LMFDB - Embedded newform 555.2.bm.a.14.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(14,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 11]))

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

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

chi := DirichletCharacter("555.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.bm (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$72$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			14.12
Character	$\chi$	$=$	555.14
Dual form			555.2.bm.a.119.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.03267 + 0.544653i) q^{2} +(1.70701 - 0.293434i) q^{3} +(2.10306 - 1.21420i) q^{4} +(2.18710 + 0.465380i) q^{5} +(-3.30998 + 1.52619i) q^{6} +(-3.21898 + 1.85848i) q^{7} +(-0.637478 + 0.637478i) q^{8} +(2.82779 - 1.00179i) q^{9} +O(q^{10})$	\(q+(-2.03267 + 0.544653i) q^{2} +(1.70701 - 0.293434i) q^{3} +(2.10306 - 1.21420i) q^{4} +(2.18710 + 0.465380i) q^{5} +(-3.30998 + 1.52619i) q^{6} +(-3.21898 + 1.85848i) q^{7} +(-0.637478 + 0.637478i) q^{8} +(2.82779 - 1.00179i) q^{9} +(-4.69914 + 0.245246i) q^{10} -0.842372 q^{11} +(3.23367 - 2.68977i) q^{12} +(-1.80930 + 6.75239i) q^{13} +(5.53090 - 5.53090i) q^{14} +(3.86997 + 0.152640i) q^{15} +(-1.47983 + 2.56313i) q^{16} +(0.861531 + 3.21528i) q^{17} +(-5.20235 + 3.57648i) q^{18} +(-3.80441 - 1.01939i) q^{19} +(5.16468 - 1.67686i) q^{20} +(-4.94950 + 4.11700i) q^{21} +(1.71227 - 0.458800i) q^{22} +(-3.42164 + 3.42164i) q^{23} +(-0.901127 + 1.27524i) q^{24} +(4.56684 + 2.03567i) q^{25} -14.7108i q^{26} +(4.53312 - 2.53984i) q^{27} +(-4.51314 + 7.81698i) q^{28} +(4.61569 - 4.61569i) q^{29} +(-7.94953 + 1.79753i) q^{30} +(2.37322 + 2.37322i) q^{31} +(2.07865 - 7.75763i) q^{32} +(-1.43794 + 0.247181i) q^{33} +(-3.50242 - 6.06637i) q^{34} +(-7.90513 + 2.56663i) q^{35} +(4.73064 - 5.54035i) q^{36} +(5.69629 - 2.13360i) q^{37} +8.28833 q^{38} +(-1.10711 + 12.0573i) q^{39} +(-1.69090 + 1.09756i) q^{40} +(2.90888 + 5.03832i) q^{41} +(7.81837 - 11.0643i) q^{42} +(-1.86227 - 1.86227i) q^{43} +(-1.77156 + 1.02281i) q^{44} +(6.65089 - 0.875024i) q^{45} +(5.09147 - 8.81868i) q^{46} -0.845254 q^{47} +(-1.77397 + 4.80954i) q^{48} +(3.40787 - 5.90260i) q^{49} +(-10.3916 - 1.65051i) q^{50} +(2.41412 + 5.23572i) q^{51} +(4.39371 + 16.3975i) q^{52} +(2.46608 - 4.27138i) q^{53} +(-7.83102 + 7.63165i) q^{54} +(-1.84235 - 0.392023i) q^{55} +(0.867289 - 3.23677i) q^{56} +(-6.79330 - 0.623766i) q^{57} +(-6.86824 + 11.8961i) q^{58} +(0.648455 - 0.173753i) q^{59} +(8.32413 - 4.37792i) q^{60} +(-2.58029 + 9.62977i) q^{61} +(-6.11656 - 3.53140i) q^{62} +(-7.24079 + 8.48013i) q^{63} +10.9816i q^{64} +(-7.09955 + 13.9262i) q^{65} +(2.78824 - 1.28562i) q^{66} +(-1.09340 - 1.89382i) q^{67} +(5.71585 + 5.71585i) q^{68} +(-4.83676 + 6.84481i) q^{69} +(14.6706 - 9.52268i) q^{70} +(-8.09195 + 4.67189i) q^{71} +(-1.16404 + 2.44128i) q^{72} -11.6345 q^{73} +(-10.4166 + 7.43942i) q^{74} +(8.39300 + 2.13485i) q^{75} +(-9.23865 + 2.47549i) q^{76} +(2.71157 - 1.56553i) q^{77} +(-4.31666 - 25.1116i) q^{78} +(15.3576 + 4.11506i) q^{79} +(-4.42937 + 4.91716i) q^{80} +(6.99282 - 5.66572i) q^{81} +(-8.65693 - 8.65693i) q^{82} +(1.51988 - 2.63251i) q^{83} +(-5.41022 + 14.6680i) q^{84} +(0.387930 + 7.43308i) q^{85} +(4.79969 + 2.77110i) q^{86} +(6.52464 - 9.23344i) q^{87} +(0.536994 - 0.536994i) q^{88} +(-3.08875 - 11.5274i) q^{89} +(-13.0425 + 5.40107i) q^{90} +(-6.72507 - 25.0983i) q^{91} +(-3.04135 + 11.3505i) q^{92} +(4.74750 + 3.35473i) q^{93} +(1.71812 - 0.460370i) q^{94} +(-7.84623 - 4.00000i) q^{95} +(1.27193 - 13.8523i) q^{96} +(11.8508 + 11.8508i) q^{97} +(-3.71221 + 13.8542i) q^{98} +(-2.38205 + 0.843882i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 24 q^{4} - 16 q^{6}+O(q^{10}) $ 288 * q - 24 * q^4 - 16 * q^6	$ 288 q - 24 q^{4} - 16 q^{6} - 16 q^{10} - 6 q^{15} + 112 q^{16} - 8 q^{19} - 12 q^{21} + 44 q^{24} - 12 q^{25} - 30 q^{30} - 72 q^{31} - 32 q^{34} - 4 q^{39} + 12 q^{40} + 16 q^{46} + 80 q^{49} + 12 q^{51} - 52 q^{54} - 28 q^{55} - 92 q^{60} - 8 q^{61} + 100 q^{66} - 104 q^{69} + 16 q^{70} + 52 q^{75} - 24 q^{76} + 16 q^{79} - 8 q^{81} - 192 q^{84} - 52 q^{90} - 168 q^{91} - 72 q^{94} - 112 q^{96} - 60 q^{99}+O(q^{100}) $ 288 * q - 24 * q^4 - 16 * q^6 - 16 * q^10 - 6 * q^15 + 112 * q^16 - 8 * q^19 - 12 * q^21 + 44 * q^24 - 12 * q^25 - 30 * q^30 - 72 * q^31 - 32 * q^34 - 4 * q^39 + 12 * q^40 + 16 * q^46 + 80 * q^49 + 12 * q^51 - 52 * q^54 - 28 * q^55 - 92 * q^60 - 8 * q^61 + 100 * q^66 - 104 * q^69 + 16 * q^70 + 52 * q^75 - 24 * q^76 + 16 * q^79 - 8 * q^81 - 192 * q^84 - 52 * q^90 - 168 * q^91 - 72 * q^94 - 112 * q^96 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$-1$	$-1$

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 $

$2$	−2.03267	+	0.544653i	−1.43732	+	0.385128i	−0.891593	−	0.452837i	$-0.850412\pi$
$2$	−2.03267	+	0.544653i	−1.43732	+	0.385128i	−0.545724	+	0.837965i	$0.683745\pi$
$3$	1.70701	−	0.293434i	0.985545	−	0.169414i
$3$	1.70701	−	0.293434i	0.985545	−	0.169414i
$4$	2.10306	−	1.21420i	1.05153	−	0.607102i
$5$	2.18710	+	0.465380i	0.978102	+	0.208124i
$5$	2.18710	+	0.465380i	0.978102	+	0.208124i
$6$	−3.30998	+	1.52619i	−1.35129	+	0.623063i
$7$	−3.21898	+	1.85848i	−1.21666	+	0.702438i	−0.964202	−	0.265170i	$-0.914572\pi$
$7$	−3.21898	+	1.85848i	−1.21666	+	0.702438i	−0.252457	+	0.967608i	$0.581239\pi$
$8$	−0.637478	+	0.637478i	−0.225383	+	0.225383i
$9$	2.82779	−	1.00179i	0.942598	−	0.333931i
$10$	−4.69914	+	0.245246i	−1.48600	+	0.0775537i
$11$	−0.842372			−0.253985			−0.126992	−	0.991904i	$-0.540532\pi$
$11$	−0.842372			−0.253985			−0.126992	+	0.991904i	$0.540532\pi$
$12$	3.23367	−	2.68977i	0.933479	−	0.776470i
$13$	−1.80930	+	6.75239i	−0.501809	+	1.87277i	−0.0138574	+	0.999904i	$0.504411\pi$
$13$	−1.80930	+	6.75239i	−0.501809	+	1.87277i	−0.487951	+	0.872871i	$0.662256\pi$
$14$	5.53090	−	5.53090i	1.47820	−	1.47820i
$15$	3.86997	+	0.152640i	0.999223	+	0.0394115i
$16$	−1.47983	+	2.56313i	−0.369957	+	0.640784i
$17$	0.861531	+	3.21528i	0.208952	+	0.779819i	0.988209	+	0.153114i	$0.0489302\pi$
$17$	0.861531	+	3.21528i	0.208952	+	0.779819i	−0.779257	+	0.626705i	$0.784403\pi$
$18$	−5.20235	+	3.57648i	−1.22621	+	0.842985i
$19$	−3.80441	−	1.01939i	−0.872791	−	0.233864i	−0.205497	−	0.978658i	$-0.565881\pi$
$19$	−3.80441	−	1.01939i	−0.872791	−	0.233864i	−0.667294	+	0.744794i	$0.732548\pi$
$20$	5.16468	−	1.67686i	1.15486	−	0.374958i
$21$	−4.94950	+	4.11700i	−1.08007	+	0.898404i
$22$	1.71227	−	0.458800i	0.365056	−	0.0978166i
$23$	−3.42164	+	3.42164i	−0.713461	+	0.713461i	−0.967258	−	0.253796i	$-0.918321\pi$
$23$	−3.42164	+	3.42164i	−0.713461	+	0.713461i	0.253796	+	0.967258i	$0.418321\pi$
$24$	−0.901127	+	1.27524i	−0.183942	+	0.260308i
$25$	4.56684	+	2.03567i	0.913368	+	0.407134i
$26$		−	14.7108i		−	2.88503i
$27$	4.53312	−	2.53984i	0.872400	−	0.488793i
$28$	−4.51314	+	7.81698i	−0.852903	+	1.47727i
$29$	4.61569	−	4.61569i	0.857112	−	0.857112i	−0.133885	−	0.990997i	$-0.542745\pi$
$29$	4.61569	−	4.61569i	0.857112	−	0.857112i	0.990997	+	0.133885i	$0.0427453\pi$
$30$	−7.94953	+	1.79753i	−1.45138	+	0.328182i
$31$	2.37322	+	2.37322i	0.426243	+	0.426243i	0.887346	−	0.461104i	$-0.152546\pi$
$31$	2.37322	+	2.37322i	0.426243	+	0.426243i	−0.461104	+	0.887346i	$0.652546\pi$
$32$	2.07865	−	7.75763i	0.367457	−	1.37137i
$33$	−1.43794	+	0.247181i	−0.250313	+	0.0430286i
$34$	−3.50242	−	6.06637i	−0.600660	−	1.04037i
$35$	−7.90513	+	2.56663i	−1.33621	+	0.433840i
$36$	4.73064	−	5.54035i	0.788441	−	0.923391i
$37$	5.69629	−	2.13360i	0.936465	−	0.350762i
$37$	5.69629	−	2.13360i	0.936465	−	0.350762i
$38$	8.28833			1.34454
$39$	−1.10711	+	12.0573i	−0.177280	+	1.93072i
$40$	−1.69090	+	1.09756i	−0.267355	+	0.173540i
$41$	2.90888	+	5.03832i	0.454290	+	0.786854i	0.998647	−	0.0520001i	$-0.0165596\pi$
$41$	2.90888	+	5.03832i	0.454290	+	0.786854i	−0.544357	+	0.838854i	$0.683226\pi$
$42$	7.81837	−	11.0643i	1.20640	−	1.70726i
$43$	−1.86227	−	1.86227i	−0.283994	−	0.283994i	0.550706	−	0.834700i	$-0.314359\pi$
$43$	−1.86227	−	1.86227i	−0.283994	−	0.283994i	−0.834700	+	0.550706i	$0.814359\pi$
$44$	−1.77156	+	1.02281i	−0.267073	+	0.154195i
$45$	6.65089	−	0.875024i	0.991456	−	0.130441i
$46$	5.09147	−	8.81868i	0.750696	−	1.30024i
$47$	−0.845254			−0.123293			−0.0616465	−	0.998098i	$-0.519635\pi$
$47$	−0.845254			−0.123293			−0.0616465	+	0.998098i	$0.519635\pi$
$48$	−1.77397	+	4.80954i	−0.256051	+	0.694197i
$49$	3.40787	−	5.90260i	0.486839	−	0.843229i
$50$	−10.3916	−	1.65051i	−1.46960	−	0.233417i
$51$	2.41412	+	5.23572i	0.338044	+	0.733147i
$52$	4.39371	+	16.3975i	0.609298	+	2.27393i
$53$	2.46608	−	4.27138i	0.338743	−	0.586719i	−0.645454	−	0.763799i	$-0.723332\pi$
$53$	2.46608	−	4.27138i	0.338743	−	0.586719i	0.984196	+	0.177080i	$0.0566651\pi$
$54$	−7.83102	+	7.63165i	−1.06567	+	1.03854i
$55$	−1.84235	−	0.392023i	−0.248423	−	0.0528604i
$56$	0.867289	−	3.23677i	0.115896	−	0.432531i
$57$	−6.79330	−	0.623766i	−0.899794	−	0.0826198i
$58$	−6.86824	+	11.8961i	−0.901844	+	1.56204i
$59$	0.648455	−	0.173753i	0.0844216	−	0.0226207i	−0.216361	−	0.976313i	$-0.569419\pi$
$59$	0.648455	−	0.173753i	0.0844216	−	0.0226207i	0.300783	+	0.953693i	$0.402752\pi$
$60$	8.32413	−	4.37792i	1.07464	−	0.565188i
$61$	−2.58029	+	9.62977i	−0.330372	+	1.23297i	0.578428	+	0.815734i	$0.303666\pi$
$61$	−2.58029	+	9.62977i	−0.330372	+	1.23297i	−0.908800	+	0.417232i	$0.863000\pi$
$62$	−6.11656	−	3.53140i	−0.776804	−	0.448488i
$63$	−7.24079	+	8.48013i	−0.912254	+	1.06840i
$64$			10.9816i			1.37270i
$65$	−7.09955	+	13.9262i	−0.880590	+	1.72733i
$66$	2.78824	−	1.28562i	0.343208	−	0.158248i
$67$	−1.09340	−	1.89382i	−0.133580	−	0.231367i	0.791474	−	0.611203i	$-0.209314\pi$
$67$	−1.09340	−	1.89382i	−0.133580	−	0.231367i	−0.925054	+	0.379835i	$0.875981\pi$
$68$	5.71585	+	5.71585i	0.693149	+	0.693149i
$69$	−4.83676	+	6.84481i	−0.582278	+	0.824019i
$70$	14.6706	−	9.52268i	1.75347	−	1.13818i
$71$	−8.09195	+	4.67189i	−0.960338	+	0.554451i	−0.896277	−	0.443495i	$-0.853738\pi$
$71$	−8.09195	+	4.67189i	−0.960338	+	0.554451i	−0.0640607	+	0.997946i	$0.520405\pi$
$72$	−1.16404	+	2.44128i	−0.137183	+	0.287707i
$73$	−11.6345			−1.36172			−0.680858	−	0.732415i	$-0.738393\pi$
$73$	−11.6345			−1.36172			−0.680858	+	0.732415i	$0.738393\pi$
$74$	−10.4166	+	7.43942i	−1.21091	+	0.864815i
$75$	8.39300	+	2.13485i	0.969140	+	0.246511i
$76$	−9.23865	+	2.47549i	−1.05975	+	0.283958i
$77$	2.71157	−	1.56553i	0.309013	−	0.178409i
$78$	−4.31666	−	25.1116i	−0.488766	−	2.84333i
$79$	15.3576	+	4.11506i	1.72787	+	0.462981i	0.979690	−	0.200517i	$-0.0642622\pi$
$79$	15.3576	+	4.11506i	1.72787	+	0.462981i	0.748178	+	0.663498i	$0.230929\pi$
$80$	−4.42937	+	4.91716i	−0.495218	+	0.549755i
$81$	6.99282	−	5.66572i	0.776981	−	0.629525i
$82$	−8.65693	−	8.65693i	−0.955998	−	0.955998i
$83$	1.51988	−	2.63251i	0.166828	−	0.288955i	−0.770475	−	0.637471i	$-0.779981\pi$
$83$	1.51988	−	2.63251i	0.166828	−	0.288955i	0.937303	+	0.348515i	$0.113314\pi$
$84$	−5.41022	+	14.6680i	−0.590303	+	1.60041i
$85$	0.387930	+	7.43308i	0.0420769	+	0.806231i
$86$	4.79969	+	2.77110i	0.517563	+	0.298815i
$87$	6.52464	−	9.23344i	0.699515	−	0.989929i
$88$	0.536994	−	0.536994i	0.0572437	−	0.0572437i
$89$	−3.08875	−	11.5274i	−0.327406	−	1.22190i	−0.911871	−	0.410478i	$-0.865362\pi$
$89$	−3.08875	−	11.5274i	−0.327406	−	1.22190i	0.584464	−	0.811419i	$-0.301305\pi$
$90$	−13.0425	+	5.40107i	−1.37480	+	0.569322i
$91$	−6.72507	−	25.0983i	−0.704979	−	2.63102i
$92$	−3.04135	+	11.3505i	−0.317083	+	1.18337i
$93$	4.74750	+	3.35473i	0.492293	+	0.347870i
$94$	1.71812	−	0.460370i	0.177211	−	0.0474836i
$95$	−7.84623	−	4.00000i	−0.805006	−	0.410392i
$96$	1.27193	−	13.8523i	0.129816	−	1.41380i
$97$	11.8508	+	11.8508i	1.20327	+	1.20327i	0.973166	+	0.230104i	$0.0739066\pi$
$97$	11.8508	+	11.8508i	1.20327	+	1.20327i	0.230104	+	0.973166i	$0.426093\pi$
$98$	−3.71221	+	13.8542i	−0.374990	+	1.39948i
$99$	−2.38205	+	0.843882i	−0.239405	+	0.0848133i
$100$	12.0761	−	1.26393i	1.20761	−	0.126393i
$101$	11.9032			1.18441			0.592205	−	0.805788i	$-0.298258\pi$
$101$	11.9032			1.18441			0.592205	+	0.805788i	$0.298258\pi$
$102$	−7.75876	−	9.32765i	−0.768232	−	0.923575i
$103$	2.76353	−	2.76353i	0.272299	−	0.272299i	−0.557726	−	0.830025i	$-0.688326\pi$
$103$	2.76353	−	2.76353i	0.272299	−	0.272299i	0.830025	+	0.557726i	$0.188326\pi$
$104$	−3.15111	−	5.45789i	−0.308992	−	0.535190i
$105$	−12.7410	+	6.70091i	−1.24340	+	0.653942i
$106$	−2.68632	+	10.0255i	−0.260918	+	0.973761i
$107$	−1.25482	−	2.17340i	−0.121308	−	0.210111i	0.798976	−	0.601363i	$-0.205375\pi$
$107$	−1.25482	−	2.17340i	−0.121308	−	0.210111i	−0.920284	+	0.391252i	$0.872042\pi$
$108$	6.44955	−	10.8456i	0.620608	−	1.04362i
$109$	0.304553	+	1.13661i	0.0291708	+	0.108867i	0.978976	−	0.203974i	$-0.0653859\pi$
$109$	0.304553	+	1.13661i	0.0291708	+	0.108867i	−0.949805	+	0.312841i	$0.898719\pi$
$110$	3.95842	−	0.206589i	0.377421	−	0.0196975i
$111$	9.09758	−	5.31357i	0.863504	−	0.504342i
$112$		−	11.0009i		−	1.03949i
$113$	11.4797	−	3.07597i	1.07992	−	0.289363i	0.325355	−	0.945592i	$-0.394516\pi$
$113$	11.4797	−	3.07597i	1.07992	−	0.289363i	0.754562	+	0.656229i	$0.227850\pi$
$114$	14.1483	−	2.43208i	1.32511	−	0.227785i
$115$	−9.07584	+	5.89112i	−0.846327	+	0.549349i
$116$	4.10269	−	15.3115i	0.380926	−	1.42163i
$117$	1.64817	+	20.9069i	0.152374	+	1.93284i
$118$	−1.22346	+	0.706366i	−0.112629	+	0.0650262i
$119$	−8.74876	−	8.74876i	−0.801998	−	0.801998i
$120$	−2.56433	+	2.36972i	−0.234090	+	0.216325i
$121$	−10.2904			−0.935492
$122$		−	20.9795i		−	1.89940i
$123$	6.44391	+	7.74692i	0.581028	+	0.698516i
$124$	7.87260	+	2.10946i	0.706980	+	0.189435i
$125$	9.04079	+	6.57754i	0.808633	+	0.588313i
$126$	10.0994	−	21.1811i	0.899729	−	1.88696i
$127$	−13.7274	−	7.92553i	−1.21811	−	0.703277i	−0.253598	−	0.967310i	$-0.581614\pi$
$127$	−13.7274	−	7.92553i	−1.21811	−	0.703277i	−0.964514	+	0.264033i	$0.914947\pi$
$128$	−1.82384	−	6.80667i	−0.161206	−	0.601630i
$129$	−3.72538	−	2.63247i	−0.328001	−	0.231776i
$130$	6.84613	−	32.1741i	0.600446	−	2.82186i
$131$	−1.26475	−	4.72011i	−0.110502	−	0.412398i	0.888409	−	0.459052i	$-0.151811\pi$
$131$	−1.26475	−	4.72011i	−0.110502	−	0.412398i	−0.998911	+	0.0466540i	$0.985144\pi$
$132$	−2.72395	+	2.26579i	−0.237089	+	0.197212i
$133$	14.1408	−	3.78902i	1.22616	−	0.328549i
$134$	3.25400	+	3.25400i	0.281103	+	0.281103i
$135$	11.0964	−	3.44528i	0.955026	−	0.296522i
$136$	−2.59888	−	1.50046i	−0.222852	−	0.128664i
$137$	−9.06430			−0.774415			−0.387208	−	0.921993i	$-0.626560\pi$
$137$	−9.06430			−0.774415			−0.387208	+	0.921993i	$0.626560\pi$
$138$	6.10350	−	16.5476i	0.519565	−	1.40863i
$139$	−0.587369	−	0.339118i	−0.0498200	−	0.0287636i	0.474883	−	0.880049i	$-0.342490\pi$
$139$	−0.587369	−	0.339118i	−0.0498200	−	0.0287636i	−0.524703	+	0.851285i	$0.675824\pi$
$140$	−13.5086	+	14.9962i	−1.14168	+	1.26741i
$141$	−1.44286	+	0.248026i	−0.121511	+	0.0208876i
$142$	13.9037	−	13.9037i	1.16677	−	1.16677i
$143$	1.52410	−	5.68802i	0.127452	−	0.475656i
$144$	−1.61691	+	8.73049i	−0.134743	+	0.727541i
$145$	12.2430	−	7.94694i	1.01673	−	0.659957i
$146$	23.6492	−	6.33677i	1.95722	−	0.524435i
$147$	4.08526	−	11.0758i	0.336946	−	0.913518i
$148$	9.38903	−	11.4036i	0.771773	−	0.937367i
$149$		−	11.1626i		−	0.914479i	−0.889344	−	0.457240i	$-0.848838\pi$
$149$		−	11.1626i		−	0.914479i	0.889344	−	0.457240i	$-0.151162\pi$
$150$	−18.2230	+	0.231820i	−1.48790	+	0.0189280i
$151$	10.2727	−	5.93092i	0.835977	−	0.482651i	−0.0199178	−	0.999802i	$-0.506340\pi$
$151$	10.2727	−	5.93092i	0.835977	−	0.482651i	0.855895	+	0.517150i	$0.173007\pi$
$152$	3.07506	−	1.77539i	0.249421	−	0.144003i
$153$	5.65727	+	8.22906i	0.457363	+	0.665280i
$154$	−4.65908	+	4.65908i	−0.375439	+	0.375439i
$155$	4.08603	+	6.29492i	0.328197	+	0.505621i
$156$	12.3117	+	26.7016i	0.985726	+	2.13784i
$157$	−5.76756	−	3.32990i	−0.460302	−	0.265755i	0.251869	−	0.967761i	$-0.418955\pi$
$157$	−5.76756	−	3.32990i	−0.460302	−	0.265755i	−0.712171	+	0.702006i	$0.752288\pi$
$158$	−33.4583			−2.66180
$159$	2.95627	−	8.01494i	0.234447	−	0.635626i
$160$	8.15647	−	15.9994i	0.644826	−	1.26486i
$161$	4.65514	−	17.3732i	0.366876	−	1.36920i
$162$	−11.1283	+	15.3252i	−0.874320	+	1.20406i
$163$	−3.98003	−	14.8537i	−0.311740	−	1.16343i	−0.926986	−	0.375095i	$-0.877610\pi$
$163$	−3.98003	−	14.8537i	−0.311740	−	1.16343i	0.615246	−	0.788335i	$-0.289057\pi$
$164$	12.2351	+	7.06393i	0.955400	+	0.551601i
$165$	−3.25996	−	0.128580i	−0.253787	−	0.0100099i
$166$	−1.65561	+	6.17884i	−0.128501	+	0.479571i
$167$	8.87381	+	2.37773i	0.686676	+	0.183994i	0.585255	−	0.810849i	$-0.300994\pi$
$167$	8.87381	+	2.37773i	0.686676	+	0.183994i	0.101421	+	0.994844i	$0.467661\pi$
$168$	0.530697	−	5.77970i	0.0409441	−	0.445913i
$169$	−31.0628	−	17.9341i	−2.38945	−	1.37955i
$170$	−4.83699	−	14.8977i	−0.370980	−	1.14260i
$171$	−11.7793	+	0.928608i	−0.900785	+	0.0710124i
$172$	−6.17766	−	1.65530i	−0.471042	−	0.126215i
$173$	−8.72406	−	5.03684i	−0.663278	−	0.382944i	0.130247	−	0.991482i	$-0.458423\pi$
$173$	−8.72406	−	5.03684i	−0.663278	−	0.382944i	−0.793525	+	0.608538i	$0.791756\pi$
$174$	−8.23344	+	22.3222i	−0.624176	+	1.69224i
$175$	−18.4838	+	1.93460i	−1.39724	+	0.146242i
$176$	1.24656	−	2.15911i	0.0939633	−	0.162749i
$177$	1.05594	−	0.486877i	0.0793690	−	0.0365959i
$178$	12.5568	+	21.7490i	0.941173	+	1.63016i
$179$	11.5579	−	11.5579i	0.863881	−	0.863881i	−0.127905	−	0.991786i	$-0.540825\pi$
$179$	11.5579	−	11.5579i	0.863881	−	0.863881i	0.991786	+	0.127905i	$0.0408253\pi$
$180$	12.9248	−	9.91576i	0.963356	−	0.739077i
$181$	−1.21207	−	2.09936i	−0.0900921	−	0.156044i	0.817458	−	0.575989i	$-0.195383\pi$
$181$	−1.21207	−	2.09936i	−0.0900921	−	0.156044i	−0.907550	+	0.419945i	$0.862049\pi$
$182$	27.3397	+	47.3538i	2.02656	+	3.51010i
$183$	−1.57889	+	17.1953i	−0.116715	+	1.27111i
$184$		−	4.36244i		−	0.321604i
$185$	13.4513	−	2.01547i	0.988960	−	0.148180i
$186$	−11.4773	−	4.23334i	−0.841555	−	0.310403i
$187$	−0.725729	−	2.70846i	−0.0530706	−	0.198062i
$188$	−1.77762	+	1.02631i	−0.129646	+	0.0748514i
$189$	−9.87177	+	16.6004i	−0.718065	+	1.20750i
$190$	18.1274	+	3.85723i	1.31510	+	0.279833i
$191$	5.59320	+	5.59320i	0.404710	+	0.404710i	0.879889	−	0.475179i	$-0.157617\pi$
$191$	5.59320	+	5.59320i	0.404710	+	0.404710i	−0.475179	+	0.879889i	$0.657617\pi$
$192$	3.22237	+	18.7457i	0.232554	+	1.35285i
$193$	−2.40019	−	2.40019i	−0.172770	−	0.172770i	0.615426	−	0.788195i	$-0.288984\pi$
$193$	−2.40019	−	2.40019i	−0.172770	−	0.172770i	−0.788195	+	0.615426i	$0.788984\pi$
$194$	−30.5435	−	17.6343i	−2.19289	−	1.26607i
$195$	−8.03262	+	25.8554i	−0.575228	+	1.85154i
$196$		−	16.5514i		−	1.18224i
$197$	3.67925	−	6.37265i	0.262136	−	0.454032i	−0.704674	−	0.709532i	$-0.748907\pi$
$197$	3.67925	−	6.37265i	0.262136	−	0.454032i	0.966809	+	0.255499i	$0.0822399\pi$
$198$	4.38231	−	3.01273i	0.311437	−	0.214105i
$199$	10.4925	+	10.4925i	0.743797	+	0.743797i	0.973306	−	0.229509i	$-0.0737122\pi$
$199$	10.4925	+	10.4925i	0.743797	+	0.743797i	−0.229509	+	0.973306i	$0.573712\pi$
$200$	−4.20896	+	1.61357i	−0.297618	+	0.114096i
$201$	−2.42216	−	2.91194i	−0.170846	−	0.205393i
$202$	−24.1952	+	6.48310i	−1.70237	+	0.456149i
$203$	−6.27964	+	23.4359i	−0.440744	+	1.64488i
$204$	11.4343	+	8.07982i	0.800559	+	0.565700i
$205$	4.01728	+	12.3731i	0.280579	+	0.864172i
$206$	−4.11219	+	7.12252i	−0.286510	+	0.496250i
$207$	−6.24792	+	13.1035i	−0.434260	+	0.910753i
$208$	−14.6298	−	14.6298i	−1.01440	−	1.01440i
$209$	3.20472	+	0.858703i	0.221675	+	0.0593978i
$210$	22.2487	−	20.5602i	1.53530	−	1.41879i
$211$	21.7834			1.49963			0.749816	−	0.661647i	$-0.230142\pi$
$211$	21.7834			1.49963			0.749816	+	0.661647i	$0.230142\pi$
$212$		−	11.9773i		−	0.822605i
$213$	−12.4422	+	10.3494i	−0.852524	+	0.709131i
$214$	3.73438	+	3.73438i	0.255277	+	0.255277i
$215$	−3.20632	−	4.93965i	−0.218669	−	0.336881i
$216$	−1.27067	+	4.50886i	−0.0864582	+	0.306789i
$217$	−12.0499	−	3.22876i	−0.818001	−	0.219183i
$218$	−1.23811	−	2.14447i	−0.0838555	−	0.145242i
$219$	−19.8603	+	3.41396i	−1.34203	+	0.230694i
$220$	−4.35058	+	1.41254i	−0.293316	+	0.0952337i
$221$	−23.2696			−1.56528
$222$	−15.5983	+	15.7558i	−1.04689	+	1.05746i
$223$			13.4309i			0.899399i	0.893180	+	0.449699i	$0.148469\pi$
$223$			13.4309i			0.899399i	−0.893180	+	0.449699i	$0.851531\pi$
$224$	7.72625	+	28.8347i	0.516232	+	1.92660i
$225$	14.9534	+	1.18143i	0.996893	+	0.0787618i
$226$	−21.6591	+	12.5049i	−1.44074	+	0.831812i
$227$	−9.58896	−	2.56936i	−0.636442	−	0.170534i	−0.0738507	−	0.997269i	$-0.523529\pi$
$227$	−9.58896	−	2.56936i	−0.636442	−	0.170534i	−0.562591	+	0.826735i	$0.690195\pi$
$228$	−15.0441	+	6.93663i	−0.996320	+	0.459389i
$229$	0.00345389	+	0.00598232i	0.000228240	+	0.000395323i	0.866140	−	0.499802i	$-0.166594\pi$
$229$	0.00345389	+	0.00598232i	0.000228240	+	0.000395323i	−0.865911	+	0.500198i	$0.833261\pi$
$230$	15.2396	−	16.9179i	1.00487	−	1.11553i
$231$	4.16932	−	3.46805i	0.274321	−	0.228181i
$232$			5.88480i			0.386356i
$233$		−	26.2554i		−	1.72005i	−0.510255	−	0.860023i	$-0.670449\pi$
$233$		−	26.2554i		−	1.72005i	0.510255	−	0.860023i	$-0.329551\pi$
$234$	−14.7372	−	41.5992i	−0.963401	−	2.71942i
$235$	−1.84866	−	0.393365i	−0.120593	−	0.0256603i
$236$	1.15277	−	1.15277i	0.0750389	−	0.0750389i
$237$	27.4232	+	2.51802i	1.78133	+	0.163563i
$238$	22.5484	+	13.0183i	1.46160	+	0.843853i
$239$	13.0240	−	3.48978i	0.842454	−	0.225735i	0.188314	−	0.982109i	$-0.439698\pi$
$239$	13.0240	−	3.48978i	0.842454	−	0.225735i	0.654139	+	0.756374i	$0.273031\pi$
$240$	−6.11813	+	9.69338i	−0.394923	+	0.625705i
$241$	6.20235	+	1.66191i	0.399528	+	0.107053i	0.452988	−	0.891517i	$-0.350358\pi$
$241$	6.20235	+	1.66191i	0.399528	+	0.107053i	−0.0534594	+	0.998570i	$0.517025\pi$
$242$	20.9170	−	5.60470i	1.34460	−	0.360284i
$243$	10.2743	−	11.7234i	0.659099	−	0.752056i
$244$	6.26599	+	23.3850i	0.401139	+	1.49707i
$245$	10.2003	−	11.3236i	0.651675	−	0.723441i
$246$	−17.3177	−	12.2373i	−1.10414	−	0.780219i
$247$	13.7666	−	23.8444i	0.875948	−	1.51719i
$248$	−3.02575			−0.192135
$249$	1.82199	−	4.93971i	0.115464	−	0.313042i
$250$	−21.9595	−	8.44589i	−1.38884	−	0.534165i
$251$	−5.98677	+	5.98677i	−0.377882	+	0.377882i	−0.870337	−	0.492456i	$-0.836099\pi$
$251$	−5.98677	+	5.98677i	−0.377882	+	0.377882i	0.492456	+	0.870337i	$0.336099\pi$
$252$	−4.93122	+	26.6260i	−0.310638	+	1.67728i
$253$	2.88229	−	2.88229i	0.181208	−	0.181208i
$254$	32.2200	+	8.63333i	2.02166	+	0.541703i
$255$	2.84332	+	12.5745i	0.178056	+	0.787448i
$256$	−3.56702	−	6.17825i	−0.222938	−	0.386141i
$257$	5.08054	+	18.9608i	0.316915	+	1.18274i	0.922193	+	0.386729i	$0.126395\pi$
$257$	5.08054	+	18.9608i	0.316915	+	1.18274i	−0.605278	+	0.796014i	$0.706938\pi$
$258$	9.00627	+	3.32191i	0.560706	+	0.206813i
$259$	−14.3710	+	17.4544i	−0.892969	+	1.08457i
$260$	1.97840	+	37.9079i	0.122695	+	2.35095i
$261$	8.42825	−	17.6762i	0.521696	−	1.09413i
$262$	5.14165	+	8.90559i	0.317652	+	0.550189i
$263$	14.2831	−	8.24633i	0.880731	−	0.508490i	0.00983168	−	0.999952i	$-0.496870\pi$
$263$	14.2831	−	8.24633i	0.880731	−	0.508490i	0.870899	+	0.491461i	$0.163537\pi$
$264$	0.759084	−	1.07423i	0.0467184	−	0.0661142i
$265$	7.38140	−	8.19429i	0.453436	−	0.503371i
$266$	−26.6799	+	15.4037i	−1.63585	+	0.944459i
$267$	−8.65505	−	18.7710i	−0.529680	−	1.14877i
$268$	−4.59897	−	2.65522i	−0.280927	−	0.162193i
$269$		−	4.56979i		−	0.278625i	−0.990248	−	0.139313i	$-0.955511\pi$
$269$		−	4.56979i		−	0.278625i	0.990248	−	0.139313i	$-0.0444893\pi$
$270$	−20.6789	+	13.0468i	−1.25848	+	0.794003i
$271$	−14.2806	+	24.7347i	−0.867484	+	1.50253i	−0.00292538	+	0.999996i	$0.500931\pi$
$271$	−14.2806	+	24.7347i	−0.867484	+	1.50253i	−0.864559	+	0.502531i	$0.832402\pi$
$272$	−9.51610	−	2.54983i	−0.576999	−	0.154606i
$273$	−18.8445	−	40.8698i	−1.14052	−	2.47355i
$274$	18.4248	−	4.93690i	1.11308	−	0.298249i
$275$	−3.84698	−	1.71479i	−0.231982	−	0.103406i
$276$	−1.86101	+	20.2679i	−0.112020	+	1.21998i
$277$	21.3418	+	5.71852i	1.28230	+	0.343592i	0.834733	−	0.550656i	$-0.185622\pi$
$277$	21.3418	+	5.71852i	1.28230	+	0.343592i	0.447572	+	0.894248i	$0.352289\pi$
$278$	1.37863	+	0.369403i	0.0826848	+	0.0221553i
$279$	9.08844	+	4.33350i	0.544111	+	0.259440i
$280$	3.40318	−	6.67552i	0.203379	−	0.398939i
$281$	−18.4881	+	4.95388i	−1.10291	+	0.295524i	−0.763949	−	0.645277i	$-0.776742\pi$
$281$	−18.4881	+	4.95388i	−1.10291	+	0.295524i	−0.338960	+	0.940801i	$0.610075\pi$
$282$	2.79777	−	1.29001i	0.166605	−	0.0768193i
$283$	−4.34494	−	1.16422i	−0.258280	−	0.0692060i	0.127355	−	0.991857i	$-0.459351\pi$
$283$	−4.34494	−	1.16422i	−0.258280	−	0.0692060i	−0.385636	+	0.922651i	$0.626018\pi$
$284$	−11.3452	+	19.6505i	−0.673217	+	1.16605i
$285$	−14.5674	−	4.52571i	−0.862896	−	0.268080i
$286$			12.3920i			0.732754i
$287$	−18.7272	−	10.8122i	−1.10543	−	0.638221i
$288$	−1.89354	−	24.0193i	−0.111578	−	1.41535i
$289$	5.12666	−	2.95988i	0.301568	−	0.174111i
$290$	−20.5578	+	22.8217i	−1.20719	+	1.34014i
$291$	23.7070	+	16.7521i	1.38973	+	0.982026i
$292$	−24.4681	+	14.1267i	−1.43189	+	0.826701i
$293$	8.17496	+	14.1594i	0.477586	+	0.827203i	0.999670	−	0.0256909i	$-0.00817856\pi$
$293$	8.17496	+	14.1594i	0.477586	+	0.827203i	−0.522084	+	0.852894i	$0.674845\pi$
$294$	−2.27151	+	24.7386i	−0.132477	+	1.44278i
$295$	1.49910	−	0.0782374i	0.0872809	−	0.00455516i
$296$	−2.27114	+	4.99139i	−0.132007	+	0.290119i
$297$	−3.81857	+	2.13949i	−0.221576	+	0.124146i
$298$	6.07977	+	22.6900i	0.352191	+	1.31440i
$299$	−16.9135	−	29.2950i	−0.978131	−	1.69417i
$300$	20.2431	−	5.70109i	1.16874	−	0.329152i
$301$	9.45560	+	2.53362i	0.545012	+	0.146036i
$302$	−17.6507	+	17.6507i	−1.01568	+	1.01568i
$303$	20.3189	−	3.49280i	1.16729	−	0.200656i
$304$	8.24269	−	8.24269i	0.472751	−	0.472751i
$305$	−10.1249	+	19.8605i	−0.579748	+	1.13721i
$306$	−15.9814	−	13.6457i	−0.913594	−	0.780075i
$307$	−14.8798			−0.849232			−0.424616	−	0.905373i	$-0.639591\pi$
$307$	−14.8798			−0.849232			−0.424616	+	0.905373i	$0.639591\pi$
$308$	3.80174	−	6.58481i	0.216624	−	0.375204i
$309$	3.90647	−	5.52830i	0.222231	−	0.314494i
$310$	−11.7341	−	10.5701i	−0.666452	−	0.600339i
$311$	7.85854	+	29.3285i	0.445617	+	1.66307i	0.714302	+	0.699838i	$0.246744\pi$
$311$	7.85854	+	29.3285i	0.445617	+	1.66307i	−0.268685	+	0.963228i	$0.586589\pi$
$312$	−6.98052	−	8.39205i	−0.395194	−	0.475106i
$313$	27.8776	−	7.46978i	1.57574	−	0.422217i	0.638133	−	0.769926i	$-0.279707\pi$
$313$	27.8776	−	7.46978i	1.57574	−	0.422217i	0.937602	+	0.347709i	$0.113040\pi$
$314$	13.5372	+	3.62728i	0.763949	+	0.204700i
$315$	−19.7828	+	15.1772i	−1.11464	+	0.855138i
$316$	37.2946	−	9.99305i	2.09798	−	0.562153i
$317$	−22.6926	−	13.1016i	−1.27454	−	0.735857i	−0.298703	−	0.954346i	$-0.596554\pi$
$317$	−22.6926	−	13.1016i	−1.27454	−	0.735857i	−0.975839	+	0.218489i	$0.929887\pi$
$318$	−1.64377	+	17.9019i	−0.0921779	+	1.00389i
$319$	−3.88813	+	3.88813i	−0.217693	+	0.217693i
$320$	−5.11061	+	24.0178i	−0.285692	+	1.34264i
$321$	−2.77974	−	3.34183i	−0.155150	−	0.186522i
$322$			37.8495i			2.10927i
$323$		−	13.1105i		−	0.729485i
$324$	7.82701	−	20.4061i	0.434834	−	1.13367i
$325$	−22.0084	+	27.1540i	−1.22081	+	1.50623i
$326$	16.1802	+	28.0249i	0.896139	+	1.55216i
$327$	0.853394	+	1.85084i	0.0471928	+	0.102351i
$328$	−5.06617	−	1.35748i	−0.279732	−	0.0749540i
$329$	2.72085	−	1.57088i	0.150005	−	0.0866057i
$330$	6.69646	−	1.51419i	0.368628	−	0.0833532i
$331$	−2.59343	−	9.67883i	−0.142548	−	0.531997i	−0.999852	−	0.0171865i	$-0.994529\pi$
$331$	−2.59343	−	9.67883i	−0.142548	−	0.531997i	0.857304	−	0.514810i	$-0.172138\pi$
$332$		−	7.38177i		−	0.405127i
$333$	13.9705	−	11.7399i	0.765579	−	0.643342i
$334$	−19.3326			−1.05783
$335$	−1.51003	−	4.65083i	−0.0825017	−	0.254102i
$336$	−3.22804	−	18.7787i	−0.176104	−	1.02446i
$337$	1.42715	+	2.47190i	0.0777420	+	0.134653i	0.902275	−	0.431160i	$-0.141896\pi$
$337$	1.42715	+	2.47190i	0.0777420	+	0.134653i	−0.824533	+	0.565813i	$0.808562\pi$
$338$	72.9085	+	19.5358i	3.96570	+	1.06261i
$339$	18.6934	−	8.61925i	1.01528	−	0.468133i
$340$	9.84112	+	15.1612i	0.533709	+	0.822232i
$341$	−1.99913	−	1.99913i	−0.108259	−	0.108259i
$342$	23.4377	−	8.30318i	1.26736	−	0.448985i
$343$		−	0.684886i		−	0.0369804i
$344$	2.37432			0.128015
$345$	−13.7639	+	12.7194i	−0.741025	+	0.684788i
$346$	20.4765	+	5.48666i	1.10082	+	0.294965i
$347$	−7.59820	−	7.59820i	−0.407893	−	0.407893i	0.473110	−	0.881003i	$-0.343131\pi$
$347$	−7.59820	−	7.59820i	−0.407893	−	0.407893i	−0.881003	+	0.473110i	$0.843131\pi$
$348$	2.51045	−	27.3408i	0.134574	−	1.46562i
$349$	−2.44346	+	4.23220i	−0.130796	+	0.226545i	−0.923983	−	0.382432i	$-0.875086\pi$
$349$	−2.44346	+	4.23220i	−0.130796	+	0.226545i	0.793188	+	0.608977i	$0.208420\pi$
$350$	36.5178	−	13.9997i	1.95196	−	0.748313i
$351$	8.94825	+	35.2047i	0.477622	+	1.87909i
$352$	−1.75100	+	6.53481i	−0.0933285	+	0.348307i
$353$	−0.387502	+	0.103831i	−0.0206247	+	0.00552636i	−0.269117	−	0.963108i	$-0.586732\pi$
$353$	−0.387502	+	0.103831i	−0.0206247	+	0.00552636i	0.248492	+	0.968634i	$0.420065\pi$
$354$	−1.88119	+	1.56478i	−0.0999843	+	0.0831672i
$355$	−19.8721	+	6.45207i	−1.05470	+	0.342440i
$356$	−20.4924	−	20.4924i	−1.08609	−	1.08609i
$357$	−17.5014	−	12.3671i	−0.926275	−	0.654535i
$358$	−17.1985	+	29.7886i	−0.908966	+	1.57438i
$359$		−	13.7704i		−	0.726773i	−0.931639	−	0.363386i	$-0.881621\pi$
$359$		−	13.7704i		−	0.726773i	0.931639	−	0.363386i	$-0.118379\pi$
$360$	−3.68199	+	4.79761i	−0.194058	+	0.252856i
$361$	−3.02013	−	1.74367i	−0.158954	−	0.0917722i
$362$	3.60716	+	3.60716i	0.189588	+	0.189588i
$363$	−17.5659	+	3.01956i	−0.921969	+	0.158486i
$364$	−44.6177	−	44.6177i	−2.33860	−	2.33860i
$365$	−25.4459	−	5.41448i	−1.33190	−	0.283407i
$366$	−6.15611	−	35.8124i	−0.321785	−	1.87194i
$367$	27.2648	−	15.7414i	1.42321	−	0.821692i	0.426640	−	0.904421i	$-0.359697\pi$
$367$	27.2648	−	15.7414i	1.42321	−	0.821692i	0.996572	+	0.0827293i	$0.0263637\pi$
$368$	−3.70669	−	13.8336i	−0.193225	−	0.721124i
$369$	13.2730	+	11.3332i	0.690967	+	0.589985i
$370$	−26.2444	+	11.4231i	−1.36438	+	0.593858i
$371$			18.3326i			0.951783i
$372$	14.0576	+	1.29078i	0.728854	+	0.0669239i
$373$	10.9243	+	18.9215i	0.565641	+	0.979719i	0.996990	+	0.0775335i	$0.0247045\pi$
$373$	10.9243	+	18.9215i	0.565641	+	0.979719i	−0.431349	+	0.902185i	$0.641962\pi$
$374$	2.95034	+	5.11014i	0.152559	+	0.264239i
$375$	17.3628	+	8.57507i	0.896613	+	0.442815i
$376$	0.538831	−	0.538831i	0.0277881	−	0.0277881i
$377$	22.8158	+	39.5181i	1.17507	+	2.03528i
$378$	11.0246	−	39.1199i	0.567045	−	2.01211i
$379$	−5.35156	+	9.26918i	−0.274891	+	0.476126i	−0.970108	−	0.242675i	$-0.921975\pi$
$379$	−5.35156	+	9.26918i	−0.274891	+	0.476126i	0.695216	+	0.718801i	$0.255309\pi$
$380$	−21.3579	+	1.11466i	−1.09564	+	0.0571810i
$381$	−25.7585	−	9.50090i	−1.31965	−	0.486746i
$382$	−14.4155	−	8.32279i	−0.737561	−	0.425831i
$383$	−35.0831	−	9.40048i	−1.79266	−	0.480342i	−0.799868	−	0.600176i	$-0.795097\pi$
$383$	−35.0831	−	9.40048i	−1.79266	−	0.480342i	−0.992794	+	0.119834i	$0.961764\pi$
$384$	−5.11063	−	11.0839i	−0.260801	−	0.565623i
$385$	6.65906	−	2.16206i	0.339377	−	0.110189i
$386$	6.18608	+	3.57153i	0.314863	+	0.181786i
$387$	−7.13173	−	3.40051i	−0.362526	−	0.172858i
$388$	39.3124	+	10.5337i	1.99578	+	0.534769i
$389$	−1.27055	+	4.74175i	−0.0644193	+	0.240416i	−0.990626	−	0.136599i	$-0.956383\pi$
$389$	−1.27055	+	4.74175i	−0.0644193	+	0.240416i	0.926207	+	0.377015i	$0.123049\pi$
$390$	2.24546	−	56.9305i	0.113703	−	2.88279i
$391$	−13.9494	−	8.05367i	−0.705450	−	0.407292i
$392$	1.59034	+	5.93523i	0.0803242	+	0.299774i
$393$	−3.54399	−	7.68617i	−0.178770	−	0.387716i
$394$	−4.00783	+	14.9574i	−0.201912	+	0.753544i
$395$	31.6737	+	16.1472i	1.59367	+	0.812454i
$396$	−3.98496	+	4.66703i	−0.200252	+	0.234527i
$397$	3.76056			0.188737			0.0943686	−	0.995537i	$-0.469917\pi$
$397$	3.76056			0.188737			0.0943686	+	0.995537i	$0.469917\pi$
$398$	−27.0427	−	15.6131i	−1.35553	−	0.782615i
$399$	23.0267	−	10.6173i	1.15278	−	0.531530i
$400$	−11.9758	+	8.69299i	−0.598792	+	0.434650i
$401$	16.2806	−	16.2806i	0.813017	−	0.813017i	−0.172068	−	0.985085i	$-0.555045\pi$
$401$	16.2806	−	16.2806i	0.813017	−	0.813017i	0.985085	+	0.172068i	$0.0550450\pi$
$402$	6.50946	+	4.59979i	0.324662	+	0.229417i
$403$	−20.3187	+	11.7310i	−1.01215	+	0.584364i
$404$	25.0331	−	14.4529i	1.24544	−	0.719057i
$405$	17.9307	−	9.13720i	0.890986	−	0.454031i
$406$		−	51.0578i		−	2.53396i
$407$	−4.79840	+	1.79729i	−0.237848	+	0.0890882i
$408$	−4.87661	−	1.79871i	−0.241428	−	0.0890495i
$409$	11.7232	−	3.14121i	0.579673	−	0.155323i	0.0429436	−	0.999077i	$-0.486326\pi$
$409$	11.7232	−	3.14121i	0.579673	−	0.155323i	0.536729	+	0.843755i	$0.319660\pi$
$410$	−14.9048	−	22.9624i	−0.736097	−	1.13403i
$411$	−15.4729	+	2.65977i	−0.763221	+	0.131197i
$412$	2.45639	−	9.16737i	0.121018	−	0.451644i
$413$	−1.76444	+	1.76444i	−0.0868226	+	0.0868226i
$414$	5.56313	−	30.0380i	0.273413	−	1.47629i
$415$	4.54925	−	5.05024i	0.223314	−	0.247907i
$416$	48.6216	+	28.0717i	2.38387	+	1.37633i
$417$	−1.10216	−	0.406525i	−0.0539728	−	0.0199076i
$418$	−6.98185			−0.341494
$419$	−11.7096	−	6.76057i	−0.572054	−	0.330275i	0.185915	−	0.982566i	$-0.440475\pi$
$419$	−11.7096	−	6.76057i	−0.572054	−	0.330275i	−0.757969	+	0.652290i	$0.773808\pi$
$420$	−18.6589	+	29.5626i	−0.910462	+	1.44251i
$421$	−17.7870	−	17.7870i	−0.866887	−	0.866887i	0.125239	−	0.992127i	$-0.460030\pi$
$421$	−17.7870	−	17.7870i	−0.866887	−	0.866887i	−0.992127	+	0.125239i	$0.960030\pi$
$422$	−44.2785	+	11.8644i	−2.15545	+	0.577550i
$423$	−2.39020	+	0.846769i	−0.116216	+	0.0411713i
$424$	1.15084	+	4.29499i	0.0558897	+	0.208583i
$425$	−2.61077	+	16.4375i	−0.126641	+	0.797334i
$426$	19.6540	−	27.8137i	0.952241	−	1.34758i
$427$	−9.59081	−	35.7934i	−0.464132	−	1.73216i
$428$	−5.27791	−	3.04720i	−0.255117	−	0.147292i
$429$	0.932601	−	10.1568i	0.0450264	−	0.490373i
$430$	9.20779	+	8.29436i	0.444039	+	0.399990i
$431$	12.0723	+	3.23476i	0.581502	+	0.155813i	0.537566	−	0.843221i	$-0.319344\pi$
$431$	12.0723	+	3.23476i	0.581502	+	0.155813i	0.0439355	+	0.999034i	$0.486010\pi$
$432$	−0.198271	+	15.3775i	−0.00953931	+	0.739852i
$433$			0.168804i			0.00811219i	0.999992	+	0.00405610i	$0.00129110\pi$
$433$			0.168804i			0.00811219i	−0.999992	+	0.00405610i	$0.998709\pi$
$434$	26.2521			1.26014
$435$	18.5671	−	17.1581i	0.890226	−	0.822666i
$436$	2.02056	+	2.02056i	0.0967674	+	0.0967674i
$437$	16.5053	−	9.52933i	0.789555	−	0.455850i
$438$	38.5100	−	17.7564i	1.84008	−	0.848435i
$439$	5.22471	−	19.4989i	0.249362	−	0.930630i	−0.721779	−	0.692123i	$-0.756675\pi$
$439$	5.22471	−	19.4989i	0.249362	−	0.930630i	0.971141	−	0.238507i	$-0.0766580\pi$
$440$	1.42437	−	0.924555i	0.0679041	−	0.0440764i
$441$	3.72357	−	20.1053i	0.177313	−	0.957396i
$442$	47.2994	−	12.6738i	2.24980	−	0.602833i
$443$			29.9711i			1.42397i	0.702195	+	0.711985i	$0.252204\pi$
$443$			29.9711i			1.42397i	−0.702195	+	0.711985i	$0.747796\pi$
$444$	12.6810	−	22.2211i	0.601814	−	1.05457i
$445$	−1.39080	−	26.6490i	−0.0659302	−	1.26328i
$446$	−7.31517	−	27.3006i	−0.346384	−	1.29272i
$447$	−3.27550	−	19.0548i	−0.154926	−	0.901260i
$448$	−20.4090	−	35.3494i	−0.964234	−	1.67010i
$449$	0.951429	−	3.55078i	0.0449007	−	0.167572i	−0.939835	−	0.341629i	$-0.889021\pi$
$449$	0.951429	−	3.55078i	0.0449007	−	0.167572i	0.984735	+	0.174058i	$0.0556879\pi$
$450$	−31.0388	+	5.74296i	−1.46319	+	0.270726i
$451$	−2.45036	−	4.24414i	−0.115383	−	0.199849i
$452$	20.4076	−	20.4076i	0.959893	−	0.959893i
$453$	15.7952	−	13.1385i	0.742125	−	0.617301i
$454$	20.8906			0.980446
$455$	−3.02816	−	58.0223i	−0.141963	−	2.72013i
$456$	4.72822	−	3.93294i	0.221419	−	0.184177i
$457$	−5.76350	+	21.5097i	−0.269605	+	1.00618i	0.689765	+	0.724033i	$0.257714\pi$
$457$	−5.76350	+	21.5097i	−0.269605	+	1.00618i	−0.959371	+	0.282148i	$0.908953\pi$
$458$	−0.0102789	−	0.0102789i	−0.000480303	−	0.000480303i
$459$	12.0717	+	12.3871i	0.563460	+	0.578180i
$460$	−11.9341	+	23.4093i	−0.556428	+	1.09146i
$461$	−30.2866	+	8.11526i	−1.41059	+	0.377965i	−0.882134	−	0.470998i	$-0.843894\pi$
$461$	−30.2866	+	8.11526i	−1.41059	+	0.377965i	−0.528451	+	0.848964i	$0.677227\pi$
$462$	−6.58597	+	9.32024i	−0.306407	+	0.433617i
$463$	−2.99509	+	11.1778i	−0.139194	+	0.519477i	0.860752	+	0.509025i	$0.169994\pi$
$463$	−2.99509	+	11.1778i	−0.139194	+	0.519477i	−0.999945	+	0.0104525i	$0.996673\pi$
$464$	5.00021	+	18.6610i	0.232129	+	0.866317i
$465$	8.82205	+	9.54654i	0.409113	+	0.442710i
$466$	14.3001	+	53.3686i	0.662438	+	2.47225i
$467$	10.3142	−	10.3142i	0.477283	−	0.477283i	−0.426979	−	0.904262i	$-0.640422\pi$
$467$	10.3142	−	10.3142i	0.477283	−	0.477283i	0.904262	+	0.426979i	$0.140422\pi$
$468$	28.8514	+	41.9673i	1.33366	+	1.93994i
$469$	7.03925	+	4.06411i	0.325042	+	0.187663i
$470$	3.97196	−	0.207295i	0.183213	−	0.00956183i
$471$	−10.8224	−	3.99179i	−0.498671	−	0.183932i
$472$	−0.302612	+	0.524139i	−0.0139288	+	0.0241255i
$473$	1.56873	+	1.56873i	0.0721301	+	0.0721301i
$474$	−57.1138	+	9.81781i	−2.62332	+	0.450947i
$475$	−15.2990	−	12.3999i	−0.701966	−	0.568946i
$476$	−29.0220	−	7.77642i	−1.33022	−	0.356431i
$477$	2.69454	−	14.5491i	0.123374	−	0.666157i
$478$	−24.5729	+	14.1871i	−1.12394	+	0.648905i
$479$	−5.84249	+	1.56549i	−0.266950	+	0.0715291i	−0.389811	−	0.920895i	$-0.627460\pi$
$479$	−5.84249	+	1.56549i	−0.266950	+	0.0715291i	0.122861	+	0.992424i	$0.460793\pi$
$480$	9.22845	−	29.7045i	0.421219	−	1.35582i
$481$	4.10062	+	42.3239i	0.186972	+	1.92980i
$482$	−13.5125			−0.615478
$483$	2.84849	−	31.0223i	0.129611	−	1.41156i
$484$	−21.6414	+	12.4947i	−0.983699	+	0.567939i
$485$	20.4039	+	31.4341i	0.926491	+	1.42735i
$486$	−14.4992	+	29.4258i	−0.657696	+	1.33478i
$487$	4.23368	+	4.23368i	0.191846	+	0.191846i	0.796493	−	0.604647i	$-0.206686\pi$
$487$	4.23368	+	4.23368i	0.191846	+	0.191846i	−0.604647	+	0.796493i	$0.706686\pi$
$488$	−4.49389	−	7.78365i	−0.203429	−	0.352349i
$489$	−11.1525	−	24.1876i	−0.504336	−	1.09380i
$490$	−14.5665	+	28.5729i	−0.658045	+	1.29079i
$491$		−	2.27178i		−	0.102524i	−0.998685	−	0.0512619i	$-0.983676\pi$
$491$		−	2.27178i		−	0.102524i	0.998685	−	0.0512619i	$-0.0163243\pi$
$492$	22.9583	+	8.46804i	1.03504	+	0.381769i
$493$	18.8173	+	10.8642i	0.847487	+	0.489297i
$494$	−14.9960	+	55.9660i	−0.674704	+	2.51803i
$495$	−5.60252	+	0.737095i	−0.251815	+	0.0331300i
$496$	−9.59483	+	2.57093i	−0.430821	+	0.115438i
$497$	17.3652	−	30.0774i	0.778935	−	1.34916i
$498$	−1.01307	+	11.0332i	−0.0453970	+	0.494408i
$499$	−0.910380	+	3.39758i	−0.0407542	+	0.152097i	−0.983305	−	0.181967i	$-0.941754\pi$
$499$	−0.910380	+	3.39758i	−0.0407542	+	0.152097i	0.942550	+	0.334064i	$0.108420\pi$
$500$	26.9998	+	2.85561i	1.20747	+	0.127707i
$501$	15.8454	+	1.45494i	0.707922	+	0.0650019i
$502$	8.90844	−	15.4299i	0.397603	−	0.688669i
$503$	0.913292	+	3.40845i	0.0407217	+	0.151975i	0.983293	−	0.182029i	$-0.0582666\pi$
$503$	0.913292	+	3.40845i	0.0407217	+	0.151975i	−0.942571	+	0.334005i	$0.891600\pi$
$504$	−0.790054	−	10.0217i	−0.0351918	−	0.446404i
$505$	26.0335	+	5.53950i	1.15847	+	0.246505i
$506$	−4.28891	+	7.42861i	−0.190665	+	0.330242i
$507$	−58.2872	−	21.4989i	−2.58862	−	0.954801i
$508$	−38.4928			−1.70784
$509$	10.2502	−	17.7539i	0.454334	−	0.786929i	−0.544316	−	0.838880i	$-0.683211\pi$
$509$	10.2502	−	17.7539i	0.454334	−	0.786929i	0.998650	+	0.0519512i	$0.0165440\pi$
$510$	−12.6283	−	24.0113i	−0.559191	−	1.06324i
$511$	37.4512	−	21.6225i	1.65674	−	0.956522i
$512$	20.5812	+	20.5812i	0.909571	+	0.909571i
$513$	−19.8349	+	5.04159i	−0.875733	+	0.222592i
$514$	−20.6541	−	35.7740i	−0.911015	−	1.57792i
$515$	7.33022	−	4.75804i	0.323008	−	0.209664i
$516$	−11.0311	−	1.01288i	−0.485616	−	0.0445896i
$517$	0.712018			0.0313145
$518$	19.7049	−	43.3064i	0.865783	−	1.90277i
$519$	−16.3701	−	6.03802i	−0.718566	−	0.265039i
$520$	−4.35182	−	13.4034i	−0.190840	−	0.587779i
$521$	17.8768	+	30.9634i	0.783195	+	1.35653i	0.930072	+	0.367378i	$0.119745\pi$
$521$	17.8768	+	30.9634i	0.783195	+	1.35653i	−0.146877	+	0.989155i	$0.546922\pi$
$522$	−7.50449	+	40.5203i	−0.328463	+	1.77353i
$523$	6.83607	−	25.5126i	0.298921	−	1.11559i	−0.639133	−	0.769096i	$-0.720707\pi$
$523$	6.83607	−	25.5126i	0.298921	−	1.11559i	0.938053	−	0.346490i	$-0.112627\pi$
$524$	−8.39102	−	8.39102i	−0.366564	−	0.366564i
$525$	−30.9844	+	8.72616i	−1.35227	+	0.380841i
$526$	−24.5414	+	24.5414i	−1.07006	+	1.07006i
$527$	−5.58595	+	9.67516i	−0.243328	+	0.421456i
$528$	1.49435	−	4.05142i	0.0650330	−	0.176315i
$529$		−	0.415233i		−	0.0180536i
$530$	−10.5409	+	20.6766i	−0.457868	+	0.898134i
$531$	1.65963	−	1.14095i	0.0720218	−	0.0495132i
$532$	25.1383	−	25.1383i	1.08989	−	1.08989i
$533$	−39.2837	+	10.5260i	−1.70157	+	0.455933i
$534$	27.8166	+	33.4413i	1.20374	+	1.44715i
$535$	−1.73295	−	5.33743i	−0.0749220	−	0.230757i
$536$	1.90429	+	0.510253i	0.0822528	+	0.0220396i
$537$	16.3381	−	23.1211i	0.705040	−	0.997748i
$538$	2.48895	+	9.28890i	0.107306	+	0.400473i
$539$	−2.87069	+	4.97219i	−0.123650	+	0.214167i
$540$	19.1532	−	20.7189i	0.824220	−	0.891600i
$541$	14.1598	−	14.1598i	0.608775	−	0.608775i	−0.333851	−	0.942626i	$-0.608348\pi$
$541$	14.1598	−	14.1598i	0.608775	−	0.608775i	0.942626	+	0.333851i	$0.108348\pi$
$542$	15.5559	−	58.0556i	0.668185	−	2.49370i
$543$	−2.68504	−	3.22797i	−0.115226	−	0.138526i
$544$	26.7338			1.14620
$545$	0.137134	+	2.62761i	0.00587417	+	0.112554i
$546$	60.5645	+	72.8112i	2.59192	+	3.11603i
$547$	16.8134	−	16.8134i	0.718890	−	0.718890i	−0.249488	−	0.968378i	$-0.580262\pi$
$547$	16.8134	−	16.8134i	0.718890	−	0.718890i	0.968378	+	0.249488i	$0.0802622\pi$
$548$	−19.0628	+	11.0059i	−0.814322	+	0.470149i
$549$	2.35051	+	29.8159i	0.100317	+	1.27251i
$550$	8.75362	+	1.39034i	0.373256	+	0.0592843i
$551$	−22.2651	+	12.8548i	−0.948526	+	0.547632i
$552$	−1.28009	−	7.44675i	−0.0544842	−	0.316955i
$553$	−57.0836	+	15.2955i	−2.42744	+	0.650431i
$554$	−46.4955			−1.97540
$555$	22.3702	−	7.38750i	0.949561	−	0.313582i
$556$	−1.64703			−0.0698497
$557$	6.04305	−	1.61923i	0.256052	−	0.0686089i	−0.128510	−	0.991708i	$-0.541019\pi$
$557$	6.04305	−	1.61923i	0.256052	−	0.0686089i	0.384562	+	0.923099i	$0.374353\pi$
$558$	−20.8341	−	3.85854i	−0.881977	−	0.163345i
$559$	15.9442	−	9.20538i	0.674367	−	0.389346i
$560$	5.11960	−	24.0601i	0.216343	−	1.01672i
$561$	−2.03358	−	4.41042i	−0.0858580	−	0.186208i
$562$	34.8822	−	20.1392i	1.47142	−	0.849522i
$563$	−22.0943	+	22.0943i	−0.931165	+	0.931165i	−0.997779	−	0.0666142i	$-0.978780\pi$
$563$	−22.0943	+	22.0943i	−0.931165	+	0.931165i	0.0666142	+	0.997779i	$0.478780\pi$
$564$	−2.73327	+	2.27354i	−0.115091	+	0.0957333i
$565$	26.5387	−	1.38505i	1.11649	−	0.0582694i
$566$	9.46595			0.397884
$567$	−11.9801	+	31.2338i	−0.503118	+	1.31170i
$568$	2.18021	−	8.13667i	0.0914798	−	0.341407i
$569$	−19.7201	+	19.7201i	−0.826708	+	0.826708i	−0.987060	−	0.160352i	$-0.948737\pi$
$569$	−19.7201	+	19.7201i	−0.826708	+	0.826708i	0.160352	+	0.987060i	$0.448737\pi$
$570$	32.0756	+	1.26513i	1.34350	+	0.0529905i
$571$	1.56962	−	2.71867i	0.0656867	−	0.113773i	−0.831312	−	0.555806i	$-0.812410\pi$
$571$	1.56962	−	2.71867i	0.0656867	−	0.113773i	0.896998	+	0.442034i	$0.145743\pi$
$572$	−3.70114	−	13.8128i	−0.154752	−	0.577543i
$573$	11.1889	+	7.90643i	0.467423	+	0.330296i
$574$	43.9552	+	11.7777i	1.83465	+	0.491594i
$575$	−22.5914	+	8.66076i	−0.942127	+	0.361179i
$576$	11.0012	+	31.0536i	0.458385	+	1.29390i
$577$	−5.52015	+	1.47912i	−0.229807	+	0.0615765i	−0.371885	−	0.928279i	$-0.621288\pi$
$577$	−5.52015	+	1.47912i	−0.229807	+	0.0615765i	0.142078	+	0.989855i	$0.454622\pi$
$578$	−8.80872	+	8.80872i	−0.366394	+	0.366394i
$579$	−4.80146	−	3.39286i	−0.199542	−	0.141003i
$580$	16.0987	−	31.5784i	0.668461	−	1.31122i
$581$			11.2986i			0.468747i
$582$	−57.3126	−	21.1395i	−2.37568	−	0.876259i
$583$	−2.07736	+	3.59809i	−0.0860354	+	0.149018i
$584$	7.41675	−	7.41675i	0.306907	−	0.306907i
$585$	−6.12493	+	46.4926i	−0.253235	+	1.92223i
$586$	−24.3290	−	24.3290i	−1.00502	−	1.00502i
$587$	11.0780	−	41.3437i	0.457239	−	1.70644i	−0.224183	−	0.974547i	$-0.571971\pi$
$587$	11.0780	−	41.3437i	0.457239	−	1.70644i	0.681421	−	0.731891i	$-0.261362\pi$
$588$	−4.85674	−	28.2535i	−0.200289	−	1.16515i
$589$	−6.60946	−	11.4479i	−0.272338	−	0.471703i
$590$	−3.00456	+	0.975520i	−0.123696	+	0.0401615i
$591$	4.41058	−	11.9578i	0.181427	−	0.491879i
$592$	−2.96081	+	17.7577i	−0.121689	+	0.729838i
$593$	18.1194			0.744073			0.372037	−	0.928218i	$-0.378660\pi$
$593$	18.1194			0.744073			0.372037	+	0.928218i	$0.378660\pi$
$594$	6.59663	−	6.42869i	0.270663	−	0.263772i
$595$	−15.0629	−	23.2060i	−0.617521	−	0.951351i
$596$	−13.5537	−	23.4757i	−0.555182	−	0.961603i
$597$	20.9898	+	14.8321i	0.859055	+	0.607035i
$598$	50.3352	+	50.3352i	2.05836	+	2.05836i
$599$	−15.1148	+	8.72652i	−0.617573	+	0.356556i	−0.775923	−	0.630827i	$-0.782716\pi$
$599$	−15.1148	+	8.72652i	−0.617573	+	0.356556i	0.158351	+	0.987383i	$0.449382\pi$
$600$	−6.71128	+	3.98943i	−0.273987	+	0.162868i
$601$	−15.0899	+	26.1365i	−0.615531	+	1.06613i	0.374761	+	0.927122i	$0.377725\pi$
$601$	−15.0899	+	26.1365i	−0.615531	+	1.06613i	−0.990291	+	0.139009i	$0.955608\pi$
$602$	−20.6001			−0.839597
$603$	−4.98912	−	4.25998i	−0.203173	−	0.173480i
$604$	14.4027	−	24.9462i	0.586037	−	1.01505i
$605$	−22.5062	−	4.78896i	−0.915007	−	0.194699i
$606$	−39.3993	+	18.1664i	−1.60049	+	0.737962i
$607$	−6.15250	−	22.9615i	−0.249722	−	0.931977i	−0.970951	−	0.239279i	$-0.923089\pi$
$607$	−6.15250	−	22.9615i	−0.249722	−	0.931977i	0.721228	−	0.692697i	$-0.243578\pi$
$608$	−15.8161	+	27.3942i	−0.641426	+	1.11098i
$609$	−3.84253	+	41.8481i	−0.155707	+	1.69577i
$610$	9.76347	−	45.8844i	0.395311	−	1.85781i
$611$	1.52931	−	5.70748i	0.0618695	−	0.230900i
$612$	21.8893	+	10.4372i	0.884825	+	0.421897i
$613$	3.26217	−	5.65024i	0.131758	−	0.228211i	−0.792596	−	0.609747i	$-0.791271\pi$
$613$	3.26217	−	5.65024i	0.131758	−	0.228211i	0.924354	+	0.381535i	$0.124605\pi$
$614$	30.2457	−	8.10430i	1.22062	−	0.327063i
$615$	10.4882	+	19.9422i	0.422926	+	0.804146i
$616$	−0.730580	+	2.72656i	−0.0294359	+	0.109856i
$617$	9.19280	+	5.30746i	0.370088	+	0.213670i	0.673497	−	0.739190i	$-0.264791\pi$
$617$	9.19280	+	5.30746i	0.370088	+	0.213670i	−0.303409	+	0.952860i	$0.598125\pi$
$618$	−4.92958	+	13.3649i	−0.198297	+	0.537615i
$619$			45.6214i			1.83368i	0.399256	+	0.916839i	$0.369268\pi$
$619$			45.6214i			1.83368i	−0.399256	+	0.916839i	$0.630732\pi$
$620$	16.2365	+	8.27735i	0.652073	+	0.332426i
$621$	−6.82028	+	24.2011i	−0.273688	+	0.971158i
$622$	−31.9477	−	55.3350i	−1.28099	−	2.21873i
$623$	31.3659	+	31.3659i	1.25665	+	1.25665i
$624$	−29.2662	−	20.6804i	−1.17159	−	0.827880i
$625$	16.7121	+	18.5932i	0.668484	+	0.743727i
$626$	−52.5976	+	30.3672i	−2.10222	+	1.21372i
$627$	5.72248	+	0.525443i	0.228534	+	0.0209842i
$628$	−16.1727			−0.645362
$629$	11.7677	+	16.4770i	0.469207	+	0.656981i
$630$	31.9457	−	41.6251i	1.27275	−	1.65838i
$631$	32.0858	−	8.59738i	1.27732	−	0.342256i	0.444487	−	0.895785i	$-0.353386\pi$
$631$	32.0858	−	8.59738i	1.27732	−	0.342256i	0.832830	+	0.553529i	$0.186719\pi$
$632$	−12.4134	+	7.16689i	−0.493779	+	0.285084i
$633$	37.1846	−	6.39199i	1.47795	−	0.254059i
$634$	53.2624	+	14.2716i	2.11532	+	0.566798i
$635$	−26.3349	−	23.7224i	−1.04507	−	0.941396i
$636$	−3.51455	−	20.4454i	−0.139361	−	0.810714i
$637$	33.6908	+	33.6908i	1.33488	+	1.33488i
$638$	5.78561	−	10.0210i	0.229054	−	0.396734i
$639$	−18.2021	+	21.3176i	−0.720064	+	0.843311i
$640$	−0.821239	−	15.7357i	−0.0324623	−	0.622007i
$641$	24.9030	+	14.3778i	0.983610	+	0.567887i	0.903358	−	0.428887i	$-0.141094\pi$
$641$	24.9030	+	14.3778i	0.983610	+	0.567887i	0.0802518	+	0.996775i	$0.474428\pi$
$642$	7.47043	+	5.27885i	0.294835	+	0.208339i
$643$	−15.9374	+	15.9374i	−0.628510	+	0.628510i	−0.947693	−	0.319183i	$-0.896592\pi$
$643$	−15.9374	+	15.9374i	−0.628510	+	0.628510i	0.319183	+	0.947693i	$0.396592\pi$
$644$	−11.3046	−	42.1892i	−0.445462	−	1.66249i
$645$	−6.92269	−	7.49121i	−0.272581	−	0.294966i
$646$	7.14065	+	26.6493i	0.280945	+	1.04850i
$647$	−9.49956	+	35.4528i	−0.373466	+	1.39379i	0.482107	+	0.876112i	$0.339872\pi$
$647$	−9.49956	+	35.4528i	−0.373466	+	1.39379i	−0.855573	+	0.517682i	$0.826795\pi$
$648$	−0.845999	+	8.06955i	−0.0332340	+	0.317002i
$649$	−0.546240	+	0.146365i	−0.0214418	+	0.00574531i
$650$	29.9464	−	67.1821i	1.17459	−	2.63510i
$651$	−21.5168	−	1.97569i	−0.843309	−	0.0774334i
$652$	−26.4056	−	26.4056i	−1.03412	−	1.03412i
$653$	0.729608	−	2.72293i	0.0285518	−	0.106557i	−0.950179	−	0.311703i	$-0.899100\pi$
$653$	0.729608	−	2.72293i	0.0285518	−	0.106557i	0.978731	+	0.205147i	$0.0657672\pi$
$654$	−2.74274	−	3.29734i	−0.107249	−	0.128936i
$655$	−0.569491	−	10.9120i	−0.0222519	−	0.426366i
$656$	−17.2185			−0.672271
$657$	−32.9000	+	11.6554i	−1.28355	+	0.454719i
$658$	−4.67501	+	4.67501i	−0.182251	+	0.182251i
$659$	−15.8277	−	27.4143i	−0.616559	−	1.06791i	−0.990109	−	0.140301i	$-0.955193\pi$
$659$	−15.8277	−	27.4143i	−0.616559	−	1.06791i	0.373550	−	0.927610i	$-0.378140\pi$
$660$	−7.01202	+	3.68784i	−0.272942	+	0.143549i
$661$	−4.24383	+	15.8382i	−0.165066	+	0.616034i	0.832966	+	0.553324i	$0.186641\pi$
$661$	−4.24383	+	15.8382i	−0.165066	+	0.616034i	−0.998032	+	0.0627097i	$0.980026\pi$
$662$	10.5432	+	18.2614i	0.409773	+	0.709748i
$663$	−39.7215	+	6.82808i	−1.54265	+	0.265181i
$664$	0.709277	+	2.64706i	0.0275253	+	0.102726i
$665$	32.6907	−	1.70612i	1.26769	−	0.0661604i
$666$	−22.0033	+	31.4724i	−0.852611	+	1.21953i
$667$			31.5864i			1.22303i
$668$	21.5492	−	5.77410i	0.833765	−	0.223407i
$669$	3.94108	+	22.9267i	0.152371	+	0.886398i
$670$	5.60249	+	8.63118i	0.216443	+	0.333452i
$671$	2.17356	−	8.11185i	0.0839095	−	0.313154i
$672$	21.6499	+	46.9542i	0.835163	+	1.81130i
$673$	5.37015	−	3.10046i	0.207004	−	0.119514i	−0.392914	−	0.919575i	$-0.628533\pi$
$673$	5.37015	−	3.10046i	0.207004	−	0.119514i	0.599918	+	0.800061i	$0.295200\pi$
$674$	−4.24727	−	4.24727i	−0.163599	−	0.163599i
$675$	25.8723	−	2.37113i	0.995827	−	0.0912647i
$676$	−87.1028			−3.35011
$677$		−	32.7413i		−	1.25835i	−0.777263	−	0.629175i	$-0.783393\pi$
$677$		−	32.7413i		−	1.25835i	0.777263	−	0.629175i	$-0.216607\pi$
$678$	−33.3030	+	27.7015i	−1.27899	+	1.06387i
$679$	−60.1720	−	16.1231i	−2.30919	−	0.618746i
$680$	−4.98573	−	4.49113i	−0.191194	−	0.172227i
$681$	−17.1224	−	1.57220i	−0.656133	−	0.0602467i
$682$	5.15242	+	2.97475i	0.197296	+	0.113909i
$683$	8.78624	+	32.7907i	0.336196	+	1.25470i	0.902567	+	0.430550i	$0.141680\pi$
$683$	8.78624	+	32.7907i	0.336196	+	1.25470i	−0.566371	+	0.824151i	$0.691653\pi$
$684$	−23.6451	+	16.2554i	−0.904091	+	0.621540i
$685$	−19.8246	−	4.21835i	−0.757457	−	0.161175i
$686$	0.373026	+	1.39215i	0.0142422	+	0.0531525i
$687$	0.00765126	+	0.00919841i	0.000291914	+	0.000350941i
$688$	7.52910	−	2.01742i	0.287044	−	0.0769133i
$689$	24.3801	+	24.3801i	0.928809	+	0.928809i
$690$	21.0499	−	33.3509i	0.801357	−	1.26965i
$691$	−39.0696	−	22.5569i	−1.48628	−	0.858104i	−0.486401	−	0.873736i	$-0.661691\pi$
$691$	−39.0696	−	22.5569i	−1.48628	−	0.858104i	−0.999878	+	0.0156321i	$0.995024\pi$
$692$	−24.4630			−0.929943
$693$	6.09944	−	7.14342i	0.231698	−	0.271356i
$694$	19.5830	+	11.3063i	0.743362	+	0.429180i
$695$	−1.12682	−	1.01504i	−0.0427427	−	0.0385025i
$696$	1.72680	+	10.0454i	0.0654543	+	0.380771i
$697$	−13.6935	+	13.6935i	−0.518679	+	0.518679i
$698$	2.66168	−	9.93352i	0.100746	−	0.375989i
$699$	−7.70422	−	44.8183i	−0.291400	−	1.69518i
$700$	−36.5236	+	26.5117i	−1.38046	+	1.00205i
$701$	20.4180	−	5.47098i	0.771176	−	0.206636i	0.148285	−	0.988945i	$-0.452625\pi$
$701$	20.4180	−	5.47098i	0.771176	−	0.206636i	0.622891	+	0.782309i	$0.285958\pi$
$702$	−37.3632	−	66.6860i	−1.41018	−	2.51690i
$703$	−23.8460	+	2.31036i	−0.899368	+	0.0871368i
$704$		−	9.25056i		−	0.348644i
$705$	−3.27111	−	0.129020i	−0.123197	−	0.00485916i
$706$	0.731114	−	0.422109i	0.0275158	−	0.0158863i
$707$	−38.3160	+	22.1218i	−1.44102	+	0.831974i
$708$	1.62953	−	2.30605i	0.0612415	−	0.0866668i
$709$	−8.73503	+	8.73503i	−0.328051	+	0.328051i	−0.851845	−	0.523794i	$-0.824516\pi$
$709$	−8.73503	+	8.73503i	−0.328051	+	0.328051i	0.523794	+	0.851845i	$0.324516\pi$
$710$	36.8794	−	23.9384i	1.38406	−	0.898391i
$711$	47.5506	−	3.74860i	1.78329	−	0.140584i
$712$	9.31745	+	5.37943i	0.349186	+	0.201603i
$713$	−16.2406			−0.608215
$714$	42.3105	+	15.6060i	1.58343	+	0.584040i
$715$	5.98046	−	11.7310i	0.223656	−	0.438715i
$716$	10.2734	−	38.3408i	0.383934	−	1.43286i
$717$	21.2082	−	9.77879i	0.792033	−	0.365196i
$718$	7.50008	+	27.9907i	0.279900	+	1.04460i
$719$	−21.9194	−	12.6552i	−0.817457	−	0.471959i	0.0320820	−	0.999485i	$-0.489786\pi$
$719$	−21.9194	−	12.6552i	−0.817457	−	0.471959i	−0.849539	+	0.527526i	$0.823120\pi$
$720$	−7.59936	+	18.3420i	−0.283211	+	0.683566i
$721$	−3.75978	+	14.0317i	−0.140022	+	0.522568i
$722$	7.08863	+	1.89939i	0.263811	+	0.0706880i
$723$	11.0752	+	1.01693i	0.411889	+	0.0378200i
$724$	−5.09810	−	2.94339i	−0.189469	−	0.109390i
$725$	30.4751	−	11.6831i	1.13182	−	0.433899i
$726$	34.0611	−	15.7051i	1.26412	−	0.582870i
$727$	6.03570	+	1.61726i	0.223852	+	0.0599809i	0.369001	−	0.929429i	$-0.379700\pi$
$727$	6.03570	+	1.61726i	0.223852	+	0.0599809i	−0.145150	+	0.989410i	$0.546366\pi$
$728$	20.2867	+	11.7125i	0.751876	+	0.434096i
$729$	14.0984	−	23.0268i	0.522162	−	0.852846i
$730$	54.6722	−	2.85332i	2.02351	−	0.105606i
$731$	4.38332	−	7.59213i	0.162123	−	0.280805i
$732$	17.5581	+	38.0799i	0.648966	+	1.40747i
$733$	18.4205	+	31.9053i	0.680377	+	1.17845i	0.974866	+	0.222793i	$0.0715175\pi$
$733$	18.4205	+	31.9053i	0.680377	+	1.17845i	−0.294488	+	0.955655i	$0.595149\pi$
$734$	−46.8469	+	46.8469i	−1.72915	+	1.72915i
$735$	14.0893	−	22.3227i	0.519693	−	0.823387i
$736$	19.4314	+	33.6562i	0.716252	+	1.24058i
$737$	0.921049	+	1.59530i	0.0339273	+	0.0587637i
$738$	−33.1525	−	15.8076i	−1.22036	−	0.581884i
$739$			13.9962i			0.514858i	0.966297	+	0.257429i	$0.0828753\pi$
$739$			13.9962i			0.514858i	−0.966297	+	0.257429i	$0.917125\pi$
$740$	25.8418	−	20.5713i	0.949962	−	0.756215i
$741$	16.5030	−	44.7424i	0.606253	−	1.64365i
$742$	−9.98492	−	37.2642i	−0.366558	−	1.36801i
$743$	36.3991	−	21.0150i	1.33535	−	0.770966i	0.349238	−	0.937034i	$-0.386441\pi$
$743$	36.3991	−	21.0150i	1.33535	−	0.770966i	0.986114	+	0.166068i	$0.0531073\pi$
$744$	−5.16500	+	0.887859i	−0.189358	+	0.0325505i
$745$	5.19487	−	24.4138i	0.190325	−	0.894454i
$746$	−32.5113	−	32.5113i	−1.19032	−	1.19032i
$747$	1.66068	−	8.96679i	0.0607610	−	0.328078i
$748$	−4.81487	−	4.81487i	−0.176049	−	0.176049i
$749$	8.07844	+	4.66409i	0.295180	+	0.170422i
$750$	−39.9634	−	7.97360i	−1.45926	−	0.291155i
$751$		−	7.61919i		−	0.278028i	−0.990290	−	0.139014i	$-0.955607\pi$
$751$		−	7.61919i		−	0.278028i	0.990290	−	0.139014i	$-0.0443933\pi$
$752$	1.25083	−	2.16650i	0.0456130	−	0.0790041i
$753$	−8.46278	+	11.9762i	−0.308401	+	0.436438i
$754$	−67.9006	−	67.9006i	−2.47279	−	2.47279i
$755$	25.2275	−	8.19084i	0.918123	−	0.298095i
$756$	−0.604681	+	46.8980i	−0.0219921	+	1.70566i
$757$	16.3724	−	4.38698i	0.595066	−	0.159448i	0.0512986	−	0.998683i	$-0.483664\pi$
$757$	16.3724	−	4.38698i	0.595066	−	0.159448i	0.543768	+	0.839236i	$0.316997\pi$
$758$	5.82949	−	21.7560i	0.211737	−	0.790212i
$759$	4.07435	−	5.76588i	0.147890	−	0.209288i
$760$	7.55172	−	2.45188i	0.273929	−	0.0889392i
$761$	3.23631	−	5.60546i	0.117316	−	0.203198i	−0.801387	−	0.598146i	$-0.795904\pi$
$761$	3.23631	−	5.60546i	0.117316	−	0.203198i	0.918703	+	0.394948i	$0.129238\pi$
$762$	57.5333	+	5.28276i	2.08421	+	0.191374i
$763$	−3.09270	−	3.09270i	−0.111963	−	0.111963i
$764$	18.5541	+	4.97156i	0.671265	+	0.179865i
$765$	8.54339	+	20.6306i	0.308887	+	0.745901i
$766$	76.4325			2.76162
$767$			4.69299i			0.169454i
$768$	−7.90186	−	9.49968i	−0.285134	−	0.342790i
$769$	−5.62804	−	5.62804i	−0.202952	−	0.202952i	0.598311	−	0.801264i	$-0.295839\pi$
$769$	−5.62804	−	5.62804i	−0.202952	−	0.202952i	−0.801264	+	0.598311i	$0.795839\pi$
$770$	−12.3581	+	8.02164i	−0.445356	+	0.289080i
$771$	14.2363	+	30.8756i	0.512708	+	1.11196i
$772$	−7.96207	−	2.13343i	−0.286561	−	0.0767839i
$773$	2.12581	+	3.68201i	0.0764600	+	0.132433i	0.901720	−	0.432320i	$-0.142305\pi$
$773$	2.12581	+	3.68201i	0.0764600	+	0.132433i	−0.825260	+	0.564753i	$0.808972\pi$
$774$	16.3486	+	3.02781i	0.587638	+	0.108832i
$775$	6.00702	+	15.6692i	0.215779	+	0.562855i
$776$	−15.1093			−0.542392
$777$	−19.4097	+	34.0119i	−0.696320	+	1.22017i
$778$		−	10.3304i		−	0.370364i
$779$	−5.93054	−	22.1331i	−0.212484	−	0.793000i
$780$	14.5006	+	64.1287i	0.519205	+	2.29618i
$781$	6.81643	−	3.93547i	0.243911	−	0.140822i
$782$	32.7410	+	8.77291i	1.17081	+	0.313719i
$783$	9.20035	−	32.6466i	0.328794	−	1.16669i
$784$	10.0861	+	17.4697i	0.360218	+	0.623916i
$785$	−11.0646	−	9.96695i	−0.394912	−	0.355736i
$786$	11.3901	+	13.6932i	0.406270	+	0.488422i
$787$		−	0.369424i		−	0.0131686i	−0.999978	−	0.00658428i	$-0.997904\pi$
$787$		−	0.369424i		−	0.0131686i	0.999978	−	0.00658428i	$-0.00209586\pi$
$788$		−	17.8694i		−	0.636572i
$789$	21.9616	−	18.2677i	0.781855	−	0.650348i
$790$	−73.1768	−	15.5708i	−2.60351	−	0.553986i
$791$	−31.2362	+	31.2362i	−1.11063	+	1.11063i
$792$	0.980551	−	2.05646i	0.0348424	−	0.0730733i
$793$	−60.3554	−	34.8462i	−2.14328	−	1.23743i
$794$	−7.64399	+	2.04820i	−0.271275	+	0.0726880i
$795$	10.1957	−	16.1537i	0.361603	−	0.572913i
$796$	34.8066	+	9.32639i	1.23369	+	0.330565i
$797$	−6.04540	+	1.61986i	−0.214139	+	0.0573784i	−0.364294	−	0.931284i	$-0.618690\pi$
$797$	−6.04540	+	1.61986i	−0.214139	+	0.0573784i	0.150155	+	0.988663i	$0.452023\pi$
$798$	−41.0230	+	34.1231i	−1.45220	+	1.20794i
$799$	−0.728212	−	2.71773i	−0.0257623	−	0.0961462i
$800$	25.2848	−	31.1964i	0.893954	−	1.10296i
$801$	−20.2823	−	29.5027i	−0.716641	−	1.04243i
$802$	−24.2259	+	41.9605i	−0.855447	+	1.48168i
$803$	9.80059			0.345855
$804$	−8.62964	−	3.18300i	−0.304344	−	0.112256i
$805$	18.2664	−	35.8306i	0.643807	−	1.26286i
$806$	34.9120	−	34.9120i	1.22972	−	1.22972i
$807$	−1.34093	−	7.80070i	−0.0472031	−	0.274598i
$808$	−7.58801	+	7.58801i	−0.266945	+	0.266945i
$809$	41.9563	+	11.2421i	1.47510	+	0.395253i	0.904678	−	0.426096i	$-0.140111\pi$
$809$	41.9563	+	11.2421i	1.47510	+	0.395253i	0.570426	+	0.821349i	$0.306778\pi$
$810$	−31.4707	+	28.3390i	−1.10577	+	0.995730i
$811$	10.7115	+	18.5528i	0.376130	+	0.651476i	0.990495	−	0.137545i	$-0.0439213\pi$
$811$	10.7115	+	18.5528i	0.376130	+	0.651476i	−0.614366	+	0.789022i	$0.710588\pi$
$812$	15.2495	+	56.9120i	0.535153	+	1.99722i
$813$	−17.1192	+	46.4129i	−0.600395	+	1.62777i
$814$	8.77467	−	6.26676i	0.307552	−	0.219650i
$815$	−1.79213	−	34.3388i	−0.0627755	−	1.20283i
$816$	−16.9923	−	1.56025i	−0.594851	−	0.0546197i
$817$	5.18647	+	8.98322i	0.181451	+	0.314283i
$818$	−22.1185	+	12.7701i	−0.773354	+	0.446496i
$819$	−44.1604	−	64.2357i	−1.54309	−	2.24458i
$820$	23.4720	+	21.1435i	0.819678	+	0.738364i
$821$	1.62437	−	0.937830i	0.0566909	−	0.0327305i	−0.471387	−	0.881927i	$-0.656246\pi$
$821$	1.62437	−	0.937830i	0.0566909	−	0.0327305i	0.528078	+	0.849196i	$0.322913\pi$
$822$	30.0027	−	13.8338i	1.04646	−	0.482509i
$823$	19.5427	+	11.2830i	0.681217	+	0.393301i	0.800313	−	0.599582i	$-0.204667\pi$
$823$	19.5427	+	11.2830i	0.681217	+	0.393301i	−0.119097	+	0.992883i	$0.538000\pi$
$824$			3.52338i			0.122743i
$825$	−7.07003	−	1.79834i	−0.246147	−	0.0626101i
$826$	2.62553	−	4.54755i	0.0913538	−	0.158229i
$827$	−19.3199	−	5.17675i	−0.671818	−	0.180013i	−0.0932445	−	0.995643i	$-0.529724\pi$
$827$	−19.3199	−	5.17675i	−0.671818	−	0.180013i	−0.578574	+	0.815630i	$0.696391\pi$
$828$	2.77051	+	35.1436i	0.0962819	+	1.22133i
$829$	−37.3307	+	10.0027i	−1.29655	+	0.347409i	−0.840144	−	0.542364i	$-0.817529\pi$
$829$	−37.3307	+	10.0027i	−1.29655	+	0.347409i	−0.456404	+	0.889773i	$0.650863\pi$
$830$	−6.49651	+	12.7433i	−0.225497	+	0.442325i
$831$	38.1088	+	3.49918i	1.32198	+	0.121385i
$832$	−74.1518	−	19.8689i	−2.57075	−	0.688830i
$833$	21.9145	+	5.87197i	0.759292	+	0.203452i
$834$	2.46174	+	0.226039i	0.0852430	+	0.00782708i
$835$	18.3014	+	9.33004i	0.633346	+	0.322879i
$836$	7.78238	−	2.08528i	0.269159	−	0.0721210i
$837$	16.7857	+	4.73048i	0.580199	+	0.163509i
$838$	27.4841	+	7.36433i	0.949421	+	0.254397i
$839$	1.97476	−	3.42038i	0.0681761	−	0.118084i	−0.829922	−	0.557879i	$-0.811615\pi$
$839$	1.97476	−	3.42038i	0.0681761	−	0.118084i	0.898098	+	0.439794i	$0.144949\pi$
$840$	3.85045	−	12.3938i	0.132853	−	0.427627i
$841$		−	13.6092i		−	0.469281i
$842$	45.8430	+	26.4675i	1.57985	+	0.912129i
$843$	−30.1059	+	13.8814i	−1.03690	+	0.478100i
$844$	45.8118	−	26.4495i	1.57691	−	0.910429i
$845$	−59.5914	−	53.6798i	−2.05001	−	1.84664i
$846$	4.39731	−	3.02304i	0.151182	−	0.103934i
$847$	33.1246	−	19.1245i	1.13817	−	0.657125i
$848$	7.29875	+	12.6418i	0.250640	+	0.434121i
$849$	−7.75850	−	0.712392i	−0.266271	−	0.0244492i
$850$	−3.64587	−	34.8339i	−0.125052	−	1.19479i
$851$	−12.1902	+	26.7911i	−0.417876	+	0.918386i
$852$	−13.6004	+	36.8728i	−0.465940	+	1.26324i
$853$	−9.56236	−	35.6872i	−0.327409	−	1.22191i	−0.911868	−	0.410484i	$-0.865360\pi$
$853$	−9.56236	−	35.6872i	−0.327409	−	1.22191i	0.584459	−	0.811423i	$-0.301307\pi$
$854$	38.9900	+	67.5326i	1.33421	+	2.31092i
$855$	−26.1947	−	3.45089i	−0.895839	−	0.118018i
$856$	2.18542	+	0.585580i	0.0746960	+	0.0200147i
$857$	−15.9042	+	15.9042i	−0.543278	+	0.543278i	−0.924488	−	0.381210i	$-0.875507\pi$
$857$	−15.9042	+	15.9042i	−0.543278	+	0.543278i	0.381210	+	0.924488i	$0.375507\pi$
$858$	3.63623	+	21.1533i	0.124139	+	0.722162i
$859$	3.14774	−	3.14774i	0.107399	−	0.107399i	−0.651365	−	0.758764i	$-0.725803\pi$
$859$	3.14774	−	3.14774i	0.107399	−	0.107399i	0.758764	+	0.651365i	$0.225803\pi$
$860$	−12.7408	−	6.49527i	−0.434459	−	0.221487i
$861$	−35.1402	−	12.9613i	−1.19758	−	0.441720i
$862$	−26.3009			−0.895811
$863$	22.9542	−	39.7578i	0.781368	−	1.35337i	−0.149776	−	0.988720i	$-0.547855\pi$
$863$	22.9542	−	39.7578i	0.781368	−	1.35337i	0.931145	−	0.364650i	$-0.118811\pi$
$864$	−10.2804	−	40.4457i	−0.349746	−	1.37599i
$865$	−16.7364	−	15.0761i	−0.569054	−	0.512603i
$866$	−0.0919395	−	0.343123i	−0.00312423	−	0.0116598i
$867$	7.88275	−	6.55689i	0.267712	−	0.222684i
$868$	−29.2621	+	7.84075i	−0.993220	+	0.266132i
$869$	−12.9368	−	3.46641i	−0.438852	−	0.117590i
$870$	−28.3957	+	44.9894i	−0.962705	+	1.52528i
$871$	14.7661	−	3.95657i	0.500330	−	0.134063i
$872$	−0.918707	−	0.530416i	−0.0311114	−	0.0179621i
$873$	45.3838	+	21.6396i	1.53601	+	0.732391i
$874$	−28.3597	+	28.3597i	−0.959280	+	0.959280i
$875$	−41.3263	−	4.37084i	−1.39708	−	0.147761i
$876$	−37.6222	+	31.2942i	−1.27113	+	1.05733i
$877$			37.3219i			1.26027i	0.776485	+	0.630135i	$0.217001\pi$
$877$			37.3219i			1.26027i	−0.776485	+	0.630135i	$0.782999\pi$
$878$			42.4805i			1.43365i
$879$	18.1096	+	21.7715i	0.610822	+	0.734336i
$880$	3.73117	−	4.14208i	0.125778	−	0.139629i
$881$	−18.4413	−	31.9412i	−0.621303	−	1.07613i	−0.989243	−	0.146279i	$-0.953270\pi$
$881$	−18.4413	−	31.9412i	−0.621303	−	1.07613i	0.367941	−	0.929849i	$-0.380063\pi$
$882$	3.38163	+	42.8956i	0.113865	+	1.44437i
$883$	39.6542	+	10.6253i	1.33447	+	0.357571i	0.854380	−	0.519648i	$-0.173937\pi$
$883$	39.6542	+	10.6253i	1.33447	+	0.357571i	0.480091	+	0.877219i	$0.340604\pi$
$884$	−48.9373	+	28.2540i	−1.64594	+	0.950284i
$885$	2.53602	−	0.573439i	0.0852475	−	0.0192759i
$886$	−16.3239	−	60.9214i	−0.548411	−	2.04670i
$887$			9.46558i			0.317823i	0.987293	+	0.158912i	$0.0507985\pi$
$887$			9.46558i			0.317823i	−0.987293	+	0.158912i	$0.949202\pi$
$888$	−2.41222	+	9.18680i	−0.0809488	+	0.308289i
$889$	58.9176			1.97603
$890$	17.3415	+	53.4111i	0.581288	+	1.79034i
$891$	−5.89056	+	4.77264i	−0.197341	+	0.159890i
$892$	16.3078	+	28.2460i	0.546027	+	0.945746i
$893$	3.21569	+	0.861641i	0.107609	+	0.0288337i
$894$	17.0363	+	36.9481i	0.569778	+	1.23573i
$895$	30.6573	−	19.8996i	1.02476	−	0.665169i
$896$	18.5209	+	18.5209i	0.618741	+	0.618741i
$897$	−37.4677	−	45.0440i	−1.25101	−	1.50397i
$898$			7.73578i			0.258146i
$899$	21.9081			0.730675
$900$	32.8824	−	15.6719i	1.09608	−	0.522395i
$901$	15.8583	+	4.24921i	0.528316	+	0.141562i
$902$	7.29236	+	7.29236i	0.242809	+	0.242809i
$903$	16.8843	+	1.55033i	0.561874	+	0.0515918i
$904$	−5.35718	+	9.27891i	−0.178177	+	0.308612i
$905$	−1.67391	−	5.15559i	−0.0556427	−	0.171378i
$906$	−24.9506	+	35.3092i	−0.828929	+	1.17307i
$907$	−6.59995	+	24.6313i	−0.219148	+	0.817870i	0.765517	+	0.643415i	$0.222483\pi$
$907$	−6.59995	+	24.6313i	−0.219148	+	0.817870i	−0.984665	+	0.174455i	$0.944184\pi$
$908$	−23.2859	+	6.23944i	−0.772770	+	0.207063i
$909$	33.6597	−	11.9245i	1.11642	−	0.395511i
$910$	37.7573	+	116.291i	1.25164	+	3.85501i
$911$	−6.80584	−	6.80584i	−0.225488	−	0.225488i	0.585317	−	0.810805i	$-0.300970\pi$
$911$	−6.80584	−	6.80584i	−0.225488	−	0.225488i	−0.810805	+	0.585317i	$0.800970\pi$
$912$	11.6517	−	16.4891i	0.385826	−	0.546008i
$913$	−1.28030	+	2.21755i	−0.0423719	+	0.0733902i
$914$		−	46.8613i		−	1.55003i
$915$	−11.4555	+	36.8731i	−0.378709	+	1.21899i
$916$	0.0145275	+	0.00838746i	0.000480002	+	0.000277129i
$917$	12.8434	+	12.8434i	0.424127	+	0.424127i
$918$	−31.2845	−	18.6040i	−1.03254	−	0.614023i
$919$	−10.0880	−	10.0880i	−0.332771	−	0.332771i	0.520867	−	0.853638i	$-0.325609\pi$
$919$	−10.0880	−	10.0880i	−0.332771	−	0.332771i	−0.853638	+	0.520867i	$0.825609\pi$
$920$	2.03020	−	9.54111i	0.0669336	−	0.314561i
$921$	−25.3999	+	4.36623i	−0.836957	+	0.143872i
$922$	57.1427	−	32.9913i	1.88189	−	1.08651i
$923$	−16.9057	−	63.0928i	−0.556457	−	2.07672i
$924$	4.55742	−	12.3559i	0.149928	−	0.406480i
$925$	30.3574	+	1.85195i	0.998144	+	0.0608917i
$926$		−	24.3521i		−	0.800261i
$927$	5.04621	−	10.5832i	0.165739	−	0.347597i
$928$	−26.2124	−	45.4012i	−0.860464	−	1.49037i
$929$	−21.8196	−	37.7926i	−0.715876	−	1.23993i	−0.962621	−	0.270854i	$-0.912694\pi$
$929$	−21.8196	−	37.7926i	−0.715876	−	1.23993i	0.246744	−	0.969081i	$-0.420639\pi$
$930$	−23.1319	−	14.6000i	−0.758525	−	0.478754i
$931$	−18.9820	+	18.9820i	−0.622109	+	0.622109i
$932$	−31.8794	−	55.2167i	−1.04424	−	1.80868i
$933$	22.0206	+	47.7582i	0.720923	+	1.56353i
$934$	−15.3477	+	26.5830i	−0.502192	+	0.869822i
$935$	−0.326781	−	6.26142i	−0.0106869	−	0.204770i
$936$	−14.3784	−	12.2770i	−0.469972	−	0.401287i
$937$	−26.9553	−	15.5626i	−0.880590	−	0.508409i	−0.00973736	−	0.999953i	$-0.503100\pi$
$937$	−26.9553	−	15.5626i	−0.880590	−	0.508409i	−0.870853	+	0.491543i	$0.836433\pi$
$938$	−16.5220	−	4.42706i	−0.539463	−	0.144549i
$939$	45.3956	−	20.9313i	1.48143	−	0.683066i
$940$	−4.36547	+	1.41738i	−0.142386	+	0.0462297i
$941$	36.1912	+	20.8950i	1.17980	+	0.681157i	0.955968	−	0.293471i	$-0.0948103\pi$
$941$	36.1912	+	20.8950i	1.17980	+	0.681157i	0.223831	+	0.974628i	$0.428144\pi$
$942$	24.1726	+	2.21955i	0.787585	+	0.0723167i
$943$	−27.1924	−	7.28619i	−0.885508	−	0.237271i
$944$	−0.514248	+	1.91920i	−0.0167374	+	0.0624647i
$945$	−29.3161	+	31.7127i	−0.953652	+	1.03161i
$946$	−4.04312	−	2.33430i	−0.131453	−	0.0758945i
$947$	9.84307	+	36.7348i	0.319857	+	1.19372i	0.919382	+	0.393366i	$0.128689\pi$
$947$	9.84307	+	36.7348i	0.319857	+	1.19372i	−0.599525	+	0.800356i	$0.704644\pi$
$948$	60.7301	−	28.0018i	1.97242	−	0.909455i
$949$	21.0503	−	78.5607i	0.683321	−	2.55019i
$950$	37.8515	+	16.8723i	1.22806	+	0.547410i
$951$	−42.5810	−	15.7058i	−1.38078	−	0.509295i
$952$	11.1543			0.361513
$953$	−9.44073	−	5.45061i	−0.305815	−	0.176562i	0.339237	−	0.940701i	$-0.389831\pi$
$953$	−9.44073	−	5.45061i	−0.305815	−	0.176562i	−0.645052	+	0.764138i	$0.723164\pi$
$954$	2.44709	+	31.0411i	0.0792276	+	1.00499i
$955$	9.62994	+	14.8359i	0.311618	+	0.480077i
$956$	23.1530	−	23.1530i	0.748822	−	0.748822i
$957$	−5.49618	+	7.77799i	−0.177666	+	0.251427i
$958$	11.0232	−	6.36427i	0.356144	−	0.205620i
$959$	29.1777	−	16.8458i	0.942199	−	0.543979i
$960$	−1.67623	+	42.4984i	−0.0541000	+	1.37163i
$961$		−	19.7357i		−	0.636634i
$962$	−31.3871	−	83.7972i	−1.01196	−	2.70173i
$963$	−5.72566	−	4.88887i	−0.184507	−	0.157542i
$964$	15.0618	−	4.03580i	0.485109	−	0.129984i
$965$	−4.13246	−	6.36647i	−0.133029	−	0.204944i
$966$	11.1063	+	64.6096i	0.357340	+	2.07878i
$967$	−11.4976	+	42.9097i	−0.369738	+	1.37988i	0.491144	+	0.871078i	$0.336579\pi$
$967$	−11.4976	+	42.9097i	−0.369738	+	1.37988i	−0.860882	+	0.508804i	$0.830088\pi$
$968$	6.55991	−	6.55991i	0.210844	−	0.210844i
$969$	−3.84705	−	22.3797i	−0.123585	−	0.718940i
$970$	−58.5951	−	52.7823i	−1.88137	−	1.69474i
$971$	−5.05899	−	2.92081i	−0.162351	−	0.0937333i	0.416623	−	0.909079i	$-0.363213\pi$
$971$	−5.05899	−	2.92081i	−0.162351	−	0.0937333i	−0.578974	+	0.815346i	$0.696547\pi$
$972$	7.37297	−	37.1302i	0.236488	−	1.19095i
$973$	2.52097			0.0808186
$974$	−10.9116	−	6.29980i	−0.349629	−	0.201859i
$975$	−29.6008	+	52.8102i	−0.947983	+	1.69128i
$976$	−20.8640	−	20.8640i	−0.667841	−	0.667841i
$977$	29.4657	−	7.89532i	0.942692	−	0.252594i	0.245434	−	0.969413i	$-0.421070\pi$
$977$	29.4657	−	7.89532i	0.942692	−	0.252594i	0.697259	+	0.716820i	$0.254403\pi$
$978$	35.8433	+	43.0911i	1.14614	+	1.37790i
$979$	2.60187	+	9.71032i	0.0831562	+	0.310343i
$980$	7.70269	−	36.1996i	0.246054	−	1.15635i
$981$	1.99985	+	2.90899i	0.0638504	+	0.0928768i
$982$	1.23733	+	4.61778i	0.0394848	+	0.147359i
$983$	12.5666	+	7.25536i	0.400814	+	0.231410i	0.686835	−	0.726813i	$-0.258999\pi$
$983$	12.5666	+	7.25536i	0.400814	+	0.231410i	−0.286021	+	0.958223i	$0.592333\pi$
$984$	−9.04635	−	0.830643i	−0.288387	−	0.0264799i
$985$	11.0126	−	12.2254i	0.350891	−	0.389533i
$986$	−44.1666	−	11.8344i	−1.40655	−	0.376884i
$987$	4.18358	−	3.47991i	0.133165	−	0.110767i
$988$		−	66.8618i		−	2.12716i
$989$	12.7441			0.405237
$990$	10.9866	−	4.54971i	0.349178	−	0.144599i
$991$	−4.84279	−	4.84279i	−0.153836	−	0.153836i	0.625993	−	0.779829i	$-0.284694\pi$
$991$	−4.84279	−	4.84279i	−0.153836	−	0.153836i	−0.779829	+	0.625993i	$0.784694\pi$
$992$	23.3436	−	13.4775i	0.741162	−	0.427910i
$993$	−7.26713	−	15.7609i	−0.230615	−	0.500157i
$994$	−18.9160	+	70.5955i	−0.599979	+	2.23915i
$995$	18.0653	+	27.8313i	0.572707	+	0.882312i
$996$	−2.16606	−	12.6008i	−0.0686343	−	0.399271i
$997$	27.7368	−	7.43204i	0.878432	−	0.235375i	0.208702	−	0.977979i	$-0.433076\pi$
$997$	27.7368	−	7.43204i	0.878432	−	0.235375i	0.669731	+	0.742604i	$0.266410\pi$
$998$		−	7.40202i		−	0.234307i
$999$	20.4030	−	24.1396i	0.645521	−	0.763742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.bm.a.14.12	yes	288
3.2	odd	2	inner	555.2.bm.a.14.62	yes	288
5.4	even	2	inner	555.2.bm.a.14.61	yes	288
15.14	odd	2	inner	555.2.bm.a.14.11	✓	288
37.8	odd	12	inner	555.2.bm.a.119.11	yes	288
111.8	even	12	inner	555.2.bm.a.119.61	yes	288
185.119	odd	12	inner	555.2.bm.a.119.62	yes	288
555.119	even	12	inner	555.2.bm.a.119.12	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bm.a.14.11	✓	288	15.14	odd	2	inner
555.2.bm.a.14.12	yes	288	1.1	even	1	trivial
555.2.bm.a.14.61	yes	288	5.4	even	2	inner
555.2.bm.a.14.62	yes	288	3.2	odd	2	inner
555.2.bm.a.119.11	yes	288	37.8	odd	12	inner
555.2.bm.a.119.12	yes	288	555.119	even	12	inner
555.2.bm.a.119.61	yes	288	111.8	even	12	inner
555.2.bm.a.119.62	yes	288	185.119	odd	12	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:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.bm (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.03267 + 0.544653i) q^{2} +(1.70701 - 0.293434i) q^{3} +(2.10306 - 1.21420i) q^{4} +(2.18710 + 0.465380i) q^{5} +(-3.30998 + 1.52619i) q^{6} +(-3.21898 + 1.85848i) q^{7} +(-0.637478 + 0.637478i) q^{8} +(2.82779 - 1.00179i) q^{9} +O(q^{10})\)	\(q+(-2.03267 + 0.544653i) q^{2} +(1.70701 - 0.293434i) q^{3} +(2.10306 - 1.21420i) q^{4} +(2.18710 + 0.465380i) q^{5} +(-3.30998 + 1.52619i) q^{6} +(-3.21898 + 1.85848i) q^{7} +(-0.637478 + 0.637478i) q^{8} +(2.82779 - 1.00179i) q^{9} +(-4.69914 + 0.245246i) q^{10} -0.842372 q^{11} +(3.23367 - 2.68977i) q^{12} +(-1.80930 + 6.75239i) q^{13} +(5.53090 - 5.53090i) q^{14} +(3.86997 + 0.152640i) q^{15} +(-1.47983 + 2.56313i) q^{16} +(0.861531 + 3.21528i) q^{17} +(-5.20235 + 3.57648i) q^{18} +(-3.80441 - 1.01939i) q^{19} +(5.16468 - 1.67686i) q^{20} +(-4.94950 + 4.11700i) q^{21} +(1.71227 - 0.458800i) q^{22} +(-3.42164 + 3.42164i) q^{23} +(-0.901127 + 1.27524i) q^{24} +(4.56684 + 2.03567i) q^{25} -14.7108i q^{26} +(4.53312 - 2.53984i) q^{27} +(-4.51314 + 7.81698i) q^{28} +(4.61569 - 4.61569i) q^{29} +(-7.94953 + 1.79753i) q^{30} +(2.37322 + 2.37322i) q^{31} +(2.07865 - 7.75763i) q^{32} +(-1.43794 + 0.247181i) q^{33} +(-3.50242 - 6.06637i) q^{34} +(-7.90513 + 2.56663i) q^{35} +(4.73064 - 5.54035i) q^{36} +(5.69629 - 2.13360i) q^{37} +8.28833 q^{38} +(-1.10711 + 12.0573i) q^{39} +(-1.69090 + 1.09756i) q^{40} +(2.90888 + 5.03832i) q^{41} +(7.81837 - 11.0643i) q^{42} +(-1.86227 - 1.86227i) q^{43} +(-1.77156 + 1.02281i) q^{44} +(6.65089 - 0.875024i) q^{45} +(5.09147 - 8.81868i) q^{46} -0.845254 q^{47} +(-1.77397 + 4.80954i) q^{48} +(3.40787 - 5.90260i) q^{49} +(-10.3916 - 1.65051i) q^{50} +(2.41412 + 5.23572i) q^{51} +(4.39371 + 16.3975i) q^{52} +(2.46608 - 4.27138i) q^{53} +(-7.83102 + 7.63165i) q^{54} +(-1.84235 - 0.392023i) q^{55} +(0.867289 - 3.23677i) q^{56} +(-6.79330 - 0.623766i) q^{57} +(-6.86824 + 11.8961i) q^{58} +(0.648455 - 0.173753i) q^{59} +(8.32413 - 4.37792i) q^{60} +(-2.58029 + 9.62977i) q^{61} +(-6.11656 - 3.53140i) q^{62} +(-7.24079 + 8.48013i) q^{63} +10.9816i q^{64} +(-7.09955 + 13.9262i) q^{65} +(2.78824 - 1.28562i) q^{66} +(-1.09340 - 1.89382i) q^{67} +(5.71585 + 5.71585i) q^{68} +(-4.83676 + 6.84481i) q^{69} +(14.6706 - 9.52268i) q^{70} +(-8.09195 + 4.67189i) q^{71} +(-1.16404 + 2.44128i) q^{72} -11.6345 q^{73} +(-10.4166 + 7.43942i) q^{74} +(8.39300 + 2.13485i) q^{75} +(-9.23865 + 2.47549i) q^{76} +(2.71157 - 1.56553i) q^{77} +(-4.31666 - 25.1116i) q^{78} +(15.3576 + 4.11506i) q^{79} +(-4.42937 + 4.91716i) q^{80} +(6.99282 - 5.66572i) q^{81} +(-8.65693 - 8.65693i) q^{82} +(1.51988 - 2.63251i) q^{83} +(-5.41022 + 14.6680i) q^{84} +(0.387930 + 7.43308i) q^{85} +(4.79969 + 2.77110i) q^{86} +(6.52464 - 9.23344i) q^{87} +(0.536994 - 0.536994i) q^{88} +(-3.08875 - 11.5274i) q^{89} +(-13.0425 + 5.40107i) q^{90} +(-6.72507 - 25.0983i) q^{91} +(-3.04135 + 11.3505i) q^{92} +(4.74750 + 3.35473i) q^{93} +(1.71812 - 0.460370i) q^{94} +(-7.84623 - 4.00000i) q^{95} +(1.27193 - 13.8523i) q^{96} +(11.8508 + 11.8508i) q^{97} +(-3.71221 + 13.8542i) q^{98} +(-2.38205 + 0.843882i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 24 q^{4} - 16 q^{6}+O(q^{10}) \) 288 * q - 24 * q^4 - 16 * q^6	\( 288 q - 24 q^{4} - 16 q^{6} - 16 q^{10} - 6 q^{15} + 112 q^{16} - 8 q^{19} - 12 q^{21} + 44 q^{24} - 12 q^{25} - 30 q^{30} - 72 q^{31} - 32 q^{34} - 4 q^{39} + 12 q^{40} + 16 q^{46} + 80 q^{49} + 12 q^{51} - 52 q^{54} - 28 q^{55} - 92 q^{60} - 8 q^{61} + 100 q^{66} - 104 q^{69} + 16 q^{70} + 52 q^{75} - 24 q^{76} + 16 q^{79} - 8 q^{81} - 192 q^{84} - 52 q^{90} - 168 q^{91} - 72 q^{94} - 112 q^{96} - 60 q^{99}+O(q^{100}) \) 288 * q - 24 * q^4 - 16 * q^6 - 16 * q^10 - 6 * q^15 + 112 * q^16 - 8 * q^19 - 12 * q^21 + 44 * q^24 - 12 * q^25 - 30 * q^30 - 72 * q^31 - 32 * q^34 - 4 * q^39 + 12 * q^40 + 16 * q^46 + 80 * q^49 + 12 * q^51 - 52 * q^54 - 28 * q^55 - 92 * q^60 - 8 * q^61 + 100 * q^66 - 104 * q^69 + 16 * q^70 + 52 * q^75 - 24 * q^76 + 16 * q^79 - 8 * q^81 - 192 * q^84 - 52 * q^90 - 168 * q^91 - 72 * q^94 - 112 * q^96 - 60 * q^99

Introduction

L-functions

Modular forms

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