LMFDB - Embedded newform 570.2.u.i.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} + 24x^{10} + 216x^{8} + 905x^{6} + 1770x^{4} + 1395x^{2} + 361 $ x^12 + 24x^10 + 216x^8 + 905x^6 + 1770x^4 + 1395*x^2 + 361
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			$2.88811i$ of defining polynomial
Character	$\chi$	$=$	570.61
Dual form			570.2.u.i.271.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.939693 - 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(0.487791 - 0.844879i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(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} +(0.487791 - 0.844879i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(-1.31414 - 2.27616i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.09464 - 6.20799i) q^{13} +(-0.747339 + 0.627092i) q^{14} +(0.766044 + 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.43463 - 0.886131i) q^{17} +1.00000 q^{18} +(4.21986 - 1.09216i) q^{19} +1.00000 q^{20} +(0.916747 + 0.333669i) q^{21} +(0.456397 + 2.58836i) q^{22} +(0.535155 + 0.449048i) q^{23} +(0.766044 - 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-3.15188 + 5.45921i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(0.916747 - 0.333669i) q^{28} +(-0.522946 + 0.190337i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-2.09664 + 3.63148i) q^{31} +(0.173648 - 0.984808i) q^{32} +(2.01338 - 1.68943i) q^{33} +(1.98473 + 1.66538i) q^{34} +(-0.169408 - 0.960761i) q^{35} +(-0.939693 - 0.342020i) q^{36} +4.66169 q^{37} +(-4.33891 - 0.416977i) q^{38} +6.30375 q^{39} +(-0.939693 - 0.342020i) q^{40} +(-0.676824 - 3.83846i) q^{41} +(-0.747339 - 0.627092i) q^{42} +(6.60945 - 5.54599i) q^{43} +(0.456397 - 2.58836i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-0.349297 - 0.605001i) q^{46} +(5.19270 - 1.88999i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(3.02412 + 5.23793i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.449901 - 2.55151i) q^{51} +(4.82896 - 4.05198i) q^{52} +(-9.11468 - 7.64812i) q^{53} +(0.173648 + 0.984808i) q^{54} +(-2.46978 - 0.898927i) q^{55} -0.975582 q^{56} +(1.80834 + 3.96609i) q^{57} +0.556507 q^{58} +(3.56715 + 1.29834i) q^{59} +(0.173648 + 0.984808i) q^{60} +(5.76791 + 4.83985i) q^{61} +(3.21223 - 2.69538i) q^{62} +(-0.169408 + 0.960761i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-3.15188 - 5.45921i) q^{65} +(-2.46978 + 0.898927i) q^{66} +(2.53054 - 0.921040i) q^{67} +(-1.29544 - 2.24376i) q^{68} +(-0.349297 + 0.605001i) q^{69} +(-0.169408 + 0.960761i) q^{70} +(-2.57286 + 2.15889i) q^{71} +(0.766044 + 0.642788i) q^{72} +(-2.04255 - 11.5839i) q^{73} +(-4.38056 - 1.59439i) q^{74} +1.00000 q^{75} +(3.93463 + 1.87582i) q^{76} -2.56411 q^{77} +(-5.92359 - 2.15601i) q^{78} +(1.24146 + 7.04067i) q^{79} +(0.766044 + 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-0.676824 + 3.83846i) q^{82} +(4.16612 - 7.21593i) q^{83} +(0.487791 + 0.844879i) q^{84} +(-2.43463 + 0.886131i) q^{85} +(-8.10769 + 2.95096i) q^{86} +(-0.278253 - 0.481949i) q^{87} +(-1.31414 + 2.27616i) q^{88} +(-1.26869 + 7.19511i) q^{89} +(0.766044 - 0.642788i) q^{90} +(-4.71104 - 3.95303i) q^{91} +(0.121310 + 0.687981i) q^{92} +(-3.94039 - 1.43418i) q^{93} -5.52596 q^{94} +(2.53057 - 3.54912i) q^{95} +1.00000 q^{96} +(-14.0819 - 5.12540i) q^{97} +(-1.05027 - 5.95635i) q^{98} +(2.01338 + 1.68943i) 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} - 9 q^{11} - 6 q^{12} - 3 q^{13} + 3 q^{14} + 9 q^{17} + 12 q^{18} - 3 q^{19} + 12 q^{20} + 3 q^{21} - 6 q^{22} + 12 q^{23} - 9 q^{26} - 6 q^{27} + 3 q^{28} - 3 q^{29} - 6 q^{30} - 12 q^{31} + 3 q^{33} - 9 q^{34} - 6 q^{35} + 42 q^{37} + 18 q^{39} + 21 q^{41} + 3 q^{42} + 9 q^{43} - 6 q^{44} - 6 q^{45} - 3 q^{46} + 3 q^{49} - 6 q^{50} - 3 q^{52} - 18 q^{53} + 3 q^{55} + 6 q^{56} + 6 q^{58} - 15 q^{59} + 9 q^{61} + 12 q^{62} - 6 q^{63} - 6 q^{64} - 9 q^{65} + 3 q^{66} + 18 q^{67} - 6 q^{68} - 3 q^{69} - 6 q^{70} + 12 q^{71} - 9 q^{73} + 12 q^{75} + 9 q^{76} - 54 q^{77} + 6 q^{78} - 9 q^{79} + 21 q^{82} + 15 q^{83} - 3 q^{84} + 9 q^{85} - 27 q^{86} - 3 q^{87} - 9 q^{88} + 3 q^{89} - 51 q^{91} + 3 q^{92} - 15 q^{93} + 12 q^{96} - 48 q^{97} - 15 q^{98} + 3 q^{99}+O(q^{100}) $ 12 * q - 3 * q^7 - 6 * q^8 - 9 * q^11 - 6 * q^12 - 3 * q^13 + 3 * q^14 + 9 * q^17 + 12 * q^18 - 3 * q^19 + 12 * q^20 + 3 * q^21 - 6 * q^22 + 12 * q^23 - 9 * q^26 - 6 * q^27 + 3 * q^28 - 3 * q^29 - 6 * q^30 - 12 * q^31 + 3 * q^33 - 9 * q^34 - 6 * q^35 + 42 * q^37 + 18 * q^39 + 21 * q^41 + 3 * q^42 + 9 * q^43 - 6 * q^44 - 6 * q^45 - 3 * q^46 + 3 * q^49 - 6 * q^50 - 3 * q^52 - 18 * q^53 + 3 * q^55 + 6 * q^56 + 6 * q^58 - 15 * q^59 + 9 * q^61 + 12 * q^62 - 6 * q^63 - 6 * q^64 - 9 * q^65 + 3 * q^66 + 18 * q^67 - 6 * q^68 - 3 * q^69 - 6 * q^70 + 12 * q^71 - 9 * q^73 + 12 * q^75 + 9 * q^76 - 54 * q^77 + 6 * q^78 - 9 * q^79 + 21 * q^82 + 15 * q^83 - 3 * q^84 + 9 * q^85 - 27 * q^86 - 3 * q^87 - 9 * q^88 + 3 * q^89 - 51 * q^91 + 3 * q^92 - 15 * q^93 + 12 * q^96 - 48 * 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
$7$	0.487791	−	0.844879i	0.184368	−	0.319334i	−0.758996	−	0.651096i	$-0.774310\pi$
$7$	0.487791	−	0.844879i	0.184368	−	0.319334i	0.943363	+	0.331762i	$0.107643\pi$
$8$	−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
$11$	−1.31414	−	2.27616i	−0.396229	−	0.686289i	0.597028	−	0.802220i	$-0.296348\pi$
$11$	−1.31414	−	2.27616i	−0.396229	−	0.686289i	−0.993257	+	0.115932i	$0.963015\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	1.09464	−	6.20799i	0.303597	−	1.72179i	−0.326438	−	0.945219i	$-0.605848\pi$
$13$	1.09464	−	6.20799i	0.303597	−	1.72179i	0.630035	−	0.776567i	$-0.283041\pi$
$14$	−0.747339	+	0.627092i	−0.199735	+	0.167597i
$15$	0.766044	+	0.642788i	0.197792	+	0.165967i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	−2.43463	−	0.886131i	−0.590484	−	0.214918i	0.0294586	−	0.999566i	$-0.490622\pi$
$17$	−2.43463	−	0.886131i	−0.590484	−	0.214918i	−0.619942	+	0.784648i	$0.712844\pi$
$18$	1.00000			0.235702
$19$	4.21986	−	1.09216i	0.968101	−	0.250560i
$19$	4.21986	−	1.09216i	0.968101	−	0.250560i
$20$	1.00000			0.223607
$21$	0.916747	+	0.333669i	0.200051	+	0.0728125i
$22$	0.456397	+	2.58836i	0.0973042	+	0.551839i
$23$	0.535155	+	0.449048i	0.111587	+	0.0936330i	0.696874	−	0.717193i	$-0.254574\pi$
$23$	0.535155	+	0.449048i	0.111587	+	0.0936330i	−0.585287	+	0.810826i	$0.699018\pi$
$24$	0.766044	−	0.642788i	0.156368	−	0.131208i
$25$	0.173648	−	0.984808i	0.0347296	−	0.196962i
$26$	−3.15188	+	5.45921i	−0.618134	+	1.07064i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	0.916747	−	0.333669i	0.173249	−	0.0630574i
$29$	−0.522946	+	0.190337i	−0.0971085	+	0.0353446i	−0.390118	−	0.920765i	$-0.627566\pi$
$29$	−0.522946	+	0.190337i	−0.0971085	+	0.0353446i	0.293009	+	0.956110i	$0.405343\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−2.09664	+	3.63148i	−0.376567	+	0.652233i	−0.990560	−	0.137078i	$-0.956229\pi$
$31$	−2.09664	+	3.63148i	−0.376567	+	0.652233i	0.613993	+	0.789311i	$0.289562\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$	2.01338	−	1.68943i	0.350485	−	0.294092i
$34$	1.98473	+	1.66538i	0.340378	+	0.285611i
$35$	−0.169408	−	0.960761i	−0.0286352	−	0.162398i
$36$	−0.939693	−	0.342020i	−0.156615	−	0.0570034i
$37$	4.66169			0.766378			0.383189	−	0.923670i	$-0.374826\pi$
$37$	4.66169			0.766378			0.383189	+	0.923670i	$0.374826\pi$
$38$	−4.33891	−	0.416977i	−0.703864	−	0.0676427i
$39$	6.30375			1.00941
$40$	−0.939693	−	0.342020i	−0.148578	−	0.0540781i
$41$	−0.676824	−	3.83846i	−0.105702	−	0.599466i	−0.990938	−	0.134323i	$-0.957114\pi$
$41$	−0.676824	−	3.83846i	−0.105702	−	0.599466i	0.885235	−	0.465143i	$-0.153997\pi$
$42$	−0.747339	−	0.627092i	−0.115317	−	0.0967624i
$43$	6.60945	−	5.54599i	1.00793	−	0.845755i	0.0198680	−	0.999803i	$-0.493675\pi$
$43$	6.60945	−	5.54599i	1.00793	−	0.845755i	0.988063	+	0.154048i	$0.0492309\pi$
$44$	0.456397	−	2.58836i	0.0688044	−	0.390209i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−0.349297	−	0.605001i	−0.0515011	−	0.0892025i
$47$	5.19270	−	1.88999i	0.757433	−	0.275683i	0.0657031	−	0.997839i	$-0.479071\pi$
$47$	5.19270	−	1.88999i	0.757433	−	0.275683i	0.691730	+	0.722156i	$0.256849\pi$
$48$	−0.939693	+	0.342020i	−0.135633	+	0.0493664i
$49$	3.02412	+	5.23793i	0.432017	+	0.748276i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	0.449901	−	2.55151i	0.0629987	−	0.357283i
$52$	4.82896	−	4.05198i	0.669656	−	0.561908i
$53$	−9.11468	−	7.64812i	−1.25200	−	1.05055i	−0.996487	−	0.0837442i	$-0.973312\pi$
$53$	−9.11468	−	7.64812i	−1.25200	−	1.05055i	−0.255510	−	0.966806i	$-0.582243\pi$
$54$	0.173648	+	0.984808i	0.0236305	+	0.134015i
$55$	−2.46978	−	0.898927i	−0.333025	−	0.121211i
$56$	−0.975582			−0.130368
$57$	1.80834	+	3.96609i	0.239521	+	0.525322i
$58$	0.556507			0.0730729
$59$	3.56715	+	1.29834i	0.464404	+	0.169029i	0.563616	−	0.826037i	$-0.309410\pi$
$59$	3.56715	+	1.29834i	0.464404	+	0.169029i	−0.0992120	+	0.995066i	$0.531632\pi$
$60$	0.173648	+	0.984808i	0.0224179	+	0.127138i
$61$	5.76791	+	4.83985i	0.738506	+	0.619680i	0.932436	−	0.361335i	$-0.117679\pi$
$61$	5.76791	+	4.83985i	0.738506	+	0.619680i	−0.193930	+	0.981015i	$0.562124\pi$
$62$	3.21223	−	2.69538i	0.407954	−	0.342314i
$63$	−0.169408	+	0.960761i	−0.0213434	+	0.121044i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−3.15188	−	5.45921i	−0.390942	−	0.677132i
$66$	−2.46978	+	0.898927i	−0.304009	+	0.110650i
$67$	2.53054	−	0.921040i	0.309154	−	0.112523i	−0.182784	−	0.983153i	$-0.558511\pi$
$67$	2.53054	−	0.921040i	0.309154	−	0.112523i	0.491938	+	0.870630i	$0.336289\pi$
$68$	−1.29544	−	2.24376i	−0.157095	−	0.272096i
$69$	−0.349297	+	0.605001i	−0.0420505	+	0.0728335i
$70$	−0.169408	+	0.960761i	−0.0202481	+	0.114833i
$71$	−2.57286	+	2.15889i	−0.305343	+	0.256213i	−0.782564	−	0.622570i	$-0.786089\pi$
$71$	−2.57286	+	2.15889i	−0.305343	+	0.256213i	0.477221	+	0.878783i	$0.341644\pi$
$72$	0.766044	+	0.642788i	0.0902792	+	0.0757532i
$73$	−2.04255	−	11.5839i	−0.239063	−	1.35579i	−0.833887	−	0.551936i	$-0.813889\pi$
$73$	−2.04255	−	11.5839i	−0.239063	−	1.35579i	0.594824	−	0.803856i	$-0.297222\pi$
$74$	−4.38056	−	1.59439i	−0.509230	−	0.185344i
$75$	1.00000			0.115470
$76$	3.93463	+	1.87582i	0.451333	+	0.215172i
$77$	−2.56411			−0.292207
$78$	−5.92359	−	2.15601i	−0.670715	−	0.244120i
$79$	1.24146	+	7.04067i	0.139675	+	0.792137i	0.971489	+	0.237083i	$0.0761913\pi$
$79$	1.24146	+	7.04067i	0.139675	+	0.792137i	−0.831814	+	0.555054i	$0.812698\pi$
$80$	0.766044	+	0.642788i	0.0856464	+	0.0718658i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−0.676824	+	3.83846i	−0.0747427	+	0.423887i
$83$	4.16612	−	7.21593i	0.457291	−	0.792051i	−0.541526	−	0.840684i	$-0.682153\pi$
$83$	4.16612	−	7.21593i	0.457291	−	0.792051i	0.998817	+	0.0486330i	$0.0154865\pi$
$84$	0.487791	+	0.844879i	0.0532224	+	0.0921838i
$85$	−2.43463	+	0.886131i	−0.264072	+	0.0961144i
$86$	−8.10769	+	2.95096i	−0.874275	+	0.318210i
$87$	−0.278253	−	0.481949i	−0.0298319	−	0.0516704i
$88$	−1.31414	+	2.27616i	−0.140088	+	0.242640i
$89$	−1.26869	+	7.19511i	−0.134481	+	0.762680i	0.840739	+	0.541441i	$0.182121\pi$
$89$	−1.26869	+	7.19511i	−0.134481	+	0.762680i	−0.975220	+	0.221239i	$0.928990\pi$
$90$	0.766044	−	0.642788i	0.0807482	−	0.0677558i
$91$	−4.71104	−	3.95303i	−0.493851	−	0.414391i
$92$	0.121310	+	0.687981i	0.0126474	+	0.0717270i
$93$	−3.94039	−	1.43418i	−0.408599	−	0.148718i
$94$	−5.52596			−0.569959
$95$	2.53057	−	3.54912i	0.259631	−	0.364132i
$96$	1.00000			0.102062
$97$	−14.0819	−	5.12540i	−1.42980	−	0.520406i	−0.492928	−	0.870070i	$-0.664073\pi$
$97$	−14.0819	−	5.12540i	−1.42980	−	0.520406i	−0.936875	+	0.349664i	$0.886296\pi$
$98$	−1.05027	−	5.95635i	−0.106093	−	0.601683i
$99$	2.01338	+	1.68943i	0.202353	+	0.169794i
$100$	0.766044	−	0.642788i	0.0766044	−	0.0642788i
$101$	−0.146719	+	0.832083i	−0.0145991	+	0.0827954i	−0.991237	−	0.132097i	$-0.957829\pi$
$101$	−0.146719	+	0.832083i	−0.0145991	+	0.0827954i	0.976638	+	0.214892i	$0.0689401\pi$
$102$	−1.29544	+	2.24376i	−0.128267	+	0.222166i
$103$	3.42192	+	5.92695i	0.337172	+	0.583999i	0.983900	−	0.178722i	$-0.0571962\pi$
$103$	3.42192	+	5.92695i	0.337172	+	0.583999i	−0.646727	+	0.762721i	$0.723863\pi$
$104$	−5.92359	+	2.15601i	−0.580856	+	0.211414i
$105$	0.916747	−	0.333669i	0.0894654	−	0.0325627i
$106$	5.94918	+	10.3043i	0.577836	+	1.00084i
$107$	−9.54069	+	16.5250i	−0.922334	+	1.59753i	−0.126539	+	0.991962i	$0.540387\pi$
$107$	−9.54069	+	16.5250i	−0.922334	+	1.59753i	−0.795794	+	0.605567i	$0.792946\pi$
$108$	0.173648	−	0.984808i	0.0167093	−	0.0947632i
$109$	−5.44694	+	4.57053i	−0.521723	+	0.437777i	−0.865232	−	0.501372i	$-0.832829\pi$
$109$	−5.44694	+	4.57053i	−0.521723	+	0.437777i	0.343509	+	0.939149i	$0.388384\pi$
$110$	2.01338	+	1.68943i	0.191969	+	0.161081i
$111$	0.809495	+	4.59087i	0.0768338	+	0.435746i
$112$	0.916747	+	0.333669i	0.0866245	+	0.0315287i
$113$	−6.02268			−0.566566			−0.283283	−	0.959036i	$-0.591424\pi$
$113$	−6.02268			−0.566566			−0.283283	+	0.959036i	$0.591424\pi$
$114$	−0.342801	−	4.34540i	−0.0321063	−	0.406984i
$115$	0.698595			0.0651443
$116$	−0.522946	−	0.190337i	−0.0485543	−	0.0176723i
$117$	1.09464	+	6.20799i	0.101199	+	0.573929i
$118$	−2.90797	−	2.44008i	−0.267700	−	0.224627i
$119$	−1.93626	+	1.62472i	−0.177497	+	0.148938i
$120$	0.173648	−	0.984808i	0.0158518	−	0.0899002i
$121$	2.04606	−	3.54388i	0.186005	−	0.322171i
$122$	−3.76474	−	6.52072i	−0.340843	−	0.590358i
$123$	3.66261	−	1.33308i	0.330247	−	0.120200i
$124$	−3.94039	+	1.43418i	−0.353857	+	0.128794i
$125$	−0.500000	−	0.866025i	−0.0447214	−	0.0774597i
$126$	0.487791	−	0.844879i	0.0434559	−	0.0752678i
$127$	−2.00035	+	11.3446i	−0.177502	+	1.00667i	0.757713	+	0.652588i	$0.226317\pi$
$127$	−2.00035	+	11.3446i	−0.177502	+	1.00667i	−0.935216	+	0.354079i	$0.884794\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$	6.60945	+	5.54599i	0.581930	+	0.488297i
$130$	1.09464	+	6.20799i	0.0960059	+	0.544476i
$131$	9.16093	+	3.33431i	0.800394	+	0.291320i	0.709650	−	0.704555i	$-0.248853\pi$
$131$	9.16093	+	3.33431i	0.800394	+	0.291320i	0.0907443	+	0.995874i	$0.471075\pi$
$132$	2.62829			0.228763
$133$	1.13566	−	4.09801i	0.0984743	−	0.355343i
$134$	−2.69294			−0.232635
$135$	−0.939693	−	0.342020i	−0.0808759	−	0.0294364i
$136$	0.449901	+	2.55151i	0.0385787	+	0.218790i
$137$	16.0247	+	13.4463i	1.36908	+	1.14880i	0.973058	+	0.230560i	$0.0740557\pi$
$137$	16.0247	+	13.4463i	1.36908	+	1.14880i	0.396027	+	0.918239i	$0.370389\pi$
$138$	0.535155	−	0.449048i	0.0455554	−	0.0382255i
$139$	1.49255	−	8.46469i	0.126597	−	0.717966i	−0.853750	−	0.520683i	$-0.825677\pi$
$139$	1.49255	−	8.46469i	0.126597	−	0.717966i	0.980347	−	0.197283i	$-0.0632116\pi$
$140$	0.487791	−	0.844879i	0.0412259	−	0.0714053i
$141$	2.76298	+	4.78562i	0.232685	+	0.403022i
$142$	3.15609	−	1.14872i	0.264853	−	0.0963985i
$143$	−15.5689	+	5.66661i	−1.30194	+	0.473866i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.278253	+	0.481949i	−0.0231077	+	0.0400237i
$146$	−2.04255	+	11.5839i	−0.169043	+	0.958689i
$147$	−4.63322	+	3.88773i	−0.382142	+	0.320655i
$148$	3.57106	+	2.99648i	0.293540	+	0.246309i
$149$	2.12715	+	12.0636i	0.174263	+	0.988292i	0.938992	+	0.343940i	$0.111762\pi$
$149$	2.12715	+	12.0636i	0.174263	+	0.988292i	−0.764729	+	0.644352i	$0.777127\pi$
$150$	−0.939693	−	0.342020i	−0.0767256	−	0.0279258i
$151$	3.21332			0.261496			0.130748	−	0.991416i	$-0.458262\pi$
$151$	3.21332			0.261496			0.130748	+	0.991416i	$0.458262\pi$
$152$	−3.05577	−	3.10842i	−0.247856	−	0.252126i
$153$	2.59087			0.209460
$154$	2.40947	+	0.876977i	0.194161	+	0.0706688i
$155$	0.728154	+	4.12957i	0.0584868	+	0.331695i
$156$	4.82896	+	4.05198i	0.386626	+	0.324418i
$157$	−13.2695	+	11.1345i	−1.05903	+	0.888628i	−0.994014	−	0.109257i	$-0.965153\pi$
$157$	−13.2695	+	11.1345i	−1.05903	+	0.888628i	−0.0650116	+	0.997885i	$0.520708\pi$
$158$	1.24146	−	7.04067i	0.0987652	−	0.560125i
$159$	5.94918	−	10.3043i	0.471801	−	0.817183i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	0.640435	−	0.233099i	0.0504733	−	0.0183708i
$162$	−0.939693	+	0.342020i	−0.0738292	+	0.0268716i
$163$	9.49461	+	16.4452i	0.743675	+	1.28808i	0.950811	+	0.309771i	$0.100253\pi$
$163$	9.49461	+	16.4452i	0.743675	+	1.28808i	−0.207136	+	0.978312i	$0.566414\pi$
$164$	1.94884	−	3.37548i	0.152179	−	0.263581i
$165$	0.456397	−	2.58836i	0.0355305	−	0.201503i
$166$	−6.38286	+	5.35586i	−0.495406	+	0.415695i
$167$	−5.17214	−	4.33994i	−0.400232	−	0.335834i	0.420351	−	0.907361i	$-0.361907\pi$
$167$	−5.17214	−	4.33994i	−0.400232	−	0.335834i	−0.820583	+	0.571527i	$0.806351\pi$
$168$	−0.169408	−	0.960761i	−0.0130701	−	0.0741243i
$169$	−25.1249	−	9.14470i	−1.93268	−	0.703439i
$170$	2.59087			0.198711
$171$	−3.59182	+	2.46957i	−0.274674	+	0.188853i
$172$	8.62802			0.657881
$173$	−12.7096	−	4.62592i	−0.966294	−	0.351702i	−0.189797	−	0.981823i	$-0.560783\pi$
$173$	−12.7096	−	4.62592i	−0.966294	−	0.351702i	−0.776497	+	0.630121i	$0.783005\pi$
$174$	0.0966364	+	0.548052i	0.00732599	+	0.0415477i
$175$	−0.747339	−	0.627092i	−0.0564935	−	0.0474037i
$176$	2.01338	−	1.68943i	0.151764	−	0.127346i
$177$	−0.659183	+	3.73841i	−0.0495472	+	0.280996i
$178$	3.65305	−	6.32727i	0.273808	−	0.474249i
$179$	0.0211142	+	0.0365709i	0.00157815	+	0.00273344i	0.866813	−	0.498633i	$-0.166164\pi$
$179$	0.0211142	+	0.0365709i	0.00157815	+	0.00273344i	−0.865235	+	0.501366i	$0.832831\pi$
$180$	−0.939693	+	0.342020i	−0.0700406	+	0.0254927i
$181$	−10.5154	+	3.82731i	−0.781607	+	0.284482i	−0.701843	−	0.712332i	$-0.747639\pi$
$181$	−10.5154	+	3.82731i	−0.781607	+	0.284482i	−0.0797645	+	0.996814i	$0.525417\pi$
$182$	3.07491	+	5.32591i	0.227928	+	0.394783i
$183$	−3.76474	+	6.52072i	−0.278297	+	0.482025i
$184$	0.121310	−	0.687981i	0.00894307	−	0.0507187i
$185$	3.57106	−	2.99648i	0.262550	−	0.220306i
$186$	3.21223	+	2.69538i	0.235532	+	0.197635i
$187$	1.18247	+	6.70611i	0.0864706	+	0.490399i
$188$	5.19270	+	1.88999i	0.378717	+	0.137842i
$189$	−0.975582			−0.0709631
$190$	−3.59182	+	2.46957i	−0.260578	+	0.179162i
$191$	8.25553			0.597349			0.298674	−	0.954355i	$-0.403456\pi$
$191$	8.25553			0.597349			0.298674	+	0.954355i	$0.403456\pi$
$192$	−0.939693	−	0.342020i	−0.0678165	−	0.0246832i
$193$	−3.25140	−	18.4396i	−0.234041	−	1.32731i	−0.844624	−	0.535360i	$-0.820176\pi$
$193$	−3.25140	−	18.4396i	−0.234041	−	1.32731i	0.610583	−	0.791952i	$-0.290935\pi$
$194$	11.4797	+	9.63260i	0.824194	+	0.691581i
$195$	4.82896	−	4.05198i	0.345809	−	0.290168i
$196$	−1.05027	+	5.95635i	−0.0750190	+	0.425454i
$197$	7.81022	−	13.5277i	0.556455	−	0.963809i	−0.441333	−	0.897343i	$-0.645494\pi$
$197$	7.81022	−	13.5277i	0.556455	−	0.963809i	0.997789	−	0.0664656i	$-0.0211723\pi$
$198$	−1.31414	−	2.27616i	−0.0933921	−	0.161760i
$199$	−15.5664	+	5.66572i	−1.10348	+	0.401633i	−0.828597	−	0.559846i	$-0.810860\pi$
$199$	−15.5664	+	5.66572i	−1.10348	+	0.401633i	−0.274880	+	0.961479i	$0.588638\pi$
$200$	−0.939693	+	0.342020i	−0.0664463	+	0.0241845i
$201$	1.34647	+	2.33215i	0.0949727	+	0.164497i
$202$	0.422460	−	0.731722i	0.0297242	−	0.0514838i
$203$	−0.0942767	+	0.534670i	−0.00661693	+	0.0375265i
$204$	1.98473	−	1.66538i	0.138959	−	0.116600i
$205$	−2.98579	−	2.50538i	−0.208537	−	0.174983i
$206$	−1.18842	−	6.73987i	−0.0828013	−	0.469589i
$207$	−0.656464	−	0.238933i	−0.0456274	−	0.0166070i
$208$	6.30375			0.437087
$209$	−8.03143	−	8.16982i	−0.555546	−	0.565118i
$210$	−0.975582			−0.0673215
$211$	−1.19414	−	0.434631i	−0.0822079	−	0.0299212i	0.300589	−	0.953754i	$-0.402817\pi$
$211$	−1.19414	−	0.434631i	−0.0822079	−	0.0299212i	−0.382797	+	0.923833i	$0.625039\pi$
$212$	−2.06613	−	11.7176i	−0.141902	−	0.804768i
$213$	−2.57286	−	2.15889i	−0.176290	−	0.147925i
$214$	14.6172	−	12.2653i	0.999210	−	0.838437i
$215$	1.49824	−	8.49694i	0.102179	−	0.579487i
$216$	−0.500000	+	0.866025i	−0.0340207	+	0.0589256i
$217$	2.04544	+	3.54281i	0.138854	+	0.240501i
$218$	6.68167	−	2.43193i	0.452540	−	0.164711i
$219$	11.0532	−	4.02304i	0.746907	−	0.271852i
$220$	−1.31414	−	2.27616i	−0.0885995	−	0.153459i
$221$	−8.16612	+	14.1441i	−0.549313	+	0.951437i
$222$	0.809495	−	4.59087i	0.0543297	−	0.308119i
$223$	9.38140	−	7.87193i	0.628225	−	0.527143i	−0.272152	−	0.962254i	$-0.587735\pi$
$223$	9.38140	−	7.87193i	0.628225	−	0.527143i	0.900377	+	0.435111i	$0.143291\pi$
$224$	−0.747339	−	0.627092i	−0.0499337	−	0.0418993i
$225$	0.173648	+	0.984808i	0.0115765	+	0.0656539i
$226$	5.65947	+	2.05988i	0.376462	+	0.137021i
$227$	26.1062			1.73273			0.866364	−	0.499413i	$-0.166451\pi$
$227$	26.1062			1.73273			0.866364	+	0.499413i	$0.166451\pi$
$228$	−1.16409	+	4.20058i	−0.0770935	+	0.278190i
$229$	−12.3537			−0.816356			−0.408178	−	0.912902i	$-0.633836\pi$
$229$	−12.3537			−0.816356			−0.408178	+	0.912902i	$0.633836\pi$
$230$	−0.656464	−	0.238933i	−0.0432860	−	0.0157548i
$231$	−0.445253	−	2.52515i	−0.0292955	−	0.166143i
$232$	0.426309	+	0.357716i	0.0279886	+	0.0234852i
$233$	−6.86499	+	5.76041i	−0.449741	+	0.377377i	−0.839340	−	0.543607i	$-0.817058\pi$
$233$	−6.86499	+	5.76041i	−0.449741	+	0.377377i	0.389599	+	0.920985i	$0.372614\pi$
$234$	1.09464	−	6.20799i	0.0715586	−	0.405829i
$235$	2.76298	−	4.78562i	0.180237	−	0.312179i
$236$	1.89804	+	3.28750i	0.123552	+	0.213998i
$237$	−6.71813	+	2.44520i	−0.436389	+	0.158833i
$238$	2.37518	−	0.864494i	0.153960	−	0.0560368i
$239$	4.23738	+	7.33935i	0.274093	+	0.474743i	0.969906	−	0.243480i	$-0.0782890\pi$
$239$	4.23738	+	7.33935i	0.274093	+	0.474743i	−0.695813	+	0.718223i	$0.744956\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	2.10570	−	11.9420i	0.135640	−	0.769253i	−0.838772	−	0.544483i	$-0.816726\pi$
$241$	2.10570	−	11.9420i	0.135640	−	0.769253i	0.974412	−	0.224770i	$-0.0721630\pi$
$242$	−3.13474	+	2.63036i	−0.201509	+	0.169086i
$243$	0.766044	+	0.642788i	0.0491418	+	0.0412348i
$244$	1.30748	+	7.41509i	0.0837028	+	0.474702i
$245$	5.68349	+	2.06862i	0.363105	+	0.132159i
$246$	−3.89767			−0.248506
$247$	−2.16093	−	27.3923i	−0.137497	−	1.74293i
$248$	4.19327			0.266273
$249$	7.82974	+	2.84979i	0.496190	+	0.180598i
$250$	0.173648	+	0.984808i	0.0109825	+	0.0622847i
$251$	4.66523	+	3.91459i	0.294467	+	0.247087i	0.778037	−	0.628219i	$-0.216216\pi$
$251$	4.66523	+	3.91459i	0.294467	+	0.247087i	−0.483570	+	0.875306i	$0.660660\pi$
$252$	−0.747339	+	0.627092i	−0.0470779	+	0.0395031i
$253$	0.318837	−	1.80821i	0.0200451	−	0.113681i
$254$	5.75978	−	9.97623i	0.361401	−	0.625965i
$255$	−1.29544	−	2.24376i	−0.0811234	−	0.140510i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−14.0120	+	5.09995i	−0.874044	+	0.318126i	−0.739804	−	0.672823i	$-0.765082\pi$
$257$	−14.0120	+	5.09995i	−0.874044	+	0.318126i	−0.134240	+	0.990949i	$0.542859\pi$
$258$	−4.31401	−	7.47209i	−0.268579	−	0.465192i
$259$	2.27393	−	3.93857i	0.141295	−	0.244731i
$260$	1.09464	−	6.20799i	0.0678864	−	0.385003i
$261$	0.426309	−	0.357716i	0.0263879	−	0.0221421i
$262$	−7.46806	−	6.26644i	−0.461378	−	0.387142i
$263$	−2.16722	−	12.2909i	−0.133637	−	0.757892i	−0.975799	−	0.218668i	$-0.929829\pi$
$263$	−2.16722	−	12.2909i	−0.133637	−	0.757892i	0.842163	−	0.539224i	$-0.181282\pi$
$264$	−2.46978	−	0.898927i	−0.152004	−	0.0553251i
$265$	−11.8984			−0.730911
$266$	−2.46878	+	3.46245i	−0.151370	+	0.212297i
$267$	−7.30610			−0.447126
$268$	2.53054	+	0.921040i	0.154577	+	0.0562614i
$269$	−1.17152	−	6.64402i	−0.0714288	−	0.405093i	−0.999468	−	0.0326107i	$-0.989618\pi$
$269$	−1.17152	−	6.64402i	−0.0714288	−	0.405093i	0.928039	−	0.372482i	$-0.121493\pi$
$270$	0.766044	+	0.642788i	0.0466200	+	0.0391188i
$271$	10.6812	−	8.96256i	0.648834	−	0.544437i	−0.257883	−	0.966176i	$-0.583025\pi$
$271$	10.6812	−	8.96256i	0.648834	−	0.544437i	0.906717	+	0.421740i	$0.138580\pi$
$272$	0.449901	−	2.55151i	0.0272792	−	0.154708i
$273$	3.07491	−	5.32591i	0.186102	−	0.322339i
$274$	−10.4594	−	18.1162i	−0.631875	−	1.09444i
$275$	−2.46978	+	0.898927i	−0.148933	+	0.0542073i
$276$	−0.656464	+	0.238933i	−0.0395145	+	0.0143821i
$277$	5.76809	+	9.99063i	0.346571	+	0.600279i	0.985638	−	0.168872i	$-0.0540126\pi$
$277$	5.76809	+	9.99063i	0.346571	+	0.600279i	−0.639067	+	0.769151i	$0.720679\pi$
$278$	−4.29764	+	7.44373i	−0.257755	+	0.446445i
$279$	0.728154	−	4.12957i	0.0435935	−	0.247231i
$280$	−0.747339	+	0.627092i	−0.0446621	+	0.0374759i
$281$	11.4571	+	9.61366i	0.683474	+	0.573503i	0.917019	−	0.398843i	$-0.130588\pi$
$281$	11.4571	+	9.61366i	0.683474	+	0.573503i	−0.233545	+	0.972346i	$0.575033\pi$
$282$	−0.959572	−	5.44201i	−0.0571417	−	0.324067i
$283$	−25.6735	−	9.34439i	−1.52613	−	0.555466i	−0.563460	−	0.826143i	$-0.690530\pi$
$283$	−25.6735	−	9.34439i	−1.52613	−	0.555466i	−0.962670	+	0.270677i	$0.912752\pi$
$284$	−3.35864			−0.199298
$285$	3.93463	+	1.87582i	0.233067	+	0.111114i
$286$	16.5681			0.979690
$287$	−3.57318	−	1.30053i	−0.210918	−	0.0767679i
$288$	0.173648	+	0.984808i	0.0102323	+	0.0580304i
$289$	−7.88058	−	6.61259i	−0.463564	−	0.388976i
$290$	0.426309	−	0.357716i	0.0250337	−	0.0210058i
$291$	2.60223	−	14.7580i	0.152546	−	0.865130i
$292$	5.88129	−	10.1867i	0.344177	−	0.596132i
$293$	14.9150	+	25.8336i	0.871346	+	1.50922i	0.860605	+	0.509273i	$0.170086\pi$
$293$	14.9150	+	25.8336i	0.871346	+	1.50922i	0.0107405	+	0.999942i	$0.496581\pi$
$294$	5.68349	−	2.06862i	0.331468	−	0.120644i
$295$	3.56715	−	1.29834i	0.207688	−	0.0755921i
$296$	−2.33085	−	4.03715i	−0.135478	−	0.234654i
$297$	−1.31414	+	2.27616i	−0.0762543	+	0.132076i
$298$	2.12715	−	12.0636i	0.123222	−	0.698828i
$299$	3.37348	−	2.83069i	0.195094	−	0.163703i
$300$	0.766044	+	0.642788i	0.0442276	+	0.0371114i
$301$	−1.46166	−	8.28946i	−0.0842485	−	0.477797i
$302$	−3.01953	−	1.09902i	−0.173755	−	0.0632415i
$303$	−0.844920			−0.0485394
$304$	1.80834	+	3.96609i	0.103715	+	0.227471i
$305$	7.52948			0.431137
$306$	−2.43463	−	0.886131i	−0.139178	−	0.0506568i
$307$	5.63562	+	31.9612i	0.321642	+	1.82412i	0.532293	+	0.846560i	$0.321331\pi$
$307$	5.63562	+	31.9612i	0.321642	+	1.82412i	−0.210651	+	0.977561i	$0.567558\pi$
$308$	−1.96422	−	1.64818i	−0.111922	−	0.0939136i
$309$	−5.24269	+	4.39914i	−0.298246	+	0.250258i
$310$	0.728154	−	4.12957i	0.0413564	−	0.234544i
$311$	15.7025	−	27.1975i	0.890405	−	1.54223i	0.0510137	−	0.998698i	$-0.483755\pi$
$311$	15.7025	−	27.1975i	0.890405	−	1.54223i	0.839391	−	0.543528i	$-0.182912\pi$
$312$	−3.15188	−	5.45921i	−0.178440	−	0.309067i
$313$	29.5814	−	10.7667i	1.67204	−	0.608572i	0.679853	−	0.733349i	$-0.262044\pi$
$313$	29.5814	−	10.7667i	1.67204	−	0.608572i	0.992185	+	0.124777i	$0.0398215\pi$
$314$	16.2775	−	5.92453i	0.918593	−	0.334340i
$315$	0.487791	+	0.844879i	0.0274839	+	0.0476035i
$316$	−3.57464	+	6.19146i	−0.201089	+	0.348297i
$317$	1.56025	−	8.84862i	0.0876324	−	0.496988i	−0.909125	−	0.416523i	$-0.863248\pi$
$317$	1.56025	−	8.84862i	0.0876324	−	0.496988i	0.996757	−	0.0804649i	$-0.0256405\pi$
$318$	−9.11468	+	7.64812i	−0.511126	+	0.428885i
$319$	1.12046	+	0.940179i	0.0627338	+	0.0526399i
$320$	0.173648	+	0.984808i	0.00970723	+	0.0550524i
$321$	−17.9306	−	6.52622i	−1.00079	−	0.364258i
$322$	−0.681536			−0.0379805
$323$	−11.2416	−	1.08034i	−0.625498	−	0.0601115i
$324$	1.00000			0.0555556
$325$	−5.92359	−	2.15601i	−0.328582	−	0.119594i
$326$	−3.29744	−	18.7007i	−0.182629	−	1.03574i
$327$	−5.44694	−	4.57053i	−0.301217	−	0.252751i
$328$	−2.98579	+	2.50538i	−0.164863	+	0.138336i
$329$	0.936142	−	5.30912i	0.0516112	−	0.292701i
$330$	−1.31414	+	2.27616i	−0.0723412	+	0.125299i
$331$	7.05795	+	12.2247i	0.387940	+	0.671932i	0.992172	−	0.124876i	$-0.0398534\pi$
$331$	7.05795	+	12.2247i	0.387940	+	0.671932i	−0.604232	+	0.796808i	$0.706520\pi$
$332$	7.82974	−	2.84979i	0.429713	−	0.156403i
$333$	−4.38056	+	1.59439i	−0.240053	+	0.0873722i
$334$	3.37587	+	5.84718i	0.184719	+	0.319944i
$335$	1.34647	−	2.33215i	0.0735655	−	0.127419i
$336$	−0.169408	+	0.960761i	−0.00924197	+	0.0524138i
$337$	−11.1388	+	9.34658i	−0.606770	+	0.509140i	−0.893614	−	0.448837i	$-0.851838\pi$
$337$	−11.1388	+	9.34658i	−0.606770	+	0.509140i	0.286844	+	0.957977i	$0.407394\pi$
$338$	20.4820	+	17.1864i	1.11407	+	0.934818i
$339$	−1.04583	−	5.93118i	−0.0568015	−	0.322138i
$340$	−2.43463	−	0.886131i	−0.132036	−	0.0480572i
$341$	11.0211			0.596827
$342$	4.21986	−	1.09216i	0.228184	−	0.0590574i
$343$	12.7296			0.687335
$344$	−8.10769	−	2.95096i	−0.437137	−	0.159105i
$345$	0.121310	+	0.687981i	0.00653109	+	0.0370397i
$346$	10.3610	+	8.69388i	0.557009	+	0.467386i
$347$	8.80866	−	7.39134i	0.472874	−	0.396788i	−0.374968	−	0.927038i	$-0.622346\pi$
$347$	8.80866	−	7.39134i	0.472874	−	0.396788i	0.847841	+	0.530250i	$0.177902\pi$
$348$	0.0966364	−	0.548052i	0.00518026	−	0.0293787i
$349$	−11.8789	+	20.5748i	−0.635861	+	1.10134i	0.350471	+	0.936574i	$0.386022\pi$
$349$	−11.8789	+	20.5748i	−0.635861	+	1.10134i	−0.986332	+	0.164771i	$0.947312\pi$
$350$	0.487791	+	0.844879i	0.0260735	+	0.0451607i
$351$	−5.92359	+	2.15601i	−0.316178	+	0.115079i
$352$	−2.46978	+	0.898927i	−0.131640	+	0.0479129i
$353$	17.4674	+	30.2544i	0.929694	+	1.61028i	0.783833	+	0.620971i	$0.213262\pi$
$353$	17.4674	+	30.2544i	0.929694	+	1.61028i	0.145860	+	0.989305i	$0.453405\pi$
$354$	1.89804	−	3.28750i	0.100880	−	0.174729i
$355$	−0.583221	+	3.30761i	−0.0309542	+	0.175550i
$356$	−5.59680	+	4.69627i	−0.296630	+	0.248902i
$357$	−1.93626	−	1.62472i	−0.102478	−	0.0859891i
$358$	−0.00733290	−	0.0415869i	−0.000387556	−	0.00219794i
$359$	−18.1902	−	6.62067i	−0.960040	−	0.349426i	−0.185991	−	0.982552i	$-0.559549\pi$
$359$	−18.1902	−	6.62067i	−0.960040	−	0.349426i	−0.774049	+	0.633126i	$0.781772\pi$
$360$	1.00000			0.0527046
$361$	16.6144	−	9.21754i	0.874440	−	0.485134i
$362$	11.1903			0.588149
$363$	3.84533	+	1.39959i	0.201828	+	0.0734592i
$364$	−1.06791	−	6.05640i	−0.0559735	−	0.317442i
$365$	−9.01067	−	7.56085i	−0.471640	−	0.395753i
$366$	5.76791	−	4.83985i	0.301494	−	0.252983i
$367$	2.24944	−	12.7572i	0.117420	−	0.665921i	−0.868104	−	0.496383i	$-0.834661\pi$
$367$	2.24944	−	12.7572i	0.117420	−	0.665921i	0.985524	−	0.169538i	$-0.0542277\pi$
$368$	−0.349297	+	0.605001i	−0.0182084	+	0.0315378i
$369$	1.94884	+	3.37548i	0.101452	+	0.175721i
$370$	−4.38056	+	1.59439i	−0.227734	+	0.0828886i
$371$	−10.9078	+	3.97011i	−0.566304	+	0.206118i
$372$	−2.09664	−	3.63148i	−0.108706	−	0.188284i
$373$	2.15986	−	3.74099i	0.111833	−	0.193701i	−0.804676	−	0.593714i	$-0.797661\pi$
$373$	2.15986	−	3.74099i	0.111833	−	0.193701i	0.916509	+	0.400013i	$0.130994\pi$
$374$	1.18247	−	6.70611i	0.0611439	−	0.346765i
$375$	0.766044	−	0.642788i	0.0395584	−	0.0331934i
$376$	−4.23313	−	3.55202i	−0.218307	−	0.183181i
$377$	0.609172	+	3.45479i	0.0313740	+	0.177931i
$378$	0.916747	+	0.333669i	0.0471524	+	0.0171621i
$379$	−13.4543			−0.691102			−0.345551	−	0.938400i	$-0.612308\pi$
$379$	−13.4543			−0.691102			−0.345551	+	0.938400i	$0.612308\pi$
$380$	4.21986	−	1.09216i	0.216474	−	0.0560268i
$381$	−11.5196			−0.590165
$382$	−7.75766	−	2.82356i	−0.396916	−	0.144466i
$383$	−0.588794	−	3.33922i	−0.0300860	−	0.170626i	0.966063	−	0.258308i	$-0.0831651\pi$
$383$	−0.588794	−	3.33922i	−0.0300860	−	0.170626i	−0.996148	+	0.0876823i	$0.972054\pi$
$384$	0.766044	+	0.642788i	0.0390920	+	0.0328021i
$385$	−1.96422	+	1.64818i	−0.100106	+	0.0839989i
$386$	−3.25140	+	18.4396i	−0.165492	+	0.938551i
$387$	−4.31401	+	7.47209i	−0.219294	+	0.379828i
$388$	−7.49284	−	12.9780i	−0.380391	−	0.658857i
$389$	12.9130	−	4.69996i	0.654717	−	0.238298i	0.00676324	−	0.999977i	$-0.497847\pi$
$389$	12.9130	−	4.69996i	0.654717	−	0.238298i	0.647954	+	0.761680i	$0.275625\pi$
$390$	−5.92359	+	2.15601i	−0.299953	+	0.109174i
$391$	−0.904986	−	1.56748i	−0.0457671	−	0.0792709i
$392$	3.02412	−	5.23793i	0.152741	−	0.264555i
$393$	−1.69287	+	9.60075i	−0.0853941	+	0.484294i
$394$	−11.9660	+	10.0406i	−0.602836	+	0.505839i
$395$	5.47667	+	4.59547i	0.275561	+	0.231223i
$396$	0.456397	+	2.58836i	0.0229348	+	0.130070i
$397$	−18.4063	−	6.69935i	−0.923787	−	0.336231i	−0.164043	−	0.986453i	$-0.552453\pi$
$397$	−18.4063	−	6.69935i	−0.923787	−	0.336231i	−0.759744	+	0.650222i	$0.774676\pi$
$398$	16.5655			0.830352
$399$	4.23296	+	0.406796i	0.211913	+	0.0203653i
$400$	1.00000			0.0500000
$401$	6.17006	+	2.24572i	0.308118	+	0.112146i	0.491451	−	0.870905i	$-0.336467\pi$
$401$	6.17006	+	2.24572i	0.308118	+	0.112146i	−0.183333	+	0.983051i	$0.558689\pi$
$402$	−0.467624	−	2.65203i	−0.0233230	−	0.132271i
$403$	20.2491	+	16.9910i	1.00868	+	0.846384i
$404$	−0.647246	+	0.543104i	−0.0322017	+	0.0270204i
$405$	0.173648	−	0.984808i	0.00862865	−	0.0489355i
$406$	0.271459	−	0.470181i	0.0134723	−	0.0233347i
$407$	−6.12613	−	10.6108i	−0.303661	−	0.525956i
$408$	−2.43463	+	0.886131i	−0.120532	+	0.0438700i
$409$	−18.5405	+	6.74819i	−0.916768	+	0.333676i	−0.756952	−	0.653470i	$-0.773312\pi$
$409$	−18.5405	+	6.74819i	−0.916768	+	0.333676i	−0.159816	+	0.987147i	$0.551090\pi$
$410$	1.94884	+	3.37548i	0.0962461	+	0.166703i
$411$	−10.4594	+	18.1162i	−0.515924	+	0.893607i
$412$	−1.18842	+	6.73987i	−0.0585493	+	0.332050i
$413$	2.83696	−	2.38049i	0.139598	−	0.117136i
$414$	0.535155	+	0.449048i	0.0263014	+	0.0220695i
$415$	−1.44688	−	8.20565i	−0.0710244	−	0.402800i
$416$	−5.92359	−	2.15601i	−0.290428	−	0.105707i
$417$	8.59527			0.420912
$418$	4.75284	+	10.4240i	0.232469	+	0.509856i
$419$	39.6244			1.93578			0.967888	−	0.251380i	$-0.0808845\pi$
$419$	39.6244			1.93578			0.967888	+	0.251380i	$0.0808845\pi$
$420$	0.916747	+	0.333669i	0.0447327	+	0.0162814i
$421$	−4.35511	−	24.6991i	−0.212255	−	1.20376i	−0.885606	−	0.464437i	$-0.846257\pi$
$421$	−4.35511	−	24.6991i	−0.212255	−	1.20376i	0.673351	−	0.739323i	$-0.264854\pi$
$422$	0.973471	+	0.816839i	0.0473878	+	0.0397631i
$423$	−4.23313	+	3.55202i	−0.205822	+	0.172705i
$424$	−2.06613	+	11.7176i	−0.100340	+	0.569057i
$425$	−1.29544	+	2.24376i	−0.0628379	+	0.108839i
$426$	1.67932	+	2.90866i	0.0813632	+	0.140925i
$427$	6.90263	−	2.51235i	0.334041	−	0.121581i
$428$	−17.9306	+	6.52622i	−0.866710	+	0.315457i
$429$	−8.28403	−	14.3484i	−0.399957	−	0.692746i
$430$	−4.31401	+	7.47209i	−0.208040	+	0.360336i
$431$	1.20410	−	6.82880i	0.0579996	−	0.328932i	−0.941978	−	0.335675i	$-0.891035\pi$
$431$	1.20410	−	6.82880i	0.0579996	−	0.328932i	0.999977	+	0.00674361i	$0.00214657\pi$
$432$	0.766044	−	0.642788i	0.0368563	−	0.0309261i
$433$	21.1542	+	17.7505i	1.01661	+	0.853035i	0.989197	−	0.146589i	$-0.0468294\pi$
$433$	21.1542	+	17.7505i	1.01661	+	0.853035i	0.0274104	+	0.999624i	$0.491274\pi$
$434$	−0.710374	−	4.02873i	−0.0340990	−	0.193385i
$435$	−0.522946	−	0.190337i	−0.0250733	−	0.00912594i
$436$	−7.11048			−0.340530
$437$	2.74871	+	1.31044i	0.131489	+	0.0626869i
$438$	−11.7626			−0.562038
$439$	33.7221	+	12.2738i	1.60947	+	0.585798i	0.981335	−	0.192308i	$-0.0615973\pi$
$439$	33.7221	+	12.2738i	1.60947	+	0.585798i	0.628133	+	0.778106i	$0.283819\pi$
$440$	0.456397	+	2.58836i	0.0217579	+	0.123395i
$441$	−4.63322	−	3.88773i	−0.220630	−	0.185130i
$442$	12.5112	−	10.4982i	0.595098	−	0.499347i
$443$	−2.35792	+	13.3724i	−0.112028	+	0.635343i	0.876151	+	0.482037i	$0.160103\pi$
$443$	−2.35792	+	13.3724i	−0.112028	+	0.635343i	−0.988179	+	0.153306i	$0.951008\pi$
$444$	−2.33085	+	4.03715i	−0.110617	+	0.191594i
$445$	3.65305	+	6.32727i	0.173171	+	0.299941i
$446$	−11.5080	+	4.18856i	−0.544919	+	0.198334i
$447$	−11.5110	+	4.18966i	−0.544451	+	0.198164i
$448$	0.487791	+	0.844879i	0.0230460	+	0.0399168i
$449$	3.81996	−	6.61636i	0.180275	−	0.312245i	−0.761699	−	0.647931i	$-0.775635\pi$
$449$	3.81996	−	6.61636i	0.180275	−	0.312245i	0.941974	+	0.335685i	$0.108968\pi$
$450$	0.173648	−	0.984808i	0.00818585	−	0.0464243i
$451$	−7.84751	+	6.58484i	−0.369525	+	0.310068i
$452$	−4.61364	−	3.87130i	−0.217007	−	0.182091i
$453$	0.557987	+	3.16450i	0.0262165	+	0.148681i
$454$	−24.5318	−	8.92884i	−1.15133	−	0.419051i
$455$	−6.14983			−0.288308
$456$	2.53057	−	3.54912i	0.118505	−	0.166203i
$457$	27.6364			1.29278			0.646389	−	0.763008i	$-0.276278\pi$
$457$	27.6364			1.29278			0.646389	+	0.763008i	$0.276278\pi$
$458$	11.6087	+	4.22522i	0.542439	+	0.197431i
$459$	0.449901	+	2.55151i	0.0209996	+	0.119094i
$460$	0.535155	+	0.449048i	0.0249517	+	0.0209370i
$461$	−23.7597	+	19.9367i	−1.10660	+	0.928545i	−0.997851	−	0.0655242i	$-0.979128\pi$
$461$	−23.7597	+	19.9367i	−1.10660	+	0.928545i	−0.108746	+	0.994070i	$0.534684\pi$
$462$	−0.445253	+	2.52515i	−0.0207150	+	0.117481i
$463$	−18.6734	+	32.3432i	−0.867824	+	1.50312i	−0.00360891	+	0.999993i	$0.501149\pi$
$463$	−18.6734	+	32.3432i	−0.867824	+	1.50312i	−0.864215	+	0.503122i	$0.832185\pi$
$464$	−0.278253	−	0.481949i	−0.0129176	−	0.0223739i
$465$	−3.94039	+	1.43418i	−0.182731	+	0.0665087i
$466$	8.42116	−	3.06505i	0.390103	−	0.141986i
$467$	14.9958	+	25.9735i	0.693924	+	1.20191i	0.970542	+	0.240932i	$0.0774529\pi$
$467$	14.9958	+	25.9735i	0.693924	+	1.20191i	−0.276618	+	0.960980i	$0.589214\pi$
$468$	−3.15188	+	5.45921i	−0.145696	+	0.252352i
$469$	0.456206	−	2.58727i	0.0210656	−	0.119469i
$470$	−4.23313	+	3.55202i	−0.195260	+	0.163842i
$471$	−13.2695	−	11.1345i	−0.611428	−	0.513049i
$472$	−0.659183	−	3.73841i	−0.0303414	−	0.172074i
$473$	−21.3093	−	7.75596i	−0.979804	−	0.356619i
$474$	7.14928			0.328377
$475$	−0.342801	−	4.34540i	−0.0157288	−	0.199381i
$476$	−2.52761			−0.115853
$477$	11.1808	+	4.06948i	0.511934	+	0.186329i
$478$	−1.47163	−	8.34601i	−0.0673106	−	0.381737i
$479$	15.0968	+	12.6677i	0.689788	+	0.578801i	0.918848	−	0.394611i	$-0.129121\pi$
$479$	15.0968	+	12.6677i	0.689788	+	0.578801i	−0.229060	+	0.973412i	$0.573565\pi$
$480$	0.766044	−	0.642788i	0.0349650	−	0.0293391i
$481$	5.10286	−	28.9397i	0.232670	−	1.31954i
$482$	−6.06312	+	10.5016i	−0.276167	+	0.478336i
$483$	0.340768	+	0.590228i	0.0155055	+	0.0268563i
$484$	3.84533	−	1.39959i	0.174788	−	0.0636175i
$485$	−14.0819	+	5.12540i	−0.639427	+	0.232732i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−10.7365	+	18.5962i	−0.486519	+	0.842676i	−0.999880	−	0.0154971i	$-0.995067\pi$
$487$	−10.7365	+	18.5962i	−0.486519	+	0.842676i	0.513361	+	0.858173i	$0.328400\pi$
$488$	1.30748	−	7.41509i	0.0591868	−	0.335665i
$489$	−14.5466	+	12.2060i	−0.657820	+	0.551976i
$490$	−4.63322	−	3.88773i	−0.209308	−	0.175630i
$491$	−1.35138	−	7.66406i	−0.0609870	−	0.345874i	−0.999998	−	0.00198735i	$-0.999367\pi$
$491$	−1.35138	−	7.66406i	−0.0609870	−	0.345874i	0.939011	−	0.343887i	$-0.111744\pi$
$492$	3.66261	+	1.33308i	0.165123	+	0.0601000i
$493$	1.44184			0.0649372
$494$	−7.33811	+	26.4794i	−0.330157	+	1.19137i
$495$	2.62829			0.118133
$496$	−3.94039	−	1.43418i	−0.176929	−	0.0643968i
$497$	0.568980	+	3.22685i	0.0255222	+	0.144744i
$498$	−6.38286	−	5.35586i	−0.286023	−	0.240002i
$499$	−24.2649	+	20.3607i	−1.08625	+	0.911469i	−0.996424	−	0.0844885i	$-0.973074\pi$
$499$	−24.2649	+	20.3607i	−1.08625	+	0.911469i	−0.0898224	+	0.995958i	$0.528630\pi$
$500$	0.173648	−	0.984808i	0.00776578	−	0.0440419i
$501$	3.37587	−	5.84718i	0.150823	−	0.261233i
$502$	−3.04501	−	5.27411i	−0.135905	−	0.235395i
$503$	−15.8859	+	5.78200i	−0.708318	+	0.257807i	−0.670958	−	0.741495i	$-0.734117\pi$
$503$	−15.8859	+	5.78200i	−0.708318	+	0.257807i	−0.0373601	+	0.999302i	$0.511895\pi$
$504$	0.916747	−	0.333669i	0.0408352	−	0.0148628i
$505$	0.422460	+	0.731722i	0.0187992	+	0.0325612i
$506$	−0.918053	+	1.59011i	−0.0408124	+	0.0706892i
$507$	4.64289	−	26.3311i	0.206198	−	1.16941i
$508$	−8.82450	+	7.40463i	−0.391524	+	0.328527i
$509$	20.7746	+	17.4319i	0.920817	+	0.772658i	0.974146	−	0.225919i	$-0.0725386\pi$
$509$	20.7746	+	17.4319i	0.920817	+	0.772658i	−0.0533285	+	0.998577i	$0.516983\pi$
$510$	0.449901	+	2.55151i	0.0199219	+	0.112983i
$511$	−10.7833	−	3.92481i	−0.477026	−	0.173623i
$512$	1.00000			0.0441942
$513$	−3.05577	−	3.10842i	−0.134916	−	0.137240i
$514$	14.9112			0.657707
$515$	6.43111	+	2.34073i	0.283389	+	0.103145i
$516$	1.49824	+	8.49694i	0.0659564	+	0.374057i
$517$	−11.1259	−	9.33571i	−0.489315	−	0.410584i
$518$	−3.48387	+	2.92331i	−0.153072	+	0.128443i
$519$	2.34864	−	13.3198i	0.103094	−	0.584674i
$520$	−3.15188	+	5.45921i	−0.138219	+	0.239402i
$521$	−4.01435	−	6.95306i	−0.175872	−	0.304619i	0.764591	−	0.644516i	$-0.222941\pi$
$521$	−4.01435	−	6.95306i	−0.175872	−	0.304619i	−0.940463	+	0.339897i	$0.889608\pi$
$522$	−0.522946	+	0.190337i	−0.0228887	+	0.00833081i
$523$	9.57921	−	3.48655i	0.418870	−	0.152456i	−0.123982	−	0.992284i	$-0.539567\pi$
$523$	9.57921	−	3.48655i	0.418870	−	0.152456i	0.542852	+	0.839828i	$0.317344\pi$
$524$	4.87443	+	8.44276i	0.212940	+	0.368824i
$525$	0.487791	−	0.844879i	0.0212889	−	0.0368735i
$526$	−2.16722	+	12.2909i	−0.0944954	+	0.535910i
$527$	8.32249	−	6.98340i	0.362534	−	0.304202i
$528$	2.01338	+	1.68943i	0.0876213	+	0.0735230i
$529$	−3.90916	−	22.1700i	−0.169964	−	0.963911i
$530$	11.1808	+	4.06948i	0.485663	+	0.176767i
$531$	−3.79608			−0.164736
$532$	3.50412	−	2.40927i	0.151923	−	0.104455i
$533$	−24.5700			−1.06424
$534$	6.86549	+	2.49883i	0.297099	+	0.108135i
$535$	3.31345	+	18.7915i	0.143253	+	0.812427i
$536$	−2.06291	−	1.73099i	−0.0891042	−	0.0747673i
$537$	−0.0323489	+	0.0271439i	−0.00139596	+	0.00117135i
$538$	−1.17152	+	6.64402i	−0.0505078	+	0.286444i
$539$	7.94825	−	13.7668i	0.342355	−	0.592977i
$540$	−0.500000	−	0.866025i	−0.0215166	−	0.0372678i
$541$	7.04323	−	2.56353i	0.302812	−	0.110215i	−0.186145	−	0.982522i	$-0.559600\pi$
$541$	7.04323	−	2.56353i	0.302812	−	0.110215i	0.488958	+	0.872308i	$0.337377\pi$
$542$	−13.1024	+	4.76888i	−0.562796	+	0.204841i
$543$	−5.59515	−	9.69109i	−0.240111	−	0.415884i
$544$	−1.29544	+	2.24376i	−0.0555414	+	0.0962006i
$545$	−1.23472	+	7.00246i	−0.0528897	+	0.299952i
$546$	−4.71104	+	3.95303i	−0.201614	+	0.169174i
$547$	9.88894	+	8.29780i	0.422820	+	0.354788i	0.829235	−	0.558900i	$-0.188777\pi$
$547$	9.88894	+	8.29780i	0.422820	+	0.354788i	−0.406414	+	0.913689i	$0.633221\pi$
$548$	3.63251	+	20.6010i	0.155173	+	0.880031i
$549$	−7.07539	−	2.57523i	−0.301970	−	0.109908i
$550$	2.62829			0.112070
$551$	−1.99888	+	1.37434i	−0.0851550	+	0.0585486i
$552$	0.698595			0.0297342
$553$	6.55408	+	2.38549i	0.278708	+	0.101441i
$554$	−2.00324	−	11.3609i	−0.0851094	−	0.482680i
$555$	3.57106	+	2.99648i	0.151583	+	0.127193i
$556$	6.58436	−	5.52494i	0.279239	−	0.234309i
$557$	−1.19224	+	6.76151i	−0.0505167	+	0.286494i	−0.999592	−	0.0285541i	$-0.990910\pi$
$557$	−1.19224	+	6.76151i	−0.0505167	+	0.286494i	0.949076	+	0.315049i	$0.102021\pi$
$558$	−2.09664	+	3.63148i	−0.0887577	+	0.153733i
$559$	−27.1945	−	47.1022i	−1.15020	−	1.99221i
$560$	0.916747	−	0.333669i	0.0387396	−	0.0141001i
$561$	−6.39889	+	2.32901i	−0.270161	+	0.0983307i
$562$	−7.47810	−	12.9524i	−0.315444	−	0.546366i
$563$	−4.22139	+	7.31165i	−0.177910	+	0.308149i	−0.941165	−	0.337949i	$-0.890267\pi$
$563$	−4.22139	+	7.31165i	−0.177910	+	0.308149i	0.763254	+	0.646098i	$0.223600\pi$
$564$	−0.959572	+	5.44201i	−0.0404053	+	0.229150i
$565$	−4.61364	+	3.87130i	−0.194097	+	0.162867i
$566$	20.9292	+	17.5617i	0.879721	+	0.738173i
$567$	−0.169408	−	0.960761i	−0.00711447	−	0.0403482i
$568$	3.15609	+	1.14872i	0.132426	+	0.0481993i
$569$	9.96825			0.417891			0.208945	−	0.977927i	$-0.432997\pi$
$569$	9.96825			0.417891			0.208945	+	0.977927i	$0.432997\pi$
$570$	−3.05577	−	3.10842i	−0.127992	−	0.130197i
$571$	4.00704			0.167690			0.0838448	−	0.996479i	$-0.473280\pi$
$571$	4.00704			0.167690			0.0838448	+	0.996479i	$0.473280\pi$
$572$	−15.5689	−	5.66661i	−0.650968	−	0.236933i
$573$	1.43356	+	8.13011i	0.0598877	+	0.339640i
$574$	2.91288	+	2.44420i	0.121581	+	0.102019i
$575$	0.535155	−	0.449048i	0.0223175	−	0.0187266i
$576$	0.173648	−	0.984808i	0.00723534	−	0.0410337i
$577$	14.0151	−	24.2749i	0.583458	−	1.01058i	−0.411608	−	0.911361i	$-0.635033\pi$
$577$	14.0151	−	24.2749i	0.583458	−	1.01058i	0.995066	−	0.0992173i	$-0.0316339\pi$
$578$	5.14368	+	8.90912i	0.213949	+	0.370571i
$579$	17.5949	−	6.40401i	0.731218	−	0.266142i
$580$	−0.522946	+	0.190337i	−0.0217141	+	0.00790330i
$581$	−4.06439	−	7.03973i	−0.168619	−	0.292057i
$582$	−7.49284	+	12.9780i	−0.310588	+	0.537954i
$583$	−5.43038	+	30.7972i	−0.224903	+	1.27549i
$584$	−9.01067	+	7.56085i	−0.372864	+	0.312870i
$585$	4.82896	+	4.05198i	0.199653	+	0.167529i
$586$	−5.17994	−	29.3769i	−0.213981	−	1.21355i
$587$	25.7339	+	9.36639i	1.06215	+	0.386592i	0.813237	−	0.581933i	$-0.197703\pi$
$587$	25.7339	+	9.36639i	1.06215	+	0.386592i	0.248916	+	0.968525i	$0.419926\pi$
$588$	−6.04824			−0.249425
$589$	−4.88133	+	17.6142i	−0.201132	+	0.725780i
$590$	−3.79608			−0.156282
$591$	14.6784	+	5.34251i	0.603789	+	0.219761i
$592$	0.809495	+	4.59087i	0.0332700	+	0.188684i
$593$	−9.70147	−	8.14050i	−0.398392	−	0.334290i	0.421480	−	0.906838i	$-0.361511\pi$
$593$	−9.70147	−	8.14050i	−0.398392	−	0.334290i	−0.819872	+	0.572547i	$0.805955\pi$
$594$	2.01338	−	1.68943i	0.0826101	−	0.0693181i
$595$	−0.438915	+	2.48921i	−0.0179938	+	0.102048i
$596$	−6.12487	+	10.6086i	−0.250885	+	0.434545i
$597$	−8.28273	−	14.3461i	−0.338990	−	0.587148i
$598$	−4.13819	+	1.50618i	−0.169223	+	0.0615922i
$599$	−14.0783	+	5.12408i	−0.575224	+	0.209364i	−0.613218	−	0.789914i	$-0.710125\pi$
$599$	−14.0783	+	5.12408i	−0.575224	+	0.209364i	0.0379944	+	0.999278i	$0.487903\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	−2.57485	+	4.45976i	−0.105030	+	0.181918i	−0.913751	−	0.406276i	$-0.866827\pi$
$601$	−2.57485	+	4.45976i	−0.105030	+	0.181918i	0.808720	+	0.588193i	$0.200161\pi$
$602$	−1.46166	+	8.28946i	−0.0595727	+	0.337853i
$603$	−2.06291	+	1.73099i	−0.0840082	+	0.0704913i
$604$	2.46155	+	2.06548i	0.100159	+	0.0840433i
$605$	−0.710588	−	4.02995i	−0.0288895	−	0.163841i
$606$	0.793965	+	0.288980i	0.0322526	+	0.0117390i
$607$	−16.9757			−0.689022			−0.344511	−	0.938782i	$-0.611955\pi$
$607$	−16.9757			−0.689022			−0.344511	+	0.938782i	$0.611955\pi$
$608$	−0.342801	−	4.34540i	−0.0139024	−	0.176229i
$609$	−0.542918			−0.0220002
$610$	−7.07539	−	2.57523i	−0.286474	−	0.104268i
$611$	−6.04891	−	34.3051i	−0.244713	−	1.38783i
$612$	1.98473	+	1.66538i	0.0802278	+	0.0673191i
$613$	23.6149	−	19.8152i	0.953795	−	0.800329i	−0.0261372	−	0.999658i	$-0.508321\pi$
$613$	23.6149	−	19.8152i	0.953795	−	0.800329i	0.979933	+	0.199329i	$0.0638762\pi$
$614$	5.63562	−	31.9612i	0.227435	−	1.28985i
$615$	1.94884	−	3.37548i	0.0785847	−	0.136113i
$616$	1.28205	+	2.22058i	0.0516554	+	0.0894698i
$617$	−29.1822	+	10.6215i	−1.17483	+	0.427604i	−0.854374	−	0.519658i	$-0.826059\pi$
$617$	−29.1822	+	10.6215i	−1.17483	+	0.427604i	−0.320459	+	0.947263i	$0.603837\pi$
$618$	6.43111	−	2.34073i	0.258697	−	0.0941581i
$619$	16.8170	+	29.1278i	0.675931	+	1.17075i	0.976196	+	0.216890i	$0.0695914\pi$
$619$	16.8170	+	29.1278i	0.675931	+	1.17075i	−0.300265	+	0.953856i	$0.597075\pi$
$620$	−2.09664	+	3.63148i	−0.0842029	+	0.145844i
$621$	0.121310	−	0.687981i	0.00486799	−	0.0276077i
$622$	−24.0576	+	20.1867i	−0.964620	+	0.809413i
$623$	5.46014	+	4.58160i	0.218756	+	0.183558i
$624$	1.09464	+	6.20799i	0.0438205	+	0.248518i
$625$	−0.939693	−	0.342020i	−0.0375877	−	0.0136808i
$626$	−31.4798			−1.25819
$627$	6.65105	−	9.32809i	0.265618	−	0.372528i
$628$	−17.3222			−0.691230
$629$	−11.3495	−	4.13087i	−0.452533	−	0.164709i
$630$	−0.169408	−	0.960761i	−0.00674938	−	0.0382776i
$631$	−2.27913	−	1.91242i	−0.0907307	−	0.0761321i	0.596294	−	0.802766i	$-0.296639\pi$
$631$	−2.27913	−	1.91242i	−0.0907307	−	0.0761321i	−0.687025	+	0.726634i	$0.741084\pi$
$632$	5.47667	−	4.59547i	0.217850	−	0.182798i
$633$	0.220668	−	1.25147i	0.00877077	−	0.0497415i
$634$	−4.49256	+	7.78135i	−0.178423	+	0.309037i
$635$	5.75978	+	9.97623i	0.228570	+	0.395895i
$636$	11.1808	−	4.06948i	0.443348	−	0.161365i
$637$	35.8273	−	13.0401i	1.41953	−	0.516666i
$638$	−0.731330	−	1.26670i	−0.0289536	−	0.0501491i
$639$	1.67932	−	2.90866i	0.0664328	−	0.115065i
$640$	0.173648	−	0.984808i	0.00686405	−	0.0389279i
$641$	30.6875	−	25.7498i	1.21208	−	1.01706i	0.212881	−	0.977078i	$-0.431715\pi$
$641$	30.6875	−	25.7498i	1.21208	−	1.01706i	0.999201	−	0.0399793i	$-0.0127292\pi$
$642$	14.6172	+	12.2653i	0.576894	+	0.484072i
$643$	3.34155	+	18.9509i	0.131778	+	0.747350i	0.977049	+	0.213013i	$0.0683276\pi$
$643$	3.34155	+	18.9509i	0.131778	+	0.747350i	−0.845272	+	0.534337i	$0.820561\pi$
$644$	0.640435	+	0.233099i	0.0252367	+	0.00918539i
$645$	8.62802			0.339728
$646$	10.1941	+	4.86003i	0.401082	+	0.191215i
$647$	−24.3135			−0.955863			−0.477931	−	0.878397i	$-0.658613\pi$
$647$	−24.3135			−0.955863			−0.477931	+	0.878397i	$0.658613\pi$
$648$	−0.939693	−	0.342020i	−0.0369146	−	0.0134358i
$649$	−1.73252	−	9.82562i	−0.0680074	−	0.385689i
$650$	4.82896	+	4.05198i	0.189407	+	0.158932i
$651$	−3.13380	+	2.62957i	−0.122823	+	0.103061i
$652$	−3.29744	+	18.7007i	−0.129138	+	0.732377i
$653$	21.2380	−	36.7854i	0.831109	−	1.43952i	−0.0660504	−	0.997816i	$-0.521040\pi$
$653$	21.2380	−	36.7854i	0.831109	−	1.43952i	0.897159	−	0.441707i	$-0.145627\pi$
$654$	3.55524	+	6.15786i	0.139021	+	0.240791i
$655$	9.16093	−	3.33431i	0.357947	−	0.130282i
$656$	3.66261	−	1.33308i	0.143001	−	0.0520481i
$657$	5.88129	+	10.1867i	0.229451	+	0.397421i
$658$	−2.69551	+	4.66876i	−0.105082	+	0.182007i
$659$	7.71698	−	43.7652i	0.300611	−	1.70485i	−0.342867	−	0.939384i	$-0.611398\pi$
$659$	7.71698	−	43.7652i	0.300611	−	1.70485i	0.643478	−	0.765465i	$-0.277491\pi$
$660$	2.01338	−	1.68943i	0.0783708	−	0.0657609i
$661$	−11.4810	−	9.63374i	−0.446561	−	0.374709i	0.391597	−	0.920137i	$-0.371923\pi$
$661$	−11.4810	−	9.63374i	−0.446561	−	0.374709i	−0.838158	+	0.545428i	$0.816367\pi$
$662$	−2.45120	−	13.9015i	−0.0952687	−	0.540295i
$663$	−15.3473	−	5.58595i	−0.596039	−	0.216940i
$664$	−8.33224			−0.323354
$665$	−1.76419	−	3.86925i	−0.0684122	−	0.150043i
$666$	4.66169			0.180637
$667$	−0.365327	−	0.132968i	−0.0141455	−	0.00514855i
$668$	−1.17243	−	6.64917i	−0.0453626	−	0.257264i
$669$	9.38140	+	7.87193i	0.362706	+	0.304346i
$670$	−2.06291	+	1.73099i	−0.0796972	+	0.0668739i
$671$	3.43643	−	19.4890i	0.132662	−	0.752363i
$672$	0.487791	−	0.844879i	0.0188169	−	0.0325919i
$673$	4.25742	+	7.37408i	0.164112	+	0.284250i	0.936339	−	0.351096i	$-0.114191\pi$
$673$	4.25742	+	7.37408i	0.164112	+	0.284250i	−0.772228	+	0.635346i	$0.780858\pi$
$674$	13.6638	−	4.97321i	0.526309	−	0.191561i
$675$	−0.939693	+	0.342020i	−0.0361688	+	0.0131644i
$676$	−13.3687	−	23.1552i	−0.514179	−	0.890584i
$677$	10.4409	−	18.0841i	0.401275	−	0.695029i	−0.592605	−	0.805493i	$-0.701900\pi$
$677$	10.4409	−	18.0841i	0.401275	−	0.695029i	0.993880	+	0.110464i	$0.0352337\pi$
$678$	−1.04583	+	5.93118i	−0.0401648	+	0.227786i
$679$	−11.1994	+	9.39739i	−0.429793	+	0.360639i
$680$	1.98473	+	1.66538i	0.0761107	+	0.0638645i
$681$	4.53329	+	25.7096i	0.173716	+	0.985193i
$682$	−10.3565	−	3.76944i	−0.396569	−	0.144339i
$683$	−28.4039			−1.08684			−0.543422	−	0.839459i	$-0.682872\pi$
$683$	−28.4039			−1.08684			−0.543422	+	0.839459i	$0.682872\pi$
$684$	−4.33891	−	0.416977i	−0.165902	−	0.0159435i
$685$	20.9188			0.799266
$686$	−11.9619	−	4.35379i	−0.456709	−	0.166228i
$687$	−2.14520	−	12.1660i	−0.0818445	−	0.464163i
$688$	6.60945	+	5.54599i	0.251983	+	0.211439i
$689$	−57.4567	+	48.2119i	−2.18893	+	1.83673i
$690$	0.121310	−	0.687981i	0.00461818	−	0.0261910i
$691$	10.5263	−	18.2321i	0.400439	−	0.693580i	−0.593340	−	0.804952i	$-0.702191\pi$
$691$	10.5263	−	18.2321i	0.400439	−	0.693580i	0.993779	+	0.111372i	$0.0355244\pi$
$692$	−6.76264	−	11.7132i	−0.257077	−	0.445270i
$693$	2.40947	−	0.876977i	0.0915283	−	0.0333136i
$694$	−10.8054	+	3.93285i	−0.410168	+	0.149289i
$695$	−4.29764	−	7.44373i	−0.163019	−	0.282357i
$696$	−0.278253	+	0.481949i	−0.0105472	+	0.0182682i
$697$	−1.75357	+	9.94496i	−0.0664210	+	0.376692i
$698$	18.1995	−	15.2712i	0.688861	−	0.578023i
$699$	−6.86499	−	5.76041i	−0.259658	−	0.217879i
$700$	−0.169408	−	0.960761i	−0.00640302	−	0.0363133i
$701$	10.6908	+	3.89115i	0.403788	+	0.146967i	0.535927	−	0.844264i	$-0.319962\pi$
$701$	10.6908	+	3.89115i	0.403788	+	0.146967i	−0.132139	+	0.991231i	$0.542185\pi$
$702$	6.30375			0.237920
$703$	19.6717	−	5.09133i	0.741931	−	0.192023i
$704$	2.62829			0.0990572
$705$	5.19270	+	1.88999i	0.195568	+	0.0711811i
$706$	−6.06635	−	34.4040i	−0.228310	−	1.29481i
$707$	0.631442	+	0.529842i	0.0237478	+	0.0199268i
$708$	−2.90797	+	2.44008i	−0.109288	+	0.0917037i
$709$	−2.47193	+	14.0190i	−0.0928351	+	0.526494i	0.902554	+	0.430576i	$0.141690\pi$
$709$	−2.47193	+	14.0190i	−0.0928351	+	0.526494i	−0.995389	+	0.0959177i	$0.969421\pi$
$710$	1.67932	−	2.90866i	0.0630237	−	0.109160i
$711$	−3.57464	−	6.19146i	−0.134060	−	0.232198i
$712$	6.86549	−	2.49883i	0.257295	−	0.0936478i
$713$	−2.75273	+	1.00191i	−0.103091	+	0.0375219i
$714$	1.26381	+	2.18897i	0.0472967	+	0.0819203i
$715$	−8.28403	+	14.3484i	−0.309805	+	0.536598i
$716$	−0.00733290	+	0.0415869i	−0.000274043	+	0.00155418i
$717$	−6.49204	+	5.44747i	−0.242450	+	0.203439i
$718$	14.8287	+	12.4428i	0.553404	+	0.464361i
$719$	−1.55342	−	8.80991i	−0.0579330	−	0.328554i	0.942043	−	0.335492i	$-0.108903\pi$
$719$	−1.55342	−	8.80991i	−0.0579330	−	0.328554i	−0.999976	+	0.00693805i	$0.997792\pi$
$720$	−0.939693	−	0.342020i	−0.0350203	−	0.0127463i
$721$	6.67673			0.248655
$722$	−18.7650	+	2.97921i	−0.698360	+	0.110875i
$723$	12.1262			0.450980
$724$	−10.5154	−	3.82731i	−0.390804	−	0.142241i
$725$	0.0966364	+	0.548052i	0.00358899	+	0.0203542i
$726$	−3.13474	−	2.63036i	−0.116341	−	0.0976219i
$727$	−3.98515	+	3.34394i	−0.147801	+	0.124020i	−0.713690	−	0.700462i	$-0.752977\pi$
$727$	−3.98515	+	3.34394i	−0.147801	+	0.124020i	0.565889	+	0.824481i	$0.308533\pi$
$728$	−1.06791	+	6.05640i	−0.0395792	+	0.224465i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	5.88129	+	10.1867i	0.217676	+	0.377027i
$731$	−21.0060	+	7.64556i	−0.776935	+	0.282781i
$732$	−7.07539	+	2.57523i	−0.261514	+	0.0951833i
$733$	11.2461	+	19.4788i	0.415383	+	0.719465i	0.995469	−	0.0950907i	$-0.0303141\pi$
$733$	11.2461	+	19.4788i	0.415383	+	0.719465i	−0.580085	+	0.814556i	$0.696981\pi$
$734$	−6.47701	+	11.2185i	−0.239071	+	0.414083i
$735$	−1.05027	+	5.95635i	−0.0387396	+	0.219703i
$736$	0.535155	−	0.449048i	0.0197261	−	0.0165521i
$737$	−5.42192	−	4.54953i	−0.199719	−	0.167584i
$738$	−0.676824	−	3.83846i	−0.0249142	−	0.141296i
$739$	37.4937	+	13.6466i	1.37923	+	0.501998i	0.921944	−	0.387323i	$-0.126600\pi$
$739$	37.4937	+	13.6466i	1.37923	+	0.501998i	0.457283	+	0.889321i	$0.348822\pi$
$740$	4.66169			0.171367
$741$	26.6009	−	6.88473i	0.977210	−	0.252917i
$742$	11.6078			0.426137
$743$	−8.74588	−	3.18324i	−0.320855	−	0.116782i	0.176571	−	0.984288i	$-0.443499\pi$
$743$	−8.74588	−	3.18324i	−0.320855	−	0.116782i	−0.497426	+	0.867506i	$0.665722\pi$
$744$	0.728154	+	4.12957i	0.0266954	+	0.151397i
$745$	9.38385	+	7.87398i	0.343798	+	0.288480i
$746$	−3.30910	+	2.77666i	−0.121155	+	0.101661i
$747$	−1.44688	+	8.20565i	−0.0529385	+	0.300229i
$748$	−3.40478	+	5.89725i	−0.124491	+	0.215625i
$749$	9.30773	+	16.1215i	0.340097	+	0.589065i
$750$	−0.939693	+	0.342020i	−0.0343127	+	0.0124888i
$751$	−22.7469	+	8.27920i	−0.830047	+	0.302112i	−0.721878	−	0.692020i	$-0.756721\pi$
$751$	−22.7469	+	8.27920i	−0.830047	+	0.302112i	−0.108169	+	0.994133i	$0.534499\pi$
$752$	2.76298	+	4.78562i	0.100755	+	0.174514i
$753$	−3.04501	+	5.27411i	−0.110966	+	0.192199i
$754$	0.609172	−	3.45479i	0.0221847	−	0.125816i
$755$	2.46155	−	2.06548i	0.0895848	−	0.0751706i
$756$	−0.747339	−	0.627092i	−0.0271805	−	0.0228071i
$757$	−5.63674	−	31.9675i	−0.204871	−	1.16188i	−0.897643	−	0.440723i	$-0.854722\pi$
$757$	−5.63674	−	31.9675i	−0.204871	−	1.16188i	0.692773	−	0.721156i	$-0.256389\pi$
$758$	12.6429	+	4.60165i	0.459211	+	0.167139i
$759$	1.83611			0.0666464
$760$	−4.33891	−	0.416977i	−0.157389	−	0.0151254i
$761$	10.5224			0.381437			0.190719	−	0.981645i	$-0.438918\pi$
$761$	10.5224			0.381437			0.190719	+	0.981645i	$0.438918\pi$
$762$	10.8248	+	3.93992i	0.392143	+	0.142728i
$763$	1.20457	+	6.83147i	0.0436085	+	0.247316i
$764$	6.32410	+	5.30655i	0.228798	+	0.191984i
$765$	1.98473	−	1.66538i	0.0717579	−	0.0602120i
$766$	−0.588794	+	3.33922i	−0.0212740	+	0.120651i
$767$	11.9648	−	20.7236i	0.432023	−	0.748287i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	45.5570	−	16.5814i	1.64283	−	0.597940i	0.655296	−	0.755372i	$-0.272544\pi$
$769$	45.5570	−	16.5814i	1.64283	−	0.597940i	0.987530	+	0.157432i	$0.0503216\pi$
$770$	2.40947	−	0.876977i	0.0868314	−	0.0316040i
$771$	−7.45562	−	12.9135i	−0.268508	−	0.465069i
$772$	9.36203	−	16.2155i	0.336947	−	0.583609i
$773$	−3.33706	+	18.9254i	−0.120026	+	0.680700i	0.864113	+	0.503298i	$0.167880\pi$
$773$	−3.33706	+	18.9254i	−0.120026	+	0.680700i	−0.984139	+	0.177402i	$0.943231\pi$
$774$	6.60945	−	5.54599i	0.237572	−	0.199346i
$775$	3.21223	+	2.69538i	0.115387	+	0.0968210i
$776$	2.60223	+	14.7580i	0.0934148	+	0.529782i
$777$	4.27359	+	1.55546i	0.153314	+	0.0558019i
$778$	−13.7418			−0.492666
$779$	−7.04832	−	15.4585i	−0.252532	−	0.553859i
$780$	6.30375			0.225711
$781$	8.29509	+	3.01917i	0.296822	+	0.108034i
$782$	0.314298	+	1.78247i	0.0112393	+	0.0637411i
$783$	0.426309	+	0.357716i	0.0152350	+	0.0127837i
$784$	−4.63322	+	3.88773i	−0.165472	+	0.138848i
$785$	−3.00796	+	17.0590i	−0.107359	+	0.608862i
$786$	4.87443	−	8.44276i	0.173865	−	0.301143i
$787$	−10.9649	−	18.9918i	−0.390858	−	0.676986i	0.601705	−	0.798718i	$-0.294488\pi$
$787$	−10.9649	−	18.9918i	−0.390858	−	0.676986i	−0.992563	+	0.121733i	$0.961155\pi$
$788$	14.6784	−	5.34251i	0.522897	−	0.190319i
$789$	11.7279	−	4.26860i	0.417523	−	0.151966i
$790$	−3.57464	−	6.19146i	−0.127180	−	0.220282i
$791$	−2.93781	+	5.08843i	−0.104456	+	0.180924i
$792$	0.456397	−	2.58836i	0.0162174	−	0.0919732i
$793$	36.3595	−	30.5093i	1.29116	−	1.08342i
$794$	15.0050	+	12.5907i	0.532506	+	0.446826i
$795$	−2.06613	−	11.7176i	−0.0732781	−	0.415581i
$796$	−15.5664	−	5.66572i	−0.551738	−	0.200816i
$797$	44.2314			1.56676			0.783378	−	0.621546i	$-0.213495\pi$
$797$	44.2314			1.56676			0.783378	+	0.621546i	$0.213495\pi$
$798$	−3.83855	−	1.83002i	−0.135883	−	0.0647820i
$799$	−14.3171			−0.506501
$800$	−0.939693	−	0.342020i	−0.0332232	−	0.0120922i
$801$	−1.26869	−	7.19511i	−0.0448270	−	0.254227i
$802$	−5.02988	−	4.22057i	−0.177611	−	0.149033i
$803$	−23.6826	+	19.8721i	−0.835741	+	0.701270i
$804$	−0.467624	+	2.65203i	−0.0164918	+	0.0935298i
$805$	0.340768	−	0.590228i	0.0120105	−	0.0208028i
$806$	−13.2167	−	22.8920i	−0.465538	−	0.806335i
$807$	6.33965	−	2.30744i	0.223166	−	0.0812259i
$808$	0.793965	−	0.288980i	0.0279316	−	0.0101663i
$809$	17.2425	+	29.8648i	0.606212	+	1.04999i	0.991859	+	0.127344i	$0.0406452\pi$
$809$	17.2425	+	29.8648i	0.606212	+	1.04999i	−0.385646	+	0.922647i	$0.626022\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	−3.76489	+	21.3517i	−0.132203	+	0.749761i	0.844564	+	0.535455i	$0.179860\pi$
$811$	−3.76489	+	21.3517i	−0.132203	+	0.749761i	−0.976767	+	0.214305i	$0.931251\pi$
$812$	−0.415899	+	0.348981i	−0.0145952	+	0.0122468i
$813$	10.6812	+	8.96256i	0.374605	+	0.314331i
$814$	2.12758	+	12.0661i	0.0745718	+	0.422917i
$815$	17.8440	+	6.49470i	0.625049	+	0.227499i
$816$	2.59087			0.0906988
$817$	21.8338	−	30.6219i	0.763868	−	1.07132i
$818$	19.7304			0.689857
$819$	5.77895	+	2.10337i	0.201933	+	0.0734975i
$820$	−0.676824	−	3.83846i	−0.0236357	−	0.134045i
$821$	3.07991	+	2.58435i	0.107489	+	0.0901944i	0.694948	−	0.719060i	$-0.255427\pi$
$821$	3.07991	+	2.58435i	0.107489	+	0.0901944i	−0.587459	+	0.809254i	$0.699872\pi$
$822$	16.0247	−	13.4463i	0.558927	−	0.468995i
$823$	3.67755	−	20.8564i	0.128191	−	0.727009i	−0.851170	−	0.524890i	$-0.824106\pi$
$823$	3.67755	−	20.8564i	0.128191	−	0.727009i	0.979361	−	0.202118i	$-0.0647826\pi$
$824$	3.42192	−	5.92695i	0.119208	−	0.206475i
$825$	−1.31414	−	2.27616i	−0.0457526	−	0.0792458i
$826$	−3.48005	+	1.26663i	−0.121086	+	0.0440718i
$827$	−38.5138	+	14.0179i	−1.33926	+	0.487449i	−0.909578	−	0.415534i	$-0.863595\pi$
$827$	−38.5138	+	14.0179i	−1.33926	+	0.487449i	−0.429677	+	0.902983i	$0.641373\pi$
$828$	−0.349297	−	0.605001i	−0.0121389	−	0.0210252i
$829$	−2.63006	+	4.55540i	−0.0913458	+	0.158216i	−0.908078	−	0.418802i	$-0.862450\pi$
$829$	−2.63006	+	4.55540i	−0.0913458	+	0.158216i	0.816732	+	0.577017i	$0.195784\pi$
$830$	−1.44688	+	8.20565i	−0.0502219	+	0.284822i
$831$	−8.83723	+	7.41532i	−0.306560	+	0.257235i
$832$	4.82896	+	4.05198i	0.167414	+	0.140477i
$833$	−2.72111	−	15.4322i	−0.0942808	−	0.534693i
$834$	−8.07692	−	2.93976i	−0.279681	−	0.101795i
$835$	−6.75174			−0.233654
$836$	−0.900979	−	11.4209i	−0.0311610	−	0.395002i
$837$	4.19327			0.144941
$838$	−37.2347	−	13.5523i	−1.28625	−	0.468157i
$839$	−7.44162	−	42.2035i	−0.256913	−	1.45703i	−0.791113	−	0.611669i	$-0.790498\pi$
$839$	−7.44162	−	42.2035i	−0.256913	−	1.45703i	0.534200	−	0.845358i	$-0.320613\pi$
$840$	−0.747339	−	0.627092i	−0.0257856	−	0.0216367i
$841$	−21.9780	+	18.4418i	−0.757864	+	0.635923i
$842$	−4.35511	+	24.6991i	−0.150087	+	0.851187i
$843$	−7.47810	+	12.9524i	−0.257559	+	0.446106i
$844$	−0.635388	−	1.10052i	−0.0218710	−	0.0378816i
$845$	−25.1249	+	9.14470i	−0.864321	+	0.314587i
$846$	5.19270	−	1.88999i	0.178529	−	0.0649792i
$847$	−1.99610	−	3.45734i	−0.0685867	−	0.118796i
$848$	5.94918	−	10.3043i	0.204296	−	0.353851i
$849$	4.74427	−	26.9061i	0.162823	−	0.923415i
$850$	1.98473	−	1.66538i	0.0680755	−	0.0571221i
$851$	2.49473	+	2.09332i	0.0855181	+	0.0717582i
$852$	−0.583221	−	3.30761i	−0.0199808	−	0.113317i
$853$	−11.6058	−	4.22416i	−0.397374	−	0.144632i	0.135600	−	0.990764i	$-0.456704\pi$
$853$	−11.6058	−	4.22416i	−0.397374	−	0.144632i	−0.532975	+	0.846131i	$0.678926\pi$
$854$	−7.34562			−0.251362
$855$	−1.16409	+	4.20058i	−0.0398109	+	0.143657i
$856$	19.0814			0.652188
$857$	−36.2644	−	13.1992i	−1.23877	−	0.450875i	−0.362177	−	0.932109i	$-0.617966\pi$
$857$	−36.2644	−	13.1992i	−1.23877	−	0.450875i	−0.876592	+	0.481234i	$0.840189\pi$
$858$	2.87701	+	16.3164i	0.0982197	+	0.557031i
$859$	16.2561	+	13.6405i	0.554651	+	0.465408i	0.876513	−	0.481379i	$-0.159864\pi$
$859$	16.2561	+	13.6405i	0.554651	+	0.465408i	−0.321861	+	0.946787i	$0.604308\pi$
$860$	6.60945	−	5.54599i	0.225380	−	0.189117i
$861$	0.660297	−	3.74473i	0.0225029	−	0.127620i
$862$	−3.46707	+	6.00515i	−0.118089	+	0.204536i
$863$	−6.88580	−	11.9266i	−0.234396	−	0.405985i	0.724701	−	0.689063i	$-0.241978\pi$
$863$	−6.88580	−	11.9266i	−0.234396	−	0.405985i	−0.959097	+	0.283078i	$0.908644\pi$
$864$	−0.939693	+	0.342020i	−0.0319690	+	0.0116358i
$865$	−12.7096	+	4.62592i	−0.432140	+	0.157286i
$866$	−13.8075	−	23.9152i	−0.469196	−	0.812672i
$867$	5.14368	−	8.90912i	0.174689	−	0.302570i
$868$	−0.710374	+	4.02873i	−0.0241117	+	0.136744i
$869$	14.3942	−	12.0782i	0.488291	−	0.409725i
$870$	0.426309	+	0.357716i	0.0144532	+	0.0121277i
$871$	−2.94779	−	16.7177i	−0.0998820	−	0.566459i
$872$	6.68167	+	2.43193i	0.226270	+	0.0823555i
$873$	14.9857			0.507188
$874$	−2.13474	−	2.17153i	−0.0722088	−	0.0734530i
$875$	−0.975582			−0.0329807
$876$	11.0532	+	4.02304i	0.373454	+	0.135926i
$877$	2.93928	+	16.6695i	0.0992525	+	0.562889i	0.993361	+	0.115038i	$0.0366991\pi$
$877$	2.93928	+	16.6695i	0.0992525	+	0.562889i	−0.894109	+	0.447850i	$0.852190\pi$
$878$	−27.4905	−	23.0673i	−0.927759	−	0.778482i
$879$	−22.8512	+	19.1744i	−0.770751	+	0.646736i
$880$	0.456397	−	2.58836i	0.0153851	−	0.0872535i
$881$	27.1342	−	46.9978i	0.914174	−	1.58340i	0.106068	−	0.994359i	$-0.466174\pi$
$881$	27.1342	−	46.9978i	0.914174	−	1.58340i	0.808106	−	0.589037i	$-0.200493\pi$
$882$	3.02412	+	5.23793i	0.101827	+	0.176370i
$883$	−19.0473	+	6.93266i	−0.640994	+	0.233303i	−0.642009	−	0.766697i	$-0.721899\pi$
$883$	−19.0473	+	6.93266i	−0.640994	+	0.233303i	0.00101557	+	0.999999i	$0.499677\pi$
$884$	−15.3473	+	5.58595i	−0.516185	+	0.187876i
$885$	1.89804	+	3.28750i	0.0638020	+	0.110508i
$886$	6.78936	−	11.7595i	0.228093	−	0.395069i
$887$	−5.45136	+	30.9162i	−0.183039	+	1.03806i	0.745411	+	0.666605i	$0.232253\pi$
$887$	−5.45136	+	30.9162i	−0.183039	+	1.03806i	−0.928449	+	0.371459i	$0.878858\pi$
$888$	3.57106	−	2.99648i	0.119837	−	0.100555i
$889$	8.60902	+	7.22383i	0.288737	+	0.242279i
$890$	−1.26869	−	7.19511i	−0.0425266	−	0.241181i
$891$	−2.46978	−	0.898927i	−0.0827408	−	0.0301152i
$892$	12.2465			0.410045
$893$	19.8483	−	13.6468i	0.664197	−	0.456671i
$894$	12.2497			0.409693
$895$	0.0396818	+	0.0144430i	0.00132642	+	0.000482776i
$896$	−0.169408	−	0.960761i	−0.00565952	−	0.0320968i
$897$	3.37348	+	2.83069i	0.112637	+	0.0945139i
$898$	−5.85251	+	4.91084i	−0.195301	+	0.163877i
$899$	0.405223	−	2.29813i	0.0135149	−	0.0766470i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	15.4136	+	26.6971i	0.513501	+	0.889410i
$902$	9.62639	−	3.50372i	0.320524	−	0.116661i
$903$	7.90971	−	2.87890i	0.263219	−	0.0958038i
$904$	3.01134	+	5.21579i	0.100156	+	0.173475i
$905$	−5.59515	+	9.69109i	−0.185989	+	0.322143i
$906$	0.557987	−	3.16450i	0.0185379	−	0.105134i
$907$	3.96751	−	3.32914i	0.131739	−	0.110542i	−0.574537	−	0.818478i	$-0.694818\pi$
$907$	3.96751	−	3.32914i	0.131739	−	0.110542i	0.706276	+	0.707936i	$0.250374\pi$
$908$	19.9985	+	16.7807i	0.663674	+	0.556888i
$909$	−0.146719	−	0.832083i	−0.00486635	−	0.0275985i
$910$	5.77895	+	2.10337i	0.191570	+	0.0697259i
$911$	−48.2911			−1.59995			−0.799977	−	0.600030i	$-0.795155\pi$
$911$	−48.2911			−1.59995			−0.799977	+	0.600030i	$0.795155\pi$
$912$	−3.59182	+	2.46957i	−0.118937	+	0.0817758i
$913$	−21.8995			−0.724768
$914$	−25.9698	−	9.45222i	−0.859003	−	0.312652i
$915$	1.30748	+	7.41509i	0.0432240	+	0.245135i
$916$	−9.46349	−	7.94081i	−0.312683	−	0.262372i
$917$	7.28570	−	6.11343i	0.240595	−	0.201883i
$918$	0.449901	−	2.55151i	0.0148489	−	0.0842125i
$919$	−12.9892	+	22.4980i	−0.428474	+	0.742139i	−0.996738	−	0.0807074i	$-0.974282\pi$
$919$	−12.9892	+	22.4980i	−0.428474	+	0.742139i	0.568264	+	0.822847i	$0.307615\pi$
$920$	−0.349297	−	0.605001i	−0.0115160	−	0.0199463i
$921$	−30.4970	+	11.1000i	−1.00491	+	0.365758i
$922$	29.1455	−	10.6081i	0.959857	−	0.349359i
$923$	10.5860	+	18.3355i	0.348443	+	0.603520i
$924$	1.28205	−	2.22058i	0.0421765	−	0.0730518i
$925$	0.809495	−	4.59087i	0.0266160	−	0.150947i
$926$	28.6092	−	24.0060i	0.940158	−	0.788886i
$927$	−5.24269	−	4.39914i	−0.172193	−	0.144487i
$928$	0.0966364	+	0.548052i	0.00317225	+	0.0179907i
$929$	36.4252	+	13.2577i	1.19507	+	0.434971i	0.861502	−	0.507754i	$-0.169524\pi$
$929$	36.4252	+	13.2577i	1.19507	+	0.434971i	0.333571	+	0.942725i	$0.391746\pi$
$930$	4.19327			0.137503
$931$	18.4820	+	18.8005i	0.605724	+	0.616161i
$932$	−8.96161			−0.293547
$933$	29.5110	+	10.7411i	0.966146	+	0.351648i
$934$	−5.20799	−	29.5360i	−0.170411	−	0.966448i
$935$	5.21642	+	4.37710i	0.170595	+	0.143146i
$936$	4.82896	−	4.05198i	0.157839	−	0.132443i
$937$	−9.16495	+	51.9770i	−0.299406	+	1.69802i	0.349329	+	0.937000i	$0.386410\pi$
$937$	−9.16495	+	51.9770i	−0.299406	+	1.69802i	−0.648734	+	0.761015i	$0.724701\pi$
$938$	−1.31359	+	2.27521i	−0.0428903	+	0.0742882i
$939$	15.7399	+	27.2623i	0.513653	+	0.889673i
$940$	5.19270	−	1.88999i	0.169367	−	0.0616446i
$941$	42.2100	−	15.3632i	1.37601	−	0.500825i	0.455041	−	0.890471i	$-0.349625\pi$
$941$	42.2100	−	15.3632i	1.37601	−	0.500825i	0.920965	+	0.389645i	$0.127402\pi$
$942$	8.66108	+	15.0014i	0.282193	+	0.488773i
$943$	1.36145	−	2.35809i	0.0443348	−	0.0767901i
$944$	−0.659183	+	3.73841i	−0.0214546	+	0.121675i
$945$	−0.747339	+	0.627092i	−0.0243109	+	0.0203993i
$946$	17.3715	+	14.5764i	0.564797	+	0.473921i
$947$	−5.87998	−	33.3470i	−0.191074	−	1.08363i	−0.917900	−	0.396812i	$-0.870117\pi$
$947$	−5.87998	−	33.3470i	−0.191074	−	1.08363i	0.726826	−	0.686821i	$-0.240995\pi$
$948$	−6.71813	−	2.44520i	−0.218195	−	0.0794164i
$949$	−74.1485			−2.40696
$950$	−1.16409	+	4.20058i	−0.0377679	+	0.136285i
$951$	8.98513			0.291363
$952$	2.37518	+	0.864494i	0.0769799	+	0.0280184i
$953$	−2.96222	−	16.7996i	−0.0959556	−	0.544191i	−0.994450	−	0.105207i	$-0.966449\pi$
$953$	−2.96222	−	16.7996i	−0.0959556	−	0.544191i	0.898495	−	0.438984i	$-0.144662\pi$
$954$	−9.11468	−	7.64812i	−0.295099	−	0.247617i
$955$	6.32410	−	5.30655i	0.204643	−	0.171716i
$956$	−1.47163	+	8.34601i	−0.0475958	+	0.269929i
$957$	−0.731330	+	1.26670i	−0.0236405	+	0.0409466i
$958$	−9.85371	−	17.0671i	−0.318359	−	0.551414i
$959$	19.1772	−	6.97995i	0.619266	−	0.225394i
$960$	−0.939693	+	0.342020i	−0.0303284	+	0.0110387i
$961$	6.70823	+	11.6190i	0.216395	+	0.374806i
$962$	−14.6931	+	25.4492i	−0.473724	+	0.820514i
$963$	3.31345	−	18.7915i	0.106774	−	0.605548i
$964$	9.28924	−	7.79459i	0.299186	−	0.251047i
$965$	−14.3435	−	12.0356i	−0.461733	−	0.387440i
$966$	−0.118348	−	0.671182i	−0.00380777	−	0.0215949i
$967$	−42.7198	−	15.5487i	−1.37377	−	0.500013i	−0.453490	−	0.891262i	$-0.649821\pi$
$967$	−42.7198	−	15.5487i	−1.37377	−	0.500013i	−0.920285	+	0.391248i	$0.872043\pi$
$968$	−4.09212			−0.131526
$969$	−0.888155	−	11.2584i	−0.0285316	−	0.361671i
$970$	14.9857			0.481161
$971$	12.4090	+	4.51652i	0.398225	+	0.144942i	0.533366	−	0.845884i	$-0.320927\pi$
$971$	12.4090	+	4.51652i	0.398225	+	0.144942i	−0.135142	+	0.990826i	$0.543149\pi$
$972$	0.173648	+	0.984808i	0.00556977	+	0.0315877i
$973$	−6.42358	−	5.39003i	−0.205931	−	0.172796i
$974$	16.4493	−	13.8026i	0.527071	−	0.442265i
$975$	1.09464	−	6.20799i	0.0350564	−	0.198815i
$976$	−3.76474	+	6.52072i	−0.120506	+	0.208723i
$977$	−26.0750	−	45.1632i	−0.834212	−	1.44490i	−0.894670	−	0.446727i	$-0.852589\pi$
$977$	−26.0750	−	45.1632i	−0.834212	−	1.44490i	0.0604577	−	0.998171i	$-0.480744\pi$
$978$	17.8440	−	6.49470i	0.570589	−	0.207678i
$979$	18.0445	−	6.56765i	0.576704	−	0.209903i
$980$	3.02412	+	5.23793i	0.0966020	+	0.167320i
$981$	3.55524	−	6.15786i	0.113510	−	0.196605i
$982$	−1.35138	+	7.66406i	−0.0431243	+	0.244570i
$983$	−42.8135	+	35.9248i	−1.36554	+	1.14582i	−0.391309	+	0.920259i	$0.627978\pi$
$983$	−42.8135	+	35.9248i	−1.36554	+	1.14582i	−0.974229	+	0.225563i	$0.927578\pi$
$984$	−2.98579	−	2.50538i	−0.0951835	−	0.0798684i
$985$	−2.71246	−	15.3831i	−0.0864262	−	0.490147i
$986$	−1.35489	−	0.493138i	−0.0431484	−	0.0157047i
$987$	5.39102			0.171598
$988$	15.9521	−	22.3728i	0.507503	−	0.711772i
$989$	6.02749			0.191663
$990$	−2.46978	−	0.898927i	−0.0784948	−	0.0285698i
$991$	7.55802	+	42.8637i	0.240088	+	1.36161i	0.831628	+	0.555333i	$0.187409\pi$
$991$	7.55802	+	42.8637i	0.240088	+	1.36161i	−0.591540	+	0.806276i	$0.701480\pi$
$992$	3.21223	+	2.69538i	0.101989	+	0.0855785i
$993$	−10.8134	+	9.07353i	−0.343153	+	0.287940i
$994$	0.568980	−	3.22685i	0.0180469	−	0.102349i
$995$	−8.28273	+	14.3461i	−0.262580	+	0.454803i
$996$	4.16612	+	7.21593i	0.132009	+	0.228645i
$997$	−11.7614	+	4.28080i	−0.372488	+	0.135574i	−0.521479	−	0.853264i	$-0.674620\pi$
$997$	−11.7614	+	4.28080i	−0.372488	+	0.135574i	0.148991	+	0.988838i	$0.452397\pi$
$998$	29.7653	−	10.8337i	0.942205	−	0.342935i
$999$	−2.33085	−	4.03715i	−0.0737447	−	0.127730i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.i.61.2	✓	12	1.1	even	1	trivial
570.2.u.i.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)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.173648 + 0.984808i) q^{3} +(0.766044 + 0.642788i) q^{4} +(0.766044 - 0.642788i) q^{5} +(0.173648 - 0.984808i) q^{6} +(0.487791 - 0.844879i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(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} +(0.487791 - 0.844879i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(-0.939693 + 0.342020i) q^{10} +(-1.31414 - 2.27616i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(1.09464 - 6.20799i) q^{13} +(-0.747339 + 0.627092i) q^{14} +(0.766044 + 0.642788i) q^{15} +(0.173648 + 0.984808i) q^{16} +(-2.43463 - 0.886131i) q^{17} +1.00000 q^{18} +(4.21986 - 1.09216i) q^{19} +1.00000 q^{20} +(0.916747 + 0.333669i) q^{21} +(0.456397 + 2.58836i) q^{22} +(0.535155 + 0.449048i) q^{23} +(0.766044 - 0.642788i) q^{24} +(0.173648 - 0.984808i) q^{25} +(-3.15188 + 5.45921i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(0.916747 - 0.333669i) q^{28} +(-0.522946 + 0.190337i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(-2.09664 + 3.63148i) q^{31} +(0.173648 - 0.984808i) q^{32} +(2.01338 - 1.68943i) q^{33} +(1.98473 + 1.66538i) q^{34} +(-0.169408 - 0.960761i) q^{35} +(-0.939693 - 0.342020i) q^{36} +4.66169 q^{37} +(-4.33891 - 0.416977i) q^{38} +6.30375 q^{39} +(-0.939693 - 0.342020i) q^{40} +(-0.676824 - 3.83846i) q^{41} +(-0.747339 - 0.627092i) q^{42} +(6.60945 - 5.54599i) q^{43} +(0.456397 - 2.58836i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-0.349297 - 0.605001i) q^{46} +(5.19270 - 1.88999i) q^{47} +(-0.939693 + 0.342020i) q^{48} +(3.02412 + 5.23793i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.449901 - 2.55151i) q^{51} +(4.82896 - 4.05198i) q^{52} +(-9.11468 - 7.64812i) q^{53} +(0.173648 + 0.984808i) q^{54} +(-2.46978 - 0.898927i) q^{55} -0.975582 q^{56} +(1.80834 + 3.96609i) q^{57} +0.556507 q^{58} +(3.56715 + 1.29834i) q^{59} +(0.173648 + 0.984808i) q^{60} +(5.76791 + 4.83985i) q^{61} +(3.21223 - 2.69538i) q^{62} +(-0.169408 + 0.960761i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-3.15188 - 5.45921i) q^{65} +(-2.46978 + 0.898927i) q^{66} +(2.53054 - 0.921040i) q^{67} +(-1.29544 - 2.24376i) q^{68} +(-0.349297 + 0.605001i) q^{69} +(-0.169408 + 0.960761i) q^{70} +(-2.57286 + 2.15889i) q^{71} +(0.766044 + 0.642788i) q^{72} +(-2.04255 - 11.5839i) q^{73} +(-4.38056 - 1.59439i) q^{74} +1.00000 q^{75} +(3.93463 + 1.87582i) q^{76} -2.56411 q^{77} +(-5.92359 - 2.15601i) q^{78} +(1.24146 + 7.04067i) q^{79} +(0.766044 + 0.642788i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-0.676824 + 3.83846i) q^{82} +(4.16612 - 7.21593i) q^{83} +(0.487791 + 0.844879i) q^{84} +(-2.43463 + 0.886131i) q^{85} +(-8.10769 + 2.95096i) q^{86} +(-0.278253 - 0.481949i) q^{87} +(-1.31414 + 2.27616i) q^{88} +(-1.26869 + 7.19511i) q^{89} +(0.766044 - 0.642788i) q^{90} +(-4.71104 - 3.95303i) q^{91} +(0.121310 + 0.687981i) q^{92} +(-3.94039 - 1.43418i) q^{93} -5.52596 q^{94} +(2.53057 - 3.54912i) q^{95} +1.00000 q^{96} +(-14.0819 - 5.12540i) q^{97} +(-1.05027 - 5.95635i) q^{98} +(2.01338 + 1.68943i) 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	\( 12 q - 3 q^{7} - 6 q^{8} - 9 q^{11} - 6 q^{12} - 3 q^{13} + 3 q^{14} + 9 q^{17} + 12 q^{18} - 3 q^{19} + 12 q^{20} + 3 q^{21} - 6 q^{22} + 12 q^{23} - 9 q^{26} - 6 q^{27} + 3 q^{28} - 3 q^{29} - 6 q^{30} - 12 q^{31} + 3 q^{33} - 9 q^{34} - 6 q^{35} + 42 q^{37} + 18 q^{39} + 21 q^{41} + 3 q^{42} + 9 q^{43} - 6 q^{44} - 6 q^{45} - 3 q^{46} + 3 q^{49} - 6 q^{50} - 3 q^{52} - 18 q^{53} + 3 q^{55} + 6 q^{56} + 6 q^{58} - 15 q^{59} + 9 q^{61} + 12 q^{62} - 6 q^{63} - 6 q^{64} - 9 q^{65} + 3 q^{66} + 18 q^{67} - 6 q^{68} - 3 q^{69} - 6 q^{70} + 12 q^{71} - 9 q^{73} + 12 q^{75} + 9 q^{76} - 54 q^{77} + 6 q^{78} - 9 q^{79} + 21 q^{82} + 15 q^{83} - 3 q^{84} + 9 q^{85} - 27 q^{86} - 3 q^{87} - 9 q^{88} + 3 q^{89} - 51 q^{91} + 3 q^{92} - 15 q^{93} + 12 q^{96} - 48 q^{97} - 15 q^{98} + 3 q^{99}+O(q^{100}) \) 12 * q - 3 * q^7 - 6 * q^8 - 9 * q^11 - 6 * q^12 - 3 * q^13 + 3 * q^14 + 9 * q^17 + 12 * q^18 - 3 * q^19 + 12 * q^20 + 3 * q^21 - 6 * q^22 + 12 * q^23 - 9 * q^26 - 6 * q^27 + 3 * q^28 - 3 * q^29 - 6 * q^30 - 12 * q^31 + 3 * q^33 - 9 * q^34 - 6 * q^35 + 42 * q^37 + 18 * q^39 + 21 * q^41 + 3 * q^42 + 9 * q^43 - 6 * q^44 - 6 * q^45 - 3 * q^46 + 3 * q^49 - 6 * q^50 - 3 * q^52 - 18 * q^53 + 3 * q^55 + 6 * q^56 + 6 * q^58 - 15 * q^59 + 9 * q^61 + 12 * q^62 - 6 * q^63 - 6 * q^64 - 9 * q^65 + 3 * q^66 + 18 * q^67 - 6 * q^68 - 3 * q^69 - 6 * q^70 + 12 * q^71 - 9 * q^73 + 12 * q^75 + 9 * q^76 - 54 * q^77 + 6 * q^78 - 9 * q^79 + 21 * q^82 + 15 * q^83 - 3 * q^84 + 9 * q^85 - 27 * q^86 - 3 * q^87 - 9 * q^88 + 3 * q^89 - 51 * q^91 + 3 * q^92 - 15 * q^93 + 12 * q^96 - 48 * q^97 - 15 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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