LMFDB - Embedded newform 162.7.d.e.107.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{12} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.2
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	162.107
Dual form			162.7.d.e.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(190.398 - 109.926i) q^{5} +(-180.868 + 313.272i) q^{7} -181.019i q^{8} +O(q^{10})$	\(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(190.398 - 109.926i) q^{5} +(-180.868 + 313.272i) q^{7} -181.019i q^{8} -1243.68 q^{10} +(56.7490 + 32.7641i) q^{11} +(1625.09 + 2814.73i) q^{13} +(1772.13 - 1023.14i) q^{14} +(-512.000 + 886.810i) q^{16} +6323.99i q^{17} -8697.81 q^{19} +(6092.74 + 3517.65i) q^{20} +(-185.342 - 321.021i) q^{22} +(-11341.0 + 6547.73i) q^{23} +(16355.1 - 28327.9i) q^{25} -18385.7i q^{26} -11575.5 q^{28} +(-6575.38 - 3796.30i) q^{29} +(-18876.0 - 32694.2i) q^{31} +(5016.55 - 2896.31i) q^{32} +(17887.0 - 30981.1i) q^{34} +79528.5i q^{35} -21446.1 q^{37} +(42610.4 + 24601.1i) q^{38} +(-19898.8 - 34465.7i) q^{40} +(17879.8 - 10322.9i) q^{41} +(-61213.4 + 106025. i) q^{43} +2096.90i q^{44} +74079.1 q^{46} +(-13663.3 - 7888.54i) q^{47} +(-6601.63 - 11434.4i) q^{49} +(-160247. + 92518.6i) q^{50} +(-52002.7 + 90071.4i) q^{52} +241230. i q^{53} +14406.5 q^{55} +(56708.2 + 32740.5i) q^{56} +(21475.1 + 37196.0i) q^{58} +(64406.8 - 37185.3i) q^{59} +(-96844.7 + 167740. i) q^{61} +213557. i q^{62} -32768.0 q^{64} +(618827. + 357280. i) q^{65} +(67898.5 + 117604. i) q^{67} +(-175256. + 101184. i) q^{68} +(224940. - 389608. i) q^{70} +262767. i q^{71} +418432. q^{73} +(105064. + 60658.7i) q^{74} +(-139165. - 241041. i) q^{76} +(-20528.1 + 11851.9i) q^{77} +(341157. - 590902. i) q^{79} +225129. i q^{80} -116790. q^{82} +(-514668. - 297144. i) q^{83} +(695174. + 1.20408e6i) q^{85} +(599766. - 346275. i) q^{86} +(5930.93 - 10272.7i) q^{88} +652205. i q^{89} -1.17570e6 q^{91} +(-362912. - 209527. i) q^{92} +(44624.3 + 77291.6i) q^{94} +(-1.65605e6 + 956119. i) q^{95} +(-877305. + 1.51954e6i) q^{97} +74688.9i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 128 q^{4} - 836 q^{7}+O(q^{10}) $ 8 * q + 128 * q^4 - 836 * q^7	$ 8 q + 128 q^{4} - 836 q^{7} - 3840 q^{10} - 440 q^{13} - 4096 q^{16} - 13376 q^{19} - 19200 q^{22} + 39200 q^{25} - 53504 q^{28} - 160172 q^{31} + 78336 q^{34} - 301088 q^{37} - 61440 q^{40} - 90152 q^{43} + 274944 q^{46} + 202560 q^{49} + 14080 q^{52} - 269640 q^{55} - 86016 q^{58} - 584144 q^{61} - 262144 q^{64} + 766792 q^{67} + 867840 q^{70} + 3149512 q^{73} - 214016 q^{76} - 323000 q^{79} + 2081280 q^{82} + 2720520 q^{85} + 614400 q^{88} - 3921808 q^{91} - 1970688 q^{94} - 4432940 q^{97}+O(q^{100}) $ 8 * q + 128 * q^4 - 836 * q^7 - 3840 * q^10 - 440 * q^13 - 4096 * q^16 - 13376 * q^19 - 19200 * q^22 + 39200 * q^25 - 53504 * q^28 - 160172 * q^31 + 78336 * q^34 - 301088 * q^37 - 61440 * q^40 - 90152 * q^43 + 274944 * q^46 + 202560 * q^49 + 14080 * q^52 - 269640 * q^55 - 86016 * q^58 - 584144 * q^61 - 262144 * q^64 + 766792 * q^67 + 867840 * q^70 + 3149512 * q^73 - 214016 * q^76 - 323000 * q^79 + 2081280 * q^82 + 2720520 * q^85 + 614400 * q^88 - 3921808 * q^91 - 1970688 * q^94 - 4432940 * 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
$5$	190.398	−	109.926i	1.52318	−	0.879411i	0.523561	−	0.851988i	$-0.324603\pi$
$5$	190.398	−	109.926i	1.52318	−	0.879411i	0.999624	−	0.0274231i	$-0.00873014\pi$
$6$		0			0
$7$	−180.868	+	313.272i	−0.527311	+	0.913329i	0.472183	+	0.881501i	$0.343466\pi$
$7$	−180.868	+	313.272i	−0.527311	+	0.913329i	−0.999493	+	0.0318281i	$0.989867\pi$
$8$		−	181.019i		−	0.353553i
$9$		0			0
$10$	−1243.68			−1.24368
$11$	56.7490	+	32.7641i	0.0426364	+	0.0246161i	0.521167	−	0.853455i	$-0.325497\pi$
$11$	56.7490	+	32.7641i	0.0426364	+	0.0246161i	−0.478530	+	0.878071i	$0.658830\pi$
$12$		0			0
$13$	1625.09	+	2814.73i	0.739684	+	1.28117i	0.952638	+	0.304108i	$0.0983583\pi$
$13$	1625.09	+	2814.73i	0.739684	+	1.28117i	−0.212954	+	0.977062i	$0.568308\pi$
$14$	1772.13	−	1023.14i	0.645821	−	0.372865i
$15$		0			0
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$			6323.99i			1.28720i	0.765364	+	0.643598i	$0.222559\pi$
$17$			6323.99i			1.28720i	−0.765364	+	0.643598i	$0.777441\pi$
$18$		0			0
$19$	−8697.81			−1.26809			−0.634044	−	0.773297i	$-0.718606\pi$
$19$	−8697.81			−1.26809			−0.634044	+	0.773297i	$0.718606\pi$
$20$	6092.74	+	3517.65i	0.761592	+	0.439706i
$21$		0			0
$22$	−185.342	−	321.021i	−0.0174062	−	0.0301485i
$23$	−11341.0	+	6547.73i	−0.932112	+	0.538155i	−0.887479	−	0.460849i	$-0.847545\pi$
$23$	−11341.0	+	6547.73i	−0.932112	+	0.538155i	−0.0446328	+	0.999003i	$0.514212\pi$
$24$		0			0
$25$	16355.1	−	28327.9i	1.04673	−	1.81299i
$26$		−	18385.7i		−	1.04607i
$27$		0			0
$28$	−11575.5			−0.527311
$29$	−6575.38	−	3796.30i	−0.269604	−	0.155656i	0.359104	−	0.933298i	$-0.383083\pi$
$29$	−6575.38	−	3796.30i	−0.269604	−	0.155656i	−0.628708	+	0.777642i	$0.716416\pi$
$30$		0			0
$31$	−18876.0	−	32694.2i	−0.633614	−	1.09745i	−0.986807	−	0.161901i	$-0.948238\pi$
$31$	−18876.0	−	32694.2i	−0.633614	−	1.09745i	0.353193	−	0.935550i	$-0.385096\pi$
$32$	5016.55	−	2896.31i	0.153093	−	0.0883883i
$33$		0			0
$34$	17887.0	−	30981.1i	0.455093	−	0.788243i
$35$			79528.5i			1.85489i
$36$		0			0
$37$	−21446.1			−0.423392			−0.211696	−	0.977336i	$-0.567899\pi$
$37$	−21446.1			−0.423392			−0.211696	+	0.977336i	$0.567899\pi$
$38$	42610.4	+	24601.1i	0.776542	+	0.448337i
$39$		0			0
$40$	−19898.8	−	34465.7i	−0.310919	−	0.538527i
$41$	17879.8	−	10322.9i	0.259424	−	0.149779i	−0.364648	−	0.931146i	$-0.618811\pi$
$41$	17879.8	−	10322.9i	0.259424	−	0.149779i	0.624072	+	0.781367i	$0.285477\pi$
$42$		0			0
$43$	−61213.4	+	106025.i	−0.769912	+	1.33353i	0.167699	+	0.985838i	$0.446366\pi$
$43$	−61213.4	+	106025.i	−0.769912	+	1.33353i	−0.937610	+	0.347688i	$0.886967\pi$
$44$			2096.90i			0.0246161i
$45$		0			0
$46$	74079.1			0.761066
$47$	−13663.3	−	7888.54i	−0.131602	−	0.0759806i	0.432753	−	0.901512i	$-0.357542\pi$
$47$	−13663.3	−	7888.54i	−0.131602	−	0.0759806i	−0.564356	+	0.825532i	$0.690875\pi$
$48$		0			0
$49$	−6601.63	−	11434.4i	−0.0561129	−	0.0971904i
$50$	−160247.	+	92518.6i	−1.28198	+	0.740149i
$51$		0			0
$52$	−52002.7	+	90071.4i	−0.369842	+	0.640585i
$53$			241230.i			1.62033i	0.586203	+	0.810164i	$0.300622\pi$
$53$			241230.i			1.62033i	−0.586203	+	0.810164i	$0.699378\pi$
$54$		0			0
$55$	14406.5			0.0865908
$56$	56708.2	+	32740.5i	0.322910	+	0.186432i
$57$		0			0
$58$	21475.1	+	37196.0i	0.110065	+	0.190639i
$59$	64406.8	−	37185.3i	0.313600	−	0.181057i	−0.334936	−	0.942241i	$-0.608715\pi$
$59$	64406.8	−	37185.3i	0.313600	−	0.181057i	0.648536	+	0.761184i	$0.275381\pi$
$60$		0			0
$61$	−96844.7	+	167740.i	−0.426664	+	0.739004i	−0.996574	−	0.0827030i	$-0.973645\pi$
$61$	−96844.7	+	167740.i	−0.426664	+	0.739004i	0.569910	+	0.821707i	$0.306978\pi$
$62$			213557.i			0.896065i
$63$		0			0
$64$	−32768.0			−0.125000
$65$	618827.	+	357280.i	2.25335	+	1.30097i
$66$		0			0
$67$	67898.5	+	117604.i	0.225754	+	0.391018i	0.956545	−	0.291583i	$-0.0941821\pi$
$67$	67898.5	+	117604.i	0.225754	+	0.391018i	−0.730791	+	0.682601i	$0.760849\pi$
$68$	−175256.	+	101184.i	−0.557372	+	0.321799i
$69$		0			0
$70$	224940.	−	389608.i	0.655803	−	1.13588i
$71$			262767.i			0.734168i	0.930188	+	0.367084i	$0.119644\pi$
$71$			262767.i			0.734168i	−0.930188	+	0.367084i	$0.880356\pi$
$72$		0			0
$73$	418432.			1.07561			0.537807	−	0.843068i	$-0.319253\pi$
$73$	418432.			1.07561			0.537807	+	0.843068i	$0.319253\pi$
$74$	105064.	+	60658.7i	0.259274	+	0.149692i
$75$		0			0
$76$	−139165.	−	241041.i	−0.317022	−	0.549098i
$77$	−20528.1	+	11851.9i	−0.0449652	+	0.0259607i
$78$		0			0
$79$	341157.	−	590902.i	0.691948	−	1.19849i	−0.279251	−	0.960218i	$-0.590086\pi$
$79$	341157.	−	590902.i	0.691948	−	1.19849i	0.971199	−	0.238270i	$-0.0765805\pi$
$80$			225129.i			0.439706i
$81$		0			0
$82$	−116790.			−0.211819
$83$	−514668.	−	297144.i	−0.900105	−	0.519676i	−0.0228706	−	0.999738i	$-0.507281\pi$
$83$	−514668.	−	297144.i	−0.900105	−	0.519676i	−0.877234	+	0.480063i	$0.840614\pi$
$84$		0			0
$85$	695174.	+	1.20408e6i	1.13197	+	1.96064i
$86$	599766.	−	346275.i	0.942945	−	0.544410i
$87$		0			0
$88$	5930.93	−	10272.7i	0.00870312	−	0.0150742i
$89$			652205.i			0.925155i	0.886579	+	0.462577i	$0.153075\pi$
$89$			652205.i			0.925155i	−0.886579	+	0.462577i	$0.846925\pi$
$90$		0			0
$91$	−1.17570e6			−1.56017
$92$	−362912.	−	209527.i	−0.466056	−	0.269077i
$93$		0			0
$94$	44624.3	+	77291.6i	0.0537264	+	0.0930569i
$95$	−1.65605e6	+	956119.i	−1.93153	+	1.11517i
$96$		0			0
$97$	−877305.	+	1.51954e6i	−0.961248	+	1.66493i	−0.241873	+	0.970308i	$0.577762\pi$
$97$	−877305.	+	1.51954e6i	−0.961248	+	1.66493i	−0.719375	+	0.694622i	$0.755572\pi$
$98$			74688.9i			0.0793556i
$99$		0			0
$100$	1.04673e6			1.04673
$101$	1.46721e6	+	847093.i	1.42406	+	0.822180i	0.996643	−	0.0818750i	$-0.0260908\pi$
$101$	1.46721e6	+	847093.i	1.42406	+	0.822180i	0.427416	+	0.904055i	$0.359424\pi$
$102$		0			0
$103$	−189841.	−	328814.i	−0.173731	−	0.300911i	0.765990	−	0.642852i	$-0.222249\pi$
$103$	−189841.	−	328814.i	−0.173731	−	0.300911i	−0.939721	+	0.341941i	$0.888916\pi$
$104$	509521.	−	294172.i	0.452962	−	0.261518i
$105$		0			0
$106$	682300.	−	1.18178e6i	0.572872	−	0.992244i
$107$		−	322980.i		−	0.263648i	−0.991273	−	0.131824i	$-0.957917\pi$
$107$		−	322980.i		−	0.263648i	0.991273	−	0.131824i	$-0.0420833\pi$
$108$		0			0
$109$	−749380.			−0.578659			−0.289329	−	0.957230i	$-0.593432\pi$
$109$	−749380.			−0.578659			−0.289329	+	0.957230i	$0.593432\pi$
$110$	−70577.4	−	40747.9i	−0.0530258	−	0.0306145i
$111$		0			0
$112$	−185208.	−	320790.i	−0.131828	−	0.228332i
$113$	−81251.0	+	46910.3i	−0.0563110	+	0.0325112i	−0.527891	−	0.849312i	$-0.677017\pi$
$113$	−81251.0	+	46910.3i	−0.0563110	+	0.0325112i	0.471580	+	0.881823i	$0.343684\pi$
$114$		0			0
$115$	−1.43954e6	+	2.49335e6i	−0.946519	+	1.63942i
$116$		−	242963.i		−	0.155656i
$117$		0			0
$118$	−420704.			−0.256053
$119$	−1.98113e6	−	1.14381e6i	−1.17563	−	0.678752i
$120$		0			0
$121$	−883634.	−	1.53050e6i	−0.498788	−	0.863926i
$122$	948880.	−	547836.i	0.522555	−	0.301697i
$123$		0			0
$124$	604032.	−	1.04621e6i	0.316807	−	0.548726i
$125$		−	3.75624e6i		−	1.92320i
$126$		0			0
$127$	2.04352e6			0.997626			0.498813	−	0.866710i	$-0.333770\pi$
$127$	2.04352e6			0.997626			0.498813	+	0.866710i	$0.333770\pi$
$128$	160530.	+	92681.9i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−2.02108e6	−	3.50061e6i	−0.919927	−	1.59336i
$131$	3.20242e6	−	1.84892e6i	1.42451	−	0.822439i	0.427827	−	0.903861i	$-0.359279\pi$
$131$	3.20242e6	−	1.84892e6i	1.42451	−	0.822439i	0.996680	+	0.0814215i	$0.0259460\pi$
$132$		0			0
$133$	1.57315e6	−	2.72478e6i	0.668676	−	1.15818i
$134$		−	768184.i		−	0.319265i
$135$		0			0
$136$	1.14477e6			0.455093
$137$	1.32750e6	+	766433.i	0.516266	+	0.298066i	0.735405	−	0.677627i	$-0.236992\pi$
$137$	1.32750e6	+	766433.i	0.516266	+	0.298066i	−0.219140	+	0.975693i	$0.570325\pi$
$138$		0			0
$139$	46860.8	+	81165.4i	0.0174488	+	0.0302222i	0.874618	−	0.484813i	$-0.161112\pi$
$139$	46860.8	+	81165.4i	0.0174488	+	0.0302222i	−0.857169	+	0.515035i	$0.827779\pi$
$140$	−2.20396e6	+	1.27246e6i	−0.803192	+	0.463723i
$141$		0			0
$142$	743217.	−	1.28729e6i	0.259568	−	0.449584i
$143$			212978.i			0.0728326i
$144$		0			0
$145$	−1.66925e6			−0.547543
$146$	−2.04989e6	−	1.18350e6i	−0.658676	−	0.380287i
$147$		0			0
$148$	−343137.	−	594331.i	−0.105848	−	0.183334i
$149$	1.57794e6	−	911021.i	0.477013	−	0.275404i	−0.242158	−	0.970237i	$-0.577855\pi$
$149$	1.57794e6	−	911021.i	0.477013	−	0.275404i	0.719171	+	0.694833i	$0.244522\pi$
$150$		0			0
$151$	−1.47276e6	+	2.55089e6i	−0.427761	+	0.740903i	−0.996674	−	0.0814942i	$-0.974031\pi$
$151$	−1.47276e6	+	2.55089e6i	−0.427761	+	0.740903i	0.568913	+	0.822398i	$0.307364\pi$
$152$			1.57447e6i			0.448337i
$153$		0			0
$154$	134089.			0.0367140
$155$	−7.18790e6	−	4.14994e6i	−1.93022	−	1.11441i
$156$		0			0
$157$	1.87975e6	+	3.25582e6i	0.485737	+	0.841322i	0.999866	−	0.0163916i	$-0.00521785\pi$
$157$	1.87975e6	+	3.25582e6i	0.485737	+	0.841322i	−0.514128	+	0.857713i	$0.671885\pi$
$158$	−3.34264e6	+	1.92988e6i	−0.847459	+	0.489281i
$159$		0			0
$160$	636762.	−	1.10290e6i	0.155459	−	0.269264i
$161$		−	4.73709e6i		−	1.13510i
$162$		0			0
$163$	−3.82184e6			−0.882490			−0.441245	−	0.897387i	$-0.645463\pi$
$163$	−3.82184e6			−0.882490			−0.441245	+	0.897387i	$0.645463\pi$
$164$	572152.	+	330332.i	0.129712	+	0.0748893i
$165$		0			0
$166$	1.68090e6	+	2.91140e6i	0.367466	+	0.636470i
$167$	3.86966e6	−	2.23415e6i	0.830852	−	0.479692i	−0.0232925	−	0.999729i	$-0.507415\pi$
$167$	3.86966e6	−	2.23415e6i	0.830852	−	0.479692i	0.854144	+	0.520036i	$0.174082\pi$
$168$		0			0
$169$	−2.86840e6	+	4.96822e6i	−0.594265	+	1.02930i
$170$		−	7.86500e6i		−	1.60085i
$171$		0			0
$172$	−3.91766e6			−0.769912
$173$	−424489.	−	245079.i	−0.0819837	−	0.0473333i	0.458448	−	0.888721i	$-0.348406\pi$
$173$	−424489.	−	245079.i	−0.0819837	−	0.0473333i	−0.540431	+	0.841388i	$0.681739\pi$
$174$		0			0
$175$	5.91622e6	+	1.02472e7i	1.10390	+	1.91201i
$176$	−58111.0	+	33550.4i	−0.0106591	+	0.00615403i
$177$		0			0
$178$	1.84472e6	−	3.19514e6i	0.327092	−	0.566539i
$179$		−	4.26181e6i		−	0.743079i	−0.928417	−	0.371540i	$-0.878830\pi$
$179$		−	4.26181e6i		−	0.743079i	0.928417	−	0.371540i	$-0.121170\pi$
$180$		0			0
$181$	−203844.			−0.0343765			−0.0171883	−	0.999852i	$-0.505471\pi$
$181$	−203844.			−0.0343765			−0.0171883	+	0.999852i	$0.505471\pi$
$182$	5.75973e6	+	3.32538e6i	0.955407	+	0.551604i
$183$		0			0
$184$	1.18527e6	+	2.05294e6i	0.190266	+	0.329551i
$185$	−4.08329e6	+	2.35749e6i	−0.644905	+	0.372336i
$186$		0			0
$187$	−207200.	+	358881.i	−0.0316858	+	0.0548814i
$188$		−	504866.i		−	0.0759806i
$189$		0			0
$190$	1.08173e7			1.57709
$191$	−838858.	−	484315.i	−0.120389	−	0.0695068i	0.438596	−	0.898684i	$-0.355476\pi$
$191$	−838858.	−	484315.i	−0.120389	−	0.0695068i	−0.558985	+	0.829177i	$0.688809\pi$
$192$		0			0
$193$	−1.47212e6	−	2.54978e6i	−0.204772	−	0.354676i	0.745288	−	0.666743i	$-0.232312\pi$
$193$	−1.47212e6	−	2.54978e6i	−0.204772	−	0.354676i	−0.950060	+	0.312067i	$0.898979\pi$
$194$	8.59580e6	−	4.96279e6i	1.17728	−	0.679705i
$195$		0			0
$196$	211252.	−	365899.i	0.0280565	−	0.0485952i
$197$			6.11122e6i			0.799336i	0.916660	+	0.399668i	$0.130875\pi$
$197$			6.11122e6i			0.799336i	−0.916660	+	0.399668i	$0.869125\pi$
$198$		0			0
$199$	742860.			0.0942644			0.0471322	−	0.998889i	$-0.484992\pi$
$199$	742860.			0.0942644			0.0471322	+	0.998889i	$0.484992\pi$
$200$	−5.12790e6	−	2.96059e6i	−0.640988	−	0.370074i
$201$		0			0
$202$	−4.79188e6	−	8.29978e6i	−0.581369	−	1.00696i
$203$	2.37855e6	−	1.37325e6i	0.284330	−	0.164158i
$204$		0			0
$205$	2.26952e6	−	3.93092e6i	0.263434	−	0.456281i
$206$			2.14780e6i			0.245693i
$207$		0			0
$208$	−3.32818e6			−0.369842
$209$	−493592.	−	284976.i	−0.0540667	−	0.0312154i
$210$		0			0
$211$	−1.89091e6	−	3.27515e6i	−0.201291	−	0.348646i	0.747654	−	0.664089i	$-0.231180\pi$
$211$	−1.89091e6	−	3.27515e6i	−0.201291	−	0.348646i	−0.948945	+	0.315443i	$0.897847\pi$
$212$	−6.68515e6	+	3.85967e6i	−0.701623	+	0.405082i
$213$		0			0
$214$	−913524.	+	1.58227e6i	−0.0932135	+	0.161451i
$215$			2.69159e7i			2.70828i
$216$		0			0
$217$	1.36562e7			1.33644
$218$	3.67120e6	+	2.11957e6i	0.354355	+	0.204587i
$219$		0			0
$220$	230505.	+	399246.i	0.0216477	+	0.0374949i
$221$	−1.78003e7	+	1.02770e7i	−1.64912	+	0.952118i
$222$		0			0
$223$	−31399.7	+	54385.9i	−0.00283146	+	0.00490424i	−0.867438	−	0.497546i	$-0.834235\pi$
$223$	−31399.7	+	54385.9i	−0.00283146	+	0.00490424i	0.864606	+	0.502450i	$0.167568\pi$
$224$			2.09539e6i			0.186432i
$225$		0			0
$226$	530729.			0.0459777
$227$	1.78525e7	+	1.03072e7i	1.52624	+	0.881173i	0.999515	+	0.0311352i	$0.00991223\pi$
$227$	1.78525e7	+	1.03072e7i	1.52624	+	0.881173i	0.526721	+	0.850038i	$0.323421\pi$
$228$		0			0
$229$	−7.34627e6	−	1.27241e7i	−0.611731	−	1.05955i	−0.990949	−	0.134242i	$-0.957140\pi$
$229$	−7.34627e6	−	1.27241e7i	−0.611731	−	1.05955i	0.379217	−	0.925308i	$-0.376193\pi$
$230$	1.41045e7	−	8.14325e6i	1.15924	−	0.669290i
$231$		0			0
$232$	−687203.	+	1.19027e6i	−0.0550327	+	0.0953195i
$233$		−	1.85059e7i		−	1.46299i	−0.681845	−	0.731497i	$-0.738822\pi$
$233$		−	1.85059e7i		−	1.46299i	0.681845	−	0.731497i	$-0.261178\pi$
$234$		0			0
$235$	−3.46863e6			−0.267273
$236$	2.06102e6	+	1.18993e6i	0.156800	+	0.0905285i
$237$		0			0
$238$	6.47034e6	+	1.12070e7i	0.479950	+	0.831298i
$239$	7.43494e6	−	4.29257e6i	0.544608	−	0.314430i	−0.202336	−	0.979316i	$-0.564853\pi$
$239$	7.43494e6	−	4.29257e6i	0.544608	−	0.314430i	0.746944	+	0.664887i	$0.231520\pi$
$240$		0			0
$241$	−2.91154e6	+	5.04294e6i	−0.208004	+	0.360274i	−0.951086	−	0.308927i	$-0.900030\pi$
$241$	−2.91154e6	+	5.04294e6i	−0.208004	+	0.360274i	0.743082	+	0.669201i	$0.233363\pi$
$242$			9.99717e6i			0.705393i
$243$		0			0
$244$	−6.19806e6			−0.426664
$245$	−2.51388e6	−	1.45139e6i	−0.170941	−	0.0986927i
$246$		0			0
$247$	−1.41347e7	−	2.44820e7i	−0.937984	−	1.62464i
$248$	−5.91828e6	+	3.41692e6i	−0.388008	+	0.224016i
$249$		0			0
$250$	−1.06243e7	+	1.84018e7i	−0.679953	+	1.17771i
$251$			7.28405e6i			0.460629i	0.973116	+	0.230315i	$0.0739755\pi$
$251$			7.28405e6i			0.460629i	−0.973116	+	0.230315i	$0.926024\pi$
$252$		0			0
$253$	−858121.			−0.0529892
$254$	−1.00112e7	−	5.77995e6i	−0.610918	−	0.352714i
$255$		0			0
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	−1.12484e7	+	6.49429e6i	−0.662663	+	0.382589i	−0.793291	−	0.608843i	$-0.791634\pi$
$257$	−1.12484e7	+	6.49429e6i	−0.662663	+	0.382589i	0.130628	+	0.991431i	$0.458301\pi$
$258$		0			0
$259$	3.87890e6	−	6.71845e6i	0.223259	−	0.386696i
$260$			2.28659e7i			1.30097i
$261$		0			0
$262$	−2.09181e7			−1.16310
$263$	2.87471e7	+	1.65971e7i	1.58025	+	0.912358i	0.994822	+	0.101635i	$0.0324074\pi$
$263$	2.87471e7	+	1.65971e7i	1.58025	+	0.912358i	0.585429	+	0.810723i	$0.300926\pi$
$264$		0			0
$265$	2.65175e7	+	4.59297e7i	1.42493	+	2.46806i
$266$	−1.54137e7	+	8.89909e6i	−0.818958	+	0.472825i
$267$		0			0
$268$	−2.17275e6	+	3.76332e6i	−0.112877	+	0.195509i
$269$			1.11187e6i			0.0571209i	0.999592	+	0.0285605i	$0.00909232\pi$
$269$			1.11187e6i			0.0571209i	−0.999592	+	0.0285605i	$0.990908\pi$
$270$		0			0
$271$	−1.07882e7			−0.542053			−0.271027	−	0.962572i	$-0.587363\pi$
$271$	−1.07882e7			−0.542053			−0.271027	+	0.962572i	$0.587363\pi$
$272$	−5.60818e6	−	3.23789e6i	−0.278686	−	0.160900i
$273$		0			0
$274$	−4.33560e6	−	7.50948e6i	−0.210765	−	0.365055i
$275$	1.85628e6	−	1.07172e6i	0.0892574	−	0.0515328i
$276$		0			0
$277$	1.86746e7	−	3.23454e7i	0.878644	−	1.52186i	0.0258150	−	0.999667i	$-0.491782\pi$
$277$	1.86746e7	−	3.23454e7i	0.878644	−	1.52186i	0.852829	−	0.522190i	$-0.174885\pi$
$278$		−	530170.i		−	0.0246763i
$279$		0			0
$280$	1.43962e7			0.655803
$281$	1.05319e7	+	6.08060e6i	0.474666	+	0.274048i	0.718191	−	0.695846i	$-0.244970\pi$
$281$	1.05319e7	+	6.08060e6i	0.474666	+	0.274048i	−0.243525	+	0.969895i	$0.578304\pi$
$282$		0			0
$283$	−1.00643e7	−	1.74318e7i	−0.444040	−	0.769100i	0.553945	−	0.832554i	$-0.313122\pi$
$283$	−1.00643e7	−	1.74318e7i	−0.444040	−	0.769100i	−0.997985	+	0.0634533i	$0.979789\pi$
$284$	−7.28201e6	+	4.20427e6i	−0.317904	+	0.183542i
$285$		0			0
$286$	602392.	−	1.04337e6i	0.0257502	−	0.0446007i
$287$			7.46830e6i			0.315919i
$288$		0			0
$289$	−1.58553e7			−0.656874
$290$	8.17764e6	+	4.72136e6i	0.335300	+	0.193586i
$291$		0			0
$292$	6.69491e6	+	1.15959e7i	0.268903	+	0.465754i
$293$	1.42159e7	−	8.20754e6i	0.565159	−	0.326295i	−0.190055	−	0.981774i	$-0.560866\pi$
$293$	1.42159e7	−	8.20754e6i	0.565159	−	0.326295i	0.755214	+	0.655479i	$0.227533\pi$
$294$		0			0
$295$	8.17529e6	−	1.41600e7i	0.318447	−	0.551566i
$296$			3.88216e6i			0.149692i
$297$		0			0
$298$	−1.03070e7			−0.389480
$299$	−3.68602e7	−	2.12812e7i	−1.37894	−	0.796129i
$300$		0			0
$301$	−2.21430e7	−	3.83528e7i	−0.811965	−	1.40636i
$302$	1.44300e7	−	8.33119e6i	0.523898	−	0.302473i
$303$		0			0
$304$	4.45328e6	−	7.71331e6i	0.158511	−	0.274549i
$305$			4.25831e7i			1.50085i
$306$		0			0
$307$	−1.26276e7			−0.436422			−0.218211	−	0.975902i	$-0.570022\pi$
$307$	−1.26276e7			−0.436422			−0.218211	+	0.975902i	$0.570022\pi$
$308$	−656900.	−	379261.i	−0.0224826	−	0.0129803i
$309$		0			0
$310$	2.34756e7	+	4.06609e7i	0.788010	+	1.36487i
$311$	−2.32452e6	+	1.34206e6i	−0.0772773	+	0.0446161i	−0.538141	−	0.842855i	$-0.680873\pi$
$311$	−2.32452e6	+	1.34206e6i	−0.0772773	+	0.0446161i	0.460863	+	0.887471i	$0.347540\pi$
$312$		0			0
$313$	2.06293e7	−	3.57311e7i	0.672748	−	1.16523i	−0.304374	−	0.952553i	$-0.598447\pi$
$313$	2.06293e7	−	3.57311e7i	0.672748	−	1.16523i	0.977122	−	0.212681i	$-0.0682195\pi$
$314$		−	2.12670e7i		−	0.686936i
$315$		0			0
$316$	2.18341e7			0.691948
$317$	−1.39503e7	−	8.05420e6i	−0.437931	−	0.252839i	0.264789	−	0.964306i	$-0.414698\pi$
$317$	−1.39503e7	−	8.05420e6i	−0.437931	−	0.252839i	−0.702719	+	0.711467i	$0.748031\pi$
$318$		0			0
$319$	−248764.	−	430872.i	−0.00766330	−	0.0132732i
$320$	−6.23897e6	+	3.60207e6i	−0.190398	+	0.109926i
$321$		0			0
$322$	−1.33985e7	+	2.32069e7i	−0.401318	+	0.695103i
$323$		−	5.50049e7i		−	1.63228i
$324$		0			0
$325$	1.06314e8			3.09699
$326$	1.87231e7	+	1.08098e7i	0.540413	+	0.312008i
$327$		0			0
$328$	−1.86864e6	−	3.23658e6i	−0.0529547	−	0.0917203i
$329$	4.94251e6	−	2.85356e6i	0.138791	−	0.0801308i
$330$		0			0
$331$	−2.45722e7	+	4.25604e7i	−0.677580	+	1.17360i	0.298127	+	0.954526i	$0.403638\pi$
$331$	−2.45722e7	+	4.25604e7i	−0.677580	+	1.17360i	−0.975708	+	0.219077i	$0.929695\pi$
$332$		−	1.90172e7i		−	0.519676i
$333$		0			0
$334$	−2.52765e7			−0.678388
$335$	2.58555e7	+	1.49277e7i	0.687731	+	0.397061i
$336$		0			0
$337$	3.50384e6	+	6.06883e6i	0.0915493	+	0.158568i	0.908163	−	0.418616i	$-0.137485\pi$
$337$	3.50384e6	+	6.06883e6i	0.0915493	+	0.158568i	−0.816614	+	0.577184i	$0.804151\pi$
$338$	2.81045e7	−	1.62261e7i	0.727823	−	0.420209i
$339$		0			0
$340$	−2.22456e7	+	3.85305e7i	−0.565987	+	0.980319i
$341$		−	2.47382e6i		−	0.0623885i
$342$		0			0
$343$	−3.77817e7			−0.936265
$344$	1.91925e7	+	1.10808e7i	0.471473	+	0.272205i
$345$		0			0
$346$	1.38637e6	+	2.40127e6i	0.0334697	+	0.0579713i
$347$	−1.95668e7	+	1.12969e7i	−0.468308	+	0.270378i	−0.715531	−	0.698581i	$-0.753815\pi$
$347$	−1.95668e7	+	1.12969e7i	−0.468308	+	0.270378i	0.247223	+	0.968959i	$0.420482\pi$
$348$		0			0
$349$	−8.93245e6	+	1.54715e7i	−0.210133	+	0.363961i	−0.951756	−	0.306856i	$-0.900723\pi$
$349$	−8.93245e6	+	1.54715e7i	−0.210133	+	0.363961i	0.741623	+	0.670817i	$0.234056\pi$
$350$		−	6.69344e7i		−	1.56115i
$351$		0			0
$352$	379580.			0.00870312
$353$	−4.27196e7	−	2.46642e7i	−0.971188	−	0.560716i	−0.0715897	−	0.997434i	$-0.522807\pi$
$353$	−4.27196e7	−	2.46642e7i	−0.971188	−	0.560716i	−0.899598	+	0.436719i	$0.856141\pi$
$354$		0			0
$355$	2.88850e7	+	5.00303e7i	0.645636	+	1.11827i
$356$	−1.80744e7	+	1.04353e7i	−0.400604	+	0.231289i
$357$		0			0
$358$	−1.20542e7	+	2.08785e7i	−0.262718	+	0.455041i
$359$			9.23078e6i			0.199505i	0.995012	+	0.0997527i	$0.0318052\pi$
$359$			9.23078e6i			0.199505i	−0.995012	+	0.0997527i	$0.968195\pi$
$360$		0			0
$361$	2.86061e7			0.608046
$362$	998627.	+	576558.i	0.0210512	+	0.0121539i
$363$		0			0
$364$	−1.88112e7	−	3.25820e7i	−0.390043	−	0.675575i
$365$	7.96687e7	−	4.59967e7i	1.63836	−	0.945907i
$366$		0			0
$367$	−1.61616e7	+	2.79927e7i	−0.326953	+	0.566299i	−0.981906	−	0.189371i	$-0.939355\pi$
$367$	−1.61616e7	+	2.79927e7i	−0.326953	+	0.566299i	0.654953	+	0.755670i	$0.272689\pi$
$368$		−	1.34098e7i		−	0.269077i
$369$		0			0
$370$	2.66720e7			0.526562
$371$	−7.55704e7	−	4.36306e7i	−1.47989	−	0.854416i
$372$		0			0
$373$	−331610.	−	574365.i	−0.00639000	−	0.0110678i	0.862813	−	0.505524i	$-0.168701\pi$
$373$	−331610.	−	574365.i	−0.00639000	−	0.0110678i	−0.869203	+	0.494456i	$0.835367\pi$
$374$	2.03014e6	−	1.17210e6i	0.0388070	−	0.0224052i
$375$		0			0
$376$	−1.42798e6	+	2.47333e6i	−0.0268632	+	0.0465284i
$377$		−	2.46772e7i		−	0.460545i
$378$		0			0
$379$	1.06169e7			0.195020			0.0975098	−	0.995235i	$-0.468912\pi$
$379$	1.06169e7			0.195020			0.0975098	+	0.995235i	$0.468912\pi$
$380$	−5.29935e7	−	3.05958e7i	−0.965766	−	0.557585i
$381$		0			0
$382$	2.73970e6	+	4.74530e6i	0.0491488	+	0.0851282i
$383$	−6.97322e7	+	4.02599e7i	−1.24119	+	0.716600i	−0.969336	−	0.245739i	$-0.920969\pi$
$383$	−6.97322e7	+	4.02599e7i	−1.24119	+	0.716600i	−0.271851	+	0.962339i	$0.587636\pi$
$384$		0			0
$385$	−2.60568e6	+	4.51316e6i	−0.0456602	+	0.0790859i
$386$			1.66551e7i			0.289592i
$387$		0			0
$388$	−5.61475e7			−0.961248
$389$	−4.50119e7	−	2.59877e7i	−0.764679	−	0.441487i	0.0662945	−	0.997800i	$-0.478882\pi$
$389$	−4.50119e7	−	2.59877e7i	−0.764679	−	0.441487i	−0.830973	+	0.556313i	$0.812216\pi$
$390$		0			0
$391$	−4.14078e7	−	7.17204e7i	−0.692711	−	1.19981i
$392$	−2.06984e6	+	1.19502e6i	−0.0343620	+	0.0198389i
$393$		0			0
$394$	1.72852e7	−	2.99388e7i	0.282608	−	0.489491i
$395$		−	1.50009e8i		−	2.43403i
$396$		0			0
$397$	2.94852e7			0.471230			0.235615	−	0.971846i	$-0.424290\pi$
$397$	2.94852e7			0.471230			0.235615	+	0.971846i	$0.424290\pi$
$398$	−3.63926e6	−	2.10113e6i	−0.0577249	−	0.0333275i
$399$		0			0
$400$	1.67477e7	+	2.90078e7i	0.261682	+	0.453247i
$401$	1.14443e7	−	6.60738e6i	0.177483	−	0.102470i	−0.408626	−	0.912702i	$-0.633992\pi$
$401$	1.14443e7	−	6.60738e6i	0.177483	−	0.102470i	0.586110	+	0.810232i	$0.300659\pi$
$402$		0			0
$403$	6.13502e7	−	1.06262e8i	0.937348	−	1.62353i
$404$			5.42140e7i			0.822180i
$405$		0			0
$406$	−1.55366e7			−0.232155
$407$	−1.21704e6	−	702661.i	−0.0180519	−	0.0104223i
$408$		0			0
$409$	−6.20547e6	−	1.07482e7i	−0.0906995	−	0.157096i	0.817106	−	0.576487i	$-0.195577\pi$
$409$	−6.20547e6	−	1.07482e7i	−0.0906995	−	0.157096i	−0.907806	+	0.419391i	$0.862244\pi$
$410$	−2.22366e7	+	1.28383e7i	−0.322639	+	0.186276i
$411$		0			0
$412$	6.07491e6	−	1.05220e7i	0.0868656	−	0.150456i
$413$			2.69025e7i			0.381893i
$414$		0			0
$415$	−1.30656e8			−1.82803
$416$	1.63047e7	+	9.41350e6i	0.226481	+	0.130759i
$417$		0			0
$418$	1.61207e6	+	2.79218e6i	0.0220726	+	0.0382309i
$419$	8.91041e7	−	5.14443e7i	1.21131	−	0.699351i	0.248266	−	0.968692i	$-0.420139\pi$
$419$	8.91041e7	−	5.14443e7i	1.21131	−	0.699351i	0.963045	+	0.269341i	$0.0868059\pi$
$420$		0			0
$421$	5.02269e7	−	8.69956e7i	0.673117	−	1.16587i	−0.303899	−	0.952704i	$-0.598288\pi$
$421$	5.02269e7	−	8.69956e7i	0.673117	−	1.16587i	0.977016	−	0.213168i	$-0.0683782\pi$
$422$			2.13932e7i			0.284668i
$423$		0			0
$424$	4.36672e7			0.572872
$425$	1.79146e8	+	1.03430e8i	2.33367	+	1.34734i
$426$		0			0
$427$	−3.50321e7	−	6.06774e7i	−0.449969	−	0.779369i
$428$	8.95067e6	−	5.16767e6i	0.114163	−	0.0659119i
$429$		0			0
$430$	7.61296e7	−	1.31860e8i	0.957520	−	1.65847i
$431$			4.20064e7i			0.524667i	0.964977	+	0.262333i	$0.0844920\pi$
$431$			4.20064e7i			0.524667i	−0.964977	+	0.262333i	$0.915508\pi$
$432$		0			0
$433$	−1.00183e8			−1.23404			−0.617022	−	0.786946i	$-0.711661\pi$
$433$	−1.00183e8			−1.23404			−0.617022	+	0.786946i	$0.711661\pi$
$434$	−6.69015e7	−	3.86256e7i	−0.818402	−	0.472505i
$435$		0			0
$436$	−1.19901e7	−	2.07674e7i	−0.144665	−	0.250567i
$437$	9.86419e7	−	5.69509e7i	1.18200	−	0.682428i
$438$		0			0
$439$	−6.57077e7	+	1.13809e8i	−0.776645	+	1.34519i	0.157220	+	0.987564i	$0.449747\pi$
$439$	−6.57077e7	+	1.13809e8i	−0.776645	+	1.34519i	−0.933865	+	0.357625i	$0.883587\pi$
$440$		−	2.60786e6i		−	0.0306145i
$441$		0			0
$442$	1.16271e8			1.34650
$443$	6.39716e6	+	3.69340e6i	0.0735828	+	0.0424830i	0.536340	−	0.844002i	$-0.319806\pi$
$443$	6.39716e6	+	3.69340e6i	0.0735828	+	0.0424830i	−0.462757	+	0.886485i	$0.653140\pi$
$444$		0			0
$445$	7.16946e7	+	1.24179e8i	0.813592	+	1.40918i
$446$	307653.	−	177623.i	0.00346782	−	0.00200215i
$447$		0			0
$448$	5.92667e6	−	1.02653e7i	0.0659138	−	0.114166i
$449$		−	9.38627e7i		−	1.03694i	−0.855095	−	0.518471i	$-0.826502\pi$
$449$		−	9.38627e7i		−	1.03694i	0.855095	−	0.518471i	$-0.173498\pi$
$450$		0			0
$451$	1.35288e6			0.0147479
$452$	−2.60003e6	−	1.50113e6i	−0.0281555	−	0.0162556i
$453$		0			0
$454$	−5.83061e7	−	1.00989e8i	−0.623083	−	1.07921i
$455$	−2.23851e8	+	1.29241e8i	−2.37643	+	1.37203i
$456$		0			0
$457$	−1.25273e7	+	2.16979e7i	−0.131253	+	0.227336i	−0.924160	−	0.382006i	$-0.875233\pi$
$457$	−1.25273e7	+	2.16979e7i	−0.131253	+	0.227336i	0.792907	+	0.609343i	$0.208567\pi$
$458$			8.31136e7i			0.865119i
$459$		0			0
$460$	−9.21304e7			−0.946519
$461$	−3.99451e7	−	2.30623e7i	−0.407719	−	0.235397i	0.282090	−	0.959388i	$-0.408972\pi$
$461$	−3.99451e7	−	2.30623e7i	−0.407719	−	0.235397i	−0.689809	+	0.723991i	$0.742306\pi$
$462$		0			0
$463$	7.06199e7	+	1.22317e8i	0.711515	+	1.23238i	0.964288	+	0.264854i	$0.0853238\pi$
$463$	7.06199e7	+	1.22317e8i	0.711515	+	1.23238i	−0.252774	+	0.967525i	$0.581343\pi$
$464$	6.73319e6	−	3.88741e6i	0.0674011	−	0.0389140i
$465$		0			0
$466$	−5.23426e7	+	9.06600e7i	−0.517246	+	0.895897i
$467$		−	1.30520e8i		−	1.28152i	−0.767741	−	0.640760i	$-0.778619\pi$
$467$		−	1.30520e8i		−	1.28152i	0.767741	−	0.640760i	$-0.221381\pi$
$468$		0			0
$469$	−4.91225e7			−0.476170
$470$	1.69928e7	+	9.81078e6i	0.163671	+	0.0944952i
$471$		0			0
$472$	−6.73126e6	−	1.16589e7i	−0.0640133	−	0.110874i
$473$	−6.94760e6	+	4.01120e6i	−0.0656525	+	0.0379045i
$474$		0			0
$475$	−1.42254e8	+	2.46391e8i	−1.32734	+	2.29903i
$476$		−	7.32035e7i		−	0.678752i
$477$		0			0
$478$	−4.85648e7			−0.444671
$479$	1.67635e8	+	9.67841e7i	1.52531	+	0.880638i	0.999550	+	0.0300057i	$0.00955254\pi$
$479$	1.67635e8	+	9.67841e7i	1.52531	+	0.880638i	0.525761	+	0.850633i	$0.323781\pi$
$480$		0			0
$481$	−3.48517e7	−	6.03650e7i	−0.313176	−	0.542437i
$482$	2.85272e7	−	1.64702e7i	0.254752	−	0.147081i
$483$		0			0
$484$	2.82763e7	−	4.89759e7i	0.249394	−	0.431963i
$485$			3.85756e8i			3.38133i
$486$		0			0
$487$	3.79815e7			0.328840			0.164420	−	0.986390i	$-0.447425\pi$
$487$	3.79815e7			0.328840			0.164420	+	0.986390i	$0.447425\pi$
$488$	3.03642e7	+	1.75308e7i	0.261277	+	0.150849i
$489$		0			0
$490$	8.21028e6	+	1.42206e7i	0.0697862	+	0.120873i
$491$	−6.41311e7	+	3.70261e7i	−0.541782	+	0.312798i	−0.745801	−	0.666169i	$-0.767933\pi$
$491$	−6.41311e7	+	3.70261e7i	−0.541782	+	0.312798i	0.204019	+	0.978967i	$0.434600\pi$
$492$		0			0
$493$	2.40078e7	−	4.15827e7i	0.200360	−	0.347034i
$494$			1.59916e8i			1.32651i
$495$		0			0
$496$	3.86580e7			0.316807
$497$	−8.23174e7	−	4.75260e7i	−0.670537	−	0.387135i
$498$		0			0
$499$	7.27421e6	+	1.25993e7i	0.0585442	+	0.101402i	0.893812	−	0.448442i	$-0.148021\pi$
$499$	7.27421e6	+	1.25993e7i	0.0585442	+	0.101402i	−0.835268	+	0.549843i	$0.814687\pi$
$500$	1.04096e8	−	6.00999e7i	0.832768	−	0.480799i
$501$		0			0
$502$	2.06024e7	−	3.56844e7i	0.162857	−	0.282077i
$503$			2.43812e8i			1.91580i	0.287094	+	0.957902i	$0.407311\pi$
$503$			2.43812e8i			1.91580i	−0.287094	+	0.957902i	$0.592689\pi$
$504$		0			0
$505$	3.72472e8			2.89214
$506$	4.20392e6	+	2.42713e6i	0.0324491	+	0.0187345i
$507$		0			0
$508$	3.26963e7	+	5.66317e7i	0.249406	+	0.431985i
$509$	−1.75953e8	+	1.01586e8i	−1.33427	+	0.770339i	−0.985950	−	0.167038i	$-0.946580\pi$
$509$	−1.75953e8	+	1.01586e8i	−1.33427	+	0.770339i	−0.348316	+	0.937377i	$0.613246\pi$
$510$		0			0
$511$	−7.56808e7	+	1.31083e8i	−0.567183	+	0.982389i
$512$			5.93164e6i			0.0441942i
$513$		0			0
$514$	7.34745e7			0.541062
$515$	−7.22907e7	−	4.17370e7i	−0.529250	−	0.305562i
$516$		0			0
$517$	−516921.	−	895334.i	−0.00374070	−	0.00647908i
$518$	−3.80053e7	+	2.19424e7i	−0.273436	+	0.157868i
$519$		0			0
$520$	6.46745e7	−	1.12020e8i	0.459963	−	0.796680i
$521$			4.76973e7i			0.337272i	0.985678	+	0.168636i	$0.0539363\pi$
$521$			4.76973e7i			0.337272i	−0.985678	+	0.168636i	$0.946064\pi$
$522$		0			0
$523$	−1.71156e8			−1.19643			−0.598216	−	0.801335i	$-0.704123\pi$
$523$	−1.71156e8			−1.19643			−0.598216	+	0.801335i	$0.704123\pi$
$524$	1.02477e8	+	5.91654e7i	0.712253	+	0.411220i
$525$		0			0
$526$	−9.38875e7	−	1.62618e8i	−0.645135	−	1.11741i
$527$	2.06758e8	−	1.19372e8i	1.41263	−	0.815585i
$528$		0			0
$529$	1.17276e7	−	2.03128e7i	0.0792214	−	0.137215i
$530$		−	3.00011e8i		−	2.01516i
$531$		0			0
$532$	1.00682e8			0.668676
$533$	5.81123e7	+	3.35512e7i	0.383784	+	0.221578i
$534$		0			0
$535$	−3.55040e7	−	6.14947e7i	−0.231855	−	0.401584i
$536$	2.12885e7	−	1.22909e7i	0.138246	−	0.0798161i
$537$		0			0
$538$	3.14483e6	−	5.44700e6i	0.0201953	−	0.0349793i
$539$		−	865185.i		−	0.00552513i
$540$		0			0
$541$	1.88549e8			1.19078			0.595392	−	0.803435i	$-0.296997\pi$
$541$	1.88549e8			1.19078			0.595392	+	0.803435i	$0.296997\pi$
$542$	5.28513e7	+	3.05137e7i	0.331938	+	0.191645i
$543$		0			0
$544$	1.83162e7	+	3.17247e7i	0.113773	+	0.197061i
$545$	−1.42681e8	+	8.23767e7i	−0.881405	+	0.508879i
$546$		0			0
$547$	6.46145e7	−	1.11916e8i	0.394792	−	0.683799i	−0.598283	−	0.801285i	$-0.704150\pi$
$547$	6.46145e7	−	1.11916e8i	0.394792	−	0.683799i	0.993075	+	0.117486i	$0.0374835\pi$
$548$			4.90517e7i			0.298066i
$549$		0			0
$550$	−1.21251e7			−0.0728784
$551$	5.71914e7	+	3.30195e7i	0.341882	+	0.197386i
$552$		0			0
$553$	1.23409e8	+	2.13750e8i	0.729743	+	1.26395i
$554$	−1.82973e8	+	1.05640e8i	−1.07612	+	0.621295i
$555$		0			0
$556$	−1.49955e6	+	2.59729e6i	−0.00872440	+	0.0151111i
$557$		−	2.12891e8i		−	1.23194i	−0.787768	−	0.615972i	$-0.788763\pi$
$557$		−	2.12891e8i		−	1.23194i	0.787768	−	0.615972i	$-0.211237\pi$
$558$		0			0
$559$	−3.97908e8			−2.27797
$560$	−7.05266e7	−	4.07186e7i	−0.401596	−	0.231861i
$561$		0			0
$562$	−3.43970e7	−	5.95774e7i	−0.193781	−	0.335639i
$563$	8.70527e7	−	5.02599e7i	0.487817	−	0.281641i	−0.235851	−	0.971789i	$-0.575788\pi$
$563$	8.70527e7	−	5.02599e7i	0.487817	−	0.281641i	0.723668	+	0.690148i	$0.242455\pi$
$564$		0			0
$565$	−1.03134e7	+	1.78633e7i	−0.0571814	+	0.0990411i
$566$			1.13864e8i			0.627968i
$567$		0			0
$568$	4.75659e7			0.259568
$569$	−4.33807e6	−	2.50458e6i	−0.0235483	−	0.0135956i	0.488180	−	0.872743i	$-0.337661\pi$
$569$	−4.33807e6	−	2.50458e6i	−0.0235483	−	0.0135956i	−0.511728	+	0.859148i	$0.670994\pi$
$570$		0			0
$571$	−7.51494e6	−	1.30163e7i	−0.0403662	−	0.0699162i	0.845136	−	0.534551i	$-0.179519\pi$
$571$	−7.51494e6	−	1.30163e7i	−0.0403662	−	0.0699162i	−0.885503	+	0.464634i	$0.846186\pi$
$572$	−5.90221e6	+	3.40764e6i	−0.0315375	+	0.0182082i
$573$		0			0
$574$	2.11235e7	−	3.65871e7i	0.111694	−	0.193460i
$575$			4.28356e8i			2.25321i
$576$		0			0
$577$	3.09641e8			1.61187			0.805936	−	0.592003i	$-0.201662\pi$
$577$	3.09641e8			1.61187			0.805936	+	0.592003i	$0.201662\pi$
$578$	7.76750e7	+	4.48457e7i	0.402252	+	0.232240i
$579$		0			0
$580$	−2.67081e7	−	4.62597e7i	−0.136886	−	0.237093i
$581$	1.86174e8	−	1.07487e8i	0.949270	−	0.548061i
$582$		0			0
$583$	−7.90366e6	+	1.36895e7i	−0.0398862	+	0.0690849i
$584$		−	7.57443e7i		−	0.380287i
$585$		0			0
$586$	−9.28577e7			−0.461450
$587$	2.10377e8	+	1.21461e8i	1.04012	+	0.600513i	0.919867	−	0.392230i	$-0.128296\pi$
$587$	2.10377e8	+	1.21461e8i	1.04012	+	0.600513i	0.120252	+	0.992743i	$0.461630\pi$
$588$		0			0
$589$	1.64180e8	+	2.84368e8i	0.803478	+	1.39166i
$590$	−8.01012e7	+	4.62464e7i	−0.390016	+	0.225176i
$591$		0			0
$592$	1.09804e7	−	1.90186e7i	0.0529240	−	0.0916671i
$593$		−	2.09148e8i		−	1.00297i	−0.865165	−	0.501487i	$-0.832787\pi$
$593$		−	2.09148e8i		−	1.00297i	0.865165	−	0.501487i	$-0.167213\pi$
$594$		0			0
$595$	−5.02938e8			−2.38761
$596$	5.04939e7	+	2.91527e7i	0.238507	+	0.137702i
$597$		0			0
$598$	1.20385e8	+	2.08513e8i	0.562948	+	0.975055i
$599$	1.30597e8	−	7.54002e7i	0.607649	−	0.350826i	−0.164396	−	0.986394i	$-0.552567\pi$
$599$	1.30597e8	−	7.54002e7i	0.607649	−	0.350826i	0.772045	+	0.635568i	$0.219234\pi$
$600$		0			0
$601$	1.49782e6	−	2.59431e6i	0.00689981	−	0.0119508i	−0.862555	−	0.505964i	$-0.831137\pi$
$601$	1.49782e6	−	2.59431e6i	0.00689981	−	0.0119508i	0.869455	+	0.494013i	$0.164470\pi$
$602$			2.50520e8i			1.14829i
$603$		0			0
$604$	−9.42566e7			−0.427761
$605$	−3.36484e8	−	1.94269e8i	−1.51949	−	0.877280i
$606$		0			0
$607$	−2.48947e7	−	4.31190e7i	−0.111312	−	0.192798i	0.804988	−	0.593292i	$-0.202172\pi$
$607$	−2.48947e7	−	4.31190e7i	−0.111312	−	0.192798i	−0.916299	+	0.400494i	$0.868839\pi$
$608$	−4.36331e7	+	2.51916e7i	−0.194135	+	0.112084i
$609$		0			0
$610$	1.20443e8	−	2.08614e8i	0.530632	−	0.919081i
$611$		−	5.12782e7i		−	0.224807i
$612$		0			0
$613$	−3.42067e8			−1.48501			−0.742506	−	0.669839i	$-0.766363\pi$
$613$	−3.42067e8			−1.48501			−0.742506	+	0.669839i	$0.766363\pi$
$614$	6.18625e7	+	3.57163e7i	0.267253	+	0.154298i
$615$		0			0
$616$	2.14543e6	+	3.71599e6i	0.00917849	+	0.0158976i
$617$	−2.50835e8	+	1.44820e8i	−1.06790	+	0.616555i	−0.927608	−	0.373554i	$-0.878139\pi$
$617$	−2.50835e8	+	1.44820e8i	−1.06790	+	0.616555i	−0.140297	+	0.990110i	$0.544806\pi$
$618$		0			0
$619$	−2.09811e8	+	3.63404e8i	−0.884620	+	1.53221i	−0.0384713	+	0.999260i	$0.512249\pi$
$619$	−2.09811e8	+	3.63404e8i	−0.884620	+	1.53221i	−0.846149	+	0.532947i	$0.821085\pi$
$620$		−	2.65596e8i		−	1.11441i
$621$		0			0
$622$	1.51837e7			0.0630967
$623$	−2.04318e8	−	1.17963e8i	−0.844970	−	0.487844i
$624$		0			0
$625$	−1.57361e8	−	2.72558e8i	−0.644552	−	1.11640i
$626$	−2.02125e8	+	1.16697e8i	−0.823945	+	0.475705i
$627$		0			0
$628$	−6.01520e7	+	1.04186e8i	−0.242869	+	0.420661i
$629$		−	1.35625e8i		−	0.544989i
$630$		0			0
$631$	4.29471e8			1.70941			0.854705	−	0.519114i	$-0.173738\pi$
$631$	4.29471e8			1.70941			0.854705	+	0.519114i	$0.173738\pi$
$632$	−1.06965e8	−	6.17560e7i	−0.423730	−	0.244640i
$633$		0			0
$634$	4.55614e7	+	7.89147e7i	0.178784	+	0.309664i
$635$	3.89082e8	−	2.24637e8i	1.51957	−	0.877323i
$636$		0			0
$637$	2.14564e7	−	3.71636e7i	0.0830117	−	0.143780i
$638$			2.81445e6i			0.0108375i
$639$		0			0
$640$	4.07528e7			0.155459
$641$	1.95331e8	+	1.12775e8i	0.741649	+	0.428191i	0.822668	−	0.568521i	$-0.192484\pi$
$641$	1.95331e8	+	1.12775e8i	0.741649	+	0.428191i	−0.0810198	+	0.996712i	$0.525818\pi$
$642$		0			0
$643$	−9.59974e7	−	1.66272e8i	−0.361099	−	0.625442i	0.627043	−	0.778985i	$-0.284265\pi$
$643$	−9.59974e7	−	1.66272e8i	−0.361099	−	0.625442i	−0.988142	+	0.153543i	$0.950932\pi$
$644$	1.31278e8	−	7.57934e7i	0.491512	−	0.283775i
$645$		0			0
$646$	−1.55577e8	+	2.69468e8i	−0.577097	+	0.999562i
$647$		−	3.48634e8i		−	1.28723i	−0.765348	−	0.643617i	$-0.777433\pi$
$647$		−	3.48634e8i		−	1.28723i	0.765348	−	0.643617i	$-0.222567\pi$
$648$		0			0
$649$	4.87337e6			0.0178277
$650$	−5.20830e8	−	3.00701e8i	−1.89651	−	1.09495i
$651$		0			0
$652$	−6.11495e7	−	1.05914e8i	−0.220623	−	0.382130i
$653$	2.77818e8	−	1.60399e8i	0.997750	−	0.576051i	0.0901680	−	0.995927i	$-0.471260\pi$
$653$	2.77818e8	−	1.60399e8i	0.997750	−	0.576051i	0.907582	+	0.419875i	$0.137926\pi$
$654$		0			0
$655$	4.06490e8	−	7.04061e8i	1.44652	−	2.50545i
$656$			2.11413e7i			0.0748893i
$657$		0			0
$658$	−3.22843e7			−0.113322
$659$	−1.18002e8	−	6.81284e7i	−0.412318	−	0.238052i	0.279467	−	0.960155i	$-0.409842\pi$
$659$	−1.18002e8	−	6.81284e7i	−0.412318	−	0.238052i	−0.691785	+	0.722103i	$0.743176\pi$
$660$		0			0
$661$	−5.18236e7	−	8.97612e7i	−0.179442	−	0.310802i	0.762248	−	0.647285i	$-0.224096\pi$
$661$	−5.18236e7	−	8.97612e7i	−0.179442	−	0.310802i	−0.941689	+	0.336483i	$0.890762\pi$
$662$	2.40758e8	−	1.39002e8i	0.829863	−	0.479121i
$663$		0			0
$664$	−5.37888e7	+	9.31649e7i	−0.183733	+	0.318235i
$665$		−	6.91724e8i		−	2.35216i
$666$		0			0
$667$	9.94285e7			0.335068
$668$	1.23829e8	+	7.14928e7i	0.415426	+	0.239846i
$669$		0			0
$670$	−8.44437e7	−	1.46261e8i	−0.280765	−	0.486299i
$671$	−1.09917e7	+	6.34605e6i	−0.0363828	+	0.0210056i
$672$		0			0
$673$	2.40953e8	−	4.17343e8i	0.790473	−	1.36914i	−0.135201	−	0.990818i	$-0.543168\pi$
$673$	2.40953e8	−	4.17343e8i	0.790473	−	1.36914i	0.925674	−	0.378322i	$-0.123499\pi$
$674$		−	3.96414e7i		−	0.129470i
$675$		0			0
$676$	−1.83578e8			−0.594265
$677$	−2.71713e8	−	1.56874e8i	−0.875679	−	0.505574i	−0.00644805	−	0.999979i	$-0.502052\pi$
$677$	−2.71713e8	−	1.56874e8i	−0.875679	−	0.505574i	−0.869231	+	0.494405i	$0.835386\pi$
$678$		0			0
$679$	−3.17352e8	−	5.49670e8i	−1.01375	−	1.75587i
$680$	2.17961e8	−	1.25840e8i	0.693190	−	0.400214i
$681$		0			0
$682$	−6.99701e6	+	1.21192e7i	−0.0220577	+	0.0382050i
$683$			4.79568e7i			0.150518i	0.997164	+	0.0752590i	$0.0239783\pi$
$683$			4.79568e7i			0.150518i	−0.997164	+	0.0752590i	$0.976022\pi$
$684$		0			0
$685$	3.37005e8			1.04849
$686$	1.85092e8	+	1.06863e8i	0.573343	+	0.331020i
$687$		0			0
$688$	−6.26825e7	−	1.08569e8i	−0.192478	−	0.333382i
$689$	−6.78996e8	+	3.92019e8i	−2.07592	+	1.19853i
$690$		0			0
$691$	−1.69731e8	+	2.93983e8i	−0.514432	+	0.891022i	0.485428	+	0.874277i	$0.338664\pi$
$691$	−1.69731e8	+	2.93983e8i	−0.514432	+	0.891022i	−0.999860	+	0.0167457i	$0.994669\pi$
$692$		−	1.56850e7i		−	0.0473333i
$693$		0			0
$694$	1.27810e8			0.382372
$695$	1.78444e7	+	1.03025e7i	0.0531555	+	0.0306894i
$696$		0			0
$697$	6.52819e7	+	1.13072e8i	0.192794	+	0.333930i
$698$	8.75197e7	−	5.05295e7i	0.257359	−	0.148586i
$699$		0			0
$700$	−1.89319e8	+	3.27910e8i	−0.551951	+	0.956007i
$701$			3.15780e8i			0.916706i	0.888770	+	0.458353i	$0.151560\pi$
$701$			3.15780e8i			0.916706i	−0.888770	+	0.458353i	$0.848440\pi$
$702$		0			0
$703$	1.86534e8			0.536898
$704$	−1.85955e6	−	1.07361e6i	−0.00532955	−	0.00307702i
$705$		0			0
$706$	1.39522e8	+	2.41659e8i	0.396486	+	0.686734i
$707$	−5.30741e8	+	3.06423e8i	−1.50184	+	0.867089i
$708$		0			0
$709$	−3.53011e6	+	6.11432e6i	−0.00990488	+	0.0171558i	−0.870935	−	0.491398i	$-0.836486\pi$
$709$	−3.53011e6	+	6.11432e6i	−0.00990488	+	0.0171558i	0.861030	+	0.508553i	$0.169820\pi$
$710$		−	3.26797e8i		−	0.913067i
$711$		0			0
$712$	1.18062e8			0.327092
$713$	4.28145e8	+	2.47190e8i	1.18120	+	0.681965i
$714$		0			0
$715$	2.34119e7	+	4.05506e7i	0.0640498	+	0.110938i
$716$	1.18107e8	−	6.81890e7i	0.321763	−	0.185770i
$717$		0			0
$718$	2.61086e7	−	4.52214e7i	0.0705358	−	0.122172i
$719$		−	4.97883e8i		−	1.33949i	−0.742589	−	0.669747i	$-0.766402\pi$
$719$		−	4.97883e8i		−	1.33949i	0.742589	−	0.669747i	$-0.233598\pi$
$720$		0			0
$721$	1.37344e8			0.366441
$722$	−1.40141e8	−	8.09102e7i	−0.372351	−	0.214977i
$723$		0			0
$724$	−3.26150e6	−	5.64909e6i	−0.00859413	−	0.0148855i
$725$	−2.15082e8	+	1.24178e8i	−0.564405	+	0.325859i
$726$		0			0
$727$	−3.33387e8	+	5.77443e8i	−0.867651	+	1.50282i	−0.00326047	+	0.999995i	$0.501038\pi$
$727$	−3.33387e8	+	5.77443e8i	−0.867651	+	1.50282i	−0.864391	+	0.502821i	$0.832295\pi$
$728$			2.12825e8i			0.551604i
$729$		0			0
$730$	−5.20394e8			−1.33771
$731$	−6.70499e8	−	3.87113e8i	−1.71651	−	0.991027i
$732$		0			0
$733$	3.98165e7	+	6.89641e7i	0.101100	+	0.175110i	0.912138	−	0.409883i	$-0.134430\pi$
$733$	3.98165e7	+	6.89641e7i	0.101100	+	0.175110i	−0.811038	+	0.584993i	$0.801097\pi$
$734$	1.58350e8	−	9.14237e7i	0.400434	−	0.231191i
$735$		0			0
$736$	−3.79285e7	+	6.56941e7i	−0.0951332	+	0.164776i
$737$			8.89852e6i			0.0222288i
$738$		0			0
$739$	−2.70841e7			−0.0671091			−0.0335546	−	0.999437i	$-0.510683\pi$
$739$	−2.70841e7			−0.0671091			−0.0335546	+	0.999437i	$0.510683\pi$
$740$	−1.30665e8	−	7.54397e7i	−0.322452	−	0.186168i
$741$		0			0
$742$	2.46812e8	+	4.27491e8i	0.604163	+	1.04644i
$743$	6.16010e8	−	3.55654e8i	1.50183	−	0.867083i	0.501835	−	0.864963i	$-0.332658\pi$
$743$	6.16010e8	−	3.55654e8i	1.50183	−	0.867083i	0.999998	−	0.00212005i	$-0.000674834\pi$
$744$		0			0
$745$	2.00291e8	−	3.46914e8i	0.484386	−	0.838982i
$746$			3.75174e6i			0.00903682i
$747$		0			0
$748$	−1.32608e7			−0.0316858
$749$	1.01180e8	+	5.84165e7i	0.240797	+	0.139024i
$750$		0			0
$751$	1.88126e8	+	3.25844e8i	0.444150	+	0.769291i	0.997993	−	0.0633309i	$-0.0201723\pi$
$751$	1.88126e8	+	3.25844e8i	0.444150	+	0.769291i	−0.553842	+	0.832622i	$0.686839\pi$
$752$	1.39913e7	−	8.07786e6i	0.0329006	−	0.0189952i
$753$		0			0
$754$	−6.97978e7	+	1.20893e8i	−0.162827	+	0.282025i
$755$			6.47581e8i			1.50471i
$756$		0			0
$757$	5.61588e8			1.29458			0.647292	−	0.762242i	$-0.275901\pi$
$757$	5.61588e8			1.29458			0.647292	+	0.762242i	$0.275901\pi$
$758$	−5.20117e7	−	3.00290e7i	−0.119425	−	0.0689498i
$759$		0			0
$760$	1.73076e8	+	2.99777e8i	0.394272	+	0.682900i
$761$	4.66525e8	−	2.69348e8i	1.05857	−	0.611167i	0.133536	−	0.991044i	$-0.457367\pi$
$761$	4.66525e8	−	2.69348e8i	1.05857	−	0.611167i	0.925037	+	0.379877i	$0.124034\pi$
$762$		0			0
$763$	1.35539e8	−	2.34760e8i	0.305133	−	0.528506i
$764$		−	3.09961e7i		−	0.0695068i
$765$		0			0
$766$	4.55489e8			1.01343
$767$	2.09333e8	+	1.20859e8i	0.463930	+	0.267850i
$768$		0			0
$769$	6.66254e7	+	1.15399e8i	0.146508	+	0.253759i	0.929934	−	0.367725i	$-0.119863\pi$
$769$	6.66254e7	+	1.15399e8i	0.146508	+	0.253759i	−0.783427	+	0.621484i	$0.786530\pi$
$770$	2.55303e7	−	1.47399e7i	0.0559222	−	0.0322867i
$771$		0			0
$772$	4.71078e7	−	8.15931e7i	0.102386	−	0.177338i
$773$		−	1.49887e8i		−	0.324509i	−0.986749	−	0.162254i	$-0.948124\pi$
$773$		−	1.49887e8i		−	0.324509i	0.986749	−	0.162254i	$-0.0518765\pi$
$774$		0			0
$775$	−1.23488e9			−2.65289
$776$	2.75066e8	+	1.58809e8i	0.588642	+	0.339852i
$777$		0			0
$778$	1.47008e8	+	2.54626e8i	0.312179	+	0.540709i
$779$	−1.55515e8	+	8.97865e7i	−0.328972	+	0.189932i
$780$		0			0
$781$	−8.60931e6	+	1.49118e7i	−0.0180724	+	0.0313023i
$782$			4.68476e8i			0.979641i
$783$		0			0
$784$	1.35201e7			0.0280565
$785$	7.15802e8	+	4.13269e8i	1.47974	+	0.854326i
$786$		0			0
$787$	3.97219e8	+	6.88004e8i	0.814903	+	1.41145i	0.909397	+	0.415928i	$0.136543\pi$
$787$	3.97219e8	+	6.88004e8i	0.814903	+	1.41145i	−0.0944940	+	0.995525i	$0.530123\pi$
$788$	−1.69359e8	+	9.77796e7i	−0.346123	+	0.199834i
$789$		0			0
$790$	−4.24289e8	+	7.34890e8i	−0.860558	+	1.49053i
$791$		−	3.39382e7i		−	0.0685740i
$792$		0			0
$793$	−6.29524e8			−1.26239
$794$	−1.44448e8	−	8.33968e7i	−0.288568	−	0.166605i
$795$		0			0
$796$	1.18858e7	+	2.05867e7i	0.0235661	+	0.0408177i
$797$	5.41648e8	−	3.12721e8i	1.06990	−	0.617706i	0.141744	−	0.989903i	$-0.454729\pi$
$797$	5.41648e8	−	3.12721e8i	1.06990	−	0.617706i	0.928154	+	0.372198i	$0.121396\pi$
$798$		0			0
$799$	4.98871e7	−	8.64069e7i	0.0978020	−	0.169398i
$800$		−	1.89478e8i		−	0.370074i
$801$		0			0
$802$	−7.47540e7			−0.144914
$803$	2.37456e7	+	1.37095e7i	0.0458603	+	0.0264775i
$804$		0			0
$805$	−5.20731e8	−	9.01933e8i	−0.998219	−	1.72897i
$806$	−6.01107e8	+	3.47049e8i	−1.14801	+	0.662805i
$807$		0			0
$808$	1.53340e8	−	2.65593e8i	0.290685	−	0.503481i
$809$			5.59378e7i			0.105648i	0.998604	+	0.0528238i	$0.0168222\pi$
$809$			5.59378e7i			0.105648i	−0.998604	+	0.0528238i	$0.983178\pi$
$810$		0			0
$811$	4.01030e8			0.751820			0.375910	−	0.926656i	$-0.377330\pi$
$811$	4.01030e8			0.751820			0.375910	+	0.926656i	$0.377330\pi$
$812$	7.61134e7	+	4.39441e7i	0.142165	+	0.0820791i
$813$		0			0
$814$	3.97485e6	+	6.88464e6i	0.00736966	+	0.0127646i
$815$	−7.27672e8	+	4.20121e8i	−1.34420	+	0.776072i
$816$		0			0
$817$	5.32422e8	−	9.22183e8i	0.976315	−	1.69103i
$818$			7.02069e7i			0.128268i
$819$		0			0
$820$	1.45249e8			0.263434
$821$	4.03601e7	+	2.33019e7i	0.0729327	+	0.0421077i	0.536023	−	0.844203i	$-0.319926\pi$
$821$	4.03601e7	+	2.33019e7i	0.0729327	+	0.0421077i	−0.463090	+	0.886311i	$0.653259\pi$
$822$		0			0
$823$	1.63594e8	+	2.83352e8i	0.293472	+	0.508309i	0.974628	−	0.223830i	$-0.0718559\pi$
$823$	1.63594e8	+	2.83352e8i	0.293472	+	0.508309i	−0.681156	+	0.732138i	$0.738523\pi$
$824$	−5.95217e7	+	3.43649e7i	−0.106388	+	0.0614233i
$825$		0			0
$826$	7.60916e7	−	1.31795e8i	0.135020	−	0.233861i
$827$			7.18675e8i			1.27062i	0.772257	+	0.635310i	$0.219128\pi$
$827$			7.18675e8i			1.27062i	−0.772257	+	0.635310i	$0.780872\pi$
$828$		0			0
$829$	6.45599e8			1.13318			0.566591	−	0.823999i	$-0.308262\pi$
$829$	6.45599e8			1.13318			0.566591	+	0.823999i	$0.308262\pi$
$830$	6.40080e8	+	3.69550e8i	1.11944	+	0.646308i
$831$		0			0
$832$	−5.32508e7	−	9.22331e7i	−0.0924605	−	0.160146i
$833$	7.23108e7	−	4.17487e7i	0.125103	−	0.0722283i
$834$		0			0
$835$	4.91184e8	−	8.50756e8i	0.843694	−	1.46132i
$836$		−	1.82384e7i		−	0.0312154i
$837$		0			0
$838$	−5.82026e8			−0.989031
$839$	−9.50166e8	−	5.48579e8i	−1.60884	−	0.928866i	−0.989630	−	0.143642i	$-0.954118\pi$
$839$	−9.50166e8	−	5.48579e8i	−1.60884	−	0.928866i	−0.619213	−	0.785223i	$-0.712548\pi$
$840$		0			0
$841$	−2.68588e8	−	4.65208e8i	−0.451542	−	0.782094i
$842$	−4.92122e8	+	2.84126e8i	−0.824396	+	0.475965i
$843$		0			0
$844$	6.05091e7	−	1.04805e8i	0.100645	−	0.174323i
$845$			1.26125e9i			2.09041i
$846$		0			0
$847$	6.39282e8			1.05206
$848$	−2.13925e8	−	1.23510e8i	−0.350811	−	0.202541i
$849$		0			0
$850$	−5.85087e8	−	1.01340e9i	−0.952717	−	1.65015i
$851$	2.43220e8	−	1.40423e8i	0.394649	−	0.227851i
$852$		0			0
$853$	−4.24040e8	+	7.34458e8i	−0.683218	+	1.18337i	0.290775	+	0.956791i	$0.406087\pi$
$853$	−4.24040e8	+	7.34458e8i	−0.683218	+	1.18337i	−0.973993	+	0.226577i	$0.927247\pi$
$854$			3.96343e8i			0.636352i
$855$		0			0
$856$	−5.84656e7			−0.0932135
$857$	3.09471e8	+	1.78673e8i	0.491675	+	0.283868i	0.725269	−	0.688466i	$-0.241715\pi$
$857$	3.09471e8	+	1.78673e8i	0.491675	+	0.283868i	−0.233594	+	0.972334i	$0.575049\pi$
$858$		0			0
$859$	−3.41375e8	−	5.91279e8i	−0.538582	−	0.932852i	−0.998981	−	0.0451395i	$-0.985627\pi$
$859$	−3.41375e8	−	5.91279e8i	−0.538582	−	0.932852i	0.460398	−	0.887712i	$-0.347707\pi$
$860$	−7.45914e8	+	4.30654e8i	−1.17272	+	0.677069i
$861$		0			0
$862$	1.18812e8	−	2.05789e8i	0.185498	−	0.321292i
$863$		−	5.78425e8i		−	0.899943i	−0.893043	−	0.449971i	$-0.851434\pi$
$863$		−	5.78425e8i		−	0.899943i	0.893043	−	0.449971i	$-0.148566\pi$
$864$		0			0
$865$	−1.07762e8			−0.166502
$866$	4.90795e8	+	2.83360e8i	0.755694	+	0.436300i
$867$		0			0
$868$	2.18499e8	+	3.78452e8i	0.334111	+	0.578698i
$869$	3.87207e7	−	2.23554e7i	0.0590043	−	0.0340661i
$870$		0			0
$871$	−2.20682e8	+	3.82232e8i	−0.333973	+	0.578459i
$872$			1.35652e8i			0.204587i
$873$		0			0
$874$	−6.44326e8			−0.965098
$875$	1.17672e9	+	6.79382e8i	1.75651	+	1.01412i
$876$		0			0
$877$	2.08409e8	+	3.60975e8i	0.308971	+	0.535154i	0.978138	−	0.207959i	$-0.0666820\pi$
$877$	2.08409e8	+	3.60975e8i	0.308971	+	0.535154i	−0.669166	+	0.743113i	$0.733349\pi$
$878$	6.43801e8	−	3.71699e8i	0.951192	−	0.549171i
$879$		0			0
$880$	−7.37615e6	+	1.27759e7i	−0.0108239	+	0.0187475i
$881$			6.78099e7i			0.0991666i	0.998770	+	0.0495833i	$0.0157893\pi$
$881$			6.78099e7i			0.0991666i	−0.998770	+	0.0495833i	$0.984211\pi$
$882$		0			0
$883$	1.00573e9			1.46083			0.730416	−	0.683002i	$-0.239326\pi$
$883$	1.00573e9			1.46083			0.730416	+	0.683002i	$0.239326\pi$
$884$	−5.69611e8	−	3.28865e8i	−0.824559	−	0.476059i
$885$		0			0
$886$	−2.08930e7	−	3.61878e7i	−0.0300400	−	0.0520309i
$887$	−2.24227e8	+	1.29457e8i	−0.321304	+	0.185505i	−0.651974	−	0.758241i	$-0.726059\pi$
$887$	−2.24227e8	+	1.29457e8i	−0.321304	+	0.185505i	0.330669	+	0.943747i	$0.392725\pi$
$888$		0			0
$889$	−3.69606e8	+	6.40177e8i	−0.526059	+	0.911160i
$890$		−	8.11132e8i		−	1.15059i
$891$		0			0
$892$	−2.00958e6			−0.00283146
$893$	1.18841e8	+	6.86130e7i	0.166883	+	0.0963501i
$894$		0			0
$895$	−4.68486e8	−	8.11441e8i	−0.653472	−	1.13185i
$896$	−5.80692e7	+	3.35263e7i	−0.0807276	+	0.0466081i
$897$		0			0
$898$	−2.65484e8	+	4.59832e8i	−0.366614	+	0.634994i
$899$			2.86635e8i			0.394503i
$900$		0			0
$901$	−1.52553e9			−2.08568
$902$	−6.62773e6	−	3.82652e6i	−0.00903119	−	0.00521416i
$903$		0			0
$904$	8.49167e6	+	1.47080e7i	0.0114944	+	0.0199089i
$905$	−3.88115e7	+	2.24078e7i	−0.0523618	+	0.0302311i
$906$		0			0
$907$	−5.96770e7	+	1.03364e8i	−0.0799807	+	0.138531i	−0.903241	−	0.429133i	$-0.858819\pi$
$907$	−5.96770e7	+	1.03364e8i	−0.0799807	+	0.138531i	0.823261	+	0.567664i	$0.192153\pi$
$908$			6.59658e8i			0.881173i
$909$		0			0
$910$	1.46219e9			1.94035
$911$	−5.87402e8	−	3.39137e8i	−0.776928	−	0.448559i	0.0584127	−	0.998293i	$-0.481396\pi$
$911$	−5.87402e8	−	3.39137e8i	−0.776928	−	0.448559i	−0.835340	+	0.549733i	$0.814729\pi$
$912$		0			0
$913$	−1.94713e7	−	3.37252e7i	−0.0255848	−	0.0443142i
$914$	1.22742e8	−	7.08650e7i	0.160751	−	0.0928097i
$915$		0			0
$916$	2.35081e8	−	4.07172e8i	0.305866	−	0.529775i
$917$			1.33764e9i			1.73472i
$918$		0			0
$919$	−6.67058e8			−0.859444			−0.429722	−	0.902961i	$-0.641388\pi$
$919$	−6.67058e8			−0.859444			−0.429722	+	0.902961i	$0.641388\pi$
$920$	4.51345e8	+	2.60584e8i	0.579622	+	0.334645i
$921$		0			0
$922$	1.30460e8	+	2.25964e8i	0.166451	+	0.288301i
$923$	−7.39618e8	+	4.27019e8i	−0.940594	+	0.543052i
$924$		0			0
$925$	−3.50753e8	+	6.07523e8i	−0.443177	+	0.767604i
$926$		−	7.98972e8i		−	1.00623i
$927$		0			0
$928$	−4.39810e7			−0.0550327
$929$	−9.87168e8	−	5.69942e8i	−1.23124	−	0.710859i	−0.263954	−	0.964535i	$-0.585027\pi$
$929$	−9.87168e8	−	5.69942e8i	−1.23124	−	0.710859i	−0.967289	+	0.253676i	$0.918360\pi$
$930$		0			0
$931$	5.74197e7	+	9.94539e7i	0.0711561	+	0.123246i
$932$	5.12850e8	−	2.96094e8i	0.633495	−	0.365748i
$933$		0			0
$934$	−3.69165e8	+	6.39413e8i	−0.453086	+	0.784767i
$935$			9.11069e7i			0.111459i
$936$		0			0
$937$	2.17868e8			0.264835			0.132417	−	0.991194i	$-0.457726\pi$
$937$	2.17868e8			0.264835			0.132417	+	0.991194i	$0.457726\pi$
$938$	2.40650e8	+	1.38939e8i	0.291593	+	0.168352i
$939$		0			0
$940$	−5.54981e7	−	9.61256e7i	−0.0668182	−	0.115733i
$941$	1.28999e9	−	7.44778e8i	1.54817	−	0.893836i	0.549887	−	0.835239i	$-0.314671\pi$
$941$	1.28999e9	−	7.44778e8i	1.54817	−	0.893836i	0.998282	−	0.0585969i	$-0.0186627\pi$
$942$		0			0
$943$	−1.35183e8	+	2.34144e8i	−0.161208	+	0.279221i
$944$			7.61555e7i			0.0905285i
$945$		0			0
$946$	4.53815e7			0.0536050
$947$	1.22623e9	+	7.07962e8i	1.44385	+	0.833605i	0.998104	−	0.0615564i	$-0.0196064\pi$
$947$	1.22623e9	+	7.07962e8i	1.44385	+	0.833605i	0.445742	+	0.895161i	$0.352940\pi$
$948$		0			0
$949$	6.79988e8	+	1.17777e9i	0.795614	+	1.37804i
$950$	1.39380e9	−	8.04709e8i	1.62566	−	0.938573i
$951$		0			0
$952$	−2.07051e8	+	3.58623e8i	−0.239975	+	0.415649i
$953$			1.83513e8i			0.212026i	0.994365	+	0.106013i	$0.0338085\pi$
$953$			1.83513e8i			0.212026i	−0.994365	+	0.106013i	$0.966191\pi$
$954$		0			0
$955$	−2.12956e8			−0.244500
$956$	2.37918e8	+	1.37362e8i	0.272304	+	0.157215i
$957$		0			0
$958$	−5.47494e8	−	9.48287e8i	−0.622705	−	1.07856i
$959$	−4.80204e8	+	2.77246e8i	−0.544465	+	0.314347i
$960$		0			0
$961$	−2.68854e8	+	4.65669e8i	−0.302933	+	0.524695i
$962$			3.94302e8i			0.442898i
$963$		0			0
$964$	−1.86339e8			−0.208004
$965$	−5.60577e8	−	3.23649e8i	−0.623812	−	0.360158i
$966$		0			0
$967$	−2.79334e8	−	4.83820e8i	−0.308919	−	0.535063i	0.669208	−	0.743076i	$-0.266634\pi$
$967$	−2.79334e8	−	4.83820e8i	−0.308919	−	0.535063i	−0.978126	+	0.208013i	$0.933300\pi$
$968$	−2.77050e8	+	1.59955e8i	−0.305444	+	0.176348i
$969$		0			0
$970$	1.09108e9	−	1.88981e9i	1.19548	−	2.07063i
$971$		−	7.94310e8i		−	0.867626i	−0.901003	−	0.433813i	$-0.857168\pi$
$971$		−	7.94310e8i		−	0.867626i	0.901003	−	0.433813i	$-0.142832\pi$
$972$		0			0
$973$	−3.39024e7			−0.0368038
$974$	−1.86070e8	−	1.07428e8i	−0.201373	−	0.116263i
$975$		0			0
$976$	−9.91689e7	−	1.71766e8i	−0.106666	−	0.184751i
$977$	−1.16354e9	+	6.71772e8i	−1.24767	+	0.720341i	−0.970644	−	0.240522i	$-0.922681\pi$
$977$	−1.16354e9	+	6.71772e8i	−1.24767	+	0.720341i	−0.277023	+	0.960863i	$0.589348\pi$
$978$		0			0
$979$	−2.13689e7	+	3.70120e7i	−0.0227737	+	0.0394453i
$980$		−	9.28887e7i		−	0.0986927i
$981$		0			0
$982$	4.18903e8			0.442363
$983$	7.37631e8	+	4.25871e8i	0.776566	+	0.448351i	0.835212	−	0.549928i	$-0.185345\pi$
$983$	7.37631e8	+	4.25871e8i	0.776566	+	0.448351i	−0.0586456	+	0.998279i	$0.518678\pi$
$984$		0			0
$985$	6.71785e8	+	1.16357e9i	0.702945	+	1.21754i
$986$	−2.35227e8	+	1.35808e8i	−0.245390	+	0.141676i
$987$		0			0
$988$	4.52310e8	−	7.83424e8i	0.468992	−	0.812318i
$989$		−	1.60323e9i		−	1.65733i
$990$		0			0
$991$	−8.03759e8			−0.825857			−0.412928	−	0.910763i	$-0.635494\pi$
$991$	−8.03759e8			−0.825857			−0.412928	+	0.910763i	$0.635494\pi$
$992$	−1.89385e8	−	1.09341e8i	−0.194004	−	0.112008i
$993$		0			0
$994$	2.68848e8	+	4.65658e8i	0.273746	+	0.474141i
$995$	1.41439e8	−	8.16600e7i	0.143582	−	0.0828972i
$996$		0			0
$997$	5.35681e8	−	9.27826e8i	0.540531	−	0.936227i	−0.458343	−	0.888776i	$-0.651557\pi$
$997$	5.35681e8	−	9.27826e8i	0.540531	−	0.936227i	0.998874	−	0.0474514i	$-0.0151099\pi$
$998$		−	8.22983e7i		−	0.0827941i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.d.e.107.2		8
3.2	odd	2	inner	162.7.d.e.107.3		8
9.2	odd	6		54.7.b.c.53.1	✓	4
9.4	even	3	inner	162.7.d.e.53.3		8
9.5	odd	6	inner	162.7.d.e.53.2		8
9.7	even	3		54.7.b.c.53.4	yes	4
36.7	odd	6		432.7.e.h.161.4		4
36.11	even	6		432.7.e.h.161.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.7.b.c.53.1	✓	4	9.2	odd	6
54.7.b.c.53.4	yes	4	9.7	even	3
162.7.d.e.53.2		8	9.5	odd	6	inner
162.7.d.e.53.3		8	9.4	even	3	inner
162.7.d.e.107.2		8	1.1	even	1	trivial
162.7.d.e.107.3		8	3.2	odd	2	inner
432.7.e.h.161.1		4	36.11	even	6
432.7.e.h.161.4		4	36.7	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(190.398 - 109.926i) q^{5} +(-180.868 + 313.272i) q^{7} -181.019i q^{8} +O(q^{10})\)	\(q+(-4.89898 - 2.82843i) q^{2} +(16.0000 + 27.7128i) q^{4} +(190.398 - 109.926i) q^{5} +(-180.868 + 313.272i) q^{7} -181.019i q^{8} -1243.68 q^{10} +(56.7490 + 32.7641i) q^{11} +(1625.09 + 2814.73i) q^{13} +(1772.13 - 1023.14i) q^{14} +(-512.000 + 886.810i) q^{16} +6323.99i q^{17} -8697.81 q^{19} +(6092.74 + 3517.65i) q^{20} +(-185.342 - 321.021i) q^{22} +(-11341.0 + 6547.73i) q^{23} +(16355.1 - 28327.9i) q^{25} -18385.7i q^{26} -11575.5 q^{28} +(-6575.38 - 3796.30i) q^{29} +(-18876.0 - 32694.2i) q^{31} +(5016.55 - 2896.31i) q^{32} +(17887.0 - 30981.1i) q^{34} +79528.5i q^{35} -21446.1 q^{37} +(42610.4 + 24601.1i) q^{38} +(-19898.8 - 34465.7i) q^{40} +(17879.8 - 10322.9i) q^{41} +(-61213.4 + 106025. i) q^{43} +2096.90i q^{44} +74079.1 q^{46} +(-13663.3 - 7888.54i) q^{47} +(-6601.63 - 11434.4i) q^{49} +(-160247. + 92518.6i) q^{50} +(-52002.7 + 90071.4i) q^{52} +241230. i q^{53} +14406.5 q^{55} +(56708.2 + 32740.5i) q^{56} +(21475.1 + 37196.0i) q^{58} +(64406.8 - 37185.3i) q^{59} +(-96844.7 + 167740. i) q^{61} +213557. i q^{62} -32768.0 q^{64} +(618827. + 357280. i) q^{65} +(67898.5 + 117604. i) q^{67} +(-175256. + 101184. i) q^{68} +(224940. - 389608. i) q^{70} +262767. i q^{71} +418432. q^{73} +(105064. + 60658.7i) q^{74} +(-139165. - 241041. i) q^{76} +(-20528.1 + 11851.9i) q^{77} +(341157. - 590902. i) q^{79} +225129. i q^{80} -116790. q^{82} +(-514668. - 297144. i) q^{83} +(695174. + 1.20408e6i) q^{85} +(599766. - 346275. i) q^{86} +(5930.93 - 10272.7i) q^{88} +652205. i q^{89} -1.17570e6 q^{91} +(-362912. - 209527. i) q^{92} +(44624.3 + 77291.6i) q^{94} +(-1.65605e6 + 956119. i) q^{95} +(-877305. + 1.51954e6i) q^{97} +74688.9i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 128 q^{4} - 836 q^{7}+O(q^{10}) \) 8 * q + 128 * q^4 - 836 * q^7	\( 8 q + 128 q^{4} - 836 q^{7} - 3840 q^{10} - 440 q^{13} - 4096 q^{16} - 13376 q^{19} - 19200 q^{22} + 39200 q^{25} - 53504 q^{28} - 160172 q^{31} + 78336 q^{34} - 301088 q^{37} - 61440 q^{40} - 90152 q^{43} + 274944 q^{46} + 202560 q^{49} + 14080 q^{52} - 269640 q^{55} - 86016 q^{58} - 584144 q^{61} - 262144 q^{64} + 766792 q^{67} + 867840 q^{70} + 3149512 q^{73} - 214016 q^{76} - 323000 q^{79} + 2081280 q^{82} + 2720520 q^{85} + 614400 q^{88} - 3921808 q^{91} - 1970688 q^{94} - 4432940 q^{97}+O(q^{100}) \) 8 * q + 128 * q^4 - 836 * q^7 - 3840 * q^10 - 440 * q^13 - 4096 * q^16 - 13376 * q^19 - 19200 * q^22 + 39200 * q^25 - 53504 * q^28 - 160172 * q^31 + 78336 * q^34 - 301088 * q^37 - 61440 * q^40 - 90152 * q^43 + 274944 * q^46 + 202560 * q^49 + 14080 * q^52 - 269640 * q^55 - 86016 * q^58 - 584144 * q^61 - 262144 * q^64 + 766792 * q^67 + 867840 * q^70 + 3149512 * q^73 - 214016 * q^76 - 323000 * q^79 + 2081280 * q^82 + 2720520 * q^85 + 614400 * q^88 - 3921808 * q^91 - 1970688 * q^94 - 4432940 * q^97

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