LMFDB - Embedded newform 731.2.m.b.87.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, 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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$29$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.15
Character	$\chi$	$=$	731.87
Dual form			731.2.m.b.689.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0607158 - 0.0607158i) q^{2} +(-1.28452 + 0.532068i) q^{3} -1.99263i q^{4} +(-0.430997 - 1.04052i) q^{5} +(0.110296 + 0.0456861i) q^{6} +(-0.993514 + 2.39855i) q^{7} +(-0.242416 + 0.242416i) q^{8} +(-0.754412 + 0.754412i) q^{9} +O(q^{10})$	\(q+(-0.0607158 - 0.0607158i) q^{2} +(-1.28452 + 0.532068i) q^{3} -1.99263i q^{4} +(-0.430997 - 1.04052i) q^{5} +(0.110296 + 0.0456861i) q^{6} +(-0.993514 + 2.39855i) q^{7} +(-0.242416 + 0.242416i) q^{8} +(-0.754412 + 0.754412i) q^{9} +(-0.0370077 + 0.0893444i) q^{10} +(2.44652 + 1.01338i) q^{11} +(1.06021 + 2.55958i) q^{12} +0.100617i q^{13} +(0.205952 - 0.0853082i) q^{14} +(1.10725 + 1.10725i) q^{15} -3.95582 q^{16} +(4.12281 - 0.0497885i) q^{17} +0.0916095 q^{18} +(2.33291 + 2.33291i) q^{19} +(-2.07337 + 0.858817i) q^{20} -3.60962i q^{21} +(-0.0870140 - 0.210070i) q^{22} +(2.67536 + 1.10817i) q^{23} +(0.182407 - 0.440371i) q^{24} +(2.63861 - 2.63861i) q^{25} +(0.00610904 - 0.00610904i) q^{26} +(2.16387 - 5.22403i) q^{27} +(4.77942 + 1.97970i) q^{28} +(-1.18303 - 2.85608i) q^{29} -0.134456i q^{30} +(2.11873 - 0.877607i) q^{31} +(0.725012 + 0.725012i) q^{32} -3.68180 q^{33} +(-0.253343 - 0.247297i) q^{34} +2.92394 q^{35} +(1.50326 + 1.50326i) q^{36} +(3.30417 - 1.36863i) q^{37} -0.283289i q^{38} +(-0.0535350 - 0.129245i) q^{39} +(0.356719 + 0.147758i) q^{40} +(3.17825 - 7.67297i) q^{41} +(-0.219161 + 0.219161i) q^{42} +(0.707107 - 0.707107i) q^{43} +(2.01929 - 4.87499i) q^{44} +(1.11013 + 0.459831i) q^{45} +(-0.0951533 - 0.229720i) q^{46} +5.70822i q^{47} +(5.08135 - 2.10476i) q^{48} +(0.183756 + 0.183756i) q^{49} -0.320411 q^{50} +(-5.26936 + 2.25757i) q^{51} +0.200492 q^{52} +(6.81913 + 6.81913i) q^{53} +(-0.448563 + 0.185801i) q^{54} -2.98241i q^{55} +(-0.340604 - 0.822291i) q^{56} +(-4.23794 - 1.75541i) q^{57} +(-0.101581 + 0.245238i) q^{58} +(-4.57438 + 4.57438i) q^{59} +(2.20634 - 2.20634i) q^{60} +(2.07032 - 4.99819i) q^{61} +(-0.181925 - 0.0753559i) q^{62} +(-1.05998 - 2.55902i) q^{63} +7.82360i q^{64} +(0.104694 - 0.0433656i) q^{65} +(0.223543 + 0.223543i) q^{66} +2.17540 q^{67} +(-0.0992098 - 8.21521i) q^{68} -4.02619 q^{69} +(-0.177530 - 0.177530i) q^{70} +(-0.600699 + 0.248818i) q^{71} -0.365763i q^{72} +(2.14351 + 5.17489i) q^{73} +(-0.283713 - 0.117518i) q^{74} +(-1.98544 + 4.79328i) q^{75} +(4.64861 - 4.64861i) q^{76} +(-4.86129 + 4.86129i) q^{77} +(-0.00459679 + 0.0110976i) q^{78} +(8.82331 + 3.65473i) q^{79} +(1.70495 + 4.11611i) q^{80} +4.66103i q^{81} +(-0.658841 + 0.272901i) q^{82} +(6.39878 + 6.39878i) q^{83} -7.19262 q^{84} +(-1.82872 - 4.26840i) q^{85} -0.0858652 q^{86} +(3.03926 + 3.03926i) q^{87} +(-0.838733 + 0.347415i) q^{88} +13.1159i q^{89} +(-0.0394835 - 0.0953215i) q^{90} +(-0.241335 - 0.0999643i) q^{91} +(2.20817 - 5.33100i) q^{92} +(-2.25462 + 2.25462i) q^{93} +(0.346579 - 0.346579i) q^{94} +(1.42196 - 3.43291i) q^{95} +(-1.31705 - 0.545541i) q^{96} +(0.661166 + 1.59619i) q^{97} -0.0223138i q^{98} +(-2.61019 + 1.08117i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 8 q^{6}+O(q^{10}) $ 116 * q - 8 * q^6	$ 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) $ 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0607158	−	0.0607158i	−0.0429326	−	0.0429326i	0.685315	−	0.728247i	$-0.259665\pi$
$2$	−0.0607158	−	0.0607158i	−0.0429326	−	0.0429326i	−0.728247	+	0.685315i	$0.759665\pi$
$3$	−1.28452	+	0.532068i	−0.741621	+	0.307189i	−0.721318	−	0.692604i	$-0.756463\pi$
$3$	−1.28452	+	0.532068i	−0.741621	+	0.307189i	−0.0203032	+	0.999794i	$0.506463\pi$
$4$		−	1.99263i		−	0.996314i
$5$	−0.430997	−	1.04052i	−0.192748	−	0.465335i	0.797729	−	0.603017i	$-0.206035\pi$
$5$	−0.430997	−	1.04052i	−0.192748	−	0.465335i	−0.990476	+	0.137682i	$0.956035\pi$
$6$	0.110296	+	0.0456861i	0.0450281	+	0.0186513i
$7$	−0.993514	+	2.39855i	−0.375513	+	0.906568i	0.617282	+	0.786742i	$0.288234\pi$
$7$	−0.993514	+	2.39855i	−0.375513	+	0.906568i	−0.992795	+	0.119826i	$0.961766\pi$
$8$	−0.242416	+	0.242416i	−0.0857069	+	0.0857069i
$9$	−0.754412	+	0.754412i	−0.251471	+	0.251471i
$10$	−0.0370077	+	0.0893444i	−0.0117029	+	0.0282532i
$11$	2.44652	+	1.01338i	0.737652	+	0.305546i	0.719692	−	0.694293i	$-0.244283\pi$
$11$	2.44652	+	1.01338i	0.737652	+	0.305546i	0.0179599	+	0.999839i	$0.494283\pi$
$12$	1.06021	+	2.55958i	0.306057	+	0.738887i
$13$			0.100617i			0.0279061i	0.999903	+	0.0139531i	$0.00444154\pi$
$13$			0.100617i			0.0279061i	−0.999903	+	0.0139531i	$0.995558\pi$
$14$	0.205952	−	0.0853082i	0.0550431	−	0.0227996i
$15$	1.10725	+	1.10725i	0.285892	+	0.285892i
$16$	−3.95582			−0.988954
$17$	4.12281	−	0.0497885i	0.999927	−	0.0120755i
$17$	4.12281	−	0.0497885i	0.999927	−	0.0120755i
$18$	0.0916095			0.0215926
$19$	2.33291	+	2.33291i	0.535206	+	0.535206i	0.922117	−	0.386911i	$-0.126458\pi$
$19$	2.33291	+	2.33291i	0.535206	+	0.535206i	−0.386911	+	0.922117i	$0.626458\pi$
$20$	−2.07337	+	0.858817i	−0.463619	+	0.192037i
$21$		−	3.60962i		−	0.787683i
$22$	−0.0870140	−	0.210070i	−0.0185515	−	0.0447872i
$23$	2.67536	+	1.10817i	0.557851	+	0.231070i	0.643752	−	0.765234i	$-0.277377\pi$
$23$	2.67536	+	1.10817i	0.557851	+	0.231070i	−0.0859007	+	0.996304i	$0.527377\pi$
$24$	0.182407	−	0.440371i	0.0372338	−	0.0898903i
$25$	2.63861	−	2.63861i	0.527722	−	0.527722i
$26$	0.00610904	−	0.00610904i	0.00119808	−	0.00119808i
$27$	2.16387	−	5.22403i	0.416436	−	1.00537i
$28$	4.77942	+	1.97970i	0.903226	+	0.374129i
$29$	−1.18303	−	2.85608i	−0.219683	−	0.530361i	0.775163	−	0.631761i	$-0.217668\pi$
$29$	−1.18303	−	2.85608i	−0.219683	−	0.530361i	−0.994846	+	0.101400i	$0.967668\pi$
$30$		−	0.134456i		−	0.0245481i
$31$	2.11873	−	0.877607i	0.380535	−	0.157623i	−0.184212	−	0.982886i	$-0.558973\pi$
$31$	2.11873	−	0.877607i	0.380535	−	0.157623i	0.564748	+	0.825264i	$0.308973\pi$
$32$	0.725012	+	0.725012i	0.128165	+	0.128165i
$33$	−3.68180			−0.640919
$34$	−0.253343	−	0.247297i	−0.0434479	−	0.0424110i
$35$	2.92394			0.494237
$36$	1.50326	+	1.50326i	0.250544	+	0.250544i
$37$	3.30417	−	1.36863i	0.543202	−	0.225002i	−0.0941722	−	0.995556i	$-0.530020\pi$
$37$	3.30417	−	1.36863i	0.543202	−	0.225002i	0.637375	+	0.770554i	$0.280020\pi$
$38$		−	0.283289i		−	0.0459555i
$39$	−0.0535350	−	0.129245i	−0.00857246	−	0.0206958i
$40$	0.356719	+	0.147758i	0.0564022	+	0.0233626i
$41$	3.17825	−	7.67297i	0.496359	−	1.19832i	−0.455072	−	0.890455i	$-0.650387\pi$
$41$	3.17825	−	7.67297i	0.496359	−	1.19832i	0.951431	−	0.307862i	$-0.0996134\pi$
$42$	−0.219161	+	0.219161i	−0.0338173	+	0.0338173i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$43$	0.707107	−	0.707107i	0.107833	−	0.107833i
$44$	2.01929	−	4.87499i	0.304419	−	0.734933i
$45$	1.11013	+	0.459831i	0.165488	+	0.0685476i
$46$	−0.0951533	−	0.229720i	−0.0140296	−	0.0338704i
$47$			5.70822i			0.832630i	0.909221	+	0.416315i	$0.136679\pi$
$47$			5.70822i			0.832630i	−0.909221	+	0.416315i	$0.863321\pi$
$48$	5.08135	−	2.10476i	0.733429	−	0.303796i
$49$	0.183756	+	0.183756i	0.0262508	+	0.0262508i
$50$	−0.320411			−0.0453130
$51$	−5.26936	+	2.25757i	−0.737857	+	0.316122i
$52$	0.200492			0.0278032
$53$	6.81913	+	6.81913i	0.936680	+	0.936680i	0.998111	−	0.0614318i	$-0.0195667\pi$
$53$	6.81913	+	6.81913i	0.936680	+	0.936680i	−0.0614318	+	0.998111i	$0.519567\pi$
$54$	−0.448563	+	0.185801i	−0.0610416	+	0.0252843i
$55$		−	2.98241i		−	0.402148i
$56$	−0.340604	−	0.822291i	−0.0455151	−	0.109883i
$57$	−4.23794	−	1.75541i	−0.561329	−	0.232510i
$58$	−0.101581	+	0.245238i	−0.0133382	+	0.0322013i
$59$	−4.57438	+	4.57438i	−0.595534	+	0.595534i	−0.939121	−	0.343587i	$-0.888358\pi$
$59$	−4.57438	+	4.57438i	−0.595534	+	0.595534i	0.343587	+	0.939121i	$0.388358\pi$
$60$	2.20634	−	2.20634i	0.284838	−	0.284838i
$61$	2.07032	−	4.99819i	0.265077	−	0.639952i	−0.734161	−	0.678975i	$-0.762424\pi$
$61$	2.07032	−	4.99819i	0.265077	−	0.639952i	0.999238	+	0.0390227i	$0.0124245\pi$
$62$	−0.181925	−	0.0753559i	−0.0231045	−	0.00957021i
$63$	−1.05998	−	2.55902i	−0.133545	−	0.322406i
$64$			7.82360i			0.977949i
$65$	0.104694	−	0.0433656i	0.0129857	−	0.00537885i
$66$	0.223543	+	0.223543i	0.0275163	+	0.0275163i
$67$	2.17540			0.265767			0.132884	−	0.991132i	$-0.457576\pi$
$67$	2.17540			0.265767			0.132884	+	0.991132i	$0.457576\pi$
$68$	−0.0992098	−	8.21521i	−0.0120310	−	0.996241i
$69$	−4.02619			−0.484696
$70$	−0.177530	−	0.177530i	−0.0212189	−	0.0212189i
$71$	−0.600699	+	0.248818i	−0.0712898	+	0.0295292i	−0.418043	−	0.908427i	$-0.637284\pi$
$71$	−0.600699	+	0.248818i	−0.0712898	+	0.0295292i	0.346754	+	0.937956i	$0.387284\pi$
$72$		−	0.365763i		−	0.0431055i
$73$	2.14351	+	5.17489i	0.250879	+	0.605675i	0.998275	−	0.0587030i	$-0.0186965\pi$
$73$	2.14351	+	5.17489i	0.250879	+	0.605675i	−0.747397	+	0.664378i	$0.768696\pi$
$74$	−0.283713	−	0.117518i	−0.0329810	−	0.0136612i
$75$	−1.98544	+	4.79328i	−0.229259	+	0.553480i
$76$	4.64861	−	4.64861i	0.533233	−	0.533233i
$77$	−4.86129	+	4.86129i	−0.553996	+	0.553996i
$78$	−0.00459679	+	0.0110976i	−0.000520484	+	0.00125656i
$79$	8.82331	+	3.65473i	0.992700	+	0.411190i	0.819115	−	0.573629i	$-0.194465\pi$
$79$	8.82331	+	3.65473i	0.992700	+	0.411190i	0.173585	+	0.984819i	$0.444465\pi$
$80$	1.70495	+	4.11611i	0.190619	+	0.460195i
$81$			4.66103i			0.517892i
$82$	−0.658841	+	0.272901i	−0.0727568	+	0.0301368i
$83$	6.39878	+	6.39878i	0.702357	+	0.702357i	0.964916	−	0.262559i	$-0.0845664\pi$
$83$	6.39878	+	6.39878i	0.702357	+	0.702357i	−0.262559	+	0.964916i	$0.584566\pi$
$84$	−7.19262			−0.784780
$85$	−1.82872	−	4.26840i	−0.198353	−	0.462973i
$86$	−0.0858652			−0.00925908
$87$	3.03926	+	3.03926i	0.325843	+	0.325843i
$88$	−0.838733	+	0.347415i	−0.0894092	+	0.0370345i
$89$			13.1159i			1.39028i	0.718873	+	0.695142i	$0.244658\pi$
$89$			13.1159i			1.39028i	−0.718873	+	0.695142i	$0.755342\pi$
$90$	−0.0394835	−	0.0953215i	−0.00416192	−	0.0100478i
$91$	−0.241335	−	0.0999643i	−0.0252988	−	0.0104791i
$92$	2.20817	−	5.33100i	0.230218	−	0.555795i
$93$	−2.25462	+	2.25462i	−0.233793	+	0.233793i
$94$	0.346579	−	0.346579i	0.0357469	−	0.0357469i
$95$	1.42196	−	3.43291i	0.145890	−	0.352210i
$96$	−1.31705	−	0.545541i	−0.134421	−	0.0556790i
$97$	0.661166	+	1.59619i	0.0671312	+	0.162069i	0.953884	−	0.300174i	$-0.0970448\pi$
$97$	0.661166	+	1.59619i	0.0671312	+	0.162069i	−0.886753	+	0.462243i	$0.847045\pi$
$98$		−	0.0223138i		−	0.00225403i
$99$	−2.61019	+	1.08117i	−0.262334	+	0.108662i
$100$	−5.25777	−	5.25777i	−0.525777	−	0.525777i
$101$	−11.0676			−1.10126			−0.550631	−	0.834748i	$-0.685613\pi$
$101$	−11.0676			−1.10126			−0.550631	+	0.834748i	$0.685613\pi$
$102$	0.457003	+	0.182863i	0.0452501	+	0.0181062i
$103$	14.6505			1.44355			0.721776	−	0.692126i	$-0.243326\pi$
$103$	14.6505			1.44355			0.721776	+	0.692126i	$0.243326\pi$
$104$	−0.0243911	−	0.0243911i	−0.00239175	−	0.00239175i
$105$	−3.75588	+	1.55574i	−0.366536	+	0.151824i
$106$		−	0.828058i		−	0.0804282i
$107$	1.77237	+	4.27888i	0.171342	+	0.413655i	0.986102	−	0.166143i	$-0.0531314\pi$
$107$	1.77237	+	4.27888i	0.171342	+	0.413655i	−0.814760	+	0.579798i	$0.803131\pi$
$108$	−10.4096	−	4.31178i	−1.00166	−	0.414901i
$109$	0.108071	−	0.260907i	0.0103513	−	0.0249904i	−0.918619	−	0.395144i	$-0.870695\pi$
$109$	0.108071	−	0.260907i	0.0103513	−	0.0249904i	0.928971	+	0.370153i	$0.120695\pi$
$110$	−0.181080	+	0.181080i	−0.0172653	+	0.0172653i
$111$	−3.51608	+	3.51608i	−0.333732	+	0.333732i
$112$	3.93016	−	9.48824i	0.371365	−	0.896555i
$113$	−12.0883	−	5.00714i	−1.13717	−	0.471033i	−0.266960	−	0.963708i	$-0.586019\pi$
$113$	−12.0883	−	5.00714i	−1.13717	−	0.471033i	−0.870213	+	0.492675i	$0.836019\pi$
$114$	0.150729	+	0.363892i	0.0141171	+	0.0340816i
$115$		−	3.26139i		−	0.304126i
$116$	−5.69111	+	2.35733i	−0.528406	+	0.218873i
$117$	−0.0759066	−	0.0759066i	−0.00701757	−	0.00701757i
$118$	0.555475			0.0511356
$119$	−3.97664	+	9.93824i	−0.364538	+	0.911037i
$120$	−0.536832			−0.0490058
$121$	−2.81968	−	2.81968i	−0.256334	−	0.256334i
$122$	−0.429170	+	0.177768i	−0.0388552	+	0.0160944i
$123$			11.5472i			1.04117i
$124$	−1.74874	−	4.22184i	−0.157042	−	0.379133i
$125$	−9.08536	−	3.76328i	−0.812619	−	0.336598i
$126$	−0.0910153	+	0.219730i	−0.00810829	+	0.0195751i
$127$	10.5124	−	10.5124i	0.932825	−	0.932825i	−0.0650569	−	0.997882i	$-0.520723\pi$
$127$	10.5124	−	10.5124i	0.932825	−	0.932825i	0.997882	+	0.0650569i	$0.0207229\pi$
$128$	1.92504	−	1.92504i	0.170151	−	0.170151i
$129$	−0.532068	+	1.28452i	−0.0468459	+	0.113096i
$130$	−0.00898956	−	0.00372360i	−0.000788437	−	0.000326581i
$131$	0.0396335	+	0.0956838i	0.00346280	+	0.00835993i	0.925601	−	0.378500i	$-0.123560\pi$
$131$	0.0396335	+	0.0956838i	0.00346280	+	0.00835993i	−0.922139	+	0.386859i	$0.873560\pi$
$132$			7.33645i			0.638556i
$133$	−7.91338	+	3.27783i	−0.686177	+	0.284224i
$134$	−0.132081	−	0.132081i	−0.0114101	−	0.0114101i
$135$	−6.36833			−0.548099
$136$	−0.987363	+	1.01150i	−0.0846657	+	0.0867356i
$137$	−9.99216			−0.853688			−0.426844	−	0.904325i	$-0.640375\pi$
$137$	−9.99216			−0.853688			−0.426844	+	0.904325i	$0.640375\pi$
$138$	0.244454	+	0.244454i	0.0208093	+	0.0208093i
$139$	−6.23700	+	2.58345i	−0.529016	+	0.219125i	−0.631172	−	0.775643i	$-0.717426\pi$
$139$	−6.23700	+	2.58345i	−0.529016	+	0.219125i	0.102156	+	0.994768i	$0.467426\pi$
$140$		−	5.82633i		−	0.492415i
$141$	−3.03716	−	7.33235i	−0.255775	−	0.617496i
$142$	0.0515791	+	0.0213648i	0.00432842	+	0.00179289i
$143$	−0.101963	+	0.246161i	−0.00852659	+	0.0205850i
$144$	2.98432	−	2.98432i	0.248693	−	0.248693i
$145$	−2.46193	+	2.46193i	−0.204452	+	0.204452i
$146$	0.184053	−	0.444343i	0.0152323	−	0.0367741i
$147$	−0.333809	−	0.138268i	−0.0275321	−	0.0114042i
$148$	−2.72717	−	6.58398i	−0.224172	−	0.541200i
$149$		−	3.70790i		−	0.303763i	−0.988399	−	0.151882i	$-0.951467\pi$
$149$		−	3.70790i		−	0.303763i	0.988399	−	0.151882i	$-0.0485332\pi$
$150$	0.411576	−	0.170480i	0.0336050	−	0.0139197i
$151$	−5.69426	−	5.69426i	−0.463392	−	0.463392i	0.436374	−	0.899766i	$-0.356263\pi$
$151$	−5.69426	−	5.69426i	−0.463392	−	0.463392i	−0.899766	+	0.436374i	$0.856263\pi$
$152$	−1.13107			−0.0917416
$153$	−3.07273	+	3.14785i	−0.248416	+	0.254489i
$154$	0.590315			0.0475689
$155$	−1.82634	−	1.82634i	−0.146695	−	0.146695i
$156$	−0.257537	+	0.106675i	−0.0206195	+	0.00854086i
$157$		−	10.4242i		−	0.831942i	−0.909378	−	0.415971i	$-0.863442\pi$
$157$		−	10.4242i		−	0.831942i	0.909378	−	0.415971i	$-0.136558\pi$
$158$	−0.313814	−	0.757615i	−0.0249657	−	0.0602726i
$159$	−12.3876	−	5.13110i	−0.982399	−	0.406923i
$160$	0.441911	−	1.06687i	0.0349362	−	0.0843433i
$161$	−5.31602	+	5.31602i	−0.418961	+	0.418961i
$162$	0.282998	−	0.282998i	0.0222344	−	0.0222344i
$163$	4.64443	−	11.2126i	0.363780	−	0.878242i	−0.630961	−	0.775815i	$-0.717339\pi$
$163$	4.64443	−	11.2126i	0.363780	−	0.878242i	0.994740	−	0.102427i	$-0.0326609\pi$
$164$	−15.2894	−	6.33306i	−1.19390	−	0.494529i
$165$	1.58685	+	3.83098i	0.123536	+	0.298242i
$166$		−	0.777014i		−	0.0603080i
$167$	9.76029	−	4.04285i	0.755274	−	0.312845i	0.0283827	−	0.999597i	$-0.490964\pi$
$167$	9.76029	−	4.04285i	0.755274	−	0.312845i	0.726891	+	0.686752i	$0.240964\pi$
$168$	0.875028	+	0.875028i	0.0675099	+	0.0675099i
$169$	12.9899			0.999221
$170$	−0.148127	+	0.370192i	−0.0113608	+	0.0283924i
$171$	−3.51995			−0.269177
$172$	−1.40900	−	1.40900i	−0.107435	−	0.107435i
$173$	−10.1098	+	4.18763i	−0.768636	+	0.318380i	−0.732320	−	0.680961i	$-0.761562\pi$
$173$	−10.1098	+	4.18763i	−0.768636	+	0.318380i	−0.0363165	+	0.999340i	$0.511562\pi$
$174$		−	0.369062i		−	0.0279785i
$175$	3.70736	+	8.95035i	0.280250	+	0.676583i
$176$	−9.67797	−	4.00875i	−0.729504	−	0.302171i
$177$	3.44203	−	8.30979i	0.258719	−	0.624602i
$178$	0.796343	−	0.796343i	0.0596885	−	0.0596885i
$179$	−10.6815	+	10.6815i	−0.798375	+	0.798375i	−0.982839	−	0.184464i	$-0.940945\pi$
$179$	−10.6815	+	10.6815i	−0.798375	+	0.798375i	0.184464	+	0.982839i	$0.440945\pi$
$180$	0.916272	−	2.21208i	0.0682949	−	0.164878i
$181$	−11.8413	−	4.90484i	−0.880160	−	0.364574i	−0.103601	−	0.994619i	$-0.533037\pi$
$181$	−11.8413	−	4.90484i	−0.880160	−	0.364574i	−0.776559	+	0.630045i	$0.783037\pi$
$182$	0.00858345	+	0.0207223i	0.000636248	+	0.00153604i
$183$			7.52185i			0.556031i
$184$	−0.917188	+	0.379912i	−0.0676160	+	0.0280075i
$185$	−2.84818	−	2.84818i	−0.209402	−	0.209402i
$186$	0.273782			0.0200747
$187$	10.1370	+	4.05616i	0.741288	+	0.296616i
$188$	11.3744			0.829560
$189$	10.3803	+	10.3803i	0.755056	+	0.755056i
$190$	−0.294768	+	0.122097i	−0.0213847	+	0.00885783i
$191$		−	10.1681i		−	0.735737i	−0.929878	−	0.367869i	$-0.880088\pi$
$191$		−	10.1681i		−	0.735737i	0.929878	−	0.367869i	$-0.119912\pi$
$192$	−4.16268	−	10.0496i	−0.300416	−	0.725268i
$193$	13.0558	+	5.40791i	0.939780	+	0.389270i	0.799381	−	0.600825i	$-0.205161\pi$
$193$	13.0558	+	5.40791i	0.939780	+	0.389270i	0.140400	+	0.990095i	$0.455161\pi$
$194$	0.0567711	−	0.137058i	0.00407593	−	0.00984016i
$195$	−0.111408	+	0.111408i	−0.00797813	+	0.00797813i
$196$	0.366157	−	0.366157i	0.0261541	−	0.0261541i
$197$	3.66539	−	8.84905i	0.261149	−	0.630468i	−0.737862	−	0.674952i	$-0.764164\pi$
$197$	3.66539	−	8.84905i	0.261149	−	0.630468i	0.999010	+	0.0444837i	$0.0141643\pi$
$198$	0.224124	+	0.0928352i	0.0159278	+	0.00659751i
$199$	1.80969	+	4.36898i	0.128286	+	0.309709i	0.974952	−	0.222415i	$-0.0713940\pi$
$199$	1.80969	+	4.36898i	0.128286	+	0.309709i	−0.846666	+	0.532124i	$0.821394\pi$
$200$			1.27928i			0.0904589i
$201$	−2.79435	+	1.15746i	−0.197099	+	0.0816409i
$202$	0.671976	+	0.671976i	0.0472801	+	0.0472801i
$203$	8.02582			0.563302
$204$	4.49849	+	10.4999i	0.314957	+	0.735137i
$205$	−9.35369			−0.653290
$206$	−0.889515	−	0.889515i	−0.0619754	−	0.0619754i
$207$	−2.85434	+	1.18231i	−0.198390	+	0.0821760i
$208$		−	0.398022i		−	0.0275979i
$209$	3.34337	+	8.07162i	0.231266	+	0.558325i
$210$	0.322499	+	0.133584i	0.0222546	+	0.00921814i
$211$	−0.867918	+	2.09534i	−0.0597500	+	0.144249i	−0.950935	−	0.309391i	$-0.899875\pi$
$211$	−0.867918	+	2.09534i	−0.0597500	+	0.144249i	0.891185	+	0.453640i	$0.149875\pi$
$212$	13.5880	−	13.5880i	0.933227	−	0.933227i
$213$	0.639225	−	0.639225i	0.0437990	−	0.0437990i
$214$	0.152185	−	0.367407i	0.0104031	−	0.0251154i
$215$	−1.04052	−	0.430997i	−0.0709629	−	0.0293938i
$216$	0.741833	+	1.79094i	0.0504753	+	0.121858i
$217$			5.95381i			0.404171i
$218$	−0.0224028	+	0.00927956i	−0.00151731	+	0.000628491i
$219$	−5.50678	−	5.50678i	−0.372114	−	0.372114i
$220$	−5.94284			−0.400666
$221$	0.00500956	+	0.414824i	0.000336980	+	0.0279041i
$222$	0.426964			0.0286560
$223$	12.4277	+	12.4277i	0.832221	+	0.832221i	0.987820	−	0.155599i	$-0.0497309\pi$
$223$	12.4277	+	12.4277i	0.832221	+	0.832221i	−0.155599	+	0.987820i	$0.549731\pi$
$224$	−2.45929	+	1.01867i	−0.164318	+	0.0680629i
$225$			3.98120i			0.265413i
$226$	0.429939	+	1.03797i	0.0285991	+	0.0690444i
$227$	7.25472	+	3.00500i	0.481513	+	0.199449i	0.610218	−	0.792234i	$-0.291082\pi$
$227$	7.25472	+	3.00500i	0.481513	+	0.199449i	−0.128705	+	0.991683i	$0.541082\pi$
$228$	−3.49788	+	8.44464i	−0.231653	+	0.559260i
$229$	−14.9142	+	14.9142i	−0.985561	+	0.985561i	−0.999897	−	0.0143362i	$-0.995436\pi$
$229$	−14.9142	+	14.9142i	−0.985561	+	0.985561i	0.0143362	+	0.999897i	$0.495436\pi$
$230$	−0.198018	+	0.198018i	−0.0130569	+	0.0130569i
$231$	3.65792	−	8.83099i	0.240673	−	0.581036i
$232$	0.979144	+	0.405575i	0.0642840	+	0.0266273i
$233$	5.25492	+	12.6865i	0.344261	+	0.831121i	0.997275	+	0.0737744i	$0.0235045\pi$
$233$	5.25492	+	12.6865i	0.344261	+	0.831121i	−0.653014	+	0.757346i	$0.726496\pi$
$234$			0.00921747i			0.000602565i
$235$	5.93952	−	2.46023i	0.387451	−	0.160488i
$236$	9.11504	+	9.11504i	0.593339	+	0.593339i
$237$	−13.2783			−0.862520
$238$	0.844854	−	0.361963i	0.0547637	−	0.0234626i
$239$	−10.7267			−0.693856			−0.346928	−	0.937892i	$-0.612775\pi$
$239$	−10.7267			−0.693856			−0.346928	+	0.937892i	$0.612775\pi$
$240$	−4.38009	−	4.38009i	−0.282734	−	0.282734i
$241$	−11.5742	+	4.79419i	−0.745559	+	0.308821i	−0.722928	−	0.690923i	$-0.757204\pi$
$241$	−11.5742	+	4.79419i	−0.745559	+	0.308821i	−0.0226309	+	0.999744i	$0.507204\pi$
$242$			0.342398i			0.0220102i
$243$	4.01162	+	9.68490i	0.257345	+	0.621286i
$244$	−9.95952	−	4.12537i	−0.637593	−	0.264100i
$245$	0.112003	−	0.270400i	0.00715563	−	0.0172752i
$246$	0.701096	−	0.701096i	0.0447002	−	0.0447002i
$247$	−0.234730	+	0.234730i	−0.0149355	+	0.0149355i
$248$	−0.300868	+	0.726360i	−0.0191051	+	0.0461239i
$249$	−11.6240	−	4.81481i	−0.736639	−	0.305126i
$250$	0.323135	+	0.780116i	0.0204368	+	0.0493389i
$251$		−	1.25312i		−	0.0790960i	−0.999218	−	0.0395480i	$-0.987408\pi$
$251$		−	1.25312i		−	0.0790960i	0.999218	−	0.0395480i	$-0.0125918\pi$
$252$	−5.09917	+	2.11214i	−0.321217	+	0.133053i
$253$	5.42232	+	5.42232i	0.340898	+	0.340898i
$254$	−1.27654			−0.0800972
$255$	4.62012	+	4.50986i	0.289323	+	0.282419i
$256$	15.4134			0.963339
$257$	18.8745	+	18.8745i	1.17736	+	1.17736i	0.980415	+	0.196943i	$0.0631014\pi$
$257$	18.8745	+	18.8745i	1.17736	+	1.17736i	0.196943	+	0.980415i	$0.436899\pi$
$258$	0.110296	−	0.0456861i	0.00686673	−	0.00284429i
$259$			9.28499i			0.576941i
$260$	−0.0864116	−	0.208616i	−0.00535902	−	0.0129378i
$261$	3.04715	+	1.26217i	0.188614	+	0.0781265i
$262$	0.00340314	−	0.00821591i	0.000210247	−	0.000507580i
$263$	−6.13503	+	6.13503i	−0.378302	+	0.378302i	−0.870489	−	0.492187i	$-0.836198\pi$
$263$	−6.13503	+	6.13503i	−0.378302	+	0.378302i	0.492187	+	0.870489i	$0.336198\pi$
$264$	0.892526	−	0.892526i	0.0549311	−	0.0549311i
$265$	4.15641	−	10.0345i	0.255326	−	0.616412i
$266$	0.679484	+	0.281451i	0.0416618	+	0.0172569i
$267$	−6.97855	−	16.8477i	−0.427080	−	1.03106i
$268$		−	4.33476i		−	0.264788i
$269$	9.56902	−	3.96362i	0.583434	−	0.241666i	−0.0713892	−	0.997449i	$-0.522743\pi$
$269$	9.56902	−	3.96362i	0.583434	−	0.241666i	0.654823	+	0.755782i	$0.272743\pi$
$270$	0.386659	+	0.386659i	0.0235313	+	0.0235313i
$271$	10.7854			0.655165			0.327582	−	0.944823i	$-0.393766\pi$
$271$	10.7854			0.655165			0.327582	+	0.944823i	$0.393766\pi$
$272$	−16.3091	+	0.196954i	−0.988882	+	0.0119421i
$273$	0.363189			0.0219812
$274$	0.606683	+	0.606683i	0.0366510	+	0.0366510i
$275$	9.12932	−	3.78149i	0.550519	−	0.228032i
$276$			8.02270i			0.482910i
$277$	−10.4364	−	25.1956i	−0.627060	−	1.51386i	−0.843258	−	0.537508i	$-0.819366\pi$
$277$	−10.4364	−	25.1956i	−0.627060	−	1.51386i	0.216198	−	0.976350i	$-0.430634\pi$
$278$	0.535541	+	0.221828i	0.0321196	+	0.0133044i
$279$	−0.936319	+	2.26047i	−0.0560559	+	0.135331i
$280$	−0.708810	+	0.708810i	−0.0423595	+	0.0423595i
$281$	−16.1463	+	16.1463i	−0.963209	+	0.963209i	−0.999347	−	0.0361376i	$-0.988495\pi$
$281$	−16.1463	+	16.1463i	−0.963209	+	0.963209i	0.0361376	+	0.999347i	$0.488495\pi$
$282$	−0.260786	+	0.629594i	−0.0155296	+	0.0374918i
$283$	−2.25407	−	0.933666i	−0.133991	−	0.0555007i	0.314681	−	0.949198i	$-0.398103\pi$
$283$	−2.25407	−	0.933666i	−0.133991	−	0.0555007i	−0.448671	+	0.893697i	$0.648103\pi$
$284$	0.495801	+	1.19697i	0.0294204	+	0.0710270i
$285$			5.16624i			0.306022i
$286$	0.0211366	−	0.00875509i	0.00124984	−	0.000517699i
$287$	15.2464	+	15.2464i	0.899966	+	0.899966i
$288$	−1.09392			−0.0644596
$289$	16.9950	−	0.410536i	0.999708	−	0.0241492i
$290$	0.298956			0.0175553
$291$	−1.69857	−	1.69857i	−0.0995718	−	0.0995718i
$292$	10.3116	−	4.27122i	0.603442	−	0.249954i
$293$		−	22.4750i		−	1.31300i	−0.754325	−	0.656501i	$-0.772036\pi$
$293$		−	22.4750i		−	1.31300i	0.754325	−	0.656501i	$-0.227964\pi$
$294$	0.0118724	+	0.0286626i	0.000692415	+	0.00167164i
$295$	6.73128	+	2.78819i	0.391910	+	0.162335i
$296$	−0.469205	+	1.13276i	−0.0272720	+	0.0658404i
$297$	10.5879	−	10.5879i	0.614370	−	0.614370i
$298$	−0.225128	+	0.225128i	−0.0130413	+	0.0130413i
$299$	−0.111501	+	0.269187i	−0.00644826	+	0.0155675i
$300$	9.55122	+	3.95625i	0.551440	+	0.228414i
$301$	0.993514	+	2.39855i	0.0572652	+	0.138250i
$302$			0.691463i			0.0397892i
$303$	14.2166	−	5.88869i	0.816719	−	0.338296i
$304$	−9.22856	−	9.22856i	−0.529294	−	0.529294i
$305$	−6.09301			−0.348885
$306$	0.377688	−	0.00456110i	0.0215910	−	0.000260741i
$307$	14.8526			0.847683			0.423841	−	0.905736i	$-0.360681\pi$
$307$	14.8526			0.847683			0.423841	+	0.905736i	$0.360681\pi$
$308$	9.68674	+	9.68674i	0.551953	+	0.551953i
$309$	−18.8189	+	7.79504i	−1.07057	+	0.443444i
$310$			0.221775i			0.0125960i
$311$	−0.635063	−	1.53318i	−0.0360111	−	0.0869385i	0.904851	−	0.425729i	$-0.139982\pi$
$311$	−0.635063	−	1.53318i	−0.0360111	−	0.0869385i	−0.940862	+	0.338790i	$0.889982\pi$
$312$	0.0443087	+	0.0183533i	0.00250849	+	0.00103905i
$313$	7.29315	−	17.6072i	0.412233	−	0.995220i	−0.572303	−	0.820042i	$-0.693950\pi$
$313$	7.29315	−	17.6072i	0.412233	−	0.995220i	0.984537	−	0.175178i	$-0.0560500\pi$
$314$	−0.632914	+	0.632914i	−0.0357174	+	0.0357174i
$315$	−2.20586	+	2.20586i	−0.124286	+	0.124286i
$316$	7.28252	−	17.5816i	0.409674	−	0.989040i
$317$	−22.9500	−	9.50621i	−1.28900	−	0.533922i	−0.370314	−	0.928907i	$-0.620750\pi$
$317$	−22.9500	−	9.50621i	−1.28900	−	0.533922i	−0.918688	+	0.394984i	$0.870750\pi$
$318$	0.440583	+	1.06366i	0.0247067	+	0.0596472i
$319$		−	8.18631i		−	0.458345i
$320$	8.14061	−	3.37195i	0.455074	−	0.188498i
$321$	−4.55331	−	4.55331i	−0.254141	−	0.254141i
$322$	0.645533			0.0359741
$323$	9.73427	+	9.50197i	0.541630	+	0.528704i
$324$	9.28769			0.515983
$325$	0.265489	+	0.265489i	0.0147267	+	0.0147267i
$326$	−0.962776	+	0.398795i	−0.0533232	+	0.0220872i
$327$			0.392643i			0.0217132i
$328$	1.08959	+	2.63051i	0.0601626	+	0.145245i
$329$	−13.6915	−	5.67120i	−0.754836	−	0.312663i
$330$	0.136255	−	0.328948i	0.00750058	−	0.0181080i
$331$	19.6828	−	19.6828i	1.08186	−	1.08186i	0.0855263	−	0.996336i	$-0.472743\pi$
$331$	19.6828	−	19.6828i	1.08186	−	1.08186i	0.996336	−	0.0855263i	$-0.0272572\pi$
$332$	12.7504	−	12.7504i	0.699768	−	0.699768i
$333$	−1.46019	+	3.52522i	−0.0800181	+	0.193181i
$334$	−0.838069	−	0.347140i	−0.0458571	−	0.0189946i
$335$	−0.937591	−	2.26355i	−0.0512261	−	0.123671i
$336$			14.2790i			0.778983i
$337$	−21.0819	+	8.73243i	−1.14841	+	0.475686i	−0.873999	−	0.485928i	$-0.838482\pi$
$337$	−21.0819	+	8.73243i	−1.14841	+	0.475686i	−0.274408	+	0.961613i	$0.588482\pi$
$338$	−0.788691	−	0.788691i	−0.0428992	−	0.0428992i
$339$	18.1919			0.988048
$340$	−8.50533	+	3.64397i	−0.461266	+	0.197622i
$341$	6.07286			0.328864
$342$	0.213717	+	0.213717i	0.0115565	+	0.0115565i
$343$	−17.4132	+	7.21278i	−0.940224	+	0.389453i
$344$			0.342828i			0.0184840i
$345$	1.73528	+	4.18933i	0.0934242	+	0.225546i
$346$	0.868083	+	0.359572i	0.0466684	+	0.0193307i
$347$	5.39002	−	13.0127i	0.289352	−	0.698556i	−0.710636	−	0.703560i	$-0.751593\pi$
$347$	5.39002	−	13.0127i	0.289352	−	0.698556i	0.999987	+	0.00500346i	$0.00159266\pi$
$348$	6.05611	−	6.05611i	0.324642	−	0.324642i
$349$	−18.9400	+	18.9400i	−1.01384	+	1.01384i	−0.0139336	+	0.999903i	$0.504435\pi$
$349$	−18.9400	+	18.9400i	−1.01384	+	1.01384i	−0.999903	+	0.0139336i	$0.995565\pi$
$350$	0.318333	−	0.768523i	0.0170156	−	0.0410793i
$351$	0.525626	+	0.217722i	0.0280559	+	0.0116211i
$352$	1.03904	+	2.50847i	0.0553811	+	0.133702i
$353$			7.46904i			0.397537i	0.980046	+	0.198768i	$0.0636942\pi$
$353$			7.46904i			0.397537i	−0.980046	+	0.198768i	$0.936306\pi$
$354$	−0.713522	+	0.295550i	−0.0379232	+	0.0157083i
$355$	0.517799	+	0.517799i	0.0274819	+	0.0274819i
$356$	26.1351			1.38516
$357$	−0.179717	−	14.8818i	−0.00951165	−	0.787626i
$358$	1.29708			0.0685526
$359$	−7.36022	−	7.36022i	−0.388457	−	0.388457i	0.485680	−	0.874137i	$-0.338572\pi$
$359$	−7.36022	−	7.36022i	−0.388457	−	0.388457i	−0.874137	+	0.485680i	$0.838572\pi$
$360$	−0.380583	+	0.157643i	−0.0200585	+	0.00830850i
$361$		−	8.11509i		−	0.427110i
$362$	0.421155	+	1.01676i	0.0221354	+	0.0534396i
$363$	5.12220	+	2.12169i	0.268846	+	0.111360i
$364$	−0.199192	+	0.480891i	−0.0104405	+	0.0252055i
$365$	4.46073	−	4.46073i	0.233485	−	0.233485i
$366$	0.456695	−	0.456695i	0.0238718	−	0.0238718i
$367$	13.0548	−	31.5170i	0.681453	−	1.64517i	−0.0798727	−	0.996805i	$-0.525451\pi$
$367$	13.0548	−	31.5170i	0.681453	−	1.64517i	0.761326	−	0.648369i	$-0.224549\pi$
$368$	−10.5832	−	4.38372i	−0.551690	−	0.228517i
$369$	3.39087	+	8.18629i	0.176522	+	0.426161i
$370$			0.345859i			0.0179804i
$371$	−23.1309	+	9.58115i	−1.20090	+	0.497429i
$372$	4.49261	+	4.49261i	0.232931	+	0.232931i
$373$	28.0241			1.45103			0.725515	−	0.688206i	$-0.241601\pi$
$373$	28.0241			1.45103			0.725515	+	0.688206i	$0.241601\pi$
$374$	−0.369201	−	0.861747i	−0.0190909	−	0.0445599i
$375$	13.6727			0.706055
$376$	−1.38376	−	1.38376i	−0.0713621	−	0.0713621i
$377$	0.287370	−	0.119033i	0.0148003	−	0.00613049i
$378$		−	1.26050i		−	0.0648330i
$379$	−4.43074	−	10.6968i	−0.227592	−	0.549455i	0.768291	−	0.640100i	$-0.221107\pi$
$379$	−4.43074	−	10.6968i	−0.227592	−	0.549455i	−0.995883	+	0.0906450i	$0.971107\pi$
$380$	−6.84052	−	2.83343i	−0.350911	−	0.145352i
$381$	−7.91013	+	19.0967i	−0.405248	+	0.978356i
$382$	−0.617364	+	0.617364i	−0.0315871	+	0.0315871i
$383$	−24.5350	+	24.5350i	−1.25368	+	1.25368i	−0.299623	+	0.954058i	$0.596861\pi$
$383$	−24.5350	+	24.5350i	−1.25368	+	1.25368i	−0.954058	+	0.299623i	$0.903139\pi$
$384$	−1.44851	+	3.49701i	−0.0739190	+	0.178456i
$385$	7.15348	+	2.96307i	0.364575	+	0.151012i
$386$	−0.464351	−	1.12104i	−0.0236348	−	0.0570596i
$387$			1.06690i			0.0542336i
$388$	3.18062	−	1.31746i	0.161472	−	0.0668837i
$389$	−19.5025	−	19.5025i	−0.988815	−	0.988815i	0.0111227	−	0.999938i	$-0.496459\pi$
$389$	−19.5025	−	19.5025i	−0.988815	−	0.988815i	−0.999938	+	0.0111227i	$0.996459\pi$
$390$	0.0135285			0.000685043
$391$	11.0852	+	4.43557i	0.560601	+	0.224316i
$392$	−0.0890906			−0.00449976
$393$	−0.101821	−	0.101821i	−0.00513617	−	0.00513617i
$394$	−0.759825	+	0.314730i	−0.0382794	+	0.0158559i
$395$		−	10.7560i		−	0.541194i
$396$	2.15438	+	5.20113i	0.108262	+	0.261367i
$397$	17.0996	+	7.08289i	0.858205	+	0.355480i	0.768005	−	0.640444i	$-0.221249\pi$
$397$	17.0996	+	7.08289i	0.858205	+	0.355480i	0.0901997	+	0.995924i	$0.471249\pi$
$398$	0.155390	−	0.375144i	0.00778897	−	0.0188042i
$399$	8.42091	−	8.42091i	0.421573	−	0.421573i
$400$	−10.4379	+	10.4379i	−0.521893	+	0.521893i
$401$	−7.17975	+	17.3335i	−0.358540	+	0.865592i	0.636966	+	0.770892i	$0.280189\pi$
$401$	−7.17975	+	17.3335i	−0.358540	+	0.865592i	−0.995506	+	0.0946999i	$0.969811\pi$
$402$	0.239938	+	0.0993854i	0.0119670	+	0.00495690i
$403$	0.0883021	+	0.213180i	0.00439864	+	0.0106193i
$404$			22.0535i			1.09720i
$405$	4.84989	−	2.00889i	0.240993	−	0.0998226i
$406$	−0.487295	−	0.487295i	−0.0241840	−	0.0241840i
$407$	9.47065			0.469443
$408$	0.730105	−	1.82464i	0.0361456	−	0.0903333i
$409$	−25.9227			−1.28180			−0.640898	−	0.767626i	$-0.721438\pi$
$409$	−25.9227			−1.28180			−0.640898	+	0.767626i	$0.721438\pi$
$410$	0.567917	+	0.567917i	0.0280474	+	0.0280474i
$411$	12.8352	−	5.31651i	0.633113	−	0.262244i
$412$		−	29.1929i		−	1.43823i
$413$	−6.42719	−	15.5166i	−0.316261	−	0.763523i
$414$	0.245089	+	0.101519i	0.0120454	+	0.00498939i
$415$	3.90020	−	9.41591i	0.191453	−	0.462209i
$416$	−0.0729485	+	0.0729485i	−0.00357660	+	0.00357660i
$417$	6.63701	−	6.63701i	0.325016	−	0.325016i
$418$	0.287079	−	0.693071i	0.0140415	−	0.0338992i
$419$	5.59061	+	2.31571i	0.273119	+	0.113130i	0.515040	−	0.857166i	$-0.327777\pi$
$419$	5.59061	+	2.31571i	0.273119	+	0.113130i	−0.241920	+	0.970296i	$0.577777\pi$
$420$	3.10000	+	7.48407i	0.151265	+	0.365185i
$421$		−	0.678435i		−	0.0330649i	−0.999863	−	0.0165325i	$-0.994737\pi$
$421$		−	0.678435i		−	0.0330649i	0.999863	−	0.0165325i	$-0.00526268\pi$
$422$	0.179917	−	0.0745239i	0.00875821	−	0.00362777i
$423$	−4.30635	−	4.30635i	−0.209382	−	0.209382i
$424$	−3.30613			−0.160560
$425$	10.7471	−	11.0099i	0.521311	−	0.534056i
$426$	−0.0776222			−0.00376081
$427$	9.93153	+	9.93153i	0.480621	+	0.480621i
$428$	8.52621	−	3.53167i	0.412130	−	0.170710i
$429$		−	0.370451i		−	0.0178855i
$430$	0.0370077	+	0.0893444i	0.00178467	+	0.00430857i
$431$	10.8685	+	4.50188i	0.523518	+	0.216848i	0.628761	−	0.777598i	$-0.283562\pi$
$431$	10.8685	+	4.50188i	0.523518	+	0.216848i	−0.105244	+	0.994446i	$0.533562\pi$
$432$	−8.55986	+	20.6653i	−0.411836	+	0.994261i
$433$	0.651350	−	0.651350i	0.0313019	−	0.0313019i	−0.691283	−	0.722584i	$-0.742954\pi$
$433$	0.651350	−	0.651350i	0.0313019	−	0.0313019i	0.722584	+	0.691283i	$0.242954\pi$
$434$	0.361490	−	0.361490i	0.0173521	−	0.0173521i
$435$	1.85250	−	4.47232i	0.0888204	−	0.214431i
$436$	−0.519891	−	0.215346i	−0.0248982	−	0.0103132i
$437$	3.65611	+	8.82663i	0.174895	+	0.422235i
$438$			0.668698i			0.0319516i
$439$	8.16388	−	3.38159i	0.389641	−	0.161394i	−0.179258	−	0.983802i	$-0.557370\pi$
$439$	8.16388	−	3.38159i	0.389641	−	0.161394i	0.568899	+	0.822408i	$0.307370\pi$
$440$	0.722984	+	0.722984i	0.0344669	+	0.0344669i
$441$	−0.277255			−0.0132026
$442$	0.0248822	−	0.0254906i	0.00118353	−	0.00121246i
$443$	−4.66895			−0.221829			−0.110914	−	0.993830i	$-0.535378\pi$
$443$	−4.66895			−0.221829			−0.110914	+	0.993830i	$0.535378\pi$
$444$	7.00625	+	7.00625i	0.332502	+	0.332502i
$445$	13.6474	−	5.65292i	0.646947	−	0.267974i
$446$		−	1.50912i		−	0.0714588i
$447$	1.97285	+	4.76289i	0.0933128	+	0.225277i
$448$	−18.7653	−	7.77285i	−0.886578	−	0.367233i
$449$	8.00905	−	19.3356i	0.377971	−	0.912502i	−0.614376	−	0.789014i	$-0.710592\pi$
$449$	8.00905	−	19.3356i	0.377971	−	0.912502i	0.992346	−	0.123488i	$-0.0394080\pi$
$450$	0.241722	−	0.241722i	0.0113949	−	0.0113949i
$451$	15.5513	−	15.5513i	0.732280	−	0.732280i
$452$	−9.97737	+	24.0875i	−0.469296	+	1.13298i
$453$	10.3441	+	4.28468i	0.486010	+	0.201312i
$454$	−0.258025	−	0.622928i	−0.0121097	−	0.0292354i
$455$			0.294198i			0.0137922i
$456$	1.45288	−	0.601804i	0.0680375	−	0.0281821i
$457$	−14.6344	−	14.6344i	−0.684567	−	0.684567i	0.276459	−	0.961026i	$-0.410839\pi$
$457$	−14.6344	−	14.6344i	−0.684567	−	0.684567i	−0.961026	+	0.276459i	$0.910839\pi$
$458$	1.81106			0.0846254
$459$	8.66110	−	21.6454i	0.404266	−	1.01032i
$460$	−6.49873			−0.303005
$461$	11.5910	+	11.5910i	0.539848	+	0.539848i	0.923484	−	0.383636i	$-0.125328\pi$
$461$	11.5910	+	11.5910i	0.539848	+	0.539848i	−0.383636	+	0.923484i	$0.625328\pi$
$462$	−0.758274	+	0.314088i	−0.0352781	+	0.0146127i
$463$		−	3.75116i		−	0.174331i	−0.996194	−	0.0871656i	$-0.972219\pi$
$463$		−	3.75116i		−	0.174331i	0.996194	−	0.0871656i	$-0.0277809\pi$
$464$	4.67984	+	11.2981i	0.217256	+	0.524503i
$465$	3.31771	+	1.37424i	0.153855	+	0.0637288i
$466$	0.451215	−	1.08933i	0.0209021	−	0.0504622i
$467$	−17.5386	+	17.5386i	−0.811587	+	0.811587i	−0.984872	−	0.173284i	$-0.944562\pi$
$467$	−17.5386	+	17.5386i	−0.811587	+	0.811587i	0.173284	+	0.984872i	$0.444562\pi$
$468$	−0.151254	+	0.151254i	−0.00699170	+	0.00699170i
$469$	−2.16129	+	5.21781i	−0.0997990	+	0.240936i
$470$	−0.509998	−	0.211248i	−0.0235244	−	0.00974414i
$471$	5.54638	+	13.3901i	0.255564	+	0.616986i
$472$		−	2.21780i		−	0.102083i
$473$	2.44652	−	1.01338i	0.112491	−	0.0465953i
$474$	0.806205	+	0.806205i	0.0370302	+	0.0370302i
$475$	12.3113			0.564880
$476$	19.8032	+	7.92397i	0.907678	+	0.363194i
$477$	−10.2889			−0.471095
$478$	0.651284	+	0.651284i	0.0297890	+	0.0297890i
$479$	−9.21951	+	3.81885i	−0.421250	+	0.174487i	−0.583231	−	0.812306i	$-0.698212\pi$
$479$	−9.21951	+	3.81885i	−0.421250	+	0.174487i	0.161981	+	0.986794i	$0.448212\pi$
$480$			1.60555i			0.0732828i
$481$	0.137708	+	0.332456i	0.00627893	+	0.0151587i
$482$	0.993820	+	0.411654i	0.0452672	+	0.0187503i
$483$	4.00007	−	9.65704i	0.182010	−	0.439410i
$484$	−5.61856	+	5.61856i	−0.255389	+	0.255389i
$485$	1.37591	−	1.37591i	0.0624769	−	0.0624769i
$486$	0.344458	−	0.831595i	0.0156249	−	0.0377219i
$487$	−26.7485	−	11.0796i	−1.21209	−	0.502064i	−0.317203	−	0.948358i	$-0.602744\pi$
$487$	−26.7485	−	11.0796i	−1.21209	−	0.502064i	−0.894886	+	0.446294i	$0.852744\pi$
$488$	0.709762	+	1.71352i	0.0321294	+	0.0775673i
$489$			16.8741i			0.763072i
$490$	−0.0232179	+	0.00961718i	−0.00104888	+	0.000434460i
$491$	12.6834	+	12.6834i	0.572395	+	0.572395i	0.932797	−	0.360402i	$-0.117361\pi$
$491$	12.6834	+	12.6834i	0.572395	+	0.572395i	−0.360402	+	0.932797i	$0.617361\pi$
$492$	23.0092			1.03733
$493$	−5.01959	−	11.7162i	−0.226071	−	0.527670i
$494$	0.0285037			0.00128244
$495$	2.24997	+	2.24997i	0.101129	+	0.101129i
$496$	−8.38131	+	3.47165i	−0.376332	+	0.155882i
$497$		−	1.68801i		−	0.0757177i
$498$	0.413424	+	0.998094i	0.0185260	+	0.0447257i
$499$	−16.5882	−	6.87105i	−0.742589	−	0.307590i	−0.0208750	−	0.999782i	$-0.506645\pi$
$499$	−16.5882	−	6.87105i	−0.742589	−	0.307590i	−0.721714	+	0.692192i	$0.756645\pi$
$500$	−7.49881	+	18.1037i	−0.335357	+	0.809624i
$501$	−10.3863	+	10.3863i	−0.464024	+	0.464024i
$502$	−0.0760840	+	0.0760840i	−0.00339580	+	0.00339580i
$503$	−1.21238	+	2.92694i	−0.0540573	+	0.130506i	−0.948601	−	0.316475i	$-0.897501\pi$
$503$	−1.21238	+	2.92694i	−0.0540573	+	0.130506i	0.894544	+	0.446981i	$0.147501\pi$
$504$	0.877301	+	0.363390i	0.0390781	+	0.0161867i
$505$	4.77009	+	11.5160i	0.212266	+	0.512456i
$506$		−	0.658441i		−	0.0292713i
$507$	−16.6858	+	6.91149i	−0.741043	+	0.306950i
$508$	−20.9473	−	20.9473i	−0.929386	−	0.929386i
$509$	38.4758			1.70541			0.852705	−	0.522392i	$-0.174960\pi$
$509$	38.4758			1.70541			0.852705	+	0.522392i	$0.174960\pi$
$510$	−0.00669434	−	0.554335i	−0.000296431	−	0.0245464i
$511$	−14.5419			−0.643294
$512$	−4.78592	−	4.78592i	−0.211510	−	0.211510i
$513$	17.2353	−	7.13909i	0.760956	−	0.315198i
$514$		−	2.29196i		−	0.101094i
$515$	−6.31431	−	15.2441i	−0.278242	−	0.671735i
$516$	2.55958	+	1.06021i	0.112679	+	0.0466733i
$517$	−5.78460	+	13.9653i	−0.254406	+	0.614191i
$518$	0.563746	−	0.563746i	0.0247696	−	0.0247696i
$519$	10.7582	−	10.7582i	0.472234	−	0.472234i
$520$	−0.0148669	+	0.0358920i	−0.000651958	+	0.00157397i
$521$	−4.11510	−	1.70453i	−0.180286	−	0.0746768i	0.290715	−	0.956810i	$-0.406107\pi$
$521$	−4.11510	−	1.70453i	−0.180286	−	0.0746768i	−0.471000	+	0.882133i	$0.656107\pi$
$522$	−0.108377	−	0.261644i	−0.00474352	−	0.0114519i
$523$			13.2428i			0.579068i	0.957168	+	0.289534i	$0.0935003\pi$
$523$			13.2428i			0.579068i	−0.957168	+	0.289534i	$0.906500\pi$
$524$	0.190662	−	0.0789748i	0.00832911	−	0.00345003i
$525$	−9.52438	−	9.52438i	−0.415678	−	0.415678i
$526$	0.744987			0.0324830
$527$	8.69142	−	3.72369i	0.378604	−	0.162207i
$528$	14.5645			0.633839
$529$	−10.3339	−	10.3339i	−0.449302	−	0.449302i
$530$	−0.861611	+	0.356891i	−0.0374260	+	0.0155024i
$531$		−	6.90194i		−	0.299519i
$532$	6.53149	+	15.7684i	0.283176	+	0.683647i
$533$	0.772031	+	0.319786i	0.0334404	+	0.0138514i
$534$	−0.599214	+	1.44663i	−0.0259305	+	0.0626019i
$535$	3.68837	−	3.68837i	0.159462	−	0.159462i
$536$	−0.527351	+	0.527351i	−0.0227781	+	0.0227781i
$537$	8.03740	−	19.4040i	0.346839	−	0.837344i
$538$	−0.821646	−	0.340337i	−0.0354237	−	0.0146730i
$539$	0.263347	+	0.635776i	0.0113432	+	0.0273848i
$540$			12.6897i			0.546078i
$541$	27.5522	−	11.4125i	1.18456	−	0.490661i	0.298580	−	0.954385i	$-0.403487\pi$
$541$	27.5522	−	11.4125i	1.18456	−	0.490661i	0.885980	+	0.463724i	$0.153487\pi$
$542$	−0.654843	−	0.654843i	−0.0281279	−	0.0281279i
$543$	17.8202			0.764738
$544$	3.02518	+	2.95299i	0.129704	+	0.126608i
$545$	−0.318057			−0.0136241
$546$	−0.0220513	−	0.0220513i	−0.000943709	−	0.000943709i
$547$	2.39171	−	0.990680i	0.102262	−	0.0423584i	−0.330966	−	0.943643i	$-0.607374\pi$
$547$	2.39171	−	0.990680i	0.102262	−	0.0423584i	0.433228	+	0.901284i	$0.357374\pi$
$548$			19.9107i			0.850541i
$549$	2.20882	+	5.33256i	0.0942702	+	0.227588i
$550$	−0.783891	−	0.324698i	−0.0334252	−	0.0138452i
$551$	3.90308	−	9.42287i	0.166277	−	0.401428i
$552$	0.976012	−	0.976012i	0.0415418	−	0.0415418i
$553$	−17.5322	+	17.5322i	−0.745543	+	0.745543i
$554$	−0.896120	+	2.16343i	−0.0380725	+	0.0919152i
$555$	5.17398	+	2.14313i	0.219623	+	0.0909709i
$556$	5.14785	+	12.4280i	0.218318	+	0.527065i
$557$			19.5452i			0.828157i	0.910241	+	0.414078i	$0.135896\pi$
$557$			19.5452i			0.828157i	−0.910241	+	0.414078i	$0.864104\pi$
$558$	0.194096	−	0.0803972i	0.00821674	−	0.00340348i
$559$	0.0711469	+	0.0711469i	0.00300919	+	0.00300919i
$560$	−11.5666			−0.488778
$561$	−15.1793	+	0.183311i	−0.640872	+	0.00773940i
$562$	1.96068			0.0827061
$563$	−28.7033	−	28.7033i	−1.20970	−	1.20970i	−0.971124	−	0.238574i	$-0.923320\pi$
$563$	−28.7033	−	28.7033i	−1.20970	−	1.20970i	−0.238574	−	0.971124i	$-0.576680\pi$
$564$	−14.6106	+	6.05193i	−0.615219	+	0.254832i
$565$			14.7362i			0.619957i
$566$	0.0801694	+	0.193546i	0.00336977	+	0.00813535i
$567$	−11.1797	−	4.63079i	−0.469504	−	0.194475i
$568$	0.0853016	−	0.205936i	0.00357917	−	0.00864089i
$569$	−4.70738	+	4.70738i	−0.197343	+	0.197343i	−0.798860	−	0.601517i	$-0.794563\pi$
$569$	−4.70738	+	4.70738i	−0.197343	+	0.197343i	0.601517	+	0.798860i	$0.294563\pi$
$570$	0.313673	−	0.313673i	0.0131383	−	0.0131383i
$571$	11.2450	−	27.1478i	0.470588	−	1.13610i	−0.493316	−	0.869850i	$-0.664215\pi$
$571$	11.2450	−	27.1478i	0.470588	−	1.13610i	0.963904	−	0.266250i	$-0.0857847\pi$
$572$	0.490507	+	0.203175i	0.0205091	+	0.00849516i
$573$	5.41011	+	13.0612i	0.226011	+	0.545638i
$574$		−	1.85140i		−	0.0772758i
$575$	9.98327	−	4.13521i	0.416331	−	0.172450i
$576$	−5.90221	−	5.90221i	−0.245926	−	0.245926i
$577$	25.9166			1.07892			0.539461	−	0.842011i	$-0.318628\pi$
$577$	25.9166			1.07892			0.539461	+	0.842011i	$0.318628\pi$
$578$	−1.05679	−	1.00694i	−0.0439569	−	0.0418833i
$579$	−19.6479			−0.816540
$580$	4.90571	+	4.90571i	0.203698	+	0.203698i
$581$	−21.7051	+	8.99054i	−0.900479	+	0.372990i
$582$			0.206260i			0.00854975i
$583$	9.77274	+	23.5935i	0.404745	+	0.977142i
$584$	−1.77410	−	0.734854i	−0.0734126	−	0.0304085i
$585$	−0.0462668	+	0.111698i	−0.00191290	+	0.00461814i
$586$	−1.36459	+	1.36459i	−0.0563706	+	0.0563706i
$587$	18.1277	−	18.1277i	0.748208	−	0.748208i	−0.225934	−	0.974143i	$-0.572543\pi$
$587$	18.1277	−	18.1277i	0.748208	−	0.748208i	0.974143	+	0.225934i	$0.0725435\pi$
$588$	−0.275517	+	0.665158i	−0.0113621	+	0.0274306i
$589$	6.99018	+	2.89543i	0.288025	+	0.119304i
$590$	−0.239408	−	0.577983i	−0.00985628	−	0.0237952i
$591$			13.3171i			0.547791i
$592$	−13.0707	+	5.41406i	−0.537202	+	0.222516i
$593$	11.0587	+	11.0587i	0.454128	+	0.454128i	0.896722	−	0.442594i	$-0.145942\pi$
$593$	11.0587	+	11.0587i	0.454128	+	0.454128i	−0.442594	+	0.896722i	$0.645942\pi$
$594$	−1.28570			−0.0527530
$595$	12.0549	−	0.145579i	0.494201	−	0.00596815i
$596$	−7.38847			−0.302643
$597$	−4.64919	−	4.64919i	−0.190279	−	0.190279i
$598$	0.0231138	−	0.00957403i	0.000945192	−	0.000391511i
$599$		−	24.4403i		−	0.998602i	−0.866429	−	0.499301i	$-0.833590\pi$
$599$		−	24.4403i		−	0.998602i	0.866429	−	0.499301i	$-0.166410\pi$
$600$	−0.680664	−	1.64327i	−0.0277880	−	0.0670862i
$601$	−24.0356	−	9.95587i	−0.980432	−	0.406108i	−0.165847	−	0.986152i	$-0.553036\pi$
$601$	−24.0356	−	9.95587i	−0.980432	−	0.406108i	−0.814586	+	0.580043i	$0.803036\pi$
$602$	0.0853082	−	0.205952i	0.00347690	−	0.00839399i
$603$	−1.64115	+	1.64115i	−0.0668327	+	0.0668327i
$604$	−11.3465	+	11.3465i	−0.461684	+	0.461684i
$605$	−1.71866	+	4.14920i	−0.0698733	+	0.168689i
$606$	−1.22071	−	0.505633i	−0.0495878	−	0.0205399i
$607$	12.1450	+	29.3207i	0.492952	+	1.19009i	0.953211	+	0.302306i	$0.0977565\pi$
$607$	12.1450	+	29.3207i	0.492952	+	1.19009i	−0.460259	+	0.887785i	$0.652243\pi$
$608$			3.38277i			0.137190i
$609$	−10.3094	+	4.27028i	−0.417757	+	0.173041i
$610$	0.369943	+	0.369943i	0.0149785	+	0.0149785i
$611$	−0.574344			−0.0232355
$612$	6.27250	+	6.12281i	0.253551	+	0.247500i
$613$	−27.3776			−1.10577			−0.552886	−	0.833257i	$-0.686473\pi$
$613$	−27.3776			−1.10577			−0.552886	+	0.833257i	$0.686473\pi$
$614$	−0.901788	−	0.901788i	−0.0363932	−	0.0363932i
$615$	12.0151	−	4.97680i	0.484494	−	0.200684i
$616$		−	2.35691i		−	0.0949625i
$617$	1.55335	+	3.75011i	0.0625354	+	0.150974i	0.952058	−	0.305917i	$-0.0989630\pi$
$617$	1.55335	+	3.75011i	0.0625354	+	0.150974i	−0.889523	+	0.456891i	$0.848963\pi$
$618$	1.61589	+	0.669322i	0.0650005	+	0.0269241i
$619$	−5.25717	+	12.6919i	−0.211304	+	0.510132i	−0.993624	−	0.112744i	$-0.964036\pi$
$619$	−5.25717	+	12.6919i	−0.211304	+	0.510132i	0.782320	+	0.622876i	$0.214036\pi$
$620$	−3.63921	+	3.63921i	−0.146154	+	0.146154i
$621$	11.5782	−	11.5782i	0.464619	−	0.464619i
$622$	−0.0545298	+	0.131646i	−0.00218644	+	0.00527854i
$623$	−31.4592	−	13.0308i	−1.26039	−	0.522069i
$624$	0.211775	+	0.511269i	0.00847778	+	0.0204672i
$625$		−	7.58234i		−	0.303293i
$626$	−1.51185	+	0.626228i	−0.0604256	+	0.0250291i
$627$	−8.58929	−	8.58929i	−0.343023	−	0.343023i
$628$	−20.7716			−0.828875
$629$	13.5543	−	5.80711i	0.540446	−	0.231545i
$630$	0.267861			0.0106718
$631$	−18.8503	−	18.8503i	−0.750417	−	0.750417i	0.224140	−	0.974557i	$-0.428043\pi$
$631$	−18.8503	−	18.8503i	−0.750417	−	0.750417i	−0.974557	+	0.224140i	$0.928043\pi$
$632$	−3.02487	+	1.25294i	−0.120323	+	0.0498394i
$633$		−	3.15331i		−	0.125333i
$634$	0.816253	+	1.97061i	0.0324175	+	0.0782628i
$635$	−15.4692	−	6.40754i	−0.613876	−	0.254276i
$636$	−10.2244	+	24.6838i	−0.405423	+	0.978778i
$637$	−0.0184889	+	0.0184889i	−0.000732559	+	0.000732559i
$638$	−0.497039	+	0.497039i	−0.0196779	+	0.0196779i
$639$	0.265463	−	0.640885i	0.0105016	−	0.0253530i
$640$	−2.83273	−	1.17336i	−0.111974	−	0.0463809i
$641$	−0.641589	−	1.54893i	−0.0253412	−	0.0611792i	0.910702	−	0.413063i	$-0.135541\pi$
$641$	−0.641589	−	1.54893i	−0.0253412	−	0.0611792i	−0.936044	+	0.351884i	$0.885541\pi$
$642$			0.552916i			0.0218219i
$643$	28.5075	−	11.8082i	1.12423	−	0.465670i	0.258412	−	0.966035i	$-0.416801\pi$
$643$	28.5075	−	11.8082i	1.12423	−	0.465670i	0.865815	+	0.500365i	$0.166801\pi$
$644$	10.5928	+	10.5928i	0.417416	+	0.417416i
$645$	1.56589			0.0616570
$646$	−0.0141045	−	1.16794i	−0.000554935	−	0.0459522i
$647$	−26.6585			−1.04805			−0.524027	−	0.851702i	$-0.675571\pi$
$647$	−26.6585			−1.04805			−0.524027	+	0.851702i	$0.675571\pi$
$648$	−1.12991	−	1.12991i	−0.0443869	−	0.0443869i
$649$	−15.8269	+	6.55571i	−0.621260	+	0.257334i
$650$		−	0.0322388i		−	0.00126451i
$651$	−3.16783	−	7.64781i	−0.124157	−	0.299741i
$652$	−22.3426	−	9.25462i	−0.875005	−	0.362439i
$653$	9.88428	−	23.8628i	0.386802	−	0.933822i	−0.603812	−	0.797127i	$-0.706352\pi$
$653$	9.88428	−	23.8628i	0.386802	−	0.933822i	0.990613	−	0.136695i	$-0.0436479\pi$
$654$	0.0238396	−	0.0238396i	0.000932204	−	0.000932204i
$655$	0.0824790	−	0.0824790i	0.00322272	−	0.00322272i
$656$	−12.5726	+	30.3529i	−0.490876	+	1.18508i
$657$	−5.52109	−	2.28691i	−0.215398	−	0.0892208i
$658$	0.486958	+	1.17562i	0.0189836	+	0.0458305i
$659$			34.3736i			1.33901i	0.742810	+	0.669503i	$0.233493\pi$
$659$			34.3736i			1.33901i	−0.742810	+	0.669503i	$0.766507\pi$
$660$	7.63372	−	3.16199i	0.297142	−	0.123080i
$661$	15.1375	+	15.1375i	0.588780	+	0.588780i	0.937301	−	0.348521i	$-0.113316\pi$
$661$	15.1375	+	15.1375i	0.588780	+	0.588780i	−0.348521	+	0.937301i	$0.613316\pi$
$662$	−2.39011			−0.0928943
$663$	−0.227149	−	0.530186i	−0.00882175	−	0.0205907i
$664$	−3.10233			−0.120394
$665$	6.82129	+	6.82129i	0.264518	+	0.264518i
$666$	0.302693	−	0.125380i	0.0117291	−	0.00485837i
$667$		−	8.95205i		−	0.346625i
$668$	−8.05588	−	19.4486i	−0.311692	−	0.752490i
$669$	−22.5761	−	9.35132i	−0.872842	−	0.361543i
$670$	−0.0805064	+	0.194360i	−0.00311023	+	0.00750877i
$671$	10.1301	−	10.1301i	0.391069	−	0.391069i
$672$	2.61702	−	2.61702i	0.100954	−	0.100954i
$673$	−0.283213	+	0.683736i	−0.0109170	+	0.0263561i	−0.929244	−	0.369466i	$-0.879540\pi$
$673$	−0.283213	+	0.683736i	−0.0109170	+	0.0263561i	0.918327	+	0.395823i	$0.129540\pi$
$674$	1.81020	+	0.749811i	0.0697265	+	0.0288817i
$675$	−8.07459	−	19.4938i	−0.310791	−	0.750317i
$676$		−	25.8840i		−	0.995538i
$677$	−13.9758	+	5.78895i	−0.537132	+	0.222487i	−0.634724	−	0.772739i	$-0.718886\pi$
$677$	−13.9758	+	5.78895i	−0.537132	+	0.222487i	0.0975916	+	0.995227i	$0.468886\pi$
$678$	−1.10454	−	1.10454i	−0.0424194	−	0.0424194i
$679$	−4.48544			−0.172135
$680$	1.47804	+	0.591416i	0.0566802	+	0.0226798i
$681$	−10.9177			−0.418368
$682$	−0.368719	−	0.368719i	−0.0141190	−	0.0141190i
$683$	−22.5343	+	9.33403i	−0.862252	+	0.357157i	−0.769588	−	0.638541i	$-0.779538\pi$
$683$	−22.5343	+	9.33403i	−0.862252	+	0.357157i	−0.0926644	+	0.995697i	$0.529538\pi$
$684$			7.01394i			0.268185i
$685$	4.30660	+	10.3970i	0.164547	+	0.397251i
$686$	1.49519	+	0.619327i	0.0570865	+	0.0236460i
$687$	11.2223	−	27.0931i	0.428159	−	1.03367i
$688$	−2.79719	+	2.79719i	−0.106642	+	0.106642i
$689$	−0.686120	+	0.686120i	−0.0261391	+	0.0261391i
$690$	0.149000	−	0.359718i	0.00567233	−	0.0136942i
$691$	−8.99732	−	3.72681i	−0.342274	−	0.141775i	0.204924	−	0.978778i	$-0.434305\pi$
$691$	−8.99732	−	3.72681i	−0.342274	−	0.141775i	−0.547198	+	0.837003i	$0.684305\pi$
$692$	8.34439	+	20.1451i	0.317206	+	0.765803i
$693$		−	7.33483i		−	0.278627i
$694$	−1.11733	+	0.462815i	−0.0424134	+	0.0175682i
$695$	5.37626	+	5.37626i	0.203933	+	0.203933i
$696$	−1.47353			−0.0558539
$697$	12.7213	−	31.7924i	0.481852	−	1.20422i
$698$	2.29992			0.0870533
$699$	−13.5002	−	13.5002i	−0.510623	−	0.510623i
$700$	17.8347	−	7.38738i	0.674088	−	0.279217i
$701$		−	39.9663i		−	1.50950i	−0.656010	−	0.754752i	$-0.727757\pi$
$701$		−	39.9663i		−	1.50950i	0.656010	−	0.754752i	$-0.272243\pi$
$702$	−0.0186947	−	0.0451330i	−0.000705586	−	0.00170344i
$703$	10.9012	+	4.51543i	0.411147	+	0.170303i
$704$	−7.92827	+	19.1405i	−0.298808	+	0.721387i
$705$	−6.32045	+	6.32045i	−0.238042	+	0.238042i
$706$	0.453489	−	0.453489i	0.0170673	−	0.0170673i
$707$	10.9958	−	26.5461i	0.413538	−	0.998370i
$708$	−16.5583	−	6.85868i	−0.622300	−	0.257765i
$709$	−8.28749	−	20.0078i	−0.311243	−	0.751408i	−0.999660	−	0.0260918i	$-0.991694\pi$
$709$	−8.28749	−	20.0078i	−0.311243	−	0.751408i	0.688416	−	0.725316i	$-0.258306\pi$
$710$		−	0.0628773i		−	0.00235974i
$711$	−9.41358	+	3.89923i	−0.353037	+	0.146233i
$712$	−3.17950	−	3.17950i	−0.119157	−	0.119157i
$713$	6.64091			0.248704
$714$	−0.892647	+	0.914470i	−0.0334065	+	0.0342232i
$715$	0.300081			0.0112224
$716$	21.2843	+	21.2843i	0.795432	+	0.795432i
$717$	13.7788	−	5.70736i	0.514578	−	0.213145i
$718$			0.893764i			0.0333550i
$719$	2.78835	+	6.73167i	0.103988	+	0.251049i	0.967306	−	0.253610i	$-0.0816181\pi$
$719$	2.78835	+	6.73167i	0.103988	+	0.251049i	−0.863319	+	0.504659i	$0.831618\pi$
$720$	−4.39147	−	1.81901i	−0.163661	−	0.0677904i
$721$	−14.5554	+	35.1399i	−0.542073	+	1.30868i
$722$	−0.492714	+	0.492714i	−0.0183369	+	0.0183369i
$723$	12.3165	−	12.3165i	0.458056	−	0.458056i
$724$	−9.77352	+	23.5954i	−0.363230	+	0.876915i
$725$	−10.6576	−	4.41454i	−0.395815	−	0.163952i
$726$	−0.182179	−	0.439819i	−0.00676129	−	0.0163232i
$727$			28.5890i			1.06031i	0.847902	+	0.530153i	$0.177866\pi$
$727$			28.5890i			1.06031i	−0.847902	+	0.530153i	$0.822134\pi$
$728$	0.0827364	−	0.0342705i	0.00306641	−	0.00127015i
$729$	−20.1936	−	20.1936i	−0.747910	−	0.747910i
$730$	−0.541674			−0.0200483
$731$	2.88006	−	2.95047i	0.106523	−	0.109127i
$732$	14.9882			0.553981
$733$	−30.3480	−	30.3480i	−1.12093	−	1.12093i	−0.991602	−	0.129329i	$-0.958718\pi$
$733$	−30.3480	−	30.3480i	−1.12093	−	1.12093i	−0.129329	−	0.991602i	$-0.541282\pi$
$734$	−2.70621	+	1.12095i	−0.0998881	+	0.0413750i
$735$			0.406929i			0.0150098i
$736$	1.13623	+	2.74311i	0.0418821	+	0.101112i
$737$	5.32215	+	2.20451i	0.196044	+	0.0812040i
$738$	0.291158	−	0.702917i	0.0107177	−	0.0258747i
$739$	−31.6336	+	31.6336i	−1.16366	+	1.16366i	−0.179991	+	0.983668i	$0.557607\pi$
$739$	−31.6336	+	31.6336i	−1.16366	+	1.16366i	−0.983668	+	0.179991i	$0.942393\pi$
$740$	−5.67536	+	5.67536i	−0.208630	+	0.208630i
$741$	0.176624	−	0.426409i	0.00648846	−	0.0156645i
$742$	1.98614	+	0.822687i	0.0729136	+	0.0302018i
$743$	2.11160	+	5.09786i	0.0774671	+	0.187022i	0.957869	−	0.287207i	$-0.0927268\pi$
$743$	2.11160	+	5.09786i	0.0774671	+	0.187022i	−0.880401	+	0.474229i	$0.842727\pi$
$744$		−	1.09311i		−	0.0400753i
$745$	−3.85815	+	1.59810i	−0.141351	+	0.0585497i
$746$	−1.70150	−	1.70150i	−0.0622965	−	0.0622965i
$747$	−9.65463			−0.353244
$748$	8.08241	−	20.1992i	0.295522	−	0.738555i
$749$	−12.0240			−0.439347
$750$	−0.830149	−	0.830149i	−0.0303128	−	0.0303128i
$751$	−17.7497	+	7.35218i	−0.647697	+	0.268285i	−0.682251	−	0.731118i	$-0.738999\pi$
$751$	−17.7497	+	7.35218i	−0.647697	+	0.268285i	0.0345539	+	0.999403i	$0.488999\pi$
$752$		−	22.5807i		−	0.823433i
$753$	0.666743	+	1.60966i	0.0242975	+	0.0586593i
$754$	−0.0246751	−	0.0102208i	−0.000898614	−	0.000372218i
$755$	−3.47078	+	8.37920i	−0.126314	+	0.304950i
$756$	20.6841	−	20.6841i	0.752272	−	0.752272i
$757$	13.3103	−	13.3103i	0.483770	−	0.483770i	−0.422563	−	0.906333i	$-0.638870\pi$
$757$	13.3103	−	13.3103i	0.483770	−	0.483770i	0.906333	+	0.422563i	$0.138870\pi$
$758$	−0.380446	+	0.918478i	−0.0138184	+	0.0333606i
$759$	−9.85014	−	4.08006i	−0.357537	−	0.148097i
$760$	0.487487	+	1.17690i	0.0176830	+	0.0426906i
$761$			4.27753i			0.155060i	0.996990	+	0.0775301i	$0.0247034\pi$
$761$			4.27753i			0.155060i	−0.996990	+	0.0775301i	$0.975297\pi$
$762$	1.63975	−	0.679205i	0.0594017	−	0.0246050i
$763$	0.518429	+	0.518429i	0.0187684	+	0.0187684i
$764$	−20.2612			−0.733025
$765$	4.59974	+	1.84052i	0.166304	+	0.0665442i
$766$	2.97933			0.107647
$767$	−0.460260	−	0.460260i	−0.0166190	−	0.0166190i
$768$	−19.7989	+	8.20099i	−0.714433	+	0.295928i
$769$			53.6321i			1.93402i	0.254732	+	0.967012i	$0.418013\pi$
$769$			53.6321i			1.93402i	−0.254732	+	0.967012i	$0.581987\pi$
$770$	−0.254424	−	0.614234i	−0.00916881	−	0.0221355i
$771$	−34.2872	−	14.2022i	−1.23483	−	0.511481i
$772$	10.7759	−	26.0154i	0.387835	−	0.936316i
$773$	−26.9939	+	26.9939i	−0.970904	+	0.970904i	−0.999589	−	0.0286843i	$-0.990868\pi$
$773$	−26.9939	+	26.9939i	−0.970904	+	0.970904i	0.0286843	+	0.999589i	$0.490868\pi$
$774$	0.0647777	−	0.0647777i	0.00232839	−	0.00232839i
$775$	3.27484	−	7.90617i	0.117636	−	0.283998i
$776$	−0.547220	−	0.226666i	−0.0196440	−	0.00813683i
$777$	−4.94024	−	11.9268i	−0.177230	−	0.427871i
$778$			2.36822i			0.0849048i
$779$	25.3149	−	10.4858i	0.907000	−	0.375692i
$780$	0.221996	+	0.221996i	0.00794872	+	0.00794872i
$781$	−1.72177			−0.0616096
$782$	−0.403736	−	0.942355i	−0.0144376	−	0.0336985i
$783$	−17.4802			−0.624691
$784$	−0.726904	−	0.726904i	−0.0259609	−	0.0259609i
$785$	−10.8466	+	4.49280i	−0.387131	+	0.160355i
$786$			0.0123642i			0.000441018i
$787$	13.7960	+	33.3066i	0.491775	+	1.18725i	0.953816	+	0.300392i	$0.0971175\pi$
$787$	13.7960	+	33.3066i	0.491775	+	1.18725i	−0.462041	+	0.886859i	$0.652883\pi$
$788$	−17.6328	−	7.30377i	−0.628144	−	0.260186i
$789$	4.61635	−	11.1448i	0.164346	−	0.396767i
$790$	−0.653060	+	0.653060i	−0.0232348	+	0.0232348i
$791$	24.0198	−	24.0198i	0.854046	−	0.854046i
$792$	0.370657	−	0.894844i	0.0131707	−	0.0317969i
$793$	0.502902	+	0.208309i	0.0178586	+	0.00739727i
$794$	−0.608174	−	1.46826i	−0.0215833	−	0.0521066i
$795$			15.1010i			0.535578i
$796$	8.70576	−	3.60604i	0.308567	−	0.127813i
$797$	−10.3975	−	10.3975i	−0.368299	−	0.368299i	0.498557	−	0.866857i	$-0.333863\pi$
$797$	−10.3975	−	10.3975i	−0.368299	−	0.368299i	−0.866857	+	0.498557i	$0.833863\pi$
$798$	−1.02256			−0.0361984
$799$	0.284204	+	23.5339i	0.0100544	+	0.832569i
$800$	3.82605			0.135271
$801$	−9.89480	−	9.89480i	−0.349615	−	0.349615i
$802$	1.48834	−	0.616491i	0.0525551	−	0.0217690i
$803$			14.8326i			0.523432i
$804$	2.30638	+	5.56811i	0.0813399	+	0.196372i
$805$	7.82261	+	3.24023i	0.275711	+	0.114203i
$806$	0.00758208	−	0.0183048i	0.000267067	−	0.000644758i
$807$	−10.1827	+	10.1827i	−0.358449	+	0.358449i
$808$	2.68295	−	2.68295i	0.0943858	−	0.0943858i
$809$	−11.5283	+	27.8317i	−0.405313	+	0.978512i	0.581041	+	0.813874i	$0.302646\pi$
$809$	−11.5283	+	27.8317i	−0.405313	+	0.978512i	−0.986354	+	0.164638i	$0.947354\pi$
$810$	−0.416437	−	0.172494i	−0.0146321	−	0.00606081i
$811$	−0.217067	−	0.524046i	−0.00762225	−	0.0184018i	0.920023	−	0.391865i	$-0.128170\pi$
$811$	−0.217067	−	0.524046i	−0.00762225	−	0.0184018i	−0.927645	+	0.373464i	$0.878170\pi$
$812$		−	15.9925i		−	0.561226i
$813$	−13.8541	+	5.73855i	−0.485884	+	0.201260i
$814$	−0.575018	−	0.575018i	−0.0201544	−	0.0201544i
$815$	−13.6687			−0.478794
$816$	20.8446	−	8.93052i	0.729707	−	0.312631i
$817$	3.29923			0.115425
$818$	1.57392	+	1.57392i	0.0550308	+	0.0550308i
$819$	0.257480	−	0.106652i	0.00899709	−	0.00372672i
$820$			18.6384i			0.650882i
$821$	−14.6956	−	35.4783i	−0.512880	−	1.23820i	−0.942201	−	0.335049i	$-0.891247\pi$
$821$	−14.6956	−	35.4783i	−0.512880	−	1.23820i	0.429321	−	0.903152i	$-0.358753\pi$
$822$	−1.10210	−	0.456503i	−0.0384400	−	0.0159224i
$823$	−1.73437	+	4.18714i	−0.0604563	+	0.145954i	−0.951221	−	0.308510i	$-0.900170\pi$
$823$	−1.73437	+	4.18714i	−0.0604563	+	0.145954i	0.890765	+	0.454465i	$0.150170\pi$
$824$	−3.55150	+	3.55150i	−0.123722	+	0.123722i
$825$	−9.71483	+	9.71483i	−0.338227	+	0.338227i
$826$	−0.551872	+	1.33234i	−0.0192021	+	0.0463579i
$827$	−39.2643	−	16.2638i	−1.36535	−	0.565548i	−0.424830	−	0.905273i	$-0.639666\pi$
$827$	−39.2643	−	16.2638i	−1.36535	−	0.565548i	−0.940525	+	0.339725i	$0.889666\pi$
$828$	2.35590	+	5.68764i	0.0818731	+	0.197659i
$829$		−	23.1975i		−	0.805683i	−0.915270	−	0.402841i	$-0.868023\pi$
$829$		−	23.1975i		−	0.805683i	0.915270	−	0.402841i	$-0.131977\pi$
$830$	−0.808499	+	0.334891i	−0.0280634	+	0.0116242i
$831$	26.8115	+	26.8115i	0.930082	+	0.930082i
$832$	−0.787186			−0.0272908
$833$	0.766738	+	0.748440i	0.0265659	+	0.0259319i
$834$	−0.805944			−0.0279076
$835$	−8.41332	−	8.41332i	−0.291155	−	0.291155i
$836$	16.0837	−	6.66210i	0.556267	−	0.230413i
$837$		−	12.9673i		−	0.448217i
$838$	−0.198839	−	0.480039i	−0.00686877	−	0.0165827i
$839$	4.71856	+	1.95449i	0.162903	+	0.0674765i	0.462645	−	0.886544i	$-0.346901\pi$
$839$	4.71856	+	1.95449i	0.162903	+	0.0674765i	−0.299742	+	0.954020i	$0.596901\pi$
$840$	0.533349	−	1.28762i	0.0184023	−	0.0444271i
$841$	13.7484	−	13.7484i	0.474084	−	0.474084i
$842$	−0.0411918	+	0.0411918i	−0.00141956	+	0.00141956i
$843$	12.1494	−	29.3313i	0.418448	−	1.01022i
$844$	4.17523	+	1.72944i	0.143717	+	0.0595297i
$845$	−5.59860	−	13.5162i	−0.192598	−	0.464972i
$846$			0.522927i			0.0179786i
$847$	9.56453	−	3.96176i	0.328641	−	0.136128i
$848$	−26.9752	−	26.9752i	−0.926333	−	0.926333i
$849$	3.39218			0.116419
$850$	−1.32099	+	0.0159528i	−0.0453097	+	0.000547176i
$851$	10.3565			0.355017
$852$	−1.27374	−	1.27374i	−0.0436375	−	0.0436375i
$853$	−36.9974	+	15.3248i	−1.26677	+	0.524713i	−0.911980	−	0.410234i	$-0.865447\pi$
$853$	−36.9974	+	15.3248i	−1.26677	+	0.524713i	−0.354788	+	0.934947i	$0.615447\pi$
$854$		−	1.20600i		−	0.0412686i
$855$	1.51709	+	3.66257i	0.0518833	+	0.125257i
$856$	−1.46692	−	0.607618i	−0.0501382	−	0.0207679i
$857$	18.1109	−	43.7237i	0.618658	−	1.49357i	−0.234605	−	0.972091i	$-0.575380\pi$
$857$	18.1109	−	43.7237i	0.618658	−	1.49357i	0.853263	−	0.521481i	$-0.174620\pi$
$858$	−0.0224923	+	0.0224923i	−0.000767873	+	0.000767873i
$859$	8.67075	−	8.67075i	0.295842	−	0.295842i	−0.543541	−	0.839383i	$-0.682917\pi$
$859$	8.67075	−	8.67075i	0.295842	−	0.295842i	0.839383	+	0.543541i	$0.182917\pi$
$860$	−0.858817	+	2.07337i	−0.0292854	+	0.0707013i
$861$	−27.6965	−	11.4723i	−0.943894	−	0.390974i
$862$	−0.386555	−	0.933226i	−0.0131661	−	0.0317858i
$863$			36.7117i			1.24968i	0.780753	+	0.624840i	$0.214836\pi$
$863$			36.7117i			1.24968i	−0.780753	+	0.624840i	$0.785164\pi$
$864$	5.35632	−	2.21866i	0.182226	−	0.0754803i
$865$	8.71463	+	8.71463i	0.296306	+	0.296306i
$866$	−0.0790945			−0.00268774
$867$	−21.6121	+	9.56986i	−0.733986	+	0.325009i
$868$	11.8637			0.402681
$869$	17.8827	+	17.8827i	0.606630	+	0.606630i
$870$	−0.384017	+	0.159065i	−0.0130194	+	0.00539281i
$871$			0.218882i			0.00741653i
$872$	0.0370498	+	0.0894462i	0.00125466	+	0.00302903i
$873$	−1.70298	−	0.705397i	−0.0576371	−	0.0238741i
$874$	0.313933	−	0.757900i	0.0106189	−	0.0256364i
$875$	18.0529	−	18.0529i	0.610298	−	0.610298i
$876$	−10.9730	+	10.9730i	−0.370742	+	0.370742i
$877$	9.05747	−	21.8667i	0.305849	−	0.738385i	−0.693982	−	0.719993i	$-0.744145\pi$
$877$	9.05747	−	21.8667i	0.305849	−	0.738385i	0.999831	−	0.0183925i	$-0.00585484\pi$
$878$	−0.700993	−	0.290361i	−0.0236574	−	0.00979920i
$879$	11.9582	+	28.8697i	0.403340	+	0.973750i
$880$			11.7979i			0.397706i
$881$	48.9003	−	20.2552i	1.64749	−	0.682415i	0.650472	−	0.759530i	$-0.274571\pi$
$881$	48.9003	−	20.2552i	1.64749	−	0.682415i	0.997022	+	0.0771153i	$0.0245710\pi$
$882$	0.0168338	+	0.0168338i	0.000566823	+	0.000566823i
$883$	26.9205			0.905948			0.452974	−	0.891524i	$-0.350363\pi$
$883$	26.9205			0.905948			0.452974	+	0.891524i	$0.350363\pi$
$884$	0.826590	−	0.00998219i	0.0278012	−	0.000335737i
$885$	−10.1300			−0.340516
$886$	0.283479	+	0.283479i	0.00952367	+	0.00952367i
$887$	1.71598	−	0.710783i	0.0576171	−	0.0238658i	−0.353689	−	0.935363i	$-0.615073\pi$
$887$	1.71598	−	0.710783i	0.0576171	−	0.0238658i	0.411306	+	0.911497i	$0.365073\pi$
$888$		−	1.70471i		−	0.0572063i
$889$	14.7703	+	35.6588i	0.495382	+	1.19596i
$890$	−1.17183	−	0.485389i	−0.0392799	−	0.0162703i
$891$	−4.72339	+	11.4033i	−0.158240	+	0.382024i
$892$	24.7638	−	24.7638i	0.829153	−	0.829153i
$893$	−13.3168	+	13.3168i	−0.445628	+	0.445628i
$894$	0.169399	−	0.408967i	0.00566557	−	0.0136779i
$895$	15.7181	+	6.51063i	0.525397	+	0.217627i
$896$	2.70476	+	6.52987i	0.0903597	+	0.218148i
$897$		−	0.405103i		−	0.0135260i
$898$	−1.66025	+	0.687699i	−0.0554033	+	0.0229488i
$899$	−5.01304	−	5.01304i	−0.167194	−	0.167194i
$900$	7.93305			0.264435
$901$	28.4535	+	27.7744i	0.947922	+	0.925300i
$902$	−1.88842			−0.0628774
$903$	−2.55239	−	2.55239i	−0.0849381	−	0.0849381i
$904$	4.14421	−	1.71659i	0.137834	−	0.0570929i
$905$			14.4351i			0.479840i
$906$	−0.367905	−	0.888202i	−0.0122228	−	0.0295085i
$907$	54.1979	+	22.4495i	1.79961	+	0.745423i	0.986596	+	0.163179i	$0.0521748\pi$
$907$	54.1979	+	22.4495i	1.79961	+	0.745423i	0.813014	+	0.582244i	$0.197825\pi$
$908$	5.98785	−	14.4559i	0.198714	−	0.479738i
$909$	8.34950	−	8.34950i	0.276935	−	0.276935i
$910$	0.0178625	−	0.0178625i	0.000592136	−	0.000592136i
$911$	−16.9894	+	41.0161i	−0.562884	+	1.35892i	0.344566	+	0.938762i	$0.388026\pi$
$911$	−16.9894	+	41.0161i	−0.562884	+	1.35892i	−0.907450	+	0.420160i	$0.861974\pi$
$912$	16.7645	+	6.94409i	0.555129	+	0.229942i
$913$	9.17032	+	22.1391i	0.303493	+	0.732697i
$914$			1.77708i			0.0587804i
$915$	7.82663	−	3.24190i	0.258740	−	0.107174i
$916$	29.7185	+	29.7185i	0.981928	+	0.981928i
$917$	−0.268879			−0.00887917
$918$	−1.84009	+	0.788353i	−0.0607319	+	0.0260195i
$919$	−4.90420			−0.161775			−0.0808873	−	0.996723i	$-0.525775\pi$
$919$	−4.90420			−0.161775			−0.0808873	+	0.996723i	$0.525775\pi$
$920$	0.790611	+	0.790611i	0.0260657	+	0.0260657i
$921$	−19.0785	+	7.90259i	−0.628659	+	0.260399i
$922$		−	1.40752i		−	0.0463542i
$923$	−0.0250353	−	0.0604405i	−0.000824046	−	0.00198942i
$924$	−17.5969	−	7.28886i	−0.578894	−	0.239786i
$925$	5.10713	−	12.3297i	0.167922	−	0.405398i
$926$	−0.227755	+	0.227755i	−0.00748449	+	0.00748449i
$927$	−11.0525	+	11.0525i	−0.363011	+	0.363011i
$928$	1.21299	−	2.92840i	0.0398182	−	0.0961296i
$929$	40.0797	+	16.6015i	1.31497	+	0.544679i	0.926331	−	0.376710i	$-0.122945\pi$
$929$	40.0797	+	16.6015i	1.31497	+	0.544679i	0.388641	+	0.921389i	$0.372945\pi$
$930$	−0.117999	−	0.284876i	−0.00386935	−	0.00934144i
$931$			0.857371i			0.0280992i
$932$	25.2795	−	10.4711i	0.828057	−	0.342992i
$933$	1.63151	+	1.63151i	0.0534132	+	0.0534132i
$934$	2.12974			0.0696871
$935$	−0.148490	−	12.2959i	−0.00485613	−	0.402119i
$936$	0.0368019			0.00120291
$937$	26.7269	+	26.7269i	0.873128	+	0.873128i	0.992812	−	0.119684i	$-0.0381881\pi$
$937$	26.7269	+	26.7269i	0.873128	+	0.873128i	−0.119684	+	0.992812i	$0.538188\pi$
$938$	0.448028	−	0.185579i	0.0146286	−	0.00605938i
$939$			26.4974i			0.864709i
$940$	−4.90232	−	11.8352i	−0.159896	−	0.386023i
$941$	−14.3672	−	5.95108i	−0.468356	−	0.194000i	0.136008	−	0.990708i	$-0.456573\pi$
$941$	−14.3672	−	5.95108i	−0.468356	−	0.194000i	−0.604364	+	0.796708i	$0.706573\pi$
$942$	0.476241	−	1.14975i	0.0155168	−	0.0374608i
$943$	17.0059	−	17.0059i	0.553789	−	0.553789i
$944$	18.0954	−	18.0954i	0.588956	−	0.588956i
$945$	6.32702	−	15.2748i	0.205818	−	0.496889i
$946$	−0.210070	−	0.0870140i	−0.00682998	−	0.00282907i
$947$	−9.36045	−	22.5981i	−0.304174	−	0.734341i	−0.999872	−	0.0160062i	$-0.994905\pi$
$947$	−9.36045	−	22.5981i	−0.304174	−	0.734341i	0.695698	−	0.718334i	$-0.255095\pi$
$948$			26.4588i			0.859340i
$949$	−0.520682	+	0.215673i	−0.0169020	+	0.00700105i
$950$	−0.747489	−	0.747489i	−0.0242518	−	0.0242518i
$951$	34.5378			1.11997
$952$	−1.44518	−	3.37319i	−0.0468387	−	0.109326i
$953$	6.33856			0.205326			0.102663	−	0.994716i	$-0.467264\pi$
$953$	6.33856			0.205326			0.102663	+	0.994716i	$0.467264\pi$
$954$	0.624697	+	0.624697i	0.0202253	+	0.0202253i
$955$	−10.5801	+	4.38242i	−0.342364	+	0.141812i
$956$			21.3744i			0.691298i
$957$	4.35567	+	10.5155i	0.140799	+	0.339918i
$958$	0.791635	+	0.327906i	0.0255766	+	0.0105942i
$959$	9.92735	−	23.9667i	0.320571	−	0.773926i
$960$	−8.66271	+	8.66271i	−0.279588	+	0.279588i
$961$	−18.2015	+	18.2015i	−0.587145	+	0.587145i
$962$	0.0118243	−	0.0285464i	0.000381230	−	0.000920371i
$963$	−4.56514	−	1.89094i	−0.147109	−	0.0609347i
$964$	9.55302	+	23.0630i	0.307682	+	0.742811i
$965$		−	15.9157i		−	0.512343i
$966$	−0.829203	+	0.343467i	−0.0266792	+	0.0110509i
$967$	0.157051	+	0.157051i	0.00505042	+	0.00505042i	0.709627	−	0.704577i	$-0.248863\pi$
$967$	0.157051	+	0.157051i	0.00505042	+	0.00505042i	−0.704577	+	0.709627i	$0.748863\pi$
$968$	1.36707			0.0439392
$969$	−17.5596	−	7.02623i	−0.564096	−	0.225715i
$970$	−0.167079			−0.00536459
$971$	14.6011	+	14.6011i	0.468573	+	0.468573i	0.901452	−	0.432879i	$-0.142502\pi$
$971$	14.6011	+	14.6011i	0.468573	+	0.468573i	−0.432879	+	0.901452i	$0.642502\pi$
$972$	19.2984	−	7.99365i	0.618996	−	0.256397i
$973$		−	17.5265i		−	0.561873i
$974$	0.951350	+	2.29676i	0.0304832	+	0.0735930i
$975$	−0.482285	−	0.199769i	−0.0154455	−	0.00639773i
$976$	−8.18980	+	19.7719i	−0.262149	+	0.632884i
$977$	16.4443	−	16.4443i	0.526100	−	0.526100i	−0.393307	−	0.919407i	$-0.628669\pi$
$977$	16.4443	−	16.4443i	0.526100	−	0.526100i	0.919407	+	0.393307i	$0.128669\pi$
$978$	1.02452	−	1.02452i	0.0327607	−	0.0327607i
$979$	−13.2914	+	32.0883i	−0.424795	+	1.02555i
$980$	−0.538806	−	0.223181i	−0.0172115	−	0.00712925i
$981$	0.115301	+	0.278362i	0.00368128	+	0.00888740i
$982$		−	1.54017i		−	0.0491488i
$983$	−50.3519	+	20.8564i	−1.60598	+	0.665217i	−0.992245	−	0.124297i	$-0.960332\pi$
$983$	−50.3519	+	20.8564i	−1.60598	+	0.665217i	−0.613732	+	0.789515i	$0.710332\pi$
$984$	−2.79921	−	2.79921i	−0.0892357	−	0.0892357i
$985$	−10.7874			−0.343715
$986$	−0.406588	+	1.01613i	−0.0129484	+	0.0323600i
$987$	20.6045			0.655849
$988$	0.467729	+	0.467729i	0.0148805	+	0.0148805i
$989$	2.67536	−	1.10817i	0.0850715	−	0.0352378i
$990$		−	0.273217i		−	0.00868342i
$991$	3.76667	+	9.09354i	0.119652	+	0.288866i	0.972346	−	0.233545i	$-0.0750327\pi$
$991$	3.76667	+	9.09354i	0.119652	+	0.288866i	−0.852694	+	0.522411i	$0.825033\pi$
$992$	2.17238	+	0.899830i	0.0689732	+	0.0285696i
$993$	−14.8104	+	35.7556i	−0.469995	+	1.13467i
$994$	−0.102489	+	0.102489i	−0.00325076	+	0.00325076i
$995$	3.76604	−	3.76604i	0.119392	−	0.119392i
$996$	−9.59412	+	23.1622i	−0.304001	+	0.733924i
$997$	−8.46587	−	3.50668i	−0.268117	−	0.111058i	0.244575	−	0.969630i	$-0.421352\pi$
$997$	−8.46587	−	3.50668i	−0.268117	−	0.111058i	−0.512692	+	0.858573i	$0.671352\pi$
$998$	0.589984	+	1.42435i	0.0186756	+	0.0450869i
$999$		−	20.2226i		−	0.639816i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.b.87.15	✓	116
17.9	even	8	inner	731.2.m.b.689.15	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.b.87.15	✓	116	1.1	even	1	trivial
731.2.m.b.689.15	yes	116	17.9	even	8	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0607158 - 0.0607158i) q^{2} +(-1.28452 + 0.532068i) q^{3} -1.99263i q^{4} +(-0.430997 - 1.04052i) q^{5} +(0.110296 + 0.0456861i) q^{6} +(-0.993514 + 2.39855i) q^{7} +(-0.242416 + 0.242416i) q^{8} +(-0.754412 + 0.754412i) q^{9} +O(q^{10})\)	\(q+(-0.0607158 - 0.0607158i) q^{2} +(-1.28452 + 0.532068i) q^{3} -1.99263i q^{4} +(-0.430997 - 1.04052i) q^{5} +(0.110296 + 0.0456861i) q^{6} +(-0.993514 + 2.39855i) q^{7} +(-0.242416 + 0.242416i) q^{8} +(-0.754412 + 0.754412i) q^{9} +(-0.0370077 + 0.0893444i) q^{10} +(2.44652 + 1.01338i) q^{11} +(1.06021 + 2.55958i) q^{12} +0.100617i q^{13} +(0.205952 - 0.0853082i) q^{14} +(1.10725 + 1.10725i) q^{15} -3.95582 q^{16} +(4.12281 - 0.0497885i) q^{17} +0.0916095 q^{18} +(2.33291 + 2.33291i) q^{19} +(-2.07337 + 0.858817i) q^{20} -3.60962i q^{21} +(-0.0870140 - 0.210070i) q^{22} +(2.67536 + 1.10817i) q^{23} +(0.182407 - 0.440371i) q^{24} +(2.63861 - 2.63861i) q^{25} +(0.00610904 - 0.00610904i) q^{26} +(2.16387 - 5.22403i) q^{27} +(4.77942 + 1.97970i) q^{28} +(-1.18303 - 2.85608i) q^{29} -0.134456i q^{30} +(2.11873 - 0.877607i) q^{31} +(0.725012 + 0.725012i) q^{32} -3.68180 q^{33} +(-0.253343 - 0.247297i) q^{34} +2.92394 q^{35} +(1.50326 + 1.50326i) q^{36} +(3.30417 - 1.36863i) q^{37} -0.283289i q^{38} +(-0.0535350 - 0.129245i) q^{39} +(0.356719 + 0.147758i) q^{40} +(3.17825 - 7.67297i) q^{41} +(-0.219161 + 0.219161i) q^{42} +(0.707107 - 0.707107i) q^{43} +(2.01929 - 4.87499i) q^{44} +(1.11013 + 0.459831i) q^{45} +(-0.0951533 - 0.229720i) q^{46} +5.70822i q^{47} +(5.08135 - 2.10476i) q^{48} +(0.183756 + 0.183756i) q^{49} -0.320411 q^{50} +(-5.26936 + 2.25757i) q^{51} +0.200492 q^{52} +(6.81913 + 6.81913i) q^{53} +(-0.448563 + 0.185801i) q^{54} -2.98241i q^{55} +(-0.340604 - 0.822291i) q^{56} +(-4.23794 - 1.75541i) q^{57} +(-0.101581 + 0.245238i) q^{58} +(-4.57438 + 4.57438i) q^{59} +(2.20634 - 2.20634i) q^{60} +(2.07032 - 4.99819i) q^{61} +(-0.181925 - 0.0753559i) q^{62} +(-1.05998 - 2.55902i) q^{63} +7.82360i q^{64} +(0.104694 - 0.0433656i) q^{65} +(0.223543 + 0.223543i) q^{66} +2.17540 q^{67} +(-0.0992098 - 8.21521i) q^{68} -4.02619 q^{69} +(-0.177530 - 0.177530i) q^{70} +(-0.600699 + 0.248818i) q^{71} -0.365763i q^{72} +(2.14351 + 5.17489i) q^{73} +(-0.283713 - 0.117518i) q^{74} +(-1.98544 + 4.79328i) q^{75} +(4.64861 - 4.64861i) q^{76} +(-4.86129 + 4.86129i) q^{77} +(-0.00459679 + 0.0110976i) q^{78} +(8.82331 + 3.65473i) q^{79} +(1.70495 + 4.11611i) q^{80} +4.66103i q^{81} +(-0.658841 + 0.272901i) q^{82} +(6.39878 + 6.39878i) q^{83} -7.19262 q^{84} +(-1.82872 - 4.26840i) q^{85} -0.0858652 q^{86} +(3.03926 + 3.03926i) q^{87} +(-0.838733 + 0.347415i) q^{88} +13.1159i q^{89} +(-0.0394835 - 0.0953215i) q^{90} +(-0.241335 - 0.0999643i) q^{91} +(2.20817 - 5.33100i) q^{92} +(-2.25462 + 2.25462i) q^{93} +(0.346579 - 0.346579i) q^{94} +(1.42196 - 3.43291i) q^{95} +(-1.31705 - 0.545541i) q^{96} +(0.661166 + 1.59619i) q^{97} -0.0223138i q^{98} +(-2.61019 + 1.08117i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 8 q^{6}+O(q^{10}) \) 116 * q - 8 * q^6	\( 116 q - 8 q^{6} - 8 q^{10} + 8 q^{14} + 4 q^{15} - 68 q^{16} - 4 q^{17} - 44 q^{18} + 12 q^{19} + 8 q^{20} - 16 q^{22} - 28 q^{23} - 12 q^{24} - 4 q^{25} - 8 q^{26} + 24 q^{28} + 80 q^{33} + 32 q^{34} - 112 q^{35} + 160 q^{36} - 20 q^{37} + 8 q^{39} - 112 q^{40} + 8 q^{41} + 4 q^{42} + 32 q^{44} - 52 q^{45} - 40 q^{46} + 40 q^{48} + 8 q^{49} + 100 q^{50} - 32 q^{51} - 152 q^{52} + 28 q^{53} - 36 q^{54} + 124 q^{56} - 104 q^{57} - 32 q^{58} - 36 q^{59} - 24 q^{60} + 52 q^{61} - 68 q^{62} + 20 q^{63} + 20 q^{65} - 60 q^{66} + 64 q^{67} - 128 q^{69} + 188 q^{70} + 52 q^{73} - 104 q^{74} + 36 q^{75} - 112 q^{76} + 28 q^{77} + 56 q^{78} - 108 q^{79} - 44 q^{80} + 52 q^{82} - 52 q^{83} + 120 q^{84} + 12 q^{85} - 20 q^{86} + 56 q^{87} + 36 q^{88} + 144 q^{90} - 16 q^{92} - 176 q^{93} - 8 q^{94} + 164 q^{95} - 164 q^{96} - 8 q^{97} - 24 q^{99}+O(q^{100}) \) 116 * q - 8 * q^6 - 8 * q^10 + 8 * q^14 + 4 * q^15 - 68 * q^16 - 4 * q^17 - 44 * q^18 + 12 * q^19 + 8 * q^20 - 16 * q^22 - 28 * q^23 - 12 * q^24 - 4 * q^25 - 8 * q^26 + 24 * q^28 + 80 * q^33 + 32 * q^34 - 112 * q^35 + 160 * q^36 - 20 * q^37 + 8 * q^39 - 112 * q^40 + 8 * q^41 + 4 * q^42 + 32 * q^44 - 52 * q^45 - 40 * q^46 + 40 * q^48 + 8 * q^49 + 100 * q^50 - 32 * q^51 - 152 * q^52 + 28 * q^53 - 36 * q^54 + 124 * q^56 - 104 * q^57 - 32 * q^58 - 36 * q^59 - 24 * q^60 + 52 * q^61 - 68 * q^62 + 20 * q^63 + 20 * q^65 - 60 * q^66 + 64 * q^67 - 128 * q^69 + 188 * q^70 + 52 * q^73 - 104 * q^74 + 36 * q^75 - 112 * q^76 + 28 * q^77 + 56 * q^78 - 108 * q^79 - 44 * q^80 + 52 * q^82 - 52 * q^83 + 120 * q^84 + 12 * q^85 - 20 * q^86 + 56 * q^87 + 36 * q^88 + 144 * q^90 - 16 * q^92 - 176 * q^93 - 8 * q^94 + 164 * q^95 - 164 * q^96 - 8 * q^97 - 24 * q^99

Introduction

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