LMFDB - Embedded newform 378.2.w.a.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(25,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("378.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.w (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.4
Character	$\chi$	$=$	378.25
Dual form			378.2.w.a.121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 + 0.342020i) q^{2} +(-1.03071 - 1.39199i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.69961 - 1.34655i) q^{5} +(1.44464 + 0.955517i) q^{6} +(0.644767 + 2.56598i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.875266 + 2.86948i) q^{9} +O(q^{10})$	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.03071 - 1.39199i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.69961 - 1.34655i) q^{5} +(1.44464 + 0.955517i) q^{6} +(0.644767 + 2.56598i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.875266 + 2.86948i) q^{9} +3.93704 q^{10} +(-1.54857 + 0.563632i) q^{11} +(-1.68432 - 0.403796i) q^{12} +(-0.258932 - 1.46848i) q^{13} +(-1.48350 - 2.19071i) q^{14} +(1.93885 + 6.53772i) q^{15} +(0.173648 - 0.984808i) q^{16} +6.00293 q^{17} +(-0.158939 - 2.99579i) q^{18} +3.99319 q^{19} +(-3.69961 + 1.34655i) q^{20} +(2.90725 - 3.54230i) q^{21} +(1.26240 - 1.05928i) q^{22} +(0.514517 + 2.91797i) q^{23} +(1.72085 - 0.196628i) q^{24} +(8.04371 + 6.74947i) q^{25} +(0.745566 + 1.29136i) q^{26} +(4.89643 - 1.73925i) q^{27} +(2.14330 + 1.55121i) q^{28} +(0.387255 - 2.19623i) q^{29} +(-4.05796 - 5.48032i) q^{30} +(-0.770601 + 0.646611i) q^{31} +(0.173648 + 0.984808i) q^{32} +(2.38070 + 1.57464i) q^{33} +(-5.64091 + 2.05312i) q^{34} +(1.06984 - 10.3614i) q^{35} +(1.17397 + 2.76076i) q^{36} +(-5.77615 + 10.0046i) q^{37} +(-3.75237 + 1.36575i) q^{38} +(-1.77722 + 1.87401i) q^{39} +(3.01595 - 2.53068i) q^{40} +(0.699279 + 3.96581i) q^{41} +(-1.52039 + 4.32301i) q^{42} +(-3.28674 - 2.75790i) q^{43} +(-0.823975 + 1.42717i) q^{44} +(7.10204 - 9.43737i) q^{45} +(-1.48149 - 2.56602i) q^{46} +(6.93636 + 5.82030i) q^{47} +(-1.54982 + 0.773337i) q^{48} +(-6.16855 + 3.30892i) q^{49} +(-9.86707 - 3.59132i) q^{50} +(-6.18730 - 8.35602i) q^{51} +(-1.14227 - 0.958481i) q^{52} +(-5.68396 + 9.84491i) q^{53} +(-4.00628 + 3.30903i) q^{54} +6.48805 q^{55} +(-2.54459 - 0.724608i) q^{56} +(-4.11583 - 5.55847i) q^{57} +(0.387255 + 2.19623i) q^{58} +(-0.334598 - 1.89760i) q^{59} +(5.68761 + 3.76191i) q^{60} +(-0.583656 - 0.489745i) q^{61} +(0.502974 - 0.871176i) q^{62} +(-7.92738 - 0.395774i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.01943 + 5.78146i) q^{65} +(-2.77568 - 0.665436i) q^{66} +(12.9811 + 4.72473i) q^{67} +(4.59851 - 3.85861i) q^{68} +(3.53146 - 3.72379i) q^{69} +(2.53847 + 10.1024i) q^{70} +(0.162856 + 0.282076i) q^{71} +(-2.04741 - 2.19274i) q^{72} +(-0.171482 - 0.297016i) q^{73} +(2.00604 - 11.3768i) q^{74} +(1.10444 - 18.1535i) q^{75} +(3.05896 - 2.56677i) q^{76} +(-2.44474 - 3.61019i) q^{77} +(1.02909 - 2.36884i) q^{78} +(12.9389 - 4.70937i) q^{79} +(-1.96852 + 3.40958i) q^{80} +(-7.46782 - 5.02311i) q^{81} +(-2.01349 - 3.48747i) q^{82} +(-2.11023 + 11.9677i) q^{83} +(-0.0498608 - 4.58230i) q^{84} +(-22.2085 - 8.08324i) q^{85} +(4.03178 + 1.46745i) q^{86} +(-3.45628 + 1.72463i) q^{87} +(0.286164 - 1.62291i) q^{88} -6.67813 q^{89} +(-3.44596 + 11.2973i) q^{90} +(3.60114 - 1.61124i) q^{91} +(2.26978 + 1.90457i) q^{92} +(1.69434 + 0.406198i) q^{93} +(-8.50871 - 3.09692i) q^{94} +(-14.7732 - 5.37702i) q^{95} +(1.19186 - 1.25677i) q^{96} +(-4.05678 - 3.40404i) q^{97} +(4.66482 - 5.21914i) q^{98} +(-0.261923 - 4.93691i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9}+O(q^{10}) $ 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9	$ 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9} + 12 q^{10} - 6 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} + 36 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} + 9 q^{35} + 9 q^{36} + 3 q^{39} - 6 q^{41} + 3 q^{42} + 24 q^{43} - 30 q^{45} - 9 q^{47} - 6 q^{48} + 51 q^{49} + 6 q^{50} + 12 q^{51} + 6 q^{52} - 15 q^{53} - 27 q^{54} + 72 q^{55} + 6 q^{56} - 63 q^{57} + 3 q^{58} + 15 q^{59} - 3 q^{60} - 18 q^{61} - 24 q^{62} - 48 q^{63} - 36 q^{64} - 18 q^{65} - 36 q^{66} + 66 q^{67} - 18 q^{68} - 21 q^{69} - 6 q^{70} + 12 q^{71} - 12 q^{72} - 66 q^{73} + 9 q^{74} + 15 q^{75} - 15 q^{77} + 30 q^{78} + 9 q^{79} - 6 q^{80} - 33 q^{82} - 18 q^{83} - 12 q^{84} + 21 q^{85} - 12 q^{86} - 48 q^{87} + 12 q^{88} + 72 q^{89} + 69 q^{90} + 12 q^{91} + 30 q^{92} + 60 q^{93} - 36 q^{94} + 93 q^{95} - 48 q^{97} + 6 q^{98} - 54 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9 + 12 * q^10 - 6 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 + 36 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 + 9 * q^35 + 9 * q^36 + 3 * q^39 - 6 * q^41 + 3 * q^42 + 24 * q^43 - 30 * q^45 - 9 * q^47 - 6 * q^48 + 51 * q^49 + 6 * q^50 + 12 * q^51 + 6 * q^52 - 15 * q^53 - 27 * q^54 + 72 * q^55 + 6 * q^56 - 63 * q^57 + 3 * q^58 + 15 * q^59 - 3 * q^60 - 18 * q^61 - 24 * q^62 - 48 * q^63 - 36 * q^64 - 18 * q^65 - 36 * q^66 + 66 * q^67 - 18 * q^68 - 21 * q^69 - 6 * q^70 + 12 * q^71 - 12 * q^72 - 66 * q^73 + 9 * q^74 + 15 * q^75 - 15 * q^77 + 30 * q^78 + 9 * q^79 - 6 * q^80 - 33 * q^82 - 18 * q^83 - 12 * q^84 + 21 * q^85 - 12 * q^86 - 48 * q^87 + 12 * q^88 + 72 * q^89 + 69 * q^90 + 12 * q^91 + 30 * q^92 + 60 * q^93 - 36 * q^94 + 93 * q^95 - 48 * q^97 + 6 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$2$	−0.939693	+	0.342020i	−0.664463	+	0.241845i
$3$	−1.03071	−	1.39199i	−0.595082	−	0.803665i
$3$	−1.03071	−	1.39199i	−0.595082	−	0.803665i
$4$	0.766044	−	0.642788i	0.383022	−	0.321394i
$5$	−3.69961	−	1.34655i	−1.65452	−	0.602195i	−0.665029	−	0.746817i	$-0.731581\pi$
$5$	−3.69961	−	1.34655i	−1.65452	−	0.602195i	−0.989487	+	0.144622i	$0.953803\pi$
$6$	1.44464	+	0.955517i	0.589772	+	0.390088i
$7$	0.644767	+	2.56598i	0.243699	+	0.969851i
$7$	0.644767	+	2.56598i	0.243699	+	0.969851i
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.875266	+	2.86948i	−0.291755	+	0.956493i
$10$	3.93704			1.24500
$11$	−1.54857	+	0.563632i	−0.466910	+	0.169941i	−0.564752	−	0.825260i	$-0.691028\pi$
$11$	−1.54857	+	0.563632i	−0.466910	+	0.169941i	0.0978419	+	0.995202i	$0.468806\pi$
$12$	−1.68432	−	0.403796i	−0.486223	−	0.116566i
$13$	−0.258932	−	1.46848i	−0.0718149	−	0.407282i	−0.999430	−	0.0337461i	$-0.989256\pi$
$13$	−0.258932	−	1.46848i	−0.0718149	−	0.407282i	0.927616	−	0.373536i	$-0.121855\pi$
$14$	−1.48350	−	2.19071i	−0.396482	−	0.585493i
$15$	1.93885	+	6.53772i	0.500610	+	1.68803i
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	6.00293			1.45593			0.727963	−	0.685617i	$-0.240467\pi$
$17$	6.00293			1.45593			0.727963	+	0.685617i	$0.240467\pi$
$18$	−0.158939	−	2.99579i	−0.0374622	−	0.706114i
$19$	3.99319			0.916100			0.458050	−	0.888926i	$-0.348548\pi$
$19$	3.99319			0.916100			0.458050	+	0.888926i	$0.348548\pi$
$20$	−3.69961	+	1.34655i	−0.827258	+	0.301097i
$21$	2.90725	−	3.54230i	0.634415	−	0.772993i
$22$	1.26240	−	1.05928i	0.269145	−	0.225840i
$23$	0.514517	+	2.91797i	0.107284	+	0.608439i	0.990283	+	0.139064i	$0.0444095\pi$
$23$	0.514517	+	2.91797i	0.107284	+	0.608439i	−0.882999	+	0.469375i	$0.844479\pi$
$24$	1.72085	−	0.196628i	0.351268	−	0.0401366i
$25$	8.04371	+	6.74947i	1.60874	+	1.34989i
$26$	0.745566	+	1.29136i	0.146217	+	0.253256i
$27$	4.89643	−	1.73925i	0.942318	−	0.334718i
$28$	2.14330	+	1.55121i	0.405046	+	0.293151i
$29$	0.387255	−	2.19623i	0.0719114	−	0.407830i	−0.927509	−	0.373800i	$-0.878055\pi$
$29$	0.387255	−	2.19623i	0.0719114	−	0.407830i	0.999421	−	0.0340301i	$-0.0108342\pi$
$30$	−4.05796	−	5.48032i	−0.740878	−	1.00057i
$31$	−0.770601	+	0.646611i	−0.138404	+	0.116135i	−0.709361	−	0.704845i	$-0.751017\pi$
$31$	−0.770601	+	0.646611i	−0.138404	+	0.116135i	0.570957	+	0.820980i	$0.306572\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	2.38070	+	1.57464i	0.414426	+	0.274111i
$34$	−5.64091	+	2.05312i	−0.967409	+	0.352108i
$35$	1.06984	−	10.3614i	0.180835	−	1.75139i
$36$	1.17397	+	2.76076i	0.195662	+	0.460126i
$37$	−5.77615	+	10.0046i	−0.949593	+	1.64474i	−0.203310	+	0.979114i	$0.565170\pi$
$37$	−5.77615	+	10.0046i	−0.949593	+	1.64474i	−0.746283	+	0.665629i	$0.768163\pi$
$38$	−3.75237	+	1.36575i	−0.608715	+	0.221554i
$39$	−1.77722	+	1.87401i	−0.284583	+	0.300081i
$40$	3.01595	−	2.53068i	0.476864	−	0.400136i
$41$	0.699279	+	3.96581i	0.109209	+	0.619355i	0.989455	+	0.144838i	$0.0462662\pi$
$41$	0.699279	+	3.96581i	0.109209	+	0.619355i	−0.880246	+	0.474517i	$0.842623\pi$
$42$	−1.52039	+	4.32301i	−0.234601	+	0.667055i
$43$	−3.28674	−	2.75790i	−0.501223	−	0.420576i	0.356805	−	0.934179i	$-0.383866\pi$
$43$	−3.28674	−	2.75790i	−0.501223	−	0.420576i	−0.858028	+	0.513603i	$0.828310\pi$
$44$	−0.823975	+	1.42717i	−0.124219	+	0.215153i
$45$	7.10204	−	9.43737i	1.05871	−	1.40684i
$46$	−1.48149	−	2.56602i	−0.218434	−	0.378339i
$47$	6.93636	+	5.82030i	1.01177	+	0.848978i	0.988571	−	0.150753i	$-0.0481697\pi$
$47$	6.93636	+	5.82030i	1.01177	+	0.848978i	0.0232011	+	0.999731i	$0.492614\pi$
$48$	−1.54982	+	0.773337i	−0.223698	+	0.111622i
$49$	−6.16855	+	3.30892i	−0.881222	+	0.472703i
$50$	−9.86707	−	3.59132i	−1.39541	−	0.507889i
$51$	−6.18730	−	8.35602i	−0.866395	−	1.17008i
$52$	−1.14227	−	0.958481i	−0.158405	−	0.132917i
$53$	−5.68396	+	9.84491i	−0.780752	+	1.35230i	0.150753	+	0.988572i	$0.451830\pi$
$53$	−5.68396	+	9.84491i	−0.780752	+	1.35230i	−0.931504	+	0.363730i	$0.881503\pi$
$54$	−4.00628	+	3.30903i	−0.545186	+	0.450303i
$55$	6.48805			0.874849
$56$	−2.54459	−	0.724608i	−0.340035	−	0.0968298i
$57$	−4.11583	−	5.55847i	−0.545155	−	0.736238i
$58$	0.387255	+	2.19623i	0.0508491	+	0.288379i
$59$	−0.334598	−	1.89760i	−0.0435610	−	0.247047i	0.955250	−	0.295800i	$-0.0955862\pi$
$59$	−0.334598	−	1.89760i	−0.0435610	−	0.247047i	−0.998811	+	0.0487536i	$0.984475\pi$
$60$	5.68761	+	3.76191i	0.734268	+	0.485661i
$61$	−0.583656	−	0.489745i	−0.0747295	−	0.0627055i	0.604658	−	0.796485i	$-0.293310\pi$
$61$	−0.583656	−	0.489745i	−0.0747295	−	0.0627055i	−0.679387	+	0.733780i	$0.737754\pi$
$62$	0.502974	−	0.871176i	0.0638777	−	0.110639i
$63$	−7.92738	−	0.395774i	−0.998756	−	0.0498628i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−1.01943	+	5.78146i	−0.126444	+	0.717102i
$66$	−2.77568	−	0.665436i	−0.341663	−	0.0819096i
$67$	12.9811	+	4.72473i	1.58589	+	0.577218i	0.976475	−	0.215630i	$-0.0691807\pi$
$67$	12.9811	+	4.72473i	1.58589	+	0.577218i	0.609419	+	0.792849i	$0.291403\pi$
$68$	4.59851	−	3.85861i	0.557652	−	0.467925i
$69$	3.53146	−	3.72379i	0.425138	−	0.448291i
$70$	2.53847	+	10.1024i	0.303406	+	1.20747i
$71$	0.162856	+	0.282076i	0.0193275	+	0.0334762i	0.875527	−	0.483168i	$-0.160514\pi$
$71$	0.162856	+	0.282076i	0.0193275	+	0.0334762i	−0.856200	+	0.516645i	$0.827181\pi$
$72$	−2.04741	−	2.19274i	−0.241289	−	0.258417i
$73$	−0.171482	−	0.297016i	−0.0200705	−	0.0347631i	0.855816	−	0.517281i	$-0.173056\pi$
$73$	−0.171482	−	0.297016i	−0.0200705	−	0.0347631i	−0.875886	+	0.482518i	$0.839722\pi$
$74$	2.00604	−	11.3768i	0.233197	−	1.32253i
$75$	1.10444	−	18.1535i	0.127530	−	2.09619i
$76$	3.05896	−	2.56677i	0.350887	−	0.294429i
$77$	−2.44474	−	3.61019i	−0.278603	−	0.411419i
$78$	1.02909	−	2.36884i	0.116522	−	0.268218i
$79$	12.9389	−	4.70937i	1.45574	−	0.529845i	0.511550	−	0.859253i	$-0.329071\pi$
$79$	12.9389	−	4.70937i	1.45574	−	0.529845i	0.944188	+	0.329408i	$0.106849\pi$
$80$	−1.96852	+	3.40958i	−0.220087	+	0.381203i
$81$	−7.46782	−	5.02311i	−0.829758	−	0.558124i
$82$	−2.01349	−	3.48747i	−0.222353	−	0.385127i
$83$	−2.11023	+	11.9677i	−0.231628	+	1.31363i	0.617972	+	0.786200i	$0.287955\pi$
$83$	−2.11023	+	11.9677i	−0.231628	+	1.31363i	−0.849600	+	0.527428i	$0.823157\pi$
$84$	−0.0498608	−	4.58230i	−0.00544026	−	0.499970i
$85$	−22.2085	−	8.08324i	−2.40885	−	0.876751i
$86$	4.03178	+	1.46745i	0.434758	+	0.158239i
$87$	−3.45628	+	1.72463i	−0.370552	+	0.184899i
$88$	0.286164	−	1.62291i	0.0305051	−	0.173003i
$89$	−6.67813			−0.707880			−0.353940	−	0.935268i	$-0.615158\pi$
$89$	−6.67813			−0.707880			−0.353940	+	0.935268i	$0.615158\pi$
$90$	−3.44596	+	11.2973i	−0.363236	+	1.19084i
$91$	3.60114	−	1.61124i	0.377502	−	0.168904i
$92$	2.26978	+	1.90457i	0.236641	+	0.198565i
$93$	1.69434	+	0.406198i	0.175695	+	0.0421208i
$94$	−8.50871	−	3.09692i	−0.877606	−	0.319423i
$95$	−14.7732	−	5.37702i	−1.51570	−	0.551671i
$96$	1.19186	−	1.25677i	0.121644	−	0.128268i
$97$	−4.05678	−	3.40404i	−0.411903	−	0.345628i	0.413170	−	0.910654i	$-0.364422\pi$
$97$	−4.05678	−	3.40404i	−0.411903	−	0.345628i	−0.825073	+	0.565026i	$0.808866\pi$
$98$	4.66482	−	5.21914i	0.471218	−	0.527213i
$99$	−0.261923	−	4.93691i	−0.0263243	−	0.496178i
$100$	10.5003			1.05003
$101$	1.80325	−	10.2268i	0.179430	−	1.01760i	−0.753474	−	0.657477i	$-0.771624\pi$
$101$	1.80325	−	10.2268i	0.179430	−	1.01760i	0.932905	−	0.360123i	$-0.117265\pi$
$102$	8.67208	+	5.73591i	0.858664	+	0.567940i
$103$	−13.8059	−	5.02494i	−1.36034	−	0.495122i	−0.444178	−	0.895939i	$-0.646504\pi$
$103$	−13.8059	−	5.02494i	−1.36034	−	0.495122i	−0.916158	+	0.400817i	$0.868726\pi$
$104$	1.40121	+	0.509997i	0.137399	+	0.0500093i
$105$	−15.5256	+	9.19037i	−1.51514	+	0.896888i
$106$	1.97402	−	11.1952i	0.191734	−	1.08738i
$107$	6.80229	+	11.7819i	0.657602	+	1.13900i	0.981235	+	0.192818i	$0.0617626\pi$
$107$	6.80229	+	11.7819i	0.657602	+	1.13900i	−0.323632	+	0.946183i	$0.604904\pi$
$108$	2.63292	−	4.47970i	0.253353	−	0.431060i
$109$	−4.78613	+	8.28982i	−0.458428	+	0.794021i	−0.998878	−	0.0473552i	$-0.984921\pi$
$109$	−4.78613	+	8.28982i	−0.458428	+	0.794021i	0.540450	+	0.841376i	$0.318254\pi$
$110$	−6.09677	+	2.21904i	−0.581305	+	0.211578i
$111$	19.8798	−	2.27151i	1.88691	−	0.215602i
$112$	2.63896	−	0.189393i	0.249359	−	0.0178959i
$113$	1.41520	−	1.18749i	0.133131	−	0.111710i	−0.573791	−	0.819002i	$-0.694528\pi$
$113$	1.41520	−	1.18749i	0.133131	−	0.111710i	0.706922	+	0.707292i	$0.250083\pi$
$114$	5.76872	+	3.81556i	0.540290	+	0.357360i
$115$	2.02568	−	11.4882i	0.188895	−	1.07128i
$116$	−1.11506	−	1.93133i	−0.103530	−	0.179320i
$117$	4.44040	+	0.542308i	0.410515	+	0.0501364i
$118$	0.963437	+	1.66872i	0.0886916	+	0.153618i
$119$	3.87049	+	15.4034i	0.354807	+	1.41203i
$120$	−6.63126	−	1.58976i	−0.605348	−	0.145125i
$121$	−6.34611	+	5.32502i	−0.576919	+	0.484093i
$122$	0.715960	+	0.260588i	0.0648200	+	0.0235925i
$123$	4.79961	−	5.06100i	0.432766	−	0.456335i
$124$	−0.174681	+	0.990665i	−0.0156868	+	0.0889644i
$125$	−10.8275	−	18.7538i	−0.968440	−	1.67739i
$126$	7.58466	−	2.33942i	0.675696	−	0.208412i
$127$	4.80221	−	8.31767i	0.426127	−	0.738074i	−0.570398	−	0.821369i	$-0.693211\pi$
$127$	4.80221	−	8.31767i	0.426127	−	0.738074i	0.996525	+	0.0832946i	$0.0265443\pi$
$128$	0.766044	+	0.642788i	0.0677094	+	0.0568149i
$129$	−0.451287	+	7.41770i	−0.0397336	+	0.653092i
$130$	−1.01943	−	5.78146i	−0.0894097	−	0.507068i
$131$	−2.28695	−	12.9699i	−0.199811	−	1.13319i	−0.905398	−	0.424563i	$-0.860428\pi$
$131$	−2.28695	−	12.9699i	−0.199811	−	1.13319i	0.705587	−	0.708623i	$-0.250683\pi$
$132$	2.83588	−	0.324034i	0.246832	−	0.0282035i
$133$	2.57467	+	10.2465i	0.223253	+	0.888481i
$134$	−13.8142			−1.19336
$135$	−20.4569	−	0.158746i	−1.76065	−	0.0136626i
$136$	−3.00147	+	5.19869i	−0.257374	+	0.445784i
$137$	14.9574	+	12.5508i	1.27790	+	1.07229i	0.993530	+	0.113571i	$0.0362290\pi$
$137$	14.9574	+	12.5508i	1.27790	+	1.07229i	0.284370	+	0.958714i	$0.408215\pi$
$138$	−2.04488	+	4.70705i	−0.174072	+	0.400690i
$139$	−4.31051	−	1.56890i	−0.365613	−	0.133072i	0.152680	−	0.988276i	$-0.451210\pi$
$139$	−4.31051	−	1.56890i	−0.365613	−	0.133072i	−0.518292	+	0.855204i	$0.673432\pi$
$140$	−5.84061	−	8.62493i	−0.493621	−	0.728940i
$141$	0.952400	−	15.6544i	0.0802066	−	1.31834i
$142$	−0.249511	−	0.209364i	−0.0209385	−	0.0175695i
$143$	1.22866	+	2.12809i	0.102745	+	0.177960i
$144$	2.67390	+	1.36025i	0.222825	+	0.113354i
$145$	−4.39002	+	7.60374i	−0.364572	+	0.631457i
$146$	0.262726	+	0.220453i	0.0217433	+	0.0182448i
$147$	10.9640	+	5.17601i	0.904294	+	0.426910i
$148$	2.00604	+	11.3768i	0.164895	+	0.935167i
$149$	5.79518	−	4.86273i	0.474759	−	0.398370i	−0.373768	−	0.927522i	$-0.621934\pi$
$149$	5.79518	−	4.86273i	0.474759	−	0.398370i	0.848527	+	0.529152i	$0.177490\pi$
$150$	5.17103	+	17.4365i	0.422213	+	1.42368i
$151$	19.2977	−	7.02377i	1.57042	−	0.571587i	0.597328	−	0.801997i	$-0.296229\pi$
$151$	19.2977	−	7.02377i	1.57042	−	0.571587i	0.973093	+	0.230411i	$0.0740069\pi$
$152$	−1.99659	+	3.45820i	−0.161945	+	0.280497i
$153$	−5.25416	+	17.2253i	−0.424774	+	1.39258i
$154$	3.53206	+	2.55632i	0.284621	+	0.205994i
$155$	3.72162	−	1.35456i	0.298927	−	0.108801i
$156$	−0.156840	+	2.57795i	−0.0125573	+	0.206401i
$157$	1.22564	+	6.95097i	0.0978170	+	0.554748i	0.993848	+	0.110756i	$0.0353271\pi$
$157$	1.22564	+	6.95097i	0.0978170	+	0.554748i	−0.896031	+	0.443992i	$0.853562\pi$
$158$	−10.5479	+	8.85072i	−0.839144	+	0.704125i
$159$	19.5625	−	2.23525i	1.55141	−	0.177267i
$160$	0.683660	−	3.87723i	0.0540481	−	0.306522i
$161$	−7.15572	+	3.20165i	−0.563950	+	0.252326i
$162$	8.73546	+	2.16604i	0.686323	+	0.170180i
$163$	−0.867735	−	1.50296i	−0.0679662	−	0.117721i	0.830040	−	0.557704i	$-0.188318\pi$
$163$	−0.867735	−	1.50296i	−0.0679662	−	0.117721i	−0.898006	+	0.439983i	$0.854984\pi$
$164$	3.08485	+	2.58850i	0.240886	+	0.202128i
$165$	−6.68731	−	9.03130i	−0.520607	−	0.703085i
$166$	−2.11023	−	11.9677i	−0.163786	−	0.928875i
$167$	−0.597809	+	0.501622i	−0.0462599	+	0.0388166i	−0.665624	−	0.746287i	$-0.731835\pi$
$167$	−0.597809	+	0.501622i	−0.0462599	+	0.0388166i	0.619365	+	0.785103i	$0.287390\pi$
$168$	1.61409	+	4.28890i	0.124530	+	0.330896i
$169$	10.1266	−	3.68579i	0.778971	−	0.283522i
$170$	23.6338			1.81263
$171$	−3.49510	+	11.4584i	−0.267277	+	0.876243i
$172$	−4.29053			−0.327150
$173$	−2.43576	+	13.8139i	−0.185187	+	1.05025i	0.740528	+	0.672026i	$0.234576\pi$
$173$	−2.43576	+	13.8139i	−0.185187	+	1.05025i	−0.925715	+	0.378222i	$0.876536\pi$
$174$	2.65798	−	2.80274i	0.201501	−	0.212475i
$175$	−12.1327	+	24.9919i	−0.917148	+	1.88921i
$176$	0.286164	+	1.62291i	0.0215704	+	0.122332i
$177$	−2.29656	+	2.42164i	−0.172620	+	0.182021i
$178$	6.27539	−	2.28405i	0.470360	−	0.171197i
$179$	23.8828			1.78508			0.892542	−	0.450964i	$-0.148920\pi$
$179$	23.8828			1.78508			0.892542	+	0.450964i	$0.148920\pi$
$180$	−0.625749	−	11.7945i	−0.0466406	−	0.879113i
$181$	−12.6683	+	21.9421i	−0.941624	+	1.63094i	−0.179249	+	0.983804i	$0.557367\pi$
$181$	−12.6683	+	21.9421i	−0.941624	+	1.63094i	−0.762374	+	0.647136i	$0.775966\pi$
$182$	−2.83289	+	2.74573i	−0.209988	+	0.203527i
$183$	−0.0801391	+	1.31723i	−0.00592405	+	0.0973723i
$184$	−2.78429	−	1.01340i	−0.205261	−	0.0747089i
$185$	34.8412	−	29.2352i	2.56157	−	2.14941i
$186$	−1.73109	+	0.197798i	−0.126930	+	0.0145032i
$187$	−9.29594	+	3.38345i	−0.679787	+	0.247422i
$188$	9.05478			0.660388
$189$	7.61993	+	11.4428i	0.554269	+	0.832338i
$190$	15.7214			1.14055
$191$	−23.0060	+	8.37348i	−1.66465	+	0.605884i	−0.991084	−	0.133240i	$-0.957462\pi$
$191$	−23.0060	+	8.37348i	−1.66465	+	0.605884i	−0.673569	+	0.739124i	$0.735240\pi$
$192$	−0.690142	+	1.58862i	−0.0498067	+	0.114649i
$193$	−10.6510	+	8.93726i	−0.766676	+	0.643318i	−0.939855	−	0.341572i	$-0.889041\pi$
$193$	−10.6510	+	8.93726i	−0.766676	+	0.643318i	0.173179	+	0.984890i	$0.444596\pi$
$194$	4.97638	+	1.81125i	0.357283	+	0.130040i
$195$	9.09847	−	4.53999i	0.651555	−	0.325115i
$196$	−2.59845	+	6.49985i	−0.185604	+	0.464275i
$197$	−6.22118	+	10.7754i	−0.443241	+	0.767716i	−0.997928	−	0.0643433i	$-0.979505\pi$
$197$	−6.22118	+	10.7754i	−0.443241	+	0.767716i	0.554687	+	0.832059i	$0.312838\pi$
$198$	1.93465	+	4.54959i	0.137490	+	0.323325i
$199$	−19.2374			−1.36370			−0.681851	−	0.731491i	$-0.738825\pi$
$199$	−19.2374			−1.36370			−0.681851	+	0.731491i	$0.738825\pi$
$200$	−9.86707	+	3.59132i	−0.697707	+	0.253945i
$201$	−6.80300	−	22.9394i	−0.479846	−	1.61802i
$202$	1.80325	+	10.2268i	0.126876	+	0.719552i
$203$	5.88518	−	0.422367i	0.413059	−	0.0296443i
$204$	−10.1109	−	2.42396i	−0.707904	−	0.169711i
$205$	2.75309	−	15.6136i	0.192284	−	1.09050i
$206$	14.6919			1.02364
$207$	−8.82339	−	1.07760i	−0.613268	−	0.0748987i
$208$	−1.49113			−0.103391
$209$	−6.18372	+	2.25069i	−0.427737	+	0.155683i
$210$	11.4460	−	13.9462i	0.789848	−	0.962378i
$211$	7.78357	−	6.53119i	0.535843	−	0.449626i	−0.334270	−	0.942477i	$-0.608490\pi$
$211$	7.78357	−	6.53119i	0.535843	−	0.449626i	0.870114	+	0.492851i	$0.164045\pi$
$212$	1.97402	+	11.1952i	0.135576	+	0.768890i
$213$	0.224788	−	0.517433i	0.0154022	−	0.0354539i
$214$	−10.4217	−	8.74486i	−0.712414	−	0.597786i
$215$	8.44600	+	14.6289i	0.576013	+	0.997683i
$216$	−0.941984	+	5.11006i	−0.0640939	+	0.347695i
$217$	−2.15605	−	1.56044i	−0.146362	−	0.105929i
$218$	1.66221	−	9.42684i	0.112579	−	0.638466i
$219$	−0.236694	+	0.544839i	−0.0159943	+	0.0368168i
$220$	4.97014	−	4.17044i	0.335086	−	0.281171i
$221$	−1.55435	−	8.81518i	−0.104557	−	0.592973i
$222$	−17.9040	+	8.93382i	−1.20164	+	0.599599i
$223$	6.14714	−	2.23738i	0.411643	−	0.149826i	−0.127894	−	0.991788i	$-0.540822\pi$
$223$	6.14714	−	2.23738i	0.411643	−	0.149826i	0.539537	+	0.841962i	$0.318599\pi$
$224$	−2.41504	+	1.08055i	−0.161362	+	0.0721973i
$225$	−26.4078	+	17.1737i	−1.76052	+	1.14491i
$226$	−0.923705	+	1.59990i	−0.0614439	+	0.106424i
$227$	12.2458	−	4.45712i	0.812785	−	0.295830i	0.0980114	−	0.995185i	$-0.468752\pi$
$227$	12.2458	−	4.45712i	0.812785	−	0.295830i	0.714774	+	0.699356i	$0.246530\pi$
$228$	−6.72582	−	1.61244i	−0.445429	−	0.106786i
$229$	−7.71527	+	6.47388i	−0.509839	+	0.427806i	−0.861073	−	0.508482i	$-0.830207\pi$
$229$	−7.71527	+	6.47388i	−0.509839	+	0.427806i	0.351233	+	0.936288i	$0.385762\pi$
$230$	2.02568	+	11.4882i	0.133569	+	0.757508i
$231$	−2.50552	+	7.12411i	−0.164851	+	0.468732i
$232$	1.70836	+	1.43349i	0.112160	+	0.0941131i
$233$	−0.953881	+	1.65217i	−0.0624908	+	0.108237i	−0.895578	−	0.444904i	$-0.853238\pi$
$233$	−0.953881	+	1.65217i	−0.0624908	+	0.108237i	0.833087	+	0.553141i	$0.186571\pi$
$234$	−4.35809	+	1.00910i	−0.284897	+	0.0659672i
$235$	−17.8245	−	30.8730i	−1.16274	−	2.01393i
$236$	−1.47607	−	1.23857i	−0.0960840	−	0.0806241i
$237$	−19.8916	−	13.1568i	−1.29210	−	0.854624i
$238$	−8.90536	−	13.1507i	−0.577249	−	0.852434i
$239$	−6.84005	−	2.48957i	−0.442446	−	0.161037i	0.111184	−	0.993800i	$-0.464536\pi$
$239$	−6.84005	−	2.48957i	−0.442446	−	0.161037i	−0.553630	+	0.832763i	$0.686758\pi$
$240$	6.77508	−	0.774134i	0.437329	−	0.0499701i
$241$	−8.88346	−	7.45411i	−0.572234	−	0.480161i	0.310152	−	0.950687i	$-0.399620\pi$
$241$	−8.88346	−	7.45411i	−0.572234	−	0.480161i	−0.882386	+	0.470525i	$0.844064\pi$
$242$	4.14213	−	7.17438i	0.266266	−	0.461187i
$243$	0.705052	+	15.5725i	0.0452291	+	0.998977i
$244$	−0.761908			−0.0487762
$245$	27.2769	−	3.93547i	1.74266	−	0.251428i
$246$	−2.77919	+	6.39734i	−0.177195	+	0.407880i
$247$	−1.03397	−	5.86391i	−0.0657896	−	0.373111i
$248$	−0.174681	−	0.990665i	−0.0110923	−	0.0629073i
$249$	18.8340	−	9.39785i	1.19355	−	0.595565i
$250$	16.5887	+	13.9196i	1.04916	+	0.880350i
$251$	6.61645	−	11.4600i	0.417627	−	0.723351i	−0.578074	−	0.815985i	$-0.696195\pi$
$251$	6.61645	−	11.4600i	0.417627	−	0.723351i	0.995700	+	0.0926340i	$0.0295287\pi$
$252$	−6.32712	+	4.79244i	−0.398571	+	0.301895i
$253$	−2.44143	−	4.22867i	−0.153491	−	0.265854i
$254$	−1.66779	+	9.45851i	−0.104646	+	0.593480i
$255$	11.6388	+	39.2455i	0.728850	+	2.45765i
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	12.8705	−	10.7997i	0.802842	−	0.673664i	−0.146046	−	0.989278i	$-0.546655\pi$
$257$	12.8705	−	10.7997i	0.802842	−	0.673664i	0.948888	+	0.315614i	$0.102210\pi$
$258$	−2.11293	−	7.12471i	−0.131545	−	0.443565i
$259$	−29.3959	−	8.37089i	−1.82657	−	0.520142i
$260$	2.93532	+	5.08413i	0.182041	+	0.315304i
$261$	5.96309	+	3.03351i	0.369106	+	0.187769i
$262$	6.58500	+	11.4055i	0.406822	+	0.704637i
$263$	0.796803	−	4.51890i	0.0491330	−	0.278647i	−0.950336	−	0.311225i	$-0.899261\pi$
$263$	0.796803	−	4.51890i	0.0491330	−	0.278647i	0.999469	+	0.0325781i	$0.0103718\pi$
$264$	−2.55403	+	1.27442i	−0.157190	+	0.0784352i
$265$	34.2851	−	28.7686i	2.10612	−	1.76724i
$266$	−5.92390	−	8.74793i	−0.363217	−	0.536370i
$267$	6.88323	+	9.29588i	0.421247	+	0.568899i
$268$	12.9811	−	4.72473i	0.792947	−	0.288609i
$269$	10.3614	−	17.9465i	0.631748	−	1.09422i	−0.355446	−	0.934697i	$-0.615671\pi$
$269$	10.3614	−	17.9465i	0.631748	−	1.09422i	0.987194	−	0.159523i	$-0.0509957\pi$
$270$	19.2775	−	6.84749i	1.17319	−	0.416725i
$271$	3.94725	+	6.83683i	0.239778	+	0.415308i	0.960651	−	0.277760i	$-0.0895920\pi$
$271$	3.94725	+	6.83683i	0.239778	+	0.415308i	−0.720872	+	0.693068i	$0.756259\pi$
$272$	1.04240	−	5.91174i	0.0632047	−	0.358452i
$273$	−5.95457	−	3.35202i	−0.360387	−	0.202874i
$274$	−18.3480	−	6.67813i	−1.10844	−	0.403441i
$275$	−16.2604	−	5.91831i	−0.980541	−	0.356888i
$276$	0.311653	−	5.12257i	0.0187593	−	0.308342i
$277$	−0.729812	+	4.13897i	−0.0438502	+	0.248687i	−0.998851	−	0.0479151i	$-0.984742\pi$
$277$	−0.729812	+	4.13897i	−0.0438502	+	0.248687i	0.955001	+	0.296602i	$0.0958534\pi$
$278$	4.58715			0.275119
$279$	−1.18096	−	2.77718i	−0.0707020	−	0.166265i
$280$	8.43828	+	6.10718i	0.504284	+	0.364974i
$281$	6.32170	+	5.30454i	0.377121	+	0.316442i	0.811571	−	0.584254i	$-0.198613\pi$
$281$	6.32170	+	5.30454i	0.377121	+	0.316442i	−0.434450	+	0.900696i	$0.643057\pi$
$282$	4.45915	+	15.0361i	0.265539	+	0.895384i
$283$	13.0319	+	4.74321i	0.774664	+	0.281955i	0.698946	−	0.715175i	$-0.253653\pi$
$283$	13.0319	+	4.74321i	0.774664	+	0.281955i	0.0757182	+	0.997129i	$0.475875\pi$
$284$	0.306070	+	0.111400i	0.0181619	+	0.00661040i
$285$	7.74220	+	26.1063i	0.458609	+	1.54641i
$286$	−1.88241	−	1.57953i	−0.111309	−	0.0933995i
$287$	−9.72533	+	4.35136i	−0.574068	+	0.256853i
$288$	−2.97787	−	0.363689i	−0.175473	−	0.0214306i
$289$	19.0352			1.11972
$290$	1.52464	−	8.64666i	0.0895299	−	0.507749i
$291$	−0.557018	+	9.15558i	−0.0326529	+	0.536709i
$292$	−0.322281	−	0.117301i	−0.0188601	−	0.00686450i
$293$	4.43361	+	1.61370i	0.259014	+	0.0942736i	0.468264	−	0.883589i	$-0.344880\pi$
$293$	4.43361	+	1.61370i	0.259014	+	0.0942736i	−0.209249	+	0.977862i	$0.567102\pi$
$294$	−12.0731	−	1.11395i	−0.704116	−	0.0649672i
$295$	−1.31733	+	7.47094i	−0.0766978	+	0.434975i
$296$	−5.77615	−	10.0046i	−0.335732	−	0.581505i
$297$	−6.60215	+	5.45312i	−0.383096	+	0.316422i
$298$	−3.78253	+	6.55154i	−0.219116	+	0.379520i
$299$	4.15175	−	1.51111i	0.240102	−	0.0873899i
$300$	−10.8228	−	14.6163i	−0.624855	−	0.843874i
$301$	4.95755	−	10.2119i	0.285748	−	0.588605i
$302$	−15.7316	+	13.2004i	−0.905252	+	0.759596i
$303$	−16.0942	+	8.03073i	−0.924586	+	0.461354i
$304$	0.693410	−	3.93252i	0.0397698	−	0.225546i
$305$	1.49983	+	2.59779i	0.0858802	+	0.148749i
$306$	−0.954099	−	17.9835i	−0.0545422	−	1.02805i
$307$	9.95456	+	17.2418i	0.568137	+	0.984042i	0.996750	+	0.0805537i	$0.0256688\pi$
$307$	9.95456	+	17.2418i	0.568137	+	0.984042i	−0.428614	+	0.903488i	$0.640998\pi$
$308$	−4.19336	−	1.19412i	−0.238939	−	0.0680412i
$309$	7.23525	+	24.3969i	0.411599	+	1.38789i
$310$	−3.03389	+	2.54573i	−0.172313	+	0.144588i
$311$	12.6383	+	4.59995i	0.716651	+	0.260839i	0.674503	−	0.738272i	$-0.264358\pi$
$311$	12.6383	+	4.59995i	0.716651	+	0.260839i	0.0421474	+	0.999111i	$0.486580\pi$
$312$	−0.734329	−	2.47612i	−0.0415732	−	0.140183i
$313$	1.70203	−	9.65269i	0.0962044	−	0.545602i	−0.898167	−	0.439654i	$-0.855101\pi$
$313$	1.70203	−	9.65269i	0.0962044	−	0.545602i	0.994372	−	0.105948i	$-0.0337878\pi$
$314$	−3.52910	−	6.11258i	−0.199159	−	0.344953i
$315$	28.7953	+	12.1388i	1.62243	+	0.683944i
$316$	6.88463	−	11.9245i	0.387291	−	0.670808i
$317$	−24.8425	−	20.8454i	−1.39530	−	1.17079i	−0.963142	−	0.268992i	$-0.913309\pi$
$317$	−24.8425	−	20.8454i	−1.39530	−	1.17079i	−0.432154	−	0.901800i	$-0.642246\pi$
$318$	−17.6183	+	8.79123i	−0.987983	+	0.492988i
$319$	0.638177	+	3.61928i	0.0357310	+	0.202641i
$320$	0.683660	+	3.87723i	0.0382178	+	0.216744i
$321$	9.38909	−	21.6125i	0.524048	−	1.20629i
$322$	5.62915	−	5.45597i	0.313700	−	0.304049i
$323$	23.9708			1.33377
$324$	−8.94948	+	0.952293i	−0.497193	+	0.0529052i
$325$	7.82867	−	13.5597i	0.434257	−	0.752155i
$326$	1.32945	+	1.11554i	0.0736312	+	0.0617839i
$327$	16.4725	−	1.88218i	0.910929	−	0.104085i
$328$	−3.78413	−	1.37731i	−0.208944	−	0.0760493i
$329$	−10.4625	+	21.5513i	−0.576814	+	1.18816i
$330$	9.37290	+	6.19945i	0.515961	+	0.341268i
$331$	−7.69589	−	6.45762i	−0.423005	−	0.354943i	0.406300	−	0.913740i	$-0.366819\pi$
$331$	−7.69589	−	6.45762i	−0.423005	−	0.354943i	−0.829305	+	0.558797i	$0.811263\pi$
$332$	6.07617	+	10.5242i	0.333473	+	0.577592i
$333$	−23.6523	−	25.3312i	−1.29614	−	1.38814i
$334$	0.390192	−	0.675833i	0.0213504	−	0.0369799i
$335$	−41.6629	−	34.9594i	−2.27629	−	1.91003i
$336$	−2.98364	−	3.47820i	−0.162771	−	0.189751i
$337$	−3.78662	−	21.4750i	−0.206270	−	1.16982i	−0.895429	−	0.445205i	$-0.853131\pi$
$337$	−3.78662	−	21.4750i	−0.206270	−	1.16982i	0.689158	−	0.724611i	$-0.257980\pi$
$338$	−8.25530	+	6.92702i	−0.449029	+	0.376780i
$339$	−3.11164	−	0.745978i	−0.169001	−	0.0405159i
$340$	−22.2085	+	8.08324i	−1.20443	+	0.438375i
$341$	0.828876	−	1.43565i	0.0448861	−	0.0777451i
$342$	−0.634672	−	11.9627i	−0.0343191	−	0.646871i
$343$	−12.4679	−	13.6949i	−0.673204	−	0.739456i
$344$	4.03178	−	1.46745i	0.217379	−	0.0791195i
$345$	−18.0793	+	9.02128i	−0.973357	+	0.485689i
$346$	−2.43576	−	13.8139i	−0.130947	−	0.742638i
$347$	−18.1553	+	15.2341i	−0.974628	+	0.817810i	−0.983270	−	0.182153i	$-0.941693\pi$
$347$	−18.1553	+	15.2341i	−0.974628	+	0.817810i	0.00864253	+	0.999963i	$0.497249\pi$
$348$	−1.53909	+	3.54279i	−0.0825041	+	0.189914i
$349$	0.965025	−	5.47293i	0.0516566	−	0.292959i	−0.948025	−	0.318196i	$-0.896923\pi$
$349$	0.965025	−	5.47293i	0.0516566	−	0.292959i	0.999681	+	0.0252370i	$0.00803404\pi$
$350$	2.85331	−	27.6343i	0.152516	−	1.47712i
$351$	−3.82189	−	6.73995i	−0.203997	−	0.359752i
$352$	−0.823975	−	1.42717i	−0.0439180	−	0.0760682i
$353$	−2.73930	−	2.29854i	−0.145798	−	0.122339i	0.566971	−	0.823737i	$-0.308115\pi$
$353$	−2.73930	−	2.29854i	−0.145798	−	0.122339i	−0.712770	+	0.701398i	$0.752559\pi$
$354$	1.32982	−	3.06106i	0.0706789	−	0.162694i
$355$	−0.222677	−	1.26286i	−0.0118185	−	0.0670259i
$356$	−5.11574	+	4.29262i	−0.271134	+	0.227508i
$357$	17.4520	−	21.2642i	0.923660	−	1.12542i
$358$	−22.4425	+	8.16840i	−1.18612	+	0.431713i
$359$	10.5758			0.558169			0.279084	−	0.960267i	$-0.409969\pi$
$359$	10.5758			0.558169			0.279084	+	0.960267i	$0.409969\pi$
$360$	4.62198	+	10.8692i	0.243600	+	0.572859i
$361$	−3.05445			−0.160761
$362$	4.39964	−	24.9516i	0.231240	−	1.31143i
$363$	13.9534	+	3.34516i	0.732363	+	0.175575i
$364$	1.72295	−	3.54905i	0.0903070	−	0.186021i
$365$	0.234471	+	1.32975i	0.0122728	+	0.0696024i
$366$	−0.375213	−	1.26520i	−0.0196127	−	0.0661330i
$367$	−9.01723	+	3.28200i	−0.470696	+	0.171319i	−0.566467	−	0.824084i	$-0.691690\pi$
$367$	−9.01723	+	3.28200i	−0.470696	+	0.171319i	0.0957718	+	0.995403i	$0.469468\pi$
$368$	2.96298			0.154456
$369$	−11.9919	−	1.46457i	−0.624271	−	0.0762425i
$370$	−22.7410	+	39.3885i	−1.18225	+	2.04771i
$371$	−28.9267	−	8.23728i	−1.50180	−	0.427658i
$372$	1.55904	−	0.777936i	0.0808325	−	0.0403341i
$373$	28.3323	+	10.3121i	1.46699	+	0.533941i	0.947281	−	0.320403i	$-0.103818\pi$
$373$	28.3323	+	10.3121i	1.46699	+	0.533941i	0.519708	+	0.854344i	$0.326041\pi$
$374$	7.57812	−	6.35880i	0.391855	−	0.328806i
$375$	−14.9450	+	34.4015i	−0.771757	+	1.77648i
$376$	−8.50871	+	3.09692i	−0.438803	+	0.159711i
$377$	−3.32539			−0.171266
$378$	−11.0740	−	8.14650i	−0.569588	−	0.419011i
$379$	−3.98054			−0.204467			−0.102233	−	0.994760i	$-0.532599\pi$
$379$	−3.98054			−0.204467			−0.102233	+	0.994760i	$0.532599\pi$
$380$	−14.7732	+	5.37702i	−0.757851	+	0.275835i
$381$	−16.5278	+	1.88850i	−0.846745	+	0.0967508i
$382$	18.7546	−	15.7370i	0.959570	−	0.805175i
$383$	−3.25270	−	1.18389i	−0.166205	−	0.0604938i	0.257577	−	0.966258i	$-0.417076\pi$
$383$	−3.25270	−	1.18389i	−0.166205	−	0.0604938i	−0.423783	+	0.905764i	$0.639298\pi$
$384$	0.105182	−	1.72885i	0.00536755	−	0.0882252i
$385$	4.18328	+	16.6482i	0.213200	+	0.848473i
$386$	6.95195	−	12.0411i	0.353845	−	0.612878i
$387$	10.7905	−	7.01733i	0.548512	−	0.356711i
$388$	−5.29575			−0.268851
$389$	−25.3142	+	9.21362i	−1.28348	+	0.467149i	−0.891582	−	0.452859i	$-0.850404\pi$
$389$	−25.3142	+	9.21362i	−1.28348	+	0.467149i	−0.391899	+	0.920008i	$0.628182\pi$
$390$	−6.99699	+	7.37805i	−0.354307	+	0.373602i
$391$	3.08861	+	17.5164i	0.156198	+	0.885841i
$392$	0.218665	−	6.99658i	0.0110442	−	0.353381i
$393$	−15.6968	+	16.5516i	−0.791798	+	0.834920i
$394$	2.16059	−	12.2533i	0.108849	−	0.617314i
$395$	−54.2102			−2.72761
$396$	−3.37403	−	3.61353i	−0.169551	−	0.181587i
$397$	11.4755			0.575937			0.287969	−	0.957640i	$-0.407020\pi$
$397$	11.4755			0.575937			0.287969	+	0.957640i	$0.407020\pi$
$398$	18.0772	−	6.57957i	0.906129	−	0.329804i
$399$	11.6092	−	14.1451i	0.581187	−	0.708139i
$400$	8.04371	−	6.74947i	0.402185	−	0.337474i
$401$	−1.57144	−	8.91205i	−0.0784737	−	0.445047i	−0.998575	−	0.0533662i	$-0.983005\pi$
$401$	−1.57144	−	8.91205i	−0.0784737	−	0.445047i	0.920101	−	0.391681i	$-0.128106\pi$
$402$	14.2385	+	19.2292i	0.710150	+	0.959066i
$403$	1.14907	+	0.964182i	0.0572391	+	0.0480293i
$404$	−5.19226	−	8.99326i	−0.258325	−	0.447431i
$405$	20.8642	+	28.6393i	1.03675	+	1.42310i
$406$	−5.38581	+	2.40975i	−0.267293	+	0.119594i
$407$	3.30585	−	18.7484i	0.163865	−	0.929323i
$408$	10.3302	−	1.18035i	0.511420	−	0.0584359i
$409$	−28.5110	+	23.9236i	−1.40978	+	1.18294i	−0.453220	+	0.891398i	$0.649725\pi$
$409$	−28.5110	+	23.9236i	−1.40978	+	1.18294i	−0.956557	+	0.291545i	$0.905831\pi$
$410$	2.75309	+	15.6136i	0.135966	+	0.771099i
$411$	2.05374	−	33.7568i	0.101303	−	1.66510i
$412$	−13.8059	+	5.02494i	−0.680168	+	0.247561i
$413$	4.65347	−	2.08208i	0.228983	−	0.102453i
$414$	8.65984	−	2.00516i	0.425608	−	0.0985483i
$415$	23.9221	−	41.4344i	1.17429	−	2.03393i
$416$	1.40121	−	0.509997i	0.0686997	−	0.0250047i
$417$	2.25901	+	7.61726i	0.110624	+	0.373019i
$418$	5.04101	−	4.22991i	0.246564	−	0.206892i
$419$	2.25461	+	12.7865i	0.110145	+	0.624662i	0.989040	+	0.147647i	$0.0471700\pi$
$419$	2.25461	+	12.7865i	0.110145	+	0.624662i	−0.878895	+	0.477015i	$0.841719\pi$
$420$	−5.98583	+	17.0199i	−0.292079	+	0.830485i
$421$	5.20931	+	4.37113i	0.253886	+	0.213036i	0.760844	−	0.648935i	$-0.224785\pi$
$421$	5.20931	+	4.37113i	0.253886	+	0.213036i	−0.506957	+	0.861971i	$0.669230\pi$
$422$	−5.08037	+	8.79945i	−0.247308	+	0.428351i
$423$	−22.7724	+	14.8094i	−1.10723	+	0.720060i
$424$	−5.68396	−	9.84491i	−0.276037	−	0.478111i
$425$	48.2858	+	40.5166i	2.34221	+	1.96535i
$426$	−0.0342591	+	0.563110i	−0.00165986	+	0.0272828i
$427$	0.880357	−	1.81342i	0.0426035	−	0.0877577i
$428$	12.7841	+	4.65304i	0.617944	+	0.224913i
$429$	1.69589	−	3.90372i	0.0818784	−	0.188474i
$430$	−12.9400	−	10.8580i	−0.624023	−	0.523618i
$431$	7.27375	−	12.5985i	0.350364	−	0.606848i	−0.635949	−	0.771731i	$-0.719391\pi$
$431$	7.27375	−	12.5985i	0.350364	−	0.606848i	0.986313	+	0.164883i	$0.0527245\pi$
$432$	−0.862567	−	5.12406i	−0.0415003	−	0.246531i
$433$	9.39529			0.451509			0.225755	−	0.974184i	$-0.427515\pi$
$433$	9.39529			0.451509			0.225755	+	0.974184i	$0.427515\pi$
$434$	2.55973	+	0.728918i	0.122871	+	0.0349892i
$435$	15.1092	−	1.72641i	0.724430	−	0.0827748i
$436$	1.66221	+	9.42684i	0.0796052	+	0.451464i
$437$	2.05456	+	11.6520i	0.0982830	+	0.557391i
$438$	0.0360737	−	0.592935i	0.00172367	−	0.0283315i
$439$	−5.39351	−	4.52569i	−0.257418	−	0.215999i	0.504941	−	0.863154i	$-0.331514\pi$
$439$	−5.39351	−	4.52569i	−0.257418	−	0.215999i	−0.762359	+	0.647155i	$0.775959\pi$
$440$	−3.24403	+	5.61882i	−0.154653	+	0.267867i
$441$	−4.09576	−	20.5967i	−0.195036	−	0.980796i
$442$	4.47558	+	7.75194i	0.212882	+	0.368722i
$443$	1.00352	−	5.69125i	0.0476787	−	0.270400i	−0.951644	−	0.307204i	$-0.900607\pi$
$443$	1.00352	−	5.69125i	0.0476787	−	0.270400i	0.999322	+	0.0368042i	$0.0117178\pi$
$444$	13.7687	−	14.5186i	0.653435	−	0.689021i
$445$	24.7065	+	8.99242i	1.17120	+	0.426282i
$446$	−5.01120	+	4.20489i	−0.237287	+	0.199107i
$447$	−12.7420	−	3.05475i	−0.602677	−	0.144485i
$448$	1.89982	−	1.84138i	0.0897583	−	0.0869969i
$449$	12.3215	+	21.3415i	0.581488	+	1.00717i	0.995303	+	0.0968063i	$0.0308628\pi$
$449$	12.3215	+	21.3415i	0.581488	+	1.00717i	−0.413815	+	0.910361i	$0.635804\pi$
$450$	18.9415	−	25.1700i	0.892912	−	1.18652i
$451$	−3.31814	−	5.74718i	−0.156245	−	0.270624i
$452$	0.320799	−	1.81934i	0.0150891	−	0.0855747i
$453$	−29.6673	−	19.6226i	−1.39389	−	0.921952i
$454$	−9.98291	+	8.37665i	−0.468521	+	0.393136i
$455$	−15.4924	+	1.11186i	−0.726296	+	0.0521247i
$456$	6.87169	−	0.785174i	0.321796	−	0.0367691i
$457$	3.43970	−	1.25195i	0.160902	−	0.0585636i	−0.260313	−	0.965524i	$-0.583826\pi$
$457$	3.43970	−	1.25195i	0.160902	−	0.0585636i	0.421215	+	0.906961i	$0.361604\pi$
$458$	5.03578	−	8.72223i	0.235307	−	0.407563i
$459$	29.3929	−	10.4406i	1.37195	−	0.487325i
$460$	−5.83270	−	10.1025i	−0.271951	−	0.471033i
$461$	1.56879	−	8.89702i	0.0730656	−	0.414376i	−0.926234	−	0.376950i	$-0.876973\pi$
$461$	1.56879	−	8.89702i	0.0730656	−	0.414376i	0.999299	−	0.0374261i	$-0.0119159\pi$
$462$	−0.0821681	−	7.55141i	−0.00382281	−	0.351323i
$463$	15.3762	+	5.59649i	0.714594	+	0.260091i	0.673629	−	0.739070i	$-0.264735\pi$
$463$	15.3762	+	5.59649i	0.714594	+	0.260091i	0.0409649	+	0.999161i	$0.486957\pi$
$464$	−2.09562	−	0.762743i	−0.0972867	−	0.0354095i
$465$	−5.72144	−	3.78429i	−0.265325	−	0.175492i
$466$	0.331279	−	1.87878i	0.0153462	−	0.0870328i
$467$	−5.44705			−0.252059			−0.126030	−	0.992026i	$-0.540223\pi$
$467$	−5.44705			−0.252059			−0.126030	+	0.992026i	$0.540223\pi$
$468$	3.75013	−	2.43880i	0.173350	−	0.112734i
$469$	−3.75381	+	36.3557i	−0.173335	+	1.67875i
$470$	27.3088	+	22.9148i	1.25966	+	1.05698i
$471$	8.41239	−	8.87053i	0.387622	−	0.408732i
$472$	1.81067	+	0.659030i	0.0833428	+	0.0303343i
$473$	6.64417	+	2.41828i	0.305499	+	0.111193i
$474$	23.1919	+	5.55998i	1.06524	+	0.255378i
$475$	32.1200	+	26.9519i	1.47377	+	1.23664i
$476$	12.8661	+	9.31181i	0.589717	+	0.426806i
$477$	−23.2748	−	24.9269i	−1.06568	−	1.14132i
$478$	7.27903			0.332935
$479$	−4.73161	+	26.8343i	−0.216193	+	1.22609i	0.662632	+	0.748946i	$0.269440\pi$
$479$	−4.73161	+	26.8343i	−0.216193	+	1.22609i	−0.878824	+	0.477145i	$0.841672\pi$
$480$	−6.10172	+	3.04466i	−0.278504	+	0.138969i
$481$	16.1871	+	5.89164i	0.738070	+	0.268636i
$482$	10.8972	+	3.96625i	0.496353	+	0.180658i
$483$	11.8322	+	6.66070i	0.538382	+	0.303073i
$484$	−1.43855	+	8.15840i	−0.0653885	+	0.370837i
$485$	10.4248	+	18.0563i	0.473366	+	0.819893i
$486$	−5.98864	−	14.3922i	−0.271650	−	0.652845i
$487$	−16.3844	+	28.3786i	−0.742448	+	1.28596i	0.208930	+	0.977931i	$0.433002\pi$
$487$	−16.3844	+	28.3786i	−0.742448	+	1.28596i	−0.951378	+	0.308027i	$0.900331\pi$
$488$	0.715960	−	0.260588i	0.0324100	−	0.0117963i
$489$	−1.19772	+	2.75700i	−0.0541628	+	0.124676i
$490$	−24.2859	+	13.0274i	−1.09712	+	0.588517i
$491$	4.38515	−	3.67958i	0.197899	−	0.166057i	−0.538453	−	0.842655i	$-0.680991\pi$
$491$	4.38515	−	3.67958i	0.197899	−	0.166057i	0.736352	+	0.676598i	$0.236547\pi$
$492$	0.423567	−	6.96208i	0.0190959	−	0.313875i
$493$	2.32467	−	13.1838i	0.104698	−	0.593770i
$494$	2.97718	+	5.15663i	0.133950	+	0.232008i
$495$	−5.67877	+	18.6173i	−0.255242	+	0.836787i
$496$	0.502974	+	0.871176i	0.0225842	+	0.0391170i
$497$	−0.618797	+	0.599760i	−0.0277569	+	0.0269029i
$498$	−14.4839	+	15.2727i	−0.649039	+	0.684386i
$499$	−5.46161	+	4.58284i	−0.244495	+	0.205156i	−0.756798	−	0.653649i	$-0.773237\pi$
$499$	−5.46161	+	4.58284i	−0.244495	+	0.205156i	0.512302	+	0.858805i	$0.328793\pi$
$500$	−20.3490	−	7.40644i	−0.910036	−	0.331226i
$501$	1.31442	+	0.315117i	0.0587240	+	0.0140784i
$502$	−2.29787	+	13.0319i	−0.102559	+	0.581641i
$503$	−11.8867	−	20.5883i	−0.530001	−	0.917989i	−0.999387	−	0.0349962i	$-0.988858\pi$
$503$	−11.8867	−	20.5883i	−0.530001	−	0.917989i	0.469386	−	0.882993i	$-0.344475\pi$
$504$	4.30644	−	6.66743i	0.191824	−	0.296991i
$505$	−20.4422	+	35.4069i	−0.909664	+	1.57558i
$506$	3.74048	+	3.13864i	0.166285	+	0.139529i
$507$	−15.5682	−	10.2972i	−0.691408	−	0.457313i
$508$	−1.66779	−	9.45851i	−0.0739962	−	0.419653i
$509$	5.89632	+	33.4397i	0.261350	+	1.48219i	0.779232	+	0.626735i	$0.215609\pi$
$509$	5.89632	+	33.4397i	0.261350	+	1.48219i	−0.517882	+	0.855452i	$0.673280\pi$
$510$	−24.3597	−	32.8980i	−1.07866	−	1.45675i
$511$	0.651572	−	0.631526i	0.0288238	−	0.0279371i
$512$	1.00000			0.0441942
$513$	19.5524	−	6.94514i	0.863258	−	0.306635i
$514$	−8.40064	+	14.5503i	−0.370537	+	0.641788i
$515$	44.3102	+	37.1806i	1.95254	+	1.63837i
$516$	4.42230	+	5.97237i	0.194681	+	0.262919i
$517$	−14.0219	−	5.10356i	−0.616684	−	0.224455i
$518$	30.4861	−	2.18792i	1.33948	−	0.0961317i
$519$	21.7393	−	10.8476i	0.954249	−	0.476155i
$520$	−4.49718	−	3.77358i	−0.197214	−	0.165482i
$521$	−11.9928	−	20.7721i	−0.525414	−	0.910043i	−0.999562	−	0.0295981i	$-0.990577\pi$
$521$	−11.9928	−	20.7721i	−0.525414	−	0.910043i	0.474148	−	0.880445i	$-0.342756\pi$
$522$	−6.64099	−	0.811067i	−0.290668	−	0.0354994i
$523$	17.0514	−	29.5340i	0.745608	−	1.29143i	−0.204303	−	0.978908i	$-0.565493\pi$
$523$	17.0514	−	29.5340i	0.745608	−	1.29143i	0.949910	−	0.312523i	$-0.101174\pi$
$524$	−10.0888	−	8.46551i	−0.440731	−	0.369817i
$525$	47.2937	−	8.87079i	2.06407	−	0.387153i
$526$	0.796803	+	4.51890i	0.0347423	+	0.197033i
$527$	−4.62587	+	3.88156i	−0.201506	+	0.169083i
$528$	1.96413	−	2.07109i	0.0854776	−	0.0901328i
$529$	13.3631	−	4.86377i	0.581005	−	0.211468i
$530$	−22.3780	+	38.7598i	−0.972038	+	1.68362i
$531$	5.73799	+	0.700782i	0.249007	+	0.0304114i
$532$	8.55861	+	6.19427i	0.371063	+	0.268556i
$533$	5.64264	−	2.05375i	0.244410	−	0.0889579i
$534$	−9.64749	−	6.38107i	−0.417488	−	0.276136i
$535$	−9.30092	−	52.7481i	−0.402114	−	2.28050i
$536$	−10.5823	+	8.87960i	−0.457085	+	0.383540i
$537$	−24.6163	−	33.2446i	−1.06227	−	1.43461i
$538$	−3.59849	+	20.4081i	−0.155142	+	0.879854i
$539$	7.68740	−	8.60088i	0.331120	−	0.370466i
$540$	−15.7729	+	13.0278i	−0.678758	+	0.560628i
$541$	−2.94791	−	5.10593i	−0.126740	−	0.219521i	0.795671	−	0.605728i	$-0.207118\pi$
$541$	−2.94791	−	5.10593i	−0.126740	−	0.219521i	−0.922412	+	0.386208i	$0.873785\pi$
$542$	−6.04753	−	5.07448i	−0.259764	−	0.217968i
$543$	43.6004	−	4.98187i	1.87107	−	0.213793i
$544$	1.04240	+	5.91174i	0.0446925	+	0.253464i
$545$	28.8695	−	24.2244i	1.23663	−	1.03766i
$546$	6.74192	+	1.11329i	0.288528	+	0.0476443i
$547$	25.5550	−	9.30125i	1.09265	−	0.397693i	0.268049	−	0.963405i	$-0.413621\pi$
$547$	25.5550	−	9.30125i	1.09265	−	0.397693i	0.824602	+	0.565713i	$0.191399\pi$
$548$	19.5256			0.834090
$549$	1.91617	−	1.24613i	0.0817801	−	0.0531836i
$550$	17.3040			0.737845
$551$	1.54638	−	8.76996i	0.0658781	−	0.373613i
$552$	1.45916	+	4.92023i	0.0621061	+	0.209419i
$553$	20.4267	+	30.1645i	0.868633	+	1.28273i
$554$	−0.729812	−	4.13897i	−0.0310067	−	0.175848i
$555$	−76.6063	−	18.3654i	−3.25176	−	0.779569i
$556$	−4.31051	+	1.56890i	−0.182806	+	0.0665360i
$557$	−34.4851			−1.46118			−0.730590	−	0.682817i	$-0.760755\pi$
$557$	−34.4851			−1.46118			−0.730590	+	0.682817i	$0.760755\pi$
$558$	2.05959	+	2.20578i	0.0871892	+	0.0933783i
$559$	−3.19887	+	5.54061i	−0.135298	+	0.234343i
$560$	−10.0182	−	2.85281i	−0.423345	−	0.120553i
$561$	14.2912	+	9.45249i	0.603373	+	0.399084i
$562$	−7.75471	−	2.82248i	−0.327113	−	0.119059i
$563$	−12.6312	+	10.5988i	−0.532342	+	0.446688i	−0.868909	−	0.494972i	$-0.835178\pi$
$563$	−12.6312	+	10.5988i	−0.532342	+	0.446688i	0.336567	+	0.941659i	$0.390734\pi$
$564$	−9.33287	−	12.6042i	−0.392985	−	0.530731i
$565$	−6.83470	+	2.48763i	−0.287538	+	0.104655i
$566$	−13.8682			−0.582925
$567$	8.07423	−	22.4010i	0.339086	−	0.940755i
$568$	−0.325713			−0.0136666
$569$	−14.6582	+	5.33516i	−0.614505	+	0.223662i	−0.630473	−	0.776211i	$-0.717139\pi$
$569$	−14.6582	+	5.33516i	−0.614505	+	0.223662i	0.0159683	+	0.999872i	$0.494917\pi$
$570$	−16.2042	−	21.8840i	−0.678719	−	0.916618i
$571$	−15.3597	+	12.8883i	−0.642784	+	0.539360i	−0.904872	−	0.425684i	$-0.860033\pi$
$571$	−15.3597	+	12.8883i	−0.642784	+	0.539360i	0.262088	+	0.965044i	$0.415589\pi$
$572$	2.30912	+	0.840450i	0.0965490	+	0.0351410i
$573$	35.3683	+	23.3934i	1.47753	+	0.977273i
$574$	7.65057	−	7.41520i	0.319329	−	0.309505i
$575$	−15.5561	+	26.9440i	−0.648736	+	1.12364i
$576$	2.92267	−	0.676737i	0.121778	−	0.0281974i
$577$	−32.4759			−1.35199			−0.675995	−	0.736907i	$-0.736286\pi$
$577$	−32.4759			−1.35199			−0.675995	+	0.736907i	$0.736286\pi$
$578$	−17.8873	+	6.51043i	−0.744012	+	0.270798i
$579$	23.4187	+	5.61435i	0.973247	+	0.233324i
$580$	1.52464	+	8.64666i	0.0633072	+	0.359033i
$581$	−32.0696	+	2.30156i	−1.33047	+	0.0954850i
$582$	−2.60797	−	8.79394i	−0.108104	−	0.364521i
$583$	3.25308	−	18.4492i	0.134729	−	0.764086i
$584$	0.342964			0.0141920
$585$	−15.6975	−	7.98554i	−0.649012	−	0.330162i
$586$	−4.71815			−0.194905
$587$	−10.5599	+	3.84350i	−0.435855	+	0.158638i	−0.550623	−	0.834754i	$-0.685610\pi$
$587$	−10.5599	+	3.84350i	−0.435855	+	0.158638i	0.114768	+	0.993392i	$0.463387\pi$
$588$	11.7260	−	3.08246i	0.483571	−	0.127118i
$589$	−3.07715	+	2.58204i	−0.126792	+	0.106391i
$590$	−1.31733	−	7.47094i	−0.0542335	−	0.307574i
$591$	21.4115	−	2.44652i	0.880751	−	0.100636i
$592$	8.84957	+	7.42567i	0.363715	+	0.305193i
$593$	−16.0355	−	27.7743i	−0.658498	−	1.14055i	−0.981004	−	0.193985i	$-0.937859\pi$
$593$	−16.0355	−	27.7743i	−0.658498	−	1.14055i	0.322506	−	0.946567i	$-0.395475\pi$
$594$	4.33892	−	7.38233i	0.178028	−	0.302901i
$595$	6.42215	−	62.1985i	0.263283	−	2.54989i
$596$	1.31366	−	7.45014i	0.0538096	−	0.305169i
$597$	19.8282	+	26.7782i	0.811514	+	1.09596i
$598$	−3.38454	+	2.83996i	−0.138404	+	0.116135i
$599$	−5.55647	−	31.5123i	−0.227031	−	1.28756i	−0.858764	−	0.512371i	$-0.828767\pi$
$599$	−5.55647	−	31.5123i	−0.227031	−	1.28756i	0.631733	−	0.775186i	$-0.282344\pi$
$600$	15.1692	+	10.0332i	0.619279	+	0.409605i
$601$	23.5574	−	8.57420i	0.960928	−	0.349749i	0.186531	−	0.982449i	$-0.440276\pi$
$601$	23.5574	−	8.57420i	0.960928	−	0.349749i	0.774397	+	0.632700i	$0.218053\pi$
$602$	−1.16589	+	11.2916i	−0.0475182	+	0.460213i
$603$	−24.9194	+	33.1136i	−1.01480	+	1.34849i
$604$	10.2681	−	17.7848i	0.417802	−	0.723654i
$605$	30.6485	−	11.1552i	1.24604	−	0.453522i
$606$	12.3769	−	13.0509i	0.502777	−	0.530159i
$607$	7.27167	−	6.10166i	0.295148	−	0.247659i	−0.483173	−	0.875525i	$-0.660516\pi$
$607$	7.27167	−	6.10166i	0.295148	−	0.247659i	0.778321	+	0.627866i	$0.216071\pi$
$608$	0.693410	+	3.93252i	0.0281215	+	0.159485i
$609$	−6.65386	−	7.75677i	−0.269628	−	0.314320i
$610$	−2.29788	−	1.92815i	−0.0930384	−	0.0780685i
$611$	6.75093	−	11.6930i	0.273114	−	0.473046i
$612$	7.04728	+	16.5727i	0.284870	+	0.669910i
$613$	2.19597	+	3.80354i	0.0886945	+	0.153623i	0.906960	−	0.421218i	$-0.138397\pi$
$613$	2.19597	+	3.80354i	0.0886945	+	0.153623i	−0.818265	+	0.574841i	$0.805064\pi$
$614$	−15.2513	−	12.7973i	−0.615491	−	0.516458i
$615$	−24.5716	+	12.2608i	−0.990821	+	0.494404i
$616$	4.34888	−	0.312110i	0.175221	−	0.0125753i
$617$	6.80897	+	2.47826i	0.274119	+	0.0997710i	0.475422	−	0.879758i	$-0.342295\pi$
$617$	6.80897	+	2.47826i	0.274119	+	0.0997710i	−0.201303	+	0.979529i	$0.564518\pi$
$618$	−15.1432	−	20.4510i	−0.609147	−	0.822660i
$619$	3.32923	+	2.79356i	0.133813	+	0.112282i	0.707238	−	0.706976i	$-0.249941\pi$
$619$	3.32923	+	2.79356i	0.133813	+	0.112282i	−0.573425	+	0.819258i	$0.694385\pi$
$620$	1.98023	−	3.42986i	0.0795280	−	0.137746i
$621$	7.59436	+	13.3928i	0.304751	+	0.537433i
$622$	−13.4494			−0.539270
$623$	−4.30583	−	17.1360i	−0.172510	−	0.686538i
$624$	1.53693	+	2.07564i	0.0615263	+	0.0830920i
$625$	5.68785	+	32.2574i	0.227514	+	1.29030i
$626$	1.70203	+	9.65269i	0.0680268	+	0.385799i
$627$	9.50656	+	6.28785i	0.379656	+	0.251113i
$628$	5.40689	+	4.53692i	0.215759	+	0.181043i
$629$	−34.6738	+	60.0569i	−1.38254	+	2.39462i
$630$	−31.2104	−	1.55818i	−1.24345	−	0.0620794i
$631$	6.75224	+	11.6952i	0.268802	+	0.465579i	0.968553	−	0.248808i	$-0.0800388\pi$
$631$	6.75224	+	11.6952i	0.268802	+	0.465579i	−0.699750	+	0.714387i	$0.746705\pi$
$632$	−2.39101	+	13.5601i	−0.0951092	+	0.539391i
$633$	−17.1140	−	4.10287i	−0.680219	−	0.163074i
$634$	30.4739	+	11.0916i	1.21027	+	0.440503i
$635$	−28.9665	+	24.3057i	−1.14950	+	0.964544i
$636$	13.5490	−	14.2869i	0.537252	−	0.566511i
$637$	6.45632	+	8.20159i	0.255809	+	0.324959i
$638$	−1.83756	−	3.18274i	−0.0727496	−	0.126006i
$639$	−0.951953	+	0.220422i	−0.0376587	+	0.00871976i
$640$	−1.96852	−	3.40958i	−0.0778127	−	0.134775i
$641$	7.52296	−	42.6648i	0.297139	−	1.68516i	−0.361241	−	0.932473i	$-0.617647\pi$
$641$	7.52296	−	42.6648i	0.297139	−	1.68516i	0.658380	−	0.752686i	$-0.271242\pi$
$642$	−1.43096	+	23.5203i	−0.0564754	+	0.928274i
$643$	−22.2887	+	18.7024i	−0.878979	+	0.737551i	−0.965969	−	0.258659i	$-0.916720\pi$
$643$	−22.2887	+	18.7024i	−0.878979	+	0.737551i	0.0869902	+	0.996209i	$0.472275\pi$
$644$	−3.42362	+	7.05222i	−0.134909	+	0.277896i
$645$	11.6579	−	26.8349i	0.459028	−	1.05662i
$646$	−22.5252	+	8.19851i	−0.886243	+	0.322566i
$647$	−19.7654	+	34.2347i	−0.777058	+	1.34590i	0.156572	+	0.987667i	$0.449956\pi$
$647$	−19.7654	+	34.2347i	−0.777058	+	1.34590i	−0.933630	+	0.358238i	$0.883378\pi$
$648$	8.08405	−	3.95576i	0.317572	−	0.155397i
$649$	1.58770	+	2.74997i	0.0623225	+	0.107946i
$650$	−2.71887	+	15.4195i	−0.106643	+	0.604802i
$651$	0.0501574	+	4.60956i	0.00196582	+	0.180663i
$652$	−1.63081	−	0.593565i	−0.0638674	−	0.0232458i
$653$	22.4132	+	8.15775i	0.877098	+	0.319238i	0.741038	−	0.671463i	$-0.234334\pi$
$653$	22.4132	+	8.15775i	0.877098	+	0.319238i	0.136060	+	0.990701i	$0.456556\pi$
$654$	−14.8353	+	7.40258i	−0.580106	+	0.289464i
$655$	−9.00380	+	51.0631i	−0.351808	+	1.99520i
$656$	4.02699			0.157227
$657$	1.00237	−	0.232097i	0.0391063	−	0.00905495i
$658$	2.46051	−	23.8300i	0.0959206	−	0.928990i
$659$	2.79688	+	2.34686i	0.108951	+	0.0914208i	0.695636	−	0.718395i	$-0.255123\pi$
$659$	2.79688	+	2.34686i	0.108951	+	0.0914208i	−0.586685	+	0.809815i	$0.699567\pi$
$660$	−10.9280	−	2.61985i	−0.425371	−	0.101978i
$661$	34.5660	+	12.5810i	1.34446	+	0.489343i	0.911214	−	0.411932i	$-0.135146\pi$
$661$	34.5660	+	12.5810i	1.34446	+	0.489343i	0.433246	+	0.901276i	$0.357368\pi$
$662$	9.44041	+	3.43603i	0.366912	+	0.133545i
$663$	−10.6685	+	11.2495i	−0.414332	+	0.436896i
$664$	−9.30923	−	7.81137i	−0.361268	−	0.303140i
$665$	4.27206	−	41.3748i	0.165663	−	1.60445i
$666$	30.8897	+	15.7140i	1.19695	+	0.608905i
$667$	6.60779			0.255855
$668$	−0.135512	+	0.768529i	−0.00524313	+	0.0297353i
$669$	−9.45034	−	6.25066i	−0.365371	−	0.241665i
$670$	51.1072	+	18.6015i	1.97444	+	0.718638i
$671$	1.17987	+	0.429436i	0.0455482	+	0.0165782i
$672$	3.99332	+	2.24797i	0.154046	+	0.0867174i
$673$	0.548582	−	3.11116i	0.0211463	−	0.119927i	−0.972407	−	0.233289i	$-0.925051\pi$
$673$	0.548582	−	3.11116i	0.0211463	−	0.119927i	0.993554	+	0.113363i	$0.0361622\pi$
$674$	10.9031	+	18.8848i	0.419973	+	0.727414i
$675$	51.1244	+	19.0583i	1.96778	+	0.733555i
$676$	5.38826	−	9.33275i	0.207241	−	0.358952i
$677$	−16.1742	+	5.88693i	−0.621625	+	0.226253i	−0.633582	−	0.773676i	$-0.718416\pi$
$677$	−16.1742	+	5.88693i	−0.621625	+	0.226253i	0.0119571	+	0.999929i	$0.496194\pi$
$678$	3.17912	−	0.363253i	0.122093	−	0.0139507i
$679$	6.11904	−	12.6044i	0.234827	−	0.483714i
$680$	18.1046	−	15.1915i	0.694278	−	0.582568i
$681$	−18.8262	−	12.4521i	−0.721422	−	0.477164i
$682$	−0.287866	+	1.63257i	−0.0110229	+	0.0625142i
$683$	−20.4691	−	35.4535i	−0.783228	−	1.35659i	−0.930052	−	0.367428i	$-0.880238\pi$
$683$	−20.4691	−	35.4535i	−0.783228	−	1.35659i	0.146824	−	0.989163i	$-0.453095\pi$
$684$	4.68789	+	11.0242i	0.179246	+	0.421522i
$685$	−38.4365	−	66.5739i	−1.46858	−	2.54366i
$686$	16.4000	+	8.60474i	0.626153	+	0.328530i
$687$	16.9638	+	4.06686i	0.647209	+	0.155161i
$688$	−3.28674	+	2.75790i	−0.125306	+	0.105144i
$689$	15.9288	+	5.79760i	0.606838	+	0.220871i
$690$	13.9035	−	14.6607i	0.529298	−	0.558124i
$691$	−4.84377	+	27.4704i	−0.184266	+	1.04502i	0.742630	+	0.669702i	$0.233578\pi$
$691$	−4.84377	+	27.4704i	−0.184266	+	1.04502i	−0.926895	+	0.375320i	$0.877533\pi$
$692$	7.01348	+	12.1477i	0.266612	+	0.461786i
$693$	12.4991	−	3.85524i	0.474803	−	0.146449i
$694$	11.8500	−	20.5249i	0.449821	−	0.779113i
$695$	13.8346	+	11.6086i	0.524777	+	0.440340i
$696$	0.234568	−	3.85554i	0.00889127	−	0.146144i
$697$	4.19773	+	23.8065i	0.159000	+	0.901735i
$698$	0.965025	+	5.47293i	0.0365267	+	0.207153i
$699$	3.28298	−	0.375120i	0.124174	−	0.0141883i
$700$	6.77025	+	26.9436i	0.255891	+	1.01837i
$701$	−3.10143			−0.117139			−0.0585697	−	0.998283i	$-0.518654\pi$
$701$	−3.10143			−0.117139			−0.0585697	+	0.998283i	$0.518654\pi$
$702$	5.89660	+	5.02632i	0.222553	+	0.189706i
$703$	−23.0652	+	39.9502i	−0.869922	+	1.50675i
$704$	1.26240	+	1.05928i	0.0475786	+	0.0399232i
$705$	−24.6029	+	56.6327i	−0.926599	+	2.13291i
$706$	3.36025	+	1.22303i	0.126465	+	0.0460293i
$707$	27.4044	−	1.96675i	1.03065	−	0.0739674i
$708$	−0.202673	+	3.33128i	−0.00761690	+	0.125197i
$709$	−25.4425	−	21.3488i	−0.955513	−	0.801771i	0.0247042	−	0.999695i	$-0.492136\pi$
$709$	−25.4425	−	21.3488i	−0.955513	−	0.801771i	−0.980217	+	0.197924i	$0.936580\pi$
$710$	0.641173	+	1.11054i	0.0240628	+	0.0416780i
$711$	2.18847	+	41.2498i	0.0820741	+	1.54699i
$712$	3.33906	−	5.78343i	0.125137	−	0.216743i
$713$	−2.28328	−	1.91590i	−0.0855094	−	0.0717509i
$714$	−9.12678	+	25.9508i	−0.341561	+	0.971182i
$715$	−1.67997	−	9.52756i	−0.0628272	−	0.356311i
$716$	18.2953	−	15.3516i	0.683727	−	0.573715i
$717$	3.58466	+	12.0873i	0.133872	+	0.451409i
$718$	−9.93799	+	3.61713i	−0.370883	+	0.134990i
$719$	0.833463	−	1.44360i	0.0310829	−	0.0538372i	−0.850065	−	0.526677i	$-0.823438\pi$
$719$	0.833463	−	1.44360i	0.0310829	−	0.0538372i	0.881148	+	0.472840i	$0.156771\pi$
$720$	−8.06074	−	8.63292i	−0.300406	−	0.321730i
$721$	3.99233	−	38.6657i	0.148682	−	1.43998i
$722$	2.87025	−	1.04468i	0.106819	−	0.0388791i
$723$	−1.21975	+	20.0487i	−0.0453629	+	0.745620i
$724$	4.39964	+	24.9516i	0.163511	+	0.927318i
$725$	17.9384	−	15.0521i	0.666214	−	0.559020i
$726$	−14.2560	+	1.62892i	−0.529090	+	0.0604549i
$727$	3.81640	−	21.6439i	0.141543	−	0.802728i	−0.828536	−	0.559936i	$-0.810826\pi$
$727$	3.81640	−	21.6439i	0.141543	−	0.802728i	0.970078	−	0.242792i	$-0.0780632\pi$
$728$	−0.405194	+	3.92430i	−0.0150175	+	0.145444i
$729$	20.9500	−	17.0322i	0.775928	−	0.630822i
$730$	−0.675133	−	1.16936i	−0.0249878	−	0.0432801i
$731$	−19.7301	−	16.5555i	−0.729743	−	0.612327i
$732$	0.785308	+	1.06057i	0.0290258	+	0.0391997i
$733$	−8.20858	−	46.5532i	−0.303191	−	1.71948i	−0.631901	−	0.775049i	$-0.717725\pi$
$733$	−8.20858	−	46.5532i	−0.303191	−	1.71948i	0.328710	−	0.944431i	$-0.393386\pi$
$734$	7.35091	−	6.16815i	0.271327	−	0.227671i
$735$	−33.5927	−	33.9128i	−1.23909	−	1.25089i
$736$	−2.78429	+	1.01340i	−0.102630	+	0.0373544i
$737$	−22.7651			−0.838564
$738$	11.7696	−	2.72521i	0.433244	−	0.100316i
$739$	26.4823			0.974168			0.487084	−	0.873355i	$-0.338061\pi$
$739$	26.4823			0.974168			0.487084	+	0.873355i	$0.338061\pi$
$740$	7.89785	−	44.7909i	0.290331	−	1.64655i
$741$	−7.09677	+	7.48327i	−0.260706	+	0.274905i
$742$	29.9995	−	2.15300i	1.10132	−	0.0790391i
$743$	−0.664390	−	3.76794i	−0.0243741	−	0.138232i	0.970192	−	0.242336i	$-0.0779137\pi$
$743$	−0.664390	−	3.76794i	−0.0243741	−	0.138232i	−0.994566	+	0.104104i	$0.966803\pi$
$744$	−1.19895	+	1.26424i	−0.0439556	+	0.0463494i
$745$	−27.9878	+	10.1867i	−1.02539	+	0.373213i
$746$	−30.1506			−1.10389
$747$	−32.4941	−	16.5302i	−1.18890	−	0.604808i
$748$	−4.94627	+	8.56719i	−0.180853	+	0.313247i
$749$	−25.8463	+	25.0512i	−0.944404	+	0.915349i
$750$	2.27771	−	37.4383i	0.0831704	−	1.36705i
$751$	16.9214	+	6.15890i	0.617472	+	0.224741i	0.631769	−	0.775156i	$-0.282329\pi$
$751$	16.9214	+	6.15890i	0.617472	+	0.224741i	−0.0142975	+	0.999898i	$0.504551\pi$
$752$	6.93636	−	5.82030i	0.252943	−	0.212245i
$753$	−22.7719	+	2.60196i	−0.829854	+	0.0948208i
$754$	3.12484	−	1.13735i	0.113800	−	0.0414199i
$755$	−80.8517			−2.94249
$756$	13.1925	+	3.86766i	0.479805	+	0.140665i
$757$	7.06319			0.256716			0.128358	−	0.991728i	$-0.459029\pi$
$757$	7.06319			0.256716			0.128358	+	0.991728i	$0.459029\pi$
$758$	3.74049	−	1.36143i	0.135861	−	0.0494492i
$759$	−3.36986	+	7.75698i	−0.122318	+	0.281561i
$760$	12.0433	−	10.1055i	0.436855	−	0.366565i
$761$	−16.0747	−	5.85071i	−0.582707	−	0.212088i	0.0338115	−	0.999428i	$-0.489235\pi$
$761$	−16.0747	−	5.85071i	−0.582707	−	0.212088i	−0.616519	+	0.787340i	$0.711458\pi$
$762$	14.8851	−	7.42745i	0.539232	−	0.269068i
$763$	−24.3575	−	6.93614i	−0.881800	−	0.251105i
$764$	−12.2412	+	21.2024i	−0.442872	+	0.767076i
$765$	42.6331	−	56.6519i	1.54140	−	2.04825i
$766$	3.46145			0.125067
$767$	−2.69995	+	0.982700i	−0.0974894	+	0.0354832i
$768$	0.492464	+	1.66057i	0.0177703	+	0.0599205i
$769$	−4.29109	−	24.3360i	−0.154741	−	0.877578i	−0.959022	−	0.283330i	$-0.908561\pi$
$769$	−4.29109	−	24.3360i	−0.154741	−	0.877578i	0.804282	−	0.594248i	$-0.202550\pi$
$770$	−9.62503	−	14.2135i	−0.346862	−	0.512218i
$771$	−28.2988	−	6.78430i	−1.01916	−	0.244331i
$772$	−2.41439	+	13.6927i	−0.0868957	+	0.492810i
$773$	41.1095			1.47861			0.739304	−	0.673372i	$-0.235155\pi$
$773$	41.1095			1.47861			0.739304	+	0.673372i	$0.235155\pi$
$774$	−7.73969	+	10.2847i	−0.278197	+	0.369676i
$775$	−10.5628			−0.379426
$776$	4.97638	−	1.81125i	0.178641	−	0.0650202i
$777$	18.6465	+	49.5467i	0.668939	+	1.77748i
$778$	20.6363	−	17.3159i	0.739848	−	0.620806i
$779$	2.79235	+	15.8362i	0.100046	+	0.567392i
$780$	4.05158	−	9.32621i	0.145070	−	0.333932i
$781$	−0.411181	−	0.345022i	−0.0147132	−	0.0123458i
$782$	−8.89330	−	15.4036i	−0.318024	−	0.550833i
$783$	−1.92362	−	11.4272i	−0.0687446	−	0.408376i
$784$	2.18749	+	6.64943i	0.0781248	+	0.237480i
$785$	4.82541	−	27.3663i	0.172226	−	0.976744i
$786$	9.08916	−	20.9221i	0.324200	−	0.746266i
$787$	−6.18172	+	5.18708i	−0.220354	+	0.184899i	−0.746282	−	0.665630i	$-0.768163\pi$
$787$	−6.18172	+	5.18708i	−0.220354	+	0.184899i	0.525927	+	0.850530i	$0.323718\pi$
$788$	2.16059	+	12.2533i	0.0769680	+	0.436507i
$789$	−7.11153	+	3.54854i	−0.253177	+	0.126331i
$790$	50.9409	−	18.5410i	1.81240	−	0.659659i
$791$	3.95956	+	2.86572i	0.140786	+	0.101893i
$792$	4.40645	+	2.24162i	0.156576	+	0.0796525i
$793$	−0.568053	+	0.983896i	−0.0201721	+	0.0349392i
$794$	−10.7834	+	3.92484i	−0.382689	+	0.139287i
$795$	−75.3836	−	18.0723i	−2.67358	−	0.640959i
$796$	−14.7367	+	12.3655i	−0.522328	+	0.438285i
$797$	−3.33880	−	18.9353i	−0.118266	−	0.670723i	−0.985081	−	0.172092i	$-0.944947\pi$
$797$	−3.33880	−	18.9353i	−0.118266	−	0.670723i	0.866814	−	0.498631i	$-0.166164\pi$
$798$	−6.07119	+	17.2626i	−0.214918	+	0.611089i
$799$	41.6385	+	34.9389i	1.47307	+	1.23605i
$800$	−5.25016	+	9.09354i	−0.185621	+	0.321505i
$801$	5.84514	−	19.1627i	0.206528	−	0.677082i
$802$	4.52477	+	7.83713i	0.159775	+	0.276739i
$803$	0.432959	+	0.363296i	0.0152788	+	0.0128204i
$804$	−19.9566	−	13.1997i	−0.703813	−	0.465518i
$805$	30.7846	−	2.20934i	1.08501	−	0.0778691i
$806$	−1.40954	−	0.513030i	−0.0496489	−	0.0180707i
$807$	−35.6610	+	4.07470i	−1.25533	+	0.143436i
$808$	7.95501	+	6.67504i	0.279856	+	0.234827i
$809$	11.0783	−	19.1883i	0.389494	−	0.674623i	−0.602888	−	0.797826i	$-0.705983\pi$
$809$	11.0783	−	19.1883i	0.389494	−	0.674623i	0.992381	+	0.123203i	$0.0393166\pi$
$810$	−29.4011	−	19.7762i	−1.03305	−	0.694866i
$811$	1.80869			0.0635116			0.0317558	−	0.999496i	$-0.489890\pi$
$811$	1.80869			0.0635116			0.0317558	+	0.999496i	$0.489890\pi$
$812$	4.23682	−	4.10648i	0.148683	−	0.144109i
$813$	5.44832	−	12.5413i	0.191081	−	0.439843i
$814$	3.30585	+	18.7484i	0.115870	+	0.657131i
$815$	1.18647	+	6.72882i	0.0415603	+	0.235700i
$816$	−9.30348	+	4.64229i	−0.325687	+	0.162513i
$817$	−13.1246	−	11.0128i	−0.459170	−	0.385289i
$818$	18.6092	−	32.2321i	0.650656	−	1.12697i
$819$	1.47147	+	11.7437i	0.0514173	+	0.410357i
$820$	−7.92721	−	13.7303i	−0.276830	−	0.479484i
$821$	−1.02699	+	5.82435i	−0.0358422	+	0.203271i	−0.997470	−	0.0710853i	$-0.977354\pi$
$821$	−1.02699	+	5.82435i	−0.0358422	+	0.203271i	0.961628	+	0.274357i	$0.0884649\pi$
$822$	9.61563	+	32.4235i	0.335384	+	1.13090i
$823$	−21.1441	−	7.69583i	−0.737037	−	0.268260i	−0.0538966	−	0.998547i	$-0.517164\pi$
$823$	−21.1441	−	7.69583i	−0.737037	−	0.268260i	−0.683141	+	0.730287i	$0.739386\pi$
$824$	11.2547	−	9.44380i	0.392075	−	0.328990i
$825$	8.52160	+	28.7344i	0.296684	+	1.00040i
$826$	−3.66072	+	3.54810i	−0.127373	+	0.123454i
$827$	−5.20366	−	9.01301i	−0.180949	−	0.313413i	0.761255	−	0.648453i	$-0.224584\pi$
$827$	−5.20366	−	9.01301i	−0.180949	−	0.313413i	−0.942204	+	0.335040i	$0.891250\pi$
$828$	−7.45178	+	4.84607i	−0.258967	+	0.168413i
$829$	8.98438	+	15.5614i	0.312040	+	0.540470i	0.978804	−	0.204799i	$-0.0656542\pi$
$829$	8.98438	+	15.5614i	0.312040	+	0.540470i	−0.666764	+	0.745269i	$0.732321\pi$
$830$	−8.30807	+	47.1174i	−0.288377	+	1.63547i
$831$	6.51363	−	3.25020i	0.225955	−	0.112748i
$832$	−1.14227	+	0.958481i	−0.0396012	+	0.0332293i
$833$	−37.0294	+	19.8632i	−1.28299	+	0.688221i
$834$	−4.72803	−	6.38526i	−0.163718	−	0.221103i
$835$	2.88712	−	1.05083i	0.0999129	−	0.0363653i
$836$	−3.29029	+	5.69894i	−0.113797	+	0.197102i
$837$	−2.64858	+	4.50635i	−0.0915482	+	0.155762i
$838$	−6.49188	−	11.2443i	−0.224258	−	0.388427i
$839$	5.57985	−	31.6449i	0.192638	−	1.09250i	−0.723105	−	0.690739i	$-0.757286\pi$
$839$	5.57985	−	31.6449i	0.192638	−	1.09250i	0.915743	−	0.401766i	$-0.131603\pi$
$840$	−0.196304	−	18.0407i	−0.00677314	−	0.622464i
$841$	22.5776	+	8.21758i	0.778539	+	0.283365i
$842$	−6.39017	−	2.32583i	−0.220220	−	0.0801535i
$843$	0.868003	−	14.2672i	0.0298956	−	0.491388i
$844$	1.76439	−	10.0064i	0.0607329	−	0.344433i
$845$	−42.4277			−1.45956
$846$	16.3339	−	21.7049i	0.561572	−	0.746231i
$847$	−17.7557	−	12.8506i	−0.610092	−	0.441553i
$848$	8.70833	+	7.30716i	0.299045	+	0.250929i
$849$	−6.82960	−	23.0291i	−0.234391	−	0.790357i
$850$	−59.2314	−	21.5585i	−2.03162	−	0.739449i
$851$	−32.1650	−	11.7071i	−1.10260	−	0.401314i
$852$	−0.160402	−	0.540868i	−0.00549528	−	0.0185298i
$853$	23.5020	+	19.7205i	0.804693	+	0.675218i	0.949335	−	0.314266i	$-0.101758\pi$
$853$	23.5020	+	19.7205i	0.804693	+	0.675218i	−0.144642	+	0.989484i	$0.546203\pi$
$854$	−0.207038	+	2.00516i	−0.00708469	+	0.0686152i
$855$	28.3598	−	37.6852i	0.969883	−	1.28881i
$856$	−13.6046			−0.464995
$857$	−1.55544	+	8.82135i	−0.0531329	+	0.301331i	−0.999781	−	0.0209382i	$-0.993335\pi$
$857$	−1.55544	+	8.82135i	−0.0531329	+	0.301331i	0.946648	+	0.322270i	$0.104446\pi$
$858$	−0.258465	+	4.24833i	−0.00882385	+	0.145036i
$859$	24.0354	+	8.74818i	0.820078	+	0.298484i	0.717780	−	0.696270i	$-0.245158\pi$
$859$	24.0354	+	8.74818i	0.820078	+	0.298484i	0.102298	+	0.994754i	$0.467380\pi$
$860$	15.8733	+	5.77741i	0.541275	+	0.197008i
$861$	16.0811	+	9.05255i	0.548041	+	0.308510i
$862$	−2.52615	+	14.3265i	−0.0860409	+	0.487962i
$863$	28.3242	+	49.0589i	0.964165	+	1.66998i	0.711841	+	0.702341i	$0.247862\pi$
$863$	28.3242	+	49.0589i	0.964165	+	1.66998i	0.252325	+	0.967643i	$0.418805\pi$
$864$	2.56308	+	4.52003i	0.0871977	+	0.153774i
$865$	27.6124	−	47.8260i	0.938849	−	1.62613i
$866$	−8.82869	+	3.21338i	−0.300011	+	0.109195i
$867$	−19.6198	−	26.4968i	−0.666324	−	0.899879i
$868$	−2.65466	+	0.190519i	−0.0901050	+	0.00646664i
$869$	−17.3824	+	14.5855i	−0.589656	+	0.494780i
$870$	−13.6075	+	6.78993i	−0.461338	+	0.230200i
$871$	3.57694	−	20.2858i	0.121200	−	0.687360i
$872$	−4.78613	−	8.28982i	−0.162079	−	0.280729i
$873$	13.3186	−	8.66140i	0.450766	−	0.293144i
$874$	−5.91588	−	10.2466i	−0.200108	−	0.346596i
$875$	41.1407	−	39.8750i	1.39081	−	1.34802i
$876$	0.168898	+	0.569515i	0.00570652	+	0.0192421i
$877$	−36.3289	+	30.4835i	−1.22674	+	1.02936i	−0.228294	+	0.973592i	$0.573315\pi$
$877$	−36.3289	+	30.4835i	−1.22674	+	1.02936i	−0.998444	+	0.0557635i	$0.982241\pi$
$878$	6.61612	+	2.40807i	0.223283	+	0.0812684i
$879$	−2.32352	−	7.83480i	−0.0783704	−	0.264261i
$880$	1.12664	−	6.38948i	0.0379790	−	0.215389i
$881$	16.3599	+	28.3361i	0.551178	+	0.954668i	0.998190	+	0.0601398i	$0.0191546\pi$
$881$	16.3599	+	28.3361i	0.551178	+	0.954668i	−0.447012	+	0.894528i	$0.647512\pi$
$882$	10.8932	+	17.9538i	0.366795	+	0.604534i
$883$	10.3640	−	17.9510i	0.348777	−	0.604099i	−0.637256	−	0.770653i	$-0.719930\pi$
$883$	10.3640	−	17.9510i	0.348777	−	0.604099i	0.986032	+	0.166553i	$0.0532638\pi$
$884$	−6.85699	−	5.75370i	−0.230626	−	0.193518i
$885$	11.7572	−	5.86668i	0.395215	−	0.197206i
$886$	1.00352	+	5.69125i	0.0337140	+	0.191201i
$887$	1.78331	+	10.1136i	0.0598776	+	0.339583i	0.999999	−	0.00125631i	$-0.000399896\pi$
$887$	1.78331	+	10.1136i	0.0598776	+	0.339583i	−0.940122	+	0.340839i	$0.889289\pi$
$888$	−7.97272	+	18.3522i	−0.267547	+	0.615859i
$889$	24.4393	+	6.95944i	0.819669	+	0.233412i
$890$	−26.2921			−0.881313
$891$	14.3956	+	3.56952i	0.482271	+	0.119584i
$892$	3.27083	−	5.66524i	0.109515	−	0.189686i
$893$	27.6982	+	23.2416i	0.926885	+	0.777749i
$894$	13.0184	−	1.48751i	0.435399	−	0.0497496i
$895$	−88.3571	−	32.1594i	−2.95345	−	1.07497i
$896$	−1.15546	+	2.38011i	−0.0386013	+	0.0795138i
$897$	−6.38271	−	4.22167i	−0.213112	−	0.140957i
$898$	−18.8777	−	15.8402i	−0.629956	−	0.528596i
$899$	1.12169	+	1.94282i	0.0374104	+	0.0647967i
$900$	−9.19057	+	30.1304i	−0.306352	+	1.00435i
$901$	−34.1204	+	59.0983i	−1.13672	+	1.96885i
$902$	5.08368	+	4.26572i	0.169268	+	0.142033i
$903$	−19.3247	+	3.62469i	−0.643085	+	0.120622i
$904$	0.320799	+	1.81934i	0.0106696	+	0.0605105i
$905$	76.4136	−	64.1187i	2.54008	−	2.13138i
$906$	34.5895	+	8.29242i	1.14916	+	0.275497i
$907$	−20.8609	+	7.59275i	−0.692676	+	0.252113i	−0.664280	−	0.747484i	$-0.731262\pi$
$907$	−20.8609	+	7.59275i	−0.692676	+	0.252113i	−0.0283951	+	0.999597i	$0.509040\pi$
$908$	6.51588	−	11.2858i	0.216237	−	0.374534i
$909$	27.7671	+	14.1255i	0.920978	+	0.468514i
$910$	14.1778	−	6.34353i	0.469991	−	0.210286i
$911$	−17.7185	+	6.44902i	−0.587041	+	0.213665i	−0.618427	−	0.785842i	$-0.712230\pi$
$911$	−17.7185	+	6.44902i	−0.587041	+	0.213665i	0.0313865	+	0.999507i	$0.490008\pi$
$912$	−6.18873	+	3.08808i	−0.204929	+	0.102257i
$913$	−3.47756	−	19.7222i	−0.115090	−	0.652710i
$914$	−2.80407	+	2.35289i	−0.0927503	+	0.0778267i
$915$	2.07020	−	4.76532i	0.0684385	−	0.157537i
$916$	−1.74891	+	9.91856i	−0.0577856	+	0.327718i
$917$	31.8060	−	14.2308i	1.05033	−	0.469943i
$918$	−24.0494	+	19.8639i	−0.793750	+	0.655607i
$919$	13.3670	+	23.1523i	0.440936	+	0.763724i	0.997759	−	0.0669071i	$-0.0213131\pi$
$919$	13.3670	+	23.1523i	0.440936	+	0.763724i	−0.556823	+	0.830631i	$0.687980\pi$
$920$	8.93621	+	7.49837i	0.294618	+	0.247214i
$921$	13.7401	−	31.6280i	0.452752	−	1.04218i
$922$	1.56879	+	8.89702i	0.0516652	+	0.293008i
$923$	0.372053	−	0.312190i	0.0122463	−	0.0102758i
$924$	2.65995	+	7.06790i	0.0875058	+	0.232517i
$925$	−113.987	+	41.4880i	−3.74788	+	1.36412i
$926$	−16.3630			−0.537723
$927$	26.5028	−	35.2176i	0.870466	−	1.15670i
$928$	2.23011			0.0732070
$929$	2.69250	−	15.2699i	0.0883379	−	0.500989i	−0.908248	−	0.418432i	$-0.862580\pi$
$929$	2.69250	−	15.2699i	0.0883379	−	0.500989i	0.996586	−	0.0825578i	$-0.0263089\pi$
$930$	6.67070	+	1.59922i	0.218741	+	0.0524405i
$931$	−24.6322	+	13.2131i	−0.807287	+	0.433043i
$932$	0.331279	+	1.87878i	0.0108514	+	0.0615415i
$933$	−6.62333	−	22.3336i	−0.216838	−	0.731168i
$934$	5.11855	−	1.86300i	0.167484	−	0.0609592i
$935$	38.9473			1.27371
$936$	−2.68985	+	3.57435i	−0.0879206	+	0.116831i
$937$	−10.1638	+	17.6042i	−0.332037	+	0.575106i	−0.982911	−	0.184080i	$-0.941069\pi$
$937$	−10.1638	+	17.6042i	−0.332037	+	0.575106i	0.650874	+	0.759186i	$0.274403\pi$
$938$	−8.90693	−	35.4470i	−0.290822	−	1.15739i
$939$	−15.1907	+	7.57994i	−0.495731	+	0.247362i
$940$	−33.4992	−	12.1927i	−1.09262	−	0.397682i
$941$	18.3468	−	15.3948i	0.598090	−	0.501857i	−0.292741	−	0.956192i	$-0.594567\pi$
$941$	18.3468	−	15.3948i	0.598090	−	0.501857i	0.890831	+	0.454335i	$0.150123\pi$
$942$	−4.87116	+	11.2128i	−0.158711	+	0.365332i
$943$	−11.2123	+	4.08095i	−0.365123	+	0.132894i
$944$	−1.92687			−0.0627144
$945$	−12.7826	−	52.5943i	−0.415817	−	1.71089i
$946$	−7.07058			−0.229884
$947$	20.4243	−	7.43385i	0.663701	−	0.241568i	0.0118678	−	0.999930i	$-0.496222\pi$
$947$	20.4243	−	7.43385i	0.663701	−	0.241568i	0.651834	+	0.758362i	$0.274000\pi$
$948$	−23.6949	+	2.70743i	−0.769574	+	0.0879332i
$949$	−0.391759	+	0.328725i	−0.0127170	+	0.0106709i
$950$	−39.4011	−	14.3408i	−1.27834	−	0.465277i
$951$	−3.41101	+	56.0661i	−0.110610	+	1.81807i
$952$	−15.2750	−	4.34977i	−0.495066	−	0.140977i
$953$	13.4821	−	23.3517i	0.436729	−	0.756437i	−0.560706	−	0.828015i	$-0.689470\pi$
$953$	13.4821	−	23.3517i	0.436729	−	0.756437i	0.997435	+	0.0715782i	$0.0228035\pi$
$954$	30.3966	+	15.4632i	0.984128	+	0.500639i
$955$	96.3884			3.11906
$956$	−6.84005	+	2.48957i	−0.221223	+	0.0805186i
$957$	4.38022	−	4.61877i	0.141592	−	0.149304i
$958$	−4.73161	−	26.8343i	−0.152871	−	0.866977i
$959$	−22.5611	+	46.4729i	−0.728534	+	1.50069i
$960$	4.69241	−	4.94796i	0.151447	−	0.159695i
$961$	−5.20737	+	29.5325i	−0.167980	+	0.952661i
$962$	−17.2260			−0.555388
$963$	−39.7618	+	9.20673i	−1.28131	+	0.296683i
$964$	−11.5965			−0.373499
$965$	51.4390	−	18.7223i	1.65588	−	0.602691i
$966$	−13.3967	−	2.21218i	−0.431031	−	0.0711757i
$967$	19.9540	−	16.7434i	0.641678	−	0.538432i	−0.262855	−	0.964835i	$-0.584664\pi$
$967$	19.9540	−	16.7434i	0.641678	−	0.538432i	0.904533	+	0.426404i	$0.140220\pi$
$968$	−1.43855	−	8.15840i	−0.0462366	−	0.262221i
$969$	−24.7070	−	33.3671i	−0.793704	−	1.07191i
$970$	−15.9717	−	13.4019i	−0.512821	−	0.430308i
$971$	0.268228	+	0.464584i	0.00860784	+	0.0149092i	0.870297	−	0.492527i	$-0.163927\pi$
$971$	0.268228	+	0.464584i	0.00860784	+	0.0149092i	−0.861689	+	0.507436i	$0.830593\pi$
$972$	10.5499	+	11.4760i	0.338389	+	0.368094i
$973$	1.24649	−	12.0723i	0.0399607	−	0.387019i
$974$	5.69024	−	32.2710i	0.182327	−	1.03403i
$975$	−26.9440	+	3.07868i	−0.862899	+	0.0985966i
$976$	−0.583656	+	0.489745i	−0.0186824	+	0.0156764i
$977$	0.137769	+	0.781324i	0.00440761	+	0.0249968i	0.986932	−	0.161136i	$-0.0515157\pi$
$977$	0.137769	+	0.781324i	0.00440761	+	0.0249968i	−0.982525	+	0.186133i	$0.940405\pi$
$978$	0.182540	−	3.00037i	0.00583699	−	0.0959414i
$979$	10.3415	−	3.76401i	0.330517	−	0.120298i
$980$	18.3656	−	20.5480i	0.586668	−	0.656381i
$981$	−19.5983	−	20.9895i	−0.625727	−	0.670143i
$982$	−2.86220	+	4.95748i	−0.0913366	+	0.158200i
$983$	−9.05946	+	3.29737i	−0.288952	+	0.105170i	−0.482430	−	0.875935i	$-0.660246\pi$
$983$	−9.05946	+	3.29737i	−0.288952	+	0.105170i	0.193478	+	0.981105i	$0.438023\pi$
$984$	1.98315	+	6.68708i	0.0632204	+	0.213176i
$985$	37.5256	−	31.4877i	1.19566	−	1.00328i
$986$	2.32467	+	13.1838i	0.0740324	+	0.419859i
$987$	40.7830	−	7.64959i	1.29814	−	0.243489i
$988$	−4.56131	−	3.82739i	−0.145115	−	0.121766i
$989$	6.35639	−	11.0096i	0.202121	−	0.350084i
$990$	−1.03120	−	19.4368i	−0.0327738	−	0.617743i
$991$	4.30217	+	7.45157i	0.136663	+	0.236707i	0.926231	−	0.376955i	$-0.123029\pi$
$991$	4.30217	+	7.45157i	0.136663	+	0.236707i	−0.789569	+	0.613662i	$0.789696\pi$
$992$	−0.770601	−	0.646611i	−0.0244666	−	0.0205299i
$993$	−1.05669	+	17.3685i	−0.0335330	+	0.551174i
$994$	0.376349	−	0.775231i	0.0119371	−	0.0245888i
$995$	71.1708	+	25.9041i	2.25627	+	0.821214i
$996$	8.38684	−	19.3054i	0.265747	−	0.611715i
$997$	−35.5192	−	29.8042i	−1.12490	−	0.943907i	−0.126063	−	0.992022i	$-0.540234\pi$
$997$	−35.5192	−	29.8042i	−1.12490	−	0.943907i	−0.998842	+	0.0481152i	$0.984679\pi$
$998$	3.56482	−	6.17444i	0.112842	−	0.195449i
$999$	−10.8821	+	59.0329i	−0.344294	+	1.86772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.a.25.4	yes	72
7.2	even	3		378.2.v.b.79.12	yes	72
27.13	even	9		378.2.v.b.67.12	✓	72
189.121	even	9	inner	378.2.w.a.121.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.b.67.12	✓	72	27.13	even	9
378.2.v.b.79.12	yes	72	7.2	even	3
378.2.w.a.25.4	yes	72	1.1	even	1	trivial
378.2.w.a.121.4	yes	72	189.121	even	9	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.03071 - 1.39199i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.69961 - 1.34655i) q^{5} +(1.44464 + 0.955517i) q^{6} +(0.644767 + 2.56598i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.875266 + 2.86948i) q^{9} +O(q^{10})\)	\(q+(-0.939693 + 0.342020i) q^{2} +(-1.03071 - 1.39199i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-3.69961 - 1.34655i) q^{5} +(1.44464 + 0.955517i) q^{6} +(0.644767 + 2.56598i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.875266 + 2.86948i) q^{9} +3.93704 q^{10} +(-1.54857 + 0.563632i) q^{11} +(-1.68432 - 0.403796i) q^{12} +(-0.258932 - 1.46848i) q^{13} +(-1.48350 - 2.19071i) q^{14} +(1.93885 + 6.53772i) q^{15} +(0.173648 - 0.984808i) q^{16} +6.00293 q^{17} +(-0.158939 - 2.99579i) q^{18} +3.99319 q^{19} +(-3.69961 + 1.34655i) q^{20} +(2.90725 - 3.54230i) q^{21} +(1.26240 - 1.05928i) q^{22} +(0.514517 + 2.91797i) q^{23} +(1.72085 - 0.196628i) q^{24} +(8.04371 + 6.74947i) q^{25} +(0.745566 + 1.29136i) q^{26} +(4.89643 - 1.73925i) q^{27} +(2.14330 + 1.55121i) q^{28} +(0.387255 - 2.19623i) q^{29} +(-4.05796 - 5.48032i) q^{30} +(-0.770601 + 0.646611i) q^{31} +(0.173648 + 0.984808i) q^{32} +(2.38070 + 1.57464i) q^{33} +(-5.64091 + 2.05312i) q^{34} +(1.06984 - 10.3614i) q^{35} +(1.17397 + 2.76076i) q^{36} +(-5.77615 + 10.0046i) q^{37} +(-3.75237 + 1.36575i) q^{38} +(-1.77722 + 1.87401i) q^{39} +(3.01595 - 2.53068i) q^{40} +(0.699279 + 3.96581i) q^{41} +(-1.52039 + 4.32301i) q^{42} +(-3.28674 - 2.75790i) q^{43} +(-0.823975 + 1.42717i) q^{44} +(7.10204 - 9.43737i) q^{45} +(-1.48149 - 2.56602i) q^{46} +(6.93636 + 5.82030i) q^{47} +(-1.54982 + 0.773337i) q^{48} +(-6.16855 + 3.30892i) q^{49} +(-9.86707 - 3.59132i) q^{50} +(-6.18730 - 8.35602i) q^{51} +(-1.14227 - 0.958481i) q^{52} +(-5.68396 + 9.84491i) q^{53} +(-4.00628 + 3.30903i) q^{54} +6.48805 q^{55} +(-2.54459 - 0.724608i) q^{56} +(-4.11583 - 5.55847i) q^{57} +(0.387255 + 2.19623i) q^{58} +(-0.334598 - 1.89760i) q^{59} +(5.68761 + 3.76191i) q^{60} +(-0.583656 - 0.489745i) q^{61} +(0.502974 - 0.871176i) q^{62} +(-7.92738 - 0.395774i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.01943 + 5.78146i) q^{65} +(-2.77568 - 0.665436i) q^{66} +(12.9811 + 4.72473i) q^{67} +(4.59851 - 3.85861i) q^{68} +(3.53146 - 3.72379i) q^{69} +(2.53847 + 10.1024i) q^{70} +(0.162856 + 0.282076i) q^{71} +(-2.04741 - 2.19274i) q^{72} +(-0.171482 - 0.297016i) q^{73} +(2.00604 - 11.3768i) q^{74} +(1.10444 - 18.1535i) q^{75} +(3.05896 - 2.56677i) q^{76} +(-2.44474 - 3.61019i) q^{77} +(1.02909 - 2.36884i) q^{78} +(12.9389 - 4.70937i) q^{79} +(-1.96852 + 3.40958i) q^{80} +(-7.46782 - 5.02311i) q^{81} +(-2.01349 - 3.48747i) q^{82} +(-2.11023 + 11.9677i) q^{83} +(-0.0498608 - 4.58230i) q^{84} +(-22.2085 - 8.08324i) q^{85} +(4.03178 + 1.46745i) q^{86} +(-3.45628 + 1.72463i) q^{87} +(0.286164 - 1.62291i) q^{88} -6.67813 q^{89} +(-3.44596 + 11.2973i) q^{90} +(3.60114 - 1.61124i) q^{91} +(2.26978 + 1.90457i) q^{92} +(1.69434 + 0.406198i) q^{93} +(-8.50871 - 3.09692i) q^{94} +(-14.7732 - 5.37702i) q^{95} +(1.19186 - 1.25677i) q^{96} +(-4.05678 - 3.40404i) q^{97} +(4.66482 - 5.21914i) q^{98} +(-0.261923 - 4.93691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9}+O(q^{10}) \) 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9	\( 72 q + 3 q^{6} - 3 q^{7} - 36 q^{8} - 12 q^{9} + 12 q^{10} - 6 q^{11} - 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} + 36 q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} - 30 q^{25} - 18 q^{26} - 6 q^{27} + 3 q^{29} + 3 q^{30} + 9 q^{31} - 18 q^{33} + 9 q^{34} + 9 q^{35} + 9 q^{36} + 3 q^{39} - 6 q^{41} + 3 q^{42} + 24 q^{43} - 30 q^{45} - 9 q^{47} - 6 q^{48} + 51 q^{49} + 6 q^{50} + 12 q^{51} + 6 q^{52} - 15 q^{53} - 27 q^{54} + 72 q^{55} + 6 q^{56} - 63 q^{57} + 3 q^{58} + 15 q^{59} - 3 q^{60} - 18 q^{61} - 24 q^{62} - 48 q^{63} - 36 q^{64} - 18 q^{65} - 36 q^{66} + 66 q^{67} - 18 q^{68} - 21 q^{69} - 6 q^{70} + 12 q^{71} - 12 q^{72} - 66 q^{73} + 9 q^{74} + 15 q^{75} - 15 q^{77} + 30 q^{78} + 9 q^{79} - 6 q^{80} - 33 q^{82} - 18 q^{83} - 12 q^{84} + 21 q^{85} - 12 q^{86} - 48 q^{87} + 12 q^{88} + 72 q^{89} + 69 q^{90} + 12 q^{91} + 30 q^{92} + 60 q^{93} - 36 q^{94} + 93 q^{95} - 48 q^{97} + 6 q^{98} - 54 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 - 3 * q^7 - 36 * q^8 - 12 * q^9 + 12 * q^10 - 6 * q^11 - 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 + 36 * q^19 - 12 * q^21 - 6 * q^22 + 12 * q^23 - 30 * q^25 - 18 * q^26 - 6 * q^27 + 3 * q^29 + 3 * q^30 + 9 * q^31 - 18 * q^33 + 9 * q^34 + 9 * q^35 + 9 * q^36 + 3 * q^39 - 6 * q^41 + 3 * q^42 + 24 * q^43 - 30 * q^45 - 9 * q^47 - 6 * q^48 + 51 * q^49 + 6 * q^50 + 12 * q^51 + 6 * q^52 - 15 * q^53 - 27 * q^54 + 72 * q^55 + 6 * q^56 - 63 * q^57 + 3 * q^58 + 15 * q^59 - 3 * q^60 - 18 * q^61 - 24 * q^62 - 48 * q^63 - 36 * q^64 - 18 * q^65 - 36 * q^66 + 66 * q^67 - 18 * q^68 - 21 * q^69 - 6 * q^70 + 12 * q^71 - 12 * q^72 - 66 * q^73 + 9 * q^74 + 15 * q^75 - 15 * q^77 + 30 * q^78 + 9 * q^79 - 6 * q^80 - 33 * q^82 - 18 * q^83 - 12 * q^84 + 21 * q^85 - 12 * q^86 - 48 * q^87 + 12 * q^88 + 72 * q^89 + 69 * q^90 + 12 * q^91 + 30 * q^92 + 60 * q^93 - 36 * q^94 + 93 * q^95 - 48 * q^97 + 6 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more