LMFDB - Embedded newform 966.2.y.d.151.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			151.4
Character	$\chi$	$=$	966.151
Dual form			966.2.y.d.499.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.527443 + 0.0503647i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.62119 - 0.359704i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})$	\(q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.527443 + 0.0503647i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.62119 - 0.359704i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(0.124915 - 0.514906i) q^{10} +(0.160191 + 0.462842i) q^{11} +(0.981929 + 0.189251i) q^{12} +(5.66480 - 1.66334i) q^{13} +(1.19723 - 2.35937i) q^{14} +(0.445731 - 0.286454i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-2.41091 - 0.965183i) q^{17} +(0.580057 + 0.814576i) q^{18} +(4.27692 - 1.71222i) q^{19} +(0.445731 + 0.286454i) q^{20} +(2.49463 - 0.881379i) q^{21} -0.489780 q^{22} +(1.79785 + 4.44609i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.63398 + 0.893127i) q^{25} +(-0.280921 + 5.89726i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(1.83804 + 1.90306i) q^{28} +(-0.437820 - 3.04510i) q^{29} +(0.124915 + 0.514906i) q^{30} +(0.404709 + 8.49588i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(-0.354470 - 0.337987i) q^{33} +(1.70063 - 1.96263i) q^{34} +(1.40064 + 0.0577081i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(0.265313 - 0.372579i) q^{37} +(0.219206 + 4.60171i) q^{38} +(-4.27289 + 4.07419i) q^{39} +(-0.416484 + 0.327526i) q^{40} +(-3.55317 + 7.78035i) q^{41} +(0.0169908 + 2.64570i) q^{42} +(4.93850 + 3.17378i) q^{43} +(0.160191 - 0.462842i) q^{44} +(-0.264921 + 0.458856i) q^{45} +(-4.78958 + 0.244795i) q^{46} +(2.00283 + 3.46901i) q^{47} +(-0.654861 - 0.755750i) q^{48} +(6.74123 + 1.88570i) q^{49} +(0.671622 - 4.67123i) q^{50} +(2.58517 - 0.246854i) q^{51} +(-5.48104 - 2.19428i) q^{52} +(3.95128 - 3.76754i) q^{53} +(-0.888835 - 0.458227i) q^{54} +(-0.107803 - 0.236055i) q^{55} +(-2.39955 + 1.11452i) q^{56} +(-3.01690 + 3.48168i) q^{57} +(3.02082 + 0.582216i) q^{58} +(-2.10742 + 8.68690i) q^{59} +(-0.527443 - 0.0503647i) q^{60} +(0.487442 + 0.251294i) q^{61} +(-8.16098 - 2.39628i) q^{62} +(-1.81344 + 1.92651i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-2.90408 + 1.16262i) q^{65} +(0.435333 - 0.224430i) q^{66} +(12.2470 - 2.36042i) q^{67} +(1.29847 + 2.24901i) q^{68} +(-3.63531 - 3.12802i) q^{69} +(-0.512639 + 1.30473i) q^{70} +(9.19771 + 10.6147i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(-4.92420 - 3.87243i) q^{73} +(0.265313 + 0.372579i) q^{74} +(3.70959 - 2.91726i) q^{75} +(-4.42031 - 1.29792i) q^{76} +(-0.253405 - 1.27082i) q^{77} +(-2.45259 - 5.37042i) q^{78} +(-9.39036 - 8.95369i) q^{79} +(-0.173294 - 0.500701i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(-6.19031 - 5.90245i) q^{82} +(4.97875 + 10.9019i) q^{83} +(-2.50574 - 0.849266i) q^{84} +(1.32023 + 0.387654i) q^{85} +(-4.61445 + 3.62885i) q^{86} +(1.78450 + 2.50598i) q^{87} +(0.384993 + 0.302762i) q^{88} +(-0.472941 + 9.92825i) q^{89} +(-0.346973 - 0.400428i) q^{90} +(-15.4468 + 2.32226i) q^{91} +(1.33519 - 4.60622i) q^{92} +(-4.25276 - 7.36599i) q^{93} +(-3.93328 + 0.758078i) q^{94} +(-2.16960 + 1.11850i) q^{95} +(0.928368 - 0.371662i) q^{96} +(4.17538 - 9.14281i) q^{97} +(-3.98683 + 5.75371i) q^{98} +(0.469940 + 0.137987i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	−0.327068	+	0.945001i	−0.231272	+	0.668216i
$2$	−0.327068	+	0.945001i	−0.231272	+	0.668216i
$3$	−0.888835	+	0.458227i	−0.513169	+	0.264557i
$3$	−0.888835	+	0.458227i	−0.513169	+	0.264557i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−0.527443	+	0.0503647i	−0.235880	+	0.0225238i	−0.212326	−	0.977199i	$-0.568104\pi$
$5$	−0.527443	+	0.0503647i	−0.235880	+	0.0225238i	−0.0235532	+	0.999723i	$0.507498\pi$
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	−2.62119	−	0.359704i	−0.990715	−	0.135955i
$7$	−2.62119	−	0.359704i	−0.990715	−	0.135955i
$8$	0.841254	−	0.540641i	0.297428	−	0.191145i
$9$	0.580057	−	0.814576i	0.193352	−	0.271525i
$10$	0.124915	−	0.514906i	0.0395016	−	0.162828i
$11$	0.160191	+	0.462842i	0.0482995	+	0.139552i	0.966571	−	0.256399i	$-0.0825361\pi$
$11$	0.160191	+	0.462842i	0.0482995	+	0.139552i	−0.918272	+	0.395951i	$0.870415\pi$
$12$	0.981929	+	0.189251i	0.283458	+	0.0546321i
$13$	5.66480	−	1.66334i	1.57113	−	0.461326i	0.623802	−	0.781583i	$-0.285587\pi$
$13$	5.66480	−	1.66334i	1.57113	−	0.461326i	0.947331	+	0.320256i	$0.103769\pi$
$14$	1.19723	−	2.35937i	0.319972	−	0.630569i
$15$	0.445731	−	0.286454i	0.115087	−	0.0739621i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−2.41091	−	0.965183i	−0.584732	−	0.234091i	0.0603853	−	0.998175i	$-0.480767\pi$
$17$	−2.41091	−	0.965183i	−0.584732	−	0.234091i	−0.645117	+	0.764084i	$0.723191\pi$
$18$	0.580057	+	0.814576i	0.136721	+	0.191997i
$19$	4.27692	−	1.71222i	0.981194	−	0.392811i	0.175069	−	0.984556i	$-0.443985\pi$
$19$	4.27692	−	1.71222i	0.981194	−	0.392811i	0.806125	+	0.591746i	$0.201561\pi$
$20$	0.445731	+	0.286454i	0.0996685	+	0.0640531i
$21$	2.49463	−	0.881379i	0.544373	−	0.192333i
$22$	−0.489780			−0.104421
$23$	1.79785	+	4.44609i	0.374878	+	0.927074i
$23$	1.79785	+	4.44609i	0.374878	+	0.927074i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−4.63398	+	0.893127i	−0.926797	+	0.178625i
$26$	−0.280921	+	5.89726i	−0.0550932	+	1.15655i
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$	1.83804	+	1.90306i	0.347356	+	0.359644i
$29$	−0.437820	−	3.04510i	−0.0813011	−	0.565461i	−0.989234	−	0.146345i	$-0.953249\pi$
$29$	−0.437820	−	3.04510i	−0.0813011	−	0.565461i	0.907933	−	0.419116i	$-0.137660\pi$
$30$	0.124915	+	0.514906i	0.0228062	+	0.0940086i
$31$	0.404709	+	8.49588i	0.0726878	+	1.52591i	0.681045	+	0.732242i	$0.261526\pi$
$31$	0.404709	+	8.49588i	0.0726878	+	1.52591i	−0.608357	+	0.793664i	$0.708171\pi$
$32$	−0.995472	−	0.0950560i	−0.175976	−	0.0168037i
$33$	−0.354470	−	0.337987i	−0.0617053	−	0.0588359i
$34$	1.70063	−	1.96263i	0.291656	−	0.336589i
$35$	1.40064	+	0.0577081i	0.236752	+	0.00975446i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	0.265313	−	0.372579i	0.0436171	−	0.0612517i	−0.792191	−	0.610273i	$-0.791060\pi$
$37$	0.265313	−	0.372579i	0.0436171	−	0.0612517i	0.835809	+	0.549021i	$0.184999\pi$
$38$	0.219206	+	4.60171i	0.0355600	+	0.746496i
$39$	−4.27289	+	4.07419i	−0.684210	+	0.652393i
$40$	−0.416484	+	0.327526i	−0.0658519	+	0.0517865i
$41$	−3.55317	+	7.78035i	−0.554911	+	1.21509i	0.399539	+	0.916716i	$0.369170\pi$
$41$	−3.55317	+	7.78035i	−0.554911	+	1.21509i	−0.954450	+	0.298370i	$0.903557\pi$
$42$	0.0169908	+	2.64570i	0.00262173	+	0.408240i
$43$	4.93850	+	3.17378i	0.753114	+	0.483997i	0.860013	−	0.510273i	$-0.170456\pi$
$43$	4.93850	+	3.17378i	0.753114	+	0.483997i	−0.106898	+	0.994270i	$0.534092\pi$
$44$	0.160191	−	0.462842i	0.0241497	−	0.0697761i
$45$	−0.264921	+	0.458856i	−0.0394921	+	0.0684023i
$46$	−4.78958	+	0.244795i	−0.706185	+	0.0360931i
$47$	2.00283	+	3.46901i	0.292143	+	0.506007i	0.974316	−	0.225184i	$-0.0722982\pi$
$47$	2.00283	+	3.46901i	0.292143	+	0.506007i	−0.682173	+	0.731191i	$0.738965\pi$
$48$	−0.654861	−	0.755750i	−0.0945210	−	0.109083i
$49$	6.74123	+	1.88570i	0.963032	+	0.269386i
$50$	0.671622	−	4.67123i	0.0949817	−	0.660612i
$51$	2.58517	−	0.246854i	0.361997	−	0.0345665i
$52$	−5.48104	−	2.19428i	−0.760083	−	0.304291i
$53$	3.95128	−	3.76754i	0.542750	−	0.517511i	−0.368355	−	0.929685i	$-0.620079\pi$
$53$	3.95128	−	3.76754i	0.542750	−	0.517511i	0.911105	+	0.412174i	$0.135230\pi$
$54$	−0.888835	−	0.458227i	−0.120955	−	0.0623567i
$55$	−0.107803	−	0.236055i	−0.0145361	−	0.0318296i
$56$	−2.39955	+	1.11452i	−0.320654	+	0.148934i
$57$	−3.01690	+	3.48168i	−0.399598	+	0.461160i
$58$	3.02082	+	0.582216i	0.396653	+	0.0764487i
$59$	−2.10742	+	8.68690i	−0.274363	+	1.13094i	0.653174	+	0.757208i	$0.273437\pi$
$59$	−2.10742	+	8.68690i	−0.274363	+	1.13094i	−0.927537	+	0.373731i	$0.878078\pi$
$60$	−0.527443	−	0.0503647i	−0.0680926	−	0.00650205i
$61$	0.487442	+	0.251294i	0.0624106	+	0.0321749i	0.489149	−	0.872200i	$-0.337307\pi$
$61$	0.487442	+	0.251294i	0.0624106	+	0.0321749i	−0.426739	+	0.904375i	$0.640338\pi$
$62$	−8.16098	−	2.39628i	−1.03645	−	0.304328i
$63$	−1.81344	+	1.92651i	−0.228472	+	0.242717i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−2.90408	+	1.16262i	−0.360207	+	0.144205i
$66$	0.435333	−	0.224430i	0.0535858	−	0.0276254i
$67$	12.2470	−	2.36042i	1.49621	−	0.288371i	0.625523	−	0.780206i	$-0.284886\pi$
$67$	12.2470	−	2.36042i	1.49621	−	0.288371i	0.870688	+	0.491835i	$0.163674\pi$
$68$	1.29847	+	2.24901i	0.157462	+	0.272733i
$69$	−3.63531	−	3.12802i	−0.437640	−	0.376570i
$70$	−0.512639	+	1.30473i	−0.0612721	+	0.155945i
$71$	9.19771	+	10.6147i	1.09157	+	1.25974i	0.963424	+	0.267981i	$0.0863564\pi$
$71$	9.19771	+	10.6147i	1.09157	+	1.25974i	0.128144	+	0.991756i	$0.459098\pi$
$72$	0.0475819	−	0.998867i	0.00560758	−	0.117718i
$73$	−4.92420	−	3.87243i	−0.576333	−	0.453234i	0.286955	−	0.957944i	$-0.407357\pi$
$73$	−4.92420	−	3.87243i	−0.576333	−	0.453234i	−0.863289	+	0.504710i	$0.831599\pi$
$74$	0.265313	+	0.372579i	0.0308420	+	0.0433115i
$75$	3.70959	−	2.91726i	0.428347	−	0.336856i
$76$	−4.42031	−	1.29792i	−0.507045	−	0.148882i
$77$	−0.253405	−	1.27082i	−0.0288781	−	0.144823i
$78$	−2.45259	−	5.37042i	−0.277701	−	0.608081i
$79$	−9.39036	−	8.95369i	−1.05650	−	1.00737i	−0.999960	−	0.00896847i	$-0.997145\pi$
$79$	−9.39036	−	8.95369i	−1.05650	−	1.00737i	−0.0565383	−	0.998400i	$-0.518006\pi$
$80$	−0.173294	−	0.500701i	−0.0193749	−	0.0559801i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	−6.19031	−	5.90245i	−0.683605	−	0.651816i
$83$	4.97875	+	10.9019i	0.546489	+	1.19664i	0.958402	+	0.285420i	$0.0921332\pi$
$83$	4.97875	+	10.9019i	0.546489	+	1.19664i	−0.411914	+	0.911223i	$0.635139\pi$
$84$	−2.50574	−	0.849266i	−0.273399	−	0.0926626i
$85$	1.32023	+	0.387654i	0.143199	+	0.0420470i
$86$	−4.61445	+	3.62885i	−0.497589	+	0.391308i
$87$	1.78450	+	2.50598i	0.191318	+	0.268669i
$88$	0.384993	+	0.302762i	0.0410404	+	0.0322745i
$89$	−0.472941	+	9.92825i	−0.0501316	+	1.05239i	0.823965	+	0.566641i	$0.191757\pi$
$89$	−0.472941	+	9.92825i	−0.0501316	+	1.05239i	−0.874097	+	0.485752i	$0.838546\pi$
$90$	−0.346973	−	0.400428i	−0.0365741	−	0.0422088i
$91$	−15.4468	+	2.32226i	−1.61926	+	0.243439i
$92$	1.33519	−	4.60622i	0.139203	−	0.480232i
$93$	−4.25276	−	7.36599i	−0.440990	−	0.763818i
$94$	−3.93328	+	0.758078i	−0.405687	+	0.0781898i
$95$	−2.16960	+	1.11850i	−0.222596	+	0.114756i
$96$	0.928368	−	0.371662i	0.0947512	−	0.0379326i
$97$	4.17538	−	9.14281i	0.423946	−	0.928312i	−0.570325	−	0.821419i	$-0.693183\pi$
$97$	4.17538	−	9.14281i	0.423946	−	0.928312i	0.994271	−	0.106893i	$-0.0340902\pi$
$98$	−3.98683	+	5.75371i	−0.402731	+	0.581213i
$99$	0.469940	+	0.137987i	0.0472308	+	0.0138682i
$100$	4.19465	+	2.16249i	0.419465	+	0.216249i
$101$	−13.4086	−	1.28037i	−1.33421	−	0.127402i	−0.596551	−	0.802575i	$-0.703463\pi$
$101$	−13.4086	−	1.28037i	−1.33421	−	0.127402i	−0.737659	+	0.675174i	$0.764069\pi$
$102$	−0.612250	+	2.52373i	−0.0606218	+	0.249887i
$103$	3.96014	+	0.763255i	0.390204	+	0.0752057i	0.380580	−	0.924748i	$-0.375724\pi$
$103$	3.96014	+	0.763255i	0.390204	+	0.0752057i	0.00962432	+	0.999954i	$0.496936\pi$
$104$	3.86627	−	4.46191i	0.379119	−	0.437526i
$105$	−1.27138	+	0.590518i	−0.124074	+	0.0576287i
$106$	2.26799	+	4.96620i	0.220287	+	0.482360i
$107$	5.69401	+	2.93546i	0.550460	+	0.283782i	0.710935	−	0.703258i	$-0.248272\pi$
$107$	5.69401	+	2.93546i	0.550460	+	0.283782i	−0.160474	+	0.987040i	$0.551302\pi$
$108$	0.723734	−	0.690079i	0.0696413	−	0.0664029i
$109$	4.77891	+	1.91319i	0.457737	+	0.183250i	0.589060	−	0.808090i	$-0.299498\pi$
$109$	4.77891	+	1.91319i	0.457737	+	0.183250i	−0.131323	+	0.991340i	$0.541923\pi$
$110$	0.258331	−	0.0246676i	0.0246309	−	0.00235196i
$111$	−0.0650935	+	0.452735i	−0.00617840	+	0.0429717i
$112$	−0.268403	−	2.63210i	−0.0253617	−	0.248710i
$113$	8.59236	+	9.91611i	0.808301	+	0.932829i	0.998806	−	0.0488574i	$-0.0155580\pi$
$113$	8.59236	+	9.91611i	0.808301	+	0.932829i	−0.190505	+	0.981686i	$0.561013\pi$
$114$	−2.30346	−	3.98972i	−0.215739	−	0.373671i
$115$	−1.17219	−	2.25451i	−0.109307	−	0.210234i
$116$	−1.53821	+	2.66426i	−0.142819	+	0.247370i
$117$	1.93099	−	5.57924i	0.178520	−	0.515801i
$118$	−7.51986	−	4.83272i	−0.692259	−	0.444888i
$119$	5.97226	+	3.39714i	0.547476	+	0.311415i
$120$	0.220104	−	0.481961i	0.0200927	−	0.0439968i
$121$	8.45802	−	6.65146i	0.768911	−	0.604678i
$122$	−0.396900	+	0.378443i	−0.0359336	+	0.0342626i
$123$	−0.406982	−	8.54360i	−0.0366963	−	0.770351i
$124$	4.93368	−	6.92839i	0.443058	−	0.622188i
$125$	4.94108	−	1.45083i	0.441943	−	0.129766i
$126$	−1.22743	−	2.34380i	−0.109348	−	0.208803i
$127$	−0.531394	+	0.613261i	−0.0471536	+	0.0544181i	−0.778836	−	0.627227i	$-0.784190\pi$
$127$	−0.531394	+	0.613261i	−0.0471536	+	0.0544181i	0.731683	+	0.681645i	$0.238735\pi$
$128$	0.723734	+	0.690079i	0.0639697	+	0.0609949i
$129$	−5.84383	−	0.558018i	−0.514520	−	0.0491307i
$130$	−0.148844	−	3.12462i	−0.0130545	−	0.274047i
$131$	3.07568	+	12.6781i	0.268724	+	1.10769i	0.932905	+	0.360122i	$0.117265\pi$
$131$	3.07568	+	12.6781i	0.268724	+	1.10769i	−0.664182	+	0.747571i	$0.731220\pi$
$132$	0.0697029	+	0.484794i	0.00606686	+	0.0421959i
$133$	−11.8265	+	2.94962i	−1.02549	+	0.255765i
$134$	−1.77501	+	12.3455i	−0.153337	+	1.06649i
$135$	0.0252109	−	0.529242i	0.00216981	−	0.0455499i
$136$	−2.55000	+	0.491473i	−0.218661	+	0.0421435i
$137$	2.86259	−	4.95815i	0.244567	−	0.423603i	−0.717442	−	0.696618i	$-0.754687\pi$
$137$	2.86259	−	4.95815i	0.244567	−	0.423603i	0.962010	+	0.273015i	$0.0880207\pi$
$138$	4.14498	−	2.41230i	0.352844	−	0.205348i
$139$	−15.5979			−1.32300			−0.661499	−	0.749946i	$-0.730079\pi$
$139$	−15.5979			−1.32300			−0.661499	+	0.749946i	$0.730079\pi$
$140$	−1.06531	−	0.911181i	−0.0900348	−	0.0770088i
$141$	−3.36978	−	2.16563i	−0.283787	−	0.182379i
$142$	−13.0392	+	5.22011i	−1.09423	+	0.438062i
$143$	1.67731	+	2.35546i	0.140264	+	0.196973i
$144$	0.928368	+	0.371662i	0.0773640	+	0.0309719i
$145$	0.384290	+	1.58407i	0.0319136	+	0.131550i
$146$	5.27000	−	3.38682i	0.436148	−	0.280295i
$147$	−6.85592	+	1.41293i	−0.565467	+	0.116536i
$148$	−0.438863	+	0.128862i	−0.0360743	+	0.0105924i
$149$	−6.01283	−	1.15888i	−0.492591	−	0.0949391i	−0.0630941	−	0.998008i	$-0.520097\pi$
$149$	−6.01283	−	1.15888i	−0.492591	−	0.0949391i	−0.429497	+	0.903069i	$0.641309\pi$
$150$	1.54352	+	4.45971i	0.126028	+	0.364134i
$151$	4.49304	−	18.5206i	0.365638	−	1.50718i	−0.430792	−	0.902451i	$-0.641766\pi$
$151$	4.49304	−	18.5206i	0.365638	−	1.50718i	0.796430	−	0.604730i	$-0.206719\pi$
$152$	2.67228	−	3.75269i	0.216751	−	0.304384i
$153$	−2.18468	+	1.40401i	−0.176621	+	0.113507i
$154$	1.28380	+	0.176176i	0.103452	+	0.0141966i
$155$	−0.641353	−	4.46071i	−0.0515147	−	0.358293i
$156$	5.87722	−	0.561206i	0.470554	−	0.0449325i
$157$	18.0739	+	14.2134i	1.44245	+	1.13436i	0.967050	+	0.254586i	$0.0819391\pi$
$157$	18.0739	+	14.2134i	1.44245	+	1.13436i	0.475400	+	0.879770i	$0.342303\pi$
$158$	11.5325	−	5.94543i	0.917479	−	0.472993i
$159$	−1.78565	+	5.15930i	−0.141611	+	0.409159i
$160$	0.529842			0.0418877
$161$	−3.11322	−	12.3007i	−0.245356	−	0.969433i
$162$	1.00000			0.0785674
$163$	0.943938	−	2.72733i	0.0739349	−	0.213621i	−0.901978	−	0.431783i	$-0.857885\pi$
$163$	0.943938	−	2.72733i	0.0739349	−	0.213621i	0.975913	+	0.218162i	$0.0700060\pi$
$164$	7.60247	−	3.91935i	0.593653	−	0.306049i
$165$	0.203985	+	0.160416i	0.0158802	+	0.0124884i
$166$	−11.9307	+	1.13925i	−0.926004	+	0.0884227i
$167$	−1.21756	−	8.46828i	−0.0942173	−	0.655295i	−0.981129	−	0.193356i	$-0.938063\pi$
$167$	−1.21756	−	8.46828i	−0.0942173	−	0.655295i	0.886911	−	0.461940i	$-0.152846\pi$
$168$	1.62211	−	2.09016i	0.125148	−	0.161259i
$169$	18.3870	−	11.8166i	1.41438	−	0.908968i
$170$	−0.798137	+	1.12083i	−0.0612143	+	0.0859635i
$171$	1.08612	−	4.47707i	0.0830580	−	0.342370i
$172$	−1.92002	−	5.54754i	−0.146400	−	0.422996i
$173$	−6.86266	−	1.32267i	−0.521759	−	0.100561i	−0.0784295	−	0.996920i	$-0.524991\pi$
$173$	−6.86266	−	1.32267i	−0.521759	−	0.100561i	−0.443329	+	0.896359i	$0.646203\pi$
$174$	−2.95180	+	0.866727i	−0.223775	+	0.0657064i
$175$	12.4678	−	0.674189i	0.942477	−	0.0509639i
$176$	−0.412029	+	0.264795i	−0.0310578	+	0.0199597i
$177$	−2.10742	−	8.68690i	−0.158403	−	0.652948i
$178$	−9.22752	−	3.69414i	−0.691632	−	0.276888i
$179$	−12.9181	−	18.1410i	−0.965548	−	1.35592i	−0.934330	−	0.356409i	$-0.884001\pi$
$179$	−12.9181	−	18.1410i	−0.965548	−	1.35592i	−0.0312176	−	0.999513i	$-0.509938\pi$
$180$	0.491888	−	0.196922i	0.0366632	−	0.0146777i
$181$	15.7199	+	10.1026i	1.16845	+	0.750919i	0.973228	−	0.229840i	$-0.0738203\pi$
$181$	15.7199	+	10.1026i	1.16845	+	0.750919i	0.195224	+	0.980759i	$0.437457\pi$
$182$	2.85762	−	15.3568i	0.211821	−	1.13832i
$183$	−0.548405			−0.0405393
$184$	3.91619	+	2.76830i	0.288705	+	0.204082i
$185$	−0.121172	+	0.209877i	−0.00890877	+	0.0154304i
$186$	8.35181	−	1.60968i	0.612384	−	0.118027i
$187$	0.0605206	−	1.27048i	0.00442571	−	0.0929070i
$188$	0.570066	−	3.96490i	0.0415764	−	0.289170i
$189$	0.729076	−	2.54331i	0.0530325	−	0.184999i
$190$	−0.347382	−	2.41610i	−0.0252018	−	0.175282i
$191$	−1.39567	−	5.75304i	−0.100987	−	0.416275i	0.898767	−	0.438426i	$-0.144464\pi$
$191$	−1.39567	−	5.75304i	−0.100987	−	0.416275i	−0.999755	+	0.0221507i	$0.992949\pi$
$192$	0.0475819	+	0.998867i	0.00343393	+	0.0720870i
$193$	1.40245	+	0.133918i	0.100951	+	0.00963963i	0.145409	−	0.989372i	$-0.453550\pi$
$193$	1.40245	+	0.133918i	0.100951	+	0.00963963i	−0.0444584	+	0.999011i	$0.514156\pi$
$194$	7.27433	+	6.93606i	0.522267	+	0.497980i
$195$	2.04851	−	2.36411i	0.146697	−	0.169297i
$196$	−4.13330	−	5.64941i	−0.295236	−	0.403529i
$197$	7.35845	−	2.16064i	0.524268	−	0.153939i	−0.00888063	−	0.999961i	$-0.502827\pi$
$197$	7.35845	−	2.16064i	0.524268	−	0.153939i	0.533149	+	0.846022i	$0.321009\pi$
$198$	−0.284100	+	0.398963i	−0.0201901	+	0.0283530i
$199$	0.549660	+	11.5388i	0.0389643	+	0.817962i	0.930784	+	0.365571i	$0.119126\pi$
$199$	0.549660	+	11.5388i	0.0389643	+	0.817962i	−0.891819	+	0.452392i	$0.850571\pi$
$200$	−3.41549	+	3.25667i	−0.241512	+	0.230281i
$201$	−9.80398	+	7.70993i	−0.691519	+	0.543817i
$202$	5.59549	−	12.2524i	0.393697	−	0.862076i
$203$	0.0522707	+	8.13927i	0.00366868	+	0.571264i
$204$	−2.18468	−	1.40401i	−0.152958	−	0.0983002i
$205$	1.48224	−	4.28264i	0.103524	−	0.299113i
$206$	−2.01651	+	3.49270i	−0.140497	+	0.243348i
$207$	4.66454	+	1.11450i	0.324208	+	0.0774632i
$208$	2.95198	+	5.11297i	0.204683	+	0.354521i
$209$	1.47761	+	1.70526i	0.102209	+	0.117955i
$210$	−0.142211	−	1.39460i	−0.00981351	−	0.0962364i
$211$	−0.274281	+	1.90767i	−0.0188823	+	0.131329i	−0.997082	−	0.0763366i	$-0.975678\pi$
$211$	−0.274281	+	1.90767i	−0.0188823	+	0.131329i	0.978200	+	0.207666i	$0.0665867\pi$
$212$	−5.43485	+	0.518965i	−0.373267	+	0.0356427i
$213$	−13.0392	−	5.22011i	−0.893432	−	0.357676i
$214$	−4.63634	+	4.42074i	−0.316934	+	0.302196i
$215$	−2.76462	−	1.42526i	−0.188546	−	0.0972021i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	1.99519	−	22.4149i	0.135442	−	1.52162i
$218$	−3.37099	+	3.89033i	−0.228312	+	0.263486i
$219$	6.15125	+	1.18556i	0.415663	+	0.0801125i
$220$	−0.0611808	+	0.252191i	−0.00412481	+	0.0170027i
$221$	−15.2627	−	1.45742i	−1.02668	−	0.0980364i
$222$	−0.406545	−	0.209589i	−0.0272855	−	0.0140667i
$223$	2.62280	+	0.770124i	0.175636	+	0.0515713i	0.368368	−	0.929680i	$-0.379917\pi$
$223$	2.62280	+	0.770124i	0.175636	+	0.0515713i	−0.192732	+	0.981251i	$0.561735\pi$
$224$	2.57512	+	0.607235i	0.172058	+	0.0405726i
$225$	−1.96045	+	4.29280i	−0.130697	+	0.286186i
$226$	−12.1810	+	4.87654i	−0.810269	+	0.324383i
$227$	20.5459	−	10.5921i	1.36368	−	0.703024i	0.387881	−	0.921709i	$-0.373207\pi$
$227$	20.5459	−	10.5921i	1.36368	−	0.703024i	0.975795	+	0.218685i	$0.0701769\pi$
$228$	4.52367	−	0.871867i	0.299588	−	0.0577408i
$229$	−7.07959	−	12.2622i	−0.467832	−	0.810309i	0.531492	−	0.847063i	$-0.321632\pi$
$229$	−7.07959	−	12.2622i	−0.467832	−	0.810309i	−0.999324	+	0.0367540i	$0.988298\pi$
$230$	2.51390	−	0.370341i	0.165762	−	0.0244196i
$231$	0.807557	+	1.01343i	0.0531333	+	0.0666788i
$232$	−2.01462	−	2.32500i	−0.132267	−	0.152644i
$233$	0.415668	−	8.72595i	0.0272313	−	0.571656i	−0.943483	−	0.331420i	$-0.892472\pi$
$233$	0.415668	−	8.72595i	0.0272313	−	0.571656i	0.970715	−	0.240236i	$-0.0772248\pi$
$234$	4.64082	+	3.64958i	0.303380	+	0.238581i
$235$	−1.23110	−	1.72883i	−0.0803079	−	0.112777i
$236$	7.02643	−	5.52565i	0.457382	−	0.359689i
$237$	12.4493	+	3.65545i	0.808669	+	0.237447i
$238$	−5.16363	+	4.53270i	−0.334709	+	0.293811i
$239$	11.9545	+	26.1767i	0.773271	+	1.69323i	0.719315	+	0.694684i	$0.244456\pi$
$239$	11.9545	+	26.1767i	0.773271	+	1.69323i	0.0539554	+	0.998543i	$0.482817\pi$
$240$	0.383465	+	0.365633i	0.0247525	+	0.0236015i
$241$	5.83608	+	16.8622i	0.375935	+	1.08619i	0.961319	+	0.275437i	$0.0888225\pi$
$241$	5.83608	+	16.8622i	0.375935	+	1.08619i	−0.585384	+	0.810756i	$0.699056\pi$
$242$	3.51929	+	10.1683i	0.226228	+	0.653644i
$243$	0.723734	+	0.690079i	0.0464276	+	0.0442686i
$244$	−0.227816	−	0.498847i	−0.0145844	−	0.0319354i
$245$	−3.65058	−	0.655080i	−0.233227	−	0.0418515i
$246$	8.20682	+	2.40974i	0.523248	+	0.153639i
$247$	21.3799	−	16.8134i	1.36037	−	1.06981i
$248$	4.93368	+	6.92839i	0.313289	+	0.439953i
$249$	−9.42085	−	7.40864i	−0.597022	−	0.469503i
$250$	−0.245031	+	5.14384i	−0.0154971	+	0.325325i
$251$	−9.91314	−	11.4404i	−0.625712	−	0.722110i	0.351069	−	0.936349i	$-0.385818\pi$
$251$	−9.91314	−	11.4404i	−0.625712	−	0.722110i	−0.976781	+	0.214240i	$0.931273\pi$
$252$	2.61635	−	0.393340i	0.164815	−	0.0247781i
$253$	−1.76984	+	1.54435i	−0.111269	+	0.0970922i
$254$	−0.405730	−	0.702745i	−0.0254578	−	0.0440942i
$255$	−1.35110	+	0.260403i	−0.0846091	+	0.0163071i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	0.190530	−	0.0762768i	0.0118849	−	0.00475802i	−0.365712	−	0.930728i	$-0.619175\pi$
$257$	0.190530	−	0.0762768i	0.0118849	−	0.00475802i	0.377597	+	0.925970i	$0.376750\pi$
$258$	2.43866	−	5.33991i	0.151824	−	0.332448i
$259$	−0.829452	+	0.881166i	−0.0515396	+	0.0547530i
$260$	3.00145	+	0.881305i	0.186142	+	0.0546562i
$261$	−2.73443	−	1.40970i	−0.169257	−	0.0872580i
$262$	−12.9868	−	1.24009i	−0.802327	−	0.0766130i
$263$	−3.13061	+	12.9045i	−0.193041	+	0.795728i	0.790115	+	0.612959i	$0.210021\pi$
$263$	−3.13061	+	12.9045i	−0.193041	+	0.795728i	−0.983156	+	0.182768i	$0.941494\pi$
$264$	−0.480929	−	0.0926914i	−0.0295991	−	0.00570476i
$265$	−1.89432	+	2.18616i	−0.116367	+	0.134295i
$266$	1.08067	−	12.1408i	0.0662603	−	0.744399i
$267$	−4.12902	−	9.04129i	−0.252692	−	0.553318i
$268$	−11.0859	−	5.71519i	−0.677180	−	0.349111i
$269$	7.88911	−	7.52225i	0.481007	−	0.458640i	−0.410358	−	0.911924i	$-0.634596\pi$
$269$	7.88911	−	7.52225i	0.481007	−	0.458640i	0.891366	+	0.453285i	$0.149748\pi$
$270$	0.491888	+	0.196922i	0.0299354	+	0.0119843i
$271$	−5.86941	+	0.560461i	−0.356541	+	0.0340456i	−0.271790	−	0.962357i	$-0.587616\pi$
$271$	−5.86941	+	0.560461i	−0.356541	+	0.0340456i	−0.0847512	+	0.996402i	$0.527010\pi$
$272$	0.369582	−	2.57050i	0.0224092	−	0.155859i
$273$	12.6655	−	9.14224i	0.766553	−	0.553313i
$274$	3.74919	+	4.32680i	0.226497	+	0.261392i
$275$	−1.15570	−	2.00173i	−0.0696914	−	0.120709i
$276$	0.923932	+	4.70599i	0.0556142	+	0.283267i
$277$	−5.61848	+	9.73150i	−0.337582	+	0.584709i	−0.983977	−	0.178294i	$-0.942942\pi$
$277$	−5.61848	+	9.73150i	−0.337582	+	0.584709i	0.646395	+	0.763003i	$0.276276\pi$
$278$	5.10158	−	14.7400i	0.305972	−	0.884049i
$279$	7.15529	+	4.59843i	0.428376	+	0.275301i
$280$	1.20949	−	0.708697i	0.0722811	−	0.0423527i
$281$	11.3461	−	24.8445i	0.676852	−	1.48210i	−0.189092	−	0.981959i	$-0.560555\pi$
$281$	11.3461	−	24.8445i	0.676852	−	1.48210i	0.865944	−	0.500140i	$-0.166718\pi$
$282$	3.14867	−	2.47614i	0.187501	−	0.147452i
$283$	−15.2448	+	14.5359i	−0.906212	+	0.864071i	−0.991208	−	0.132310i	$-0.957761\pi$
$283$	−15.2448	+	14.5359i	−0.906212	+	0.864071i	0.0849966	+	0.996381i	$0.472912\pi$
$284$	−0.668302	−	14.0294i	−0.0396564	−	0.832491i
$285$	1.41589	−	1.98833i	0.0838698	−	0.117779i
$286$	−2.77450	+	0.814668i	−0.164060	+	0.0481723i
$287$	12.1121	−	19.1156i	0.714956	−	1.12836i
$288$	−0.654861	+	0.755750i	−0.0385880	+	0.0445330i
$289$	−7.42257	−	7.07741i	−0.436622	−	0.416318i
$290$	−1.62263	−	0.154943i	−0.0952843	−	0.00909855i
$291$	0.478251	+	10.0397i	0.0280356	+	0.588539i
$292$	1.47690	+	6.08787i	0.0864291	+	0.356266i
$293$	1.75517	+	12.2075i	0.102538	+	0.713169i	0.974629	+	0.223825i	$0.0718545\pi$
$293$	1.75517	+	12.2075i	0.102538	+	0.713169i	−0.872091	+	0.489344i	$0.837236\pi$
$294$	0.907132	−	6.94097i	0.0529050	−	0.404806i
$295$	0.674030	−	4.68798i	0.0392436	−	0.272945i
$296$	0.0217635	−	0.456873i	0.00126498	−	0.0265552i
$297$	−0.480929	+	0.0926914i	−0.0279063	+	0.00537850i
$298$	3.06175	−	5.30310i	0.177362	−	0.307200i
$299$	17.5798	+	22.1958i	1.01667	+	1.28362i
$300$	−4.71927			−0.272467
$301$	−11.8031	−	10.0955i	−0.680320	−	0.581893i
$302$	16.0324	+	10.3034i	0.922561	+	0.592894i
$303$	12.5048	−	5.00616i	0.718380	−	0.287596i
$304$	2.67228	+	3.75269i	0.153266	+	0.215232i
$305$	−0.269754	−	0.107993i	−0.0154461	−	0.00618368i
$306$	−0.612250	−	2.52373i	−0.0350000	−	0.144272i
$307$	1.43121	−	0.919785i	0.0816837	−	0.0524949i	−0.499161	−	0.866509i	$-0.666359\pi$
$307$	1.43121	−	0.919785i	0.0816837	−	0.0524949i	0.580845	+	0.814014i	$0.302722\pi$
$308$	−0.586377	+	1.15557i	−0.0334119	+	0.0658449i
$309$	−3.86966	+	1.13623i	−0.220137	+	0.0646381i
$310$	4.42514	+	0.852875i	0.251331	+	0.0484401i
$311$	3.88681	+	11.2302i	0.220401	+	0.636806i	0.999945	+	0.0104593i	$0.00332936\pi$
$311$	3.88681	+	11.2302i	0.220401	+	0.636806i	−0.779545	+	0.626347i	$0.784549\pi$
$312$	−1.39191	+	5.73753i	−0.0788013	+	0.324824i
$313$	15.2452	−	21.4089i	0.861708	−	1.21010i	−0.114534	−	0.993419i	$-0.536538\pi$
$313$	15.2452	−	21.4089i	0.861708	−	1.21010i	0.976243	−	0.216680i	$-0.0695230\pi$
$314$	−19.3431	+	12.4310i	−1.09159	+	0.701524i
$315$	0.859459	−	1.10745i	0.0484250	−	0.0623980i
$316$	1.84652	+	12.8428i	0.103875	+	0.722465i
$317$	−1.63731	+	0.156344i	−0.0919603	+	0.00878115i	−0.140935	−	0.990019i	$-0.545011\pi$
$317$	−1.63731	+	0.156344i	−0.0919603	+	0.00878115i	0.0489744	+	0.998800i	$0.484405\pi$
$318$	−4.29151	−	3.37488i	−0.240656	−	0.189254i
$319$	1.33927	−	0.690440i	0.0749846	−	0.0386572i
$320$	−0.173294	+	0.500701i	−0.00968744	+	0.0279900i
$321$	−6.40614			−0.357556
$322$	12.6424	+	1.08118i	0.704535	+	0.0602516i
$323$	−11.9639			−0.665688
$324$	−0.327068	+	0.945001i	−0.0181704	+	0.0525000i
$325$	−24.7650	+	12.7673i	−1.37372	+	0.708200i
$326$	2.26860	+	1.78404i	0.125646	+	0.0988091i
$327$	−5.12434	+	0.489315i	−0.283376	+	0.0270592i
$328$	1.21726	+	8.46623i	0.0672120	+	0.467469i
$329$	−4.00198	−	9.81335i	−0.220637	−	0.541028i
$330$	−0.218310	+	0.140299i	−0.0120176	+	0.00772323i
$331$	8.08526	−	11.3542i	0.444406	−	0.624081i	−0.530236	−	0.847850i	$-0.677897\pi$
$331$	8.08526	−	11.3542i	0.444406	−	0.624081i	0.974642	+	0.223769i	$0.0718361\pi$
$332$	2.82557	−	11.6472i	0.155073	−	0.639221i
$333$	−0.149598	−	0.432235i	−0.00819791	−	0.0236863i
$334$	8.40076	+	1.61911i	0.459669	+	0.0885939i
$335$	−6.34072	+	1.86180i	−0.346430	+	0.101721i
$336$	1.44467	+	2.21652i	0.0788129	+	0.120921i
$337$	−21.8507	+	14.0426i	−1.19028	+	0.764949i	−0.977249	−	0.212095i	$-0.931971\pi$
$337$	−21.8507	+	14.0426i	−1.19028	+	0.764949i	−0.213035	+	0.977044i	$0.568335\pi$
$338$	5.15290	+	21.2405i	0.280281	+	1.15533i
$339$	−12.1810	−	4.87654i	−0.661582	−	0.264857i
$340$	−0.798137	−	1.12083i	−0.0432851	−	0.0607854i
$341$	−3.86742	+	1.54828i	−0.209433	+	0.0838442i
$342$	3.87559	+	2.49069i	0.209568	+	0.134681i
$343$	−16.9917	−	7.36762i	−0.917466	−	0.397814i
$344$	5.87041			0.316511
$345$	2.07496	+	1.46676i	0.111712	+	0.0789678i
$346$	3.49448	−	6.05262i	0.187864	−	0.325391i
$347$	−25.6380	+	4.94132i	−1.37632	+	0.265264i	−0.823159	−	0.567811i	$-0.807790\pi$
$347$	−25.6380	+	4.94132i	−1.37632	+	0.265264i	−0.553160	+	0.833075i	$0.686578\pi$
$348$	0.146382	−	3.07293i	0.00784689	−	0.164726i
$349$	−2.82972	+	19.6811i	−0.151471	+	1.05351i	0.762284	+	0.647243i	$0.224078\pi$
$349$	−2.82972	+	19.6811i	−0.151471	+	1.05351i	−0.913756	+	0.406264i	$0.866831\pi$
$350$	−3.44071	+	12.0026i	−0.183914	+	0.641565i
$351$	0.840220	+	5.84386i	0.0448476	+	0.311922i
$352$	−0.115470	−	0.475973i	−0.00615457	−	0.0253695i
$353$	−0.846514	−	17.7705i	−0.0450554	−	0.945829i	−0.902350	−	0.431003i	$-0.858160\pi$
$353$	−0.846514	−	17.7705i	−0.0450554	−	0.945829i	0.857295	−	0.514826i	$-0.172143\pi$
$354$	8.89840	+	0.849694i	0.472945	+	0.0451607i
$355$	−5.38587	−	5.13542i	−0.285853	−	0.272560i
$356$	6.50899	−	7.51178i	0.344976	−	0.398123i
$357$	−6.86502	−	0.282847i	−0.363335	−	0.0149699i
$358$	21.3684	−	6.27432i	1.12935	−	0.331608i
$359$	−18.0806	+	25.3906i	−0.954256	+	1.34007i	−0.0138890	+	0.999904i	$0.504421\pi$
$359$	−18.0806	+	25.3906i	−0.954256	+	1.34007i	−0.940367	+	0.340162i	$0.889518\pi$
$360$	0.0252109	+	0.529242i	0.00132873	+	0.0278935i
$361$	1.60942	−	1.53458i	0.0847066	−	0.0807676i
$362$	−14.6884	+	11.5511i	−0.772007	+	0.607113i
$363$	−4.46991	+	9.78775i	−0.234610	+	0.513723i
$364$	13.5775	+	7.72316i	0.711656	+	0.404804i
$365$	2.79226	+	1.79448i	0.146154	+	0.0939273i
$366$	0.179366	−	0.518244i	0.00937560	−	0.0270890i
$367$	−5.62890	+	9.74955i	−0.293826	+	0.508922i	−0.974711	−	0.223468i	$-0.928262\pi$
$367$	−5.62890	+	9.74955i	−0.293826	+	0.508922i	0.680885	+	0.732390i	$0.261595\pi$
$368$	−3.89690	+	2.79538i	−0.203140	+	0.145719i
$369$	4.27665	+	7.40737i	0.222633	+	0.385612i
$370$	−0.158702	−	0.183152i	−0.00825053	−	0.00952162i
$371$	−11.7122	+	8.45412i	−0.608069	+	0.438916i
$372$	−1.21046	+	8.41894i	−0.0627595	+	0.436502i
$373$	23.3024	−	2.22511i	1.20655	−	0.115212i	0.527665	−	0.849452i	$-0.323068\pi$
$373$	23.3024	−	2.22511i	1.20655	−	0.115212i	0.678889	+	0.734240i	$0.262462\pi$
$374$	1.18081	+	0.472727i	0.0610585	+	0.0244441i
$375$	−3.72699	+	3.55368i	−0.192461	+	0.183511i
$376$	3.56038	+	1.83550i	0.183613	+	0.0946589i
$377$	−7.54519	−	16.5217i	−0.388597	−	0.850909i
$378$	2.16498	+	1.52081i	0.111354	+	0.0782223i
$379$	−1.28643	+	1.48462i	−0.0660796	+	0.0762600i	−0.787827	−	0.615897i	$-0.788794\pi$
$379$	−1.28643	+	1.48462i	−0.0660796	+	0.0762600i	0.721747	+	0.692157i	$0.243339\pi$
$380$	2.39683	+	0.461951i	0.122955	+	0.0236976i
$381$	0.191309	−	0.788587i	0.00980106	−	0.0404005i
$382$	5.89310	+	0.562723i	0.301517	+	0.0287914i
$383$	1.34469	+	0.693237i	0.0687105	+	0.0354227i	0.492239	−	0.870460i	$-0.336178\pi$
$383$	1.34469	+	0.693237i	0.0687105	+	0.0354227i	−0.423529	+	0.905883i	$0.639209\pi$
$384$	−0.959493	−	0.281733i	−0.0489639	−	0.0143771i
$385$	0.197661	+	0.657520i	0.0100737	+	0.0335103i
$386$	−0.585250	+	1.28152i	−0.0297884	+	0.0652276i
$387$	5.44990	−	2.18181i	0.277034	−	0.110908i
$388$	−8.93379	+	4.60569i	−0.453544	+	0.233818i
$389$	−15.5540	+	2.99778i	−0.788617	+	0.151994i	−0.567631	−	0.823283i	$-0.692140\pi$
$389$	−15.5540	+	2.99778i	−0.788617	+	0.151994i	−0.220987	+	0.975277i	$0.570928\pi$
$390$	1.56408	+	2.70907i	0.0792003	+	0.137179i
$391$	−0.0431631	−	12.4544i	−0.00218285	−	0.629845i
$392$	6.69057	−	2.05823i	0.337925	−	0.103956i
$393$	−8.54323	−	9.85941i	−0.430949	−	0.497342i
$394$	−0.364911	+	7.66042i	−0.0183839	+	0.385926i
$395$	5.40383	+	4.24962i	0.271896	+	0.213821i
$396$	−0.284100	−	0.398963i	−0.0142766	−	0.0200486i
$397$	−16.7083	+	13.1396i	−0.838568	+	0.659457i	−0.942160	−	0.335163i	$-0.891209\pi$
$397$	−16.7083	+	13.1396i	−0.838568	+	0.659457i	0.103592	+	0.994620i	$0.466966\pi$
$398$	−11.0839	−	3.25454i	−0.555587	−	0.163135i
$399$	9.16022	−	8.04095i	0.458585	−	0.402551i
$400$	−1.96045	−	4.29280i	−0.0980227	−	0.214640i
$401$	−27.2944	−	26.0252i	−1.36302	−	1.29964i	−0.913771	−	0.406229i	$-0.866843\pi$
$401$	−27.2944	−	26.0252i	−1.36302	−	1.29964i	−0.449248	−	0.893407i	$-0.648308\pi$
$402$	−4.07933	−	11.7864i	−0.203458	−	0.587854i
$403$	16.4241	+	47.4543i	0.818142	+	2.36387i
$404$	9.74843	+	9.29511i	0.485002	+	0.462449i
$405$	0.220104	+	0.481961i	0.0109371	+	0.0239488i
$406$	−7.70871	−	2.61270i	−0.382577	−	0.129666i
$407$	0.214946	+	0.0631139i	0.0106545	+	0.00312844i
$408$	2.04133	−	1.60532i	0.101061	−	0.0794751i
$409$	−21.3633	−	30.0006i	−1.05635	−	1.48343i	−0.864908	−	0.501931i	$-0.832623\pi$
$409$	−21.3633	−	30.0006i	−1.05635	−	1.48343i	−0.191441	−	0.981504i	$-0.561316\pi$
$410$	3.56231	+	2.80143i	0.175930	+	0.138353i
$411$	−0.272415	+	5.71869i	−0.0134372	+	0.282082i
$412$	−2.64107	−	3.04796i	−0.130116	−	0.150162i
$413$	8.64865	−	22.0119i	0.425572	−	1.08314i
$414$	−2.57882	+	4.04347i	−0.126742	+	0.198726i
$415$	−3.17508	−	5.49939i	−0.155858	−	0.269955i
$416$	−5.79726	+	1.11733i	−0.284234	+	0.0547816i
$417$	13.8640	−	7.14738i	0.678922	−	0.350009i
$418$	−2.09475	+	0.838611i	−0.102458	+	0.0410178i
$419$	3.48268	−	7.62601i	0.170140	−	0.372555i	−0.805284	−	0.592889i	$-0.797987\pi$
$419$	3.48268	−	7.62601i	0.170140	−	0.372555i	0.975425	+	0.220334i	$0.0707146\pi$
$420$	1.36441	+	0.321738i	0.0665763	+	0.0156992i
$421$	35.2015	+	10.3361i	1.71562	+	0.503750i	0.984030	−	0.178000i	$-0.0569627\pi$
$421$	35.2015	+	10.3361i	1.71562	+	0.503750i	0.731585	+	0.681750i	$0.238781\pi$
$422$	−1.71304	−	0.883134i	−0.0833895	−	0.0429903i
$423$	3.98753	+	0.380763i	0.193880	+	0.0185133i
$424$	1.28714	−	5.30568i	0.0625092	−	0.257666i
$425$	12.0341	+	2.31939i	0.583742	+	0.112507i
$426$	9.19771	−	10.6147i	0.445631	−	0.514285i
$427$	−1.18728	−	0.834023i	−0.0574567	−	0.0403612i
$428$	−2.66121	−	5.82723i	−0.128634	−	0.281670i
$429$	−2.57019	−	1.32502i	−0.124090	−	0.0639727i
$430$	2.25109	−	2.14641i	0.108557	−	0.103509i
$431$	−17.5259	−	7.01632i	−0.844194	−	0.337964i	−0.0910713	−	0.995844i	$-0.529029\pi$
$431$	−17.5259	−	7.01632i	−0.844194	−	0.337964i	−0.753123	+	0.657880i	$0.771453\pi$
$432$	−0.995472	+	0.0950560i	−0.0478947	+	0.00457339i
$433$	1.63038	−	11.3396i	0.0783512	−	0.544944i	−0.912405	−	0.409289i	$-0.865777\pi$
$433$	1.63038	−	11.3396i	0.0783512	−	0.544944i	0.990756	−	0.135656i	$-0.0433140\pi$
$434$	20.5295	+	9.21663i	0.985447	+	0.442413i
$435$	−1.06743	−	1.23188i	−0.0511795	−	0.0590642i
$436$	−2.57382	−	4.45799i	−0.123264	−	0.213499i
$437$	15.3020	+	15.9373i	0.731992	+	0.762383i
$438$	−3.13223	+	5.42518i	−0.149664	+	0.259225i
$439$	−11.2429	+	32.4842i	−0.536594	+	1.55039i	0.272167	+	0.962250i	$0.412260\pi$
$439$	−11.2429	+	32.4842i	−0.536594	+	1.55039i	−0.808761	+	0.588137i	$0.799862\pi$
$440$	−0.218310	−	0.140299i	−0.0104075	−	0.00668851i
$441$	5.44634	−	4.39743i	0.259350	−	0.209401i
$442$	6.36921	−	13.9466i	0.302953	−	0.663374i
$443$	27.6660	−	21.7568i	1.31445	−	1.03370i	0.318128	−	0.948048i	$-0.396946\pi$
$443$	27.6660	−	21.7568i	1.31445	−	1.03370i	0.996325	−	0.0856492i	$-0.0272964\pi$
$444$	0.331029	−	0.315636i	0.0157100	−	0.0149794i
$445$	−0.250584	−	5.26040i	−0.0118788	−	0.249367i
$446$	−1.58560	+	2.22667i	−0.0750805	+	0.105436i
$447$	5.87545	−	1.72519i	0.277899	−	0.0815986i
$448$	−1.41608	+	2.23489i	−0.0669034	+	0.105589i
$449$	−10.7132	+	12.3637i	−0.505585	+	0.583477i	−0.949963	−	0.312363i	$-0.898879\pi$
$449$	−10.7132	+	12.3637i	−0.505585	+	0.583477i	0.444377	+	0.895840i	$0.353425\pi$
$450$	−3.41549	−	3.25667i	−0.161008	−	0.153521i
$451$	−4.17026	−	0.398211i	−0.196370	−	0.0187510i
$452$	−0.624317	−	13.1060i	−0.0293654	−	0.616456i
$453$	4.49304	+	18.5206i	0.211101	+	0.870171i
$454$	3.28968	+	22.8802i	0.154392	+	1.07382i
$455$	8.03034	−	2.00283i	0.376468	−	0.0938942i
$456$	−0.655634	+	4.56004i	−0.0307029	+	0.213543i
$457$	1.13545	−	23.8361i	0.0531143	−	1.11501i	−0.802253	−	0.596984i	$-0.796366\pi$
$457$	1.13545	−	23.8361i	0.0531143	−	1.11501i	0.855367	−	0.518022i	$-0.173331\pi$
$458$	13.9033	−	2.67964i	0.649658	−	0.125211i
$459$	1.29847	−	2.24901i	0.0606072	−	0.104975i
$460$	−0.472243	+	2.49676i	−0.0220185	+	0.116412i
$461$	−31.0067			−1.44413			−0.722064	−	0.691826i	$-0.756806\pi$
$461$	−31.0067			−1.44413			−0.722064	+	0.691826i	$0.756806\pi$
$462$	−1.22182	+	0.431681i	−0.0568441	+	0.0200836i
$463$	17.7305	+	11.3947i	0.824007	+	0.529557i	0.883368	−	0.468680i	$-0.155270\pi$
$463$	17.7305	+	11.3947i	0.824007	+	0.529557i	−0.0593615	+	0.998237i	$0.518906\pi$
$464$	2.85605	−	1.14339i	0.132589	−	0.0530805i
$465$	2.61407	+	3.67095i	0.121225	+	0.170236i
$466$	8.11008	+	3.24679i	0.375692	+	0.150404i
$467$	−1.06541	−	4.39168i	−0.0493013	−	0.203223i	0.941834	−	0.336078i	$-0.109101\pi$
$467$	−1.06541	−	4.39168i	−0.0493013	−	0.203223i	−0.991135	+	0.132855i	$0.957585\pi$
$468$	−4.96672	+	3.19192i	−0.229587	+	0.147546i
$469$	−32.9508	+	1.78179i	−1.52152	+	0.0822756i
$470$	2.03640	−	0.597941i	0.0939321	−	0.0275810i
$471$	−22.5777	−	4.35149i	−1.04032	−	0.200506i
$472$	2.92362	+	8.44725i	0.134571	+	0.388816i
$473$	−0.677855	+	2.79416i	−0.0311678	+	0.128476i
$474$	−7.52617	+	10.5690i	−0.345688	+	0.485451i
$475$	−18.2900	+	11.7542i	−0.839201	+	0.539322i
$476$	−2.59454	−	6.36214i	−0.118921	−	0.291608i
$477$	−0.776978	−	5.40400i	−0.0355754	−	0.247432i
$478$	−28.6469	+	2.73545i	−1.31028	+	0.125116i
$479$	11.4595	+	9.01186i	0.523598	+	0.411762i	0.844666	−	0.535294i	$-0.179799\pi$
$479$	11.4595	+	9.01186i	0.523598	+	0.411762i	−0.321067	+	0.947056i	$0.604042\pi$
$480$	−0.470942	+	0.242788i	−0.0214955	+	0.0110817i
$481$	0.883218	−	2.55189i	0.0402713	−	0.116356i
$482$	−17.8436			−0.812755
$483$	8.40366	+	9.50676i	0.382380	+	0.432573i
$484$	−10.7601			−0.489096
$485$	−1.74180	+	5.03260i	−0.0790911	+	0.228519i
$486$	−0.888835	+	0.458227i	−0.0403184	+	0.0207856i
$487$	−14.9427	−	11.7510i	−0.677117	−	0.532490i	0.219325	−	0.975652i	$-0.429614\pi$
$487$	−14.9427	−	11.7510i	−0.677117	−	0.532490i	−0.896442	+	0.443161i	$0.853857\pi$
$488$	0.545922	−	0.0521292i	0.0247127	−	0.00235978i
$489$	0.410729	+	2.85669i	0.0185738	+	0.129184i
$490$	1.81304	−	3.23555i	0.0819048	−	0.146167i
$491$	5.04460	−	3.24197i	0.227660	−	0.146308i	−0.421839	−	0.906671i	$-0.638615\pi$
$491$	5.04460	−	3.24197i	0.227660	−	0.146308i	0.649499	+	0.760363i	$0.274979\pi$
$492$	−4.96140	+	6.96731i	−0.223677	+	0.314110i
$493$	−1.88354	+	7.76405i	−0.0848302	+	0.349675i
$494$	8.89595	+	25.7031i	0.400248	+	1.15644i
$495$	−0.254816	−	0.0491118i	−0.0114531	−	0.00220741i
$496$	−8.16098	+	2.39628i	−0.366439	+	0.107596i
$497$	−20.2908	−	31.1316i	−0.910165	−	1.39644i
$498$	10.0824	−	6.47958i	0.451804	−	0.290357i
$499$	4.81702	+	19.8560i	0.215640	+	0.888879i	0.972049	+	0.234780i	$0.0754369\pi$
$499$	4.81702	+	19.8560i	0.215640	+	0.888879i	−0.756409	+	0.654099i	$0.773048\pi$
$500$	−4.78079	−	1.91394i	−0.213804	−	0.0855940i
$501$	4.96260	+	6.96899i	0.221713	+	0.311352i
$502$	14.0534	−	5.62614i	0.627235	−	0.251107i
$503$	−10.9199	−	7.01782i	−0.486896	−	0.312909i	0.274060	−	0.961713i	$-0.411633\pi$
$503$	−10.9199	−	7.01782i	−0.486896	−	0.312909i	−0.760956	+	0.648803i	$0.775270\pi$
$504$	−0.484018	+	2.60110i	−0.0215599	+	0.115862i
$505$	7.13677			0.317582
$506$	−0.880550	−	2.17761i	−0.0391452	−	0.0968064i
$507$	−10.9283	+	18.9284i	−0.485344	+	0.840640i
$508$	0.796796	−	0.153570i	0.0353521	−	0.00681356i
$509$	−1.30213	+	27.3351i	−0.0577159	+	1.21161i	0.765333	+	0.643635i	$0.222574\pi$
$509$	−1.30213	+	27.3351i	−0.0577159	+	1.21161i	−0.823049	+	0.567971i	$0.807729\pi$
$510$	0.195820	−	1.36196i	0.00867106	−	0.0603085i
$511$	11.5143	+	11.9216i	0.509363	+	0.527381i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$	1.08612	+	4.47707i	0.0479536	+	0.197667i
$514$	0.00976530	+	0.204999i	0.000430729	+	0.00904211i
$515$	−2.12719	−	0.203122i	−0.0937352	−	0.00895062i
$516$	4.24861	+	4.05105i	0.187035	+	0.178337i
$517$	−1.28477	+	1.48270i	−0.0565040	+	0.0652091i
$518$	−0.561415	−	1.07203i	−0.0246672	−	0.0471025i
$519$	6.70586	−	1.96902i	0.294355	−	0.0864303i
$520$	−1.81451	+	2.54812i	−0.0795716	+	0.111743i
$521$	1.75023	+	36.7419i	0.0766790	+	1.60969i	0.629913	+	0.776665i	$0.283090\pi$
$521$	1.75023	+	36.7419i	0.0766790	+	1.60969i	−0.553234	+	0.833026i	$0.686607\pi$
$522$	2.22651	−	2.12297i	0.0974516	−	0.0929199i
$523$	−15.9843	+	12.5702i	−0.698945	+	0.549657i	−0.903178	−	0.429266i	$-0.858772\pi$
$523$	−15.9843	+	12.5702i	−0.698945	+	0.549657i	0.204233	+	0.978922i	$0.434530\pi$
$524$	5.41945	−	11.8669i	0.236750	−	0.518410i
$525$	−10.7729	+	6.31232i	−0.470167	+	0.275492i
$526$	−11.1709	−	7.17909i	−0.487073	−	0.313023i
$527$	7.22436	−	20.8734i	0.314698	−	0.909261i
$528$	0.244890	−	0.424162i	0.0106575	−	0.0184593i
$529$	−16.5355	+	15.9868i	−0.718934	+	0.695079i
$530$	−1.44636	−	2.50516i	−0.0628257	−	0.108817i
$531$	5.85372	+	6.75555i	0.254030	+	0.293166i
$532$	11.1196	+	4.99210i	0.482096	+	0.216435i
$533$	−7.18665	+	49.9842i	−0.311288	+	2.16506i
$534$	9.89450	−	0.944810i	0.428177	−	0.0408859i
$535$	−3.15111	−	1.26151i	−0.136234	−	0.0545399i
$536$	9.02671	−	8.60695i	0.389894	−	0.371764i
$537$	19.7948	+	10.2049i	0.854208	+	0.440375i
$538$	4.52826	+	9.91550i	0.195227	+	0.427487i
$539$	0.207103	+	3.42220i	0.00892055	+	0.147404i
$540$	−0.346973	+	0.400428i	−0.0149313	+	0.0172317i
$541$	−6.88058	−	1.32612i	−0.295819	−	0.0570145i	0.0391822	−	0.999232i	$-0.487525\pi$
$541$	−6.88058	−	1.32612i	−0.295819	−	0.0570145i	−0.335002	+	0.942218i	$0.608737\pi$
$542$	1.39006	−	5.72991i	0.0597082	−	0.246121i
$543$	−18.6017	−	1.77625i	−0.798275	−	0.0762260i
$544$	2.30825	+	1.18998i	0.0989653	+	0.0510201i
$545$	−2.61696	−	0.768408i	−0.112098	−	0.0329150i
$546$	4.49693	+	14.9591i	0.192451	+	0.640190i
$547$	9.75896	−	21.3691i	0.417263	−	0.913678i	−0.577962	−	0.816064i	$-0.696152\pi$
$547$	9.75896	−	21.3691i	0.417263	−	0.913678i	0.995224	−	0.0976141i	$-0.0311211\pi$
$548$	−5.31507	+	2.12783i	−0.227049	+	0.0908965i
$549$	0.487442	−	0.251294i	0.0208035	−	0.0107250i
$550$	2.26963	−	0.437436i	0.0967774	−	0.0186523i
$551$	−7.08641	−	12.2740i	−0.301891	−	0.522891i
$552$	−4.74935	−	0.666062i	−0.202146	−	0.0283495i
$553$	21.3932	+	26.8470i	0.909731	+	1.14165i
$554$	−7.35865	−	8.49233i	−0.312639	−	0.360805i
$555$	0.0115312	−	0.242070i	0.000489473	−	0.0102753i
$556$	12.2608	+	9.64199i	0.519973	+	0.408911i
$557$	−8.65934	−	12.1603i	−0.366908	−	0.515250i	0.589310	−	0.807907i	$-0.299400\pi$
$557$	−8.65934	−	12.1603i	−0.366908	−	0.515250i	−0.956217	+	0.292657i	$0.905460\pi$
$558$	−6.68579	+	5.25776i	−0.283032	+	0.222579i
$559$	33.2547	+	9.76446i	1.40652	+	0.412992i
$560$	0.274132	+	1.37476i	0.0115842	+	0.0580944i
$561$	0.528377	+	1.15698i	0.0223081	+	0.0488479i
$562$	19.7671	+	18.8479i	0.833826	+	0.795052i
$563$	−13.6240	−	39.3639i	−0.574182	−	1.65899i	−0.739822	−	0.672803i	$-0.765090\pi$
$563$	−13.6240	−	39.3639i	−0.574182	−	1.65899i	0.165641	−	0.986186i	$-0.447031\pi$
$564$	1.31013	+	3.78536i	0.0551663	+	0.159392i
$565$	−5.03140	−	4.79743i	−0.211672	−	0.201829i
$566$	−8.75036	−	19.1606i	−0.367805	−	0.805381i
$567$	0.517385	+	2.59467i	0.0217281	+	0.108966i
$568$	13.4764	+	3.95702i	0.565456	+	0.166033i
$569$	−2.07938	+	1.63524i	−0.0871721	+	0.0685529i	−0.660794	−	0.750567i	$-0.729780\pi$
$569$	−2.07938	+	1.63524i	−0.0871721	+	0.0685529i	0.573622	+	0.819120i	$0.305538\pi$
$570$	1.41589	+	1.98833i	0.0593049	+	0.0832821i
$571$	23.2536	+	18.2868i	0.973131	+	0.765279i	0.972063	−	0.234721i	$-0.0754176\pi$
$571$	23.2536	+	18.2868i	0.973131	+	0.765279i	0.00106810	+	0.999999i	$0.499660\pi$
$572$	0.137590	−	2.88836i	0.00575291	−	0.120768i
$573$	3.87672	+	4.47397i	0.161952	+	0.186903i
$574$	14.1028	+	17.6981i	0.588640	+	0.738704i
$575$	−12.3021	−	18.9974i	−0.513034	−	0.792247i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−22.3457	+	4.30679i	−0.930265	+	0.179294i	−0.631804	−	0.775128i	$-0.717685\pi$
$577$	−22.3457	+	4.30679i	−0.930265	+	0.179294i	−0.298461	+	0.954422i	$0.596473\pi$
$578$	9.11584	−	4.69954i	0.379169	−	0.195475i
$579$	−1.30791	+	0.523610i	−0.0543551	+	0.0217605i
$580$	0.677132	−	1.48271i	0.0281164	−	0.0615663i
$581$	−9.12875	−	30.3669i	−0.378724	−	1.25983i
$582$	−9.64397	−	2.83173i	−0.399756	−	0.117379i
$583$	2.37673	+	1.22529i	0.0984343	+	0.0507464i
$584$	−6.23609	−	0.595474i	−0.258051	−	0.0246409i
$585$	−0.737492	+	3.03998i	−0.0304915	+	0.125688i
$586$	−12.1101	−	2.33404i	−0.500266	−	0.0964183i
$587$	−23.4688	+	27.0844i	−0.968659	+	1.11789i	0.0243319	+	0.999704i	$0.492254\pi$
$587$	−23.4688	+	27.0844i	−0.968659	+	1.11789i	−0.992991	+	0.118188i	$0.962291\pi$
$588$	6.26253	+	3.12741i	0.258262	+	0.128972i
$589$	16.2777	+	35.6433i	0.670713	+	1.46866i
$590$	4.20969	+	2.17025i	0.173310	+	0.0893477i
$591$	−5.55039	+	5.29229i	−0.228313	+	0.217696i
$592$	0.424627	+	0.169995i	0.0174521	+	0.00698675i
$593$	29.2607	−	2.79406i	1.20159	−	0.114738i	0.525004	−	0.851100i	$-0.324064\pi$
$593$	29.2607	−	2.79406i	1.20159	−	0.114738i	0.676588	+	0.736361i	$0.263458\pi$
$594$	0.0697029	−	0.484794i	0.00285994	−	0.0198914i
$595$	−3.32112	−	1.49100i	−0.136153	−	0.0611252i
$596$	4.01004	+	4.62783i	0.164257	+	0.189563i
$597$	−5.77593	−	10.0042i	−0.236393	−	0.409445i
$598$	−26.7248	+	9.35339i	−1.09286	+	0.382489i
$599$	−11.6183	+	20.1235i	−0.474711	+	0.822223i	−0.999581	−	0.0289591i	$-0.990781\pi$
$599$	−11.6183	+	20.1235i	−0.474711	+	0.822223i	0.524870	+	0.851183i	$0.324114\pi$
$600$	1.54352	−	4.45971i	0.0630140	−	0.182067i
$601$	−0.353584	−	0.227235i	−0.0144230	−	0.00926909i	0.533409	−	0.845857i	$-0.320911\pi$
$601$	−0.353584	−	0.227235i	−0.0144230	−	0.00926909i	−0.547832	+	0.836588i	$0.684547\pi$
$602$	13.4006	−	7.85204i	0.546170	−	0.320025i
$603$	5.18123	−	11.3453i	0.210996	−	0.462016i
$604$	−14.9804	+	11.7807i	−0.609544	+	0.479351i
$605$	−4.12612	+	3.93425i	−0.167751	+	0.159950i
$606$	0.640911	+	13.4544i	0.0260352	+	0.546547i
$607$	20.5247	−	28.8229i	0.833071	−	1.16988i	−0.150365	−	0.988631i	$-0.548045\pi$
$607$	20.5247	−	28.8229i	0.833071	−	1.16988i	0.983436	−	0.181254i	$-0.0580157\pi$
$608$	−4.42031	+	1.29792i	−0.179267	+	0.0526377i
$609$	−3.77609	−	7.21052i	−0.153015	−	0.292185i
$610$	0.190282	−	0.219597i	0.00770428	−	0.00889121i
$611$	17.1158	+	16.3199i	0.692431	+	0.660231i
$612$	2.58517	+	0.246854i	0.104499	+	0.00997849i
$613$	−0.470961	−	9.88670i	−0.0190220	−	0.399320i	−0.988220	−	0.153038i	$-0.951094\pi$
$613$	−0.470961	−	9.88670i	−0.0190220	−	0.399320i	0.969198	−	0.246282i	$-0.0792088\pi$
$614$	0.401094	+	1.65333i	0.0161868	+	0.0667230i
$615$	0.644955	+	4.48576i	0.0260071	+	0.180883i
$616$	−0.900233	−	0.932078i	−0.0362714	−	0.0375545i
$617$	1.13150	−	7.86979i	0.0455527	−	0.316826i	−0.954287	−	0.298893i	$-0.903383\pi$
$617$	1.13150	−	7.86979i	0.0455527	−	0.316826i	0.999839	−	0.0179324i	$-0.00570837\pi$
$618$	0.191899	−	4.02846i	0.00771931	−	0.162048i
$619$	−9.65616	+	1.86107i	−0.388114	+	0.0748028i	−0.379575	−	0.925161i	$-0.623930\pi$
$619$	−9.65616	+	1.86107i	−0.388114	+	0.0748028i	−0.00853817	+	0.999964i	$0.502718\pi$
$620$	−2.25329	+	3.90281i	−0.0904942	+	0.156741i
$621$	−4.65670	+	1.14681i	−0.186867	+	0.0460197i
$622$	−11.8838			−0.476497
$623$	4.81090	−	25.8537i	0.192745	−	1.03581i
$624$	−4.96672	−	3.19192i	−0.198828	−	0.127779i
$625$	19.3730	−	7.75579i	0.774921	−	0.310231i
$626$	15.2452	+	21.4089i	0.609320	+	0.855670i
$627$	−2.09475	−	0.838611i	−0.0836563	−	0.0334909i
$628$	−5.42084	−	22.3450i	−0.216315	−	0.891664i
$629$	−0.999252	+	0.642180i	−0.0398428	+	0.0256054i
$630$	0.765444	+	1.17440i	0.0304960	+	0.0467893i
$631$	−30.8607	+	9.06152i	−1.22854	+	0.360733i	−0.830700	−	0.556720i	$-0.812060\pi$
$631$	−30.8607	+	9.06152i	−1.22854	+	0.360733i	−0.397844	+	0.917453i	$0.630242\pi$
$632$	−12.7404	−	2.45551i	−0.506786	−	0.0976750i
$633$	−0.630354	−	1.82129i	−0.0250543	−	0.0723897i
$634$	0.387766	−	1.59839i	0.0154001	−	0.0634802i
$635$	0.249393	−	0.350223i	0.00989686	−	0.0138982i
$636$	4.59289	−	2.95167i	0.182120	−	0.117041i
$637$	41.3242	−	0.530794i	1.63733	−	0.0210308i
$638$	0.214435	+	1.49143i	0.00848957	+	0.0590463i
$639$	13.9817	−	1.33509i	0.553108	−	0.0528154i
$640$	−0.416484	−	0.327526i	−0.0164630	−	0.0129466i
$641$	−2.71609	+	1.40024i	−0.107279	+	0.0553062i	−0.511031	−	0.859562i	$-0.670736\pi$
$641$	−2.71609	+	1.40024i	−0.107279	+	0.0553062i	0.403752	+	0.914869i	$0.367706\pi$
$642$	2.09524	−	6.05381i	0.0826927	−	0.238925i
$643$	29.1838			1.15090			0.575448	−	0.817839i	$-0.304828\pi$
$643$	29.1838			1.15090			0.575448	+	0.817839i	$0.304828\pi$
$644$	−5.15665	+	11.5935i	−0.203200	+	0.456847i
$645$	3.11039			0.122471
$646$	3.91300	−	11.3059i	0.153955	−	0.444824i
$647$	18.8497	−	9.71770i	0.741058	−	0.382042i	−0.0459832	−	0.998942i	$-0.514642\pi$
$647$	18.8497	−	9.71770i	0.741058	−	0.382042i	0.787041	+	0.616900i	$0.211612\pi$
$648$	−0.786053	−	0.618159i	−0.0308791	−	0.0242836i
$649$	−4.35826	+	0.416163i	−0.171076	+	0.0163358i
$650$	−3.96522	−	27.5787i	−0.155529	−	1.08173i
$651$	8.49769	+	20.8374i	0.333051	+	0.816681i
$652$	−2.42791	+	1.56032i	−0.0950843	+	0.0611069i
$653$	−10.7371	+	15.0781i	−0.420174	+	0.590052i	−0.969359	−	0.245649i	$-0.920999\pi$
$653$	−10.7371	+	15.0781i	−0.420174	+	0.590052i	0.549185	+	0.835701i	$0.314938\pi$
$654$	1.21360	−	5.00254i	0.0474557	−	0.195615i
$655$	−2.26078	−	6.53208i	−0.0883358	−	0.255230i
$656$	−8.39872	−	1.61872i	−0.327915	−	0.0632004i
$657$	−6.01070	+	1.76490i	−0.234500	+	0.0688554i
$658$	10.5825	−	0.572245i	0.412551	−	0.0223084i
$659$	7.38875	−	4.74846i	0.287825	−	0.184974i	−0.388759	−	0.921340i	$-0.627096\pi$
$659$	7.38875	−	4.74846i	0.287825	−	0.184974i	0.676584	+	0.736366i	$0.263460\pi$
$660$	−0.0611808	−	0.252191i	−0.00238146	−	0.00981651i
$661$	10.1775	+	4.07446i	0.395860	+	0.158478i	0.561047	−	0.827784i	$-0.310399\pi$
$661$	10.1775	+	4.07446i	0.395860	+	0.158478i	−0.165187	+	0.986262i	$0.552823\pi$
$662$	8.08526	+	11.3542i	0.314243	+	0.441292i
$663$	14.2339	−	5.69839i	0.552799	−	0.221307i
$664$	10.0824	+	6.47958i	0.391274	+	0.251456i
$665$	6.08925	−	2.15140i	0.236131	−	0.0834275i
$666$	0.457391			0.0177235
$667$	12.7517	−	7.42123i	0.493747	−	0.287351i
$668$	−4.27768	+	7.40916i	−0.165508	+	0.286669i
$669$	−2.68413	+	0.517324i	−0.103775	+	0.0200009i
$670$	0.314441	−	6.60092i	0.0121479	−	0.255016i
$671$	−0.0382254	+	0.265864i	−0.00147568	+	0.0102636i
$672$	−2.56711	+	0.640258i	−0.0990285	+	0.0246985i
$673$	−4.52388	−	31.4643i	−0.174383	−	1.21286i	−0.869489	−	0.493952i	$-0.835552\pi$
$673$	−4.52388	−	31.4643i	−0.174383	−	1.21286i	0.695106	−	0.718907i	$-0.255357\pi$
$674$	−6.12360	−	25.2418i	−0.235872	−	0.972279i
$675$	−0.224552	−	4.71392i	−0.00864300	−	0.181439i
$676$	−21.7577	−	2.07761i	−0.836833	−	0.0799079i
$677$	−24.4327	−	23.2965i	−0.939025	−	0.895358i	0.0556470	−	0.998451i	$-0.482278\pi$
$677$	−24.4327	−	23.2965i	−0.939025	−	0.895358i	−0.994672	+	0.103092i	$0.967126\pi$
$678$	8.59236	−	9.91611i	0.329987	−	0.380826i
$679$	−14.2332	+	22.4631i	−0.546219	+	0.862055i
$680$	1.32023	−	0.387654i	0.0506284	−	0.0148658i
$681$	−13.4083	+	18.8293i	−0.513807	+	0.721541i
$682$	−0.198218	−	4.16111i	−0.00759016	−	0.159337i
$683$	6.31833	−	6.02451i	0.241764	−	0.230522i	−0.559503	−	0.828828i	$-0.689008\pi$
$683$	6.31833	−	6.02451i	0.241764	−	0.230522i	0.801267	+	0.598307i	$0.204160\pi$
$684$	−3.62129	+	2.84781i	−0.138463	+	0.108889i
$685$	−1.26014	+	2.75931i	−0.0481473	+	0.105428i
$686$	12.5199	−	13.6475i	0.478010	−	0.521063i
$687$	11.9115	+	7.65503i	0.454450	+	0.292057i
$688$	−1.92002	+	5.54754i	−0.0732002	+	0.211498i
$689$	16.1165	−	27.9146i	0.613991	−	1.06346i
$690$	−2.06474	+	1.48111i	−0.0786034	+	0.0563848i
$691$	8.90578	+	15.4253i	0.338792	+	0.586805i	0.984206	−	0.177028i	$-0.0566484\pi$
$691$	8.90578	+	15.4253i	0.338792	+	0.586805i	−0.645414	+	0.763833i	$0.723315\pi$
$692$	4.57680	+	5.28191i	0.173984	+	0.200788i
$693$	−1.18217	−	0.530728i	−0.0449068	−	0.0201607i
$694$	3.71582	−	25.8441i	0.141050	−	0.981027i
$695$	8.22700	−	0.785584i	0.312068	−	0.0297989i
$696$	2.85605	+	1.14339i	0.108258	+	0.0433400i
$697$	16.0758	−	15.3283i	0.608915	−	0.580599i
$698$	−17.6732	−	9.11116i	−0.668940	−	0.344862i
$699$	3.62900	+	7.94641i	0.137261	+	0.300561i
$700$	−10.2171	−	7.17713i	−0.386170	−	0.271270i
$701$	24.4678	−	28.2374i	0.924136	−	1.06651i	−0.0734655	−	0.997298i	$-0.523406\pi$
$701$	24.4678	−	28.2374i	0.924136	−	1.06651i	0.997602	−	0.0692125i	$-0.0220486\pi$
$702$	−5.79726	−	1.11733i	−0.218803	−	0.0421709i
$703$	0.496783	−	2.04777i	0.0187365	−	0.0772330i
$704$	0.487562	+	0.0465565i	0.0183757	+	0.00175466i
$705$	1.88644	+	0.972527i	0.0710474	+	0.0366275i
$706$	17.0700	+	5.01221i	0.642439	+	0.188637i
$707$	34.6860	+	8.17923i	1.30450	+	0.307612i
$708$	−3.71334	+	8.13109i	−0.139556	+	0.305585i
$709$	4.34603	−	1.73989i	0.163219	−	0.0653429i	−0.288614	−	0.957445i	$-0.593195\pi$
$709$	4.34603	−	1.73989i	0.163219	−	0.0653429i	0.451833	+	0.892103i	$0.350770\pi$
$710$	6.61452	−	3.41002i	0.248239	−	0.127976i
$711$	−12.7404	+	2.45551i	−0.477803	+	0.0920889i
$712$	4.96975	+	8.60787i	0.186249	+	0.322593i
$713$	−37.0459	+	17.0737i	−1.38738	+	0.639415i
$714$	2.51262	−	6.39494i	0.0940324	−	0.239324i
$715$	−1.00332	−	1.15789i	−0.0375220	−	0.0433027i
$716$	−1.05967	+	22.2453i	−0.0396018	+	0.831344i
$717$	−22.6204	−	17.7889i	−0.844774	−	0.664338i
$718$	−18.0806	−	25.3906i	−0.674761	−	0.947569i
$719$	−2.04745	+	1.61013i	−0.0763571	+	0.0600479i	−0.655608	−	0.755101i	$-0.727588\pi$
$719$	−2.04745	+	1.61013i	−0.0763571	+	0.0600479i	0.579251	+	0.815149i	$0.303345\pi$
$720$	−0.508379	−	0.149274i	−0.0189462	−	0.00556310i
$721$	−10.1057	−	3.42511i	−0.376357	−	0.127558i
$722$	0.923791	+	2.02282i	0.0343800	+	0.0752816i
$723$	−12.9140	−	12.3135i	−0.480278	−	0.457945i
$724$	−6.11169	−	17.6586i	−0.227139	−	0.656276i
$725$	4.74851	+	13.7199i	0.176355	+	0.509545i
$726$	−7.78746	−	7.42533i	−0.289020	−	0.275580i
$727$	−4.12443	−	9.03123i	−0.152966	−	0.334950i	0.817599	−	0.575788i	$-0.195305\pi$
$727$	−4.12443	−	9.03123i	−0.152966	−	0.334950i	−0.970565	+	0.240839i	$0.922578\pi$
$728$	−11.7392	+	10.3048i	−0.435082	+	0.381920i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−2.60904	+	2.05178i	−0.0965651	+	0.0759396i
$731$	−8.84300	−	12.4183i	−0.327070	−	0.459306i
$732$	0.431076	+	0.339002i	0.0159330	+	0.0125299i
$733$	−1.42122	+	29.8352i	−0.0524941	+	1.10199i	0.806905	+	0.590682i	$0.201141\pi$
$733$	−1.42122	+	29.8352i	−0.0524941	+	1.10199i	−0.859399	+	0.511306i	$0.829162\pi$
$734$	−7.37229	−	8.50808i	−0.272116	−	0.314039i
$735$	3.54494	−	1.09054i	0.130757	−	0.0402250i
$736$	−1.36708	−	4.59686i	−0.0503913	−	0.169442i
$737$	3.05437	+	5.29032i	0.112509	+	0.194871i
$738$	−8.39872	+	1.61872i	−0.309161	+	0.0595860i
$739$	−8.60344	+	4.43538i	−0.316483	+	0.163158i	−0.609147	−	0.793057i	$-0.708488\pi$
$739$	−8.60344	+	4.43538i	−0.316483	+	0.163158i	0.292665	+	0.956215i	$0.405458\pi$
$740$	0.224985	−	0.0900704i	0.00827062	−	0.00331106i
$741$	−11.2989	+	24.7411i	−0.415076	+	0.908889i
$742$	−4.15846	−	13.8331i	−0.152662	−	0.507831i
$743$	3.38787	+	0.994768i	0.124289	+	0.0364945i	0.343285	−	0.939231i	$-0.388460\pi$
$743$	3.38787	+	0.994768i	0.124289	+	0.0364945i	−0.218997	+	0.975726i	$0.570278\pi$
$744$	−7.56000	−	3.89745i	−0.277163	−	0.142888i
$745$	3.22979	+	0.308408i	0.118330	+	0.0112992i
$746$	−5.51875	+	22.7486i	−0.202056	+	0.832885i
$747$	11.7684	+	2.26818i	0.430584	+	0.0829882i
$748$	−0.832934	+	0.961257i	−0.0304551	+	0.0351470i
$749$	−13.8691	−	9.74255i	−0.506768	−	0.355985i
$750$	−2.13925	−	4.68431i	−0.0781144	−	0.171047i
$751$	5.51908	+	2.84528i	0.201394	+	0.103826i	0.555973	−	0.831200i	$-0.312346\pi$
$751$	5.51908	+	2.84528i	0.201394	+	0.103826i	−0.354579	+	0.935026i	$0.615376\pi$
$752$	−2.89904	+	2.76423i	−0.105717	+	0.100801i
$753$	14.0534	+	5.62614i	0.512135	+	0.205028i
$754$	18.0808	−	1.72650i	0.658463	−	0.0628756i
$755$	−1.43704	+	9.99482i	−0.0522992	+	0.363749i
$756$	−2.14527	+	1.54849i	−0.0780225	+	0.0563182i
$757$	27.8111	+	32.0958i	1.01081	+	1.16654i	0.985982	+	0.166849i	$0.0533592\pi$
$757$	27.8111	+	32.0958i	1.01081	+	1.16654i	0.0248307	+	0.999692i	$0.492095\pi$
$758$	−0.982219	−	1.70125i	−0.0356758	−	0.0617923i
$759$	0.865435	−	2.18366i	0.0314133	−	0.0792617i
$760$	−1.22047	+	2.11392i	−0.0442711	+	0.0766799i
$761$	−1.00448	+	2.90225i	−0.0364123	+	0.105206i	−0.961742	−	0.273958i	$-0.911667\pi$
$761$	−1.00448	+	2.90225i	−0.0364123	+	0.105206i	0.925329	+	0.379164i	$0.123788\pi$
$762$	0.682644	+	0.438709i	0.0247296	+	0.0158927i
$763$	−11.8382	−	6.73381i	−0.428573	−	0.243780i
$764$	−2.45922	+	5.38494i	−0.0889714	+	0.194820i
$765$	1.08158	−	0.850565i	0.0391046	−	0.0307522i
$766$	−1.09491	+	1.04400i	−0.0395609	+	0.0377212i
$767$	2.51112	+	52.7149i	0.0906713	+	1.90343i
$768$	0.580057	−	0.814576i	0.0209310	−	0.0293935i
$769$	−4.91752	+	1.44391i	−0.177330	+	0.0520689i	−0.369192	−	0.929353i	$-0.620366\pi$
$769$	−4.91752	+	1.44391i	−0.177330	+	0.0520689i	0.191862	+	0.981422i	$0.438547\pi$
$770$	−0.686006	−	0.0282643i	−0.0247219	−	0.00101857i
$771$	−0.134398	+	0.155104i	−0.00484022	+	0.00558592i
$772$	−1.01962	−	0.972205i	−0.0366969	−	0.0349904i
$773$	25.6172	+	2.44615i	0.921387	+	0.0879818i	0.544958	−	0.838464i	$-0.316546\pi$
$773$	25.6172	+	2.44615i	0.921387	+	0.0879818i	0.376429	+	0.926445i	$0.377152\pi$
$774$	0.279325	+	5.86376i	0.0100401	+	0.210768i
$775$	−9.46332	−	39.0083i	−0.339932	−	1.40122i
$776$	−1.43042	−	9.94881i	−0.0513492	−	0.357141i
$777$	0.333473	−	1.16329i	0.0119633	−	0.0417327i
$778$	2.25430	−	15.6790i	0.0808205	−	0.562119i
$779$	−1.87494	+	39.3598i	−0.0671766	+	1.41021i
$780$	−3.07163	+	0.592008i	−0.109982	+	0.0211973i
$781$	−3.43955	+	5.95748i	−0.123077	+	0.213175i
$782$	11.7835	+	4.03264i	0.421378	+	0.144207i
$783$	3.07642			0.109942
$784$	−0.243243	+	6.99577i	−0.00868725	+	0.249849i
$785$	−10.2488	−	6.58649i	−0.365794	−	0.235082i
$786$	12.1114	−	4.84866i	0.431998	−	0.172946i
$787$	−27.6798	−	38.8709i	−0.986679	−	1.38560i	−0.921783	−	0.387705i	$-0.873268\pi$
$787$	−27.6798	−	38.8709i	−0.986679	−	1.38560i	−0.0648958	−	0.997892i	$-0.520672\pi$
$788$	−7.11975	−	2.85032i	−0.253631	−	0.101538i
$789$	−3.13061	−	12.9045i	−0.111453	−	0.459414i
$790$	−5.78331	+	3.71671i	−0.205761	+	0.132235i
$791$	−18.9553	−	29.0827i	−0.673973	−	1.03406i
$792$	0.469940	−	0.137987i	0.0166986	−	0.00490315i
$793$	3.17925	+	0.612750i	0.112898	+	0.0217594i
$794$	−6.95216	−	20.0869i	−0.246723	−	0.712859i
$795$	0.681982	−	2.81117i	0.0241874	−	0.0997019i
$796$	6.70074	−	9.40987i	0.237501	−	0.333524i
$797$	10.0836	−	6.48035i	0.357180	−	0.229546i	−0.349728	−	0.936851i	$-0.613726\pi$
$797$	10.0836	−	6.48035i	0.357180	−	0.229546i	0.706908	+	0.707306i	$0.250090\pi$
$798$	4.60269	+	11.2864i	0.162933	+	0.399532i
$799$	−1.48042	−	10.2966i	−0.0523736	−	0.364267i
$800$	4.69790	−	0.448595i	0.166096	−	0.0158602i
$801$	7.81298	+	6.14420i	0.276058	+	0.217094i
$802$	33.5210	−	17.2813i	1.18367	−	0.610223i
$803$	1.00351	−	2.89945i	0.0354131	−	0.102320i
$804$	12.4724			0.439868
$805$	2.26157	+	6.33113i	0.0797098	+	0.223143i
$806$	−50.2161			−1.76879
$807$	−3.56522	+	10.3010i	−0.125502	+	0.362614i
$808$	−11.9723	+	6.17214i	−0.421183	+	0.217135i
$809$	7.58105	+	5.96180i	0.266535	+	0.209606i	0.742478	−	0.669871i	$-0.233650\pi$
$809$	7.58105	+	5.96180i	0.266535	+	0.209606i	−0.475942	+	0.879476i	$0.657893\pi$
$810$	−0.527443	+	0.0503647i	−0.0185324	+	0.00176963i
$811$	−3.95935	−	27.5379i	−0.139032	−	0.966986i	−0.933218	−	0.359311i	$-0.883012\pi$
$811$	−3.95935	−	27.5379i	−0.139032	−	0.966986i	0.794186	−	0.607674i	$-0.207897\pi$
$812$	4.99027	−	6.43021i	0.175124	−	0.225656i
$813$	4.96012	−	3.18768i	0.173959	−	0.111797i
$814$	−0.129945	+	0.182482i	−0.00455456	+	0.00639598i
$815$	−0.360512	+	1.48605i	−0.0126282	+	0.0520541i
$816$	0.849374	+	2.45410i	0.0297340	+	0.0859108i
$817$	26.5558	+	5.11821i	0.929070	+	0.179064i
$818$	35.3379	−	10.3761i	1.23556	−	0.362793i
$819$	−7.06837	+	13.9296i	−0.246989	+	0.486741i
$820$	−3.81247	+	2.45013i	−0.133137	+	0.0855621i
$821$	−11.9637	−	49.3150i	−0.417536	−	1.72111i	−0.660284	−	0.751016i	$-0.729564\pi$
$821$	−11.9637	−	49.3150i	−0.417536	−	1.72111i	0.242748	−	0.970089i	$-0.421951\pi$
$822$	−5.31507	−	2.12783i	−0.185384	−	0.0742167i
$823$	1.30357	+	1.83061i	0.0454397	+	0.0638111i	0.836671	−	0.547706i	$-0.184499\pi$
$823$	1.30357	+	1.83061i	0.0454397	+	0.0638111i	−0.791231	+	0.611517i	$0.790559\pi$
$824$	3.74413	−	1.49892i	0.130433	−	0.0522175i
$825$	1.94447	+	1.24964i	0.0676979	+	0.0435068i
$826$	17.9726	+	15.3724i	0.625347	+	0.534874i
$827$	−13.6008			−0.472946			−0.236473	−	0.971638i	$-0.575991\pi$
$827$	−13.6008			−0.472946			−0.236473	+	0.971638i	$0.575991\pi$
$828$	−2.97763	−	3.75948i	−0.103480	−	0.130651i
$829$	19.0256	−	32.9533i	0.660787	−	1.14452i	−0.319623	−	0.947545i	$-0.603556\pi$
$829$	19.0256	−	32.9533i	0.660787	−	1.14452i	0.980409	−	0.196971i	$-0.0631105\pi$
$830$	6.23540	−	1.20177i	0.216434	−	0.0417142i
$831$	0.534676	−	11.2242i	0.0185477	−	0.389365i
$832$	0.840220	−	5.84386i	0.0291294	−	0.202599i
$833$	−14.4324	−	11.0528i	−0.500054	−	0.382956i
$834$	2.21981	+	15.4391i	0.0768659	+	0.534614i
$835$	1.06869	+	4.40521i	0.0369836	+	0.152449i
$836$	−0.107363	−	2.25382i	−0.00371322	−	0.0779501i
$837$	−8.46700	−	0.808501i	−0.292662	−	0.0279459i
$838$	6.06751	+	5.78536i	0.209599	+	0.199852i
$839$	36.0181	−	41.5671i	1.24348	−	1.43506i	0.384444	−	0.923148i	$-0.374393\pi$
$839$	36.0181	−	41.5671i	1.24348	−	1.43506i	0.859040	−	0.511909i	$-0.171061\pi$
$840$	−0.750297	+	1.18414i	−0.0258877	+	0.0408566i
$841$	18.7443	−	5.50383i	0.646356	−	0.189787i
$842$	−21.2809	+	29.8848i	−0.733388	+	1.02990i
$843$	1.29959	+	27.2818i	0.0447603	+	0.939634i
$844$	1.39484	−	1.32998i	0.0480125	−	0.0457798i
$845$	−9.10294	+	7.15863i	−0.313150	+	0.246264i
$846$	−1.66402	+	3.64369i	−0.0572100	+	0.125272i
$847$	−24.5626	+	14.3923i	−0.843981	+	0.494526i
$848$	4.59289	+	2.95167i	0.157720	+	0.101361i
$849$	6.88941	−	19.9056i	0.236444	−	0.683160i
$850$	−6.12781	+	10.6137i	−0.210182	+	0.364046i
$851$	2.13352	+	0.509762i	0.0731360	+	0.0174744i
$852$	7.02265	+	12.1636i	0.240592	+	0.416718i
$853$	19.0989	+	22.0413i	0.653934	+	0.754680i	0.981774	−	0.190054i	$-0.0608662\pi$
$853$	19.0989	+	22.0413i	0.653934	+	0.754680i	−0.327840	+	0.944733i	$0.606321\pi$
$854$	1.17648	−	0.849203i	0.0402582	−	0.0290591i
$855$	−0.347382	+	2.41610i	−0.0118802	+	0.0826288i
$856$	6.37714	−	0.608943i	0.217966	−	0.0208132i
$857$	29.4539	+	11.7916i	1.00613	+	0.402792i	0.815429	−	0.578857i	$-0.196501\pi$
$857$	29.4539	+	11.7916i	1.00613	+	0.402792i	0.190696	+	0.981649i	$0.438925\pi$
$858$	2.09277	−	1.99546i	0.0714461	−	0.0681238i
$859$	−31.5844	−	16.2829i	−1.07765	−	0.555565i	−0.174394	−	0.984676i	$-0.555797\pi$
$859$	−31.5844	−	16.2829i	−1.07765	−	0.555565i	−0.903252	+	0.429111i	$0.858827\pi$
$860$	1.29210	+	2.82931i	0.0440603	+	0.0964786i
$861$	−2.00639	+	22.5408i	−0.0683777	+	0.768187i
$862$	12.3626	−	14.2672i	0.421072	−	0.485943i
$863$	−15.8245	−	3.04991i	−0.538671	−	0.103820i	−0.0873426	−	0.996178i	$-0.527837\pi$
$863$	−15.8245	−	3.04991i	−0.538671	−	0.103820i	−0.451328	+	0.892358i	$0.649050\pi$
$864$	0.235759	−	0.971812i	0.00802068	−	0.0330617i
$865$	3.68628	+	0.351997i	0.125337	+	0.0119682i
$866$	10.1826	+	5.24952i	0.346020	+	0.178386i
$867$	9.84050	+	2.88943i	0.334201	+	0.0981302i
$868$	−15.4243	+	16.3859i	−0.523534	+	0.556174i
$869$	2.63989	−	5.78056i	0.0895522	−	0.196092i
$870$	1.51325	−	0.605815i	0.0513041	−	0.0205391i
$871$	65.4507	−	33.7422i	2.21771	−	1.14331i
$872$	5.05462	−	0.974198i	0.171171	−	0.0329905i
$873$	−5.02556	−	8.70452i	−0.170089	−	0.294603i
$874$	−20.0655	+	9.24780i	−0.678726	+	0.312811i
$875$	−13.4733	+	2.02557i	−0.455482	+	0.0684768i
$876$	−4.10235	−	4.73436i	−0.138605	−	0.159959i
$877$	0.623063	−	13.0797i	0.0210394	−	0.441670i	−0.963630	−	0.267240i	$-0.913888\pi$
$877$	0.623063	−	13.0797i	0.0210394	−	0.441670i	0.984669	−	0.174431i	$-0.0558085\pi$
$878$	−27.0204	−	21.2491i	−0.911895	−	0.717122i
$879$	−7.15385	−	10.0462i	−0.241294	−	0.338849i
$880$	0.203985	−	0.160416i	0.00687634	−	0.00540761i
$881$	−12.5328	−	3.67997i	−0.422241	−	0.123981i	0.0637073	−	0.997969i	$-0.479708\pi$
$881$	−12.5328	−	3.67997i	−0.422241	−	0.123981i	−0.485949	+	0.873987i	$0.661526\pi$
$882$	2.37425	+	6.58506i	0.0799451	+	0.221730i
$883$	−6.06321	−	13.2766i	−0.204043	−	0.446792i	0.779752	−	0.626089i	$-0.215345\pi$
$883$	−6.06321	−	13.2766i	−0.204043	−	0.446792i	−0.983795	+	0.179296i	$0.942618\pi$
$884$	11.0964	+	10.5804i	0.373213	+	0.355858i
$885$	1.54906	+	4.47570i	0.0520710	+	0.150449i
$886$	11.5115	+	33.2604i	0.386737	+	1.11740i
$887$	−27.3344	−	26.0633i	−0.917800	−	0.875120i	0.0747201	−	0.997205i	$-0.476194\pi$
$887$	−27.3344	−	26.0633i	−0.917800	−	0.875120i	−0.992520	+	0.122084i	$0.961042\pi$
$888$	0.190007	+	0.416057i	0.00637622	+	0.0139620i
$889$	1.61347	−	1.41633i	0.0541142	−	0.0475021i
$890$	5.05304	+	1.48371i	0.169378	+	0.0497340i
$891$	0.384993	−	0.302762i	0.0128977	−	0.0101429i
$892$	−1.58560	−	2.22667i	−0.0530899	−	0.0745543i
$893$	14.5057	+	11.4074i	0.485414	+	0.381734i
$894$	−0.291368	+	6.11656i	−0.00974479	+	0.204568i
$895$	7.72725	+	8.91772i	0.258293	+	0.298086i
$896$	−1.64882	−	2.06916i	−0.0550831	−	0.0691256i
$897$	−25.7963	−	11.6729i	−0.861312	−	0.389746i
$898$	−8.17973	−	14.1677i	−0.272961	−	0.472782i
$899$	25.6936	−	4.95204i	0.856931	−	0.165160i
$900$	4.19465	−	2.16249i	0.139822	−	0.0720831i
$901$	−13.1625	+	5.26949i	−0.438508	+	0.175552i
$902$	1.74027	−	3.81066i	0.0579446	−	0.126881i
$903$	15.1170	+	3.56472i	0.503063	+	0.118626i
$904$	12.5894	+	3.69658i	0.418717	+	0.122946i
$905$	−8.80017	−	4.53680i	−0.292527	−	0.150808i
$906$	−18.9715	−	1.81156i	−0.630285	−	0.0601849i
$907$	9.76668	−	40.2588i	0.324297	−	1.33677i	−0.543314	−	0.839529i	$-0.682831\pi$
$907$	9.76668	−	40.2588i	0.324297	−	1.33677i	0.867612	−	0.497243i	$-0.165654\pi$
$908$	−22.6978	−	4.37463i	−0.753251	−	0.145177i
$909$	−8.82073	+	10.1797i	−0.292565	+	0.337638i
$910$	−0.733790	+	8.24374i	−0.0243249	+	0.273277i
$911$	−14.5467	−	31.8528i	−0.481953	−	1.05533i	−0.981922	−	0.189286i	$-0.939383\pi$
$911$	−14.5467	−	31.8528i	−0.481953	−	1.05533i	0.499969	−	0.866043i	$-0.333345\pi$
$912$	−4.09480	−	2.11102i	−0.135592	−	0.0699027i
$913$	−4.24832	+	4.05077i	−0.140599	+	0.134061i
$914$	22.1538	+	8.86903i	0.732781	+	0.293361i
$915$	0.289252	−	0.0276203i	0.00956239	−	0.000913098i
$916$	−2.01506	+	14.0151i	−0.0665795	+	0.463070i
$917$	−3.50156	−	34.3381i	−0.115632	−	1.13394i
$918$	1.70063	+	1.96263i	0.0561291	+	0.0647765i
$919$	16.1647	+	27.9981i	0.533224	+	0.923571i	0.999247	+	0.0387983i	$0.0123530\pi$
$919$	16.1647	+	27.9981i	0.533224	+	0.923571i	−0.466023	+	0.884772i	$0.654314\pi$
$920$	−2.20499	−	1.26288i	−0.0726963	−	0.0416360i
$921$	−0.850643	+	1.47336i	−0.0280297	+	0.0485488i
$922$	10.1413	−	29.3014i	0.333986	−	0.964990i
$923$	69.7591	+	44.8314i	2.29615	+	1.47564i
$924$	−0.00832173	−	1.29581i	−0.000273765	−	0.0426290i
$925$	−0.896694	+	1.96349i	−0.0294831	+	0.0645590i
$926$	−16.5671	+	13.0285i	−0.544428	+	0.428143i
$927$	2.91884	−	2.78311i	0.0958672	−	0.0914092i
$928$	0.146382	+	3.07293i	0.00480522	+	0.100874i
$929$	11.9165	−	16.7344i	0.390969	−	0.549039i	−0.571440	−	0.820644i	$-0.693615\pi$
$929$	11.9165	−	16.7344i	0.390969	−	0.549039i	0.962409	+	0.271605i	$0.0875544\pi$
$930$	−4.32403	+	1.26965i	−0.141791	+	0.0416334i
$931$	32.0604	−	3.47747i	1.05074	−	0.113969i
$932$	−5.72076	+	6.60211i	−0.187390	+	0.216259i
$933$	−8.60071	−	8.20076i	−0.281575	−	0.268481i
$934$	4.49860	+	0.429565i	0.147199	+	0.0140558i
$935$	0.0320664	+	0.673156i	0.00104868	+	0.0220145i
$936$	−1.39191	−	5.73753i	−0.0454960	−	0.187537i
$937$	−4.24134	−	29.4992i	−0.138559	−	0.963696i	−0.933900	−	0.357534i	$-0.883617\pi$
$937$	−4.24134	−	29.4992i	−0.138559	−	0.963696i	0.795341	−	0.606162i	$-0.207292\pi$
$938$	9.09334	−	31.7213i	0.296908	−	1.03574i
$939$	−3.74035	+	26.0147i	−0.122062	+	0.848957i
$940$	−0.100986	+	2.11997i	−0.00329382	+	0.0691457i
$941$	5.06771	−	0.976721i	0.165203	−	0.0318402i	−0.105979	−	0.994368i	$-0.533798\pi$
$941$	5.06771	−	0.976721i	0.165203	−	0.0318402i	0.271182	+	0.962528i	$0.412586\pi$
$942$	11.4966	−	19.9127i	0.374579	−	0.648790i
$943$	−40.9802	−	1.80980i	−1.33450	−	0.0589353i
$944$	−8.93888			−0.290936
$945$	−0.256453	+	1.37817i	−0.00834241	+	0.0448319i
$946$	−2.41878	−	1.55445i	−0.0786412	−	0.0505396i
$947$	−30.3925	+	12.1673i	−0.987623	+	0.395385i	−0.808535	−	0.588449i	$-0.799739\pi$
$947$	−30.3925	+	12.1673i	−0.987623	+	0.395385i	−0.179088	+	0.983833i	$0.557315\pi$
$948$	−7.52617	−	10.5690i	−0.244439	−	0.343266i
$949$	−34.3357	−	13.7460i	−1.11458	−	0.446213i
$950$	−5.12571	−	21.1285i	−0.166300	−	0.685498i
$951$	1.38366	−	0.889221i	0.0448681	−	0.0288350i
$952$	6.86082	−	0.370995i	0.222360	−	0.0120240i
$953$	16.8859	−	4.95814i	0.546987	−	0.160610i	0.00344862	−	0.999994i	$-0.498902\pi$
$953$	16.8859	−	4.95814i	0.546987	−	0.160610i	0.543539	+	0.839384i	$0.317084\pi$
$954$	5.36091	+	1.03323i	0.173566	+	0.0334521i
$955$	1.02589	+	2.96410i	0.0331969	+	0.0959162i
$956$	6.78448	−	27.9660i	0.219426	−	0.904485i
$957$	−0.874010	+	1.22738i	−0.0282527	+	0.0396754i
$958$	−12.2643	+	7.88176i	−0.396240	+	0.254648i
$959$	−9.28684	+	11.9665i	−0.299888	+	0.386420i
$960$	−0.0754044	−	0.524449i	−0.00243366	−	0.0169265i
$961$	−41.1566	+	3.92998i	−1.32763	+	0.126773i
$962$	2.12267	+	1.66928i	0.0684375	+	0.0538199i
$963$	5.69401	−	2.93546i	0.183487	−	0.0945940i
$964$	5.83608	−	16.8622i	0.187967	−	0.543096i
$965$	−0.746458			−0.0240293
$966$	−11.7325	+	4.83211i	−0.377486	+	0.155471i
$967$	−35.3204			−1.13583			−0.567913	−	0.823089i	$-0.692249\pi$
$967$	−35.3204			−1.13583			−0.567913	+	0.823089i	$0.692249\pi$
$968$	3.51929	−	10.1683i	0.113114	−	0.326822i
$969$	10.6339	−	5.48217i	0.341611	−	0.176113i
$970$	−4.18613	−	3.29201i	−0.134408	−	0.105700i
$971$	−32.4313	+	3.09681i	−1.04077	+	0.0993813i	−0.601418	−	0.798934i	$-0.705397\pi$
$971$	−32.4313	+	3.09681i	−1.04077	+	0.0993813i	−0.439350	+	0.898316i	$0.644791\pi$
$972$	−0.142315	−	0.989821i	−0.00456475	−	0.0317485i
$973$	40.8850	+	5.61063i	1.31071	+	0.179869i
$974$	15.9920	−	10.2774i	0.512417	−	0.329310i
$975$	16.1617	−	22.6960i	0.517590	−	0.726853i
$976$	−0.129291	+	0.532947i	−0.00413852	+	0.0170592i
$977$	1.83388	+	5.29864i	0.0586710	+	0.169519i	0.970527	−	0.240990i	$-0.0774722\pi$
$977$	1.83388	+	5.29864i	0.0586710	+	0.169519i	−0.911857	+	0.410509i	$0.865351\pi$
$978$	−2.83391	−	0.546191i	−0.0906183	−	0.0174653i
$979$	−4.67097	+	1.37152i	−0.149285	+	0.0438340i
$980$	2.46461	+	2.77157i	0.0787290	+	0.0885345i
$981$	4.33048	−	2.78303i	0.138261	−	0.0888552i
$982$	1.41373	+	5.82750i	0.0451141	+	0.185963i
$983$	48.7853	+	19.5307i	1.55601	+	0.622932i	0.980790	−	0.195068i	$-0.0624926\pi$
$983$	48.7853	+	19.5307i	1.55601	+	0.622932i	0.575219	+	0.817999i	$0.304917\pi$
$984$	−4.96140	−	6.96731i	−0.158164	−	0.222110i
$985$	−3.77234	+	1.51022i	−0.120197	+	0.0481195i
$986$	−6.72099	−	4.31931i	−0.214040	−	0.137555i
$987$	8.05384	+	6.88864i	0.256357	+	0.219268i
$988$	−27.1991			−0.865318
$989$	−5.23224	+	27.6630i	−0.166376	+	0.879633i
$990$	0.129753	−	0.224739i	0.00412382	−	0.00714266i
$991$	20.7220	−	3.99385i	0.658257	−	0.126869i	0.150825	−	0.988560i	$-0.451807\pi$
$991$	20.7220	−	3.99385i	0.658257	−	0.126869i	0.507432	+	0.861692i	$0.330595\pi$
$992$	0.404709	−	8.49588i	0.0128495	−	0.269744i
$993$	−1.98369	+	13.7969i	−0.0629505	+	0.437830i
$994$	36.0559	−	8.99262i	1.14362	−	0.285229i
$995$	−0.871061	−	6.05836i	−0.0276145	−	0.192063i
$996$	2.82557	+	11.6472i	0.0895316	+	0.369054i
$997$	0.794140	+	16.6711i	0.0251507	+	0.527978i	0.975927	+	0.218099i	$0.0699855\pi$
$997$	0.794140	+	16.6711i	0.0251507	+	0.527978i	−0.950776	+	0.309879i	$0.899711\pi$
$998$	−20.3395	−	1.94218i	−0.643835	−	0.0614788i
$999$	0.331029	+	0.315636i	0.0104733	+	0.00998627i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.d.151.4	✓	160
7.2	even	3	inner	966.2.y.d.289.5	yes	160
23.16	even	11	inner	966.2.y.d.361.5	yes	160
161.16	even	33	inner	966.2.y.d.499.4	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.d.151.4	✓	160	1.1	even	1	trivial
966.2.y.d.289.5	yes	160	7.2	even	3	inner
966.2.y.d.361.5	yes	160	23.16	even	11	inner
966.2.y.d.499.4	yes	160	161.16	even	33	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.527443 + 0.0503647i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.62119 - 0.359704i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})\)	\(q+(-0.327068 + 0.945001i) q^{2} +(-0.888835 + 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.527443 + 0.0503647i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-2.62119 - 0.359704i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(0.124915 - 0.514906i) q^{10} +(0.160191 + 0.462842i) q^{11} +(0.981929 + 0.189251i) q^{12} +(5.66480 - 1.66334i) q^{13} +(1.19723 - 2.35937i) q^{14} +(0.445731 - 0.286454i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-2.41091 - 0.965183i) q^{17} +(0.580057 + 0.814576i) q^{18} +(4.27692 - 1.71222i) q^{19} +(0.445731 + 0.286454i) q^{20} +(2.49463 - 0.881379i) q^{21} -0.489780 q^{22} +(1.79785 + 4.44609i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.63398 + 0.893127i) q^{25} +(-0.280921 + 5.89726i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(1.83804 + 1.90306i) q^{28} +(-0.437820 - 3.04510i) q^{29} +(0.124915 + 0.514906i) q^{30} +(0.404709 + 8.49588i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(-0.354470 - 0.337987i) q^{33} +(1.70063 - 1.96263i) q^{34} +(1.40064 + 0.0577081i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(0.265313 - 0.372579i) q^{37} +(0.219206 + 4.60171i) q^{38} +(-4.27289 + 4.07419i) q^{39} +(-0.416484 + 0.327526i) q^{40} +(-3.55317 + 7.78035i) q^{41} +(0.0169908 + 2.64570i) q^{42} +(4.93850 + 3.17378i) q^{43} +(0.160191 - 0.462842i) q^{44} +(-0.264921 + 0.458856i) q^{45} +(-4.78958 + 0.244795i) q^{46} +(2.00283 + 3.46901i) q^{47} +(-0.654861 - 0.755750i) q^{48} +(6.74123 + 1.88570i) q^{49} +(0.671622 - 4.67123i) q^{50} +(2.58517 - 0.246854i) q^{51} +(-5.48104 - 2.19428i) q^{52} +(3.95128 - 3.76754i) q^{53} +(-0.888835 - 0.458227i) q^{54} +(-0.107803 - 0.236055i) q^{55} +(-2.39955 + 1.11452i) q^{56} +(-3.01690 + 3.48168i) q^{57} +(3.02082 + 0.582216i) q^{58} +(-2.10742 + 8.68690i) q^{59} +(-0.527443 - 0.0503647i) q^{60} +(0.487442 + 0.251294i) q^{61} +(-8.16098 - 2.39628i) q^{62} +(-1.81344 + 1.92651i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-2.90408 + 1.16262i) q^{65} +(0.435333 - 0.224430i) q^{66} +(12.2470 - 2.36042i) q^{67} +(1.29847 + 2.24901i) q^{68} +(-3.63531 - 3.12802i) q^{69} +(-0.512639 + 1.30473i) q^{70} +(9.19771 + 10.6147i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(-4.92420 - 3.87243i) q^{73} +(0.265313 + 0.372579i) q^{74} +(3.70959 - 2.91726i) q^{75} +(-4.42031 - 1.29792i) q^{76} +(-0.253405 - 1.27082i) q^{77} +(-2.45259 - 5.37042i) q^{78} +(-9.39036 - 8.95369i) q^{79} +(-0.173294 - 0.500701i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(-6.19031 - 5.90245i) q^{82} +(4.97875 + 10.9019i) q^{83} +(-2.50574 - 0.849266i) q^{84} +(1.32023 + 0.387654i) q^{85} +(-4.61445 + 3.62885i) q^{86} +(1.78450 + 2.50598i) q^{87} +(0.384993 + 0.302762i) q^{88} +(-0.472941 + 9.92825i) q^{89} +(-0.346973 - 0.400428i) q^{90} +(-15.4468 + 2.32226i) q^{91} +(1.33519 - 4.60622i) q^{92} +(-4.25276 - 7.36599i) q^{93} +(-3.93328 + 0.758078i) q^{94} +(-2.16960 + 1.11850i) q^{95} +(0.928368 - 0.371662i) q^{96} +(4.17538 - 9.14281i) q^{97} +(-3.98683 + 5.75371i) q^{98} +(0.469940 + 0.137987i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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