LMFDB - Embedded newform 370.2.o.a.201.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 21 x^{16} - 20 x^{15} + 180 x^{14} - 126 x^{13} + 1002 x^{12} - 270 x^{11} + \cdots + 81 $ x^18 - 3x^17 + 21x^16 - 20x^15 + 180x^14 - 126x^13 + 1002x^12 - 270x^11 + 3294x^10 - 1172x^9 + 6585x^8 - 1464x^7 + 8092x^6 - 2088x^5 + 5598x^4 + 180x^3 + 972x^2 - 162*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			201.3
Root			$0.620701 - 1.07509i$ of defining polynomial
Character	$\chi$	$=$	370.201
Dual form			370.2.o.a.81.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(2.25600 - 0.821116i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.173648 - 0.984808i) q^{5} -2.40078 q^{6} +(0.201324 - 1.14177i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.11716 - 1.77651i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(2.25600 - 0.821116i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.173648 - 0.984808i) q^{5} -2.40078 q^{6} +(0.201324 - 1.14177i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.11716 - 1.77651i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.27810 - 3.94578i) q^{11} +(2.25600 + 0.821116i) q^{12} +(0.690926 + 0.579755i) q^{13} +(-0.579690 + 1.00405i) q^{14} +(-0.416892 - 2.36431i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-0.622093 + 0.521998i) q^{17} +(-2.59709 + 0.945262i) q^{18} +(5.58610 - 2.03317i) q^{19} +(0.766044 - 0.642788i) q^{20} +(-0.483336 - 2.74114i) q^{21} +(0.791174 + 4.48697i) q^{22} +(-1.45985 + 2.52853i) q^{23} +(-1.83911 - 1.54319i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(-0.450970 - 0.781102i) q^{26} +(-0.283578 + 0.491171i) q^{27} +(0.888137 - 0.745236i) q^{28} +(3.06163 + 5.30289i) q^{29} +(-0.416892 + 2.36431i) q^{30} +1.34327 q^{31} +(0.173648 - 0.984808i) q^{32} +(-8.37932 - 7.03109i) q^{33} +(0.763110 - 0.277749i) q^{34} +(-1.08946 - 0.396532i) q^{35} +2.76376 q^{36} +(4.64115 + 3.93188i) q^{37} -5.94460 q^{38} +(2.03477 + 0.740597i) q^{39} +(-0.939693 + 0.342020i) q^{40} +(-3.23604 - 2.71536i) q^{41} +(-0.483336 + 2.74114i) q^{42} -6.60514 q^{43} +(0.791174 - 4.48697i) q^{44} +(-1.38188 - 2.39349i) q^{45} +(2.23661 - 1.87674i) q^{46} +(2.37481 - 4.11328i) q^{47} +(1.20039 + 2.07914i) q^{48} +(5.31475 + 1.93441i) q^{49} +(0.766044 + 0.642788i) q^{50} +(-0.974820 + 1.68844i) q^{51} +(0.156620 + 0.888237i) q^{52} +(-0.718172 - 4.07296i) q^{53} +(0.434466 - 0.364560i) q^{54} +(-4.28142 + 1.55831i) q^{55} +(-1.08946 + 0.396532i) q^{56} +(10.9328 - 9.17368i) q^{57} +(-1.06329 - 6.03022i) q^{58} +(-0.0686079 - 0.389095i) q^{59} +(1.20039 - 2.07914i) q^{60} +(1.73526 + 1.45605i) q^{61} +(-1.26226 - 0.459424i) q^{62} +(-1.60213 - 2.77497i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.690926 - 0.579755i) q^{65} +(5.46922 + 9.47296i) q^{66} +(-1.34403 + 7.62238i) q^{67} -0.812085 q^{68} +(-1.21720 + 6.90306i) q^{69} +(0.888137 + 0.745236i) q^{70} +(7.78047 - 2.83186i) q^{71} +(-2.59709 - 0.945262i) q^{72} -8.59898 q^{73} +(-3.01647 - 5.28213i) q^{74} -2.40078 q^{75} +(5.58610 + 2.03317i) q^{76} +(-4.96380 + 1.80667i) q^{77} +(-1.65876 - 1.39187i) q^{78} +(-0.991412 + 5.62258i) q^{79} +1.00000 q^{80} +(-1.67621 + 9.50626i) q^{81} +(2.11218 + 3.65840i) q^{82} +(-5.50607 + 4.62014i) q^{83} +(1.39171 - 2.41052i) q^{84} +(0.406042 + 0.703286i) q^{85} +(6.20680 + 2.25909i) q^{86} +(11.2613 + 9.44936i) q^{87} +(-2.27810 + 3.94578i) q^{88} +(1.19521 + 6.77836i) q^{89} +(0.479922 + 2.72177i) q^{90} +(0.801046 - 0.672157i) q^{91} +(-2.74361 + 0.998594i) q^{92} +(3.03041 - 1.10298i) q^{93} +(-3.63841 + 3.05299i) q^{94} +(-1.03227 - 5.85429i) q^{95} +(-0.416892 - 2.36431i) q^{96} +(-5.13754 + 8.89849i) q^{97} +(-4.33262 - 3.63550i) q^{98} +(-11.8328 - 4.30680i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9}+O(q^{10}) $ 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9	$ 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9} - 9 q^{10} + 3 q^{11} + 9 q^{13} - 6 q^{17} + 6 q^{18} + 9 q^{19} - 6 q^{21} + 21 q^{23} + 6 q^{26} + 12 q^{27} - 3 q^{28} + 6 q^{29} - 30 q^{31} - 45 q^{33} - 15 q^{34} + 6 q^{35} + 24 q^{36} + 6 q^{37} - 12 q^{38} + 24 q^{39} + 15 q^{41} - 6 q^{42} - 12 q^{43} - 12 q^{45} + 24 q^{47} + 3 q^{48} + 33 q^{49} - 42 q^{51} - 12 q^{53} + 27 q^{54} + 6 q^{56} + 51 q^{57} - 15 q^{58} - 15 q^{59} + 3 q^{60} + 72 q^{61} - 57 q^{62} - 30 q^{63} - 9 q^{64} + 9 q^{65} - 3 q^{66} + 18 q^{67} + 24 q^{69} - 3 q^{70} + 6 q^{72} - 66 q^{73} - 24 q^{74} - 6 q^{75} + 9 q^{76} - 66 q^{77} + 6 q^{78} - 12 q^{79} + 18 q^{80} + 66 q^{81} + 45 q^{82} + 9 q^{83} + 42 q^{84} + 12 q^{86} + 48 q^{87} + 3 q^{88} + 6 q^{90} - 78 q^{91} + 18 q^{92} + 24 q^{94} - 3 q^{97} - 48 q^{98} - 96 q^{99}+O(q^{100}) $ 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9 - 9 * q^10 + 3 * q^11 + 9 * q^13 - 6 * q^17 + 6 * q^18 + 9 * q^19 - 6 * q^21 + 21 * q^23 + 6 * q^26 + 12 * q^27 - 3 * q^28 + 6 * q^29 - 30 * q^31 - 45 * q^33 - 15 * q^34 + 6 * q^35 + 24 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^39 + 15 * q^41 - 6 * q^42 - 12 * q^43 - 12 * q^45 + 24 * q^47 + 3 * q^48 + 33 * q^49 - 42 * q^51 - 12 * q^53 + 27 * q^54 + 6 * q^56 + 51 * q^57 - 15 * q^58 - 15 * q^59 + 3 * q^60 + 72 * q^61 - 57 * q^62 - 30 * q^63 - 9 * q^64 + 9 * q^65 - 3 * q^66 + 18 * q^67 + 24 * q^69 - 3 * q^70 + 6 * q^72 - 66 * q^73 - 24 * q^74 - 6 * q^75 + 9 * q^76 - 66 * q^77 + 6 * q^78 - 12 * q^79 + 18 * q^80 + 66 * q^81 + 45 * q^82 + 9 * q^83 + 42 * q^84 + 12 * q^86 + 48 * q^87 + 3 * q^88 + 6 * q^90 - 78 * q^91 + 18 * q^92 + 24 * q^94 - 3 * q^97 - 48 * q^98 - 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$	2.25600	−	0.821116i	1.30250	−	0.474072i	0.404691	−	0.914454i	$-0.367379\pi$
$3$	2.25600	−	0.821116i	1.30250	−	0.474072i	0.897811	+	0.440382i	$0.145157\pi$
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$5$	0.173648	−	0.984808i	0.0776578	−	0.440419i
$6$	−2.40078			−0.980116
$7$	0.201324	−	1.14177i	0.0760935	−	0.431548i	−0.922832	−	0.385203i	$-0.874132\pi$
$7$	0.201324	−	1.14177i	0.0760935	−	0.431548i	0.998925	−	0.0463449i	$-0.0147573\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.11716	−	1.77651i	0.705722	−	0.592171i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	−2.27810	−	3.94578i	−0.686872	−	1.18970i	−0.972845	−	0.231459i	$-0.925650\pi$
$11$	−2.27810	−	3.94578i	−0.686872	−	1.18970i	0.285973	−	0.958238i	$-0.407683\pi$
$12$	2.25600	+	0.821116i	0.651251	+	0.237036i
$13$	0.690926	+	0.579755i	0.191628	+	0.160795i	0.733554	−	0.679631i	$-0.237860\pi$
$13$	0.690926	+	0.579755i	0.191628	+	0.160795i	−0.541926	+	0.840426i	$0.682305\pi$
$14$	−0.579690	+	1.00405i	−0.154929	+	0.268345i
$15$	−0.416892	−	2.36431i	−0.107641	−	0.610462i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−0.622093	+	0.521998i	−0.150880	+	0.126603i	−0.715103	−	0.699019i	$-0.753620\pi$
$17$	−0.622093	+	0.521998i	−0.150880	+	0.126603i	0.564223	+	0.825622i	$0.309176\pi$
$18$	−2.59709	+	0.945262i	−0.612139	+	0.222800i
$19$	5.58610	−	2.03317i	1.28154	−	0.466442i	0.390598	−	0.920561i	$-0.372268\pi$
$19$	5.58610	−	2.03317i	1.28154	−	0.466442i	0.890941	+	0.454119i	$0.150046\pi$
$20$	0.766044	−	0.642788i	0.171293	−	0.143732i
$21$	−0.483336	−	2.74114i	−0.105473	−	0.598165i
$22$	0.791174	+	4.48697i	0.168679	+	0.956626i
$23$	−1.45985	+	2.52853i	−0.304399	+	0.527234i	−0.977127	−	0.212655i	$-0.931789\pi$
$23$	−1.45985	+	2.52853i	−0.304399	+	0.527234i	0.672728	+	0.739890i	$0.265122\pi$
$24$	−1.83911	−	1.54319i	−0.375406	−	0.315003i
$25$	−0.939693	−	0.342020i	−0.187939	−	0.0684040i
$26$	−0.450970	−	0.781102i	−0.0884424	−	0.153187i
$27$	−0.283578	+	0.491171i	−0.0545745	+	0.0945259i
$28$	0.888137	−	0.745236i	0.167842	−	0.140836i
$29$	3.06163	+	5.30289i	0.568530	+	0.984722i	0.996712	+	0.0810296i	$0.0258208\pi$
$29$	3.06163	+	5.30289i	0.568530	+	0.984722i	−0.428182	+	0.903692i	$0.640846\pi$
$30$	−0.416892	+	2.36431i	−0.0761137	+	0.431662i
$31$	1.34327			0.241258			0.120629	−	0.992698i	$-0.461509\pi$
$31$	1.34327			0.241258			0.120629	+	0.992698i	$0.461509\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	−8.37932	−	7.03109i	−1.45865	−	1.22396i
$34$	0.763110	−	0.277749i	0.130872	−	0.0476336i
$35$	−1.08946	−	0.396532i	−0.184153	−	0.0670261i
$36$	2.76376			0.460627
$37$	4.64115	+	3.93188i	0.763001	+	0.646398i
$37$	4.64115	+	3.93188i	0.763001	+	0.646398i
$38$	−5.94460			−0.964342
$39$	2.03477	+	0.740597i	0.325825	+	0.118590i
$40$	−0.939693	+	0.342020i	−0.148578	+	0.0540781i
$41$	−3.23604	−	2.71536i	−0.505385	−	0.424068i	0.354117	−	0.935201i	$-0.384782\pi$
$41$	−3.23604	−	2.71536i	−0.505385	−	0.424068i	−0.859502	+	0.511133i	$0.829226\pi$
$42$	−0.483336	+	2.74114i	−0.0745804	+	0.422967i
$43$	−6.60514			−1.00727			−0.503637	−	0.863915i	$-0.668005\pi$
$43$	−6.60514			−1.00727			−0.503637	+	0.863915i	$0.668005\pi$
$44$	0.791174	−	4.48697i	0.119274	−	0.676437i
$45$	−1.38188	−	2.39349i	−0.205999	−	0.356800i
$46$	2.23661	−	1.87674i	0.329771	−	0.276710i
$47$	2.37481	−	4.11328i	0.346401	−	0.599984i	−0.639206	−	0.769035i	$-0.720737\pi$
$47$	2.37481	−	4.11328i	0.346401	−	0.599984i	0.985607	+	0.169051i	$0.0540703\pi$
$48$	1.20039	+	2.07914i	0.173262	+	0.300098i
$49$	5.31475	+	1.93441i	0.759250	+	0.276344i
$50$	0.766044	+	0.642788i	0.108335	+	0.0909039i
$51$	−0.974820	+	1.68844i	−0.136502	+	0.236429i
$52$	0.156620	+	0.888237i	0.0217193	+	0.123176i
$53$	−0.718172	−	4.07296i	−0.0986486	−	0.559464i	−0.993568	−	0.113236i	$-0.963878\pi$
$53$	−0.718172	−	4.07296i	−0.0986486	−	0.559464i	0.894920	−	0.446228i	$-0.147233\pi$
$54$	0.434466	−	0.364560i	0.0591233	−	0.0496104i
$55$	−4.28142	+	1.55831i	−0.577307	+	0.210122i
$56$	−1.08946	+	0.396532i	−0.145585	+	0.0529888i
$57$	10.9328	−	9.17368i	1.44808	−	1.21508i
$58$	−1.06329	−	6.03022i	−0.139617	−	0.791807i
$59$	−0.0686079	−	0.389095i	−0.00893199	−	0.0506558i	0.980016	−	0.198919i	$-0.0637430\pi$
$59$	−0.0686079	−	0.389095i	−0.00893199	−	0.0506558i	−0.988948	+	0.148263i	$0.952632\pi$
$60$	1.20039	−	2.07914i	0.154970	−	0.268416i
$61$	1.73526	+	1.45605i	0.222177	+	0.186429i	0.747081	−	0.664733i	$-0.231455\pi$
$61$	1.73526	+	1.45605i	0.222177	+	0.186429i	−0.524905	+	0.851161i	$0.675899\pi$
$62$	−1.26226	−	0.459424i	−0.160307	−	0.0583469i
$63$	−1.60213	−	2.77497i	−0.201849	−	0.349613i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.690926	−	0.579755i	0.0856988	−	0.0719098i
$66$	5.46922	+	9.47296i	0.673214	+	1.16604i
$67$	−1.34403	+	7.62238i	−0.164200	+	0.931222i	0.785686	+	0.618625i	$0.212310\pi$
$67$	−1.34403	+	7.62238i	−0.164200	+	0.931222i	−0.949886	+	0.312597i	$0.898801\pi$
$68$	−0.812085			−0.0984797
$69$	−1.21720	+	6.90306i	−0.146533	+	0.831031i
$70$	0.888137	+	0.745236i	0.106153	+	0.0890727i
$71$	7.78047	−	2.83186i	0.923371	−	0.336080i	0.163792	−	0.986495i	$-0.447627\pi$
$71$	7.78047	−	2.83186i	0.923371	−	0.336080i	0.759579	+	0.650415i	$0.225405\pi$
$72$	−2.59709	−	0.945262i	−0.306070	−	0.111400i
$73$	−8.59898			−1.00643			−0.503217	−	0.864160i	$-0.667850\pi$
$73$	−8.59898			−1.00643			−0.503217	+	0.864160i	$0.667850\pi$
$74$	−3.01647	−	5.28213i	−0.350658	−	0.614035i
$75$	−2.40078			−0.277219
$76$	5.58610	+	2.03317i	0.640770	+	0.233221i
$77$	−4.96380	+	1.80667i	−0.565677	+	0.205890i
$78$	−1.65876	−	1.39187i	−0.187818	−	0.157598i
$79$	−0.991412	+	5.62258i	−0.111543	+	0.632589i	0.876862	+	0.480743i	$0.159633\pi$
$79$	−0.991412	+	5.62258i	−0.111543	+	0.632589i	−0.988404	+	0.151846i	$0.951478\pi$
$80$	1.00000			0.111803
$81$	−1.67621	+	9.50626i	−0.186245	+	1.05625i
$82$	2.11218	+	3.65840i	0.233251	+	0.404002i
$83$	−5.50607	+	4.62014i	−0.604370	+	0.507127i	−0.892847	−	0.450360i	$-0.851296\pi$
$83$	−5.50607	+	4.62014i	−0.604370	+	0.507127i	0.288477	+	0.957487i	$0.406851\pi$
$84$	1.39171	−	2.41052i	0.151848	−	0.263009i
$85$	0.406042	+	0.703286i	0.0440415	+	0.0762821i
$86$	6.20680	+	2.25909i	0.669297	+	0.243604i
$87$	11.2613	+	9.44936i	1.20734	+	1.01308i
$88$	−2.27810	+	3.94578i	−0.242846	+	0.420621i
$89$	1.19521	+	6.77836i	0.126692	+	0.718505i	0.980289	+	0.197571i	$0.0633052\pi$
$89$	1.19521	+	6.77836i	0.126692	+	0.718505i	−0.853597	+	0.520934i	$0.825584\pi$
$90$	0.479922	+	2.72177i	0.0505883	+	0.286900i
$91$	0.801046	−	0.672157i	0.0839724	−	0.0704612i
$92$	−2.74361	+	0.998594i	−0.286041	+	0.104111i
$93$	3.03041	−	1.10298i	0.314238	−	0.114373i
$94$	−3.63841	+	3.05299i	−0.375274	+	0.314892i
$95$	−1.03227	−	5.85429i	−0.105909	−	0.600638i
$96$	−0.416892	−	2.36431i	−0.0425488	−	0.241306i
$97$	−5.13754	+	8.89849i	−0.521639	+	0.903505i	0.478045	+	0.878336i	$0.341346\pi$
$97$	−5.13754	+	8.89849i	−0.521639	+	0.903505i	−0.999683	+	0.0251691i	$0.991988\pi$
$98$	−4.33262	−	3.63550i	−0.437661	−	0.367241i
$99$	−11.8328	−	4.30680i	−1.18924	−	0.432849i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−7.62377	+	13.2048i	−0.758593	+	1.31392i	0.184975	+	0.982743i	$0.440780\pi$
$101$	−7.62377	+	13.2048i	−0.758593	+	1.31392i	−0.943568	+	0.331179i	$0.892554\pi$
$102$	1.49351	−	1.25320i	0.147880	−	0.124086i
$103$	9.06631	+	15.7033i	0.893330	+	1.54729i	0.835858	+	0.548946i	$0.184971\pi$
$103$	9.06631	+	15.7033i	0.893330	+	1.54729i	0.0574717	+	0.998347i	$0.481696\pi$
$104$	0.156620	−	0.888237i	0.0153579	−	0.0870988i
$105$	−2.78342			−0.271634
$106$	−0.718172	+	4.07296i	−0.0697551	+	0.395601i
$107$	−5.58445	−	4.68591i	−0.539869	−	0.453004i	0.331624	−	0.943412i	$-0.392403\pi$
$107$	−5.58445	−	4.68591i	−0.539869	−	0.453004i	−0.871493	+	0.490408i	$0.836848\pi$
$108$	−0.532952	+	0.193979i	−0.0512833	+	0.0186656i
$109$	16.7288	+	6.08879i	1.60233	+	0.583200i	0.979902	−	0.199477i	$-0.0639244\pi$
$109$	16.7288	+	6.08879i	1.60233	+	0.583200i	0.622427	+	0.782678i	$0.286147\pi$
$110$	4.55619			0.434416
$111$	13.6990	+	5.05940i	1.30025	+	0.480217i
$112$	1.15938			0.109551
$113$	−4.29184	−	1.56210i	−0.403743	−	0.146950i	0.132163	−	0.991228i	$-0.457808\pi$
$113$	−4.29184	−	1.56210i	−0.403743	−	0.146950i	−0.535906	+	0.844278i	$0.680030\pi$
$114$	−13.4110	+	4.88121i	−1.25606	+	0.457167i
$115$	2.23661	+	1.87674i	0.208565	+	0.175007i
$116$	−1.06329	+	6.03022i	−0.0987241	+	0.559892i
$117$	2.49275			0.230454
$118$	−0.0686079	+	0.389095i	−0.00631587	+	0.0358191i
$119$	0.470758	+	0.815376i	0.0431543	+	0.0747454i
$120$	−1.83911	+	1.54319i	−0.167887	+	0.140874i
$121$	−4.87944	+	8.45144i	−0.443586	+	0.768313i
$122$	−1.13261	−	1.96174i	−0.102542	−	0.177607i
$123$	−9.53013	−	3.46868i	−0.859303	−	0.312761i
$124$	1.02900	+	0.863434i	0.0924070	+	0.0775387i
$125$	−0.500000	+	0.866025i	−0.0447214	+	0.0774597i
$126$	0.556413	+	3.15557i	0.0495692	+	0.281121i
$127$	−3.03702	−	17.2238i	−0.269492	−	1.52837i	−0.755931	−	0.654652i	$-0.772815\pi$
$127$	−3.03702	−	17.2238i	−0.269492	−	1.52837i	0.486439	−	0.873715i	$-0.338296\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	−14.9012	+	5.42359i	−1.31198	+	0.477520i
$130$	−0.847546	+	0.308481i	−0.0743347	+	0.0270556i
$131$	8.95108	−	7.51085i	0.782059	−	0.656226i	−0.161707	−	0.986839i	$-0.551700\pi$
$131$	8.95108	−	7.51085i	0.782059	−	0.656226i	0.943766	+	0.330613i	$0.107255\pi$
$132$	−1.89944	−	10.7723i	−0.165325	−	0.937604i
$133$	−1.19679	−	6.78736i	−0.103775	−	0.588538i
$134$	3.86998	−	6.70301i	0.334316	−	0.579052i
$135$	0.434466	+	0.364560i	0.0373929	+	0.0313764i
$136$	0.763110	+	0.277749i	0.0654361	+	0.0238168i
$137$	−6.39681	−	11.0796i	−0.546517	−	0.946594i	−0.998510	−	0.0545730i	$-0.982620\pi$
$137$	−6.39681	−	11.0796i	−0.546517	−	0.946594i	0.451993	−	0.892021i	$-0.350713\pi$
$138$	3.50477	−	6.07045i	0.298346	−	0.516751i
$139$	10.4864	−	8.79917i	0.889448	−	0.746336i	−0.0786512	−	0.996902i	$-0.525061\pi$
$139$	10.4864	−	8.79917i	0.889448	−	0.746336i	0.968099	+	0.250567i	$0.0806169\pi$
$140$	−0.579690	−	1.00405i	−0.0489928	−	0.0848580i
$141$	1.98007	−	11.2296i	0.166752	−	0.945699i
$142$	−8.27980			−0.694825
$143$	0.713591	−	4.04698i	0.0596735	−	0.338425i
$144$	2.11716	+	1.77651i	0.176430	+	0.148043i
$145$	5.75397	−	2.09428i	0.477841	−	0.173920i
$146$	8.08040	+	2.94102i	0.668738	+	0.243401i
$147$	13.5784			1.11993
$148$	1.02796	+	5.99527i	0.0844980	+	0.492808i
$149$	−20.7158			−1.69710			−0.848551	−	0.529114i	$-0.822524\pi$
$149$	−20.7158			−1.69710			−0.848551	+	0.529114i	$0.822524\pi$
$150$	2.25600	+	0.821116i	0.184202	+	0.0670439i
$151$	11.3659	−	4.13685i	0.924945	−	0.336652i	0.164741	−	0.986337i	$-0.447321\pi$
$151$	11.3659	−	4.13685i	0.924945	−	0.336652i	0.760204	+	0.649684i	$0.225099\pi$
$152$	−4.55383	−	3.82112i	−0.369365	−	0.309934i
$153$	−0.389738	+	2.21031i	−0.0315084	+	0.178693i
$154$	5.28236			0.425665
$155$	0.233256	−	1.32286i	0.0187355	−	0.106255i
$156$	1.08268	+	1.87526i	0.0866838	+	0.150141i
$157$	−12.8611	+	10.7918i	−1.02643	+	0.861278i	−0.990422	−	0.138073i	$-0.955909\pi$
$157$	−12.8611	+	10.7918i	−1.02643	+	0.861278i	−0.0360093	+	0.999351i	$0.511465\pi$
$158$	2.85466	−	4.94441i	0.227104	−	0.393356i
$159$	−4.96457	−	8.59889i	−0.393716	−	0.681936i
$160$	−0.939693	−	0.342020i	−0.0742892	−	0.0270391i
$161$	2.59309	+	2.17586i	0.204364	+	0.171482i
$162$	4.82645	−	8.35966i	0.379202	−	0.656797i
$163$	2.96515	+	16.8162i	0.232248	+	1.31715i	0.848332	+	0.529465i	$0.177607\pi$
$163$	2.96515	+	16.8162i	0.232248	+	1.31715i	−0.616083	+	0.787681i	$0.711282\pi$
$164$	−0.733551	−	4.16017i	−0.0572807	−	0.324855i
$165$	−8.37932	+	7.03109i	−0.652330	+	0.547369i
$166$	6.75420	−	2.45833i	0.524228	−	0.190803i
$167$	−3.25411	+	1.18440i	−0.251810	+	0.0916515i	−0.464841	−	0.885394i	$-0.653889\pi$
$167$	−3.25411	+	1.18440i	−0.251810	+	0.0916515i	0.213031	+	0.977045i	$0.431666\pi$
$168$	−2.13223	+	1.78915i	−0.164505	+	0.138036i
$169$	−2.11616	−	12.0014i	−0.162782	−	0.923182i
$170$	−0.141017	−	0.799747i	−0.0108155	−	0.0613378i
$171$	8.21474	−	14.2283i	0.628197	−	1.08807i
$172$	−5.05983	−	4.24570i	−0.385809	−	0.323732i
$173$	−4.25795	−	1.54977i	−0.323726	−	0.117827i	0.175045	−	0.984560i	$-0.443993\pi$
$173$	−4.25795	−	1.54977i	−0.323726	−	0.117827i	−0.498771	+	0.866734i	$0.666215\pi$
$174$	−7.35030	−	12.7311i	−0.557225	−	0.965142i
$175$	−0.579690	+	1.00405i	−0.0438205	+	0.0758993i
$176$	3.49025	−	2.92866i	0.263087	−	0.220756i
$177$	−0.474271	−	0.821462i	−0.0356484	−	0.0617449i
$178$	1.19521	−	6.77836i	0.0895846	−	0.508060i
$179$	19.4080			1.45062			0.725309	−	0.688423i	$-0.241697\pi$
$179$	19.4080			1.45062			0.725309	+	0.688423i	$0.241697\pi$
$180$	0.479922	−	2.72177i	0.0357713	−	0.202869i
$181$	−12.0148	−	10.0816i	−0.893049	−	0.749357i	0.0757700	−	0.997125i	$-0.475859\pi$
$181$	−12.0148	−	10.0816i	−0.893049	−	0.749357i	−0.968819	+	0.247768i	$0.920303\pi$
$182$	−0.982628	+	0.357647i	−0.0728373	+	0.0265106i
$183$	5.11033	+	1.86001i	0.377766	+	0.137496i
$184$	2.91969			0.215243
$185$	4.67808	−	3.88788i	0.343939	−	0.285842i
$186$	−3.22489			−0.236460
$187$	3.47688	+	1.26548i	0.254254	+	0.0925410i
$188$	4.46317	−	1.62446i	0.325510	−	0.118476i
$189$	0.503712	+	0.422664i	0.0366396	+	0.0307443i
$190$	−1.03227	+	5.85429i	−0.0748887	+	0.424715i
$191$	−6.68727			−0.483874			−0.241937	−	0.970292i	$-0.577783\pi$
$191$	−6.68727			−0.483874			−0.241937	+	0.970292i	$0.577783\pi$
$192$	−0.416892	+	2.36431i	−0.0300866	+	0.170629i
$193$	−11.2608	−	19.5043i	−0.810572	−	1.40395i	−0.912464	−	0.409156i	$-0.865823\pi$
$193$	−11.2608	−	19.5043i	−0.810572	−	1.40395i	0.101892	−	0.994795i	$-0.467510\pi$
$194$	7.87118	−	6.60470i	0.565117	−	0.474190i
$195$	1.08268	−	1.87526i	0.0775324	−	0.134290i
$196$	2.82792	+	4.89810i	0.201994	+	0.349864i
$197$	20.0417	+	7.29457i	1.42791	+	0.519716i	0.936331	−	0.351117i	$-0.114198\pi$
$197$	20.0417	+	7.29457i	1.42791	+	0.519716i	0.491578	+	0.870834i	$0.336420\pi$
$198$	9.64621	+	8.09413i	0.685526	+	0.575225i
$199$	5.04539	−	8.73888i	0.357658	−	0.619482i	−0.629911	−	0.776667i	$-0.716909\pi$
$199$	5.04539	−	8.73888i	0.357658	−	0.619482i	0.987569	+	0.157185i	$0.0502419\pi$
$200$	0.173648	+	0.984808i	0.0122788	+	0.0696364i
$201$	3.22673	+	18.2997i	0.227596	+	1.29076i
$202$	11.6803	−	9.80093i	0.821822	−	0.689591i
$203$	6.67105	−	2.42806i	0.468216	−	0.170417i
$204$	−1.83206	+	0.666816i	−0.128270	+	0.0466865i
$205$	−3.23604	+	2.71536i	−0.226015	+	0.189649i
$206$	−3.14870	−	17.8571i	−0.219380	−	1.24417i
$207$	1.40123	+	7.94674i	0.0973919	+	0.552337i
$208$	−0.450970	+	0.781102i	−0.0312691	+	0.0541597i
$209$	−20.7481	−	17.4097i	−1.43518	−	1.20426i
$210$	2.61556	+	0.951987i	0.180491	+	0.0656933i
$211$	−11.2993	−	19.5709i	−0.777874	−	1.34732i	−0.933165	−	0.359449i	$-0.882965\pi$
$211$	−11.2993	−	19.5709i	−0.777874	−	1.34732i	0.155290	−	0.987869i	$-0.450369\pi$
$212$	2.06790	−	3.58170i	0.142024	−	0.245992i
$213$	15.2274	−	12.7773i	1.04337	−	0.875489i
$214$	3.64499	+	6.31330i	0.249166	+	0.431569i
$215$	−1.14697	+	6.50479i	−0.0782228	+	0.443623i
$216$	0.567155			0.0385900
$217$	0.270432	−	1.53370i	0.0183581	−	0.104114i
$218$	−13.6375	−	11.4432i	−0.923645	−	0.775030i
$219$	−19.3993	+	7.06076i	−1.31088	+	0.477122i
$220$	−4.28142	−	1.55831i	−0.288653	−	0.105061i
$221$	−0.732451			−0.0492700
$222$	−11.1424	−	9.43960i	−0.747829	−	0.633545i
$223$	26.7589			1.79191			0.895953	−	0.444148i	$-0.146494\pi$
$223$	26.7589			1.79191			0.895953	+	0.444148i	$0.146494\pi$
$224$	−1.08946	−	0.396532i	−0.0727927	−	0.0264944i
$225$	−2.59709	+	0.945262i	−0.173139	+	0.0630175i
$226$	3.49874	+	2.93579i	0.232733	+	0.195286i
$227$	−2.48385	+	14.0866i	−0.164859	+	0.934963i	0.784350	+	0.620318i	$0.212996\pi$
$227$	−2.48385	+	14.0866i	−0.164859	+	0.934963i	−0.949210	+	0.314645i	$0.898115\pi$
$228$	14.2717			0.945167
$229$	−0.414503	+	2.35076i	−0.0273911	+	0.155343i	−0.995436	−	0.0954359i	$-0.969576\pi$
$229$	−0.414503	+	2.35076i	−0.0273911	+	0.155343i	0.968044	+	0.250779i	$0.0806866\pi$
$230$	−1.45985	−	2.52853i	−0.0962594	−	0.166726i
$231$	−9.71483	+	8.15171i	−0.639189	+	0.536343i
$232$	3.06163	−	5.30289i	0.201006	−	0.348152i
$233$	−4.18679	−	7.25172i	−0.274285	−	0.475076i	0.695669	−	0.718362i	$-0.255108\pi$
$233$	−4.18679	−	7.25172i	−0.274285	−	0.475076i	−0.969955	+	0.243286i	$0.921775\pi$
$234$	−2.34242	−	0.852569i	−0.153128	−	0.0557342i
$235$	−3.63841	−	3.05299i	−0.237344	−	0.199155i
$236$	0.197549	−	0.342164i	0.0128593	−	0.0222730i
$237$	2.38017	+	13.4986i	0.154608	+	0.876828i
$238$	−0.163492	−	0.927212i	−0.0105976	−	0.0601022i
$239$	3.37415	−	2.83125i	0.218256	−	0.183138i	−0.527104	−	0.849801i	$-0.676722\pi$
$239$	3.37415	−	2.83125i	0.218256	−	0.183138i	0.745360	+	0.666663i	$0.232278\pi$
$240$	2.25600	−	0.821116i	0.145624	−	0.0530028i
$241$	−17.5489	+	6.38727i	−1.13042	+	0.411440i	−0.838446	−	0.544985i	$-0.816535\pi$
$241$	−17.5489	+	6.38727i	−1.13042	+	0.411440i	−0.291977	+	0.956425i	$0.594313\pi$
$242$	7.47574	−	6.27289i	0.480559	−	0.403237i
$243$	3.72876	+	21.1468i	0.239200	+	1.35657i
$244$	0.393351	+	2.23080i	0.0251817	+	0.142813i
$245$	2.82792	−	4.89810i	0.180669	−	0.312928i
$246$	7.76904	+	6.51899i	0.495336	+	0.415636i
$247$	5.03832	+	1.83380i	0.320581	+	0.116682i
$248$	−0.671633	−	1.16330i	−0.0426487	−	0.0738698i
$249$	−8.62802	+	14.9442i	−0.546779	+	0.947048i
$250$	0.766044	−	0.642788i	0.0484489	−	0.0406535i
$251$	−2.19959	−	3.80981i	−0.138837	−	0.240473i	0.788220	−	0.615394i	$-0.211003\pi$
$251$	−2.19959	−	3.80981i	−0.138837	−	0.240473i	−0.927057	+	0.374921i	$0.877670\pi$
$252$	0.556413	−	3.15557i	0.0350507	−	0.198782i
$253$	13.3027			0.836332
$254$	−3.03702	+	17.2238i	−0.190560	+	1.08072i
$255$	1.49351	+	1.25320i	0.0935273	+	0.0784787i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−2.98547	−	1.08662i	−0.186228	−	0.0677815i	0.247223	−	0.968959i	$-0.420482\pi$
$257$	−2.98547	−	1.08662i	−0.186228	−	0.0677815i	−0.433451	+	0.901177i	$0.642704\pi$
$258$	15.8575			0.987246
$259$	5.42367	−	4.50753i	0.337011	−	0.280084i
$260$	0.901939			0.0559359
$261$	15.9026	+	5.78808i	0.984347	+	0.358273i
$262$	−10.9801	+	3.99644i	−0.678354	+	0.246901i
$263$	4.17207	+	3.50078i	0.257261	+	0.215867i	0.762291	−	0.647234i	$-0.224074\pi$
$263$	4.17207	+	3.50078i	0.257261	+	0.215867i	−0.505031	+	0.863101i	$0.668519\pi$
$264$	−1.89944	+	10.7723i	−0.116902	+	0.662986i
$265$	−4.13579			−0.254060
$266$	−1.19679	+	6.78736i	−0.0733801	+	0.416159i
$267$	8.26221	+	14.3106i	0.505639	+	0.875793i
$268$	−5.92916	+	4.97515i	−0.362181	+	0.303906i
$269$	−0.359764	+	0.623130i	−0.0219352	+	0.0379929i	−0.876785	−	0.480883i	$-0.840316\pi$
$269$	−0.359764	+	0.623130i	−0.0219352	+	0.0379929i	0.854849	+	0.518876i	$0.173649\pi$
$270$	−0.283578	−	0.491171i	−0.0172580	−	0.0298917i
$271$	−19.1335	−	6.96403i	−1.16228	−	0.423035i	−0.312367	−	0.949961i	$-0.601122\pi$
$271$	−19.1335	−	6.96403i	−1.16228	−	0.423035i	−0.849911	+	0.526927i	$0.823344\pi$
$272$	−0.622093	−	0.521998i	−0.0377199	−	0.0316508i
$273$	1.25524	−	2.17414i	0.0759705	−	0.131585i
$274$	2.22159	+	12.5993i	0.134211	+	0.761149i
$275$	0.791174	+	4.48697i	0.0477096	+	0.270575i
$276$	−5.36963	+	4.50565i	−0.323214	+	0.271208i
$277$	−24.0828	+	8.76543i	−1.44700	+	0.526664i	−0.941751	−	0.336312i	$-0.890820\pi$
$277$	−24.0828	+	8.76543i	−1.44700	+	0.526664i	−0.505246	+	0.862976i	$0.668598\pi$
$278$	−12.8635	+	4.68194i	−0.771503	+	0.280804i
$279$	2.84391	−	2.38633i	0.170261	−	0.142866i
$280$	0.201324	+	1.14177i	0.0120314	+	0.0682337i
$281$	−4.82239	−	27.3491i	−0.287679	−	1.63151i	−0.695555	−	0.718473i	$-0.744841\pi$
$281$	−4.82239	−	27.3491i	−0.287679	−	1.63151i	0.407875	−	0.913038i	$-0.366270\pi$
$282$	−5.70139	+	9.87510i	−0.339513	+	0.588054i
$283$	−19.9027	−	16.7003i	−1.18309	−	0.992732i	−0.999953	−	0.00964513i	$-0.996930\pi$
$283$	−19.9027	−	16.7003i	−1.18309	−	0.992732i	−0.183139	−	0.983087i	$-0.558626\pi$
$284$	7.78047	+	2.83186i	0.461686	+	0.168040i
$285$	−7.13586	−	12.3597i	−0.422692	−	0.732123i
$286$	−2.05470	+	3.55885i	−0.121497	+	0.210439i
$287$	−3.75180	+	3.14814i	−0.221462	+	0.185829i
$288$	−1.38188	−	2.39349i	−0.0814281	−	0.141038i
$289$	−2.83750	+	16.0923i	−0.166912	+	0.946604i
$290$	−6.12325			−0.359570
$291$	−4.28360	+	24.2935i	−0.251109	+	1.42411i
$292$	−6.58720	−	5.52732i	−0.385487	−	0.323462i
$293$	8.03742	−	2.92538i	0.469551	−	0.170903i	−0.0963979	−	0.995343i	$-0.530732\pi$
$293$	8.03742	−	2.92538i	0.469551	−	0.170903i	0.565949	+	0.824440i	$0.308510\pi$
$294$	−12.7596	−	4.64410i	−0.744153	−	0.270849i
$295$	−0.395097			−0.0230034
$296$	1.08454	−	5.98530i	0.0630373	−	0.347888i
$297$	2.58407			0.149943
$298$	19.4664	+	7.08521i	1.12766	+	0.410435i
$299$	−2.47457	+	0.900671i	−0.143108	+	0.0520871i
$300$	−1.83911	−	1.54319i	−0.106181	−	0.0890963i
$301$	−1.32978	+	7.54154i	−0.0766470	+	0.434687i
$302$	−12.0954			−0.696009
$303$	−6.35657	+	36.0499i	−0.365175	+	2.07101i
$304$	2.97230	+	5.14818i	0.170473	+	0.295268i
$305$	1.73526	−	1.45605i	0.0993605	−	0.0833734i
$306$	1.12220	−	1.94372i	0.0641522	−	0.111115i
$307$	−12.8859	−	22.3190i	−0.735436	−	1.27381i	−0.954532	−	0.298109i	$-0.903644\pi$
$307$	−12.8859	−	22.3190i	−0.735436	−	1.27381i	0.219096	−	0.975703i	$-0.429689\pi$
$308$	−4.96380	−	1.80667i	−0.282839	−	0.102945i
$309$	33.3478	+	27.9821i	1.89709	+	1.59185i
$310$	−0.671633	+	1.16330i	−0.0381462	+	0.0660711i
$311$	−2.17005	−	12.3070i	−0.123052	−	0.697865i	−0.982446	−	0.186550i	$-0.940269\pi$
$311$	−2.17005	−	12.3070i	−0.123052	−	0.697865i	0.859393	−	0.511316i	$-0.170842\pi$
$312$	−0.376011	−	2.13246i	−0.0212874	−	0.120727i
$313$	−13.9627	+	11.7161i	−0.789220	+	0.662234i	−0.945552	−	0.325470i	$-0.894477\pi$
$313$	−13.9627	+	11.7161i	−0.789220	+	0.662234i	0.156332	+	0.987705i	$0.450033\pi$
$314$	15.7765	−	5.74219i	0.890321	−	0.324050i
$315$	−3.01101	+	1.09592i	−0.169651	+	0.0617481i
$316$	−4.37359	+	3.66988i	−0.246034	+	0.206447i
$317$	4.60790	+	26.1327i	0.258806	+	1.46776i	0.786112	+	0.618084i	$0.212091\pi$
$317$	4.60790	+	26.1327i	0.258806	+	1.46776i	−0.527306	+	0.849675i	$0.676798\pi$
$318$	1.72418	+	9.77829i	0.0966870	+	0.548339i
$319$	13.9494	−	24.1610i	0.781014	−	1.35276i
$320$	0.766044	+	0.642788i	0.0428232	+	0.0359329i
$321$	−16.4462	−	5.98592i	−0.917936	−	0.334101i
$322$	−1.69252	−	2.93153i	−0.0943203	−	0.163368i
$323$	−2.41376	+	4.18076i	−0.134305	+	0.232624i
$324$	−7.39455	+	6.20477i	−0.410809	+	0.344709i
$325$	−0.450970	−	0.781102i	−0.0250153	−	0.0433278i
$326$	2.96515	−	16.8162i	0.164224	−	0.931363i
$327$	42.7398			2.36352
$328$	−0.733551	+	4.16017i	−0.0405036	+	0.229707i
$329$	−4.21831	−	3.53958i	−0.232563	−	0.195143i
$330$	10.2788	−	3.74116i	0.565827	−	0.205944i
$331$	−12.3002	−	4.47690i	−0.676079	−	0.246073i	−0.0189159	−	0.999821i	$-0.506021\pi$
$331$	−12.3002	−	4.47690i	−0.676079	−	0.246073i	−0.657163	+	0.753748i	$0.728244\pi$
$332$	−7.18767			−0.394475
$333$	16.8111	+	0.0793829i	0.921244	+	0.00435016i
$334$	3.46295			0.189484
$335$	7.27319	+	2.64722i	0.397377	+	0.144633i
$336$	2.61556	−	0.951987i	0.142691	−	0.0519351i
$337$	7.93364	+	6.65711i	0.432173	+	0.362636i	0.832771	−	0.553618i	$-0.186753\pi$
$337$	7.93364	+	6.65711i	0.432173	+	0.362636i	−0.400598	+	0.916254i	$0.631198\pi$
$338$	−2.11616	+	12.0014i	−0.115104	+	0.652788i
$339$	−10.9651			−0.595540
$340$	−0.141017	+	0.799747i	−0.00764772	+	0.0433724i
$341$	−3.06009	−	5.30023i	−0.165713	−	0.287023i
$342$	−12.5857	+	10.5607i	−0.680557	+	0.571055i
$343$	7.33647	−	12.7071i	0.396132	−	0.686121i
$344$	3.30257	+	5.72022i	0.178063	+	0.308414i
$345$	6.58682	+	2.39741i	0.354623	+	0.129072i
$346$	3.47111	+	2.91261i	0.186608	+	0.156583i
$347$	6.89466	−	11.9419i	0.370125	−	0.641075i	−0.619460	−	0.785028i	$-0.712648\pi$
$347$	6.89466	−	11.9419i	0.370125	−	0.641075i	0.989584	+	0.143954i	$0.0459816\pi$
$348$	2.55273	+	14.4773i	0.136841	+	0.776063i
$349$	−2.72464	−	15.4522i	−0.145847	−	0.827139i	−0.966683	−	0.255975i	$-0.917603\pi$
$349$	−2.72464	−	15.4522i	−0.145847	−	0.827139i	0.820836	−	0.571163i	$-0.193508\pi$
$350$	0.888137	−	0.745236i	0.0474729	−	0.0398345i
$351$	−0.480690	+	0.174957i	−0.0256573	+	0.00933851i
$352$	−4.28142	+	1.55831i	−0.228200	+	0.0830582i
$353$	15.4181	−	12.9373i	0.820622	−	0.688584i	−0.132496	−	0.991184i	$-0.542299\pi$
$353$	15.4181	−	12.9373i	0.820622	−	0.688584i	0.953118	+	0.302600i	$0.0978546\pi$
$354$	0.164713	+	0.934132i	0.00875438	+	0.0496486i
$355$	−1.43777	−	8.15401i	−0.0763090	−	0.432770i
$356$	−3.44146	+	5.96079i	−0.182397	+	0.315921i
$357$	1.73155	+	1.45294i	0.0916432	+	0.0768978i
$358$	−18.2375	−	6.63791i	−0.963882	−	0.350825i
$359$	14.5156	+	25.1418i	0.766106	+	1.32694i	0.939660	+	0.342111i	$0.111142\pi$
$359$	14.5156	+	25.1418i	0.766106	+	1.32694i	−0.173553	+	0.984824i	$0.555525\pi$
$360$	−1.38188	+	2.39349i	−0.0728315	+	0.126148i
$361$	12.5159	−	10.5021i	0.658731	−	0.552741i
$362$	7.84207	+	13.5829i	0.412170	+	0.713900i
$363$	−4.06840	+	23.0730i	−0.213536	+	1.21102i
$364$	1.04569			0.0548091
$365$	−1.49320	+	8.46834i	−0.0781575	+	0.443253i
$366$	−4.16598	−	3.49567i	−0.217759	−	0.182722i
$367$	24.2593	−	8.82965i	1.26632	−	0.460904i	0.380437	−	0.924807i	$-0.375774\pi$
$367$	24.2593	−	8.82965i	1.26632	−	0.460904i	0.885886	+	0.463903i	$0.153551\pi$
$368$	−2.74361	−	0.998594i	−0.143021	−	0.0520553i
$369$	−11.6751			−0.607782
$370$	−5.72569	+	2.05341i	−0.297664	+	0.106752i
$371$	−4.79496			−0.248942
$372$	3.03041	+	1.10298i	0.157119	+	0.0571867i
$373$	−2.38761	+	0.869020i	−0.123626	+	0.0449961i	−0.403092	−	0.915159i	$-0.632065\pi$
$373$	−2.38761	+	0.869020i	−0.123626	+	0.0449961i	0.279466	+	0.960155i	$0.409842\pi$
$374$	−2.83437	−	2.37832i	−0.146562	−	0.122980i
$375$	−0.416892	+	2.36431i	−0.0215282	+	0.122092i
$376$	−4.74961			−0.244942
$377$	−0.959024	+	5.43890i	−0.0493923	+	0.280117i
$378$	−0.328774	−	0.569454i	−0.0169103	−	0.0292896i
$379$	15.5448	−	13.0436i	0.798481	−	0.670005i	−0.149348	−	0.988785i	$-0.547717\pi$
$379$	15.5448	−	13.0436i	0.798481	−	0.670005i	0.947829	+	0.318780i	$0.103273\pi$
$380$	2.97230	−	5.14818i	0.152476	−	0.264096i
$381$	−20.9943	−	36.3632i	−1.07557	−	1.86294i
$382$	6.28398	+	2.28718i	0.321516	+	0.117022i
$383$	8.16469	+	6.85099i	0.417196	+	0.350069i	0.827095	−	0.562062i	$-0.189992\pi$
$383$	8.16469	+	6.85099i	0.417196	+	0.350069i	−0.409899	+	0.912131i	$0.634436\pi$
$384$	1.20039	−	2.07914i	0.0612572	−	0.106101i
$385$	0.917273	+	5.20211i	0.0467485	+	0.265124i
$386$	3.91084	+	22.1795i	0.199057	+	1.12891i
$387$	−13.9842	+	11.7341i	−0.710855	+	0.596479i
$388$	−9.65543	+	3.51429i	−0.490180	+	0.178411i
$389$	4.00246	−	1.45678i	0.202933	−	0.0738615i	−0.238554	−	0.971129i	$-0.576673\pi$
$389$	4.00246	−	1.45678i	0.202933	−	0.0738615i	0.441487	+	0.897268i	$0.354451\pi$
$390$	−1.65876	+	1.39187i	−0.0839947	+	0.0704799i
$391$	−0.411726	−	2.33502i	−0.0208219	−	0.118087i
$392$	−0.982126	−	5.56991i	−0.0496048	−	0.281323i
$393$	14.0263	−	24.2943i	0.707535	−	1.22549i
$394$	−16.3381	−	13.7093i	−0.823102	−	0.690665i
$395$	5.36500	+	1.95270i	0.269942	+	0.0982510i
$396$	−6.29612	−	10.9052i	−0.316392	−	0.548007i
$397$	2.23263	−	3.86702i	0.112052	−	0.194080i	−0.804545	−	0.593891i	$-0.797591\pi$
$397$	2.23263	−	3.86702i	0.112052	−	0.194080i	0.916598	+	0.399811i	$0.130924\pi$
$398$	−7.72999	+	6.48623i	−0.387469	+	0.325125i
$399$	−8.27317	−	14.3296i	−0.414177	−	0.717375i
$400$	0.173648	−	0.984808i	0.00868241	−	0.0492404i
$401$	5.64259			0.281778			0.140889	−	0.990025i	$-0.455004\pi$
$401$	5.64259			0.281778			0.140889	+	0.990025i	$0.455004\pi$
$402$	3.22673	−	18.2997i	0.160935	−	0.912705i
$403$	0.928097	+	0.778766i	0.0462318	+	0.0387931i
$404$	−14.3280	+	5.21496i	−0.712844	+	0.259454i
$405$	9.07076	+	3.30149i	0.450730	+	0.164052i
$406$	−7.09918			−0.352326
$407$	4.94135	−	27.2702i	0.244934	−	1.35173i
$408$	1.94964			0.0965215
$409$	14.5029	+	5.27864i	0.717124	+	0.261012i	0.674704	−	0.738088i	$-0.264271\pi$
$409$	14.5029	+	5.27864i	0.717124	+	0.261012i	0.0424197	+	0.999100i	$0.486493\pi$
$410$	3.96959	−	1.44481i	0.196044	−	0.0713543i
$411$	−23.5288	−	19.7430i	−1.16059	−	0.973853i
$412$	−3.14870	+	17.8571i	−0.155125	+	0.879758i
$413$	−0.458068			−0.0225401
$414$	1.40123	−	7.94674i	0.0688665	−	0.390561i
$415$	3.59383	+	6.22470i	0.176414	+	0.305559i
$416$	0.690926	−	0.579755i	0.0338754	−	0.0284248i
$417$	16.4323	−	28.4615i	0.804691	−	1.39377i
$418$	13.5424	+	23.4561i	0.662379	+	1.14727i
$419$	−15.5623	−	5.66421i	−0.760267	−	0.276715i	−0.0673477	−	0.997730i	$-0.521454\pi$
$419$	−15.5623	−	5.66421i	−0.760267	−	0.276715i	−0.692920	+	0.721015i	$0.743676\pi$
$420$	−2.13223	−	1.78915i	−0.104042	−	0.0873016i
$421$	7.87656	−	13.6426i	0.383880	−	0.664900i	−0.607733	−	0.794142i	$-0.707921\pi$
$421$	7.87656	−	13.6426i	0.383880	−	0.664900i	0.991613	+	0.129241i	$0.0412542\pi$
$422$	3.92420	+	22.2552i	0.191027	+	1.08337i
$423$	−2.27944	−	12.9274i	−0.110830	−	0.628550i
$424$	−3.16820	+	2.65843i	−0.153861	+	0.129105i
$425$	0.763110	−	0.277749i	0.0370163	−	0.0134728i
$426$	−18.6792	+	6.79868i	−0.905011	+	0.329397i
$427$	2.01182	−	1.68812i	0.0973590	−	0.0816939i
$428$	−1.26589	−	7.17922i	−0.0611891	−	0.347021i
$429$	−1.71318	−	9.71592i	−0.0827130	−	0.469089i
$430$	3.30257	−	5.72022i	0.159264	−	0.275854i
$431$	1.05461	+	0.884921i	0.0507987	+	0.0426252i	0.667834	−	0.744311i	$-0.267222\pi$
$431$	1.05461	+	0.884921i	0.0507987	+	0.0426252i	−0.617035	+	0.786936i	$0.711666\pi$
$432$	−0.532952	−	0.193979i	−0.0256416	−	0.00933280i
$433$	4.98241	+	8.62979i	0.239440	+	0.414721i	0.960554	−	0.278095i	$-0.0897030\pi$
$433$	4.98241	+	8.62979i	0.239440	+	0.414721i	−0.721114	+	0.692816i	$0.756370\pi$
$434$	−0.778678	+	1.34871i	−0.0373778	+	0.0647402i
$435$	11.2613	−	9.44936i	0.539939	−	0.453062i
$436$	8.90122	+	15.4174i	0.426291	+	0.738358i
$437$	−3.01391	+	17.0927i	−0.144175	+	0.817656i
$438$	20.6443			0.986422
$439$	0.581516	−	3.29794i	0.0277542	−	0.157402i	−0.967781	−	0.251794i	$-0.918980\pi$
$439$	0.581516	−	3.29794i	0.0277542	−	0.157402i	0.995535	+	0.0943917i	$0.0300906\pi$
$440$	3.49025	+	2.92866i	0.166391	+	0.139619i
$441$	14.6887	−	5.34625i	0.699462	−	0.254583i
$442$	0.688279	+	0.250513i	0.0327381	+	0.0119157i
$443$	−17.2812			−0.821055			−0.410527	−	0.911848i	$-0.634655\pi$
$443$	−17.2812			−0.821055			−0.410527	+	0.911848i	$0.634655\pi$
$444$	7.24190	+	12.6813i	0.343685	+	0.601826i
$445$	6.88293			0.326282
$446$	−25.1451	−	9.15207i	−1.19066	−	0.433363i
$447$	−46.7347	+	17.0100i	−2.21048	+	0.804548i
$448$	0.888137	+	0.745236i	0.0419605	+	0.0352091i
$449$	−1.96198	+	11.1269i	−0.0925914	+	0.525112i	0.902867	+	0.429919i	$0.141458\pi$
$449$	−1.96198	+	11.1269i	−0.0925914	+	0.525112i	−0.995459	+	0.0951929i	$0.969653\pi$
$450$	2.76376			0.130285
$451$	−3.34220	+	18.9546i	−0.157378	+	0.892535i
$452$	−2.28364	−	3.95538i	−0.107413	−	0.186046i
$453$	22.2446	−	18.6655i	1.04514	−	0.876981i
$454$	7.15197	−	12.3876i	0.335659	−	0.581378i
$455$	−0.522846	−	0.905595i	−0.0245114	−	0.0424550i
$456$	−13.4110	−	4.88121i	−0.628029	−	0.228584i
$457$	−21.0642	−	17.6750i	−0.985341	−	0.826799i	−0.000454644	−	1.00000i	$-0.500145\pi$
$457$	−21.0642	−	17.6750i	−0.985341	−	0.826799i	−0.984887	+	0.173200i	$0.944589\pi$
$458$	1.19351	−	2.06723i	0.0557692	−	0.0965951i
$459$	−0.0799785	−	0.453581i	−0.00373308	−	0.0211713i
$460$	0.506999	+	2.87534i	0.0236390	+	0.134063i
$461$	−18.1614	+	15.2392i	−0.845862	+	0.709762i	−0.958874	−	0.283831i	$-0.908394\pi$
$461$	−18.1614	+	15.2392i	−0.845862	+	0.709762i	0.113012	+	0.993594i	$0.463950\pi$
$462$	11.9170	−	4.33743i	0.554429	−	0.201796i
$463$	2.75435	−	1.00250i	0.128005	−	0.0465902i	−0.277223	−	0.960806i	$-0.589414\pi$
$463$	2.75435	−	1.00250i	0.128005	−	0.0465902i	0.405229	+	0.914215i	$0.367192\pi$
$464$	−4.69068	+	3.93595i	−0.217759	+	0.182722i
$465$	−0.559996	−	3.17590i	−0.0259692	−	0.147279i
$466$	1.45406	+	8.24636i	0.0673578	+	0.382005i
$467$	−17.2405	+	29.8614i	−0.797796	+	1.38182i	0.123253	+	0.992375i	$0.460667\pi$
$467$	−17.2405	+	29.8614i	−0.797796	+	1.38182i	−0.921049	+	0.389448i	$0.872666\pi$
$468$	1.90955	+	1.60231i	0.0882692	+	0.0740666i
$469$	8.43240	+	3.06914i	0.389372	+	0.141720i
$470$	2.37481	+	4.11328i	0.109542	+	0.189732i
$471$	−20.1534	+	34.9067i	−0.928621	+	1.60842i
$472$	−0.302662	+	0.253964i	−0.0139311	+	0.0116896i
$473$	15.0471	+	26.0624i	0.691869	+	1.19835i
$474$	2.38017	−	13.4986i	0.109325	−	0.620011i
$475$	−5.94460			−0.272757
$476$	−0.163492	+	0.927212i	−0.00749366	+	0.0424987i
$477$	−8.75615	−	7.34728i	−0.400917	−	0.336409i
$478$	−4.13901	+	1.50648i	−0.189314	+	0.0689046i
$479$	−28.9454	−	10.5353i	−1.32255	−	0.481368i	−0.418274	−	0.908321i	$-0.637365\pi$
$479$	−28.9454	−	10.5353i	−1.32255	−	0.481368i	−0.904274	+	0.426953i	$0.859587\pi$
$480$	−2.40078			−0.109580
$481$	0.927160	+	5.40737i	0.0422748	+	0.246555i
$482$	18.6751			0.850629
$483$	7.63664	+	2.77951i	0.347479	+	0.126472i
$484$	−9.17035	+	3.33774i	−0.416834	+	0.151715i
$485$	7.87118	+	6.60470i	0.357412	+	0.299904i
$486$	3.72876	−	21.1468i	0.169140	−	0.959240i
$487$	−12.6573			−0.573555			−0.286777	−	0.957997i	$-0.592584\pi$
$487$	−12.6573			−0.573555			−0.286777	+	0.957997i	$0.592584\pi$
$488$	0.393351	−	2.23080i	0.0178062	−	0.100984i
$489$	20.4974	+	35.5026i	0.926926	+	1.60548i
$490$	−4.33262	+	3.63550i	−0.195728	+	0.164235i
$491$	2.47133	−	4.28047i	0.111529	−	0.193175i	−0.804858	−	0.593468i	$-0.797758\pi$
$491$	2.47133	−	4.28047i	0.111529	−	0.193175i	0.916387	+	0.400293i	$0.131092\pi$
$492$	−5.07088	−	8.78302i	−0.228613	−	0.395969i
$493$	−4.67271	−	1.70073i	−0.210448	−	0.0765970i
$494$	−4.10728	−	3.44642i	−0.184795	−	0.155062i
$495$	−6.29612	+	10.9052i	−0.282989	+	0.490152i
$496$	0.233256	+	1.32286i	0.0104735	+	0.0593981i
$497$	−1.66693	−	9.45360i	−0.0747718	−	0.424052i
$498$	13.2189	−	11.0920i	0.592353	−	0.497043i
$499$	21.4898	−	7.82166i	0.962017	−	0.350146i	0.187193	−	0.982323i	$-0.440061\pi$
$499$	21.4898	−	7.82166i	0.962017	−	0.350146i	0.774824	+	0.632178i	$0.217839\pi$
$500$	−0.939693	+	0.342020i	−0.0420243	+	0.0152956i
$501$	−6.36874	+	5.34400i	−0.284534	+	0.238752i
$502$	0.763910	+	4.33235i	0.0340950	+	0.193362i
$503$	5.92404	+	33.5969i	0.264140	+	1.49801i	0.771474	+	0.636261i	$0.219520\pi$
$503$	5.92404	+	33.5969i	0.264140	+	1.49801i	−0.507334	+	0.861749i	$0.669369\pi$
$504$	−1.60213	+	2.77497i	−0.0713644	+	0.123607i
$505$	11.6803	+	9.80093i	0.519766	+	0.436135i
$506$	−12.5004	−	4.54978i	−0.555712	−	0.202263i
$507$	−14.6286	−	25.3374i	−0.649678	−	1.12528i
$508$	8.74476	−	15.1464i	0.387986	−	0.672011i
$509$	−1.82001	+	1.52717i	−0.0806704	+	0.0676905i	−0.682231	−	0.731137i	$-0.738990\pi$
$509$	−1.82001	+	1.52717i	−0.0806704	+	0.0676905i	0.601561	+	0.798827i	$0.294546\pi$
$510$	−0.974820	−	1.68844i	−0.0431657	−	0.0747653i
$511$	−1.73118	+	9.81803i	−0.0765831	+	0.434324i
$512$	1.00000			0.0441942
$513$	−0.585457	+	3.32029i	−0.0258486	+	0.146595i
$514$	2.43377	+	2.04218i	0.107349	+	0.0900767i
$515$	17.0391	−	6.20172i	0.750832	−	0.273280i
$516$	−14.9012	−	5.42359i	−0.655988	−	0.238760i
$517$	−21.6401			−0.951732
$518$	−6.63825	+	2.38069i	−0.291668	+	0.104601i
$519$	−10.8785			−0.477512
$520$	−0.847546	−	0.308481i	−0.0371673	−	0.0135278i
$521$	1.38251	−	0.503191i	0.0605687	−	0.0220452i	−0.311558	−	0.950227i	$-0.600851\pi$
$521$	1.38251	−	0.503191i	0.0605687	−	0.0220452i	0.372127	+	0.928182i	$0.378629\pi$
$522$	−12.9639	−	10.8780i	−0.567416	−	0.476118i
$523$	2.67182	−	15.1526i	0.116830	−	0.662578i	−0.868997	−	0.494817i	$-0.835235\pi$
$523$	2.67182	−	15.1526i	0.116830	−	0.662578i	0.985828	−	0.167761i	$-0.0536537\pi$
$524$	11.6848			0.510453
$525$	−0.483336	+	2.74114i	−0.0210945	+	0.119633i
$526$	−2.72312	−	4.71659i	−0.118734	−	0.205653i
$527$	−0.835636	+	0.701182i	−0.0364009	+	0.0305440i
$528$	5.46922	−	9.47296i	0.238017	−	0.412258i
$529$	7.23770	+	12.5361i	0.314683	+	0.545046i
$530$	3.88637	+	1.41452i	0.168813	+	0.0614430i
$531$	−0.836486	−	0.701895i	−0.0363004	−	0.0304596i
$532$	3.44603	−	5.96870i	0.149404	−	0.258776i
$533$	−0.661619	−	3.75223i	−0.0286579	−	0.162527i
$534$	−2.86944	−	16.2734i	−0.124173	−	0.704218i
$535$	−5.58445	+	4.68591i	−0.241437	+	0.202589i
$536$	7.27319	−	2.64722i	0.314154	−	0.114343i
$537$	43.7843	−	15.9362i	1.88943	−	0.687697i
$538$	0.551191	−	0.462504i	0.0237635	−	0.0199400i
$539$	−4.47475	−	25.3776i	−0.192741	−	1.09309i
$540$	0.0984855	+	0.558539i	0.00423814	+	0.0240357i
$541$	19.5968	−	33.9426i	0.842531	−	1.45931i	−0.0452173	−	0.998977i	$-0.514398\pi$
$541$	19.5968	−	33.9426i	0.842531	−	1.45931i	0.887748	−	0.460329i	$-0.152269\pi$
$542$	15.5978	+	13.0881i	0.669982	+	0.562182i
$543$	−35.3834	−	12.8785i	−1.51845	−	0.552670i
$544$	0.406042	+	0.703286i	0.0174089	+	0.0301531i
$545$	8.90122	−	15.4174i	0.381286	−	0.660407i
$546$	−1.92314	+	1.61370i	−0.0823027	+	0.0690602i
$547$	−22.6391	−	39.2121i	−0.967978	−	1.67659i	−0.701392	−	0.712775i	$-0.747438\pi$
$547$	−22.6391	−	39.2121i	−0.967978	−	1.67659i	−0.266585	−	0.963811i	$-0.585895\pi$
$548$	2.22159	−	12.5993i	0.0949016	−	0.538214i
$549$	6.26052			0.267193
$550$	0.791174	−	4.48697i	0.0337358	−	0.191325i
$551$	27.8843	+	23.3977i	1.18791	+	0.996774i
$552$	6.58682	−	2.39741i	0.280354	−	0.102040i
$553$	6.22008	+	2.26392i	0.264505	+	0.0962718i
$554$	25.6284			1.08885
$555$	7.36134	−	12.6123i	0.312471	−	0.535362i
$556$	13.6891			0.580546
$557$	−22.0541	−	8.02702i	−0.934461	−	0.340116i	−0.170484	−	0.985360i	$-0.554533\pi$
$557$	−22.0541	−	8.02702i	−0.934461	−	0.340116i	−0.763976	+	0.645245i	$0.776756\pi$
$558$	−3.48858	+	1.26974i	−0.147683	+	0.0537523i
$559$	−4.56366	−	3.82937i	−0.193022	−	0.161965i
$560$	0.201324	−	1.14177i	0.00850751	−	0.0482485i
$561$	8.88293			0.375038
$562$	−4.82239	+	27.3491i	−0.203420	+	1.15365i
$563$	3.62092	+	6.27162i	0.152604	+	0.264317i	0.932184	−	0.361985i	$-0.117901\pi$
$563$	3.62092	+	6.27162i	0.152604	+	0.264317i	−0.779580	+	0.626302i	$0.784568\pi$
$564$	8.73504	−	7.32957i	0.367812	−	0.308631i
$565$	−2.28364	+	3.95538i	−0.0960735	+	0.166404i
$566$	12.9906	+	22.5003i	0.546034	+	0.945759i
$567$	10.5165	+	3.82768i	0.441650	+	0.160748i
$568$	−6.34269	−	5.32215i	−0.266134	−	0.223313i
$569$	−3.34725	+	5.79761i	−0.140324	+	0.243049i	−0.927619	−	0.373529i	$-0.878148\pi$
$569$	−3.34725	+	5.79761i	−0.140324	+	0.243049i	0.787295	+	0.616577i	$0.211481\pi$
$570$	2.47826	+	14.0549i	0.103803	+	0.588695i
$571$	3.84973	+	21.8329i	0.161106	+	0.913679i	0.952989	+	0.303005i	$0.0979900\pi$
$571$	3.84973	+	21.8329i	0.161106	+	0.913679i	−0.791883	+	0.610673i	$0.790899\pi$
$572$	3.14799	−	2.64148i	0.131624	−	0.110446i
$573$	−15.0865	+	5.49102i	−0.630246	+	0.229391i
$574$	4.60227	−	1.67509i	0.192095	−	0.0699169i
$575$	2.23661	−	1.87674i	0.0932732	−	0.0782655i
$576$	0.479922	+	2.72177i	0.0199968	+	0.113407i
$577$	−1.41912	−	8.04822i	−0.0590787	−	0.335052i	0.940915	−	0.338643i	$-0.109968\pi$
$577$	−1.41912	−	8.04822i	−0.0590787	−	0.335052i	−0.999994	+	0.00359136i	$0.998857\pi$
$578$	8.17026	−	14.1513i	0.339838	−	0.588617i
$579$	−41.4197	−	34.7553i	−1.72134	−	1.44438i
$580$	5.75397	+	2.09428i	0.238921	+	0.0869600i
$581$	4.16662	+	7.21680i	0.172861	+	0.299403i
$582$	12.3341	−	21.3633i	0.511266	−	0.885539i
$583$	−14.4349	+	12.1123i	−0.597833	+	0.501642i
$584$	4.29949	+	7.44693i	0.177914	+	0.308156i
$585$	0.432861	−	2.45488i	0.0178966	−	0.101497i
$586$	−8.55325			−0.353331
$587$	2.21425	−	12.5576i	0.0913918	−	0.518308i	−0.904402	−	0.426682i	$-0.859682\pi$
$587$	2.21425	−	12.5576i	0.0913918	−	0.518308i	0.995793	−	0.0916264i	$-0.0292065\pi$
$588$	10.4017	+	8.72805i	0.428958	+	0.359939i
$589$	7.50362	−	2.73109i	0.309181	−	0.112533i
$590$	0.371270	+	0.135131i	0.0152849	+	0.00556326i
$591$	51.2036			2.10624
$592$	−3.06622	+	5.25341i	−0.126021	+	0.215914i
$593$	23.0683			0.947301			0.473650	−	0.880713i	$-0.342936\pi$
$593$	23.0683			0.947301			0.473650	+	0.880713i	$0.342936\pi$
$594$	−2.42823	−	0.883803i	−0.0996315	−	0.0362629i
$595$	0.884735	−	0.322017i	0.0362706	−	0.0132014i
$596$	−15.8692	−	13.3158i	−0.650027	−	0.545438i
$597$	4.20676	−	23.8577i	0.172171	−	0.976433i
$598$	2.63339			0.107687
$599$	−8.21438	+	46.5861i	−0.335630	+	1.90346i	0.0852876	+	0.996356i	$0.472819\pi$
$599$	−8.21438	+	46.5861i	−0.335630	+	1.90346i	−0.420918	+	0.907099i	$0.638292\pi$
$600$	1.20039	+	2.07914i	0.0490058	+	0.0848805i
$601$	−2.30480	+	1.93396i	−0.0940148	+	0.0788878i	−0.688584	−	0.725157i	$-0.741767\pi$
$601$	−2.30480	+	1.93396i	−0.0940148	+	0.0788878i	0.594569	+	0.804045i	$0.297323\pi$
$602$	3.82894	−	6.63191i	0.156056	−	0.270297i
$603$	10.6957	+	18.5255i	0.435563	+	0.754417i
$604$	11.3659	+	4.13685i	0.462472	+	0.168326i
$605$	7.47574	+	6.27289i	0.303932	+	0.255029i
$606$	18.3030	−	31.7018i	0.743509	−	1.28780i
$607$	1.48549	+	8.42464i	0.0602942	+	0.341946i	1.00000		3.84527e-5i	$-1.22399e-5\pi$
$607$	1.48549	+	8.42464i	0.0602942	+	0.341946i	−0.939706	+	0.341984i	$0.888901\pi$
$608$	−1.03227	−	5.85429i	−0.0418641	−	0.237423i
$609$	13.0562	−	10.9554i	0.529062	−	0.443936i
$610$	−2.12861	+	0.774750i	−0.0861848	+	0.0313687i
$611$	4.02551	−	1.46517i	0.162855	−	0.0592743i
$612$	−1.71932	+	1.44268i	−0.0694993	+	0.0583168i
$613$	0.387267	+	2.19630i	0.0156416	+	0.0887078i	0.991629	−	0.129118i	$-0.0412146\pi$
$613$	0.387267	+	2.19630i	0.0156416	+	0.0887078i	−0.975988	+	0.217826i	$0.930104\pi$
$614$	4.47522	+	25.3802i	0.180605	+	1.02426i
$615$	−5.07088	+	8.78302i	−0.204478	+	0.354165i
$616$	4.04652	+	3.39544i	0.163039	+	0.136806i
$617$	18.0496	+	6.56953i	0.726651	+	0.264479i	0.678747	−	0.734373i	$-0.262523\pi$
$617$	18.0496	+	6.56953i	0.726651	+	0.264479i	0.0479044	+	0.998852i	$0.484746\pi$
$618$	−21.7662	−	37.7002i	−0.875567	−	1.51653i
$619$	2.70957	−	4.69312i	0.108907	−	0.188632i	−0.806421	−	0.591342i	$-0.798598\pi$
$619$	2.70957	−	4.69312i	0.108907	−	0.188632i	0.915328	+	0.402710i	$0.131932\pi$
$620$	1.02900	−	0.863434i	0.0413257	−	0.0346764i
$621$	−0.827959	−	1.43407i	−0.0332249	−	0.0575472i
$622$	−2.17005	+	12.3070i	−0.0870112	+	0.493465i
$623$	7.97994			0.319709
$624$	−0.376011	+	2.13246i	−0.0150525	+	0.0853669i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	17.1278	−	6.23402i	0.684565	−	0.249161i
$627$	−61.1032	−	22.2397i	−2.44023	−	0.888170i
$628$	−16.7890			−0.669955
$629$	−4.93966	−	0.0233253i	−0.196957	−	0.000930041i
$630$	3.20425			0.127661
$631$	−37.9753	−	13.8219i	−1.51177	−	0.550240i	−0.552694	−	0.833384i	$-0.686400\pi$
$631$	−37.9753	−	13.8219i	−1.51177	−	0.550240i	−0.959077	+	0.283144i	$0.908622\pi$
$632$	5.36500	−	1.95270i	0.213408	−	0.0776742i
$633$	−41.5612	−	34.8740i	−1.65191	−	1.38612i
$634$	4.60790	−	26.1327i	0.183003	−	1.03786i
$635$	−17.4895			−0.694050
$636$	1.72418	−	9.77829i	0.0683681	−	0.387735i
$637$	2.55061	+	4.41779i	0.101059	+	0.175039i
$638$	−21.3716	+	17.9329i	−0.846112	+	0.709972i
$639$	11.4417	−	19.8176i	0.452627	−	0.783972i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	41.2654	+	15.0194i	1.62988	+	0.593230i	0.985229	−	0.171243i	$-0.0547784\pi$
$641$	41.2654	+	15.0194i	1.62988	+	0.593230i	0.644656	+	0.764473i	$0.277001\pi$
$642$	13.4070	+	11.2498i	0.529134	+	0.443996i
$643$	0.238081	−	0.412368i	0.00938899	−	0.0162622i	−0.861293	−	0.508109i	$-0.830345\pi$
$643$	0.238081	−	0.412368i	0.00938899	−	0.0162622i	0.870682	+	0.491847i	$0.163678\pi$
$644$	0.587805	+	3.33361i	0.0231628	+	0.131363i
$645$	2.75363	+	15.6166i	0.108424	+	0.614903i
$646$	3.69810	−	3.10307i	0.145500	−	0.122089i
$647$	10.6395	−	3.87246i	0.418282	−	0.152242i	−0.124301	−	0.992245i	$-0.539669\pi$
$647$	10.6395	−	3.87246i	0.418282	−	0.152242i	0.542582	+	0.840003i	$0.317447\pi$
$648$	9.07076	−	3.30149i	0.356333	−	0.129695i
$649$	−1.37899	+	1.15711i	−0.0541299	+	0.0454204i
$650$	0.156620	+	0.888237i	0.00614315	+	0.0348395i
$651$	−0.649249	−	3.68207i	−0.0254461	−	0.144312i
$652$	−8.53781	+	14.7879i	−0.334366	+	0.579139i
$653$	−11.8678	−	9.95830i	−0.464425	−	0.389698i	0.380331	−	0.924850i	$-0.375810\pi$
$653$	−11.8678	−	9.95830i	−0.464425	−	0.389698i	−0.844756	+	0.535152i	$0.820254\pi$
$654$	−40.1623	−	14.6179i	−1.57047	−	0.571604i
$655$	−5.84240	−	10.1193i	−0.228282	−	0.395395i
$656$	2.11218	−	3.65840i	0.0824666	−	0.142836i
$657$	−18.2055	+	15.2762i	−0.710263	+	0.595981i
$658$	2.75330	+	4.76886i	0.107335	+	0.185910i
$659$	−6.98887	+	39.6358i	−0.272248	+	1.54399i	0.475323	+	0.879811i	$0.342331\pi$
$659$	−6.98887	+	39.6358i	−0.272248	+	1.54399i	−0.747571	+	0.664182i	$0.768780\pi$
$660$	−10.9384			−0.425778
$661$	−6.00658	+	34.0650i	−0.233629	+	1.32498i	0.611853	+	0.790972i	$0.290424\pi$
$661$	−6.00658	+	34.0650i	−0.233629	+	1.32498i	−0.845482	+	0.534004i	$0.820687\pi$
$662$	10.0272	+	8.41382i	0.389718	+	0.327012i
$663$	−1.65241	+	0.601428i	−0.0641742	+	0.0233575i
$664$	6.75420	+	2.45833i	0.262114	+	0.0954016i
$665$	−6.89206			−0.267263
$666$	−15.7701	−	5.82434i	−0.611080	−	0.225689i
$667$	−17.8780			−0.692239
$668$	−3.25411	−	1.18440i	−0.125905	−	0.0458258i
$669$	60.3680	−	21.9721i	2.33396	−	0.849492i
$670$	−5.92916	−	4.97515i	−0.229063	−	0.192207i
$671$	1.79218	−	10.1640i	0.0691864	−	0.392376i
$672$	−2.78342			−0.107373
$673$	4.05972	−	23.0238i	0.156491	−	0.887504i	−0.800919	−	0.598772i	$-0.795655\pi$
$673$	4.05972	−	23.0238i	0.156491	−	0.887504i	0.957410	−	0.288731i	$-0.0932334\pi$
$674$	−5.17831	−	8.96910i	−0.199461	−	0.345477i
$675$	0.434466	−	0.364560i	0.0167226	−	0.0140319i
$676$	6.09325	−	10.5538i	0.234356	−	0.405916i
$677$	−24.9222	−	43.1665i	−0.957837	−	1.65902i	−0.727737	−	0.685856i	$-0.759428\pi$
$677$	−24.9222	−	43.1665i	−0.957837	−	1.65902i	−0.230100	−	0.973167i	$-0.573905\pi$
$678$	10.3038	+	3.75027i	0.395715	+	0.144028i
$679$	9.12569	+	7.65736i	0.350212	+	0.293863i
$680$	0.406042	−	0.703286i	0.0155710	−	0.0269698i
$681$	5.96319	+	33.8190i	0.228510	+	1.29595i
$682$	1.06276	+	6.02720i	0.0406951	+	0.230793i
$683$	−8.55703	+	7.18020i	−0.327426	+	0.274743i	−0.791650	−	0.610975i	$-0.790778\pi$
$683$	−8.55703	+	7.18020i	−0.327426	+	0.274743i	0.464224	+	0.885718i	$0.346333\pi$
$684$	15.4387	−	5.61921i	0.590312	−	0.214856i
$685$	−12.0221	+	4.37568i	−0.459340	+	0.167186i
$686$	−11.2401	+	9.43158i	−0.429150	+	0.360099i
$687$	0.995132	+	5.64367i	0.0379666	+	0.215320i
$688$	−1.14697	−	6.50479i	−0.0437279	−	0.247993i
$689$	1.86512	−	3.23048i	0.0710553	−	0.123071i
$690$	−5.36963	−	4.50565i	−0.204418	−	0.171527i
$691$	1.31718	+	0.479413i	0.0501078	+	0.0182377i	0.366952	−	0.930240i	$-0.380401\pi$
$691$	1.31718	+	0.479413i	0.0501078	+	0.0182377i	−0.316845	+	0.948477i	$0.602623\pi$
$692$	−2.26561	−	3.92415i	−0.0861255	−	0.149174i
$693$	−7.29960	+	12.6433i	−0.277289	+	0.480278i
$694$	−10.5632	+	8.86361i	−0.400975	+	0.336458i
$695$	−6.84454	−	11.8551i	−0.259628	−	0.449689i
$696$	2.55273	−	14.4773i	0.0967611	−	0.548759i
$697$	3.43053			0.129941
$698$	−2.72464	+	15.4522i	−0.103129	+	0.584875i
$699$	−15.3999	−	12.9220i	−0.582477	−	0.488757i
$700$	−1.08946	+	0.396532i	−0.0411778	+	0.0149875i
$701$	15.4237	+	5.61375i	0.582543	+	0.212028i	0.616447	−	0.787397i	$-0.288572\pi$
$701$	15.4237	+	5.61375i	0.582543	+	0.212028i	−0.0339033	+	0.999425i	$0.510794\pi$
$702$	0.511540			0.0193068
$703$	33.9202	+	12.5276i	1.27932	+	0.472488i
$704$	4.55619			0.171718
$705$	−10.7151	−	3.89998i	−0.403555	−	0.146882i
$706$	−18.9131	+	6.88380i	−0.711803	+	0.259075i
$707$	13.5419	+	11.3630i	0.509296	+	0.427350i
$708$	0.164713	−	0.934132i	0.00619028	−	0.0351068i
$709$	−17.1809			−0.645243			−0.322621	−	0.946528i	$-0.604564\pi$
$709$	−17.1809			−0.645243			−0.322621	+	0.946528i	$0.604564\pi$
$710$	−1.43777	+	8.15401i	−0.0539586	+	0.306015i
$711$	7.88959	+	13.6652i	0.295883	+	0.512484i
$712$	5.27263	−	4.42426i	0.197600	−	0.165806i
$713$	−1.96096	+	3.39648i	−0.0734386	+	0.127199i
$714$	−1.13019	−	1.95754i	−0.0422962	−	0.0732592i
$715$	−3.86158	−	1.40550i	−0.144415	−	0.0525627i
$716$	14.8674	+	12.4752i	0.555619	+	0.466220i
$717$	5.28729	−	9.15786i	0.197458	−	0.342007i
$718$	−5.04123	−	28.5902i	−0.188137	−	1.06698i
$719$	−1.35772	−	7.70002i	−0.0506345	−	0.287162i	0.948967	−	0.315374i	$-0.102130\pi$
$719$	−1.35772	−	7.70002i	−0.0506345	−	0.287162i	−0.999602	+	0.0282115i	$0.991019\pi$
$720$	2.11716	−	1.77651i	0.0789021	−	0.0662067i
$721$	19.7548	−	7.19016i	0.735707	−	0.267775i
$722$	−15.3530	+	5.58804i	−0.571380	+	0.207965i
$723$	−34.3456	+	28.8194i	−1.27733	+	1.07180i
$724$	−2.72352	−	15.4459i	−0.101219	−	0.574041i
$725$	−1.06329	−	6.03022i	−0.0394896	−	0.223957i
$726$	11.7145	−	20.2901i	0.434765	−	0.753036i
$727$	6.65529	+	5.58445i	0.246831	+	0.207116i	0.757806	−	0.652480i	$-0.226271\pi$
$727$	6.65529	+	5.58445i	0.246831	+	0.207116i	−0.510975	+	0.859595i	$0.670716\pi$
$728$	−0.982628	−	0.357647i	−0.0364186	−	0.0132553i
$729$	11.2967	+	19.5665i	0.418398	+	0.724686i
$730$	4.29949	−	7.44693i	0.159131	−	0.275623i
$731$	4.10901	−	3.44787i	0.151977	−	0.127524i
$732$	2.71915	+	4.70970i	0.100503	+	0.174076i
$733$	1.76966	−	10.0363i	0.0653640	−	0.370698i	−0.934526	−	0.355894i	$-0.884176\pi$
$733$	1.76966	−	10.0363i	0.0653640	−	0.370698i	0.999890	−	0.0148039i	$-0.00471239\pi$
$734$	−25.8162			−0.952892
$735$	2.35787	−	13.3722i	0.0869714	−	0.493239i
$736$	2.23661	+	1.87674i	0.0824427	+	0.0691776i
$737$	33.1380	−	12.0613i	1.22066	−	0.444282i
$738$	10.9710	+	3.99312i	0.403848	+	0.146989i
$739$	−53.5770			−1.97086			−0.985430	−	0.170079i	$-0.945598\pi$
$739$	−53.5770			−1.97086			−0.985430	+	0.170079i	$0.945598\pi$
$740$	6.08269	+	0.0287228i	0.223604	+	0.00105587i
$741$	12.8722			0.472873
$742$	4.50579	+	1.63997i	0.165413	+	0.0602053i
$743$	−9.64139	+	3.50918i	−0.353708	+	0.128739i	−0.512762	−	0.858531i	$-0.671378\pi$
$743$	−9.64139	+	3.50918i	−0.353708	+	0.128739i	0.159054	+	0.987270i	$0.449156\pi$
$744$	−2.47041	−	2.07292i	−0.0905696	−	0.0759969i
$745$	−3.59725	+	20.4010i	−0.131793	+	0.747436i
$746$	2.54084			0.0930269
$747$	−3.44952	+	19.5632i	−0.126211	+	0.715781i
$748$	1.85001	+	3.20431i	0.0676429	+	0.117161i
$749$	−6.47450	+	5.43275i	−0.236573	+	0.198508i
$750$	1.20039	−	2.07914i	0.0438321	−	0.0759194i
$751$	21.2249	+	36.7625i	0.774506	+	1.34148i	0.935072	+	0.354459i	$0.115335\pi$
$751$	21.2249	+	36.7625i	0.774506	+	1.34148i	−0.160565	+	0.987025i	$0.551332\pi$
$752$	4.46317	+	1.62446i	0.162755	+	0.0592381i
$753$	−8.09057	−	6.78880i	−0.294837	−	0.247397i
$754$	2.76140	−	4.78289i	0.100564	−	0.174182i
$755$	−2.10034	−	11.9116i	−0.0764391	−	0.433507i
$756$	0.114182	+	0.647559i	0.00415277	+	0.0235515i
$757$	−37.6170	+	31.5644i	−1.36721	+	1.14723i	−0.393532	+	0.919311i	$0.628747\pi$
$757$	−37.6170	+	31.5644i	−1.36721	+	1.14723i	−0.973681	+	0.227917i	$0.926809\pi$
$758$	−19.0685	+	6.94036i	−0.692598	+	0.252085i
$759$	30.0108	−	10.9230i	1.08932	−	0.396481i
$760$	−4.55383	+	3.82112i	−0.165185	+	0.138607i
$761$	0.157293	+	0.892054i	0.00570187	+	0.0323369i	0.987526	−	0.157456i	$-0.0503293\pi$
$761$	0.157293	+	0.892054i	0.00570187	+	0.0323369i	−0.981824	+	0.189793i	$0.939218\pi$
$762$	7.29124	+	41.3507i	0.264134	+	1.49798i
$763$	10.3199	−	17.8746i	0.373605	−	0.647104i
$764$	−5.12274	−	4.29849i	−0.185334	−	0.155514i
$765$	2.10905	+	0.767633i	0.0762530	+	0.0277538i
$766$	−5.32912	−	9.23031i	−0.192549	−	0.333505i
$767$	0.178177	−	0.308611i	0.00643359	−	0.0111433i
$768$	−1.83911	+	1.54319i	−0.0663631	+	0.0556852i
$769$	24.6200	+	42.6431i	0.887820	+	1.53775i	0.842447	+	0.538779i	$0.181114\pi$
$769$	24.6200	+	42.6431i	0.887820	+	1.53775i	0.0453733	+	0.998970i	$0.485552\pi$
$770$	0.917273	−	5.20211i	0.0330562	−	0.187471i
$771$	−7.62745			−0.274696
$772$	3.91084	−	22.1795i	0.140754	−	0.798257i
$773$	8.81324	+	7.39519i	0.316990	+	0.265986i	0.787374	−	0.616476i	$-0.211440\pi$
$773$	8.81324	+	7.39519i	0.316990	+	0.265986i	−0.470384	+	0.882462i	$0.655885\pi$
$774$	17.1541	−	6.24359i	0.616592	−	0.224421i
$775$	−1.26226	−	0.459424i	−0.0453416	−	0.0165030i
$776$	10.2751			0.368854
$777$	8.53459	−	14.6225i	0.306177	−	0.524578i
$778$	−4.25933			−0.152704
$779$	−23.5977	−	8.58885i	−0.845474	−	0.307727i
$780$	2.03477	−	0.740597i	0.0728566	−	0.0265176i
$781$	−28.8985	−	24.2487i	−1.03407	−	0.867688i
$782$	−0.411726	+	2.33502i	−0.0147233	+	0.0835000i
$783$	−3.47283			−0.124109
$784$	−0.982126	+	5.56991i	−0.0350759	+	0.198925i
$785$	8.39452	+	14.5397i	0.299613	+	0.518945i
$786$	−21.4896	+	18.0319i	−0.766509	+	0.643177i
$787$	−0.825722	+	1.43019i	−0.0294338	+	0.0509808i	−0.880367	−	0.474293i	$-0.842704\pi$
$787$	−0.825722	+	1.43019i	−0.0294338	+	0.0509808i	0.850933	+	0.525274i	$0.176037\pi$
$788$	10.6639	+	18.4705i	0.379887	+	0.657984i
$789$	12.2867	+	4.47200i	0.437419	+	0.159207i
$790$	−4.37359	−	3.66988i	−0.155605	−	0.130568i
$791$	−2.64761	+	4.58580i	−0.0941382	+	0.163052i
$792$	2.18662	+	12.4009i	0.0776981	+	0.440648i
$793$	0.354779	+	2.01205i	0.0125986	+	0.0714500i
$794$	−3.42058	+	2.87021i	−0.121392	+	0.101860i
$795$	−9.33034	+	3.39597i	−0.330913	+	0.120442i
$796$	9.48224	−	3.45125i	0.336089	−	0.122326i
$797$	5.55890	−	4.66447i	0.196906	−	0.165224i	−0.539004	−	0.842303i	$-0.681199\pi$
$797$	5.55890	−	4.66447i	0.196906	−	0.165224i	0.735910	+	0.677079i	$0.236755\pi$
$798$	2.87324	+	16.2950i	0.101712	+	0.576836i
$799$	0.669776	+	3.79849i	0.0236950	+	0.134381i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	14.5723	+	12.2276i	0.514887	+	0.432041i
$802$	−5.30230	−	1.92988i	−0.187231	−	0.0681464i
$803$	19.5893	+	33.9297i	0.691291	+	1.19735i
$804$	−9.29099	+	16.0925i	−0.327668	+	0.567538i
$805$	2.59309	−	2.17586i	0.0913943	−	0.0766889i
$806$	−0.605772	−	1.04923i	−0.0213374	−	0.0369575i
$807$	−0.299965	+	1.70119i	−0.0105593	+	0.0598847i
$808$	15.2475			0.536406
$809$	−8.62779	+	48.9306i	−0.303337	+	1.72031i	0.327893	+	0.944715i	$0.393661\pi$
$809$	−8.62779	+	48.9306i	−0.303337	+	1.72031i	−0.631230	+	0.775595i	$0.717450\pi$
$810$	−7.39455	−	6.20477i	−0.259818	−	0.218013i
$811$	23.5387	−	8.56740i	0.826557	−	0.300842i	0.106112	−	0.994354i	$-0.466160\pi$
$811$	23.5387	−	8.56740i	0.826557	−	0.300842i	0.720445	+	0.693512i	$0.243938\pi$
$812$	6.67105	+	2.42806i	0.234108	+	0.0852083i
$813$	−48.8835			−1.71442
$814$	−13.9703	+	23.9355i	−0.489659	+	0.838940i
$815$	17.0756			0.598133
$816$	−1.83206	−	0.666816i	−0.0641350	−	0.0233432i
$817$	−36.8970	+	13.4294i	−1.29086	+	0.469835i
$818$	−11.8229	−	9.92059i	−0.413378	−	0.346865i
$819$	0.501851	−	2.84614i	0.0175361	−	0.0994520i
$820$	−4.22435			−0.147521
$821$	−6.53015	+	37.0343i	−0.227904	+	1.29251i	0.629152	+	0.777282i	$0.283402\pi$
$821$	−6.53015	+	37.0343i	−0.227904	+	1.29251i	−0.857056	+	0.515224i	$0.827709\pi$
$822$	15.3574	+	26.5997i	0.535649	+	0.927772i
$823$	27.7503	−	23.2852i	0.967313	−	0.811672i	−0.0148139	−	0.999890i	$-0.504716\pi$
$823$	27.7503	−	23.2852i	0.967313	−	0.811672i	0.982127	+	0.188218i	$0.0602711\pi$
$824$	9.06631	−	15.7033i	0.315840	−	0.547051i
$825$	5.46922	+	9.47296i	0.190414	+	0.329806i
$826$	0.430443	+	0.156668i	0.0149770	+	0.00545119i
$827$	38.3362	+	32.1679i	1.33308	+	1.11859i	0.983347	+	0.181740i	$0.0581729\pi$
$827$	38.3362	+	32.1679i	1.33308	+	1.11859i	0.349735	+	0.936849i	$0.386272\pi$
$828$	−4.03467	+	6.98825i	−0.140214	+	0.242858i
$829$	−4.35442	−	24.6952i	−0.151235	−	0.857698i	−0.962147	−	0.272530i	$-0.912140\pi$
$829$	−4.35442	−	24.6952i	−0.151235	−	0.857698i	0.810912	−	0.585168i	$-0.198971\pi$
$830$	−1.24813	−	7.07847i	−0.0433231	−	0.245697i
$831$	−47.1334	+	39.5496i	−1.63504	+	1.37196i
$832$	−0.847546	+	0.308481i	−0.0293834	+	0.0106947i
$833$	−4.31602	+	1.57090i	−0.149541	+	0.0544286i
$834$	−25.1757	+	21.1249i	−0.871762	+	0.731495i
$835$	0.601335	+	3.41034i	0.0208101	+	0.118020i
$836$	−4.70322	−	26.6733i	−0.162664	−	0.922515i
$837$	−0.380920	+	0.659773i	−0.0131665	+	0.0228051i
$838$	12.6865	+	10.6452i	0.438248	+	0.367733i
$839$	−32.2645	−	11.7433i	−1.11389	−	0.405424i	−0.281473	−	0.959569i	$-0.590823\pi$
$839$	−32.2645	−	11.7433i	−1.11389	−	0.405424i	−0.832420	+	0.554145i	$0.813045\pi$
$840$	1.39171	+	2.41052i	0.0480186	+	0.0831707i
$841$	−4.24710	+	7.35619i	−0.146452	+	0.253662i
$842$	−12.0676	+	10.1259i	−0.415877	+	0.348962i
$843$	−33.3361	−	57.7398i	−1.14816	−	1.98866i
$844$	3.92420	−	22.2552i	0.135076	−	0.766057i
$845$	−12.1865			−0.419229
$846$	−2.27944	+	12.9274i	−0.0783689	+	0.444452i
$847$	8.66723	+	7.27267i	0.297810	+	0.249892i
$848$	3.88637	−	1.41452i	0.133459	−	0.0485749i
$849$	−58.6134	−	21.3335i	−2.01161	−	0.732165i
$850$	−0.812085			−0.0278543
$851$	−16.7172	+	5.99534i	−0.573060	+	0.205517i
$852$	19.8780			0.681009
$853$	8.11353	+	2.95308i	0.277802	+	0.101112i	0.477164	−	0.878814i	$-0.341665\pi$
$853$	8.11353	+	2.95308i	0.277802	+	0.101112i	−0.199362	+	0.979926i	$0.563887\pi$
$854$	−2.46787	+	0.898230i	−0.0844487	+	0.0307368i
$855$	−12.5857	−	10.5607i	−0.430422	−	0.361167i
$856$	−1.26589	+	7.17922i	−0.0432673	+	0.245381i
$857$	47.4548			1.62102			0.810512	−	0.585722i	$-0.199189\pi$
$857$	47.4548			1.62102			0.810512	+	0.585722i	$0.199189\pi$
$858$	−1.71318	+	9.71592i	−0.0584869	+	0.331696i
$859$	7.54508	+	13.0685i	0.257435	+	0.445890i	0.965554	−	0.260203i	$-0.0837894\pi$
$859$	7.54508	+	13.0685i	0.257435	+	0.445890i	−0.708119	+	0.706093i	$0.750456\pi$
$860$	−5.05983	+	4.24570i	−0.172539	+	0.144777i
$861$	−5.87908	+	10.1829i	−0.200358	+	0.347031i
$862$	−0.688347	−	1.19225i	−0.0234452	−	0.0406082i
$863$	25.9044	+	9.42844i	0.881797	+	0.320948i	0.742935	−	0.669364i	$-0.233433\pi$
$863$	25.9044	+	9.42844i	0.881797	+	0.320948i	0.138862	+	0.990312i	$0.455656\pi$
$864$	0.434466	+	0.364560i	0.0147808	+	0.0124026i
$865$	−2.26561	+	3.92415i	−0.0770330	+	0.133425i
$866$	−1.73037	−	9.81344i	−0.0588005	−	0.333474i
$867$	6.81223	+	38.6341i	0.231355	+	1.31208i
$868$	1.19300	−	1.00105i	0.0404932	−	0.0339778i
$869$	24.4440	−	8.89688i	0.829205	−	0.301806i
$870$	−13.8140	+	5.02790i	−0.468340	+	0.170462i
$871$	−5.34774	+	4.48729i	−0.181201	+	0.152046i
$872$	−3.09136	−	17.5320i	−0.104687	−	0.593708i
$873$	4.93124	+	27.9665i	0.166897	+	0.946522i
$874$	8.67821	−	15.0311i	0.293545	−	0.508434i
$875$	0.888137	+	0.745236i	0.0300245	+	0.0251936i
$876$	−19.3993	−	7.06076i	−0.655441	−	0.238561i
$877$	5.05277	+	8.75166i	0.170620	+	0.295523i	0.938637	−	0.344907i	$-0.112090\pi$
$877$	5.05277	+	8.75166i	0.170620	+	0.295523i	−0.768017	+	0.640430i	$0.778756\pi$
$878$	−1.67441	+	2.90016i	−0.0565086	+	0.0978757i
$879$	15.7303	−	13.1993i	0.530571	−	0.445202i
$880$	−2.27810	−	3.94578i	−0.0767946	−	0.133012i
$881$	9.55282	−	54.1768i	0.321843	−	1.82526i	−0.209148	−	0.977884i	$-0.567069\pi$
$881$	9.55282	−	54.1768i	0.321843	−	1.82526i	0.530991	−	0.847377i	$-0.321820\pi$
$882$	−15.6314			−0.526336
$883$	4.88641	−	27.7122i	0.164441	−	0.932590i	−0.785198	−	0.619244i	$-0.787439\pi$
$883$	4.88641	−	27.7122i	0.164441	−	0.932590i	0.949639	−	0.313345i	$-0.101450\pi$
$884$	−0.561090	−	0.470810i	−0.0188715	−	0.0158351i
$885$	−0.891338	+	0.324421i	−0.0299620	+	0.0109053i
$886$	16.2390	+	5.91052i	0.545560	+	0.198568i
$887$	−3.90764			−0.131206			−0.0656028	−	0.997846i	$-0.520897\pi$
$887$	−3.90764			−0.131206			−0.0656028	+	0.997846i	$0.520897\pi$
$888$	−2.46792	−	14.3934i	−0.0828178	−	0.483009i
$889$	−20.2770			−0.680069
$890$	−6.46784	−	2.35410i	−0.216802	−	0.0789096i
$891$	41.3281	−	15.0422i	1.38454	−	0.503933i
$892$	20.4985	+	17.2003i	0.686340	+	0.575908i
$893$	4.90288	−	27.8056i	0.164069	−	0.930479i
$894$	49.7341			1.66336
$895$	3.37016	−	19.1131i	0.112652	−	0.638881i
$896$	−0.579690	−	1.00405i	−0.0193661	−	0.0335431i
$897$	−4.84308	+	4.06382i	−0.161706	+	0.135687i
$898$	5.64929	−	9.78485i	0.188519	−	0.326525i
$899$	4.11258	+	7.12319i	0.137162	+	0.237572i
$900$	−2.59709	−	0.945262i	−0.0865696	−	0.0315087i
$901$	2.57285	+	2.15887i	0.0857139	+	0.0719225i
$902$	9.62348	−	16.6684i	0.320427	−	0.554996i
$903$	3.19250	+	18.1056i	0.106240	+	0.602516i
$904$	0.793101	+	4.49790i	0.0263781	+	0.149598i
$905$	−12.0148	+	10.0816i	−0.399384	+	0.335123i
$906$	−27.2871	+	9.93169i	−0.906553	+	0.329958i
$907$	−43.2131	+	15.7283i	−1.43487	+	0.522249i	−0.938322	−	0.345763i	$-0.887620\pi$
$907$	−43.2131	+	15.7283i	−1.43487	+	0.522249i	−0.496544	+	0.868011i	$0.665398\pi$
$908$	−10.9575	+	9.19440i	−0.363636	+	0.305127i
$909$	7.31763	+	41.5004i	0.242711	+	1.37648i
$910$	0.181582	+	1.02980i	0.00601940	+	0.0341377i
$911$	−5.67795	+	9.83449i	−0.188119	+	0.325831i	−0.944623	−	0.328158i	$-0.893572\pi$
$911$	−5.67795	+	9.83449i	−0.188119	+	0.325831i	0.756504	+	0.653989i	$0.226906\pi$
$912$	10.9328	+	9.17368i	0.362020	+	0.303771i
$913$	30.7734	+	11.2006i	1.01845	+	0.370686i
$914$	13.7487	+	23.8134i	0.454766	+	0.787677i
$915$	2.71915	−	4.70970i	0.0898923	−	0.155698i
$916$	−1.82857	+	1.53435i	−0.0604176	+	0.0506964i
$917$	−6.77357	−	11.7322i	−0.223683	−	0.387430i
$918$	−0.0799785	+	0.453581i	−0.00263969	+	0.0149704i
$919$	27.8995			0.920320			0.460160	−	0.887836i	$-0.347792\pi$
$919$	27.8995			0.920320			0.460160	+	0.887836i	$0.347792\pi$
$920$	0.506999	−	2.87534i	0.0167153	−	0.0947970i
$921$	−47.3970	−	39.7708i	−1.56178	−	1.31049i
$922$	22.2783	−	8.10863i	0.733696	−	0.267044i
$923$	7.01751	+	2.55416i	0.230984	+	0.0840713i
$924$	−12.6818			−0.417201
$925$	−3.01647	−	5.28213i	−0.0991810	−	0.173675i
$926$	−2.93112			−0.0963224
$927$	47.0920	+	17.1401i	1.54670	+	0.562954i
$928$	5.75397	−	2.09428i	0.188883	−	0.0687479i
$929$	−29.6636	−	24.8907i	−0.973231	−	0.816637i	0.00982380	−	0.999952i	$-0.496873\pi$
$929$	−29.6636	−	24.8907i	−0.973231	−	0.816637i	−0.983054	+	0.183314i	$0.941317\pi$
$930$	−0.559996	+	3.17590i	−0.0183630	+	0.104142i
$931$	33.6217			1.10191
$932$	1.45406	−	8.24636i	0.0476292	−	0.270118i
$933$	−15.0011	−	25.9827i	−0.491114	−	0.850635i
$934$	26.4140	−	22.1640i	0.864292	−	0.725227i
$935$	1.85001	−	3.20431i	0.0605017	−	0.104792i
$936$	−1.24637	−	2.15878i	−0.0407390	−	0.0705620i
$937$	48.9579	+	17.8192i	1.59938	+	0.582128i	0.979301	−	0.202407i	$-0.0648765\pi$
$937$	48.9579	+	17.8192i	1.59938	+	0.582128i	0.620083	+	0.784536i	$0.287099\pi$
$938$	−6.87415	−	5.76810i	−0.224449	−	0.188335i
$939$	−21.8796	+	37.8966i	−0.714014	+	1.23671i
$940$	−0.824761	−	4.67745i	−0.0269007	−	0.152562i
$941$	−3.06845	−	17.4021i	−0.100029	−	0.567291i	−0.993090	−	0.117356i	$-0.962558\pi$
$941$	−3.06845	−	17.4021i	−0.100029	−	0.567291i	0.893061	−	0.449935i	$-0.148553\pi$
$942$	30.8768	−	25.9087i	1.00602	−	0.844152i
$943$	11.5900	−	4.21841i	0.377422	−	0.137370i
$944$	0.371270	−	0.135131i	0.0120838	−	0.00439814i
$945$	0.503712	−	0.422664i	0.0163857	−	0.0137493i
$946$	−5.22582	−	29.6371i	−0.169906	−	0.963585i
$947$	7.39080	+	41.9153i	0.240169	+	1.36206i	0.831450	+	0.555599i	$0.187511\pi$
$947$	7.39080	+	41.9153i	0.240169	+	1.36206i	−0.591282	+	0.806465i	$0.701378\pi$
$948$	−6.85341	+	11.8705i	−0.222589	+	0.385535i
$949$	−5.94126	−	4.98531i	−0.192861	−	0.161830i
$950$	5.58610	+	2.03317i	0.181237	+	0.0659649i
$951$	31.8534	+	55.1718i	1.03292	+	1.78907i
$952$	0.470758	−	0.815376i	0.0152573	−	0.0264265i
$953$	−27.4536	+	23.0363i	−0.889308	+	0.746218i	−0.968071	−	0.250675i	$-0.919347\pi$
$953$	−27.4536	+	23.0363i	−0.889308	+	0.746218i	0.0787630	+	0.996893i	$0.474903\pi$
$954$	5.71517	+	9.89897i	0.185035	+	0.320491i
$955$	−1.16123	+	6.58567i	−0.0375766	+	0.213107i
$956$	4.40464			0.142456
$957$	11.6307	−	65.9612i	0.375968	−	2.13222i
$958$	23.5965	+	19.7998i	0.762368	+	0.639702i
$959$	−13.9382	+	5.07308i	−0.450087	+	0.163818i
$960$	2.25600	+	0.821116i	0.0728120	+	0.0265014i
$961$	−29.1956			−0.941795
$962$	0.978185	−	5.39838i	0.0315380	−	0.174051i
$963$	−20.1478			−0.649253
$964$	−17.5489	−	6.38727i	−0.565212	−	0.205720i
$965$	−21.1634	+	7.70286i	−0.681275	+	0.247964i
$966$	−6.22544	−	5.22377i	−0.200300	−	0.168072i
$967$	−1.39557	+	7.91468i	−0.0448785	+	0.254519i	−0.998990	−	0.0449328i	$-0.985693\pi$
$967$	−1.39557	+	7.91468i	−0.0448785	+	0.254519i	0.954111	+	0.299452i	$0.0968037\pi$
$968$	9.75888			0.313662
$969$	−2.01255	+	11.4138i	−0.0646525	+	0.366663i
$970$	−5.13754	−	8.89849i	−0.164957	−	0.285713i
$971$	40.7076	−	34.1577i	1.30637	−	1.09617i	0.317362	−	0.948304i	$-0.397203\pi$
$971$	40.7076	−	34.1577i	1.30637	−	1.09617i	0.989007	−	0.147869i	$-0.0472415\pi$
$972$	−10.7365	+	18.5962i	−0.344375	+	0.596474i
$973$	−7.93543	−	13.7446i	−0.254398	−	0.440630i
$974$	11.8939	+	4.32904i	0.381106	+	0.138711i
$975$	−1.65876	−	1.39187i	−0.0531229	−	0.0445754i
$976$	−1.13261	+	1.96174i	−0.0362539	+	0.0627936i
$977$	−8.13007	−	46.1079i	−0.260104	−	1.47512i	−0.782623	−	0.622496i	$-0.786119\pi$
$977$	−8.13007	−	46.1079i	−0.260104	−	1.47512i	0.522519	−	0.852627i	$-0.324992\pi$
$978$	−7.11868	−	40.3720i	−0.227630	−	1.29096i
$979$	24.0231	−	20.1578i	0.767782	−	0.644246i
$980$	5.31475	−	1.93441i	0.169773	−	0.0617925i
$981$	46.2345	−	16.8280i	1.47615	−	0.537276i
$982$	−3.78629	+	3.17708i	−0.120826	+	0.101385i
$983$	−5.30001	−	30.0579i	−0.169044	−	0.958697i	−0.944796	−	0.327659i	$-0.893740\pi$
$983$	−5.30001	−	30.0579i	−0.169044	−	0.958697i	0.775752	−	0.631038i	$-0.217371\pi$
$984$	1.76110	+	9.98768i	0.0561417	+	0.318396i
$985$	10.6639	−	18.4705i	0.339782	−	0.588519i
$986$	3.80923	+	3.19632i	0.121311	+	0.101792i
$987$	−12.4229	−	4.52157i	−0.395425	−	0.143923i
$988$	2.68084	+	4.64334i	0.0852888	+	0.147724i
$989$	9.64249	−	16.7013i	0.306613	−	0.531070i
$990$	9.64621	−	8.09413i	0.306577	−	0.257248i
$991$	−24.8870	−	43.1056i	−0.790563	−	1.36929i	−0.925619	−	0.378457i	$-0.876455\pi$
$991$	−24.8870	−	43.1056i	−0.790563	−	1.36929i	0.135057	−	0.990838i	$-0.456878\pi$
$992$	0.233256	−	1.32286i	0.00740587	−	0.0420008i
$993$	−31.4252			−0.997250
$994$	−1.66693	+	9.45360i	−0.0528717	+	0.299850i
$995$	−7.72999	−	6.48623i	−0.245057	−	0.205627i
$996$	−16.2154	+	5.90191i	−0.513804	+	0.187009i
$997$	−49.4737	−	18.0069i	−1.56685	−	0.570286i	−0.594555	−	0.804055i	$-0.702672\pi$
$997$	−49.4737	−	18.0069i	−1.56685	−	0.570286i	−0.972292	+	0.233769i	$0.924894\pi$
$998$	−22.8690			−0.723906
$999$	−3.24735	+	1.16460i	−0.102742	+	0.0368464i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.a.201.3	yes	18
37.7	even	9	inner	370.2.o.a.81.3	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.a.81.3	✓	18	37.7	even	9	inner
370.2.o.a.201.3	yes	18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(2.25600 - 0.821116i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.173648 - 0.984808i) q^{5} -2.40078 q^{6} +(0.201324 - 1.14177i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.11716 - 1.77651i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(2.25600 - 0.821116i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.173648 - 0.984808i) q^{5} -2.40078 q^{6} +(0.201324 - 1.14177i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.11716 - 1.77651i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-2.27810 - 3.94578i) q^{11} +(2.25600 + 0.821116i) q^{12} +(0.690926 + 0.579755i) q^{13} +(-0.579690 + 1.00405i) q^{14} +(-0.416892 - 2.36431i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-0.622093 + 0.521998i) q^{17} +(-2.59709 + 0.945262i) q^{18} +(5.58610 - 2.03317i) q^{19} +(0.766044 - 0.642788i) q^{20} +(-0.483336 - 2.74114i) q^{21} +(0.791174 + 4.48697i) q^{22} +(-1.45985 + 2.52853i) q^{23} +(-1.83911 - 1.54319i) q^{24} +(-0.939693 - 0.342020i) q^{25} +(-0.450970 - 0.781102i) q^{26} +(-0.283578 + 0.491171i) q^{27} +(0.888137 - 0.745236i) q^{28} +(3.06163 + 5.30289i) q^{29} +(-0.416892 + 2.36431i) q^{30} +1.34327 q^{31} +(0.173648 - 0.984808i) q^{32} +(-8.37932 - 7.03109i) q^{33} +(0.763110 - 0.277749i) q^{34} +(-1.08946 - 0.396532i) q^{35} +2.76376 q^{36} +(4.64115 + 3.93188i) q^{37} -5.94460 q^{38} +(2.03477 + 0.740597i) q^{39} +(-0.939693 + 0.342020i) q^{40} +(-3.23604 - 2.71536i) q^{41} +(-0.483336 + 2.74114i) q^{42} -6.60514 q^{43} +(0.791174 - 4.48697i) q^{44} +(-1.38188 - 2.39349i) q^{45} +(2.23661 - 1.87674i) q^{46} +(2.37481 - 4.11328i) q^{47} +(1.20039 + 2.07914i) q^{48} +(5.31475 + 1.93441i) q^{49} +(0.766044 + 0.642788i) q^{50} +(-0.974820 + 1.68844i) q^{51} +(0.156620 + 0.888237i) q^{52} +(-0.718172 - 4.07296i) q^{53} +(0.434466 - 0.364560i) q^{54} +(-4.28142 + 1.55831i) q^{55} +(-1.08946 + 0.396532i) q^{56} +(10.9328 - 9.17368i) q^{57} +(-1.06329 - 6.03022i) q^{58} +(-0.0686079 - 0.389095i) q^{59} +(1.20039 - 2.07914i) q^{60} +(1.73526 + 1.45605i) q^{61} +(-1.26226 - 0.459424i) q^{62} +(-1.60213 - 2.77497i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.690926 - 0.579755i) q^{65} +(5.46922 + 9.47296i) q^{66} +(-1.34403 + 7.62238i) q^{67} -0.812085 q^{68} +(-1.21720 + 6.90306i) q^{69} +(0.888137 + 0.745236i) q^{70} +(7.78047 - 2.83186i) q^{71} +(-2.59709 - 0.945262i) q^{72} -8.59898 q^{73} +(-3.01647 - 5.28213i) q^{74} -2.40078 q^{75} +(5.58610 + 2.03317i) q^{76} +(-4.96380 + 1.80667i) q^{77} +(-1.65876 - 1.39187i) q^{78} +(-0.991412 + 5.62258i) q^{79} +1.00000 q^{80} +(-1.67621 + 9.50626i) q^{81} +(2.11218 + 3.65840i) q^{82} +(-5.50607 + 4.62014i) q^{83} +(1.39171 - 2.41052i) q^{84} +(0.406042 + 0.703286i) q^{85} +(6.20680 + 2.25909i) q^{86} +(11.2613 + 9.44936i) q^{87} +(-2.27810 + 3.94578i) q^{88} +(1.19521 + 6.77836i) q^{89} +(0.479922 + 2.72177i) q^{90} +(0.801046 - 0.672157i) q^{91} +(-2.74361 + 0.998594i) q^{92} +(3.03041 - 1.10298i) q^{93} +(-3.63841 + 3.05299i) q^{94} +(-1.03227 - 5.85429i) q^{95} +(-0.416892 - 2.36431i) q^{96} +(-5.13754 + 8.89849i) q^{97} +(-4.33262 - 3.63550i) q^{98} +(-11.8328 - 4.30680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9}+O(q^{10}) \) 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9	\( 18 q - 6 q^{6} - 3 q^{7} - 9 q^{8} - 12 q^{9} - 9 q^{10} + 3 q^{11} + 9 q^{13} - 6 q^{17} + 6 q^{18} + 9 q^{19} - 6 q^{21} + 21 q^{23} + 6 q^{26} + 12 q^{27} - 3 q^{28} + 6 q^{29} - 30 q^{31} - 45 q^{33} - 15 q^{34} + 6 q^{35} + 24 q^{36} + 6 q^{37} - 12 q^{38} + 24 q^{39} + 15 q^{41} - 6 q^{42} - 12 q^{43} - 12 q^{45} + 24 q^{47} + 3 q^{48} + 33 q^{49} - 42 q^{51} - 12 q^{53} + 27 q^{54} + 6 q^{56} + 51 q^{57} - 15 q^{58} - 15 q^{59} + 3 q^{60} + 72 q^{61} - 57 q^{62} - 30 q^{63} - 9 q^{64} + 9 q^{65} - 3 q^{66} + 18 q^{67} + 24 q^{69} - 3 q^{70} + 6 q^{72} - 66 q^{73} - 24 q^{74} - 6 q^{75} + 9 q^{76} - 66 q^{77} + 6 q^{78} - 12 q^{79} + 18 q^{80} + 66 q^{81} + 45 q^{82} + 9 q^{83} + 42 q^{84} + 12 q^{86} + 48 q^{87} + 3 q^{88} + 6 q^{90} - 78 q^{91} + 18 q^{92} + 24 q^{94} - 3 q^{97} - 48 q^{98} - 96 q^{99}+O(q^{100}) \) 18 * q - 6 * q^6 - 3 * q^7 - 9 * q^8 - 12 * q^9 - 9 * q^10 + 3 * q^11 + 9 * q^13 - 6 * q^17 + 6 * q^18 + 9 * q^19 - 6 * q^21 + 21 * q^23 + 6 * q^26 + 12 * q^27 - 3 * q^28 + 6 * q^29 - 30 * q^31 - 45 * q^33 - 15 * q^34 + 6 * q^35 + 24 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^39 + 15 * q^41 - 6 * q^42 - 12 * q^43 - 12 * q^45 + 24 * q^47 + 3 * q^48 + 33 * q^49 - 42 * q^51 - 12 * q^53 + 27 * q^54 + 6 * q^56 + 51 * q^57 - 15 * q^58 - 15 * q^59 + 3 * q^60 + 72 * q^61 - 57 * q^62 - 30 * q^63 - 9 * q^64 + 9 * q^65 - 3 * q^66 + 18 * q^67 + 24 * q^69 - 3 * q^70 + 6 * q^72 - 66 * q^73 - 24 * q^74 - 6 * q^75 + 9 * q^76 - 66 * q^77 + 6 * q^78 - 12 * q^79 + 18 * q^80 + 66 * q^81 + 45 * q^82 + 9 * q^83 + 42 * q^84 + 12 * q^86 + 48 * q^87 + 3 * q^88 + 6 * q^90 - 78 * q^91 + 18 * q^92 + 24 * q^94 - 3 * q^97 - 48 * q^98 - 96 * q^99

Introduction

L-functions

Modular forms

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Database

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