LMFDB - Embedded newform 570.2.u.d.61.1

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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	570.61
Dual form			570.2.u.d.271.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(-1.43969 + 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(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} +(-1.43969 + 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(2.14543 + 3.71599i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.205737 + 1.16679i) q^{13} +(-2.20574 + 1.85083i) q^{14} +(0.766044 + 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(1.32635 + 0.482753i) q^{17} -1.00000 q^{18} +(3.50000 + 2.59808i) q^{19} -1.00000 q^{20} +(2.70574 + 0.984808i) q^{21} +(0.745100 + 4.22567i) q^{22} +(-0.390530 - 0.327693i) q^{23} +(0.766044 - 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-0.592396 + 1.02606i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-2.70574 + 0.984808i) q^{28} +(-3.26604 + 1.18874i) q^{29} +(0.500000 + 0.866025i) q^{30} +(3.29813 - 5.71253i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(3.28699 - 2.75811i) q^{33} +(1.08125 + 0.907278i) q^{34} +(-0.500000 - 2.83564i) q^{35} +(-0.939693 - 0.342020i) q^{36} -2.29086 q^{37} +(2.40033 + 3.63846i) q^{38} +1.18479 q^{39} +(-0.939693 - 0.342020i) q^{40} +(0.886659 + 5.02849i) q^{41} +(2.20574 + 1.85083i) q^{42} +(7.60607 - 6.38225i) q^{43} +(-0.745100 + 4.22567i) q^{44} +(0.500000 - 0.866025i) q^{45} +(-0.254900 - 0.441500i) q^{46} +(-4.23783 + 1.54244i) q^{47} +(0.939693 - 0.342020i) q^{48} +(-0.645430 - 1.11792i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.245100 - 1.39003i) q^{51} +(-0.907604 + 0.761570i) q^{52} +(-8.36618 - 7.02006i) q^{53} +(0.173648 + 0.984808i) q^{54} +(-4.03209 - 1.46756i) q^{55} -2.87939 q^{56} +(1.95084 - 3.89798i) q^{57} -3.47565 q^{58} +(-6.68479 - 2.43307i) q^{59} +(0.173648 + 0.984808i) q^{60} +(10.3380 + 8.67458i) q^{61} +(5.05303 - 4.24000i) q^{62} +(0.500000 - 2.83564i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.592396 - 1.02606i) q^{65} +(4.03209 - 1.46756i) q^{66} +(-5.15910 + 1.87776i) q^{67} +(0.705737 + 1.22237i) q^{68} +(-0.254900 + 0.441500i) q^{69} +(0.500000 - 2.83564i) q^{70} +(5.10220 - 4.28125i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(1.20961 + 6.86002i) q^{73} +(-2.15270 - 0.783520i) q^{74} -1.00000 q^{75} +(1.01114 + 4.24000i) q^{76} -12.3550 q^{77} +(1.11334 + 0.405223i) q^{78} +(-3.05556 - 17.3289i) q^{79} +(-0.766044 - 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-0.886659 + 5.02849i) q^{82} +(-1.02094 + 1.76833i) q^{83} +(1.43969 + 2.49362i) q^{84} +(-1.32635 + 0.482753i) q^{85} +(9.33022 - 3.39592i) q^{86} +(1.73783 + 3.01000i) q^{87} +(-2.14543 + 3.71599i) q^{88} +(-0.435822 + 2.47167i) q^{89} +(0.766044 - 0.642788i) q^{90} +(-2.61334 - 2.19285i) q^{91} +(-0.0885259 - 0.502055i) q^{92} +(-6.19846 - 2.25606i) q^{93} -4.50980 q^{94} +(-4.35117 + 0.259515i) q^{95} +1.00000 q^{96} +(10.1099 + 3.67972i) q^{97} +(-0.224155 - 1.27125i) q^{98} +(-3.28699 - 2.75811i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 3 * q^7 + 3 * q^8	$ 6 q - 3 q^{7} + 3 q^{8} - 3 q^{11} + 3 q^{12} + 9 q^{13} - 3 q^{14} + 9 q^{17} - 6 q^{18} + 21 q^{19} - 6 q^{20} + 6 q^{21} + 3 q^{22} + 15 q^{23} + 3 q^{27} - 6 q^{28} - 15 q^{29} + 3 q^{30} + 6 q^{31} + 12 q^{33} + 9 q^{34} - 3 q^{35} + 18 q^{37} + 12 q^{41} + 3 q^{42} + 21 q^{43} - 3 q^{44} + 3 q^{45} - 3 q^{46} - 6 q^{47} + 12 q^{49} + 3 q^{50} - 9 q^{52} + 6 q^{53} - 15 q^{55} - 6 q^{56} + 18 q^{58} - 33 q^{59} - 9 q^{61} + 18 q^{62} + 3 q^{63} - 3 q^{64} + 15 q^{66} + 6 q^{67} - 6 q^{68} - 3 q^{69} + 3 q^{70} + 30 q^{71} - 27 q^{73} - 15 q^{74} - 6 q^{75} - 24 q^{77} + 9 q^{79} - 12 q^{82} - 3 q^{83} + 3 q^{84} - 9 q^{85} + 33 q^{86} - 9 q^{87} + 3 q^{88} - 21 q^{89} - 9 q^{91} - 21 q^{92} - 9 q^{93} - 30 q^{94} + 6 q^{96} + 12 q^{97} - 3 q^{98} - 12 q^{99}+O(q^{100}) $ 6 * q - 3 * q^7 + 3 * q^8 - 3 * q^11 + 3 * q^12 + 9 * q^13 - 3 * q^14 + 9 * q^17 - 6 * q^18 + 21 * q^19 - 6 * q^20 + 6 * q^21 + 3 * q^22 + 15 * q^23 + 3 * q^27 - 6 * q^28 - 15 * q^29 + 3 * q^30 + 6 * q^31 + 12 * q^33 + 9 * q^34 - 3 * q^35 + 18 * q^37 + 12 * q^41 + 3 * q^42 + 21 * q^43 - 3 * q^44 + 3 * q^45 - 3 * q^46 - 6 * q^47 + 12 * q^49 + 3 * q^50 - 9 * q^52 + 6 * q^53 - 15 * q^55 - 6 * q^56 + 18 * q^58 - 33 * q^59 - 9 * q^61 + 18 * q^62 + 3 * q^63 - 3 * q^64 + 15 * q^66 + 6 * q^67 - 6 * q^68 - 3 * q^69 + 3 * q^70 + 30 * q^71 - 27 * q^73 - 15 * q^74 - 6 * q^75 - 24 * q^77 + 9 * q^79 - 12 * q^82 - 3 * q^83 + 3 * q^84 - 9 * q^85 + 33 * q^86 - 9 * q^87 + 3 * q^88 - 21 * q^89 - 9 * q^91 - 21 * q^92 - 9 * q^93 - 30 * q^94 + 6 * q^96 + 12 * q^97 - 3 * q^98 - 12 * 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
$7$	−1.43969	+	2.49362i	−0.544153	+	0.942500i	0.454507	+	0.890743i	$0.349815\pi$
$7$	−1.43969	+	2.49362i	−0.544153	+	0.942500i	−0.998660	+	0.0517569i	$0.983518\pi$
$8$	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
$11$	2.14543	+	3.71599i	0.646871	+	1.12041i	0.983866	+	0.178907i	$0.0572563\pi$
$11$	2.14543	+	3.71599i	0.646871	+	1.12041i	−0.336995	+	0.941507i	$0.609410\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−0.205737	+	1.16679i	−0.0570612	+	0.323610i	−0.999955	−	0.00948328i	$-0.996981\pi$
$13$	−0.205737	+	1.16679i	−0.0570612	+	0.323610i	0.942894	+	0.333093i	$0.108092\pi$
$14$	−2.20574	+	1.85083i	−0.589508	+	0.494656i
$15$	0.766044	+	0.642788i	0.197792	+	0.165967i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	1.32635	+	0.482753i	0.321688	+	0.117085i	0.497816	−	0.867282i	$-0.334135\pi$
$17$	1.32635	+	0.482753i	0.321688	+	0.117085i	−0.176129	+	0.984367i	$0.556358\pi$
$18$	−1.00000			−0.235702
$19$	3.50000	+	2.59808i	0.802955	+	0.596040i
$19$	3.50000	+	2.59808i	0.802955	+	0.596040i
$20$	−1.00000			−0.223607
$21$	2.70574	+	0.984808i	0.590440	+	0.214903i
$22$	0.745100	+	4.22567i	0.158856	+	0.900916i
$23$	−0.390530	−	0.327693i	−0.0814310	−	0.0683288i	0.601164	−	0.799126i	$-0.294704\pi$
$23$	−0.390530	−	0.327693i	−0.0814310	−	0.0683288i	−0.682595	+	0.730797i	$0.739148\pi$
$24$	0.766044	−	0.642788i	0.156368	−	0.131208i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	−0.592396	+	1.02606i	−0.116178	+	0.201227i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−2.70574	+	0.984808i	−0.511336	+	0.186111i
$29$	−3.26604	+	1.18874i	−0.606489	+	0.220744i	−0.626966	−	0.779046i	$-0.715704\pi$
$29$	−3.26604	+	1.18874i	−0.606489	+	0.220744i	0.0204772	+	0.999790i	$0.493481\pi$
$30$	0.500000	+	0.866025i	0.0912871	+	0.158114i
$31$	3.29813	−	5.71253i	0.592362	−	1.02600i	−0.401551	−	0.915837i	$-0.631529\pi$
$31$	3.29813	−	5.71253i	0.592362	−	1.02600i	0.993913	−	0.110165i	$-0.0351379\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	3.28699	−	2.75811i	0.572191	−	0.480126i
$34$	1.08125	+	0.907278i	0.185433	+	0.155597i
$35$	−0.500000	−	2.83564i	−0.0845154	−	0.479311i
$36$	−0.939693	−	0.342020i	−0.156615	−	0.0570034i
$37$	−2.29086			−0.376615			−0.188307	−	0.982110i	$-0.560300\pi$
$37$	−2.29086			−0.376615			−0.188307	+	0.982110i	$0.560300\pi$
$38$	2.40033	+	3.63846i	0.389385	+	0.590237i
$39$	1.18479			0.189719
$40$	−0.939693	−	0.342020i	−0.148578	−	0.0540781i
$41$	0.886659	+	5.02849i	0.138473	+	0.785319i	0.972378	+	0.233411i	$0.0749888\pi$
$41$	0.886659	+	5.02849i	0.138473	+	0.785319i	−0.833905	+	0.551908i	$0.813900\pi$
$42$	2.20574	+	1.85083i	0.340353	+	0.285590i
$43$	7.60607	−	6.38225i	1.15991	−	0.973284i	0.160010	−	0.987115i	$-0.448847\pi$
$43$	7.60607	−	6.38225i	1.15991	−	0.973284i	0.999904	+	0.0138317i	$0.00440291\pi$
$44$	−0.745100	+	4.22567i	−0.112328	+	0.637044i
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	−0.254900	−	0.441500i	−0.0375830	−	0.0650956i
$47$	−4.23783	+	1.54244i	−0.618150	+	0.224988i	−0.632066	−	0.774915i	$-0.717793\pi$
$47$	−4.23783	+	1.54244i	−0.618150	+	0.224988i	0.0139152	+	0.999903i	$0.495570\pi$
$48$	0.939693	−	0.342020i	0.135633	−	0.0493664i
$49$	−0.645430	−	1.11792i	−0.0922042	−	0.159702i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	0.245100	−	1.39003i	0.0343209	−	0.194643i
$52$	−0.907604	+	0.761570i	−0.125862	+	0.105611i
$53$	−8.36618	−	7.02006i	−1.14918	−	0.964279i	−0.149483	−	0.988764i	$-0.547761\pi$
$53$	−8.36618	−	7.02006i	−1.14918	−	0.964279i	−0.999700	+	0.0244849i	$0.992205\pi$
$54$	0.173648	+	0.984808i	0.0236305	+	0.134015i
$55$	−4.03209	−	1.46756i	−0.543687	−	0.197886i
$56$	−2.87939			−0.384774
$57$	1.95084	−	3.89798i	0.258395	−	0.516300i
$58$	−3.47565			−0.456375
$59$	−6.68479	−	2.43307i	−0.870286	−	0.316758i	−0.132003	−	0.991249i	$-0.542141\pi$
$59$	−6.68479	−	2.43307i	−0.870286	−	0.316758i	−0.738283	+	0.674491i	$0.764363\pi$
$60$	0.173648	+	0.984808i	0.0224179	+	0.127138i
$61$	10.3380	+	8.67458i	1.32364	+	1.11067i	0.985519	+	0.169564i	$0.0542359\pi$
$61$	10.3380	+	8.67458i	1.32364	+	1.11067i	0.338121	+	0.941103i	$0.390209\pi$
$62$	5.05303	−	4.24000i	0.641736	−	0.538480i
$63$	0.500000	−	2.83564i	0.0629941	−	0.357257i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.592396	−	1.02606i	−0.0734777	−	0.127267i
$66$	4.03209	−	1.46756i	0.496316	−	0.180644i
$67$	−5.15910	+	1.87776i	−0.630284	+	0.229405i	−0.637355	−	0.770570i	$-0.719972\pi$
$67$	−5.15910	+	1.87776i	−0.630284	+	0.229405i	0.00707068	+	0.999975i	$0.497749\pi$
$68$	0.705737	+	1.22237i	0.0855832	+	0.148234i
$69$	−0.254900	+	0.441500i	−0.0306864	+	0.0531503i
$70$	0.500000	−	2.83564i	0.0597614	−	0.338924i
$71$	5.10220	−	4.28125i	0.605519	−	0.508091i	−0.287695	−	0.957722i	$-0.592889\pi$
$71$	5.10220	−	4.28125i	0.605519	−	0.508091i	0.893214	+	0.449631i	$0.148445\pi$
$72$	−0.766044	−	0.642788i	−0.0902792	−	0.0757532i
$73$	1.20961	+	6.86002i	0.141574	+	0.802905i	0.970054	+	0.242887i	$0.0780946\pi$
$73$	1.20961	+	6.86002i	0.141574	+	0.802905i	−0.828481	+	0.560018i	$0.810794\pi$
$74$	−2.15270	−	0.783520i	−0.250247	−	0.0910824i
$75$	−1.00000			−0.115470
$76$	1.01114	+	4.24000i	0.115986	+	0.486361i
$77$	−12.3550			−1.40799
$78$	1.11334	+	0.405223i	0.126061	+	0.0458825i
$79$	−3.05556	−	17.3289i	−0.343777	−	1.94966i	−0.311727	−	0.950172i	$-0.600907\pi$
$79$	−3.05556	−	17.3289i	−0.343777	−	1.94966i	−0.0320506	−	0.999486i	$-0.510204\pi$
$80$	−0.766044	−	0.642788i	−0.0856464	−	0.0718658i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−0.886659	+	5.02849i	−0.0979151	+	0.555304i
$83$	−1.02094	+	1.76833i	−0.112063	+	0.194099i	−0.916602	−	0.399801i	$-0.869079\pi$
$83$	−1.02094	+	1.76833i	−0.112063	+	0.194099i	0.804539	+	0.593900i	$0.202413\pi$
$84$	1.43969	+	2.49362i	0.157083	+	0.272076i
$85$	−1.32635	+	0.482753i	−0.143863	+	0.0523619i
$86$	9.33022	−	3.39592i	1.00610	−	0.366192i
$87$	1.73783	+	3.01000i	0.186314	+	0.322706i
$88$	−2.14543	+	3.71599i	−0.228704	+	0.396126i
$89$	−0.435822	+	2.47167i	−0.0461971	+	0.261997i	−0.999155	−	0.0411068i	$-0.986912\pi$
$89$	−0.435822	+	2.47167i	−0.0461971	+	0.261997i	0.952958	+	0.303103i	$0.0980227\pi$
$90$	0.766044	−	0.642788i	0.0807482	−	0.0677558i
$91$	−2.61334	−	2.19285i	−0.273953	−	0.229873i
$92$	−0.0885259	−	0.502055i	−0.00922946	−	0.0523429i
$93$	−6.19846	−	2.25606i	−0.642751	−	0.233942i
$94$	−4.50980			−0.465150
$95$	−4.35117	+	0.259515i	−0.446420	+	0.0266257i
$96$	1.00000			0.102062
$97$	10.1099	+	3.67972i	1.02651	+	0.373619i	0.799750	−	0.600333i	$-0.204965\pi$
$97$	10.1099	+	3.67972i	1.02651	+	0.373619i	0.226758	+	0.973951i	$0.427187\pi$
$98$	−0.224155	−	1.27125i	−0.0226431	−	0.128415i
$99$	−3.28699	−	2.75811i	−0.330355	−	0.277201i
$100$	0.766044	−	0.642788i	0.0766044	−	0.0642788i
$101$	−0.563711	+	3.19696i	−0.0560913	+	0.318110i	−0.999924	−	0.0123135i	$-0.996080\pi$
$101$	−0.563711	+	3.19696i	−0.0560913	+	0.318110i	0.943833	+	0.330423i	$0.107191\pi$
$102$	0.705737	−	1.22237i	0.0698784	−	0.121033i
$103$	−2.63176	−	4.55834i	−0.259315	−	0.449147i	0.706744	−	0.707470i	$-0.250163\pi$
$103$	−2.63176	−	4.55834i	−0.259315	−	0.449147i	−0.966059	+	0.258323i	$0.916830\pi$
$104$	−1.11334	+	0.405223i	−0.109172	+	0.0397354i
$105$	−2.70574	+	0.984808i	−0.264053	+	0.0961074i
$106$	−5.46064	−	9.45810i	−0.530384	−	0.918652i
$107$	9.14930	−	15.8471i	0.884496	−	1.53199i	0.0382063	−	0.999270i	$-0.487836\pi$
$107$	9.14930	−	15.8471i	0.884496	−	1.53199i	0.846290	−	0.532723i	$-0.178831\pi$
$108$	−0.173648	+	0.984808i	−0.0167093	+	0.0947632i
$109$	8.35710	−	7.01244i	0.800465	−	0.671670i	−0.147847	−	0.989010i	$-0.547234\pi$
$109$	8.35710	−	7.01244i	0.800465	−	0.671670i	0.948312	+	0.317341i	$0.102790\pi$
$110$	−3.28699	−	2.75811i	−0.313402	−	0.262976i
$111$	0.397804	+	2.25606i	0.0377578	+	0.214135i
$112$	−2.70574	−	0.984808i	−0.255668	−	0.0930556i
$113$	−15.8871			−1.49454			−0.747268	−	0.664523i	$-0.768635\pi$
$113$	−15.8871			−1.49454			−0.747268	+	0.664523i	$0.768635\pi$
$114$	3.16637	−	2.99568i	0.296558	−	0.280571i
$115$	0.509800			0.0475391
$116$	−3.26604	−	1.18874i	−0.303245	−	0.110372i
$117$	−0.205737	−	1.16679i	−0.0190204	−	0.107870i
$118$	−5.44949	−	4.57267i	−0.501666	−	0.420948i
$119$	−3.11334	+	2.61240i	−0.285399	+	0.239479i
$120$	−0.173648	+	0.984808i	−0.0158518	+	0.0899002i
$121$	−3.70574	+	6.41852i	−0.336885	+	0.583502i
$122$	6.74763	+	11.6872i	0.610901	+	1.05811i
$123$	4.79813	−	1.74638i	0.432633	−	0.157466i
$124$	6.19846	−	2.25606i	0.556638	−	0.202600i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	1.43969	−	2.49362i	0.128258	−	0.222149i
$127$	0.698463	−	3.96118i	0.0619786	−	0.351498i	−0.938009	−	0.346610i	$-0.887333\pi$
$127$	0.698463	−	3.96118i	0.0619786	−	0.351498i	0.999988	−	0.00488837i	$-0.00155602\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	−7.60607	−	6.38225i	−0.669677	−	0.561926i
$130$	−0.205737	−	1.16679i	−0.0180443	−	0.102335i
$131$	9.74422	+	3.54661i	0.851357	+	0.309868i	0.730593	−	0.682813i	$-0.239244\pi$
$131$	9.74422	+	3.54661i	0.851357	+	0.309868i	0.120763	+	0.992681i	$0.461466\pi$
$132$	4.29086			0.373471
$133$	−11.5175	+	4.98724i	−0.998697	+	0.432449i
$134$	−5.49020			−0.474281
$135$	−0.939693	−	0.342020i	−0.0808759	−	0.0294364i
$136$	0.245100	+	1.39003i	0.0210171	+	0.119194i
$137$	4.80200	+	4.02936i	0.410263	+	0.344251i	0.824444	−	0.565943i	$-0.191488\pi$
$137$	4.80200	+	4.02936i	0.410263	+	0.344251i	−0.414182	+	0.910194i	$0.635932\pi$
$138$	−0.390530	+	0.327693i	−0.0332441	+	0.0278951i
$139$	2.51027	−	14.2364i	0.212918	−	1.20752i	−0.671565	−	0.740946i	$-0.734378\pi$
$139$	2.51027	−	14.2364i	0.212918	−	1.20752i	0.884483	−	0.466573i	$-0.154511\pi$
$140$	1.43969	−	2.49362i	0.121676	−	0.210749i
$141$	2.25490	+	3.90560i	0.189897	+	0.328911i
$142$	6.25877	−	2.27801i	0.525224	−	0.191166i
$143$	−4.77719	+	1.73875i	−0.399489	+	0.145402i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.73783	−	3.01000i	0.144319	−	0.249967i
$146$	−1.20961	+	6.86002i	−0.100108	+	0.567740i
$147$	−0.988856	+	0.829748i	−0.0815594	+	0.0684365i
$148$	−1.75490	−	1.47254i	−0.144252	−	0.121042i
$149$	0.812681	+	4.60894i	0.0665774	+	0.377579i	0.999831	+	0.0183622i	$0.00584519\pi$
$149$	0.812681	+	4.60894i	0.0665774	+	0.377579i	−0.933254	+	0.359217i	$0.883044\pi$
$150$	−0.939693	−	0.342020i	−0.0767256	−	0.0279258i
$151$	14.9564			1.21713			0.608566	−	0.793504i	$-0.291745\pi$
$151$	14.9564			1.21713			0.608566	+	0.793504i	$0.291745\pi$
$152$	−0.500000	+	4.33013i	−0.0405554	+	0.351220i
$153$	−1.41147			−0.114111
$154$	−11.6099	−	4.22567i	−0.935555	−	0.340514i
$155$	1.14543	+	6.49605i	0.0920031	+	0.521776i
$156$	0.907604	+	0.761570i	0.0726665	+	0.0609744i
$157$	12.7135	−	10.6679i	1.01465	−	0.851389i	0.0257007	−	0.999670i	$-0.491818\pi$
$157$	12.7135	−	10.6679i	1.01465	−	0.851389i	0.988945	+	0.148281i	$0.0473739\pi$
$158$	3.05556	−	17.3289i	0.243087	−	1.37862i
$159$	−5.46064	+	9.45810i	−0.433057	+	0.750076i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	1.37939	−	0.502055i	0.108711	−	0.0395675i
$162$	0.939693	−	0.342020i	0.0738292	−	0.0268716i
$163$	−2.78446	−	4.82283i	−0.218096	−	0.377753i	0.736130	−	0.676840i	$-0.236651\pi$
$163$	−2.78446	−	4.82283i	−0.218096	−	0.377753i	−0.954226	+	0.299087i	$0.903318\pi$
$164$	−2.55303	+	4.42198i	−0.199358	+	0.345299i
$165$	−0.745100	+	4.22567i	−0.0580059	+	0.328968i
$166$	−1.56418	+	1.31250i	−0.121404	+	0.101870i
$167$	−11.6591	−	9.78315i	−0.902208	−	0.757043i	0.0684125	−	0.997657i	$-0.478207\pi$
$167$	−11.6591	−	9.78315i	−0.902208	−	0.757043i	−0.970621	+	0.240614i	$0.922651\pi$
$168$	0.500000	+	2.83564i	0.0385758	+	0.218774i
$169$	10.8969	+	3.96616i	0.838225	+	0.305089i
$170$	−1.41147			−0.108255
$171$	−4.17752	−	1.24432i	−0.319463	−	0.0951557i
$172$	9.92902			0.757080
$173$	−9.01501	−	3.28120i	−0.685399	−	0.249465i	−0.0242350	−	0.999706i	$-0.507715\pi$
$173$	−9.01501	−	3.28120i	−0.685399	−	0.249465i	−0.661164	+	0.750241i	$0.729937\pi$
$174$	0.603541	+	3.42285i	0.0457543	+	0.259486i
$175$	2.20574	+	1.85083i	0.166738	+	0.139910i
$176$	−3.28699	+	2.75811i	−0.247766	+	0.207900i
$177$	−1.23530	+	7.00573i	−0.0928508	+	0.526583i
$178$	−1.25490	+	2.17355i	−0.0940587	+	0.162915i
$179$	10.1284	+	17.5428i	0.757029	+	1.31121i	0.944359	+	0.328915i	$0.106683\pi$
$179$	10.1284	+	17.5428i	0.757029	+	1.31121i	−0.187331	+	0.982297i	$0.559984\pi$
$180$	0.939693	−	0.342020i	0.0700406	−	0.0254927i
$181$	5.07145	−	1.84586i	0.376958	−	0.137202i	−0.146591	−	0.989197i	$-0.546830\pi$
$181$	5.07145	−	1.84586i	0.376958	−	0.137202i	0.523549	+	0.851996i	$0.324608\pi$
$182$	−1.70574	−	2.95442i	−0.126438	−	0.218996i
$183$	6.74763	−	11.6872i	0.498799	−	0.863945i
$184$	0.0885259	−	0.502055i	0.00652621	−	0.0370120i
$185$	1.75490	−	1.47254i	0.129023	−	0.108263i
$186$	−5.05303	−	4.24000i	−0.370506	−	0.310892i
$187$	1.05169	+	5.96443i	0.0769071	+	0.436162i
$188$	−4.23783	−	1.54244i	−0.309075	−	0.112494i
$189$	−2.87939			−0.209444
$190$	−4.17752	−	1.24432i	−0.303069	−	0.0902726i
$191$	−8.47296			−0.613082			−0.306541	−	0.951857i	$-0.599172\pi$
$191$	−8.47296			−0.613082			−0.306541	+	0.951857i	$0.599172\pi$
$192$	0.939693	+	0.342020i	0.0678165	+	0.0246832i
$193$	1.87299	+	10.6222i	0.134821	+	0.764606i	0.974984	+	0.222273i	$0.0713477\pi$
$193$	1.87299	+	10.6222i	0.134821	+	0.764606i	−0.840164	+	0.542333i	$0.817541\pi$
$194$	8.24170	+	6.91560i	0.591719	+	0.496511i
$195$	−0.907604	+	0.761570i	−0.0649949	+	0.0545372i
$196$	0.224155	−	1.27125i	0.0160111	−	0.0908035i
$197$	10.7476	−	18.6154i	0.765737	−	1.32629i	−0.174120	−	0.984725i	$-0.555708\pi$
$197$	10.7476	−	18.6154i	0.765737	−	1.32629i	0.939856	−	0.341570i	$-0.110959\pi$
$198$	−2.14543	−	3.71599i	−0.152469	−	0.264084i
$199$	8.44609	−	3.07413i	0.598727	−	0.217919i	−0.0248363	−	0.999692i	$-0.507906\pi$
$199$	8.44609	−	3.07413i	0.598727	−	0.217919i	0.623564	+	0.781773i	$0.285684\pi$
$200$	0.939693	−	0.342020i	0.0664463	−	0.0241845i
$201$	2.74510	+	4.75465i	0.193624	+	0.335367i
$202$	−1.62314	+	2.81136i	−0.114204	+	0.197807i
$203$	1.73783	−	9.85570i	0.121971	−	0.691735i
$204$	1.08125	−	0.907278i	0.0757028	−	0.0635222i
$205$	−3.91147	−	3.28212i	−0.273189	−	0.229233i
$206$	−0.914000	−	5.18355i	−0.0636814	−	0.361155i
$207$	0.479055	+	0.174362i	0.0332967	+	0.0121190i
$208$	−1.18479			−0.0821506
$209$	−2.14543	+	18.5800i	−0.148402	+	1.28520i
$210$	−2.87939			−0.198696
$211$	10.6912	+	3.89127i	0.736012	+	0.267886i	0.682707	−	0.730692i	$-0.260802\pi$
$211$	10.6912	+	3.89127i	0.736012	+	0.267886i	0.0533045	+	0.998578i	$0.483025\pi$
$212$	−1.89646	−	10.7554i	−0.130249	−	0.738681i
$213$	−5.10220	−	4.28125i	−0.349597	−	0.293346i
$214$	14.0175	−	11.7621i	0.958219	−	0.804042i
$215$	−1.72416	+	9.77817i	−0.117586	+	0.666866i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	9.49660	+	16.4486i	0.644671	+	1.11660i
$218$	10.2515	−	3.73124i	0.694319	−	0.252711i
$219$	6.54576	−	2.38246i	0.442321	−	0.160992i
$220$	−2.14543	−	3.71599i	−0.144645	−	0.250532i
$221$	−0.836152	+	1.44826i	−0.0562457	+	0.0974204i
$222$	−0.397804	+	2.25606i	−0.0266988	+	0.151417i
$223$	6.12314	−	5.13793i	0.410036	−	0.344061i	−0.414322	−	0.910131i	$-0.635981\pi$
$223$	6.12314	−	5.13793i	0.410036	−	0.344061i	0.824357	+	0.566070i	$0.191537\pi$
$224$	−2.20574	−	1.85083i	−0.147377	−	0.123664i
$225$	0.173648	+	0.984808i	0.0115765	+	0.0656539i
$226$	−14.9290	−	5.43372i	−0.993063	−	0.361445i
$227$	6.59627			0.437810			0.218905	−	0.975746i	$-0.429752\pi$
$227$	6.59627			0.437810			0.218905	+	0.975746i	$0.429752\pi$
$228$	4.00000	−	1.73205i	0.264906	−	0.114708i
$229$	−15.4543			−1.02125			−0.510624	−	0.859804i	$-0.670586\pi$
$229$	−15.4543			−1.02125			−0.510624	+	0.859804i	$0.670586\pi$
$230$	0.479055	+	0.174362i	0.0315880	+	0.0114971i
$231$	2.14543	+	12.1673i	0.141159	+	0.800552i
$232$	−2.66250	−	2.23411i	−0.174802	−	0.146676i
$233$	−7.60401	+	6.38052i	−0.498155	+	0.418002i	−0.856938	−	0.515419i	$-0.827636\pi$
$233$	−7.60401	+	6.38052i	−0.498155	+	0.418002i	0.358783	+	0.933421i	$0.383192\pi$
$234$	0.205737	−	1.16679i	0.0134495	−	0.0762756i
$235$	2.25490	−	3.90560i	0.147093	−	0.254773i
$236$	−3.55690	−	6.16074i	−0.231535	−	0.401030i
$237$	−16.5351	+	6.01828i	−1.07407	+	0.390929i
$238$	−3.81908	+	1.39003i	−0.247554	+	0.0901023i
$239$	7.97952	+	13.8209i	0.516152	+	0.894002i	0.999824	+	0.0187527i	$0.00596952\pi$
$239$	7.97952	+	13.8209i	0.516152	+	0.894002i	−0.483672	+	0.875249i	$0.660697\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	−2.53462	+	14.3745i	−0.163269	+	0.925944i	0.787562	+	0.616235i	$0.211343\pi$
$241$	−2.53462	+	14.3745i	−0.163269	+	0.925944i	−0.950831	+	0.309709i	$0.899768\pi$
$242$	−5.67752	+	4.76400i	−0.364965	+	0.306242i
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$	2.34343	+	13.2902i	0.150022	+	0.850820i
$245$	1.21301	+	0.441500i	0.0774964	+	0.0282064i
$246$	5.10607			0.325551
$247$	−3.75150	+	3.54925i	−0.238702	+	0.225834i
$248$	6.59627			0.418863
$249$	1.91875	+	0.698367i	0.121596	+	0.0442572i
$250$	0.173648	+	0.984808i	0.0109825	+	0.0622847i
$251$	16.8346	+	14.1259i	1.06259	+	0.891617i	0.994361	−	0.106053i	$-0.0338212\pi$
$251$	16.8346	+	14.1259i	1.06259	+	0.891617i	0.0682275	+	0.997670i	$0.478266\pi$
$252$	2.20574	−	1.85083i	0.138948	−	0.116592i
$253$	0.379852	−	2.15425i	0.0238811	−	0.135436i
$254$	2.01114	−	3.48340i	0.126190	−	0.218568i
$255$	0.705737	+	1.22237i	0.0441950	+	0.0765479i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−7.47818	+	2.72183i	−0.466476	+	0.169783i	−0.564555	−	0.825395i	$-0.690952\pi$
$257$	−7.47818	+	2.72183i	−0.466476	+	0.169783i	0.0980794	+	0.995179i	$0.468730\pi$
$258$	−4.96451	−	8.59878i	−0.309077	−	0.535337i
$259$	3.29813	−	5.71253i	0.204936	−	0.354960i
$260$	0.205737	−	1.16679i	0.0127593	−	0.0723614i
$261$	2.66250	−	2.23411i	0.164805	−	0.138288i
$262$	7.94356	+	6.66544i	0.490755	+	0.411792i
$263$	0.535492	+	3.03693i	0.0330199	+	0.187265i	0.996856	−	0.0792290i	$-0.0252458\pi$
$263$	0.535492	+	3.03693i	0.0330199	+	0.187265i	−0.963837	+	0.266494i	$0.914135\pi$
$264$	4.03209	+	1.46756i	0.248158	+	0.0903221i
$265$	10.9213			0.670889
$266$	−12.5287	+	0.747243i	−0.768183	+	0.0458164i
$267$	2.50980			0.153597
$268$	−5.15910	−	1.87776i	−0.315142	−	0.114702i
$269$	−1.09745	−	6.22394i	−0.0669126	−	0.379480i	−0.999813	−	0.0193455i	$-0.993842\pi$
$269$	−1.09745	−	6.22394i	−0.0669126	−	0.379480i	0.932900	−	0.360135i	$-0.117269\pi$
$270$	−0.766044	−	0.642788i	−0.0466200	−	0.0391188i
$271$	−22.5804	+	18.9472i	−1.37166	+	1.15096i	−0.399475	+	0.916744i	$0.630808\pi$
$271$	−22.5804	+	18.9472i	−1.37166	+	1.15096i	−0.972185	+	0.234216i	$0.924748\pi$
$272$	−0.245100	+	1.39003i	−0.0148614	+	0.0842830i
$273$	−1.70574	+	2.95442i	−0.103236	+	0.178810i
$274$	3.13429	+	5.42874i	0.189349	+	0.327962i
$275$	4.03209	−	1.46756i	0.243144	−	0.0884972i
$276$	−0.479055	+	0.174362i	−0.0288358	+	0.0104954i
$277$	−14.6702	−	25.4096i	−0.881450	−	1.52672i	−0.849730	−	0.527219i	$-0.823235\pi$
$277$	−14.6702	−	25.4096i	−0.881450	−	1.52672i	−0.0317199	−	0.999497i	$-0.510098\pi$
$278$	7.22803	−	12.5193i	0.433508	−	0.750858i
$279$	−1.14543	+	6.49605i	−0.0685751	+	0.388909i
$280$	2.20574	−	1.85083i	0.131818	−	0.110608i
$281$	−11.7003	−	9.81770i	−0.697980	−	0.585675i	0.223218	−	0.974768i	$-0.428344\pi$
$281$	−11.7003	−	9.81770i	−0.697980	−	0.585675i	−0.921198	+	0.389094i	$0.872788\pi$
$282$	0.783119	+	4.44129i	0.0466340	+	0.264475i
$283$	−5.27719	−	1.92074i	−0.313696	−	0.114176i	0.180374	−	0.983598i	$-0.442269\pi$
$283$	−5.27719	−	1.92074i	−0.313696	−	0.114176i	−0.494070	+	0.869422i	$0.664491\pi$
$284$	6.66044			0.395225
$285$	1.01114	+	4.24000i	0.0598950	+	0.251156i
$286$	−5.08378			−0.300610
$287$	−13.8157	−	5.02849i	−0.815513	−	0.296823i
$288$	−0.173648	−	0.984808i	−0.0102323	−	0.0580304i
$289$	−11.4966	−	9.64679i	−0.676270	−	0.567458i
$290$	2.66250	−	2.23411i	0.156348	−	0.131191i
$291$	1.86824	−	10.5953i	0.109518	−	0.621109i
$292$	−3.48293	+	6.03260i	−0.203823	+	0.353031i
$293$	3.92855	+	6.80445i	0.229508	+	0.397520i	0.957662	−	0.287893i	$-0.0929549\pi$
$293$	3.92855	+	6.80445i	0.229508	+	0.397520i	−0.728154	+	0.685413i	$0.759622\pi$
$294$	−1.21301	+	0.441500i	−0.0707442	+	0.0257488i
$295$	6.68479	−	2.43307i	0.389204	−	0.141659i
$296$	−1.14543	−	1.98394i	−0.0665767	−	0.115314i
$297$	−2.14543	+	3.71599i	−0.124490	+	0.215624i
$298$	−0.812681	+	4.60894i	−0.0470774	+	0.266989i
$299$	0.462697	−	0.388249i	0.0267584	−	0.0224530i
$300$	−0.766044	−	0.642788i	−0.0442276	−	0.0371114i
$301$	4.96451	+	28.1551i	0.286149	+	1.62283i
$302$	14.0544	+	5.11538i	0.808739	+	0.294357i
$303$	3.24628			0.186494
$304$	−1.95084	+	3.89798i	−0.111888	+	0.223564i
$305$	−13.4953			−0.772736
$306$	−1.32635	−	0.482753i	−0.0758225	−	0.0275971i
$307$	3.80406	+	21.5739i	0.217109	+	1.23129i	0.877208	+	0.480110i	$0.159403\pi$
$307$	3.80406	+	21.5739i	0.217109	+	1.23129i	−0.660099	+	0.751179i	$0.729486\pi$
$308$	−9.46451	−	7.94166i	−0.539290	−	0.452518i
$309$	−4.03209	+	3.38332i	−0.229378	+	0.192471i
$310$	−1.14543	+	6.49605i	−0.0650560	+	0.368951i
$311$	−3.72328	+	6.44891i	−0.211128	+	0.365684i	−0.952068	−	0.305887i	$-0.901047\pi$
$311$	−3.72328	+	6.44891i	−0.211128	+	0.365684i	0.740940	+	0.671571i	$0.234380\pi$
$312$	0.592396	+	1.02606i	0.0335378	+	0.0580892i
$313$	−14.8478	+	5.40414i	−0.839245	+	0.305460i	−0.725648	−	0.688067i	$-0.758460\pi$
$313$	−14.8478	+	5.40414i	−0.839245	+	0.305460i	−0.113598	+	0.993527i	$0.536237\pi$
$314$	15.5954	−	5.67626i	0.880099	−	0.320330i
$315$	1.43969	+	2.49362i	0.0811175	+	0.140500i
$316$	8.79813	−	15.2388i	0.494934	−	0.857250i
$317$	−2.61112	+	14.8084i	−0.146655	+	0.831722i	0.819368	+	0.573267i	$0.194324\pi$
$317$	−2.61112	+	14.8084i	−0.146655	+	0.831722i	−0.966023	+	0.258455i	$0.916787\pi$
$318$	−8.36618	+	7.02006i	−0.469152	+	0.393665i
$319$	−11.4244	−	9.58623i	−0.639645	−	0.536726i
$320$	−0.173648	−	0.984808i	−0.00970723	−	0.0550524i
$321$	−17.1951	−	6.25849i	−0.959735	−	0.349315i
$322$	1.46791			0.0818035
$323$	3.38800	+	5.13560i	0.188514	+	0.285752i
$324$	1.00000			0.0555556
$325$	1.11334	+	0.405223i	0.0617570	+	0.0224777i
$326$	−0.967034	−	5.48432i	−0.0535590	−	0.303748i
$327$	−8.35710	−	7.01244i	−0.462148	−	0.387789i
$328$	−3.91147	+	3.28212i	−0.215975	+	0.181225i
$329$	2.25490	−	12.7882i	0.124317	−	0.705035i
$330$	−2.14543	+	3.71599i	−0.118102	+	0.204559i
$331$	−5.03343	−	8.71816i	−0.276663	−	0.479194i	0.693891	−	0.720080i	$-0.255895\pi$
$331$	−5.03343	−	8.71816i	−0.276663	−	0.479194i	−0.970553	+	0.240887i	$0.922562\pi$
$332$	−1.91875	+	0.698367i	−0.105305	+	0.0383279i
$333$	2.15270	−	0.783520i	0.117967	−	0.0429366i
$334$	−7.60994	−	13.1808i	−0.416397	−	0.721221i
$335$	2.74510	−	4.75465i	0.149981	−	0.259774i
$336$	−0.500000	+	2.83564i	−0.0272772	+	0.154697i
$337$	−12.8648	+	10.7949i	−0.700792	+	0.588035i	−0.921999	−	0.387192i	$-0.873445\pi$
$337$	−12.8648	+	10.7949i	−0.700792	+	0.588035i	0.221207	+	0.975227i	$0.429000\pi$
$338$	8.88326	+	7.45394i	0.483185	+	0.405441i
$339$	2.75877	+	15.6458i	0.149836	+	0.849761i
$340$	−1.32635	−	0.482753i	−0.0719315	−	0.0261809i
$341$	28.3037			1.53273
$342$	−3.50000	−	2.59808i	−0.189258	−	0.140488i
$343$	−16.4388			−0.887613
$344$	9.33022	+	3.39592i	0.503052	+	0.183096i
$345$	−0.0885259	−	0.502055i	−0.00476607	−	0.0270297i
$346$	−7.34911	−	6.16663i	−0.395090	−	0.331520i
$347$	25.6839	−	21.5514i	1.37878	−	1.15694i	0.409125	−	0.912478i	$-0.365834\pi$
$347$	25.6839	−	21.5514i	1.37878	−	1.15694i	0.969659	−	0.244460i	$-0.0786106\pi$
$348$	−0.603541	+	3.42285i	−0.0323532	+	0.183484i
$349$	3.00253	−	5.20053i	0.160722	−	0.278378i	−0.774406	−	0.632689i	$-0.781951\pi$
$349$	3.00253	−	5.20053i	0.160722	−	0.278378i	0.935128	+	0.354311i	$0.115285\pi$
$350$	1.43969	+	2.49362i	0.0769548	+	0.133290i
$351$	−1.11334	+	0.405223i	−0.0594257	+	0.0216292i
$352$	−4.03209	+	1.46756i	−0.214911	+	0.0782212i
$353$	11.4561	+	19.8425i	0.609744	+	1.05611i	0.991282	+	0.131755i	$0.0420611\pi$
$353$	11.4561	+	19.8425i	0.609744	+	1.05611i	−0.381538	+	0.924353i	$0.624606\pi$
$354$	−3.55690	+	6.16074i	−0.189047	+	0.327440i
$355$	−1.15657	+	6.55926i	−0.0613846	+	0.348129i
$356$	−1.92262	+	1.61327i	−0.101899	+	0.0855031i
$357$	3.11334	+	2.61240i	0.164775	+	0.138263i
$358$	3.51754	+	19.9490i	0.185908	+	1.05434i
$359$	14.1951	+	5.16658i	0.749187	+	0.272682i	0.688263	−	0.725461i	$-0.258373\pi$
$359$	14.1951	+	5.16658i	0.749187	+	0.272682i	0.0609231	+	0.998142i	$0.480596\pi$
$360$	1.00000			0.0527046
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$	5.39693			0.283656
$363$	6.96451	+	2.53487i	0.365542	+	0.133046i
$364$	−0.592396	−	3.35965i	−0.0310500	−	0.176093i
$365$	−5.33615	−	4.47756i	−0.279307	−	0.234366i
$366$	10.3380	−	8.67458i	0.540374	−	0.453428i
$367$	2.99407	−	16.9802i	0.156289	−	0.886360i	−0.801309	−	0.598251i	$-0.795862\pi$
$367$	2.99407	−	16.9802i	0.156289	−	0.886360i	0.957598	−	0.288109i	$-0.0930265\pi$
$368$	0.254900	−	0.441500i	0.0132876	−	0.0230148i
$369$	−2.55303	−	4.42198i	−0.132906	−	0.230199i
$370$	2.15270	−	0.783520i	0.111914	−	0.0407333i
$371$	29.5501	−	10.7554i	1.53416	−	0.558390i
$372$	−3.29813	−	5.71253i	−0.171000	−	0.296181i
$373$	−11.9534	+	20.7038i	−0.618922	+	1.07200i	0.370761	+	0.928728i	$0.379097\pi$
$373$	−11.9534	+	20.7038i	−0.618922	+	1.07200i	−0.989683	+	0.143276i	$0.954236\pi$
$374$	−1.05169	+	5.96443i	−0.0543816	+	0.308413i
$375$	0.766044	−	0.642788i	0.0395584	−	0.0331934i
$376$	−3.45471	−	2.89884i	−0.178163	−	0.149496i
$377$	−0.715070	−	4.05537i	−0.0368280	−	0.208862i
$378$	−2.70574	−	0.984808i	−0.139168	−	0.0506530i
$379$	30.7151			1.57773			0.788865	−	0.614566i	$-0.210669\pi$
$379$	30.7151			1.57773			0.788865	+	0.614566i	$0.210669\pi$
$380$	−3.50000	−	2.59808i	−0.179546	−	0.133278i
$381$	−4.02229			−0.206068
$382$	−7.96198	−	2.89792i	−0.407370	−	0.148271i
$383$	1.49882	+	8.50022i	0.0765860	+	0.434341i	0.998857	+	0.0477971i	$0.0152201\pi$
$383$	1.49882	+	8.50022i	0.0765860	+	0.434341i	−0.922271	+	0.386544i	$0.873669\pi$
$384$	0.766044	+	0.642788i	0.0390920	+	0.0328021i
$385$	9.46451	−	7.94166i	0.482356	−	0.404745i
$386$	−1.87299	+	10.6222i	−0.0953326	+	0.540658i
$387$	−4.96451	+	8.59878i	−0.252360	+	0.437101i
$388$	5.37939	+	9.31737i	0.273097	+	0.473018i
$389$	3.99185	−	1.45291i	0.202395	−	0.0736657i	−0.238834	−	0.971060i	$-0.576765\pi$
$389$	3.99185	−	1.45291i	0.202395	−	0.0736657i	0.441228	+	0.897395i	$0.354543\pi$
$390$	−1.11334	+	0.405223i	−0.0563762	+	0.0205193i
$391$	−0.359785	−	0.623166i	−0.0181951	−	0.0315148i
$392$	0.645430	−	1.11792i	0.0325991	−	0.0564633i
$393$	1.80066	−	10.2120i	0.0908313	−	0.515130i
$394$	16.4663	−	13.8169i	0.829561	−	0.696084i
$395$	13.4795	+	11.3107i	0.678228	+	0.569101i
$396$	−0.745100	−	4.22567i	−0.0374427	−	0.212348i
$397$	26.7986	+	9.75389i	1.34498	+	0.489534i	0.911378	−	0.411569i	$-0.135019\pi$
$397$	26.7986	+	9.75389i	1.34498	+	0.489534i	0.433605	+	0.901103i	$0.357241\pi$
$398$	8.98814			0.450535
$399$	6.91147	+	10.4765i	0.346006	+	0.524483i
$400$	1.00000			0.0500000
$401$	−7.58987	−	2.76249i	−0.379020	−	0.137952i	0.145483	−	0.989361i	$-0.453527\pi$
$401$	−7.58987	−	2.76249i	−0.379020	−	0.137952i	−0.524503	+	0.851409i	$0.675749\pi$
$402$	0.953363	+	5.40679i	0.0475494	+	0.269666i
$403$	5.98680	+	5.02352i	0.298224	+	0.250239i
$404$	−2.48680	+	2.08667i	−0.123723	+	0.103816i
$405$	−0.173648	+	0.984808i	−0.00862865	+	0.0489355i
$406$	5.00387	−	8.66696i	0.248338	−	0.430134i
$407$	−4.91488	−	8.51282i	−0.243621	−	0.421965i
$408$	1.32635	−	0.482753i	0.0656642	−	0.0238998i
$409$	−5.30706	+	1.93161i	−0.262417	+	0.0955120i	−0.469878	−	0.882731i	$-0.655702\pi$
$409$	−5.30706	+	1.93161i	−0.262417	+	0.0955120i	0.207461	+	0.978243i	$0.433480\pi$
$410$	−2.55303	−	4.42198i	−0.126085	−	0.218386i
$411$	3.13429	−	5.42874i	0.154603	−	0.267780i
$412$	0.914000	−	5.18355i	0.0450296	−	0.255375i
$413$	15.6912	−	13.1665i	0.772113	−	0.647880i
$414$	0.390530	+	0.327693i	0.0191935	+	0.0161052i
$415$	−0.354570	−	2.01087i	−0.0174052	−	0.0987096i
$416$	−1.11334	−	0.405223i	−0.0545860	−	0.0198677i
$417$	−14.4561			−0.707916
$418$	−8.37077	+	16.7257i	−0.409428	+	0.818080i
$419$	−20.5544			−1.00415			−0.502074	−	0.864825i	$-0.667429\pi$
$419$	−20.5544			−1.00415			−0.502074	+	0.864825i	$0.667429\pi$
$420$	−2.70574	−	0.984808i	−0.132026	−	0.0480537i
$421$	1.20873	+	6.85505i	0.0589099	+	0.334095i	0.999992	−	0.00408448i	$-0.00130013\pi$
$421$	1.20873	+	6.85505i	0.0589099	+	0.334095i	−0.941082	+	0.338179i	$0.890189\pi$
$422$	8.71554	+	7.31320i	0.424266	+	0.356001i
$423$	3.45471	−	2.89884i	0.167974	−	0.140947i
$424$	1.89646	−	10.7554i	0.0921002	−	0.522326i
$425$	0.705737	−	1.22237i	0.0342333	−	0.0592938i
$426$	−3.33022	−	5.76811i	−0.161350	−	0.279466i
$427$	−36.5146	+	13.2902i	−1.76707	+	0.643159i
$428$	17.1951	−	6.25849i	0.831155	−	0.302516i
$429$	2.54189	+	4.40268i	0.122724	+	0.212563i
$430$	−4.96451	+	8.59878i	−0.239410	+	0.414670i
$431$	4.37733	−	24.8250i	0.210848	−	1.19578i	−0.677119	−	0.735874i	$-0.736772\pi$
$431$	4.37733	−	24.8250i	0.210848	−	1.19578i	0.887967	−	0.459907i	$-0.152117\pi$
$432$	−0.766044	+	0.642788i	−0.0368563	+	0.0309261i
$433$	−9.08306	−	7.62159i	−0.436504	−	0.366270i	0.397895	−	0.917431i	$-0.369741\pi$
$433$	−9.08306	−	7.62159i	−0.436504	−	0.366270i	−0.834399	+	0.551160i	$0.814185\pi$
$434$	3.29813	+	18.7046i	0.158315	+	0.897852i
$435$	−3.26604	−	1.18874i	−0.156595	−	0.0569959i
$436$	10.9094			0.522466
$437$	−0.515482	−	2.16155i	−0.0246588	−	0.103401i
$438$	6.96585			0.332841
$439$	16.6138	+	6.04693i	0.792934	+	0.288604i	0.706555	−	0.707658i	$-0.250248\pi$
$439$	16.6138	+	6.04693i	0.792934	+	0.288604i	0.0863787	+	0.996262i	$0.472470\pi$
$440$	−0.745100	−	4.22567i	−0.0355212	−	0.201451i
$441$	0.988856	+	0.829748i	0.0470884	+	0.0395118i
$442$	−1.28106	+	1.07494i	−0.0609338	+	0.0511295i
$443$	3.35844	−	19.0467i	0.159564	−	0.904934i	−0.794929	−	0.606702i	$-0.792492\pi$
$443$	3.35844	−	19.0467i	0.159564	−	0.904934i	0.954493	−	0.298232i	$-0.0963969\pi$
$444$	−1.14543	+	1.98394i	−0.0543597	+	0.0941537i
$445$	−1.25490	−	2.17355i	−0.0594880	−	0.103036i
$446$	7.51114	−	2.73383i	0.355663	−	0.129451i
$447$	4.39780	−	1.60067i	0.208009	−	0.0757091i
$448$	−1.43969	−	2.49362i	−0.0680191	−	0.117813i
$449$	13.9055	−	24.0851i	0.656243	−	1.13665i	−0.325337	−	0.945598i	$-0.605478\pi$
$449$	13.9055	−	24.0851i	0.656243	−	1.13665i	0.981581	−	0.191049i	$-0.0611888\pi$
$450$	−0.173648	+	0.984808i	−0.00818585	+	0.0464243i
$451$	−16.7836	+	14.0831i	−0.790308	+	0.663147i
$452$	−12.1702	−	10.2120i	−0.572440	−	0.480334i
$453$	−2.59714	−	14.7291i	−0.122024	−	0.692035i
$454$	6.19846	+	2.25606i	0.290908	+	0.105882i
$455$	3.41147			0.159932
$456$	4.35117	−	0.259515i	0.203762	−	0.0121529i
$457$	−20.9659			−0.980741			−0.490371	−	0.871514i	$-0.663139\pi$
$457$	−20.9659			−0.980741			−0.490371	+	0.871514i	$0.663139\pi$
$458$	−14.5223	−	5.28568i	−0.678582	−	0.246984i
$459$	0.245100	+	1.39003i	0.0114403	+	0.0648811i
$460$	0.390530	+	0.327693i	0.0182085	+	0.0152788i
$461$	−0.809278	+	0.679065i	−0.0376918	+	0.0316272i	−0.661439	−	0.749999i	$-0.730054\pi$
$461$	−0.809278	+	0.679065i	−0.0376918	+	0.0316272i	0.623747	+	0.781626i	$0.285609\pi$
$462$	−2.14543	+	12.1673i	−0.0998144	+	0.566076i
$463$	−16.5829	+	28.7224i	−0.770673	+	1.33484i	0.166522	+	0.986038i	$0.446746\pi$
$463$	−16.5829	+	28.7224i	−0.770673	+	1.33484i	−0.937195	+	0.348807i	$0.886587\pi$
$464$	−1.73783	−	3.01000i	−0.0806765	−	0.139736i
$465$	6.19846	−	2.25606i	0.287447	−	0.104622i
$466$	−9.32770	+	3.39500i	−0.432097	+	0.157271i
$467$	−0.979522	−	1.69658i	−0.0453269	−	0.0785085i	0.842472	−	0.538740i	$-0.181100\pi$
$467$	−0.979522	−	1.69658i	−0.0453269	−	0.0785085i	−0.887799	+	0.460232i	$0.847766\pi$
$468$	0.592396	−	1.02606i	0.0273835	−	0.0474297i
$469$	2.74510	−	15.5682i	0.126757	−	0.718874i
$470$	3.45471	−	2.89884i	0.159354	−	0.133714i
$471$	−12.7135	−	10.6679i	−0.585806	−	0.491550i
$472$	−1.23530	−	7.00573i	−0.0568593	−	0.322465i
$473$	40.0347	+	14.5714i	1.84080	+	0.669995i
$474$	−17.5963			−0.808223
$475$	3.16637	−	2.99568i	0.145283	−	0.137451i
$476$	−4.06418			−0.186281
$477$	10.2626	+	3.73530i	0.469894	+	0.171027i
$478$	2.77126	+	15.7166i	0.126754	+	0.718860i
$479$	−14.8237	−	12.4385i	−0.677310	−	0.568331i	0.237909	−	0.971288i	$-0.423538\pi$
$479$	−14.8237	−	12.4385i	−0.677310	−	0.568331i	−0.915219	+	0.402957i	$0.867983\pi$
$480$	−0.766044	+	0.642788i	−0.0349650	+	0.0293391i
$481$	0.471315	−	2.67296i	0.0214901	−	0.121876i
$482$	−7.29813	+	12.6407i	−0.332421	+	0.575770i
$483$	−0.733956	−	1.27125i	−0.0333961	−	0.0578438i
$484$	−6.96451	+	2.53487i	−0.316569	+	0.115222i
$485$	−10.1099	+	3.67972i	−0.459069	+	0.167087i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	8.28446	−	14.3491i	0.375405	−	0.650220i	−0.614983	−	0.788541i	$-0.710837\pi$
$487$	8.28446	−	14.3491i	0.375405	−	0.650220i	0.990388	+	0.138320i	$0.0441704\pi$
$488$	−2.34343	+	13.2902i	−0.106082	+	0.601620i
$489$	−4.26604	+	3.57964i	−0.192917	+	0.161877i
$490$	0.988856	+	0.829748i	0.0446719	+	0.0374842i
$491$	−4.96626	−	28.1651i	−0.224124	−	1.27107i	−0.864352	−	0.502887i	$-0.832271\pi$
$491$	−4.96626	−	28.1651i	−0.224124	−	1.27107i	0.640228	−	0.768185i	$-0.278840\pi$
$492$	4.79813	+	1.74638i	0.216317	+	0.0787328i
$493$	−4.90579			−0.220946
$494$	−4.73917	+	2.05212i	−0.213225	+	0.0923293i
$495$	4.29086			0.192860
$496$	6.19846	+	2.25606i	0.278319	+	0.101300i
$497$	3.33022	+	18.8866i	0.149381	+	0.847181i
$498$	1.56418	+	1.31250i	0.0700925	+	0.0588146i
$499$	−25.1234	+	21.0810i	−1.12468	+	0.943715i	−0.998831	−	0.0483347i	$-0.984609\pi$
$499$	−25.1234	+	21.0810i	−1.12468	+	0.943715i	−0.125845	+	0.992050i	$0.540164\pi$
$500$	−0.173648	+	0.984808i	−0.00776578	+	0.0440419i
$501$	−7.60994	+	13.1808i	−0.339987	+	0.588875i
$502$	10.9880	+	19.0317i	0.490417	+	0.849428i
$503$	−16.2643	+	5.91972i	−0.725189	+	0.263947i	−0.678127	−	0.734945i	$-0.737208\pi$
$503$	−16.2643	+	5.91972i	−0.725189	+	0.263947i	−0.0470619	+	0.998892i	$0.514986\pi$
$504$	2.70574	−	0.984808i	0.120523	−	0.0438668i
$505$	−1.62314	−	2.81136i	−0.0722288	−	0.125104i
$506$	1.09374	−	1.89441i	0.0486227	−	0.0842170i
$507$	2.01367	−	11.4201i	0.0894302	−	0.507184i
$508$	3.08125	−	2.58548i	0.136708	−	0.114712i
$509$	−13.2344	−	11.1050i	−0.586605	−	0.492220i	0.300503	−	0.953781i	$-0.402845\pi$
$509$	−13.2344	−	11.1050i	−0.586605	−	0.492220i	−0.887109	+	0.461560i	$0.847290\pi$
$510$	0.245100	+	1.39003i	0.0108532	+	0.0615516i
$511$	−18.8478	−	6.86002i	−0.833776	−	0.303470i
$512$	−1.00000			−0.0441942
$513$	−0.500000	+	4.33013i	−0.0220755	+	0.191180i
$514$	−7.95811			−0.351017
$515$	4.94609	+	1.80023i	0.217951	+	0.0793276i
$516$	−1.72416	−	9.77817i	−0.0759017	−	0.430460i
$517$	−14.8237	−	12.4385i	−0.651944	−	0.547046i
$518$	5.05303	−	4.24000i	0.222018	−	0.186295i
$519$	−1.66591	+	9.44783i	−0.0731252	+	0.414714i
$520$	0.592396	−	1.02606i	0.0259783	−	0.0449957i
$521$	−17.8969	−	30.9984i	−0.784079	−	1.35806i	−0.929548	−	0.368701i	$-0.879803\pi$
$521$	−17.8969	−	30.9984i	−0.784079	−	1.35806i	0.145469	−	0.989363i	$-0.453531\pi$
$522$	3.26604	−	1.18874i	0.142951	−	0.0520299i
$523$	23.7361	−	8.63922i	1.03791	−	0.377767i	0.233820	−	0.972280i	$-0.424877\pi$
$523$	23.7361	−	8.63922i	1.03791	−	0.377767i	0.804086	+	0.594513i	$0.202655\pi$
$524$	5.18479	+	8.98032i	0.226499	+	0.392307i
$525$	1.43969	−	2.49362i	0.0628333	−	0.108831i
$526$	−0.535492	+	3.03693i	−0.0233486	+	0.132416i
$527$	7.13223	−	5.98465i	0.310685	−	0.260695i
$528$	3.28699	+	2.75811i	0.143048	+	0.120031i
$529$	−3.94878	−	22.3946i	−0.171686	−	0.973680i
$530$	10.2626	+	3.73530i	0.445781	+	0.162251i
$531$	7.11381			0.308713
$532$	−12.0287	−	3.58288i	−0.521510	−	0.155338i
$533$	−6.04963			−0.262039
$534$	2.35844	+	0.858402i	0.102060	+	0.0371467i
$535$	3.17752	+	18.0206i	0.137376	+	0.779099i
$536$	−4.20574	−	3.52903i	−0.181660	−	0.152431i
$537$	15.5175	−	13.0208i	0.669631	−	0.561887i
$538$	1.09745	−	6.22394i	0.0473144	−	0.268333i
$539$	2.76945	−	4.79682i	0.119289	−	0.206614i
$540$	−0.500000	−	0.866025i	−0.0215166	−	0.0372678i
$541$	0.868241	−	0.316014i	0.0373286	−	0.0135865i	−0.323288	−	0.946300i	$-0.604788\pi$
$541$	0.868241	−	0.316014i	0.0373286	−	0.0135865i	0.360617	+	0.932714i	$0.382566\pi$
$542$	−27.6989	+	10.0816i	−1.18977	+	0.433041i
$543$	−2.69846	−	4.67388i	−0.115802	−	0.200575i
$544$	−0.705737	+	1.22237i	−0.0302582	+	0.0524088i
$545$	−1.89440	+	10.7437i	−0.0811472	+	0.460209i
$546$	−2.61334	+	2.19285i	−0.111841	+	0.0938455i
$547$	−25.6728	−	21.5420i	−1.09769	−	0.921070i	−0.100421	−	0.994945i	$-0.532019\pi$
$547$	−25.6728	−	21.5420i	−1.09769	−	0.921070i	−0.997268	+	0.0738751i	$0.976463\pi$
$548$	1.08853	+	6.17334i	0.0464995	+	0.263712i
$549$	−12.6814	−	4.61565i	−0.541228	−	0.196991i
$550$	4.29086			0.182963
$551$	−14.5196	−	4.32483i	−0.618556	−	0.184244i
$552$	−0.509800			−0.0216985
$553$	47.6109	+	17.3289i	2.02462	+	0.736901i
$554$	−5.09492	−	28.8947i	−0.216463	−	1.22762i
$555$	−1.75490	−	1.47254i	−0.0744914	−	0.0625057i
$556$	11.0740	−	9.29217i	0.469641	−	0.394076i
$557$	5.80035	−	32.8954i	0.245769	−	1.39382i	−0.572931	−	0.819603i	$-0.694194\pi$
$557$	5.80035	−	32.8954i	0.245769	−	1.39382i	0.818700	−	0.574221i	$-0.194695\pi$
$558$	−3.29813	+	5.71253i	−0.139621	+	0.241831i
$559$	5.88191	+	10.1878i	0.248778	+	0.430897i
$560$	2.70574	−	0.984808i	0.114338	−	0.0416157i
$561$	5.69119	−	2.07142i	0.240282	−	0.0874556i
$562$	−7.63681	−	13.2273i	−0.322139	−	0.557962i
$563$	22.7729	−	39.4438i	0.959764	−	1.66236i	0.236694	−	0.971584i	$-0.423936\pi$
$563$	22.7729	−	39.4438i	0.959764	−	1.66236i	0.723070	−	0.690775i	$-0.242731\pi$
$564$	−0.783119	+	4.44129i	−0.0329752	+	0.187012i
$565$	12.1702	−	10.2120i	0.512006	−	0.429624i
$566$	−4.30200	−	3.60981i	−0.180827	−	0.151732i
$567$	0.500000	+	2.83564i	0.0209980	+	0.119086i
$568$	6.25877	+	2.27801i	0.262612	+	0.0955830i
$569$	−16.9135			−0.709052			−0.354526	−	0.935046i	$-0.615358\pi$
$569$	−16.9135			−0.709052			−0.354526	+	0.935046i	$0.615358\pi$
$570$	−0.500000	+	4.33013i	−0.0209427	+	0.181369i
$571$	−34.2131			−1.43177			−0.715886	−	0.698217i	$-0.753977\pi$
$571$	−34.2131			−1.43177			−0.715886	+	0.698217i	$0.753977\pi$
$572$	−4.77719	−	1.73875i	−0.199744	−	0.0727010i
$573$	1.47131	+	8.34424i	0.0614651	+	0.348586i
$574$	−11.2626	−	9.45048i	−0.470094	−	0.394455i
$575$	−0.390530	+	0.327693i	−0.0162862	+	0.0136658i
$576$	0.173648	−	0.984808i	0.00723534	−	0.0410337i
$577$	7.65523	−	13.2592i	0.318691	−	0.551990i	−0.661524	−	0.749924i	$-0.730090\pi$
$577$	7.65523	−	13.2592i	0.318691	−	0.551990i	0.980215	+	0.197934i	$0.0634233\pi$
$578$	−7.50387	−	12.9971i	−0.312120	−	0.540607i
$579$	10.1356	−	3.68907i	0.421222	−	0.153312i
$580$	3.26604	−	1.18874i	0.135615	−	0.0493599i
$581$	−2.93969	−	5.09170i	−0.121959	−	0.211239i
$582$	5.37939	−	9.31737i	0.222983	−	0.386217i
$583$	8.13744	−	46.1497i	0.337018	−	1.91133i
$584$	−5.33615	+	4.47756i	−0.220812	+	0.185283i
$585$	0.907604	+	0.761570i	0.0375248	+	0.0314870i
$586$	1.36437	+	7.73773i	0.0563616	+	0.319643i
$587$	21.3332	+	7.76466i	0.880516	+	0.320482i	0.742418	−	0.669937i	$-0.233679\pi$
$587$	21.3332	+	7.76466i	0.880516	+	0.320482i	0.138098	+	0.990419i	$0.455901\pi$
$588$	−1.29086			−0.0532341
$589$	26.3851	−	11.4251i	1.08718	−	0.470762i
$590$	7.11381			0.292871
$591$	−20.1989	−	7.35181i	−0.830873	−	0.302413i
$592$	−0.397804	−	2.25606i	−0.0163496	−	0.0927233i
$593$	−4.83615	−	4.05801i	−0.198597	−	0.166643i	0.538066	−	0.842903i	$-0.319155\pi$
$593$	−4.83615	−	4.05801i	−0.198597	−	0.166643i	−0.736663	+	0.676260i	$0.763600\pi$
$594$	−3.28699	+	2.75811i	−0.134867	+	0.113167i
$595$	0.705737	−	4.00243i	0.0289324	−	0.164084i
$596$	−2.34002	+	4.05304i	−0.0958511	+	0.166019i
$597$	−4.49407	−	7.78396i	−0.183930	−	0.318576i
$598$	0.567581	−	0.206583i	0.0232101	−	0.00844780i
$599$	−37.0813	+	13.4965i	−1.51510	+	0.551452i	−0.959919	−	0.280277i	$-0.909574\pi$
$599$	−37.0813	+	13.4965i	−1.51510	+	0.551452i	−0.555182	+	0.831729i	$0.687351\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	2.95424	−	5.11689i	0.120506	−	0.208722i	−0.799461	−	0.600718i	$-0.794882\pi$
$601$	2.95424	−	5.11689i	0.120506	−	0.208722i	0.919967	+	0.391995i	$0.128215\pi$
$602$	−4.96451	+	28.1551i	−0.202338	+	1.14752i
$603$	4.20574	−	3.52903i	0.171271	−	0.143713i
$604$	11.4572	+	9.61376i	0.466188	+	0.391178i
$605$	−1.28699	−	7.29888i	−0.0523235	−	0.296742i
$606$	3.05051	+	1.11029i	0.123918	+	0.0451026i
$607$	−11.2422			−0.456305			−0.228153	−	0.973625i	$-0.573269\pi$
$607$	−11.2422			−0.456305			−0.228153	+	0.973625i	$0.573269\pi$
$608$	−3.16637	+	2.99568i	−0.128413	+	0.121491i
$609$	−10.0077			−0.405534
$610$	−12.6814	−	4.61565i	−0.513454	−	0.186882i
$611$	−0.927833	−	5.26200i	−0.0375361	−	0.212878i
$612$	−1.08125	−	0.907278i	−0.0437070	−	0.0366745i
$613$	10.7829	−	9.04790i	0.435516	−	0.365441i	−0.398512	−	0.917163i	$-0.630473\pi$
$613$	10.7829	−	9.04790i	0.435516	−	0.365441i	0.834028	+	0.551722i	$0.186029\pi$
$614$	−3.80406	+	21.5739i	−0.153519	+	0.870652i
$615$	−2.55303	+	4.42198i	−0.102948	+	0.178312i
$616$	−6.17752	−	10.6998i	−0.248899	−	0.431106i
$617$	−24.7824	+	9.02006i	−0.997702	+	0.363134i	−0.788698	−	0.614781i	$-0.789244\pi$
$617$	−24.7824	+	9.02006i	−0.997702	+	0.363134i	−0.209004	+	0.977915i	$0.567022\pi$
$618$	−4.94609	+	1.80023i	−0.198961	+	0.0724158i
$619$	−9.03209	−	15.6440i	−0.363030	−	0.628787i	0.625428	−	0.780282i	$-0.284925\pi$
$619$	−9.03209	−	15.6440i	−0.363030	−	0.628787i	−0.988458	+	0.151495i	$0.951591\pi$
$620$	−3.29813	+	5.71253i	−0.132456	+	0.229421i
$621$	0.0885259	−	0.502055i	0.00355242	−	0.0201468i
$622$	−5.70439	+	4.78655i	−0.228725	+	0.191923i
$623$	−5.53596	−	4.64522i	−0.221794	−	0.186107i
$624$	0.205737	+	1.16679i	0.00823607	+	0.0467091i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	−15.8007			−0.631521
$627$	18.6702	−	1.11354i	0.745618	−	0.0444706i
$628$	16.5963			0.662263
$629$	−3.03849	−	1.10592i	−0.121152	−	0.0440958i
$630$	0.500000	+	2.83564i	0.0199205	+	0.112975i
$631$	−32.4654	−	27.2417i	−1.29243	−	1.08448i	−0.991401	−	0.130861i	$-0.958226\pi$
$631$	−32.4654	−	27.2417i	−1.29243	−	1.08448i	−0.301028	−	0.953615i	$-0.597330\pi$
$632$	13.4795	−	11.3107i	0.536187	−	0.449914i
$633$	1.97565	−	11.2045i	0.0785251	−	0.445338i
$634$	−7.51842	+	13.0223i	−0.298595	+	0.517181i
$635$	2.01114	+	3.48340i	0.0798098	+	0.138235i
$636$	−10.2626	+	3.73530i	−0.406940	+	0.148114i
$637$	1.43717	−	0.523086i	0.0569426	−	0.0207254i
$638$	−7.45677	−	12.9155i	−0.295216	−	0.511329i
$639$	−3.33022	+	5.76811i	−0.131742	+	0.228183i
$640$	0.173648	−	0.984808i	0.00686405	−	0.0389279i
$641$	33.5435	−	28.1464i	1.32489	−	1.11171i	0.339647	−	0.940553i	$-0.389692\pi$
$641$	33.5435	−	28.1464i	1.32489	−	1.11171i	0.985243	−	0.171162i	$-0.0547521\pi$
$642$	−14.0175	−	11.7621i	−0.553228	−	0.464214i
$643$	1.00862	+	5.72016i	0.0397760	+	0.225581i	0.998215	−	0.0597150i	$-0.0190192\pi$
$643$	1.00862	+	5.72016i	0.0397760	+	0.225581i	−0.958439	+	0.285296i	$0.907908\pi$
$644$	1.37939	+	0.502055i	0.0543554	+	0.0197837i
$645$	9.92902			0.390955
$646$	1.42720	+	5.98465i	0.0561526	+	0.235463i
$647$	42.8221			1.68351			0.841756	−	0.539859i	$-0.181522\pi$
$647$	42.8221			1.68351			0.841756	+	0.539859i	$0.181522\pi$
$648$	0.939693	+	0.342020i	0.0369146	+	0.0134358i
$649$	−5.30050	−	30.0606i	−0.208063	−	1.17998i
$650$	0.907604	+	0.761570i	0.0355991	+	0.0298712i
$651$	14.5496	−	12.2086i	0.570245	−	0.478492i
$652$	0.967034	−	5.48432i	0.0378720	−	0.214783i
$653$	−13.5398	+	23.4517i	−0.529854	+	0.917735i	0.469539	+	0.882912i	$0.344420\pi$
$653$	−13.5398	+	23.4517i	−0.529854	+	0.917735i	−0.999393	+	0.0348232i	$0.988913\pi$
$654$	−5.45471	−	9.44783i	−0.213296	−	0.369439i
$655$	−9.74422	+	3.54661i	−0.380738	+	0.138577i
$656$	−4.79813	+	1.74638i	−0.187336	+	0.0681846i
$657$	−3.48293	−	6.03260i	−0.135882	−	0.235354i
$658$	6.49273	−	11.2457i	0.253113	−	0.438404i
$659$	−8.27332	+	46.9203i	−0.322283	+	1.82776i	0.205837	+	0.978586i	$0.434008\pi$
$659$	−8.27332	+	46.9203i	−0.322283	+	1.82776i	−0.528120	+	0.849170i	$0.677103\pi$
$660$	−3.28699	+	2.75811i	−0.127946	+	0.107359i
$661$	−18.8969	−	15.8564i	−0.735005	−	0.616743i	0.196486	−	0.980507i	$-0.437047\pi$
$661$	−18.8969	−	15.8564i	−0.735005	−	0.616743i	−0.931491	+	0.363764i	$0.881491\pi$
$662$	−1.74809	−	9.91393i	−0.0679416	−	0.385316i
$663$	1.57145	+	0.571962i	0.0610301	+	0.0222132i
$664$	−2.04189			−0.0792407
$665$	5.61721	−	11.2238i	0.217826	−	0.435240i
$666$	2.29086			0.0887690
$667$	1.66503	+	0.606021i	0.0644702	+	0.0234652i
$668$	−2.64290	−	14.9887i	−0.102257	−	0.579928i
$669$	−6.12314	−	5.13793i	−0.236734	−	0.198644i
$670$	4.20574	−	3.52903i	0.162482	−	0.136338i
$671$	−10.0553	+	57.0265i	−0.388181	+	2.20148i
$672$	−1.43969	+	2.49362i	−0.0555373	+	0.0961935i
$673$	21.9013	+	37.9341i	0.844232	+	1.46225i	0.886287	+	0.463137i	$0.153276\pi$
$673$	21.9013	+	37.9341i	0.844232	+	1.46225i	−0.0420551	+	0.999115i	$0.513391\pi$
$674$	−15.7811	+	5.74384i	−0.607864	+	0.221244i
$675$	0.939693	−	0.342020i	0.0361688	−	0.0131644i
$676$	5.79813	+	10.0427i	0.223005	+	0.386256i
$677$	−21.4920	+	37.2253i	−0.826005	+	1.43068i	0.0751437	+	0.997173i	$0.476058\pi$
$677$	−21.4920	+	37.2253i	−0.826005	+	1.43068i	−0.901149	+	0.433510i	$0.857275\pi$
$678$	−2.75877	+	15.6458i	−0.105950	+	0.600872i
$679$	−23.7310	+	19.9127i	−0.910713	+	0.764179i
$680$	−1.08125	−	0.907278i	−0.0414641	−	0.0347925i
$681$	−1.14543	−	6.49605i	−0.0438930	−	0.248929i
$682$	26.5967	+	9.68042i	1.01844	+	0.370682i
$683$	7.08553			0.271120			0.135560	−	0.990769i	$-0.456717\pi$
$683$	7.08553			0.271120			0.135560	+	0.990769i	$0.456717\pi$
$684$	−2.40033	−	3.63846i	−0.0917789	−	0.139120i
$685$	−6.26857			−0.239510
$686$	−15.4474	−	5.62241i	−0.589786	−	0.214664i
$687$	2.68361	+	15.2195i	0.102386	+	0.580661i
$688$	7.60607	+	6.38225i	0.289979	+	0.243321i
$689$	9.91219	−	8.31731i	0.377624	−	0.316864i
$690$	0.0885259	−	0.502055i	0.00337012	−	0.0191129i
$691$	14.9829	−	25.9512i	0.569977	−	0.987230i	−0.426590	−	0.904445i	$-0.640285\pi$
$691$	14.9829	−	25.9512i	0.569977	−	0.987230i	0.996567	−	0.0827847i	$-0.0263814\pi$
$692$	−4.79679	−	8.30828i	−0.182347	−	0.315834i
$693$	11.6099	−	4.22567i	0.441025	−	0.160520i
$694$	31.5060	−	11.4672i	1.19595	−	0.435291i
$695$	7.22803	+	12.5193i	0.274175	+	0.474884i
$696$	−1.73783	+	3.01000i	−0.0658721	+	0.114094i
$697$	−1.25150	+	7.09759i	−0.0474038	+	0.268840i
$698$	4.60014	−	3.85997i	0.174118	−	0.146102i
$699$	7.60401	+	6.38052i	0.287610	+	0.241333i
$700$	0.500000	+	2.83564i	0.0188982	+	0.107177i
$701$	30.5171	+	11.1073i	1.15262	+	0.419518i	0.846454	−	0.532462i	$-0.178733\pi$
$701$	30.5171	+	11.1073i	1.15262	+	0.419518i	0.306162	+	0.951979i	$0.400955\pi$
$702$	−1.18479			−0.0447171
$703$	−8.01801	−	5.95183i	−0.302405	−	0.224477i
$704$	−4.29086			−0.161718
$705$	−4.23783	−	1.54244i	−0.159606	−	0.0580917i
$706$	3.97864	+	22.5640i	0.149738	+	0.849208i
$707$	−7.16044	−	6.00833i	−0.269296	−	0.225966i
$708$	−5.44949	+	4.57267i	−0.204804	+	0.171851i
$709$	1.72762	−	9.79779i	0.0648820	−	0.367964i	−0.935028	−	0.354573i	$-0.884626\pi$
$709$	1.72762	−	9.79779i	0.0648820	−	0.367964i	0.999910	−	0.0133910i	$-0.00426260\pi$
$710$	−3.33022	+	5.76811i	−0.124981	+	0.216473i
$711$	8.79813	+	15.2388i	0.329956	+	0.571500i
$712$	−2.35844	+	0.858402i	−0.0883863	+	0.0321700i
$713$	−3.15998	+	1.15014i	−0.118342	+	0.0430730i
$714$	2.03209	+	3.51968i	0.0760490	+	0.131721i
$715$	2.54189	−	4.40268i	0.0950613	−	0.164651i
$716$	−3.51754	+	19.9490i	−0.131457	+	0.745528i
$717$	12.2253	−	10.2583i	0.456564	−	0.383102i
$718$	11.5719	+	9.70999i	0.431860	+	0.362374i
$719$	−3.04173	−	17.2505i	−0.113437	−	0.643335i	−0.987512	−	0.157543i	$-0.949643\pi$
$719$	−3.04173	−	17.2505i	−0.113437	−	0.643335i	0.874075	−	0.485791i	$-0.161469\pi$
$720$	0.939693	+	0.342020i	0.0350203	+	0.0127463i
$721$	15.1557			0.564428
$722$	−1.05185	+	18.9709i	−0.0391459	+	0.706022i
$723$	14.5963			0.542841
$724$	5.07145	+	1.84586i	0.188479	+	0.0686008i
$725$	0.603541	+	3.42285i	0.0224149	+	0.127121i
$726$	5.67752	+	4.76400i	0.210712	+	0.176809i
$727$	−32.1446	+	26.9725i	−1.19218	+	1.00035i	−0.192357	+	0.981325i	$0.561613\pi$
$727$	−32.1446	+	26.9725i	−1.19218	+	1.00035i	−0.999819	+	0.0190289i	$0.993943\pi$
$728$	0.592396	−	3.35965i	0.0219557	−	0.124517i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−3.48293	−	6.03260i	−0.128909	−	0.223277i
$731$	13.1694	−	4.79326i	0.487087	−	0.177285i
$732$	12.6814	−	4.61565i	0.468718	−	0.170599i
$733$	10.5813	+	18.3273i	0.390827	+	0.676933i	0.992559	−	0.121765i	$-0.0388556\pi$
$733$	10.5813	+	18.3273i	0.390827	+	0.676933i	−0.601731	+	0.798698i	$0.705522\pi$
$734$	8.62108	−	14.9322i	0.318210	−	0.551156i
$735$	0.224155	−	1.27125i	0.00826810	−	0.0468907i
$736$	0.390530	−	0.327693i	0.0143951	−	0.0120789i
$737$	−18.0462	−	15.1426i	−0.664741	−	0.557784i
$738$	−0.886659	−	5.02849i	−0.0326384	−	0.185101i
$739$	−29.0967	−	10.5903i	−1.07034	−	0.389572i	−0.254037	−	0.967195i	$-0.581758\pi$
$739$	−29.0967	−	10.5903i	−1.07034	−	0.389572i	−0.816304	+	0.577622i	$0.803981\pi$
$740$	2.29086			0.0842137
$741$	4.14677	+	3.07818i	0.152336	+	0.113080i
$742$	31.4466			1.15444
$743$	6.77244	+	2.46497i	0.248457	+	0.0904309i	0.463247	−	0.886229i	$-0.346684\pi$
$743$	6.77244	+	2.46497i	0.248457	+	0.0904309i	−0.214790	+	0.976660i	$0.568907\pi$
$744$	−1.14543	−	6.49605i	−0.0419935	−	0.238157i
$745$	−3.58512	−	3.00827i	−0.131349	−	0.110215i
$746$	−18.3136	+	15.3669i	−0.670509	+	0.562624i
$747$	0.354570	−	2.01087i	0.0129730	−	0.0735738i
$748$	−3.02822	+	5.24503i	−0.110723	+	0.191777i
$749$	26.3444	+	45.6298i	0.962602	+	1.66728i
$750$	0.939693	−	0.342020i	0.0343127	−	0.0124888i
$751$	−2.49912	+	0.909606i	−0.0911943	+	0.0331920i	−0.387214	−	0.921990i	$-0.626563\pi$
$751$	−2.49912	+	0.909606i	−0.0911943	+	0.0331920i	0.296020	+	0.955182i	$0.404340\pi$
$752$	−2.25490	−	3.90560i	−0.0822277	−	0.142423i
$753$	10.9880	−	19.0317i	0.400424	−	0.693555i
$754$	0.715070	−	4.05537i	0.0260413	−	0.147688i
$755$	−11.4572	+	9.61376i	−0.416971	+	0.349881i
$756$	−2.20574	−	1.85083i	−0.0802219	−	0.0673142i
$757$	−3.68155	−	20.8791i	−0.133808	−	0.758864i	−0.975682	−	0.219190i	$-0.929659\pi$
$757$	−3.68155	−	20.8791i	−0.133808	−	0.758864i	0.841874	−	0.539674i	$-0.181453\pi$
$758$	28.8628	+	10.5052i	1.04834	+	0.381566i
$759$	−2.18748			−0.0794005
$760$	−2.40033	−	3.63846i	−0.0870691	−	0.131981i
$761$	−26.9632			−0.977414			−0.488707	−	0.872448i	$-0.662531\pi$
$761$	−26.9632			−0.977414			−0.488707	+	0.872448i	$0.662531\pi$
$762$	−3.77972	−	1.37570i	−0.136925	−	0.0498365i
$763$	5.45471	+	30.9352i	0.197474	+	1.11993i
$764$	−6.49067	−	5.44632i	−0.234824	−	0.197041i
$765$	1.08125	−	0.907278i	0.0390927	−	0.0328027i
$766$	−1.49882	+	8.50022i	−0.0541545	+	0.307125i
$767$	4.21419	−	7.29920i	0.152166	−	0.263559i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	18.4538	−	6.71664i	0.665462	−	0.242208i	0.0128693	−	0.999917i	$-0.495903\pi$
$769$	18.4538	−	6.71664i	0.665462	−	0.242208i	0.652593	+	0.757709i	$0.273681\pi$
$770$	11.6099	−	4.22567i	0.418393	−	0.152283i
$771$	3.97906	+	6.89193i	0.143302	+	0.248207i
$772$	−5.39306	+	9.34105i	−0.194100	+	0.336192i
$773$	−7.97549	+	45.2313i	−0.286858	+	1.62685i	0.411712	+	0.911314i	$0.364931\pi$
$773$	−7.97549	+	45.2313i	−0.286858	+	1.62685i	−0.698571	+	0.715541i	$0.746180\pi$
$774$	−7.60607	+	6.38225i	−0.273394	+	0.229405i
$775$	−5.05303	−	4.24000i	−0.181510	−	0.152305i
$776$	1.86824	+	10.5953i	0.0670659	+	0.380350i
$777$	−6.19846	−	2.25606i	−0.222369	−	0.0809356i
$778$	4.24804			0.152299
$779$	−9.96110	+	19.9033i	−0.356894	+	0.713111i
$780$	−1.18479			−0.0424224
$781$	26.8555	+	9.77460i	0.960965	+	0.349763i
$782$	−0.124952	−	0.708638i	−0.00446827	−	0.0253408i
$783$	−2.66250	−	2.23411i	−0.0951501	−	0.0798404i
$784$	0.988856	−	0.829748i	0.0353163	−	0.0296339i
$785$	−2.88191	+	16.3441i	−0.102860	+	0.583347i
$786$	5.18479	−	8.98032i	0.184935	−	0.320318i
$787$	−9.14425	−	15.8383i	−0.325957	−	0.564574i	0.655748	−	0.754979i	$-0.272353\pi$
$787$	−9.14425	−	15.8383i	−0.325957	−	0.564574i	−0.981706	+	0.190405i	$0.939020\pi$
$788$	20.1989	−	7.35181i	0.719557	−	0.261897i
$789$	2.89780	−	1.05471i	0.103165	−	0.0375488i
$790$	8.79813	+	15.2388i	0.313024	+	0.542173i
$791$	22.8726	−	39.6165i	0.813255	−	1.40860i
$792$	0.745100	−	4.22567i	0.0264760	−	0.150153i
$793$	−12.2483	+	10.2776i	−0.434951	+	0.364968i
$794$	21.8464	+	18.3313i	0.775300	+	0.650554i
$795$	−1.89646	−	10.7554i	−0.0672605	−	0.381453i
$796$	8.44609	+	3.07413i	0.299364	+	0.108959i
$797$	15.8108			0.560046			0.280023	−	0.959993i	$-0.409658\pi$
$797$	15.8108			0.560046			0.280023	+	0.959993i	$0.409658\pi$
$798$	2.91147	+	12.2086i	0.103065	+	0.432179i
$799$	−6.36547			−0.225194
$800$	0.939693	+	0.342020i	0.0332232	+	0.0120922i
$801$	−0.435822	−	2.47167i	−0.0153990	−	0.0873322i
$802$	−6.18732	−	5.19178i	−0.218482	−	0.183328i
$803$	−22.8967	+	19.2126i	−0.808006	+	0.677998i
$804$	−0.953363	+	5.40679i	−0.0336225	+	0.190683i
$805$	−0.733956	+	1.27125i	−0.0258685	+	0.0448056i
$806$	3.90760	+	6.76817i	0.137639	+	0.238399i
$807$	−5.93882	+	2.16155i	−0.209056	+	0.0760902i
$808$	−3.05051	+	1.11029i	−0.107316	+	0.0390600i
$809$	−13.6977	−	23.7252i	−0.481587	−	0.834133i	0.518190	−	0.855266i	$-0.326606\pi$
$809$	−13.6977	−	23.7252i	−0.481587	−	0.834133i	−0.999777	+	0.0211324i	$0.993273\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	−1.84735	+	10.4769i	−0.0648693	+	0.367892i	0.935042	+	0.354538i	$0.115362\pi$
$811$	−1.84735	+	10.4769i	−0.0648693	+	0.367892i	−0.999911	+	0.0133540i	$0.995749\pi$
$812$	7.66637	−	6.43285i	0.269037	−	0.225749i
$813$	22.5804	+	18.9472i	0.791928	+	0.664507i
$814$	−1.70692	−	9.68042i	−0.0598275	−	0.339299i
$815$	5.23308	+	1.90468i	0.183307	+	0.0667182i
$816$	1.41147			0.0494115
$817$	43.2028	−	2.57673i	1.51147	−	0.0901482i
$818$	−5.64765			−0.197465
$819$	3.20574	+	1.16679i	0.112018	+	0.0407710i
$820$	−0.886659	−	5.02849i	−0.0309635	−	0.175603i
$821$	−17.1793	−	14.4152i	−0.599563	−	0.503093i	0.291742	−	0.956497i	$-0.405765\pi$
$821$	−17.1793	−	14.4152i	−0.599563	−	0.503093i	−0.891305	+	0.453404i	$0.850209\pi$
$822$	4.80200	−	4.02936i	0.167489	−	0.140540i
$823$	−1.12345	+	6.37138i	−0.0391609	+	0.222092i	−0.998107	−	0.0614946i	$-0.980413\pi$
$823$	−1.12345	+	6.37138i	−0.0391609	+	0.222092i	0.958947	+	0.283587i	$0.0915244\pi$
$824$	2.63176	−	4.55834i	0.0916817	−	0.158797i
$825$	−2.14543	−	3.71599i	−0.0746943	−	0.129374i
$826$	19.2481	−	7.00573i	0.669727	−	0.243761i
$827$	−6.52094	+	2.37343i	−0.226755	+	0.0825322i	−0.452899	−	0.891562i	$-0.649610\pi$
$827$	−6.52094	+	2.37343i	−0.226755	+	0.0825322i	0.226144	+	0.974094i	$0.427388\pi$
$828$	0.254900	+	0.441500i	0.00885839	+	0.0153432i
$829$	1.68954	−	2.92637i	0.0586802	−	0.101637i	−0.835193	−	0.549957i	$-0.814644\pi$
$829$	1.68954	−	2.92637i	0.0586802	−	0.101637i	0.893873	+	0.448320i	$0.147977\pi$
$830$	0.354570	−	2.01087i	0.0123073	−	0.0697983i
$831$	−22.4761	+	18.8597i	−0.779688	+	0.654236i
$832$	−0.907604	−	0.761570i	−0.0314655	−	0.0264027i
$833$	−0.316390	−	1.79433i	−0.0109622	−	0.0621700i
$834$	−13.5842	−	4.94426i	−0.470384	−	0.171206i
$835$	15.2199			0.526705
$836$	−13.5865	+	12.8540i	−0.469898	+	0.444566i
$837$	6.59627			0.228000
$838$	−19.3148	−	7.03001i	−0.667219	−	0.242848i
$839$	−2.58693	−	14.6712i	−0.0893109	−	0.506507i	−0.996343	−	0.0854453i	$-0.972769\pi$
$839$	−2.58693	−	14.6712i	−0.0893109	−	0.506507i	0.907032	−	0.421062i	$-0.138342\pi$
$840$	−2.20574	−	1.85083i	−0.0761052	−	0.0638598i
$841$	−12.9614	+	10.8759i	−0.446943	+	0.375030i
$842$	−1.20873	+	6.85505i	−0.0416556	+	0.236241i
$843$	−7.63681	+	13.2273i	−0.263026	+	0.455574i
$844$	5.68866	+	9.85305i	0.195812	+	0.339156i
$845$	−10.8969	+	3.96616i	−0.374866	+	0.136440i
$846$	4.23783	−	1.54244i	0.145699	−	0.0530303i
$847$	−10.6702	−	18.4814i	−0.366634	−	0.635029i
$848$	5.46064	−	9.45810i	0.187519	−	0.324793i
$849$	−0.975185	+	5.53055i	−0.0334683	+	0.189808i
$850$	1.08125	−	0.907278i	0.0370866	−	0.0311194i
$851$	0.894648	+	0.750699i	0.0306682	+	0.0257336i
$852$	−1.15657	−	6.55926i	−0.0396236	−	0.224716i
$853$	1.30453	+	0.474810i	0.0446663	+	0.0162572i	0.364257	−	0.931299i	$-0.381323\pi$
$853$	1.30453	+	0.474810i	0.0446663	+	0.0162572i	−0.319590	+	0.947556i	$0.603545\pi$
$854$	−38.8580			−1.32969
$855$	4.00000	−	1.73205i	0.136797	−	0.0592349i
$856$	18.2986			0.625433
$857$	4.00165	+	1.45648i	0.136694	+	0.0497524i	0.409461	−	0.912328i	$-0.365717\pi$
$857$	4.00165	+	1.45648i	0.136694	+	0.0497524i	−0.272767	+	0.962080i	$0.587939\pi$
$858$	0.882789	+	5.00654i	0.0301379	+	0.170921i
$859$	14.8346	+	12.4477i	0.506149	+	0.424709i	0.859771	−	0.510679i	$-0.170606\pi$
$859$	14.8346	+	12.4477i	0.506149	+	0.424709i	−0.353623	+	0.935388i	$0.615050\pi$
$860$	−7.60607	+	6.38225i	−0.259365	+	0.217633i
$861$	−2.55303	+	14.4790i	−0.0870071	+	0.493442i
$862$	12.6040	−	21.8308i	0.429294	−	0.743559i
$863$	22.5030	+	38.9763i	0.766011	+	1.32677i	0.939711	+	0.341971i	$0.111094\pi$
$863$	22.5030	+	38.9763i	0.766011	+	1.32677i	−0.173700	+	0.984799i	$0.555572\pi$
$864$	−0.939693	+	0.342020i	−0.0319690	+	0.0116358i
$865$	9.01501	−	3.28120i	0.306520	−	0.111564i
$866$	−5.92855	−	10.2685i	−0.201460	−	0.348939i
$867$	−7.50387	+	12.9971i	−0.254845	+	0.441404i
$868$	−3.29813	+	18.7046i	−0.111946	+	0.634877i
$869$	57.8387	−	48.5325i	1.96204	−	1.64635i
$870$	−2.66250	−	2.23411i	−0.0902673	−	0.0757433i
$871$	−1.12954	−	6.40593i	−0.0382729	−	0.217057i
$872$	10.2515	+	3.73124i	0.347159	+	0.126356i
$873$	−10.7588			−0.364129
$874$	0.254900	−	2.20750i	0.00862212	−	0.0746698i
$875$	−2.87939			−0.0973410
$876$	6.54576	+	2.38246i	0.221161	+	0.0804959i
$877$	5.64930	+	32.0388i	0.190763	+	1.08187i	0.918324	+	0.395829i	$0.129543\pi$
$877$	5.64930	+	32.0388i	0.190763	+	1.08187i	−0.727561	+	0.686043i	$0.759346\pi$
$878$	13.5437	+	11.3645i	0.457078	+	0.383534i
$879$	6.01889	−	5.05044i	0.203012	−	0.170347i
$880$	0.745100	−	4.22567i	0.0251173	−	0.142447i
$881$	−22.6634	+	39.2542i	−0.763551	+	1.32251i	0.177459	+	0.984128i	$0.443212\pi$
$881$	−22.6634	+	39.2542i	−0.763551	+	1.32251i	−0.941009	+	0.338380i	$0.890121\pi$
$882$	0.645430	+	1.11792i	0.0217327	+	0.0376422i
$883$	31.7254	−	11.5471i	1.06764	−	0.388591i	0.252349	−	0.967636i	$-0.418797\pi$
$883$	31.7254	−	11.5471i	1.06764	−	0.388591i	0.815295	+	0.579045i	$0.196575\pi$
$884$	−1.57145	+	0.571962i	−0.0528536	+	0.0192372i
$885$	−3.55690	−	6.16074i	−0.119564	−	0.207091i
$886$	9.67024	−	16.7494i	0.324878	−	0.562706i
$887$	−7.71982	+	43.7813i	−0.259206	+	1.47003i	0.525835	+	0.850587i	$0.323753\pi$
$887$	−7.71982	+	43.7813i	−0.259206	+	1.47003i	−0.785041	+	0.619444i	$0.787358\pi$
$888$	−1.75490	+	1.47254i	−0.0588906	+	0.0494151i
$889$	8.87211	+	7.44459i	0.297561	+	0.249683i
$890$	−0.435822	−	2.47167i	−0.0146088	−	0.0828506i
$891$	4.03209	+	1.46756i	0.135080	+	0.0491651i
$892$	7.99319			0.267632
$893$	−18.8398	−	5.61165i	−0.630449	−	0.187787i
$894$	4.68004			0.156524
$895$	−19.0351	−	6.92820i	−0.636273	−	0.231584i
$896$	−0.500000	−	2.83564i	−0.0167038	−	0.0947321i
$897$	−0.462697	−	0.388249i	−0.0154490	−	0.0129632i
$898$	21.3045	−	17.8766i	0.710941	−	0.596551i
$899$	−3.98111	+	22.5780i	−0.132778	+	0.753019i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−7.70755	−	13.3499i	−0.256776	−	0.444748i
$902$	−20.5881	+	7.49346i	−0.685509	+	0.249505i
$903$	26.8653	−	9.77817i	0.894021	−	0.325397i
$904$	−7.94356	−	13.7587i	−0.264199	−	0.457606i
$905$	−2.69846	+	4.67388i	−0.0896999	+	0.155365i
$906$	2.59714	−	14.7291i	0.0862843	−	0.489343i
$907$	34.2861	−	28.7695i	1.13845	−	0.955274i	0.139065	−	0.990283i	$-0.455590\pi$
$907$	34.2861	−	28.7695i	1.13845	−	0.955274i	0.999387	+	0.0350089i	$0.0111460\pi$
$908$	5.05303	+	4.24000i	0.167691	+	0.140709i
$909$	−0.563711	−	3.19696i	−0.0186971	−	0.106037i
$910$	3.20574	+	1.16679i	0.106269	+	0.0386788i
$911$	−48.7015			−1.61355			−0.806777	−	0.590857i	$-0.798790\pi$
$911$	−48.7015			−1.61355			−0.806777	+	0.590857i	$0.798790\pi$
$912$	4.17752	+	1.24432i	0.138331	+	0.0412036i
$913$	−8.76146			−0.289962
$914$	−19.7015	−	7.17074i	−0.651666	−	0.237187i
$915$	2.34343	+	13.2902i	0.0774713	+	0.439361i
$916$	−11.8387	−	9.93383i	−0.391161	−	0.328223i
$917$	−22.8726	+	19.1924i	−0.755319	+	0.633788i
$918$	−0.245100	+	1.39003i	−0.00808950	+	0.0458778i
$919$	−13.2208	+	22.8990i	−0.436112	+	0.755369i	−0.997386	−	0.0722617i	$-0.976978\pi$
$919$	−13.2208	+	22.8990i	−0.436112	+	0.755369i	0.561273	+	0.827630i	$0.310312\pi$
$920$	0.254900	+	0.441500i	0.00840381	+	0.0145558i
$921$	20.5856	−	7.49254i	0.678318	−	0.246888i
$922$	−0.992726	+	0.361323i	−0.0326937	+	0.0118995i
$923$	3.94562	+	6.83402i	0.129872	+	0.224944i
$924$	−6.17752	+	10.6998i	−0.203225	+	0.351997i
$925$	−0.397804	+	2.25606i	−0.0130797	+	0.0741787i
$926$	−25.4065	+	21.3186i	−0.834909	+	0.700572i
$927$	4.03209	+	3.38332i	0.132431	+	0.111123i
$928$	−0.603541	−	3.42285i	−0.0198122	−	0.112361i
$929$	−29.9206	−	10.8902i	−0.981662	−	0.357296i	−0.199176	−	0.979964i	$-0.563826\pi$
$929$	−29.9206	−	10.8902i	−0.981662	−	0.357296i	−0.782486	+	0.622668i	$0.786049\pi$
$930$	6.59627			0.216300
$931$	0.645430	−	5.58959i	0.0211531	−	0.183191i
$932$	−9.92633			−0.325148
$933$	6.99747	+	2.54687i	0.229087	+	0.0833809i
$934$	−0.340185	−	1.92928i	−0.0111312	−	0.0631280i
$935$	−4.63950	−	3.89300i	−0.151728	−	0.127315i
$936$	0.907604	−	0.761570i	0.0296660	−	0.0248927i
$937$	−8.08749	+	45.8664i	−0.264207	+	1.49839i	0.507078	+	0.861900i	$0.330726\pi$
$937$	−8.08749	+	45.8664i	−0.264207	+	1.49839i	−0.771285	+	0.636490i	$0.780386\pi$
$938$	7.90420	−	13.6905i	0.258081	−	0.447010i
$939$	7.90033	+	13.6838i	0.257818	+	0.446553i
$940$	4.23783	−	1.54244i	0.138223	−	0.0503089i
$941$	27.3221	−	9.94442i	0.890674	−	0.324179i	0.144165	−	0.989554i	$-0.453951\pi$
$941$	27.3221	−	9.94442i	0.890674	−	0.324179i	0.746509	+	0.665375i	$0.231728\pi$
$942$	−8.29813	−	14.3728i	−0.270368	−	0.468291i
$943$	1.30154	−	2.25433i	0.0423839	−	0.0734110i
$944$	1.23530	−	7.00573i	0.0402056	−	0.228017i
$945$	2.20574	−	1.85083i	0.0717526	−	0.0602076i
$946$	32.6366	+	27.3853i	1.06111	+	0.890374i
$947$	4.60472	+	26.1147i	0.149633	+	0.848613i	0.963529	+	0.267603i	$0.0862314\pi$
$947$	4.60472	+	26.1147i	0.149633	+	0.848613i	−0.813896	+	0.581011i	$0.802657\pi$
$948$	−16.5351	−	6.01828i	−0.537034	−	0.195465i
$949$	−8.25309			−0.267907
$950$	4.00000	−	1.73205i	0.129777	−	0.0561951i
$951$	15.0368			0.487603
$952$	−3.81908	−	1.39003i	−0.123777	−	0.0450512i
$953$	−6.25150	−	35.4540i	−0.202506	−	1.14847i	−0.901317	−	0.433161i	$-0.857398\pi$
$953$	−6.25150	−	35.4540i	−0.202506	−	1.14847i	0.698811	−	0.715307i	$-0.253713\pi$
$954$	8.36618	+	7.02006i	0.270865	+	0.227283i
$955$	6.49067	−	5.44632i	0.210033	−	0.176239i
$956$	−2.77126	+	15.7166i	−0.0896289	+	0.508311i
$957$	−7.45677	+	12.9155i	−0.241043	+	0.417499i
$958$	−9.67546	−	16.7584i	−0.312600	−	0.541439i
$959$	−16.9611	+	6.17334i	−0.547703	+	0.199347i
$960$	−0.939693	+	0.342020i	−0.0303284	+	0.0110387i
$961$	−6.25537	−	10.8346i	−0.201786	−	0.349504i
$962$	1.35710	−	2.35056i	0.0437545	−	0.0757851i
$963$	−3.17752	+	18.0206i	−0.102394	+	0.580706i
$964$	−11.1814	+	9.38230i	−0.360128	+	0.302184i
$965$	−8.26264	−	6.93318i	−0.265984	−	0.223187i
$966$	−0.254900	−	1.44561i	−0.00820128	−	0.0465117i
$967$	54.6306	+	19.8839i	1.75680	+	0.639424i	0.999901	−	0.0141043i	$-0.00448967\pi$
$967$	54.6306	+	19.8839i	1.75680	+	0.639424i	0.756902	+	0.653528i	$0.226712\pi$
$968$	−7.41147			−0.238214
$969$	4.46926	−	4.22832i	0.143573	−	0.135833i
$970$	−10.7588			−0.345443
$971$	3.33022	+	1.21210i	0.106872	+	0.0388982i	0.394903	−	0.918723i	$-0.370778\pi$
$971$	3.33022	+	1.21210i	0.106872	+	0.0388982i	−0.288031	+	0.957621i	$0.593001\pi$
$972$	−0.173648	−	0.984808i	−0.00556977	−	0.0315877i
$973$	31.8862	+	26.7557i	1.02223	+	0.857750i
$974$	12.6925	−	10.6503i	0.406695	−	0.341258i
$975$	0.205737	−	1.16679i	0.00658886	−	0.0373673i
$976$	−6.74763	+	11.6872i	−0.215986	+	0.374099i
$977$	0.791326	+	1.37062i	0.0253168	+	0.0438499i	0.878406	−	0.477915i	$-0.158607\pi$
$977$	0.791326	+	1.37062i	0.0253168	+	0.0438499i	−0.853089	+	0.521765i	$0.825274\pi$
$978$	−5.23308	+	1.90468i	−0.167335	+	0.0609051i
$979$	−10.1197	+	3.68328i	−0.323428	+	0.117718i
$980$	0.645430	+	1.11792i	0.0206175	+	0.0357105i
$981$	−5.45471	+	9.44783i	−0.174155	+	0.301646i
$982$	4.96626	−	28.1651i	0.158480	−	0.898784i
$983$	−3.27016	+	2.74399i	−0.104302	+	0.0875198i	−0.693447	−	0.720507i	$-0.743909\pi$
$983$	−3.27016	+	2.74399i	−0.104302	+	0.0875198i	0.589145	+	0.808027i	$0.299465\pi$
$984$	3.91147	+	3.28212i	0.124693	+	0.104630i
$985$	3.73261	+	21.1687i	0.118931	+	0.674491i
$986$	−4.60994	−	1.67788i	−0.146810	−	0.0534346i
$987$	−12.9855			−0.413331
$988$	−5.15523	+	0.307471i	−0.164010	+	0.00978196i
$989$	−5.06181			−0.160956
$990$	4.03209	+	1.46756i	0.128148	+	0.0466421i
$991$	6.37851	+	36.1743i	0.202620	+	1.14912i	0.901141	+	0.433526i	$0.142731\pi$
$991$	6.37851	+	36.1743i	0.202620	+	1.14912i	−0.698521	+	0.715589i	$0.746158\pi$
$992$	5.05303	+	4.24000i	0.160434	+	0.134620i
$993$	−7.71167	+	6.47086i	−0.244722	+	0.205346i
$994$	−3.33022	+	18.8866i	−0.105628	+	0.599047i
$995$	−4.49407	+	7.78396i	−0.142472	+	0.246768i
$996$	1.02094	+	1.76833i	0.0323499	+	0.0560316i
$997$	−16.0865	+	5.85499i	−0.509464	+	0.185430i	−0.583946	−	0.811793i	$-0.698492\pi$
$997$	−16.0865	+	5.85499i	−0.509464	+	0.185430i	0.0744821	+	0.997222i	$0.476270\pi$
$998$	−30.8184	+	11.2170i	−0.975538	+	0.355067i
$999$	−1.14543	−	1.98394i	−0.0362398	−	0.0627692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.d.61.1	✓	6
19.5	even	9	inner	570.2.u.d.271.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.d.61.1	✓	6	1.1	even	1	trivial
570.2.u.d.271.1	yes	6	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)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-0.766044 + 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(-1.43969 + 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(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} +(-1.43969 + 2.49362i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(2.14543 + 3.71599i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-0.205737 + 1.16679i) q^{13} +(-2.20574 + 1.85083i) q^{14} +(0.766044 + 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(1.32635 + 0.482753i) q^{17} -1.00000 q^{18} +(3.50000 + 2.59808i) q^{19} -1.00000 q^{20} +(2.70574 + 0.984808i) q^{21} +(0.745100 + 4.22567i) q^{22} +(-0.390530 - 0.327693i) q^{23} +(0.766044 - 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-0.592396 + 1.02606i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-2.70574 + 0.984808i) q^{28} +(-3.26604 + 1.18874i) q^{29} +(0.500000 + 0.866025i) q^{30} +(3.29813 - 5.71253i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(3.28699 - 2.75811i) q^{33} +(1.08125 + 0.907278i) q^{34} +(-0.500000 - 2.83564i) q^{35} +(-0.939693 - 0.342020i) q^{36} -2.29086 q^{37} +(2.40033 + 3.63846i) q^{38} +1.18479 q^{39} +(-0.939693 - 0.342020i) q^{40} +(0.886659 + 5.02849i) q^{41} +(2.20574 + 1.85083i) q^{42} +(7.60607 - 6.38225i) q^{43} +(-0.745100 + 4.22567i) q^{44} +(0.500000 - 0.866025i) q^{45} +(-0.254900 - 0.441500i) q^{46} +(-4.23783 + 1.54244i) q^{47} +(0.939693 - 0.342020i) q^{48} +(-0.645430 - 1.11792i) q^{49} +(0.500000 - 0.866025i) q^{50} +(0.245100 - 1.39003i) q^{51} +(-0.907604 + 0.761570i) q^{52} +(-8.36618 - 7.02006i) q^{53} +(0.173648 + 0.984808i) q^{54} +(-4.03209 - 1.46756i) q^{55} -2.87939 q^{56} +(1.95084 - 3.89798i) q^{57} -3.47565 q^{58} +(-6.68479 - 2.43307i) q^{59} +(0.173648 + 0.984808i) q^{60} +(10.3380 + 8.67458i) q^{61} +(5.05303 - 4.24000i) q^{62} +(0.500000 - 2.83564i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.592396 - 1.02606i) q^{65} +(4.03209 - 1.46756i) q^{66} +(-5.15910 + 1.87776i) q^{67} +(0.705737 + 1.22237i) q^{68} +(-0.254900 + 0.441500i) q^{69} +(0.500000 - 2.83564i) q^{70} +(5.10220 - 4.28125i) q^{71} +(-0.766044 - 0.642788i) q^{72} +(1.20961 + 6.86002i) q^{73} +(-2.15270 - 0.783520i) q^{74} -1.00000 q^{75} +(1.01114 + 4.24000i) q^{76} -12.3550 q^{77} +(1.11334 + 0.405223i) q^{78} +(-3.05556 - 17.3289i) q^{79} +(-0.766044 - 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-0.886659 + 5.02849i) q^{82} +(-1.02094 + 1.76833i) q^{83} +(1.43969 + 2.49362i) q^{84} +(-1.32635 + 0.482753i) q^{85} +(9.33022 - 3.39592i) q^{86} +(1.73783 + 3.01000i) q^{87} +(-2.14543 + 3.71599i) q^{88} +(-0.435822 + 2.47167i) q^{89} +(0.766044 - 0.642788i) q^{90} +(-2.61334 - 2.19285i) q^{91} +(-0.0885259 - 0.502055i) q^{92} +(-6.19846 - 2.25606i) q^{93} -4.50980 q^{94} +(-4.35117 + 0.259515i) q^{95} +1.00000 q^{96} +(10.1099 + 3.67972i) q^{97} +(-0.224155 - 1.27125i) q^{98} +(-3.28699 - 2.75811i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 3 * q^7 + 3 * q^8	\( 6 q - 3 q^{7} + 3 q^{8} - 3 q^{11} + 3 q^{12} + 9 q^{13} - 3 q^{14} + 9 q^{17} - 6 q^{18} + 21 q^{19} - 6 q^{20} + 6 q^{21} + 3 q^{22} + 15 q^{23} + 3 q^{27} - 6 q^{28} - 15 q^{29} + 3 q^{30} + 6 q^{31} + 12 q^{33} + 9 q^{34} - 3 q^{35} + 18 q^{37} + 12 q^{41} + 3 q^{42} + 21 q^{43} - 3 q^{44} + 3 q^{45} - 3 q^{46} - 6 q^{47} + 12 q^{49} + 3 q^{50} - 9 q^{52} + 6 q^{53} - 15 q^{55} - 6 q^{56} + 18 q^{58} - 33 q^{59} - 9 q^{61} + 18 q^{62} + 3 q^{63} - 3 q^{64} + 15 q^{66} + 6 q^{67} - 6 q^{68} - 3 q^{69} + 3 q^{70} + 30 q^{71} - 27 q^{73} - 15 q^{74} - 6 q^{75} - 24 q^{77} + 9 q^{79} - 12 q^{82} - 3 q^{83} + 3 q^{84} - 9 q^{85} + 33 q^{86} - 9 q^{87} + 3 q^{88} - 21 q^{89} - 9 q^{91} - 21 q^{92} - 9 q^{93} - 30 q^{94} + 6 q^{96} + 12 q^{97} - 3 q^{98} - 12 q^{99}+O(q^{100}) \) 6 * q - 3 * q^7 + 3 * q^8 - 3 * q^11 + 3 * q^12 + 9 * q^13 - 3 * q^14 + 9 * q^17 - 6 * q^18 + 21 * q^19 - 6 * q^20 + 6 * q^21 + 3 * q^22 + 15 * q^23 + 3 * q^27 - 6 * q^28 - 15 * q^29 + 3 * q^30 + 6 * q^31 + 12 * q^33 + 9 * q^34 - 3 * q^35 + 18 * q^37 + 12 * q^41 + 3 * q^42 + 21 * q^43 - 3 * q^44 + 3 * q^45 - 3 * q^46 - 6 * q^47 + 12 * q^49 + 3 * q^50 - 9 * q^52 + 6 * q^53 - 15 * q^55 - 6 * q^56 + 18 * q^58 - 33 * q^59 - 9 * q^61 + 18 * q^62 + 3 * q^63 - 3 * q^64 + 15 * q^66 + 6 * q^67 - 6 * q^68 - 3 * q^69 + 3 * q^70 + 30 * q^71 - 27 * q^73 - 15 * q^74 - 6 * q^75 - 24 * q^77 + 9 * q^79 - 12 * q^82 - 3 * q^83 + 3 * q^84 - 9 * q^85 + 33 * q^86 - 9 * q^87 + 3 * q^88 - 21 * q^89 - 9 * q^91 - 21 * q^92 - 9 * q^93 - 30 * q^94 + 6 * q^96 + 12 * q^97 - 3 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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