LMFDB - Embedded newform 525.2.w.a.104.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(104,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1, 5]))

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

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

chi := DirichletCharacter("525.104");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.w (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			104.18
Character	$\chi$	$=$	525.104
Dual form			525.2.w.a.419.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.534897 + 1.64624i) q^{2} +(1.66454 - 0.478872i) q^{3} +(-0.805968 - 0.585570i) q^{4} +(2.04228 + 0.910555i) q^{5} +(-0.102015 + 2.99638i) q^{6} +(-0.846893 + 2.50655i) q^{7} +(-1.40566 + 1.02127i) q^{8} +(2.54136 - 1.59420i) q^{9} +O(q^{10})$	\(q+(-0.534897 + 1.64624i) q^{2} +(1.66454 - 0.478872i) q^{3} +(-0.805968 - 0.585570i) q^{4} +(2.04228 + 0.910555i) q^{5} +(-0.102015 + 2.99638i) q^{6} +(-0.846893 + 2.50655i) q^{7} +(-1.40566 + 1.02127i) q^{8} +(2.54136 - 1.59420i) q^{9} +(-2.59140 + 2.87503i) q^{10} +(-3.47332 - 1.12855i) q^{11} +(-1.62198 - 0.588747i) q^{12} +(1.76748 + 5.43976i) q^{13} +(-3.67338 - 2.73493i) q^{14} +(3.83548 + 0.537663i) q^{15} +(-1.54508 - 4.75527i) q^{16} +(-2.25783 - 3.10763i) q^{17} +(1.26508 + 5.03643i) q^{18} +(0.435470 + 0.599373i) q^{19} +(-1.11281 - 1.92977i) q^{20} +(-0.209368 + 4.57779i) q^{21} +(3.71574 - 5.11427i) q^{22} +(-0.104552 + 0.321779i) q^{23} +(-1.85071 + 2.37307i) q^{24} +(3.34178 + 3.71921i) q^{25} -9.90058 q^{26} +(3.46677 - 3.87059i) q^{27} +(2.15033 - 1.52428i) q^{28} +(5.21620 - 7.17948i) q^{29} +(-2.93671 + 6.02654i) q^{30} +(0.409018 + 0.562964i) q^{31} +5.17981 q^{32} +(-6.32190 - 0.215235i) q^{33} +(6.32363 - 2.05467i) q^{34} +(-4.01194 + 4.34791i) q^{35} +(-2.98177 - 0.203271i) q^{36} +(7.22692 - 2.34817i) q^{37} +(-1.21965 + 0.396287i) q^{38} +(5.54699 + 8.20827i) q^{39} +(-3.80066 + 0.805785i) q^{40} +(2.78467 + 8.57032i) q^{41} +(-7.42417 - 2.79332i) q^{42} +3.39864i q^{43} +(2.13854 + 2.94345i) q^{44} +(6.64177 - 0.941746i) q^{45} +(-0.473802 - 0.344237i) q^{46} +(-0.756806 + 1.04165i) q^{47} +(-4.84901 - 7.17542i) q^{48} +(-5.56555 - 4.24555i) q^{49} +(-7.91023 + 3.51198i) q^{50} +(-5.24640 - 4.09156i) q^{51} +(1.76082 - 5.41925i) q^{52} +(-2.03163 - 1.47607i) q^{53} +(4.51757 + 7.77752i) q^{54} +(-6.06587 - 5.46746i) q^{55} +(-1.36942 - 4.38825i) q^{56} +(1.01188 + 0.789144i) q^{57} +(9.02904 + 12.4274i) q^{58} +(-2.74649 - 8.45283i) q^{59} +(-2.77644 - 2.67928i) q^{60} +(1.15184 + 0.374257i) q^{61} +(-1.14556 + 0.372214i) q^{62} +(1.84368 + 7.72016i) q^{63} +(0.319495 - 0.983304i) q^{64} +(-1.34351 + 12.7189i) q^{65} +(3.73589 - 10.2923i) q^{66} +(-7.91572 - 10.8950i) q^{67} +3.82677i q^{68} +(-0.0199401 + 0.585680i) q^{69} +(-5.01175 - 8.93031i) q^{70} +(3.10015 - 4.26699i) q^{71} +(-1.94417 + 4.83631i) q^{72} +(3.43330 - 10.5666i) q^{73} +13.1533i q^{74} +(7.34354 + 4.59047i) q^{75} -0.738074i q^{76} +(5.77029 - 7.75028i) q^{77} +(-16.4799 + 4.74112i) q^{78} +(-10.0715 - 7.31737i) q^{79} +(1.17446 - 11.1185i) q^{80} +(3.91705 - 8.10289i) q^{81} -15.5983 q^{82} +(10.3911 + 14.3021i) q^{83} +(2.84936 - 3.56695i) q^{84} +(-1.78143 - 8.40252i) q^{85} +(-5.59499 - 1.81792i) q^{86} +(5.24450 - 14.4484i) q^{87} +(6.03485 - 1.96084i) q^{88} +(-3.29410 + 10.1382i) q^{89} +(-2.00232 + 11.4377i) q^{90} +(-15.1319 - 0.176610i) q^{91} +(0.272690 - 0.198121i) q^{92} +(0.950413 + 0.741207i) q^{93} +(-1.31000 - 1.80306i) q^{94} +(0.343588 + 1.62061i) q^{95} +(8.62199 - 2.48047i) q^{96} +(9.38121 + 6.81585i) q^{97} +(9.96620 - 6.89131i) q^{98} +(-10.6261 + 2.66912i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q - 84 q^{4} - 6 q^{9}+O(q^{10}) $ 304 * q - 84 * q^4 - 6 * q^9	$ 304 q - 84 q^{4} - 6 q^{9} - 36 q^{15} - 60 q^{16} - 18 q^{21} - 40 q^{22} - 8 q^{25} + 60 q^{28} + 14 q^{30} + 28 q^{36} - 20 q^{37} - 2 q^{39} - 35 q^{42} - 24 q^{46} - 20 q^{49} - 52 q^{51} - 80 q^{58} + 4 q^{60} + 55 q^{63} - 76 q^{64} - 20 q^{67} + 6 q^{70} + 30 q^{72} - 40 q^{78} - 68 q^{79} - 10 q^{81} + 80 q^{84} - 88 q^{85} - 20 q^{88} - 82 q^{91} - 36 q^{99}+O(q^{100}) $ 304 * q - 84 * q^4 - 6 * q^9 - 36 * q^15 - 60 * q^16 - 18 * q^21 - 40 * q^22 - 8 * q^25 + 60 * q^28 + 14 * q^30 + 28 * q^36 - 20 * q^37 - 2 * q^39 - 35 * q^42 - 24 * q^46 - 20 * q^49 - 52 * q^51 - 80 * q^58 + 4 * q^60 + 55 * q^63 - 76 * q^64 - 20 * q^67 + 6 * q^70 + 30 * q^72 - 40 * q^78 - 68 * q^79 - 10 * q^81 + 80 * q^84 - 88 * q^85 - 20 * q^88 - 82 * q^91 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$-1$

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 $

$2$	−0.534897	+	1.64624i	−0.378229	+	1.16407i	0.563045	+	0.826426i	$0.309630\pi$
$2$	−0.534897	+	1.64624i	−0.378229	+	1.16407i	−0.941274	+	0.337643i	$0.890370\pi$
$3$	1.66454	−	0.478872i	0.961020	−	0.276477i
$3$	1.66454	−	0.478872i	0.961020	−	0.276477i
$4$	−0.805968	−	0.585570i	−0.402984	−	0.292785i
$5$	2.04228	+	0.910555i	0.913333	+	0.407213i
$5$	2.04228	+	0.910555i	0.913333	+	0.407213i
$6$	−0.102015	+	2.99638i	−0.0416473	+	1.22327i
$7$	−0.846893	+	2.50655i	−0.320095	+	0.947385i
$7$	−0.846893	+	2.50655i	−0.320095	+	0.947385i
$8$	−1.40566	+	1.02127i	−0.496974	+	0.361073i
$9$	2.54136	−	1.59420i	0.847121	−	0.531400i
$10$	−2.59140	+	2.87503i	−0.819473	+	0.909164i
$11$	−3.47332	−	1.12855i	−1.04725	−	0.340271i	−0.265659	−	0.964067i	$-0.585589\pi$
$11$	−3.47332	−	1.12855i	−1.04725	−	0.340271i	−0.781587	+	0.623796i	$0.785589\pi$
$12$	−1.62198	−	0.588747i	−0.468224	−	0.169956i
$13$	1.76748	+	5.43976i	0.490212	+	1.50872i	0.824288	+	0.566171i	$0.191576\pi$
$13$	1.76748	+	5.43976i	0.490212	+	1.50872i	−0.334076	+	0.942546i	$0.608424\pi$
$14$	−3.67338	−	2.73493i	−0.981753	−	0.730942i
$15$	3.83548	+	0.537663i	0.990317	+	0.138824i
$16$	−1.54508	−	4.75527i	−0.386270	−	1.18882i
$17$	−2.25783	−	3.10763i	−0.547604	−	0.753712i	0.442081	−	0.896975i	$-0.354240\pi$
$17$	−2.25783	−	3.10763i	−0.547604	−	0.753712i	−0.989685	+	0.143263i	$0.954240\pi$
$18$	1.26508	+	5.03643i	0.298181	+	1.18710i
$19$	0.435470	+	0.599373i	0.0999037	+	0.137506i	0.856042	−	0.516906i	$-0.172916\pi$
$19$	0.435470	+	0.599373i	0.0999037	+	0.137506i	−0.756138	+	0.654412i	$0.772916\pi$
$20$	−1.11281	−	1.92977i	−0.248833	−	0.431510i
$21$	−0.209368	+	4.57779i	−0.0456878	+	0.998956i
$22$	3.71574	−	5.11427i	0.792198	−	1.09037i
$23$	−0.104552	+	0.321779i	−0.0218007	+	0.0670956i	−0.961365	−	0.275277i	$-0.911230\pi$
$23$	−0.104552	+	0.321779i	−0.0218007	+	0.0670956i	0.939564	+	0.342372i	$0.111230\pi$
$24$	−1.85071	+	2.37307i	−0.377774	+	0.484401i
$25$	3.34178	+	3.71921i	0.668356	+	0.743842i
$26$	−9.90058			−1.94166
$27$	3.46677	−	3.87059i	0.667180	−	0.744896i
$28$	2.15033	−	1.52428i	0.406373	−	0.288062i
$29$	5.21620	−	7.17948i	0.968624	−	1.33320i	0.0258844	−	0.999665i	$-0.491760\pi$
$29$	5.21620	−	7.17948i	0.968624	−	1.33320i	0.942739	−	0.333531i	$-0.108240\pi$
$30$	−2.93671	+	6.02654i	−0.536168	+	1.10029i
$31$	0.409018	+	0.562964i	0.0734617	+	0.101111i	0.844167	−	0.536081i	$-0.180096\pi$
$31$	0.409018	+	0.562964i	0.0734617	+	0.101111i	−0.770705	+	0.637192i	$0.780096\pi$
$32$	5.17981			0.915670
$33$	−6.32190	−	0.215235i	−1.10050	−	0.0374677i
$34$	6.32363	−	2.05467i	1.08449	−	0.352373i
$35$	−4.01194	+	4.34791i	−0.678141	+	0.734932i
$36$	−2.98177	−	0.203271i	−0.496962	−	0.0338784i
$37$	7.22692	−	2.34817i	1.18810	−	0.386036i	0.352728	−	0.935726i	$-0.385254\pi$
$37$	7.22692	−	2.34817i	1.18810	−	0.386036i	0.835369	+	0.549689i	$0.185254\pi$
$38$	−1.21965	+	0.396287i	−0.197853	+	0.0642862i
$39$	5.54699	+	8.20827i	0.888229	+	1.31438i
$40$	−3.80066	+	0.805785i	−0.600937	+	0.127406i
$41$	2.78467	+	8.57032i	0.434892	+	1.33846i	0.893198	+	0.449664i	$0.148456\pi$
$41$	2.78467	+	8.57032i	0.434892	+	1.33846i	−0.458306	+	0.888794i	$0.651544\pi$
$42$	−7.42417	−	2.79332i	−1.14557	−	0.431018i
$43$			3.39864i			0.518288i	0.965839	+	0.259144i	$0.0834404\pi$
$43$			3.39864i			0.518288i	−0.965839	+	0.259144i	$0.916560\pi$
$44$	2.13854	+	2.94345i	0.322397	+	0.443741i
$45$	6.64177	−	0.941746i	0.990097	−	0.140387i
$46$	−0.473802	−	0.344237i	−0.0698583	−	0.0507550i
$47$	−0.756806	+	1.04165i	−0.110392	+	0.151941i	−0.860638	−	0.509217i	$-0.829935\pi$
$47$	−0.756806	+	1.04165i	−0.110392	+	0.151941i	0.750246	+	0.661158i	$0.229935\pi$
$48$	−4.84901	−	7.17542i	−0.699894	−	1.03568i
$49$	−5.56555	−	4.24555i	−0.795078	−	0.606507i
$50$	−7.91023	+	3.51198i	−1.11868	+	0.496670i
$51$	−5.24640	−	4.09156i	−0.734643	−	0.572933i
$52$	1.76082	−	5.41925i	0.244182	−	0.751515i
$53$	−2.03163	−	1.47607i	−0.279066	−	0.202753i	0.439444	−	0.898270i	$-0.355176\pi$
$53$	−2.03163	−	1.47607i	−0.279066	−	0.202753i	−0.718510	+	0.695517i	$0.755176\pi$
$54$	4.51757	+	7.77752i	0.614764	+	1.05839i
$55$	−6.06587	−	5.46746i	−0.817922	−	0.737232i
$56$	−1.36942	−	4.38825i	−0.182996	−	0.586404i
$57$	1.01188	+	0.789144i	0.134027	+	0.104525i
$58$	9.02904	+	12.4274i	1.18557	+	1.63180i
$59$	−2.74649	−	8.45283i	−0.357563	−	1.10047i	−0.954509	−	0.298184i	$-0.903619\pi$
$59$	−2.74649	−	8.45283i	−0.357563	−	1.10047i	0.596946	−	0.802282i	$-0.296381\pi$
$60$	−2.77644	−	2.67928i	−0.358436	−	0.345894i
$61$	1.15184	+	0.374257i	0.147479	+	0.0479187i	0.381826	−	0.924234i	$-0.375295\pi$
$61$	1.15184	+	0.374257i	0.147479	+	0.0479187i	−0.234347	+	0.972153i	$0.575295\pi$
$62$	−1.14556	+	0.372214i	−0.145486	+	0.0472713i
$63$	1.84368	+	7.72016i	0.232281	+	0.972649i
$64$	0.319495	−	0.983304i	0.0399369	−	0.122913i
$65$	−1.34351	+	12.7189i	−0.166642	+	1.57758i
$66$	3.73589	−	10.2923i	0.459857	−	1.26689i
$67$	−7.91572	−	10.8950i	−0.967059	−	1.33104i	−0.943519	−	0.331319i	$-0.892506\pi$
$67$	−7.91572	−	10.8950i	−0.967059	−	1.33104i	−0.0235400	−	0.999723i	$-0.507494\pi$
$68$			3.82677i			0.464064i
$69$	−0.0199401	+	0.585680i	−0.00240050	+	0.0705076i
$70$	−5.01175	−	8.93031i	−0.599019	−	1.06738i
$71$	3.10015	−	4.26699i	0.367920	−	0.506399i	−0.584414	−	0.811456i	$-0.698676\pi$
$71$	3.10015	−	4.26699i	0.367920	−	0.506399i	0.952334	+	0.305057i	$0.0986755\pi$
$72$	−1.94417	+	4.83631i	−0.229123	+	0.569965i
$73$	3.43330	−	10.5666i	0.401838	−	1.23673i	−0.521669	−	0.853148i	$-0.674690\pi$
$73$	3.43330	−	10.5666i	0.401838	−	1.23673i	0.923507	−	0.383582i	$-0.125310\pi$
$74$			13.1533i			1.52904i
$75$	7.34354	+	4.59047i	0.847959	+	0.530062i
$76$		−	0.738074i		−	0.0846629i
$77$	5.77029	−	7.75028i	0.657586	−	0.883226i
$78$	−16.4799	+	4.74112i	−1.86598	+	0.536826i
$79$	−10.0715	−	7.31737i	−1.13313	−	0.823269i	−0.146985	−	0.989139i	$-0.546957\pi$
$79$	−10.0715	−	7.31737i	−1.13313	−	0.823269i	−0.986148	+	0.165870i	$0.946957\pi$
$80$	1.17446	−	11.1185i	0.131308	−	1.24308i
$81$	3.91705	−	8.10289i	0.435227	−	0.900321i
$82$	−15.5983			−1.72255
$83$	10.3911	+	14.3021i	1.14057	+	1.56986i	0.766224	+	0.642574i	$0.222133\pi$
$83$	10.3911	+	14.3021i	1.14057	+	1.56986i	0.374348	+	0.927288i	$0.377867\pi$
$84$	2.84936	−	3.56695i	0.310891	−	0.389186i
$85$	−1.78143	−	8.40252i	−0.193224	−	0.911381i
$86$	−5.59499	−	1.81792i	−0.603323	−	0.196032i
$87$	5.24450	−	14.4484i	0.562269	−	1.54903i
$88$	6.03485	−	1.96084i	0.643317	−	0.209026i
$89$	−3.29410	+	10.1382i	−0.349174	+	1.07465i	0.610138	+	0.792295i	$0.291114\pi$
$89$	−3.29410	+	10.1382i	−0.349174	+	1.07465i	−0.959311	+	0.282350i	$0.908886\pi$
$90$	−2.00232	+	11.4377i	−0.211063	+	1.20564i
$91$	−15.1319	−	0.176610i	−1.58625	−	0.0185138i
$92$	0.272690	−	0.198121i	0.0284299	−	0.0206555i
$93$	0.950413	+	0.741207i	0.0985532	+	0.0768596i
$94$	−1.31000	−	1.80306i	−0.135117	−	0.185972i
$95$	0.343588	+	1.62061i	0.0352513	+	0.166271i
$96$	8.62199	−	2.48047i	0.879978	−	0.253162i
$97$	9.38121	+	6.81585i	0.952518	+	0.692045i	0.951401	−	0.307955i	$-0.0996446\pi$
$97$	9.38121	+	6.81585i	0.952518	+	0.692045i	0.00111666	+	0.999999i	$0.499645\pi$
$98$	9.96620	−	6.89131i	1.00674	−	0.696127i
$99$	−10.6261	+	2.66912i	−1.06796	+	0.268256i
$100$	−0.515508	−	4.95441i	−0.0515508	−	0.495441i
$101$	−1.32182			−0.131526			−0.0657632	−	0.997835i	$-0.520948\pi$
$101$	−1.32182			−0.131526			−0.0657632	+	0.997835i	$0.520948\pi$
$102$	9.54198	−	6.44828i	0.944797	−	0.638475i
$103$	5.63619	+	4.09494i	0.555351	+	0.403486i	0.829754	−	0.558129i	$-0.188480\pi$
$103$	5.63619	+	4.09494i	0.555351	+	0.403486i	−0.274404	+	0.961615i	$0.588480\pi$
$104$	−8.03993	−	5.84135i	−0.788380	−	0.572792i
$105$	−4.59592	+	9.15847i	−0.448516	+	0.893775i
$106$	3.51668	−	2.55502i	0.341570	−	0.248165i
$107$	−7.72366			−0.746674			−0.373337	−	0.927696i	$-0.621786\pi$
$107$	−7.72366			−0.746674			−0.373337	+	0.927696i	$0.621786\pi$
$108$	−5.06061	+	1.08954i	−0.486957	+	0.104841i
$109$	1.23299	+	3.79474i	0.118099	+	0.363470i	0.992581	−	0.121587i	$-0.0387985\pi$
$109$	1.23299	+	3.79474i	0.118099	+	0.363470i	−0.874482	+	0.485058i	$0.838798\pi$
$110$	12.2454	−	7.06137i	1.16755	−	0.673275i
$111$	10.9050	−	7.36938i	1.03506	−	0.699471i
$112$	13.2278	+	0.154387i	1.24991	+	0.0145882i
$113$	−3.80265	−	11.7034i	−0.357723	−	1.10096i	−0.954413	−	0.298488i	$-0.903518\pi$
$113$	−3.80265	−	11.7034i	−0.357723	−	1.10096i	0.596690	−	0.802472i	$-0.296482\pi$
$114$	−1.84037	+	1.24369i	−0.172367	+	0.116482i
$115$	−0.506523	+	0.561961i	−0.0472335	+	0.0524031i
$116$	−8.40817	+	2.73198i	−0.780679	+	0.253658i
$117$	13.1639	+	11.0067i	1.21700	+	1.01757i
$118$	15.3845			1.41626
$119$	9.70157	−	3.02752i	0.889341	−	0.277532i
$120$	−5.94047	+	3.16129i	−0.542288	+	0.288585i
$121$	1.89114	+	1.37400i	0.171922	+	0.124909i
$122$	−1.23224	+	1.69603i	−0.111561	+	0.153551i
$123$	8.73927	+	12.9321i	0.787993	+	1.16605i
$124$		−	0.693239i		−	0.0622547i
$125$	3.43828	+	10.6385i	0.307529	+	0.951539i
$126$	−13.6954	−	1.09435i	−1.22009	−	0.0974923i
$127$	17.2746	+	5.61285i	1.53287	+	0.498060i	0.949398	−	0.314074i	$-0.101694\pi$
$127$	17.2746	+	5.61285i	1.53287	+	0.498060i	0.583471	+	0.812134i	$0.301694\pi$
$128$	9.82898	+	7.14117i	0.868767	+	0.631196i
$129$	1.62752	+	5.65716i	0.143295	+	0.498085i
$130$	−20.2197	−	9.01503i	−1.77339	−	0.790670i
$131$	5.21767	−	3.79086i	0.455870	−	0.331209i	−0.336039	−	0.941848i	$-0.609087\pi$
$131$	5.21767	−	3.79086i	0.455870	−	0.331209i	0.791909	+	0.610639i	$0.209087\pi$
$132$	4.96921	+	3.87539i	0.432514	+	0.337309i
$133$	−1.87115	+	0.583921i	−0.162250	+	0.0506324i
$134$	22.1700	−	7.20347i	1.91520	−	0.622285i
$135$	10.6045	−	4.74813i	0.912689	−	0.408654i
$136$	6.34746	+	2.06241i	0.544290	+	0.176851i
$137$	0.181781	+	0.559463i	0.0155306	+	0.0477982i	0.958521	−	0.285020i	$-0.0920004\pi$
$137$	0.181781	+	0.559463i	0.0155306	+	0.0477982i	−0.942991	+	0.332818i	$0.892000\pi$
$138$	−0.953507	−	0.346105i	−0.0811679	−	0.0294624i
$139$	−2.96084	−	0.962036i	−0.251135	−	0.0815988i	0.180744	−	0.983530i	$-0.442149\pi$
$139$	−2.96084	−	0.962036i	−0.251135	−	0.0815988i	−0.431879	+	0.901931i	$0.642149\pi$
$140$	5.77950	−	1.15501i	0.488457	−	0.0976161i
$141$	−0.760912	+	2.09629i	−0.0640804	+	0.176539i
$142$	5.36624	+	7.38600i	0.450325	+	0.619819i
$143$		−	20.8887i		−	1.74680i
$144$	−11.5075	−	9.62169i	−0.958955	−	0.801808i
$145$	17.1902	−	9.91284i	1.42757	−	0.823216i
$146$	15.5588	+	11.3041i	1.28765	+	0.935535i
$147$	−11.2971	−	4.40169i	−0.931772	−	0.363045i
$148$	−7.19968	−	2.33932i	−0.591810	−	0.192291i
$149$		−	4.95693i		−	0.406088i	−0.979170	−	0.203044i	$-0.934917\pi$
$149$		−	4.95693i		−	0.406088i	0.979170	−	0.203044i	$-0.0650834\pi$
$150$	−11.4851	+	9.63382i	−0.937752	+	0.786598i
$151$	−3.70182			−0.301250			−0.150625	−	0.988591i	$-0.548129\pi$
$151$	−3.70182			−0.301250			−0.150625	+	0.988591i	$0.548129\pi$
$152$	−1.22424	−	0.397781i	−0.0992992	−	0.0322643i
$153$	−10.6922	−	4.29819i	−0.864409	−	0.347488i
$154$	9.67233	+	13.6449i	0.779418	+	1.09954i
$155$	0.322716	+	1.52216i	0.0259212	+	0.122263i
$156$	0.335822	−	9.86375i	0.0268872	−	0.789732i
$157$	9.05409			0.722595			0.361297	−	0.932451i	$-0.382334\pi$
$157$	9.05409			0.722595			0.361297	+	0.932451i	$0.382334\pi$
$158$	17.4334	−	12.6661i	1.38693	−	1.00766i
$159$	−4.08857	−	1.48407i	−0.324245	−	0.117695i
$160$	10.5786	+	4.71651i	0.836312	+	0.372873i
$161$	−0.718010	−	0.534578i	−0.0565871	−	0.0421306i
$162$	11.2441	+	10.7826i	0.883420	+	0.847162i
$163$	−2.80924	+	0.912776i	−0.220036	+	0.0714941i	−0.416961	−	0.908925i	$-0.636905\pi$
$163$	−2.80924	+	0.912776i	−0.220036	+	0.0714941i	0.196924	+	0.980419i	$0.436905\pi$
$164$	2.77417	−	8.53802i	0.216626	−	0.666707i
$165$	−12.7151	−	6.19601i	−0.989867	−	0.482359i
$166$	−29.1029	+	9.45612i	−2.25883	+	0.733937i
$167$	−8.98230	−	12.3631i	−0.695071	−	0.956683i	−0.999991	−	0.00430529i	$-0.998630\pi$
$167$	−8.98230	−	12.3631i	−0.695071	−	0.956683i	0.304920	−	0.952378i	$-0.401370\pi$
$168$	−4.38086	−	6.64862i	−0.337990	−	0.512952i
$169$	−15.9497	+	11.5882i	−1.22690	+	0.891397i
$170$	14.7855	+	1.56181i	1.13399	+	0.119785i
$171$	2.06221	+	0.828998i	0.157701	+	0.0633951i
$172$	1.99014	−	2.73920i	0.151747	−	0.208862i
$173$	−0.748728	−	0.243277i	−0.0569248	−	0.0184960i	0.280416	−	0.959879i	$-0.409528\pi$
$173$	−0.748728	−	0.243277i	−0.0569248	−	0.0184960i	−0.337341	+	0.941383i	$0.609528\pi$
$174$	20.9803	+	16.3621i	1.59051	+	1.24041i
$175$	−12.1525	+	5.22655i	−0.918642	+	0.395090i
$176$			18.2603i			1.37642i
$177$	−8.61946	−	12.7548i	−0.647879	−	0.958712i
$178$	−14.9279	−	10.8458i	−1.11889	−	0.812925i
$179$	−7.97589	+	10.9779i	−0.596146	+	0.820525i	−0.995349	−	0.0963381i	$-0.969287\pi$
$179$	−7.97589	+	10.9779i	−0.596146	+	0.820525i	0.399203	+	0.916863i	$0.369287\pi$
$180$	−5.90451	−	3.13020i	−0.440096	−	0.233312i
$181$	−9.58472	−	13.1922i	−0.712427	−	0.980572i	−0.999742	−	0.0227353i	$-0.992762\pi$
$181$	−9.58472	−	13.1922i	−0.712427	−	0.980572i	0.287315	−	0.957836i	$-0.407238\pi$
$182$	8.38473	−	24.8163i	0.621518	−	1.83950i
$183$	2.09651	+	0.0713777i	0.154978	+	0.00527639i
$184$	−0.181658	−	0.559087i	−0.0133920	−	0.0412164i
$185$	16.8975	+	1.78490i	1.24233	+	0.131229i
$186$	−1.72858	+	1.16814i	−0.126746	+	0.0856522i
$187$	4.33504	+	13.3419i	0.317010	+	0.975655i
$188$	1.21992	−	0.396377i	0.0889720	−	0.0289088i
$189$	6.76584	+	11.9676i	0.492142	+	0.870515i
$190$	−2.85169	−	0.301228i	−0.206884	−	0.0218534i
$191$	2.65091	−	0.861332i	0.191813	−	0.0623238i	−0.211535	−	0.977370i	$-0.567846\pi$
$191$	2.65091	−	0.861332i	0.191813	−	0.0623238i	0.403348	+	0.915047i	$0.367846\pi$
$192$	0.0609336	−	1.78974i	0.00439751	−	0.129164i
$193$		−	15.4056i		−	1.10892i	−0.832210	−	0.554460i	$-0.812925\pi$
$193$		−	15.4056i		−	1.10892i	0.832210	−	0.554460i	$-0.187075\pi$
$194$	−16.2385	+	11.7980i	−1.16586	+	0.847045i
$195$	3.85440	+	21.8144i	0.276019	+	1.56216i
$196$	1.99958	+	6.68079i	0.142827	+	0.477199i
$197$	−19.9742	−	14.5121i	−1.42310	−	1.03395i	−0.991250	−	0.132001i	$-0.957860\pi$
$197$	−19.9742	−	14.5121i	−1.42310	−	1.03395i	−0.431854	−	0.901944i	$-0.642140\pi$
$198$	1.28985	−	18.9208i	0.0916659	−	1.34465i
$199$			4.48568i			0.317981i	0.987280	+	0.158991i	$0.0508240\pi$
$199$			4.48568i			0.317981i	−0.987280	+	0.158991i	$0.949176\pi$
$200$	−8.49570	−	1.81508i	−0.600737	−	0.128345i
$201$	−18.3933	−	14.3446i	−1.29737	−	1.01179i
$202$	0.707039	−	2.17604i	0.0497471	−	0.153106i
$203$	13.5781	+	19.1549i	0.952998	+	1.34441i
$204$	1.83253	+	6.36980i	0.128303	+	0.445975i
$205$	−2.11670	+	20.0385i	−0.147836	+	1.39955i
$206$	−9.75604	+	7.08818i	−0.679736	+	0.493857i
$207$	0.247275	+	0.984435i	0.0171868	+	0.0684230i
$208$	23.1366	−	16.8097i	1.60423	−	1.16554i
$209$	−0.836105	−	2.57327i	−0.0578346	−	0.177997i
$210$	−12.6187	−	12.4648i	−0.870775	−	0.860155i
$211$	3.27368	−	10.0754i	0.225370	−	0.693617i	−0.772884	−	0.634547i	$-0.781187\pi$
$211$	3.27368	−	10.0754i	0.225370	−	0.693617i	0.998254	−	0.0590694i	$-0.0188133\pi$
$212$	0.773090	+	2.37933i	0.0530960	+	0.163413i
$213$	3.11697	−	8.58714i	0.213571	−	0.588381i
$214$	4.13136	−	12.7150i	0.282414	−	0.869180i
$215$	−3.09465	+	6.94096i	−0.211053	+	0.473370i
$216$	−0.920171	+	8.98123i	−0.0626097	+	0.611095i
$217$	−1.75749	+	0.548451i	−0.119306	+	0.0372313i
$218$	−6.90659			−0.467773
$219$	0.654795	−	19.2326i	0.0442469	−	1.29962i
$220$	1.68731	+	7.95859i	0.113759	+	0.536568i
$221$	12.9141	−	17.7747i	0.868696	−	1.19566i
$222$	6.29875	+	21.8941i	0.422744	+	1.46944i
$223$	1.18320	−	3.64152i	0.0792330	−	0.243854i	−0.903592	−	0.428394i	$-0.859080\pi$
$223$	1.18320	−	3.64152i	0.0792330	−	0.243854i	0.982825	+	0.184540i	$0.0590795\pi$
$224$	−4.38675	+	12.9834i	−0.293102	+	0.867493i
$225$	14.4218	+	4.12439i	0.961456	+	0.274960i
$226$	21.3006			1.41690
$227$	−0.934484	−	0.303632i	−0.0620239	−	0.0201528i	0.277841	−	0.960627i	$-0.410381\pi$
$227$	−0.934484	−	0.303632i	−0.0620239	−	0.0201528i	−0.339865	+	0.940474i	$0.610381\pi$
$228$	−0.353443	−	1.22855i	−0.0234073	−	0.0813628i
$229$	13.7839	−	18.9719i	0.910864	−	1.25370i	−0.0560067	−	0.998430i	$-0.517837\pi$
$229$	13.7839	−	18.9719i	0.910864	−	1.25370i	0.966871	−	0.255266i	$-0.0821632\pi$
$230$	−0.654187	−	1.13445i	−0.0431358	−	0.0748035i
$231$	5.89347	−	15.6639i	0.387762	−	1.03061i
$232$			15.4190i			1.01231i
$233$	−6.11888	+	4.44563i	−0.400861	+	0.291243i	−0.769892	−	0.638175i	$-0.779690\pi$
$233$	−6.11888	+	4.44563i	−0.400861	+	0.291243i	0.369031	+	0.929417i	$0.379690\pi$
$234$	−25.1610	+	15.7835i	−1.64482	+	1.03180i
$235$	−2.49409	+	1.43823i	−0.162697	+	0.0938199i
$236$	−2.73614	+	8.42097i	−0.178108	+	0.548159i
$237$	−20.2685	−	7.35707i	−1.31658	−	0.477893i
$238$	−0.205306	+	17.5905i	−0.0133080	+	1.14023i
$239$	−3.28356	−	1.06689i	−0.212396	−	0.0690115i	0.200887	−	0.979615i	$-0.435618\pi$
$239$	−3.28356	−	1.06689i	−0.212396	−	0.0690115i	−0.413282	+	0.910603i	$0.635618\pi$
$240$	−3.36939	−	19.0695i	−0.217493	−	1.23093i
$241$	−7.66549	+	2.49067i	−0.493778	+	0.160438i	−0.545312	−	0.838233i	$-0.683589\pi$
$241$	−7.66549	+	2.49067i	−0.493778	+	0.160438i	0.0515344	+	0.998671i	$0.483589\pi$
$242$	−3.27350	+	2.37834i	−0.210428	+	0.152885i
$243$	2.63982	−	15.3633i	0.169344	−	0.985557i
$244$	−0.709196	−	0.976124i	−0.0454016	−	0.0624900i
$245$	−7.50057	−	13.7383i	−0.479194	−	0.877709i
$246$	−25.9640	+	7.46961i	−1.65540	+	0.476245i
$247$	−2.49076	+	3.42824i	−0.158483	+	0.218133i
$248$	−1.14988	−	0.373617i	−0.0730172	−	0.0237247i
$249$	24.1453	+	18.8304i	1.53014	+	1.19333i
$250$	−19.3527	−	0.0302620i	−1.22397	−	0.00191394i
$251$	−25.9722			−1.63935			−0.819674	−	0.572830i	$-0.805846\pi$
$251$	−25.9722			−1.63935			−0.819674	+	0.572830i	$0.805846\pi$
$252$	3.03475	−	7.30180i	0.191171	−	0.459970i
$253$	0.726288	−	0.999650i	0.0456613	−	0.0628474i
$254$	−18.4802	+	25.4358i	−1.15955	+	1.59599i
$255$	−6.98900	−	13.1332i	−0.437668	−	0.822434i
$256$	−15.3407	+	11.1457i	−0.958793	+	0.696604i
$257$		−	9.19835i		−	0.573777i	−0.957964	−	0.286889i	$-0.907379\pi$
$257$		−	9.19835i		−	0.573777i	0.957964	−	0.286889i	$-0.0926209\pi$
$258$	−10.1836	−	0.346712i	−0.634004	−	0.0215853i
$259$	−0.234633	+	20.1032i	−0.0145794	+	1.24915i
$260$	8.53062	−	9.46428i	0.529046	−	0.586950i
$261$	1.81071	−	26.5613i	0.112080	−	1.64410i
$262$	3.44976	+	10.6173i	0.213127	+	0.655937i
$263$	5.95773	+	18.3360i	0.367369	+	1.13065i	0.948484	+	0.316824i	$0.102617\pi$
$263$	5.95773	+	18.3360i	0.367369	+	1.13065i	−0.581115	+	0.813821i	$0.697383\pi$
$264$	9.10623	−	6.15381i	0.560450	−	0.378741i
$265$	−2.80511	−	4.86445i	−0.172317	−	0.298821i
$266$	0.0395977	−	3.39271i	0.00242789	−	0.208020i
$267$	−0.628245	+	18.4528i	−0.0384480	+	1.12929i
$268$			13.4163i			0.819529i
$269$	0.467762	−	0.339849i	0.0285199	−	0.0207209i	−0.573434	−	0.819252i	$-0.694389\pi$
$269$	0.467762	−	0.339849i	0.0285199	−	0.0207209i	0.601954	+	0.798531i	$0.294389\pi$
$270$	2.14427	+	19.9973i	0.130496	+	1.21700i
$271$	−1.84407	+	2.53814i	−0.112019	+	0.154181i	−0.861345	−	0.508020i	$-0.830378\pi$
$271$	−1.84407	+	2.53814i	−0.112019	+	0.154181i	0.749326	+	0.662201i	$0.230378\pi$
$272$	−11.2891	+	15.5381i	−0.684503	+	0.942137i
$273$	−25.2721	+	6.95226i	−1.52954	+	0.420770i
$274$	−1.01825			−0.0615145
$275$	−7.40975	−	16.6894i	−0.446825	−	1.00641i
$276$	0.359028	−	0.460363i	0.0216109	−	0.0277106i
$277$	−10.5082	−	3.41433i	−0.631378	−	0.205147i	−0.0241928	−	0.999707i	$-0.507702\pi$
$277$	−10.5082	−	3.41433i	−0.631378	−	0.205147i	−0.607186	+	0.794560i	$0.707702\pi$
$278$	3.16749	−	4.35968i	0.189973	−	0.261476i
$279$	1.93694	+	0.778640i	0.115962	+	0.0466160i
$280$	1.19901	−	10.2089i	0.0716548	−	0.610101i
$281$	18.1113	+	24.9280i	1.08043	+	1.48708i	0.859048	+	0.511895i	$0.171056\pi$
$281$	18.1113	+	24.9280i	1.08043	+	1.48708i	0.221381	+	0.975187i	$0.428944\pi$
$282$	−3.04399	−	2.37394i	−0.181267	−	0.141366i
$283$	−15.4152	+	11.1998i	−0.916341	+	0.665761i	−0.942611	−	0.333894i	$-0.891637\pi$
$283$	−15.4152	+	11.1998i	−0.916341	+	0.665761i	0.0262693	+	0.999655i	$0.491637\pi$
$284$	−4.99724	+	1.62370i	−0.296532	+	0.0963490i
$285$	1.34798	+	2.53302i	0.0798473	+	0.150043i
$286$	34.3879	+	11.1733i	2.03340	+	0.660691i
$287$	−23.8402	−	0.278249i	−1.40724	−	0.0164245i
$288$	13.1638	−	8.25767i	0.775684	−	0.486588i
$289$	0.693689	−	2.13495i	0.0408052	−	0.125586i
$290$	7.12394	+	33.6016i	0.418332	+	1.97316i
$291$	18.8793	+	6.85282i	1.10672	+	0.401720i
$292$	−8.95463	+	6.50592i	−0.524030	+	0.380730i
$293$			18.9992i			1.10995i	0.831868	+	0.554973i	$0.187272\pi$
$293$			18.9992i			1.10995i	−0.831868	+	0.554973i	$0.812728\pi$
$294$	13.2890	−	16.2434i	0.775033	−	0.947333i
$295$	2.08768	−	19.7638i	0.121549	−	1.15070i
$296$	−7.76045	+	10.6813i	−0.451067	+	0.620840i
$297$	−16.4094	+	9.53139i	−0.952168	+	0.553067i
$298$	8.16031	+	2.65145i	0.472714	+	0.153594i
$299$	−1.93520			−0.111915
$300$	−3.23061	−	7.99993i	−0.186519	−	0.461876i
$301$	−8.51885	−	2.87828i	−0.491018	−	0.165902i
$302$	1.98009	−	6.09409i	0.113941	−	0.350676i
$303$	−2.20022	+	0.632985i	−0.126400	+	0.0363640i
$304$	2.17735	−	2.99686i	0.124879	−	0.171882i
$305$	2.01160	+	1.81315i	0.115184	+	0.103821i
$306$	12.7951	−	15.3028i	0.731445	−	0.874802i
$307$	−1.44282			−0.0823462			−0.0411731	−	0.999152i	$-0.513110\pi$
$307$	−1.44282			−0.0823462			−0.0411731	+	0.999152i	$0.513110\pi$
$308$	−9.18900	+	2.86756i	−0.523592	+	0.163395i
$309$	11.3426	+	4.11715i	0.645258	+	0.234216i
$310$	−2.67847	−	0.282930i	−0.152127	−	0.0160693i
$311$	−0.638989	+	1.96661i	−0.0362338	+	0.111516i	−0.967538	−	0.252727i	$-0.918672\pi$
$311$	−0.638989	+	1.96661i	−0.0362338	+	0.111516i	0.931304	+	0.364243i	$0.118672\pi$
$312$	−16.1800	−	5.87304i	−0.916013	−	0.332495i
$313$	9.11988	+	28.0681i	0.515486	+	1.58650i	0.782396	+	0.622781i	$0.213997\pi$
$313$	9.11988	+	28.0681i	0.515486	+	1.58650i	−0.266910	+	0.963722i	$0.586003\pi$
$314$	−4.84300	+	14.9052i	−0.273306	+	0.841151i
$315$	−3.26434	+	17.4455i	−0.183925	+	0.982940i
$316$	3.83247	+	11.7951i	0.215593	+	0.663528i
$317$	−28.2933	+	20.5562i	−1.58911	+	1.15455i	−0.683907	+	0.729570i	$0.739720\pi$
$317$	−28.2933	+	20.5562i	−1.58911	+	1.15455i	−0.905201	+	0.424984i	$0.860280\pi$
$318$	4.63011	−	5.93696i	0.259644	−	0.332928i
$319$	−26.2199	+	19.0499i	−1.46803	+	1.06659i
$320$	1.54785	−	1.71726i	0.0865274	−	0.0959978i
$321$	−12.8563	+	3.69865i	−0.717569	+	0.206438i
$322$	1.26411	−	0.896075i	0.0704459	−	0.0499363i
$323$	0.879416	−	2.70656i	0.0489320	−	0.150597i
$324$	−7.90182	+	4.23696i	−0.438990	+	0.235387i
$325$	−14.3251	+	24.7521i	−0.794611	+	1.37300i
$326$		−	5.11293i		−	0.283179i
$327$	3.86955	+	5.72604i	0.213987	+	0.316651i
$328$	−12.6669	−	9.20303i	−0.699412	−	0.508152i
$329$	−1.97002	−	2.77914i	−0.108611	−	0.153219i
$330$	17.0014	−	17.6179i	0.935896	−	0.969832i
$331$	10.7371	−	7.80095i	0.590163	−	0.428779i	−0.252210	−	0.967672i	$-0.581158\pi$
$331$	10.7371	−	7.80095i	0.590163	−	0.428779i	0.842374	+	0.538894i	$0.181158\pi$
$332$		−	17.6118i		−	0.966571i
$333$	14.6228	−	17.4887i	0.801322	−	0.958375i
$334$	25.1572	−	8.17408i	1.37654	−	0.447266i
$335$	−6.24553	−	29.4584i	−0.341230	−	1.60948i
$336$	22.0921	−	6.07745i	1.20522	−	0.331552i
$337$	−25.6570	+	8.33646i	−1.39762	+	0.454116i	−0.908422	−	0.418054i	$-0.862712\pi$
$337$	−25.6570	+	8.33646i	−1.39762	+	0.454116i	−0.489203	+	0.872170i	$0.662712\pi$
$338$	−10.5455	−	32.4556i	−0.573598	−	1.76535i
$339$	−11.9341	−	17.6597i	−0.648170	−	0.959142i
$340$	−3.48448	+	7.81532i	−0.188973	+	0.423845i
$341$	−0.785315	−	2.41695i	−0.0425272	−	0.130885i
$342$	−2.46780	+	2.95147i	−0.133443	+	0.159597i
$343$	15.3551	−	10.3548i	0.829097	−	0.559105i
$344$	−3.47093	−	4.77732i	−0.187140	−	0.257576i
$345$	−0.574018	+	1.17796i	−0.0309041	+	0.0634195i
$346$	0.800985	−	1.10246i	0.0430612	−	0.0592687i
$347$	4.66866	+	3.39198i	0.250627	+	0.182091i	0.706004	−	0.708207i	$-0.250496\pi$
$347$	4.66866	+	3.39198i	0.250627	+	0.182091i	−0.455378	+	0.890298i	$0.650496\pi$
$348$	−12.6874	+	8.57392i	−0.680118	+	0.459611i
$349$		−	3.20920i		−	0.171784i	−0.996304	−	0.0858921i	$-0.972626\pi$
$349$		−	3.20920i		−	0.171784i	0.996304	−	0.0858921i	$-0.0273740\pi$
$350$	−2.10384	−	22.8016i	−0.112455	−	1.21880i
$351$	27.1826	+	12.0172i	1.45090	+	0.641430i
$352$	−17.9912	−	5.84568i	−0.958932	−	0.311576i
$353$	−4.04392	+	5.56598i	−0.215236	+	0.296247i	−0.902960	−	0.429726i	$-0.858610\pi$
$353$	−4.04392	+	5.56598i	−0.215236	+	0.296247i	0.687723	+	0.725973i	$0.258610\pi$
$354$	25.6081	−	7.36722i	1.36105	−	0.391563i
$355$	10.2167	−	5.89151i	0.542246	−	0.312689i
$356$	8.59155	−	6.24213i	0.455351	−	0.330832i
$357$	14.6988	−	9.68523i	0.777944	−	0.512596i
$358$	−13.8060	−	19.0023i	−0.729668	−	1.00430i
$359$	6.16835	−	2.00422i	0.325553	−	0.105779i	−0.141681	−	0.989912i	$-0.545251\pi$
$359$	6.16835	−	2.00422i	0.325553	−	0.105779i	0.467234	+	0.884134i	$0.345251\pi$
$360$	−8.37427	+	8.10681i	−0.441363	+	0.427266i
$361$	5.70171	−	17.5481i	0.300090	−	0.923582i
$362$	26.8445	−	8.72230i	1.41091	−	0.458434i
$363$	3.80585	+	1.38145i	0.199755	+	0.0725073i
$364$	12.0924	+	9.00311i	0.633813	+	0.471891i
$365$	16.6333	−	18.4537i	0.870624	−	0.965913i
$366$	−1.23892	+	3.41318i	−0.0647594	+	0.178410i
$367$	−12.7138	+	9.23714i	−0.663657	+	0.482175i	−0.867896	−	0.496746i	$-0.834528\pi$
$367$	−12.7138	+	9.23714i	−0.663657	+	0.482175i	0.204239	+	0.978921i	$0.434528\pi$
$368$	1.69169			0.0881854
$369$	20.7397	+	17.3410i	1.07966	+	0.902735i
$370$	−11.9768	+	26.8626i	−0.622644	+	1.39652i
$371$	5.42040	−	3.84231i	0.281413	−	0.199483i
$372$	−0.331973	−	1.15392i	−0.0172120	−	0.0598281i
$373$	10.5736	+	3.43557i	0.547480	+	0.177887i	0.569680	−	0.821867i	$-0.307067\pi$
$373$	10.5736	+	3.43557i	0.547480	+	0.177887i	−0.0222004	+	0.999754i	$0.507067\pi$
$374$	−24.2828			−1.25563
$375$	10.8176	+	16.0617i	0.558621	+	0.829423i
$376$		−	2.23711i		−	0.115370i
$377$	48.2742	+	15.6852i	2.48625	+	0.807830i
$378$	−23.3206	+	4.73678i	−1.19948	+	0.243634i
$379$	−7.56769	−	5.49825i	−0.388726	−	0.282426i	0.376207	−	0.926536i	$-0.377228\pi$
$379$	−7.56769	−	5.49825i	−0.388726	−	0.282426i	−0.764933	+	0.644109i	$0.777228\pi$
$380$	0.672057	−	1.50735i	0.0344758	−	0.0773254i
$381$	31.4420	+	1.07047i	1.61082	+	0.0548420i
$382$			4.82476i			0.246856i
$383$	2.12988	+	2.93153i	0.108832	+	0.149794i	0.859959	−	0.510364i	$-0.170489\pi$
$383$	2.12988	+	2.93153i	0.108832	+	0.149794i	−0.751127	+	0.660158i	$0.770489\pi$
$384$	19.7804	+	7.17991i	1.00941	+	0.366398i
$385$	18.8416	−	10.5740i	0.960256	−	0.538902i
$386$	25.3614	+	8.24041i	1.29086	+	0.419426i
$387$	5.41812	+	8.63718i	0.275418	+	0.439053i
$388$	−3.56980	−	10.9867i	−0.181229	−	0.557766i
$389$	−2.21635	−	0.720135i	−0.112373	−	0.0365123i	0.252291	−	0.967652i	$-0.418816\pi$
$389$	−2.21635	−	0.720135i	−0.112373	−	0.0365123i	−0.364664	+	0.931139i	$0.618816\pi$
$390$	−37.9735	−	5.32318i	−1.92286	−	0.269550i
$391$	1.23603	−	0.401612i	0.0625089	−	0.0203104i
$392$	12.1591	+	0.283866i	0.614127	+	0.0143374i
$393$	6.86966	−	8.80862i	0.346529	−	0.444336i
$394$	34.5746	−	25.1199i	1.74184	−	1.26552i
$395$	−13.9059	−	24.1148i	−0.699682	−	1.21334i
$396$	10.1272	+	4.07110i	0.508913	+	0.204581i
$397$	14.5926	+	10.6021i	0.732380	+	0.532105i	0.890315	−	0.455344i	$-0.150484\pi$
$397$	14.5926	+	10.6021i	0.732380	+	0.532105i	−0.157935	+	0.987449i	$0.550484\pi$
$398$	−7.38452	−	2.39938i	−0.370153	−	0.120270i
$399$	−2.83498	+	1.86800i	−0.141926	+	0.0935171i
$400$	12.5225	−	21.6375i	0.626126	−	1.08188i
$401$			11.8897i			0.593741i	0.954918	+	0.296871i	$0.0959430\pi$
$401$			11.8897i			0.593741i	−0.954918	+	0.296871i	$0.904057\pi$
$402$	33.4532	−	22.6070i	1.66849	−	1.12754i
$403$	−2.33946	+	3.21999i	−0.116537	+	0.160399i
$404$	1.06535	+	0.774020i	0.0530030	+	0.0385089i
$405$	15.3778	−	12.9816i	0.764130	−	0.645063i
$406$	−38.7965	+	12.1070i	−1.92544	+	0.600862i
$407$	−27.7514			−1.37559
$408$	11.5532	+	0.393341i	0.571969	+	0.0194733i
$409$	−9.58901	+	3.11566i	−0.474146	+	0.154059i	−0.536335	−	0.844005i	$-0.680192\pi$
$409$	−9.58901	+	3.11566i	−0.474146	+	0.154059i	0.0621893	+	0.998064i	$0.480192\pi$
$410$	−31.8561	−	14.2031i	−1.57326	−	0.701444i
$411$	0.570492	+	0.844197i	0.0281403	+	0.0416412i
$412$	−2.14472	−	6.60077i	−0.105663	−	0.325197i
$413$	23.5134	+	0.274434i	1.15702	+	0.0135040i
$414$	−1.75289	−	0.119496i	−0.0861497	−	0.00587291i
$415$	8.19861	+	38.6706i	0.402454	+	1.89826i
$416$	9.15524	+	28.1769i	0.448873	+	1.38149i
$417$	−5.38912	−	0.183478i	−0.263906	−	0.00898496i
$418$	4.68345			0.229075
$419$	−7.00552	+	5.08981i	−0.342242	+	0.248654i	−0.745607	−	0.666386i	$-0.767840\pi$
$419$	−7.00552	+	5.08981i	−0.342242	+	0.248654i	0.403365	+	0.915039i	$0.367840\pi$
$420$	9.06708	−	4.69020i	0.442428	−	0.228858i
$421$	22.0505	+	16.0207i	1.07468	+	0.780799i	0.976747	−	0.214394i	$-0.0687778\pi$
$421$	22.0505	+	16.0207i	1.07468	+	0.780799i	0.0979303	+	0.995193i	$0.468778\pi$
$422$	14.8354	+	10.7786i	0.722177	+	0.524692i
$423$	−0.262712	+	3.85372i	−0.0127735	+	0.187374i
$424$	4.36324			0.211898
$425$	4.01278	−	18.7824i	0.194649	−	0.911078i
$426$	12.4693	+	9.72452i	0.604138	+	0.471155i
$427$	−1.91358	+	2.57020i	−0.0926047	+	0.124380i
$428$	6.22502	+	4.52274i	0.300898	+	0.218615i
$429$	−10.0030	−	34.7700i	−0.482951	−	1.67871i
$430$	−9.77119	−	8.80725i	−0.471209	−	0.424723i
$431$	−18.7675	−	25.8313i	−0.903999	−	1.24425i	−0.969175	−	0.246375i	$-0.920761\pi$
$431$	−18.7675	−	25.8313i	−0.903999	−	1.24425i	0.0651752	−	0.997874i	$-0.479239\pi$
$432$	−23.7622	−	10.5050i	−1.14326	−	0.505424i
$433$	−15.6104	+	11.3416i	−0.750189	+	0.545044i	−0.895885	−	0.444285i	$-0.853458\pi$
$433$	−15.6104	+	11.3416i	−0.750189	+	0.545044i	0.145697	+	0.989329i	$0.453458\pi$
$434$	0.0371923	−	3.18662i	0.00178529	−	0.152963i
$435$	23.8668	−	24.7322i	1.14432	−	1.18582i
$436$	1.22834	−	3.78044i	0.0588268	−	0.181050i
$437$	−0.238395	+	0.0774593i	−0.0114040	+	0.00370538i
$438$	31.3114	+	11.3654i	1.49611	+	0.543061i
$439$	−21.1491	−	6.87177i	−1.00939	−	0.327972i	−0.242780	−	0.970081i	$-0.578059\pi$
$439$	−21.1491	−	6.87177i	−1.00939	−	0.327972i	−0.766613	+	0.642110i	$0.778059\pi$
$440$	14.1103	+	1.49049i	0.672681	+	0.0710561i
$441$	−20.9123	−	1.91689i	−0.995825	−	0.0912802i
$442$	22.3538	+	30.7674i	1.06326	+	1.46346i
$443$	21.6740			1.02976			0.514882	−	0.857261i	$-0.327836\pi$
$443$	21.6740			1.02976			0.514882	+	0.857261i	$0.327836\pi$
$444$	−13.1044	−	0.446151i	−0.621905	−	0.0211734i
$445$	−15.9588	+	17.7055i	−0.756521	+	0.839322i
$446$	5.36193	+	3.89567i	0.253895	+	0.184465i
$447$	−2.37374	−	8.25099i	−0.112274	−	0.390259i
$448$	2.19412	+	1.63358i	0.103662	+	0.0771795i
$449$		−	21.5302i		−	1.01607i	−0.861336	−	0.508036i	$-0.830372\pi$
$449$		−	21.5302i		−	1.01607i	0.861336	−	0.508036i	$-0.169628\pi$
$450$	−14.5040	+	21.5357i	−0.683723	+	1.01520i
$451$		−	32.9101i		−	1.54968i
$452$	−3.78832	+	11.6593i	−0.178188	+	0.548405i
$453$	−6.16181	+	1.77270i	−0.289507	+	0.0832887i
$454$	0.999705	−	1.37598i	0.0469185	−	0.0645777i
$455$	−30.7426	−	14.1391i	−1.44124	−	0.662851i
$456$	−2.22828	−	0.0758642i	−0.104349	−	0.00355266i
$457$		−	10.1239i		−	0.473576i	−0.971561	−	0.236788i	$-0.923905\pi$
$457$		−	10.1239i		−	0.473576i	0.971561	−	0.236788i	$-0.0760946\pi$
$458$	23.8594	+	32.8396i	1.11488	+	1.53449i
$459$	−19.8558	−	2.03432i	−0.926788	−	0.0949539i
$460$	0.737308	−	0.156318i	0.0343772	−	0.00728837i
$461$	−3.13306	+	9.64256i	−0.145921	+	0.449099i	−0.997128	−	0.0757308i	$-0.975871\pi$
$461$	−3.13306	+	9.64256i	−0.145921	+	0.449099i	0.851207	+	0.524830i	$0.175871\pi$
$462$	22.6341	+	18.0806i	1.05303	+	0.841187i
$463$	−38.2449	+	12.4265i	−1.77739	+	0.577509i	−0.998751	−	0.0499636i	$-0.984089\pi$
$463$	−38.2449	+	12.4265i	−1.77739	+	0.577509i	−0.778639	+	0.627473i	$0.784089\pi$
$464$	−42.1998	−	13.7115i	−1.95908	−	0.636543i
$465$	1.26609	+	2.37915i	0.0587137	+	0.110331i
$466$	−4.04561	−	12.4511i	−0.187409	−	0.576787i
$467$	−20.7132	−	28.5093i	−0.958493	−	1.31925i	−0.947650	−	0.319311i	$-0.896549\pi$
$467$	−20.7132	−	28.5093i	−0.958493	−	1.31925i	−0.0108425	−	0.999941i	$-0.503451\pi$
$468$	−4.16449	−	16.5794i	−0.192504	−	0.766383i
$469$	34.0127	−	10.6142i	1.57056	−	0.490117i
$470$	−1.03360	−	4.87519i	−0.0476763	−	0.224876i
$471$	15.0709	−	4.33575i	0.694428	−	0.199781i
$472$	12.4932	+	9.07687i	0.575048	+	0.417797i
$473$	3.83554	−	11.8046i	0.176358	−	0.542775i
$474$	22.9531	−	29.4316i	1.05427	−	1.35184i
$475$	−0.773951	+	3.62258i	−0.0355113	+	0.166215i
$476$	−9.59197	−	3.24086i	−0.439647	−	0.148545i
$477$	−7.51626	−	0.512391i	−0.344146	−	0.0234608i
$478$	3.51273	−	4.83486i	0.160668	−	0.221141i
$479$	18.8038	+	13.6617i	0.859166	+	0.624220i	0.927658	−	0.373431i	$-0.121819\pi$
$479$	18.8038	+	13.6617i	0.859166	+	0.624220i	−0.0684922	+	0.997652i	$0.521819\pi$
$480$	19.8671	+	2.78500i	0.906804	+	0.127117i
$481$	25.5469	+	35.1623i	1.16484	+	1.60326i
$482$		−	13.9515i		−	0.635474i
$483$	−1.45115	−	0.545989i	−0.0660295	−	0.0248434i
$484$	−0.719630	−	2.21479i	−0.0327105	−	0.100672i
$485$	12.9528	+	22.4620i	0.588157	+	1.01994i
$486$	23.8797	+	12.5636i	1.08321	+	0.569895i
$487$	−20.5661	+	6.68233i	−0.931939	+	0.302805i	−0.735355	−	0.677682i	$-0.762985\pi$
$487$	−20.5661	+	6.68233i	−0.931939	+	0.302805i	−0.196584	+	0.980487i	$0.562985\pi$
$488$	−2.00131	+	0.650266i	−0.0905952	+	0.0294362i
$489$	−4.23897	+	2.86461i	−0.191693	+	0.129542i
$490$	26.6286	−	4.99917i	1.20296	−	0.225840i
$491$	−3.71463	+	1.20696i	−0.167639	+	0.0544692i	−0.391634	−	0.920121i	$-0.628090\pi$
$491$	−3.71463	+	1.20696i	−0.167639	+	0.0544692i	0.223995	+	0.974590i	$0.428090\pi$
$492$	0.529086	−	15.5403i	0.0238530	−	0.700611i
$493$	−34.0885			−1.53527
$494$	−4.31141	−	5.93415i	−0.193980	−	0.266990i
$495$	−24.1318	−	4.22458i	−1.08464	−	0.189881i
$496$	2.04508	−	2.81481i	0.0918269	−	0.126389i
$497$	8.06991	+	11.3844i	0.361985	+	0.510658i
$498$	−43.9146	+	29.6766i	−1.96786	+	1.32984i
$499$	−22.2181			−0.994619			−0.497309	−	0.867573i	$-0.665679\pi$
$499$	−22.2181			−0.994619			−0.497309	+	0.867573i	$0.665679\pi$
$500$	3.45845	−	10.5877i	0.154667	−	0.473495i
$501$	−20.8717	−	16.2774i	−0.932479	−	0.727221i
$502$	13.8924	−	42.7565i	0.620049	−	1.90832i
$503$	3.26441	−	4.49308i	0.145553	−	0.200337i	−0.730015	−	0.683431i	$-0.760487\pi$
$503$	3.26441	−	4.49308i	0.145553	−	0.200337i	0.875568	+	0.483094i	$0.160487\pi$
$504$	−10.4759	−	8.96900i	−0.466635	−	0.399511i
$505$	−2.69953	−	1.20359i	−0.120127	−	0.0535592i
$506$	1.25718	+	1.73036i	0.0558883	+	0.0769237i
$507$	−20.9997	+	26.9268i	−0.932628	+	1.19586i
$508$	−10.6360	−	14.6392i	−0.471897	−	0.649511i
$509$	−4.62704	−	14.2406i	−0.205090	−	0.631202i	−0.999710	−	0.0240945i	$-0.992330\pi$
$509$	−4.62704	−	14.2406i	−0.205090	−	0.631202i	0.794620	−	0.607107i	$-0.207670\pi$
$510$	25.3589	−	4.48067i	1.12291	−	0.198407i
$511$	23.5781	+	17.5545i	1.04303	+	0.776567i
$512$	−2.63412	−	8.10698i	−0.116413	−	0.358281i
$513$	3.82961	+	0.392362i	0.169081	+	0.0173232i
$514$	15.1427	+	4.92017i	0.667916	+	0.217019i
$515$	7.78200	+	13.4951i	0.342916	+	0.594663i
$516$	2.00094	−	5.51251i	0.0880864	−	0.242675i
$517$	3.80419	−	2.76391i	0.167308	−	0.121556i
$518$	−32.9693	−	11.1394i	−1.44859	−	0.489438i
$519$	−1.36278	−	0.0463974i	−0.0598196	−	0.00203662i
$520$	−11.1009	−	19.2504i	−0.486806	−	0.844188i
$521$	15.2172	+	11.0560i	0.666679	+	0.484370i	0.868912	−	0.494967i	$-0.164820\pi$
$521$	15.2172	+	11.0560i	0.666679	+	0.484370i	−0.202233	+	0.979337i	$0.564820\pi$
$522$	42.7579	+	17.1884i	1.87146	+	0.752318i
$523$	0.413173	−	1.27161i	0.0180668	−	0.0556038i	−0.941617	−	0.336687i	$-0.890694\pi$
$523$	0.413173	−	1.27161i	0.0180668	−	0.0556038i	0.959683	+	0.281083i	$0.0906936\pi$
$524$	−6.42509			−0.280681
$525$	−17.7254	+	14.5193i	−0.773601	+	0.633673i
$526$	−33.3723			−1.45510
$527$	0.825996	−	2.54215i	0.0359809	−	0.110738i
$528$	8.74434	+	30.3949i	0.380549	+	1.32277i
$529$	18.5148	+	13.4518i	0.804990	+	0.584860i
$530$	9.50851	−	2.01592i	0.413023	−	0.0875658i
$531$	−20.4553	−	17.1033i	−0.887686	−	0.742218i
$532$	1.85002	+	0.625069i	0.0802084	+	0.0271002i
$533$	−41.6986	+	30.2958i	−1.80617	+	1.31226i
$534$	−30.0418	−	10.9046i	−1.30004	−	0.471888i
$535$	−15.7738	−	7.03282i	−0.681962	−	0.304055i
$536$	22.2536	+	7.23062i	0.961207	+	0.312315i
$537$	−8.01916	+	22.0925i	−0.346052	+	0.953362i
$538$	0.309269	+	0.951834i	0.0133336	+	0.0410365i
$539$	14.5396	+	21.0272i	0.626265	+	0.905704i
$540$	−11.3272	−	2.38283i	−0.487447	−	0.102541i
$541$	9.20019	+	28.3153i	0.395547	+	1.21737i	0.928535	+	0.371245i	$0.121069\pi$
$541$	9.20019	+	28.3153i	0.395547	+	1.21737i	−0.532988	+	0.846123i	$0.678931\pi$
$542$	−3.19201	−	4.39343i	−0.137109	−	0.188714i
$543$	−22.2715	−	17.3691i	−0.955763	−	0.745380i
$544$	−11.6951	−	16.0970i	−0.501425	−	0.690152i
$545$	−0.937225	+	8.87261i	−0.0401463	+	0.380061i
$546$	2.07286	−	45.3228i	0.0887104	−	1.93964i
$547$	13.5830	−	18.6954i	0.580767	−	0.799357i	−0.413012	−	0.910725i	$-0.635523\pi$
$547$	13.5830	−	18.6954i	0.580767	−	0.799357i	0.993779	+	0.111368i	$0.0355233\pi$
$548$	0.181095	−	0.557355i	0.00773601	−	0.0238090i
$549$	3.52389	−	0.885149i	0.150396	−	0.0377772i
$550$	31.4382	−	3.27116i	1.34053	−	0.139483i
$551$	6.57469			0.280091
$552$	−0.570108	−	0.843630i	−0.0242654	−	0.0359073i
$553$	26.8708	−	19.0476i	1.14266	−	0.809988i
$554$	11.2416	−	15.4728i	0.477611	−	0.657376i
$555$	28.9812	−	5.12071i	1.23018	−	0.217362i
$556$	1.82300	+	2.50915i	0.0773126	+	0.106412i
$557$	5.03112			0.213175			0.106588	−	0.994303i	$-0.466008\pi$
$557$	5.03112			0.213175			0.106588	+	0.994303i	$0.466008\pi$
$558$	−2.31789	+	2.77218i	−0.0981243	+	0.117356i
$559$	−18.4878	+	6.00705i	−0.781950	+	0.254071i
$560$	26.8743	+	12.3600i	1.13565	+	0.522304i
$561$	13.6049	+	20.1321i	0.574399	+	0.849979i
$562$	−50.7253	+	16.4816i	−2.13972	+	0.695236i
$563$	19.8446	−	6.44789i	0.836348	−	0.271746i	0.140631	−	0.990062i	$-0.455087\pi$
$563$	19.8446	−	6.44789i	0.836348	−	0.271746i	0.695717	+	0.718316i	$0.255087\pi$
$564$	1.84079	−	1.24397i	0.0775113	−	0.0523806i
$565$	2.89050	−	27.3640i	0.121604	−	1.15121i
$566$	−10.1921	−	31.3680i	−0.428405	−	1.31850i
$567$	16.9929	+	16.6805i	0.713636	+	0.700516i
$568$			9.16401i			0.384513i
$569$	10.3352	+	14.2252i	0.433276	+	0.596353i	0.968701	−	0.248230i	$-0.0798488\pi$
$569$	10.3352	+	14.2252i	0.433276	+	0.596353i	−0.535426	+	0.844582i	$0.679849\pi$
$570$	−4.89100	+	0.864193i	−0.204861	+	0.0361970i
$571$	−13.0415	−	9.47522i	−0.545771	−	0.396526i	0.280453	−	0.959868i	$-0.409515\pi$
$571$	−13.0415	−	9.47522i	−0.545771	−	0.396526i	−0.826224	+	0.563342i	$0.809515\pi$
$572$	−12.2318	+	16.8356i	−0.511437	+	0.703933i
$573$	4.00007	−	2.70317i	0.167105	−	0.112926i
$574$	13.2101	−	39.0979i	0.551380	−	1.63192i
$575$	−1.54616	+	0.686462i	−0.0644791	+	0.0286275i
$576$	−0.755632	−	3.00827i	−0.0314847	−	0.125345i
$577$	11.5740	−	35.6212i	0.481833	−	1.48293i	−0.354682	−	0.934987i	$-0.615411\pi$
$577$	11.5740	−	35.6212i	0.481833	−	1.48293i	0.836516	−	0.547943i	$-0.184589\pi$
$578$	3.14360	+	2.28396i	0.130757	+	0.0950002i
$579$	−7.37732	−	25.6432i	−0.306591	−	1.06569i
$580$	−19.6594	−	2.07665i	−0.816313	−	0.0862282i
$581$	−44.6491	+	13.9334i	−1.85236	+	0.578055i
$582$	−21.3799	+	27.4143i	−0.886225	+	1.13636i
$583$	5.39069	+	7.41965i	0.223260	+	0.307291i
$584$	5.96532	+	18.3594i	0.246847	+	0.759716i
$585$	16.8621	+	34.4651i	0.697162	+	1.42496i
$586$	−31.2773	−	10.1626i	−1.29206	−	0.419814i
$587$	8.06560	−	2.62067i	0.332903	−	0.108167i	−0.137796	−	0.990461i	$-0.544002\pi$
$587$	8.06560	−	2.62067i	0.332903	−	0.108167i	0.470699	+	0.882294i	$0.344002\pi$
$588$	6.52763	+	10.1629i	0.269195	+	0.419110i
$589$	−0.159311	+	0.490308i	−0.00656429	+	0.0202028i
$590$	31.4194	+	14.0084i	1.29352	+	0.576719i
$591$	−40.1972	−	14.5908i	−1.65349	−	0.600187i
$592$	−22.3323	−	30.7378i	−0.917853	−	1.26332i
$593$			35.6722i			1.46488i	0.680830	+	0.732442i	$0.261619\pi$
$593$			35.6722i			1.46488i	−0.680830	+	0.732442i	$0.738381\pi$
$594$	−6.91366	−	32.1121i	−0.283671	−	1.31758i
$595$	22.5700	+	2.65079i	0.925279	+	0.108672i
$596$	−2.90263	+	3.99513i	−0.118896	+	0.163647i
$597$	2.14807	+	7.46658i	0.0879146	+	0.305587i
$598$	1.03513	−	3.18580i	0.0423296	−	0.130277i
$599$			11.1523i			0.455671i	0.973700	+	0.227835i	$0.0731648\pi$
$599$			11.1523i			0.455671i	−0.973700	+	0.227835i	$0.926835\pi$
$600$	−15.0106	+	1.04710i	−0.612805	+	0.0427476i
$601$		−	3.17192i		−	0.129385i	−0.997905	−	0.0646927i	$-0.979393\pi$
$601$		−	3.17192i		−	0.129385i	0.997905	−	0.0646927i	$-0.0206067\pi$
$602$	9.29506	−	12.4845i	0.378838	−	0.508831i
$603$	−37.4856	−	15.0690i	−1.52653	−	0.613658i
$604$	2.98355	+	2.16767i	0.121399	+	0.0882014i
$605$	2.61114	+	4.52807i	0.106158	+	0.184092i
$606$	0.134846	−	3.96068i	0.00547772	−	0.160892i
$607$	−38.4168			−1.55929			−0.779644	−	0.626223i	$-0.784600\pi$
$607$	−38.4168			−1.55929			−0.779644	+	0.626223i	$0.784600\pi$
$608$	2.25566	+	3.10464i	0.0914789	+	0.125910i
$609$	31.7740	+	25.3818i	1.28755	+	1.02852i
$610$	−4.06089	+	2.34174i	−0.164421	+	0.0948141i
$611$	−7.00399	−	2.27573i	−0.283351	−	0.0920664i
$612$	6.10064	+	9.72521i	0.246604	+	0.393118i
$613$	−4.76772	+	1.54913i	−0.192566	+	0.0625686i	−0.403712	−	0.914886i	$-0.632280\pi$
$613$	−4.76772	+	1.54913i	−0.192566	+	0.0625686i	0.211146	+	0.977454i	$0.432280\pi$
$614$	0.771761	−	2.37524i	0.0311457	−	0.0958567i
$615$	6.07259	+	34.3685i	0.244870	+	1.38587i
$616$	−0.195931	+	16.7872i	−0.00789427	+	0.676377i
$617$	−3.75011	+	2.72461i	−0.150974	+	0.109689i	−0.660708	−	0.750643i	$-0.729744\pi$
$617$	−3.75011	+	2.72461i	−0.150974	+	0.109689i	0.509734	+	0.860332i	$0.329744\pi$
$618$	−12.8450	+	16.4704i	−0.516700	+	0.662538i
$619$	9.57107	+	13.1734i	0.384694	+	0.529486i	0.956820	−	0.290680i	$-0.0938814\pi$
$619$	9.57107	+	13.1734i	0.384694	+	0.529486i	−0.572127	+	0.820165i	$0.693881\pi$
$620$	0.631233	−	1.41579i	0.0253509	−	0.0568593i
$621$	0.883017	+	1.52021i	0.0354343	+	0.0610041i
$622$	−2.89572	−	2.10386i	−0.116108	−	0.0843573i
$623$	−22.6221	−	16.8428i	−0.906335	−	0.674791i
$624$	30.4620	−	39.0599i	1.21946	−	1.56365i
$625$	−2.66504	+	24.8575i	−0.106602	+	0.994302i
$626$	−51.0851			−2.04177
$627$	−2.62399	−	3.88291i	−0.104792	−	0.155068i
$628$	−7.29730	−	5.30180i	−0.291194	−	0.211565i
$629$	−23.6144	−	17.1568i	−0.941567	−	0.684088i
$630$	−26.9734	−	14.7054i	−1.07465	−	0.585878i
$631$	−27.7041	+	20.1282i	−1.10288	+	0.801293i	−0.981528	−	0.191316i	$-0.938724\pi$
$631$	−27.7041	+	20.1282i	−1.10288	+	0.801293i	−0.121356	+	0.992609i	$0.538724\pi$
$632$	21.6301			0.860398
$633$	0.624352	−	18.3385i	0.0248158	−	0.728889i
$634$	−18.7066	−	57.5730i	−0.742935	−	2.28652i
$635$	30.1686	+	27.1924i	1.19720	+	1.07910i
$636$	2.42623	+	3.59026i	0.0962062	+	0.142363i
$637$	13.2578	−	37.7792i	0.525291	−	1.49686i
$638$	−17.3358	−	53.3541i	−0.686331	−	2.11231i
$639$	1.07616	−	15.7862i	0.0425724	−	0.624494i
$640$	13.5710	+	23.5341i	0.536443	+	0.930266i
$641$	10.5525	−	3.42870i	0.416797	−	0.135425i	−0.0931087	−	0.995656i	$-0.529680\pi$
$641$	10.5525	−	3.42870i	0.416797	−	0.135425i	0.509905	+	0.860230i	$0.329680\pi$
$642$	0.787927	−	23.1430i	0.0310970	−	0.913381i
$643$	14.6395			0.577325			0.288663	−	0.957431i	$-0.406789\pi$
$643$	14.6395			0.577325			0.288663	+	0.957431i	$0.406789\pi$
$644$	0.265660	+	0.851297i	0.0104685	+	0.0335458i
$645$	−1.82732	+	13.0354i	−0.0719508	+	0.513269i
$646$	3.98527	+	2.89547i	0.156798	+	0.113921i
$647$	3.28093	−	4.51582i	0.128987	−	0.177535i	−0.739639	−	0.673004i	$-0.765004\pi$
$647$	3.28093	−	4.51582i	0.128987	−	0.177535i	0.868626	+	0.495469i	$0.165004\pi$
$648$	2.76921	+	15.3902i	0.108785	+	0.604585i
$649$			32.4590i			1.27413i
$650$	−33.0856	−	36.8223i	−1.29772	−	1.44429i
$651$	−2.66277	+	1.75453i	−0.104362	+	0.0687654i
$652$	2.79865	+	0.909336i	0.109604	+	0.0356123i
$653$	2.71149	+	1.97001i	0.106109	+	0.0770926i	0.639574	−	0.768729i	$-0.279111\pi$
$653$	2.71149	+	1.97001i	0.106109	+	0.0770926i	−0.533466	+	0.845822i	$0.679111\pi$
$654$	−11.4963	+	3.30738i	−0.449540	+	0.129329i
$655$	14.1077	−	2.99100i	0.551234	−	0.116868i
$656$	36.4516	−	26.4837i	1.42320	−	1.03401i
$657$	−8.12005	−	32.3270i	−0.316793	−	1.26120i
$658$	5.62890	−	1.75658i	0.219437	−	0.0684787i
$659$	15.5256	−	5.04457i	0.604791	−	0.196508i	0.00941477	−	0.999956i	$-0.497003\pi$
$659$	15.5256	−	5.04457i	0.604791	−	0.196508i	0.595376	+	0.803447i	$0.297003\pi$
$660$	6.61975	+	12.4394i	0.257673	+	0.484201i
$661$	28.6360	+	9.30440i	1.11381	+	0.361899i	0.807402	−	0.590001i	$-0.200873\pi$
$661$	28.6360	+	9.30440i	1.11381	+	0.361899i	0.306408	+	0.951900i	$0.400873\pi$
$662$	7.09902	+	21.8485i	0.275911	+	0.849168i
$663$	12.9842	−	35.7709i	0.504263	−	1.38923i
$664$	−29.2126	−	9.49176i	−1.13367	−	0.368352i
$665$	−4.35310	−	0.511261i	−0.168806	−	0.0198258i
$666$	20.9690	+	33.4273i	0.812532	+	1.29528i
$667$	1.76484	+	2.42910i	0.0683349	+	0.0940550i
$668$			15.2240i			0.589034i
$669$	0.225658	−	6.62804i	0.00872446	−	0.256255i
$670$	51.8364	+	5.47554i	2.00261	+	0.211539i
$671$	−3.57836	−	2.59983i	−0.138141	−	0.100365i
$672$	−1.08449	+	23.7121i	−0.0418350	+	0.914714i
$673$	4.07666	+	1.32459i	0.157144	+	0.0510591i	0.386532	−	0.922276i	$-0.373673\pi$
$673$	4.07666	+	1.32459i	0.157144	+	0.0510591i	−0.229389	+	0.973335i	$0.573673\pi$
$674$		−	46.6968i		−	1.79869i
$675$	25.9807	−	0.0410153i	0.999999	−	0.00157868i
$676$	19.6406			0.755410
$677$	−28.1020	−	9.13091i	−1.08005	−	0.350929i	−0.285656	−	0.958332i	$-0.592211\pi$
$677$	−28.1020	−	9.13091i	−1.08005	−	0.350929i	−0.794394	+	0.607403i	$0.792211\pi$
$678$	35.4556	−	10.2003i	1.36167	−	0.391739i
$679$	−25.0291	+	17.7421i	−0.960529	+	0.680881i
$680$	11.0853	+	9.99173i	0.425103	+	0.383165i
$681$	−1.70088	−	0.0579083i	−0.0651780	−	0.00221905i
$682$	4.39895			0.168445
$683$	−32.5229	+	23.6293i	−1.24445	+	0.904148i	−0.997887	−	0.0649775i	$-0.979302\pi$
$683$	−32.5229	+	23.6293i	−1.24445	+	0.904148i	−0.246567	+	0.969126i	$0.579302\pi$
$684$	−1.17664	−	1.87571i	−0.0449899	−	0.0717197i
$685$	−0.138176	+	1.30810i	−0.00527944	+	0.0499799i
$686$	8.83308	+	30.8169i	0.337249	+	1.17660i
$687$	13.8587	−	38.1801i	0.528741	−	1.45666i
$688$	16.1615	−	5.25118i	0.616150	−	0.200199i
$689$	4.43857	−	13.6605i	0.169096	−	0.520424i
$690$	−1.63218	−	1.57506i	−0.0621359	−	0.0599616i
$691$	42.9333	−	13.9499i	1.63326	−	0.530679i	0.658244	−	0.752805i	$-0.271300\pi$
$691$	42.9333	−	13.9499i	1.63326	−	0.530679i	0.975018	+	0.222126i	$0.0712997\pi$
$692$	0.460995	+	0.634506i	0.0175244	+	0.0241203i
$693$	2.30891	−	28.8953i	0.0877081	−	1.09764i
$694$	−8.08127	+	5.87139i	−0.306761	+	0.222875i
$695$	−5.17087	−	4.66075i	−0.196142	−	0.176792i
$696$	7.38374	+	25.6655i	0.279880	+	0.972849i
$697$	20.3461	−	28.0040i	0.770664	−	1.06073i
$698$	5.28312	+	1.71659i	0.199969	+	0.0649738i
$699$	−8.05621	+	10.3301i	−0.304714	+	0.390719i
$700$	12.8550	+	2.90371i	0.485874	+	0.109750i
$701$			25.5630i			0.965501i	0.875758	+	0.482751i	$0.160362\pi$
$701$			25.5630i			0.965501i	−0.875758	+	0.482751i	$0.839638\pi$
$702$	−34.3231	+	38.3211i	−1.29544	+	1.44634i
$703$	4.55454	+	3.30906i	0.171778	+	0.124804i
$704$	−2.21942	+	3.05477i	−0.0836474	+	0.115131i
$705$	−3.46278	+	3.58834i	−0.130416	+	0.135145i
$706$	−6.99988	−	9.63451i	−0.263444	−	0.362600i
$707$	1.11944	−	3.31321i	0.0421010	−	0.124606i
$708$	−0.521833	+	15.3273i	−0.0196117	+	0.576034i
$709$	1.18188	+	3.63747i	0.0443866	+	0.136608i	0.970794	−	0.239915i	$-0.0771196\pi$
$709$	1.18188	+	3.63747i	0.0443866	+	0.136608i	−0.926407	+	0.376523i	$0.877120\pi$
$710$	4.23398	+	19.9705i	0.158899	+	0.749480i
$711$	−37.2607	−	2.54010i	−1.39739	−	0.0952612i
$712$	−5.72345	−	17.6150i	−0.214495	−	0.660149i
$713$	−0.223914	+	0.0727541i	−0.00838564	+	0.00272466i
$714$	8.08189	+	29.3784i	0.302457	+	1.09946i
$715$	19.0203	−	42.6605i	0.711320	−	1.59541i
$716$	12.8566	−	4.17737i	0.480474	−	0.156116i
$717$	−5.97651	−	0.203476i	−0.223197	−	0.00759896i
$718$			11.2267i			0.418975i
$719$	37.7698	−	27.4413i	1.40857	−	1.02339i	0.415047	−	0.909800i	$-0.363765\pi$
$719$	37.7698	−	27.4413i	1.40857	−	1.02339i	0.993528	−	0.113589i	$-0.0362348\pi$
$720$	−14.7403	−	30.1283i	−0.549340	−	1.12282i
$721$	−15.0374	+	10.6594i	−0.560022	+	0.396977i
$722$	25.8385	+	18.7728i	0.961611	+	0.698651i
$723$	−11.5668	+	7.81660i	−0.430173	+	0.290703i
$724$			16.2450i			0.603742i
$725$	44.1334	−	4.59209i	1.63907	−	0.170546i
$726$	−4.30994	+	5.52641i	−0.159957	+	0.205104i
$727$	−15.6812	+	48.2617i	−0.581582	+	1.78993i	0.0310003	+	0.999519i	$0.490131\pi$
$727$	−15.6812	+	48.2617i	−0.581582	+	1.78993i	−0.612583	+	0.790407i	$0.709869\pi$
$728$	21.4506	−	15.2055i	0.795011	−	0.563552i
$729$	−2.96300	−	26.8369i	−0.109741	−	0.993960i
$730$	21.4823	+	37.2532i	0.795095	+	1.37880i
$731$	10.5617	−	7.67355i	0.390640	−	0.283816i
$732$	−1.64792	−	1.28518i	−0.0609089	−	0.0475016i
$733$	−36.0783	+	26.2125i	−1.33258	+	0.968179i	−0.332902	+	0.942961i	$0.608028\pi$
$733$	−36.0783	+	26.2125i	−1.33258	+	0.968179i	−0.999682	+	0.0252178i	$0.991972\pi$
$734$	−8.40599	−	25.8710i	−0.310271	−	0.954915i
$735$	−19.0639	−	19.2761i	−0.703181	−	0.711010i
$736$	−0.541562	+	1.66676i	−0.0199622	+	0.0614375i
$737$	15.1982	+	46.7753i	0.559833	+	1.72299i
$738$	−39.6410	+	24.8669i	−1.45921	+	0.915363i
$739$	10.0080	−	30.8014i	0.368150	−	1.13305i	−0.579835	−	0.814734i	$-0.696883\pi$
$739$	10.0080	−	30.8014i	0.368150	−	1.13305i	0.947985	−	0.318315i	$-0.103117\pi$
$740$	−12.5736	−	11.3332i	−0.462216	−	0.416618i
$741$	−2.50427	+	6.89918i	−0.0919967	+	0.253448i
$742$	3.42602	+	10.9785i	0.125773	+	0.403035i
$743$	2.86157			0.104981			0.0524904	−	0.998621i	$-0.483284\pi$
$743$	2.86157			0.104981			0.0524904	+	0.998621i	$0.483284\pi$
$744$	−2.09293	−	0.0712558i	−0.0767304	−	0.00261236i
$745$	4.51356	−	10.1234i	0.165364	−	0.370893i
$746$	−11.3116	+	15.5690i	−0.414145	+	0.570022i
$747$	49.2080	+	19.7814i	1.80043	+	0.723763i
$748$	4.31870	−	13.2916i	0.157907	−	0.485989i
$749$	6.54111	−	19.3597i	0.239007	−	0.707388i
$750$	−32.2278	+	9.21711i	−1.17679	+	0.336561i
$751$	47.0641			1.71739			0.858697	−	0.512484i	$-0.171275\pi$
$751$	47.0641			1.71739			0.858697	+	0.512484i	$0.171275\pi$
$752$	6.12267	+	1.98938i	0.223271	+	0.0725451i
$753$	−43.2316	+	12.4374i	−1.57545	+	0.453242i
$754$	−51.6434	+	71.0810i	−1.88074	+	2.58862i
$755$	−7.56013	−	3.37071i	−0.275141	−	0.122673i
$756$	1.55482	−	13.6074i	0.0565482	−	0.494895i
$757$		−	29.5049i		−	1.07237i	−0.844099	−	0.536187i	$-0.819864\pi$
$757$		−	29.5049i		−	1.07237i	0.844099	−	0.536187i	$-0.180136\pi$
$758$	13.0994	−	9.51727i	0.475791	−	0.345683i
$759$	0.730228	−	2.01175i	0.0265056	−	0.0730220i
$760$	−2.13804	−	1.92712i	−0.0775549	−	0.0699039i
$761$	−7.14013	+	21.9751i	−0.258830	+	0.796596i	0.734221	+	0.678910i	$0.237547\pi$
$761$	−7.14013	+	21.9751i	−0.258830	+	0.796596i	−0.993051	+	0.117686i	$0.962453\pi$
$762$	−18.5805	+	51.1885i	−0.673099	+	1.85437i
$763$	−10.5559	−	0.123202i	−0.382149	−	0.00446022i
$764$	−2.64092	−	0.858086i	−0.0955450	−	0.0310445i
$765$	−17.9226	−	18.5139i	−0.647992	−	0.669371i
$766$	−5.96529	+	1.93824i	−0.215535	+	0.0700314i
$767$	41.1270	−	29.8805i	1.48501	−	1.07892i
$768$	−20.1978	+	25.8986i	−0.728825	+	0.934535i
$769$	15.3165	+	21.0813i	0.552326	+	0.760211i	0.990325	−	0.138764i	$-0.0443130\pi$
$769$	15.3165	+	21.0813i	0.552326	+	0.760211i	−0.438000	+	0.898975i	$0.644313\pi$
$770$	7.32912	+	36.6738i	0.264123	+	1.32163i
$771$	−4.40483	−	15.3110i	−0.158636	−	0.551412i
$772$	−9.02106	+	12.4164i	−0.324675	+	0.446877i
$773$	−11.4715	−	3.72733i	−0.412603	−	0.134063i	0.0953578	−	0.995443i	$-0.469600\pi$
$773$	−11.4715	−	3.72733i	−0.412603	−	0.134063i	−0.507961	+	0.861380i	$0.669600\pi$
$774$	−17.1170	+	4.29954i	−0.615259	+	0.154544i
$775$	−0.726937	+	3.40252i	−0.0261123	+	0.122222i
$776$	−20.1476			−0.723256
$777$	9.23633	+	33.5749i	0.331352	+	1.20449i
$778$	2.37103	−	3.26345i	0.0850057	−	0.117000i
$779$	−3.92418	+	5.40117i	−0.140598	+	0.193517i
$780$	9.66734	−	19.8387i	0.346146	−	0.710340i
$781$	−15.5833	+	11.3220i	−0.557615	+	0.405131i
$782$			2.24963i			0.0804467i
$783$	−9.70549	−	45.0794i	−0.346846	−	1.61101i
$784$	−11.5895	+	33.0254i	−0.413911	+	1.17948i
$785$	18.4909	+	8.24425i	0.659970	+	0.294250i
$786$	10.8266	+	16.0208i	0.386171	+	0.571444i
$787$	13.6488	+	42.0068i	0.486529	+	1.49738i	0.829755	+	0.558128i	$0.188480\pi$
$787$	13.6488	+	42.0068i	0.486529	+	1.49738i	−0.343226	+	0.939253i	$0.611520\pi$
$788$	7.60071	+	23.3926i	0.270764	+	0.833326i
$789$	18.6975	+	27.6679i	0.665647	+	0.985005i
$790$	47.1370	−	9.99359i	1.67706	−	0.355556i
$791$	32.5555	+	0.379968i	1.15754	+	0.0135101i
$792$	12.2108	−	14.6040i	0.433890	−	0.518929i
$793$			6.92725i			0.245994i
$794$	−25.2592	+	18.3519i	−0.896415	+	0.651284i
$795$	−6.99866	−	6.75376i	−0.248217	−	0.239531i
$796$	2.62668	−	3.61531i	0.0931002	−	0.128141i
$797$	3.04549	−	4.19176i	0.107877	−	0.148480i	−0.751665	−	0.659545i	$-0.770749\pi$
$797$	3.04549	−	4.19176i	0.107877	−	0.148480i	0.859542	+	0.511065i	$0.170749\pi$
$798$	−1.55876	−	5.66625i	−0.0551796	−	0.200583i
$799$	4.94582			0.174971
$800$	17.3098	+	19.2648i	0.611993	+	0.681114i
$801$	7.79081	+	31.0163i	0.275275	+	1.09591i
$802$	−19.5733	−	6.35974i	−0.691156	−	0.224570i
$803$	−23.8499	+	32.8266i	−0.841646	+	1.15843i
$804$	6.42468	+	22.3319i	0.226581	+	0.787584i
$805$	−0.979611	−	1.74554i	−0.0345267	−	0.0615223i
$806$	−4.04951	−	5.57368i	−0.142638	−	0.196324i
$807$	0.615862	−	0.789689i	0.0216794	−	0.0277984i
$808$	1.85803	−	1.34994i	0.0653653	−	0.0474906i
$809$	−14.6113	+	4.74750i	−0.513706	+	0.166913i	−0.554387	−	0.832259i	$-0.687047\pi$
$809$	−14.6113	+	4.74750i	−0.513706	+	0.166913i	0.0406812	+	0.999172i	$0.487047\pi$
$810$	13.1454	+	32.2595i	0.461882	+	1.13348i
$811$	−29.6342	−	9.62873i	−1.04060	−	0.338110i	−0.261625	−	0.965170i	$-0.584258\pi$
$811$	−29.6342	−	9.62873i	−1.04060	−	0.338110i	−0.778972	+	0.627059i	$0.784258\pi$
$812$	0.272984	−	23.3892i	0.00957988	−	0.820799i
$813$	−1.85407	+	5.10790i	−0.0650252	+	0.179142i
$814$	14.8441	−	45.6856i	0.520287	−	1.60128i
$815$	−6.56837	−	0.693825i	−0.230080	−	0.0243036i
$816$	−11.3504	+	31.2698i	−0.397342	+	1.09466i
$817$	−2.03706	+	1.48001i	−0.0712675	+	0.0517789i
$818$		−	17.4524i		−	0.610209i
$819$	−38.7371	+	23.6744i	−1.35358	+	0.827251i
$820$	13.4400	−	14.9109i	0.469344	−	0.520713i
$821$	21.6858	−	29.8479i	0.756839	−	1.04170i	−0.240631	−	0.970617i	$-0.577354\pi$
$821$	21.6858	−	29.8479i	0.756839	−	1.04170i	0.997470	−	0.0710833i	$-0.0226456\pi$
$822$	−1.69491	+	0.487610i	−0.0591167	+	0.0170074i
$823$	−21.4369	−	6.96526i	−0.747242	−	0.242794i	−0.0894480	−	0.995991i	$-0.528510\pi$
$823$	−21.4369	−	6.96526i	−0.747242	−	0.242794i	−0.657794	+	0.753198i	$0.728510\pi$
$824$	−12.1046			−0.421683
$825$	−20.3259	−	24.2317i	−0.707656	−	0.843641i
$826$	−13.0290	+	38.5620i	−0.453338	+	1.34174i
$827$	−11.0775	+	34.0931i	−0.385204	+	1.18553i	0.551129	+	0.834420i	$0.314197\pi$
$827$	−11.0775	+	34.0931i	−0.385204	+	1.18553i	−0.936332	+	0.351115i	$0.885803\pi$
$828$	0.377160	−	0.938220i	0.0131072	−	0.0326054i
$829$	25.8242	−	35.5440i	0.896912	−	1.23449i	−0.0745301	−	0.997219i	$-0.523746\pi$
$829$	25.8242	−	35.5440i	0.896912	−	1.23449i	0.971442	−	0.237275i	$-0.0762543\pi$
$830$	−68.0465	−	7.18784i	−2.36193	−	0.249494i
$831$	−19.1264	−	0.651176i	−0.663486	−	0.0225891i
$832$	5.91364			0.205019
$833$	−0.627573	+	26.8814i	−0.0217441	+	0.931385i
$834$	3.18467	−	8.77366i	0.110276	−	0.303807i
$835$	−7.08706	−	33.4277i	−0.245258	−	1.15681i
$836$	−0.832953	+	2.56357i	−0.0288083	+	0.0886628i
$837$	3.59698	+	0.368528i	0.124330	+	0.0127382i
$838$	−4.63183	−	14.2553i	−0.160004	−	0.492442i
$839$	5.49167	−	16.9016i	0.189593	−	0.583509i	−0.810404	−	0.585872i	$-0.800752\pi$
$839$	5.49167	−	16.9016i	0.189593	−	0.583509i	0.999997	+	0.00236320i	$0.000752229\pi$
$840$	−2.89298	−	17.5673i	−0.0998172	−	0.606130i
$841$	−15.3747	−	47.3185i	−0.530163	−	1.63167i
$842$	−38.1687	+	27.7311i	−1.31538	+	0.955679i
$843$	42.0842	+	32.8206i	1.44946	+	1.13040i
$844$	−8.53831	+	6.20345i	−0.293901	+	0.213531i
$845$	−43.1254	+	9.14310i	−1.48356	+	0.314532i
$846$	−6.20364	−	2.49383i	−0.213286	−	0.0857397i
$847$	−5.04558	+	3.57661i	−0.173368	+	0.122894i
$848$	−3.88006	+	11.9416i	−0.133242	+	0.410076i
$849$	−20.2959	+	26.0245i	−0.696555	+	0.893157i
$850$	28.7739	+	16.6526i	0.986937	+	0.571181i
$851$			2.57098i			0.0881320i
$852$	−7.54055	+	5.09575i	−0.258335	+	0.174578i
$853$	−18.0027	−	13.0797i	−0.616399	−	0.447840i	0.235263	−	0.971932i	$-0.424405\pi$
$853$	−18.0027	−	13.0797i	−0.616399	−	0.447840i	−0.851662	+	0.524092i	$0.824405\pi$
$854$	−3.20760	−	4.52501i	−0.109762	−	0.154843i
$855$	3.45675	+	3.57080i	0.118218	+	0.122119i
$856$	10.8568	−	7.88793i	0.371078	−	0.269604i
$857$		−	24.8740i		−	0.849678i	−0.905269	−	0.424839i	$-0.860331\pi$
$857$		−	24.8740i		−	0.849678i	0.905269	−	0.424839i	$-0.139669\pi$
$858$	62.5905	+	2.13096i	2.13680	+	0.0727497i
$859$	−30.7282	+	9.98418i	−1.04843	+	0.340656i	−0.782053	−	0.623213i	$-0.785827\pi$
$859$	−30.7282	+	9.98418i	−1.04843	+	0.340656i	−0.266379	+	0.963868i	$0.585827\pi$
$860$	6.55861	−	3.78206i	0.223647	−	0.128967i
$861$	−39.8161	+	10.9533i	−1.35693	+	0.373286i
$862$	52.5632	−	17.0788i	1.79031	−	0.581707i
$863$	−3.06880	−	9.44481i	−0.104463	−	0.321505i	0.885141	−	0.465323i	$-0.154062\pi$
$863$	−3.06880	−	9.44481i	−0.104463	−	0.321505i	−0.989604	+	0.143818i	$0.954062\pi$
$864$	17.9572	−	20.0490i	0.610917	−	0.682079i
$865$	−1.30759	−	1.17860i	−0.0444595	−	0.0400735i
$866$	−10.3211	−	31.7651i	−0.350726	−	1.07942i
$867$	0.132299	−	3.88590i	0.00449312	−	0.131972i
$868$	1.73764	+	0.587099i	0.0589792	+	0.0199275i
$869$	26.7235	+	36.7818i	0.906534	+	1.24774i
$870$	27.9490	+	52.5197i	0.947559	+	1.78058i
$871$	45.2755	−	62.3164i	1.53410	−	2.11151i
$872$	−5.60861	−	4.07489i	−0.189931	−	0.137993i
$873$	34.7069	+	2.36600i	1.17465	+	0.0800771i
$874$		−	0.433889i		−	0.0146765i
$875$	−29.5778	−	0.391473i	−0.999912	−	0.0132342i
$876$	−11.7898	+	15.1175i	−0.398340	+	0.510772i
$877$	−9.95225	−	3.23368i	−0.336064	−	0.109194i	0.136124	−	0.990692i	$-0.456535\pi$
$877$	−9.95225	−	3.23368i	−0.336064	−	0.109194i	−0.472188	+	0.881498i	$0.656535\pi$
$878$	22.6252	−	31.1409i	0.763564	−	1.05096i
$879$	9.09821	+	31.6249i	0.306875	+	1.06668i
$880$	−16.6270	+	37.2925i	−0.560496	+	1.25713i
$881$	32.6611	−	23.7297i	1.10038	−	0.799474i	0.119260	−	0.992863i	$-0.461948\pi$
$881$	32.6611	−	23.7297i	1.10038	−	0.799474i	0.981122	+	0.193389i	$0.0619479\pi$
$882$	14.3416	−	33.4014i	0.482907	−	1.12469i
$883$	−19.9088	−	27.4021i	−0.669984	−	0.922154i	0.329776	−	0.944059i	$-0.393027\pi$
$883$	−19.9088	−	27.4021i	−0.669984	−	0.922154i	−0.999760	+	0.0219053i	$0.993027\pi$
$884$	−20.8167	+	6.76375i	−0.700141	+	0.227490i
$885$	−5.98934	−	33.8974i	−0.201330	−	1.13945i
$886$	−11.5934	+	35.6807i	−0.389487	+	1.19872i
$887$	15.2616	−	4.95879i	0.512434	−	0.166500i	−0.0413748	−	0.999144i	$-0.513174\pi$
$887$	15.2616	−	4.95879i	0.512434	−	0.166500i	0.553809	+	0.832644i	$0.313174\pi$
$888$	−7.80255	+	21.4957i	−0.261836	+	0.721350i
$889$	−28.6986	+	38.5460i	−0.962519	+	1.29279i
$890$	−20.6112	−	35.7427i	−0.690891	−	1.19810i
$891$	−22.7497	+	23.7233i	−0.762143	+	0.794762i
$892$	−3.08599	+	2.24210i	−0.103326	+	0.0750710i
$893$	−0.953907			−0.0319213
$894$	14.8528	+	0.505680i	0.496753	+	0.0169125i
$895$	−26.2849	+	15.1573i	−0.878608	+	0.506654i
$896$	−26.2238	+	18.5890i	−0.876074	+	0.621014i
$897$	−3.22120	+	0.926712i	−0.107553	+	0.0309420i
$898$	35.4439	+	11.5164i	1.18278	+	0.384308i
$899$	6.17531			0.205958
$900$	−9.20841	−	11.7691i	−0.306947	−	0.392304i
$901$			9.64628i			0.321364i
$902$	54.1780	+	17.6035i	1.80393	+	0.586133i
$903$	−15.5583	−	0.711567i	−0.517747	−	0.0236795i
$904$	17.2975	+	12.5674i	0.575306	+	0.417985i
$905$	−7.56238	−	35.6696i	−0.251382	−	1.18570i
$906$	0.377640	−	11.0921i	0.0125463	−	0.368509i
$907$			50.0182i			1.66083i	0.557147	+	0.830414i	$0.311896\pi$
$907$			50.0182i			1.66083i	−0.557147	+	0.830414i	$0.688104\pi$
$908$	0.575366	+	0.791923i	0.0190942	+	0.0262809i
$909$	−3.35923	+	2.10725i	−0.111419	+	0.0698932i
$910$	39.7205	−	43.0469i	1.31672	−	1.42699i
$911$	−30.4761	−	9.90229i	−1.00972	−	0.328078i	−0.242976	−	0.970032i	$-0.578124\pi$
$911$	−30.4761	−	9.90229i	−1.00972	−	0.328078i	−0.766743	+	0.641955i	$0.778124\pi$
$912$	2.18916	−	6.03105i	0.0724902	−	0.199708i
$913$	−19.9510	−	61.4027i	−0.660280	−	2.03213i
$914$	16.6664	+	5.41524i	0.551275	+	0.179120i
$915$	4.21665	+	2.05476i	0.139398	+	0.0679283i
$916$	−22.2187	+	7.21930i	−0.734127	+	0.238532i
$917$	5.08316	+	16.2888i	0.167861	+	0.537903i
$918$	13.9698	−	31.5993i	0.461071	−	1.04293i
$919$	−3.64709	+	2.64977i	−0.120306	+	0.0874078i	−0.646311	−	0.763074i	$-0.723689\pi$
$919$	−3.64709	+	2.64977i	−0.120306	+	0.0874078i	0.526005	+	0.850481i	$0.323689\pi$
$920$	0.138083	−	1.30722i	0.00455247	−	0.0430978i
$921$	−2.40163	+	0.690928i	−0.0791364	+	0.0227668i
$922$	−14.1981	−	10.3156i	−0.467591	−	0.339725i
$923$	28.6909	+	9.32223i	0.944371	+	0.306845i
$924$	−13.9222	+	9.17352i	−0.458008	+	0.301787i
$925$	32.8841	+	19.0314i	1.08122	+	0.625747i
$926$		−	69.6072i		−	2.28744i
$927$	20.8518	+	1.42149i	0.684862	+	0.0466877i
$928$	27.0189	−	37.1884i	0.886940	−	1.22077i
$929$	−11.2061	−	8.14172i	−0.367661	−	0.267121i	0.388580	−	0.921415i	$-0.372966\pi$
$929$	−11.2061	−	8.14172i	−0.367661	−	0.267121i	−0.756240	+	0.654294i	$0.772966\pi$
$930$	−4.59389	+	0.811697i	−0.150640	+	0.0266166i
$931$	0.121041	−	5.18465i	0.00396695	−	0.169920i
$932$	7.53484			0.246812
$933$	−0.121867	+	3.57948i	−0.00398975	+	0.117187i
$934$	58.0126	−	18.8494i	1.89823	−	0.616773i
$935$	−3.29518	+	31.1951i	−0.107764	+	1.02019i
$936$	−29.7447	−	2.02772i	−0.972235	−	0.0662783i
$937$	−16.5690	−	50.9941i	−0.541285	−	1.66590i	−0.729663	−	0.683807i	$-0.760323\pi$
$937$	−16.5690	−	50.9941i	−0.541285	−	1.66590i	0.188378	−	0.982097i	$-0.439677\pi$
$938$	−0.719783	+	61.6707i	−0.0235018	+	2.01362i
$939$	28.6214	+	42.3531i	0.934024	+	1.38214i
$940$	2.85234	+	0.301296i	0.0930331	+	0.00982721i
$941$	−11.2970	−	34.7684i	−0.368270	−	1.13342i	−0.947908	−	0.318545i	$-0.896806\pi$
$941$	−11.2970	−	34.7684i	−0.368270	−	1.13342i	0.579638	−	0.814874i	$-0.303194\pi$
$942$	−0.923650	+	27.1295i	−0.0300942	+	0.883926i
$943$	−3.04889			−0.0992856
$944$	−35.9519	+	26.1206i	−1.17014	+	0.850154i
$945$	2.92054	+	30.6018i	0.0950053	+	0.995477i
$946$	17.3816	+	12.6285i	0.565124	+	0.410587i
$947$	12.4088	+	9.01555i	0.403233	+	0.292966i	0.770857	−	0.637009i	$-0.219829\pi$
$947$	12.4088	+	9.01555i	0.403233	+	0.292966i	−0.367624	+	0.929975i	$0.619829\pi$
$948$	12.0277	+	17.7982i	0.390640	+	0.578057i
$949$	63.5482			2.06286
$950$	−5.54966	−	3.21182i	−0.180055	−	0.104205i
$951$	−37.2513	+	47.7655i	−1.20796	+	1.54890i
$952$	−10.5452	+	14.1636i	−0.341770	+	0.459043i
$953$	20.9529	+	15.2232i	0.678732	+	0.493128i	0.872937	−	0.487833i	$-0.162213\pi$
$953$	20.9529	+	15.2232i	0.678732	+	0.493128i	−0.194205	+	0.980961i	$0.562213\pi$
$954$	4.86395	−	12.0995i	0.157476	−	0.391736i
$955$	6.19818	+	0.654721i	0.200568	+	0.0211863i
$956$	2.02170	+	2.78263i	0.0653865	+	0.0899968i
$957$	−34.5216	+	44.2652i	−1.11592	+	1.43089i
$958$	−32.5486	+	23.6479i	−1.05160	+	0.764030i
$959$	−1.55627	−	0.0181638i	−0.0502545	−	0.000586541i
$960$	1.75410	−	3.59967i	0.0566134	−	0.116179i
$961$	9.42989	−	29.0222i	0.304190	−	0.936201i
$962$	−71.5507	+	23.2482i	−2.30689	+	0.749553i
$963$	−19.6286	+	12.3131i	−0.632523	+	0.396783i
$964$	7.63660	+	2.48128i	0.245958	+	0.0799167i
$965$	14.0277	−	31.4625i	0.451566	−	1.01281i
$966$	1.67505	−	2.09689i	0.0538937	−	0.0674665i
$967$	−11.0652	−	15.2300i	−0.355834	−	0.489764i	0.593148	−	0.805094i	$-0.297885\pi$
$967$	−11.0652	−	15.2300i	−0.355834	−	0.489764i	−0.948982	+	0.315330i	$0.897885\pi$
$968$	−4.06152			−0.130542
$969$	0.167721	−	4.92630i	0.00538797	−	0.158256i
$970$	−43.9063	+	9.30864i	−1.40974	+	0.298883i
$971$	34.4636	+	25.0393i	1.10599	+	0.803548i	0.982027	−	0.188739i	$-0.0604400\pi$
$971$	34.4636	+	25.0393i	1.10599	+	0.803548i	0.123962	+	0.992287i	$0.460440\pi$
$972$	−11.1239	+	10.8365i	−0.356799	+	0.347582i
$973$	4.91890	−	6.60674i	0.157693	−	0.211803i
$974$		−	37.4312i		−	1.19937i
$975$	−11.9915	+	48.0606i	−0.384035	+	1.53917i
$976$		−	6.05559i		−	0.193835i
$977$	11.1514	−	34.3205i	0.356765	−	1.09801i	−0.598214	−	0.801336i	$-0.704123\pi$
$977$	11.1514	−	34.3205i	0.356765	−	1.09801i	0.954979	−	0.296674i	$-0.0958773\pi$
$978$	−2.44844	−	8.51065i	−0.0782925	−	0.272141i
$979$	22.8829	−	31.4956i	0.731341	−	1.00660i
$980$	−1.99953	+	15.4648i	−0.0638727	+	0.494003i
$981$	9.18305	+	7.67819i	0.293192	+	0.245146i
$982$		−	6.76079i		−	0.215745i
$983$	−11.2869	−	15.5350i	−0.359995	−	0.495490i	0.590153	−	0.807292i	$-0.299068\pi$
$983$	−11.2869	−	15.5350i	−0.359995	−	0.495490i	−0.950147	+	0.311802i	$0.899068\pi$
$984$	−25.4916	−	9.25295i	−0.812641	−	0.294973i
$985$	−27.5787	−	47.8253i	−0.878732	−	1.52384i
$986$	18.2338	−	56.1179i	0.580683	−	1.78716i
$987$	−4.61003	−	3.68259i	−0.146739	−	0.117218i
$988$	4.01494	−	1.30453i	0.127732	−	0.0415028i
$989$	−1.09361	−	0.355336i	−0.0347748	−	0.0112990i
$990$	19.8627	−	37.4671i	0.631279	−	1.19078i
$991$	−12.0358	−	37.0424i	−0.382330	−	1.17669i	−0.938399	−	0.345554i	$-0.887691\pi$
$991$	−12.0358	−	37.0424i	−0.382330	−	1.17669i	0.556069	−	0.831136i	$-0.312309\pi$
$992$	2.11863	+	2.91605i	0.0672667	+	0.0925847i
$993$	14.1366	−	18.1267i	0.448612	−	0.575232i
$994$	−23.0580	+	7.19559i	−0.731355	+	0.228230i
$995$	−4.08446	+	9.16100i	−0.129486	+	0.290423i
$996$	−8.43379	−	29.3154i	−0.267235	−	0.928895i
$997$	33.5966	+	24.4094i	1.06402	+	0.773053i	0.974827	−	0.222961i	$-0.0715724\pi$
$997$	33.5966	+	24.4094i	1.06402	+	0.773053i	0.0891892	+	0.996015i	$0.471572\pi$
$998$	11.8844	−	36.5764i	0.376194	−	1.15781i
$999$	15.9653	−	36.1130i	0.505118	−	1.14257i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.w.a.104.18	yes	304
3.2	odd	2	inner	525.2.w.a.104.60	yes	304
7.6	odd	2	inner	525.2.w.a.104.17	✓	304
21.20	even	2	inner	525.2.w.a.104.59	yes	304
25.19	even	10	inner	525.2.w.a.419.59	yes	304
75.44	odd	10	inner	525.2.w.a.419.17	yes	304
175.69	odd	10	inner	525.2.w.a.419.60	yes	304
525.419	even	10	inner	525.2.w.a.419.18	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.w.a.104.17	✓	304	7.6	odd	2	inner
525.2.w.a.104.18	yes	304	1.1	even	1	trivial
525.2.w.a.104.59	yes	304	21.20	even	2	inner
525.2.w.a.104.60	yes	304	3.2	odd	2	inner
525.2.w.a.419.17	yes	304	75.44	odd	10	inner
525.2.w.a.419.18	yes	304	525.419	even	10	inner
525.2.w.a.419.59	yes	304	25.19	even	10	inner
525.2.w.a.419.60	yes	304	175.69	odd	10	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.534897 + 1.64624i) q^{2} +(1.66454 - 0.478872i) q^{3} +(-0.805968 - 0.585570i) q^{4} +(2.04228 + 0.910555i) q^{5} +(-0.102015 + 2.99638i) q^{6} +(-0.846893 + 2.50655i) q^{7} +(-1.40566 + 1.02127i) q^{8} +(2.54136 - 1.59420i) q^{9} +O(q^{10})\)	\(q+(-0.534897 + 1.64624i) q^{2} +(1.66454 - 0.478872i) q^{3} +(-0.805968 - 0.585570i) q^{4} +(2.04228 + 0.910555i) q^{5} +(-0.102015 + 2.99638i) q^{6} +(-0.846893 + 2.50655i) q^{7} +(-1.40566 + 1.02127i) q^{8} +(2.54136 - 1.59420i) q^{9} +(-2.59140 + 2.87503i) q^{10} +(-3.47332 - 1.12855i) q^{11} +(-1.62198 - 0.588747i) q^{12} +(1.76748 + 5.43976i) q^{13} +(-3.67338 - 2.73493i) q^{14} +(3.83548 + 0.537663i) q^{15} +(-1.54508 - 4.75527i) q^{16} +(-2.25783 - 3.10763i) q^{17} +(1.26508 + 5.03643i) q^{18} +(0.435470 + 0.599373i) q^{19} +(-1.11281 - 1.92977i) q^{20} +(-0.209368 + 4.57779i) q^{21} +(3.71574 - 5.11427i) q^{22} +(-0.104552 + 0.321779i) q^{23} +(-1.85071 + 2.37307i) q^{24} +(3.34178 + 3.71921i) q^{25} -9.90058 q^{26} +(3.46677 - 3.87059i) q^{27} +(2.15033 - 1.52428i) q^{28} +(5.21620 - 7.17948i) q^{29} +(-2.93671 + 6.02654i) q^{30} +(0.409018 + 0.562964i) q^{31} +5.17981 q^{32} +(-6.32190 - 0.215235i) q^{33} +(6.32363 - 2.05467i) q^{34} +(-4.01194 + 4.34791i) q^{35} +(-2.98177 - 0.203271i) q^{36} +(7.22692 - 2.34817i) q^{37} +(-1.21965 + 0.396287i) q^{38} +(5.54699 + 8.20827i) q^{39} +(-3.80066 + 0.805785i) q^{40} +(2.78467 + 8.57032i) q^{41} +(-7.42417 - 2.79332i) q^{42} +3.39864i q^{43} +(2.13854 + 2.94345i) q^{44} +(6.64177 - 0.941746i) q^{45} +(-0.473802 - 0.344237i) q^{46} +(-0.756806 + 1.04165i) q^{47} +(-4.84901 - 7.17542i) q^{48} +(-5.56555 - 4.24555i) q^{49} +(-7.91023 + 3.51198i) q^{50} +(-5.24640 - 4.09156i) q^{51} +(1.76082 - 5.41925i) q^{52} +(-2.03163 - 1.47607i) q^{53} +(4.51757 + 7.77752i) q^{54} +(-6.06587 - 5.46746i) q^{55} +(-1.36942 - 4.38825i) q^{56} +(1.01188 + 0.789144i) q^{57} +(9.02904 + 12.4274i) q^{58} +(-2.74649 - 8.45283i) q^{59} +(-2.77644 - 2.67928i) q^{60} +(1.15184 + 0.374257i) q^{61} +(-1.14556 + 0.372214i) q^{62} +(1.84368 + 7.72016i) q^{63} +(0.319495 - 0.983304i) q^{64} +(-1.34351 + 12.7189i) q^{65} +(3.73589 - 10.2923i) q^{66} +(-7.91572 - 10.8950i) q^{67} +3.82677i q^{68} +(-0.0199401 + 0.585680i) q^{69} +(-5.01175 - 8.93031i) q^{70} +(3.10015 - 4.26699i) q^{71} +(-1.94417 + 4.83631i) q^{72} +(3.43330 - 10.5666i) q^{73} +13.1533i q^{74} +(7.34354 + 4.59047i) q^{75} -0.738074i q^{76} +(5.77029 - 7.75028i) q^{77} +(-16.4799 + 4.74112i) q^{78} +(-10.0715 - 7.31737i) q^{79} +(1.17446 - 11.1185i) q^{80} +(3.91705 - 8.10289i) q^{81} -15.5983 q^{82} +(10.3911 + 14.3021i) q^{83} +(2.84936 - 3.56695i) q^{84} +(-1.78143 - 8.40252i) q^{85} +(-5.59499 - 1.81792i) q^{86} +(5.24450 - 14.4484i) q^{87} +(6.03485 - 1.96084i) q^{88} +(-3.29410 + 10.1382i) q^{89} +(-2.00232 + 11.4377i) q^{90} +(-15.1319 - 0.176610i) q^{91} +(0.272690 - 0.198121i) q^{92} +(0.950413 + 0.741207i) q^{93} +(-1.31000 - 1.80306i) q^{94} +(0.343588 + 1.62061i) q^{95} +(8.62199 - 2.48047i) q^{96} +(9.38121 + 6.81585i) q^{97} +(9.96620 - 6.89131i) q^{98} +(-10.6261 + 2.66912i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q - 84 q^{4} - 6 q^{9}+O(q^{10}) \) 304 * q - 84 * q^4 - 6 * q^9	\( 304 q - 84 q^{4} - 6 q^{9} - 36 q^{15} - 60 q^{16} - 18 q^{21} - 40 q^{22} - 8 q^{25} + 60 q^{28} + 14 q^{30} + 28 q^{36} - 20 q^{37} - 2 q^{39} - 35 q^{42} - 24 q^{46} - 20 q^{49} - 52 q^{51} - 80 q^{58} + 4 q^{60} + 55 q^{63} - 76 q^{64} - 20 q^{67} + 6 q^{70} + 30 q^{72} - 40 q^{78} - 68 q^{79} - 10 q^{81} + 80 q^{84} - 88 q^{85} - 20 q^{88} - 82 q^{91} - 36 q^{99}+O(q^{100}) \) 304 * q - 84 * q^4 - 6 * q^9 - 36 * q^15 - 60 * q^16 - 18 * q^21 - 40 * q^22 - 8 * q^25 + 60 * q^28 + 14 * q^30 + 28 * q^36 - 20 * q^37 - 2 * q^39 - 35 * q^42 - 24 * q^46 - 20 * q^49 - 52 * q^51 - 80 * q^58 + 4 * q^60 + 55 * q^63 - 76 * q^64 - 20 * q^67 + 6 * q^70 + 30 * q^72 - 40 * q^78 - 68 * q^79 - 10 * q^81 + 80 * q^84 - 88 * q^85 - 20 * q^88 - 82 * q^91 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more