LMFDB - Embedded newform 456.2.j.e.419.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [456,2,Mod(419,456)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(456, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("456.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.j (of order $2$, degree $1$, 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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.3
Character	$\chi$	$=$	456.419
Dual form			456.2.j.e.419.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16880 - 0.796176i) q^{2} +(-0.732208 + 1.56967i) q^{3} +(0.732208 + 1.86115i) q^{4} -4.19368 q^{5} +(2.10554 - 1.25167i) q^{6} -1.07444i q^{7} +(0.625992 - 2.75828i) q^{8} +(-1.92774 - 2.29865i) q^{9} +O(q^{10})$	\(q+(-1.16880 - 0.796176i) q^{2} +(-0.732208 + 1.56967i) q^{3} +(0.732208 + 1.86115i) q^{4} -4.19368 q^{5} +(2.10554 - 1.25167i) q^{6} -1.07444i q^{7} +(0.625992 - 2.75828i) q^{8} +(-1.92774 - 2.29865i) q^{9} +(4.90159 + 3.33891i) q^{10} +0.479460i q^{11} +(-3.45752 - 0.213421i) q^{12} -0.199168i q^{13} +(-0.855440 + 1.25581i) q^{14} +(3.07065 - 6.58270i) q^{15} +(-2.92774 + 2.72550i) q^{16} +1.44408i q^{17} +(0.423021 + 4.22150i) q^{18} +1.00000 q^{19} +(-3.07065 - 7.80506i) q^{20} +(1.68651 + 0.786711i) q^{21} +(0.381735 - 0.560395i) q^{22} +4.44453 q^{23} +(3.87125 + 3.00224i) q^{24} +12.5869 q^{25} +(-0.158573 + 0.232788i) q^{26} +(5.01964 - 1.34283i) q^{27} +(1.99969 - 0.786711i) q^{28} +3.42323 q^{29} +(-8.82997 + 5.24912i) q^{30} -7.13939i q^{31} +(5.59193 - 0.854574i) q^{32} +(-0.752595 - 0.351065i) q^{33} +(1.14974 - 1.68785i) q^{34} +4.50584i q^{35} +(2.86663 - 5.27091i) q^{36} +7.53773i q^{37} +(-1.16880 - 0.796176i) q^{38} +(0.312628 + 0.145832i) q^{39} +(-2.62521 + 11.5674i) q^{40} -4.55195i q^{41} +(-1.34484 - 2.26227i) q^{42} -1.12359 q^{43} +(-0.892346 + 0.351065i) q^{44} +(8.08433 + 9.63982i) q^{45} +(-5.19479 - 3.53863i) q^{46} -2.57434 q^{47} +(-2.13442 - 6.59123i) q^{48} +5.84559 q^{49} +(-14.7117 - 10.0214i) q^{50} +(-2.26673 - 1.05737i) q^{51} +(0.370681 - 0.145832i) q^{52} +9.25642 q^{53} +(-6.93611 - 2.42701i) q^{54} -2.01070i q^{55} +(-2.96360 - 0.672589i) q^{56} +(-0.732208 + 1.56967i) q^{57} +(-4.00109 - 2.72550i) q^{58} -9.13463i q^{59} +(14.4997 + 0.895018i) q^{60} -14.3459i q^{61} +(-5.68421 + 8.34455i) q^{62} +(-2.46976 + 2.07124i) q^{63} +(-7.21627 - 3.45333i) q^{64} +0.835246i q^{65} +(0.600128 + 1.00952i) q^{66} -15.4293 q^{67} +(-2.68765 + 1.05737i) q^{68} +(-3.25432 + 6.97646i) q^{69} +(3.58744 - 5.26645i) q^{70} +6.76802 q^{71} +(-7.54709 + 3.87832i) q^{72} -3.91675 q^{73} +(6.00136 - 8.81013i) q^{74} +(-9.21627 + 19.7574i) q^{75} +(0.732208 + 1.86115i) q^{76} +0.515150 q^{77} +(-0.249293 - 0.419356i) q^{78} -10.0625i q^{79} +(12.2780 - 11.4299i) q^{80} +(-1.56762 + 8.86242i) q^{81} +(-3.62415 + 5.32034i) q^{82} -12.5824i q^{83} +(-0.229307 + 3.71489i) q^{84} -6.05601i q^{85} +(1.31326 + 0.894576i) q^{86} +(-2.50652 + 5.37335i) q^{87} +(1.32249 + 0.300138i) q^{88} +14.3091i q^{89} +(-1.77402 - 17.7036i) q^{90} -0.213993 q^{91} +(3.25432 + 8.27193i) q^{92} +(11.2065 + 5.22752i) q^{93} +(3.00890 + 2.04963i) q^{94} -4.19368 q^{95} +(-2.75306 + 9.40323i) q^{96} -5.39431 q^{97} +(-6.83235 - 4.65411i) q^{98} +(1.10211 - 0.924276i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{3} - 6 q^{4} + q^{6} - 6 q^{9}+O(q^{10}) $ 24 * q + 6 * q^3 - 6 * q^4 + q^6 - 6 * q^9	$ 24 q + 6 q^{3} - 6 q^{4} + q^{6} - 6 q^{9} + 4 q^{10} - 33 q^{12} - 30 q^{16} - 19 q^{18} + 24 q^{19} - 28 q^{22} + 21 q^{24} + 96 q^{25} + 34 q^{28} + 8 q^{30} + 24 q^{33} + 58 q^{34} - 9 q^{36} - 24 q^{40} - 31 q^{42} + 16 q^{43} - 6 q^{46} + 3 q^{48} - 36 q^{49} + 38 q^{51} - 6 q^{52} - 8 q^{54} + 6 q^{57} - 42 q^{58} - 50 q^{60} + 18 q^{64} + 10 q^{66} + 20 q^{67} - 96 q^{70} - 33 q^{72} - 12 q^{73} - 30 q^{75} - 6 q^{76} - 17 q^{78} + 34 q^{81} + 68 q^{82} - 29 q^{84} - 76 q^{88} - 70 q^{90} - 36 q^{91} - 12 q^{94} + 29 q^{96} - 104 q^{97} + 56 q^{99}+O(q^{100}) $ 24 * q + 6 * q^3 - 6 * q^4 + q^6 - 6 * q^9 + 4 * q^10 - 33 * q^12 - 30 * q^16 - 19 * q^18 + 24 * q^19 - 28 * q^22 + 21 * q^24 + 96 * q^25 + 34 * q^28 + 8 * q^30 + 24 * q^33 + 58 * q^34 - 9 * q^36 - 24 * q^40 - 31 * q^42 + 16 * q^43 - 6 * q^46 + 3 * q^48 - 36 * q^49 + 38 * q^51 - 6 * q^52 - 8 * q^54 + 6 * q^57 - 42 * q^58 - 50 * q^60 + 18 * q^64 + 10 * q^66 + 20 * q^67 - 96 * q^70 - 33 * q^72 - 12 * q^73 - 30 * q^75 - 6 * q^76 - 17 * q^78 + 34 * q^81 + 68 * q^82 - 29 * q^84 - 76 * q^88 - 70 * q^90 - 36 * q^91 - 12 * q^94 + 29 * q^96 - 104 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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 $

$2$	−1.16880	−	0.796176i	−0.826470	−	0.562981i
$2$	−1.16880	−	0.796176i	−0.826470	−	0.562981i
$3$	−0.732208	+	1.56967i	−0.422741	+	0.906251i
$3$	−0.732208	+	1.56967i	−0.422741	+	0.906251i
$4$	0.732208	+	1.86115i	0.366104	+	0.930574i
$5$	−4.19368			−1.87547			−0.937735	−	0.347351i	$-0.887081\pi$
$5$	−4.19368			−1.87547			−0.937735	+	0.347351i	$0.887081\pi$
$6$	2.10554	−	1.25167i	0.859584	−	0.510994i
$7$		−	1.07444i		−	0.406099i	−0.979168	−	0.203049i	$-0.934915\pi$
$7$		−	1.07444i		−	0.406099i	0.979168	−	0.203049i	$-0.0650852\pi$
$8$	0.625992	−	2.75828i	0.221322	−	0.975201i
$9$	−1.92774	−	2.29865i	−0.642581	−	0.766218i
$10$	4.90159	+	3.33891i	1.55002	+	1.05585i
$11$			0.479460i			0.144563i	0.997384	+	0.0722813i	$0.0230279\pi$
$11$			0.479460i			0.144563i	−0.997384	+	0.0722813i	$0.976972\pi$
$12$	−3.45752	−	0.213421i	−0.998100	−	0.0616093i
$13$		−	0.199168i		−	0.0552392i	−0.999619	−	0.0276196i	$-0.991207\pi$
$13$		−	0.199168i		−	0.0552392i	0.999619	−	0.0276196i	$-0.00879271\pi$
$14$	−0.855440	+	1.25581i	−0.228626	+	0.335628i
$15$	3.07065	−	6.58270i	0.792838	−	1.69965i
$16$	−2.92774	+	2.72550i	−0.731936	+	0.681374i
$17$			1.44408i			0.350241i	0.984547	+	0.175120i	$0.0560315\pi$
$17$			1.44408i			0.350241i	−0.984547	+	0.175120i	$0.943969\pi$
$18$	0.423021	+	4.22150i	0.0997071	+	0.995017i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−3.07065	−	7.80506i	−0.686617	−	1.74526i
$21$	1.68651	+	0.786711i	0.368027	+	0.171674i
$22$	0.381735	−	0.560395i	0.0813861	−	0.119477i
$23$	4.44453			0.926749			0.463374	−	0.886163i	$-0.346638\pi$
$23$	4.44453			0.926749			0.463374	+	0.886163i	$0.346638\pi$
$24$	3.87125	+	3.00224i	0.790215	+	0.612830i
$25$	12.5869			2.51739
$26$	−0.158573	+	0.232788i	−0.0310986	+	0.0456535i
$27$	5.01964	−	1.34283i	0.966031	−	0.258428i
$28$	1.99969	−	0.786711i	0.377905	−	0.148674i
$29$	3.42323			0.635678			0.317839	−	0.948145i	$-0.397043\pi$
$29$	3.42323			0.635678			0.317839	+	0.948145i	$0.397043\pi$
$30$	−8.82997	+	5.24912i	−1.61213	+	0.958353i
$31$		−	7.13939i		−	1.28227i	−0.767427	−	0.641136i	$-0.778463\pi$
$31$		−	7.13939i		−	1.28227i	0.767427	−	0.641136i	$-0.221537\pi$
$32$	5.59193	−	0.854574i	0.988523	−	0.151069i
$33$	−0.752595	−	0.351065i	−0.131010	−	0.0611125i
$34$	1.14974	−	1.68785i	0.197179	−	0.289463i
$35$			4.50584i			0.761626i
$36$	2.86663	−	5.27091i	0.477771	−	0.878484i
$37$			7.53773i			1.23919i	0.784920	+	0.619597i	$0.212704\pi$
$37$			7.53773i			1.23919i	−0.784920	+	0.619597i	$0.787296\pi$
$38$	−1.16880	−	0.796176i	−0.189605	−	0.129157i
$39$	0.312628	+	0.145832i	0.0500606	+	0.0233519i
$40$	−2.62521	+	11.5674i	−0.415082	+	1.82896i
$41$		−	4.55195i		−	0.710895i	−0.934696	−	0.355448i	$-0.884328\pi$
$41$		−	4.55195i		−	0.710895i	0.934696	−	0.355448i	$-0.115672\pi$
$42$	−1.34484	−	2.26227i	−0.207514	−	0.349076i
$43$	−1.12359			−0.171346			−0.0856730	−	0.996323i	$-0.527304\pi$
$43$	−1.12359			−0.171346			−0.0856730	+	0.996323i	$0.527304\pi$
$44$	−0.892346	+	0.351065i	−0.134526	+	0.0529250i
$45$	8.08433	+	9.63982i	1.20514	+	1.43702i
$46$	−5.19479	−	3.53863i	−0.765930	−	0.521742i
$47$	−2.57434			−0.375506			−0.187753	−	0.982216i	$-0.560121\pi$
$47$	−2.57434			−0.375506			−0.187753	+	0.982216i	$0.560121\pi$
$48$	−2.13442	−	6.59123i	−0.308077	−	0.951362i
$49$	5.84559			0.835084
$50$	−14.7117	−	10.0214i	−2.08055	−	1.41724i
$51$	−2.26673	−	1.05737i	−0.317406	−	0.148061i
$52$	0.370681	−	0.145832i	0.0514042	−	0.0202233i
$53$	9.25642			1.27147			0.635733	−	0.771909i	$-0.280698\pi$
$53$	9.25642			1.27147			0.635733	+	0.771909i	$0.280698\pi$
$54$	−6.93611	−	2.42701i	−0.943885	−	0.330274i
$55$		−	2.01070i		−	0.271123i
$56$	−2.96360	−	0.672589i	−0.396028	−	0.0898785i
$57$	−0.732208	+	1.56967i	−0.0969834	+	0.207908i
$58$	−4.00109	−	2.72550i	−0.525369	−	0.357875i
$59$		−	9.13463i		−	1.18923i	−0.804012	−	0.594613i	$-0.797305\pi$
$59$		−	9.13463i		−	1.18923i	0.804012	−	0.594613i	$-0.202695\pi$
$60$	14.4997	+	0.895018i	1.87191	+	0.115546i
$61$		−	14.3459i		−	1.83680i	−0.395652	−	0.918400i	$-0.629481\pi$
$61$		−	14.3459i		−	1.83680i	0.395652	−	0.918400i	$-0.370519\pi$
$62$	−5.68421	+	8.34455i	−0.721896	+	1.05976i
$63$	−2.46976	+	2.07124i	−0.311160	+	0.260951i
$64$	−7.21627	−	3.45333i	−0.902033	−	0.431666i
$65$			0.835246i			0.103600i
$66$	0.600128	+	1.00952i	0.0738706	+	0.124264i
$67$	−15.4293			−1.88499			−0.942494	−	0.334223i	$-0.891526\pi$
$67$	−15.4293			−1.88499			−0.942494	+	0.334223i	$0.891526\pi$
$68$	−2.68765	+	1.05737i	−0.325925	+	0.128225i
$69$	−3.25432	+	6.97646i	−0.391774	+	0.839867i
$70$	3.58744	−	5.26645i	0.428781	−	0.629461i
$71$	6.76802			0.803216			0.401608	−	0.915812i	$-0.368451\pi$
$71$	6.76802			0.803216			0.401608	+	0.915812i	$0.368451\pi$
$72$	−7.54709	+	3.87832i	−0.889434	+	0.457065i
$73$	−3.91675			−0.458421			−0.229211	−	0.973377i	$-0.573614\pi$
$73$	−3.91675			−0.458421			−0.229211	+	0.973377i	$0.573614\pi$
$74$	6.00136	−	8.81013i	0.697644	−	1.02416i
$75$	−9.21627	+	19.7574i	−1.06420	+	2.28139i
$76$	0.732208	+	1.86115i	0.0839900	+	0.213488i
$77$	0.515150			0.0587067
$78$	−0.249293	−	0.419356i	−0.0282269	−	0.0474828i
$79$		−	10.0625i		−	1.13211i	−0.824366	−	0.566057i	$-0.808468\pi$
$79$		−	10.0625i		−	1.13211i	0.824366	−	0.566057i	$-0.191532\pi$
$80$	12.2780	−	11.4299i	1.37272	−	1.27790i
$81$	−1.56762	+	8.86242i	−0.174180	+	0.984714i
$82$	−3.62415	+	5.32034i	−0.400221	+	0.587533i
$83$		−	12.5824i		−	1.38110i	−0.723285	−	0.690549i	$-0.757369\pi$
$83$		−	12.5824i		−	1.38110i	0.723285	−	0.690549i	$-0.242631\pi$
$84$	−0.229307	+	3.71489i	−0.0250195	+	0.405327i
$85$		−	6.05601i		−	0.656866i
$86$	1.31326	+	0.894576i	0.141612	+	0.0964646i
$87$	−2.50652	+	5.37335i	−0.268727	+	0.576084i
$88$	1.32249	+	0.300138i	0.140978	+	0.0319949i
$89$			14.3091i			1.51677i	0.651809	+	0.758383i	$0.274010\pi$
$89$			14.3091i			1.51677i	−0.651809	+	0.758383i	$0.725990\pi$
$90$	−1.77402	−	17.7036i	−0.186998	−	1.86612i
$91$	−0.213993			−0.0224326
$92$	3.25432	+	8.27193i	0.339287	+	0.862408i
$93$	11.2065	+	5.22752i	1.16206	+	0.542069i
$94$	3.00890	+	2.04963i	0.310345	+	0.211403i
$95$	−4.19368			−0.430262
$96$	−2.75306	+	9.40323i	−0.280983	+	0.959713i
$97$	−5.39431			−0.547709			−0.273855	−	0.961771i	$-0.588299\pi$
$97$	−5.39431			−0.547709			−0.273855	+	0.961771i	$0.588299\pi$
$98$	−6.83235	−	4.65411i	−0.690171	−	0.470137i
$99$	1.10211	−	0.924276i	0.110767	−	0.0928932i
$100$	9.21627	+	23.4262i	0.921627	+	2.34262i
$101$	15.6284			1.55508			0.777542	−	0.628831i	$-0.216466\pi$
$101$	15.6284			1.55508			0.777542	+	0.628831i	$0.216466\pi$
$102$	1.80752	+	3.04057i	0.178971	+	0.301062i
$103$			9.80115i			0.965736i	0.875693	+	0.482868i	$0.160405\pi$
$103$			9.80115i			0.965736i	−0.875693	+	0.482868i	$0.839595\pi$
$104$	−0.549361	−	0.124678i	−0.0538693	−	0.0122256i
$105$	−7.07270	−	3.29921i	−0.690224	−	0.321970i
$106$	−10.8189	−	7.36973i	−1.05083	−	0.715812i
$107$			7.69129i			0.743545i	0.928324	+	0.371773i	$0.121250\pi$
$107$			7.69129i			0.743545i	−0.928324	+	0.371773i	$0.878750\pi$
$108$	6.17463	+	8.35906i	0.594154	+	0.804351i
$109$			12.9662i			1.24194i	0.783834	+	0.620970i	$0.213261\pi$
$109$			12.9662i			1.24194i	−0.783834	+	0.620970i	$0.786739\pi$
$110$	−1.60087	+	2.35012i	−0.152637	+	0.224075i
$111$	−11.8318	−	5.51919i	−1.12302	−	0.523858i
$112$	2.92837	+	3.14567i	0.276705	+	0.297238i
$113$			0.670669i			0.0630912i	0.999502	+	0.0315456i	$0.0100430\pi$
$113$			0.670669i			0.0630912i	−0.999502	+	0.0315456i	$0.989957\pi$
$114$	2.10554	−	1.25167i	0.197202	−	0.117230i
$115$	−18.6389			−1.73809
$116$	2.50652	+	6.37114i	0.232725	+	0.591546i
$117$	−0.457818	+	0.383944i	−0.0423253	+	0.0354957i
$118$	−7.27277	+	10.6766i	−0.669513	+	0.982860i
$119$	1.55157			0.142232
$120$	−16.2348	−	12.5904i	−1.48202	−	1.14934i
$121$	10.7701			0.979102
$122$	−11.4218	+	16.7675i	−1.03408	+	1.51806i
$123$	7.14507	+	3.33297i	0.644249	+	0.300524i
$124$	13.2875	−	5.22752i	1.19325	−	0.469445i
$125$	−31.8172			−2.84582
$126$	4.53573	−	0.454509i	0.404075	−	0.0404909i
$127$		−	11.5830i		−	1.02783i	−0.857842	−	0.513914i	$-0.828195\pi$
$127$		−	11.5830i		−	1.02783i	0.857842	−	0.513914i	$-0.171805\pi$
$128$	5.68495	+	9.78169i	0.502483	+	0.864587i
$129$	0.822703	−	1.76367i	0.0724349	−	0.155282i
$130$	0.665003	−	0.976239i	0.0583246	−	0.0856219i
$131$		−	19.1375i		−	1.67205i	−0.548693	−	0.836024i	$-0.684874\pi$
$131$		−	19.1375i		−	1.67205i	0.548693	−	0.836024i	$-0.315126\pi$
$132$	0.102327	−	1.65774i	0.00890640	−	0.144288i
$133$		−	1.07444i		−	0.0931655i
$134$	18.0338	+	12.2844i	1.55789	+	1.06121i
$135$	−21.0508	+	5.63140i	−1.81176	+	0.484674i
$136$	3.98318	+	0.903983i	0.341555	+	0.0775159i
$137$		−	15.5712i		−	1.33034i	−0.746693	−	0.665169i	$-0.768360\pi$
$137$		−	15.5712i		−	1.33034i	0.746693	−	0.665169i	$-0.231640\pi$
$138$	9.35815	−	5.56310i	0.796619	−	0.473563i
$139$	18.6295			1.58013			0.790066	−	0.613022i	$-0.210046\pi$
$139$	18.6295			1.58013			0.790066	+	0.613022i	$0.210046\pi$
$140$	−8.38604	+	3.29921i	−0.708750	+	0.278835i
$141$	1.88495	−	4.04087i	0.158742	−	0.340303i
$142$	−7.91049	−	5.38854i	−0.663834	−	0.452196i
$143$	0.0954930			0.00798553
$144$	11.9089	+	1.47581i	0.992409	+	0.122984i
$145$	−14.3559			−1.19220
$146$	4.57792	+	3.11842i	0.378871	+	0.258083i
$147$	−4.28019	+	9.17565i	−0.353024	+	0.756795i
$148$	−14.0288	+	5.51919i	−1.15316	+	0.453674i
$149$	−6.86663			−0.562536			−0.281268	−	0.959629i	$-0.590755\pi$
$149$	−6.86663			−0.562536			−0.281268	+	0.959629i	$0.590755\pi$
$150$	26.5024	−	15.7548i	2.16391	−	1.28637i
$151$			7.40070i			0.602260i	0.953583	+	0.301130i	$0.0973638\pi$
$151$			7.40070i			0.602260i	−0.953583	+	0.301130i	$0.902636\pi$
$152$	0.625992	−	2.75828i	0.0507747	−	0.223726i
$153$	3.31944	−	2.78381i	0.268361	−	0.225058i
$154$	−0.602109	−	0.410150i	−0.0485193	−	0.0330508i
$155$			29.9403i			2.40486i
$156$	−0.0425065	+	0.688627i	−0.00340325	+	0.0551343i
$157$		−	2.14887i		−	0.171499i	−0.996317	−	0.0857494i	$-0.972672\pi$
$157$		−	2.14887i		−	0.171499i	0.996317	−	0.0857494i	$-0.0273284\pi$
$158$	−8.01148	+	11.7610i	−0.637359	+	0.935658i
$159$	−6.77762	+	14.5295i	−0.537501	+	1.15227i
$160$	−23.4508	+	3.58381i	−1.85395	+	0.283325i
$161$		−	4.77537i		−	0.376352i
$162$	8.88829	−	9.11034i	0.698330	−	0.715776i
$163$	18.1405			1.42087			0.710435	−	0.703763i	$-0.248498\pi$
$163$	18.1405			1.42087			0.710435	+	0.703763i	$0.248498\pi$
$164$	8.47185	−	3.33297i	0.661540	−	0.260262i
$165$	3.15614	+	1.47225i	0.245705	+	0.114615i
$166$	−10.0178	+	14.7064i	−0.777533	+	1.14144i
$167$	−1.58981			−0.123023			−0.0615114	−	0.998106i	$-0.519592\pi$
$167$	−1.58981			−0.123023			−0.0615114	+	0.998106i	$0.519592\pi$
$168$	3.22572	−	4.15941i	0.248870	−	0.320905i
$169$	12.9603			0.996949
$170$	−4.82165	+	7.07829i	−0.369803	+	0.542880i
$171$	−1.92774	−	2.29865i	−0.147418	−	0.175782i
$172$	−0.822703	−	2.09117i	−0.0627305	−	0.159450i
$173$	−13.0908			−0.995276			−0.497638	−	0.867385i	$-0.665799\pi$
$173$	−13.0908			−0.995276			−0.497638	+	0.867385i	$0.665799\pi$
$174$	7.20777	−	4.28477i	0.546419	−	0.324828i
$175$		−	13.5239i		−	1.02231i
$176$	−1.30677	−	1.40374i	−0.0985012	−	0.105811i
$177$	14.3384	+	6.68845i	1.07774	+	0.502735i
$178$	11.3926	−	16.7246i	0.853911	−	1.25356i
$179$		−	4.63136i		−	0.346164i	−0.984907	−	0.173082i	$-0.944627\pi$
$179$		−	4.63136i		−	0.346164i	0.984907	−	0.173082i	$-0.0553726\pi$
$180$	−12.0217	+	22.1045i	−0.896045	+	1.64757i
$181$		−	11.7980i		−	0.876935i	−0.898747	−	0.438468i	$-0.855521\pi$
$181$		−	11.7980i		−	0.876935i	0.898747	−	0.438468i	$-0.144479\pi$
$182$	0.250116	+	0.170376i	0.0185398	+	0.0126291i
$183$	22.5183	+	10.5042i	1.66460	+	0.776490i
$184$	2.78224	−	12.2593i	0.205110	−	0.903766i
$185$		−	31.6108i		−	2.32407i
$186$	−8.93619	−	15.0323i	−0.655233	−	1.10222i
$187$	−0.692379			−0.0506317
$188$	−1.88495	−	4.79123i	−0.137474	−	0.349436i
$189$	−1.44279	−	5.39329i	−0.104947	−	0.392304i
$190$	4.90159	+	3.33891i	0.355599	+	0.242230i
$191$	−12.1891			−0.881971			−0.440985	−	0.897514i	$-0.645371\pi$
$191$	−12.1891			−0.881971			−0.440985	+	0.897514i	$0.645371\pi$
$192$	10.7044	−	8.79862i	0.772524	−	0.634985i
$193$	−5.28690			−0.380559			−0.190280	−	0.981730i	$-0.560939\pi$
$193$	−5.28690			−0.380559			−0.190280	+	0.981730i	$0.560939\pi$
$194$	6.30489	+	4.29482i	0.452665	+	0.308350i
$195$	−1.31106	−	0.611574i	−0.0938871	−	0.0437957i
$196$	4.28019	+	10.8795i	0.305728	+	0.777107i
$197$	5.36017			0.381896			0.190948	−	0.981600i	$-0.438844\pi$
$197$	5.36017			0.381896			0.190948	+	0.981600i	$0.438844\pi$
$198$	−2.02404	+	0.202822i	−0.143842	+	0.0144139i
$199$		−	9.05375i		−	0.641804i	−0.947112	−	0.320902i	$-0.896014\pi$
$199$		−	9.05375i		−	0.641804i	0.947112	−	0.320902i	$-0.103986\pi$
$200$	7.87933	−	34.7184i	0.557153	−	2.45496i
$201$	11.2975	−	24.2189i	0.796861	−	1.70827i
$202$	−18.2665	−	12.4430i	−1.28523	−	0.875483i
$203$		−	3.67805i		−	0.258148i
$204$	0.308197	−	4.99294i	0.0215781	−	0.349575i
$205$			19.0894i			1.33326i
$206$	7.80344	−	11.4556i	0.543691	−	0.798152i
$207$	−8.56791	−	10.2164i	−0.595511	−	0.710092i
$208$	0.542831	+	0.583112i	0.0376386	+	0.0404315i
$209$			0.479460i			0.0331650i
$210$	5.63984	+	9.48725i	0.389186	+	0.654682i
$211$	9.10224			0.626624			0.313312	−	0.949650i	$-0.398561\pi$
$211$	9.10224			0.626624			0.313312	+	0.949650i	$0.398561\pi$
$212$	6.77762	+	17.2276i	0.465489	+	1.18319i
$213$	−4.95560	+	10.6236i	−0.339552	+	0.727915i
$214$	6.12362	−	8.98962i	0.418602	−	0.614518i
$215$	4.71198			0.321354
$216$	−0.561649	−	14.6862i	−0.0382154	−	0.999270i
$217$	−7.67082			−0.520729
$218$	10.3234	−	15.1550i	0.699189	−	1.02643i
$219$	2.86788	−	6.14802i	0.193793	−	0.415445i
$220$	3.74221	−	1.47225i	0.252300	−	0.0992593i
$221$	0.287614			0.0193470
$222$	9.43478	+	15.8710i	0.633221	+	1.06519i
$223$		−	1.44534i		−	0.0967871i	−0.998828	−	0.0483935i	$-0.984590\pi$
$223$		−	1.44534i		−	0.0967871i	0.998828	−	0.0483935i	$-0.0154102\pi$
$224$	−0.918186	−	6.00818i	−0.0613489	−	0.401438i
$225$	−24.2644	−	28.9330i	−1.61763	−	1.92887i
$226$	0.533971	−	0.783881i	0.0355192	−	0.0521430i
$227$		−	6.67799i		−	0.443234i	−0.975134	−	0.221617i	$-0.928867\pi$
$227$		−	6.67799i		−	0.443234i	0.975134	−	0.221617i	$-0.0711334\pi$
$228$	−3.45752	−	0.213421i	−0.228980	−	0.0141341i
$229$		−	6.03970i		−	0.399115i	−0.979886	−	0.199557i	$-0.936050\pi$
$229$		−	6.03970i		−	0.399115i	0.979886	−	0.199557i	$-0.0639504\pi$
$230$	21.7853	+	14.8399i	1.43648	+	0.978512i
$231$	−0.377197	+	0.808616i	−0.0248177	+	0.0532030i
$232$	2.14292	−	9.44225i	0.140689	−	0.619914i
$233$			15.7283i			1.03040i	0.857071	+	0.515199i	$0.172282\pi$
$233$			15.7283i			1.03040i	−0.857071	+	0.515199i	$0.827718\pi$
$234$	0.840787	−	0.0842522i	0.0549639	−	0.00550774i
$235$	10.7960			0.704251
$236$	17.0009	−	6.68845i	1.10666	−	0.435381i
$237$	15.7948	+	7.36781i	1.02598	+	0.478591i
$238$	−1.81348	−	1.23532i	−0.117551	−	0.0800742i
$239$	6.12260			0.396038			0.198019	−	0.980198i	$-0.436549\pi$
$239$	6.12260			0.396038			0.198019	+	0.980198i	$0.436549\pi$
$240$	8.95106	+	27.6415i	0.577789	+	1.78425i
$241$	−7.89907			−0.508824			−0.254412	−	0.967096i	$-0.581882\pi$
$241$	−7.89907			−0.508824			−0.254412	+	0.967096i	$0.581882\pi$
$242$	−12.5882	−	8.57491i	−0.809198	−	0.551216i
$243$	−12.7633	−	8.94979i	−0.818765	−	0.574129i
$244$	26.6998	−	10.5042i	1.70928	−	0.672460i
$245$	−24.5145			−1.56617
$246$	−5.69756	−	9.58433i	−0.363263	−	0.611074i
$247$		−	0.199168i		−	0.0126727i
$248$	−19.6925	−	4.46921i	−1.25047	−	0.283795i
$249$	19.7503	+	9.21294i	1.25162	+	0.583846i
$250$	37.1881	+	25.3321i	2.35198	+	1.60214i
$251$		−	4.32020i		−	0.272689i	−0.990662	−	0.136344i	$-0.956465\pi$
$251$		−	4.32020i		−	0.272689i	0.990662	−	0.136344i	$-0.0435353\pi$
$252$	−5.66325	−	3.08001i	−0.356751	−	0.194022i
$253$			2.13098i			0.133973i
$254$	−9.22213	+	13.5383i	−0.578648	+	0.849469i
$255$	9.50595	+	4.43426i	0.595286	+	0.277684i
$256$	1.14335	−	15.9591i	0.0714593	−	0.997444i
$257$			24.4572i			1.52560i	0.646635	+	0.762800i	$0.276176\pi$
$257$			24.4572i			1.52560i	−0.646635	+	0.762800i	$0.723824\pi$
$258$	−2.36577	+	1.40637i	−0.147286	+	0.0875567i
$259$	8.09881			0.503236
$260$	−1.55452	+	0.611574i	−0.0964070	+	0.0379282i
$261$	−6.59911	−	7.86883i	−0.408475	−	0.487068i
$262$	−15.2368	+	22.3680i	−0.941332	+	1.38190i
$263$	18.2695			1.12655			0.563274	−	0.826270i	$-0.309542\pi$
$263$	18.2695			1.12655			0.563274	+	0.826270i	$0.309542\pi$
$264$	−1.43946	+	1.85611i	−0.0885923	+	0.114236i
$265$	−38.8184			−2.38460
$266$	−0.855440	+	1.25581i	−0.0524504	+	0.0769984i
$267$	−22.4607	−	10.4773i	−1.37457	−	0.641199i
$268$	−11.2975	−	28.7162i	−0.690102	−	1.75412i
$269$	−17.9081			−1.09187			−0.545937	−	0.837826i	$-0.683826\pi$
$269$	−17.9081			−1.09187			−0.545937	+	0.837826i	$0.683826\pi$
$270$	29.0878	+	10.1781i	1.77023	+	0.619420i
$271$		−	19.4170i		−	1.17950i	−0.807586	−	0.589750i	$-0.799226\pi$
$271$		−	19.4170i		−	1.17950i	0.807586	−	0.589750i	$-0.200774\pi$
$272$	−3.93583	−	4.22789i	−0.238645	−	0.256354i
$273$	0.156688	−	0.335899i	0.00948316	−	0.0203295i
$274$	−12.3974	+	18.1997i	−0.748955	+	1.09948i
$275$			6.03494i			0.363921i
$276$	−15.3671	−	0.948555i	−0.924988	−	0.0570963i
$277$			7.80655i			0.469050i	0.972110	+	0.234525i	$0.0753534\pi$
$277$			7.80655i			0.469050i	−0.972110	+	0.234525i	$0.924647\pi$
$278$	−21.7742	−	14.8323i	−1.30593	−	0.889584i
$279$	−16.4110	+	13.7629i	−0.982500	+	0.823964i
$280$	12.4284	+	2.82062i	0.742739	+	0.168564i
$281$			20.8459i			1.24356i	0.783192	+	0.621780i	$0.213590\pi$
$281$			20.8459i			1.24356i	−0.783192	+	0.621780i	$0.786410\pi$
$282$	−5.42039	+	3.22224i	−0.322780	+	0.191881i
$283$	−14.2754			−0.848587			−0.424294	−	0.905525i	$-0.639478\pi$
$283$	−14.2754			−0.848587			−0.424294	+	0.905525i	$0.639478\pi$
$284$	4.95560	+	12.5963i	0.294061	+	0.747452i
$285$	3.07065	−	6.58270i	0.181889	−	0.389926i
$286$	−0.111613	−	0.0760292i	−0.00659980	−	0.00449570i
$287$	−4.89078			−0.288694
$288$	−12.7442	−	11.2065i	−0.750958	−	0.660350i
$289$	14.9146			0.877331
$290$	16.7793	+	11.4299i	0.985314	+	0.671184i
$291$	3.94976	−	8.46730i	0.231539	−	0.496362i
$292$	−2.86788	−	7.28966i	−0.167830	−	0.426595i
$293$	21.2952			1.24408			0.622039	−	0.782986i	$-0.286304\pi$
$293$	21.2952			1.24408			0.622039	+	0.782986i	$0.286304\pi$
$294$	12.3081	−	7.31677i	0.717825	−	0.426722i
$295$			38.3077i			2.23036i
$296$	20.7912	+	4.71856i	1.20846	+	0.274261i
$297$	0.643833	+	2.40672i	0.0373590	+	0.139652i
$298$	8.02575	+	5.46705i	0.464919	+	0.316697i
$299$		−	0.885208i		−	0.0511929i
$300$	−43.5196	−	2.68632i	−2.51261	−	0.155095i
$301$			1.20723i			0.0695834i
$302$	5.89226	−	8.64997i	0.339061	−	0.497750i
$303$	−11.4432	+	24.5315i	−0.657397	+	1.40930i
$304$	−2.92774	+	2.72550i	−0.167918	+	0.156318i
$305$			60.1620i			3.44487i
$306$	−6.09618	+	0.610876i	−0.348495	+	0.0349215i
$307$	29.7172			1.69605			0.848026	−	0.529954i	$-0.177791\pi$
$307$	29.7172			1.69605			0.848026	+	0.529954i	$0.177791\pi$
$308$	0.377197	+	0.958769i	0.0214928	+	0.0546310i
$309$	−15.3846	−	7.17648i	−0.875199	−	0.408256i
$310$	23.8378	−	34.9944i	1.35389	−	1.98755i
$311$	−0.968960			−0.0549447			−0.0274723	−	0.999623i	$-0.508746\pi$
$311$	−0.968960			−0.0549447			−0.0274723	+	0.999623i	$0.508746\pi$
$312$	0.597950	−	0.771028i	0.0338522	−	0.0436508i
$313$	6.28796			0.355416			0.177708	−	0.984083i	$-0.443132\pi$
$313$	6.28796			0.355416			0.177708	+	0.984083i	$0.443132\pi$
$314$	−1.71088	+	2.51161i	−0.0965506	+	0.141738i
$315$	10.3574	−	8.68610i	0.583572	−	0.489406i
$316$	18.7277	−	7.36781i	1.05352	−	0.414472i
$317$	−23.9229			−1.34364			−0.671822	−	0.740713i	$-0.734488\pi$
$317$	−23.9229			−1.34364			−0.671822	+	0.740713i	$0.734488\pi$
$318$	19.4898	−	11.5860i	1.09293	−	0.649711i
$319$			1.64130i			0.0918954i
$320$	30.2627	+	14.4822i	1.69174	+	0.809577i
$321$	−12.0728	−	5.63163i	−0.673839	−	0.314327i
$322$	−3.80203	+	5.58147i	−0.211879	+	0.311043i
$323$			1.44408i			0.0803507i
$324$	−17.6421	+	3.57157i	−0.980117	+	0.198420i
$325$		−	2.50691i		−	0.139059i
$326$	−21.2027	−	14.4430i	−1.17431	−	0.799924i
$327$	−20.3527	−	9.49399i	−1.12551	−	0.525019i
$328$	−12.5556	−	2.84949i	−0.693265	−	0.157337i
$329$			2.76597i			0.152493i
$330$	−2.51674	−	4.23362i	−0.138542	−	0.233053i
$331$	−5.43015			−0.298468			−0.149234	−	0.988802i	$-0.547681\pi$
$331$	−5.43015			−0.298468			−0.149234	+	0.988802i	$0.547681\pi$
$332$	23.4177	−	9.21294i	1.28521	−	0.505626i
$333$	17.3266	−	14.5308i	0.949493	−	0.796283i
$334$	1.85817	+	1.26577i	0.101675	+	0.0692596i
$335$	64.7055			3.53524
$336$	−7.08185	+	2.29330i	−0.386347	+	0.125110i
$337$	24.1756			1.31693			0.658464	−	0.752612i	$-0.271206\pi$
$337$	24.1756			1.31693			0.658464	+	0.752612i	$0.271206\pi$
$338$	−15.1481	−	10.3187i	−0.823948	−	0.561263i
$339$	−1.05273	−	0.491070i	−0.0571765	−	0.0266712i
$340$	11.2711	−	4.43426i	0.611263	−	0.240481i
$341$	3.42305			0.185369
$342$	0.423021	+	4.22150i	0.0228744	+	0.228273i
$343$		−	13.8018i		−	0.745225i
$344$	−0.703359	+	3.09918i	−0.0379226	+	0.167097i
$345$	13.6476	−	29.2570i	0.734761	−	1.57515i
$346$	15.3006	+	10.4226i	0.822566	+	0.560322i
$347$		−	22.7286i		−	1.22014i	−0.792349	−	0.610069i	$-0.791142\pi$
$347$		−	22.7286i		−	1.22014i	0.792349	−	0.610069i	$-0.208858\pi$
$348$	−11.8359	−	0.730589i	−0.634471	−	0.0391637i
$349$		−	14.2702i		−	0.763866i	−0.924190	−	0.381933i	$-0.875258\pi$
$349$		−	14.2702i		−	0.763866i	0.924190	−	0.381933i	$-0.124742\pi$
$350$	−10.7674	+	15.8068i	−0.575541	+	0.844907i
$351$	−0.267449	−	0.999751i	−0.0142753	−	0.0533628i
$352$	0.409734	+	2.68111i	0.0218389	+	0.142904i
$353$			11.8249i			0.629375i	0.949195	+	0.314688i	$0.101900\pi$
$353$			11.8249i			0.629375i	−0.949195	+	0.314688i	$0.898100\pi$
$354$	−11.4336	−	19.2333i	−0.607687	−	1.02224i
$355$	−28.3829			−1.50641
$356$	−26.6314	+	10.4773i	−1.41146	+	0.555294i
$357$	−1.13607	+	2.43546i	−0.0601274	+	0.128898i
$358$	−3.68738	+	5.41316i	−0.194884	+	0.286094i
$359$	−5.51159			−0.290891			−0.145445	−	0.989366i	$-0.546462\pi$
$359$	−5.51159			−0.290891			−0.145445	+	0.989366i	$0.546462\pi$
$360$	31.6501	−	16.2644i	1.66811	−	0.857211i
$361$	1.00000			0.0526316
$362$	−9.39325	+	13.7895i	−0.493698	+	0.724760i
$363$	−7.88597	+	16.9056i	−0.413906	+	0.887312i
$364$	−0.156688	−	0.398273i	−0.00821266	−	0.0208752i
$365$	16.4256			0.859756
$366$	−17.9564	−	30.2059i	−0.938593	−	1.57889i
$367$			26.3259i			1.37420i	0.726563	+	0.687100i	$0.241117\pi$
$367$			26.3259i			1.37420i	−0.726563	+	0.687100i	$0.758883\pi$
$368$	−13.0124	+	12.1136i	−0.678320	+	0.631463i
$369$	−10.4634	+	8.77498i	−0.544701	+	0.456807i
$370$	−25.1678	+	36.9469i	−1.30841	+	1.92078i
$371$		−	9.94543i		−	0.516341i
$372$	−1.52369	+	24.6846i	−0.0789999	+	1.27984i
$373$		−	23.4705i		−	1.21526i	−0.794221	−	0.607629i	$-0.792121\pi$
$373$		−	23.4705i		−	1.21526i	0.794221	−	0.607629i	$-0.207879\pi$
$374$	0.809255	+	0.551255i	0.0418456	+	0.0285047i
$375$	23.2968	−	49.9426i	1.20304	−	2.57903i
$376$	−1.61152	+	7.10077i	−0.0831077	+	0.366194i
$377$		−	0.681798i		−	0.0351144i
$378$	−2.60767	+	7.45241i	−0.134124	+	0.383311i
$379$	13.6094			0.699068			0.349534	−	0.936924i	$-0.386340\pi$
$379$	13.6094			0.699068			0.349534	+	0.936924i	$0.386340\pi$
$380$	−3.07065	−	7.80506i	−0.157521	−	0.400391i
$381$	18.1816	+	8.48119i	0.931470	+	0.434505i
$382$	14.2466	+	9.70465i	0.728922	+	0.496533i
$383$	−3.59699			−0.183798			−0.0918989	−	0.995768i	$-0.529294\pi$
$383$	−3.59699			−0.183798			−0.0918989	+	0.995768i	$0.529294\pi$
$384$	−19.5166	+	1.76127i	−0.995953	+	0.0898796i
$385$	−2.16037			−0.110103
$386$	6.17935	+	4.20930i	0.314521	+	0.214248i
$387$	2.16599	+	2.58275i	0.110104	+	0.131288i
$388$	−3.94976	−	10.0396i	−0.200519	−	0.509684i
$389$	−9.83198			−0.498501			−0.249250	−	0.968439i	$-0.580184\pi$
$389$	−9.83198			−0.498501			−0.249250	+	0.968439i	$0.580184\pi$
$390$	1.04546	+	1.75865i	0.0529387	+	0.0890525i
$391$			6.41826i			0.324585i
$392$	3.65929	−	16.1238i	0.184822	−	0.814374i
$393$	30.0396	+	14.0126i	1.51530	+	0.706843i
$394$	−6.26499	−	4.26764i	−0.315626	−	0.215000i
$395$			42.1987i			2.12325i
$396$	2.52719	+	1.37443i	0.126996	+	0.0690679i
$397$			24.5889i			1.23408i	0.786932	+	0.617040i	$0.211668\pi$
$397$			24.5889i			1.23408i	−0.786932	+	0.617040i	$0.788332\pi$
$398$	−7.20838	+	10.5821i	−0.361323	+	0.530431i
$399$	1.68651	+	0.786711i	0.0844313	+	0.0393848i
$400$	−36.8513	+	34.3057i	−1.84257	+	1.71528i
$401$		−	25.8987i		−	1.29332i	−0.762778	−	0.646660i	$-0.776165\pi$
$401$		−	25.8987i		−	1.29332i	0.762778	−	0.646660i	$-0.223835\pi$
$402$	−32.4870	+	19.3124i	−1.62031	+	0.963217i
$403$	−1.42194			−0.0708317
$404$	11.4432	+	29.0868i	0.569322	+	1.44712i
$405$	6.57410	−	37.1662i	0.326670	−	1.84680i
$406$	−2.92837	+	4.29892i	−0.145333	+	0.213352i
$407$	−3.61404			−0.179141
$408$	−4.33548	+	5.59039i	−0.214638	+	0.276765i
$409$	−7.01083			−0.346663			−0.173332	−	0.984864i	$-0.555453\pi$
$409$	−7.01083			−0.346663			−0.173332	+	0.984864i	$0.555453\pi$
$410$	15.1985	−	22.3118i	0.750602	−	1.10190i
$411$	24.4417	+	11.4014i	1.20562	+	0.562388i
$412$	−18.2414	+	7.17648i	−0.898689	+	0.353560i
$413$	−9.81457			−0.482944
$414$	1.88013	+	18.7626i	0.0924034	+	0.922131i
$415$			52.7666i			2.59021i
$416$	−0.170204	−	1.11373i	−0.00834492	−	0.0546052i
$417$	−13.6407	+	29.2422i	−0.667986	+	1.43200i
$418$	0.381735	−	0.560395i	0.0186712	−	0.0274098i
$419$		−	26.9960i		−	1.31884i	−0.751773	−	0.659422i	$-0.770801\pi$
$419$		−	26.9960i		−	1.31884i	0.751773	−	0.659422i	$-0.229199\pi$
$420$	0.961640	−	15.5790i	0.0469232	−	0.760180i
$421$			34.7706i			1.69462i	0.531102	+	0.847308i	$0.321778\pi$
$421$			34.7706i			1.69462i	−0.531102	+	0.847308i	$0.678222\pi$
$422$	−10.6387	−	7.24698i	−0.517886	−	0.352777i
$423$	4.96267	+	5.91752i	0.241293	+	0.287720i
$424$	5.79445	−	25.5318i	0.281403	−	1.23994i
$425$			18.1766i			0.881692i
$426$	14.2504	−	8.47135i	0.690432	−	0.410438i
$427$	−15.4137			−0.745923
$428$	−14.3146	+	5.63163i	−0.691924	+	0.272215i
$429$	−0.0699208	+	0.149893i	−0.00337581	+	0.00723689i
$430$	−5.50738	−	3.75156i	−0.265590	−	0.180917i
$431$	−8.00443			−0.385560			−0.192780	−	0.981242i	$-0.561750\pi$
$431$	−8.00443			−0.385560			−0.192780	+	0.981242i	$0.561750\pi$
$432$	−11.0363	+	17.6125i	−0.530986	+	0.847380i
$433$	5.47544			0.263133			0.131567	−	0.991307i	$-0.457999\pi$
$433$	5.47544			0.263133			0.131567	+	0.991307i	$0.457999\pi$
$434$	8.96569	+	6.10732i	0.430367	+	0.293161i
$435$	10.5115	−	22.5341i	0.503990	−	1.08043i
$436$	−24.1321	+	9.49399i	−1.15572	+	0.454679i
$437$	4.44453			0.212611
$438$	−8.24689	+	4.90250i	−0.394052	+	0.234250i
$439$			6.36520i			0.303795i	0.988396	+	0.151897i	$0.0485383\pi$
$439$			6.36520i			0.303795i	−0.988396	+	0.151897i	$0.951462\pi$
$440$	−5.54609	−	1.25868i	−0.264399	−	0.0600054i
$441$	−11.2688	−	13.4370i	−0.536609	−	0.639856i
$442$	−0.336165	−	0.228991i	−0.0159897	−	0.0108920i
$443$		−	22.1115i		−	1.05055i	−0.850933	−	0.525274i	$-0.823963\pi$
$443$		−	22.1115i		−	1.05055i	0.850933	−	0.525274i	$-0.176037\pi$
$444$	1.60871	−	26.0619i	0.0763459	−	1.23684i
$445$		−	60.0080i		−	2.84465i
$446$	−1.15074	+	1.68932i	−0.0544893	+	0.0799916i
$447$	5.02780	−	10.7784i	0.237807	−	0.509799i
$448$	−3.71038	+	7.75342i	−0.175299	+	0.366315i
$449$		−	14.0410i		−	0.662634i	−0.943520	−	0.331317i	$-0.892507\pi$
$449$		−	14.0410i		−	0.662634i	0.943520	−	0.331317i	$-0.107493\pi$
$450$	5.32455	+	53.1358i	0.251001	+	2.50484i
$451$	2.18248			0.102769
$452$	−1.24821	+	0.491070i	−0.0587111	+	0.0230980i
$453$	−11.6167	−	5.41885i	−0.545799	−	0.254600i
$454$	−5.31685	+	7.80526i	−0.249532	+	0.366319i
$455$	0.897419			0.0420716
$456$	3.87125	+	3.00224i	0.181288	+	0.140593i
$457$	3.91027			0.182915			0.0914574	−	0.995809i	$-0.470847\pi$
$457$	3.91027			0.182915			0.0914574	+	0.995809i	$0.470847\pi$
$458$	−4.80866	+	7.05923i	−0.224694	+	0.329856i
$459$	1.93915	+	7.24876i	0.0905119	+	0.338343i
$460$	−13.6476	−	34.6898i	−0.636322	−	1.61742i
$461$	5.45629			0.254125			0.127062	−	0.991895i	$-0.459445\pi$
$461$	5.45629			0.254125			0.127062	+	0.991895i	$0.459445\pi$
$462$	1.08467	−	0.644799i	0.0504634	−	0.0299988i
$463$			0.138171i			0.00642134i	0.999995	+	0.00321067i	$0.00102199\pi$
$463$			0.138171i			0.00642134i	−0.999995	+	0.00321067i	$0.998978\pi$
$464$	−10.0223	+	9.33001i	−0.465276	+	0.433135i
$465$	−46.9965	−	21.9226i	−2.17941	−	1.01663i
$466$	12.5225	−	18.3834i	0.580095	−	0.851593i
$467$			2.69235i			0.124587i	0.998058	+	0.0622935i	$0.0198415\pi$
$467$			2.69235i			0.124587i	−0.998058	+	0.0622935i	$0.980159\pi$
$468$	−1.04979	−	0.570940i	−0.0485268	−	0.0263917i
$469$			16.5778i			0.765491i
$470$	−12.6184	−	8.59549i	−0.582042	−	0.396480i
$471$	3.37303	+	1.57342i	0.155421	+	0.0724995i
$472$	−25.1959	−	5.71821i	−1.15974	−	0.263202i
$473$		−	0.538717i		−	0.0247702i
$474$	−12.5949	−	21.1869i	−0.578503	−	0.973148i
$475$	12.5869			0.577529
$476$	1.13607	+	2.88770i	0.0520719	+	0.132358i
$477$	−17.8440	−	21.2773i	−0.817020	−	0.974220i
$478$	−7.15612	−	4.87467i	−0.327313	−	0.222962i
$479$	−18.7667			−0.857470			−0.428735	−	0.903430i	$-0.641041\pi$
$479$	−18.7667			−0.857470			−0.428735	+	0.903430i	$0.641041\pi$
$480$	11.5454	−	39.4341i	0.526975	−	1.79991i
$481$	1.50127			0.0684522
$482$	9.23247	+	6.28905i	0.420527	+	0.286458i
$483$	7.49576	+	3.49656i	0.341069	+	0.159099i
$484$	7.88597	+	20.0448i	0.358453	+	0.911126i
$485$	22.6220			1.02721
$486$	7.79217	+	20.6224i	0.353460	+	0.935450i
$487$		−	6.56034i		−	0.297277i	−0.988892	−	0.148639i	$-0.952511\pi$
$487$		−	6.56034i		−	0.297277i	0.988892	−	0.148639i	$-0.0474891\pi$
$488$	−39.5700	−	8.98041i	−1.79125	−	0.406524i
$489$	−13.2826	+	28.4746i	−0.600660	+	1.28766i
$490$	28.6527	+	19.5179i	1.29440	+	0.881727i
$491$			41.1103i			1.85528i	0.373473	+	0.927641i	$0.378167\pi$
$491$			41.1103i			1.85528i	−0.373473	+	0.927641i	$0.621833\pi$
$492$	−0.971481	+	15.7385i	−0.0437977	+	0.709545i
$493$			4.94342i			0.222641i
$494$	−0.158573	+	0.232788i	−0.00713452	+	0.0104736i
$495$	−4.62191	+	3.87612i	−0.207739	+	0.174218i
$496$	19.4584	+	20.9023i	0.873707	+	0.938541i
$497$		−	7.27181i		−	0.326185i
$498$	−15.7491	−	26.4928i	−0.705732	−	1.18717i
$499$	−1.58234			−0.0708353			−0.0354177	−	0.999373i	$-0.511276\pi$
$499$	−1.58234			−0.0708353			−0.0354177	+	0.999373i	$0.511276\pi$
$500$	−23.2968	−	59.2166i	−1.04187	−	2.64825i
$501$	1.16407	−	2.49547i	0.0520068	−	0.111490i
$502$	−3.43964	+	5.04947i	−0.153519	+	0.225369i
$503$	17.0700			0.761115			0.380558	−	0.924757i	$-0.375732\pi$
$503$	17.0700			0.761115			0.380558	+	0.924757i	$0.375732\pi$
$504$	4.16701	+	8.10887i	0.185613	+	0.361198i
$505$	−65.5405			−2.91651
$506$	1.69663	−	2.49069i	0.0754245	−	0.110725i
$507$	−9.48966	+	20.3435i	−0.421451	+	0.903485i
$508$	21.5577	−	8.48119i	0.956470	−	0.376292i
$509$	22.6322			1.00315			0.501577	−	0.865113i	$-0.332753\pi$
$509$	22.6322			1.00315			0.501577	+	0.865113i	$0.332753\pi$
$510$	−7.58015	−	12.7512i	−0.335654	−	0.564632i
$511$			4.20830i			0.186164i
$512$	−14.0426	+	17.7428i	−0.620601	+	0.784127i
$513$	5.01964	−	1.34283i	0.221623	−	0.0592874i
$514$	19.4722	−	28.5857i	0.858884	−	1.26086i
$515$		−	41.1029i		−	1.81121i
$516$	3.88484	+	0.239798i	0.171021	+	0.0105565i
$517$		−	1.23429i		−	0.0542842i
$518$	−9.46593	−	6.44808i	−0.415909	−	0.283312i
$519$	9.58520	−	20.5483i	0.420744	−	0.901970i
$520$	2.30385	+	0.522858i	0.101030	+	0.0229288i
$521$			10.7070i			0.469081i	0.972106	+	0.234540i	$0.0753585\pi$
$521$			10.7070i			0.469081i	−0.972106	+	0.234540i	$0.924642\pi$
$522$	1.44810	+	14.4512i	0.0633816	+	0.632511i
$523$	8.47438			0.370559			0.185279	−	0.982686i	$-0.440681\pi$
$523$	8.47438			0.370559			0.185279	+	0.982686i	$0.440681\pi$
$524$	35.6177	−	14.0126i	1.55596	−	0.612144i
$525$	21.2281	+	9.90229i	0.926468	+	0.432172i
$526$	−21.3535	−	14.5458i	−0.931058	−	0.634226i
$527$	10.3099			0.449104
$528$	3.16023	−	1.02337i	0.137531	−	0.0445364i
$529$	−3.24614			−0.141136
$530$	45.3712	+	30.9063i	1.97080	+	1.34248i
$531$	−20.9973	+	17.6092i	−0.911207	+	0.764174i
$532$	1.99969	−	0.786711i	0.0866973	−	0.0341083i
$533$	−0.906602			−0.0392693
$534$	17.9104	+	30.1285i	0.775058	+	1.30379i
$535$		−	32.2548i		−	1.39450i
$536$	−9.65862	+	42.5584i	−0.417189	+	1.83824i
$537$	7.26972	+	3.39112i	0.313712	+	0.146338i
$538$	20.9310	+	14.2580i	0.902401	+	0.614705i
$539$			2.80273i			0.120722i
$540$	−25.8944	−	35.0552i	−1.11432	−	1.50854i
$541$		−	41.6854i		−	1.79220i	−0.443856	−	0.896098i	$-0.646390\pi$
$541$		−	41.6854i		−	1.79220i	0.443856	−	0.896098i	$-0.353610\pi$
$542$	−15.4594	+	22.6947i	−0.664036	+	0.974821i
$543$	18.5189	+	8.63856i	0.794723	+	0.370716i
$544$	1.23407	+	8.07520i	0.0529105	+	0.346221i
$545$		−	54.3762i		−	2.32922i
$546$	−0.450572	+	0.267850i	−0.0192827	+	0.0114629i
$547$	−40.8541			−1.74680			−0.873398	−	0.487008i	$-0.838088\pi$
$547$	−40.8541			−1.74680			−0.873398	+	0.487008i	$0.838088\pi$
$548$	28.9803	−	11.4014i	1.23798	−	0.487042i
$549$	−32.9762	+	27.6551i	−1.40739	+	1.18029i
$550$	4.80487	−	7.05367i	0.204880	−	0.300769i
$551$	3.42323			0.145835
$552$	17.2059	+	13.3436i	0.732331	+	0.567940i
$553$	−10.8115			−0.459750
$554$	6.21538	−	9.12433i	0.264066	−	0.387655i
$555$	49.6186	+	23.1457i	2.10619	+	0.982480i
$556$	13.6407	+	34.6722i	0.578493	+	1.47043i
$557$	18.5432			0.785699			0.392850	−	0.919603i	$-0.371489\pi$
$557$	18.5432			0.785699			0.392850	+	0.919603i	$0.371489\pi$
$558$	30.1389	−	3.02011i	1.27588	−	0.127852i
$559$			0.223783i			0.00946502i
$560$	−12.2807	−	13.1919i	−0.518952	−	0.557461i
$561$	0.506965	−	1.08681i	0.0214041	−	0.0458851i
$562$	16.5970	−	24.3647i	0.700101	−	1.02776i
$563$			11.4988i			0.484617i	0.970199	+	0.242308i	$0.0779046\pi$
$563$			11.4988i			0.484617i	−0.970199	+	0.242308i	$0.922095\pi$
$564$	8.90084	+	0.549418i	0.374793	+	0.0231347i
$565$		−	2.81257i		−	0.118326i
$566$	16.6852	+	11.3658i	0.701332	+	0.477739i
$567$	9.52211	+	1.68431i	0.399891	+	0.0707343i
$568$	4.23673	−	18.6681i	0.177769	−	0.783297i
$569$		−	46.0162i		−	1.92910i	−0.263902	−	0.964550i	$-0.585009\pi$
$569$		−	46.0162i		−	1.92910i	0.263902	−	0.964550i	$-0.414991\pi$
$570$	−8.82997	+	5.24912i	−0.369847	+	0.219861i
$571$	17.8577			0.747320			0.373660	−	0.927566i	$-0.378103\pi$
$571$	17.8577			0.747320			0.373660	+	0.927566i	$0.378103\pi$
$572$	0.0699208	+	0.177727i	0.00292353	+	0.00743112i
$573$	8.92494	−	19.1329i	0.372845	−	0.799286i
$574$	5.71637	+	3.89392i	0.238597	+	0.162529i
$575$	55.9431			2.33299
$576$	5.97309	+	23.2448i	0.248879	+	0.968535i
$577$	−10.3462			−0.430720			−0.215360	−	0.976535i	$-0.569092\pi$
$577$	−10.3462			−0.430720			−0.215360	+	0.976535i	$0.569092\pi$
$578$	−17.4323	−	11.8747i	−0.725088	−	0.493921i
$579$	3.87111	−	8.29869i	0.160878	−	0.344882i
$580$	−10.5115	−	26.7185i	−0.436468	−	1.10943i
$581$	−13.5190			−0.560862
$582$	−11.3580	+	6.75191i	−0.470802	+	0.279876i
$583$			4.43808i			0.183807i
$584$	−2.45186	+	10.8035i	−0.101459	+	0.447053i
$585$	1.91994	−	1.61014i	0.0793798	−	0.0665710i
$586$	−24.8899	−	16.9547i	−1.02819	−	0.700393i
$587$			4.89186i			0.201909i	0.994891	+	0.100954i	$0.0321896\pi$
$587$			4.89186i			0.201909i	−0.994891	+	0.100954i	$0.967810\pi$
$588$	−20.2112	−	1.24757i	−0.833497	−	0.0514489i
$589$		−	7.13939i		−	0.294174i
$590$	30.4997	−	44.7742i	1.25565	−	1.84332i
$591$	−3.92476	+	8.41371i	−0.161443	+	0.346094i
$592$	−20.5440	−	22.0685i	−0.844355	−	0.907011i
$593$			20.2452i			0.831371i	0.909509	+	0.415685i	$0.136458\pi$
$593$			20.2452i			0.831371i	−0.909509	+	0.415685i	$0.863542\pi$
$594$	1.16366	−	3.32559i	0.0477454	−	0.136451i
$595$	−6.50680			−0.266753
$596$	−5.02780	−	12.7798i	−0.205947	−	0.523482i
$597$	14.2114	+	6.62923i	0.581635	+	0.271316i
$598$	−0.704781	+	1.03463i	−0.0288206	+	0.0423094i
$599$	−28.2577			−1.15458			−0.577288	−	0.816540i	$-0.695889\pi$
$599$	−28.2577			−1.15458			−0.577288	+	0.816540i	$0.695889\pi$
$600$	48.7272	+	37.7891i	1.98928	+	1.54273i
$601$	20.2981			0.827978			0.413989	−	0.910282i	$-0.364135\pi$
$601$	20.2981			0.827978			0.413989	+	0.910282i	$0.364135\pi$
$602$	0.961165	−	1.41101i	0.0391742	−	0.0575086i
$603$	29.7437	+	35.4666i	1.21126	+	1.44431i
$604$	−13.7738	+	5.41885i	−0.560448	+	0.220490i
$605$	−45.1664			−1.83628
$606$	32.9063	−	19.5617i	1.33673	−	0.794638i
$607$		−	13.6602i		−	0.554450i	−0.960805	−	0.277225i	$-0.910585\pi$
$607$		−	13.6602i		−	0.554450i	0.960805	−	0.277225i	$-0.0894147\pi$
$608$	5.59193	−	0.854574i	0.226783	−	0.0346576i
$609$	5.77333	+	2.69310i	0.233947	+	0.109130i
$610$	47.8995	−	70.3176i	1.93939	−	2.84708i
$611$			0.512726i			0.0207427i
$612$	7.61161	+	4.13964i	0.307681	+	0.167335i
$613$		−	37.1787i		−	1.50163i	−0.660511	−	0.750816i	$-0.729660\pi$
$613$		−	37.1787i		−	1.50163i	0.660511	−	0.750816i	$-0.270340\pi$
$614$	−34.7337	−	23.6602i	−1.40174	−	0.954846i
$615$	−29.9641	−	13.9774i	−1.20827	−	0.563624i
$616$	0.322480	−	1.42093i	0.0129931	−	0.0572509i
$617$			15.3963i			0.619833i	0.950764	+	0.309916i	$0.100301\pi$
$617$			15.3963i			0.619833i	−0.950764	+	0.309916i	$0.899699\pi$
$618$	12.2678	+	20.6367i	0.493485	+	0.830132i
$619$	−3.93937			−0.158337			−0.0791683	−	0.996861i	$-0.525226\pi$
$619$	−3.93937			−0.158337			−0.0791683	+	0.996861i	$0.525226\pi$
$620$	−55.7234	+	21.9226i	−2.23790	+	0.880431i
$621$	22.3100	−	5.96825i	0.895268	−	0.239498i
$622$	1.13253	+	0.771463i	0.0454101	+	0.0309328i
$623$	15.3743			0.615957
$624$	−1.31276	+	0.425107i	−0.0525525	+	0.0170179i
$625$	70.4965			2.81986
$626$	−7.34939	−	5.00632i	−0.293741	−	0.200093i
$627$	−0.752595	−	0.351065i	−0.0300558	−	0.0140202i
$628$	3.99937	−	1.57342i	0.159592	−	0.0627864i
$629$	−10.8851			−0.434017
$630$	−19.0214	+	1.90607i	−0.757831	+	0.0759395i
$631$			9.58947i			0.381751i	0.981614	+	0.190875i	$0.0611326\pi$
$631$			9.58947i			0.381751i	−0.981614	+	0.190875i	$0.938867\pi$
$632$	−27.7551	−	6.29902i	−1.10404	−	0.250562i
$633$	−6.66473	+	14.2875i	−0.264899	+	0.567878i
$634$	27.9612	+	19.0468i	1.11048	+	0.756446i
$635$			48.5755i			1.92766i
$636$	−32.0043	−	1.97551i	−1.26905	−	0.0783341i
$637$		−	1.16425i		−	0.0461294i
$638$	1.30677	−	1.91836i	0.0517354	−	0.0759487i
$639$	−13.0470	−	15.5573i	−0.516131	−	0.615439i
$640$	−23.8408	−	41.0213i	−0.942392	−	1.62151i
$641$			7.02048i			0.277292i	0.990342	+	0.138646i	$0.0442751\pi$
$641$			7.02048i			0.277292i	−0.990342	+	0.138646i	$0.955725\pi$
$642$	9.62699	+	16.1944i	0.379947	+	0.639140i
$643$	18.9551			0.747517			0.373758	−	0.927526i	$-0.378069\pi$
$643$	18.9551			0.747517			0.373758	+	0.927526i	$0.378069\pi$
$644$	8.88766	−	3.49656i	0.350223	−	0.137784i
$645$	−3.45015	+	7.39626i	−0.135850	+	0.291228i
$646$	1.14974	−	1.68785i	0.0452360	−	0.0664075i
$647$	29.7579			1.16990			0.584952	−	0.811068i	$-0.301113\pi$
$647$	29.7579			1.16990			0.584952	+	0.811068i	$0.301113\pi$
$648$	23.4638	+	9.87175i	0.921744	+	0.387799i
$649$	4.37969			0.171918
$650$	−1.99594	+	2.93009i	−0.0782874	+	0.114928i
$651$	5.61664	−	12.0407i	0.220134	−	0.471911i
$652$	13.2826	+	33.7621i	0.520187	+	1.32223i
$653$	−2.16318			−0.0846516			−0.0423258	−	0.999104i	$-0.513477\pi$
$653$	−2.16318			−0.0846516			−0.0423258	+	0.999104i	$0.513477\pi$
$654$	16.2295	+	27.3010i	0.634624	+	1.06755i
$655$			80.2564i			3.13588i
$656$	12.4063	+	13.3269i	0.484385	+	0.520329i
$657$	7.55049	+	9.00326i	0.294573	+	0.351251i
$658$	2.20220	−	3.23288i	0.0858506	−	0.126031i
$659$		−	17.5114i		−	0.682149i	−0.940036	−	0.341074i	$-0.889209\pi$
$659$		−	17.5114i		−	0.682149i	0.940036	−	0.341074i	$-0.110791\pi$
$660$	−0.429126	+	6.95205i	−0.0167037	+	0.270608i
$661$			16.1146i			0.626785i	0.949624	+	0.313392i	$0.101465\pi$
$661$			16.1146i			0.626785i	−0.949624	+	0.313392i	$0.898535\pi$
$662$	6.34679	+	4.32336i	0.246675	+	0.168032i
$663$	−0.210593	+	0.451460i	−0.00817877	+	0.0175333i
$664$	−34.7059	−	7.87649i	−1.34685	−	0.305667i
$665$			4.50584i			0.174729i
$666$	−31.8205	+	3.18862i	−1.23302	+	0.123556i
$667$	15.2147			0.589114
$668$	−1.16407	−	2.95886i	−0.0450392	−	0.114482i
$669$	2.26871	+	1.05829i	0.0877133	+	0.0409158i
$670$	−75.6281	−	51.5170i	−2.92177	−	1.99027i
$671$	6.87827			0.265533
$672$	10.1032	+	2.95799i	0.389738	+	0.114107i
$673$	−32.9181			−1.26890			−0.634450	−	0.772964i	$-0.718773\pi$
$673$	−32.9181			−1.26890			−0.634450	+	0.772964i	$0.718773\pi$
$674$	−28.2565	−	19.2480i	−1.08840	−	0.741406i
$675$	63.1820	−	16.9021i	2.43188	−	0.650563i
$676$	9.48966	+	24.1211i	0.364987	+	0.927734i
$677$	−11.3965			−0.438004			−0.219002	−	0.975724i	$-0.570280\pi$
$677$	−11.3965			−0.438004			−0.219002	+	0.975724i	$0.570280\pi$
$678$	0.839459	+	1.41212i	0.0322392	+	0.0542323i
$679$			5.79584i			0.222424i
$680$	−16.7042	−	3.79102i	−0.640577	−	0.145379i
$681$	10.4823	+	4.88968i	0.401681	+	0.187373i
$682$	−4.00088	−	2.72535i	−0.153202	−	0.104359i
$683$		−	30.6815i		−	1.17400i	−0.809588	−	0.586998i	$-0.800310\pi$
$683$		−	30.6815i		−	1.17400i	0.809588	−	0.586998i	$-0.199690\pi$
$684$	2.86663	−	5.27091i	0.109608	−	0.201538i
$685$			65.3006i			2.49501i
$686$	−10.9886	+	16.1316i	−0.419548	+	0.615906i
$687$	9.48035	+	4.42232i	0.361698	+	0.168722i
$688$	3.28958	−	3.06234i	0.125414	−	0.116751i
$689$		−	1.84358i		−	0.0702348i
$690$	−39.2451	+	23.3299i	−1.49404	+	0.888153i
$691$	−33.5120			−1.27486			−0.637428	−	0.770510i	$-0.720002\pi$
$691$	−33.5120			−1.27486			−0.637428	+	0.770510i	$0.720002\pi$
$692$	−9.58520	−	24.3639i	−0.364375	−	0.926178i
$693$	−0.993075	−	1.18415i	−0.0377238	−	0.0449822i
$694$	−18.0960	+	26.5653i	−0.686914	+	1.00841i
$695$	−78.1260			−2.96349
$696$	13.2522	+	10.2774i	0.502323	+	0.389563i
$697$	6.57338			0.248984
$698$	−11.3616	+	16.6791i	−0.430043	+	0.631312i
$699$	−24.6883	−	11.5164i	−0.933799	−	0.435591i
$700$	25.1699	−	9.90229i	0.951334	−	0.374272i
$701$	8.00296			0.302268			0.151134	−	0.988513i	$-0.451708\pi$
$701$	8.00296			0.302268			0.151134	+	0.988513i	$0.451708\pi$
$702$	−0.483383	+	1.38145i	−0.0182441	+	0.0521395i
$703$			7.53773i			0.284291i
$704$	1.65573	−	3.45991i	0.0624028	−	0.130400i
$705$	−7.90490	+	16.9461i	−0.297716	+	0.638228i
$706$	9.41469	−	13.8210i	0.354327	−	0.520160i
$707$		−	16.7917i		−	0.631518i
$708$	−1.94952	+	31.5832i	−0.0732674	+	1.18697i
$709$			16.9931i			0.638189i	0.947723	+	0.319094i	$0.103379\pi$
$709$			16.9931i			0.638189i	−0.947723	+	0.319094i	$0.896621\pi$
$710$	33.1741	+	22.5978i	1.24500	+	0.848080i
$711$	−23.1301	+	19.3978i	−0.867447	+	0.727475i
$712$	39.4687	+	8.95742i	1.47915	+	0.335693i
$713$		−	31.7313i		−	1.18834i
$714$	3.26690	−	1.94206i	0.122261	−	0.0726798i
$715$	−0.400467			−0.0149766
$716$	8.61965	−	3.39112i	0.322131	−	0.126732i
$717$	−4.48302	+	9.61048i	−0.167421	+	0.358910i
$718$	6.44197	+	4.38820i	0.240412	+	0.163766i
$719$	−41.5171			−1.54833			−0.774164	−	0.632985i	$-0.781829\pi$
$719$	−41.5171			−1.54833			−0.774164	+	0.632985i	$0.781829\pi$
$720$	−49.9421	−	6.18909i	−1.86123	−	0.230654i
$721$	10.5307			0.392184
$722$	−1.16880	−	0.796176i	−0.0434984	−	0.0296306i
$723$	5.78376	−	12.3990i	0.215101	−	0.461122i
$724$	21.9577	−	8.63856i	0.816053	−	0.321050i
$725$	43.0881			1.60025
$726$	22.6770	−	13.4807i	0.841621	−	0.500315i
$727$			31.1911i			1.15682i	0.815748	+	0.578408i	$0.196326\pi$
$727$			31.1911i			1.15682i	−0.815748	+	0.578408i	$0.803674\pi$
$728$	−0.133958	+	0.590254i	−0.00496482	+	0.0218763i
$729$	23.3936	−	13.4811i	0.866430	−	0.499298i
$730$	−19.1983	−	13.0777i	−0.710562	−	0.484026i
$731$		−	1.62255i		−	0.0600124i
$732$	−3.06171	+	49.6012i	−0.113164	+	1.83331i
$733$		−	2.54943i		−	0.0941652i	−0.998891	−	0.0470826i	$-0.985008\pi$
$733$		−	2.54943i		−	0.0941652i	0.998891	−	0.0470826i	$-0.0149924\pi$
$734$	20.9600	−	30.7698i	0.773649	−	1.13573i
$735$	17.9497	−	38.4798i	0.662086	−	1.41935i
$736$	24.8535	−	3.79818i	0.916113	−	0.140003i
$737$		−	7.39773i		−	0.272499i
$738$	19.2160	−	1.92557i	0.707353	−	0.0708813i
$739$	−34.0065			−1.25095			−0.625474	−	0.780245i	$-0.715095\pi$
$739$	−34.0065			−1.25095			−0.625474	+	0.780245i	$0.715095\pi$
$740$	58.8324	−	23.1457i	2.16272	−	0.850853i
$741$	0.312628	+	0.145832i	0.0114847	+	0.00535728i
$742$	−7.91831	+	11.6243i	−0.290690	+	0.426740i
$743$	−19.6554			−0.721086			−0.360543	−	0.932743i	$-0.617409\pi$
$743$	−19.6554			−0.721086			−0.360543	+	0.932743i	$0.617409\pi$
$744$	21.4342	−	27.6383i	0.785815	−	1.01327i
$745$	28.7965			1.05502
$746$	−18.6867	+	27.4325i	−0.684167	+	1.00437i
$747$	−28.9226	+	24.2556i	−1.05822	+	0.887467i
$748$	−0.506965	−	1.28862i	−0.0185365	−	0.0471166i
$749$	8.26381			0.301953
$750$	−66.9926	+	39.8248i	−2.44622	+	1.45420i
$751$			21.1165i			0.770552i	0.922801	+	0.385276i	$0.125894\pi$
$751$			21.1165i			0.770552i	−0.922801	+	0.385276i	$0.874106\pi$
$752$	7.53701	−	7.01636i	0.274847	−	0.255860i
$753$	6.78130	+	3.16329i	0.247124	+	0.115277i
$754$	−0.542831	+	0.796889i	−0.0197687	+	0.0290210i
$755$		−	31.0361i		−	1.12952i
$756$	8.98128	−	6.63425i	0.326646	−	0.241285i
$757$			21.4371i			0.779144i	0.920996	+	0.389572i	$0.127377\pi$
$757$			21.4371i			0.779144i	−0.920996	+	0.389572i	$0.872623\pi$
$758$	−15.9067	−	10.8355i	−0.577759	−	0.393562i
$759$	−3.34493	−	1.56032i	−0.121413	−	0.0566360i
$760$	−2.62521	+	11.5674i	−0.0952264	+	0.419592i
$761$			4.15418i			0.150589i	0.997161	+	0.0752945i	$0.0239897\pi$
$761$			4.15418i			0.150589i	−0.997161	+	0.0752945i	$0.976010\pi$
$762$	−14.4982	−	24.3886i	−0.525214	−	0.883505i
$763$	13.9314			0.504350
$764$	−8.92494	−	22.6857i	−0.322893	−	0.820739i
$765$	−13.9207	+	11.6744i	−0.503303	+	0.422090i
$766$	4.20418	+	2.86384i	0.151903	+	0.103475i
$767$	−1.81932			−0.0656920
$768$	24.2134	+	13.4801i	0.873725	+	0.486420i
$769$	−0.350362			−0.0126344			−0.00631720	−	0.999980i	$-0.502011\pi$
$769$	−0.350362			−0.0126344			−0.00631720	+	0.999980i	$0.502011\pi$
$770$	2.52505	+	1.72004i	0.0909966	+	0.0619858i
$771$	−38.3898	−	17.9078i	−1.38258	−	0.644933i
$772$	−3.87111	−	9.83970i	−0.139324	−	0.354138i
$773$	21.6952			0.780322			0.390161	−	0.920747i	$-0.372419\pi$
$773$	21.6952			0.780322			0.390161	+	0.920747i	$0.372419\pi$
$774$	−0.475303	−	4.74324i	−0.0170844	−	0.170492i
$775$		−	89.8632i		−	3.22798i
$776$	−3.37680	+	14.8790i	−0.121220	+	0.534126i
$777$	−5.93002	+	12.7125i	−0.212738	+	0.456058i
$778$	11.4917	+	7.82798i	0.411996	+	0.280647i
$779$		−	4.55195i		−	0.163091i
$780$	0.178259	−	2.88788i	0.00638269	−	0.103403i
$781$			3.24500i			0.116115i
$782$	5.11006	−	7.50169i	0.182735	−	0.268260i
$783$	17.1834	−	4.59682i	0.614085	−	0.164277i
$784$	−17.1144	+	15.9321i	−0.611227	+	0.569004i
$785$			9.01168i			0.321641i
$786$	−23.9539	−	40.2948i	−0.854406	−	1.43727i
$787$	−12.2043			−0.435036			−0.217518	−	0.976056i	$-0.569796\pi$
$787$	−12.2043			−0.435036			−0.217518	+	0.976056i	$0.569796\pi$
$788$	3.92476	+	9.97606i	0.139814	+	0.355383i
$789$	−13.3771	+	28.6772i	−0.476238	+	1.02094i
$790$	33.5976	−	49.3220i	1.19535	−	1.75480i
$791$	0.720591			0.0256213
$792$	−1.85950	−	3.61853i	−0.0660745	−	0.128579i
$793$	−2.85724			−0.101463
$794$	19.5771	−	28.7396i	0.694764	−	1.01993i
$795$	28.4232	−	60.9322i	1.00807	−	2.16104i
$796$	16.8504	−	6.62923i	0.597246	−	0.234967i
$797$	−2.97596			−0.105414			−0.0527070	−	0.998610i	$-0.516785\pi$
$797$	−2.97596			−0.105414			−0.0527070	+	0.998610i	$0.516785\pi$
$798$	−1.34484	−	2.26227i	−0.0476070	−	0.0800836i
$799$		−	3.71756i		−	0.131518i
$800$	70.3854	−	10.7565i	2.48850	−	0.380299i
$801$	32.8918	−	27.5843i	1.16217	−	0.974645i
$802$	−20.6199	+	30.2705i	−0.728115	+	1.06889i
$803$		−	1.87793i		−	0.0662706i
$804$	53.3471	+	3.29293i	1.88141	+	0.116133i
$805$			20.0264i			0.705836i
$806$	1.66197	+	1.13211i	0.0585403	+	0.0398769i
$807$	13.1124	−	28.1098i	0.461580	−	0.989512i
$808$	9.78326	−	43.1076i	0.344174	−	1.51652i
$809$		−	9.54842i		−	0.335705i	−0.985812	−	0.167852i	$-0.946317\pi$
$809$		−	9.54842i		−	0.335705i	0.985812	−	0.167852i	$-0.0536832\pi$
$810$	−37.2746	+	38.2058i	−1.30970	+	1.34242i
$811$	−5.42974			−0.190664			−0.0953319	−	0.995446i	$-0.530391\pi$
$811$	−5.42974			−0.190664			−0.0953319	+	0.995446i	$0.530391\pi$
$812$	6.84539	−	2.69310i	0.240226	−	0.0945092i
$813$	30.4783	+	14.2173i	1.06892	+	0.498622i
$814$	4.22411	+	2.87741i	0.148055	+	0.100853i
$815$	−76.0753			−2.66480
$816$	9.51826	−	3.08227i	0.333206	−	0.107901i
$817$	−1.12359			−0.0393095
$818$	8.19429	+	5.58185i	0.286507	+	0.195165i
$819$	0.412524	+	0.491896i	0.0144147	+	0.0171882i
$820$	−35.5282	+	13.9774i	−1.24070	+	0.488113i
$821$	44.6513			1.55834			0.779170	−	0.626813i	$-0.215641\pi$
$821$	44.6513			1.55834			0.779170	+	0.626813i	$0.215641\pi$
$822$	−19.4901	−	32.7858i	−0.679794	−	1.14354i
$823$		−	34.4623i		−	1.20128i	−0.799520	−	0.600639i	$-0.794913\pi$
$823$		−	34.4623i		−	1.20128i	0.799520	−	0.600639i	$-0.205087\pi$
$824$	27.0344	+	6.13545i	0.941787	+	0.213738i
$825$	−9.47288	−	4.41883i	−0.329803	−	0.153844i
$826$	11.4713	+	7.81413i	0.399138	+	0.271888i
$827$			20.5306i			0.713918i	0.934120	+	0.356959i	$0.116186\pi$
$827$			20.5306i			0.713918i	−0.934120	+	0.356959i	$0.883814\pi$
$828$	12.7408	−	23.4267i	0.442774	−	0.814134i
$829$		−	1.35687i		−	0.0471261i	−0.999722	−	0.0235631i	$-0.992499\pi$
$829$		−	1.35687i		−	0.0471261i	0.999722	−	0.0235631i	$-0.00750105\pi$
$830$	42.0115	−	61.6738i	1.45824	−	2.14073i
$831$	−12.2537	−	5.71602i	−0.425077	−	0.198286i
$832$	−0.687792	+	1.43725i	−0.0238449	+	0.0498276i
$833$			8.44149i			0.292480i
$834$	39.2252	−	23.3180i	1.35826	−	0.807437i
$835$	6.66714			0.230726
$836$	−0.892346	+	0.351065i	−0.0308624	+	0.0121418i
$837$	−9.58699	−	35.8372i	−0.331375	−	1.23871i
$838$	−21.4936	+	31.5531i	−0.742484	+	1.08998i
$839$	15.3270			0.529146			0.264573	−	0.964366i	$-0.414769\pi$
$839$	15.3270			0.529146			0.264573	+	0.964366i	$0.414769\pi$
$840$	−13.5276	+	17.4432i	−0.466747	+	0.601848i
$841$	−17.2815			−0.595913
$842$	27.6835	−	40.6400i	0.954037	−	1.40055i
$843$	−32.7212	−	15.2635i	−1.12698	−	0.525703i
$844$	6.66473	+	16.9406i	0.229410	+	0.583120i
$845$	−54.3515			−1.86975
$846$	−1.08900	−	10.8676i	−0.0374406	−	0.373635i
$847$		−	11.5718i		−	0.397612i
$848$	−27.1004	+	25.2283i	−0.930631	+	0.866344i
$849$	10.4526	−	22.4078i	0.358732	−	0.769033i
$850$	14.4717	−	21.2448i	0.496376	−	0.728692i
$851$			33.5017i			1.14842i
$852$	−23.4006	−	1.44444i	−0.801691	−	0.0494856i
$853$		−	42.1508i		−	1.44322i	−0.692301	−	0.721609i	$-0.743403\pi$
$853$		−	42.1508i		−	1.44322i	0.692301	−	0.721609i	$-0.256597\pi$
$854$	18.0156	+	12.2720i	0.616482	+	0.419940i
$855$	8.08433	+	9.63982i	0.276478	+	0.329675i
$856$	21.2148	+	4.81469i	0.725106	+	0.164563i
$857$		−	13.7612i		−	0.470074i	−0.971986	−	0.235037i	$-0.924479\pi$
$857$		−	13.7612i		−	0.470074i	0.971986	−	0.235037i	$-0.0755211\pi$
$858$	0.201065	−	0.119526i	0.00686424	−	0.00408055i
$859$	−29.3821			−1.00250			−0.501252	−	0.865301i	$-0.667127\pi$
$859$	−29.3821			−1.00250			−0.501252	+	0.865301i	$0.667127\pi$
$860$	3.45015	+	8.76969i	0.117649	+	0.299044i
$861$	3.58107	−	7.67692i	0.122043	−	0.261629i
$862$	9.35562	+	6.37293i	0.318654	+	0.217063i
$863$	19.6613			0.669279			0.334639	−	0.942346i	$-0.391385\pi$
$863$	19.6613			0.669279			0.334639	+	0.942346i	$0.391385\pi$
$864$	26.9219	−	11.7987i	0.915903	−	0.401399i
$865$	54.8987			1.86661
$866$	−6.39972	−	4.35942i	−0.217471	−	0.148139i
$867$	−10.9206	+	23.4111i	−0.370884	+	0.795082i
$868$	−5.61664	−	14.2765i	−0.190641	−	0.484577i
$869$	4.82455			0.163662
$870$	−30.2271	+	17.9690i	−1.02479	+	0.609205i
$871$			3.07302i			0.104125i
$872$	35.7646	+	8.11677i	1.21114	+	0.274868i
$873$	10.3988	+	12.3997i	0.351947	+	0.419665i
$874$	−5.19479	−	3.53863i	−0.175716	−	0.119696i
$875$			34.1856i			1.15568i
$876$	13.5423	+	0.835916i	0.457550	+	0.0282430i
$877$			20.2157i			0.682636i	0.939948	+	0.341318i	$0.110873\pi$
$877$			20.2157i			0.682636i	−0.939948	+	0.341318i	$0.889127\pi$
$878$	5.06782	−	7.43968i	0.171031	−	0.251077i
$879$	−15.5925	+	33.4265i	−0.525923	+	1.12745i
$880$	5.48016	+	5.88682i	0.184736	+	0.198445i
$881$		−	8.26211i		−	0.278358i	−0.990267	−	0.139179i	$-0.955554\pi$
$881$		−	8.26211i		−	0.278358i	0.990267	−	0.139179i	$-0.0444463\pi$
$882$	2.47281	+	24.6771i	0.0832637	+	0.830922i
$883$	−2.43982			−0.0821065			−0.0410532	−	0.999157i	$-0.513071\pi$
$883$	−2.43982			−0.0821065			−0.0410532	+	0.999157i	$0.513071\pi$
$884$	0.210593	+	0.535293i	0.00708303	+	0.0180038i
$885$	−60.1305	−	28.0492i	−2.02127	−	0.942864i
$886$	−17.6046	+	25.8440i	−0.591439	+	0.868246i
$887$	−26.9366			−0.904443			−0.452222	−	0.891906i	$-0.649368\pi$
$887$	−26.9366			−0.904443			−0.452222	+	0.891906i	$0.649368\pi$
$888$	−22.6301	+	29.1804i	−0.759416	+	0.979230i
$889$	−12.4452			−0.417400
$890$	−47.7769	+	70.1376i	−1.60149	+	2.35102i
$891$	−4.24918	−	0.751612i	−0.142353	−	0.0251799i
$892$	2.68999	−	1.05829i	0.0900675	−	0.0354341i
$893$	−2.57434			−0.0861471
$894$	−14.4580	+	8.59478i	−0.483548	+	0.287453i
$895$			19.4224i			0.649221i
$896$	10.5098	−	6.10812i	0.351108	−	0.204058i
$897$	1.38949	+	0.648156i	0.0463936	+	0.0216413i
$898$	−11.1791	+	16.4111i	−0.373050	+	0.547647i
$899$		−	24.4398i		−	0.815113i
$900$	36.0821	−	66.3446i	1.20274	−	2.21149i
$901$			13.3670i			0.445319i
$902$	−2.55089	−	1.73764i	−0.0849354	−	0.0578570i
$903$	−1.89495	−	0.883942i	−0.0630600	−	0.0294157i
$904$	1.84990	+	0.419834i	0.0615266	+	0.0139635i
$905$			49.4768i			1.64467i
$906$	9.26326	+	15.5825i	0.307751	+	0.517693i
$907$	−58.2268			−1.93339			−0.966695	−	0.255930i	$-0.917618\pi$
$907$	−58.2268			−1.93339			−0.966695	+	0.255930i	$0.917618\pi$
$908$	12.4287	−	4.88968i	0.412462	−	0.162270i
$909$	−30.1275	−	35.9243i	−0.999267	−	1.19153i
$910$	−1.04891	−	0.714503i	−0.0347709	−	0.0236855i
$911$	−42.9212			−1.42204			−0.711022	−	0.703170i	$-0.751767\pi$
$911$	−42.9212			−1.42204			−0.711022	+	0.703170i	$0.751767\pi$
$912$	−2.13442	−	6.59123i	−0.0706776	−	0.218257i
$913$	6.03276			0.199655
$914$	−4.57034	−	3.11326i	−0.151173	−	0.102978i
$915$	−94.4346	−	44.0511i	−3.12191	−	1.45628i
$916$	11.2408	−	4.42232i	0.371406	−	0.146118i
$917$	−20.5620			−0.679017
$918$	3.50480	−	10.0163i	0.115676	−	0.330587i
$919$		−	17.1127i		−	0.564497i	−0.959341	−	0.282249i	$-0.908920\pi$
$919$		−	17.1127i		−	0.564497i	0.959341	−	0.282249i	$-0.0910803\pi$
$920$	−11.6678	+	51.4115i	−0.384677	+	1.69499i
$921$	−21.7592	+	46.6463i	−0.716990	+	1.53705i
$922$	−6.37733	−	4.34416i	−0.210026	−	0.143067i
$923$		−	1.34797i		−	0.0443690i
$924$	−1.78114	−	0.109944i	−0.0585952	−	0.00361688i
$925$			94.8770i			3.11954i
$926$	0.110008	−	0.161495i	0.00361509	−	0.00530704i
$927$	22.5295	−	18.8941i	0.739964	−	0.620563i
$928$	19.1425	−	2.92541i	0.628383	−	0.0960312i
$929$		−	47.3015i		−	1.55191i	−0.630787	−	0.775956i	$-0.717268\pi$
$929$		−	47.3015i		−	1.55191i	0.630787	−	0.775956i	$-0.282732\pi$
$930$	37.4755	+	63.0407i	1.22887	+	2.06718i
$931$	5.84559			0.191581
$932$	−29.2728	+	11.5164i	−0.958862	+	0.377233i
$933$	0.709481	−	1.52095i	0.0232274	−	0.0497937i
$934$	2.14358	−	3.14683i	0.0701401	−	0.102967i
$935$	2.90361			0.0949583
$936$	0.772437	+	1.50314i	0.0252479	+	0.0491316i
$937$	−43.3976			−1.41774			−0.708869	−	0.705340i	$-0.750794\pi$
$937$	−43.3976			−1.41774			−0.708869	+	0.705340i	$0.750794\pi$
$938$	13.1988	−	19.3762i	0.430957	−	0.632655i
$939$	−4.60409	+	9.87003i	−0.150249	+	0.322096i
$940$	7.90490	+	20.0929i	0.257829	+	0.655358i
$941$	−26.9315			−0.877941			−0.438971	−	0.898501i	$-0.644657\pi$
$941$	−26.9315			−0.877941			−0.438971	+	0.898501i	$0.644657\pi$
$942$	−2.68969	−	4.52455i	−0.0876348	−	0.147418i
$943$		−	20.2313i		−	0.658821i
$944$	24.8964	+	26.7438i	0.810308	+	0.870437i
$945$	6.05058	+	22.6177i	0.196825	+	0.735754i
$946$	−0.428913	+	0.629655i	−0.0139452	+	0.0204718i
$947$		−	6.09197i		−	0.197962i	−0.995089	−	0.0989812i	$-0.968442\pi$
$947$		−	6.09197i		−	0.197962i	0.995089	−	0.0989812i	$-0.0315584\pi$
$948$	−2.14754	+	34.7911i	−0.0697488	+	1.12996i
$949$			0.780091i			0.0253228i
$950$	−14.7117	−	10.0214i	−0.477310	−	0.325138i
$951$	17.5165	−	37.5511i	0.568013	−	1.21768i
$952$	0.971272	−	4.27968i	0.0314791	−	0.138705i
$953$			17.6541i			0.571874i	0.958248	+	0.285937i	$0.0923048\pi$
$953$			17.6541i			0.571874i	−0.958248	+	0.285937i	$0.907695\pi$
$954$	3.91566	+	39.0759i	0.126774	+	1.26513i
$955$	51.1171			1.65411
$956$	4.48302	+	11.3951i	0.144991	+	0.368543i
$957$	−2.57631	−	1.20178i	−0.0832803	−	0.0388479i
$958$	21.9346	+	14.9416i	0.708673	+	0.482740i
$959$	−16.7303			−0.540249
$960$	−44.8909	+	36.8986i	−1.44885	+	1.19090i
$961$	−19.9709			−0.644224
$962$	−1.75469	−	1.19528i	−0.0565736	−	0.0385373i
$963$	17.6796	−	14.8268i	0.569718	−	0.477788i
$964$	−5.78376	−	14.7013i	−0.186283	−	0.473498i
$965$	22.1715			0.713727
$966$	−5.97720	−	10.0547i	−0.192313	−	0.323506i
$967$		−	39.9115i		−	1.28347i	−0.766928	−	0.641733i	$-0.778216\pi$
$967$		−	39.9115i		−	1.28347i	0.766928	−	0.641733i	$-0.221784\pi$
$968$	6.74201	−	29.7070i	0.216696	−	0.954821i
$969$	−2.26673	−	1.05737i	−0.0728179	−	0.0339675i
$970$	−26.4407	−	18.0111i	−0.848960	−	0.578301i
$971$			32.7879i			1.05221i	0.850419	+	0.526106i	$0.176349\pi$
$971$			32.7879i			1.05221i	−0.850419	+	0.526106i	$0.823651\pi$
$972$	7.31151	−	30.3075i	0.234517	−	0.972112i
$973$		−	20.0162i		−	0.641689i
$974$	−5.22318	+	7.66776i	−0.167362	+	0.245691i
$975$	3.93503	+	1.83558i	0.126022	+	0.0587857i
$976$	39.0996	+	42.0010i	1.25155	+	1.34442i
$977$		−	6.37611i		−	0.203990i	−0.994785	−	0.101995i	$-0.967477\pi$
$977$		−	6.37611i		−	0.203990i	0.994785	−	0.101995i	$-0.0325225\pi$
$978$	38.1955	−	22.7059i	1.22136	−	0.726056i
$979$	−6.86066			−0.219268
$980$	−17.9497	−	45.6251i	−0.573383	−	1.45744i
$981$	29.8049	−	24.9956i	0.951597	−	0.798047i
$982$	32.7310	−	48.0499i	1.04449	−	1.53333i
$983$	22.8835			0.729871			0.364936	−	0.931033i	$-0.381091\pi$
$983$	22.8835			0.729871			0.364936	+	0.931033i	$0.381091\pi$
$984$	13.6661	−	17.6217i	0.435658	−	0.561760i
$985$	−22.4788			−0.716235
$986$	3.93583	−	5.77789i	0.125342	−	0.184006i
$987$	−4.34166	−	2.02526i	−0.138197	−	0.0644649i
$988$	0.370681	−	0.145832i	0.0117929	−	0.00463954i
$989$	−4.99384			−0.158795
$990$	8.48818	−	0.850570i	0.269772	−	0.0270329i
$991$		−	44.1229i		−	1.40161i	−0.713353	−	0.700805i	$-0.752824\pi$
$991$		−	44.1229i		−	1.40161i	0.713353	−	0.700805i	$-0.247176\pi$
$992$	−6.10114	−	39.9230i	−0.193711	−	1.26756i
$993$	3.97600	−	8.52356i	0.126175	−	0.270487i
$994$	−5.78964	+	8.49932i	−0.183636	+	0.269582i
$995$			37.9685i			1.20368i
$996$	−2.68535	+	43.5039i	−0.0850885	+	1.37847i
$997$			34.9656i			1.10737i	0.832726	+	0.553686i	$0.186779\pi$
$997$			34.9656i			1.10737i	−0.832726	+	0.553686i	$0.813221\pi$
$998$	1.84945	+	1.25982i	0.0585433	+	0.0398790i
$999$	10.1219	+	37.8367i	0.320242	+	1.19710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.j.e.419.3	✓	24
3.2	odd	2	inner	456.2.j.e.419.22	yes	24
4.3	odd	2		1824.2.j.d.1103.17		24
8.3	odd	2	inner	456.2.j.e.419.21	yes	24
8.5	even	2		1824.2.j.d.1103.18		24
12.11	even	2		1824.2.j.d.1103.20		24
24.5	odd	2		1824.2.j.d.1103.19		24
24.11	even	2	inner	456.2.j.e.419.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.j.e.419.3	✓	24	1.1	even	1	trivial
456.2.j.e.419.4	yes	24	24.11	even	2	inner
456.2.j.e.419.21	yes	24	8.3	odd	2	inner
456.2.j.e.419.22	yes	24	3.2	odd	2	inner
1824.2.j.d.1103.17		24	4.3	odd	2
1824.2.j.d.1103.18		24	8.5	even	2
1824.2.j.d.1103.19		24	24.5	odd	2
1824.2.j.d.1103.20		24	12.11	even	2

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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.j (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16880 - 0.796176i) q^{2} +(-0.732208 + 1.56967i) q^{3} +(0.732208 + 1.86115i) q^{4} -4.19368 q^{5} +(2.10554 - 1.25167i) q^{6} -1.07444i q^{7} +(0.625992 - 2.75828i) q^{8} +(-1.92774 - 2.29865i) q^{9} +O(q^{10})\)	\(q+(-1.16880 - 0.796176i) q^{2} +(-0.732208 + 1.56967i) q^{3} +(0.732208 + 1.86115i) q^{4} -4.19368 q^{5} +(2.10554 - 1.25167i) q^{6} -1.07444i q^{7} +(0.625992 - 2.75828i) q^{8} +(-1.92774 - 2.29865i) q^{9} +(4.90159 + 3.33891i) q^{10} +0.479460i q^{11} +(-3.45752 - 0.213421i) q^{12} -0.199168i q^{13} +(-0.855440 + 1.25581i) q^{14} +(3.07065 - 6.58270i) q^{15} +(-2.92774 + 2.72550i) q^{16} +1.44408i q^{17} +(0.423021 + 4.22150i) q^{18} +1.00000 q^{19} +(-3.07065 - 7.80506i) q^{20} +(1.68651 + 0.786711i) q^{21} +(0.381735 - 0.560395i) q^{22} +4.44453 q^{23} +(3.87125 + 3.00224i) q^{24} +12.5869 q^{25} +(-0.158573 + 0.232788i) q^{26} +(5.01964 - 1.34283i) q^{27} +(1.99969 - 0.786711i) q^{28} +3.42323 q^{29} +(-8.82997 + 5.24912i) q^{30} -7.13939i q^{31} +(5.59193 - 0.854574i) q^{32} +(-0.752595 - 0.351065i) q^{33} +(1.14974 - 1.68785i) q^{34} +4.50584i q^{35} +(2.86663 - 5.27091i) q^{36} +7.53773i q^{37} +(-1.16880 - 0.796176i) q^{38} +(0.312628 + 0.145832i) q^{39} +(-2.62521 + 11.5674i) q^{40} -4.55195i q^{41} +(-1.34484 - 2.26227i) q^{42} -1.12359 q^{43} +(-0.892346 + 0.351065i) q^{44} +(8.08433 + 9.63982i) q^{45} +(-5.19479 - 3.53863i) q^{46} -2.57434 q^{47} +(-2.13442 - 6.59123i) q^{48} +5.84559 q^{49} +(-14.7117 - 10.0214i) q^{50} +(-2.26673 - 1.05737i) q^{51} +(0.370681 - 0.145832i) q^{52} +9.25642 q^{53} +(-6.93611 - 2.42701i) q^{54} -2.01070i q^{55} +(-2.96360 - 0.672589i) q^{56} +(-0.732208 + 1.56967i) q^{57} +(-4.00109 - 2.72550i) q^{58} -9.13463i q^{59} +(14.4997 + 0.895018i) q^{60} -14.3459i q^{61} +(-5.68421 + 8.34455i) q^{62} +(-2.46976 + 2.07124i) q^{63} +(-7.21627 - 3.45333i) q^{64} +0.835246i q^{65} +(0.600128 + 1.00952i) q^{66} -15.4293 q^{67} +(-2.68765 + 1.05737i) q^{68} +(-3.25432 + 6.97646i) q^{69} +(3.58744 - 5.26645i) q^{70} +6.76802 q^{71} +(-7.54709 + 3.87832i) q^{72} -3.91675 q^{73} +(6.00136 - 8.81013i) q^{74} +(-9.21627 + 19.7574i) q^{75} +(0.732208 + 1.86115i) q^{76} +0.515150 q^{77} +(-0.249293 - 0.419356i) q^{78} -10.0625i q^{79} +(12.2780 - 11.4299i) q^{80} +(-1.56762 + 8.86242i) q^{81} +(-3.62415 + 5.32034i) q^{82} -12.5824i q^{83} +(-0.229307 + 3.71489i) q^{84} -6.05601i q^{85} +(1.31326 + 0.894576i) q^{86} +(-2.50652 + 5.37335i) q^{87} +(1.32249 + 0.300138i) q^{88} +14.3091i q^{89} +(-1.77402 - 17.7036i) q^{90} -0.213993 q^{91} +(3.25432 + 8.27193i) q^{92} +(11.2065 + 5.22752i) q^{93} +(3.00890 + 2.04963i) q^{94} -4.19368 q^{95} +(-2.75306 + 9.40323i) q^{96} -5.39431 q^{97} +(-6.83235 - 4.65411i) q^{98} +(1.10211 - 0.924276i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{3} - 6 q^{4} + q^{6} - 6 q^{9}+O(q^{10}) \) 24 * q + 6 * q^3 - 6 * q^4 + q^6 - 6 * q^9	\( 24 q + 6 q^{3} - 6 q^{4} + q^{6} - 6 q^{9} + 4 q^{10} - 33 q^{12} - 30 q^{16} - 19 q^{18} + 24 q^{19} - 28 q^{22} + 21 q^{24} + 96 q^{25} + 34 q^{28} + 8 q^{30} + 24 q^{33} + 58 q^{34} - 9 q^{36} - 24 q^{40} - 31 q^{42} + 16 q^{43} - 6 q^{46} + 3 q^{48} - 36 q^{49} + 38 q^{51} - 6 q^{52} - 8 q^{54} + 6 q^{57} - 42 q^{58} - 50 q^{60} + 18 q^{64} + 10 q^{66} + 20 q^{67} - 96 q^{70} - 33 q^{72} - 12 q^{73} - 30 q^{75} - 6 q^{76} - 17 q^{78} + 34 q^{81} + 68 q^{82} - 29 q^{84} - 76 q^{88} - 70 q^{90} - 36 q^{91} - 12 q^{94} + 29 q^{96} - 104 q^{97} + 56 q^{99}+O(q^{100}) \) 24 * q + 6 * q^3 - 6 * q^4 + q^6 - 6 * q^9 + 4 * q^10 - 33 * q^12 - 30 * q^16 - 19 * q^18 + 24 * q^19 - 28 * q^22 + 21 * q^24 + 96 * q^25 + 34 * q^28 + 8 * q^30 + 24 * q^33 + 58 * q^34 - 9 * q^36 - 24 * q^40 - 31 * q^42 + 16 * q^43 - 6 * q^46 + 3 * q^48 - 36 * q^49 + 38 * q^51 - 6 * q^52 - 8 * q^54 + 6 * q^57 - 42 * q^58 - 50 * q^60 + 18 * q^64 + 10 * q^66 + 20 * q^67 - 96 * q^70 - 33 * q^72 - 12 * q^73 - 30 * q^75 - 6 * q^76 - 17 * q^78 + 34 * q^81 + 68 * q^82 - 29 * q^84 - 76 * q^88 - 70 * q^90 - 36 * q^91 - 12 * q^94 + 29 * q^96 - 104 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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