LMFDB - Embedded newform 525.2.bg.a.16.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(16,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 10]))

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

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

chi := DirichletCharacter("525.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bg (of order $15$, degree $8$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.11
Character	$\chi$	$=$	525.16
Dual form			525.2.bg.a.361.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104767 - 0.0466452i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-1.32946 + 1.47652i) q^{4} +(0.449213 + 2.19048i) q^{5} +(-0.0354385 + 0.109069i) q^{6} +(2.46049 + 0.972613i) q^{7} +(-0.141288 + 0.434840i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(0.104767 - 0.0466452i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-1.32946 + 1.47652i) q^{4} +(0.449213 + 2.19048i) q^{5} +(-0.0354385 + 0.109069i) q^{6} +(2.46049 + 0.972613i) q^{7} +(-0.141288 + 0.434840i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(0.149238 + 0.208536i) q^{10} +(-0.223328 + 2.12482i) q^{11} +(-0.207682 - 1.97596i) q^{12} +(-1.25719 + 0.913401i) q^{13} +(0.303145 - 0.0128726i) q^{14} +(-1.92843 - 1.13189i) q^{15} +(-0.409883 - 3.89978i) q^{16} +(1.07414 - 0.228316i) q^{17} +(-0.0573407 - 0.0993171i) q^{18} +(-0.991165 - 1.10080i) q^{19} +(-3.83149 - 2.24889i) q^{20} +(-2.36918 + 1.17770i) q^{21} +(0.0757153 + 0.233028i) q^{22} +(-2.57143 + 1.14487i) q^{23} +(-0.228609 - 0.395962i) q^{24} +(-4.59642 + 1.96799i) q^{25} +(-0.0891058 + 0.154336i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-4.70721 + 2.33991i) q^{28} +(0.663276 + 2.04135i) q^{29} +(-0.254832 - 0.0286324i) q^{30} +(1.50530 - 0.319961i) q^{31} +(-0.682066 - 1.18137i) q^{32} +(-1.42961 - 1.58775i) q^{33} +(0.101885 - 0.0740235i) q^{34} +(-1.02521 + 5.82657i) q^{35} +(1.60739 + 1.16784i) q^{36} +(-0.421182 - 4.00728i) q^{37} +(-0.155188 - 0.0690942i) q^{38} +(0.162434 - 1.54546i) q^{39} +(-1.01598 - 0.114153i) q^{40} +(-5.26454 + 3.82491i) q^{41} +(-0.193278 + 0.233894i) q^{42} -9.54777 q^{43} +(-2.84043 - 3.15461i) q^{44} +(2.13153 - 0.675720i) q^{45} +(-0.215997 + 0.239889i) q^{46} +(2.72406 + 0.579016i) q^{47} +(3.17237 + 2.30486i) q^{48} +(5.10805 + 4.78621i) q^{49} +(-0.389754 + 0.420580i) q^{50} +(-0.549070 + 0.951017i) q^{51} +(0.322732 - 3.07059i) q^{52} +(-1.77574 + 1.97216i) q^{53} +(0.112175 + 0.0238436i) q^{54} +(-4.75470 + 0.465302i) q^{55} +(-0.770569 + 0.932502i) q^{56} +1.48127 q^{57} +(0.164708 + 0.182927i) q^{58} +(8.11603 + 3.61349i) q^{59} +(4.23502 - 1.34255i) q^{60} +(6.30166 - 2.80568i) q^{61} +(0.142781 - 0.103736i) q^{62} +(0.710093 - 2.54868i) q^{63} +(6.21817 + 4.51777i) q^{64} +(-2.56553 - 2.34354i) q^{65} +(-0.223837 - 0.0996586i) q^{66} +(13.6827 - 2.90835i) q^{67} +(-1.09092 + 1.88953i) q^{68} +(0.869814 - 2.67701i) q^{69} +(0.164374 + 0.658252i) q^{70} +(3.60505 + 11.0952i) q^{71} +(0.447226 + 0.0950609i) q^{72} +(1.18042 - 11.2310i) q^{73} +(-0.231046 - 0.400184i) q^{74} +(1.61310 - 4.73264i) q^{75} +2.94306 q^{76} +(-2.61612 + 5.01090i) q^{77} +(-0.0550704 - 0.169489i) q^{78} +(-4.37468 - 0.929867i) q^{79} +(8.35827 - 2.64967i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-0.373135 + 0.646289i) q^{82} +(-0.0653066 + 0.200993i) q^{83} +(1.41085 - 5.06384i) q^{84} +(0.982641 + 2.25033i) q^{85} +(-1.00029 + 0.445357i) q^{86} +(-1.96084 - 0.873022i) q^{87} +(-0.892403 - 0.397324i) q^{88} +(5.70768 - 2.54123i) q^{89} +(0.191794 - 0.170218i) q^{90} +(-3.98169 + 1.02466i) q^{91} +(1.72819 - 5.31881i) q^{92} +(-0.769464 + 1.33275i) q^{93} +(0.312399 - 0.0664024i) q^{94} +(1.96604 - 2.66562i) q^{95} +(1.33432 + 0.283619i) q^{96} +(-5.03322 - 15.4907i) q^{97} +(0.758407 + 0.263170i) q^{98} +2.13653 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) $ 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.104767	−	0.0466452i	0.0740813	−	0.0329831i	−0.369362	−	0.929286i	$-0.620424\pi$
$2$	0.104767	−	0.0466452i	0.0740813	−	0.0329831i	0.443443	+	0.896303i	$0.353757\pi$
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$4$	−1.32946	+	1.47652i	−0.664730	+	0.738258i
$5$	0.449213	+	2.19048i	0.200894	+	0.979613i
$5$	0.449213	+	2.19048i	0.200894	+	0.979613i
$6$	−0.0354385	+	0.109069i	−0.0144677	+	0.0445271i
$7$	2.46049	+	0.972613i	0.929979	+	0.367613i
$7$	2.46049	+	0.972613i	0.929979	+	0.367613i
$8$	−0.141288	+	0.434840i	−0.0499529	+	0.153739i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	0.149238	+	0.208536i	0.0471932	+	0.0659449i
$11$	−0.223328	+	2.12482i	−0.0673358	+	0.640658i	0.907854	+	0.419287i	$0.137720\pi$
$11$	−0.223328	+	2.12482i	−0.0673358	+	0.640658i	−0.975190	+	0.221371i	$0.928947\pi$
$12$	−0.207682	−	1.97596i	−0.0599527	−	0.570412i
$13$	−1.25719	+	0.913401i	−0.348681	+	0.253332i	−0.748316	−	0.663343i	$-0.769137\pi$
$13$	−1.25719	+	0.913401i	−0.348681	+	0.253332i	0.399634	+	0.916675i	$0.369137\pi$
$14$	0.303145	−	0.0128726i	0.0810190	−	0.00344034i
$15$	−1.92843	−	1.13189i	−0.497918	−	0.292252i
$16$	−0.409883	−	3.89978i	−0.102471	−	0.974945i
$17$	1.07414	−	0.228316i	0.260518	−	0.0553748i	−0.0758010	−	0.997123i	$-0.524151\pi$
$17$	1.07414	−	0.228316i	0.260518	−	0.0553748i	0.336319	+	0.941748i	$0.390818\pi$
$18$	−0.0573407	−	0.0993171i	−0.0135153	−	0.0234093i
$19$	−0.991165	−	1.10080i	−0.227389	−	0.252541i	0.618644	−	0.785671i	$-0.287682\pi$
$19$	−0.991165	−	1.10080i	−0.227389	−	0.252541i	−0.846033	+	0.533130i	$0.821016\pi$
$20$	−3.83149	−	2.24889i	−0.856748	−	0.502867i
$21$	−2.36918	+	1.17770i	−0.516998	+	0.256995i
$22$	0.0757153	+	0.233028i	0.0161426	+	0.0496817i
$23$	−2.57143	+	1.14487i	−0.536179	+	0.238722i	−0.656918	−	0.753962i	$-0.728140\pi$
$23$	−2.57143	+	1.14487i	−0.536179	+	0.238722i	0.120739	+	0.992684i	$0.461474\pi$
$24$	−0.228609	−	0.395962i	−0.0466646	−	0.0808254i
$25$	−4.59642	+	1.96799i	−0.919283	+	0.393597i
$26$	−0.0891058	+	0.154336i	−0.0174751	+	0.0302677i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	−4.70721	+	2.33991i	−0.889579	+	0.442201i
$29$	0.663276	+	2.04135i	0.123167	+	0.379070i	0.993563	−	0.113283i	$-0.0361368\pi$
$29$	0.663276	+	2.04135i	0.123167	+	0.379070i	−0.870395	+	0.492353i	$0.836137\pi$
$30$	−0.254832	−	0.0286324i	−0.0465258	−	0.00522754i
$31$	1.50530	−	0.319961i	0.270360	−	0.0574667i	−0.0707368	−	0.997495i	$-0.522535\pi$
$31$	1.50530	−	0.319961i	0.270360	−	0.0574667i	0.341096	+	0.940028i	$0.389202\pi$
$32$	−0.682066	−	1.18137i	−0.120573	−	0.208839i
$33$	−1.42961	−	1.58775i	−0.248864	−	0.276391i
$34$	0.101885	−	0.0740235i	0.0174731	−	0.0126949i
$35$	−1.02521	+	5.82657i	−0.173291	+	0.984871i
$36$	1.60739	+	1.16784i	0.267899	+	0.194640i
$37$	−0.421182	−	4.00728i	−0.0692419	−	0.658793i	−0.973009	−	0.230768i	$-0.925876\pi$
$37$	−0.421182	−	4.00728i	−0.0692419	−	0.658793i	0.903767	−	0.428025i	$-0.140790\pi$
$38$	−0.155188	−	0.0690942i	−0.0251748	−	0.0112086i
$39$	0.162434	−	1.54546i	0.0260103	−	0.247471i
$40$	−1.01598	−	0.114153i	−0.160640	−	0.0180492i
$41$	−5.26454	+	3.82491i	−0.822184	+	0.597351i	−0.917337	−	0.398111i	$-0.869666\pi$
$41$	−5.26454	+	3.82491i	−0.822184	+	0.597351i	0.0951536	+	0.995463i	$0.469666\pi$
$42$	−0.193278	+	0.233894i	−0.0298234	+	0.0360907i
$43$	−9.54777			−1.45602			−0.728011	−	0.685566i	$-0.759555\pi$
$43$	−9.54777			−1.45602			−0.728011	+	0.685566i	$0.759555\pi$
$44$	−2.84043	−	3.15461i	−0.428210	−	0.475576i
$45$	2.13153	−	0.675720i	0.317749	−	0.100730i
$46$	−0.215997	+	0.239889i	−0.0318470	+	0.0353697i
$47$	2.72406	+	0.579016i	0.397345	+	0.0844582i	0.402250	−	0.915530i	$-0.368228\pi$
$47$	2.72406	+	0.579016i	0.397345	+	0.0844582i	−0.00490564	+	0.999988i	$0.501562\pi$
$48$	3.17237	+	2.30486i	0.457892	+	0.332678i
$49$	5.10805	+	4.78621i	0.729721	+	0.683745i
$50$	−0.389754	+	0.420580i	−0.0551196	+	0.0594790i
$51$	−0.549070	+	0.951017i	−0.0768851	+	0.133169i
$52$	0.322732	−	3.07059i	0.0447549	−	0.425814i
$53$	−1.77574	+	1.97216i	−0.243916	+	0.270897i	−0.852655	−	0.522474i	$-0.825009\pi$
$53$	−1.77574	+	1.97216i	−0.243916	+	0.270897i	0.608739	+	0.793371i	$0.291676\pi$
$54$	0.112175	+	0.0238436i	0.0152651	+	0.00324471i
$55$	−4.75470	+	0.465302i	−0.641124	+	0.0627413i
$56$	−0.770569	+	0.932502i	−0.102972	+	0.124611i
$57$	1.48127			0.196199
$58$	0.164708	+	0.182927i	0.0216273	+	0.0240195i
$59$	8.11603	+	3.61349i	1.05662	+	0.470436i	0.860133	−	0.510070i	$-0.170381\pi$
$59$	8.11603	+	3.61349i	1.05662	+	0.470436i	0.196485	+	0.980507i	$0.437047\pi$
$60$	4.23502	−	1.34255i	0.546739	−	0.173323i
$61$	6.30166	−	2.80568i	0.806845	−	0.359230i	0.0384935	−	0.999259i	$-0.487744\pi$
$61$	6.30166	−	2.80568i	0.806845	−	0.359230i	0.768351	+	0.640028i	$0.221077\pi$
$62$	0.142781	−	0.103736i	0.0181332	−	0.0131745i
$63$	0.710093	−	2.54868i	0.0894634	−	0.321103i
$64$	6.21817	+	4.51777i	0.777272	+	0.564721i
$65$	−2.56553	−	2.34354i	−0.318215	−	0.290680i
$66$	−0.223837	−	0.0996586i	−0.0275524	−	0.0122671i
$67$	13.6827	−	2.90835i	1.67161	−	0.355311i	0.727796	−	0.685794i	$-0.240545\pi$
$67$	13.6827	−	2.90835i	1.67161	−	0.355311i	0.943812	+	0.330483i	$0.107211\pi$
$68$	−1.09092	+	1.88953i	−0.132293	+	0.229139i
$69$	0.869814	−	2.67701i	0.104713	−	0.322274i
$70$	0.164374	+	0.658252i	0.0196465	+	0.0786761i
$71$	3.60505	+	11.0952i	0.427841	+	1.31676i	0.900247	+	0.435379i	$0.143386\pi$
$71$	3.60505	+	11.0952i	0.427841	+	1.31676i	−0.472406	+	0.881381i	$0.656614\pi$
$72$	0.447226	+	0.0950609i	0.0527061	+	0.0112030i
$73$	1.18042	−	11.2310i	0.138158	−	1.31449i	−0.677316	−	0.735693i	$-0.736857\pi$
$73$	1.18042	−	11.2310i	0.138158	−	1.31449i	0.815474	−	0.578794i	$-0.196476\pi$
$74$	−0.231046	−	0.400184i	−0.0268586	−	0.0465204i
$75$	1.61310	−	4.73264i	0.186265	−	0.546478i
$76$	2.94306			0.337592
$77$	−2.61612	+	5.01090i	−0.298135	+	0.571045i
$78$	−0.0550704	−	0.169489i	−0.00623550	−	0.0191909i
$79$	−4.37468	−	0.929867i	−0.492190	−	0.104618i	−0.0448711	−	0.998993i	$-0.514288\pi$
$79$	−4.37468	−	0.929867i	−0.492190	−	0.104618i	−0.447319	+	0.894375i	$0.647621\pi$
$80$	8.35827	−	2.64967i	0.934483	−	0.296243i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−0.373135	+	0.646289i	−0.0412059	+	0.0713707i
$83$	−0.0653066	+	0.200993i	−0.00716833	+	0.0220619i	−0.954577	−	0.297965i	$-0.903692\pi$
$83$	−0.0653066	+	0.200993i	−0.00716833	+	0.0220619i	0.947408	+	0.320027i	$0.103692\pi$
$84$	1.41085	−	5.06384i	0.153936	−	0.552510i
$85$	0.982641	+	2.25033i	0.106582	+	0.244082i
$86$	−1.00029	+	0.445357i	−0.107864	+	0.0480241i
$87$	−1.96084	−	0.873022i	−0.210224	−	0.0935978i
$88$	−0.892403	−	0.397324i	−0.0951305	−	0.0423548i
$89$	5.70768	−	2.54123i	0.605013	−	0.269369i	−0.0812833	−	0.996691i	$-0.525902\pi$
$89$	5.70768	−	2.54123i	0.605013	−	0.269369i	0.686297	+	0.727322i	$0.259235\pi$
$90$	0.191794	−	0.170218i	0.0202169	−	0.0179426i
$91$	−3.98169	+	1.02466i	−0.417394	+	0.107413i
$92$	1.72819	−	5.31881i	0.180176	−	0.554525i
$93$	−0.769464	+	1.33275i	−0.0797897	+	0.138200i
$94$	0.312399	−	0.0664024i	0.0322215	−	0.00684889i
$95$	1.96604	−	2.66562i	0.201711	−	0.273487i
$96$	1.33432	+	0.283619i	0.136184	+	0.0289467i
$97$	−5.03322	−	15.4907i	−0.511046	−	1.57284i	−0.790363	−	0.612639i	$-0.790108\pi$
$97$	−5.03322	−	15.4907i	−0.511046	−	1.57284i	0.279317	−	0.960199i	$-0.409892\pi$
$98$	0.758407	+	0.263170i	0.0766107	+	0.0265842i
$99$	2.13653			0.214729
$100$	3.20499	−	9.40304i	0.320499	−	0.940304i
$101$	4.70206	+	8.14421i	0.467872	+	0.810379i	0.999326	−	0.0367086i	$-0.0116873\pi$
$101$	4.70206	+	8.14421i	0.467872	+	0.810379i	−0.531454	+	0.847087i	$0.678354\pi$
$102$	−0.0131639	+	0.125246i	−0.00130342	+	0.0124012i
$103$	5.41772	+	1.15157i	0.533824	+	0.113468i	0.466933	−	0.884293i	$-0.345359\pi$
$103$	5.41772	+	1.15157i	0.533824	+	0.113468i	0.0668906	+	0.997760i	$0.478692\pi$
$104$	−0.219557	−	0.675728i	−0.0215294	−	0.0662606i
$105$	−3.64399	−	4.66061i	−0.355617	−	0.454829i
$106$	−0.0940467	+	0.289446i	−0.00913463	+	0.0281135i
$107$	−5.67715	+	9.83312i	−0.548831	+	0.950603i	0.449524	+	0.893268i	$0.351594\pi$
$107$	−5.67715	+	9.83312i	−0.548831	+	0.950603i	−0.998355	+	0.0573350i	$0.981740\pi$
$108$	−1.94343	+	0.413089i	−0.187007	+	0.0397495i
$109$	4.57440	+	2.03665i	0.438148	+	0.195076i	0.613942	−	0.789351i	$-0.289583\pi$
$109$	4.57440	+	2.03665i	0.438148	+	0.195076i	−0.175794	+	0.984427i	$0.556249\pi$
$110$	−0.476431	+	0.270532i	−0.0454259	+	0.0257942i
$111$	3.25982	+	2.36839i	0.309408	+	0.224798i
$112$	2.78446	−	9.99404i	0.263107	−	0.944348i
$113$	−14.5118	+	10.5434i	−1.36516	+	0.991844i	−0.367058	+	0.930198i	$0.619635\pi$
$113$	−14.5118	+	10.5434i	−1.36516	+	0.991844i	−0.998098	+	0.0616463i	$0.980365\pi$
$114$	0.155188	−	0.0690942i	0.0145347	−	0.00647126i
$115$	−3.66294	−	5.11837i	−0.341571	−	0.477290i
$116$	−3.89589	−	1.73456i	−0.361724	−	0.161050i
$117$	1.03981	+	1.15482i	0.0961304	+	0.106764i
$118$	1.01884			0.0937920
$119$	2.86498	+	0.482955i	0.262633	+	0.0442724i
$120$	0.764653	−	0.678635i	0.0698030	−	0.0619506i
$121$	6.29463	+	1.33797i	0.572239	+	0.121633i
$122$	0.529333	−	0.587884i	0.0479236	−	0.0532245i
$123$	0.680202	−	6.47169i	0.0613317	−	0.583532i
$124$	−1.52881	+	2.64797i	−0.137291	+	0.237795i
$125$	−6.37560	−	9.18432i	−0.570251	−	0.821470i
$126$	−0.0444894	−	0.300139i	−0.00396343	−	0.0267385i
$127$	−3.40304	−	2.47245i	−0.301971	−	0.219395i	0.426473	−	0.904500i	$-0.359756\pi$
$127$	−3.40304	−	2.47245i	−0.301971	−	0.219395i	−0.728444	+	0.685106i	$0.759756\pi$
$128$	3.53083	+	0.750502i	0.312084	+	0.0663356i
$129$	6.38871	−	7.09538i	0.562494	−	0.624713i
$130$	−0.378097	−	0.125855i	−0.0331613	−	0.0110382i
$131$	14.0351	+	15.5876i	1.22625	+	1.36189i	0.910745	+	0.412969i	$0.135508\pi$
$131$	14.0351	+	15.5876i	1.22625	+	1.36189i	0.315508	+	0.948923i	$0.397825\pi$
$132$	4.24495			0.369476
$133$	−1.36810	−	3.67253i	−0.118629	−	0.318449i
$134$	1.29783	−	0.942930i	0.112116	−	0.0814567i
$135$	−0.924112	+	2.03618i	−0.0795349	+	0.175246i
$136$	−0.0524826	+	0.499338i	−0.00450034	+	0.0428179i
$137$	−2.74039	−	1.22010i	−0.234128	−	0.104240i	0.286320	−	0.958134i	$-0.407568\pi$
$137$	−2.74039	−	1.22010i	−0.234128	−	0.104240i	−0.520447	+	0.853894i	$0.674235\pi$
$138$	−0.0337421	−	0.321034i	−0.00287232	−	0.0273283i
$139$	9.20763	+	6.68973i	0.780981	+	0.567416i	0.905273	−	0.424830i	$-0.139666\pi$
$139$	9.20763	+	6.68973i	0.780981	+	0.567416i	−0.124292	+	0.992246i	$0.539666\pi$
$140$	−7.24006	−	9.25993i	−0.611897	−	0.782607i
$141$	−2.25304	+	1.63693i	−0.189740	+	0.137855i
$142$	0.895228	+	0.994251i	0.0751259	+	0.0834357i
$143$	−1.66005	−	2.87529i	−0.138820	−	0.240444i
$144$	−3.83557	+	0.815276i	−0.319631	+	0.0679397i
$145$	−4.17359	+	2.36990i	−0.346598	+	0.196809i
$146$	−0.400202	−	1.23169i	−0.0331209	−	0.101936i
$147$	−6.97480	+	0.593417i	−0.575272	+	0.0489442i
$148$	6.47676	+	4.70564i	0.532386	+	0.386801i
$149$	−5.05508	+	8.75566i	−0.414129	+	0.717292i	−0.995337	−	0.0964634i	$-0.969247\pi$
$149$	−5.05508	+	8.75566i	−0.414129	+	0.717292i	0.581208	+	0.813755i	$0.302580\pi$
$150$	−0.0517551	−	0.571067i	−0.00422579	−	0.0466274i
$151$	−1.66515	−	2.88412i	−0.135508	−	0.234707i	0.790283	−	0.612741i	$-0.209933\pi$
$151$	−1.66515	−	2.88412i	−0.135508	−	0.234707i	−0.925791	+	0.378035i	$0.876600\pi$
$152$	0.618711	−	0.275468i	0.0501841	−	0.0223434i
$153$	−0.339344	−	1.04439i	−0.0274343	−	0.0844342i
$154$	−0.0403489	+	0.647005i	−0.00325140	+	0.0521371i
$155$	1.37707	+	3.15360i	0.110609	+	0.253303i
$156$	2.06594	+	2.29446i	0.165408	+	0.183704i
$157$	−1.95530	−	3.38667i	−0.156050	−	0.270286i	0.777391	−	0.629018i	$-0.216543\pi$
$157$	−1.95530	−	3.38667i	−0.156050	−	0.270286i	−0.933441	+	0.358732i	$0.883209\pi$
$158$	−0.501695	+	0.106638i	−0.0399127	+	0.00848370i
$159$	−0.277398	−	2.63926i	−0.0219991	−	0.209307i
$160$	2.28138	−	2.02474i	0.180359	−	0.160070i
$161$	−7.44049	+	0.315948i	−0.586393	+	0.0249002i
$162$	−0.0927793	+	0.0674081i	−0.00728943	+	0.00529608i
$163$	2.31668	+	22.0418i	0.181457	+	1.72644i	0.584613	+	0.811312i	$0.301246\pi$
$163$	2.31668	+	22.0418i	0.181457	+	1.72644i	−0.403157	+	0.915131i	$0.632087\pi$
$164$	1.35146	−	12.8583i	0.105531	−	1.00406i
$165$	2.83573	−	3.84478i	0.220761	−	0.299316i
$166$	0.00253339	+	0.0241036i	0.000196629	+	0.00187080i
$167$	4.99235	−	15.3649i	0.386320	−	1.18897i	−0.549199	−	0.835692i	$-0.685067\pi$
$167$	4.99235	−	15.3649i	0.386320	−	1.18897i	0.935518	−	0.353278i	$-0.114933\pi$
$168$	−0.177372	−	1.19661i	−0.0136846	−	0.0923204i
$169$	−3.27100	+	10.0671i	−0.251615	+	0.774392i
$170$	0.207915	+	0.189924i	0.0159463	+	0.0145665i
$171$	−0.991165	+	1.10080i	−0.0757963	+	0.0841803i
$172$	12.6934	−	14.0974i	0.967862	−	1.07492i
$173$	19.9349	−	8.87560i	1.51562	−	0.674800i	0.530664	−	0.847582i	$-0.321942\pi$
$173$	19.9349	−	8.87560i	1.51562	−	0.674800i	0.984960	+	0.172782i	$0.0552758\pi$
$174$	−0.246153			−0.0186608
$175$	−13.2235	+	0.371680i	−0.999605	+	0.0280964i
$176$	8.37787			0.631506
$177$	−8.11603	+	3.61349i	−0.610038	+	0.271607i
$178$	0.479440	−	0.532472i	0.0359355	−	0.0399104i
$179$	−1.46099	+	1.62259i	−0.109199	+	0.121278i	−0.795266	−	0.606260i	$-0.792669\pi$
$179$	−1.46099	+	1.62259i	−0.109199	+	0.121278i	0.686067	+	0.727538i	$0.259336\pi$
$180$	−1.83607	+	4.04558i	−0.136853	+	0.301539i
$181$	1.38946	−	4.27633i	0.103278	−	0.317857i	−0.886044	−	0.463600i	$-0.846557\pi$
$181$	1.38946	−	4.27633i	0.103278	−	0.317857i	0.989322	+	0.145743i	$0.0465574\pi$
$182$	−0.369353	+	0.293077i	−0.0273783	+	0.0217243i
$183$	−2.13161	+	6.56041i	−0.157573	+	0.484960i
$184$	−0.134524	−	1.27991i	−0.00991728	−	0.0943566i
$185$	8.58867	−	2.72271i	0.631452	−	0.200178i
$186$	−0.0184479	+	0.175520i	−0.00135266	+	0.0128697i
$187$	0.245245	+	2.33335i	0.0179341	+	0.170631i
$188$	−4.47645	+	3.25233i	−0.326479	+	0.237201i
$189$	1.41889	+	2.23310i	0.103209	+	0.162434i
$190$	0.0816370	−	0.370975i	0.00592257	−	0.0269133i
$191$	−1.77930	−	16.9290i	−0.128746	−	1.22494i	−0.847927	−	0.530113i	$-0.822149\pi$
$191$	−1.77930	−	16.9290i	−0.128746	−	1.22494i	0.719181	−	0.694823i	$-0.244517\pi$
$192$	−7.51812	+	1.59803i	−0.542574	+	0.115328i
$193$	6.38090	+	11.0520i	0.459307	+	0.795544i	0.998924	−	0.0463668i	$-0.0147643\pi$
$193$	6.38090	+	11.0520i	0.459307	+	0.795544i	−0.539617	+	0.841911i	$0.681431\pi$
$194$	−1.24988	−	1.38813i	−0.0897360	−	0.0996619i
$195$	3.45826	−	0.338431i	0.247651	−	0.0242355i
$196$	−13.8579	+	1.17903i	−0.989848	+	0.0842164i
$197$	2.97095	+	9.14363i	0.211671	+	0.651457i	0.999373	+	0.0354003i	$0.0112706\pi$
$197$	2.97095	+	9.14363i	0.211671	+	0.651457i	−0.787702	+	0.616056i	$0.788729\pi$
$198$	0.223837	−	0.0996586i	0.0159074	−	0.00708242i
$199$	6.04814	+	10.4757i	0.428741	+	0.742601i	0.996762	−	0.0804132i	$-0.0256240\pi$
$199$	6.04814	+	10.4757i	0.428741	+	0.742601i	−0.568021	+	0.823014i	$0.692291\pi$
$200$	−0.206340	−	2.27676i	−0.0145904	−	0.160991i
$201$	−6.99419	+	12.1143i	−0.493332	+	0.854476i
$202$	0.872507	+	0.633914i	0.0613894	+	0.0446020i
$203$	−0.353461	+	5.66785i	−0.0248081	+	0.397805i
$204$	−0.674225	−	2.07505i	−0.0472052	−	0.145283i
$205$	−10.7433	−	9.81368i	−0.750345	−	0.685417i
$206$	0.621312	−	0.132064i	0.0432889	−	0.00920133i
$207$	1.40739	+	2.43767i	0.0978202	+	0.169430i
$208$	4.07736	+	4.52837i	0.282714	+	0.313986i
$209$	2.56036	−	1.86021i	0.177104	−	0.128673i
$210$	−0.599164	−	0.318303i	−0.0413463	−	0.0219650i
$211$	11.4658	+	8.33039i	0.789338	+	0.573488i	0.907767	−	0.419475i	$-0.137786\pi$
$211$	11.4658	+	8.33039i	0.789338	+	0.573488i	−0.118429	+	0.992963i	$0.537786\pi$
$212$	−0.551147	−	5.24381i	−0.0378529	−	0.360147i
$213$	−10.6576	−	4.74507i	−0.730247	−	0.325127i
$214$	−0.136109	+	1.29500i	−0.00930425	+	0.0885240i
$215$	−4.28898	−	20.9142i	−0.292506	−	1.42634i
$216$	−0.369897	+	0.268746i	−0.0251683	+	0.0182858i
$217$	4.01497	+	0.676811i	0.272554	+	0.0459449i
$218$	0.574245			0.0388928
$219$	7.55639	+	8.39222i	0.510613	+	0.567093i
$220$	5.63416	−	7.63899i	0.379855	−	0.515021i
$221$	−1.14186	+	1.26816i	−0.0768095	+	0.0853056i
$222$	0.451994	+	0.0960744i	0.0303359	+	0.00644809i
$223$	7.35881	+	5.34649i	0.492783	+	0.358028i	0.806253	−	0.591570i	$-0.201492\pi$
$223$	7.35881	+	5.34649i	0.492783	+	0.358028i	−0.313471	+	0.949598i	$0.601492\pi$
$224$	−0.529199	−	3.57014i	−0.0353586	−	0.238540i
$225$	2.43766	+	4.36553i	0.162511	+	0.291035i
$226$	−1.02855	+	1.78151i	−0.0684184	+	0.118504i
$227$	−2.31491	+	22.0249i	−0.153646	+	1.46185i	0.597584	+	0.801806i	$0.296127\pi$
$227$	−2.31491	+	22.0249i	−0.153646	+	1.46185i	−0.751231	+	0.660040i	$0.770539\pi$
$228$	−1.96929	+	2.18712i	−0.130420	+	0.144846i
$229$	−21.3016	−	4.52778i	−1.40765	−	0.299204i	−0.559440	−	0.828871i	$-0.688984\pi$
$229$	−21.3016	−	4.52778i	−1.40765	−	0.299204i	−0.848206	+	0.529666i	$0.822317\pi$
$230$	−0.622501	−	0.365376i	−0.0410465	−	0.0240922i
$231$	−1.97329	−	5.29710i	−0.129833	−	0.348524i
$232$	−0.981374			−0.0644304
$233$	−17.6303	−	19.5805i	−1.15500	−	1.28276i	−0.952862	−	0.303403i	$-0.901877\pi$
$233$	−17.6303	−	19.5805i	−1.15500	−	1.28276i	−0.202140	−	0.979357i	$-0.564790\pi$
$234$	0.162804	+	0.0724852i	0.0106429	+	0.00473850i
$235$	−0.0446422	+	6.22710i	−0.00291214	+	0.406211i
$236$	−16.1253	+	7.17946i	−1.04967	+	0.467343i
$237$	3.61826	−	2.62882i	0.235031	−	0.170760i
$238$	0.322682	−	0.0830400i	0.0209164	−	0.00538268i
$239$	19.7391	+	14.3413i	1.27682	+	0.927661i	0.999452	−	0.0331036i	$-0.0105391\pi$
$239$	19.7391	+	14.3413i	1.27682	+	0.927661i	0.277364	+	0.960765i	$0.410539\pi$
$240$	−3.62368	+	7.98438i	−0.233908	+	0.515390i
$241$	−25.5177	−	11.3612i	−1.64374	−	0.731840i	−0.644283	−	0.764787i	$-0.722844\pi$
$241$	−25.5177	−	11.3612i	−1.64374	−	0.731840i	−0.999457	+	0.0329466i	$0.989511\pi$
$242$	0.721878	−	0.153440i	0.0464041	−	0.00986349i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−4.23518	+	13.0345i	−0.271130	+	0.834451i
$245$	−8.18951	+	13.3391i	−0.523209	+	0.852205i
$246$	−0.230610	−	0.709745i	−0.0147032	−	0.0452517i
$247$	2.25155	+	0.478582i	0.143263	+	0.0304515i
$248$	−0.0735488	+	0.699770i	−0.00467036	+	0.0444355i
$249$	−0.105668	−	0.183023i	−0.00669646	−	0.0115986i
$250$	−1.09636	−	0.664820i	−0.0693396	−	0.0420469i
$251$	7.15044			0.451332			0.225666	−	0.974205i	$-0.427544\pi$
$251$	7.15044			0.451332			0.225666	+	0.974205i	$0.427544\pi$
$252$	2.81912	+	4.43683i	0.177588	+	0.279494i
$253$	−1.85838	−	5.71950i	−0.116835	−	0.359582i
$254$	−0.471853	−	0.100295i	−0.0296067	−	0.00629310i
$255$	−2.32983	−	0.775518i	−0.145900	−	0.0485648i
$256$	−14.6313	+	3.10998i	−0.914458	+	0.194374i
$257$	4.70166	−	8.14352i	0.293282	−	0.507979i	−0.681302	−	0.732002i	$-0.738586\pi$
$257$	4.70166	−	8.14352i	0.293282	−	0.507979i	0.974584	+	0.224024i	$0.0719193\pi$
$258$	0.338359	−	1.04136i	0.0210653	−	0.0648323i
$259$	2.86122	−	10.2695i	0.177787	−	0.638118i
$260$	6.87104	−	0.672410i	0.426124	−	0.0417011i
$261$	1.96084	−	0.873022i	0.121373	−	0.0540387i
$262$	2.19750	+	0.978389i	0.135762	+	0.0604451i
$263$	−9.93491	−	4.42331i	−0.612613	−	0.272753i	0.0768857	−	0.997040i	$-0.475502\pi$
$263$	−9.93491	−	4.42331i	−0.612613	−	0.272753i	−0.689498	+	0.724287i	$0.742169\pi$
$264$	0.892403	−	0.397324i	0.0549236	−	0.0244536i
$265$	−5.11766	−	3.00380i	−0.314375	−	0.184522i
$266$	−0.314637	−	0.320944i	−0.0192916	−	0.0196783i
$267$	−1.93069	+	5.94205i	−0.118156	+	0.363647i
$268$	−13.8964	+	24.0693i	−0.848857	+	1.47026i
$269$	28.7006	−	6.10049i	1.74990	−	0.371954i	0.782001	−	0.623277i	$-0.214199\pi$
$269$	28.7006	−	6.10049i	1.74990	−	0.371954i	0.967903	+	0.251323i	$0.0808657\pi$
$270$	−0.00183835	+	0.256429i	−0.000111878	+	0.0156058i
$271$	13.1182	+	2.78835i	0.796871	+	0.169380i	0.588317	−	0.808631i	$-0.299791\pi$
$271$	13.1182	+	2.78835i	0.796871	+	0.169380i	0.208554	+	0.978011i	$0.433124\pi$
$272$	−1.33066	−	4.09534i	−0.0806829	−	0.248316i
$273$	1.90280	−	3.64460i	0.115163	−	0.220581i
$274$	−0.344014			−0.0207826
$275$	−3.15511	−	10.2061i	−0.190260	−	0.615449i
$276$	2.79627	+	4.84327i	0.168315	+	0.291531i
$277$	0.484220	−	4.60704i	0.0290940	−	0.276810i	−0.970297	−	0.241917i	$-0.922224\pi$
$277$	0.484220	−	4.60704i	0.0290940	−	0.276810i	0.999391	−	0.0348940i	$-0.0111093\pi$
$278$	1.27670	+	0.271370i	0.0765712	+	0.0162757i
$279$	−0.475555	−	1.46361i	−0.0284707	−	0.0876239i
$280$	−2.38878	−	1.26902i	−0.142757	−	0.0758387i
$281$	6.39924	−	19.6948i	0.381747	−	1.17490i	−0.557066	−	0.830468i	$-0.688073\pi$
$281$	6.39924	−	19.6948i	0.381747	−	1.17490i	0.938813	−	0.344427i	$-0.111927\pi$
$282$	−0.159689	+	0.276590i	−0.00950934	+	0.0164707i
$283$	7.89300	−	1.67771i	0.469190	−	0.0997294i	0.0327515	−	0.999464i	$-0.489573\pi$
$283$	7.89300	−	1.67771i	0.469190	−	0.0997294i	0.436438	+	0.899734i	$0.356240\pi$
$284$	−21.1750	−	9.42774i	−1.25651	−	0.559433i
$285$	0.665407	+	3.24470i	0.0394153	+	0.192199i
$286$	−0.308036	−	0.223801i	−0.0182146	−	0.0132337i
$287$	−16.6735	+	4.29081i	−0.984207	+	0.253279i
$288$	−1.10361	+	0.801816i	−0.0650306	+	0.0472475i
$289$	−14.4286	+	6.42403i	−0.848742	+	0.377884i
$290$	−0.326710	+	0.442964i	−0.0191850	+	0.0260117i
$291$	14.8797	+	6.62486i	0.872262	+	0.388356i
$292$	15.0134	+	16.6741i	0.878592	+	0.975776i
$293$	−12.4659			−0.728268			−0.364134	−	0.931346i	$-0.618635\pi$
$293$	−12.4659			−0.728268			−0.364134	+	0.931346i	$0.618635\pi$
$294$	−0.703047	+	0.387511i	−0.0410025	+	0.0226001i
$295$	−4.26946	+	19.4012i	−0.248577	+	1.12958i
$296$	1.80203	+	0.383034i	0.104741	+	0.0222634i
$297$	−1.42961	+	1.58775i	−0.0829546	+	0.0921305i
$298$	−0.121195	+	1.15310i	−0.00702066	+	0.0667971i
$299$	2.18704	−	3.78806i	0.126480	−	0.219069i
$300$	4.84326	+	8.67364i	0.279626	+	0.500773i
$301$	−23.4922	−	9.28629i	−1.35407	−	0.535253i
$302$	−0.308983	−	0.224489i	−0.0177799	−	0.0129179i
$303$	−9.19862	−	1.95523i	−0.528447	−	0.112325i
$304$	−3.88662	+	4.31652i	−0.222913	+	0.247570i
$305$	8.97658	+	12.5433i	0.513997	+	0.718228i
$306$	−0.0842678	−	0.0935889i	−0.00481727	−	0.00535012i
$307$	−1.30687			−0.0745868			−0.0372934	−	0.999304i	$-0.511874\pi$
$307$	−1.30687			−0.0745868			−0.0372934	+	0.999304i	$0.511874\pi$
$308$	−3.92063	−	10.5245i	−0.223399	−	0.599691i
$309$	−4.48095	+	3.25560i	−0.254912	+	0.185205i
$310$	0.291371	+	0.266159i	0.0165488	+	0.0151168i
$311$	−1.10066	+	10.4721i	−0.0624129	+	0.593819i	0.917961	+	0.396671i	$0.129835\pi$
$311$	−1.10066	+	10.4721i	−0.0624129	+	0.593819i	−0.980374	+	0.197148i	$0.936832\pi$
$312$	0.649076	+	0.288987i	0.0367467	+	0.0163607i
$313$	−1.34824	−	12.8277i	−0.0762072	−	0.725063i	−0.964195	−	0.265195i	$-0.914564\pi$
$313$	−1.34824	−	12.8277i	−0.0762072	−	0.725063i	0.887988	−	0.459868i	$-0.152103\pi$
$314$	−0.362822	−	0.263606i	−0.0204752	−	0.0148761i
$315$	5.90182	+	0.410546i	0.332530	+	0.0231317i
$316$	7.18893	−	5.22306i	0.404409	−	0.293820i
$317$	−9.20709	−	10.2255i	−0.517122	−	0.574322i	0.426861	−	0.904317i	$-0.359619\pi$
$317$	−9.20709	−	10.2255i	−0.517122	−	0.574322i	−0.943983	+	0.329995i	$0.892953\pi$
$318$	−0.152171	−	0.263568i	−0.00853332	−	0.0147801i
$319$	−4.48564	+	0.953452i	−0.251148	+	0.0533831i
$320$	−7.10280	+	15.6502i	−0.397059	+	0.874874i
$321$	−3.50867	−	10.7986i	−0.195835	−	0.602718i
$322$	−0.764779	+	0.380164i	−0.0426194	+	0.0211857i
$323$	−1.31598	−	0.956117i	−0.0732232	−	0.0531998i
$324$	0.993424	−	1.72066i	0.0551902	−	0.0955923i
$325$	3.98100	−	6.67250i	0.220826	−	0.370124i
$326$	1.27085	+	2.20118i	0.0703860	+	0.121912i
$327$	−4.57440	+	2.03665i	−0.252965	+	0.112627i
$328$	−0.919408	−	2.82965i	−0.0507658	−	0.156241i
$329$	6.13936	+	4.07412i	0.338474	+	0.224613i
$330$	0.117750	−	0.535078i	0.00648191	−	0.0294551i
$331$	2.45216	+	2.72340i	0.134783	+	0.149692i	0.806758	−	0.590882i	$-0.201220\pi$
$331$	2.45216	+	2.72340i	0.134783	+	0.149692i	−0.671975	+	0.740574i	$0.734554\pi$
$332$	−0.209947	−	0.363639i	−0.0115223	−	0.0199573i
$333$	−3.94130	+	0.837750i	−0.215982	+	0.0459084i
$334$	−0.193665	−	1.84260i	−0.0105969	−	0.100822i
$335$	12.5171	+	28.6652i	0.683884	+	1.56615i
$336$	5.56385	+	8.75658i	0.303533	+	0.477710i
$337$	−8.31014	+	6.03767i	−0.452682	+	0.328893i	−0.790654	−	0.612263i	$-0.790259\pi$
$337$	−8.31014	+	6.03767i	−0.452682	+	0.328893i	0.337972	+	0.941156i	$0.390259\pi$
$338$	0.126890	+	1.20727i	0.00690188	+	0.0656670i
$339$	1.87499	−	17.8393i	0.101835	−	0.968899i
$340$	−4.62903	−	1.54084i	−0.251044	−	0.0835636i
$341$	0.343685	+	3.26995i	0.0186116	+	0.177078i
$342$	−0.0524941	+	0.161560i	−0.00283856	+	0.00873618i
$343$	7.91318	+	16.7446i	0.427272	+	0.904123i
$344$	1.34899	−	4.15175i	0.0727324	−	0.223847i
$345$	6.25467	+	0.702762i	0.336740	+	0.0378354i
$346$	1.67451	−	1.85974i	0.0900224	−	0.0999800i
$347$	−6.88244	+	7.64372i	−0.369469	+	0.410336i	−0.898996	−	0.437956i	$-0.855702\pi$
$347$	−6.88244	+	7.64372i	−0.369469	+	0.410336i	0.529528	+	0.848293i	$0.322369\pi$
$348$	3.89589	−	1.73456i	0.208842	−	0.0929823i
$349$	7.88396			0.422019			0.211009	−	0.977484i	$-0.432325\pi$
$349$	7.88396			0.422019			0.211009	+	0.977484i	$0.432325\pi$
$350$	−1.36805	+	0.655753i	−0.0731253	+	0.0350515i
$351$	−1.55397			−0.0829448
$352$	2.66253	−	1.18543i	0.141913	−	0.0631839i
$353$	0.747544	−	0.830232i	0.0397878	−	0.0441888i	−0.722922	−	0.690929i	$-0.757202\pi$
$353$	0.747544	−	0.830232i	0.0397878	−	0.0441888i	0.762710	+	0.646740i	$0.223868\pi$
$354$	−0.681739	+	0.757147i	−0.0362340	+	0.0402419i
$355$	−22.6844	+	12.8809i	−1.20396	+	0.683648i
$356$	−3.83598	+	11.8059i	−0.203307	+	0.625714i
$357$	−2.27595	+	1.80594i	−0.120456	+	0.0955803i
$358$	−0.0773770	+	0.238142i	−0.00408950	+	0.0125862i
$359$	−3.67744	−	34.9885i	−0.194088	−	1.84662i	−0.466599	−	0.884469i	$-0.654521\pi$
$359$	−3.67744	−	34.9885i	−0.194088	−	1.84662i	0.272511	−	0.962153i	$-0.412146\pi$
$360$	−0.00732921	+	1.02234i	−0.000386283	+	0.0538822i
$361$	1.75669	−	16.7138i	0.0924573	−	0.879672i
$362$	−0.0539005	−	0.512829i	−0.00283295	−	0.0269537i
$363$	−5.20623	+	3.78255i	−0.273256	+	0.198532i
$364$	3.78057	−	7.24127i	0.198156	−	0.379546i
$365$	25.1315	−	2.45941i	1.31544	−	0.128731i
$366$	0.0826899	+	0.786742i	0.00432227	+	0.0411237i
$367$	−21.8383	+	4.64187i	−1.13995	+	0.242304i	−0.738941	−	0.673771i	$-0.764674\pi$
$367$	−21.8383	+	4.64187i	−1.13995	+	0.242304i	−0.401009	+	0.916074i	$0.631340\pi$
$368$	5.51874	+	9.55873i	0.287684	+	0.498283i
$369$	4.35426	+	4.83589i	0.226674	+	0.251746i
$370$	0.772806	−	0.685870i	0.0401763	−	0.0356567i
$371$	−6.28734	+	3.12537i	−0.326422	+	0.162261i
$372$	−0.944855	−	2.90797i	−0.0489885	−	0.150771i
$373$	11.2192	−	4.99509i	0.580906	−	0.258636i	−0.0951783	−	0.995460i	$-0.530342\pi$
$373$	11.2192	−	4.99509i	0.580906	−	0.258636i	0.676084	+	0.736824i	$0.263675\pi$
$374$	0.134533	+	0.233018i	0.00695654	+	0.0120491i
$375$	11.0914	+	1.40751i	0.572757	+	0.0726835i
$376$	−0.636656	+	1.10272i	−0.0328330	+	0.0568685i
$377$	−2.69844	−	1.96053i	−0.138977	−	0.100972i
$378$	0.252816	+	0.167770i	0.0130035	+	0.00862917i
$379$	−6.12572	−	18.8530i	−0.314657	−	0.968416i	−0.975895	−	0.218239i	$-0.929969\pi$
$379$	−6.12572	−	18.8530i	−0.314657	−	0.968416i	0.661238	−	0.750176i	$-0.270031\pi$
$380$	1.32206	+	6.44672i	0.0678204	+	0.330710i
$381$	4.11447	−	0.874557i	0.210791	−	0.0448049i
$382$	−0.976066	−	1.69060i	−0.0499399	−	0.0864984i
$383$	−22.5302	−	25.0223i	−1.15124	−	1.27858i	−0.954528	−	0.298121i	$-0.903640\pi$
$383$	−22.5302	−	25.0223i	−1.15124	−	1.27858i	−0.196712	−	0.980461i	$-0.563026\pi$
$384$	−2.92032	+	2.12174i	−0.149027	+	0.108274i
$385$	−12.1515	−	3.47961i	−0.619296	−	0.177337i
$386$	1.18403	+	0.860249i	0.0602656	+	0.0437855i
$387$	0.998014	+	9.49547i	0.0507319	+	0.482682i
$388$	29.5637	+	13.1626i	1.50087	+	0.668229i
$389$	0.0917429	−	0.872875i	0.00465155	−	0.0442565i	−0.991950	−	0.126631i	$-0.959584\pi$
$389$	0.0917429	−	0.872875i	0.00465155	−	0.0442565i	0.996601	+	0.0823743i	$0.0262503\pi$
$390$	0.346525	−	0.196767i	0.0175470	−	0.00996371i
$391$	−2.50069	+	1.81685i	−0.126465	+	0.0918823i
$392$	−2.80294	+	1.54495i	−0.141570	+	0.0780316i
$393$	−20.9751			−1.05806
$394$	0.737762	+	0.819368i	0.0371679	+	0.0412792i
$395$	0.0716928	−	10.0004i	0.00360726	−	0.503173i
$396$	−2.84043	+	3.15461i	−0.142737	+	0.158525i
$397$	29.0169	+	6.16773i	1.45632	+	0.309550i	0.866982	−	0.498340i	$-0.166057\pi$
$397$	29.0169	+	6.16773i	1.45632	+	0.309550i	0.589334	+	0.807889i	$0.299390\pi$
$398$	1.12228	+	0.815386i	0.0562550	+	0.0408716i
$399$	3.64466	+	1.44070i	0.182461	+	0.0721254i
$400$	9.55871	+	17.1184i	0.477935	+	0.855918i
$401$	13.8130	−	23.9248i	0.689787	−	1.19475i	−0.282119	−	0.959379i	$-0.591037\pi$
$401$	13.8130	−	23.9248i	0.689787	−	1.19475i	0.971907	−	0.235367i	$-0.0756293\pi$
$402$	−0.167685	+	1.59542i	−0.00836339	+	0.0795723i
$403$	−1.60019	+	1.77719i	−0.0797112	+	0.0885283i
$404$	−18.2763	−	3.88474i	−0.909278	−	0.193273i
$405$	−0.894823	−	2.04922i	−0.0444641	−	0.101826i
$406$	0.227347	+	0.610289i	0.0112830	+	0.0302881i
$407$	8.60882			0.426723
$408$	−0.335963	−	0.373125i	−0.0166326	−	0.0184724i
$409$	6.05150	+	2.69430i	0.299228	+	0.133225i	0.550859	−	0.834599i	$-0.314300\pi$
$409$	6.05150	+	2.69430i	0.299228	+	0.133225i	−0.251631	+	0.967823i	$0.580967\pi$
$410$	−1.58330	−	0.527024i	−0.0781937	−	0.0260279i
$411$	2.74039	−	1.22010i	0.135174	−	0.0601832i
$412$	−8.90296	+	6.46838i	−0.438618	+	0.318674i
$413$	16.4549	+	16.7847i	0.809693	+	0.825923i
$414$	0.261153	+	0.189739i	0.0128350	+	0.00932514i
$415$	−0.469608	−	0.0527642i	−0.0230522	−	0.00259009i
$416$	1.93655	+	0.862208i	0.0949472	+	0.0422732i
$417$	−11.1325	+	2.36630i	−0.545163	+	0.115878i
$418$	0.181471	−	0.314316i	0.00887601	−	0.0153737i
$419$	−3.98611	+	12.2680i	−0.194734	+	0.599330i	0.805245	+	0.592942i	$0.202034\pi$
$419$	−3.98611	+	12.2680i	−0.194734	+	0.599330i	−0.999980	+	0.00638867i	$0.997966\pi$
$420$	11.7260	+	0.815693i	0.572171	+	0.0398017i
$421$	−5.68104	−	17.4844i	−0.276877	−	0.852140i	−0.988717	−	0.149798i	$-0.952138\pi$
$421$	−5.68104	−	17.4844i	−0.276877	−	0.852140i	0.711840	−	0.702342i	$-0.247862\pi$
$422$	1.58981	+	0.337924i	0.0773906	+	0.0164499i
$423$	0.291103	−	2.76966i	0.0141539	−	0.134665i
$424$	−0.606682	−	1.05080i	−0.0294631	−	0.0510316i
$425$	−4.48788	+	3.16333i	−0.217694	+	0.153444i
$426$	−1.33790			−0.0648213
$427$	18.2340	−	0.774278i	0.882406	−	0.0374699i
$428$	−6.97120	−	21.4551i	−0.336966	−	1.03707i
$429$	3.24754	+	0.690287i	0.156793	+	0.0333274i
$430$	−1.42489	−	1.99105i	−0.0687143	−	0.0960171i
$431$	13.0502	−	2.77391i	0.628606	−	0.133614i	0.117417	−	0.993083i	$-0.462539\pi$
$431$	13.0502	−	2.77391i	0.628606	−	0.133614i	0.511189	+	0.859468i	$0.329205\pi$
$432$	1.96063	−	3.39591i	0.0943309	−	0.163386i
$433$	12.0663	−	37.1363i	0.579870	−	1.78466i	−0.0390903	−	0.999236i	$-0.512446\pi$
$433$	12.0663	−	37.1363i	0.579870	−	1.78466i	0.618961	−	0.785422i	$-0.287554\pi$
$434$	0.452206	−	0.116372i	0.0217066	−	0.00558603i
$435$	1.03150	−	4.68735i	0.0494568	−	0.224741i
$436$	−9.08863	+	4.04652i	−0.435267	+	0.193793i
$437$	3.80898	+	1.69587i	0.182208	+	0.0811244i
$438$	1.18311	+	0.526756i	0.0565314	+	0.0251694i
$439$	−14.8282	+	6.60193i	−0.707710	+	0.315093i	−0.728840	−	0.684684i	$-0.759940\pi$
$439$	−14.8282	+	6.60193i	−0.707710	+	0.315093i	0.0211298	+	0.999777i	$0.493274\pi$
$440$	0.469451	−	2.13328i	0.0223802	−	0.101700i
$441$	4.22606	−	5.58036i	0.201241	−	0.265731i
$442$	−0.0604750	+	0.186123i	−0.00287650	+	0.00885296i
$443$	12.0420	−	20.8574i	0.572135	−	0.990967i	−0.424211	−	0.905563i	$-0.639449\pi$
$443$	12.0420	−	20.8574i	0.572135	−	0.990967i	0.996346	−	0.0854038i	$-0.0272180\pi$
$444$	−7.83077	+	1.66448i	−0.371632	+	0.0789928i
$445$	8.13047	+	11.3610i	0.385421	+	0.538564i
$446$	1.02035	+	0.216881i	0.0483148	+	0.0102696i
$447$	−3.12421	−	9.61534i	−0.147770	−	0.454790i
$448$	10.9057	+	17.1638i	0.515247	+	0.810914i
$449$	−29.6674			−1.40009			−0.700046	−	0.714098i	$-0.746837\pi$
$449$	−29.6674			−1.40009			−0.700046	+	0.714098i	$0.746837\pi$
$450$	0.459016	+	0.343657i	0.0216382	+	0.0162001i
$451$	−6.95154	−	12.0404i	−0.327335	−	0.566961i
$452$	3.72532	−	35.4440i	0.175224	−	1.66715i
$453$	3.25752	+	0.692408i	0.153052	+	0.0325322i
$454$	0.784830	+	2.41546i	0.0368339	+	0.113363i
$455$	−4.03312	−	8.26152i	−0.189076	−	0.387306i
$456$	−0.209286	+	0.644116i	−0.00980072	+	0.0301635i
$457$	8.05191	−	13.9463i	0.376652	−	0.652381i	−0.613920	−	0.789368i	$-0.710408\pi$
$457$	8.05191	−	13.9463i	0.376652	−	0.652381i	0.990573	+	0.136987i	$0.0437418\pi$
$458$	−2.44289	+	0.519253i	−0.114149	+	0.0242631i
$459$	1.00320	+	0.446654i	0.0468254	+	0.0208480i
$460$	12.4271	+	1.39628i	0.579416	+	0.0651020i
$461$	−23.2026	−	16.8577i	−1.08065	−	0.785139i	−0.102855	−	0.994696i	$-0.532798\pi$
$461$	−23.2026	−	16.8577i	−1.08065	−	0.785139i	−0.977796	+	0.209557i	$0.932798\pi$
$462$	−0.453820	−	0.462916i	−0.0211136	−	0.0215368i
$463$	4.95781	−	3.60206i	0.230409	−	0.167402i	−0.466591	−	0.884473i	$-0.654518\pi$
$463$	4.95781	−	3.60206i	0.230409	−	0.167402i	0.697000	+	0.717071i	$0.254518\pi$
$464$	7.68896	−	3.42335i	0.356951	−	0.158925i
$465$	−3.26502	−	1.08681i	−0.151412	−	0.0503995i
$466$	−2.76041	−	1.22901i	−0.127873	−	0.0569329i
$467$	−2.43423	−	2.70349i	−0.112643	−	0.125103i	0.684186	−	0.729307i	$-0.260158\pi$
$467$	−2.43423	−	2.70349i	−0.112643	−	0.125103i	−0.796829	+	0.604205i	$0.793491\pi$
$468$	−3.08750			−0.142720
$469$	36.4949	+	6.15200i	1.68518	+	0.284073i
$470$	0.285787	+	0.654475i	0.0131824	+	0.0301887i
$471$	3.82514	+	0.813058i	0.176253	+	0.0374637i
$472$	−2.71799	+	3.01863i	−0.125106	+	0.138944i
$473$	2.13228	−	20.2873i	0.0980424	−	0.932811i
$474$	0.256451	−	0.444187i	0.0117792	−	0.0204022i
$475$	6.72216	+	3.10914i	0.308434	+	0.142657i
$476$	−4.52197	+	3.58812i	−0.207264	+	0.164461i
$477$	2.14697	+	1.55986i	0.0983030	+	0.0714213i
$478$	2.73695	+	0.581757i	0.125185	+	0.0266090i
$479$	6.46936	−	7.18495i	0.295593	−	0.328289i	−0.576994	−	0.816748i	$-0.695774\pi$
$479$	6.46936	−	7.18495i	0.295593	−	0.328289i	0.872587	+	0.488460i	$0.162441\pi$
$480$	−0.0218670	+	3.05021i	−0.000998090	+	0.139222i
$481$	4.18976	+	4.65320i	0.191037	+	0.212168i
$482$	−3.20335			−0.145909
$483$	4.74387	−	5.74077i	0.215853	−	0.261214i
$484$	−10.3440	+	7.51535i	−0.470182	+	0.341607i
$485$	31.6710	−	17.9838i	1.43811	−	0.816601i
$486$	0.0119875	−	0.114053i	0.000543763	−	0.00517356i
$487$	28.2953	+	12.5979i	1.28218	+	0.570864i	0.930855	−	0.365389i	$-0.119064\pi$
$487$	28.2953	+	12.5979i	1.28218	+	0.570864i	0.351327	+	0.936253i	$0.385731\pi$
$488$	0.329672	+	3.13662i	0.0149236	+	0.141988i
$489$	−17.9304	−	13.0272i	−0.810840	−	0.589110i
$490$	−0.235783	+	1.77950i	−0.0106516	+	0.0803894i
$491$	17.4571	−	12.6833i	0.787829	−	0.572391i	−0.119490	−	0.992835i	$-0.538126\pi$
$491$	17.4571	−	12.6833i	0.787829	−	0.572391i	0.907318	+	0.420444i	$0.138126\pi$
$492$	8.65125	+	9.60818i	0.390028	+	0.433170i
$493$	1.17853	+	2.04127i	0.0530782	+	0.0919341i
$494$	0.258211	−	0.0548845i	0.0116175	−	0.00246937i
$495$	0.959755	+	4.68002i	0.0431378	+	0.210351i
$496$	−1.86478	−	5.73919i	−0.0837309	−	0.257697i
$497$	−1.92114	+	30.8060i	−0.0861750	+	1.38184i
$498$	−0.0196077	−	0.0142458i	−0.000878640	−	0.000638369i
$499$	−14.3147	+	24.7938i	−0.640813	+	1.10992i	0.344438	+	0.938809i	$0.388069\pi$
$499$	−14.3147	+	24.7938i	−0.640813	+	1.10992i	−0.985252	+	0.171112i	$0.945264\pi$
$500$	22.0369	+	2.79651i	0.985520	+	0.125064i
$501$	8.07779	+	13.9911i	0.360889	+	0.625078i
$502$	0.749128	−	0.333533i	0.0334352	−	0.0148863i
$503$	7.69924	+	23.6958i	0.343292	+	1.05654i	0.962492	+	0.271311i	$0.0874570\pi$
$503$	7.69924	+	23.6958i	0.343292	+	1.05654i	−0.619200	+	0.785233i	$0.712543\pi$
$504$	1.00794	+	0.668875i	0.0448972	+	0.0297940i
$505$	−15.7275	+	13.9583i	−0.699865	+	0.621134i
$506$	−0.461483	−	0.512529i	−0.0205154	−	0.0227847i
$507$	−5.29259	−	9.16703i	−0.235052	−	0.407122i
$508$	8.17482	−	1.73761i	0.362699	−	0.0770941i
$509$	−0.314501	−	2.99228i	−0.0139400	−	0.132630i	0.985338	−	0.170611i	$-0.0545741\pi$
$509$	−0.314501	−	2.99228i	−0.0139400	−	0.132630i	−0.999278	+	0.0379807i	$0.987907\pi$
$510$	−0.280263	+	0.0274270i	−0.0124103	+	0.00121449i
$511$	13.8278	−	26.4856i	0.611707	−	1.17166i
$512$	−7.22845	+	5.25178i	−0.319455	+	0.232098i
$513$	−0.154835	−	1.47316i	−0.00683614	−	0.0650415i
$514$	0.112722	−	1.07248i	0.00497196	−	0.0473050i
$515$	−0.0887864	+	12.3847i	−0.00391239	+	0.545736i
$516$	1.98290	+	18.8661i	0.0872924	+	0.830532i
$517$	−1.83866	+	5.65882i	−0.0808643	+	0.248875i
$518$	−0.179263	−	1.20937i	−0.00787638	−	0.0531365i
$519$	−6.74321	+	20.7535i	−0.295994	+	0.910976i
$520$	1.38154	−	0.784482i	0.0605846	−	0.0344018i
$521$	13.3959	−	14.8776i	0.586885	−	0.651802i	−0.374429	−	0.927255i	$-0.622161\pi$
$521$	13.3959	−	14.8776i	0.586885	−	0.651802i	0.961314	+	0.275454i	$0.0888281\pi$
$522$	0.164708	−	0.182927i	0.00720909	−	0.00800651i
$523$	33.6732	−	14.9923i	1.47243	−	0.655566i	0.495395	−	0.868668i	$-0.335023\pi$
$523$	33.6732	−	14.9923i	1.47243	−	0.655566i	0.977030	+	0.213102i	$0.0683565\pi$
$524$	−41.6744			−1.82056
$525$	8.57206	−	10.0757i	0.374115	−	0.439740i
$526$	−1.24717			−0.0543794
$527$	1.54385	−	0.687368i	0.0672513	−	0.0299422i
$528$	−5.60589	+	6.22597i	−0.243965	+	0.270951i
$529$	−10.0885	+	11.2044i	−0.438631	+	0.487149i
$530$	−0.676273	−	0.0759847i	−0.0293754	−	0.00330056i
$531$	2.74534	−	8.44929i	0.119138	−	0.366668i
$532$	7.24138	+	2.86246i	0.313954	+	0.124103i
$533$	3.12484	−	9.61728i	0.135352	−	0.416570i
$534$	0.0748958	+	0.712586i	0.00324106	+	0.0308366i
$535$	−24.0895	−	8.01853i	−1.04148	−	0.346671i
$536$	−0.668536	+	6.36070i	−0.0288764	+	0.274740i
$537$	−0.228229	−	2.17145i	−0.00984880	−	0.0937051i
$538$	2.72231	−	1.97787i	0.117367	−	0.0852721i
$539$	−11.3106	+	9.78479i	−0.487183	+	0.421461i
$540$	−1.77788	−	4.07148i	−0.0765077	−	0.175209i
$541$	3.10206	+	29.5142i	0.133368	+	1.26891i	0.832542	+	0.553962i	$0.186885\pi$
$541$	3.10206	+	29.5142i	0.133368	+	1.26891i	−0.699174	+	0.714952i	$0.746449\pi$
$542$	1.50441	−	0.319772i	0.0646199	−	0.0137354i
$543$	2.24820	+	3.89400i	0.0964795	+	0.167107i
$544$	−1.00236	−	1.11324i	−0.0429759	−	0.0477296i
$545$	−2.40637	+	10.9350i	−0.103078	+	0.468405i
$546$	0.0293472	−	0.470589i	0.00125594	−	0.0201394i
$547$	2.08920	+	6.42989i	0.0893276	+	0.274922i	0.985734	−	0.168311i	$-0.0538313\pi$
$547$	2.08920	+	6.42989i	0.0893276	+	0.274922i	−0.896406	+	0.443233i	$0.853831\pi$
$548$	5.44475	−	2.42416i	0.232588	−	0.103555i
$549$	−3.44901	−	5.97386i	−0.147200	−	0.254958i
$550$	−0.806614	−	0.922086i	−0.0343941	−	0.0393179i
$551$	1.58971	−	2.75345i	0.0677237	−	0.117301i
$552$	1.04118	+	0.756459i	0.0443154	+	0.0321970i
$553$	−9.85946	−	6.54280i	−0.419267	−	0.278228i
$554$	−0.164166	−	0.505252i	−0.00697475	−	0.0214661i
$555$	−3.72357	+	8.20448i	−0.158057	+	0.348261i
$556$	−22.1187	+	4.70147i	−0.938041	+	0.199387i
$557$	2.55888	+	4.43211i	0.108423	+	0.187795i	0.915132	−	0.403155i	$-0.132086\pi$
$557$	2.55888	+	4.43211i	0.108423	+	0.187795i	−0.806708	+	0.590950i	$0.798753\pi$
$558$	−0.118093	−	0.131155i	−0.00499926	−	0.00555224i
$559$	12.0033	−	8.72094i	0.507687	−	0.368857i
$560$	23.1426	+	1.60986i	0.977952	+	0.0680290i
$561$	−1.89812	−	1.37906i	−0.0801386	−	0.0582241i
$562$	−0.248241	−	2.36186i	−0.0104714	−	0.0996289i
$563$	22.2393	+	9.90159i	0.937276	+	0.417302i	0.817779	−	0.575532i	$-0.195205\pi$
$563$	22.2393	+	9.90159i	0.937276	+	0.417302i	0.119497	+	0.992835i	$0.461872\pi$
$564$	0.578377	−	5.50289i	0.0243541	−	0.231713i
$565$	−29.6141	−	27.0516i	−1.24588	−	1.13807i
$566$	0.748667	−	0.543938i	0.0314688	−	0.0228634i
$567$	−2.60894	−	0.439794i	−0.109565	−	0.0184696i
$568$	−5.33399			−0.223809
$569$	28.2418	+	31.3657i	1.18396	+	1.31492i	0.938406	+	0.345536i	$0.112303\pi$
$569$	28.2418	+	31.3657i	1.18396	+	1.31492i	0.245553	+	0.969383i	$0.421030\pi$
$570$	0.221062	+	0.308899i	0.00925927	+	0.0129383i
$571$	19.4289	−	21.5779i	0.813073	−	0.903009i	−0.183725	−	0.982978i	$-0.558815\pi$
$571$	19.4289	−	21.5779i	0.813073	−	0.903009i	0.996797	+	0.0799690i	$0.0254821\pi$
$572$	6.45238	+	1.37150i	0.269787	+	0.0573451i
$573$	13.7713	+	10.0054i	0.575302	+	0.417982i
$574$	−1.54669	+	1.22727i	−0.0645574	+	0.0512254i
$575$	9.56625	−	10.3228i	0.398940	−	0.430492i
$576$	3.84304	−	6.65634i	0.160127	−	0.277348i
$577$	−1.55528	+	14.7975i	−0.0647473	+	0.616029i	0.913248	+	0.407404i	$0.133566\pi$
$577$	−1.55528	+	14.7975i	−0.0647473	+	0.616029i	−0.977996	+	0.208626i	$0.933101\pi$
$578$	−1.21199	+	1.34605i	−0.0504121	+	0.0559883i
$579$	−12.4829	−	2.65333i	−0.518773	−	0.110269i
$580$	2.04944	−	9.31306i	0.0850984	−	0.386704i
$581$	−0.356175	+	0.431024i	−0.0147766	+	0.0178819i
$582$	1.86791			0.0774275
$583$	−3.79391	−	4.21356i	−0.157128	−	0.174508i
$584$	4.71690	+	2.10010i	0.195187	+	0.0869027i
$585$	−2.06253	+	2.79644i	−0.0852750	+	0.115619i
$586$	−1.30602	+	0.581476i	−0.0539510	+	0.0240206i
$587$	−10.6224	+	7.71760i	−0.438432	+	0.318539i	−0.785011	−	0.619481i	$-0.787343\pi$
$587$	−10.6224	+	7.71760i	−0.438432	+	0.318539i	0.346580	+	0.938021i	$0.387343\pi$
$588$	8.39654	−	11.0873i	0.346267	−	0.457234i
$589$	−1.84421	−	1.33990i	−0.0759894	−	0.0552096i
$590$	0.457677	+	2.23175i	0.0188423	+	0.0918799i
$591$	−8.78299	−	3.91044i	−0.361284	−	0.160854i
$592$	−15.4549	+	3.28504i	−0.635192	+	0.135014i
$593$	7.34117	−	12.7153i	0.301466	−	0.522154i	−0.675002	−	0.737816i	$-0.735857\pi$
$593$	7.34117	−	12.7153i	0.301466	−	0.522154i	0.976468	+	0.215661i	$0.0691907\pi$
$594$	−0.0757153	+	0.233028i	−0.00310664	+	0.00956124i
$595$	0.229084	+	6.49264i	0.00939152	+	0.266172i
$596$	−6.20734	−	19.1042i	−0.254262	−	0.782539i
$597$	−11.8319	−	2.51496i	−0.484249	−	0.102930i
$598$	0.0524342	−	0.498878i	0.00214419	−	0.0204006i
$599$	−18.0452	−	31.2553i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$599$	−18.0452	−	31.2553i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$600$	1.83003	+	1.37011i	0.0747106	+	0.0559344i
$601$	9.48350			0.386840			0.193420	−	0.981116i	$-0.438042\pi$
$601$	9.48350			0.386840			0.193420	+	0.981116i	$0.438042\pi$
$602$	−2.89436	+	0.122904i	−0.117965	+	0.00500921i
$603$	−4.32265	−	13.3037i	−0.176032	−	0.541770i
$604$	6.47220	+	1.37571i	0.263350	+	0.0559768i
$605$	−0.103157	+	14.3893i	−0.00419394	+	0.585009i
$606$	−1.05491	+	0.224228i	−0.0428528	+	0.00910865i
$607$	1.47397	−	2.55299i	0.0598267	−	0.103623i	−0.834561	−	0.550916i	$-0.814279\pi$
$607$	1.47397	−	2.55299i	0.0598267	−	0.103623i	0.894387	+	0.447293i	$0.147612\pi$
$608$	−0.624415	+	1.92175i	−0.0253234	+	0.0779373i
$609$	−3.97552	−	4.05520i	−0.161096	−	0.164325i
$610$	1.52553	+	0.895409i	0.0617670	+	0.0362540i
$611$	−3.95353	+	1.76022i	−0.159943	+	0.0712110i
$612$	1.99321	+	0.887433i	0.0805706	+	0.0358723i
$613$	−7.89074	−	3.51318i	−0.318704	−	0.141896i	0.241149	−	0.970488i	$-0.422476\pi$
$613$	−7.89074	−	3.51318i	−0.318704	−	0.141896i	−0.559853	+	0.828592i	$0.689142\pi$
$614$	−0.136916	+	0.0609590i	−0.00552549	+	0.00246010i
$615$	14.4817	−	1.41720i	0.583957	−	0.0571469i
$616$	−1.80931	−	1.84557i	−0.0728992	−	0.0743603i
$617$	12.8306	−	39.4885i	0.516541	−	1.58975i	−0.263921	−	0.964544i	$-0.585016\pi$
$617$	12.8306	−	39.4885i	0.516541	−	1.58975i	0.780461	−	0.625204i	$-0.214984\pi$
$618$	−0.317596	+	0.550093i	−0.0127756	+	0.0221280i
$619$	−26.1299	+	5.55408i	−1.05025	+	0.223237i	−0.700534	−	0.713619i	$-0.747055\pi$
$619$	−26.1299	+	5.55408i	−1.05025	+	0.223237i	−0.349715	+	0.936856i	$0.613722\pi$
$620$	−6.48710	−	2.15932i	−0.260528	−	0.0867204i
$621$	−2.75327	−	0.585225i	−0.110485	−	0.0234843i
$622$	0.373161	+	1.14847i	0.0149624	+	0.0460495i
$623$	16.5153	−	0.701297i	0.661673	−	0.0280969i
$624$	−6.09352			−0.243936
$625$	17.2541	−	18.0914i	0.690163	−	0.723654i
$626$	−0.739600	−	1.28102i	−0.0295604	−	0.0512000i
$627$	−0.330809	+	3.14744i	−0.0132112	+	0.125697i
$628$	7.59997	+	1.61542i	0.303272	+	0.0644624i
$629$	−1.36734	−	4.20823i	−0.0545193	−	0.167793i
$630$	0.637464	−	0.232280i	0.0253972	−	0.00925424i
$631$	13.8725	−	42.6952i	0.552255	−	1.69967i	−0.150828	−	0.988560i	$-0.548194\pi$
$631$	13.8725	−	42.6952i	0.552255	−	1.69967i	0.703083	−	0.711107i	$-0.251806\pi$
$632$	1.02243	−	1.77091i	0.0406702	−	0.0704428i
$633$	−13.8628	+	2.94663i	−0.550997	+	0.117118i
$634$	−1.44157	−	0.641827i	−0.0572520	−	0.0254902i
$635$	3.88717	−	8.56495i	0.154258	−	0.339890i
$636$	4.26570	+	3.09921i	0.169146	+	0.122892i
$637$	−10.7935	−	1.35148i	−0.427654	−	0.0535475i
$638$	−0.425472	+	0.309123i	−0.0168446	+	0.0122383i
$639$	10.6576	−	4.74507i	0.421608	−	0.187712i
$640$	−0.0578638	+	8.07136i	−0.00228727	+	0.319048i
$641$	38.8151	+	17.2816i	1.53310	+	0.682582i	0.987810	−	0.155662i	$-0.0497512\pi$
$641$	38.8151	+	17.2816i	1.53310	+	0.682582i	0.545294	+	0.838245i	$0.316418\pi$
$642$	−0.871294	−	0.967670i	−0.0343872	−	0.0381909i
$643$	12.4114			0.489459			0.244730	−	0.969591i	$-0.421301\pi$
$643$	12.4114			0.489459			0.244730	+	0.969591i	$0.421301\pi$
$644$	9.42534	−	11.4060i	0.371410	−	0.449461i
$645$	18.4122	+	10.8070i	0.724979	+	0.425525i
$646$	−0.182469	−	0.0387851i	−0.00717916	−	0.00152598i
$647$	−30.3051	+	33.6572i	−1.19141	+	1.32320i	−0.257255	+	0.966343i	$0.582818\pi$
$647$	−30.3051	+	33.6572i	−1.19141	+	1.32320i	−0.934159	+	0.356856i	$0.883849\pi$
$648$	0.0477923	−	0.454713i	0.00187746	−	0.0178628i
$649$	−9.49056	+	16.4381i	−0.372537	+	0.645253i
$650$	0.105837	−	0.884750i	0.00415126	−	0.0347028i
$651$	−3.18951	+	2.53083i	−0.125007	+	0.0991912i
$652$	−35.6249	−	25.8830i	−1.39518	−	1.01366i
$653$	−0.175000	−	0.0371974i	−0.00684827	−	0.00145565i	0.204486	−	0.978869i	$-0.434448\pi$
$653$	−0.175000	−	0.0371974i	−0.00684827	−	0.00145565i	−0.211335	+	0.977414i	$0.567781\pi$
$654$	−0.384245	+	0.426747i	−0.0150252	+	0.0166871i
$655$	−27.8395	+	37.7458i	−1.08778	+	1.47485i
$656$	17.0742	+	18.9628i	0.666635	+	0.740373i
$657$	−11.2928			−0.440576
$658$	0.833239	+	0.140461i	0.0324830	+	0.00547572i
$659$	−29.7455	+	21.6114i	−1.15872	+	0.841860i	−0.989616	−	0.143738i	$-0.954088\pi$
$659$	−29.7455	+	21.6114i	−1.15872	+	0.841860i	−0.169105	+	0.985598i	$0.554088\pi$
$660$	1.90689	+	9.29849i	0.0742255	+	0.361943i
$661$	1.49538	−	14.2276i	0.0581637	−	0.553391i	−0.926174	−	0.377097i	$-0.876922\pi$
$661$	1.49538	−	14.2276i	0.0581637	−	0.553391i	0.984338	−	0.176294i	$-0.0564109\pi$
$662$	0.383939	+	0.170941i	0.0149222	+	0.00664379i
$663$	−0.178375	−	1.69713i	−0.00692752	−	0.0659110i
$664$	−0.0781727	−	0.0567958i	−0.00303369	−	0.00220411i
$665$	7.43004	−	4.64655i	0.288124	−	0.180185i
$666$	−0.373840	+	0.271611i	−0.0144860	+	0.0105247i
$667$	−4.04265	−	4.48982i	−0.156532	−	0.173847i
$668$	16.0493	+	27.7983i	0.620968	+	1.07555i
$669$	−8.89723	+	1.89116i	−0.343987	+	0.0731166i
$670$	2.64847	+	2.41930i	0.102319	+	0.0934657i
$671$	4.55423	+	14.0165i	0.175814	+	0.541100i
$672$	3.00724	+	1.99562i	0.116007	+	0.0769827i
$673$	13.6047	+	9.88440i	0.524423	+	0.381015i	0.818267	−	0.574838i	$-0.194935\pi$
$673$	13.6047	+	9.88440i	0.524423	+	0.381015i	−0.293845	+	0.955853i	$0.594935\pi$
$674$	−0.588998	+	1.02017i	−0.0226874	+	0.0392957i
$675$	−4.87533	−	1.10957i	−0.187652	−	0.0427074i
$676$	−10.5156	−	18.2135i	−0.404445	−	0.700519i
$677$	3.60120	−	1.60336i	0.138405	−	0.0616220i	−0.336365	−	0.941732i	$-0.609198\pi$
$677$	3.60120	−	1.60336i	0.138405	−	0.0616220i	0.474771	+	0.880110i	$0.342531\pi$
$678$	−0.635682	−	1.95643i	−0.0244132	−	0.0751361i
$679$	2.68221	−	43.0100i	0.102934	−	1.65057i
$680$	−1.11737	+	0.109347i	−0.0428491	+	0.00419327i
$681$	−14.8187	−	16.4579i	−0.567855	−	0.630667i
$682$	0.188534	+	0.326550i	0.00721934	+	0.0125043i
$683$	8.03575	−	1.70805i	0.307479	−	0.0653568i	−0.0515878	−	0.998668i	$-0.516428\pi$
$683$	8.03575	−	1.70805i	0.307479	−	0.0653568i	0.359067	+	0.933312i	$0.383095\pi$
$684$	−0.307634	−	2.92694i	−0.0117627	−	0.111914i
$685$	1.44159	−	6.55087i	0.0550803	−	0.250296i
$686$	1.61009	+	1.38517i	0.0614736	+	0.0528859i
$687$	17.6183	−	12.8005i	0.672181	−	0.488368i
$688$	3.91347	+	37.2342i	0.149200	+	1.41954i
$689$	0.431068	−	4.10133i	0.0164224	−	0.156248i
$690$	0.688062	−	0.218124i	0.0261941	−	0.00830384i
$691$	0.924196	+	8.79314i	0.0351581	+	0.334507i	0.997936	+	0.0642137i	$0.0204539\pi$
$691$	0.924196	+	8.79314i	0.0351581	+	0.334507i	−0.962778	+	0.270293i	$0.912879\pi$
$692$	−13.3977	+	41.2340i	−0.509306	+	1.56748i
$693$	5.25690	+	2.07801i	0.199693	+	0.0789372i
$694$	−0.364508	+	1.12184i	−0.0138365	+	0.0425845i
$695$	−10.5175	+	23.1742i	−0.398953	+	0.879049i
$696$	0.656668	−	0.729303i	0.0248909	−	0.0276442i
$697$	−4.78158	+	5.31048i	−0.181115	+	0.201149i
$698$	0.825977	−	0.367749i	0.0312637	−	0.0139195i
$699$	26.3481			0.996578
$700$	17.0314	−	20.0189i	0.643726	−	0.756643i
$701$	−23.4163			−0.884422			−0.442211	−	0.896911i	$-0.645806\pi$
$701$	−23.4163			−0.884422			−0.442211	+	0.896911i	$0.645806\pi$
$702$	−0.162804	+	0.0724852i	−0.00614466	+	0.00273578i
$703$	−3.99375	+	4.43551i	−0.150627	+	0.167288i
$704$	−10.9881	+	12.2036i	−0.414131	+	0.459939i
$705$	−4.59776	−	4.19992i	−0.173162	−	0.158178i
$706$	0.0395915	−	0.121850i	0.00149004	−	0.00458589i
$707$	3.64822	+	24.6120i	0.137206	+	0.925631i
$708$	5.45457	−	16.7874i	0.204995	−	0.630911i
$709$	−0.204285	−	1.94364i	−0.00767207	−	0.0729949i	0.990016	−	0.140955i	$-0.0450174\pi$
$709$	−0.204285	−	1.94364i	−0.00767207	−	0.0729949i	−0.997688	+	0.0679606i	$0.978351\pi$
$710$	−1.77574	+	2.40761i	−0.0666424	+	0.0903560i
$711$	−0.467494	+	4.44791i	−0.0175324	+	0.166810i
$712$	0.298598	+	2.84097i	0.0111904	+	0.106470i
$713$	−3.50445	+	2.54613i	−0.131243	+	0.0953534i
$714$	−0.154206	+	0.295364i	−0.00577101	+	0.0110537i
$715$	5.55255	−	4.92792i	0.207654	−	0.184294i
$716$	−0.453456	−	4.31435i	−0.0169465	−	0.161235i
$717$	−23.8657	+	5.07281i	−0.891281	+	0.189448i
$718$	−2.01732	−	3.49409i	−0.0752856	−	0.130398i
$719$	−27.6504	−	30.7089i	−1.03119	−	1.14525i	−0.989266	−	0.146129i	$-0.953319\pi$
$719$	−27.6504	−	30.7089i	−1.03119	−	1.14525i	−0.0419217	−	0.999121i	$-0.513348\pi$
$720$	−3.50884	−	8.03552i	−0.130767	−	0.299466i
$721$	12.2102	+	8.10278i	0.454733	+	0.301763i
$722$	−0.595574	−	1.83299i	−0.0221650	−	0.0682167i
$723$	25.5177	−	11.3612i	0.949014	−	0.422528i
$724$	4.46683	+	7.73678i	0.166008	+	0.287535i
$725$	−7.06604	−	8.07759i	−0.262426	−	0.299994i
$726$	−0.369003	+	0.639131i	−0.0136950	+	0.0237204i
$727$	25.2119	+	18.3175i	0.935058	+	0.679359i	0.947226	−	0.320567i	$-0.103873\pi$
$727$	25.2119	+	18.3175i	0.935058	+	0.679359i	−0.0121682	+	0.999926i	$0.503873\pi$
$728$	0.117003	−	1.87617i	0.00433641	−	0.0695354i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	2.51823	−	1.42993i	0.0932038	−	0.0529240i
$731$	−10.2557	+	2.17991i	−0.379320	+	0.0806269i
$732$	−6.85266	−	11.8692i	−0.253282	−	0.438697i
$733$	−29.2357	−	32.4695i	−1.07984	−	1.19929i	−0.978888	−	0.204397i	$-0.934477\pi$
$733$	−29.2357	−	32.4695i	−1.07984	−	1.19929i	−0.100956	−	0.994891i	$-0.532190\pi$
$734$	−2.07140	+	1.50496i	−0.0764569	+	0.0555492i
$735$	−4.43304	−	15.0116i	−0.163515	−	0.553711i
$736$	3.10640	+	2.25693i	0.114503	+	0.0831917i
$737$	3.12399	+	29.7228i	0.115074	+	1.09485i
$738$	0.681752	+	0.303536i	0.0250956	+	0.0111733i
$739$	2.14581	−	20.4160i	0.0789350	−	0.751016i	−0.881438	−	0.472299i	$-0.843424\pi$
$739$	2.14581	−	20.4160i	0.0789350	−	0.751016i	0.960373	−	0.278717i	$-0.0899091\pi$
$740$	−7.39817	+	16.3011i	−0.271962	+	0.599239i
$741$	−1.86224	+	1.35300i	−0.0684110	+	0.0497035i
$742$	−0.512920	+	0.620709i	−0.0188299	+	0.0227869i
$743$	−42.6740			−1.56556			−0.782779	−	0.622300i	$-0.786198\pi$
$743$	−42.6740			−1.56556			−0.782779	+	0.622300i	$0.786198\pi$
$744$	−0.470817	−	0.522895i	−0.0172610	−	0.0191703i
$745$	−21.4499	−	7.13991i	−0.785864	−	0.261586i
$746$	0.942398	−	1.04664i	0.0345036	−	0.0383202i
$747$	0.206718	+	0.0439393i	0.00756343	+	0.00160766i
$748$	−3.77127	−	2.73999i	−0.137891	−	0.100184i
$749$	−23.5324	+	18.6726i	−0.859855	+	0.682283i
$750$	1.22766	−	0.369899i	0.0448279	−	0.0135068i
$751$	−4.25602	+	7.37164i	−0.155304	+	0.268995i	−0.933170	−	0.359436i	$-0.882969\pi$
$751$	−4.25602	+	7.37164i	−0.155304	+	0.268995i	0.777866	+	0.628431i	$0.216302\pi$
$752$	1.14149	−	10.8606i	0.0416259	−	0.396044i
$753$	−4.78458	+	5.31381i	−0.174360	+	0.193646i
$754$	−0.374156	−	0.0795292i	−0.0136259	−	0.00289628i
$755$	5.56961	−	4.94306i	0.202699	−	0.179896i
$756$	−5.18357	−	0.873804i	−0.188525	−	0.0317799i
$757$	−43.7447			−1.58993			−0.794963	−	0.606657i	$-0.792510\pi$
$757$	−43.7447			−1.58993			−0.794963	+	0.606657i	$0.792510\pi$
$758$	−1.52118	−	1.68944i	−0.0552516	−	0.0613631i
$759$	5.49392	+	2.44605i	0.199417	+	0.0887860i
$760$	0.881341	+	1.23153i	0.0319696	+	0.0446723i
$761$	−24.1060	+	10.7327i	−0.873841	+	0.389059i	−0.794122	−	0.607758i	$-0.792069\pi$
$761$	−24.1060	+	10.7327i	−0.873841	+	0.389059i	−0.0797190	+	0.996817i	$0.525402\pi$
$762$	0.390265	−	0.283544i	0.0141378	−	0.0102717i
$763$	9.27440	+	9.46029i	0.335756	+	0.342485i
$764$	27.3614	+	19.8792i	0.989900	+	0.719205i
$765$	2.13529	−	1.21248i	0.0772014	−	0.0438373i
$766$	−3.52759	−	1.57058i	−0.127457	−	0.0567475i
$767$	−13.5040	+	2.87035i	−0.487599	+	0.103642i
$768$	7.47910	−	12.9542i	0.269879	−	0.467444i
$769$	−11.3505	+	34.9334i	−0.409311	+	1.25973i	0.507930	+	0.861398i	$0.330411\pi$
$769$	−11.3505	+	34.9334i	−0.409311	+	1.25973i	−0.917241	+	0.398332i	$0.869589\pi$
$770$	−1.43538	+	0.202260i	−0.0517274	+	0.00728893i
$771$	2.90579	+	8.94309i	0.104649	+	0.322078i
$772$	−24.8017	−	5.27176i	−0.892632	−	0.189735i
$773$	−5.29387	+	50.3678i	−0.190407	+	1.81160i	0.315402	+	0.948958i	$0.397861\pi$
$773$	−5.29387	+	50.3678i	−0.190407	+	1.81160i	−0.505809	+	0.862645i	$0.668806\pi$
$774$	0.547476	+	0.948257i	0.0196786	+	0.0340844i
$775$	−6.28930	+	4.43308i	−0.225918	+	0.159241i
$776$	7.44708			0.267335
$777$	5.71722	+	8.99796i	0.205104	+	0.322800i
$778$	−0.0311038	−	0.0957277i	−0.00111513	−	0.00343200i
$779$	9.42849	+	2.00409i	0.337811	+	0.0718039i
$780$	−4.09793	+	5.55611i	−0.146729	+	0.198941i
$781$	−24.3805	+	5.18223i	−0.872401	+	0.185435i
$782$	−0.177241	+	0.306991i	−0.00633813	+	0.0109780i
$783$	−0.663276	+	2.04135i	−0.0237035	+	0.0729520i
$784$	16.5715	−	21.8821i	0.591839	−	0.781502i
$785$	6.54010	−	5.80438i	0.233426	−	0.207167i
$786$	−2.19750	+	0.978389i	−0.0783821	+	0.0348980i
$787$	24.9418	+	11.1048i	0.889080	+	0.395844i	0.799873	−	0.600169i	$-0.204900\pi$
$787$	24.9418	+	11.1048i	0.889080	+	0.395844i	0.0892068	+	0.996013i	$0.471567\pi$
$788$	−17.4505	−	7.76945i	−0.621647	−	0.276775i
$789$	9.93491	−	4.42331i	0.353692	−	0.157474i
$790$	−0.458957	−	1.05105i	−0.0163290	−	0.0373947i
$791$	−45.9609	+	11.8277i	−1.63418	+	0.420545i
$792$	−0.301865	+	0.929046i	−0.0107263	+	0.0330122i
$793$	−5.35966	+	9.28321i	−0.190327	+	0.329656i
$794$	3.32770	−	0.707324i	0.118096	−	0.0251020i
$795$	5.65664	−	1.79322i	0.200620	−	0.0635991i
$796$	−23.5083	−	4.99684i	−0.833228	−	0.177108i
$797$	1.74674	+	5.37591i	0.0618727	+	0.190425i	0.977215	−	0.212252i	$-0.0680798\pi$
$797$	1.74674	+	5.37591i	0.0618727	+	0.190425i	−0.915342	+	0.402677i	$0.868080\pi$
$798$	0.449041	−	0.0190678i	0.0158959	−	0.000674992i
$799$	3.05822			0.108192
$800$	5.45998	+	4.08778i	0.193039	+	0.144525i
$801$	−3.12392	−	5.41079i	−0.110378	−	0.191181i
$802$	0.331166	−	3.15083i	0.0116939	−	0.111260i
$803$	23.6002	+	5.01638i	0.832833	+	0.177024i
$804$	−8.58844	−	26.4325i	−0.302891	−	0.932203i
$805$	−4.03444	−	16.1563i	−0.142195	−	0.569436i
$806$	−0.0847494	+	0.260832i	−0.00298517	+	0.00918741i
$807$	−14.6709	+	25.4107i	−0.516439	+	0.894499i
$808$	−4.20577	+	0.893964i	−0.147958	+	0.0314495i
$809$	21.2279	+	9.45128i	0.746334	+	0.332289i	0.744423	−	0.667709i	$-0.232725\pi$
$809$	21.2279	+	9.45128i	0.746334	+	0.332289i	0.00191155	+	0.999998i	$0.499392\pi$
$810$	−0.189334	−	0.172951i	−0.00665251	−	0.00607687i
$811$	5.05939	+	3.67586i	0.177659	+	0.129077i	0.673061	−	0.739587i	$-0.264979\pi$
$811$	5.05939	+	3.67586i	0.177659	+	0.129077i	−0.495402	+	0.868664i	$0.664979\pi$
$812$	−7.89875	−	8.05707i	−0.277192	−	0.282748i
$813$	−10.8499	+	7.88292i	−0.380523	+	0.276466i
$814$	0.901917	−	0.401560i	0.0316122	−	0.0140747i
$815$	−47.2414	+	14.9761i	−1.65479	+	0.524590i
$816$	3.93381	+	1.75145i	0.137711	+	0.0613129i
$817$	9.46341	+	10.5102i	0.331083	+	0.367705i
$818$	0.759673			0.0265613
$819$	1.43524	+	3.85277i	0.0501515	+	0.134627i
$820$	28.7729	−	2.81575i	1.00479	−	0.0983304i
$821$	−28.9734	−	6.15849i	−1.01118	−	0.214933i	−0.327606	−	0.944814i	$-0.606242\pi$
$821$	−28.9734	−	6.15849i	−1.01118	−	0.214933i	−0.683574	+	0.729882i	$0.739575\pi$
$822$	0.230190	−	0.255652i	0.00802881	−	0.00891690i
$823$	2.96595	−	28.2192i	0.103387	−	0.983659i	−0.812701	−	0.582681i	$-0.802004\pi$
$823$	2.96595	−	28.2192i	0.103387	−	0.983659i	0.916088	−	0.400978i	$-0.131330\pi$
$824$	−1.26621	+	2.19314i	−0.0441105	+	0.0764016i
$825$	9.69577	+	4.48449i	0.337563	+	0.156130i
$826$	2.50685	+	0.990939i	0.0872246	+	0.0344792i
$827$	−32.4388	−	23.5681i	−1.12801	−	0.819545i	−0.142603	−	0.989780i	$-0.545547\pi$
$827$	−32.4388	−	23.5681i	−1.12801	−	0.819545i	−0.985403	+	0.170235i	$0.945547\pi$
$828$	−5.47032	−	1.16275i	−0.190107	−	0.0404085i
$829$	−32.1931	+	35.7540i	−1.11811	+	1.24179i	−0.150699	+	0.988580i	$0.548153\pi$
$829$	−32.1931	+	35.7540i	−1.11811	+	1.24179i	−0.967412	+	0.253209i	$0.918514\pi$
$830$	−0.0516605	+	0.0163770i	−0.00179316	+	0.000568454i
$831$	3.09969	+	3.44256i	0.107527	+	0.119421i
$832$	−11.9439			−0.414082
$833$	6.57954	+	3.97483i	0.227968	+	0.137720i
$834$	−1.05594	+	0.767188i	−0.0365644	+	0.0265656i
$835$	35.8991	+	4.03355i	1.24234	+	0.139587i
$836$	−0.657267	+	6.25348i	−0.0227321	+	0.216281i
$837$	1.40588	+	0.625938i	0.0485943	+	0.0216356i
$838$	0.154630	+	1.47121i	0.00534162	+	0.0508221i
$839$	24.7923	+	18.0126i	0.855924	+	0.621865i	0.926773	−	0.375622i	$-0.122571\pi$
$839$	24.7923	+	18.0126i	0.855924	+	0.621865i	−0.0708490	+	0.997487i	$0.522571\pi$
$840$	2.54147	−	0.926064i	0.0876891	−	0.0319522i
$841$	19.7343	−	14.3378i	0.680493	−	0.494407i
$842$	−1.41075	−	1.56680i	−0.0486176	−	0.0539953i
$843$	10.3542	+	17.9340i	0.356617	+	0.617679i
$844$	−27.5433	+	5.85451i	−0.948079	+	0.201520i
$845$	−23.5212	−	2.64279i	−0.809153	−	0.0909147i
$846$	−0.0986932	−	0.303747i	−0.00339314	−	0.0104430i
$847$	14.1866	+	9.41430i	0.487457	+	0.323479i
$848$	8.41883	+	6.11664i	0.289104	+	0.210046i
$849$	−4.03467	+	6.98825i	−0.138469	+	0.239836i
$850$	−0.322627	+	0.540750i	−0.0110660	+	0.0185476i
$851$	5.67086	+	9.82222i	0.194395	+	0.336701i
$852$	21.1750	−	9.42774i	0.725445	−	0.322989i
$853$	−10.8592	−	33.4212i	−0.371812	−	1.14432i	−0.945604	−	0.325319i	$-0.894528\pi$
$853$	−10.8592	−	33.4212i	−0.371812	−	1.14432i	0.573792	−	0.819001i	$-0.305472\pi$
$854$	1.87420	−	0.931648i	0.0641339	−	0.0318803i
$855$	−2.85653	−	1.67663i	−0.0976911	−	0.0573397i
$856$	−3.47372	−	3.85795i	−0.118729	−	0.131862i
$857$	−4.88439	−	8.46001i	−0.166848	−	0.288989i	0.770462	−	0.637486i	$-0.220025\pi$
$857$	−4.88439	−	8.46001i	−0.166848	−	0.288989i	−0.937310	+	0.348497i	$0.886692\pi$
$858$	0.372433	−	0.0791631i	0.0127147	−	0.00270258i
$859$	−4.00257	−	38.0819i	−0.136566	−	1.29934i	−0.821279	−	0.570526i	$-0.806739\pi$
$859$	−4.00257	−	38.0819i	−0.136566	−	1.29934i	0.684713	−	0.728812i	$-0.259927\pi$
$860$	36.5822	+	21.4719i	1.24744	+	0.732185i
$861$	7.96808	−	15.2620i	0.271551	−	0.520126i
$862$	1.23784	−	0.899342i	0.0421609	−	0.0306317i
$863$	2.87933	+	27.3950i	0.0980136	+	0.932537i	0.927453	+	0.373940i	$0.121994\pi$
$863$	2.87933	+	27.3950i	0.0980136	+	0.932537i	−0.829439	+	0.558597i	$0.811340\pi$
$864$	0.142591	−	1.35666i	0.00485103	−	0.0461545i
$865$	28.3969	+	39.6800i	0.965522	+	1.34916i
$866$	−0.468080	−	4.45349i	−0.0159060	−	0.151336i
$867$	4.88064	−	15.0211i	0.165755	−	0.510142i
$868$	−6.33707	+	5.02838i	−0.215094	+	0.170674i
$869$	2.95279	−	9.08774i	0.100166	−	0.308281i
$870$	−0.110575	−	0.539193i	−0.00374885	−	0.0182804i
$871$	−14.5452	+	16.1541i	−0.492847	+	0.547362i
$872$	−1.53193	+	1.70138i	−0.0518775	+	0.0576158i
$873$	−14.8797	+	6.62486i	−0.503601	+	0.224218i
$874$	0.478159			0.0161740
$875$	−6.75434	−	28.7989i	−0.228338	−	0.973582i
$876$	−22.4372			−0.758081
$877$	24.4992	−	10.9078i	0.827280	−	0.368329i	0.0509860	−	0.998699i	$-0.483764\pi$
$877$	24.4992	−	10.9078i	0.827280	−	0.368329i	0.776295	+	0.630370i	$0.217097\pi$
$878$	−1.24555	+	1.38333i	−0.0420353	+	0.0466850i
$879$	8.34135	−	9.26400i	0.281347	−	0.312467i
$880$	3.76345	+	18.3516i	0.126866	+	0.618632i
$881$	1.35227	−	4.16186i	0.0455592	−	0.140217i	−0.925689	−	0.378285i	$-0.876514\pi$
$881$	1.35227	−	4.16186i	0.0455592	−	0.140217i	0.971249	+	0.238068i	$0.0765141\pi$
$882$	0.182454	−	0.781761i	0.00614353	−	0.0263233i
$883$	−0.201608	+	0.620485i	−0.00678465	+	0.0208810i	−0.954392	−	0.298558i	$-0.903494\pi$
$883$	−0.201608	+	0.620485i	−0.00678465	+	0.0208810i	0.947607	+	0.319439i	$0.103494\pi$
$884$	−0.354405	−	3.37194i	−0.0119199	−	0.113410i
$885$	−11.5611	−	16.1548i	−0.388623	−	0.543037i
$886$	0.288708	−	2.74687i	0.00969932	−	0.0922829i
$887$	1.09229	+	10.3924i	0.0366754	+	0.348944i	0.997436	+	0.0715644i	$0.0227991\pi$
$887$	1.09229	+	10.3924i	0.0366754	+	0.348944i	−0.960761	+	0.277379i	$0.910534\pi$
$888$	−1.49044	+	1.08287i	−0.0500161	+	0.0363388i
$889$	−5.96841	−	9.39329i	−0.200174	−	0.315041i
$890$	1.38174	+	0.811010i	0.0463160	+	0.0271851i
$891$	−0.223328	−	2.12482i	−0.00748176	−	0.0711842i
$892$	−17.6774	+	3.75746i	−0.591884	+	0.125809i
$893$	−2.06261	−	3.57254i	−0.0690225	−	0.119551i
$894$	−0.775823	−	0.861638i	−0.0259474	−	0.0288175i
$895$	−4.21055	−	2.47138i	−0.140743	−	0.0826091i
$896$	7.95764	+	5.28074i	0.265846	+	0.176417i
$897$	1.35166	+	4.16000i	0.0451308	+	0.138898i
$898$	−3.10816	+	1.38384i	−0.103721	+	0.0461794i
$899$	1.65158	+	2.86062i	0.0550833	+	0.0954072i
$900$	−9.68654	−	2.20455i	−0.322885	−	0.0734850i
$901$	−1.45712	+	2.52381i	−0.0485437	+	0.0840802i
$902$	−1.28992	−	0.937180i	−0.0429496	−	0.0312047i
$903$	22.6204	−	11.2444i	0.752760	−	0.374190i
$904$	−2.53437	−	7.79998i	−0.0842918	−	0.259423i
$905$	9.99138	+	1.12261i	0.332125	+	0.0373169i
$906$	0.373577	−	0.0794063i	0.0124113	−	0.00263810i
$907$	2.58119	+	4.47075i	0.0857069	+	0.148449i	0.905692	−	0.423936i	$-0.139352\pi$
$907$	2.58119	+	4.47075i	0.0857069	+	0.148449i	−0.819985	+	0.572385i	$0.806018\pi$
$908$	−29.4426	−	32.6993i	−0.977086	−	1.08516i
$909$	7.60809	−	5.52760i	0.252345	−	0.183339i
$910$	−0.807897	−	0.677407i	−0.0267815	−	0.0224558i
$911$	−6.26367	−	4.55082i	−0.207525	−	0.150775i	0.479168	−	0.877723i	$-0.340938\pi$
$911$	−6.26367	−	4.55082i	−0.207525	−	0.150775i	−0.686693	+	0.726948i	$0.740938\pi$
$912$	−0.607149	−	5.77664i	−0.0201047	−	0.191284i
$913$	−0.412490	−	0.183652i	−0.0136514	−	0.00607800i
$914$	0.193044	−	1.83669i	0.00638533	−	0.0607524i
$915$	−15.3280	−	1.72222i	−0.506728	−	0.0569349i
$916$	35.0049	−	25.4326i	1.15660	−	0.840316i
$917$	19.3726	+	52.0038i	0.639740	+	1.71732i
$918$	0.125936			0.00415652
$919$	17.8177	+	19.7886i	0.587753	+	0.652766i	0.961513	−	0.274759i	$-0.0885982\pi$
$919$	17.8177	+	19.7886i	0.587753	+	0.652766i	−0.373760	+	0.927526i	$0.621932\pi$
$920$	2.74320	−	0.869628i	0.0904406	−	0.0286708i
$921$	0.874464	−	0.971191i	0.0288146	−	0.0320018i
$922$	−3.21719	−	0.683834i	−0.105952	−	0.0225209i
$923$	−14.6666	−	10.6559i	−0.482757	−	0.350744i
$924$	10.4447	+	4.12869i	0.343604	+	0.135824i
$925$	9.82220	+	17.5902i	0.322952	+	0.578364i
$926$	0.351395	−	0.608634i	0.0115476	−	0.0200010i
$927$	0.578958	−	5.50841i	0.0190155	−	0.180920i
$928$	1.95920	−	2.17591i	0.0643139	−	0.0714278i
$929$	−3.42442	−	0.727882i	−0.112351	−	0.0238810i	0.151393	−	0.988474i	$-0.451624\pi$
$929$	−3.42442	−	0.727882i	−0.112351	−	0.0238810i	−0.263744	+	0.964593i	$0.584957\pi$
$930$	−0.392760	+	0.0384360i	−0.0128791	+	0.00126037i
$931$	0.205747	−	10.3669i	0.00674310	−	0.339760i
$932$	52.3497			1.71477
$933$	−7.04581	−	7.82517i	−0.230670	−	0.256185i
$934$	−0.381131	−	0.169691i	−0.0124710	−	0.00555245i
$935$	−5.00099	+	1.58538i	−0.163550	+	0.0518473i
$936$	−0.649076	+	0.288987i	−0.0212157	+	0.00944585i
$937$	8.91977	−	6.48060i	0.291396	−	0.211712i	−0.432477	−	0.901645i	$-0.642360\pi$
$937$	8.91977	−	6.48060i	0.291396	−	0.211712i	0.723873	+	0.689933i	$0.242360\pi$
$938$	4.11041	−	1.05778i	0.134210	−	0.0345379i
$939$	10.4350	+	7.58145i	0.340532	+	0.247411i
$940$	−9.13506	−	8.34460i	−0.297953	−	0.272171i
$941$	21.3360	+	9.49940i	0.695534	+	0.309672i	0.723879	−	0.689927i	$-0.242357\pi$
$941$	21.3360	+	9.49940i	0.695534	+	0.309672i	−0.0283456	+	0.999598i	$0.509024\pi$
$942$	0.438672	−	0.0932427i	0.0142927	−	0.00303801i
$943$	9.15834	−	15.8627i	0.298237	−	0.516561i
$944$	10.7652	−	33.1319i	0.350377	−	1.07835i
$945$	−4.25418	+	4.11120i	−0.138389	+	0.133737i
$946$	−0.722912	−	2.22490i	−0.0235039	−	0.0723376i
$947$	−31.6683	−	6.73131i	−1.02908	−	0.218738i	−0.337720	−	0.941247i	$-0.609656\pi$
$947$	−31.6683	−	6.73131i	−1.02908	−	0.218738i	−0.691362	+	0.722508i	$0.742989\pi$
$948$	−0.928840	+	8.83732i	−0.0301673	+	0.287023i
$949$	8.77437	+	15.1977i	0.284828	+	0.493337i
$950$	0.849285	+	0.0121777i	0.0275544	+	0.000395097i
$951$	13.7598			0.446192
$952$	−0.614796	+	1.17757i	−0.0199256	+	0.0381654i
$953$	−5.99560	−	18.4526i	−0.194217	−	0.597737i	−0.999985	−	0.00550620i	$-0.998247\pi$
$953$	−5.99560	−	18.4526i	−0.194217	−	0.597737i	0.805768	−	0.592231i	$-0.201753\pi$
$954$	0.297691	+	0.0632762i	0.00963810	+	0.00204864i
$955$	36.2833	−	11.5022i	1.17410	−	0.372204i
$956$	−47.4175	+	10.0789i	−1.53359	+	0.325975i
$957$	2.29292	−	3.97146i	0.0741197	−	0.128379i
$958$	0.342631	−	1.05451i	0.0110699	−	0.0340696i
$959$	−5.55603	−	5.66740i	−0.179414	−	0.183010i
$960$	−6.87769	−	15.7505i	−0.221976	−	0.508344i
$961$	−26.1564	+	11.6456i	−0.843754	+	0.375663i
$962$	0.655996	+	0.292068i	0.0211502	+	0.00941666i
$963$	10.3727	+	4.61821i	0.334255	+	0.148820i
$964$	50.6998	−	22.5730i	1.63293	−	0.727028i
$965$	−21.3429	+	18.9420i	−0.687053	+	0.609764i
$966$	0.229220	−	0.822720i	0.00737503	−	0.0264706i
$967$	9.99007	−	30.7463i	0.321259	−	0.988733i	−0.651842	−	0.758355i	$-0.726003\pi$
$967$	9.99007	−	30.7463i	0.321259	−	0.988733i	0.973101	−	0.230379i	$-0.0739965\pi$
$968$	−1.47116	+	2.54812i	−0.0472848	+	0.0818996i
$969$	1.59110	−	0.338198i	0.0511134	−	0.0108645i
$970$	2.47921	−	3.36140i	0.0796027	−	0.107928i
$971$	11.1750	+	2.37531i	0.358621	+	0.0762273i	0.383699	−	0.923458i	$-0.374650\pi$
$971$	11.1750	+	2.37531i	0.358621	+	0.0762273i	−0.0250777	+	0.999686i	$0.507983\pi$
$972$	0.613970	+	1.88960i	0.0196931	+	0.0606091i
$973$	16.1488	+	25.4155i	0.517706	+	0.814783i
$974$	3.55203			0.113815
$975$	2.29482	+	7.42323i	0.0734931	+	0.237734i
$976$	−13.5245	−	23.4251i	−0.432908	−	0.749819i
$977$	0.673544	−	6.40834i	0.0215486	−	0.205021i	−0.978450	−	0.206482i	$-0.933798\pi$
$977$	0.673544	−	6.40834i	0.0215486	−	0.205021i	0.999999	+	0.00146114i	$0.000465097\pi$
$978$	−2.48616	−	0.528450i	−0.0794987	−	0.0168980i
$979$	4.12496	+	12.6953i	0.131834	+	0.405745i
$980$	−8.80778	−	29.8258i	−0.281354	−	0.952749i
$981$	1.54734	−	4.76223i	0.0494028	−	0.152046i
$982$	1.23731	−	2.14308i	0.0394841	−	0.0683885i
$983$	3.99002	−	0.848106i	0.127262	−	0.0270504i	−0.143840	−	0.989601i	$-0.545945\pi$
$983$	3.99002	−	0.848106i	0.127262	−	0.0270504i	0.271102	+	0.962551i	$0.412612\pi$
$984$	2.71804	+	1.21015i	0.0866480	+	0.0385782i
$985$	−18.6944	+	10.6152i	−0.595652	+	0.338230i
$986$	0.218686	+	0.158884i	0.00696437	+	0.00505991i
$987$	−7.13570	+	1.83632i	−0.227132	+	0.0584507i
$988$	−3.69998	+	2.68820i	−0.117712	+	0.0855229i
$989$	24.5514	−	10.9310i	0.780689	−	0.347585i
$990$	0.318851	+	0.445542i	0.0101337	+	0.0141603i
$991$	31.0490	+	13.8239i	0.986303	+	0.439130i	0.835534	−	0.549439i	$-0.185158\pi$
$991$	31.0490	+	13.8239i	0.986303	+	0.439130i	0.150769	+	0.988569i	$0.451825\pi$
$992$	−1.40471	−	1.56008i	−0.0445995	−	0.0495327i
$993$	−3.66470			−0.116296
$994$	1.23568	+	3.31706i	0.0391934	+	0.105211i
$995$	−20.2299	+	17.9541i	−0.641330	+	0.569184i
$996$	0.410718	+	0.0873008i	0.0130141	+	0.00276623i
$997$	5.08880	−	5.65168i	0.161164	−	0.178990i	−0.657154	−	0.753756i	$-0.728240\pi$
$997$	5.08880	−	5.65168i	0.161164	−	0.178990i	0.818318	+	0.574765i	$0.194907\pi$
$998$	−0.343194	+	3.26527i	−0.0108636	+	0.103360i
$999$	2.01468	−	3.48952i	0.0637415	−	0.110404i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bg.a.16.11	✓	160
7.4	even	3	inner	525.2.bg.a.466.10	yes	160
25.11	even	5	inner	525.2.bg.a.436.10	yes	160
175.11	even	15	inner	525.2.bg.a.361.11	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.a.16.11	✓	160	1.1	even	1	trivial
525.2.bg.a.361.11	yes	160	175.11	even	15	inner
525.2.bg.a.436.10	yes	160	25.11	even	5	inner
525.2.bg.a.466.10	yes	160	7.4	even	3	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104767 - 0.0466452i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-1.32946 + 1.47652i) q^{4} +(0.449213 + 2.19048i) q^{5} +(-0.0354385 + 0.109069i) q^{6} +(2.46049 + 0.972613i) q^{7} +(-0.141288 + 0.434840i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.104767 - 0.0466452i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-1.32946 + 1.47652i) q^{4} +(0.449213 + 2.19048i) q^{5} +(-0.0354385 + 0.109069i) q^{6} +(2.46049 + 0.972613i) q^{7} +(-0.141288 + 0.434840i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(0.149238 + 0.208536i) q^{10} +(-0.223328 + 2.12482i) q^{11} +(-0.207682 - 1.97596i) q^{12} +(-1.25719 + 0.913401i) q^{13} +(0.303145 - 0.0128726i) q^{14} +(-1.92843 - 1.13189i) q^{15} +(-0.409883 - 3.89978i) q^{16} +(1.07414 - 0.228316i) q^{17} +(-0.0573407 - 0.0993171i) q^{18} +(-0.991165 - 1.10080i) q^{19} +(-3.83149 - 2.24889i) q^{20} +(-2.36918 + 1.17770i) q^{21} +(0.0757153 + 0.233028i) q^{22} +(-2.57143 + 1.14487i) q^{23} +(-0.228609 - 0.395962i) q^{24} +(-4.59642 + 1.96799i) q^{25} +(-0.0891058 + 0.154336i) q^{26} +(0.809017 + 0.587785i) q^{27} +(-4.70721 + 2.33991i) q^{28} +(0.663276 + 2.04135i) q^{29} +(-0.254832 - 0.0286324i) q^{30} +(1.50530 - 0.319961i) q^{31} +(-0.682066 - 1.18137i) q^{32} +(-1.42961 - 1.58775i) q^{33} +(0.101885 - 0.0740235i) q^{34} +(-1.02521 + 5.82657i) q^{35} +(1.60739 + 1.16784i) q^{36} +(-0.421182 - 4.00728i) q^{37} +(-0.155188 - 0.0690942i) q^{38} +(0.162434 - 1.54546i) q^{39} +(-1.01598 - 0.114153i) q^{40} +(-5.26454 + 3.82491i) q^{41} +(-0.193278 + 0.233894i) q^{42} -9.54777 q^{43} +(-2.84043 - 3.15461i) q^{44} +(2.13153 - 0.675720i) q^{45} +(-0.215997 + 0.239889i) q^{46} +(2.72406 + 0.579016i) q^{47} +(3.17237 + 2.30486i) q^{48} +(5.10805 + 4.78621i) q^{49} +(-0.389754 + 0.420580i) q^{50} +(-0.549070 + 0.951017i) q^{51} +(0.322732 - 3.07059i) q^{52} +(-1.77574 + 1.97216i) q^{53} +(0.112175 + 0.0238436i) q^{54} +(-4.75470 + 0.465302i) q^{55} +(-0.770569 + 0.932502i) q^{56} +1.48127 q^{57} +(0.164708 + 0.182927i) q^{58} +(8.11603 + 3.61349i) q^{59} +(4.23502 - 1.34255i) q^{60} +(6.30166 - 2.80568i) q^{61} +(0.142781 - 0.103736i) q^{62} +(0.710093 - 2.54868i) q^{63} +(6.21817 + 4.51777i) q^{64} +(-2.56553 - 2.34354i) q^{65} +(-0.223837 - 0.0996586i) q^{66} +(13.6827 - 2.90835i) q^{67} +(-1.09092 + 1.88953i) q^{68} +(0.869814 - 2.67701i) q^{69} +(0.164374 + 0.658252i) q^{70} +(3.60505 + 11.0952i) q^{71} +(0.447226 + 0.0950609i) q^{72} +(1.18042 - 11.2310i) q^{73} +(-0.231046 - 0.400184i) q^{74} +(1.61310 - 4.73264i) q^{75} +2.94306 q^{76} +(-2.61612 + 5.01090i) q^{77} +(-0.0550704 - 0.169489i) q^{78} +(-4.37468 - 0.929867i) q^{79} +(8.35827 - 2.64967i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-0.373135 + 0.646289i) q^{82} +(-0.0653066 + 0.200993i) q^{83} +(1.41085 - 5.06384i) q^{84} +(0.982641 + 2.25033i) q^{85} +(-1.00029 + 0.445357i) q^{86} +(-1.96084 - 0.873022i) q^{87} +(-0.892403 - 0.397324i) q^{88} +(5.70768 - 2.54123i) q^{89} +(0.191794 - 0.170218i) q^{90} +(-3.98169 + 1.02466i) q^{91} +(1.72819 - 5.31881i) q^{92} +(-0.769464 + 1.33275i) q^{93} +(0.312399 - 0.0664024i) q^{94} +(1.96604 - 2.66562i) q^{95} +(1.33432 + 0.283619i) q^{96} +(-5.03322 - 15.4907i) q^{97} +(0.758407 + 0.263170i) q^{98} +2.13653 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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