LMFDB - Embedded newform 43.2.g.a.25.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,2,Mod(9,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, degree $12$, 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:	$0.343356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			25.2
Character	$\chi$	$=$	43.25
Dual form			43.2.g.a.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.118393 + 0.0570152i) q^{2} +(1.09131 + 0.744044i) q^{3} +(-1.23621 - 1.55016i) q^{4} +(-1.30537 + 1.21121i) q^{5} +(0.0867822 + 0.150311i) q^{6} +(-0.00749281 + 0.0129779i) q^{7} +(-0.116458 - 0.510236i) q^{8} +(-0.458662 - 1.16865i) q^{9} +O(q^{10})$	\(q+(0.118393 + 0.0570152i) q^{2} +(1.09131 + 0.744044i) q^{3} +(-1.23621 - 1.55016i) q^{4} +(-1.30537 + 1.21121i) q^{5} +(0.0867822 + 0.150311i) q^{6} +(-0.00749281 + 0.0129779i) q^{7} +(-0.116458 - 0.510236i) q^{8} +(-0.458662 - 1.16865i) q^{9} +(-0.223604 + 0.0689728i) q^{10} +(-1.29669 + 1.62599i) q^{11} +(-0.195705 - 2.61151i) q^{12} +(-1.55224 - 0.478804i) q^{13} +(-0.00162704 + 0.00110929i) q^{14} +(-2.32576 + 0.350552i) q^{15} +(-0.867096 + 3.79899i) q^{16} +(4.42356 + 4.10446i) q^{17} +(0.0123284 - 0.164511i) q^{18} +(2.78497 - 7.09598i) q^{19} +(3.49129 + 0.526227i) q^{20} +(-0.0178331 + 0.00858798i) q^{21} +(-0.246225 + 0.118576i) q^{22} +(5.24284 + 0.790231i) q^{23} +(0.252546 - 0.643476i) q^{24} +(-0.136680 + 1.82386i) q^{25} +(-0.156476 - 0.145189i) q^{26} +(1.25072 - 5.47974i) q^{27} +(0.0293806 - 0.00442841i) q^{28} +(-5.92981 + 4.04287i) q^{29} +(-0.295341 - 0.0911007i) q^{30} +(0.178251 + 2.37860i) q^{31} +(-0.971874 + 1.21869i) q^{32} +(-2.62490 + 0.809675i) q^{33} +(0.289703 + 0.738150i) q^{34} +(-0.00593807 - 0.0260164i) q^{35} +(-1.24460 + 2.15571i) q^{36} +(-2.52043 - 4.36551i) q^{37} +(0.734300 - 0.681331i) q^{38} +(-1.33773 - 1.67746i) q^{39} +(0.770022 + 0.524992i) q^{40} +(-3.20110 - 1.54157i) q^{41} -0.00260097 q^{42} +(-1.84169 - 6.29350i) q^{43} +4.12354 q^{44} +(2.01421 + 0.969991i) q^{45} +(0.575662 + 0.392479i) q^{46} +(-6.24911 - 7.83614i) q^{47} +(-3.77289 + 3.50073i) q^{48} +(3.49989 + 6.06198i) q^{49} +(-0.120170 + 0.208140i) q^{50} +(1.77358 + 7.77057i) q^{51} +(1.17668 + 2.99813i) q^{52} +(-6.55236 + 2.02113i) q^{53} +(0.460505 - 0.577454i) q^{54} +(-0.276759 - 3.69309i) q^{55} +(0.00749439 + 0.00231171i) q^{56} +(8.31899 - 5.67179i) q^{57} +(-0.932554 + 0.140560i) q^{58} +(0.370875 - 1.62491i) q^{59} +(3.41855 + 3.17195i) q^{60} +(-0.452207 + 6.03428i) q^{61} +(-0.114512 + 0.291773i) q^{62} +(0.0186034 + 0.00280400i) q^{63} +(6.83705 - 3.29255i) q^{64} +(2.60619 - 1.25507i) q^{65} +(-0.356934 - 0.0537992i) q^{66} +(0.523545 - 1.33397i) q^{67} +(0.894122 - 11.9312i) q^{68} +(5.13361 + 4.76329i) q^{69} +(0.000780301 - 0.00341872i) q^{70} +(6.96679 - 1.05007i) q^{71} +(-0.542873 + 0.370125i) q^{72} +(9.32817 + 2.87736i) q^{73} +(-0.0495013 - 0.660549i) q^{74} +(-1.50620 + 1.88871i) q^{75} +(-14.4427 + 4.45500i) q^{76} +(-0.0113862 - 0.0290116i) q^{77} +(-0.0627375 - 0.274871i) q^{78} +(-6.00573 + 10.4022i) q^{79} +(-3.46949 - 6.00933i) q^{80} +(2.68119 - 2.48778i) q^{81} +(-0.291096 - 0.365023i) q^{82} +(7.49232 + 5.10817i) q^{83} +(0.0353583 + 0.0170277i) q^{84} -10.7457 q^{85} +(0.140781 - 0.850113i) q^{86} -9.47935 q^{87} +(0.980650 + 0.472256i) q^{88} +(-13.1407 - 8.95920i) q^{89} +(0.183164 + 0.229681i) q^{90} +(0.0178445 - 0.0165573i) q^{91} +(-5.25628 - 9.10415i) q^{92} +(-1.57525 + 2.72842i) q^{93} +(-0.293074 - 1.28404i) q^{94} +(4.95929 + 12.6361i) q^{95} +(-1.96738 + 0.606856i) q^{96} +(8.44749 - 10.5928i) q^{97} +(0.0687380 + 0.917245i) q^{98} +(2.49496 + 0.769595i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) $ 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{21}\right)$

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 $

$2$	0.118393	+	0.0570152i	0.0837167	+	0.0403158i	0.475274	−	0.879838i	$-0.342349\pi$
$2$	0.118393	+	0.0570152i	0.0837167	+	0.0403158i	−0.391557	+	0.920154i	$0.628063\pi$
$3$	1.09131	+	0.744044i	0.630069	+	0.429574i	0.835800	−	0.549035i	$-0.185005\pi$
$3$	1.09131	+	0.744044i	0.630069	+	0.429574i	−0.205730	+	0.978609i	$0.565957\pi$
$4$	−1.23621	−	1.55016i	−0.618107	−	0.775081i
$5$	−1.30537	+	1.21121i	−0.583780	+	0.541669i	−0.915816	−	0.401598i	$-0.868455\pi$
$5$	−1.30537	+	1.21121i	−0.583780	+	0.541669i	0.332036	+	0.943267i	$0.392264\pi$
$6$	0.0867822	+	0.150311i	0.0354287	+	0.0613643i
$7$	−0.00749281	+	0.0129779i	−0.00283201	+	0.00490519i	−0.867438	−	0.497545i	$-0.834235\pi$
$7$	−0.00749281	+	0.0129779i	−0.00283201	+	0.00490519i	0.864606	+	0.502451i	$0.167568\pi$
$8$	−0.116458	−	0.510236i	−0.0411741	−	0.180396i
$9$	−0.458662	−	1.16865i	−0.152887	−	0.389551i
$10$	−0.223604	+	0.0689728i	−0.0707099	+	0.0218111i
$11$	−1.29669	+	1.62599i	−0.390966	+	0.490256i	−0.937893	−	0.346924i	$-0.887226\pi$
$11$	−1.29669	+	1.62599i	−0.390966	+	0.490256i	0.546927	+	0.837180i	$0.315797\pi$
$12$	−0.195705	−	2.61151i	−0.0564953	−	0.753877i
$13$	−1.55224	−	0.478804i	−0.430515	−	0.132796i	0.0719219	−	0.997410i	$-0.477087\pi$
$13$	−1.55224	−	0.478804i	−0.430515	−	0.132796i	−0.502437	+	0.864614i	$0.667563\pi$
$14$	−0.00162704	+	0.00110929i	−0.000434844	+	0.000296471i
$15$	−2.32576	+	0.350552i	−0.600509	+	0.0905121i
$16$	−0.867096	+	3.79899i	−0.216774	+	0.949748i
$17$	4.42356	+	4.10446i	1.07287	+	0.995478i	0.999998	−	0.00186302i	$-0.000593018\pi$
$17$	4.42356	+	4.10446i	1.07287	+	0.995478i	0.0728722	+	0.997341i	$0.476783\pi$
$18$	0.0123284	−	0.164511i	0.00290584	−	0.0387757i
$19$	2.78497	−	7.09598i	0.638916	−	1.62793i	−0.132191	−	0.991224i	$-0.542201\pi$
$19$	2.78497	−	7.09598i	0.638916	−	1.62793i	0.771107	−	0.636706i	$-0.219704\pi$
$20$	3.49129	+	0.526227i	0.780676	+	0.117668i
$21$	−0.0178331	+	0.00858798i	−0.00389151	+	0.00187405i
$22$	−0.246225	+	0.118576i	−0.0524954	+	0.0252805i
$23$	5.24284	+	0.790231i	1.09321	+	0.164775i	0.670805	−	0.741634i	$-0.265949\pi$
$23$	5.24284	+	0.790231i	1.09321	+	0.164775i	0.422403	+	0.906408i	$0.361187\pi$
$24$	0.252546	−	0.643476i	0.0515507	−	0.131349i
$25$	−0.136680	+	1.82386i	−0.0273359	+	0.364773i
$26$	−0.156476	−	0.145189i	−0.0306875	−	0.0284738i
$27$	1.25072	−	5.47974i	0.240700	−	1.05458i
$28$	0.0293806	−	0.00442841i	0.00555241	−	0.000836891i
$29$	−5.92981	+	4.04287i	−1.10114	+	0.750743i	−0.970599	−	0.240700i	$-0.922623\pi$
$29$	−5.92981	+	4.04287i	−1.10114	+	0.750743i	−0.130538	+	0.991443i	$0.541671\pi$
$30$	−0.295341	−	0.0911007i	−0.0539217	−	0.0166326i
$31$	0.178251	+	2.37860i	0.0320149	+	0.427209i	0.990065	+	0.140609i	$0.0449060\pi$
$31$	0.178251	+	2.37860i	0.0320149	+	0.427209i	−0.958050	+	0.286600i	$0.907475\pi$
$32$	−0.971874	+	1.21869i	−0.171805	+	0.215436i
$33$	−2.62490	+	0.809675i	−0.456937	+	0.140946i
$34$	0.289703	+	0.738150i	0.0496836	+	0.126592i
$35$	−0.00593807	−	0.0260164i	−0.00100372	−	0.00439757i
$36$	−1.24460	+	2.15571i	−0.207433	+	0.359284i
$37$	−2.52043	−	4.36551i	−0.414356	−	0.717685i	0.581005	−	0.813900i	$-0.302660\pi$
$37$	−2.52043	−	4.36551i	−0.414356	−	0.717685i	−0.995361	+	0.0962150i	$0.969326\pi$
$38$	0.734300	−	0.681331i	0.119119	−	0.110526i
$39$	−1.33773	−	1.67746i	−0.214208	−	0.268609i
$40$	0.770022	+	0.524992i	0.121751	+	0.0830086i
$41$	−3.20110	−	1.54157i	−0.499928	−	0.240753i	0.166887	−	0.985976i	$-0.446629\pi$
$41$	−3.20110	−	1.54157i	−0.499928	−	0.240753i	−0.666815	+	0.745223i	$0.732343\pi$
$42$	−0.00260097			−0.000401338
$43$	−1.84169	−	6.29350i	−0.280856	−	0.959750i
$43$	−1.84169	−	6.29350i	−0.280856	−	0.959750i
$44$	4.12354			0.621647
$45$	2.01421	+	0.969991i	0.300260	+	0.144598i
$46$	0.575662	+	0.392479i	0.0848767	+	0.0578679i
$47$	−6.24911	−	7.83614i	−0.911527	−	1.14302i	−0.989278	−	0.146046i	$-0.953345\pi$
$47$	−6.24911	−	7.83614i	−0.911527	−	1.14302i	0.0777509	−	0.996973i	$-0.475226\pi$
$48$	−3.77289	+	3.50073i	−0.544570	+	0.505287i
$49$	3.49989	+	6.06198i	0.499984	+	0.865998i
$50$	−0.120170	+	0.208140i	−0.0169946	+	0.0294355i
$51$	1.77358	+	7.77057i	0.248351	+	1.08810i
$52$	1.17668	+	2.99813i	0.163176	+	0.415766i
$53$	−6.55236	+	2.02113i	−0.900035	+	0.277624i	−0.710040	−	0.704161i	$-0.751323\pi$
$53$	−6.55236	+	2.02113i	−0.900035	+	0.277624i	−0.189995	+	0.981785i	$0.560847\pi$
$54$	0.460505	−	0.577454i	0.0626667	−	0.0785816i
$55$	−0.276759	−	3.69309i	−0.0373181	−	0.497976i
$56$	0.00749439	+	0.00231171i	0.00100148	+	0.000308916i
$57$	8.31899	−	5.67179i	1.10188	−	0.751247i
$58$	−0.932554	+	0.140560i	−0.122450	+	0.0184564i
$59$	0.370875	−	1.62491i	0.0482838	−	0.211545i	−0.945031	−	0.326980i	$-0.893969\pi$
$59$	0.370875	−	1.62491i	0.0482838	−	0.211545i	0.993315	+	0.115435i	$0.0368261\pi$
$60$	3.41855	+	3.17195i	0.441333	+	0.409497i
$61$	−0.452207	+	6.03428i	−0.0578992	+	0.772611i	0.890389	+	0.455200i	$0.150432\pi$
$61$	−0.452207	+	6.03428i	−0.0578992	+	0.772611i	−0.948288	+	0.317411i	$0.897187\pi$
$62$	−0.114512	+	0.291773i	−0.0145431	+	0.0370552i
$63$	0.0186034	+	0.00280400i	0.00234380	+	0.000353271i
$64$	6.83705	−	3.29255i	0.854631	−	0.411569i
$65$	2.60619	−	1.25507i	0.323258	−	0.155673i
$66$	−0.356934	−	0.0537992i	−0.0439356	−	0.00662222i
$67$	0.523545	−	1.33397i	0.0639612	−	0.162970i	−0.895320	−	0.445424i	$-0.853053\pi$
$67$	0.523545	−	1.33397i	0.0639612	−	0.162970i	0.959281	+	0.282453i	$0.0911483\pi$
$68$	0.894122	−	11.9312i	0.108428	−	1.44687i
$69$	5.13361	+	4.76329i	0.618014	+	0.573433i
$70$	0.000780301	−	0.00341872i	9.32638e−5	−	0.000408615i
$71$	6.96679	−	1.05007i	0.826805	−	0.124621i	0.278011	−	0.960578i	$-0.410325\pi$
$71$	6.96679	−	1.05007i	0.826805	−	0.124621i	0.548795	+	0.835957i	$0.315087\pi$
$72$	−0.542873	+	0.370125i	−0.0639782	+	0.0436196i
$73$	9.32817	+	2.87736i	1.09178	+	0.336770i	0.787814	−	0.615913i	$-0.211213\pi$
$73$	9.32817	+	2.87736i	1.09178	+	0.336770i	0.303966	+	0.952683i	$0.401689\pi$
$74$	−0.0495013	−	0.660549i	−0.00575441	−	0.0767873i
$75$	−1.50620	+	1.88871i	−0.173920	+	0.218089i
$76$	−14.4427	+	4.45500i	−1.65670	+	0.511023i
$77$	−0.0113862	−	0.0290116i	−0.00129758	−	0.00330617i
$78$	−0.0627375	−	0.274871i	−0.00710362	−	0.0311230i
$79$	−6.00573	+	10.4022i	−0.675697	+	1.17034i	0.300567	+	0.953761i	$0.402824\pi$
$79$	−6.00573	+	10.4022i	−0.675697	+	1.17034i	−0.976265	+	0.216581i	$0.930509\pi$
$80$	−3.46949	−	6.00933i	−0.387901	−	0.671864i
$81$	2.68119	−	2.48778i	0.297910	−	0.276420i
$82$	−0.291096	−	0.365023i	−0.0321462	−	0.0403100i
$83$	7.49232	+	5.10817i	0.822389	+	0.560695i	0.899799	−	0.436304i	$-0.143713\pi$
$83$	7.49232	+	5.10817i	0.822389	+	0.560695i	−0.0774107	+	0.996999i	$0.524665\pi$
$84$	0.0353583	+	0.0170277i	0.00385791	+	0.00185787i
$85$	−10.7457			−1.16554
$86$	0.140781	−	0.850113i	0.0151808	−	0.0916700i
$87$	−9.47935			−1.01629
$88$	0.980650	+	0.472256i	0.104538	+	0.0503427i
$89$	−13.1407	−	8.95920i	−1.39291	−	0.949673i	−0.999541	−	0.0302945i	$-0.990355\pi$
$89$	−13.1407	−	8.95920i	−1.39291	−	0.949673i	−0.393374	−	0.919379i	$-0.628692\pi$
$90$	0.183164	+	0.229681i	0.0193072	+	0.0242105i
$91$	0.0178445	−	0.0165573i	0.00187061	−	0.00173568i
$92$	−5.25628	−	9.10415i	−0.548005	−	0.949173i
$93$	−1.57525	+	2.72842i	−0.163346	+	0.282924i
$94$	−0.293074	−	1.28404i	−0.0302283	−	0.132439i
$95$	4.95929	+	12.6361i	0.508813	+	1.29643i
$96$	−1.96738	+	0.606856i	−0.200795	+	0.0619370i
$97$	8.44749	−	10.5928i	0.857712	−	1.07554i	−0.138652	−	0.990341i	$-0.544277\pi$
$97$	8.44749	−	10.5928i	0.857712	−	1.07554i	0.996364	−	0.0851960i	$-0.0271516\pi$
$98$	0.0687380	+	0.917245i	0.00694358	+	0.0926557i
$99$	2.49496	+	0.769595i	0.250753	+	0.0773472i
$100$	2.99625	−	2.04281i	0.299625	−	0.204281i
$101$	−3.08833	+	0.465490i	−0.307300	+	0.0463180i	−0.300882	−	0.953661i	$-0.597281\pi$
$101$	−3.08833	+	0.465490i	−0.307300	+	0.0463180i	−0.00641794	+	0.999979i	$0.502043\pi$
$102$	−0.233060	+	1.02110i	−0.0230764	+	0.101104i
$103$	0.386491	+	0.358612i	0.0380821	+	0.0353351i	0.698984	−	0.715137i	$-0.253636\pi$
$103$	0.386491	+	0.358612i	0.0380821	+	0.0353351i	−0.660902	+	0.750472i	$0.729826\pi$
$104$	−0.0635316	+	0.847770i	−0.00622978	+	0.0831307i
$105$	0.0128770	−	0.0328102i	0.00125667	−	0.00320194i
$106$	−0.890990	−	0.134295i	−0.0865406	−	0.0130439i
$107$	−1.02320	+	0.492747i	−0.0989164	+	0.0476356i	−0.482688	−	0.875793i	$-0.660339\pi$
$107$	−1.02320	+	0.492747i	−0.0989164	+	0.0476356i	0.383771	+	0.923428i	$0.374625\pi$
$108$	−10.0406	+	4.83532i	−0.966161	+	0.465279i
$109$	12.0642	+	1.81839i	1.15554	+	0.174170i	0.698725	−	0.715391i	$-0.253751\pi$
$109$	12.0642	+	1.81839i	1.15554	+	0.174170i	0.456817	+	0.889561i	$0.348989\pi$
$110$	0.177796	−	0.453016i	0.0169521	−	0.0431934i
$111$	0.497557	−	6.63944i	0.0472260	−	0.630188i
$112$	−0.0428061	−	0.0397182i	−0.00404479	−	0.00375302i
$113$	0.981156	−	4.29873i	0.0922994	−	0.404390i	−0.907581	−	0.419878i	$-0.862073\pi$
$113$	0.981156	−	4.29873i	0.0922994	−	0.404390i	0.999880	+	0.0154876i	$0.00493006\pi$
$114$	1.30829	−	0.197193i	0.122533	−	0.0184688i
$115$	−7.80099	+	5.31863i	−0.727446	+	0.495964i
$116$	13.5976	+	4.19431i	1.26251	+	0.389432i
$117$	0.152400	+	2.03364i	0.0140894	+	0.188010i
$118$	0.136554	−	0.171233i	0.0125708	−	0.0157633i
$119$	−0.0864122	+	0.0266546i	−0.00792140	+	0.00244343i
$120$	0.449717	+	1.14586i	0.0410534	+	0.104602i
$121$	1.48527	+	6.50740i	0.135025	+	0.591581i
$122$	−0.397584	+	0.688636i	−0.0359956	+	0.0623462i
$123$	−2.34641	−	4.06410i	−0.211568	−	0.366447i
$124$	3.46686	−	3.21677i	0.311333	−	0.288875i
$125$	−7.58202	−	9.50755i	−0.678156	−	0.850381i
$126$	0.00204264	+	0.00139265i	0.000181973	+	0.000124067i
$127$	8.11611	+	3.90851i	0.720188	+	0.346824i	0.757817	−	0.652468i	$-0.226266\pi$
$127$	8.11611	+	3.90851i	0.720188	+	0.346824i	−0.0376287	+	0.999292i	$0.511980\pi$
$128$	4.11472			0.363693
$129$	2.67278	−	8.23848i	0.235325	−	0.725357i
$130$	0.380113			0.0333381
$131$	4.11246	+	1.98046i	0.359307	+	0.173033i	0.604824	−	0.796359i	$-0.293243\pi$
$131$	4.11246	+	1.98046i	0.359307	+	0.173033i	−0.245517	+	0.969392i	$0.578958\pi$
$132$	4.50007	+	3.06809i	0.391680	+	0.267043i
$133$	0.0712239	+	0.0893119i	0.00617589	+	0.00774433i
$134$	0.138041	−	0.128083i	0.0119249	−	0.0110647i
$135$	5.00446	+	8.66798i	0.430715	+	0.746021i
$136$	1.57908	−	2.73505i	0.135405	−	0.234529i
$137$	3.46135	+	15.1652i	0.295723	+	1.29565i	0.876428	+	0.481534i	$0.159920\pi$
$137$	3.46135	+	15.1652i	0.295723	+	1.29565i	−0.580704	+	0.814115i	$0.697223\pi$
$138$	0.336204	+	0.856635i	0.0286196	+	0.0729216i
$139$	−6.55460	+	2.02183i	−0.555954	+	0.171489i	−0.559985	−	0.828503i	$-0.689193\pi$
$139$	−6.55460	+	2.02183i	−0.555954	+	0.171489i	0.00403085	+	0.999992i	$0.498717\pi$
$140$	−0.0329889	+	0.0413667i	−0.00278807	+	0.00349613i
$141$	−0.989300	−	13.2013i	−0.0833141	−	1.11175i
$142$	0.884690	+	0.272891i	0.0742416	+	0.0229005i
$143$	2.79131	−	1.90308i	0.233421	−	0.159144i
$144$	4.83741	−	0.729122i	0.403117	−	0.0607602i
$145$	2.84384	−	12.4597i	0.236168	−	1.03472i
$146$	0.940339	+	0.872507i	0.0778230	+	0.0722092i
$147$	−0.690912	+	9.21959i	−0.0569855	+	0.760419i
$148$	−3.65146	+	9.30377i	−0.300148	+	0.764765i
$149$	−20.4091	−	3.07618i	−1.67198	−	0.252010i	−0.756389	−	0.654122i	$-0.773038\pi$
$149$	−20.4091	−	3.07618i	−1.67198	−	0.252010i	−0.915591	+	0.402112i	$0.868276\pi$
$150$	−0.286008	+	0.137734i	−0.0233525	+	0.0112460i
$151$	3.49495	−	1.68308i	0.284415	−	0.136967i	−0.286238	−	0.958159i	$-0.592405\pi$
$151$	3.49495	−	1.68308i	0.284415	−	0.136967i	0.570652	+	0.821192i	$0.306690\pi$
$152$	−3.94496	−	0.594606i	−0.319978	−	0.0482289i
$153$	2.76777	−	7.05217i	0.223761	−	0.570134i
$154$	0.000306050	−	0.00408396i	2.46622e−5	−	0.000329095i
$155$	−3.11366	−	2.88906i	−0.250095	−	0.232055i
$156$	−0.946617	+	4.14740i	−0.0757900	+	0.332058i
$157$	−1.36351	+	0.205515i	−0.108820	+	0.0164019i	−0.203226	−	0.979132i	$-0.565143\pi$
$157$	−1.36351	+	0.205515i	−0.108820	+	0.0164019i	0.0944067	+	0.995534i	$0.469905\pi$
$158$	−1.30412	+	0.889136i	−0.103750	+	0.0707358i
$159$	−8.65448	−	2.66955i	−0.686345	−	0.211709i
$160$	−0.207432	−	2.76799i	−0.0163989	−	0.218829i
$161$	−0.0495391	+	0.0621201i	−0.00390423	+	0.00489575i
$162$	0.459276	−	0.141668i	0.0360841	−	0.0111305i
$163$	−1.19480	−	3.04431i	−0.0935843	−	0.238449i	0.876415	−	0.481557i	$-0.159928\pi$
$163$	−1.19480	−	3.04431i	−0.0935843	−	0.238449i	−0.969999	+	0.243108i	$0.921833\pi$
$164$	1.56756	+	6.86794i	0.122406	+	0.536296i
$165$	2.44579	−	4.23623i	0.190404	−	0.329790i
$166$	0.595796	+	1.03195i	0.0462427	+	0.0800948i
$167$	−2.54387	+	2.36037i	−0.196851	+	0.182651i	−0.772439	−	0.635089i	$-0.780964\pi$
$167$	−2.54387	+	2.36037i	−0.196851	+	0.182651i	0.575588	+	0.817740i	$0.304773\pi$
$168$	0.00645870	+	0.00809896i	0.000498300	+	0.000624848i
$169$	−8.56090	−	5.83672i	−0.658531	−	0.448979i
$170$	−1.27222	−	0.612671i	−0.0975751	−	0.0469897i
$171$	−9.57010			−0.731844
$172$	−7.47922	+	10.6350i	−0.570285	+	0.810914i
$173$	16.9268			1.28692			0.643459	−	0.765480i	$-0.277499\pi$
$173$	16.9268			1.28692			0.643459	+	0.765480i	$0.277499\pi$
$174$	−1.12229	−	0.540467i	−0.0850806	−	0.0409727i
$175$	−0.0226458	−	0.0154397i	−0.00171187	−	0.00116713i
$176$	−5.05279	−	6.33600i	−0.380868	−	0.477594i
$177$	1.61374	−	1.49734i	0.121296	−	0.112547i
$178$	−1.04496	−	1.80993i	−0.0783233	−	0.135660i
$179$	−4.71887	+	8.17331i	−0.352705	+	0.610902i	−0.986722	−	0.162416i	$-0.948071\pi$
$179$	−4.71887	+	8.17331i	−0.352705	+	0.610902i	0.634018	+	0.773318i	$0.281405\pi$
$180$	−0.986346	−	4.32146i	−0.0735179	−	0.322103i
$181$	−2.69238	−	6.86008i	−0.200123	−	0.509906i	0.795218	−	0.606324i	$-0.207357\pi$
$181$	−2.69238	−	6.86008i	−0.200123	−	0.509906i	−0.995341	+	0.0964185i	$0.969261\pi$
$182$	0.00305669		0.000942864i	0.000226577		6.98897e-5i
$183$	−4.98327	+	6.24883i	−0.368374	+	0.461926i
$184$	−0.207366	−	2.76711i	−0.0152873	−	0.203994i
$185$	8.57763	+	2.64585i	0.630640	+	0.194527i
$186$	−0.342061	+	0.233213i	−0.0250811	+	0.0171000i
$187$	−12.4098	+	1.87048i	−0.907495	+	0.136783i
$188$	−4.42205	+	19.3743i	−0.322511	+	1.41301i
$189$	0.0617443	+	0.0572903i	0.00449124	+	0.00416726i
$190$	−0.133301	+	1.77878i	−0.00967069	+	0.129046i
$191$	7.05849	−	17.9847i	0.510735	−	1.30133i	−0.410336	−	0.911935i	$-0.634588\pi$
$191$	7.05849	−	17.9847i	0.510735	−	1.30133i	0.921070	−	0.389396i	$-0.127316\pi$
$192$	9.91116	+	1.49387i	0.715276	+	0.107811i
$193$	−1.90871	+	0.919185i	−0.137392	+	0.0661644i	−0.501317	−	0.865264i	$-0.667151\pi$
$193$	−1.90871	+	0.919185i	−0.137392	+	0.0661644i	0.363925	+	0.931428i	$0.381437\pi$
$194$	1.60408	−	0.772482i	0.115166	−	0.0554610i
$195$	3.77799	+	0.569441i	0.270548	+	0.0407785i
$196$	5.07045	−	12.9193i	0.362175	−	0.922807i
$197$	−1.38864	+	18.5301i	−0.0989366	+	1.32022i	0.697975	+	0.716122i	$0.254085\pi$
$197$	−1.38864	+	18.5301i	−0.0989366	+	1.32022i	−0.796912	+	0.604096i	$0.793534\pi$
$198$	0.251508	+	0.233366i	0.0178739	+	0.0165846i
$199$	1.75537	−	7.69076i	0.124435	−	0.545184i	−0.873827	−	0.486238i	$-0.838369\pi$
$199$	1.75537	−	7.69076i	0.124435	−	0.545184i	0.998261	−	0.0589460i	$-0.0187740\pi$
$200$	0.946518	−	0.142665i	0.0669289	−	0.0100879i
$201$	1.56388	−	1.06624i	0.110308	−	0.0752066i
$202$	−0.392177	−	0.120971i	−0.0275935	−	0.00851146i
$203$	−0.00803721	−	0.107249i	−0.000564101	−	0.00752741i
$204$	9.85312	−	12.3554i	0.689857	−	0.865053i
$205$	6.04579	−	1.86488i	0.422257	−	0.130249i
$206$	0.0253117	+	0.0644931i	0.00176355	+	0.00449344i
$207$	−1.48119	−	6.48951i	−0.102950	−	0.451052i
$208$	3.16491	−	5.48179i	0.219447	−	0.380094i
$209$	7.92680	+	13.7296i	0.548308	+	0.949697i
$210$	0.00339523	−	0.00315031i	0.000234293	−	0.000217392i
$211$	5.02386	+	6.29972i	0.345857	+	0.433691i	0.924087	−	0.382183i	$-0.124828\pi$
$211$	5.02386	+	6.29972i	0.345857	+	0.433691i	−0.578230	+	0.815874i	$0.696256\pi$
$212$	11.2332	+	7.65866i	0.771499	+	0.525999i
$213$	8.38424	+	4.03764i	0.574479	+	0.276654i
$214$	−0.149234			−0.0102014
$215$	10.0268	+	5.98469i	0.683825	+	0.408152i
$216$	−2.94161			−0.200151
$217$	−0.0322049	−	0.0155090i	−0.00218621	−	0.00105282i
$218$	1.32465	+	0.903128i	0.0897163	+	0.0611675i
$219$	8.03907	+	10.0807i	0.543230	+	0.681188i
$220$	−5.38275	+	4.99446i	−0.362905	+	0.336727i
$221$	−4.90121	−	8.48914i	−0.329691	−	0.571041i
$222$	0.437456	−	0.757696i	0.0293601	−	0.0508532i
$223$	−4.52520	−	19.8262i	−0.303030	−	1.32766i	−0.865527	−	0.500862i	$-0.833016\pi$
$223$	−4.52520	−	19.8262i	−0.303030	−	1.32766i	0.562497	−	0.826799i	$-0.309841\pi$
$224$	−0.00853402	−	0.0217443i	−0.000570203	−	0.00145285i
$225$	2.19415	−	0.676807i	0.146277	−	0.0451205i
$226$	0.361255	−	0.452999i	0.0240303	−	0.0301331i
$227$	0.383627	+	5.11915i	0.0254622	+	0.339770i	0.995357	+	0.0962474i	$0.0306840\pi$
$227$	0.383627	+	5.11915i	0.0254622	+	0.339770i	−0.969895	+	0.243523i	$0.921697\pi$
$228$	−19.0763	−	5.88425i	−1.26336	−	0.389694i
$229$	−2.36542	+	1.61272i	−0.156312	+	0.106571i	−0.638950	−	0.769248i	$-0.720631\pi$
$229$	−2.36542	+	1.61272i	−0.156312	+	0.106571i	0.482638	+	0.875820i	$0.339679\pi$
$230$	−1.22683	+	0.184914i	−0.0808946	+	0.0121929i
$231$	0.00915998	−	0.0401325i	0.000602683	−	0.00264052i
$232$	2.75339	+	2.55477i	0.180769	+	0.167729i
$233$	0.927985	−	12.3831i	0.0607943	−	0.811244i	−0.880584	−	0.473890i	$-0.842849\pi$
$233$	0.927985	−	12.3831i	0.0607943	−	0.811244i	0.941378	−	0.337353i	$-0.109532\pi$
$234$	−0.0979053	+	0.249459i	−0.00640027	+	0.0163076i
$235$	17.6486	+	2.66010i	1.15127	+	0.173526i
$236$	−2.97735	+	1.43382i	−0.193809	+	0.0933336i
$237$	−14.2938	+	6.88355i	−0.928485	+	0.447135i
$238$	−0.0117503	−	0.00177108i	−0.000761662	−	0.000114802i
$239$	−8.50273	+	21.6646i	−0.549996	+	1.40137i	0.337838	+	0.941204i	$0.390304\pi$
$239$	−8.50273	+	21.6646i	−0.549996	+	1.40137i	−0.887834	+	0.460163i	$0.847791\pi$
$240$	0.684912	−	9.13951i	0.0442109	−	0.589953i
$241$	−2.57706	−	2.39116i	−0.166003	−	0.154028i	0.592797	−	0.805352i	$-0.298024\pi$
$241$	−2.57706	−	2.39116i	−0.166003	−	0.154028i	−0.758800	+	0.651324i	$0.774214\pi$
$242$	−0.195174	+	0.855115i	−0.0125463	+	0.0549688i
$243$	−11.8966	+	1.79313i	−0.763169	+	0.115029i
$244$	9.91315	−	6.75867i	0.634624	−	0.432679i
$245$	−11.9110	−	3.67405i	−0.760965	−	0.234726i
$246$	−0.0460836	−	0.614942i	−0.00293818	−	0.0392073i
$247$	−7.72053	+	9.68124i	−0.491246	+	0.616002i
$248$	1.19289	−	0.367957i	0.0757484	−	0.0233653i
$249$	4.37575	+	11.1492i	0.277302	+	0.706553i
$250$	−0.355585	−	1.55792i	−0.0224892	−	0.0985315i
$251$	6.92415	−	11.9930i	0.437048	−	0.756990i	−0.560412	−	0.828214i	$-0.689357\pi$
$251$	6.92415	−	11.9930i	0.437048	−	0.756990i	0.997460	+	0.0712240i	$0.0226905\pi$
$252$	−0.0186511	−	0.0323046i	−0.00117491	−	0.00203500i
$253$	−8.08323	+	7.50014i	−0.508189	+	0.471530i
$254$	0.738048	+	0.925482i	0.0463092	+	0.0580699i
$255$	−11.7270	−	7.99531i	−0.734371	−	0.500686i
$256$	−13.1869	−	6.35050i	−0.824184	−	0.396906i
$257$	24.5832			1.53346			0.766728	−	0.641972i	$-0.221883\pi$
$257$	24.5832			1.53346			0.766728	+	0.641972i	$0.221883\pi$
$258$	0.786157	−	0.822991i	0.0489440	−	0.0512372i
$259$	0.0755403			0.00469384
$260$	−5.16737	−	2.48847i	−0.320467	−	0.154329i
$261$	7.44450	+	5.07557i	0.460803	+	0.314170i
$262$	0.373971	+	0.468945i	0.0231040	+	0.0289715i
$263$	5.19039	−	4.81598i	0.320053	−	0.296966i	−0.503741	−	0.863855i	$-0.668044\pi$
$263$	5.19039	−	4.81598i	0.320053	−	0.296966i	0.823794	+	0.566889i	$0.191853\pi$
$264$	0.718816	+	1.24502i	0.0442400	+	0.0766260i
$265$	6.10525	−	10.5746i	0.375042	−	0.649593i
$266$	0.00334029	+	0.0146348i	0.000204806	+	0.000897315i
$267$	−7.67460	−	19.5546i	−0.469678	−	1.19672i
$268$	−2.71508	+	0.837492i	−0.165850	+	0.0511580i
$269$	−5.70535	+	7.15429i	−0.347862	+	0.436205i	−0.924725	−	0.380636i	$-0.875705\pi$
$269$	−5.70535	+	7.15429i	−0.347862	+	0.436205i	0.576863	+	0.816841i	$0.304276\pi$
$270$	0.0982878	+	1.31156i	0.00598161	+	0.0798190i
$271$	3.16958	+	0.977687i	0.192539	+	0.0593903i	0.389525	−	0.921016i	$-0.372639\pi$
$271$	3.16958	+	0.977687i	0.192539	+	0.0593903i	−0.196986	+	0.980406i	$0.563115\pi$
$272$	−19.4285	+	13.2461i	−1.17802	+	0.803163i
$273$	0.0317933	−	0.00479207i	0.00192422	−	0.000290029i
$274$	−0.454844	+	1.99280i	−0.0274782	+	0.120390i
$275$	−2.78836	−	2.58722i	−0.168145	−	0.156015i
$276$	1.03764	−	13.8464i	0.0624587	−	0.833454i
$277$	−0.698305	+	1.77925i	−0.0419571	+	0.106905i	−0.950316	−	0.311286i	$-0.899240\pi$
$277$	−0.698305	+	1.77925i	−0.0419571	+	0.106905i	0.908359	+	0.418191i	$0.137336\pi$
$278$	−0.891296	−	0.134341i	−0.0534564	−	0.00805725i
$279$	2.69800	−	1.29929i	0.161525	−	0.0777863i
$280$	−0.0125829	+	0.00605962i	−0.000751974	+	0.000362132i
$281$	−19.5257	−	2.94302i	−1.16480	−	0.175566i	−0.461954	−	0.886904i	$-0.652852\pi$
$281$	−19.5257	−	2.94302i	−1.16480	−	0.175566i	−0.702850	+	0.711338i	$0.748090\pi$
$282$	0.635547	−	1.61935i	0.0378463	−	0.0964308i
$283$	−1.31220	+	17.5101i	−0.0780020	+	1.04086i	0.811626	+	0.584178i	$0.198583\pi$
$283$	−1.31220	+	17.5101i	−0.0780020	+	1.04086i	−0.889628	+	0.456687i	$0.849036\pi$
$284$	−10.2402	−	9.50154i	−0.607645	−	0.563812i
$285$	−3.98966	+	17.4798i	−0.236327	+	1.03542i
$286$	0.438976	−	0.0661650i	0.0259572	−	0.00391242i
$287$	0.0439916	−	0.0299930i	0.00259674	−	0.00177043i
$288$	1.86999	+	0.576816i	0.110190	+	0.0339892i
$289$	1.45085	+	19.3602i	0.0853439	+	1.13883i
$290$	1.04708	−	1.31300i	0.0614868	−	0.0771020i
$291$	17.1004	−	5.27476i	1.00244	−	0.309212i
$292$	−7.07124	−	18.0172i	−0.413813	−	1.05438i
$293$	−1.28000	−	5.60806i	−0.0747786	−	0.327626i	0.923678	−	0.383170i	$-0.125168\pi$
$293$	−1.28000	−	5.60806i	−0.0747786	−	0.327626i	−0.998456	+	0.0555441i	$0.982311\pi$
$294$	−0.607456	+	1.05214i	−0.0354275	+	0.0613623i
$295$	1.48397	+	2.57032i	0.0864003	+	0.149650i
$296$	−1.93391	+	1.79441i	−0.112406	+	0.104298i
$297$	7.28824	+	9.13916i	0.422907	+	0.530308i
$298$	−2.24091	−	1.52783i	−0.129813	−	0.0885047i
$299$	−7.75980	−	3.73692i	−0.448761	−	0.216112i
$300$	4.78978			0.276538
$301$	0.0954760	+	0.0232546i	0.00550315	+	0.00134037i
$302$	0.509739			0.0293322
$303$	−3.71667	−	1.78985i	−0.213517	−	0.102824i
$304$	24.5428	+	16.7330i	1.40762	+	0.959702i
$305$	−6.71848	−	8.42470i	−0.384699	−	0.482397i
$306$	0.729766	−	0.677124i	0.0417179	−	0.0387086i
$307$	7.61789	+	13.1946i	0.434776	+	0.753054i	0.997277	−	0.0737425i	$-0.0234943\pi$
$307$	7.61789	+	13.1946i	0.434776	+	0.753054i	−0.562502	+	0.826796i	$0.690161\pi$
$308$	−0.0308969	+	0.0535149i	−0.00176051	+	0.00304930i
$309$	0.154960	+	0.678924i	0.00881536	+	0.0386226i
$310$	−0.203916	−	0.519571i	−0.0115817	−	0.0295096i
$311$	31.3624	−	9.67402i	1.77840	−	0.548563i	0.781263	−	0.624202i	$-0.214576\pi$
$311$	31.3624	−	9.67402i	1.77840	−	0.548563i	0.997135	+	0.0756385i	$0.0240995\pi$
$312$	−0.700111	+	0.877911i	−0.0396360	+	0.0497019i
$313$	1.45692	+	19.4413i	0.0823502	+	1.09889i	0.873357	+	0.487080i	$0.161938\pi$
$313$	1.45692	+	19.4413i	0.0823502	+	1.09889i	−0.791007	+	0.611807i	$0.790443\pi$
$314$	−0.173147	−	0.0534089i	−0.00977127	−	0.00301404i
$315$	−0.0276805	+	0.0188723i	−0.00155962	+	0.00106333i
$316$	23.5495	−	3.54952i	1.32476	−	0.199676i
$317$	3.76022	−	16.4746i	0.211195	−	0.925306i	−0.752561	−	0.658522i	$-0.771182\pi$
$317$	3.76022	−	16.4746i	0.211195	−	0.925306i	0.963756	−	0.266784i	$-0.0859610\pi$
$318$	−0.872427	−	0.809494i	−0.0489233	−	0.0453942i
$319$	1.11541	−	14.8842i	0.0624512	−	0.833354i
$320$	−4.93693	+	12.5791i	−0.275983	+	0.703193i
$321$	−1.48325	−	0.223565i	−0.0827872	−	0.0124782i
$322$	−0.00940689	+	0.00453012i	−0.000524225	+	0.000252454i
$323$	41.4447	−	19.9587i	2.30604	−	1.11053i
$324$	−7.17098	−	1.08085i	−0.398388	−	0.0600473i
$325$	1.08543	−	2.76564i	0.0602090	−	0.153410i
$326$	0.0321152	−	0.428548i	0.00177870	−	0.0237351i
$327$	11.8129	+	10.9607i	0.653252	+	0.606130i
$328$	−0.413770	+	1.81284i	−0.0228466	+	0.100098i
$329$	0.148520	−	0.0223858i	0.00818818	−	0.00123417i
$330$	0.531094	−	0.362094i	0.0292358	−	0.0199326i
$331$	−27.4650	−	8.47184i	−1.50962	−	0.465655i	−0.574053	−	0.818818i	$-0.694630\pi$
$331$	−27.4650	−	8.47184i	−1.50962	−	0.465655i	−0.935562	+	0.353163i	$0.885106\pi$
$332$	−1.34360	−	17.9291i	−0.0737397	−	0.983987i
$333$	−3.94574	+	4.94780i	−0.216225	+	0.271138i
$334$	−0.435754	+	0.134412i	−0.0238434	+	0.00735471i
$335$	0.932295	+	2.37545i	0.0509367	+	0.129785i
$336$	−0.0171627	−	0.0751946i	−0.000936300	−	0.00410220i
$337$	−8.51965	+	14.7565i	−0.464095	+	0.803836i	−0.999160	−	0.0409748i	$-0.986954\pi$
$337$	−8.51965	+	14.7565i	−0.464095	+	0.803836i	0.535065	+	0.844811i	$0.320287\pi$
$338$	−0.680771	−	1.17913i	−0.0370290	−	0.0641362i
$339$	4.26919	−	3.96123i	0.231871	−	0.215144i
$340$	13.2840	+	16.6577i	0.720428	+	0.903388i
$341$	−4.09872	−	2.79446i	−0.221958	−	0.151329i
$342$	−1.13304	−	0.545641i	−0.0612675	−	0.0295049i
$343$	−0.209795			−0.0113279
$344$	−2.99669	+	1.67263i	−0.161571	+	0.0901820i
$345$	−12.4706			−0.671395
$346$	2.00401	+	0.965083i	0.107736	+	0.0518832i
$347$	−22.9814	−	15.6684i	−1.23371	−	0.841126i	−0.242078	−	0.970257i	$-0.577829\pi$
$347$	−22.9814	−	15.6684i	−1.23371	−	0.841126i	−0.991628	+	0.129131i	$0.958781\pi$
$348$	11.7185	+	14.6945i	0.628177	+	0.787709i
$349$	9.18897	−	8.52612i	0.491874	−	0.456393i	−0.394814	−	0.918761i	$-0.629191\pi$
$349$	9.18897	−	8.52612i	0.491874	−	0.456393i	0.886688	+	0.462369i	$0.153000\pi$
$350$	−0.00180082	−	0.00311911i	−9.62578e−5	−	0.000166723i
$351$	−4.56513	+	7.90704i	−0.243669	+	0.422047i
$352$	−0.721369	−	3.16052i	−0.0384491	−	0.168456i
$353$	−0.273094	−	0.695831i	−0.0145353	−	0.0370353i	0.923422	−	0.383786i	$-0.125380\pi$
$353$	−0.273094	−	0.695831i	−0.0145353	−	0.0370353i	−0.937957	+	0.346751i	$0.887285\pi$
$354$	0.276427	−	0.0852665i	0.0146919	−	0.00453187i
$355$	−7.82239	+	9.80897i	−0.415169	+	0.520606i
$356$	2.35653	+	31.4458i	0.124896	+	1.66662i
$357$	−0.114135	−	0.0352060i	−0.00604066	−	0.00186330i
$358$	−1.02468	+	0.698618i	−0.0541563	+	0.0369231i
$359$	−0.374896	+	0.0565064i	−0.0197862	+	0.00298230i	−0.158928	−	0.987290i	$-0.550804\pi$
$359$	−0.374896	+	0.0565064i	−0.0197862	+	0.00298230i	0.139142	+	0.990272i	$0.455566\pi$
$360$	0.260354	−	1.14068i	0.0137218	−	0.0601193i
$361$	−28.6690	−	26.6009i	−1.50889	−	1.40005i
$362$	0.0723687	−	0.965693i	0.00380362	−	0.0507557i
$363$	−3.22089	+	8.20671i	−0.169053	+	0.430740i
$364$	−0.0477262	−	0.00719356i	−0.00250153	−	0.000377045i
$365$	−15.6618	+	7.54233i	−0.819777	+	0.394784i
$366$	−0.946264	+	0.455696i	−0.0494620	+	0.0238196i
$367$	−17.0718	−	2.57316i	−0.891142	−	0.134318i	−0.312517	−	0.949912i	$-0.601172\pi$
$367$	−17.0718	−	2.57316i	−0.891142	−	0.134318i	−0.578624	+	0.815594i	$0.696410\pi$
$368$	−7.54813	+	19.2323i	−0.393473	+	1.00255i
$369$	−0.333334	+	4.44804i	−0.0173527	+	0.231556i
$370$	0.864680	+	0.802306i	0.0449526	+	0.0417099i
$371$	0.0228654	−	0.100180i	0.00118711	−	0.00520108i
$372$	6.17684	−	0.931009i	0.320254	−	0.0482706i
$373$	23.7980	−	16.2252i	1.23221	−	0.840108i	0.240760	−	0.970585i	$-0.422603\pi$
$373$	23.7980	−	16.2252i	1.23221	−	0.840108i	0.991451	+	0.130477i	$0.0416509\pi$
$374$	−1.57588	−	0.486095i	−0.0814869	−	0.0251354i
$375$	−1.20031	−	16.0171i	−0.0619839	−	0.827117i
$376$	−3.27052	+	4.10110i	−0.168664	+	0.211498i
$377$	11.1402	−	3.43631i	0.573752	−	0.176979i
$378$	0.00404369	+	0.0103031i	0.000207985	+	0.000529937i
$379$	−4.28454	−	18.7718i	−0.220082	−	0.964242i	−0.957416	−	0.288713i	$-0.906773\pi$
$379$	−4.28454	−	18.7718i	−0.220082	−	0.964242i	0.737334	−	0.675529i	$-0.236085\pi$
$380$	13.4572	−	23.3086i	0.690341	−	1.19571i
$381$	5.94910	+	10.3041i	0.304782	+	0.527897i
$382$	1.86108	−	1.72683i	0.0952212	−	0.0883524i
$383$	−8.54764	−	10.7184i	−0.436764	−	0.547685i	0.513923	−	0.857836i	$-0.328192\pi$
$383$	−8.54764	−	10.7184i	−0.436764	−	0.547685i	−0.950687	+	0.310151i	$0.899620\pi$
$384$	4.49044	+	3.06153i	0.229152	+	0.156233i
$385$	0.0500023	+	0.0240798i	0.00254835	+	0.00122722i
$386$	−0.278386			−0.0141695
$387$	−6.51020	+	5.03889i	−0.330932	+	0.256141i
$388$	−26.8635			−1.36379
$389$	−26.3431	−	12.6862i	−1.33565	−	0.643215i	−0.376579	−	0.926384i	$-0.622900\pi$
$389$	−26.3431	−	12.6862i	−1.33565	−	0.643215i	−0.959070	+	0.283170i	$0.908614\pi$
$390$	0.414822	+	0.282821i	0.0210053	+	0.0143212i
$391$	19.9485	+	25.0147i	1.00884	+	1.26505i
$392$	2.68545	−	2.49173i	0.135636	−	0.125852i
$393$	3.01443	+	5.22114i	0.152058	+	0.263372i
$394$	−1.22090	+	2.11467i	−0.0615083	+	0.106536i
$395$	−4.75955	−	20.8530i	−0.239479	−	1.04923i
$396$	−1.89131	−	4.81898i	−0.0950420	−	0.242163i
$397$	17.8679	−	5.51152i	0.896764	−	0.276615i	0.188091	−	0.982152i	$-0.439770\pi$
$397$	17.8679	−	5.51152i	0.896764	−	0.276615i	0.708674	+	0.705536i	$0.249294\pi$
$398$	0.646314	−	0.810452i	0.0323968	−	0.0406243i
$399$	0.0112755	+	0.150461i	0.000564480	+	0.00753247i
$400$	−6.81033	−	2.10071i	−0.340517	−	0.105035i
$401$	−4.37678	+	2.98404i	−0.218566	+	0.149016i	−0.667654	−	0.744472i	$-0.732701\pi$
$401$	−4.37678	+	2.98404i	−0.218566	+	0.149016i	0.449088	+	0.893488i	$0.351749\pi$
$402$	0.245945	−	0.0370702i	0.0122666	−	0.00184890i
$403$	0.862192	−	3.77751i	0.0429488	−	0.188171i
$404$	4.53941	+	4.21196i	0.225844	+	0.209553i
$405$	−0.486730	+	6.49495i	−0.0241858	+	0.322737i
$406$	0.00516327	−	0.0131558i	0.000256249	−	0.000652912i
$407$	10.3665	+	1.56250i	0.513848	+	0.0774501i
$408$	3.75827	−	1.80989i	0.186062	−	0.0896029i
$409$	−5.49230	+	2.64495i	−0.271577	+	0.130784i	−0.564716	−	0.825285i	$-0.691014\pi$
$409$	−5.49230	+	2.64495i	−0.271577	+	0.130784i	0.293139	+	0.956070i	$0.405300\pi$
$410$	0.822108	+	0.123913i	0.0406010	+	0.00611962i
$411$	−7.50614	+	19.1253i	−0.370251	+	0.943383i
$412$	0.0781204	−	1.04244i	0.00384872	−	0.0513576i
$413$	0.0183091	+	0.0169883i	0.000900930	+	0.000835941i
$414$	0.194638	−	0.852764i	0.00956593	−	0.0419111i
$415$	−15.9673	+	2.40669i	−0.783805	+	0.118140i
$416$	2.09210	−	1.42637i	0.102574	−	0.0699335i
$417$	−8.65745	−	2.67047i	−0.423957	−	0.130773i
$418$	0.155683	+	2.07744i	0.00761469	+	0.101611i
$419$	3.35789	−	4.21066i	0.164044	−	0.205704i	−0.693015	−	0.720923i	$-0.743718\pi$
$419$	3.35789	−	4.21066i	0.164044	−	0.205704i	0.857059	+	0.515219i	$0.172289\pi$
$420$	−0.0667798	+	0.0205989i	−0.00325852	+	0.00100512i
$421$	13.0829	+	33.3348i	0.637623	+	1.62464i	0.773415	+	0.633900i	$0.218547\pi$
$421$	13.0829	+	33.3348i	0.637623	+	1.62464i	−0.135791	+	0.990737i	$0.543358\pi$
$422$	0.235611	+	1.03228i	0.0114694	+	0.0502506i
$423$	−6.29149	+	10.8972i	−0.305903	+	0.529839i
$424$	1.79433	+	3.10787i	0.0871403	+	0.150931i
$425$	−8.09059	+	7.50697i	−0.392451	+	0.364142i
$426$	0.762431	+	0.956058i	0.0369399	+	0.0463211i
$427$	−0.0749242	−	0.0510824i	−0.00362583	−	0.00247205i
$428$	2.02873	+	0.976985i	0.0980624	+	0.0472243i
$429$	4.46216			0.215435
$430$	0.845892	+	1.28023i	0.0407925	+	0.0617381i
$431$	2.38810			0.115031			0.0575153	−	0.998345i	$-0.481682\pi$
$431$	2.38810			0.115031			0.0575153	+	0.998345i	$0.481682\pi$
$432$	19.7330	+	9.50292i	0.949405	+	0.457209i
$433$	−6.98440	−	4.76188i	−0.335649	−	0.228841i	0.383753	−	0.923436i	$-0.374631\pi$
$433$	−6.98440	−	4.76188i	−0.335649	−	0.228841i	−0.719402	+	0.694594i	$0.755584\pi$
$434$	−0.00292859	−	0.00367233i	−0.000140577	−	0.000176278i
$435$	12.3741	−	11.4815i	0.593292	−	0.550494i
$436$	−12.0951	−	20.9494i	−0.579252	−	1.00329i
$437$	20.2086	−	35.0023i	0.966709	−	1.67439i
$438$	0.377020	+	1.65183i	0.0180147	+	0.0789276i
$439$	1.42478	+	3.63029i	0.0680013	+	0.173264i	0.960834	−	0.277123i	$-0.0893810\pi$
$439$	1.42478	+	3.63029i	0.0680013	+	0.173264i	−0.892833	+	0.450388i	$0.851286\pi$
$440$	−1.85211	+	0.571301i	−0.0882960	+	0.0272357i
$441$	5.47909	−	6.87056i	0.260909	−	0.327169i
$442$	−0.0962599	−	1.28450i	−0.00457862	−	0.0610974i
$443$	24.1906	+	7.46180i	1.14933	+	0.354521i	0.810162	−	0.586205i	$-0.199379\pi$
$443$	24.1906	+	7.46180i	1.14933	+	0.354521i	0.339166	+	0.940726i	$0.389855\pi$
$444$	−10.9073	+	7.43647i	−0.517637	+	0.352919i
$445$	28.0050	−	4.22107i	1.32756	−	0.200098i
$446$	0.594642	−	2.60529i	0.0281571	−	0.123364i
$447$	−19.9839	−	18.5423i	−0.945206	−	0.877023i
$448$	−0.00849824	+	0.113401i	−0.000401504	+	0.00535770i
$449$	−13.0603	+	33.2771i	−0.616353	+	1.57044i	0.191778	+	0.981438i	$0.438575\pi$
$449$	−13.0603	+	33.2771i	−0.616353	+	1.57044i	−0.808131	+	0.589003i	$0.799520\pi$
$450$	0.298361	+	0.0449707i	0.0140649	+	0.00211994i
$451$	6.65741	−	3.20604i	0.313485	−	0.150967i
$452$	−7.87664	+	3.79319i	−0.370486	+	0.178417i
$453$	5.06636	+	0.763631i	0.238038	+	0.0358785i
$454$	−0.246450	+	0.627946i	−0.0115665	+	0.0294709i
$455$	−0.00323941	+	0.0432269i	−0.000151866	+	0.00202651i
$456$	−3.86276	−	3.58412i	−0.180890	−	0.167842i
$457$	−4.21771	+	18.4790i	−0.197296	+	0.864411i	0.775241	+	0.631665i	$0.217628\pi$
$457$	−4.21771	+	18.4790i	−0.197296	+	0.864411i	−0.972538	+	0.232746i	$0.925229\pi$
$458$	−0.372000	+	0.0560699i	−0.0173824	+	0.00261998i
$459$	28.0240	−	19.1064i	1.30805	−	0.891812i
$460$	17.8884	+	5.51785i	0.834052	+	0.257271i
$461$	1.05220	+	14.0407i	0.0490060	+	0.653940i	0.966578	+	0.256371i	$0.0825269\pi$
$461$	1.05220	+	14.0407i	0.0490060	+	0.653940i	−0.917572	+	0.397569i	$0.869854\pi$
$462$	0.00337264	−	0.00422916i	0.000156909	−	0.000196758i
$463$	17.8943	−	5.51965i	0.831618	−	0.256520i	0.150422	−	0.988622i	$-0.451937\pi$
$463$	17.8943	−	5.51965i	0.831618	−	0.256520i	0.681195	+	0.732102i	$0.261460\pi$
$464$	−10.2171	−	26.0329i	−0.474319	−	1.20855i
$465$	−1.24839	−	5.46956i	−0.0578928	−	0.253645i
$466$	0.815892	−	1.41317i	0.0377955	−	0.0654636i
$467$	1.07575	+	1.86325i	0.0497796	+	0.0862208i	0.889842	−	0.456270i	$-0.150815\pi$
$467$	1.07575	+	1.86325i	0.0497796	+	0.0862208i	−0.840062	+	0.542491i	$0.817481\pi$
$468$	2.96408	−	2.75026i	0.137015	−	0.127131i
$469$	0.0133893	+	0.0167897i	0.000618262	+	0.000775276i
$470$	1.93781	+	1.32118i	0.0893845	+	0.0609413i
$471$	−1.64092	−	0.790227i	−0.0756097	−	0.0364117i
$472$	−0.872278			−0.0401499
$473$	12.6213	+	5.16612i	0.580328	+	0.237538i
$474$	−2.08476			−0.0957562
$475$	12.5615	+	6.04928i	0.576359	+	0.277560i
$476$	0.148143	+	0.101002i	0.00679012	+	0.00462943i
$477$	5.36732	+	6.73041i	0.245753	+	0.308164i
$478$	−2.24188	+	2.08016i	−0.102541	+	0.0951442i
$479$	−14.0491	−	24.3337i	−0.641919	−	1.11184i	−0.985004	−	0.172532i	$-0.944805\pi$
$479$	−14.0491	−	24.3337i	−0.641919	−	1.11184i	0.343085	−	0.939304i	$-0.388528\pi$
$480$	1.83313	−	3.17508i	0.0836706	−	0.144922i
$481$	1.82209	+	7.98312i	0.0830804	+	0.363999i
$482$	−0.168774	−	0.430029i	−0.00768744	−	0.0195873i
$483$	−0.100283	+	0.0309331i	−0.00456302	+	0.00140751i
$484$	8.25141	−	10.3469i	0.375064	−	0.470315i
$485$	1.80299	+	24.0592i	0.0818696	+	1.09247i
$486$	−1.51072	−	0.465994i	−0.0685274	−	0.0211379i
$487$	−15.6116	+	10.6438i	−0.707431	+	0.482318i	−0.862805	−	0.505538i	$-0.831294\pi$
$487$	−15.6116	+	10.6438i	−0.707431	+	0.482318i	0.155374	+	0.987856i	$0.450342\pi$
$488$	3.13157	−	0.472008i	0.141759	−	0.0213668i
$489$	0.961197	−	4.21128i	0.0434668	−	0.190441i
$490$	−1.20070	−	1.11409i	−0.0542422	−	0.0503294i
$491$	−2.02122	+	26.9713i	−0.0912165	+	1.21720i	0.744342	+	0.667798i	$0.232763\pi$
$491$	−2.02122	+	26.9713i	−0.0912165	+	1.21720i	−0.835559	+	0.549401i	$0.814856\pi$
$492$	−3.39935	+	8.66140i	−0.153255	+	0.390486i
$493$	−42.8247	−	6.45478i	−1.92873	−	0.290709i
$494$	−1.46604	+	0.706006i	−0.0659601	+	0.0317647i
$495$	−4.18900	+	2.01731i	−0.188281	+	0.0906715i
$496$	−9.19084	−	1.38530i	−0.412681	−	0.0622016i
$497$	−0.0385730	+	0.0982824i	−0.00173024	+	0.00440857i
$498$	−0.117616	+	1.56948i	−0.00527050	+	0.0703299i
$499$	−5.20488	−	4.82942i	−0.233002	−	0.216195i	0.555027	−	0.831832i	$-0.312708\pi$
$499$	−5.20488	−	4.82942i	−0.233002	−	0.216195i	−0.788029	+	0.615638i	$0.788898\pi$
$500$	−5.36525	+	23.5067i	−0.239941	+	1.05125i
$501$	−4.53238	+	0.683146i	−0.202492	+	0.0305207i
$502$	1.50355	−	1.02511i	0.0671069	−	0.0457527i
$503$	−18.5296	−	5.71564i	−0.826196	−	0.254848i	−0.147309	−	0.989091i	$-0.547061\pi$
$503$	−18.5296	−	5.71564i	−0.826196	−	0.254848i	−0.678887	+	0.734243i	$0.737537\pi$
$504$	−0.000735805	−	0.00981864i	−3.27754e−5	−	0.000437357i
$505$	3.46761	−	4.34824i	0.154307	−	0.193494i
$506$	−1.38462	+	0.427099i	−0.0615540	+	0.0189869i
$507$	−4.99983	−	12.7394i	−0.222050	−	0.565775i
$508$	−3.97441	−	17.4130i	−0.176336	−	0.772579i
$509$	12.0737	−	20.9122i	0.535156	−	0.926917i	−0.464000	−	0.885835i	$-0.653586\pi$
$509$	12.0737	−	20.9122i	0.535156	−	0.926917i	0.999156	−	0.0410815i	$-0.0130803\pi$
$510$	−0.932539	−	1.61521i	−0.0412935	−	0.0715225i
$511$	−0.107236	+	0.0995008i	−0.00474386	+	0.00440166i
$512$	−6.33014	−	7.93774i	−0.279755	−	0.350802i
$513$	−35.4010	−	24.1360i	−1.56299	−	1.06563i
$514$	2.91048	+	1.40161i	0.128376	+	0.0618226i
$515$	−0.938868			−0.0413715
$516$	−16.0751	+	6.04127i	−0.707667	+	0.265952i
$517$	20.8447			0.916747
$518$	0.00894346	+	0.00430694i	0.000392953	+	0.000189236i
$519$	18.4724	+	12.5943i	0.810848	+	0.552827i
$520$	−0.943894	−	1.18361i	−0.0413925	−	0.0519045i
$521$	−1.66226	+	1.54235i	−0.0728250	+	0.0675718i	−0.715746	−	0.698361i	$-0.753913\pi$
$521$	−1.66226	+	1.54235i	−0.0728250	+	0.0675718i	0.642921	+	0.765933i	$0.277723\pi$
$522$	0.591993	+	1.02536i	0.0259109	+	0.0448789i
$523$	−15.7289	+	27.2432i	−0.687775	+	1.19126i	0.284780	+	0.958593i	$0.408079\pi$
$523$	−15.7289	+	27.2432i	−0.687775	+	1.19126i	−0.972556	+	0.232669i	$0.925254\pi$
$524$	−2.01385	−	8.82324i	−0.0879753	−	0.385445i
$525$	−0.0132259	−	0.0336990i	−0.000577225	−	0.00147075i
$526$	0.889090	−	0.274248i	0.0387662	−	0.0119578i
$527$	−8.97436	+	11.2535i	−0.390929	+	0.490210i
$528$	−0.799909	−	10.6740i	−0.0348116	−	0.464528i
$529$	4.88473	+	1.50674i	0.212380	+	0.0655104i
$530$	1.32573	−	0.903869i	0.0575862	−	0.0392616i
$531$	−2.06906	+	0.311861i	−0.0897896	+	0.0135336i
$532$	0.0504001	−	0.220817i	0.00218512	−	0.00957364i
$533$	4.23078	+	3.92559i	0.183255	+	0.170036i
$534$	0.206286	−	2.75270i	0.00892687	−	0.119121i
$535$	0.738837	−	1.88253i	0.0319427	−	0.0813887i
$536$	−0.741610	−	0.111780i	−0.0320327	−	0.00482815i
$537$	−11.2311	+	5.40859i	−0.484656	+	0.233398i
$538$	−1.08338	+	0.521727i	−0.0467077	+	0.0224933i
$539$	−14.3950	−	2.16970i	−0.620037	−	0.0934555i
$540$	7.25019	−	18.4732i	0.311999	−	0.794960i
$541$	−0.0680679	+	0.908302i	−0.00292647	+	0.0390510i	−0.998476	−	0.0551903i	$-0.982423\pi$
$541$	−0.0680679	+	0.908302i	−0.00292647	+	0.0390510i	0.995549	+	0.0942413i	$0.0300425\pi$
$542$	0.319514	+	0.296466i	0.0137243	+	0.0127343i
$543$	2.16597	−	9.48974i	0.0929507	−	0.407244i
$544$	−9.30122	+	1.40193i	−0.398786	+	0.0601074i
$545$	−17.9507	+	12.2386i	−0.768925	+	0.524244i
$546$	0.00403733	+	0.00124535i	0.000172782	+	5.32962e-5i
$547$	−2.81219	−	37.5260i	−0.120240	−	1.60450i	−0.652415	−	0.757862i	$-0.726244\pi$
$547$	−2.81219	−	37.5260i	−0.120240	−	1.60450i	0.532175	−	0.846635i	$-0.321375\pi$
$548$	19.2295	−	24.1131i	0.821444	−	1.03006i
$549$	7.25939	−	2.23923i	0.309823	−	0.0955679i
$550$	−0.182612	−	0.465288i	−0.00778661	−	0.0198400i
$551$	12.1738	+	53.3371i	0.518623	+	2.27224i
$552$	1.83255	−	3.17407i	0.0779986	−	0.135097i
$553$	−0.0899995	−	0.155884i	−0.00382717	−	0.00662885i
$554$	−0.184119	+	0.170838i	−0.00782247	+	0.00725819i
$555$	7.39225	+	9.26958i	0.313783	+	0.393472i
$556$	11.2370	+	7.66129i	0.476557	+	0.324911i
$557$	37.3275	+	17.9760i	1.58162	+	0.761667i	0.998705	−	0.0508683i	$-0.0161989\pi$
$557$	37.3275	+	17.9760i	1.58162	+	0.761667i	0.582912	+	0.812535i	$0.301913\pi$
$558$	0.393504			0.0166583
$559$	−0.154594	+	10.6509i	−0.00653861	+	0.450483i
$560$	0.103985			0.00439416
$561$	−14.9347	−	7.19216i	−0.630543	−	0.303653i
$562$	−2.14391	−	1.46169i	−0.0904355	−	0.0616579i
$563$	14.7605	+	18.5091i	0.622083	+	0.780067i	0.988636	−	0.150330i	$-0.0480336\pi$
$563$	14.7605	+	18.5091i	0.622083	+	0.780067i	−0.366553	+	0.930397i	$0.619462\pi$
$564$	−19.2412	+	17.8532i	−0.810199	+	0.751755i
$565$	3.92588	+	6.79982i	0.165163	+	0.286071i
$566$	−1.15369	+	1.99826i	−0.0484934	+	0.0839930i
$567$	0.0121966	+	0.0534367i	0.000512208	+	0.00224413i
$568$	−1.34712	−	3.43241i	−0.0565240	−	0.144021i
$569$	4.53414	−	1.39860i	0.190081	−	0.0586322i	−0.198253	−	0.980151i	$-0.563527\pi$
$569$	4.53414	−	1.39860i	0.190081	−	0.0586322i	0.388334	+	0.921519i	$0.373051\pi$
$570$	−1.46896	+	1.84202i	−0.0615282	+	0.0771539i
$571$	−2.70647	−	36.1153i	−0.113262	−	1.51138i	−0.707284	−	0.706930i	$-0.750080\pi$
$571$	−2.70647	−	36.1153i	−0.113262	−	1.51138i	0.594021	−	0.804449i	$-0.297539\pi$
$572$	−6.40073	−	1.97436i	−0.267628	−	0.0825523i
$573$	21.0845	−	14.3751i	0.880816	−	0.600530i
$574$	0.00691837	−	0.00104278i	0.000288767	−	4.35246e-5i
$575$	−2.15786	+	9.45422i	−0.0899891	+	0.394268i
$576$	−6.98375	−	6.47997i	−0.290989	−	0.269999i
$577$	1.54710	−	20.6446i	0.0644065	−	0.859445i	−0.867660	−	0.497158i	$-0.834377\pi$
$577$	1.54710	−	20.6446i	0.0644065	−	0.859445i	0.932067	−	0.362287i	$-0.118004\pi$
$578$	−0.932054	+	2.37484i	−0.0387683	+	0.0987801i
$579$	−2.76691	−	0.417045i	−0.114989	−	0.0173318i
$580$	−22.8301	+	10.9944i	−0.947970	+	0.456518i
$581$	−0.122432	+	0.0589601i	−0.00507933	+	0.00244608i
$582$	2.32531	+	0.350484i	0.0963871	+	0.0145280i
$583$	5.21000	−	13.2749i	0.215776	−	0.549789i
$584$	0.381792	−	5.09466i	0.0157987	−	0.210818i
$585$	−2.66210	−	2.47007i	−0.110064	−	0.102125i
$586$	0.168201	−	0.736936i	0.00694831	−	0.0304425i
$587$	22.4886	−	3.38961i	0.928203	−	0.139904i	0.332495	−	0.943105i	$-0.392110\pi$
$587$	22.4886	−	3.38961i	0.928203	−	0.139904i	0.595708	+	0.803201i	$0.296872\pi$
$588$	15.1460	−	10.3263i	0.624609	−	0.425851i
$589$	17.3749	+	5.35945i	0.715921	+	0.220832i
$590$	0.0291453	+	0.388917i	0.00119989	+	0.0160115i
$591$	−15.3027	+	19.1890i	−0.629468	+	0.789328i
$592$	18.7700	−	5.78977i	0.771442	−	0.237958i
$593$	−3.19236	−	8.13401i	−0.131095	−	0.334024i	0.850222	−	0.526425i	$-0.176468\pi$
$593$	−3.19236	−	8.13401i	−0.131095	−	0.334024i	−0.981316	+	0.192401i	$0.938373\pi$
$594$	0.341807	+	1.49756i	0.0140245	+	0.0614454i
$595$	0.0805158	−	0.139457i	0.00330083	−	0.00571720i
$596$	20.4614	+	35.4403i	0.838133	+	1.45169i
$597$	7.63792	−	7.08695i	0.312599	−	0.290050i
$598$	−0.705646	−	0.884852i	−0.0288560	−	0.0361843i
$599$	17.4200	+	11.8767i	0.711760	+	0.485270i	0.864268	−	0.503032i	$-0.167782\pi$
$599$	17.4200	+	11.8767i	0.711760	+	0.485270i	−0.152507	+	0.988302i	$0.548735\pi$
$600$	1.13909	+	0.548559i	0.0465034	+	0.0223948i
$601$	−9.25003			−0.377316			−0.188658	−	0.982043i	$-0.560414\pi$
$601$	−9.25003			−0.377316			−0.188658	+	0.982043i	$0.560414\pi$
$602$	0.00997785	+	0.00819677i	0.000406667	+	0.000334075i
$603$	−1.79908			−0.0732641
$604$	−6.92954	−	3.33709i	−0.281959	−	0.135784i
$605$	−9.82064	−	6.69560i	−0.399266	−	0.272215i
$606$	−0.337980	−	0.423813i	−0.0137295	−	0.0172162i
$607$	26.3944	−	24.4904i	1.07132	−	0.994035i	0.0713212	−	0.997453i	$-0.477278\pi$
$607$	26.3944	−	24.4904i	1.07132	−	0.994035i	0.999994	+	0.00341803i	$0.00108800\pi$
$608$	5.94118	+	10.2904i	0.240947	+	0.417332i
$609$	0.0710269	−	0.123022i	0.00287816	−	0.00498511i
$610$	−0.315086	−	1.38048i	−0.0127575	−	0.0558941i
$611$	5.94817	+	15.1557i	0.240637	+	0.613134i
$612$	−14.3536	+	4.42749i	−0.580208	+	0.178971i
$613$	−4.70938	+	5.90537i	−0.190210	+	0.238516i	−0.867787	−	0.496936i	$-0.834458\pi$
$613$	−4.70938	+	5.90537i	−0.190210	+	0.238516i	0.677577	+	0.735452i	$0.263030\pi$
$614$	0.149616	+	1.99648i	0.00603800	+	0.0805715i
$615$	7.98540	+	2.46317i	0.322002	+	0.0993246i
$616$	−0.0134767	+	0.00918827i	−0.000542992	+	0.000370206i
$617$	−13.9051	+	2.09586i	−0.559798	+	0.0843760i	−0.422846	−	0.906202i	$-0.638969\pi$
$617$	−13.9051	+	2.09586i	−0.559798	+	0.0843760i	−0.136952	+	0.990578i	$0.543731\pi$
$618$	−0.0203628	+	0.0892150i	−0.000819110	+	0.00358876i
$619$	4.50835	+	4.18313i	0.181206	+	0.168134i	0.765560	−	0.643364i	$-0.222462\pi$
$619$	4.50835	+	4.18313i	0.181206	+	0.168134i	−0.584355	+	0.811498i	$0.698652\pi$
$620$	−0.629356	+	8.39817i	−0.0252755	+	0.337279i
$621$	10.8876	−	27.7410i	0.436903	−	1.11321i
$622$	4.26466	+	0.642794i	0.170997	+	0.0257737i
$623$	0.214733	−	0.103410i	0.00860308	−	0.00414303i
$624$	7.53260	−	3.62751i	0.301546	−	0.145217i
$625$	12.3702	+	1.86451i	0.494809	+	0.0745804i
$626$	−0.935959	+	2.38479i	−0.0374085	+	0.0953152i
$627$	−1.56483	+	20.8812i	−0.0624932	+	0.833914i
$628$	2.00417	+	1.85960i	0.0799750	+	0.0742059i
$629$	6.76880	−	29.6561i	0.269890	−	1.18246i
$630$	−0.00435319		0.000656138i	−0.000173435		2.61412e-5i
$631$	−25.7287	+	17.5415i	−1.02424	+	0.698317i	−0.954182	−	0.299226i	$-0.903272\pi$
$631$	−25.7287	+	17.5415i	−1.02424	+	0.698317i	−0.0700608	+	0.997543i	$0.522319\pi$
$632$	6.00700	+	1.85291i	0.238946	+	0.0737050i
$633$	0.795329	+	10.6129i	0.0316115	+	0.421826i
$634$	1.38449	−	1.73609i	0.0549850	−	0.0689490i
$635$	−15.3286	+	4.72823i	−0.608295	+	0.187634i
$636$	6.56054	+	16.7160i	0.260142	+	0.662832i
$637$	−2.53018	−	11.0854i	−0.100249	−	0.439221i
$638$	0.980682	−	1.69859i	0.0388256	−	0.0672478i
$639$	−4.42258	−	7.66013i	−0.174954	−	0.303030i
$640$	−5.37124	+	4.98378i	−0.212317	+	0.197001i
$641$	−16.5022	−	20.6931i	−0.651798	−	0.817329i	0.340625	−	0.940199i	$-0.389361\pi$
$641$	−16.5022	−	20.6931i	−0.651798	−	0.817329i	−0.992423	+	0.122871i	$0.960790\pi$
$642$	−0.162861	−	0.111037i	−0.00642760	−	0.00438226i
$643$	−15.1982	−	7.31905i	−0.599357	−	0.288635i	0.109501	−	0.993987i	$-0.465075\pi$
$643$	−15.1982	−	7.31905i	−0.599357	−	0.288635i	−0.708858	+	0.705352i	$0.750789\pi$
$644$	0.157537			0.00620784
$645$	6.48954	+	13.9916i	0.255525	+	0.550917i
$646$	6.04472			0.237826
$647$	−7.97769	−	3.84185i	−0.313635	−	0.151039i	0.270443	−	0.962736i	$-0.412830\pi$
$647$	−7.97769	−	3.84185i	−0.313635	−	0.151039i	−0.584079	+	0.811697i	$0.698544\pi$
$648$	−1.58160	−	1.07832i	−0.0621311	−	0.0423602i
$649$	2.16118	+	2.71004i	0.0848339	+	0.106378i
$650$	0.286191	−	0.265547i	0.0112253	−	0.0104156i
$651$	−0.0236061	−	0.0408870i	−0.000925198	−	0.00160249i
$652$	−3.24214	+	5.61556i	−0.126972	+	0.219922i
$653$	−0.952035	−	4.17114i	−0.0372560	−	0.163229i	0.952878	−	0.303354i	$-0.0981066\pi$
$653$	−0.952035	−	4.17114i	−0.0372560	−	0.163229i	−0.990134	+	0.140125i	$0.955249\pi$
$654$	0.773634	+	1.97119i	0.0302515	+	0.0770796i
$655$	−7.76703	+	2.39581i	−0.303483	+	0.0936121i
$656$	8.63208	−	10.8243i	0.337026	−	0.422617i
$657$	−0.915847	−	12.2211i	−0.0357306	−	0.476792i
$658$	0.0188601	+	0.00581758i	0.000735244	+	0.000226793i
$659$	−18.1765	+	12.3925i	−0.708056	+	0.482744i	−0.863016	−	0.505176i	$-0.831427\pi$
$659$	−18.1765	+	12.3925i	−0.708056	+	0.482744i	0.154960	+	0.987921i	$0.450475\pi$
$660$	−9.59036	+	1.44551i	−0.373304	+	0.0562666i
$661$	3.37614	−	14.7918i	0.131317	−	0.575336i	−0.865863	−	0.500281i	$-0.833230\pi$
$661$	3.37614	−	14.7918i	0.131317	−	0.575336i	0.997179	−	0.0750541i	$-0.0239130\pi$
$662$	−2.76865	−	2.56893i	−0.107607	−	0.0998444i
$663$	0.967547	−	12.9110i	0.0375764	−	0.501422i
$664$	1.73383	−	4.41773i	0.0672858	−	0.171441i
$665$	−0.201149	−	0.0303183i	−0.00780022	−	0.00117569i
$666$	−0.749248	+	0.360819i	−0.0290328	+	0.0139814i
$667$	−34.2838	+	16.5102i	−1.32748	+	0.639279i
$668$	6.80372	+	1.02550i	0.263244	+	0.0396776i
$669$	9.81316	−	25.0035i	0.379399	−	0.966693i
$670$	−0.0250592	+	0.334392i	−0.000968122	+	0.0129187i
$671$	−9.22534	−	8.55986i	−0.356140	−	0.330450i
$672$	0.00686546	−	0.0300795i	0.000264841	−	0.00116034i
$673$	−18.2365	+	2.74871i	−0.702965	+	0.105955i	−0.490791	−	0.871277i	$-0.663292\pi$
$673$	−18.2365	+	2.74871i	−0.702965	+	0.105955i	−0.212174	+	0.977232i	$0.568054\pi$
$674$	−1.85001	+	1.26132i	−0.0712598	+	0.0485841i
$675$	9.82335	+	3.03010i	0.378101	+	0.116629i
$676$	1.53523	+	20.4862i	0.0590473	+	0.787931i
$677$	14.3763	−	18.0274i	0.552528	−	0.692848i	−0.424629	−	0.905367i	$-0.639595\pi$
$677$	14.3763	−	18.0274i	0.552528	−	0.692848i	0.977157	+	0.212520i	$0.0681669\pi$
$678$	0.731293	−	0.225574i	0.0280852	−	0.00866312i
$679$	0.0741773	+	0.189001i	0.00284666	+	0.00725318i
$680$	1.25143	+	5.48286i	0.0479901	+	0.210258i
$681$	−3.39022	+	5.87203i	−0.129913	+	0.225017i
$682$	−0.325934	−	0.564535i	−0.0124807	−	0.0216172i
$683$	−34.9487	+	32.4277i	−1.33728	+	1.24081i	−0.389833	+	0.920886i	$0.627467\pi$
$683$	−34.9487	+	32.4277i	−1.33728	+	1.24081i	−0.947443	+	0.319925i	$0.896342\pi$
$684$	11.8307	+	14.8352i	0.452358	+	0.567239i
$685$	−22.8865	−	15.6038i	−0.874450	−	0.596190i
$686$	−0.0248383	−	0.0119615i	−0.000948332	−	0.000456693i
$687$	−3.78135			−0.144268
$688$	25.5059	−	1.53952i	0.972403	−	0.0586936i
$689$	11.1386			0.424346
$690$	−1.47644	−	0.711014i	−0.0562069	−	0.0270678i
$691$	13.3788	+	9.12151i	0.508953	+	0.346998i	0.790413	−	0.612575i	$-0.209866\pi$
$691$	13.3788	+	9.12151i	0.508953	+	0.346998i	−0.281459	+	0.959573i	$0.590819\pi$
$692$	−20.9251	−	26.2392i	−0.795453	−	0.997466i
$693$	−0.0286820	+	0.0266130i	−0.00108954	+	0.00101095i
$694$	−1.82750	−	3.16533i	−0.0693710	−	0.120154i
$695$	6.10734	−	10.5782i	0.231665	−	0.401255i
$696$	1.10395	+	4.83670i	0.0418449	+	0.183335i
$697$	−7.83295	−	19.9580i	−0.296694	−	0.755964i
$698$	1.57403	−	0.485524i	0.0595779	−	0.0183773i
$699$	10.2263	−	12.8234i	0.386794	−	0.485024i
$700$	0.00406109	+	0.0541915i	0.000153495	+	0.00204825i
$701$	−28.2831	−	8.72419i	−1.06824	−	0.329508i	−0.289708	−	0.957115i	$-0.593558\pi$
$701$	−28.2831	−	8.72419i	−1.06824	−	0.329508i	−0.778530	+	0.627607i	$0.784035\pi$
$702$	−0.991302	+	0.675858i	−0.0374143	+	0.0255086i
$703$	−37.9969	+	5.72711i	−1.43308	+	0.216002i
$704$	−3.51185	+	15.3864i	−0.132358	+	0.579897i
$705$	17.2809	+	16.0343i	0.650837	+	0.603888i
$706$	0.00734050	−	0.0979522i	0.000276263	−	0.00368648i
$707$	0.0170991	−	0.0435679i	0.000643079	−	0.00163854i
$708$	−4.31605	−	0.650539i	−0.162207	−	0.0244488i
$709$	16.3466	−	7.87211i	0.613910	−	0.295643i	−0.100971	−	0.994889i	$-0.532195\pi$
$709$	16.3466	−	7.87211i	0.613910	−	0.295643i	0.714881	+	0.699246i	$0.246481\pi$
$710$	−1.48538	+	0.715320i	−0.0557452	+	0.0268455i
$711$	14.9112	+	2.24750i	0.559213	+	0.0842879i
$712$	−3.04096	+	7.74824i	−0.113965	+	0.290377i
$713$	−0.945099	+	12.6115i	−0.0353942	+	0.472303i
$714$	−0.0115055	−	0.0106756i	−0.000430584	−	0.000399523i
$715$	−1.33867	+	5.86508i	−0.0500633	+	0.219342i
$716$	18.5035	−	2.78895i	0.691508	−	0.104228i
$717$	−25.3986	+	17.3164i	−0.948527	+	0.646694i
$718$	−0.0476068	−	0.0146848i	−0.00177667	−	0.000548031i
$719$	1.34139	+	17.8996i	0.0500254	+	0.667542i	0.964700	+	0.263351i	$0.0848279\pi$
$719$	1.34139	+	17.8996i	0.0500254	+	0.667542i	−0.914675	+	0.404191i	$0.867553\pi$
$720$	−5.43150	+	6.81089i	−0.202420	+	0.253827i
$721$	−0.00754994	+	0.00232885i	−0.000281174	+	8.67308e-5i
$722$	−1.87756	−	4.78393i	−0.0698754	−	0.178040i
$723$	−1.03325	−	4.52695i	−0.0384268	−	0.168359i
$724$	−7.30588	+	12.6541i	−0.271521	+	0.470288i
$725$	−6.56317	−	11.3677i	−0.243750	−	0.422187i
$726$	−0.849239	+	0.787979i	−0.0315182	+	0.0292446i
$727$	7.71422	+	9.67332i	0.286105	+	0.358764i	0.904027	−	0.427475i	$-0.140597\pi$
$727$	7.71422	+	9.67332i	0.286105	+	0.358764i	−0.617923	+	0.786239i	$0.712025\pi$
$728$	−0.0105263	−	0.00717668i	−0.000390129	−	0.000265986i
$729$	−24.2032	−	11.6556i	−0.896413	−	0.431690i
$730$	−2.28428			−0.0845450
$731$	17.6846	−	35.3988i	0.654088	−	1.30927i
$732$	15.8471			0.585725
$733$	17.8504	+	8.59631i	0.659320	+	0.317512i	0.733457	−	0.679736i	$-0.237906\pi$
$733$	17.8504	+	8.59631i	0.659320	+	0.317512i	−0.0741364	+	0.997248i	$0.523620\pi$
$734$	−1.87448	−	1.27800i	−0.0691883	−	0.0471718i
$735$	−10.2649	−	12.8718i	−0.378628	−	0.474785i
$736$	−6.05843	+	5.62140i	−0.223317	+	0.207208i
$737$	1.49015	+	2.58102i	0.0548905	+	0.0950732i
$738$	−0.293070	+	0.507613i	−0.0107881	+	0.0186855i
$739$	6.50578	+	28.5037i	0.239319	+	1.04852i	0.941629	+	0.336653i	$0.109295\pi$
$739$	6.50578	+	28.5037i	0.239319	+	1.04852i	−0.702310	+	0.711871i	$0.747848\pi$
$740$	−6.50229	−	16.5676i	−0.239029	−	0.609036i
$741$	−15.6288	+	4.82084i	−0.574137	+	0.177098i
$742$	0.00841889	−	0.0105570i	0.000309067	−	0.000387558i
$743$	−1.38658	−	18.5026i	−0.0508686	−	0.678795i	−0.963104	−	0.269129i	$-0.913264\pi$
$743$	−1.38658	−	18.5026i	−0.0508686	−	0.678795i	0.912236	−	0.409666i	$-0.134355\pi$
$744$	1.57559	+	0.486004i	0.0577638	+	0.0178178i
$745$	30.3674	−	20.7041i	1.11257	−	0.758541i
$746$	3.74260	−	0.564106i	0.137026	−	0.0206534i
$747$	2.53324	−	11.0988i	0.0926864	−	0.406086i
$748$	18.2407	+	16.9249i	0.666946	+	0.618836i
$749$	0.00127180	−	0.0169711i	4.64707e−5	−	0.000620109i
$750$	0.771106	−	1.96475i	0.0281568	−	0.0717424i
$751$	41.0993	+	6.19473i	1.49974	+	0.226049i	0.847023	−	0.531557i	$-0.178393\pi$
$751$	41.0993	+	6.19473i	1.49974	+	0.226049i	0.652713	+	0.757606i	$0.273631\pi$
$752$	35.1880	−	16.9457i	1.28318	−	0.617945i
$753$	16.4797	−	7.93621i	0.600554	−	0.289212i
$754$	1.51485	+	0.228327i	0.0551676	+	0.00831518i
$755$	−2.52365	+	6.43015i	−0.0918449	+	0.234017i
$756$	0.0124802	−	0.166537i	0.000453901	−	0.00605688i
$757$	18.4171	+	17.0886i	0.669381	+	0.621095i	0.939831	−	0.341639i	$-0.110982\pi$
$757$	18.4171	+	17.0886i	0.669381	+	0.621095i	−0.270450	+	0.962734i	$0.587172\pi$
$758$	0.563016	−	2.46674i	0.0204497	−	0.0895959i
$759$	−14.4018	+	2.17072i	−0.522751	+	0.0787920i
$760$	5.86983	−	4.00198i	0.212921	−	0.145167i
$761$	2.55267	+	0.787394i	0.0925342	+	0.0285430i	0.340677	−	0.940181i	$-0.389344\pi$
$761$	2.55267	+	0.787394i	0.0925342	+	0.0285430i	−0.248142	+	0.968724i	$0.579820\pi$
$762$	0.116841	+	1.55913i	0.00423269	+	0.0564813i
$763$	−0.113994	+	0.142944i	−0.00412685	+	0.00517490i
$764$	−36.6051	+	11.2912i	−1.32433	+	0.408500i
$765$	4.92867	+	12.5580i	0.178196	+	0.454037i
$766$	−0.400871	−	1.75633i	−0.0144841	−	0.0634588i
$767$	−1.35370	+	2.34468i	−0.0488793	+	0.0846614i
$768$	−9.66602	−	16.7420i	−0.348793	−	0.604126i
$769$	27.1593	−	25.2001i	0.979389	−	0.908741i	−0.0164501	−	0.999865i	$-0.505236\pi$
$769$	27.1593	−	25.2001i	0.979389	−	0.908741i	0.995840	+	0.0911240i	$0.0290460\pi$
$770$	0.00454701	+	0.00570178i	0.000163863	+	0.000205478i
$771$	26.8279	+	18.2910i	0.966184	+	0.658733i
$772$	3.78446	+	1.82250i	0.136206	+	0.0655931i
$773$	46.2293			1.66275			0.831376	−	0.555711i	$-0.187554\pi$
$773$	46.2293			1.66275			0.831376	+	0.555711i	$0.187554\pi$
$774$	−1.05806	+	0.225391i	−0.0380311	+	0.00810150i
$775$	−4.36260			−0.156709
$776$	−6.38861	−	3.07659i	−0.229338	−	0.110443i
$777$	0.0824380	+	0.0562053i	0.00295745	+	0.00201635i
$778$	−2.39554	−	3.00392i	−0.0858844	−	0.107696i
$779$	−19.8539	+	18.4218i	−0.711341	+	0.660028i
$780$	−3.78768	−	6.56045i	−0.135621	−	0.234902i
$781$	−7.32633	+	12.6896i	−0.262157	+	0.454069i
$782$	0.935556	+	4.09894i	0.0334554	+	0.146578i
$783$	14.7374	+	37.5503i	0.526672	+	1.34194i
$784$	−26.0642	+	8.03973i	−0.930863	+	0.287133i
$785$	1.53096	−	1.91976i	0.0546423	−	0.0685193i
$786$	0.0592035	+	0.790016i	0.00211172	+	0.0281790i
$787$	12.3410	+	3.80671i	0.439911	+	0.135695i	0.506796	−	0.862066i	$-0.330830\pi$
$787$	12.3410	+	3.80671i	0.439911	+	0.135695i	−0.0668849	+	0.997761i	$0.521306\pi$
$788$	30.4414	−	20.7546i	1.08443	−	0.739351i
$789$	9.24763	−	1.39386i	0.329224	−	0.0496226i
$790$	0.625437	−	2.74022i	0.0222520	−	0.0974925i
$791$	0.0484369	+	0.0449429i	0.00172222	+	0.00159799i
$792$	0.102116	−	1.36265i	0.00362854	−	0.0484195i
$793$	3.59117	−	9.15016i	0.127526	−	0.324932i
$794$	2.42968	+	0.366215i	0.0862261	+	0.0129965i
$795$	14.5307	−	6.99762i	0.515351	−	0.248180i
$796$	−14.0919	+	6.78632i	−0.499476	+	0.240535i
$797$	−34.6051	−	5.21589i	−1.22578	−	0.184756i	−0.495928	−	0.868364i	$-0.665172\pi$
$797$	−34.6051	−	5.21589i	−1.22578	−	0.184756i	−0.729850	+	0.683608i	$0.760410\pi$
$798$	−0.00724361	+	0.0184564i	−0.000256421	+	0.000653350i
$799$	4.51983	−	60.3129i	0.159900	−	2.13372i
$800$	−2.08989	−	1.93914i	−0.0738889	−	0.0685588i
$801$	−4.44303	+	19.4662i	−0.156987	+	0.687804i
$802$	−0.688316	+	0.103747i	−0.0243053	+	0.00366343i
$803$	−16.7743	+	11.4365i	−0.591952	+	0.403586i
$804$	−3.58613	−	1.10618i	−0.126473	−	0.0390118i
$805$	−0.0105734	−	0.141092i	−0.000372663	−	0.00497284i
$806$	0.317453	−	0.398073i	0.0111818	−	0.0140215i
$807$	−11.5494	+	3.56253i	−0.406559	+	0.125407i
$808$	0.597170	+	1.52156i	0.0210084	+	0.0535284i
$809$	4.51483	+	19.7807i	0.158733	+	0.695454i	0.990174	+	0.139841i	$0.0446592\pi$
$809$	4.51483	+	19.7807i	0.158733	+	0.695454i	−0.831441	+	0.555613i	$0.812484\pi$
$810$	−0.427936	+	0.741208i	−0.0150362	+	0.0260434i
$811$	−3.52831	−	6.11121i	−0.123896	−	0.214593i	0.797405	−	0.603444i	$-0.206205\pi$
$811$	−3.52831	−	6.11121i	−0.123896	−	0.214593i	−0.921301	+	0.388851i	$0.872872\pi$
$812$	−0.156318	+	0.145042i	−0.00548568	+	0.00508997i
$813$	2.73156	+	3.42527i	0.0958001	+	0.120130i
$814$	1.13824	+	0.776037i	0.0398952	+	0.0272001i
$815$	5.24696	+	2.52680i	0.183793	+	0.0885100i
$816$	−31.0582			−1.08726
$817$	−49.7876	−	4.45857i	−1.74185	−	0.155986i
$818$	−0.801053			−0.0280082
$819$	−0.0275344	−	0.0132598i	−0.000962128	−	0.000463337i
$820$	−10.3648	−	7.06657i	−0.361953	−	0.246775i
$821$	−18.1800	−	22.7970i	−0.634486	−	0.795621i	0.355815	−	0.934556i	$-0.384203\pi$
$821$	−18.1800	−	22.7970i	−0.634486	−	0.795621i	−0.990301	+	0.138936i	$0.955632\pi$
$822$	−1.97911	+	1.83635i	−0.0690294	+	0.0640499i
$823$	24.5454	+	42.5140i	0.855600	+	1.48194i	0.876087	+	0.482153i	$0.160145\pi$
$823$	24.5454	+	42.5140i	0.855600	+	1.48194i	−0.0204864	+	0.999790i	$0.506521\pi$
$824$	0.137966	−	0.238965i	0.00480629	−	0.00832473i
$825$	−1.11797	−	4.89813i	−0.0389226	−	0.170531i
$826$	0.00119908	+	0.00305520i	4.17212e−5	+	0.000106304i
$827$	4.63646	−	1.43016i	0.161225	−	0.0497314i	−0.213092	−	0.977032i	$-0.568353\pi$
$827$	4.63646	−	1.43016i	0.161225	−	0.0497314i	0.374317	+	0.927301i	$0.377877\pi$
$828$	−8.22873	+	10.3185i	−0.285968	+	0.358593i
$829$	2.29136	+	30.5761i	0.0795823	+	1.06195i	0.883876	+	0.467721i	$0.154925\pi$
$829$	2.29136	+	30.5761i	0.0795823	+	1.06195i	−0.804294	+	0.594231i	$0.797456\pi$
$830$	−2.02764	−	0.625444i	−0.0703804	−	0.0217095i
$831$	−2.08591	+	1.42215i	−0.0723595	+	0.0493339i
$832$	−12.1892	+	1.83723i	−0.422586	+	0.0636946i
$833$	−9.39922	+	41.1807i	−0.325664	+	1.42683i
$834$	−0.872726	−	0.809771i	−0.0302200	−	0.0280401i
$835$	0.461802	−	6.16232i	0.0159813	−	0.213256i
$836$	11.4839	−	29.2606i	0.397180	−	1.01200i
$837$	13.2570	+	1.99818i	0.458230	+	0.0690671i
$838$	0.637624	−	0.307063i	0.0220263	−	0.0106073i
$839$	28.7846	−	13.8619i	0.993755	−	0.478567i	0.134941	−	0.990854i	$-0.456916\pi$
$839$	28.7846	−	13.8619i	0.993755	−	0.478567i	0.858815	+	0.512286i	$0.171201\pi$
$840$	−0.0182405	−	0.00274932i	−0.000629358	−	9.48605e-5i
$841$	8.22290	−	20.9516i	0.283548	−	0.722469i
$842$	−0.351657	+	4.69254i	−0.0121189	+	0.161716i
$843$	−19.1189	−	17.7397i	−0.658489	−	0.610989i
$844$	3.55503	−	15.5756i	0.122369	−	0.536134i
$845$	18.2446	−	2.74994i	0.627635	−	0.0946007i
$846$	−1.36618	+	0.931443i	−0.0469701	+	0.0320237i
$847$	−0.0955813	−	0.0294829i	−0.00328421	−	0.00101305i
$848$	−1.99676	−	26.6449i	−0.0685689	−	0.914989i
$849$	−14.4603	+	18.1326i	−0.496275	+	0.622309i
$850$	−1.38588	+	0.427488i	−0.0475354	+	0.0146627i
$851$	−9.76444	−	24.8794i	−0.334721	−	0.852854i
$852$	−4.10572	−	17.9883i	−0.140659	−	0.616269i
$853$	−12.0620	+	20.8920i	−0.412996	+	0.715330i	−0.995216	−	0.0977017i	$-0.968851\pi$
$853$	−12.0620	+	20.8920i	−0.412996	+	0.715330i	0.582220	+	0.813031i	$0.302184\pi$
$854$	−0.00595804	−	0.0103196i	−0.000203880	−	0.000353130i
$855$	12.4925	−	11.5914i	0.427236	−	0.396417i
$856$	0.370577	+	0.464688i	0.0126660	+	0.0158827i
$857$	37.7821	+	25.7594i	1.29061	+	0.879924i	0.997105	−	0.0760330i	$-0.0242254\pi$
$857$	37.7821	+	25.7594i	1.29061	+	0.879924i	0.293506	+	0.955957i	$0.405178\pi$
$858$	0.528290	+	0.254411i	0.0180355	+	0.00868544i
$859$	−31.4601			−1.07341			−0.536703	−	0.843771i	$-0.680330\pi$
$859$	−31.4601			−1.07341			−0.536703	+	0.843771i	$0.680330\pi$
$860$	−3.11808	−	22.9416i	−0.106325	−	0.782301i
$861$	0.0703247			0.00239666
$862$	0.282734	+	0.136158i	0.00962997	+	0.00463755i
$863$	−7.50021	−	5.11356i	−0.255310	−	0.174068i	0.428901	−	0.903352i	$-0.358901\pi$
$863$	−7.50021	−	5.11356i	−0.255310	−	0.174068i	−0.684211	+	0.729284i	$0.739853\pi$
$864$	5.46258	+	6.84986i	0.185841	+	0.233037i
$865$	−22.0957	+	20.5018i	−0.751277	+	0.697083i
$866$	−0.555406	−	0.961991i	−0.0188735	−	0.0326898i
$867$	−12.8215	+	22.2075i	−0.435441	+	0.754206i
$868$	0.0157705	+	0.0690952i	0.000535287	+	0.00234525i
$869$	−9.12641	−	23.2537i	−0.309592	−	0.788828i
$870$	2.11962	−	0.653818i	0.0718620	−	0.0221665i
$871$	−1.45138	+	1.81997i	−0.0491781	+	0.0616674i
$872$	−0.477167	−	6.36735i	−0.0161589	−	0.215626i
$873$	−16.2539	−	5.01365i	−0.550110	−	0.169686i
$874$	4.38823	−	2.99184i	0.148434	−	0.101201i
$875$	0.180199	−	0.0271606i	0.00609183	−	0.000918196i
$876$	5.68868	−	24.9237i	0.192203	−	0.842094i
$877$	32.2254	+	29.9008i	1.08817	+	1.00968i	0.999908	+	0.0135802i	$0.00432285\pi$
$877$	32.2254	+	29.9008i	1.08817	+	1.00968i	0.0882654	+	0.996097i	$0.471868\pi$
$878$	−0.0382969	+	0.511036i	−0.00129246	+	0.0172466i
$879$	2.77576	−	7.07252i	0.0936241	−	0.238550i
$880$	14.2700	+	2.15085i	0.481041	+	0.0725053i
$881$	−18.7576	+	9.03321i	−0.631961	+	0.304336i	−0.722305	−	0.691574i	$-0.756918\pi$
$881$	−18.7576	+	9.03321i	−0.631961	+	0.304336i	0.0903444	+	0.995911i	$0.471203\pi$
$882$	1.04041	−	0.501036i	0.0350325	−	0.0168708i
$883$	50.0003	+	7.53634i	1.68264	+	0.253618i	0.919636	−	0.392771i	$-0.128483\pi$
$883$	50.0003	+	7.53634i	1.68264	+	0.253618i	0.763008	+	0.646389i	$0.223721\pi$
$884$	−7.10061	+	18.0921i	−0.238819	+	0.608502i
$885$	−0.292951	+	3.90916i	−0.00984745	+	0.131405i
$886$	2.43856	+	2.26266i	0.0819252	+	0.0760154i
$887$	12.3944	−	54.3035i	0.416164	−	1.82333i	−0.137389	−	0.990517i	$-0.543871\pi$
$887$	12.3944	−	54.3035i	0.416164	−	1.82333i	0.553552	−	0.832814i	$-0.313272\pi$
$888$	−3.44562	+	0.519344i	−0.115628	+	0.0174280i
$889$	−0.111537	+	0.0760445i	−0.00374082	+	0.00255045i
$890$	3.55627	+	1.09696i	0.119206	+	0.0367703i
$891$	0.568452	+	7.58547i	0.0190439	+	0.254123i
$892$	−25.1397	+	31.5242i	−0.841741	+	1.05551i
$893$	−73.0087	+	22.5202i	−2.44314	+	0.753610i
$894$	−1.30876	−	3.33467i	−0.0437716	−	0.111528i
$895$	−3.73971	−	16.3847i	−0.125005	−	0.547682i
$896$	−0.0308308	+	0.0534005i	−0.00102998	+	0.00178398i
$897$	−5.68793	−	9.85178i	−0.189914	−	0.328941i
$898$	−3.44355	+	3.19514i	−0.114913	+	0.106623i
$899$	−10.6734	−	13.3840i	−0.355977	−	0.446381i
$900$	−3.76160	−	2.56462i	−0.125387	−	0.0854873i
$901$	−37.2804	−	17.9533i	−1.24199	−	0.598111i
$902$	0.970986			0.0323303
$903$	0.0868917	+	0.0964164i	0.00289157	+	0.00320854i
$904$	−2.30763			−0.0767505
$905$	11.8235	+	5.69392i	0.393028	+	0.189272i
$906$	0.556284	+	0.379268i	0.0184813	+	0.0126003i
$907$	−26.2597	−	32.9286i	−0.871939	−	1.09338i	−0.994890	−	0.100964i	$-0.967807\pi$
$907$	−26.2597	−	32.9286i	−0.871939	−	1.09338i	0.122951	−	0.992413i	$-0.460764\pi$
$908$	7.46127	−	6.92305i	0.247611	−	0.229749i
$909$	1.96050	+	3.39568i	0.0650255	+	0.112628i
$910$	−0.00284811	+	0.00493308i	−9.44140e−5	+	0.000163530i
$911$	3.51500	+	15.4002i	0.116457	+	0.510232i	0.999186	+	0.0403485i	$0.0128468\pi$
$911$	3.51500	+	15.4002i	0.116457	+	0.510232i	−0.882729	+	0.469883i	$0.844296\pi$
$912$	14.3337	+	36.5218i	0.474638	+	1.20936i
$913$	−18.0211	+	5.55876i	−0.596410	+	0.183968i
$914$	−1.55293	+	1.94732i	−0.0513664	+	0.0644115i
$915$	−1.06360	−	14.1928i	−0.0351617	−	0.469200i
$916$	5.42415	+	1.67313i	0.179219	+	0.0552817i
$917$	−0.0565160	+	0.0385320i	−0.00186632	+	0.00127244i
$918$	4.40721	−	0.664280i	0.145460	−	0.0219245i
$919$	−6.32627	+	27.7172i	−0.208684	+	0.914306i	0.756759	+	0.653694i	$0.226782\pi$
$919$	−6.32627	+	27.7172i	−0.208684	+	0.914306i	−0.965444	+	0.260612i	$0.916076\pi$
$920$	3.62224	+	3.36095i	0.119422	+	0.110807i
$921$	−1.50385	+	20.0674i	−0.0495534	+	0.661244i
$922$	−0.675958	+	1.72231i	−0.0222615	+	0.0567214i
$923$	−11.3169	−	1.70575i	−0.372501	−	0.0561455i
$924$	−0.0735356	+	0.0354129i	−0.00241914	+	0.00116500i
$925$	8.30658	−	4.00024i	0.273119	−	0.131527i
$926$	2.43327	+	0.366756i	0.0799621	+	0.0120523i
$927$	0.241823	−	0.616156i	0.00794252	−	0.0202372i
$928$	0.836010	−	11.1558i	0.0274434	−	0.366206i
$929$	32.4893	+	30.1457i	1.06594	+	0.989047i	0.999962	−	0.00877413i	$-0.00279293\pi$
$929$	32.4893	+	30.1457i	1.06594	+	0.989047i	0.0659776	+	0.997821i	$0.478983\pi$
$930$	0.164047	−	0.718736i	0.00537931	−	0.0235683i
$931$	52.7628	−	7.95271i	1.72923	−	0.260640i
$932$	−20.3430	+	13.8696i	−0.666357	+	0.454315i
$933$	41.4241	+	12.7776i	1.35616	+	0.418321i
$934$	0.0211277	+	0.281930i	0.000691320	+	0.00922502i
$935$	13.9339	−	17.4725i	0.455686	−	0.571413i
$936$	1.01989	−	0.314594i	0.0333361	−	0.0102828i
$937$	11.1997	+	28.5364i	0.365879	+	0.932245i	0.988704	+	0.149883i	$0.0478897\pi$
$937$	11.1997	+	28.5364i	0.365879	+	0.932245i	−0.622825	+	0.782361i	$0.714015\pi$
$938$	0.000627940		0.00275118i	2.05030e−5		8.98293e-5i
$939$	−12.8752	+	22.3005i	−0.420167	+	0.727751i
$940$	−17.6939	−	30.6467i	−0.577110	−	0.999584i
$941$	26.1851	−	24.2962i	0.853609	−	0.792033i	−0.126193	−	0.992006i	$-0.540276\pi$
$941$	26.1851	−	24.2962i	0.853609	−	0.792033i	0.979802	+	0.199973i	$0.0640853\pi$
$942$	−0.149219	−	0.187115i	−0.00486183	−	0.00609654i
$943$	−15.5647	−	10.6118i	−0.506856	−	0.345568i
$944$	5.85144	+	2.81790i	0.190448	+	0.0917150i
$945$	−0.149990			−0.00487917
$946$	1.19973	+	1.33124i	0.0390066	+	0.0432823i
$947$	−40.7779			−1.32510			−0.662552	−	0.749016i	$-0.730527\pi$
$947$	−40.7779			−1.32510			−0.662552	+	0.749016i	$0.730527\pi$
$948$	28.3409	+	13.6482i	0.920468	+	0.443274i
$949$	−13.1019	−	8.93272i	−0.425306	−	0.289969i
$950$	1.14229	+	1.43239i	0.0370608	+	0.0464728i
$951$	16.3614	−	15.1812i	0.530555	−	0.492283i
$952$	0.0236635	+	0.0409865i	0.000766940	+	0.00132838i
$953$	12.4281	−	21.5261i	0.402586	−	0.697300i	−0.591451	−	0.806341i	$-0.701445\pi$
$953$	12.4281	−	21.5261i	0.402586	−	0.697300i	0.994037	+	0.109041i	$0.0347781\pi$
$954$	0.251719	+	1.10285i	0.00814971	+	0.0357062i
$955$	12.5693	+	32.0261i	0.406734	+	1.03634i
$956$	44.0949	−	13.6015i	1.42613	−	0.439903i
$957$	12.2917	−	15.4134i	0.397336	−	0.498243i
$958$	−0.275925	−	3.68196i	−0.00891472	−	0.118959i
$959$	−0.222748	−	0.0687086i	−0.00719290	−	0.00221872i
$960$	−14.7471	+	10.0544i	−0.475962	+	0.324505i
$961$	25.0278	−	3.77233i	0.807348	−	0.121688i
$962$	−0.239435	+	1.04903i	−0.00771970	+	0.0338222i
$963$	1.04515	+	0.969760i	0.0336796	+	0.0312501i
$964$	−0.520894	+	6.95085i	−0.0167769	+	0.223872i
$965$	1.37825	−	3.51172i	0.0443674	−	0.113046i
$966$	−0.0136365	−	0.00205537i	−0.000438746	−	6.61303e-5i
$967$	11.2144	−	5.40056i	0.360630	−	0.173670i	−0.244791	−	0.969576i	$-0.578719\pi$
$967$	11.2144	−	5.40056i	0.360630	−	0.173670i	0.605421	+	0.795906i	$0.293005\pi$
$968$	3.14733	−	1.51568i	0.101159	−	0.0487157i
$969$	60.0792	+	9.05549i	1.93002	+	0.290904i
$970$	−1.15828	+	2.95125i	−0.0371901	+	0.0947588i
$971$	2.26263	−	30.1927i	0.0726113	−	0.968931i	−0.835307	−	0.549784i	$-0.814710\pi$
$971$	2.26263	−	30.1927i	0.0726113	−	0.968931i	0.907918	−	0.419147i	$-0.137671\pi$
$972$	17.4864	+	16.2250i	0.560877	+	0.520417i
$973$	0.0228733	−	0.100214i	0.000733283	−	0.00321272i
$974$	−2.45517	+	0.370058i	−0.0786688	+	0.0118574i
$975$	3.24230	−	2.21056i	0.103837	−	0.0707947i
$976$	−22.5321	−	6.95023i	−0.721235	−	0.222472i
$977$	2.68390	+	35.8142i	0.0858656	+	1.14580i	0.859145	+	0.511732i	$0.170996\pi$
$977$	2.68390	+	35.8142i	0.0858656	+	1.14580i	−0.773280	+	0.634065i	$0.781385\pi$
$978$	0.353906	−	0.443784i	0.0113167	−	0.0141907i
$979$	31.6070	−	9.74947i	1.01016	−	0.311595i
$980$	9.02914	+	23.0059i	0.288425	+	0.734895i
$981$	−3.40834	−	14.9329i	−0.108820	−	0.476771i
$982$	−1.77707	+	3.07798i	−0.0567087	+	0.0982224i
$983$	−24.1540	−	41.8359i	−0.770392	−	1.33436i	−0.937348	−	0.348394i	$-0.886727\pi$
$983$	−24.1540	−	41.8359i	−0.770392	−	1.33436i	0.166956	−	0.985964i	$-0.446606\pi$
$984$	−1.80039	+	1.67052i	−0.0573943	+	0.0532541i
$985$	−20.6312	−	25.8707i	−0.657364	−	0.824308i
$986$	−4.70213	−	3.20586i	−0.149746	−	0.102095i
$987$	0.178738	+	0.0860756i	0.00568929	+	0.00273982i
$988$	24.5517			0.781094
$989$	−4.68239	−	34.4512i	−0.148891	−	1.09548i
$990$	−0.610966			−0.0194178
$991$	10.0373	+	4.83373i	0.318847	+	0.153548i	0.586461	−	0.809978i	$-0.300521\pi$
$991$	10.0373	+	4.83373i	0.318847	+	0.153548i	−0.267614	+	0.963526i	$0.586235\pi$
$992$	−3.07202	−	2.09446i	−0.0975366	−	0.0664993i
$993$	−23.6695	−	29.6806i	−0.751129	−	0.941886i
$994$	−0.0101704	+	0.00943672i	−0.000322585	+	0.000299315i
$995$	7.02371	+	12.1654i	0.222667	+	0.385670i
$996$	11.8738	−	20.5659i	0.376234	−	0.651657i
$997$	8.80699	+	38.5859i	0.278920	+	1.22203i	0.899161	+	0.437618i	$0.144178\pi$
$997$	8.80699	+	38.5859i	0.278920	+	1.22203i	−0.620241	+	0.784411i	$0.712965\pi$
$998$	−0.340872	−	0.868528i	−0.0107901	−	0.0274928i
$999$	−27.0742	+	8.35128i	−0.856589	+	0.264223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.2.g.a.25.2	✓	36
3.2	odd	2		387.2.y.c.154.2		36
4.3	odd	2		688.2.bg.c.369.1		36
43.17	even	21		1849.2.a.n.1.10		18
43.26	odd	42		1849.2.a.o.1.9		18
43.31	even	21	inner	43.2.g.a.31.2	yes	36
129.74	odd	42		387.2.y.c.289.2		36
172.31	odd	42		688.2.bg.c.289.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.25.2	✓	36	1.1	even	1	trivial
43.2.g.a.31.2	yes	36	43.31	even	21	inner
387.2.y.c.154.2		36	3.2	odd	2
387.2.y.c.289.2		36	129.74	odd	42
688.2.bg.c.289.1		36	172.31	odd	42
688.2.bg.c.369.1		36	4.3	odd	2
1849.2.a.n.1.10		18	43.17	even	21
1849.2.a.o.1.9		18	43.26	odd	42

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.118393 + 0.0570152i) q^{2} +(1.09131 + 0.744044i) q^{3} +(-1.23621 - 1.55016i) q^{4} +(-1.30537 + 1.21121i) q^{5} +(0.0867822 + 0.150311i) q^{6} +(-0.00749281 + 0.0129779i) q^{7} +(-0.116458 - 0.510236i) q^{8} +(-0.458662 - 1.16865i) q^{9} +O(q^{10})\)	\(q+(0.118393 + 0.0570152i) q^{2} +(1.09131 + 0.744044i) q^{3} +(-1.23621 - 1.55016i) q^{4} +(-1.30537 + 1.21121i) q^{5} +(0.0867822 + 0.150311i) q^{6} +(-0.00749281 + 0.0129779i) q^{7} +(-0.116458 - 0.510236i) q^{8} +(-0.458662 - 1.16865i) q^{9} +(-0.223604 + 0.0689728i) q^{10} +(-1.29669 + 1.62599i) q^{11} +(-0.195705 - 2.61151i) q^{12} +(-1.55224 - 0.478804i) q^{13} +(-0.00162704 + 0.00110929i) q^{14} +(-2.32576 + 0.350552i) q^{15} +(-0.867096 + 3.79899i) q^{16} +(4.42356 + 4.10446i) q^{17} +(0.0123284 - 0.164511i) q^{18} +(2.78497 - 7.09598i) q^{19} +(3.49129 + 0.526227i) q^{20} +(-0.0178331 + 0.00858798i) q^{21} +(-0.246225 + 0.118576i) q^{22} +(5.24284 + 0.790231i) q^{23} +(0.252546 - 0.643476i) q^{24} +(-0.136680 + 1.82386i) q^{25} +(-0.156476 - 0.145189i) q^{26} +(1.25072 - 5.47974i) q^{27} +(0.0293806 - 0.00442841i) q^{28} +(-5.92981 + 4.04287i) q^{29} +(-0.295341 - 0.0911007i) q^{30} +(0.178251 + 2.37860i) q^{31} +(-0.971874 + 1.21869i) q^{32} +(-2.62490 + 0.809675i) q^{33} +(0.289703 + 0.738150i) q^{34} +(-0.00593807 - 0.0260164i) q^{35} +(-1.24460 + 2.15571i) q^{36} +(-2.52043 - 4.36551i) q^{37} +(0.734300 - 0.681331i) q^{38} +(-1.33773 - 1.67746i) q^{39} +(0.770022 + 0.524992i) q^{40} +(-3.20110 - 1.54157i) q^{41} -0.00260097 q^{42} +(-1.84169 - 6.29350i) q^{43} +4.12354 q^{44} +(2.01421 + 0.969991i) q^{45} +(0.575662 + 0.392479i) q^{46} +(-6.24911 - 7.83614i) q^{47} +(-3.77289 + 3.50073i) q^{48} +(3.49989 + 6.06198i) q^{49} +(-0.120170 + 0.208140i) q^{50} +(1.77358 + 7.77057i) q^{51} +(1.17668 + 2.99813i) q^{52} +(-6.55236 + 2.02113i) q^{53} +(0.460505 - 0.577454i) q^{54} +(-0.276759 - 3.69309i) q^{55} +(0.00749439 + 0.00231171i) q^{56} +(8.31899 - 5.67179i) q^{57} +(-0.932554 + 0.140560i) q^{58} +(0.370875 - 1.62491i) q^{59} +(3.41855 + 3.17195i) q^{60} +(-0.452207 + 6.03428i) q^{61} +(-0.114512 + 0.291773i) q^{62} +(0.0186034 + 0.00280400i) q^{63} +(6.83705 - 3.29255i) q^{64} +(2.60619 - 1.25507i) q^{65} +(-0.356934 - 0.0537992i) q^{66} +(0.523545 - 1.33397i) q^{67} +(0.894122 - 11.9312i) q^{68} +(5.13361 + 4.76329i) q^{69} +(0.000780301 - 0.00341872i) q^{70} +(6.96679 - 1.05007i) q^{71} +(-0.542873 + 0.370125i) q^{72} +(9.32817 + 2.87736i) q^{73} +(-0.0495013 - 0.660549i) q^{74} +(-1.50620 + 1.88871i) q^{75} +(-14.4427 + 4.45500i) q^{76} +(-0.0113862 - 0.0290116i) q^{77} +(-0.0627375 - 0.274871i) q^{78} +(-6.00573 + 10.4022i) q^{79} +(-3.46949 - 6.00933i) q^{80} +(2.68119 - 2.48778i) q^{81} +(-0.291096 - 0.365023i) q^{82} +(7.49232 + 5.10817i) q^{83} +(0.0353583 + 0.0170277i) q^{84} -10.7457 q^{85} +(0.140781 - 0.850113i) q^{86} -9.47935 q^{87} +(0.980650 + 0.472256i) q^{88} +(-13.1407 - 8.95920i) q^{89} +(0.183164 + 0.229681i) q^{90} +(0.0178445 - 0.0165573i) q^{91} +(-5.25628 - 9.10415i) q^{92} +(-1.57525 + 2.72842i) q^{93} +(-0.293074 - 1.28404i) q^{94} +(4.95929 + 12.6361i) q^{95} +(-1.96738 + 0.606856i) q^{96} +(8.44749 - 10.5928i) q^{97} +(0.0687380 + 0.917245i) q^{98} +(2.49496 + 0.769595i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9}+O(q^{10}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9	\( 36 q - 10 q^{2} - 16 q^{3} - 18 q^{4} - 17 q^{5} - 4 q^{6} + 6 q^{7} + 18 q^{8} - q^{9} - 7 q^{10} - 4 q^{11} + 2 q^{12} + 18 q^{14} - 3 q^{15} - 10 q^{16} - 10 q^{17} + 11 q^{18} + 10 q^{19} - 3 q^{20} - 21 q^{21} - 3 q^{22} + 4 q^{23} + 31 q^{24} - 2 q^{25} - 15 q^{26} - 4 q^{27} + 20 q^{28} + 9 q^{29} + 88 q^{30} + 40 q^{31} + 48 q^{32} - 11 q^{33} - 42 q^{34} + 11 q^{35} - 47 q^{36} - 19 q^{37} - 21 q^{38} - q^{39} - 97 q^{40} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 14 q^{44} - 46 q^{45} - 61 q^{46} - 30 q^{47} - 97 q^{48} + 6 q^{49} - 3 q^{50} + 57 q^{51} - 8 q^{52} - 24 q^{53} + 6 q^{54} + 14 q^{55} + 39 q^{56} + 52 q^{57} + 64 q^{58} - q^{59} + 111 q^{60} - 14 q^{61} + 33 q^{62} + 47 q^{63} + 48 q^{64} + 38 q^{65} + 79 q^{66} + 66 q^{67} + 66 q^{68} - 7 q^{69} + 47 q^{70} - 33 q^{71} + 26 q^{72} + 29 q^{73} - 40 q^{74} - 55 q^{75} - 39 q^{76} - 27 q^{77} - 126 q^{78} - 17 q^{79} + 8 q^{80} + 38 q^{81} - 54 q^{82} - 23 q^{83} - 155 q^{84} - 56 q^{85} - 45 q^{86} - 86 q^{87} - 17 q^{88} - 19 q^{89} - 127 q^{90} - 13 q^{91} - 18 q^{92} - 30 q^{93} + 44 q^{94} + q^{95} - 36 q^{96} - 31 q^{97} - 5 q^{98} - 31 q^{99}+O(q^{100}) \) 36 * q - 10 * q^2 - 16 * q^3 - 18 * q^4 - 17 * q^5 - 4 * q^6 + 6 * q^7 + 18 * q^8 - q^9 - 7 * q^10 - 4 * q^11 + 2 * q^12 + 18 * q^14 - 3 * q^15 - 10 * q^16 - 10 * q^17 + 11 * q^18 + 10 * q^19 - 3 * q^20 - 21 * q^21 - 3 * q^22 + 4 * q^23 + 31 * q^24 - 2 * q^25 - 15 * q^26 - 4 * q^27 + 20 * q^28 + 9 * q^29 + 88 * q^30 + 40 * q^31 + 48 * q^32 - 11 * q^33 - 42 * q^34 + 11 * q^35 - 47 * q^36 - 19 * q^37 - 21 * q^38 - q^39 - 97 * q^40 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 14 * q^44 - 46 * q^45 - 61 * q^46 - 30 * q^47 - 97 * q^48 + 6 * q^49 - 3 * q^50 + 57 * q^51 - 8 * q^52 - 24 * q^53 + 6 * q^54 + 14 * q^55 + 39 * q^56 + 52 * q^57 + 64 * q^58 - q^59 + 111 * q^60 - 14 * q^61 + 33 * q^62 + 47 * q^63 + 48 * q^64 + 38 * q^65 + 79 * q^66 + 66 * q^67 + 66 * q^68 - 7 * q^69 + 47 * q^70 - 33 * q^71 + 26 * q^72 + 29 * q^73 - 40 * q^74 - 55 * q^75 - 39 * q^76 - 27 * q^77 - 126 * q^78 - 17 * q^79 + 8 * q^80 + 38 * q^81 - 54 * q^82 - 23 * q^83 - 155 * q^84 - 56 * q^85 - 45 * q^86 - 86 * q^87 - 17 * q^88 - 19 * q^89 - 127 * q^90 - 13 * q^91 - 18 * q^92 - 30 * q^93 + 44 * q^94 + q^95 - 36 * q^96 - 31 * q^97 - 5 * q^98 - 31 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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