LMFDB - Embedded newform 162.7.d.g.107.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,7,Mod(53,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("162.53");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	162.d (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:	$37.2687615464$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 485774x^{12} + 87183614355x^{8} + 6839940225440174x^{4} + 198392288899684017121 $ x^16 + 485774x^12 + 87183614355x^8 + 6839940225440174*x^4 + 198392288899684017121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{36} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.8
Root			$14.2877 + 13.5806i$ of defining polynomial
Character	$\chi$	$=$	162.107
Dual form			162.7.d.g.53.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(132.984 - 76.7783i) q^{5} +(-336.136 + 582.205i) q^{7} +181.019i q^{8} +O(q^{10})$	\(q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(132.984 - 76.7783i) q^{5} +(-336.136 + 582.205i) q^{7} +181.019i q^{8} +868.648 q^{10} +(-2216.94 - 1279.95i) q^{11} +(885.045 + 1532.94i) q^{13} +(-3293.45 + 1901.47i) q^{14} +(-512.000 + 886.810i) q^{16} -3978.79i q^{17} -7767.58 q^{19} +(4255.49 + 2456.91i) q^{20} +(-7240.51 - 12540.9i) q^{22} +(-2263.42 + 1306.79i) q^{23} +(3977.33 - 6888.93i) q^{25} +10013.1i q^{26} -21512.7 q^{28} +(-12531.5 - 7235.06i) q^{29} +(22206.0 + 38462.0i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(11253.7 - 19492.0i) q^{34} +103232. i q^{35} -39519.1 q^{37} +(-38053.2 - 21970.0i) q^{38} +(13898.4 + 24072.7i) q^{40} +(14131.5 - 8158.84i) q^{41} +(-27602.8 + 47809.4i) q^{43} -81917.0i q^{44} -14784.6 q^{46} +(-103331. - 59658.1i) q^{47} +(-167150. - 289513. i) q^{49} +(38969.7 - 22499.1i) q^{50} +(-28321.5 + 49054.2i) q^{52} +5933.28i q^{53} -393091. q^{55} +(-105390. - 60847.1i) q^{56} +(-40927.7 - 70888.8i) q^{58} +(-6434.10 + 3714.73i) q^{59} +(-27266.1 + 47226.2i) q^{61} +251232. i q^{62} -32768.0 q^{64} +(235394. + 135905. i) q^{65} +(111770. + 193591. i) q^{67} +(110264. - 63660.7i) q^{68} +(-291984. + 505731. i) q^{70} +72415.7i q^{71} -317041. q^{73} +(-193603. - 111777. i) q^{74} +(-124281. - 215262. i) q^{76} +(1.49039e6 - 860477. i) q^{77} +(-86430.6 + 149702. i) q^{79} +157242. i q^{80} +92306.7 q^{82} +(12699.3 + 7331.94i) q^{83} +(-305485. - 529116. i) q^{85} +(-270451. + 156145. i) q^{86} +(231696. - 401310. i) q^{88} +800260. i q^{89} -1.18998e6 q^{91} +(-72429.6 - 41817.2i) q^{92} +(-337477. - 584528. i) q^{94} +(-1.03296e6 + 596382. i) q^{95} +(83923.0 - 145359. i) q^{97} -1.89109e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 256 q^{4} - 964 q^{7}+O(q^{10}) $ 16 * q + 256 * q^4 - 964 * q^7	$ 16 q + 256 q^{4} - 964 q^{7} - 1536 q^{10} - 4540 q^{13} - 8192 q^{16} - 47368 q^{19} - 27072 q^{22} + 32392 q^{25} - 61696 q^{28} - 77056 q^{31} + 52608 q^{34} - 22696 q^{37} - 24576 q^{40} + 226604 q^{43} - 325440 q^{46} - 1298088 q^{49} + 145280 q^{52} - 2921832 q^{55} - 867456 q^{58} + 327476 q^{61} - 524288 q^{64} - 1713292 q^{67} + 176352 q^{70} - 4378432 q^{73} - 757888 q^{76} + 1326884 q^{79} - 2317632 q^{82} - 3483180 q^{85} + 866304 q^{88} + 2260648 q^{91} + 26400 q^{94} + 2200064 q^{97}+O(q^{100}) $ 16 * q + 256 * q^4 - 964 * q^7 - 1536 * q^10 - 4540 * q^13 - 8192 * q^16 - 47368 * q^19 - 27072 * q^22 + 32392 * q^25 - 61696 * q^28 - 77056 * q^31 + 52608 * q^34 - 22696 * q^37 - 24576 * q^40 + 226604 * q^43 - 325440 * q^46 - 1298088 * q^49 + 145280 * q^52 - 2921832 * q^55 - 867456 * q^58 + 327476 * q^61 - 524288 * q^64 - 1713292 * q^67 + 176352 * q^70 - 4378432 * q^73 - 757888 * q^76 + 1326884 * q^79 - 2317632 * q^82 - 3483180 * q^85 + 866304 * q^88 + 2260648 * q^91 + 26400 * q^94 + 2200064 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	4.89898	+	2.82843i	0.612372	+	0.353553i
$2$	4.89898	+	2.82843i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	16.0000	+	27.7128i	0.250000	+	0.433013i
$5$	132.984	−	76.7783i	1.06387	−	0.614227i	0.137371	−	0.990520i	$-0.456135\pi$
$5$	132.984	−	76.7783i	1.06387	−	0.614227i	0.926501	+	0.376293i	$0.122801\pi$
$6$		0			0
$7$	−336.136	+	582.205i	−0.979989	+	1.69739i	−0.317609	+	0.948222i	$0.602880\pi$
$7$	−336.136	+	582.205i	−0.979989	+	1.69739i	−0.662380	+	0.749168i	$0.730453\pi$
$8$			181.019i			0.353553i
$9$		0			0
$10$	868.648			0.868648
$11$	−2216.94	−	1279.95i	−1.66562	−	0.961647i	−0.969955	−	0.243283i	$-0.921776\pi$
$11$	−2216.94	−	1279.95i	−1.66562	−	0.961647i	−0.695667	−	0.718365i	$-0.744891\pi$
$12$		0			0
$13$	885.045	+	1532.94i	0.402843	+	0.697744i	0.994068	−	0.108763i	$-0.0346888\pi$
$13$	885.045	+	1532.94i	0.402843	+	0.697744i	−0.591225	+	0.806507i	$0.701356\pi$
$14$	−3293.45	+	1901.47i	−1.20024	+	0.692957i
$15$		0			0
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$		−	3978.79i		−	0.809850i	−0.914350	−	0.404925i	$-0.867298\pi$
$17$		−	3978.79i		−	0.809850i	0.914350	−	0.404925i	$-0.132702\pi$
$18$		0			0
$19$	−7767.58			−1.13247			−0.566233	−	0.824245i	$-0.691600\pi$
$19$	−7767.58			−1.13247			−0.566233	+	0.824245i	$0.691600\pi$
$20$	4255.49	+	2456.91i	0.531936	+	0.307113i
$21$		0			0
$22$	−7240.51	−	12540.9i	−0.679987	−	1.17777i
$23$	−2263.42	+	1306.79i	−0.186030	+	0.107404i	−0.590123	−	0.807314i	$-0.700921\pi$
$23$	−2263.42	+	1306.79i	−0.186030	+	0.107404i	0.404093	+	0.914718i	$0.367587\pi$
$24$		0			0
$25$	3977.33	−	6888.93i	0.254549	−	0.440891i
$26$			10013.1i			0.569706i
$27$		0			0
$28$	−21512.7			−0.979989
$29$	−12531.5	−	7235.06i	−0.513817	−	0.296652i	0.220584	−	0.975368i	$-0.429204\pi$
$29$	−12531.5	−	7235.06i	−0.513817	−	0.296652i	−0.734401	+	0.678715i	$0.762537\pi$
$30$		0			0
$31$	22206.0	+	38462.0i	0.745394	+	1.29106i	0.950011	+	0.312218i	$0.101072\pi$
$31$	22206.0	+	38462.0i	0.745394	+	1.29106i	−0.204617	+	0.978842i	$0.565595\pi$
$32$	−5016.55	+	2896.31i	−0.153093	+	0.0883883i
$33$		0			0
$34$	11253.7	−	19492.0i	0.286325	−	0.495930i
$35$			103232.i			2.40774i
$36$		0			0
$37$	−39519.1			−0.780193			−0.390097	−	0.920774i	$-0.627558\pi$
$37$	−39519.1			−0.780193			−0.390097	+	0.920774i	$0.627558\pi$
$38$	−38053.2	−	21970.0i	−0.693491	−	0.400387i
$39$		0			0
$40$	13898.4	+	24072.7i	0.217162	+	0.376135i
$41$	14131.5	−	8158.84i	0.205039	−	0.118380i	−0.393964	−	0.919126i	$-0.628897\pi$
$41$	14131.5	−	8158.84i	0.205039	−	0.118380i	0.599004	+	0.800746i	$0.295563\pi$
$42$		0			0
$43$	−27602.8	+	47809.4i	−0.347174	+	0.601323i	−0.985746	−	0.168239i	$-0.946192\pi$
$43$	−27602.8	+	47809.4i	−0.347174	+	0.601323i	0.638572	+	0.769562i	$0.279525\pi$
$44$		−	81917.0i		−	0.961647i
$45$		0			0
$46$	−14784.6			−0.151893
$47$	−103331.	−	59658.1i	−0.995261	−	0.574614i	−0.0884180	−	0.996083i	$-0.528181\pi$
$47$	−103331.	−	59658.1i	−0.995261	−	0.574614i	−0.906843	+	0.421470i	$0.861514\pi$
$48$		0			0
$49$	−167150.	−	289513.i	−1.42076	−	2.46082i
$50$	38969.7	−	22499.1i	0.311757	−	0.179993i
$51$		0			0
$52$	−28321.5	+	49054.2i	−0.201421	+	0.348872i
$53$			5933.28i			0.0398536i	0.999801	+	0.0199268i	$0.00634331\pi$
$53$			5933.28i			0.0398536i	−0.999801	+	0.0199268i	$0.993657\pi$
$54$		0			0
$55$	−393091.			−2.36268
$56$	−105390.	−	60847.1i	−0.600118	−	0.346478i
$57$		0			0
$58$	−40927.7	−	70888.8i	−0.209765	−	0.363324i
$59$	−6434.10	+	3714.73i	−0.0313279	+	0.0180872i	−0.515582	−	0.856840i	$-0.672424\pi$
$59$	−6434.10	+	3714.73i	−0.0313279	+	0.0180872i	0.484254	+	0.874927i	$0.339091\pi$
$60$		0			0
$61$	−27266.1	+	47226.2i	−0.120125	+	0.208062i	−0.919817	−	0.392348i	$-0.871663\pi$
$61$	−27266.1	+	47226.2i	−0.120125	+	0.208062i	0.799692	+	0.600411i	$0.204996\pi$
$62$			251232.i			1.05415i
$63$		0			0
$64$	−32768.0			−0.125000
$65$	235394.	+	135905.i	0.857146	+	0.494873i
$66$		0			0
$67$	111770.	+	193591.i	0.371621	+	0.643666i	0.989815	−	0.142359i	$-0.0454688\pi$
$67$	111770.	+	193591.i	0.371621	+	0.643666i	−0.618194	+	0.786026i	$0.712135\pi$
$68$	110264.	−	63660.7i	0.350675	−	0.202462i
$69$		0			0
$70$	−291984.	+	505731.i	−0.851265	+	1.47443i
$71$			72415.7i			0.202329i	0.994870	+	0.101164i	$0.0322568\pi$
$71$			72415.7i			0.202329i	−0.994870	+	0.101164i	$0.967743\pi$
$72$		0			0
$73$	−317041.			−0.814979			−0.407489	−	0.913210i	$-0.633596\pi$
$73$	−317041.			−0.814979			−0.407489	+	0.913210i	$0.633596\pi$
$74$	−193603.	−	111777.i	−0.477769	−	0.275840i
$75$		0			0
$76$	−124281.	−	215262.i	−0.283116	−	0.490372i
$77$	1.49039e6	−	860477.i	3.26458	−	1.88481i
$78$		0			0
$79$	−86430.6	+	149702.i	−0.175302	+	0.303632i	−0.940266	−	0.340442i	$-0.889423\pi$
$79$	−86430.6	+	149702.i	−0.175302	+	0.303632i	0.764964	+	0.644073i	$0.222757\pi$
$80$			157242.i			0.307113i
$81$		0			0
$82$	92306.7			0.167414
$83$	12699.3	+	7331.94i	0.0222098	+	0.0128229i	0.511064	−	0.859543i	$-0.329252\pi$
$83$	12699.3	+	7331.94i	0.0222098	+	0.0128229i	−0.488854	+	0.872366i	$0.662585\pi$
$84$		0			0
$85$	−305485.	−	529116.i	−0.497431	−	0.861576i
$86$	−270451.	+	156145.i	−0.425200	+	0.245489i
$87$		0			0
$88$	231696.	−	401310.i	0.339994	−	0.588886i
$89$			800260.i			1.13517i	0.823315	+	0.567585i	$0.192122\pi$
$89$			800260.i			1.13517i	−0.823315	+	0.567585i	$0.807878\pi$
$90$		0			0
$91$	−1.18998e6			−1.57913
$92$	−72429.6	−	41817.2i	−0.0930149	−	0.0537022i
$93$		0			0
$94$	−337477.	−	584528.i	−0.406313	−	0.703755i
$95$	−1.03296e6	+	596382.i	−1.20480	+	0.695591i
$96$		0			0
$97$	83923.0	−	145359.i	0.0919529	−	0.159267i	−0.816380	−	0.577515i	$-0.804022\pi$
$97$	83923.0	−	145359.i	0.0919529	−	0.159267i	0.908333	+	0.418248i	$0.137356\pi$
$98$		−	1.89109e6i		−	2.00925i
$99$		0			0
$100$	254549.			0.254549
$101$	−221787.	−	128049.i	−0.215264	−	0.124283i	0.388492	−	0.921452i	$-0.372996\pi$
$101$	−221787.	−	128049.i	−0.215264	−	0.124283i	−0.603755	+	0.797170i	$0.706330\pi$
$102$		0			0
$103$	−40307.0	−	69813.8i	−0.0368866	−	0.0638895i	0.846993	−	0.531605i	$-0.178411\pi$
$103$	−40307.0	−	69813.8i	−0.0368866	−	0.0638895i	−0.883879	+	0.467715i	$0.845077\pi$
$104$	−277492.	+	160210.i	−0.246690	+	0.142426i
$105$		0			0
$106$	−16781.9	+	29067.0i	−0.0140904	+	0.0244052i
$107$			991514.i			0.809371i	0.914456	+	0.404685i	$0.132619\pi$
$107$			991514.i			0.809371i	−0.914456	+	0.404685i	$0.867381\pi$
$108$		0			0
$109$	2.01080e6			1.55270			0.776352	−	0.630300i	$-0.217068\pi$
$109$	2.01080e6			1.55270			0.776352	+	0.630300i	$0.217068\pi$
$110$	−1.92574e6	−	1.11183e6i	−1.44684	−	0.835333i
$111$		0			0
$112$	−344203.	−	596178.i	−0.244997	−	0.424348i
$113$	238211.	−	137531.i	0.165092	−	0.0953159i	−0.415178	−	0.909740i	$-0.636281\pi$
$113$	238211.	−	137531.i	0.165092	−	0.0953159i	0.580270	+	0.814424i	$0.302947\pi$
$114$		0			0
$115$	−200666.	+	347564.i	−0.131941	+	0.228529i
$116$		−	463044.i		−	0.296652i
$117$		0			0
$118$	−42027.4			−0.0255791
$119$	2.31647e6	+	1.33742e6i	1.37463	+	0.793644i
$120$		0			0
$121$	2.39078e6	+	4.14095e6i	1.34953	+	2.33746i
$122$	−267152.	+	154240.i	−0.147122	+	0.0849411i
$123$		0			0
$124$	−710593.	+	1.23078e6i	−0.372697	+	0.645530i
$125$			1.17783e6i			0.603051i
$126$		0			0
$127$	−864483.			−0.422032			−0.211016	−	0.977483i	$-0.567677\pi$
$127$	−864483.			−0.422032			−0.211016	+	0.977483i	$0.567677\pi$
$128$	−160530.	−	92681.9i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	768793.	+	1.33159e6i	0.349928	+	0.606094i
$131$	−1.03882e6	+	599764.i	−0.462091	+	0.266788i	−0.712923	−	0.701242i	$-0.752629\pi$
$131$	−1.03882e6	+	599764.i	−0.462091	+	0.266788i	0.250832	+	0.968031i	$0.419296\pi$
$132$		0			0
$133$	2.61097e6	−	4.52232e6i	1.10980	−	1.92224i
$134$			1.26453e6i			0.525551i
$135$		0			0
$136$	720238.			0.286325
$137$	2.16875e6	+	1.25213e6i	0.843426	+	0.486952i	0.858427	−	0.512935i	$-0.171442\pi$
$137$	2.16875e6	+	1.25213e6i	0.843426	+	0.486952i	−0.0150012	+	0.999887i	$0.504775\pi$
$138$		0			0
$139$	1.07273e6	+	1.85802e6i	0.399434	+	0.691841i	0.993656	−	0.112460i	$-0.0358732\pi$
$139$	1.07273e6	+	1.85802e6i	0.399434	+	0.691841i	−0.594222	+	0.804301i	$0.702540\pi$
$140$	−2.86085e6	+	1.65171e6i	−1.04258	+	0.601935i
$141$		0			0
$142$	−204823.	+	354763.i	−0.0715341	+	0.123901i
$143$		−	4.53126e6i		−	1.54957i
$144$		0			0
$145$	−2.22198e6			−0.728847
$146$	−1.55318e6	−	896726.i	−0.499071	−	0.288139i
$147$		0			0
$148$	−632306.	−	1.09519e6i	−0.195048	−	0.337834i
$149$	−3.18418e6	+	1.83838e6i	−0.962583	+	0.555748i	−0.896967	−	0.442097i	$-0.854235\pi$
$149$	−3.18418e6	+	1.83838e6i	−0.962583	+	0.555748i	−0.0656159	+	0.997845i	$0.520901\pi$
$150$		0			0
$151$	1.81065e6	−	3.13614e6i	0.525901	−	0.910886i	−0.473644	−	0.880716i	$-0.657062\pi$
$151$	1.81065e6	−	3.13614e6i	0.525901	−	0.910886i	0.999545	−	0.0301702i	$-0.00960493\pi$
$152$		−	1.40608e6i		−	0.400387i
$153$		0			0
$154$	9.73518e6			2.66552
$155$	5.90609e6	+	3.40988e6i	1.58601	+	0.915681i
$156$		0			0
$157$	−2.13140e6	−	3.69169e6i	−0.550765	−	0.953952i	−0.998220	−	0.0596459i	$-0.981003\pi$
$157$	−2.13140e6	−	3.69169e6i	−0.550765	−	0.953952i	0.447455	−	0.894306i	$-0.352330\pi$
$158$	−846844.	+	488925.i	−0.214700	+	0.123957i
$159$		0			0
$160$	−444748.	+	770325.i	−0.108581	+	0.188068i
$161$		−	1.75703e6i		−	0.421020i
$162$		0			0
$163$	6.80481e6			1.57128			0.785639	−	0.618685i	$-0.212334\pi$
$163$	6.80481e6			1.57128			0.785639	+	0.618685i	$0.212334\pi$
$164$	452209.	+	261083.i	0.102520	+	0.0591898i
$165$		0			0
$166$	41475.7	+	71838.1i	0.00906713	+	0.0157047i
$167$	6.56268e6	−	3.78897e6i	1.40907	−	0.813526i	0.413770	−	0.910381i	$-0.364212\pi$
$167$	6.56268e6	−	3.78897e6i	1.40907	−	0.813526i	0.995298	+	0.0968555i	$0.0308785\pi$
$168$		0			0
$169$	846794.	−	1.46669e6i	0.175436	−	0.303863i
$170$		−	3.45617e6i		−	0.703474i
$171$		0			0
$172$	−1.76658e6			−0.347174
$173$	−3.61959e6	−	2.08977e6i	−0.699070	−	0.403608i	0.107931	−	0.994158i	$-0.465578\pi$
$173$	−3.61959e6	−	2.08977e6i	−0.699070	−	0.403608i	−0.807001	+	0.590550i	$0.798911\pi$
$174$		0			0
$175$	2.67385e6	+	4.63124e6i	0.498910	+	0.864137i
$176$	2.27015e6	−	1.31067e6i	0.416406	−	0.240412i
$177$		0			0
$178$	−2.26348e6	+	3.92046e6i	−0.401343	+	0.695147i
$179$			5.42321e6i			0.945578i	0.881176	+	0.472789i	$0.156753\pi$
$179$			5.42321e6i			0.945578i	−0.881176	+	0.472789i	$0.843247\pi$
$180$		0			0
$181$	4.86015e6			0.819623			0.409812	−	0.912170i	$-0.365594\pi$
$181$	4.86015e6			0.819623			0.409812	+	0.912170i	$0.365594\pi$
$182$	−5.82970e6	−	3.36578e6i	−0.967013	−	0.558305i
$183$		0			0
$184$	−236554.	−	409723.i	−0.0379732	−	0.0657714i
$185$	−5.25541e6	+	3.03421e6i	−0.830025	+	0.479215i
$186$		0			0
$187$	−5.09266e6	+	8.82075e6i	−0.778790	+	1.34890i
$188$		−	3.81812e6i		−	0.574614i
$189$		0			0
$190$	−6.74729e6			−0.983714
$191$	2.75428e6	+	1.59018e6i	0.395282	+	0.228216i	0.684446	−	0.729063i	$-0.260044\pi$
$191$	2.75428e6	+	1.59018e6i	0.395282	+	0.228216i	−0.289164	+	0.957280i	$0.593377\pi$
$192$		0			0
$193$	3.34346e6	+	5.79105e6i	0.465077	+	0.805537i	0.999205	−	0.0398667i	$-0.0126933\pi$
$193$	3.34346e6	+	5.79105e6i	0.465077	+	0.805537i	−0.534128	+	0.845404i	$0.679360\pi$
$194$	822274.	−	474740.i	0.112619	−	0.0650205i
$195$		0			0
$196$	5.34881e6	−	9.26442e6i	0.710378	−	1.23041i
$197$		−	1.54760e6i		−	0.202423i	−0.994865	−	0.101212i	$-0.967728\pi$
$197$		−	1.54760e6i		−	0.202423i	0.994865	−	0.101212i	$-0.0322719\pi$
$198$		0			0
$199$	1.08352e7			1.37493			0.687463	−	0.726219i	$-0.258724\pi$
$199$	1.08352e7			1.37493			0.687463	+	0.726219i	$0.258724\pi$
$200$	1.24703e6	+	719973.i	0.155879	+	0.0899966i
$201$		0			0
$202$	−724352.	−	1.25461e6i	−0.0878811	−	0.152215i
$203$	8.42457e6	−	4.86393e6i	1.00707	−	0.581432i
$204$		0			0
$205$	1.25284e6	−	2.16999e6i	0.145424	−	0.251881i
$206$		−	456022.i		−	0.0521656i
$207$		0			0
$208$	−1.81257e6			−0.201421
$209$	1.72203e7	+	9.94214e6i	1.88626	+	1.08903i
$210$		0			0
$211$	−6.89727e6	−	1.19464e7i	−0.734226	−	1.27172i	−0.955062	−	0.296406i	$-0.904212\pi$
$211$	−6.89727e6	−	1.19464e7i	−0.734226	−	1.27172i	0.220835	−	0.975311i	$-0.429122\pi$
$212$	−164428.	+	94932.5i	−0.0172571	+	0.00996339i
$213$		0			0
$214$	−2.80442e6	+	4.85741e6i	−0.286156	+	0.495636i
$215$			8.47718e6i			0.852974i
$216$		0			0
$217$	−2.98570e7			−2.92191
$218$	9.85085e6	+	5.68739e6i	0.950833	+	0.548963i
$219$		0			0
$220$	−6.28945e6	−	1.08936e7i	−0.590669	−	1.02307i
$221$	6.09926e6	−	3.52141e6i	0.565068	−	0.326242i
$222$		0			0
$223$	253620.	−	439282.i	0.0228701	−	0.0396122i	−0.854364	−	0.519675i	$-0.826053\pi$
$223$	253620.	−	439282.i	0.0228701	−	0.0396122i	0.877234	+	0.480063i	$0.159386\pi$
$224$		−	3.89422e6i		−	0.346478i
$225$		0			0
$226$	1.55599e6			0.134797
$227$	−1.74677e7	−	1.00850e7i	−1.49334	−	0.862178i	−0.493366	−	0.869822i	$-0.664234\pi$
$227$	−1.74677e7	−	1.00850e7i	−1.49334	−	0.862178i	−0.999971	+	0.00764350i	$0.997567\pi$
$228$		0			0
$229$	1.79949e6	+	3.11681e6i	0.149845	+	0.259540i	0.931170	−	0.364585i	$-0.118789\pi$
$229$	1.79949e6	+	3.11681e6i	0.149845	+	0.259540i	−0.781325	+	0.624125i	$0.785456\pi$
$230$	−1.96612e6	+	1.13514e6i	−0.161594	+	0.0932965i
$231$		0			0
$232$	1.30969e6	−	2.26844e6i	0.104882	−	0.181662i
$233$		−	4.20593e6i		−	0.332502i	−0.986083	−	0.166251i	$-0.946834\pi$
$233$		−	4.20593e6i		−	0.332502i	0.986083	−	0.166251i	$-0.0531662\pi$
$234$		0			0
$235$	−1.83218e7			−1.41177
$236$	−205891.	−	118871.i	−0.0156640	−	0.00904359i
$237$		0			0
$238$	7.56556e6	+	1.31039e7i	0.561191	+	0.972011i
$239$	−1.46389e7	+	8.45177e6i	−1.07230	+	0.619090i	−0.928808	−	0.370562i	$-0.879165\pi$
$239$	−1.46389e7	+	8.45177e6i	−1.07230	+	0.619090i	−0.143488	+	0.989652i	$0.545832\pi$
$240$		0			0
$241$	−1.08021e7	+	1.87097e7i	−0.771712	+	1.33664i	0.164912	+	0.986308i	$0.447266\pi$
$241$	−1.08021e7	+	1.87097e7i	−0.771712	+	1.33664i	−0.936624	+	0.350337i	$0.886067\pi$
$242$			2.70486e7i			1.90853i
$243$		0			0
$244$	−1.74503e6			−0.120125
$245$	−4.44567e7	−	2.56671e7i	−3.02300	−	1.74533i
$246$		0			0
$247$	−6.87466e6	−	1.19073e7i	−0.456206	−	0.790171i
$248$	−6.96236e6	+	4.01972e6i	−0.456459	+	0.263536i
$249$		0			0
$250$	−3.33142e6	+	5.77018e6i	−0.213211	+	0.369292i
$251$			9.17726e6i			0.580352i	0.956973	+	0.290176i	$0.0937139\pi$
$251$			9.17726e6i			0.580352i	−0.956973	+	0.290176i	$0.906286\pi$
$252$		0			0
$253$	6.69051e6			0.413140
$254$	−4.23508e6	−	2.44513e6i	−0.258441	−	0.149211i
$255$		0			0
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	1.67068e7	−	9.64565e6i	0.984221	−	0.568240i	0.0806793	−	0.996740i	$-0.474291\pi$
$257$	1.67068e7	−	9.64565e6i	0.984221	−	0.568240i	0.903542	+	0.428500i	$0.140958\pi$
$258$		0			0
$259$	1.32838e7	−	2.30082e7i	0.764580	−	1.32429i
$260$			8.69790e6i			0.494873i
$261$		0			0
$262$	−6.78556e6			−0.377296
$263$	−1.67748e7	−	9.68495e6i	−0.922127	−	0.532390i	−0.0378141	−	0.999285i	$-0.512039\pi$
$263$	−1.67748e7	−	9.68495e6i	−0.922127	−	0.532390i	−0.884313	+	0.466894i	$0.845373\pi$
$264$		0			0
$265$	455547.	+	789031.i	0.0244791	+	0.0423991i
$266$	2.55821e7	−	1.47698e7i	1.35923	−	0.784750i
$267$		0			0
$268$	−3.57664e6	+	6.19491e6i	−0.185811	+	0.321833i
$269$		−	2.18670e7i		−	1.12340i	−0.827343	−	0.561698i	$-0.810148\pi$
$269$		−	2.18670e7i		−	1.12340i	0.827343	−	0.561698i	$-0.189852\pi$
$270$		0			0
$271$	−8.52403e6			−0.428289			−0.214145	−	0.976802i	$-0.568696\pi$
$271$	−8.52403e6			−0.428289			−0.214145	+	0.976802i	$0.568696\pi$
$272$	3.52843e6	+	2.03714e6i	0.175338	+	0.101231i
$273$		0			0
$274$	7.08310e6	+	1.22683e7i	0.344327	+	0.596392i
$275$	−1.76350e7	+	1.01816e7i	−0.847964	+	0.489572i
$276$		0			0
$277$	−1.21342e7	+	2.10170e7i	−0.570914	+	0.988853i	0.425558	+	0.904931i	$0.360078\pi$
$277$	−1.21342e7	+	2.10170e7i	−0.570914	+	0.988853i	−0.996472	+	0.0839216i	$0.973255\pi$
$278$			1.21365e7i			0.564886i
$279$		0			0
$280$	−1.86870e7			−0.851265
$281$	3.60862e7	+	2.08344e7i	1.62638	+	0.938990i	0.985161	+	0.171631i	$0.0549038\pi$
$281$	3.60862e7	+	2.08344e7i	1.62638	+	0.938990i	0.641218	+	0.767359i	$0.278429\pi$
$282$		0			0
$283$	−1.67549e7	−	2.90204e7i	−0.739237	−	1.28040i	−0.952839	−	0.303475i	$-0.901853\pi$
$283$	−1.67549e7	−	2.90204e7i	−0.739237	−	1.28040i	0.213602	−	0.976921i	$-0.431480\pi$
$284$	−2.00684e6	+	1.15865e6i	−0.0876110	+	0.0505822i
$285$		0			0
$286$	1.28164e7	−	2.21986e7i	0.547856	−	0.948914i
$287$			1.09699e7i			0.464043i
$288$		0			0
$289$	8.30679e6			0.344143
$290$	−1.08854e7	−	6.28472e6i	−0.446326	−	0.257687i
$291$		0			0
$292$	−5.07265e6	−	8.78609e6i	−0.203745	−	0.352896i
$293$	−1.01473e7	+	5.85854e6i	−0.403411	+	0.232909i	−0.687955	−	0.725754i	$-0.741491\pi$
$293$	−1.01473e7	+	5.85854e6i	−0.403411	+	0.232909i	0.284544	+	0.958663i	$0.408158\pi$
$294$		0			0
$295$	−570421.	+	987999.i	−0.0222193	+	0.0384849i
$296$		−	7.15372e6i		−	0.275840i
$297$		0			0
$298$	−2.07989e7			−0.785946
$299$	−4.00647e6	−	2.31313e6i	−0.149881	−	0.0865341i
$300$		0			0
$301$	−1.85566e7	−	3.21409e7i	−0.680453	−	1.17858i
$302$	1.77407e7	−	1.02426e7i	0.644094	−	0.371868i
$303$		0			0
$304$	3.97700e6	−	6.88837e6i	0.141558	−	0.245186i
$305$			8.37377e6i			0.295136i
$306$		0			0
$307$	−1.61170e7			−0.557019			−0.278510	−	0.960433i	$-0.589840\pi$
$307$	−1.61170e7			−0.557019			−0.278510	+	0.960433i	$0.589840\pi$
$308$	4.76925e7	+	2.75353e7i	1.63229	+	0.942403i
$309$		0			0
$310$	1.92892e7	+	3.34099e7i	0.647484	+	1.12148i
$311$	−3.01350e7	+	1.73984e7i	−1.00182	+	0.578401i	−0.908786	−	0.417262i	$-0.862990\pi$
$311$	−3.01350e7	+	1.73984e7i	−1.00182	+	0.578401i	−0.0930334	+	0.995663i	$0.529656\pi$
$312$		0			0
$313$	−601891.	+	1.04251e6i	−0.0196284	+	0.0339974i	−0.875673	−	0.482905i	$-0.839582\pi$
$313$	−601891.	+	1.04251e6i	−0.0196284	+	0.0339974i	0.856044	+	0.516902i	$0.172915\pi$
$314$		−	2.41140e7i		−	0.778899i
$315$		0			0
$316$	−5.53156e6			−0.175302
$317$	−3.78377e7	−	2.18456e7i	−1.18781	−	0.685783i	−0.230002	−	0.973190i	$-0.573873\pi$
$317$	−3.78377e7	−	2.18456e7i	−1.18781	−	0.685783i	−0.957808	+	0.287408i	$0.907207\pi$
$318$		0			0
$319$	1.85211e7	+	3.20794e7i	0.570550	+	0.988222i
$320$	−4.35762e6	+	2.51587e6i	−0.132984	+	0.0767783i
$321$		0			0
$322$	4.96964e6	−	8.60768e6i	0.148853	−	0.257821i
$323$			3.09056e7i			0.917127i
$324$		0			0
$325$	1.40805e7			0.410173
$326$	3.33366e7	+	1.92469e7i	0.962208	+	0.555531i
$327$		0			0
$328$	1.47691e6	+	2.55808e6i	0.0418535	+	0.0724924i
$329$	6.94665e7	−	4.01065e7i	1.95069	−	1.12623i
$330$		0			0
$331$	−2.80293e7	+	4.85481e7i	−0.772908	+	1.33872i	0.163054	+	0.986617i	$0.447865\pi$
$331$	−2.80293e7	+	4.85481e7i	−0.772908	+	1.33872i	−0.935963	+	0.352099i	$0.885468\pi$
$332$			469244.i			0.0128229i
$333$		0			0
$334$	4.28673e7			1.15050
$335$	2.97272e7	+	1.71630e7i	0.790714	+	0.456519i
$336$		0			0
$337$	2.43291e7	+	4.21392e7i	0.635676	+	1.10102i	0.986371	+	0.164534i	$0.0526120\pi$
$337$	2.43291e7	+	4.21392e7i	0.635676	+	1.10102i	−0.350695	+	0.936490i	$0.614055\pi$
$338$	8.29685e6	−	4.79019e6i	0.214864	−	0.124052i
$339$		0			0
$340$	9.77552e6	−	1.69317e7i	0.248716	−	0.430788i
$341$		−	1.13691e8i		−	2.86722i
$342$		0			0
$343$	1.45649e8			3.60932
$344$	−8.65443e6	−	4.99664e6i	−0.212600	−	0.122745i
$345$		0			0
$346$	−1.18215e7	−	2.04755e7i	−0.285394	−	0.494317i
$347$	−578894.	+	334225.i	−0.0138551	+	0.00799927i	−0.506912	−	0.861998i	$-0.669213\pi$
$347$	−578894.	+	334225.i	−0.0138551	+	0.00799927i	0.493056	+	0.869997i	$0.335880\pi$
$348$		0			0
$349$	−3.30947e6	+	5.73217e6i	−0.0778542	+	0.134847i	−0.902324	−	0.431059i	$-0.858140\pi$
$349$	−3.30947e6	+	5.73217e6i	−0.0778542	+	0.134847i	0.824470	+	0.565906i	$0.191474\pi$
$350$			3.02511e7i			0.705565i
$351$		0			0
$352$	1.48286e7			0.339994
$353$	−3.34516e7	−	1.93133e7i	−0.760490	−	0.439069i	0.0689819	−	0.997618i	$-0.478025\pi$
$353$	−3.34516e7	−	1.93133e7i	−0.760490	−	0.439069i	−0.829471	+	0.558549i	$0.811358\pi$
$354$		0			0
$355$	5.55996e6	+	9.63013e6i	0.124276	+	0.215252i
$356$	−2.21775e7	+	1.28042e7i	−0.491543	+	0.283793i
$357$		0			0
$358$	−1.53392e7	+	2.65682e7i	−0.334312	+	0.579046i
$359$		−	4.14923e7i		−	0.896776i	−0.893839	−	0.448388i	$-0.851998\pi$
$359$		−	4.14923e7i		−	0.896776i	0.893839	−	0.448388i	$-0.148002\pi$
$360$		0			0
$361$	1.32895e7			0.282479
$362$	2.38098e7	+	1.37466e7i	0.501915	+	0.289781i
$363$		0			0
$364$	−1.90397e7	−	3.29778e7i	−0.394781	−	0.683781i
$365$	−4.21613e7	+	2.43419e7i	−0.867033	+	0.500582i
$366$		0			0
$367$	−1.22127e7	+	2.11530e7i	−0.247066	+	0.427931i	−0.962710	−	0.270534i	$-0.912800\pi$
$367$	−1.22127e7	+	2.11530e7i	−0.247066	+	0.427931i	0.715645	+	0.698465i	$0.246133\pi$
$368$		−	2.67630e6i		−	0.0537022i
$369$		0			0
$370$	−3.43282e7			−0.677713
$371$	−3.45438e6	−	1.99439e6i	−0.0676471	−	0.0390560i
$372$		0			0
$373$	−1.26112e7	−	2.18432e7i	−0.243013	−	0.420911i	0.718558	−	0.695467i	$-0.244803\pi$
$373$	−1.26112e7	−	2.18432e7i	−0.243013	−	0.420911i	−0.961571	+	0.274556i	$0.911469\pi$
$374$	−4.98977e7	+	2.88085e7i	−0.953819	+	0.550688i
$375$		0			0
$376$	1.07993e7	−	1.87049e7i	0.203157	−	0.351878i
$377$		−	2.56134e7i		−	0.478017i
$378$		0			0
$379$	−6.95718e6			−0.127795			−0.0638977	−	0.997956i	$-0.520353\pi$
$379$	−6.95718e6			−0.127795			−0.0638977	+	0.997956i	$0.520353\pi$
$380$	−3.30548e7	−	1.90842e7i	−0.602399	−	0.347795i
$381$		0			0
$382$	8.99543e6	+	1.55805e7i	0.161373	+	0.279507i
$383$	−3.11534e7	+	1.79864e7i	−0.554509	+	0.320146i	−0.750939	−	0.660372i	$-0.770399\pi$
$383$	−3.11534e7	+	1.79864e7i	−0.554509	+	0.320146i	0.196429	+	0.980518i	$0.437065\pi$
$384$		0			0
$385$	1.32132e8	−	2.28859e8i	2.31540	−	4.01039i
$386$			3.78270e7i			0.657718i
$387$		0			0
$388$	5.37107e6			0.0919529
$389$	4.35374e7	+	2.51364e7i	0.739629	+	0.427025i	0.821935	−	0.569582i	$-0.192895\pi$
$389$	4.35374e7	+	2.51364e7i	0.739629	+	0.427025i	−0.0823052	+	0.996607i	$0.526228\pi$
$390$		0			0
$391$	5.19944e6	+	9.00569e6i	0.0869813	+	0.150656i
$392$	5.24075e7	−	3.02575e7i	0.870031	−	0.502313i
$393$		0			0
$394$	4.37727e6	−	7.58166e6i	0.0715674	−	0.123958i
$395$			2.65440e7i			0.430700i
$396$		0			0
$397$	2.70307e7			0.432002			0.216001	−	0.976393i	$-0.430699\pi$
$397$	2.70307e7			0.432002			0.216001	+	0.976393i	$0.430699\pi$
$398$	5.30816e7	+	3.06467e7i	0.841967	+	0.486110i
$399$		0			0
$400$	4.07278e6	+	7.05426e6i	0.0636372	+	0.110223i
$401$	−7.00834e7	+	4.04627e7i	−1.08688	+	0.627511i	−0.932744	−	0.360539i	$-0.882593\pi$
$401$	−7.00834e7	+	4.04627e7i	−1.08688	+	0.627511i	−0.154137	+	0.988050i	$0.549260\pi$
$402$		0			0
$403$	−3.93067e7	+	6.80812e7i	−0.600553	+	1.04019i
$404$		−	8.19511e6i		−	0.124283i
$405$		0			0
$406$	5.50291e7			0.822269
$407$	8.76116e7	+	5.05826e7i	1.29951	+	0.750271i
$408$		0			0
$409$	3.21740e7	+	5.57270e7i	0.470257	+	0.814509i	0.999421	−	0.0340102i	$-0.0108279\pi$
$409$	3.21740e7	+	5.57270e7i	0.470257	+	0.814509i	−0.529164	+	0.848519i	$0.677495\pi$
$410$	1.22753e7	−	7.08716e6i	0.178107	−	0.102830i
$411$		0			0
$412$	1.28983e6	−	2.23404e6i	0.0184433	−	0.0319448i
$413$		−	4.99462e6i		−	0.0709009i
$414$		0			0
$415$	2.25174e6			0.0315046
$416$	−8.87976e6	−	5.12673e6i	−0.123345	−	0.0712132i
$417$		0			0
$418$	5.62412e7	+	9.74127e7i	0.770062	+	1.33379i
$419$	4.80649e7	−	2.77503e7i	0.653410	−	0.377247i	−0.136351	−	0.990661i	$-0.543538\pi$
$419$	4.80649e7	−	2.77503e7i	0.653410	−	0.377247i	0.789762	+	0.613414i	$0.210204\pi$
$420$		0			0
$421$	−1.37634e7	+	2.38390e7i	−0.184451	+	0.319478i	−0.943391	−	0.331682i	$-0.892384\pi$
$421$	−1.37634e7	+	2.38390e7i	−0.184451	+	0.319478i	0.758941	+	0.651160i	$0.225717\pi$
$422$		−	7.80337e7i		−	1.03835i
$423$		0			0
$424$	−1.07404e6			−0.0140904
$425$	−2.74096e7	−	1.58249e7i	−0.357056	−	0.206146i
$426$		0			0
$427$	−1.83302e7	−	3.17489e7i	−0.235442	−	0.407797i
$428$	−2.74776e7	+	1.58642e7i	−0.350468	+	0.202343i
$429$		0			0
$430$	−2.39771e7	+	4.15295e7i	−0.301572	+	0.522338i
$431$			1.36305e8i			1.70248i	0.524779	+	0.851238i	$0.324148\pi$
$431$			1.36305e8i			1.70248i	−0.524779	+	0.851238i	$0.675852\pi$
$432$		0			0
$433$	−1.06153e8			−1.30758			−0.653792	−	0.756675i	$-0.726823\pi$
$433$	−1.06153e8			−1.30758			−0.653792	+	0.756675i	$0.726823\pi$
$434$	−1.46269e8	−	8.44483e7i	−1.78930	−	1.03305i
$435$		0			0
$436$	3.21727e7	+	5.57248e7i	0.388176	+	0.672340i
$437$	1.75813e7	−	1.01506e7i	0.210672	−	0.121632i
$438$		0			0
$439$	−3.15647e7	+	5.46717e7i	−0.373086	+	0.646203i	−0.990039	−	0.140797i	$-0.955034\pi$
$439$	−3.15647e7	+	5.46717e7i	−0.373086	+	0.646203i	0.616953	+	0.787000i	$0.288367\pi$
$440$		−	7.11570e7i		−	0.835333i
$441$		0			0
$442$	3.98402e7			0.461376
$443$	4.11188e7	+	2.37399e7i	0.472965	+	0.273066i	0.717480	−	0.696579i	$-0.245295\pi$
$443$	4.11188e7	+	2.37399e7i	0.472965	+	0.273066i	−0.244515	+	0.969645i	$0.578629\pi$
$444$		0			0
$445$	6.14426e7	+	1.06422e8i	0.697252	+	1.20768i
$446$	2.48496e6	−	1.43469e6i	0.0280101	−	0.0161716i
$447$		0			0
$448$	1.10145e7	−	1.90777e7i	0.122499	−	0.212174i
$449$			1.11141e8i			1.22782i	0.789376	+	0.613910i	$0.210404\pi$
$449$			1.11141e8i			1.22782i	−0.789376	+	0.613910i	$0.789596\pi$
$450$		0			0
$451$	−4.17717e7			−0.455358
$452$	7.62275e6	+	4.40099e6i	0.0825460	+	0.0476580i
$453$		0			0
$454$	−5.70492e7	−	9.88121e7i	−0.609652	−	1.05595i
$455$	−1.58249e8	+	9.13649e7i	−1.67999	+	0.969941i
$456$		0			0
$457$	4.40606e7	−	7.63153e7i	0.461639	−	0.799582i	−0.537404	−	0.843325i	$-0.680595\pi$
$457$	4.40606e7	−	7.63153e7i	0.461639	−	0.799582i	0.999043	+	0.0437431i	$0.0139283\pi$
$458$			2.03589e7i			0.211913i
$459$		0			0
$460$	−1.28426e7			−0.131941
$461$	−1.21222e8	−	6.99877e7i	−1.23731	−	0.714363i	−0.268769	−	0.963205i	$-0.586617\pi$
$461$	−1.21222e8	−	6.99877e7i	−1.23731	−	0.714363i	−0.968544	+	0.248842i	$0.919950\pi$
$462$		0			0
$463$	−6.56085e7	−	1.13637e8i	−0.661024	−	1.14493i	−0.980347	−	0.197281i	$-0.936789\pi$
$463$	−6.56085e7	−	1.13637e8i	−0.661024	−	1.14493i	0.319323	−	0.947646i	$-0.396544\pi$
$464$	1.28322e7	−	7.40870e6i	0.128454	−	0.0741631i
$465$		0			0
$466$	1.18962e7	−	2.06048e7i	0.117557	−	0.203615i
$467$		−	8.32231e7i		−	0.817134i	−0.912728	−	0.408567i	$-0.866029\pi$
$467$		−	8.32231e7i		−	0.817134i	0.912728	−	0.408567i	$-0.133971\pi$
$468$		0			0
$469$	−1.50280e8			−1.45674
$470$	−8.97582e7	−	5.18219e7i	−0.864531	−	0.499137i
$471$		0			0
$472$	−672438.	−	1.16470e6i	−0.00639479	−	0.0110761i
$473$	1.22388e8	−	7.06605e7i	1.15652	−	0.667718i
$474$		0			0
$475$	−3.08942e7	+	5.35103e7i	−0.288268	+	0.499295i
$476$			8.55946e7i			0.793644i
$477$		0			0
$478$	−9.56208e7			−0.875525
$479$	1.28601e8	+	7.42478e7i	1.17014	+	0.675580i	0.953713	−	0.300719i	$-0.0972266\pi$
$479$	1.28601e8	+	7.42478e7i	1.17014	+	0.675580i	0.216426	+	0.976299i	$0.430560\pi$
$480$		0			0
$481$	−3.49762e7	−	6.05806e7i	−0.314295	−	0.544375i
$482$	−1.05838e8	+	6.11057e7i	−0.945151	+	0.545683i
$483$		0			0
$484$	−7.65049e7	+	1.32510e8i	−0.674766	+	1.16873i
$485$		−	2.57739e7i		−	0.225920i
$486$		0			0
$487$	1.02978e8			0.891571			0.445785	−	0.895140i	$-0.352924\pi$
$487$	1.02978e8			0.891571			0.445785	+	0.895140i	$0.352924\pi$
$488$	−8.54885e6	−	4.93568e6i	−0.0735611	−	0.0424705i
$489$		0			0
$490$	−1.45195e8	−	2.51485e8i	−1.23414	−	2.13759i
$491$	1.13163e8	−	6.53345e7i	0.956001	−	0.551948i	0.0610613	−	0.998134i	$-0.480551\pi$
$491$	1.13163e8	−	6.53345e7i	0.956001	−	0.551948i	0.894940	+	0.446186i	$0.147218\pi$
$492$		0			0
$493$	−2.87868e7	+	4.98602e7i	−0.240244	+	0.416115i
$494$		−	7.77779e7i		−	0.645172i
$495$		0			0
$496$	−4.54779e7			−0.372697
$497$	−4.21608e7	−	2.43415e7i	−0.343431	−	0.198280i
$498$		0			0
$499$	−7.41479e7	−	1.28428e8i	−0.596757	−	1.03361i	−0.993296	−	0.115596i	$-0.963122\pi$
$499$	−7.41479e7	−	1.28428e8i	−0.596757	−	1.03361i	0.396539	−	0.918018i	$-0.370211\pi$
$500$	−3.26411e7	+	1.88453e7i	−0.261129	+	0.150763i
$501$		0			0
$502$	−2.59572e7	+	4.49592e7i	−0.205186	+	0.355392i
$503$		−	4.70389e6i		−	0.0369618i	−0.999829	−	0.0184809i	$-0.994117\pi$
$503$		−	4.70389e6i		−	0.0369618i	0.999829	−	0.0184809i	$-0.00588300\pi$
$504$		0			0
$505$	−3.93254e7			−0.305351
$506$	3.27767e7	+	1.89236e7i	0.252996	+	0.146067i
$507$		0			0
$508$	−1.38317e7	−	2.39573e7i	−0.105508	−	0.182745i
$509$	1.99743e8	−	1.15322e8i	1.51467	−	0.874496i	0.514820	−	0.857298i	$-0.327859\pi$
$509$	1.99743e8	−	1.15322e8i	1.51467	−	0.874496i	0.999852	−	0.0171979i	$-0.00547454\pi$
$510$		0			0
$511$	1.06569e8	−	1.84583e8i	0.798670	−	1.38334i
$512$		−	5.93164e6i		−	0.0441942i
$513$		0			0
$514$	1.09128e8			0.803613
$515$	−1.07204e7	−	6.18941e6i	−0.0784853	−	0.0453135i
$516$		0			0
$517$	1.52719e8	+	2.64517e8i	1.10515	+	1.91418i
$518$	1.30154e8	−	7.51445e7i	0.936416	−	0.540640i
$519$		0			0
$520$	−2.46014e7	+	4.26108e7i	−0.174964	+	0.303047i
$521$		−	1.23094e8i		−	0.870413i	−0.900331	−	0.435207i	$-0.856675\pi$
$521$		−	1.23094e8i		−	0.870413i	0.900331	−	0.435207i	$-0.143325\pi$
$522$		0			0
$523$	−2.36329e8			−1.65201			−0.826004	−	0.563664i	$-0.809391\pi$
$523$	−2.36329e8			−1.65201			−0.826004	+	0.563664i	$0.809391\pi$
$524$	−3.32423e7	−	1.91925e7i	−0.231045	−	0.133394i
$525$		0			0
$526$	−5.47864e7	−	9.48928e7i	−0.376457	−	0.652042i
$527$	1.53032e8	−	8.83531e7i	1.04556	−	0.603657i
$528$		0			0
$529$	−7.06026e7	+	1.22287e8i	−0.476929	+	0.826065i
$530$			5.15393e6i			0.0346187i
$531$		0			0
$532$	1.67102e8			1.10980
$533$	2.50141e7	+	1.44419e7i	0.165197	+	0.0953767i
$534$		0			0
$535$	7.61268e7	+	1.31855e8i	0.497137	+	0.861067i
$536$	−3.50437e7	+	2.02325e7i	−0.227570	+	0.131388i
$537$		0			0
$538$	6.18492e7	−	1.07126e8i	0.397180	−	0.687936i
$539$			8.55779e8i			5.46506i
$540$		0			0
$541$	−2.15827e8			−1.36306			−0.681529	−	0.731791i	$-0.738685\pi$
$541$	−2.15827e8			−1.36306			−0.681529	+	0.731791i	$0.738685\pi$
$542$	−4.17590e7	−	2.41096e7i	−0.262272	−	0.151423i
$543$		0			0
$544$	1.15238e7	+	1.99598e7i	0.0715813	+	0.123982i
$545$	2.67404e8	−	1.54386e8i	1.65188	−	0.953712i
$546$		0			0
$547$	−8.28182e7	+	1.43445e8i	−0.506015	+	0.876444i	0.493961	+	0.869484i	$0.335549\pi$
$547$	−8.28182e7	+	1.43445e8i	−0.506015	+	0.876444i	−0.999976	+	0.00695972i	$0.997785\pi$
$548$			8.01361e7i			0.486952i
$549$		0			0
$550$	−1.15191e8			−0.692360
$551$	9.73394e7	+	5.61989e7i	0.581880	+	0.335949i
$552$		0			0
$553$	−5.81049e7	−	1.00641e8i	−0.343588	−	0.595111i
$554$	−1.18890e8	+	6.86413e7i	−0.699225	+	0.403697i
$555$		0			0
$556$	−3.43273e7	+	5.94567e7i	−0.199717	+	0.345920i
$557$		−	3.30976e8i		−	1.91527i	−0.287979	−	0.957637i	$-0.592983\pi$
$557$		−	3.30976e8i		−	1.91527i	0.287979	−	0.957637i	$-0.407017\pi$
$558$		0			0
$559$	−9.77188e7			−0.559426
$560$	−9.15471e7	−	5.28547e7i	−0.521291	−	0.300968i
$561$		0			0
$562$	1.17857e8	+	2.04134e8i	0.663966	+	1.15002i
$563$	−2.19267e8	+	1.26594e8i	−1.22871	+	0.709395i	−0.966760	−	0.255687i	$-0.917698\pi$
$563$	−2.19267e8	+	1.26594e8i	−1.22871	+	0.709395i	−0.261948	+	0.965082i	$0.584365\pi$
$564$		0			0
$565$	2.11188e7	−	3.65789e7i	0.117091	−	0.202808i
$566$		−	1.89561e8i		−	1.04544i
$567$		0			0
$568$	−1.31087e7			−0.0715341
$569$	−1.95145e7	−	1.12667e7i	−0.105930	−	0.0611589i	0.446099	−	0.894984i	$-0.352813\pi$
$569$	−1.95145e7	−	1.12667e7i	−0.105930	−	0.0611589i	−0.552029	+	0.833825i	$0.686146\pi$
$570$		0			0
$571$	−1.18639e8	−	2.05490e8i	−0.637266	−	1.10378i	−0.986030	−	0.166567i	$-0.946732\pi$
$571$	−1.18639e8	−	2.05490e8i	−0.637266	−	1.10378i	0.348764	−	0.937211i	$-0.386602\pi$
$572$	1.25574e8	−	7.25002e7i	0.670984	−	0.387393i
$573$		0			0
$574$	−3.10276e7	+	5.37414e7i	−0.164064	+	0.284167i
$575$			2.07901e7i			0.109359i
$576$		0			0
$577$	1.32757e8			0.691085			0.345542	−	0.938403i	$-0.387695\pi$
$577$	1.32757e8			0.691085			0.345542	+	0.938403i	$0.387695\pi$
$578$	4.06948e7	+	2.34951e7i	0.210744	+	0.121673i
$579$		0			0
$580$	−3.55517e7	−	6.15774e7i	−0.182212	−	0.315600i
$581$	−8.53739e6	+	4.92906e6i	−0.0435308	+	0.0251325i
$582$		0			0
$583$	7.59432e6	−	1.31537e7i	0.0383251	−	0.0663810i
$584$		−	5.73905e7i		−	0.288139i
$585$		0			0
$586$	−6.62818e7			−0.329383
$587$	−7.32912e7	−	4.23147e7i	−0.362358	−	0.209207i	0.307757	−	0.951465i	$-0.400422\pi$
$587$	−7.32912e7	−	4.23147e7i	−0.362358	−	0.209207i	−0.670115	+	0.742258i	$0.733755\pi$
$588$		0			0
$589$	−1.72487e8	−	2.98756e8i	−0.844133	−	1.46208i
$590$	−5.58896e6	+	3.22679e6i	−0.0272129	+	0.0157114i
$591$		0			0
$592$	2.02338e7	−	3.50460e7i	0.0975241	−	0.168917i
$593$		−	2.84449e8i		−	1.36408i	−0.731313	−	0.682042i	$-0.761092\pi$
$593$		−	2.84449e8i		−	1.36408i	0.731313	−	0.682042i	$-0.238908\pi$
$594$		0			0
$595$	4.10738e8			1.94991
$596$	−1.01894e8	−	5.88283e7i	−0.481291	−	0.277874i
$597$		0			0
$598$	−1.30851e7	−	2.26640e7i	−0.0611888	−	0.105982i
$599$	−3.56833e8	+	2.06018e8i	−1.66029	+	0.958570i	−0.687717	+	0.725979i	$0.741387\pi$
$599$	−3.56833e8	+	2.06018e8i	−1.66029	+	0.958570i	−0.972575	+	0.232591i	$0.925280\pi$
$600$		0			0
$601$	−8.06263e7	+	1.39649e8i	−0.371410	+	0.643301i	−0.989783	−	0.142584i	$-0.954459\pi$
$601$	−8.06263e7	+	1.39649e8i	−0.371410	+	0.643301i	0.618373	+	0.785885i	$0.287792\pi$
$602$		−	2.09944e8i		−	0.962306i
$603$		0			0
$604$	1.15882e8			0.525901
$605$	6.35870e8	+	3.67120e8i	2.87146	+	1.65784i
$606$		0			0
$607$	2.35372e7	+	4.07677e7i	0.105242	+	0.182285i	0.913837	−	0.406081i	$-0.133105\pi$
$607$	2.35372e7	+	4.07677e7i	0.105242	+	0.182285i	−0.808595	+	0.588366i	$0.799772\pi$
$608$	3.89665e7	−	2.24973e7i	0.173373	−	0.100097i
$609$		0			0
$610$	−2.36846e7	+	4.10229e7i	−0.104346	+	0.180733i
$611$		−	2.11201e8i		−	0.925916i
$612$		0			0
$613$	−2.39685e8			−1.04054			−0.520271	−	0.854002i	$-0.674169\pi$
$613$	−2.39685e8			−1.04054			−0.520271	+	0.854002i	$0.674169\pi$
$614$	−7.89570e7	−	4.55859e7i	−0.341103	−	0.196936i
$615$		0			0
$616$	1.55763e8	+	2.69789e8i	0.666380	+	1.15420i
$617$	−3.48514e8	+	2.01215e8i	−1.48376	+	0.856652i	−0.999830	−	0.0184517i	$-0.994126\pi$
$617$	−3.48514e8	+	2.01215e8i	−1.48376	+	0.856652i	−0.483935	+	0.875104i	$0.660793\pi$
$618$		0			0
$619$	1.45928e8	−	2.52754e8i	0.615271	−	1.06568i	−0.375066	−	0.926998i	$-0.622380\pi$
$619$	1.45928e8	−	2.52754e8i	0.615271	−	1.06568i	0.990337	−	0.138682i	$-0.0442866\pi$
$620$			2.18233e8i			0.915681i
$621$		0			0
$622$	−1.96841e8			−0.817982
$623$	−4.65915e8	−	2.68996e8i	−1.92683	−	1.11245i
$624$		0			0
$625$	1.52578e8	+	2.64272e8i	0.624959	+	1.08246i
$626$	−5.89730e6	+	3.40481e6i	−0.0240398	+	0.0138794i
$627$		0			0
$628$	6.82048e7	−	1.18134e8i	0.275382	−	0.476976i
$629$			1.57238e8i			0.631839i
$630$		0			0
$631$	2.90786e8			1.15740			0.578702	−	0.815539i	$-0.303559\pi$
$631$	2.90786e8			1.15740			0.578702	+	0.815539i	$0.303559\pi$
$632$	−2.70990e7	−	1.56456e7i	−0.107350	−	0.0619785i
$633$		0			0
$634$	−1.23577e8	−	2.14042e8i	−0.484922	−	0.839909i
$635$	−1.14962e8	+	6.63736e7i	−0.448988	+	0.259223i
$636$		0			0
$637$	2.95871e8	−	5.12464e8i	1.14468	−	1.98265i
$638$			2.09542e8i			0.806880i
$639$		0			0
$640$	−2.84638e7			−0.108581
$641$	−3.02356e8	−	1.74565e8i	−1.14801	−	0.662803i	−0.199607	−	0.979876i	$-0.563967\pi$
$641$	−3.02356e8	−	1.74565e8i	−1.14801	−	0.662803i	−0.948401	+	0.317073i	$0.897300\pi$
$642$		0			0
$643$	1.87713e8	+	3.25128e8i	0.706091	+	1.22298i	0.966296	+	0.257432i	$0.0828763\pi$
$643$	1.87713e8	+	3.25128e8i	0.706091	+	1.22298i	−0.260206	+	0.965553i	$0.583790\pi$
$644$	4.86924e7	−	2.81126e7i	0.182307	−	0.105255i
$645$		0			0
$646$	−8.74142e7	+	1.51406e8i	−0.324253	+	0.561623i
$647$			3.70870e8i			1.36933i	0.728856	+	0.684667i	$0.240052\pi$
$647$			3.70870e8i			1.36933i	−0.728856	+	0.684667i	$0.759948\pi$
$648$		0			0
$649$	1.90187e7			0.0695740
$650$	6.89799e7	+	3.98255e7i	0.251178	+	0.145018i
$651$		0			0
$652$	1.08877e8	+	1.88580e8i	0.392820	+	0.680383i
$653$	1.12878e8	−	6.51700e7i	0.405386	−	0.234050i	−0.283419	−	0.958996i	$-0.591469\pi$
$653$	1.12878e8	−	6.51700e7i	0.405386	−	0.234050i	0.688805	+	0.724946i	$0.258135\pi$
$654$		0			0
$655$	−9.20978e7	+	1.59518e8i	−0.327737	+	0.567657i
$656$			1.67093e7i			0.0591898i
$657$		0			0
$658$	4.53753e8			1.59273
$659$	1.69874e8	+	9.80768e7i	0.593568	+	0.342697i	0.766507	−	0.642236i	$-0.221993\pi$
$659$	1.69874e8	+	9.80768e7i	0.593568	+	0.342697i	−0.172939	+	0.984933i	$0.555326\pi$
$660$		0			0
$661$	1.71370e8	+	2.96822e8i	0.593378	+	1.02776i	0.993774	+	0.111418i	$0.0355393\pi$
$661$	1.71370e8	+	2.96822e8i	0.593378	+	1.02776i	−0.400396	+	0.916342i	$0.631127\pi$
$662$	−2.74630e8	+	1.58558e8i	−0.946616	+	0.546529i
$663$		0			0
$664$	−1.32722e6	+	2.29882e6i	−0.00453356	+	0.00785236i
$665$		−	8.01862e8i		−	2.72668i
$666$		0			0
$667$	3.78187e7			0.127447
$668$	2.10006e8	+	1.21247e8i	0.704534	+	0.406763i
$669$		0			0
$670$	9.70886e7	+	1.68162e8i	0.322808	+	0.559119i
$671$	1.20895e8	−	6.97985e7i	0.400165	−	0.231035i
$672$		0			0
$673$	−1.55010e8	+	2.68485e8i	−0.508528	+	0.880796i	0.491423	+	0.870921i	$0.336477\pi$
$673$	−1.55010e8	+	2.68485e8i	−0.508528	+	0.880796i	−0.999951	+	0.00987551i	$0.996856\pi$
$674$			2.75252e8i			0.898982i
$675$		0			0
$676$	5.41948e7			0.175436
$677$	−2.21658e8	−	1.27975e8i	−0.714362	−	0.412437i	0.0983121	−	0.995156i	$-0.468656\pi$
$677$	−2.21658e8	−	1.27975e8i	−0.714362	−	0.412437i	−0.812674	+	0.582719i	$0.801989\pi$
$678$		0			0
$679$	5.64191e7	+	9.77207e7i	0.180226	+	0.312160i
$680$	9.57801e7	−	5.52987e7i	0.304613	−	0.175869i
$681$		0			0
$682$	3.21566e8	−	5.56968e8i	1.01372	−	1.75581i
$683$		−	4.96369e7i		−	0.155791i	−0.996962	−	0.0778955i	$-0.975180\pi$
$683$		−	4.96369e7i		−	0.155791i	0.996962	−	0.0778955i	$-0.0248200\pi$
$684$		0			0
$685$	3.84545e8			1.19640
$686$	7.13532e8	+	4.11958e8i	2.21025	+	1.27609i
$687$		0			0
$688$	−2.82652e7	−	4.89568e7i	−0.0867935	−	0.150331i
$689$	−9.09538e6	+	5.25122e6i	−0.0278076	+	0.0160547i
$690$		0			0
$691$	1.62210e7	−	2.80956e7i	0.0491636	−	0.0851539i	−0.840396	−	0.541972i	$-0.817678\pi$
$691$	1.62210e7	−	2.80956e7i	0.0491636	−	0.0851539i	0.889560	+	0.456818i	$0.151011\pi$
$692$		−	1.33745e8i		−	0.403608i
$693$		0			0
$694$	−3.78132e6			−0.0113127
$695$	2.85311e8	+	1.64725e8i	0.849894	+	0.490687i
$696$		0			0
$697$	−3.24623e7	−	5.62264e7i	−0.0958697	−	0.166051i
$698$	−3.24261e7	+	1.87212e7i	−0.0953516	+	0.0550513i
$699$		0			0
$700$	−8.55630e7	+	1.48200e8i	−0.249455	+	0.432069i
$701$			2.92826e8i			0.850071i	0.905177	+	0.425035i	$0.139738\pi$
$701$			2.92826e8i			0.850071i	−0.905177	+	0.425035i	$0.860262\pi$
$702$		0			0
$703$	3.06968e8			0.883542
$704$	7.26448e7	+	4.19415e7i	0.208203	+	0.120206i
$705$		0			0
$706$	−1.09253e8	−	1.89231e8i	−0.310469	−	0.537747i
$707$	1.49101e8	−	8.60835e7i	0.421912	−	0.243591i
$708$		0			0
$709$	2.42304e8	−	4.19683e8i	0.679863	−	1.17756i	−0.295158	−	0.955448i	$-0.595372\pi$
$709$	2.42304e8	−	4.19683e8i	0.679863	−	1.17756i	0.975022	−	0.222110i	$-0.0712943\pi$
$710$			6.29038e7i			0.175753i
$711$		0			0
$712$	−1.44862e8			−0.401343
$713$	−1.00523e8	−	5.80371e7i	−0.277331	−	0.160117i
$714$		0			0
$715$	−3.47903e8	−	6.02586e8i	−0.951788	−	1.64854i
$716$	−1.50292e8	+	8.67714e7i	−0.409447	+	0.236395i
$717$		0			0
$718$	1.17358e8	−	2.03270e8i	0.317058	−	0.549161i
$719$		−	2.30795e8i		−	0.620927i	−0.950585	−	0.310463i	$-0.899516\pi$
$719$		−	2.30795e8i		−	0.620927i	0.950585	−	0.310463i	$-0.100484\pi$
$720$		0			0
$721$	5.41946e7			0.144594
$722$	6.51048e7	+	3.75883e7i	0.172982	+	0.0998713i
$723$		0			0
$724$	7.77625e7	+	1.34689e8i	0.204906	+	0.354907i
$725$	−9.96836e7	+	5.75524e7i	−0.261583	+	0.151025i
$726$		0			0
$727$	1.73396e7	−	3.00331e7i	0.0451271	−	0.0781624i	−0.842580	−	0.538572i	$-0.818964\pi$
$727$	1.73396e7	−	3.00331e7i	0.0451271	−	0.0781624i	0.887707	+	0.460409i	$0.152297\pi$
$728$		−	2.15410e8i		−	0.558305i
$729$		0			0
$730$	−2.75397e8			−0.707929
$731$	1.90224e8	+	1.09826e8i	0.486981	+	0.281159i
$732$		0			0
$733$	2.27856e8	+	3.94658e8i	0.578560	+	1.00210i	0.995645	+	0.0932276i	$0.0297184\pi$
$733$	2.27856e8	+	3.94658e8i	0.578560	+	1.00210i	−0.417085	+	0.908868i	$0.636948\pi$
$734$	−1.19659e8	+	6.90853e7i	−0.302593	+	0.174702i
$735$		0			0
$736$	7.56973e6	−	1.31111e7i	0.0189866	−	0.0328857i
$737$		−	5.72240e8i		−	1.42947i
$738$		0			0
$739$	4.45251e8			1.10324			0.551621	−	0.834095i	$-0.314009\pi$
$739$	4.45251e8			1.10324			0.551621	+	0.834095i	$0.314009\pi$
$740$	−1.68173e8	−	9.70948e7i	−0.415013	−	0.239608i
$741$		0			0
$742$	−1.12820e7	−	1.95409e7i	−0.0276168	−	0.0478337i
$743$	−5.06865e8	+	2.92639e8i	−1.23574	+	0.713453i	−0.968220	−	0.250101i	$-0.919536\pi$
$743$	−5.06865e8	+	2.92639e8i	−1.23574	+	0.713453i	−0.267516	+	0.963553i	$0.586203\pi$
$744$		0			0
$745$	−2.82296e8	+	4.88951e8i	−0.682710	+	1.18249i
$746$		−	1.42679e8i		−	0.343673i
$747$		0			0
$748$	−3.25931e8			−0.778790
$749$	−5.77264e8	−	3.33284e8i	−1.37382	−	0.793174i
$750$		0			0
$751$	−1.91807e8	−	3.32219e8i	−0.452840	−	0.784341i	0.545722	−	0.837967i	$-0.316256\pi$
$751$	−1.91807e8	−	3.32219e8i	−0.452840	−	0.784341i	−0.998561	+	0.0536254i	$0.982922\pi$
$752$	1.05811e8	−	6.10899e7i	0.248815	−	0.143653i
$753$		0			0
$754$	7.24457e7	−	1.25480e8i	0.169005	−	0.292725i
$755$		−	5.56075e8i		−	1.29209i
$756$		0			0
$757$	−7.52012e7			−0.173355			−0.0866777	−	0.996236i	$-0.527625\pi$
$757$	−7.52012e7			−0.173355			−0.0866777	+	0.996236i	$0.527625\pi$
$758$	−3.40831e7	−	1.96779e7i	−0.0782584	−	0.0451825i
$759$		0			0
$760$	−1.07957e8	−	1.86986e8i	−0.245928	−	0.425961i
$761$	−1.49064e8	+	8.60624e7i	−0.338236	+	0.195281i	−0.659492	−	0.751712i	$-0.729228\pi$
$761$	−1.49064e8	+	8.60624e7i	−0.338236	+	0.195281i	0.321256	+	0.946992i	$0.395895\pi$
$762$		0			0
$763$	−6.75901e8	+	1.17069e9i	−1.52163	+	2.63554i
$764$			1.01772e8i			0.228216i
$765$		0			0
$766$	−2.03493e8			−0.452755
$767$	−1.13889e7	−	6.57541e6i	−0.0252405	−	0.0145726i
$768$		0			0
$769$	−5.99791e7	−	1.03887e8i	−0.131893	−	0.228445i	0.792513	−	0.609855i	$-0.208772\pi$
$769$	−5.99791e7	−	1.03887e8i	−0.131893	−	0.228445i	−0.924406	+	0.381409i	$0.875439\pi$
$770$	1.29462e9	−	7.47451e8i	2.83577	−	1.63723i
$771$		0			0
$772$	−1.06991e8	+	1.85314e8i	−0.232538	+	0.402768i
$773$			7.73357e8i			1.67433i	0.546949	+	0.837166i	$0.315789\pi$
$773$			7.73357e8i			1.67433i	−0.546949	+	0.837166i	$0.684211\pi$
$774$		0			0
$775$	3.53282e8			0.758956
$776$	2.63128e7	+	1.51917e7i	0.0563094	+	0.0325103i
$777$		0			0
$778$	1.42193e8	+	2.46285e8i	0.301952	+	0.522997i
$779$	−1.09768e8	+	6.33745e7i	−0.232200	+	0.134061i
$780$		0			0
$781$	9.26887e7	−	1.60542e8i	0.194569	−	0.337004i
$782$			5.88249e7i			0.123010i
$783$		0			0
$784$	3.42324e8			0.710378
$785$	−5.66884e8	−	3.27291e8i	−1.17189	−	0.676589i
$786$		0			0
$787$	−7.38293e7	−	1.27876e8i	−0.151462	−	0.262340i	0.780303	−	0.625402i	$-0.215065\pi$
$787$	−7.38293e7	−	1.27876e8i	−0.151462	−	0.262340i	−0.931765	+	0.363061i	$0.881732\pi$
$788$	4.28884e7	−	2.47616e7i	0.0876518	−	0.0506058i
$789$		0			0
$790$	−7.50778e7	+	1.30038e8i	−0.152275	+	0.263749i
$791$			1.84917e8i			0.373634i
$792$		0			0
$793$	−9.65268e7			−0.193566
$794$	1.32423e8	+	7.64544e7i	0.264546	+	0.152736i
$795$		0			0
$796$	1.73364e8	+	3.00275e8i	0.343731	+	0.595360i
$797$	8.74127e8	−	5.04677e8i	1.72663	−	0.996870i	0.823789	−	0.566897i	$-0.191856\pi$
$797$	8.74127e8	−	5.04677e8i	1.72663	−	0.996870i	0.902842	−	0.429973i	$-0.141477\pi$
$798$		0			0
$799$	−2.37367e8	+	4.11132e8i	−0.465351	+	0.806011i
$800$			4.60783e7i			0.0899966i
$801$		0			0
$802$	−4.57783e8			−0.887435
$803$	7.02861e8	+	4.05797e8i	1.35745	+	0.783722i
$804$		0			0
$805$	−1.34902e8	−	2.33657e8i	−0.258602	−	0.447911i
$806$	−3.85125e8	+	2.22352e8i	−0.735524	+	0.424655i
$807$		0			0
$808$	2.31793e7	−	4.01477e7i	0.0439405	−	0.0761073i
$809$			3.05870e8i			0.577686i	0.957376	+	0.288843i	$0.0932705\pi$
$809$			3.05870e8i			0.577686i	−0.957376	+	0.288843i	$0.906729\pi$
$810$		0			0
$811$	−2.24649e8			−0.421156			−0.210578	−	0.977577i	$-0.567535\pi$
$811$	−2.24649e8			−0.421156			−0.210578	+	0.977577i	$0.567535\pi$
$812$	2.69586e8	+	1.55646e8i	0.503535	+	0.290716i
$813$		0			0
$814$	2.86138e8	+	4.95606e8i	0.530521	+	0.918890i
$815$	9.04931e8	−	5.22462e8i	1.67164	−	0.965121i
$816$		0			0
$817$	2.14407e8	−	3.71363e8i	0.393163	−	0.680978i
$818$			3.64007e8i			0.665044i
$819$		0			0
$820$	8.01820e7			0.145424
$821$	−1.65568e8	−	9.55909e7i	−0.299190	−	0.172738i	0.342889	−	0.939376i	$-0.388595\pi$
$821$	−1.65568e8	−	9.55909e7i	−0.299190	−	0.172738i	−0.642079	+	0.766638i	$0.721928\pi$
$822$		0			0
$823$	−3.04419e8	−	5.27268e8i	−0.546099	−	0.945872i	−0.998537	−	0.0540757i	$-0.982779\pi$
$823$	−3.04419e8	−	5.27268e8i	−0.546099	−	0.945872i	0.452437	−	0.891796i	$-0.350555\pi$
$824$	1.26377e7	−	7.29635e6i	0.0225884	−	0.0130414i
$825$		0			0
$826$	1.41269e7	−	2.44685e7i	0.0250673	−	0.0434178i
$827$			4.70812e7i			0.0832398i	0.999134	+	0.0416199i	$0.0132519\pi$
$827$			4.70812e7i			0.0832398i	−0.999134	+	0.0416199i	$0.986748\pi$
$828$		0			0
$829$	1.01177e8			0.177589			0.0887947	−	0.996050i	$-0.471698\pi$
$829$	1.01177e8			0.177589			0.0887947	+	0.996050i	$0.471698\pi$
$830$	1.10312e7	+	6.36888e6i	0.0192925	+	0.0111385i
$831$		0			0
$832$	−2.90012e7	−	5.02315e7i	−0.0503553	−	0.0872180i
$833$	−1.15191e9	+	6.65057e8i	−1.99289	+	1.15060i
$834$		0			0
$835$	5.81821e8	−	1.00774e9i	0.999379	−	1.73097i
$836$			6.36297e8i			1.08903i
$837$		0			0
$838$	3.13959e8			0.533507
$839$	−3.61246e8	−	2.08565e8i	−0.611670	−	0.353148i	0.161949	−	0.986799i	$-0.448222\pi$
$839$	−3.61246e8	−	2.08565e8i	−0.611670	−	0.353148i	−0.773619	+	0.633651i	$0.781555\pi$
$840$		0			0
$841$	−1.92720e8	−	3.33800e8i	−0.323995	−	0.561175i
$842$	−1.34854e8	+	7.78577e7i	−0.225905	+	0.130426i
$843$		0			0
$844$	2.20713e8	−	3.82286e8i	0.367113	−	0.635859i
$845$		−	2.60062e8i		−	0.431029i
$846$		0			0
$847$	−3.21451e9			−5.29010
$848$	−5.26169e6	−	3.03784e6i	−0.00862855	−	0.00498170i
$849$		0			0
$850$	−8.95194e7	−	1.55052e8i	−0.145767	−	0.252477i
$851$	8.94485e7	−	5.16431e7i	0.145139	−	0.0837961i
$852$		0			0
$853$	2.32676e7	−	4.03007e7i	0.0374891	−	0.0649330i	−0.846672	−	0.532115i	$-0.821397\pi$
$853$	2.32676e7	−	4.03007e7i	0.0374891	−	0.0649330i	0.884161	+	0.467182i	$0.154731\pi$
$854$		−	2.07383e8i		−	0.332965i
$855$		0			0
$856$	−1.79483e8			−0.286156
$857$	−3.92039e8	−	2.26344e8i	−0.622855	−	0.359606i	0.155125	−	0.987895i	$-0.450422\pi$
$857$	−3.92039e8	−	2.26344e8i	−0.622855	−	0.359606i	−0.777980	+	0.628289i	$0.783755\pi$
$858$		0			0
$859$	−7.76503e7	−	1.34494e8i	−0.122508	−	0.212190i	0.798248	−	0.602329i	$-0.205760\pi$
$859$	−7.76503e7	−	1.34494e8i	−0.122508	−	0.212190i	−0.920756	+	0.390139i	$0.872427\pi$
$860$	−2.34926e8	+	1.35635e8i	−0.369349	+	0.213244i
$861$		0			0
$862$	−3.85530e8	+	6.67757e8i	−0.601916	+	1.04255i
$863$		−	3.43497e7i		−	0.0534430i	−0.999643	−	0.0267215i	$-0.991493\pi$
$863$		−	3.43497e7i		−	0.0534430i	0.999643	−	0.0267215i	$-0.00850672\pi$
$864$		0			0
$865$	−6.41796e8			−0.991628
$866$	−5.20042e8	−	3.00247e8i	−0.800728	−	0.462301i
$867$		0			0
$868$	−4.77712e8	−	8.27421e8i	−0.730477	−	1.26522i
$869$	3.83224e8	−	2.21254e8i	0.583973	−	0.337157i
$870$		0			0
$871$	−1.97843e8	+	3.42674e8i	−0.299410	+	0.518593i
$872$			3.63993e8i			0.548963i
$873$		0			0
$874$	1.14841e8			0.172013
$875$	−6.85740e8	−	3.95912e8i	−1.02361	−	0.590983i
$876$		0			0
$877$	−2.49548e8	−	4.32231e8i	−0.369961	−	0.640792i	0.619598	−	0.784919i	$-0.287296\pi$
$877$	−2.49548e8	−	4.32231e8i	−0.369961	−	0.640792i	−0.989559	+	0.144128i	$0.953962\pi$
$878$	−3.09270e8	+	1.78557e8i	−0.456935	+	0.263811i
$879$		0			0
$880$	2.01262e8	−	3.48597e8i	0.295335	−	0.511535i
$881$			9.97853e8i			1.45928i	0.683831	+	0.729640i	$0.260312\pi$
$881$			9.97853e8i			1.45928i	−0.683831	+	0.729640i	$0.739688\pi$
$882$		0			0
$883$	5.39800e8			0.784062			0.392031	−	0.919952i	$-0.371773\pi$
$883$	5.39800e8			0.784062			0.392031	+	0.919952i	$0.371773\pi$
$884$	1.95176e8	+	1.12685e8i	0.282534	+	0.163121i
$885$		0			0
$886$	1.34293e8	+	2.32603e8i	0.193087	+	0.334437i
$887$	−1.56993e8	+	9.06399e7i	−0.224962	+	0.129882i	−0.608246	−	0.793749i	$-0.708126\pi$
$887$	−1.56993e8	+	9.06399e7i	−0.224962	+	0.129882i	0.383284	+	0.923631i	$0.374793\pi$
$888$		0			0
$889$	2.90584e8	−	5.03306e8i	0.413587	−	0.716353i
$890$			6.95144e8i			0.986063i
$891$		0			0
$892$	1.62317e7			0.0228701
$893$	8.02632e8	+	4.63400e8i	1.12710	+	0.650731i
$894$		0			0
$895$	4.16385e8	+	7.21200e8i	0.580799	+	1.00597i
$896$	1.07920e8	−	6.23075e7i	0.150030	−	0.0866196i
$897$		0			0
$898$	−3.14354e8	+	5.44477e8i	−0.434100	+	0.751883i
$899$		−	6.42647e8i		−	0.884492i
$900$		0			0
$901$	2.36073e7			0.0322754
$902$	−2.04639e8	−	1.18148e8i	−0.278849	−	0.160993i
$903$		0			0
$904$	2.48958e7	+	4.31208e7i	0.0336993	+	0.0583688i
$905$	6.46323e8	−	3.73155e8i	0.871974	−	0.503435i
$906$		0			0
$907$	−5.12818e8	+	8.88227e8i	−0.687292	+	1.19042i	0.285419	+	0.958403i	$0.407867\pi$
$907$	−5.12818e8	+	8.88227e8i	−0.687292	+	1.19042i	−0.972711	+	0.232022i	$0.925466\pi$
$908$		−	6.45438e8i		−	0.862178i
$909$		0			0
$910$	−1.03368e9			−1.37170
$911$	−7.96109e8	−	4.59633e8i	−1.05297	−	0.607934i	−0.129493	−	0.991580i	$-0.541335\pi$
$911$	−7.96109e8	−	4.59633e8i	−1.05297	−	0.607934i	−0.923480	+	0.383646i	$0.874668\pi$
$912$		0			0
$913$	−1.87691e7	−	3.25090e7i	−0.0246621	−	0.0427161i
$914$	4.31704e8	−	2.49245e8i	0.565390	−	0.326428i
$915$		0			0
$916$	−5.75837e7	+	9.97379e7i	−0.0749226	+	0.129770i
$917$		−	8.06410e8i		−	1.04580i
$918$		0			0
$919$	1.20573e9			1.55347			0.776737	−	0.629826i	$-0.216874\pi$
$919$	1.20573e9			1.55347			0.776737	+	0.629826i	$0.216874\pi$
$920$	−6.29158e7	−	3.63244e7i	−0.0807971	−	0.0466482i
$921$		0			0
$922$	−3.95910e8	−	6.85737e8i	−0.505131	−	0.874913i
$923$	−1.11009e8	+	6.40912e7i	−0.141174	+	0.0815067i
$924$		0			0
$925$	−1.57180e8	+	2.72244e8i	−0.198597	+	0.343980i
$926$		−	7.42275e8i		−	0.934829i
$927$		0			0
$928$	8.38199e7			0.104882
$929$	8.85812e7	+	5.11424e7i	0.110483	+	0.0637872i	0.554223	−	0.832368i	$-0.313015\pi$
$929$	8.85812e7	+	5.11424e7i	0.110483	+	0.0637872i	−0.443740	+	0.896155i	$0.646349\pi$
$930$		0			0
$931$	1.29836e9	+	2.24882e9i	1.60896	+	2.78680i
$932$	1.16558e8	−	6.72949e7i	0.143978	−	0.0831256i
$933$		0			0
$934$	2.35390e8	−	4.07708e8i	0.288900	−	0.500390i
$935$			1.56403e9i			1.91341i
$936$		0			0
$937$	4.70010e8			0.571332			0.285666	−	0.958329i	$-0.407785\pi$
$937$	4.70010e8			0.571332			0.285666	+	0.958329i	$0.407785\pi$
$938$	−7.36216e8	−	4.25055e8i	−0.892066	−	0.515034i
$939$		0			0
$940$	−2.93149e8	−	5.07749e8i	−0.352943	−	0.611316i
$941$	−7.71639e8	+	4.45506e8i	−0.926073	+	0.534668i	−0.885567	−	0.464511i	$-0.846230\pi$
$941$	−7.71639e8	+	4.45506e8i	−0.926073	+	0.534668i	−0.0405053	+	0.999179i	$0.512897\pi$
$942$		0			0
$943$	−2.13238e7	+	3.69338e7i	−0.0254290	+	0.0440442i
$944$		−	7.60776e6i		−	0.00904359i
$945$		0			0
$946$	7.99432e8			0.944296
$947$	−7.74400e8	−	4.47100e8i	−0.911833	−	0.526447i	−0.0308127	−	0.999525i	$-0.509810\pi$
$947$	−7.74400e8	−	4.47100e8i	−0.911833	−	0.526447i	−0.881021	+	0.473078i	$0.843143\pi$
$948$		0			0
$949$	−2.80595e8	−	4.86005e8i	−0.328308	−	0.568647i
$950$	−3.02700e8	+	1.74764e8i	−0.353055	+	0.203836i
$951$		0			0
$952$	−2.42098e8	+	4.19326e8i	−0.280595	+	0.486005i
$953$			1.03289e9i			1.19337i	0.802476	+	0.596684i	$0.203516\pi$
$953$			1.03289e9i			1.19337i	−0.802476	+	0.596684i	$0.796484\pi$
$954$		0			0
$955$	4.88366e8			0.560707
$956$	−4.68444e8	−	2.70457e8i	−0.536148	−	0.309545i
$957$		0			0
$958$	4.20009e8	+	7.27477e8i	0.477707	+	0.827413i
$959$	−1.45799e9	+	8.41770e8i	−1.65310	+	0.954415i
$960$		0			0
$961$	−5.42463e8	+	9.39574e8i	−0.611223	+	1.05867i
$962$		−	3.95711e8i		−	0.444480i
$963$		0			0
$964$	−6.91332e8			−0.771712
$965$	8.89254e8	+	5.13411e8i	0.989564	+	0.571325i
$966$		0			0
$967$	−1.54335e8	−	2.67316e8i	−0.170681	−	0.295628i	0.767977	−	0.640477i	$-0.221263\pi$
$967$	−1.54335e8	−	2.67316e8i	−0.170681	−	0.295628i	−0.938658	+	0.344849i	$0.887930\pi$
$968$	−7.49592e8	+	4.32777e8i	−0.826416	+	0.477131i
$969$		0			0
$970$	7.28995e7	−	1.26266e8i	0.0798747	−	0.138347i
$971$			2.10002e8i			0.229386i	0.993401	+	0.114693i	$0.0365884\pi$
$971$			2.10002e8i			0.229386i	−0.993401	+	0.114693i	$0.963412\pi$
$972$		0			0
$973$	−1.44233e9			−1.56576
$974$	5.04485e8	+	2.91265e8i	0.545973	+	0.315218i
$975$		0			0
$976$	−2.79204e7	−	4.83596e7i	−0.0300312	−	0.0520156i
$977$	1.15124e9	−	6.64670e8i	1.23448	−	0.712725i	0.266517	−	0.963830i	$-0.414127\pi$
$977$	1.15124e9	−	6.64670e8i	1.23448	−	0.712725i	0.967960	+	0.251105i	$0.0807939\pi$
$978$		0			0
$979$	1.02429e9	−	1.77413e9i	1.09163	−	1.89076i
$980$		−	1.64269e9i		−	1.74533i
$981$		0			0
$982$	7.39175e8			0.780572
$983$	1.13268e9	+	6.53951e8i	1.19246	+	0.688469i	0.958864	−	0.283864i	$-0.0916165\pi$
$983$	1.13268e9	+	6.53951e8i	1.19246	+	0.688469i	0.233599	+	0.972333i	$0.424950\pi$
$984$		0			0
$985$	−1.18822e8	−	2.05806e8i	−0.124334	−	0.215352i
$986$	−2.82052e8	+	1.62843e8i	−0.294238	+	0.169878i
$987$		0			0
$988$	2.19989e8	−	3.81033e8i	0.228103	−	0.395086i
$989$		−	1.44284e8i		−	0.149152i
$990$		0			0
$991$	−6.02119e8			−0.618673			−0.309337	−	0.950953i	$-0.600107\pi$
$991$	−6.02119e8			−0.618673			−0.309337	+	0.950953i	$0.600107\pi$
$992$	−2.22795e8	−	1.28631e8i	−0.228229	−	0.131768i
$993$		0			0
$994$	−1.37697e8	−	2.38497e8i	−0.140205	−	0.242842i
$995$	1.44091e9	−	8.31912e8i	1.46274	−	0.844516i
$996$		0			0
$997$	−4.08795e8	+	7.08053e8i	−0.412496	+	0.714464i	−0.995162	−	0.0982476i	$-0.968676\pi$
$997$	−4.08795e8	+	7.08053e8i	−0.412496	+	0.714464i	0.582666	+	0.812712i	$0.302010\pi$
$998$		−	8.38888e8i		−	0.843942i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.d.g.107.8		16
3.2	odd	2	inner	162.7.d.g.107.1		16
9.2	odd	6		162.7.b.b.161.5	yes	8
9.4	even	3	inner	162.7.d.g.53.1		16
9.5	odd	6	inner	162.7.d.g.53.8		16
9.7	even	3		162.7.b.b.161.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.7.b.b.161.4	✓	8	9.7	even	3
162.7.b.b.161.5	yes	8	9.2	odd	6
162.7.d.g.53.1		16	9.4	even	3	inner
162.7.d.g.53.8		16	9.5	odd	6	inner
162.7.d.g.107.1		16	3.2	odd	2	inner
162.7.d.g.107.8		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(132.984 - 76.7783i) q^{5} +(-336.136 + 582.205i) q^{7} +181.019i q^{8} +O(q^{10})\)	\(q+(4.89898 + 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(132.984 - 76.7783i) q^{5} +(-336.136 + 582.205i) q^{7} +181.019i q^{8} +868.648 q^{10} +(-2216.94 - 1279.95i) q^{11} +(885.045 + 1532.94i) q^{13} +(-3293.45 + 1901.47i) q^{14} +(-512.000 + 886.810i) q^{16} -3978.79i q^{17} -7767.58 q^{19} +(4255.49 + 2456.91i) q^{20} +(-7240.51 - 12540.9i) q^{22} +(-2263.42 + 1306.79i) q^{23} +(3977.33 - 6888.93i) q^{25} +10013.1i q^{26} -21512.7 q^{28} +(-12531.5 - 7235.06i) q^{29} +(22206.0 + 38462.0i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(11253.7 - 19492.0i) q^{34} +103232. i q^{35} -39519.1 q^{37} +(-38053.2 - 21970.0i) q^{38} +(13898.4 + 24072.7i) q^{40} +(14131.5 - 8158.84i) q^{41} +(-27602.8 + 47809.4i) q^{43} -81917.0i q^{44} -14784.6 q^{46} +(-103331. - 59658.1i) q^{47} +(-167150. - 289513. i) q^{49} +(38969.7 - 22499.1i) q^{50} +(-28321.5 + 49054.2i) q^{52} +5933.28i q^{53} -393091. q^{55} +(-105390. - 60847.1i) q^{56} +(-40927.7 - 70888.8i) q^{58} +(-6434.10 + 3714.73i) q^{59} +(-27266.1 + 47226.2i) q^{61} +251232. i q^{62} -32768.0 q^{64} +(235394. + 135905. i) q^{65} +(111770. + 193591. i) q^{67} +(110264. - 63660.7i) q^{68} +(-291984. + 505731. i) q^{70} +72415.7i q^{71} -317041. q^{73} +(-193603. - 111777. i) q^{74} +(-124281. - 215262. i) q^{76} +(1.49039e6 - 860477. i) q^{77} +(-86430.6 + 149702. i) q^{79} +157242. i q^{80} +92306.7 q^{82} +(12699.3 + 7331.94i) q^{83} +(-305485. - 529116. i) q^{85} +(-270451. + 156145. i) q^{86} +(231696. - 401310. i) q^{88} +800260. i q^{89} -1.18998e6 q^{91} +(-72429.6 - 41817.2i) q^{92} +(-337477. - 584528. i) q^{94} +(-1.03296e6 + 596382. i) q^{95} +(83923.0 - 145359. i) q^{97} -1.89109e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 256 q^{4} - 964 q^{7}+O(q^{10}) \) 16 * q + 256 * q^4 - 964 * q^7	\( 16 q + 256 q^{4} - 964 q^{7} - 1536 q^{10} - 4540 q^{13} - 8192 q^{16} - 47368 q^{19} - 27072 q^{22} + 32392 q^{25} - 61696 q^{28} - 77056 q^{31} + 52608 q^{34} - 22696 q^{37} - 24576 q^{40} + 226604 q^{43} - 325440 q^{46} - 1298088 q^{49} + 145280 q^{52} - 2921832 q^{55} - 867456 q^{58} + 327476 q^{61} - 524288 q^{64} - 1713292 q^{67} + 176352 q^{70} - 4378432 q^{73} - 757888 q^{76} + 1326884 q^{79} - 2317632 q^{82} - 3483180 q^{85} + 866304 q^{88} + 2260648 q^{91} + 26400 q^{94} + 2200064 q^{97}+O(q^{100}) \) 16 * q + 256 * q^4 - 964 * q^7 - 1536 * q^10 - 4540 * q^13 - 8192 * q^16 - 47368 * q^19 - 27072 * q^22 + 32392 * q^25 - 61696 * q^28 - 77056 * q^31 + 52608 * q^34 - 22696 * q^37 - 24576 * q^40 + 226604 * q^43 - 325440 * q^46 - 1298088 * q^49 + 145280 * q^52 - 2921832 * q^55 - 867456 * q^58 + 327476 * q^61 - 524288 * q^64 - 1713292 * q^67 + 176352 * q^70 - 4378432 * q^73 - 757888 * q^76 + 1326884 * q^79 - 2317632 * q^82 - 3483180 * q^85 + 866304 * q^88 + 2260648 * q^91 + 26400 * q^94 + 2200064 * q^97

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