LMFDB - Embedded newform 162.7.d.e.53.1

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			53.1
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	162.53
Dual form			162.7.d.e.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-43.4287 - 25.0736i) q^{5} +(-28.1325 - 48.7269i) q^{7} +181.019i q^{8} +O(q^{10})$	\(q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-43.4287 - 25.0736i) q^{5} +(-28.1325 - 48.7269i) q^{7} +181.019i q^{8} +283.675 q^{10} +(1412.94 - 815.764i) q^{11} +(-1735.09 + 3005.26i) q^{13} +(275.641 + 159.141i) q^{14} +(-512.000 - 886.810i) q^{16} -599.995i q^{17} +5353.81 q^{19} +(-1389.72 + 802.355i) q^{20} +(-4614.66 + 7992.82i) q^{22} +(817.994 + 472.269i) q^{23} +(-6555.13 - 11353.8i) q^{25} -19630.3i q^{26} -1800.48 q^{28} +(13159.6 - 7597.70i) q^{29} +(-21167.0 + 36662.3i) q^{31} +(5016.55 + 2896.31i) q^{32} +(1697.04 + 2939.36i) q^{34} +2821.53i q^{35} -53825.9 q^{37} +(-26228.2 + 15142.9i) q^{38} +(4538.81 - 7861.44i) q^{40} +(-97537.2 - 56313.1i) q^{41} +(38675.4 + 66987.7i) q^{43} -52208.9i q^{44} -5343.12 q^{46} +(164513. - 94981.5i) q^{47} +(57241.6 - 99145.4i) q^{49} +(64226.9 + 37081.4i) q^{50} +(55522.7 + 96168.2i) q^{52} -243552. i q^{53} -81816.5 q^{55} +(8820.50 - 5092.52i) q^{56} +(-42979.1 + 74442.0i) q^{58} +(-72989.8 - 42140.7i) q^{59} +(-49191.3 - 85201.9i) q^{61} -239477. i q^{62} -32768.0 q^{64} +(150705. - 87009.7i) q^{65} +(123800. - 214427. i) q^{67} +(-16627.5 - 9599.92i) q^{68} +(-7980.49 - 13822.6i) q^{70} -411915. i q^{71} +368946. q^{73} +(263692. - 152243. i) q^{74} +(85661.0 - 148369. i) q^{76} +(-79499.2 - 45898.9i) q^{77} +(-421907. - 730765. i) q^{79} +51350.7i q^{80} +637110. q^{82} +(407498. - 235269. i) q^{83} +(-15044.0 + 26057.0i) q^{85} +(-378940. - 218781. i) q^{86} +(147669. + 255770. i) q^{88} -752753. i q^{89} +195249. q^{91} +(26175.8 - 15112.6i) q^{92} +(-537296. + 930624. i) q^{94} +(-232509. - 134239. i) q^{95} +(-230930. - 399983. i) q^{97} +647615. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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
$5$	−43.4287	−	25.0736i	−0.347430	−	0.200589i	0.316123	−	0.948718i	$-0.397619\pi$
$5$	−43.4287	−	25.0736i	−0.347430	−	0.200589i	−0.663553	+	0.748130i	$0.730952\pi$
$6$		0			0
$7$	−28.1325	−	48.7269i	−0.0820189	−	0.142061i	0.822098	−	0.569346i	$-0.192803\pi$
$7$	−28.1325	−	48.7269i	−0.0820189	−	0.142061i	−0.904117	+	0.427285i	$0.859470\pi$
$8$			181.019i			0.353553i
$9$		0			0
$10$	283.675			0.283675
$11$	1412.94	−	815.764i	1.06157	−	0.612896i	0.135701	−	0.990750i	$-0.456671\pi$
$11$	1412.94	−	815.764i	1.06157	−	0.612896i	0.925865	+	0.377854i	$0.123338\pi$
$12$		0			0
$13$	−1735.09	+	3005.26i	−0.789752	+	1.36789i	0.136366	+	0.990658i	$0.456458\pi$
$13$	−1735.09	+	3005.26i	−0.789752	+	1.36789i	−0.926119	+	0.377233i	$0.876876\pi$
$14$	275.641	+	159.141i	0.100452	+	0.0579961i
$15$		0			0
$16$	−512.000	−	886.810i	−0.125000	−	0.216506i
$17$		−	599.995i		−	0.122124i	−0.998134	−	0.0610620i	$-0.980551\pi$
$17$		−	599.995i		−	0.122124i	0.998134	−	0.0610620i	$-0.0194487\pi$
$18$		0			0
$19$	5353.81			0.780553			0.390276	−	0.920698i	$-0.372379\pi$
$19$	5353.81			0.780553			0.390276	+	0.920698i	$0.372379\pi$
$20$	−1389.72	+	802.355i	−0.173715	+	0.100294i
$21$		0			0
$22$	−4614.66	+	7992.82i	−0.433383	+	0.750641i
$23$	817.994	+	472.269i	0.0672306	+	0.0388156i	0.533238	−	0.845965i	$-0.320975\pi$
$23$	817.994	+	472.269i	0.0672306	+	0.0388156i	−0.466008	+	0.884781i	$0.654308\pi$
$24$		0			0
$25$	−6555.13	−	11353.8i	−0.419528	−	0.726644i
$26$		−	19630.3i		−	1.11688i
$27$		0			0
$28$	−1800.48			−0.0820189
$29$	13159.6	−	7597.70i	0.539571	−	0.311522i	−0.205334	−	0.978692i	$-0.565828\pi$
$29$	13159.6	−	7597.70i	0.539571	−	0.311522i	0.744905	+	0.667170i	$0.232495\pi$
$30$		0			0
$31$	−21167.0	+	36662.3i	−0.710517	+	1.23065i	0.254146	+	0.967166i	$0.418206\pi$
$31$	−21167.0	+	36662.3i	−0.710517	+	1.23065i	−0.964663	+	0.263486i	$0.915128\pi$
$32$	5016.55	+	2896.31i	0.153093	+	0.0883883i
$33$		0			0
$34$	1697.04	+	2939.36i	0.0431773	+	0.0747853i
$35$			2821.53i			0.0658082i
$36$		0			0
$37$	−53825.9			−1.06264			−0.531320	−	0.847171i	$-0.678304\pi$
$37$	−53825.9			−1.06264			−0.531320	+	0.847171i	$0.678304\pi$
$38$	−26228.2	+	15142.9i	−0.477989	+	0.275967i
$39$		0			0
$40$	4538.81	−	7861.44i	0.0709188	−	0.122835i
$41$	−97537.2	−	56313.1i	−1.41520	−	0.817068i	−0.419330	−	0.907834i	$-0.637735\pi$
$41$	−97537.2	−	56313.1i	−1.41520	−	0.817068i	−0.995872	+	0.0907662i	$0.971068\pi$
$42$		0			0
$43$	38675.4	+	66987.7i	0.486440	+	0.842538i	0.999879	−	0.0155879i	$-0.00496197\pi$
$43$	38675.4	+	66987.7i	0.486440	+	0.842538i	−0.513439	+	0.858126i	$0.671629\pi$
$44$		−	52208.9i		−	0.612896i
$45$		0			0
$46$	−5343.12			−0.0548935
$47$	164513.	−	94981.5i	1.58455	−	0.914840i	0.590367	−	0.807135i	$-0.298983\pi$
$47$	164513.	−	94981.5i	1.58455	−	0.914840i	0.994183	−	0.107705i	$-0.0343503\pi$
$48$		0			0
$49$	57241.6	−	99145.4i	0.486546	−	0.842722i
$50$	64226.9	+	37081.4i	0.513815	+	0.296651i
$51$		0			0
$52$	55522.7	+	96168.2i	0.394876	+	0.683946i
$53$		−	243552.i		−	1.63592i	−0.575272	−	0.817962i	$-0.695104\pi$
$53$		−	243552.i		−	1.63592i	0.575272	−	0.817962i	$-0.304896\pi$
$54$		0			0
$55$	−81816.5			−0.491760
$56$	8820.50	−	5092.52i	0.0502261	−	0.0289980i
$57$		0			0
$58$	−42979.1	+	74442.0i	−0.220279	+	0.381535i
$59$	−72989.8	−	42140.7i	−0.355391	−	0.205185i	0.311666	−	0.950192i	$-0.399113\pi$
$59$	−72989.8	−	42140.7i	−0.355391	−	0.205185i	−0.667057	+	0.745007i	$0.732446\pi$
$60$		0			0
$61$	−49191.3	−	85201.9i	−0.216720	−	0.375370i	0.737083	−	0.675802i	$-0.236203\pi$
$61$	−49191.3	−	85201.9i	−0.216720	−	0.375370i	−0.953803	+	0.300432i	$0.902869\pi$
$62$		−	239477.i		−	1.00482i
$63$		0			0
$64$	−32768.0			−0.125000
$65$	150705.	−	87009.7i	0.548767	−	0.316831i
$66$		0			0
$67$	123800.	−	214427.i	0.411618	−	0.712944i	−0.583449	−	0.812150i	$-0.698297\pi$
$67$	123800.	−	214427.i	0.411618	−	0.712944i	0.995067	+	0.0992064i	$0.0316304\pi$
$68$	−16627.5	−	9599.92i	−0.0528812	−	0.0305310i
$69$		0			0
$70$	−7980.49	−	13822.6i	−0.0232667	−	0.0402992i
$71$		−	411915.i		−	1.15089i	−0.817842	−	0.575443i	$-0.804830\pi$
$71$		−	411915.i		−	1.15089i	0.817842	−	0.575443i	$-0.195170\pi$
$72$		0			0
$73$	368946.			0.948406			0.474203	−	0.880416i	$-0.342736\pi$
$73$	368946.			0.948406			0.474203	+	0.880416i	$0.342736\pi$
$74$	263692.	−	152243.i	0.650732	−	0.375700i
$75$		0			0
$76$	85661.0	−	148369.i	0.195138	−	0.337989i
$77$	−79499.2	−	45898.9i	−0.174137	−	0.100538i
$78$		0			0
$79$	−421907.	−	730765.i	−0.855728	−	1.48216i	−0.875968	−	0.482369i	$-0.839776\pi$
$79$	−421907.	−	730765.i	−0.855728	−	1.48216i	0.0202403	−	0.999795i	$-0.493557\pi$
$80$			51350.7i			0.100294i
$81$		0			0
$82$	637110.			1.15551
$83$	407498.	−	235269.i	0.712675	−	0.411463i	−0.0993759	−	0.995050i	$-0.531685\pi$
$83$	407498.	−	235269.i	0.712675	−	0.411463i	0.812051	+	0.583587i	$0.198351\pi$
$84$		0			0
$85$	−15044.0	+	26057.0i	−0.0244967	+	0.0424295i
$86$	−378940.	−	218781.i	−0.595765	−	0.343965i
$87$		0			0
$88$	147669.	+	255770.i	0.216691	+	0.375320i
$89$		−	752753.i		−	1.06778i	−0.845553	−	0.533891i	$-0.820729\pi$
$89$		−	752753.i		−	1.06778i	0.845553	−	0.533891i	$-0.179271\pi$
$90$		0			0
$91$	195249.			0.259098
$92$	26175.8	−	15112.6i	0.0336153	−	0.0194078i
$93$		0			0
$94$	−537296.	+	930624.i	−0.646890	+	1.12045i
$95$	−232509.	−	134239.i	−0.271187	−	0.156570i
$96$		0			0
$97$	−230930.	−	399983.i	−0.253026	−	0.438254i	0.711331	−	0.702857i	$-0.248093\pi$
$97$	−230930.	−	399983.i	−0.253026	−	0.438254i	−0.964358	+	0.264603i	$0.914759\pi$
$98$			647615.i			0.688080i
$99$		0			0
$100$	−419528.			−0.419528
$101$	−1.06425e6	+	614444.i	−1.03295	+	0.596373i	−0.917828	−	0.396978i	$-0.870059\pi$
$101$	−1.06425e6	+	614444.i	−1.03295	+	0.596373i	−0.115121	+	0.993352i	$0.536725\pi$
$102$		0			0
$103$	273863.	−	474344.i	0.250623	−	0.434092i	−0.713074	−	0.701088i	$-0.752698\pi$
$103$	273863.	−	474344.i	0.250623	−	0.434092i	0.963698	+	0.266996i	$0.0860311\pi$
$104$	−544010.	−	314084.i	−0.483623	−	0.279220i
$105$		0			0
$106$	688868.	+	1.19315e6i	0.578387	+	1.00180i
$107$		−	90822.4i		−	0.0741381i	−0.999313	−	0.0370690i	$-0.988198\pi$
$107$		−	90822.4i		−	0.0741381i	0.999313	−	0.0370690i	$-0.0118021\pi$
$108$		0			0
$109$	−1.08845e6			−0.840485			−0.420242	−	0.907412i	$-0.638055\pi$
$109$	−1.08845e6			−0.840485			−0.420242	+	0.907412i	$0.638055\pi$
$110$	400818.	−	231412.i	0.301140	−	0.173863i
$111$		0			0
$112$	−28807.6	+	49896.3i	−0.0205047	+	0.0355152i
$113$	2.15675e6	+	1.24520e6i	1.49474	+	0.862987i	0.999982	−	0.00604466i	$-0.00192409\pi$
$113$	2.15675e6	+	1.24520e6i	1.49474	+	0.862987i	0.494756	+	0.869032i	$0.335257\pi$
$114$		0			0
$115$	−23683.0	−	41020.1i	−0.0155719	−	0.0269714i
$116$		−	486253.i		−	0.311522i
$117$		0			0
$118$	476768.			0.290175
$119$	−29235.9	+	16879.3i	−0.0173490	+	0.0100165i
$120$		0			0
$121$	445162.	−	771042.i	0.251282	−	0.435233i
$122$	481975.	+	278268.i	0.265427	+	0.153244i
$123$		0			0
$124$	677344.	+	1.17319e6i	0.355259	+	0.615326i
$125$			1.44099e6i			0.737788i
$126$		0			0
$127$	−3.12962e6			−1.52785			−0.763924	−	0.645306i	$-0.776730\pi$
$127$	−3.12962e6			−1.52785			−0.763924	+	0.645306i	$0.776730\pi$
$128$	160530.	−	92681.9i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−492201.	+	852517.i	−0.224033	+	0.388037i
$131$	−973306.	−	561939.i	−0.432948	−	0.249963i	0.267654	−	0.963515i	$-0.413752\pi$
$131$	−973306.	−	561939.i	−0.432948	−	0.249963i	−0.700602	+	0.713553i	$0.747085\pi$
$132$		0			0
$133$	−150616.	−	260875.i	−0.0640201	−	0.110886i
$134$			1.40063e6i			0.582116i
$135$		0			0
$136$	108611.			0.0431773
$137$	−1.82514e6	+	1.05374e6i	−0.709797	+	0.409802i	−0.810986	−	0.585066i	$-0.801069\pi$
$137$	−1.82514e6	+	1.05374e6i	−0.709797	+	0.409802i	0.101189	+	0.994867i	$0.467735\pi$
$138$		0			0
$139$	−78992.8	+	136820.i	−0.0294133	+	0.0509453i	−0.880357	−	0.474311i	$-0.842697\pi$
$139$	−78992.8	+	136820.i	−0.0294133	+	0.0509453i	0.850944	+	0.525256i	$0.176031\pi$
$140$	78192.5	+	45144.5i	0.0284958	+	0.0164521i
$141$		0			0
$142$	1.16507e6	+	2.01796e6i	0.406900	+	0.704771i
$143$			5.66168e6i			1.93614i
$144$		0			0
$145$	−762007.			−0.249951
$146$	−1.80746e6	+	1.04354e6i	−0.580777	+	0.335312i
$147$		0			0
$148$	−861215.	+	1.49167e6i	−0.265660	+	0.460137i
$149$	−176935.	−	102154.i	−0.0534879	−	0.0308812i	0.473018	−	0.881053i	$-0.343165\pi$
$149$	−176935.	−	102154.i	−0.0534879	−	0.0308812i	−0.526505	+	0.850172i	$0.676498\pi$
$150$		0			0
$151$	−1.48147e6	−	2.56597e6i	−0.430289	−	0.745283i	0.566609	−	0.823987i	$-0.308255\pi$
$151$	−1.48147e6	−	2.56597e6i	−0.430289	−	0.745283i	−0.996898	+	0.0787039i	$0.974922\pi$
$152$			969144.i			0.275967i
$153$		0			0
$154$	519287.			0.142182
$155$	1.83851e6	−	1.06147e6i	0.493710	−	0.285043i
$156$		0			0
$157$	1.30241e6	−	2.25585e6i	0.336550	−	0.582922i	−0.647231	−	0.762294i	$-0.724073\pi$
$157$	1.30241e6	−	2.25585e6i	0.336550	−	0.582922i	0.983781	+	0.179372i	$0.0574065\pi$
$158$	4.13383e6	+	2.38667e6i	1.04805	+	0.605091i
$159$		0			0
$160$	−145242.	−	251566.i	−0.0354594	−	0.0614175i
$161$		−	53144.4i		−	0.0127344i
$162$		0			0
$163$	5.62696e6			1.29930			0.649652	−	0.760232i	$-0.274915\pi$
$163$	5.62696e6			1.29930			0.649652	+	0.760232i	$0.274915\pi$
$164$	−3.12119e6	+	1.80202e6i	−0.707601	+	0.408534i
$165$		0			0
$166$	−1.33088e6	+	2.30516e6i	−0.290948	+	0.503937i
$167$	−1.52697e6	−	881596.i	−0.327854	−	0.189287i	0.327034	−	0.945013i	$-0.393951\pi$
$167$	−1.52697e6	−	881596.i	−0.327854	−	0.189287i	−0.654888	+	0.755726i	$0.727284\pi$
$168$		0			0
$169$	−3.60764e6	−	6.24862e6i	−0.747417	−	1.29456i
$170$		−	170204.i		−	0.0346435i
$171$		0			0
$172$	2.47522e6			0.486440
$173$	−6.95934e6	+	4.01798e6i	−1.34409	+	0.776013i	−0.987406	−	0.158210i	$-0.949428\pi$
$173$	−6.95934e6	+	4.01798e6i	−1.34409	+	0.776013i	−0.356689	+	0.934223i	$0.616094\pi$
$174$		0			0
$175$	−368824.	+	638822.i	−0.0688185	+	0.119197i
$176$	−1.44686e6	−	835342.i	−0.265392	−	0.153224i
$177$		0			0
$178$	2.12911e6	+	3.68772e6i	0.377518	+	0.653880i
$179$			9.88186e6i			1.72298i	0.507776	+	0.861489i	$0.330468\pi$
$179$			9.88186e6i			1.72298i	−0.507776	+	0.861489i	$0.669532\pi$
$180$		0			0
$181$	3.82714e6			0.645414			0.322707	−	0.946499i	$-0.395407\pi$
$181$	3.82714e6			0.645414			0.322707	+	0.946499i	$0.395407\pi$
$182$	−956521.	+	552247.i	−0.158665	+	0.0916051i
$183$		0			0
$184$	−85489.9	+	148073.i	−0.0137234	+	0.0237696i
$185$	2.33759e6	+	1.34961e6i	0.369193	+	0.213154i
$186$		0			0
$187$	−489454.	−	847760.i	−0.0748492	−	0.129643i
$188$		−	6.07881e6i		−	0.914840i
$189$		0			0
$190$	1.51874e6			0.221424
$191$	3.79194e6	−	2.18928e6i	0.544204	−	0.314196i	−0.202577	−	0.979266i	$-0.564932\pi$
$191$	3.79194e6	−	2.18928e6i	0.544204	−	0.314196i	0.746781	+	0.665070i	$0.231598\pi$
$192$		0			0
$193$	445928.	−	772370.i	0.0620287	−	0.107437i	−0.833343	−	0.552756i	$-0.813576\pi$
$193$	445928.	−	772370.i	0.0620287	−	0.107437i	0.895372	+	0.445319i	$0.146910\pi$
$194$	2.26264e6	+	1.30634e6i	0.309892	+	0.178916i
$195$		0			0
$196$	−1.83173e6	−	3.17265e6i	−0.243273	−	0.421361i
$197$		−	4.90719e6i		−	0.641850i	−0.947105	−	0.320925i	$-0.896006\pi$
$197$		−	4.90719e6i		−	0.641850i	0.947105	−	0.320925i	$-0.103994\pi$
$198$		0			0
$199$	−8.34946e6			−1.05950			−0.529748	−	0.848155i	$-0.677713\pi$
$199$	−8.34946e6			−1.05950			−0.529748	+	0.848155i	$0.677713\pi$
$200$	2.05526e6	−	1.18661e6i	0.256908	−	0.148326i
$201$		0			0
$202$	3.47582e6	−	6.02029e6i	0.421699	−	0.730405i
$203$	−740424.	−	427484.i	−0.0885101	−	0.0511013i
$204$		0			0
$205$	2.82394e6	+	4.89121e6i	0.327789	+	0.567747i
$206$			3.09840e6i			0.354435i
$207$		0			0
$208$	3.55346e6			0.394876
$209$	7.56464e6	−	4.36745e6i	0.828609	−	0.478398i
$210$		0			0
$211$	6.48355e6	−	1.12298e7i	0.690185	−	1.19544i	−0.281592	−	0.959534i	$-0.590862\pi$
$211$	6.48355e6	−	1.12298e7i	0.690185	−	1.19544i	0.971777	−	0.235902i	$-0.0758044\pi$
$212$	−6.74950e6	−	3.89682e6i	−0.708376	−	0.408981i
$213$		0			0
$214$	256884.	+	444937.i	0.0262118	+	0.0454001i
$215$		−	3.87892e6i		−	0.390297i
$216$		0			0
$217$	2.38192e6			0.233103
$218$	5.33230e6	−	3.07861e6i	0.514690	−	0.297156i
$219$		0			0
$220$	−1.30906e6	+	2.26737e6i	−0.122940	+	0.212938i
$221$	1.80314e6	+	1.04104e6i	0.167052	+	0.0964476i
$222$		0			0
$223$	−1.88621e6	−	3.26702e6i	−0.170089	−	0.294603i	0.768362	−	0.640016i	$-0.221072\pi$
$223$	−1.88621e6	−	3.26702e6i	−0.170089	−	0.294603i	−0.938451	+	0.345413i	$0.887739\pi$
$224$		−	325921.i		−	0.0289980i
$225$		0			0
$226$	−1.40878e7			−1.22045
$227$	4.35856e6	−	2.51641e6i	0.372619	−	0.215132i	−0.301983	−	0.953313i	$-0.597649\pi$
$227$	4.35856e6	−	2.51641e6i	0.372619	−	0.215132i	0.674602	+	0.738182i	$0.264315\pi$
$228$		0			0
$229$	−1.43726e6	+	2.48941e6i	−0.119682	+	0.207295i	−0.919642	−	0.392758i	$-0.871521\pi$
$229$	−1.43726e6	+	2.48941e6i	−0.119682	+	0.207295i	0.799960	+	0.600054i	$0.204854\pi$
$230$	232045.	+	133971.i	0.0190717	+	0.0110110i
$231$		0			0
$232$	1.37533e6	+	2.38214e6i	0.110140	+	0.190767i
$233$		−	2.23245e7i		−	1.76487i	−0.470431	−	0.882437i	$-0.655902\pi$
$233$		−	2.23245e7i		−	1.76487i	0.470431	−	0.882437i	$-0.344098\pi$
$234$		0			0
$235$	−9.52611e6			−0.734027
$236$	−2.33567e6	+	1.34850e6i	−0.177695	+	0.102593i
$237$		0			0
$238$	95483.9	−	165383.i	0.00708271	−	0.0122676i
$239$	−1.01660e7	−	5.86937e6i	−0.744661	−	0.429930i	0.0791008	−	0.996867i	$-0.474795\pi$
$239$	−1.01660e7	−	5.86937e6i	−0.744661	−	0.429930i	−0.823761	+	0.566937i	$0.808128\pi$
$240$		0			0
$241$	1.32692e7	+	2.29829e7i	0.947969	+	1.64193i	0.749696	+	0.661783i	$0.230200\pi$
$241$	1.32692e7	+	2.29829e7i	0.947969	+	1.64193i	0.198273	+	0.980147i	$0.436467\pi$
$242$			5.03643e6i			0.355367i
$243$		0			0
$244$	−3.14825e6			−0.216720
$245$	−4.97186e6	+	2.87051e6i	−0.338081	+	0.195191i
$246$		0			0
$247$	−9.28932e6	+	1.60896e7i	−0.616443	+	1.06771i
$248$	−6.63659e6	−	3.83164e6i	−0.435101	−	0.251206i
$249$		0			0
$250$	−4.07574e6	−	7.05939e6i	−0.260847	−	0.451801i
$251$		−	2.64855e7i		−	1.67489i	−0.546521	−	0.837446i	$-0.684048\pi$
$251$		−	2.64855e7i		−	1.67489i	0.546521	−	0.837446i	$-0.315952\pi$
$252$		0			0
$253$	1.54104e6			0.0951596
$254$	1.53319e7	−	8.85189e6i	0.935612	−	0.540176i
$255$		0			0
$256$	−524288.	+	908093.i	−0.0312500	+	0.0541266i
$257$	1.93078e7	+	1.11473e7i	1.13745	+	0.656708i	0.945798	−	0.324755i	$-0.105282\pi$
$257$	1.93078e7	+	1.11473e7i	1.13745	+	0.656708i	0.191653	+	0.981463i	$0.438615\pi$
$258$		0			0
$259$	1.51426e6	+	2.62277e6i	0.0871565	+	0.150960i
$260$		−	5.56862e6i		−	0.316831i
$261$		0			0
$262$	6.35761e6			0.353501
$263$	−1.50734e6	+	870261.i	−0.0828596	+	0.0478390i	−0.540857	−	0.841114i	$-0.681900\pi$
$263$	−1.50734e6	+	870261.i	−0.0828596	+	0.0478390i	0.457998	+	0.888953i	$0.348567\pi$
$264$		0			0
$265$	−6.10671e6	+	1.05771e7i	−0.328148	+	0.568369i
$266$	1.47573e6	+	852013.i	0.0784082	+	0.0452690i
$267$		0			0
$268$	−3.96158e6	−	6.86167e6i	−0.205809	−	0.356472i
$269$		−	3.21970e6i		−	0.165409i	−0.996574	−	0.0827044i	$-0.973644\pi$
$269$		−	3.21970e6i		−	0.165409i	0.996574	−	0.0827044i	$-0.0263557\pi$
$270$		0			0
$271$	8.71025e6			0.437646			0.218823	−	0.975765i	$-0.429778\pi$
$271$	8.71025e6			0.437646			0.218823	+	0.975765i	$0.429778\pi$
$272$	−532081.	+	307197.i	−0.0264406	+	0.0152655i
$273$		0			0
$274$	5.96088e6	−	1.03245e7i	0.289774	−	0.501903i
$275$	−1.85241e7	−	1.06949e7i	−0.890714	−	0.514254i
$276$		0			0
$277$	−2.37163e6	−	4.10779e6i	−0.111586	−	0.193272i	0.804824	−	0.593513i	$-0.202260\pi$
$277$	−2.37163e6	−	4.10779e6i	−0.111586	−	0.193272i	−0.916410	+	0.400241i	$0.868926\pi$
$278$		−	893702.i		−	0.0415967i
$279$		0			0
$280$	−510751.			−0.0232667
$281$	6.35229e6	−	3.66750e6i	0.286294	−	0.165292i	−0.349976	−	0.936759i	$-0.613810\pi$
$281$	6.35229e6	−	3.66750e6i	0.286294	−	0.165292i	0.636269	+	0.771467i	$0.280477\pi$
$282$		0			0
$283$	−1.93466e7	+	3.35093e7i	−0.853581	+	1.47845i	0.0243739	+	0.999703i	$0.492241\pi$
$283$	−1.93466e7	+	3.35093e7i	−0.853581	+	1.47845i	−0.877955	+	0.478743i	$0.841093\pi$
$284$	−1.14153e7	−	6.59064e6i	−0.498348	−	0.287722i
$285$		0			0
$286$	−1.60137e7	−	2.77365e7i	−0.684530	−	1.18564i
$287$			6.33691e6i			0.268060i
$288$		0			0
$289$	2.37776e7			0.985086
$290$	3.73306e6	−	2.15528e6i	0.153063	−	0.0883710i
$291$		0			0
$292$	5.90313e6	−	1.02245e7i	0.237101	−	0.410672i
$293$	−2.03760e7	−	1.17641e7i	−0.810058	−	0.467687i	0.0369179	−	0.999318i	$-0.488246\pi$
$293$	−2.03760e7	−	1.17641e7i	−0.810058	−	0.467687i	−0.846976	+	0.531631i	$0.821579\pi$
$294$		0			0
$295$	2.11324e6	+	3.66023e6i	0.0823156	+	0.142575i
$296$		−	9.74353e6i		−	0.375700i
$297$		0			0
$298$	1.15574e6			0.0436727
$299$	−2.83858e6	+	1.63886e6i	−0.106191	+	0.0613094i
$300$		0			0
$301$	2.17607e6	−	3.76906e6i	0.0797945	−	0.138208i
$302$	1.45153e7	+	8.38043e6i	0.526995	+	0.304261i
$303$		0			0
$304$	−2.74115e6	−	4.74781e6i	−0.0975691	−	0.168995i
$305$			4.93361e6i			0.173886i
$306$		0			0
$307$	−1.92808e7			−0.666360			−0.333180	−	0.942863i	$-0.608122\pi$
$307$	−1.92808e7			−0.666360			−0.333180	+	0.942863i	$0.608122\pi$
$308$	−2.54398e6	+	1.46877e6i	−0.0870685	+	0.0502690i
$309$		0			0
$310$	−6.00456e6	+	1.04002e7i	−0.201556	+	0.349105i
$311$	2.70295e7	+	1.56055e7i	0.898582	+	0.518796i	0.876740	−	0.480965i	$-0.159714\pi$
$311$	2.70295e7	+	1.56055e7i	0.898582	+	0.518796i	0.0218419	+	0.999761i	$0.493047\pi$
$312$		0			0
$313$	1.76015e6	+	3.04866e6i	0.0574005	+	0.0994206i	0.893298	−	0.449465i	$-0.148385\pi$
$313$	1.76015e6	+	3.04866e6i	0.0574005	+	0.0994206i	−0.835897	+	0.548886i	$0.815052\pi$
$314$			1.47351e7i			0.475954i
$315$		0			0
$316$	−2.70021e7			−0.855728
$317$	4.11426e7	−	2.37537e7i	1.29156	−	0.745682i	0.312629	−	0.949875i	$-0.398790\pi$
$317$	4.11426e7	−	2.37537e7i	1.29156	−	0.745682i	0.978931	+	0.204193i	$0.0654570\pi$
$318$		0			0
$319$	1.23959e7	−	2.14703e7i	0.381861	−	0.661402i
$320$	1.42307e6	+	821611.i	0.0434287	+	0.0250736i
$321$		0			0
$322$	150315.	+	260353.i	0.00450230	+	0.00779822i
$323$		−	3.21226e6i		−	0.0953242i
$324$		0			0
$325$	4.54948e7			1.32529
$326$	−2.75664e7	+	1.59154e7i	−0.795658	+	0.459374i
$327$		0			0
$328$	1.01938e7	−	1.76561e7i	0.288877	−	0.500350i
$329$	−9.25630e6	−	5.34413e6i	−0.259926	−	0.150068i
$330$		0			0
$331$	5.44968e6	+	9.43912e6i	0.150275	+	0.260284i	0.931329	−	0.364180i	$-0.118651\pi$
$331$	5.44968e6	+	9.43912e6i	0.150275	+	0.260284i	−0.781053	+	0.624464i	$0.785317\pi$
$332$		−	1.50572e7i		−	0.411463i
$333$		0			0
$334$	9.97412e6			0.267692
$335$	−1.07529e7	+	6.20820e6i	−0.286017	+	0.165132i
$336$		0			0
$337$	2.38414e7	−	4.12946e7i	0.622935	−	1.07895i	−0.366001	−	0.930614i	$-0.619273\pi$
$337$	2.38414e7	−	4.12946e7i	0.622935	−	1.07895i	0.988936	−	0.148341i	$-0.0473932\pi$
$338$	3.53475e7	+	2.04079e7i	0.915395	+	0.528504i
$339$		0			0
$340$	481409.	+	833825.i	0.0122483	+	0.0212147i
$341$			6.90692e7i			1.74189i
$342$		0			0
$343$	−1.30609e7			−0.323661
$344$	−1.21261e7	+	7.00099e6i	−0.297882	+	0.171982i
$345$		0			0
$346$	2.27291e7	−	3.93680e7i	0.548724	−	0.950418i
$347$	2.23319e7	+	1.28933e7i	0.534487	+	0.308586i	0.742842	−	0.669467i	$-0.233477\pi$
$347$	2.23319e7	+	1.28933e7i	0.534487	+	0.308586i	−0.208355	+	0.978053i	$0.566811\pi$
$348$		0			0
$349$	2.94007e7	+	5.09235e7i	0.691642	+	1.19796i	0.971300	+	0.237859i	$0.0764457\pi$
$349$	2.94007e7	+	5.09235e7i	0.691642	+	1.19796i	−0.279658	+	0.960100i	$0.590221\pi$
$350$		−	4.17277e6i		−	0.0973240i
$351$		0			0
$352$	9.45082e6			0.216691
$353$	−6.54573e7	+	3.77918e7i	−1.48811	+	0.859159i	−0.999908	−	0.0135736i	$-0.995679\pi$
$353$	−6.54573e7	+	3.77918e7i	−1.48811	+	0.859159i	−0.488199	+	0.872732i	$0.662346\pi$
$354$		0			0
$355$	−1.03282e7	+	1.78889e7i	−0.230855	+	0.399852i
$356$	−2.08609e7	−	1.20441e7i	−0.462363	−	0.266946i
$357$		0			0
$358$	−2.79501e7	−	4.84110e7i	−0.609165	−	1.05510i
$359$			4.56033e7i			0.985628i	0.870135	+	0.492814i	$0.164032\pi$
$359$			4.56033e7i			0.985628i	−0.870135	+	0.492814i	$0.835968\pi$
$360$		0			0
$361$	−1.83826e7			−0.390737
$362$	−1.87491e7	+	1.08248e7i	−0.395234	+	0.228188i
$363$		0			0
$364$	3.12398e6	−	5.41090e6i	0.0647746	−	0.112193i
$365$	−1.60229e7	−	9.25080e6i	−0.329504	−	0.190239i
$366$		0			0
$367$	1.57052e7	+	2.72022e7i	0.317721	+	0.550309i	0.980012	−	0.198938i	$-0.0637491\pi$
$367$	1.57052e7	+	2.72022e7i	0.317721	+	0.550309i	−0.662291	+	0.749247i	$0.730416\pi$
$368$		−	967207.i		−	0.0194078i
$369$		0			0
$370$	−1.52691e7			−0.301445
$371$	−1.18675e7	+	6.85171e6i	−0.232401	+	0.134177i
$372$		0			0
$373$	−5.69047e6	+	9.85619e6i	−0.109653	+	0.189925i	−0.915630	−	0.402022i	$-0.868307\pi$
$373$	−5.69047e6	+	9.85619e6i	−0.109653	+	0.189925i	0.805977	+	0.591948i	$0.201641\pi$
$374$	4.79565e6	+	2.76877e6i	0.0916712	+	0.0529264i
$375$		0			0
$376$	1.71935e7	+	2.97800e7i	0.323445	+	0.560223i
$377$			5.27307e7i			0.984100i
$378$		0			0
$379$	−4.52964e7			−0.832044			−0.416022	−	0.909355i	$-0.636576\pi$
$379$	−4.52964e7			−0.832044			−0.416022	+	0.909355i	$0.636576\pi$
$380$	−7.44030e6	+	4.29566e6i	−0.135594	+	0.0782851i
$381$		0			0
$382$	−1.23844e7	+	2.14505e7i	−0.222170	+	0.384810i
$383$	2.83885e7	+	1.63901e7i	0.505297	+	0.291733i	0.730898	−	0.682486i	$-0.239101\pi$
$383$	2.83885e7	+	1.63901e7i	0.505297	+	0.291733i	−0.225602	+	0.974220i	$0.572435\pi$
$384$		0			0
$385$	2.30170e6	+	3.98666e6i	0.0403336	+	0.0698598i
$386$			5.04510e6i			0.0877219i
$387$		0			0
$388$	−1.47795e7			−0.253026
$389$	2.98843e7	−	1.72537e7i	0.507686	−	0.293113i	−0.224196	−	0.974544i	$-0.571976\pi$
$389$	2.98843e7	−	1.72537e7i	0.507686	−	0.293113i	0.731882	+	0.681432i	$0.238642\pi$
$390$		0			0
$391$	283359.	−	490792.i	0.00474031	−	0.00821046i
$392$	1.79472e7	+	1.03618e7i	0.297947	+	0.172020i
$393$		0			0
$394$	1.38796e7	+	2.40402e7i	0.226928	+	0.393051i
$395$			4.23149e7i			0.686597i
$396$		0			0
$397$	5.72396e7			0.914798			0.457399	−	0.889262i	$-0.348781\pi$
$397$	5.72396e7			0.914798			0.457399	+	0.889262i	$0.348781\pi$
$398$	4.09038e7	−	2.36158e7i	0.648806	−	0.374588i
$399$		0			0
$400$	−6.71245e6	+	1.16263e7i	−0.104882	+	0.181661i
$401$	−6.90479e7	−	3.98648e7i	−1.07082	−	0.618239i	−0.142416	−	0.989807i	$-0.545487\pi$
$401$	−6.90479e7	−	3.98648e7i	−1.07082	−	0.618239i	−0.928406	+	0.371568i	$0.878820\pi$
$402$		0			0
$403$	−7.34532e7	−	1.27225e8i	−1.12226	−	1.94382i
$404$			3.93244e7i			0.596373i
$405$		0			0
$406$	4.83643e6			0.0722682
$407$	−7.60531e7	+	4.39092e7i	−1.12806	+	0.651288i
$408$		0			0
$409$	−2.39594e7	+	4.14989e7i	−0.350192	+	0.606550i	−0.986283	−	0.165064i	$-0.947217\pi$
$409$	−2.39594e7	+	4.14989e7i	−0.350192	+	0.606550i	0.636091	+	0.771614i	$0.280550\pi$
$410$	−2.76689e7	−	1.59746e7i	−0.401458	−	0.231782i
$411$		0			0
$412$	−8.76361e6	−	1.51790e7i	−0.125312	−	0.217046i
$413$			4.74209e6i			0.0673162i
$414$		0			0
$415$	−2.35962e7			−0.330139
$416$	−1.74083e7	+	1.00507e7i	−0.241811	+	0.139610i
$417$		0			0
$418$	−2.47060e7	+	4.27921e7i	−0.338278	+	0.585915i
$419$	9.53262e7	+	5.50366e7i	1.29590	+	0.748186i	0.979693	−	0.200505i	$-0.0642582\pi$
$419$	9.53262e7	+	5.50366e7i	1.29590	+	0.748186i	0.316204	+	0.948691i	$0.397592\pi$
$420$		0			0
$421$	1.87470e7	+	3.24708e7i	0.251238	+	0.435158i	0.963867	−	0.266384i	$-0.0858289\pi$
$421$	1.87470e7	+	3.24708e7i	0.251238	+	0.435158i	−0.712629	+	0.701541i	$0.752496\pi$
$422$			7.33530e7i			0.976070i
$423$		0			0
$424$	4.40875e7			0.578387
$425$	−6.81223e6	+	3.93304e6i	−0.0887407	+	0.0512344i
$426$		0			0
$427$	−2.76775e6	+	4.79388e6i	−0.0355503	+	0.0615749i
$428$	−2.51694e6	−	1.45316e6i	−0.0321027	−	0.0185345i
$429$		0			0
$430$	1.09712e7	+	1.90028e7i	0.137991	+	0.239007i
$431$		−	1.35605e8i		−	1.69373i	−0.531810	−	0.846864i	$-0.678488\pi$
$431$		−	1.35605e8i		−	1.69373i	0.531810	−	0.846864i	$-0.321512\pi$
$432$		0			0
$433$	1.18161e8			1.45549			0.727746	−	0.685846i	$-0.240568\pi$
$433$	1.18161e8			1.45549			0.727746	+	0.685846i	$0.240568\pi$
$434$	−1.16690e7	+	6.73709e6i	−0.142746	+	0.0824144i
$435$		0			0
$436$	−1.74152e7	+	3.01641e7i	−0.210121	+	0.363941i
$437$	4.37939e6	+	2.52844e6i	0.0524770	+	0.0302976i
$438$		0			0
$439$	−4.59907e7	−	7.96582e7i	−0.543596	−	0.941535i	−0.998694	−	0.0510942i	$-0.983729\pi$
$439$	−4.59907e7	−	7.96582e7i	−0.543596	−	0.941535i	0.455098	−	0.890441i	$-0.349604\pi$
$440$		−	1.48104e7i		−	0.173863i
$441$		0			0
$442$	−1.17781e7			−0.136398
$443$	1.70594e7	−	9.84924e6i	0.196224	−	0.113290i	−0.398669	−	0.917095i	$-0.630528\pi$
$443$	1.70594e7	−	9.84924e6i	0.196224	−	0.113290i	0.594893	+	0.803805i	$0.297194\pi$
$444$		0			0
$445$	−1.88742e7	+	3.26911e7i	−0.214185	+	0.370980i
$446$	1.84811e7	+	1.06700e7i	0.208316	+	0.120271i
$447$		0			0
$448$	921845.	+	1.59668e6i	0.0102524	+	0.0177576i
$449$		−	1.38530e7i		−	0.153040i	−0.997068	−	0.0765199i	$-0.975619\pi$
$449$		−	1.38530e7i		−	0.153040i	0.997068	−	0.0765199i	$-0.0243809\pi$
$450$		0			0
$451$	−1.83753e8			−2.00311
$452$	6.90161e7	−	3.98465e7i	0.747369	−	0.431494i
$453$		0			0
$454$	−1.42350e7	+	2.46557e7i	−0.152121	+	0.263481i
$455$	−8.47942e6	−	4.89559e6i	−0.0900185	−	0.0519722i
$456$		0			0
$457$	3.69186e7	+	6.39448e7i	0.386809	+	0.669972i	0.992018	−	0.126094i	$-0.0402441\pi$
$457$	3.69186e7	+	6.39448e7i	0.386809	+	0.669972i	−0.605210	+	0.796066i	$0.706911\pi$
$458$		−	1.62607e7i		−	0.169256i
$459$		0			0
$460$	−1.51571e6			−0.0155719
$461$	4.60339e7	−	2.65777e7i	0.469867	−	0.271278i	−0.246317	−	0.969189i	$-0.579220\pi$
$461$	4.60339e7	−	2.65777e7i	0.469867	−	0.271278i	0.716184	+	0.697912i	$0.245887\pi$
$462$		0			0
$463$	−4.74332e7	+	8.21567e7i	−0.477903	+	0.827752i	−0.999679	−	0.0253305i	$-0.991936\pi$
$463$	−4.74332e7	+	8.21567e7i	−0.477903	+	0.827752i	0.521776	+	0.853082i	$0.325270\pi$
$464$	−1.34754e7	−	7.78005e6i	−0.134893	−	0.0778804i
$465$		0			0
$466$	6.31432e7	+	1.09367e8i	0.623977	+	1.08076i
$467$		−	1.90459e8i		−	1.87004i	−0.354598	−	0.935019i	$-0.615382\pi$
$467$		−	1.90459e8i		−	1.87004i	0.354598	−	0.935019i	$-0.384618\pi$
$468$		0			0
$469$	−1.39311e7			−0.135042
$470$	4.66682e7	−	2.69439e7i	0.449498	−	0.259518i
$471$		0			0
$472$	7.62828e6	−	1.32126e7i	0.0725439	−	0.125650i
$473$	1.09292e8	+	6.30999e7i	1.03278	+	0.596274i
$474$		0			0
$475$	−3.50949e7	−	6.07862e7i	−0.327464	−	0.567184i
$476$			1.08028e6i			0.0100165i
$477$		0			0
$478$	6.64043e7			0.608013
$479$	2.45490e7	−	1.41734e7i	0.223371	−	0.128963i	−0.384139	−	0.923275i	$-0.625502\pi$
$479$	2.45490e7	−	1.41734e7i	0.223371	−	0.128963i	0.607510	+	0.794312i	$0.292168\pi$
$480$		0			0
$481$	9.33926e7	−	1.61761e8i	0.839223	−	1.45358i
$482$	−1.30011e8	−	7.50620e7i	−1.16102	−	0.670315i
$483$		0			0
$484$	−1.42452e7	−	2.46734e7i	−0.125641	−	0.217617i
$485$			2.31610e7i			0.203017i
$486$		0			0
$487$	−6.06414e7			−0.525028			−0.262514	−	0.964928i	$-0.584552\pi$
$487$	−6.06414e7			−0.525028			−0.262514	+	0.964928i	$0.584552\pi$
$488$	1.54232e7	−	8.90458e6i	0.132713	−	0.0766221i
$489$		0			0
$490$	1.62380e7	−	2.81251e7i	0.138021	−	0.239059i
$491$	−1.34714e8	−	7.77769e7i	−1.13806	−	0.657062i	−0.192114	−	0.981373i	$-0.561534\pi$
$491$	−1.34714e8	−	7.77769e7i	−1.13806	−	0.657062i	−0.945951	+	0.324311i	$0.894868\pi$
$492$		0			0
$493$	−4.55858e6	−	7.89570e6i	−0.0380443	−	0.0658946i
$494$		−	1.05097e8i		−	0.871783i
$495$		0			0
$496$	4.33500e7			0.355259
$497$	−2.00713e7	+	1.15882e7i	−0.163496	+	0.0943944i
$498$		0			0
$499$	6.46864e7	−	1.12040e8i	0.520609	−	0.901721i	−0.479104	−	0.877758i	$-0.659038\pi$
$499$	6.46864e7	−	1.12040e8i	0.520609	−	0.901721i	0.999713	−	0.0239626i	$-0.00762826\pi$
$500$	3.99340e7	+	2.30559e7i	0.319472	+	0.184447i
$501$		0			0
$502$	7.49122e7	+	1.29752e8i	0.592163	+	1.02566i
$503$			1.43279e8i			1.12585i	0.826509	+	0.562923i	$0.190323\pi$
$503$			1.43279e8i			1.12585i	−0.826509	+	0.562923i	$0.809677\pi$
$504$		0			0
$505$	6.16253e7			0.478503
$506$	−7.54953e6	+	4.35872e6i	−0.0582731	+	0.0336440i
$507$		0			0
$508$	−5.00739e7	+	8.67305e7i	−0.381962	+	0.661577i
$509$	−1.37466e8	−	7.93661e7i	−1.04242	−	0.601841i	−0.121901	−	0.992542i	$-0.538899\pi$
$509$	−1.37466e8	−	7.93661e7i	−1.04242	−	0.601841i	−0.920517	+	0.390702i	$0.872232\pi$
$510$		0			0
$511$	−1.03794e7	−	1.79776e7i	−0.0777871	−	0.134731i
$512$		−	5.93164e6i		−	0.0441942i
$513$		0			0
$514$	−1.26118e8			−0.928725
$515$	−2.37870e7	+	1.37335e7i	−0.174148	+	0.100544i
$516$		0			0
$517$	1.54965e8	−	2.68407e8i	1.12140	−	1.94233i
$518$	−1.48366e7	−	8.56592e6i	−0.106745	−	0.0616290i
$519$		0			0
$520$	1.57504e7	+	2.72805e7i	0.112017	+	0.194018i
$521$		−	2.21508e8i		−	1.56630i	−0.621831	−	0.783152i	$-0.713611\pi$
$521$		−	2.21508e8i		−	1.56630i	0.621831	−	0.783152i	$-0.286389\pi$
$522$		0			0
$523$	5.17660e7			0.361859			0.180930	−	0.983496i	$-0.442089\pi$
$523$	5.17660e7			0.361859			0.180930	+	0.983496i	$0.442089\pi$
$524$	−3.11458e7	+	1.79820e7i	−0.216474	+	0.124981i
$525$		0			0
$526$	4.92294e6	−	8.52678e6i	0.0338273	−	0.0585906i
$527$	2.19972e7	+	1.27001e7i	0.150292	+	0.0867711i
$528$		0			0
$529$	−7.35719e7	−	1.27430e8i	−0.496987	−	0.860806i
$530$		−	6.90896e7i		−	0.464071i
$531$		0			0
$532$	−9.63942e6			−0.0640201
$533$	3.38471e8	−	1.95416e8i	2.23532	−	1.29056i
$534$		0			0
$535$	−2.27724e6	+	3.94430e6i	−0.0148713	+	0.0257578i
$536$	3.88154e7	+	2.24101e7i	0.252064	+	0.145529i
$537$		0			0
$538$	9.10669e6	+	1.57733e7i	0.0584809	+	0.101292i
$539$		−	1.86783e8i		−	1.19281i
$540$		0			0
$541$	1.49689e7			0.0945361			0.0472681	−	0.998882i	$-0.484949\pi$
$541$	1.49689e7			0.0945361			0.0472681	+	0.998882i	$0.484949\pi$
$542$	−4.26713e7	+	2.46363e7i	−0.268002	+	0.154731i
$543$		0			0
$544$	1.73777e6	−	3.00991e6i	0.0107943	−	0.0186963i
$545$	4.72701e7	+	2.72914e7i	0.292009	+	0.168592i
$546$		0			0
$547$	4.60003e7	+	7.96749e7i	0.281060	+	0.486810i	0.971646	−	0.236440i	$-0.0759807\pi$
$547$	4.60003e7	+	7.96749e7i	0.281060	+	0.486810i	−0.690586	+	0.723250i	$0.742647\pi$
$548$			6.74397e7i			0.409802i
$549$		0			0
$550$	1.20999e8			0.727265
$551$	7.04541e7	−	4.06767e7i	0.421164	−	0.243159i
$552$		0			0
$553$	−2.37386e7	+	4.11164e7i	−0.140372	+	0.243131i
$554$	2.32372e7	+	1.34160e7i	0.136664	+	0.0789030i
$555$		0			0
$556$	2.52777e6	+	4.37823e6i	0.0147066	+	0.0254726i
$557$			1.53984e8i			0.891066i	0.895266	+	0.445533i	$0.146986\pi$
$557$			1.53984e8i			0.891066i	−0.895266	+	0.445533i	$0.853014\pi$
$558$		0			0
$559$	−2.68420e8			−1.53667
$560$	2.50216e6	−	1.44462e6i	0.0142479	−	0.00822603i
$561$		0			0
$562$	−2.07465e7	+	3.59340e7i	−0.116879	+	0.202440i
$563$	−9.62471e7	−	5.55683e7i	−0.539340	−	0.311388i	0.205471	−	0.978663i	$-0.434127\pi$
$563$	−9.62471e7	−	5.55683e7i	−0.539340	−	0.311388i	−0.744811	+	0.667275i	$0.767461\pi$
$564$		0			0
$565$	−6.24434e7	−	1.08155e8i	−0.346211	−	0.599655i
$566$		−	2.18882e8i		−	1.20715i
$567$		0			0
$568$	7.45646e7			0.406900
$569$	−2.79773e8	+	1.61527e8i	−1.51869	+	0.876817i	−0.518934	+	0.854814i	$0.673671\pi$
$569$	−2.79773e8	+	1.61527e8i	−1.51869	+	0.876817i	−0.999758	+	0.0220026i	$0.992996\pi$
$570$		0			0
$571$	−2.71860e7	+	4.70875e7i	−0.146028	+	0.252928i	−0.929756	−	0.368176i	$-0.879982\pi$
$571$	−2.71860e7	+	4.70875e7i	−0.146028	+	0.252928i	0.783728	+	0.621104i	$0.213316\pi$
$572$	1.56901e8	+	9.05869e7i	0.838374	+	0.484036i
$573$		0			0
$574$	−1.79235e7	−	3.10444e7i	−0.0947734	−	0.164152i
$575$		−	1.23831e7i		−	0.0651370i
$576$		0			0
$577$	2.74190e8			1.42733			0.713665	−	0.700487i	$-0.247034\pi$
$577$	2.74190e8			1.42733			0.713665	+	0.700487i	$0.247034\pi$
$578$	−1.16486e8	+	6.72531e7i	−0.603239	+	0.348280i
$579$		0			0
$580$	−1.21921e7	+	2.11174e7i	−0.0624877	+	0.108232i
$581$	−2.29279e7	−	1.32374e7i	−0.116906	−	0.0674954i
$582$		0			0
$583$	−1.98681e8	−	3.44125e8i	−1.00265	−	1.73664i
$584$			6.67863e7i			0.335312i
$585$		0			0
$586$	1.33096e8			0.661410
$587$	2.14847e8	−	1.24042e8i	1.06222	−	0.613274i	0.136176	−	0.990685i	$-0.456519\pi$
$587$	2.14847e8	−	1.24042e8i	1.06222	−	0.613274i	0.926046	+	0.377411i	$0.123186\pi$
$588$		0			0
$589$	−1.13324e8	+	1.96283e8i	−0.554596	+	0.960589i
$590$	−2.07054e7	−	1.19543e7i	−0.100816	−	0.0582059i
$591$		0			0
$592$	2.75589e7	+	4.77334e7i	0.132830	+	0.230068i
$593$		−	2.27716e8i		−	1.09202i	−0.837779	−	0.546009i	$-0.816146\pi$
$593$		−	2.27716e8i		−	1.09202i	0.837779	−	0.546009i	$-0.183854\pi$
$594$		0			0
$595$	1.69290e6			0.00803676
$596$	−5.66192e6	+	3.26891e6i	−0.0267439	+	0.0154406i
$597$		0			0
$598$	9.27077e6	−	1.60574e7i	0.0433523	−	0.0750884i
$599$	−7.43379e7	−	4.29190e7i	−0.345884	−	0.199696i	0.316987	−	0.948430i	$-0.397329\pi$
$599$	−7.43379e7	−	4.29190e7i	−0.345884	−	0.199696i	−0.662871	+	0.748734i	$0.730662\pi$
$600$		0			0
$601$	1.73833e8	+	3.01088e8i	0.800774	+	1.38698i	0.919108	+	0.394007i	$0.128911\pi$
$601$	1.73833e8	+	3.01088e8i	0.800774	+	1.38698i	−0.118334	+	0.992974i	$0.537755\pi$
$602$			2.46194e7i			0.112846i
$603$		0			0
$604$	−9.48138e7			−0.430289
$605$	−3.86656e7	+	2.23236e7i	−0.174606	+	0.100809i
$606$		0			0
$607$	−4.35211e7	+	7.53807e7i	−0.194596	+	0.337050i	−0.946768	−	0.321917i	$-0.895673\pi$
$607$	−4.35211e7	+	7.53807e7i	−0.194596	+	0.337050i	0.752172	+	0.658967i	$0.229006\pi$
$608$	2.68577e7	+	1.55063e7i	0.119497	+	0.0689918i
$609$		0			0
$610$	−1.39544e7	−	2.41697e7i	−0.0614781	−	0.106483i
$611$			6.59204e8i			2.88999i
$612$		0			0
$613$	3.18298e8			1.38182			0.690912	−	0.722939i	$-0.257209\pi$
$613$	3.18298e8			1.38182			0.690912	+	0.722939i	$0.257209\pi$
$614$	9.44560e7	−	5.45342e7i	0.408061	−	0.235594i
$615$		0			0
$616$	8.30859e6	−	1.43909e7i	0.0355455	−	0.0615667i
$617$	1.18589e8	+	6.84674e7i	0.504881	+	0.291493i	0.730727	−	0.682670i	$-0.239181\pi$
$617$	1.18589e8	+	6.84674e7i	0.504881	+	0.291493i	−0.225846	+	0.974163i	$0.572515\pi$
$618$		0			0
$619$	−8.03059e7	−	1.39094e8i	−0.338591	−	0.586457i	0.645577	−	0.763695i	$-0.276617\pi$
$619$	−8.03059e7	−	1.39094e8i	−0.338591	−	0.586457i	−0.984168	+	0.177238i	$0.943284\pi$
$620$		−	6.79338e7i		−	0.285043i
$621$		0			0
$622$	−1.76556e8			−0.733689
$623$	−3.66793e7	+	2.11768e7i	−0.151690	+	0.0875783i
$624$		0			0
$625$	−6.62930e7	+	1.14823e8i	−0.271536	+	0.470315i
$626$	−1.72458e7	−	9.95689e6i	−0.0703010	−	0.0405883i
$627$		0			0
$628$	−4.16772e7	−	7.21870e7i	−0.168275	−	0.291461i
$629$			3.22953e7i			0.129774i
$630$		0			0
$631$	−4.09279e8			−1.62904			−0.814519	−	0.580136i	$-0.802999\pi$
$631$	−4.09279e8			−1.62904			−0.814519	+	0.580136i	$0.802999\pi$
$632$	1.32283e8	−	7.63734e7i	0.524024	−	0.302545i
$633$		0			0
$634$	−1.34371e8	+	2.32738e8i	−0.527277	+	0.913271i
$635$	1.35915e8	+	7.84708e7i	0.530820	+	0.306469i
$636$		0			0
$637$	1.98638e8	+	3.44052e8i	0.768501	+	1.33108i
$638$			1.40243e8i			0.540032i
$639$		0			0
$640$	−9.29547e6			−0.0354594
$641$	−6.47552e7	+	3.73865e7i	−0.245867	+	0.141952i	−0.617870	−	0.786280i	$-0.712004\pi$
$641$	−6.47552e7	+	3.73865e7i	−0.245867	+	0.141952i	0.372003	+	0.928231i	$0.378671\pi$
$642$		0			0
$643$	−1.35130e8	+	2.34052e8i	−0.508298	+	0.880399i	0.491655	+	0.870790i	$0.336392\pi$
$643$	−1.35130e8	+	2.34052e8i	−0.508298	+	0.880399i	−0.999954	+	0.00960888i	$0.996941\pi$
$644$	−1.47278e6	−	850310.i	−0.00551417	−	0.00318361i
$645$		0			0
$646$	9.08564e6	+	1.57368e7i	0.0337022	+	0.0583739i
$647$			2.04687e8i			0.755749i	0.925857	+	0.377874i	$0.123345\pi$
$647$			2.04687e8i			0.755749i	−0.925857	+	0.377874i	$0.876655\pi$
$648$		0			0
$649$	−1.37507e8			−0.503028
$650$	−2.22878e8	+	1.28679e8i	−0.811573	+	0.468562i
$651$		0			0
$652$	9.00313e7	−	1.55939e8i	0.324826	−	0.562615i
$653$	−1.10498e8	−	6.37963e7i	−0.396841	−	0.229116i	0.288279	−	0.957546i	$-0.406917\pi$
$653$	−1.10498e8	−	6.37963e7i	−0.396841	−	0.229116i	−0.685120	+	0.728430i	$0.740250\pi$
$654$		0			0
$655$	2.81796e7	+	4.88086e7i	0.100279	+	0.173689i
$656$			1.15329e8i			0.408534i
$657$		0			0
$658$	6.04619e7			0.212229
$659$	−2.79267e8	+	1.61235e8i	−0.975807	+	0.563383i	−0.901002	−	0.433816i	$-0.857167\pi$
$659$	−2.79267e8	+	1.61235e8i	−0.975807	+	0.563383i	−0.0748056	+	0.997198i	$0.523834\pi$
$660$		0			0
$661$	2.17389e8	−	3.76529e8i	0.752721	−	1.30375i	−0.193779	−	0.981045i	$-0.562074\pi$
$661$	2.17389e8	−	3.76529e8i	0.752721	−	1.30375i	0.946500	−	0.322705i	$-0.104592\pi$
$662$	−5.33957e7	−	3.08280e7i	−0.184049	−	0.106260i
$663$		0			0
$664$	4.25883e7	+	7.37650e7i	0.145474	+	0.251969i
$665$			1.51059e7i			0.0513668i
$666$		0			0
$667$	1.43526e7			0.0483676
$668$	−4.88630e7	+	2.82111e7i	−0.163927	+	0.0946434i
$669$		0			0
$670$	3.51189e7	−	6.08277e7i	0.116766	−	0.202245i
$671$	−1.39009e8	−	8.02570e7i	−0.460125	−	0.265654i
$672$		0			0
$673$	4.31783e7	+	7.47869e7i	0.141651	+	0.245347i	0.928119	−	0.372285i	$-0.121426\pi$
$673$	4.31783e7	+	7.47869e7i	0.141651	+	0.245347i	−0.786467	+	0.617632i	$0.788092\pi$
$674$			2.69735e8i			0.880963i
$675$		0			0
$676$	−2.30889e8			−0.747417
$677$	−4.92732e8	+	2.84479e8i	−1.58798	+	0.916820i	−0.594340	+	0.804214i	$0.702587\pi$
$677$	−4.92732e8	+	2.84479e8i	−1.58798	+	0.916820i	−0.993640	+	0.112606i	$0.964080\pi$
$678$		0			0
$679$	−1.29933e7	+	2.25050e7i	−0.0415058	+	0.0718902i
$680$	−4.71682e6	−	2.72326e6i	−0.0150011	−	0.00866089i
$681$		0			0
$682$	−1.95357e8	−	3.38368e8i	−0.615852	−	1.06669i
$683$		−	1.34652e8i		−	0.422622i	−0.977419	−	0.211311i	$-0.932227\pi$
$683$		−	1.34652e8i		−	0.422622i	0.977419	−	0.211311i	$-0.0677733\pi$
$684$		0			0
$685$	1.05685e8			0.328806
$686$	6.39851e7	−	3.69418e7i	0.198201	−	0.114432i
$687$		0			0
$688$	3.96036e7	−	6.85954e7i	0.121610	−	0.210635i
$689$	7.31935e8	+	4.22583e8i	2.23777	+	1.29198i
$690$		0			0
$691$	5.35612e7	+	9.27707e7i	0.162336	+	0.281175i	0.935706	−	0.352780i	$-0.114764\pi$
$691$	5.35612e7	+	9.27707e7i	0.162336	+	0.281175i	−0.773370	+	0.633955i	$0.781430\pi$
$692$			2.57151e8i			0.776013i
$693$		0			0
$694$	−1.45871e8			−0.436407
$695$	6.86112e6	−	3.96127e6i	0.0204381	−	0.0117999i
$696$		0			0
$697$	−3.37876e7	+	5.85218e7i	−0.0997835	+	0.172830i
$698$	−2.88067e8	−	1.66315e8i	−0.847085	−	0.489065i
$699$		0			0
$700$	1.18024e7	+	2.04423e7i	0.0344092	+	0.0595985i
$701$			2.39134e8i			0.694204i	0.937827	+	0.347102i	$0.112834\pi$
$701$			2.39134e8i			0.694204i	−0.937827	+	0.347102i	$0.887166\pi$
$702$		0			0
$703$	−2.88174e8			−0.829447
$704$	−4.62994e7	+	2.67310e7i	−0.132696	+	0.0766120i
$705$		0			0
$706$	2.13783e8	−	3.70282e8i	0.607517	−	1.05225i
$707$	5.98798e7	+	3.45716e7i	0.169443	+	0.0978277i
$708$		0			0
$709$	1.85010e8	+	3.20446e8i	0.519106	+	0.899118i	0.999753	+	0.0222038i	$0.00706826\pi$
$709$	1.85010e8	+	3.20446e8i	0.519106	+	0.899118i	−0.480648	+	0.876914i	$0.659598\pi$
$710$		−	1.16850e8i		−	0.326478i
$711$		0			0
$712$	1.36263e8			0.377518
$713$	−3.46290e7	+	1.99931e7i	−0.0955369	+	0.0551583i
$714$		0			0
$715$	1.41959e8	−	2.45880e8i	0.388368	−	0.672674i
$716$	2.73854e8	+	1.58110e8i	0.746071	+	0.430744i
$717$		0			0
$718$	−1.28986e8	−	2.23410e8i	−0.348472	−	0.603571i
$719$			1.59561e8i			0.429279i	0.976693	+	0.214639i	$0.0688576\pi$
$719$			1.59561e8i			0.429279i	−0.976693	+	0.214639i	$0.931142\pi$
$720$		0			0
$721$	−3.08177e7			−0.0822233
$722$	9.00558e7	−	5.19938e7i	0.239277	−	0.138146i
$723$		0			0
$724$	6.12342e7	−	1.06061e8i	0.161354	−	0.279473i
$725$	−1.72526e8	−	9.96079e7i	−0.452731	−	0.261384i
$726$		0			0
$727$	1.24125e8	+	2.14991e8i	0.323040	+	0.559522i	0.981114	−	0.193432i	$-0.0619617\pi$
$727$	1.24125e8	+	2.14991e8i	0.323040	+	0.559522i	−0.658073	+	0.752954i	$0.728628\pi$
$728$			3.53438e7i			0.0916051i
$729$		0			0
$730$	1.04661e8			0.269039
$731$	4.01923e7	−	2.32050e7i	0.102894	−	0.0594059i
$732$		0			0
$733$	−2.13730e8	+	3.70190e8i	−0.542691	+	0.939968i	0.456057	+	0.889950i	$0.349261\pi$
$733$	−2.13730e8	+	3.70190e8i	−0.542691	+	0.939968i	−0.998748	+	0.0500180i	$0.984072\pi$
$734$	−1.53879e8	−	8.88422e7i	−0.389127	−	0.224663i
$735$		0			0
$736$	2.73568e6	+	4.73833e6i	0.00686169	+	0.0118848i
$737$		−	4.03965e8i		−	1.00912i
$738$		0			0
$739$	2.68169e8			0.664469			0.332234	−	0.943197i	$-0.392197\pi$
$739$	2.68169e8			0.664469			0.332234	+	0.943197i	$0.392197\pi$
$740$	7.48029e7	−	4.31875e7i	0.184596	−	0.106577i
$741$		0			0
$742$	3.87591e7	−	6.71327e7i	0.0948772	−	0.164332i
$743$	1.46273e8	+	8.44510e7i	0.356614	+	0.205891i	0.667595	−	0.744525i	$-0.267324\pi$
$743$	1.46273e8	+	8.44510e7i	0.356614	+	0.205891i	−0.310980	+	0.950416i	$0.600657\pi$
$744$		0			0
$745$	5.12271e6	+	8.87280e6i	0.0123889	+	0.0214581i
$746$		−	6.43803e7i		−	0.155073i
$747$		0			0
$748$	−3.13251e7			−0.0748492
$749$	−4.42549e6	+	2.55506e6i	−0.0105321	+	0.00608072i
$750$		0			0
$751$	−1.90204e8	+	3.29444e8i	−0.449056	+	0.777788i	−0.998325	−	0.0578577i	$-0.981573\pi$
$751$	−1.90204e8	+	3.29444e8i	−0.449056	+	0.777788i	0.549269	+	0.835646i	$0.314906\pi$
$752$	−1.68461e8	−	9.72610e7i	−0.396137	−	0.228710i
$753$		0			0
$754$	−1.49145e8	−	2.58326e8i	−0.347932	−	0.602636i
$755$			1.48583e8i			0.345245i
$756$		0			0
$757$	5.93762e8			1.36875			0.684376	−	0.729129i	$-0.260075\pi$
$757$	5.93762e8			1.36875			0.684376	+	0.729129i	$0.260075\pi$
$758$	2.21906e8	−	1.28118e8i	0.509521	−	0.294172i
$759$		0			0
$760$	2.42999e7	−	4.20887e7i	0.0553559	−	0.0958792i
$761$	2.02904e8	+	1.17147e8i	0.460401	+	0.265813i	0.712213	−	0.701964i	$-0.247693\pi$
$761$	2.02904e8	+	1.17147e8i	0.460401	+	0.265813i	−0.251812	+	0.967776i	$0.581026\pi$
$762$		0			0
$763$	3.06208e7	+	5.30368e7i	0.0689356	+	0.119400i
$764$		−	1.40114e8i		−	0.314196i
$765$		0			0
$766$	−1.85433e8			−0.412573
$767$	2.53287e8	−	1.46235e8i	0.561342	−	0.324091i
$768$		0			0
$769$	1.58571e8	−	2.74653e8i	0.348694	−	0.603956i	−0.637324	−	0.770596i	$-0.719959\pi$
$769$	1.58571e8	−	2.74653e8i	0.348694	−	0.603956i	0.986018	+	0.166640i	$0.0532919\pi$
$770$	−2.25520e7	−	1.30204e7i	−0.0493983	−	0.0285201i
$771$		0			0
$772$	−1.42697e7	−	2.47158e7i	−0.0310144	−	0.0537184i
$773$			3.31391e8i			0.717468i	0.933440	+	0.358734i	$0.116791\pi$
$773$			3.31391e8i			0.717468i	−0.933440	+	0.358734i	$0.883209\pi$
$774$		0			0
$775$	5.55010e8			1.19233
$776$	7.24046e7	−	4.18028e7i	0.154946	−	0.0894582i
$777$		0			0
$778$	−9.76019e7	+	1.69051e8i	−0.207262	+	0.358988i
$779$	−5.22196e8	−	3.01490e8i	−1.10464	−	0.637765i
$780$		0			0
$781$	−3.36025e8	−	5.82013e8i	−0.705373	−	1.22174i
$782$			3.20584e6i			0.00670381i
$783$		0			0
$784$	−1.17231e8			−0.243273
$785$	−1.13124e8	+	6.53123e7i	−0.233855	+	0.135016i
$786$		0			0
$787$	9.60758e7	−	1.66408e8i	0.197101	−	0.341390i	−0.750486	−	0.660886i	$-0.770181\pi$
$787$	9.60758e7	−	1.66408e8i	0.197101	−	0.341390i	0.947587	+	0.319497i	$0.103514\pi$
$788$	−1.35992e8	−	7.85150e7i	−0.277929	−	0.160463i
$789$		0			0
$790$	−1.19685e8	−	2.07300e8i	−0.242749	−	0.420453i
$791$		−	1.40122e8i		−	0.283125i
$792$		0			0
$793$	3.41405e8			0.684621
$794$	−2.80416e8	+	1.61898e8i	−0.560197	+	0.323430i
$795$		0			0
$796$	−1.33591e8	+	2.31387e8i	−0.264874	+	0.458775i
$797$	−1.18277e8	−	6.82872e7i	−0.233628	−	0.134885i	0.378617	−	0.925554i	$-0.376400\pi$
$797$	−1.18277e8	−	6.82872e7i	−0.233628	−	0.134885i	−0.612245	+	0.790668i	$0.709733\pi$
$798$		0			0
$799$	−5.69884e7	−	9.87068e7i	−0.111724	−	0.193511i
$800$		−	7.59427e7i		−	0.148326i
$801$		0			0
$802$	4.51019e8			0.874322
$803$	5.21300e8	−	3.00973e8i	1.00680	−	0.581274i
$804$		0			0
$805$	−1.33252e6	+	2.30799e6i	−0.00255439	+	0.00442433i
$806$	7.19691e8	+	4.15514e8i	1.37449	+	0.793561i
$807$		0			0
$808$	−1.11226e8	−	1.92649e8i	−0.210850	−	0.365202i
$809$		−	6.82631e8i		−	1.28926i	−0.764495	−	0.644630i	$-0.777011\pi$
$809$		−	6.82631e8i		−	1.28926i	0.764495	−	0.644630i	$-0.222989\pi$
$810$		0			0
$811$	−8.02342e7			−0.150417			−0.0752085	−	0.997168i	$-0.523962\pi$
$811$	−8.02342e7			−0.150417			−0.0752085	+	0.997168i	$0.523962\pi$
$812$	−2.36936e7	+	1.36795e7i	−0.0442550	+	0.0255507i
$813$		0			0
$814$	2.48388e8	−	4.30221e8i	0.460530	−	0.797661i
$815$	−2.44372e8	−	1.41088e8i	−0.451417	−	0.260626i
$816$		0			0
$817$	2.07061e8	+	3.58640e8i	0.379692	+	0.657646i
$818$		−	2.71070e8i		−	0.495246i
$819$		0			0
$820$	1.80732e8			0.327789
$821$	7.33039e8	−	4.23220e8i	1.32464	−	0.764781i	0.340174	−	0.940362i	$-0.389514\pi$
$821$	7.33039e8	−	4.23220e8i	1.32464	−	0.764781i	0.984465	+	0.175582i	$0.0561806\pi$
$822$		0			0
$823$	−3.00433e8	+	5.20365e8i	−0.538949	+	0.933487i	0.460012	+	0.887913i	$0.347845\pi$
$823$	−3.00433e8	+	5.20365e8i	−0.538949	+	0.933487i	−0.998961	+	0.0455745i	$0.985488\pi$
$824$	8.58655e7	+	4.95745e7i	0.153475	+	0.0886087i
$825$		0			0
$826$	−1.34126e7	−	2.32314e7i	−0.0237999	−	0.0412226i
$827$		−	8.30480e8i		−	1.46829i	−0.678991	−	0.734146i	$-0.737583\pi$
$827$		−	8.30480e8i		−	1.46829i	0.678991	−	0.734146i	$-0.262417\pi$
$828$		0			0
$829$	−9.87908e8			−1.73402			−0.867008	−	0.498294i	$-0.833960\pi$
$829$	−9.87908e8			−1.73402			−0.867008	+	0.498294i	$0.833960\pi$
$830$	1.15597e8	−	6.67401e7i	0.202168	−	0.116722i
$831$		0			0
$832$	5.68553e7	−	9.84762e7i	0.0987190	−	0.170986i
$833$	−5.94867e7	−	3.43447e7i	−0.102917	−	0.0594189i
$834$		0			0
$835$	4.42096e7	+	7.65732e7i	0.0759376	+	0.131528i
$836$		−	2.79517e8i		−	0.478398i
$837$		0			0
$838$	−6.22668e8			−1.05810
$839$	−3.20618e8	+	1.85109e8i	−0.542878	+	0.313431i	−0.746245	−	0.665672i	$-0.768145\pi$
$839$	−3.20618e8	+	1.85109e8i	−0.542878	+	0.313431i	0.203367	+	0.979103i	$0.434812\pi$
$840$		0			0
$841$	−1.81961e8	+	3.15167e8i	−0.305908	+	0.529849i
$842$	−1.83683e8	−	1.06049e8i	−0.307703	−	0.177652i
$843$		0			0
$844$	−2.07474e8	−	3.59355e8i	−0.345093	−	0.597718i
$845$			3.61826e8i			0.599694i
$846$		0			0
$847$	−5.00940e7			−0.0824395
$848$	−2.15984e8	+	1.24698e8i	−0.354188	+	0.204491i
$849$		0			0
$850$	2.22487e7	−	3.85358e7i	0.0362282	−	0.0627491i
$851$	−4.40293e7	−	2.54203e7i	−0.0714419	−	0.0412470i
$852$		0			0
$853$	−1.82273e7	−	3.15707e7i	−0.0293681	−	0.0508671i	0.850968	−	0.525218i	$-0.176016\pi$
$853$	−1.82273e7	−	3.15707e7i	−0.0293681	−	0.0508671i	−0.880336	+	0.474351i	$0.842683\pi$
$854$		−	3.13135e7i		−	0.0502757i
$855$		0			0
$856$	1.64406e7			0.0262118
$857$	−2.18436e8	+	1.26114e8i	−0.347042	+	0.200365i	−0.663382	−	0.748281i	$-0.730879\pi$
$857$	−2.18436e8	+	1.26114e8i	−0.347042	+	0.200365i	0.316339	+	0.948646i	$0.397546\pi$
$858$		0			0
$859$	−7.74242e7	+	1.34103e8i	−0.122151	+	0.211572i	−0.920616	−	0.390470i	$-0.872313\pi$
$859$	−7.74242e7	+	1.34103e8i	−0.122151	+	0.211572i	0.798465	+	0.602042i	$0.205646\pi$
$860$	−1.07496e8	−	6.20627e7i	−0.169004	−	0.0975743i
$861$		0			0
$862$	3.83549e8	+	6.64326e8i	0.598823	+	1.03719i
$863$		−	8.16338e8i		−	1.27010i	−0.772472	−	0.635049i	$-0.780980\pi$
$863$		−	8.16338e8i		−	1.27010i	0.772472	−	0.635049i	$-0.219020\pi$
$864$		0			0
$865$	4.02981e8			0.622638
$866$	−5.78868e8	+	3.34209e8i	−0.891304	+	0.514594i
$867$		0			0
$868$	3.81107e7	−	6.60097e7i	0.0582758	−	0.100937i
$869$	−1.19226e9	−	6.88353e8i	−1.81682	−	1.04894i
$870$		0			0
$871$	4.29606e8	+	7.44099e8i	0.650153	+	1.12610i
$872$		−	1.97031e8i		−	0.297156i
$873$		0			0
$874$	−2.86060e7			−0.0428473
$875$	7.02150e7	−	4.05387e7i	0.104811	−	0.0605125i
$876$		0			0
$877$	1.75984e7	−	3.04813e7i	0.0260900	−	0.0451892i	−0.852686	−	0.522424i	$-0.825028\pi$
$877$	1.75984e7	−	3.04813e7i	0.0260900	−	0.0451892i	0.878776	+	0.477235i	$0.158361\pi$
$878$	4.50615e8	+	2.60162e8i	0.665766	+	0.384380i
$879$		0			0
$880$	4.18901e7	+	7.25557e7i	0.0614700	+	0.106469i
$881$		−	1.48112e8i		−	0.216602i	−0.994118	−	0.108301i	$-0.965459\pi$
$881$		−	1.48112e8i		−	0.216602i	0.994118	−	0.108301i	$-0.0345410\pi$
$882$		0			0
$883$	−1.03227e9			−1.49937			−0.749686	−	0.661794i	$-0.769795\pi$
$883$	−1.03227e9			−1.49937			−0.749686	+	0.661794i	$0.769795\pi$
$884$	5.77004e7	−	3.33134e7i	0.0835261	−	0.0482238i
$885$		0			0
$886$	−5.57157e7	+	9.65025e7i	−0.0801081	+	0.138751i
$887$	2.13506e8	+	1.23268e8i	0.305943	+	0.176636i	0.645109	−	0.764090i	$-0.276812\pi$
$887$	2.13506e8	+	1.23268e8i	0.305943	+	0.176636i	−0.339167	+	0.940726i	$0.610145\pi$
$888$		0			0
$889$	8.80439e7	+	1.52496e8i	0.125312	+	0.217047i
$890$		−	2.13538e8i		−	0.302904i
$891$		0			0
$892$	−1.20718e8			−0.170089
$893$	8.80770e8	−	5.08513e8i	1.23683	−	0.714081i
$894$		0			0
$895$	2.47774e8	−	4.29157e8i	0.345610	−	0.598614i
$896$	−9.03220e6	−	5.21474e6i	−0.0125565	−	0.00724951i
$897$		0			0
$898$	3.91822e7	+	6.78655e7i	0.0541078	+	0.0937174i
$899$			6.43283e8i			0.885366i
$900$		0			0
$901$	−1.46130e8			−0.199786
$902$	9.00201e8	−	5.19732e8i	1.22665	−	0.708206i
$903$		0			0
$904$	−2.25406e8	+	3.90414e8i	−0.305112	+	0.528470i
$905$	−1.66208e8	−	9.59601e7i	−0.224236	−	0.129463i
$906$		0			0
$907$	−3.47798e8	−	6.02404e8i	−0.466128	−	0.807357i	0.533124	−	0.846037i	$-0.321018\pi$
$907$	−3.47798e8	−	6.02404e8i	−0.466128	−	0.807357i	−0.999252	+	0.0386800i	$0.987685\pi$
$908$		−	1.61050e8i		−	0.215132i
$909$		0			0
$910$	5.53873e7			0.0734998
$911$	8.66691e8	−	5.00385e8i	1.14633	−	0.661833i	0.198339	−	0.980133i	$-0.436445\pi$
$911$	8.66691e8	−	5.00385e8i	1.14633	−	0.661833i	0.947990	+	0.318300i	$0.103112\pi$
$912$		0			0
$913$	3.83848e8	−	6.64845e8i	0.504368	−	0.873590i
$914$	−3.61726e8	−	2.08843e8i	−0.473742	−	0.273515i
$915$		0			0
$916$	4.59923e7	+	7.96610e7i	0.0598410	+	0.103648i
$917$			6.32349e7i			0.0820066i
$918$		0			0
$919$	3.63664e8			0.468548			0.234274	−	0.972171i	$-0.424729\pi$
$919$	3.63664e8			0.468548			0.234274	+	0.972171i	$0.424729\pi$
$920$	7.42543e6	−	4.28708e6i	0.00953583	−	0.00550551i
$921$		0			0
$922$	−1.50346e8	+	2.60407e8i	−0.191822	+	0.332246i
$923$	1.23791e9	+	7.14708e8i	1.57429	+	0.908915i
$924$		0			0
$925$	3.52836e8	+	6.11130e8i	0.445808	+	0.772162i
$926$		−	5.36645e8i		−	0.675856i
$927$		0			0
$928$	8.80212e7			0.110140
$929$	−3.37250e8	+	1.94711e8i	−0.420634	+	0.242853i	−0.695349	−	0.718673i	$-0.744750\pi$
$929$	−3.37250e8	+	1.94711e8i	−0.420634	+	0.242853i	0.274715	+	0.961526i	$0.411417\pi$
$930$		0			0
$931$	3.06461e8	−	5.30806e8i	0.379775	−	0.657789i
$932$	−6.18674e8	−	3.57192e8i	−0.764213	−	0.441218i
$933$		0			0
$934$	5.38699e8	+	9.33054e8i	0.661158	+	1.14516i
$935$			4.90895e7i			0.0600556i
$936$		0			0
$937$	−7.33744e8			−0.891920			−0.445960	−	0.895053i	$-0.647138\pi$
$937$	−7.33744e8			−0.891920			−0.445960	+	0.895053i	$0.647138\pi$
$938$	6.82484e7	−	3.94032e7i	0.0826959	−	0.0477445i
$939$		0			0
$940$	−1.52418e8	+	2.63995e8i	−0.183507	+	0.317843i
$941$	−2.41096e8	−	1.39197e8i	−0.289348	−	0.167055i	0.348300	−	0.937383i	$-0.386759\pi$
$941$	−2.41096e8	−	1.39197e8i	−0.289348	−	0.167055i	−0.637648	+	0.770328i	$0.720092\pi$
$942$		0			0
$943$	−5.31899e7	−	9.21276e7i	−0.0634299	−	0.109864i
$944$			8.63042e7i			0.102593i
$945$		0			0
$946$	−7.13894e8			−0.843258
$947$	−7.22272e8	+	4.17004e8i	−0.850454	+	0.491010i	−0.860804	−	0.508937i	$-0.830039\pi$
$947$	−7.22272e8	+	4.17004e8i	−0.850454	+	0.491010i	0.0103502	+	0.999946i	$0.496705\pi$
$948$		0			0
$949$	−6.40153e8	+	1.10878e9i	−0.749006	+	1.29732i
$950$	3.43859e8	+	1.98527e8i	0.401060	+	0.231552i
$951$		0			0
$952$	−3.05549e6	−	5.29226e6i	−0.00354135	−	0.00613381i
$953$		−	1.27101e8i		−	0.146849i	−0.997301	−	0.0734245i	$-0.976607\pi$
$953$		−	1.27101e8i		−	0.146849i	0.997301	−	0.0734245i	$-0.0233928\pi$
$954$		0			0
$955$	−2.19572e8			−0.252097
$956$	−3.25313e8	+	1.87820e8i	−0.372330	+	0.214965i
$957$		0			0
$958$	−8.01766e7	+	1.38870e8i	−0.0911908	+	0.157947i
$959$	1.02691e8	+	5.92889e7i	0.116434	+	0.0672229i
$960$		0			0
$961$	−4.52333e8	−	7.83464e8i	−0.509669	−	0.882772i
$962$			1.05662e9i			1.18684i
$963$		0			0
$964$	8.49229e8			0.947969
$965$	−3.87322e7	+	2.23620e7i	−0.0431013	+	0.0248845i
$966$		0			0
$967$	1.78470e8	−	3.09120e8i	0.197373	−	0.341859i	−0.750303	−	0.661094i	$-0.770092\pi$
$967$	1.78470e8	−	3.09120e8i	0.197373	−	0.341859i	0.947676	+	0.319235i	$0.103426\pi$
$968$	1.39574e8	+	8.05828e7i	0.153878	+	0.0888416i
$969$		0			0
$970$	−6.55092e7	−	1.13465e8i	−0.0717773	−	0.124322i
$971$			2.79662e8i			0.305476i	0.988267	+	0.152738i	$0.0488090\pi$
$971$			2.79662e8i			0.305476i	−0.988267	+	0.152738i	$0.951191\pi$
$972$		0			0
$973$	8.88905e6			0.00964977
$974$	2.97081e8	−	1.71520e8i	0.321513	−	0.185625i
$975$		0			0
$976$	−5.03719e7	+	8.72467e7i	−0.0541800	+	0.0938425i
$977$	7.08671e7	+	4.09152e7i	0.0759908	+	0.0438733i	0.537514	−	0.843255i	$-0.319364\pi$
$977$	7.08671e7	+	4.09152e7i	0.0759908	+	0.0438733i	−0.461523	+	0.887128i	$0.652697\pi$
$978$		0			0
$979$	−6.14069e8	−	1.06360e9i	−0.654439	−	1.13352i
$980$			1.83712e8i			0.195191i
$981$		0			0
$982$	8.79946e8			0.929226
$983$	−7.65774e8	+	4.42120e8i	−0.806195	+	0.465457i	−0.845633	−	0.533765i	$-0.820777\pi$
$983$	−7.65774e8	+	4.42120e8i	−0.806195	+	0.465457i	0.0394375	+	0.999222i	$0.487443\pi$
$984$		0			0
$985$	−1.23041e8	+	2.13113e8i	−0.128748	+	0.222998i
$986$	4.46648e7	+	2.57872e7i	0.0465945	+	0.0269013i
$987$		0			0
$988$	2.97258e8	+	5.14867e8i	0.308222	+	0.533856i
$989$			7.30607e7i			0.0755258i
$990$		0			0
$991$	1.35522e9			1.39248			0.696239	−	0.717810i	$-0.254855\pi$
$991$	1.35522e9			1.39248			0.696239	+	0.717810i	$0.254855\pi$
$992$	−2.12371e8	+	1.22612e8i	−0.217551	+	0.125603i
$993$		0			0
$994$	6.55527e7	−	1.13541e8i	0.0667469	−	0.115609i
$995$	3.62606e8	+	2.09351e8i	0.368100	+	0.212523i
$996$		0			0
$997$	−4.59348e8	−	7.95613e8i	−0.463507	−	0.802817i	0.535626	−	0.844455i	$-0.320076\pi$
$997$	−4.59348e8	−	7.95613e8i	−0.463507	−	0.802817i	−0.999133	+	0.0416381i	$0.986742\pi$
$998$			7.31843e8i			0.736252i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.7.d.e.53.1		8
3.2	odd	2	inner	162.7.d.e.53.4		8
9.2	odd	6	inner	162.7.d.e.107.1		8
9.4	even	3		54.7.b.c.53.2	✓	4
9.5	odd	6		54.7.b.c.53.3	yes	4
9.7	even	3	inner	162.7.d.e.107.4		8
36.23	even	6		432.7.e.h.161.2		4
36.31	odd	6		432.7.e.h.161.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.7.b.c.53.2	✓	4	9.4	even	3
54.7.b.c.53.3	yes	4	9.5	odd	6
162.7.d.e.53.1		8	1.1	even	1	trivial
162.7.d.e.53.4		8	3.2	odd	2	inner
162.7.d.e.107.1		8	9.2	odd	6	inner
162.7.d.e.107.4		8	9.7	even	3	inner
432.7.e.h.161.2		4	36.23	even	6
432.7.e.h.161.3		4	36.31	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)

\(f(q)\)	\(=\)	\(q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-43.4287 - 25.0736i) q^{5} +(-28.1325 - 48.7269i) q^{7} +181.019i q^{8} +O(q^{10})\)	\(q+(-4.89898 + 2.82843i) q^{2} +(16.0000 - 27.7128i) q^{4} +(-43.4287 - 25.0736i) q^{5} +(-28.1325 - 48.7269i) q^{7} +181.019i q^{8} +283.675 q^{10} +(1412.94 - 815.764i) q^{11} +(-1735.09 + 3005.26i) q^{13} +(275.641 + 159.141i) q^{14} +(-512.000 - 886.810i) q^{16} -599.995i q^{17} +5353.81 q^{19} +(-1389.72 + 802.355i) q^{20} +(-4614.66 + 7992.82i) q^{22} +(817.994 + 472.269i) q^{23} +(-6555.13 - 11353.8i) q^{25} -19630.3i q^{26} -1800.48 q^{28} +(13159.6 - 7597.70i) q^{29} +(-21167.0 + 36662.3i) q^{31} +(5016.55 + 2896.31i) q^{32} +(1697.04 + 2939.36i) q^{34} +2821.53i q^{35} -53825.9 q^{37} +(-26228.2 + 15142.9i) q^{38} +(4538.81 - 7861.44i) q^{40} +(-97537.2 - 56313.1i) q^{41} +(38675.4 + 66987.7i) q^{43} -52208.9i q^{44} -5343.12 q^{46} +(164513. - 94981.5i) q^{47} +(57241.6 - 99145.4i) q^{49} +(64226.9 + 37081.4i) q^{50} +(55522.7 + 96168.2i) q^{52} -243552. i q^{53} -81816.5 q^{55} +(8820.50 - 5092.52i) q^{56} +(-42979.1 + 74442.0i) q^{58} +(-72989.8 - 42140.7i) q^{59} +(-49191.3 - 85201.9i) q^{61} -239477. i q^{62} -32768.0 q^{64} +(150705. - 87009.7i) q^{65} +(123800. - 214427. i) q^{67} +(-16627.5 - 9599.92i) q^{68} +(-7980.49 - 13822.6i) q^{70} -411915. i q^{71} +368946. q^{73} +(263692. - 152243. i) q^{74} +(85661.0 - 148369. i) q^{76} +(-79499.2 - 45898.9i) q^{77} +(-421907. - 730765. i) q^{79} +51350.7i q^{80} +637110. q^{82} +(407498. - 235269. i) q^{83} +(-15044.0 + 26057.0i) q^{85} +(-378940. - 218781. i) q^{86} +(147669. + 255770. i) q^{88} -752753. i q^{89} +195249. q^{91} +(26175.8 - 15112.6i) q^{92} +(-537296. + 930624. i) q^{94} +(-232509. - 134239. i) q^{95} +(-230930. - 399983. i) q^{97} +647615. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 128 q^{4} - 836 q^{7}+O(q^{10}) \) 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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