LMFDB - Embedded newform 289.2.h.a.115.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,2,Mod(4,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(68))

chi = DirichletCharacter(H, H._module([27]))

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

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

chi := DirichletCharacter("289.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	289.h (of order $68$, degree $32$, 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:	$2.30767661842$
Analytic rank:	$0$
Dimension:	$768$
Relative dimension:	$24$ over $\Q(\zeta_{68})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{68}]$

Embedding invariants

Embedding label			115.18
Character	$\chi$	$=$	289.115
Dual form			289.2.h.a.191.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.985664 - 1.08122i) q^{2} +(-0.197896 + 0.355292i) q^{3} +(-0.0129704 - 0.139973i) q^{4} +(-0.163469 + 1.17187i) q^{5} +(0.189090 + 0.564168i) q^{6} +(-0.426911 + 1.81511i) q^{7} +(2.17098 + 1.63945i) q^{8} +(1.49223 + 2.41003i) q^{9} +O(q^{10})$	\(q+(0.985664 - 1.08122i) q^{2} +(-0.197896 + 0.355292i) q^{3} +(-0.0129704 - 0.139973i) q^{4} +(-0.163469 + 1.17187i) q^{5} +(0.189090 + 0.564168i) q^{6} +(-0.426911 + 1.81511i) q^{7} +(2.17098 + 1.63945i) q^{8} +(1.49223 + 2.41003i) q^{9} +(1.10593 + 1.33182i) q^{10} +(-0.629677 - 0.522877i) q^{11} +(0.0522980 + 0.0230918i) q^{12} +(1.29970 - 1.72108i) q^{13} +(1.54175 + 2.25068i) q^{14} +(-0.384006 - 0.289988i) q^{15} +(4.18883 - 0.783027i) q^{16} +(-0.474450 - 4.09572i) q^{17} +(4.07661 + 0.762050i) q^{18} +(-3.58930 - 3.93728i) q^{19} +(0.166151 + 0.00768160i) q^{20} +(-0.560411 - 0.510882i) q^{21} +(-1.18600 + 0.165439i) q^{22} +(-0.346600 + 1.47365i) q^{23} +(-1.01211 + 0.446891i) q^{24} +(3.46257 + 0.985186i) q^{25} +(-0.579802 - 3.10166i) q^{26} +(-2.37033 + 0.109587i) q^{27} +(0.259604 + 0.0362132i) q^{28} +(-0.635545 + 0.765358i) q^{29} +(-0.692042 + 0.129365i) q^{30} +(1.44402 - 0.201432i) q^{31} +(0.417860 - 0.674867i) q^{32} +(0.310384 - 0.120244i) q^{33} +(-4.89603 - 3.52401i) q^{34} +(-2.05729 - 0.796999i) q^{35} +(0.317984 - 0.240130i) q^{36} +(-0.945619 - 2.14162i) q^{37} -7.79491 q^{38} +(0.354279 + 0.802366i) q^{39} +(-2.27611 + 2.27611i) q^{40} +(0.258606 + 0.144043i) q^{41} +(-1.10475 + 0.102370i) q^{42} +(0.913317 - 4.88582i) q^{43} +(-0.0650215 + 0.0949196i) q^{44} +(-3.06818 + 1.35473i) q^{45} +(1.25171 + 1.82728i) q^{46} +(-0.232760 - 0.144119i) q^{47} +(-0.550750 + 1.64321i) q^{48} +(3.15376 + 1.57039i) q^{49} +(4.47813 - 2.77274i) q^{50} +(1.54907 + 0.641959i) q^{51} +(-0.257762 - 0.159599i) q^{52} +(-3.71898 - 6.00636i) q^{53} +(-2.21786 + 2.67087i) q^{54} +(0.715677 - 0.652426i) q^{55} +(-3.90260 + 3.24068i) q^{56} +(2.10919 - 0.496077i) q^{57} +(0.201088 + 1.44155i) q^{58} +(0.927826 - 0.462002i) q^{59} +(-0.0356098 + 0.0575117i) q^{60} +(-2.67673 - 7.98627i) q^{61} +(1.20552 - 1.75985i) q^{62} +(-5.01152 + 1.67969i) q^{63} +(2.01455 + 7.08043i) q^{64} +(1.80442 + 1.80442i) q^{65} +(0.175925 - 0.454114i) q^{66} +(0.708941 - 0.646285i) q^{67} +(-0.567136 + 0.119533i) q^{68} +(-0.454986 - 0.414774i) q^{69} +(-2.88953 + 1.43882i) q^{70} +(-14.1971 - 3.33914i) q^{71} +(-0.711524 + 7.67857i) q^{72} +(0.928237 + 0.635857i) q^{73} +(-3.24763 - 1.08850i) q^{74} +(-1.03526 + 1.03526i) q^{75} +(-0.504557 + 0.553473i) q^{76} +(1.21790 - 0.919713i) q^{77} +(1.21674 + 0.407809i) q^{78} +(-0.126489 + 2.73591i) q^{79} +(0.232864 + 5.03677i) q^{80} +(-3.36033 + 6.74846i) q^{81} +(0.410641 - 0.137633i) q^{82} +(10.9563 + 3.11732i) q^{83} +(-0.0642409 + 0.0850687i) q^{84} +(4.87721 + 0.113529i) q^{85} +(-4.38243 - 5.80327i) q^{86} +(-0.146153 - 0.377265i) q^{87} +(-0.509787 - 2.16748i) q^{88} +(-3.25221 - 4.30662i) q^{89} +(-1.55942 + 4.65269i) q^{90} +(2.56910 + 3.09384i) q^{91} +(0.210767 + 0.0294007i) q^{92} +(-0.214199 + 0.552910i) q^{93} +(-0.385247 + 0.109612i) q^{94} +(5.20072 - 3.56258i) q^{95} +(0.157082 + 0.282016i) q^{96} +(11.0261 + 2.59331i) q^{97} +(4.80648 - 1.86204i) q^{98} +(0.320528 - 2.29779i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 768 q - 34 q^{2} - 34 q^{3} + 14 q^{4} - 34 q^{5} - 34 q^{6} - 34 q^{7} - 34 q^{8} - 34 q^{9}+O(q^{10}) $ 768 * q - 34 * q^2 - 34 * q^3 + 14 * q^4 - 34 * q^5 - 34 * q^6 - 34 * q^7 - 34 * q^8 - 34 * q^9	\( 768 q - 34 q^{2} - 34 q^{3} + 14 q^{4} - 34 q^{5} - 34 q^{6} - 34 q^{7} - 34 q^{8} - 34 q^{9} + 34 q^{10} - 34 q^{11} - 34 q^{12} - 30 q^{13} - 34 q^{14} - 34 q^{15} - 82 q^{16} - 34 q^{17} - 42 q^{18} - 34 q^{19} - 34 q^{20} - 26 q^{21} - 34 q^{22} - 34 q^{23} - 204 q^{24} + 170 q^{25} - 34 q^{26} - 34 q^{27} - 34 q^{28} - 34 q^{29} - 14 q^{30} - 34 q^{31} - 34 q^{32} + 56 q^{33} - 34 q^{34} - 42 q^{35} - 34 q^{36} - 34 q^{37} + 144 q^{38} - 170 q^{39} - 34 q^{40} - 34 q^{41} - 34 q^{42} - 34 q^{43} - 34 q^{44} - 34 q^{45} + 102 q^{46} - 30 q^{47} - 34 q^{48} - 34 q^{49} - 62 q^{50} + 238 q^{51} - 50 q^{52} + 136 q^{54} - 14 q^{55} - 34 q^{56} - 34 q^{57} - 34 q^{58} - 34 q^{59} - 34 q^{60} - 34 q^{61} - 238 q^{62} - 34 q^{63} + 38 q^{64} - 34 q^{65} + 476 q^{66} + 82 q^{67} - 34 q^{68} - 62 q^{69} - 34 q^{70} - 34 q^{71} + 10 q^{72} - 34 q^{73} - 34 q^{74} + 102 q^{75} - 102 q^{76} - 374 q^{77} - 34 q^{78} + 68 q^{79} - 34 q^{80} + 30 q^{81} - 34 q^{82} + 102 q^{83} - 82 q^{84} - 204 q^{85} - 62 q^{86} - 34 q^{87} + 170 q^{88} - 22 q^{89} - 34 q^{90} - 34 q^{91} + 34 q^{92} - 34 q^{93} + 238 q^{94} - 34 q^{95} + 544 q^{96} - 34 q^{97} + 10 q^{98} - 34 q^{99}+O(q^{100}) \) 768 * q - 34 * q^2 - 34 * q^3 + 14 * q^4 - 34 * q^5 - 34 * q^6 - 34 * q^7 - 34 * q^8 - 34 * q^9 + 34 * q^10 - 34 * q^11 - 34 * q^12 - 30 * q^13 - 34 * q^14 - 34 * q^15 - 82 * q^16 - 34 * q^17 - 42 * q^18 - 34 * q^19 - 34 * q^20 - 26 * q^21 - 34 * q^22 - 34 * q^23 - 204 * q^24 + 170 * q^25 - 34 * q^26 - 34 * q^27 - 34 * q^28 - 34 * q^29 - 14 * q^30 - 34 * q^31 - 34 * q^32 + 56 * q^33 - 34 * q^34 - 42 * q^35 - 34 * q^36 - 34 * q^37 + 144 * q^38 - 170 * q^39 - 34 * q^40 - 34 * q^41 - 34 * q^42 - 34 * q^43 - 34 * q^44 - 34 * q^45 + 102 * q^46 - 30 * q^47 - 34 * q^48 - 34 * q^49 - 62 * q^50 + 238 * q^51 - 50 * q^52 + 136 * q^54 - 14 * q^55 - 34 * q^56 - 34 * q^57 - 34 * q^58 - 34 * q^59 - 34 * q^60 - 34 * q^61 - 238 * q^62 - 34 * q^63 + 38 * q^64 - 34 * q^65 + 476 * q^66 + 82 * q^67 - 34 * q^68 - 62 * q^69 - 34 * q^70 - 34 * q^71 + 10 * q^72 - 34 * q^73 - 34 * q^74 + 102 * q^75 - 102 * q^76 - 374 * q^77 - 34 * q^78 + 68 * q^79 - 34 * q^80 + 30 * q^81 - 34 * q^82 + 102 * q^83 - 82 * q^84 - 204 * q^85 - 62 * q^86 - 34 * q^87 + 170 * q^88 - 22 * q^89 - 34 * q^90 - 34 * q^91 + 34 * q^92 - 34 * q^93 + 238 * q^94 - 34 * q^95 + 544 * q^96 - 34 * q^97 + 10 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{45}{68}\right)$

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 $

$2$	0.985664	−	1.08122i	0.696969	−	0.764539i	−0.283974	−	0.958832i	$-0.591653\pi$
$2$	0.985664	−	1.08122i	0.696969	−	0.764539i	0.980944	+	0.194293i	$0.0622412\pi$
$3$	−0.197896	+	0.355292i	−0.114255	+	0.205128i	−0.924709	−	0.380676i	$-0.875691\pi$
$3$	−0.197896	+	0.355292i	−0.114255	+	0.205128i	0.810453	+	0.585803i	$0.199221\pi$
$4$	−0.0129704	−	0.139973i	−0.00648520	−	0.0699865i
$5$	−0.163469	+	1.17187i	−0.0731056	+	0.524077i	0.918564	+	0.395272i	$0.129350\pi$
$5$	−0.163469	+	1.17187i	−0.0731056	+	0.524077i	−0.991670	+	0.128805i	$0.958886\pi$
$6$	0.189090	+	0.564168i	0.0771956	+	0.230320i
$7$	−0.426911	+	1.81511i	−0.161357	+	0.686048i	0.830319	+	0.557289i	$0.188158\pi$
$7$	−0.426911	+	1.81511i	−0.161357	+	0.686048i	−0.991676	+	0.128760i	$0.958900\pi$
$8$	2.17098	+	1.63945i	0.767558	+	0.579633i
$9$	1.49223	+	2.41003i	0.497409	+	0.803343i
$10$	1.10593	+	1.33182i	0.349725	+	0.421158i
$11$	−0.629677	−	0.522877i	−0.189855	−	0.157653i	0.539038	−	0.842282i	$-0.318788\pi$
$11$	−0.629677	−	0.522877i	−0.189855	−	0.157653i	−0.728892	+	0.684628i	$0.759965\pi$
$12$	0.0522980	+	0.0230918i	0.0150971	+	0.00666604i
$13$	1.29970	−	1.72108i	0.360471	−	0.477341i	−0.581255	−	0.813722i	$-0.697438\pi$
$13$	1.29970	−	1.72108i	0.360471	−	0.477341i	0.941726	+	0.336380i	$0.109203\pi$
$14$	1.54175	+	2.25068i	0.412050	+	0.601518i
$15$	−0.384006	−	0.289988i	−0.0991500	−	0.0748746i
$16$	4.18883	−	0.783027i	1.04721	−	0.195757i
$17$	−0.474450	−	4.09572i	−0.115071	−	0.993357i
$17$	−0.474450	−	4.09572i	−0.115071	−	0.993357i
$18$	4.07661	+	0.762050i	0.960866	+	0.179617i
$19$	−3.58930	−	3.93728i	−0.823442	−	0.903273i	0.173222	−	0.984883i	$-0.444582\pi$
$19$	−3.58930	−	3.93728i	−0.823442	−	0.903273i	−0.996664	+	0.0816099i	$0.973994\pi$
$20$	0.166151	+	0.00768160i	0.0371524	+	0.00171766i
$21$	−0.560411	−	0.510882i	−0.122292	−	0.111484i
$22$	−1.18600	+	0.165439i	−0.252855	+	0.0352718i
$23$	−0.346600	+	1.47365i	−0.0722711	+	0.307278i	−0.997373	−	0.0724420i	$-0.976921\pi$
$23$	−0.346600	+	1.47365i	−0.0722711	+	0.307278i	0.925102	+	0.379720i	$0.123980\pi$
$24$	−1.01211	+	0.446891i	−0.206597	+	0.0912213i
$25$	3.46257	+	0.985186i	0.692514	+	0.197037i
$26$	−0.579802	−	3.10166i	−0.113708	−	0.608286i
$27$	−2.37033	+	0.109587i	−0.456170	+	0.0210900i
$28$	0.259604	+	0.0362132i	0.0490605	+	0.00684365i
$29$	−0.635545	+	0.765358i	−0.118018	+	0.142123i	−0.825054	−	0.565054i	$-0.808855\pi$
$29$	−0.635545	+	0.765358i	−0.118018	+	0.142123i	0.707036	+	0.707177i	$0.250032\pi$
$30$	−0.692042	+	0.129365i	−0.126349	+	0.0236187i
$31$	1.44402	−	0.201432i	0.259353	−	0.0361782i	−0.00729037	−	0.999973i	$-0.502321\pi$
$31$	1.44402	−	0.201432i	0.259353	−	0.0361782i	0.266644	+	0.963795i	$0.414085\pi$
$32$	0.417860	−	0.674867i	0.0738679	−	0.119301i
$33$	0.310384	−	0.120244i	0.0540310	−	0.0209317i
$34$	−4.89603	−	3.52401i	−0.839661	−	0.604363i
$35$	−2.05729	−	0.796999i	−0.347746	−	0.134717i
$36$	0.317984	−	0.240130i	0.0529974	−	0.0400217i
$37$	−0.945619	−	2.14162i	−0.155459	−	0.352081i	0.819966	−	0.572412i	$-0.193992\pi$
$37$	−0.945619	−	2.14162i	−0.155459	−	0.352081i	−0.975425	+	0.220331i	$0.929286\pi$
$38$	−7.79491			−1.26450
$39$	0.354279	+	0.802366i	0.0567301	+	0.128481i
$40$	−2.27611	+	2.27611i	−0.359885	+	0.359885i
$41$	0.258606	+	0.144043i	0.0403875	+	0.0224957i	0.506668	−	0.862141i	$-0.330877\pi$
$41$	0.258606	+	0.144043i	0.0403875	+	0.0224957i	−0.466281	+	0.884637i	$0.654406\pi$
$42$	−1.10475	+	0.102370i	−0.170467	+	0.0157961i
$43$	0.913317	−	4.88582i	0.139280	−	0.745080i	−0.840003	−	0.542582i	$-0.817447\pi$
$43$	0.913317	−	4.88582i	0.139280	−	0.745080i	0.979283	−	0.202498i	$-0.0649060\pi$
$44$	−0.0650215	+	0.0949196i	−0.00980235	+	0.0143097i
$45$	−3.06818	+	1.35473i	−0.457377	+	0.201952i
$46$	1.25171	+	1.82728i	0.184555	+	0.269417i
$47$	−0.232760	−	0.144119i	−0.0339515	−	0.0210219i	0.509351	−	0.860559i	$-0.329885\pi$
$47$	−0.232760	−	0.144119i	−0.0339515	−	0.0210219i	−0.543303	+	0.839537i	$0.682827\pi$
$48$	−0.550750	+	1.64321i	−0.0794938	+	0.237177i
$49$	3.15376	+	1.57039i	0.450537	+	0.224341i
$50$	4.47813	−	2.77274i	0.633303	−	0.392125i
$51$	1.54907	+	0.641959i	0.216913	+	0.0898922i
$52$	−0.257762	−	0.159599i	−0.0357451	−	0.0221325i
$53$	−3.71898	−	6.00636i	−0.510841	−	0.825037i	0.488016	−	0.872835i	$-0.337721\pi$
$53$	−3.71898	−	6.00636i	−0.510841	−	0.825037i	−0.998857	+	0.0477977i	$0.984780\pi$
$54$	−2.21786	+	2.67087i	−0.301813	+	0.363459i
$55$	0.715677	−	0.652426i	0.0965019	−	0.0879731i
$56$	−3.90260	+	3.24068i	−0.521507	+	0.433054i
$57$	2.10919	−	0.496077i	0.279369	−	0.0657070i
$58$	0.201088	+	1.44155i	0.0264041	+	0.189285i
$59$	0.927826	−	0.462002i	0.120793	−	0.0601476i	−0.384326	−	0.923197i	$-0.625566\pi$
$59$	0.927826	−	0.462002i	0.120793	−	0.0601476i	0.505119	+	0.863050i	$0.331449\pi$
$60$	−0.0356098	+	0.0575117i	−0.00459720	+	0.00742473i
$61$	−2.67673	−	7.98627i	−0.342720	−	1.02254i	−0.969867	−	0.243636i	$-0.921660\pi$
$61$	−2.67673	−	7.98627i	−0.342720	−	1.02254i	0.627147	−	0.778901i	$-0.284222\pi$
$62$	1.20552	−	1.75985i	0.153102	−	0.223501i
$63$	−5.01152	+	1.67969i	−0.631393	+	0.211622i
$64$	2.01455	+	7.08043i	0.251819	+	0.885053i
$65$	1.80442	+	1.80442i	0.223811	+	0.223811i
$66$	0.175925	−	0.454114i	0.0216548	−	0.0558976i
$67$	0.708941	−	0.646285i	0.0866110	−	0.0789563i	−0.629232	−	0.777217i	$-0.716631\pi$
$67$	0.708941	−	0.646285i	0.0866110	−	0.0789563i	0.715843	+	0.698261i	$0.246042\pi$
$68$	−0.567136	+	0.119533i	−0.0687753	+	0.0144955i
$69$	−0.454986	−	0.414774i	−0.0547738	−	0.0499329i
$70$	−2.88953	+	1.43882i	−0.345365	+	0.171971i
$71$	−14.1971	−	3.33914i	−1.68489	−	0.396283i	−0.727735	−	0.685858i	$-0.759427\pi$
$71$	−14.1971	−	3.33914i	−1.68489	−	0.396283i	−0.957155	+	0.289576i	$0.906486\pi$
$72$	−0.711524	+	7.67857i	−0.0838539	+	0.904928i
$73$	0.928237	+	0.635857i	0.108642	+	0.0744215i	0.618231	−	0.785996i	$-0.287850\pi$
$73$	0.928237	+	0.635857i	0.108642	+	0.0744215i	−0.509589	+	0.860418i	$0.670203\pi$
$74$	−3.24763	−	1.08850i	−0.377530	−	0.126535i
$75$	−1.03526	+	1.03526i	−0.119541	+	0.119541i
$76$	−0.504557	+	0.553473i	−0.0578767	+	0.0634877i
$77$	1.21790	−	0.919713i	0.138792	−	0.104811i
$78$	1.21674	+	0.407809i	0.137768	+	0.0461753i
$79$	−0.126489	+	2.73591i	−0.0142311	+	0.307814i	0.979890	+	0.199539i	$0.0639445\pi$
$79$	−0.126489	+	2.73591i	−0.0142311	+	0.307814i	−0.994121	+	0.108275i	$0.965467\pi$
$80$	0.232864	+	5.03677i	0.0260350	+	0.563128i
$81$	−3.36033	+	6.74846i	−0.373370	+	0.749829i
$82$	0.410641	−	0.137633i	0.0453477	−	0.0151990i
$83$	10.9563	+	3.11732i	1.20261	+	0.342171i	0.814894	−	0.579610i	$-0.196795\pi$
$83$	10.9563	+	3.11732i	1.20261	+	0.342171i	0.387712	+	0.921781i	$0.373266\pi$
$84$	−0.0642409	+	0.0850687i	−0.00700925	+	0.00928175i
$85$	4.87721	+	0.113529i	0.529008	+	0.0123139i
$86$	−4.38243	−	5.80327i	−0.472569	−	0.625783i
$87$	−0.146153	−	0.377265i	−0.0156693	−	0.0404471i
$88$	−0.509787	−	2.16748i	−0.0543435	−	0.231054i
$89$	−3.25221	−	4.30662i	−0.344733	−	0.456500i	0.592312	−	0.805709i	$-0.298215\pi$
$89$	−3.25221	−	4.30662i	−0.344733	−	0.456500i	−0.937045	+	0.349208i	$0.886451\pi$
$90$	−1.55942	+	4.65269i	−0.164378	+	0.490437i
$91$	2.56910	+	3.09384i	0.269314	+	0.324323i
$92$	0.210767	+	0.0294007i	0.0219740	+	0.00306524i
$93$	−0.214199	+	0.552910i	−0.0222114	+	0.0573341i
$94$	−0.385247	+	0.109612i	−0.0397352	+	0.0113056i
$95$	5.20072	−	3.56258i	0.533583	−	0.365513i
$96$	0.157082	+	0.282016i	0.0160321	+	0.0287831i
$97$	11.0261	+	2.59331i	1.11953	+	0.263311i	0.747075	−	0.664739i	$-0.231457\pi$
$97$	11.0261	+	2.59331i	1.11953	+	0.263311i	0.372455	+	0.928050i	$0.378516\pi$
$98$	4.80648	−	1.86204i	0.485528	−	0.188095i
$99$	0.320528	−	2.29779i	0.0322143	−	0.230937i
$100$	0.0929884	−	0.497444i	0.00929884	−	0.0497444i
$101$	3.16733	−	6.36085i	0.315161	−	0.632929i	−0.679777	−	0.733419i	$-0.737923\pi$
$101$	3.16733	−	6.36085i	0.315161	−	0.632929i	0.994938	+	0.100490i	$0.0320411\pi$
$102$	2.22096	−	1.04213i	0.219908	−	0.103186i
$103$	−4.08682	−	8.20744i	−0.402686	−	0.808703i	−0.999978	−	0.00667850i	$-0.997874\pi$
$103$	−4.08682	−	8.20744i	−0.402686	−	0.808703i	0.597292	−	0.802024i	$-0.296243\pi$
$104$	5.64324	−	1.60564i	0.553366	−	0.157446i
$105$	0.690297	−	0.573216i	0.0673661	−	0.0559401i
$106$	−10.1599	−	1.89921i	−0.986814	−	0.184468i
$107$	−17.9580	−	0.830251i	−1.73607	−	0.0802633i	−0.845180	−	0.534482i	$-0.820507\pi$
$107$	−17.9580	−	0.830251i	−1.73607	−	0.0802633i	−0.890890	+	0.454219i	$0.849918\pi$
$108$	0.0460834	+	0.330361i	0.00443437	+	0.0317890i
$109$	9.38885	+	16.8562i	0.899289	+	1.61453i	0.783616	+	0.621245i	$0.213373\pi$
$109$	9.38885	+	16.8562i	0.899289	+	1.61453i	0.115673	+	0.993287i	$0.463098\pi$
$110$		−	1.41688i		−	0.135094i
$111$	0.948035	+	0.0878484i	0.0899835	+	0.00833820i
$112$	−0.366972	+	7.93748i	−0.0346756	+	0.750021i
$113$	0.281995	+	0.157070i	0.0265279	+	0.0147759i	0.499812	−	0.866134i	$-0.333402\pi$
$113$	0.281995	+	0.157070i	0.0265279	+	0.0147759i	−0.473284	+	0.880910i	$0.656932\pi$
$114$	1.54258	−	2.76947i	0.144476	−	0.259384i
$115$	−1.67027	−	0.647067i	−0.155754	−	0.0603393i
$116$	0.115373	+	0.0790321i	0.0107121	+	0.00733795i
$117$	6.08729	+	0.564071i	0.562770	+	0.0521484i
$118$	0.414997	−	1.45856i	0.0382036	−	0.134272i
$119$	7.63674	+	0.887325i	0.700059	+	0.0813410i
$120$	−0.358250	−	1.25912i	−0.0327036	−	0.114941i
$121$	−1.89815	−	10.1542i	−0.172559	−	0.923111i
$122$	−11.2733	−	4.97764i	−1.02063	−	0.450654i
$123$	−0.102354	+	0.0633752i	−0.00922899	+	0.00571435i
$124$	−0.0469245	−	0.199511i	−0.00421395	−	0.0179166i
$125$	−4.11017	+	9.30864i	−0.367624	+	0.832590i
$126$	−3.12356	+	7.07418i	−0.278269	+	0.630218i
$127$	3.92274	+	10.1258i	0.348087	+	0.898516i	0.991155	+	0.132707i	$0.0423669\pi$
$127$	3.92274	+	10.1258i	0.348087	+	0.898516i	−0.643068	+	0.765809i	$0.722339\pi$
$128$	11.0623	+	5.50836i	0.977776	+	0.486874i
$129$	1.55515	+	1.29138i	0.136923	+	0.113700i
$130$	3.72953	−	0.172427i	0.327102	−	0.0151228i
$131$	−8.53023	−	8.53023i	−0.745290	−	0.745290i	0.228301	−	0.973591i	$-0.426683\pi$
$131$	−8.53023	−	8.53023i	−0.745290	−	0.745290i	−0.973591	+	0.228301i	$0.926683\pi$
$132$	−0.0208567	−	0.0418858i	−0.00181534	−	0.00364569i
$133$	8.67891	−	4.83412i	0.752557	−	0.419172i
$134$		−	1.40354i		−	0.121248i
$135$	0.259054	−	2.79564i	0.0222958	−	0.240610i
$136$	5.68470	−	9.66957i	0.487459	−	0.829159i
$137$	−1.71204	−	18.4758i	−0.146269	−	1.57850i	−0.680237	−	0.732992i	$-0.738123\pi$
$137$	−1.71204	−	18.4758i	−0.146269	−	1.57850i	0.533968	−	0.845505i	$-0.320700\pi$
$138$	−0.896926	+	0.0831124i	−0.0763514	+	0.00707500i
$139$	−0.616469	−	13.3340i	−0.0522883	−	1.13098i	−0.849606	−	0.527418i	$-0.823160\pi$
$139$	−0.616469	−	13.3340i	−0.0522883	−	1.13098i	0.797318	−	0.603560i	$-0.206252\pi$
$140$	−0.0848744	+	0.298303i	−0.00717320	+	0.0252112i
$141$	0.0972665	−	0.0541771i	0.00819132	−	0.00456253i
$142$	−17.6039	+	12.0590i	−1.47729	+	1.01197i
$143$	−1.71830	+	0.404141i	−0.143692	+	0.0337959i
$144$	8.13780	+	8.92674i	0.678150	+	0.743895i
$145$	−0.793009	−	0.869890i	−0.0658558	−	0.0722404i
$146$	1.60243	−	0.376889i	0.132618	−	0.0311915i
$147$	−1.18206	+	0.809731i	−0.0974948	+	0.0667855i
$148$	−0.287504	+	0.160139i	−0.0236327	+	0.0131633i
$149$	−2.07295	+	7.28567i	−0.169823	+	0.596865i	0.829444	+	0.558589i	$0.188657\pi$
$149$	−2.07295	+	7.28567i	−0.169823	+	0.596865i	−0.999267	+	0.0382761i	$0.987813\pi$
$150$	0.0989270	+	2.13976i	0.00807735	+	0.174710i
$151$	11.5429	−	1.06961i	0.939349	−	0.0870435i	0.388315	−	0.921527i	$-0.373057\pi$
$151$	11.5429	−	1.06961i	0.939349	−	0.0870435i	0.551033	+	0.834483i	$0.314234\pi$
$152$	−1.33734	−	14.4322i	−0.108473	−	1.17061i
$153$	9.16281	−	7.25518i	0.740769	−	0.586546i
$154$	0.206023	−	2.22334i	0.0166018	−	0.179162i
$155$			1.72513i			0.138566i
$156$	0.107714	−	0.0599965i	0.00862406	−	0.00480357i
$157$	1.43508	+	2.88203i	0.114532	+	0.230011i	0.945011	−	0.327039i	$-0.106051\pi$
$157$	1.43508	+	2.88203i	0.114532	+	0.230011i	−0.830479	+	0.557050i	$0.811933\pi$
$158$	2.83345	+	2.83345i	0.225417	+	0.225417i
$159$	2.86998	−	0.132687i	0.227604	−	0.0105228i
$160$	0.722550	+	0.599998i	0.0571226	+	0.0474340i
$161$	−2.52688	−	1.25824i	−0.199146	−	0.0991629i
$162$	3.98442	+	10.2850i	0.313046	+	0.808064i
$163$	1.48489	−	3.36295i	0.116305	−	0.263406i	−0.847111	−	0.531416i	$-0.821660\pi$
$163$	1.48489	−	3.36295i	0.116305	−	0.263406i	0.963416	+	0.268010i	$0.0863660\pi$
$164$	0.0168079	−	0.0380662i	0.00131247	−	0.00297247i
$165$	0.0901717	+	0.383387i	0.00701986	+	0.0298466i
$166$	14.1697	−	8.77351i	1.09978	−	0.680956i
$167$	3.26041	+	1.43961i	0.252298	+	0.111401i	0.526211	−	0.850354i	$-0.323612\pi$
$167$	3.26041	+	1.43961i	0.252298	+	0.111401i	−0.273913	+	0.961755i	$0.588318\pi$
$168$	−0.379077	−	2.02788i	−0.0292464	−	0.156454i
$169$	2.28472	+	8.02997i	0.175748	+	0.617690i
$170$	4.93004	−	5.16144i	0.378117	−	0.395865i
$171$	4.13290	−	14.5256i	0.316051	−	1.11080i
$172$	−0.695728	−	0.0644687i	−0.0530488	−	0.00491569i
$173$	1.78873	+	1.22531i	0.135994	+	0.0931583i	0.631211	−	0.775611i	$-0.282558\pi$
$173$	1.78873	+	1.22531i	0.135994	+	0.0931583i	−0.495216	+	0.868770i	$0.664911\pi$
$174$	−0.551965	−	0.213833i	−0.0418444	−	0.0162106i
$175$	−3.26643	+	5.86437i	−0.246919	+	0.443304i
$176$	−3.04703	−	1.69719i	−0.229679	−	0.127930i
$177$	−0.0194676	+	0.421077i	−0.00146327	+	0.0316501i
$178$	−7.86199	−	0.728520i	−0.589281	−	0.0546049i
$179$			17.9563i			1.34212i	0.741403	+	0.671060i	$0.234161\pi$
$179$			17.9563i			1.34212i	−0.741403	+	0.671060i	$0.765839\pi$
$180$	0.229421	+	0.411890i	0.0171001	+	0.0307005i
$181$	1.40727	+	10.0884i	0.104602	+	0.749866i	0.969000	+	0.247059i	$0.0794642\pi$
$181$	1.40727	+	10.0884i	0.104602	+	0.749866i	−0.864399	+	0.502807i	$0.832301\pi$
$182$	5.87740	+	0.271728i	0.435662	+	0.0201418i
$183$	3.36717	+	0.629433i	0.248908	+	0.0465290i
$184$	−3.16844	+	2.63104i	−0.233581	+	0.193963i
$185$	2.66429	−	0.758055i	0.195882	−	0.0557333i
$186$	0.386691	+	0.776579i	0.0283535	+	0.0569416i
$187$	−1.84281	+	2.82706i	−0.134759	+	0.206735i
$188$	−0.0171537	+	0.0344494i	−0.00125107	+	0.00251248i
$189$	0.813007	−	4.34920i	0.0591376	−	0.316358i
$190$	1.27423	−	9.13463i	0.0924421	−	0.662696i
$191$	−24.5133	+	9.49648i	−1.77372	+	0.687141i	−0.775258	+	0.631645i	$0.782380\pi$
$191$	−24.5133	+	9.49648i	−1.77372	+	0.687141i	−0.998459	+	0.0554964i	$0.982326\pi$
$192$	−2.91429	−	0.685435i	−0.210321	−	0.0494670i
$193$	9.27780	+	16.6568i	0.667831	+	1.19899i	0.969387	+	0.245537i	$0.0789644\pi$
$193$	9.27780	+	16.6568i	0.667831	+	1.19899i	−0.301556	+	0.953448i	$0.597506\pi$
$194$	13.6720	−	9.36551i	0.981590	−	0.672405i
$195$	−0.998184	+	0.284008i	−0.0714814	+	0.0203382i
$196$	0.178906	−	0.461810i	0.0127790	−	0.0329864i
$197$	11.0139	+	1.53637i	0.784706	+	0.109462i	0.519206	−	0.854649i	$-0.326228\pi$
$197$	11.0139	+	1.53637i	0.784706	+	0.109462i	0.265500	+	0.964111i	$0.414463\pi$
$198$	−2.16849	−	2.61141i	−0.154108	−	0.185585i
$199$	−3.28209	+	9.79241i	−0.232661	+	0.694166i	0.766020	+	0.642817i	$0.222234\pi$
$199$	−3.28209	+	9.79241i	−0.232661	+	0.694166i	−0.998681	+	0.0513488i	$0.983648\pi$
$200$	5.90201	+	7.81553i	0.417335	+	0.552641i
$201$	0.0893231	+	0.379778i	0.00630036	+	0.0267875i
$202$	−3.75557	−	9.69424i	−0.264241	−	0.682085i
$203$	−1.11789	−	1.48033i	−0.0784605	−	0.103899i
$204$	0.0697648	−	0.225154i	0.00488451	−	0.0157639i
$205$	−0.211074	+	0.279507i	−0.0147420	+	0.0195216i
$206$	−12.9023	−	3.67102i	−0.898945	−	0.255772i
$207$	−4.06875	+	1.36371i	−0.282798	+	0.0947843i
$208$	4.09656	−	8.22699i	0.284045	−	0.570439i
$209$	0.201389	+	4.35597i	0.0139304	+	0.301309i
$210$	0.0606279	−	1.31136i	0.00418373	−	0.0904926i
$211$	−5.48416	−	1.83811i	−0.377545	−	0.126540i	0.122657	−	0.992449i	$-0.460859\pi$
$211$	−5.48416	−	1.83811i	−0.377545	−	0.126540i	−0.500202	+	0.865909i	$0.666741\pi$
$212$	−0.792491	+	0.598462i	−0.0544285	+	0.0411025i
$213$	3.99593	−	4.38332i	0.273796	−	0.300340i
$214$	−18.5983	+	18.5983i	−1.27135	+	1.27135i
$215$	5.57625	+	1.86897i	0.380297	+	0.127463i
$216$	−5.32561	−	3.64813i	−0.362362	−	0.248224i
$217$	−0.250845	+	2.70705i	−0.0170285	+	0.183766i
$218$	27.4796	+	6.46313i	1.86115	+	0.437739i
$219$	−0.409609	+	0.203961i	−0.0276788	+	0.0137824i
$220$	−0.100605	−	0.0917132i	−0.00678276	−	0.00618330i
$221$	−7.66569	−	4.50663i	−0.515650	−	0.303149i
$222$	1.02943	−	0.938447i	0.0690907	−	0.0629845i
$223$	−4.84493	+	12.5062i	−0.324441	+	0.837478i	0.670944	+	0.741508i	$0.265889\pi$
$223$	−4.84493	+	12.5062i	−0.324441	+	0.837478i	−0.995384	+	0.0959694i	$0.969405\pi$
$224$	1.04657	+	1.04657i	0.0699270	+	0.0699270i
$225$	2.79261	+	9.81501i	0.186174	+	0.654334i
$226$	0.447780	−	0.150081i	0.0297859	−	0.00998323i
$227$	1.87544	−	2.73780i	0.124477	−	0.181714i	−0.757741	−	0.652556i	$-0.773697\pi$
$227$	1.87544	−	2.73780i	0.124477	−	0.181714i	0.882218	+	0.470842i	$0.156050\pi$
$228$	−0.0967944	−	0.288795i	−0.00641036	−	0.0191259i
$229$	0.0724145	−	0.116953i	0.00478529	−	0.00772850i	−0.847816	−	0.530291i	$-0.822083\pi$
$229$	0.0724145	−	0.116953i	0.00478529	−	0.00772850i	0.852601	+	0.522562i	$0.175024\pi$
$230$	−2.34595	+	1.16814i	−0.154687	+	0.0770252i
$231$	0.0857492	+	0.614716i	0.00564189	+	0.0404454i
$232$	−2.63452	+	0.619634i	−0.172965	+	0.0406810i
$233$	6.21494	−	5.16082i	0.407154	−	0.338096i	−0.412498	−	0.910959i	$-0.635343\pi$
$233$	6.21494	−	5.16082i	0.407154	−	0.338096i	0.819652	+	0.572862i	$0.194167\pi$
$234$	6.60991	−	6.02573i	0.432103	−	0.393914i
$235$	0.206938	−	0.249206i	0.0134991	−	0.0162564i
$236$	−0.0767021	−	0.123878i	−0.00499288	−	0.00806378i
$237$	−0.947015	−	0.586367i	−0.0615152	−	0.0380886i
$238$	8.48665	−	7.38240i	0.550108	−	0.478530i
$239$	−10.4138	+	6.44792i	−0.673610	+	0.417081i	−0.820170	−	0.572120i	$-0.806121\pi$
$239$	−10.4138	+	6.44792i	−0.673610	+	0.417081i	0.146560	+	0.989202i	$0.453180\pi$
$240$	−1.83560	−	0.914022i	−0.118488	−	0.0589999i
$241$	−5.64504	+	16.8425i	−0.363629	+	1.08492i	0.595839	+	0.803104i	$0.296820\pi$
$241$	−5.64504	+	16.8425i	−0.363629	+	1.08492i	−0.959468	+	0.281817i	$0.909063\pi$
$242$	−12.8499	−	7.95632i	−0.826023	−	0.511452i
$243$	−5.75565	−	8.40221i	−0.369225	−	0.539002i
$244$	−1.08314	+	0.478254i	−0.0693411	+	0.0306171i
$245$	−2.35583	+	3.43909i	−0.150509	+	0.219715i
$246$	−0.0323644	+	0.173134i	−0.00206348	+	0.0110386i
$247$	−11.4414	+	1.06020i	−0.727996	+	0.0674588i
$248$	3.46518	+	1.93009i	0.220039	+	0.122561i
$249$	−3.27576	+	3.27576i	−0.207593	+	0.207593i
$250$	6.01346	+	13.6192i	0.380325	+	0.861353i
$251$	−12.5955			−0.795023			−0.397511	−	0.917597i	$-0.630126\pi$
$251$	−12.5955			−0.795023			−0.397511	+	0.917597i	$0.630126\pi$
$252$	0.300113	+	0.679692i	0.0189054	+	0.0428165i
$253$	0.988785	−	0.746696i	0.0621644	−	0.0469444i
$254$	14.8147	+	5.73924i	0.929556	+	0.360112i
$255$	−1.00552	+	1.71037i	−0.0629679	+	0.107107i
$256$	3.13074	−	1.21286i	0.195671	−	0.0758035i
$257$	1.24428	−	2.00957i	0.0776158	−	0.125354i	−0.809096	−	0.587677i	$-0.800043\pi$
$257$	1.24428	−	2.00957i	0.0776158	−	0.125354i	0.886712	+	0.462323i	$0.152984\pi$
$258$	2.92912	−	0.408595i	0.182359	−	0.0254380i
$259$	4.29098	−	0.802124i	0.266629	−	0.0498416i
$260$	0.229166	−	0.275974i	0.0142123	−	0.0171152i
$261$	−2.79291	−	0.389595i	−0.172877	−	0.0241153i
$262$	−17.6310	+	0.815131i	−1.08925	+	0.0503589i
$263$	−0.514643	−	2.75309i	−0.0317342	−	0.169763i	0.963434	−	0.267945i	$-0.0863445\pi$
$263$	−0.514643	−	2.75309i	−0.0317342	−	0.169763i	−0.995169	+	0.0981816i	$0.968697\pi$
$264$	0.870973	+	0.247813i	0.0536047	+	0.0152518i
$265$	7.64662	−	3.37631i	0.469728	−	0.207405i
$266$	3.32773	−	14.1486i	0.204036	−	0.867509i
$267$	2.17370	−	0.303219i	0.133029	−	0.0185567i
$268$	−0.0996577	−	0.0908500i	−0.00608756	−	0.00554955i
$269$	−5.22377	−	0.241510i	−0.318499	−	0.0147251i	−0.113657	−	0.993520i	$-0.536256\pi$
$269$	−5.22377	−	0.241510i	−0.318499	−	0.0147251i	−0.204842	+	0.978795i	$0.565668\pi$
$270$	−2.76736	−	3.03565i	−0.168416	−	0.184744i
$271$	−1.04966	−	0.196215i	−0.0637622	−	0.0119192i	0.151772	−	0.988416i	$-0.451502\pi$
$271$	−1.04966	−	0.196215i	−0.0637622	−	0.0119192i	−0.215534	+	0.976496i	$0.569149\pi$
$272$	−5.19445	−	16.7847i	−0.314960	−	1.01772i
$273$	−1.60763	+	0.300518i	−0.0972983	+	0.0181882i
$274$	−21.6640	−	16.3599i	−1.30877	−	0.988336i
$275$	−1.66517	−	2.43085i	−0.100413	−	0.146586i
$276$	−0.0521558	+	0.0690655i	−0.00313941	+	0.00415725i
$277$	−0.218369	−	0.0964192i	−0.0131205	−	0.00579327i	0.397350	−	0.917667i	$-0.369930\pi$
$277$	−0.218369	−	0.0964192i	−0.0131205	−	0.00579327i	−0.410471	+	0.911874i	$0.634636\pi$
$278$	−15.0247	−	12.4763i	−0.901120	−	0.748280i
$279$	2.64026	+	3.17954i	0.158068	+	0.190354i
$280$	−3.15971	−	5.10310i	−0.188829	−	0.304969i
$281$	−15.2887	−	11.5455i	−0.912047	−	0.688746i	0.0385228	−	0.999258i	$-0.487735\pi$
$281$	−15.2887	−	11.5455i	−0.912047	−	0.688746i	−0.950569	+	0.310512i	$0.899499\pi$
$282$	0.0372946	−	0.158567i	0.00222086	−	0.00944253i
$283$	1.50408	+	4.48758i	0.0894085	+	0.266759i	0.983437	−	0.181252i	$-0.0580150\pi$
$283$	1.50408	+	4.48758i	0.0894085	+	0.266759i	−0.894028	+	0.448011i	$0.852133\pi$
$284$	−0.283246	+	2.03052i	−0.0168076	+	0.120489i
$285$	0.236551	+	2.55279i	0.0140121	+	0.151214i
$286$	−1.25670	+	2.25621i	−0.0743103	+	0.133413i
$287$	−0.371856	+	0.407906i	−0.0219500	+	0.0240780i
$288$	2.24999			0.132582
$289$	−16.5498	+	3.88642i	−0.973517	+	0.228613i
$290$	−1.72218			−0.101130
$291$	−3.10340	+	3.40427i	−0.181925	+	0.199562i
$292$	0.0769632	−	0.138175i	0.00450393	−	0.00808610i
$293$	−2.14282	−	23.1248i	−0.125185	−	1.35096i	−0.794174	−	0.607690i	$-0.792096\pi$
$293$	−2.14282	−	23.1248i	−0.125185	−	1.35096i	0.668989	−	0.743272i	$-0.266727\pi$
$294$	−0.289617	+	2.07619i	−0.0168908	+	0.121086i
$295$	0.389736	+	1.16282i	0.0226913	+	0.0677017i
$296$	1.45816	−	6.19973i	0.0847540	−	0.360352i
$297$	1.54984	+	1.17039i	0.0899310	+	0.0679128i
$298$	5.83419	+	9.42254i	0.337966	+	0.545833i
$299$	2.08580	+	2.51183i	0.120625	+	0.145263i
$300$	0.158336	+	0.131480i	0.00914151	+	0.00759102i
$301$	8.47840	+	3.74358i	0.488687	+	0.215776i
$302$	10.2209	−	13.5347i	0.588149	−	0.778835i
$303$	1.63316	+	2.38411i	0.0938223	+	0.136964i
$304$	−18.1180	−	13.6820i	−1.03914	−	0.784719i
$305$	9.79644	−	1.83127i	0.560942	−	0.104858i
$306$	1.18700	−	17.0582i	0.0678560	−	0.975152i
$307$	−0.846961	−	0.158324i	−0.0483386	−	0.00903606i	0.159525	−	0.987194i	$-0.449004\pi$
$307$	−0.846961	−	0.158324i	−0.0483386	−	0.00903606i	−0.207863	+	0.978158i	$0.566651\pi$
$308$	−0.144532	−	0.158544i	−0.00823545	−	0.00903386i
$309$	3.72480	+	0.172208i	0.211896	+	0.00979656i
$310$	1.86525	+	1.70040i	0.105939	+	0.0965762i
$311$	−29.9926	+	4.18379i	−1.70072	+	0.237241i	−0.921188	−	0.389117i	$-0.872780\pi$
$311$	−29.9926	+	4.18379i	−1.70072	+	0.237241i	−0.779536	+	0.626358i	$0.784545\pi$
$312$	−0.546305	+	2.32275i	−0.0309284	+	0.131500i
$313$	−22.2369	+	9.81856i	−1.25691	+	0.554978i	−0.921969	−	0.387263i	$-0.873421\pi$
$313$	−22.2369	+	9.81856i	−1.25691	+	0.554978i	−0.334936	+	0.942241i	$0.608715\pi$
$314$	4.53062	+	1.28907i	0.255678	+	0.0727466i
$315$	−1.14916	−	6.14744i	−0.0647476	−	0.346369i
$316$	0.384594	−	0.0177809i	0.0216351	−	0.00100025i
$317$	28.3792	+	3.95872i	1.59393	+	0.222344i	0.878990	−	0.476840i	$-0.158218\pi$
$317$	28.3792	+	3.95872i	1.59393	+	0.222344i	0.714942	+	0.699184i	$0.246453\pi$
$318$	2.68537	−	3.23387i	0.150588	−	0.181347i
$319$	0.800376	−	0.149616i	0.0448125	−	0.00837690i
$320$	−8.62667	+	1.20337i	−0.482245	+	0.0672703i
$321$	3.84881	−	6.21604i	0.214820	−	0.346946i
$322$	−3.85108	+	1.49192i	−0.214613	+	0.0831413i
$323$	−14.4230	+	16.5688i	−0.802518	+	0.921913i
$324$	0.988186	+	0.382825i	0.0548992	+	0.0212681i
$325$	6.19587	−	4.67891i	0.343685	−	0.259539i
$326$	−2.17249	−	4.92023i	−0.120323	−	0.272506i
$327$	−7.84689			−0.433934
$328$	0.325279	+	0.736687i	0.0179605	+	0.0406767i
$329$	0.360960	−	0.360960i	0.0199003	−	0.0199003i
$330$	0.503405	+	0.280395i	0.0277115	+	0.0154352i
$331$	−17.4655	+	1.61842i	−0.959992	+	0.0889564i	−0.560836	−	0.827927i	$-0.689520\pi$
$331$	−17.4655	+	1.61842i	−0.959992	+	0.0889564i	−0.399156	+	0.916883i	$0.630697\pi$
$332$	0.294234	−	1.57401i	0.0161482	−	0.0863852i
$333$	3.75030	−	5.47476i	0.205515	−	0.300015i
$334$	4.77021	−	2.10626i	0.261014	−	0.115249i
$335$	0.641473	+	0.936436i	0.0350474	+	0.0511629i
$336$	−2.74750	−	1.70118i	−0.149888	−	0.0928069i
$337$	8.42436	−	25.1349i	0.458904	−	1.36918i	−0.426553	−	0.904463i	$-0.640272\pi$
$337$	8.42436	−	25.1349i	0.458904	−	1.36918i	0.885457	−	0.464721i	$-0.153846\pi$
$338$	10.9341	+	5.44456i	0.594739	+	0.296145i
$339$	−0.111612	+	0.0691070i	−0.00606191	+	0.00375338i
$340$	−0.0473684	−	0.684150i	−0.00256891	−	0.0371032i
$341$	−1.01459	−	0.628207i	−0.0549431	−	0.0340193i
$342$	−11.6318	−	18.7860i	−0.628974	−	1.01583i
$343$	−12.5353	+	15.0957i	−0.676845	+	0.815093i
$344$	9.99285	−	9.10969i	0.538778	−	0.491161i
$345$	0.560438	−	0.465382i	0.0301730	−	0.0250553i
$346$	3.08791	−	0.726270i	0.166007	−	0.0390445i
$347$	−0.990855	−	7.10321i	−0.0531919	−	0.381320i	−0.998482	−	0.0550878i	$-0.982456\pi$
$347$	−0.990855	−	7.10321i	−0.0531919	−	0.381320i	0.945290	−	0.326232i	$-0.105779\pi$
$348$	−0.0509113	+	0.0253508i	−0.00272913	+	0.00135895i
$349$	−18.2063	+	29.4042i	−0.974562	+	1.57397i	−0.165532	+	0.986204i	$0.552934\pi$
$349$	−18.2063	+	29.4042i	−0.974562	+	1.57397i	−0.809030	+	0.587767i	$0.800007\pi$
$350$	3.12108	+	9.31203i	0.166829	+	0.497749i
$351$	−2.89211	+	4.22195i	−0.154369	+	0.225351i
$352$	−0.615989	+	0.206459i	−0.0328323	+	0.0110043i
$353$	1.22054	+	4.28975i	0.0649627	+	0.228320i	0.987508	−	0.157568i	$-0.0503655\pi$
$353$	1.22054	+	4.28975i	0.0649627	+	0.228320i	−0.922545	+	0.385889i	$0.873895\pi$
$354$	0.436089	+	0.436089i	0.0231779	+	0.0231779i
$355$	6.23383	−	16.0914i	0.330857	−	0.854041i
$356$	−0.560627	+	0.511079i	−0.0297132	+	0.0270872i
$357$	−1.82654	+	2.53767i	−0.0966708	+	0.134308i
$358$	19.4148	+	17.6989i	1.02610	+	0.935417i
$359$	2.52853	−	1.25906i	0.133451	−	0.0664506i	−0.377773	−	0.925898i	$-0.623310\pi$
$359$	2.52853	−	1.25906i	0.133451	−	0.0664506i	0.511224	+	0.859448i	$0.329192\pi$
$360$	−8.88198	−	2.08902i	−0.468121	−	0.110101i
$361$	−0.865958	+	9.34518i	−0.0455768	+	0.491852i
$362$	12.2949	+	8.42221i	0.646206	+	0.442662i
$363$	3.98335	+	1.33508i	0.209071	+	0.0700737i
$364$	0.399732	−	0.399732i	0.0209517	−	0.0209517i
$365$	−0.896881	+	0.983832i	−0.0469449	+	0.0514961i
$366$	3.99945	−	3.02024i	0.209055	−	0.157871i
$367$	24.4910	+	8.20856i	1.27842	+	0.428483i	0.873927	−	0.486057i	$-0.161565\pi$
$367$	24.4910	+	8.20856i	1.27842	+	0.428483i	0.404494	+	0.914541i	$0.367448\pi$
$368$	−0.297937	+	6.44427i	−0.0155310	+	0.335931i
$369$	0.0387520	+	0.838194i	0.00201735	+	0.0436346i
$370$	1.80647	−	3.62787i	0.0939137	−	0.188604i
$371$	12.4899	−	4.18619i	0.648443	−	0.217336i
$372$	0.0801707	+	0.0228105i	0.00415666	+	0.00118267i
$373$	4.75243	−	6.29323i	0.246071	−	0.325851i	−0.658173	−	0.752867i	$-0.728670\pi$
$373$	4.75243	−	6.29323i	0.246071	−	0.325851i	0.904244	+	0.427016i	$0.140435\pi$
$374$	1.24029	+	4.77901i	0.0641338	+	0.247117i
$375$	−2.49390	−	3.30245i	−0.128784	−	0.170538i
$376$	−0.269042	−	0.694478i	−0.0138748	−	0.0358150i
$377$	0.491224	+	2.08856i	0.0252993	+	0.107566i
$378$	−3.90110	−	5.16589i	−0.200651	−	0.265705i
$379$	6.37987	−	19.0349i	0.327712	−	0.977760i	−0.648551	−	0.761171i	$-0.724625\pi$
$379$	6.37987	−	19.0349i	0.327712	−	0.977760i	0.976263	−	0.216588i	$-0.0694930\pi$
$380$	−0.566120	−	0.681752i	−0.0290413	−	0.0349731i
$381$	−4.37389	−	0.610132i	−0.224081	−	0.0312580i
$382$	−13.8940	+	35.8646i	−0.710880	+	1.83499i
$383$	1.44732	−	0.411799i	0.0739548	−	0.0210419i	−0.236483	−	0.971636i	$-0.575995\pi$
$383$	1.44732	−	0.411799i	0.0739548	−	0.0210419i	0.310438	+	0.950594i	$0.399524\pi$
$384$	−4.14625	+	2.84025i	−0.211588	+	0.144941i
$385$	0.878697	+	1.57756i	0.0447825	+	0.0804000i
$386$	27.1545	+	6.38669i	1.38213	+	0.325074i
$387$	13.1378	−	5.08963i	0.667834	−	0.258720i
$388$	0.219981	−	1.57699i	0.0111678	−	0.0800596i
$389$	−4.93078	+	26.3773i	−0.250000	+	1.33738i	0.595477	+	0.803373i	$0.296963\pi$
$389$	−4.93078	+	26.3773i	−0.250000	+	1.33738i	−0.845477	+	0.534012i	$0.820684\pi$
$390$	−0.676798	+	1.35919i	−0.0342710	+	0.0688255i
$391$	6.20011	+	0.720401i	0.313553	+	0.0364322i
$392$	4.27219	+	8.57971i	0.215778	+	0.433341i
$393$	4.71882	−	1.34262i	0.238033	−	0.0677262i
$394$	12.5171	−	10.3941i	0.630604	−	0.523647i
$395$	−3.18546	−	0.595466i	−0.160278	−	0.0299611i
$396$	−0.325786	−	0.0150620i	−0.0163714	−	0.000756894i
$397$	−2.84901	−	20.4239i	−0.142988	−	1.02505i	−0.918980	−	0.394303i	$-0.870986\pi$
$397$	−2.84901	−	20.4239i	−0.142988	−	1.02505i	0.775993	−	0.630742i	$-0.217249\pi$
$398$	7.35273	+	13.2007i	0.368559	+	0.661691i
$399$			4.04020i			0.202263i
$400$	15.2755	+	1.41549i	0.763776	+	0.0707743i
$401$	−1.06630	+	23.0636i	−0.0532483	+	1.15174i	0.789611	+	0.613608i	$0.210283\pi$
$401$	−1.06630	+	23.0636i	−0.0532483	+	1.15174i	−0.842859	+	0.538135i	$0.819129\pi$
$402$	0.498667	+	0.277756i	0.0248712	+	0.0138532i
$403$	1.53011	−	2.74707i	0.0762200	−	0.136841i
$404$	−0.931429	−	0.360837i	−0.0463403	−	0.0179523i
$405$	−7.35901	−	5.04104i	−0.365672	−	0.250491i
$406$	−2.70242	−	0.250416i	−0.134119	−	0.0124280i
$407$	−0.524371	+	1.84297i	−0.0259921	+	0.0913528i
$408$	2.31054	+	3.93330i	0.114389	+	0.194727i
$409$	−0.380735	−	1.33815i	−0.0188262	−	0.0661671i	0.951843	−	0.306585i	$-0.0991862\pi$
$409$	−0.380735	−	1.33815i	−0.0188262	−	0.0661671i	−0.970670	+	0.240418i	$0.922716\pi$
$410$	0.0941611	+	0.503717i	0.00465028	+	0.0248768i
$411$	6.90312	+	3.04802i	0.340506	+	0.150348i
$412$	−1.09581	+	0.678498i	−0.0539867	+	0.0334272i
$413$	0.442488	+	1.88134i	0.0217734	+	0.0925748i
$414$	−2.53595	+	5.74338i	−0.124635	+	0.282272i
$415$	−5.44411	+	12.3297i	−0.267241	+	0.605243i
$416$	−0.618407	−	1.59629i	−0.0303199	−	0.0782647i
$417$	4.85947	+	2.41973i	0.237969	+	0.118495i
$418$	4.90827	+	4.07578i	0.240072	+	0.199353i
$419$	18.2539	−	0.843929i	0.891761	−	0.0412286i	0.404553	−	0.914514i	$-0.367427\pi$
$419$	18.2539	−	0.843929i	0.891761	−	0.0412286i	0.487208	+	0.873286i	$0.338015\pi$
$420$	−0.0891881	−	0.0891881i	−0.00435193	−	0.00435193i
$421$	−0.104027	−	0.208915i	−0.00506998	−	0.0101819i	0.892614	−	0.450822i	$-0.148869\pi$
$421$	−0.104027	−	0.208915i	−0.00506998	−	0.0101819i	−0.897684	+	0.440640i	$0.854751\pi$
$422$	−7.39294	+	4.11784i	−0.359883	+	0.200453i
$423$		−	0.776016i		−	0.0377312i
$424$	1.77329	−	19.1368i	0.0861183	−	0.929365i
$425$	2.39223	−	14.6491i	0.116040	−	0.710587i
$426$	−0.800703	−	8.64096i	−0.0387942	−	0.418656i
$427$	15.6387	−	1.44914i	0.756810	−	0.0701287i
$428$	0.116710	+	2.52441i	0.00564141	+	0.122022i
$429$	0.196457	−	0.690476i	0.00948505	−	0.0333365i
$430$	7.51708	−	4.18698i	0.362506	−	0.201914i
$431$	1.01180	−	0.693097i	0.0487365	−	0.0333853i	−0.540522	−	0.841330i	$-0.681773\pi$
$431$	1.01180	−	0.693097i	0.0487365	−	0.0333853i	0.589258	+	0.807945i	$0.299420\pi$
$432$	−9.84310	+	2.31508i	−0.473576	+	0.111384i
$433$	12.0773	+	13.2481i	0.580397	+	0.636665i	0.957131	−	0.289657i	$-0.0935411\pi$
$433$	12.0773	+	13.2481i	0.580397	+	0.636665i	−0.376734	+	0.926322i	$0.622953\pi$
$434$	2.67967	+	2.93946i	0.128628	+	0.141099i
$435$	0.465998	−	0.109602i	0.0223429	−	0.00525500i
$436$	2.23764	−	1.53282i	0.107163	−	0.0734086i
$437$	7.04623	−	3.92472i	0.337067	−	0.187745i
$438$	−0.183210	+	0.643916i	−0.00875410	+	0.0307675i
$439$	−1.42391	−	30.7988i	−0.0679597	−	1.46995i	−0.710502	−	0.703696i	$-0.751532\pi$
$439$	−1.42391	−	30.7988i	−0.0679597	−	1.46995i	0.642542	−	0.766251i	$-0.277880\pi$
$440$	2.62334	−	0.243089i	0.125063	−	0.0115888i
$441$	0.921450	+	9.94403i	0.0438786	+	0.473525i
$442$	−12.4285	+	3.84629i	−0.591161	+	0.182949i
$443$	−0.477468	+	5.15270i	−0.0226852	+	0.244812i	0.976839	+	0.213974i	$0.0686409\pi$
$443$	−0.477468	+	5.15270i	−0.0226852	+	0.244812i	−0.999524	+	0.0308374i	$0.990183\pi$
$444$		−	0.133839i		−	0.00635171i
$445$	5.57844	−	3.10717i	0.264443	−	0.147294i
$446$	8.74651	+	17.5654i	0.414159	+	0.831744i
$447$	−2.17831	−	2.17831i	−0.103030	−	0.103030i
$448$	−13.7118	+	0.633935i	−0.647822	+	0.0299506i
$449$	−0.814978	−	0.676749i	−0.0384612	−	0.0319378i	0.619417	−	0.785062i	$-0.287369\pi$
$449$	−0.814978	−	0.676749i	−0.0384612	−	0.0319378i	−0.657878	+	0.753125i	$0.728546\pi$
$450$	13.3648	+	6.65487i	0.630022	+	0.313714i
$451$	−0.0875218	−	0.225920i	−0.00412124	−	0.0106381i
$452$	0.0183280	−	0.0415090i	0.000862077	−	0.00195242i
$453$	−1.90427	+	4.31277i	−0.0894706	+	0.202632i
$454$	−1.11162	−	4.72631i	−0.0521708	−	0.221817i
$455$	−4.04556	+	2.50490i	−0.189659	+	0.117432i
$456$	5.39231	+	2.38094i	0.252518	+	0.111498i
$457$	−3.75090	−	20.0656i	−0.175460	−	0.938627i	−0.951432	−	0.307860i	$-0.900387\pi$
$457$	−3.75090	−	20.0656i	−0.175460	−	0.938627i	0.775972	−	0.630767i	$-0.217260\pi$
$458$	−0.0550763	−	0.193573i	−0.00257354	−	0.00904507i
$459$	1.57344	+	9.65621i	0.0734419	+	0.450713i
$460$	−0.0689078	+	0.242186i	−0.00321284	+	0.0112920i
$461$	30.6158	+	2.83697i	1.42592	+	0.132131i	0.777371	−	0.629043i	$-0.216553\pi$
$461$	30.6158	+	2.83697i	1.42592	+	0.132131i	0.648548	+	0.761174i	$0.275376\pi$
$462$	0.749164	+	0.513189i	0.0348543	+	0.0238757i
$463$	27.5241	+	10.6629i	1.27915	+	0.495546i	0.902452	−	0.430790i	$-0.141765\pi$
$463$	27.5241	+	10.6629i	1.27915	+	0.495546i	0.376699	+	0.926336i	$0.377059\pi$
$464$	−2.06289	+	3.70360i	−0.0957674	+	0.171935i
$465$	−0.612925	−	0.341397i	−0.0284237	−	0.0158319i
$466$	0.545850	−	11.8066i	0.0252860	−	0.546928i
$467$	−22.4457	−	2.07990i	−1.03866	−	0.0962464i	−0.440607	−	0.897700i	$-0.645237\pi$
$467$	−22.4457	−	2.07990i	−1.03866	−	0.0962464i	−0.598057	+	0.801454i	$0.704060\pi$
$468$		−	0.859372i		−	0.0397245i
$469$	0.870427	+	1.56271i	0.0401926	+	0.0721595i
$470$	−0.0654755	−	0.469378i	−0.00302016	−	0.0216508i
$471$	−1.30796	−	0.0604706i	−0.0602675	−	0.00278634i
$472$	2.77172	+	0.518125i	0.127579	+	0.0238486i
$473$	−3.12978	+	2.59893i	−0.143907	+	0.119499i
$474$	−1.56743	+	0.445972i	−0.0719945	+	0.0204842i
$475$	−8.54925	−	17.1692i	−0.392267	−	0.787777i
$476$	0.0251500	−	1.08045i	0.00115275	−	0.0495221i
$477$	8.92594	−	17.9257i	0.408691	−	0.820762i
$478$	−3.29282	+	17.6151i	−0.150610	+	0.805694i
$479$	0.829173	−	5.94415i	0.0378859	−	0.271595i	−0.962114	−	0.272649i	$-0.912100\pi$
$479$	0.829173	−	5.94415i	0.0378859	−	0.271595i	0.999999	+	0.00105405i	$0.000335514\pi$
$480$	−0.356164	+	0.137979i	−0.0162566	+	0.00629784i
$481$	−4.91492	−	1.15598i	−0.224101	−	0.0527081i
$482$	12.6464	+	22.7046i	0.576026	+	1.03417i
$483$	0.947100	−	0.648779i	0.0430946	−	0.0295205i
$484$	−1.39670	+	0.397394i	−0.0634862	+	0.0180634i
$485$	−4.84145	+	12.4972i	−0.219839	+	0.567470i
$486$	−14.7578	−	2.05862i	−0.669427	−	0.0933810i
$487$	23.8049	+	28.6671i	1.07870	+	1.29903i	0.951666	+	0.307133i	$0.0993698\pi$
$487$	23.8049	+	28.6671i	1.07870	+	1.29903i	0.127036	+	0.991898i	$0.459454\pi$
$488$	7.28196	−	21.7264i	0.329639	−	0.983508i
$489$	0.900974	+	1.19308i	0.0407434	+	0.0539530i
$490$	1.39636	+	5.93696i	0.0630812	+	0.268205i
$491$	7.88367	+	20.3501i	0.355785	+	0.918387i	0.989462	+	0.144790i	$0.0462506\pi$
$491$	7.88367	+	20.3501i	0.355785	+	0.918387i	−0.633677	+	0.773597i	$0.718455\pi$
$492$	0.0101984	+	0.0135048i	0.000459779	+	0.000608846i
$493$	3.43622	+	2.23989i	0.154760	+	0.100880i
$494$	−10.1310	+	13.4156i	−0.455816	+	0.603598i
$495$	2.64032	+	0.751236i	0.118674	+	0.0337655i
$496$	5.89101	−	1.97447i	0.264514	−	0.0886563i
$497$	12.1218	−	24.3439i	0.543738	−	1.09197i
$498$	0.313025	+	6.77062i	0.0140270	+	0.303399i
$499$	1.82506	−	39.4755i	0.0817011	−	1.76717i	−0.425139	−	0.905128i	$-0.639775\pi$
$499$	1.82506	−	39.4755i	0.0817011	−	1.76717i	0.506841	−	0.862040i	$-0.330813\pi$
$500$	1.35627	+	0.454575i	0.0606542	+	0.0203292i
$501$	−1.15671	+	0.873504i	−0.0516778	+	0.0390253i
$502$	−12.4150	+	13.6186i	−0.554107	+	0.607826i
$503$	−26.4431	+	26.4431i	−1.17904	+	1.17904i	−0.199048	+	0.979990i	$0.563785\pi$
$503$	−26.4431	+	26.4431i	−1.17904	+	1.17904i	−0.979990	+	0.199048i	$0.936215\pi$
$504$	−13.6337	−	4.56956i	−0.607294	−	0.203544i
$505$	6.93634	+	4.75150i	0.308663	+	0.211439i
$506$	0.167266	−	1.80509i	0.00743588	−	0.0802459i
$507$	−3.30512	−	0.777357i	−0.146786	−	0.0345236i
$508$	1.36645	−	0.680413i	0.0606265	−	0.0301884i
$509$	−18.9228	−	17.2504i	−0.838737	−	0.764610i	0.135347	−	0.990798i	$-0.456785\pi$
$509$	−18.9228	−	17.2504i	−0.838737	−	0.764610i	−0.974084	+	0.226189i	$0.927373\pi$
$510$	0.858182	+	2.77303i	0.0380009	+	0.122792i
$511$	−1.55043	+	1.41340i	−0.0685869	+	0.0625252i
$512$	−7.15383	+	18.4662i	−0.316158	+	0.816097i
$513$	8.93931	+	8.93931i	0.394680	+	0.394680i
$514$	−0.946357	−	3.32610i	−0.0417420	−	0.146708i
$515$	10.2861	−	3.44756i	0.453261	−	0.151918i
$516$	0.160587	−	0.234428i	0.00706945	−	0.0103201i
$517$	0.0712071	+	0.212453i	0.00313168	+	0.00934367i
$518$	3.36219	−	5.43013i	0.147726	−	0.238586i
$519$	−0.789323	+	0.393036i	−0.0346474	+	0.0172524i
$520$	0.959109	+	6.87563i	0.0420597	+	0.301516i
$521$	−22.7488	+	5.35048i	−0.996644	+	0.234409i	−0.694998	−	0.719011i	$-0.744595\pi$
$521$	−22.7488	+	5.35048i	−0.996644	+	0.234409i	−0.301646	+	0.953420i	$0.597536\pi$
$522$	−3.17411	+	2.63575i	−0.138927	+	0.115364i
$523$	28.9868	−	26.4249i	1.26750	−	1.15548i	0.287223	−	0.957864i	$-0.407268\pi$
$523$	28.9868	−	26.4249i	1.26750	−	1.15548i	0.980279	−	0.197617i	$-0.0633204\pi$
$524$	−1.08336	+	1.30464i	−0.0473268	+	0.0569936i
$525$	−1.43715	−	2.32107i	−0.0627222	−	0.101300i
$526$	−3.48397	−	2.15718i	−0.151908	−	0.0940576i
$527$	−1.51012	−	5.81872i	−0.0657820	−	0.253467i
$528$	1.20599	−	0.746719i	0.0524841	−	0.0324968i
$529$	18.5372	+	9.23045i	0.805967	+	0.401324i
$530$	3.88645	−	11.5956i	0.168817	−	0.503681i
$531$	2.49797	+	1.54668i	0.108402	+	0.0671200i
$532$	−0.789215	−	1.15211i	−0.0342168	−	0.0499504i
$533$	0.584019	−	0.257870i	0.0252967	−	0.0111696i
$534$	1.81469	−	2.64913i	0.0785295	−	0.114639i
$535$	3.90853	−	20.9088i	0.168981	−	0.903966i
$536$	2.59865	−	0.240801i	0.112245	−	0.0104010i
$537$	−6.37974	−	3.55349i	−0.275306	−	0.153344i
$538$	−5.41001	+	5.41001i	−0.233242	+	0.233242i
$539$	−1.16473	−	2.63786i	−0.0501685	−	0.113621i
$540$	−0.394674			−0.0169840
$541$	−13.8902	−	31.4582i	−0.597185	−	1.35250i	−0.914658	−	0.404228i	$-0.867540\pi$
$541$	−13.8902	−	31.4582i	−0.597185	−	1.35250i	0.317473	−	0.948267i	$-0.397166\pi$
$542$	−1.24676	+	0.941511i	−0.0535530	+	0.0404413i
$543$	−3.86283	−	1.49647i	−0.165770	−	0.0642195i
$544$	−2.96232	−	1.39125i	−0.127008	−	0.0596492i
$545$	−21.2881	+	8.24706i	−0.911882	+	0.353265i
$546$	−1.25966	+	2.03442i	−0.0539083	+	0.0870649i
$547$	−19.3329	+	2.69683i	−0.826616	+	0.115308i	−0.538860	−	0.842396i	$-0.681145\pi$
$547$	−19.3329	+	2.69683i	−0.826616	+	0.115308i	−0.287757	+	0.957704i	$0.592909\pi$
$548$	−2.56391	+	0.479278i	−0.109525	+	0.0204737i
$549$	15.2529	−	18.3683i	0.650976	−	0.783941i
$550$	−4.26958	−	0.595581i	−0.182055	−	0.0253956i
$551$	5.29459	−	0.244784i	0.225557	−	0.0104281i
$552$	−0.307764	−	1.64639i	−0.0130993	−	0.0700752i
$553$	−4.91199	−	1.39758i	−0.208879	−	0.0594312i
$554$	−0.319489	+	0.141068i	−0.0135738	+	0.00599341i
$555$	−0.257922	+	1.09662i	−0.0109482	+	0.0465487i
$556$	−1.85841	+	0.259237i	−0.0788140	+	0.0109941i
$557$	−1.64111	−	1.49607i	−0.0695360	−	0.0633904i	0.638182	−	0.769886i	$-0.279687\pi$
$557$	−1.64111	−	1.49607i	−0.0695360	−	0.0633904i	−0.707718	+	0.706495i	$0.750275\pi$
$558$	6.04020	+	0.279255i	0.255702	+	0.0118218i
$559$	−7.22183	−	7.92197i	−0.305451	−	0.335064i
$560$	−9.24171	−	1.72758i	−0.390534	−	0.0730034i
$561$	−0.639745	−	1.21420i	−0.0270101	−	0.0512634i
$562$	−27.5527	+	5.15050i	−1.16224	+	0.217261i
$563$	15.6809	+	11.8417i	0.660871	+	0.499067i	0.878981	−	0.476857i	$-0.158224\pi$
$563$	15.6809	+	11.8417i	0.660871	+	0.499067i	−0.218109	+	0.975924i	$0.569989\pi$
$564$	−0.00884491	−	0.0129120i	−0.000372438	−	0.000543692i
$565$	−0.230164	+	0.304786i	−0.00968306	+	0.0128224i
$566$	6.33459	+	2.79699i	0.266263	+	0.117566i
$567$	−10.8147	−	8.98037i	−0.454173	−	0.377140i
$568$	−25.3474	−	30.5247i	−1.06355	−	1.28079i
$569$	−5.73164	−	9.25691i	−0.240283	−	0.388070i	0.707639	−	0.706575i	$-0.249761\pi$
$569$	−5.73164	−	9.25691i	−0.240283	−	0.388070i	−0.947921	+	0.318505i	$0.896819\pi$
$570$	2.99329	+	2.26043i	0.125375	+	0.0946790i
$571$	9.11990	−	38.7754i	0.381656	−	1.62270i	−0.347031	−	0.937854i	$-0.612810\pi$
$571$	9.11990	−	38.7754i	0.381656	−	1.62270i	0.728687	−	0.684847i	$-0.240131\pi$
$572$	0.0788558	+	0.235274i	0.00329713	+	0.00983729i
$573$	1.47706	−	10.5887i	0.0617049	−	0.442348i
$574$	0.0745124	+	0.804117i	0.00311009	+	0.0335632i
$575$	−2.65195	+	4.76116i	−0.110594	+	0.198554i
$576$	−14.0579	+	15.4207i	−0.585744	+	0.642531i
$577$	−34.7470			−1.44654			−0.723269	−	0.690567i	$-0.757361\pi$
$577$	−34.7470			−1.44654			−0.723269	+	0.690567i	$0.757361\pi$
$578$	−12.1104	+	21.7247i	−0.503728	+	0.903628i
$579$	−7.75408			−0.322248
$580$	−0.111475	+	0.122283i	−0.00462876	+	0.00507751i
$581$	−10.3356	+	18.5560i	−0.428795	+	0.769834i
$582$	0.621860	+	6.71093i	0.0257769	+	0.278177i
$583$	−0.798832	+	5.72664i	−0.0330842	+	0.237173i
$584$	0.972731	+	2.90223i	0.0402519	+	0.120095i
$585$	−1.65610	+	7.04132i	−0.0684714	+	0.291123i
$586$	−27.1151	−	20.4764i	−1.12011	−	0.845871i
$587$	−6.95221	−	11.2282i	−0.286948	−	0.463437i	0.674557	−	0.738222i	$-0.264335\pi$
$587$	−6.95221	−	11.2282i	−0.286948	−	0.463437i	−0.961506	+	0.274785i	$0.911393\pi$
$588$	0.128672	+	0.154954i	0.00530636	+	0.00639020i
$589$	−5.97611	−	4.96250i	−0.246241	−	0.204476i
$590$	1.64141	+	0.724753i	0.0675758	+	0.0298376i
$591$	−2.72546	+	3.60909i	−0.112110	+	0.148458i
$592$	−5.63799	−	8.23044i	−0.231720	−	0.338269i
$593$	14.5485	+	10.9865i	0.597435	+	0.451162i	0.857539	−	0.514419i	$-0.171992\pi$
$593$	14.5485	+	10.9865i	0.597435	+	0.451162i	−0.260104	+	0.965581i	$0.583757\pi$
$594$	2.79307	−	0.522116i	0.114601	−	0.0214227i
$595$	−2.28820	+	8.80422i	−0.0938071	+	0.360938i
$596$	1.04668	+	0.195659i	0.0428738	+	0.00801451i
$597$	−2.82965	−	3.10398i	−0.115810	−	0.127037i
$598$	4.77173	+	0.220611i	0.195131	+	0.00902144i
$599$	24.1449	+	22.0110i	0.986533	+	0.899344i	0.994925	−	0.100621i	$-0.0320830\pi$
$599$	24.1449	+	22.0110i	0.986533	+	0.899344i	−0.00839187	+	0.999965i	$0.502671\pi$
$600$	−3.94478	+	0.550273i	−0.161045	+	0.0224648i
$601$	10.1560	−	43.1805i	0.414271	−	1.76137i	−0.207563	−	0.978222i	$-0.566553\pi$
$601$	10.1560	−	43.1805i	0.414271	−	1.76137i	0.621833	−	0.783150i	$-0.286388\pi$
$602$	12.4045	−	5.47712i	0.505569	−	0.223231i
$603$	2.61547	+	0.744165i	0.106510	+	0.0303047i
$604$	−0.299432	−	1.60182i	−0.0121837	−	0.0651772i
$605$	12.2097	−	0.564490i	0.496396	−	0.0229498i
$606$	4.18750	+	0.584131i	0.170105	+	0.0237287i
$607$	−4.17183	+	5.02394i	−0.169329	+	0.203915i	−0.847213	−	0.531254i	$-0.821721\pi$
$607$	−4.17183	+	5.02394i	−0.169329	+	0.203915i	0.677883	+	0.735170i	$0.262897\pi$
$608$	−4.15696	+	0.777071i	−0.168587	+	0.0315144i
$609$	0.747174	−	0.104226i	0.0302770	−	0.00422346i
$610$	7.67598	−	12.3971i	0.310791	−	0.501945i
$611$	−0.550557	+	0.213287i	−0.0222732	+	0.00862867i
$612$	−1.13437	−	1.18844i	−0.0458544	−	0.0480400i
$613$	8.85196	+	3.42927i	0.357527	+	0.138507i	0.533305	−	0.845923i	$-0.320950\pi$
$613$	8.85196	+	3.42927i	0.357527	+	0.138507i	−0.175778	+	0.984430i	$0.556244\pi$
$614$	−1.00600	+	0.759698i	−0.0405990	+	0.0306589i
$615$	−0.0575358	−	0.130306i	−0.00232007	−	0.00525445i
$616$	4.15186			0.167283
$617$	−12.1474	−	27.5112i	−0.489035	−	1.10756i	−0.972650	−	0.232277i	$-0.925382\pi$
$617$	−12.1474	−	27.5112i	−0.489035	−	1.10756i	0.483615	−	0.875281i	$-0.339324\pi$
$618$	3.85759	−	3.85759i	0.155175	−	0.155175i
$619$	−25.3170	−	14.1015i	−1.01758	−	0.566787i	−0.113223	−	0.993570i	$-0.536117\pi$
$619$	−25.3170	−	14.1015i	−1.01758	−	0.566787i	−0.904354	+	0.426783i	$0.859647\pi$
$620$	0.241472	−	0.0223756i	0.00969774	−	0.000898628i
$621$	0.660063	−	3.53103i	0.0264874	−	0.141695i
$622$	−25.0390	+	36.5524i	−1.00397	+	1.46562i
$623$	9.20540	−	4.06458i	0.368806	−	0.162844i
$624$	2.11229	+	3.08356i	0.0845593	+	0.123441i
$625$	5.06725	+	3.13751i	0.202690	+	0.125500i
$626$	−11.3021	+	33.7208i	−0.451722	+	1.34776i
$627$	−1.58750	−	0.790479i	−0.0633984	−	0.0315687i
$628$	0.384793	−	0.238254i	0.0153549	−	0.00950735i
$629$	−8.32284	+	4.88908i	−0.331853	+	0.194940i
$630$	−7.77942	−	4.81682i	−0.309940	−	0.191907i
$631$	−0.241793	−	0.390508i	−0.00962561	−	0.0155459i	0.845369	−	0.534183i	$-0.179381\pi$
$631$	−0.241793	−	0.390508i	−0.00962561	−	0.0155459i	−0.854994	+	0.518637i	$0.826440\pi$
$632$	−4.76000	+	5.73225i	−0.189343	+	0.228017i
$633$	1.73836	−	1.58472i	0.0690935	−	0.0629871i
$634$	32.2526	−	26.7822i	1.28091	−	1.06366i
$635$	−12.5073	+	2.94170i	−0.496338	+	0.116738i
$636$	−0.0557975	−	0.399999i	−0.00221251	−	0.0158610i
$637$	6.80169	−	3.38684i	0.269493	−	0.134191i
$638$	0.627133	−	1.01286i	0.0248284	−	0.0400993i
$639$	−13.1379	−	39.1983i	−0.519729	−	1.55066i
$640$	−8.26342	+	12.0631i	−0.326640	+	0.476836i
$641$	−6.04445	+	2.02590i	−0.238742	+	0.0800181i	−0.434634	−	0.900607i	$-0.643122\pi$
$641$	−6.04445	+	2.02590i	−0.238742	+	0.0800181i	0.195892	+	0.980625i	$0.437240\pi$
$642$	−2.92728	−	10.2883i	−0.115531	−	0.406048i
$643$	8.57619	+	8.57619i	0.338212	+	0.338212i	0.855694	−	0.517482i	$-0.173131\pi$
$643$	8.57619	+	8.57619i	0.338212	+	0.338212i	−0.517482	+	0.855694i	$0.673131\pi$
$644$	−0.143344	+	0.370015i	−0.00564856	+	0.0145806i
$645$	−1.76755	+	1.61133i	−0.0695971	+	0.0634462i
$646$	3.69829	+	31.9257i	0.145507	+	1.25610i
$647$	5.56793	+	5.07584i	0.218898	+	0.199552i	0.775715	−	0.631083i	$-0.217389\pi$
$647$	5.56793	+	5.07584i	0.218898	+	0.199552i	−0.556817	+	0.830635i	$0.687978\pi$
$648$	−18.3590	+	9.14169i	−0.721209	+	0.359119i
$649$	−0.825801	−	0.194227i	−0.0324155	−	0.00762406i
$650$	1.04811	−	11.3109i	0.0411104	−	0.443651i
$651$	−0.912151	−	0.624838i	−0.0357500	−	0.0244893i
$652$	−0.489981	−	0.164225i	−0.0191891	−	0.00643155i
$653$	3.04838	−	3.04838i	0.119292	−	0.119292i	−0.644940	−	0.764233i	$-0.723118\pi$
$653$	3.04838	−	3.04838i	0.119292	−	0.119292i	0.764233	+	0.644940i	$0.223118\pi$
$654$	−7.73439	+	8.48423i	−0.302439	+	0.331760i
$655$	11.3908	−	8.60190i	0.445074	−	0.336104i
$656$	1.19605	+	0.400874i	0.0466978	+	0.0156515i
$657$	−0.147294	+	3.18592i	−0.00574649	+	0.124295i
$658$	−0.0344925	−	0.746062i	−0.00134466	−	0.0290845i
$659$	−8.84584	+	17.7648i	−0.344585	+	0.692020i	−0.997880	−	0.0650837i	$-0.979269\pi$
$659$	−8.84584	+	17.7648i	−0.344585	+	0.692020i	0.653295	+	0.757104i	$0.273386\pi$
$660$	0.0524942	−	0.0175943i	0.00204333	−	0.000684857i
$661$	−29.5973	−	8.42117i	−1.15120	−	0.327545i	−0.356353	−	0.934352i	$-0.615980\pi$
$661$	−29.5973	−	8.42117i	−1.15120	−	0.327545i	−0.794850	+	0.606806i	$0.792450\pi$
$662$	−15.4653	+	20.4793i	−0.601075	+	0.795951i
$663$	3.11818	−	1.83171i	0.121100	−	0.0711377i
$664$	18.6752	+	24.7299i	0.724737	+	0.959706i
$665$	4.24624	+	10.9608i	0.164662	+	0.425041i
$666$	−2.22290	−	9.45117i	−0.0861355	−	0.366226i
$667$	−0.907592	−	1.20185i	−0.0351421	−	0.0465357i
$668$	0.159218	−	0.475042i	0.00616033	−	0.0183799i
$669$	−3.48456	−	4.19629i	−0.134721	−	0.162238i
$670$	1.64477	+	0.229436i	0.0635431	+	0.00886388i
$671$	−2.49036	+	6.42836i	−0.0961394	+	0.248164i
$672$	−0.578951	+	0.164726i	−0.0223335	+	0.00635443i
$673$	18.5084	−	12.6786i	0.713448	−	0.488723i	−0.152851	−	0.988249i	$-0.548845\pi$
$673$	18.5084	−	12.6786i	0.713448	−	0.488723i	0.866299	+	0.499526i	$0.166493\pi$
$674$	−18.8728	−	33.8831i	−0.726952	−	1.30513i
$675$	−8.31540	−	1.95576i	−0.320060	−	0.0752774i
$676$	1.09435	−	0.423952i	0.0420902	−	0.0163058i
$677$	0.698843	−	5.00984i	0.0268587	−	0.192544i	−0.972291	−	0.233774i	$-0.924892\pi$
$677$	0.698843	−	5.00984i	0.0268587	−	0.192544i	0.999150	+	0.0412302i	$0.0131277\pi$
$678$	−0.0352915	+	0.188793i	−0.00135536	+	0.00725055i
$679$	−9.41431	+	18.9065i	−0.361288	+	0.725564i
$680$	10.4022	+	8.24242i	0.398907	+	0.316082i
$681$	0.601576	+	1.20813i	0.0230524	+	0.0462955i
$682$	−1.67927	+	0.477795i	−0.0643027	+	0.0182957i
$683$	30.0723	−	24.9717i	1.15069	−	0.955517i	0.151230	−	0.988499i	$-0.451677\pi$
$683$	30.0723	−	24.9717i	1.15069	−	0.955517i	0.999456	+	0.0329812i	$0.0105001\pi$
$684$	−2.08680	−	0.390091i	−0.0797908	−	0.0149155i
$685$	21.9312	+	1.01394i	0.837947	+	0.0387406i
$686$	3.96621	+	28.4328i	0.151430	+	1.08557i
$687$	0.0272220	+	0.0488729i	0.00103859	+	0.00186462i
$688$		−	21.1810i		−	0.807518i
$689$	−15.1710	−	1.40580i	−0.577968	−	0.0535566i
$690$	0.0492226	−	1.06467i	0.00187387	−	0.0405312i
$691$	26.7681	+	14.9097i	1.01831	+	0.567193i	0.904573	−	0.426319i	$-0.140190\pi$
$691$	26.7681	+	14.9097i	1.01831	+	0.567193i	0.113733	+	0.993511i	$0.463719\pi$
$692$	0.148309	−	0.266266i	0.00563787	−	0.0101219i
$693$	4.03391	+	1.56275i	0.153236	+	0.0593638i
$694$	−8.65679	−	5.93004i	−0.328607	−	0.225101i
$695$	15.7265	+	1.45728i	0.596542	+	0.0552777i
$696$	0.301211	−	1.05865i	0.0114174	−	0.0401279i
$697$	0.467263	−	1.12752i	0.0176988	−	0.0427079i
$698$	13.8472	+	48.6677i	0.524123	+	1.84210i
$699$	0.603683	+	3.22942i	0.0228334	+	0.122148i
$700$	0.863220	+	0.381149i	0.0326266	+	0.0144061i
$701$	−36.4756	+	22.5848i	−1.37767	+	0.853015i	−0.997414	−	0.0718684i	$-0.977104\pi$
$701$	−36.4756	+	22.5848i	−1.37767	+	0.853015i	−0.380252	+	0.924883i	$0.624163\pi$
$702$	1.71422	+	7.28843i	0.0646992	+	0.275084i
$703$	−5.03805	+	11.4101i	−0.190014	+	0.430340i
$704$	2.43367	−	5.51174i	0.0917225	−	0.207732i
$705$	0.0475885	+	0.122840i	0.00179229	+	0.00462642i
$706$	5.84121	+	2.90857i	0.219837	+	0.109466i
$707$	10.1935	+	8.46458i	0.383366	+	0.318343i
$708$	0.0591919	−	0.00273661i	0.00222457	−	0.000102848i
$709$	−8.53398	−	8.53398i	−0.320500	−	0.320500i	0.528459	−	0.848959i	$-0.322770\pi$
$709$	−8.53398	−	8.53398i	−0.320500	−	0.320500i	−0.848959	+	0.528459i	$0.822770\pi$
$710$	−11.2539	−	22.6008i	−0.422350	−	0.848194i
$711$	−6.78238	+	3.77776i	−0.254359	+	0.141677i
$712$		−	14.6814i		−	0.550210i
$713$	−0.203656	+	2.19780i	−0.00762697	+	0.0823081i
$714$	0.943430	+	4.47618i	0.0353070	+	0.167517i
$715$	−0.192712	−	2.07969i	−0.00720702	−	0.0777761i
$716$	2.51340	−	0.232901i	0.0939302	−	0.00870392i
$717$	−0.230052	−	4.97594i	−0.00859143	−	0.185830i
$718$	1.13096	−	3.97491i	0.0422070	−	0.148342i
$719$	−16.4501	+	9.16263i	−0.613484	+	0.341708i	−0.762366	−	0.647147i	$-0.775962\pi$
$719$	−16.4501	+	9.16263i	−0.613484	+	0.341708i	0.148881	+	0.988855i	$0.452433\pi$
$720$	−11.7913	+	8.07721i	−0.439435	+	0.301020i
$721$	16.6421	−	3.91419i	0.619785	−	0.145772i
$722$	9.25066	+	10.1475i	0.344274	+	0.377651i
$723$	−4.86687	−	5.33870i	−0.181001	−	0.198549i
$724$	1.39385	−	0.327831i	0.0518021	−	0.0121838i
$725$	−2.95464	+	2.02397i	−0.109732	+	0.0751685i
$726$	5.36976	−	2.99094i	0.199290	−	0.111004i
$727$	7.77991	−	27.3435i	0.288541	−	1.01412i	−0.673043	−	0.739603i	$-0.735013\pi$
$727$	7.77991	−	27.3435i	0.288541	−	1.01412i	0.961584	−	0.274512i	$-0.0885163\pi$
$728$	0.505259	+	10.9286i	0.0187262	+	0.405040i
$729$	−18.3957	+	1.70461i	−0.681321	+	0.0631337i
$730$	0.179717	+	1.93945i	0.00665162	+	0.0717824i
$731$	−20.4442	−	1.42261i	−0.756158	−	0.0526173i
$732$	0.0444300	−	0.479476i	0.00164218	−	0.0177220i
$733$			32.7818i			1.21082i	0.795913	+	0.605411i	$0.206991\pi$
$733$			32.7818i			1.21082i	−0.795913	+	0.605411i	$0.793009\pi$
$734$	33.0152	−	18.3893i	1.21861	−	0.678763i
$735$	−0.755670	−	1.51759i	−0.0278733	−	0.0559772i
$736$	0.849690	+	0.849690i	0.0313200	+	0.0313200i
$737$	−0.784332	+	0.0362618i	−0.0288912	+	0.00133572i
$738$	0.944470	+	0.784278i	0.0347664	+	0.0288697i
$739$	12.0637	+	6.00700i	0.443770	+	0.220971i	0.653713	−	0.756742i	$-0.273210\pi$
$739$	12.0637	+	6.00700i	0.443770	+	0.220971i	−0.209943	+	0.977714i	$0.567328\pi$
$740$	−0.140664	−	0.363096i	−0.00517091	−	0.0133477i
$741$	1.88752	−	4.27483i	0.0693398	−	0.157040i
$742$	7.78464	−	17.6305i	0.285783	−	0.647237i
$743$	7.64489	+	32.5041i	0.280464	+	1.19246i	0.909707	+	0.415250i	$0.136306\pi$
$743$	7.64489	+	32.5041i	0.280464	+	1.19246i	−0.629243	+	0.777208i	$0.716635\pi$
$744$	−1.37149	+	0.849191i	−0.0502813	+	0.0311328i
$745$	−8.19901	−	3.62021i	−0.300388	−	0.132634i
$746$	−2.12008	−	11.3414i	−0.0776217	−	0.415240i
$747$	8.83638	+	31.0567i	0.323306	+	1.13630i
$748$	0.419613	+	0.221275i	0.0153426	+	0.00809061i
$749$	9.17348	−	32.2414i	0.335192	−	1.17808i
$750$	−6.02882	−	0.558653i	−0.220142	−	0.0203991i
$751$	19.9351	+	13.6559i	0.727443	+	0.498310i	0.870970	−	0.491337i	$-0.163491\pi$
$751$	19.9351	+	13.6559i	0.727443	+	0.498310i	−0.143527	+	0.989646i	$0.545844\pi$
$752$	−1.08784	−	0.421431i	−0.0396694	−	0.0153680i
$753$	2.49261	−	4.47509i	0.0908356	−	0.163081i
$754$	2.74237	+	1.52749i	0.0998714	+	0.0556280i
$755$	−0.633466	+	13.7017i	−0.0230542	+	0.498654i
$756$	−0.619316	−	0.0573881i	−0.0225243	−	0.00208718i
$757$			10.4089i			0.378320i	0.981946	+	0.189160i	$0.0605764\pi$
$757$			10.4089i			0.378320i	−0.981946	+	0.189160i	$0.939424\pi$
$758$	−14.2926	−	25.6601i	−0.519130	−	0.932017i
$759$	0.0696180	+	0.499075i	0.00252697	+	0.0181153i
$760$	17.1313	+	0.792030i	0.621419	+	0.0287299i
$761$	−39.0350	−	7.29691i	−1.41502	−	0.264513i	−0.579947	−	0.814654i	$-0.696927\pi$
$761$	−39.0350	−	7.29691i	−1.41502	−	0.264513i	−0.835071	+	0.550142i	$0.814574\pi$
$762$	−4.97087	+	4.12776i	−0.180076	+	0.149533i
$763$	−34.6041	+	9.84573i	−1.25275	+	0.356439i
$764$	1.64720	+	3.30802i	0.0595935	+	0.119680i
$765$	7.00430	+	11.9236i	0.253241	+	0.431100i
$766$	0.981328	−	1.97077i	0.0354568	−	0.0712069i
$767$	0.410751	−	2.19732i	0.0148314	−	0.0793407i
$768$	−0.188644	+	1.35235i	−0.00680712	+	0.0487986i
$769$	22.0772	−	8.55276i	0.796125	−	0.308420i	0.0713903	−	0.997448i	$-0.477256\pi$
$769$	22.0772	−	8.55276i	0.796125	−	0.308420i	0.724735	+	0.689028i	$0.241962\pi$
$770$	2.57179	+	0.604880i	0.0926810	+	0.0217984i
$771$	0.467747	+	0.839767i	0.0168455	+	0.0302435i
$772$	2.21117	−	1.51469i	0.0795818	−	0.0545148i
$773$	−12.8969	+	3.66950i	−0.463871	+	0.131983i	−0.497523	−	0.867451i	$-0.665757\pi$
$773$	−12.8969	+	3.66950i	−0.463871	+	0.131983i	0.0336517	+	0.999434i	$0.489286\pi$
$774$	7.44648	−	19.2216i	0.267658	−	0.690905i
$775$	5.19846	+	0.725154i	0.186734	+	0.0260483i
$776$	19.6859	+	23.7068i	0.706681	+	0.851023i
$777$	−0.564181	+	1.68329i	−0.0202399	+	0.0603876i
$778$	23.6597	+	31.3304i	0.848240	+	1.12325i
$779$	−0.361080	−	1.53522i	−0.0129370	−	0.0550049i
$780$	0.0527002	+	0.136035i	0.00188697	+	0.00487084i
$781$	7.19365	+	9.52593i	0.257409	+	0.340865i
$782$	6.89013	−	5.99362i	0.246391	−	0.214331i
$783$	1.42258	−	1.88380i	0.0508388	−	0.0673215i
$784$	14.4402	+	4.10859i	0.515722	+	0.146735i
$785$	−3.61196	+	1.21061i	−0.128916	+	0.0432084i
$786$	3.19950	−	6.42546i	0.114122	−	0.229189i
$787$	−1.93120	−	41.7712i	−0.0688398	−	1.48898i	−0.700454	−	0.713698i	$-0.747019\pi$
$787$	−1.93120	−	41.7712i	−0.0688398	−	1.48898i	0.631614	−	0.775283i	$-0.282393\pi$
$788$	0.0721958	−	1.56157i	0.00257187	−	0.0556287i
$789$	1.08000	+	0.361979i	0.0384489	+	0.0128868i
$790$	−3.78362	+	2.85726i	−0.134615	+	0.101657i
$791$	−0.405487	+	0.444798i	−0.0144175	+	0.0158152i
$792$	4.46298	−	4.46298i	0.158585	−	0.158585i
$793$	−17.2239	−	5.77288i	−0.611639	−	0.205001i
$794$	−24.8909	−	17.0507i	−0.883345	−	0.605105i
$795$	−0.313661	+	3.38494i	−0.0111244	+	0.120051i
$796$	1.41324	+	0.332392i	0.0500911	+	0.0117813i
$797$	27.5371	−	13.7119i	0.975415	−	0.485699i	0.113933	−	0.993488i	$-0.463655\pi$
$797$	27.5371	−	13.7119i	0.975415	−	0.485699i	0.861481	+	0.507790i	$0.169537\pi$
$798$	4.36835	+	3.98228i	0.154638	+	0.140971i
$799$	−0.479837	+	1.02170i	−0.0169754	+	0.0361450i
$800$	2.11174	−	1.92510i	0.0746612	−	0.0680627i
$801$	5.52604	−	14.2644i	0.195253	−	0.504006i
$802$	23.8859	+	23.8859i	0.843440	+	0.843440i
$803$	−0.252014	−	0.885738i	−0.00889339	−	0.0312570i
$804$	0.0520001	−	0.0174287i	0.00183390	−	0.000614662i
$805$	1.88756	−	2.75549i	0.0665277	−	0.0971184i
$806$	−1.46202	−	4.36207i	−0.0514974	−	0.153647i
$807$	1.11957	−	1.80817i	0.0394108	−	0.0636506i
$808$	17.3045	−	8.61663i	0.608771	−	0.303132i
$809$	2.65475	+	19.0313i	0.0933361	+	0.669105i	0.978863	+	0.204517i	$0.0655623\pi$
$809$	2.65475	+	19.0313i	0.0933361	+	0.669105i	−0.885527	+	0.464588i	$0.846202\pi$
$810$	−12.7040	+	2.98795i	−0.446373	+	0.104986i
$811$	−1.65791	+	1.37671i	−0.0582169	+	0.0483427i	−0.667498	−	0.744612i	$-0.732635\pi$
$811$	−1.65791	+	1.37671i	−0.0582169	+	0.0483427i	0.609281	+	0.792954i	$0.291458\pi$
$812$	−0.192706	+	0.175675i	−0.00676266	+	0.00616498i
$813$	0.277437	−	0.334105i	0.00973014	−	0.0117176i
$814$	1.47581	+	2.38351i	0.0517271	+	0.0835421i
$815$	3.69821	+	2.28983i	0.129543	+	0.0802094i
$816$	6.99144	+	1.47609i	0.244749	+	0.0516736i
$817$	−22.5150	+	13.9407i	−0.787699	+	0.487723i
$818$	−1.82211	−	0.907303i	−0.0637086	−	0.0317231i
$819$	−3.62258	+	10.8083i	−0.126583	+	0.377673i
$820$	0.0418611	+	0.0259193i	0.00146185	+	0.000905141i
$821$	6.09181	+	8.89295i	0.212606	+	0.310366i	0.916574	−	0.399865i	$-0.130943\pi$
$821$	6.09181	+	8.89295i	0.212606	+	0.310366i	−0.703968	+	0.710232i	$0.748590\pi$
$822$	10.0997	−	4.45947i	0.352269	−	0.155542i
$823$	4.99245	−	7.28807i	0.174026	−	0.254046i	−0.728147	−	0.685421i	$-0.759618\pi$
$823$	4.99245	−	7.28807i	0.174026	−	0.254046i	0.902173	+	0.431375i	$0.141971\pi$
$824$	4.58327	−	24.5183i	0.159666	−	0.854137i
$825$	1.19319	−	0.110565i	0.0415415	−	0.00384939i
$826$	2.47029	+	1.37594i	0.0859524	+	0.0478752i
$827$	33.7607	−	33.7607i	1.17397	−	1.17397i	0.192720	−	0.981254i	$-0.438269\pi$
$827$	33.7607	−	33.7607i	1.17397	−	1.17397i	0.981254	−	0.192720i	$-0.0617310\pi$
$828$	0.243656	+	0.551827i	0.00846762	+	0.0191773i
$829$	−35.8677			−1.24574			−0.622869	−	0.782326i	$-0.714033\pi$
$829$	−35.8677			−1.24574			−0.622869	+	0.782326i	$0.714033\pi$
$830$	7.96512	+	18.0393i	0.276473	+	0.626152i
$831$	0.0774713	−	0.0585036i	0.00268745	−	0.00202947i
$832$	14.8043	+	5.73521i	0.513246	+	0.198833i
$833$	4.93556	−	13.6620i	0.171007	−	0.473359i
$834$	7.40606	−	2.86912i	0.256451	−	0.0993496i
$835$	−2.22002	+	3.58545i	−0.0768269	+	0.124080i
$836$	0.607106	−	0.0846877i	0.0209972	−	0.00292899i
$837$	−3.40073	+	0.635706i	−0.117546	+	0.0219732i
$838$	17.0797	−	20.5683i	0.590010	−	0.710521i
$839$	43.4580	+	6.06213i	1.50034	+	0.209288i	0.840372	−	0.542010i	$-0.182336\pi$
$839$	43.4580	+	6.06213i	1.50034	+	0.209288i	0.659964	+	0.751297i	$0.270572\pi$
$840$	2.43838	−	0.112733i	0.0841322	−	0.00388967i
$841$	5.14688	+	27.5334i	0.177479	+	0.949427i
$842$	−0.328419	−	0.0934433i	−0.0113181	−	0.00322027i
$843$	7.12759	−	3.14714i	0.245487	−	0.108393i
$844$	−0.186153	+	0.791475i	−0.00640766	+	0.0272437i
$845$	−9.78358	+	1.36475i	−0.336565	+	0.0469488i
$846$	−0.839045	−	0.764891i	−0.0288470	−	0.0262975i
$847$	19.2414	+	0.889583i	0.661142	+	0.0305664i
$848$	−20.2813	−	22.2475i	−0.696463	−	0.763984i
$849$	−1.89205	−	0.353686i	−0.0649350	−	0.0121385i
$850$	−13.4810	−	17.0256i	−0.462395	−	0.583974i
$851$	3.48376	−	0.651228i	0.119422	−	0.0223238i
$852$	−0.665375	−	0.502468i	−0.0227954	−	0.0172143i
$853$	18.0124	+	26.2949i	0.616734	+	0.900321i	0.999725	−	0.0234310i	$-0.00745900\pi$
$853$	18.0124	+	26.2949i	0.616734	+	0.900321i	−0.382991	+	0.923752i	$0.625106\pi$
$854$	13.8477	−	18.3373i	0.473857	−	0.627488i
$855$	16.3466	+	7.21772i	0.559041	+	0.246841i
$856$	−37.6255	−	31.2438i	−1.28601	−	1.06789i
$857$	30.3608	+	36.5622i	1.03711	+	1.24894i	0.967899	+	0.251338i	$0.0808706\pi$
$857$	30.3608	+	36.5622i	1.03711	+	1.24894i	0.0692075	+	0.997602i	$0.477953\pi$
$858$	−0.552917	−	0.892991i	−0.0188763	−	0.0304862i
$859$	−17.9618	−	13.5641i	−0.612848	−	0.462802i	0.250013	−	0.968242i	$-0.419565\pi$
$859$	−17.9618	−	13.5641i	−0.612848	−	0.462802i	−0.862861	+	0.505441i	$0.831330\pi$
$860$	0.189279	−	0.804765i	0.00645436	−	0.0274423i
$861$	−0.0713369	−	0.212840i	−0.00243116	−	0.00725358i
$862$	0.247900	−	1.77714i	0.00844351	−	0.0605295i
$863$	2.00695	+	21.6585i	0.0683175	+	0.737264i	0.959144	+	0.282919i	$0.0913029\pi$
$863$	2.00695	+	21.6585i	0.0683175	+	0.737264i	−0.890826	+	0.454344i	$0.849874\pi$
$864$	−0.916510	+	1.64545i	−0.0311803	+	0.0559794i
$865$	−1.72830	+	1.89586i	−0.0587640	+	0.0644611i
$866$	26.2283			0.891274
$867$	1.89433	−	6.64911i	0.0643347	−	0.225816i
$868$	0.382167			0.0129716
$869$	1.51019	−	1.65660i	0.0512298	−	0.0561964i
$870$	0.340813	−	0.611877i	0.0115547	−	0.0207446i
$871$	−0.190898	−	2.06012i	−0.00646834	−	0.0698045i
$872$	−7.25189	+	51.9871i	−0.245580	+	1.76051i
$873$	10.2035	+	30.4430i	0.345335	+	1.03034i
$874$	2.70172	−	11.4870i	0.0913869	−	0.388553i
$875$	−15.1416	−	11.4344i	−0.511878	−	0.386552i
$876$	0.0338618	+	0.0546888i	0.00114409	+	0.00184776i
$877$	−18.6078	−	22.4086i	−0.628342	−	0.756684i	0.355703	−	0.934599i	$-0.384241\pi$
$877$	−18.6078	−	22.4086i	−0.628342	−	0.756684i	−0.984046	+	0.177915i	$0.943065\pi$
$878$	−34.7038	−	28.8177i	−1.17120	−	0.972550i
$879$	8.64009	+	3.81497i	0.291423	+	0.128676i
$880$	2.48698	−	3.29329i	0.0838361	−	0.111017i
$881$	−20.8779	−	30.4780i	−0.703396	−	1.02683i	−0.997473	−	0.0710495i	$-0.977365\pi$
$881$	−20.8779	−	30.4780i	−0.703396	−	1.02683i	0.294077	−	0.955782i	$-0.404988\pi$
$882$	11.6599	+	8.80518i	0.392610	+	0.296486i
$883$	−30.9164	+	5.77927i	−1.04042	+	0.194488i	−0.676118	−	0.736793i	$-0.736339\pi$
$883$	−30.9164	+	5.77927i	−1.04042	+	0.194488i	−0.364301	+	0.931281i	$0.618692\pi$
$884$	−0.531379	+	1.13144i	−0.0178722	+	0.0380545i
$885$	−0.490266	−	0.0916466i	−0.0164801	−	0.00308067i
$886$	5.10058	+	5.59507i	0.171357	+	0.187970i
$887$	1.45725	+	0.0673727i	0.0489296	+	0.00226215i	0.0706344	−	0.997502i	$-0.477498\pi$
$887$	1.45725	+	0.0673727i	0.0489296	+	0.00226215i	−0.0217048	+	0.999764i	$0.506909\pi$
$888$	1.91415	+	1.74497i	0.0642345	+	0.0585575i
$889$	−20.0541	+	2.79742i	−0.672591	+	0.0938225i
$890$	2.13892	−	9.09415i	0.0716969	−	0.304836i
$891$	5.64454	−	2.49231i	0.189099	−	0.0834954i
$892$	1.81337	+	0.515949i	0.0607162	+	0.0172752i
$893$	0.268010	+	1.43373i	0.00896860	+	0.0479778i
$894$	−4.50231	+	0.208155i	−0.150580	+	0.00696173i
$895$	−21.0425	−	2.93531i	−0.703374	−	0.0981165i
$896$	−14.7209	+	17.7277i	−0.491790	+	0.592241i
$897$	−1.30520	+	0.243985i	−0.0435794	+	0.00814641i
$898$	−1.53501	+	0.214125i	−0.0512239	+	0.00714543i
$899$	−0.763571	+	1.23321i	−0.0254665	+	0.0411298i
$900$	1.33761	−	0.518195i	0.0445872	−	0.0172732i
$901$	−22.8359	+	18.0816i	−0.760774	+	0.602386i
$902$	−0.330536	−	0.128050i	−0.0110057	−	0.00426361i
$903$	−3.00791	+	2.27147i	−0.100097	+	0.0755896i
$904$	0.354698	+	0.803315i	0.0117971	+	0.0267178i
$905$	−12.0524			−0.400635
$906$	2.78609	+	6.30988i	0.0925615	+	0.209632i
$907$	13.9001	−	13.9001i	0.461545	−	0.461545i	−0.437616	−	0.899162i	$-0.644177\pi$
$907$	13.9001	−	13.9001i	0.461545	−	0.461545i	0.899162	+	0.437616i	$0.144177\pi$
$908$	−0.407543	−	0.227000i	−0.0135248	−	0.00753326i
$909$	20.0562	−	1.85848i	0.665223	−	0.0616420i
$910$	−1.27920	+	6.84313i	−0.0424052	+	0.226848i
$911$	12.3371	−	18.0099i	0.408746	−	0.596696i	−0.564788	−	0.825236i	$-0.691042\pi$
$911$	12.3371	−	18.0099i	0.408746	−	0.596696i	0.973535	+	0.228540i	$0.0733951\pi$
$912$	8.44659	−	3.72953i	0.279694	−	0.123497i
$913$	−5.26892	−	7.69168i	−0.174376	−	0.254558i
$914$	−25.3924	−	15.7223i	−0.839907	−	0.520049i
$915$	−1.28804	+	3.84299i	−0.0425813	+	0.127045i
$916$	−0.0173096	−	0.00861914i	−0.000571924	−	0.000284784i
$917$	19.1250	−	11.8417i	0.631563	−	0.391047i
$918$	11.9914	+	7.81654i	0.395775	+	0.257984i
$919$	9.61312	+	5.95219i	0.317108	+	0.196345i	0.675751	−	0.737130i	$-0.263819\pi$
$919$	9.61312	+	5.95219i	0.317108	+	0.196345i	−0.358643	+	0.933475i	$0.616761\pi$
$920$	−2.56530	−	4.14310i	−0.0845754	−	0.136594i
$921$	0.223862	−	0.269586i	0.00737650	−	0.00888318i
$922$	33.2443	−	30.3061i	1.09484	−	0.998080i
$923$	−24.1989	+	20.0945i	−0.796516	+	0.661419i
$924$	0.0849314	−	0.0199757i	0.00279404	−	0.000657152i
$925$	−1.16437	−	8.34713i	−0.0382844	−	0.274452i
$926$	38.6584	−	19.2496i	1.27039	−	0.632581i
$927$	13.6817	−	22.0967i	0.449366	−	0.725751i
$928$	0.250946	+	0.748721i	0.00823771	+	0.0245780i
$929$	−20.3321	+	29.6813i	−0.667076	+	0.973811i	0.332453	+	0.943120i	$0.392124\pi$
$929$	−20.3321	+	29.6813i	−0.667076	+	0.973811i	−0.999529	+	0.0306911i	$0.990229\pi$
$930$	−0.973263	+	0.326205i	−0.0319146	+	0.0106967i
$931$	−5.13675	−	18.0538i	−0.168350	−	0.591690i
$932$	−0.802985	−	0.802985i	−0.0263027	−	0.0263027i
$933$	4.44895	−	11.4841i	0.145652	−	0.375972i
$934$	−24.3728	+	22.2187i	−0.797501	+	0.727018i
$935$	−3.01171	−	2.62167i	−0.0984933	−	0.0857377i
$936$	12.2906	+	11.2044i	0.401732	+	0.366227i
$937$	−4.78373	+	2.38202i	−0.156278	+	0.0778171i	−0.522176	−	0.852838i	$-0.674880\pi$
$937$	−4.78373	+	2.38202i	−0.156278	+	0.0778171i	0.365898	+	0.930655i	$0.380762\pi$
$938$	2.54759	+	0.599187i	0.0831817	+	0.0195642i
$939$	0.912148	−	9.84365i	0.0297668	−	0.321235i
$940$	−0.0375661	−	0.0257334i	−0.00122527	−	0.000839330i
$941$	55.0292	+	18.4439i	1.79390	+	0.601255i	0.999977	−	0.00676337i	$-0.00215286\pi$
$941$	55.0292	+	18.4439i	1.79390	+	0.601255i	0.793923	+	0.608018i	$0.208035\pi$
$942$	−1.35459	+	1.35459i	−0.0441349	+	0.0441349i
$943$	−0.301902	+	0.331171i	−0.00983128	+	0.0107844i
$944$	3.52474	−	2.66176i	0.114721	−	0.0866329i
$945$	4.96381	+	1.66370i	0.161473	+	0.0541202i
$946$	−0.274884	+	5.94565i	−0.00893725	+	0.193310i
$947$	−1.18367	−	25.6024i	−0.0384641	−	0.831965i	−0.927431	−	0.373994i	$-0.877988\pi$
$947$	−1.18367	−	25.6024i	−0.0384641	−	0.831965i	0.888967	−	0.457971i	$-0.151424\pi$
$948$	−0.0697923	+	0.140162i	−0.00226675	+	0.00455225i
$949$	2.30079	−	0.771146i	0.0746867	−	0.0250325i
$950$	−26.9904	−	7.67943i	−0.875684	−	0.249154i
$951$	−7.02263	+	9.29946i	−0.227724	+	0.301556i
$952$	15.1245	+	14.4464i	0.490188	+	0.468211i
$953$	17.6946	+	23.4314i	0.573183	+	0.759017i	0.988592	−	0.150618i	$-0.0481263\pi$
$953$	17.6946	+	23.4314i	0.573183	+	0.759017i	−0.415409	+	0.909635i	$0.636362\pi$
$954$	−10.5837	−	27.3196i	−0.342660	−	0.884506i
$955$	−7.12150	−	30.2788i	−0.230446	−	0.979798i
$956$	1.03761	+	1.37401i	0.0335586	+	0.0444387i
$957$	−0.105234	+	0.313975i	−0.00340173	+	0.0101494i
$958$	−5.60965	−	6.75545i	−0.181240	−	0.218259i
$959$	34.2666	+	4.77999i	1.10653	+	0.154354i
$960$	1.27964	−	3.30312i	0.0413001	−	0.106608i
$961$	−27.7720	+	7.90181i	−0.895870	+	0.254897i
$962$	−6.09433	+	4.17471i	−0.196489	+	0.134598i
$963$	−24.7966	−	44.5183i	−0.799058	−	1.43458i
$964$	2.43071	+	0.571699i	0.0782880	+	0.0184132i
$965$	−21.0363	+	8.14951i	−0.677183	+	0.262342i
$966$	0.232049	−	1.66350i	0.00746605	−	0.0535223i
$967$	−9.31437	+	49.8275i	−0.299530	+	1.60234i	0.419761	+	0.907635i	$0.362114\pi$
$967$	−9.31437	+	49.8275i	−0.299530	+	1.60234i	−0.719291	+	0.694709i	$0.755533\pi$
$968$	12.5265	−	25.1566i	0.402616	−	0.808563i
$969$	−3.03250	−	8.40328i	−0.0974178	−	0.269952i
$970$	8.74023	+	17.5528i	0.280632	+	0.563585i
$971$	27.4443	−	7.80858i	0.880729	−	0.250589i	0.197069	−	0.980390i	$-0.436858\pi$
$971$	27.4443	−	7.80858i	0.880729	−	0.250589i	0.683660	+	0.729800i	$0.260387\pi$
$972$	−1.10143	+	0.914615i	−0.0353284	+	0.0293363i
$973$	24.4659	+	4.57348i	0.784342	+	0.146619i
$974$	54.4591	+	2.51780i	1.74498	+	0.0806754i
$975$	0.436237	+	3.12728i	0.0139708	+	0.100153i
$976$	−17.4658	−	31.3571i	−0.559067	−	1.00372i
$977$		−	10.3929i		−	0.332498i	−0.986084	−	0.166249i	$-0.946834\pi$
$977$		−	10.3929i		−	0.332498i	0.986084	−	0.166249i	$-0.0531655\pi$
$978$	2.17804	+	0.201825i	0.0696461	+	0.00645366i
$979$	−0.203992	+	4.41228i	−0.00651961	+	0.141017i
$980$	0.511936	+	0.285146i	0.0163532	+	0.00910867i
$981$	−26.6137	+	47.7807i	−0.849710	+	1.52552i
$982$	29.7736	+	11.5344i	0.950114	+	0.368076i
$983$	32.8487	+	22.5019i	1.04771	+	0.717699i	0.960440	−	0.278486i	$-0.0898324\pi$
$983$	32.8487	+	22.5019i	1.04771	+	0.717699i	0.0872711	+	0.996185i	$0.472185\pi$
$984$	−0.326110	−	0.0302186i	−0.0103960	−	0.000963333i
$985$	−3.60085	+	12.6557i	−0.114733	+	0.403244i
$986$	5.80878	−	1.50754i	0.184989	−	0.0480099i
$987$	0.0568134	+	0.199678i	0.00180839	+	0.00635583i
$988$	0.296798	+	1.58773i	0.00944241	+	0.0505124i
$989$	6.88344	+	3.03934i	0.218881	+	0.0966453i
$990$	3.41472	−	2.11430i	0.108527	−	0.0671970i
$991$	−2.39969	−	10.2028i	−0.0762286	−	0.324104i	0.921740	−	0.387808i	$-0.126768\pi$
$991$	−2.39969	−	10.2028i	−0.0762286	−	0.324104i	−0.997969	+	0.0637037i	$0.979709\pi$
$992$	0.467458	−	1.05869i	0.0148418	−	0.0336135i
$993$	2.88135	−	6.52563i	0.0914369	−	0.207085i
$994$	−14.3731	−	37.1013i	−0.455887	−	1.17678i
$995$	−10.9389	−	5.44694i	−0.346787	−	0.172680i
$996$	0.501006	+	0.416030i	0.0158750	+	0.0131824i
$997$	−44.2481	+	2.04571i	−1.40135	+	0.0647883i	−0.733592	−	0.679590i	$-0.762158\pi$
$997$	−44.2481	+	2.04571i	−1.40135	+	0.0647883i	−0.667758	+	0.744378i	$0.732746\pi$
$998$	−40.8829	−	40.8829i	−1.29413	−	1.29413i
$999$	2.47613	+	4.97273i	0.0783411	+	0.157330i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.2.h.a.115.18	✓	768
289.191	even	68	inner	289.2.h.a.191.18	yes	768

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.2.h.a.115.18	✓	768	1.1	even	1	trivial
289.2.h.a.191.18	yes	768	289.191	even	68	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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	289.h (of order \(68\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(0.985664 - 1.08122i) q^{2} +(-0.197896 + 0.355292i) q^{3} +(-0.0129704 - 0.139973i) q^{4} +(-0.163469 + 1.17187i) q^{5} +(0.189090 + 0.564168i) q^{6} +(-0.426911 + 1.81511i) q^{7} +(2.17098 + 1.63945i) q^{8} +(1.49223 + 2.41003i) q^{9} +O(q^{10})\)	\(q+(0.985664 - 1.08122i) q^{2} +(-0.197896 + 0.355292i) q^{3} +(-0.0129704 - 0.139973i) q^{4} +(-0.163469 + 1.17187i) q^{5} +(0.189090 + 0.564168i) q^{6} +(-0.426911 + 1.81511i) q^{7} +(2.17098 + 1.63945i) q^{8} +(1.49223 + 2.41003i) q^{9} +(1.10593 + 1.33182i) q^{10} +(-0.629677 - 0.522877i) q^{11} +(0.0522980 + 0.0230918i) q^{12} +(1.29970 - 1.72108i) q^{13} +(1.54175 + 2.25068i) q^{14} +(-0.384006 - 0.289988i) q^{15} +(4.18883 - 0.783027i) q^{16} +(-0.474450 - 4.09572i) q^{17} +(4.07661 + 0.762050i) q^{18} +(-3.58930 - 3.93728i) q^{19} +(0.166151 + 0.00768160i) q^{20} +(-0.560411 - 0.510882i) q^{21} +(-1.18600 + 0.165439i) q^{22} +(-0.346600 + 1.47365i) q^{23} +(-1.01211 + 0.446891i) q^{24} +(3.46257 + 0.985186i) q^{25} +(-0.579802 - 3.10166i) q^{26} +(-2.37033 + 0.109587i) q^{27} +(0.259604 + 0.0362132i) q^{28} +(-0.635545 + 0.765358i) q^{29} +(-0.692042 + 0.129365i) q^{30} +(1.44402 - 0.201432i) q^{31} +(0.417860 - 0.674867i) q^{32} +(0.310384 - 0.120244i) q^{33} +(-4.89603 - 3.52401i) q^{34} +(-2.05729 - 0.796999i) q^{35} +(0.317984 - 0.240130i) q^{36} +(-0.945619 - 2.14162i) q^{37} -7.79491 q^{38} +(0.354279 + 0.802366i) q^{39} +(-2.27611 + 2.27611i) q^{40} +(0.258606 + 0.144043i) q^{41} +(-1.10475 + 0.102370i) q^{42} +(0.913317 - 4.88582i) q^{43} +(-0.0650215 + 0.0949196i) q^{44} +(-3.06818 + 1.35473i) q^{45} +(1.25171 + 1.82728i) q^{46} +(-0.232760 - 0.144119i) q^{47} +(-0.550750 + 1.64321i) q^{48} +(3.15376 + 1.57039i) q^{49} +(4.47813 - 2.77274i) q^{50} +(1.54907 + 0.641959i) q^{51} +(-0.257762 - 0.159599i) q^{52} +(-3.71898 - 6.00636i) q^{53} +(-2.21786 + 2.67087i) q^{54} +(0.715677 - 0.652426i) q^{55} +(-3.90260 + 3.24068i) q^{56} +(2.10919 - 0.496077i) q^{57} +(0.201088 + 1.44155i) q^{58} +(0.927826 - 0.462002i) q^{59} +(-0.0356098 + 0.0575117i) q^{60} +(-2.67673 - 7.98627i) q^{61} +(1.20552 - 1.75985i) q^{62} +(-5.01152 + 1.67969i) q^{63} +(2.01455 + 7.08043i) q^{64} +(1.80442 + 1.80442i) q^{65} +(0.175925 - 0.454114i) q^{66} +(0.708941 - 0.646285i) q^{67} +(-0.567136 + 0.119533i) q^{68} +(-0.454986 - 0.414774i) q^{69} +(-2.88953 + 1.43882i) q^{70} +(-14.1971 - 3.33914i) q^{71} +(-0.711524 + 7.67857i) q^{72} +(0.928237 + 0.635857i) q^{73} +(-3.24763 - 1.08850i) q^{74} +(-1.03526 + 1.03526i) q^{75} +(-0.504557 + 0.553473i) q^{76} +(1.21790 - 0.919713i) q^{77} +(1.21674 + 0.407809i) q^{78} +(-0.126489 + 2.73591i) q^{79} +(0.232864 + 5.03677i) q^{80} +(-3.36033 + 6.74846i) q^{81} +(0.410641 - 0.137633i) q^{82} +(10.9563 + 3.11732i) q^{83} +(-0.0642409 + 0.0850687i) q^{84} +(4.87721 + 0.113529i) q^{85} +(-4.38243 - 5.80327i) q^{86} +(-0.146153 - 0.377265i) q^{87} +(-0.509787 - 2.16748i) q^{88} +(-3.25221 - 4.30662i) q^{89} +(-1.55942 + 4.65269i) q^{90} +(2.56910 + 3.09384i) q^{91} +(0.210767 + 0.0294007i) q^{92} +(-0.214199 + 0.552910i) q^{93} +(-0.385247 + 0.109612i) q^{94} +(5.20072 - 3.56258i) q^{95} +(0.157082 + 0.282016i) q^{96} +(11.0261 + 2.59331i) q^{97} +(4.80648 - 1.86204i) q^{98} +(0.320528 - 2.29779i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 768 q - 34 q^{2} - 34 q^{3} + 14 q^{4} - 34 q^{5} - 34 q^{6} - 34 q^{7} - 34 q^{8} - 34 q^{9}+O(q^{10}) \) 768 * q - 34 * q^2 - 34 * q^3 + 14 * q^4 - 34 * q^5 - 34 * q^6 - 34 * q^7 - 34 * q^8 - 34 * q^9	\( 768 q - 34 q^{2} - 34 q^{3} + 14 q^{4} - 34 q^{5} - 34 q^{6} - 34 q^{7} - 34 q^{8} - 34 q^{9} + 34 q^{10} - 34 q^{11} - 34 q^{12} - 30 q^{13} - 34 q^{14} - 34 q^{15} - 82 q^{16} - 34 q^{17} - 42 q^{18} - 34 q^{19} - 34 q^{20} - 26 q^{21} - 34 q^{22} - 34 q^{23} - 204 q^{24} + 170 q^{25} - 34 q^{26} - 34 q^{27} - 34 q^{28} - 34 q^{29} - 14 q^{30} - 34 q^{31} - 34 q^{32} + 56 q^{33} - 34 q^{34} - 42 q^{35} - 34 q^{36} - 34 q^{37} + 144 q^{38} - 170 q^{39} - 34 q^{40} - 34 q^{41} - 34 q^{42} - 34 q^{43} - 34 q^{44} - 34 q^{45} + 102 q^{46} - 30 q^{47} - 34 q^{48} - 34 q^{49} - 62 q^{50} + 238 q^{51} - 50 q^{52} + 136 q^{54} - 14 q^{55} - 34 q^{56} - 34 q^{57} - 34 q^{58} - 34 q^{59} - 34 q^{60} - 34 q^{61} - 238 q^{62} - 34 q^{63} + 38 q^{64} - 34 q^{65} + 476 q^{66} + 82 q^{67} - 34 q^{68} - 62 q^{69} - 34 q^{70} - 34 q^{71} + 10 q^{72} - 34 q^{73} - 34 q^{74} + 102 q^{75} - 102 q^{76} - 374 q^{77} - 34 q^{78} + 68 q^{79} - 34 q^{80} + 30 q^{81} - 34 q^{82} + 102 q^{83} - 82 q^{84} - 204 q^{85} - 62 q^{86} - 34 q^{87} + 170 q^{88} - 22 q^{89} - 34 q^{90} - 34 q^{91} + 34 q^{92} - 34 q^{93} + 238 q^{94} - 34 q^{95} + 544 q^{96} - 34 q^{97} + 10 q^{98} - 34 q^{99}+O(q^{100}) \) 768 * q - 34 * q^2 - 34 * q^3 + 14 * q^4 - 34 * q^5 - 34 * q^6 - 34 * q^7 - 34 * q^8 - 34 * q^9 + 34 * q^10 - 34 * q^11 - 34 * q^12 - 30 * q^13 - 34 * q^14 - 34 * q^15 - 82 * q^16 - 34 * q^17 - 42 * q^18 - 34 * q^19 - 34 * q^20 - 26 * q^21 - 34 * q^22 - 34 * q^23 - 204 * q^24 + 170 * q^25 - 34 * q^26 - 34 * q^27 - 34 * q^28 - 34 * q^29 - 14 * q^30 - 34 * q^31 - 34 * q^32 + 56 * q^33 - 34 * q^34 - 42 * q^35 - 34 * q^36 - 34 * q^37 + 144 * q^38 - 170 * q^39 - 34 * q^40 - 34 * q^41 - 34 * q^42 - 34 * q^43 - 34 * q^44 - 34 * q^45 + 102 * q^46 - 30 * q^47 - 34 * q^48 - 34 * q^49 - 62 * q^50 + 238 * q^51 - 50 * q^52 + 136 * q^54 - 14 * q^55 - 34 * q^56 - 34 * q^57 - 34 * q^58 - 34 * q^59 - 34 * q^60 - 34 * q^61 - 238 * q^62 - 34 * q^63 + 38 * q^64 - 34 * q^65 + 476 * q^66 + 82 * q^67 - 34 * q^68 - 62 * q^69 - 34 * q^70 - 34 * q^71 + 10 * q^72 - 34 * q^73 - 34 * q^74 + 102 * q^75 - 102 * q^76 - 374 * q^77 - 34 * q^78 + 68 * q^79 - 34 * q^80 + 30 * q^81 - 34 * q^82 + 102 * q^83 - 82 * q^84 - 204 * q^85 - 62 * q^86 - 34 * q^87 + 170 * q^88 - 22 * q^89 - 34 * q^90 - 34 * q^91 + 34 * q^92 - 34 * q^93 + 238 * q^94 - 34 * q^95 + 544 * q^96 - 34 * q^97 + 10 * q^98 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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