LMFDB - Embedded newform 572.2.e.b.131.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(131,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("572.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.e (of order $2$, degree $1$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.7
Character	$\chi$	$=$	572.131
Dual form			572.2.e.b.131.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33395 - 0.469670i) q^{2} +3.04863i q^{3} +(1.55882 + 1.25303i) q^{4} -2.77923 q^{5} +(1.43185 - 4.06671i) q^{6} -0.398342 q^{7} +(-1.49087 - 2.40360i) q^{8} -6.29417 q^{9} +O(q^{10})$	\(q+(-1.33395 - 0.469670i) q^{2} +3.04863i q^{3} +(1.55882 + 1.25303i) q^{4} -2.77923 q^{5} +(1.43185 - 4.06671i) q^{6} -0.398342 q^{7} +(-1.49087 - 2.40360i) q^{8} -6.29417 q^{9} +(3.70734 + 1.30532i) q^{10} +(1.84401 - 2.75674i) q^{11} +(-3.82002 + 4.75227i) q^{12} -1.00000i q^{13} +(0.531366 + 0.187089i) q^{14} -8.47286i q^{15} +(0.859843 + 3.90649i) q^{16} -4.37142i q^{17} +(8.39608 + 2.95618i) q^{18} -5.64036 q^{19} +(-4.33232 - 3.48245i) q^{20} -1.21440i q^{21} +(-3.75457 + 2.81127i) q^{22} +0.542331i q^{23} +(7.32770 - 4.54512i) q^{24} +2.72413 q^{25} +(-0.469670 + 1.33395i) q^{26} -10.0427i q^{27} +(-0.620944 - 0.499134i) q^{28} +2.16310i q^{29} +(-3.97945 + 11.3023i) q^{30} +3.59359i q^{31} +(0.687778 - 5.61489i) q^{32} +(8.40430 + 5.62172i) q^{33} +(-2.05312 + 5.83124i) q^{34} +1.10708 q^{35} +(-9.81149 - 7.88677i) q^{36} +10.6214 q^{37} +(7.52394 + 2.64911i) q^{38} +3.04863 q^{39} +(4.14348 + 6.68017i) q^{40} -10.6003i q^{41} +(-0.570367 + 1.61994i) q^{42} +1.79968 q^{43} +(6.32876 - 1.98667i) q^{44} +17.4930 q^{45} +(0.254716 - 0.723440i) q^{46} -3.13709i q^{47} +(-11.9095 + 2.62135i) q^{48} -6.84132 q^{49} +(-3.63384 - 1.27944i) q^{50} +13.3269 q^{51} +(1.25303 - 1.55882i) q^{52} -2.00293 q^{53} +(-4.71677 + 13.3965i) q^{54} +(-5.12494 + 7.66162i) q^{55} +(0.593877 + 0.957455i) q^{56} -17.1954i q^{57} +(1.01594 - 2.88546i) q^{58} -3.35411i q^{59} +(10.6167 - 13.2077i) q^{60} +5.99977i q^{61} +(1.68780 - 4.79366i) q^{62} +2.50723 q^{63} +(-3.55460 + 7.16692i) q^{64} +2.77923i q^{65} +(-8.57052 - 11.4463i) q^{66} -1.31372i q^{67} +(5.47751 - 6.81426i) q^{68} -1.65337 q^{69} +(-1.47679 - 0.519964i) q^{70} -2.74132i q^{71} +(9.38381 + 15.1287i) q^{72} -11.0605i q^{73} +(-14.1684 - 4.98855i) q^{74} +8.30488i q^{75} +(-8.79231 - 7.06753i) q^{76} +(-0.734547 + 1.09813i) q^{77} +(-4.06671 - 1.43185i) q^{78} -15.8741 q^{79} +(-2.38970 - 10.8570i) q^{80} +11.7341 q^{81} +(-4.97866 + 14.1403i) q^{82} -12.6524 q^{83} +(1.52168 - 1.89303i) q^{84} +12.1492i q^{85} +(-2.40067 - 0.845253i) q^{86} -6.59450 q^{87} +(-9.37529 - 0.322321i) q^{88} -10.5207 q^{89} +(-23.3347 - 8.21592i) q^{90} +0.398342i q^{91} +(-0.679555 + 0.845396i) q^{92} -10.9556 q^{93} +(-1.47340 + 4.18471i) q^{94} +15.6759 q^{95} +(17.1177 + 2.09678i) q^{96} +12.5793 q^{97} +(9.12595 + 3.21316i) q^{98} +(-11.6065 + 17.3514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	$ 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) $ 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−1.33395	−	0.469670i	−0.943242	−	0.332107i
$2$	−1.33395	−	0.469670i	−0.943242	−	0.332107i
$3$			3.04863i			1.76013i	0.474853	+	0.880065i	$0.342501\pi$
$3$			3.04863i			1.76013i	−0.474853	+	0.880065i	$0.657499\pi$
$4$	1.55882	+	1.25303i	0.779410	+	0.626514i
$5$	−2.77923			−1.24291			−0.621455	−	0.783450i	$-0.713458\pi$
$5$	−2.77923			−1.24291			−0.621455	+	0.783450i	$0.713458\pi$
$6$	1.43185	−	4.06671i	0.584551	−	1.66023i
$7$	−0.398342			−0.150559			−0.0752795	−	0.997162i	$-0.523985\pi$
$7$	−0.398342			−0.150559			−0.0752795	+	0.997162i	$0.523985\pi$
$8$	−1.49087	−	2.40360i	−0.527103	−	0.849801i
$9$	−6.29417			−2.09806
$10$	3.70734	+	1.30532i	1.17237	+	0.412779i
$11$	1.84401	−	2.75674i	0.555990	−	0.831189i
$11$	1.84401	−	2.75674i	0.555990	−	0.831189i
$12$	−3.82002	+	4.75227i	−1.10275	+	1.37186i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	0.531366	+	0.187089i	0.142014	+	0.0500017i
$15$		−	8.47286i		−	2.18768i
$16$	0.859843	+	3.90649i	0.214961	+	0.976623i
$17$		−	4.37142i		−	1.06023i	−0.847927	−	0.530113i	$-0.822150\pi$
$17$		−	4.37142i		−	1.06023i	0.847927	−	0.530113i	$-0.177850\pi$
$18$	8.39608	+	2.95618i	1.97898	+	0.696779i
$19$	−5.64036			−1.29399			−0.646994	−	0.762495i	$-0.723974\pi$
$19$	−5.64036			−1.29399			−0.646994	+	0.762495i	$0.723974\pi$
$20$	−4.33232	−	3.48245i	−0.968737	−	0.778701i
$21$		−	1.21440i		−	0.265004i
$22$	−3.75457	+	2.81127i	−0.800477	+	0.599364i
$23$			0.542331i			0.113084i	0.998400	+	0.0565419i	$0.0180074\pi$
$23$			0.542331i			0.113084i	−0.998400	+	0.0565419i	$0.981993\pi$
$24$	7.32770	−	4.54512i	1.49576	−	0.927770i
$25$	2.72413			0.544826
$26$	−0.469670	+	1.33395i	−0.0921098	+	0.261608i
$27$		−	10.0427i		−	1.93272i
$28$	−0.620944	−	0.499134i	−0.117347	−	0.0943274i
$29$			2.16310i			0.401678i	0.979624	+	0.200839i	$0.0643667\pi$
$29$			2.16310i			0.401678i	−0.979624	+	0.200839i	$0.935633\pi$
$30$	−3.97945	+	11.3023i	−0.726544	+	2.06351i
$31$			3.59359i			0.645429i	0.946496	+	0.322714i	$0.104595\pi$
$31$			3.59359i			0.645429i	−0.946496	+	0.322714i	$0.895405\pi$
$32$	0.687778	−	5.61489i	0.121583	−	0.992581i
$33$	8.40430	+	5.62172i	1.46300	+	0.978615i
$34$	−2.05312	+	5.83124i	−0.352108	+	1.00005i
$35$	1.10708			0.187131
$36$	−9.81149	−	7.88677i	−1.63525	−	1.31446i
$37$	10.6214			1.74615			0.873074	−	0.487588i	$-0.162123\pi$
$37$	10.6214			1.74615			0.873074	+	0.487588i	$0.162123\pi$
$38$	7.52394	+	2.64911i	1.22054	+	0.429742i
$39$	3.04863			0.488172
$40$	4.14348	+	6.68017i	0.655142	+	1.05623i
$41$		−	10.6003i		−	1.65550i	−0.561100	−	0.827748i	$-0.689622\pi$
$41$		−	10.6003i		−	1.65550i	0.561100	−	0.827748i	$-0.310378\pi$
$42$	−0.570367	+	1.61994i	−0.0880095	+	0.249962i
$43$	1.79968			0.274448			0.137224	−	0.990540i	$-0.456182\pi$
$43$	1.79968			0.274448			0.137224	+	0.990540i	$0.456182\pi$
$44$	6.32876	−	1.98667i	0.954096	−	0.299501i
$45$	17.4930			2.60770
$46$	0.254716	−	0.723440i	0.0375559	−	0.106665i
$47$		−	3.13709i		−	0.457592i	−0.973474	−	0.228796i	$-0.926521\pi$
$47$		−	3.13709i		−	0.457592i	0.973474	−	0.228796i	$-0.0734789\pi$
$48$	−11.9095	+	2.62135i	−1.71898	+	0.378359i
$49$	−6.84132			−0.977332
$50$	−3.63384	−	1.27944i	−0.513903	−	0.180940i
$51$	13.3269			1.86613
$52$	1.25303	−	1.55882i	0.173764	−	0.216170i
$53$	−2.00293			−0.275124			−0.137562	−	0.990493i	$-0.543927\pi$
$53$	−2.00293			−0.275124			−0.137562	+	0.990493i	$0.543927\pi$
$54$	−4.71677	+	13.3965i	−0.641871	+	1.82303i
$55$	−5.12494	+	7.66162i	−0.691046	+	1.03309i
$56$	0.593877	+	0.957455i	0.0793601	+	0.127945i
$57$		−	17.1954i		−	2.27759i
$58$	1.01594	−	2.88546i	0.133400	−	0.378879i
$59$		−	3.35411i		−	0.436668i	−0.975874	−	0.218334i	$-0.929938\pi$
$59$		−	3.35411i		−	0.436668i	0.975874	−	0.218334i	$-0.0700622\pi$
$60$	10.6167	−	13.2077i	1.37061	−	1.70510i
$61$			5.99977i			0.768192i	0.923293	+	0.384096i	$0.125487\pi$
$61$			5.99977i			0.768192i	−0.923293	+	0.384096i	$0.874513\pi$
$62$	1.68780	−	4.79366i	0.214351	−	0.608795i
$63$	2.50723			0.315882
$64$	−3.55460	+	7.16692i	−0.444325	+	0.895866i
$65$			2.77923i			0.344721i
$66$	−8.57052	−	11.4463i	−1.05496	−	1.40894i
$67$		−	1.31372i		−	0.160496i	−0.996775	−	0.0802481i	$-0.974429\pi$
$67$		−	1.31372i		−	0.160496i	0.996775	−	0.0802481i	$-0.0255713\pi$
$68$	5.47751	−	6.81426i	0.664246	−	0.826350i
$69$	−1.65337			−0.199042
$70$	−1.47679	−	0.519964i	−0.176510	−	0.0621476i
$71$		−	2.74132i		−	0.325334i	−0.986681	−	0.162667i	$-0.947990\pi$
$71$		−	2.74132i		−	0.325334i	0.986681	−	0.162667i	$-0.0520097\pi$
$72$	9.38381	+	15.1287i	1.10589	+	1.78293i
$73$		−	11.0605i		−	1.29454i	−0.762263	−	0.647268i	$-0.775911\pi$
$73$		−	11.0605i		−	1.29454i	0.762263	−	0.647268i	$-0.224089\pi$
$74$	−14.1684	−	4.98855i	−1.64704	−	0.579907i
$75$			8.30488i			0.958965i
$76$	−8.79231	−	7.06753i	−1.00855	−	0.810701i
$77$	−0.734547	+	1.09813i	−0.0837094	+	0.125143i
$78$	−4.06671	−	1.43185i	−0.460464	−	0.162125i
$79$	−15.8741			−1.78598			−0.892990	−	0.450076i	$-0.851397\pi$
$79$	−15.8741			−1.78598			−0.892990	+	0.450076i	$0.851397\pi$
$80$	−2.38970	−	10.8570i	−0.267177	−	1.21385i
$81$	11.7341			1.30379
$82$	−4.97866	+	14.1403i	−0.549801	+	1.56153i
$83$	−12.6524			−1.38878			−0.694391	−	0.719598i	$-0.744326\pi$
$83$	−12.6524			−1.38878			−0.694391	+	0.719598i	$0.744326\pi$
$84$	1.52168	−	1.89303i	0.166028	−	0.206547i
$85$			12.1492i			1.31776i
$86$	−2.40067	−	0.845253i	−0.258871	−	0.0911460i
$87$	−6.59450			−0.707005
$88$	−9.37529	−	0.322321i	−0.999410	−	0.0343595i
$89$	−10.5207			−1.11519			−0.557595	−	0.830113i	$-0.688276\pi$
$89$	−10.5207			−1.11519			−0.557595	+	0.830113i	$0.688276\pi$
$90$	−23.3347	−	8.21592i	−2.45969	−	0.866034i
$91$			0.398342i			0.0417576i
$92$	−0.679555	+	0.845396i	−0.0708486	+	0.0881387i
$93$	−10.9556			−1.13604
$94$	−1.47340	+	4.18471i	−0.151969	+	0.431620i
$95$	15.6759			1.60831
$96$	17.1177	+	2.09678i	1.74707	+	0.214002i
$97$	12.5793			1.27724			0.638619	−	0.769523i	$-0.279506\pi$
$97$	12.5793			1.27724			0.638619	+	0.769523i	$0.279506\pi$
$98$	9.12595	+	3.21316i	0.921860	+	0.324579i
$99$	−11.6065	+	17.3514i	−1.16650	+	1.74388i
$100$	4.24643	+	3.41341i	0.424643	+	0.341341i
$101$		−	9.24664i		−	0.920075i	−0.887899	−	0.460038i	$-0.847836\pi$
$101$		−	9.24664i		−	0.920075i	0.887899	−	0.460038i	$-0.152164\pi$
$102$	−17.7773	−	6.25923i	−1.76022	−	0.619756i
$103$		−	16.2399i		−	1.60017i	−0.599887	−	0.800084i	$-0.704788\pi$
$103$		−	16.2399i		−	1.60017i	0.599887	−	0.800084i	$-0.295212\pi$
$104$	−2.40360	+	1.49087i	−0.235693	+	0.146192i
$105$			3.37510i			0.329376i
$106$	2.67180	+	0.940717i	0.259508	+	0.0913705i
$107$	3.19262			0.308642			0.154321	−	0.988021i	$-0.450681\pi$
$107$	3.19262			0.308642			0.154321	+	0.988021i	$0.450681\pi$
$108$	12.5838	−	15.6548i	1.21088	−	1.50638i
$109$		−	1.52765i		−	0.146323i	−0.997320	−	0.0731614i	$-0.976691\pi$
$109$		−	1.52765i		−	0.146323i	0.997320	−	0.0731614i	$-0.0233088\pi$
$110$	10.4348	−	7.81316i	0.994921	−	0.744955i
$111$			32.3808i			3.07345i
$112$	−0.342511	−	1.55612i	−0.0323643	−	0.147039i
$113$	4.50879			0.424151			0.212076	−	0.977253i	$-0.431978\pi$
$113$	4.50879			0.424151			0.212076	+	0.977253i	$0.431978\pi$
$114$	−8.07616	+	22.9377i	−0.756402	+	2.14832i
$115$		−	1.50726i		−	0.140553i
$116$	−2.71042	+	3.37188i	−0.251657	+	0.313072i
$117$			6.29417i			0.581896i
$118$	−1.57532	+	4.47420i	−0.145020	+	0.411883i
$119$			1.74132i			0.159627i
$120$	−20.3654	+	12.6320i	−1.85910	+	1.15313i
$121$	−4.19924	−	10.1669i	−0.381749	−	0.924266i
$122$	2.81791	−	8.00337i	0.255122	−	0.724591i
$123$	32.3166			2.91389
$124$	−4.50287	+	5.60177i	−0.404370	+	0.503054i
$125$	6.32517			0.565740
$126$	−3.34451	−	1.17757i	−0.297953	−	0.104906i
$127$	3.98567			0.353671			0.176835	−	0.984240i	$-0.443414\pi$
$127$	3.98567			0.353671			0.176835	+	0.984240i	$0.443414\pi$
$128$	8.10773	−	7.89080i	0.716629	−	0.697455i
$129$			5.48655i			0.483064i
$130$	1.30532	−	3.70734i	0.114484	−	0.325156i
$131$	−10.5958			−0.925755			−0.462878	−	0.886422i	$-0.653183\pi$
$131$	−10.5958			−0.925755			−0.462878	+	0.886422i	$0.653183\pi$
$132$	6.05662	+	19.2941i	0.527161	+	1.67933i
$133$	2.24679			0.194822
$134$	−0.617013	+	1.75243i	−0.0533018	+	0.151387i
$135$			27.9111i			2.40220i
$136$	−10.5072	+	6.51723i	−0.900981	+	0.558848i
$137$	−20.2489			−1.72998			−0.864992	−	0.501786i	$-0.832677\pi$
$137$	−20.2489			−1.72998			−0.864992	+	0.501786i	$0.832677\pi$
$138$	2.20550	+	0.776537i	0.187745	+	0.0661032i
$139$	2.34340			0.198765			0.0993823	−	0.995049i	$-0.468313\pi$
$139$	2.34340			0.198765			0.0993823	+	0.995049i	$0.468313\pi$
$140$	1.72575	+	1.38721i	0.145852	+	0.117240i
$141$	9.56385			0.805422
$142$	−1.28751	+	3.65677i	−0.108046	+	0.306869i
$143$	−2.75674	−	1.84401i	−0.230530	−	0.154204i
$144$	−5.41200	−	24.5881i	−0.451000	−	2.04901i
$145$		−	6.01176i		−	0.499249i
$146$	−5.19479	+	14.7541i	−0.429924	+	1.22106i
$147$		−	20.8567i		−	1.72023i
$148$	16.5569	+	13.3089i	1.36097	+	1.09399i
$149$			20.6774i			1.69396i	0.531625	+	0.846980i	$0.321582\pi$
$149$			20.6774i			1.69396i	−0.531625	+	0.846980i	$0.678418\pi$
$150$	3.90055	−	11.0783i	0.318479	−	0.904536i
$151$	−22.6843			−1.84602			−0.923009	−	0.384778i	$-0.874278\pi$
$151$	−22.6843			−1.84602			−0.923009	+	0.384778i	$0.874278\pi$
$152$	8.40906	+	13.5572i	0.682065	+	1.09963i
$153$			27.5145i			2.22441i
$154$	1.49560	−	1.11984i	0.120519	−	0.0902397i
$155$		−	9.98743i		−	0.802210i
$156$	4.75227	+	3.82002i	0.380486	+	0.305847i
$157$	20.0985			1.60403			0.802016	−	0.597303i	$-0.203761\pi$
$157$	20.0985			1.60403			0.802016	+	0.597303i	$0.203761\pi$
$158$	21.1752	+	7.45560i	1.68461	+	0.593136i
$159$		−	6.10621i		−	0.484254i
$160$	−1.91149	+	15.6051i	−0.151117	+	1.23369i
$161$		−	0.216033i		−	0.0170258i
$162$	−15.6526	−	5.51115i	−1.22979	−	0.432997i
$163$		−	7.36228i		−	0.576658i	−0.957531	−	0.288329i	$-0.906900\pi$
$163$		−	7.36228i		−	0.576658i	0.957531	−	0.288329i	$-0.0930998\pi$
$164$	13.2825	−	16.5240i	1.03719	−	1.29031i
$165$	−23.3575	−	15.6241i	−1.81838	−	1.21633i
$166$	16.8776	+	5.94245i	1.30996	+	0.461224i
$167$	−20.9937			−1.62454			−0.812271	−	0.583280i	$-0.801769\pi$
$167$	−20.9937			−1.62454			−0.812271	+	0.583280i	$0.801769\pi$
$168$	−2.91893	+	1.81051i	−0.225200	+	0.139684i
$169$	−1.00000			−0.0769231
$170$	5.70611	−	16.2064i	0.437639	−	1.24297i
$171$	35.5014			2.71486
$172$	2.80537	+	2.25504i	0.213908	+	0.171945i
$173$			18.2803i			1.38982i	0.719095	+	0.694912i	$0.244557\pi$
$173$			18.2803i			1.38982i	−0.719095	+	0.694912i	$0.755443\pi$
$174$	8.79670	+	3.09724i	0.666876	+	0.234801i
$175$	−1.08514			−0.0820285
$176$	12.3547	+	4.83325i	0.931274	+	0.364320i
$177$	10.2255			0.768592
$178$	14.0340	+	4.94124i	1.05189	+	0.370362i
$179$		−	14.0224i		−	1.04808i	−0.851692	−	0.524042i	$-0.824423\pi$
$179$		−	14.0224i		−	1.04808i	0.851692	−	0.524042i	$-0.175577\pi$
$180$	27.2684	+	21.9192i	2.03247	+	1.63376i
$181$	−8.16756			−0.607090			−0.303545	−	0.952817i	$-0.598170\pi$
$181$	−8.16756			−0.607090			−0.303545	+	0.952817i	$0.598170\pi$
$182$	0.187089	−	0.531366i	0.0138680	−	0.0393875i
$183$	−18.2911			−1.35212
$184$	1.30355	−	0.808546i	0.0960988	−	0.0596068i
$185$	−29.5193			−2.17030
$186$	14.6141	+	5.14549i	1.07156	+	0.377286i
$187$	−12.0509	−	8.06095i	−0.881247	−	0.589475i
$188$	3.93087	−	4.89017i	0.286688	−	0.356652i
$189$			4.00044i			0.290989i
$190$	−20.9108	−	7.36249i	−1.51703	−	0.534131i
$191$			13.3593i			0.966648i	0.875441	+	0.483324i	$0.160571\pi$
$191$			13.3593i			0.966648i	−0.875441	+	0.483324i	$0.839429\pi$
$192$	−21.8493	−	10.8367i	−1.57684	−	0.782070i
$193$			18.5956i			1.33854i	0.743018	+	0.669271i	$0.233393\pi$
$193$			18.5956i			1.33854i	−0.743018	+	0.669271i	$0.766607\pi$
$194$	−16.7802	−	5.90814i	−1.20474	−	0.424180i
$195$	−8.47286			−0.606754
$196$	−10.6644	−	8.57237i	−0.761743	−	0.612312i
$197$		−	2.33017i		−	0.166018i	−0.996549	−	0.0830090i	$-0.973547\pi$
$197$		−	2.33017i		−	0.166018i	0.996549	−	0.0830090i	$-0.0264530\pi$
$198$	23.6319	−	17.6946i	1.67945	−	1.25750i
$199$			10.2603i			0.727331i	0.931530	+	0.363665i	$0.118475\pi$
$199$			10.2603i			0.727331i	−0.931530	+	0.363665i	$0.881525\pi$
$200$	−4.06133	−	6.54772i	−0.287179	−	0.462994i
$201$	4.00504			0.282494
$202$	−4.34287	+	12.3345i	−0.305563	+	0.867853i
$203$		−	0.861653i		−	0.0604762i
$204$	20.7742	+	16.6989i	1.45448	+	1.16916i
$205$			29.4608i			2.05763i
$206$	−7.62741	+	21.6632i	−0.531427	+	1.50935i
$207$		−	3.41352i		−	0.237256i
$208$	3.90649	−	0.859843i	0.270866	−	0.0596194i
$209$	−10.4009	+	15.5490i	−0.719445	+	1.07555i
$210$	1.58518	−	4.50219i	0.109388	−	0.310681i
$211$	26.2772			1.80899			0.904497	−	0.426479i	$-0.140246\pi$
$211$	26.2772			1.80899			0.904497	+	0.426479i	$0.140246\pi$
$212$	−3.12221	−	2.50973i	−0.214434	−	0.172369i
$213$	8.35727			0.572631
$214$	−4.25878	−	1.49948i	−0.291124	−	0.102502i
$215$	−5.00172			−0.341114
$216$	−24.1387	+	14.9724i	−1.64243	+	1.01874i
$217$		−	1.43148i		−	0.0971752i
$218$	−0.717493	+	2.03781i	−0.0485948	+	0.138018i
$219$	33.7195			2.27855
$220$	−17.5891	+	5.52141i	−1.18586	+	0.372253i
$221$	−4.37142			−0.294054
$222$	15.2083	−	43.1942i	1.02071	−	2.89900i
$223$		−	23.7985i		−	1.59366i	−0.604202	−	0.796831i	$-0.706508\pi$
$223$		−	23.7985i		−	1.59366i	0.604202	−	0.796831i	$-0.293492\pi$
$224$	−0.273971	+	2.23665i	−0.0183054	+	0.149442i
$225$	−17.1461			−1.14308
$226$	−6.01448	−	2.11764i	−0.400077	−	0.140864i
$227$	−13.8822			−0.921397			−0.460699	−	0.887557i	$-0.652401\pi$
$227$	−13.8822			−0.921397			−0.460699	+	0.887557i	$0.652401\pi$
$228$	21.5463	−	26.8045i	1.42694	−	1.77517i
$229$	−25.6686			−1.69623			−0.848113	−	0.529815i	$-0.822261\pi$
$229$	−25.6686			−1.69623			−0.848113	+	0.529815i	$0.822261\pi$
$230$	−0.707916	+	2.01061i	−0.0466786	+	0.132575i
$231$	−3.34778	−	2.23937i	−0.220268	−	0.147339i
$232$	5.19923	−	3.22491i	0.341346	−	0.211725i
$233$		−	8.23801i		−	0.539690i	−0.962904	−	0.269845i	$-0.913027\pi$
$233$		−	8.23801i		−	0.539690i	0.962904	−	0.269845i	$-0.0869725\pi$
$234$	2.95618	−	8.39608i	0.193252	−	0.548869i
$235$			8.71871i			0.568746i
$236$	4.20279	−	5.22845i	0.273578	−	0.340343i
$237$		−	48.3945i		−	3.14356i
$238$	0.817845	−	2.32283i	0.0530130	−	0.150566i
$239$	4.50382			0.291328			0.145664	−	0.989334i	$-0.453468\pi$
$239$	4.50382			0.291328			0.145664	+	0.989334i	$0.453468\pi$
$240$	33.0992	−	7.28533i	2.13654	−	0.470266i
$241$		−	26.5414i		−	1.70968i	−0.518892	−	0.854840i	$-0.673655\pi$
$241$		−	26.5414i		−	1.70968i	0.518892	−	0.854840i	$-0.326345\pi$
$242$	0.826463	+	15.5344i	0.0531271	+	0.998588i
$243$			5.64477i			0.362112i
$244$	−7.51788	+	9.35257i	−0.481283	+	0.598737i
$245$	19.0136			1.21474
$246$	−43.1085	−	15.1781i	−2.74850	−	0.967722i
$247$			5.64036i			0.358888i
$248$	8.63757	−	5.35759i	0.548486	−	0.340207i
$249$		−	38.5726i		−	2.44444i
$250$	−8.43743	−	2.97074i	−0.533630	−	0.187886i
$251$		−	24.5386i		−	1.54886i	−0.632660	−	0.774430i	$-0.718037\pi$
$251$		−	24.5386i		−	1.54886i	0.632660	−	0.774430i	$-0.281963\pi$
$252$	3.90833	+	3.14163i	0.246201	+	0.197904i
$253$	1.49507	+	1.00006i	0.0939940	+	0.0628735i
$254$	−5.31666	−	1.87195i	−0.333597	−	0.117456i
$255$	−37.0384			−2.31944
$256$	−14.5213	+	6.71794i	−0.907584	+	0.419871i
$257$	−7.69395			−0.479935			−0.239968	−	0.970781i	$-0.577137\pi$
$257$	−7.69395			−0.479935			−0.239968	+	0.970781i	$0.577137\pi$
$258$	2.57687	−	7.31876i	0.160429	−	0.455646i
$259$	−4.23095			−0.262898
$260$	−3.48245	+	4.33232i	−0.215973	+	0.268679i
$261$		−	13.6149i		−	0.842743i
$262$	14.1342	+	4.97651i	0.873211	+	0.307450i
$263$	20.1790			1.24429			0.622147	−	0.782901i	$-0.286261\pi$
$263$	20.1790			1.24429			0.622147	+	0.782901i	$0.286261\pi$
$264$	0.982638	−	28.5818i	0.0604772	−	1.75909i
$265$	5.56661			0.341954
$266$	−2.99710	−	1.05525i	−0.183764	−	0.0647016i
$267$		−	32.0737i		−	1.96288i
$268$	1.64612	−	2.04785i	0.100553	−	0.125092i
$269$	9.03850			0.551087			0.275544	−	0.961289i	$-0.411142\pi$
$269$	9.03850			0.551087			0.275544	+	0.961289i	$0.411142\pi$
$270$	13.1090	−	37.2318i	0.797788	−	2.26586i
$271$	−9.82055			−0.596556			−0.298278	−	0.954479i	$-0.596412\pi$
$271$	−9.82055			−0.596556			−0.298278	+	0.954479i	$0.596412\pi$
$272$	17.0769	−	3.75873i	1.03544	−	0.227907i
$273$	−1.21440			−0.0734988
$274$	27.0110	+	9.51032i	1.63179	+	0.574539i
$275$	5.02333	−	7.50972i	0.302918	−	0.452853i
$276$	−2.57730	−	2.07172i	−0.155135	−	0.124703i
$277$			10.0070i			0.601265i	0.953740	+	0.300632i	$0.0971978\pi$
$277$			10.0070i			0.601265i	−0.953740	+	0.300632i	$0.902802\pi$
$278$	−3.12597	−	1.10062i	−0.187483	−	0.0660110i
$279$		−	22.6187i		−	1.35415i
$280$	−1.65052	−	2.66099i	−0.0986375	−	0.159025i
$281$			10.9285i			0.651937i	0.945381	+	0.325968i	$0.105690\pi$
$281$			10.9285i			0.651937i	−0.945381	+	0.325968i	$0.894310\pi$
$282$	−12.7577	−	4.49185i	−0.759708	−	0.267486i
$283$	9.99728			0.594277			0.297138	−	0.954834i	$-0.403968\pi$
$283$	9.99728			0.594277			0.297138	+	0.954834i	$0.403968\pi$
$284$	3.43495	−	4.27322i	0.203827	−	0.253569i
$285$			47.7900i			2.83084i
$286$	2.81127	+	3.75457i	0.166234	+	0.222012i
$287$			4.22256i			0.249250i
$288$	−4.32899	+	35.3411i	−0.255088	+	2.08249i
$289$	−2.10931			−0.124077
$290$	−2.82354	+	8.01935i	−0.165804	+	0.470913i
$291$			38.3498i			2.24811i
$292$	13.8591	−	17.2414i	0.811045	−	1.00897i
$293$			8.30235i			0.485029i	0.970148	+	0.242514i	$0.0779721\pi$
$293$			8.30235i			0.485029i	−0.970148	+	0.242514i	$0.922028\pi$
$294$	−9.79576	+	27.8217i	−0.571300	+	1.62259i
$295$			9.32185i			0.542739i
$296$	−15.8351	−	25.5296i	−0.920399	−	1.48388i
$297$	−27.6852	−	18.5189i	−1.60646	−	1.07458i
$298$	9.71156	−	27.5825i	0.562575	−	1.59781i
$299$	0.542331			0.0313638
$300$	−10.4062	+	12.9458i	−0.600805	+	0.747427i
$301$	−0.716886			−0.0413206
$302$	30.2596	+	10.6541i	1.74124	+	0.613075i
$303$	28.1896			1.61945
$304$	−4.84982	−	22.0340i	−0.278157	−	1.26374i
$305$		−	16.6748i		−	0.954794i
$306$	12.9227	−	36.7028i	0.738743	−	2.09816i
$307$	−14.5500			−0.830412			−0.415206	−	0.909727i	$-0.636290\pi$
$307$	−14.5500			−0.830412			−0.415206	+	0.909727i	$0.636290\pi$
$308$	−2.52101	+	0.791373i	−0.143648	+	0.0450926i
$309$	49.5096			2.81651
$310$	−4.69080	+	13.3227i	−0.266419	+	0.756678i
$311$			6.87576i			0.389889i	0.980814	+	0.194944i	$0.0624526\pi$
$311$			6.87576i			0.389889i	−0.980814	+	0.194944i	$0.937547\pi$
$312$	−4.54512	−	7.32770i	−0.257317	−	0.414849i
$313$	−11.2456			−0.635637			−0.317819	−	0.948152i	$-0.602950\pi$
$313$	−11.2456			−0.635637			−0.317819	+	0.948152i	$0.602950\pi$
$314$	−26.8102	−	9.43964i	−1.51299	−	0.532710i
$315$	−6.96818			−0.392613
$316$	−24.7449	−	19.8907i	−1.39201	−	1.11894i
$317$	12.1388			0.681784			0.340892	−	0.940102i	$-0.389271\pi$
$317$	12.1388			0.681784			0.340892	+	0.940102i	$0.389271\pi$
$318$	−2.86790	+	8.14535i	−0.160824	+	0.456769i
$319$	5.96311	+	3.98878i	0.333870	+	0.223329i
$320$	9.87906	−	19.9185i	0.552256	−	1.11348i
$321$			9.73313i			0.543250i
$322$	−0.101464	+	0.288176i	−0.00565438	+	0.0160594i
$323$			24.6564i			1.37192i
$324$	18.2913	+	14.7031i	1.01619	+	0.816841i
$325$		−	2.72413i		−	0.151108i
$326$	−3.45784	+	9.82088i	−0.191512	+	0.543928i
$327$	4.65726			0.257547
$328$	−25.4790	+	15.8038i	−1.40684	+	0.872616i
$329$			1.24964i			0.0688947i
$330$	23.8195	+	31.8119i	1.31122	+	1.75119i
$331$			32.4843i			1.78550i	0.450556	+	0.892748i	$0.351226\pi$
$331$			32.4843i			1.78550i	−0.450556	+	0.892748i	$0.648774\pi$
$332$	−19.7228	−	15.8538i	−1.08243	−	0.870091i
$333$	−66.8529			−3.66352
$334$	28.0045	+	9.86011i	1.53234	+	0.539521i
$335$			3.65113i			0.199482i
$336$	4.74404	−	1.04419i	0.258809	−	0.0569654i
$337$		−	17.7181i		−	0.965164i	−0.875851	−	0.482582i	$-0.839699\pi$
$337$		−	17.7181i		−	0.965164i	0.875851	−	0.482582i	$-0.160301\pi$
$338$	1.33395	+	0.469670i	0.0725571	+	0.0255467i
$339$			13.7457i			0.746562i
$340$	−15.2233	+	18.9384i	−0.825598	+	1.02708i
$341$	9.90661	+	6.62663i	0.536473	+	0.358852i
$342$	−47.3569	−	16.6739i	−2.56077	−	0.901624i
$343$	5.51358			0.297705
$344$	−2.68309	−	4.32570i	−0.144662	−	0.233226i
$345$	4.59509			0.247392
$346$	8.58570	−	24.3849i	0.461570	−	1.31094i
$347$	−3.14912			−0.169054			−0.0845269	−	0.996421i	$-0.526938\pi$
$347$	−3.14912			−0.169054			−0.0845269	+	0.996421i	$0.526938\pi$
$348$	−10.2796	−	8.26309i	−0.551047	−	0.442948i
$349$		−	18.5071i		−	0.990663i	−0.868704	−	0.495332i	$-0.835047\pi$
$349$		−	18.5071i		−	0.990663i	0.868704	−	0.495332i	$-0.164953\pi$
$350$	1.44751	+	0.509655i	0.0773727	+	0.0272422i
$351$	−10.0427			−0.536041
$352$	−14.2105	−	12.2499i	−0.757423	−	0.652924i
$353$	−17.3977			−0.925987			−0.462994	−	0.886362i	$-0.653225\pi$
$353$	−17.3977			−0.925987			−0.462994	+	0.886362i	$0.653225\pi$
$354$	−13.6402	−	4.80259i	−0.724968	−	0.255255i
$355$			7.61876i			0.404362i
$356$	−16.3998	−	13.1827i	−0.869190	−	0.698682i
$357$	−5.30865			−0.280963
$358$	−6.58591	+	18.7051i	−0.348076	+	0.988597i
$359$	30.6959			1.62007			0.810033	−	0.586384i	$-0.199449\pi$
$359$	30.6959			1.62007			0.810033	+	0.586384i	$0.199449\pi$
$360$	−26.0798	−	42.0461i	−1.37452	−	2.21603i
$361$	12.8137			0.674405
$362$	10.8951	+	3.83606i	0.572633	+	0.201619i
$363$	30.9952	−	12.8020i	1.62683	−	0.671929i
$364$	−0.499134	+	0.620944i	−0.0261617	+	0.0325463i
$365$			30.7398i			1.60899i
$366$	24.3994	+	8.59079i	1.27537	+	0.449048i
$367$			1.67921i			0.0876542i	0.999039	+	0.0438271i	$0.0139551\pi$
$367$			1.67921i			0.0876542i	−0.999039	+	0.0438271i	$0.986045\pi$
$368$	−2.11861	+	0.466319i	−0.110440	+	0.0243086i
$369$			66.7204i			3.47332i
$370$	39.3772	+	13.8643i	2.04712	+	0.720773i
$371$	0.797852			0.0414224
$372$	−17.0777	−	13.7276i	−0.885440	−	0.711744i
$373$		−	9.13778i		−	0.473136i	−0.971615	−	0.236568i	$-0.923977\pi$
$373$		−	9.13778i		−	0.473136i	0.971615	−	0.236568i	$-0.0760226\pi$
$374$	12.2892	+	16.4128i	0.635461	+	0.848686i
$375$			19.2831i			0.995776i
$376$	−7.54032	+	4.67701i	−0.388863	+	0.241198i
$377$	2.16310			0.111405
$378$	1.87889	−	5.33637i	0.0966395	−	0.274473i
$379$			5.76958i			0.296363i	0.988960	+	0.148182i	$0.0473420\pi$
$379$			5.76958i			0.296363i	−0.988960	+	0.148182i	$0.952658\pi$
$380$	24.4359	+	19.6423i	1.25353	+	1.00763i
$381$			12.1508i			0.622507i
$382$	6.27448	−	17.8206i	0.321030	−	0.911783i
$383$			13.1633i			0.672615i	0.941752	+	0.336308i	$0.109178\pi$
$383$			13.1633i			0.672615i	−0.941752	+	0.336308i	$0.890822\pi$
$384$	24.0562	+	24.7175i	1.22761	+	1.26136i
$385$	2.04148	−	3.05195i	0.104043	−	0.155542i
$386$	8.73380	−	24.8055i	0.444539	−	1.26257i
$387$	−11.3275			−0.575808
$388$	19.6089	+	15.7623i	0.995493	+	0.800208i
$389$	−25.5589			−1.29589			−0.647943	−	0.761688i	$-0.724371\pi$
$389$	−25.5589			−1.29589			−0.647943	+	0.761688i	$0.724371\pi$
$390$	11.3023	+	3.97945i	0.572316	+	0.201507i
$391$	2.37076			0.119894
$392$	10.1995	+	16.4438i	0.515154	+	0.830538i
$393$		−	32.3026i		−	1.62945i
$394$	−1.09441	+	3.10832i	−0.0551357	+	0.156595i
$395$	44.1179			2.21981
$396$	−39.8343	+	12.5044i	−2.00175	+	0.628371i
$397$	−5.52154			−0.277118			−0.138559	−	0.990354i	$-0.544247\pi$
$397$	−5.52154			−0.277118			−0.138559	+	0.990354i	$0.544247\pi$
$398$	4.81894	−	13.6866i	0.241551	−	0.686049i
$399$			6.84965i			0.342911i
$400$	2.34232	+	10.6418i	0.117116	+	0.532090i
$401$	−18.2270			−0.910214			−0.455107	−	0.890437i	$-0.650399\pi$
$401$	−18.2270			−0.910214			−0.455107	+	0.890437i	$0.650399\pi$
$402$	−5.34251	−	1.88105i	−0.266460	−	0.0938182i
$403$	3.59359			0.179010
$404$	11.5863	−	14.4139i	0.576440	−	0.717116i
$405$	−32.6118			−1.62049
$406$	−0.404693	+	1.14940i	−0.0200846	+	0.0570437i
$407$	19.5860	−	29.2804i	0.970841	−	1.45138i
$408$	−19.8686	−	32.0325i	−0.983645	−	1.58584i
$409$			24.0118i			1.18730i	0.804722	+	0.593652i	$0.202315\pi$
$409$			24.0118i			1.18730i	−0.804722	+	0.593652i	$0.797685\pi$
$410$	13.8369	−	39.2991i	0.683354	−	1.94084i
$411$		−	61.7316i		−	3.04500i
$412$	20.3491	−	25.3152i	1.00253	−	1.24719i
$413$			1.33608i			0.0657443i
$414$	−1.60323	+	4.55345i	−0.0787944	+	0.223790i
$415$	35.1640			1.72613
$416$	−5.61489	−	0.687778i	−0.275293	−	0.0337211i
$417$			7.14417i			0.349851i
$418$	21.1771	−	15.8566i	1.03581	−	0.775570i
$419$			19.6547i			0.960195i	0.877215	+	0.480098i	$0.159399\pi$
$419$			19.6547i			0.960195i	−0.877215	+	0.480098i	$0.840601\pi$
$420$	−4.22909	+	5.26117i	−0.206358	+	0.256719i
$421$	15.0542			0.733699			0.366849	−	0.930280i	$-0.380436\pi$
$421$	15.0542			0.733699			0.366849	+	0.930280i	$0.380436\pi$
$422$	−35.0523	−	12.3416i	−1.70632	−	0.600779i
$423$			19.7454i			0.960055i
$424$	2.98612	+	4.81425i	0.145019	+	0.233801i
$425$		−	11.9083i		−	0.577638i
$426$	−11.1481	−	3.92516i	−0.540129	−	0.190175i
$427$		−	2.38996i		−	0.115658i
$428$	4.97672	+	4.00044i	0.240559	+	0.193369i
$429$	5.62172	−	8.40430i	0.271419	−	0.405763i
$430$	6.67202	+	2.34916i	0.321753	+	0.113286i
$431$	−24.4855			−1.17942			−0.589711	−	0.807614i	$-0.700759\pi$
$431$	−24.4855			−1.17942			−0.589711	+	0.807614i	$0.700759\pi$
$432$	39.2318	−	8.63517i	1.88754	−	0.415460i
$433$	18.6992			0.898627			0.449313	−	0.893374i	$-0.351669\pi$
$433$	18.6992			0.898627			0.449313	+	0.893374i	$0.351669\pi$
$434$	−0.672323	+	1.90952i	−0.0322725	+	0.0916597i
$435$	18.3276			0.878743
$436$	1.91419	−	2.38134i	0.0916732	−	0.114045i
$437$		−	3.05894i		−	0.146329i
$438$	−44.9799	−	15.8370i	−2.14923	−	0.756722i
$439$	12.8816			0.614806			0.307403	−	0.951579i	$-0.400540\pi$
$439$	12.8816			0.614806			0.307403	+	0.951579i	$0.400540\pi$
$440$	26.0561	+	0.895804i	1.24218	+	0.0427058i
$441$	43.0605			2.05050
$442$	5.83124	+	2.05312i	0.277364	+	0.0976572i
$443$			21.8314i			1.03724i	0.855005	+	0.518620i	$0.173554\pi$
$443$			21.8314i			1.03724i	−0.855005	+	0.518620i	$0.826446\pi$
$444$	−40.5740	+	50.4758i	−1.92556	+	2.39548i
$445$	29.2394			1.38608
$446$	−11.1774	+	31.7458i	−0.529266	+	1.50321i
$447$	−63.0379			−2.98159
$448$	1.41595	−	2.85489i	0.0668972	−	0.134881i
$449$	23.8044			1.12340			0.561699	−	0.827341i	$-0.310148\pi$
$449$	23.8044			1.12340			0.561699	+	0.827341i	$0.310148\pi$
$450$	22.8720	+	8.05303i	1.07820	+	0.379623i
$451$	−29.2224	−	19.5472i	−1.37603	−	0.920440i
$452$	7.02840	+	5.64964i	0.330588	+	0.265737i
$453$		−	69.1560i		−	3.24923i
$454$	18.5182	+	6.52007i	0.869100	+	0.306002i
$455$		−	1.10708i		−	0.0519009i
$456$	−41.3309	+	25.6361i	−1.93550	+	1.20052i
$457$			31.0035i			1.45028i	0.688599	+	0.725142i	$0.258226\pi$
$457$			31.0035i			1.45028i	−0.688599	+	0.725142i	$0.741774\pi$
$458$	34.2405	+	12.0558i	1.59995	+	0.563328i
$459$	−43.9010			−2.04912
$460$	1.88864	−	2.34955i	0.0880584	−	0.109548i
$461$		−	6.53832i		−	0.304520i	−0.988340	−	0.152260i	$-0.951345\pi$
$461$		−	6.53832i		−	0.304520i	0.988340	−	0.152260i	$-0.0486551\pi$
$462$	3.41400	+	4.55954i	0.158834	+	0.212129i
$463$		−	4.13457i		−	0.192150i	−0.995374	−	0.0960750i	$-0.969371\pi$
$463$		−	4.13457i		−	0.192150i	0.995374	−	0.0960750i	$-0.0306289\pi$
$464$	−8.45013	+	1.85993i	−0.392287	+	0.0863449i
$465$	30.4480			1.41199
$466$	−3.86915	+	10.9891i	−0.179235	+	0.509058i
$467$		−	18.9956i		−	0.879014i	−0.898239	−	0.439507i	$-0.855153\pi$
$467$		−	18.9956i		−	0.879014i	0.898239	−	0.439507i	$-0.144847\pi$
$468$	−7.88677	+	9.81149i	−0.364566	+	0.453536i
$469$			0.523309i			0.0241642i
$470$	4.09492	−	11.6303i	0.188884	−	0.536465i
$471$			61.2729i			2.82330i
$472$	−8.06194	+	5.00055i	−0.371081	+	0.230169i
$473$	3.31862	−	4.96124i	0.152590	−	0.228118i
$474$	−22.7294	+	64.5556i	−1.04400	+	2.96513i
$475$	−15.3651			−0.704998
$476$	−2.18192	+	2.71441i	−0.100008	+	0.124415i
$477$	12.6068			0.577226
$478$	−6.00784	−	2.11531i	−0.274792	−	0.0967519i
$479$	−13.2771			−0.606644			−0.303322	−	0.952888i	$-0.598096\pi$
$479$	−13.2771			−0.606644			−0.303322	+	0.952888i	$0.598096\pi$
$480$	−47.5742	−	5.82745i	−2.17145	−	0.265985i
$481$		−	10.6214i		−	0.484294i
$482$	−12.4657	+	35.4047i	−0.567796	+	1.61264i
$483$	0.658606			0.0299676
$484$	6.19357	−	21.1102i	0.281526	−	0.959554i
$485$	−34.9609			−1.58749
$486$	2.65118	−	7.52981i	0.120260	−	0.341559i
$487$		−	21.6937i		−	0.983036i	−0.870867	−	0.491518i	$-0.836442\pi$
$487$		−	21.6937i		−	0.983036i	0.870867	−	0.491518i	$-0.163558\pi$
$488$	14.4211	−	8.94490i	0.652811	−	0.404916i
$489$	22.4449			1.01499
$490$	−25.3631	−	8.93013i	−1.14579	−	0.403422i
$491$	17.5909			0.793867			0.396933	−	0.917847i	$-0.370074\pi$
$491$	17.5909			0.793867			0.396933	+	0.917847i	$0.370074\pi$
$492$	50.3757	+	40.4936i	2.27111	+	1.82559i
$493$	9.45582			0.425869
$494$	2.64911	−	7.52394i	0.119189	−	0.338518i
$495$	32.2572	−	48.2236i	1.44985	−	2.16749i
$496$	−14.0383	+	3.08993i	−0.630340	+	0.138742i
$497$			1.09198i			0.0489821i
$498$	−18.1164	+	51.4537i	−0.811814	+	2.30569i
$499$		−	24.1164i		−	1.07960i	−0.841794	−	0.539799i	$-0.818500\pi$
$499$		−	24.1164i		−	1.07960i	0.841794	−	0.539799i	$-0.181500\pi$
$500$	9.85980	+	7.92561i	0.440944	+	0.354444i
$501$		−	64.0021i		−	2.85940i
$502$	−11.5250	+	32.7331i	−0.514387	+	1.46095i
$503$	10.6931			0.476781			0.238390	−	0.971169i	$-0.423380\pi$
$503$	10.6931			0.476781			0.238390	+	0.971169i	$0.423380\pi$
$504$	−3.73796	−	6.02639i	−0.166502	−	0.268437i
$505$			25.6986i			1.14357i
$506$	−1.52464	−	2.03622i	−0.0677783	−	0.0905209i
$507$		−	3.04863i		−	0.135395i
$508$	6.21294	+	4.99415i	0.275655	+	0.221580i
$509$	4.63668			0.205517			0.102759	−	0.994706i	$-0.467233\pi$
$509$	4.63668			0.205517			0.102759	+	0.994706i	$0.467233\pi$
$510$	49.4073	+	17.3958i	2.18779	+	0.770301i
$511$			4.40587i			0.194904i
$512$	22.5259	−	2.14112i	0.995513	−	0.0946252i
$513$			56.6446i			2.50092i
$514$	10.2633	+	3.61361i	0.452695	+	0.159390i
$515$			45.1346i			1.98887i
$516$	−6.87480	+	8.55255i	−0.302646	+	0.376505i
$517$	−8.64816	−	5.78484i	−0.380346	−	0.254417i
$518$	5.64385	+	1.98715i	0.247977	+	0.0873103i
$519$	−55.7299			−2.44627
$520$	6.68017	−	4.14348i	0.292945	−	0.181704i
$521$	21.2044			0.928982			0.464491	−	0.885578i	$-0.346237\pi$
$521$	21.2044			0.928982			0.464491	+	0.885578i	$0.346237\pi$
$522$	−6.39452	+	18.1616i	−0.279880	+	0.794910i
$523$	−41.4207			−1.81120			−0.905599	−	0.424134i	$-0.860579\pi$
$523$	−41.4207			−1.81120			−0.905599	+	0.424134i	$0.860579\pi$
$524$	−16.5169	−	13.2768i	−0.721543	−	0.579999i
$525$		−	3.30818i		−	0.144381i
$526$	−26.9177	−	9.47749i	−1.17367	−	0.413238i
$527$	15.7091			0.684300
$528$	−14.7348	+	37.6651i	−0.641250	+	1.63916i
$529$	22.7059			0.987212
$530$	−7.42556	−	2.61447i	−0.322546	−	0.113565i
$531$			21.1113i			0.916154i
$532$	3.50235	+	2.81529i	0.151846	+	0.122058i
$533$	−10.6003			−0.459152
$534$	−15.0640	+	42.7846i	−0.651885	+	1.85147i
$535$	−8.87303			−0.383614
$536$	−3.15765	+	1.95858i	−0.136390	+	0.0845980i
$537$	42.7492			1.84477
$538$	−12.0569	−	4.24511i	−0.519808	−	0.183020i
$539$	−12.6155	+	18.8598i	−0.543387	+	0.812347i
$540$	−34.9733	+	43.5084i	−1.50501	+	1.87230i
$541$			27.5097i			1.18274i	0.806402	+	0.591368i	$0.201412\pi$
$541$			27.5097i			1.18274i	−0.806402	+	0.591368i	$0.798588\pi$
$542$	13.1001	+	4.61242i	0.562696	+	0.198120i
$543$		−	24.8999i		−	1.06856i
$544$	−24.5450	−	3.00657i	−1.05236	−	0.128905i
$545$			4.24570i			0.181866i
$546$	1.61994	+	0.570367i	0.0693271	+	0.0244094i
$547$	0.394737			0.0168777			0.00843887	−	0.999964i	$-0.497314\pi$
$547$	0.394737			0.0168777			0.00843887	+	0.999964i	$0.497314\pi$
$548$	−31.5645	−	25.3725i	−1.34837	−	1.08386i
$549$		−	37.7636i		−	1.61171i
$550$	−10.2279	+	7.65825i	−0.436121	+	0.326549i
$551$		−	12.2007i		−	0.519766i
$552$	2.46496	+	3.97404i	0.104916	+	0.169146i
$553$	6.32334			0.268896
$554$	4.70001	−	13.3488i	0.199684	−	0.567138i
$555$		−	89.9937i		−	3.82002i
$556$	3.65294	+	2.93634i	0.154919	+	0.124529i
$557$			21.0202i			0.890654i	0.895368	+	0.445327i	$0.146913\pi$
$557$			21.0202i			0.890654i	−0.895368	+	0.445327i	$0.853087\pi$
$558$	−10.6233	+	30.1721i	−0.449721	+	1.27729i
$559$		−	1.79968i		−	0.0761182i
$560$	0.951919	+	4.32482i	0.0402259	+	0.182757i
$561$	24.5749	−	36.7387i	1.03755	−	1.55111i
$562$	5.13276	−	14.5780i	0.216513	−	0.614934i
$563$	24.4448			1.03023			0.515113	−	0.857122i	$-0.327750\pi$
$563$	24.4448			1.03023			0.515113	+	0.857122i	$0.327750\pi$
$564$	14.9083	+	11.9838i	0.627754	+	0.504608i
$565$	−12.5310			−0.527182
$566$	−13.3358	−	4.69542i	−0.560547	−	0.197363i
$567$	−4.67418			−0.196297
$568$	−6.58903	+	4.08695i	−0.276470	+	0.171485i
$569$			0.868758i			0.0364202i	0.999834	+	0.0182101i	$0.00579678\pi$
$569$			0.868758i			0.0364202i	−0.999834	+	0.0182101i	$0.994203\pi$
$570$	22.4455	−	63.7493i	0.940140	−	2.67016i
$571$	−3.23890			−0.135544			−0.0677719	−	0.997701i	$-0.521589\pi$
$571$	−3.23890			−0.135544			−0.0677719	+	0.997701i	$0.521589\pi$
$572$	−1.98667	−	6.32876i	−0.0830667	−	0.264619i
$573$	−40.7278			−1.70143
$574$	1.98321	−	5.63267i	0.0827776	−	0.235103i
$575$			1.47738i			0.0616110i
$576$	22.3733	−	45.1099i	0.932220	−	1.87958i
$577$	14.9094			0.620687			0.310344	−	0.950624i	$-0.399556\pi$
$577$	14.9094			0.620687			0.310344	+	0.950624i	$0.399556\pi$
$578$	2.81371	+	0.990681i	0.117035	+	0.0412069i
$579$	−56.6912			−2.35601
$580$	7.53290	−	9.37125i	0.312787	−	0.389120i
$581$	5.03998			0.209094
$582$	18.0118	−	51.1566i	0.746611	−	2.12051i
$583$	−3.69343	+	5.52157i	−0.152966	+	0.228680i
$584$	−26.5851	+	16.4898i	−1.10010	+	0.682354i
$585$		−	17.4930i		−	0.723245i
$586$	3.89936	−	11.0749i	0.161081	−	0.457499i
$587$			39.7810i			1.64194i	0.570974	+	0.820968i	$0.306566\pi$
$587$			39.7810i			1.64194i	−0.570974	+	0.820968i	$0.693434\pi$
$588$	26.1340	−	32.5118i	1.07775	−	1.34077i
$589$		−	20.2692i		−	0.835177i
$590$	4.37819	−	12.4348i	0.180247	−	0.511934i
$591$	7.10385			0.292213
$592$	9.13273	+	41.4924i	0.375353	+	1.70533i
$593$		−	19.6509i		−	0.806966i	−0.914987	−	0.403483i	$-0.867800\pi$
$593$		−	19.6509i		−	0.806966i	0.914987	−	0.403483i	$-0.132200\pi$
$594$	28.2328	+	37.7061i	1.15840	+	1.54710i
$595$		−	4.83953i		−	0.198401i
$596$	−25.9094	+	32.2324i	−1.06129	+	1.32029i
$597$	−31.2798			−1.28020
$598$	−0.723440	−	0.254716i	−0.0295836	−	0.0104161i
$599$		−	17.3473i		−	0.708793i	−0.935095	−	0.354397i	$-0.884686\pi$
$599$		−	17.3473i		−	0.708793i	0.935095	−	0.354397i	$-0.115314\pi$
$600$	19.9616	−	12.3815i	0.814930	−	0.505473i
$601$			16.1383i			0.658293i	0.944279	+	0.329147i	$0.106761\pi$
$601$			16.1383i			0.658293i	−0.944279	+	0.329147i	$0.893239\pi$
$602$	0.956287	+	0.336700i	0.0389754	+	0.0137229i
$603$			8.26876i			0.336730i
$604$	−35.3607	−	28.4240i	−1.43881	−	1.15656i
$605$	11.6707	+	28.2562i	0.474480	+	1.14878i
$606$	−37.6034	−	13.2398i	−1.52753	−	0.537831i
$607$	17.2287			0.699291			0.349645	−	0.936882i	$-0.386302\pi$
$607$	17.2287			0.699291			0.349645	+	0.936882i	$0.386302\pi$
$608$	−3.87932	+	31.6700i	−0.157327	+	1.28439i
$609$	2.62687			0.106446
$610$	−7.83163	+	22.2432i	−0.317094	+	0.900602i
$611$	−3.13709			−0.126913
$612$	−34.4764	+	42.8901i	−1.39363	+	1.73373i
$613$			4.08340i			0.164927i	0.996594	+	0.0824634i	$0.0262788\pi$
$613$			4.08340i			0.164927i	−0.996594	+	0.0824634i	$0.973721\pi$
$614$	19.4089	+	6.83369i	0.783279	+	0.275785i
$615$	−89.8153			−3.62170
$616$	3.73457	+	0.128394i	0.150470	+	0.00517314i
$617$	−15.6375			−0.629540			−0.314770	−	0.949168i	$-0.601927\pi$
$617$	−15.6375			−0.629540			−0.314770	+	0.949168i	$0.601927\pi$
$618$	−66.0432	−	23.2532i	−2.65665	−	0.935380i
$619$		−	3.23623i		−	0.130075i	−0.997883	−	0.0650375i	$-0.979283\pi$
$619$		−	3.23623i		−	0.130075i	0.997883	−	0.0650375i	$-0.0207167\pi$
$620$	12.5145	−	15.5686i	0.502596	−	0.625251i
$621$	5.44648			0.218560
$622$	3.22934	−	9.17189i	0.129485	−	0.367759i
$623$	4.19083			0.167902
$624$	2.62135	+	11.9095i	0.104938	+	0.476760i
$625$	−31.1998			−1.24799
$626$	15.0010	+	5.28170i	0.599560	+	0.211099i
$627$	−47.4033	−	31.7085i	−1.89310	−	1.26632i
$628$	31.3299	+	25.1839i	1.25020	+	1.00495i
$629$		−	46.4306i		−	1.85131i
$630$	9.29517	+	3.27274i	0.370329	+	0.130389i
$631$		−	16.8096i		−	0.669178i	−0.942364	−	0.334589i	$-0.891402\pi$
$631$		−	16.8096i		−	0.669178i	0.942364	−	0.334589i	$-0.108598\pi$
$632$	23.6663	+	38.1551i	0.941395	+	1.51773i
$633$			80.1095i			3.18407i
$634$	−16.1925	−	5.70124i	−0.643087	−	0.226425i
$635$	−11.0771			−0.439581
$636$	7.65125	−	9.51849i	0.303392	−	0.377432i
$637$			6.84132i			0.271063i
$638$	−6.08105	−	8.12151i	−0.240751	−	0.321534i
$639$			17.2543i			0.682570i
$640$	−22.5333	+	21.9304i	−0.890706	+	0.866873i
$641$	−19.6035			−0.774292			−0.387146	−	0.922018i	$-0.626539\pi$
$641$	−19.6035			−0.774292			−0.387146	+	0.922018i	$0.626539\pi$
$642$	4.57136	−	12.9835i	0.180417	−	0.512416i
$643$			30.6343i			1.20810i	0.796947	+	0.604049i	$0.206447\pi$
$643$			30.6343i			1.20810i	−0.796947	+	0.604049i	$0.793553\pi$
$644$	0.270695	−	0.336757i	0.0106669	−	0.0132701i
$645$		−	15.2484i		−	0.600405i
$646$	11.5804	−	32.8903i	0.455623	−	1.29405i
$647$			5.31737i			0.209047i	0.994522	+	0.104524i	$0.0333318\pi$
$647$			5.31737i			0.209047i	−0.994522	+	0.104524i	$0.966668\pi$
$648$	−17.4940	−	28.2041i	−0.687230	−	1.10796i
$649$	−9.24641	−	6.18501i	−0.362953	−	0.242783i
$650$	−1.27944	+	3.63384i	−0.0501838	+	0.142531i
$651$	4.36406			0.171041
$652$	9.22514	−	11.4765i	0.361285	−	0.449454i
$653$	−20.2079			−0.790796			−0.395398	−	0.918510i	$-0.629393\pi$
$653$	−20.2079			−0.790796			−0.395398	+	0.918510i	$0.629393\pi$
$654$	−6.21253	−	2.18737i	−0.242929	−	0.0855331i
$655$	29.4481			1.15063
$656$	41.4101	−	9.11463i	1.61679	−	0.355866i
$657$			69.6168i			2.71601i
$658$	0.586916	−	1.66695i	0.0228804	−	0.0649843i
$659$	−26.7656			−1.04264			−0.521320	−	0.853361i	$-0.674560\pi$
$659$	−26.7656			−1.04264			−0.521320	+	0.853361i	$0.674560\pi$
$660$	−16.8328	−	53.6227i	−0.655214	−	2.08726i
$661$	−26.7508			−1.04048			−0.520242	−	0.854019i	$-0.674158\pi$
$661$	−26.7508			−1.04048			−0.520242	+	0.854019i	$0.674158\pi$
$662$	15.2569	−	43.3322i	0.592975	−	1.68415i
$663$		−	13.3269i		−	0.517572i
$664$	18.8631	+	30.4113i	0.732031	+	1.18019i
$665$	−6.24436			−0.242146
$666$	89.1781	+	31.3988i	3.45558	+	1.21668i
$667$	−1.17312			−0.0454232
$668$	−32.7254	−	26.3057i	−1.26618	−	1.01780i
$669$	72.5528			2.80505
$670$	1.71482	−	4.87040i	0.0662494	−	0.188160i
$671$	16.5398	+	11.0637i	0.638513	+	0.427108i
$672$	−6.81871	−	0.835236i	−0.263038	−	0.0322199i
$673$			1.05814i			0.0407881i	0.999792	+	0.0203941i	$0.00649208\pi$
$673$			1.05814i			0.0407881i	−0.999792	+	0.0203941i	$0.993508\pi$
$674$	−8.32164	+	23.6349i	−0.320538	+	0.910383i
$675$		−	27.3577i		−	1.05300i
$676$	−1.55882	−	1.25303i	−0.0599546	−	0.0481934i
$677$		−	6.91957i		−	0.265941i	−0.991120	−	0.132970i	$-0.957548\pi$
$677$		−	6.91957i		−	0.265941i	0.991120	−	0.132970i	$-0.0424515\pi$
$678$	6.45592	−	18.3360i	0.247938	−	0.704188i
$679$	−5.01088			−0.192300
$680$	29.2018	−	18.1129i	1.11984	−	0.694598i
$681$		−	42.3219i		−	1.62178i
$682$	−10.1025	−	13.4924i	−0.386847	−	0.516651i
$683$		−	24.2529i		−	0.928010i	−0.885833	−	0.464005i	$-0.846412\pi$
$683$		−	24.2529i		−	0.928010i	0.885833	−	0.464005i	$-0.153588\pi$
$684$	55.3403	+	44.4843i	2.11599	+	1.70090i
$685$	56.2765			2.15022
$686$	−7.35481	−	2.58956i	−0.280808	−	0.0988699i
$687$		−	78.2541i		−	2.98558i
$688$	1.54744	+	7.03042i	0.0589955	+	0.268032i
$689$			2.00293i			0.0763057i
$690$	−6.12960	−	2.15818i	−0.233350	−	0.0821604i
$691$			3.44537i			0.131068i	0.997850	+	0.0655341i	$0.0208751\pi$
$691$			3.44537i			0.131068i	−0.997850	+	0.0655341i	$0.979125\pi$
$692$	−22.9057	+	28.4957i	−0.870744	+	1.08324i
$693$	4.62337	−	6.91179i	0.175627	−	0.262557i
$694$	4.20076	+	1.47905i	0.159459	+	0.0561439i
$695$	−6.51285			−0.247047
$696$	9.83156	+	15.8506i	0.372664	+	0.600814i
$697$	−46.3386			−1.75520
$698$	−8.69223	+	24.6875i	−0.329006	+	0.934435i
$699$	25.1147			0.949925
$700$	−1.69153	−	1.35970i	−0.0639339	−	0.0513920i
$701$			0.151692i			0.00572934i	0.999996	+	0.00286467i	$0.000911854\pi$
$701$			0.151692i			0.00572934i	−0.999996	+	0.00286467i	$0.999088\pi$
$702$	13.3965	+	4.71677i	0.505616	+	0.178023i
$703$	−59.9085			−2.25949
$704$	13.2026	+	23.0150i	0.497593	+	0.867411i
$705$	−26.5802			−1.00107
$706$	23.2076	+	8.17118i	0.873430	+	0.307527i
$707$			3.68332i			0.138526i
$708$	15.9396	+	12.8128i	0.599048	+	0.481534i
$709$	47.3746			1.77919			0.889595	−	0.456750i	$-0.150987\pi$
$709$	47.3746			1.77919			0.889595	+	0.456750i	$0.150987\pi$
$710$	3.57830	−	10.1630i	0.134291	−	0.381411i
$711$	99.9146			3.74709
$712$	15.6850	+	25.2875i	0.587819	+	0.947690i
$713$	−1.94892			−0.0729875
$714$	7.08145	+	2.49331i	0.265016	+	0.0933099i
$715$	7.66162	+	5.12494i	0.286528	+	0.191662i
$716$	17.5705	−	21.8584i	0.656640	−	0.816888i
$717$			13.7305i			0.512774i
$718$	−40.9466	−	14.4169i	−1.52811	−	0.538035i
$719$			7.18100i			0.267806i	0.990994	+	0.133903i	$0.0427511\pi$
$719$			7.18100i			0.267806i	−0.990994	+	0.133903i	$0.957249\pi$
$720$	15.0412	+	68.3361i	0.560552	+	2.54674i
$721$			6.46905i			0.240920i
$722$	−17.0928	−	6.01820i	−0.636127	−	0.223974i
$723$	80.9149			3.00926
$724$	−12.7318	−	10.2342i	−0.473172	−	0.380350i
$725$			5.89257i			0.218844i
$726$	−47.3586	+	2.51958i	−1.75764	+	0.0935105i
$727$			4.27355i			0.158497i	0.996855	+	0.0792486i	$0.0252521\pi$
$727$			4.27355i			0.158497i	−0.996855	+	0.0792486i	$0.974748\pi$
$728$	0.957455	−	0.593877i	0.0354857	−	0.0220105i
$729$	17.9934			0.666423
$730$	14.4375	−	41.0051i	0.534357	−	1.51767i
$731$		−	7.86714i		−	0.290977i
$732$	−28.5126	−	22.9193i	−1.05386	−	0.847121i
$733$		−	18.8094i		−	0.694741i	−0.937728	−	0.347371i	$-0.887075\pi$
$733$		−	18.8094i		−	0.694741i	0.937728	−	0.347371i	$-0.112925\pi$
$734$	0.788675	−	2.23998i	0.0291105	−	0.0826791i
$735$			57.9656i			2.13809i
$736$	3.04513	+	0.373003i	0.112245	+	0.0137491i
$737$	−3.62158	−	2.42251i	−0.133403	−	0.0892343i
$738$	31.3366	−	89.0014i	1.15351	−	3.27619i
$739$	15.2080			0.559435			0.279718	−	0.960082i	$-0.409759\pi$
$739$	15.2080			0.559435			0.279718	+	0.960082i	$0.409759\pi$
$740$	−46.0153	−	36.9885i	−1.69156	−	1.35973i
$741$	−17.1954			−0.631689
$742$	−1.06429	−	0.374727i	−0.0390714	−	0.0137567i
$743$	−7.71852			−0.283165			−0.141583	−	0.989926i	$-0.545219\pi$
$743$	−7.71852			−0.283165			−0.141583	+	0.989926i	$0.545219\pi$
$744$	16.3333	+	26.3328i	0.598809	+	0.965407i
$745$		−	57.4673i		−	2.10544i
$746$	−4.29174	+	12.1893i	−0.157132	+	0.446282i
$747$	79.6364			2.91374
$748$	−8.68456	−	27.6657i	−0.317539	−	1.01156i
$749$	−1.27175			−0.0464689
$750$	9.05670	−	25.7226i	0.330704	−	0.939258i
$751$			13.8636i			0.505891i	0.967481	+	0.252945i	$0.0813993\pi$
$751$			13.8636i			0.505891i	−0.967481	+	0.252945i	$0.918601\pi$
$752$	12.2550	−	2.69741i	0.446895	−	0.0983643i
$753$	74.8091			2.72619
$754$	−2.88546	−	1.01594i	−0.105082	−	0.0369985i
$755$	63.0448			2.29444
$756$	−5.01266	+	6.23597i	−0.182309	+	0.226800i
$757$	13.5309			0.491790			0.245895	−	0.969296i	$-0.420918\pi$
$757$	13.5309			0.491790			0.245895	+	0.969296i	$0.420918\pi$
$758$	2.70980	−	7.69630i	0.0984243	−	0.279542i
$759$	−3.04883	+	4.55791i	−0.110666	+	0.165442i
$760$	−23.3707	−	37.6786i	−0.847745	−	1.36674i
$761$			17.1462i			0.621549i	0.950484	+	0.310775i	$0.100588\pi$
$761$			17.1462i			0.621549i	−0.950484	+	0.310775i	$0.899412\pi$
$762$	5.70688	−	16.2086i	0.206739	−	0.587174i
$763$			0.608529i			0.0220302i
$764$	−16.7396	+	20.8248i	−0.605619	+	0.753416i
$765$		−	76.4691i		−	2.76475i
$766$	6.18242	−	17.5592i	0.223380	−	0.634439i
$767$	−3.35411			−0.121110
$768$	−20.4805	−	44.2703i	−0.739027	−	1.59747i
$769$		−	20.8264i		−	0.751018i	−0.926819	−	0.375509i	$-0.877468\pi$
$769$		−	20.8264i		−	0.751018i	0.926819	−	0.375509i	$-0.122532\pi$
$770$	−4.15663	+	3.11231i	−0.149794	+	0.112160i
$771$		−	23.4560i		−	0.844748i
$772$	−23.3008	+	28.9872i	−0.838615	+	1.04327i
$773$	−2.70966			−0.0974595			−0.0487298	−	0.998812i	$-0.515517\pi$
$773$	−2.70966			−0.0974595			−0.0487298	+	0.998812i	$0.515517\pi$
$774$	15.1102	+	5.32017i	0.543126	+	0.191230i
$775$			9.78942i			0.351646i
$776$	−18.7542	−	30.2357i	−0.673236	−	1.08540i
$777$		−	12.8986i		−	0.462735i
$778$	34.0942	+	12.0042i	1.22233	+	0.430373i
$779$			59.7898i			2.14219i
$780$	−13.2077	−	10.6167i	−0.472911	−	0.380140i
$781$	−7.55710	−	5.05502i	−0.270414	−	0.180883i
$782$	−3.16246	−	1.11347i	−0.113089	−	0.0398177i
$783$	21.7234			0.776332
$784$	−5.88246	−	26.7256i	−0.210088	−	0.954485i
$785$	−55.8583			−1.99367
$786$	−15.1715	+	43.0899i	−0.541151	+	1.53697i
$787$	11.8080			0.420908			0.210454	−	0.977604i	$-0.432506\pi$
$787$	11.8080			0.420908			0.210454	+	0.977604i	$0.432506\pi$
$788$	2.91977	−	3.63232i	0.104013	−	0.129396i
$789$			61.5185i			2.19012i
$790$	−58.8509	−	20.7209i	−2.09382	−	0.737215i
$791$	−1.79604			−0.0638599
$792$	59.0097	+	2.02874i	2.09682	+	0.0720882i
$793$	5.99977			0.213058
$794$	7.36544	+	2.59330i	0.261390	+	0.0920329i
$795$			16.9706i			0.601884i
$796$	−12.8564	+	15.9939i	−0.455683	+	0.566889i
$797$	−8.02123			−0.284127			−0.142063	−	0.989858i	$-0.545374\pi$
$797$	−8.02123			−0.284127			−0.142063	+	0.989858i	$0.545374\pi$
$798$	3.21707	−	9.13706i	0.113883	−	0.323448i
$799$	−13.7136			−0.485151
$800$	1.87360	−	15.2957i	0.0662416	−	0.540784i
$801$	66.2189			2.33973
$802$	24.3139	+	8.56068i	0.858552	+	0.302288i
$803$	−30.4910	−	20.3957i	−1.07600	−	0.719750i
$804$	6.24315	+	5.01843i	0.220179	+	0.176986i
$805$			0.600406i			0.0211615i
$806$	−4.79366	−	1.68780i	−0.168849	−	0.0594503i
$807$			27.5551i			0.969985i
$808$	−22.2252	+	13.7856i	−0.781881	+	0.484974i
$809$		−	21.2989i		−	0.748829i	−0.927262	−	0.374414i	$-0.877844\pi$
$809$		−	21.2989i		−	0.748829i	0.927262	−	0.374414i	$-0.122156\pi$
$810$	43.5023	+	15.3168i	1.52852	+	0.538176i
$811$	42.2055			1.48203			0.741017	−	0.671486i	$-0.234344\pi$
$811$	42.2055			1.48203			0.741017	+	0.671486i	$0.234344\pi$
$812$	1.07968	−	1.34316i	0.0378892	−	0.0471358i
$813$		−	29.9393i		−	1.05002i
$814$	−39.8788	+	29.8596i	−1.39775	+	1.04658i
$815$			20.4615i			0.716735i
$816$	11.4590	+	52.0613i	0.401145	+	1.82251i
$817$	−10.1508			−0.355132
$818$	11.2776	−	32.0304i	0.394312	−	1.11992i
$819$		−	2.50723i		−	0.0876098i
$820$	−36.9152	+	45.9241i	−1.28914	+	1.60374i
$821$		−	6.73040i		−	0.234893i	−0.993079	−	0.117446i	$-0.962529\pi$
$821$		−	6.73040i		−	0.234893i	0.993079	−	0.117446i	$-0.0374708\pi$
$822$	−28.9935	+	82.3466i	−1.01126	+	2.87217i
$823$			3.03370i			0.105748i	0.998601	+	0.0528740i	$0.0168382\pi$
$823$			3.03370i			0.105748i	−0.998601	+	0.0528740i	$0.983162\pi$
$824$	−39.0343	+	24.2117i	−1.35983	+	0.843454i
$825$	22.8944	+	15.3143i	0.797081	+	0.533175i
$826$	0.627517	−	1.78226i	0.0218341	−	0.0620128i
$827$	−31.7649			−1.10457			−0.552286	−	0.833654i	$-0.686244\pi$
$827$	−31.7649			−1.10457			−0.552286	+	0.833654i	$0.686244\pi$
$828$	4.27724	−	5.32107i	0.148644	−	0.184920i
$829$	−39.2573			−1.36346			−0.681732	−	0.731602i	$-0.738773\pi$
$829$	−39.2573			−1.36346			−0.681732	+	0.731602i	$0.738773\pi$
$830$	−46.9068	−	16.5155i	−1.62816	−	0.573260i
$831$	−30.5078			−1.05830
$832$	7.16692	+	3.55460i	0.248468	+	0.123234i
$833$			29.9063i			1.03619i
$834$	3.35540	−	9.52993i	0.116188	−	0.329995i
$835$	58.3464			2.01916
$836$	−35.6965	+	11.2055i	−1.23459	+	0.387551i
$837$	36.0895			1.24744
$838$	9.23122	−	26.2183i	0.318887	−	0.905696i
$839$			15.8911i			0.548621i	0.961641	+	0.274311i	$0.0884497\pi$
$839$			15.8911i			0.548621i	−0.961641	+	0.274311i	$0.911550\pi$
$840$	8.11239	−	5.03184i	0.279904	−	0.173615i
$841$	24.3210			0.838655
$842$	−20.0815	−	7.07052i	−0.692056	−	0.243666i
$843$	−33.3169			−1.14749
$844$	40.9614	+	32.9260i	1.40995	+	1.13336i
$845$	2.77923			0.0956085
$846$	9.27382	−	26.3393i	0.318841	−	0.905564i
$847$	1.67273	+	4.04991i	0.0574758	+	0.139157i
$848$	−1.72221	−	7.82444i	−0.0591408	−	0.268692i
$849$			30.4781i			1.04600i
$850$	−5.59298	+	15.8850i	−0.191838	+	0.544853i
$851$			5.76031i			0.197461i
$852$	13.0275	+	10.4719i	0.446314	+	0.358761i
$853$		−	38.2952i		−	1.31120i	−0.755107	−	0.655602i	$-0.772415\pi$
$853$		−	38.2952i		−	1.31120i	0.755107	−	0.655602i	$-0.227585\pi$
$854$	−1.12249	+	3.18808i	−0.0384109	+	0.109094i
$855$	−98.6667			−3.37433
$856$	−4.75978	−	7.67378i	−0.162686	−	0.262284i
$857$			34.9983i			1.19552i	0.801675	+	0.597760i	$0.203942\pi$
$857$			34.9983i			1.19552i	−0.801675	+	0.597760i	$0.796058\pi$
$858$	−11.4463	+	8.57052i	−0.390771	+	0.292593i
$859$			19.2913i			0.658212i	0.944293	+	0.329106i	$0.106747\pi$
$859$			19.2913i			0.658212i	−0.944293	+	0.329106i	$0.893253\pi$
$860$	−7.79678	−	6.26729i	−0.265868	−	0.213713i
$861$	−12.8730			−0.438712
$862$	32.6623	+	11.5001i	1.11248	+	0.391694i
$863$		−	21.2878i		−	0.724644i	−0.932053	−	0.362322i	$-0.881984\pi$
$863$		−	21.2878i		−	0.724644i	0.932053	−	0.362322i	$-0.118016\pi$
$864$	−56.3888	−	6.90716i	−1.91839	−	0.234986i
$865$		−	50.8052i		−	1.72743i
$866$	−24.9437	−	8.78246i	−0.847623	−	0.298440i
$867$		−	6.43053i		−	0.218392i
$868$	1.79368	−	2.23142i	0.0608816	−	0.0757393i
$869$	−29.2721	+	43.7609i	−0.992988	+	1.48449i
$870$	−24.4481	−	8.60794i	−0.828868	−	0.291837i
$871$	−1.31372			−0.0445136
$872$	−3.67187	+	2.27754i	−0.124345	+	0.0771271i
$873$	−79.1766			−2.67972
$874$	−1.43669	+	4.08046i	−0.0485969	+	0.138024i
$875$	−2.51958			−0.0851774
$876$	52.5626	+	42.2514i	1.77593	+	1.42754i
$877$			25.5294i			0.862065i	0.902336	+	0.431033i	$0.141851\pi$
$877$			25.5294i			0.862065i	−0.902336	+	0.431033i	$0.858149\pi$
$878$	−17.1834	−	6.05011i	−0.579911	−	0.204181i
$879$	−25.3108			−0.853713
$880$	−34.3367	−	13.4327i	−1.15749	−	0.452817i
$881$	−16.6394			−0.560595			−0.280297	−	0.959913i	$-0.590433\pi$
$881$	−16.6394			−0.560595			−0.280297	+	0.959913i	$0.590433\pi$
$882$	−57.4403	−	20.2242i	−1.93412	−	0.680984i
$883$		−	23.3708i		−	0.786489i	−0.919434	−	0.393245i	$-0.871353\pi$
$883$		−	23.3708i		−	0.786489i	0.919434	−	0.393245i	$-0.128647\pi$
$884$	−6.81426	−	5.47751i	−0.229188	−	0.184229i
$885$	−28.4189			−0.955291
$886$	10.2535	−	29.1218i	0.344474	−	0.978367i
$887$	24.0995			0.809181			0.404590	−	0.914498i	$-0.367414\pi$
$887$	24.0995			0.809181			0.404590	+	0.914498i	$0.367414\pi$
$888$	77.8305	−	48.2756i	2.61182	−	1.62002i
$889$	−1.58766			−0.0532484
$890$	−39.0038	−	13.7329i	−1.30741	−	0.460327i
$891$	21.6378	−	32.3479i	0.724894	−	1.08369i
$892$	29.8201	−	37.0975i	0.998452	−	1.24212i
$893$			17.6943i			0.592119i
$894$	84.0891	+	29.6070i	2.81236	+	0.990206i
$895$			38.9715i			1.30268i
$896$	−3.22965	+	3.14324i	−0.107895	+	0.105008i
$897$			1.65337i			0.0552044i
$898$	−31.7538	−	11.1802i	−1.05964	−	0.373088i
$899$	−7.77330			−0.259254
$900$	−26.7278	−	21.4846i	−0.890926	−	0.716153i
$901$			8.75566i			0.291693i
$902$	29.8004	+	39.7997i	0.992244	+	1.32519i
$903$		−	2.18552i		−	0.0727297i
$904$	−6.72203	−	10.8373i	−0.223571	−	0.360445i
$905$	22.6996			0.754559
$906$	−32.4805	+	92.2503i	−1.07909	+	3.06481i
$907$		−	7.57714i		−	0.251595i	−0.992056	−	0.125797i	$-0.959851\pi$
$907$		−	7.57714i		−	0.251595i	0.992056	−	0.125797i	$-0.0401489\pi$
$908$	−21.6399	−	17.3948i	−0.718146	−	0.577268i
$909$			58.2000i			1.93037i
$910$	−0.519964	+	1.47679i	−0.0172366	+	0.0489551i
$911$		−	20.2403i		−	0.670592i	−0.942113	−	0.335296i	$-0.891164\pi$
$911$		−	20.2403i		−	0.670592i	0.942113	−	0.335296i	$-0.108836\pi$
$912$	67.1737	−	14.7853i	2.22434	−	0.489592i
$913$	−23.3312	+	34.8794i	−0.772149	+	1.15434i
$914$	14.5614	−	41.3570i	0.481649	−	1.36797i
$915$	50.8353			1.68056
$916$	−40.0127	−	32.1634i	−1.32206	−	1.06271i
$917$	4.22073			0.139381
$918$	58.5615	+	20.6190i	1.93282	+	0.680527i
$919$	−19.8045			−0.653292			−0.326646	−	0.945147i	$-0.605918\pi$
$919$	−19.8045			−0.653292			−0.326646	+	0.945147i	$0.605918\pi$
$920$	−3.62286	+	2.24714i	−0.119442	+	0.0740859i
$921$		−	44.3576i		−	1.46163i
$922$	−3.07085	+	8.72176i	−0.101133	+	0.287236i
$923$	−2.74132			−0.0902315
$924$	−2.41261	−	7.68564i	−0.0793689	−	0.252839i
$925$	28.9341			0.951347
$926$	−1.94188	+	5.51529i	−0.0638143	+	0.181244i
$927$			102.217i			3.35725i
$928$	12.1456	+	1.48773i	0.398698	+	0.0488372i
$929$	29.5708			0.970186			0.485093	−	0.874463i	$-0.338786\pi$
$929$	29.5708			0.970186			0.485093	+	0.874463i	$0.338786\pi$
$930$	−40.6160	−	14.3005i	−1.33185	−	0.468933i
$931$	38.5875			1.26466
$932$	10.3225	−	12.8416i	0.338123	−	0.420640i
$933$	−20.9617			−0.686255
$934$	−8.92168	+	25.3392i	−0.291926	+	0.829123i
$935$	33.4922	+	22.4032i	1.09531	+	0.732665i
$936$	15.1287	−	9.38381i	0.494496	−	0.306719i
$937$		−	30.9032i		−	1.00956i	−0.863247	−	0.504782i	$-0.831573\pi$
$937$		−	30.9032i		−	1.00956i	0.863247	−	0.504782i	$-0.168427\pi$
$938$	0.245782	−	0.698065i	0.00802508	−	0.0227926i
$939$		−	34.2836i		−	1.11880i
$940$	−10.9248	+	13.5909i	−0.356327	+	0.443287i
$941$			7.58140i			0.247147i	0.992335	+	0.123573i	$0.0394354\pi$
$941$			7.58140i			0.247147i	−0.992335	+	0.123573i	$0.960565\pi$
$942$	28.7780	−	81.7346i	0.937638	−	2.66306i
$943$	5.74889			0.187210
$944$	13.1028	−	2.88401i	0.426460	−	0.0938664i
$945$		−	11.1182i		−	0.361673i
$946$	−6.75701	+	5.05937i	−0.219689	+	0.164494i
$947$			49.0637i			1.59436i	0.603744	+	0.797178i	$0.293675\pi$
$947$			49.0637i			1.59436i	−0.603744	+	0.797178i	$0.706325\pi$
$948$	60.6396	−	75.4383i	1.96948	−	2.45012i
$949$	−11.0605			−0.359040
$950$	20.4962	+	7.21652i	0.664984	+	0.234135i
$951$			37.0068i			1.20003i
$952$	4.18544	−	2.59609i	0.135651	−	0.0841396i
$953$		−	21.8247i		−	0.706973i	−0.935440	−	0.353486i	$-0.884996\pi$
$953$		−	21.8247i		−	0.706973i	0.935440	−	0.353486i	$-0.115004\pi$
$954$	−16.8168	−	5.92104i	−0.544464	−	0.191701i
$955$		−	37.1287i		−	1.20146i
$956$	7.02064	+	5.64341i	0.227064	+	0.182521i
$957$	−12.1603	+	18.1793i	−0.393088	+	0.587654i
$958$	17.7109	+	6.23583i	0.572212	+	0.201471i
$959$	8.06600			0.260465
$960$	60.7244	+	30.1176i	1.95987	+	0.972043i
$961$	18.0861			0.583422
$962$	−4.98855	+	14.1684i	−0.160837	+	0.456806i
$963$	−20.0949			−0.647549
$964$	33.2571	−	41.3732i	1.07114	−	1.33254i
$965$		−	51.6815i		−	1.66369i
$966$	−0.878544	−	0.309327i	−0.0282667	−	0.00995244i
$967$	21.1479			0.680071			0.340036	−	0.940413i	$-0.389561\pi$
$967$	21.1479			0.680071			0.340036	+	0.940413i	$0.389561\pi$
$968$	−18.1767	+	25.2509i	−0.584221	+	0.811594i
$969$	−75.1683			−2.41475
$970$	46.6359	+	16.4201i	1.49739	+	0.527217i
$971$		−	17.7242i		−	0.568798i	−0.958706	−	0.284399i	$-0.908206\pi$
$971$		−	17.7242i		−	0.568798i	0.958706	−	0.284399i	$-0.0917941\pi$
$972$	−7.07305	+	8.79918i	−0.226868	+	0.282234i
$973$	−0.933474			−0.0299258
$974$	−10.1889	+	28.9382i	−0.326473	+	0.927241i
$975$	8.30488			0.265969
$976$	−23.4381	+	5.15886i	−0.750234	+	0.165131i
$977$	47.7847			1.52877			0.764384	−	0.644761i	$-0.223043\pi$
$977$	47.7847			1.52877			0.764384	+	0.644761i	$0.223043\pi$
$978$	−29.9403	−	10.5417i	−0.957385	−	0.337086i
$979$	−19.4002	+	29.0028i	−0.620035	+	0.926933i
$980$	29.6388	+	23.8246i	0.946778	+	0.761049i
$981$			9.61532i			0.306993i
$982$	−23.4653	−	8.26192i	−0.748808	−	0.263648i
$983$		−	16.4652i		−	0.525158i	−0.964911	−	0.262579i	$-0.915427\pi$
$983$		−	16.4652i		−	0.525158i	0.964911	−	0.262579i	$-0.0845730\pi$
$984$	−48.1799	−	77.6762i	−1.53592	−	2.47623i
$985$			6.47609i			0.206345i
$986$	−12.6135	−	4.44111i	−0.401697	−	0.141434i
$987$	−3.80968			−0.121264
$988$	−7.06753	+	8.79231i	−0.224848	+	0.279721i
$989$			0.976019i			0.0310356i
$990$	−65.6785	+	49.1774i	−2.08740	+	1.56296i
$991$		−	20.8552i		−	0.662486i	−0.943545	−	0.331243i	$-0.892532\pi$
$991$		−	20.8552i		−	0.662486i	0.943545	−	0.331243i	$-0.107468\pi$
$992$	20.1776	+	2.47159i	0.640640	+	0.0784732i
$993$	−99.0326			−3.14271
$994$	0.512871	−	1.45664i	0.0162673	−	0.0462019i
$995$		−	28.5157i		−	0.904007i
$996$	48.3325	−	60.1277i	1.53147	−	1.90522i
$997$		−	40.7675i		−	1.29112i	−0.763709	−	0.645561i	$-0.776624\pi$
$997$		−	40.7675i		−	1.29112i	0.763709	−	0.645561i	$-0.223376\pi$
$998$	−11.3267	+	32.1700i	−0.358542	+	1.01832i
$999$		−	106.668i		−	3.37482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.e.b.131.7	✓	64
4.3	odd	2	inner	572.2.e.b.131.57	yes	64
11.10	odd	2	inner	572.2.e.b.131.58	yes	64
44.43	even	2	inner	572.2.e.b.131.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.e.b.131.7	✓	64	1.1	even	1	trivial
572.2.e.b.131.8	yes	64	44.43	even	2	inner
572.2.e.b.131.57	yes	64	4.3	odd	2	inner
572.2.e.b.131.58	yes	64	11.10	odd	2	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33395 - 0.469670i) q^{2} +3.04863i q^{3} +(1.55882 + 1.25303i) q^{4} -2.77923 q^{5} +(1.43185 - 4.06671i) q^{6} -0.398342 q^{7} +(-1.49087 - 2.40360i) q^{8} -6.29417 q^{9} +O(q^{10})\)	\(q+(-1.33395 - 0.469670i) q^{2} +3.04863i q^{3} +(1.55882 + 1.25303i) q^{4} -2.77923 q^{5} +(1.43185 - 4.06671i) q^{6} -0.398342 q^{7} +(-1.49087 - 2.40360i) q^{8} -6.29417 q^{9} +(3.70734 + 1.30532i) q^{10} +(1.84401 - 2.75674i) q^{11} +(-3.82002 + 4.75227i) q^{12} -1.00000i q^{13} +(0.531366 + 0.187089i) q^{14} -8.47286i q^{15} +(0.859843 + 3.90649i) q^{16} -4.37142i q^{17} +(8.39608 + 2.95618i) q^{18} -5.64036 q^{19} +(-4.33232 - 3.48245i) q^{20} -1.21440i q^{21} +(-3.75457 + 2.81127i) q^{22} +0.542331i q^{23} +(7.32770 - 4.54512i) q^{24} +2.72413 q^{25} +(-0.469670 + 1.33395i) q^{26} -10.0427i q^{27} +(-0.620944 - 0.499134i) q^{28} +2.16310i q^{29} +(-3.97945 + 11.3023i) q^{30} +3.59359i q^{31} +(0.687778 - 5.61489i) q^{32} +(8.40430 + 5.62172i) q^{33} +(-2.05312 + 5.83124i) q^{34} +1.10708 q^{35} +(-9.81149 - 7.88677i) q^{36} +10.6214 q^{37} +(7.52394 + 2.64911i) q^{38} +3.04863 q^{39} +(4.14348 + 6.68017i) q^{40} -10.6003i q^{41} +(-0.570367 + 1.61994i) q^{42} +1.79968 q^{43} +(6.32876 - 1.98667i) q^{44} +17.4930 q^{45} +(0.254716 - 0.723440i) q^{46} -3.13709i q^{47} +(-11.9095 + 2.62135i) q^{48} -6.84132 q^{49} +(-3.63384 - 1.27944i) q^{50} +13.3269 q^{51} +(1.25303 - 1.55882i) q^{52} -2.00293 q^{53} +(-4.71677 + 13.3965i) q^{54} +(-5.12494 + 7.66162i) q^{55} +(0.593877 + 0.957455i) q^{56} -17.1954i q^{57} +(1.01594 - 2.88546i) q^{58} -3.35411i q^{59} +(10.6167 - 13.2077i) q^{60} +5.99977i q^{61} +(1.68780 - 4.79366i) q^{62} +2.50723 q^{63} +(-3.55460 + 7.16692i) q^{64} +2.77923i q^{65} +(-8.57052 - 11.4463i) q^{66} -1.31372i q^{67} +(5.47751 - 6.81426i) q^{68} -1.65337 q^{69} +(-1.47679 - 0.519964i) q^{70} -2.74132i q^{71} +(9.38381 + 15.1287i) q^{72} -11.0605i q^{73} +(-14.1684 - 4.98855i) q^{74} +8.30488i q^{75} +(-8.79231 - 7.06753i) q^{76} +(-0.734547 + 1.09813i) q^{77} +(-4.06671 - 1.43185i) q^{78} -15.8741 q^{79} +(-2.38970 - 10.8570i) q^{80} +11.7341 q^{81} +(-4.97866 + 14.1403i) q^{82} -12.6524 q^{83} +(1.52168 - 1.89303i) q^{84} +12.1492i q^{85} +(-2.40067 - 0.845253i) q^{86} -6.59450 q^{87} +(-9.37529 - 0.322321i) q^{88} -10.5207 q^{89} +(-23.3347 - 8.21592i) q^{90} +0.398342i q^{91} +(-0.679555 + 0.845396i) q^{92} -10.9556 q^{93} +(-1.47340 + 4.18471i) q^{94} +15.6759 q^{95} +(17.1177 + 2.09678i) q^{96} +12.5793 q^{97} +(9.12595 + 3.21316i) q^{98} +(-11.6065 + 17.3514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9}+O(q^{10}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9	\( 64 q + 6 q^{4} + 12 q^{5} - 104 q^{9} - 8 q^{12} - 34 q^{14} + 26 q^{16} + 14 q^{20} - 8 q^{22} + 76 q^{25} + 2 q^{26} - 16 q^{33} + 32 q^{34} - 24 q^{36} - 32 q^{37} - 30 q^{38} + 54 q^{42} + 10 q^{44} + 12 q^{45} + 34 q^{48} - 36 q^{49} - 32 q^{53} - 36 q^{56} + 62 q^{58} + 4 q^{60} - 18 q^{64} - 30 q^{66} - 24 q^{69} - 30 q^{70} + 88 q^{77} - 10 q^{78} - 46 q^{80} + 64 q^{81} - 46 q^{82} + 98 q^{86} + 16 q^{88} + 24 q^{89} + 84 q^{92} + 8 q^{93} - 88 q^{97}+O(q^{100}) \) 64 * q + 6 * q^4 + 12 * q^5 - 104 * q^9 - 8 * q^12 - 34 * q^14 + 26 * q^16 + 14 * q^20 - 8 * q^22 + 76 * q^25 + 2 * q^26 - 16 * q^33 + 32 * q^34 - 24 * q^36 - 32 * q^37 - 30 * q^38 + 54 * q^42 + 10 * q^44 + 12 * q^45 + 34 * q^48 - 36 * q^49 - 32 * q^53 - 36 * q^56 + 62 * q^58 + 4 * q^60 - 18 * q^64 - 30 * q^66 - 24 * q^69 - 30 * q^70 + 88 * q^77 - 10 * q^78 - 46 * q^80 + 64 * q^81 - 46 * q^82 + 98 * q^86 + 16 * q^88 + 24 * q^89 + 84 * q^92 + 8 * q^93 - 88 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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