LMFDB - Embedded newform 804.2.bf.a.7.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(7,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 0, 23]))

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

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

chi := DirichletCharacter("804.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.bf (of order $66$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$680$
Relative dimension:	$34$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			7.17
Character	$\chi$	$=$	804.7
Dual form			804.2.bf.a.115.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0531079 + 1.41322i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-1.99436 + 0.150106i) q^{4} +(1.40058 + 1.21361i) q^{5} +(0.347192 - 1.37093i) q^{6} +(0.0696355 - 1.46183i) q^{7} +(-0.318048 - 2.81049i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(0.0531079 + 1.41322i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-1.99436 + 0.150106i) q^{4} +(1.40058 + 1.21361i) q^{5} +(0.347192 - 1.37093i) q^{6} +(0.0696355 - 1.46183i) q^{7} +(-0.318048 - 2.81049i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-1.64071 + 2.04377i) q^{10} +(-2.06492 - 0.397981i) q^{11} +(1.95586 + 0.417850i) q^{12} +(1.54128 - 3.84994i) q^{13} +(2.06958 + 0.0207754i) q^{14} +(-1.00193 - 1.55904i) q^{15} +(3.95494 - 0.598730i) q^{16} +(-2.37622 - 3.33693i) q^{17} +(-0.719365 + 1.21759i) q^{18} +(1.67257 - 0.0796743i) q^{19} +(-2.97542 - 2.21013i) q^{20} +(-0.478660 + 1.38300i) q^{21} +(0.452770 - 2.93932i) q^{22} +(-0.0725662 - 0.0761052i) q^{23} +(-0.486641 + 2.78625i) q^{24} +(-0.222800 - 1.54961i) q^{25} +(5.52265 + 1.97371i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(0.0805509 + 2.92587i) q^{28} +(-0.889671 - 1.54096i) q^{29} +(2.15004 - 1.49874i) q^{30} +(4.69976 - 1.88150i) q^{31} +(1.05617 + 5.55738i) q^{32} +(1.86915 + 0.963616i) q^{33} +(4.58961 - 3.53533i) q^{34} +(1.87162 - 1.96290i) q^{35} +(-1.75891 - 0.951955i) q^{36} +(2.09972 - 3.63682i) q^{37} +(0.201424 + 2.35947i) q^{38} +(-2.56351 + 3.25976i) q^{39} +(2.96538 - 4.32229i) q^{40} +(0.459467 + 4.81176i) q^{41} +(-1.97989 - 0.603002i) q^{42} +(2.01414 - 4.41034i) q^{43} +(4.17794 + 0.483760i) q^{44} +(0.522115 + 1.77816i) q^{45} +(0.103699 - 0.106593i) q^{46} +(0.254296 - 0.0616916i) q^{47} +(-3.96342 - 0.539757i) q^{48} +(4.83621 + 0.461802i) q^{49} +(2.17810 - 0.397160i) q^{50} +(1.33984 + 3.87122i) q^{51} +(-2.49598 + 7.90952i) q^{52} +(7.13649 - 3.25913i) q^{53} +(1.03326 - 0.965596i) q^{54} +(-2.40909 - 3.06341i) q^{55} +(-4.13060 + 0.269222i) q^{56} +(-1.62727 - 0.394770i) q^{57} +(2.13046 - 1.33913i) q^{58} +(-4.07415 - 0.585775i) q^{59} +(2.23223 + 2.95888i) q^{60} +(0.194598 + 1.00967i) q^{61} +(2.90856 + 6.54185i) q^{62} +(0.848906 - 1.19212i) q^{63} +(-7.79769 + 1.78774i) q^{64} +(6.83100 - 3.52163i) q^{65} +(-1.26253 + 2.69269i) q^{66} +(-3.32362 + 7.48021i) q^{67} +(5.23993 + 6.29836i) q^{68} +(0.0481854 + 0.0934667i) q^{69} +(2.87339 + 2.54075i) q^{70} +(6.72948 + 4.79204i) q^{71} +(1.25191 - 2.53628i) q^{72} +(2.21377 - 0.426669i) q^{73} +(5.25113 + 2.77422i) q^{74} +(-0.222800 + 1.54961i) q^{75} +(-3.32374 + 0.409962i) q^{76} +(-0.725573 + 2.99085i) q^{77} +(-4.74289 - 3.44967i) q^{78} +(9.31399 - 7.32460i) q^{79} +(6.26582 + 3.96117i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-6.77565 + 0.904868i) q^{82} +(-5.68253 + 1.96674i) q^{83} +(0.747024 - 2.83004i) q^{84} +(0.721647 - 7.55743i) q^{85} +(6.33973 + 2.61218i) q^{86} +(0.419496 + 1.72919i) q^{87} +(-0.461777 + 5.93002i) q^{88} +(13.7426 - 4.03520i) q^{89} +(-2.48520 + 0.832296i) q^{90} +(-5.52063 - 2.52119i) q^{91} +(0.156147 + 0.140889i) q^{92} +(-5.03947 + 0.481211i) q^{93} +(0.100689 + 0.356099i) q^{94} +(2.43926 + 1.91825i) q^{95} +(0.552305 - 5.62983i) q^{96} +(-12.3985 - 7.15828i) q^{97} +(-0.395785 + 6.85913i) q^{98} +(-1.52196 - 1.45118i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 680 q - 68 q^{3} + 2 q^{4} - 11 q^{6} + 4 q^{7} - 39 q^{8} - 68 q^{9}+O(q^{10}) $ 680 * q - 68 * q^3 + 2 * q^4 - 11 * q^6 + 4 * q^7 - 39 * q^8 - 68 * q^9	$ 680 q - 68 q^{3} + 2 q^{4} - 11 q^{6} + 4 q^{7} - 39 q^{8} - 68 q^{9} + 39 q^{10} - 9 q^{12} - 6 q^{13} - 10 q^{14} + 2 q^{16} + 12 q^{20} + 4 q^{21} + 33 q^{22} - 6 q^{24} + 68 q^{25} + 19 q^{26} - 68 q^{27} - 92 q^{28} + 8 q^{29} + 6 q^{30} + 2 q^{31} + 40 q^{32} - 9 q^{36} - 12 q^{37} - 4 q^{38} - 6 q^{39} + 37 q^{40} - 10 q^{42} - 4 q^{43} + 159 q^{44} - 93 q^{46} + 2 q^{48} + 46 q^{49} + 6 q^{50} - 28 q^{52} + 17 q^{56} - 66 q^{57} + 92 q^{58} - 98 q^{60} - 6 q^{61} + 34 q^{62} - 18 q^{63} - 49 q^{64} + 22 q^{66} - 18 q^{67} + 208 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} - 72 q^{73} - 11 q^{74} + 68 q^{75} + 162 q^{76} + 4 q^{77} + 19 q^{78} + 28 q^{79} - 41 q^{80} - 68 q^{81} - 84 q^{82} + 12 q^{83} + 7 q^{84} - 77 q^{86} + 8 q^{87} - 132 q^{88} + 39 q^{90} - 186 q^{92} + 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} - 18 q^{97} + 65 q^{98}+O(q^{100}) $ 680 * q - 68 * q^3 + 2 * q^4 - 11 * q^6 + 4 * q^7 - 39 * q^8 - 68 * q^9 + 39 * q^10 - 9 * q^12 - 6 * q^13 - 10 * q^14 + 2 * q^16 + 12 * q^20 + 4 * q^21 + 33 * q^22 - 6 * q^24 + 68 * q^25 + 19 * q^26 - 68 * q^27 - 92 * q^28 + 8 * q^29 + 6 * q^30 + 2 * q^31 + 40 * q^32 - 9 * q^36 - 12 * q^37 - 4 * q^38 - 6 * q^39 + 37 * q^40 - 10 * q^42 - 4 * q^43 + 159 * q^44 - 93 * q^46 + 2 * q^48 + 46 * q^49 + 6 * q^50 - 28 * q^52 + 17 * q^56 - 66 * q^57 + 92 * q^58 - 98 * q^60 - 6 * q^61 + 34 * q^62 - 18 * q^63 - 49 * q^64 + 22 * q^66 - 18 * q^67 + 208 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 - 72 * q^73 - 11 * q^74 + 68 * q^75 + 162 * q^76 + 4 * q^77 + 19 * q^78 + 28 * q^79 - 41 * q^80 - 68 * q^81 - 84 * q^82 + 12 * q^83 + 7 * q^84 - 77 * q^86 + 8 * q^87 - 132 * q^88 + 39 * q^90 - 186 * q^92 + 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 - 18 * q^97 + 65 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{23}{66}\right)$	$-1$

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 $

$2$	0.0531079	+	1.41322i	0.0375530	+	0.999295i
$2$	0.0531079	+	1.41322i	0.0375530	+	0.999295i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$	−1.99436	+	0.150106i	−0.997180	+	0.0750529i
$5$	1.40058	+	1.21361i	0.626357	+	0.542742i	0.909166	−	0.416435i	$-0.136721\pi$
$5$	1.40058	+	1.21361i	0.626357	+	0.542742i	−0.282808	+	0.959176i	$0.591266\pi$
$6$	0.347192	−	1.37093i	0.141741	−	0.559681i
$7$	0.0696355	−	1.46183i	0.0263198	−	0.552520i	−0.946745	−	0.321986i	$-0.895650\pi$
$7$	0.0696355	−	1.46183i	0.0263198	−	0.552520i	0.973064	−	0.230534i	$-0.0740473\pi$
$8$	−0.318048	−	2.81049i	−0.112447	−	0.993658i
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$	−1.64071	+	2.04377i	−0.518837	+	0.646297i
$11$	−2.06492	−	0.397981i	−0.622598	−	0.119996i	−0.131810	−	0.991275i	$-0.542079\pi$
$11$	−2.06492	−	0.397981i	−0.622598	−	0.119996i	−0.490788	+	0.871279i	$0.663291\pi$
$12$	1.95586	+	0.417850i	0.564609	+	0.120623i
$13$	1.54128	−	3.84994i	0.427475	−	1.06778i	−0.545754	−	0.837945i	$-0.683757\pi$
$13$	1.54128	−	3.84994i	0.427475	−	1.06778i	0.973229	−	0.229836i	$-0.0738191\pi$
$14$	2.06958	+	0.0207754i	0.553118	+	0.00555245i
$15$	−1.00193	−	1.55904i	−0.258698	−	0.402541i
$16$	3.95494	−	0.598730i	0.988734	−	0.149682i
$17$	−2.37622	−	3.33693i	−0.576318	−	0.809325i	0.418794	−	0.908081i	$-0.362453\pi$
$17$	−2.37622	−	3.33693i	−0.576318	−	0.809325i	−0.995112	+	0.0987563i	$0.968514\pi$
$18$	−0.719365	+	1.21759i	−0.169556	+	0.286988i
$19$	1.67257	−	0.0796743i	0.383714	−	0.0182785i	0.145161	−	0.989408i	$-0.453630\pi$
$19$	1.67257	−	0.0796743i	0.383714	−	0.0182785i	0.238553	+	0.971130i	$0.423327\pi$
$20$	−2.97542	−	2.21013i	−0.665325	−	0.494201i
$21$	−0.478660	+	1.38300i	−0.104452	+	0.301795i
$22$	0.452770	−	2.93932i	0.0965308	−	0.626665i
$23$	−0.0725662	−	0.0761052i	−0.0151311	−	0.0158690i	0.716125	−	0.697972i	$-0.245914\pi$
$23$	−0.0725662	−	0.0761052i	−0.0151311	−	0.0158690i	−0.731256	+	0.682103i	$0.761066\pi$
$24$	−0.486641	+	2.78625i	−0.0993352	+	0.568741i
$25$	−0.222800	−	1.54961i	−0.0445599	−	0.309921i
$26$	5.52265	+	1.97371i	1.08308	+	0.387075i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	0.0805509	+	2.92587i	0.0152227	+	0.552937i
$29$	−0.889671	−	1.54096i	−0.165208	−	0.286148i	0.771521	−	0.636204i	$-0.219496\pi$
$29$	−0.889671	−	1.54096i	−0.165208	−	0.286148i	−0.936729	+	0.350055i	$0.886163\pi$
$30$	2.15004	−	1.49874i	0.392543	−	0.273632i
$31$	4.69976	−	1.88150i	0.844102	−	0.337927i	0.0910159	−	0.995849i	$-0.470989\pi$
$31$	4.69976	−	1.88150i	0.844102	−	0.337927i	0.753086	+	0.657922i	$0.228564\pi$
$32$	1.05617	+	5.55738i	0.186707	+	0.982416i
$33$	1.86915	+	0.963616i	0.325378	+	0.167744i
$34$	4.58961	−	3.53533i	0.787112	−	0.606304i
$35$	1.87162	−	1.96290i	0.316361	−	0.331790i
$36$	−1.75891	−	0.951955i	−0.293152	−	0.158659i
$37$	2.09972	−	3.63682i	0.345192	−	0.597890i	−0.640197	−	0.768211i	$-0.721147\pi$
$37$	2.09972	−	3.63682i	0.345192	−	0.597890i	0.985389	+	0.170321i	$0.0544805\pi$
$38$	0.201424	+	2.35947i	0.0326752	+	0.382757i
$39$	−2.56351	+	3.25976i	−0.410489	+	0.521980i
$40$	2.96538	−	4.32229i	0.468867	−	0.683414i
$41$	0.459467	+	4.81176i	0.0717567	+	0.751470i	0.957718	+	0.287710i	$0.0928939\pi$
$41$	0.459467	+	4.81176i	0.0717567	+	0.751470i	−0.885961	+	0.463760i	$0.846500\pi$
$42$	−1.97989	−	0.603002i	−0.305504	−	0.0930452i
$43$	2.01414	−	4.41034i	0.307153	−	0.672571i	−0.691611	−	0.722270i	$-0.743099\pi$
$43$	2.01414	−	4.41034i	0.307153	−	0.672571i	0.998764	+	0.0496989i	$0.0158262\pi$
$44$	4.17794	+	0.483760i	0.629848	+	0.0729296i
$45$	0.522115	+	1.77816i	0.0778323	+	0.265073i
$46$	0.103699	−	0.106593i	0.0152896	−	0.0157163i
$47$	0.254296	−	0.0616916i	0.0370929	−	0.00899865i	−0.217170	−	0.976134i	$-0.569682\pi$
$47$	0.254296	−	0.0616916i	0.0370929	−	0.00899865i	0.254262	+	0.967135i	$0.418167\pi$
$48$	−3.96342	−	0.539757i	−0.572070	−	0.0779072i
$49$	4.83621	+	0.461802i	0.690887	+	0.0659717i
$50$	2.17810	−	0.397160i	0.308029	−	0.0561670i
$51$	1.33984	+	3.87122i	0.187616	+	0.542079i
$52$	−2.49598	+	7.90952i	−0.346129	+	1.09685i
$53$	7.13649	−	3.25913i	0.980272	−	0.447675i	0.140184	−	0.990125i	$-0.455230\pi$
$53$	7.13649	−	3.25913i	0.980272	−	0.447675i	0.840088	+	0.542450i	$0.182503\pi$
$54$	1.03326	−	0.965596i	0.140609	−	0.131401i
$55$	−2.40909	−	3.06341i	−0.324842	−	0.413070i
$56$	−4.13060	+	0.269222i	−0.551975	+	0.0359764i
$57$	−1.62727	−	0.394770i	−0.215537	−	0.0522886i
$58$	2.13046	−	1.33913i	0.279742	−	0.175837i
$59$	−4.07415	−	0.585775i	−0.530410	−	0.0762614i	−0.128093	−	0.991762i	$-0.540886\pi$
$59$	−4.07415	−	0.585775i	−0.530410	−	0.0762614i	−0.402316	+	0.915501i	$0.631795\pi$
$60$	2.23223	+	2.95888i	0.288180	+	0.381990i
$61$	0.194598	+	1.00967i	0.0249158	+	0.129275i	0.992257	−	0.124203i	$-0.0396374\pi$
$61$	0.194598	+	1.00967i	0.0249158	+	0.129275i	−0.967341	+	0.253478i	$0.918425\pi$
$62$	2.90856	+	6.54185i	0.369388	+	0.830816i
$63$	0.848906	−	1.19212i	0.106952	−	0.150193i
$64$	−7.79769	+	1.78774i	−0.974711	+	0.223468i
$65$	6.83100	−	3.52163i	0.847282	−	0.436804i
$66$	−1.26253	+	2.69269i	−0.155407	+	0.331448i
$67$	−3.32362	+	7.48021i	−0.406044	+	0.913853i
$67$	−3.32362	+	7.48021i	−0.406044	+	0.913853i
$68$	5.23993	+	6.29836i	0.635434	+	0.763788i
$69$	0.0481854	+	0.0934667i	0.00580084	+	0.0112521i
$70$	2.87339	+	2.54075i	0.343436	+	0.303678i
$71$	6.72948	+	4.79204i	0.798642	+	0.568711i	0.904898	−	0.425628i	$-0.139947\pi$
$71$	6.72948	+	4.79204i	0.798642	+	0.568711i	−0.106256	+	0.994339i	$0.533886\pi$
$72$	1.25191	−	2.53628i	0.147538	−	0.298904i
$73$	2.21377	−	0.426669i	0.259102	−	0.0499378i	−0.0580460	−	0.998314i	$-0.518487\pi$
$73$	2.21377	−	0.426669i	0.259102	−	0.0499378i	0.317148	+	0.948376i	$0.397275\pi$
$74$	5.25113	+	2.77422i	0.610431	+	0.322496i
$75$	−0.222800	+	1.54961i	−0.0257267	+	0.178933i
$76$	−3.32374	+	0.409962i	−0.381260	+	0.0470258i
$77$	−0.725573	+	2.99085i	−0.0826867	+	0.340839i
$78$	−4.74289	−	3.44967i	−0.537027	−	0.390598i
$79$	9.31399	−	7.32460i	1.04791	−	0.824082i	0.0631459	−	0.998004i	$-0.479887\pi$
$79$	9.31399	−	7.32460i	1.04791	−	0.824082i	0.984759	+	0.173923i	$0.0556442\pi$
$80$	6.26582	+	3.96117i	0.700540	+	0.442872i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−6.77565	+	0.904868i	−0.748245	+	0.0999260i
$83$	−5.68253	+	1.96674i	−0.623739	+	0.215878i	−0.620613	−	0.784117i	$-0.713116\pi$
$83$	−5.68253	+	1.96674i	−0.623739	+	0.215878i	−0.00312604	+	0.999995i	$0.500995\pi$
$84$	0.747024	−	2.83004i	0.0815070	−	0.308783i
$85$	0.721647	−	7.55743i	0.0782736	−	0.819718i
$86$	6.33973	+	2.61218i	0.683631	+	0.281679i
$87$	0.419496	+	1.72919i	0.0449747	+	0.185388i
$88$	−0.461777	+	5.93002i	−0.0492256	+	0.632142i
$89$	13.7426	−	4.03520i	1.45671	−	0.427730i	0.544959	−	0.838463i	$-0.316545\pi$
$89$	13.7426	−	4.03520i	1.45671	−	0.427730i	0.911756	+	0.410733i	$0.134727\pi$
$90$	−2.48520	+	0.832296i	−0.261963	+	0.0877317i
$91$	−5.52063	−	2.52119i	−0.578719	−	0.264292i
$92$	0.156147	+	0.140889i	0.0162794	+	0.0146886i
$93$	−5.03947	+	0.481211i	−0.522568	+	0.0498992i
$94$	0.100689	+	0.356099i	0.0103853	+	0.0367289i
$95$	2.43926	+	1.91825i	0.250262	+	0.196808i
$96$	0.552305	−	5.62983i	0.0563694	−	0.574592i
$97$	−12.3985	−	7.15828i	−1.25888	−	0.726814i	−0.286022	−	0.958223i	$-0.592333\pi$
$97$	−12.3985	−	7.15828i	−1.25888	−	0.726814i	−0.972856	+	0.231409i	$0.925666\pi$
$98$	−0.395785	+	6.85913i	−0.0399803	+	0.692877i
$99$	−1.52196	−	1.45118i	−0.152963	−	0.145850i
$100$	0.676948	+	3.05703i	0.0676948	+	0.305703i
$101$	−0.364585	+	0.707196i	−0.0362775	+	0.0703686i	−0.906278	−	0.422683i	$-0.861088\pi$
$101$	−0.364585	+	0.707196i	−0.0362775	+	0.0703686i	0.870000	+	0.493052i	$0.164119\pi$
$102$	−5.39972	+	2.09908i	−0.534652	+	0.207840i
$103$	−5.13427	−	12.8248i	−0.505895	−	1.26366i	−0.933135	−	0.359526i	$-0.882938\pi$
$103$	−5.13427	−	12.8248i	−0.505895	−	1.26366i	0.427240	−	0.904138i	$-0.359486\pi$
$104$	−11.3104	−	3.10729i	−1.10908	−	0.304695i
$105$	−2.34882	+	1.35609i	−0.229221	+	0.132341i
$106$	4.98485	+	9.91232i	0.484172	+	0.962769i
$107$	−2.14959	+	1.86263i	−0.207809	+	0.180068i	−0.752547	−	0.658539i	$-0.771175\pi$
$107$	−2.14959	+	1.86263i	−0.207809	+	0.180068i	0.544737	+	0.838607i	$0.316629\pi$
$108$	1.41947	+	1.40894i	0.136589	+	0.135575i
$109$	−17.4599	+	2.51035i	−1.67235	+	0.240448i	−0.912332	−	0.409452i	$-0.865720\pi$
$109$	−17.4599	+	2.51035i	−1.67235	+	0.240448i	−0.760020	+	0.649900i	$0.774811\pi$
$110$	4.20132	−	3.56726i	0.400580	−	0.340125i
$111$	−3.03928	+	2.89795i	−0.288476	+	0.275061i
$112$	−0.599837	−	5.82314i	−0.0566793	−	0.550235i
$113$	−5.59417	−	1.93616i	−0.526256	−	0.182139i	0.0510056	−	0.998698i	$-0.483757\pi$
$113$	−5.59417	−	1.93616i	−0.526256	−	0.182139i	−0.577261	+	0.816560i	$0.695879\pi$
$114$	0.471475	−	2.32064i	0.0441577	−	0.217348i
$115$	−0.00927271	−	0.194658i	−0.000864684	−	0.0181520i
$116$	2.00563	+	2.93967i	0.186218	+	0.272942i
$117$	3.37805	−	2.40550i	0.312300	−	0.222388i
$118$	0.611457	−	5.78877i	0.0562892	−	0.532899i
$119$	−5.04350	+	3.24126i	−0.462337	+	0.297126i
$120$	−4.06299	+	3.31177i	−0.370899	+	0.302321i
$121$	−6.10653	−	2.44469i	−0.555139	−	0.222244i
$122$	−1.41655	+	0.328631i	−0.128248	+	0.0297529i
$123$	0.914773	−	4.74629i	0.0824823	−	0.427959i
$124$	−9.09059	+	4.45785i	−0.816359	+	0.400327i
$125$	6.57822	−	10.2359i	0.588374	−	0.915528i
$126$	1.72981	+	1.13638i	0.154104	+	0.101236i
$127$	−7.95323	−	0.378859i	−0.705735	−	0.0336183i	−0.308354	−	0.951272i	$-0.599778\pi$
$127$	−7.95323	−	0.378859i	−0.705735	−	0.0336183i	−0.397381	+	0.917654i	$0.630081\pi$
$128$	−2.94058	−	10.9249i	−0.259913	−	0.965632i
$129$	−3.17509	+	3.66424i	−0.279551	+	0.322619i
$130$	5.33960	+	9.46666i	0.468314	+	0.830281i
$131$	−0.501780	+	1.70891i	−0.0438407	+	0.149308i	−0.978505	−	0.206225i	$-0.933882\pi$
$131$	−0.501780	+	1.70891i	−0.0438407	+	0.149308i	0.934664	+	0.355532i	$0.115700\pi$
$132$	−3.87241	−	1.64123i	−0.337050	−	0.142850i
$133$		−	2.45056i		−	0.212490i
$134$	−10.7477	−	4.29973i	−0.928457	−	0.371440i
$135$		−	1.85323i		−	0.159501i
$136$	−8.62266	+	7.73964i	−0.739387	+	0.663669i
$137$	2.93573	−	9.99818i	0.250816	−	0.854202i	−0.733784	−	0.679383i	$-0.762248\pi$
$137$	2.93573	−	9.99818i	0.250816	−	0.854202i	0.984601	−	0.174819i	$-0.0559342\pi$
$138$	−0.129530	+	0.0730602i	−0.0110263	+	0.00621930i
$139$	−5.89265	+	6.80048i	−0.499808	+	0.576809i	−0.948460	−	0.316898i	$-0.897359\pi$
$139$	−5.89265	+	6.80048i	−0.499808	+	0.576809i	0.448652	+	0.893707i	$0.351904\pi$
$140$	−3.43803	+	4.19566i	−0.290567	+	0.354598i
$141$	−0.261376	−	0.0124509i	−0.0220118	−	0.00104855i
$142$	−6.41480	+	9.76471i	−0.538318	+	0.819436i
$143$	−4.71484	+	7.33643i	−0.394274	+	0.613503i
$144$	3.65080	+	1.63452i	0.304234	+	0.136210i
$145$	0.624062	−	3.23794i	0.0518255	−	0.268896i
$146$	0.720543	+	3.10587i	0.0596326	+	0.257044i
$147$	−4.51020	−	1.80561i	−0.371995	−	0.148924i
$148$	−3.64169	+	7.56831i	−0.299345	+	0.622111i
$149$	−4.79672	+	3.08266i	−0.392962	+	0.252542i	−0.722169	−	0.691716i	$-0.756855\pi$
$149$	−4.79672	+	3.08266i	−0.392962	+	0.252542i	0.329207	+	0.944258i	$0.393219\pi$
$150$	−2.20176	−	0.232568i	−0.179773	−	0.0189891i
$151$	10.4125	−	7.41469i	0.847355	−	0.603399i	−0.0717449	−	0.997423i	$-0.522857\pi$
$151$	10.4125	−	7.41469i	0.847355	−	0.603399i	0.919100	+	0.394024i	$0.128917\pi$
$152$	−0.755881	−	4.67540i	−0.0613101	−	0.379225i
$153$	−0.194921	−	4.09189i	−0.0157584	−	0.330809i
$154$	−4.26525	−	0.866553i	−0.343704	−	0.0698288i
$155$	8.86578	+	3.06848i	0.712117	+	0.246466i
$156$	4.62324	−	6.88593i	0.370155	−	0.551316i
$157$	−5.79976	+	5.53006i	−0.462871	+	0.441347i	−0.885280	−	0.465059i	$-0.846033\pi$
$157$	−5.79976	+	5.53006i	−0.462871	+	0.441347i	0.422409	+	0.906406i	$0.361185\pi$
$158$	10.8459	+	12.7737i	0.862852	+	1.01622i
$159$	−7.76561	+	1.11653i	−0.615853	+	0.0885463i
$160$	−5.26523	+	9.06532i	−0.416253	+	0.716677i
$161$	−0.116306	+	0.100780i	−0.00916620	+	0.00794256i
$162$	−1.26344	+	0.635380i	−0.0992656	+	0.0499202i
$163$	13.7956	−	7.96487i	1.08055	−	0.623857i	0.149506	−	0.988761i	$-0.452232\pi$
$163$	13.7956	−	7.96487i	1.08055	−	0.623857i	0.931045	+	0.364904i	$0.118898\pi$
$164$	−1.63861	−	9.52740i	−0.127954	−	0.743965i
$165$	1.44844	+	3.61804i	0.112761	+	0.281664i
$166$	−3.08122	−	7.92620i	−0.239149	−	0.615192i
$167$	−2.56440	+	4.97425i	−0.198440	+	0.384919i	−0.966968	−	0.254896i	$-0.917959\pi$
$167$	−2.56440	+	4.97425i	−0.198440	+	0.384919i	0.768529	+	0.639815i	$0.220989\pi$
$168$	4.03913	+	0.905408i	0.311626	+	0.0698538i
$169$	−3.03795	−	2.89668i	−0.233689	−	0.222822i
$170$	10.7186	+	0.618484i	0.822079	+	0.0474355i
$171$	1.45013	+	0.837233i	0.110894	+	0.0640248i
$172$	−3.35489	+	9.09814i	−0.255808	+	0.693727i
$173$	7.64859	+	6.01492i	0.581512	+	0.457306i	0.865071	−	0.501649i	$-0.167273\pi$
$173$	7.64859	+	6.01492i	0.581512	+	0.457306i	−0.283560	+	0.958955i	$0.591515\pi$
$174$	−2.42143	+	0.684672i	−0.183568	+	0.0519048i
$175$	−2.28077	+	0.217788i	−0.172410	+	0.0164632i
$176$	−8.40492	−	0.337659i	−0.633545	−	0.0254520i
$177$	3.74409	+	1.70987i	0.281423	+	0.128522i
$178$	6.43244	+	19.2070i	0.482132	+	1.43962i
$179$	−11.8658	+	3.48411i	−0.886890	+	0.260415i	−0.693284	−	0.720665i	$-0.743837\pi$
$179$	−11.8658	+	3.48411i	−0.886890	+	0.260415i	−0.193607	+	0.981079i	$0.562019\pi$
$180$	−1.30820	−	3.46792i	−0.0975073	−	0.258483i
$181$	−3.02274	−	12.4599i	−0.224678	−	0.926137i	−0.966731	−	0.255795i	$-0.917663\pi$
$181$	−3.02274	−	12.4599i	−0.224678	−	0.926137i	0.742053	−	0.670342i	$-0.233852\pi$
$182$	3.26979	−	7.93574i	0.242373	−	0.588236i
$183$	0.0977417	−	1.02360i	0.00722528	−	0.0756665i
$184$	−0.190813	+	0.228152i	−0.0140669	+	0.0168196i
$185$	7.35450	−	2.54542i	0.540713	−	0.187143i
$186$	−0.947690	−	7.09630i	−0.0694880	−	0.520326i
$187$	3.57867	+	7.83620i	0.261698	+	0.573040i
$188$	−0.497898	+	0.161207i	−0.0363130	+	0.0117572i
$189$	−1.15038	+	0.904668i	−0.0836777	+	0.0658049i
$190$	−2.58136	+	3.54907i	−0.187272	+	0.257477i
$191$	−3.63576	+	14.9868i	−0.263074	+	1.08441i	0.674957	+	0.737857i	$0.264162\pi$
$191$	−3.63576	+	14.9868i	−0.263074	+	1.08441i	−0.938031	+	0.346551i	$0.887353\pi$
$192$	7.98549	+	0.481538i	0.576303	+	0.0347520i
$193$	−0.747615	+	5.19978i	−0.0538145	+	0.374288i	0.945062	+	0.326892i	$0.106001\pi$
$193$	−0.747615	+	5.19978i	−0.0538145	+	0.374288i	−0.998876	+	0.0473960i	$0.984908\pi$
$194$	9.45774	−	17.9019i	0.679026	−	1.28528i
$195$	−7.54646	+	1.45446i	−0.540413	+	0.104156i
$196$	−9.71445	−	0.195056i	−0.693889	−	0.0139325i
$197$	11.1738	+	7.95679i	0.796097	+	0.566898i	0.904134	−	0.427249i	$-0.140517\pi$
$197$	11.1738	+	7.95679i	0.796097	+	0.566898i	−0.108037	+	0.994147i	$0.534457\pi$
$198$	1.97001	−	2.22793i	0.140002	−	0.158332i
$199$	−6.78844	−	13.1677i	−0.481220	−	0.933436i	−0.997051	−	0.0767455i	$-0.975547\pi$
$199$	−6.78844	−	13.1677i	−0.481220	−	0.933436i	0.515831	−	0.856690i	$-0.327483\pi$
$200$	−4.28429	+	1.11903i	−0.302945	+	0.0791270i
$201$	5.29641	−	6.24084i	0.373580	−	0.440195i
$202$	−1.01878	−	0.477679i	−0.0716813	−	0.0336094i
$203$	−2.31457	+	1.19324i	−0.162451	+	0.0837492i
$204$	−3.25322	−	7.51949i	−0.227771	−	0.526469i
$205$	−5.19606	+	7.29685i	−0.362909	+	0.509634i
$206$	17.8515	−	7.93693i	1.24377	−	0.552992i
$207$	−0.0199010	−	0.103256i	−0.00138321	−	0.00717679i
$208$	3.79061	−	16.1491i	0.262831	−	1.11974i
$209$	−3.48543	−	0.501130i	−0.241093	−	0.0346639i
$210$	−2.04119	−	3.24736i	−0.140855	−	0.224089i
$211$	8.14060	+	1.97489i	0.560422	+	0.135957i	0.505957	−	0.862559i	$-0.331140\pi$
$211$	8.14060	+	1.97489i	0.560422	+	0.135957i	0.0544650	+	0.998516i	$0.482655\pi$
$212$	−13.7435	+	7.57110i	−0.943908	+	0.519985i
$213$	−5.10682	−	6.49384i	−0.349913	−	0.444951i
$214$	−2.74646	−	2.93892i	−0.187744	−	0.200900i
$215$	8.17338	−	3.73266i	0.557420	−	0.254565i
$216$	−1.91575	+	2.08084i	−0.130350	+	0.141583i
$217$	−2.42316	−	7.00127i	−0.164495	−	0.475277i
$218$	−4.47492	−	24.5412i	−0.303080	−	1.66214i
$219$	−2.24430	−	0.214305i	−0.151656	−	0.0144814i
$220$	5.26443	+	5.74792i	0.354928	+	0.387524i
$221$	−16.5094	+	4.00514i	−1.11054	+	0.269415i
$222$	−4.25683	−	4.14125i	−0.285700	−	0.277943i
$223$	−4.47846	−	15.2522i	−0.299900	−	1.02136i	−0.962249	−	0.272170i	$-0.912259\pi$
$223$	−4.47846	−	15.2522i	−0.299900	−	1.02136i	0.662349	−	0.749195i	$-0.269559\pi$
$224$	8.19749	−	1.15695i	0.547718	−	0.0773022i
$225$	0.650349	−	1.42407i	0.0433566	−	0.0949377i
$226$	2.43912	−	8.00860i	0.162248	−	0.532724i
$227$	0.599182	+	6.27492i	0.0397691	+	0.416481i	0.993332	+	0.115288i	$0.0367790\pi$
$227$	0.599182	+	6.27492i	0.0397691	+	0.416481i	−0.953563	+	0.301194i	$0.902615\pi$
$228$	3.30461	+	0.543052i	0.218853	+	0.0359645i
$229$	−3.50904	+	4.46211i	−0.231884	+	0.294865i	−0.888045	−	0.459756i	$-0.847937\pi$
$229$	−3.50904	+	4.46211i	−0.231884	+	0.294865i	0.656161	+	0.754621i	$0.272179\pi$
$230$	0.274601	−	0.0234422i	0.0181067	−	0.00154573i
$231$	1.53880	−	2.66528i	0.101246	−	0.175363i
$232$	−4.04788	+	2.99051i	−0.265756	+	0.196337i
$233$	10.7625	−	11.2874i	0.705074	−	0.739461i	−0.269629	−	0.962964i	$-0.586901\pi$
$233$	10.7625	−	11.2874i	0.705074	−	0.739461i	0.974703	+	0.223504i	$0.0717494\pi$
$234$	3.57889	+	4.64616i	0.233959	+	0.303729i
$235$	0.431031	+	0.222212i	0.0281174	+	0.0144955i
$236$	8.21325	+	0.556691i	0.534637	+	0.0362375i
$237$	−11.0003	+	4.40385i	−0.714545	+	0.286061i
$238$	−4.84845	−	6.95541i	−0.314278	−	0.450853i
$239$	−7.35834	−	12.7450i	−0.475972	−	0.824407i	0.523649	−	0.851934i	$-0.324570\pi$
$239$	−7.35834	−	12.7450i	−0.475972	−	0.824407i	−0.999621	+	0.0275269i	$0.991237\pi$
$240$	−4.89602	−	5.56600i	−0.316037	−	0.359284i
$241$	2.41470	+	2.78672i	0.155545	+	0.179508i	0.828173	−	0.560472i	$-0.189380\pi$
$241$	2.41470	+	2.78672i	0.155545	+	0.179508i	−0.672629	+	0.739980i	$0.734835\pi$
$242$	3.13057	−	8.75968i	0.201240	−	0.563094i
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$	−0.539657	−	1.98444i	−0.0345480	−	0.127041i
$245$	6.21303	+	6.51604i	0.396936	+	0.416295i
$246$	6.75612	+	1.04071i	0.430754	+	0.0663530i
$247$	2.27116	−	6.56209i	0.144511	−	0.417536i
$248$	−6.78269	−	12.6102i	−0.430701	−	0.800749i
$249$	6.00645	−	0.286122i	0.380643	−	0.0181323i
$250$	14.8149	+	8.75284i	0.936977	+	0.553578i
$251$	0.813998	+	1.14310i	0.0513791	+	0.0721519i	0.839466	−	0.543412i	$-0.182868\pi$
$251$	0.813998	+	1.14310i	0.0513791	+	0.0721519i	−0.788087	+	0.615564i	$0.788928\pi$
$252$	−1.51408	+	2.50494i	−0.0953780	+	0.157797i
$253$	0.119555	+	0.186031i	0.00751636	+	0.0116957i
$254$	0.113030	−	11.2598i	0.00709216	−	0.706500i
$255$	−2.82159	+	7.04799i	−0.176695	+	0.441362i
$256$	15.2830	−	4.73588i	0.955190	−	0.295992i
$257$	−0.401215	−	0.0773279i	−0.0250271	−	0.00482358i	0.176722	−	0.984261i	$-0.443451\pi$
$257$	−0.401215	−	0.0773279i	−0.0250271	−	0.00482358i	−0.201749	+	0.979437i	$0.564663\pi$
$258$	−5.34699	−	4.29248i	−0.332889	−	0.267238i
$259$	−5.17020	−	3.32269i	−0.321261	−	0.206462i
$260$	−13.0949	+	8.04876i	−0.812109	+	0.499163i
$261$	0.0846645	−	1.77733i	0.00524060	−	0.110014i
$262$	−2.44170	−	0.618367i	−0.150849	−	0.0382029i
$263$	6.82141	+	5.91078i	0.420626	+	0.364474i	0.839306	−	0.543659i	$-0.182962\pi$
$263$	6.82141	+	5.91078i	0.420626	+	0.364474i	−0.418680	+	0.908134i	$0.637507\pi$
$264$	2.11375	−	5.55971i	0.130092	−	0.342177i
$265$	13.9505	+	4.09624i	0.856973	+	0.251630i
$266$	3.46317	−	0.130144i	0.212341	−	0.00797964i
$267$	−14.3228			−0.876540
$268$	5.50566	−	15.4171i	0.336312	−	0.941751i
$269$	−30.1831			−1.84030			−0.920149	−	0.391568i	$-0.871933\pi$
$269$	−30.1831			−1.84030			−0.920149	+	0.391568i	$0.871933\pi$
$270$	2.61901	−	0.0984211i	0.159388	−	0.00598972i
$271$	23.7761	+	6.98130i	1.44430	+	0.424084i	0.907651	−	0.419725i	$-0.137873\pi$
$271$	23.7761	+	6.98130i	1.44430	+	0.424084i	0.536645	+	0.843808i	$0.319692\pi$
$272$	−11.3957	−	11.7746i	−0.690967	−	0.713943i
$273$	4.58671	+	3.97440i	0.277600	+	0.240542i
$274$	14.2855	+	3.61784i	0.863019	+	0.218562i
$275$	−0.156650	+	3.28849i	−0.00944634	+	0.198303i
$276$	−0.110129	−	0.179173i	−0.00662898	−	0.0107850i
$277$	11.7950	+	7.58017i	0.708692	+	0.455448i	0.844687	−	0.535261i	$-0.179787\pi$
$277$	11.7950	+	7.58017i	0.708692	+	0.455448i	−0.135995	+	0.990710i	$0.543423\pi$
$278$	−9.92349	−	7.96642i	−0.595171	−	0.477794i
$279$	4.97091	+	0.958064i	0.297600	+	0.0573578i
$280$	−6.11196	−	4.63586i	−0.365259	−	0.277046i
$281$	−4.60500	+	11.5027i	−0.274711	+	0.686195i	−0.999997	−	0.00225195i	$-0.999283\pi$
$281$	−4.60500	+	11.5027i	−0.274711	+	0.686195i	0.725286	+	0.688447i	$0.241707\pi$
$282$	0.00371465	−	0.370042i	0.000221204	−	0.0220357i
$283$	8.37933	+	13.0385i	0.498100	+	0.775058i	0.995728	−	0.0923320i	$-0.0294321\pi$
$283$	8.37933	+	13.0385i	0.498100	+	0.775058i	−0.497629	+	0.867390i	$0.665796\pi$
$284$	−14.1403	−	8.54692i	−0.839073	−	0.507166i
$285$	−1.80001	−	2.52777i	−0.106624	−	0.149732i
$286$	−10.6184	−	6.27346i	−0.627876	−	0.370957i
$287$	7.06596	−	0.336593i	0.417091	−	0.0198685i
$288$	−2.11604	+	5.24618i	−0.124689	+	0.309134i
$289$	0.0714527	−	0.206449i	0.00420310	−	0.0121441i
$290$	4.60905	+	0.709974i	0.270653	+	0.0416911i
$291$	9.87956	+	10.3614i	0.579150	+	0.607395i
$292$	−4.35100	+	1.18323i	−0.254623	+	0.0692433i
$293$	3.31535	+	23.0588i	0.193685	+	1.34711i	0.822150	+	0.569271i	$0.192775\pi$
$293$	3.31535	+	23.0588i	0.193685	+	1.34711i	−0.628465	+	0.777838i	$0.716316\pi$
$294$	2.31219	−	6.46978i	0.134850	−	0.377325i
$295$	−4.99527	−	5.76485i	−0.290836	−	0.335642i
$296$	−10.8891	−	4.74456i	−0.632914	−	0.275772i
$297$	1.05146	+	1.82119i	0.0610120	+	0.105676i
$298$	−4.61121	−	6.61508i	−0.267120	−	0.383201i
$299$	−0.404846	+	0.162076i	−0.0234128	+	0.00937308i
$300$	0.211738	−	3.12391i	0.0122247	−	0.180359i
$301$	−6.30691	−	3.25144i	−0.363524	−	0.187410i
$302$	11.0315	+	14.3213i	0.634794	+	0.824098i
$303$	0.549056	−	0.575834i	0.0315425	−	0.0330808i
$304$	6.56720	−	1.31652i	0.376655	−	0.0755078i
$305$	−0.952795	+	1.65029i	−0.0545569	+	0.0944953i
$306$	5.77237	−	0.492776i	0.329984	−	0.0281702i
$307$	9.20032	−	11.6992i	0.525090	−	0.667706i	−0.449088	−	0.893487i	$-0.648251\pi$
$307$	9.20032	−	11.6992i	0.525090	−	0.667706i	0.974178	+	0.225781i	$0.0724935\pi$
$308$	0.998108	−	6.07374i	0.0568725	−	0.346084i
$309$	1.31314	+	13.7518i	0.0747017	+	0.782312i
$310$	−3.86558	+	12.6922i	−0.219550	+	0.720870i
$311$	−14.3903	+	31.5104i	−0.816001	+	1.78679i	−0.236908	+	0.971532i	$0.576134\pi$
$311$	−14.3903	+	31.5104i	−0.816001	+	1.78679i	−0.579093	+	0.815262i	$0.696593\pi$
$312$	9.97684	+	6.16794i	0.564827	+	0.349191i
$313$	7.51870	+	25.6063i	0.424982	+	1.44736i	0.842504	+	0.538690i	$0.181080\pi$
$313$	7.51870	+	25.6063i	0.424982	+	1.44736i	−0.417522	+	0.908667i	$0.637101\pi$
$314$	−8.12318	−	7.90262i	−0.458418	−	0.445971i
$315$	2.63573	−	0.639420i	0.148506	−	0.0360272i
$316$	−17.4760	+	16.0060i	−0.983100	+	0.900406i
$317$	4.37493	+	0.417755i	0.245721	+	0.0234635i	0.217190	−	0.976129i	$-0.430311\pi$
$317$	4.37493	+	0.417755i	0.245721	+	0.0234635i	0.0285310	+	0.999593i	$0.490917\pi$
$318$	−1.99031	−	10.9152i	−0.111611	−	0.612094i
$319$	1.22383	+	3.53603i	0.0685214	+	0.197980i
$320$	−13.0909	−	6.95946i	−0.731803	−	0.389046i
$321$	2.58729	−	1.18157i	0.144408	−	0.0659490i
$322$	−0.148600	−	0.159013i	−0.00828117	−	0.00886147i
$323$	−4.24026	−	5.39193i	−0.235934	−	0.300015i
$324$	−0.965028	−	1.75178i	−0.0536127	−	0.0973209i
$325$	−6.30929	−	1.53062i	−0.349976	−	0.0849034i
$326$	11.9887	+	19.0731i	0.663995	+	1.05636i
$327$	17.4599	+	2.51035i	0.965532	+	0.138823i
$328$	13.3773	−	2.82170i	0.738635	−	0.155802i
$329$	−0.0724746	−	0.376034i	−0.00399566	−	0.0207314i
$330$	−5.03615	+	2.23911i	−0.277231	+	0.123259i
$331$	−3.22723	+	4.53201i	−0.177385	+	0.249102i	−0.893690	−	0.448685i	$-0.851892\pi$
$331$	−3.22723	+	4.53201i	−0.177385	+	0.249102i	0.716305	+	0.697787i	$0.245832\pi$
$332$	11.0378	−	4.77538i	0.605778	−	0.262083i
$333$	3.73261	−	1.92430i	0.204546	−	0.105451i
$334$	−7.16588	−	3.35988i	−0.392099	−	0.183845i
$335$	−13.7330	+	6.44305i	−0.750315	+	0.352021i
$336$	−1.06503	+	5.75625i	−0.0581020	+	0.314029i
$337$	8.30865	+	16.1165i	0.452601	+	0.877924i	0.999179	+	0.0405154i	$0.0129000\pi$
$337$	8.30865	+	16.1165i	0.452601	+	0.877924i	−0.546578	+	0.837408i	$0.684070\pi$
$338$	3.93230	−	4.44712i	0.213889	−	0.241891i
$339$	4.82209	+	3.43380i	0.261900	+	0.186498i
$340$	−0.304809	+	15.1805i	−0.0165306	+	0.823281i
$341$	−10.4534	+	2.01474i	−0.566086	+	0.109104i
$342$	−1.10618	+	2.09381i	−0.0598152	+	0.113220i
$343$	2.46978	−	17.1777i	0.133356	−	0.927508i
$344$	−13.0358	−	4.25800i	−0.702844	−	0.229576i
$345$	−0.0459444	+	0.189385i	−0.00247356	+	0.0101962i
$346$	−8.09418	+	11.1286i	−0.435146	+	0.598275i
$347$	20.3388	−	15.9946i	1.09185	−	0.858638i	0.101170	−	0.994869i	$-0.467742\pi$
$347$	20.3388	−	15.9946i	1.09185	−	0.858638i	0.990677	+	0.136232i	$0.0434991\pi$
$348$	−1.09619	−	3.38565i	−0.0587618	−	0.181490i
$349$	6.24554	+	13.6758i	0.334316	+	0.732050i	0.999898	−	0.0142746i	$-0.00454390\pi$
$349$	6.24554	+	13.6758i	0.334316	+	0.732050i	−0.665582	+	0.746325i	$0.731817\pi$
$350$	−0.428908	−	3.21166i	−0.0229261	−	0.171671i
$351$	−3.91892	+	1.35635i	−0.209176	+	0.0723966i
$352$	0.0308181	−	11.8959i	0.00164261	−	0.634054i
$353$	1.92299	−	20.1385i	0.102351	−	1.07186i	−0.787718	−	0.616036i	$-0.788738\pi$
$353$	1.92299	−	20.1385i	0.102351	−	1.07186i	0.890068	−	0.455827i	$-0.150656\pi$
$354$	−2.21757	+	5.38202i	−0.117863	+	0.286051i
$355$	3.60950	+	14.8786i	0.191572	+	0.789673i
$356$	−26.8020	+	10.1105i	−1.42050	+	0.535854i
$357$	5.75237	−	1.68905i	0.304448	−	0.0893939i
$358$	−5.55397	−	16.5839i	−0.293536	−	0.876486i
$359$	13.5183	+	6.17362i	0.713471	+	0.325831i	0.738872	−	0.673846i	$-0.235359\pi$
$359$	13.5183	+	6.17362i	0.713471	+	0.325831i	−0.0254008	+	0.999677i	$0.508086\pi$
$360$	4.83144	−	2.03294i	0.254639	−	0.107145i
$361$	−16.1228	+	1.53954i	−0.848570	+	0.0810286i
$362$	17.4480	−	4.93350i	0.917046	−	0.259299i
$363$	5.17043	+	4.06607i	0.271377	+	0.213413i
$364$	11.3886	+	4.19947i	0.596923	+	0.220112i
$365$	3.61836	+	2.08906i	0.189394	+	0.109346i
$366$	1.45176	+	0.0837691i	0.0758845	+	0.00437868i
$367$	17.2396	+	16.4379i	0.899898	+	0.858051i	0.990454	−	0.137840i	$-0.0440161\pi$
$367$	17.2396	+	16.4379i	0.899898	+	0.858051i	−0.0905565	+	0.995891i	$0.528865\pi$
$368$	−0.332561	−	0.257544i	−0.0173359	−	0.0134254i
$369$	−2.21490	+	4.29631i	−0.115303	+	0.223657i
$370$	3.98780	+	10.2583i	0.207316	+	0.533304i
$371$	−4.26733	−	10.6593i	−0.221549	−	0.553403i
$372$	9.97827	−	1.71616i	0.517349	−	0.0889788i
$373$	−13.1261	+	7.57834i	−0.679642	+	0.392391i	−0.799720	−	0.600373i	$-0.795019\pi$
$373$	−13.1261	+	7.57834i	−0.679642	+	0.392391i	0.120078	+	0.992764i	$0.461685\pi$
$374$	−10.8842	+	5.47360i	−0.562808	+	0.283033i
$375$	−9.19555	+	7.96799i	−0.474856	+	0.411465i
$376$	−0.254262	−	0.695076i	−0.0131126	−	0.0358458i
$377$	−7.30383	+	1.05013i	−0.376166	+	0.0540845i
$378$	−1.33959	−	1.57769i	−0.0689008	−	0.0811476i
$379$	−9.49419	+	9.05269i	−0.487684	+	0.465005i	−0.893574	−	0.448916i	$-0.851810\pi$
$379$	−9.49419	+	9.05269i	−0.487684	+	0.465005i	0.405890	+	0.913922i	$0.366962\pi$
$380$	−5.15269	−	3.45954i	−0.264328	−	0.177470i
$381$	7.52433	+	2.60420i	0.385483	+	0.133417i
$382$	−21.3727	−	4.34220i	−1.09352	−	0.222166i
$383$	−0.950909	−	19.9620i	−0.0485892	−	1.02001i	−0.883148	−	0.469094i	$-0.844581\pi$
$383$	−0.950909	−	19.9620i	−0.0485892	−	1.02001i	0.834559	−	0.550919i	$-0.185723\pi$
$384$	−0.256424	+	11.3108i	−0.0130856	+	0.577202i
$385$	−4.64594	+	3.30836i	−0.236779	+	0.168610i
$386$	−7.38811	−	0.780392i	−0.376045	−	0.0397209i
$387$	4.07881	−	2.62129i	0.207338	−	0.133248i
$388$	25.8016	+	12.4151i	1.30988	+	0.630281i
$389$	−15.8524	−	6.34633i	−0.803746	−	0.321772i	−0.0668378	−	0.997764i	$-0.521291\pi$
$389$	−15.8524	−	6.34633i	−0.803746	−	0.321772i	−0.736909	+	0.675992i	$0.763715\pi$
$390$	−2.45624	−	10.5875i	−0.124377	−	0.536121i
$391$	−0.0815248	+	0.422991i	−0.00412289	+	0.0213916i
$392$	−0.240258	−	13.7390i	−0.0121349	−	0.693923i
$393$	0.962909	−	1.49832i	0.0485723	−	0.0755800i
$394$	−10.6513	+	16.2135i	−0.536602	+	0.816824i
$395$	21.9341	+	1.04485i	1.10363	+	0.0525722i
$396$	3.25316	+	2.66573i	0.163478	+	0.133958i
$397$	−18.3852	+	21.2177i	−0.922727	+	1.06488i	0.0749785	+	0.997185i	$0.476111\pi$
$397$	−18.3852	+	21.2177i	−0.922727	+	1.06488i	−0.997706	+	0.0676989i	$0.978434\pi$
$398$	18.2483	−	10.2928i	0.914706	−	0.515933i
$399$	−0.690402	+	2.35129i	−0.0345634	+	0.117712i
$400$	−1.80895	−	5.99520i	−0.0904477	−	0.299760i
$401$			22.1578i			1.10651i	0.833012	+	0.553255i	$0.186614\pi$
$401$			22.1578i			1.10651i	−0.833012	+	0.553255i	$0.813386\pi$
$402$	9.10094	+	7.15353i	0.453913	+	0.356786i
$403$		−	20.9937i		−	1.04577i
$404$	0.620959	−	1.46513i	0.0308938	−	0.0728929i
$405$	−0.522115	+	1.77816i	−0.0259441	+	0.0883575i
$406$	−1.80923	−	3.20761i	−0.0897907	−	0.159191i
$407$	−5.78315	+	6.67411i	−0.286660	+	0.330823i
$408$	10.4539	−	4.99685i	0.517545	−	0.247381i
$409$	34.9425	+	1.66451i	1.72779	+	0.0823050i	0.887782	−	0.460264i	$-0.152245\pi$
$409$	34.9425	+	1.66451i	1.72779	+	0.0823050i	0.840011	+	0.542569i	$0.182548\pi$
$410$	−10.5880	−	6.95564i	−0.522903	−	0.343514i
$411$	−5.63363	+	8.76609i	−0.277886	+	0.432399i
$412$	12.1647	+	24.8065i	0.599309	+	1.22213i
$413$	−1.14001	+	5.91493i	−0.0560962	+	0.291055i
$414$	0.144866	−	0.0336081i	0.00711978	−	0.00165175i
$415$	−10.3457	−	4.14179i	−0.507850	−	0.203312i
$416$	23.0235	+	4.49930i	1.12882	+	0.220596i
$417$	7.56987	−	4.86486i	0.370698	−	0.238233i
$418$	0.523101	−	4.95229i	0.0255857	−	0.242224i
$419$	27.4026	−	19.5133i	1.33870	−	0.953287i	0.338781	−	0.940865i	$-0.389985\pi$
$419$	27.4026	−	19.5133i	1.33870	−	0.953287i	0.999923	−	0.0124213i	$-0.00395394\pi$
$420$	4.48082	−	3.05710i	0.218642	−	0.149171i
$421$	0.744063	+	15.6198i	0.0362634	+	0.761263i	0.941634	+	0.336640i	$0.109290\pi$
$421$	0.744063	+	15.6198i	0.0362634	+	0.761263i	−0.905370	+	0.424623i	$0.860407\pi$
$422$	−2.35861	+	11.6093i	−0.114815	+	0.565132i
$423$	0.247281	+	0.0855847i	0.0120232	+	0.00416127i
$424$	−11.4295	−	19.0205i	−0.555065	−	0.923715i
$425$	−4.64151	+	4.42567i	−0.225146	+	0.214677i
$426$	8.90599	−	7.56191i	0.431497	−	0.366376i
$427$	1.48952	−	0.214161i	0.0720829	−	0.0103640i
$428$	4.00747	−	4.03743i	0.193708	−	0.195156i
$429$	6.59076	−	5.71093i	0.318205	−	0.275726i
$430$	5.70912	+	11.3525i	0.275318	+	0.547467i
$431$	2.89354	−	1.67059i	0.139377	−	0.0804693i	−0.428690	−	0.903452i	$-0.641025\pi$
$431$	2.89354	−	1.67059i	0.139377	−	0.0804693i	0.568067	+	0.822982i	$0.307691\pi$
$432$	−3.04242	−	2.59686i	−0.146379	−	0.124941i
$433$	−12.7132	−	31.7561i	−0.610959	−	1.52610i	−0.834271	−	0.551354i	$-0.814111\pi$
$433$	−12.7132	−	31.7561i	−0.610959	−	1.52610i	0.223312	−	0.974747i	$-0.428313\pi$
$434$	9.76562	−	3.79628i	0.468765	−	0.182227i
$435$	−1.51102	+	2.93096i	−0.0724477	+	0.140529i
$436$	34.4444	−	7.62736i	1.64959	−	0.365284i
$437$	−0.127436	−	0.121510i	−0.00609607	−	0.00581259i
$438$	0.183669	−	3.18306i	0.00877603	−	0.152093i
$439$	5.03853	+	2.90900i	0.240476	+	0.138839i	0.615395	−	0.788219i	$-0.288996\pi$
$439$	5.03853	+	2.90900i	0.240476	+	0.138839i	−0.374920	+	0.927057i	$0.622330\pi$
$440$	−7.84347	+	7.74503i	−0.373923	+	0.369230i
$441$	3.81881	+	3.00314i	0.181848	+	0.143007i
$442$	−6.53691	−	23.1187i	−0.310929	−	1.09964i
$443$	5.76376	−	0.550373i	0.273845	−	0.0261490i	0.0427697	−	0.999085i	$-0.486382\pi$
$443$	5.76376	−	0.550373i	0.273845	−	0.0261490i	0.231075	+	0.972936i	$0.425776\pi$
$444$	5.62641	−	6.23576i	0.267018	−	0.295936i
$445$	24.1447	+	11.0265i	1.14457	+	0.522708i
$446$	21.3169	−	7.13904i	1.00938	−	0.338043i
$447$	5.47090	−	1.60640i	0.258765	−	0.0759802i
$448$	2.07038	+	11.5234i	0.0978161	+	0.544429i
$449$	−2.60843	−	10.7521i	−0.123100	−	0.507424i	−0.999659	−	0.0261290i	$-0.991682\pi$
$449$	−2.60843	−	10.7521i	−0.123100	−	0.507424i	0.876559	−	0.481294i	$-0.159833\pi$
$450$	2.04705	+	0.843455i	0.0964989	+	0.0397608i
$451$	0.966224	−	10.1188i	0.0454977	−	0.476474i
$452$	11.4474	+	3.02169i	0.538441	+	0.142128i
$453$	−12.0797	+	4.18081i	−0.567552	+	0.196432i
$454$	−8.83600	+	1.18002i	−0.414694	+	0.0553812i
$455$	−4.67234	−	10.2310i	−0.219043	−	0.479637i
$456$	−0.591948	+	4.69897i	−0.0277205	+	0.220049i
$457$	−1.66470	+	1.30913i	−0.0778712	+	0.0612386i	−0.656336	−	0.754469i	$-0.727895\pi$
$457$	−1.66470	+	1.30913i	−0.0778712	+	0.0612386i	0.578465	+	0.815708i	$0.303652\pi$
$458$	−6.49229	−	4.72206i	−0.303365	−	0.220648i
$459$	−0.965793	+	3.98105i	−0.0450794	+	0.185820i
$460$	0.0477124	+	0.386826i	0.00222460	+	0.0180359i
$461$	−5.05656	+	35.1692i	−0.235508	+	1.63799i	0.438117	+	0.898918i	$0.355645\pi$
$461$	−5.05656	+	35.1692i	−0.235508	+	1.63799i	−0.673625	+	0.739073i	$0.735264\pi$
$462$	3.84834	+	2.03311i	0.179041	+	0.0945889i
$463$	15.6236	−	3.01121i	0.726091	−	0.139943i	0.187205	−	0.982321i	$-0.440057\pi$
$463$	15.6236	−	3.01121i	0.726091	−	0.139943i	0.538887	+	0.842378i	$0.318845\pi$
$464$	−4.44121	−	5.56171i	−0.206178	−	0.258196i
$465$	−7.64216	−	5.44196i	−0.354397	−	0.252365i
$466$	16.5231	+	14.6103i	0.765417	+	0.676808i
$467$	2.38021	+	4.61697i	0.110143	+	0.213648i	0.937464	−	0.348081i	$-0.113167\pi$
$467$	2.38021	+	4.61697i	0.110143	+	0.213648i	−0.827321	+	0.561729i	$0.810136\pi$
$468$	−6.37596	+	5.30449i	−0.294729	+	0.245200i
$469$	10.7034	+	5.37945i	0.494235	+	0.248400i
$470$	−0.291142	+	0.620941i	−0.0134294	+	0.0286419i
$471$	7.12283	−	3.67207i	0.328203	−	0.169200i
$472$	−0.350536	+	11.6367i	−0.0161347	+	0.535621i
$473$	−5.91427	+	8.30543i	−0.271938	+	0.381884i
$474$	−6.80779	−	15.3119i	−0.312692	−	0.703299i
$475$	−0.496112	−	2.57407i	−0.0227632	−	0.118106i
$476$	9.57201	−	7.22129i	0.438732	−	0.330987i
$477$	7.76561	+	1.11653i	0.355563	+	0.0511223i
$478$	17.6207	−	11.0758i	0.805951	−	0.506595i
$479$	−15.6956	−	3.80770i	−0.717149	−	0.173978i	−0.139451	−	0.990229i	$-0.544534\pi$
$479$	−15.6956	−	3.80770i	−0.717149	−	0.173978i	−0.577698	+	0.816251i	$0.696049\pi$
$480$	7.60594	−	7.21473i	0.347162	−	0.329306i
$481$	−10.7653	−	13.6892i	−0.490855	−	0.624173i
$482$	−3.80999	+	3.56049i	−0.173540	+	0.162176i
$483$	0.139988	−	0.0639303i	0.00636966	−	0.00290893i
$484$	12.5456	+	3.95896i	0.570254	+	0.179953i
$485$	−8.67773	−	25.0727i	−0.394035	−	1.13849i
$486$	1.39127	−	0.253689i	0.0631094	−	0.0115076i
$487$	38.7935	+	3.70433i	1.75790	+	0.167859i	0.923576	−	0.383415i	$-0.125252\pi$
$487$	38.7935	+	3.70433i	1.75790	+	0.167859i	0.834324	+	0.551274i	$0.185858\pi$
$488$	2.77578	−	0.868041i	0.125654	−	0.0392944i
$489$	−15.4807	+	3.75558i	−0.700062	+	0.169833i
$490$	−8.87862	+	9.12641i	−0.401095	+	0.412289i
$491$	6.99656	+	23.8281i	0.315750	+	1.07535i	0.952566	+	0.304331i	$0.0984328\pi$
$491$	6.99656	+	23.8281i	0.315750	+	1.07535i	−0.636816	+	0.771016i	$0.719749\pi$
$492$	−1.11194	+	9.60312i	−0.0501301	+	0.432942i
$493$	−3.02801	+	6.63042i	−0.136375	+	0.298619i
$494$	9.39427	+	2.86114i	0.422668	+	0.128729i
$495$	−0.370453	−	3.87956i	−0.0166506	−	0.174373i
$496$	17.4607	−	10.2551i	0.784011	−	0.460468i
$497$	7.47376	−	9.50366i	0.335244	−	0.426297i
$498$	0.723343	+	8.47321i	0.0324138	+	0.379694i
$499$	−17.1092	+	29.6340i	−0.765912	+	1.32660i	0.173851	+	0.984772i	$0.444379\pi$
$499$	−17.1092	+	29.6340i	−0.765912	+	1.32660i	−0.939763	+	0.341826i	$0.888955\pi$
$500$	−11.5829	+	21.4015i	−0.518002	+	0.957105i
$501$	3.86194	−	4.05028i	0.172539	−	0.180953i
$502$	−1.57222	+	1.21106i	−0.0701716	+	0.0540524i
$503$	−25.0431	−	12.9106i	−1.11661	−	0.575655i	−0.201759	−	0.979435i	$-0.564666\pi$
$503$	−25.0431	−	12.9106i	−1.11661	−	0.575655i	−0.914856	+	0.403780i	$0.867696\pi$
$504$	−3.62044	−	2.00669i	−0.161267	−	0.0893850i
$505$	−1.36889	+	0.548020i	−0.0609147	+	0.0243865i
$506$	−0.256553	+	0.178837i	−0.0114052	+	0.00795027i
$507$	2.09880	+	3.63523i	0.0932111	+	0.161446i
$508$	15.9185	−	0.438245i	0.706268	−	0.0194440i
$509$	18.0691	+	20.8528i	0.800898	+	0.924286i	0.998430	−	0.0560106i	$-0.0178381\pi$
$509$	18.0691	+	20.8528i	0.800898	+	0.924286i	−0.197532	+	0.980296i	$0.563293\pi$
$510$	−10.1102	−	3.61321i	−0.447686	−	0.159996i
$511$	−0.469560	−	3.26586i	−0.0207721	−	0.144473i
$512$	7.50447	+	21.3467i	0.331654	+	0.943401i
$513$	−1.15551	−	1.21187i	−0.0510172	−	0.0535053i
$514$	0.0879734	−	0.571111i	0.00388034	−	0.0251906i
$515$	8.37331	−	24.1931i	0.368972	−	1.06608i
$516$	5.78224	−	7.78442i	0.254549	−	0.342690i
$517$	−0.549655	+	0.0261833i	−0.0241738	+	0.00115154i
$518$	4.42110	−	7.48307i	0.194252	−	0.328787i
$519$	−5.64417	−	7.92613i	−0.247752	−	0.347919i
$520$	−12.0701	−	18.0784i	−0.529308	−	0.792791i
$521$	−3.65153	−	5.68190i	−0.159977	−	0.248928i	0.752007	−	0.659155i	$-0.229086\pi$
$521$	−3.65153	−	5.68190i	−0.159977	−	0.248928i	−0.911984	+	0.410227i	$0.865450\pi$
$522$	2.51624	+	0.0252592i	0.110133	+	0.00110556i
$523$	5.91771	−	14.7817i	0.258763	−	0.646360i	−0.740918	−	0.671595i	$-0.765609\pi$
$523$	5.91771	−	14.7817i	0.258763	−	0.646360i	0.999682	+	0.0252357i	$0.00803361\pi$
$524$	0.744213	−	3.48349i	0.0325111	−	0.152177i
$525$	2.24975	+	0.433603i	0.0981869	+	0.0189240i
$526$	−7.99094	+	9.95403i	−0.348422	+	0.434016i
$527$	−17.4461	−	11.2119i	−0.759964	−	0.488399i
$528$	7.96933	+	2.69192i	0.346821	+	0.117151i
$529$	1.09386	−	22.9629i	0.0475590	−	0.998387i
$530$	−5.04799	+	19.9326i	−0.219271	+	0.865818i
$531$	−3.11070	−	2.69544i	−0.134993	−	0.116972i
$532$	0.367843	+	4.88730i	0.0159480	+	0.211891i
$533$	19.2331	+	5.64736i	0.833080	+	0.244614i
$534$	−0.760653	−	20.2412i	−0.0329167	−	0.875922i
$535$	−5.27118			−0.227893
$536$	22.0801	+	6.96192i	0.953716	+	0.300709i
$537$	12.3667			0.533664
$538$	−1.60296	−	42.6553i	−0.0691086	−	1.83900i
$539$	−9.80260	−	2.87830i	−0.422228	−	0.123977i
$540$	0.278181	+	3.69600i	0.0119710	+	0.159051i
$541$	−13.4972	−	11.6954i	−0.580290	−	0.502825i	0.314532	−	0.949247i	$-0.398152\pi$
$541$	−13.4972	−	11.6954i	−0.580290	−	0.502825i	−0.894822	+	0.446422i	$0.852698\pi$
$542$	−8.60338	+	33.9715i	−0.369547	+	1.45920i
$543$	−0.610062	+	12.8068i	−0.0261803	+	0.549592i
$544$	16.0349	−	16.7299i	0.687491	−	0.717290i
$545$	−27.5005	−	17.6735i	−1.17799	−	0.757048i
$546$	−5.37310	+	6.69308i	−0.229947	+	0.286437i
$547$	15.1449	+	2.91895i	0.647551	+	0.124805i	0.502442	−	0.864611i	$-0.332435\pi$
$547$	15.1449	+	2.91895i	0.647551	+	0.124805i	0.145108	+	0.989416i	$0.453647\pi$
$548$	−4.35412	+	20.3806i	−0.185999	+	0.870617i
$549$	−0.382163	+	0.954598i	−0.0163103	+	0.0407412i
$550$	−4.65566	−	0.0467356i	−0.198518	−	0.00199281i
$551$	−1.61081	−	2.50647i	−0.0686229	−	0.106779i
$552$	0.247362	−	0.165151i	0.0105284	−	0.00702931i
$553$	−10.0587	−	14.1255i	−0.427741	−	0.600678i
$554$	−10.0860	+	17.0714i	−0.428514	+	0.725295i
$555$	−7.77371	+	0.370308i	−0.329976	+	0.0157187i
$556$	10.7313	−	14.4471i	0.455107	−	0.612694i
$557$	−13.3659	+	38.6184i	−0.566333	+	1.63631i	0.189746	+	0.981833i	$0.439234\pi$
$557$	−13.3659	+	38.6184i	−0.566333	+	1.63631i	−0.756079	+	0.654480i	$0.772888\pi$
$558$	−1.08996	+	7.07585i	−0.0461415	+	0.299544i
$559$	−13.8752	−	14.5519i	−0.586859	−	0.615480i
$560$	6.22688	−	8.88372i	0.263134	−	0.375406i
$561$	−1.22600	−	8.52700i	−0.0517617	−	0.360010i
$562$	−16.5004	−	5.89697i	−0.696028	−	0.248749i
$563$	−18.9490	−	21.8683i	−0.798606	−	0.921640i	0.199698	−	0.979857i	$-0.436004\pi$
$563$	−18.9490	−	21.8683i	−0.798606	−	0.921640i	−0.998304	+	0.0582173i	$0.981458\pi$
$564$	0.523147	−	0.0144026i	0.0220285	−	0.000606457i
$565$	−5.48533	−	9.50088i	−0.230770	−	0.399705i
$566$	−17.9812	+	12.5343i	−0.755806	+	0.526854i
$567$	1.35865	−	0.543923i	0.0570581	−	0.0228426i
$568$	11.3277	−	20.4372i	0.475299	−	0.857527i
$569$	12.9880	+	6.69579i	0.544486	+	0.280702i	0.708446	−	0.705765i	$-0.249396\pi$
$569$	12.9880	+	6.69579i	0.544486	+	0.280702i	−0.163960	+	0.986467i	$0.552427\pi$
$570$	3.47669	−	2.67805i	0.145622	−	0.112171i
$571$	−3.90217	+	4.09248i	−0.163301	+	0.171265i	−0.800301	−	0.599599i	$-0.795327\pi$
$571$	−3.90217	+	4.09248i	−0.163301	+	0.171265i	0.637000	+	0.770864i	$0.280175\pi$
$572$	8.30184	−	15.3392i	0.347117	−	0.641364i
$573$	7.71076	−	13.3554i	0.322122	−	0.557931i
$574$	0.850937	+	9.96786i	0.0355174	+	0.416050i
$575$	−0.101765	+	0.129405i	−0.00424391	+	0.00539657i
$576$	−7.52636	−	2.71181i	−0.313598	−	0.112992i
$577$	−4.11479	−	43.0920i	−0.171301	−	1.79395i	−0.517397	−	0.855746i	$-0.673099\pi$
$577$	−4.11479	−	43.0920i	−0.171301	−	1.79395i	0.346096	−	0.938199i	$-0.387507\pi$
$578$	0.295552	+	0.0900140i	0.0122933	+	0.00374409i
$579$	2.18228	−	4.77852i	0.0906924	−	0.198589i
$580$	−0.758569	+	6.55129i	−0.0314979	+	0.272027i
$581$	2.47934	+	8.44385i	0.102860	+	0.350310i
$582$	−14.1182	+	14.5122i	−0.585218	+	0.601551i
$583$	−16.0334	+	3.88965i	−0.664034	+	0.161093i
$584$	−1.90323	−	6.08606i	−0.0787563	−	0.251843i
$585$	7.65054	+	0.730538i	0.316311	+	0.0302040i
$586$	−32.4110	+	5.90992i	−1.33889	+	0.244136i
$587$	−7.83594	−	22.6405i	−0.323424	−	0.934472i	−0.983124	−	0.182943i	$-0.941438\pi$
$587$	−7.83594	−	22.6405i	−0.323424	−	0.934472i	0.659700	−	0.751529i	$-0.270683\pi$
$588$	9.26599	+	2.92403i	0.382123	+	0.120585i
$589$	7.71077	−	3.52139i	0.317717	−	0.145096i
$590$	7.88168	−	7.36555i	0.324484	−	0.303235i
$591$	−8.47945	−	10.7825i	−0.348798	−	0.443533i
$592$	6.12679	−	15.6406i	0.251809	−	0.642823i
$593$	−3.46612	−	0.840871i	−0.142336	−	0.0345304i	0.163958	−	0.986467i	$-0.447574\pi$
$593$	−3.46612	−	0.840871i	−0.142336	−	0.0345304i	−0.306294	+	0.951937i	$0.599089\pi$
$594$	−2.51789	+	1.58266i	−0.103310	+	0.0649375i
$595$	−10.9974	−	1.58119i	−0.450850	−	0.0648225i
$596$	9.10365	−	6.86795i	0.372900	−	0.281322i
$597$	2.80368	+	14.5469i	0.114747	+	0.595364i
$598$	−0.250549	−	0.563527i	−0.0102457	−	0.0230443i
$599$	−3.03978	+	4.26877i	−0.124202	+	0.174417i	−0.871995	−	0.489514i	$-0.837174\pi$
$599$	−3.03978	+	4.26877i	−0.124202	+	0.174417i	0.747793	+	0.663932i	$0.231113\pi$
$600$	4.42601	+	0.133327i	0.180691	+	0.00544304i
$601$	26.5918	−	13.7090i	1.08470	−	0.559203i	0.179316	−	0.983792i	$-0.442612\pi$
$601$	26.5918	−	13.7090i	1.08470	−	0.559203i	0.905386	+	0.424589i	$0.139581\pi$
$602$	4.26004	−	9.08571i	0.173626	−	0.370306i
$603$	−6.84011	+	4.49587i	−0.278551	+	0.183086i
$604$	−19.6532	+	16.3505i	−0.799678	+	0.665294i
$605$	−5.58578	−	10.8349i	−0.227094	−	0.440501i
$606$	0.842937	+	0.745354i	0.0342420	+	0.0302779i
$607$	15.9310	+	11.3444i	0.646620	+	0.460456i	0.855721	−	0.517438i	$-0.173114\pi$
$607$	15.9310	+	11.3444i	0.646620	+	0.460456i	−0.209101	+	0.977894i	$0.567054\pi$
$608$	2.20930	+	9.21096i	0.0895991	+	0.373554i
$609$	2.55699	−	0.492819i	0.103614	−	0.0199700i
$610$	−2.38282	−	1.25886i	−0.0964774	−	0.0509698i
$611$	0.154434	−	1.07411i	0.00624772	−	0.0434539i
$612$	1.00296	+	8.13143i	0.0405422	+	0.328694i
$613$	−1.40872	+	5.80680i	−0.0568975	+	0.234535i	−0.993159	−	0.116769i	$-0.962746\pi$
$613$	−1.40872	+	5.80680i	−0.0568975	+	0.234535i	0.936262	+	0.351304i	$0.114261\pi$
$614$	17.0220	+	12.3807i	0.686954	+	0.499645i
$615$	7.04134	−	5.53737i	0.283934	−	0.223288i
$616$	8.63652	+	1.08798i	0.347975	+	0.0438359i
$617$	6.43596	+	14.0928i	0.259102	+	0.567354i	0.993818	−	0.111021i	$-0.0354119\pi$
$617$	6.43596	+	14.0928i	0.259102	+	0.567354i	−0.734716	+	0.678375i	$0.762685\pi$
$618$	−19.3645	+	2.58607i	−0.778955	+	0.104027i
$619$	−4.40044	+	1.52301i	−0.176869	+	0.0612148i	−0.414067	−	0.910246i	$-0.635892\pi$
$619$	−4.40044	+	1.52301i	−0.176869	+	0.0612148i	0.237198	+	0.971461i	$0.423771\pi$
$620$	−18.1421	−	4.78884i	−0.728606	−	0.192324i
$621$	−0.00999574	+	0.104680i	−0.000401115	+	0.00420067i
$622$	−45.2953	−	18.6632i	−1.81618	−	0.748326i
$623$	−4.94180	−	20.3704i	−0.197989	−	0.816121i
$624$	−8.18678	+	14.4270i	−0.327734	+	0.577542i
$625$	14.1251	−	4.14749i	0.565002	−	0.165900i
$626$	−35.7880	+	11.9855i	−1.43038	+	0.479035i
$627$	3.20307	+	1.46279i	0.127918	+	0.0584182i
$628$	10.7367	−	11.8995i	0.428441	−	0.474842i
$629$	−17.1252	+	1.63526i	−0.682828	+	0.0652021i
$630$	1.04362	+	3.69089i	0.0415787	+	0.147049i
$631$	13.9897	+	11.0016i	0.556922	+	0.437968i	0.856532	−	0.516093i	$-0.172614\pi$
$631$	13.9897	+	11.0016i	0.556922	+	0.437968i	−0.299610	+	0.954062i	$0.596857\pi$
$632$	−23.5480	−	23.8473i	−0.936689	−	0.948594i
$633$	−7.25446	−	4.18836i	−0.288339	−	0.166472i
$634$	−0.358035	+	6.20491i	−0.0142194	+	0.246428i
$635$	−10.6793	−	10.1827i	−0.423796	−	0.404089i
$636$	15.3198	−	3.39242i	0.607471	−	0.134518i
$637$	9.23188	−	17.9073i	0.365780	−	0.709515i
$638$	−4.93217	+	1.91733i	−0.195267	+	0.0759078i
$639$	3.07043	+	7.66955i	0.121464	+	0.303403i
$640$	9.14000	−	18.8699i	0.361290	−	0.745896i
$641$	−10.6596	+	6.15431i	−0.421028	+	0.243081i	−0.695517	−	0.718510i	$-0.744825\pi$
$641$	−10.6596	+	6.15431i	−0.421028	+	0.243081i	0.274489	+	0.961590i	$0.411491\pi$
$642$	1.80722	+	3.59364i	0.0713254	+	0.141830i
$643$	−19.2188	+	16.6532i	−0.757914	+	0.656737i	−0.945541	−	0.325504i	$-0.894466\pi$
$643$	−19.2188	+	16.6532i	−0.757914	+	0.656737i	0.187626	+	0.982240i	$0.439921\pi$
$644$	0.216828	−	0.218449i	0.00854424	−	0.00860811i
$645$	−8.89391	+	1.27875i	−0.350197	+	0.0503508i
$646$	7.39477	−	6.27875i	0.290943	−	0.247034i
$647$	26.3654	−	25.1394i	1.03653	−	0.988330i	0.0365915	−	0.999330i	$-0.488350\pi$
$647$	26.3654	−	25.1394i	1.03653	−	0.988330i	0.999939	+	0.0110000i	$0.00350147\pi$
$648$	2.42439	−	1.45683i	0.0952390	−	0.0572295i
$649$	8.17968	+	2.83102i	0.321081	+	0.111127i
$650$	1.82802	−	8.99768i	0.0717008	−	0.352918i
$651$	0.352522	+	7.40035i	0.0138164	+	0.290043i
$652$	−26.3177	+	17.9556i	−1.03068	+	0.703196i
$653$	−11.6867	+	8.32206i	−0.457336	+	0.325667i	−0.785401	−	0.618988i	$-0.787543\pi$
$653$	−11.6867	+	8.32206i	−0.457336	+	0.325667i	0.328065	+	0.944655i	$0.393604\pi$
$654$	−2.62041	+	24.8079i	−0.102466	+	0.970065i
$655$	−2.77672	+	1.78449i	−0.108496	+	0.0697259i
$656$	4.69810	+	18.7551i	0.183430	+	0.732263i
$657$	2.09301	+	0.837916i	0.0816562	+	0.0326902i
$658$	0.527568	−	0.122393i	0.0205668	−	0.00477136i
$659$	−0.455966	+	2.36578i	−0.0177619	+	0.0921576i	−0.989728	−	0.142964i	$-0.954337\pi$
$659$	−0.455966	+	2.36578i	−0.0177619	+	0.0921576i	0.971966	+	0.235122i	$0.0755488\pi$
$660$	−3.43181	−	6.99825i	−0.133583	−	0.272406i
$661$	−14.8484	+	23.1046i	−0.577536	+	0.898663i	−0.999970	−	0.00773029i	$-0.997539\pi$
$661$	−14.8484	+	23.1046i	−0.577536	+	0.898663i	0.422434	+	0.906394i	$0.361176\pi$
$662$	−6.57610	−	4.32009i	−0.255587	−	0.167905i
$663$	16.9691	+	0.808336i	0.659024	+	0.0313932i
$664$	7.33483	+	15.3452i	0.284647	+	0.595508i
$665$	2.97402	−	3.43220i	0.115327	−	0.133095i
$666$	2.91768	+	5.17279i	0.113058	+	0.200442i
$667$	−0.0527147	+	0.179530i	−0.00204112	+	0.00695143i
$668$	4.36768	−	10.3054i	0.168991	−	0.398727i
$669$			15.8961i			0.614580i
$670$	−9.83475	−	19.0655i	−0.379950	−	0.736566i
$671$		−	2.16234i		−	0.0834762i
$672$	−8.19139	−	1.19941i	−0.315990	−	0.0462683i
$673$	8.99266	−	30.6262i	0.346642	−	1.18055i	−0.583119	−	0.812387i	$-0.698168\pi$
$673$	8.99266	−	30.6262i	0.346642	−	1.18055i	0.929760	−	0.368166i	$-0.120014\pi$
$674$	−22.3349	+	12.5978i	−0.860308	+	0.485250i
$675$	−1.02521	+	1.18316i	−0.0394604	+	0.0455397i
$676$	6.49357	+	5.32101i	0.249753	+	0.204654i
$677$	29.3905	+	1.40004i	1.12957	+	0.0538080i	0.604030	−	0.796961i	$-0.293561\pi$
$677$	29.3905	+	1.40004i	1.12957	+	0.0538080i	0.525539	+	0.850769i	$0.323864\pi$
$678$	−4.59660	+	6.99702i	−0.176532	+	0.268719i
$679$	−11.3276	+	17.6260i	−0.434712	+	0.676426i
$680$	−21.4696	+	0.375446i	−0.823321	+	0.0143977i
$681$	1.19294	−	6.18955i	0.0457135	−	0.237184i
$682$	−3.40242	−	14.6660i	−0.130285	−	0.561589i
$683$	26.4253	+	10.5791i	1.01114	+	0.404798i	0.817285	−	0.576233i	$-0.195478\pi$
$683$	26.4253	+	10.5791i	1.01114	+	0.404798i	0.193851	+	0.981031i	$0.437902\pi$
$684$	−3.01775	−	1.45207i	−0.115387	−	0.0555213i
$685$	16.2456	−	10.4404i	0.620712	−	0.398907i
$686$	24.4070	+	2.57806i	0.931862	+	0.0984308i
$687$	4.62403	−	3.29275i	0.176418	−	0.125626i
$688$	5.32518	−	18.6485i	0.203020	−	0.710969i
$689$	−1.54809	−	32.4983i	−0.0589774	−	1.23809i
$690$	−0.270083	−	0.0548715i	−0.0102819	−	0.00208892i
$691$	6.89620	+	2.38680i	0.262344	+	0.0907981i	0.455074	−	0.890454i	$-0.349613\pi$
$691$	6.89620	+	2.38680i	0.262344	+	0.0907981i	−0.192730	+	0.981252i	$0.561734\pi$
$692$	−16.1569	−	10.8478i	−0.614194	−	0.412372i
$693$	−2.22737	+	2.12379i	−0.0846107	+	0.0806761i
$694$	23.6840	+	27.8937i	0.899034	+	1.05883i
$695$	−16.5062	+	2.37323i	−0.626116	+	0.0900219i
$696$	4.72644	−	1.72895i	0.179155	−	0.0655358i
$697$	14.9647	−	12.9670i	0.566829	−	0.491160i
$698$	−18.9952	+	9.55259i	−0.718979	+	0.361571i
$699$	−13.5066	+	7.79802i	−0.510865	+	0.294948i
$700$	4.51599	−	0.776704i	0.170688	−	0.0293567i
$701$	−3.36136	−	8.39627i	−0.126957	−	0.317123i	0.851249	−	0.524763i	$-0.175846\pi$
$701$	−3.36136	−	8.39627i	−0.126957	−	0.317123i	−0.978205	+	0.207640i	$0.933422\pi$
$702$	−2.12494	−	5.46625i	−0.0802008	−	0.206310i
$703$	3.22217	−	6.25013i	0.121526	−	0.235728i
$704$	16.8131	−	0.588214i	0.633668	−	0.0221691i
$705$	−0.350967	−	0.334646i	−0.0132182	−	0.0126035i
$706$	28.5621	+	1.64809i	1.07495	+	0.0620267i
$707$	1.00841	+	0.582207i	0.0379252	+	0.0218961i
$708$	−7.72372	−	2.84808i	−0.290275	−	0.107037i
$709$	−3.92445	−	3.08623i	−0.147386	−	0.115906i	0.541743	−	0.840544i	$-0.317764\pi$
$709$	−3.92445	−	3.08623i	−0.147386	−	0.115906i	−0.689129	+	0.724638i	$0.742007\pi$
$710$	−20.8349	+	5.89118i	−0.781921	+	0.221092i
$711$	11.7954	−	1.12632i	0.442362	−	0.0422405i
$712$	−15.7117	−	37.3401i	−0.588820	−	1.39938i
$713$	−0.484236	−	0.221143i	−0.0181348	−	0.00828187i
$714$	2.69249	+	8.03964i	0.100764	+	0.300876i
$715$	−15.5070	+	4.55328i	−0.579930	+	0.170283i
$716$	23.1417	−	8.72969i	0.864844	−	0.326244i
$717$	3.46959	+	14.3018i	0.129574	+	0.534112i
$718$	−8.00673	+	19.4322i	−0.298808	+	0.725204i
$719$	1.33001	−	13.9285i	0.0496012	−	0.519447i	−0.936193	−	0.351487i	$-0.885676\pi$
$719$	1.33001	−	13.9285i	0.0496012	−	0.519447i	0.985794	−	0.167960i	$-0.0537179\pi$
$720$	3.12957	+	6.71991i	0.116632	+	0.250436i
$721$	−19.1052	+	6.61237i	−0.711514	+	0.246257i
$722$	−3.03196	−	22.7033i	−0.112838	−	0.844928i
$723$	−1.53178	−	3.35413i	−0.0569676	−	0.124742i
$724$	7.89873	+	24.3958i	0.293554	+	0.906662i
$725$	−2.18966	+	1.72196i	−0.0813218	+	0.0639522i
$726$	−5.47164	+	7.52287i	−0.203072	+	0.279200i
$727$	−2.92988	+	12.0771i	−0.108663	+	0.447917i	−0.999985	−	0.00545469i	$-0.998264\pi$
$727$	−2.92988	+	12.0771i	−0.108663	+	0.447917i	0.891322	+	0.453371i	$0.149779\pi$
$728$	−5.32994	+	16.3175i	−0.197541	+	0.604768i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−2.76013	+	5.22447i	−0.102157	+	0.193366i
$731$	−19.5030	+	3.75890i	−0.721346	+	0.139028i
$732$	−0.0412841	+	2.05609i	−0.00152590	+	0.0759954i
$733$	31.5439	+	22.4623i	1.16510	+	0.829665i	0.987989	−	0.154526i	$-0.0493849\pi$
$733$	31.5439	+	22.4623i	1.16510	+	0.829665i	0.177113	+	0.984191i	$0.443324\pi$
$734$	−22.3147	+	25.2362i	−0.823652	+	0.931486i
$735$	−4.12558	−	8.00251i	−0.152174	−	0.295177i
$736$	0.346303	−	0.483658i	0.0127649	−	0.0178279i
$737$	9.83999	−	14.1233i	0.362461	−	0.520239i
$738$	−6.18925	−	2.90197i	−0.227829	−	0.106823i
$739$	−18.3002	+	9.43439i	−0.673182	+	0.347050i	−0.760691	−	0.649114i	$-0.775140\pi$
$739$	−18.3002	+	9.43439i	−0.673182	+	0.347050i	0.0875086	+	0.996164i	$0.472109\pi$
$740$	−14.2854	+	6.18043i	−0.525143	+	0.227197i
$741$	−4.02792	+	5.65642i	−0.147969	+	0.207794i
$742$	14.8372	−	6.59676i	0.544692	−	0.242175i
$743$	8.39060	+	43.5346i	0.307821	+	1.59713i	0.725294	+	0.688440i	$0.241704\pi$
$743$	8.39060	+	43.5346i	0.307821	+	1.59713i	−0.417472	+	0.908690i	$0.637084\pi$
$744$	2.95523	+	14.0103i	0.108344	+	0.513643i
$745$	−10.4593	−	1.50382i	−0.383200	−	0.0550958i
$746$	−11.4069	−	18.1475i	−0.417637	−	0.664427i
$747$	−5.84375	−	1.41768i	−0.213812	−	0.0518702i
$748$	−8.31341	−	15.0910i	−0.303969	−	0.551782i
$749$	2.57317	+	3.27205i	0.0940214	+	0.119558i
$750$	−11.7488	−	12.5721i	−0.429007	−	0.459069i
$751$	−45.0574	+	20.5770i	−1.64417	+	0.750867i	−0.999903	−	0.0139354i	$-0.995564\pi$
$751$	−45.0574	+	20.5770i	−1.64417	+	0.750867i	−0.644265	+	0.764802i	$0.722837\pi$
$752$	0.968790	−	0.396241i	0.0353281	−	0.0144494i
$753$	−0.458977	−	1.32613i	−0.0167261	−	0.0483268i
$754$	−1.87195	−	10.2661i	−0.0681725	−	0.373870i
$755$	23.5820	+	2.25181i	0.858237	+	0.0819517i
$756$	2.15847	−	1.97691i	0.0785029	−	0.0718996i
$757$	−32.4971	+	7.88370i	−1.18113	+	0.286538i	−0.777796	−	0.628517i	$-0.783662\pi$
$757$	−32.4971	+	7.88370i	−1.18113	+	0.286538i	−0.403330	+	0.915055i	$0.632147\pi$
$758$	−13.2976	−	12.9366i	−0.482991	−	0.469877i
$759$	−0.0623012	−	0.212178i	−0.00226139	−	0.00770158i
$760$	4.61542	−	7.46560i	0.167419	−	0.270806i
$761$	−12.5157	+	27.4056i	−0.453694	+	0.993452i	0.535185	+	0.844735i	$0.320242\pi$
$761$	−12.5157	+	27.4056i	−0.453694	+	0.993452i	−0.988880	+	0.148717i	$0.952486\pi$
$762$	−3.28069	+	10.7718i	−0.118847	+	0.390221i
$763$	2.45388	+	25.6982i	0.0888363	+	0.930336i
$764$	5.00141	−	30.4348i	0.180945	−	1.10109i
$765$	4.69294	−	5.96756i	0.169674	−	0.215758i
$766$	28.1602	−	2.40398i	1.01747	−	0.0868594i
$767$	−8.53463	+	14.7824i	−0.308168	+	0.533762i
$768$	−15.9982	+	0.238310i	−0.577286	+	0.00859927i
$769$	37.2048	−	39.0192i	1.34164	−	1.40707i	0.501025	−	0.865433i	$-0.332956\pi$
$769$	37.2048	−	39.0192i	1.34164	−	1.40707i	0.840613	−	0.541636i	$-0.182195\pi$
$770$	−4.92216	−	6.39002i	−0.177382	−	0.230280i
$771$	0.363178	+	0.187231i	0.0130795	+	0.00674296i
$772$	0.710496	−	10.4824i	0.0255713	−	0.377271i
$773$	12.4794	−	4.99599i	0.448852	−	0.179693i	−0.136213	−	0.990680i	$-0.543493\pi$
$773$	12.4794	−	4.99599i	0.448852	−	0.179693i	0.585065	+	0.810986i	$0.301069\pi$
$774$	3.92107	+	5.62503i	0.140940	+	0.202187i
$775$	−3.96269	−	6.86358i	−0.142344	−	0.246547i
$776$	−16.1750	+	37.1226i	−0.580647	+	1.33262i
$777$	4.02466	+	4.64471i	0.144384	+	0.166628i
$778$	8.12685	−	22.7398i	0.291362	−	0.815263i
$779$	1.15186	+	8.01139i	0.0412698	+	0.287038i
$780$	14.8320	−	4.03348i	0.531072	−	0.144422i
$781$	−11.9887	−	12.5734i	−0.428990	−	0.449912i
$782$	−0.602107	−	0.0927481i	−0.0215313	−	0.00331666i
$783$	−0.581966	+	1.68148i	−0.0207978	+	0.0600912i
$784$	19.4034	−	1.06919i	0.692978	−	0.0381852i
$785$	−14.8343	+	0.706646i	−0.529460	+	0.0252213i
$786$	2.16858	+	1.28123i	0.0773508	+	0.0456998i
$787$	−4.73124	−	6.64409i	−0.168650	−	0.236836i	0.721597	−	0.692313i	$-0.243408\pi$
$787$	−4.73124	−	6.64409i	−0.168650	−	0.236836i	−0.890248	+	0.455477i	$0.849469\pi$
$788$	−23.4788	−	14.1915i	−0.836399	−	0.505550i
$789$	−4.87983	−	7.59317i	−0.173727	−	0.270324i
$790$	−0.311726	+	31.0532i	−0.0110907	+	1.10482i
$791$	−3.21989	+	8.04291i	−0.114486	+	0.285973i
$792$	−3.59448	+	4.73899i	−0.127724	+	0.168393i
$793$	4.18711	+	0.806999i	0.148689	+	0.0286574i
$794$	−30.9615	−	24.8555i	−1.09878	−	0.882087i
$795$	−12.2314	−	7.86062i	−0.433802	−	0.278788i
$796$	15.5151	+	25.2422i	0.549919	+	0.894686i
$797$	1.33272	−	27.9772i	0.0472073	−	0.991003i	−0.843699	−	0.536816i	$-0.819627\pi$
$797$	1.33272	−	27.9772i	0.0472073	−	0.991003i	0.890906	−	0.454187i	$-0.150070\pi$
$798$	−3.35955	−	0.850815i	−0.118927	−	0.0301185i
$799$	−0.810125	−	0.701977i	−0.0286602	−	0.0248342i
$800$	8.37644	−	2.87484i	0.296152	−	0.101641i
$801$	13.7426	+	4.03520i	0.485571	+	0.142577i
$802$	−31.3138	+	1.17676i	−1.10573	+	0.0415527i
$803$	−4.74106			−0.167308
$804$	−9.62615	+	13.2415i	−0.339488	+	0.466992i
$805$	−0.285203			−0.0100521
$806$	29.6687	−	1.11493i	1.04503	−	0.0392718i
$807$	28.9605	+	8.50357i	1.01946	+	0.299340i
$808$	2.10352	+	0.799739i	0.0740016	+	0.0281347i
$809$	−25.3717	−	21.9847i	−0.892020	−	0.772940i	0.0826521	−	0.996578i	$-0.473661\pi$
$809$	−25.3717	−	21.9847i	−0.892020	−	0.772940i	−0.974672	+	0.223639i	$0.928206\pi$
$810$	−2.54065	−	0.643427i	−0.0892695	−	0.0226077i
$811$	1.83777	−	38.5795i	0.0645328	−	1.35471i	−0.701849	−	0.712325i	$-0.747642\pi$
$811$	1.83777	−	38.5795i	0.0645328	−	1.35471i	0.766382	−	0.642385i	$-0.222055\pi$
$812$	4.43697	−	2.72718i	0.155707	−	0.0957054i
$813$	−20.8462	−	13.3970i	−0.731107	−	0.469854i
$814$	−9.73909	−	7.81839i	−0.341355	−	0.274034i
$815$	28.9880	+	5.58697i	1.01540	+	0.195703i
$816$	7.61681	+	14.5082i	0.266642	+	0.507890i
$817$	3.01739	−	7.53708i	0.105565	−	0.263689i
$818$	−0.496598	+	49.4696i	−0.0173632	+	1.72967i
$819$	−3.28119	−	5.10564i	−0.114654	−	0.178405i
$820$	9.26751	−	15.3325i	0.323636	−	0.535434i
$821$	−13.1399	−	18.4524i	−0.458587	−	0.643995i	0.518939	−	0.854811i	$-0.326327\pi$
$821$	−13.1399	−	18.4524i	−0.458587	−	0.643995i	−0.977526	+	0.210816i	$0.932388\pi$
$822$	−12.6876	−	7.49598i	−0.442530	−	0.261452i
$823$	−13.2907	+	0.633113i	−0.463284	+	0.0220689i	−0.277927	−	0.960602i	$-0.589647\pi$
$823$	−13.2907	+	0.633113i	−0.463284	+	0.0220689i	−0.185357	+	0.982671i	$0.559344\pi$
$824$	−34.4110	+	18.5087i	−1.19876	+	0.644781i
$825$	1.07678	−	3.11115i	0.0374886	−	0.108316i
$826$	−8.41962	−	1.29695i	−0.292956	−	0.0451267i
$827$	20.0592	+	21.0375i	0.697527	+	0.731545i	0.973264	−	0.229688i	$-0.0737706\pi$
$827$	20.0592	+	21.0375i	0.697527	+	0.731545i	−0.275738	+	0.961233i	$0.588922\pi$
$828$	0.0551890	+	0.202942i	0.00191795	+	0.00705273i
$829$	2.94616	+	20.4910i	0.102324	+	0.711681i	0.974809	+	0.223040i	$0.0715981\pi$
$829$	2.94616	+	20.4910i	0.102324	+	0.711681i	−0.872485	+	0.488641i	$0.837493\pi$
$830$	5.30380	−	14.8406i	0.184098	−	0.515126i
$831$	−9.18162	−	10.5962i	−0.318507	−	0.367576i
$832$	−5.13576	+	32.7761i	−0.178050	+	1.13631i
$833$	−9.95088	−	17.2354i	−0.344778	−	0.597172i
$834$	7.27712	+	10.4395i	0.251986	+	0.361490i
$835$	−9.62843	+	3.85464i	−0.333206	+	0.133395i
$836$	7.02643	+	0.476249i	0.243014	+	0.0164714i
$837$	−4.49963	−	2.31972i	−0.155530	−	0.0801813i
$838$	29.0318	+	37.6895i	1.00289	+	1.30196i
$839$	−35.5628	+	37.2972i	−1.22776	+	1.28764i	−0.283299	+	0.959032i	$0.591429\pi$
$839$	−35.5628	+	37.2972i	−1.22776	+	1.28764i	−0.944466	+	0.328610i	$0.893420\pi$
$840$	4.55831	+	6.17002i	0.157277	+	0.212886i
$841$	12.9170	−	22.3728i	0.445413	−	0.771478i
$842$	−22.0346	+	1.88106i	−0.759364	+	0.0648255i
$843$	7.65916	−	9.73941i	0.263795	−	0.335443i
$844$	−16.5317	−	2.71668i	−0.569045	−	0.0935121i
$845$	−0.739453	−	7.74390i	−0.0254380	−	0.266398i
$846$	−0.107817	+	0.354006i	−0.00370683	+	0.0121710i
$847$	−3.99895	+	8.75647i	−0.137405	+	0.300876i
$848$	26.2730	−	17.1625i	0.902220	−	0.589362i
$849$	−4.36654	−	14.8711i	−0.149859	−	0.510374i
$850$	−6.50093	−	6.32442i	−0.222980	−	0.216926i
$851$	−0.429150	+	0.104111i	−0.0147111	+	0.00356887i
$852$	11.1596	+	12.1845i	0.382321	+	0.417434i
$853$	15.5494	+	1.48479i	0.532403	+	0.0508383i	0.357796	−	0.933800i	$-0.383528\pi$
$853$	15.5494	+	1.48479i	0.532403	+	0.0508383i	0.174607	+	0.984638i	$0.444134\pi$
$854$	0.381760	+	2.09364i	0.0130636	+	0.0716429i
$855$	1.01495	+	2.93250i	0.0347105	+	0.100289i
$856$	5.91859	+	5.44900i	0.202293	+	0.186243i
$857$	44.1780	−	20.1754i	1.50909	−	0.689179i	0.522537	−	0.852617i	$-0.324986\pi$
$857$	44.1780	−	20.1754i	1.50909	−	0.689179i	0.986554	+	0.163438i	$0.0522584\pi$
$858$	8.42080	+	9.01088i	0.287481	+	0.307626i
$859$	15.0444	+	19.1306i	0.513310	+	0.652726i	0.971754	−	0.235997i	$-0.0758355\pi$
$859$	15.0444	+	19.1306i	0.513310	+	0.652726i	−0.458444	+	0.888723i	$0.651593\pi$
$860$	−15.7404	+	8.67113i	−0.536742	+	0.295683i
$861$	−6.87457	−	1.66775i	−0.234285	−	0.0568369i
$862$	2.51457	+	4.00048i	0.0856465	+	0.136257i
$863$	−35.1303	−	5.05098i	−1.19585	−	0.171937i	−0.484511	−	0.874785i	$-0.661002\pi$
$863$	−35.1303	−	5.05098i	−1.19585	−	0.171937i	−0.711340	+	0.702848i	$0.751911\pi$
$864$	3.50834	−	4.43751i	0.119356	−	0.150967i
$865$	3.41270	+	17.7068i	0.116035	+	0.602048i
$866$	44.2031	−	19.6530i	1.50208	−	0.667837i
$867$	−0.126722	+	0.177956i	−0.00430369	+	0.00604369i
$868$	5.88359	+	13.5993i	0.199702	+	0.461591i
$869$	−22.1477	+	11.4179i	−0.751310	+	0.387327i
$870$	−4.22233	−	1.97973i	−0.143150	−	0.0671193i
$871$	23.6757	+	24.3249i	0.802222	+	0.824217i
$872$	12.6084	+	48.2723i	0.426974	+	1.63471i
$873$	−6.56023	−	12.7251i	−0.222030	−	0.430679i
$874$	0.164951	−	0.186547i	0.00557957	−	0.00631005i
$875$	−14.5051	−	10.3290i	−0.490361	−	0.349185i
$876$	4.50811	+	0.0905179i	0.152315	+	0.00305832i
$877$	−26.5945	+	5.12566i	−0.898031	+	0.173081i	−0.617321	−	0.786711i	$-0.711782\pi$
$877$	−26.5945	+	5.12566i	−0.898031	+	0.173081i	−0.280710	+	0.959793i	$0.590570\pi$
$878$	−3.84345	+	7.27502i	−0.129710	+	0.245520i
$879$	3.31535	−	23.0588i	0.111824	−	0.777754i
$880$	−11.3620	−	10.6732i	−0.383011	−	0.359793i
$881$	2.12267	−	8.74977i	0.0715146	−	0.294787i	−0.924812	−	0.380425i	$-0.875778\pi$
$881$	2.12267	−	8.74977i	0.0715146	−	0.294787i	0.996326	+	0.0856380i	$0.0272928\pi$
$882$	−4.04128	+	5.55629i	−0.136077	+	0.187090i
$883$	−26.0385	+	20.4769i	−0.876265	+	0.689103i	−0.951363	−	0.308074i	$-0.900316\pi$
$883$	−26.0385	+	20.4769i	−0.876265	+	0.689103i	0.0750973	+	0.997176i	$0.476073\pi$
$884$	32.3245	−	10.4659i	1.08719	−	0.352005i
$885$	3.16878	+	6.93866i	0.106517	+	0.233240i
$886$	1.08390	+	8.11621i	0.0364142	+	0.272669i
$887$	7.83233	−	2.71079i	0.262984	−	0.0910196i	−0.192394	−	0.981318i	$-0.561625\pi$
$887$	7.83233	−	2.71079i	0.262984	−	0.0910196i	0.455378	+	0.890298i	$0.349504\pi$
$888$	9.11128	+	7.62017i	0.305755	+	0.255716i
$889$	−1.10765	+	11.5999i	−0.0371495	+	0.389048i
$890$	−14.3006	+	34.7073i	−0.479357	+	1.16339i
$891$	−0.495783	−	2.04365i	−0.0166094	−	0.0684647i
$892$	11.2211	+	29.7462i	0.375710	+	0.995976i
$893$	0.420413	−	0.123444i	0.0140686	−	0.00413091i
$894$	2.56074	+	7.64625i	0.0856440	+	0.255729i
$895$	−20.8473	−	9.52064i	−0.696848	−	0.318240i
$896$	−16.1751	+	3.53787i	−0.540372	+	0.118192i
$897$	0.434109	−	0.0414523i	0.0144945	−	0.00138405i
$898$	15.0565	−	4.25730i	0.502443	−	0.142068i
$899$	−7.08055	−	5.56821i	−0.236150	−	0.185710i
$900$	−1.08327	+	2.93772i	−0.0361090	+	0.0979240i
$901$	−27.8333	−	16.0696i	−0.927263	−	0.535356i
$902$	14.3513	+	0.828098i	0.477846	+	0.0275726i
$903$	5.13540	+	4.89660i	0.170896	+	0.162949i
$904$	−3.66235	+	16.3382i	−0.121808	+	0.543399i
$905$	10.8878	−	21.1195i	0.361924	−	0.702035i
$906$	−6.54991	−	16.8491i	−0.217606	−	0.559775i
$907$	−4.48120	−	11.1935i	−0.148796	−	0.371674i	0.835180	−	0.549977i	$-0.185363\pi$
$907$	−4.48120	−	11.1935i	−0.148796	−	0.371674i	−0.983976	+	0.178303i	$0.942939\pi$
$908$	−2.13689	−	12.4245i	−0.0709151	−	0.412322i
$909$	−0.689047	+	0.397821i	−0.0228542	+	0.0131949i
$910$	14.2105	−	7.14637i	0.471072	−	0.236900i
$911$	−26.6996	+	23.1353i	−0.884598	+	0.766508i	−0.973297	−	0.229550i	$-0.926274\pi$
$911$	−26.6996	+	23.1353i	−0.884598	+	0.766508i	0.0886992	+	0.996058i	$0.471729\pi$
$912$	−6.67209	−	0.586999i	−0.220935	−	0.0194375i
$913$	12.5167	−	1.79963i	0.414243	−	0.0595592i
$914$	−1.93850	−	2.28305i	−0.0641197	−	0.0755166i
$915$	1.37914	−	1.31501i	0.0455930	−	0.0434728i
$916$	6.32851	−	9.42578i	0.209100	−	0.311437i
$917$	2.46319	+	0.852518i	0.0813417	+	0.0281526i
$918$	−5.67738	−	1.15345i	−0.187381	−	0.0380695i
$919$	−0.926683	−	19.4535i	−0.0305684	−	0.641711i	−0.961216	−	0.275795i	$-0.911059\pi$
$919$	−0.926683	−	19.4535i	−0.0305684	−	0.641711i	0.930648	−	0.365916i	$-0.119244\pi$
$920$	−0.544135	+	0.0879715i	−0.0179396	+	0.00290033i
$921$	−12.1237	+	8.63323i	−0.399489	+	0.284475i
$922$	−49.9702	−	5.27825i	−1.64568	−	0.173830i
$923$	28.8211	−	18.5222i	0.948659	−	0.609666i
$924$	−2.66885	+	5.54652i	−0.0877987	+	0.182467i
$925$	−6.10346	−	2.44346i	−0.200681	−	0.0803404i
$926$	5.08522	+	21.9196i	0.167111	+	0.720324i
$927$	2.61438	−	13.5647i	0.0858675	−	0.445523i
$928$	7.62403	−	6.57176i	0.250271	−	0.215729i
$929$	20.1626	−	31.3736i	0.661514	−	1.02934i	−0.334694	−	0.942327i	$-0.608633\pi$
$929$	20.1626	−	31.3736i	0.661514	−	1.02934i	0.996208	−	0.0870086i	$-0.0277308\pi$
$930$	7.28481	−	11.0890i	0.238878	−	0.363624i
$931$	8.12568	+	0.387074i	0.266308	+	0.0126858i
$932$	−19.7700	+	24.1266i	−0.647587	+	0.790293i
$933$	22.6849	−	26.1798i	0.742672	−	0.857089i
$934$	−6.39836	+	3.60895i	−0.209361	+	0.118088i
$935$	−4.49786	+	15.3183i	−0.147096	+	0.500962i
$936$	−7.83500	−	8.72890i	−0.256095	−	0.285313i
$937$			40.2877i			1.31614i	0.752955	+	0.658072i	$0.228628\pi$
$937$			40.2877i			1.31614i	−0.752955	+	0.658072i	$0.771372\pi$
$938$	−7.03389	+	15.4118i	−0.229665	+	0.503215i
$939$		−	26.6874i		−	0.870910i
$940$	−0.892986	−	0.378470i	−0.0291260	−	0.0123443i
$941$	6.55426	−	22.3217i	0.213663	−	0.727668i	−0.781004	−	0.624526i	$-0.785292\pi$
$941$	6.55426	−	22.3217i	0.213663	−	0.727668i	0.994667	−	0.103142i	$-0.0328896\pi$
$942$	5.56771	+	9.87108i	0.181406	+	0.321617i
$943$	0.332858	−	0.384138i	0.0108393	−	0.0125093i
$944$	−16.4637	+	0.122615i	−0.535849	+	0.00399079i
$945$	−2.70911	−	0.129051i	−0.0881272	−	0.00419802i
$946$	−12.0515	−	7.91705i	−0.391827	−	0.257406i
$947$	−11.8526	+	18.4429i	−0.385156	+	0.599315i	−0.978653	−	0.205522i	$-0.934111\pi$
$947$	−11.8526	+	18.4429i	−0.385156	+	0.599315i	0.593496	+	0.804837i	$0.297747\pi$
$948$	21.2775	−	10.4341i	0.691060	−	0.338883i
$949$	1.76939	−	9.18049i	0.0574370	−	0.298011i
$950$	3.61137	−	0.837816i	0.117168	−	0.0271824i
$951$	−4.08002	−	1.63339i	−0.132304	−	0.0529664i
$952$	10.7136	+	13.1438i	0.347230	+	0.425993i
$953$	41.6882	−	26.7914i	1.35041	−	0.867857i	0.352718	−	0.935730i	$-0.385257\pi$
$953$	41.6882	−	26.7914i	1.35041	−	0.867857i	0.997694	+	0.0678724i	$0.0216211\pi$
$954$	−1.16548	+	11.0338i	−0.0377337	+	0.357232i
$955$	−23.2803	+	16.5778i	−0.753332	+	0.536445i
$956$	16.5883	+	24.3136i	0.536503	+	0.786359i
$957$	−0.178043	−	3.73759i	−0.00575532	−	0.120819i
$958$	4.54755	−	22.3834i	0.146925	−	0.723176i
$959$	−14.4112	−	4.98777i	−0.465362	−	0.161063i
$960$	10.5999	+	10.3657i	0.342110	+	0.334551i
$961$	−3.88805	+	3.70725i	−0.125421	+	0.119589i
$962$	18.7740	−	15.9407i	0.605300	−	0.513948i
$963$	−2.81537	+	0.404789i	−0.0907240	+	0.0130441i
$964$	−5.23409	−	5.19525i	−0.168579	−	0.167328i
$965$	−7.35758	+	6.37538i	−0.236849	+	0.205231i
$966$	0.0977817	+	0.194438i	0.00314608	+	0.00625593i
$967$	11.1430	−	6.43339i	0.358334	−	0.206884i	−0.310016	−	0.950731i	$-0.600334\pi$
$967$	11.1430	−	6.43339i	0.358334	−	0.206884i	0.668350	+	0.743847i	$0.267001\pi$
$968$	−4.92859	+	17.9399i	−0.158411	+	0.576609i
$969$	2.54942	+	6.36813i	0.0818991	+	0.204574i
$970$	34.9722	−	13.5951i	1.12289	−	0.436511i
$971$	20.1399	−	39.0659i	0.646320	−	1.25369i	−0.306996	−	0.951711i	$-0.599324\pi$
$971$	20.1399	−	39.0659i	0.646320	−	1.25369i	0.953316	−	0.301975i	$-0.0976458\pi$
$972$	0.432405	+	1.95270i	0.0138694	+	0.0626328i
$973$	9.53080	+	9.08760i	0.305543	+	0.291335i
$974$	−3.17478	+	55.0203i	−0.101726	+	1.76296i
$975$	5.62249	+	3.24615i	0.180064	+	0.103960i
$976$	1.37414	+	3.87668i	0.0439853	+	0.124089i
$977$	17.6316	+	13.8656i	0.564085	+	0.443601i	0.859039	−	0.511910i	$-0.171062\pi$
$977$	17.6316	+	13.8656i	0.564085	+	0.443601i	−0.294954	+	0.955511i	$0.595304\pi$
$978$	−6.12959	−	21.6781i	−0.196003	−	0.693190i
$979$	−29.9834	+	2.86306i	−0.958273	+	0.0915039i
$980$	−13.3691	−	12.0627i	−0.427061	−	0.385329i
$981$	−16.0454	−	7.32767i	−0.512289	−	0.233955i
$982$	−33.3027	+	11.1531i	−1.06273	+	0.355910i
$983$	−35.2552	+	10.3519i	−1.12447	+	0.330173i	−0.790530	−	0.612423i	$-0.790195\pi$
$983$	−35.2552	+	10.3519i	−1.12447	+	0.330173i	−0.333936	+	0.942596i	$0.608377\pi$
$984$	−13.6303	−	1.06141i	−0.434519	−	0.0338365i
$985$	5.99328	+	24.7046i	0.190962	+	0.787156i
$986$	−9.53103	−	3.92711i	−0.303530	−	0.125065i
$987$	−0.0364021	+	0.381220i	−0.00115869	+	0.0121344i
$988$	−3.54451	+	13.4281i	−0.112766	+	0.427204i
$989$	−0.481808	+	0.166755i	−0.0153206	+	0.00530251i
$990$	5.46298	−	0.729565i	0.173625	−	0.0231871i
$991$	14.2843	+	31.2782i	0.453755	+	0.993584i	0.988867	+	0.148803i	$0.0475421\pi$
$991$	14.2843	+	31.2782i	0.453755	+	0.993584i	−0.535112	+	0.844781i	$0.679731\pi$
$992$	15.4200	+	24.1312i	0.489585	+	0.766166i
$993$	4.37332	−	3.43922i	0.138783	−	0.109140i
$994$	13.8276	+	10.0573i	0.438586	+	0.318999i
$995$	6.47272	−	26.6809i	0.205199	−	0.845842i
$996$	−11.9361	+	1.47223i	−0.378209	+	0.0466495i
$997$	−0.0982733	+	0.683506i	−0.00311235	+	0.0216468i	−0.991318	−	0.131483i	$-0.958026\pi$
$997$	−0.0982733	+	0.683506i	−0.00311235	+	0.0216468i	0.988206	+	0.153130i	$0.0489352\pi$
$998$	−42.7878	−	22.6052i	−1.35442	−	0.715554i
$999$	−4.12355	+	0.794750i	−0.130463	+	0.0251448i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.bf.a.7.17	✓	680
4.3	odd	2		804.2.bf.b.7.28	yes	680
67.48	odd	66		804.2.bf.b.115.28	yes	680
268.115	even	66	inner	804.2.bf.a.115.17	yes	680

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.bf.a.7.17	✓	680	1.1	even	1	trivial
804.2.bf.a.115.17	yes	680	268.115	even	66	inner
804.2.bf.b.7.28	yes	680	4.3	odd	2
804.2.bf.b.115.28	yes	680	67.48	odd	66

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.bf (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0531079 + 1.41322i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-1.99436 + 0.150106i) q^{4} +(1.40058 + 1.21361i) q^{5} +(0.347192 - 1.37093i) q^{6} +(0.0696355 - 1.46183i) q^{7} +(-0.318048 - 2.81049i) q^{8} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(0.0531079 + 1.41322i) q^{2} +(-0.959493 - 0.281733i) q^{3} +(-1.99436 + 0.150106i) q^{4} +(1.40058 + 1.21361i) q^{5} +(0.347192 - 1.37093i) q^{6} +(0.0696355 - 1.46183i) q^{7} +(-0.318048 - 2.81049i) q^{8} +(0.841254 + 0.540641i) q^{9} +(-1.64071 + 2.04377i) q^{10} +(-2.06492 - 0.397981i) q^{11} +(1.95586 + 0.417850i) q^{12} +(1.54128 - 3.84994i) q^{13} +(2.06958 + 0.0207754i) q^{14} +(-1.00193 - 1.55904i) q^{15} +(3.95494 - 0.598730i) q^{16} +(-2.37622 - 3.33693i) q^{17} +(-0.719365 + 1.21759i) q^{18} +(1.67257 - 0.0796743i) q^{19} +(-2.97542 - 2.21013i) q^{20} +(-0.478660 + 1.38300i) q^{21} +(0.452770 - 2.93932i) q^{22} +(-0.0725662 - 0.0761052i) q^{23} +(-0.486641 + 2.78625i) q^{24} +(-0.222800 - 1.54961i) q^{25} +(5.52265 + 1.97371i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(0.0805509 + 2.92587i) q^{28} +(-0.889671 - 1.54096i) q^{29} +(2.15004 - 1.49874i) q^{30} +(4.69976 - 1.88150i) q^{31} +(1.05617 + 5.55738i) q^{32} +(1.86915 + 0.963616i) q^{33} +(4.58961 - 3.53533i) q^{34} +(1.87162 - 1.96290i) q^{35} +(-1.75891 - 0.951955i) q^{36} +(2.09972 - 3.63682i) q^{37} +(0.201424 + 2.35947i) q^{38} +(-2.56351 + 3.25976i) q^{39} +(2.96538 - 4.32229i) q^{40} +(0.459467 + 4.81176i) q^{41} +(-1.97989 - 0.603002i) q^{42} +(2.01414 - 4.41034i) q^{43} +(4.17794 + 0.483760i) q^{44} +(0.522115 + 1.77816i) q^{45} +(0.103699 - 0.106593i) q^{46} +(0.254296 - 0.0616916i) q^{47} +(-3.96342 - 0.539757i) q^{48} +(4.83621 + 0.461802i) q^{49} +(2.17810 - 0.397160i) q^{50} +(1.33984 + 3.87122i) q^{51} +(-2.49598 + 7.90952i) q^{52} +(7.13649 - 3.25913i) q^{53} +(1.03326 - 0.965596i) q^{54} +(-2.40909 - 3.06341i) q^{55} +(-4.13060 + 0.269222i) q^{56} +(-1.62727 - 0.394770i) q^{57} +(2.13046 - 1.33913i) q^{58} +(-4.07415 - 0.585775i) q^{59} +(2.23223 + 2.95888i) q^{60} +(0.194598 + 1.00967i) q^{61} +(2.90856 + 6.54185i) q^{62} +(0.848906 - 1.19212i) q^{63} +(-7.79769 + 1.78774i) q^{64} +(6.83100 - 3.52163i) q^{65} +(-1.26253 + 2.69269i) q^{66} +(-3.32362 + 7.48021i) q^{67} +(5.23993 + 6.29836i) q^{68} +(0.0481854 + 0.0934667i) q^{69} +(2.87339 + 2.54075i) q^{70} +(6.72948 + 4.79204i) q^{71} +(1.25191 - 2.53628i) q^{72} +(2.21377 - 0.426669i) q^{73} +(5.25113 + 2.77422i) q^{74} +(-0.222800 + 1.54961i) q^{75} +(-3.32374 + 0.409962i) q^{76} +(-0.725573 + 2.99085i) q^{77} +(-4.74289 - 3.44967i) q^{78} +(9.31399 - 7.32460i) q^{79} +(6.26582 + 3.96117i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-6.77565 + 0.904868i) q^{82} +(-5.68253 + 1.96674i) q^{83} +(0.747024 - 2.83004i) q^{84} +(0.721647 - 7.55743i) q^{85} +(6.33973 + 2.61218i) q^{86} +(0.419496 + 1.72919i) q^{87} +(-0.461777 + 5.93002i) q^{88} +(13.7426 - 4.03520i) q^{89} +(-2.48520 + 0.832296i) q^{90} +(-5.52063 - 2.52119i) q^{91} +(0.156147 + 0.140889i) q^{92} +(-5.03947 + 0.481211i) q^{93} +(0.100689 + 0.356099i) q^{94} +(2.43926 + 1.91825i) q^{95} +(0.552305 - 5.62983i) q^{96} +(-12.3985 - 7.15828i) q^{97} +(-0.395785 + 6.85913i) q^{98} +(-1.52196 - 1.45118i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 680 q - 68 q^{3} + 2 q^{4} - 11 q^{6} + 4 q^{7} - 39 q^{8} - 68 q^{9}+O(q^{10}) \) 680 * q - 68 * q^3 + 2 * q^4 - 11 * q^6 + 4 * q^7 - 39 * q^8 - 68 * q^9	\( 680 q - 68 q^{3} + 2 q^{4} - 11 q^{6} + 4 q^{7} - 39 q^{8} - 68 q^{9} + 39 q^{10} - 9 q^{12} - 6 q^{13} - 10 q^{14} + 2 q^{16} + 12 q^{20} + 4 q^{21} + 33 q^{22} - 6 q^{24} + 68 q^{25} + 19 q^{26} - 68 q^{27} - 92 q^{28} + 8 q^{29} + 6 q^{30} + 2 q^{31} + 40 q^{32} - 9 q^{36} - 12 q^{37} - 4 q^{38} - 6 q^{39} + 37 q^{40} - 10 q^{42} - 4 q^{43} + 159 q^{44} - 93 q^{46} + 2 q^{48} + 46 q^{49} + 6 q^{50} - 28 q^{52} + 17 q^{56} - 66 q^{57} + 92 q^{58} - 98 q^{60} - 6 q^{61} + 34 q^{62} - 18 q^{63} - 49 q^{64} + 22 q^{66} - 18 q^{67} + 208 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} - 72 q^{73} - 11 q^{74} + 68 q^{75} + 162 q^{76} + 4 q^{77} + 19 q^{78} + 28 q^{79} - 41 q^{80} - 68 q^{81} - 84 q^{82} + 12 q^{83} + 7 q^{84} - 77 q^{86} + 8 q^{87} - 132 q^{88} + 39 q^{90} - 186 q^{92} + 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} - 18 q^{97} + 65 q^{98}+O(q^{100}) \) 680 * q - 68 * q^3 + 2 * q^4 - 11 * q^6 + 4 * q^7 - 39 * q^8 - 68 * q^9 + 39 * q^10 - 9 * q^12 - 6 * q^13 - 10 * q^14 + 2 * q^16 + 12 * q^20 + 4 * q^21 + 33 * q^22 - 6 * q^24 + 68 * q^25 + 19 * q^26 - 68 * q^27 - 92 * q^28 + 8 * q^29 + 6 * q^30 + 2 * q^31 + 40 * q^32 - 9 * q^36 - 12 * q^37 - 4 * q^38 - 6 * q^39 + 37 * q^40 - 10 * q^42 - 4 * q^43 + 159 * q^44 - 93 * q^46 + 2 * q^48 + 46 * q^49 + 6 * q^50 - 28 * q^52 + 17 * q^56 - 66 * q^57 + 92 * q^58 - 98 * q^60 - 6 * q^61 + 34 * q^62 - 18 * q^63 - 49 * q^64 + 22 * q^66 - 18 * q^67 + 208 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 - 72 * q^73 - 11 * q^74 + 68 * q^75 + 162 * q^76 + 4 * q^77 + 19 * q^78 + 28 * q^79 - 41 * q^80 - 68 * q^81 - 84 * q^82 + 12 * q^83 + 7 * q^84 - 77 * q^86 + 8 * q^87 - 132 * q^88 + 39 * q^90 - 186 * q^92 + 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 - 18 * q^97 + 65 * q^98

Introduction

L-functions

Modular forms

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