LMFDB - Embedded newform 31.2.g.a.14.1

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			14.1
Root			$-1.14660i$ of defining polynomial
Character	$\chi$	$=$	31.14
Dual form			31.2.g.a.20.1

$q$-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 $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{15}\right)$

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	−0.000184800		1.00000i	$0.500059\pi$
$2$	−0.831304	+	2.55849i	−0.587821	+	1.80913i	−0.587636	+	0.809126i	$0.699941\pi$
$3$	0.949606	−	1.05464i	0.548255	−	0.608899i	−0.403792	−	0.914851i	$-0.632308\pi$
$3$	0.949606	−	1.05464i	0.548255	−	0.608899i	0.952047	+	0.305952i	$0.0989746\pi$
$4$	−4.23677	−	3.07819i	−2.11839	−	1.53910i
$5$	−0.304192	+	0.526876i	−0.136039	+	0.235626i	−0.925994	−	0.377539i	$-0.876770\pi$
$5$	−0.304192	+	0.526876i	−0.136039	+	0.235626i	0.789955	+	0.613165i	$0.210104\pi$
$6$	1.90889	+	3.30629i	0.779300	+	1.34979i
$7$	0.180508	−	1.71742i	0.0682256	−	0.649123i	−0.905958	−	0.423367i	$-0.860848\pi$
$7$	0.180508	−	1.71742i	0.0682256	−	0.649123i	0.974184	−	0.225756i	$-0.0724853\pi$
$8$	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	−0.582572	−	0.812779i	$-0.697954\pi$
$11$	−1.22177	+	0.543967i	−0.368377	+	0.164012i	0.214195	+	0.976791i	$0.431287\pi$
$12$	−7.26966	+	1.54521i	−2.09857	+	0.446065i
$13$	−3.59045	−	0.763174i	−0.995812	−	0.211666i	−0.318946	−	0.947773i	$-0.603329\pi$
$13$	−3.59045	−	0.763174i	−0.995812	−	0.211666i	−0.676866	+	0.736106i	$0.736662\pi$
$14$	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	0.0771534	−	0.997019i	$-0.475417\pi$
$17$	−2.52396	−	1.12374i	−0.612150	−	0.272547i	−0.689304	+	0.724472i	$0.742084\pi$
$18$	−2.59446	−	0.551469i	−0.611520	−	0.129983i
$19$	2.51157	−	0.533850i	0.576193	−	0.122474i	0.0894075	−	0.995995i	$-0.471503\pi$
$19$	2.51157	−	0.533850i	0.576193	−	0.122474i	0.486786	+	0.873522i	$0.338169\pi$
$20$	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	−0.541371	−	0.840784i	$-0.682095\pi$
$23$	0.436271	−	0.316969i	0.0909688	−	0.0660927i	0.632340	+	0.774691i	$0.282095\pi$
$24$	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	0.390419	+	0.920637i	$0.372330\pi$
$29$	−2.51258	+	7.73291i	−0.466574	+	1.43597i	−0.856993	+	0.515329i	$0.827670\pi$
$30$	−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	−0.986167	−	0.165757i	$-0.946993\pi$
$37$	−3.87249	−	6.70735i	−0.636633	−	1.10268i	0.349533	−	0.936924i	$-0.386340\pi$
$38$	−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	0.737684	−	0.675147i	$-0.235920\pi$
$41$	−0.0696243	−	0.0773256i	−0.0108735	−	0.0120762i	−0.748557	+	0.663070i	$0.769253\pi$
$42$	6.02285	−	2.68155i	0.929346	−	0.413772i
$43$	2.93904	−	0.624713i	0.448200	−	0.0952678i	0.0217184	−	0.999764i	$-0.493086\pi$
$43$	2.93904	−	0.624713i	0.448200	−	0.0952678i	0.426481	+	0.904496i	$0.359753\pi$
$44$	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	−0.980370	−	0.197169i	$-0.936825\pi$
$47$	−2.07813	−	6.39584i	−0.303127	−	0.932929i	0.677243	−	0.735760i	$-0.263175\pi$
$48$	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	−0.996068	−	0.0885864i	$-0.971765\pi$
$53$	−0.292549	−	2.78341i	−0.0401846	−	0.382331i	0.955884	−	0.293745i	$-0.0949016\pi$
$54$	−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	−0.722495	−	0.691376i	$-0.757005\pi$
$59$	0.311970	−	0.346478i	0.0406151	−	0.0451076i	0.763110	+	0.646269i	$0.223671\pi$
$60$	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	0.493058	+	0.869996i	$0.335879\pi$
$67$	−4.14923	+	7.18668i	−0.506910	+	0.877993i	−0.999968	+	0.00799701i	$0.997454\pi$
$68$	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	−0.983565	−	0.180556i	$-0.942210\pi$
$71$	−0.497420	−	4.73264i	−0.0590329	−	0.561661i	0.924532	−	0.381105i	$-0.124456\pi$
$72$	5.74497	+	6.38043i	0.677051	+	0.751941i
$73$	6.85725	−	3.05304i	0.802580	−	0.357332i	0.0358953	−	0.999356i	$-0.488572\pi$
$73$	6.85725	−	3.05304i	0.802580	−	0.357332i	0.766685	+	0.642024i	$0.221905\pi$
$74$	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	−0.157577	−	0.987507i	$-0.550368\pi$
$79$	−8.86044	−	3.94492i	−0.996877	−	0.443838i	−0.839300	+	0.543668i	$0.817035\pi$
$80$	−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	−0.911380	−	0.411567i	$-0.864982\pi$
$83$	−11.1642	−	12.3991i	−1.22543	−	1.36097i	−0.314047	−	0.949407i	$-0.601685\pi$
$84$	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	0.999989	+	0.00468333i	$0.00149075\pi$
$89$	12.3911	+	9.00268i	1.31346	+	0.954282i	0.313468	+	0.949599i	$0.398509\pi$
$90$	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	0.639082	−	0.769138i	$-0.279314\pi$
$97$	1.03488	+	0.751881i	0.105076	+	0.0763420i	−0.534007	+	0.845480i	$0.679314\pi$
$98$	−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	−0.864523	−	0.502593i	$-0.832379\pi$
$101$	−6.56941	+	4.77296i	−0.653681	+	0.474927i	0.210842	+	0.977520i	$0.432379\pi$
$102$	−1.10255	−	10.4900i	−0.109168	−	1.03867i
$103$	10.1390	+	11.2605i	0.999026	+	1.10953i	0.993982	+	0.109544i	$0.0349389\pi$
$103$	10.1390	+	11.2605i	0.999026	+	1.10953i	0.00504416	+	0.999987i	$0.498394\pi$
$104$	−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	−0.220543	−	0.975377i	$-0.570783\pi$
$107$	−11.3057	−	5.03362i	−1.09296	−	0.486618i	−0.872419	+	0.488759i	$0.837450\pi$
$108$	−9.15433	−	28.1741i	−0.880876	−	2.71106i
$109$	2.22788	+	6.85672i	0.213392	+	0.656755i	0.999264	+	0.0383645i	$0.0122148\pi$
$109$	2.22788	+	6.85672i	0.213392	+	0.656755i	−0.785871	+	0.618390i	$0.787785\pi$
$110$	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	0.463984	−	0.885844i	$-0.346420\pi$
$113$	15.2304	−	6.78103i	1.43276	−	0.637906i	0.968776	+	0.247938i	$0.0797528\pi$
$114$	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	−0.992425	−	0.122854i	$-0.960795\pi$
$127$	−8.63810	+	9.59358i	−0.766507	+	0.851293i	0.225918	+	0.974146i	$0.427462\pi$
$128$	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	−0.977735	−	0.209846i	$-0.932704\pi$
$131$	0.254818	−	2.42443i	0.0222635	−	0.211823i	0.999998	−	0.00197767i	$-0.000629511\pi$
$132$	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	−0.145360	−	0.989379i	$-0.546434\pi$
$137$	−7.96586	−	1.69320i	−0.680570	−	0.144660i	−0.535210	+	0.844719i	$0.679767\pi$
$138$	1.88078	+	0.837379i	0.160103	+	0.0712824i
$139$	−0.418212	−	1.28712i	−0.0354723	−	0.109172i	0.931753	−	0.363094i	$-0.118280\pi$
$139$	−0.418212	−	1.28712i	−0.0354723	−	0.109172i	−0.967225	+	0.253921i	$0.918280\pi$
$140$	−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	0.989380	−	0.145351i	$-0.0464313\pi$
$149$	4.50192	+	7.79756i	0.368812	+	0.638801i	−0.620568	+	0.784153i	$0.713098\pi$
$150$	−8.83789	+	15.3077i	−0.721611	+	1.24987i
$151$	2.59566	+	1.88585i	0.211232	+	0.153469i	0.688371	−	0.725359i	$-0.258326\pi$
$151$	2.59566	+	1.88585i	0.211232	+	0.153469i	−0.477139	+	0.878828i	$0.658326\pi$
$152$	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	−0.983662	−	0.180027i	$-0.942382\pi$
$157$	−1.02803	+	3.16395i	−0.0820456	+	0.252510i	0.901616	+	0.432537i	$0.142382\pi$
$158$	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	−0.641559	−	0.767074i	$-0.721712\pi$
$163$	−1.40797	+	1.02295i	−0.110281	+	0.0801236i	0.531278	+	0.847198i	$0.321712\pi$
$164$	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	0.355780	−	0.934570i	$-0.384215\pi$
$167$	13.7102	−	2.91419i	1.06093	−	0.225507i	0.705145	+	0.709063i	$0.250882\pi$
$168$	−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	0.208357	−	0.978053i	$-0.433188\pi$
$173$	0.0117191	+	0.00249097i	0.000890985	+	0.000189385i	−0.207466	+	0.978242i	$0.566522\pi$
$174$	−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	−0.883812	−	0.467842i	$-0.845032\pi$
$179$	1.04299	−	9.92334i	0.0779564	−	0.741706i	0.961769	−	0.273864i	$-0.0883017\pi$
$180$	1.57069	+	2.72051i	0.117072	+	0.202775i
$181$	9.30158	−	16.1108i	0.691381	−	1.19751i	−0.280004	−	0.959999i	$-0.590336\pi$
$181$	9.30158	−	16.1108i	0.691381	−	1.19751i	0.971385	−	0.237509i	$-0.0763308\pi$
$182$	−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	−0.886885	−	0.461991i	$-0.847135\pi$
$191$	−0.599059	+	1.03760i	−0.0433464	+	0.0750782i	0.843538	+	0.537069i	$0.180469\pi$
$192$	−14.8841	−	25.7800i	−1.07417	−	1.86051i
$193$	−1.33029	+	12.6568i	−0.0957562	+	0.911059i	0.836184	+	0.548448i	$0.184781\pi$
$193$	−1.33029	+	12.6568i	−0.0957562	+	0.911059i	−0.931941	+	0.362611i	$0.881885\pi$
$194$	−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	−0.501065	−	0.865410i	$-0.667058\pi$
$197$	−2.71195	+	1.20744i	−0.193218	+	0.0860263i	0.307847	+	0.951436i	$0.400392\pi$
$198$	3.46981	−	0.737531i	0.246589	−	0.0524140i
$199$	12.8960	+	2.74112i	0.914170	+	0.194313i	0.640900	−	0.767625i	$-0.278561\pi$
$199$	12.8960	+	2.74112i	0.914170	+	0.194313i	0.273270	+	0.961937i	$0.411895\pi$
$200$	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	−0.987343	−	0.158600i	$-0.949302\pi$
$211$	−9.16614	−	15.8762i	−0.631023	−	1.09296i	0.356320	−	0.934364i	$-0.384031\pi$
$212$	−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	0.664751	−	0.747065i	$-0.268538\pi$
$223$	−4.69801	−	8.13718i	−0.314602	−	0.544906i	−0.979353	+	0.202159i	$0.935204\pi$
$224$	−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	0.901108	−	0.433594i	$-0.142755\pi$
$227$	5.66046	+	6.28658i	0.375698	+	0.417255i	−0.525410	+	0.850849i	$0.676088\pi$
$228$	−17.4333	+	7.76182i	−1.15455	+	0.514039i
$229$	−22.3443	+	4.74942i	−1.47655	+	0.313850i	−0.874663	−	0.484731i	$-0.838917\pi$
$229$	−22.3443	+	4.74942i	−1.47655	+	0.313850i	−0.601887	+	0.798582i	$0.705584\pi$
$230$	−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	0.969583	+	0.244762i	$0.0787099\pi$
$233$	5.02260	+	15.4580i	0.329042	+	1.01269i	−0.640542	+	0.767923i	$0.721290\pi$
$234$	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	−0.864035	−	0.503433i	$-0.832070\pi$
$239$	−1.91005	−	18.1729i	−0.123551	−	1.17551i	0.740484	−	0.672074i	$-0.234596\pi$
$240$	−9.04675	+	6.57285i	−0.583965	+	0.424275i
$241$	1.89944	−	18.0720i	0.122354	−	1.16412i	−0.745222	−	0.666816i	$-0.767657\pi$
$241$	1.89944	−	18.0720i	0.122354	−	1.16412i	0.867576	−	0.497304i	$-0.165677\pi$
$242$	−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	0.0286471	+	0.999590i	$0.490880\pi$
$251$	−15.3433	+	17.0405i	−0.968461	+	1.07558i	−0.997108	+	0.0759953i	$0.975787\pi$
$252$	−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	0.994170	−	0.107822i	$-0.0343876\pi$
$257$	−0.0111002	−	0.105611i	−0.000692411	−	0.00658785i	−0.994863	+	0.101234i	$0.967721\pi$
$258$	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	0.857149	−	0.515068i	$-0.172234\pi$
$263$	−2.25499	−	6.94015i	−0.139049	−	0.427948i	−0.996198	+	0.0871204i	$0.972234\pi$
$264$	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	0.976799	−	0.214158i	$-0.0687007\pi$
$269$	10.8529	+	12.0533i	0.661711	+	0.734905i	−0.315088	+	0.949063i	$0.602034\pi$
$270$	−0.967735	−	9.20739i	−0.0588945	−	0.560344i
$271$	4.16291	−	3.02453i	0.252879	−	0.183727i	−0.454123	−	0.890939i	$-0.650047\pi$
$271$	4.16291	−	3.02453i	0.252879	−	0.183727i	0.707002	+	0.707212i	$0.250047\pi$
$272$	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	0.661873	+	0.749616i	$0.269762\pi$
$277$	−5.22944	+	16.0946i	−0.314207	+	0.967029i	−0.976080	+	0.217413i	$0.930238\pi$
$278$	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	−0.931943	−	0.362605i	$-0.881888\pi$
$281$	0.589193	−	1.81335i	0.0351483	−	0.108175i	0.967091	+	0.254429i	$0.0818876\pi$
$282$	17.1796	−	19.0798i	1.02303	−	1.13619i
$283$	12.3859	+	8.99888i	0.736265	+	0.534928i	0.891539	−	0.452944i	$-0.149626\pi$
$283$	12.3859	+	8.99888i	0.736265	+	0.534928i	−0.155274	+	0.987871i	$0.549626\pi$
$284$	−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	0.968165	−	0.250313i	$-0.0805334\pi$
$293$	24.4772	+	10.8980i	1.42998	+	0.636666i	0.461810	+	0.886979i	$0.347200\pi$
$294$	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	−0.547570	−	0.836760i	$-0.684447\pi$
$307$	5.98956	−	6.65208i	0.341842	−	0.379654i	0.889413	+	0.457105i	$0.151114\pi$
$308$	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	−0.734550	−	0.678555i	$-0.762606\pi$
$313$	0.301993	−	0.335397i	0.0170696	−	0.0189577i	0.751619	+	0.659597i	$0.229273\pi$
$314$	−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	−0.965849	−	0.259104i	$-0.916573\pi$
$317$	0.583357	−	5.55027i	0.0327646	−	0.311734i	0.998614	−	0.0526304i	$-0.0167605\pi$
$318$	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	0.999986	−	0.00524168i	$-0.00166849\pi$
$331$	16.1966	+	17.9882i	0.890246	+	0.988719i	−0.109740	+	0.993960i	$0.535002\pi$
$332$	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	0.317426	−	0.948283i	$-0.397182\pi$
$337$	−8.92830	−	6.48679i	−0.486355	−	0.353358i	−0.803781	+	0.594925i	$0.797182\pi$
$338$	−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	0.999998	−	0.00187589i	$-0.000597114\pi$
$347$	9.28369	+	16.0798i	0.498375	+	0.863210i	−0.501624	+	0.865086i	$0.667264\pi$
$348$	6.31657	−	60.0982i	0.338604	−	3.22160i
$349$	26.0298	−	18.9118i	1.39334	−	1.01232i	0.397855	−	0.917448i	$-0.369755\pi$
$349$	26.0298	−	18.9118i	1.39334	−	1.01232i	0.995489	−	0.0948756i	$-0.0302453\pi$
$350$	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	−0.945585	−	0.325375i	$-0.894510\pi$
$353$	−31.5094	+	6.69754i	−1.67708	+	0.356474i	−0.731493	+	0.681849i	$0.761176\pi$
$354$	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	−0.373777	−	0.927519i	$-0.621937\pi$
$359$	−20.6998	−	4.39988i	−1.09249	−	0.232217i	−0.718718	+	0.695302i	$0.755271\pi$
$360$	−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	−0.984283	−	0.176597i	$-0.943491\pi$
$367$	−6.49822	+	11.2552i	−0.339204	+	0.587519i	0.645079	+	0.764116i	$0.276824\pi$
$368$	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	−0.878078	−	0.478518i	$-0.841174\pi$
$379$	1.56330	−	14.8738i	0.0803013	−	0.764016i	0.958379	−	0.285498i	$-0.0921591\pi$
$380$	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	−0.660220	−	0.751072i	$-0.729537\pi$
$383$	−10.6431	+	4.73862i	−0.543838	+	0.242132i	0.116382	+	0.993205i	$0.462870\pi$
$384$	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	0.712197	−	0.701980i	$-0.247700\pi$
$389$	13.1568	+	5.85779i	0.667077	+	0.297002i	−0.0451198	+	0.998982i	$0.514367\pi$
$390$	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	0.597017	−	0.802229i	$-0.296352\pi$
$397$	−7.89506	−	13.6746i	−0.396242	−	0.686311i	−0.993259	+	0.115918i	$0.963019\pi$
$398$	−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	−0.362114	−	0.932134i	$-0.617945\pi$
$401$	9.58670	−	29.5048i	0.478737	−	1.47340i	0.840851	−	0.541267i	$-0.182055\pi$
$402$	−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	0.773056	−	0.634337i	$-0.218727\pi$
$409$	−3.29291	−	5.70349i	−0.162824	−	0.282019i	−0.935880	+	0.352318i	$0.885394\pi$
$410$	−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	−0.998628	−	0.0523559i	$-0.983327\pi$
$419$	−4.53389	−	13.9539i	−0.221495	−	0.681692i	0.777133	−	0.629336i	$-0.216673\pi$
$420$	−7.13312	−	3.17587i	−0.348061	−	0.154967i
$421$	26.1321	+	5.55454i	1.27360	+	0.270712i	0.794616	−	0.607112i	$-0.207672\pi$
$421$	26.1321	+	5.55454i	1.27360	+	0.270712i	0.478983	+	0.877824i	$0.341006\pi$
$422$	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	−0.675441	−	0.737414i	$-0.736046\pi$
$431$	2.66850	−	2.96367i	0.128537	−	0.142755i	0.803978	+	0.594660i	$0.202713\pi$
$432$	−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	0.451815	+	0.892112i	$0.350777\pi$
$439$	−11.4543	+	19.8394i	−0.546684	+	0.946884i	−0.998499	+	0.0547723i	$0.982557\pi$
$440$	−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	0.908509	+	0.417866i	$0.137222\pi$
$443$	2.24645	+	21.3736i	0.106732	+	1.01549i	−0.801777	+	0.597624i	$0.796112\pi$
$444$	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	0.989440	+	0.144945i	$0.0463005\pi$
$449$	5.80940	+	17.8795i	0.274163	+	0.843786i	−0.715277	+	0.698841i	$0.753700\pi$
$450$	−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	−0.662763	−	0.748830i	$-0.730616\pi$
$457$	−3.32182	+	2.41344i	−0.155388	+	0.112896i	0.507374	+	0.861726i	$0.330616\pi$
$458$	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	0.928408	−	0.371563i	$-0.121178\pi$
$461$	18.5063	+	13.4456i	0.861924	+	0.626225i	−0.0664836	+	0.997788i	$0.521178\pi$
$462$	−5.89986	+	6.55246i	−0.274486	+	0.304848i
$463$	−5.11947	+	15.7561i	−0.237922	+	0.732249i	0.758798	+	0.651326i	$0.225787\pi$
$463$	−5.11947	+	15.7561i	−0.237922	+	0.732249i	−0.996720	+	0.0809233i	$0.974213\pi$
$464$	−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	−0.174379	−	0.984679i	$-0.555792\pi$
$467$	11.7878	−	36.2792i	0.545476	−	1.67880i	0.719855	−	0.694124i	$-0.244208\pi$
$468$	−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	−0.443279	−	0.896383i	$-0.646185\pi$
$479$	−30.7726	−	13.7008i	−1.40603	−	0.626007i	−0.962755	+	0.270377i	$0.912852\pi$
$480$	−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	0.927606	+	0.373560i	$0.121863\pi$
$487$	2.16130	+	20.5634i	0.0979379	+	0.931817i	−0.829668	+	0.558257i	$0.811470\pi$
$488$	−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	0.439570	+	0.898209i	$0.355131\pi$
$491$	−12.3664	+	21.4192i	−0.558087	+	0.966634i	−0.997656	+	0.0684258i	$0.978202\pi$
$492$	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	−0.988622	−	0.150422i	$-0.951937\pi$
$499$	−16.4340	+	18.2518i	−0.735685	+	0.817061i	0.252937	+	0.967483i	$0.418604\pi$
$500$	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	0.904951	+	0.425517i	$0.139908\pi$
$503$	−1.54066	+	14.6584i	−0.0686946	+	0.653585i	−0.973645	+	0.228068i	$0.926759\pi$
$504$	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	−0.140893	−	0.990025i	$-0.544997\pi$
$509$	−15.1674	−	3.22394i	−0.672285	−	0.142899i	−0.531392	+	0.847126i	$0.678331\pi$
$510$	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	−0.984454	−	0.175642i	$-0.943800\pi$
$521$	−14.7073	−	25.4738i	−0.644337	−	1.11603i	0.340117	−	0.940383i	$-0.389533\pi$
$522$	10.7832	−	18.6771i	0.471970	−	0.817475i
$523$	−36.4268	−	26.4656i	−1.59283	−	1.15726i	−0.899754	−	0.436397i	$-0.856254\pi$
$523$	−36.4268	−	26.4656i	−1.59283	−	1.15726i	−0.693078	−	0.720863i	$-0.743746\pi$
$524$	−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	0.979234	−	0.202731i	$-0.0649818\pi$
$541$	34.5126	+	15.3660i	1.48381	+	0.660635i	0.504577	+	0.863367i	$0.331648\pi$
$542$	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	−0.730274	−	0.683154i	$-0.760608\pi$
$547$	−16.6345	+	7.40617i	−0.711241	+	0.316665i	0.0190333	+	0.999819i	$0.493941\pi$
$548$	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	−0.179790	−	0.983705i	$-0.557542\pi$
$563$	18.0809	−	31.3170i	0.762019	−	1.31986i	0.941808	−	0.336150i	$-0.109125\pi$
$564$	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	0.594047	−	0.804430i	$-0.297529\pi$
$569$	37.9119	−	16.8795i	1.58935	−	0.707624i	0.995303	+	0.0968056i	$0.0308625\pi$
$570$	−5.83354	+	1.23996i	−0.244340	+	0.0519361i
$571$	31.6853	+	6.73491i	1.32599	+	0.281847i	0.815859	−	0.578251i	$-0.196265\pi$
$571$	31.6853	+	6.73491i	1.32599	+	0.281847i	0.510128	+	0.860099i	$0.329598\pi$
$572$	−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	−0.942911	−	0.333044i	$-0.891924\pi$
$577$	−40.0870	+	8.52075i	−1.66884	+	0.354723i	−0.725931	+	0.687768i	$0.758591\pi$
$578$	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	−0.645511	−	0.763751i	$-0.723356\pi$
$587$	7.88963	−	24.2818i	0.325640	−	1.00222i	0.971151	−	0.238466i	$-0.0766445\pi$
$588$	−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	−0.977734	−	0.209850i	$-0.932702\pi$
$593$	−36.0269	−	26.1751i	−1.47945	−	1.07488i	−0.501716	−	0.865033i	$-0.667298\pi$
$594$	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	0.944460	−	0.328627i	$-0.106586\pi$
$599$	12.7001	+	14.1049i	0.518911	+	0.576309i	−0.425549	+	0.904935i	$0.639919\pi$
$600$	52.2689	−	23.2716i	2.13387	−	0.950059i
$601$	12.5592	−	2.66955i	0.512301	−	0.108893i	0.0554947	−	0.998459i	$-0.482326\pi$
$601$	12.5592	−	2.66955i	0.512301	−	0.108893i	0.456807	+	0.889566i	$0.348993\pi$
$602$	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	0.888742	−	0.458407i	$-0.151580\pi$
$607$	37.3059	+	7.92960i	1.51420	+	0.321853i	0.625456	+	0.780260i	$0.284913\pi$
$608$	−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	−0.883022	−	0.469332i	$-0.844495\pi$
$613$	1.93821	−	18.4408i	0.0782834	−	0.744817i	0.961305	−	0.275485i	$-0.0888385\pi$
$614$	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	−0.623534	−	0.781796i	$-0.714304\pi$
$617$	5.44374	−	6.04589i	0.219157	−	0.243398i	0.842691	+	0.538398i	$0.180970\pi$
$618$	−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	0.196324	−	0.980539i	$-0.437100\pi$
$631$	26.5358	−	11.8145i	1.05637	−	0.470327i	0.860049	+	0.510212i	$0.170433\pi$
$632$	−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	0.258200	−	0.966092i	$-0.416871\pi$
$641$	−18.4717	−	20.5149i	−0.729589	−	0.810290i	−0.987788	+	0.155801i	$0.950204\pi$
$642$	−4.93868	−	46.9884i	−0.194914	−	1.85449i
$643$	3.42136	−	2.48577i	0.134925	−	0.0980291i	−0.518275	−	0.855214i	$-0.673426\pi$
$643$	3.42136	−	2.48577i	0.134925	−	0.0980291i	0.653201	+	0.757185i	$0.273426\pi$
$644$	−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	0.921217	−	0.389048i	$-0.127196\pi$
$647$	21.2617	+	15.4475i	0.835883	+	0.607304i	−0.0853349	+	0.996352i	$0.527196\pi$
$648$	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	−0.998758	−	0.0498246i	$-0.984134\pi$
$653$	−4.12592	+	12.6983i	−0.161460	+	0.496922i	0.837298	+	0.546746i	$0.184134\pi$
$654$	−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	−0.317750	−	0.948174i	$-0.602927\pi$
$659$	12.4717	−	9.06119i	0.485827	−	0.352974i	0.803577	+	0.595200i	$0.202927\pi$
$660$	0.632093	+	6.01396i	0.0246042	+	0.234093i
$661$	−3.16035	−	3.50992i	−0.122923	−	0.136520i	0.678542	−	0.734562i	$-0.262612\pi$
$661$	−3.16035	−	3.50992i	−0.122923	−	0.136520i	−0.801465	+	0.598042i	$0.795946\pi$
$662$	−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	0.859046	+	0.511898i	$0.171057\pi$
$673$	3.24801	+	30.9028i	0.125202	+	1.19121i	−0.733845	+	0.679317i	$0.762276\pi$
$674$	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	−0.766000	−	0.642841i	$-0.777756\pi$
$677$	4.51998	−	7.82883i	0.173717	−	0.300886i	0.939716	+	0.341955i	$0.111089\pi$
$678$	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	−0.788749	−	0.614716i	$-0.789271\pi$
$691$	−3.81272	−	36.2756i	−0.145043	−	1.37999i	0.643706	−	0.765273i	$-0.277396\pi$
$692$	−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	−0.177993	−	0.984032i	$-0.556960\pi$
$701$	1.57916	−	0.335661i	0.0596441	−	0.0126777i	0.237637	+	0.971354i	$0.423627\pi$
$702$	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	0.399425	−	0.916766i	$-0.369210\pi$
$709$	−9.29395	−	6.75245i	−0.349042	−	0.253594i	−0.748467	+	0.663172i	$0.769210\pi$
$710$	−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	0.967365	−	0.253386i	$-0.0815441\pi$
$719$	7.08549	+	12.2724i	0.264244	+	0.457685i	−0.703121	+	0.711070i	$0.748211\pi$
$720$	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	−0.104205	−	0.994556i	$-0.533230\pi$
$727$	−24.6180	−	10.9606i	−0.913030	−	0.406507i	−0.808826	+	0.588049i	$0.799896\pi$
$728$	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	−0.825735	−	0.564058i	$-0.809239\pi$
$733$	−25.9662	+	11.5609i	−0.959083	+	0.427011i	−0.133348	+	0.991069i	$0.542573\pi$
$734$	−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	−0.859541	−	0.511066i	$-0.829251\pi$
$739$	0.348653	−	0.603885i	0.0128254	−	0.0222143i	0.872367	+	0.488852i	$0.162584\pi$
$740$	−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	−0.661920	−	0.749574i	$-0.730258\pi$
$751$	3.87445	−	36.8629i	0.141381	−	1.34515i	0.803301	−	0.595573i	$-0.203075\pi$
$752$	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	0.0926997	−	0.995694i	$-0.470450\pi$
$757$	−6.26211	−	1.33105i	−0.227600	−	0.0483779i	−0.320300	+	0.947316i	$0.603784\pi$
$758$	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	0.0217552	−	0.999763i	$-0.493075\pi$
$761$	−19.4940	−	8.67928i	−0.706657	−	0.314624i	−0.728412	+	0.685140i	$0.759741\pi$
$762$	−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	0.955109	−	0.296254i	$-0.0957374\pi$
$769$	6.12828	+	10.6145i	0.220991	+	0.382768i	−0.734118	+	0.679022i	$0.762404\pi$
$770$	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	0.550247	+	0.835002i	$0.314534\pi$
$773$	−10.7240	+	33.0050i	−0.385714	+	1.18711i	−0.935961	+	0.352104i	$0.885466\pi$
$774$	−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	0.156646	−	0.987655i	$-0.449932\pi$
$787$	19.6786	−	4.18281i	0.701465	−	0.149101i	0.544819	+	0.838554i	$0.316598\pi$
$788$	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	−0.929459	−	0.368926i	$-0.879725\pi$
$797$	−2.73885	−	26.0584i	−0.0970150	−	0.923036i	0.832444	−	0.554110i	$-0.186941\pi$
$798$	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	−0.141791	−	0.989897i	$-0.545286\pi$
$809$	24.3899	−	27.0877i	0.857504	−	0.952354i	0.999295	+	0.0375423i	$0.0119529\pi$
$810$	−6.71298	−	4.87727i	−0.235870	−	0.171370i
$811$	9.55322	−	16.5467i	0.335459	−	0.581032i	−0.648114	−	0.761543i	$-0.724442\pi$
$811$	9.55322	−	16.5467i	0.335459	−	0.581032i	0.983573	+	0.180511i	$0.0577753\pi$
$812$	−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	0.902453	+	0.430789i	$0.141765\pi$
$821$	12.1937	+	37.5285i	0.425565	+	1.30975i	−0.476888	+	0.878964i	$0.658235\pi$
$822$	−9.60773	−	29.5696i	−0.335108	−	1.03136i
$823$	−28.8571	−	12.8480i	−1.00589	−	0.447853i	−0.163401	−	0.986560i	$-0.552246\pi$
$823$	−28.8571	−	12.8480i	−1.00589	−	0.447853i	−0.842493	+	0.538707i	$0.818913\pi$
$824$	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	0.928279	−	0.371885i	$-0.121288\pi$
$827$	13.2688	+	14.7364i	0.461400	+	0.512436i	−0.466879	+	0.884321i	$0.654622\pi$
$828$	−0.291055	−	2.76921i	−0.0101149	−	0.0962366i
$829$	−7.28104	+	5.28999i	−0.252881	+	0.183729i	−0.707003	−	0.707211i	$-0.749953\pi$
$829$	−7.28104	+	5.28999i	−0.252881	+	0.183729i	0.454122	+	0.890940i	$0.349953\pi$
$830$	−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	0.624602	+	0.780944i	$0.285261\pi$
$839$	−9.84070	+	30.2866i	−0.339739	+	1.04561i	−0.964340	+	0.264665i	$0.914739\pi$
$840$	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	−0.775099	−	0.631839i	$-0.782300\pi$
$853$	−15.1702	−	46.6890i	−0.519417	−	1.59860i	0.255683	−	0.966761i	$-0.417700\pi$
$854$	−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	−0.0839371	−	0.996471i	$-0.526749\pi$
$857$	17.5770	−	7.82580i	0.600420	−	0.267324i	0.684357	+	0.729147i	$0.260083\pi$
$858$	12.5408	+	13.9279i	0.428135	+	0.475492i
$859$	−0.485236	−	4.61672i	−0.0165561	−	0.157520i	0.983120	−	0.182960i	$-0.0585680\pi$
$859$	−0.485236	−	4.61672i	−0.0165561	−	0.157520i	−0.999676	+	0.0254400i	$0.991901\pi$
$860$	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	−0.325899	−	0.945405i	$-0.605667\pi$
$863$	19.2652	−	33.3683i	0.655795	−	1.13587i	0.981694	−	0.190466i	$-0.0609999\pi$
$864$	−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	0.998636	+	0.0522162i	$0.0166285\pi$
$877$	0.967760	+	9.20763i	0.0326789	+	0.310919i	−0.965957	+	0.258703i	$0.916705\pi$
$878$	−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	0.492857	−	0.870110i	$-0.335953\pi$
$881$	17.4884	+	3.71727i	0.589198	+	0.125238i	0.0963414	+	0.995348i	$0.469286\pi$
$882$	−9.73577	−	4.33465i	−0.327821	−	0.145955i
$883$	−14.9303	−	45.9509i	−0.502446	−	1.54637i	−0.805022	−	0.593244i	$-0.797847\pi$
$883$	−14.9303	−	45.9509i	−0.502446	−	1.54637i	0.302577	−	0.953125i	$-0.402153\pi$
$884$	−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	−0.577134	−	0.816649i	$-0.695829\pi$
$887$	−22.9984	+	4.88847i	−0.772211	+	0.164139i	−0.195077	+	0.980788i	$0.562496\pi$
$888$	−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	−0.405821	−	0.913952i	$-0.633014\pi$
$907$	10.1792	−	7.39560i	0.337994	−	0.245567i	0.743815	+	0.668386i	$0.233014\pi$
$908$	−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	0.636939	−	0.770914i	$-0.280200\pi$
$911$	46.2512	−	9.83100i	1.53237	−	0.325715i	0.895432	+	0.445199i	$0.146867\pi$
$912$	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	−0.724511	−	0.689263i	$-0.757934\pi$
$919$	−21.1320	+	9.40858i	−0.697081	+	0.310360i	0.0274300	+	0.999624i	$0.491268\pi$
$920$	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	0.907797	+	0.419409i	$0.137763\pi$
$937$	−2.06200	+	19.6186i	−0.0673625	+	0.640911i	−0.975160	+	0.221502i	$0.928904\pi$
$938$	−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	−0.533890	−	0.845554i	$-0.679270\pi$
$941$	−8.06045	+	3.58874i	−0.262763	+	0.116990i	0.271127	+	0.962544i	$0.412604\pi$
$942$	−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	0.624498	−	0.781026i	$-0.285304\pi$
$947$	14.2158	+	6.32930i	0.461953	+	0.205675i	−0.162545	+	0.986701i	$0.551970\pi$
$948$	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	−0.707028	−	0.707185i	$-0.749965\pi$
$953$	−7.80840	+	5.67314i	−0.252939	+	0.183771i	0.454089	+	0.890956i	$0.349965\pi$
$954$	−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	0.542177	−	0.840264i	$-0.317600\pi$
$967$	−14.1988	−	24.5930i	−0.456602	−	0.790858i	−0.998779	+	0.0494066i	$0.984267\pi$
$968$	−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	0.457156	−	0.889386i	$-0.348868\pi$
$971$	−14.8059	−	16.4436i	−0.475144	−	0.527701i	−0.932300	+	0.361686i	$0.882201\pi$
$972$	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	−0.999950	−	0.0100140i	$-0.996812\pi$
$977$	−6.15324	−	18.9377i	−0.196859	−	0.605871i	0.803090	−	0.595857i	$-0.203188\pi$
$978$	−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	0.954100	+	0.299488i	$0.0968158\pi$
$983$	2.60593	+	24.7938i	0.0831164	+	0.790800i	−0.870984	+	0.491312i	$0.836518\pi$
$984$	−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	−0.957527	−	0.288344i	$-0.906895\pi$
$997$	−7.23233	+	12.5268i	−0.229050	+	0.396727i	0.728477	+	0.685071i	$0.240229\pi$
$998$	−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.14.1	✓	16
3.2	odd	2		279.2.y.c.262.2		16
4.3	odd	2		496.2.bg.c.417.1		16
5.2	odd	4		775.2.ck.a.324.1		32
5.3	odd	4		775.2.ck.a.324.4		32
5.4	even	2		775.2.bl.a.76.2		16
31.2	even	5		961.2.c.j.521.1		16
31.3	odd	30		961.2.d.q.374.4		16
31.4	even	5		961.2.g.k.844.1		16
31.5	even	3		961.2.g.k.846.1		16
31.6	odd	6		961.2.d.n.628.1		16
31.7	even	15		961.2.d.o.531.1		16
31.8	even	5		961.2.g.t.338.2		16
31.9	even	15		961.2.g.s.235.2		16
31.10	even	15		961.2.c.j.439.1		16
31.11	odd	30		961.2.g.l.547.1		16
31.12	odd	30		961.2.a.j.1.1		8
31.13	odd	30		961.2.g.n.816.2		16
31.14	even	15		961.2.d.p.388.4		16
31.15	odd	10		961.2.g.m.732.2		16
31.16	even	5		961.2.g.s.732.2		16
31.17	odd	30		961.2.d.q.388.4		16
31.18	even	15		961.2.g.t.816.2		16
31.19	even	15		961.2.a.i.1.1		8
31.20	even	15	inner	31.2.g.a.20.1	yes	16
31.21	odd	30		961.2.c.i.439.1		16
31.22	odd	30		961.2.g.m.235.2		16
31.23	odd	10		961.2.g.n.338.2		16
31.24	odd	30		961.2.d.n.531.1		16
31.25	even	3		961.2.d.o.628.1		16
31.26	odd	6		961.2.g.j.846.1		16
31.27	odd	10		961.2.g.j.844.1		16
31.28	even	15		961.2.d.p.374.4		16
31.29	odd	10		961.2.c.i.521.1		16
31.30	odd	2		961.2.g.l.448.1		16
93.20	odd	30		279.2.y.c.82.2		16
93.50	odd	30		8649.2.a.bf.1.8		8
93.74	even	30		8649.2.a.be.1.8		8
124.51	odd	30		496.2.bg.c.113.1		16
155.82	odd	60		775.2.ck.a.299.4		32
155.113	odd	60		775.2.ck.a.299.1		32
155.144	even	30		775.2.bl.a.51.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.1	✓	16	1.1	even	1	trivial
31.2.g.a.20.1	yes	16	31.20	even	15	inner
279.2.y.c.82.2		16	93.20	odd	30
279.2.y.c.262.2		16	3.2	odd	2
496.2.bg.c.113.1		16	124.51	odd	30
496.2.bg.c.417.1		16	4.3	odd	2
775.2.bl.a.51.2		16	155.144	even	30
775.2.bl.a.76.2		16	5.4	even	2
775.2.ck.a.299.1		32	155.113	odd	60
775.2.ck.a.299.4		32	155.82	odd	60
775.2.ck.a.324.1		32	5.2	odd	4
775.2.ck.a.324.4		32	5.3	odd	4
961.2.a.i.1.1		8	31.19	even	15
961.2.a.j.1.1		8	31.12	odd	30
961.2.c.i.439.1		16	31.21	odd	30
961.2.c.i.521.1		16	31.29	odd	10
961.2.c.j.439.1		16	31.10	even	15
961.2.c.j.521.1		16	31.2	even	5
961.2.d.n.531.1		16	31.24	odd	30
961.2.d.n.628.1		16	31.6	odd	6
961.2.d.o.531.1		16	31.7	even	15
961.2.d.o.628.1		16	31.25	even	3
961.2.d.p.374.4		16	31.28	even	15
961.2.d.p.388.4		16	31.14	even	15
961.2.d.q.374.4		16	31.3	odd	30
961.2.d.q.388.4		16	31.17	odd	30
961.2.g.j.844.1		16	31.27	odd	10
961.2.g.j.846.1		16	31.26	odd	6
961.2.g.k.844.1		16	31.4	even	5
961.2.g.k.846.1		16	31.5	even	3
961.2.g.l.448.1		16	31.30	odd	2
961.2.g.l.547.1		16	31.11	odd	30
961.2.g.m.235.2		16	31.22	odd	30
961.2.g.m.732.2		16	31.15	odd	10
961.2.g.n.338.2		16	31.23	odd	10
961.2.g.n.816.2		16	31.13	odd	30
961.2.g.s.235.2		16	31.9	even	15
961.2.g.s.732.2		16	31.16	even	5
961.2.g.t.338.2		16	31.8	even	5
961.2.g.t.816.2		16	31.18	even	15
8649.2.a.be.1.8		8	93.74	even	30
8649.2.a.bf.1.8		8	93.50	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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