LMFDB - Embedded newform 31.2.g.a.20.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [31,2,Mod(7,31)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(31, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([28]))

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

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

chi := DirichletCharacter("31.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, degree $8$, 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:	$0.247536246266$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			20.1
Root			$1.14660i$ of defining polynomial
Character	$\chi$	$=$	31.20
Dual form			31.2.g.a.14.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.831304 - 2.55849i) q^{2} +(0.949606 + 1.05464i) q^{3} +(-4.23677 + 3.07819i) q^{4} +(-0.304192 - 0.526876i) q^{5} +(1.90889 - 3.30629i) q^{6} +(0.180508 + 1.71742i) q^{7} +(7.04481 + 5.11835i) q^{8} +(0.103062 - 0.980572i) q^{9} +O(q^{10})$	\(q+(-0.831304 - 2.55849i) q^{2} +(0.949606 + 1.05464i) q^{3} +(-4.23677 + 3.07819i) q^{4} +(-0.304192 - 0.526876i) q^{5} +(1.90889 - 3.30629i) q^{6} +(0.180508 + 1.71742i) q^{7} +(7.04481 + 5.11835i) q^{8} +(0.103062 - 0.980572i) q^{9} +(-1.09513 + 1.21627i) q^{10} +(-1.22177 - 0.543967i) q^{11} +(-7.26966 - 1.54521i) q^{12} +(-3.59045 + 0.763174i) q^{13} +(4.24394 - 1.88952i) q^{14} +(0.266804 - 0.821139i) q^{15} +(4.00227 - 12.3177i) q^{16} +(-2.52396 + 1.12374i) q^{17} +(-2.59446 + 0.551469i) q^{18} +(2.51157 + 0.533850i) q^{19} +(2.91062 + 1.29589i) q^{20} +(-1.63986 + 1.82124i) q^{21} +(-0.376072 + 3.57808i) q^{22} +(0.436271 + 0.316969i) q^{23} +(1.29175 + 12.2902i) q^{24} +(2.31493 - 4.00958i) q^{25} +(4.93733 + 8.55171i) q^{26} +(4.57641 - 3.32495i) q^{27} +(-6.05132 - 6.72067i) q^{28} +(-2.51258 - 7.73291i) q^{29} -2.32267 q^{30} +(4.75081 + 2.90341i) q^{31} -17.4262 q^{32} +(-0.586508 - 1.80509i) q^{33} +(4.97326 + 5.52336i) q^{34} +(0.849957 - 0.617530i) q^{35} +(2.58174 + 4.47170i) q^{36} +(-3.87249 + 6.70735i) q^{37} +(-0.722025 - 6.86961i) q^{38} +(-4.21439 - 3.06194i) q^{39} +(0.553763 - 5.26870i) q^{40} +(-0.0696243 + 0.0773256i) q^{41} +(6.02285 + 2.68155i) q^{42} +(2.93904 + 0.624713i) q^{43} +(6.85079 - 1.45618i) q^{44} +(-0.547990 + 0.243981i) q^{45} +(0.448289 - 1.37969i) q^{46} +(-2.07813 + 6.39584i) q^{47} +(16.7914 - 7.47602i) q^{48} +(3.93009 - 0.835366i) q^{49} +(-12.1829 - 2.58955i) q^{50} +(-3.58192 - 1.59477i) q^{51} +(12.8627 - 14.2855i) q^{52} +(-0.292549 + 2.78341i) q^{53} +(-12.3112 - 8.94464i) q^{54} +(0.0850494 + 0.809191i) q^{55} +(-7.51871 + 13.0228i) q^{56} +(1.82198 + 3.15576i) q^{57} +(-17.6959 + 12.8568i) q^{58} +(0.311970 + 0.346478i) q^{59} +(1.39724 + 4.30025i) q^{60} -5.11468 q^{61} +(3.47898 - 14.5685i) q^{62} +1.70266 q^{63} +(6.48190 + 19.9492i) q^{64} +(1.49428 + 1.65957i) q^{65} +(-4.13073 + 3.00115i) q^{66} +(-4.14923 - 7.18668i) q^{67} +(7.23436 - 12.5303i) q^{68} +(0.0799956 + 0.761107i) q^{69} +(-2.28652 - 1.66125i) q^{70} +(-0.497420 + 4.73264i) q^{71} +(5.74497 - 6.38043i) q^{72} +(6.85725 + 3.05304i) q^{73} +(20.3799 + 4.33188i) q^{74} +(6.42696 - 1.36609i) q^{75} +(-12.2842 + 5.46929i) q^{76} +(0.713679 - 2.19648i) q^{77} +(-4.33049 + 13.3279i) q^{78} +(-8.86044 + 3.94492i) q^{79} +(-7.70738 + 1.63825i) q^{80} +(4.95915 + 1.05410i) q^{81} +(0.255716 + 0.113852i) q^{82} +(-11.1642 + 12.3991i) q^{83} +(1.34155 - 12.7640i) q^{84} +(1.35984 + 0.987981i) q^{85} +(-0.844916 - 8.03884i) q^{86} +(5.76952 - 9.99310i) q^{87} +(-5.82292 - 10.0856i) q^{88} +(12.3911 - 9.00268i) q^{89} +(1.07977 + 1.19920i) q^{90} +(-1.95880 - 6.02855i) q^{91} -2.82407 q^{92} +(1.44933 + 7.76751i) q^{93} +18.0912 q^{94} +(-0.482726 - 1.48568i) q^{95} +(-16.5480 - 18.3784i) q^{96} +(1.03488 - 0.751881i) q^{97} +(-5.40437 - 9.36065i) q^{98} +(-0.659316 + 1.14197i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9	\( 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9} - 2 q^{10} - 7 q^{11} + 5 q^{12} - 7 q^{13} - 6 q^{14} + 14 q^{15} - 2 q^{16} - 6 q^{17} - 3 q^{18} + 16 q^{19} + 37 q^{20} + 9 q^{21} + 9 q^{22} + q^{23} - 20 q^{24} - 13 q^{25} + 9 q^{26} + 9 q^{27} - 30 q^{28} - 14 q^{29} - 22 q^{30} + 15 q^{31} - 42 q^{32} - 13 q^{33} - 32 q^{34} - 9 q^{35} + q^{36} - 8 q^{37} + 8 q^{38} - 3 q^{39} - q^{40} - 8 q^{41} + 69 q^{42} + 23 q^{43} + 39 q^{44} + 65 q^{45} + 34 q^{46} + 14 q^{47} + 34 q^{48} + 2 q^{49} + 3 q^{50} - 42 q^{51} + 29 q^{52} + 6 q^{53} - 46 q^{54} - 7 q^{55} - 30 q^{56} - 17 q^{57} - 15 q^{58} + 4 q^{59} - 75 q^{60} - 60 q^{61} - 25 q^{62} - 46 q^{63} + 23 q^{64} - 12 q^{65} - 30 q^{66} + 13 q^{67} + 30 q^{68} + 38 q^{69} + 12 q^{70} - 14 q^{71} + 37 q^{72} + 2 q^{73} + 13 q^{74} + 13 q^{75} - 12 q^{76} + 18 q^{77} - 15 q^{78} + 18 q^{79} + 36 q^{80} + 23 q^{81} + 14 q^{82} - 16 q^{83} + 8 q^{84} + 37 q^{85} - 26 q^{86} + 15 q^{87} - 17 q^{88} + q^{89} - 23 q^{90} + 8 q^{91} - 64 q^{92} + 17 q^{93} + 44 q^{94} - 22 q^{95} + 8 q^{96} + 3 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9 - 2 * q^10 - 7 * q^11 + 5 * q^12 - 7 * q^13 - 6 * q^14 + 14 * q^15 - 2 * q^16 - 6 * q^17 - 3 * q^18 + 16 * q^19 + 37 * q^20 + 9 * q^21 + 9 * q^22 + q^23 - 20 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 - 30 * q^28 - 14 * q^29 - 22 * q^30 + 15 * q^31 - 42 * q^32 - 13 * q^33 - 32 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 8 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 69 * q^42 + 23 * q^43 + 39 * q^44 + 65 * q^45 + 34 * q^46 + 14 * q^47 + 34 * q^48 + 2 * q^49 + 3 * q^50 - 42 * q^51 + 29 * q^52 + 6 * q^53 - 46 * q^54 - 7 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 + 4 * q^59 - 75 * q^60 - 60 * q^61 - 25 * q^62 - 46 * q^63 + 23 * q^64 - 12 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 + 38 * q^69 + 12 * q^70 - 14 * q^71 + 37 * q^72 + 2 * q^73 + 13 * q^74 + 13 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 + 18 * q^79 + 36 * q^80 + 23 * q^81 + 14 * q^82 - 16 * q^83 + 8 * q^84 + 37 * q^85 - 26 * q^86 + 15 * q^87 - 17 * q^88 + q^89 - 23 * q^90 + 8 * q^91 - 64 * q^92 + 17 * q^93 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{15}\right)$

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 $

$2$	−0.831304	−	2.55849i	−0.587821	−	1.80913i	−0.587636	−	0.809126i	$-0.699941\pi$
$2$	−0.831304	−	2.55849i	−0.587821	−	1.80913i	−0.000184800	−	1.00000i	$-0.500059\pi$
$3$	0.949606	+	1.05464i	0.548255	+	0.608899i	0.952047	−	0.305952i	$-0.0989746\pi$
$3$	0.949606	+	1.05464i	0.548255	+	0.608899i	−0.403792	+	0.914851i	$0.632308\pi$
$4$	−4.23677	+	3.07819i	−2.11839	+	1.53910i
$5$	−0.304192	−	0.526876i	−0.136039	−	0.235626i	0.789955	−	0.613165i	$-0.210104\pi$
$5$	−0.304192	−	0.526876i	−0.136039	−	0.235626i	−0.925994	+	0.377539i	$0.876770\pi$
$6$	1.90889	−	3.30629i	0.779300	−	1.34979i
$7$	0.180508	+	1.71742i	0.0682256	+	0.649123i	0.974184	+	0.225756i	$0.0724853\pi$
$7$	0.180508	+	1.71742i	0.0682256	+	0.649123i	−0.905958	+	0.423367i	$0.860848\pi$
$8$	7.04481	+	5.11835i	2.49072	+	1.80961i
$9$	0.103062	−	0.980572i	0.0343541	−	0.326857i
$10$	−1.09513	+	1.21627i	−0.346311	+	0.384617i
$11$	−1.22177	−	0.543967i	−0.368377	−	0.164012i	0.214195	−	0.976791i	$-0.431287\pi$
$11$	−1.22177	−	0.543967i	−0.368377	−	0.164012i	−0.582572	+	0.812779i	$0.697954\pi$
$12$	−7.26966	−	1.54521i	−2.09857	−	0.446065i
$13$	−3.59045	+	0.763174i	−0.995812	+	0.211666i	−0.676866	−	0.736106i	$-0.736662\pi$
$13$	−3.59045	+	0.763174i	−0.995812	+	0.211666i	−0.318946	+	0.947773i	$0.603329\pi$
$14$	4.24394	−	1.88952i	1.13424	−	0.504997i
$15$	0.266804	−	0.821139i	0.0688885	−	0.212017i
$16$	4.00227	−	12.3177i	1.00057	−	3.07943i
$17$	−2.52396	+	1.12374i	−0.612150	+	0.272547i	−0.689304	−	0.724472i	$-0.742084\pi$
$17$	−2.52396	+	1.12374i	−0.612150	+	0.272547i	0.0771534	+	0.997019i	$0.475417\pi$
$18$	−2.59446	+	0.551469i	−0.611520	+	0.129983i
$19$	2.51157	+	0.533850i	0.576193	+	0.122474i	0.486786	−	0.873522i	$-0.338169\pi$
$19$	2.51157	+	0.533850i	0.576193	+	0.122474i	0.0894075	+	0.995995i	$0.471503\pi$
$20$	2.91062	+	1.29589i	0.650834	+	0.289770i
$21$	−1.63986	+	1.82124i	−0.357846	+	0.397428i
$22$	−0.376072	+	3.57808i	−0.0801788	+	0.762850i
$23$	0.436271	+	0.316969i	0.0909688	+	0.0660927i	0.632340	−	0.774691i	$-0.282095\pi$
$23$	0.436271	+	0.316969i	0.0909688	+	0.0660927i	−0.541371	+	0.840784i	$0.682095\pi$
$24$	1.29175	+	12.2902i	0.263678	+	2.50872i
$25$	2.31493	−	4.00958i	0.462987	−	0.801917i
$26$	4.93733	+	8.55171i	0.968290	+	1.67713i
$27$	4.57641	−	3.32495i	0.880730	−	0.639888i
$28$	−6.05132	−	6.72067i	−1.14359	−	1.27009i
$29$	−2.51258	−	7.73291i	−0.466574	−	1.43597i	−0.856993	−	0.515329i	$-0.827670\pi$
$29$	−2.51258	−	7.73291i	−0.466574	−	1.43597i	0.390419	−	0.920637i	$-0.372330\pi$
$30$	−2.32267			−0.424060
$31$	4.75081	+	2.90341i	0.853271	+	0.521468i
$31$	4.75081	+	2.90341i	0.853271	+	0.521468i
$32$	−17.4262			−3.08054
$33$	−0.586508	−	1.80509i	−0.102098	−	0.314225i
$34$	4.97326	+	5.52336i	0.852906	+	0.947248i
$35$	0.849957	−	0.617530i	0.143669	−	0.104382i
$36$	2.58174	+	4.47170i	0.430290	+	0.745284i
$37$	−3.87249	+	6.70735i	−0.636633	+	1.10268i	0.349533	+	0.936924i	$0.386340\pi$
$37$	−3.87249	+	6.70735i	−0.636633	+	1.10268i	−0.986167	+	0.165757i	$0.946993\pi$
$38$	−0.722025	−	6.86961i	−0.117128	−	1.11440i
$39$	−4.21439	−	3.06194i	−0.674843	−	0.490302i
$40$	0.553763	−	5.26870i	0.0875576	−	0.833055i
$41$	−0.0696243	+	0.0773256i	−0.0108735	+	0.0120762i	−0.748557	−	0.663070i	$-0.769253\pi$
$41$	−0.0696243	+	0.0773256i	−0.0108735	+	0.0120762i	0.737684	+	0.675147i	$0.235920\pi$
$42$	6.02285	+	2.68155i	0.929346	+	0.413772i
$43$	2.93904	+	0.624713i	0.448200	+	0.0952678i	0.426481	−	0.904496i	$-0.359753\pi$
$43$	2.93904	+	0.624713i	0.448200	+	0.0952678i	0.0217184	+	0.999764i	$0.493086\pi$
$44$	6.85079	−	1.45618i	1.03280	−	0.219527i
$45$	−0.547990	+	0.243981i	−0.0816895	+	0.0363705i
$46$	0.448289	−	1.37969i	0.0660967	−	0.203425i
$47$	−2.07813	+	6.39584i	−0.303127	+	0.932929i	0.677243	+	0.735760i	$0.263175\pi$
$47$	−2.07813	+	6.39584i	−0.303127	+	0.932929i	−0.980370	+	0.197169i	$0.936825\pi$
$48$	16.7914	−	7.47602i	2.42363	−	1.07907i
$49$	3.93009	−	0.835366i	0.561441	−	0.119338i
$50$	−12.1829	−	2.58955i	−1.72292	−	0.366218i
$51$	−3.58192	−	1.59477i	−0.501568	−	0.223313i
$52$	12.8627	−	14.2855i	1.78374	−	1.98104i
$53$	−0.292549	+	2.78341i	−0.0401846	+	0.382331i	0.955884	+	0.293745i	$0.0949016\pi$
$53$	−0.292549	+	2.78341i	−0.0401846	+	0.382331i	−0.996068	+	0.0885864i	$0.971765\pi$
$54$	−12.3112	−	8.94464i	−1.67535	−	1.21721i
$55$	0.0850494	+	0.809191i	0.0114681	+	0.109111i
$56$	−7.51871	+	13.0228i	−1.00473	+	1.74024i
$57$	1.82198	+	3.15576i	0.241327	+	0.417990i
$58$	−17.6959	+	12.8568i	−2.32358	+	1.68818i
$59$	0.311970	+	0.346478i	0.0406151	+	0.0451076i	0.763110	−	0.646269i	$-0.223671\pi$
$59$	0.311970	+	0.346478i	0.0406151	+	0.0451076i	−0.722495	+	0.691376i	$0.757005\pi$
$60$	1.39724	+	4.30025i	0.180382	+	0.555160i
$61$	−5.11468			−0.654867			−0.327434	−	0.944874i	$-0.606184\pi$
$61$	−5.11468			−0.654867			−0.327434	+	0.944874i	$0.606184\pi$
$62$	3.47898	−	14.5685i	0.441831	−	1.85020i
$63$	1.70266			0.214514
$64$	6.48190	+	19.9492i	0.810238	+	2.49365i
$65$	1.49428	+	1.65957i	0.185343	+	0.205844i
$66$	−4.13073	+	3.00115i	−0.508457	+	0.369416i
$67$	−4.14923	−	7.18668i	−0.506910	−	0.877993i	−0.999968	−	0.00799701i	$-0.997454\pi$
$67$	−4.14923	−	7.18668i	−0.506910	−	0.877993i	0.493058	−	0.869996i	$-0.335879\pi$
$68$	7.23436	−	12.5303i	0.877294	−	1.51952i
$69$	0.0799956	+	0.761107i	0.00963034	+	0.0916265i
$70$	−2.28652	−	1.66125i	−0.273291	−	0.198558i
$71$	−0.497420	+	4.73264i	−0.0590329	+	0.561661i	0.924532	+	0.381105i	$0.124456\pi$
$71$	−0.497420	+	4.73264i	−0.0590329	+	0.561661i	−0.983565	+	0.180556i	$0.942210\pi$
$72$	5.74497	−	6.38043i	0.677051	−	0.751941i
$73$	6.85725	+	3.05304i	0.802580	+	0.357332i	0.766685	−	0.642024i	$-0.221905\pi$
$73$	6.85725	+	3.05304i	0.802580	+	0.357332i	0.0358953	+	0.999356i	$0.488572\pi$
$74$	20.3799	+	4.33188i	2.36911	+	0.503571i
$75$	6.42696	−	1.36609i	0.742122	−	0.157743i
$76$	−12.2842	+	5.46929i	−1.40910	+	0.627371i
$77$	0.713679	−	2.19648i	0.0813313	−	0.250312i
$78$	−4.33049	+	13.3279i	−0.490332	+	1.50909i
$79$	−8.86044	+	3.94492i	−0.996877	+	0.443838i	−0.839300	−	0.543668i	$-0.817035\pi$
$79$	−8.86044	+	3.94492i	−0.996877	+	0.443838i	−0.157577	+	0.987507i	$0.550368\pi$
$80$	−7.70738	+	1.63825i	−0.861711	+	0.183162i
$81$	4.95915	+	1.05410i	0.551017	+	0.117122i
$82$	0.255716	+	0.113852i	0.0282391	+	0.0125728i
$83$	−11.1642	+	12.3991i	−1.22543	+	1.36097i	−0.314047	+	0.949407i	$0.601685\pi$
$83$	−11.1642	+	12.3991i	−1.22543	+	1.36097i	−0.911380	+	0.411567i	$0.864982\pi$
$84$	1.34155	−	12.7640i	0.146375	−	1.39266i
$85$	1.35984	+	0.987981i	0.147495	+	0.107162i
$86$	−0.844916	−	8.03884i	−0.0911096	−	0.866850i
$87$	5.76952	−	9.99310i	0.618557	−	1.07137i
$88$	−5.82292	−	10.0856i	−0.620725	−	1.07513i
$89$	12.3911	−	9.00268i	1.31346	−	0.954282i	0.313468	−	0.949599i	$-0.398509\pi$
$89$	12.3911	−	9.00268i	1.31346	−	0.954282i	0.999989	−	0.00468333i	$-0.00149075\pi$
$90$	1.07977	+	1.19920i	0.113818	+	0.126407i
$91$	−1.95880	−	6.02855i	−0.205338	−	0.631964i
$92$	−2.82407			−0.294430
$93$	1.44933	+	7.76751i	0.150289	+	0.805454i
$94$	18.0912			1.86597
$95$	−0.482726	−	1.48568i	−0.0495266	−	0.152427i
$96$	−16.5480	−	18.3784i	−1.68892	−	1.87574i
$97$	1.03488	−	0.751881i	0.105076	−	0.0763420i	−0.534007	−	0.845480i	$-0.679314\pi$
$97$	1.03488	−	0.751881i	0.105076	−	0.0763420i	0.639082	+	0.769138i	$0.279314\pi$
$98$	−5.40437	−	9.36065i	−0.545924	−	0.945568i
$99$	−0.659316	+	1.14197i	−0.0662638	+	0.114772i
$100$	2.53443	+	24.1135i	0.253443	+	2.41135i
$101$	−6.56941	−	4.77296i	−0.653681	−	0.474927i	0.210842	−	0.977520i	$-0.432379\pi$
$101$	−6.56941	−	4.77296i	−0.653681	−	0.474927i	−0.864523	+	0.502593i	$0.832379\pi$
$102$	−1.10255	+	10.4900i	−0.109168	+	1.03867i
$103$	10.1390	−	11.2605i	0.999026	−	1.10953i	0.00504416	−	0.999987i	$-0.498394\pi$
$103$	10.1390	−	11.2605i	0.999026	−	1.10953i	0.993982	−	0.109544i	$-0.0349389\pi$
$104$	−29.2002	−	13.0008i	−2.86332	−	1.27483i
$105$	1.45840	+	0.309992i	0.142325	+	0.0302522i
$106$	7.36453	−	1.56538i	0.715307	−	0.152043i
$107$	−11.3057	+	5.03362i	−1.09296	+	0.486618i	−0.872419	−	0.488759i	$-0.837450\pi$
$107$	−11.3057	+	5.03362i	−1.09296	+	0.486618i	−0.220543	+	0.975377i	$0.570783\pi$
$108$	−9.15433	+	28.1741i	−0.880876	+	2.71106i
$109$	2.22788	−	6.85672i	0.213392	−	0.656755i	−0.785871	−	0.618390i	$-0.787785\pi$
$109$	2.22788	−	6.85672i	0.213392	−	0.656755i	0.999264	−	0.0383645i	$-0.0122148\pi$
$110$	1.99960	−	0.890281i	0.190655	−	0.0848850i
$111$	−10.7512	+	2.28524i	−1.02046	+	0.216905i
$112$	21.8772	+	4.65013i	2.06720	+	0.439396i
$113$	15.2304	+	6.78103i	1.43276	+	0.637906i	0.968776	−	0.247938i	$-0.0797528\pi$
$113$	15.2304	+	6.78103i	1.43276	+	0.637906i	0.463984	+	0.885844i	$0.346420\pi$
$114$	6.55936	−	7.28491i	0.614340	−	0.682294i
$115$	0.0342934	−	0.326280i	0.00319788	−	0.0304258i
$116$	34.4486	+	25.0284i	3.19847	+	2.32383i
$117$	0.378307	+	3.59935i	0.0349745	+	0.332760i
$118$	0.627119	−	1.08620i	0.0577310	−	0.0999930i
$119$	−2.38553	−	4.13185i	−0.218681	−	0.378767i
$120$	6.08246	−	4.41917i	0.555250	−	0.403413i
$121$	−6.16362	−	6.84539i	−0.560329	−	0.622308i
$122$	4.25185	+	13.0859i	0.384944	+	1.18474i
$123$	−0.147667			−0.0133147
$124$	−29.0654	+	2.32284i	−2.61015	+	0.208597i
$125$	−5.85866			−0.524014
$126$	−1.41542	−	4.35623i	−0.126096	−	0.388084i
$127$	−8.63810	−	9.59358i	−0.766507	−	0.851293i	0.225918	−	0.974146i	$-0.427462\pi$
$127$	−8.63810	−	9.59358i	−0.766507	−	0.851293i	−0.992425	+	0.122854i	$0.960795\pi$
$128$	17.4553	−	12.6820i	1.54285	−	1.12095i
$129$	2.13208	+	3.69288i	0.187720	+	0.325140i
$130$	3.00379	−	5.20272i	0.263450	−	0.456309i
$131$	0.254818	+	2.42443i	0.0222635	+	0.211823i	0.999998	+	0.00197767i	$0.000629511\pi$
$131$	0.254818	+	2.42443i	0.0222635	+	0.211823i	−0.977735	+	0.209846i	$0.932704\pi$
$132$	8.04130	+	5.84235i	0.699906	+	0.508511i
$133$	−0.463486	+	4.40978i	−0.0401894	+	0.382376i
$134$	−14.9378	+	16.5901i	−1.29043	+	1.43317i
$135$	−3.14394	−	1.39977i	−0.270588	−	0.120473i
$136$	−23.5325	−	5.00199i	−2.01790	−	0.428917i
$137$	−7.96586	+	1.69320i	−0.680570	+	0.144660i	−0.535210	−	0.844719i	$-0.679767\pi$
$137$	−7.96586	+	1.69320i	−0.680570	+	0.144660i	−0.145360	+	0.989379i	$0.546434\pi$
$138$	1.88078	−	0.837379i	0.160103	−	0.0712824i
$139$	−0.418212	+	1.28712i	−0.0354723	+	0.109172i	−0.967225	−	0.253921i	$-0.918280\pi$
$139$	−0.418212	+	1.28712i	−0.0354723	+	0.109172i	0.931753	+	0.363094i	$0.118280\pi$
$140$	−1.70020	+	5.23267i	−0.143693	+	0.442241i
$141$	−8.71874	+	3.88183i	−0.734251	+	0.326909i
$142$	12.5219	−	2.66162i	1.05082	−	0.223358i
$143$	4.80184	+	1.02066i	0.401550	+	0.0853522i
$144$	−11.6659	−	5.19401i	−0.972161	−	0.432834i
$145$	−3.30998	+	3.67611i	−0.274879	+	0.305284i
$146$	2.11072	−	20.0822i	0.174685	−	1.66201i
$147$	4.61305	+	3.35158i	0.380478	+	0.276433i
$148$	−4.23967	−	40.3378i	−0.348499	−	3.31574i
$149$	4.50192	−	7.79756i	0.368812	−	0.638801i	−0.620568	−	0.784153i	$-0.713098\pi$
$149$	4.50192	−	7.79756i	0.368812	−	0.638801i	0.989380	+	0.145351i	$0.0464313\pi$
$150$	−8.83789	−	15.3077i	−0.721611	−	1.24987i
$151$	2.59566	−	1.88585i	0.211232	−	0.153469i	−0.477139	−	0.878828i	$-0.658326\pi$
$151$	2.59566	−	1.88585i	0.211232	−	0.153469i	0.688371	+	0.725359i	$0.258326\pi$
$152$	14.9611	+	16.6160i	1.21350	+	1.34773i
$153$	0.841782	+	2.59074i	0.0680541	+	0.209449i
$154$	−6.21295			−0.500654
$155$	0.0845781	−	3.38628i	0.00679348	−	0.271993i
$156$	27.2807			2.18420
$157$	−1.02803	−	3.16395i	−0.0820456	−	0.252510i	0.901616	−	0.432537i	$-0.142382\pi$
$157$	−1.02803	−	3.16395i	−0.0820456	−	0.252510i	−0.983662	+	0.180027i	$0.942382\pi$
$158$	17.4588	+	19.3899i	1.38894	+	1.54258i
$159$	−3.21332	+	2.33461i	−0.254833	+	0.185147i
$160$	5.30090	+	9.18143i	0.419073	+	0.725856i
$161$	−0.465619	+	0.806476i	−0.0366959	+	0.0635592i
$162$	−1.42566	−	13.5642i	−0.112010	−	1.06570i
$163$	−1.40797	−	1.02295i	−0.110281	−	0.0801236i	0.531278	−	0.847198i	$-0.321712\pi$
$163$	−1.40797	−	1.02295i	−0.110281	−	0.0801236i	−0.641559	+	0.767074i	$0.721712\pi$
$164$	0.0569589	−	0.541928i	0.00444774	−	0.0423175i
$165$	−0.772645	+	0.858109i	−0.0601503	+	0.0668037i
$166$	41.0037	+	18.2560i	3.18250	+	1.41694i
$167$	13.7102	+	2.91419i	1.06093	+	0.225507i	0.705145	−	0.709063i	$-0.250882\pi$
$167$	13.7102	+	2.91419i	1.06093	+	0.225507i	0.355780	+	0.934570i	$0.384215\pi$
$168$	−20.8742	+	4.43696i	−1.61048	+	0.342319i
$169$	0.432821	−	0.192704i	0.0332939	−	0.0148234i
$170$	1.39730	−	4.30045i	0.107168	−	0.329829i
$171$	0.782326	−	2.40775i	0.0598260	−	0.184125i
$172$	−14.3750	+	6.40018i	−1.09609	+	0.488009i
$173$	0.0117191	−	0.00249097i	0.000890985	−	0.000189385i	−0.207466	−	0.978242i	$-0.566522\pi$
$173$	0.0117191	−	0.00249097i	0.000890985	−	0.000189385i	0.208357	+	0.978053i	$0.433188\pi$
$174$	−30.3635	−	6.45395i	−2.30185	−	0.489273i
$175$	7.30400	+	3.25195i	0.552131	+	0.245824i
$176$	−11.5903	+	12.8723i	−0.873651	+	0.970288i
$177$	−0.0691624	+	0.658036i	−0.00519856	+	0.0494610i
$178$	−33.3341	−	24.2186i	−2.49849	−	1.81526i
$179$	1.04299	+	9.92334i	0.0779564	+	0.741706i	0.961769	+	0.273864i	$0.0883017\pi$
$179$	1.04299	+	9.92334i	0.0779564	+	0.741706i	−0.883812	+	0.467842i	$0.845032\pi$
$180$	1.57069	−	2.72051i	0.117072	−	0.202775i
$181$	9.30158	+	16.1108i	0.691381	+	1.19751i	0.971385	+	0.237509i	$0.0763308\pi$
$181$	9.30158	+	16.1108i	0.691381	+	1.19751i	−0.280004	+	0.959999i	$0.590336\pi$
$182$	−13.7956	+	10.0231i	−1.02260	+	0.742963i
$183$	−4.85693	−	5.39417i	−0.359035	−	0.398748i
$184$	1.45108	+	4.46598i	0.106975	+	0.329236i
$185$	4.71192			0.346427
$186$	18.6683	−	10.1653i	1.36882	−	0.745354i
$187$	3.69497			0.270203
$188$	−10.8831	−	33.4946i	−0.793728	−	2.44284i
$189$	6.53642	+	7.25943i	0.475454	+	0.528046i
$190$	−3.39980	+	2.47010i	−0.246647	+	0.179200i
$191$	−0.599059	−	1.03760i	−0.0433464	−	0.0750782i	0.843538	−	0.537069i	$-0.180469\pi$
$191$	−0.599059	−	1.03760i	−0.0433464	−	0.0750782i	−0.886885	+	0.461991i	$0.847135\pi$
$192$	−14.8841	+	25.7800i	−1.07417	+	1.86051i
$193$	−1.33029	−	12.6568i	−0.0957562	−	0.911059i	−0.931941	−	0.362611i	$-0.881885\pi$
$193$	−1.33029	−	12.6568i	−0.0957562	−	0.911059i	0.836184	−	0.548448i	$-0.184781\pi$
$194$	−2.78398	−	2.02268i	−0.199878	−	0.145220i
$195$	−0.331276	+	3.15188i	−0.0237231	+	0.225711i
$196$	−14.0795	+	15.6368i	−1.00568	+	1.11692i
$197$	−2.71195	−	1.20744i	−0.193218	−	0.0860263i	0.307847	−	0.951436i	$-0.400392\pi$
$197$	−2.71195	−	1.20744i	−0.193218	−	0.0860263i	−0.501065	+	0.865410i	$0.667058\pi$
$198$	3.46981	+	0.737531i	0.246589	+	0.0524140i
$199$	12.8960	−	2.74112i	0.914170	−	0.194313i	0.273270	−	0.961937i	$-0.411895\pi$
$199$	12.8960	−	2.74112i	0.914170	−	0.194313i	0.640900	+	0.767625i	$0.278561\pi$
$200$	36.8307	−	16.3981i	2.60433	−	1.15952i
$201$	3.63926	−	11.2005i	0.256694	−	0.790021i
$202$	−6.75039	+	20.7755i	−0.474955	+	1.46176i
$203$	12.8271	−	5.71100i	0.900287	−	0.400834i
$204$	20.0848	−	4.26915i	1.40622	−	0.298900i
$205$	0.0619201	+	0.0131615i	0.00432469	+	0.000919241i
$206$	−37.2385	−	16.5796i	−2.59453	−	1.15516i
$207$	0.355774	−	0.395127i	0.0247280	−	0.0274633i
$208$	−4.96940	+	47.2807i	−0.344566	+	3.27832i
$209$	−2.77816	−	2.01845i	−0.192169	−	0.139619i
$210$	−0.419261	−	3.98900i	−0.0289317	−	0.275267i
$211$	−9.16614	+	15.8762i	−0.631023	+	1.09296i	0.356320	+	0.934364i	$0.384031\pi$
$211$	−9.16614	+	15.8762i	−0.631023	+	1.09296i	−0.987343	+	0.158600i	$0.949302\pi$
$212$	−7.32843	−	12.6932i	−0.503318	−	0.871773i
$213$	−5.46361	+	3.96954i	−0.374360	+	0.271989i
$214$	22.2769	+	24.7410i	1.52282	+	1.69126i
$215$	−0.564887	−	1.73854i	−0.0385250	−	0.118568i
$216$	49.2582			3.35160
$217$	−4.12881	+	8.68322i	−0.280282	+	0.589456i
$218$	−19.3949			−1.31359
$219$	3.29181	+	10.1311i	0.222440	+	0.684599i
$220$	−2.85118	−	3.16656i	−0.192227	−	0.213489i
$221$	8.20455	−	5.96096i	0.551898	−	0.400977i
$222$	14.7843	+	25.6071i	0.992256	+	1.71864i
$223$	−4.69801	+	8.13718i	−0.314602	+	0.544906i	−0.979353	−	0.202159i	$-0.935204\pi$
$223$	−4.69801	+	8.13718i	−0.314602	+	0.544906i	0.664751	+	0.747065i	$0.268538\pi$
$224$	−3.14557	−	29.9281i	−0.210172	−	1.99965i
$225$	−3.69310	−	2.68320i	−0.246207	−	0.178880i
$226$	4.68807	−	44.6040i	0.311846	−	2.96702i
$227$	5.66046	−	6.28658i	0.375698	−	0.417255i	−0.525410	−	0.850849i	$-0.676088\pi$
$227$	5.66046	−	6.28658i	0.375698	−	0.417255i	0.901108	+	0.433594i	$0.142755\pi$
$228$	−17.4333	−	7.76182i	−1.15455	−	0.514039i
$229$	−22.3443	−	4.74942i	−1.47655	−	0.313850i	−0.601887	−	0.798582i	$-0.705584\pi$
$229$	−22.3443	−	4.74942i	−1.47655	−	0.313850i	−0.874663	+	0.484731i	$0.838917\pi$
$230$	−0.863293	+	0.183499i	−0.0569238	+	0.0120995i
$231$	2.99422	−	1.33311i	0.197005	−	0.0877123i
$232$	21.8792	−	67.3372i	1.43644	−	4.42090i
$233$	5.02260	−	15.4580i	0.329042	−	1.01269i	−0.640542	−	0.767923i	$-0.721290\pi$
$233$	5.02260	−	15.4580i	0.329042	−	1.01269i	0.969583	−	0.244762i	$-0.0787099\pi$
$234$	8.89441	−	3.96005i	0.581446	−	0.258876i
$235$	4.00196	−	0.850643i	0.261059	−	0.0554899i
$236$	−2.38828	−	0.507644i	−0.155463	−	0.0330448i
$237$	−12.5744	−	5.59849i	−0.816796	−	0.363661i
$238$	−8.58821	+	9.53817i	−0.556691	+	0.618268i
$239$	−1.91005	+	18.1729i	−0.123551	+	1.17551i	0.740484	+	0.672074i	$0.234596\pi$
$239$	−1.91005	+	18.1729i	−0.123551	+	1.17551i	−0.864035	+	0.503433i	$0.832070\pi$
$240$	−9.04675	−	6.57285i	−0.583965	−	0.424275i
$241$	1.89944	+	18.0720i	0.122354	+	1.16412i	0.867576	+	0.497304i	$0.165677\pi$
$241$	1.89944	+	18.0720i	0.122354	+	1.16412i	−0.745222	+	0.666816i	$0.767657\pi$
$242$	−12.3900	+	21.4602i	−0.796461	+	1.37951i
$243$	−4.88759	−	8.46555i	−0.313539	−	0.543065i
$244$	21.6697	−	15.7440i	1.38726	−	1.00790i
$245$	−1.63564	−	1.81656i	−0.104497	−	0.116056i
$246$	0.122756	+	0.377804i	0.00782663	+	0.0240879i
$247$	−9.42508			−0.599704
$248$	18.6079	+	44.7703i	1.18160	+	2.84292i
$249$	−23.6782			−1.50054
$250$	4.87032	+	14.9893i	0.308026	+	0.948007i
$251$	−15.3433	−	17.0405i	−0.968461	−	1.07558i	−0.997108	−	0.0759953i	$-0.975787\pi$
$251$	−15.3433	−	17.0405i	−0.968461	−	1.07558i	0.0286471	−	0.999590i	$-0.490880\pi$
$252$	−7.21376	+	5.24111i	−0.454424	+	0.330159i
$253$	−0.360602	−	0.624580i	−0.0226708	−	0.0392670i
$254$	−17.3642	+	30.0757i	−1.08953	+	1.88712i
$255$	0.249343	+	2.37234i	0.0156145	+	0.148562i
$256$	−13.0179	−	9.45807i	−0.813620	−	0.591129i
$257$	−0.0111002	+	0.105611i	−0.000692411	+	0.00658785i	−0.994863	−	0.101234i	$-0.967721\pi$
$257$	−0.0111002	+	0.105611i	−0.000692411	+	0.00658785i	0.994170	+	0.107822i	$0.0343876\pi$
$258$	7.67578	−	8.52482i	0.477873	−	0.530732i
$259$	−12.2183	−	5.43996i	−0.759211	−	0.338022i
$260$	−11.4394	−	2.43152i	−0.709443	−	0.150797i
$261$	−7.84163	+	1.66679i	−0.485385	+	0.103172i
$262$	5.99105	−	2.66739i	0.370128	−	0.164792i
$263$	−2.25499	+	6.94015i	−0.139049	+	0.427948i	−0.996198	−	0.0871204i	$-0.972234\pi$
$263$	−2.25499	+	6.94015i	−0.139049	+	0.427948i	0.857149	+	0.515068i	$0.172234\pi$
$264$	5.10723	−	15.7184i	0.314328	−	0.967403i
$265$	1.55550	−	0.692555i	0.0955539	−	0.0425433i
$266$	11.6677	−	2.48004i	0.715391	−	0.152061i
$267$	21.2613	+	4.51923i	1.30117	+	0.276573i
$268$	39.7014	+	17.6762i	2.42515	+	1.07974i
$269$	10.8529	−	12.0533i	0.661711	−	0.734905i	−0.315088	−	0.949063i	$-0.602034\pi$
$269$	10.8529	−	12.0533i	0.661711	−	0.734905i	0.976799	+	0.214158i	$0.0687007\pi$
$270$	−0.967735	+	9.20739i	−0.0588945	+	0.560344i
$271$	4.16291	+	3.02453i	0.252879	+	0.183727i	0.707002	−	0.707212i	$-0.250047\pi$
$271$	4.16291	+	3.02453i	0.252879	+	0.183727i	−0.454123	+	0.890939i	$0.650047\pi$
$272$	3.74034	+	35.5870i	0.226792	+	2.15778i
$273$	4.49790	−	7.79058i	0.272225	−	0.471508i
$274$	10.9541	+	18.9730i	0.661760	+	1.14620i
$275$	−5.00939	+	3.63954i	−0.302078	+	0.219472i
$276$	−2.68176	−	2.97839i	−0.161423	−	0.179278i
$277$	−5.22944	−	16.0946i	−0.314207	−	0.967029i	−0.976080	−	0.217413i	$-0.930238\pi$
$277$	−5.22944	−	16.0946i	−0.314207	−	0.967029i	0.661873	−	0.749616i	$-0.269762\pi$
$278$	3.64076			0.218358
$279$	3.33663	−	4.35928i	0.199759	−	0.260983i
$280$	9.14853			0.546729
$281$	0.589193	+	1.81335i	0.0351483	+	0.108175i	0.967091	−	0.254429i	$-0.0818876\pi$
$281$	0.589193	+	1.81335i	0.0351483	+	0.108175i	−0.931943	+	0.362605i	$0.881888\pi$
$282$	17.1796	+	19.0798i	1.02303	+	1.13619i
$283$	12.3859	−	8.99888i	0.736265	−	0.534928i	−0.155274	−	0.987871i	$-0.549626\pi$
$283$	12.3859	−	8.99888i	0.736265	−	0.534928i	0.891539	+	0.452944i	$0.149626\pi$
$284$	−12.4605	−	21.5823i	−0.739396	−	1.28067i
$285$	1.10846	−	1.91991i	0.0656596	−	0.113726i
$286$	−1.38043	−	13.1339i	−0.0816268	−	0.776627i
$287$	−0.145368	−	0.105616i	−0.00858081	−	0.00623433i
$288$	−1.79598	+	17.0876i	−0.105829	+	1.00690i
$289$	−6.26763	+	6.96091i	−0.368684	+	0.409465i
$290$	12.1569	+	5.41259i	0.713876	+	0.317838i
$291$	1.77569	+	0.377435i	0.104093	+	0.0221256i
$292$	−38.4504	+	8.17289i	−2.25014	+	0.478282i
$293$	24.4772	−	10.8980i	1.42998	−	0.636666i	0.461810	−	0.886979i	$-0.347200\pi$
$293$	24.4772	−	10.8980i	1.42998	−	0.636666i	0.968165	+	0.250313i	$0.0805334\pi$
$294$	4.74013	−	14.5886i	0.276450	−	0.850826i
$295$	0.0876522	−	0.269766i	0.00510331	−	0.0157064i
$296$	−61.6115	+	27.4312i	−3.58110	+	1.59441i
$297$	−7.39998	+	1.57291i	−0.429390	+	0.0912697i
$298$	−23.6924	−	5.03599i	−1.37247	−	0.291727i
$299$	−1.80831	−	0.805113i	−0.104577	−	0.0465609i
$300$	−23.0245	+	25.5713i	−1.32932	+	1.47636i
$301$	−0.542373	+	5.16033i	−0.0312619	+	0.297437i
$302$	−6.98272	−	5.07324i	−0.401810	−	0.291932i
$303$	−1.20458	−	11.4608i	−0.0692014	−	0.658407i
$304$	16.6278	−	28.8002i	0.953670	−	1.65181i
$305$	1.55584	+	2.69480i	0.0890873	+	0.154304i
$306$	5.92860	−	4.30738i	0.338916	−	0.246237i
$307$	5.98956	+	6.65208i	0.341842	+	0.379654i	0.889413	−	0.457105i	$-0.151114\pi$
$307$	5.98956	+	6.65208i	0.341842	+	0.379654i	−0.547570	+	0.836760i	$0.684447\pi$
$308$	3.73749	+	11.5028i	0.212963	+	0.655434i
$309$	21.5039			1.22331
$310$	−8.73408	+	2.59864i	−0.496062	+	0.147593i
$311$	20.6556			1.17127			0.585637	−	0.810574i	$-0.300844\pi$
$311$	20.6556			1.17127			0.585637	+	0.810574i	$0.300844\pi$
$312$	−14.0175	−	43.1415i	−0.793586	−	2.44241i
$313$	0.301993	+	0.335397i	0.0170696	+	0.0189577i	0.751619	−	0.659597i	$-0.229273\pi$
$313$	0.301993	+	0.335397i	0.0170696	+	0.0189577i	−0.734550	+	0.678555i	$0.762606\pi$
$314$	−7.24032	+	5.26040i	−0.408595	+	0.296862i
$315$	−0.517934	−	0.897088i	−0.0291823	−	0.0505452i
$316$	25.3964	−	43.9879i	1.42866	−	2.47451i
$317$	0.583357	+	5.55027i	0.0327646	+	0.311734i	0.998614	+	0.0526304i	$0.0167605\pi$
$317$	0.583357	+	5.55027i	0.0327646	+	0.311734i	−0.965849	+	0.259104i	$0.916573\pi$
$318$	8.64432	+	6.28047i	0.484750	+	0.352191i
$319$	−1.13666	+	10.8146i	−0.0636407	+	0.605501i
$320$	8.53903	−	9.48355i	0.477346	−	0.530147i
$321$	−16.0446	−	7.14353i	−0.895524	−	0.398713i
$322$	2.45043	+	0.520855i	0.136557	+	0.0290261i
$323$	−6.93901	+	1.47493i	−0.386097	+	0.0820674i
$324$	−24.2555	+	10.7992i	−1.34753	+	0.599958i
$325$	−5.25165	+	16.1629i	−0.291309	+	0.896557i
$326$	−1.44676	+	4.45266i	−0.0801284	+	0.246610i
$327$	9.34701	−	4.16156i	0.516891	−	0.230135i
$328$	−0.886270	+	0.188382i	−0.0489360	+	0.0104017i
$329$	−11.3595	−	2.41453i	−0.626267	−	0.133117i
$330$	2.83777	+	1.26346i	0.156214	+	0.0695509i
$331$	16.1966	−	17.9882i	0.890246	−	0.988719i	−0.109740	−	0.993960i	$-0.535002\pi$
$331$	16.1966	−	17.9882i	0.890246	−	0.988719i	0.999986	+	0.00524168i	$0.00166849\pi$
$332$	9.13329	−	86.8975i	0.501255	−	4.76912i
$333$	6.17793	+	4.48853i	0.338548	+	0.245970i
$334$	−3.94140	−	37.4999i	−0.215664	−	2.05191i
$335$	−2.52433	+	4.37226i	−0.137919	+	0.238882i
$336$	15.8704	+	27.4884i	0.865804	+	1.49962i
$337$	−8.92830	+	6.48679i	−0.486355	+	0.353358i	−0.803781	−	0.594925i	$-0.797182\pi$
$337$	−8.92830	+	6.48679i	−0.486355	+	0.353358i	0.317426	+	0.948283i	$0.397182\pi$
$338$	−0.852838	−	0.947173i	−0.0463883	−	0.0515194i
$339$	7.31135	+	22.5020i	0.397098	+	1.22214i
$340$	−8.80253			−0.477384
$341$	−4.22504	−	6.13158i	−0.228799	−	0.332044i
$342$	−6.81056			−0.368273
$343$	5.87953	+	18.0953i	0.317465	+	0.977056i
$344$	17.5075	+	19.4440i	0.943941	+	1.04835i
$345$	0.376675	−	0.273670i	0.0202795	−	0.0147339i
$346$	−0.0161152	−	0.0279124i	−0.000866360	−	0.00150058i
$347$	9.28369	−	16.0798i	0.498375	−	0.863210i	−0.501624	−	0.865086i	$-0.667264\pi$
$347$	9.28369	−	16.0798i	0.498375	−	0.863210i	0.999998	+	0.00187589i	$0.000597114\pi$
$348$	6.31657	+	60.0982i	0.338604	+	3.22160i
$349$	26.0298	+	18.9118i	1.39334	+	1.01232i	0.995489	+	0.0948756i	$0.0302453\pi$
$349$	26.0298	+	18.9118i	1.39334	+	1.01232i	0.397855	+	0.917448i	$0.369755\pi$
$350$	2.24824	−	21.3906i	0.120173	−	1.14337i
$351$	−13.8939	+	15.4307i	−0.741599	+	0.823629i
$352$	21.2908	+	9.47926i	1.13480	+	0.505246i
$353$	−31.5094	−	6.69754i	−1.67708	−	0.356474i	−0.731493	−	0.681849i	$-0.761176\pi$
$353$	−31.5094	−	6.69754i	−1.67708	−	0.356474i	−0.945585	+	0.325375i	$0.894510\pi$
$354$	1.74107	−	0.370077i	0.0925370	−	0.0196693i
$355$	2.64482	−	1.17755i	0.140373	−	0.0624980i
$356$	−24.7864	+	76.2846i	−1.31367	+	4.04307i
$357$	2.09233	−	6.43952i	0.110738	−	0.340815i
$358$	24.5217	−	10.9178i	1.29601	−	0.577023i
$359$	−20.6998	+	4.39988i	−1.09249	+	0.232217i	−0.718718	−	0.695302i	$-0.755271\pi$
$359$	−20.6998	+	4.39988i	−1.09249	+	0.232217i	−0.373777	+	0.927519i	$0.621937\pi$
$360$	−5.10927	−	1.08601i	−0.269282	−	0.0572377i
$361$	−11.3344	−	5.04639i	−0.596547	−	0.265600i
$362$	33.4869	−	37.1910i	1.76003	−	1.95472i
$363$	1.36644	−	13.0009i	0.0717197	−	0.682368i
$364$	26.8560	+	19.5120i	1.40764	+	1.02271i
$365$	−0.477344	−	4.54163i	−0.0249853	−	0.237720i
$366$	−9.76334	+	16.9106i	−0.510338	+	0.883931i
$367$	−6.49822	−	11.2552i	−0.339204	−	0.587519i	0.645079	−	0.764116i	$-0.276824\pi$
$367$	−6.49822	−	11.2552i	−0.339204	−	0.587519i	−0.984283	+	0.176597i	$0.943491\pi$
$368$	5.65042	−	4.10527i	0.294549	−	0.214002i
$369$	0.0686477	+	0.0762409i	0.00357365	+	0.00396894i
$370$	−3.91704	−	12.0554i	−0.203637	−	0.626730i
$371$	−4.83309			−0.250922
$372$	−30.0504	−	28.4478i	−1.55804	−	1.47495i
$373$	−4.42592			−0.229166			−0.114583	−	0.993414i	$-0.536553\pi$
$373$	−4.42592			−0.229166			−0.114583	+	0.993414i	$0.536553\pi$
$374$	−3.07165	−	9.45355i	−0.158831	−	0.488832i
$375$	−5.56342	−	6.17880i	−0.287294	−	0.319072i
$376$	−47.3762	+	34.4208i	−2.44324	+	1.77512i
$377$	14.9228	+	25.8471i	0.768566	+	1.33119i
$378$	13.1394	−	22.7581i	0.675819	−	1.17055i
$379$	1.56330	+	14.8738i	0.0803013	+	0.764016i	0.958379	+	0.285498i	$0.0921591\pi$
$379$	1.56330	+	14.8738i	0.0803013	+	0.764016i	−0.878078	+	0.478518i	$0.841174\pi$
$380$	6.61840	+	4.80855i	0.339517	+	0.246673i
$381$	1.91503	−	18.2202i	0.0981097	−	0.933452i
$382$	−2.15669	+	2.39525i	−0.110346	+	0.122552i
$383$	−10.6431	−	4.73862i	−0.543838	−	0.242132i	0.116382	−	0.993205i	$-0.462870\pi$
$383$	−10.6431	−	4.73862i	−0.543838	−	0.242132i	−0.660220	+	0.751072i	$0.729537\pi$
$384$	29.9508	+	6.36623i	1.52842	+	0.324875i
$385$	−1.37437	+	0.292131i	−0.0700442	+	0.0148884i
$386$	−31.2765	+	13.9252i	−1.59193	+	0.708774i
$387$	0.915480	−	2.81756i	0.0465365	−	0.143225i
$388$	−2.07009	+	6.37110i	−0.105093	+	0.323443i
$389$	13.1568	−	5.85779i	0.667077	−	0.297002i	−0.0451198	−	0.998982i	$-0.514367\pi$
$389$	13.1568	−	5.85779i	0.667077	−	0.297002i	0.712197	+	0.701980i	$0.247700\pi$
$390$	8.33944	−	1.77260i	0.422284	−	0.0897592i
$391$	−1.45732	−	0.309763i	−0.0737000	−	0.0156654i
$392$	31.9624	+	14.2306i	1.61435	+	0.718753i
$393$	−2.31493	+	2.57100i	−0.116773	+	0.129690i
$394$	−0.834763	+	7.94224i	−0.0420547	+	0.400124i
$395$	4.77376	+	3.46834i	0.240194	+	0.174511i
$396$	−0.721831	−	6.86777i	−0.0362734	−	0.345118i
$397$	−7.89506	+	13.6746i	−0.396242	+	0.686311i	−0.993259	−	0.115918i	$-0.963019\pi$
$397$	−7.89506	+	13.6746i	−0.396242	+	0.686311i	0.597017	+	0.802229i	$0.296352\pi$
$398$	−17.7336	−	30.7155i	−0.888904	−	1.53963i
$399$	−5.09088	+	3.69874i	−0.254863	+	0.185169i
$400$	−40.1240	−	44.5622i	−2.00620	−	2.22811i
$401$	9.58670	+	29.5048i	0.478737	+	1.47340i	0.840851	+	0.541267i	$0.182055\pi$
$401$	9.58670	+	29.5048i	0.478737	+	1.47340i	−0.362114	+	0.932134i	$0.617945\pi$
$402$	−31.6817			−1.58014
$403$	−19.2734	−	6.79886i	−0.960075	−	0.338675i
$404$	42.5252			2.11571
$405$	−0.953153	−	2.93350i	−0.0473626	−	0.145767i
$406$	−25.2748	−	28.0705i	−1.25437	−	1.39311i
$407$	8.37986	−	6.08832i	0.415374	−	0.301787i
$408$	−17.0713	−	29.5684i	−0.845156	−	1.46385i
$409$	−3.29291	+	5.70349i	−0.162824	+	0.282019i	−0.935880	−	0.352318i	$-0.885394\pi$
$409$	−3.29291	+	5.70349i	−0.162824	+	0.282019i	0.773056	+	0.634337i	$0.218727\pi$
$410$	−0.0178008	−	0.169363i	−0.000879119	−	0.00836425i
$411$	−9.35015	−	6.79328i	−0.461209	−	0.335088i
$412$	−8.29462	+	78.9180i	−0.408647	+	3.88801i
$413$	−0.538735	+	0.598326i	−0.0265094	+	0.0294417i
$414$	−1.30669	−	0.581774i	−0.0642201	−	0.0285926i
$415$	9.92882	+	2.11043i	0.487386	+	0.103597i
$416$	62.5679	−	13.2992i	3.06764	−	0.652047i
$417$	−1.75460	+	0.781196i	−0.0859229	+	0.0382554i
$418$	−2.85469	+	8.78583i	−0.139627	+	0.429729i
$419$	−4.53389	+	13.9539i	−0.221495	+	0.681692i	0.777133	+	0.629336i	$0.216673\pi$
$419$	−4.53389	+	13.9539i	−0.221495	+	0.681692i	−0.998628	+	0.0523559i	$0.983327\pi$
$420$	−7.13312	+	3.17587i	−0.348061	+	0.154967i
$421$	26.1321	−	5.55454i	1.27360	−	0.270712i	0.478983	−	0.877824i	$-0.341006\pi$
$421$	26.1321	−	5.55454i	1.27360	−	0.270712i	0.794616	+	0.607112i	$0.207672\pi$
$422$	48.2390	+	10.2535i	2.34824	+	0.499133i
$423$	6.05740	+	2.69693i	0.294521	+	0.131129i
$424$	−16.3074	+	18.1113i	−0.791959	+	0.879560i
$425$	−1.33708	+	12.7214i	−0.0648577	+	0.617079i
$426$	14.6980	+	10.6787i	0.712118	+	0.517384i
$427$	−0.923240	−	8.78404i	−0.0446787	−	0.425090i
$428$	32.4052	−	56.1274i	1.56636	−	2.71302i
$429$	3.48342	+	6.03347i	0.168181	+	0.291299i
$430$	−3.97845	+	2.89052i	−0.191858	+	0.139393i
$431$	2.66850	+	2.96367i	0.128537	+	0.142755i	0.803978	−	0.594660i	$-0.202713\pi$
$431$	2.66850	+	2.96367i	0.128537	+	0.142755i	−0.675441	+	0.737414i	$0.736046\pi$
$432$	−22.6399	−	69.6783i	−1.08926	−	3.35240i
$433$	18.0766			0.868704			0.434352	−	0.900743i	$-0.356977\pi$
$433$	18.0766			0.868704			0.434352	+	0.900743i	$0.356977\pi$
$434$	25.6482	+	3.34513i	1.23115	+	0.160571i
$435$	−7.02016			−0.336591
$436$	11.6673	+	35.9082i	0.558762	+	1.71969i
$437$	0.926510	+	1.02899i	0.0443210	+	0.0492234i
$438$	23.1839	−	16.8441i	1.10777	−	0.804843i
$439$	−11.4543	−	19.8394i	−0.546684	−	0.946884i	−0.998499	−	0.0547723i	$-0.982557\pi$
$439$	−11.4543	−	19.8394i	−0.546684	−	0.946884i	0.451815	−	0.892112i	$-0.350777\pi$
$440$	−3.54257	+	6.13591i	−0.168885	+	0.292518i
$441$	−0.414093	−	3.93983i	−0.0197187	−	0.187611i
$442$	−22.0715	−	16.0359i	−1.04984	−	0.762750i
$443$	2.24645	−	21.3736i	0.106732	−	1.01549i	−0.801777	−	0.597624i	$-0.796112\pi$
$443$	2.24645	−	21.3736i	0.106732	−	1.01549i	0.908509	−	0.417866i	$-0.137222\pi$
$444$	38.5160	−	42.7763i	1.82789	−	2.03008i
$445$	−8.51257	−	3.79004i	−0.403535	−	0.179665i
$446$	24.7244	+	5.25533i	1.17073	+	0.248847i
$447$	12.4987	−	2.65668i	0.591169	−	0.125657i
$448$	−33.0912	+	14.7331i	−1.56341	+	0.696075i
$449$	5.80940	−	17.8795i	0.274163	−	0.843786i	−0.715277	−	0.698841i	$-0.753700\pi$
$449$	5.80940	−	17.8795i	0.274163	−	0.843786i	0.989440	−	0.144945i	$-0.0463005\pi$
$450$	−3.79484	+	11.6793i	−0.178890	+	0.550568i
$451$	0.127127	−	0.0566007i	0.00598619	−	0.00266522i
$452$	−85.4012	+	18.1526i	−4.01694	+	0.853826i
$453$	4.45376	+	0.946676i	0.209256	+	0.0444787i
$454$	−20.7897	−	9.25617i	−0.975709	−	0.434414i
$455$	−2.58045	+	2.86588i	−0.120973	+	0.134354i
$456$	−3.31680	+	31.5572i	−0.155323	+	1.47780i
$457$	−3.32182	−	2.41344i	−0.155388	−	0.112896i	0.507374	−	0.861726i	$-0.330616\pi$
$457$	−3.32182	−	2.41344i	−0.155388	−	0.112896i	−0.662763	+	0.748830i	$0.730616\pi$
$458$	6.42352	+	61.1158i	0.300152	+	2.85575i
$459$	−7.81429	+	13.5347i	−0.364740	+	0.631748i
$460$	0.859060	+	1.48794i	0.0400539	+	0.0693754i
$461$	18.5063	−	13.4456i	0.861924	−	0.626225i	−0.0664836	−	0.997788i	$-0.521178\pi$
$461$	18.5063	−	13.4456i	0.861924	−	0.626225i	0.928408	+	0.371563i	$0.121178\pi$
$462$	−5.89986	−	6.55246i	−0.274486	−	0.304848i
$463$	−5.11947	−	15.7561i	−0.237922	−	0.732249i	−0.996720	−	0.0809233i	$-0.974213\pi$
$463$	−5.11947	−	15.7561i	−0.237922	−	0.732249i	0.758798	−	0.651326i	$-0.225787\pi$
$464$	−105.308			−4.88880
$465$	3.65164	−	3.12643i	0.169341	−	0.144985i
$466$	−43.7244			−2.02549
$467$	11.7878	+	36.2792i	0.545476	+	1.67880i	0.719855	+	0.694124i	$0.244208\pi$
$467$	11.7878	+	36.2792i	0.545476	+	1.67880i	−0.174379	+	0.984679i	$0.555792\pi$
$468$	−12.6823	−	14.0851i	−0.586239	−	0.651085i
$469$	11.5936	−	8.42323i	0.535342	−	0.388949i
$470$	−5.50321	−	9.53184i	−0.253844	−	0.439671i
$471$	2.36062	−	4.08871i	0.108771	−	0.188398i
$472$	0.424374	+	4.03765i	0.0195334	+	0.185848i
$473$	−3.25101	−	2.36200i	−0.149482	−	0.108605i
$474$	−3.87052	+	36.8256i	−0.177779	+	1.69145i
$475$	7.95463	−	8.83451i	0.364984	−	0.405355i
$476$	22.8256	+	10.1626i	1.04621	+	0.465802i
$477$	2.69919	+	0.573730i	0.123587	+	0.0262693i
$478$	48.0830	−	10.2204i	2.19926	−	0.467468i
$479$	−30.7726	+	13.7008i	−1.40603	+	0.626007i	−0.962755	−	0.270377i	$-0.912852\pi$
$479$	−30.7726	+	13.7008i	−1.40603	+	0.626007i	−0.443279	+	0.896383i	$0.646185\pi$
$480$	−4.64938	+	14.3093i	−0.212214	+	0.653128i
$481$	8.78511	−	27.0378i	0.400567	−	1.23282i
$482$	44.6580	−	19.8830i	2.03412	−	0.905647i
$483$	−1.29270	+	0.274772i	−0.0588199	+	0.0125026i
$484$	47.1853	+	10.0295i	2.14479	+	0.455888i
$485$	−0.710949	−	0.316535i	−0.0322825	−	0.0143731i
$486$	−17.5960	+	19.5423i	−0.798169	+	0.886456i
$487$	2.16130	−	20.5634i	0.0979379	−	0.931817i	−0.829668	−	0.558257i	$-0.811470\pi$
$487$	2.16130	−	20.5634i	0.0979379	−	0.931817i	0.927606	−	0.373560i	$-0.121863\pi$
$488$	−36.0319	−	26.1787i	−1.63109	−	1.18506i
$489$	−0.258168	−	2.45631i	−0.0116748	−	0.111078i
$490$	−3.28793	+	5.69487i	−0.148534	+	0.257268i
$491$	−12.3664	−	21.4192i	−0.558087	−	0.966634i	−0.997656	−	0.0684258i	$-0.978202\pi$
$491$	−12.3664	−	21.4192i	−0.558087	−	0.966634i	0.439570	−	0.898209i	$-0.355131\pi$
$492$	0.625630	−	0.454547i	0.0282056	−	0.0204925i
$493$	15.0314	+	16.6941i	0.676982	+	0.751864i
$494$	7.83511	+	24.1140i	0.352518	+	1.08494i
$495$	0.802235			0.0360578
$496$	54.7775	−	46.8990i	2.45958	−	2.10583i
$497$	−8.21771			−0.368615
$498$	19.6838	+	60.5804i	0.882050	+	2.71467i
$499$	−16.4340	−	18.2518i	−0.735685	−	0.817061i	0.252937	−	0.967483i	$-0.418604\pi$
$499$	−16.4340	−	18.2518i	−0.735685	−	0.817061i	−0.988622	+	0.150422i	$0.951937\pi$
$500$	24.8218	−	18.0341i	1.11006	−	0.806509i
$501$	9.94584	+	17.2267i	0.444347	+	0.769632i
$502$	−30.8429	+	53.4215i	−1.37659	+	2.38432i
$503$	−1.54066	−	14.6584i	−0.0686946	−	0.653585i	−0.973645	−	0.228068i	$-0.926759\pi$
$503$	−1.54066	−	14.6584i	−0.0686946	−	0.653585i	0.904951	−	0.425517i	$-0.139908\pi$
$504$	11.9949	+	8.71479i	0.534295	+	0.388188i
$505$	−0.516394	+	4.91316i	−0.0229792	+	0.218633i
$506$	−1.29821	+	1.44181i	−0.0577126	+	0.0640963i
$507$	0.614244	+	0.273479i	0.0272795	+	0.0121456i
$508$	66.1285	+	14.0561i	2.93398	+	0.623637i
$509$	−15.1674	+	3.22394i	−0.672285	+	0.142899i	−0.531392	−	0.847126i	$-0.678331\pi$
$509$	−15.1674	+	3.22394i	−0.672285	+	0.142899i	−0.140893	+	0.990025i	$0.544997\pi$
$510$	5.86233	−	2.61008i	0.259588	−	0.115576i
$511$	−4.00557	+	12.3279i	−0.177196	+	0.545353i
$512$	−0.0418393	+	0.128768i	−0.00184905	+	0.00569080i
$513$	13.2690	−	5.90773i	0.585840	−	0.260833i
$514$	0.279433	−	0.0593953i	0.0123253	−	0.00261982i
$515$	−9.01709	−	1.91664i	−0.397341	−	0.0844574i
$516$	−20.4005	−	9.08291i	−0.898084	−	0.399853i
$517$	6.01812	−	6.68380i	0.264677	−	0.293953i
$518$	−3.76092	+	35.7828i	−0.165245	+	1.57220i
$519$	0.0137556	+	0.00999402i	0.000603803	+	0.000438689i
$520$	2.03268	+	19.3396i	0.0891388	+	0.848099i
$521$	−14.7073	+	25.4738i	−0.644337	+	1.11603i	0.340117	+	0.940383i	$0.389533\pi$
$521$	−14.7073	+	25.4738i	−0.644337	+	1.11603i	−0.984454	+	0.175642i	$0.943800\pi$
$522$	10.7832	+	18.6771i	0.471970	+	0.817475i
$523$	−36.4268	+	26.4656i	−1.59283	+	1.15726i	−0.693078	+	0.720863i	$0.743746\pi$
$523$	−36.4268	+	26.4656i	−1.59283	+	1.15726i	−0.899754	+	0.436397i	$0.856254\pi$
$524$	−8.54247	−	9.48737i	−0.373180	−	0.414458i
$525$	3.50627	+	10.7912i	0.153026	+	0.470966i
$526$	19.6309			0.855947
$527$	−15.2535	−	1.98942i	−0.664455	−	0.0866604i
$528$	−24.5819			−1.06979
$529$	−7.01753	−	21.5977i	−0.305110	−	0.939032i
$530$	−3.06499	−	3.40402i	−0.133135	−	0.147861i
$531$	0.371899	−	0.270201i	0.0161391	−	0.0117257i
$532$	−11.6105	−	20.1099i	−0.503378	−	0.871876i
$533$	0.190970	−	0.330769i	0.00827182	−	0.0143272i
$534$	−6.11220	−	58.1537i	−0.264501	−	2.51656i
$535$	6.09119	+	4.42551i	0.263345	+	0.191331i
$536$	7.55343	−	71.8661i	0.326258	−	3.10414i
$537$	−9.47518	+	10.5232i	−0.408884	+	0.454112i
$538$	−39.8604	−	17.7470i	−1.71850	−	0.765127i
$539$	−5.25607	−	1.11721i	−0.226395	−	0.0481217i
$540$	17.6289	−	3.74715i	0.758629	−	0.161252i
$541$	34.5126	−	15.3660i	1.48381	−	0.660635i	0.504577	−	0.863367i	$-0.331648\pi$
$541$	34.5126	−	15.3660i	1.48381	−	0.660635i	0.979234	+	0.202731i	$0.0649818\pi$
$542$	4.27759	−	13.1651i	0.183738	−	0.565488i
$543$	−8.15834	+	25.1088i	−0.350108	+	1.07752i
$544$	43.9830	−	19.5825i	1.88576	−	0.839593i
$545$	−4.29034	+	0.911941i	−0.183778	+	0.0390632i
$546$	−23.6712	−	5.03148i	−1.01304	−	0.215327i
$547$	−16.6345	−	7.40617i	−0.711241	−	0.316665i	0.0190333	−	0.999819i	$-0.493941\pi$
$547$	−16.6345	−	7.40617i	−0.711241	−	0.316665i	−0.730274	+	0.683154i	$0.760608\pi$
$548$	28.5375	−	31.6942i	1.21906	−	1.35391i
$549$	−0.527130	+	5.01531i	−0.0224974	+	0.214048i
$550$	13.4761	+	9.79092i	0.574621	+	0.417486i
$551$	−2.18229	−	20.7631i	−0.0929686	−	0.884537i
$552$	−3.33206	+	5.77130i	−0.141822	+	0.245643i
$553$	−8.37446	−	14.5050i	−0.356118	−	0.616815i
$554$	−36.8305	+	26.7590i	−1.56478	+	1.13688i
$555$	4.47447	+	4.96940i	0.189931	+	0.210939i
$556$	−2.19015	−	6.74059i	−0.0928831	−	0.285865i
$557$	−9.19760			−0.389715			−0.194857	−	0.980832i	$-0.562424\pi$
$557$	−9.19760			−0.389715			−0.194857	+	0.980832i	$0.562424\pi$
$558$	−13.9269	−	4.91285i	−0.589574	−	0.207978i
$559$	−11.0293			−0.466488
$560$	−4.20481	−	12.9411i	−0.177686	−	0.546860i
$561$	3.50877	+	3.89688i	0.148140	+	0.164527i
$562$	4.14964	−	3.01489i	0.175042	−	0.127175i
$563$	18.0809	+	31.3170i	0.762019	+	1.31986i	0.941808	+	0.336150i	$0.109125\pi$
$563$	18.0809	+	31.3170i	0.762019	+	1.31986i	−0.179790	+	0.983705i	$0.557542\pi$
$564$	24.9903	−	43.2844i	1.05228	−	1.82260i
$565$	−1.06022	−	10.0873i	−0.0446037	−	0.424375i
$566$	−33.3200	−	24.2084i	−1.40054	−	1.01755i
$567$	−0.915165	+	8.70721i	−0.0384333	+	0.365668i
$568$	−27.7276	+	30.7946i	−1.16342	+	1.29211i
$569$	37.9119	+	16.8795i	1.58935	+	0.707624i	0.995303	−	0.0968056i	$-0.0308625\pi$
$569$	37.9119	+	16.8795i	1.58935	+	0.707624i	0.594047	+	0.804430i	$0.297529\pi$
$570$	−5.83354	−	1.23996i	−0.244340	−	0.0519361i
$571$	31.6853	−	6.73491i	1.32599	−	0.281847i	0.510128	−	0.860099i	$-0.329598\pi$
$571$	31.6853	−	6.73491i	1.32599	−	0.281847i	0.815859	+	0.578251i	$0.196265\pi$
$572$	−23.4861	+	10.4567i	−0.982004	+	0.437216i
$573$	0.525430	−	1.61711i	0.0219501	−	0.0675556i
$574$	−0.149373	+	0.459722i	−0.00623470	+	0.0191884i
$575$	2.28085	−	1.01550i	0.0951182	−	0.0423494i
$576$	20.2297	−	4.29995i	0.842904	−	0.179165i
$577$	−40.0870	−	8.52075i	−1.66884	−	0.354723i	−0.725931	−	0.687768i	$-0.758591\pi$
$577$	−40.0870	−	8.52075i	−1.66884	−	0.354723i	−0.942911	+	0.333044i	$0.891924\pi$
$578$	23.0197	+	10.2490i	0.957494	+	0.426304i
$579$	12.0852	−	13.4220i	0.502245	−	0.557799i
$580$	2.70786	−	25.7636i	0.112438	−	1.06977i
$581$	−23.3096	−	16.9354i	−0.967046	−	0.702600i
$582$	−0.510476	−	4.85685i	−0.0211599	−	0.201323i
$583$	1.87151	−	3.24155i	0.0775100	−	0.134251i
$584$	32.6814	+	56.6059i	1.35237	+	2.34237i
$585$	1.78133	−	1.29421i	0.0736490	−	0.0535092i
$586$	−48.2304	−	53.5652i	−1.99238	−	2.21276i
$587$	7.88963	+	24.2818i	0.325640	+	1.00222i	0.971151	+	0.238466i	$0.0766445\pi$
$587$	7.88963	+	24.2818i	0.325640	+	1.00222i	−0.645511	+	0.763751i	$0.723356\pi$
$588$	−29.8612			−1.23146
$589$	10.3820	+	9.82833i	0.427783	+	0.404969i
$590$	−0.763058			−0.0314146
$591$	−1.30187	−	4.00673i	−0.0535516	−	0.164815i
$592$	67.1206	+	74.5449i	2.75864	+	3.06378i
$593$	−36.0269	+	26.1751i	−1.47945	+	1.07488i	−0.501716	+	0.865033i	$0.667298\pi$
$593$	−36.0269	+	26.1751i	−1.47945	+	1.07488i	−0.977734	+	0.209850i	$0.932702\pi$
$594$	10.1759	+	17.6252i	0.417523	+	0.723170i
$595$	−1.45132	+	2.51375i	−0.0594982	+	0.103054i
$596$	4.92879	+	46.8943i	0.201891	+	1.92086i
$597$	15.1370	+	10.9977i	0.619515	+	0.450104i
$598$	−0.556616	+	5.29584i	−0.0227617	+	0.216563i
$599$	12.7001	−	14.1049i	0.518911	−	0.576309i	−0.425549	−	0.904935i	$-0.639919\pi$
$599$	12.7001	−	14.1049i	0.518911	−	0.576309i	0.944460	+	0.328627i	$0.106586\pi$
$600$	52.2689	+	23.2716i	2.13387	+	0.950059i
$601$	12.5592	+	2.66955i	0.512301	+	0.108893i	0.456807	−	0.889566i	$-0.348993\pi$
$601$	12.5592	+	2.66955i	0.512301	+	0.108893i	0.0554947	+	0.998459i	$0.482326\pi$
$602$	13.6535	−	2.90215i	0.556477	−	0.118283i
$603$	−7.47469	+	3.32795i	−0.304393	+	0.135524i
$604$	−5.19217	+	15.9799i	−0.211267	+	0.650212i
$605$	−1.73175	+	5.32977i	−0.0704056	+	0.216686i
$606$	−28.3210	+	12.6093i	−1.15046	+	0.512219i
$607$	37.3059	−	7.92960i	1.51420	−	0.321853i	0.625456	−	0.780260i	$-0.284913\pi$
$607$	37.3059	−	7.92960i	1.51420	−	0.321853i	0.888742	+	0.458407i	$0.151580\pi$
$608$	−43.7670	−	9.30297i	−1.77499	−	0.377285i
$609$	18.2038	+	8.10485i	0.737654	+	0.328425i
$610$	5.60124	−	6.22081i	0.226788	−	0.251873i
$611$	2.58030	−	24.5499i	0.104388	−	0.993184i
$612$	−11.5412	−	8.38520i	−0.466527	−	0.338952i
$613$	1.93821	+	18.4408i	0.0782834	+	0.744817i	0.961305	+	0.275485i	$0.0888385\pi$
$613$	1.93821	+	18.4408i	0.0782834	+	0.744817i	−0.883022	+	0.469332i	$0.844495\pi$
$614$	12.0401	−	20.8541i	0.485901	−	0.841605i
$615$	0.0449190	+	0.0778020i	0.00181131	+	0.00313728i
$616$	16.2701	−	11.8209i	0.655541	−	0.476278i
$617$	5.44374	+	6.04589i	0.219157	+	0.243398i	0.842691	−	0.538398i	$-0.180970\pi$
$617$	5.44374	+	6.04589i	0.219157	+	0.243398i	−0.623534	+	0.781796i	$0.714304\pi$
$618$	−17.8763	−	55.0175i	−0.719089	−	2.21313i
$619$	−5.36063			−0.215462			−0.107731	−	0.994180i	$-0.534359\pi$
$619$	−5.36063			−0.215462			−0.107731	+	0.994180i	$0.534359\pi$
$620$	10.0653	+	14.6072i	0.404232	+	0.586641i
$621$	3.05046			0.122411
$622$	−17.1711	−	52.8472i	−0.688499	−	2.11898i
$623$	17.6981	+	19.6557i	0.709058	+	0.787489i
$624$	−54.5833	+	39.6571i	−2.18508	+	1.58755i
$625$	−9.79252	−	16.9611i	−0.391701	−	0.678446i
$626$	0.607062	−	1.05146i	0.0242631	−	0.0420249i
$627$	−0.509409	−	4.84670i	−0.0203438	−	0.193559i
$628$	14.0948	+	10.2404i	0.562442	+	0.408638i
$629$	2.23670	−	21.2808i	0.0891830	−	0.848519i
$630$	−1.86463	+	2.07088i	−0.0742887	+	0.0825059i
$631$	26.5358	+	11.8145i	1.05637	+	0.470327i	0.860049	−	0.510212i	$-0.170433\pi$
$631$	26.5358	+	11.8145i	1.05637	+	0.470327i	0.196324	+	0.980539i	$0.437100\pi$
$632$	−82.6116	−	17.5596i	−3.28611	−	0.698485i
$633$	−25.4480	+	5.40914i	−1.01147	+	0.214994i
$634$	13.7154	−	6.10647i	0.544707	−	0.242519i
$635$	−2.42699	+	7.46949i	−0.0963120	+	0.296418i
$636$	6.42770	−	19.7824i	0.254875	−	0.784424i
$637$	−13.4733	+	5.99868i	−0.533830	+	0.237677i
$638$	28.6139	−	6.08208i	1.13284	−	0.240792i
$639$	4.58943	+	0.975513i	0.181555	+	0.0385907i
$640$	−11.9916	−	5.33902i	−0.474011	−	0.211043i
$641$	−18.4717	+	20.5149i	−0.729589	+	0.810290i	−0.987788	−	0.155801i	$-0.950204\pi$
$641$	−18.4717	+	20.5149i	−0.729589	+	0.810290i	0.258200	+	0.966092i	$0.416871\pi$
$642$	−4.93868	+	46.9884i	−0.194914	+	1.85449i
$643$	3.42136	+	2.48577i	0.134925	+	0.0980291i	0.653201	−	0.757185i	$-0.273426\pi$
$643$	3.42136	+	2.48577i	0.134925	+	0.0980291i	−0.518275	+	0.855214i	$0.673426\pi$
$644$	−0.509768	−	4.85012i	−0.0200877	−	0.191121i
$645$	1.29713	−	2.24669i	0.0510742	−	0.0884632i
$646$	9.54202	+	16.5273i	0.375426	+	0.650257i
$647$	21.2617	−	15.4475i	0.835883	−	0.607304i	−0.0853349	−	0.996352i	$-0.527196\pi$
$647$	21.2617	−	15.4475i	0.835883	−	0.607304i	0.921217	+	0.389048i	$0.127196\pi$
$648$	29.5410	+	32.8086i	1.16048	+	1.28884i
$649$	−0.192683	−	0.593018i	−0.00756348	−	0.0232780i
$650$	45.7184			1.79322
$651$	−13.0785	+	3.89121i	−0.512585	+	0.152509i
$652$	9.11408			0.356935
$653$	−4.12592	−	12.6983i	−0.161460	−	0.496922i	0.837298	−	0.546746i	$-0.184134\pi$
$653$	−4.12592	−	12.6983i	−0.161460	−	0.496922i	−0.998758	+	0.0498246i	$0.984134\pi$
$654$	−18.4175	−	20.4547i	−0.720182	−	0.799843i
$655$	1.19986	−	0.871749i	0.0468824	−	0.0340621i
$656$	0.673821	+	1.16709i	0.0263083	+	0.0455673i
$657$	3.70045	−	6.40937i	0.144368	−	0.250053i
$658$	3.26561	+	31.0702i	0.127307	+	1.21124i
$659$	12.4717	+	9.06119i	0.485827	+	0.352974i	0.803577	−	0.595200i	$-0.202927\pi$
$659$	12.4717	+	9.06119i	0.485827	+	0.352974i	−0.317750	+	0.948174i	$0.602927\pi$
$660$	0.632093	−	6.01396i	0.0246042	−	0.234093i
$661$	−3.16035	+	3.50992i	−0.122923	+	0.136520i	−0.801465	−	0.598042i	$-0.795946\pi$
$661$	−3.16035	+	3.50992i	−0.122923	+	0.136520i	0.678542	+	0.734562i	$0.262612\pi$
$662$	−59.4868	−	26.4852i	−2.31202	−	1.02938i
$663$	14.0778	+	2.99233i	0.546736	+	0.116212i
$664$	−142.112	+	30.2069i	−5.51502	+	1.17225i
$665$	2.46439	−	1.09722i	0.0955651	−	0.0425483i
$666$	6.34812	−	19.5375i	0.245984	−	0.757062i
$667$	1.35493	−	4.17006i	0.0524632	−	0.161465i
$668$	−67.0573	+	29.8558i	−2.59453	+	1.15516i
$669$	−13.0431	+	2.77239i	−0.504275	+	0.107187i
$670$	13.2849	+	2.82379i	0.513239	+	0.109092i
$671$	6.24895	+	2.78221i	0.241238	+	0.107406i
$672$	28.5764	−	31.7373i	1.10236	−	1.22429i
$673$	3.24801	−	30.9028i	0.125202	−	1.19121i	−0.733845	−	0.679317i	$-0.762276\pi$
$673$	3.24801	−	30.9028i	0.125202	−	1.19121i	0.859046	−	0.511898i	$-0.171057\pi$
$674$	24.0185	+	17.4505i	0.925158	+	0.672167i
$675$	−2.73760	−	26.0465i	−0.105370	−	1.00253i
$676$	−1.24058	+	2.14875i	−0.0477147	+	0.0826443i
$677$	4.51998	+	7.82883i	0.173717	+	0.300886i	0.939716	−	0.341955i	$-0.111089\pi$
$677$	4.51998	+	7.82883i	0.173717	+	0.300886i	−0.766000	+	0.642841i	$0.777756\pi$
$678$	51.4932	−	37.4120i	1.97759	−	1.43680i
$679$	1.47810	+	1.64159i	0.0567242	+	0.0629986i
$680$	4.52297	+	13.9203i	0.173448	+	0.533818i
$681$	12.0053			0.460044
$682$	−12.1753	+	15.9069i	−0.466216	+	0.609107i
$683$	7.13535			0.273027			0.136513	−	0.990638i	$-0.456410\pi$
$683$	7.13535			0.273027			0.136513	+	0.990638i	$0.456410\pi$
$684$	4.09699	+	12.6092i	0.156652	+	0.482127i
$685$	3.31525	+	3.68196i	0.126669	+	0.140681i
$686$	41.4091	−	30.0854i	1.58101	−	1.14867i
$687$	−16.2093	−	28.0753i	−0.618423	−	1.07114i
$688$	19.4579	−	33.7021i	0.741826	−	1.28488i
$689$	−1.07385	−	10.2170i	−0.0409103	−	0.389236i
$690$	−1.01331	−	0.736216i	−0.0385762	−	0.0280273i
$691$	−3.81272	+	36.2756i	−0.145043	+	1.37999i	0.643706	+	0.765273i	$0.277396\pi$
$691$	−3.81272	+	36.2756i	−0.145043	+	1.37999i	−0.788749	+	0.614716i	$0.789271\pi$
$692$	−0.0419833	+	0.0466272i	−0.00159597	+	0.00177250i
$693$	−2.08025	−	0.926188i	−0.0790222	−	0.0351830i
$694$	−48.8576	−	10.3850i	−1.85461	−	0.394210i
$695$	0.805371	−	0.171187i	0.0305495	−	0.00649349i
$696$	91.7934	−	40.8690i	3.47942	−	1.54914i
$697$	0.0888351	−	0.273406i	0.00336487	−	0.0103560i
$698$	26.7469	−	82.3185i	1.01238	−	3.11580i
$699$	21.0722	−	9.38193i	0.797022	−	0.354857i
$700$	−40.9555	+	8.70536i	−1.54797	+	0.329032i
$701$	1.57916	+	0.335661i	0.0596441	+	0.0126777i	0.237637	−	0.971354i	$-0.423627\pi$
$701$	1.57916	+	0.335661i	0.0596441	+	0.0126777i	−0.177993	+	0.984032i	$0.556960\pi$
$702$	51.0293	+	22.7197i	1.92598	+	0.857500i
$703$	−13.3067	+	14.7786i	−0.501873	+	0.557386i
$704$	2.93233	−	27.8993i	0.110516	−	1.05149i
$705$	4.69742	+	3.41287i	0.176915	+	0.128536i
$706$	9.05833	+	86.1843i	0.340915	+	3.24359i
$707$	7.01134	−	12.1440i	0.263688	−	0.456722i
$708$	−1.73254	−	3.00084i	−0.0651127	−	0.112779i
$709$	−9.29395	+	6.75245i	−0.349042	+	0.253594i	−0.748467	−	0.663172i	$-0.769210\pi$
$709$	−9.29395	+	6.75245i	−0.349042	+	0.253594i	0.399425	+	0.916766i	$0.369210\pi$
$710$	−5.21141	−	5.78785i	−0.195581	−	0.217214i
$711$	2.95510	+	9.09487i	0.110825	+	0.341084i
$712$	133.372			4.99833
$713$	1.15235	+	2.77254i	0.0431558	+	0.103832i
$714$	−18.2148			−0.681672
$715$	−0.922919	−	2.84045i	−0.0345152	−	0.106227i
$716$	−34.9649	−	38.8324i	−1.30670	−	1.45124i
$717$	−20.9797	+	15.2427i	−0.783503	+	0.569248i
$718$	28.4649	+	49.3026i	1.06230	+	1.83996i
$719$	7.08549	−	12.2724i	0.264244	−	0.457685i	−0.703121	−	0.711070i	$-0.748211\pi$
$719$	7.08549	−	12.2724i	0.264244	−	0.457685i	0.967365	+	0.253386i	$0.0815441\pi$
$720$	0.812085	+	7.72648i	0.0302646	+	0.287949i
$721$	21.1692	+	15.3803i	0.788382	+	0.572793i
$722$	−3.48883	+	33.1940i	−0.129841	+	1.23535i
$723$	−17.2558	+	19.1645i	−0.641751	+	0.712736i
$724$	−89.0009	−	39.6258i	−3.30769	−	1.47268i
$725$	−36.8222	−	7.82681i	−1.36754	−	0.290680i
$726$	−34.3985	+	7.31162i	−1.27665	+	0.271360i
$727$	−24.6180	+	10.9606i	−0.913030	+	0.406507i	−0.808826	−	0.588049i	$-0.799896\pi$
$727$	−24.6180	+	10.9606i	−0.913030	+	0.406507i	−0.104205	+	0.994556i	$0.533230\pi$
$728$	17.0569	−	52.4958i	0.632172	−	1.94562i
$729$	8.98695	−	27.6590i	0.332850	−	1.02441i
$730$	−11.2229	+	4.99675i	−0.415378	+	0.184938i
$731$	−8.12005	+	1.72597i	−0.300331	+	0.0638373i
$732$	37.1820	+	7.90328i	1.37429	+	0.292113i
$733$	−25.9662	−	11.5609i	−0.959083	−	0.427011i	−0.133348	−	0.991069i	$-0.542573\pi$
$733$	−25.9662	−	11.5609i	−0.959083	−	0.427011i	−0.825735	+	0.564058i	$0.809239\pi$
$734$	−23.3944	+	25.9822i	−0.863504	+	0.959019i
$735$	0.362612	−	3.45003i	0.0133752	−	0.127256i
$736$	−7.60254	−	5.52357i	−0.280233	−	0.203601i
$737$	1.16009	+	11.0375i	0.0427324	+	0.406572i
$738$	0.137995	−	0.239014i	0.00507965	−	0.00879822i
$739$	0.348653	+	0.603885i	0.0128254	+	0.0222143i	0.872367	−	0.488852i	$-0.162584\pi$
$739$	0.348653	+	0.603885i	0.0128254	+	0.0222143i	−0.859541	+	0.511066i	$0.829251\pi$
$740$	−19.9633	+	14.5042i	−0.733866	+	0.533185i
$741$	−8.95012	−	9.94011i	−0.328791	−	0.365159i
$742$	4.01777	+	12.3654i	0.147497	+	0.453949i
$743$	−18.1815			−0.667015			−0.333508	−	0.942747i	$-0.608232\pi$
$743$	−18.1815			−0.667015			−0.333508	+	0.942747i	$0.608232\pi$
$744$	−29.5466	+	62.1389i	−1.08323	+	2.27812i
$745$	−5.47779			−0.200691
$746$	3.67929	+	11.3237i	0.134708	+	0.414589i
$747$	11.0076	+	12.2251i	0.402746	+	0.447295i
$748$	−15.6548	+	11.3738i	−0.572395	+	0.415869i
$749$	−10.6856	−	18.5080i	−0.390443	−	0.676267i
$750$	−11.1835	+	19.3704i	−0.408364	+	0.707307i
$751$	3.87445	+	36.8629i	0.141381	+	1.34515i	0.803301	+	0.595573i	$0.203075\pi$
$751$	3.87445	+	36.8629i	0.141381	+	1.34515i	−0.661920	+	0.749574i	$0.730258\pi$
$752$	70.4650	+	51.1958i	2.56959	+	1.86692i
$753$	3.40154	−	32.3635i	0.123959	−	1.17939i
$754$	53.7242	−	59.6668i	1.95652	−	2.17294i
$755$	−1.78319	−	0.793927i	−0.0648969	−	0.0288940i
$756$	−50.0392	−	10.6362i	−1.81991	−	0.386834i
$757$	−6.26211	+	1.33105i	−0.227600	+	0.0483779i	−0.320300	−	0.947316i	$-0.603784\pi$
$757$	−6.26211	+	1.33105i	−0.227600	+	0.0483779i	0.0926997	+	0.995694i	$0.470450\pi$
$758$	36.7549	−	16.3643i	1.33500	−	0.594380i
$759$	0.316281	−	0.973412i	0.0114803	−	0.0353326i
$760$	4.20351	−	12.9371i	0.152477	−	0.469277i
$761$	−19.4940	+	8.67928i	−0.706657	+	0.314624i	−0.728412	−	0.685140i	$-0.759741\pi$
$761$	−19.4940	+	8.67928i	−0.706657	+	0.314624i	0.0217552	+	0.999763i	$0.493075\pi$
$762$	−48.2083	+	10.2470i	−1.74640	+	0.371209i
$763$	12.1780	+	2.58852i	0.440874	+	0.0937106i
$764$	5.73201	+	2.55206i	0.207377	+	0.0923302i
$765$	1.10893	−	1.23160i	0.0400936	−	0.0445285i
$766$	−3.27605	+	31.1696i	−0.118369	+	1.12620i
$767$	−1.38454	−	1.00593i	−0.0499928	−	0.0363219i
$768$	−2.38699	−	22.7107i	−0.0861332	−	0.819502i
$769$	6.12828	−	10.6145i	0.220991	−	0.382768i	−0.734118	−	0.679022i	$-0.762404\pi$
$769$	6.12828	−	10.6145i	0.220991	−	0.382768i	0.955109	+	0.296254i	$0.0957374\pi$
$770$	1.88993	+	3.27346i	0.0681084	+	0.117967i
$771$	−0.121923	+	0.0885824i	−0.00439096	+	0.00319022i
$772$	44.5963	+	49.5292i	1.60506	+	1.78260i
$773$	−10.7240	−	33.0050i	−0.385714	−	1.18711i	−0.935961	−	0.352104i	$-0.885466\pi$
$773$	−10.7240	−	33.0050i	−0.385714	−	1.18711i	0.550247	−	0.835002i	$-0.314534\pi$
$774$	−7.96974			−0.286466
$775$	22.6393	−	12.3276i	0.813227	−	0.442820i
$776$	11.1389			0.399863
$777$	−5.86539	−	18.0518i	−0.210420	−	0.647605i
$778$	−25.9244	−	28.7920i	−0.929435	−	1.03224i
$779$	−0.216146	+	0.157040i	−0.00774425	+	0.00562652i
$780$	−8.29855	−	14.3735i	−0.297136	−	0.514654i
$781$	3.18213	−	5.51161i	0.113866	−	0.197221i
$782$	0.418951	+	3.98605i	0.0149817	+	0.142541i
$783$	−37.2102	−	27.0348i	−1.32978	−	0.966144i
$784$	5.43948	−	51.7532i	0.194267	−	1.84833i
$785$	−1.35429	+	1.50409i	−0.0483366	+	0.0536833i
$786$	8.50228	+	3.78546i	0.303266	+	0.135023i
$787$	19.6786	+	4.18281i	0.701465	+	0.149101i	0.544819	−	0.838554i	$-0.316598\pi$
$787$	19.6786	+	4.18281i	0.701465	+	0.149101i	0.156646	+	0.987655i	$0.449932\pi$
$788$	15.2066	−	3.23227i	0.541714	−	0.115145i
$789$	−9.46075	+	4.21220i	−0.336812	+	0.149958i
$790$	4.90526	−	15.0968i	0.174521	−	0.537122i
$791$	−8.89666	+	27.3811i	−0.316329	+	0.973559i
$792$	−10.4898	+	4.67034i	−0.372737	+	0.165953i
$793$	18.3640	−	3.90339i	0.652125	−	0.138613i
$794$	41.5496	+	8.83165i	1.47454	+	0.313423i
$795$	2.20752	+	0.982849i	0.0782925	+	0.0348581i
$796$	−46.1995	+	51.3097i	−1.63750	+	1.81863i
$797$	−2.73885	+	26.0584i	−0.0970150	+	0.923036i	0.832444	+	0.554110i	$0.186941\pi$
$797$	−2.73885	+	26.0584i	−0.0970150	+	0.923036i	−0.929459	+	0.368926i	$0.879725\pi$
$798$	13.6953	+	9.95018i	0.484807	+	0.352233i
$799$	−1.94213	−	18.4781i	−0.0687076	−	0.653709i
$800$	−40.3405	+	69.8717i	−1.42625	+	2.47034i
$801$	−7.55072	−	13.0782i	−0.266791	−	0.462096i
$802$	67.5183	−	49.0549i	2.38416	−	1.73219i
$803$	−6.71722	−	7.46022i	−0.237045	−	0.263266i
$804$	19.0586	+	58.6562i	0.672144	+	2.06865i
$805$	0.566550			0.0199683
$806$	−1.37278	+	54.9626i	−0.0483543	+	1.93598i
$807$	23.0179			0.810270
$808$	−21.8506	−	67.2491i	−0.768700	−	2.36582i
$809$	24.3899	+	27.0877i	0.857504	+	0.952354i	0.999295	−	0.0375423i	$-0.0119529\pi$
$809$	24.3899	+	27.0877i	0.857504	+	0.952354i	−0.141791	+	0.989897i	$0.545286\pi$
$810$	−6.71298	+	4.87727i	−0.235870	+	0.171370i
$811$	9.55322	+	16.5467i	0.335459	+	0.581032i	0.983573	−	0.180511i	$-0.0577753\pi$
$811$	9.55322	+	16.5467i	0.335459	+	0.581032i	−0.648114	+	0.761543i	$0.724442\pi$
$812$	−36.7660	+	63.6805i	−1.29023	+	2.23475i
$813$	0.763320	+	7.26250i	0.0267708	+	0.254707i
$814$	−22.5431	−	16.3785i	−0.790136	−	0.574067i
$815$	−0.110675	+	1.05300i	−0.00387676	+	0.0368849i
$816$	−33.9798	+	37.7384i	−1.18953	+	1.32111i
$817$	7.04810	+	3.13802i	0.246582	+	0.109785i
$818$	17.3297	+	3.68355i	0.605920	+	0.128792i
$819$	−6.11330	+	1.29942i	−0.213616	+	0.0454055i
$820$	−0.302855	+	0.134840i	−0.0105762	+	0.00470881i
$821$	12.1937	−	37.5285i	0.425565	−	1.30975i	−0.476888	−	0.878964i	$-0.658235\pi$
$821$	12.1937	−	37.5285i	0.425565	−	1.30975i	0.902453	−	0.430789i	$-0.141765\pi$
$822$	−9.60773	+	29.5696i	−0.335108	+	1.03136i
$823$	−28.8571	+	12.8480i	−1.00589	+	0.447853i	−0.842493	−	0.538707i	$-0.818913\pi$
$823$	−28.8571	+	12.8480i	−1.00589	+	0.447853i	−0.163401	+	0.986560i	$0.552246\pi$
$824$	129.063	−	27.4331i	4.49611	−	0.955678i
$825$	−8.59537	−	1.82700i	−0.299252	−	0.0636081i
$826$	1.97866	+	0.880958i	0.0688465	+	0.0306525i
$827$	13.2688	−	14.7364i	0.461400	−	0.512436i	−0.466879	−	0.884321i	$-0.654622\pi$
$827$	13.2688	−	14.7364i	0.461400	−	0.512436i	0.928279	+	0.371885i	$0.121288\pi$
$828$	−0.291055	+	2.76921i	−0.0101149	+	0.0962366i
$829$	−7.28104	−	5.28999i	−0.252881	−	0.183729i	0.454122	−	0.890940i	$-0.349953\pi$
$829$	−7.28104	−	5.28999i	−0.252881	−	0.183729i	−0.707003	+	0.707211i	$0.749953\pi$
$830$	−2.85434	−	27.1572i	−0.0990754	−	0.942640i
$831$	12.0081	−	20.7987i	0.416558	−	0.721499i
$832$	−38.4977	−	66.6800i	−1.33467	−	2.31171i
$833$	−8.98066	+	6.52483i	−0.311161	+	0.226072i
$834$	3.45729	+	3.83970i	0.119716	+	0.132958i
$835$	−2.63511	−	8.11003i	−0.0911917	−	0.280659i
$836$	17.9836			0.621976
$837$	31.3954	−	2.50905i	1.08518	−	0.0867253i
$838$	39.4699			1.36347
$839$	−9.84070	−	30.2866i	−0.339739	−	1.04561i	−0.964340	−	0.264665i	$-0.914739\pi$
$839$	−9.84070	−	30.2866i	−0.339739	−	1.04561i	0.624602	−	0.780944i	$-0.285261\pi$
$840$	8.68750	+	9.64844i	0.299747	+	0.332903i
$841$	−30.0234	+	21.8133i	−1.03529	+	0.752183i
$842$	−35.9349	−	62.2411i	−1.23840	−	2.14497i
$843$	−1.35294	+	2.34336i	−0.0465976	+	0.0807095i
$844$	−10.0353	−	95.4791i	−0.345428	−	3.28652i
$845$	−0.233192	−	0.169424i	−0.00802205	−	0.00582836i
$846$	1.86452	−	17.7398i	0.0641037	−	0.609906i
$847$	10.6438	−	11.8212i	0.365726	−	0.406180i
$848$	33.1145	+	14.7435i	1.13716	+	0.506295i
$849$	21.2523	+	4.51733i	0.729379	+	0.155034i
$850$	33.6591	−	7.15447i	1.15450	−	0.245396i
$851$	−3.81548	+	1.69876i	−0.130793	+	0.0582328i
$852$	10.9290	−	33.6361i	0.374422	−	1.15235i
$853$	−15.1702	+	46.6890i	−0.519417	+	1.59860i	0.255683	+	0.966761i	$0.417700\pi$
$853$	−15.1702	+	46.6890i	−0.519417	+	1.59860i	−0.775099	+	0.631839i	$0.782300\pi$
$854$	−21.7064	+	9.66431i	−0.742778	+	0.330706i
$855$	−1.50656	+	0.320230i	−0.0515234	+	0.0109516i
$856$	−105.410	−	22.4056i	−3.60285	−	0.765809i
$857$	17.5770	+	7.82580i	0.600420	+	0.267324i	0.684357	−	0.729147i	$-0.260083\pi$
$857$	17.5770	+	7.82580i	0.600420	+	0.267324i	−0.0839371	+	0.996471i	$0.526749\pi$
$858$	12.5408	−	13.9279i	0.428135	−	0.475492i
$859$	−0.485236	+	4.61672i	−0.0165561	+	0.157520i	−0.999676	−	0.0254400i	$-0.991901\pi$
$859$	−0.485236	+	4.61672i	−0.0165561	+	0.157520i	0.983120	+	0.182960i	$0.0585680\pi$
$860$	7.74487	+	5.62698i	0.264098	+	0.191878i
$861$	−0.0266550	−	0.253606i	−0.000908401	−	0.00864285i
$862$	5.36418	−	9.29104i	0.182705	−	0.316454i
$863$	19.2652	+	33.3683i	0.655795	+	1.13587i	0.981694	+	0.190466i	$0.0609999\pi$
$863$	19.2652	+	33.3683i	0.655795	+	1.13587i	−0.325899	+	0.945405i	$0.605667\pi$
$864$	−79.7493	+	57.9413i	−2.71313	+	1.97120i
$865$	−0.00487728	−	0.00541676i	−0.000165832	−	0.000184175i
$866$	−15.0271	−	46.2487i	−0.510642	−	1.57159i
$867$	−13.2931			−0.451456
$868$	−9.23582	−	49.4981i	−0.313484	−	1.68008i
$869$	12.9713			0.440022
$870$	5.83589	+	17.9610i	0.197855	+	0.608935i
$871$	20.3823	+	22.6369i	0.690629	+	0.767021i
$872$	50.7901	−	36.9012i	1.71997	−	1.24963i
$873$	−0.630617	−	1.09226i	−0.0213431	−	0.0369674i
$874$	1.86246	−	3.22587i	0.0629986	−	0.109117i
$875$	−1.05753	−	10.0618i	−0.0357512	−	0.340150i
$876$	−45.1323	−	32.7905i	−1.52488	−	1.10789i
$877$	0.967760	−	9.20763i	0.0326789	−	0.310919i	−0.965957	−	0.258703i	$-0.916705\pi$
$877$	0.967760	−	9.20763i	0.0326789	−	0.310919i	0.998636	−	0.0522162i	$-0.0166285\pi$
$878$	−41.2370	+	45.7983i	−1.39168	+	1.54562i
$879$	34.7372	+	15.4660i	1.17166	+	0.521655i
$880$	10.3078	+	2.19099i	0.347475	+	0.0738582i
$881$	17.4884	−	3.71727i	0.589198	−	0.125238i	0.0963414	−	0.995348i	$-0.469286\pi$
$881$	17.4884	−	3.71727i	0.589198	−	0.125238i	0.492857	+	0.870110i	$0.335953\pi$
$882$	−9.73577	+	4.33465i	−0.327821	+	0.145955i
$883$	−14.9303	+	45.9509i	−0.502446	+	1.54637i	0.302577	+	0.953125i	$0.402153\pi$
$883$	−14.9303	+	45.9509i	−0.502446	+	1.54637i	−0.805022	+	0.593244i	$0.797847\pi$
$884$	−16.4118	+	50.5104i	−0.551990	+	1.69885i
$885$	0.367742	−	0.163729i	0.0123615	−	0.00550370i
$886$	−56.5516	+	12.0204i	−1.89989	+	0.403834i
$887$	−22.9984	−	4.88847i	−0.772211	−	0.164139i	−0.195077	−	0.980788i	$-0.562496\pi$
$887$	−22.9984	−	4.88847i	−0.772211	−	0.164139i	−0.577134	+	0.816649i	$0.695829\pi$
$888$	−87.4369	−	38.9294i	−2.93419	−	1.30639i
$889$	14.9170	−	16.5670i	0.500298	−	0.555638i
$890$	−2.62025	+	24.9300i	−0.0878310	+	0.835656i
$891$	−5.48554	−	3.98548i	−0.183772	−	0.133518i
$892$	−5.14346	−	48.9368i	−0.172216	−	1.63852i
$893$	−8.63379	+	14.9542i	−0.288919	+	0.500422i
$894$	−17.1873	−	29.7693i	−0.574830	−	0.995635i
$895$	4.91110	−	3.56812i	0.164160	−	0.119269i
$896$	24.9312	+	27.6889i	0.832894	+	0.925022i
$897$	−0.868078	−	2.67167i	−0.0289843	−	0.0892044i
$898$	−50.5739			−1.68767
$899$	10.5150	−	44.0327i	0.350696	−	1.46857i
$900$	23.9062			0.796874
$901$	−2.38945	−	7.35398i	−0.0796042	−	0.244996i
$902$	−0.250494	−	0.278202i	−0.00834053	−	0.00926310i
$903$	−5.95736	+	4.32827i	−0.198249	+	0.144036i
$904$	72.5879	+	125.726i	2.41424	+	4.18158i
$905$	5.65893	−	9.80156i	0.188109	−	0.325815i
$906$	−1.28037	−	12.1819i	−0.0425373	−	0.404716i
$907$	10.1792	+	7.39560i	0.337994	+	0.245567i	0.743815	−	0.668386i	$-0.233014\pi$
$907$	10.1792	+	7.39560i	0.337994	+	0.245567i	−0.405821	+	0.913952i	$0.633014\pi$
$908$	−4.63076	+	44.0588i	−0.153677	+	1.46214i
$909$	−5.35728	+	5.94987i	−0.177690	+	0.197345i
$910$	9.47746	+	4.21964i	0.314175	+	0.139880i
$911$	46.2512	+	9.83100i	1.53237	+	0.325715i	0.895432	−	0.445199i	$-0.146867\pi$
$911$	46.2512	+	9.83100i	1.53237	+	0.325715i	0.636939	+	0.770914i	$0.280200\pi$
$912$	46.1639	−	9.81243i	1.52864	−	0.324922i
$913$	20.3847	−	9.07586i	0.674635	−	0.300367i
$914$	−3.41333	+	10.5051i	−0.112903	+	0.347479i
$915$	−1.36462	+	4.19986i	−0.0451129	+	0.138843i
$916$	109.287	−	48.6578i	3.61095	−	1.60770i
$917$	−4.11776	+	0.875258i	−0.135981	+	0.0289036i
$918$	41.1246	+	8.74130i	1.35731	+	0.288506i
$919$	−21.1320	−	9.40858i	−0.697081	−	0.310360i	0.0274300	−	0.999624i	$-0.491268\pi$
$919$	−21.1320	−	9.40858i	−0.697081	−	0.310360i	−0.724511	+	0.689263i	$0.757934\pi$
$920$	1.91161	−	2.12306i	0.0630238	−	0.0699951i
$921$	−1.32786	+	12.6337i	−0.0437544	+	0.416295i
$922$	−49.7848	−	36.1708i	−1.63958	−	1.19122i
$923$	−1.82586	−	17.3719i	−0.0600990	−	0.571804i
$924$	−8.58224	+	14.8649i	−0.282335	+	0.489019i
$925$	17.9291	+	31.0541i	0.589506	+	1.02105i
$926$	−36.0560	+	26.1962i	−1.18488	+	0.860862i
$927$	−9.99679	−	11.1026i	−0.328338	−	0.364656i
$928$	43.7846	+	134.755i	1.43730	+	4.42355i
$929$	1.68694			0.0553468			0.0276734	−	0.999617i	$-0.491190\pi$
$929$	1.68694			0.0553468			0.0276734	+	0.999617i	$0.491190\pi$
$930$	−11.0346	−	6.74367i	−0.361838	−	0.221133i
$931$	10.3166			0.338114
$932$	26.3030	+	80.9524i	0.861585	+	2.65169i
$933$	19.6147	+	21.7844i	0.642157	+	0.713188i
$934$	83.0208	−	60.3181i	2.71652	−	1.97367i
$935$	−1.12398	−	1.94679i	−0.0367581	−	0.0636669i
$936$	−15.7576	+	27.2930i	−0.515055	+	0.892101i
$937$	−2.06200	−	19.6186i	−0.0673625	−	0.640911i	−0.975160	−	0.221502i	$-0.928904\pi$
$937$	−2.06200	−	19.6186i	−0.0673625	−	0.640911i	0.907797	−	0.419409i	$-0.137763\pi$
$938$	−31.1885	−	22.6598i	−1.01834	−	0.739868i
$939$	−0.0669503	+	0.636990i	−0.00218484	+	0.0207874i
$940$	−14.3370	+	15.9228i	−0.467620	+	0.519344i
$941$	−8.06045	−	3.58874i	−0.262763	−	0.116990i	0.271127	−	0.962544i	$-0.412604\pi$
$941$	−8.06045	−	3.58874i	−0.262763	−	0.116990i	−0.533890	+	0.845554i	$0.679270\pi$
$942$	−12.4233	−	2.64066i	−0.404773	−	0.0860372i
$943$	−0.0548849	+	0.0116661i	−0.00178730	+	0.000379902i
$944$	5.51642	−	2.45607i	0.179544	−	0.0799382i
$945$	1.83649	−	5.65214i	0.0597411	−	0.183864i
$946$	−3.34057	+	10.2812i	−0.108611	+	0.334271i
$947$	14.2158	−	6.32930i	0.461953	−	0.205675i	−0.162545	−	0.986701i	$-0.551970\pi$
$947$	14.2158	−	6.32930i	0.461953	−	0.205675i	0.624498	+	0.781026i	$0.285304\pi$
$948$	70.5082	−	14.9870i	2.29000	−	0.486754i
$949$	−26.9506	−	5.72853i	−0.874854	−	0.185956i
$950$	−29.2157	−	13.0077i	−0.947883	−	0.422025i
$951$	−5.29960	+	5.88581i	−0.171851	+	0.190860i
$952$	4.34271	−	41.3181i	0.140748	−	1.33913i
$953$	−7.80840	−	5.67314i	−0.252939	−	0.183771i	0.454089	−	0.890956i	$-0.349965\pi$
$953$	−7.80840	−	5.67314i	−0.252939	−	0.183771i	−0.707028	+	0.707185i	$0.749965\pi$
$954$	−0.775962	−	7.38278i	−0.0251227	−	0.239026i
$955$	−0.364458	+	0.631260i	−0.0117936	+	0.0204271i
$956$	−47.8473	−	82.8739i	−1.54749	−	2.68033i
$957$	−12.4849	+	9.07083i	−0.403580	+	0.293218i
$958$	60.6348	+	67.3417i	1.95902	+	2.17571i
$959$	−4.34583	−	13.3751i	−0.140334	−	0.431904i
$960$	18.1105			0.584514
$961$	14.1404	+	27.5871i	0.456143	+	0.889907i
$962$	−76.4790			−2.46578
$963$	3.77063	+	11.6048i	0.121507	+	0.373960i
$964$	−63.6766	−	70.7201i	−2.05089	−	2.27774i
$965$	−6.26392	+	4.55100i	−0.201643	+	0.146502i
$966$	1.77763	+	3.07894i	0.0571942	+	0.0990633i
$967$	−14.1988	+	24.5930i	−0.456602	+	0.790858i	−0.998779	−	0.0494066i	$-0.984267\pi$
$967$	−14.1988	+	24.5930i	−0.456602	+	0.790858i	0.542177	+	0.840264i	$0.317600\pi$
$968$	−8.38438	−	79.7720i	−0.269484	−	2.56397i
$969$	−8.14485	−	5.91758i	−0.261650	−	0.190100i
$970$	−0.218837	+	2.08209i	−0.00702642	+	0.0668519i
$971$	−14.8059	+	16.4436i	−0.475144	+	0.527701i	−0.932300	−	0.361686i	$-0.882201\pi$
$971$	−14.8059	+	16.4436i	−0.475144	+	0.527701i	0.457156	+	0.889386i	$0.348868\pi$
$972$	46.7662	+	20.8217i	1.50003	+	0.667855i
$973$	−2.28602	−	0.485909i	−0.0732865	−	0.0155775i
$974$	−54.4080	+	11.5648i	−1.74334	+	0.370559i
$975$	−22.0331	+	9.80978i	−0.705625	+	0.314165i
$976$	−20.4703	+	63.0012i	−0.655240	+	2.01662i
$977$	−6.15324	+	18.9377i	−0.196859	+	0.605871i	0.803090	+	0.595857i	$0.203188\pi$
$977$	−6.15324	+	18.9377i	−0.196859	+	0.605871i	−0.999950	+	0.0100140i	$0.996812\pi$
$978$	−6.06982	+	2.70246i	−0.194091	+	0.0864151i
$979$	−20.0362	+	4.25884i	−0.640361	+	0.136113i
$980$	12.5215	+	2.66153i	0.399985	+	0.0850195i
$981$	−6.49389	−	2.89127i	−0.207334	−	0.0923111i
$982$	−44.5206	+	49.4451i	−1.42071	+	1.57786i
$983$	2.60593	−	24.7938i	0.0831164	−	0.790800i	−0.870984	−	0.491312i	$-0.836518\pi$
$983$	2.60593	−	24.7938i	0.0831164	−	0.790800i	0.954100	−	0.299488i	$-0.0968158\pi$
$984$	−1.04028	−	0.755810i	−0.0331630	−	0.0240944i
$985$	0.188783	+	1.79615i	0.00601513	+	0.0572302i
$986$	30.2160	−	52.3356i	0.962273	−	1.66671i
$987$	−8.24054	−	14.2730i	−0.262299	−	0.454316i
$988$	39.9319	−	29.0122i	1.27040	−	0.923002i
$989$	1.08420	+	1.20413i	0.0344757	+	0.0382891i
$990$	−0.666901	−	2.05251i	−0.0211955	−	0.0652330i
$991$	−42.0512			−1.33580			−0.667900	−	0.744251i	$-0.732807\pi$
$991$	−42.0512			−1.33580			−0.667900	+	0.744251i	$0.732807\pi$
$992$	−82.7885	−	50.5953i	−2.62854	−	1.60640i
$993$	34.3515			1.09011
$994$	6.83142	+	21.0249i	0.216679	+	0.666871i
$995$	−5.36707	−	5.96074i	−0.170148	−	0.188968i
$996$	100.319	−	72.8860i	3.17873	−	2.30948i
$997$	−7.23233	−	12.5268i	−0.229050	−	0.396727i	0.728477	−	0.685071i	$-0.240229\pi$
$997$	−7.23233	−	12.5268i	−0.229050	−	0.396727i	−0.957527	+	0.288344i	$0.906895\pi$
$998$	−33.0353	+	57.2189i	−1.04572	+	1.81123i
$999$	4.57954	+	43.5714i	0.144890	+	1.37854i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.2.g.a.20.1	yes	16
3.2	odd	2		279.2.y.c.82.2		16
4.3	odd	2		496.2.bg.c.113.1		16
5.2	odd	4		775.2.ck.a.299.4		32
5.3	odd	4		775.2.ck.a.299.1		32
5.4	even	2		775.2.bl.a.51.2		16
31.2	even	5		961.2.g.s.235.2		16
31.3	odd	30		961.2.c.i.521.1		16
31.4	even	5		961.2.g.t.816.2		16
31.5	even	3		961.2.d.o.531.1		16
31.6	odd	6		961.2.g.j.844.1		16
31.7	even	15		961.2.g.s.732.2		16
31.8	even	5		961.2.g.k.846.1		16
31.9	even	15		961.2.d.o.628.1		16
31.10	even	15		961.2.d.p.388.4		16
31.11	odd	30		961.2.d.q.374.4		16
31.12	odd	30		961.2.g.n.338.2		16
31.13	odd	30		961.2.a.j.1.1		8
31.14	even	15	inner	31.2.g.a.14.1	✓	16
31.15	odd	10		961.2.c.i.439.1		16
31.16	even	5		961.2.c.j.439.1		16
31.17	odd	30		961.2.g.l.448.1		16
31.18	even	15		961.2.a.i.1.1		8
31.19	even	15		961.2.g.t.338.2		16
31.20	even	15		961.2.d.p.374.4		16
31.21	odd	30		961.2.d.q.388.4		16
31.22	odd	30		961.2.d.n.628.1		16
31.23	odd	10		961.2.g.j.846.1		16
31.24	odd	30		961.2.g.m.732.2		16
31.25	even	3		961.2.g.k.844.1		16
31.26	odd	6		961.2.d.n.531.1		16
31.27	odd	10		961.2.g.n.816.2		16
31.28	even	15		961.2.c.j.521.1		16
31.29	odd	10		961.2.g.m.235.2		16
31.30	odd	2		961.2.g.l.547.1		16
93.14	odd	30		279.2.y.c.262.2		16
93.44	even	30		8649.2.a.be.1.8		8
93.80	odd	30		8649.2.a.bf.1.8		8
124.107	odd	30		496.2.bg.c.417.1		16
155.14	even	30		775.2.bl.a.76.2		16
155.107	odd	60		775.2.ck.a.324.1		32
155.138	odd	60		775.2.ck.a.324.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.1	✓	16	31.14	even	15	inner
31.2.g.a.20.1	yes	16	1.1	even	1	trivial
279.2.y.c.82.2		16	3.2	odd	2
279.2.y.c.262.2		16	93.14	odd	30
496.2.bg.c.113.1		16	4.3	odd	2
496.2.bg.c.417.1		16	124.107	odd	30
775.2.bl.a.51.2		16	5.4	even	2
775.2.bl.a.76.2		16	155.14	even	30
775.2.ck.a.299.1		32	5.3	odd	4
775.2.ck.a.299.4		32	5.2	odd	4
775.2.ck.a.324.1		32	155.107	odd	60
775.2.ck.a.324.4		32	155.138	odd	60
961.2.a.i.1.1		8	31.18	even	15
961.2.a.j.1.1		8	31.13	odd	30
961.2.c.i.439.1		16	31.15	odd	10
961.2.c.i.521.1		16	31.3	odd	30
961.2.c.j.439.1		16	31.16	even	5
961.2.c.j.521.1		16	31.28	even	15
961.2.d.n.531.1		16	31.26	odd	6
961.2.d.n.628.1		16	31.22	odd	30
961.2.d.o.531.1		16	31.5	even	3
961.2.d.o.628.1		16	31.9	even	15
961.2.d.p.374.4		16	31.20	even	15
961.2.d.p.388.4		16	31.10	even	15
961.2.d.q.374.4		16	31.11	odd	30
961.2.d.q.388.4		16	31.21	odd	30
961.2.g.j.844.1		16	31.6	odd	6
961.2.g.j.846.1		16	31.23	odd	10
961.2.g.k.844.1		16	31.25	even	3
961.2.g.k.846.1		16	31.8	even	5
961.2.g.l.448.1		16	31.17	odd	30
961.2.g.l.547.1		16	31.30	odd	2
961.2.g.m.235.2		16	31.29	odd	10
961.2.g.m.732.2		16	31.24	odd	30
961.2.g.n.338.2		16	31.12	odd	30
961.2.g.n.816.2		16	31.27	odd	10
961.2.g.s.235.2		16	31.2	even	5
961.2.g.s.732.2		16	31.7	even	15
961.2.g.t.338.2		16	31.19	even	15
961.2.g.t.816.2		16	31.4	even	5
8649.2.a.be.1.8		8	93.44	even	30
8649.2.a.bf.1.8		8	93.80	odd	30

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.831304 - 2.55849i) q^{2} +(0.949606 + 1.05464i) q^{3} +(-4.23677 + 3.07819i) q^{4} +(-0.304192 - 0.526876i) q^{5} +(1.90889 - 3.30629i) q^{6} +(0.180508 + 1.71742i) q^{7} +(7.04481 + 5.11835i) q^{8} +(0.103062 - 0.980572i) q^{9} +O(q^{10})\)	\(q+(-0.831304 - 2.55849i) q^{2} +(0.949606 + 1.05464i) q^{3} +(-4.23677 + 3.07819i) q^{4} +(-0.304192 - 0.526876i) q^{5} +(1.90889 - 3.30629i) q^{6} +(0.180508 + 1.71742i) q^{7} +(7.04481 + 5.11835i) q^{8} +(0.103062 - 0.980572i) q^{9} +(-1.09513 + 1.21627i) q^{10} +(-1.22177 - 0.543967i) q^{11} +(-7.26966 - 1.54521i) q^{12} +(-3.59045 + 0.763174i) q^{13} +(4.24394 - 1.88952i) q^{14} +(0.266804 - 0.821139i) q^{15} +(4.00227 - 12.3177i) q^{16} +(-2.52396 + 1.12374i) q^{17} +(-2.59446 + 0.551469i) q^{18} +(2.51157 + 0.533850i) q^{19} +(2.91062 + 1.29589i) q^{20} +(-1.63986 + 1.82124i) q^{21} +(-0.376072 + 3.57808i) q^{22} +(0.436271 + 0.316969i) q^{23} +(1.29175 + 12.2902i) q^{24} +(2.31493 - 4.00958i) q^{25} +(4.93733 + 8.55171i) q^{26} +(4.57641 - 3.32495i) q^{27} +(-6.05132 - 6.72067i) q^{28} +(-2.51258 - 7.73291i) q^{29} -2.32267 q^{30} +(4.75081 + 2.90341i) q^{31} -17.4262 q^{32} +(-0.586508 - 1.80509i) q^{33} +(4.97326 + 5.52336i) q^{34} +(0.849957 - 0.617530i) q^{35} +(2.58174 + 4.47170i) q^{36} +(-3.87249 + 6.70735i) q^{37} +(-0.722025 - 6.86961i) q^{38} +(-4.21439 - 3.06194i) q^{39} +(0.553763 - 5.26870i) q^{40} +(-0.0696243 + 0.0773256i) q^{41} +(6.02285 + 2.68155i) q^{42} +(2.93904 + 0.624713i) q^{43} +(6.85079 - 1.45618i) q^{44} +(-0.547990 + 0.243981i) q^{45} +(0.448289 - 1.37969i) q^{46} +(-2.07813 + 6.39584i) q^{47} +(16.7914 - 7.47602i) q^{48} +(3.93009 - 0.835366i) q^{49} +(-12.1829 - 2.58955i) q^{50} +(-3.58192 - 1.59477i) q^{51} +(12.8627 - 14.2855i) q^{52} +(-0.292549 + 2.78341i) q^{53} +(-12.3112 - 8.94464i) q^{54} +(0.0850494 + 0.809191i) q^{55} +(-7.51871 + 13.0228i) q^{56} +(1.82198 + 3.15576i) q^{57} +(-17.6959 + 12.8568i) q^{58} +(0.311970 + 0.346478i) q^{59} +(1.39724 + 4.30025i) q^{60} -5.11468 q^{61} +(3.47898 - 14.5685i) q^{62} +1.70266 q^{63} +(6.48190 + 19.9492i) q^{64} +(1.49428 + 1.65957i) q^{65} +(-4.13073 + 3.00115i) q^{66} +(-4.14923 - 7.18668i) q^{67} +(7.23436 - 12.5303i) q^{68} +(0.0799956 + 0.761107i) q^{69} +(-2.28652 - 1.66125i) q^{70} +(-0.497420 + 4.73264i) q^{71} +(5.74497 - 6.38043i) q^{72} +(6.85725 + 3.05304i) q^{73} +(20.3799 + 4.33188i) q^{74} +(6.42696 - 1.36609i) q^{75} +(-12.2842 + 5.46929i) q^{76} +(0.713679 - 2.19648i) q^{77} +(-4.33049 + 13.3279i) q^{78} +(-8.86044 + 3.94492i) q^{79} +(-7.70738 + 1.63825i) q^{80} +(4.95915 + 1.05410i) q^{81} +(0.255716 + 0.113852i) q^{82} +(-11.1642 + 12.3991i) q^{83} +(1.34155 - 12.7640i) q^{84} +(1.35984 + 0.987981i) q^{85} +(-0.844916 - 8.03884i) q^{86} +(5.76952 - 9.99310i) q^{87} +(-5.82292 - 10.0856i) q^{88} +(12.3911 - 9.00268i) q^{89} +(1.07977 + 1.19920i) q^{90} +(-1.95880 - 6.02855i) q^{91} -2.82407 q^{92} +(1.44933 + 7.76751i) q^{93} +18.0912 q^{94} +(-0.482726 - 1.48568i) q^{95} +(-16.5480 - 18.3784i) q^{96} +(1.03488 - 0.751881i) q^{97} +(-5.40437 - 9.36065i) q^{98} +(-0.659316 + 1.14197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9	\( 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9} - 2 q^{10} - 7 q^{11} + 5 q^{12} - 7 q^{13} - 6 q^{14} + 14 q^{15} - 2 q^{16} - 6 q^{17} - 3 q^{18} + 16 q^{19} + 37 q^{20} + 9 q^{21} + 9 q^{22} + q^{23} - 20 q^{24} - 13 q^{25} + 9 q^{26} + 9 q^{27} - 30 q^{28} - 14 q^{29} - 22 q^{30} + 15 q^{31} - 42 q^{32} - 13 q^{33} - 32 q^{34} - 9 q^{35} + q^{36} - 8 q^{37} + 8 q^{38} - 3 q^{39} - q^{40} - 8 q^{41} + 69 q^{42} + 23 q^{43} + 39 q^{44} + 65 q^{45} + 34 q^{46} + 14 q^{47} + 34 q^{48} + 2 q^{49} + 3 q^{50} - 42 q^{51} + 29 q^{52} + 6 q^{53} - 46 q^{54} - 7 q^{55} - 30 q^{56} - 17 q^{57} - 15 q^{58} + 4 q^{59} - 75 q^{60} - 60 q^{61} - 25 q^{62} - 46 q^{63} + 23 q^{64} - 12 q^{65} - 30 q^{66} + 13 q^{67} + 30 q^{68} + 38 q^{69} + 12 q^{70} - 14 q^{71} + 37 q^{72} + 2 q^{73} + 13 q^{74} + 13 q^{75} - 12 q^{76} + 18 q^{77} - 15 q^{78} + 18 q^{79} + 36 q^{80} + 23 q^{81} + 14 q^{82} - 16 q^{83} + 8 q^{84} + 37 q^{85} - 26 q^{86} + 15 q^{87} - 17 q^{88} + q^{89} - 23 q^{90} + 8 q^{91} - 64 q^{92} + 17 q^{93} + 44 q^{94} - 22 q^{95} + 8 q^{96} + 3 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9 - 2 * q^10 - 7 * q^11 + 5 * q^12 - 7 * q^13 - 6 * q^14 + 14 * q^15 - 2 * q^16 - 6 * q^17 - 3 * q^18 + 16 * q^19 + 37 * q^20 + 9 * q^21 + 9 * q^22 + q^23 - 20 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 - 30 * q^28 - 14 * q^29 - 22 * q^30 + 15 * q^31 - 42 * q^32 - 13 * q^33 - 32 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 8 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 69 * q^42 + 23 * q^43 + 39 * q^44 + 65 * q^45 + 34 * q^46 + 14 * q^47 + 34 * q^48 + 2 * q^49 + 3 * q^50 - 42 * q^51 + 29 * q^52 + 6 * q^53 - 46 * q^54 - 7 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 + 4 * q^59 - 75 * q^60 - 60 * q^61 - 25 * q^62 - 46 * q^63 + 23 * q^64 - 12 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 + 38 * q^69 + 12 * q^70 - 14 * q^71 + 37 * q^72 + 2 * q^73 + 13 * q^74 + 13 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 + 18 * q^79 + 36 * q^80 + 23 * q^81 + 14 * q^82 - 16 * q^83 + 8 * q^84 + 37 * q^85 - 26 * q^86 + 15 * q^87 - 17 * q^88 + q^89 - 23 * q^90 + 8 * q^91 - 64 * q^92 + 17 * q^93 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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