	+	0.629549i	$0.783240\pi$
$374$	−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	0.151862	−	0.988402i	$-0.451473\pi$
$379$	21.8652	−	14.6099i	1.12314	−	0.750459i	0.971279	+	0.237943i	$0.0764732\pi$
$380$	−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	0.0316735	−	0.999498i	$-0.489916\pi$
$383$	−12.7732	−	5.29085i	−0.652682	−	0.270350i	−0.684355	+	0.729149i	$0.739916\pi$
$384$	−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	0.470050	−	0.882640i	$-0.344236\pi$
$389$	28.1359	−	11.6543i	1.42655	−	0.590895i	0.956496	+	0.291745i	$0.0942360\pi$
$390$	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	−0.797244	−	0.603658i	$-0.793709\pi$
$397$	−5.81201	−	29.2189i	−0.291696	−	1.46646i	0.505547	−	0.862799i	$-0.331291\pi$
$398$	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	−0.855122	−	0.518427i	$-0.826518\pi$
$401$	−0.979570	+	1.46603i	−0.0489174	+	0.0732100i	0.806205	+	0.591637i	$0.201518\pi$
$402$	−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	−0.680208	−	0.733019i	$-0.738111\pi$
$419$	−21.0452	+	4.18615i	−1.02812	+	0.204507i	−0.347916	+	0.937526i	$0.613111\pi$
$420$	10.6626	−	63.0191i	0.520280	−	3.07502i
$421$	6.24485	−	6.24485i	0.304355	−	0.304355i	−0.538360	−	0.842715i	$-0.680956\pi$
$421$	6.24485	−	6.24485i	0.304355	−	0.304355i	0.842715	+	0.538360i	$0.180956\pi$
$422$	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	−0.00695775	−	0.999976i	$-0.502215\pi$
$431$	7.66662	−	1.52499i	0.369288	−	0.0734560i	0.376246	+	0.926520i	$0.377215\pi$
$432$	36.7153	−	23.7763i	1.76647	−	1.14394i
$433$	15.6913	+	6.49954i	0.754075	+	0.312348i	0.726403	−	0.687269i	$-0.241191\pi$
$433$	15.6913	+	6.49954i	0.754075	+	0.312348i	0.0276718	+	0.999617i	$0.491191\pi$
$434$	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	−0.992353	−	0.123431i	$-0.960610\pi$
$439$	−0.593019	+	2.98131i	−0.0283033	+	0.142290i	0.964050	+	0.265721i	$0.0856101\pi$
$440$	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	$0.335508\pi$
$443$			36.5984i			1.73884i	−0.494071	+	0.869422i	$0.664492\pi$
$444$	−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	−0.239894	−	0.970799i	$-0.577113\pi$
$449$	−26.0335	−	17.3951i	−1.22860	−	0.820923i	−0.988705	+	0.149876i	$0.952113\pi$
$450$	−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	−0.427302	−	0.904109i	$-0.640536\pi$
$457$	−1.92714	+	0.798247i	−0.0901477	+	0.0373404i	0.337154	+	0.941450i	$0.390536\pi$
$458$	−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	0.867070	−	0.498185i	$-0.166000\pi$
$461$	−2.11083	−	5.09600i	−0.0983113	−	0.237344i	−0.965382	+	0.260841i	$0.916000\pi$
$462$	−45.4538	−	13.9668i	−2.11470	−	0.649795i
$463$	−12.5310	+	12.5310i	−0.582367	+	0.582367i	−0.935553	−	0.353186i	$-0.885098\pi$
$463$	−12.5310	+	12.5310i	−0.582367	+	0.582367i	0.353186	+	0.935553i	$0.385098\pi$
$464$	−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	0.138601	−	0.990348i	$-0.455740\pi$
$467$	−10.0201	−	4.15047i	−0.463676	−	0.192061i	−0.602277	+	0.798287i	$0.705740\pi$
$468$	−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	−0.641509	−	0.767115i	$-0.721692\pi$
$479$	−33.4364	−	6.65092i	−1.52775	−	0.303888i	−0.886240	+	0.463227i	$0.846692\pi$
$480$	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	−0.236100	−	0.971729i	$-0.575869\pi$
$487$	−1.81761	+	0.361545i	−0.0823638	+	0.0163832i	0.153736	+	0.988112i	$0.450869\pi$
$488$	−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	0.777682	−	0.628658i	$-0.216395\pi$
$491$	−4.80286	−	11.5951i	−0.216750	−	0.523281i	−0.994432	+	0.105376i	$0.966395\pi$
$492$	−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	−0.809751	−	0.586774i	$-0.800398\pi$
$499$	−6.39294	−	32.1395i	−0.286187	−	1.43876i	0.523564	−	0.851987i	$-0.324602\pi$
$500$	−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	−0.236072	−	0.971736i	$-0.575860\pi$
$503$	16.8664	−	25.2424i	0.752036	−	1.12550i	0.988107	−	0.153766i	$-0.0491400\pi$
$504$	−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	−0.0735790	−	0.997289i	$-0.523442\pi$
$521$	5.48013	−	1.09007i	0.240089	−	0.0477567i	0.313668	+	0.949533i	$0.398442\pi$
$522$	48.1251	−	25.5015i	2.10638	−	1.11617i
$523$	−14.3521	+	14.3521i	−0.627573	+	0.627573i	−0.947457	−	0.319884i	$-0.896356\pi$
$523$	−14.3521	+	14.3521i	−0.627573	+	0.627573i	0.319884	+	0.947457i	$0.396356\pi$
$524$	−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	−0.998742	−	0.0501457i	$-0.984031\pi$
$541$	−1.32194	+	6.64586i	−0.0568348	+	0.285728i	0.941907	+	0.335873i	$0.109031\pi$
$542$	−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	0.206148	−	0.978521i	$-0.433907\pi$
$547$	0.517804	+	0.102998i	0.0221397	+	0.00440386i	−0.184008	+	0.982925i	$0.558907\pi$
$548$	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	0.541257	−	0.840857i	$-0.317949\pi$
$557$	−7.07083	−	7.07083i	−0.299601	−	0.299601i	−0.840857	+	0.541257i	$0.817949\pi$
$558$	−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	0.782240	−	0.622978i	$-0.214077\pi$
$563$	−5.01599	−	12.1097i	−0.211399	−	0.510362i	−0.993639	+	0.112615i	$0.964077\pi$
$564$	−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	−0.782991	−	0.622033i	$-0.786307\pi$
$569$	5.02147	−	12.1229i	0.210511	−	0.508219i	0.993502	+	0.113814i	$0.0363069\pi$
$570$	−34.5266	−	59.8559i	−1.44616	−	2.50709i
$571$	6.28432	−	9.40515i	0.262991	−	0.393593i	−0.676349	−	0.736581i	$-0.736439\pi$
$571$	6.28432	−	9.40515i	0.262991	−	0.393593i	0.939340	+	0.342988i	$0.111439\pi$
$572$	−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	−0.837319	−	0.546714i	$-0.815878\pi$
$587$	3.42440	−	8.26724i	0.141340	−	0.341226i	0.978659	+	0.205489i	$0.0658784\pi$
$588$	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	−0.761177	−	0.648544i	$-0.775378\pi$
$593$	−20.4753	+	8.48116i	−0.840821	+	0.348280i	−0.0796440	+	0.996823i	$0.525378\pi$
$594$	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	0.497584	−	0.867416i	$-0.334221\pi$
$599$	−9.05146	−	9.05146i	−0.369832	−	0.369832i	−0.867416	+	0.497584i	$0.834221\pi$
$600$	−32.0119	+	29.7206i	−1.30688	+	1.21334i
$601$	−4.90373	−	24.6527i	−0.200027	−	1.00561i	−0.942112	−	0.335299i	$-0.891163\pi$
$601$	−4.90373	−	24.6527i	−0.200027	−	1.00561i	0.742084	−	0.670306i	$-0.233837\pi$
$602$	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	0.962239	+	0.272207i	$0.0877534\pi$
$607$	20.8307	+	31.1753i	0.845492	+	1.26537i	−0.116747	+	0.993162i	$0.537247\pi$
$608$	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	0.976588	−	0.215120i	$-0.0690143\pi$
$617$	10.0381	+	15.0231i	0.404119	+	0.604806i	−0.572469	+	0.819926i	$0.694014\pi$
$618$	−36.4869	+	3.46131i	−1.46772	+	0.139234i
$619$	−17.1673	−	11.4709i	−0.690014	−	0.461053i	0.160479	−	0.987039i	$-0.448696\pi$
$619$	−17.1673	−	11.4709i	−0.690014	−	0.461053i	−0.850493	+	0.525987i	$0.823696\pi$
$620$	−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	0.835644	−	0.549272i	$-0.185095\pi$
$631$	−3.60818	−	8.71092i	−0.143639	−	0.346776i	−0.979283	+	0.202496i	$0.935095\pi$
$632$	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	0.463915	−	0.885880i	$-0.346444\pi$
$641$	−13.4708	−	20.1605i	−0.532064	−	0.796290i	−0.995979	+	0.0895896i	$0.971444\pi$
$642$	14.2595	+	17.5031i	0.562776	+	0.690792i
$643$	3.81347	−	19.1716i	0.150388	−	0.756054i	−0.829812	−	0.558044i	$-0.811552\pi$
$643$	3.81347	−	19.1716i	0.150388	−	0.756054i	0.980200	−	0.198010i	$-0.0634479\pi$
$644$	−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	−0.267859	−	0.963458i	$-0.586316\pi$
$653$	−32.2102	−	21.5222i	−1.26048	−	0.842228i	−0.992624	+	0.121230i	$0.961316\pi$
$654$	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	0.389572	−	0.920996i	$-0.372623\pi$
$659$	−13.6422	−	13.6422i	−0.531424	−	0.531424i	−0.920996	+	0.389572i	$0.872623\pi$
$660$	18.8241	+	26.4912i	0.732726	+	1.03117i
$661$	−19.3537	+	8.01657i	−0.752772	+	0.311808i	−0.725872	−	0.687830i	$-0.758564\pi$
$661$	−19.3537	+	8.01657i	−0.752772	+	0.311808i	−0.0269000	+	0.999638i	$0.508564\pi$
$662$	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	0.997204	−	0.0747236i	$-0.0238074\pi$
$673$	33.9787	+	22.7038i	1.30978	+	0.875169i	0.312578	+	0.949892i	$0.398807\pi$
$674$	−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	0.776490	−	0.630130i	$-0.216998\pi$
$677$	32.5951	+	6.48358i	1.25273	+	0.249184i	0.476243	+	0.879314i	$0.341998\pi$
$678$	−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	0.889244	−	0.457433i	$-0.151231\pi$
$683$	40.1356	+	7.98347i	1.53575	+	0.305479i	0.646503	+	0.762912i	$0.276231\pi$
$684$	−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	−0.932997	−	0.359884i	$-0.882816\pi$
$691$	−43.5640	+	8.66542i	−1.65725	+	0.329648i	−0.724255	+	0.689532i	$0.757816\pi$
$692$	−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	0.0560536	−	0.998428i	$-0.482148\pi$
$701$	−24.9507	−	24.9507i	−0.942374	−	0.942374i	−0.998428	+	0.0560536i	$0.982148\pi$
$702$	−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	−0.521051	+	0.853525i	$0.674460\pi$
$709$	−40.1803	+	26.8476i	−1.50900	+	1.00828i	−0.987952	+	0.154758i	$0.950540\pi$
$710$	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	0.981193	−	0.193027i	$-0.0618307\pi$
$719$	11.4596	+	17.1506i	0.427373	+	0.639609i	−0.553821	+	0.832636i	$0.686831\pi$
$720$	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	0.889383	−	0.457163i	$-0.151134\pi$
$727$	11.6539	+	11.6539i	0.432220	+	0.432220i	−0.457163	+	0.889383i	$0.651134\pi$
$728$	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	−0.692535	−	0.721384i	$-0.743506\pi$
$733$	−18.1974	+	7.53760i	−0.672136	+	0.278408i	0.0203994	+	0.999792i	$0.493506\pi$
$734$	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	0.380551	+	0.924760i	$0.375734\pi$
$739$	−14.7461	+	35.6002i	−0.542443	+	1.30957i	−0.922994	+	0.384814i	$0.874266\pi$
$740$	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	0.609614	−	0.792698i	$-0.291324\pi$
$743$	−9.70475	−	14.5242i	−0.356033	−	0.532841i	−0.965647	+	0.259858i	$0.916324\pi$
$744$	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	0.848472	−	0.529240i	$-0.177523\pi$
$751$	39.1835	+	7.79408i	1.42983	+	0.284410i	0.581354	+	0.813650i	$0.302523\pi$
$752$	−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	0.168827	−	0.985646i	$-0.446002\pi$
$757$	−11.2462	−	4.65834i	−0.408751	−	0.169310i	−0.577578	+	0.816335i	$0.696002\pi$
$758$	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	0.995629	−	0.0933975i	$-0.0297727\pi$
$761$	24.8892	+	24.8892i	0.902231	+	0.902231i	−0.0933975	+	0.995629i	$0.529773\pi$
$762$	−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	−0.597777	−	0.801662i	$-0.703949\pi$
$769$	5.65391	−	5.65391i	0.203885	−	0.203885i	0.801662	+	0.597777i	$0.203949\pi$
$770$	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	−0.357042	−	0.934089i	$-0.616215\pi$
$773$	15.4563	−	37.3149i	0.555925	−	1.34212i	0.912967	−	0.408034i	$-0.133785\pi$
$774$	−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	0.957721	−	0.287699i	$-0.0928902\pi$
$787$	9.12912	+	13.6627i	0.325418	+	0.487022i	−0.632303	+	0.774721i	$0.717890\pi$
$788$	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	−0.896002	−	0.444050i	$-0.853541\pi$
$797$	−16.2731	−	39.2868i	−0.576424	−	1.39161i	0.319578	−	0.947560i	$-0.396459\pi$
$798$	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	−0.936287	−	0.351235i	$-0.885762\pi$
$809$	−7.20992	+	10.7904i	−0.253487	+	0.379371i	0.682800	+	0.730605i	$0.260762\pi$
$810$	−19.8142	+	40.1397i	−0.696200	+	1.41036i
$811$	0.282462	+	0.422734i	0.00991857	+	0.0148442i	0.836396	−	0.548126i	$-0.184659\pi$
$811$	0.282462	+	0.422734i	0.00991857	+	0.0148442i	−0.826477	+	0.562970i	$0.809659\pi$
$812$	−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	0.565845	−	0.824512i	$-0.308550\pi$
$821$	−11.8178	−	17.6866i	−0.412444	−	0.617267i	−0.978289	+	0.207245i	$0.933550\pi$
$822$	7.47095	+	78.7539i	0.260579	+	2.74686i
$823$	30.9347	+	20.6699i	1.07832	+	0.720507i	0.962095	−	0.272716i	$-0.0879220\pi$
$823$	30.9347	+	20.6699i	1.07832	+	0.720507i	0.116221	+	0.993223i	$0.462922\pi$
$824$	−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	−0.794231	−	0.607616i	$-0.792126\pi$
$827$	−8.42546	−	42.3576i	−0.292982	−	1.47292i	0.501249	−	0.865303i	$-0.332874\pi$
$828$	33.1654	+	81.7245i	1.15258	+	2.84012i
$829$	25.1539	−	25.1539i	0.873632	−	0.873632i	−0.119234	−	0.992866i	$-0.538044\pi$
$829$	25.1539	−	25.1539i	0.873632	−	0.873632i	0.992866	+	0.119234i	$0.0380439\pi$
$830$	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	0.406292	−	0.913743i	$-0.366822\pi$
$839$	32.7696	−	6.51827i	1.13133	−	0.225036i	0.725039	+	0.688707i	$0.241822\pi$
$840$	−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	0.821395	+	0.570360i	$0.193196\pi$
$853$	−4.54863	+	22.8675i	−0.155742	+	0.782969i	−0.977137	+	0.212609i	$0.931804\pi$
$854$	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	−0.489663	−	0.871912i	$-0.662880\pi$
$857$	14.7329	−	22.0493i	0.503265	−	0.753189i	0.992927	+	0.118723i	$0.0378800\pi$
$858$	−6.06900	−	3.27204i	−0.207192	−	0.111706i
$859$	−25.9168	−	10.7351i	−0.884270	−	0.366277i	−0.106119	−	0.994353i	$-0.533842\pi$
$859$	−25.9168	−	10.7351i	−0.884270	−	0.366277i	−0.778151	+	0.628077i	$0.783842\pi$
$860$	−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	0.319618	−	0.947546i	$-0.396445\pi$
$863$	−18.4466	−	18.4466i	−0.627928	−	0.627928i	−0.947546	+	0.319618i	$0.896445\pi$
$864$	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	−0.985227	−	0.171253i	$-0.945219\pi$
$877$	−13.3258	+	19.9435i	−0.449980	+	0.673443i	0.535247	+	0.844696i	$0.320219\pi$
$878$	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	−0.628154	−	0.778089i	$-0.716189\pi$
$881$	−44.7081	−	8.89300i	−1.50625	−	0.299613i	−0.878101	+	0.478476i	$0.841189\pi$
$882$	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	0.757875	+	0.652400i	$0.226238\pi$
$887$	−5.71744	+	28.7435i	−0.191973	+	0.965113i	−0.949848	+	0.312713i	$0.898762\pi$
$888$	−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	−0.475743	−	0.879584i	$-0.657821\pi$
$907$	−17.4275	+	3.46654i	−0.578669	+	0.115104i	−0.102927	+	0.994689i	$0.532821\pi$
$908$	−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	0.826318	−	0.563203i	$-0.190431\pi$
$911$	18.7799	+	12.5483i	0.622205	+	0.415744i	−0.204114	+	0.978947i	$0.565431\pi$
$912$	−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	$0.0392531\pi$
$919$			7.45779i			0.246010i	−0.992406	+	0.123005i	$0.960747\pi$
$920$	−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	0.586230	−	0.810145i	$-0.300612\pi$
$929$	43.8254	−	8.71741i	1.43786	−	0.286009i	0.851635	+	0.524136i	$0.175612\pi$
$930$	−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	−0.987937	−	0.154859i	$-0.950508\pi$
$937$	−12.2093	−	29.4759i	−0.398862	−	0.962937i	0.589075	−	0.808078i	$-0.299492\pi$
$938$	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	−0.956619	−	0.291341i	$-0.905899\pi$
$941$	−53.0362	+	10.5495i	−1.72893	+	0.343905i	−0.772310	+	0.635246i	$0.780899\pi$
$942$	−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	−0.499157	−	0.866512i	$-0.666357\pi$
$947$	3.39667	−	2.26958i	0.110377	−	0.0737515i	0.609534	+	0.792760i	$0.291357\pi$
$948$	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	$-0.936123\pi$
$953$		−	12.3069i		−	0.398660i	0.979932	−	0.199330i	$-0.0638766\pi$
$954$	−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	0.688463	+	0.725272i	$0.258286\pi$
$967$	22.2182	+	53.6396i	0.714491	+	1.72493i	0.0260278	+	0.999661i	$0.491714\pi$
$968$	−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	−0.0669895	−	0.997754i	$-0.521339\pi$
$971$	18.4211	−	7.63026i	0.591160	−	0.244867i	0.658150	+	0.752887i	$0.271339\pi$
$972$	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	0.0721243	−	0.997396i	$-0.477022\pi$
$977$	−18.1960	−	7.53703i	−0.582141	−	0.241131i	−0.654266	+	0.756265i	$0.727022\pi$
$978$	−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	−0.180498	−	0.983575i	$-0.557771\pi$
$983$	−22.6886	−	4.51305i	−0.723655	−	0.143944i	−0.543157	+	0.839631i	$0.682771\pi$
$984$	−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	−0.999653	−	0.0263313i	$-0.991618\pi$
$991$	−20.1923	−	30.2199i	−0.641429	−	0.959967i	0.358224	−	0.933636i	$-0.383382\pi$
$992$	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	−0.617749	−	0.786375i	$-0.711955\pi$
$997$	−28.0244	+	5.57440i	−0.887542	+	0.176543i	−0.269793	+	0.962918i	$0.586955\pi$
$998$	−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.99.94	yes	832
5.4	even	2	inner	680.2.co.a.99.11	✓	832
8.3	odd	2	inner	680.2.co.a.99.16	yes	832
17.11	odd	16	inner	680.2.co.a.419.89	yes	832
40.19	odd	2	inner	680.2.co.a.99.89	yes	832
85.79	odd	16	inner	680.2.co.a.419.16	yes	832
136.11	even	16	inner	680.2.co.a.419.11	yes	832
680.419	even	16	inner	680.2.co.a.419.94	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.co.a.99.11	✓	832	5.4	even	2	inner
680.2.co.a.99.16	yes	832	8.3	odd	2	inner
680.2.co.a.99.89	yes	832	40.19	odd	2	inner
680.2.co.a.99.94	yes	832	1.1	even	1	trivial
680.2.co.a.419.11	yes	832	136.11	even	16	inner
680.2.co.a.419.16	yes	832	85.79	odd	16	inner
680.2.co.a.419.89	yes	832	17.11	odd	16	inner
680.2.co.a.419.94	yes	832	680.419	even	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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
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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