LMFDB - Embedded newform 399.2.bo.b.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [399,2,Mod(43,399)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(399, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("399.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 399 = 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	399.bo (of order $9$, degree $6$, 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:	$3.18603104065$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 18 x^{16} - 41 x^{15} + 177 x^{14} - 369 x^{13} + 1063 x^{12} - 1788 x^{11} + \cdots + 1 $ x^18 - 3x^17 + 18x^16 - 41x^15 + 177x^14 - 369x^13 + 1063x^12 - 1788x^11 + 4005x^10 - 5773x^9 + 9162x^8 - 8208x^7 + 7150x^6 - 2445x^5 + 1476x^4 - 120x^3 + 339x^2 + 18*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			169.2
Root			$0.358173 - 0.620373i$ of defining polynomial
Character	$\chi$	$=$	399.169
Dual form			399.2.bo.b.85.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.124392 + 0.705462i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(1.39718 + 0.508532i) q^{4} +(-0.780211 + 0.283974i) q^{5} +(0.548752 - 0.460458i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-1.24889 + 2.16315i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.103281 - 0.585733i) q^{10} +(-1.78098 + 3.08475i) q^{11} +(-0.743425 - 1.28765i) q^{12} +(0.608032 - 0.510199i) q^{13} +(-0.673144 + 0.245004i) q^{14} +(0.780211 + 0.283974i) q^{15} +(0.907319 + 0.761331i) q^{16} +(-0.0572261 + 0.324545i) q^{17} -0.716345 q^{18} +(3.95637 + 1.82951i) q^{19} -1.23451 q^{20} +(0.173648 - 0.984808i) q^{21} +(-1.95464 - 1.64014i) q^{22} +(3.33452 + 1.21367i) q^{23} +(2.34715 - 0.854294i) q^{24} +(-3.30213 + 2.77082i) q^{25} +(0.284292 + 0.492408i) q^{26} +(0.500000 - 0.866025i) q^{27} +(0.258189 + 1.46426i) q^{28} +(0.746560 + 4.23395i) q^{29} +(-0.297385 + 0.515085i) q^{30} +(-0.512645 - 0.887927i) q^{31} +(-4.47679 + 3.75647i) q^{32} +(3.34715 - 1.21826i) q^{33} +(-0.221836 - 0.0807417i) q^{34} +(-0.636034 - 0.533696i) q^{35} +(-0.258189 + 1.46426i) q^{36} +0.180743 q^{37} +(-1.78279 + 2.56349i) q^{38} -0.793729 q^{39} +(0.360124 - 2.04236i) q^{40} +(-1.39485 - 1.17042i) q^{41} +(0.673144 + 0.245004i) q^{42} +(2.89168 - 1.05249i) q^{43} +(-4.05705 + 3.40427i) q^{44} +(-0.415142 - 0.719046i) q^{45} +(-1.27098 + 2.20141i) q^{46} +(-0.317862 - 1.80269i) q^{47} +(-0.205672 - 1.16643i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-1.54395 - 2.67420i) q^{50} +(0.252451 - 0.211832i) q^{51} +(1.10898 - 0.403637i) q^{52} +(-5.35983 - 1.95082i) q^{53} +(0.548752 + 0.460458i) q^{54} +(0.513554 - 2.91251i) q^{55} -2.49779 q^{56} +(-1.85477 - 3.94460i) q^{57} -3.07976 q^{58} +(1.16966 - 6.63347i) q^{59} +(0.945686 + 0.793525i) q^{60} +(11.8818 + 4.32463i) q^{61} +(0.690168 - 0.251201i) q^{62} +(-0.766044 + 0.642788i) q^{63} +(-0.908751 - 1.57400i) q^{64} +(-0.329510 + 0.570728i) q^{65} +(0.443080 + 2.51283i) q^{66} +(-1.26660 - 7.18325i) q^{67} +(-0.244997 + 0.424347i) q^{68} +(-1.77426 - 3.07311i) q^{69} +(0.455620 - 0.382310i) q^{70} +(12.3340 - 4.48919i) q^{71} +(-2.34715 - 0.854294i) q^{72} +(-2.95316 - 2.47800i) q^{73} +(-0.0224830 + 0.127508i) q^{74} +4.31063 q^{75} +(4.59740 + 4.56811i) q^{76} -3.56197 q^{77} +(0.0987336 - 0.559946i) q^{78} +(-4.44302 - 3.72813i) q^{79} +(-0.924098 - 0.336344i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(0.999198 - 0.838426i) q^{82} +(-4.77855 - 8.27669i) q^{83} +(0.743425 - 1.28765i) q^{84} +(-0.0475139 - 0.269464i) q^{85} +(0.382787 + 2.17089i) q^{86} +(2.14963 - 3.72328i) q^{87} +(-4.44852 - 7.70506i) q^{88} +(0.984013 - 0.825685i) q^{89} +(0.558900 - 0.203423i) q^{90} +(0.745862 + 0.271471i) q^{91} +(4.04174 + 3.39142i) q^{92} +(-0.178040 + 1.00971i) q^{93} +1.31127 q^{94} +(-3.60634 - 0.303903i) q^{95} +5.84403 q^{96} +(1.42760 - 8.09632i) q^{97} +(-0.548752 - 0.460458i) q^{98} +(-3.34715 - 1.21826i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} + 3 q^{4} + 12 q^{5} + 3 q^{6} + 9 q^{7} - 6 q^{8} + 6 q^{10} + 12 q^{11} + 9 q^{12} - 6 q^{14} - 12 q^{15} + 27 q^{16} - 3 q^{17} - 6 q^{18} - 3 q^{19} + 3 q^{22} - 18 q^{23} - 21 q^{24}+ \cdots + 3 q^{99}+O(q^{100}) $ 18 * q - 3 * q^2 + 3 * q^4 + 12 * q^5 + 3 * q^6 + 9 * q^7 - 6 * q^8 + 6 * q^10 + 12 * q^11 + 9 * q^12 - 6 * q^14 - 12 * q^15 + 27 * q^16 - 3 * q^17 - 6 * q^18 - 3 * q^19 + 3 * q^22 - 18 * q^23 - 21 * q^24 - 6 * q^25 + 21 * q^26 + 9 * q^27 - 3 * q^28 - 15 * q^29 - 6 * q^30 - 27 * q^31 - 21 * q^32 - 3 * q^33 + 21 * q^34 + 6 * q^35 + 3 * q^36 - 60 * q^38 - 18 * q^39 + 24 * q^41 + 6 * q^42 + 3 * q^43 - 27 * q^44 + 3 * q^46 - 3 * q^47 - 9 * q^49 + 15 * q^50 + 12 * q^51 - 57 * q^52 + 45 * q^53 + 3 * q^54 - 12 * q^56 - 42 * q^58 + 45 * q^59 + 18 * q^60 - 30 * q^61 - 27 * q^62 + 24 * q^64 - 48 * q^65 - 12 * q^66 - 66 * q^67 + 18 * q^68 - 21 * q^69 - 6 * q^70 - 12 * q^71 + 21 * q^72 + 27 * q^73 + 12 * q^74 + 18 * q^75 - 27 * q^76 + 24 * q^77 - 3 * q^78 - 12 * q^79 + 36 * q^80 + 57 * q^82 - 30 * q^83 - 9 * q^84 + 18 * q^85 + 69 * q^86 - 15 * q^87 - 42 * q^88 - 21 * q^89 - 12 * q^90 + 48 * q^92 - 15 * q^93 + 114 * q^94 + 24 * q^95 + 12 * q^96 + 36 * q^97 - 3 * q^98 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/399\mathbb{Z}\right)^\times$.

$n$	$115$	$134$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.124392	+	0.705462i	−0.0879585	+	0.498837i	0.908720	+	0.417405i	$0.137060\pi$
$2$	−0.124392	+	0.705462i	−0.0879585	+	0.498837i	−0.996679	+	0.0814319i	$0.974051\pi$
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$4$	1.39718	+	0.508532i	0.698591	+	0.254266i
$5$	−0.780211	+	0.283974i	−0.348921	+	0.126997i	−0.510534	−	0.859857i	$-0.670552\pi$
$5$	−0.780211	+	0.283974i	−0.348921	+	0.126997i	0.161614	+	0.986854i	$0.448330\pi$
$6$	0.548752	−	0.460458i	0.224027	−	0.187981i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−1.24889	+	2.16315i	−0.441551	+	0.764788i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	−0.103281	−	0.585733i	−0.0326602	−	0.185225i
$11$	−1.78098	+	3.08475i	−0.536987	+	0.930088i	0.462078	+	0.886839i	$0.347104\pi$
$11$	−1.78098	+	3.08475i	−0.536987	+	0.930088i	−0.999064	+	0.0432486i	$0.986229\pi$
$12$	−0.743425	−	1.28765i	−0.214608	−	0.371712i
$13$	0.608032	−	0.510199i	0.168638	−	0.141504i	−0.554563	−	0.832142i	$-0.687115\pi$
$13$	0.608032	−	0.510199i	0.168638	−	0.141504i	0.723201	+	0.690638i	$0.242670\pi$
$14$	−0.673144	+	0.245004i	−0.179905	+	0.0654802i
$15$	0.780211	+	0.283974i	0.201450	+	0.0733217i
$16$	0.907319	+	0.761331i	0.226830	+	0.190333i
$17$	−0.0572261	+	0.324545i	−0.0138794	+	0.0787138i	−0.990961	−	0.134153i	$-0.957169\pi$
$17$	−0.0572261	+	0.324545i	−0.0138794	+	0.0787138i	0.977081	+	0.212866i	$0.0682799\pi$
$18$	−0.716345			−0.168844
$19$	3.95637	+	1.82951i	0.907654	+	0.419720i
$19$	3.95637	+	1.82951i	0.907654	+	0.419720i
$20$	−1.23451			−0.276044
$21$	0.173648	−	0.984808i	0.0378931	−	0.214903i
$22$	−1.95464	−	1.64014i	−0.416730	−	0.349678i
$23$	3.33452	+	1.21367i	0.695296	+	0.253067i	0.665401	−	0.746486i	$-0.268261\pi$
$23$	3.33452	+	1.21367i	0.695296	+	0.253067i	0.0298946	+	0.999553i	$0.490483\pi$
$24$	2.34715	−	0.854294i	0.479111	−	0.174382i
$25$	−3.30213	+	2.77082i	−0.660427	+	0.554164i
$26$	0.284292	+	0.492408i	0.0557543	+	0.0965692i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	0.258189	+	1.46426i	0.0487931	+	0.276719i
$29$	0.746560	+	4.23395i	0.138633	+	0.786225i	0.972261	+	0.233899i	$0.0751486\pi$
$29$	0.746560	+	4.23395i	0.138633	+	0.786225i	−0.833628	+	0.552326i	$0.813740\pi$
$30$	−0.297385	+	0.515085i	−0.0542948	+	0.0940413i
$31$	−0.512645	−	0.887927i	−0.0920738	−	0.159476i	0.816310	−	0.577614i	$-0.196016\pi$
$31$	−0.512645	−	0.887927i	−0.0920738	−	0.159476i	−0.908384	+	0.418138i	$0.862683\pi$
$32$	−4.47679	+	3.75647i	−0.791392	+	0.664056i
$33$	3.34715	−	1.21826i	0.582665	−	0.212073i
$34$	−0.221836	−	0.0807417i	−0.0380446	−	0.0138471i
$35$	−0.636034	−	0.533696i	−0.107509	−	0.0902110i
$36$	−0.258189	+	1.46426i	−0.0430315	+	0.244043i
$37$	0.180743			0.0297140			0.0148570	−	0.999890i	$-0.495271\pi$
$37$	0.180743			0.0297140			0.0148570	+	0.999890i	$0.495271\pi$
$38$	−1.78279	+	2.56349i	−0.289208	+	0.415854i
$39$	−0.793729			−0.127098
$40$	0.360124	−	2.04236i	0.0569406	−	0.322926i
$41$	−1.39485	−	1.17042i	−0.217840	−	0.182789i	0.527337	−	0.849656i	$-0.323191\pi$
$41$	−1.39485	−	1.17042i	−0.217840	−	0.182789i	−0.745177	+	0.666867i	$0.767635\pi$
$42$	0.673144	+	0.245004i	0.103868	+	0.0378050i
$43$	2.89168	−	1.05249i	0.440977	−	0.160503i	−0.111983	−	0.993710i	$-0.535720\pi$
$43$	2.89168	−	1.05249i	0.440977	−	0.160503i	0.552961	+	0.833207i	$0.313498\pi$
$44$	−4.05705	+	3.40427i	−0.611624	+	0.513213i
$45$	−0.415142	−	0.719046i	−0.0618856	−	0.107189i
$46$	−1.27098	+	2.20141i	−0.187396	+	0.324580i
$47$	−0.317862	−	1.80269i	−0.0463650	−	0.262949i	0.952810	−	0.303568i	$-0.0981780\pi$
$47$	−0.317862	−	1.80269i	−0.0463650	−	0.262949i	−0.999175	+	0.0406193i	$0.987067\pi$
$48$	−0.205672	−	1.16643i	−0.0296863	−	0.168359i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−1.54395	−	2.67420i	−0.218347	−	0.378189i
$51$	0.252451	−	0.211832i	0.0353503	−	0.0296624i
$52$	1.10898	−	0.403637i	0.153788	−	0.0559744i
$53$	−5.35983	−	1.95082i	−0.736229	−	0.267966i	−0.0534301	−	0.998572i	$-0.517015\pi$
$53$	−5.35983	−	1.95082i	−0.736229	−	0.267966i	−0.682799	+	0.730606i	$0.739238\pi$
$54$	0.548752	+	0.460458i	0.0746757	+	0.0626604i
$55$	0.513554	−	2.91251i	0.0692476	−	0.392723i
$56$	−2.49779			−0.333781
$57$	−1.85477	−	3.94460i	−0.245670	−	0.522475i
$58$	−3.07976			−0.404392
$59$	1.16966	−	6.63347i	0.152277	−	0.863604i	−0.808957	−	0.587868i	$-0.799967\pi$
$59$	1.16966	−	6.63347i	0.152277	−	0.863604i	0.961233	−	0.275736i	$-0.0889215\pi$
$60$	0.945686	+	0.793525i	0.122088	+	0.102444i
$61$	11.8818	+	4.32463i	1.52131	+	0.553712i	0.961475	−	0.274892i	$-0.0886423\pi$
$61$	11.8818	+	4.32463i	1.52131	+	0.553712i	0.559835	+	0.828604i	$0.310864\pi$
$62$	0.690168	−	0.251201i	0.0876514	−	0.0319025i
$63$	−0.766044	+	0.642788i	−0.0965125	+	0.0809836i
$64$	−0.908751	−	1.57400i	−0.113594	−	0.196750i
$65$	−0.329510	+	0.570728i	−0.0408707	+	0.0707901i
$66$	0.443080	+	2.51283i	0.0545394	+	0.309308i
$67$	−1.26660	−	7.18325i	−0.154740	−	0.877574i	−0.959023	−	0.283328i	$-0.908562\pi$
$67$	−1.26660	−	7.18325i	−0.154740	−	0.877574i	0.804283	−	0.594246i	$-0.202550\pi$
$68$	−0.244997	+	0.424347i	−0.0297103	+	0.0514597i
$69$	−1.77426	−	3.07311i	−0.213596	−	0.369959i
$70$	0.455620	−	0.382310i	0.0544570	−	0.0456948i
$71$	12.3340	−	4.48919i	1.46377	−	0.532769i	0.517370	−	0.855762i	$-0.326911\pi$
$71$	12.3340	−	4.48919i	1.46377	−	0.532769i	0.946402	+	0.322992i	$0.104689\pi$
$72$	−2.34715	−	0.854294i	−0.276615	−	0.100679i
$73$	−2.95316	−	2.47800i	−0.345641	−	0.290027i	0.453396	−	0.891309i	$-0.350212\pi$
$73$	−2.95316	−	2.47800i	−0.345641	−	0.290027i	−0.799037	+	0.601282i	$0.794657\pi$
$74$	−0.0224830	+	0.127508i	−0.00261360	+	0.0148225i
$75$	4.31063			0.497749
$76$	4.59740	+	4.56811i	0.527358	+	0.523998i
$77$	−3.56197			−0.405924
$78$	0.0987336	−	0.559946i	0.0111794	−	0.0634014i
$79$	−4.44302	−	3.72813i	−0.499878	−	0.419448i	0.357672	−	0.933847i	$-0.383570\pi$
$79$	−4.44302	−	3.72813i	−0.499878	−	0.419448i	−0.857551	+	0.514399i	$0.828015\pi$
$80$	−0.924098	−	0.336344i	−0.103317	−	0.0376044i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	0.999198	−	0.838426i	0.110343	−	0.0925887i
$83$	−4.77855	−	8.27669i	−0.524514	−	0.908484i	−0.999593	−	0.0285412i	$-0.990914\pi$
$83$	−4.77855	−	8.27669i	−0.524514	−	0.908484i	0.475079	−	0.879943i	$-0.342420\pi$
$84$	0.743425	−	1.28765i	0.0811143	−	0.140494i
$85$	−0.0475139	−	0.269464i	−0.00515360	−	0.0292275i
$86$	0.382787	+	2.17089i	0.0412770	+	0.234094i
$87$	2.14963	−	3.72328i	0.230465	−	0.399177i
$88$	−4.44852	−	7.70506i	−0.474214	−	0.821362i
$89$	0.984013	−	0.825685i	0.104305	−	0.0875224i	−0.589144	−	0.808028i	$-0.700535\pi$
$89$	0.984013	−	0.825685i	0.104305	−	0.0875224i	0.693449	+	0.720506i	$0.256090\pi$
$90$	0.558900	−	0.203423i	0.0589133	−	0.0214427i
$91$	0.745862	+	0.271471i	0.0781875	+	0.0284579i
$92$	4.04174	+	3.39142i	0.421381	+	0.353580i
$93$	−0.178040	+	1.00971i	−0.0184619	+	0.104702i
$94$	1.31127			0.135247
$95$	−3.60634	−	0.303903i	−0.370002	−	0.0311798i
$96$	5.84403			0.596454
$97$	1.42760	−	8.09632i	0.144951	−	0.822056i	−0.822456	−	0.568829i	$-0.807397\pi$
$97$	1.42760	−	8.09632i	0.144951	−	0.822056i	0.967407	−	0.253228i	$-0.0814922\pi$
$98$	−0.548752	−	0.460458i	−0.0554324	−	0.0465133i
$99$	−3.34715	−	1.21826i	−0.336402	−	0.122440i
$100$	−6.02273	+	2.19210i	−0.602273	+	0.219210i
$101$	−6.80854	+	5.71304i	−0.677475	+	0.568469i	−0.915267	−	0.402847i	$-0.868021\pi$
$101$	−6.80854	+	5.71304i	−0.677475	+	0.568469i	0.237792	+	0.971316i	$0.423576\pi$
$102$	0.118036	+	0.204445i	0.0116874	+	0.0202431i
$103$	9.41003	−	16.2987i	0.927198	−	1.60595i	0.139211	−	0.990263i	$-0.455543\pi$
$103$	9.41003	−	16.2987i	0.927198	−	1.60595i	0.787987	−	0.615692i	$-0.211123\pi$
$104$	0.344269	+	1.95245i	0.0337584	+	0.191453i
$105$	0.144177	+	0.817669i	0.0140702	+	0.0797963i
$106$	2.04295	−	3.53849i	0.198429	−	0.343689i
$107$	−2.97404	−	5.15118i	−0.287511	−	0.497984i	0.685704	−	0.727881i	$-0.259494\pi$
$107$	−2.97404	−	5.15118i	−0.287511	−	0.497984i	−0.973215	+	0.229897i	$0.926161\pi$
$108$	1.13899	−	0.955728i	0.109600	−	0.0919650i
$109$	−5.02428	+	1.82869i	−0.481239	+	0.175157i	−0.571237	−	0.820785i	$-0.693536\pi$
$109$	−5.02428	+	1.82869i	−0.481239	+	0.175157i	0.0899978	+	0.995942i	$0.471314\pi$
$110$	1.99078	+	0.724586i	0.189814	+	0.0690866i
$111$	−0.138457	−	0.116180i	−0.0131418	−	0.0110273i
$112$	−0.205672	+	1.16643i	−0.0194342	+	0.110217i
$113$	20.5092			1.92935			0.964673	−	0.263450i	$-0.0848605\pi$
$113$	20.5092			1.92935			0.964673	+	0.263450i	$0.0848605\pi$
$114$	3.01348	−	0.817792i	0.282238	−	0.0765932i
$115$	−2.94628			−0.274742
$116$	−1.11002	+	6.29525i	−0.103063	+	0.584499i
$117$	0.608032	+	0.510199i	0.0562126	+	0.0471680i
$118$	4.53416	+	1.65030i	0.417404	+	0.151923i
$119$	−0.309677	+	0.112713i	−0.0283881	+	0.0103324i
$120$	−1.58868	+	1.33306i	−0.145026	+	0.121691i
$121$	−0.843800	−	1.46150i	−0.0767091	−	0.132864i
$122$	−4.52886	+	7.84422i	−0.410024	+	0.710182i
$123$	0.316188	+	1.79319i	0.0285097	+	0.161687i
$124$	−0.264718	−	1.50129i	−0.0237724	−	0.134820i
$125$	3.86523	−	6.69477i	0.345717	−	0.598799i
$126$	−0.358173	−	0.620373i	−0.0319086	−	0.0552672i
$127$	1.83438	−	1.53923i	0.162775	−	0.136584i	−0.557762	−	0.830001i	$-0.688340\pi$
$127$	1.83438	−	1.53923i	0.162775	−	0.136584i	0.720537	+	0.693417i	$0.243895\pi$
$128$	−9.75974	+	3.55226i	−0.862648	+	0.313978i
$129$	−2.89168	−	1.05249i	−0.254598	−	0.0926663i
$130$	−0.361639	−	0.303451i	−0.0317178	−	0.0266144i
$131$	1.22065	−	6.92263i	0.106648	−	0.604833i	−0.883901	−	0.467674i	$-0.845092\pi$
$131$	1.22065	−	6.92263i	0.106648	−	0.604833i	0.990549	−	0.137158i	$-0.0437969\pi$
$132$	5.29611			0.460967
$133$	0.393779	+	4.34108i	0.0341450	+	0.376419i
$134$	5.22507			0.451377
$135$	−0.144177	+	0.817669i	−0.0124088	+	0.0703738i
$136$	−0.630570	−	0.529111i	−0.0540709	−	0.0453709i
$137$	8.84518	+	3.21938i	0.755695	+	0.275050i	0.691000	−	0.722855i	$-0.257170\pi$
$137$	8.84518	+	3.21938i	0.755695	+	0.275050i	0.0646948	+	0.997905i	$0.479393\pi$
$138$	2.38867	−	0.869404i	0.203337	−	0.0740086i
$139$	−9.60343	+	8.05824i	−0.814553	+	0.683491i	−0.951690	−	0.307061i	$-0.900654\pi$
$139$	−9.60343	+	8.05824i	−0.814553	+	0.683491i	0.137137	+	0.990552i	$0.456210\pi$
$140$	−0.617253	−	1.06911i	−0.0521674	−	0.0903566i
$141$	−0.915248	+	1.58526i	−0.0770778	+	0.133503i
$142$	1.63271	+	9.25956i	0.137014	+	0.777045i
$143$	0.490945	+	2.78428i	0.0410548	+	0.232834i
$144$	−0.592210	+	1.02574i	−0.0493509	+	0.0854782i
$145$	−1.78480	−	3.09137i	−0.148220	−	0.256725i
$146$	2.11548	−	1.77510i	0.175079	−	0.146908i
$147$	0.939693	−	0.342020i	0.0775045	−	0.0282093i
$148$	0.252531	+	0.0919138i	0.0207579	+	0.00755527i
$149$	5.12684	+	4.30193i	0.420007	+	0.352428i	0.828166	−	0.560483i	$-0.189385\pi$
$149$	5.12684	+	4.30193i	0.420007	+	0.352428i	−0.408159	+	0.912911i	$0.633829\pi$
$150$	−0.536208	+	3.04099i	−0.0437812	+	0.248296i
$151$	12.6254			1.02744			0.513722	−	0.857957i	$-0.328266\pi$
$151$	12.6254			1.02744			0.513722	+	0.857957i	$0.328266\pi$
$152$	−8.89860	+	6.27335i	−0.721772	+	0.508836i
$153$	−0.329552			−0.0266427
$154$	0.443080	−	2.51283i	0.0357044	−	0.202490i
$155$	0.652119	+	0.547193i	0.0523795	+	0.0439516i
$156$	−1.10898	−	0.403637i	−0.0887898	−	0.0323168i
$157$	−21.4093	+	7.79235i	−1.70865	+	0.621897i	−0.996763	−	0.0803973i	$-0.974381\pi$
$157$	−21.4093	+	7.79235i	−1.70865	+	0.621897i	−0.711886	+	0.702295i	$0.752159\pi$
$158$	3.18273	−	2.67063i	0.253205	−	0.212464i
$159$	2.85191	+	4.93965i	0.226171	+	0.391740i
$160$	2.42610	−	4.20213i	0.191800	−	0.332207i
$161$	0.616194	+	3.49461i	0.0485629	+	0.275414i
$162$	−0.124392	−	0.705462i	−0.00977316	−	0.0554264i
$163$	1.28984	−	2.23408i	0.101028	−	0.174986i	−0.811080	−	0.584935i	$-0.801120\pi$
$163$	1.28984	−	2.23408i	0.101028	−	0.174986i	0.912109	+	0.409949i	$0.134453\pi$
$164$	−1.35367	−	2.34462i	−0.105704	−	0.183084i
$165$	−2.26553	+	1.90101i	−0.176371	+	0.147993i
$166$	6.43330	−	2.34153i	0.499321	−	0.181738i
$167$	−2.63471	−	0.958954i	−0.203880	−	0.0742061i	0.238062	−	0.971250i	$-0.423488\pi$
$167$	−2.63471	−	0.958954i	−0.203880	−	0.0742061i	−0.441941	+	0.897044i	$0.645710\pi$
$168$	1.91342	+	1.60555i	0.147623	+	0.123871i
$169$	−2.14803	+	12.1821i	−0.165233	+	0.937082i
$170$	0.196007			0.0150331
$171$	−1.11470	+	4.21396i	−0.0852435	+	0.322249i
$172$	4.57543			0.348873
$173$	1.28569	−	7.29151i	0.0977492	−	0.554363i	−0.896121	−	0.443810i	$-0.853627\pi$
$173$	1.28569	−	7.29151i	0.0977492	−	0.554363i	0.993870	−	0.110553i	$-0.0352623\pi$
$174$	2.35923	+	1.97963i	0.178853	+	0.150075i
$175$	−4.05067	−	1.47432i	−0.306202	−	0.111448i
$176$	−3.96444	+	1.44294i	−0.298831	+	0.108765i
$177$	−5.15992	+	4.32969i	−0.387843	+	0.325439i
$178$	0.460086	+	0.796892i	0.0344849	+	0.0597296i
$179$	−6.35320	+	11.0041i	−0.474860	+	0.822482i	−0.999585	−	0.0287895i	$-0.990835\pi$
$179$	−6.35320	+	11.0041i	−0.474860	+	0.822482i	0.524725	+	0.851272i	$0.324168\pi$
$180$	−0.214370	−	1.21575i	−0.0159782	−	0.0906167i
$181$	2.84975	+	16.1618i	0.211820	+	1.20129i	0.886339	+	0.463036i	$0.153240\pi$
$181$	2.84975	+	16.1618i	0.211820	+	1.20129i	−0.674519	+	0.738258i	$0.735649\pi$
$182$	−0.284292	+	0.492408i	−0.0210731	+	0.0364997i
$183$	−6.32218	−	10.9503i	−0.467349	−	0.809472i
$184$	−6.78980	+	5.69732i	−0.500551	+	0.420012i
$185$	−0.141018	+	0.0513263i	−0.0103678	+	0.00377359i
$186$	−0.690168	−	0.251201i	−0.0506056	−	0.0184189i
$187$	−0.899223	−	0.754538i	−0.0657577	−	0.0551773i
$188$	0.472613	−	2.68032i	0.0344689	−	0.195483i
$189$	1.00000			0.0727393
$190$	0.662992	−	2.50633i	0.0480985	−	0.181828i
$191$	−6.39701			−0.462871			−0.231436	−	0.972850i	$-0.574342\pi$
$191$	−6.39701			−0.462871			−0.231436	+	0.972850i	$0.574342\pi$
$192$	−0.315606	+	1.78989i	−0.0227769	+	0.129174i
$193$	−13.9307	−	11.6893i	−1.00276	−	0.841412i	−0.0153914	−	0.999882i	$-0.504899\pi$
$193$	−13.9307	−	11.6893i	−1.00276	−	0.841412i	−0.987364	+	0.158470i	$0.949344\pi$
$194$	5.53406	+	2.01423i	0.397323	+	0.144614i
$195$	0.619276	−	0.225398i	0.0443473	−	0.0161411i
$196$	−1.13899	+	0.955728i	−0.0813566	+	0.0682663i
$197$	0.895310	+	1.55072i	0.0637882	+	0.110484i	0.896156	−	0.443740i	$-0.146348\pi$
$197$	0.895310	+	1.55072i	0.0637882	+	0.110484i	−0.832368	+	0.554224i	$0.813015\pi$
$198$	1.27580	−	2.20975i	0.0906671	−	0.157040i
$199$	2.02733	+	11.4975i	0.143713	+	0.815039i	0.968391	+	0.249436i	$0.0802452\pi$
$199$	2.02733	+	11.4975i	0.143713	+	0.815039i	−0.824678	+	0.565603i	$0.808644\pi$
$200$	−1.86968	−	10.6035i	−0.132206	−	0.749778i
$201$	−3.64703	+	6.31685i	−0.257242	+	0.445556i
$202$	−3.18341	−	5.51382i	−0.223984	−	0.387951i
$203$	−3.29343	+	2.76352i	−0.231153	+	0.193961i
$204$	0.460444	−	0.167588i	0.0322375	−	0.0117335i
$205$	1.42065	+	0.517074i	0.0992225	+	0.0361140i
$206$	10.3276	+	8.66585i	0.719555	+	0.603778i
$207$	−0.616194	+	3.49461i	−0.0428285	+	0.242892i
$208$	0.940109			0.0651849
$209$	−12.6898	+	8.94609i	−0.877774	+	0.618814i
$210$	−0.594769			−0.0410430
$211$	−1.03030	+	5.84313i	−0.0709288	+	0.402257i	0.928586	+	0.371117i	$0.121025\pi$
$211$	−1.03030	+	5.84313i	−0.0709288	+	0.402257i	−0.999515	+	0.0311405i	$0.990086\pi$
$212$	−6.49660	−	5.45130i	−0.446188	−	0.374397i
$213$	−12.3340	−	4.48919i	−0.845109	−	0.307595i
$214$	4.00391	−	1.45731i	0.273702	−	0.0996193i
$215$	−1.95724	+	1.64232i	−0.133483	+	0.112005i
$216$	1.24889	+	2.16315i	0.0849765	+	0.147184i
$217$	0.512645	−	0.887927i	0.0348006	−	0.0602764i
$218$	−0.665091	−	3.77192i	−0.0450456	−	0.255466i
$219$	0.669427	+	3.79651i	0.0452357	+	0.256544i
$220$	2.19863	−	3.80815i	0.148232	−	0.256745i
$221$	0.130788	+	0.226531i	0.00879772	+	0.0152381i
$222$	0.0991833	−	0.0832247i	0.00665675	−	0.00558567i
$223$	−7.90600	+	2.87755i	−0.529425	+	0.192695i	−0.592881	−	0.805290i	$-0.702010\pi$
$223$	−7.90600	+	2.87755i	−0.529425	+	0.192695i	0.0634568	+	0.997985i	$0.479787\pi$
$224$	−5.49159	−	1.99878i	−0.366922	−	0.133549i
$225$	−3.30213	−	2.77082i	−0.220142	−	0.184721i
$226$	−2.55118	+	14.4685i	−0.169702	+	0.962430i
$227$	23.1566			1.53696			0.768478	−	0.639876i	$-0.221014\pi$
$227$	23.1566			1.53696			0.768478	+	0.639876i	$0.221014\pi$
$228$	−0.585491	−	6.45453i	−0.0387751	−	0.427461i
$229$	−13.5968			−0.898499			−0.449250	−	0.893406i	$-0.648309\pi$
$229$	−13.5968			−0.898499			−0.449250	+	0.893406i	$0.648309\pi$
$230$	0.366494	−	2.07849i	0.0241659	−	0.137051i
$231$	2.72862	+	2.28959i	0.179530	+	0.150644i
$232$	−10.0910	−	3.67284i	−0.662509	−	0.241134i
$233$	11.3144	−	4.11810i	0.741229	−	0.269785i	0.0563190	−	0.998413i	$-0.482064\pi$
$233$	11.3144	−	4.11810i	0.741229	−	0.269785i	0.684910	+	0.728627i	$0.259841\pi$
$234$	−0.435561	+	0.365479i	−0.0284735	+	0.0238921i
$235$	0.759915	+	1.31621i	0.0495714	+	0.0858601i
$236$	5.00756	−	8.67335i	0.325964	−	0.564587i
$237$	1.00715	+	5.71183i	0.0654214	+	0.371023i
$238$	−0.0409936	−	0.232486i	−0.00265722	−	0.0150699i
$239$	15.0852	−	26.1283i	0.975777	−	1.69010i	0.298432	−	0.954431i	$-0.403536\pi$
$239$	15.0852	−	26.1283i	0.975777	−	1.69010i	0.677345	−	0.735665i	$-0.263130\pi$
$240$	0.491702	+	0.851653i	0.0317392	+	0.0549740i
$241$	−9.23583	+	7.74978i	−0.594932	+	0.499207i	−0.889812	−	0.456327i	$-0.849165\pi$
$241$	−9.23583	+	7.74978i	−0.594932	+	0.499207i	0.294880	+	0.955534i	$0.404720\pi$
$242$	1.13600	−	0.413470i	0.0730247	−	0.0265788i
$243$	0.939693	+	0.342020i	0.0602813	+	0.0219406i
$244$	14.4018	+	12.0846i	0.921983	+	0.773636i
$245$	0.144177	−	0.817669i	0.00921114	−	0.0522390i
$246$	−1.30436			−0.0831629
$247$	3.33902	−	0.906135i	0.212457	−	0.0576560i
$248$	2.56096			0.162621
$249$	−1.65957	+	9.41190i	−0.105171	+	0.596455i
$250$	4.24211	+	3.55955i	0.268294	+	0.225126i
$251$	10.1406	+	3.69087i	0.640067	+	0.232965i	0.641607	−	0.767033i	$-0.278268\pi$
$251$	10.1406	+	3.69087i	0.640067	+	0.232965i	−0.00154001	+	0.999999i	$0.500490\pi$
$252$	−1.39718	+	0.508532i	−0.0880142	+	0.0320345i
$253$	−9.68258	+	8.12465i	−0.608739	+	0.510792i
$254$	0.857685	+	1.48555i	0.0538159	+	0.0932119i
$255$	−0.136811	+	0.236963i	−0.00856742	+	0.0148392i
$256$	−1.92316	−	10.9068i	−0.120198	−	0.681674i
$257$	−0.620077	−	3.51663i	−0.0386794	−	0.219362i	0.959341	−	0.282249i	$-0.0910803\pi$
$257$	−0.620077	−	3.51663i	−0.0386794	−	0.219362i	−0.998021	+	0.0628871i	$0.979969\pi$
$258$	1.10219	−	1.90905i	0.0686195	−	0.118852i
$259$	0.0903716	+	0.156528i	0.00561542	+	0.00972619i
$260$	−0.750619	+	0.629844i	−0.0465514	+	0.0390613i
$261$	−4.03999	+	1.47044i	−0.250069	+	0.0910177i
$262$	4.73181	+	1.72224i	0.292333	+	0.106400i
$263$	3.41991	+	2.86964i	0.210881	+	0.176950i	0.742110	−	0.670278i	$-0.233825\pi$
$263$	3.41991	+	2.86964i	0.210881	+	0.176950i	−0.531229	+	0.847228i	$0.678270\pi$
$264$	−1.54495	+	8.76187i	−0.0950853	+	0.539256i
$265$	4.73578			0.290917
$266$	−3.11145	−	0.262199i	−0.190775	−	0.0160764i
$267$	−1.28454			−0.0786124
$268$	1.88325	−	10.6804i	0.115038	−	0.652410i
$269$	−1.18081	−	0.990819i	−0.0719954	−	0.0604113i	0.606080	−	0.795404i	$-0.292741\pi$
$269$	−1.18081	−	0.990819i	−0.0719954	−	0.0604113i	−0.678075	+	0.734993i	$0.737186\pi$
$270$	−0.558900	−	0.203423i	−0.0340136	−	0.0123799i
$271$	27.7161	−	10.0878i	1.68363	−	0.612791i	0.689830	−	0.723971i	$-0.257685\pi$
$271$	27.7161	−	10.0878i	1.68363	−	0.612791i	0.993800	+	0.111180i	$0.0354629\pi$
$272$	−0.299009	+	0.250898i	−0.0181301	+	0.0152129i
$273$	−0.396865	−	0.687390i	−0.0240193	−	0.0416027i
$274$	−3.37142	+	5.83948i	−0.203675	+	0.352776i
$275$	−2.66625	−	15.1210i	−0.160781	−	0.911834i
$276$	−0.916188	−	5.19596i	−0.0551481	−	0.312760i
$277$	−10.7350	+	18.5936i	−0.645006	+	1.11718i	0.339294	+	0.940680i	$0.389812\pi$
$277$	−10.7350	+	18.5936i	−0.645006	+	1.11718i	−0.984300	+	0.176503i	$0.943522\pi$
$278$	−4.49019	−	7.77724i	−0.269304	−	0.466448i
$279$	0.785418	−	0.659044i	0.0470217	−	0.0394559i
$280$	1.94880	−	0.709306i	0.116463	−	0.0423891i
$281$	23.8677	+	8.68714i	1.42383	+	0.518232i	0.935156	−	0.354235i	$-0.115259\pi$
$281$	23.8677	+	8.68714i	1.42383	+	0.518232i	0.488673	+	0.872467i	$0.337481\pi$
$282$	−1.00449	−	0.842866i	−0.0598164	−	0.0501919i
$283$	−2.32682	+	13.1960i	−0.138315	+	0.784423i	0.834179	+	0.551494i	$0.185942\pi$
$283$	−2.32682	+	13.1960i	−0.138315	+	0.784423i	−0.972494	+	0.232929i	$0.925169\pi$
$284$	19.5157			1.15804
$285$	2.56727	+	2.55091i	0.152072	+	0.151103i
$286$	−2.02528			−0.119757
$287$	0.316188	−	1.79319i	0.0186640	−	0.105849i
$288$	−4.47679	−	3.75647i	−0.263797	−	0.221352i
$289$	15.8727	+	5.77720i	0.933689	+	0.339835i
$290$	2.40286	−	0.874570i	0.141101	−	0.0513565i
$291$	−6.29782	+	5.28449i	−0.369185	+	0.309783i
$292$	−2.86596	−	4.96399i	−0.167718	−	0.290495i
$293$	−4.76144	+	8.24706i	−0.278166	+	0.481798i	−0.970929	−	0.239367i	$-0.923060\pi$
$293$	−4.76144	+	8.24706i	−0.278166	+	0.481798i	0.692763	+	0.721166i	$0.256393\pi$
$294$	0.124392	+	0.705462i	0.00725469	+	0.0411434i
$295$	0.971148	+	5.50766i	0.0565424	+	0.320668i
$296$	−0.225729	+	0.390974i	−0.0131202	+	0.0227249i
$297$	1.78098	+	3.08475i	0.103343	+	0.178996i
$298$	−3.67259	+	3.08167i	−0.212747	+	0.178516i
$299$	2.64671	−	0.963322i	0.153063	−	0.0557104i
$300$	6.02273	+	2.19210i	0.347723	+	0.126561i
$301$	2.35732	+	1.97803i	0.135874	+	0.114012i
$302$	−1.57050	+	8.90677i	−0.0903723	+	0.512527i
$303$	8.88791			0.510597
$304$	2.19682	+	4.67206i	0.125997	+	0.267961i
$305$	−10.4984			−0.601137
$306$	0.0409936	−	0.232486i	0.00234345	−	0.0132904i
$307$	18.0352	+	15.1333i	1.02932	+	0.863705i	0.990770	−	0.135552i	$-0.0432807\pi$
$307$	18.0352	+	15.1333i	1.02932	+	0.863705i	0.0385532	+	0.999257i	$0.487725\pi$
$308$	−4.97671	−	1.81138i	−0.283575	−	0.103213i
$309$	−17.6851	+	6.43684i	−1.00607	+	0.366179i
$310$	−0.467142	+	0.391979i	−0.0265319	+	0.0222629i
$311$	−5.07975	−	8.79838i	−0.288046	−	0.498910i	0.685297	−	0.728264i	$-0.259672\pi$
$311$	−5.07975	−	8.79838i	−0.288046	−	0.498910i	−0.973343	+	0.229353i	$0.926339\pi$
$312$	0.991284	−	1.71695i	0.0561204	−	0.0972034i
$313$	−0.0756136	−	0.428826i	−0.00427393	−	0.0242387i	0.982596	−	0.185754i	$-0.0594729\pi$
$313$	−0.0756136	−	0.428826i	−0.00427393	−	0.0242387i	−0.986870	+	0.161516i	$0.948362\pi$
$314$	−2.83406	−	16.0728i	−0.159935	−	0.907039i
$315$	0.415142	−	0.719046i	0.0233906	−	0.0405137i
$316$	−4.31182	−	7.46830i	−0.242559	−	0.420125i
$317$	−10.8789	+	9.12850i	−0.611021	+	0.512708i	−0.894967	−	0.446133i	$-0.852801\pi$
$317$	−10.8789	+	9.12850i	−0.611021	+	0.512708i	0.283946	+	0.958840i	$0.408357\pi$
$318$	−3.83949	+	1.39746i	−0.215308	+	0.0783657i
$319$	−14.3903	−	5.23764i	−0.805703	−	0.293252i
$320$	1.15599	+	0.969993i	0.0646219	+	0.0542242i
$321$	−1.03287	+	5.85771i	−0.0576493	+	0.326946i
$322$	−2.54197			−0.141658
$323$	−0.820168	+	1.17933i	−0.0456354	+	0.0656194i
$324$	−1.48685			−0.0826028
$325$	−0.594133	+	3.36949i	−0.0329566	+	0.186906i
$326$	1.41561	+	1.18784i	0.0784034	+	0.0657883i
$327$	5.02428	+	1.82869i	0.277843	+	0.101127i
$328$	4.27382	−	1.55554i	0.235982	−	0.0858905i
$329$	1.40224	−	1.17662i	0.0773081	−	0.0648692i
$330$	−1.05927	−	1.83472i	−0.0583111	−	0.100998i
$331$	10.6861	−	18.5089i	0.587361	−	1.01734i	−0.407216	−	0.913332i	$-0.633500\pi$
$331$	10.6861	−	18.5089i	0.587361	−	1.01734i	0.994577	−	0.104007i	$-0.0331664\pi$
$332$	−2.46753	−	13.9941i	−0.135424	−	0.768025i
$333$	0.0313857	+	0.177997i	0.00171993	+	0.00975420i
$334$	1.00424	−	1.73940i	0.0549497	−	0.0951757i
$335$	3.02807	+	5.24477i	0.165441	+	0.286552i
$336$	0.907319	−	0.761331i	0.0494983	−	0.0415340i
$337$	−11.2366	+	4.08978i	−0.612095	+	0.222785i	−0.629420	−	0.777065i	$-0.716707\pi$
$337$	−11.2366	+	4.08978i	−0.612095	+	0.222785i	0.0173245	+	0.999850i	$0.494485\pi$
$338$	−8.32679	−	3.03070i	−0.452918	−	0.164849i
$339$	−15.7110	−	13.1831i	−0.853303	−	0.716007i
$340$	0.0706459	−	0.400653i	0.00383131	−	0.0217285i
$341$	3.65205			0.197769
$342$	−2.83413	−	1.31056i	−0.153252	−	0.0708672i
$343$	−1.00000			−0.0539949
$344$	−1.33472	+	7.56958i	−0.0719633	+	0.408124i
$345$	2.25698	+	1.89383i	0.121512	+	0.101960i
$346$	4.98396	+	1.81401i	0.267939	+	0.0975219i
$347$	29.1466	−	10.6085i	1.56467	−	0.569493i	0.592869	−	0.805299i	$-0.297995\pi$
$347$	29.1466	−	10.6085i	1.56467	−	0.569493i	0.971800	+	0.235806i	$0.0757730\pi$
$348$	4.89684	−	4.10893i	0.262498	−	0.220262i
$349$	−9.37470	−	16.2375i	−0.501816	−	0.869171i	−0.999998	−	0.00209848i	$-0.999332\pi$
$349$	−9.37470	−	16.2375i	−0.501816	−	0.869171i	0.498182	−	0.867073i	$-0.334001\pi$
$350$	1.54395	−	2.67420i	0.0825276	−	0.142942i
$351$	−0.137830	−	0.781671i	−0.00735680	−	0.0417225i
$352$	−3.61470	−	20.5000i	−0.192664	−	1.09265i
$353$	15.8612	−	27.4724i	0.844206	−	1.46221i	−0.0421025	−	0.999113i	$-0.513406\pi$
$353$	15.8612	−	27.4724i	0.844206	−	1.46221i	0.886309	−	0.463095i	$-0.153261\pi$
$354$	−2.41258	−	4.17871i	−0.128227	−	0.222096i
$355$	−8.34828	+	7.00504i	−0.443081	+	0.371789i
$356$	1.79473	−	0.653229i	0.0951206	−	0.0346211i
$357$	0.309677	+	0.112713i	0.0163899	+	0.00596542i
$358$	−6.97266	−	5.85076i	−0.368517	−	0.309222i
$359$	1.65301	−	9.37471i	0.0872427	−	0.494778i	−0.909607	−	0.415469i	$-0.863617\pi$
$359$	1.65301	−	9.37471i	0.0872427	−	0.494778i	0.996850	−	0.0793092i	$-0.0252714\pi$
$360$	2.07387			0.109303
$361$	12.3058	+	14.4765i	0.647671	+	0.761920i
$362$	−11.7560			−0.617881
$363$	−0.293049	+	1.66196i	−0.0153811	+	0.0872304i
$364$	0.904052	+	0.758590i	0.0473852	+	0.0397609i
$365$	3.00777	+	1.09474i	0.157434	+	0.0573013i
$366$	8.51148	−	3.09792i	0.444902	−	0.161931i
$367$	9.59761	−	8.05335i	0.500991	−	0.420381i	−0.356955	−	0.934122i	$-0.616185\pi$
$367$	9.59761	−	8.05335i	0.500991	−	0.420381i	0.857946	+	0.513740i	$0.171740\pi$
$368$	2.10147	+	3.63986i	0.109547	+	0.189741i
$369$	0.910427	−	1.57691i	0.0473949	−	0.0820904i
$370$	−0.0186673	−	0.105867i	−0.000970466	−	0.00550378i
$371$	−0.990457	−	5.61716i	−0.0514220	−	0.291628i
$372$	−0.762226	+	1.32021i	−0.0395196	+	0.0684499i
$373$	−11.1924	−	19.3858i	−0.579520	−	1.00376i	−0.995534	−	0.0943995i	$-0.969907\pi$
$373$	−11.1924	−	19.3858i	−0.579520	−	1.00376i	0.416015	−	0.909358i	$-0.363426\pi$
$374$	0.644154	−	0.540510i	0.0333084	−	0.0279491i
$375$	−7.26425	+	2.64397i	−0.375125	+	0.136534i
$376$	4.29645	+	1.56378i	0.221573	+	0.0806459i
$377$	2.61409	+	2.19348i	0.134633	+	0.112970i
$378$	−0.124392	+	0.705462i	−0.00639804	+	0.0362851i
$379$	14.9865			0.769807			0.384904	−	0.922957i	$-0.374235\pi$
$379$	14.9865			0.769807			0.384904	+	0.922957i	$0.374235\pi$
$380$	−4.88416	−	2.25855i	−0.250552	−	0.115861i
$381$	−2.39461			−0.122680
$382$	0.795737	−	4.51285i	0.0407135	−	0.230898i
$383$	−19.7426	−	16.5660i	−1.00880	−	0.846483i	−0.0206201	−	0.999787i	$-0.506564\pi$
$383$	−19.7426	−	16.5660i	−1.00880	−	0.846483i	−0.988179	+	0.153304i	$0.951008\pi$
$384$	9.75974	+	3.55226i	0.498050	+	0.181275i
$385$	2.77908	−	1.01150i	0.141635	−	0.0515510i
$386$	9.97921	−	8.37355i	0.507928	−	0.426202i
$387$	1.53863	+	2.66499i	0.0782131	+	0.135469i
$388$	6.11185	−	10.5860i	0.310282	−	0.537425i
$389$	−3.55356	−	20.1533i	−0.180173	−	1.02181i	−0.932002	−	0.362453i	$-0.881939\pi$
$389$	−3.55356	−	20.1533i	−0.180173	−	1.02181i	0.751829	−	0.659358i	$-0.229172\pi$
$390$	0.0819769	+	0.464914i	0.00415106	+	0.0235418i
$391$	−0.584711	+	1.01275i	−0.0295701	+	0.0512169i
$392$	−1.24889	−	2.16315i	−0.0630787	−	0.109255i
$393$	−5.38485	+	4.51842i	−0.271630	+	0.227924i
$394$	−1.20535	+	0.438710i	−0.0607245	+	0.0221019i
$395$	4.52518	+	1.64703i	0.227687	+	0.0828711i
$396$	−4.05705	−	3.40427i	−0.203875	−	0.171071i
$397$	−4.71445	+	26.7370i	−0.236611	+	1.34189i	0.602582	+	0.798057i	$0.294139\pi$
$397$	−4.71445	+	26.7370i	−0.236611	+	1.34189i	−0.839193	+	0.543833i	$0.816973\pi$
$398$	−8.36326			−0.419212
$399$	2.48874	−	3.57857i	0.124593	−	0.179153i
$400$	−5.10560			−0.255280
$401$	3.43401	−	19.4752i	0.171486	−	0.972547i	−0.770636	−	0.637276i	$-0.780061\pi$
$401$	3.43401	−	19.4752i	0.171486	−	0.972547i	0.942122	−	0.335271i	$-0.108828\pi$
$402$	−4.00263	−	3.35861i	−0.199633	−	0.167512i
$403$	−0.764724	−	0.278337i	−0.0380936	−	0.0138650i
$404$	−12.4180	+	4.51979i	−0.617820	+	0.224868i
$405$	0.636034	−	0.533696i	0.0316048	−	0.0265196i
$406$	−1.53988	−	2.66715i	−0.0764230	−	0.132368i
$407$	−0.321901	+	0.557548i	−0.0159560	+	0.0276366i
$408$	0.142939	+	0.810645i	0.00707652	+	0.0401329i
$409$	−5.20713	−	29.5311i	−0.257476	−	1.46022i	−0.789637	−	0.613575i	$-0.789731\pi$
$409$	−5.20713	−	29.5311i	−0.257476	−	1.46022i	0.532161	−	0.846643i	$-0.321380\pi$
$410$	−0.541494	+	0.937895i	−0.0267425	+	0.0463193i
$411$	−4.70642	−	8.15176i	−0.232151	−	0.402097i
$412$	21.4359	−	17.9869i	1.05607	−	0.886150i
$413$	6.32958	−	2.30378i	0.311458	−	0.113362i
$414$	−2.38867	−	0.869404i	−0.117397	−	0.0427289i
$415$	6.07863	+	5.10058i	0.298388	+	0.250378i
$416$	−0.805481	+	4.56811i	−0.0394919	+	0.223970i
$417$	12.5364			0.613910
$418$	−4.73262	−	10.0650i	−0.231480	−	0.492296i
$419$	−33.8826			−1.65528			−0.827638	−	0.561263i	$-0.810316\pi$
$419$	−33.8826			−1.65528			−0.827638	+	0.561263i	$0.810316\pi$
$420$	−0.214370	+	1.21575i	−0.0104602	+	0.0593226i
$421$	−24.4509	−	20.5168i	−1.19167	−	0.999927i	−0.999829	−	0.0185001i	$-0.994111\pi$
$421$	−24.4509	−	20.5168i	−1.19167	−	0.999927i	−0.191838	−	0.981427i	$-0.561445\pi$
$422$	−3.99394	−	1.45368i	−0.194422	−	0.0707639i
$423$	1.72010	−	0.626066i	0.0836343	−	0.0304404i
$424$	10.9138	−	9.15774i	0.530020	−	0.444739i
$425$	−0.710288	−	1.23026i	−0.0344540	−	0.0596761i
$426$	4.70120	−	8.14272i	0.227774	−	0.394516i
$427$	2.19567	+	12.4523i	0.106256	+	0.602607i
$428$	−1.53573	−	8.70953i	−0.0742321	−	0.420991i
$429$	1.41362	−	2.44846i	0.0682501	−	0.118213i
$430$	−0.915131	−	1.58505i	−0.0441315	−	0.0764381i
$431$	−21.0811	+	17.6892i	−1.01544	+	0.852058i	−0.989048	−	0.147594i	$-0.952847\pi$
$431$	−21.0811	+	17.6892i	−1.01544	+	0.852058i	−0.0263946	+	0.999652i	$0.508403\pi$
$432$	1.11299	−	0.405096i	0.0535488	−	0.0194902i
$433$	−12.4255	−	4.52249i	−0.597129	−	0.217337i	0.0257330	−	0.999669i	$-0.491808\pi$
$433$	−12.4255	−	4.52249i	−0.597129	−	0.217337i	−0.622862	+	0.782332i	$0.714030\pi$
$434$	0.562630	+	0.472103i	0.0270071	+	0.0226617i
$435$	−0.619856	+	3.51538i	−0.0297198	+	0.168550i
$436$	−7.94978			−0.380726
$437$	10.9722	+	10.9023i	0.524871	+	0.521526i
$438$	−2.76157			−0.131953
$439$	−4.72160	+	26.7775i	−0.225350	+	1.27802i	0.636666	+	0.771140i	$0.280313\pi$
$439$	−4.72160	+	26.7775i	−0.225350	+	1.27802i	−0.862016	+	0.506881i	$0.830798\pi$
$440$	5.65881	+	4.74831i	0.269773	+	0.226367i
$441$	−0.939693	−	0.342020i	−0.0447473	−	0.0162867i
$442$	−0.176078	+	0.0640871i	−0.00837516	+	0.00304831i
$443$	−28.4882	+	23.9045i	−1.35352	+	1.13574i	−0.375591	+	0.926786i	$0.622560\pi$
$443$	−28.4882	+	23.9045i	−1.35352	+	1.13574i	−0.977926	+	0.208950i	$0.932995\pi$
$444$	−0.134369	−	0.232734i	−0.00637687	−	0.0110451i
$445$	−0.533265	+	0.923642i	−0.0252792	+	0.0437848i
$446$	−1.04656	−	5.93533i	−0.0495560	−	0.281046i
$447$	−1.16216	−	6.59094i	−0.0549683	−	0.311741i
$448$	0.908751	−	1.57400i	0.0429344	−	0.0743646i
$449$	15.4209	+	26.7097i	0.727756	+	1.26051i	0.957829	+	0.287338i	$0.0927701\pi$
$449$	15.4209	+	26.7097i	0.727756	+	1.26051i	−0.230073	+	0.973173i	$0.573897\pi$
$450$	2.36547	−	1.98486i	0.111509	−	0.0935674i
$451$	6.09468	−	2.21828i	0.286987	−	0.104455i
$452$	28.6551	+	10.4296i	1.34782	+	0.490568i
$453$	−9.67164	−	8.11547i	−0.454413	−	0.381298i
$454$	−2.88049	+	16.3361i	−0.135188	+	0.766691i
$455$	−0.659020			−0.0308953
$456$	10.8492	+	0.914248i	0.508058	+	0.0428136i
$457$	3.41452			0.159725			0.0798623	−	0.996806i	$-0.474552\pi$
$457$	3.41452			0.159725			0.0798623	+	0.996806i	$0.474552\pi$
$458$	1.69133	−	9.59200i	0.0790306	−	0.448205i
$459$	0.252451	+	0.211832i	0.0117834	+	0.00988747i
$460$	−4.11649	−	1.49828i	−0.191932	−	0.0698576i
$461$	−19.7611	+	7.19246i	−0.920367	+	0.334986i	−0.758385	−	0.651807i	$-0.774011\pi$
$461$	−19.7611	+	7.19246i	−0.920367	+	0.334986i	−0.161983	+	0.986794i	$0.551789\pi$
$462$	−1.95464	+	1.64014i	−0.0909379	+	0.0763060i
$463$	−16.3924	−	28.3924i	−0.761818	−	1.31951i	−0.941913	−	0.335857i	$-0.890974\pi$
$463$	−16.3924	−	28.3924i	−0.761818	−	1.31951i	0.180095	−	0.983649i	$-0.442359\pi$
$464$	−2.54607	+	4.40992i	−0.118198	+	0.204726i
$465$	−0.147823	−	0.838348i	−0.00685515	−	0.0388775i
$466$	1.49774	+	8.49412i	0.0693816	+	0.393483i
$467$	−10.4454	+	18.0920i	−0.483357	+	0.837199i	−0.999817	−	0.0191122i	$-0.993916\pi$
$467$	−10.4454	+	18.0920i	−0.483357	+	0.837199i	0.516460	+	0.856311i	$0.327249\pi$
$468$	0.590078	+	1.02205i	0.0272764	+	0.0472441i
$469$	5.58758	−	4.68853i	0.258010	−	0.216496i
$470$	−1.02306	+	0.372365i	−0.0471905	+	0.0171759i
$471$	21.4093	+	7.79235i	0.986489	+	0.359053i
$472$	12.8884	+	10.8146i	0.593236	+	0.497784i
$473$	−1.90338	+	10.7946i	−0.0875173	+	0.496336i
$474$	−4.15476			−0.190835
$475$	−18.1337	+	4.92109i	−0.832032	+	0.225795i
$476$	−0.489994			−0.0224588
$477$	0.990457	−	5.61716i	0.0453499	−	0.257192i
$478$	16.5560	+	13.8922i	0.757255	+	0.635412i
$479$	15.4838	+	5.63564i	0.707473	+	0.257499i	0.670598	−	0.741821i	$-0.266038\pi$
$479$	15.4838	+	5.63564i	0.707473	+	0.257499i	0.0368748	+	0.999320i	$0.488260\pi$
$480$	−4.55958	+	1.65955i	−0.208115	+	0.0757477i
$481$	0.109898	−	0.0922151i	0.00501090	−	0.00420465i
$482$	−4.31831	−	7.47954i	−0.196694	−	0.340684i
$483$	1.77426	−	3.07311i	0.0807317	−	0.139831i
$484$	−0.435719	−	2.47109i	−0.0198054	−	0.112322i
$485$	1.18531	+	6.72223i	0.0538222	+	0.305241i
$486$	−0.358173	+	0.620373i	−0.0162470	+	0.0281407i
$487$	−2.46421	−	4.26813i	−0.111664	−	0.193407i	0.804777	−	0.593577i	$-0.202285\pi$
$487$	−2.46421	−	4.26813i	−0.111664	−	0.193407i	−0.916441	+	0.400169i	$0.868951\pi$
$488$	−24.1939	+	20.3011i	−1.09521	+	0.918988i
$489$	−2.42411	+	0.882306i	−0.109622	+	0.0398992i
$490$	0.558900	+	0.203423i	0.0252485	+	0.00918972i
$491$	23.4418	+	19.6700i	1.05791	+	0.887696i	0.993904	−	0.110253i	$-0.0351662\pi$
$491$	23.4418	+	19.6700i	1.05791	+	0.887696i	0.0640112	+	0.997949i	$0.479611\pi$
$492$	−0.470124	+	2.66620i	−0.0211948	+	0.120202i
$493$	−1.41683			−0.0638109
$494$	0.223897	+	2.46827i	0.0100736	+	0.111053i
$495$	2.95744			0.132927
$496$	0.210874	−	1.19593i	0.00946852	−	0.0536986i
$497$	10.0547	+	8.43693i	0.451017	+	0.378448i
$498$	−6.43330	−	2.34153i	−0.288283	−	0.104927i
$499$	30.2753	−	11.0193i	1.35531	−	0.493292i	0.440708	−	0.897650i	$-0.354727\pi$
$499$	30.2753	−	11.0193i	1.35531	−	0.493292i	0.914601	+	0.404359i	$0.132505\pi$
$500$	8.80494	−	7.38822i	0.393769	−	0.330411i
$501$	1.40190	+	2.42816i	0.0626322	+	0.108482i
$502$	−3.86517	+	6.69468i	−0.172511	+	0.298798i
$503$	−0.424412	−	2.40696i	−0.0189236	−	0.107321i	0.973883	−	0.227051i	$-0.0729083\pi$
$503$	−0.424412	−	2.40696i	−0.0189236	−	0.107321i	−0.992807	+	0.119730i	$0.961797\pi$
$504$	−0.433736	−	2.45984i	−0.0193202	−	0.109570i
$505$	3.68974	−	6.39082i	0.164191	−	0.284388i
$506$	−4.52720	−	7.84134i	−0.201259	−	0.348590i
$507$	9.47596	−	7.95128i	0.420842	−	0.353129i
$508$	3.34571	−	1.21774i	0.148442	−	0.0540284i
$509$	−11.9167	−	4.33731i	−0.528196	−	0.192248i	0.0641365	−	0.997941i	$-0.479571\pi$
$509$	−11.9167	−	4.33731i	−0.528196	−	0.192248i	−0.592333	+	0.805693i	$0.701793\pi$
$510$	−0.150150	−	0.125991i	−0.00664877	−	0.00557898i
$511$	0.669427	−	3.79651i	0.0296137	−	0.167948i
$512$	−12.8387			−0.567394
$513$	3.56259	−	2.51156i	0.157292	−	0.110888i
$514$	2.55798			0.112828
$515$	−2.71342	+	15.3886i	−0.119568	+	0.678102i
$516$	−3.50498	−	2.94103i	−0.154298	−	0.129472i
$517$	6.12695	+	2.23003i	0.269463	+	0.0980765i
$518$	−0.121666	+	0.0442829i	−0.00534571	+	0.00194568i
$519$	−5.67179	+	4.75920i	−0.248964	+	0.208905i
$520$	−0.823046	−	1.42556i	−0.0360930	−	0.0625148i
$521$	−5.77167	+	9.99683i	−0.252861	+	0.437969i	−0.964312	−	0.264767i	$-0.914705\pi$
$521$	−5.77167	+	9.99683i	−0.252861	+	0.437969i	0.711451	+	0.702736i	$0.248038\pi$
$522$	−0.534795	−	3.03297i	−0.0234073	−	0.132750i
$523$	0.0353734	+	0.200613i	0.00154677	+	0.00877218i	0.985571	−	0.169260i	$-0.0541379\pi$
$523$	0.0353734	+	0.200613i	0.00154677	+	0.00877218i	−0.984025	+	0.178033i	$0.943027\pi$
$524$	5.22585	−	9.05143i	0.228292	−	0.395414i
$525$	2.15531	+	3.73312i	0.0940657	+	0.162926i
$526$	−2.44984	+	2.05566i	−0.106818	+	0.0896309i
$527$	0.317509	−	0.115564i	0.0138309	−	0.00503404i
$528$	3.96444	+	1.44294i	0.172530	+	0.0627958i
$529$	−7.97298	−	6.69013i	−0.346651	−	0.290875i
$530$	−0.589093	+	3.34091i	−0.0255886	+	0.145120i
$531$	6.73580			0.292309
$532$	−1.65740	+	6.26552i	−0.0718573	+	0.271645i
$533$	−1.44527			−0.0626014
$534$	0.159786	−	0.906193i	0.00691462	−	0.0392148i
$535$	3.78318	+	3.17446i	0.163561	+	0.137244i
$536$	17.1203	+	6.23127i	0.739484	+	0.269150i
$537$	11.9401	−	4.34584i	0.515254	−	0.187537i
$538$	0.845869	−	0.709768i	0.0364680	−	0.0306003i
$539$	−1.78098	−	3.08475i	−0.0767124	−	0.132870i
$540$	−0.617253	+	1.06911i	−0.0265623	+	0.0460073i
$541$	6.92816	+	39.2915i	0.297865	+	1.68928i	0.655325	+	0.755347i	$0.272532\pi$
$541$	6.92816	+	39.2915i	0.297865	+	1.68928i	−0.357460	+	0.933928i	$0.616357\pi$
$542$	3.66892	+	20.8075i	0.157594	+	0.893758i
$543$	8.20554	−	14.2124i	0.352133	−	0.609913i
$544$	−0.962956	−	1.66789i	−0.0412864	−	0.0715101i
$545$	3.40070	−	2.85353i	0.145670	−	0.122232i
$546$	0.534294	−	0.194467i	0.0228657	−	0.00832243i
$547$	−5.38208	−	1.95892i	−0.230121	−	0.0837572i	0.224386	−	0.974500i	$-0.427962\pi$
$547$	−5.38208	−	1.95892i	−0.230121	−	0.0837572i	−0.454507	+	0.890743i	$0.650185\pi$
$548$	10.7212	+	8.99612i	0.457985	+	0.384295i
$549$	−2.19567	+	12.4523i	−0.0937089	+	0.531450i
$550$	10.9990			0.468999
$551$	−4.79241	+	18.1169i	−0.204164	+	0.771807i
$552$	8.86346			0.377254
$553$	1.00715	−	5.71183i	0.0428284	−	0.242892i
$554$	−11.7818	−	9.88606i	−0.500559	−	0.420019i
$555$	0.141018	+	0.0513263i	0.00598588	+	0.00217868i
$556$	−17.5156	+	6.37516i	−0.742828	+	0.270367i
$557$	17.7139	−	14.8637i	0.750563	−	0.629797i	−0.185089	−	0.982722i	$-0.559257\pi$
$557$	17.7139	−	14.8637i	0.750563	−	0.629797i	0.935652	+	0.352925i	$0.114813\pi$
$558$	0.367231	+	0.636062i	0.0155461	+	0.0269267i
$559$	1.22126	−	2.11528i	0.0516537	−	0.0894668i
$560$	−0.170766	−	0.968464i	−0.00721620	−	0.0409251i
$561$	0.203837	+	1.15602i	0.00860602	+	0.0488072i
$562$	−9.09741	+	15.7572i	−0.383751	+	0.664676i
$563$	16.8996	+	29.2709i	0.712233	+	1.23362i	0.964017	+	0.265840i	$0.0856493\pi$
$563$	16.8996	+	29.2709i	0.712233	+	1.23362i	−0.251784	+	0.967783i	$0.581017\pi$
$564$	−2.08492	+	1.74946i	−0.0877910	+	0.0736654i
$565$	−16.0015	+	5.82408i	−0.673189	+	0.245021i
$566$	−9.01987	−	3.28297i	−0.379134	−	0.137993i
$567$	−0.766044	−	0.642788i	−0.0321708	−	0.0269945i
$568$	−5.69302	+	32.2867i	−0.238874	+	1.35472i
$569$	−9.16448			−0.384195			−0.192097	−	0.981376i	$-0.561529\pi$
$569$	−9.16448			−0.384195			−0.192097	+	0.981376i	$0.561529\pi$
$570$	−2.11892	+	1.49380i	−0.0887518	+	0.0625684i
$571$	−7.33201			−0.306835			−0.153418	−	0.988161i	$-0.549028\pi$
$571$	−7.33201			−0.306835			−0.153418	+	0.988161i	$0.549028\pi$
$572$	−0.729961	+	4.13981i	−0.0305212	+	0.173094i
$573$	4.90039	+	4.11192i	0.204717	+	0.171778i
$574$	1.22570	+	0.446117i	0.0511596	+	0.0186206i
$575$	−14.3739	+	5.23167i	−0.599432	+	0.218176i
$576$	1.39229	−	1.16827i	0.0580120	−	0.0486778i
$577$	−8.78407	−	15.2145i	−0.365685	−	0.633386i	0.623200	−	0.782062i	$-0.285832\pi$
$577$	−8.78407	−	15.2145i	−0.365685	−	0.633386i	−0.988886	+	0.148676i	$0.952499\pi$
$578$	−6.05004	+	10.4790i	−0.251648	+	0.435868i
$579$	3.15784	+	17.9090i	0.131235	+	0.744272i
$580$	−0.921633	−	5.22684i	−0.0382687	−	0.217033i
$581$	4.77855	−	8.27669i	0.198248	−	0.343375i
$582$	−2.94461	−	5.10022i	−0.122058	−	0.211411i
$583$	15.5636	−	13.0594i	0.644577	−	0.540864i
$584$	9.04845	−	3.29337i	0.374428	−	0.136281i
$585$	−0.619276	−	0.225398i	−0.0256039	−	0.00931907i
$586$	−5.22570	−	4.38488i	−0.215872	−	0.181138i
$587$	2.30686	−	13.0829i	0.0952144	−	0.539987i	−0.899467	−	0.436988i	$-0.856045\pi$
$587$	2.30686	−	13.0829i	0.0952144	−	0.539987i	0.994681	−	0.102999i	$-0.0328438\pi$
$588$	1.48685			0.0613166
$589$	−0.403738	−	4.45086i	−0.0166357	−	0.183395i
$590$	−4.00625			−0.164935
$591$	0.310938	−	1.76342i	0.0127903	−	0.0725373i
$592$	0.163992	+	0.137605i	0.00674002	+	0.00565555i
$593$	−13.6023	−	4.95084i	−0.558580	−	0.203307i	0.0472744	−	0.998882i	$-0.484946\pi$
$593$	−13.6023	−	4.95084i	−0.558580	−	0.203307i	−0.605855	+	0.795575i	$0.707169\pi$
$594$	−2.39772	+	0.872698i	−0.0983795	+	0.0358072i
$595$	0.209606	−	0.175880i	0.00859301	−	0.00721039i
$596$	4.97545	+	8.61774i	0.203803	+	0.352996i
$597$	5.83745	−	10.1108i	0.238911	−	0.413806i
$598$	0.350358	+	1.98698i	0.0143272	+	0.0812537i
$599$	−5.93021	−	33.6319i	−0.242302	−	1.37416i	−0.826676	−	0.562678i	$-0.809771\pi$
$599$	−5.93021	−	33.6319i	−0.242302	−	1.37416i	0.584374	−	0.811484i	$-0.301340\pi$
$600$	−5.38352	+	9.32453i	−0.219781	+	0.380672i
$601$	5.68031	+	9.83859i	0.231705	+	0.401324i	0.958310	−	0.285731i	$-0.0922364\pi$
$601$	5.68031	+	9.83859i	0.231705	+	0.401324i	−0.726605	+	0.687055i	$0.758903\pi$
$602$	−1.68866	+	1.41695i	−0.0688245	+	0.0577506i
$603$	6.85418	−	2.49472i	0.279124	−	0.101593i
$604$	17.6400	+	6.42044i	0.717762	+	0.261244i
$605$	1.07337	+	0.900665i	0.0436387	+	0.0366172i
$606$	−1.10559	+	6.27009i	−0.0449114	+	0.254705i
$607$	−15.6709			−0.636062			−0.318031	−	0.948080i	$-0.603022\pi$
$607$	−15.6709			−0.636062			−0.318031	+	0.948080i	$0.603022\pi$
$608$	−24.5843	+	6.67164i	−0.997027	+	0.270571i
$609$	4.29927			0.174215
$610$	1.30592	−	7.40622i	0.0528750	−	0.299869i
$611$	−1.11300	−	0.933918i	−0.0450272	−	0.0377823i
$612$	−0.460444	−	0.167588i	−0.0186123	−	0.00677434i
$613$	31.2612	−	11.3782i	1.26263	−	0.459559i	0.377978	−	0.925814i	$-0.376619\pi$
$613$	31.2612	−	11.3782i	1.26263	−	0.459559i	0.884650	+	0.466255i	$0.154397\pi$
$614$	−12.9194	+	10.8407i	−0.521386	+	0.437495i
$615$	−0.755912	−	1.30928i	−0.0304813	−	0.0527952i
$616$	4.44852	−	7.70506i	0.179236	−	0.310446i
$617$	7.41133	+	42.0317i	0.298369	+	1.69213i	0.653186	+	0.757198i	$0.273432\pi$
$617$	7.41133	+	42.0317i	0.298369	+	1.69213i	−0.354817	+	0.934936i	$0.615457\pi$
$618$	−2.34107	−	13.2768i	−0.0941715	−	0.534073i
$619$	6.38904	−	11.0661i	0.256797	−	0.444786i	−0.708585	−	0.705626i	$-0.750666\pi$
$619$	6.38904	−	11.0661i	0.256797	−	0.444786i	0.965382	+	0.260840i	$0.0839994\pi$
$620$	0.632863	+	1.09615i	0.0254164	+	0.0440225i
$621$	2.71833	−	2.28095i	0.109083	−	0.0915312i
$622$	6.83881	−	2.48912i	0.274211	−	0.0998047i
$623$	1.20707	+	0.439338i	0.0483602	+	0.0176017i
$624$	−0.720166	−	0.604291i	−0.0288297	−	0.0241910i
$625$	2.62811	−	14.9048i	0.105124	−	0.596190i
$626$	0.311926			0.0124671
$627$	15.4714	+	1.30376i	0.617869	+	0.0520672i
$628$	−33.8754			−1.35177
$629$	−0.0103432	+	0.0586594i	−0.000412412	+	0.00233890i
$630$	0.455620	+	0.382310i	0.0181523	+	0.0152316i
$631$	−4.09896	−	1.49190i	−0.163177	−	0.0593916i	0.259140	−	0.965840i	$-0.416561\pi$
$631$	−4.09896	−	1.49190i	−0.163177	−	0.0593916i	−0.422317	+	0.906448i	$0.638783\pi$
$632$	13.6134	−	4.95486i	0.541510	−	0.197094i
$633$	4.54514	−	3.81383i	0.180653	−	0.151586i
$634$	−5.08656	−	8.81018i	−0.202013	−	0.349897i
$635$	−0.994103	+	1.72184i	−0.0394498	+	0.0683290i
$636$	1.47266	+	8.35187i	0.0583948	+	0.331173i
$637$	0.137830	+	0.781671i	0.00546101	+	0.0309709i
$638$	5.48500	−	9.50030i	0.217153	−	0.376120i
$639$	6.56276	+	11.3670i	0.259619	+	0.449673i
$640$	6.60591	−	5.54302i	0.261122	−	0.219107i
$641$	12.5572	−	4.57044i	0.495979	−	0.180521i	−0.0819057	−	0.996640i	$-0.526101\pi$
$641$	12.5572	−	4.57044i	0.495979	−	0.180521i	0.577884	+	0.816119i	$0.303878\pi$
$642$	−4.00391	−	1.45731i	−0.158022	−	0.0575152i
$643$	−22.9644	−	19.2694i	−0.905628	−	0.759912i	0.0656542	−	0.997842i	$-0.479087\pi$
$643$	−22.9644	−	19.2694i	−0.905628	−	0.759912i	−0.971282	+	0.237930i	$0.923531\pi$
$644$	−0.916188	+	5.19596i	−0.0361029	+	0.204750i
$645$	2.55500			0.100603
$646$	−0.729947	−	0.725296i	−0.0287194	−	0.0285364i
$647$	5.32431			0.209320			0.104660	−	0.994508i	$-0.466625\pi$
$647$	5.32431			0.209320			0.104660	+	0.994508i	$0.466625\pi$
$648$	0.433736	−	2.45984i	0.0170388	−	0.0966317i
$649$	18.3795	+	15.4222i	0.721457	+	0.605374i
$650$	−2.30315	−	0.838276i	−0.0903368	−	0.0328799i
$651$	−0.963457	+	0.350670i	−0.0377609	+	0.0137438i
$652$	2.93825	−	2.46548i	0.115071	−	0.0965557i
$653$	6.83802	+	11.8438i	0.267592	+	0.463483i	0.968240	−	0.250024i	$-0.0804387\pi$
$653$	6.83802	+	11.8438i	0.267592	+	0.463483i	−0.700647	+	0.713508i	$0.747105\pi$
$654$	−1.91505	+	3.31697i	−0.0748845	+	0.129704i
$655$	1.01348	+	5.74774i	0.0396000	+	0.224583i
$656$	−0.374499	−	2.12389i	−0.0146217	−	0.0829241i
$657$	1.92754	−	3.33859i	0.0752004	−	0.130251i
$658$	0.655633	+	1.13559i	0.0255593	+	0.0442699i
$659$	3.71484	−	3.11712i	0.144710	−	0.121426i	−0.567559	−	0.823333i	$-0.692112\pi$
$659$	3.71484	−	3.11712i	0.144710	−	0.121426i	0.712269	+	0.701907i	$0.247668\pi$
$660$	−4.13208	+	1.50395i	−0.160841	+	0.0585413i
$661$	−44.7501	−	16.2877i	−1.74058	−	0.633518i	−0.741285	−	0.671190i	$-0.765783\pi$
$661$	−44.7501	−	16.2877i	−1.74058	−	0.633518i	−0.999290	+	0.0376723i	$0.988006\pi$
$662$	11.7280	+	9.84099i	0.455823	+	0.382481i
$663$	0.0454220	−	0.257601i	0.00176405	−	0.0100044i
$664$	23.8716			0.926398
$665$	−1.53998	−	3.27513i	−0.0597179	−	0.127004i
$666$	−0.129475			−0.00501704
$667$	−2.64918	+	15.0243i	−0.102577	+	0.581742i
$668$	−3.19350	−	2.67967i	−0.123560	−	0.103679i
$669$	7.90600	+	2.87755i	0.305663	+	0.111252i
$670$	−4.07666	+	1.48378i	−0.157495	+	0.0573235i
$671$	−34.5017	+	28.9504i	−1.33192	+	1.11762i
$672$	2.92201	+	5.06108i	0.112719	+	0.195235i
$673$	14.7209	−	25.4973i	0.567449	−	0.982851i	−0.429368	−	0.903130i	$-0.641264\pi$
$673$	14.7209	−	25.4973i	0.567449	−	0.982851i	0.996817	−	0.0797211i	$-0.0254030\pi$
$674$	−1.48744	−	8.43572i	−0.0572942	−	0.324932i
$675$	0.748533	+	4.24514i	0.0288111	+	0.163396i
$676$	−9.19616	+	15.9282i	−0.353698	+	0.612624i
$677$	9.46249	+	16.3895i	0.363673	+	0.629900i	0.988562	−	0.150813i	$-0.0481892\pi$
$677$	9.46249	+	16.3895i	0.363673	+	0.629900i	−0.624889	+	0.780713i	$0.714856\pi$
$678$	11.2545	−	9.44364i	0.432226	−	0.362681i
$679$	7.72541	−	2.81182i	0.296474	−	0.107908i
$680$	0.642231	+	0.233753i	0.0246284	+	0.00896402i
$681$	−17.7390	−	14.8848i	−0.679759	−	0.570385i
$682$	−0.454286	+	2.57638i	−0.0173955	+	0.0986548i
$683$	−41.7889			−1.59901			−0.799504	−	0.600661i	$-0.794904\pi$
$683$	−41.7889			−1.59901			−0.799504	+	0.600661i	$0.794904\pi$
$684$	−3.70038	+	5.32080i	−0.141487	+	0.203446i
$685$	−7.81533			−0.298608
$686$	0.124392	−	0.705462i	0.00474931	−	0.0269347i
$687$	10.4157	+	8.73983i	0.397385	+	0.333445i
$688$	3.42497	+	1.24659i	0.130576	+	0.0475257i
$689$	−4.25426	+	1.54842i	−0.162074	+	0.0589902i
$690$	−1.61678	+	1.35664i	−0.0615496	+	0.0516463i
$691$	9.02531	+	15.6323i	0.343339	+	0.594680i	0.985051	−	0.172266i	$-0.0551087\pi$
$691$	9.02531	+	15.6323i	0.343339	+	0.594680i	−0.641712	+	0.766946i	$0.721775\pi$
$692$	5.50431	−	9.53375i	0.209243	−	0.362419i
$693$	−0.618529	−	3.50785i	−0.0234960	−	0.133252i
$694$	3.85828	+	21.8814i	0.146458	+	0.830607i
$695$	5.20438	−	9.01425i	0.197413	−	0.341930i
$696$	5.36933	+	9.29995i	0.203524	+	0.352514i
$697$	0.459677	−	0.385715i	0.0174115	−	0.0146100i
$698$	12.6211	−	4.59369i	0.477714	−	0.173874i
$699$	−11.3144	−	4.11810i	−0.427949	−	0.155761i
$700$	−4.90978	−	4.11979i	−0.185572	−	0.155713i
$701$	1.05086	−	5.95971i	0.0396903	−	0.225095i	−0.958510	−	0.285058i	$-0.907987\pi$
$701$	1.05086	−	5.95971i	0.0396903	−	0.225095i	0.998201	+	0.0599629i	$0.0190982\pi$
$702$	0.568584			0.0214598
$703$	0.715088	+	0.330673i	0.0269700	+	0.0124716i
$704$	6.47388			0.243993
$705$	0.263916	−	1.49674i	0.00993964	−	0.0563705i
$706$	17.4077	+	14.6068i	0.655149	+	0.549735i
$707$	−8.35191	−	3.03985i	−0.314106	−	0.114325i
$708$	−9.41113	+	3.42537i	−0.353692	+	0.128733i
$709$	−5.16727	+	4.33586i	−0.194061	+	0.162837i	−0.734641	−	0.678456i	$-0.762649\pi$
$709$	−5.16727	+	4.33586i	−0.194061	+	0.162837i	0.540580	+	0.841293i	$0.318205\pi$
$710$	−3.90333	−	6.76077i	−0.146489	−	0.253727i
$711$	2.89997	−	5.02290i	0.108757	−	0.188373i
$712$	0.557150	+	3.15976i	0.0208801	+	0.118417i
$713$	−0.631778	−	3.58299i	−0.0236603	−	0.134184i
$714$	−0.118036	+	0.204445i	−0.00441740	+	0.00765117i
$715$	−1.17370	−	2.03291i	−0.0438940	−	0.0760267i
$716$	−14.4725	+	12.1439i	−0.540862	+	0.453838i
$717$	−28.3508	+	10.3189i	−1.05878	+	0.385365i
$718$	6.40788	+	2.33228i	0.239140	+	0.0870399i
$719$	−24.8355	−	20.8394i	−0.926206	−	0.777179i	0.0489262	−	0.998802i	$-0.484420\pi$
$719$	−24.8355	−	20.8394i	−0.926206	−	0.777179i	−0.975132	+	0.221623i	$0.928865\pi$
$720$	0.170766	−	0.968464i	0.00636409	−	0.0360925i
$721$	18.8201			0.700896
$722$	−11.7433	+	6.88048i	−0.437042	+	0.256065i
$723$	12.0565			0.448387
$724$	−4.23715	+	24.0301i	−0.157473	+	0.893071i
$725$	−14.1968	−	11.9125i	−0.527254	−	0.442419i
$726$	−1.13600	−	0.413470i	−0.0421609	−	0.0153453i
$727$	−13.7636	+	5.00956i	−0.510465	+	0.185794i	−0.584395	−	0.811469i	$-0.698668\pi$
$727$	−13.7636	+	5.00956i	−0.510465	+	0.185794i	0.0739298	+	0.997263i	$0.476446\pi$
$728$	−1.51873	+	1.27437i	−0.0562881	+	0.0472313i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−1.14644	+	1.98569i	−0.0424317	+	0.0734938i
$731$	0.176100	+	0.998711i	0.00651329	+	0.0369387i
$732$	−3.26463	−	18.5146i	−0.120664	−	0.684321i
$733$	4.75964	−	8.24393i	0.175801	−	0.304497i	−0.764637	−	0.644461i	$-0.777082\pi$
$733$	4.75964	−	8.24393i	0.175801	−	0.304497i	0.940438	+	0.339965i	$0.110415\pi$
$734$	4.48747	+	7.77252i	0.165635	+	0.286889i
$735$	−0.636034	+	0.533696i	−0.0234605	+	0.0196857i
$736$	−19.4870	+	7.09270i	−0.718302	+	0.261440i
$737$	24.4144	+	8.88610i	0.899314	+	0.327324i
$738$	0.999198	+	0.838426i	0.0367810	+	0.0308629i
$739$	7.04937	−	39.9789i	0.259315	−	1.47065i	−0.525433	−	0.850835i	$-0.676097\pi$
$739$	7.04937	−	39.9789i	0.259315	−	1.47065i	0.784748	−	0.619814i	$-0.212792\pi$
$740$	−0.223129			−0.00820237
$741$	−3.14029	−	1.45214i	−0.115361	−	0.0533457i
$742$	4.08590			0.149998
$743$	−2.32379	+	13.1789i	−0.0852517	+	0.483486i	0.912050	+	0.410078i	$0.134499\pi$
$743$	−2.32379	+	13.1789i	−0.0852517	+	0.483486i	−0.997302	+	0.0734079i	$0.976612\pi$
$744$	−1.96181	−	1.64615i	−0.0719233	−	0.0603508i
$745$	−5.22165	−	1.90053i	−0.191306	−	0.0696299i
$746$	15.0682	−	5.48437i	0.551685	−	0.200797i
$747$	7.32116	−	6.14318i	0.267867	−	0.224767i
$748$	−0.872671	−	1.51151i	−0.0319080	−	0.0552663i
$749$	2.97404	−	5.15118i	0.108669	−	0.188220i
$750$	−0.961608	−	5.45355i	−0.0351129	−	0.199135i
$751$	1.97270	+	11.1878i	0.0719850	+	0.408247i	0.999413	+	0.0342465i	$0.0109031\pi$
$751$	1.97270	+	11.1878i	0.0719850	+	0.408247i	−0.927428	+	0.374001i	$0.877986\pi$
$752$	1.08404	−	1.87761i	0.0395308	−	0.0684694i
$753$	−5.39568	−	9.34560i	−0.196630	−	0.340573i
$754$	−1.87259	+	1.57129i	−0.0681958	+	0.0572231i
$755$	−9.85050	+	3.58529i	−0.358496	+	0.130482i
$756$	1.39718	+	0.508532i	0.0508150	+	0.0184951i
$757$	15.6270	+	13.1126i	0.567971	+	0.476585i	0.880972	−	0.473168i	$-0.156890\pi$
$757$	15.6270	+	13.1126i	0.567971	+	0.476585i	−0.313001	+	0.949753i	$0.601334\pi$
$758$	−1.86421	+	10.5724i	−0.0677110	+	0.384008i
$759$	12.6397			0.458793
$760$	5.16132	−	7.42150i	0.187221	−	0.269206i
$761$	−44.7223			−1.62118			−0.810591	−	0.585612i	$-0.800854\pi$
$761$	−44.7223			−1.62118			−0.810591	+	0.585612i	$0.800854\pi$
$762$	0.297871	−	1.68931i	0.0107907	−	0.0611972i
$763$	−4.09583	−	3.43681i	−0.148279	−	0.124421i
$764$	−8.93779	−	3.25309i	−0.323358	−	0.117693i
$765$	0.257120	−	0.0935840i	0.00929619	−	0.00338354i
$766$	14.1425	−	11.8670i	0.510990	−	0.428771i
$767$	−2.67320	−	4.63012i	−0.0965237	−	0.167184i
$768$	−5.53752	+	9.59126i	−0.199818	+	0.346095i
$769$	−0.0947392	−	0.537293i	−0.00341638	−	0.0193753i	0.983052	−	0.183327i	$-0.0586868\pi$
$769$	−0.0947392	−	0.537293i	−0.00341638	−	0.0193753i	−0.986468	+	0.163952i	$0.947576\pi$
$770$	0.367882	+	2.08636i	0.0132575	+	0.0751873i
$771$	−1.78544	+	3.09248i	−0.0643011	+	0.111373i
$772$	−13.5194	−	23.4162i	−0.486573	−	0.842769i
$773$	−19.5167	+	16.3764i	−0.701966	+	0.589019i	−0.922332	−	0.386398i	$-0.873719\pi$
$773$	−19.5167	+	16.3764i	−0.701966	+	0.589019i	0.220366	+	0.975417i	$0.429275\pi$
$774$	−2.07144	+	0.753944i	−0.0744565	+	0.0270999i
$775$	4.15311	+	1.51161i	0.149184	+	0.0542986i
$776$	15.7306	+	13.1995i	0.564696	+	0.473836i
$777$	0.0313857	−	0.177997i	0.00112596	−	0.00638562i
$778$	14.6594			0.525565
$779$	−3.37726	−	7.18253i	−0.121003	−	0.257341i
$780$	0.979864			0.0350847
$781$	−8.11852	+	46.0424i	−0.290503	+	1.64753i
$782$	−0.641723	−	0.538470i	−0.0229480	−	0.0192556i
$783$	4.03999	+	1.47044i	0.144377	+	0.0525491i
$784$	−1.11299	+	0.405096i	−0.0397497	+	0.0144677i
$785$	14.4910	−	12.1594i	0.517204	−	0.433986i
$786$	−2.51775	−	4.36086i	−0.0898050	−	0.155547i
$787$	13.2356	−	22.9247i	0.471798	−	0.817178i	−0.527682	−	0.849442i	$-0.676939\pi$
$787$	13.2356	−	22.9247i	0.471798	−	0.817178i	0.999479	+	0.0322646i	$0.0102719\pi$
$788$	0.462318	+	2.62194i	0.0164694	+	0.0934026i
$789$	−0.775231	−	4.39655i	−0.0275989	−	0.156521i
$790$	−1.72481	+	2.98747i	−0.0613662	+	0.106289i
$791$	10.2546	+	17.7615i	0.364612	+	0.631527i
$792$	6.81552	−	5.71890i	0.242179	−	0.203212i
$793$	9.43094	−	3.43258i	0.334903	−	0.121895i
$794$	−18.2755	−	6.65173i	−0.648573	−	0.236061i
$795$	−3.62782	−	3.04410i	−0.128665	−	0.107963i
$796$	−3.01433	+	17.0951i	−0.106840	+	0.605920i
$797$	4.77103			0.168999			0.0844994	−	0.996424i	$-0.473071\pi$
$797$	4.77103			0.168999			0.0844994	+	0.996424i	$0.473071\pi$
$798$	2.21497	+	2.20086i	0.0784091	+	0.0779095i
$799$	0.603243			0.0213412
$800$	4.37445	−	24.8087i	0.154660	−	0.877121i
$801$	0.984013	+	0.825685i	0.0347684	+	0.0291741i
$802$	13.3119	+	4.84513i	0.470059	+	0.171087i
$803$	12.9035	−	4.69650i	0.455356	−	0.165736i
$804$	−8.30789	+	6.97115i	−0.292997	+	0.245853i
$805$	−1.47314	−	2.55155i	−0.0519213	−	0.0899304i
$806$	0.291482	−	0.504861i	0.0102670	−	0.0177830i
$807$	0.267668	+	1.51802i	0.00942237	+	0.0534369i
$808$	−3.85501	−	21.8629i	−0.135619	−	0.769133i
$809$	23.2647	−	40.2957i	0.817944	−	1.41672i	−0.0892506	−	0.996009i	$-0.528447\pi$
$809$	23.2647	−	40.2957i	0.817944	−	1.41672i	0.907195	−	0.420711i	$-0.138219\pi$
$810$	0.297385	+	0.515085i	0.0104490	+	0.0180983i
$811$	16.0493	−	13.4670i	0.563569	−	0.472890i	−0.315936	−	0.948781i	$-0.602318\pi$
$811$	16.0493	−	13.4670i	0.563569	−	0.472890i	0.879505	+	0.475890i	$0.157874\pi$
$812$	−6.00686	+	2.18632i	−0.210799	+	0.0767247i
$813$	−27.7161	−	10.0878i	−0.972045	−	0.353795i
$814$	−0.353287	−	0.296443i	−0.0123827	−	0.0103903i
$815$	−0.371932	+	2.10933i	−0.0130282	+	0.0738867i
$816$	0.390328			0.0136642
$817$	13.3661	+	1.12635i	0.467621	+	0.0394060i
$818$	21.4808			0.751058
$819$	−0.137830	+	0.781671i	−0.00481616	+	0.0273138i
$820$	1.72196	+	1.44489i	0.0601333	+	0.0504579i
$821$	1.65273	+	0.601544i	0.0576806	+	0.0209940i	0.370699	−	0.928753i	$-0.379118\pi$
$821$	1.65273	+	0.601544i	0.0576806	+	0.0209940i	−0.313019	+	0.949747i	$0.601340\pi$
$822$	6.33620	−	2.30619i	0.221000	−	0.0804376i
$823$	17.8512	−	14.9790i	0.622255	−	0.522134i	−0.276256	−	0.961084i	$-0.589094\pi$
$823$	17.8512	−	14.9790i	0.622255	−	0.522134i	0.898512	+	0.438950i	$0.144649\pi$
$824$	23.5043	+	40.7106i	0.818810	+	1.41822i
$825$	−7.67716	+	13.2972i	−0.267284	+	0.462950i
$826$	0.837880	+	4.75185i	0.0291536	+	0.165338i
$827$	3.19686	+	18.1303i	0.111166	+	0.630453i	0.988577	+	0.150714i	$0.0481573\pi$
$827$	3.19686	+	18.1303i	0.111166	+	0.630453i	−0.877412	+	0.479738i	$0.840732\pi$
$828$	−2.63806	+	4.56925i	−0.0916789	+	0.158793i
$829$	2.24913	+	3.89560i	0.0781154	+	0.135300i	0.902437	−	0.430822i	$-0.141776\pi$
$829$	2.24913	+	3.89560i	0.0781154	+	0.135300i	−0.824321	+	0.566122i	$0.808443\pi$
$830$	−4.35440	+	3.65378i	−0.151143	+	0.126824i
$831$	20.1753	−	7.34320i	0.699872	−	0.254733i
$832$	−1.35560	−	0.493400i	−0.0469971	−	0.0171056i
$833$	−0.252451	−	0.211832i	−0.00874692	−	0.00733954i
$834$	−1.55943	+	8.84395i	−0.0539986	+	0.306241i
$835$	2.32794			0.0805618
$836$	−22.2794	+	6.04613i	−0.770548	+	0.209110i
$837$	−1.02529			−0.0354392
$838$	4.21473	−	23.9029i	0.145595	−	0.825713i
$839$	−34.0489	−	28.5705i	−1.17550	−	0.986362i	−0.999998	−	0.00188261i	$-0.999401\pi$
$839$	−34.0489	−	28.5705i	−1.17550	−	0.986362i	−0.175502	−	0.984479i	$-0.556155\pi$
$840$	−1.94880	−	0.709306i	−0.0672400	−	0.0244734i
$841$	9.88208	−	3.59678i	0.340762	−	0.124027i
$842$	17.5153	−	14.6971i	0.603618	−	0.506495i
$843$	−12.6998	−	21.9966i	−0.437403	−	0.757604i
$844$	−4.41094	+	7.63997i	−0.151831	+	0.262978i
$845$	−1.78347	−	10.1146i	−0.0613532	−	0.347952i
$846$	0.227699	+	1.29135i	0.00782846	+	0.0443974i
$847$	0.843800	−	1.46150i	0.0289933	−	0.0502179i
$848$	−3.37786	−	5.85062i	−0.115996	−	0.200911i
$849$	10.2647	−	8.61311i	0.352284	−	0.295601i
$850$	0.956253	−	0.348048i	0.0327992	−	0.0119379i
$851$	0.602692	+	0.219362i	0.0206600	+	0.00751963i
$852$	−14.9499	−	12.5444i	−0.512174	−	0.429765i
$853$	7.73416	−	43.8626i	0.264813	−	1.50183i	−0.504756	−	0.863262i	$-0.668417\pi$
$853$	7.73416	−	43.8626i	0.264813	−	1.50183i	0.769568	−	0.638564i	$-0.220471\pi$
$854$	−9.05773			−0.309949
$855$	−0.326948	−	3.60432i	−0.0111814	−	0.123265i
$856$	14.8570			0.507803
$857$	2.12811	−	12.0691i	0.0726948	−	0.412273i	−0.926645	−	0.375938i	$-0.877321\pi$
$857$	2.12811	−	12.0691i	0.0726948	−	0.412273i	0.999340	−	0.0363350i	$-0.0115683\pi$
$858$	1.55145	+	1.30182i	0.0529657	+	0.0444435i
$859$	−4.49970	−	1.63776i	−0.153528	−	0.0558796i	0.264113	−	0.964492i	$-0.414921\pi$
$859$	−4.49970	−	1.63776i	−0.153528	−	0.0558796i	−0.417641	+	0.908612i	$0.637143\pi$
$860$	−3.56980	+	1.29930i	−0.121729	+	0.0443058i
$861$	−1.39485	+	1.17042i	−0.0475365	+	0.0398879i
$862$	−9.85672	−	17.0723i	−0.335721	−	0.581486i
$863$	−7.89493	+	13.6744i	−0.268746	+	0.465483i	−0.968538	−	0.248864i	$-0.919943\pi$
$863$	−7.89493	+	13.6744i	−0.268746	+	0.465483i	0.699792	+	0.714347i	$0.253276\pi$
$864$	1.01481	+	5.75525i	0.0345244	+	0.195797i
$865$	1.06749	+	6.05402i	0.0362956	+	0.205843i
$866$	4.73608	−	8.20313i	0.160938	−	0.278754i
$867$	−8.44570	−	14.6284i	−0.286831	−	0.496806i
$868$	1.16780	−	0.979899i	0.0396376	−	0.0332599i
$869$	19.4133	−	7.06587i	0.658551	−	0.239693i
$870$	−2.40286	−	0.874570i	−0.0814647	−	0.0296507i
$871$	−4.43502	−	3.72143i	−0.150275	−	0.126096i
$872$	2.31907	−	13.1521i	0.0785337	−	0.445387i
$873$	8.22121			0.278246
$874$	−9.05599	+	6.38430i	−0.306323	+	0.215952i
$875$	7.73046			0.261337
$876$	−0.995337	+	5.64484i	−0.0336293	+	0.190721i
$877$	−33.9499	−	28.4873i	−1.14641	−	0.961949i	−0.146777	−	0.989170i	$-0.546890\pi$
$877$	−33.9499	−	28.4873i	−1.14641	−	0.961949i	−0.999629	+	0.0272203i	$0.991334\pi$
$878$	−18.3032	−	6.66182i	−0.617703	−	0.224825i
$879$	8.94858	−	3.25702i	0.301828	−	0.109856i
$880$	2.68334	−	2.25159i	0.0904554	−	0.0759011i
$881$	4.61067	+	7.98591i	0.155337	+	0.269052i	0.933182	−	0.359405i	$-0.117020\pi$
$881$	4.61067	+	7.98591i	0.155337	+	0.269052i	−0.777844	+	0.628457i	$0.783687\pi$
$882$	0.358173	−	0.620373i	0.0120603	−	0.0208891i
$883$	1.97595	+	11.2062i	0.0664962	+	0.377119i	0.999836	+	0.0181238i	$0.00576929\pi$
$883$	1.97595	+	11.2062i	0.0664962	+	0.377119i	−0.933340	+	0.358995i	$0.883120\pi$
$884$	0.0675357	+	0.383014i	0.00227147	+	0.0128822i
$885$	2.79631	−	4.84335i	0.0939969	−	0.162807i
$886$	−13.3200	−	23.0709i	−0.447494	−	0.775082i
$887$	−25.4743	+	21.3755i	−0.855344	+	0.717719i	−0.960960	−	0.276688i	$-0.910763\pi$
$887$	−25.4743	+	21.3755i	−0.855344	+	0.717719i	0.105615	+	0.994407i	$0.466319\pi$
$888$	0.424232	−	0.154408i	0.0142363	−	0.00518159i
$889$	2.25020	+	0.819006i	0.0754693	+	0.0274686i
$890$	−0.585260	−	0.491092i	−0.0196180	−	0.0164614i
$891$	0.618529	−	3.50785i	0.0207215	−	0.117517i
$892$	−12.5094			−0.418847
$893$	2.04046	−	7.71363i	0.0682814	−	0.258127i
$894$	4.79422			0.160343
$895$	1.83197	−	10.3896i	0.0612361	−	0.347287i
$896$	−7.95622	−	6.67606i	−0.265798	−	0.223031i
$897$	−2.64671	−	0.963322i	−0.0883710	−	0.0321644i
$898$	−20.7610	+	7.55637i	−0.692802	+	0.252159i
$899$	3.37672	−	2.83341i	0.112620	−	0.0944994i
$900$	−3.20463	−	5.55058i	−0.106821	−	0.185019i
$901$	0.939851	−	1.62787i	0.0313110	−	0.0542322i
$902$	0.806784	+	4.57550i	0.0268630	+	0.152348i
$903$	−0.534361	−	3.03051i	−0.0177824	−	0.100849i
$904$	−25.6139	+	44.3645i	−0.851904	+	1.47554i
$905$	−6.81292	−	11.8003i	−0.226469	−	0.392256i
$906$	6.92824	−	5.81348i	0.230175	−	0.193140i
$907$	1.04303	−	0.379633i	0.0346334	−	0.0126055i	−0.324645	−	0.945836i	$-0.605245\pi$
$907$	1.04303	−	0.379633i	0.0346334	−	0.0126055i	0.359279	+	0.933230i	$0.383023\pi$
$908$	32.3539	+	11.7759i	1.07370	+	0.390796i
$909$	−6.80854	−	5.71304i	−0.225825	−	0.189490i
$910$	0.0819769	−	0.464914i	0.00271751	−	0.0154117i
$911$	−36.2811			−1.20205			−0.601024	−	0.799231i	$-0.705240\pi$
$911$	−36.2811			−1.20205			−0.601024	+	0.799231i	$0.705240\pi$
$912$	1.32028	−	4.99110i	0.0437188	−	0.165272i
$913$	34.0420			1.12663
$914$	−0.424739	+	2.40882i	−0.0140491	+	0.0796766i
$915$	8.04224	+	6.74824i	0.265868	+	0.223090i
$916$	−18.9971	−	6.91440i	−0.627683	−	0.228458i
$917$	6.60550	−	2.40420i	0.218133	−	0.0793938i
$918$	−0.180842	+	0.151745i	−0.00596869	+	0.00500832i
$919$	21.5751	+	37.3691i	0.711696	+	1.23269i	0.964220	+	0.265102i	$0.0854058\pi$
$919$	21.5751	+	37.3691i	0.711696	+	1.23269i	−0.252525	+	0.967590i	$0.581261\pi$
$920$	3.67959	−	6.37323i	0.121312	−	0.210119i
$921$	−4.08825	−	23.1856i	−0.134712	−	0.763992i
$922$	−2.61588	−	14.8354i	−0.0861495	−	0.488578i
$923$	5.20906	−	9.02235i	0.171458	−	0.296974i
$924$	2.64805	+	4.58656i	0.0871146	+	0.150887i
$925$	−0.596839	+	0.500807i	−0.0196239	+	0.0164664i
$926$	22.0688	−	8.03240i	0.725227	−	0.263961i
$927$	17.6851	+	6.43684i	0.580854	+	0.211414i
$928$	−19.2469	−	16.1501i	−0.631811	−	0.530152i
$929$	9.90248	−	56.1598i	0.324890	−	1.84254i	−0.185558	−	0.982633i	$-0.559409\pi$
$929$	9.90248	−	56.1598i	0.324890	−	1.84254i	0.510448	−	0.859909i	$-0.329480\pi$
$930$	0.609811			0.0199965
$931$	−3.56259	+	2.51156i	−0.116759	+	0.0823131i
$932$	17.9024			0.586413
$933$	−1.76418	+	10.0052i	−0.0577566	+	0.327554i
$934$	−11.4639	−	9.61936i	−0.375111	−	0.314755i
$935$	0.915853	+	0.333343i	0.0299516	+	0.0109015i
$936$	−1.86300	+	0.678078i	−0.0608942	+	0.0221637i
$937$	5.58903	−	4.68975i	0.182586	−	0.153208i	−0.546914	−	0.837189i	$-0.684197\pi$
$937$	5.58903	−	4.68975i	0.182586	−	0.153208i	0.729500	+	0.683981i	$0.239753\pi$
$938$	2.61253	+	4.52504i	0.0853023	+	0.147748i
$939$	−0.217721	+	0.377103i	−0.00710505	+	0.0123063i
$940$	0.392403	+	2.22543i	0.0127988	+	0.0725854i
$941$	2.69317	+	15.2737i	0.0877947	+	0.497909i	0.996718	+	0.0809463i	$0.0257942\pi$
$941$	2.69317	+	15.2737i	0.0877947	+	0.497909i	−0.908924	+	0.416962i	$0.863095\pi$
$942$	−8.16036	+	14.1342i	−0.265879	+	0.460516i
$943$	−3.23067	−	5.59568i	−0.105205	−	0.182221i
$944$	6.11152	−	5.12817i	0.198913	−	0.166908i
$945$	−0.780211	+	0.283974i	−0.0253803	+	0.00923766i
$946$	−7.37841	−	2.68552i	−0.239893	−	0.0873138i
$947$	2.14161	+	1.79703i	0.0695930	+	0.0583955i	0.676921	−	0.736056i	$-0.263314\pi$
$947$	2.14161	+	1.79703i	0.0695930	+	0.0583955i	−0.607328	+	0.794451i	$0.707758\pi$
$948$	−1.49748	+	8.49263i	−0.0486359	+	0.275828i
$949$	−3.05989			−0.0993281
$950$	−1.21595	−	13.4048i	−0.0394507	−	0.434909i
$951$	14.2014			0.460513
$952$	0.142939	−	0.810645i	0.00463267	−	0.0262732i
$953$	−36.6100	−	30.7194i	−1.18591	−	0.995099i	−0.999921	−	0.0125482i	$-0.996006\pi$
$953$	−36.6100	−	30.7194i	−1.18591	−	0.995099i	−0.185992	−	0.982551i	$-0.559550\pi$
$954$	3.83949	+	1.39746i	0.124308	+	0.0452444i
$955$	4.99102	−	1.81658i	0.161506	−	0.0587832i
$956$	34.3638	−	28.8346i	1.11140	−	0.932578i
$957$	7.65692	+	13.2622i	0.247513	+	0.428705i
$958$	−5.90180	+	10.2222i	−0.190678	+	0.330265i
$959$	1.63452	+	9.26984i	0.0527815	+	0.299339i
$960$	−0.262042	−	1.48612i	−0.00845738	−	0.0479642i
$961$	14.9744	−	25.9364i	0.483045	−	0.836658i
$962$	0.0513839	+	0.0889995i	0.00165668	+	0.00286946i
$963$	4.55649	−	3.82335i	0.146831	−	0.123206i
$964$	−16.8451	+	6.13113i	−0.542545	+	0.197470i
$965$	14.1883	+	5.16413i	0.456739	+	0.166239i
$966$	1.94726	+	1.63394i	0.0626521	+	0.0525713i
$967$	0.474390	−	2.69040i	0.0152554	−	0.0865175i	−0.976230	−	0.216739i	$-0.930458\pi$
$967$	0.474390	−	2.69040i	0.0152554	−	0.0865175i	0.991485	+	0.130222i	$0.0415690\pi$
$968$	4.21527			0.135484
$969$	1.38634	−	0.376222i	0.0445357	−	0.0120860i
$970$	−4.88973			−0.157000
$971$	0.601985	−	3.41402i	0.0193186	−	0.109561i	−0.973624	−	0.228160i	$-0.926729\pi$
$971$	0.601985	−	3.41402i	0.0193186	−	0.109561i	0.992942	+	0.118599i	$0.0378402\pi$
$972$	1.13899	+	0.955728i	0.0365332	+	0.0306550i
$973$	−11.7804	−	4.28770i	−0.377661	−	0.137457i
$974$	3.31753	−	1.20748i	0.106301	−	0.0386903i
$975$	2.62100	−	2.19928i	0.0839392	−	0.0704334i
$976$	7.48812	+	12.9698i	0.239689	+	0.415153i
$977$	−21.8537	+	37.8517i	−0.699161	+	1.21098i	0.269596	+	0.962973i	$0.413110\pi$
$977$	−21.8537	+	37.8517i	−0.699161	+	1.21098i	−0.968758	+	0.248009i	$0.920224\pi$
$978$	−0.320893	−	1.81987i	−0.0102610	−	0.0581931i
$979$	0.794523	+	4.50597i	0.0253931	+	0.144011i
$980$	0.617253	−	1.06911i	0.0197174	−	0.0341516i
$981$	−2.67337	−	4.63040i	−0.0853540	−	0.147837i
$982$	−16.7924	+	14.0905i	−0.535868	+	0.449647i
$983$	38.4836	−	14.0069i	1.22744	−	0.446750i	0.354718	−	0.934973i	$-0.384577\pi$
$983$	38.4836	−	14.0069i	1.22744	−	0.446750i	0.872719	+	0.488223i	$0.162355\pi$
$984$	−4.27382	−	1.55554i	−0.136244	−	0.0495889i
$985$	−1.13890	−	0.955647i	−0.0362882	−	0.0304494i
$986$	0.176243	−	0.999522i	0.00561271	−	0.0318312i
$987$	−1.83050			−0.0582653
$988$	5.12601	+	0.431964i	0.163080	+	0.0137426i
$989$	10.9197			0.347228
$990$	−0.367882	+	2.08636i	−0.0116921	+	0.0663090i
$991$	17.3138	+	14.5280i	0.549990	+	0.461496i	0.874937	−	0.484236i	$-0.160902\pi$
$991$	17.3138	+	14.5280i	0.549990	+	0.461496i	−0.324948	+	0.945732i	$0.605347\pi$
$992$	5.63047	+	2.04933i	0.178768	+	0.0650661i
$993$	−20.0833	+	7.30972i	−0.637324	+	0.231967i
$994$	−7.20266	+	6.04375i	−0.228455	+	0.191696i
$995$	−4.84674	−	8.39479i	−0.153652	−	0.266133i
$996$	−7.10498	+	12.3062i	−0.225130	+	0.389936i
$997$	7.77462	+	44.0920i	0.246225	+	1.39641i	0.817631	+	0.575742i	$0.195287\pi$
$997$	7.77462	+	44.0920i	0.246225	+	1.39641i	−0.571407	+	0.820667i	$0.693602\pi$
$998$	4.00770	+	22.7288i	0.126862	+	0.719468i
$999$	0.0903716	−	0.156528i	0.00285923	−	0.00495234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	399.2.bo.b.169.2	yes	18
19.3	odd	18		7581.2.a.bh.1.5		9
19.9	even	9	inner	399.2.bo.b.85.2	✓	18
19.16	even	9		7581.2.a.bg.1.5		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.bo.b.85.2	✓	18	19.9	even	9	inner
399.2.bo.b.169.2	yes	18	1.1	even	1	trivial
7581.2.a.bg.1.5		9	19.16	even	9
7581.2.a.bh.1.5		9	19.3	odd	18

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:	\( N \)	\(=\)	\( 399 = 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	399.bo (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.124392 + 0.705462i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(1.39718 + 0.508532i) q^{4} +(-0.780211 + 0.283974i) q^{5} +(0.548752 - 0.460458i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-1.24889 + 2.16315i) q^{8} +(0.173648 + 0.984808i) q^{9} +(-0.103281 - 0.585733i) q^{10} +(-1.78098 + 3.08475i) q^{11} +(-0.743425 - 1.28765i) q^{12} +(0.608032 - 0.510199i) q^{13} +(-0.673144 + 0.245004i) q^{14} +(0.780211 + 0.283974i) q^{15} +(0.907319 + 0.761331i) q^{16} +(-0.0572261 + 0.324545i) q^{17} -0.716345 q^{18} +(3.95637 + 1.82951i) q^{19} -1.23451 q^{20} +(0.173648 - 0.984808i) q^{21} +(-1.95464 - 1.64014i) q^{22} +(3.33452 + 1.21367i) q^{23} +(2.34715 - 0.854294i) q^{24} +(-3.30213 + 2.77082i) q^{25} +(0.284292 + 0.492408i) q^{26} +(0.500000 - 0.866025i) q^{27} +(0.258189 + 1.46426i) q^{28} +(0.746560 + 4.23395i) q^{29} +(-0.297385 + 0.515085i) q^{30} +(-0.512645 - 0.887927i) q^{31} +(-4.47679 + 3.75647i) q^{32} +(3.34715 - 1.21826i) q^{33} +(-0.221836 - 0.0807417i) q^{34} +(-0.636034 - 0.533696i) q^{35} +(-0.258189 + 1.46426i) q^{36} +0.180743 q^{37} +(-1.78279 + 2.56349i) q^{38} -0.793729 q^{39} +(0.360124 - 2.04236i) q^{40} +(-1.39485 - 1.17042i) q^{41} +(0.673144 + 0.245004i) q^{42} +(2.89168 - 1.05249i) q^{43} +(-4.05705 + 3.40427i) q^{44} +(-0.415142 - 0.719046i) q^{45} +(-1.27098 + 2.20141i) q^{46} +(-0.317862 - 1.80269i) q^{47} +(-0.205672 - 1.16643i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-1.54395 - 2.67420i) q^{50} +(0.252451 - 0.211832i) q^{51} +(1.10898 - 0.403637i) q^{52} +(-5.35983 - 1.95082i) q^{53} +(0.548752 + 0.460458i) q^{54} +(0.513554 - 2.91251i) q^{55} -2.49779 q^{56} +(-1.85477 - 3.94460i) q^{57} -3.07976 q^{58} +(1.16966 - 6.63347i) q^{59} +(0.945686 + 0.793525i) q^{60} +(11.8818 + 4.32463i) q^{61} +(0.690168 - 0.251201i) q^{62} +(-0.766044 + 0.642788i) q^{63} +(-0.908751 - 1.57400i) q^{64} +(-0.329510 + 0.570728i) q^{65} +(0.443080 + 2.51283i) q^{66} +(-1.26660 - 7.18325i) q^{67} +(-0.244997 + 0.424347i) q^{68} +(-1.77426 - 3.07311i) q^{69} +(0.455620 - 0.382310i) q^{70} +(12.3340 - 4.48919i) q^{71} +(-2.34715 - 0.854294i) q^{72} +(-2.95316 - 2.47800i) q^{73} +(-0.0224830 + 0.127508i) q^{74} +4.31063 q^{75} +(4.59740 + 4.56811i) q^{76} -3.56197 q^{77} +(0.0987336 - 0.559946i) q^{78} +(-4.44302 - 3.72813i) q^{79} +(-0.924098 - 0.336344i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(0.999198 - 0.838426i) q^{82} +(-4.77855 - 8.27669i) q^{83} +(0.743425 - 1.28765i) q^{84} +(-0.0475139 - 0.269464i) q^{85} +(0.382787 + 2.17089i) q^{86} +(2.14963 - 3.72328i) q^{87} +(-4.44852 - 7.70506i) q^{88} +(0.984013 - 0.825685i) q^{89} +(0.558900 - 0.203423i) q^{90} +(0.745862 + 0.271471i) q^{91} +(4.04174 + 3.39142i) q^{92} +(-0.178040 + 1.00971i) q^{93} +1.31127 q^{94} +(-3.60634 - 0.303903i) q^{95} +5.84403 q^{96} +(1.42760 - 8.09632i) q^{97} +(-0.548752 - 0.460458i) q^{98} +(-3.34715 - 1.21826i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} + 3 q^{4} + 12 q^{5} + 3 q^{6} + 9 q^{7} - 6 q^{8} + 6 q^{10} + 12 q^{11} + 9 q^{12} - 6 q^{14} - 12 q^{15} + 27 q^{16} - 3 q^{17} - 6 q^{18} - 3 q^{19} + 3 q^{22} - 18 q^{23} - 21 q^{24}+ \cdots + 3 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 + 3 * q^4 + 12 * q^5 + 3 * q^6 + 9 * q^7 - 6 * q^8 + 6 * q^10 + 12 * q^11 + 9 * q^12 - 6 * q^14 - 12 * q^15 + 27 * q^16 - 3 * q^17 - 6 * q^18 - 3 * q^19 + 3 * q^22 - 18 * q^23 - 21 * q^24 - 6 * q^25 + 21 * q^26 + 9 * q^27 - 3 * q^28 - 15 * q^29 - 6 * q^30 - 27 * q^31 - 21 * q^32 - 3 * q^33 + 21 * q^34 + 6 * q^35 + 3 * q^36 - 60 * q^38 - 18 * q^39 + 24 * q^41 + 6 * q^42 + 3 * q^43 - 27 * q^44 + 3 * q^46 - 3 * q^47 - 9 * q^49 + 15 * q^50 + 12 * q^51 - 57 * q^52 + 45 * q^53 + 3 * q^54 - 12 * q^56 - 42 * q^58 + 45 * q^59 + 18 * q^60 - 30 * q^61 - 27 * q^62 + 24 * q^64 - 48 * q^65 - 12 * q^66 - 66 * q^67 + 18 * q^68 - 21 * q^69 - 6 * q^70 - 12 * q^71 + 21 * q^72 + 27 * q^73 + 12 * q^74 + 18 * q^75 - 27 * q^76 + 24 * q^77 - 3 * q^78 - 12 * q^79 + 36 * q^80 + 57 * q^82 - 30 * q^83 - 9 * q^84 + 18 * q^85 + 69 * q^86 - 15 * q^87 - 42 * q^88 - 21 * q^89 - 12 * q^90 + 48 * q^92 - 15 * q^93 + 114 * q^94 + 24 * q^95 + 12 * q^96 + 36 * q^97 - 3 * q^98 + 3 * q^99

Introduction

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