LMFDB - Embedded newform 570.2.u.j.61.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
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			61.2
Root			$0.500000 - 0.677980i$ of defining polynomial
Character	$\chi$	$=$	570.61
Dual form			570.2.u.j.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-0.308023 + 0.533512i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-0.308023 + 0.533512i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(-2.55943 - 4.43306i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.222674 + 1.26285i) q^{13} +(0.471919 - 0.395987i) q^{14} +(-0.766044 - 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(0.754567 + 0.274640i) q^{17} +1.00000 q^{18} +(-1.20199 - 4.18990i) q^{19} +1.00000 q^{20} +(0.578894 + 0.210700i) q^{21} +(0.888879 + 5.04109i) q^{22} +(-4.27867 - 3.59023i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(0.641164 - 1.11053i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-0.578894 + 0.210700i) q^{28} +(6.97573 - 2.53896i) q^{29} +(0.500000 + 0.866025i) q^{30} +(1.45698 - 2.52356i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-3.92127 + 3.29033i) q^{33} +(-0.615128 - 0.516154i) q^{34} +(0.106975 + 0.606687i) q^{35} +(-0.939693 - 0.342020i) q^{36} -8.92589 q^{37} +(-0.303530 + 4.34832i) q^{38} +1.28233 q^{39} +(-0.939693 - 0.342020i) q^{40} +(-0.716761 - 4.06495i) q^{41} +(-0.471919 - 0.395987i) q^{42} +(-7.33788 + 6.15721i) q^{43} +(0.888879 - 5.04109i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(2.79270 + 4.83710i) q^{46} +(2.00731 - 0.730599i) q^{47} +(0.939693 - 0.342020i) q^{48} +(3.31024 + 5.73351i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.139438 - 0.790794i) q^{51} +(-0.982320 + 0.824264i) q^{52} +(-10.8441 - 9.09928i) q^{53} +(-0.173648 - 0.984808i) q^{54} +(-4.81015 - 1.75075i) q^{55} +0.616046 q^{56} +(-3.91752 + 1.91129i) q^{57} -7.42341 q^{58} +(-4.56957 - 1.66319i) q^{59} +(-0.173648 - 0.984808i) q^{60} +(-6.59177 - 5.53115i) q^{61} +(-2.23222 + 1.87305i) q^{62} +(0.106975 - 0.606687i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.641164 + 1.11053i) q^{65} +(4.81015 - 1.75075i) q^{66} +(10.0105 - 3.64352i) q^{67} +(0.401497 + 0.695413i) q^{68} +(-2.79270 + 4.83710i) q^{69} +(0.106975 - 0.606687i) q^{70} +(6.09117 - 5.11110i) q^{71} +(0.766044 + 0.642788i) q^{72} +(1.72818 + 9.80098i) q^{73} +(8.38760 + 3.05284i) q^{74} -1.00000 q^{75} +(1.77244 - 3.98227i) q^{76} +3.15345 q^{77} +(-1.20499 - 0.438582i) q^{78} +(-0.0499818 - 0.283461i) q^{79} +(0.766044 + 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-0.716761 + 4.06495i) q^{82} +(-1.30961 + 2.26831i) q^{83} +(0.308023 + 0.533512i) q^{84} +(0.754567 - 0.274640i) q^{85} +(9.00124 - 3.27618i) q^{86} +(-3.71171 - 6.42886i) q^{87} +(-2.55943 + 4.43306i) q^{88} +(1.09825 - 6.22849i) q^{89} +(0.766044 - 0.642788i) q^{90} +(-0.605154 - 0.507785i) q^{91} +(-0.969895 - 5.50055i) q^{92} +(-2.73822 - 0.996631i) q^{93} -2.13613 q^{94} +(-3.61399 - 2.43702i) q^{95} -1.00000 q^{96} +(17.1128 + 6.22854i) q^{97} +(-1.14964 - 6.51991i) q^{98} +(3.92127 + 3.29033i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{7} - 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^7 - 6 * q^8	$ 12 q + 3 q^{7} - 6 q^{8} + 3 q^{11} + 6 q^{12} + 9 q^{13} + 9 q^{14} + 9 q^{17} + 12 q^{18} + 9 q^{19} + 12 q^{20} + 9 q^{21} - 6 q^{22} + 12 q^{23} + 9 q^{26} + 6 q^{27} - 9 q^{28} + 27 q^{29} + 6 q^{30} + 12 q^{31} - 3 q^{33} - 9 q^{34} - 42 q^{37} + 18 q^{38} + 18 q^{39} - 27 q^{41} - 9 q^{42} - 27 q^{43} - 6 q^{44} - 6 q^{45} + 9 q^{46} - 6 q^{47} + 3 q^{49} - 6 q^{50} + 9 q^{52} - 18 q^{53} + 3 q^{55} - 6 q^{56} + 6 q^{58} - 15 q^{59} - 9 q^{61} - 18 q^{62} - 6 q^{64} + 9 q^{65} - 3 q^{66} + 42 q^{67} + 6 q^{68} - 9 q^{69} + 24 q^{71} + 15 q^{73} + 18 q^{74} - 12 q^{75} + 3 q^{76} - 6 q^{77} + 18 q^{78} - 57 q^{79} - 27 q^{82} + 21 q^{83} - 3 q^{84} + 9 q^{85} + 9 q^{86} + 3 q^{87} + 3 q^{88} - 57 q^{89} + 21 q^{91} - 15 q^{92} - 9 q^{93} - 24 q^{94} - 18 q^{95} - 12 q^{96} - 6 q^{97} - 15 q^{98} + 3 q^{99}+O(q^{100}) $ 12 * q + 3 * q^7 - 6 * q^8 + 3 * q^11 + 6 * q^12 + 9 * q^13 + 9 * q^14 + 9 * q^17 + 12 * q^18 + 9 * q^19 + 12 * q^20 + 9 * q^21 - 6 * q^22 + 12 * q^23 + 9 * q^26 + 6 * q^27 - 9 * q^28 + 27 * q^29 + 6 * q^30 + 12 * q^31 - 3 * q^33 - 9 * q^34 - 42 * q^37 + 18 * q^38 + 18 * q^39 - 27 * q^41 - 9 * q^42 - 27 * q^43 - 6 * q^44 - 6 * q^45 + 9 * q^46 - 6 * q^47 + 3 * q^49 - 6 * q^50 + 9 * q^52 - 18 * q^53 + 3 * q^55 - 6 * q^56 + 6 * q^58 - 15 * q^59 - 9 * q^61 - 18 * q^62 - 6 * q^64 + 9 * q^65 - 3 * q^66 + 42 * q^67 + 6 * q^68 - 9 * q^69 + 24 * q^71 + 15 * q^73 + 18 * q^74 - 12 * q^75 + 3 * q^76 - 6 * q^77 + 18 * q^78 - 57 * q^79 - 27 * q^82 + 21 * q^83 - 3 * q^84 + 9 * q^85 + 9 * q^86 + 3 * q^87 + 3 * q^88 - 57 * q^89 + 21 * q^91 - 15 * q^92 - 9 * q^93 - 24 * q^94 - 18 * q^95 - 12 * q^96 - 6 * q^97 - 15 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

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
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$5$	0.766044	−	0.642788i	0.342585	−	0.287463i
$6$	−0.173648	+	0.984808i	−0.0708916	+	0.402046i
$7$	−0.308023	+	0.533512i	−0.116422	+	0.201649i	−0.918347	−	0.395776i	$-0.870476\pi$
$7$	−0.308023	+	0.533512i	−0.116422	+	0.201649i	0.801925	+	0.597424i	$0.203809\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	−0.939693	+	0.342020i	−0.297157	+	0.108156i
$11$	−2.55943	−	4.43306i	−0.771696	−	1.33662i	−0.936633	−	0.350313i	$-0.886075\pi$
$11$	−2.55943	−	4.43306i	−0.771696	−	1.33662i	0.164937	−	0.986304i	$-0.447258\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−0.222674	+	1.26285i	−0.0617586	+	0.350250i	0.938232	+	0.346006i	$0.112462\pi$
$13$	−0.222674	+	1.26285i	−0.0617586	+	0.350250i	−0.999991	+	0.00424464i	$0.998649\pi$
$14$	0.471919	−	0.395987i	0.126126	−	0.105832i
$15$	−0.766044	−	0.642788i	−0.197792	−	0.165967i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	0.754567	+	0.274640i	0.183009	+	0.0666099i	0.431899	−	0.901922i	$-0.357844\pi$
$17$	0.754567	+	0.274640i	0.183009	+	0.0666099i	−0.248890	+	0.968532i	$0.580066\pi$
$18$	1.00000			0.235702
$19$	−1.20199	−	4.18990i	−0.275755	−	0.961228i
$19$	−1.20199	−	4.18990i	−0.275755	−	0.961228i
$20$	1.00000			0.223607
$21$	0.578894	+	0.210700i	0.126325	+	0.0459786i
$22$	0.888879	+	5.04109i	0.189510	+	1.07476i
$23$	−4.27867	−	3.59023i	−0.892163	−	0.748614i	0.0764795	−	0.997071i	$-0.475632\pi$
$23$	−4.27867	−	3.59023i	−0.892163	−	0.748614i	−0.968643	+	0.248457i	$0.920076\pi$
$24$	−0.766044	+	0.642788i	−0.156368	+	0.131208i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	0.641164	−	1.11053i	0.125743	−	0.217792i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−0.578894	+	0.210700i	−0.109401	+	0.0398186i
$29$	6.97573	−	2.53896i	1.29536	−	0.471472i	0.399877	−	0.916569i	$-0.369053\pi$
$29$	6.97573	−	2.53896i	1.29536	−	0.471472i	0.895483	+	0.445096i	$0.146831\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	1.45698	−	2.52356i	0.261681	−	0.453245i	−0.705008	−	0.709199i	$-0.749057\pi$
$31$	1.45698	−	2.52356i	0.261681	−	0.453245i	0.966689	+	0.255955i	$0.0823899\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	−3.92127	+	3.29033i	−0.682605	+	0.572774i
$34$	−0.615128	−	0.516154i	−0.105494	−	0.0885197i
$35$	0.106975	+	0.606687i	0.0180821	+	0.102549i
$36$	−0.939693	−	0.342020i	−0.156615	−	0.0570034i
$37$	−8.92589			−1.46741			−0.733704	−	0.679469i	$-0.762210\pi$
$37$	−8.92589			−1.46741			−0.733704	+	0.679469i	$0.762210\pi$
$38$	−0.303530	+	4.34832i	−0.0492391	+	0.705390i
$39$	1.28233			0.205337
$40$	−0.939693	−	0.342020i	−0.148578	−	0.0540781i
$41$	−0.716761	−	4.06495i	−0.111939	−	0.634839i	−0.988220	−	0.153038i	$-0.951094\pi$
$41$	−0.716761	−	4.06495i	−0.111939	−	0.634839i	0.876281	−	0.481800i	$-0.160017\pi$
$42$	−0.471919	−	0.395987i	−0.0728187	−	0.0611021i
$43$	−7.33788	+	6.15721i	−1.11902	+	0.938966i	−0.998554	−	0.0537518i	$-0.982882\pi$
$43$	−7.33788	+	6.15721i	−1.11902	+	0.938966i	−0.120462	+	0.992718i	$0.538438\pi$
$44$	0.888879	−	5.04109i	0.134004	−	0.759972i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	2.79270	+	4.83710i	0.411761	+	0.713191i
$47$	2.00731	−	0.730599i	0.292796	−	0.106569i	−0.191446	−	0.981503i	$-0.561318\pi$
$47$	2.00731	−	0.730599i	0.292796	−	0.106569i	0.484242	+	0.874934i	$0.339096\pi$
$48$	0.939693	−	0.342020i	0.135633	−	0.0493664i
$49$	3.31024	+	5.73351i	0.472892	+	0.819073i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	0.139438	−	0.790794i	0.0195253	−	0.110733i
$52$	−0.982320	+	0.824264i	−0.136223	+	0.114305i
$53$	−10.8441	−	9.09928i	−1.48955	−	1.24988i	−0.895191	−	0.445682i	$-0.852961\pi$
$53$	−10.8441	−	9.09928i	−1.48955	−	1.24988i	−0.594360	−	0.804199i	$-0.702594\pi$
$54$	−0.173648	−	0.984808i	−0.0236305	−	0.134015i
$55$	−4.81015	−	1.75075i	−0.648600	−	0.236071i
$56$	0.616046			0.0823227
$57$	−3.91752	+	1.91129i	−0.518888	+	0.253157i
$58$	−7.42341			−0.974742
$59$	−4.56957	−	1.66319i	−0.594907	−	0.216528i	0.0269792	−	0.999636i	$-0.491411\pi$
$59$	−4.56957	−	1.66319i	−0.594907	−	0.216528i	−0.621886	+	0.783108i	$0.713633\pi$
$60$	−0.173648	−	0.984808i	−0.0224179	−	0.127138i
$61$	−6.59177	−	5.53115i	−0.843990	−	0.708192i	0.114467	−	0.993427i	$-0.463484\pi$
$61$	−6.59177	−	5.53115i	−0.843990	−	0.708192i	−0.958458	+	0.285235i	$0.907928\pi$
$62$	−2.23222	+	1.87305i	−0.283492	+	0.237878i
$63$	0.106975	−	0.606687i	0.0134776	−	0.0764354i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.641164	+	1.11053i	0.0795265	+	0.137744i
$66$	4.81015	−	1.75075i	0.592088	−	0.215503i
$67$	10.0105	−	3.64352i	1.22298	−	0.445127i	0.351790	−	0.936079i	$-0.385573\pi$
$67$	10.0105	−	3.64352i	1.22298	−	0.445127i	0.871187	+	0.490952i	$0.163351\pi$
$68$	0.401497	+	0.695413i	0.0486886	+	0.0843312i
$69$	−2.79270	+	4.83710i	−0.336202	+	0.582318i
$70$	0.106975	−	0.606687i	0.0127860	−	0.0725130i
$71$	6.09117	−	5.11110i	0.722889	−	0.606575i	−0.205294	−	0.978700i	$-0.565815\pi$
$71$	6.09117	−	5.11110i	0.722889	−	0.606575i	0.928183	+	0.372125i	$0.121371\pi$
$72$	0.766044	+	0.642788i	0.0902792	+	0.0757532i
$73$	1.72818	+	9.80098i	0.202268	+	1.14712i	0.901681	+	0.432401i	$0.142334\pi$
$73$	1.72818	+	9.80098i	0.202268	+	1.14712i	−0.699413	+	0.714717i	$0.746555\pi$
$74$	8.38760	+	3.05284i	0.975038	+	0.354885i
$75$	−1.00000			−0.115470
$76$	1.77244	−	3.98227i	0.203312	−	0.456798i
$77$	3.15345			0.359369
$78$	−1.20499	−	0.438582i	−0.136439	−	0.0496596i
$79$	−0.0499818	−	0.283461i	−0.00562339	−	0.0318919i	0.981867	−	0.189571i	$-0.0607098\pi$
$79$	−0.0499818	−	0.283461i	−0.00562339	−	0.0318919i	−0.987490	+	0.157679i	$0.949599\pi$
$80$	0.766044	+	0.642788i	0.0856464	+	0.0718658i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−0.716761	+	4.06495i	−0.0791530	+	0.448899i
$83$	−1.30961	+	2.26831i	−0.143748	+	0.248980i	−0.928905	−	0.370317i	$-0.879249\pi$
$83$	−1.30961	+	2.26831i	−0.143748	+	0.248980i	0.785157	+	0.619297i	$0.212582\pi$
$84$	0.308023	+	0.533512i	0.0336081	+	0.0582109i
$85$	0.754567	−	0.274640i	0.0818443	−	0.0297889i
$86$	9.00124	−	3.27618i	0.970629	−	0.353280i
$87$	−3.71171	−	6.42886i	−0.397937	−	0.689247i
$88$	−2.55943	+	4.43306i	−0.272836	+	0.472565i
$89$	1.09825	−	6.22849i	0.116414	−	0.660218i	−0.869626	−	0.493711i	$-0.835640\pi$
$89$	1.09825	−	6.22849i	0.116414	−	0.660218i	0.986040	−	0.166507i	$-0.0532489\pi$
$90$	0.766044	−	0.642788i	0.0807482	−	0.0677558i
$91$	−0.605154	−	0.507785i	−0.0634374	−	0.0532303i
$92$	−0.969895	−	5.50055i	−0.101119	−	0.573472i
$93$	−2.73822	−	0.996631i	−0.283940	−	0.103346i
$94$	−2.13613			−0.220325
$95$	−3.61399	−	2.43702i	−0.370787	−	0.250033i
$96$	−1.00000			−0.102062
$97$	17.1128	+	6.22854i	1.73754	+	0.632412i	0.999120	−	0.0419314i	$-0.0133511\pi$
$97$	17.1128	+	6.22854i	1.73754	+	0.632412i	0.738418	+	0.674344i	$0.235573\pi$
$98$	−1.14964	−	6.51991i	−0.116131	−	0.658610i
$99$	3.92127	+	3.29033i	0.394102	+	0.330691i
$100$	0.766044	−	0.642788i	0.0766044	−	0.0642788i
$101$	−2.64839	+	15.0198i	−0.263525	+	1.49452i	0.509679	+	0.860365i	$0.329764\pi$
$101$	−2.64839	+	15.0198i	−0.263525	+	1.49452i	−0.773204	+	0.634158i	$0.781347\pi$
$102$	−0.401497	+	0.695413i	−0.0397541	+	0.0688561i
$103$	0.495734	+	0.858636i	0.0488461	+	0.0846039i	0.889415	−	0.457101i	$-0.151112\pi$
$103$	0.495734	+	0.858636i	0.0488461	+	0.0846039i	−0.840569	+	0.541705i	$0.817779\pi$
$104$	1.20499	−	0.438582i	0.118159	−	0.0430065i
$105$	0.578894	−	0.210700i	0.0564943	−	0.0205622i
$106$	7.07798	+	12.2594i	0.687474	+	1.19074i
$107$	5.49292	−	9.51401i	0.531020	−	0.919754i	−0.468324	−	0.883557i	$-0.655142\pi$
$107$	5.49292	−	9.51401i	0.531020	−	0.919754i	0.999345	−	0.0361974i	$-0.0115245\pi$
$108$	−0.173648	+	0.984808i	−0.0167093	+	0.0947632i
$109$	9.33761	−	7.83518i	0.894380	−	0.750474i	−0.0747034	−	0.997206i	$-0.523801\pi$
$109$	9.33761	−	7.83518i	0.894380	−	0.750474i	0.969084	+	0.246732i	$0.0793566\pi$
$110$	3.92127	+	3.29033i	0.373878	+	0.313721i
$111$	1.54997	+	8.79029i	0.147116	+	0.834337i
$112$	−0.578894	−	0.210700i	−0.0547004	−	0.0199093i
$113$	−6.00943			−0.565320			−0.282660	−	0.959220i	$-0.591217\pi$
$113$	−6.00943			−0.565320			−0.282660	+	0.959220i	$0.591217\pi$
$114$	4.33496	−	0.456159i	0.406007	−	0.0427232i
$115$	−5.58540			−0.520841
$116$	6.97573	+	2.53896i	0.647680	+	0.235736i
$117$	−0.222674	−	1.26285i	−0.0205862	−	0.116750i
$118$	3.72515	+	3.12577i	0.342928	+	0.287750i
$119$	−0.378948	+	0.317975i	−0.0347381	+	0.0291487i
$120$	−0.173648	+	0.984808i	−0.0158518	+	0.0899002i
$121$	−7.60132	+	13.1659i	−0.691029	+	1.19690i
$122$	4.30247	+	7.45210i	0.389528	+	0.674682i
$123$	−3.87873	+	1.41174i	−0.349733	+	0.127293i
$124$	2.73822	−	0.996631i	0.245900	−	0.0895001i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	−0.308023	+	0.533512i	−0.0274409	+	0.0475290i
$127$	0.749393	−	4.25002i	0.0664979	−	0.377128i	−0.933338	−	0.358999i	$-0.883118\pi$
$127$	0.749393	−	4.25002i	0.0664979	−	0.377128i	0.999836	−	0.0181289i	$-0.00577091\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	7.33788	+	6.15721i	0.646064	+	0.542112i
$130$	−0.222674	−	1.26285i	−0.0195298	−	0.110759i
$131$	14.5034	+	5.27879i	1.26716	+	0.461210i	0.886167	−	0.463366i	$-0.153358\pi$
$131$	14.5034	+	5.27879i	1.26716	+	0.461210i	0.380997	+	0.924576i	$0.375581\pi$
$132$	−5.11885			−0.445539
$133$	2.60560	+	0.649311i	0.225934	+	0.0563024i
$134$	−10.6529			−0.920274
$135$	0.939693	+	0.342020i	0.0808759	+	0.0294364i
$136$	−0.139438	−	0.790794i	−0.0119567	−	0.0678100i
$137$	17.2636	+	14.4859i	1.47493	+	1.23761i	0.911402	+	0.411518i	$0.135001\pi$
$137$	17.2636	+	14.4859i	1.47493	+	1.23761i	0.563530	+	0.826096i	$0.309443\pi$
$138$	4.27867	−	3.59023i	0.364224	−	0.305620i
$139$	2.87518	−	16.3060i	0.243870	−	1.38305i	−0.579234	−	0.815161i	$-0.696648\pi$
$139$	2.87518	−	16.3060i	0.243870	−	1.38305i	0.823103	−	0.567892i	$-0.192241\pi$
$140$	−0.308023	+	0.533512i	−0.0260327	+	0.0450900i
$141$	−1.06806	−	1.84994i	−0.0899473	−	0.155793i
$142$	−7.47192	+	2.71956i	−0.627030	+	0.228220i
$143$	6.16818	−	2.24503i	0.515809	−	0.187739i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	3.71171	−	6.42886i	0.308240	−	0.533888i
$146$	1.72818	−	9.80098i	0.143025	−	0.811135i
$147$	5.07159	−	4.25557i	0.418297	−	0.350993i
$148$	−6.83763	−	5.73745i	−0.562050	−	0.471616i
$149$	2.76667	+	15.6906i	0.226655	+	1.28542i	0.859497	+	0.511141i	$0.170777\pi$
$149$	2.76667	+	15.6906i	0.226655	+	1.28542i	−0.632842	+	0.774281i	$0.718112\pi$
$150$	0.939693	+	0.342020i	0.0767256	+	0.0279258i
$151$	7.64372			0.622037			0.311019	−	0.950404i	$-0.399330\pi$
$151$	7.64372			0.622037			0.311019	+	0.950404i	$0.399330\pi$
$152$	−3.02756	+	3.13590i	−0.245568	+	0.254355i
$153$	−0.802993			−0.0649182
$154$	−2.96327	−	1.07854i	−0.238787	−	0.0869115i
$155$	−0.506003	−	2.86969i	−0.0406431	−	0.230499i
$156$	0.982320	+	0.824264i	0.0786485	+	0.0659939i
$157$	7.25804	−	6.09021i	0.579254	−	0.486052i	−0.305448	−	0.952209i	$-0.598806\pi$
$157$	7.25804	−	6.09021i	0.579254	−	0.486052i	0.884702	+	0.466157i	$0.154362\pi$
$158$	−0.0499818	+	0.283461i	−0.00397634	+	0.0225509i
$159$	−7.07798	+	12.2594i	−0.561320	+	0.972235i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	3.23336	−	1.17685i	0.254824	−	0.0927484i
$162$	−0.939693	+	0.342020i	−0.0738292	+	0.0268716i
$163$	−1.90574	−	3.30083i	−0.149269	−	0.258541i	0.781689	−	0.623669i	$-0.214359\pi$
$163$	−1.90574	−	3.30083i	−0.149269	−	0.258541i	−0.930957	+	0.365128i	$0.881025\pi$
$164$	2.06383	−	3.57466i	0.161158	−	0.279134i
$165$	−0.888879	+	5.04109i	−0.0691992	+	0.392448i
$166$	2.00644	−	1.68360i	0.155730	−	0.130673i
$167$	8.94777	+	7.50807i	0.692399	+	0.580992i	0.919600	−	0.392856i	$-0.128513\pi$
$167$	8.94777	+	7.50807i	0.692399	+	0.580992i	−0.227201	+	0.973848i	$0.572957\pi$
$168$	−0.106975	−	0.606687i	−0.00825333	−	0.0468069i
$169$	10.6708	+	3.88386i	0.820831	+	0.298758i
$170$	−0.802993			−0.0615868
$171$	2.56253	+	3.52611i	0.195961	+	0.269648i
$172$	−9.57892			−0.730386
$173$	−5.35014	−	1.94729i	−0.406763	−	0.148050i	0.130532	−	0.991444i	$-0.458332\pi$
$173$	−5.35014	−	1.94729i	−0.406763	−	0.148050i	−0.537295	+	0.843394i	$0.680554\pi$
$174$	1.28906	+	7.31064i	0.0977236	+	0.554218i
$175$	0.471919	+	0.395987i	0.0356737	+	0.0299338i
$176$	3.92127	−	3.29033i	0.295577	−	0.248018i
$177$	−0.844422	+	4.78896i	−0.0634707	+	0.359960i
$178$	−3.16229	+	5.47724i	−0.237023	+	0.410536i
$179$	−3.21619	−	5.57061i	−0.240389	−	0.416367i	0.720436	−	0.693522i	$-0.243942\pi$
$179$	−3.21619	−	5.57061i	−0.240389	−	0.416367i	−0.960825	+	0.277155i	$0.910608\pi$
$180$	−0.939693	+	0.342020i	−0.0700406	+	0.0254927i
$181$	18.5199	−	6.74068i	1.37657	−	0.501030i	0.455433	−	0.890270i	$-0.349484\pi$
$181$	18.5199	−	6.74068i	1.37657	−	0.501030i	0.921137	+	0.389239i	$0.127262\pi$
$182$	0.394987	+	0.684137i	0.0292783	+	0.0507116i
$183$	−4.30247	+	7.45210i	−0.318048	+	0.550875i
$184$	−0.969895	+	5.50055i	−0.0715016	+	0.405506i
$185$	−6.83763	+	5.73745i	−0.502713	+	0.421826i
$186$	2.23222	+	1.87305i	0.163674	+	0.137339i
$187$	−0.713764	−	4.04796i	−0.0521956	−	0.296016i
$188$	2.00731	+	0.730599i	0.146398	+	0.0532844i
$189$	−0.616046			−0.0448108
$190$	2.56253	+	3.52611i	0.185905	+	0.255811i
$191$	−14.1291			−1.02234			−0.511172	−	0.859478i	$-0.670789\pi$
$191$	−14.1291			−1.02234			−0.511172	+	0.859478i	$0.670789\pi$
$192$	0.939693	+	0.342020i	0.0678165	+	0.0246832i
$193$	0.154673	+	0.877192i	0.0111336	+	0.0631417i	0.989868	−	0.141988i	$-0.0453495\pi$
$193$	0.154673	+	0.877192i	0.0111336	+	0.0631417i	−0.978735	+	0.205130i	$0.934238\pi$
$194$	−13.9505	−	11.7058i	−1.00158	−	0.840429i
$195$	0.982320	−	0.824264i	0.0703454	−	0.0590268i
$196$	−1.14964	+	6.51991i	−0.0821168	+	0.465708i
$197$	0.745537	−	1.29131i	0.0531173	−	0.0920019i	−0.838244	−	0.545295i	$-0.816418\pi$
$197$	0.745537	−	1.29131i	0.0531173	−	0.0920019i	0.891361	+	0.453293i	$0.149751\pi$
$198$	−2.55943	−	4.43306i	−0.181890	−	0.315044i
$199$	−6.19396	+	2.25442i	−0.439078	+	0.159811i	−0.552094	−	0.833782i	$-0.686171\pi$
$199$	−6.19396	+	2.25442i	−0.439078	+	0.159811i	0.113016	+	0.993593i	$0.463949\pi$
$200$	−0.939693	+	0.342020i	−0.0664463	+	0.0241845i
$201$	−5.32647	−	9.22572i	−0.375700	−	0.650732i
$202$	7.62573	−	13.2082i	0.536545	−	0.929323i
$203$	−0.794122	+	4.50369i	−0.0557365	+	0.316097i
$204$	0.615128	−	0.516154i	0.0430676	−	0.0361380i
$205$	−3.16197	−	2.65321i	−0.220842	−	0.185308i
$206$	−0.172167	−	0.976405i	−0.0119954	−	0.0680294i
$207$	5.24856	+	1.91032i	0.364800	+	0.132776i
$208$	−1.28233			−0.0889134
$209$	−15.4976	+	16.0522i	−1.07199	+	1.11035i
$210$	−0.616046			−0.0425112
$211$	−9.92544	−	3.61256i	−0.683295	−	0.248699i	−0.0230335	−	0.999735i	$-0.507332\pi$
$211$	−9.92544	−	3.61256i	−0.683295	−	0.248699i	−0.660262	+	0.751036i	$0.729555\pi$
$212$	−2.45816	−	13.9409i	−0.168827	−	0.957465i
$213$	−6.09117	−	5.11110i	−0.417360	−	0.350207i
$214$	−8.41564	+	7.06156i	−0.575281	+	0.482718i
$215$	−1.66336	+	9.43340i	−0.113440	+	0.643352i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	0.897566	+	1.55463i	0.0609307	+	0.105535i
$218$	−11.4543	+	4.16901i	−0.775781	+	0.282361i
$219$	9.35199	−	3.40385i	0.631949	−	0.230011i
$220$	−2.55943	−	4.43306i	−0.172556	−	0.298877i
$221$	−0.514850	+	0.891746i	−0.0346326	+	0.0599853i
$222$	1.54997	−	8.79029i	0.104027	−	0.589966i
$223$	−4.65533	+	3.90629i	−0.311744	+	0.261584i	−0.785212	−	0.619227i	$-0.787446\pi$
$223$	−4.65533	+	3.90629i	−0.311744	+	0.261584i	0.473468	+	0.880811i	$0.343002\pi$
$224$	0.471919	+	0.395987i	0.0315314	+	0.0264580i
$225$	0.173648	+	0.984808i	0.0115765	+	0.0656539i
$226$	5.64702	+	2.05535i	0.375634	+	0.136720i
$227$	−3.57215			−0.237092			−0.118546	−	0.992949i	$-0.537823\pi$
$227$	−3.57215			−0.237092			−0.118546	+	0.992949i	$0.537823\pi$
$228$	−4.22955	−	1.05400i	−0.280109	−	0.0698026i
$229$	4.34585			0.287182			0.143591	−	0.989637i	$-0.454135\pi$
$229$	4.34585			0.287182			0.143591	+	0.989637i	$0.454135\pi$
$230$	5.24856	+	1.91032i	0.346080	+	0.125963i
$231$	−0.547591	−	3.10554i	−0.0360288	−	0.204330i
$232$	−5.68666	−	4.77168i	−0.373348	−	0.313276i
$233$	7.43854	−	6.24168i	0.487315	−	0.408906i	−0.365748	−	0.930714i	$-0.619187\pi$
$233$	7.43854	−	6.24168i	0.487315	−	0.408906i	0.853063	+	0.521808i	$0.174742\pi$
$234$	−0.222674	+	1.26285i	−0.0145566	+	0.0825548i
$235$	1.06806	−	1.84994i	0.0696729	−	0.120677i
$236$	−2.43142	−	4.21134i	−0.158272	−	0.274135i
$237$	−0.270475	+	0.0984450i	−0.0175693	+	0.00639469i
$238$	0.464848	−	0.169191i	0.0301316	−	0.0109670i
$239$	−4.94331	−	8.56207i	−0.319756	−	0.553834i	0.660681	−	0.750667i	$-0.270268\pi$
$239$	−4.94331	−	8.56207i	−0.319756	−	0.553834i	−0.980437	+	0.196833i	$0.936934\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	0.697919	−	3.95810i	0.0449569	−	0.254963i	−0.954043	−	0.299669i	$-0.903124\pi$
$241$	0.697919	−	3.95810i	0.0449569	−	0.254963i	0.999000	+	0.0447054i	$0.0142349\pi$
$242$	11.6459	−	9.77207i	0.748627	−	0.628173i
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$	−1.49423	−	8.47422i	−0.0956585	−	0.542506i
$245$	6.22122	+	2.26434i	0.397459	+	0.144663i
$246$	4.12766			0.263170
$247$	5.55884	−	0.584945i	0.353701	−	0.0372192i
$248$	−2.91395			−0.185036
$249$	2.46126	+	0.895827i	0.155976	+	0.0567707i
$250$	0.173648	+	0.984808i	0.0109825	+	0.0622847i
$251$	−7.94863	−	6.66969i	−0.501713	−	0.420987i	0.356489	−	0.934300i	$-0.383974\pi$
$251$	−7.94863	−	6.66969i	−0.501713	−	0.420987i	−0.858202	+	0.513312i	$0.828418\pi$
$252$	0.471919	−	0.395987i	0.0297281	−	0.0249448i
$253$	−4.96475	+	28.1565i	−0.312131	+	1.77018i
$254$	−2.15779	+	3.73741i	−0.135392	+	0.234506i
$255$	−0.401497	−	0.695413i	−0.0251427	−	0.0435484i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−14.9150	+	5.42862i	−0.930373	+	0.338628i	−0.762357	−	0.647156i	$-0.775958\pi$
$257$	−14.9150	+	5.42862i	−0.930373	+	0.338628i	−0.168015	+	0.985784i	$0.553736\pi$
$258$	−4.78946	−	8.29559i	−0.298179	−	0.516461i
$259$	2.74938	−	4.76207i	0.170838	−	0.295901i
$260$	−0.222674	+	1.26285i	−0.0138096	+	0.0783184i
$261$	−5.68666	+	4.77168i	−0.351996	+	0.295359i
$262$	−11.8232	−	9.92088i	−0.730443	−	0.612914i
$263$	−2.45437	−	13.9194i	−0.151343	−	0.858310i	−0.962053	−	0.272862i	$-0.912030\pi$
$263$	−2.45437	−	13.9194i	−0.151343	−	0.858310i	0.810710	−	0.585448i	$-0.199081\pi$
$264$	4.81015	+	1.75075i	0.296044	+	0.107751i
$265$	−14.1560			−0.869594
$266$	−2.22639	−	1.50132i	−0.136508	−	0.0920518i
$267$	−6.32457			−0.387057
$268$	10.0105	+	3.64352i	0.611488	+	0.222564i
$269$	2.11201	+	11.9778i	0.128771	+	0.730298i	0.978996	+	0.203878i	$0.0653547\pi$
$269$	2.11201	+	11.9778i	0.128771	+	0.730298i	−0.850225	+	0.526420i	$0.823534\pi$
$270$	−0.766044	−	0.642788i	−0.0466200	−	0.0391188i
$271$	12.2642	−	10.2909i	0.744995	−	0.625125i	−0.189179	−	0.981943i	$-0.560583\pi$
$271$	12.2642	−	10.2909i	0.744995	−	0.625125i	0.934174	+	0.356818i	$0.116138\pi$
$272$	−0.139438	+	0.790794i	−0.00845469	+	0.0479489i
$273$	−0.394987	+	0.684137i	−0.0239057	+	0.0414058i
$274$	−11.2680	−	19.5168i	−0.680727	−	1.17905i
$275$	−4.81015	+	1.75075i	−0.290063	+	0.105574i
$276$	−5.24856	+	1.91032i	−0.315926	+	0.114988i
$277$	−6.32863	−	10.9615i	−0.380251	−	0.658614i	0.610847	−	0.791749i	$-0.290829\pi$
$277$	−6.32863	−	10.9615i	−0.380251	−	0.658614i	−0.991098	+	0.133135i	$0.957496\pi$
$278$	−8.27875	+	14.3392i	−0.496526	+	0.860009i
$279$	−0.506003	+	2.86969i	−0.0302936	+	0.171804i
$280$	0.471919	−	0.395987i	0.0282026	−	0.0236648i
$281$	6.73494	+	5.65129i	0.401773	+	0.337127i	0.821178	−	0.570672i	$-0.193317\pi$
$281$	6.73494	+	5.65129i	0.401773	+	0.337127i	−0.419406	+	0.907799i	$0.637761\pi$
$282$	0.370935	+	2.10368i	0.0220889	+	0.125272i
$283$	12.6738	+	4.61287i	0.753377	+	0.274207i	0.690026	−	0.723785i	$-0.257599\pi$
$283$	12.6738	+	4.61287i	0.753377	+	0.274207i	0.0633507	+	0.997991i	$0.479821\pi$
$284$	7.95145			0.471832
$285$	−1.77244	+	3.98227i	−0.104990	+	0.235889i
$286$	−6.56404			−0.388140
$287$	2.38948	+	0.869699i	0.141046	+	0.0513367i
$288$	0.173648	+	0.984808i	0.0102323	+	0.0580304i
$289$	−12.5288	−	10.5129i	−0.736989	−	0.618407i
$290$	−5.68666	+	4.77168i	−0.333932	+	0.280203i
$291$	3.16231	−	17.9344i	0.185378	−	1.05133i
$292$	−4.97609	+	8.61884i	−0.291204	+	0.504379i
$293$	−2.91006	−	5.04038i	−0.170008	−	0.294462i	0.768415	−	0.639952i	$-0.221046\pi$
$293$	−2.91006	−	5.04038i	−0.170008	−	0.294462i	−0.938422	+	0.345490i	$0.887713\pi$
$294$	−6.22122	+	2.26434i	−0.362829	+	0.132059i
$295$	−4.56957	+	1.66319i	−0.266051	+	0.0968345i
$296$	4.46295	+	7.73005i	0.259404	+	0.449300i
$297$	2.55943	−	4.43306i	0.148513	−	0.257232i
$298$	2.76667	−	15.6906i	0.160269	−	0.908930i
$299$	5.48665	−	4.60384i	0.317301	−	0.266247i
$300$	−0.766044	−	0.642788i	−0.0442276	−	0.0371114i
$301$	−1.02471	−	5.81141i	−0.0590632	−	0.334964i
$302$	−7.18275	−	2.61431i	−0.413321	−	0.150436i
$303$	15.2515			0.876174
$304$	3.91752	−	1.91129i	0.224685	−	0.109620i
$305$	−8.60495			−0.492718
$306$	0.754567	+	0.274640i	0.0431357	+	0.0157001i
$307$	0.487721	+	2.76601i	0.0278357	+	0.157864i	0.995557	−	0.0941574i	$-0.0300157\pi$
$307$	0.487721	+	2.76601i	0.0278357	+	0.157864i	−0.967722	+	0.252022i	$0.918905\pi$
$308$	2.41568	+	2.02700i	0.137646	+	0.115499i
$309$	0.759508	−	0.637303i	0.0432069	−	0.0362549i
$310$	−0.506003	+	2.86969i	−0.0287390	+	0.162987i
$311$	−4.70806	+	8.15461i	−0.266970	+	0.462405i	−0.968078	−	0.250650i	$-0.919356\pi$
$311$	−4.70806	+	8.15461i	−0.266970	+	0.462405i	0.701108	+	0.713055i	$0.252689\pi$
$312$	−0.641164	−	1.11053i	−0.0362987	−	0.0628713i
$313$	12.0775	−	4.39585i	0.682661	−	0.248468i	0.0226715	−	0.999743i	$-0.492783\pi$
$313$	12.0775	−	4.39585i	0.682661	−	0.248468i	0.659990	+	0.751275i	$0.270561\pi$
$314$	−8.90330	+	3.24054i	−0.502442	+	0.182874i
$315$	−0.308023	−	0.533512i	−0.0173551	−	0.0300600i
$316$	0.143917	−	0.249271i	0.00809596	−	0.0140226i
$317$	−2.18784	+	12.4078i	−0.122881	+	0.696893i	0.859663	+	0.510862i	$0.170674\pi$
$317$	−2.18784	+	12.4078i	−0.122881	+	0.696893i	−0.982544	+	0.186031i	$0.940437\pi$
$318$	10.8441	−	9.09928i	0.608107	−	0.510262i
$319$	−29.1092	−	24.4255i	−1.62980	−	1.36757i
$320$	0.173648	+	0.984808i	0.00970723	+	0.0550524i
$321$	−10.3233	−	3.75738i	−0.576191	−	0.209716i
$322$	−3.44087			−0.191752
$323$	0.243732	−	3.49167i	0.0135616	−	0.194282i
$324$	1.00000			0.0555556
$325$	1.20499	+	0.438582i	0.0668410	+	0.0243281i
$326$	0.661855	+	3.75357i	0.0366568	+	0.207891i
$327$	−9.33761	−	7.83518i	−0.516371	−	0.433287i
$328$	−3.16197	+	2.65321i	−0.174591	+	0.146499i
$329$	−0.228513	+	1.29596i	−0.0125983	+	0.0714487i
$330$	2.55943	−	4.43306i	0.140892	−	0.244032i
$331$	8.09975	+	14.0292i	0.445202	+	0.771113i	0.998066	−	0.0621583i	$-0.0197984\pi$
$331$	8.09975	+	14.0292i	0.445202	+	0.771113i	−0.552864	+	0.833272i	$0.686465\pi$
$332$	−2.46126	+	0.895827i	−0.135079	+	0.0491649i
$333$	8.38760	−	3.05284i	0.459637	−	0.167294i
$334$	−5.84024	−	10.1156i	−0.319564	−	0.553501i
$335$	5.32647	−	9.22572i	0.291016	−	0.504055i
$336$	−0.106975	+	0.606687i	−0.00583598	+	0.0330975i
$337$	14.2893	−	11.9901i	0.778387	−	0.653144i	−0.164455	−	0.986385i	$-0.552586\pi$
$337$	14.2893	−	11.9901i	0.778387	−	0.653144i	0.942842	+	0.333240i	$0.108142\pi$
$338$	−8.69892	−	7.29926i	−0.473159	−	0.397028i
$339$	1.04353	+	5.91813i	0.0566766	+	0.321429i
$340$	0.754567	+	0.274640i	0.0409221	+	0.0148944i
$341$	−14.9161			−0.807752
$342$	−1.20199	−	4.18990i	−0.0649960	−	0.226564i
$343$	−8.39085			−0.453063
$344$	9.00124	+	3.27618i	0.485315	+	0.176640i
$345$	0.969895	+	5.50055i	0.0522174	+	0.296139i
$346$	4.36147	+	3.65971i	0.234474	+	0.196747i
$347$	−5.09796	+	4.27770i	−0.273673	+	0.229639i	−0.769286	−	0.638905i	$-0.779388\pi$
$347$	−5.09796	+	4.27770i	−0.273673	+	0.229639i	0.495613	+	0.868543i	$0.334943\pi$
$348$	1.28906	−	7.31064i	0.0691010	−	0.391891i
$349$	−4.79224	+	8.30041i	−0.256523	+	0.444311i	−0.965308	−	0.261114i	$-0.915910\pi$
$349$	−4.79224	+	8.30041i	−0.256523	+	0.444311i	0.708785	+	0.705424i	$0.249244\pi$
$350$	−0.308023	−	0.533512i	−0.0164645	−	0.0285174i
$351$	−1.20499	+	0.438582i	−0.0643178	+	0.0234098i
$352$	−4.81015	+	1.75075i	−0.256382	+	0.0933153i
$353$	−12.5316	−	21.7054i	−0.666992	−	1.15526i	−0.978741	−	0.205099i	$-0.934248\pi$
$353$	−12.5316	−	21.7054i	−0.666992	−	1.15526i	0.311750	−	0.950164i	$-0.399085\pi$
$354$	2.43142	−	4.21134i	0.129228	−	0.223830i
$355$	1.38076	−	7.83065i	0.0732829	−	0.415608i
$356$	4.84490	−	4.06536i	0.256779	−	0.215463i
$357$	0.378948	+	0.317975i	0.0200560	+	0.0168290i
$358$	1.11697	+	6.33466i	0.0590338	+	0.334797i
$359$	27.5961	+	10.0442i	1.45647	+	0.530111i	0.944390	−	0.328829i	$-0.106654\pi$
$359$	27.5961	+	10.0442i	1.45647	+	0.530111i	0.512077	+	0.858939i	$0.328876\pi$
$360$	1.00000			0.0527046
$361$	−16.1105	+	10.0724i	−0.847919	+	0.530127i
$362$	−19.7084			−1.03585
$363$	14.2858	+	5.19961i	0.749811	+	0.272909i
$364$	−0.137177	−	0.777972i	−0.00719005	−	0.0407768i
$365$	7.62381	+	6.39714i	0.399049	+	0.334841i
$366$	6.59177	−	5.53115i	0.344558	−	0.289118i
$367$	−4.25955	+	24.1571i	−0.222347	+	1.26099i	0.645346	+	0.763890i	$0.276713\pi$
$367$	−4.25955	+	24.1571i	−0.222347	+	1.26099i	−0.867693	+	0.497100i	$0.834398\pi$
$368$	2.79270	−	4.83710i	0.145580	−	0.252151i
$369$	2.06383	+	3.57466i	0.107439	+	0.186089i
$370$	8.38760	−	3.05284i	0.436050	−	0.158709i
$371$	8.19480	−	2.98266i	0.425453	−	0.154852i
$372$	−1.45698	−	2.52356i	−0.0755408	−	0.130840i
$373$	11.1791	−	19.3628i	0.578832	−	1.00257i	−0.416782	−	0.909007i	$-0.636842\pi$
$373$	11.1791	−	19.3628i	0.578832	−	1.00257i	0.995614	−	0.0935598i	$-0.0298246\pi$
$374$	−0.713764	+	4.04796i	−0.0369079	+	0.209315i
$375$	−0.766044	+	0.642788i	−0.0395584	+	0.0331934i
$376$	−1.63637	−	1.37308i	−0.0843893	−	0.0708111i
$377$	1.65300	+	9.37463i	0.0851338	+	0.482818i
$378$	0.578894	+	0.210700i	0.0297751	+	0.0108373i
$379$	−18.0800			−0.928709			−0.464355	−	0.885649i	$-0.653714\pi$
$379$	−18.0800			−0.928709			−0.464355	+	0.885649i	$0.653714\pi$
$380$	−1.20199	−	4.18990i	−0.0616607	−	0.214937i
$381$	−4.31558			−0.221094
$382$	13.2770	+	4.83243i	0.679310	+	0.247249i
$383$	−1.66303	−	9.43149i	−0.0849766	−	0.481926i	−0.997362	−	0.0725933i	$-0.976872\pi$
$383$	−1.66303	−	9.43149i	−0.0849766	−	0.481926i	0.912385	−	0.409333i	$-0.134239\pi$
$384$	−0.766044	−	0.642788i	−0.0390920	−	0.0328021i
$385$	2.41568	−	2.02700i	0.123115	−	0.103305i
$386$	0.154673	−	0.877192i	0.00787263	−	0.0446479i
$387$	4.78946	−	8.29559i	0.243462	−	0.421689i
$388$	9.10551	+	15.7712i	0.462262	+	0.800662i
$389$	−22.6312	+	8.23708i	−1.14745	+	0.417637i	−0.844597	−	0.535402i	$-0.820160\pi$
$389$	−22.6312	+	8.23708i	−1.14745	+	0.417637i	−0.302850	+	0.953038i	$0.597938\pi$
$390$	−1.20499	+	0.438582i	−0.0610172	+	0.0222084i
$391$	−2.24252	−	3.88416i	−0.113409	−	0.196430i
$392$	3.31024	−	5.73351i	0.167193	−	0.289586i
$393$	2.68011	−	15.1997i	0.135194	−	0.766722i
$394$	−1.14223	+	0.958444i	−0.0575447	+	0.0482857i
$395$	−0.220493	−	0.185016i	−0.0110942	−	0.00930917i
$396$	0.888879	+	5.04109i	0.0446679	+	0.253324i
$397$	−14.6026	−	5.31493i	−0.732886	−	0.266749i	−0.0514998	−	0.998673i	$-0.516400\pi$
$397$	−14.6026	−	5.31493i	−0.732886	−	0.266749i	−0.681386	+	0.731924i	$0.738622\pi$
$398$	6.59148			0.330401
$399$	0.186989	−	2.67877i	0.00936113	−	0.134106i
$400$	1.00000			0.0500000
$401$	−26.8999	−	9.79075i	−1.34332	−	0.488927i	−0.432460	−	0.901653i	$-0.642354\pi$
$401$	−26.8999	−	9.79075i	−1.34332	−	0.488927i	−0.910855	+	0.412726i	$0.864577\pi$
$402$	1.84986	+	10.4911i	0.0922629	+	0.523249i
$403$	2.86243	+	2.40187i	0.142588	+	0.119646i
$404$	−11.6833	+	9.80346i	−0.581266	+	0.487740i
$405$	0.173648	−	0.984808i	0.00862865	−	0.0489355i
$406$	2.28658	−	3.96048i	0.113481	−	0.196555i
$407$	22.8452	+	39.5690i	1.13239	+	1.96136i
$408$	−0.754567	+	0.274640i	−0.0373566	+	0.0135967i
$409$	35.8037	−	13.0315i	1.77038	−	0.644365i	0.770402	−	0.637559i	$-0.220056\pi$
$409$	35.8037	−	13.0315i	1.77038	−	0.644365i	0.999977	−	0.00680639i	$-0.00216656\pi$
$410$	2.06383	+	3.57466i	0.101925	+	0.176540i
$411$	11.2680	−	19.5168i	0.555811	−	0.962693i
$412$	−0.172167	+	0.976405i	−0.00848204	+	0.0481040i
$413$	2.29486	−	1.92562i	0.112923	−	0.0947535i
$414$	−4.27867	−	3.59023i	−0.210285	−	0.176450i
$415$	0.454823	+	2.57943i	0.0223264	+	0.126619i
$416$	1.20499	+	0.438582i	0.0590797	+	0.0215032i
$417$	−16.5575			−0.810824
$418$	20.0532	−	9.78363i	0.980834	−	0.478533i
$419$	12.5098			0.611142			0.305571	−	0.952169i	$-0.401153\pi$
$419$	12.5098			0.611142			0.305571	+	0.952169i	$0.401153\pi$
$420$	0.578894	+	0.210700i	0.0282471	+	0.0102811i
$421$	5.52419	+	31.3293i	0.269233	+	1.52690i	0.756705	+	0.653757i	$0.226808\pi$
$421$	5.52419	+	31.3293i	0.269233	+	1.52690i	−0.487472	+	0.873139i	$0.662081\pi$
$422$	8.09129	+	6.78940i	0.393878	+	0.330503i
$423$	−1.63637	+	1.37308i	−0.0795630	+	0.0667613i
$424$	−2.45816	+	13.9409i	−0.119379	+	0.677030i
$425$	0.401497	−	0.695413i	0.0194754	−	0.0337325i
$426$	3.97573	+	6.88616i	0.192625	+	0.333636i
$427$	4.98136	−	1.81307i	0.241065	−	0.0877404i
$428$	10.3233	−	3.75738i	0.498996	−	0.181620i
$429$	−3.28202	−	5.68463i	−0.158457	−	0.274456i
$430$	4.78946	−	8.29559i	0.230968	−	0.400049i
$431$	−1.34094	+	7.60487i	−0.0645910	+	0.366314i	0.935330	+	0.353775i	$0.115102\pi$
$431$	−1.34094	+	7.60487i	−0.0645910	+	0.366314i	−0.999921	+	0.0125383i	$0.996009\pi$
$432$	−0.766044	+	0.642788i	−0.0368563	+	0.0309261i
$433$	15.4919	+	12.9992i	0.744491	+	0.624703i	0.934040	−	0.357169i	$-0.116258\pi$
$433$	15.4919	+	12.9992i	0.744491	+	0.624703i	−0.189548	+	0.981871i	$0.560702\pi$
$434$	−0.311721	−	1.76786i	−0.0149631	−	0.0848600i
$435$	−6.97573	−	2.53896i	−0.334461	−	0.121734i
$436$	12.1894			0.583765
$437$	−9.89977	+	22.2426i	−0.473570	+	1.06401i
$438$	−9.95218			−0.475534
$439$	−17.4060	−	6.33526i	−0.830742	−	0.302365i	−0.108578	−	0.994088i	$-0.534630\pi$
$439$	−17.4060	−	6.33526i	−0.830742	−	0.302365i	−0.722163	+	0.691723i	$0.756852\pi$
$440$	0.888879	+	5.04109i	0.0423757	+	0.240324i
$441$	−5.07159	−	4.25557i	−0.241504	−	0.202646i
$442$	0.788796	−	0.661878i	0.0375192	−	0.0314823i
$443$	−2.30451	+	13.0695i	−0.109490	+	0.620951i	0.879841	+	0.475268i	$0.157649\pi$
$443$	−2.30451	+	13.0695i	−0.109490	+	0.620951i	−0.989331	+	0.145683i	$0.953462\pi$
$444$	−4.46295	+	7.73005i	−0.211802	+	0.366852i
$445$	−3.16229	−	5.47724i	−0.149907	−	0.259646i
$446$	5.71061	−	2.07849i	0.270405	−	0.0984194i
$447$	14.9718	−	5.44928i	0.708140	−	0.257742i
$448$	−0.308023	−	0.533512i	−0.0145527	−	0.0252061i
$449$	−12.2404	+	21.2009i	−0.577658	+	1.00053i	0.418089	+	0.908406i	$0.362700\pi$
$449$	−12.2404	+	21.2009i	−0.577658	+	1.00053i	−0.995747	+	0.0921276i	$0.970633\pi$
$450$	0.173648	−	0.984808i	0.00818585	−	0.0464243i
$451$	−16.1857	+	13.5814i	−0.762153	+	0.639522i
$452$	−4.60349	−	3.86279i	−0.216530	−	0.181690i
$453$	−1.32732	−	7.52760i	−0.0623629	−	0.353677i
$454$	3.35673	+	1.22175i	0.157539	+	0.0573395i
$455$	−0.789973			−0.0370345
$456$	3.61399	+	2.43702i	0.169241	+	0.114124i
$457$	2.19624			0.102736			0.0513678	−	0.998680i	$-0.483642\pi$
$457$	2.19624			0.102736			0.0513678	+	0.998680i	$0.483642\pi$
$458$	−4.08376	−	1.48637i	−0.190822	−	0.0694534i
$459$	0.139438	+	0.790794i	0.00650842	+	0.0369111i
$460$	−4.27867	−	3.59023i	−0.199494	−	0.167395i
$461$	−23.0192	+	19.3154i	−1.07211	+	0.899607i	−0.995242	−	0.0974339i	$-0.968937\pi$
$461$	−23.0192	+	19.3154i	−1.07211	+	0.899607i	−0.0768683	+	0.997041i	$0.524492\pi$
$462$	−0.547591	+	3.10554i	−0.0254762	+	0.144483i
$463$	−15.7000	+	27.1932i	−0.729641	+	1.26378i	0.227394	+	0.973803i	$0.426979\pi$
$463$	−15.7000	+	27.1932i	−0.729641	+	1.26378i	−0.957035	+	0.289972i	$0.906354\pi$
$464$	3.71171	+	6.42886i	0.172312	+	0.298453i
$465$	−2.73822	+	0.996631i	−0.126982	+	0.0462177i
$466$	−9.12473	+	3.32113i	−0.422695	+	0.153848i
$467$	−15.1508	−	26.2420i	−0.701096	−	1.21433i	−0.968082	−	0.250633i	$-0.919361\pi$
$467$	−15.1508	−	26.2420i	−0.701096	−	1.21433i	0.266986	−	0.963700i	$-0.413972\pi$
$468$	0.641164	−	1.11053i	0.0296378	−	0.0513342i
$469$	−1.13960	+	6.46301i	−0.0526220	+	0.298434i
$470$	−1.63637	+	1.37308i	−0.0754801	+	0.0633353i
$471$	−7.25804	−	6.09021i	−0.334433	−	0.280622i
$472$	0.844422	+	4.78896i	0.0388677	+	0.220430i
$473$	46.0760	+	16.7703i	2.11858	+	0.771099i
$474$	0.287834			0.0132206
$475$	−4.33496	+	0.456159i	−0.198902	+	0.0209300i
$476$	−0.494681			−0.0226737
$477$	13.3023	+	4.84162i	0.609068	+	0.221683i
$478$	1.71679	+	9.73642i	0.0785243	+	0.445334i
$479$	27.3756	+	22.9709i	1.25082	+	1.04957i	0.996598	+	0.0824202i	$0.0262650\pi$
$479$	27.3756	+	22.9709i	1.25082	+	1.04957i	0.254225	+	0.967145i	$0.418179\pi$
$480$	−0.766044	+	0.642788i	−0.0349650	+	0.0293391i
$481$	1.98756	−	11.2720i	0.0906250	−	0.513960i
$482$	−2.00958	+	3.48069i	−0.0915338	+	0.158541i
$483$	−1.72043	−	2.97988i	−0.0782824	−	0.135589i
$484$	−14.2858	+	5.19961i	−0.649355	+	0.236346i
$485$	17.1128	−	6.22854i	0.777051	−	0.282823i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−1.10121	+	1.90735i	−0.0499006	+	0.0864304i	−0.889897	−	0.456162i	$-0.849224\pi$
$487$	−1.10121	+	1.90735i	−0.0499006	+	0.0864304i	0.839996	+	0.542592i	$0.182557\pi$
$488$	−1.49423	+	8.47422i	−0.0676408	+	0.383610i
$489$	−2.91976	+	2.44997i	−0.132036	+	0.110791i
$490$	−5.07159	−	4.25557i	−0.229111	−	0.192247i
$491$	1.18706	+	6.73217i	0.0535714	+	0.303819i	0.999807	−	0.0196605i	$-0.00625852\pi$
$491$	1.18706	+	6.73217i	0.0535714	+	0.303819i	−0.946235	+	0.323479i	$0.895147\pi$
$492$	−3.87873	−	1.41174i	−0.174867	−	0.0636463i
$493$	5.96095			0.268468
$494$	−5.42367	−	1.35157i	−0.244022	−	0.0608099i
$495$	5.11885			0.230075
$496$	2.73822	+	0.996631i	0.122950	+	0.0447501i
$497$	0.850609	+	4.82405i	0.0381551	+	0.216388i
$498$	−2.00644	−	1.68360i	−0.0899107	−	0.0754441i
$499$	33.6786	−	28.2597i	1.50766	−	1.26508i	0.639502	−	0.768789i	$-0.279140\pi$
$499$	33.6786	−	28.2597i	1.50766	−	1.26508i	0.868158	−	0.496288i	$-0.165304\pi$
$500$	0.173648	−	0.984808i	0.00776578	−	0.0440419i
$501$	5.84024	−	10.1156i	0.260923	−	0.451931i
$502$	5.18810	+	8.98605i	0.231556	+	0.401067i
$503$	9.27404	−	3.37548i	0.413509	−	0.150505i	−0.126884	−	0.991918i	$-0.540498\pi$
$503$	9.27404	−	3.37548i	0.413509	−	0.150505i	0.540393	+	0.841412i	$0.318275\pi$
$504$	−0.578894	+	0.210700i	−0.0257860	+	0.00938534i
$505$	7.62573	+	13.2082i	0.339341	+	0.587755i
$506$	14.2954	−	24.7604i	0.635509	−	1.10073i
$507$	1.97189	−	11.1831i	0.0875745	−	0.496660i
$508$	3.30593	−	2.77400i	0.146677	−	0.123077i
$509$	−17.1278	−	14.3720i	−0.759178	−	0.637026i	0.178735	−	0.983897i	$-0.442800\pi$
$509$	−17.1278	−	14.3720i	−0.759178	−	0.637026i	−0.937913	+	0.346871i	$0.887244\pi$
$510$	0.139438	+	0.790794i	0.00617443	+	0.0350169i
$511$	−5.76126	−	2.09693i	−0.254863	−	0.0927626i
$512$	1.00000			0.0441942
$513$	3.02756	−	3.13590i	0.133670	−	0.138453i
$514$	15.8722			0.700094
$515$	0.931675	+	0.339102i	0.0410545	+	0.0149426i
$516$	1.66336	+	9.43340i	0.0732255	+	0.415282i
$517$	−8.37634	−	7.02858i	−0.368391	−	0.309117i
$518$	−4.21230	+	3.53454i	−0.185078	+	0.155299i
$519$	−0.988665	+	5.60700i	−0.0433976	+	0.246120i
$520$	0.641164	−	1.11053i	0.0281169	−	0.0486999i
$521$	−7.79971	−	13.5095i	−0.341712	−	0.591862i	0.643039	−	0.765833i	$-0.277673\pi$
$521$	−7.79971	−	13.5095i	−0.341712	−	0.591862i	−0.984751	+	0.173971i	$0.944340\pi$
$522$	6.97573	−	2.53896i	0.305319	−	0.111127i
$523$	40.4323	−	14.7162i	1.76798	−	0.643493i	0.767986	−	0.640467i	$-0.221259\pi$
$523$	40.4323	−	14.7162i	1.76798	−	0.643493i	0.999995	−	0.00302595i	$-0.000963192\pi$
$524$	7.71708	+	13.3664i	0.337122	+	0.583913i
$525$	0.308023	−	0.533512i	0.0134432	−	0.0232844i
$526$	−2.45437	+	13.9194i	−0.107016	+	0.606917i
$527$	1.79246	−	1.50405i	0.0780806	−	0.0655174i
$528$	−3.92127	−	3.29033i	−0.170651	−	0.143193i
$529$	1.42334	+	8.07217i	0.0618844	+	0.350964i
$530$	13.3023	+	4.84162i	0.577813	+	0.210307i
$531$	4.86283			0.211029
$532$	1.57864	+	2.17225i	0.0684425	+	0.0941789i
$533$	5.29301			0.229266
$534$	5.94315	+	2.16313i	0.257185	+	0.0936078i
$535$	−1.90767	−	10.8189i	−0.0824758	−	0.467743i
$536$	−8.16063	−	6.84758i	−0.352486	−	0.295770i
$537$	−4.92749	+	4.13466i	−0.212637	+	0.178424i
$538$	2.11201	−	11.9778i	0.0910550	−	0.516399i
$539$	16.9446	−	29.3490i	0.729858	−	1.26415i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	24.3171	−	8.85071i	1.04547	−	0.380522i	0.238521	−	0.971137i	$-0.423337\pi$
$541$	24.3171	−	8.85071i	1.04547	−	0.380522i	0.806953	+	0.590616i	$0.201115\pi$
$542$	−15.0442	+	5.47565i	−0.646204	+	0.235199i
$543$	−9.85421	−	17.0680i	−0.422885	−	0.732458i
$544$	0.401497	−	0.695413i	0.0172140	−	0.0298156i
$545$	2.11666	−	12.0042i	0.0906679	−	0.514203i
$546$	0.605154	−	0.507785i	0.0258982	−	0.0217312i
$547$	29.1739	+	24.4798i	1.24739	+	1.04668i	0.996909	+	0.0785594i	$0.0250320\pi$
$547$	29.1739	+	24.4798i	1.24739	+	1.04668i	0.250477	+	0.968122i	$0.419412\pi$
$548$	3.91335	+	22.1937i	0.167170	+	0.948067i
$549$	8.08601	+	2.94307i	0.345102	+	0.125607i
$550$	5.11885			0.218269
$551$	−19.0227	−	26.1758i	−0.810394	−	1.11513i
$552$	5.58540			0.237730
$553$	0.166625	+	0.0606467i	0.00708563	+	0.00257896i
$554$	2.19791	+	12.4650i	0.0933803	+	0.529586i
$555$	6.83763	+	5.73745i	0.290241	+	0.243541i
$556$	12.6838	−	10.6430i	0.537912	−	0.451362i
$557$	5.48641	−	31.1150i	0.232467	−	1.31838i	−0.615417	−	0.788201i	$-0.711013\pi$
$557$	5.48641	−	31.1150i	0.232467	−	1.31838i	0.847884	−	0.530182i	$-0.177876\pi$
$558$	1.45698	−	2.52356i	0.0616788	−	0.106831i
$559$	−6.14166	−	10.6377i	−0.259764	−	0.449925i
$560$	−0.578894	+	0.210700i	−0.0244627	+	0.00890371i
$561$	−3.86252	+	1.40584i	−0.163076	+	0.0593546i
$562$	−4.39592	−	7.61396i	−0.185431	−	0.321175i
$563$	9.63382	−	16.6863i	0.406017	−	0.703242i	−0.588422	−	0.808554i	$-0.700251\pi$
$563$	9.63382	−	16.6863i	0.406017	−	0.703242i	0.994439	+	0.105312i	$0.0335841\pi$
$564$	0.370935	−	2.10368i	0.0156192	−	0.0885808i
$565$	−4.60349	+	3.86279i	−0.193670	+	0.162509i
$566$	−10.3317	−	8.66936i	−0.434275	−	0.364400i
$567$	0.106975	+	0.606687i	0.00449254	+	0.0254785i
$568$	−7.47192	−	2.71956i	−0.313515	−	0.114110i
$569$	29.7508			1.24722			0.623610	−	0.781736i	$-0.285666\pi$
$569$	29.7508			1.24722			0.623610	+	0.781736i	$0.285666\pi$
$570$	3.02756	−	3.13590i	0.126811	−	0.131348i
$571$	1.42905			0.0598041			0.0299020	−	0.999553i	$-0.490480\pi$
$571$	1.42905			0.0598041			0.0299020	+	0.999553i	$0.490480\pi$
$572$	6.16818	+	2.24503i	0.257905	+	0.0938696i
$573$	2.45349	+	13.9144i	0.102496	+	0.581284i
$574$	−1.94792	−	1.63450i	−0.0813046	−	0.0682227i
$575$	−4.27867	+	3.59023i	−0.178433	+	0.149723i
$576$	0.173648	−	0.984808i	0.00723534	−	0.0410337i
$577$	−11.8770	+	20.5716i	−0.494448	+	0.856409i	−0.999980	−	0.00639919i	$-0.997963\pi$
$577$	−11.8770	+	20.5716i	−0.494448	+	0.856409i	0.505532	+	0.862808i	$0.331296\pi$
$578$	8.17760	+	14.1640i	0.340143	+	0.589146i
$579$	0.837007	−	0.304646i	0.0347848	−	0.0126606i
$580$	6.97573	−	2.53896i	0.289651	−	0.105424i
$581$	−0.806781	−	1.39739i	−0.0334709	−	0.0579733i
$582$	−9.10551	+	15.7712i	−0.377436	+	0.653738i
$583$	−12.5829	+	71.3614i	−0.521132	+	2.95549i
$584$	7.62381	−	6.39714i	0.315476	−	0.264715i
$585$	−0.982320	−	0.824264i	−0.0406139	−	0.0340791i
$586$	1.01065	+	5.73171i	0.0417498	+	0.236775i
$587$	21.1603	+	7.70172i	0.873379	+	0.317884i	0.739535	−	0.673119i	$-0.235046\pi$
$587$	21.1603	+	7.70172i	0.873379	+	0.317884i	0.133844	+	0.991002i	$0.457268\pi$
$588$	6.62049			0.273024
$589$	−12.3247	−	3.07130i	−0.507831	−	0.126551i
$590$	4.86283			0.200200
$591$	−1.40115	−	0.509978i	−0.0576357	−	0.0209777i
$592$	−1.54997	−	8.79029i	−0.0637032	−	0.361279i
$593$	−36.8134	−	30.8901i	−1.51175	−	1.26851i	−0.860271	−	0.509837i	$-0.829706\pi$
$593$	−36.8134	−	30.8901i	−1.51175	−	1.26851i	−0.651476	−	0.758670i	$-0.725850\pi$
$594$	−3.92127	+	3.29033i	−0.160892	+	0.135004i
$595$	−0.0859005	+	0.487166i	−0.00352158	+	0.0199718i
$596$	−7.96631	+	13.7981i	−0.326313	+	0.565190i
$597$	3.29574	+	5.70839i	0.134886	+	0.233629i
$598$	−6.73037	+	2.44965i	−0.275225	+	0.100174i
$599$	−33.2480	+	12.1013i	−1.35848	+	0.494446i	−0.915584	−	0.402128i	$-0.868271\pi$
$599$	−33.2480	+	12.1013i	−1.35848	+	0.494446i	−0.442895	+	0.896574i	$0.646049\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	6.91666	−	11.9800i	0.282136	−	0.488674i	−0.689774	−	0.724024i	$-0.742290\pi$
$601$	6.91666	−	11.9800i	0.282136	−	0.488674i	0.971911	+	0.235350i	$0.0756236\pi$
$602$	−1.02471	+	5.81141i	−0.0417640	+	0.236855i
$603$	−8.16063	+	6.84758i	−0.332327	+	0.278855i
$604$	5.85543	+	4.91329i	0.238254	+	0.199919i
$605$	2.63991	+	14.9717i	0.107328	+	0.608686i
$606$	−14.3317	−	5.21631i	−0.582185	−	0.211898i
$607$	−39.3475			−1.59707			−0.798533	−	0.601950i	$-0.794390\pi$
$607$	−39.3475			−1.59707			−0.798533	+	0.601950i	$0.794390\pi$
$608$	−4.33496	+	0.456159i	−0.175806	+	0.0184997i
$609$	4.57317			0.185314
$610$	8.08601	+	2.94307i	0.327393	+	0.119161i
$611$	0.475660	+	2.69760i	0.0192431	+	0.109133i
$612$	−0.615128	−	0.516154i	−0.0248651	−	0.0208643i
$613$	10.9754	−	9.20948i	0.443293	−	0.371967i	−0.393647	−	0.919262i	$-0.628787\pi$
$613$	10.9754	−	9.20948i	0.443293	−	0.371967i	0.836940	+	0.547294i	$0.184342\pi$
$614$	0.487721	−	2.76601i	0.0196828	−	0.111627i
$615$	−2.06383	+	3.57466i	−0.0832216	+	0.144144i
$616$	−1.57673	−	2.73097i	−0.0635281	−	0.110034i
$617$	11.8843	−	4.32554i	0.478445	−	0.174140i	−0.0915290	−	0.995802i	$-0.529175\pi$
$617$	11.8843	−	4.32554i	0.478445	−	0.174140i	0.569974	+	0.821663i	$0.306953\pi$
$618$	−0.931675	+	0.339102i	−0.0374775	+	0.0136407i
$619$	−18.8900	−	32.7185i	−0.759254	−	1.31507i	−0.943232	−	0.332135i	$-0.892231\pi$
$619$	−18.8900	−	32.7185i	−0.759254	−	1.31507i	0.183978	−	0.982930i	$-0.441102\pi$
$620$	1.45698	−	2.52356i	0.0585136	−	0.101349i
$621$	0.969895	−	5.50055i	0.0389205	−	0.220729i
$622$	7.21317	−	6.05257i	0.289222	−	0.242686i
$623$	2.98468	+	2.50445i	0.119579	+	0.100339i
$624$	0.222674	+	1.26285i	0.00891408	+	0.0505543i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	−12.8526			−0.513694
$627$	18.4995	+	12.4748i	0.738798	+	0.498194i
$628$	9.47469			0.378081
$629$	−6.73518	−	2.45141i	−0.268549	−	0.0977440i
$630$	0.106975	+	0.606687i	0.00426200	+	0.0241710i
$631$	−24.7160	−	20.7392i	−0.983928	−	0.825613i	0.000749607	−	1.00000i	$-0.499761\pi$
$631$	−24.7160	−	20.7392i	−0.983928	−	0.825613i	−0.984677	+	0.174386i	$0.944206\pi$
$632$	−0.220493	+	0.185016i	−0.00877076	+	0.00735954i
$633$	−1.83415	+	10.4020i	−0.0729008	+	0.413441i
$634$	6.29962	−	10.9113i	0.250190	−	0.433342i
$635$	−2.15779	−	3.73741i	−0.0856294	−	0.148314i
$636$	−13.3023	+	4.84162i	−0.527469	+	0.191983i
$637$	−7.97764	+	2.90362i	−0.316086	+	0.115046i
$638$	18.9997	+	32.9084i	0.752204	+	1.30286i
$639$	−3.97573	+	6.88616i	−0.157277	+	0.272412i
$640$	0.173648	−	0.984808i	0.00686405	−	0.0389279i
$641$	6.39746	−	5.36810i	0.252684	−	0.212027i	−0.507643	−	0.861568i	$-0.669483\pi$
$641$	6.39746	−	5.36810i	0.252684	−	0.212027i	0.760327	+	0.649540i	$0.225039\pi$
$642$	8.41564	+	7.06156i	0.332139	+	0.278697i
$643$	−5.11132	−	28.9877i	−0.201571	−	1.14316i	−0.902746	−	0.430175i	$-0.858452\pi$
$643$	−5.11132	−	28.9877i	−0.201571	−	1.14316i	0.701175	−	0.712989i	$-0.252659\pi$
$644$	3.23336	+	1.17685i	0.127412	+	0.0463742i
$645$	9.57892			0.377170
$646$	−1.42325	+	3.19773i	−0.0559972	+	0.125813i
$647$	−49.5568			−1.94828			−0.974140	−	0.225944i	$-0.927453\pi$
$647$	−49.5568			−1.94828			−0.974140	+	0.225944i	$0.927453\pi$
$648$	−0.939693	−	0.342020i	−0.0369146	−	0.0134358i
$649$	4.32247	+	24.5140i	0.169672	+	0.962257i
$650$	−0.982320	−	0.824264i	−0.0385297	−	0.0323303i
$651$	1.37515	−	1.15389i	0.0538964	−	0.0452244i
$652$	0.661855	−	3.75357i	0.0259202	−	0.147001i
$653$	20.2128	−	35.0096i	0.790988	−	1.37003i	−0.134368	−	0.990931i	$-0.542901\pi$
$653$	20.2128	−	35.0096i	0.790988	−	1.37003i	0.925356	−	0.379099i	$-0.123766\pi$
$654$	6.09469	+	10.5563i	0.238321	+	0.412784i
$655$	14.5034	−	5.27879i	0.566693	−	0.206259i
$656$	3.87873	−	1.41174i	0.151439	−	0.0551193i
$657$	−4.97609	−	8.61884i	−0.194136	−	0.336253i
$658$	0.657977	−	1.13965i	0.0256506	−	0.0444282i
$659$	−6.09139	+	34.5460i	−0.237287	+	1.34572i	0.600457	+	0.799657i	$0.294986\pi$
$659$	−6.09139	+	34.5460i	−0.237287	+	1.34572i	−0.837744	+	0.546064i	$0.816126\pi$
$660$	−3.92127	+	3.29033i	−0.152635	+	0.128076i
$661$	−17.5262	−	14.7062i	−0.681691	−	0.572006i	0.234809	−	0.972042i	$-0.424554\pi$
$661$	−17.5262	−	14.7062i	−0.681691	−	0.572006i	−0.916500	+	0.400035i	$0.868998\pi$
$662$	−2.81301	−	15.9534i	−0.109331	−	0.620046i
$663$	0.967601	+	0.352178i	0.0375785	+	0.0136775i
$664$	2.61922			0.101646
$665$	2.41337	−	1.17745i	0.0935866	−	0.0456594i
$666$	−8.92589			−0.345871
$667$	−38.9622	−	14.1811i	−1.50862	−	0.549094i
$668$	2.02829	+	11.5030i	0.0784771	+	0.445066i
$669$	4.65533	+	3.90629i	0.179985	+	0.151026i
$670$	−8.16063	+	6.84758i	−0.315273	+	0.264545i
$671$	−7.64876	+	43.3783i	−0.295277	+	1.67460i
$672$	0.308023	−	0.533512i	0.0118823	−	0.0205807i
$673$	5.20125	+	9.00884i	0.200494	+	0.347265i	0.948688	−	0.316215i	$-0.102412\pi$
$673$	5.20125	+	9.00884i	0.200494	+	0.347265i	−0.748194	+	0.663480i	$0.769079\pi$
$674$	−17.5284	+	6.37982i	−0.675169	+	0.245741i
$675$	0.939693	−	0.342020i	0.0361688	−	0.0131644i
$676$	5.67782	+	9.83427i	0.218378	+	0.378241i
$677$	20.2409	−	35.0583i	0.777921	−	1.34740i	−0.155216	−	0.987880i	$-0.549607\pi$
$677$	20.2409	−	35.0583i	0.777921	−	1.34740i	0.933138	−	0.359519i	$-0.117059\pi$
$678$	1.04353	−	5.91813i	0.0400764	−	0.227285i
$679$	−8.59413	+	7.21133i	−0.329812	+	0.276745i
$680$	−0.615128	−	0.516154i	−0.0235891	−	0.0197936i
$681$	0.620298	+	3.51788i	0.0237699	+	0.134806i
$682$	14.0166	+	5.10161i	0.536722	+	0.195351i
$683$	20.3480			0.778595			0.389297	−	0.921112i	$-0.372718\pi$
$683$	20.3480			0.778595			0.389297	+	0.921112i	$0.372718\pi$
$684$	−0.303530	+	4.34832i	−0.0116058	+	0.166262i
$685$	22.5361			0.861059
$686$	7.88482	+	2.86984i	0.301044	+	0.109571i
$687$	−0.754649	−	4.27983i	−0.0287917	−	0.163286i
$688$	−7.33788	−	6.15721i	−0.279754	−	0.234742i
$689$	13.9057	−	11.6682i	0.529764	−	0.444525i
$690$	0.969895	−	5.50055i	0.0369233	−	0.209402i
$691$	−17.6293	+	30.5348i	−0.670649	+	1.16160i	0.307071	+	0.951687i	$0.400651\pi$
$691$	−17.6293	+	30.5348i	−0.670649	+	1.16160i	−0.977720	+	0.209912i	$0.932682\pi$
$692$	−2.84675	−	4.93071i	−0.108217	−	0.187438i
$693$	−2.96327	+	1.07854i	−0.112565	+	0.0409705i
$694$	6.25357	−	2.27611i	0.237382	−	0.0864001i
$695$	−8.27875	−	14.3392i	−0.314031	−	0.543917i
$696$	−3.71171	+	6.42886i	−0.140692	+	0.243685i
$697$	0.575554	−	3.26413i	0.0218007	−	0.123638i
$698$	7.34214	−	6.16079i	0.277904	−	0.233189i
$699$	−7.43854	−	6.24168i	−0.281352	−	0.236082i
$700$	0.106975	+	0.606687i	0.00404329	+	0.0229306i
$701$	32.1698	+	11.7088i	1.21504	+	0.442237i	0.868448	−	0.495781i	$-0.165118\pi$
$701$	32.1698	+	11.7088i	1.21504	+	0.442237i	0.346588	+	0.938018i	$0.387340\pi$
$702$	1.28233			0.0483983
$703$	10.7288	+	37.3986i	0.404645	+	1.41051i
$704$	5.11885			0.192924
$705$	−2.00731	−	0.730599i	−0.0755995	−	0.0275160i
$706$	4.35219	+	24.6825i	0.163797	+	0.928938i
$707$	−7.19746	−	6.03938i	−0.270688	−	0.227134i
$708$	−3.72515	+	3.12577i	−0.140000	+	0.117474i
$709$	0.0284560	−	0.161382i	0.00106869	−	0.00606082i	−0.984269	−	0.176678i	$-0.943465\pi$
$709$	0.0284560	−	0.161382i	0.00106869	−	0.00606082i	0.985337	+	0.170617i	$0.0545761\pi$
$710$	−3.97573	+	6.88616i	−0.149206	+	0.258433i
$711$	0.143917	+	0.249271i	0.00539731	+	0.00934841i
$712$	−5.94315	+	2.16313i	−0.222729	+	0.0810667i
$713$	−15.2941	+	5.56658i	−0.572767	+	0.208470i
$714$	−0.247341	−	0.428406i	−0.00925649	−	0.0160327i
$715$	3.28202	−	5.68463i	0.122741	−	0.212593i
$716$	1.11697	−	6.33466i	0.0417432	−	0.236737i
$717$	−7.57359	+	6.35500i	−0.282841	+	0.237332i
$718$	−22.4966	−	18.8768i	−0.839564	−	0.704478i
$719$	−7.08262	−	40.1675i	−0.264137	−	1.49800i	−0.771481	−	0.636253i	$-0.780484\pi$
$719$	−7.08262	−	40.1675i	−0.264137	−	1.49800i	0.507344	−	0.861744i	$-0.330628\pi$
$720$	−0.939693	−	0.342020i	−0.0350203	−	0.0127463i
$721$	−0.610790			−0.0227470
$722$	18.5838	−	3.95487i	0.691619	−	0.147185i
$723$	−4.01916			−0.149474
$724$	18.5199	+	6.74068i	0.688285	+	0.250515i
$725$	−1.28906	−	7.31064i	−0.0478746	−	0.271510i
$726$	−11.6459	−	9.77207i	−0.432220	−	0.362676i
$727$	−3.27005	+	2.74390i	−0.121280	+	0.101766i	−0.701410	−	0.712758i	$-0.747446\pi$
$727$	−3.27005	+	2.74390i	−0.121280	+	0.101766i	0.580131	+	0.814523i	$0.303001\pi$
$728$	−0.137177	+	0.777972i	−0.00508413	+	0.0288335i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−4.97609	−	8.61884i	−0.184173	−	0.318998i
$731$	−7.22794	+	2.63075i	−0.267335	+	0.0973019i
$732$	−8.08601	+	2.94307i	−0.298867	+	0.108779i
$733$	−13.8354	−	23.9636i	−0.511021	−	0.885115i	−0.999918	−	0.0127735i	$-0.995934\pi$
$733$	−13.8354	−	23.9636i	−0.511021	−	0.885115i	0.488897	−	0.872342i	$-0.337399\pi$
$734$	12.2649	−	21.2434i	0.452705	−	0.784108i
$735$	1.14964	−	6.51991i	0.0424049	−	0.240490i
$736$	−4.27867	+	3.59023i	−0.157714	+	0.132337i
$737$	−41.7731	−	35.0518i	−1.53873	−	1.29115i
$738$	−0.716761	−	4.06495i	−0.0263843	−	0.149633i
$739$	−1.34389	−	0.489135i	−0.0494357	−	0.0179931i	0.317184	−	0.948364i	$-0.397263\pi$
$739$	−1.34389	−	0.489135i	−0.0494357	−	0.0179931i	−0.366620	+	0.930371i	$0.619485\pi$
$740$	−8.92589			−0.328122
$741$	−1.54134	−	5.37282i	−0.0566226	−	0.197375i
$742$	−8.72073			−0.320148
$743$	−1.35480	−	0.493106i	−0.0497027	−	0.0180903i	0.317049	−	0.948409i	$-0.397308\pi$
$743$	−1.35480	−	0.493106i	−0.0497027	−	0.0180903i	−0.366752	+	0.930319i	$0.619530\pi$
$744$	0.506003	+	2.86969i	0.0185510	+	0.105208i
$745$	12.2051	+	10.2413i	0.447160	+	0.375212i
$746$	−17.1274	+	14.3716i	−0.627078	+	0.526181i
$747$	0.454823	−	2.57943i	0.0166411	−	0.0943764i
$748$	2.05520	−	3.55971i	0.0751456	−	0.130156i
$749$	3.38389	+	5.86107i	0.123645	+	0.214159i
$750$	0.939693	−	0.342020i	0.0343127	−	0.0124888i
$751$	−32.6764	+	11.8932i	−1.19238	+	0.433991i	−0.860558	−	0.509352i	$-0.829885\pi$
$751$	−32.6764	+	11.8932i	−1.19238	+	0.433991i	−0.331821	+	0.943342i	$0.607663\pi$
$752$	1.06806	+	1.84994i	0.0389483	+	0.0674605i
$753$	−5.18810	+	8.98605i	−0.189065	+	0.327470i
$754$	1.65300	−	9.37463i	0.0601987	−	0.341404i
$755$	5.85543	−	4.91329i	0.213101	−	0.178813i
$756$	−0.471919	−	0.395987i	−0.0171635	−	0.0144019i
$757$	5.41724	+	30.7227i	0.196893	+	1.11664i	0.909697	+	0.415273i	$0.136314\pi$
$757$	5.41724	+	30.7227i	0.196893	+	1.11664i	−0.712804	+	0.701363i	$0.752575\pi$
$758$	16.9897	+	6.18374i	0.617093	+	0.224603i
$759$	28.5908			1.03778
$760$	−0.303530	+	4.34832i	−0.0110102	+	0.157730i
$761$	−32.4832			−1.17751			−0.588757	−	0.808310i	$-0.700382\pi$
$761$	−32.4832			−1.17751			−0.588757	+	0.808310i	$0.700382\pi$
$762$	4.05532	+	1.47602i	0.146909	+	0.0534704i
$763$	1.30396	+	7.39514i	0.0472066	+	0.267722i
$764$	−10.8235	−	9.08200i	−0.391581	−	0.328575i
$765$	−0.615128	+	0.516154i	−0.0222400	+	0.0186616i
$766$	−1.66303	+	9.43149i	−0.0600876	+	0.340773i
$767$	3.11787	−	5.40031i	0.112580	−	0.194994i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−7.08211	+	2.57768i	−0.255387	+	0.0929534i	−0.466541	−	0.884499i	$-0.654500\pi$
$769$	−7.08211	+	2.57768i	−0.255387	+	0.0929534i	0.211154	+	0.977453i	$0.432278\pi$
$770$	−2.96327	+	1.07854i	−0.106789	+	0.0388680i
$771$	7.93611	+	13.7457i	0.285812	+	0.495041i
$772$	−0.445362	+	0.771390i	−0.0160289	+	0.0277629i
$773$	−0.0108738	+	0.0616682i	−0.000391102	+	0.00221805i	−0.985003	−	0.172539i	$-0.944803\pi$
$773$	−0.0108738	+	0.0616682i	−0.000391102	+	0.00221805i	0.984612	+	0.174757i	$0.0559140\pi$
$774$	−7.33788	+	6.15721i	−0.263755	+	0.221316i
$775$	−2.23222	−	1.87305i	−0.0801837	−	0.0672821i
$776$	−3.16231	−	17.9344i	−0.113520	−	0.643806i
$777$	−5.16715	−	1.88069i	−0.185370	−	0.0674693i
$778$	24.0836			0.863439
$779$	−16.1702	+	7.88917i	−0.579357	+	0.282659i
$780$	1.28233			0.0459147
$781$	−38.2477	−	13.9210i	−1.36861	−	0.498133i
$782$	0.778819	+	4.41690i	0.0278505	+	0.157948i
$783$	5.68666	+	4.77168i	0.203225	+	0.170526i
$784$	−5.07159	+	4.25557i	−0.181128	+	0.151985i
$785$	1.64526	−	9.33075i	0.0587220	−	0.333029i
$786$	−7.71708	+	13.3664i	−0.275259	+	0.476763i
$787$	−11.6631	−	20.2012i	−0.415746	−	0.720094i	0.579760	−	0.814787i	$-0.303146\pi$
$787$	−11.6631	−	20.2012i	−0.415746	−	0.720094i	−0.995506	+	0.0946934i	$0.969813\pi$
$788$	1.40115	−	0.509978i	0.0499140	−	0.0181672i
$789$	−13.2818	+	4.83417i	−0.472844	+	0.172101i
$790$	0.143917	+	0.249271i	0.00512033	+	0.00886868i
$791$	1.85104	−	3.20610i	0.0658156	−	0.113996i
$792$	0.888879	−	5.04109i	0.0315850	−	0.179127i
$793$	8.45281	−	7.09275i	0.300168	−	0.251871i
$794$	11.9042	+	9.98880i	0.422464	+	0.354489i
$795$	2.45816	+	13.9409i	0.0871818	+	0.494433i
$796$	−6.19396	−	2.25442i	−0.219539	−	0.0799057i
$797$	18.6256			0.659752			0.329876	−	0.944024i	$-0.392993\pi$
$797$	18.6256			0.659752			0.329876	+	0.944024i	$0.392993\pi$
$798$	−1.09190	+	2.45326i	−0.0386530	+	0.0868446i
$799$	1.71530			0.0606829
$800$	−0.939693	−	0.342020i	−0.0332232	−	0.0120922i
$801$	1.09825	+	6.22849i	0.0388048	+	0.220073i
$802$	21.9290	+	18.4006i	0.774339	+	0.649747i
$803$	39.0252	−	32.7460i	1.37717	−	1.15558i
$804$	1.84986	−	10.4911i	0.0652397	−	0.369993i
$805$	1.72043	−	2.97988i	0.0606373	−	0.105027i
$806$	−1.86832	−	3.23603i	−0.0658088	−	0.113984i
$807$	11.4291	−	4.15984i	0.402322	−	0.146433i
$808$	14.3317	−	5.21631i	0.504187	−	0.183509i
$809$	16.8840	+	29.2440i	0.593610	+	1.02816i	0.993741	+	0.111705i	$0.0356312\pi$
$809$	16.8840	+	29.2440i	0.593610	+	1.02816i	−0.400131	+	0.916458i	$0.631035\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	−5.15432	+	29.2316i	−0.180992	+	1.02646i	0.750005	+	0.661433i	$0.230051\pi$
$811$	−5.15432	+	29.2316i	−0.180992	+	1.02646i	−0.930997	+	0.365027i	$0.881060\pi$
$812$	−3.50325	+	2.93958i	−0.122940	+	0.103159i
$813$	−12.2642	−	10.2909i	−0.430123	−	0.360916i
$814$	−7.93404	−	44.9962i	−0.278088	−	1.57712i
$815$	−3.58161	−	1.30360i	−0.125458	−	0.0456631i
$816$	0.802993			0.0281104
$817$	34.6181	+	23.3441i	1.21113	+	0.816705i
$818$	−38.1015			−1.33219
$819$	0.742332	+	0.270187i	0.0259392	+	0.00944109i
$820$	−0.716761	−	4.06495i	−0.0250304	−	0.141954i
$821$	−24.6024	−	20.6439i	−0.858631	−	0.720477i	0.103041	−	0.994677i	$-0.467143\pi$
$821$	−24.6024	−	20.6439i	−0.858631	−	0.720477i	−0.961673	+	0.274200i	$0.911587\pi$
$822$	−17.2636	+	14.4859i	−0.602138	+	0.505254i
$823$	−2.94586	+	16.7068i	−0.102686	+	0.582363i	0.889433	+	0.457066i	$0.151100\pi$
$823$	−2.94586	+	16.7068i	−0.102686	+	0.582363i	−0.992119	+	0.125297i	$0.960012\pi$
$824$	0.495734	−	0.858636i	0.0172697	−	0.0299120i
$825$	2.55943	+	4.43306i	0.0891078	+	0.154339i
$826$	−2.81507	+	1.02460i	−0.0979487	+	0.0356504i
$827$	9.78454	−	3.56128i	0.340242	−	0.123838i	−0.166248	−	0.986084i	$-0.553165\pi$
$827$	9.78454	−	3.56128i	0.340242	−	0.123838i	0.506490	+	0.862246i	$0.330943\pi$
$828$	2.79270	+	4.83710i	0.0970530	+	0.168101i
$829$	13.3992	−	23.2081i	0.465373	−	0.806049i	−0.533846	−	0.845582i	$-0.679254\pi$
$829$	13.3992	−	23.2081i	0.465373	−	0.806049i	0.999218	+	0.0395330i	$0.0125870\pi$
$830$	0.454823	−	2.57943i	0.0157871	−	0.0895333i
$831$	−9.69603	+	8.13594i	−0.336352	+	0.282232i
$832$	−0.982320	−	0.824264i	−0.0340558	−	0.0285762i
$833$	0.923149	+	5.23544i	0.0319852	+	0.181397i
$834$	15.5590	+	5.66300i	0.538763	+	0.196094i
$835$	11.6805			0.404220
$836$	−22.1900	+	2.33501i	−0.767459	+	0.0807580i
$837$	2.91395			0.100721
$838$	−11.7553	−	4.27859i	−0.406082	−	0.147802i
$839$	−2.38410	−	13.5209i	−0.0823083	−	0.466793i	−0.997905	−	0.0646957i	$-0.979392\pi$
$839$	−2.38410	−	13.5209i	−0.0823083	−	0.466793i	0.915597	−	0.402098i	$-0.131719\pi$
$840$	−0.471919	−	0.395987i	−0.0162828	−	0.0136629i
$841$	19.9992	−	16.7813i	0.689627	−	0.578666i
$842$	5.52419	−	31.3293i	0.190376	−	1.07968i
$843$	4.39592	−	7.61396i	0.151404	−	0.262239i
$844$	−5.28122	−	9.14733i	−0.181787	−	0.314864i
$845$	10.6708	−	3.88386i	0.367087	−	0.133609i
$846$	2.00731	−	0.730599i	0.0690126	−	0.0251185i
$847$	−4.68277	−	8.11079i	−0.160902	−	0.278690i
$848$	7.07798	−	12.2594i	0.243059	−	0.420990i
$849$	2.34202	−	13.2822i	0.0803778	−	0.455845i
$850$	−0.615128	+	0.516154i	−0.0210987	+	0.0177039i
$851$	38.1909	+	32.0460i	1.30917	+	1.09852i
$852$	−1.38076	−	7.83065i	−0.0473039	−	0.268274i
$853$	−31.2742	−	11.3829i	−1.07081	−	0.389743i	−0.254330	−	0.967117i	$-0.581855\pi$
$853$	−31.2742	−	11.3829i	−1.07081	−	0.389743i	−0.816479	+	0.577375i	$0.804077\pi$
$854$	−5.30105			−0.181398
$855$	4.22955	+	1.05400i	0.144648	+	0.0360459i
$856$	−10.9858			−0.375488
$857$	−35.0211	−	12.7466i	−1.19630	−	0.435417i	−0.334367	−	0.942443i	$-0.608523\pi$
$857$	−35.0211	−	12.7466i	−1.19630	−	0.435417i	−0.861931	+	0.507026i	$0.830745\pi$
$858$	1.13983	+	6.46432i	0.0389133	+	0.220688i
$859$	−23.6058	−	19.8076i	−0.805420	−	0.675828i	0.144090	−	0.989565i	$-0.453975\pi$
$859$	−23.6058	−	19.8076i	−0.805420	−	0.675828i	−0.949510	+	0.313737i	$0.898419\pi$
$860$	−7.33788	+	6.15721i	−0.250220	+	0.209959i
$861$	0.441558	−	2.50420i	0.0150482	−	0.0853429i
$862$	3.86109	−	6.68761i	0.131509	−	0.227781i
$863$	10.0682	+	17.4386i	0.342724	+	0.593616i	0.984938	−	0.172910i	$-0.0553171\pi$
$863$	10.0682	+	17.4386i	0.342724	+	0.593616i	−0.642213	+	0.766526i	$0.721984\pi$
$864$	0.939693	−	0.342020i	0.0319690	−	0.0116358i
$865$	−5.35014	+	1.94729i	−0.181910	+	0.0662099i
$866$	−10.1116	−	17.5138i	−0.343606	−	0.595143i
$867$	−8.17760	+	14.1640i	−0.277726	+	0.481035i
$868$	−0.311721	+	1.76786i	−0.0105805	+	0.0600051i
$869$	−1.12867	+	0.947070i	−0.0382876	+	0.0321271i
$870$	5.68666	+	4.77168i	0.192796	+	0.161775i
$871$	2.37213	+	13.4530i	0.0803766	+	0.455838i
$872$	−11.4543	−	4.16901i	−0.387891	−	0.141181i
$873$	−18.2110			−0.616350
$874$	16.9101	−	17.5153i	0.571994	−	0.592462i
$875$	0.616046			0.0208262
$876$	9.35199	+	3.40385i	0.315974	+	0.115005i
$877$	−6.39427	−	36.2637i	−0.215919	−	1.22454i	−0.879304	−	0.476260i	$-0.841992\pi$
$877$	−6.39427	−	36.2637i	−0.215919	−	1.22454i	0.663385	−	0.748278i	$-0.269119\pi$
$878$	14.1895	+	11.9064i	0.478872	+	0.401821i
$879$	−4.45848	+	3.74111i	−0.150381	+	0.126184i
$880$	0.888879	−	5.04109i	0.0299641	−	0.169935i
$881$	0.359687	−	0.622996i	0.0121182	−	0.0209893i	−0.859903	−	0.510458i	$-0.829476\pi$
$881$	0.359687	−	0.622996i	0.0121182	−	0.0209893i	0.872021	+	0.489469i	$0.162809\pi$
$882$	3.31024	+	5.73351i	0.111462	+	0.193057i
$883$	−32.9246	+	11.9836i	−1.10800	+	0.403280i	−0.830260	−	0.557376i	$-0.811808\pi$
$883$	−32.9246	+	11.9836i	−1.10800	+	0.403280i	−0.277742	+	0.960656i	$0.589586\pi$
$884$	−0.967601	+	0.352178i	−0.0325440	+	0.0118450i
$885$	2.43142	+	4.21134i	0.0817312	+	0.141563i
$886$	6.63557	−	11.4931i	0.222926	−	0.386119i
$887$	−6.20615	+	35.1968i	−0.208382	+	1.18179i	0.683646	+	0.729813i	$0.260393\pi$
$887$	−6.20615	+	35.1968i	−0.208382	+	1.18179i	−0.892028	+	0.451979i	$0.850718\pi$
$888$	6.83763	−	5.73745i	0.229456	−	0.192536i
$889$	2.03661	+	1.70892i	0.0683056	+	0.0573152i
$890$	1.09825	+	6.22849i	0.0368134	+	0.208779i
$891$	−4.81015	−	1.75075i	−0.161146	−	0.0586524i
$892$	−6.07710			−0.203476
$893$	−5.47389	−	7.53223i	−0.183177	−	0.252056i
$894$	−15.9326			−0.532867
$895$	−6.04446	−	2.20000i	−0.202044	−	0.0735380i
$896$	0.106975	+	0.606687i	0.00357380	+	0.0202680i
$897$	−5.48665	−	4.60384i	−0.183194	−	0.153718i
$898$	18.7533	−	15.7359i	0.625806	−	0.525114i
$899$	3.75627	−	21.3029i	0.125279	−	0.710490i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−5.68357	−	9.84423i	−0.189347	−	0.327959i
$902$	19.8547	−	7.22650i	0.661088	−	0.240616i
$903$	−5.54518	+	2.01828i	−0.184532	+	0.0671642i
$904$	3.00472	+	5.20432i	0.0999353	+	0.173093i
$905$	9.85421	−	17.0680i	0.327565	−	0.567359i
$906$	−1.32732	+	7.52760i	−0.0440972	+	0.250088i
$907$	13.1570	−	11.0400i	0.436871	−	0.366579i	−0.397666	−	0.917530i	$-0.630180\pi$
$907$	13.1570	−	11.0400i	0.436871	−	0.366579i	0.834537	+	0.550952i	$0.185735\pi$
$908$	−2.73643	−	2.29614i	−0.0908116	−	0.0762000i
$909$	−2.64839	−	15.0198i	−0.0878415	−	0.498174i
$910$	0.742332	+	0.270187i	0.0246081	+	0.00895660i
$911$	39.7860			1.31817			0.659085	−	0.752069i	$-0.270944\pi$
$911$	39.7860			1.31817			0.659085	+	0.752069i	$0.270944\pi$
$912$	−2.56253	−	3.52611i	−0.0848538	−	0.116761i
$913$	13.4074			0.443721
$914$	−2.06379	−	0.751158i	−0.0682641	−	0.0248461i
$915$	1.49423	+	8.47422i	0.0493978	+	0.280149i
$916$	3.32911	+	2.79346i	0.109997	+	0.0922985i
$917$	−7.28367	+	6.11172i	−0.240528	+	0.201827i
$918$	0.139438	−	0.790794i	0.00460215	−	0.0261001i
$919$	−19.8303	+	34.3471i	−0.654141	+	1.13301i	0.327968	+	0.944689i	$0.393636\pi$
$919$	−19.8303	+	34.3471i	−0.654141	+	1.13301i	−0.982108	+	0.188316i	$0.939697\pi$
$920$	2.79270	+	4.83710i	0.0920726	+	0.159474i
$921$	2.63929	−	0.960624i	0.0869676	−	0.0316536i
$922$	28.2372	−	10.2775i	0.929943	−	0.338472i
$923$	5.09818	+	8.83031i	0.167809	+	0.290653i
$924$	1.57673	−	2.73097i	0.0518705	−	0.0898423i
$925$	−1.54997	+	8.79029i	−0.0509625	+	0.289023i
$926$	24.0538	−	20.1835i	0.790457	−	0.663272i
$927$	−0.759508	−	0.637303i	−0.0249455	−	0.0209318i
$928$	−1.28906	−	7.31064i	−0.0423155	−	0.239983i
$929$	13.2871	+	4.83611i	0.435935	+	0.158668i	0.550660	−	0.834730i	$-0.314376\pi$
$929$	13.2871	+	4.83611i	0.435935	+	0.158668i	−0.114724	+	0.993397i	$0.536598\pi$
$930$	2.91395			0.0955523
$931$	20.0439	−	20.7612i	0.656913	−	0.680420i
$932$	9.71033			0.318072
$933$	8.84827	+	3.22051i	0.289679	+	0.105435i
$934$	5.26182	+	29.8413i	0.172172	+	0.976436i
$935$	−3.14875	−	2.64212i	−0.102975	−	0.0864064i
$936$	−0.982320	+	0.824264i	−0.0321081	+	0.0269419i
$937$	5.44402	−	30.8746i	0.177848	−	1.00863i	−0.756956	−	0.653465i	$-0.773314\pi$
$937$	5.44402	−	30.8746i	0.177848	−	1.00863i	0.934805	−	0.355162i	$-0.115574\pi$
$938$	3.28135	−	5.68347i	0.107140	−	0.185572i
$939$	−6.42631	−	11.1307i	−0.209715	−	0.363236i
$940$	2.00731	−	0.730599i	0.0654711	−	0.0238295i
$941$	34.8731	−	12.6928i	1.13683	−	0.413772i	0.296063	−	0.955168i	$-0.404326\pi$
$941$	34.8731	−	12.6928i	1.13683	−	0.413772i	0.840768	+	0.541396i	$0.182104\pi$
$942$	4.73735	+	8.20532i	0.154351	+	0.267344i
$943$	−11.5273	+	19.9659i	−0.375381	+	0.650179i
$944$	0.844422	−	4.78896i	0.0274836	−	0.155867i
$945$	−0.471919	+	0.395987i	−0.0153515	+	0.0128815i
$946$	−37.5615	−	31.5179i	−1.22123	−	1.02473i
$947$	8.43523	+	47.8386i	0.274108	+	1.55454i	0.741780	+	0.670643i	$0.233982\pi$
$947$	8.43523	+	47.8386i	0.274108	+	1.55454i	−0.467672	+	0.883902i	$0.654907\pi$
$948$	−0.270475	−	0.0984450i	−0.00878463	−	0.00319734i
$949$	−12.7619			−0.414270
$950$	4.22955	+	1.05400i	0.137225	+	0.0341961i
$951$	12.5992			0.408558
$952$	0.464848	+	0.169191i	0.0150658	+	0.00548351i
$953$	−8.92394	−	50.6102i	−0.289075	−	1.63943i	−0.690356	−	0.723470i	$-0.742546\pi$
$953$	−8.92394	−	50.6102i	−0.289075	−	1.63943i	0.401281	−	0.915955i	$-0.368565\pi$
$954$	−10.8441	−	9.09928i	−0.351091	−	0.294600i
$955$	−10.8235	+	9.08200i	−0.350240	+	0.293887i
$956$	1.71679	−	9.73642i	0.0555251	−	0.314898i
$957$	−18.9997	+	32.9084i	−0.614172	+	1.06378i
$958$	−17.8682	−	30.9486i	−0.577294	−	0.999902i
$959$	−13.0460	+	4.74836i	−0.421277	+	0.153332i
$960$	0.939693	−	0.342020i	0.0303284	−	0.0110387i
$961$	11.2544	+	19.4933i	0.363046	+	0.628815i
$962$	−5.72296	+	9.91245i	−0.184516	+	0.319590i
$963$	−1.90767	+	10.8189i	−0.0614738	+	0.348635i
$964$	3.07885	−	2.58346i	0.0991632	−	0.0832078i
$965$	0.682335	+	0.572547i	0.0219651	+	0.0184309i
$966$	0.597500	+	3.38859i	0.0192243	+	0.109026i
$967$	2.15660	+	0.784936i	0.0693514	+	0.0252419i	0.376463	−	0.926432i	$-0.377140\pi$
$967$	2.15660	+	0.784936i	0.0693514	+	0.0252419i	−0.307111	+	0.951674i	$0.599362\pi$
$968$	15.2026			0.488632
$969$	−3.48095	+	0.366292i	−0.111824	+	0.0117670i
$970$	−18.2110			−0.584721
$971$	44.2144	+	16.0927i	1.41891	+	0.516441i	0.933731	−	0.357975i	$-0.116533\pi$
$971$	44.2144	+	16.0927i	1.41891	+	0.516441i	0.485178	+	0.874416i	$0.338755\pi$
$972$	−0.173648	−	0.984808i	−0.00556977	−	0.0315877i
$973$	7.81380	+	6.55655i	0.250499	+	0.210193i
$974$	1.68715	−	1.41569i	0.0540599	−	0.0453616i
$975$	0.222674	−	1.26285i	0.00713127	−	0.0404434i
$976$	4.30247	−	7.45210i	0.137719	−	0.238536i
$977$	−28.4898	−	49.3458i	−0.911470	−	1.57871i	−0.811988	−	0.583673i	$-0.801615\pi$
$977$	−28.4898	−	49.3458i	−0.911470	−	1.57871i	−0.0994818	−	0.995039i	$-0.531719\pi$
$978$	3.58161	−	1.30360i	0.114527	−	0.0416845i
$979$	−30.4221	+	11.0727i	−0.972295	+	0.353887i
$980$	3.31024	+	5.73351i	0.105742	+	0.183150i
$981$	−6.09469	+	10.5563i	−0.194588	+	0.337037i
$982$	1.18706	−	6.73217i	0.0378807	−	0.214832i
$983$	−8.18750	+	6.87013i	−0.261141	+	0.219123i	−0.763952	−	0.645273i	$-0.776744\pi$
$983$	−8.18750	+	6.87013i	−0.261141	+	0.219123i	0.502811	+	0.864396i	$0.332299\pi$
$984$	3.16197	+	2.65321i	0.100800	+	0.0845812i
$985$	−0.258922	−	1.46842i	−0.00824995	−	0.0467878i
$986$	−5.60146	−	2.03877i	−0.178387	−	0.0649275i
$987$	1.31595			0.0418873
$988$	4.63432	+	3.12506i	0.147437	+	0.0994214i
$989$	53.5021			1.70127
$990$	−4.81015	−	1.75075i	−0.152877	−	0.0556425i
$991$	−5.54054	−	31.4220i	−0.176001	−	0.998152i	−0.936982	−	0.349377i	$-0.886393\pi$
$991$	−5.54054	−	31.4220i	−0.176001	−	0.998152i	0.760981	−	0.648774i	$-0.224718\pi$
$992$	−2.23222	−	1.87305i	−0.0708730	−	0.0594695i
$993$	12.4095	−	10.4128i	0.393805	−	0.330441i
$994$	0.850609	−	4.82405i	0.0269797	−	0.153009i
$995$	−3.29574	+	5.70839i	−0.104482	+	0.180968i
$996$	1.30961	+	2.26831i	0.0414966	+	0.0718742i
$997$	−5.69707	+	2.07356i	−0.180428	+	0.0656704i	−0.430654	−	0.902517i	$-0.641717\pi$
$997$	−5.69707	+	2.07356i	−0.180428	+	0.0656704i	0.250226	+	0.968187i	$0.419495\pi$
$998$	−41.3129	+	15.0367i	−1.30774	+	0.475977i
$999$	−4.46295	−	7.73005i	−0.141201	−	0.244568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.j.61.2	✓	12
19.5	even	9	inner	570.2.u.j.271.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.j.61.2	✓	12	1.1	even	1	trivial
570.2.u.j.271.2	yes	12	19.5	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-0.308023 + 0.533512i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(-0.939693 - 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(-0.173648 + 0.984808i) q^{6} +(-0.308023 + 0.533512i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(-2.55943 - 4.43306i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.222674 + 1.26285i) q^{13} +(0.471919 - 0.395987i) q^{14} +(-0.766044 - 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(0.754567 + 0.274640i) q^{17} +1.00000 q^{18} +(-1.20199 - 4.18990i) q^{19} +1.00000 q^{20} +(0.578894 + 0.210700i) q^{21} +(0.888879 + 5.04109i) q^{22} +(-4.27867 - 3.59023i) q^{23} +(-0.766044 + 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(0.641164 - 1.11053i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-0.578894 + 0.210700i) q^{28} +(6.97573 - 2.53896i) q^{29} +(0.500000 + 0.866025i) q^{30} +(1.45698 - 2.52356i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-3.92127 + 3.29033i) q^{33} +(-0.615128 - 0.516154i) q^{34} +(0.106975 + 0.606687i) q^{35} +(-0.939693 - 0.342020i) q^{36} -8.92589 q^{37} +(-0.303530 + 4.34832i) q^{38} +1.28233 q^{39} +(-0.939693 - 0.342020i) q^{40} +(-0.716761 - 4.06495i) q^{41} +(-0.471919 - 0.395987i) q^{42} +(-7.33788 + 6.15721i) q^{43} +(0.888879 - 5.04109i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(2.79270 + 4.83710i) q^{46} +(2.00731 - 0.730599i) q^{47} +(0.939693 - 0.342020i) q^{48} +(3.31024 + 5.73351i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.139438 - 0.790794i) q^{51} +(-0.982320 + 0.824264i) q^{52} +(-10.8441 - 9.09928i) q^{53} +(-0.173648 - 0.984808i) q^{54} +(-4.81015 - 1.75075i) q^{55} +0.616046 q^{56} +(-3.91752 + 1.91129i) q^{57} -7.42341 q^{58} +(-4.56957 - 1.66319i) q^{59} +(-0.173648 - 0.984808i) q^{60} +(-6.59177 - 5.53115i) q^{61} +(-2.23222 + 1.87305i) q^{62} +(0.106975 - 0.606687i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.641164 + 1.11053i) q^{65} +(4.81015 - 1.75075i) q^{66} +(10.0105 - 3.64352i) q^{67} +(0.401497 + 0.695413i) q^{68} +(-2.79270 + 4.83710i) q^{69} +(0.106975 - 0.606687i) q^{70} +(6.09117 - 5.11110i) q^{71} +(0.766044 + 0.642788i) q^{72} +(1.72818 + 9.80098i) q^{73} +(8.38760 + 3.05284i) q^{74} -1.00000 q^{75} +(1.77244 - 3.98227i) q^{76} +3.15345 q^{77} +(-1.20499 - 0.438582i) q^{78} +(-0.0499818 - 0.283461i) q^{79} +(0.766044 + 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-0.716761 + 4.06495i) q^{82} +(-1.30961 + 2.26831i) q^{83} +(0.308023 + 0.533512i) q^{84} +(0.754567 - 0.274640i) q^{85} +(9.00124 - 3.27618i) q^{86} +(-3.71171 - 6.42886i) q^{87} +(-2.55943 + 4.43306i) q^{88} +(1.09825 - 6.22849i) q^{89} +(0.766044 - 0.642788i) q^{90} +(-0.605154 - 0.507785i) q^{91} +(-0.969895 - 5.50055i) q^{92} +(-2.73822 - 0.996631i) q^{93} -2.13613 q^{94} +(-3.61399 - 2.43702i) q^{95} -1.00000 q^{96} +(17.1128 + 6.22854i) q^{97} +(-1.14964 - 6.51991i) q^{98} +(3.92127 + 3.29033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{7} - 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^7 - 6 * q^8	\( 12 q + 3 q^{7} - 6 q^{8} + 3 q^{11} + 6 q^{12} + 9 q^{13} + 9 q^{14} + 9 q^{17} + 12 q^{18} + 9 q^{19} + 12 q^{20} + 9 q^{21} - 6 q^{22} + 12 q^{23} + 9 q^{26} + 6 q^{27} - 9 q^{28} + 27 q^{29} + 6 q^{30} + 12 q^{31} - 3 q^{33} - 9 q^{34} - 42 q^{37} + 18 q^{38} + 18 q^{39} - 27 q^{41} - 9 q^{42} - 27 q^{43} - 6 q^{44} - 6 q^{45} + 9 q^{46} - 6 q^{47} + 3 q^{49} - 6 q^{50} + 9 q^{52} - 18 q^{53} + 3 q^{55} - 6 q^{56} + 6 q^{58} - 15 q^{59} - 9 q^{61} - 18 q^{62} - 6 q^{64} + 9 q^{65} - 3 q^{66} + 42 q^{67} + 6 q^{68} - 9 q^{69} + 24 q^{71} + 15 q^{73} + 18 q^{74} - 12 q^{75} + 3 q^{76} - 6 q^{77} + 18 q^{78} - 57 q^{79} - 27 q^{82} + 21 q^{83} - 3 q^{84} + 9 q^{85} + 9 q^{86} + 3 q^{87} + 3 q^{88} - 57 q^{89} + 21 q^{91} - 15 q^{92} - 9 q^{93} - 24 q^{94} - 18 q^{95} - 12 q^{96} - 6 q^{97} - 15 q^{98} + 3 q^{99}+O(q^{100}) \) 12 * q + 3 * q^7 - 6 * q^8 + 3 * q^11 + 6 * q^12 + 9 * q^13 + 9 * q^14 + 9 * q^17 + 12 * q^18 + 9 * q^19 + 12 * q^20 + 9 * q^21 - 6 * q^22 + 12 * q^23 + 9 * q^26 + 6 * q^27 - 9 * q^28 + 27 * q^29 + 6 * q^30 + 12 * q^31 - 3 * q^33 - 9 * q^34 - 42 * q^37 + 18 * q^38 + 18 * q^39 - 27 * q^41 - 9 * q^42 - 27 * q^43 - 6 * q^44 - 6 * q^45 + 9 * q^46 - 6 * q^47 + 3 * q^49 - 6 * q^50 + 9 * q^52 - 18 * q^53 + 3 * q^55 - 6 * q^56 + 6 * q^58 - 15 * q^59 - 9 * q^61 - 18 * q^62 - 6 * q^64 + 9 * q^65 - 3 * q^66 + 42 * q^67 + 6 * q^68 - 9 * q^69 + 24 * q^71 + 15 * q^73 + 18 * q^74 - 12 * q^75 + 3 * q^76 - 6 * q^77 + 18 * q^78 - 57 * q^79 - 27 * q^82 + 21 * q^83 - 3 * q^84 + 9 * q^85 + 9 * q^86 + 3 * q^87 + 3 * q^88 - 57 * q^89 + 21 * q^91 - 15 * q^92 - 9 * q^93 - 24 * q^94 - 18 * q^95 - 12 * q^96 - 6 * q^97 - 15 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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