LMFDB - Embedded newform 588.2.x.a.559.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(55,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 0, 9]))

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

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

chi := DirichletCharacter("588.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.x (of order $14$, 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			559.21
Character	$\chi$	$=$	588.559
Dual form			588.2.x.a.223.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.981280 - 1.01838i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(-0.0741801 - 1.99862i) q^{4} +(2.53335 - 0.578222i) q^{5} +(-1.21120 - 0.730067i) q^{6} +(-1.72629 - 2.00497i) q^{7} +(-2.10814 - 1.88567i) q^{8} +(-0.900969 + 0.433884i) q^{9} +O(q^{10})$	\(q+(0.981280 - 1.01838i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(-0.0741801 - 1.99862i) q^{4} +(2.53335 - 0.578222i) q^{5} +(-1.21120 - 0.730067i) q^{6} +(-1.72629 - 2.00497i) q^{7} +(-2.10814 - 1.88567i) q^{8} +(-0.900969 + 0.433884i) q^{9} +(1.89708 - 3.14730i) q^{10} +(-0.428593 + 0.889983i) q^{11} +(-1.93201 + 0.517056i) q^{12} +(0.697693 - 1.44877i) q^{13} +(-3.73579 - 0.209420i) q^{14} +(-1.12745 - 2.34117i) q^{15} +(-3.98899 + 0.296516i) q^{16} +(3.94421 + 3.14540i) q^{17} +(-0.442246 + 1.34329i) q^{18} -2.99862 q^{19} +(-1.34357 - 5.02033i) q^{20} +(-1.57056 + 2.12916i) q^{21} +(0.485768 + 1.30979i) q^{22} +(2.65508 - 2.11735i) q^{23} +(-1.36928 + 2.47489i) q^{24} +(1.57870 - 0.760262i) q^{25} +(-0.790765 - 2.13217i) q^{26} +(0.623490 + 0.781831i) q^{27} +(-3.87913 + 3.59894i) q^{28} +(0.154534 - 0.193780i) q^{29} +(-3.49054 - 1.14918i) q^{30} +1.95638 q^{31} +(-3.61235 + 4.35326i) q^{32} +(0.963040 + 0.219808i) q^{33} +(7.07358 - 0.930170i) q^{34} +(-5.53263 - 4.08112i) q^{35} +(0.934004 + 1.76851i) q^{36} +(2.49400 - 3.12738i) q^{37} +(-2.94248 + 3.05372i) q^{38} +(-1.56770 - 0.357818i) q^{39} +(-6.43100 - 3.55809i) q^{40} +(-2.68486 + 0.612801i) q^{41} +(0.627123 + 3.68873i) q^{42} +(12.5134 + 2.85610i) q^{43} +(1.81053 + 0.790578i) q^{44} +(-2.03159 + 1.62014i) q^{45} +(0.449112 - 4.78159i) q^{46} +(-5.73142 - 2.76011i) q^{47} +(1.17672 + 3.82300i) q^{48} +(-1.03981 + 6.92234i) q^{49} +(0.774914 - 2.35374i) q^{50} +(2.18887 - 4.54524i) q^{51} +(-2.94731 - 1.28696i) q^{52} +(2.44059 + 3.06040i) q^{53} +(1.40802 + 0.132248i) q^{54} +(-0.571171 + 2.50246i) q^{55} +(-0.141430 + 7.48198i) q^{56} +(0.667255 + 2.92343i) q^{57} +(-0.0456993 - 0.347526i) q^{58} +(1.47606 - 6.46703i) q^{59} +(-4.59549 + 2.42701i) q^{60} +(-5.41157 - 4.31558i) q^{61} +(1.91976 - 1.99233i) q^{62} +(2.42526 + 1.05740i) q^{63} +(0.888528 + 7.95050i) q^{64} +(0.929791 - 4.07368i) q^{65} +(1.16886 - 0.765045i) q^{66} +14.9209i q^{67} +(5.99390 - 8.11632i) q^{68} +(-2.65508 - 2.11735i) q^{69} +(-9.58518 + 1.62958i) q^{70} +(3.75696 - 2.99607i) q^{71} +(2.71753 + 0.784238i) q^{72} +(-3.48651 - 7.23981i) q^{73} +(-0.737534 - 5.60866i) q^{74} +(-1.09249 - 1.36994i) q^{75} +(0.222438 + 5.99311i) q^{76} +(2.52427 - 0.677056i) q^{77} +(-1.90275 + 1.24539i) q^{78} -3.43155i q^{79} +(-9.93409 + 3.05770i) q^{80} +(0.623490 - 0.781831i) q^{81} +(-2.01053 + 3.33552i) q^{82} +(1.36655 - 0.658097i) q^{83} +(4.37190 + 2.98103i) q^{84} +(11.8108 + 5.68780i) q^{85} +(15.1877 - 9.94069i) q^{86} +(-0.223308 - 0.107540i) q^{87} +(2.58175 - 1.06803i) q^{88} +(-1.91459 - 3.97568i) q^{89} +(-0.343648 + 3.65874i) q^{90} +(-4.10917 + 1.10216i) q^{91} +(-4.42875 - 5.14944i) q^{92} +(-0.435335 - 1.90733i) q^{93} +(-8.43496 + 3.12831i) q^{94} +(-7.59656 + 1.73386i) q^{95} +(5.04794 + 2.55309i) q^{96} +3.46477i q^{97} +(6.02920 + 7.85167i) q^{98} -0.987807i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) $ 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9	$ 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9} + 20 q^{10} - 12 q^{14} + 36 q^{16} + 12 q^{19} - 25 q^{20} + 2 q^{21} - 6 q^{22} - 15 q^{24} + 32 q^{25} + 6 q^{26} - 28 q^{27} - 66 q^{28} - 8 q^{30} - 4 q^{31} + 25 q^{32} - 68 q^{34} - 12 q^{35} - 10 q^{37} + 35 q^{38} + 14 q^{39} + 16 q^{40} + 9 q^{42} + 20 q^{44} - 28 q^{46} - 8 q^{47} + 8 q^{48} - 8 q^{49} + 114 q^{50} + 20 q^{52} - 8 q^{53} - q^{56} + 12 q^{57} - 6 q^{58} + 20 q^{59} + 10 q^{60} - 14 q^{61} - 16 q^{62} - 12 q^{63} + 42 q^{64} - 8 q^{65} - 6 q^{66} - 16 q^{68} + 59 q^{70} + 28 q^{71} - 15 q^{72} + 22 q^{74} + 18 q^{75} + 7 q^{76} + 8 q^{77} + 6 q^{78} + 26 q^{80} - 28 q^{81} + 12 q^{82} + 10 q^{83} + 11 q^{84} - 24 q^{85} - 6 q^{86} - 242 q^{88} + 20 q^{90} - 16 q^{91} + 7 q^{92} - 4 q^{93} - 53 q^{94} - 10 q^{96} - 118 q^{98}+O(q^{100}) $ 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9 + 20 * q^10 - 12 * q^14 + 36 * q^16 + 12 * q^19 - 25 * q^20 + 2 * q^21 - 6 * q^22 - 15 * q^24 + 32 * q^25 + 6 * q^26 - 28 * q^27 - 66 * q^28 - 8 * q^30 - 4 * q^31 + 25 * q^32 - 68 * q^34 - 12 * q^35 - 10 * q^37 + 35 * q^38 + 14 * q^39 + 16 * q^40 + 9 * q^42 + 20 * q^44 - 28 * q^46 - 8 * q^47 + 8 * q^48 - 8 * q^49 + 114 * q^50 + 20 * q^52 - 8 * q^53 - q^56 + 12 * q^57 - 6 * q^58 + 20 * q^59 + 10 * q^60 - 14 * q^61 - 16 * q^62 - 12 * q^63 + 42 * q^64 - 8 * q^65 - 6 * q^66 - 16 * q^68 + 59 * q^70 + 28 * q^71 - 15 * q^72 + 22 * q^74 + 18 * q^75 + 7 * q^76 + 8 * q^77 + 6 * q^78 + 26 * q^80 - 28 * q^81 + 12 * q^82 + 10 * q^83 + 11 * q^84 - 24 * q^85 - 6 * q^86 - 242 * q^88 + 20 * q^90 - 16 * q^91 + 7 * q^92 - 4 * q^93 - 53 * q^94 - 10 * q^96 - 118 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{14}\right)$

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 $

$2$	0.981280	−	1.01838i	0.693870	−	0.720101i
$2$	0.981280	−	1.01838i	0.693870	−	0.720101i
$3$	−0.222521	−	0.974928i	−0.128473	−	0.562875i
$3$	−0.222521	−	0.974928i	−0.128473	−	0.562875i
$4$	−0.0741801	−	1.99862i	−0.0370900	−	0.999312i
$5$	2.53335	−	0.578222i	1.13295	−	0.258589i	0.385372	−	0.922761i	$-0.374073\pi$
$5$	2.53335	−	0.578222i	1.13295	−	0.258589i	0.747579	+	0.664173i	$0.231216\pi$
$6$	−1.21120	−	0.730067i	−0.494470	−	0.298049i
$7$	−1.72629	−	2.00497i	−0.652478	−	0.757808i
$7$	−1.72629	−	2.00497i	−0.652478	−	0.757808i
$8$	−2.10814	−	1.88567i	−0.745341	−	0.666684i
$9$	−0.900969	+	0.433884i	−0.300323	+	0.144628i
$10$	1.89708	−	3.14730i	0.599910	−	0.995265i
$11$	−0.428593	+	0.889983i	−0.129226	+	0.268340i	−0.955536	−	0.294876i	$-0.904722\pi$
$11$	−0.428593	+	0.889983i	−0.129226	+	0.268340i	0.826310	+	0.563216i	$0.190436\pi$
$12$	−1.93201	+	0.517056i	−0.557723	+	0.149261i
$13$	0.697693	−	1.44877i	0.193505	−	0.401818i	−0.781530	−	0.623868i	$-0.785560\pi$
$13$	0.697693	−	1.44877i	0.193505	−	0.401818i	0.975035	+	0.222050i	$0.0712748\pi$
$14$	−3.73579	−	0.209420i	−0.998432	−	0.0559697i
$15$	−1.12745	−	2.34117i	−0.291106	−	0.604488i
$16$	−3.98899	+	0.296516i	−0.997249	+	0.0741290i
$17$	3.94421	+	3.14540i	0.956612	+	0.762873i	0.971506	−	0.237016i	$-0.0761695\pi$
$17$	3.94421	+	3.14540i	0.956612	+	0.762873i	−0.0148936	+	0.999889i	$0.504741\pi$
$18$	−0.442246	+	1.34329i	−0.104238	+	0.316616i
$19$	−2.99862			−0.687930			−0.343965	−	0.938983i	$-0.611770\pi$
$19$	−2.99862			−0.687930			−0.343965	+	0.938983i	$0.611770\pi$
$20$	−1.34357	−	5.02033i	−0.300432	−	1.12258i
$21$	−1.57056	+	2.12916i	−0.342725	+	0.464621i
$22$	0.485768	+	1.30979i	0.103566	+	0.279249i
$23$	2.65508	−	2.11735i	0.553622	−	0.441499i	−0.306292	−	0.951938i	$-0.599088\pi$
$23$	2.65508	−	2.11735i	0.553622	−	0.441499i	0.859914	+	0.510439i	$0.170517\pi$
$24$	−1.36928	+	2.47489i	−0.279504	+	0.505184i
$25$	1.57870	−	0.760262i	0.315740	−	0.152052i
$26$	−0.790765	−	2.13217i	−0.155082	−	0.418152i
$27$	0.623490	+	0.781831i	0.119991	+	0.150464i
$28$	−3.87913	+	3.59894i	−0.733086	+	0.680136i
$29$	0.154534	−	0.193780i	0.0286962	−	0.0359840i	−0.767276	−	0.641317i	$-0.778389\pi$
$29$	0.154534	−	0.193780i	0.0286962	−	0.0359840i	0.795973	+	0.605333i	$0.206960\pi$
$30$	−3.49054	−	1.14918i	−0.637282	−	0.209810i
$31$	1.95638			0.351376			0.175688	−	0.984446i	$-0.443785\pi$
$31$	1.95638			0.351376			0.175688	+	0.984446i	$0.443785\pi$
$32$	−3.61235	+	4.35326i	−0.638580	+	0.769555i
$33$	0.963040	+	0.219808i	0.167644	+	0.0382636i
$34$	7.07358	−	0.930170i	1.21311	−	0.159523i
$35$	−5.53263	−	4.08112i	−0.935186	−	0.689835i
$36$	0.934004	+	1.76851i	0.155667	+	0.294752i
$37$	2.49400	−	3.12738i	0.410011	−	0.514137i	−0.533355	−	0.845892i	$-0.679069\pi$
$37$	2.49400	−	3.12738i	0.410011	−	0.514137i	0.943366	+	0.331754i	$0.107640\pi$
$38$	−2.94248	+	3.05372i	−0.477334	+	0.495379i
$39$	−1.56770	−	0.357818i	−0.251033	−	0.0572967i
$40$	−6.43100	−	3.55809i	−1.01683	−	0.562583i
$41$	−2.68486	+	0.612801i	−0.419304	+	0.0957035i	−0.426967	−	0.904267i	$-0.640418\pi$
$41$	−2.68486	+	0.612801i	−0.419304	+	0.0957035i	0.00766276	+	0.999971i	$0.497561\pi$
$42$	0.627123	+	3.68873i	0.0967672	+	0.569183i
$43$	12.5134	+	2.85610i	1.90827	+	0.435551i	0.999847	+	0.0175019i	$0.00557130\pi$
$43$	12.5134	+	2.85610i	1.90827	+	0.435551i	0.908425	+	0.418049i	$0.137286\pi$
$44$	1.81053	+	0.790578i	0.272948	+	0.119184i
$45$	−2.03159	+	1.62014i	−0.302852	+	0.241516i
$46$	0.449112	−	4.78159i	0.0662179	−	0.705006i
$47$	−5.73142	−	2.76011i	−0.836014	−	0.402603i	−0.0336466	−	0.999434i	$-0.510712\pi$
$47$	−5.73142	−	2.76011i	−0.836014	−	0.402603i	−0.802367	+	0.596831i	$0.796426\pi$
$48$	1.17672	+	3.82300i	0.169844	+	0.551803i
$49$	−1.03981	+	6.92234i	−0.148545	+	0.988906i
$50$	0.774914	−	2.35374i	0.109589	−	0.332869i
$51$	2.18887	−	4.54524i	0.306504	−	0.636461i
$52$	−2.94731	−	1.28696i	−0.408718	−	0.178469i
$53$	2.44059	+	3.06040i	0.335240	+	0.420378i	0.920668	−	0.390347i	$-0.127645\pi$
$53$	2.44059	+	3.06040i	0.335240	+	0.420378i	−0.585428	+	0.810725i	$0.699073\pi$
$54$	1.40802	+	0.132248i	0.191607	+	0.0179967i
$55$	−0.571171	+	2.50246i	−0.0770167	+	0.337432i
$56$	−0.141430	+	7.48198i	−0.0188993	+	0.999821i
$57$	0.667255	+	2.92343i	0.0883801	+	0.387218i
$58$	−0.0456993	−	0.347526i	−0.00600062	−	0.0456324i
$59$	1.47606	−	6.46703i	0.192166	−	0.841935i	−0.783275	−	0.621675i	$-0.786452\pi$
$59$	1.47606	−	6.46703i	0.192166	−	0.841935i	0.975441	−	0.220260i	$-0.0706905\pi$
$60$	−4.59549	+	2.42701i	−0.593275	+	0.313326i
$61$	−5.41157	−	4.31558i	−0.692880	−	0.552554i	0.212497	−	0.977162i	$-0.431840\pi$
$61$	−5.41157	−	4.31558i	−0.692880	−	0.552554i	−0.905377	+	0.424608i	$0.860412\pi$
$62$	1.91976	−	1.99233i	0.243809	−	0.253026i
$63$	2.42526	+	1.05740i	0.305554	+	0.133220i
$64$	0.888528	+	7.95050i	0.111066	+	0.993813i
$65$	0.929791	−	4.07368i	0.115326	−	0.505278i
$66$	1.16886	−	0.765045i	0.143877	−	0.0941705i
$67$			14.9209i			1.82288i	0.411434	+	0.911440i	$0.365028\pi$
$67$			14.9209i			1.82288i	−0.411434	+	0.911440i	$0.634972\pi$
$68$	5.99390	−	8.11632i	0.726867	−	0.984249i
$69$	−2.65508	−	2.11735i	−0.319634	−	0.254900i
$70$	−9.58518	+	1.62958i	−1.14565	+	0.194772i
$71$	3.75696	−	2.99607i	0.445869	−	0.355569i	−0.374671	−	0.927158i	$-0.622244\pi$
$71$	3.75696	−	2.99607i	0.445869	−	0.355569i	0.820540	+	0.571589i	$0.193673\pi$
$72$	2.71753	+	0.784238i	0.320264	+	0.0924233i
$73$	−3.48651	−	7.23981i	−0.408065	−	0.847356i	−0.999169	−	0.0407606i	$-0.987022\pi$
$73$	−3.48651	−	7.23981i	−0.408065	−	0.847356i	0.591104	−	0.806596i	$-0.298692\pi$
$74$	−0.737534	−	5.60866i	−0.0857366	−	0.651993i
$75$	−1.09249	−	1.36994i	−0.126150	−	0.158188i
$76$	0.222438	+	5.99311i	0.0255153	+	0.687456i
$77$	2.52427	−	0.677056i	0.287667	−	0.0771577i
$78$	−1.90275	+	1.24539i	−0.215444	+	0.141013i
$79$		−	3.43155i		−	0.386080i	−0.981191	−	0.193040i	$-0.938165\pi$
$79$		−	3.43155i		−	0.386080i	0.981191	−	0.193040i	$-0.0618347\pi$
$80$	−9.93409	+	3.05770i	−1.11066	+	0.341862i
$81$	0.623490	−	0.781831i	0.0692766	−	0.0868702i
$82$	−2.01053	+	3.33552i	−0.222026	+	0.368347i
$83$	1.36655	−	0.658097i	0.149999	−	0.0722355i	−0.357379	−	0.933960i	$-0.616329\pi$
$83$	1.36655	−	0.658097i	0.149999	−	0.0722355i	0.507377	+	0.861724i	$0.330615\pi$
$84$	4.37190	+	2.98103i	0.477013	+	0.325257i
$85$	11.8108	+	5.68780i	1.28106	+	0.616928i
$86$	15.1877	−	9.94069i	1.63773	−	1.07193i
$87$	−0.223308	−	0.107540i	−0.0239411	−	0.0115294i
$88$	2.58175	−	1.06803i	0.275215	−	0.113852i
$89$	−1.91459	−	3.97568i	−0.202946	−	0.421421i	0.774510	−	0.632562i	$-0.217997\pi$
$89$	−1.91459	−	3.97568i	−0.202946	−	0.421421i	−0.977456	+	0.211141i	$0.932282\pi$
$90$	−0.343648	+	3.65874i	−0.0362236	+	0.385665i
$91$	−4.10917	+	1.10216i	−0.430758	+	0.115538i
$92$	−4.42875	−	5.14944i	−0.461729	−	0.536866i
$93$	−0.435335	−	1.90733i	−0.0451422	−	0.197781i
$94$	−8.43496	+	3.12831i	−0.869999	+	0.322660i
$95$	−7.59656	+	1.73386i	−0.779390	+	0.177891i
$96$	5.04794	+	2.55309i	0.515203	+	0.260574i
$97$			3.46477i			0.351794i	0.984409	+	0.175897i	$0.0562825\pi$
$97$			3.46477i			0.351794i	−0.984409	+	0.175897i	$0.943717\pi$
$98$	6.02920	+	7.85167i	0.609041	+	0.793139i
$99$		−	0.987807i		−	0.0992783i
$100$	−1.63659	−	3.09883i	−0.163659	−	0.309883i
$101$	18.3822	−	4.19562i	1.82910	−	0.417480i	0.837457	−	0.546503i	$-0.184041\pi$
$101$	18.3822	−	4.19562i	1.82910	−	0.417480i	0.991642	+	0.129023i	$0.0411841\pi$
$102$	−2.48087	−	6.68925i	−0.245643	−	0.662334i
$103$	2.76355	+	12.1079i	0.272301	+	1.19303i	0.907289	+	0.420507i	$0.138148\pi$
$103$	2.76355	+	12.1079i	0.272301	+	1.19303i	−0.634988	+	0.772522i	$0.718995\pi$
$104$	−4.20274	+	1.73861i	−0.412113	+	0.170484i
$105$	−2.74767	+	6.30205i	−0.268145	+	0.615017i
$106$	5.51154	+	0.517672i	0.535328	+	0.0502808i
$107$	1.42015	+	2.94897i	0.137291	+	0.285088i	0.958267	−	0.285875i	$-0.0922842\pi$
$107$	1.42015	+	2.94897i	0.137291	+	0.285088i	−0.820976	+	0.570963i	$0.806570\pi$
$108$	1.51634	−	1.30412i	0.145910	−	0.125489i
$109$	16.1046	+	7.75557i	1.54254	+	0.742848i	0.995545	−	0.0942871i	$-0.0300572\pi$
$109$	16.1046	+	7.75557i	1.54254	+	0.742848i	0.546996	+	0.837135i	$0.315771\pi$
$110$	1.98797	+	3.03729i	0.189546	+	0.289594i
$111$	−3.60393	−	1.73556i	−0.342070	−	0.164732i
$112$	7.48069	+	7.48594i	0.706858	+	0.707355i
$113$	12.5191	−	6.02886i	1.17769	−	0.567147i	0.260455	−	0.965486i	$-0.416127\pi$
$113$	12.5191	−	6.02886i	1.17769	−	0.567147i	0.917238	+	0.398339i	$0.130413\pi$
$114$	3.63192	+	2.18919i	0.340161	+	0.205037i
$115$	5.50196	−	6.89923i	0.513060	−	0.643357i
$116$	−0.398756	−	0.294481i	−0.0370235	−	0.0273419i
$117$			1.60802i			0.148661i
$118$	−5.13744	−	7.84914i	−0.472940	−	0.722572i
$119$	−0.502430	−	13.3379i	−0.0460577	−	1.22269i
$120$	−2.03784	+	7.06151i	−0.186029	+	0.644625i
$121$	6.25001	+	7.83726i	0.568183	+	0.712479i
$122$	−9.70515	+	1.27622i	−0.878663	+	0.115543i
$123$	1.19487	+	2.48118i	0.107738	+	0.223721i
$124$	−0.145124	−	3.91007i	−0.0130325	−	0.351134i
$125$	−6.59816	+	5.26185i	−0.590157	+	0.470634i
$126$	3.45670	−	1.43222i	0.307947	−	0.127592i
$127$	6.84131	+	5.45576i	0.607068	+	0.484121i	0.878118	−	0.478445i	$-0.158799\pi$
$127$	6.84131	+	5.45576i	0.607068	+	0.484121i	−0.271049	+	0.962565i	$0.587371\pi$
$128$	8.96850	+	6.89681i	0.792711	+	0.609598i
$129$		−	12.8352i		−	1.13007i
$130$	−3.23615	−	4.94430i	−0.283829	−	0.433644i
$131$	0.761492	−	3.33631i	0.0665319	−	0.291495i	−0.930706	−	0.365768i	$-0.880806\pi$
$131$	0.761492	−	3.33631i	0.0665319	−	0.291495i	0.997238	+	0.0742728i	$0.0236635\pi$
$132$	0.367874	−	1.94106i	0.0320194	−	0.168948i
$133$	5.17650	+	6.01214i	0.448859	+	0.521318i
$134$	15.1951	+	14.6416i	1.31266	+	1.26484i
$135$	2.03159	+	1.62014i	0.174852	+	0.139440i
$136$	−2.38378	−	14.0684i	−0.204407	−	1.20636i
$137$	2.02745	−	8.88283i	0.173216	−	0.758911i	−0.811444	−	0.584430i	$-0.801318\pi$
$137$	2.02745	−	8.88283i	0.173216	−	0.758911i	0.984661	−	0.174481i	$-0.0558247\pi$
$138$	−4.76164	+	0.626152i	−0.405338	+	0.0533016i
$139$	2.90366	+	12.7218i	0.246285	+	1.07905i	0.935177	+	0.354181i	$0.115240\pi$
$139$	2.90366	+	12.7218i	0.246285	+	1.07905i	−0.688892	+	0.724864i	$0.741902\pi$
$140$	−7.74621	+	11.3604i	−0.654674	+	0.960128i
$141$	−1.41554	+	6.20190i	−0.119210	+	0.522295i
$142$	0.635497	−	6.76598i	0.0533297	−	0.567789i
$143$	0.990358	+	1.24187i	0.0828179	+	0.103850i
$144$	3.46531	−	1.99791i	0.288776	−	0.166493i
$145$	0.279442	−	0.580267i	0.0232064	−	0.0481886i
$146$	−10.7941	−	3.55370i	−0.893326	−	0.294107i
$147$	6.98016	−	0.526623i	0.575714	−	0.0434351i
$148$	−6.43545	−	4.75258i	−0.528991	−	0.390659i
$149$	−1.10446	−	0.531881i	−0.0904812	−	0.0435734i	0.388096	−	0.921619i	$-0.373133\pi$
$149$	−1.10446	−	0.531881i	−0.0904812	−	0.0435734i	−0.478577	+	0.878046i	$0.658847\pi$
$150$	−2.46716	−	0.231729i	−0.201443	−	0.0189206i
$151$	−3.33498	+	2.65956i	−0.271397	+	0.216432i	−0.749725	−	0.661749i	$-0.769814\pi$
$151$	−3.33498	+	2.65956i	−0.271397	+	0.216432i	0.478328	+	0.878181i	$0.341243\pi$
$152$	6.32151	+	5.65439i	0.512742	+	0.458632i
$153$	−4.91835	−	1.12258i	−0.397625	−	0.0907554i
$154$	1.78752	−	3.23504i	0.144042	−	0.260687i
$155$	4.95620	−	1.13122i	0.398092	−	0.0908618i
$156$	−0.598851	+	3.15979i	−0.0479464	+	0.252986i
$157$	−11.1304	−	2.54044i	−0.888304	−	0.202750i	−0.246064	−	0.969254i	$-0.579137\pi$
$157$	−11.1304	−	2.54044i	−0.888304	−	0.202750i	−0.642240	+	0.766504i	$0.721995\pi$
$158$	−3.49461	−	3.36731i	−0.278016	−	0.267889i
$159$	2.44059	−	3.06040i	0.193551	−	0.242705i
$160$	−6.63422	+	13.1171i	−0.524482	+	1.03700i
$161$	−8.82868	−	1.66818i	−0.695798	−	0.131471i
$162$	−0.184381	−	1.40214i	−0.0144863	−	0.110163i
$163$	−21.0851	−	4.81254i	−1.65151	−	0.376947i	−0.707463	−	0.706751i	$-0.750160\pi$
$163$	−21.0851	−	4.81254i	−1.65151	−	0.376947i	−0.944050	+	0.329804i	$0.893017\pi$
$164$	1.42392	+	5.32056i	0.111190	+	0.415466i
$165$	2.56682			0.199827
$166$	0.670780	−	2.03744i	0.0520626	−	0.158136i
$167$	−2.30847	+	2.89473i	−0.178635	+	0.224001i	−0.863085	−	0.505059i	$-0.831471\pi$
$167$	−2.30847	+	2.89473i	−0.178635	+	0.224001i	0.684450	+	0.729060i	$0.260042\pi$
$168$	7.32586	−	1.52701i	0.565202	−	0.117812i
$169$	6.49320	+	8.14221i	0.499477	+	0.626324i
$170$	17.3820	−	6.44655i	1.33314	−	0.494428i
$171$	2.70166	−	1.30105i	0.206601	−	0.0994939i
$172$	4.78002	−	25.2214i	0.364473	−	1.92311i
$173$	−15.5213	+	12.3779i	−1.18007	+	0.941071i	−0.999100	−	0.0424186i	$-0.986494\pi$
$173$	−15.5213	+	12.3779i	−1.18007	+	0.941071i	−0.180966	+	0.983489i	$0.557922\pi$
$174$	−0.328643	+	0.121885i	−0.0249144	+	0.00924010i
$175$	−4.24960	−	1.85281i	−0.321240	−	0.140059i
$176$	1.44576	−	3.67722i	0.108978	−	0.277181i
$177$	−6.63334			−0.498592
$178$	−5.92748	−	1.95148i	−0.444283	−	0.146270i
$179$	−19.0019	−	15.1535i	−1.42027	−	1.13263i	−0.970956	−	0.239256i	$-0.923096\pi$
$179$	−19.0019	−	15.1535i	−1.42027	−	1.13263i	−0.449316	−	0.893373i	$-0.648332\pi$
$180$	3.38876	+	3.94021i	0.252583	+	0.293686i
$181$	−10.7401	−	22.3021i	−0.798307	−	1.65770i	−0.752355	−	0.658758i	$-0.771082\pi$
$181$	−10.7401	−	22.3021i	−0.798307	−	1.65770i	−0.0459516	−	0.998944i	$-0.514632\pi$
$182$	−2.90984	+	5.26621i	−0.215692	+	0.390357i
$183$	−3.00319	+	6.23620i	−0.222002	+	0.460993i
$184$	−9.58991	−	0.542907i	−0.706977	−	0.0400236i
$185$	4.50987	−	9.36484i	0.331572	−	0.688516i
$186$	−2.36956	−	1.42829i	−0.173745	−	0.104727i
$187$	−4.48982	+	2.16218i	−0.328328	+	0.158115i
$188$	−5.09126	+	11.6597i	−0.371318	+	0.850371i
$189$	0.491222	−	2.59975i	0.0357311	−	0.189104i
$190$	−5.68862	+	9.43756i	−0.412696	+	0.684673i
$191$	7.99385	−	1.82454i	0.578415	−	0.132019i	0.0767026	−	0.997054i	$-0.475561\pi$
$191$	7.99385	−	1.82454i	0.578415	−	0.132019i	0.501712	+	0.865035i	$0.332704\pi$
$192$	7.55345	−	2.63540i	0.545123	−	0.190194i
$193$	−2.15173	−	9.42736i	−0.154885	−	0.678596i	−0.991424	−	0.130688i	$-0.958281\pi$
$193$	−2.15173	−	9.42736i	−0.154885	−	0.678596i	0.836538	−	0.547908i	$-0.184576\pi$
$194$	3.52843	+	3.39990i	0.253327	+	0.244099i
$195$	−4.17844			−0.299224
$196$	13.9123	+	1.56470i	0.993735	+	0.111764i
$197$	−24.4781			−1.74400			−0.871998	−	0.489510i	$-0.837176\pi$
$197$	−24.4781			−1.74400			−0.871998	+	0.489510i	$0.837176\pi$
$198$	−1.00596	−	0.969315i	−0.0714904	−	0.0688862i
$199$	3.30952	+	14.5000i	0.234606	+	1.02788i	0.945767	+	0.324846i	$0.105313\pi$
$199$	3.30952	+	14.5000i	0.234606	+	1.02788i	−0.711161	+	0.703029i	$0.751830\pi$
$200$	−4.76172	−	1.37416i	−0.336705	−	0.0971678i
$201$	14.5468	−	3.32021i	1.02605	−	0.234190i
$202$	13.7654	−	22.8371i	0.968528	−	1.60681i
$203$	−0.655293	+	0.0246844i	−0.0459926	+	0.00173251i
$204$	−9.24660	−	4.03757i	−0.647391	−	0.282686i
$205$	−6.44736	+	3.10489i	−0.450303	+	0.216855i
$206$	15.0422	+	9.06692i	1.04804	+	0.631722i
$207$	−1.47346	+	3.05967i	−0.102412	+	0.212662i
$208$	−2.35351	+	5.98603i	−0.163186	+	0.415057i
$209$	1.28519	−	2.66872i	0.0888982	−	0.184599i
$210$	3.72163	+	8.98224i	0.256817	+	0.619833i
$211$	7.95957	+	16.5282i	0.547959	+	1.13785i	0.972600	+	0.232487i	$0.0746863\pi$
$211$	7.95957	+	16.5282i	0.547959	+	1.13785i	−0.424640	+	0.905362i	$0.639599\pi$
$212$	5.93554	−	5.10484i	0.407655	−	0.350602i
$213$	−3.75696	−	2.99607i	−0.257423	−	0.205288i
$214$	4.39673	+	1.44752i	0.300554	+	0.0989505i
$215$	33.3523			2.27461
$216$	0.159868	−	2.82391i	0.0108776	−	0.192142i
$217$	−3.37729	−	3.92248i	−0.229265	−	0.266275i
$218$	23.7012	−	8.79016i	1.60525	−	0.595345i
$219$	−6.28248	+	5.01011i	−0.424530	+	0.338552i
$220$	5.04386	+	0.955923i	0.340057	+	0.0644483i
$221$	7.30883	−	3.51975i	0.491645	−	0.236764i
$222$	−5.30392	+	1.96709i	−0.355976	+	0.132022i
$223$	10.9364	+	13.7139i	0.732359	+	0.918349i	0.998966	−	0.0454565i	$-0.0144742\pi$
$223$	10.9364	+	13.7139i	0.732359	+	0.918349i	−0.266608	+	0.963805i	$0.585903\pi$
$224$	14.9642	−	0.272349i	0.999834	−	0.0181971i
$225$	−1.09249	+	1.36994i	−0.0728330	+	0.0913296i
$226$	6.14505	−	18.6651i	0.408762	−	1.24158i
$227$	−23.6644			−1.57066			−0.785331	−	0.619076i	$-0.787507\pi$
$227$	−23.6644			−1.57066			−0.785331	+	0.619076i	$0.787507\pi$
$228$	5.79335	−	1.55045i	0.383674	−	0.102681i
$229$	−17.1048	−	3.90406i	−1.13032	−	0.257987i	−0.383840	−	0.923400i	$-0.625399\pi$
$229$	−17.1048	−	3.90406i	−1.13032	−	0.257987i	−0.746476	+	0.665412i	$0.768256\pi$
$230$	−1.62706	−	12.3731i	−0.107285	−	0.815861i
$231$	−1.22178	−	2.31032i	−0.0803875	−	0.152008i
$232$	−0.691183	+	0.117115i	−0.0453784	+	0.00768900i
$233$	−7.77353	+	9.74769i	−0.509261	+	0.638593i	−0.968290	−	0.249828i	$-0.919626\pi$
$233$	−7.77353	+	9.74769i	−0.509261	+	0.638593i	0.459029	+	0.888421i	$0.348197\pi$
$234$	1.63757	+	1.57792i	0.107051	+	0.103152i
$235$	−16.1157	−	3.67830i	−1.05127	−	0.239946i
$236$	−13.0346	−	2.47036i	−0.848483	−	0.160807i
$237$	−3.34552	+	0.763592i	−0.217315	+	0.0496006i
$238$	−14.0760	−	12.5766i	−0.912415	−	0.815218i
$239$	20.7288	+	4.73122i	1.34084	+	0.306037i	0.831976	−	0.554812i	$-0.187210\pi$
$239$	20.7288	+	4.73122i	1.34084	+	0.306037i	0.508861	+	0.860849i	$0.330067\pi$
$240$	5.19158	+	9.00461i	0.335115	+	0.581245i
$241$	−7.13366	+	5.68890i	−0.459519	+	0.366454i	−0.825719	−	0.564082i	$-0.809230\pi$
$241$	−7.13366	+	5.68890i	−0.459519	+	0.366454i	0.366199	+	0.930536i	$0.380659\pi$
$242$	14.1143	+	1.32569i	0.907301	+	0.0852184i
$243$	−0.900969	−	0.433884i	−0.0577972	−	0.0278337i
$244$	−8.22379	+	11.1358i	−0.526475	+	0.712898i
$245$	1.36843	+	18.1380i	0.0874259	+	1.15879i
$246$	3.69928	+	1.21790i	0.235858	+	0.0776506i
$247$	−2.09211	+	4.34432i	−0.133118	+	0.276422i
$248$	−4.12433	−	3.68908i	−0.261895	−	0.234257i
$249$	−0.945683	−	1.18585i	−0.0599302	−	0.0751501i
$250$	−1.11609	+	11.8828i	−0.0705877	+	0.751531i
$251$	−5.08565	+	22.2817i	−0.321004	+	1.40641i	0.514767	+	0.857330i	$0.327878\pi$
$251$	−5.08565	+	22.2817i	−0.321004	+	1.40641i	−0.835771	+	0.549079i	$0.814979\pi$
$252$	1.93345	−	4.92562i	0.121796	−	0.310285i
$253$	0.746461	+	3.27046i	0.0469296	+	0.205612i
$254$	12.2693	−	1.61340i	0.769842	−	0.101234i
$255$	2.91703	−	12.7804i	0.182672	−	0.800337i
$256$	15.8242	−	2.36560i	0.989010	−	0.147850i
$257$	−24.5549	−	19.5818i	−1.53169	−	1.22148i	−0.891284	−	0.453446i	$-0.850195\pi$
$257$	−24.5549	−	19.5818i	−1.53169	−	1.22148i	−0.640406	−	0.768036i	$-0.721234\pi$
$258$	−13.0710	−	12.5949i	−0.813767	−	0.784124i
$259$	−10.5757	+	0.398378i	−0.657140	+	0.0247540i
$260$	−8.21073	−	1.55612i	−0.509208	−	0.0965062i
$261$	−0.0551526	+	0.241639i	−0.00341386	+	0.0149571i
$262$	−2.65039	−	4.04934i	−0.163741	−	0.250169i
$263$			6.05266i			0.373223i	0.982434	+	0.186611i	$0.0597506\pi$
$263$			6.05266i			0.373223i	−0.982434	+	0.186611i	$0.940249\pi$
$264$	−1.61574	−	2.27936i	−0.0994421	−	0.140285i
$265$	7.95246	+	6.34188i	0.488516	+	0.389578i
$266$	11.2022	+	0.627969i	0.686851	+	0.0385032i
$267$	−3.44996	+	2.75125i	−0.211134	+	0.168374i
$268$	29.8213	−	1.10683i	1.82163	−	0.0676106i
$269$	4.80604	+	9.97985i	0.293030	+	0.608482i	0.994561	−	0.104156i	$-0.0332142\pi$
$269$	4.80604	+	9.97985i	0.293030	+	0.608482i	−0.701531	+	0.712639i	$0.747500\pi$
$270$	3.64347	−	0.479114i	0.221735	−	0.0291579i
$271$	−6.89277	−	8.64326i	−0.418706	−	0.525041i	0.527087	−	0.849812i	$-0.323284\pi$
$271$	−6.89277	−	8.64326i	−0.418706	−	0.525041i	−0.945793	+	0.324771i	$0.894713\pi$
$272$	−16.6661	−	11.3775i	−1.01053	−	0.689861i
$273$	1.98890	+	3.76089i	0.120374	+	0.227620i
$274$	−7.05657	−	10.7812i	−0.426303	−	0.651319i
$275$			1.73086i			0.104375i
$276$	−4.03484	+	5.46357i	−0.242869	+	0.328868i
$277$	−9.40027	+	11.7876i	−0.564807	+	0.708246i	−0.979438	−	0.201744i	$-0.935339\pi$
$277$	−9.40027	+	11.7876i	−0.564807	+	0.708246i	0.414631	+	0.909990i	$0.363911\pi$
$278$	15.8048	+	9.52659i	0.947911	+	0.571367i
$279$	−1.76264	+	0.848841i	−0.105526	+	0.0508188i
$280$	3.96795	+	19.0363i	0.237130	+	1.13764i
$281$	−10.7240	−	5.16442i	−0.639742	−	0.308084i	0.0857473	−	0.996317i	$-0.472672\pi$
$281$	−10.7240	−	5.16442i	−0.639742	−	0.308084i	−0.725489	+	0.688233i	$0.758387\pi$
$282$	4.92683	+	7.52736i	0.293388	+	0.448248i
$283$	13.3151	+	6.41221i	0.791500	+	0.381166i	0.785536	−	0.618816i	$-0.212387\pi$
$283$	13.3151	+	6.41221i	0.791500	+	0.381166i	0.00596384	+	0.999982i	$0.498102\pi$
$284$	−6.26672	−	7.28650i	−0.371861	−	0.432374i
$285$	3.38079	+	7.02028i	0.200261	+	0.415845i
$286$	2.23651	+	0.210065i	0.132248	+	0.0124214i
$287$	5.86350	+	4.32518i	0.346112	+	0.255308i
$288$	1.36581	−	5.48950i	0.0804811	−	0.323472i
$289$	1.88039	+	8.23851i	0.110611	+	0.484619i
$290$	−0.316720	−	0.853981i	−0.0185984	−	0.0501475i
$291$	3.37790	−	0.770983i	0.198016	−	0.0451958i
$292$	−14.2110	+	7.50527i	−0.831638	+	0.439213i
$293$			10.4632i			0.611267i	0.952149	+	0.305633i	$0.0988682\pi$
$293$			10.4632i			0.611267i	−0.952149	+	0.305633i	$0.901132\pi$
$294$	6.31319	−	7.62520i	0.368193	−	0.444710i
$295$		−	17.2368i		−	1.00356i
$296$	−11.1549	+	1.89010i	−0.648365	+	0.109860i
$297$	−0.963040	+	0.219808i	−0.0558813	+	0.0127545i
$298$	−1.62544	+	0.602835i	−0.0941594	+	0.0349213i
$299$	−1.21514	−	5.32387i	−0.0702733	−	0.307888i
$300$	−2.65696	+	2.28511i	−0.153400	+	0.131931i
$301$	−15.8754	−	30.0194i	−0.915042	−	1.73029i
$302$	−0.564118	+	6.00603i	−0.0324613	+	0.345608i
$303$	−8.18086	−	16.9877i	−0.469978	−	0.975919i
$304$	11.9615	−	0.889138i	0.686037	−	0.0509956i
$305$	−16.2048	−	7.80381i	−0.927883	−	0.446845i
$306$	−5.96949	+	3.90717i	−0.341253	+	0.223358i
$307$	−15.6919	−	7.55682i	−0.895584	−	0.431291i	−0.0712923	−	0.997455i	$-0.522712\pi$
$307$	−15.6919	−	7.55682i	−0.895584	−	0.431291i	−0.824292	+	0.566165i	$0.808427\pi$
$308$	−1.54043	−	4.99484i	−0.0877742	−	0.284607i
$309$	11.1894	−	5.38853i	0.636543	−	0.306543i
$310$	3.71141	−	6.15732i	0.210794	−	0.349712i
$311$	11.6839	−	14.6512i	0.662534	−	0.830791i	−0.331083	−	0.943602i	$-0.607414\pi$
$311$	11.6839	−	14.6512i	0.662534	−	0.830791i	0.993616	+	0.112811i	$0.0359854\pi$
$312$	2.63021	+	3.71049i	0.148907	+	0.210065i
$313$		−	13.5438i		−	0.765544i	−0.923843	−	0.382772i	$-0.874970\pi$
$313$		−	13.5438i		−	0.765544i	0.923843	−	0.382772i	$-0.125030\pi$
$314$	−13.5092	+	8.84206i	−0.762367	+	0.498986i
$315$	6.75546	+	1.27644i	0.380627	+	0.0719194i
$316$	−6.85838	+	0.254553i	−0.385814	+	0.0143197i
$317$	12.9121	+	16.1913i	0.725218	+	0.909395i	0.998621	−	0.0525048i	$-0.0167205\pi$
$317$	12.9121	+	16.1913i	0.725218	+	0.909395i	−0.273402	+	0.961900i	$0.588149\pi$
$318$	−0.721739	−	5.48854i	−0.0404731	−	0.307782i
$319$	0.106228	+	0.220585i	0.00594764	+	0.0123504i
$320$	6.84811	+	19.6277i	0.382821	+	1.09722i
$321$	2.55902	−	2.04075i	0.142831	−	0.113904i
$322$	−10.3622	+	7.35397i	−0.577465	+	0.409821i
$323$	−11.8272	−	9.43186i	−0.658082	−	0.524803i
$324$	−1.60884	−	1.18813i	−0.0893799	−	0.0660070i
$325$		−	2.81761i		−	0.156293i
$326$	−25.5914	+	16.7501i	−1.41737	+	0.927703i
$327$	3.97751	−	17.4266i	0.219957	−	0.963693i
$328$	6.81560	+	3.77087i	0.376329	+	0.208212i
$329$	4.36019	+	16.2561i	0.240385	+	0.896227i
$330$	2.51877	−	2.61399i	0.138654	−	0.143895i
$331$	−11.0653	−	8.82429i	−0.608205	−	0.485027i	0.270290	−	0.962779i	$-0.412880\pi$
$331$	−11.0653	−	8.82429i	−0.608205	−	0.485027i	−0.878495	+	0.477752i	$0.841452\pi$
$332$	−1.41666	−	2.68241i	−0.0777492	−	0.147216i
$333$	−0.890098	+	3.89977i	−0.0487771	+	0.213706i
$334$	0.682669	+	5.19143i	0.0373540	+	0.284062i
$335$	8.62759	+	37.8000i	0.471376	+	2.06523i
$336$	5.63364	−	8.95891i	0.307341	−	0.488749i
$337$	−7.23961	+	31.7188i	−0.394367	+	1.72783i	0.254626	+	0.967040i	$0.418048\pi$
$337$	−7.23961	+	31.7188i	−0.394367	+	1.72783i	−0.648993	+	0.760795i	$0.724809\pi$
$338$	14.6635	+	1.37727i	0.797588	+	0.0749136i
$339$	−8.66345	−	10.8636i	−0.470534	−	0.590031i
$340$	10.4916	−	24.0273i	0.568989	−	1.30306i
$341$	−0.838491	+	1.74114i	−0.0454068	+	0.0942883i
$342$	1.32613	−	4.02800i	0.0717086	−	0.217809i
$343$	15.6741	−	9.86520i	0.846322	−	0.532671i
$344$	−20.9943	−	29.6171i	−1.13194	−	1.59685i
$345$	−7.95056	−	3.82879i	−0.428044	−	0.206135i
$346$	−2.62546	+	27.9527i	−0.141146	+	1.50275i
$347$	−6.65631	+	5.30823i	−0.357329	+	0.284961i	−0.785656	−	0.618663i	$-0.787675\pi$
$347$	−6.65631	+	5.30823i	−0.357329	+	0.284961i	0.428327	+	0.903624i	$0.359103\pi$
$348$	−0.198366	+	0.454286i	−0.0106335	+	0.0243523i
$349$	−17.4002	−	3.97149i	−0.931413	−	0.212589i	−0.270215	−	0.962800i	$-0.587095\pi$
$349$	−17.4002	−	3.97149i	−0.931413	−	0.212589i	−0.661198	+	0.750211i	$0.729952\pi$
$350$	−6.05691	+	2.50957i	−0.323755	+	0.134142i
$351$	1.56770	−	0.357818i	0.0836777	−	0.0190989i
$352$	−2.32610	−	5.08071i	−0.123981	−	0.270803i
$353$	−7.92257	−	1.80827i	−0.421676	−	0.0962447i	0.00641736	−	0.999979i	$-0.497957\pi$
$353$	−7.92257	−	1.80827i	−0.421676	−	0.0962447i	−0.428093	+	0.903735i	$0.640814\pi$
$354$	−6.50916	+	6.75523i	−0.345958	+	0.359037i
$355$	7.78531	−	9.76247i	0.413201	−	0.518138i
$356$	−7.80386	+	4.12145i	−0.413604	+	0.218437i
$357$	−12.8917	+	3.45780i	−0.682302	+	0.183006i
$358$	−34.0782	+	4.48126i	−1.80109	+	0.236842i
$359$	−23.6046	−	5.38760i	−1.24580	−	0.284347i	−0.451723	−	0.892158i	$-0.649190\pi$
$359$	−23.6046	−	5.38760i	−1.24580	−	0.284347i	−0.794081	+	0.607812i	$0.792048\pi$
$360$	7.33793	+	0.415417i	0.386743	+	0.0218944i
$361$	−10.0083			−0.526753
$362$	−33.2510	−	10.9471i	−1.74763	−	0.575367i
$363$	6.25001	−	7.83726i	0.328040	−	0.411350i
$364$	2.50762	+	8.13093i	0.131435	+	0.426177i
$365$	−13.0188	−	16.3250i	−0.681434	−	0.854492i
$366$	3.40382	+	9.17783i	0.177921	+	0.479733i
$367$	28.6537	−	13.7989i	1.49571	−	0.720298i	0.505890	−	0.862598i	$-0.331164\pi$
$367$	28.6537	−	13.7989i	1.49571	−	0.720298i	0.989824	+	0.142301i	$0.0454499\pi$
$368$	−9.96327	+	9.23339i	−0.519371	+	0.481324i
$369$	2.15309	−	1.71703i	0.112085	−	0.0893851i
$370$	−5.11148	−	13.7823i	−0.265733	−	0.716506i
$371$	1.92284	−	10.1765i	0.0998288	−	0.528335i
$372$	−3.77974	+	1.01156i	−0.195970	+	0.0524468i
$373$	36.8438			1.90770			0.953850	−	0.300285i	$-0.0970817\pi$
$373$	36.8438			1.90770			0.953850	+	0.300285i	$0.0970817\pi$
$374$	−2.20385	+	6.69403i	−0.113959	+	0.346140i
$375$	6.59816	+	5.26185i	0.340727	+	0.271721i
$376$	6.87801	+	16.6262i	0.354706	+	0.857433i
$377$	−0.172926	−	0.359084i	−0.00890612	−	0.0184937i
$378$	−2.16550	−	3.05133i	−0.111381	−	0.156944i
$379$	−4.66785	+	9.69289i	−0.239771	+	0.497890i	−0.985779	−	0.168047i	$-0.946254\pi$
$379$	−4.66785	+	9.69289i	−0.239771	+	0.497890i	0.746008	+	0.665937i	$0.231968\pi$
$380$	4.02886	+	15.0540i	0.206676	+	0.772256i
$381$	3.79664	−	7.88381i	0.194508	−	0.403900i
$382$	5.98613	−	9.93114i	0.306277	−	0.508121i
$383$	17.2042	−	8.28512i	0.879095	−	0.423350i	0.0608011	−	0.998150i	$-0.480634\pi$
$383$	17.2042	−	8.28512i	0.879095	−	0.423350i	0.818294	+	0.574800i	$0.194920\pi$
$384$	4.72822	−	10.2783i	0.241286	−	0.524514i
$385$	6.00338	−	3.17481i	0.305960	−	0.161803i
$386$	−11.7121	−	7.05961i	−0.596128	−	0.359324i
$387$	−12.5134	+	2.85610i	−0.636090	+	0.145184i
$388$	6.92476	−	0.257017i	0.351552	−	0.0130480i
$389$	−0.690134	−	3.02367i	−0.0349912	−	0.153306i	0.954414	−	0.298485i	$-0.0964814\pi$
$389$	−0.690134	−	3.02367i	−0.0349912	−	0.153306i	−0.989405	+	0.145179i	$0.953624\pi$
$390$	−4.10022	+	4.25523i	−0.207623	+	0.215472i
$391$	17.1321			0.866409
$392$	15.2453	−	12.6325i	0.770004	−	0.638039i
$393$	−3.42211			−0.172623
$394$	−24.0199	+	24.9280i	−1.21011	+	1.25585i
$395$	−1.98420	−	8.69334i	−0.0998358	−	0.437409i
$396$	−1.97425	+	0.0732756i	−0.0992100	+	0.00368224i
$397$	−20.7431	+	4.73448i	−1.04107	+	0.237617i	−0.708683	−	0.705527i	$-0.750710\pi$
$397$	−20.7431	+	4.73448i	−1.04107	+	0.237617i	−0.332385	+	0.943144i	$0.607853\pi$
$398$	18.0140	+	10.8582i	0.902960	+	0.544272i
$399$	4.70952	−	6.38454i	0.235771	−	0.319627i
$400$	−6.07200	+	3.50079i	−0.303600	+	0.175040i
$401$	15.9599	−	7.68589i	0.797001	−	0.383815i	0.00936459	−	0.999956i	$-0.497019\pi$
$401$	15.9599	−	7.68589i	0.797001	−	0.383815i	0.787636	+	0.616141i	$0.211305\pi$
$402$	10.8933	−	18.0722i	0.543307	−	0.901359i
$403$	1.36495	−	2.83435i	0.0679931	−	0.141189i
$404$	−9.74906	−	36.4279i	−0.485034	−	1.81236i
$405$	1.12745	−	2.34117i	0.0560234	−	0.116334i
$406$	−0.617888	+	0.691558i	−0.0306653	+	0.0343214i
$407$	1.71440	+	3.55999i	0.0849797	+	0.176462i
$408$	−13.1853	+	5.45453i	−0.652768	+	0.270040i
$409$	11.4419	+	9.12462i	0.565766	+	0.451183i	0.864130	−	0.503269i	$-0.167869\pi$
$409$	11.4419	+	9.12462i	0.565766	+	0.451183i	−0.298364	+	0.954452i	$0.596441\pi$
$410$	−3.16472	+	9.61260i	−0.156295	+	0.474732i
$411$	−9.11126			−0.449426
$412$	23.9942	−	6.42147i	1.18211	−	0.316363i
$413$	−15.5143	+	8.20454i	−0.763409	+	0.403719i
$414$	1.67002	+	4.50292i	0.0820769	+	0.221307i
$415$	3.08143	−	2.45736i	0.151262	−	0.120627i
$416$	3.78658	+	8.27073i	0.185652	+	0.405506i
$417$	11.7567	−	5.66172i	0.575727	−	0.277255i
$418$	−1.45663	−	3.92756i	−0.0712462	−	0.192103i
$419$	−0.660675	−	0.828461i	−0.0322761	−	0.0404730i	0.765431	−	0.643517i	$-0.222526\pi$
$419$	−0.660675	−	0.828461i	−0.0322761	−	0.0404730i	−0.797708	+	0.603044i	$0.793954\pi$
$420$	12.7993	+	5.02407i	0.624540	+	0.245150i
$421$	12.7095	−	15.9372i	0.619423	−	0.776732i	−0.368840	−	0.929493i	$-0.620245\pi$
$421$	12.7095	−	15.9372i	0.619423	−	0.776732i	0.988263	+	0.152761i	$0.0488163\pi$
$422$	24.6425	+	8.11297i	1.19958	+	0.394933i
$423$	6.36140			0.309302
$424$	0.625786	−	11.0539i	0.0303909	−	0.536824i
$425$	8.61806	+	1.96702i	0.418037	+	0.0954143i
$426$	−6.73776	+	0.886010i	−0.326445	+	0.0429273i
$427$	0.689348	+	18.3000i	0.0333599	+	0.885599i
$428$	5.78854	−	3.05710i	0.279800	−	0.147771i
$429$	0.990358	−	1.24187i	0.0478149	−	0.0599580i
$430$	32.7279	−	33.9652i	1.57828	−	1.63795i
$431$	−18.6172	−	4.24926i	−0.896760	−	0.204680i	−0.250789	−	0.968042i	$-0.580690\pi$
$431$	−18.6172	−	4.24926i	−0.896760	−	0.204680i	−0.645971	+	0.763362i	$0.723547\pi$
$432$	−2.71892	−	2.93385i	−0.130814	−	0.141155i
$433$	28.1087	−	6.41562i	1.35082	−	0.308315i	0.514937	−	0.857228i	$-0.327815\pi$
$433$	28.1087	−	6.41562i	1.35082	−	0.308315i	0.835879	+	0.548913i	$0.184958\pi$
$434$	−7.30863	−	0.409704i	−0.350825	−	0.0196664i
$435$	−0.627900	−	0.143314i	−0.0301055	−	0.00687139i
$436$	14.3058	−	32.7623i	0.685124	−	1.56903i
$437$	−7.96156	+	6.34914i	−0.380853	+	0.303720i
$438$	−1.06269	+	11.3142i	−0.0507774	+	0.540615i
$439$	−24.0154	−	11.5652i	−1.14619	−	0.551977i	−0.238304	−	0.971191i	$-0.576591\pi$
$439$	−24.0154	−	11.5652i	−1.14619	−	0.551977i	−0.907887	+	0.419214i	$0.862306\pi$
$440$	5.92292	−	4.19851i	0.282364	−	0.200156i
$441$	−2.06665	−	6.68797i	−0.0984120	−	0.318475i
$442$	3.58758	−	10.8970i	0.170644	−	0.518317i
$443$	−15.9059	+	33.0289i	−0.755711	+	1.56925i	0.0649849	+	0.997886i	$0.479300\pi$
$443$	−15.9059	+	33.0289i	−0.755711	+	1.56925i	−0.820696	+	0.571365i	$0.806414\pi$
$444$	−3.20140	+	7.33165i	−0.151932	+	0.347945i
$445$	−7.14915	−	8.96475i	−0.338902	−	0.424970i
$446$	24.6976	+	2.31973i	1.16946	+	0.109842i
$447$	−0.272780	+	1.19513i	−0.0129020	+	0.0565276i
$448$	14.4067	−	15.5064i	0.680651	−	0.732608i
$449$	−3.40970	−	14.9389i	−0.160914	−	0.705008i	−0.989426	−	0.145038i	$-0.953670\pi$
$449$	−3.40970	−	14.9389i	−0.160914	−	0.705008i	0.828513	−	0.559970i	$-0.189187\pi$
$450$	0.323076	+	2.45687i	0.0152300	+	0.115818i
$451$	0.605329	−	2.65212i	0.0285038	−	0.124883i
$452$	−12.9781	−	24.5737i	−0.610438	−	1.15585i
$453$	3.33498	+	2.65956i	0.156691	+	0.124957i
$454$	−23.2214	+	24.0993i	−1.08983	+	1.13103i
$455$	−9.77270	+	5.16817i	−0.458151	+	0.242288i
$456$	4.10595	−	7.42124i	0.192279	−	0.347531i
$457$	−1.84599	+	8.08779i	−0.0863516	+	0.378331i	−0.999576	−	0.0291265i	$-0.990727\pi$
$457$	−1.84599	+	8.08779i	−0.0863516	+	0.378331i	0.913224	+	0.407458i	$0.133585\pi$
$458$	−20.7604	+	13.5881i	−0.970069	+	0.634932i
$459$			5.04484i			0.235473i
$460$	−14.1971	−	10.4846i	−0.661944	−	0.488845i
$461$	24.5205	+	19.5544i	1.14203	+	0.910740i	0.996900	−	0.0786727i	$-0.0250682\pi$
$461$	24.5205	+	19.5544i	1.14203	+	0.910740i	0.145131	+	0.989412i	$0.453640\pi$
$462$	−3.55169	−	1.02284i	−0.165239	−	0.0475866i
$463$	−1.51558	+	1.20863i	−0.0704348	+	0.0561699i	−0.658074	−	0.752953i	$-0.728629\pi$
$463$	−1.51558	+	1.20863i	−0.0704348	+	0.0561699i	0.587640	+	0.809123i	$0.300057\pi$
$464$	−0.558977	+	0.818807i	−0.0259498	+	0.0380122i
$465$	−2.20572	−	4.58022i	−0.102288	−	0.212403i
$466$	2.29882	+	17.4816i	0.106491	+	0.809819i
$467$	−19.2579	−	24.1486i	−0.891148	−	1.11746i	−0.992455	−	0.122610i	$-0.960874\pi$
$467$	−19.2579	−	24.1486i	−0.891148	−	1.11746i	0.101307	−	0.994855i	$-0.467698\pi$
$468$	3.21382	−	0.119283i	0.148559	−	0.00551385i
$469$	29.9160	−	25.7579i	1.38139	−	1.18939i
$470$	−19.5599	+	12.8024i	−0.902230	+	0.590530i
$471$			11.4167i			0.526052i
$472$	−15.3064	+	10.8501i	−0.704534	+	0.499415i
$473$	−7.90502	+	9.91259i	−0.363473	+	0.455781i
$474$	−2.50526	+	4.15629i	−0.115071	+	0.190905i
$475$	−4.73392	+	2.27973i	−0.217207	+	0.104601i
$476$	−26.6202	+	1.99358i	−1.22014	+	0.0913754i
$477$	−3.52675	−	1.69839i	−0.161479	−	0.0777641i
$478$	25.1589	−	16.4671i	1.15074	−	0.753187i
$479$	14.2689	+	6.87155i	0.651964	+	0.313969i	0.730470	−	0.682944i	$-0.239301\pi$
$479$	14.2689	+	6.87155i	0.651964	+	0.313969i	−0.0785065	+	0.996914i	$0.525015\pi$
$480$	14.2645	+	3.54906i	0.651081	+	0.161992i
$481$	−2.79082	−	5.79519i	−0.127250	−	0.264238i
$482$	−1.20667	+	12.8472i	−0.0549624	+	0.585172i
$483$	0.338215	+	8.97853i	0.0153893	+	0.408537i
$484$	15.2001	−	13.0728i	0.690914	−	0.594218i
$485$	2.00340	+	8.77748i	0.0909698	+	0.398565i
$486$	−1.32596	+	0.491764i	−0.0601467	+	0.0223069i
$487$	12.1194	−	2.76617i	0.549181	−	0.125347i	0.0610781	−	0.998133i	$-0.480546\pi$
$487$	12.1194	−	2.76617i	0.549181	−	0.125347i	0.488103	+	0.872786i	$0.337689\pi$
$488$	3.27061	+	19.3023i	0.148054	+	0.873773i
$489$			21.6273i			0.978022i
$490$	19.8141	+	16.4049i	0.895110	+	0.741096i
$491$			24.4628i			1.10399i	0.833847	+	0.551995i	$0.186133\pi$
$491$			24.4628i			1.10399i	−0.833847	+	0.551995i	$0.813867\pi$
$492$	4.87031	−	2.57216i	0.219571	−	0.115962i
$493$	1.21903	−	0.278236i	0.0549024	−	0.0125311i
$494$	2.37120	+	6.39355i	0.106685	+	0.287659i
$495$	−0.571171	−	2.50246i	−0.0256722	−	0.112477i
$496$	−7.80399	+	0.580098i	−0.350409	+	0.0260472i
$497$	−12.4927	−	2.36048i	−0.560372	−	0.105882i
$498$	−2.13562	−	0.200589i	−0.0956994	−	0.00898859i
$499$	−17.8968	−	37.1631i	−0.801171	−	1.66365i	−0.746725	−	0.665133i	$-0.768375\pi$
$499$	−17.8968	−	37.1631i	−0.801171	−	1.66365i	−0.0544459	−	0.998517i	$-0.517339\pi$
$500$	11.0059	+	12.7969i	0.492200	+	0.572295i
$501$	3.33584	+	1.60645i	0.149034	+	0.0717711i
$502$	17.7007	+	27.0437i	0.790021	+	1.20702i
$503$	20.2001	+	9.72786i	0.900678	+	0.433744i	0.826134	−	0.563474i	$-0.190535\pi$
$503$	20.2001	+	9.72786i	0.900678	+	0.433744i	0.0745443	+	0.997218i	$0.476250\pi$
$504$	−3.11888	−	6.80239i	−0.138926	−	0.303003i
$505$	44.1427	−	21.2580i	1.96432	−	0.945968i
$506$	4.06305	+	2.44906i	0.180624	+	0.108874i
$507$	6.49320	−	8.14221i	0.288373	−	0.361608i
$508$	10.3965	−	14.0779i	0.461272	−	0.624607i
$509$		−	1.60217i		−	0.0710150i	−0.999369	−	0.0355075i	$-0.988695\pi$
$509$		−	1.60217i		−	0.0710150i	0.999369	−	0.0355075i	$-0.0113048\pi$
$510$	−10.1528	−	15.5117i	−0.449573	−	0.686872i
$511$	−8.49687	+	19.4884i	−0.375879	+	0.862116i
$512$	13.1189	−	18.4363i	0.579777	−	0.814775i
$513$	−1.86961	−	2.34441i	−0.0825452	−	0.103508i
$514$	−44.0369	+	5.79081i	−1.94238	+	0.255422i
$515$	14.0021	+	29.0757i	0.617007	+	1.28123i
$516$	−25.6527	+	0.952114i	−1.12930	+	0.0419145i
$517$	4.91290	−	3.91791i	0.216069	−	0.172309i
$518$	−9.97200	+	11.1609i	−0.438144	+	0.490383i
$519$	15.5213	+	12.3779i	0.681311	+	0.543328i
$520$	−9.64173	+	6.83462i	−0.422818	+	0.299718i
$521$		−	35.2662i		−	1.54504i	−0.634990	−	0.772520i	$-0.718996\pi$
$521$		−	35.2662i		−	1.54504i	0.634990	−	0.772520i	$-0.281004\pi$
$522$	0.191959	+	0.293282i	0.00840184	+	0.0128366i
$523$	−0.172653	+	0.756443i	−0.00754959	+	0.0330769i	−0.978562	−	0.205950i	$-0.933971\pi$
$523$	−0.172653	+	0.756443i	−0.00754959	+	0.0330769i	0.971013	+	0.239027i	$0.0768286\pi$
$524$	−6.72452	−	1.27445i	−0.293762	−	0.0556745i
$525$	−0.860731	+	4.55535i	−0.0375654	+	0.198812i
$526$	6.16388	+	5.93935i	0.268758	+	0.258968i
$527$	7.71637	+	6.15360i	0.336131	+	0.268055i
$528$	−3.90674	−	0.591255i	−0.170019	−	0.0257311i
$529$	−2.55173	+	11.1799i	−0.110945	+	0.486081i
$530$	14.2620	−	1.87544i	0.619502	−	0.0814640i
$531$	1.47606	+	6.46703i	0.0640554	+	0.280645i
$532$	11.6320	−	10.7918i	0.504312	−	0.467886i
$533$	−0.985396	+	4.31730i	−0.0426822	+	0.187003i
$534$	−0.583568	+	6.21311i	−0.0252535	+	0.268868i
$535$	5.30291	+	6.64964i	0.229265	+	0.287489i
$536$	28.1359	−	31.4554i	1.21528	−	1.35867i
$537$	−10.5453	+	21.8975i	−0.455063	+	0.944947i
$538$	14.8793	+	4.89867i	0.641493	+	0.211197i
$539$	−5.71511	−	3.89228i	−0.246167	−	0.167653i
$540$	3.08735	−	4.18057i	0.132858	−	0.179903i
$541$	7.09670	+	3.41759i	0.305111	+	0.146934i	0.580174	−	0.814492i	$-0.302984\pi$
$541$	7.09670	+	3.41759i	0.305111	+	0.146934i	−0.275063	+	0.961426i	$0.588699\pi$
$542$	−15.5658	−	1.46202i	−0.668610	−	0.0627993i
$543$	−19.3530	+	15.4335i	−0.830518	+	0.662316i
$544$	−27.9407	+	5.80787i	−1.19795	+	0.249011i
$545$	45.2831	+	10.3356i	1.93971	+	0.442727i
$546$	5.78167	+	1.66504i	0.247433	+	0.0712571i
$547$	4.71169	−	1.07541i	0.201457	−	0.0459813i	−0.120601	−	0.992701i	$-0.538482\pi$
$547$	4.71169	−	1.07541i	0.201457	−	0.0459813i	0.322059	+	0.946720i	$0.395625\pi$
$548$	−17.9038	−	3.39318i	−0.764813	−	0.144949i
$549$	6.74812	+	1.54021i	0.288003	+	0.0657347i
$550$	1.76267	+	1.69846i	0.0751603	+	0.0724225i
$551$	−0.463388	+	0.581070i	−0.0197410	+	0.0247544i
$552$	1.60466	+	9.47028i	0.0682989	+	0.403082i
$553$	−6.88016	+	5.92387i	−0.292574	+	0.251909i
$554$	2.77988	+	21.1399i	0.118106	+	0.898148i
$555$	−10.1336	−	2.31292i	−0.430146	−	0.0981781i
$556$	25.2106	−	6.74702i	1.06917	−	0.286137i
$557$	−8.54172			−0.361924			−0.180962	−	0.983490i	$-0.557921\pi$
$557$	−8.54172			−0.361924			−0.180962	+	0.983490i	$0.557921\pi$
$558$	−0.865200	+	2.62798i	−0.0366268	+	0.111251i
$559$	12.8683	−	16.1364i	0.544272	−	0.682496i
$560$	23.2798	+	14.6391i	0.983750	+	0.618613i
$561$	3.10705	+	3.89612i	0.131180	+	0.164494i
$562$	−15.7826	+	5.85336i	−0.665749	+	0.246909i
$563$	3.46915	−	1.67065i	0.146207	−	0.0704096i	−0.359350	−	0.933203i	$-0.617001\pi$
$563$	3.46915	−	1.67065i	0.146207	−	0.0704096i	0.505557	+	0.862793i	$0.331287\pi$
$564$	12.5003	+	2.36908i	0.526357	+	0.0997564i
$565$	28.2292	−	22.5120i	1.18761	−	0.947088i
$566$	19.5959	−	7.26760i	0.823676	−	0.305480i
$567$	−2.64388	+	0.0995929i	−0.111032	+	0.00418251i
$568$	−13.5698	−	0.768217i	−0.569376	−	0.0322337i
$569$	−36.2227			−1.51854			−0.759268	−	0.650778i	$-0.774443\pi$
$569$	−36.2227			−1.51854			−0.759268	+	0.650778i	$0.774443\pi$
$570$	10.4668	+	3.44594i	0.438405	+	0.144335i
$571$	12.3542	+	9.85212i	0.517006	+	0.412298i	0.846926	−	0.531710i	$-0.178451\pi$
$571$	12.3542	+	9.85212i	0.517006	+	0.412298i	−0.329921	+	0.944009i	$0.607022\pi$
$572$	2.40857	−	2.07148i	0.100707	−	0.0866127i
$573$	−3.55760	−	7.38743i	−0.148621	−	0.308614i
$574$	10.1584	−	1.72704i	0.424004	−	0.0720851i
$575$	2.58183	−	5.36122i	0.107670	−	0.223578i
$576$	−4.25013	−	6.77764i	−0.177089	−	0.282402i
$577$	−11.1534	+	23.1603i	−0.464322	+	0.964174i	0.528981	+	0.848634i	$0.322574\pi$
$577$	−11.1534	+	23.1603i	−0.464322	+	0.964174i	−0.993303	+	0.115540i	$0.963140\pi$
$578$	10.2351	+	6.16935i	0.425724	+	0.256611i
$579$	−8.71219	+	4.19557i	−0.362066	+	0.174362i
$580$	−1.18046	−	0.515455i	−0.0490161	−	0.0214031i
$581$	−3.67854	−	1.60383i	−0.152611	−	0.0665380i
$582$	2.52951	−	4.19652i	0.104852	−	0.173951i
$583$	−3.76972	+	0.860415i	−0.156126	+	0.0356347i
$584$	−6.30181	+	21.8370i	−0.260771	+	0.903620i
$585$	0.929791	+	4.07368i	0.0384421	+	0.168426i
$586$	10.6555	+	10.2673i	0.440174	+	0.424140i
$587$	−12.0178			−0.496027			−0.248014	−	0.968757i	$-0.579778\pi$
$587$	−12.0178			−0.496027			−0.248014	+	0.968757i	$0.579778\pi$
$588$	−1.57031	−	13.9117i	−0.0647585	−	0.573707i
$589$	−5.86643			−0.241722
$590$	−17.5535	−	16.9141i	−0.722666	−	0.696342i
$591$	5.44690	+	23.8644i	0.224055	+	0.981651i
$592$	−9.02123	+	13.2146i	−0.370770	+	0.543117i
$593$	30.8888	−	7.05016i	1.26845	−	0.289515i	0.465226	−	0.885192i	$-0.345973\pi$
$593$	30.8888	−	7.05016i	1.26845	−	0.289515i	0.803224	+	0.595677i	$0.203116\pi$
$594$	−0.721165	+	1.19643i	−0.0295898	+	0.0490901i
$595$	−8.98511	−	33.4992i	−0.368354	−	1.37333i
$596$	−0.981102	+	2.24686i	−0.0401875	+	0.0920350i
$597$	13.4000	−	6.45309i	0.548425	−	0.264107i
$598$	−6.61410	−	3.98674i	−0.270471	−	0.163030i
$599$	12.9409	−	26.8720i	0.528749	−	1.09796i	−0.450025	−	0.893016i	$-0.648585\pi$
$599$	12.9409	−	26.8720i	0.528749	−	1.09796i	0.978774	−	0.204943i	$-0.0657009\pi$
$600$	−0.280124	+	4.94812i	−0.0114360	+	0.202006i
$601$	−8.38228	+	17.4060i	−0.341920	+	0.710005i	−0.999041	−	0.0437806i	$-0.986060\pi$
$601$	−8.38228	+	17.4060i	−0.341920	+	0.710005i	0.657121	+	0.753785i	$0.271774\pi$
$602$	−46.1492	−	13.2903i	−1.88090	−	0.541673i
$603$	−6.47394	−	13.4433i	−0.263639	−	0.547452i
$604$	5.56284	+	6.46808i	0.226349	+	0.263183i
$605$	20.3652	+	16.2407i	0.827962	+	0.660277i
$606$	−25.3276	−	8.33852i	−1.02886	−	0.338729i
$607$	−0.344296			−0.0139745			−0.00698727	−	0.999976i	$-0.502224\pi$
$607$	−0.344296			−0.0139745			−0.00698727	+	0.999976i	$0.502224\pi$
$608$	10.8321	−	13.0538i	0.439298	−	0.529400i
$609$	0.169882	+	0.633371i	0.00688397	+	0.0256655i
$610$	−23.8486	+	8.84484i	−0.965603	+	0.358117i
$611$	−7.99755	+	6.37783i	−0.323546	+	0.258019i
$612$	−1.87878	+	9.91321i	−0.0759450	+	0.400718i
$613$	1.27025	−	0.611720i	0.0513049	−	0.0247071i	−0.408055	−	0.912957i	$-0.633793\pi$
$613$	1.27025	−	0.611720i	0.0513049	−	0.0247071i	0.459360	+	0.888250i	$0.348079\pi$
$614$	−23.0938	+	8.56491i	−0.931992	+	0.345651i
$615$	4.46171	+	5.59481i	0.179914	+	0.225605i
$616$	−6.59822	−	3.33260i	−0.265850	−	0.134274i
$617$	−14.9988	+	18.8079i	−0.603829	+	0.757178i	−0.985969	−	0.166927i	$-0.946616\pi$
$617$	−14.9988	+	18.8079i	−0.603829	+	0.757178i	0.382140	+	0.924104i	$0.375187\pi$
$618$	5.49238	−	16.6827i	0.220936	−	0.671076i
$619$	−11.1721			−0.449043			−0.224521	−	0.974469i	$-0.572082\pi$
$619$	−11.1721			−0.449043			−0.224521	+	0.974469i	$0.572082\pi$
$620$	−2.62854	−	9.82167i	−0.105565	−	0.394448i
$621$	3.31083	+	0.755675i	0.132859	+	0.0303242i
$622$	−3.45521	−	26.2755i	−0.138541	−	1.05355i
$623$	−4.66598	+	10.7019i	−0.186938	+	0.428762i
$624$	6.35965	+	0.962484i	0.254590	+	0.0385302i
$625$	−19.1354	+	23.9951i	−0.765417	+	0.959802i
$626$	−13.7927	−	13.2903i	−0.551268	−	0.531187i
$627$	−2.88779	−	0.659119i	−0.115327	−	0.0263227i
$628$	−4.25174	+	22.4340i	−0.169663	+	0.895212i
$629$	19.6737	−	4.49040i	0.784443	−	0.179044i
$630$	7.92890	−	5.62705i	0.315895	−	0.224187i
$631$	12.2055	+	2.78583i	0.485895	+	0.110902i	0.458448	−	0.888721i	$-0.348405\pi$
$631$	12.2055	+	2.78583i	0.485895	+	0.110902i	0.0274461	+	0.999623i	$0.491263\pi$
$632$	−6.47076	+	7.23420i	−0.257393	+	0.287761i
$633$	14.3426	−	11.4379i	0.570069	−	0.454615i
$634$	29.1593	+	2.73879i	1.15806	+	0.108771i
$635$	20.4861	+	9.86559i	0.812967	+	0.391504i
$636$	−6.29763	−	4.65079i	−0.249717	−	0.184416i
$637$	9.30344	+	6.33612i	0.368616	+	0.251046i
$638$	0.328878	+	0.108276i	0.0130204	+	0.00428667i
$639$	−2.08495	+	4.32945i	−0.0824795	+	0.171271i
$640$	26.7083	+	12.2863i	1.05574	+	0.485658i
$641$	3.98346	+	4.99511i	0.157337	+	0.197295i	0.854252	−	0.519859i	$-0.174016\pi$
$641$	3.98346	+	4.99511i	0.157337	+	0.197295i	−0.696914	+	0.717154i	$0.745444\pi$
$642$	0.432864	−	4.60860i	0.0170838	−	0.181887i
$643$	−1.53651	+	6.73191i	−0.0605942	+	0.265481i	−0.996146	−	0.0877084i	$-0.972046\pi$
$643$	−1.53651	+	6.73191i	−0.0605942	+	0.265481i	0.935552	+	0.353189i	$0.114903\pi$
$644$	−2.67915	+	17.7690i	−0.105573	+	0.700195i
$645$	−7.42158	−	32.5161i	−0.292224	−	1.28032i
$646$	−21.2110	+	2.78922i	−0.834534	+	0.109741i
$647$	1.58369	−	6.93862i	0.0622614	−	0.272785i	−0.934209	−	0.356725i	$-0.883893\pi$
$647$	1.58369	−	6.93862i	0.0622614	−	0.272785i	0.996471	+	0.0839400i	$0.0267504\pi$
$648$	−2.78868	+	0.472519i	−0.109550	+	0.0185623i
$649$	5.12292	+	4.08539i	0.201092	+	0.160366i
$650$	−2.86939	−	2.76486i	−0.112547	−	0.108447i
$651$	−3.07262	+	4.16545i	−0.120425	+	0.163257i
$652$	−8.05436	+	42.4982i	−0.315433	+	1.66436i
$653$	5.85169	−	25.6379i	0.228994	−	1.00329i	−0.721467	−	0.692448i	$-0.756532\pi$
$653$	5.85169	−	25.6379i	0.228994	−	1.00329i	0.950462	−	0.310841i	$-0.100611\pi$
$654$	−13.8438	−	21.1510i	−0.541335	−	0.827068i
$655$		−	8.89238i		−	0.347454i
$656$	10.5282	−	3.24056i	0.411056	−	0.126523i
$657$	6.28248	+	5.01011i	0.245103	+	0.195463i
$658$	20.8334	+	11.5115i	0.812170	+	0.448763i
$659$	36.4397	−	29.0597i	1.41949	−	1.13200i	0.448246	−	0.893910i	$-0.352049\pi$
$659$	36.4397	−	29.0597i	1.41949	−	1.13200i	0.971242	−	0.238094i	$-0.0765225\pi$
$660$	−0.190407	−	5.13011i	−0.00741158	−	0.199689i
$661$	9.66945	+	20.0788i	0.376098	+	0.780976i	1.00000		0.000527070i	$-0.000167772\pi$
$661$	9.66945	+	20.0788i	0.376098	+	0.780976i	−0.623902	+	0.781503i	$0.714453\pi$
$662$	−19.8446	+	2.60955i	−0.771283	+	0.101423i
$663$	−5.05787	−	6.34237i	−0.196431	−	0.246317i
$664$	−4.12184	−	1.18950i	−0.159958	−	0.0461615i
$665$	16.5902	+	12.2377i	0.643342	+	0.474558i
$666$	3.09800	+	4.73322i	0.120045	+	0.183409i
$667$		−	0.841703i		−	0.0325909i
$668$	5.95672	+	4.39903i	0.230472	+	0.170204i
$669$	10.9364	−	13.7139i	0.422827	−	0.530209i
$670$	46.9607	+	28.3062i	1.81425	+	1.09356i
$671$	6.16016	−	2.96658i	0.237810	−	0.114523i
$672$	−3.59536	−	14.5284i	−0.138694	−	0.560444i
$673$	8.02593	+	3.86508i	0.309377	+	0.148988i	0.582129	−	0.813096i	$-0.302220\pi$
$673$	8.02593	+	3.86508i	0.309377	+	0.148988i	−0.272752	+	0.962084i	$0.587934\pi$
$674$	25.1976	+	38.4977i	0.970575	+	1.48288i
$675$	1.57870	+	0.760262i	0.0607642	+	0.0292625i
$676$	15.7915	−	13.5814i	0.607367	−	0.522363i
$677$	12.4926	+	25.9412i	0.480131	+	0.997002i	0.990560	+	0.137082i	$0.0437724\pi$
$677$	12.4926	+	25.9412i	0.480131	+	0.997002i	−0.510429	+	0.859920i	$0.670513\pi$
$678$	−19.5645	−	1.83760i	−0.751371	−	0.0705727i
$679$	6.94675	−	5.98121i	0.266592	−	0.229538i
$680$	−14.1736	−	34.2620i	−0.543534	−	1.31389i
$681$	5.26583	+	23.0711i	0.201787	+	0.884086i
$682$	0.950346	+	2.56245i	0.0363906	+	0.0981212i
$683$	12.7199	−	2.90323i	0.486712	−	0.111089i	0.0278790	−	0.999611i	$-0.491125\pi$
$683$	12.7199	−	2.90323i	0.486712	−	0.111089i	0.458833	+	0.888522i	$0.348268\pi$
$684$	−2.80072	−	5.30309i	−0.107088	−	0.202769i
$685$		−	23.6757i		−	0.904600i
$686$	5.33420	−	25.6427i	0.203661	−	0.979042i
$687$			17.5447i			0.669371i
$688$	−50.7627	−	7.68253i	−1.93531	−	0.292894i
$689$	6.13661	−	1.40064i	0.233786	−	0.0533602i
$690$	−11.7009	+	4.33955i	−0.445444	+	0.165204i
$691$	3.69503	+	16.1890i	0.140566	+	0.615859i	0.995304	+	0.0967994i	$0.0308605\pi$
$691$	3.69503	+	16.1890i	0.140566	+	0.615859i	−0.854738	+	0.519059i	$0.826282\pi$
$692$	25.8900	+	30.1031i	0.984192	+	1.14435i
$693$	−1.98052	+	1.70525i	−0.0752339	+	0.0647769i
$694$	−1.12593	+	11.9875i	−0.0427396	+	0.455039i
$695$	14.7120	+	30.5498i	0.558058	+	1.15882i
$696$	0.267982	+	0.647793i	0.0101578	+	0.0245545i
$697$	−12.5172	−	6.02795i	−0.474121	−	0.228325i
$698$	−21.1190	+	13.8228i	−0.799364	+	0.523202i
$699$	11.2331	+	5.40956i	0.424874	+	0.204608i
$700$	−3.38784	+	8.63080i	−0.128048	+	0.326214i
$701$	26.0437	−	12.5420i	0.983658	−	0.473705i	0.128296	−	0.991736i	$-0.459049\pi$
$701$	26.0437	−	12.5420i	0.983658	−	0.473705i	0.855362	+	0.518031i	$0.173335\pi$
$702$	1.17396	−	1.94763i	0.0443083	−	0.0735085i
$703$	−7.47855	+	9.37780i	−0.282059	+	0.353690i
$704$	−7.45663	−	2.61676i	−0.281032	−	0.0986228i
$705$			16.5301i			0.622560i
$706$	−9.61576	+	6.29373i	−0.361894	+	0.236868i
$707$	−40.1452	−	29.6129i	−1.50982	−	1.11371i
$708$	0.492061	+	13.2575i	0.0184928	+	0.498249i
$709$	6.84905	+	8.58844i	0.257222	+	0.322546i	0.893628	−	0.448808i	$-0.148151\pi$
$709$	6.84905	+	8.58844i	0.257222	+	0.322546i	−0.636407	+	0.771354i	$0.719580\pi$
$710$	−2.30230	−	17.5081i	−0.0864038	−	0.657067i
$711$	1.48889	+	3.09172i	0.0558379	+	0.115949i
$712$	−3.46058	+	11.9916i	−0.129691	+	0.449403i
$713$	5.19434	−	4.14235i	0.194530	−	0.155132i
$714$	−9.12904	+	16.5217i	−0.341646	+	0.618309i
$715$	3.22700	+	2.57345i	0.120683	+	0.0962416i
$716$	−28.8767	+	39.1018i	−1.07917	+	1.46130i
$717$		−	21.2619i		−	0.794041i
$718$	−28.6493	+	18.7516i	−1.06918	+	0.699805i
$719$	8.94445	−	39.1882i	0.333572	−	1.46147i	−0.478589	−	0.878039i	$-0.658852\pi$
$719$	8.94445	−	39.1882i	0.333572	−	1.46147i	0.812161	−	0.583434i	$-0.198291\pi$
$720$	7.62361	−	7.06513i	0.284115	−	0.263302i
$721$	19.5053	−	26.4427i	0.726416	−	0.984777i
$722$	−9.82094	+	10.1922i	−0.365498	+	0.379315i
$723$	7.13366	+	5.68890i	0.265304	+	0.211573i
$724$	−43.7768	+	23.1198i	−1.62695	+	0.859242i
$725$	0.0966397	−	0.423406i	0.00358911	−	0.0157249i
$726$	−1.84828	−	14.0554i	−0.0685959	−	0.521645i
$727$	−0.806567	−	3.53380i	−0.0299139	−	0.131061i	0.957766	−	0.287548i	$-0.0928402\pi$
$727$	−0.806567	−	3.53380i	−0.0299139	−	0.131061i	−0.987680	+	0.156487i	$0.949983\pi$
$728$	10.7410	+	5.42502i	0.398089	+	0.201065i
$729$	−0.222521	+	0.974928i	−0.00824152	+	0.0361084i
$730$	−29.4001	−	2.76141i	−1.08815	−	0.102204i
$731$	40.3718	+	50.6247i	1.49321	+	1.87242i
$732$	12.6866	+	5.53965i	0.468910	+	0.204751i
$733$	−17.9413	+	37.2555i	−0.662676	+	1.37606i	0.250348	+	0.968156i	$0.419455\pi$
$733$	−17.9413	+	37.2555i	−0.662676	+	1.37606i	−0.913024	+	0.407905i	$0.866259\pi$
$734$	14.0649	−	42.7209i	0.519143	−	1.57686i
$735$	17.3787	−	5.37020i	0.641024	−	0.198083i
$736$	−0.373686	+	19.2069i	−0.0137743	+	0.707975i
$737$	−13.2794	−	6.39500i	−0.489151	−	0.235563i
$738$	0.364199	−	3.87754i	0.0134063	−	0.142734i
$739$	−25.8182	+	20.5893i	−0.949738	+	0.757391i	−0.970176	−	0.242400i	$-0.922065\pi$
$739$	−25.8182	+	20.5893i	−0.949738	+	0.757391i	0.0204383	+	0.999791i	$0.493494\pi$
$740$	−19.0513	−	8.31884i	−0.700341	−	0.305807i
$741$	4.70094	+	1.07296i	0.172693	+	0.0394161i
$742$	−8.47662	−	11.9441i	−0.311186	−	0.438482i
$743$	−0.291054	+	0.0664312i	−0.0106777	+	0.00243712i	−0.227856	−	0.973695i	$-0.573172\pi$
$743$	−0.291054	+	0.0664312i	−0.0106777	+	0.00243712i	0.217179	+	0.976132i	$0.430315\pi$
$744$	−2.67884	+	4.84182i	−0.0982109	+	0.177510i
$745$	−3.10554	−	0.708820i	−0.113778	−	0.0259691i
$746$	36.1541	−	37.5208i	1.32369	−	1.37374i
$747$	−0.945683	+	1.18585i	−0.0346007	+	0.0433879i
$748$	4.65445	+	8.81307i	0.170183	+	0.322238i
$749$	3.46101	−	7.93816i	0.126462	−	0.290054i
$750$	11.8332	−	1.55605i	0.432087	−	0.0568191i
$751$	27.7196	+	6.32681i	1.01150	+	0.230869i	0.695989	−	0.718053i	$-0.254966\pi$
$751$	27.7196	+	6.32681i	1.01150	+	0.230869i	0.315513	+	0.948921i	$0.397824\pi$
$752$	23.6810	+	9.31059i	0.863558	+	0.339522i
$753$	22.8547			0.832872
$754$	−0.535370	−	0.176258i	−0.0194970	−	0.00641894i
$755$	−6.91087	+	8.66596i	−0.251512	+	0.315387i
$756$	−5.23236	−	0.788918i	−0.190299	−	0.0286927i
$757$	−29.5374	−	37.0387i	−1.07355	−	1.34619i	−0.934522	−	0.355905i	$-0.884173\pi$
$757$	−29.5374	−	37.0387i	−1.07355	−	1.34619i	−0.139031	−	0.990288i	$-0.544399\pi$
$758$	5.29054	+	14.2651i	0.192161	+	0.518131i
$759$	3.02236	−	1.45549i	0.109705	−	0.0528310i
$760$	19.2841	+	10.6693i	0.699508	+	0.387018i
$761$	37.4360	−	29.8542i	1.35705	−	1.08221i	0.368782	−	0.929516i	$-0.379775\pi$
$761$	37.4360	−	29.8542i	1.35705	−	1.08221i	0.988273	−	0.152699i	$-0.0487964\pi$
$762$	−4.30311	−	11.6026i	−0.155885	−	0.420319i
$763$	−12.2516	−	45.6776i	−0.443538	−	1.65364i
$764$	−4.23956	−	15.8414i	−0.153382	−	0.573120i
$765$	−13.1090			−0.473958
$766$	8.44479	−	25.6504i	0.305123	−	0.926786i
$767$	−8.33943	−	6.65047i	−0.301119	−	0.240135i
$768$	−5.82750	−	14.9010i	−0.210282	−	0.537694i
$769$	−5.22384	−	10.8474i	−0.188376	−	0.391168i	0.785296	−	0.619121i	$-0.212511\pi$
$769$	−5.22384	−	10.8474i	−0.188376	−	0.391168i	−0.973672	+	0.227953i	$0.926797\pi$
$770$	2.65784	−	9.22907i	0.0957820	−	0.332593i
$771$	−13.6269	+	28.2966i	−0.490762	+	1.01908i
$772$	−18.6821	+	4.99983i	−0.672385	+	0.179948i
$773$	−12.3141	+	25.5704i	−0.442906	+	0.919705i	0.553325	+	0.832966i	$0.313359\pi$
$773$	−12.3141	+	25.5704i	−0.442906	+	0.919705i	−0.996231	+	0.0867390i	$0.972355\pi$
$774$	−9.37054	+	15.5459i	−0.336817	+	0.558788i
$775$	3.08854	−	1.48736i	0.110943	−	0.0534276i
$776$	6.53339	−	7.30422i	0.234535	−	0.262206i
$777$	2.74170	+	10.2219i	0.0983579	+	0.366708i
$778$	−3.75645	−	2.26425i	−0.134675	−	0.0811774i
$779$	8.05086	−	1.83756i	0.288452	−	0.0658373i
$780$	0.309957	+	8.35113i	0.0110982	+	0.299019i
$781$	1.05625	+	4.62773i	0.0377955	+	0.165593i
$782$	16.8114	−	17.4470i	0.601175	−	0.623902i
$783$	0.247853			0.00885755
$784$	2.09522	−	27.9215i	0.0748294	−	0.997196i
$785$	−29.6662			−1.05883
$786$	−3.35805	+	3.48500i	−0.119778	+	0.124306i
$787$	−4.51706	−	19.7905i	−0.161016	−	0.705456i	−0.989390	−	0.145281i	$-0.953591\pi$
$787$	−4.51706	−	19.7905i	−0.161016	−	0.705456i	0.828375	−	0.560174i	$-0.189266\pi$
$788$	1.81579	+	48.9226i	0.0646848	+	1.74280i
$789$	5.90091	−	1.34684i	0.210078	−	0.0479489i
$790$	−10.8001	−	6.50994i	−0.384252	−	0.231613i
$791$	−33.6993	−	14.6927i	−1.19821	−	0.522414i
$792$	−1.86267	+	2.08244i	−0.0661872	+	0.0739962i
$793$	−10.0279	+	4.82919i	−0.356102	+	0.171490i
$794$	−15.5333	+	25.7702i	−0.551257	+	0.914549i
$795$	4.41328	−	9.16428i	0.156523	−	0.325023i
$796$	28.7345	−	7.69010i	1.01847	−	0.272568i
$797$	4.72829	−	9.81839i	0.167485	−	0.347785i	−0.800286	−	0.599618i	$-0.795319\pi$
$797$	4.72829	−	9.81839i	0.167485	−	0.347785i	0.967771	+	0.251833i	$0.0810334\pi$
$798$	−1.88050	−	11.0611i	−0.0665690	−	0.391558i
$799$	−13.9243	−	28.9141i	−0.492606	−	1.02291i
$800$	−2.39321	+	9.61883i	−0.0846126	+	0.340077i
$801$	3.44996	+	2.75125i	0.121899	+	0.0972108i
$802$	7.83402	−	23.7952i	0.276629	−	0.840238i
$803$	7.93761			0.280112
$804$	−7.71494	−	28.8273i	−0.272085	−	1.01666i
$805$	−23.3308	+	0.878853i	−0.822301	+	0.0309755i
$806$	−1.54704	−	4.17133i	−0.0544920	−	0.146929i
$807$	8.66019	−	6.90627i	0.304853	−	0.243112i
$808$	−46.6639	−	25.8178i	−1.64163	−	0.908265i
$809$	29.7134	−	14.3092i	1.04467	−	0.503085i	0.168806	−	0.985649i	$-0.446009\pi$
$809$	29.7134	−	14.3092i	1.04467	−	0.503085i	0.875861	+	0.482564i	$0.160294\pi$
$810$	−1.27785	−	3.44551i	−0.0448991	−	0.121063i
$811$	−34.0601	−	42.7100i	−1.19601	−	1.49975i	−0.819247	−	0.573441i	$-0.805608\pi$
$811$	−34.0601	−	42.7100i	−1.19601	−	1.49975i	−0.376764	−	0.926309i	$-0.622963\pi$
$812$	0.0979446	+	1.30785i	0.00343718	+	0.0458967i
$813$	−6.89277	+	8.64326i	−0.241740	+	0.303133i
$814$	5.30771	+	1.74744i	0.186035	+	0.0612478i
$815$	−56.1987			−1.96856
$816$	−7.38367	+	18.7800i	−0.258480	+	0.657431i
$817$	−37.5228	−	8.56434i	−1.31276	−	0.299628i
$818$	20.5200	−	2.69836i	0.717465	−	0.0943461i
$819$	3.22403	−	2.77591i	0.112657	−	0.0969983i
$820$	6.68376	+	12.6555i	0.233407	+	0.441950i
$821$	13.9635	−	17.5097i	0.487330	−	0.611093i	−0.475989	−	0.879451i	$-0.657910\pi$
$821$	13.9635	−	17.5097i	0.487330	−	0.611093i	0.963319	+	0.268358i	$0.0864812\pi$
$822$	−8.94070	+	9.27869i	−0.311843	+	0.323632i
$823$	−0.705802	−	0.161095i	−0.0246027	−	0.00561541i	0.210202	−	0.977658i	$-0.432588\pi$
$823$	−0.705802	−	0.161095i	−0.0246027	−	0.00561541i	−0.234805	+	0.972043i	$0.575445\pi$
$824$	17.0055	−	30.7364i	0.592416	−	1.07075i
$825$	1.68746	−	0.385153i	0.0587499	−	0.0134093i
$826$	−6.86856	+	23.8503i	−0.238988	+	0.829860i
$827$	−27.8146	−	6.34851i	−0.967209	−	0.220759i	−0.290390	−	0.956908i	$-0.593785\pi$
$827$	−27.8146	−	6.34851i	−0.967209	−	0.220759i	−0.676819	+	0.736149i	$0.736642\pi$
$828$	6.22442	+	2.71792i	0.216314	+	0.0944543i
$829$	−35.3273	+	28.1726i	−1.22697	+	0.978473i	−0.226977	+	0.973900i	$0.572884\pi$
$829$	−35.3273	+	28.1726i	−1.22697	+	0.978473i	−0.999990	+	0.00457344i	$0.998544\pi$
$830$	0.521230	−	5.54942i	0.0180922	−	0.192623i
$831$	13.5838	+	6.54160i	0.471216	+	0.226926i
$832$	12.1384	+	4.25973i	0.420824	+	0.147680i
$833$	−25.8748	+	24.0325i	−0.896509	+	0.832678i
$834$	5.77083	−	17.5284i	0.199827	−	0.606960i
$835$	−4.17438	+	8.66818i	−0.144460	+	0.299975i
$836$	−5.42910	−	2.37064i	−0.187769	−	0.0819903i
$837$	1.21978	+	1.52956i	0.0421618	+	0.0528693i
$838$	−1.49199	−	0.140136i	−0.0515400	−	0.00484091i
$839$	−2.39483	+	10.4924i	−0.0826786	+	0.362239i	−0.999296	−	0.0375280i	$-0.988052\pi$
$839$	−2.39483	+	10.4924i	−0.0826786	+	0.362239i	0.916617	+	0.399767i	$0.130909\pi$
$840$	17.6760	−	8.10444i	0.609882	−	0.279630i
$841$	6.43944	+	28.2130i	0.222050	+	0.972863i
$842$	−3.75850	−	28.5819i	−0.129526	−	0.984998i
$843$	−2.64862	+	11.6044i	−0.0912232	+	0.399675i
$844$	32.4432	−	17.1342i	1.11674	−	0.589785i
$845$	21.1576	+	16.8726i	0.727842	+	0.580435i
$846$	6.24231	−	6.47830i	0.214615	−	0.222728i
$847$	4.92413	−	26.0605i	0.169195	−	0.895450i
$848$	−10.6429	−	11.4842i	−0.365480	−	0.394370i
$849$	3.28856	−	14.4081i	0.112863	−	0.494485i
$850$	10.4599	−	6.84623i	0.358771	−	0.234824i
$851$		−	13.5841i		−	0.465657i
$852$	−5.70933	+	7.73100i	−0.195599	+	0.264860i
$853$	−22.9082	−	18.2686i	−0.784361	−	0.625507i	0.147194	−	0.989108i	$-0.452976\pi$
$853$	−22.9082	−	18.2686i	−0.784361	−	0.625507i	−0.931555	+	0.363601i	$0.881547\pi$
$854$	19.3127	+	17.2554i	0.660868	+	0.590468i
$855$	6.09197	−	4.85818i	0.208341	−	0.166146i
$856$	2.56690	−	8.89479i	0.0877348	−	0.304018i
$857$	−8.94439	−	18.5732i	−0.305534	−	0.634449i	0.690508	−	0.723324i	$-0.257387\pi$
$857$	−8.94439	−	18.5732i	−0.305534	−	0.634449i	−0.996043	+	0.0888757i	$0.971673\pi$
$858$	−0.292872	−	2.22718i	−0.00999849	−	0.0760346i
$859$	−8.90985	−	11.1726i	−0.304000	−	0.381204i	0.606242	−	0.795280i	$-0.292676\pi$
$859$	−8.90985	−	11.1726i	−0.304000	−	0.381204i	−0.910242	+	0.414076i	$0.864105\pi$
$860$	−2.47407	−	66.6586i	−0.0843652	−	2.27304i
$861$	2.91199	−	6.67894i	0.0992404	−	0.227618i
$862$	−22.5960	+	14.7896i	−0.769624	+	0.503736i
$863$		−	48.1759i		−	1.63993i	−0.572416	−	0.819963i	$-0.693994\pi$
$863$		−	48.1759i		−	1.63993i	0.572416	−	0.819963i	$-0.306006\pi$
$864$	−5.65578	−	0.110038i	−0.192414	−	0.00374357i
$865$	−32.1639	+	40.3323i	−1.09361	+	1.37134i
$866$	21.0489	−	34.9207i	0.715272	−	1.18665i
$867$	7.61353	−	3.66648i	0.258569	−	0.124520i
$868$	−7.58904	+	7.04090i	−0.257589	+	0.238984i
$869$	3.05402	+	1.47074i	0.103601	+	0.0498914i
$870$	−0.762094	+	0.498807i	−0.0258374	+	0.0169112i
$871$	21.6170	+	10.4102i	0.732465	+	0.352737i
$872$	−19.3264	−	46.7177i	−0.654474	−	1.58206i
$873$	−1.50331	−	3.12165i	−0.0508792	−	0.105652i
$874$	−1.34671	+	14.3381i	−0.0455533	+	0.484995i
$875$	21.9402	+	4.14560i	0.741715	+	0.140147i
$876$	10.4794	+	12.1847i	0.354065	+	0.411681i
$877$	3.20063	+	14.0229i	0.108078	+	0.473519i	0.999782	+	0.0209001i	$0.00665321\pi$
$877$	3.20063	+	14.0229i	0.108078	+	0.473519i	−0.891704	+	0.452619i	$0.850490\pi$
$878$	−35.3435	+	13.1080i	−1.19279	+	0.442373i
$879$	10.2009	−	2.32828i	0.344067	−	0.0785310i
$880$	1.53638	−	10.1517i	0.0517913	−	0.342213i
$881$			33.0470i			1.11338i	0.830719	+	0.556692i	$0.187929\pi$
$881$			33.0470i			1.11338i	−0.830719	+	0.556692i	$0.812071\pi$
$882$	−8.83883	−	4.45814i	−0.297619	−	0.150113i
$883$		−	16.6683i		−	0.560932i	−0.959864	−	0.280466i	$-0.909511\pi$
$883$		−	16.6683i		−	0.560932i	0.959864	−	0.280466i	$-0.0904890\pi$
$884$	−7.57682	−	14.3465i	−0.254836	−	0.482525i
$885$	−16.8046	+	3.83554i	−0.564880	+	0.128930i
$886$	18.0277	+	48.6088i	0.605654	+	1.63304i
$887$	−1.28490	−	5.62950i	−0.0431426	−	0.189020i	0.948765	−	0.315983i	$-0.102334\pi$
$887$	−1.28490	−	5.62950i	−0.0431426	−	0.189020i	−0.991907	+	0.126963i	$0.959477\pi$
$888$	4.32491	+	10.4546i	0.145135	+	0.350834i
$889$	−0.871474	−	23.1349i	−0.0292283	−	0.775919i
$890$	−16.1448	−	1.51640i	−0.541175	−	0.0508300i
$891$	0.428593	+	0.889983i	0.0143584	+	0.0298156i
$892$	26.5976	−	22.8751i	0.890554	−	0.765916i
$893$	17.1863	+	8.27650i	0.575119	+	0.276963i
$894$	0.949415	+	1.45055i	0.0317532	+	0.0485135i
$895$	−56.9008	−	27.4020i	−1.90198	−	0.915947i
$896$	−1.65436	−	29.8875i	−0.0552685	−	0.998472i
$897$	−4.92000	+	2.36935i	−0.164274	+	0.0791102i
$898$	−18.5592	−	11.1868i	−0.619330	−	0.373310i
$899$	0.302327	−	0.379106i	0.0100832	−	0.0126439i
$900$	2.81905	+	2.08186i	0.0939682	+	0.0693954i
$901$			19.7475i			0.657885i
$902$	−2.10686	−	3.21893i	−0.0701507	−	0.107178i
$903$	−25.7342	+	22.1573i	−0.856379	+	0.737349i
$904$	−37.7604	−	10.8971i	−1.25589	−	0.362431i
$905$	−40.1041	−	50.2889i	−1.33310	−	1.67166i
$906$	5.98098	−	0.786494i	0.198705	−	0.0261295i
$907$	21.1674	+	43.9546i	0.702852	+	1.45949i	0.879838	+	0.475274i	$0.157651\pi$
$907$	21.1674	+	43.9546i	0.702852	+	1.45949i	−0.176986	+	0.984213i	$0.556635\pi$
$908$	1.75543	+	47.2962i	0.0582559	+	1.56958i
$909$	−14.7414	+	11.7559i	−0.488941	+	0.389918i
$910$	−4.32661	+	15.0237i	−0.143426	+	0.498031i
$911$	−18.0024	−	14.3564i	−0.596445	−	0.475649i	0.278127	−	0.960544i	$-0.410286\pi$
$911$	−18.0024	−	14.3564i	−0.596445	−	0.475649i	−0.874572	+	0.484895i	$0.838858\pi$
$912$	−3.52852	−	11.4637i	−0.116841	−	0.379602i
$913$			1.49826i			0.0495853i
$914$	6.42499	+	9.81630i	0.212520	+	0.324694i
$915$	−4.00225	+	17.5350i	−0.132310	+	0.579689i
$916$	−6.53390	+	34.4756i	−0.215886	+	1.13911i
$917$	−8.00377	+	4.23269i	−0.264308	+	0.139776i
$918$	5.13754	+	4.95040i	0.169564	+	0.163387i
$919$	7.99302	+	6.37422i	0.263665	+	0.210266i	0.746395	−	0.665503i	$-0.231783\pi$
$919$	7.99302	+	6.37422i	0.263665	+	0.210266i	−0.482729	+	0.875770i	$0.660355\pi$
$920$	−24.6086	+	4.16972i	−0.811320	+	0.137472i
$921$	−3.87558	+	16.9800i	−0.127705	+	0.559511i
$922$	43.9752	−	5.78270i	1.44825	−	0.190443i
$923$	−1.71943	−	7.53333i	−0.0565958	−	0.247962i
$924$	−4.52683	+	2.61327i	−0.148922	+	0.0859701i
$925$	1.55965	−	6.83328i	0.0512810	−	0.224677i
$926$	−0.256363	+	2.72943i	−0.00842460	+	0.0896948i
$927$	−7.74330	−	9.70980i	−0.254323	−	0.318912i
$928$	0.285341	+	1.37273i	0.00936679	+	0.0450620i
$929$	23.5452	−	48.8921i	0.772493	−	1.60410i	−0.0241961	−	0.999707i	$-0.507703\pi$
$929$	23.5452	−	48.8921i	0.772493	−	1.60410i	0.796689	−	0.604390i	$-0.206583\pi$
$930$	−6.82881	−	2.24823i	−0.223926	−	0.0737222i
$931$	3.11800	−	20.7574i	0.102188	−	0.680298i
$932$	20.0586	+	14.8133i	0.657042	+	0.485225i
$933$	−16.8837	−	8.13078i	−0.552749	−	0.266190i
$934$	−43.4897	−	4.08478i	−1.42303	−	0.133658i
$935$	−10.1241	+	8.07369i	−0.331093	+	0.264038i
$936$	3.03219	−	3.38993i	0.0991101	−	0.110803i
$937$	−8.30952	−	1.89659i	−0.271460	−	0.0619590i	0.0846238	−	0.996413i	$-0.473031\pi$
$937$	−8.30952	−	1.89659i	−0.271460	−	0.0619590i	−0.356084	+	0.934454i	$0.615888\pi$
$938$	3.12473	−	55.7414i	0.102026	−	1.82002i
$939$	−13.2043	+	3.01379i	−0.430905	+	0.0983513i
$940$	−6.15607	+	32.4820i	−0.200789	+	1.05945i
$941$	−30.8733	−	7.04663i	−1.00644	−	0.229714i	−0.312633	−	0.949874i	$-0.601211\pi$
$941$	−30.8733	−	7.04663i	−1.00644	−	0.229714i	−0.693808	+	0.720160i	$0.744068\pi$
$942$	11.6264	+	11.2029i	0.378810	+	0.365011i
$943$	−5.83099	+	7.31183i	−0.189883	+	0.238106i
$944$	−3.97040	+	26.2346i	−0.129226	+	0.853864i
$945$	−0.258793	−	6.87012i	−0.00841852	−	0.223485i
$946$	2.33770	+	17.7773i	0.0760053	+	0.577990i
$947$	−11.8741	−	2.71020i	−0.385858	−	0.0880695i	0.0251915	−	0.999683i	$-0.491980\pi$
$947$	−11.8741	−	2.71020i	−0.385858	−	0.0880695i	−0.411049	+	0.911613i	$0.634838\pi$
$948$	1.77430	+	6.62978i	0.0576267	+	0.215325i
$949$	−12.9214			−0.419445
$950$	−2.32367	+	7.05796i	−0.0753898	+	0.228991i
$951$	12.9121	−	16.1913i	0.418705	−	0.525039i
$952$	−24.0917	+	29.0657i	−0.780816	+	0.942023i
$953$	13.9173	+	17.4517i	0.450824	+	0.565316i	0.954360	−	0.298659i	$-0.0965392\pi$
$953$	13.9173	+	17.4517i	0.450824	+	0.565316i	−0.503536	+	0.863974i	$0.667968\pi$
$954$	−5.19033	+	1.92496i	−0.168043	+	0.0623229i
$955$	19.1963	−	9.24443i	0.621177	−	0.299143i
$956$	7.91826	−	41.7801i	0.256095	−	1.35126i
$957$	0.191417	−	0.152650i	0.00618762	−	0.00493447i
$958$	20.9996	−	7.78822i	0.678467	−	0.251626i
$959$	−21.3098	+	11.2694i	−0.688129	+	0.363908i
$960$	17.6117	−	11.0440i	0.568416	−	0.356443i
$961$	−27.1726			−0.876535
$962$	−8.64026	−	2.84460i	−0.278573	−	0.0917136i
$963$	−2.55902	−	2.04075i	−0.0824634	−	0.0657624i
$964$	11.8992	+	13.8355i	0.383246	+	0.445611i
$965$	−10.9022	−	22.6387i	−0.350955	−	0.728765i
$966$	9.47541	+	8.46602i	0.304866	+	0.272390i
$967$	−0.894560	+	1.85757i	−0.0287671	+	0.0597355i	−0.914857	−	0.403777i	$-0.867697\pi$
$967$	−0.894560	+	1.85757i	−0.0287671	+	0.0597355i	0.886090	+	0.463513i	$0.153411\pi$
$968$	1.60255	−	28.3075i	0.0515080	−	0.909838i
$969$	−6.56359	+	13.6294i	−0.210853	+	0.437841i
$970$	10.9047	+	6.57295i	0.350128	+	0.211045i
$971$	15.2051	−	7.32240i	0.487955	−	0.234987i	−0.173695	−	0.984800i	$-0.555571\pi$
$971$	15.2051	−	7.32240i	0.487955	−	0.234987i	0.661650	+	0.749813i	$0.269856\pi$
$972$	−0.800336	+	1.83288i	−0.0256708	+	0.0587898i
$973$	20.4942	−	27.7833i	0.657013	−	0.890690i
$974$	9.07550	−	15.0565i	0.290798	−	0.482440i
$975$	−2.74697	+	0.626977i	−0.0879733	+	0.0200793i
$976$	22.8664	+	15.6102i	0.731934	+	0.499671i
$977$	7.30359	+	31.9991i	0.233663	+	1.02374i	0.946574	+	0.322488i	$0.104519\pi$
$977$	7.30359	+	31.9991i	0.233663	+	1.02374i	−0.712911	+	0.701254i	$0.752624\pi$
$978$	22.0248	+	21.2225i	0.704274	+	0.678620i
$979$	4.35887			0.139310
$980$	36.1495	−	4.08046i	1.15475	−	0.130345i
$981$	−17.8748			−0.570697
$982$	24.9123	+	24.0048i	0.794984	+	0.766025i
$983$	7.14940	+	31.3236i	0.228030	+	0.999067i	0.951243	+	0.308441i	$0.0998074\pi$
$983$	7.14940	+	31.3236i	0.228030	+	0.999067i	−0.723213	+	0.690625i	$0.757335\pi$
$984$	2.15972	−	7.48382i	0.0688492	−	0.238575i
$985$	−62.0118	+	14.1538i	−1.97586	+	0.450977i
$986$	0.912861	−	1.51446i	0.0290714	−	0.0482302i
$987$	14.8783	−	7.86819i	0.473581	−	0.250447i
$988$	8.83785	+	3.85909i	0.281170	+	0.122774i
$989$	39.2714	−	18.9121i	1.24876	−	0.601370i
$990$	−3.10893	−	1.87395i	−0.0988083	−	0.0595581i
$991$	8.18111	−	16.9883i	0.259882	−	0.539650i	−0.729675	−	0.683794i	$-0.760329\pi$
$991$	8.18111	−	16.9883i	0.259882	−	0.539650i	0.989557	+	0.144144i	$0.0460429\pi$
$992$	−7.06714	+	8.51663i	−0.224382	+	0.270403i
$993$	−6.14079	+	12.7515i	−0.194872	+	0.404656i
$994$	−14.6627	+	10.4059i	−0.465071	+	0.330056i
$995$	16.7684	+	34.8199i	0.531594	+	1.10387i
$996$	−2.29992	+	1.97803i	−0.0728756	+	0.0626763i
$997$	−5.07010	−	4.04327i	−0.160572	−	0.128052i	0.539908	−	0.841724i	$-0.318459\pi$
$997$	−5.07010	−	4.04327i	−0.160572	−	0.128052i	−0.700480	+	0.713672i	$0.747030\pi$
$998$	−55.4078	−	18.2417i	−1.75390	−	0.577432i
$999$	4.00006			0.126556

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.x.a.559.21	yes	168
4.3	odd	2		588.2.x.b.559.13	yes	168
49.27	odd	14		588.2.x.b.223.13	yes	168
196.27	even	14	inner	588.2.x.a.223.21	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.x.a.223.21	✓	168	196.27	even	14	inner
588.2.x.a.559.21	yes	168	1.1	even	1	trivial
588.2.x.b.223.13	yes	168	49.27	odd	14
588.2.x.b.559.13	yes	168	4.3	odd	2

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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.x (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.981280 - 1.01838i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(-0.0741801 - 1.99862i) q^{4} +(2.53335 - 0.578222i) q^{5} +(-1.21120 - 0.730067i) q^{6} +(-1.72629 - 2.00497i) q^{7} +(-2.10814 - 1.88567i) q^{8} +(-0.900969 + 0.433884i) q^{9} +O(q^{10})\)	\(q+(0.981280 - 1.01838i) q^{2} +(-0.222521 - 0.974928i) q^{3} +(-0.0741801 - 1.99862i) q^{4} +(2.53335 - 0.578222i) q^{5} +(-1.21120 - 0.730067i) q^{6} +(-1.72629 - 2.00497i) q^{7} +(-2.10814 - 1.88567i) q^{8} +(-0.900969 + 0.433884i) q^{9} +(1.89708 - 3.14730i) q^{10} +(-0.428593 + 0.889983i) q^{11} +(-1.93201 + 0.517056i) q^{12} +(0.697693 - 1.44877i) q^{13} +(-3.73579 - 0.209420i) q^{14} +(-1.12745 - 2.34117i) q^{15} +(-3.98899 + 0.296516i) q^{16} +(3.94421 + 3.14540i) q^{17} +(-0.442246 + 1.34329i) q^{18} -2.99862 q^{19} +(-1.34357 - 5.02033i) q^{20} +(-1.57056 + 2.12916i) q^{21} +(0.485768 + 1.30979i) q^{22} +(2.65508 - 2.11735i) q^{23} +(-1.36928 + 2.47489i) q^{24} +(1.57870 - 0.760262i) q^{25} +(-0.790765 - 2.13217i) q^{26} +(0.623490 + 0.781831i) q^{27} +(-3.87913 + 3.59894i) q^{28} +(0.154534 - 0.193780i) q^{29} +(-3.49054 - 1.14918i) q^{30} +1.95638 q^{31} +(-3.61235 + 4.35326i) q^{32} +(0.963040 + 0.219808i) q^{33} +(7.07358 - 0.930170i) q^{34} +(-5.53263 - 4.08112i) q^{35} +(0.934004 + 1.76851i) q^{36} +(2.49400 - 3.12738i) q^{37} +(-2.94248 + 3.05372i) q^{38} +(-1.56770 - 0.357818i) q^{39} +(-6.43100 - 3.55809i) q^{40} +(-2.68486 + 0.612801i) q^{41} +(0.627123 + 3.68873i) q^{42} +(12.5134 + 2.85610i) q^{43} +(1.81053 + 0.790578i) q^{44} +(-2.03159 + 1.62014i) q^{45} +(0.449112 - 4.78159i) q^{46} +(-5.73142 - 2.76011i) q^{47} +(1.17672 + 3.82300i) q^{48} +(-1.03981 + 6.92234i) q^{49} +(0.774914 - 2.35374i) q^{50} +(2.18887 - 4.54524i) q^{51} +(-2.94731 - 1.28696i) q^{52} +(2.44059 + 3.06040i) q^{53} +(1.40802 + 0.132248i) q^{54} +(-0.571171 + 2.50246i) q^{55} +(-0.141430 + 7.48198i) q^{56} +(0.667255 + 2.92343i) q^{57} +(-0.0456993 - 0.347526i) q^{58} +(1.47606 - 6.46703i) q^{59} +(-4.59549 + 2.42701i) q^{60} +(-5.41157 - 4.31558i) q^{61} +(1.91976 - 1.99233i) q^{62} +(2.42526 + 1.05740i) q^{63} +(0.888528 + 7.95050i) q^{64} +(0.929791 - 4.07368i) q^{65} +(1.16886 - 0.765045i) q^{66} +14.9209i q^{67} +(5.99390 - 8.11632i) q^{68} +(-2.65508 - 2.11735i) q^{69} +(-9.58518 + 1.62958i) q^{70} +(3.75696 - 2.99607i) q^{71} +(2.71753 + 0.784238i) q^{72} +(-3.48651 - 7.23981i) q^{73} +(-0.737534 - 5.60866i) q^{74} +(-1.09249 - 1.36994i) q^{75} +(0.222438 + 5.99311i) q^{76} +(2.52427 - 0.677056i) q^{77} +(-1.90275 + 1.24539i) q^{78} -3.43155i q^{79} +(-9.93409 + 3.05770i) q^{80} +(0.623490 - 0.781831i) q^{81} +(-2.01053 + 3.33552i) q^{82} +(1.36655 - 0.658097i) q^{83} +(4.37190 + 2.98103i) q^{84} +(11.8108 + 5.68780i) q^{85} +(15.1877 - 9.94069i) q^{86} +(-0.223308 - 0.107540i) q^{87} +(2.58175 - 1.06803i) q^{88} +(-1.91459 - 3.97568i) q^{89} +(-0.343648 + 3.65874i) q^{90} +(-4.10917 + 1.10216i) q^{91} +(-4.42875 - 5.14944i) q^{92} +(-0.435335 - 1.90733i) q^{93} +(-8.43496 + 3.12831i) q^{94} +(-7.59656 + 1.73386i) q^{95} +(5.04794 + 2.55309i) q^{96} +3.46477i q^{97} +(6.02920 + 7.85167i) q^{98} -0.987807i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9}+O(q^{10}) \) 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9	\( 168 q - 28 q^{3} + 2 q^{7} + 6 q^{8} - 28 q^{9} + 20 q^{10} - 12 q^{14} + 36 q^{16} + 12 q^{19} - 25 q^{20} + 2 q^{21} - 6 q^{22} - 15 q^{24} + 32 q^{25} + 6 q^{26} - 28 q^{27} - 66 q^{28} - 8 q^{30} - 4 q^{31} + 25 q^{32} - 68 q^{34} - 12 q^{35} - 10 q^{37} + 35 q^{38} + 14 q^{39} + 16 q^{40} + 9 q^{42} + 20 q^{44} - 28 q^{46} - 8 q^{47} + 8 q^{48} - 8 q^{49} + 114 q^{50} + 20 q^{52} - 8 q^{53} - q^{56} + 12 q^{57} - 6 q^{58} + 20 q^{59} + 10 q^{60} - 14 q^{61} - 16 q^{62} - 12 q^{63} + 42 q^{64} - 8 q^{65} - 6 q^{66} - 16 q^{68} + 59 q^{70} + 28 q^{71} - 15 q^{72} + 22 q^{74} + 18 q^{75} + 7 q^{76} + 8 q^{77} + 6 q^{78} + 26 q^{80} - 28 q^{81} + 12 q^{82} + 10 q^{83} + 11 q^{84} - 24 q^{85} - 6 q^{86} - 242 q^{88} + 20 q^{90} - 16 q^{91} + 7 q^{92} - 4 q^{93} - 53 q^{94} - 10 q^{96} - 118 q^{98}+O(q^{100}) \) 168 * q - 28 * q^3 + 2 * q^7 + 6 * q^8 - 28 * q^9 + 20 * q^10 - 12 * q^14 + 36 * q^16 + 12 * q^19 - 25 * q^20 + 2 * q^21 - 6 * q^22 - 15 * q^24 + 32 * q^25 + 6 * q^26 - 28 * q^27 - 66 * q^28 - 8 * q^30 - 4 * q^31 + 25 * q^32 - 68 * q^34 - 12 * q^35 - 10 * q^37 + 35 * q^38 + 14 * q^39 + 16 * q^40 + 9 * q^42 + 20 * q^44 - 28 * q^46 - 8 * q^47 + 8 * q^48 - 8 * q^49 + 114 * q^50 + 20 * q^52 - 8 * q^53 - q^56 + 12 * q^57 - 6 * q^58 + 20 * q^59 + 10 * q^60 - 14 * q^61 - 16 * q^62 - 12 * q^63 + 42 * q^64 - 8 * q^65 - 6 * q^66 - 16 * q^68 + 59 * q^70 + 28 * q^71 - 15 * q^72 + 22 * q^74 + 18 * q^75 + 7 * q^76 + 8 * q^77 + 6 * q^78 + 26 * q^80 - 28 * q^81 + 12 * q^82 + 10 * q^83 + 11 * q^84 - 24 * q^85 - 6 * q^86 - 242 * q^88 + 20 * q^90 - 16 * q^91 + 7 * q^92 - 4 * q^93 - 53 * q^94 - 10 * q^96 - 118 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more