LMFDB - Embedded newform 225.2.q.a.16.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.20
Character	$\chi$	$=$	225.16
Dual form			225.2.q.a.211.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00759 - 0.448609i) q^{2} +(1.00870 + 1.40802i) q^{3} +(-0.524267 + 0.582258i) q^{4} +(1.72966 - 1.41714i) q^{5} +(1.64801 + 0.966199i) q^{6} +(0.860383 - 1.49023i) q^{7} +(-0.948701 + 2.91980i) q^{8} +(-0.965042 + 2.84054i) q^{9} +O(q^{10})$	\(q+(1.00759 - 0.448609i) q^{2} +(1.00870 + 1.40802i) q^{3} +(-0.524267 + 0.582258i) q^{4} +(1.72966 - 1.41714i) q^{5} +(1.64801 + 0.966199i) q^{6} +(0.860383 - 1.49023i) q^{7} +(-0.948701 + 2.91980i) q^{8} +(-0.965042 + 2.84054i) q^{9} +(1.10705 - 2.20384i) q^{10} +(0.0672106 - 0.0299241i) q^{11} +(-1.34866 - 0.150855i) q^{12} +(-2.55665 - 1.13830i) q^{13} +(0.198386 - 1.88752i) q^{14} +(3.74007 + 1.00592i) q^{15} +(0.190149 + 1.80914i) q^{16} +(0.268852 - 0.827443i) q^{17} +(0.301925 + 3.29504i) q^{18} +(0.867657 - 2.67037i) q^{19} +(-0.0816614 + 1.75007i) q^{20} +(2.96614 - 0.291758i) q^{21} +(0.0542967 - 0.0603026i) q^{22} +(-0.295519 + 2.81167i) q^{23} +(-5.06810 + 1.60942i) q^{24} +(0.983426 - 4.90233i) q^{25} -3.08672 q^{26} +(-4.97298 + 1.50646i) q^{27} +(0.416626 + 1.28224i) q^{28} +(-3.13652 - 0.666689i) q^{29} +(4.21974 - 0.664273i) q^{30} +(-0.118483 + 0.0251844i) q^{31} +(-2.06687 - 3.57992i) q^{32} +(0.109929 + 0.0644494i) q^{33} +(-0.100305 - 0.954336i) q^{34} +(-0.623694 - 3.79687i) q^{35} +(-1.14799 - 2.05111i) q^{36} +(1.86002 - 1.35138i) q^{37} +(-0.323709 - 3.07989i) q^{38} +(-0.976157 - 4.74802i) q^{39} +(2.49684 + 6.39470i) q^{40} +(-10.1034 - 4.49833i) q^{41} +(2.85778 - 1.62461i) q^{42} +(4.98237 - 8.62972i) q^{43} +(-0.0178128 + 0.0548221i) q^{44} +(2.35626 + 6.28077i) q^{45} +(0.963580 + 2.96559i) q^{46} +(-10.7907 - 2.29364i) q^{47} +(-2.35551 + 2.09262i) q^{48} +(2.01948 + 3.49785i) q^{49} +(-1.20834 - 5.38073i) q^{50} +(1.43625 - 0.456093i) q^{51} +(2.00315 - 0.891860i) q^{52} +(2.96839 + 9.13577i) q^{53} +(-4.33493 + 3.74883i) q^{54} +(0.0738447 - 0.147005i) q^{55} +(3.53492 + 3.92593i) q^{56} +(4.63515 - 1.47193i) q^{57} +(-3.45942 + 0.735323i) q^{58} +(6.95253 + 3.09547i) q^{59} +(-2.54650 + 1.65031i) q^{60} +(-11.6667 + 5.19434i) q^{61} +(-0.108085 + 0.0785282i) q^{62} +(3.40275 + 3.88209i) q^{63} +(-6.63193 - 4.81838i) q^{64} +(-6.03526 + 1.65428i) q^{65} +(0.139677 + 0.0156235i) q^{66} +(15.7155 - 3.34044i) q^{67} +(0.340834 + 0.590342i) q^{68} +(-4.25698 + 2.42004i) q^{69} +(-2.33174 - 3.54590i) q^{70} +(3.68727 + 11.3483i) q^{71} +(-7.37829 - 5.51256i) q^{72} +(2.94814 + 2.14195i) q^{73} +(1.26790 - 2.19607i) q^{74} +(7.89457 - 3.56031i) q^{75} +(1.09996 + 1.90519i) q^{76} +(0.0132332 - 0.125905i) q^{77} +(-3.11358 - 4.34616i) q^{78} +(-0.221403 - 0.0470606i) q^{79} +(2.89270 + 2.85973i) q^{80} +(-7.13739 - 5.48249i) q^{81} -12.1981 q^{82} +(2.50430 + 2.78131i) q^{83} +(-1.38517 + 1.88002i) q^{84} +(-0.707580 - 1.81219i) q^{85} +(1.14883 - 10.9304i) q^{86} +(-2.22510 - 5.08878i) q^{87} +(0.0236096 + 0.224631i) q^{88} +(1.26081 + 0.916033i) q^{89} +(5.19176 + 5.27142i) q^{90} +(-3.89602 + 2.83062i) q^{91} +(-1.48219 - 1.64614i) q^{92} +(-0.154974 - 0.141423i) q^{93} +(-11.9016 + 2.52976i) q^{94} +(-2.28354 - 5.84842i) q^{95} +(2.95575 - 6.52127i) q^{96} +(10.1344 + 2.15414i) q^{97} +(3.60398 + 2.61845i) q^{98} +(0.0201397 + 0.219793i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	1.00759	−	0.448609i	0.712476	−	0.317215i	−0.0182995	−	0.999833i	$-0.505825\pi$
$2$	1.00759	−	0.448609i	0.712476	−	0.317215i	0.730776	+	0.682618i	$0.239159\pi$
$3$	1.00870	+	1.40802i	0.582374	+	0.812921i
$3$	1.00870	+	1.40802i	0.582374	+	0.812921i
$4$	−0.524267	+	0.582258i	−0.262134	+	0.291129i
$5$	1.72966	−	1.41714i	0.773526	−	0.633764i
$5$	1.72966	−	1.41714i	0.773526	−	0.633764i
$6$	1.64801	+	0.966199i	0.672798	+	0.394449i
$7$	0.860383	−	1.49023i	0.325194	−	0.563253i	−0.656357	−	0.754450i	$-0.727904\pi$
$7$	0.860383	−	1.49023i	0.325194	−	0.563253i	0.981552	+	0.191197i	$0.0612370\pi$
$8$	−0.948701	+	2.91980i	−0.335417	+	1.03231i
$9$	−0.965042	+	2.84054i	−0.321681	+	0.946848i
$10$	1.10705	−	2.20384i	0.350079	−	0.696916i
$11$	0.0672106	−	0.0299241i	0.0202648	−	0.00902245i	−0.396579	−	0.918000i	$-0.629803\pi$
$11$	0.0672106	−	0.0299241i	0.0202648	−	0.00902245i	0.416844	+	0.908978i	$0.363136\pi$
$12$	−1.34866	−	0.150855i	−0.389325	−	0.0435479i
$13$	−2.55665	−	1.13830i	−0.709088	−	0.315706i	0.0203122	−	0.999794i	$-0.493534\pi$
$13$	−2.55665	−	1.13830i	−0.709088	−	0.315706i	−0.729400	+	0.684087i	$0.760201\pi$
$14$	0.198386	−	1.88752i	0.0530210	−	0.504461i
$15$	3.74007	+	1.00592i	0.965682	+	0.259727i
$16$	0.190149	+	1.80914i	0.0475372	+	0.452286i
$17$	0.268852	−	0.827443i	0.0652063	−	0.200684i	−0.913145	−	0.407634i	$-0.866354\pi$
$17$	0.268852	−	0.827443i	0.0652063	−	0.200684i	0.978351	+	0.206950i	$0.0663538\pi$
$18$	0.301925	+	3.29504i	0.0711645	+	0.776649i
$19$	0.867657	−	2.67037i	0.199054	−	0.612626i	−0.800851	−	0.598863i	$-0.795619\pi$
$19$	0.867657	−	2.67037i	0.199054	−	0.612626i	0.999905	−	0.0137621i	$-0.00438076\pi$
$20$	−0.0816614	+	1.75007i	−0.0182600	+	0.391327i
$21$	2.96614	−	0.291758i	0.647265	−	0.0636668i
$22$	0.0542967	−	0.0603026i	0.0115761	−	0.0128566i
$23$	−0.295519	+	2.81167i	−0.0616199	+	0.586274i	0.919529	+	0.393022i	$0.128570\pi$
$23$	−0.295519	+	2.81167i	−0.0616199	+	0.586274i	−0.981149	+	0.193252i	$0.938096\pi$
$24$	−5.06810	+	1.60942i	−1.03452	+	0.328521i
$25$	0.983426	−	4.90233i	0.196685	−	0.980467i
$26$	−3.08672			−0.605355
$27$	−4.97298	+	1.50646i	−0.957051	+	0.289919i
$28$	0.416626	+	1.28224i	0.0787348	+	0.242321i
$29$	−3.13652	−	0.666689i	−0.582438	−	0.123801i	−0.0927356	−	0.995691i	$-0.529561\pi$
$29$	−3.13652	−	0.666689i	−0.582438	−	0.123801i	−0.489702	+	0.871890i	$0.662894\pi$
$30$	4.21974	−	0.664273i	0.770415	−	0.121279i
$31$	−0.118483	+	0.0251844i	−0.0212802	+	0.00452324i	−0.218539	−	0.975828i	$-0.570129\pi$
$31$	−0.118483	+	0.0251844i	−0.0212802	+	0.00452324i	0.197259	+	0.980351i	$0.436796\pi$
$32$	−2.06687	−	3.57992i	−0.365374	−	0.632847i
$33$	0.109929	+	0.0644494i	0.0191362	+	0.0112192i
$34$	−0.100305	−	0.954336i	−0.0172021	−	0.163667i
$35$	−0.623694	−	3.79687i	−0.105423	−	0.641787i
$36$	−1.14799	−	2.05111i	−0.191332	−	0.341851i
$37$	1.86002	−	1.35138i	0.305785	−	0.222166i	−0.424301	−	0.905521i	$-0.639480\pi$
$37$	1.86002	−	1.35138i	0.305785	−	0.222166i	0.730086	+	0.683355i	$0.239480\pi$
$38$	−0.323709	−	3.07989i	−0.0525126	−	0.499624i
$39$	−0.976157	−	4.74802i	−0.156310	−	0.760291i
$40$	2.49684	+	6.39470i	0.394785	+	1.01109i
$41$	−10.1034	−	4.49833i	−1.57789	−	0.702521i	−0.583880	−	0.811840i	$-0.698466\pi$
$41$	−10.1034	−	4.49833i	−1.57789	−	0.702521i	−0.994007	+	0.109319i	$0.965133\pi$
$42$	2.85778	−	1.62461i	0.440965	−	0.250683i
$43$	4.98237	−	8.62972i	0.759804	−	1.31602i	−0.183146	−	0.983086i	$-0.558628\pi$
$43$	4.98237	−	8.62972i	0.759804	−	1.31602i	0.942950	−	0.332934i	$-0.108038\pi$
$44$	−0.0178128	+	0.0548221i	−0.00268538	+	0.00826475i
$45$	2.35626	+	6.28077i	0.351250	+	0.936282i
$46$	0.963580	+	2.96559i	0.142072	+	0.437253i
$47$	−10.7907	−	2.29364i	−1.57399	−	0.334562i	−0.663526	−	0.748153i	$-0.730941\pi$
$47$	−10.7907	−	2.29364i	−1.57399	−	0.334562i	−0.910462	+	0.413592i	$0.864274\pi$
$48$	−2.35551	+	2.09262i	−0.339988	+	0.302044i
$49$	2.01948	+	3.49785i	0.288497	+	0.499692i
$50$	−1.20834	−	5.38073i	−0.170885	−	0.760951i
$51$	1.43625	−	0.456093i	0.201115	−	0.0638658i
$52$	2.00315	−	0.891860i	0.277787	−	0.123679i
$53$	2.96839	+	9.13577i	0.407740	+	1.25489i	0.918586	+	0.395222i	$0.129332\pi$
$53$	2.96839	+	9.13577i	0.407740	+	1.25489i	−0.510846	+	0.859673i	$0.670668\pi$
$54$	−4.33493	+	3.74883i	−0.589910	+	0.510151i
$55$	0.0738447	−	0.147005i	0.00995721	−	0.0198222i
$56$	3.53492	+	3.92593i	0.472374	+	0.524624i
$57$	4.63515	−	1.47193i	0.613940	−	0.194962i
$58$	−3.45942	+	0.735323i	−0.454244	+	0.0965526i
$59$	6.95253	+	3.09547i	0.905143	+	0.402995i	0.805889	−	0.592067i	$-0.201688\pi$
$59$	6.95253	+	3.09547i	0.905143	+	0.402995i	0.0992537	+	0.995062i	$0.468354\pi$
$60$	−2.54650	+	1.65031i	−0.328752	+	0.213055i
$61$	−11.6667	+	5.19434i	−1.49377	+	0.665068i	−0.981097	−	0.193518i	$-0.938010\pi$
$61$	−11.6667	+	5.19434i	−1.49377	+	0.665068i	−0.512670	+	0.858586i	$0.671343\pi$
$62$	−0.108085	+	0.0785282i	−0.0137268	+	0.00997310i
$63$	3.40275	+	3.88209i	0.428706	+	0.489097i
$64$	−6.63193	−	4.81838i	−0.828992	−	0.602298i
$65$	−6.03526	+	1.65428i	−0.748581	+	0.205188i
$66$	0.139677	+	0.0156235i	0.0171930	+	0.00192312i
$67$	15.7155	−	3.34044i	1.91996	−	0.408099i	0.920091	−	0.391705i	$-0.128115\pi$
$67$	15.7155	−	3.34044i	1.91996	−	0.408099i	0.999866	−	0.0163944i	$-0.00521872\pi$
$68$	0.340834	+	0.590342i	0.0413322	+	0.0715895i
$69$	−4.25698	+	2.42004i	−0.512480	+	0.291339i
$70$	−2.33174	−	3.54590i	−0.278696	−	0.423816i
$71$	3.68727	+	11.3483i	0.437599	+	1.34679i	0.890400	+	0.455179i	$0.150425\pi$
$71$	3.68727	+	11.3483i	0.437599	+	1.34679i	−0.452801	+	0.891612i	$0.649575\pi$
$72$	−7.37829	−	5.51256i	−0.869540	−	0.649662i
$73$	2.94814	+	2.14195i	0.345054	+	0.250696i	0.746791	−	0.665059i	$-0.231593\pi$
$73$	2.94814	+	2.14195i	0.345054	+	0.250696i	−0.401737	+	0.915755i	$0.631593\pi$
$74$	1.26790	−	2.19607i	0.147390	−	0.255288i
$75$	7.89457	−	3.56031i	0.911586	−	0.411109i
$76$	1.09996	+	1.90519i	0.126174	+	0.218540i
$77$	0.0132332	−	0.125905i	0.00150806	−	0.0143482i
$78$	−3.11358	−	4.34616i	−0.352543	−	0.492106i
$79$	−0.221403	−	0.0470606i	−0.0249098	−	0.00529473i	0.195440	−	0.980716i	$-0.437387\pi$
$79$	−0.221403	−	0.0470606i	−0.0249098	−	0.00529473i	−0.220350	+	0.975421i	$0.570720\pi$
$80$	2.89270	+	2.85973i	0.323414	+	0.319728i
$81$	−7.13739	−	5.48249i	−0.793043	−	0.609166i
$82$	−12.1981			−1.34706
$83$	2.50430	+	2.78131i	0.274883	+	0.305288i	0.864741	−	0.502219i	$-0.167483\pi$
$83$	2.50430	+	2.78131i	0.274883	+	0.305288i	−0.589858	+	0.807507i	$0.700816\pi$
$84$	−1.38517	+	1.88002i	−0.151135	+	0.205127i
$85$	−0.707580	−	1.81219i	−0.0767478	−	0.196560i
$86$	1.14883	−	10.9304i	0.123881	−	1.17865i
$87$	−2.22510	−	5.08878i	−0.238556	−	0.545574i
$88$	0.0236096	+	0.224631i	0.00251680	+	0.0239457i
$89$	1.26081	+	0.916033i	0.133646	+	0.0970993i	0.652600	−	0.757703i	$-0.273678\pi$
$89$	1.26081	+	0.916033i	0.133646	+	0.0970993i	−0.518954	+	0.854802i	$0.673678\pi$
$90$	5.19176	+	5.27142i	0.547260	+	0.555656i
$91$	−3.89602	+	2.83062i	−0.408414	+	0.296730i
$92$	−1.48219	−	1.64614i	−0.154529	−	0.171621i
$93$	−0.154974	−	0.141423i	−0.0160701	−	0.0146649i
$94$	−11.9016	+	2.52976i	−1.22756	+	0.260925i
$95$	−2.28354	−	5.84842i	−0.234287	−	0.600035i
$96$	2.95575	−	6.52127i	0.301670	−	0.665574i
$97$	10.1344	+	2.15414i	1.02900	+	0.218720i	0.691324	−	0.722545i	$-0.257028\pi$
$97$	10.1344	+	2.15414i	1.02900	+	0.218720i	0.337671	+	0.941264i	$0.390361\pi$
$98$	3.60398	+	2.61845i	0.364057	+	0.264503i
$99$	0.0201397	+	0.219793i	0.00202411	+	0.0220900i
$100$	2.33884	+	3.14274i	0.233884	+	0.314274i
$101$	−5.57016	+	9.64780i	−0.554251	+	0.959992i	0.443710	+	0.896170i	$0.353662\pi$
$101$	−5.57016	+	9.64780i	−0.554251	+	0.959992i	−0.997961	+	0.0638212i	$0.979671\pi$
$102$	1.24255	−	1.10387i	0.123030	−	0.109300i
$103$	9.40302	−	10.4431i	0.926508	−	1.02899i	−0.0729912	−	0.997333i	$-0.523255\pi$
$103$	9.40302	−	10.4431i	0.926508	−	1.02899i	0.999499	−	0.0316583i	$-0.0100788\pi$
$104$	5.74910	−	6.38502i	0.563745	−	0.626103i
$105$	4.71694	−	4.70808i	0.460326	−	0.459461i
$106$	7.08933	+	7.87349i	0.688576	+	0.764741i
$107$	2.07941			0.201024			0.100512	−	0.994936i	$-0.467952\pi$
$107$	2.07941			0.201024			0.100512	+	0.994936i	$0.467952\pi$
$108$	1.73002	−	3.68535i	0.166471	−	0.354623i
$109$	−4.81227	+	3.49632i	−0.460932	+	0.334887i	−0.793897	−	0.608053i	$-0.791951\pi$
$109$	−4.81227	+	3.49632i	−0.460932	+	0.334887i	0.332965	+	0.942939i	$0.391951\pi$
$110$	0.00845742	−	0.181249i	0.000806384	−	0.0172814i
$111$	3.77898	+	1.25580i	0.358685	+	0.119196i
$112$	2.85964	+	1.27319i	0.270210	+	0.120305i
$113$	15.9127	+	7.08477i	1.49694	+	0.666479i	0.981677	−	0.190554i	$-0.0610286\pi$
$113$	15.9127	+	7.08477i	1.49694	+	0.666479i	0.515260	+	0.857034i	$0.327695\pi$
$114$	4.01002	−	3.56248i	0.375573	−	0.333657i
$115$	3.47339	+	5.28202i	0.323895	+	0.492551i
$116$	2.03256	−	1.47674i	0.188719	−	0.137112i
$117$	5.70066	−	6.16378i	0.527026	−	0.569842i
$118$	8.39398			0.772729
$119$	−1.00176	−	1.11257i	−0.0918313	−	0.101989i
$120$	−6.48530	+	9.96595i	−0.592024	+	0.909763i
$121$	−7.35681	+	8.17057i	−0.668801	+	0.742779i
$122$	−9.42505	+	10.4676i	−0.853304	+	0.947690i
$123$	−3.85759	−	18.7633i	−0.347827	−	1.69183i
$124$	0.0474530	−	0.0821910i	0.00426141	−	0.00738097i
$125$	−5.24631	−	9.87301i	−0.469244	−	0.883069i
$126$	5.17013	+	2.38506i	0.460592	+	0.212478i
$127$	−1.39966	−	1.01691i	−0.124199	−	0.0902362i	0.523951	−	0.851748i	$-0.324457\pi$
$127$	−1.39966	−	1.01691i	−0.124199	−	0.0902362i	−0.648151	+	0.761512i	$0.724457\pi$
$128$	−0.757049	−	0.160916i	−0.0669143	−	0.0142231i
$129$	17.1765	−	1.68953i	1.51231	−	0.148755i
$130$	−5.33896	+	4.37431i	−0.468258	+	0.383652i
$131$	−1.61913	+	0.344156i	−0.141464	+	0.0300690i	−0.278099	−	0.960552i	$-0.589704\pi$
$131$	−1.61913	+	0.344156i	−0.141464	+	0.0300690i	0.136636	+	0.990621i	$0.456371\pi$
$132$	−0.0951584	+	0.0302184i	−0.00828248	+	0.00263017i
$133$	−3.23294	−	3.59055i	−0.280332	−	0.311340i
$134$	14.3363	−	10.4159i	1.23847	−	0.899800i
$135$	−6.46669	+	9.65308i	−0.556564	+	0.830805i
$136$	2.16091	+	1.56999i	0.185296	+	0.134626i
$137$	0.125787	+	1.19678i	0.0107467	+	0.102248i	0.998580	−	0.0532662i	$-0.0169632\pi$
$137$	0.125787	+	1.19678i	0.0107467	+	0.102248i	−0.987834	+	0.155514i	$0.950297\pi$
$138$	−3.20365	+	4.34814i	−0.272713	+	0.370138i
$139$	0.920830	−	8.76112i	0.0781038	−	0.743108i	−0.883456	−	0.468514i	$-0.844790\pi$
$139$	0.920830	−	8.76112i	0.0781038	−	0.743108i	0.961560	−	0.274595i	$-0.0885436\pi$
$140$	2.53774	+	1.62742i	0.214478	+	0.137542i
$141$	−7.65513	−	17.5071i	−0.644678	−	1.47437i
$142$	8.80621	+	9.78029i	0.739001	+	0.820744i
$143$	−0.205897			−0.0172179
$144$	−5.32246	−	1.20577i	−0.443538	−	0.100481i
$145$	−6.36990	+	3.29175i	−0.528991	+	0.273365i
$146$	3.93143	+	0.835651i	0.325367	+	0.0691589i
$147$	−2.88798	+	6.37175i	−0.238197	+	0.525533i
$148$	−0.188294	+	1.79150i	−0.0154777	+	0.147260i
$149$	4.66331	+	8.07709i	0.382033	+	0.661701i	0.991353	−	0.131224i	$-0.0418907\pi$
$149$	4.66331	+	8.07709i	0.382033	+	0.661701i	−0.609320	+	0.792925i	$0.708557\pi$
$150$	6.35733	−	7.12892i	0.519074	−	0.582074i
$151$	−8.58646	+	14.8722i	−0.698756	+	1.21028i	0.270142	+	0.962821i	$0.412929\pi$
$151$	−8.58646	+	14.8722i	−0.698756	+	1.21028i	−0.968898	+	0.247461i	$0.920404\pi$
$152$	6.97381	+	5.06677i	0.565651	+	0.410970i
$153$	2.09093	+	1.56220i	0.169042	+	0.126297i
$154$	−0.0431486	−	0.132798i	−0.00347702	−	0.0107012i
$155$	−0.169245	+	0.211467i	−0.0135941	+	0.0169855i
$156$	3.27634	+	1.92086i	0.262317	+	0.153792i
$157$	0.129733	+	0.224705i	0.0103539	+	0.0179334i	0.871156	−	0.491006i	$-0.163371\pi$
$157$	0.129733	+	0.224705i	0.0103539	+	0.0179334i	−0.860802	+	0.508940i	$0.830038\pi$
$158$	−0.244196	+	0.0519054i	−0.0194272	+	0.00412938i
$159$	−9.86913	+	13.3948i	−0.782673	+	1.06228i
$160$	−8.64823	−	3.26300i	−0.683703	−	0.257962i
$161$	3.93577	+	2.85950i	0.310182	+	0.225361i
$162$	−9.65108	−	2.32222i	−0.758261	−	0.182451i
$163$	−10.2542	+	7.45009i	−0.803168	+	0.583536i	−0.911842	−	0.410542i	$-0.865340\pi$
$163$	−10.2542	+	7.45009i	−0.803168	+	0.583536i	0.108674	+	0.994077i	$0.465340\pi$
$164$	7.91607	−	3.52446i	0.618141	−	0.275214i
$165$	0.281474	−	0.0443097i	0.0219127	−	0.00344951i
$166$	3.77104	+	1.67897i	0.292689	+	0.130314i
$167$	15.2366	−	3.23863i	1.17904	−	0.250613i	0.423612	−	0.905844i	$-0.360762\pi$
$167$	15.2366	−	3.23863i	1.17904	−	0.250613i	0.755429	+	0.655231i	$0.227429\pi$
$168$	−1.96211	+	8.93733i	−0.151380	+	0.689530i
$169$	−3.45794	−	3.84043i	−0.265995	−	0.295418i
$170$	−1.52592	−	1.50853i	−0.117033	−	0.115699i
$171$	6.74799	+	5.04164i	0.516032	+	0.385544i
$172$	2.41263	+	7.42530i	0.183961	+	0.566174i
$173$	−14.2185	+	6.33050i	−1.08101	+	0.481299i	−0.868414	−	0.495840i	$-0.834860\pi$
$173$	−14.2185	+	6.33050i	−1.08101	+	0.481299i	−0.212601	+	0.977139i	$0.568194\pi$
$174$	−4.52487	−	4.12922i	−0.343030	−	0.313035i
$175$	−6.45947	−	5.68341i	−0.488290	−	0.429626i
$176$	0.0669170	+	0.115904i	0.00504406	+	0.00873657i
$177$	2.65455	+	12.9117i	0.199528	+	0.970504i
$178$	1.68133	+	0.357377i	0.126021	+	0.0267865i
$179$	−2.80001	−	8.61753i	−0.209282	−	0.644105i	−0.999510	−	0.0312917i	$-0.990038\pi$
$179$	−2.80001	−	8.61753i	−0.209282	−	0.644105i	0.790228	−	0.612813i	$-0.209962\pi$
$180$	−4.89233	−	1.92085i	−0.364653	−	0.143172i
$181$	5.73308	−	17.6446i	0.426137	−	1.31151i	−0.475765	−	0.879572i	$-0.657829\pi$
$181$	5.73308	−	17.6446i	0.426137	−	1.31151i	0.901902	−	0.431941i	$-0.142171\pi$
$182$	−2.65576	+	4.59991i	−0.196858	+	0.340968i
$183$	−19.0819	−	11.1874i	−1.41058	−	0.826996i
$184$	−7.92917	−	3.53029i	−0.584546	−	0.260257i
$185$	1.30210	−	4.97334i	0.0957320	−	0.365647i
$186$	−0.219595	−	0.0729741i	−0.0161015	−	0.00535072i
$187$	−0.00669074	−	0.0636581i	−0.000489275	−	0.00465514i
$188$	6.99271	−	5.08050i	0.509996	−	0.370534i
$189$	−2.03370	+	8.70701i	−0.147930	+	0.633342i
$190$	−4.92454	−	4.86841i	−0.357264	−	0.353192i
$191$	−1.91046	−	18.1768i	−0.138236	−	1.31523i	−0.815187	−	0.579198i	$-0.803366\pi$
$191$	−1.91046	−	18.1768i	−0.138236	−	1.31523i	0.676951	−	0.736028i	$-0.263301\pi$
$192$	0.0947368	−	14.1982i	0.00683704	−	1.02467i
$193$	−13.4226	−	23.2487i	−0.966182	−	1.67348i	−0.706405	−	0.707808i	$-0.749684\pi$
$193$	−13.4226	−	23.2487i	−0.966182	−	1.67348i	−0.259778	−	0.965668i	$-0.583649\pi$
$194$	11.1777	−	2.37590i	0.802516	−	0.170580i
$195$	−8.41703	−	6.82909i	−0.602756	−	0.489041i
$196$	−3.09540	−	0.657947i	−0.221100	−	0.0469962i
$197$	7.98062	+	24.5618i	0.568596	+	1.74996i	0.657019	+	0.753874i	$0.271817\pi$
$197$	7.98062	+	24.5618i	0.568596	+	1.74996i	−0.0884231	+	0.996083i	$0.528183\pi$
$198$	0.118894	+	0.212427i	0.00844941	+	0.0150965i
$199$	17.2648			1.22387			0.611933	−	0.790909i	$-0.290392\pi$
$199$	17.2648			1.22387			0.611933	+	0.790909i	$0.290392\pi$
$200$	13.3809	+	7.52226i	0.946170	+	0.531904i
$201$	20.5557	+	18.7583i	1.44989	+	1.32311i
$202$	−1.28436	+	12.2199i	−0.0903673	+	0.859788i
$203$	−3.69213	+	4.10052i	−0.259137	+	0.287800i
$204$	−0.487414	+	1.07538i	−0.0341258	+	0.0752917i
$205$	−23.8502	+	6.53739i	−1.66577	+	0.456591i
$206$	4.78954	−	14.7407i	0.333703	−	1.02703i
$207$	−7.70149	−	3.55282i	−0.535291	−	0.246938i
$208$	1.57320	−	4.84180i	0.109082	−	0.335718i
$209$	−0.0215927	−	0.205441i	−0.00149360	−	0.0142107i
$210$	2.64067	−	6.85989i	0.182224	−	0.473378i
$211$	1.80003	−	17.1262i	0.123919	−	1.17901i	−0.739012	−	0.673692i	$-0.764707\pi$
$211$	1.80003	−	17.1262i	0.123919	−	1.17901i	0.862931	−	0.505322i	$-0.168626\pi$
$212$	−6.87560	−	3.06122i	−0.472218	−	0.210245i
$213$	−12.2592	+	16.6388i	−0.839988	+	1.14007i
$214$	2.09520	−	0.932843i	0.143225	−	0.0637678i
$215$	−3.61173	−	21.9872i	−0.246318	−	1.49951i
$216$	0.319301	−	15.9493i	0.0217257	−	1.08521i
$217$	−0.0644104	+	0.198235i	−0.00437246	+	0.0134571i
$218$	−3.28033	+	5.68170i	−0.222172	+	0.384813i
$219$	−0.0421140	+	6.31163i	−0.00284580	+	0.426500i
$220$	0.0468806	+	0.120067i	0.00316069	+	0.00809489i
$221$	−1.62924	+	1.80945i	−0.109594	+	0.121717i
$222$	4.37104	−	0.429948i	0.293365	−	0.0288562i
$223$	−7.14582	+	3.18152i	−0.478520	+	0.213051i	−0.631799	−	0.775132i	$-0.717683\pi$
$223$	−7.14582	+	3.18152i	−0.478520	+	0.213051i	0.153279	+	0.988183i	$0.451017\pi$
$224$	−7.11320			−0.475271
$225$	12.9762	+	7.52442i	0.865083	+	0.501628i
$226$	19.2118			1.27795
$227$	−4.35782	+	1.94023i	−0.289239	+	0.128777i	−0.546227	−	0.837637i	$-0.683936\pi$
$227$	−4.35782	+	1.94023i	−0.289239	+	0.128777i	0.256988	+	0.966415i	$0.417270\pi$
$228$	−1.57301	+	3.47053i	−0.104175	+	0.229842i
$229$	−12.8062	+	14.2227i	−0.846258	+	0.939865i	−0.998827	−	0.0484278i	$-0.984579\pi$
$229$	−12.8062	+	14.2227i	−0.846258	+	0.939865i	0.152568	+	0.988293i	$0.451246\pi$
$230$	5.86933	+	3.76393i	0.387012	+	0.248186i
$231$	0.190626	−	0.108368i	0.0125422	−	0.00713011i
$232$	4.92222	−	8.52554i	0.323160	−	0.559729i
$233$	−1.95135	+	6.00565i	−0.127837	+	0.393443i	−0.994407	−	0.105613i	$-0.966320\pi$
$233$	−1.95135	+	6.00565i	−0.127837	+	0.393443i	0.866570	+	0.499056i	$0.166320\pi$
$234$	2.97881	−	8.76796i	0.194731	−	0.573179i
$235$	−21.9147	+	11.3248i	−1.42955	+	0.738746i
$236$	−5.44734	+	2.42531i	−0.354592	+	0.157874i
$237$	−0.157067	−	0.359210i	−0.0102026	−	0.0233332i
$238$	−1.50848	−	0.671617i	−0.0977801	−	0.0435345i
$239$	−2.13485	+	20.3117i	−0.138092	+	1.31386i	0.677626	+	0.735407i	$0.263009\pi$
$239$	−2.13485	+	20.3117i	−0.138092	+	1.31386i	−0.815718	+	0.578450i	$0.803658\pi$
$240$	−1.10869	+	6.95760i	−0.0715653	+	0.449111i
$241$	0.423906	+	4.03319i	0.0273062	+	0.259801i	0.999655	+	0.0262674i	$0.00836214\pi$
$241$	0.423906	+	4.03319i	0.0273062	+	0.259801i	−0.972349	+	0.233533i	$0.924971\pi$
$242$	−3.74728	+	11.5330i	−0.240884	+	0.741366i
$243$	0.519962	−	15.5798i	0.0333556	−	0.999444i
$244$	3.09201	−	9.51624i	0.197946	−	0.609215i
$245$	8.44995	+	3.18818i	0.539847	+	0.203686i
$246$	−12.3043	−	17.1752i	−0.784491	−	1.09505i
$247$	−5.25797	+	5.83957i	−0.334557	+	0.371563i
$248$	0.0388717	−	0.369840i	0.00246836	−	0.0234848i
$249$	−1.39005	+	6.33162i	−0.0880906	+	0.401250i
$250$	−9.71527	−	7.59444i	−0.614447	−	0.480314i
$251$	−15.4647			−0.976121			−0.488060	−	0.872810i	$-0.662295\pi$
$251$	−15.4647			−0.976121			−0.488060	+	0.872810i	$0.662295\pi$
$252$	−4.04433	−	0.0539735i	−0.254769	−	0.00340001i
$253$	0.0642747	+	0.197817i	0.00404092	+	0.0124367i
$254$	−1.86648	−	0.396733i	−0.117113	−	0.0248932i
$255$	1.83787	−	2.82425i	0.115092	−	0.176861i
$256$	15.2018	−	3.23124i	0.950112	−	0.201952i
$257$	−12.7683	−	22.1153i	−0.796464	−	1.37952i	−0.921906	−	0.387414i	$-0.873368\pi$
$257$	−12.7683	−	22.1153i	−0.796464	−	1.37952i	0.125442	−	0.992101i	$-0.459965\pi$
$258$	16.5490	−	9.40792i	1.03030	−	0.585711i
$259$	−0.413539	−	3.93456i	−0.0256961	−	0.244482i
$260$	2.20087	−	4.38136i	0.136492	−	0.271720i
$261$	4.92063	−	8.26605i	0.304580	−	0.511656i
$262$	−1.47703	+	1.07312i	−0.0912511	+	0.0662978i
$263$	−2.73540	−	26.0256i	−0.168672	−	1.60481i	−0.671892	−	0.740649i	$-0.734518\pi$
$263$	−2.73540	−	26.0256i	−0.168672	−	1.60481i	0.503220	−	0.864158i	$-0.332149\pi$
$264$	−0.292470	+	0.259828i	−0.0180003	+	0.0159913i
$265$	18.0810	+	11.5951i	1.11071	+	0.712283i
$266$	−4.86825	−	2.16748i	−0.298491	−	0.132897i
$267$	−0.0180106	+	2.69925i	−0.00110223	+	0.165191i
$268$	−6.29414	+	10.9018i	−0.384476	+	0.665931i
$269$	−1.12202	+	3.45323i	−0.0684109	+	0.210547i	−0.979418	−	0.201844i	$-0.935306\pi$
$269$	−1.12202	+	3.45323i	−0.0684109	+	0.210547i	0.911007	+	0.412392i	$0.135306\pi$
$270$	−2.18533	+	12.6274i	−0.132995	+	0.768479i
$271$	−2.08198	−	6.40767i	−0.126471	−	0.389238i	0.867695	−	0.497097i	$-0.165601\pi$
$271$	−2.08198	−	6.40767i	−0.126471	−	0.389238i	−0.994166	+	0.107859i	$0.965601\pi$
$272$	1.54809	+	0.329056i	0.0938665	+	0.0199519i
$273$	−7.91550	−	2.63042i	−0.479068	−	0.159200i
$274$	0.663631	+	1.14944i	0.0400914	+	0.0694403i
$275$	−0.0806012	−	0.358917i	−0.00486044	−	0.0216435i
$276$	0.822707	−	3.74741i	0.0495212	−	0.225567i
$277$	9.97918	−	4.44302i	0.599591	−	0.266955i	−0.0844159	−	0.996431i	$-0.526902\pi$
$277$	9.97918	−	4.44302i	0.599591	−	0.266955i	0.684007	+	0.729475i	$0.260236\pi$
$278$	−3.00250	−	9.24074i	−0.180078	−	0.554223i
$279$	0.0428039	−	0.360860i	0.00256260	−	0.0216042i
$280$	11.6778	+	1.78103i	0.697882	+	0.106437i
$281$	−8.88116	−	9.86352i	−0.529805	−	0.588409i	0.417525	−	0.908665i	$-0.362897\pi$
$281$	−8.88116	−	9.86352i	−0.529805	−	0.588409i	−0.947331	+	0.320257i	$0.896231\pi$
$282$	−15.5671	−	14.2059i	−0.927009	−	0.845951i
$283$	9.43123	−	2.00467i	0.560628	−	0.119165i	0.0811229	−	0.996704i	$-0.474149\pi$
$283$	9.43123	−	2.00467i	0.560628	−	0.119165i	0.479506	+	0.877539i	$0.340816\pi$
$284$	−8.54073	−	3.80258i	−0.506799	−	0.225642i
$285$	5.93128	−	9.11459i	0.351339	−	0.539902i
$286$	−0.207460	+	0.0923672i	−0.0122674	+	0.00546179i
$287$	−15.3963	+	11.1861i	−0.908817	+	0.660294i
$288$	12.1636	−	2.41626i	0.716744	−	0.142379i
$289$	13.1409	+	9.54743i	0.772995	+	0.561613i
$290$	−4.94156	+	6.17434i	−0.290178	+	0.362570i
$291$	7.18954	+	16.4424i	0.421458	+	0.963868i
$292$	−2.79278	+	0.593624i	−0.163435	+	0.0347392i
$293$	0.00920116	+	0.0159369i	0.000537537	+	0.000931042i	0.866294	−	0.499534i	$-0.166496\pi$
$293$	0.00920116	+	0.0159369i	0.000537537	+	0.000931042i	−0.865757	+	0.500465i	$0.833162\pi$
$294$	−0.0514827	+	7.71571i	−0.00300253	+	0.449990i
$295$	16.4122	−	4.49862i	0.955556	−	0.261920i
$296$	2.18117	+	6.71295i	0.126778	+	0.390182i
$297$	−0.289158	+	0.250062i	−0.0167786	+	0.0145101i
$298$	8.32218	+	6.04642i	0.482091	+	0.350259i
$299$	3.95605	−	6.85208i	0.228784	−	0.396266i
$300$	−2.06585	+	6.46323i	−0.119272	+	0.373155i
$301$	−8.57349	−	14.8497i	−0.494168	−	0.855924i
$302$	−1.97986	+	18.8371i	−0.113928	+	1.08395i
$303$	−19.2029	+	1.88885i	−1.10318	+	0.108512i
$304$	4.99607	+	1.06195i	0.286545	+	0.0609069i
$305$	−12.8183	+	25.5178i	−0.733971	+	1.46114i
$306$	2.80763	+	0.636054i	0.160502	+	0.0363608i
$307$	−8.63956			−0.493086			−0.246543	−	0.969132i	$-0.579295\pi$
$307$	−8.63956			−0.493086			−0.246543	+	0.969132i	$0.579295\pi$
$308$	0.0663716	+	0.0737131i	0.00378187	+	0.00420020i
$309$	24.1890	+	2.70566i	1.37606	+	0.153920i
$310$	−0.0756642	+	0.288998i	−0.00429744	+	0.0164140i
$311$	1.34053	−	12.7543i	0.0760143	−	0.723228i	−0.888443	−	0.458988i	$-0.848212\pi$
$311$	1.34053	−	12.7543i	0.0760143	−	0.723228i	0.964457	−	0.264240i	$-0.0851212\pi$
$312$	14.7894	+	1.65427i	0.837283	+	0.0936544i
$313$	0.261032	+	2.48355i	0.0147544	+	0.140379i	0.999419	−	0.0340785i	$-0.0108496\pi$
$313$	0.261032	+	2.48355i	0.0147544	+	0.140379i	−0.984665	+	0.174457i	$0.944183\pi$
$314$	0.231523	+	0.168212i	0.0130656	+	0.00949273i
$315$	11.3871	+	1.89250i	0.641588	+	0.106631i
$316$	0.143476	−	0.104241i	0.00807114	−	0.00586402i
$317$	11.2785	+	12.5261i	0.633465	+	0.703534i	0.971350	−	0.237653i	$-0.0763782\pi$
$317$	11.2785	+	12.5261i	0.633465	+	0.703534i	−0.337885	+	0.941187i	$0.609712\pi$
$318$	−3.93502	+	17.9239i	−0.220665	+	1.00512i
$319$	−0.230758	+	0.0490491i	−0.0129200	+	0.00274622i
$320$	−18.2993	+	1.06423i	−1.02296	+	0.0594925i
$321$	2.09750	+	2.92785i	0.117071	+	0.163417i
$322$	5.24846	+	1.11559i	0.292485	+	0.0621696i
$323$	−1.97631	−	1.43587i	−0.109965	−	0.0798941i
$324$	6.93412	−	1.28151i	0.385229	−	0.0711950i
$325$	−8.09458	+	11.4141i	−0.449007	+	0.633142i
$326$	−6.98985	+	12.1068i	−0.387132	+	0.670532i
$327$	−9.77704	−	3.24903i	−0.540671	−	0.179672i
$328$	22.7193	−	25.2324i	1.25447	−	1.39323i
$329$	−12.7022	+	14.1072i	−0.700295	+	0.777756i
$330$	0.263733	−	0.170918i	0.0145180	−	0.00940872i
$331$	21.0641	+	23.3941i	1.15779	+	1.28585i	0.951599	+	0.307342i	$0.0994397\pi$
$331$	21.0641	+	23.3941i	1.15779	+	1.28585i	0.206190	+	0.978512i	$0.433894\pi$
$332$	−2.93236			−0.160934
$333$	2.04367	+	6.58761i	0.111992	+	0.360999i
$334$	13.8994	−	10.0985i	0.760540	−	0.552565i
$335$	22.4486	−	28.0489i	1.22650	−	1.53248i
$336$	1.09184	+	5.31070i	0.0595648	+	0.289722i
$337$	7.27103	+	3.23727i	0.396078	+	0.176345i	0.595104	−	0.803649i	$-0.297111\pi$
$337$	7.27103	+	3.23727i	0.396078	+	0.176345i	−0.199025	+	0.979994i	$0.563778\pi$
$338$	−5.20705	−	2.31833i	−0.283226	−	0.126100i
$339$	6.07562	+	29.5518i	0.329983	+	1.60503i
$340$	1.42612	+	0.538080i	0.0773425	+	0.0291815i
$341$	−0.00720970	+	0.00523816i	−0.000390427	+	0.000283662i
$342$	9.06096	+	2.05271i	0.489960	+	0.110998i
$343$	18.9955			1.02566
$344$	20.4703	+	22.7346i	1.10368	+	1.22577i
$345$	−3.93358	+	10.2186i	−0.211777	+	0.550150i
$346$	−11.4866	+	12.7571i	−0.617522	+	0.685828i
$347$	8.40921	−	9.33938i	0.451430	−	0.501364i	−0.473872	−	0.880593i	$-0.657144\pi$
$347$	8.40921	−	9.33938i	0.451430	−	0.501364i	0.925303	+	0.379229i	$0.123811\pi$
$348$	4.12953	+	1.37229i	0.221366	+	0.0735627i
$349$	10.8487	−	18.7905i	0.580718	−	1.00583i	−0.414677	−	0.909969i	$-0.636105\pi$
$349$	10.8487	−	18.7905i	0.580718	−	1.00583i	0.995394	−	0.0958636i	$-0.0305613\pi$
$350$	−9.05815	−	2.82879i	−0.484178	−	0.151205i
$351$	14.4290	+	1.80922i	0.770163	+	0.0965690i
$352$	−0.246042	−	0.178760i	−0.0131141	−	0.00952792i
$353$	1.53544	+	0.326367i	0.0817230	+	0.0173708i	0.248592	−	0.968608i	$-0.420032\pi$
$353$	1.53544	+	0.326367i	0.0817230	+	0.0173708i	−0.166869	+	0.985979i	$0.553366\pi$
$354$	8.46702	+	11.8189i	0.450017	+	0.628167i
$355$	22.4598	+	14.4032i	1.19204	+	0.764443i
$356$	−1.19437	+	0.253871i	−0.0633014	+	0.0134551i
$357$	0.556041	−	2.53275i	0.0294288	−	0.134047i
$358$	−6.68717	−	7.42686i	−0.353428	−	0.392522i
$359$	−3.14788	+	2.28707i	−0.166139	+	0.120707i	−0.667748	−	0.744387i	$-0.732742\pi$
$359$	−3.14788	+	2.28707i	−0.166139	+	0.120707i	0.501609	+	0.865094i	$0.332742\pi$
$360$	−20.5740	+	0.921239i	−1.08434	+	0.0485535i
$361$	8.99326	+	6.53399i	0.473330	+	0.343894i
$362$	−2.13892	−	20.3505i	−0.112419	−	1.06960i
$363$	−18.9252	−	2.11688i	−0.993313	−	0.111107i
$364$	0.394403	−	3.75249i	0.0206723	−	0.196684i
$365$	8.13472	−	0.473092i	0.425791	−	0.0247627i
$366$	−24.2456	−	2.71200i	−1.26734	−	0.141758i
$367$	−14.0367	−	15.5893i	−0.732709	−	0.813756i	0.255509	−	0.966807i	$-0.417757\pi$
$367$	−14.0367	−	15.5893i	−0.732709	−	0.813756i	−0.988218	+	0.153051i	$0.951090\pi$
$368$	−5.14291			−0.268093
$369$	22.5279	−	24.3581i	1.17276	−	1.26803i
$370$	−0.919104	−	5.59524i	−0.0477819	−	0.290882i
$371$	16.1683	+	3.43668i	0.839418	+	0.178424i
$372$	0.163593	−	0.0160914i	0.00848188	−	0.000834301i
$373$	−2.54774	+	24.2401i	−0.131917	+	1.25510i	0.705567	+	0.708643i	$0.250692\pi$
$373$	−2.54774	+	24.2401i	−0.131917	+	1.25510i	−0.837484	+	0.546462i	$0.815974\pi$
$374$	−0.0352992	−	0.0611400i	−0.00182528	−	0.00316147i
$375$	8.60944	−	17.3458i	0.444589	−	0.895734i
$376$	16.9341	−	29.3308i	0.873312	−	1.51262i
$377$	7.26011	+	5.27478i	0.373915	+	0.271665i
$378$	1.85691	+	9.68546i	0.0955090	+	0.498166i
$379$	−2.82883	−	8.70624i	−0.145307	−	0.447209i	0.851743	−	0.523959i	$-0.175546\pi$
$379$	−2.82883	−	8.70624i	−0.145307	−	0.447209i	−0.997050	+	0.0767501i	$0.975546\pi$
$380$	4.60247	+	1.73652i	0.236102	+	0.0890818i
$381$	0.0199940	−	2.99650i	0.00102432	−	0.153516i
$382$	−10.0792	−	17.4577i	−0.515699	−	0.893216i
$383$	3.39470	−	0.721566i	0.173461	−	0.0368703i	−0.120362	−	0.992730i	$-0.538406\pi$
$383$	3.39470	−	0.721566i	0.173461	−	0.0368703i	0.293823	+	0.955860i	$0.405072\pi$
$384$	−0.537064	−	1.22826i	−0.0274069	−	0.0626792i
$385$	−0.155537	−	0.236526i	−0.00792688	−	0.0120545i
$386$	−23.9541	−	17.4037i	−1.21923	−	0.885825i
$387$	19.7049	+	22.4807i	1.00166	+	1.14276i
$388$	−6.56741	+	4.77150i	−0.333410	+	0.242236i
$389$	1.01305	−	0.451038i	0.0513635	−	0.0228685i	−0.380894	−	0.924619i	$-0.624384\pi$
$389$	1.01305	−	0.451038i	0.0513635	−	0.0228685i	0.432258	+	0.901750i	$0.357717\pi$
$390$	−11.5445	−	3.10499i	−0.584580	−	0.157227i
$391$	2.24705	+	1.00045i	0.113638	+	0.0505949i
$392$	−12.1289	+	2.57808i	−0.612602	+	0.130213i
$393$	−2.11779	−	1.93261i	−0.106829	−	0.0974873i
$394$	19.0599	+	21.1681i	0.960223	+	1.06644i
$395$	−0.449643	+	0.232360i	−0.0226240	+	0.0116913i
$396$	−0.138535	−	0.103504i	−0.00696163	−	0.00520126i
$397$	−10.6072	−	32.6455i	−0.532358	−	1.63843i	−0.749289	−	0.662243i	$-0.769605\pi$
$397$	−10.6072	−	32.6455i	−0.532358	−	1.63843i	0.216931	−	0.976187i	$-0.430395\pi$
$398$	17.3959	−	7.74514i	0.871976	−	0.388229i
$399$	1.79449	−	8.17384i	0.0898368	−	0.409204i
$400$	9.05603	+	0.846987i	0.452801	+	0.0423494i
$401$	−5.42797	−	9.40152i	−0.271060	−	0.469490i	0.698074	−	0.716026i	$-0.254041\pi$
$401$	−5.42797	−	9.40152i	−0.271060	−	0.469490i	−0.969134	+	0.246536i	$0.920708\pi$
$402$	29.1269	+	9.67924i	1.45272	+	0.482756i
$403$	0.331587	+	0.0704811i	0.0165175	+	0.00351091i
$404$	−2.69725	−	8.30129i	−0.134193	−	0.413005i
$405$	−20.1147	+	0.631855i	−0.999507	+	0.0313971i
$406$	−1.88063	+	5.78798i	−0.0933341	+	0.287253i
$407$	0.0845742	−	0.146487i	0.00419219	−	0.00726108i
$408$	−0.0308685	+	4.62626i	−0.00152822	+	0.229034i
$409$	−21.0478	−	9.37110i	−1.04075	−	0.463371i	−0.186074	−	0.982536i	$-0.559576\pi$
$409$	−21.0478	−	9.37110i	−1.04075	−	0.463371i	−0.854674	+	0.519165i	$0.826243\pi$
$410$	−21.0986	+	17.2864i	−1.04198	+	0.853717i
$411$	−1.55821	+	1.38431i	−0.0768610	+	0.0682829i
$412$	1.15089	+	10.9500i	0.0567002	+	0.539466i
$413$	10.5948	−	7.69757i	0.521336	−	0.378772i
$414$	−9.35380	−	0.124831i	−0.459714	−	0.00613511i
$415$	8.27309	+	1.26176i	0.406110	+	0.0619375i
$416$	1.20926	+	11.5053i	0.0592888	+	0.564095i
$417$	13.2647	−	7.54080i	0.649574	−	0.369275i
$418$	−0.113920	−	0.197315i	−0.00557199	−	0.00965097i
$419$	−0.262852	+	0.0558710i	−0.0128412	+	0.00272948i	−0.214328	−	0.976762i	$-0.568756\pi$
$419$	−0.262852	+	0.0558710i	−0.0128412	+	0.00272948i	0.201487	+	0.979491i	$0.435423\pi$
$420$	0.268376	+	5.21477i	0.0130954	+	0.254455i
$421$	−31.8293	−	6.76552i	−1.55126	−	0.329731i	−0.648957	−	0.760825i	$-0.724794\pi$
$421$	−31.8293	−	6.76552i	−1.55126	−	0.329731i	−0.902307	+	0.431094i	$0.858128\pi$
$422$	−5.86926	−	18.0637i	−0.285711	−	0.879328i
$423$	16.9287	−	28.4381i	0.823101	−	1.38271i
$424$	−29.4908			−1.43220
$425$	−3.79200	−	2.13173i	−0.183939	−	0.103404i
$426$	−4.88801	+	22.2647i	−0.236825	+	1.07873i
$427$	−2.29707	+	21.8551i	−0.111163	+	1.05764i
$428$	−1.09017	+	1.21075i	−0.0526952	+	0.0585239i
$429$	−0.207688	−	0.289907i	−0.0100273	−	0.0139968i
$430$	−13.5028	−	20.5339i	−0.651163	−	0.990231i
$431$	6.87180	−	21.1492i	0.331003	−	1.01872i	−0.637655	−	0.770322i	$-0.720095\pi$
$431$	6.87180	−	21.1492i	0.331003	−	1.01872i	0.968658	−	0.248400i	$-0.0799047\pi$
$432$	−3.67102	−	8.71039i	−0.176622	−	0.419079i
$433$	3.53683	−	10.8853i	0.169969	−	0.523112i	−0.829399	−	0.558657i	$-0.811317\pi$
$433$	3.53683	−	10.8853i	0.169969	−	0.523112i	0.999368	+	0.0355453i	$0.0113168\pi$
$434$	0.0240305	+	0.228635i	0.00115350	+	0.0109748i
$435$	−11.0602	−	5.64855i	−0.530295	−	0.270827i
$436$	0.487157	−	4.63499i	0.0233306	−	0.221976i
$437$	7.25180	+	3.22871i	0.346901	+	0.154450i
$438$	2.78902	+	6.37845i	0.133265	+	0.304774i
$439$	−4.38848	+	1.95388i	−0.209451	+	0.0932536i	−0.508781	−	0.860896i	$-0.669904\pi$
$439$	−4.38848	+	1.95388i	−0.209451	+	0.0932536i	0.299330	+	0.954150i	$0.403237\pi$
$440$	0.359170	+	0.355076i	0.0171228	+	0.0169276i
$441$	−11.8847	+	2.36086i	−0.565937	+	0.112422i
$442$	−0.829871	+	2.55408i	−0.0394729	+	0.121485i
$443$	−7.69824	+	13.3337i	−0.365754	+	0.633505i	−0.988897	−	0.148603i	$-0.952522\pi$
$443$	−7.69824	+	13.3337i	−0.365754	+	0.633505i	0.623143	+	0.782108i	$0.285856\pi$
$444$	−2.71240	+	1.54196i	−0.128725	+	0.0731784i
$445$	3.47892	−	0.202324i	0.164916	−	0.00959106i
$446$	−5.77282	+	6.41137i	−0.273351	+	0.303587i
$447$	−6.66882	+	14.7134i	−0.315424	+	0.695920i
$448$	−12.8865	+	5.73743i	−0.608829	+	0.271068i
$449$	−37.4902			−1.76927			−0.884635	−	0.466284i	$-0.845593\pi$
$449$	−37.4902			−1.76927			−0.884635	+	0.466284i	$0.845593\pi$
$450$	16.4503	+	1.76029i	0.775475	+	0.0829809i
$451$	−0.813665			−0.0383140
$452$	−12.4676	+	5.55095i	−0.586429	+	0.261095i
$453$	−29.6015	+	2.91169i	−1.39080	+	0.136803i
$454$	−3.52051	+	3.90992i	−0.165226	+	0.183502i
$455$	−2.72739	+	10.4172i	−0.127862	+	0.488366i
$456$	−0.0996206	+	14.9301i	−0.00466516	+	0.699168i
$457$	14.5265	−	25.1606i	0.679520	−	1.17696i	−0.295606	−	0.955310i	$-0.595522\pi$
$457$	14.5265	−	25.1606i	0.679520	−	1.17696i	0.975126	−	0.221652i	$-0.0711451\pi$
$458$	−6.52300	+	20.0757i	−0.304800	+	0.938077i
$459$	−0.0904867	+	4.51988i	−0.00422356	+	0.210970i
$460$	−4.89648	−	0.746782i	−0.228300	−	0.0348189i
$461$	6.74253	−	3.00197i	0.314031	−	0.139816i	−0.243668	−	0.969859i	$-0.578351\pi$
$461$	6.74253	−	3.00197i	0.314031	−	0.139816i	0.557699	+	0.830043i	$0.311684\pi$
$462$	0.143458	−	0.194708i	0.00667427	−	0.00905862i
$463$	7.19200	+	3.20209i	0.334241	+	0.148814i	0.566993	−	0.823722i	$-0.308107\pi$
$463$	7.19200	+	3.20209i	0.334241	+	0.148814i	−0.232753	+	0.972536i	$0.574773\pi$
$464$	0.609730	−	5.80119i	0.0283060	−	0.269314i
$465$	−0.468469	−	0.0249932i	−0.0217247	−	0.00115903i
$466$	0.728020	+	6.92664i	0.0337249	+	0.320871i
$467$	6.90367	−	21.2473i	0.319464	−	0.983209i	−0.654414	−	0.756137i	$-0.727085\pi$
$467$	6.90367	−	21.2473i	0.319464	−	0.983209i	0.973878	−	0.227072i	$-0.0729154\pi$
$468$	0.600244	+	6.55072i	0.0277463	+	0.302807i
$469$	8.54336	−	26.2938i	0.394496	−	1.21413i
$470$	−17.0007	+	21.2419i	−0.784182	+	0.979815i
$471$	−0.185527	+	0.409328i	−0.00854862	+	0.0188608i
$472$	−15.6340	+	17.3633i	−0.719615	+	0.799213i
$473$	0.0766316	−	0.729101i	0.00352353	−	0.0335241i
$474$	−0.319405	−	0.291476i	−0.0146707	−	0.0133879i
$475$	−12.2378	−	6.87966i	−0.561508	−	0.315660i
$476$	1.17299			0.0537640
$477$	−28.8152	−	0.384553i	−1.31936	−	0.0176075i
$478$	6.96097	+	21.4237i	0.318388	+	0.979896i
$479$	1.22171	+	0.259683i	0.0558215	+	0.0118652i	0.235738	−	0.971817i	$-0.424249\pi$
$479$	1.22171	+	0.259683i	0.0558215	+	0.0118652i	−0.179916	+	0.983682i	$0.557583\pi$
$480$	−4.12912	−	15.4683i	−0.188468	−	0.706027i
$481$	−6.29370	+	1.33777i	−0.286968	+	0.0609969i
$482$	2.23645	+	3.87365i	0.101868	+	0.176440i
$483$	−0.0562223	+	8.42603i	−0.00255820	+	0.383398i
$484$	−0.900441	−	8.56712i	−0.0409291	−	0.389415i
$485$	20.5818	−	10.6360i	0.934571	−	0.482955i
$486$	−6.46533	−	15.9313i	−0.293273	−	0.722661i
$487$	−7.11621	+	5.17023i	−0.322466	+	0.234286i	−0.737227	−	0.675645i	$-0.763865\pi$
$487$	−7.11621	+	5.17023i	−0.322466	+	0.234286i	0.414761	+	0.909930i	$0.363865\pi$
$488$	−4.09826	−	38.9923i	−0.185519	−	1.76510i
$489$	−20.8333	−	6.92316i	−0.942113	−	0.313076i
$490$	9.94436	−	0.578335i	0.449240	−	0.0261265i
$491$	19.8886	+	8.85500i	0.897562	+	0.399620i	0.803056	−	0.595904i	$-0.203206\pi$
$491$	19.8886	+	8.85500i	0.897562	+	0.399620i	0.0945064	+	0.995524i	$0.469873\pi$
$492$	12.9475	+	7.59086i	0.583717	+	0.342222i
$493$	−1.39491	+	2.41605i	−0.0628235	+	0.108814i
$494$	−2.67821	+	8.24268i	−0.120498	+	0.370856i
$495$	0.346312	+	0.351625i	0.0155656	+	0.0158044i
$496$	−0.0680916	−	0.209564i	−0.00305740	−	0.00940971i
$497$	20.0840	+	4.26898i	0.900889	+	0.191490i
$498$	1.43982	+	7.00328i	0.0645200	+	0.313825i
$499$	7.50240	+	12.9945i	0.335854	+	0.581715i	0.983648	−	0.180099i	$-0.0576419\pi$
$499$	7.50240	+	12.9945i	0.335854	+	0.581715i	−0.647795	+	0.761815i	$0.724309\pi$
$500$	8.49910	+	2.12139i	0.380091	+	0.0948715i
$501$	19.9292	+	18.1866i	0.890371	+	0.812516i
$502$	−15.5821	+	6.93760i	−0.695463	+	0.309640i
$503$	−9.75336	−	30.0177i	−0.434881	−	1.33842i	−0.893209	−	0.449642i	$-0.851552\pi$
$503$	−9.75336	−	30.0177i	−0.434881	−	1.33842i	0.458328	−	0.888783i	$-0.348448\pi$
$504$	−14.5631	+	6.25242i	−0.648693	+	0.278505i
$505$	4.03782	+	24.5811i	0.179681	+	1.09384i
$506$	0.153506	+	0.170485i	0.00682415	+	0.00757899i
$507$	1.91938	−	8.74270i	0.0852425	−	0.388277i
$508$	1.32590	−	0.281828i	0.0588272	−	0.0125041i
$509$	−16.1555	−	7.19291i	−0.716081	−	0.318820i	0.0161561	−	0.999869i	$-0.494857\pi$
$509$	−16.1555	−	7.19291i	−0.716081	−	0.318820i	−0.732237	+	0.681050i	$0.761524\pi$
$510$	0.584839	−	3.67018i	0.0258971	−	0.162518i
$511$	5.72852	−	2.55050i	0.253415	−	0.112828i
$512$	15.1200	−	10.9853i	0.668214	−	0.485486i
$513$	−0.292024	+	14.5868i	−0.0128932	+	0.644024i
$514$	−22.7864	−	16.5553i	−1.00506	−	0.730222i
$515$	1.46464	−	31.3884i	0.0645399	−	1.38314i
$516$	−8.02135	+	10.8869i	−0.353120	+	0.479271i
$517$	−0.793886	+	0.168746i	−0.0349151	+	0.00742143i
$518$	−2.18176	−	3.77892i	−0.0958610	−	0.166036i
$519$	−23.2557	−	13.6344i	−1.02081	−	0.598484i
$520$	0.895497	−	19.1912i	0.0392701	−	0.841588i
$521$	6.89659	+	21.2255i	0.302145	+	0.929907i	0.980727	+	0.195382i	$0.0625947\pi$
$521$	6.89659	+	21.2255i	0.302145	+	0.929907i	−0.678582	+	0.734524i	$0.737405\pi$
$522$	1.24977	−	10.5363i	0.0547010	−	0.461160i
$523$	17.1151	+	12.4349i	0.748392	+	0.543738i	0.895328	−	0.445408i	$-0.146941\pi$
$523$	17.1151	+	12.4349i	0.748392	+	0.543738i	−0.146936	+	0.989146i	$0.546941\pi$
$524$	0.648467	−	1.12318i	0.0283284	−	0.0490663i
$525$	1.48668	−	14.8279i	0.0648842	−	0.647144i
$526$	−14.4315	−	24.9961i	−0.629244	−	1.08988i
$527$	−0.0110159	+	0.104809i	−0.000479858	+	0.00456554i
$528$	−0.0956954	+	0.211133i	−0.00416461	+	0.00918838i
$529$	14.6792	+	3.12017i	0.638227	+	0.135659i
$530$	23.4199	+	3.57187i	1.01730	+	0.155152i
$531$	−15.5023	+	16.7617i	−0.672742	+	0.727397i
$532$	3.78555			0.164124
$533$	20.7105	+	23.0013i	0.897070	+	0.996298i
$534$	1.19276	+	2.72783i	0.0516159	+	0.118045i
$535$	3.59666	−	2.94681i	0.155497	−	0.127402i
$536$	−5.15592	+	49.0553i	−0.222702	+	2.11887i
$537$	9.30929	−	12.6350i	0.401725	−	0.545240i
$538$	0.418609	+	3.98280i	0.0180475	+	0.171711i
$539$	0.240401	+	0.174661i	0.0103548	+	0.00752319i
$540$	−2.23031	−	8.82607i	−0.0959773	−	0.379814i
$541$	2.18565	−	1.58797i	0.0939686	−	0.0682722i	−0.539809	−	0.841788i	$-0.681503\pi$
$541$	2.18565	−	1.58797i	0.0939686	−	0.0682722i	0.633777	+	0.773515i	$0.281503\pi$
$542$	−4.97233	−	5.52233i	−0.213580	−	0.237204i
$543$	30.6269	−	9.72585i	1.31433	−	0.417376i
$544$	−3.51786	+	0.747745i	−0.150827	+	0.0320593i
$545$	−3.36880	+	12.8671i	−0.144304	+	0.551166i
$546$	−9.15563	+	0.900574i	−0.391825	+	0.0385410i
$547$	−22.6251	−	4.80910i	−0.967378	−	0.205622i	−0.302976	−	0.952998i	$-0.597980\pi$
$547$	−22.6251	−	4.80910i	−0.967378	−	0.205622i	−0.664402	+	0.747376i	$0.731314\pi$
$548$	−0.762783	−	0.554194i	−0.0325845	−	0.0236740i
$549$	−3.49592	−	38.1525i	−0.149202	−	1.62831i
$550$	−0.242227	−	0.325484i	−0.0103286	−	0.0138787i
$551$	−4.50173	+	7.79723i	−0.191780	+	0.332173i
$552$	−3.02744	−	14.7254i	−0.128856	−	0.626756i
$553$	−0.260622	+	0.289450i	−0.0110828	+	0.0123087i
$554$	8.06178	−	8.95351i	0.342512	−	0.380398i
$555$	8.31599	−	3.18324i	0.352994	−	0.135121i
$556$	4.61847	+	5.12933i	0.195867	+	0.217532i
$557$	2.75385			0.116684			0.0583422	−	0.998297i	$-0.481419\pi$
$557$	2.75385			0.116684			0.0583422	+	0.998297i	$0.481419\pi$
$558$	−0.118757	−	0.382803i	−0.00502737	−	0.0162053i
$559$	−22.5613	+	16.3918i	−0.954243	+	0.693298i
$560$	6.75048	−	1.85032i	0.285260	−	0.0781903i
$561$	0.0828829	−	0.0736327i	0.00349932	−	0.00310878i
$562$	−13.3735	−	5.95425i	−0.564126	−	0.251165i
$563$	23.9656	+	10.6702i	1.01003	+	0.449694i	0.843952	−	0.536419i	$-0.180223\pi$
$563$	23.9656	+	10.6702i	1.01003	+	0.449694i	0.166077	+	0.986113i	$0.446890\pi$
$564$	14.2070	+	4.72117i	0.598223	+	0.198797i
$565$	37.5636	−	10.2962i	1.58031	−	0.433166i
$566$	8.60353	−	6.25083i	0.361633	−	0.262742i
$567$	−14.3110	+	5.91929i	−0.601007	+	0.248587i
$568$	−36.6328			−1.53708
$569$	−18.4167	−	20.4538i	−0.772068	−	0.857469i	0.220968	−	0.975281i	$-0.429079\pi$
$569$	−18.4167	−	20.4538i	−0.772068	−	0.857469i	−0.993036	+	0.117812i	$0.962412\pi$
$570$	1.88743	−	11.8446i	0.0790556	−	0.496117i
$571$	−18.0991	+	20.1011i	−0.757424	+	0.841205i	−0.991377	−	0.131043i	$-0.958167\pi$
$571$	−18.0991	+	20.1011i	−0.757424	+	0.841205i	0.233952	+	0.972248i	$0.424834\pi$
$572$	0.107945	−	0.119885i	0.00451340	−	0.00501264i
$573$	23.6662	−	21.0249i	0.988669	−	0.878328i
$574$	−10.4951	+	18.1780i	−0.438055	+	0.758734i
$575$	13.4931	+	4.21380i	0.562702	+	0.175728i
$576$	20.0869	−	14.1884i	0.836955	−	0.591182i
$577$	8.01728	+	5.82489i	0.333764	+	0.242493i	0.742026	−	0.670371i	$-0.233865\pi$
$577$	8.01728	+	5.82489i	0.333764	+	0.242493i	−0.408262	+	0.912865i	$0.633865\pi$
$578$	17.5238	+	3.72479i	0.728892	+	0.154931i
$579$	19.1952	−	42.3503i	0.797725	−	1.76002i
$580$	1.42288	−	5.43468i	0.0590820	−	0.225663i
$581$	6.29944	−	1.33899i	0.261345	−	0.0555506i
$582$	14.6203	+	13.3419i	0.606032	+	0.553040i
$583$	0.472887	+	0.525194i	0.0195850	+	0.0217513i
$584$	−9.05098	+	6.57592i	−0.374532	+	0.272113i
$585$	1.12523	−	18.7399i	0.0465226	−	0.774798i
$586$	0.0164205	+	0.0119302i	0.000678323	+	0.000492830i
$587$	0.933648	+	8.88307i	0.0385358	+	0.366643i	0.996748	+	0.0805845i	$0.0256787\pi$
$587$	0.933648	+	8.88307i	0.0385358	+	0.366643i	−0.958212	+	0.286059i	$0.907655\pi$
$588$	−2.19593	−	5.02205i	−0.0905586	−	0.207106i
$589$	−0.0355510	+	0.338245i	−0.00146485	+	0.0139372i
$590$	14.5187	−	11.8955i	0.597726	−	0.489728i
$591$	−26.5335	+	36.0124i	−1.09144	+	1.48135i
$592$	2.79853	+	3.10808i	0.115019	+	0.127741i
$593$	−2.95431			−0.121319			−0.0606594	−	0.998159i	$-0.519320\pi$
$593$	−2.95431			−0.121319			−0.0606594	+	0.998159i	$0.519320\pi$
$594$	−0.179173	+	0.381680i	−0.00735156	+	0.0156605i
$595$	−3.30937	−	0.504726i	−0.135671	−	0.0206917i
$596$	−7.14777	−	1.51930i	−0.292784	−	0.0622331i
$597$	17.4150	+	24.3091i	0.712748	+	0.994907i
$598$	0.912182	−	8.67883i	0.0373019	−	0.354904i
$599$	−0.577510	−	1.00028i	−0.0235964	−	0.0408702i	0.853986	−	0.520296i	$-0.174178\pi$
$599$	−0.577510	−	1.00028i	−0.0235964	−	0.0408702i	−0.877582	+	0.479426i	$0.840845\pi$
$600$	2.90581	+	26.4283i	0.118629	+	1.07893i
$601$	6.94255	−	12.0248i	0.283192	−	0.490504i	−0.688977	−	0.724783i	$-0.741940\pi$
$601$	6.94255	−	12.0248i	0.283192	−	0.490504i	0.972169	+	0.234280i	$0.0752732\pi$
$602$	−15.3003	−	11.1163i	−0.623594	−	0.453068i
$603$	−5.67748	+	47.8643i	−0.231205	+	1.94919i
$604$	−4.15785	−	12.7965i	−0.169180	−	0.520683i
$605$	−1.14592	+	24.5579i	−0.0465883	+	0.998422i
$606$	−18.5014	+	10.5178i	−0.751567	+	0.427257i
$607$	21.1355	+	36.6078i	0.857866	+	1.48587i	0.873961	+	0.485996i	$0.161543\pi$
$607$	21.1355	+	36.6078i	0.857866	+	1.48587i	−0.0160954	+	0.999870i	$0.505124\pi$
$608$	−11.3531	+	2.41317i	−0.460428	+	0.0978669i
$609$	−9.49788	−	1.06239i	−0.384873	−	0.0430501i
$610$	−1.46807	+	31.4619i	−0.0594406	+	1.27386i
$611$	24.9773	+	18.1471i	1.01047	+	0.734151i
$612$	−2.00581	+	0.398450i	−0.0810802	+	0.0161064i
$613$	−13.1852	+	9.57962i	−0.532546	+	0.386917i	−0.821309	−	0.570483i	$-0.806756\pi$
$613$	−13.1852	+	9.57962i	−0.532546	+	0.386917i	0.288763	+	0.957401i	$0.406756\pi$
$614$	−8.70516	+	3.87579i	−0.351312	+	0.156414i
$615$	−33.2625	−	26.9873i	−1.34127	−	1.08823i
$616$	0.355064	+	0.158085i	0.0143059	+	0.00636942i
$617$	31.4538	−	6.68571i	1.26628	−	0.269157i	0.474661	−	0.880169i	$-0.342571\pi$
$617$	31.4538	−	6.68571i	1.26628	−	0.269157i	0.791621	+	0.611012i	$0.209237\pi$
$618$	25.5864	−	8.12519i	1.02924	−	0.326843i
$619$	29.5371	+	32.8042i	1.18720	+	1.31851i	0.936591	+	0.350424i	$0.113963\pi$
$619$	29.5371	+	32.8042i	1.18720	+	1.31851i	0.250604	+	0.968090i	$0.419371\pi$
$620$	−0.0343988	−	0.209410i	−0.00138149	−	0.00841010i
$621$	−2.76607	−	14.4276i	−0.110999	−	0.578959i
$622$	−4.37098	−	13.4525i	−0.175260	−	0.539395i
$623$	2.44988	−	1.09076i	0.0981522	−	0.0437002i
$624$	8.40424	−	2.66884i	0.336439	−	0.106839i
$625$	−23.0657	−	9.64216i	−0.922630	−	0.385687i
$626$	1.37716	+	2.38531i	0.0550424	+	0.0953361i
$627$	0.267485	−	0.237632i	0.0106823	−	0.00949011i
$628$	−0.198851	−	0.0422671i	−0.00793502	−	0.00168664i
$629$	−0.618122	−	1.90238i	−0.0246461	−	0.0758530i
$630$	12.3225	−	3.20147i	0.490941	−	0.127549i
$631$	−3.76108	+	11.5754i	−0.149726	+	0.460811i	−0.997588	−	0.0694064i	$-0.977889\pi$
$631$	−3.76108	+	11.5754i	−0.149726	+	0.460811i	0.847862	+	0.530217i	$0.177889\pi$
$632$	0.347453	−	0.601806i	0.0138209	−	0.0239386i
$633$	25.9297	−	14.7407i	1.03061	−	0.585891i
$634$	16.9835	+	7.56153i	0.674500	+	0.300307i
$635$	−3.86203	+	0.224605i	−0.153260	+	0.00891316i
$636$	−2.62518	−	12.7688i	−0.104095	−	0.506318i
$637$	−1.18153	−	11.2415i	−0.0468141	−	0.445406i
$638$	−0.210506	+	0.152942i	−0.00833401	+	0.00605502i
$639$	−35.7936	−	0.477684i	−1.41597	−	0.0188969i
$640$	−1.53748	+	0.794516i	−0.0607741	+	0.0314060i
$641$	−0.0873812	−	0.831377i	−0.00345135	−	0.0328374i	0.992661	−	0.120933i	$-0.0385886\pi$
$641$	−0.0873812	−	0.831377i	−0.00345135	−	0.0328374i	−0.996112	+	0.0880955i	$0.971922\pi$
$642$	3.42689	+	2.00912i	0.135249	+	0.0792937i
$643$	5.78414	+	10.0184i	0.228104	+	0.395088i	0.957246	−	0.289274i	$-0.0934140\pi$
$643$	5.78414	+	10.0184i	0.228104	+	0.395088i	−0.729142	+	0.684362i	$0.760081\pi$
$644$	−3.72836	+	0.792488i	−0.146918	+	0.0312284i
$645$	27.3152	−	27.2639i	1.07554	−	1.07351i
$646$	−2.63546	−	0.560185i	−0.103691	−	0.0220402i
$647$	−9.03550	−	27.8084i	−0.355222	−	1.09326i	−0.955881	−	0.293756i	$-0.905095\pi$
$647$	−9.03550	−	27.8084i	−0.355222	−	1.09326i	0.600658	−	0.799506i	$-0.294905\pi$
$648$	22.7790	−	15.6385i	0.894845	−	0.614339i
$649$	0.559913			0.0219785
$650$	−3.03556	+	15.1321i	−0.119064	+	0.593530i
$651$	−0.344090	+	0.109269i	−0.0134859	+	0.00428258i
$652$	1.03805	−	9.87640i	0.0406532	−	0.386790i
$653$	−6.65329	+	7.38923i	−0.260363	+	0.289163i	−0.859126	−	0.511763i	$-0.828992\pi$
$653$	−6.65329	+	7.38923i	−0.260363	+	0.289163i	0.598763	+	0.800926i	$0.295659\pi$
$654$	−11.3088	+	1.11237i	−0.442210	+	0.0434970i
$655$	−2.31281	+	2.88980i	−0.0903691	+	0.112914i
$656$	6.21697	−	19.1339i	0.242732	−	0.747052i
$657$	−8.92938	+	6.30725i	−0.348368	+	0.246069i
$658$	−6.47002	+	19.9127i	−0.252228	+	0.776276i
$659$	1.31489	+	12.5103i	0.0512207	+	0.487333i	0.989820	+	0.142324i	$0.0454574\pi$
$659$	1.31489	+	12.5103i	0.0512207	+	0.487333i	−0.938599	+	0.345009i	$0.887876\pi$
$660$	−0.121768	+	0.187120i	−0.00473980	+	0.00728365i
$661$	1.25194	−	11.9114i	0.0486949	−	0.463301i	−0.942820	−	0.333304i	$-0.891837\pi$
$661$	1.25194	−	11.9114i	0.0486949	−	0.463301i	0.991514	−	0.129997i	$-0.0414968\pi$
$662$	31.7189	+	14.1221i	1.23279	+	0.548873i
$663$	−4.19116	−	0.468802i	−0.162771	−	0.0182068i
$664$	−10.4967	+	4.67343i	−0.407351	+	0.181364i
$665$	−10.6802	−	1.62888i	−0.414160	−	0.0631653i
$666$	5.01445	+	5.72082i	0.194306	+	0.221677i
$667$	2.80141	−	8.62185i	0.108471	−	0.333840i
$668$	−6.10231	+	10.5695i	−0.236105	+	0.408947i
$669$	−11.6877	−	6.85225i	−0.451871	−	0.264923i
$670$	10.0360	−	38.3325i	0.387726	−	1.48092i
$671$	−0.628689	+	0.698230i	−0.0242703	+	0.0269549i
$672$	−7.17510	−	10.0155i	−0.276785	−	0.386357i
$673$	−24.2839	+	10.8119i	−0.936076	+	0.416768i	−0.817338	−	0.576158i	$-0.804551\pi$
$673$	−24.2839	+	10.8119i	−0.936076	+	0.416768i	−0.118737	+	0.992926i	$0.537885\pi$
$674$	8.77851			0.338136
$675$	2.49462	+	25.8607i	0.0960181	+	0.995380i
$676$	4.04901			0.155731
$677$	26.1107	−	11.6252i	1.00351	−	0.446793i	0.161862	−	0.986813i	$-0.448250\pi$
$677$	26.1107	−	11.6252i	1.00351	−	0.446793i	0.841652	+	0.540020i	$0.181583\pi$
$678$	19.3790	+	27.0506i	0.744244	+	1.03887i
$679$	11.9296	−	13.2492i	0.457818	−	0.508458i
$680$	5.96253	−	0.346763i	0.228653	−	0.0132978i
$681$	−7.12762	−	4.17879i	−0.273131	−	0.160132i
$682$	−0.00491456	+	0.00851227i	−0.000188188	+	0.000325952i
$683$	−10.0969	+	31.0752i	−0.386349	+	1.18906i	0.549148	+	0.835725i	$0.314952\pi$
$683$	−10.0969	+	31.0752i	−0.386349	+	1.18906i	−0.935497	+	0.353335i	$0.885048\pi$
$684$	−6.47328	+	1.28590i	−0.247512	+	0.0491677i
$685$	1.91358	+	1.89177i	0.0731141	+	0.0722807i
$686$	19.1397	−	8.52155i	0.730758	−	0.325354i
$687$	−32.9436	−	3.68491i	−1.25687	−	0.140588i
$688$	16.5598	+	7.37290i	0.631336	+	0.281089i
$689$	2.81006	−	26.7359i	0.107055	−	1.01856i
$690$	0.620706	+	12.0608i	0.0236299	+	0.459147i
$691$	4.38833	+	41.7522i	0.166940	+	1.58833i	0.682117	+	0.731243i	$0.261060\pi$
$691$	4.38833	+	41.7522i	0.166940	+	1.58833i	−0.515177	+	0.857084i	$0.672274\pi$
$692$	3.76833	−	11.5977i	0.143250	−	0.440879i
$693$	0.344869	+	0.159093i	0.0131005	+	0.00604346i
$694$	4.28333	−	13.1827i	0.162593	−	0.500410i
$695$	−10.8230	−	16.4587i	−0.410540	−	0.624313i
$696$	16.9692	−	1.66914i	0.643215	−	0.0632685i
$697$	−6.43843	+	7.15060i	−0.243873	+	0.270848i
$698$	2.50148	−	23.8000i	0.0946825	−	0.900844i
$699$	−10.4244	+	3.31036i	−0.394287	+	0.125209i
$700$	6.69570	−	0.781448i	0.253074	−	0.0295360i
$701$	−19.3944			−0.732517			−0.366258	−	0.930513i	$-0.619361\pi$
$701$	−19.3944			−0.732517			−0.366258	+	0.930513i	$0.619361\pi$
$702$	15.3502	−	4.65003i	0.579356	−	0.175504i
$703$	−1.99484	−	6.13948i	−0.0752368	−	0.231555i
$704$	−0.589922	−	0.125392i	−0.0222335	−	0.00472588i
$705$	−38.0508	−	19.4330i	−1.43308	−	0.731888i
$706$	1.69351	−	0.359966i	0.0637360	−	0.0135475i
$707$	9.58494	+	16.6016i	0.360479	+	0.624367i
$708$	−8.90964	−	5.22355i	−0.334845	−	0.196313i
$709$	3.41022	+	32.4461i	0.128074	+	1.21854i	0.850080	+	0.526653i	$0.176553\pi$
$709$	3.41022	+	32.4461i	0.128074	+	1.21854i	−0.722007	+	0.691886i	$0.756780\pi$
$710$	29.0918	+	4.43691i	1.09179	+	0.166514i
$711$	0.347341	−	0.583489i	0.0130263	−	0.0218826i
$712$	−3.87077	+	2.81228i	−0.145063	+	0.105395i
$713$	−0.0357962	−	0.340578i	−0.00134058	−	0.0127547i
$714$	−0.575953	−	2.80143i	−0.0215545	−	0.104841i
$715$	−0.356131	+	0.291784i	−0.0133185	+	0.0109121i
$716$	6.48558	+	2.88756i	0.242377	+	0.107913i
$717$	−30.7527	+	17.4826i	−1.14848	+	0.652898i
$718$	−2.14578	+	3.71661i	−0.0800799	+	0.138703i
$719$	−9.39727	+	28.9218i	−0.350459	+	1.07860i	0.608137	+	0.793832i	$0.291917\pi$
$719$	−9.39727	+	28.9218i	−0.350459	+	1.07860i	−0.958596	+	0.284770i	$0.908083\pi$
$720$	−10.9148	+	5.45709i	−0.406770	+	0.203374i
$721$	−7.47241	−	22.9977i	−0.278287	−	0.856480i
$722$	11.9928	+	2.54914i	0.446324	+	0.0948692i
$723$	−5.25122	+	4.66516i	−0.195295	+	0.173499i
$724$	7.26804	+	12.5886i	0.270115	+	0.467852i
$725$	−6.35287	+	14.7206i	−0.235940	+	0.546711i
$726$	−20.0185	+	6.35706i	−0.742957	+	0.235932i
$727$	−2.33978	+	1.04174i	−0.0867778	+	0.0386360i	−0.449667	−	0.893197i	$-0.648457\pi$
$727$	−2.33978	+	1.04174i	−0.0867778	+	0.0386360i	0.362889	+	0.931832i	$0.381791\pi$
$728$	−4.56870	−	14.0610i	−0.169327	−	0.521136i
$729$	22.4611	−	14.9832i	0.831894	−	0.554935i
$730$	7.98425	−	4.12599i	0.295510	−	0.152710i
$731$	−5.80107	−	6.44274i	−0.214560	−	0.238293i
$732$	16.5180	−	5.24543i	0.610522	−	0.193877i
$733$	−16.3291	+	3.47085i	−0.603129	+	0.128199i	−0.499348	−	0.866401i	$-0.666427\pi$
$733$	−16.3291	+	3.47085i	−0.603129	+	0.128199i	−0.103780	+	0.994600i	$0.533094\pi$
$734$	−21.1368	−	9.41070i	−0.780173	−	0.347355i
$735$	4.03445	+	15.1136i	0.148813	+	0.557474i
$736$	10.6764	−	4.75343i	0.393536	−	0.175214i
$737$	0.956290	−	0.694786i	0.0352254	−	0.0255928i
$738$	11.7717	−	34.6493i	0.433322	−	1.27546i
$739$	26.7420	+	19.4292i	0.983720	+	0.714714i	0.958537	−	0.284968i	$-0.0919831\pi$
$739$	26.7420	+	19.4292i	0.983720	+	0.714714i	0.0251831	+	0.999683i	$0.491983\pi$
$740$	2.21312	+	3.36551i	0.0813559	+	0.123719i
$741$	−13.5259	−	1.51295i	−0.496888	−	0.0555795i
$742$	17.8328	−	3.79049i	0.654664	−	0.139153i
$743$	−8.24520	−	14.2811i	−0.302487	−	0.523923i	0.674212	−	0.738538i	$-0.264484\pi$
$743$	−8.24520	−	14.2811i	−0.302487	−	0.523923i	−0.976699	+	0.214615i	$0.931150\pi$
$744$	0.559952	−	0.318326i	0.0205288	−	0.0116704i
$745$	19.5123	+	7.36203i	0.714875	+	0.269724i
$746$	8.30725	+	25.5671i	0.304150	+	0.936078i
$747$	−10.3172	+	4.42950i	−0.377486	+	0.162067i
$748$	0.0405732	+	0.0294781i	0.00148350	+	0.00107783i
$749$	1.78909	−	3.09879i	0.0653719	−	0.113227i
$750$	0.893312	−	21.3398i	0.0326191	−	0.779220i
$751$	−25.3638	−	43.9313i	−0.925537	−	1.60308i	−0.790696	−	0.612209i	$-0.790281\pi$
$751$	−25.3638	−	43.9313i	−0.925537	−	1.60308i	−0.134841	−	0.990867i	$-0.543052\pi$
$752$	2.09768	−	19.9581i	0.0764946	−	0.727797i
$753$	−15.5992	−	21.7746i	−0.568468	−	0.793509i
$754$	9.68156	+	2.05788i	0.352581	+	0.0749435i
$755$	6.22435	+	37.8920i	0.226527	+	1.37903i
$756$	−4.00352	−	5.74894i	−0.145607	−	0.209087i
$757$	−39.6630			−1.44158			−0.720788	−	0.693156i	$-0.756220\pi$
$757$	−39.6630			−1.44158			−0.720788	+	0.693156i	$0.756220\pi$
$758$	−6.75601	−	7.50331i	−0.245389	−	0.272532i
$759$	−0.213697	+	0.290039i	−0.00775670	+	0.0105277i
$760$	19.2426	−	1.11910i	0.698004	−	0.0405939i
$761$	1.78434	−	16.9769i	0.0646823	−	0.615411i	−0.913381	−	0.407105i	$-0.866538\pi$
$761$	1.78434	−	16.9769i	0.0646823	−	0.615411i	0.978064	−	0.208306i	$-0.0667950\pi$
$762$	−1.32411	−	3.02823i	−0.0479676	−	0.109701i
$763$	1.06991	+	10.1796i	0.0387335	+	0.368525i
$764$	11.5852	+	8.41711i	0.419136	+	0.304520i
$765$	5.83046	−	0.261070i	0.210801	−	0.00943900i
$766$	3.09678	−	2.24994i	0.111891	−	0.0812937i
$767$	−14.2517	−	15.8281i	−0.514597	−	0.571518i
$768$	19.8837	+	18.1451i	0.717492	+	0.654754i
$769$	−21.2454	+	4.51585i	−0.766129	+	0.162846i	−0.574370	−	0.818596i	$-0.694753\pi$
$769$	−21.2454	+	4.51585i	−0.766129	+	0.162846i	−0.191760	+	0.981442i	$0.561419\pi$
$770$	−0.262826	−	0.168547i	−0.00947158	−	0.00607401i
$771$	18.2594	−	40.2858i	0.657597	−	1.45086i
$772$	20.5738	+	4.37309i	0.740466	+	0.157391i
$773$	9.92325	+	7.20966i	0.356914	+	0.259314i	0.751764	−	0.659432i	$-0.229203\pi$
$773$	9.92325	+	7.20966i	0.356914	+	0.259314i	−0.394850	+	0.918746i	$0.629203\pi$
$774$	29.9396	+	13.8116i	1.07616	+	0.496447i
$775$	0.00694278	+	0.605611i	0.000249392	+	0.0217542i
$776$	−15.9042	+	27.5469i	−0.570928	+	0.988876i
$777$	5.12280	−	4.55107i	0.183780	−	0.163269i
$778$	0.818400	−	0.908925i	0.0293411	−	0.0325865i
$779$	−20.7785	+	23.0769i	−0.744467	+	0.826814i
$780$	8.38906	−	1.32061i	0.300377	−	0.0472854i
$781$	0.587411	+	0.652386i	0.0210192	+	0.0233442i
$782$	2.71292			0.0970138
$783$	16.6022	−	1.40963i	0.593315	−	0.0503759i
$784$	−5.94411	+	4.31865i	−0.212290	+	0.154237i
$785$	0.542833	+	0.204812i	0.0193745	+	0.00731005i
$786$	−3.00086	−	0.997224i	−0.107037	−	0.0355698i
$787$	−15.6076	−	6.94895i	−0.556351	−	0.247703i	0.109246	−	0.994015i	$-0.465156\pi$
$787$	−15.6076	−	6.94895i	−0.556351	−	0.247703i	−0.665597	+	0.746311i	$0.731823\pi$
$788$	−18.4853	−	8.23018i	−0.658511	−	0.293188i
$789$	33.8854	−	30.1036i	1.20635	−	1.07172i
$790$	−0.348818	+	0.435839i	−0.0124104	+	0.0155064i
$791$	24.2489	−	17.6179i	0.862192	−	0.626419i
$792$	−0.660858	−	0.149714i	−0.0234826	−	0.00531985i
$793$	35.7404			1.26918
$794$	−25.3328	−	28.1349i	−0.899027	−	0.998470i
$795$	1.91214	+	37.1544i	0.0678166	+	1.31773i
$796$	−9.05135	+	10.0525i	−0.320817	+	0.356303i
$797$	3.89797	−	4.32913i	0.138073	−	0.153346i	−0.670142	−	0.742233i	$-0.733767\pi$
$797$	3.89797	−	4.32913i	0.138073	−	0.153346i	0.808216	+	0.588887i	$0.200434\pi$
$798$	−1.85875	−	9.04094i	−0.0657990	−	0.320046i
$799$	−4.79897	+	8.31205i	−0.169775	+	0.294059i
$800$	−19.5826	+	6.61190i	−0.692349	+	0.233766i
$801$	−3.81877	+	2.69738i	−0.134929	+	0.0953072i
$802$	−9.68680	−	7.03787i	−0.342053	−	0.248516i
$803$	0.262242	+	0.0557413i	0.00925433	+	0.00196707i
$804$	−21.6988	+	2.13436i	−0.765258	+	0.0752729i
$805$	10.8599	−	0.631578i	0.382759	−	0.0222602i
$806$	0.365724	−	0.0777370i	0.0128821	−	0.00273817i
$807$	−5.99401	+	1.90345i	−0.210999	+	0.0670046i
$808$	−22.8852	−	25.4166i	−0.805100	−	0.894154i
$809$	33.8455	−	24.5902i	1.18995	−	0.864546i	0.196687	−	0.980466i	$-0.436982\pi$
$809$	33.8455	−	24.5902i	1.18995	−	0.864546i	0.993259	+	0.115920i	$0.0369817\pi$
$810$	−19.9840	+	9.66029i	−0.702165	+	0.339428i
$811$	11.3088	+	8.21632i	0.397105	+	0.288514i	0.768361	−	0.640017i	$-0.221073\pi$
$811$	11.3088	+	8.21632i	0.397105	+	0.288514i	−0.371256	+	0.928531i	$0.621073\pi$
$812$	−0.451900	−	4.29954i	−0.0158586	−	0.150884i
$813$	6.92203	−	9.39489i	0.242766	−	0.329493i
$814$	0.0195010	−	0.185540i	0.000683511	−	0.00650317i
$815$	−7.17837	+	27.4177i	−0.251447	+	0.960399i
$816$	1.09824	+	2.51165i	0.0384461	+	0.0879255i
$817$	−18.7216	−	20.7924i	−0.654985	−	0.727434i
$818$	−25.4116			−0.888497
$819$	−4.28069	−	13.7985i	−0.149579	−	0.482158i
$820$	8.69743	−	17.3143i	0.303727	−	0.604641i
$821$	28.6943	+	6.09917i	1.00144	+	0.212862i	0.679324	−	0.733838i	$-0.262273\pi$
$821$	28.6943	+	6.09917i	1.00144	+	0.212862i	0.322114	+	0.946701i	$0.395606\pi$
$822$	−0.949032	+	2.09385i	−0.0331013	+	0.0730314i
$823$	−3.98337	+	37.8993i	−0.138852	+	1.32108i	0.674051	+	0.738685i	$0.264553\pi$
$823$	−3.98337	+	37.8993i	−0.138852	+	1.32108i	−0.812902	+	0.582400i	$0.802114\pi$
$824$	21.5712	+	37.3624i	0.751468	+	1.30158i
$825$	0.424060	−	0.475528i	0.0147639	−	0.0165558i
$826$	7.22204	−	12.5089i	0.251287	−	0.435242i
$827$	−29.2916	−	21.2816i	−1.01857	−	0.740034i	−0.0525800	−	0.998617i	$-0.516744\pi$
$827$	−29.2916	−	21.2816i	−1.01857	−	0.740034i	−0.965989	+	0.258583i	$0.916744\pi$
$828$	6.10629	−	2.62163i	0.212208	−	0.0911079i
$829$	5.45513	+	16.7892i	0.189465	+	0.583112i	0.999997	−	0.00258211i	$-0.000821911\pi$
$829$	5.45513	+	16.7892i	0.189465	+	0.583112i	−0.810532	+	0.585694i	$0.800822\pi$
$830$	8.90195	−	2.44004i	0.308991	−	0.0846951i
$831$	16.3219	+	9.56921i	0.566200	+	0.331952i
$832$	11.4708	+	19.8680i	0.397679	+	0.688800i
$833$	3.43721	−	0.730601i	0.119092	−	0.0253138i
$834$	9.98252	−	13.5487i	0.345666	−	0.469154i
$835$	21.7644	−	27.1941i	0.753189	−	0.941089i
$836$	0.130940	+	0.0951336i	0.00452866	+	0.00329026i
$837$	0.551275	−	0.303732i	0.0190549	−	0.0104985i
$838$	−0.239784	+	0.174213i	−0.00828320	+	0.00601810i
$839$	−11.2539	+	5.01058i	−0.388529	+	0.172984i	−0.591699	−	0.806159i	$-0.701542\pi$
$839$	−11.2539	+	5.01058i	−0.388529	+	0.172984i	0.203169	+	0.979144i	$0.434876\pi$
$840$	9.27169	+	18.2391i	0.319904	+	0.629309i
$841$	−17.0995	−	7.61320i	−0.589638	−	0.262524i
$842$	−35.1060	+	7.46202i	−1.20983	+	0.257158i
$843$	4.92960	−	22.4542i	0.169785	−	0.773364i
$844$	9.02814	+	10.0268i	0.310762	+	0.345136i
$845$	−11.4235	−	1.74224i	−0.392980	−	0.0599350i
$846$	4.29964	−	36.2484i	0.147825	−	1.24624i
$847$	5.84633	+	17.9931i	0.200882	+	0.618252i
$848$	−15.9635	+	7.10741i	−0.548189	+	0.244069i
$849$	12.3359	+	11.2572i	0.423367	+	0.386348i
$850$	−4.77711	−	0.446791i	−0.163854	−	0.0153248i
$851$	3.24998	+	5.62912i	0.111408	+	0.192964i
$852$	−3.26094	−	15.8612i	−0.111718	−	0.543395i
$853$	−12.3489	−	2.62483i	−0.422817	−	0.0898726i	−0.00841113	−	0.999965i	$-0.502677\pi$
$853$	−12.3489	−	2.62483i	−0.422817	−	0.0898726i	−0.414406	+	0.910092i	$0.636011\pi$
$854$	7.48991	+	23.0516i	0.256300	+	0.788809i
$855$	18.8164	−	0.842540i	0.643508	−	0.0288143i
$856$	−1.97274	+	6.07146i	−0.0674268	+	0.207518i
$857$	−10.4245	+	18.0557i	−0.356094	+	0.616773i	−0.987305	−	0.158839i	$-0.949225\pi$
$857$	−10.4245	+	18.0557i	−0.356094	+	0.616773i	0.631211	+	0.775611i	$0.282558\pi$
$858$	−0.339320	−	0.198937i	−0.0115842	−	0.00679160i
$859$	46.8602	+	20.8635i	1.59885	+	0.711854i	0.996277	−	0.0862097i	$-0.0274755\pi$
$859$	46.8602	+	20.8635i	1.59885	+	0.711854i	0.602573	+	0.798064i	$0.294142\pi$
$860$	14.6957	+	9.42419i	0.501119	+	0.321362i
$861$	−31.2805	−	10.3949i	−1.06604	−	0.354258i
$862$	−2.56376	−	24.3926i	−0.0873221	−	0.830814i
$863$	−15.1856	+	11.0330i	−0.516922	+	0.375566i	−0.815443	−	0.578837i	$-0.803507\pi$
$863$	−15.1856	+	11.0330i	−0.516922	+	0.375566i	0.298521	+	0.954403i	$0.403507\pi$
$864$	15.6715	+	14.6892i	0.533156	+	0.499738i
$865$	−15.6220	+	31.0992i	−0.531163	+	1.05741i
$866$	−1.31954	−	12.5546i	−0.0448397	−	0.426621i
$867$	−0.187717	+	28.1332i	−0.00637521	+	0.955453i
$868$	−0.0816555	−	0.141432i	−0.00277157	−	0.00480050i
$869$	−0.0162889	+	0.00346231i	−0.000552562	+	0.000117451i
$870$	−13.6782	−	0.729743i	−0.463733	−	0.0247406i
$871$	−43.9815	−	9.34856i	−1.49026	−	0.316764i
$872$	−5.64316	−	17.3679i	−0.191101	−	0.588150i
$873$	−15.8991	+	26.7085i	−0.538102	+	0.903944i
$874$	8.75530			0.296152
$875$	−19.2269	−	0.676381i	−0.649986	−	0.0228659i
$876$	−3.65292	−	3.33350i	−0.123421	−	0.112629i
$877$	4.79481	−	45.6196i	0.161909	−	1.54046i	−0.548184	−	0.836358i	$-0.684681\pi$
$877$	4.79481	−	45.6196i	0.161909	−	1.54046i	0.710094	−	0.704107i	$-0.248653\pi$
$878$	−3.54528	+	3.93743i	−0.119647	+	0.132882i
$879$	−0.0131582	+	0.0290310i	−0.000443816	+	0.000979190i
$880$	0.279995	+	0.105643i	0.00943864	+	0.00356122i
$881$	−7.06458	+	21.7426i	−0.238012	+	0.732525i	0.758696	+	0.651445i	$0.225837\pi$
$881$	−7.06458	+	21.7426i	−0.238012	+	0.732525i	−0.996708	+	0.0810801i	$0.974163\pi$
$882$	−10.9158	+	7.71036i	−0.367554	+	0.259621i
$883$	2.94101	−	9.05149i	0.0989728	−	0.304607i	−0.889296	−	0.457332i	$-0.848805\pi$
$883$	2.94101	−	9.05149i	0.0989728	−	0.304607i	0.988269	+	0.152725i	$0.0488050\pi$
$884$	−0.199411	−	1.89727i	−0.00670692	−	0.0638121i
$885$	22.8892	+	18.5710i	0.769411	+	0.624256i
$886$	−1.77505	+	16.8885i	−0.0596341	+	0.567380i
$887$	−23.7011	−	10.5524i	−0.795804	−	0.354315i	−0.0317739	−	0.999495i	$-0.510116\pi$
$887$	−23.7011	−	10.5524i	−0.795804	−	0.354315i	−0.764030	+	0.645180i	$0.776782\pi$
$888$	−7.25182	+	9.84250i	−0.243355	+	0.330293i
$889$	−2.71967	+	1.21087i	−0.0912147	+	0.0406114i
$890$	3.41457	−	1.76454i	0.114457	−	0.0591474i
$891$	−0.643767	−	0.154902i	−0.0215670	−	0.00518940i
$892$	1.89385	−	5.82868i	0.0634109	−	0.195159i
$893$	−15.4875	+	26.8252i	−0.518270	+	0.897670i
$894$	−0.118882	+	17.8168i	−0.00397600	+	0.595884i
$895$	−17.0553	−	10.9374i	−0.570096	−	0.365596i
$896$	−0.891154	+	0.989726i	−0.0297714	+	0.0330644i
$897$	13.6383	−	1.34151i	0.455371	−	0.0447916i
$898$	−37.7748	+	16.8184i	−1.26056	+	0.561239i
$899$	0.388415			0.0129544
$900$	−11.1842	+	3.61071i	−0.372806	+	0.120357i
$901$	8.35739			0.278425
$902$	−0.819843	+	0.365018i	−0.0272978	+	0.0121538i
$903$	12.2606	−	27.0506i	0.408008	−	0.900187i
$904$	−35.7825	+	39.7405i	−1.19011	+	1.32175i
$905$	−15.0886	−	38.6437i	−0.501563	−	1.28456i
$906$	−28.5201	+	16.2133i	−0.947516	+	0.538651i
$907$	−5.31025	+	9.19762i	−0.176324	+	0.305402i	−0.940619	−	0.339465i	$-0.889754\pi$
$907$	−5.31025	+	9.19762i	−0.176324	+	0.305402i	0.764295	+	0.644867i	$0.223087\pi$
$908$	1.15495	−	3.55457i	0.0383284	−	0.117963i
$909$	−22.0296	−	25.1328i	−0.730674	−	0.833603i
$910$	1.92517	+	11.7198i	0.0638186	+	0.388509i
$911$	18.6869	−	8.31993i	0.619124	−	0.275652i	−0.0731112	−	0.997324i	$-0.523293\pi$
$911$	18.6869	−	8.31993i	0.619124	−	0.275652i	0.692235	+	0.721672i	$0.256626\pi$
$912$	3.54430	+	8.10576i	0.117364	+	0.268409i
$913$	0.251544	+	0.111995i	0.00832488	+	0.00370648i
$914$	3.34950	−	31.8683i	0.110792	−	1.05411i
$915$	−48.8593	+	7.69146i	−1.61524	+	0.254272i
$916$	−1.56742	−	14.9130i	−0.0517891	−	0.492740i
$917$	−0.880198	+	2.70897i	−0.0290667	+	0.0894581i
$918$	1.93649	+	4.59479i	0.0639135	+	0.151651i
$919$	5.59584	−	17.2222i	0.184590	−	0.568108i	−0.815351	−	0.578966i	$-0.803456\pi$
$919$	5.59584	−	17.2222i	0.184590	−	0.568108i	0.999941	+	0.0108579i	$0.00345625\pi$
$920$	−18.7177	+	5.13055i	−0.617103	+	0.169149i
$921$	−8.71474	−	12.1647i	−0.287160	−	0.400840i
$922$	5.44702	−	6.04953i	0.179388	−	0.199231i
$923$	3.49059	−	33.2108i	0.114894	−	1.09315i
$924$	−0.0368404	+	0.167807i	−0.00121196	+	0.00552045i
$925$	−4.79574	−	10.4474i	−0.157683	−	0.343509i
$926$	8.68310			0.285344
$927$	20.5898	+	36.7878i	0.676259	+	1.20827i
$928$	4.09609	+	12.6065i	0.134461	+	0.413828i
$929$	9.16979	+	1.94910i	0.300851	+	0.0639479i	0.355864	−	0.934538i	$-0.384187\pi$
$929$	9.16979	+	1.94910i	0.300851	+	0.0639479i	−0.0550128	+	0.998486i	$0.517520\pi$
$930$	−0.483238	+	0.184976i	−0.0158460	+	0.00606562i
$931$	11.0928	−	2.35784i	0.363551	−	0.0772751i
$932$	−2.47380	−	4.28475i	−0.0810321	−	0.140352i
$933$	19.3105	−	10.9778i	0.632196	−	0.359396i
$934$	−2.57565	−	24.5057i	−0.0842780	−	0.801852i
$935$	−0.101785	−	0.100625i	−0.00332873	−	0.00329079i
$936$	12.5888	+	22.4924i	0.411478	+	0.735186i
$937$	20.0768	−	14.5867i	0.655881	−	0.476526i	−0.209388	−	0.977833i	$-0.567147\pi$
$937$	20.0768	−	14.5867i	0.655881	−	0.476526i	0.865270	+	0.501307i	$0.167147\pi$
$938$	−3.18740	−	30.3260i	−0.104072	−	0.990180i
$939$	−3.23359	+	2.87270i	−0.105524	+	0.0937471i
$940$	4.89520	−	18.6972i	0.159664	−	0.609835i
$941$	34.6228	+	15.4151i	1.12867	+	0.502517i	0.884185	−	0.467136i	$-0.154714\pi$
$941$	34.6228	+	15.4151i	1.12867	+	0.502517i	0.244486	+	0.969653i	$0.421381\pi$
$942$	−0.00330730	+	0.495665i	−0.000107758	+	0.0161496i
$943$	15.6336	−	27.0781i	0.509099	−	0.881785i
$944$	−4.27813	+	13.1667i	−0.139241	+	0.428541i
$945$	8.82146	+	17.9422i	0.286962	+	0.583659i
$946$	−0.249868	−	0.769015i	−0.00812392	−	0.0250028i
$947$	−15.6882	−	3.33463i	−0.509798	−	0.108361i	−0.0541710	−	0.998532i	$-0.517252\pi$
$947$	−15.6882	−	3.33463i	−0.509798	−	0.108361i	−0.455627	+	0.890171i	$0.650585\pi$
$948$	0.291498	+	0.0968684i	0.00946741	+	0.00314614i
$949$	−5.09920	−	8.83208i	−0.165527	−	0.286701i
$950$	−15.4170	−	1.44191i	−0.500193	−	0.0467818i
$951$	−6.26029	+	28.5155i	−0.203004	+	0.924677i
$952$	4.19885	−	1.86945i	0.136086	−	0.0605892i
$953$	−16.6285	−	51.1773i	−0.538650	−	1.65779i	−0.735627	−	0.677386i	$-0.763113\pi$
$953$	−16.6285	−	51.1773i	−0.538650	−	1.65779i	0.196977	−	0.980408i	$-0.436887\pi$
$954$	−29.2065	+	12.5393i	−0.945596	+	0.405975i
$955$	−29.0635	−	28.7322i	−0.940472	−	0.929752i
$956$	−10.7074	−	11.8918i	−0.346303	−	0.384608i
$957$	−0.301828	−	0.275436i	−0.00975671	−	0.00890357i
$958$	1.34749	−	0.286417i	0.0435353	−	0.00925372i
$959$	1.89170	+	0.842241i	0.0610863	+	0.0271974i
$960$	−19.9570	−	24.6923i	−0.644109	−	0.796940i
$961$	−28.3065	+	12.6029i	−0.913113	+	0.406544i
$962$	−5.74135	+	4.17134i	−0.185109	+	0.134489i
$963$	−2.00672	+	5.90665i	−0.0646656	+	0.190339i
$964$	−2.57060	−	1.86765i	−0.0827934	−	0.0601529i
$965$	−56.1632	−	21.1905i	−1.80796	−	0.682146i
$966$	3.72335	+	8.51524i	0.119797	+	0.273973i
$967$	−36.3072	+	7.71734i	−1.16756	+	0.248173i	−0.750604	−	0.660753i	$-0.770237\pi$
$967$	−36.3072	+	7.71734i	−1.16756	+	0.248173i	−0.416958	+	0.908926i	$0.636904\pi$
$968$	−16.8770	−	29.2319i	−0.542448	−	0.939548i
$969$	0.0282315	−	4.23105i	0.000906925	−	0.135921i
$970$	15.9667	−	19.9499i	0.512659	−	0.640554i
$971$	0.254854	+	0.784361i	0.00817866	+	0.0251713i	0.955063	−	0.296404i	$-0.0957876\pi$
$971$	0.254854	+	0.784361i	0.00817866	+	0.0251713i	−0.946884	+	0.321576i	$0.895788\pi$
$972$	8.79885	+	8.47072i	0.282223	+	0.271698i
$973$	−12.2638	−	8.91016i	−0.393159	−	0.285647i
$974$	−4.85083	+	8.40189i	−0.155431	+	0.269214i
$975$	−24.2363	+	0.116123i	−0.776184	+	0.00371892i
$976$	−11.6157	−	20.1190i	−0.371810	−	0.643994i
$977$	2.00962	−	19.1202i	0.0642933	−	0.611710i	−0.914176	−	0.405318i	$-0.867161\pi$
$977$	2.00962	−	19.1202i	0.0642933	−	0.611710i	0.978469	−	0.206393i	$-0.0661724\pi$
$978$	−24.0973	+	2.37027i	−0.770545	+	0.0757930i
$979$	0.112151	+	0.0238385i	0.00358437	+	0.000761882i
$980$	−6.28637	+	3.24859i	−0.200811	+	0.103772i
$981$	−5.28741	−	17.0436i	−0.168814	−	0.544159i
$982$	24.0121			0.766257
$983$	31.1539	+	34.5999i	0.993655	+	1.10357i	0.994623	+	0.103566i	$0.0330252\pi$
$983$	31.1539	+	34.5999i	0.993655	+	1.10357i	−0.000968038		1.00000i	$0.500308\pi$
$984$	58.4448	+	6.53735i	1.86315	+	0.208403i
$985$	48.6113	+	31.1739i	1.54888	+	0.993282i
$986$	−0.321637	+	3.06017i	−0.0102430	+	0.0974556i
$987$	−32.6760	−	3.65498i	−1.04009	−	0.116339i
$988$	−0.643552	−	6.12299i	−0.0204741	−	0.194798i
$989$	22.7915	+	16.5590i	0.724729	+	0.526546i
$990$	0.506684	+	0.198937i	0.0161035	+	0.00632262i
$991$	33.2013	−	24.1222i	1.05467	−	0.766265i	0.0815781	−	0.996667i	$-0.474004\pi$
$991$	33.2013	−	24.1222i	1.05467	−	0.766265i	0.973096	+	0.230402i	$0.0740040\pi$
$992$	0.335047	+	0.372108i	0.0106378	+	0.0118144i
$993$	−11.6919	+	53.2563i	−0.371032	+	1.69004i
$994$	22.1516	−	4.70846i	0.702605	−	0.149343i
$995$	29.8621	−	24.4666i	0.946693	−	0.775643i
$996$	−2.95788	−	4.12882i	−0.0937239	−	0.130827i
$997$	5.49444	+	1.16788i	0.174011	+	0.0369871i	0.294093	−	0.955777i	$-0.404982\pi$
$997$	5.49444	+	1.16788i	0.174011	+	0.0369871i	−0.120082	+	0.992764i	$0.538316\pi$
$998$	13.3888	+	9.72756i	0.423816	+	0.307921i
$999$	−7.21404	+	9.52246i	−0.228242	+	0.301277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.16.20	✓	224
3.2	odd	2		675.2.r.a.316.9		224
9.4	even	3	inner	225.2.q.a.166.9	yes	224
9.5	odd	6		675.2.r.a.91.20		224
25.11	even	5	inner	225.2.q.a.61.9	yes	224
75.11	odd	10		675.2.r.a.586.20		224
225.86	odd	30		675.2.r.a.361.9		224
225.211	even	15	inner	225.2.q.a.211.20	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.20	✓	224	1.1	even	1	trivial
225.2.q.a.61.9	yes	224	25.11	even	5	inner
225.2.q.a.166.9	yes	224	9.4	even	3	inner
225.2.q.a.211.20	yes	224	225.211	even	15	inner
675.2.r.a.91.20		224	9.5	odd	6
675.2.r.a.316.9		224	3.2	odd	2
675.2.r.a.361.9		224	225.86	odd	30
675.2.r.a.586.20		224	75.11	odd	10

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00759 - 0.448609i) q^{2} +(1.00870 + 1.40802i) q^{3} +(-0.524267 + 0.582258i) q^{4} +(1.72966 - 1.41714i) q^{5} +(1.64801 + 0.966199i) q^{6} +(0.860383 - 1.49023i) q^{7} +(-0.948701 + 2.91980i) q^{8} +(-0.965042 + 2.84054i) q^{9} +O(q^{10})\)	\(q+(1.00759 - 0.448609i) q^{2} +(1.00870 + 1.40802i) q^{3} +(-0.524267 + 0.582258i) q^{4} +(1.72966 - 1.41714i) q^{5} +(1.64801 + 0.966199i) q^{6} +(0.860383 - 1.49023i) q^{7} +(-0.948701 + 2.91980i) q^{8} +(-0.965042 + 2.84054i) q^{9} +(1.10705 - 2.20384i) q^{10} +(0.0672106 - 0.0299241i) q^{11} +(-1.34866 - 0.150855i) q^{12} +(-2.55665 - 1.13830i) q^{13} +(0.198386 - 1.88752i) q^{14} +(3.74007 + 1.00592i) q^{15} +(0.190149 + 1.80914i) q^{16} +(0.268852 - 0.827443i) q^{17} +(0.301925 + 3.29504i) q^{18} +(0.867657 - 2.67037i) q^{19} +(-0.0816614 + 1.75007i) q^{20} +(2.96614 - 0.291758i) q^{21} +(0.0542967 - 0.0603026i) q^{22} +(-0.295519 + 2.81167i) q^{23} +(-5.06810 + 1.60942i) q^{24} +(0.983426 - 4.90233i) q^{25} -3.08672 q^{26} +(-4.97298 + 1.50646i) q^{27} +(0.416626 + 1.28224i) q^{28} +(-3.13652 - 0.666689i) q^{29} +(4.21974 - 0.664273i) q^{30} +(-0.118483 + 0.0251844i) q^{31} +(-2.06687 - 3.57992i) q^{32} +(0.109929 + 0.0644494i) q^{33} +(-0.100305 - 0.954336i) q^{34} +(-0.623694 - 3.79687i) q^{35} +(-1.14799 - 2.05111i) q^{36} +(1.86002 - 1.35138i) q^{37} +(-0.323709 - 3.07989i) q^{38} +(-0.976157 - 4.74802i) q^{39} +(2.49684 + 6.39470i) q^{40} +(-10.1034 - 4.49833i) q^{41} +(2.85778 - 1.62461i) q^{42} +(4.98237 - 8.62972i) q^{43} +(-0.0178128 + 0.0548221i) q^{44} +(2.35626 + 6.28077i) q^{45} +(0.963580 + 2.96559i) q^{46} +(-10.7907 - 2.29364i) q^{47} +(-2.35551 + 2.09262i) q^{48} +(2.01948 + 3.49785i) q^{49} +(-1.20834 - 5.38073i) q^{50} +(1.43625 - 0.456093i) q^{51} +(2.00315 - 0.891860i) q^{52} +(2.96839 + 9.13577i) q^{53} +(-4.33493 + 3.74883i) q^{54} +(0.0738447 - 0.147005i) q^{55} +(3.53492 + 3.92593i) q^{56} +(4.63515 - 1.47193i) q^{57} +(-3.45942 + 0.735323i) q^{58} +(6.95253 + 3.09547i) q^{59} +(-2.54650 + 1.65031i) q^{60} +(-11.6667 + 5.19434i) q^{61} +(-0.108085 + 0.0785282i) q^{62} +(3.40275 + 3.88209i) q^{63} +(-6.63193 - 4.81838i) q^{64} +(-6.03526 + 1.65428i) q^{65} +(0.139677 + 0.0156235i) q^{66} +(15.7155 - 3.34044i) q^{67} +(0.340834 + 0.590342i) q^{68} +(-4.25698 + 2.42004i) q^{69} +(-2.33174 - 3.54590i) q^{70} +(3.68727 + 11.3483i) q^{71} +(-7.37829 - 5.51256i) q^{72} +(2.94814 + 2.14195i) q^{73} +(1.26790 - 2.19607i) q^{74} +(7.89457 - 3.56031i) q^{75} +(1.09996 + 1.90519i) q^{76} +(0.0132332 - 0.125905i) q^{77} +(-3.11358 - 4.34616i) q^{78} +(-0.221403 - 0.0470606i) q^{79} +(2.89270 + 2.85973i) q^{80} +(-7.13739 - 5.48249i) q^{81} -12.1981 q^{82} +(2.50430 + 2.78131i) q^{83} +(-1.38517 + 1.88002i) q^{84} +(-0.707580 - 1.81219i) q^{85} +(1.14883 - 10.9304i) q^{86} +(-2.22510 - 5.08878i) q^{87} +(0.0236096 + 0.224631i) q^{88} +(1.26081 + 0.916033i) q^{89} +(5.19176 + 5.27142i) q^{90} +(-3.89602 + 2.83062i) q^{91} +(-1.48219 - 1.64614i) q^{92} +(-0.154974 - 0.141423i) q^{93} +(-11.9016 + 2.52976i) q^{94} +(-2.28354 - 5.84842i) q^{95} +(2.95575 - 6.52127i) q^{96} +(10.1344 + 2.15414i) q^{97} +(3.60398 + 2.61845i) q^{98} +(0.0201397 + 0.219793i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Introduction

L-functions

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