LMFDB - Embedded newform 448.2.bn.a.205.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [448,2,Mod(37,448)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(448, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 27, 16]))

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

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

chi := DirichletCharacter("448.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 448 = 2^{6} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	448.bn (of order $48$, degree $16$, 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:	$3.57729801055$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$62$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			205.19
Character	$\chi$	$=$	448.205
Dual form			448.2.bn.a.389.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.830506 + 1.14467i) q^{2} +(-1.36442 - 0.672855i) q^{3} +(-0.620519 - 1.90130i) q^{4} +(1.13691 - 3.34924i) q^{5} +(1.90335 - 1.00299i) q^{6} +(2.22748 - 1.42771i) q^{7} +(2.69170 + 0.868758i) q^{8} +(-0.417389 - 0.543952i) q^{9} +O(q^{10})$	\(q+(-0.830506 + 1.14467i) q^{2} +(-1.36442 - 0.672855i) q^{3} +(-0.620519 - 1.90130i) q^{4} +(1.13691 - 3.34924i) q^{5} +(1.90335 - 1.00299i) q^{6} +(2.22748 - 1.42771i) q^{7} +(2.69170 + 0.868758i) q^{8} +(-0.417389 - 0.543952i) q^{9} +(2.88955 + 4.08295i) q^{10} +(-1.88729 - 0.123699i) q^{11} +(-0.432657 + 3.01169i) q^{12} +(-6.25362 - 1.24392i) q^{13} +(-0.215687 + 3.73544i) q^{14} +(-3.80478 + 3.80478i) q^{15} +(-3.22991 + 2.35959i) q^{16} +(-0.836885 + 3.12330i) q^{17} +(0.969288 - 0.0260154i) q^{18} +(3.94420 + 3.45897i) q^{19} +(-7.07340 - 0.0833518i) q^{20} +(-3.99984 + 0.449215i) q^{21} +(1.70900 - 2.05758i) q^{22} +(3.49170 - 2.67928i) q^{23} +(-3.08805 - 2.99647i) q^{24} +(-5.95807 - 4.57179i) q^{25} +(6.61755 - 6.12522i) q^{26} +(1.09387 + 5.49923i) q^{27} +(-4.09670 - 3.34919i) q^{28} +(-4.54188 - 6.79740i) q^{29} +(-1.19531 - 7.51509i) q^{30} +(-4.58956 + 2.64978i) q^{31} +(-0.0184792 - 5.65682i) q^{32} +(2.49181 + 1.43865i) q^{33} +(-2.88009 - 3.55187i) q^{34} +(-2.24928 - 9.08354i) q^{35} +(-0.775221 + 1.13112i) q^{36} +(-1.48538 - 0.504220i) q^{37} +(-7.23504 + 1.64209i) q^{38} +(7.69556 + 5.90501i) q^{39} +(5.96991 - 8.02745i) q^{40} +(9.60237 + 3.97743i) q^{41} +(2.80769 - 4.95156i) q^{42} +(-5.74894 - 3.84132i) q^{43} +(0.935908 + 3.66507i) q^{44} +(-2.29636 + 0.779510i) q^{45} +(0.166996 + 6.22199i) q^{46} +(4.47655 - 1.19949i) q^{47} +(5.99460 - 1.04620i) q^{48} +(2.92331 - 6.36037i) q^{49} +(10.1814 - 3.02310i) q^{50} +(3.24339 - 3.69837i) q^{51} +(1.51542 + 12.6619i) q^{52} +(-8.06804 - 0.528807i) q^{53} +(-7.20325 - 3.31504i) q^{54} +(-2.55998 + 6.18035i) q^{55} +(7.23604 - 1.90782i) q^{56} +(-3.05414 - 7.37334i) q^{57} +(11.5528 + 0.446352i) q^{58} +(3.99664 + 4.55729i) q^{59} +(9.59497 + 4.87310i) q^{60} +(-0.377061 - 5.75285i) q^{61} +(0.778542 - 7.45418i) q^{62} +(-1.70633 - 0.615732i) q^{63} +(6.49052 + 4.67687i) q^{64} +(-11.2760 + 19.5307i) q^{65} +(-3.71624 + 1.65749i) q^{66} +(1.70857 + 0.842575i) q^{67} +(6.45764 - 0.346893i) q^{68} +(-6.56690 + 1.30624i) q^{69} +(12.2657 + 4.96926i) q^{70} +(-2.47554 - 5.97649i) q^{71} +(-0.650925 - 1.82677i) q^{72} +(-12.6883 + 1.67045i) q^{73} +(1.81079 - 1.28151i) q^{74} +(5.05313 + 10.2467i) q^{75} +(4.12910 - 9.64547i) q^{76} +(-4.38050 + 2.41896i) q^{77} +(-13.1505 + 3.90469i) q^{78} +(-1.82895 - 6.82573i) q^{79} +(4.23070 + 13.5004i) q^{80} +(1.67533 - 6.25243i) q^{81} +(-12.5277 + 7.68822i) q^{82} +(0.334426 - 1.68127i) q^{83} +(3.33607 + 7.32617i) q^{84} +(9.50921 + 6.35385i) q^{85} +(9.17155 - 3.39037i) q^{86} +(1.62334 + 12.3305i) q^{87} +(-4.97255 - 1.97256i) q^{88} +(0.834940 - 6.34200i) q^{89} +(1.01487 - 3.27596i) q^{90} +(-15.7058 + 6.15753i) q^{91} +(-7.26079 - 4.97624i) q^{92} +(8.04499 - 0.527297i) q^{93} +(-2.34479 + 6.12033i) q^{94} +(16.0691 - 9.27752i) q^{95} +(-3.78101 + 7.73069i) q^{96} +3.69260i q^{97} +(4.85267 + 8.62854i) q^{98} +(0.720448 + 1.07823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 32 q^{6} - 16 q^{7} - 32 q^{8} - 8 q^{9}+O(q^{10}) $ 992 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 32 * q^6 - 16 * q^7 - 32 * q^8 - 8 * q^9	\( 992 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 32 q^{6} - 16 q^{7} - 32 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 32 q^{13} - 16 q^{14} - 32 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 32 q^{20} - 16 q^{21} - 16 q^{22} - 8 q^{23} - 88 q^{24} - 8 q^{25} - 8 q^{26} - 32 q^{27} - 56 q^{28} - 32 q^{29} - 88 q^{30} - 8 q^{32} - 32 q^{34} - 16 q^{35} + 128 q^{36} - 8 q^{37} - 88 q^{38} - 8 q^{39} - 8 q^{40} - 32 q^{41} - 56 q^{42} - 32 q^{43} - 16 q^{44} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 32 q^{48} - 16 q^{49} + 16 q^{50} - 8 q^{51} - 56 q^{52} - 8 q^{53} - 8 q^{54} - 32 q^{55} - 16 q^{56} - 32 q^{57} - 8 q^{58} + 56 q^{59} + 88 q^{60} - 8 q^{61} - 64 q^{62} - 32 q^{63} + 160 q^{64} - 16 q^{65} - 136 q^{66} - 88 q^{67} - 8 q^{68} - 32 q^{69} - 16 q^{70} - 160 q^{71} - 8 q^{72} - 8 q^{73} + 48 q^{74} - 8 q^{75} - 32 q^{76} - 16 q^{77} + 64 q^{78} - 8 q^{79} - 32 q^{80} - 8 q^{81} + 72 q^{82} - 32 q^{83} - 128 q^{84} - 32 q^{85} - 8 q^{86} - 8 q^{87} - 8 q^{88} - 8 q^{89} - 320 q^{90} - 16 q^{91} - 32 q^{92} - 56 q^{93} - 8 q^{94} + 128 q^{96} - 152 q^{98} - 80 q^{99}+O(q^{100}) \) 992 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 32 * q^6 - 16 * q^7 - 32 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 32 * q^13 - 16 * q^14 - 32 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 32 * q^20 - 16 * q^21 - 16 * q^22 - 8 * q^23 - 88 * q^24 - 8 * q^25 - 8 * q^26 - 32 * q^27 - 56 * q^28 - 32 * q^29 - 88 * q^30 - 8 * q^32 - 32 * q^34 - 16 * q^35 + 128 * q^36 - 8 * q^37 - 88 * q^38 - 8 * q^39 - 8 * q^40 - 32 * q^41 - 56 * q^42 - 32 * q^43 - 16 * q^44 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 32 * q^48 - 16 * q^49 + 16 * q^50 - 8 * q^51 - 56 * q^52 - 8 * q^53 - 8 * q^54 - 32 * q^55 - 16 * q^56 - 32 * q^57 - 8 * q^58 + 56 * q^59 + 88 * q^60 - 8 * q^61 - 64 * q^62 - 32 * q^63 + 160 * q^64 - 16 * q^65 - 136 * q^66 - 88 * q^67 - 8 * q^68 - 32 * q^69 - 16 * q^70 - 160 * q^71 - 8 * q^72 - 8 * q^73 + 48 * q^74 - 8 * q^75 - 32 * q^76 - 16 * q^77 + 64 * q^78 - 8 * q^79 - 32 * q^80 - 8 * q^81 + 72 * q^82 - 32 * q^83 - 128 * q^84 - 32 * q^85 - 8 * q^86 - 8 * q^87 - 8 * q^88 - 8 * q^89 - 320 * q^90 - 16 * q^91 - 32 * q^92 - 56 * q^93 - 8 * q^94 + 128 * q^96 - 152 * q^98 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/448\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{15}{16}\right)$

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 $

$2$	−0.830506	+	1.14467i	−0.587257	+	0.809401i
$2$	−0.830506	+	1.14467i	−0.587257	+	0.809401i
$3$	−1.36442	−	0.672855i	−0.787746	−	0.388473i	0.00348281	−	0.999994i	$-0.498891\pi$
$3$	−1.36442	−	0.672855i	−0.787746	−	0.388473i	−0.791228	+	0.611521i	$0.790558\pi$
$4$	−0.620519	−	1.90130i	−0.310259	−	0.950652i
$5$	1.13691	−	3.34924i	0.508443	−	1.49783i	−0.325266	−	0.945623i	$-0.605454\pi$
$5$	1.13691	−	3.34924i	0.508443	−	1.49783i	0.833709	−	0.552203i	$-0.186213\pi$
$6$	1.90335	−	1.00299i	0.777039	−	0.409469i
$7$	2.22748	−	1.42771i	0.841907	−	0.539622i
$7$	2.22748	−	1.42771i	0.841907	−	0.539622i
$8$	2.69170	+	0.868758i	0.951660	+	0.307152i
$9$	−0.417389	−	0.543952i	−0.139130	−	0.181317i
$10$	2.88955	+	4.08295i	0.913755	+	1.29114i
$11$	−1.88729	−	0.123699i	−0.569039	−	0.0372968i	−0.221831	−	0.975085i	$-0.571203\pi$
$11$	−1.88729	−	0.123699i	−0.569039	−	0.0372968i	−0.347208	+	0.937788i	$0.612870\pi$
$12$	−0.432657	+	3.01169i	−0.124897	+	0.869399i
$13$	−6.25362	−	1.24392i	−1.73444	−	0.345002i	−0.776097	−	0.630613i	$-0.782804\pi$
$13$	−6.25362	−	1.24392i	−1.73444	−	0.345002i	−0.958346	+	0.285611i	$0.907804\pi$
$14$	−0.215687	+	3.73544i	−0.0576448	+	0.998337i
$15$	−3.80478	+	3.80478i	−0.982389	+	0.982389i
$16$	−3.22991	+	2.35959i	−0.807478	+	0.589897i
$17$	−0.836885	+	3.12330i	−0.202975	+	0.757511i	0.787083	+	0.616847i	$0.211590\pi$
$17$	−0.836885	+	3.12330i	−0.202975	+	0.757511i	−0.990057	+	0.140664i	$0.955076\pi$
$18$	0.969288	−	0.0260154i	0.228463	−	0.00613189i
$19$	3.94420	+	3.45897i	0.904861	+	0.793542i	0.979033	−	0.203704i	$-0.0652979\pi$
$19$	3.94420	+	3.45897i	0.904861	+	0.793542i	−0.0741716	+	0.997245i	$0.523631\pi$
$20$	−7.07340	−	0.0833518i	−1.58166	−	0.0186380i
$21$	−3.99984	+	0.449215i	−0.872837	+	0.0980268i
$22$	1.70900	−	2.05758i	0.364360	−	0.438678i
$23$	3.49170	−	2.67928i	0.728070	−	0.558668i	−0.176856	−	0.984237i	$-0.556593\pi$
$23$	3.49170	−	2.67928i	0.728070	−	0.558668i	0.904926	+	0.425569i	$0.139926\pi$
$24$	−3.08805	−	2.99647i	−0.630346	−	0.611652i
$25$	−5.95807	−	4.57179i	−1.19161	−	0.914358i
$26$	6.61755	−	6.12522i	1.29781	−	1.20125i
$27$	1.09387	+	5.49923i	0.210515	+	1.05833i
$28$	−4.09670	−	3.34919i	−0.774203	−	0.632938i
$29$	−4.54188	−	6.79740i	−0.843405	−	1.26225i	−0.963021	−	0.269425i	$-0.913166\pi$
$29$	−4.54188	−	6.79740i	−0.843405	−	1.26225i	0.119616	−	0.992820i	$-0.461834\pi$
$30$	−1.19531	−	7.51509i	−0.218232	−	1.37206i
$31$	−4.58956	+	2.64978i	−0.824310	+	0.475915i	−0.851900	−	0.523704i	$-0.824550\pi$
$31$	−4.58956	+	2.64978i	−0.824310	+	0.475915i	0.0275907	+	0.999619i	$0.491217\pi$
$32$	−0.0184792	−	5.65682i	−0.00326670	−	0.999995i
$33$	2.49181	+	1.43865i	0.433769	+	0.250437i
$34$	−2.88009	−	3.55187i	−0.493932	−	0.609141i
$35$	−2.24928	−	9.08354i	−0.380198	−	1.53540i
$36$	−0.775221	+	1.13112i	−0.129203	+	0.188519i
$37$	−1.48538	−	0.504220i	−0.244196	−	0.0828933i	0.196658	−	0.980472i	$-0.436991\pi$
$37$	−1.48538	−	0.504220i	−0.244196	−	0.0828933i	−0.440854	+	0.897579i	$0.645324\pi$
$38$	−7.23504	+	1.64209i	−1.17368	+	0.266383i
$39$	7.69556	+	5.90501i	1.23228	+	0.945558i
$40$	5.96991	−	8.02745i	0.943926	−	1.26925i
$41$	9.60237	+	3.97743i	1.49964	+	0.621171i	0.973389	−	0.229159i	$-0.0735977\pi$
$41$	9.60237	+	3.97743i	1.49964	+	0.621171i	0.526250	+	0.850330i	$0.323598\pi$
$42$	2.80769	−	4.95156i	0.433237	−	0.764042i
$43$	−5.74894	−	3.84132i	−0.876705	−	0.585796i	0.0337377	−	0.999431i	$-0.489259\pi$
$43$	−5.74894	−	3.84132i	−0.876705	−	0.585796i	−0.910443	+	0.413635i	$0.864259\pi$
$44$	0.935908	+	3.66507i	0.141093	+	0.552530i
$45$	−2.29636	+	0.779510i	−0.342322	+	0.116203i
$46$	0.166996	+	6.22199i	0.0246223	+	0.917382i
$47$	4.47655	−	1.19949i	0.652972	−	0.174963i	0.0828996	−	0.996558i	$-0.473582\pi$
$47$	4.47655	−	1.19949i	0.652972	−	0.174963i	0.570072	+	0.821595i	$0.306915\pi$
$48$	5.99460	−	1.04620i	0.865247	−	0.151006i
$49$	2.92331	−	6.36037i	0.417616	−	0.908624i
$50$	10.1814	−	3.02310i	1.43987	−	0.427531i
$51$	3.24339	−	3.69837i	0.454165	−	0.517876i
$52$	1.51542	+	12.6619i	0.210150	+	1.75589i
$53$	−8.06804	−	0.528807i	−1.10823	−	0.0726372i	−0.499723	−	0.866185i	$-0.666565\pi$
$53$	−8.06804	−	0.528807i	−1.10823	−	0.0726372i	−0.608507	+	0.793548i	$0.708231\pi$
$54$	−7.20325	−	3.31504i	−0.980238	−	0.451119i
$55$	−2.55998	+	6.18035i	−0.345188	+	0.833358i
$56$	7.23604	−	1.90782i	0.966956	−	0.254943i
$57$	−3.05414	−	7.37334i	−0.404531	−	0.976623i
$58$	11.5528	+	0.446352i	1.51696	+	0.0586088i
$59$	3.99664	+	4.55729i	0.520318	+	0.593309i	0.950999	−	0.309195i	$-0.100060\pi$
$59$	3.99664	+	4.55729i	0.520318	+	0.593309i	−0.430680	+	0.902505i	$0.641726\pi$
$60$	9.59497	+	4.87310i	1.23871	+	0.629115i
$61$	−0.377061	−	5.75285i	−0.0482778	−	0.736577i	−0.951547	−	0.307503i	$-0.900507\pi$
$61$	−0.377061	−	5.75285i	−0.0482778	−	0.736577i	0.903269	−	0.429074i	$-0.141160\pi$
$62$	0.778542	−	7.45418i	0.0988749	−	0.946681i
$63$	−1.70633	−	0.615732i	−0.214977	−	0.0775749i
$64$	6.49052	+	4.67687i	0.811315	+	0.584609i
$65$	−11.2760	+	19.5307i	−1.39862	+	2.42248i
$66$	−3.71624	+	1.65749i	−0.457437	+	0.204022i
$67$	1.70857	+	0.842575i	0.208735	+	0.102937i	0.543652	−	0.839311i	$-0.317041\pi$
$67$	1.70857	+	0.842575i	0.208735	+	0.102937i	−0.334916	+	0.942248i	$0.608708\pi$
$68$	6.45764	−	0.346893i	0.783104	−	0.0420669i
$69$	−6.56690	+	1.30624i	−0.790561	+	0.157252i
$70$	12.2657	+	4.96926i	1.46603	+	0.593940i
$71$	−2.47554	−	5.97649i	−0.293793	−	0.709279i	−0.999999	−	0.00127269i	$-0.999595\pi$
$71$	−2.47554	−	5.97649i	−0.293793	−	0.709279i	0.706206	−	0.708006i	$-0.250405\pi$
$72$	−0.650925	−	1.82677i	−0.0767122	−	0.215287i
$73$	−12.6883	+	1.67045i	−1.48505	+	0.195511i	−0.829019	−	0.559221i	$-0.811100\pi$
$73$	−12.6883	+	1.67045i	−1.48505	+	0.195511i	−0.656034	+	0.754732i	$0.727767\pi$
$74$	1.81079	−	1.28151i	0.210499	−	0.148973i
$75$	5.05313	+	10.2467i	0.583486	+	1.18319i
$76$	4.12910	−	9.64547i	0.473640	−	1.10641i
$77$	−4.38050	+	2.41896i	−0.499204	+	0.275666i
$78$	−13.1505	+	3.90469i	−1.48900	+	0.442120i
$79$	−1.82895	−	6.82573i	−0.205773	−	0.767955i	−0.989213	−	0.146487i	$-0.953203\pi$
$79$	−1.82895	−	6.82573i	−0.205773	−	0.767955i	0.783440	−	0.621468i	$-0.213463\pi$
$80$	4.23070	+	13.5004i	0.473007	+	1.50939i
$81$	1.67533	−	6.25243i	0.186148	−	0.694714i
$82$	−12.5277	+	7.68822i	−1.38345	+	0.849022i
$83$	0.334426	−	1.68127i	0.0367080	−	0.184544i	−0.958081	−	0.286497i	$-0.907509\pi$
$83$	0.334426	−	1.68127i	0.0367080	−	0.184544i	0.994789	+	0.101953i	$0.0325092\pi$
$84$	3.33607	+	7.32617i	0.363995	+	0.799351i
$85$	9.50921	+	6.35385i	1.03142	+	0.689172i
$86$	9.17155	−	3.39037i	0.988994	−	0.365593i
$87$	1.62334	+	12.3305i	0.174040	+	1.32197i
$88$	−4.97255	−	1.97256i	−0.530076	−	0.210276i
$89$	0.834940	−	6.34200i	0.0885035	−	0.672251i	−0.888477	−	0.458921i	$-0.848236\pi$
$89$	0.834940	−	6.34200i	0.0885035	−	0.672251i	0.976980	−	0.213329i	$-0.0684307\pi$
$90$	1.01487	−	3.27596i	0.106976	−	0.345316i
$91$	−15.7058	+	6.15753i	−1.64641	+	0.645484i
$92$	−7.26079	−	4.97624i	−0.756989	−	0.518809i
$93$	8.04499	−	0.527297i	0.834227	−	0.0546781i
$94$	−2.34479	+	6.12033i	−0.241847	+	0.631264i
$95$	16.0691	−	9.27752i	1.64866	−	0.951853i
$96$	−3.78101	+	7.73069i	−0.385898	+	0.789010i
$97$			3.69260i			0.374927i	0.982272	+	0.187463i	$0.0600266\pi$
$97$			3.69260i			0.374927i	−0.982272	+	0.187463i	$0.939973\pi$
$98$	4.85267	+	8.62854i	0.490193	+	0.871614i
$99$	0.720448	+	1.07823i	0.0724077	+	0.108366i
$100$	−4.99526	+	14.1650i	−0.499526	+	1.41650i
$101$	10.5516	−	9.25353i	1.04993	−	0.920760i	0.0529596	−	0.998597i	$-0.483135\pi$
$101$	10.5516	−	9.25353i	1.04993	−	0.920760i	0.996966	+	0.0778365i	$0.0248012\pi$
$102$	1.53975	+	6.78412i	0.152458	+	0.671728i
$103$	−1.25158	+	9.50671i	−0.123322	+	0.936724i	0.812181	+	0.583406i	$0.198280\pi$
$103$	−1.25158	+	9.50671i	−0.123322	+	0.936724i	−0.935503	+	0.353319i	$0.885053\pi$
$104$	−15.7522	−	8.78115i	−1.54463	−	0.861063i
$105$	−3.04295	+	13.9072i	−0.296961	+	1.35720i
$106$	7.30586	−	8.79603i	0.709608	−	0.854346i
$107$	4.17942	−	2.06106i	0.404039	−	0.199250i	−0.228903	−	0.973449i	$-0.573514\pi$
$107$	4.17942	−	2.06106i	0.404039	−	0.199250i	0.632942	+	0.774199i	$0.281847\pi$
$108$	9.77695	−	5.49215i	0.940788	−	0.528482i
$109$	6.37623	−	2.16444i	0.610732	−	0.207316i	0.00109925	−	0.999999i	$-0.499650\pi$
$109$	6.37623	−	2.16444i	0.610732	−	0.207316i	0.609633	+	0.792684i	$0.291317\pi$
$110$	−4.94835	−	8.06314i	−0.471807	−	0.768791i
$111$	1.68741	+	1.68741i	0.160162	+	0.160162i
$112$	−3.82575	+	9.86730i	−0.361500	+	0.932372i
$113$	4.35155	−	4.35155i	0.409360	−	0.409360i	−0.472156	−	0.881515i	$-0.656524\pi$
$113$	4.35155	−	4.35155i	0.409360	−	0.409360i	0.881515	+	0.472156i	$0.156524\pi$
$114$	10.9765	+	2.62764i	1.02804	+	0.246101i
$115$	−5.00378	−	14.7407i	−0.466605	−	1.37457i
$116$	−10.1056	+	12.8534i	−0.938281	+	1.19341i
$117$	1.93356	+	3.92087i	0.178758	+	0.362485i
$118$	−8.53581	+	0.789955i	−0.785785	+	0.0727213i
$119$	2.59501	+	8.15190i	0.237884	+	0.747284i
$120$	−13.5468	+	6.93589i	−1.23664	+	0.633158i
$121$	−7.35934	−	0.968875i	−0.669031	−	0.0880795i
$122$	6.89824	+	4.34617i	0.624537	+	0.393483i
$123$	−10.4254	−	11.8879i	−0.940026	−	1.07189i
$124$	7.88596	+	7.08191i	0.708180	+	0.635974i
$125$	−7.38152	+	4.93218i	−0.660224	+	0.441147i
$126$	2.12192	−	1.44181i	0.189036	−	0.128446i
$127$	2.42066			0.214798			0.107399	−	0.994216i	$-0.465748\pi$
$127$	2.42066			0.214798			0.107399	+	0.994216i	$0.465748\pi$
$128$	−10.7439	+	3.54530i	−0.949633	+	0.313363i
$129$	5.25929	+	9.10936i	0.463055	+	0.802034i
$130$	−12.9913	−	29.1276i	−1.13941	−	2.55466i
$131$	−1.35129	−	20.6168i	−0.118063	−	1.80130i	−0.488632	−	0.872490i	$-0.662504\pi$
$131$	−1.35129	−	20.6168i	−0.118063	−	1.80130i	0.370569	−	0.928805i	$-0.379163\pi$
$132$	1.18909	−	5.63040i	0.103497	−	0.490064i
$133$	13.7240	+	2.07362i	1.19002	+	0.179805i
$134$	−2.38345	+	1.25598i	−0.205898	+	0.108500i
$135$	19.6619	+	2.58854i	1.69223	+	0.222786i
$136$	−4.96604	+	7.67994i	−0.425834	+	0.658549i
$137$	10.0532	−	1.32352i	0.858900	−	0.113076i	0.311804	−	0.950146i	$-0.399067\pi$
$137$	10.0532	−	1.32352i	0.858900	−	0.113076i	0.547096	+	0.837070i	$0.315733\pi$
$138$	3.95864	−	8.60174i	0.336982	−	0.732229i
$139$	−3.73522	+	5.59015i	−0.316817	+	0.474151i	−0.955364	−	0.295433i	$-0.904536\pi$
$139$	−3.73522	+	5.59015i	−0.316817	+	0.474151i	0.638546	+	0.769584i	$0.279536\pi$
$140$	−15.8748	+	9.91308i	−1.34167	+	0.837808i
$141$	−6.91495	−	1.37547i	−0.582344	−	0.115835i
$142$	8.89704	+	2.12984i	0.746623	+	0.178732i
$143$	11.6485	+	3.12121i	0.974098	+	0.261009i
$144$	2.63164	+	0.772051i	0.219303	+	0.0643376i
$145$	−27.9298	+	7.48378i	−2.31945	+	0.621494i
$146$	8.62561	−	15.9112i	0.713860	−	1.31682i
$147$	−8.26821	+	6.71122i	−0.681951	+	0.553532i
$148$	−0.0369664	+	3.13705i	−0.00303862	+	0.257864i
$149$	14.4213	−	7.11182i	1.18144	−	0.582623i	0.257919	−	0.966167i	$-0.416963\pi$
$149$	14.4213	−	7.11182i	1.18144	−	0.582623i	0.923523	+	0.383544i	$0.125297\pi$
$150$	−15.9257	−	2.72583i	−1.30033	−	0.222563i
$151$	0.960238	+	7.29373i	0.0781430	+	0.593555i	0.985056	+	0.172236i	$0.0550993\pi$
$151$	0.960238	+	7.29373i	0.0781430	+	0.593555i	−0.906913	+	0.421319i	$0.861567\pi$
$152$	7.61160	+	12.7371i	0.617382	+	1.03311i
$153$	2.04823	−	0.848406i	0.165590	−	0.0685896i
$154$	0.869135	−	7.02317i	0.0700369	−	0.565943i
$155$	3.65683	+	18.3841i	0.293724	+	1.47665i
$156$	6.45198	−	18.2958i	0.516572	−	1.46483i
$157$	−2.43074	+	4.92906i	−0.193994	+	0.393382i	−0.972036	−	0.234831i	$-0.924546\pi$
$157$	−2.43074	+	4.92906i	−0.193994	+	0.393382i	0.778042	+	0.628212i	$0.216213\pi$
$158$	9.33213	+	3.57528i	0.742424	+	0.284434i
$159$	10.6523	+	6.15013i	0.844786	+	0.487737i
$160$	−18.9671	−	6.36943i	−1.49948	−	0.503548i
$161$	3.95246	−	10.9532i	0.311498	−	0.863229i
$162$	5.76557	+	7.11038i	0.452986	+	0.558644i
$163$	−12.0038	+	0.786770i	−0.940209	+	0.0616245i	−0.527795	−	0.849372i	$-0.676981\pi$
$163$	−12.0038	+	0.786770i	−0.940209	+	0.0616245i	−0.412414	+	0.910996i	$0.635314\pi$
$164$	1.60385	−	20.7251i	0.125240	−	1.61836i
$165$	7.65136	−	6.71006i	0.595658	−	0.522378i
$166$	1.64675	+	1.77911i	0.127813	+	0.138086i
$167$	11.3703	−	4.70975i	0.879863	−	0.364451i	0.103419	−	0.994638i	$-0.467022\pi$
$167$	11.3703	−	4.70975i	0.879863	−	0.364451i	0.776444	+	0.630187i	$0.217022\pi$
$168$	−11.1566	−	2.26574i	−0.860754	−	0.174806i
$169$	25.5500	+	10.5832i	1.96539	+	0.814090i
$170$	−15.1705	+	5.60796i	−1.16352	+	0.430111i
$171$	0.235248	−	3.58919i	0.0179899	−	0.274472i
$172$	−3.73619	+	13.3141i	−0.284882	+	1.01519i
$173$	−5.85037	−	5.13064i	−0.444795	−	0.390075i	0.407441	−	0.913231i	$-0.366421\pi$
$173$	−5.85037	−	5.13064i	−0.444795	−	0.390075i	−0.852237	+	0.523156i	$0.824754\pi$
$174$	−15.4625	−	8.38237i	−1.17221	−	0.635466i
$175$	−19.7986	−	1.67718i	−1.49664	−	0.126783i
$176$	6.38766	−	4.05369i	0.481488	−	0.305558i
$177$	−2.38668	−	8.90720i	−0.179394	−	0.669506i
$178$	6.56605	+	6.22280i	0.492146	+	0.466418i
$179$	6.32233	+	18.6250i	0.472553	+	1.39210i	0.878299	+	0.478111i	$0.158678\pi$
$179$	6.32233	+	18.6250i	0.472553	+	1.39210i	−0.405746	+	0.913986i	$0.632988\pi$
$180$	2.90702	+	3.88238i	0.216677	+	0.289376i
$181$	12.4092	−	18.5716i	0.922367	−	1.38042i	−0.00244569	−	0.999997i	$-0.500778\pi$
$181$	12.4092	−	18.5716i	0.922367	−	1.38042i	0.924813	−	0.380423i	$-0.124222\pi$
$182$	5.99542	−	23.0917i	0.444410	−	1.71167i
$183$	−3.35636	+	8.10298i	−0.248110	+	0.598989i
$184$	11.7263	−	4.17837i	0.864472	−	0.308034i
$185$	−3.37751	+	4.40166i	−0.248319	+	0.323616i
$186$	−6.07784	+	9.64675i	−0.445649	+	0.707334i
$187$	1.96579	−	5.79105i	0.143753	−	0.423483i
$188$	−5.05837	−	7.76697i	−0.368920	−	0.566465i
$189$	10.2879	+	10.6877i	0.748331	+	0.777416i
$190$	−2.72586	+	26.0988i	−0.197754	+	1.89341i
$191$	2.99441	−	5.18648i	0.216668	−	0.375280i	−0.737119	−	0.675763i	$-0.763814\pi$
$191$	2.99441	−	5.18648i	0.216668	−	0.375280i	0.953787	+	0.300483i	$0.0971477\pi$
$192$	−5.70890	−	10.7484i	−0.412005	−	0.775697i
$193$	−8.76468	−	15.1809i	−0.630896	−	1.09274i	−0.987369	−	0.158438i	$-0.949354\pi$
$193$	−8.76468	−	15.1809i	−0.630896	−	1.09274i	0.356473	−	0.934305i	$-0.383979\pi$
$194$	−4.22679	−	3.06673i	−0.303466	−	0.220178i
$195$	28.5265	−	19.0608i	2.04282	−	1.36497i
$196$	−13.9070	−	1.61137i	−0.993354	−	0.115098i
$197$	−3.54603	+	0.705349i	−0.252644	+	0.0502540i	−0.319787	−	0.947489i	$-0.603611\pi$
$197$	−3.54603	+	0.705349i	−0.252644	+	0.0502540i	0.0671435	+	0.997743i	$0.478611\pi$
$198$	−1.83254	−	0.0708018i	−0.130233	−	0.00503166i
$199$	−3.47592	+	4.52991i	−0.246401	+	0.321117i	−0.900137	−	0.435606i	$-0.856534\pi$
$199$	−3.47592	+	4.52991i	−0.246401	+	0.321117i	0.653736	+	0.756723i	$0.273201\pi$
$200$	−12.0656	−	17.4820i	−0.853165	−	1.23617i
$201$	−1.76427	−	2.29924i	−0.124442	−	0.162176i
$202$	1.82900	+	19.7632i	0.128688	+	1.39053i
$203$	−19.8216	−	8.65658i	−1.39120	−	0.607573i
$204$	−9.04432	−	3.87175i	−0.633229	−	0.271077i
$205$	24.2385	−	27.6387i	1.69289	−	1.93037i
$206$	−9.84256	−	9.32803i	−0.685764	−	0.649914i
$207$	−2.91480	−	0.781018i	−0.202592	−	0.0542845i
$208$	23.1338	−	10.7382i	1.60404	−	0.744562i
$209$	−7.01597	−	7.01597i	−0.485305	−	0.485305i
$210$	−13.3919	−	15.0331i	−0.924126	−	1.03739i
$211$	3.01778	−	15.1714i	0.207753	−	1.04444i	−0.726319	−	0.687358i	$-0.758770\pi$
$211$	3.01778	−	15.1714i	0.207753	−	1.04444i	0.934072	−	0.357086i	$-0.116230\pi$
$212$	4.00095	+	15.6679i	0.274786	+	1.07608i
$213$	−0.643643	+	9.82010i	−0.0441017	+	0.672862i
$214$	−1.11181	+	6.49576i	−0.0760015	+	0.444041i
$215$	−19.4015	+	14.8873i	−1.32317	+	1.01531i
$216$	−1.83314	+	15.7526i	−0.124730	+	1.07183i
$217$	−6.44003	+	12.4549i	−0.437178	+	0.845493i
$218$	−2.81794	+	9.09624i	−0.190855	+	0.616075i
$219$	18.4361	+	6.25820i	1.24579	+	0.422890i
$220$	13.3392	+	1.03228i	0.899331	+	0.0695966i
$221$	9.11871	−	18.4909i	0.613391	−	1.24383i
$222$	−3.33293	+	0.530117i	−0.223692	+	0.0355791i
$223$			20.4739i			1.37104i	0.728056	+	0.685518i	$0.240424\pi$
$223$			20.4739i			1.37104i	−0.728056	+	0.685518i	$0.759576\pi$
$224$	−8.11745	−	12.5741i	−0.542370	−	0.840140i
$225$			5.14912i			0.343275i
$226$	1.36708	+	8.59507i	0.0909369	+	0.571735i
$227$	−9.42080	+	19.1035i	−0.625280	+	1.26794i	0.321758	+	0.946822i	$0.395726\pi$
$227$	−9.42080	+	19.1035i	−0.625280	+	1.26794i	−0.947038	+	0.321121i	$0.895940\pi$
$228$	−12.1238	+	10.3821i	−0.802919	+	0.687574i
$229$	11.6558	+	3.95662i	0.770239	+	0.261461i	0.678774	−	0.734347i	$-0.262512\pi$
$229$	11.6558	+	3.95662i	0.770239	+	0.261461i	0.0914651	+	0.995808i	$0.470845\pi$
$230$	21.0288	+	6.51455i	1.38660	+	0.429557i
$231$	7.60443	−	0.353020i	0.500335	−	0.0232270i
$232$	−6.32008	−	22.2424i	−0.414934	−	1.46028i
$233$	−8.34228	+	6.40126i	−0.546521	+	0.419360i	−0.844771	−	0.535127i	$-0.820264\pi$
$233$	−8.34228	+	6.40126i	−0.546521	+	0.419360i	0.298250	+	0.954488i	$0.403597\pi$
$234$	−6.09392	−	1.04303i	−0.398372	−	0.0681849i
$235$	1.07208	−	16.3568i	0.0699347	−	1.06700i
$236$	6.18481	−	10.4267i	0.402597	−	0.678721i
$237$	−2.09728	+	10.5437i	−0.136233	+	0.684890i
$238$	−11.4864	−	3.79979i	−0.744551	−	0.246304i
$239$	−10.8660	−	10.8660i	−0.702863	−	0.702863i	0.262161	−	0.965024i	$-0.415565\pi$
$239$	−10.8660	−	10.8660i	−0.702863	−	0.702863i	−0.965024	+	0.262161i	$0.915565\pi$
$240$	3.31138	−	21.2668i	0.213749	−	1.37277i
$241$	1.28018	+	0.343022i	0.0824634	+	0.0220960i	0.299815	−	0.953997i	$-0.403075\pi$
$241$	1.28018	+	0.343022i	0.0824634	+	0.0220960i	−0.217351	+	0.976093i	$0.569742\pi$
$242$	7.22101	−	7.61932i	0.464184	−	0.489789i
$243$	4.59797	−	5.24298i	0.294960	−	0.336337i
$244$	−10.7039	+	4.28666i	−0.685249	+	0.274425i
$245$	−17.9788	−	17.0221i	−1.14863	−	1.08750i
$246$	22.2660	−	2.06063i	1.41963	−	0.131381i
$247$	−20.3628	−	26.5374i	−1.29566	−	1.68853i
$248$	−14.6558	+	3.14521i	−0.930641	+	0.199721i
$249$	−1.58755	+	2.06893i	−0.100607	+	0.131113i
$250$	0.484708	−	12.5456i	0.0306556	−	0.793452i
$251$	14.6461	−	2.91329i	0.924453	−	0.183885i	0.290161	−	0.956978i	$-0.406291\pi$
$251$	14.6461	−	2.91329i	0.924453	−	0.183885i	0.634293	+	0.773093i	$0.281291\pi$
$252$	−0.111884	+	3.62632i	−0.00704802	+	0.228437i
$253$	−6.92127	+	4.62465i	−0.435137	+	0.290749i
$254$	−2.01037	+	2.77084i	−0.126142	+	0.173858i
$255$	−8.69929	−	15.0676i	−0.544771	−	0.943571i
$256$	4.86467	−	15.2425i	0.304042	−	0.952659i
$257$	8.25531	−	14.2986i	0.514952	−	0.891923i	−0.484898	−	0.874571i	$-0.661143\pi$
$257$	8.25531	−	14.2986i	0.514952	−	0.891923i	0.999849	−	0.0173519i	$-0.00552355\pi$
$258$	−14.7950	−	1.54525i	−0.921099	−	0.0962030i
$259$	−4.02854	+	0.997555i	−0.250321	+	0.0619850i
$260$	44.1307	+	9.32002i	2.73687	+	0.578003i
$261$	−1.80173	+	5.30773i	−0.111524	+	0.328540i
$262$	24.7216	+	15.5756i	1.52730	+	0.962262i
$263$	9.47384	−	12.3465i	0.584182	−	0.761320i	−0.403975	−	0.914770i	$-0.632372\pi$
$263$	9.47384	−	12.3465i	0.584182	−	0.761320i	0.988156	+	0.153450i	$0.0490383\pi$
$264$	5.45738	+	6.03720i	0.335879	+	0.371564i
$265$	−10.9438	+	26.4206i	−0.672270	+	1.62300i
$266$	−13.7715	+	13.9872i	−0.844383	+	0.857613i
$267$	−5.40645	+	8.09133i	−0.330869	+	0.495181i
$268$	0.541789	−	3.77135i	0.0330950	−	0.230372i
$269$	−4.63158	−	13.6442i	−0.282392	−	0.831900i	−0.991879	−	0.127182i	$-0.959407\pi$
$269$	−4.63158	−	13.6442i	−0.282392	−	0.831900i	0.709487	−	0.704718i	$-0.248927\pi$
$270$	−19.2923	+	20.3565i	−1.17409	+	1.23886i
$271$	0.316315	+	1.18050i	0.0192148	+	0.0717105i	0.974868	−	0.222785i	$-0.0715149\pi$
$271$	0.316315	+	1.18050i	0.0192148	+	0.0717105i	−0.955653	+	0.294496i	$0.904848\pi$
$272$	−4.66664	−	12.0627i	−0.282957	−	0.731408i
$273$	25.5723	+	2.16628i	1.54771	+	0.131109i
$274$	−6.83422	+	12.6067i	−0.412870	+	0.761599i
$275$	10.6791	+	9.36530i	0.643972	+	0.564749i
$276$	6.55844	+	11.6751i	0.394771	+	0.702760i
$277$	0.144759	−	2.20860i	0.00869774	−	0.132702i	−0.991302	−	0.131609i	$-0.957986\pi$
$277$	0.144759	−	2.20860i	0.00869774	−	0.132702i	0.999999	−	0.00109257i	$-0.000347777\pi$
$278$	−3.29673	−	8.91824i	−0.197725	−	0.534880i
$279$	3.35699	+	1.39051i	0.200978	+	0.0832477i
$280$	1.83700	−	26.4043i	0.109782	−	1.57796i
$281$	−5.49068	+	2.27432i	−0.327547	+	0.135674i	−0.540396	−	0.841411i	$-0.681726\pi$
$281$	−5.49068	+	2.27432i	−0.327547	+	0.135674i	0.212849	+	0.977085i	$0.431726\pi$
$282$	7.31736	−	6.77297i	0.435743	−	0.403325i
$283$	10.1527	−	8.90367i	0.603515	−	0.529268i	−0.302151	−	0.953260i	$-0.597705\pi$
$283$	10.1527	−	8.90367i	0.603515	−	0.529268i	0.905666	+	0.423992i	$0.139371\pi$
$284$	−9.82700	+	8.41528i	−0.583125	+	0.499355i
$285$	−28.1674	+	1.84619i	−1.66849	+	0.109359i
$286$	−13.2469	+	10.7415i	−0.783306	+	0.635157i
$287$	27.0677	−	4.84973i	1.59775	−	0.286270i
$288$	−3.06933	+	2.37115i	−0.180862	+	0.139721i
$289$	5.66781	+	3.27231i	0.333401	+	0.192489i
$290$	14.6295	−	38.1857i	0.859073	−	2.24234i
$291$	2.48459	−	5.03824i	0.145649	−	0.295347i
$292$	11.0494	+	23.0878i	0.646614	+	1.35111i
$293$	2.29359	+	11.5306i	0.133993	+	0.673628i	0.988135	+	0.153588i	$0.0490828\pi$
$293$	2.29359	+	11.5306i	0.133993	+	0.673628i	−0.854142	+	0.520040i	$0.825917\pi$
$294$	−0.815299	−	15.0380i	−0.0475492	−	0.877037i
$295$	19.8073	−	8.20446i	1.15323	−	0.477682i
$296$	−3.56017	−	2.64765i	−0.206931	−	0.153892i
$297$	−1.38419	−	10.5140i	−0.0803188	−	0.610081i
$298$	−3.83636	+	22.4140i	−0.222234	+	1.29841i
$299$	−25.1686	+	12.4118i	−1.45554	+	0.717792i
$300$	16.3466	−	15.9658i	0.943771	−	0.921788i
$301$	−18.2899	−	0.348651i	−1.05421	−	0.0200959i
$302$	−9.14637	−	4.95834i	−0.526314	−	0.285320i
$303$	−20.6231	+	5.52594i	−1.18476	+	0.317457i
$304$	−20.9012	−	1.86548i	−1.19876	−	0.106992i
$305$	−19.6964	−	5.27762i	−1.12781	−	0.302196i
$306$	−0.729929	+	3.04915i	−0.0417273	+	0.174308i
$307$	−15.0270	−	2.98906i	−0.857637	−	0.170595i	−0.253363	−	0.967371i	$-0.581537\pi$
$307$	−15.0270	−	2.98906i	−0.857637	−	0.170595i	−0.604274	+	0.796777i	$0.706537\pi$
$308$	7.31735	+	6.82765i	0.416945	+	0.389042i
$309$	8.10432	−	12.1290i	0.461039	−	0.689993i
$310$	−24.0807	−	11.0823i	−1.36769	−	0.629431i
$311$	6.40891	−	0.843748i	0.363416	−	0.0478446i	0.0533926	−	0.998574i	$-0.482997\pi$
$311$	6.40891	−	0.843748i	0.363416	−	0.0478446i	0.310023	+	0.950729i	$0.399663\pi$
$312$	15.5841	+	22.5801i	0.882277	+	1.27835i
$313$	−3.65883	−	0.481694i	−0.206809	−	0.0272270i	0.0264096	−	0.999651i	$-0.491593\pi$
$313$	−3.65883	−	0.481694i	−0.206809	−	0.0272270i	−0.233219	+	0.972424i	$0.574926\pi$
$314$	−3.62338	−	6.87600i	−0.204479	−	0.388035i
$315$	−4.00218	+	5.01487i	−0.225498	+	0.282556i
$316$	−11.8429	+	7.71288i	−0.666214	+	0.433883i
$317$	1.15159	+	17.5699i	0.0646799	+	0.986825i	0.899673	+	0.436565i	$0.143805\pi$
$317$	1.15159	+	17.5699i	0.0646799	+	0.986825i	−0.834993	+	0.550261i	$0.814528\pi$
$318$	−15.8867	+	7.08565i	−0.890881	+	0.397343i
$319$	7.73100	+	13.3905i	0.432853	+	0.749723i
$320$	23.0431	−	16.4211i	1.28815	−	0.917968i
$321$	−7.08925			−0.395684
$322$	9.25515	+	13.6209i	0.515769	+	0.759064i
$323$	−14.1042	+	9.42415i	−0.784781	+	0.524374i
$324$	−12.9273	+	0.694433i	−0.718186	+	0.0385796i
$325$	31.5726	+	36.0016i	1.75133	+	1.99701i
$326$	9.06863	−	14.3937i	0.502265	−	0.797195i
$327$	−10.1562	−	1.33709i	−0.561638	−	0.0739411i
$328$	22.3913	+	19.0482i	1.23635	+	1.05176i
$329$	8.25889	−	9.06303i	0.455328	−	0.499661i
$330$	1.32628	+	14.3310i	0.0730091	+	0.788896i
$331$	5.60506	+	11.3659i	0.308082	+	0.624728i	0.994760	−	0.102233i	$-0.0325987\pi$
$331$	5.60506	+	11.3659i	0.308082	+	0.624728i	−0.686679	+	0.726961i	$0.740932\pi$
$332$	−3.40413	+	0.407416i	−0.186826	+	0.0223599i
$333$	0.345712	+	1.01843i	0.0189449	+	0.0558099i
$334$	−4.05205	+	16.9267i	−0.221718	+	0.926188i
$335$	4.76449	−	4.76449i	0.260312	−	0.260312i
$336$	11.8592	−	10.8889i	0.646971	−	0.594039i
$337$	−5.20803	−	5.20803i	−0.283699	−	0.283699i	0.550883	−	0.834582i	$-0.314291\pi$
$337$	−5.20803	−	5.20803i	−0.283699	−	0.283699i	−0.834582	+	0.550883i	$0.814291\pi$
$338$	−33.3336	+	20.4569i	−1.81311	+	1.11271i
$339$	−8.86529	+	3.00936i	−0.481497	+	0.163446i
$340$	6.17996	−	22.0226i	0.335155	−	1.19434i
$341$	8.98961	−	4.43318i	0.486814	−	0.240070i
$342$	3.91305	+	3.25013i	0.211594	+	0.175747i
$343$	−2.56913	−	18.3412i	−0.138720	−	0.990332i
$344$	−12.1373	−	15.3341i	−0.654397	−	0.826760i
$345$	−3.09109	+	23.4792i	−0.166419	+	1.26408i
$346$	10.7316	−	2.43569i	0.576936	−	0.130944i
$347$	−7.52696	+	6.60097i	−0.404068	+	0.354358i	−0.837128	−	0.547007i	$-0.815767\pi$
$347$	−7.52696	+	6.60097i	−0.404068	+	0.354358i	0.433060	+	0.901365i	$0.357434\pi$
$348$	22.4367	−	10.7378i	1.20273	−	0.575605i
$349$	−9.07905	−	13.5878i	−0.485990	−	0.727336i	0.504726	−	0.863279i	$-0.331593\pi$
$349$	−9.07905	−	13.5878i	−0.485990	−	0.727336i	−0.990717	+	0.135944i	$0.956593\pi$
$350$	18.3627	−	21.2699i	0.981528	−	1.13693i
$351$		−	35.7508i		−	1.90824i
$352$	−0.664870	+	10.6783i	−0.0354377	+	0.569158i
$353$	4.41564	−	2.54937i	0.235021	−	0.135689i	−0.377865	−	0.925861i	$-0.623342\pi$
$353$	4.41564	−	2.54937i	0.235021	−	0.135689i	0.612886	+	0.790171i	$0.290008\pi$
$354$	12.1779	+	4.66554i	0.647249	+	0.247971i
$355$	−22.8312	+	1.49643i	−1.21175	+	0.0794225i
$356$	−12.5762	+	2.34786i	−0.666535	+	0.124436i
$357$	1.94438	−	12.8686i	0.102907	−	0.681081i
$358$	−26.5701	−	8.23121i	−1.40427	−	0.435033i
$359$	1.44360	−	10.9652i	0.0761902	−	0.578722i	−0.910184	−	0.414204i	$-0.864060\pi$
$359$	1.44360	−	10.9652i	0.0761902	−	0.578722i	0.986374	−	0.164518i	$-0.0526068\pi$
$360$	−6.85833	+	0.103226i	−0.361466	+	0.00544047i
$361$	1.11223	+	8.44826i	0.0585386	+	0.444645i
$362$	10.9524	+	29.6282i	0.575647	+	1.55723i
$363$	9.38928	+	6.27372i	0.492809	+	0.329285i
$364$	21.4531	+	26.0406i	1.12445	+	1.36490i
$365$	−8.83078	+	44.3953i	−0.462224	+	2.32376i
$366$	−6.48772	−	10.5715i	−0.339119	−	0.552581i
$367$	7.14224	−	26.6552i	0.372822	−	1.39139i	−0.483679	−	0.875245i	$-0.660700\pi$
$367$	7.14224	−	26.6552i	0.372822	−	1.39139i	0.856501	−	0.516145i	$-0.172633\pi$
$368$	−4.95590	+	16.8928i	−0.258344	+	0.880599i
$369$	−1.84439	−	6.88337i	−0.0960153	−	0.358334i
$370$	−2.23338	−	7.52172i	−0.116108	−	0.391036i
$371$	−18.7264	+	10.3409i	−0.972224	+	0.536872i
$372$	−5.99462	−	14.9688i	−0.310807	−	0.776095i
$373$	3.76043	+	7.62540i	0.194708	+	0.394828i	0.972230	−	0.234027i	$-0.0751905\pi$
$373$	3.76043	+	7.62540i	0.194708	+	0.394828i	−0.777522	+	0.628855i	$0.783524\pi$
$374$	4.99621	+	7.05968i	0.258348	+	0.365047i
$375$	13.3901	−	1.76284i	0.691462	−	0.0910327i
$376$	13.0916	+	0.660374i	0.675148	+	0.0340562i
$377$	19.9477	+	48.1581i	1.02736	+	2.48027i
$378$	−20.7780	+	2.89995i	−1.06870	+	0.149157i
$379$	24.9819	−	4.96921i	1.28323	−	0.255251i	0.494064	−	0.869425i	$-0.335511\pi$
$379$	24.9819	−	4.96921i	1.28323	−	0.255251i	0.789171	+	0.614174i	$0.210511\pi$
$380$	−27.6106	−	24.7954i	−1.41639	−	1.27198i
$381$	−3.30278	−	1.62875i	−0.169207	−	0.0834434i
$382$	3.44990	+	7.73500i	0.176512	+	0.395757i
$383$	−13.6416	+	23.6279i	−0.697052	+	1.20733i	0.272432	+	0.962175i	$0.412172\pi$
$383$	−13.6416	+	23.6279i	−0.697052	+	1.20733i	−0.969484	+	0.245155i	$0.921161\pi$
$384$	17.0446	+	2.39181i	0.869803	+	0.122056i
$385$	3.12142	+	17.4215i	0.159082	+	0.887881i
$386$	24.6561	+	2.57518i	1.25496	+	0.131073i
$387$	0.310052	+	4.73047i	0.0157608	+	0.240464i
$388$	7.02076	−	2.29133i	0.356425	−	0.116325i
$389$	−6.53396	−	7.45055i	−0.331285	−	0.377758i	0.562086	−	0.827079i	$-0.309999\pi$
$389$	−6.53396	−	7.45055i	−0.331285	−	0.377758i	−0.893370	+	0.449321i	$0.851666\pi$
$390$	−1.87319	+	48.4834i	−0.0948528	+	2.45505i
$391$	5.44603	+	13.1479i	0.275417	+	0.664917i
$392$	13.3943	−	14.5806i	0.676514	−	0.736430i
$393$	−12.0284	+	29.0391i	−0.606751	+	1.46483i
$394$	2.13761	−	4.64481i	0.107691	−	0.234002i
$395$	−24.9404	−	1.63468i	−1.25489	−	0.0822496i
$396$	1.60298	−	2.03885i	0.0805530	−	0.102456i
$397$	−13.8651	+	15.8101i	−0.695871	+	0.793488i	−0.986572	−	0.163325i	$-0.947778\pi$
$397$	−13.8651	+	15.8101i	−0.695871	+	0.793488i	0.290702	+	0.956814i	$0.406111\pi$
$398$	−2.29846	−	7.74088i	−0.115211	−	0.388015i
$399$	−17.3300	−	12.0635i	−0.867585	−	0.603932i
$400$	30.0316	+	0.707873i	1.50158	+	0.0353937i
$401$	16.0002	−	4.28725i	0.799014	−	0.214095i	0.163863	−	0.986483i	$-0.447605\pi$
$401$	16.0002	−	4.28725i	0.799014	−	0.214095i	0.635151	+	0.772388i	$0.280938\pi$
$402$	4.09711	−	0.109965i	0.204345	−	0.00548456i
$403$	31.9975	−	10.8617i	1.59391	−	0.541060i
$404$	−24.1412	−	14.3199i	−1.20107	−	0.712439i
$405$	−19.0362	−	12.7196i	−0.945915	−	0.632040i
$406$	26.3709	−	15.4998i	1.30876	−	0.769241i
$407$	2.74098	+	1.13535i	0.135865	+	0.0562772i
$408$	11.9432	−	7.13720i	0.591278	−	0.353344i
$409$	1.30346	+	1.00018i	0.0644522	+	0.0494559i	0.640485	−	0.767971i	$-0.278733\pi$
$409$	1.30346	+	1.00018i	0.0644522	+	0.0494559i	−0.576033	+	0.817427i	$0.695400\pi$
$410$	11.5068	+	50.6990i	0.568282	+	2.50385i
$411$	−14.6072	−	4.95849i	−0.720521	−	0.244584i
$412$	18.8518	−	3.51946i	0.928760	−	0.173391i
$413$	15.4089	+	4.44524i	0.758222	+	0.218736i
$414$	3.31476	−	2.68783i	0.162912	−	0.132100i
$415$	−5.25077	−	3.03153i	−0.257750	−	0.148812i
$416$	−6.92109	+	35.3986i	−0.339334	+	1.73556i
$417$	8.85776	−	5.11403i	0.433766	−	0.250435i
$418$	13.8577	−	2.20413i	0.677804	−	0.107808i
$419$	−13.7642	−	20.5996i	−0.672425	−	1.00636i	−0.998145	−	0.0608886i	$-0.980607\pi$
$419$	−13.7642	−	20.5996i	−0.672425	−	1.00636i	0.325720	−	0.945466i	$-0.394393\pi$
$420$	28.3299	−	2.84408i	1.38236	−	0.138777i
$421$	5.47034	+	27.5013i	0.266608	+	1.34033i	0.849418	+	0.527721i	$0.176953\pi$
$421$	5.47034	+	27.5013i	0.266608	+	1.34033i	−0.582809	+	0.812609i	$0.698047\pi$
$422$	14.8599	+	16.0543i	0.723369	+	0.781511i
$423$	−2.52093	−	1.93438i	−0.122572	−	0.0940526i
$424$	−21.2573	−	8.43256i	−1.03235	−	0.409521i
$425$	19.2653	−	14.7828i	0.934504	−	0.717070i
$426$	−10.7062	−	8.89241i	−0.518716	−	0.430838i
$427$	−9.05327	−	12.2760i	−0.438119	−	0.594077i
$428$	−6.51211	−	6.66741i	−0.314775	−	0.322282i
$429$	−13.7933	−	12.0964i	−0.665947	−	0.584019i
$430$	−0.927911	−	34.5723i	−0.0447478	−	1.66722i
$431$	−3.51845	+	13.1310i	−0.169478	+	0.632500i	0.827949	+	0.560804i	$0.189508\pi$
$431$	−3.51845	+	13.1310i	−0.169478	+	0.632500i	−0.997427	+	0.0716961i	$0.977159\pi$
$432$	−16.5090	−	15.1810i	−0.794291	−	0.730395i
$433$	24.6012	−	24.6012i	1.18226	−	1.18226i	0.203098	−	0.979158i	$-0.434899\pi$
$433$	24.6012	−	24.6012i	1.18226	−	1.18226i	0.979158	−	0.203098i	$-0.0651010\pi$
$434$	−8.90819	−	17.7155i	−0.427607	−	0.850373i
$435$	43.1434	+	8.58176i	2.06857	+	0.411464i
$436$	−8.07183	−	10.7801i	−0.386571	−	0.516272i
$437$	23.0395	+	1.51009i	1.10213	+	0.0722373i
$438$	−22.4748	+	15.9057i	−1.07389	+	0.760002i
$439$	−11.2297	−	14.6348i	−0.535964	−	0.698482i	0.444366	−	0.895845i	$-0.353429\pi$
$439$	−11.2297	−	14.6348i	−0.535964	−	0.698482i	−0.980330	+	0.197363i	$0.936762\pi$
$440$	−12.2599	+	14.4116i	−0.584470	+	0.687048i
$441$	−4.67989	+	1.06461i	−0.222852	+	0.0506956i
$442$	13.5928	+	25.7947i	0.646542	+	1.22693i
$443$	−7.45218	+	21.9534i	−0.354064	+	1.04304i	0.613344	+	0.789816i	$0.289824\pi$
$443$	−7.45218	+	21.9534i	−0.354064	+	1.04304i	−0.967408	+	0.253223i	$0.918509\pi$
$444$	2.16122	−	4.25536i	0.102567	−	0.201950i
$445$	−20.2916	−	10.0067i	−0.961915	−	0.474364i
$446$	−23.4358	−	17.0037i	−1.10972	−	0.805150i
$447$	−24.4619			−1.15701
$448$	21.1347	+	1.15108i	0.998520	+	0.0543832i
$449$	−16.6332			−0.784968			−0.392484	−	0.919759i	$-0.628384\pi$
$449$	−16.6332			−0.784968			−0.392484	+	0.919759i	$0.628384\pi$
$450$	−5.89403	−	4.27638i	−0.277847	−	0.201590i
$451$	−17.6304	−	8.69437i	−0.830185	−	0.409402i
$452$	−10.9738	−	5.57340i	−0.516166	−	0.262151i
$453$	3.59746	−	10.5978i	0.169023	−	0.497927i
$454$	−14.0431	−	26.6492i	−0.659074	−	1.25071i
$455$	2.76695	+	59.6029i	0.129716	+	2.79423i
$456$	−1.81518	−	22.5001i	−0.0850036	−	1.05367i
$457$	11.1552	+	14.5377i	0.521817	+	0.680046i	0.977703	−	0.209993i	$-0.0673441\pi$
$457$	11.1552	+	14.5377i	0.521817	+	0.680046i	−0.455886	+	0.890038i	$0.650677\pi$
$458$	−14.2092	+	10.0560i	−0.663955	+	0.469887i
$459$	−18.0912	−	1.18576i	−0.844425	−	0.0553465i
$460$	−24.9215	+	18.6606i	−1.16197	+	0.870053i
$461$	17.2359	+	3.42843i	0.802754	+	0.159678i	0.579383	−	0.815056i	$-0.303294\pi$
$461$	17.2359	+	3.42843i	0.802754	+	0.159678i	0.223372	+	0.974733i	$0.428294\pi$
$462$	−5.91143	+	8.99771i	−0.275025	+	0.418611i
$463$	23.0661	−	23.0661i	1.07197	−	1.07197i	0.0747731	−	0.997201i	$-0.476177\pi$
$463$	23.0661	−	23.0661i	1.07197	−	1.07197i	0.997201	−	0.0747731i	$-0.0238233\pi$
$464$	30.7089	+	11.2380i	1.42563	+	0.521713i
$465$	7.38042	−	27.5441i	0.342259	−	1.27733i
$466$	−0.398983	−	14.8654i	−0.0184825	−	0.688627i
$467$	19.2967	+	16.9227i	0.892943	+	0.783090i	0.976971	−	0.213374i	$-0.0684452\pi$
$467$	19.2967	+	16.9227i	0.892943	+	0.783090i	−0.0840279	+	0.996463i	$0.526779\pi$
$468$	6.25496	−	6.10926i	0.289136	−	0.282401i
$469$	5.00876	−	0.562524i	0.231283	−	0.0259750i
$470$	17.8326	+	14.8116i	0.822559	+	0.683206i
$471$	6.63309	−	5.08975i	0.305637	−	0.234523i
$472$	6.79858	+	15.7390i	0.312930	+	0.724446i
$473$	10.3747	+	7.96082i	0.477031	+	0.366039i
$474$	−10.3273	−	11.1573i	−0.474347	−	0.512473i
$475$	−7.68614	−	38.6408i	−0.352664	−	1.77296i
$476$	13.8890	−	9.99232i	0.636601	−	0.457997i
$477$	3.07987	+	4.60935i	0.141017	+	0.211047i
$478$	21.4622	−	3.41366i	0.981659	−	0.156137i
$479$	−3.33986	+	1.92827i	−0.152602	+	0.0881048i	−0.574357	−	0.818605i	$-0.694748\pi$
$479$	−3.33986	+	1.92827i	−0.152602	+	0.0881048i	0.421755	+	0.906710i	$0.361414\pi$
$480$	21.5933	+	21.4526i	0.985593	+	0.979175i
$481$	8.66183	+	5.00091i	0.394945	+	0.228022i
$482$	−1.45584	+	1.18049i	−0.0663117	+	0.0537699i
$483$	−12.7627	+	12.2852i	−0.580722	+	0.558997i
$484$	2.72448	+	14.5935i	0.123840	+	0.663343i
$485$	12.3674	+	4.19817i	0.561575	+	0.190629i
$486$	2.18282	+	9.61746i	0.0990145	+	0.436257i
$487$	−10.0663	−	7.72413i	−0.456147	−	0.350014i	0.354990	−	0.934870i	$-0.384484\pi$
$487$	−10.0663	−	7.72413i	−0.456147	−	0.350014i	−0.811137	+	0.584856i	$0.801151\pi$
$488$	3.98289	−	15.8125i	0.180297	−	0.715799i
$489$	16.9075	+	7.00333i	0.764585	+	0.316701i
$490$	34.4161	−	6.44285i	1.55476	−	0.291058i
$491$	−8.90213	−	5.94821i	−0.401747	−	0.268439i	0.338240	−	0.941060i	$-0.390168\pi$
$491$	−8.90213	−	5.94821i	−0.401747	−	0.268439i	−0.739987	+	0.672621i	$0.765168\pi$
$492$	−16.1333	+	27.1985i	−0.727346	+	1.22620i
$493$	25.0313	−	8.49699i	1.12735	−	0.382685i
$494$	47.2879	−	1.26919i	2.12758	−	0.0571037i
$495$	4.43033	−	1.18710i	0.199128	−	0.0533563i
$496$	8.57148	−	19.3881i	0.384871	−	0.870550i
$497$	−14.0469	−	9.77815i	−0.630089	−	0.438610i
$498$	−1.04977	−	3.53547i	−0.0470412	−	0.158428i
$499$	18.7809	−	21.4155i	0.840749	−	0.958690i	−0.158842	−	0.987304i	$-0.550776\pi$
$499$	18.7809	−	21.4155i	0.840749	−	0.958690i	0.999591	+	0.0286138i	$0.00910931\pi$
$500$	13.9579	+	10.9740i	0.624218	+	0.490773i
$501$	−18.6828	−	1.22454i	−0.834688	−	0.0547083i
$502$	−8.82893	+	19.1844i	−0.394055	+	0.856241i
$503$	−9.22047	+	22.2602i	−0.411120	+	0.992532i	0.573717	+	0.819053i	$0.305501\pi$
$503$	−9.22047	+	22.2602i	−0.411120	+	0.992532i	−0.984838	+	0.173479i	$0.944499\pi$
$504$	−4.05801	−	3.13975i	−0.180758	−	0.139856i
$505$	−18.9960	−	45.8604i	−0.845311	−	2.04076i
$506$	0.454486	−	11.7633i	0.0202044	−	0.522944i
$507$	−27.7399	−	31.6313i	−1.23197	−	1.40480i
$508$	−1.50206	−	4.60240i	−0.0666432	−	0.204199i
$509$	0.488344	+	7.45069i	0.0216455	+	0.330246i	0.994925	+	0.100622i	$0.0320832\pi$
$509$	0.488344	+	7.45069i	0.0216455	+	0.330246i	−0.973279	+	0.229625i	$0.926250\pi$
$510$	24.4722	+	2.55597i	1.08365	+	0.113180i
$511$	−25.8780	+	21.8360i	−1.14477	+	0.965970i
$512$	13.4075	+	18.2274i	0.592532	+	0.805547i
$513$	−14.7073	+	25.4737i	−0.649341	+	1.12469i
$514$	9.51105	+	21.3247i	0.419514	+	0.940590i
$515$	30.4173	+	15.0002i	1.34035	+	0.660986i
$516$	14.0562	−	15.6520i	0.618788	−	0.689042i
$517$	−8.59692	+	1.71003i	−0.378092	+	0.0752072i
$518$	2.20386	−	5.43981i	0.0968321	−	0.239011i
$519$	4.53016	+	10.9368i	0.198852	+	0.480071i
$520$	−47.3191	+	42.7746i	−2.07508	+	1.87579i
$521$	26.7195	−	3.51769i	1.17060	−	0.154113i	0.479947	−	0.877297i	$-0.340656\pi$
$521$	26.7195	−	3.51769i	1.17060	−	0.154113i	0.690655	+	0.723185i	$0.257322\pi$
$522$	−4.57922	−	6.47048i	−0.200427	−	0.283205i
$523$	14.8991	+	30.2125i	0.651494	+	1.32110i	0.932422	+	0.361370i	$0.117691\pi$
$523$	14.8991	+	30.2125i	0.651494	+	1.32110i	−0.280928	+	0.959729i	$0.590642\pi$
$524$	−38.3602	+	15.3623i	−1.67577	+	0.671106i
$525$	25.8851	+	15.6100i	1.12972	+	0.681276i
$526$	6.26458	+	21.0983i	0.273149	+	0.919928i
$527$	−4.43513	−	16.5521i	−0.193197	−	0.721023i
$528$	−11.4430	+	1.23295i	−0.497991	+	0.0536571i
$529$	−0.939383	+	3.50582i	−0.0408427	+	0.152427i
$530$	−21.1539	−	34.4694i	−0.918866	−	1.49726i
$531$	0.810796	−	4.07615i	0.0351856	−	0.176890i
$532$	−4.57343	−	27.3802i	−0.198283	−	1.18708i
$533$	−55.1020	−	36.8180i	−2.38673	−	1.59476i
$534$	−4.77177	−	12.9085i	−0.206495	−	0.558604i
$535$	−2.15135	−	16.3411i	−0.0930109	−	0.706488i
$536$	3.86698	+	3.75230i	0.167028	+	0.162075i
$537$	3.90563	−	29.6662i	0.168541	−	1.28019i
$538$	19.4646	+	6.02997i	0.839178	+	0.259971i
$539$	−6.30390	+	11.6422i	−0.271528	+	0.501467i
$540$	−7.27898	−	38.9895i	−0.313237	−	1.67784i
$541$	10.7312	−	0.703363i	0.461372	−	0.0302399i	0.167055	−	0.985948i	$-0.446574\pi$
$541$	10.7312	−	0.703363i	0.461372	−	0.0302399i	0.294318	+	0.955708i	$0.404908\pi$
$542$	−1.61398	−	0.618341i	−0.0693266	−	0.0265600i
$543$	−29.4273	+	16.9899i	−1.26285	+	0.729105i
$544$	17.6834	+	4.67640i	0.758170	+	0.200499i
$545$		−	23.8163i		−	1.02018i
$546$	−23.7176	+	27.4726i	−1.01502	+	1.17572i
$547$	6.36109	+	9.52005i	0.271981	+	0.407048i	0.942166	−	0.335146i	$-0.108785\pi$
$547$	6.36109	+	9.52005i	0.271981	+	0.407048i	−0.670186	+	0.742194i	$0.733785\pi$
$548$	−8.75460	−	18.2928i	−0.373978	−	0.781432i
$549$	−2.97189	+	2.60628i	−0.126837	+	0.111233i
$550$	−19.5892	+	4.44603i	−0.835285	+	0.189579i
$551$	5.59793	−	42.5205i	0.238480	−	1.81143i
$552$	−18.8109	−	2.18904i	−0.800646	−	0.0931718i
$553$	−13.8191	−	12.5930i	−0.587647	−	0.535507i
$554$	2.40789	+	1.99996i	0.102301	+	0.0849700i
$555$	7.57000	−	3.73311i	0.321329	−	0.158462i
$556$	12.9464	+	3.63300i	0.549048	+	0.154073i
$557$	1.94648	−	0.660742i	0.0824751	−	0.0279965i	−0.279897	−	0.960030i	$-0.590300\pi$
$557$	1.94648	−	0.660742i	0.0824751	−	0.0279965i	0.362372	+	0.932034i	$0.381967\pi$
$558$	−4.37967	+	2.68780i	−0.185406	+	0.113784i
$559$	31.1734	+	31.1734i	1.31849	+	1.31849i
$560$	28.6984	+	24.0316i	1.21273	+	1.01552i
$561$	−6.57869	+	6.57869i	−0.277753	+	0.277753i
$562$	1.95672	−	8.17383i	0.0825391	−	0.344792i
$563$	−8.33843	−	24.5642i	−0.351423	−	1.03526i	−0.968641	−	0.248466i	$-0.920073\pi$
$563$	−8.33843	−	24.5642i	−0.351423	−	1.03526i	0.617217	−	0.786793i	$-0.288260\pi$
$564$	1.67567	+	14.0009i	0.0705586	+	0.589546i
$565$	−9.62706	−	19.5217i	−0.405013	−	0.821286i
$566$	1.75985	+	19.0160i	0.0739722	+	0.799302i
$567$	−5.19487	−	16.3190i	−0.218164	−	0.685335i
$568$	−1.47130	−	18.2376i	−0.0617344	−	0.765232i
$569$	−6.34022	−	0.834706i	−0.265796	−	0.0349927i	−0.00354980	−	0.999994i	$-0.501130\pi$
$569$	−6.34022	−	0.834706i	−0.265796	−	0.0349927i	−0.262246	+	0.965001i	$0.584463\pi$
$570$	21.2799	−	33.7755i	0.891318	−	1.41470i
$571$	−11.6940	−	13.3344i	−0.489378	−	0.558029i	0.453461	−	0.891276i	$-0.350189\pi$
$571$	−11.6940	−	13.3344i	−0.489378	−	0.558029i	−0.942840	+	0.333247i	$0.891856\pi$
$572$	−1.29376	−	24.0841i	−0.0540946	−	1.00701i
$573$	−7.57537	+	5.06170i	−0.316466	+	0.211456i
$574$	−16.9286	+	35.0112i	−0.706584	+	1.46134i
$575$	−33.0529			−1.37840
$576$	−0.165076	−	5.48261i	−0.00687818	−	0.228442i
$577$	−20.2553	−	35.0833i	−0.843241	−	1.46054i	−0.887140	−	0.461500i	$-0.847312\pi$
$577$	−20.2553	−	35.0833i	−0.843241	−	1.46054i	0.0438997	−	0.999036i	$-0.486022\pi$
$578$	−8.45286	+	3.77007i	−0.351592	+	0.156814i
$579$	1.74414	+	26.6104i	0.0724838	+	1.10589i
$580$	31.5599	+	48.4593i	1.31046	+	2.01216i
$581$	−1.65544	−	4.22246i	−0.0686791	−	0.175177i
$582$	3.70364	+	7.02831i	0.153521	+	0.291333i
$583$	15.1613	+	1.99602i	0.627917	+	0.0826668i
$584$	−35.6043	−	6.52672i	−1.47332	−	0.270077i
$585$	15.3302	−	2.01826i	0.633827	−	0.0834450i
$586$	−15.1036	−	6.95088i	−0.623923	−	0.287138i
$587$	−4.98330	+	7.45803i	−0.205683	+	0.307826i	−0.919941	−	0.392056i	$-0.871764\pi$
$587$	−4.98330	+	7.45803i	−0.205683	+	0.307826i	0.714259	+	0.699882i	$0.246764\pi$
$588$	17.8906	+	11.5559i	0.737798	+	0.476559i
$589$	−27.2677	−	5.42388i	−1.12354	−	0.223487i
$590$	−7.05873	+	29.4866i	−0.290603	+	1.21394i
$591$	5.31285	+	1.42357i	0.218541	+	0.0585580i
$592$	5.98742	−	1.87631i	0.246081	−	0.0771160i
$593$	−6.60644	+	1.77019i	−0.271294	+	0.0726930i	−0.391901	−	0.920007i	$-0.628182\pi$
$593$	−6.60644	+	1.77019i	−0.271294	+	0.0726930i	0.120607	+	0.992700i	$0.461516\pi$
$594$	13.1845	+	7.14747i	0.540968	+	0.293264i
$595$	30.2530	+	0.576697i	1.24025	+	0.0236423i
$596$	−22.4704	−	23.0063i	−0.920425	−	0.942376i
$597$	7.79057	−	3.84188i	0.318847	−	0.157238i
$598$	6.69534	−	39.1177i	0.273793	−	1.59964i
$599$	2.77926	+	21.1105i	0.113557	+	0.862554i	0.949507	+	0.313747i	$0.101584\pi$
$599$	2.77926	+	21.1105i	0.113557	+	0.862554i	−0.835949	+	0.548807i	$0.815082\pi$
$600$	4.69959	+	31.9711i	0.191860	+	1.30522i
$601$	8.49990	−	3.52078i	0.346718	−	0.143615i	−0.202527	−	0.979277i	$-0.564915\pi$
$601$	8.49990	−	3.52078i	0.346718	−	0.143615i	0.549245	+	0.835661i	$0.314915\pi$
$602$	15.5890	−	20.6463i	0.635359	−	0.841479i
$603$	−0.254820	−	1.28106i	−0.0103771	−	0.0521690i
$604$	13.2718	−	6.35160i	0.540020	−	0.258443i
$605$	−11.6119	+	23.5467i	−0.472092	+	0.957308i
$606$	10.8022	−	28.1959i	0.438811	−	1.14538i
$607$	−1.64119	−	0.947543i	−0.0666139	−	0.0384596i	0.466323	−	0.884614i	$-0.345578\pi$
$607$	−1.64119	−	0.947543i	−0.0666139	−	0.0384596i	−0.532937	+	0.846155i	$0.678912\pi$
$608$	19.4939	−	22.3756i	0.790582	−	0.907448i
$609$	21.2203	+	25.1483i	0.859890	+	1.01906i
$610$	22.3991	−	18.1626i	0.906911	−	0.735384i
$611$	−29.4867	+	1.93266i	−1.19290	+	0.0781871i
$612$	−2.88404	−	3.36786i	−0.116581	−	0.136138i
$613$	−20.8061	+	18.2464i	−0.840349	+	0.736966i	−0.966944	−	0.254988i	$-0.917928\pi$
$613$	−20.8061	+	18.2464i	−0.840349	+	0.736966i	0.126595	+	0.991954i	$0.459595\pi$
$614$	15.9015	−	14.7185i	0.641732	−	0.593989i
$615$	−51.6681	+	21.4016i	−2.08346	+	0.862997i
$616$	−13.8925	+	2.70552i	−0.559744	+	0.109008i
$617$	−30.0782	−	12.4588i	−1.21090	−	0.501573i	−0.316397	−	0.948627i	$-0.602473\pi$
$617$	−30.0782	−	12.4588i	−1.21090	−	0.501573i	−0.894507	+	0.447054i	$0.852473\pi$
$618$	7.15293	+	19.3499i	0.287733	+	0.778368i
$619$	−3.16145	+	48.2344i	−0.127069	+	1.93871i	0.173272	+	0.984874i	$0.444566\pi$
$619$	−3.16145	+	48.2344i	−0.127069	+	1.93871i	−0.300341	+	0.953832i	$0.597101\pi$
$620$	32.6847	−	18.3604i	1.31265	−	0.737373i
$621$	18.5534	+	16.2709i	0.744523	+	0.652929i
$622$	−4.35683	+	8.03679i	−0.174693	+	0.322246i
$623$	−7.19470	−	15.3187i	−0.288250	−	0.613731i
$624$	−38.7894	−	0.914302i	−1.55282	−	0.0366014i
$625$	−1.59175	−	5.94048i	−0.0636699	−	0.237619i
$626$	3.59006	−	3.78809i	0.143488	−	0.151403i
$627$	4.85196	+	14.2934i	0.193769	+	0.570824i
$628$	10.8800	+	1.56301i	0.434158	+	0.0623708i
$629$	2.81793	−	4.21733i	0.112358	−	0.168156i
$630$	−2.41651	−	8.74605i	−0.0962762	−	0.348451i
$631$	11.3696	−	27.4486i	0.452617	−	1.09271i	−0.518707	−	0.854952i	$-0.673586\pi$
$631$	11.3696	−	27.4486i	0.452617	−	1.09271i	0.971324	−	0.237761i	$-0.0764135\pi$
$632$	1.00692	−	19.9617i	0.0400532	−	0.794035i
$633$	−14.3257	+	18.6696i	−0.569394	+	0.742049i
$634$	−21.0681	−	13.2737i	−0.836721	−	0.527168i
$635$	2.75208	−	8.10736i	0.109213	−	0.321731i
$636$	5.08329	−	24.0696i	0.201566	−	0.954422i
$637$	−26.1931	+	36.1390i	−1.03781	+	1.43188i
$638$	−21.7483	−	2.27147i	−0.861022	−	0.0899284i
$639$	−2.21766	+	3.84110i	−0.0877293	+	0.151952i
$640$	−0.340795	+	40.0145i	−0.0134711	+	1.58171i
$641$	8.71872	+	15.1013i	0.344369	+	0.596464i	0.985239	−	0.171185i	$-0.0547596\pi$
$641$	8.71872	+	15.1013i	0.344369	+	0.596464i	−0.640870	+	0.767649i	$0.721426\pi$
$642$	5.88767	−	8.11483i	0.232368	−	0.320267i
$643$	−10.2170	+	6.82680i	−0.402920	+	0.269223i	−0.740476	−	0.672083i	$-0.765400\pi$
$643$	−10.2170	+	6.82680i	−0.402920	+	0.269223i	0.337556	+	0.941306i	$0.390400\pi$
$644$	−23.2778	−	0.718197i	−0.917276	−	0.0283009i
$645$	36.4888	−	7.25807i	1.43674	−	0.285786i
$646$	0.926155	−	23.9714i	0.0364391	−	0.943144i
$647$	−3.61506	+	4.71124i	−0.142123	+	0.185218i	−0.858991	−	0.511991i	$-0.828908\pi$
$647$	−3.61506	+	4.71124i	−0.142123	+	0.185218i	0.716868	+	0.697209i	$0.245575\pi$
$648$	9.94135	−	15.3742i	0.390533	−	0.603956i
$649$	−6.97908	−	9.09531i	−0.273953	−	0.357022i
$650$	−67.4311	+	6.24047i	−2.64486	+	0.244772i
$651$	17.1672	−	12.6604i	0.672836	−	0.496201i
$652$	8.94446	+	22.3346i	0.350292	+	0.874692i
$653$	22.5326	−	25.6935i	0.881767	−	1.00546i	−0.118155	−	0.992995i	$-0.537698\pi$
$653$	22.5326	−	25.6935i	0.881767	−	1.00546i	0.999922	−	0.0124676i	$-0.00396867\pi$
$654$	9.96529	−	10.5150i	0.389674	−	0.411168i
$655$	−70.5868	−	18.9137i	−2.75806	−	0.739019i
$656$	−40.3999	+	9.81090i	−1.57735	+	0.383051i
$657$	6.20460	+	6.20460i	0.242065	+	0.242065i
$658$	3.51508	+	16.9806i	0.137032	+	0.661972i
$659$	1.82240	−	9.16182i	0.0709906	−	0.356894i	−0.928920	−	0.370281i	$-0.879261\pi$
$659$	1.82240	−	9.16182i	0.0709906	−	0.356894i	0.999910	+	0.0133871i	$0.00426139\pi$
$660$	−17.5057	−	10.3838i	−0.681408	−	0.404190i
$661$	−2.15313	+	32.8504i	−0.0837470	+	1.27773i	0.724660	+	0.689107i	$0.241997\pi$
$661$	−2.15313	+	32.8504i	−0.0837470	+	1.27773i	−0.808406	+	0.588625i	$0.799670\pi$
$662$	−17.6652	−	3.02356i	−0.686579	−	0.117514i
$663$	−24.8834	+	19.0937i	−0.966392	+	0.741538i
$664$	2.36079	−	4.23495i	0.0916165	−	0.164348i
$665$	22.5480	−	43.6075i	0.874376	−	1.69102i
$666$	−1.45288	−	0.450092i	−0.0562981	−	0.0174407i
$667$	−34.0710	−	11.5655i	−1.31923	−	0.447820i
$668$	−16.0102	−	18.6960i	−0.619452	−	0.723369i
$669$	13.7760	−	27.9350i	0.532611	−	1.08003i
$670$	1.49681	+	9.41068i	0.0578268	+	0.363566i
$671$			10.9039i			0.420941i
$672$	2.61504	+	22.6181i	0.100878	+	0.872513i
$673$		−	46.4295i		−	1.78973i	−0.446342	−	0.894863i	$-0.647273\pi$
$673$		−	46.4295i		−	1.78973i	0.446342	−	0.894863i	$-0.352727\pi$
$674$	10.2867	−	1.63615i	0.396231	−	0.0630222i
$675$	18.6240	−	37.7658i	0.716839	−	1.45360i
$676$	4.26754	−	55.1454i	0.164136	−	2.12098i
$677$	12.4693	+	4.23275i	0.479234	+	0.162678i	0.550595	−	0.834773i	$-0.314401\pi$
$677$	12.4693	+	4.23275i	0.479234	+	0.162678i	−0.0713610	+	0.997451i	$0.522734\pi$
$678$	3.91797	−	12.6471i	0.150469	−	0.485708i
$679$	5.27195	+	8.22518i	0.202319	+	0.315654i
$680$	20.0760	+	25.3639i	0.769880	+	0.972661i
$681$	25.7078	−	19.7263i	0.985123	−	0.755912i
$682$	−2.39141	+	13.9719i	−0.0915719	+	0.535011i
$683$	−2.08391	+	31.7944i	−0.0797388	+	1.21658i	0.751147	+	0.660135i	$0.229501\pi$
$683$	−2.08391	+	31.7944i	−0.0797388	+	1.21658i	−0.830885	+	0.556443i	$0.812166\pi$
$684$	−6.97012	+	1.77988i	−0.266509	+	0.0680555i
$685$	6.99678	−	35.1752i	0.267333	−	1.34397i
$686$	23.1282	+	12.2917i	0.883040	+	0.469299i
$687$	−13.2412	−	13.2412i	−0.505182	−	0.505182i
$688$	27.6325	−	1.15802i	1.05348	−	0.0441490i
$689$	49.7967	+	13.3430i	1.89710	+	0.508327i
$690$	−24.3087	−	23.0379i	−0.925415	−	0.877037i
$691$	9.67461	−	11.0318i	0.368040	−	0.419669i	−0.537945	−	0.842980i	$-0.680799\pi$
$691$	9.67461	−	11.0318i	0.368040	−	0.419669i	0.905984	+	0.423311i	$0.139132\pi$
$692$	−6.12463	+	14.3070i	−0.232824	+	0.543870i
$693$	3.14417	+	1.37314i	0.119437	+	0.0521611i
$694$	−1.30471	−	14.0980i	−0.0495262	−	0.535153i
$695$	14.4761	+	18.8657i	0.549112	+	0.715616i
$696$	−6.34267	+	34.6003i	−0.240418	+	1.31152i
$697$	−20.4588	+	26.6624i	−0.774932	+	1.00991i
$698$	23.0936	+	0.892241i	0.874107	+	0.0337718i
$699$	15.6895	−	3.12083i	0.593430	−	0.118040i
$700$	9.09661	+	38.6840i	0.343819	+	1.46212i
$701$	−30.5857	+	20.4367i	−1.15521	+	0.771884i	−0.977237	−	0.212152i	$-0.931953\pi$
$701$	−30.5857	+	20.4367i	−1.15521	+	0.771884i	−0.177969	+	0.984036i	$0.556953\pi$
$702$	40.9227	+	29.6913i	1.54453	+	1.12063i
$703$	−4.11457	−	7.12664i	−0.155184	−	0.268786i
$704$	−11.6710	−	9.62949i	−0.439866	−	0.362925i
$705$	−12.4685	+	21.5961i	−0.469590	+	0.813354i
$706$	−0.749038	+	7.17169i	−0.0281904	+	0.269910i
$707$	10.2922	−	35.6766i	0.387077	−	1.34176i
$708$	−15.4543	+	10.0649i	−0.580809	+	0.378262i
$709$	−11.9928	+	35.3296i	−0.450398	+	1.32683i	0.450491	+	0.892781i	$0.351249\pi$
$709$	−11.9928	+	35.3296i	−0.450398	+	1.32683i	−0.900889	+	0.434049i	$0.857084\pi$
$710$	17.2485	−	27.3769i	0.647325	−	1.02744i
$711$	−2.94949	+	3.84385i	−0.110614	+	0.144156i
$712$	7.75707	−	16.3454i	0.290709	−	0.612570i
$713$	−8.92587	+	21.5490i	−0.334277	+	0.807015i
$714$	13.1155	+	12.9132i	0.490835	+	0.483263i
$715$	23.6971	−	35.4651i	0.886220	−	1.32632i
$716$	31.4886	−	23.5778i	1.17679	−	0.881145i
$717$	7.51450	+	22.1370i	0.280634	+	0.826721i
$718$	11.3526	+	10.7591i	0.423675	+	0.401527i
$719$	9.90982	+	36.9839i	0.369574	+	1.37927i	0.861113	+	0.508413i	$0.169768\pi$
$719$	9.90982	+	36.9839i	0.369574	+	1.37927i	−0.491539	+	0.870855i	$0.663566\pi$
$720$	5.57773	−	7.93623i	0.207870	−	0.295766i
$721$	10.7849	+	22.9629i	0.401652	+	0.855182i
$722$	−10.5941	−	5.74319i	−0.394273	−	0.213740i
$723$	−1.51589	−	1.32940i	−0.0563765	−	0.0494408i
$724$	−43.0105	−	12.0696i	−1.59847	−	0.448562i
$725$	−4.01545	+	61.2639i	−0.149130	+	2.27528i
$726$	−14.9792	+	5.53722i	−0.555929	+	0.205506i
$727$	−1.98573	−	0.822517i	−0.0736467	−	0.0305055i	0.345556	−	0.938398i	$-0.387690\pi$
$727$	−1.98573	−	0.822517i	−0.0736467	−	0.0305055i	−0.419203	+	0.907893i	$0.637690\pi$
$728$	−47.6246	+	2.92973i	−1.76509	+	0.108583i
$729$	−27.7421	+	11.4912i	−1.02749	+	0.425598i
$730$	−43.4838	−	46.9789i	−1.60941	−	1.73877i
$731$	16.8088	−	14.7409i	0.621696	−	0.545212i
$732$	17.4889	+	1.35342i	0.646409	+	0.0500237i
$733$	−33.6472	+	2.20535i	−1.24279	+	0.0814566i	−0.672568	−	0.740035i	$-0.734809\pi$
$733$	−33.6472	+	2.20535i	−1.24279	+	0.0814566i	−0.570220	+	0.821492i	$0.693142\pi$
$734$	24.5796	+	30.3128i	0.907250	+	1.11887i
$735$	13.0772	+	35.3223i	0.482361	+	1.30288i
$736$	−15.2207	−	19.7024i	−0.561043	−	0.726241i
$737$	−3.12034	−	1.80153i	−0.114939	−	0.0663603i
$738$	9.41094	+	3.60547i	0.346421	+	0.132719i
$739$	7.22618	−	14.6532i	0.265819	−	0.539028i	−0.722510	−	0.691361i	$-0.757012\pi$
$739$	7.22618	−	14.6532i	0.265819	−	0.539028i	0.988329	+	0.152332i	$0.0486783\pi$
$740$	10.4647	+	3.69036i	0.384690	+	0.135660i
$741$	9.92756	+	49.9092i	0.364698	+	1.83346i
$742$	3.71550	−	30.0236i	0.136400	−	1.10220i
$743$	44.9210	−	18.6069i	1.64799	−	0.682620i	0.650924	−	0.759143i	$-0.274382\pi$
$743$	44.9210	−	18.6069i	1.64799	−	0.682620i	0.997068	+	0.0765229i	$0.0243818\pi$
$744$	22.1128	+	5.56982i	0.810695	+	0.204200i
$745$	−7.42336	−	56.3860i	−0.271971	−	2.06582i
$746$	−11.8516	−	2.02851i	−0.433918	−	0.0742688i
$747$	−1.05412	+	0.519833i	−0.0385681	+	0.0190197i
$748$	−12.2303	−	0.144120i	−0.447186	−	0.00526956i
$749$	6.36697	−	10.5579i	0.232644	−	0.385779i
$750$	−9.10270	+	16.7912i	−0.332384	+	0.613130i
$751$	−3.19397	+	0.855821i	−0.116550	+	0.0312294i	−0.316622	−	0.948552i	$-0.602549\pi$
$751$	−3.19397	+	0.855821i	−0.116550	+	0.0312294i	0.200073	+	0.979781i	$0.435882\pi$
$752$	−11.6286	+	14.4371i	−0.424050	+	0.526465i
$753$	−21.9436	−	5.87976i	−0.799669	−	0.214271i
$754$	−71.6917	−	17.1621i	−2.61086	−	0.625007i
$755$	25.5202	+	5.07628i	0.928774	+	0.184745i
$756$	13.9368	−	26.1923i	0.506875	−	0.952603i
$757$	7.80747	−	11.6847i	0.283767	−	0.424688i	−0.662014	−	0.749491i	$-0.730298\pi$
$757$	7.80747	−	11.6847i	0.283767	−	0.424688i	0.945781	+	0.324804i	$0.105298\pi$
$758$	−15.0596	+	32.7229i	−0.546987	+	1.18855i
$759$	12.5552	−	1.65292i	0.455725	−	0.0599974i
$760$	51.3132	−	11.0121i	1.86133	−	0.399452i
$761$	7.74086	+	1.01910i	0.280606	+	0.0369425i	0.269516	−	0.962996i	$-0.413136\pi$
$761$	7.74086	+	1.01910i	0.280606	+	0.0369425i	0.0110904	+	0.999939i	$0.496470\pi$
$762$	4.60735	−	2.42789i	0.166907	−	0.0879532i
$763$	11.1127	−	13.9246i	0.402308	−	0.504105i
$764$	−11.7192	−	2.47498i	−0.423984	−	0.0895417i
$765$	−0.512851	−	7.82459i	−0.0185422	−	0.282899i
$766$	−15.7166	−	35.2382i	−0.567865	−	1.27321i
$767$	−19.3246	−	33.4711i	−0.697769	−	1.20857i
$768$	−16.8935	+	17.5239i	−0.609590	+	0.632341i
$769$	15.7743			0.568837			0.284419	−	0.958700i	$-0.408199\pi$
$769$	15.7743			0.568837			0.284419	+	0.958700i	$0.408199\pi$
$770$	−22.5341	−	10.8957i	−0.812074	−	0.392653i
$771$	−20.8846	+	13.9546i	−0.752139	+	0.502563i
$772$	−23.4248	+	26.0843i	−0.843077	+	0.938796i
$773$	−5.17622	−	5.90235i	−0.186176	−	0.212293i	0.651221	−	0.758888i	$-0.274257\pi$
$773$	−5.17622	−	5.90235i	−0.186176	−	0.212293i	−0.837397	+	0.546595i	$0.815924\pi$
$774$	−5.67231	−	3.57378i	−0.203887	−	0.128457i
$775$	39.4592	+	5.19490i	1.41742	+	0.186606i
$776$	−3.20798	+	9.93938i	−0.115160	+	0.356803i
$777$	6.16781	+	1.34954i	0.221269	+	0.0484147i
$778$	13.9549	−	1.29147i	0.500307	−	0.0463014i
$779$	24.1158	+	48.9021i	0.864040	+	1.75210i
$780$	−53.9416	−	42.4099i	−1.93142	−	1.51852i
$781$	3.93278	+	11.5856i	0.140726	+	0.414565i
$782$	−19.5729	−	4.68551i	−0.699925	−	0.167554i
$783$	32.4123	−	32.4123i	1.15832	−	1.15832i
$784$	5.56583	+	27.4412i	0.198780	+	0.980044i
$785$	13.7451	+	13.7451i	0.490582	+	0.490582i
$786$	−23.2504	−	37.8856i	−0.829313	−	1.35133i
$787$	−11.7928	+	4.00310i	−0.420367	+	0.142695i	−0.523605	−	0.851961i	$-0.675413\pi$
$787$	−11.7928	+	4.00310i	−0.420367	+	0.142695i	0.103238	+	0.994657i	$0.467080\pi$
$788$	3.54146	+	6.30439i	0.126159	+	0.224585i
$789$	−21.2337	+	10.4713i	−0.755939	+	0.372788i
$790$	22.5843	−	27.1908i	0.803513	−	0.967404i
$791$	3.48024	−	15.9057i	0.123743	−	0.565543i
$792$	1.00251	+	3.52816i	0.0356227	+	0.125368i
$793$	−4.79810	+	36.4452i	−0.170385	+	1.29421i
$794$	−6.58226	−	29.0013i	−0.233596	−	1.02922i
$795$	32.7091	−	28.6851i	1.16007	−	1.01736i
$796$	10.7696	+	3.79789i	0.381718	+	0.134613i
$797$	3.16005	+	4.72935i	0.111935	+	0.167522i	0.883207	−	0.468983i	$-0.155379\pi$
$797$	3.16005	+	4.72935i	0.111935	+	0.167522i	−0.771273	+	0.636505i	$0.780379\pi$
$798$	28.2014	−	9.81820i	0.998318	−	0.347561i
$799$			14.9854i			0.530147i
$800$	−25.7517	+	33.7883i	−0.910460	+	1.19460i
$801$	−3.79824	+	2.19292i	−0.134204	+	0.0774828i
$802$	−8.38083	+	21.8755i	−0.295937	+	0.772451i
$803$	24.1531	−	1.58308i	0.852345	−	0.0558656i
$804$	−3.27680	+	4.78114i	−0.115564	+	0.168618i
$805$	−32.1911	−	25.6905i	−1.13459	−	0.905473i
$806$	−14.1411	+	45.6472i	−0.498100	+	1.60785i
$807$	−2.86117	+	21.7327i	−0.100718	+	0.765028i
$808$	36.4409	−	15.7409i	1.28199	−	0.553764i
$809$	−2.09823	−	15.9376i	−0.0737699	−	0.560338i	−0.987920	−	0.154963i	$-0.950474\pi$
$809$	−2.09823	−	15.9376i	−0.0737699	−	0.560338i	0.914150	−	0.405375i	$-0.132859\pi$
$810$	30.3693	−	11.2264i	1.06707	−	0.394455i
$811$	14.3401	+	9.58172i	0.503547	+	0.336460i	0.781261	−	0.624204i	$-0.214577\pi$
$811$	14.3401	+	9.58172i	0.503547	+	0.336460i	−0.277714	+	0.960664i	$0.589577\pi$
$812$	−4.15911	+	43.0585i	−0.145956	+	1.51106i
$813$	0.362723	−	1.82353i	0.0127213	−	0.0639541i
$814$	−3.57600	+	2.19459i	−0.125339	+	0.0769203i
$815$	−11.0122	+	41.0981i	−0.385740	+	1.43960i
$816$	−1.74921	+	19.5985i	−0.0612346	+	0.686084i
$817$	−9.38795	−	35.0363i	−0.328443	−	1.22577i
$818$	−2.22741	+	0.661372i	−0.0778796	+	0.0231243i
$819$	9.90482	+	5.97310i	0.346102	+	0.208717i
$820$	−67.5899	−	28.9344i	−2.36034	−	1.01043i
$821$	−22.8734	−	46.3827i	−0.798287	−	1.61877i	−0.785511	−	0.618847i	$-0.787600\pi$
$821$	−22.8734	−	46.3827i	−0.798287	−	1.61877i	−0.0127757	−	0.999918i	$-0.504067\pi$
$822$	17.8072	−	12.6023i	0.621097	−	0.439557i
$823$	46.9997	−	6.18763i	1.63831	−	0.215687i	0.745622	−	0.666369i	$-0.232153\pi$
$823$	46.9997	−	6.18763i	1.63831	−	0.215687i	0.892684	+	0.450682i	$0.148819\pi$
$824$	−11.6279	+	24.5019i	−0.405078	+	0.853565i
$825$	−8.26920	−	19.9636i	−0.287897	−	0.695044i
$826$	−17.8855	+	13.9462i	−0.622316	+	0.485252i
$827$	28.4511	−	5.65929i	0.989343	−	0.196793i	0.326213	−	0.945296i	$-0.394227\pi$
$827$	28.4511	−	5.65929i	0.989343	−	0.196793i	0.663131	+	0.748504i	$0.269227\pi$
$828$	0.323735	+	6.02655i	0.0112506	+	0.209437i
$829$	18.2868	+	9.01804i	0.635126	+	0.313210i	0.731199	−	0.682165i	$-0.238961\pi$
$829$	18.2868	+	9.01804i	0.635126	+	0.313210i	−0.0960722	+	0.995374i	$0.530628\pi$
$830$	7.83089	−	3.49267i	0.271814	−	0.121232i
$831$	−1.68358	+	2.91605i	−0.0584027	+	0.101156i
$832$	−34.7716	−	37.3211i	−1.20549	−	1.29388i
$833$	17.4189	+	14.4533i	0.603528	+	0.500776i
$834$	−1.50257	+	14.3864i	−0.0520297	+	0.498160i
$835$	−2.84698	−	43.4366i	−0.0985239	−	1.50318i
$836$	−8.98594	+	17.6930i	−0.310785	+	0.611926i
$837$	−19.5922	−	22.3406i	−0.677204	−	0.772203i
$838$	35.0109	+	1.35267i	1.20943	+	0.0467273i
$839$	−11.5616	−	27.9122i	−0.399152	−	0.963637i	−0.987868	−	0.155297i	$-0.950366\pi$
$839$	−11.5616	−	27.9122i	−0.399152	−	0.963637i	0.588716	−	0.808340i	$-0.299634\pi$
$840$	−20.2727	+	34.7903i	−0.699473	+	1.20038i
$841$	−14.4782	+	34.9534i	−0.499247	+	1.20529i
$842$	−36.0229	−	16.5783i	−1.24143	−	0.571325i
$843$	9.02186	+	0.591324i	0.310729	+	0.0203663i
$844$	−30.7181	+	3.67643i	−1.05736	+	0.126548i
$845$	64.4938	−	73.5410i	2.21865	−	2.52989i
$846$	4.30786	−	1.27911i	0.148107	−	0.0439766i
$847$	−17.7760	+	8.34882i	−0.610791	+	0.286869i
$848$	27.3068	−	17.3293i	0.937720	−	0.595089i
$849$	−19.8434	+	5.31701i	−0.681023	+	0.182479i
$850$	0.921394	+	34.3295i	0.0316036	+	1.17749i
$851$	−6.53747	+	2.21917i	−0.224101	+	0.0760722i
$852$	19.0704	−	4.86979i	0.653340	−	0.166836i
$853$	44.8892	+	29.9940i	1.53698	+	1.02698i	0.980594	+	0.196050i	$0.0628116\pi$
$853$	44.8892	+	29.9940i	1.53698	+	1.02698i	0.556384	+	0.830925i	$0.312188\pi$
$854$	21.5707	−	0.167675i	0.738135	−	0.00573771i
$855$	−11.7536	−	4.86850i	−0.401965	−	0.166499i
$856$	13.0403	−	1.91686i	0.445708	−	0.0655169i
$857$	−4.36331	−	3.34809i	−0.149048	−	0.114368i	0.531546	−	0.847030i	$-0.321611\pi$
$857$	−4.36331	−	3.34809i	−0.149048	−	0.114368i	−0.680594	+	0.732661i	$0.738278\pi$
$858$	25.3017	−	5.74258i	0.863787	−	0.196048i
$859$	10.1222	+	3.43604i	0.345366	+	0.117236i	0.488733	−	0.872434i	$-0.337459\pi$
$859$	10.1222	+	3.43604i	0.345366	+	0.117236i	−0.143366	+	0.989670i	$0.545793\pi$
$860$	40.3444	+	27.6504i	1.37573	+	0.942870i
$861$	−40.1947	−	11.5956i	−1.36983	−	0.395176i
$862$	−12.1086	−	14.9329i	−0.412419	−	0.508615i
$863$	31.5087	+	18.1915i	1.07257	+	0.619247i	0.928882	−	0.370377i	$-0.120771\pi$
$863$	31.5087	+	18.1915i	1.07257	+	0.619247i	0.143685	+	0.989623i	$0.454105\pi$
$864$	31.0880	−	6.28943i	1.05763	−	0.213971i
$865$	−23.8351	+	13.7612i	−0.810418	+	0.467895i
$866$	7.72869	+	48.5915i	0.262631	+	1.65121i
$867$	−5.53146	−	8.27841i	−0.187858	−	0.281150i
$868$	27.6767	+	4.51596i	0.939408	+	0.153282i
$869$	2.60742	+	13.1084i	0.0884505	+	0.444671i
$870$	−45.6541	+	42.2576i	−1.54782	+	1.43267i
$871$	−9.63667	−	7.39448i	−0.326526	−	0.250552i
$872$	19.0433	−	0.286623i	0.644887	−	0.00970628i
$873$	2.00860	−	1.54125i	0.0679808	−	0.0521635i
$874$	−20.8630	+	25.1184i	−0.705701	+	0.849642i
$875$	−9.40048	+	21.5250i	−0.317794	+	0.727677i
$876$	0.458814	−	38.9359i	0.0155019	−	1.31552i
$877$	−30.2962	−	26.5690i	−1.02303	−	0.897172i	−0.0282880	−	0.999600i	$-0.509006\pi$
$877$	−30.2962	−	26.5690i	−1.02303	−	0.897172i	−0.994740	+	0.102428i	$0.967339\pi$
$878$	26.0783	−	0.699935i	0.880100	−	0.0236217i
$879$	4.62905	−	17.2758i	0.156134	−	0.582700i
$880$	−6.31456	−	26.0025i	−0.212864	−	0.876544i
$881$	−8.36822	+	8.36822i	−0.281933	+	0.281933i	−0.833879	−	0.551947i	$-0.813885\pi$
$881$	−8.36822	+	8.36822i	−0.281933	+	0.281933i	0.551947	+	0.833879i	$0.313885\pi$
$882$	2.66806	−	6.24108i	0.0898383	−	0.210148i
$883$	−36.3104	−	7.22259i	−1.22194	−	0.243059i	−0.458358	−	0.888768i	$-0.651562\pi$
$883$	−36.3104	−	7.22259i	−1.22194	−	0.243059i	−0.763584	+	0.645708i	$0.776562\pi$
$884$	−40.8152	−	5.86348i	−1.37276	−	0.197210i
$885$	−32.5458	−	2.13316i	−1.09402	−	0.0717055i
$886$	−18.9402	−	26.7627i	−0.636310	−	0.899111i
$887$	−15.1279	−	19.7150i	−0.507944	−	0.661965i	0.467042	−	0.884235i	$-0.345320\pi$
$887$	−15.1279	−	19.7150i	−0.507944	−	0.661965i	−0.974985	+	0.222271i	$0.928653\pi$
$888$	3.07606	+	6.00797i	0.103226	+	0.201614i
$889$	5.39195	−	3.45599i	0.180840	−	0.115910i
$890$	28.3067	−	14.9165i	0.948842	−	0.500002i
$891$	−3.93526	+	11.5929i	−0.131836	+	0.388377i
$892$	38.9272	−	12.7045i	1.30338	−	0.425377i
$893$	21.8054	+	10.7532i	0.729689	+	0.359843i
$894$	20.3158	−	28.0007i	0.679461	−	0.936484i
$895$	69.5675			2.32539
$896$	−18.8701	+	23.2362i	−0.630405	+	0.776266i
$897$	42.6918			1.42544
$898$	13.8139	−	19.0394i	0.460977	−	0.635353i
$899$	38.8569	+	19.1621i	1.29595	+	0.639091i
$900$	9.79005	−	3.19513i	0.326335	−	0.106504i
$901$	8.40365	−	24.7563i	0.279966	−	0.824753i
$902$	24.5943	−	12.9602i	0.818902	−	0.431529i
$903$	24.7204	+	12.7822i	0.822645	+	0.425364i
$904$	15.4935	−	7.93264i	0.515307	−	0.263836i
$905$	−48.0928	−	62.6757i	−1.59866	−	2.08341i
$906$	9.14320	+	12.9194i	0.303762	+	0.429219i
$907$	22.7165	+	1.48892i	0.754289	+	0.0494387i	0.437696	−	0.899123i	$-0.355795\pi$
$907$	22.7165	+	1.48892i	0.754289	+	0.0494387i	0.316593	+	0.948562i	$0.397461\pi$
$908$	42.1673	+	6.05772i	1.39937	+	0.201033i
$909$	−9.43761	−	1.87726i	−0.313026	−	0.0622647i
$910$	−70.5234	−	46.3334i	−2.33783	−	1.53594i
$911$	9.32040	−	9.32040i	0.308799	−	0.308799i	−0.535645	−	0.844443i	$-0.679931\pi$
$911$	9.32040	−	9.32040i	0.308799	−	0.308799i	0.844443	+	0.535645i	$0.179931\pi$
$912$	27.2627	+	16.6087i	0.902757	+	0.549970i
$913$	−0.839130	+	3.13168i	−0.0277712	+	0.103643i
$914$	−25.9053	+	0.695290i	−0.856870	+	0.0229982i
$915$	23.3229	+	20.4537i	0.771032	+	0.676177i
$916$	0.290076	−	24.6164i	0.00958438	−	0.813350i
$917$	−32.4447	−	43.9941i	−1.07142	−	1.45281i
$918$	16.3821	−	19.7236i	0.540691	−	0.650975i
$919$	−15.4282	+	11.8384i	−0.508928	+	0.390514i	−0.831062	−	0.556180i	$-0.812267\pi$
$919$	−15.4282	+	11.8384i	−0.508928	+	0.390514i	0.322134	+	0.946694i	$0.395600\pi$
$920$	−0.662619	−	44.0245i	−0.0218459	−	1.45145i
$921$	18.4919	+	14.1893i	0.609328	+	0.467554i
$922$	−18.2389	+	16.8820i	−0.600666	+	0.555978i
$923$	8.04682	+	40.4541i	0.264864	+	1.33156i
$924$	−5.38989	−	14.2393i	−0.177314	−	0.468438i
$925$	6.54484	+	9.79505i	0.215193	+	0.322059i
$926$	7.24644	+	45.5596i	0.238133	+	1.49718i
$927$	5.69360	−	3.28720i	0.187002	−	0.107966i
$928$	−38.3678	+	25.8182i	−1.25948	+	0.847524i
$929$	8.97280	+	5.18045i	0.294388	+	0.169965i	0.639919	−	0.768442i	$-0.278968\pi$
$929$	8.97280	+	5.18045i	0.294388	+	0.169965i	−0.345531	+	0.938407i	$0.612301\pi$
$930$	25.3993	+	31.3237i	0.832876	+	1.02714i
$931$	33.5304	−	14.9749i	1.09891	−	0.490783i
$932$	17.3473	+	11.8891i	0.568229	+	0.389441i
$933$	−9.31213	−	3.16104i	−0.304865	−	0.103488i
$934$	−35.3968	+	8.03380i	−1.15822	+	0.262874i
$935$	−17.1607	−	13.1678i	−0.561214	−	0.430634i
$936$	1.79828	+	12.2336i	0.0587786	+	0.399868i
$937$	9.54006	+	3.95162i	0.311660	+	0.129094i	0.533031	−	0.846096i	$-0.321053\pi$
$937$	9.54006	+	3.95162i	0.311660	+	0.129094i	−0.221370	+	0.975190i	$0.571053\pi$
$938$	−3.51590	+	6.20053i	−0.114798	+	0.202455i
$939$	4.66806	+	3.11910i	0.152336	+	0.101788i
$940$	−31.7644	+	8.11133i	−1.03604	+	0.264562i
$941$	15.4703	−	5.25146i	0.504317	−	0.171193i	−0.0576746	−	0.998335i	$-0.518369\pi$
$941$	15.4703	−	5.25146i	0.504317	−	0.171193i	0.561992	+	0.827143i	$0.310035\pi$
$942$	0.317238	+	11.8197i	0.0103362	+	0.385108i
$943$	44.1853	−	11.8394i	1.43887	−	0.385544i
$944$	−23.6621	−	5.28923i	−0.770137	−	0.172150i
$945$	47.4921	−	22.3055i	1.54492	−	0.725598i
$946$	−17.7288	+	5.26410i	−0.576412	+	0.171151i
$947$	−27.5274	+	31.3890i	−0.894522	+	1.02001i	0.105152	+	0.994456i	$0.466467\pi$
$947$	−27.5274	+	31.3890i	−0.894522	+	1.02001i	−0.999674	+	0.0255504i	$0.991866\pi$
$948$	21.3483	−	2.55502i	0.693360	−	0.0829833i
$949$	81.4257	+	5.33692i	2.64319	+	0.173244i
$950$	50.6142	+	23.2934i	1.64214	+	0.755737i
$951$	10.2508	−	24.7475i	0.332404	−	0.802494i
$952$	−0.0970349	+	24.1969i	−0.00314492	+	0.784227i
$953$	−15.3450	−	37.0460i	−0.497072	−	1.20004i	−0.951053	−	0.309027i	$-0.899997\pi$
$953$	−15.3450	−	37.0460i	−0.497072	−	1.20004i	0.453982	−	0.891011i	$-0.350003\pi$
$954$	−7.83401	−	0.302673i	−0.253635	−	0.00979940i
$955$	−13.9664	−	15.9256i	−0.451941	−	0.515340i
$956$	−13.9170	+	27.4021i	−0.450108	+	0.886248i
$957$	−1.53844	−	23.4720i	−0.0497306	−	0.758743i
$958$	0.566551	−	5.42446i	0.0183044	−	0.175256i
$959$	20.5036	−	17.3011i	0.662095	−	0.558681i
$960$	−42.4894	+	6.90051i	−1.37134	+	0.222713i
$961$	−1.45728	+	2.52408i	−0.0470090	+	0.0814220i
$962$	−12.9181	+	5.76161i	−0.416495	+	0.185762i
$963$	−2.86556	−	1.41314i	−0.0923414	−	0.0455378i
$964$	−0.142184	−	2.64685i	−0.00457944	−	0.0852495i
$965$	−60.8091	+	12.0957i	−1.95751	+	0.389374i
$966$	−3.46297	−	24.8120i	−0.111419	−	0.798312i
$967$	16.0736	+	38.8050i	0.516891	+	1.24789i	0.939803	+	0.341715i	$0.111008\pi$
$967$	16.0736	+	38.8050i	0.516891	+	1.24789i	−0.422912	+	0.906171i	$0.638992\pi$
$968$	−18.9674	−	9.00140i	−0.609636	−	0.289316i
$969$	25.5851	−	3.36834i	0.821912	−	0.108207i
$970$	−15.0767	+	10.6699i	−0.484084	+	0.342591i
$971$	23.3780	+	47.4059i	0.750236	+	1.52133i	0.850271	+	0.526344i	$0.176438\pi$
$971$	23.3780	+	47.4059i	0.750236	+	1.52133i	−0.100035	+	0.994984i	$0.531896\pi$
$972$	−12.8216	−	5.48877i	−0.411254	−	0.176052i
$973$	−0.339022	+	17.7847i	−0.0108685	+	0.570153i
$974$	17.2017	−	5.10759i	0.551176	−	0.163658i
$975$	−18.8542	−	70.3650i	−0.603819	−	2.25348i
$976$	14.7922	+	17.6915i	0.473488	+	0.566290i
$977$	4.69854	−	17.5352i	0.150320	−	0.561001i	−0.849141	−	0.528166i	$-0.822880\pi$
$977$	4.69854	−	17.5352i	0.150320	−	0.561001i	0.999461	−	0.0328348i	$-0.0104535\pi$
$978$	−22.0583	+	13.5372i	−0.705346	+	0.432871i
$979$	−2.36027	+	11.8659i	−0.0754347	+	0.379236i
$980$	−21.2079	+	44.7458i	−0.677461	+	1.42935i
$981$	−3.83872	−	2.56495i	−0.122561	−	0.0818927i
$982$	14.2020	−	5.24993i	0.453204	−	0.167532i
$983$	3.52097	+	26.7444i	0.112302	+	0.853015i	0.951167	+	0.308676i	$0.0998860\pi$
$983$	3.52097	+	26.7444i	0.112302	+	0.853015i	−0.838866	+	0.544339i	$0.816781\pi$
$984$	−17.7344	−	41.0558i	−0.565350	−	1.30881i
$985$	−1.66915	+	12.6784i	−0.0531834	+	0.403968i
$986$	−11.0625	+	35.7093i	−0.352301	+	1.13722i
$987$	−17.3667	+	6.80870i	−0.552787	+	0.216723i
$988$	−37.8201	+	55.1829i	−1.20322	+	1.75560i
$989$	−30.3655	+	1.99026i	−0.965568	+	0.0632867i
$990$	−2.32058	+	6.05714i	−0.0737528	+	0.192508i
$991$	−28.5370	+	16.4758i	−0.906508	+	0.523373i	−0.879306	−	0.476257i	$-0.841993\pi$
$991$	−28.5370	+	16.4758i	−0.906508	+	0.523373i	−0.0272019	+	0.999630i	$0.508660\pi$
$992$	15.0742	+	25.9134i	0.478606	+	0.822751i
$993$		−	19.2792i		−	0.611808i
$994$	22.8587	−	7.95818i	0.725035	−	0.252418i
$995$	11.2199	+	16.7918i	0.355696	+	0.532336i
$996$	4.91877	+	1.73460i	0.155857	+	0.0549629i
$997$	3.96195	−	3.47453i	0.125476	−	0.110040i	−0.594308	−	0.804237i	$-0.702574\pi$
$997$	3.96195	−	3.47453i	0.125476	−	0.110040i	0.719784	+	0.694198i	$0.244241\pi$
$998$	8.91595	+	39.2836i	0.282229	+	1.24350i
$999$	1.14801	−	8.72003i	0.0363215	−	0.275890i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	448.2.bn.a.205.19	✓	992
7.4	even	3	inner	448.2.bn.a.333.24	yes	992
64.5	even	16	inner	448.2.bn.a.261.24	yes	992
448.389	even	48	inner	448.2.bn.a.389.19	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
448.2.bn.a.205.19	✓	992	1.1	even	1	trivial
448.2.bn.a.261.24	yes	992	64.5	even	16	inner
448.2.bn.a.333.24	yes	992	7.4	even	3	inner
448.2.bn.a.389.19	yes	992	448.389	even	48	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:	\( N \)	\(=\)	\( 448 = 2^{6} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	448.bn (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.830506 + 1.14467i) q^{2} +(-1.36442 - 0.672855i) q^{3} +(-0.620519 - 1.90130i) q^{4} +(1.13691 - 3.34924i) q^{5} +(1.90335 - 1.00299i) q^{6} +(2.22748 - 1.42771i) q^{7} +(2.69170 + 0.868758i) q^{8} +(-0.417389 - 0.543952i) q^{9} +O(q^{10})\)	\(q+(-0.830506 + 1.14467i) q^{2} +(-1.36442 - 0.672855i) q^{3} +(-0.620519 - 1.90130i) q^{4} +(1.13691 - 3.34924i) q^{5} +(1.90335 - 1.00299i) q^{6} +(2.22748 - 1.42771i) q^{7} +(2.69170 + 0.868758i) q^{8} +(-0.417389 - 0.543952i) q^{9} +(2.88955 + 4.08295i) q^{10} +(-1.88729 - 0.123699i) q^{11} +(-0.432657 + 3.01169i) q^{12} +(-6.25362 - 1.24392i) q^{13} +(-0.215687 + 3.73544i) q^{14} +(-3.80478 + 3.80478i) q^{15} +(-3.22991 + 2.35959i) q^{16} +(-0.836885 + 3.12330i) q^{17} +(0.969288 - 0.0260154i) q^{18} +(3.94420 + 3.45897i) q^{19} +(-7.07340 - 0.0833518i) q^{20} +(-3.99984 + 0.449215i) q^{21} +(1.70900 - 2.05758i) q^{22} +(3.49170 - 2.67928i) q^{23} +(-3.08805 - 2.99647i) q^{24} +(-5.95807 - 4.57179i) q^{25} +(6.61755 - 6.12522i) q^{26} +(1.09387 + 5.49923i) q^{27} +(-4.09670 - 3.34919i) q^{28} +(-4.54188 - 6.79740i) q^{29} +(-1.19531 - 7.51509i) q^{30} +(-4.58956 + 2.64978i) q^{31} +(-0.0184792 - 5.65682i) q^{32} +(2.49181 + 1.43865i) q^{33} +(-2.88009 - 3.55187i) q^{34} +(-2.24928 - 9.08354i) q^{35} +(-0.775221 + 1.13112i) q^{36} +(-1.48538 - 0.504220i) q^{37} +(-7.23504 + 1.64209i) q^{38} +(7.69556 + 5.90501i) q^{39} +(5.96991 - 8.02745i) q^{40} +(9.60237 + 3.97743i) q^{41} +(2.80769 - 4.95156i) q^{42} +(-5.74894 - 3.84132i) q^{43} +(0.935908 + 3.66507i) q^{44} +(-2.29636 + 0.779510i) q^{45} +(0.166996 + 6.22199i) q^{46} +(4.47655 - 1.19949i) q^{47} +(5.99460 - 1.04620i) q^{48} +(2.92331 - 6.36037i) q^{49} +(10.1814 - 3.02310i) q^{50} +(3.24339 - 3.69837i) q^{51} +(1.51542 + 12.6619i) q^{52} +(-8.06804 - 0.528807i) q^{53} +(-7.20325 - 3.31504i) q^{54} +(-2.55998 + 6.18035i) q^{55} +(7.23604 - 1.90782i) q^{56} +(-3.05414 - 7.37334i) q^{57} +(11.5528 + 0.446352i) q^{58} +(3.99664 + 4.55729i) q^{59} +(9.59497 + 4.87310i) q^{60} +(-0.377061 - 5.75285i) q^{61} +(0.778542 - 7.45418i) q^{62} +(-1.70633 - 0.615732i) q^{63} +(6.49052 + 4.67687i) q^{64} +(-11.2760 + 19.5307i) q^{65} +(-3.71624 + 1.65749i) q^{66} +(1.70857 + 0.842575i) q^{67} +(6.45764 - 0.346893i) q^{68} +(-6.56690 + 1.30624i) q^{69} +(12.2657 + 4.96926i) q^{70} +(-2.47554 - 5.97649i) q^{71} +(-0.650925 - 1.82677i) q^{72} +(-12.6883 + 1.67045i) q^{73} +(1.81079 - 1.28151i) q^{74} +(5.05313 + 10.2467i) q^{75} +(4.12910 - 9.64547i) q^{76} +(-4.38050 + 2.41896i) q^{77} +(-13.1505 + 3.90469i) q^{78} +(-1.82895 - 6.82573i) q^{79} +(4.23070 + 13.5004i) q^{80} +(1.67533 - 6.25243i) q^{81} +(-12.5277 + 7.68822i) q^{82} +(0.334426 - 1.68127i) q^{83} +(3.33607 + 7.32617i) q^{84} +(9.50921 + 6.35385i) q^{85} +(9.17155 - 3.39037i) q^{86} +(1.62334 + 12.3305i) q^{87} +(-4.97255 - 1.97256i) q^{88} +(0.834940 - 6.34200i) q^{89} +(1.01487 - 3.27596i) q^{90} +(-15.7058 + 6.15753i) q^{91} +(-7.26079 - 4.97624i) q^{92} +(8.04499 - 0.527297i) q^{93} +(-2.34479 + 6.12033i) q^{94} +(16.0691 - 9.27752i) q^{95} +(-3.78101 + 7.73069i) q^{96} +3.69260i q^{97} +(4.85267 + 8.62854i) q^{98} +(0.720448 + 1.07823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 32 q^{6} - 16 q^{7} - 32 q^{8} - 8 q^{9}+O(q^{10}) \) 992 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 32 * q^6 - 16 * q^7 - 32 * q^8 - 8 * q^9	\( 992 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 32 q^{6} - 16 q^{7} - 32 q^{8} - 8 q^{9} - 8 q^{10} - 8 q^{11} - 8 q^{12} - 32 q^{13} - 16 q^{14} - 32 q^{15} - 8 q^{16} - 8 q^{17} - 8 q^{18} - 8 q^{19} - 32 q^{20} - 16 q^{21} - 16 q^{22} - 8 q^{23} - 88 q^{24} - 8 q^{25} - 8 q^{26} - 32 q^{27} - 56 q^{28} - 32 q^{29} - 88 q^{30} - 8 q^{32} - 32 q^{34} - 16 q^{35} + 128 q^{36} - 8 q^{37} - 88 q^{38} - 8 q^{39} - 8 q^{40} - 32 q^{41} - 56 q^{42} - 32 q^{43} - 16 q^{44} - 8 q^{45} - 8 q^{46} - 8 q^{47} - 32 q^{48} - 16 q^{49} + 16 q^{50} - 8 q^{51} - 56 q^{52} - 8 q^{53} - 8 q^{54} - 32 q^{55} - 16 q^{56} - 32 q^{57} - 8 q^{58} + 56 q^{59} + 88 q^{60} - 8 q^{61} - 64 q^{62} - 32 q^{63} + 160 q^{64} - 16 q^{65} - 136 q^{66} - 88 q^{67} - 8 q^{68} - 32 q^{69} - 16 q^{70} - 160 q^{71} - 8 q^{72} - 8 q^{73} + 48 q^{74} - 8 q^{75} - 32 q^{76} - 16 q^{77} + 64 q^{78} - 8 q^{79} - 32 q^{80} - 8 q^{81} + 72 q^{82} - 32 q^{83} - 128 q^{84} - 32 q^{85} - 8 q^{86} - 8 q^{87} - 8 q^{88} - 8 q^{89} - 320 q^{90} - 16 q^{91} - 32 q^{92} - 56 q^{93} - 8 q^{94} + 128 q^{96} - 152 q^{98} - 80 q^{99}+O(q^{100}) \) 992 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 32 * q^6 - 16 * q^7 - 32 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 32 * q^13 - 16 * q^14 - 32 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 32 * q^20 - 16 * q^21 - 16 * q^22 - 8 * q^23 - 88 * q^24 - 8 * q^25 - 8 * q^26 - 32 * q^27 - 56 * q^28 - 32 * q^29 - 88 * q^30 - 8 * q^32 - 32 * q^34 - 16 * q^35 + 128 * q^36 - 8 * q^37 - 88 * q^38 - 8 * q^39 - 8 * q^40 - 32 * q^41 - 56 * q^42 - 32 * q^43 - 16 * q^44 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 32 * q^48 - 16 * q^49 + 16 * q^50 - 8 * q^51 - 56 * q^52 - 8 * q^53 - 8 * q^54 - 32 * q^55 - 16 * q^56 - 32 * q^57 - 8 * q^58 + 56 * q^59 + 88 * q^60 - 8 * q^61 - 64 * q^62 - 32 * q^63 + 160 * q^64 - 16 * q^65 - 136 * q^66 - 88 * q^67 - 8 * q^68 - 32 * q^69 - 16 * q^70 - 160 * q^71 - 8 * q^72 - 8 * q^73 + 48 * q^74 - 8 * q^75 - 32 * q^76 - 16 * q^77 + 64 * q^78 - 8 * q^79 - 32 * q^80 - 8 * q^81 + 72 * q^82 - 32 * q^83 - 128 * q^84 - 32 * q^85 - 8 * q^86 - 8 * q^87 - 8 * q^88 - 8 * q^89 - 320 * q^90 - 16 * q^91 - 32 * q^92 - 56 * q^93 - 8 * q^94 + 128 * q^96 - 152 * q^98 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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