LMFDB - Embedded newform 675.2.ba.b.482.3

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			482.3
Character	$\chi$	$=$	675.482
Dual form			675.2.ba.b.668.3

$q$-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 $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{4}\right)$

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	−0.940379	−	0.340129i	$-0.889529\pi$
$2$	−1.81626	+	0.846935i	−1.28429	+	0.598874i	−0.343910	+	0.939003i	$0.611751\pi$
$3$	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	0.497137	−	0.867672i	$-0.334385\pi$
$7$	2.21198	+	0.193523i	0.836051	+	0.0731450i	0.338914	+	0.940817i	$0.389940\pi$
$8$	−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	−0.00593305	−	0.999982i	$-0.501889\pi$
$11$	1.09616	−	0.193283i	0.330506	−	0.0582771i	0.336439	+	0.941705i	$0.390777\pi$
$12$	2.68077	+	2.23771i	0.773872	+	0.645971i
$13$	1.28211	−	2.74949i	0.355592	−	0.762570i	−0.644405	−	0.764684i	$-0.722895\pi$
$13$	1.28211	−	2.74949i	0.355592	−	0.762570i	0.999998	+	0.00211367i	$0.000672802\pi$
$14$	−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	0.847626	+	0.530594i	$0.178031\pi$
$17$	1.56207	+	5.82972i	0.378857	+	1.41391i	−0.468769	+	0.883321i	$0.655302\pi$
$18$	5.43563	−	2.56880i	1.28119	−	0.605472i
$19$	3.84801	−	2.22165i	0.882794	−	0.509681i	0.0112151	−	0.999937i	$-0.496430\pi$
$19$	3.84801	−	2.22165i	0.882794	−	0.509681i	0.871578	+	0.490256i	$0.163097\pi$
$20$		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	0.963534	+	0.267587i	$0.0862263\pi$
$23$	0.293046	+	3.34953i	0.0611042	+	0.698425i	−0.902429	+	0.430838i	$0.858218\pi$
$24$	−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	0.174710	−	0.984620i	$-0.444101\pi$
$29$	−1.74671	−	0.635749i	−0.324355	−	0.118056i	−0.499066	+	0.866564i	$0.666323\pi$
$30$		0			0
$31$	7.13252	+	5.98490i	1.28104	+	1.07492i	0.993100	+	0.117270i	$0.0374144\pi$
$31$	7.13252	+	5.98490i	1.28104	+	1.07492i	0.287939	+	0.957649i	$0.407030\pi$
$32$	−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	0.133951	−	0.990988i	$-0.457234\pi$
$37$	4.53439	−	1.21499i	0.745450	−	0.199743i	0.611499	+	0.791245i	$0.290567\pi$
$38$	−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	0.827169	−	0.561953i	$-0.189950\pi$
$41$	−1.07377	−	2.95017i	−0.167695	−	0.460739i	−0.994865	+	0.101214i	$0.967727\pi$
$42$	−2.65466	−	7.23565i	−0.409622	−	1.11649i
$43$	5.86507	+	4.10676i	0.894414	+	0.626276i	0.927764	−	0.373168i	$-0.121729\pi$
$43$	5.86507	+	4.10676i	0.894414	+	0.626276i	−0.0333495	+	0.999444i	$0.510617\pi$
$44$	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	0.305313	+	0.952252i	$0.401239\pi$
$47$	−1.10183	+	12.5940i	−0.160718	+	1.83702i	−0.466031	+	0.884768i	$0.654317\pi$
$48$	−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	0.121142	−	0.992635i	$-0.461344\pi$
$53$	−6.34457	−	6.34457i	−0.871494	−	0.871494i	−0.992635	+	0.121142i	$0.961344\pi$
$54$	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	−0.964933	−	0.262495i	$-0.915455\pi$
$59$	0.242616	−	1.37594i	0.0315859	−	0.179132i	0.996519	+	0.0833623i	$0.0265659\pi$
$60$		0			0
$61$	−2.30056	+	1.93040i	−0.294557	+	0.247163i	−0.778075	−	0.628172i	$-0.783803\pi$
$61$	−2.30056	+	1.93040i	−0.294557	+	0.247163i	0.483517	+	0.875335i	$0.339359\pi$
$62$	−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	−0.138812	−	0.990319i	$-0.544328\pi$
$67$	−8.07622	−	3.76600i	−0.986667	−	0.460090i	−0.847855	+	0.530228i	$0.822106\pi$
$68$	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	0.0399099	−	0.999203i	$-0.487293\pi$
$71$	−6.78702	−	3.91849i	−0.805471	−	0.465039i	−0.845380	+	0.534165i	$0.820626\pi$
$72$	0.0245595	−	0.0935799i	0.00289436	−	0.0110285i
$73$	0.167045	+	0.0447595i	0.0195511	+	0.00523870i	0.268581	−	0.963257i	$-0.413445\pi$
$73$	0.167045	+	0.0447595i	0.0195511	+	0.00523870i	−0.249030	+	0.968496i	$0.580112\pi$
$74$	−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	−0.972719	−	0.231986i	$-0.925478\pi$
$79$	−0.697324	+	1.91588i	−0.0784551	+	0.215554i	0.894264	+	0.447540i	$0.147700\pi$
$80$		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	0.990622	−	0.136629i	$-0.0436267\pi$
$83$	2.27031	+	4.86870i	0.249199	+	0.534409i	−0.741423	+	0.671038i	$0.765849\pi$
$84$	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	0.964504	+	0.264067i	$0.0850640\pi$
$89$	6.70700	+	11.6169i	0.710941	+	1.23139i	−0.253563	+	0.967319i	$0.581603\pi$
$90$		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	−0.113229	+	0.993569i	$0.536119\pi$
$97$	−9.92914	+	14.1803i	−1.00815	+	1.43979i	−0.894923	+	0.446221i	$0.852769\pi$
$98$	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	0.953356	−	0.301849i	$-0.0976038\pi$
$101$	4.92991	+	5.87523i	0.490544	+	0.584608i	−0.462812	+	0.886457i	$0.653159\pi$
$102$	16.0133	−	13.5071i	1.58555	−	1.33740i
$103$	−6.03654	−	8.62107i	−0.594798	−	0.849460i	0.403040	−	0.915182i	$-0.367954\pi$
$103$	−6.03654	−	8.62107i	−0.594798	−	0.849460i	−0.997838	+	0.0657227i	$0.979065\pi$
$104$	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	−0.425965	−	0.904740i	$-0.640065\pi$
$107$	4.95248	−	4.95248i	0.478774	−	0.478774i	0.904740	+	0.425965i	$0.140065\pi$
$108$	−8.07674	−	6.67167i	−0.777185	−	0.641982i
$109$			9.40170i			0.900520i	0.892898	+	0.450260i	$0.148669\pi$
$109$			9.40170i			0.900520i	−0.892898	+	0.450260i	$0.851331\pi$
$110$		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	−0.520569	−	0.853819i	$-0.674280\pi$
$113$	1.10249	−	0.771969i	0.103713	−	0.0726207i	0.624283	+	0.781199i	$0.285391\pi$
$114$	−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	−0.537513	−	0.843256i	$-0.680636\pi$
$127$	3.93996	−	14.7041i	0.349615	−	1.30478i	0.887127	−	0.461525i	$-0.152697\pi$
$128$	−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	0.184131	−	0.982902i	$-0.441053\pi$
$131$	12.8204	−	15.2788i	1.12013	−	1.33491i	0.935995	−	0.352013i	$-0.114503\pi$
$132$	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	0.324020	−	0.946050i	$-0.394966\pi$
$137$	14.7130	−	6.86076i	1.25701	−	0.586155i	0.932993	+	0.359896i	$0.117188\pi$
$138$	10.0922	−	5.86139i	0.859105	−	0.498955i
$139$	−1.79469	+	2.13883i	−0.152223	+	0.181413i	−0.836767	−	0.547559i	$-0.815557\pi$
$139$	−1.79469	+	2.13883i	−0.152223	+	0.181413i	0.684544	+	0.728972i	$0.260002\pi$
$140$		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	0.581492	−	0.813552i	$-0.302469\pi$
$149$	18.9187	−	6.88585i	1.54988	−	0.564111i	0.968390	+	0.249441i	$0.0802470\pi$
$150$		0			0
$151$	0.0907569	+	0.514708i	0.00738569	+	0.0418864i	0.988278	−	0.152666i	$-0.0487858\pi$
$151$	0.0907569	+	0.514708i	0.00738569	+	0.0418864i	−0.980892	+	0.194552i	$0.937675\pi$
$152$	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	−0.603723	−	0.797194i	$-0.706317\pi$
$157$	−0.765462	+	0.535982i	−0.0610905	+	0.0427760i	0.542632	+	0.839970i	$0.317428\pi$
$158$	−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	−0.853651	−	0.520846i	$-0.825617\pi$
$163$	−4.24897	+	4.24897i	−0.332805	+	0.332805i	0.520846	+	0.853651i	$0.325617\pi$
$164$	−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	0.596992	−	0.802247i	$-0.296362\pi$
$167$	−4.66589	−	6.66358i	−0.361057	−	0.515643i	−0.958049	+	0.286604i	$0.907474\pi$
$168$	−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	0.283917	+	0.958849i	$0.408366\pi$
$173$	−9.39399	+	13.4160i	−0.714212	+	1.02000i	−0.998129	+	0.0611509i	$0.980523\pi$
$174$	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	−0.849246	−	0.527998i	$-0.822943\pi$
$179$	0.436647	−	0.756295i	0.0326365	−	0.0565281i	0.881882	+	0.471470i	$0.156276\pi$
$180$		0			0
$181$	−0.367901	−	0.637223i	−0.0273459	−	0.0473644i	0.852029	−	0.523495i	$-0.175372\pi$
$181$	−0.367901	−	0.637223i	−0.0273459	−	0.0473644i	−0.879374	+	0.476131i	$0.842039\pi$
$182$	−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	−0.836560	−	0.547876i	$-0.815437\pi$
$191$	2.16218	−	5.94054i	0.156450	−	0.429842i	0.993010	+	0.118033i	$0.0376589\pi$
$192$	−7.00786	+	12.2104i	−0.505749	+	0.881209i
$193$	26.3618	−	2.30636i	1.89756	−	0.166015i	0.922213	−	0.386683i	$-0.126379\pi$
$193$	26.3618	−	2.30636i	1.89756	−	0.166015i	0.975349	+	0.220667i	$0.0708235\pi$
$194$	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	0.273895	−	0.961760i	$-0.411688\pi$
$197$	0.424090	+	0.113635i	0.0302152	+	0.00809613i	−0.243680	+	0.969856i	$0.578355\pi$
$198$	5.46184	−	3.86644i	0.388156	−	0.274776i
$199$	−2.06085	−	1.18983i	−0.146090	−	0.0843452i	0.425173	−	0.905112i	$-0.360213\pi$
$199$	−2.06085	−	1.18983i	−0.146090	−	0.0843452i	−0.571263	+	0.820767i	$0.693546\pi$
$200$		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	−0.854649	−	0.519206i	$-0.826228\pi$
$211$	1.83079	−	10.3830i	0.126037	−	0.714792i	0.980686	−	0.195586i	$-0.0626610\pi$
$212$	−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	0.934208	+	0.356729i	$0.116108\pi$
$223$	−0.713099	+	8.15076i	−0.0477527	+	0.545815i	−0.981960	+	0.189086i	$0.939447\pi$
$224$	−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	0.695937	−	0.718103i	$-0.254989\pi$
$227$	3.90472	+	2.73411i	0.259165	+	0.181469i	−0.436772	+	0.899572i	$0.643878\pi$
$228$	15.2870	+	2.65500i	1.01241	+	0.175831i
$229$	2.44592	+	6.72010i	0.161631	+	0.444077i	0.993899	−	0.110297i	$-0.0351801\pi$
$229$	2.44592	+	6.72010i	0.161631	+	0.444077i	−0.832268	+	0.554374i	$0.812958\pi$
$230$		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	−0.533159	−	0.846015i	$-0.678995\pi$
$233$	−8.72938	+	2.33903i	−0.571881	+	0.153235i	−0.0387217	+	0.999250i	$0.512329\pi$
$234$	−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	0.535295	−	0.844665i	$-0.320201\pi$
$239$	−3.14736	−	2.64095i	−0.203586	−	0.170829i	−0.738880	+	0.673837i	$0.764645\pi$
$240$		0			0
$241$	5.80277	+	2.11203i	0.373789	+	0.136048i	0.522082	−	0.852895i	$-0.325156\pi$
$241$	5.80277	+	2.11203i	0.373789	+	0.136048i	−0.148293	+	0.988944i	$0.547378\pi$
$242$	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	−0.904918	−	0.425585i	$-0.860068\pi$
$251$	−15.6657	+	9.04459i	−0.988810	+	0.570890i	−0.0838914	+	0.996475i	$0.526735\pi$
$252$	−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	−0.691854	−	0.722037i	$-0.743206\pi$
$257$	4.90513	−	10.5191i	0.305974	−	0.656163i	0.997828	+	0.0658743i	$0.0209837\pi$
$258$	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	0.155320	−	0.987864i	$-0.450359\pi$
$263$	2.21755	+	0.194010i	0.136740	+	0.0119632i	−0.0185804	+	0.999827i	$0.505915\pi$
$264$	−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	0.333141	−	0.942877i	$-0.391891\pi$
$277$	8.27992	+	0.724399i	0.497492	+	0.0435249i	0.164351	+	0.986402i	$0.447447\pi$
$278$	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	−0.351001	−	0.936375i	$-0.614159\pi$
$281$	−6.04432	+	1.06578i	−0.360574	+	0.0635790i	−0.00957353	+	0.999954i	$0.503047\pi$
$282$	41.1964	−	15.1144i	2.45321	−	0.900047i
$283$	−12.9205	+	27.7081i	−0.768044	+	1.64708i	−0.00563108	+	0.999984i	$0.501792\pi$
$283$	−12.9205	+	27.7081i	−0.768044	+	1.64708i	−0.762413	+	0.647091i	$0.775985\pi$
$284$	−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	−0.990935	−	0.134345i	$-0.957107\pi$
$293$	−0.657015	−	7.50972i	−0.0383833	−	0.438723i	0.952551	−	0.304378i	$-0.0984485\pi$
$294$	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	0.123719	−	0.992317i	$-0.460518\pi$
$307$	12.7384	−	3.41325i	0.727021	−	0.194805i	0.603302	+	0.797513i	$0.293851\pi$
$308$	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	0.936946	−	0.349475i	$-0.113640\pi$
$311$	−0.0958399	−	0.263318i	−0.00543458	−	0.0149314i	−0.942380	+	0.334544i	$0.891418\pi$
$312$	−0.108591	+	0.130092i	−0.00614777	+	0.00736501i
$313$	7.80530	+	5.46533i	0.441182	+	0.308919i	0.772979	−	0.634432i	$-0.218766\pi$
$313$	7.80530	+	5.46533i	0.441182	+	0.308919i	−0.331797	+	0.943351i	$0.607655\pi$
$314$	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	−0.982012	−	0.188816i	$-0.939535\pi$
$317$	0.318142	−	3.63638i	0.0178686	−	0.204239i	0.999881	−	0.0154231i	$-0.00490952\pi$
$318$	−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	−0.809532	−	0.587075i	$-0.800279\pi$
$331$	−6.76703	+	5.67821i	−0.371950	+	0.312103i	0.437583	+	0.899178i	$0.355835\pi$
$332$	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	−0.274284	−	0.961649i	$-0.588441\pi$
$337$	−21.7951	−	10.1632i	−1.18726	−	0.553627i	−0.912972	+	0.408022i	$0.866219\pi$
$338$	−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	0.371651	−	0.928372i	$-0.378792\pi$
$347$	16.7440	−	1.46491i	0.898867	−	0.0786406i	0.527215	+	0.849732i	$0.323236\pi$
$348$	−3.25990	−	5.61292i	−0.174749	−	0.300884i
$349$	11.7112	−	32.1764i	0.626888	−	1.72236i	−0.0625752	−	0.998040i	$-0.519931\pi$
$349$	11.7112	−	32.1764i	0.626888	−	1.72236i	0.689463	−	0.724321i	$-0.257846\pi$
$350$		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	−0.978142	−	0.207939i	$-0.933324\pi$
$353$	−9.55751	−	20.4961i	−0.508695	−	1.09090i	0.469447	−	0.882961i	$-0.344453\pi$
$354$	−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	−0.910720	−	0.413025i	$-0.864472\pi$
$359$	−15.4051	−	26.6824i	−0.813050	−	1.40824i	0.0976695	−	0.995219i	$-0.468861\pi$
$360$		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	−0.540510	−	0.841338i	$-0.681769\pi$
$367$	8.33253	−	11.9001i	0.434955	−	0.621179i	0.975464	+	0.220158i	$0.0706574\pi$
$368$	−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	0.988146	−	0.153520i	$-0.0490610\pi$
$373$	9.77090	+	13.9543i	0.505918	+	0.722526i	−0.482227	+	0.876046i	$0.660172\pi$
$374$	−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	$0.00868381\pi$
$379$			1.06208i			0.0545552i	−0.999628	+	0.0272776i	$0.991316\pi$
$380$		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	0.00701991	−	0.999975i	$-0.497765\pi$
$383$	18.5741	−	13.0057i	0.949090	−	0.664560i	0.942070	+	0.335415i	$0.108877\pi$
$384$	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	0.968186	−	0.250233i	$-0.0805072\pi$
$389$	−0.536388	−	3.04201i	−0.0271960	−	0.154236i	−0.995382	+	0.0959969i	$0.969396\pi$
$390$		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	−0.794966	−	0.606654i	$-0.792511\pi$
$397$	3.92165	−	14.6358i	0.196822	−	0.734549i	0.991788	−	0.127895i	$-0.0408220\pi$
$398$	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	−0.241113	−	0.970497i	$-0.577512\pi$
$401$	15.1491	−	18.0540i	0.756509	−	0.901573i	0.997622	+	0.0689246i	$0.0219568\pi$
$402$	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	−0.954238	−	0.299048i	$-0.903331\pi$
$409$	−9.99118	+	11.9070i	−0.494032	+	0.588764i	0.460206	+	0.887812i	$0.347775\pi$
$410$		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	−0.159000	−	0.987279i	$-0.550827\pi$
$419$	7.24231	−	2.63599i	0.353810	−	0.128776i	0.512810	+	0.858502i	$0.328605\pi$
$420$		0			0
$421$	−0.219552	−	1.24514i	−0.0107003	−	0.0606845i	0.978990	−	0.203908i	$-0.0653643\pi$
$421$	−0.219552	−	1.24514i	−0.0107003	−	0.0606845i	−0.989690	+	0.143223i	$0.954253\pi$
$422$	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	$-0.727228\pi$
$431$		−	31.3833i		−	1.51168i	0.654755	−	0.755841i	$-0.272772\pi$
$432$	20.2746	−	3.73648i	0.975462	−	0.179772i
$433$	24.8304	−	24.8304i	1.19327	−	1.19327i	0.217127	−	0.976143i	$-0.430331\pi$
$433$	24.8304	−	24.8304i	1.19327	−	1.19327i	0.976143	−	0.217127i	$-0.0696687\pi$
$434$	−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	0.356953	−	0.934122i	$-0.383815\pi$
$439$	−13.0944	−	15.6053i	−0.624962	−	0.744800i	−0.981915	+	0.189322i	$0.939371\pi$
$440$		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	−0.854943	−	0.518722i	$-0.826408\pi$
$443$	−1.58059	+	2.25731i	−0.0750960	+	0.107248i	0.779847	+	0.625970i	$0.215297\pi$
$444$	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	0.291059	+	0.956705i	$0.405992\pi$
$449$	−14.4725	+	25.0672i	−0.683001	+	1.18299i	−0.974060	+	0.226288i	$0.927341\pi$
$450$		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	−0.988333	−	0.152305i	$-0.951330\pi$
$457$	−10.0414	−	21.5339i	−0.469718	−	1.00731i	0.518616	−	0.855007i	$-0.326447\pi$
$458$	−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	−0.991885	−	0.127137i	$-0.959421\pi$
$461$	−3.22783	+	8.86840i	−0.150335	+	0.413043i	0.841550	+	0.540179i	$0.181644\pi$
$462$	−4.30847	−	7.41836i	−0.200448	−	0.345133i
$463$	−18.4116	+	1.61081i	−0.855659	+	0.0748605i	−0.506538	−	0.862217i	$-0.669075\pi$
$463$	−18.4116	+	1.61081i	−0.855659	+	0.0748605i	−0.349121	+	0.937078i	$0.613520\pi$
$464$	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	0.533304	−	0.845924i	$-0.320950\pi$
$467$	12.3653	+	3.31326i	0.572196	+	0.153320i	0.0388925	+	0.999243i	$0.487617\pi$
$468$	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	−0.774106	−	0.633056i	$-0.781800\pi$
$479$	−6.23949	+	5.23555i	−0.285090	+	0.239219i	0.489016	+	0.872275i	$0.337356\pi$
$480$		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	0.402337	−	0.915492i	$-0.368198\pi$
$487$	−11.3243	−	11.3243i	−0.513154	−	0.513154i	−0.915492	+	0.402337i	$0.868198\pi$
$488$	−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	0.245928	−	0.969288i	$-0.420907\pi$
$491$	3.22425	+	0.568523i	0.145508	+	0.0256571i	−0.100419	+	0.994945i	$0.532018\pi$
$492$	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	−0.919020	−	0.394211i	$-0.871018\pi$
$499$	−10.4633	−	28.7478i	−0.468404	−	1.28693i	0.450616	−	0.892718i	$-0.351204\pi$
$500$		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	−0.522993	−	0.852337i	$-0.675184\pi$
$503$	−12.3296	+	3.30370i	−0.549749	+	0.147305i	−0.0267563	+	0.999642i	$0.508518\pi$
$504$	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	−0.124493	−	0.992221i	$-0.539730\pi$
$509$	−25.3418	−	21.2643i	−1.12326	−	0.942525i	−0.998764	+	0.0496958i	$0.984175\pi$
$510$		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	0.161778	−	0.986827i	$-0.448277\pi$
$521$	25.0460	−	14.4603i	1.09728	−	0.633518i	0.935507	+	0.353309i	$0.114944\pi$
$522$	−11.1276	+	1.03124i	−0.487040	+	0.0451361i
$523$	−6.53051	−	24.3722i	−0.285559	−	1.06572i	−0.948430	−	0.316987i	$-0.897329\pi$
$523$	−6.53051	−	24.3722i	−0.285559	−	1.06572i	0.662871	−	0.748734i	$-0.269338\pi$
$524$	−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	−0.308923	−	0.951087i	$-0.599969\pi$
$547$	−18.2031	−	1.59256i	−0.778308	−	0.0680931i	−0.469384	+	0.882994i	$0.655524\pi$
$548$	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	0.985401	−	0.170248i	$-0.0544570\pi$
$557$	1.10675	+	4.13045i	0.0468945	+	0.175013i	−0.938507	+	0.345261i	$0.887790\pi$
$558$	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	−0.914121	−	0.405442i	$-0.867118\pi$
$563$	−2.00004	−	22.8606i	−0.0842918	−	0.963459i	0.829829	−	0.558018i	$-0.188438\pi$
$564$	−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	0.426767	−	0.904362i	$-0.359652\pi$
$569$	4.11183	+	1.49658i	0.172377	+	0.0627400i	−0.254390	+	0.967102i	$0.581875\pi$
$570$		0			0
$571$	16.1524	+	13.5535i	0.675958	+	0.567196i	0.914822	−	0.403857i	$-0.132331\pi$
$571$	16.1524	+	13.5535i	0.675958	+	0.567196i	−0.238864	+	0.971053i	$0.576775\pi$
$572$	−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	−0.494009	−	0.869457i	$-0.664469\pi$
$577$	−11.7007	+	3.13518i	−0.487105	+	0.130519i	0.00690397	+	0.999976i	$0.497802\pi$
$578$	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	−0.925361	−	0.379087i	$-0.876238\pi$
$587$	1.25428	−	14.3364i	0.0517695	−	0.591728i	0.977130	−	0.212641i	$-0.0682064\pi$
$588$	−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	0.711388	−	0.702800i	$-0.248067\pi$
$593$	0.209120	+	0.209120i	0.00858753	+	0.00858753i	−0.702800	+	0.711388i	$0.748067\pi$
$594$	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	−0.935036	−	0.354552i	$-0.884633\pi$
$599$	1.58777	−	9.00467i	0.0648743	−	0.367921i	0.999911	−	0.0133687i	$-0.00425551\pi$
$600$		0			0
$601$	−4.24577	+	3.56262i	−0.173188	+	0.145322i	−0.725262	−	0.688473i	$-0.758281\pi$
$601$	−4.24577	+	3.56262i	−0.173188	+	0.145322i	0.552073	+	0.833796i	$0.313837\pi$
$602$	−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	0.955932	−	0.293589i	$-0.0948498\pi$
$607$	33.1493	+	15.4578i	1.34549	+	0.627412i	0.389559	+	0.921002i	$0.372628\pi$
$608$	−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	−0.291509	−	0.956568i	$-0.594157\pi$
$613$	−25.3096	−	6.78170i	−1.02225	−	0.273910i	−0.730738	+	0.682658i	$0.760824\pi$
$614$	−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	0.145356	−	0.989379i	$-0.453567\pi$
$617$	11.4338	−	1.00033i	0.460309	−	0.0402718i	0.314952	+	0.949108i	$0.398012\pi$
$618$	−18.1840	+	31.6835i	−0.731467	+	1.27450i
$619$	9.29363	−	25.5340i	0.373542	−	1.02630i	−0.600439	−	0.799671i	$-0.705007\pi$
$619$	9.29363	−	25.5340i	0.373542	−	1.02630i	0.973981	−	0.226629i	$-0.0727704\pi$
$620$		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	−0.679652	−	0.733535i	$-0.737869\pi$
$631$	7.42122	−	12.8539i	0.295434	−	0.511707i	0.975086	+	0.221828i	$0.0712024\pi$
$632$	−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	0.719931	−	0.694046i	$-0.244173\pi$
$641$	−2.24280	−	2.67286i	−0.0885851	−	0.105572i	−0.808516	+	0.588474i	$0.799729\pi$
$642$	−22.8660	−	8.25602i	−0.902451	−	0.325839i
$643$	1.30898	+	1.86941i	0.0516210	+	0.0737225i	0.844133	−	0.536134i	$-0.180116\pi$
$643$	1.30898	+	1.86941i	0.0516210	+	0.0737225i	−0.792512	+	0.609857i	$0.791227\pi$
$644$	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	−0.518441	−	0.855113i	$-0.673488\pi$
$647$	8.56365	−	8.56365i	0.336672	−	0.336672i	0.855113	+	0.518441i	$0.173488\pi$
$648$	−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	−0.101718	−	0.994813i	$-0.532434\pi$
$653$	20.3999	−	14.2842i	0.798311	−	0.558984i	0.900029	+	0.435830i	$0.143545\pi$
$654$	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	−0.891123	−	0.453762i	$-0.850082\pi$
$659$	−5.36362	−	30.4186i	−0.208937	−	1.18494i	0.682186	−	0.731179i	$-0.261030\pi$
$660$		0			0
$661$	33.9585	−	12.3599i	1.32083	−	0.480744i	0.417109	−	0.908857i	$-0.363043\pi$
$661$	33.9585	−	12.3599i	1.32083	−	0.480744i	0.903726	+	0.428112i	$0.140821\pi$
$662$	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	−0.942689	−	0.333674i	$-0.891712\pi$
$673$	−33.5440	+	15.6418i	−1.29303	+	0.602949i	−0.350339	+	0.936623i	$0.613934\pi$
$674$	48.1932			1.85633
$675$		0			0
$676$	7.65415			0.294390
$677$	−41.5346	+	19.3679i	−1.59630	+	0.744368i	−0.998364	−	0.0571738i	$-0.981791\pi$
$677$	−41.5346	+	19.3679i	−1.59630	+	0.744368i	−0.597938	+	0.801542i	$0.704013\pi$
$678$	−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	0.826566	+	0.562840i	$0.190291\pi$
$683$	−4.46063	+	16.6473i	−0.170681	+	0.636992i	−0.997247	+	0.0741513i	$0.976375\pi$
$684$	−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	−0.852506	−	0.522717i	$-0.824918\pi$
$691$	−6.05103	−	34.3171i	−0.230192	−	1.30548i	0.622314	−	0.782768i	$-0.286193\pi$
$692$	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	$0.172399\pi$
$701$			27.2979i			1.03103i	−0.856881	+	0.515515i	$0.827601\pi$
$702$	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	0.980901	−	0.194506i	$-0.0623105\pi$
$709$	16.4826	+	19.6432i	0.619018	+	0.737717i	−0.361883	+	0.932223i	$0.617866\pi$
$710$		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	−0.852109	−	0.523364i	$-0.824677\pi$
$719$	0.729141	−	1.26291i	0.0271924	−	0.0470986i	0.879301	+	0.476266i	$0.158010\pi$
$720$		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	−0.814944	−	0.579540i	$-0.803232\pi$
$727$	−19.8194	−	42.5029i	−0.735062	−	1.57634i	0.0798819	−	0.996804i	$-0.474546\pi$
$728$	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	0.374196	−	0.927350i	$-0.377919\pi$
$733$	24.4678	−	2.14066i	0.903740	−	0.0790670i	0.529544	+	0.848283i	$0.322363\pi$
$734$	−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	0.793772	−	0.608215i	$-0.208114\pi$
$739$	18.0486	+	10.4204i	0.663928	+	0.383319i	−0.129844	+	0.991534i	$0.541448\pi$
$740$		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	−0.442923	−	0.896559i	$-0.646059\pi$
$743$	−38.5547	−	17.9783i	−1.41443	−	0.659561i	−0.971510	+	0.236998i	$0.923836\pi$
$744$	−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	−0.851091	−	0.525018i	$-0.824059\pi$
$751$	3.51433	−	19.9308i	0.128240	−	0.727284i	0.979331	−	0.202265i	$-0.0648304\pi$
$752$	−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	0.478381	−	0.878152i	$-0.341224\pi$
$757$	−10.9992	−	10.9992i	−0.399771	−	0.399771i	−0.878152	+	0.478381i	$0.841224\pi$
$758$	−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	−0.0628262	−	0.998024i	$-0.520011\pi$
$761$	−12.7782	−	2.25313i	−0.463208	−	0.0816761i	−0.400382	+	0.916348i	$0.631122\pi$
$762$	−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	0.969064	+	0.246810i	$0.0793822\pi$
$769$	10.6865	+	29.3608i	0.385364	+	1.05878i	−0.583700	+	0.811969i	$0.698396\pi$
$770$		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	−0.827088	−	0.562072i	$-0.810004\pi$
$773$	−35.0964	+	9.40406i	−1.26233	+	0.338241i	−0.435243	+	0.900313i	$0.643338\pi$
$774$	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	0.830942	+	0.556360i	$0.187802\pi$
$787$	3.06442	+	35.0265i	0.109235	+	1.24856i	−0.721707	+	0.692199i	$0.756642\pi$
$788$	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	−0.613811	−	0.789453i	$-0.710364\pi$
$797$	10.8830	−	23.3386i	0.385495	−	0.826696i	0.999306	−	0.0372435i	$-0.0118577\pi$
$798$	−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	−0.0584494	−	0.998290i	$-0.518616\pi$
$821$	6.53467	−	1.15224i	0.228061	−	0.0402134i	0.286511	+	0.958077i	$0.407505\pi$
$822$	−43.2589	−	36.1093i	−1.50883	−	1.25946i
$823$	−9.68030	+	20.7595i	−0.337434	+	0.723630i	−0.999671	−	0.0256651i	$-0.991830\pi$
$823$	−9.68030	+	20.7595i	−0.337434	+	0.723630i	0.662236	+	0.749295i	$0.269607\pi$
$824$	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	0.984054	+	0.177872i	$0.0569213\pi$
$827$	6.34894	+	23.6946i	0.220774	+	0.823941i	−0.763279	+	0.646069i	$0.776412\pi$
$828$	−16.7183	−	11.5786i	−0.581000	−	0.402383i
$829$	24.8714	−	14.3595i	0.863821	−	0.498727i	−0.00146915	−	0.999999i	$-0.500468\pi$
$829$	24.8714	−	14.3595i	0.863821	−	0.498727i	0.865290	+	0.501272i	$0.167134\pi$
$830$		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	0.798534	−	0.601950i	$-0.205609\pi$
$839$	29.6410	+	10.7884i	1.02332	+	0.372458i	0.224787	+	0.974408i	$0.427831\pi$
$840$		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	0.845757	−	0.533569i	$-0.179149\pi$
$853$	18.5060	+	12.9580i	0.633632	+	0.443674i	−0.212125	+	0.977243i	$0.568038\pi$
$854$	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	0.973896	+	0.226995i	$0.0728902\pi$
$857$	−0.720788	+	8.23864i	−0.0246216	+	0.281427i	−0.998518	+	0.0544314i	$0.982665\pi$
$858$	−11.5376	+	2.06500i	−0.393887	+	0.0704980i
$859$	11.2675	+	1.98676i	0.384442	+	0.0677875i	0.362529	−	0.931972i	$-0.381913\pi$
$859$	11.2675	+	1.98676i	0.384442	+	0.0677875i	0.0219126	+	0.999760i	$0.493024\pi$
$860$		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	0.845994	−	0.533193i	$-0.179008\pi$
$863$	9.18912	+	9.18912i	0.312801	+	0.312801i	−0.533193	+	0.845994i	$0.679008\pi$
$864$	−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	−0.633598	−	0.773663i	$-0.718423\pi$
$877$	−48.3756	−	22.5579i	−1.63353	−	0.761726i	−0.999929	+	0.0119368i	$0.996200\pi$
$878$	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	−0.204824	−	0.978799i	$-0.565662\pi$
$881$	−34.2794	−	19.7912i	−1.15490	−	0.666782i	−0.950077	+	0.312016i	$0.898996\pi$
$882$	−12.0023	+	3.28228i	−0.404140	+	0.110520i
$883$	−48.7707	−	13.0681i	−1.64127	−	0.439776i	−0.684116	−	0.729373i	$-0.739812\pi$
$883$	−48.7707	−	13.0681i	−1.64127	−	0.439776i	−0.957149	+	0.289597i	$0.906479\pi$
$884$	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	0.113336	−	0.993557i	$-0.463846\pi$
$887$	11.8379	−	1.03569i	0.397479	−	0.0347749i	0.284143	+	0.958782i	$0.408291\pi$
$888$	−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	−0.831015	−	0.556250i	$-0.812240\pi$
$907$	−0.725418	+	1.03600i	−0.0240871	+	0.0343999i	0.806928	+	0.590650i	$0.201129\pi$
$908$	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	0.780666	−	0.624949i	$-0.214880\pi$
$911$	0.894909	+	1.06651i	0.0296497	+	0.0353351i	−0.751016	+	0.660284i	$0.770436\pi$
$912$	−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	$0.0175085\pi$
$919$			3.33325i			0.109954i	−0.998488	+	0.0549769i	$0.982491\pi$
$920$		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	−0.919472	−	0.393156i	$-0.871383\pi$
$929$	−5.78861	−	32.8289i	−0.189918	−	1.07708i	0.729554	−	0.683924i	$-0.239728\pi$
$930$		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	0.515392	+	0.856955i	$0.327647\pi$
$937$	−11.0023	+	41.0610i	−0.359428	+	1.34140i	−0.874820	+	0.484449i	$0.839020\pi$
$938$	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	−0.785270	−	0.619154i	$-0.787476\pi$
$941$	−1.20131	+	1.43167i	−0.0391617	+	0.0466711i	0.746108	+	0.665825i	$0.231920\pi$
$942$	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	−0.824950	−	0.565205i	$-0.808797\pi$
$947$	−28.3806	+	13.2341i	−0.922246	+	0.430050i	−0.0972956	+	0.995256i	$0.531019\pi$
$948$	−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	−0.998060	−	0.0622534i	$-0.980171\pi$
$953$	−3.16696	+	11.8193i	−0.102588	+	0.382864i	0.895472	+	0.445117i	$0.146838\pi$
$954$	−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	−0.708106	−	0.706107i	$-0.750450\pi$
$967$	−8.91754	+	6.24413i	−0.286769	+	0.200798i	0.421337	+	0.906904i	$0.361561\pi$
$968$	−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	$0.0928563\pi$
$971$			17.9235i			0.575194i	−0.957752	+	0.287597i	$0.907144\pi$
$972$	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	0.769702	−	0.638403i	$-0.220405\pi$
$977$	−2.92108	−	4.17173i	−0.0934536	−	0.133466i	−0.863156	+	0.504937i	$0.831516\pi$
$978$	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	0.115220	−	0.993340i	$-0.463243\pi$
$983$	31.6427	−	45.1905i	1.00925	−	1.44135i	0.894027	−	0.448014i	$-0.147868\pi$
$984$	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	0.925033	−	0.379886i	$-0.124037\pi$
$991$	4.20341	+	7.28053i	0.133526	+	0.231274i	−0.791508	+	0.611159i	$0.790703\pi$
$992$	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	0.978813	+	0.204756i	$0.0656400\pi$
$997$	15.9928	+	34.2966i	0.506496	+	1.08618i	−0.472317	+	0.881429i	$0.656582\pi$
$998$	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.482.3		192
5.2	odd	4		135.2.q.a.23.3	✓	192
5.3	odd	4	inner	675.2.ba.b.293.14		192
5.4	even	2		135.2.q.a.77.14	yes	192
15.2	even	4		405.2.r.a.98.14		192
15.14	odd	2		405.2.r.a.17.3		192
27.20	odd	18	inner	675.2.ba.b.182.14		192
135.7	odd	36		405.2.r.a.143.3		192
135.34	even	18		405.2.r.a.62.14		192
135.47	even	36		135.2.q.a.128.14	yes	192
135.74	odd	18		135.2.q.a.47.3	yes	192
135.128	even	36	inner	675.2.ba.b.668.3		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.23.3	✓	192	5.2	odd	4
135.2.q.a.47.3	yes	192	135.74	odd	18
135.2.q.a.77.14	yes	192	5.4	even	2
135.2.q.a.128.14	yes	192	135.47	even	36
405.2.r.a.17.3		192	15.14	odd	2
405.2.r.a.62.14		192	135.34	even	18
405.2.r.a.98.14		192	15.2	even	4
405.2.r.a.143.3		192	135.7	odd	36
675.2.ba.b.182.14		192	27.20	odd	18	inner
675.2.ba.b.293.14		192	5.3	odd	4	inner
675.2.ba.b.482.3		192	1.1	even	1	trivial
675.2.ba.b.668.3		192	135.128	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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

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