LMFDB - Embedded newform 675.2.ba.b.668.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [192] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 135)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			668.3
Character	$\chi$	$=$	675.668
Dual form			675.2.ba.b.482.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.81626 - 0.846935i) q^{2} +(0.00445475 - 1.73205i) q^{3} +(1.29592 + 1.54442i) q^{4} +(-1.47502 + 3.14207i) q^{6} +(2.21198 - 0.193523i) q^{7} +(-0.00834683 - 0.0311508i) q^{8} +(-2.99996 - 0.0154316i) q^{9} +(1.09616 + 0.193283i) q^{11} +(2.68077 - 2.23771i) q^{12} +(1.28211 + 2.74949i) q^{13} +(-4.18143 - 1.52192i) q^{14} +(0.688959 - 3.90728i) q^{16} +(1.56207 - 5.82972i) q^{17} +(5.43563 + 2.56880i) q^{18} +(3.84801 + 2.22165i) q^{19} +(-0.325337 - 3.83212i) q^{21} +(-1.82722 - 1.27943i) q^{22} +(0.293046 - 3.34953i) q^{23} +(-0.0539918 + 0.0143183i) q^{24} -6.07964i q^{26} +(-0.0400924 + 5.19600i) q^{27} +(3.16543 + 3.16543i) q^{28} +(-1.74671 + 0.635749i) q^{29} +(7.13252 - 5.98490i) q^{31} +(-4.59753 + 6.56596i) q^{32} +(0.339658 - 1.89774i) q^{33} +(-7.77451 + 9.26530i) q^{34} +(-3.86387 - 4.65319i) q^{36} +(4.53439 + 1.21499i) q^{37} +(-5.10738 - 7.29410i) q^{38} +(4.76795 - 2.20842i) q^{39} +(-1.07377 + 2.95017i) q^{41} +(-2.65466 + 7.23565i) q^{42} +(5.86507 - 4.10676i) q^{43} +(1.12203 + 1.94341i) q^{44} +(-3.36908 + 5.83541i) q^{46} +(-1.10183 - 12.5940i) q^{47} +(-6.76452 - 1.21071i) q^{48} +(-2.03824 + 0.359397i) q^{49} +(-10.0904 - 2.73154i) q^{51} +(-2.58485 + 5.54322i) q^{52} +(-6.34457 + 6.34457i) q^{53} +(4.47349 - 9.40332i) q^{54} +(-0.0244914 - 0.0672897i) q^{56} +(3.86514 - 6.65503i) q^{57} +(3.71091 + 0.324662i) q^{58} +(0.242616 + 1.37594i) q^{59} +(-2.30056 - 1.93040i) q^{61} +(-18.0233 + 4.82933i) q^{62} +(-6.63885 + 0.546428i) q^{63} +(7.03924 - 4.06411i) q^{64} +(-2.22417 + 3.15912i) q^{66} +(-8.07622 + 3.76600i) q^{67} +(11.0278 - 5.14236i) q^{68} +(-5.80023 - 0.522490i) q^{69} +(-6.78702 + 3.91849i) q^{71} +(0.0245595 + 0.0935799i) q^{72} +(0.167045 - 0.0447595i) q^{73} +(-7.20661 - 6.04707i) q^{74} +(1.55556 + 8.82200i) q^{76} +(2.46210 + 0.215406i) q^{77} +(-10.5302 - 0.0270832i) q^{78} +(-0.697324 - 1.91588i) q^{79} +(8.99952 + 0.0925886i) q^{81} +(4.44885 - 4.44885i) q^{82} +(2.27031 - 4.86870i) q^{83} +(5.49677 - 5.46857i) q^{84} +(-14.1306 + 2.49161i) q^{86} +(1.09336 + 3.02821i) q^{87} +(-0.00312857 - 0.0357597i) q^{88} +(6.70700 - 11.6169i) q^{89} +(3.36809 + 5.83370i) q^{91} +(5.55283 - 3.88813i) q^{92} +(-10.3343 - 12.3805i) q^{93} +(-8.66507 + 23.8071i) q^{94} +(11.3521 + 7.99239i) q^{96} +(-9.92914 - 14.1803i) q^{97} +(4.00635 + 1.07350i) q^{98} +(-3.28547 - 0.596758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) $ 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.81626	−	0.846935i	−1.28429	−	0.598874i	−0.343910	−	0.939003i	$-0.611751\pi$
$2$	−1.81626	−	0.846935i	−1.28429	−	0.598874i	−0.940379	+	0.340129i	$0.889529\pi$
$3$	0.00445475	−	1.73205i	0.00257195	−	0.999997i
$3$	0.00445475	−	1.73205i	0.00257195	−	0.999997i
$4$	1.29592	+	1.54442i	0.647960	+	0.772208i
$5$		0			0
$5$		0			0
$6$	−1.47502	+	3.14207i	−0.602175	+	1.28274i
$7$	2.21198	−	0.193523i	0.836051	−	0.0731450i	0.338914	−	0.940817i	$-0.389940\pi$
$7$	2.21198	−	0.193523i	0.836051	−	0.0731450i	0.497137	+	0.867672i	$0.334385\pi$
$8$	−0.00834683	−	0.0311508i	−0.00295105	−	0.0110135i
$9$	−2.99996	−	0.0154316i	−0.999987	−	0.00514388i
$10$		0			0
$11$	1.09616	+	0.193283i	0.330506	+	0.0582771i	0.336439	−	0.941705i	$-0.390777\pi$
$11$	1.09616	+	0.193283i	0.330506	+	0.0582771i	−0.00593305	+	0.999982i	$0.501889\pi$
$12$	2.68077	−	2.23771i	0.773872	−	0.645971i
$13$	1.28211	+	2.74949i	0.355592	+	0.762570i	0.999998	−	0.00211367i	$-0.000672802\pi$
$13$	1.28211	+	2.74949i	0.355592	+	0.762570i	−0.644405	+	0.764684i	$0.722895\pi$
$14$	−4.18143	−	1.52192i	−1.11753	−	0.406749i
$15$		0			0
$16$	0.688959	−	3.90728i	0.172240	−	0.976820i
$17$	1.56207	−	5.82972i	0.378857	−	1.41391i	−0.468769	−	0.883321i	$-0.655302\pi$
$17$	1.56207	−	5.82972i	0.378857	−	1.41391i	0.847626	−	0.530594i	$-0.178031\pi$
$18$	5.43563	+	2.56880i	1.28119	+	0.605472i
$19$	3.84801	+	2.22165i	0.882794	+	0.509681i	0.871578	−	0.490256i	$-0.163097\pi$
$19$	3.84801	+	2.22165i	0.882794	+	0.509681i	0.0112151	+	0.999937i	$0.496430\pi$
$20$		0			0
$21$	−0.325337	−	3.83212i	−0.0709944	−	0.836236i
$22$	−1.82722	−	1.27943i	−0.389564	−	0.272776i
$23$	0.293046	−	3.34953i	0.0611042	−	0.698425i	−0.902429	−	0.430838i	$-0.858218\pi$
$23$	0.293046	−	3.34953i	0.0611042	−	0.698425i	0.963534	−	0.267587i	$-0.0862263\pi$
$24$	−0.0539918	+	0.0143183i	−0.0110210	+	0.00292271i
$25$		0			0
$26$		−	6.07964i		−	1.19232i
$27$	−0.0400924	+	5.19600i	−0.00771578	+	0.999970i
$28$	3.16543	+	3.16543i	0.598210	+	0.598210i
$29$	−1.74671	+	0.635749i	−0.324355	+	0.118056i	−0.499066	−	0.866564i	$-0.666323\pi$
$29$	−1.74671	+	0.635749i	−0.324355	+	0.118056i	0.174710	+	0.984620i	$0.444101\pi$
$30$		0			0
$31$	7.13252	−	5.98490i	1.28104	−	1.07492i	0.287939	−	0.957649i	$-0.407030\pi$
$31$	7.13252	−	5.98490i	1.28104	−	1.07492i	0.993100	−	0.117270i	$-0.0374144\pi$
$32$	−4.59753	+	6.56596i	−0.812737	+	1.16071i
$33$	0.339658	−	1.89774i	0.0591269	−	0.330355i
$34$	−7.77451	+	9.26530i	−1.33332	+	1.58899i
$35$		0			0
$36$	−3.86387	−	4.65319i	−0.643979	−	0.775531i
$37$	4.53439	+	1.21499i	0.745450	+	0.199743i	0.611499	−	0.791245i	$-0.290567\pi$
$37$	4.53439	+	1.21499i	0.745450	+	0.199743i	0.133951	+	0.990988i	$0.457234\pi$
$38$	−5.10738	−	7.29410i	−0.828527	−	1.18326i
$39$	4.76795	−	2.20842i	0.763482	−	0.353630i
$40$		0			0
$41$	−1.07377	+	2.95017i	−0.167695	+	0.460739i	−0.994865	−	0.101214i	$-0.967727\pi$
$41$	−1.07377	+	2.95017i	−0.167695	+	0.460739i	0.827169	+	0.561953i	$0.189950\pi$
$42$	−2.65466	+	7.23565i	−0.409622	+	1.11649i
$43$	5.86507	−	4.10676i	0.894414	−	0.626276i	−0.0333495	−	0.999444i	$-0.510617\pi$
$43$	5.86507	−	4.10676i	0.894414	−	0.626276i	0.927764	+	0.373168i	$0.121729\pi$
$44$	1.12203	+	1.94341i	0.169152	+	0.292981i
$45$		0			0
$46$	−3.36908	+	5.83541i	−0.496743	+	0.860385i
$47$	−1.10183	−	12.5940i	−0.160718	−	1.83702i	−0.466031	−	0.884768i	$-0.654317\pi$
$47$	−1.10183	−	12.5940i	−0.160718	−	1.83702i	0.305313	−	0.952252i	$-0.401239\pi$
$48$	−6.76452	−	1.21071i	−0.976374	−	0.174751i
$49$	−2.03824	+	0.359397i	−0.291177	+	0.0513424i
$50$		0			0
$51$	−10.0904	−	2.73154i	−1.41294	−	0.382492i
$52$	−2.58485	+	5.54322i	−0.358454	+	0.768706i
$53$	−6.34457	+	6.34457i	−0.871494	+	0.871494i	−0.992635	−	0.121142i	$-0.961344\pi$
$53$	−6.34457	+	6.34457i	−0.871494	+	0.871494i	0.121142	+	0.992635i	$0.461344\pi$
$54$	4.47349	−	9.40332i	0.608765	−	1.27963i
$55$		0			0
$56$	−0.0244914	−	0.0672897i	−0.00327281	−	0.00899196i
$57$	3.86514	−	6.65503i	0.511950	−	0.881480i
$58$	3.71091	+	0.324662i	0.487266	+	0.0426303i
$59$	0.242616	+	1.37594i	0.0315859	+	0.179132i	0.996519	−	0.0833623i	$-0.0265659\pi$
$59$	0.242616	+	1.37594i	0.0315859	+	0.179132i	−0.964933	+	0.262495i	$0.915455\pi$
$60$		0			0
$61$	−2.30056	−	1.93040i	−0.294557	−	0.247163i	0.483517	−	0.875335i	$-0.339359\pi$
$61$	−2.30056	−	1.93040i	−0.294557	−	0.247163i	−0.778075	+	0.628172i	$0.783803\pi$
$62$	−18.0233	+	4.82933i	−2.28896	+	0.613326i
$63$	−6.63885	+	0.546428i	−0.836416	+	0.0688435i
$64$	7.03924	−	4.06411i	0.879905	−	0.508014i
$65$		0			0
$66$	−2.22417	+	3.15912i	−0.273777	+	0.388861i
$67$	−8.07622	+	3.76600i	−0.986667	+	0.460090i	−0.847855	−	0.530228i	$-0.822106\pi$
$67$	−8.07622	+	3.76600i	−0.986667	+	0.460090i	−0.138812	+	0.990319i	$0.544328\pi$
$68$	11.0278	−	5.14236i	1.33732	−	0.623603i
$69$	−5.80023	−	0.522490i	−0.698265	−	0.0629003i
$70$		0			0
$71$	−6.78702	+	3.91849i	−0.805471	+	0.465039i	−0.845380	−	0.534165i	$-0.820626\pi$
$71$	−6.78702	+	3.91849i	−0.805471	+	0.465039i	0.0399099	+	0.999203i	$0.487293\pi$
$72$	0.0245595	+	0.0935799i	0.00289436	+	0.0110285i
$73$	0.167045	−	0.0447595i	0.0195511	−	0.00523870i	−0.249030	−	0.968496i	$-0.580112\pi$
$73$	0.167045	−	0.0447595i	0.0195511	−	0.00523870i	0.268581	+	0.963257i	$0.413445\pi$
$74$	−7.20661	−	6.04707i	−0.837752	−	0.702957i
$75$		0			0
$76$	1.55556	+	8.82200i	0.178435	+	1.01195i
$77$	2.46210	+	0.215406i	0.280582	+	0.0245478i
$78$	−10.5302	−	0.0270832i	−1.19231	−	0.00306657i
$79$	−0.697324	−	1.91588i	−0.0784551	−	0.215554i	0.894264	−	0.447540i	$-0.147700\pi$
$79$	−0.697324	−	1.91588i	−0.0784551	−	0.215554i	−0.972719	+	0.231986i	$0.925478\pi$
$80$		0			0
$81$	8.99952	+	0.0925886i	0.999947	+	0.0102876i
$82$	4.44885	−	4.44885i	0.491293	−	0.491293i
$83$	2.27031	−	4.86870i	0.249199	−	0.534409i	−0.741423	−	0.671038i	$-0.765849\pi$
$83$	2.27031	−	4.86870i	0.249199	−	0.534409i	0.990622	+	0.136629i	$0.0436267\pi$
$84$	5.49677	−	5.46857i	0.599747	−	0.596670i
$85$		0			0
$86$	−14.1306	+	2.49161i	−1.52375	+	0.268677i
$87$	1.09336	+	3.02821i	0.117221	+	0.324658i
$88$	−0.00312857	−	0.0357597i	−0.000333506	−	0.00381199i
$89$	6.70700	−	11.6169i	0.710941	−	1.23139i	−0.253563	−	0.967319i	$-0.581603\pi$
$89$	6.70700	−	11.6169i	0.710941	−	1.23139i	0.964504	−	0.264067i	$-0.0850640\pi$
$90$		0			0
$91$	3.36809	+	5.83370i	0.353072	+	0.611538i
$92$	5.55283	−	3.88813i	0.578922	−	0.405366i
$93$	−10.3343	−	12.3805i	−1.07162	−	1.28380i
$94$	−8.66507	+	23.8071i	−0.893734	+	2.45551i
$95$		0			0
$96$	11.3521	+	7.99239i	1.15861	+	0.815720i
$97$	−9.92914	−	14.1803i	−1.00815	−	1.43979i	−0.894923	−	0.446221i	$-0.852769\pi$
$97$	−9.92914	−	14.1803i	−1.00815	−	1.43979i	−0.113229	−	0.993569i	$-0.536119\pi$
$98$	4.00635	+	1.07350i	0.404703	+	0.108440i
$99$	−3.28547	−	0.596758i	−0.330202	−	0.0599764i
$100$		0			0
$101$	4.92991	−	5.87523i	0.490544	−	0.584608i	−0.462812	−	0.886457i	$-0.653159\pi$
$101$	4.92991	−	5.87523i	0.490544	−	0.584608i	0.953356	+	0.301849i	$0.0976038\pi$
$102$	16.0133	+	13.5071i	1.58555	+	1.33740i
$103$	−6.03654	+	8.62107i	−0.594798	+	0.849460i	−0.997838	−	0.0657227i	$-0.979065\pi$
$103$	−6.03654	+	8.62107i	−0.594798	+	0.849460i	0.403040	+	0.915182i	$0.367954\pi$
$104$	0.0749472	−	0.0628881i	0.00734917	−	0.00616669i
$105$		0			0
$106$	16.8968	−	6.14994i	1.64116	−	0.597335i
$107$	4.95248	+	4.95248i	0.478774	+	0.478774i	0.904740	−	0.425965i	$-0.140065\pi$
$107$	4.95248	+	4.95248i	0.478774	+	0.478774i	−0.425965	+	0.904740i	$0.640065\pi$
$108$	−8.07674	+	6.67167i	−0.777185	+	0.641982i
$109$		−	9.40170i		−	0.900520i	−0.892898	−	0.450260i	$-0.851331\pi$
$109$		−	9.40170i		−	0.900520i	0.892898	−	0.450260i	$-0.148669\pi$
$110$		0			0
$111$	2.12461	−	7.84836i	0.201659	−	0.744934i
$112$	0.767815	−	8.77616i	0.0725517	−	0.829270i
$113$	1.10249	+	0.771969i	0.103713	+	0.0726207i	0.624283	−	0.781199i	$-0.285391\pi$
$113$	1.10249	+	0.771969i	0.103713	+	0.0726207i	−0.520569	+	0.853819i	$0.674280\pi$
$114$	−12.6565	+	8.81372i	−1.18539	+	0.825481i
$115$		0			0
$116$	−3.24545	−	1.87376i	−0.301333	−	0.173974i
$117$	−3.80384	−	8.26814i	−0.351665	−	0.764389i
$118$	0.724681	−	2.70455i	0.0667123	−	0.248974i
$119$	2.32708	−	13.1975i	0.213323	−	1.20982i
$120$		0			0
$121$	−9.17240	−	3.33848i	−0.833855	−	0.303498i
$122$	2.54349	+	5.45454i	0.230277	+	0.493831i
$123$	5.10504	+	1.87297i	0.460306	+	0.168880i
$124$	18.4863	+	3.25964i	1.66012	+	0.292724i
$125$		0			0
$126$	12.5206	+	4.63022i	1.11543	+	0.412493i
$127$	3.93996	+	14.7041i	0.349615	+	1.30478i	0.887127	+	0.461525i	$0.152697\pi$
$127$	3.93996	+	14.7041i	0.349615	+	1.30478i	−0.537513	+	0.843256i	$0.680636\pi$
$128$	−0.257007	+	0.0224852i	−0.0227165	+	0.00198743i
$129$	−7.08697	−	10.1769i	−0.623973	−	0.896022i
$130$		0			0
$131$	12.8204	+	15.2788i	1.12013	+	1.33491i	0.935995	+	0.352013i	$0.114503\pi$
$131$	12.8204	+	15.2788i	1.12013	+	1.33491i	0.184131	+	0.982902i	$0.441053\pi$
$132$	3.37108	−	1.93475i	0.293415	−	0.168398i
$133$	8.94167	+	4.16957i	0.775341	+	0.361547i
$134$	17.8581			1.54270
$135$		0			0
$136$	−0.194639			−0.0166901
$137$	14.7130	+	6.86076i	1.25701	+	0.586155i	0.932993	−	0.359896i	$-0.117188\pi$
$137$	14.7130	+	6.86076i	1.25701	+	0.586155i	0.324020	+	0.946050i	$0.394966\pi$
$138$	10.0922	+	5.86139i	0.859105	+	0.498955i
$139$	−1.79469	−	2.13883i	−0.152223	−	0.181413i	0.684544	−	0.728972i	$-0.260002\pi$
$139$	−1.79469	−	2.13883i	−0.152223	−	0.181413i	−0.836767	+	0.547559i	$0.815557\pi$
$140$		0			0
$141$	−21.8182	+	1.85232i	−1.83743	+	0.155993i
$142$	15.6457	−	1.36882i	1.31296	−	0.114869i
$143$	0.873969	+	3.26170i	0.0730850	+	0.272757i
$144$	−2.12715	+	11.7111i	−0.177262	+	0.975921i
$145$		0			0
$146$	−0.341305	−	0.0601812i	−0.0282466	−	0.00498063i
$147$	0.613411	+	3.53192i	0.0505933	+	0.291308i
$148$	3.99976	+	8.57752i	0.328778	+	0.705068i
$149$	18.9187	+	6.88585i	1.54988	+	0.564111i	0.968390	−	0.249441i	$-0.0802470\pi$
$149$	18.9187	+	6.88585i	1.54988	+	0.564111i	0.581492	+	0.813552i	$0.302469\pi$
$150$		0			0
$151$	0.0907569	−	0.514708i	0.00738569	−	0.0418864i	−0.980892	−	0.194552i	$-0.937675\pi$
$151$	0.0907569	−	0.514708i	0.00738569	−	0.0418864i	0.988278	+	0.152666i	$0.0487858\pi$
$152$	0.0370874	−	0.138412i	0.00300819	−	0.0112267i
$153$	−4.77611	+	17.4648i	−0.386125	+	1.41195i
$154$	−4.28937	−	2.47647i	−0.345648	−	0.199560i
$155$		0			0
$156$	9.58959	+	4.50176i	0.767782	+	0.360430i
$157$	−0.765462	−	0.535982i	−0.0610905	−	0.0427760i	0.542632	−	0.839970i	$-0.317428\pi$
$157$	−0.765462	−	0.535982i	−0.0610905	−	0.0427760i	−0.603723	+	0.797194i	$0.706317\pi$
$158$	−0.356107	+	4.07033i	−0.0283304	+	0.323818i
$159$	10.9608	+	11.0173i	0.869249	+	0.873732i
$160$		0			0
$161$		−	7.46581i		−	0.588388i
$162$	−16.2670	−	7.79018i	−1.27806	−	0.612054i
$163$	−4.24897	−	4.24897i	−0.332805	−	0.332805i	0.520846	−	0.853651i	$-0.325617\pi$
$163$	−4.24897	−	4.24897i	−0.332805	−	0.332805i	−0.853651	+	0.520846i	$0.825617\pi$
$164$	−5.94781	+	2.16483i	−0.464446	+	0.169045i
$165$		0			0
$166$	−8.24694	+	6.92001i	−0.640087	+	0.537097i
$167$	−4.66589	+	6.66358i	−0.361057	+	0.515643i	−0.958049	−	0.286604i	$-0.907474\pi$
$167$	−4.66589	+	6.66358i	−0.361057	+	0.515643i	0.596992	+	0.802247i	$0.296362\pi$
$168$	−0.116658	+	0.0421205i	−0.00900035	+	0.00324967i
$169$	2.44036	−	2.90831i	0.187720	−	0.223716i
$170$		0			0
$171$	−11.5096	−	6.72424i	−0.880160	−	0.514215i
$172$	13.9432	+	3.73607i	1.06316	+	0.284873i
$173$	−9.39399	−	13.4160i	−0.714212	−	1.02000i	−0.998129	−	0.0611509i	$-0.980523\pi$
$173$	−9.39399	−	13.4160i	−0.714212	−	1.02000i	0.283917	−	0.958849i	$-0.408366\pi$
$174$	0.578861	−	6.42601i	0.0438833	−	0.487155i
$175$		0			0
$176$	1.51042	−	4.14985i	0.113852	−	0.312807i
$177$	2.38427	−	0.414092i	0.179213	−	0.0311251i
$178$	−22.0204	+	15.4188i	−1.65050	+	1.15569i
$179$	0.436647	+	0.756295i	0.0326365	+	0.0565281i	0.881882	−	0.471470i	$-0.156276\pi$
$179$	0.436647	+	0.756295i	0.0326365	+	0.0565281i	−0.849246	+	0.527998i	$0.822943\pi$
$180$		0			0
$181$	−0.367901	+	0.637223i	−0.0273459	+	0.0473644i	−0.879374	−	0.476131i	$-0.842039\pi$
$181$	−0.367901	+	0.637223i	−0.0273459	+	0.0473644i	0.852029	+	0.523495i	$0.175372\pi$
$182$	−1.17655	−	13.4481i	−0.0872119	−	0.996836i
$183$	−3.35379	+	3.97608i	−0.247920	+	0.293920i
$184$	−0.106786	+	0.0188293i	−0.00787240	+	0.00138812i
$185$		0			0
$186$	8.28434	+	31.2387i	0.607437	+	2.29053i
$187$	2.83907	−	6.08840i	0.207613	−	0.445228i
$188$	18.0225	−	18.0225i	1.31442	−	1.31442i
$189$	0.916863	+	11.5012i	0.0666920	+	0.836590i
$190$		0			0
$191$	2.16218	+	5.94054i	0.156450	+	0.429842i	0.993010	−	0.118033i	$-0.0376589\pi$
$191$	2.16218	+	5.94054i	0.156450	+	0.429842i	−0.836560	+	0.547876i	$0.815437\pi$
$192$	−7.00786	−	12.2104i	−0.505749	−	0.881209i
$193$	26.3618	+	2.30636i	1.89756	+	0.166015i	0.975349	−	0.220667i	$-0.0708235\pi$
$193$	26.3618	+	2.30636i	1.89756	+	0.166015i	0.922213	+	0.386683i	$0.126379\pi$
$194$	6.02411	+	34.1644i	0.432506	+	2.45286i
$195$		0			0
$196$	−3.19645	−	2.68214i	−0.228318	−	0.191582i
$197$	0.424090	−	0.113635i	0.0302152	−	0.00809613i	−0.243680	−	0.969856i	$-0.578355\pi$
$197$	0.424090	−	0.113635i	0.0302152	−	0.00809613i	0.273895	+	0.961760i	$0.411688\pi$
$198$	5.46184	+	3.86644i	0.388156	+	0.274776i
$199$	−2.06085	+	1.18983i	−0.146090	+	0.0843452i	−0.571263	−	0.820767i	$-0.693546\pi$
$199$	−2.06085	+	1.18983i	−0.146090	+	0.0843452i	0.425173	+	0.905112i	$0.360213\pi$
$200$		0			0
$201$	6.48691	+	14.0051i	0.457551	+	0.987847i
$202$	−13.9299	+	6.49563i	−0.980106	+	0.457031i
$203$	−3.74065	+	1.74429i	−0.262542	+	0.122425i
$204$	−8.85767	−	19.1236i	−0.620161	−	1.33892i
$205$		0			0
$206$	18.2654	−	10.5455i	1.27261	−	0.734742i
$207$	−0.930814	+	10.0439i	−0.0646960	+	0.698101i
$208$	11.6263	−	3.11527i	0.806141	−	0.216005i
$209$	3.78864	+	3.17905i	0.262066	+	0.219899i
$210$		0			0
$211$	1.83079	+	10.3830i	0.126037	+	0.714792i	0.980686	+	0.195586i	$0.0626610\pi$
$211$	1.83079	+	10.3830i	0.126037	+	0.714792i	−0.854649	+	0.519206i	$0.826228\pi$
$212$	−18.0207	−	1.57661i	−1.23767	−	0.108282i
$213$	6.75676	+	11.7729i	0.462966	+	0.806664i
$214$	−4.80055	−	13.1894i	−0.328159	−	0.901610i
$215$		0			0
$216$	0.162194	−	0.0421212i	0.0110359	−	0.00286598i
$217$	14.6188	−	14.6188i	0.992389	−	0.992389i
$218$	−7.96263	+	17.0759i	−0.539297	+	1.15653i
$219$	−0.0767813	−	0.289528i	−0.00518840	−	0.0195645i
$220$		0			0
$221$	18.0315	−	3.17944i	1.21293	−	0.213872i
$222$	−10.5059	+	12.4552i	−0.705110	+	0.835941i
$223$	−0.713099	−	8.15076i	−0.0477527	−	0.545815i	−0.981960	−	0.189086i	$-0.939447\pi$
$223$	−0.713099	−	8.15076i	−0.0477527	−	0.545815i	0.934208	−	0.356729i	$-0.116108\pi$
$224$	−8.89900	+	15.4135i	−0.594589	+	1.02986i
$225$		0			0
$226$	−1.34859	−	2.33583i	−0.0897069	−	0.155377i
$227$	3.90472	−	2.73411i	0.259165	−	0.181469i	−0.436772	−	0.899572i	$-0.643878\pi$
$227$	3.90472	−	2.73411i	0.259165	−	0.181469i	0.695937	+	0.718103i	$0.254989\pi$
$228$	15.2870	−	2.65500i	1.01241	−	0.175831i
$229$	2.44592	−	6.72010i	0.161631	−	0.444077i	−0.832268	−	0.554374i	$-0.812958\pi$
$229$	2.44592	−	6.72010i	0.161631	−	0.444077i	0.993899	+	0.110297i	$0.0351801\pi$
$230$		0			0
$231$	0.384061	−	4.26351i	0.0252693	−	0.280518i
$232$	0.0343835	+	0.0491048i	0.00225739	+	0.00322389i
$233$	−8.72938	−	2.33903i	−0.571881	−	0.153235i	−0.0387217	−	0.999250i	$-0.512329\pi$
$233$	−8.72938	−	2.33903i	−0.571881	−	0.153235i	−0.533159	+	0.846015i	$0.678995\pi$
$234$	−0.0938188	+	18.2387i	−0.00613313	+	1.19230i
$235$		0			0
$236$	−1.81062	+	2.15781i	−0.117861	+	0.140461i
$237$	−3.32150	+	1.19926i	−0.215755	+	0.0779004i
$238$	−15.4040	+	21.9992i	−0.998495	+	1.42600i
$239$	−3.14736	+	2.64095i	−0.203586	+	0.170829i	−0.738880	−	0.673837i	$-0.764645\pi$
$239$	−3.14736	+	2.64095i	−0.203586	+	0.170829i	0.535295	+	0.844665i	$0.320201\pi$
$240$		0			0
$241$	5.80277	−	2.11203i	0.373789	−	0.136048i	−0.148293	−	0.988944i	$-0.547378\pi$
$241$	5.80277	−	2.11203i	0.373789	−	0.136048i	0.522082	+	0.852895i	$0.325156\pi$
$242$	13.8320	+	13.8320i	0.889153	+	0.889153i
$243$	0.200458	−	15.5872i	0.0128594	−	0.999917i
$244$		−	6.05468i		−	0.387611i
$245$		0			0
$246$	−7.68579	−	7.72543i	−0.490028	−	0.492555i
$247$	−1.17484	+	13.4284i	−0.0747530	+	0.854431i
$248$	−0.245968	−	0.172229i	−0.0156190	−	0.0109365i
$249$	−8.42269	−	3.95397i	−0.533766	−	0.250573i
$250$		0			0
$251$	−15.6657	−	9.04459i	−0.988810	−	0.570890i	−0.0838914	−	0.996475i	$-0.526735\pi$
$251$	−15.6657	−	9.04459i	−0.988810	−	0.570890i	−0.904918	+	0.425585i	$0.860068\pi$
$252$	−9.44732	−	9.54502i	−0.595125	−	0.601279i
$253$	0.968633	−	3.61499i	0.0608975	−	0.227272i
$254$	5.29746	−	30.0434i	0.332392	−	1.88509i
$255$		0			0
$256$	−14.7902	−	5.38320i	−0.924389	−	0.336450i
$257$	4.90513	+	10.5191i	0.305974	+	0.656163i	0.997828	−	0.0658743i	$-0.0209837\pi$
$257$	4.90513	+	10.5191i	0.305974	+	0.656163i	−0.691854	+	0.722037i	$0.743206\pi$
$258$	4.25264	+	24.4860i	0.264758	+	1.52443i
$259$	10.2651	+	1.81002i	0.637844	+	0.112469i
$260$		0			0
$261$	5.24986	−	1.88027i	0.324958	−	0.116386i
$262$	−10.3451	−	38.6083i	−0.639120	−	2.38523i
$263$	2.21755	−	0.194010i	0.136740	−	0.0119632i	−0.0185804	−	0.999827i	$-0.505915\pi$
$263$	2.21755	−	0.194010i	0.136740	−	0.0119632i	0.155320	+	0.987864i	$0.450359\pi$
$264$	−0.0619513	+	0.00525952i	−0.00381284	+	0.000323701i
$265$		0			0
$266$	−12.7090	−	15.1460i	−0.779240	−	0.928662i
$267$	−20.0911	−	11.6686i	−1.22955	−	0.714106i
$268$	−16.2824	−	7.59261i	−0.994606	−	0.463792i
$269$	−2.60637			−0.158913			−0.0794565	−	0.996838i	$-0.525318\pi$
$269$	−2.60637			−0.158913			−0.0794565	+	0.996838i	$0.525318\pi$
$270$		0			0
$271$	−22.2817			−1.35352			−0.676759	−	0.736205i	$-0.736616\pi$
$271$	−22.2817			−1.35352			−0.676759	+	0.736205i	$0.736616\pi$
$272$	−21.7021	−	10.1199i	−1.31589	−	0.613608i
$273$	10.1192	−	5.80769i	0.612444	−	0.351497i
$274$	−20.9119	−	24.9218i	−1.26333	−	1.50558i
$275$		0			0
$276$	−6.70968	−	9.63507i	−0.403875	−	0.579963i
$277$	8.27992	−	0.724399i	0.497492	−	0.0435249i	0.164351	−	0.986402i	$-0.447447\pi$
$277$	8.27992	−	0.724399i	0.497492	−	0.0435249i	0.333141	+	0.942877i	$0.391891\pi$
$278$	1.44817	+	5.40464i	0.0868555	+	0.324149i
$279$	−21.4896	+	17.8444i	−1.28655	+	1.06832i
$280$		0			0
$281$	−6.04432	−	1.06578i	−0.360574	−	0.0635790i	−0.00957353	−	0.999954i	$-0.503047\pi$
$281$	−6.04432	−	1.06578i	−0.360574	−	0.0635790i	−0.351001	+	0.936375i	$0.614159\pi$
$282$	41.1964	+	15.1144i	2.45321	+	0.900047i
$283$	−12.9205	−	27.7081i	−0.768044	−	1.64708i	−0.762413	−	0.647091i	$-0.775985\pi$
$283$	−12.9205	−	27.7081i	−0.768044	−	1.64708i	−0.00563108	−	0.999984i	$-0.501792\pi$
$284$	−14.8472	−	5.40394i	−0.881019	−	0.320665i
$285$		0			0
$286$	1.17509	−	6.66428i	0.0694847	−	0.394067i
$287$	−1.80424	+	6.73352i	−0.106501	+	0.397467i
$288$	13.8937	−	19.6267i	0.818697	−	1.15651i
$289$	−16.8231	−	9.71284i	−0.989596	−	0.571343i
$290$		0			0
$291$	−24.6051	+	17.1346i	−1.44238	+	1.00445i
$292$	0.285604	+	0.199982i	0.0167137	+	0.0117031i
$293$	−0.657015	+	7.50972i	−0.0383833	+	0.438723i	0.952551	+	0.304378i	$0.0984485\pi$
$293$	−0.657015	+	7.50972i	−0.0383833	+	0.438723i	−0.990935	+	0.134345i	$0.957107\pi$
$294$	1.87720	−	6.93440i	0.109480	−	0.404423i
$295$		0			0
$296$		−	0.151391i		−	0.00879944i
$297$	−1.04825	+	5.68792i	−0.0608255	+	0.330046i
$298$	−28.5294	−	28.5294i	−1.65266	−	1.65266i
$299$	9.58520	−	3.48873i	0.554326	−	0.201758i
$300$		0			0
$301$	12.1787	−	10.2191i	0.701967	−	0.589020i
$302$	−0.600762	+	0.857978i	−0.0345700	+	0.0493711i
$303$	−10.1542	−	8.56499i	−0.583344	−	0.492046i
$304$	11.3317	−	13.5046i	0.649919	−	0.774543i
$305$		0			0
$306$	23.4662	−	27.6756i	1.34147	−	1.58211i
$307$	12.7384	+	3.41325i	0.727021	+	0.194805i	0.603302	−	0.797513i	$-0.293851\pi$
$307$	12.7384	+	3.41325i	0.727021	+	0.194805i	0.123719	+	0.992317i	$0.460518\pi$
$308$	2.85801	+	4.08166i	0.162850	+	0.232574i
$309$	14.9052	+	10.4940i	0.847927	+	0.596981i
$310$		0			0
$311$	−0.0958399	+	0.263318i	−0.00543458	+	0.0149314i	−0.942380	−	0.334544i	$-0.891418\pi$
$311$	−0.0958399	+	0.263318i	−0.00543458	+	0.0149314i	0.936946	+	0.349475i	$0.113640\pi$
$312$	−0.108591	−	0.130092i	−0.00614777	−	0.00736501i
$313$	7.80530	−	5.46533i	0.441182	−	0.308919i	−0.331797	−	0.943351i	$-0.607655\pi$
$313$	7.80530	−	5.46533i	0.441182	−	0.308919i	0.772979	+	0.634432i	$0.218766\pi$
$314$	0.936334	+	1.62178i	0.0528404	+	0.0915223i
$315$		0			0
$316$	2.05524	−	3.55979i	0.115617	−	0.200254i
$317$	0.318142	+	3.63638i	0.0178686	+	0.204239i	0.999881	+	0.0154231i	$0.00490952\pi$
$317$	0.318142	+	3.63638i	0.0178686	+	0.204239i	−0.982012	+	0.188816i	$0.939535\pi$
$318$	−10.5767	−	29.2934i	−0.593112	−	1.64269i
$319$	−2.03756	+	0.359276i	−0.114081	+	0.0201156i
$320$		0			0
$321$	8.59998	−	8.55586i	0.480004	−	0.477542i
$322$	−6.32305	+	13.5598i	−0.352370	+	0.755660i
$323$	18.9624	−	18.9624i	1.05510	−	1.05510i
$324$	11.5197	+	14.0190i	0.639981	+	0.778833i
$325$		0			0
$326$	4.11862	+	11.3158i	0.228109	+	0.626725i
$327$	−16.2842	−	0.0418822i	−0.900517	−	0.00231609i
$328$	0.100863	+	0.00882434i	0.00556921	+	0.000487243i
$329$	−4.87446	−	27.6444i	−0.268738	−	1.52409i
$330$		0			0
$331$	−6.76703	−	5.67821i	−0.371950	−	0.312103i	0.437583	−	0.899178i	$-0.355835\pi$
$331$	−6.76703	−	5.67821i	−0.371950	−	0.312103i	−0.809532	+	0.587075i	$0.800279\pi$
$332$	10.4614	−	2.80313i	0.574146	−	0.153842i
$333$	−13.5843	−	3.71489i	−0.744412	−	0.203575i
$334$	14.1181	−	8.15107i	0.772506	−	0.446007i
$335$		0			0
$336$	−15.1973	−	1.36899i	−0.829080	−	0.0746843i
$337$	−21.7951	+	10.1632i	−1.18726	+	0.553627i	−0.912972	−	0.408022i	$-0.866219\pi$
$337$	−21.7951	+	10.1632i	−1.18726	+	0.553627i	−0.274284	+	0.961649i	$0.588441\pi$
$338$	−6.89547	+	3.21541i	−0.375064	+	0.174895i
$339$	1.34200	−	1.90612i	0.0728872	−	0.103526i
$340$		0			0
$341$	8.97519	−	5.18183i	0.486034	−	0.280612i
$342$	15.2094	+	21.9608i	0.822429	+	1.18751i
$343$	−19.4524	+	5.21226i	−1.05033	+	0.281435i
$344$	−0.176884	−	0.148423i	−0.00953693	−	0.00800243i
$345$		0			0
$346$	5.69942	+	32.3230i	0.306403	+	1.73770i
$347$	16.7440	+	1.46491i	0.898867	+	0.0786406i	0.527215	−	0.849732i	$-0.323236\pi$
$347$	16.7440	+	1.46491i	0.898867	+	0.0786406i	0.371651	+	0.928372i	$0.378792\pi$
$348$	−3.25990	+	5.61292i	−0.174749	+	0.300884i
$349$	11.7112	+	32.1764i	0.626888	+	1.72236i	0.689463	+	0.724321i	$0.257846\pi$
$349$	11.7112	+	32.1764i	0.626888	+	1.72236i	−0.0625752	+	0.998040i	$0.519931\pi$
$350$		0			0
$351$	−14.3377	+	6.55159i	−0.765291	+	0.349698i
$352$	−6.30874	+	6.30874i	−0.336257	+	0.336257i
$353$	−9.55751	+	20.4961i	−0.508695	+	1.09090i	0.469447	+	0.882961i	$0.344453\pi$
$353$	−9.55751	+	20.4961i	−0.508695	+	1.09090i	−0.978142	+	0.207939i	$0.933324\pi$
$354$	−4.68117	−	1.26723i	−0.248801	−	0.0673524i
$355$		0			0
$356$	26.6330	−	4.69612i	1.41155	−	0.248894i
$357$	−22.8484	−	4.08940i	−1.20926	−	0.216434i
$358$	−0.152531	−	1.74344i	−0.00806152	−	0.0921436i
$359$	−15.4051	+	26.6824i	−0.813050	+	1.40824i	0.0976695	+	0.995219i	$0.468861\pi$
$359$	−15.4051	+	26.6824i	−0.813050	+	1.40824i	−0.910720	+	0.413025i	$0.864472\pi$
$360$		0			0
$361$	0.371443	+	0.643357i	0.0195496	+	0.0338609i
$362$	1.20789	−	0.845774i	0.0634853	−	0.0444529i
$363$	−5.82326	+	15.8721i	−0.305642	+	0.833071i
$364$	−4.64489	+	12.7617i	−0.243458	+	0.668897i
$365$		0			0
$366$	9.45884	−	4.38115i	0.494421	−	0.229006i
$367$	8.33253	+	11.9001i	0.434955	+	0.621179i	0.975464	−	0.220158i	$-0.0706574\pi$
$367$	8.33253	+	11.9001i	0.434955	+	0.621179i	−0.540510	+	0.841338i	$0.681769\pi$
$368$	−12.8856	−	3.45270i	−0.671711	−	0.179984i
$369$	3.26680	−	8.83382i	0.170063	−	0.459870i
$370$		0			0
$371$	−12.8063	+	15.2619i	−0.664868	+	0.792358i
$372$	5.72820	−	32.0047i	0.296993	−	1.65936i
$373$	9.77090	−	13.9543i	0.505918	−	0.722526i	−0.482227	−	0.876046i	$-0.660172\pi$
$373$	9.77090	−	13.9543i	0.505918	−	0.722526i	0.988146	+	0.153520i	$0.0490610\pi$
$374$	−10.3130	+	8.65361i	−0.533271	+	0.447467i
$375$		0			0
$376$	−0.383116	+	0.139443i	−0.0197577	+	0.00719121i
$377$	−3.98745	−	3.98745i	−0.205364	−	0.205364i
$378$	8.07552	−	21.6657i	0.415360	−	1.11436i
$379$		−	1.06208i		−	0.0545552i	−0.999628	−	0.0272776i	$-0.991316\pi$
$379$		−	1.06208i		−	0.0545552i	0.999628	−	0.0272776i	$-0.00868381\pi$
$380$		0			0
$381$	25.4858	−	6.75868i	1.30568	−	0.346258i
$382$	1.10417	−	12.6208i	0.0564945	−	0.645735i
$383$	18.5741	+	13.0057i	0.949090	+	0.664560i	0.942070	−	0.335415i	$-0.108877\pi$
$383$	18.5741	+	13.0057i	0.949090	+	0.664560i	0.00701991	+	0.999975i	$0.497765\pi$
$384$	0.0378005	+	0.445248i	0.00192900	+	0.0227215i
$385$		0			0
$386$	−45.9265	−	26.5156i	−2.33759	−	1.34961i
$387$	−17.6583	+	12.2296i	−0.897624	+	0.621666i
$388$	9.03290	−	33.7112i	0.458576	−	1.71143i
$389$	−0.536388	+	3.04201i	−0.0271960	+	0.154236i	−0.995382	−	0.0959969i	$-0.969396\pi$
$389$	−0.536388	+	3.04201i	−0.0271960	+	0.154236i	0.968186	+	0.250233i	$0.0805072\pi$
$390$		0			0
$391$	−19.0690	−	6.94056i	−0.964363	−	0.350999i
$392$	0.0282083	+	0.0604930i	0.00142474	+	0.00305536i
$393$	26.5207	−	22.1375i	1.33779	−	1.11669i
$394$	−0.866498	−	0.152787i	−0.0436535	−	0.00769729i
$395$		0			0
$396$	−3.33606	−	5.84748i	−0.167643	−	0.293847i
$397$	3.92165	+	14.6358i	0.196822	+	0.734549i	0.991788	+	0.127895i	$0.0408220\pi$
$397$	3.92165	+	14.6358i	0.196822	+	0.734549i	−0.794966	+	0.606654i	$0.792511\pi$
$398$	4.75076	−	0.415637i	0.238134	−	0.0208340i
$399$	7.26171	−	15.4688i	0.363540	−	0.774408i
$400$		0			0
$401$	15.1491	+	18.0540i	0.756509	+	0.901573i	0.997622	−	0.0689246i	$-0.0219568\pi$
$401$	15.1491	+	18.0540i	0.756509	+	0.901573i	−0.241113	+	0.970497i	$0.577512\pi$
$402$	0.0795531	−	30.9310i	0.00396775	−	1.54270i
$403$	25.6001	+	11.9375i	1.27523	+	0.594649i
$404$	15.4626			0.769292
$405$		0			0
$406$	8.27129			0.410497
$407$	4.73560	+	2.20825i	0.234735	+	0.109459i
$408$	−0.000867066		0.337123i	−4.29261e−5		0.0166901i
$409$	−9.99118	−	11.9070i	−0.494032	−	0.588764i	0.460206	−	0.887812i	$-0.347775\pi$
$409$	−9.99118	−	11.9070i	−0.494032	−	0.588764i	−0.954238	+	0.299048i	$0.903331\pi$
$410$		0			0
$411$	11.9487	−	25.4529i	0.589386	−	1.25550i
$412$	−21.1374	+	1.84928i	−1.04136	+	0.0911076i
$413$	0.802939	+	2.99661i	0.0395100	+	0.147453i
$414$	10.1972	−	17.4540i	0.501163	−	0.857818i
$415$		0			0
$416$	−23.9476	−	4.22260i	−1.17413	−	0.207030i
$417$	−3.71254	+	3.09895i	−0.181804	+	0.151756i
$418$	−4.18870	−	8.98270i	−0.204876	−	0.439358i
$419$	7.24231	+	2.63599i	0.353810	+	0.128776i	0.512810	−	0.858502i	$-0.328605\pi$
$419$	7.24231	+	2.63599i	0.353810	+	0.128776i	−0.159000	+	0.987279i	$0.550827\pi$
$420$		0			0
$421$	−0.219552	+	1.24514i	−0.0107003	+	0.0606845i	−0.989690	−	0.143223i	$-0.954253\pi$
$421$	−0.219552	+	1.24514i	−0.0107003	+	0.0606845i	0.978990	+	0.203908i	$0.0653643\pi$
$422$	5.46849	−	20.4087i	0.266202	−	0.993479i
$423$	3.11110	+	37.7984i	0.151267	+	1.83782i
$424$	0.250595	+	0.144681i	0.0121700	+	0.00702635i
$425$		0			0
$426$	−2.30116	−	27.1051i	−0.111492	−	1.31325i
$427$	−5.46239	−	3.82480i	−0.264343	−	0.185095i
$428$	−1.23068	+	14.0667i	−0.0594871	+	0.679940i
$429$	5.65330	−	1.49922i	0.272944	−	0.0723832i
$430$		0			0
$431$			31.3833i			1.51168i	0.654755	+	0.755841i	$0.272772\pi$
$431$			31.3833i			1.51168i	−0.654755	+	0.755841i	$0.727228\pi$
$432$	20.2746	+	3.73648i	0.975462	+	0.179772i
$433$	24.8304	+	24.8304i	1.19327	+	1.19327i	0.976143	+	0.217127i	$0.0696687\pi$
$433$	24.8304	+	24.8304i	1.19327	+	1.19327i	0.217127	+	0.976143i	$0.430331\pi$
$434$	−38.9327	+	14.1703i	−1.86883	+	0.680198i
$435$		0			0
$436$	14.5201	−	12.1838i	0.695389	−	0.583500i
$437$	8.56911	−	12.2380i	0.409916	−	0.585421i
$438$	−0.105757	+	0.590887i	−0.00505326	+	0.0282337i
$439$	−13.0944	+	15.6053i	−0.624962	+	0.744800i	−0.981915	−	0.189322i	$-0.939371\pi$
$439$	−13.0944	+	15.6053i	−0.624962	+	0.744800i	0.356953	+	0.934122i	$0.383815\pi$
$440$		0			0
$441$	6.12018	−	1.04672i	0.291437	−	0.0498439i
$442$	−35.4426	−	9.49681i	−1.68583	−	0.451717i
$443$	−1.58059	−	2.25731i	−0.0750960	−	0.107248i	0.779847	−	0.625970i	$-0.215297\pi$
$443$	−1.58059	−	2.25731i	−0.0750960	−	0.107248i	−0.854943	+	0.518722i	$0.826408\pi$
$444$	14.8745	−	6.88956i	0.705911	−	0.326964i
$445$		0			0
$446$	−5.60799	+	15.4078i	−0.265546	+	0.729582i
$447$	12.0109	−	32.7374i	0.568095	−	1.54843i
$448$	14.7842	−	10.3520i	0.698487	−	0.489086i
$449$	−14.4725	−	25.0672i	−0.683001	−	1.18299i	−0.974060	−	0.226288i	$-0.927341\pi$
$449$	−14.4725	−	25.0672i	−0.683001	−	1.18299i	0.291059	−	0.956705i	$-0.405992\pi$
$450$		0			0
$451$	−1.74725	+	3.02633i	−0.0822748	+	0.142504i
$452$	0.236491	+	2.70311i	0.0111236	+	0.127143i
$453$	−0.891093	−	0.159488i	−0.0418672	−	0.00749340i
$454$	−9.40759	+	1.65881i	−0.441520	+	0.0778519i
$455$		0			0
$456$	−0.239571	−	0.0648537i	−0.0112189	−	0.00303705i
$457$	−10.0414	+	21.5339i	−0.469718	+	1.00731i	0.518616	+	0.855007i	$0.326447\pi$
$457$	−10.0414	+	21.5339i	−0.469718	+	1.00731i	−0.988333	+	0.152305i	$0.951330\pi$
$458$	−10.1339	+	10.1339i	−0.473527	+	0.473527i
$459$	30.2286	+	8.35023i	1.41095	+	0.389755i
$460$		0			0
$461$	−3.22783	−	8.86840i	−0.150335	−	0.413043i	0.841550	−	0.540179i	$-0.181644\pi$
$461$	−3.22783	−	8.86840i	−0.150335	−	0.413043i	−0.991885	+	0.127137i	$0.959421\pi$
$462$	−4.30847	+	7.41836i	−0.200448	+	0.345133i
$463$	−18.4116	−	1.61081i	−0.855659	−	0.0748605i	−0.349121	−	0.937078i	$-0.613520\pi$
$463$	−18.4116	−	1.61081i	−0.855659	−	0.0748605i	−0.506538	+	0.862217i	$0.669075\pi$
$464$	1.28064	+	7.26288i	0.0594523	+	0.337171i
$465$		0			0
$466$	13.8738	+	11.6415i	0.642691	+	0.539282i
$467$	12.3653	−	3.31326i	0.572196	−	0.153320i	0.0388925	−	0.999243i	$-0.487617\pi$
$467$	12.3653	−	3.31326i	0.572196	−	0.153320i	0.533304	+	0.845924i	$0.320950\pi$
$468$	7.83998	−	16.5896i	0.362403	−	0.766852i
$469$	−17.1356	+	9.89327i	−0.791250	+	0.456829i
$470$		0			0
$471$	−0.931755	+	1.32343i	−0.0429330	+	0.0609803i
$472$	0.0408366	−	0.0190424i	0.00187966	−	0.000876499i
$473$	7.22284	−	3.36807i	0.332107	−	0.154864i
$474$	7.04840	+	0.634926i	0.323744	+	0.0291631i
$475$		0			0
$476$	23.3982	−	13.5090i	1.07245	−	0.619182i
$477$	19.1314	−	18.9355i	0.875965	−	0.866999i
$478$	7.95312	−	2.13103i	0.363767	−	0.0974712i
$479$	−6.23949	−	5.23555i	−0.285090	−	0.239219i	0.489016	−	0.872275i	$-0.337356\pi$
$479$	−6.23949	−	5.23555i	−0.285090	−	0.239219i	−0.774106	+	0.633056i	$0.781800\pi$
$480$		0			0
$481$	2.47299	+	14.0250i	0.112758	+	0.639485i
$482$	−12.3281	−	1.07857i	−0.561529	−	0.0491274i
$483$	−12.9311	−	0.0332583i	−0.588386	−	0.00151330i
$484$	−6.73069	−	18.4924i	−0.305940	−	0.840564i
$485$		0			0
$486$	−13.5654	+	28.1405i	−0.615339	+	1.27648i
$487$	−11.3243	+	11.3243i	−0.513154	+	0.513154i	−0.915492	−	0.402337i	$-0.868198\pi$
$487$	−11.3243	+	11.3243i	−0.513154	+	0.513154i	0.402337	+	0.915492i	$0.368198\pi$
$488$	−0.0409312	+	0.0877772i	−0.00185287	+	0.00397349i
$489$	−7.37833	+	7.34047i	−0.333659	+	0.331948i
$490$		0			0
$491$	3.22425	−	0.568523i	0.145508	−	0.0256571i	−0.100419	−	0.994945i	$-0.532018\pi$
$491$	3.22425	−	0.568523i	0.145508	−	0.0256571i	0.245928	+	0.969288i	$0.420907\pi$
$492$	3.72308	+	10.3115i	0.167849	+	0.464879i
$493$	0.977764	+	11.1759i	0.0440363	+	0.503337i
$494$	13.5068	−	23.3945i	0.607701	−	1.05257i
$495$		0			0
$496$	−18.4707	−	31.9921i	−0.829357	−	1.43649i
$497$	−14.2544	+	9.98107i	−0.639399	+	0.447712i
$498$	11.9490	+	14.3149i	0.535449	+	0.641466i
$499$	−10.4633	+	28.7478i	−0.468404	+	1.28693i	0.450616	+	0.892718i	$0.351204\pi$
$499$	−10.4633	+	28.7478i	−0.468404	+	1.28693i	−0.919020	+	0.394211i	$0.871018\pi$
$500$		0			0
$501$	11.5208	+	8.11121i	0.514713	+	0.362382i
$502$	20.7928	+	29.6951i	0.928026	+	1.32536i
$503$	−12.3296	−	3.30370i	−0.549749	−	0.147305i	−0.0267563	−	0.999642i	$-0.508518\pi$
$503$	−12.3296	−	3.30370i	−0.549749	−	0.147305i	−0.522993	+	0.852337i	$0.675184\pi$
$504$	0.0724350	+	0.202244i	0.00322651	+	0.00900868i
$505$		0			0
$506$	−4.82095	+	5.74538i	−0.214317	+	0.255413i
$507$	−5.02645	−	4.23977i	−0.223232	−	0.188295i
$508$	−17.6034	+	25.1403i	−0.781026	+	1.11542i
$509$	−25.3418	+	21.2643i	−1.12326	+	0.942525i	−0.998764	−	0.0496958i	$-0.984175\pi$
$509$	−25.3418	+	21.2643i	−1.12326	+	0.942525i	−0.124493	+	0.992221i	$0.539730\pi$
$510$		0			0
$511$	0.360838	−	0.131334i	0.0159625	−	0.00580988i
$512$	22.6685	+	22.6685i	1.00181	+	1.00181i
$513$	−11.6980	+	19.9052i	−0.516477	+	0.878835i
$514$		−	23.2597i		−	1.02594i
$515$		0			0
$516$	6.53316	−	24.1336i	0.287606	−	1.06242i
$517$	1.22642	−	14.0180i	0.0539378	−	0.616512i
$518$	−17.1112	−	11.9814i	−0.751821	−	0.526431i
$519$	−23.2790	+	16.2110i	−1.02183	+	0.711586i
$520$		0			0
$521$	25.0460	+	14.4603i	1.09728	+	0.633518i	0.935507	−	0.353309i	$-0.114944\pi$
$521$	25.0460	+	14.4603i	1.09728	+	0.633518i	0.161778	+	0.986827i	$0.448277\pi$
$522$	−11.1276	−	1.03124i	−0.487040	−	0.0451361i
$523$	−6.53051	+	24.3722i	−0.285559	+	1.06572i	0.662871	+	0.748734i	$0.269338\pi$
$523$	−6.53051	+	24.3722i	−0.285559	+	1.06572i	−0.948430	+	0.316987i	$0.897329\pi$
$524$	−6.98258	+	39.6002i	−0.305035	+	1.72994i
$525$		0			0
$526$	−4.19195	−	1.52575i	−0.182778	−	0.0665257i
$527$	−23.7488	−	50.9294i	−1.03451	−	2.21852i
$528$	−7.18101	−	2.63461i	−0.312513	−	0.114657i
$529$	11.5171	+	2.03078i	0.500745	+	0.0882948i
$530$		0			0
$531$	−0.706605	−	4.13152i	−0.0306640	−	0.179293i
$532$	5.14813	+	19.2131i	0.223200	+	0.832993i
$533$	−9.48814	+	0.830105i	−0.410977	+	0.0359558i
$534$	26.6080	+	38.2090i	1.15144	+	1.65346i
$535$		0			0
$536$	0.184725	+	0.220146i	0.00797889	+	0.00950888i
$537$	1.31188	−	0.752923i	0.0566119	−	0.0324910i
$538$	4.73383	+	2.20742i	0.204090	+	0.0951687i
$539$	−2.30371			−0.0992278
$540$		0			0
$541$	−5.37883			−0.231254			−0.115627	−	0.993293i	$-0.536888\pi$
$541$	−5.37883			−0.231254			−0.115627	+	0.993293i	$0.536888\pi$
$542$	40.4693	+	18.8712i	1.73831	+	0.810586i
$543$	1.10206	+	0.640060i	0.0472939	+	0.0274676i
$544$	31.0960	+	37.0588i	1.33323	+	1.58888i
$545$		0			0
$546$	−23.2979	+	1.97793i	−0.997057	+	0.0846478i
$547$	−18.2031	+	1.59256i	−0.778308	+	0.0680931i	−0.469384	−	0.882994i	$-0.655524\pi$
$547$	−18.2031	+	1.59256i	−0.778308	+	0.0680931i	−0.308923	+	0.951087i	$0.599969\pi$
$548$	8.47092	+	31.6139i	0.361860	+	1.35048i
$549$	6.87181	+	5.82663i	0.293282	+	0.248675i
$550$		0			0
$551$	−8.13375	−	1.43420i	−0.346509	−	0.0610990i
$552$	0.0321375	+	0.185043i	0.00136786	+	0.00787594i
$553$	−1.91324	−	4.10295i	−0.0813591	−	0.174475i
$554$	−15.6520	−	5.69686i	−0.664990	−	0.242036i
$555$		0			0
$556$	0.977467	−	5.54349i	0.0414538	−	0.235096i
$557$	1.10675	−	4.13045i	0.0468945	−	0.175013i	−0.938507	−	0.345261i	$-0.887790\pi$
$557$	1.10675	−	4.13045i	0.0468945	−	0.175013i	0.985401	+	0.170248i	$0.0544570\pi$
$558$	54.1438	−	14.2097i	2.29209	−	0.601544i
$559$	18.8111	+	10.8606i	0.795626	+	0.459355i
$560$		0			0
$561$	−10.5327	−	4.94452i	−0.444693	−	0.208758i
$562$	10.0754	+	7.05488i	0.425005	+	0.297592i
$563$	−2.00004	+	22.8606i	−0.0842918	+	0.963459i	0.829829	+	0.558018i	$0.188438\pi$
$563$	−2.00004	+	22.8606i	−0.0842918	+	0.963459i	−0.914121	+	0.405442i	$0.867118\pi$
$564$	−31.1354	−	31.2960i	−1.31104	−	1.31780i
$565$		0			0
$566$			61.2679i			2.57528i
$567$	19.9247	−	1.53681i	0.836759	−	0.0645401i
$568$	0.178714	+	0.178714i	0.00749867	+	0.00749867i
$569$	4.11183	−	1.49658i	0.172377	−	0.0627400i	−0.254390	−	0.967102i	$-0.581875\pi$
$569$	4.11183	−	1.49658i	0.172377	−	0.0627400i	0.426767	+	0.904362i	$0.359652\pi$
$570$		0			0
$571$	16.1524	−	13.5535i	0.675958	−	0.567196i	−0.238864	−	0.971053i	$-0.576775\pi$
$571$	16.1524	−	13.5535i	0.675958	−	0.567196i	0.914822	+	0.403857i	$0.132331\pi$
$572$	−3.90483	+	5.57667i	−0.163269	+	0.233172i
$573$	10.2989	−	3.71853i	0.430243	−	0.155344i
$574$	8.97982	−	10.7017i	0.374811	−	0.446682i
$575$		0			0
$576$	−21.1802	+	12.0835i	−0.882507	+	0.503481i
$577$	−11.7007	−	3.13518i	−0.487105	−	0.130519i	0.00690397	−	0.999976i	$-0.497802\pi$
$577$	−11.7007	−	3.13518i	−0.487105	−	0.130519i	−0.494009	+	0.869457i	$0.664469\pi$
$578$	22.3290	+	31.8891i	0.928764	+	1.32641i
$579$	4.11215	−	45.6495i	0.170895	−	1.89713i
$580$		0			0
$581$	4.07968	−	11.2088i	0.169254	−	0.465021i
$582$	59.2011	−	10.2818i	2.45397	−	0.426196i
$583$	−8.18099	+	5.72839i	−0.338822	+	0.237246i
$584$	−0.00278859	−	0.00482997i	−0.000115393	−	0.000199866i
$585$		0			0
$586$	7.55356	−	13.0831i	0.312034	−	0.540460i
$587$	1.25428	+	14.3364i	0.0517695	+	0.591728i	0.977130	+	0.212641i	$0.0682064\pi$
$587$	1.25428	+	14.3364i	0.0517695	+	0.591728i	−0.925361	+	0.379087i	$0.876238\pi$
$588$	−4.65983	+	5.52445i	−0.192168	+	0.227825i
$589$	40.7423	−	7.18397i	1.67876	−	0.296010i
$590$		0			0
$591$	−0.194931	−	0.735049i	−0.00801839	−	0.0302359i
$592$	7.87131	−	16.8801i	0.323509	−	0.693767i
$593$	0.209120	−	0.209120i	0.00858753	−	0.00858753i	−0.702800	−	0.711388i	$-0.748067\pi$
$593$	0.209120	−	0.209120i	0.00858753	−	0.00858753i	0.711388	+	0.702800i	$0.248067\pi$
$594$	6.72118	−	9.44293i	0.275773	−	0.387448i
$595$		0			0
$596$	13.8825	+	38.1419i	0.568650	+	1.56235i
$597$	2.05167	+	3.57479i	0.0839691	+	0.146307i
$598$	−20.3639	−	1.78161i	−0.832742	−	0.0728555i
$599$	1.58777	+	9.00467i	0.0648743	+	0.367921i	0.999911	+	0.0133687i	$0.00425551\pi$
$599$	1.58777	+	9.00467i	0.0648743	+	0.367921i	−0.935036	+	0.354552i	$0.884633\pi$
$600$		0			0
$601$	−4.24577	−	3.56262i	−0.173188	−	0.145322i	0.552073	−	0.833796i	$-0.313837\pi$
$601$	−4.24577	−	3.56262i	−0.173188	−	0.145322i	−0.725262	+	0.688473i	$0.758281\pi$
$602$	−30.7745	+	8.24601i	−1.25428	+	0.336082i
$603$	24.2864	−	11.1732i	0.989021	−	0.455009i
$604$	0.912537	−	0.526854i	0.0371306	−	0.0214374i
$605$		0			0
$606$	11.1887	+	24.1562i	0.454509	+	0.981278i
$607$	33.1493	−	15.4578i	1.34549	−	0.627412i	0.389559	−	0.921002i	$-0.372628\pi$
$607$	33.1493	−	15.4578i	1.34549	−	0.627412i	0.955932	+	0.293589i	$0.0948498\pi$
$608$	−32.2786	+	15.0518i	−1.30907	+	0.610429i
$609$	3.00453	+	6.48675i	0.121750	+	0.262856i
$610$		0			0
$611$	33.2143	−	19.1763i	1.34371	−	0.775790i
$612$	−33.1624	+	15.2567i	−1.34051	+	0.616716i
$613$	−25.3096	+	6.78170i	−1.02225	+	0.273910i	−0.730738	−	0.682658i	$-0.760824\pi$
$613$	−25.3096	+	6.78170i	−1.02225	+	0.273910i	−0.291509	+	0.956568i	$0.594157\pi$
$614$	−20.2455	−	16.9880i	−0.817041	−	0.685579i
$615$		0			0
$616$	−0.0138407	−	0.0784943i	−0.000557656	−	0.00316263i
$617$	11.4338	+	1.00033i	0.460309	+	0.0402718i	0.314952	−	0.949108i	$-0.398012\pi$
$617$	11.4338	+	1.00033i	0.460309	+	0.0402718i	0.145356	+	0.989379i	$0.453567\pi$
$618$	−18.1840	−	31.6835i	−0.731467	−	1.27450i
$619$	9.29363	+	25.5340i	0.373542	+	1.02630i	0.973981	+	0.226629i	$0.0727704\pi$
$619$	9.29363	+	25.5340i	0.373542	+	1.02630i	−0.600439	+	0.799671i	$0.705007\pi$
$620$		0			0
$621$	17.3924	+	1.65695i	0.697932	+	0.0664913i
$622$	0.397083	−	0.397083i	0.0159216	−	0.0159216i
$623$	12.5876	−	26.9943i	0.504313	−	1.08150i
$624$	−5.34399	−	20.1512i	−0.213931	−	0.806694i
$625$		0			0
$626$	−18.8052	+	3.31587i	−0.751608	+	0.132529i
$627$	5.52313	−	6.54793i	0.220572	−	0.261499i
$628$	−0.164197	−	1.87678i	−0.00655218	−	0.0748917i
$629$	14.1661	−	24.5363i	0.564838	−	0.978328i
$630$		0			0
$631$	7.42122	+	12.8539i	0.295434	+	0.511707i	0.975086	−	0.221828i	$-0.0712024\pi$
$631$	7.42122	+	12.8539i	0.295434	+	0.511707i	−0.679652	+	0.733535i	$0.737869\pi$
$632$	−0.0538608	+	0.0377137i	−0.00214247	+	0.00150017i
$633$	17.9919	−	3.12477i	0.715114	−	0.124198i
$634$	2.50195	−	6.87405i	0.0993651	−	0.273003i
$635$		0			0
$636$	−2.81103	+	31.2057i	−0.111465	+	1.23738i
$637$	−3.60140	−	5.14333i	−0.142693	−	0.203786i
$638$	4.00501	+	1.07314i	0.158560	+	0.0424860i
$639$	20.4212	−	11.6506i	0.807852	−	0.460889i
$640$		0			0
$641$	−2.24280	+	2.67286i	−0.0885851	+	0.105572i	−0.808516	−	0.588474i	$-0.799729\pi$
$641$	−2.24280	+	2.67286i	−0.0885851	+	0.105572i	0.719931	+	0.694046i	$0.244173\pi$
$642$	−22.8660	+	8.25602i	−0.902451	+	0.325839i
$643$	1.30898	−	1.86941i	0.0516210	−	0.0737225i	−0.792512	−	0.609857i	$-0.791227\pi$
$643$	1.30898	−	1.86941i	0.0516210	−	0.0737225i	0.844133	+	0.536134i	$0.180116\pi$
$644$	11.5303	−	9.67508i	0.454358	−	0.381252i
$645$		0			0
$646$	−50.5006	+	18.3807i	−1.98692	+	0.723180i
$647$	8.56365	+	8.56365i	0.336672	+	0.336672i	0.855113	−	0.518441i	$-0.173488\pi$
$647$	8.56365	+	8.56365i	0.336672	+	0.336672i	−0.518441	+	0.855113i	$0.673488\pi$
$648$	−0.0722333	−	0.281115i	−0.00283759	−	0.0110432i
$649$			1.55515i			0.0610450i
$650$		0			0
$651$	−25.2553	−	25.3855i	−0.989833	−	0.994938i
$652$	1.05586	−	12.0685i	0.0413505	−	0.472638i
$653$	20.3999	+	14.2842i	0.798311	+	0.558984i	0.900029	−	0.435830i	$-0.143545\pi$
$653$	20.3999	+	14.2842i	0.798311	+	0.558984i	−0.101718	+	0.994813i	$0.532434\pi$
$654$	29.5408	+	13.8677i	1.15514	+	0.542270i
$655$		0			0
$656$	10.7873	+	6.22808i	0.421175	+	0.243166i
$657$	−0.501818	+	0.131699i	−0.0195778	+	0.00513806i
$658$	−14.5598	+	54.3378i	−0.567599	+	2.11831i
$659$	−5.36362	+	30.4186i	−0.208937	+	1.18494i	0.682186	+	0.731179i	$0.261030\pi$
$659$	−5.36362	+	30.4186i	−0.208937	+	1.18494i	−0.891123	+	0.453762i	$0.850082\pi$
$660$		0			0
$661$	33.9585	+	12.3599i	1.32083	+	0.480744i	0.903726	−	0.428112i	$-0.140821\pi$
$661$	33.9585	+	12.3599i	1.32083	+	0.480744i	0.417109	+	0.908857i	$0.363043\pi$
$662$	7.48160	+	16.0443i	0.290780	+	0.623581i
$663$	−5.42660	−	31.2455i	−0.210752	−	1.21347i
$664$	−0.170614	−	0.0300838i	−0.00662109	−	0.00116748i
$665$		0			0
$666$	21.5262	+	18.2522i	0.834125	+	0.707257i
$667$	1.61759	+	6.03694i	0.0626335	+	0.233751i
$668$	−16.3379	+	1.42939i	−0.632134	+	0.0553046i
$669$	−14.1207	+	1.19881i	−0.545936	+	0.0463487i
$670$		0			0
$671$	−2.14868	−	2.56070i	−0.0829489	−	0.0988547i
$672$	26.6573	+	15.4821i	1.02833	+	0.597236i
$673$	−33.5440	−	15.6418i	−1.29303	−	0.602949i	−0.350339	−	0.936623i	$-0.613934\pi$
$673$	−33.5440	−	15.6418i	−1.29303	−	0.602949i	−0.942689	+	0.333674i	$0.891712\pi$
$674$	48.1932			1.85633
$675$		0			0
$676$	7.65415			0.294390
$677$	−41.5346	−	19.3679i	−1.59630	−	0.744368i	−0.597938	−	0.801542i	$-0.704013\pi$
$677$	−41.5346	−	19.3679i	−1.59630	−	0.744368i	−0.998364	+	0.0571738i	$0.981791\pi$
$678$	−4.05177	+	2.32541i	−0.155607	+	0.0893070i
$679$	−24.7073	−	29.4450i	−0.948179	−	1.13000i
$680$		0			0
$681$	−4.71821	−	6.77532i	−0.180802	−	0.259631i
$682$	−20.6899	+	1.81014i	−0.792259	+	0.0693137i
$683$	−4.46063	−	16.6473i	−0.170681	−	0.636992i	−0.997247	−	0.0741513i	$-0.976375\pi$
$683$	−4.46063	−	16.6473i	−0.170681	−	0.636992i	0.826566	−	0.562840i	$-0.190291\pi$
$684$	−4.53047	−	26.4897i	−0.173227	−	1.01286i
$685$		0			0
$686$	39.7450	+	7.00812i	1.51747	+	0.267571i
$687$	−11.6286	−	4.26638i	−0.443660	−	0.162772i
$688$	−12.0055	−	25.7458i	−0.457705	−	0.981551i
$689$	−25.5787	−	9.30989i	−0.974472	−	0.354679i
$690$		0			0
$691$	−6.05103	+	34.3171i	−0.230192	+	1.30548i	0.622314	+	0.782768i	$0.286193\pi$
$691$	−6.05103	+	34.3171i	−0.230192	+	1.30548i	−0.852506	+	0.522717i	$0.824918\pi$
$692$	8.54605	−	31.8943i	0.324872	−	1.21244i
$693$	−7.38288	−	0.684203i	−0.280452	−	0.0259907i
$694$	−29.1708	−	16.8418i	−1.10731	−	0.639305i
$695$		0			0
$696$	0.0852049	−	0.0593351i	0.00322968	−	0.00224909i
$697$	15.5213	+	10.8682i	0.587913	+	0.411661i
$698$	5.98066	−	68.3592i	0.226371	−	2.58743i
$699$	−4.09019	+	15.1093i	−0.154705	+	0.571485i
$700$		0			0
$701$		−	27.2979i		−	1.03103i	−0.856881	−	0.515515i	$-0.827601\pi$
$701$		−	27.2979i		−	1.03103i	0.856881	−	0.515515i	$-0.172399\pi$
$702$	31.5898	+	0.243747i	1.19228	+	0.00919964i
$703$	14.7491	+	14.7491i	0.556273	+	0.556273i
$704$	8.50169	−	3.09436i	0.320419	−	0.116623i
$705$		0			0
$706$	34.7178	−	29.1317i	1.30662	−	1.09639i
$707$	9.76787	−	13.9500i	0.367359	−	0.524642i
$708$	3.72936	+	3.14568i	0.140158	+	0.118222i
$709$	16.4826	−	19.6432i	0.619018	−	0.737717i	−0.361883	−	0.932223i	$-0.617866\pi$
$709$	16.4826	−	19.6432i	0.619018	−	0.737717i	0.980901	+	0.194506i	$0.0623105\pi$
$710$		0			0
$711$	2.06238	+	5.75833i	0.0773453	+	0.215954i
$712$	−0.417857	−	0.111964i	−0.0156598	−	0.00419604i
$713$	−17.9564	−	25.6444i	−0.672473	−	0.960391i
$714$	38.0350	+	26.7785i	1.42343	+	1.00216i
$715$		0			0
$716$	−0.602175	+	1.65446i	−0.0225043	+	0.0618302i
$717$	4.56022	+	5.46313i	0.170304	+	0.204024i
$718$	50.5779	−	35.4150i	1.88755	−	1.32168i
$719$	0.729141	+	1.26291i	0.0271924	+	0.0470986i	0.879301	−	0.476266i	$-0.158010\pi$
$719$	0.729141	+	1.26291i	0.0271924	+	0.0470986i	−0.852109	+	0.523364i	$0.824677\pi$
$720$		0			0
$721$	−11.6843	+	20.2379i	−0.435148	+	0.753698i
$722$	−0.129754	−	1.48309i	−0.00482893	−	0.0551949i
$723$	−3.63229	−	10.0601i	−0.135086	−	0.374138i
$724$	−1.46091	+	0.257598i	−0.0542942	+	0.00957354i
$725$		0			0
$726$	24.0192	−	23.8960i	0.891437	−	0.886863i
$727$	−19.8194	+	42.5029i	−0.735062	+	1.57634i	0.0798819	+	0.996804i	$0.474546\pi$
$727$	−19.8194	+	42.5029i	−0.735062	+	1.57634i	−0.814944	+	0.579540i	$0.803232\pi$
$728$	0.153611	−	0.153611i	0.00569322	−	0.00569322i
$729$	−26.9968	−	0.416640i	−0.999881	−	0.0154311i
$730$		0			0
$731$	−14.7796	−	40.6067i	−0.546645	−	1.50189i
$732$	−10.4870	−	0.0269720i	−0.387610	−	0.000996915i
$733$	24.4678	+	2.14066i	0.903740	+	0.0790670i	0.529544	−	0.848283i	$-0.322363\pi$
$733$	24.4678	+	2.14066i	0.903740	+	0.0790670i	0.374196	+	0.927350i	$0.377919\pi$
$734$	−5.05543	−	28.6707i	−0.186599	−	1.05826i
$735$		0			0
$736$	20.6456	+	17.3237i	0.761006	+	0.638560i
$737$	−9.58076	+	2.56716i	−0.352912	+	0.0945625i
$738$	−13.4150	+	13.2777i	−0.493814	+	0.488760i
$739$	18.0486	−	10.4204i	0.663928	−	0.383319i	−0.129844	−	0.991534i	$-0.541448\pi$
$739$	18.0486	−	10.4204i	0.663928	−	0.383319i	0.793772	+	0.608215i	$0.208114\pi$
$740$		0			0
$741$	23.2534	+	2.09469i	0.854236	+	0.0769503i
$742$	36.1853	−	16.8735i	1.32840	−	0.619445i
$743$	−38.5547	+	17.9783i	−1.41443	+	0.659561i	−0.971510	−	0.236998i	$-0.923836\pi$
$743$	−38.5547	+	17.9783i	−1.41443	+	0.659561i	−0.442923	+	0.896559i	$0.646059\pi$
$744$	−0.299404	+	0.425261i	−0.0109767	+	0.0155908i
$745$		0			0
$746$	−29.5649	+	17.0693i	−1.08245	+	0.624951i
$747$	−6.88597	+	14.5709i	−0.251945	+	0.533120i
$748$	13.0822	−	3.50537i	0.478334	−	0.128169i
$749$	11.9132	+	9.99638i	0.435300	+	0.365260i
$750$		0			0
$751$	3.51433	+	19.9308i	0.128240	+	0.727284i	0.979331	+	0.202265i	$0.0648304\pi$
$751$	3.51433	+	19.9308i	0.128240	+	0.727284i	−0.851091	+	0.525018i	$0.824059\pi$
$752$	−49.9673	−	4.37157i	−1.82212	−	0.159415i
$753$	−15.7354	+	27.0934i	−0.573431	+	0.987338i
$754$	3.86512	+	10.6193i	0.140760	+	0.386734i
$755$		0			0
$756$	−16.5745	+	16.3207i	−0.602808	+	0.593577i
$757$	−10.9992	+	10.9992i	−0.399771	+	0.399771i	−0.878152	−	0.478381i	$-0.841224\pi$
$757$	−10.9992	+	10.9992i	−0.399771	+	0.399771i	0.478381	+	0.878152i	$0.341224\pi$
$758$	−0.899510	+	1.92901i	−0.0326717	+	0.0700647i
$759$	−6.25701	−	1.69382i	−0.227115	−	0.0614818i
$760$		0			0
$761$	−12.7782	+	2.25313i	−0.463208	+	0.0816761i	−0.400382	−	0.916348i	$-0.631122\pi$
$761$	−12.7782	+	2.25313i	−0.463208	+	0.0816761i	−0.0628262	+	0.998024i	$0.520011\pi$
$762$	−52.0129	−	9.30927i	−1.88423	−	0.337239i
$763$	−1.81945	−	20.7964i	−0.0658685	−	0.752880i
$764$	−6.37266	+	11.0378i	−0.230555	+	0.399332i
$765$		0			0
$766$	−22.7203	−	39.3527i	−0.820918	−	1.42187i
$767$	−3.47208	+	2.43117i	−0.125369	+	0.0877846i
$768$	−9.38983	+	25.5933i	−0.338826	+	0.923520i
$769$	10.6865	−	29.3608i	0.385364	−	1.05878i	−0.583700	−	0.811969i	$-0.698396\pi$
$769$	10.6865	−	29.3608i	0.385364	−	1.05878i	0.969064	−	0.246810i	$-0.0793822\pi$
$770$		0			0
$771$	18.2414	−	8.44905i	0.656948	−	0.304285i
$772$	30.6008	+	43.7024i	1.10135	+	1.57288i
$773$	−35.0964	−	9.40406i	−1.26233	−	0.338241i	−0.435243	−	0.900313i	$-0.643338\pi$
$773$	−35.0964	−	9.40406i	−1.26233	−	0.338241i	−0.827088	+	0.562072i	$0.810004\pi$
$774$	42.4298	−	7.25668i	1.52511	−	0.260836i
$775$		0			0
$776$	−0.358850	+	0.427661i	−0.0128820	+	0.0153521i
$777$	3.18076	−	17.7716i	0.114109	−	0.637553i
$778$	3.55061	−	5.07079i	0.127295	−	0.181797i
$779$	−10.6861	+	8.96672i	−0.382870	+	0.321266i
$780$		0			0
$781$	−8.19706	+	2.98349i	−0.293314	+	0.106758i
$782$	28.7561	+	28.7561i	1.02832	+	1.02832i
$783$	−3.23332	−	9.10137i	−0.115549	−	0.325256i
$784$			8.21158i			0.293271i
$785$		0			0
$786$	−66.9174	+	17.7461i	−2.38686	+	0.632983i
$787$	3.06442	−	35.0265i	0.109235	−	1.24856i	−0.721707	−	0.692199i	$-0.756642\pi$
$787$	3.06442	−	35.0265i	0.109235	−	1.24856i	0.830942	−	0.556360i	$-0.187802\pi$
$788$	0.725085	+	0.507710i	0.0258301	+	0.0180864i
$789$	−0.326156	−	3.84175i	−0.0116115	−	0.136770i
$790$		0			0
$791$	2.58807	+	1.49422i	0.0920213	+	0.0531285i
$792$	0.00883374	+	0.107326i	0.000313893	+	0.00381366i
$793$	2.35805	−	8.80036i	0.0837367	−	0.312510i
$794$	5.27284	−	29.9037i	0.187126	−	1.06124i
$795$		0			0
$796$	−4.50830	−	1.64089i	−0.159793	−	0.0581597i
$797$	10.8830	+	23.3386i	0.385495	+	0.826696i	0.999306	+	0.0372435i	$0.0118577\pi$
$797$	10.8830	+	23.3386i	0.385495	+	0.826696i	−0.613811	+	0.789453i	$0.710364\pi$
$798$	−26.2902	+	21.9451i	−0.930663	+	0.776849i
$799$	−75.1405	−	13.2493i	−2.65828	−	0.468726i
$800$		0			0
$801$	−20.3000	+	34.7466i	−0.717266	+	1.22771i
$802$	−12.2241	−	45.6210i	−0.431648	−	1.61093i
$803$	0.191760	−	0.0167768i	0.00676705	−	0.000592040i
$804$	−13.2233	+	28.1680i	−0.466349	+	0.993410i
$805$		0			0
$806$	−36.3860	−	43.3632i	−1.28164	−	1.52740i
$807$	−0.0116107	+	4.51434i	−0.000408716	+	0.158912i
$808$	−0.224167	−	0.104531i	−0.00788618	−	0.00367739i
$809$	−14.9511			−0.525654			−0.262827	−	0.964843i	$-0.584655\pi$
$809$	−14.9511			−0.525654			−0.262827	+	0.964843i	$0.584655\pi$
$810$		0			0
$811$	14.0980			0.495049			0.247525	−	0.968882i	$-0.420383\pi$
$811$	14.0980			0.495049			0.247525	+	0.968882i	$0.420383\pi$
$812$	−7.54150	−	3.51666i	−0.264655	−	0.123411i
$813$	−0.0992594	+	38.5929i	−0.00348118	+	1.35351i
$814$	−6.73083	−	8.02149i	−0.235916	−	0.281153i
$815$		0			0
$816$	−17.6248	+	37.5440i	−0.616990	+	1.31430i
$817$	31.6926	−	2.77274i	1.10878	−	0.0970060i
$818$	8.06208	+	30.0881i	0.281884	+	1.05201i
$819$	−10.0141	−	17.5528i	−0.349921	−	0.613346i
$820$		0			0
$821$	6.53467	+	1.15224i	0.228061	+	0.0402134i	0.286511	−	0.958077i	$-0.407505\pi$
$821$	6.53467	+	1.15224i	0.228061	+	0.0402134i	−0.0584494	+	0.998290i	$0.518616\pi$
$822$	−43.2589	+	36.1093i	−1.50883	+	1.25946i
$823$	−9.68030	−	20.7595i	−0.337434	−	0.723630i	0.662236	−	0.749295i	$-0.269607\pi$
$823$	−9.68030	−	20.7595i	−0.337434	−	0.723630i	−0.999671	+	0.0256651i	$0.991830\pi$
$824$	0.318939	+	0.116084i	0.0111108	+	0.00404399i
$825$		0			0
$826$	1.07959	−	6.12265i	0.0375637	−	0.213034i
$827$	6.34894	−	23.6946i	0.220774	−	0.823941i	−0.763279	−	0.646069i	$-0.776412\pi$
$827$	6.34894	−	23.6946i	0.220774	−	0.823941i	0.984054	−	0.177872i	$-0.0569213\pi$
$828$	−16.7183	+	11.5786i	−0.581000	+	0.402383i
$829$	24.8714	+	14.3595i	0.863821	+	0.498727i	0.865290	−	0.501272i	$-0.167134\pi$
$829$	24.8714	+	14.3595i	0.863821	+	0.498727i	−0.00146915	+	0.999999i	$0.500468\pi$
$830$		0			0
$831$	−1.21781	−	14.3444i	−0.0422453	−	0.497603i
$832$	20.1993	+	14.1437i	0.700284	+	0.490344i
$833$	−1.08869	+	12.4438i	−0.0377208	+	0.431151i
$834$	9.36754	−	2.48422i	0.324371	−	0.0860215i
$835$		0			0
$836$			9.97102i			0.344855i
$837$	30.8116	+	37.3005i	1.06500	+	1.28929i
$838$	−10.9214	−	10.9214i	−0.377273	−	0.377273i
$839$	29.6410	−	10.7884i	1.02332	−	0.372458i	0.224787	−	0.974408i	$-0.427831\pi$
$839$	29.6410	−	10.7884i	1.02332	−	0.372458i	0.798534	+	0.601950i	$0.205609\pi$
$840$		0			0
$841$	−19.5685	+	16.4199i	−0.674775	+	0.566204i
$842$	1.45332	−	2.07555i	0.0500846	−	0.0715282i
$843$	−1.87290	+	10.4643i	−0.0645061	+	0.360409i
$844$	−13.6630	+	16.2830i	−0.470301	+	0.560483i
$845$		0			0
$846$	26.3623	−	71.2866i	0.906353	−	2.45088i
$847$	−20.9353	−	5.60959i	−0.719344	−	0.192748i
$848$	20.4189	+	29.1612i	0.701187	+	1.00140i
$849$	−48.0492	+	22.2554i	−1.64905	+	0.763805i
$850$		0			0
$851$	5.39842	−	14.8320i	0.185055	−	0.508435i
$852$	−9.42601	+	25.6919i	−0.322930	+	0.880191i
$853$	18.5060	−	12.9580i	0.633632	−	0.443674i	−0.212125	−	0.977243i	$-0.568038\pi$
$853$	18.5060	−	12.9580i	0.633632	−	0.443674i	0.845757	+	0.533569i	$0.179149\pi$
$854$	6.68174	+	11.5731i	0.228645	+	0.396024i
$855$		0			0
$856$	0.112936	−	0.195611i	0.00386008	−	0.00668586i
$857$	−0.720788	−	8.23864i	−0.0246216	−	0.281427i	−0.998518	−	0.0544314i	$-0.982665\pi$
$857$	−0.720788	−	8.23864i	−0.0246216	−	0.281427i	0.973896	−	0.226995i	$-0.0728902\pi$
$858$	−11.5376	−	2.06500i	−0.393887	−	0.0704980i
$859$	11.2675	−	1.98676i	0.384442	−	0.0677875i	0.0219126	−	0.999760i	$-0.493024\pi$
$859$	11.2675	−	1.98676i	0.384442	−	0.0677875i	0.362529	+	0.931972i	$0.381913\pi$
$860$		0			0
$861$	11.6547	+	3.15502i	0.397192	+	0.107523i
$862$	26.5797	−	57.0002i	0.905306	−	1.94144i
$863$	9.18912	−	9.18912i	0.312801	−	0.312801i	−0.533193	−	0.845994i	$-0.679008\pi$
$863$	9.18912	−	9.18912i	0.312801	−	0.312801i	0.845994	+	0.533193i	$0.179008\pi$
$864$	−33.9324	−	24.1520i	−1.15440	−	0.821669i
$865$		0			0
$866$	−24.0686	−	66.1280i	−0.817886	−	2.24712i
$867$	−16.8980	+	29.0951i	−0.573887	+	0.988123i
$868$	41.5223	+	3.63273i	1.40936	+	0.123303i
$869$	−0.394074	−	2.23490i	−0.0133680	−	0.0758139i
$870$		0			0
$871$	−20.7091	−	17.3770i	−0.701703	−	0.588798i
$872$	−0.292870	+	0.0784744i	−0.00991784	+	0.00265748i
$873$	29.5682	+	42.6935i	1.00073	+	1.44496i
$874$	−25.9285	+	14.9698i	−0.877044	+	0.506362i
$875$		0			0
$876$	0.347650	−	0.493788i	0.0117460	−	0.0166835i
$877$	−48.3756	+	22.5579i	−1.63353	+	0.761726i	−0.999929	−	0.0119368i	$-0.996200\pi$
$877$	−48.3756	+	22.5579i	−1.63353	+	0.761726i	−0.633598	+	0.773663i	$0.718423\pi$
$878$	36.9995	−	17.2531i	1.24867	−	0.582265i
$879$	13.0042	+	1.17143i	0.438622	+	0.0395115i
$880$		0			0
$881$	−34.2794	+	19.7912i	−1.15490	+	0.666782i	−0.950077	−	0.312016i	$-0.898996\pi$
$881$	−34.2794	+	19.7912i	−1.15490	+	0.666782i	−0.204824	+	0.978799i	$0.565662\pi$
$882$	−12.0023	−	3.28228i	−0.404140	−	0.110520i
$883$	−48.7707	+	13.0681i	−1.64127	+	0.439776i	−0.957149	−	0.289597i	$-0.906479\pi$
$883$	−48.7707	+	13.0681i	−1.64127	+	0.439776i	−0.684116	+	0.729373i	$0.739812\pi$
$884$	28.2777	+	23.7278i	0.951082	+	0.798053i
$885$		0			0
$886$	0.958958	+	5.43852i	0.0322168	+	0.182711i
$887$	11.8379	+	1.03569i	0.397479	+	0.0347749i	0.284143	−	0.958782i	$-0.408291\pi$
$887$	11.8379	+	1.03569i	0.397479	+	0.0347749i	0.113336	+	0.993557i	$0.463846\pi$
$888$	−0.262216		0.000674409i	−0.00879941		2.26317e-5i
$889$	11.5607	+	31.7628i	0.387734	+	1.06529i
$890$		0			0
$891$	9.84706	+	1.84095i	0.329889	+	0.0616741i
$892$	11.6641	−	11.6641i	0.390541	−	0.390541i
$893$	23.7395	−	50.9096i	0.794413	−	1.70362i
$894$	−49.5413	+	49.2871i	−1.65691	+	1.64841i
$895$		0			0
$896$	−0.564144	+	0.0994738i	−0.0188467	+	0.00332319i
$897$	−5.99993	−	16.6175i	−0.200332	−	0.554843i
$898$	5.05560	+	57.7858i	0.168708	+	1.92834i
$899$	−8.65353	+	14.9884i	−0.288611	+	0.499890i
$900$		0			0
$901$	27.0764	+	46.8977i	0.902046	+	1.56239i
$902$	5.73656	−	4.01678i	0.191006	−	0.133744i
$903$	−17.6457	−	21.1395i	−0.587213	−	0.703479i
$904$	0.0148452	−	0.0407868i	0.000493743	−	0.00135655i
$905$		0			0
$906$	1.48338	+	1.04437i	0.0492820	+	0.0346969i
$907$	−0.725418	−	1.03600i	−0.0240871	−	0.0343999i	0.806928	−	0.590650i	$-0.201129\pi$
$907$	−0.725418	−	1.03600i	−0.0240871	−	0.0343999i	−0.831015	+	0.556250i	$0.812240\pi$
$908$	9.28280	+	2.48732i	0.308061	+	0.0825446i
$909$	−14.8802	+	17.5494i	−0.493545	+	0.582077i
$910$		0			0
$911$	0.894909	−	1.06651i	0.0296497	−	0.0353351i	−0.751016	−	0.660284i	$-0.770436\pi$
$911$	0.894909	−	1.06651i	0.0296497	−	0.0353351i	0.780666	+	0.624949i	$0.214880\pi$
$912$	−23.3401	−	19.6872i	−0.772869	−	0.651909i
$913$	3.42967	−	4.89808i	0.113506	−	0.162103i
$914$	36.4756	−	30.6067i	1.20651	−	1.01238i
$915$		0			0
$916$	13.5484	−	4.93120i	0.447650	−	0.162931i
$917$	31.3154	+	31.3154i	1.03412	+	1.03412i
$918$	−47.8308	−	40.7678i	−1.57865	−	1.34554i
$919$		−	3.33325i		−	0.109954i	−0.998488	−	0.0549769i	$-0.982491\pi$
$919$		−	3.33325i		−	0.109954i	0.998488	−	0.0549769i	$-0.0175085\pi$
$920$		0			0
$921$	5.96866	−	22.0483i	0.196674	−	0.726518i
$922$	−1.64838	+	18.8411i	−0.0542865	+	0.620498i
$923$	−19.4755	−	13.6369i	−0.641044	−	0.448864i
$924$	7.08234	−	4.93201i	0.232992	−	0.162251i
$925$		0			0
$926$	32.0759	+	18.5191i	1.05408	+	0.608574i
$927$	18.2424	−	25.7697i	0.599160	−	0.846389i
$928$	3.85624	−	14.3917i	0.126587	−	0.472430i
$929$	−5.78861	+	32.8289i	−0.189918	+	1.07708i	0.729554	+	0.683924i	$0.239728\pi$
$929$	−5.78861	+	32.8289i	−0.189918	+	1.07708i	−0.919472	+	0.393156i	$0.871383\pi$
$930$		0			0
$931$	−8.64161	−	3.14529i	−0.283217	−	0.103083i
$932$	−7.70014	−	16.5130i	−0.252226	−	0.540901i
$933$	0.455652	+	0.167172i	0.0149174	+	0.00547297i
$934$	−25.2646	−	4.45484i	−0.826684	−	0.145767i
$935$		0			0
$936$	−0.225809	+	0.187505i	−0.00738080	+	0.00612880i
$937$	−11.0023	−	41.0610i	−0.359428	−	1.34140i	−0.874820	−	0.484449i	$-0.839020\pi$
$937$	−11.0023	−	41.0610i	−0.359428	−	1.34140i	0.515392	−	0.856955i	$-0.327647\pi$
$938$	39.5017	−	3.45595i	1.28978	−	0.112841i
$939$	−9.43143	−	13.5435i	−0.307783	−	0.441975i
$940$		0			0
$941$	−1.20131	−	1.43167i	−0.0391617	−	0.0466711i	0.746108	−	0.665825i	$-0.231920\pi$
$941$	−1.20131	−	1.43167i	−0.0391617	−	0.0466711i	−0.785270	+	0.619154i	$0.787476\pi$
$942$	2.81316	−	1.61455i	0.0916579	−	0.0526048i
$943$	9.56700	+	4.46117i	0.311544	+	0.145276i
$944$	5.54334			0.180420
$945$		0			0
$946$	−15.9711			−0.519265
$947$	−28.3806	−	13.2341i	−0.922246	−	0.430050i	−0.0972956	−	0.995256i	$-0.531019\pi$
$947$	−28.3806	−	13.2341i	−0.922246	−	0.430050i	−0.824950	+	0.565205i	$0.808797\pi$
$948$	−6.15656	−	3.57563i	−0.199956	−	0.116131i
$949$	0.337235	+	0.401901i	0.0109471	+	0.0130462i
$950$		0			0
$951$	6.29979	−	0.534837i	0.204285	−	0.0173433i
$952$	−0.430537	+	0.0376671i	−0.0139538	+	0.00122080i
$953$	−3.16696	−	11.8193i	−0.102588	−	0.382864i	0.895472	−	0.445117i	$-0.146838\pi$
$953$	−3.16696	−	11.8193i	−0.102588	−	0.382864i	−0.998060	+	0.0622534i	$0.980171\pi$
$954$	−50.7847	+	18.1888i	−1.64421	+	0.588885i
$955$		0			0
$956$	−8.15744	−	1.43838i	−0.263830	−	0.0465204i
$957$	0.613206	+	3.53074i	0.0198221	+	0.114133i
$958$	6.89835	+	14.7936i	0.222876	+	0.477958i
$959$	33.8725	+	12.3286i	1.09380	+	0.398111i
$960$		0			0
$961$	9.67079	−	54.8458i	0.311961	−	1.76922i
$962$	7.38668	−	27.5675i	0.238156	−	0.888811i
$963$	−14.7808	−	14.9337i	−0.476305	−	0.481231i
$964$	10.7818	+	6.22486i	0.347258	+	0.200489i
$965$		0			0
$966$	23.4581	+	11.0122i	0.754751	+	0.354312i
$967$	−8.91754	−	6.24413i	−0.286769	−	0.200798i	0.421337	−	0.906904i	$-0.361561\pi$
$967$	−8.91754	−	6.24413i	−0.286769	−	0.200798i	−0.708106	+	0.706107i	$0.750450\pi$
$968$	−0.0274359	+	0.313593i	−0.000881822	+	0.0100793i
$969$	−32.7593	−	32.9283i	−1.05238	−	1.05781i
$970$		0			0
$971$		−	17.9235i		−	0.575194i	−0.957752	−	0.287597i	$-0.907144\pi$
$971$		−	17.9235i		−	0.575194i	0.957752	−	0.287597i	$-0.0928563\pi$
$972$	24.3329	−	19.8901i	0.780477	−	0.637976i
$973$	−4.38373	−	4.38373i	−0.140536	−	0.140536i
$974$	30.1589	−	10.9769i	0.966353	−	0.351724i
$975$		0			0
$976$	−9.12762	+	7.65898i	−0.292168	+	0.245158i
$977$	−2.92108	+	4.17173i	−0.0934536	+	0.133466i	−0.863156	−	0.504937i	$-0.831516\pi$
$977$	−2.92108	+	4.17173i	−0.0934536	+	0.133466i	0.769702	+	0.638403i	$0.220405\pi$
$978$	19.6178	−	7.08323i	0.627310	−	0.226497i
$979$	9.59732	−	11.4376i	0.306732	−	0.365549i
$980$		0			0
$981$	−0.145084	+	28.2047i	−0.00463216	+	0.900508i
$982$	−6.33758	−	1.69815i	−0.202240	−	0.0541901i
$983$	31.6427	+	45.1905i	1.00925	+	1.44135i	0.894027	+	0.448014i	$0.147868\pi$
$983$	31.6427	+	45.1905i	1.00925	+	1.44135i	0.115220	+	0.993340i	$0.463243\pi$
$984$	0.0157335	−	0.174659i	0.000501565	−	0.00556794i
$985$		0			0
$986$	7.68938	−	21.1264i	0.244880	−	0.672802i
$987$	−47.9031	+	8.31963i	−1.52477	+	0.264817i
$988$	−22.2616	+	15.5877i	−0.708236	+	0.495912i
$989$	−12.0370	−	20.8487i	−0.382754	−	0.662949i
$990$		0			0
$991$	4.20341	−	7.28053i	0.133526	−	0.231274i	−0.791508	−	0.611159i	$-0.790703\pi$
$991$	4.20341	−	7.28053i	0.133526	−	0.231274i	0.925033	+	0.379886i	$0.124037\pi$
$992$	6.50458	+	74.3476i	0.206520	+	2.36054i
$993$	−9.86507	+	11.6955i	−0.313058	+	0.371146i
$994$	34.3431	−	6.05561i	1.08930	−	0.192072i
$995$		0			0
$996$	−4.80855	−	18.1322i	−0.152365	−	0.574540i
$997$	15.9928	−	34.2966i	0.506496	−	1.08618i	−0.472317	−	0.881429i	$-0.656582\pi$
$997$	15.9928	−	34.2966i	0.506496	−	1.08618i	0.978813	−	0.204756i	$-0.0656400\pi$
$998$	43.3517	−	43.3517i	1.37227	−	1.37227i
$999$	−6.49486	+	23.5120i	−0.205488	+	0.743886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.b.668.3		192
5.2	odd	4	inner	675.2.ba.b.182.14		192
5.3	odd	4		135.2.q.a.47.3	yes	192
5.4	even	2		135.2.q.a.128.14	yes	192
15.8	even	4		405.2.r.a.62.14		192
15.14	odd	2		405.2.r.a.143.3		192
27.23	odd	18	inner	675.2.ba.b.293.14		192
135.4	even	18		405.2.r.a.98.14		192
135.23	even	36		135.2.q.a.77.14	yes	192
135.58	odd	36		405.2.r.a.17.3		192
135.77	even	36	inner	675.2.ba.b.482.3		192
135.104	odd	18		135.2.q.a.23.3	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.23.3	✓	192	135.104	odd	18
135.2.q.a.47.3	yes	192	5.3	odd	4
135.2.q.a.77.14	yes	192	135.23	even	36
135.2.q.a.128.14	yes	192	5.4	even	2
405.2.r.a.17.3		192	135.58	odd	36
405.2.r.a.62.14		192	15.8	even	4
405.2.r.a.98.14		192	135.4	even	18
405.2.r.a.143.3		192	15.14	odd	2
675.2.ba.b.182.14		192	5.2	odd	4	inner
675.2.ba.b.293.14		192	27.23	odd	18	inner
675.2.ba.b.482.3		192	135.77	even	36	inner
675.2.ba.b.668.3		192	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.81626 - 0.846935i) q^{2} +(0.00445475 - 1.73205i) q^{3} +(1.29592 + 1.54442i) q^{4} +(-1.47502 + 3.14207i) q^{6} +(2.21198 - 0.193523i) q^{7} +(-0.00834683 - 0.0311508i) q^{8} +(-2.99996 - 0.0154316i) q^{9} +(1.09616 + 0.193283i) q^{11} +(2.68077 - 2.23771i) q^{12} +(1.28211 + 2.74949i) q^{13} +(-4.18143 - 1.52192i) q^{14} +(0.688959 - 3.90728i) q^{16} +(1.56207 - 5.82972i) q^{17} +(5.43563 + 2.56880i) q^{18} +(3.84801 + 2.22165i) q^{19} +(-0.325337 - 3.83212i) q^{21} +(-1.82722 - 1.27943i) q^{22} +(0.293046 - 3.34953i) q^{23} +(-0.0539918 + 0.0143183i) q^{24} -6.07964i q^{26} +(-0.0400924 + 5.19600i) q^{27} +(3.16543 + 3.16543i) q^{28} +(-1.74671 + 0.635749i) q^{29} +(7.13252 - 5.98490i) q^{31} +(-4.59753 + 6.56596i) q^{32} +(0.339658 - 1.89774i) q^{33} +(-7.77451 + 9.26530i) q^{34} +(-3.86387 - 4.65319i) q^{36} +(4.53439 + 1.21499i) q^{37} +(-5.10738 - 7.29410i) q^{38} +(4.76795 - 2.20842i) q^{39} +(-1.07377 + 2.95017i) q^{41} +(-2.65466 + 7.23565i) q^{42} +(5.86507 - 4.10676i) q^{43} +(1.12203 + 1.94341i) q^{44} +(-3.36908 + 5.83541i) q^{46} +(-1.10183 - 12.5940i) q^{47} +(-6.76452 - 1.21071i) q^{48} +(-2.03824 + 0.359397i) q^{49} +(-10.0904 - 2.73154i) q^{51} +(-2.58485 + 5.54322i) q^{52} +(-6.34457 + 6.34457i) q^{53} +(4.47349 - 9.40332i) q^{54} +(-0.0244914 - 0.0672897i) q^{56} +(3.86514 - 6.65503i) q^{57} +(3.71091 + 0.324662i) q^{58} +(0.242616 + 1.37594i) q^{59} +(-2.30056 - 1.93040i) q^{61} +(-18.0233 + 4.82933i) q^{62} +(-6.63885 + 0.546428i) q^{63} +(7.03924 - 4.06411i) q^{64} +(-2.22417 + 3.15912i) q^{66} +(-8.07622 + 3.76600i) q^{67} +(11.0278 - 5.14236i) q^{68} +(-5.80023 - 0.522490i) q^{69} +(-6.78702 + 3.91849i) q^{71} +(0.0245595 + 0.0935799i) q^{72} +(0.167045 - 0.0447595i) q^{73} +(-7.20661 - 6.04707i) q^{74} +(1.55556 + 8.82200i) q^{76} +(2.46210 + 0.215406i) q^{77} +(-10.5302 - 0.0270832i) q^{78} +(-0.697324 - 1.91588i) q^{79} +(8.99952 + 0.0925886i) q^{81} +(4.44885 - 4.44885i) q^{82} +(2.27031 - 4.86870i) q^{83} +(5.49677 - 5.46857i) q^{84} +(-14.1306 + 2.49161i) q^{86} +(1.09336 + 3.02821i) q^{87} +(-0.00312857 - 0.0357597i) q^{88} +(6.70700 - 11.6169i) q^{89} +(3.36809 + 5.83370i) q^{91} +(5.55283 - 3.88813i) q^{92} +(-10.3343 - 12.3805i) q^{93} +(-8.66507 + 23.8071i) q^{94} +(11.3521 + 7.99239i) q^{96} +(-9.92914 - 14.1803i) q^{97} +(4.00635 + 1.07350i) q^{98} +(-3.28547 - 0.596758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{2} + 12 q^{3} - 36 q^{6} + 12 q^{7} + 18 q^{8} - 36 q^{11} + 12 q^{12} + 12 q^{13} - 24 q^{16} + 18 q^{17} + 54 q^{18} - 24 q^{21} + 12 q^{22} + 36 q^{23} + 36 q^{27} + 24 q^{28} - 24 q^{31}+ \cdots - 324 q^{98}+O(q^{100}) \) 192 * q + 12 * q^2 + 12 * q^3 - 36 * q^6 + 12 * q^7 + 18 * q^8 - 36 * q^11 + 12 * q^12 + 12 * q^13 - 24 * q^16 + 18 * q^17 + 54 * q^18 - 24 * q^21 + 12 * q^22 + 36 * q^23 + 36 * q^27 + 24 * q^28 - 24 * q^31 + 48 * q^32 + 6 * q^33 + 12 * q^36 + 6 * q^37 - 12 * q^38 + 24 * q^41 + 24 * q^42 + 12 * q^43 - 12 * q^46 + 6 * q^47 - 12 * q^48 + 144 * q^51 - 12 * q^52 + 180 * q^56 + 12 * q^57 + 12 * q^58 - 60 * q^61 + 18 * q^62 + 54 * q^63 + 72 * q^66 - 24 * q^67 + 60 * q^68 - 36 * q^71 - 180 * q^72 + 6 * q^73 - 72 * q^76 - 132 * q^77 - 78 * q^78 + 12 * q^81 + 24 * q^82 - 48 * q^83 + 12 * q^86 - 144 * q^87 + 48 * q^88 - 12 * q^91 - 258 * q^92 - 180 * q^93 - 12 * q^96 - 24 * q^97 - 324 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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