LMFDB - Embedded newform 189.6.o.a.62.36

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,6,Mod(62,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("189.62");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	189.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$30.3125419447$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			62.36
Character	$\chi$	$=$	189.62
Dual form			189.6.o.a.125.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(8.40544 + 4.85288i) q^{2} +(31.1009 + 53.8683i) q^{4} +(-32.8857 - 56.9596i) q^{5} +(-3.05564 - 129.606i) q^{7} +293.131i q^{8} -638.361i q^{10} +(298.785 + 172.504i) q^{11} +(14.0132 - 8.09053i) q^{13} +(603.277 - 1104.22i) q^{14} +(-427.303 + 740.110i) q^{16} +1129.50 q^{17} -1621.87i q^{19} +(2045.55 - 3542.99i) q^{20} +(1674.28 + 2899.93i) q^{22} +(3737.69 - 2157.95i) q^{23} +(-600.433 + 1039.98i) q^{25} +157.050 q^{26} +(6886.61 - 4195.46i) q^{28} +(-3445.90 - 1989.49i) q^{29} +(5813.45 - 3356.40i) q^{31} +(940.164 - 542.804i) q^{32} +(9493.94 + 5481.33i) q^{34} +(-7281.81 + 4436.22i) q^{35} -12392.6 q^{37} +(7870.73 - 13632.5i) q^{38} +(16696.7 - 9639.82i) q^{40} +(5829.95 + 10097.8i) q^{41} +(-5962.62 + 10327.6i) q^{43} +21460.1i q^{44} +41889.2 q^{46} +(-5039.23 + 8728.21i) q^{47} +(-16788.3 + 792.057i) q^{49} +(-10093.8 + 5827.65i) q^{50} +(871.647 + 503.246i) q^{52} +6140.70i q^{53} -22691.6i q^{55} +(37991.5 - 895.704i) q^{56} +(-19309.5 - 33445.1i) q^{58} +(-10009.5 - 17337.0i) q^{59} +(-42680.8 - 24641.8i) q^{61} +65152.8 q^{62} +37884.0 q^{64} +(-921.668 - 532.125i) q^{65} +(8329.89 + 14427.8i) q^{67} +(35128.5 + 60844.3i) q^{68} +(-82735.2 + 1950.60i) q^{70} -8769.01i q^{71} +25373.2i q^{73} +(-104165. - 60139.6i) q^{74} +(87367.3 - 50441.5i) q^{76} +(21444.5 - 39251.4i) q^{77} +(28435.6 - 49251.9i) q^{79} +56208.5 q^{80} +113168. i q^{82} +(-60102.0 + 104100. i) q^{83} +(-37144.3 - 64335.9i) q^{85} +(-100237. + 57871.7i) q^{86} +(-50566.2 + 87583.2i) q^{88} +72575.9 q^{89} +(-1091.40 - 1791.47i) q^{91} +(232491. + 134229. i) q^{92} +(-84713.9 + 48909.6i) q^{94} +(-92380.9 + 53336.2i) q^{95} +(78010.1 + 45039.1i) q^{97} +(-144957. - 74814.2i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 6 q^{2} + 574 q^{4} - 30 q^{7} + 576 q^{11} - 1392 q^{14} - 8130 q^{16} - 130 q^{22} + 8112 q^{23} - 18752 q^{25} - 1732 q^{28} + 35826 q^{29} + 1092 q^{32} + 10308 q^{37} + 18486 q^{43} - 38056 q^{46}+ \cdots + 950328 q^{95}+O(q^{100}) $ 76 * q + 6 * q^2 + 574 * q^4 - 30 * q^7 + 576 * q^11 - 1392 * q^14 - 8130 * q^16 - 130 * q^22 + 8112 * q^23 - 18752 * q^25 - 1732 * q^28 + 35826 * q^29 + 1092 * q^32 + 10308 * q^37 + 18486 * q^43 - 38056 * q^46 + 7948 * q^49 - 76104 * q^50 - 164652 * q^56 + 9902 * q^58 - 192648 * q^64 - 12666 * q^65 + 1244 * q^67 + 33024 * q^70 - 356496 * q^74 + 16458 * q^77 + 168074 * q^79 + 2598 * q^85 - 543300 * q^86 + 69694 * q^88 + 139368 * q^91 + 211794 * q^92 + 950328 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	8.40544	+	4.85288i	1.48589	+	0.857876i	0.999871	−	0.0160747i	$-0.00511696\pi$
$2$	8.40544	+	4.85288i	1.48589	+	0.857876i	0.486014	+	0.873951i	$0.338450\pi$
$3$		0			0
$3$		0			0
$4$	31.1009	+	53.8683i	0.971903	+	1.68339i
$5$	−32.8857	−	56.9596i	−0.588276	−	1.01892i	−0.994458	−	0.105132i	$-0.966473\pi$
$5$	−32.8857	−	56.9596i	−0.588276	−	1.01892i	0.406182	−	0.913792i	$-0.366860\pi$
$6$		0			0
$7$	−3.05564	−	129.606i	−0.0235699	−	0.999722i
$7$	−3.05564	−	129.606i	−0.0235699	−	0.999722i
$8$			293.131i			1.61934i
$9$		0			0
$10$		−	638.361i		−	2.01867i
$11$	298.785	+	172.504i	0.744521	+	0.429849i	0.823711	−	0.567010i	$-0.191900\pi$
$11$	298.785	+	172.504i	0.744521	+	0.429849i	−0.0791899	+	0.996860i	$0.525233\pi$
$12$		0			0
$13$	14.0132	−	8.09053i	0.0229974	−	0.0132776i	−0.488457	−	0.872588i	$-0.662440\pi$
$13$	14.0132	−	8.09053i	0.0229974	−	0.0132776i	0.511455	+	0.859310i	$0.329107\pi$
$14$	603.277	−	1104.22i	0.822616	−	1.50569i
$15$		0			0
$16$	−427.303	+	740.110i	−0.417288	+	0.722764i
$17$	1129.50			0.947903			0.473951	−	0.880551i	$-0.342827\pi$
$17$	1129.50			0.947903			0.473951	+	0.880551i	$0.342827\pi$
$18$		0			0
$19$		−	1621.87i		−	1.03070i	−0.856981	−	0.515349i	$-0.827662\pi$
$19$		−	1621.87i		−	1.03070i	0.856981	−	0.515349i	$-0.172338\pi$
$20$	2045.55	−	3542.99i	1.14350	−	1.98059i
$21$		0			0
$22$	1674.28	+	2899.93i	0.737515	+	1.27741i
$23$	3737.69	−	2157.95i	1.47327	−	0.850594i	0.473725	−	0.880673i	$-0.342909\pi$
$23$	3737.69	−	2157.95i	1.47327	−	0.850594i	0.999548	+	0.0300784i	$0.00957570\pi$
$24$		0			0
$25$	−600.433	+	1039.98i	−0.192138	+	0.332794i
$26$	157.050			0.0455621
$27$		0			0
$28$	6886.61	−	4195.46i	1.66001	−	1.01131i
$29$	−3445.90	−	1989.49i	−0.760866	−	0.439286i	0.0687408	−	0.997635i	$-0.478102\pi$
$29$	−3445.90	−	1989.49i	−0.760866	−	0.439286i	−0.829606	+	0.558349i	$0.811435\pi$
$30$		0			0
$31$	5813.45	−	3356.40i	1.08650	−	0.627291i	0.153857	−	0.988093i	$-0.450830\pi$
$31$	5813.45	−	3356.40i	1.08650	−	0.627291i	0.932642	+	0.360802i	$0.117497\pi$
$32$	940.164	−	542.804i	0.162304	−	0.0937061i
$33$		0			0
$34$	9493.94	+	5481.33i	1.40847	+	0.813183i
$35$	−7281.81	+	4436.22i	−1.00478	+	0.612129i
$36$		0			0
$37$	−12392.6			−1.48819			−0.744093	−	0.668077i	$-0.767118\pi$
$37$	−12392.6			−1.48819			−0.744093	+	0.668077i	$0.767118\pi$
$38$	7870.73	−	13632.5i	0.884211	−	1.53150i
$39$		0			0
$40$	16696.7	−	9639.82i	1.64998	−	0.952618i
$41$	5829.95	+	10097.8i	0.541633	+	0.938135i	0.998811	+	0.0487601i	$0.0155270\pi$
$41$	5829.95	+	10097.8i	0.541633	+	0.938135i	−0.457178	+	0.889375i	$0.651140\pi$
$42$		0			0
$43$	−5962.62	+	10327.6i	−0.491774	+	0.851778i	−0.999955	−	0.00947224i	$-0.996985\pi$
$43$	−5962.62	+	10327.6i	−0.491774	+	0.851778i	0.508181	+	0.861250i	$0.330318\pi$
$44$			21460.1i			1.67109i
$45$		0			0
$46$	41889.2			2.91882
$47$	−5039.23	+	8728.21i	−0.332751	+	0.576342i	−0.983050	−	0.183336i	$-0.941310\pi$
$47$	−5039.23	+	8728.21i	−0.332751	+	0.576342i	0.650299	+	0.759678i	$0.274644\pi$
$48$		0			0
$49$	−16788.3	+	792.057i	−0.998889	+	0.0471266i
$50$	−10093.8	+	5827.65i	−0.570991	+	0.329662i
$51$		0			0
$52$	871.647	+	503.246i	0.0447026	+	0.0258090i
$53$			6140.70i			0.300281i	0.988665	+	0.150141i	$0.0479726\pi$
$53$			6140.70i			0.300281i	−0.988665	+	0.150141i	$0.952027\pi$
$54$		0			0
$55$		−	22691.6i		−	1.01148i
$56$	37991.5	−	895.704i	1.61889	−	0.0381675i
$57$		0			0
$58$	−19309.5	−	33445.1i	−0.753706	−	1.30546i
$59$	−10009.5	−	17337.0i	−0.374354	−	0.648400i	0.615876	−	0.787843i	$-0.288802\pi$
$59$	−10009.5	−	17337.0i	−0.374354	−	0.648400i	−0.990230	+	0.139443i	$0.955469\pi$
$60$		0			0
$61$	−42680.8	−	24641.8i	−1.46862	−	0.847906i	−0.469234	−	0.883074i	$-0.655470\pi$
$61$	−42680.8	−	24641.8i	−1.46862	−	0.847906i	−0.999381	+	0.0351680i	$0.988803\pi$
$62$	65152.8			2.15255
$63$		0			0
$64$	37884.0			1.15613
$65$	−921.668	−	532.125i	−0.0270577	−	0.0156218i
$66$		0			0
$67$	8329.89	+	14427.8i	0.226700	+	0.392656i	0.956828	−	0.290654i	$-0.0938729\pi$
$67$	8329.89	+	14427.8i	0.226700	+	0.392656i	−0.730128	+	0.683310i	$0.760540\pi$
$68$	35128.5	+	60844.3i	0.921270	+	1.59569i
$69$		0			0
$70$	−82735.2	+	1950.60i	−2.01811	+	0.0475798i
$71$		−	8769.01i		−	0.206445i	−0.994658	−	0.103223i	$-0.967085\pi$
$71$		−	8769.01i		−	0.206445i	0.994658	−	0.103223i	$-0.0329154\pi$
$72$		0			0
$73$			25373.2i			0.557273i	0.960397	+	0.278636i	$0.0898825\pi$
$73$			25373.2i			0.557273i	−0.960397	+	0.278636i	$0.910118\pi$
$74$	−104165.	−	60139.6i	−2.21127	−	1.27668i
$75$		0			0
$76$	87367.3	−	50441.5i	1.73506	−	1.00174i
$77$	21444.5	−	39251.4i	0.412182	−	0.754446i
$78$		0			0
$79$	28435.6	−	49251.9i	0.512619	−	0.887882i	−0.487274	−	0.873249i	$-0.662009\pi$
$79$	28435.6	−	49251.9i	0.512619	−	0.887882i	0.999893	−	0.0146326i	$-0.00465787\pi$
$80$	56208.5			0.981922
$81$		0			0
$82$			113168.i			1.85862i
$83$	−60102.0	+	104100.i	−0.957621	+	1.65865i	−0.229369	+	0.973340i	$0.573666\pi$
$83$	−60102.0	+	104100.i	−0.957621	+	1.65865i	−0.728252	+	0.685309i	$0.759667\pi$
$84$		0			0
$85$	−37144.3	−	64335.9i	−0.557629	−	0.965842i
$86$	−100237.	+	57871.7i	−1.46144	+	0.843763i
$87$		0			0
$88$	−50566.2	+	87583.2i	−0.696071	+	1.20563i
$89$	72575.9			0.971219			0.485610	−	0.874176i	$-0.338598\pi$
$89$	72575.9			0.971219			0.485610	+	0.874176i	$0.338598\pi$
$90$		0			0
$91$	−1091.40	−	1791.47i	−0.0138159	−	0.0226781i
$92$	232491.	+	134229.i	2.86376	+	1.65339i
$93$		0			0
$94$	−84713.9	+	48909.6i	−0.988860	+	0.570919i
$95$	−92380.9	+	53336.2i	−1.05020	+	0.606335i
$96$		0			0
$97$	78010.1	+	45039.1i	0.841824	+	0.486027i	0.857884	−	0.513844i	$-0.171779\pi$
$97$	78010.1	+	45039.1i	0.841824	+	0.486027i	−0.0160597	+	0.999871i	$0.505112\pi$
$98$	−144957.	−	74814.2i	−1.52466	−	0.786898i
$99$		0			0
$100$	−74696.0			−0.746960
$101$	−75246.2	+	130330.i	−0.733975	+	1.27128i	0.221197	+	0.975229i	$0.429004\pi$
$101$	−75246.2	+	130330.i	−0.733975	+	1.27128i	−0.955172	+	0.296053i	$0.904330\pi$
$102$		0			0
$103$	59960.7	−	34618.3i	0.556896	−	0.321524i	−0.195003	−	0.980803i	$-0.562472\pi$
$103$	59960.7	−	34618.3i	0.556896	−	0.321524i	0.751899	+	0.659279i	$0.229138\pi$
$104$	2371.59	+	4107.71i	0.0215009	+	0.0372406i
$105$		0			0
$106$	−29800.1	+	51615.2i	−0.257604	+	0.446183i
$107$		−	109784.i		−	0.927004i	−0.886096	−	0.463502i	$-0.846593\pi$
$107$		−	109784.i		−	0.927004i	0.886096	−	0.463502i	$-0.153407\pi$
$108$		0			0
$109$	94345.2			0.760595			0.380297	−	0.924864i	$-0.375822\pi$
$109$	94345.2			0.760595			0.380297	+	0.924864i	$0.375822\pi$
$110$	110119.	−	190732.i	0.867725	−	1.50294i
$111$		0			0
$112$	97228.2	+	53119.4i	0.732398	+	0.400136i
$113$	52826.5	−	30499.4i	0.389185	−	0.224696i	−0.292622	−	0.956228i	$-0.594528\pi$
$113$	52826.5	−	30499.4i	0.389185	−	0.224696i	0.681807	+	0.731532i	$0.261194\pi$
$114$		0			0
$115$	−245832.	−	141931.i	−1.73338	−	1.00077i
$116$		−	247500.i		−	1.70777i
$117$		0			0
$118$		−	194300.i		−	1.28460i
$119$	−3451.34	−	146390.i	−0.0223419	−	0.947639i
$120$		0			0
$121$	−21010.6	−	36391.4i	−0.130459	−	0.225962i
$122$	−239167.	−	414250.i	−1.45480	−	2.51978i
$123$		0			0
$124$	361607.	+	208774.i	2.11194	+	1.21933i
$125$	−126553.			−0.724431
$126$		0			0
$127$	247481.			1.36155			0.680774	−	0.732493i	$-0.261644\pi$
$127$	247481.			1.36155			0.680774	+	0.732493i	$0.261644\pi$
$128$	288346.	+	166477.i	1.55557	+	0.898109i
$129$		0			0
$130$	−5164.68	−	8945.49i	−0.0268031	−	0.0464243i
$131$	93216.0	+	161455.i	0.474583	+	0.822002i	0.999576	−	0.0291044i	$-0.00926552\pi$
$131$	93216.0	+	161455.i	0.474583	+	0.822002i	−0.524993	+	0.851106i	$0.675932\pi$
$132$		0			0
$133$	−210203.	+	4955.84i	−1.03041	+	0.0242934i
$134$			161696.i			0.777923i
$135$		0			0
$136$			331092.i			1.53497i
$137$	172340.	+	99500.6i	0.784485	+	0.452923i	0.838017	−	0.545643i	$-0.183715\pi$
$137$	172340.	+	99500.6i	0.784485	+	0.452923i	−0.0535323	+	0.998566i	$0.517048\pi$
$138$		0			0
$139$	256366.	−	148013.i	1.12544	−	0.649774i	0.182657	−	0.983177i	$-0.441530\pi$
$139$	256366.	−	148013.i	1.12544	−	0.649774i	0.942785	+	0.333403i	$0.108197\pi$
$140$	−465443.	−	254289.i	−2.00699	−	1.09650i
$141$		0			0
$142$	42554.9	−	73707.3i	0.177104	−	0.306754i
$143$	5582.58			0.0228294
$144$		0			0
$145$			261703.i			1.03369i
$146$	−123133.	+	213273.i	−0.478071	+	0.828044i
$147$		0			0
$148$	−385420.	−	667567.i	−1.44637	−	2.50519i
$149$	−157150.	+	90730.9i	−0.579896	+	0.334803i	−0.761092	−	0.648644i	$-0.775336\pi$
$149$	−157150.	+	90730.9i	−0.579896	+	0.334803i	0.181196	+	0.983447i	$0.442003\pi$
$150$		0			0
$151$	17230.7	−	29844.5i	0.0614980	−	0.106518i	−0.833637	−	0.552312i	$-0.813746\pi$
$151$	17230.7	−	29844.5i	0.0614980	−	0.106518i	0.895135	+	0.445795i	$0.147079\pi$
$152$	475420.			1.66905
$153$		0			0
$154$	370732.	−	225857.i	1.25968	−	0.767419i
$155$	−382358.	−	220755.i	−1.27832	−	0.738041i
$156$		0			0
$157$	−128045.	+	73926.7i	−0.414584	+	0.239360i	−0.692757	−	0.721171i	$-0.743604\pi$
$157$	−128045.	+	73926.7i	−0.414584	+	0.239360i	0.278173	+	0.960531i	$0.410271\pi$
$158$	478027.	−	275989.i	1.52338	−	0.879527i
$159$		0			0
$160$	−61835.8	−	35700.9i	−0.190959	−	0.110250i
$161$	−291104.	−	477832.i	−0.885083	−	1.45281i
$162$		0			0
$163$	−358664.			−1.05735			−0.528675	−	0.848824i	$-0.677311\pi$
$163$	−358664.			−1.05735			−0.528675	+	0.848824i	$0.677311\pi$
$164$	−362633.	+	628099.i	−1.05283	+	1.82355i
$165$		0			0
$166$	−1.01037e6	+	583336.i	−2.84583	+	1.64304i
$167$	−69945.8	−	121150.i	−0.194075	−	0.336148i	0.752522	−	0.658567i	$-0.228837\pi$
$167$	−69945.8	−	121150.i	−0.194075	−	0.336148i	−0.946597	+	0.322419i	$0.895504\pi$
$168$		0			0
$169$	−185516.	+	321322.i	−0.499647	+	0.865415i
$170$		−	721028.i		−	1.91351i
$171$		0			0
$172$	−741771.			−1.91183
$173$	−171808.	+	297580.i	−0.436443	+	0.755942i	−0.997412	−	0.0718951i	$-0.977095\pi$
$173$	−171808.	+	297580.i	−0.436443	+	0.755942i	0.560969	+	0.827837i	$0.310429\pi$
$174$		0			0
$175$	136622.	+	74641.7i	0.337230	+	0.184241i
$176$	−255343.	+	147422.i	−0.621359	+	0.358742i
$177$		0			0
$178$	610032.	+	352202.i	1.44312	+	0.833186i
$179$			726867.i			1.69560i	0.530320	+	0.847798i	$0.322072\pi$
$179$			726867.i			1.69560i	−0.530320	+	0.847798i	$0.677928\pi$
$180$		0			0
$181$		−	238798.i		−	0.541793i	−0.962608	−	0.270897i	$-0.912680\pi$
$181$		−	238798.i		−	0.541793i	0.962608	−	0.270897i	$-0.0873201\pi$
$182$	−479.887	−	20354.5i	−0.00107389	−	0.0455494i
$183$		0			0
$184$	632564.	+	1.09563e6i	1.37740	+	2.38573i
$185$	407538.	+	705876.i	0.875464	+	1.51635i
$186$		0			0
$187$	337477.	+	194843.i	0.705733	+	0.407455i
$188$	−626898.			−1.29361
$189$		0			0
$190$	−1.03534e6			−2.08064
$191$	−131564.	−	75958.3i	−0.260947	−	0.150658i	0.363819	−	0.931470i	$-0.381473\pi$
$191$	−131564.	−	75958.3i	−0.260947	−	0.150658i	−0.624767	+	0.780812i	$0.714806\pi$
$192$		0			0
$193$	138137.	+	239260.i	0.266942	+	0.462357i	0.968071	−	0.250678i	$-0.0806535\pi$
$193$	138137.	+	239260.i	0.266942	+	0.462357i	−0.701129	+	0.713035i	$0.747320\pi$
$194$	437139.	+	757147.i	0.833903	+	1.44436i
$195$		0			0
$196$	−564799.	−	879725.i	−1.05016	−	1.63571i
$197$			148825.i			0.273219i	0.990625	+	0.136609i	$0.0436205\pi$
$197$			148825.i			0.273219i	−0.990625	+	0.136609i	$0.956379\pi$
$198$		0			0
$199$			507404.i			0.908282i	0.890930	+	0.454141i	$0.150054\pi$
$199$			507404.i			0.908282i	−0.890930	+	0.454141i	$0.849946\pi$
$200$	−304851.	−	176006.i	−0.538905	−	0.311137i
$201$		0			0
$202$	−1.26495e6	+	730322.i	−2.18120	+	1.25932i
$203$	−247320.	+	452688.i	−0.421230	+	0.771008i
$204$		0			0
$205$	383443.	−	664143.i	0.637260	−	1.10377i
$206$	671995.			1.10331
$207$		0			0
$208$			13828.4i			0.0221623i
$209$	279778.	−	484589.i	0.443045	−	0.767376i
$210$		0			0
$211$	15175.5	+	26284.7i	0.0234658	+	0.0406440i	0.877520	−	0.479540i	$-0.159197\pi$
$211$	15175.5	+	26284.7i	0.0234658	+	0.0406440i	−0.854054	+	0.520184i	$0.825863\pi$
$212$	−330789.	+	190981.i	−0.505489	+	0.291844i
$213$		0			0
$214$	532771.	−	922786.i	0.795254	−	1.37742i
$215$	784338.			1.15720
$216$		0			0
$217$	−452772.	−	743201.i	−0.652725	−	1.07141i
$218$	793012.	+	457846.i	1.13016	+	0.652496i
$219$		0			0
$220$	1.22236e6	−	705728.i	1.70271	−	0.983061i
$221$	15827.9	−	9138.26i	0.0217993	−	0.0125859i
$222$		0			0
$223$	−208301.	−	120262.i	−0.280497	−	0.161945i	0.353151	−	0.935566i	$-0.385110\pi$
$223$	−208301.	−	120262.i	−0.280497	−	0.161945i	−0.633648	+	0.773621i	$0.718443\pi$
$224$	−73223.3	−	120192.i	−0.0975055	−	0.160050i
$225$		0			0
$226$	592039.			0.771045
$227$	415474.	−	719621.i	0.535154	−	0.926914i	−0.464002	−	0.885834i	$-0.653587\pi$
$227$	415474.	−	719621.i	0.535154	−	0.926914i	0.999156	−	0.0410797i	$-0.0130798\pi$
$228$		0			0
$229$	666915.	−	385043.i	0.840391	−	0.485200i	−0.0170059	−	0.999855i	$-0.505413\pi$
$229$	666915.	−	385043.i	0.840391	−	0.485200i	0.857397	+	0.514655i	$0.172080\pi$
$230$	−1.37755e6	−	2.38599e6i	−1.71707	−	2.97406i
$231$		0			0
$232$	583183.	−	1.01010e6i	0.711352	−	1.23210i
$233$			793987.i			0.958128i	0.877780	+	0.479064i	$0.159024\pi$
$233$			793987.i			0.958128i	−0.877780	+	0.479064i	$0.840976\pi$
$234$		0			0
$235$	662874.			0.782999
$236$	622609.	−	1.07839e6i	0.727671	−	1.26036i
$237$		0			0
$238$	681402.	−	1.24722e6i	0.779760	−	1.42725i
$239$	75094.8	−	43356.0i	0.0850384	−	0.0490969i	−0.456878	−	0.889529i	$-0.651032\pi$
$239$	75094.8	−	43356.0i	0.0850384	−	0.0490969i	0.541916	+	0.840433i	$0.317699\pi$
$240$		0			0
$241$	1.15078e6	+	664401.i	1.27629	+	0.736865i	0.976164	−	0.217035i	$-0.0696386\pi$
$241$	1.15078e6	+	664401.i	1.27629	+	0.736865i	0.300124	+	0.953900i	$0.402972\pi$
$242$		−	407847.i		−	0.447671i
$243$		0			0
$244$		−	3.06553e6i		−	3.29633i
$245$	597210.	+	930209.i	0.635641	+	0.990069i
$246$		0			0
$247$	−13121.8	−	22727.6i	−0.0136852	−	0.0237034i
$248$	983865.	+	1.70410e6i	1.01580	+	1.75941i
$249$		0			0
$250$	−1.06373e6	−	614146.i	−1.07642	−	0.621472i
$251$	−861013.			−0.862631			−0.431316	−	0.902201i	$-0.641950\pi$
$251$	−861013.			−0.862631			−0.431316	+	0.902201i	$0.641950\pi$
$252$		0			0
$253$	1.48902e6			1.46251
$254$	2.08019e6	+	1.20100e6i	2.02310	+	1.16804i
$255$		0			0
$256$	1.00964e6	+	1.74875e6i	0.962868	+	1.66774i
$257$	−390545.	−	676444.i	−0.368840	−	0.638850i	0.620544	−	0.784171i	$-0.286912\pi$
$257$	−390545.	−	676444.i	−0.368840	−	0.638850i	−0.989384	+	0.145322i	$0.953578\pi$
$258$		0			0
$259$	37867.2	+	1.60615e6i	0.0350763	+	1.48777i
$260$		−	66198.3i		−	0.0607314i
$261$		0			0
$262$			1.80946e6i			1.62853i
$263$	−944052.	−	545049.i	−0.841602	−	0.485899i	0.0162067	−	0.999869i	$-0.494841\pi$
$263$	−944052.	−	545049.i	−0.841602	−	0.485899i	−0.857808	+	0.513970i	$0.828174\pi$
$264$		0			0
$265$	349772.	−	201941.i	0.305964	−	0.176648i
$266$	−1.79090e6	−	978436.i	−1.55191	−	0.847868i
$267$		0			0
$268$	−518134.	+	897434.i	−0.440661	+	0.763248i
$269$	1.23916e6			1.04411			0.522057	−	0.852911i	$-0.325165\pi$
$269$	1.23916e6			1.04411			0.522057	+	0.852911i	$0.325165\pi$
$270$		0			0
$271$			1.50729e6i			1.24673i	0.781931	+	0.623365i	$0.214235\pi$
$271$			1.50729e6i			1.24673i	−0.781931	+	0.623365i	$0.785765\pi$
$272$	−482638.	+	835954.i	−0.395548	+	0.685110i
$273$		0			0
$274$	965729.	+	1.67269e6i	0.777103	+	1.34598i
$275$	−358800.	+	207153.i	−0.286102	+	0.165181i
$276$		0			0
$277$	−612568.	+	1.06100e6i	−0.479683	+	0.830836i	−0.999728	−	0.0233029i	$-0.992582\pi$
$277$	−612568.	+	1.06100e6i	−0.479683	+	0.830836i	0.520045	+	0.854139i	$0.325915\pi$
$278$	2.87315e6			2.22970
$279$		0			0
$280$	−1.30040e6	−	2.13453e6i	−0.991243	−	1.62707i
$281$	−825466.	−	476583.i	−0.623639	−	0.360058i	0.154645	−	0.987970i	$-0.450576\pi$
$281$	−825466.	−	476583.i	−0.623639	−	0.360058i	−0.778284	+	0.627912i	$0.783910\pi$
$282$		0			0
$283$	1.21115e6	−	699259.i	0.898944	−	0.519005i	0.0220864	−	0.999756i	$-0.492969\pi$
$283$	1.21115e6	−	699259.i	0.898944	−	0.519005i	0.876857	+	0.480751i	$0.159636\pi$
$284$	472372.	−	272724.i	0.347527	−	0.200645i
$285$		0			0
$286$	46924.0	+	27091.6i	0.0339219	+	0.0195848i
$287$	1.29091e6	−	786450.i	0.925109	−	0.563594i
$288$		0			0
$289$	−144087.			−0.101480
$290$	−1.27001e6	+	2.19973e6i	−0.886775	+	1.53594i
$291$		0			0
$292$	−1.36681e6	+	789129.i	−0.938105	+	0.541615i
$293$	50755.0	+	87910.3i	0.0345390	+	0.0598234i	0.882778	−	0.469790i	$-0.155670\pi$
$293$	50755.0	+	87910.3i	0.0345390	+	0.0598234i	−0.848239	+	0.529613i	$0.822337\pi$
$294$		0			0
$295$	−658338.	+	1.14027e6i	−0.440447	+	0.762877i
$296$		−	3.63265e6i		−	2.40987i
$297$		0			0
$298$	−1.76122e6			−1.14888
$299$	34918.0	−	60479.7i	0.0225877	−	0.0391230i
$300$		0			0
$301$	1.35673e6	+	741233.i	0.863133	+	0.471561i
$302$	289663.	−	167237.i	0.182758	−	0.105515i
$303$		0			0
$304$	1.20036e6	+	693028.i	0.744951	+	0.430097i
$305$			3.24144e6i			1.99521i
$306$		0			0
$307$		−	402643.i		−	0.243823i	−0.992541	−	0.121911i	$-0.961098\pi$
$307$		−	402643.i		−	0.243823i	0.992541	−	0.121911i	$-0.0389024\pi$
$308$	2.78135e6	−	65574.2i	1.67062	−	0.0393873i
$309$		0			0
$310$	−2.14259e6	−	3.71108e6i	−1.26630	−	2.19329i
$311$	788811.	+	1.36626e6i	0.462458	+	0.801000i	0.999083	−	0.0428205i	$-0.0136344\pi$
$311$	788811.	+	1.36626e6i	0.462458	+	0.801000i	−0.536625	+	0.843821i	$0.680301\pi$
$312$		0			0
$313$	649509.	+	374994.i	0.374735	+	0.216353i	0.675525	−	0.737337i	$-0.263917\pi$
$313$	649509.	+	374994.i	0.374735	+	0.216353i	−0.300790	+	0.953690i	$0.597250\pi$
$314$	−1.43503e6			−0.821366
$315$		0			0
$316$	3.53749e6			1.99286
$317$	2.01695e6	+	1.16449e6i	1.12732	+	0.650859i	0.943260	−	0.332056i	$-0.107742\pi$
$317$	2.01695e6	+	1.16449e6i	1.12732	+	0.650859i	0.184061	+	0.982915i	$0.441076\pi$
$318$		0			0
$319$	−686389.	−	1.18886e6i	−0.377654	−	0.654115i
$320$	−1.24584e6	−	2.15786e6i	−0.680123	−	1.17801i
$321$		0			0
$322$	−127998.	−	5.42908e6i	−0.0687961	−	2.91801i
$323$		−	1.83190e6i		−	0.977001i
$324$		0			0
$325$			19431.3i			0.0102045i
$326$	−3.01473e6	−	1.74055e6i	−1.57110	−	0.907076i
$327$		0			0
$328$	−2.95997e6	+	1.70894e6i	−1.51916	+	0.877086i
$329$	1.14662e6	+	626443.i	0.584025	+	0.319075i
$330$		0			0
$331$	−1.42556e6	+	2.46914e6i	−0.715180	+	1.23873i	0.247710	+	0.968834i	$0.420322\pi$
$331$	−1.42556e6	+	2.46914e6i	−0.715180	+	1.23873i	−0.962890	+	0.269894i	$0.913011\pi$
$332$	−7.47690e6			−3.72286
$333$		0			0
$334$		−	1.35775e6i		−	0.665970i
$335$	547868.	−	948934.i	0.266725	−	0.461981i
$336$		0			0
$337$	−1.11190e6	−	1.92586e6i	−0.533322	−	0.923741i	−0.999243	−	0.0389145i	$-0.987610\pi$
$337$	−1.11190e6	−	1.92586e6i	−0.533322	−	0.923741i	0.465920	−	0.884827i	$-0.345723\pi$
$338$	−3.11868e6	+	1.80057e6i	−1.48484	+	0.857271i
$339$		0			0
$340$	2.31044e6	−	4.00181e6i	1.08392	−	1.87741i
$341$	2.31596e6			1.07856
$342$		0			0
$343$	153954.	+	2.17344e6i	0.0706572	+	0.997501i
$344$	−3.02733e6	−	1.74783e6i	−1.37932	−	0.796349i
$345$		0			0
$346$	−2.88824e6	+	1.66753e6i	−1.29701	+	0.748828i
$347$	2.34080e6	−	1.35146e6i	1.04361	−	0.602531i	0.122759	−	0.992436i	$-0.460826\pi$
$347$	2.34080e6	−	1.35146e6i	1.04361	−	0.602531i	0.920855	+	0.389906i	$0.127492\pi$
$348$		0			0
$349$	922979.	+	532882.i	0.405628	+	0.234190i	0.688910	−	0.724847i	$-0.258090\pi$
$349$	922979.	+	532882.i	0.405628	+	0.234190i	−0.283281	+	0.959037i	$0.591423\pi$
$350$	786141.	+	1.29041e6i	0.343029	+	0.563063i
$351$		0			0
$352$	374542.			0.161118
$353$	−925198.	+	1.60249e6i	−0.395183	+	0.684476i	−0.993124	−	0.117063i	$-0.962652\pi$
$353$	−925198.	+	1.60249e6i	−0.395183	+	0.684476i	0.597942	+	0.801540i	$0.295985\pi$
$354$		0			0
$355$	−499479.	+	288375.i	−0.210352	+	0.121447i
$356$	2.25718e6	+	3.90954e6i	0.943931	+	1.63494i
$357$		0			0
$358$	−3.52740e6	+	6.10963e6i	−1.45461	+	2.51946i
$359$		−	55649.4i		−	0.0227889i	−0.999935	−	0.0113945i	$-0.996373\pi$
$359$		−	55649.4i		−	0.0227889i	0.999935	−	0.0113945i	$-0.00362705\pi$
$360$		0			0
$361$	−154353.			−0.0623371
$362$	1.15886e6	−	2.00720e6i	0.464791	−	0.805042i
$363$		0			0
$364$	62560.1	−	114508.i	0.0247482	−	0.0452985i
$365$	1.44525e6	−	834414.i	0.567819	−	0.327831i
$366$		0			0
$367$	−2.31805e6	−	1.33833e6i	−0.898377	−	0.518678i	−0.0217036	−	0.999764i	$-0.506909\pi$
$367$	−2.31805e6	−	1.33833e6i	−0.898377	−	0.518678i	−0.876673	+	0.481086i	$0.840242\pi$
$368$			3.68840e6i			1.41977i
$369$		0			0
$370$			7.91093e6i			3.00416i
$371$	795870.	−	18763.8i	0.300198	−	0.00707758i
$372$		0			0
$373$	−2.23379e6	−	3.86904e6i	−0.831325	−	1.43990i	−0.896988	−	0.442056i	$-0.854249\pi$
$373$	−2.23379e6	−	3.86904e6i	−0.831325	−	1.43990i	0.0656625	−	0.997842i	$-0.479084\pi$
$374$	1.89110e6	+	3.27547e6i	0.699092	+	1.21086i
$375$		0			0
$376$	−2.55851e6	−	1.47716e6i	−0.933292	−	0.538836i
$377$	−64384.2			−0.0233306
$378$		0			0
$379$	−215079.			−0.0769130			−0.0384565	−	0.999260i	$-0.512244\pi$
$379$	−215079.			−0.0769130			−0.0384565	+	0.999260i	$0.512244\pi$
$380$	−5.74626e6	−	3.31760e6i	−2.04139	−	1.17860i
$381$		0			0
$382$	−737233.	−	1.27693e6i	−0.258492	−	0.447721i
$383$	348342.	+	603346.i	0.121341	+	0.210170i	0.920297	−	0.391221i	$-0.127947\pi$
$383$	348342.	+	603346.i	0.121341	+	0.210170i	−0.798955	+	0.601390i	$0.794614\pi$
$384$		0			0
$385$	−2.94096e6	+	69337.2i	−1.01120	+	0.0238405i
$386$			2.68145e6i			0.916012i
$387$		0			0
$388$			5.60303e6i			1.88949i
$389$	−234067.	−	135138.i	−0.0784270	−	0.0452798i	0.460274	−	0.887777i	$-0.347751\pi$
$389$	−234067.	−	135138.i	−0.0784270	−	0.0452798i	−0.538701	+	0.842497i	$0.681085\pi$
$390$		0			0
$391$	4.22171e6	−	2.43741e6i	1.39652	−	0.806281i
$392$	−232177.	−	4.92118e6i	−0.0763139	−	1.61754i
$393$		0			0
$394$	−722231.	+	1.25094e6i	−0.234388	+	0.405972i
$395$	−3.74049e6			−1.20625
$396$		0			0
$397$		−	3.22623e6i		−	1.02735i	−0.857985	−	0.513675i	$-0.828284\pi$
$397$		−	3.22623e6i		−	1.02735i	0.857985	−	0.513675i	$-0.171716\pi$
$398$	−2.46237e6	+	4.26495e6i	−0.779194	+	1.34960i
$399$		0			0
$400$	−513133.	−	888772.i	−0.160354	−	0.277741i
$401$	−1.85817e6	+	1.07281e6i	−0.577064	+	0.333168i	−0.759966	−	0.649963i	$-0.774784\pi$
$401$	−1.85817e6	+	1.07281e6i	−0.577064	+	0.333168i	0.182902	+	0.983131i	$0.441451\pi$
$402$		0			0
$403$	54310.1	−	94067.8i	0.0166578	−	0.0288522i
$404$	−9.36090e6			−2.85341
$405$		0			0
$406$	−4.27568e6	+	2.60482e6i	−1.28733	+	0.784266i
$407$	−3.70271e6	−	2.13776e6i	−1.10798	−	0.639695i
$408$		0			0
$409$	−63844.0	+	36860.4i	−0.0188717	+	0.0108956i	−0.509406	−	0.860526i	$-0.670135\pi$
$409$	−63844.0	+	36860.4i	−0.0188717	+	0.0108956i	0.490534	+	0.871422i	$0.336802\pi$
$410$	6.44601e6	−	3.72161e6i	1.89379	−	1.09338i
$411$		0			0
$412$	3.72967e6	+	2.15332e6i	1.08250	+	0.624980i
$413$	−2.21638e6	+	1.35026e6i	−0.639396	+	0.389532i
$414$		0			0
$415$	7.90598e6			2.25338
$416$	8783.14	−	15212.9i	0.00248838	−	0.00431000i
$417$		0			0
$418$	4.70331e6	−	2.71546e6i	1.31663	−	0.760155i
$419$	1.84563e6	+	3.19672e6i	0.513581	+	0.889548i	0.999876	+	0.0157535i	$0.00501469\pi$
$419$	1.84563e6	+	3.19672e6i	0.513581	+	0.889548i	−0.486295	+	0.873795i	$0.661652\pi$
$420$		0			0
$421$	−361478.	+	626099.i	−0.0993979	+	0.172162i	−0.911436	−	0.411443i	$-0.865025\pi$
$421$	−361478.	+	626099.i	−0.0993979	+	0.172162i	0.812038	+	0.583605i	$0.198358\pi$
$422$			294579.i			0.0805230i
$423$		0			0
$424$	−1.80003e6			−0.486256
$425$	−678188.	+	1.17466e6i	−0.182129	+	0.315456i
$426$		0			0
$427$	−3.06330e6	+	5.60698e6i	−0.813055	+	1.48819i
$428$	5.91390e6	−	3.41439e6i	1.56050	−	0.900957i
$429$		0			0
$430$	6.59271e6	+	3.80630e6i	1.71946	+	0.992732i
$431$			2.43942e6i			0.632548i	0.948668	+	0.316274i	$0.102432\pi$
$431$			2.43942e6i			0.632548i	−0.948668	+	0.316274i	$0.897568\pi$
$432$		0			0
$433$		−	105036.i		−	0.0269227i	−0.999909	−	0.0134614i	$-0.995715\pi$
$433$		−	105036.i		−	0.0269227i	0.999909	−	0.0134614i	$-0.00428501\pi$
$434$	−199083.	−	8.44417e6i	−0.0507353	−	2.15195i
$435$		0			0
$436$	2.93422e6	+	5.08222e6i	0.739224	+	1.28037i
$437$	−3.49991e6	−	6.06203e6i	−0.876705	−	1.51850i
$438$		0			0
$439$	−3.99365e6	−	2.30573e6i	−0.989028	−	0.571015i	−0.0840441	−	0.996462i	$-0.526784\pi$
$439$	−3.99365e6	−	2.30573e6i	−0.989028	−	0.571015i	−0.904983	+	0.425447i	$0.860117\pi$
$440$	6.65161e6			1.63793
$441$		0			0
$442$	177387.			0.0431884
$443$	−417658.	−	241135.i	−0.101114	−	0.0583782i	0.448590	−	0.893738i	$-0.351926\pi$
$443$	−417658.	−	241135.i	−0.101114	−	0.0583782i	−0.549704	+	0.835359i	$0.685260\pi$
$444$		0			0
$445$	−2.38671e6	−	4.13390e6i	−0.571346	−	0.989600i
$446$	−1.16724e6	−	2.02171e6i	−0.277858	−	0.481263i
$447$		0			0
$448$	−115760.	−	4.90999e6i	−0.0272498	−	1.15581i
$449$			1.59561e6i			0.373516i	0.982406	+	0.186758i	$0.0597981\pi$
$449$			1.59561e6i			0.373516i	−0.982406	+	0.186758i	$0.940202\pi$
$450$		0			0
$451$			4.02274e6i			0.931282i
$452$	3.28590e6	+	1.89712e6i	0.756499	+	0.436765i
$453$		0			0
$454$	6.98447e6	−	4.03249e6i	1.59035	−	0.918192i
$455$	−66150.2	+	121079.i	−0.0149797	+	0.0274184i
$456$		0			0
$457$	189929.	−	328967.i	0.0425404	−	0.0736821i	−0.843971	−	0.536388i	$-0.819788\pi$
$457$	189929.	−	328967.i	0.0425404	−	0.0736821i	0.886512	+	0.462706i	$0.153122\pi$
$458$	7.47428e6			1.66497
$459$		0			0
$460$		−	1.76568e7i		−	3.89060i
$461$	4.27982e6	−	7.41287e6i	0.937937	−	1.62455i	0.168626	−	0.985680i	$-0.446067\pi$
$461$	4.27982e6	−	7.41287e6i	0.937937	−	1.62455i	0.769311	−	0.638874i	$-0.220600\pi$
$462$		0			0
$463$	−1.99695e6	−	3.45882e6i	−0.432927	−	0.749851i	0.564197	−	0.825640i	$-0.309186\pi$
$463$	−1.99695e6	−	3.45882e6i	−0.432927	−	0.749851i	−0.997124	+	0.0757888i	$0.975853\pi$
$464$	2.94489e6	−	1.70023e6i	0.635000	−	0.366617i
$465$		0			0
$466$	−3.85313e6	+	6.67381e6i	−0.821956	+	1.42367i
$467$	−7.96510e6			−1.69005			−0.845024	−	0.534729i	$-0.820414\pi$
$467$	−7.96510e6			−1.69005			−0.845024	+	0.534729i	$0.820414\pi$
$468$		0			0
$469$	1.84447e6	−	1.12369e6i	0.387204	−	0.235892i
$470$	5.57174e6	+	3.21685e6i	1.16345	+	0.671716i
$471$		0			0
$472$	5.08201e6	−	2.93410e6i	1.04998	−	0.606205i
$473$	−3.56308e6	+	2.05715e6i	−0.732273	+	0.422778i
$474$		0			0
$475$	1.68671e6	+	973822.i	0.343009	+	0.198037i
$476$	7.77843e6	−	4.73877e6i	1.57353	−	0.958624i
$477$		0			0
$478$	841606.			0.168476
$479$	−1.65799e6	+	2.87173e6i	−0.330175	+	0.571879i	−0.982546	−	0.186020i	$-0.940441\pi$
$479$	−1.65799e6	+	2.87173e6i	−0.330175	+	0.571879i	0.652371	+	0.757900i	$0.273774\pi$
$480$		0			0
$481$	−173660.	+	100262.i	−0.0342244	+	0.0197595i
$482$	6.44852e6	+	1.11692e7i	1.26428	+	2.18979i
$483$		0			0
$484$	1.30690e6	−	2.26361e6i	0.253587	−	0.439226i
$485$		−	5.92457e6i		−	1.14367i
$486$		0			0
$487$	−5.66667e6			−1.08269			−0.541347	−	0.840799i	$-0.682085\pi$
$487$	−5.66667e6			−1.08269			−0.541347	+	0.840799i	$0.682085\pi$
$488$	7.22328e6	−	1.25111e7i	1.37305	−	2.37818i
$489$		0			0
$490$	505618.	+	1.07170e7i	0.0951332	+	2.01643i
$491$	−492580.	+	284391.i	−0.0922089	+	0.0532368i	−0.545395	−	0.838179i	$-0.683620\pi$
$491$	−492580.	+	284391.i	−0.0922089	+	0.0532368i	0.453187	+	0.891416i	$0.350287\pi$
$492$		0			0
$493$	−3.89215e6	−	2.24713e6i	−0.721227	−	0.416400i
$494$		−	254713.i		−	0.0469607i
$495$		0			0
$496$			5.73679e6i			1.04704i
$497$	−1.13651e6	+	26794.9i	−0.206388	+	0.00486588i
$498$		0			0
$499$	2.74494e6	+	4.75437e6i	0.493493	+	0.854755i	0.999972	−	0.00749763i	$-0.00238659\pi$
$499$	2.74494e6	+	4.75437e6i	0.493493	+	0.854755i	−0.506479	+	0.862252i	$0.669053\pi$
$500$	−3.93591e6	−	6.81719e6i	−0.704077	−	1.21950i
$501$		0			0
$502$	−7.23719e6	−	4.17839e6i	−1.28177	−	0.740031i
$503$	3.39621e6			0.598514			0.299257	−	0.954173i	$-0.403261\pi$
$503$	3.39621e6			0.598514			0.299257	+	0.954173i	$0.403261\pi$
$504$		0			0
$505$	9.89808e6			1.72712
$506$	1.25158e7	+	7.22603e6i	2.17312	+	1.25465i
$507$		0			0
$508$	7.69689e6	+	1.33314e7i	1.32329	+	2.29201i
$509$	−3.81494e6	−	6.60767e6i	−0.652669	−	1.13046i	−0.982473	−	0.186407i	$-0.940316\pi$
$509$	−3.81494e6	−	6.60767e6i	−0.652669	−	1.13046i	0.329803	−	0.944050i	$-0.393018\pi$
$510$		0			0
$511$	3.28851e6	−	77531.3i	0.557118	−	0.0131348i
$512$			8.94414e6i			1.50787i
$513$		0			0
$514$		−	7.58107e6i		−	1.26568i
$515$	−3.94370e6	−	2.27689e6i	−0.655217	−	0.378290i
$516$		0			0
$517$	−3.01129e6	+	1.73857e6i	−0.495480	+	0.286066i
$518$	−7.47616e6	+	1.36841e7i	−1.22420	+	2.24075i
$519$		0			0
$520$	155983.	−	270170.i	0.0252969	−	0.0438155i
$521$	−1.89954e6			−0.306587			−0.153293	−	0.988181i	$-0.548988\pi$
$521$	−1.89954e6			−0.306587			−0.153293	+	0.988181i	$0.548988\pi$
$522$		0			0
$523$		−	362076.i		−	0.0578823i	−0.999581	−	0.0289412i	$-0.990786\pi$
$523$		−	362076.i		−	0.0578823i	0.999581	−	0.0289412i	$-0.00921355\pi$
$524$	−5.79820e6	+	1.00428e7i	−0.922497	+	1.59781i
$525$		0			0
$526$	−5.29011e6	−	9.16274e6i	−0.833682	−	1.44398i
$527$	6.56629e6	−	3.79105e6i	1.02990	−	0.594611i
$528$		0			0
$529$	6.09536e6	−	1.05575e7i	0.947022	−	1.64029i
$530$	3.91998e6			0.606170
$531$		0			0
$532$	−6.80447e6	−	1.11692e7i	−1.04235	−	1.71097i
$533$	163393.	+	94334.8i	0.0249123	+	0.0143831i
$534$		0			0
$535$	−6.25328e6	+	3.61033e6i	−0.944547	+	0.545334i
$536$	−4.22924e6	+	2.44175e6i	−0.635843	+	0.367104i
$537$		0			0
$538$	1.04157e7	+	6.01351e6i	1.55143	+	0.895721i
$539$	−5.15273e6	−	2.65939e6i	−0.763951	−	0.394285i
$540$		0			0
$541$	−9.79666e6			−1.43908			−0.719540	−	0.694451i	$-0.755647\pi$
$541$	−9.79666e6			−1.43908			−0.719540	+	0.694451i	$0.755647\pi$
$542$	−7.31467e6	+	1.26694e7i	−1.06954	+	1.85250i
$543$		0			0
$544$	1.06191e6	−	613097.i	0.153848	−	0.0888243i
$545$	−3.10260e6	−	5.37386e6i	−0.447440	−	0.774989i
$546$		0			0
$547$	2.85035e6	−	4.93695e6i	0.407314	−	0.705489i	−0.587274	−	0.809388i	$-0.699799\pi$
$547$	2.85035e6	−	4.93695e6i	0.407314	−	0.705489i	0.994588	+	0.103900i	$0.0331321\pi$
$548$			1.23782e7i			1.76079i
$549$		0			0
$550$	−4.02116e6			−0.566820
$551$	−3.22669e6	+	5.58879e6i	−0.452771	+	0.784222i
$552$		0			0
$553$	−6.47022e6	−	3.53492e6i	−0.899717	−	0.491549i
$554$	−1.02978e7	+	5.94543e6i	−1.42551	+	0.823018i
$555$		0			0
$556$	1.59464e7	+	9.20666e6i	2.18764	+	1.26303i
$557$		−	7.01577e6i		−	0.958159i	−0.877771	−	0.479080i	$-0.840971\pi$
$557$		−	7.01577e6i		−	0.958159i	0.877771	−	0.479080i	$-0.159029\pi$
$558$		0			0
$559$			192963.i			0.0261183i
$560$	−171753.	−	7.28495e6i	−0.0231438	−	0.981650i
$561$		0			0
$562$	−4.62560e6	−	8.01177e6i	−0.617771	−	1.07001i
$563$	6.83596e6	+	1.18402e7i	0.908926	+	1.57431i	0.815559	+	0.578674i	$0.196430\pi$
$563$	6.83596e6	+	1.18402e7i	0.908926	+	1.57431i	0.0933666	+	0.995632i	$0.470237\pi$
$564$		0			0
$565$	−3.47447e6	−	2.00598e6i	−0.457896	−	0.264367i
$566$	1.35737e7			1.78097
$567$		0			0
$568$	2.57047e6			0.334304
$569$	−5.05105e6	−	2.91623e6i	−0.654035	−	0.377607i	0.135965	−	0.990714i	$-0.456586\pi$
$569$	−5.05105e6	−	2.91623e6i	−0.654035	−	0.377607i	−0.790000	+	0.613106i	$0.789920\pi$
$570$		0			0
$571$	5.10348e6	+	8.83948e6i	0.655052	+	1.13458i	0.981881	+	0.189500i	$0.0606867\pi$
$571$	5.10348e6	+	8.83948e6i	0.655052	+	1.13458i	−0.326828	+	0.945084i	$0.605980\pi$
$572$	173623.	+	300724.i	0.0221880	+	0.0384307i
$573$		0			0
$574$	1.46672e7	−	345801.i	1.85810	−	0.0438073i
$575$			5.18282e6i			0.653727i
$576$		0			0
$577$			1.78932e6i			0.223742i	0.993723	+	0.111871i	$0.0356844\pi$
$577$			1.78932e6i			0.223742i	−0.993723	+	0.111871i	$0.964316\pi$
$578$	−1.21112e6	−	699239.i	−0.150788	−	0.0870575i
$579$		0			0
$580$	−1.40975e7	+	8.13920e6i	−1.74009	+	1.00464i
$581$	1.36756e7	+	7.47148e6i	1.68076	+	0.918261i
$582$		0			0
$583$	−1.05929e6	+	1.83475e6i	−0.129076	+	0.223566i
$584$	−7.43768e6			−0.902413
$585$		0			0
$586$			985233.i			0.118521i
$587$	168038.	−	291050.i	0.0201285	−	0.0348636i	−0.855786	−	0.517330i	$-0.826926\pi$
$587$	168038.	−	291050.i	0.0201285	−	0.0348636i	0.875914	+	0.482467i	$0.160259\pi$
$588$		0			0
$589$	−5.44363e6	−	9.42864e6i	−0.646547	−	1.11985i
$590$	−1.10672e7	+	6.38967e6i	−1.30891	+	0.755698i
$591$		0			0
$592$	5.29538e6	−	9.17186e6i	0.621001	−	1.07561i
$593$	2.65006e6			0.309470			0.154735	−	0.987956i	$-0.450548\pi$
$593$	2.65006e6			0.309470			0.154735	+	0.987956i	$0.450548\pi$
$594$		0			0
$595$	−8.22480e6	+	5.01071e6i	−0.952430	+	0.580239i
$596$	−9.77504e6	−	5.64362e6i	−1.12720	−	0.650792i
$597$		0			0
$598$	587002.	−	338906.i	0.0671253	−	0.0387548i
$599$	707016.	−	408196.i	0.0805123	−	0.0464838i	−0.459203	−	0.888331i	$-0.651865\pi$
$599$	707016.	−	408196.i	0.0805123	−	0.0464838i	0.539716	+	0.841847i	$0.318532\pi$
$600$		0			0
$601$	−9.60490e6	−	5.54539e6i	−1.08469	−	0.626247i	−0.152534	−	0.988298i	$-0.548743\pi$
$601$	−9.60490e6	−	5.54539e6i	−1.08469	−	0.626247i	−0.932158	+	0.362051i	$0.882077\pi$
$602$	7.80680e6	+	1.28144e7i	0.877975	+	1.44115i
$603$		0			0
$604$	2.14356e6			0.239080
$605$	−1.38189e6	+	2.39351e6i	−0.153492	+	0.265856i
$606$		0			0
$607$	2.81198e6	−	1.62350e6i	0.309771	−	0.178846i	−0.337053	−	0.941486i	$-0.609430\pi$
$607$	2.81198e6	−	1.62350e6i	0.309771	−	0.178846i	0.646824	+	0.762639i	$0.276097\pi$
$608$	−880355.	−	1.52482e6i	−0.0965826	−	0.167286i
$609$		0			0
$610$	−1.57303e7	+	2.72458e7i	−1.71164	+	2.96466i
$611$			163080.i			0.0176725i
$612$		0			0
$613$	1.15559e7			1.24209			0.621046	−	0.783774i	$-0.286708\pi$
$613$	1.15559e7			1.24209			0.621046	+	0.783774i	$0.286708\pi$
$614$	1.95398e6	−	3.38439e6i	0.209170	−	0.362293i
$615$		0			0
$616$	1.15058e7	+	6.28605e6i	1.22170	+	0.667461i
$617$	1.42413e6	−	822219.i	0.150604	−	0.0869510i	−0.422804	−	0.906221i	$-0.638954\pi$
$617$	1.42413e6	−	822219.i	0.150604	−	0.0869510i	0.573408	+	0.819270i	$0.305621\pi$
$618$		0			0
$619$	−1.02958e7	−	5.94427e6i	−1.08002	−	0.623551i	−0.149120	−	0.988819i	$-0.547644\pi$
$619$	−1.02958e7	−	5.94427e6i	−1.08002	−	0.623551i	−0.930902	+	0.365268i	$0.880977\pi$
$620$		−	2.74627e7i		−	2.86922i
$621$		0			0
$622$			1.53120e7i			1.58693i
$623$	−221766.	−	9.40626e6i	−0.0228915	−	0.970950i
$624$		0			0
$625$	6.03813e6	+	1.04583e7i	0.618304	+	1.07093i
$626$	3.63960e6	+	6.30398e6i	0.371209	+	0.642952i
$627$		0			0
$628$	−7.96461e6	−	4.59837e6i	−0.805871	−	0.465270i
$629$	−1.39974e7			−1.41065
$630$		0			0
$631$	−2.68920e6			−0.268875			−0.134437	−	0.990922i	$-0.542923\pi$
$631$	−2.68920e6			−0.268875			−0.134437	+	0.990922i	$0.542923\pi$
$632$	1.44373e7	+	8.33536e6i	1.43778	+	0.830103i
$633$		0			0
$634$	1.13022e7	+	1.95761e7i	1.11671	+	1.93420i
$635$	−8.13858e6	−	1.40964e7i	−0.800967	−	1.38732i
$636$		0			0
$637$	−228850.	+	146926.i	−0.0223462	+	0.0143466i
$638$		−	1.33239e7i		−	1.29592i
$639$		0			0
$640$		−	2.18988e7i		−	2.11335i
$641$	5.29002e6	+	3.05420e6i	0.508525	+	0.293597i	0.732227	−	0.681060i	$-0.238481\pi$
$641$	5.29002e6	+	3.05420e6i	0.508525	+	0.293597i	−0.223702	+	0.974658i	$0.571814\pi$
$642$		0			0
$643$	8.03058e6	−	4.63646e6i	0.765984	−	0.442241i	−0.0654561	−	0.997855i	$-0.520850\pi$
$643$	8.03058e6	−	4.63646e6i	0.765984	−	0.442241i	0.831440	+	0.555614i	$0.187517\pi$
$644$	1.66864e7	−	3.05423e7i	1.58543	−	2.90193i
$645$		0			0
$646$	8.88998e6	−	1.53979e7i	0.838146	−	1.45171i
$647$	7.17731e6			0.674063			0.337032	−	0.941493i	$-0.390577\pi$
$647$	7.17731e6			0.674063			0.337032	+	0.941493i	$0.390577\pi$
$648$		0			0
$649$		−	6.90669e6i		−	0.643663i
$650$	−94297.7	+	163328.i	−0.00875422	+	0.0151628i
$651$		0			0
$652$	−1.11548e7	−	1.93206e7i	−1.02764	−	1.77993i
$653$	1.57921e7	−	9.11758e6i	1.44930	−	0.836751i	0.450856	−	0.892597i	$-0.351119\pi$
$653$	1.57921e7	−	9.11758e6i	1.44930	−	0.836751i	0.998439	+	0.0558452i	$0.0177853\pi$
$654$		0			0
$655$	6.13094e6	−	1.06191e7i	0.558372	−	0.967129i
$656$	−9.96461e6			−0.904067
$657$		0			0
$658$	6.59782e6	+	1.08300e7i	0.594067	+	0.975129i
$659$	1.32789e7	+	7.66658e6i	1.19110	+	0.687683i	0.958556	−	0.284903i	$-0.0919614\pi$
$659$	1.32789e7	+	7.66658e6i	1.19110	+	0.687683i	0.232545	+	0.972586i	$0.425295\pi$
$660$		0			0
$661$	−7.54042e6	+	4.35346e6i	−0.671262	+	0.387553i	−0.796555	−	0.604567i	$-0.793346\pi$
$661$	−7.54042e6	+	4.35346e6i	−0.671262	+	0.387553i	0.125293	+	0.992120i	$0.460013\pi$
$662$	−2.39649e7	+	1.38361e7i	−2.12535	+	1.22707i
$663$		0			0
$664$	−3.05149e7	−	1.76178e7i	−2.68591	−	1.55071i
$665$	7.19496e6	+	1.18101e7i	0.630920	+	1.03562i
$666$		0			0
$667$	−1.71729e7			−1.49462
$668$	4.35075e6	−	7.53572e6i	0.377245	−	0.653407i
$669$		0			0
$670$	9.21013e6	−	5.31747e6i	0.792645	−	0.457634i
$671$	−8.50159e6	−	1.47252e7i	−0.728943	−	1.26257i
$672$		0			0
$673$	−8.24982e6	+	1.42891e7i	−0.702113	+	1.21610i	0.265610	+	0.964080i	$0.414427\pi$
$673$	−8.24982e6	+	1.42891e7i	−0.702113	+	1.21610i	−0.967723	+	0.252015i	$0.918907\pi$
$674$		−	2.15836e7i		−	1.83010i
$675$		0			0
$676$	−2.30788e7			−1.94244
$677$	8.91620e6	−	1.54433e7i	0.747667	−	1.29500i	−0.201272	−	0.979535i	$-0.564507\pi$
$677$	8.91620e6	−	1.54433e7i	0.747667	−	1.29500i	0.948938	−	0.315461i	$-0.102159\pi$
$678$		0			0
$679$	5.59896e6	−	1.02482e7i	0.466051	−	0.853046i
$680$	1.88589e7	−	1.08882e7i	1.56402	−	0.902989i
$681$		0			0
$682$	1.94667e7	+	1.12391e7i	1.60262	+	0.925273i
$683$			2.19057e7i			1.79683i	0.439151	+	0.898413i	$0.355279\pi$
$683$			2.19057e7i			1.79683i	−0.439151	+	0.898413i	$0.644721\pi$
$684$		0			0
$685$		−	1.30886e7i		−	1.06578i
$686$	−9.25341e6	+	1.90159e7i	−0.750744	+	1.54279i
$687$		0			0
$688$	−5.09569e6	−	8.82599e6i	−0.410423	−	0.710873i
$689$	49681.5	+	86050.9i	0.00398701	+	0.00690570i
$690$		0			0
$691$	1.56485e7	+	9.03467e6i	1.24675	+	0.719809i	0.970459	−	0.241266i	$-0.0775626\pi$
$691$	1.56485e7	+	9.03467e6i	1.24675	+	0.719809i	0.276287	+	0.961075i	$0.410896\pi$
$692$	−2.13735e7			−1.69672
$693$		0			0
$694$	2.62339e7			2.06759
$695$	−1.68615e7	−	9.73500e6i	−1.32414	−	0.764493i
$696$		0			0
$697$	6.58492e6	+	1.14054e7i	0.513415	+	0.889261i
$698$	5.17203e6	+	8.95821e6i	0.401811	+	0.695958i
$699$		0			0
$700$	228244.	+	9.68103e6i	0.0176057	+	0.746752i
$701$			6.25237e6i			0.480562i	0.970703	+	0.240281i	$0.0772396\pi$
$701$			6.25237e6i			0.480562i	−0.970703	+	0.240281i	$0.922760\pi$
$702$		0			0
$703$			2.00991e7i			1.53387i
$704$	1.13192e7	+	6.53513e6i	0.860762	+	0.496961i
$705$		0			0
$706$	−1.55534e7	+	8.97975e6i	−1.17439	+	0.678036i
$707$	1.71215e7	+	9.35410e6i	1.28823	+	0.703807i
$708$		0			0
$709$	−3.29799e6	+	5.71229e6i	−0.246396	+	0.426770i	−0.962523	−	0.271199i	$-0.912580\pi$
$709$	−3.29799e6	+	5.71229e6i	−0.246396	+	0.426770i	0.716127	+	0.697970i	$0.245913\pi$
$710$	−5.59779e6			−0.416745
$711$		0			0
$712$			2.12743e7i			1.57273i
$713$	1.44859e7	−	2.50903e7i	1.06714	−	1.84834i
$714$		0			0
$715$	−183587.	−	317982.i	−0.0134300	−	0.0232615i
$716$	−3.91551e7	+	2.26062e7i	−2.85434	+	1.64795i
$717$		0			0
$718$	270060.	−	467757.i	0.0195501	−	0.0338617i
$719$	−1.23687e7			−0.892279			−0.446140	−	0.894963i	$-0.647202\pi$
$719$	−1.23687e7			−0.892279			−0.446140	+	0.894963i	$0.647202\pi$
$720$		0			0
$721$	−4.66996e6	−	7.66548e6i	−0.334561	−	0.549163i
$722$	−1.29740e6	−	749056.i	−0.0926257	−	0.0534775i
$723$		0			0
$724$	1.28636e7	−	7.42682e6i	0.912046	−	0.526570i
$725$	4.13806e6	−	2.38911e6i	0.292383	−	0.168807i
$726$		0			0
$727$	1.72901e7	+	9.98246e6i	1.21328	+	0.700489i	0.963473	−	0.267806i	$-0.0862985\pi$
$727$	1.72901e7	+	9.98246e6i	1.21328	+	0.700489i	0.249810	+	0.968295i	$0.419632\pi$
$728$	525137.	−	319923.i	0.0367235	−	0.0223727i
$729$		0			0
$730$	1.61972e7			1.12495
$731$	−6.73478e6	+	1.16650e7i	−0.466154	+	0.807403i
$732$		0			0
$733$	−1.49470e7	+	8.62966e6i	−1.02753	+	0.593244i	−0.916276	−	0.400548i	$-0.868820\pi$
$733$	−1.49470e7	+	8.62966e6i	−1.02753	+	0.593244i	−0.111253	+	0.993792i	$0.535487\pi$
$734$	−1.29895e7	−	2.24985e7i	−0.889923	−	1.54139i
$735$		0			0
$736$	2.34269e6	−	4.05766e6i	0.159412	−	0.276109i
$737$			5.74774e6i			0.389788i
$738$		0			0
$739$	−1.58816e7			−1.06976			−0.534878	−	0.844930i	$-0.679642\pi$
$739$	−1.58816e7			−1.06976			−0.534878	+	0.844930i	$0.679642\pi$
$740$	−2.53496e7	+	4.39067e7i	−1.70173	+	2.94749i
$741$		0			0
$742$	6.78069e6	+	3.70454e6i	0.452131	+	0.247016i
$743$	−1.27508e7	+	7.36165e6i	−0.847352	+	0.489219i	−0.859756	−	0.510704i	$-0.829385\pi$
$743$	−1.27508e7	+	7.36165e6i	−0.847352	+	0.489219i	0.0124047	+	0.999923i	$0.496051\pi$
$744$		0			0
$745$	1.03360e7	+	5.96749e6i	0.682278	+	0.393913i
$746$		−	4.33613e7i		−	2.85270i
$747$		0			0
$748$			2.42391e7i			1.58403i
$749$	−1.42287e7	+	335462.i	−0.926746	+	0.0218493i
$750$		0			0
$751$	−5.01794e6	−	8.69132e6i	−0.324657	−	0.562323i	0.656786	−	0.754077i	$-0.271916\pi$
$751$	−5.01794e6	−	8.69132e6i	−0.324657	−	0.562323i	−0.981443	+	0.191754i	$0.938582\pi$
$752$	−4.30655e6	−	7.45917e6i	−0.277706	−	0.481001i
$753$		0			0
$754$	−541178.	−	312449.i	−0.0346666	−	0.0200148i
$755$	−2.26657e6			−0.144711
$756$		0			0
$757$	1.51893e7			0.963382			0.481691	−	0.876341i	$-0.340023\pi$
$757$	1.51893e7			0.963382			0.481691	+	0.876341i	$0.340023\pi$
$758$	−1.80783e6	−	1.04375e6i	−0.114284	−	0.0659818i
$759$		0			0
$760$	−1.56345e7	−	2.70797e7i	−0.981861	−	1.70063i
$761$	2.26847e6	+	3.92910e6i	0.141994	+	0.245941i	0.928248	−	0.371963i	$-0.121315\pi$
$761$	2.26847e6	+	3.92910e6i	0.141994	+	0.245941i	−0.786253	+	0.617904i	$0.787982\pi$
$762$		0			0
$763$	−288285.	−	1.22277e7i	−0.0179271	−	0.760383i
$764$		−	9.44949e6i		−	0.585699i
$765$		0			0
$766$			6.76185e6i			0.416384i
$767$	−280530.	−	161964.i	−0.0172184	−	0.00994102i
$768$		0			0
$769$	2.79698e7	−	1.61484e7i	1.70559	−	0.984721i	0.765724	−	0.643170i	$-0.222381\pi$
$769$	2.79698e7	−	1.61484e7i	1.70559	−	0.984721i	0.939863	−	0.341551i	$-0.110952\pi$
$770$	−2.50565e7	−	1.36893e7i	−1.52298	−	0.832060i
$771$		0			0
$772$	−8.59236e6	+	1.48824e7i	−0.518883	+	0.898732i
$773$	8.86307e6			0.533501			0.266751	−	0.963766i	$-0.414050\pi$
$773$	8.86307e6			0.533501			0.266751	+	0.963766i	$0.414050\pi$
$774$		0			0
$775$			8.06116e6i			0.482107i
$776$	−1.32024e7	+	2.28672e7i	−0.787042	+	1.36320i
$777$		0			0
$778$	−1.31162e6	−	2.27179e6i	−0.0776890	−	0.134561i
$779$	1.63772e7	−	9.45540e6i	0.966934	−	0.558259i
$780$		0			0
$781$	1.51268e6	−	2.62005e6i	0.0887403	−	0.153703i
$782$	4.73138e7			2.76676
$783$		0			0
$784$	6.58749e6	−	1.27637e7i	0.382763	−	0.741626i
$785$	8.42167e6	+	4.86225e6i	0.487780	+	0.281620i
$786$		0			0
$787$	8.48547e6	−	4.89909e6i	0.488359	−	0.281954i	−0.235535	−	0.971866i	$-0.575684\pi$
$787$	8.48547e6	−	4.89909e6i	0.488359	−	0.281954i	0.723893	+	0.689912i	$0.242351\pi$
$788$	−8.01696e6	+	4.62860e6i	−0.459933	+	0.265542i
$789$		0			0
$790$	−3.14405e7	−	1.81522e7i	−1.79234	−	1.03481i
$791$	−4.11432e6	−	6.75342e6i	−0.233806	−	0.383780i
$792$		0			0
$793$	−797461.			−0.0450325
$794$	1.56565e7	−	2.71178e7i	0.881340	−	1.52652i
$795$		0			0
$796$	−2.73330e7	+	1.57807e7i	−1.52899	+	0.882762i
$797$	−59096.5	−	102358.i	−0.00329546	−	0.00570791i	0.864373	−	0.502851i	$-0.167716\pi$
$797$	−59096.5	−	102358.i	−0.00329546	−	0.00570791i	−0.867668	+	0.497143i	$0.834382\pi$
$798$		0			0
$799$	−5.69181e6	+	9.85851e6i	−0.315416	+	0.546316i
$800$			1.30367e6i			0.0720182i
$801$		0			0
$802$	−2.08249e7			−1.14327
$803$	−4.37696e6	+	7.58113e6i	−0.239543	+	0.414901i
$804$		0			0
$805$	−1.76440e7	+	3.22950e7i	−0.959636	+	1.75649i
$806$	913000.	−	527121.i	0.0495032	−	0.0285807i
$807$		0			0
$808$	−3.82039e7	−	2.20570e7i	−2.05863	−	1.18855i
$809$		−	1.20598e7i		−	0.647842i	−0.946084	−	0.323921i	$-0.894999\pi$
$809$		−	1.20598e7i		−	0.647842i	0.946084	−	0.323921i	$-0.105001\pi$
$810$		0			0
$811$		−	1.31654e7i		−	0.702884i	−0.936210	−	0.351442i	$-0.885692\pi$
$811$		−	1.31654e7i		−	0.702884i	0.936210	−	0.351442i	$-0.114308\pi$
$812$	−3.20774e7	+	756271.i	−1.70730	+	0.0402520i
$813$		0			0
$814$	−2.07486e7	−	3.59376e7i	−1.09756	−	1.90103i
$815$	1.17949e7	+	2.04294e7i	0.622015	+	1.07736i
$816$		0			0
$817$	1.67499e7	+	9.67057e6i	0.877926	+	0.506871i
$818$	−715516.			−0.0373883
$819$		0			0
$820$	4.77017e7			2.47742
$821$	1.02559e7	+	5.92125e6i	0.531026	+	0.306588i	0.741434	−	0.671026i	$-0.234146\pi$
$821$	1.02559e7	+	5.92125e6i	0.531026	+	0.306588i	−0.210408	+	0.977614i	$0.567479\pi$
$822$		0			0
$823$	−1.19812e7	−	2.07521e7i	−0.616597	−	1.06798i	−0.990102	−	0.140349i	$-0.955178\pi$
$823$	−1.19812e7	−	2.07521e7i	−0.616597	−	1.06798i	0.373505	−	0.927628i	$-0.378156\pi$
$824$	1.01477e7	+	1.75764e7i	0.520656	+	0.901802i
$825$		0			0
$826$	−2.51824e7	+	593709.i	−1.28424	+	0.0302778i
$827$			1.43412e7i			0.729156i	0.931173	+	0.364578i	$0.118787\pi$
$827$			1.43412e7i			0.729156i	−0.931173	+	0.364578i	$0.881213\pi$
$828$		0			0
$829$		−	5.16778e6i		−	0.261167i	−0.991437	−	0.130583i	$-0.958315\pi$
$829$		−	5.16778e6i		−	0.261167i	0.991437	−	0.130583i	$-0.0416850\pi$
$830$	6.64532e7	+	3.83668e7i	3.34827	+	1.93312i
$831$		0			0
$832$	530877.	−	306502.i	0.0265880	−	0.0153506i
$833$	−1.89624e7	+	894628.i	−0.946850	+	0.0446715i
$834$		0			0
$835$	−4.60043e6	+	7.96817e6i	−0.228340	+	0.395496i
$836$	3.48053e7			1.72239
$837$		0			0
$838$			3.58264e7i			1.76236i
$839$	6.44770e6	−	1.11678e7i	0.316228	−	0.547723i	−0.663470	−	0.748203i	$-0.730917\pi$
$839$	6.44770e6	−	1.11678e7i	0.316228	−	0.547723i	0.979698	+	0.200480i	$0.0642502\pi$
$840$		0			0
$841$	−2.33941e6	−	4.05198e6i	−0.114056	−	0.197550i
$842$	−6.07677e6	+	3.50842e6i	−0.295388	+	0.170542i
$843$		0			0
$844$	−943940.	+	1.63495e6i	−0.0456130	+	0.0790040i
$845$	2.44032e7			1.17572
$846$		0			0
$847$	−4.65233e6	+	2.83429e6i	−0.222824	+	0.135749i
$848$	−4.54479e6	−	2.62394e6i	−0.217032	−	0.125304i
$849$		0			0
$850$	−1.14009e7	+	6.58233e6i	−0.541244	+	0.312487i
$851$	−4.63195e7	+	2.67426e7i	−2.19250	+	1.26584i
$852$		0			0
$853$	4.14857e6	+	2.39518e6i	0.195221	+	0.112711i	0.594424	−	0.804152i	$-0.297380\pi$
$853$	4.14857e6	+	2.39518e6i	0.195221	+	0.112711i	−0.399204	+	0.916862i	$0.630713\pi$
$854$	−5.29584e7	+	3.22633e7i	−2.48479	+	1.51378i
$855$		0			0
$856$	3.21813e7			1.50113
$857$	1.10039e7	−	1.90593e7i	0.511793	−	0.886451i	−0.488114	−	0.872780i	$-0.662315\pi$
$857$	1.10039e7	−	1.90593e7i	0.511793	−	0.886451i	0.999907	−	0.0136711i	$-0.00435178\pi$
$858$		0			0
$859$	−1.69532e7	+	9.78795e6i	−0.783916	+	0.452594i	−0.837816	−	0.545952i	$-0.816168\pi$
$859$	−1.69532e7	+	9.78795e6i	−0.783916	+	0.452594i	0.0539006	+	0.998546i	$0.482835\pi$
$860$	2.43936e7	+	4.22510e7i	1.12468	+	1.94801i
$861$		0			0
$862$	−1.18382e7	+	2.05044e7i	−0.542648	+	0.939894i
$863$		−	1.25803e7i		−	0.574994i	−0.957782	−	0.287497i	$-0.907177\pi$
$863$		−	1.25803e7i		−	0.574994i	0.957782	−	0.287497i	$-0.0928231\pi$
$864$		0			0
$865$	2.26000e7			1.02700
$866$	509727.	−	882874.i	0.0230963	−	0.0400040i
$867$		0			0
$868$	2.59534e7	−	4.75043e7i	1.16921	−	2.14010i
$869$	1.69922e7	−	9.81048e6i	0.763311	−	0.440698i
$870$		0			0
$871$	233457.	+	134786.i	0.0104271	+	0.00602006i
$872$			2.76555e7i			1.23166i
$873$		0			0
$874$		−	6.79386e7i		−	3.00842i
$875$	386700.	+	1.64020e7i	0.0170747	+	0.724230i
$876$		0			0
$877$	2.11122e7	+	3.65674e7i	0.926904	+	1.60545i	0.788470	+	0.615074i	$0.210874\pi$
$877$	2.11122e7	+	3.65674e7i	0.926904	+	1.60545i	0.138435	+	0.990372i	$0.455793\pi$
$878$	−2.23789e7	−	3.87614e7i	−0.979721	−	1.69693i
$879$		0			0
$880$	1.67943e7	+	9.69617e6i	0.731062	+	0.422079i
$881$	8.46050e6			0.367245			0.183623	−	0.982997i	$-0.441218\pi$
$881$	8.46050e6			0.367245			0.183623	+	0.982997i	$0.441218\pi$
$882$		0			0
$883$	−3.60726e7			−1.55696			−0.778478	−	0.627672i	$-0.784008\pi$
$883$	−3.60726e7			−1.55696			−0.778478	+	0.627672i	$0.784008\pi$
$884$	984525.	+	568416.i	0.0423737	+	0.0244645i
$885$		0			0
$886$	−2.34040e6	−	4.05368e6i	−0.100162	−	0.173486i
$887$	1.40470e7	+	2.43301e7i	0.599480	+	1.03833i	0.992898	+	0.118970i	$0.0379591\pi$
$887$	1.40470e7	+	2.43301e7i	0.599480	+	1.03833i	−0.393418	+	0.919360i	$0.628708\pi$
$888$		0			0
$889$	−756213.	−	3.20750e7i	−0.0320915	−	1.36117i
$890$		−	4.63296e7i		−	1.96057i
$891$		0			0
$892$		−	1.49611e7i		−	0.629579i
$893$	1.41560e7	+	8.17296e6i	0.594034	+	0.342966i
$894$		0			0
$895$	4.14021e7	−	2.39035e7i	1.72768	−	0.997479i
$896$	2.06953e7	−	3.78801e7i	0.861195	−	1.57631i
$897$		0			0
$898$	−7.74328e6	+	1.34118e7i	−0.320431	+	0.555002i
$899$	−2.67101e7			−1.10224
$900$		0			0
$901$			6.93592e6i			0.284637i
$902$	−1.95219e7	+	3.38129e7i	−0.798924	+	1.38378i
$903$		0			0
$904$	8.94033e6	+	1.54851e7i	0.363858	+	0.630221i
$905$	−1.36018e7	+	7.85301e6i	−0.552046	+	0.318724i
$906$		0			0
$907$	−1.42587e7	+	2.46968e7i	−0.575521	+	0.996831i	0.420464	+	0.907309i	$0.361867\pi$
$907$	−1.42587e7	+	2.46968e7i	−0.575521	+	0.996831i	−0.995985	+	0.0895222i	$0.971466\pi$
$908$	5.16864e7			2.08047
$909$		0			0
$910$	−1.14361e6	+	696706.i	−0.0457797	+	0.0278899i
$911$	−1.82419e7	−	1.05320e7i	−0.728240	−	0.420450i	0.0895379	−	0.995983i	$-0.471461\pi$
$911$	−1.82419e7	−	1.05320e7i	−0.728240	−	0.420450i	−0.817778	+	0.575534i	$0.804794\pi$
$912$		0			0
$913$	−3.59151e7	+	2.07356e7i	−1.42594	+	0.823266i
$914$	3.19288e6	−	1.84341e6i	0.126420	−	0.0729888i
$915$		0			0
$916$	4.14833e7	+	2.39504e7i	1.63356	+	0.943135i
$917$	2.06407e7	−	1.25747e7i	0.810588	−	0.493826i
$918$		0			0
$919$	3.24330e7			1.26677			0.633385	−	0.773837i	$-0.281665\pi$
$919$	3.24330e7			1.26677			0.633385	+	0.773837i	$0.281665\pi$
$920$	4.16046e7	−	7.20612e7i	1.62058	−	2.80693i
$921$		0			0
$922$	7.19476e7	−	4.15390e7i	2.78733	−	1.60927i
$923$	−70946.0	−	122882.i	−0.00274109	−	0.00474771i
$924$		0			0
$925$	7.44090e6	−	1.28880e7i	0.285938	−	0.495258i
$926$		−	3.87638e7i		−	1.48559i
$927$		0			0
$928$	−4.31962e6			−0.164655
$929$	−1.98727e6	+	3.44205e6i	−0.0755470	+	0.130851i	−0.901324	−	0.433145i	$-0.857404\pi$
$929$	−1.98727e6	+	3.44205e6i	−0.0755470	+	0.130851i	0.825777	+	0.563997i	$0.190737\pi$
$930$		0			0
$931$	1.28461e6	+	2.72284e7i	0.0485733	+	1.02955i
$932$	−4.27708e7	+	2.46937e7i	−1.61290	+	0.931208i
$933$		0			0
$934$	−6.69501e7	−	3.86537e7i	−2.51122	−	1.44985i
$935$		−	2.56301e7i		−	0.958786i
$936$		0			0
$937$		−	2.79914e7i		−	1.04154i	−0.853697	−	0.520769i	$-0.825645\pi$
$937$		−	2.79914e7i		−	1.04154i	0.853697	−	0.520769i	$-0.174355\pi$
$938$	2.09567e7	−	494084.i	0.777707	−	0.0183355i
$939$		0			0
$940$	2.06160e7	+	3.57079e7i	0.760999	+	1.31809i
$941$	1.18359e6	+	2.05004e6i	0.0435740	+	0.0754724i	0.886990	−	0.461789i	$-0.152792\pi$
$941$	1.18359e6	+	2.05004e6i	0.0435740	+	0.0754724i	−0.843416	+	0.537261i	$0.819459\pi$
$942$		0			0
$943$	4.35810e7	+	2.51615e7i	1.59595	+	0.921419i
$944$	1.71083e7			0.624853
$945$		0			0
$946$	−3.99323e7			−1.45076
$947$	−2.45114e7	−	1.41517e7i	−0.888166	−	0.512783i	−0.0148235	−	0.999890i	$-0.504719\pi$
$947$	−2.45114e7	−	1.41517e7i	−0.888166	−	0.512783i	−0.873342	+	0.487108i	$0.838052\pi$
$948$		0			0
$949$	205283.	+	355560.i	0.00739923	+	0.0128158i
$950$	9.45168e6	+	1.63708e7i	0.339782	+	0.588519i
$951$		0			0
$952$	4.29114e7	−	1.01170e6i	1.53455	−	0.0361791i
$953$			2.23096e7i			0.795718i	0.917447	+	0.397859i	$0.130247\pi$
$953$			2.23096e7i			0.795718i	−0.917447	+	0.397859i	$0.869753\pi$
$954$		0			0
$955$			9.99176e6i			0.354514i
$956$	4.67103e6	+	2.69682e6i	0.165298	+	0.0954349i
$957$		0			0
$958$	−2.78723e7	+	1.60921e7i	−0.981203	+	0.566498i
$959$	1.23692e7	−	2.26403e7i	0.434307	−	0.794943i
$960$		0			0
$961$	8.21621e6	−	1.42309e7i	0.286988	−	0.497077i
$962$	−1.94625e6			−0.0678048
$963$		0			0
$964$			8.26539e7i			2.86465i
$965$	9.08544e6	−	1.57365e7i	0.314071	−	0.543987i
$966$		0			0
$967$	1.90396e7	+	3.29775e7i	0.654774	+	1.13410i	0.981950	+	0.189138i	$0.0605694\pi$
$967$	1.90396e7	+	3.29775e7i	0.654774	+	1.13410i	−0.327177	+	0.944963i	$0.606097\pi$
$968$	1.06675e7	−	6.15886e6i	0.365908	−	0.211257i
$969$		0			0
$970$	2.87512e7	−	4.97986e7i	0.981131	−	1.69937i
$971$	−1.92906e7			−0.656596			−0.328298	−	0.944574i	$-0.606475\pi$
$971$	−1.92906e7			−0.656596			−0.328298	+	0.944574i	$0.606475\pi$
$972$		0			0
$973$	−1.99667e7	−	3.27742e7i	−0.676120	−	1.10981i
$974$	−4.76309e7	−	2.74997e7i	−1.60876	−	0.928818i
$975$		0			0
$976$	3.64753e7	−	2.10590e7i	1.22567	−	0.707641i
$977$	4.90079e7	−	2.82947e7i	1.64259	−	0.948352i	0.662686	−	0.748897i	$-0.269416\pi$
$977$	4.90079e7	−	2.82947e7i	1.64259	−	0.948352i	0.979907	−	0.199454i	$-0.0639170\pi$
$978$		0			0
$979$	2.16846e7	+	1.25196e7i	0.723093	+	0.417478i
$980$	−3.15351e7	+	6.11011e7i	−1.04889	+	2.03228i
$981$		0			0
$982$	−5.52046e6			−0.182682
$983$	−2.60190e7	+	4.50662e7i	−0.858828	+	1.48753i	0.0142191	+	0.999899i	$0.495474\pi$
$983$	−2.60190e7	+	4.50662e7i	−0.858828	+	1.48753i	−0.873047	+	0.487635i	$0.837860\pi$
$984$		0			0
$985$	8.47703e6	−	4.89421e6i	0.278390	−	0.160728i
$986$	−2.18101e7	−	3.77762e7i	−0.714440	−	1.23745i
$987$		0			0
$988$	816198.	−	1.41370e6i	0.0266013	−	0.0460748i
$989$			5.14682e7i			1.67320i
$990$		0			0
$991$	−2.61346e6			−0.0845341			−0.0422670	−	0.999106i	$-0.513458\pi$
$991$	−2.61346e6			−0.0845341			−0.0422670	+	0.999106i	$0.513458\pi$
$992$	3.64373e6	−	6.31112e6i	0.117562	−	0.203623i
$993$		0			0
$994$	−9.68293e6	−	5.29014e6i	−0.310843	−	0.169825i
$995$	2.89015e7	−	1.66863e7i	0.925471	−	0.534321i
$996$		0			0
$997$	−4.21115e7	−	2.43131e7i	−1.34172	−	0.774644i	−0.354662	−	0.934994i	$-0.615404\pi$
$997$	−4.21115e7	−	2.43131e7i	−1.34172	−	0.774644i	−0.987060	+	0.160351i	$0.948737\pi$
$998$			5.32834e7i			1.69342i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.6.o.a.62.36		76
3.2	odd	2		63.6.o.a.20.4	yes	76
7.6	odd	2	inner	189.6.o.a.62.35		76
9.4	even	3		63.6.o.a.41.3	yes	76
9.5	odd	6	inner	189.6.o.a.125.35		76
21.20	even	2		63.6.o.a.20.3	✓	76
63.13	odd	6		63.6.o.a.41.4	yes	76
63.41	even	6	inner	189.6.o.a.125.36		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.o.a.20.3	✓	76	21.20	even	2
63.6.o.a.20.4	yes	76	3.2	odd	2
63.6.o.a.41.3	yes	76	9.4	even	3
63.6.o.a.41.4	yes	76	63.13	odd	6
189.6.o.a.62.35		76	7.6	odd	2	inner
189.6.o.a.62.36		76	1.1	even	1	trivial
189.6.o.a.125.35		76	9.5	odd	6	inner
189.6.o.a.125.36		76	63.41	even	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	189.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(8.40544 + 4.85288i) q^{2} +(31.1009 + 53.8683i) q^{4} +(-32.8857 - 56.9596i) q^{5} +(-3.05564 - 129.606i) q^{7} +293.131i q^{8} -638.361i q^{10} +(298.785 + 172.504i) q^{11} +(14.0132 - 8.09053i) q^{13} +(603.277 - 1104.22i) q^{14} +(-427.303 + 740.110i) q^{16} +1129.50 q^{17} -1621.87i q^{19} +(2045.55 - 3542.99i) q^{20} +(1674.28 + 2899.93i) q^{22} +(3737.69 - 2157.95i) q^{23} +(-600.433 + 1039.98i) q^{25} +157.050 q^{26} +(6886.61 - 4195.46i) q^{28} +(-3445.90 - 1989.49i) q^{29} +(5813.45 - 3356.40i) q^{31} +(940.164 - 542.804i) q^{32} +(9493.94 + 5481.33i) q^{34} +(-7281.81 + 4436.22i) q^{35} -12392.6 q^{37} +(7870.73 - 13632.5i) q^{38} +(16696.7 - 9639.82i) q^{40} +(5829.95 + 10097.8i) q^{41} +(-5962.62 + 10327.6i) q^{43} +21460.1i q^{44} +41889.2 q^{46} +(-5039.23 + 8728.21i) q^{47} +(-16788.3 + 792.057i) q^{49} +(-10093.8 + 5827.65i) q^{50} +(871.647 + 503.246i) q^{52} +6140.70i q^{53} -22691.6i q^{55} +(37991.5 - 895.704i) q^{56} +(-19309.5 - 33445.1i) q^{58} +(-10009.5 - 17337.0i) q^{59} +(-42680.8 - 24641.8i) q^{61} +65152.8 q^{62} +37884.0 q^{64} +(-921.668 - 532.125i) q^{65} +(8329.89 + 14427.8i) q^{67} +(35128.5 + 60844.3i) q^{68} +(-82735.2 + 1950.60i) q^{70} -8769.01i q^{71} +25373.2i q^{73} +(-104165. - 60139.6i) q^{74} +(87367.3 - 50441.5i) q^{76} +(21444.5 - 39251.4i) q^{77} +(28435.6 - 49251.9i) q^{79} +56208.5 q^{80} +113168. i q^{82} +(-60102.0 + 104100. i) q^{83} +(-37144.3 - 64335.9i) q^{85} +(-100237. + 57871.7i) q^{86} +(-50566.2 + 87583.2i) q^{88} +72575.9 q^{89} +(-1091.40 - 1791.47i) q^{91} +(232491. + 134229. i) q^{92} +(-84713.9 + 48909.6i) q^{94} +(-92380.9 + 53336.2i) q^{95} +(78010.1 + 45039.1i) q^{97} +(-144957. - 74814.2i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 6 q^{2} + 574 q^{4} - 30 q^{7} + 576 q^{11} - 1392 q^{14} - 8130 q^{16} - 130 q^{22} + 8112 q^{23} - 18752 q^{25} - 1732 q^{28} + 35826 q^{29} + 1092 q^{32} + 10308 q^{37} + 18486 q^{43} - 38056 q^{46}+ \cdots + 950328 q^{95}+O(q^{100}) \) 76 * q + 6 * q^2 + 574 * q^4 - 30 * q^7 + 576 * q^11 - 1392 * q^14 - 8130 * q^16 - 130 * q^22 + 8112 * q^23 - 18752 * q^25 - 1732 * q^28 + 35826 * q^29 + 1092 * q^32 + 10308 * q^37 + 18486 * q^43 - 38056 * q^46 + 7948 * q^49 - 76104 * q^50 - 164652 * q^56 + 9902 * q^58 - 192648 * q^64 - 12666 * q^65 + 1244 * q^67 + 33024 * q^70 - 356496 * q^74 + 16458 * q^77 + 168074 * q^79 + 2598 * q^85 - 543300 * q^86 + 69694 * q^88 + 139368 * q^91 + 211794 * q^92 + 950328 * q^95

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