LMFDB - Embedded newform 240.7.bg.b.193.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [240,7,Mod(97,240)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(240, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("240.97"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	240.bg (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,60] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$55.2129800688$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1602x^{6} + 816401x^{4} + 140305200x^{2} + 7638760000 $ x^8 + 1602x^6 + 816401x^4 + 140305200*x^2 + 7638760000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3^{8}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			193.2
Root			$25.3784i$ of defining polynomial
Character	$\chi$	$=$	240.193
Dual form			240.7.bg.b.97.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-11.0227 - 11.0227i) q^{3} +(75.4773 - 99.6402i) q^{5} +(-145.451 + 145.451i) q^{7} +243.000i q^{9} -1037.11 q^{11} +(2027.16 + 2027.16i) q^{13} +(-1930.27 + 266.341i) q^{15} +(4670.49 - 4670.49i) q^{17} -9189.32i q^{19} +3206.54 q^{21} +(13577.9 + 13577.9i) q^{23} +(-4231.35 - 15041.2i) q^{25} +(2678.52 - 2678.52i) q^{27} -8478.24i q^{29} -17088.4 q^{31} +(11431.7 + 11431.7i) q^{33} +(3514.53 + 25471.1i) q^{35} +(-14956.3 + 14956.3i) q^{37} -44689.5i q^{39} +50688.1 q^{41} +(12486.6 + 12486.6i) q^{43} +(24212.6 + 18341.0i) q^{45} +(25787.6 - 25787.6i) q^{47} +75336.8i q^{49} -102963. q^{51} +(-166649. - 166649. i) q^{53} +(-78277.9 + 103337. i) q^{55} +(-101291. + 101291. i) q^{57} -247188. i q^{59} -281194. q^{61} +(-35344.7 - 35344.7i) q^{63} +(354991. - 48982.0i) q^{65} +(304343. - 304343. i) q^{67} -299331. i q^{69} +288398. q^{71} +(-487894. - 487894. i) q^{73} +(-119153. + 212435. i) q^{75} +(150848. - 150848. i) q^{77} -222009. i q^{79} -59049.0 q^{81} +(-749160. - 749160. i) q^{83} +(-112853. - 817885. i) q^{85} +(-93453.1 + 93453.1i) q^{87} +689800. i q^{89} -589705. q^{91} +(188360. + 188360. i) q^{93} +(-915626. - 693585. i) q^{95} +(820944. - 820944. i) q^{97} -252017. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 60 q^{5} - 388 q^{7} + 4192 q^{11} + 7884 q^{13} - 1296 q^{15} - 1372 q^{17} + 4536 q^{21} - 14888 q^{23} + 17932 q^{25} - 2240 q^{31} + 3564 q^{33} + 78232 q^{35} - 69996 q^{37} + 169064 q^{41} - 164136 q^{43}+ \cdots - 854736 q^{97}+O(q^{100}) $ 8 * q + 60 * q^5 - 388 * q^7 + 4192 * q^11 + 7884 * q^13 - 1296 * q^15 - 1372 * q^17 + 4536 * q^21 - 14888 * q^23 + 17932 * q^25 - 2240 * q^31 + 3564 * q^33 + 78232 * q^35 - 69996 * q^37 + 169064 * q^41 - 164136 * q^43 - 44712 * q^45 + 109248 * q^47 - 380376 * q^51 - 480740 * q^53 + 409068 * q^55 - 442584 * q^57 + 266088 * q^61 - 94284 * q^63 + 903396 * q^65 - 92488 * q^67 + 2526032 * q^71 + 324464 * q^73 + 38232 * q^75 + 2822104 * q^77 - 472392 * q^81 - 213264 * q^83 - 1537292 * q^85 + 1707156 * q^87 - 3340176 * q^91 + 1264248 * q^93 - 3084784 * q^95 - 854736 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−11.0227	−	11.0227i	−0.408248	−	0.408248i
$3$	−11.0227	−	11.0227i	−0.408248	−	0.408248i
$4$		0			0
$5$	75.4773	−	99.6402i	0.603818	−	0.797122i
$5$	75.4773	−	99.6402i	0.603818	−	0.797122i
$6$		0			0
$7$	−145.451	+	145.451i	−0.424057	+	0.424057i	−0.886598	−	0.462541i	$-0.846938\pi$
$7$	−145.451	+	145.451i	−0.424057	+	0.424057i	0.462541	+	0.886598i	$0.346938\pi$
$8$		0			0
$9$			243.000i			0.333333i
$10$		0			0
$11$	−1037.11			−0.779193			−0.389596	−	0.920986i	$-0.627385\pi$
$11$	−1037.11			−0.779193			−0.389596	+	0.920986i	$0.627385\pi$
$12$		0			0
$13$	2027.16	+	2027.16i	0.922693	+	0.922693i	0.997219	−	0.0745260i	$-0.0237444\pi$
$13$	2027.16	+	2027.16i	0.922693	+	0.922693i	−0.0745260	+	0.997219i	$0.523744\pi$
$14$		0			0
$15$	−1930.27	+	266.341i	−0.571931	+	0.0789158i
$16$		0			0
$17$	4670.49	−	4670.49i	0.950640	−	0.950640i	−0.0481978	−	0.998838i	$-0.515348\pi$
$17$	4670.49	−	4670.49i	0.950640	−	0.950640i	0.998838	+	0.0481978i	$0.0153478\pi$
$18$		0			0
$19$		−	9189.32i		−	1.33975i	−0.742476	−	0.669873i	$-0.766349\pi$
$19$		−	9189.32i		−	1.33975i	0.742476	−	0.669873i	$-0.233651\pi$
$20$		0			0
$21$	3206.54			0.346241
$22$		0			0
$23$	13577.9	+	13577.9i	1.11597	+	1.11597i	0.992327	+	0.123638i	$0.0394561\pi$
$23$	13577.9	+	13577.9i	1.11597	+	1.11597i	0.123638	+	0.992327i	$0.460544\pi$
$24$		0			0
$25$	−4231.35	−	15041.2i	−0.270807	−	0.962634i
$26$		0			0
$27$	2678.52	−	2678.52i	0.136083	−	0.136083i
$28$		0			0
$29$		−	8478.24i		−	0.347625i	−0.984779	−	0.173813i	$-0.944391\pi$
$29$		−	8478.24i		−	0.347625i	0.984779	−	0.173813i	$-0.0556087\pi$
$30$		0			0
$31$	−17088.4			−0.573609			−0.286805	−	0.957989i	$-0.592593\pi$
$31$	−17088.4			−0.573609			−0.286805	+	0.957989i	$0.592593\pi$
$32$		0			0
$33$	11431.7	+	11431.7i	0.318104	+	0.318104i
$34$		0			0
$35$	3514.53	+	25471.1i	0.0819716	+	0.594078i
$36$		0			0
$37$	−14956.3	+	14956.3i	−0.295269	+	0.295269i	−0.839158	−	0.543888i	$-0.816952\pi$
$37$	−14956.3	+	14956.3i	−0.295269	+	0.295269i	0.543888	+	0.839158i	$0.316952\pi$
$38$		0			0
$39$		−	44689.5i		−	0.753376i
$40$		0			0
$41$	50688.1			0.735452			0.367726	−	0.929934i	$-0.380136\pi$
$41$	50688.1			0.735452			0.367726	+	0.929934i	$0.380136\pi$
$42$		0			0
$43$	12486.6	+	12486.6i	0.157050	+	0.157050i	0.781258	−	0.624208i	$-0.214578\pi$
$43$	12486.6	+	12486.6i	0.157050	+	0.157050i	−0.624208	+	0.781258i	$0.714578\pi$
$44$		0			0
$45$	24212.6	+	18341.0i	0.265707	+	0.201273i
$46$		0			0
$47$	25787.6	−	25787.6i	0.248380	−	0.248380i	−0.571925	−	0.820306i	$-0.693803\pi$
$47$	25787.6	−	25787.6i	0.248380	−	0.248380i	0.820306	+	0.571925i	$0.193803\pi$
$48$		0			0
$49$			75336.8i			0.640352i
$50$		0			0
$51$	−102963.			−0.776194
$52$		0			0
$53$	−166649.	−	166649.i	−1.11937	−	1.11937i	−0.991833	−	0.127542i	$-0.959291\pi$
$53$	−166649.	−	166649.i	−1.11937	−	1.11937i	−0.127542	−	0.991833i	$-0.540709\pi$
$54$		0			0
$55$	−78277.9	+	103337.i	−0.470491	+	0.621111i
$56$		0			0
$57$	−101291.	+	101291.i	−0.546949	+	0.546949i
$58$		0			0
$59$		−	247188.i		−	1.20357i	−0.798658	−	0.601785i	$-0.794456\pi$
$59$		−	247188.i		−	1.20357i	0.798658	−	0.601785i	$-0.205544\pi$
$60$		0			0
$61$	−281194.			−1.23884			−0.619422	−	0.785058i	$-0.712633\pi$
$61$	−281194.			−1.23884			−0.619422	+	0.785058i	$0.712633\pi$
$62$		0			0
$63$	−35344.7	−	35344.7i	−0.141352	−	0.141352i
$64$		0			0
$65$	354991.	−	48982.0i	1.29264	−	0.178360i
$66$		0			0
$67$	304343.	−	304343.i	1.01190	−	1.01190i	0.0119749	−	0.999928i	$-0.496188\pi$
$67$	304343.	−	304343.i	1.01190	−	1.01190i	0.999928	−	0.0119749i	$-0.00381184\pi$
$68$		0			0
$69$		−	299331.i		−	0.911182i
$70$		0			0
$71$	288398.			0.805780			0.402890	−	0.915248i	$-0.368006\pi$
$71$	288398.			0.805780			0.402890	+	0.915248i	$0.368006\pi$
$72$		0			0
$73$	−487894.	−	487894.i	−1.25417	−	1.25417i	−0.953833	−	0.300338i	$-0.902900\pi$
$73$	−487894.	−	487894.i	−1.25417	−	1.25417i	−0.300338	−	0.953833i	$-0.597100\pi$
$74$		0			0
$75$	−119153.	+	212435.i	−0.282437	+	0.503550i
$76$		0			0
$77$	150848.	−	150848.i	0.330422	−	0.330422i
$78$		0			0
$79$		−	222009.i		−	0.450286i	−0.974326	−	0.225143i	$-0.927715\pi$
$79$		−	222009.i		−	0.450286i	0.974326	−	0.225143i	$-0.0722850\pi$
$80$		0			0
$81$	−59049.0			−0.111111
$82$		0			0
$83$	−749160.	−	749160.i	−1.31021	−	1.31021i	−0.921260	−	0.388948i	$-0.872839\pi$
$83$	−749160.	−	749160.i	−1.31021	−	1.31021i	−0.388948	−	0.921260i	$-0.627161\pi$
$84$		0			0
$85$	−112853.	−	817885.i	−0.183762	−	1.33179i
$86$		0			0
$87$	−93453.1	+	93453.1i	−0.141917	+	0.141917i
$88$		0			0
$89$			689800.i			0.978482i	0.872149	+	0.489241i	$0.162726\pi$
$89$			689800.i			0.978482i	−0.872149	+	0.489241i	$0.837274\pi$
$90$		0			0
$91$	−589705.			−0.782548
$92$		0			0
$93$	188360.	+	188360.i	0.234175	+	0.234175i
$94$		0			0
$95$	−915626.	−	693585.i	−1.06794	−	0.808963i
$96$		0			0
$97$	820944.	−	820944.i	0.899494	−	0.899494i	−0.0958974	−	0.995391i	$-0.530572\pi$
$97$	820944.	−	820944.i	0.899494	−	0.899494i	0.995391	+	0.0958974i	$0.0305721\pi$
$98$		0			0
$99$		−	252017.i		−	0.259731i
$100$		0			0
$101$	−290048.			−0.281518			−0.140759	−	0.990044i	$-0.544954\pi$
$101$	−290048.			−0.281518			−0.140759	+	0.990044i	$0.544954\pi$
$102$		0			0
$103$	−291498.	−	291498.i	−0.266762	−	0.266762i	0.561032	−	0.827794i	$-0.310404\pi$
$103$	−291498.	−	291498.i	−0.266762	−	0.266762i	−0.827794	+	0.561032i	$0.810404\pi$
$104$		0			0
$105$	242021.	−	319500.i	0.209067	−	0.275996i
$106$		0			0
$107$	−792277.	+	792277.i	−0.646734	+	0.646734i	−0.952202	−	0.305468i	$-0.901187\pi$
$107$	−792277.	+	792277.i	−0.646734	+	0.646734i	0.305468	+	0.952202i	$0.401187\pi$
$108$		0			0
$109$			165909.i			0.128112i	0.997946	+	0.0640559i	$0.0204036\pi$
$109$			165909.i			0.128112i	−0.997946	+	0.0640559i	$0.979596\pi$
$110$		0			0
$111$	329717.			0.241086
$112$		0			0
$113$	−750389.	−	750389.i	−0.520057	−	0.520057i	0.397532	−	0.917589i	$-0.369867\pi$
$113$	−750389.	−	750389.i	−0.520057	−	0.520057i	−0.917589	+	0.397532i	$0.869867\pi$
$114$		0			0
$115$	2.37774e6	−	328083.i	1.56340	−	0.215720i
$116$		0			0
$117$	−492599.	+	492599.i	−0.307564	+	0.307564i
$118$		0			0
$119$			1.35866e6i			0.806250i
$120$		0			0
$121$	−695974.			−0.392859
$122$		0			0
$123$	−558720.	−	558720.i	−0.300247	−	0.300247i
$124$		0			0
$125$	−1.81808e6	−	713653.i	−0.930854	−	0.365390i
$126$		0			0
$127$	−583066.	+	583066.i	−0.284647	+	0.284647i	−0.834959	−	0.550312i	$-0.814509\pi$
$127$	−583066.	+	583066.i	−0.284647	+	0.284647i	0.550312	+	0.834959i	$0.314509\pi$
$128$		0			0
$129$		−	275272.i		−	0.128231i
$130$		0			0
$131$	4.18868e6			1.86321			0.931607	−	0.363466i	$-0.118407\pi$
$131$	4.18868e6			1.86321			0.931607	+	0.363466i	$0.118407\pi$
$132$		0			0
$133$	1.33660e6	+	1.33660e6i	0.568128	+	0.568128i
$134$		0			0
$135$	−64720.8	−	469055.i	−0.0263053	−	0.190644i
$136$		0			0
$137$	250638.	−	250638.i	0.0974731	−	0.0974731i	−0.656689	−	0.754162i	$-0.728043\pi$
$137$	250638.	−	250638.i	0.0974731	−	0.0974731i	0.754162	+	0.656689i	$0.228043\pi$
$138$		0			0
$139$		−	4.91265e6i		−	1.82924i	−0.404309	−	0.914622i	$-0.632488\pi$
$139$		−	4.91265e6i		−	1.82924i	0.404309	−	0.914622i	$-0.367512\pi$
$140$		0			0
$141$	−568497.			−0.202801
$142$		0			0
$143$	−2.10237e6	−	2.10237e6i	−0.718956	−	0.718956i
$144$		0			0
$145$	−844774.	−	639914.i	−0.277100	−	0.209903i
$146$		0			0
$147$	830415.	−	830415.i	0.261423	−	0.261423i
$148$		0			0
$149$		−	3.77991e6i		−	1.14268i	−0.820715	−	0.571338i	$-0.806425\pi$
$149$		−	3.77991e6i		−	1.14268i	0.820715	−	0.571338i	$-0.193575\pi$
$150$		0			0
$151$	−1.19813e6			−0.347996			−0.173998	−	0.984746i	$-0.555669\pi$
$151$	−1.19813e6			−0.347996			−0.173998	+	0.984746i	$0.555669\pi$
$152$		0			0
$153$	1.13493e6	+	1.13493e6i	0.316880	+	0.316880i
$154$		0			0
$155$	−1.28979e6	+	1.70269e6i	−0.346356	+	0.457236i
$156$		0			0
$157$	2.93950e6	−	2.93950e6i	0.759582	−	0.759582i	−0.216664	−	0.976246i	$-0.569518\pi$
$157$	2.93950e6	−	2.93950e6i	0.759582	−	0.759582i	0.976246	+	0.216664i	$0.0695176\pi$
$158$		0			0
$159$			3.67385e6i			0.913966i
$160$		0			0
$161$	−3.94986e6			−0.946465
$162$		0			0
$163$	−3.63502e6	−	3.63502e6i	−0.839351	−	0.839351i	0.149422	−	0.988774i	$-0.452259\pi$
$163$	−3.63502e6	−	3.63502e6i	−0.839351	−	0.839351i	−0.988774	+	0.149422i	$0.952259\pi$
$164$		0			0
$165$	2.00189e6	−	276223.i	0.445645	−	0.0614906i
$166$		0			0
$167$	738364.	−	738364.i	0.158533	−	0.158533i	−0.623383	−	0.781917i	$-0.714242\pi$
$167$	738364.	−	738364.i	0.158533	−	0.158533i	0.781917	+	0.623383i	$0.214242\pi$
$168$		0			0
$169$			3.39192e6i			0.702725i
$170$		0			0
$171$	2.23300e6			0.446582
$172$		0			0
$173$	5.01441e6	+	5.01441e6i	0.968459	+	0.968459i	0.999518	−	0.0310584i	$-0.00988779\pi$
$173$	5.01441e6	+	5.01441e6i	0.968459	+	0.968459i	−0.0310584	+	0.999518i	$0.509888\pi$
$174$		0			0
$175$	2.80321e6	+	1.57230e6i	0.523048	+	0.293374i
$176$		0			0
$177$	−2.72468e6	+	2.72468e6i	−0.491355	+	0.491355i
$178$		0			0
$179$			7.77058e6i			1.35486i	0.735587	+	0.677430i	$0.236906\pi$
$179$			7.77058e6i			1.35486i	−0.735587	+	0.677430i	$0.763094\pi$
$180$		0			0
$181$	6.98198e6			1.17745			0.588726	−	0.808333i	$-0.299630\pi$
$181$	6.98198e6			1.17745			0.588726	+	0.808333i	$0.299630\pi$
$182$		0			0
$183$	3.09952e6	+	3.09952e6i	0.505756	+	0.505756i
$184$		0			0
$185$	361387.	+	2.61911e6i	0.0570766	+	0.413655i
$186$		0			0
$187$	−4.84379e6	+	4.84379e6i	−0.740732	+	0.740732i
$188$		0			0
$189$			779188.i			0.115414i
$190$		0			0
$191$	−1.75621e6			−0.252044			−0.126022	−	0.992027i	$-0.540221\pi$
$191$	−1.75621e6			−0.252044			−0.126022	+	0.992027i	$0.540221\pi$
$192$		0			0
$193$	−8.48929e6	−	8.48929e6i	−1.18086	−	1.18086i	−0.979521	−	0.201343i	$-0.935470\pi$
$193$	−8.48929e6	−	8.48929e6i	−1.18086	−	1.18086i	−0.201343	−	0.979521i	$-0.564530\pi$
$194$		0			0
$195$	−4.45287e6	−	3.37304e6i	−0.600532	−	0.454902i
$196$		0			0
$197$	−7.08383e6	+	7.08383e6i	−0.926552	+	0.926552i	−0.997481	−	0.0709298i	$-0.977403\pi$
$197$	−7.08383e6	+	7.08383e6i	−0.926552	+	0.926552i	0.0709298	+	0.997481i	$0.477403\pi$
$198$		0			0
$199$		−	2.34311e6i		−	0.297326i	−0.988888	−	0.148663i	$-0.952503\pi$
$199$		−	2.34311e6i		−	0.297326i	0.988888	−	0.148663i	$-0.0474970\pi$
$200$		0			0
$201$	−6.70937e6			−0.826216
$202$		0			0
$203$	1.23317e6	+	1.23317e6i	0.147413	+	0.147413i
$204$		0			0
$205$	3.82580e6	−	5.05058e6i	0.444080	−	0.586245i
$206$		0			0
$207$	−3.29944e6	+	3.29944e6i	−0.371988	+	0.371988i
$208$		0			0
$209$			9.53029e6i			1.04392i
$210$		0			0
$211$	4.10418e6			0.436897			0.218448	−	0.975848i	$-0.429900\pi$
$211$	4.10418e6			0.436897			0.218448	+	0.975848i	$0.429900\pi$
$212$		0			0
$213$	−3.17892e6	−	3.17892e6i	−0.328958	−	0.328958i
$214$		0			0
$215$	2.18662e6	−	301712.i	0.220018	−	0.0303583i
$216$		0			0
$217$	2.48553e6	−	2.48553e6i	0.243243	−	0.243243i
$218$		0			0
$219$			1.07558e7i			1.02403i
$220$		0			0
$221$	1.89356e7			1.75430
$222$		0			0
$223$	9.84643e6	+	9.84643e6i	0.887901	+	0.887901i	0.994321	−	0.106421i	$-0.0339390\pi$
$223$	9.84643e6	+	9.84643e6i	0.887901	+	0.887901i	−0.106421	+	0.994321i	$0.533939\pi$
$224$		0			0
$225$	3.65500e6	−	1.02822e6i	0.320878	−	0.0902689i
$226$		0			0
$227$	−447932.	+	447932.i	−0.0382943	+	0.0382943i	−0.725995	−	0.687700i	$-0.758620\pi$
$227$	−447932.	+	447932.i	−0.0382943	+	0.0382943i	0.687700	+	0.725995i	$0.258620\pi$
$228$		0			0
$229$			2.13385e7i			1.77688i	0.458991	+	0.888441i	$0.348211\pi$
$229$			2.13385e7i			1.77688i	−0.458991	+	0.888441i	$0.651789\pi$
$230$		0			0
$231$	−3.32551e6			−0.269788
$232$		0			0
$233$	1.19508e6	+	1.19508e6i	0.0944775	+	0.0944775i	0.752766	−	0.658288i	$-0.228719\pi$
$233$	1.19508e6	+	1.19508e6i	0.0944775	+	0.0944775i	−0.658288	+	0.752766i	$0.728719\pi$
$234$		0			0
$235$	−623103.	−	4.51586e6i	−0.0480127	−	0.347966i
$236$		0			0
$237$	−2.44714e6	+	2.44714e6i	−0.183829	+	0.183829i
$238$		0			0
$239$			2.07007e6i			0.151632i	0.997122	+	0.0758160i	$0.0241562\pi$
$239$			2.07007e6i			0.151632i	−0.997122	+	0.0758160i	$0.975844\pi$
$240$		0			0
$241$	2.35841e7			1.68487			0.842437	−	0.538795i	$-0.181120\pi$
$241$	2.35841e7			1.68487			0.842437	+	0.538795i	$0.181120\pi$
$242$		0			0
$243$	650880.	+	650880.i	0.0453609	+	0.0453609i
$244$		0			0
$245$	7.50658e6	+	5.68622e6i	0.510439	+	0.386656i
$246$		0			0
$247$	1.86282e7	−	1.86282e7i	1.23617	−	1.23617i
$248$		0			0
$249$			1.65155e7i			1.06978i
$250$		0			0
$251$	8.83541e6			0.558734			0.279367	−	0.960184i	$-0.409875\pi$
$251$	8.83541e6			0.558734			0.279367	+	0.960184i	$0.409875\pi$
$252$		0			0
$253$	−1.40818e7	−	1.40818e7i	−0.869552	−	0.869552i
$254$		0			0
$255$	−7.77137e6	+	1.02593e7i	−0.468680	+	0.618721i
$256$		0			0
$257$	−6.09969e6	+	6.09969e6i	−0.359342	+	0.359342i	−0.863570	−	0.504228i	$-0.831777\pi$
$257$	−6.09969e6	+	6.09969e6i	−0.359342	+	0.359342i	0.504228	+	0.863570i	$0.331777\pi$
$258$		0			0
$259$		−	4.35082e6i		−	0.250422i
$260$		0			0
$261$	2.06021e6			0.115875
$262$		0			0
$263$	4.35686e6	+	4.35686e6i	0.239500	+	0.239500i	0.816643	−	0.577143i	$-0.195832\pi$
$263$	4.35686e6	+	4.35686e6i	0.239500	+	0.239500i	−0.577143	+	0.816643i	$0.695832\pi$
$264$		0			0
$265$	−2.91832e7	+	4.02673e6i	−1.56818	+	0.216379i
$266$		0			0
$267$	7.60346e6	−	7.60346e6i	0.399464	−	0.399464i
$268$		0			0
$269$		−	1.36102e7i		−	0.699208i	−0.936898	−	0.349604i	$-0.886316\pi$
$269$		−	1.36102e7i		−	0.699208i	0.936898	−	0.349604i	$-0.113684\pi$
$270$		0			0
$271$	8.20889e6			0.412455			0.206228	−	0.978504i	$-0.433881\pi$
$271$	8.20889e6			0.412455			0.206228	+	0.978504i	$0.433881\pi$
$272$		0			0
$273$	6.50015e6	+	6.50015e6i	0.319474	+	0.319474i
$274$		0			0
$275$	4.38836e6	+	1.55993e7i	0.211010	+	0.750077i
$276$		0			0
$277$	2.56480e7	−	2.56480e7i	1.20674	−	1.20674i	0.234665	−	0.972076i	$-0.424601\pi$
$277$	2.56480e7	−	2.56480e7i	1.20674	−	1.20674i	0.972076	−	0.234665i	$-0.0753995\pi$
$278$		0			0
$279$		−	4.15248e6i		−	0.191203i
$280$		0			0
$281$	−2.47592e7			−1.11588			−0.557940	−	0.829881i	$-0.688408\pi$
$281$	−2.47592e7			−1.11588			−0.557940	+	0.829881i	$0.688408\pi$
$282$		0			0
$283$	1.00351e7	+	1.00351e7i	0.442753	+	0.442753i	0.892936	−	0.450183i	$-0.148641\pi$
$283$	1.00351e7	+	1.00351e7i	0.442753	+	0.442753i	−0.450183	+	0.892936i	$0.648641\pi$
$284$		0			0
$285$	2.44749e6	+	1.77379e7i	0.105727	+	0.766243i
$286$		0			0
$287$	−7.37266e6	+	7.37266e6i	−0.311873	+	0.311873i
$288$		0			0
$289$		−	1.94895e7i		−	0.807433i
$290$		0			0
$291$	−1.80980e7			−0.734434
$292$		0			0
$293$	1.88230e6	+	1.88230e6i	0.0748319	+	0.0748319i	0.743532	−	0.668700i	$-0.233149\pi$
$293$	1.88230e6	+	1.88230e6i	0.0748319	+	0.0748319i	−0.668700	+	0.743532i	$0.733149\pi$
$294$		0			0
$295$	−2.46299e7	−	1.86571e7i	−0.959392	−	0.726737i
$296$		0			0
$297$	−2.77790e6	+	2.77790e6i	−0.106035	+	0.106035i
$298$		0			0
$299$			5.50493e7i			2.05939i
$300$		0			0
$301$	−3.63238e6			−0.133196
$302$		0			0
$303$	3.19712e6	+	3.19712e6i	0.114929	+	0.114929i
$304$		0			0
$305$	−2.12238e7	+	2.80183e7i	−0.748037	+	0.987510i
$306$		0			0
$307$	3.23684e7	−	3.23684e7i	1.11868	−	1.11868i	0.126747	−	0.991935i	$-0.459547\pi$
$307$	3.23684e7	−	3.23684e7i	1.11868	−	1.11868i	0.991935	−	0.126747i	$-0.0404535\pi$
$308$		0			0
$309$			6.42620e6i			0.217810i
$310$		0			0
$311$	−1.96913e7			−0.654625			−0.327313	−	0.944916i	$-0.606143\pi$
$311$	−1.96913e7			−0.654625			−0.327313	+	0.944916i	$0.606143\pi$
$312$		0			0
$313$	1.21275e7	+	1.21275e7i	0.395493	+	0.395493i	0.876640	−	0.481147i	$-0.159780\pi$
$313$	1.21275e7	+	1.21275e7i	0.395493	+	0.395493i	−0.481147	+	0.876640i	$0.659780\pi$
$314$		0			0
$315$	−6.18947e6	+	854031.i	−0.198026	+	0.0273239i
$316$		0			0
$317$	2.36698e7	−	2.36698e7i	0.743048	−	0.743048i	−0.230116	−	0.973163i	$-0.573910\pi$
$317$	2.36698e7	−	2.36698e7i	0.743048	−	0.743048i	0.973163	+	0.230116i	$0.0739104\pi$
$318$		0			0
$319$			8.79282e6i			0.270867i
$320$		0			0
$321$	1.74661e7			0.528056
$322$		0			0
$323$	−4.29187e7	−	4.29187e7i	−1.27362	−	1.27362i
$324$		0			0
$325$	2.19132e7	−	3.90684e7i	0.638344	−	1.13809i
$326$		0			0
$327$	1.82876e6	−	1.82876e6i	0.0523014	−	0.0523014i
$328$		0			0
$329$			7.50167e6i			0.210654i
$330$		0			0
$331$	−3.78781e7			−1.04449			−0.522245	−	0.852796i	$-0.674905\pi$
$331$	−3.78781e7			−1.04449			−0.522245	+	0.852796i	$0.674905\pi$
$332$		0			0
$333$	−3.63438e6	−	3.63438e6i	−0.0984231	−	0.0984231i
$334$		0			0
$335$	−7.35382e6	−	5.32958e7i	−0.195604	−	1.41762i
$336$		0			0
$337$	−2.24435e7	+	2.24435e7i	−0.586411	+	0.586411i	−0.936657	−	0.350247i	$-0.886098\pi$
$337$	−2.24435e7	+	2.24435e7i	−0.586411	+	0.586411i	0.350247	+	0.936657i	$0.386098\pi$
$338$		0			0
$339$			1.65426e7i			0.424625i
$340$		0			0
$341$	1.77225e7			0.446952
$342$		0			0
$343$	−2.80701e7	−	2.80701e7i	−0.695602	−	0.695602i
$344$		0			0
$345$	−2.98255e7	−	2.25927e7i	−0.726323	−	0.550188i
$346$		0			0
$347$	−3.01955e7	+	3.01955e7i	−0.722692	+	0.722692i	−0.969153	−	0.246461i	$-0.920732\pi$
$347$	−3.01955e7	+	3.01955e7i	−0.722692	+	0.722692i	0.246461	+	0.969153i	$0.420732\pi$
$348$		0			0
$349$		−	7.82272e7i		−	1.84027i	−0.391600	−	0.920135i	$-0.628078\pi$
$349$		−	7.82272e7i		−	1.84027i	0.391600	−	0.920135i	$-0.371922\pi$
$350$		0			0
$351$	1.08595e7			0.251125
$352$		0			0
$353$	−9.45650e6	−	9.45650e6i	−0.214984	−	0.214984i	0.591397	−	0.806381i	$-0.298577\pi$
$353$	−9.45650e6	−	9.45650e6i	−0.214984	−	0.214984i	−0.806381	+	0.591397i	$0.798577\pi$
$354$		0			0
$355$	2.17675e7	−	2.87360e7i	0.486545	−	0.642305i
$356$		0			0
$357$	1.49761e7	−	1.49761e7i	0.329150	−	0.329150i
$358$		0			0
$359$		−	2.13996e7i		−	0.462511i	−0.972893	−	0.231256i	$-0.925717\pi$
$359$		−	2.13996e7i		−	0.462511i	0.972893	−	0.231256i	$-0.0742834\pi$
$360$		0			0
$361$	−3.73977e7			−0.794919
$362$		0			0
$363$	7.67151e6	+	7.67151e6i	0.160384	+	0.160384i
$364$		0			0
$365$	−8.54388e7	+	1.17889e7i	−1.75702	+	0.242436i
$366$		0			0
$367$	1.29658e7	−	1.29658e7i	0.262302	−	0.262302i	−0.563687	−	0.825989i	$-0.690617\pi$
$367$	1.29658e7	−	1.29658e7i	0.262302	−	0.262302i	0.825989	+	0.563687i	$0.190617\pi$
$368$		0			0
$369$			1.23172e7i			0.245151i
$370$		0			0
$371$	4.84787e7			0.949356
$372$		0			0
$373$	3.92352e6	+	3.92352e6i	0.0756048	+	0.0756048i	0.743898	−	0.668293i	$-0.232975\pi$
$373$	3.92352e6	+	3.92352e6i	0.0756048	+	0.0756048i	−0.668293	+	0.743898i	$0.732975\pi$
$374$		0			0
$375$	1.21737e7	+	2.79065e7i	0.230850	+	0.529190i
$376$		0			0
$377$	1.71867e7	−	1.71867e7i	0.320752	−	0.320752i
$378$		0			0
$379$		−	3.61170e7i		−	0.663429i	−0.943380	−	0.331714i	$-0.892373\pi$
$379$		−	3.61170e7i		−	0.663429i	0.943380	−	0.331714i	$-0.107627\pi$
$380$		0			0
$381$	1.28539e7			0.232413
$382$		0			0
$383$	774461.	+	774461.i	0.0137849	+	0.0137849i	0.713966	−	0.700181i	$-0.246897\pi$
$383$	774461.	+	774461.i	0.0137849	+	0.0137849i	−0.700181	+	0.713966i	$0.746897\pi$
$384$		0			0
$385$	−3.64494e6	−	2.64162e7i	−0.0638716	−	0.462901i
$386$		0			0
$387$	−3.03424e6	+	3.03424e6i	−0.0523500	+	0.0523500i
$388$		0			0
$389$			4.56599e7i			0.775686i	0.921726	+	0.387843i	$0.126780\pi$
$389$			4.56599e7i			0.775686i	−0.921726	+	0.387843i	$0.873220\pi$
$390$		0			0
$391$	1.26831e8			2.12176
$392$		0			0
$393$	−4.61705e7	−	4.61705e7i	−0.760654	−	0.760654i
$394$		0			0
$395$	−2.21210e7	−	1.67566e7i	−0.358933	−	0.271891i
$396$		0			0
$397$	5.08606e7	−	5.08606e7i	0.812849	−	0.812849i	−0.172211	−	0.985060i	$-0.555091\pi$
$397$	5.08606e7	−	5.08606e7i	0.812849	−	0.812849i	0.985060	+	0.172211i	$0.0550912\pi$
$398$		0			0
$399$		−	2.94659e7i		−	0.463875i
$400$		0			0
$401$	−3.46994e7			−0.538133			−0.269066	−	0.963122i	$-0.586715\pi$
$401$	−3.46994e7			−0.538133			−0.269066	+	0.963122i	$0.586715\pi$
$402$		0			0
$403$	−3.46408e7	−	3.46408e7i	−0.529265	−	0.529265i
$404$		0			0
$405$	−4.45686e6	+	5.88366e6i	−0.0670909	+	0.0885691i
$406$		0			0
$407$	1.55112e7	−	1.55112e7i	0.230072	−	0.230072i
$408$		0			0
$409$			6.63216e6i			0.0969360i	0.998825	+	0.0484680i	$0.0154339\pi$
$409$			6.63216e6i			0.0969360i	−0.998825	+	0.0484680i	$0.984566\pi$
$410$		0			0
$411$	−5.52541e6			−0.0795865
$412$		0			0
$413$	3.59538e7	+	3.59538e7i	0.510382	+	0.510382i
$414$		0			0
$415$	−1.31191e8	+	1.81019e7i	−1.83552	+	0.253268i
$416$		0			0
$417$	−5.41507e7	+	5.41507e7i	−0.746786	+	0.746786i
$418$		0			0
$419$		−	1.87567e7i		−	0.254985i	−0.991840	−	0.127493i	$-0.959307\pi$
$419$		−	1.87567e7i		−	0.254985i	0.991840	−	0.127493i	$-0.0406929\pi$
$420$		0			0
$421$	1.01392e8			1.35881			0.679406	−	0.733762i	$-0.262237\pi$
$421$	1.01392e8			1.35881			0.679406	+	0.733762i	$0.262237\pi$
$422$		0			0
$423$	6.26638e6	+	6.26638e6i	0.0827934	+	0.0827934i
$424$		0			0
$425$	−9.00121e7	−	5.04871e7i	−1.17256	−	0.657679i
$426$		0			0
$427$	4.09001e7	−	4.09001e7i	0.525340	−	0.525340i
$428$		0			0
$429$			4.63477e7i			0.587025i
$430$		0			0
$431$	2.54338e7			0.317672			0.158836	−	0.987305i	$-0.449226\pi$
$431$	2.54338e7			0.317672			0.158836	+	0.987305i	$0.449226\pi$
$432$		0			0
$433$	−4.84883e7	−	4.84883e7i	−0.597273	−	0.597273i	0.342313	−	0.939586i	$-0.388790\pi$
$433$	−4.84883e7	−	4.84883e7i	−0.597273	−	0.597273i	−0.939586	+	0.342313i	$0.888790\pi$
$434$		0			0
$435$	2.25810e6	+	1.63653e7i	0.0274331	+	0.198818i
$436$		0			0
$437$	1.24772e8	−	1.24772e8i	1.49511	−	1.49511i
$438$		0			0
$439$			3.77933e7i			0.446706i	0.974738	+	0.223353i	$0.0717002\pi$
$439$			3.77933e7i			0.446706i	−0.974738	+	0.223353i	$0.928300\pi$
$440$		0			0
$441$	−1.83068e7			−0.213451
$442$		0			0
$443$	2.16224e7	+	2.16224e7i	0.248710	+	0.248710i	0.820441	−	0.571731i	$-0.193728\pi$
$443$	2.16224e7	+	2.16224e7i	0.248710	+	0.248710i	−0.571731	+	0.820441i	$0.693728\pi$
$444$		0			0
$445$	6.87318e7	+	5.20642e7i	0.779970	+	0.590826i
$446$		0			0
$447$	−4.16648e7	+	4.16648e7i	−0.466495	+	0.466495i
$448$		0			0
$449$			9.43557e7i			1.04239i	0.853439	+	0.521193i	$0.174513\pi$
$449$			9.43557e7i			1.04239i	−0.853439	+	0.521193i	$0.825487\pi$
$450$		0			0
$451$	−5.25689e7			−0.573059
$452$		0			0
$453$	1.32067e7	+	1.32067e7i	0.142069	+	0.142069i
$454$		0			0
$455$	−4.45094e7	+	5.87584e7i	−0.472517	+	0.623786i
$456$		0			0
$457$	−3.23415e7	+	3.23415e7i	−0.338853	+	0.338853i	−0.855936	−	0.517083i	$-0.827018\pi$
$457$	−3.23415e7	+	3.23415e7i	−0.338853	+	0.338853i	0.517083	+	0.855936i	$0.327018\pi$
$458$		0			0
$459$		−	2.50200e7i		−	0.258731i
$460$		0			0
$461$	8.77131e7			0.895286			0.447643	−	0.894212i	$-0.352264\pi$
$461$	8.77131e7			0.895286			0.447643	+	0.894212i	$0.352264\pi$
$462$		0			0
$463$	−4.91700e7	−	4.91700e7i	−0.495402	−	0.495402i	0.414601	−	0.910003i	$-0.363921\pi$
$463$	−4.91700e7	−	4.91700e7i	−0.495402	−	0.495402i	−0.910003	+	0.414601i	$0.863921\pi$
$464$		0			0
$465$	3.29852e7	−	4.55133e6i	0.328065	−	0.0452668i
$466$		0			0
$467$	9.52295e7	−	9.52295e7i	0.935020	−	0.935020i	−0.0629938	−	0.998014i	$-0.520065\pi$
$467$	9.52295e7	−	9.52295e7i	0.935020	−	0.935020i	0.998014	+	0.0629938i	$0.0200648\pi$
$468$		0			0
$469$			8.85342e7i			0.858208i
$470$		0			0
$471$	−6.48025e7			−0.620196
$472$		0			0
$473$	−1.29499e7	−	1.29499e7i	−0.122372	−	0.122372i
$474$		0			0
$475$	−1.38218e8	+	3.88832e7i	−1.28968	+	0.362812i
$476$		0			0
$477$	4.04958e7	−	4.04958e7i	0.373125	−	0.373125i
$478$		0			0
$479$			2.04024e8i			1.85642i	0.372062	+	0.928208i	$0.378651\pi$
$479$			2.04024e8i			1.85642i	−0.372062	+	0.928208i	$0.621349\pi$
$480$		0			0
$481$	−6.06374e7			−0.544886
$482$		0			0
$483$	4.35382e7	+	4.35382e7i	0.386393	+	0.386393i
$484$		0			0
$485$	−1.98364e7	−	1.43762e8i	−0.173875	−	1.26014i
$486$		0			0
$487$	1.00420e8	−	1.00420e8i	0.869424	−	0.869424i	−0.122984	−	0.992409i	$-0.539247\pi$
$487$	1.00420e8	−	1.00420e8i	0.869424	−	0.869424i	0.992409	+	0.122984i	$0.0392465\pi$
$488$		0			0
$489$			8.01355e7i			0.685328i
$490$		0			0
$491$	7.28010e7			0.615025			0.307512	−	0.951544i	$-0.400503\pi$
$491$	7.28010e7			0.615025			0.307512	+	0.951544i	$0.400503\pi$
$492$		0			0
$493$	−3.95976e7	−	3.95976e7i	−0.330467	−	0.330467i
$494$		0			0
$495$	−2.51110e7	−	1.90215e7i	−0.207037	−	0.156830i
$496$		0			0
$497$	−4.19478e7	+	4.19478e7i	−0.341696	+	0.341696i
$498$		0			0
$499$			1.79824e8i			1.44726i	0.690188	+	0.723630i	$0.257528\pi$
$499$			1.79824e8i			1.44726i	−0.690188	+	0.723630i	$0.742472\pi$
$500$		0			0
$501$	−1.62775e7			−0.129442
$502$		0			0
$503$	5.58642e7	+	5.58642e7i	0.438965	+	0.438965i	0.891664	−	0.452699i	$-0.149539\pi$
$503$	5.58642e7	+	5.58642e7i	0.438965	+	0.438965i	−0.452699	+	0.891664i	$0.649539\pi$
$504$		0			0
$505$	−2.18921e7	+	2.89005e7i	−0.169986	+	0.224404i
$506$		0			0
$507$	3.73881e7	−	3.73881e7i	0.286886	−	0.286886i
$508$		0			0
$509$			2.14366e6i			0.0162556i	0.999967	+	0.00812779i	$0.00258718\pi$
$509$			2.14366e6i			0.0162556i	−0.999967	+	0.00812779i	$0.997413\pi$
$510$		0			0
$511$	1.41930e8			1.06368
$512$		0			0
$513$	−2.46137e7	−	2.46137e7i	−0.182316	−	0.182316i
$514$		0			0
$515$	−5.10465e7	+	7.04345e6i	−0.373718	+	0.0515661i
$516$		0			0
$517$	−2.67444e7	+	2.67444e7i	−0.193536	+	0.193536i
$518$		0			0
$519$		−	1.10545e8i		−	0.790744i
$520$		0			0
$521$	−5.06571e7			−0.358201			−0.179101	−	0.983831i	$-0.557319\pi$
$521$	−5.06571e7			−0.358201			−0.179101	+	0.983831i	$0.557319\pi$
$522$		0			0
$523$	1.58594e7	+	1.58594e7i	0.110862	+	0.110862i	0.760362	−	0.649500i	$-0.225022\pi$
$523$	1.58594e7	+	1.58594e7i	0.110862	+	0.110862i	−0.649500	+	0.760362i	$0.725022\pi$
$524$		0			0
$525$	−1.35680e7	−	4.82300e7i	−0.0937643	−	0.333303i
$526$		0			0
$527$	−7.98112e7	+	7.98112e7i	−0.545296	+	0.545296i
$528$		0			0
$529$			2.20686e8i			1.49076i
$530$		0			0
$531$	6.00667e7			0.401190
$532$		0			0
$533$	1.02753e8	+	1.02753e8i	0.678597	+	0.678597i
$534$		0			0
$535$	1.91437e7	+	1.38742e8i	0.125016	+	0.906036i
$536$		0			0
$537$	8.56528e7	−	8.56528e7i	0.553119	−	0.553119i
$538$		0			0
$539$		−	7.81322e7i		−	0.498958i
$540$		0			0
$541$	4.43541e7			0.280119			0.140059	−	0.990143i	$-0.455271\pi$
$541$	4.43541e7			0.280119			0.140059	+	0.990143i	$0.455271\pi$
$542$		0			0
$543$	−7.69603e7	−	7.69603e7i	−0.480692	−	0.480692i
$544$		0			0
$545$	1.65312e7	+	1.25223e7i	0.102121	+	0.0773563i
$546$		0			0
$547$	−1.89599e7	+	1.89599e7i	−0.115844	+	0.115844i	−0.762653	−	0.646808i	$-0.776103\pi$
$547$	−1.89599e7	+	1.89599e7i	−0.115844	+	0.115844i	0.646808	+	0.762653i	$0.276103\pi$
$548$		0			0
$549$		−	6.83302e7i		−	0.412948i
$550$		0			0
$551$	−7.79092e7			−0.465730
$552$		0			0
$553$	3.22915e7	+	3.22915e7i	0.190947	+	0.190947i
$554$		0			0
$555$	2.48862e7	−	3.28531e7i	0.145572	−	0.192175i
$556$		0			0
$557$	−1.03290e8	+	1.03290e8i	−0.597712	+	0.597712i	−0.939703	−	0.341991i	$-0.888899\pi$
$557$	−1.03290e8	+	1.03290e8i	−0.597712	+	0.597712i	0.341991	+	0.939703i	$0.388899\pi$
$558$		0			0
$559$			5.06245e7i			0.289818i
$560$		0			0
$561$	1.06783e8			0.604805
$562$		0			0
$563$	−1.84599e8	−	1.84599e8i	−1.03444	−	1.03444i	−0.999385	−	0.0350521i	$-0.988840\pi$
$563$	−1.84599e8	−	1.84599e8i	−1.03444	−	1.03444i	−0.0350521	−	0.999385i	$-0.511160\pi$
$564$		0			0
$565$	−1.31406e8	+	1.81316e7i	−0.728569	+	0.100529i
$566$		0			0
$567$	8.58876e6	−	8.58876e6i	0.0471174	−	0.0471174i
$568$		0			0
$569$			9.69662e7i			0.526361i	0.964747	+	0.263180i	$0.0847715\pi$
$569$			9.69662e7i			0.526361i	−0.964747	+	0.263180i	$0.915229\pi$
$570$		0			0
$571$	8.24057e7			0.442638			0.221319	−	0.975201i	$-0.428964\pi$
$571$	8.24057e7			0.442638			0.221319	+	0.975201i	$0.428964\pi$
$572$		0			0
$573$	1.93582e7	+	1.93582e7i	0.102897	+	0.102897i
$574$		0			0
$575$	1.46775e8	−	2.61681e8i	0.772055	−	1.37648i
$576$		0			0
$577$	1.75260e8	−	1.75260e8i	0.912336	−	0.912336i	−0.0841201	−	0.996456i	$-0.526808\pi$
$577$	1.75260e8	−	1.75260e8i	0.912336	−	0.912336i	0.996456	+	0.0841201i	$0.0268079\pi$
$578$		0			0
$579$			1.87150e8i			0.964171i
$580$		0			0
$581$	2.17933e8			1.11120
$582$		0			0
$583$	1.72833e8	+	1.72833e8i	0.872209	+	0.872209i
$584$		0			0
$585$	1.19026e7	+	8.62627e7i	0.0594532	+	0.430879i
$586$		0			0
$587$	5.98432e7	−	5.98432e7i	0.295870	−	0.295870i	−0.543524	−	0.839394i	$-0.682910\pi$
$587$	5.98432e7	−	5.98432e7i	0.295870	−	0.295870i	0.839394	+	0.543524i	$0.182910\pi$
$588$		0			0
$589$			1.57031e8i			0.768490i
$590$		0			0
$591$	1.56166e8			0.756526
$592$		0			0
$593$	7.10812e7	+	7.10812e7i	0.340872	+	0.340872i	0.856695	−	0.515823i	$-0.172514\pi$
$593$	7.10812e7	+	7.10812e7i	0.340872	+	0.340872i	−0.515823	+	0.856695i	$0.672514\pi$
$594$		0			0
$595$	1.35377e8	+	1.02548e8i	0.642680	+	0.486829i
$596$		0			0
$597$	−2.58274e7	+	2.58274e7i	−0.121383	+	0.121383i
$598$		0			0
$599$			1.93410e8i			0.899911i	0.893051	+	0.449955i	$0.148560\pi$
$599$			1.93410e8i			0.899911i	−0.893051	+	0.449955i	$0.851440\pi$
$600$		0			0
$601$	−2.04018e8			−0.939822			−0.469911	−	0.882714i	$-0.655714\pi$
$601$	−2.04018e8			−0.939822			−0.469911	+	0.882714i	$0.655714\pi$
$602$		0			0
$603$	7.39554e7	+	7.39554e7i	0.337301	+	0.337301i
$604$		0			0
$605$	−5.25302e7	+	6.93470e7i	−0.237215	+	0.313156i
$606$		0			0
$607$	−2.70178e8	+	2.70178e8i	−1.20805	+	1.20805i	−0.236388	+	0.971659i	$0.575964\pi$
$607$	−2.70178e8	+	2.70178e8i	−1.20805	+	1.20805i	−0.971659	+	0.236388i	$0.924036\pi$
$608$		0			0
$609$		−	2.71858e7i		−	0.120362i
$610$		0			0
$611$	1.04551e8			0.458357
$612$		0			0
$613$	−1.48040e8	−	1.48040e8i	−0.642685	−	0.642685i	0.308529	−	0.951215i	$-0.400163\pi$
$613$	−1.48040e8	−	1.48040e8i	−0.642685	−	0.642685i	−0.951215	+	0.308529i	$0.900163\pi$
$614$		0			0
$615$	−9.78417e7	+	1.35003e7i	−0.420628	+	0.0580388i
$616$		0			0
$617$	−3.46749e7	+	3.46749e7i	−0.147625	+	0.147625i	−0.777056	−	0.629431i	$-0.783288\pi$
$617$	−3.46749e7	+	3.46749e7i	−0.147625	+	0.147625i	0.629431	+	0.777056i	$0.283288\pi$
$618$		0			0
$619$			3.42044e8i			1.44215i	0.692858	+	0.721074i	$0.256351\pi$
$619$			3.42044e8i			1.44215i	−0.692858	+	0.721074i	$0.743649\pi$
$620$		0			0
$621$	7.27375e7			0.303727
$622$		0			0
$623$	−1.00332e8	−	1.00332e8i	−0.414932	−	0.414932i
$624$		0			0
$625$	−2.08332e8	+	1.27289e8i	−0.853328	+	0.521375i
$626$		0			0
$627$	1.05050e8	−	1.05050e8i	0.426179	−	0.426179i
$628$		0			0
$629$			1.39706e8i			0.561390i
$630$		0			0
$631$	−8.36979e7			−0.333140			−0.166570	−	0.986030i	$-0.553269\pi$
$631$	−8.36979e7			−0.333140			−0.166570	+	0.986030i	$0.553269\pi$
$632$		0			0
$633$	−4.52391e7	−	4.52391e7i	−0.178362	−	0.178362i
$634$		0			0
$635$	1.40886e7	+	1.02105e8i	0.0550233	+	0.398774i
$636$		0			0
$637$	−1.52719e8	+	1.52719e8i	−0.590848	+	0.590848i
$638$		0			0
$639$			7.00806e7i			0.268593i
$640$		0			0
$641$	1.80537e8			0.685475			0.342737	−	0.939431i	$-0.388646\pi$
$641$	1.80537e8			0.685475			0.342737	+	0.939431i	$0.388646\pi$
$642$		0			0
$643$	−2.11026e8	−	2.11026e8i	−0.793784	−	0.793784i	0.188324	−	0.982107i	$-0.439695\pi$
$643$	−2.11026e8	−	2.11026e8i	−0.793784	−	0.793784i	−0.982107	+	0.188324i	$0.939695\pi$
$644$		0			0
$645$	−2.74281e7	−	2.07768e7i	−0.102216	−	0.0774281i
$646$		0			0
$647$	−1.30845e8	+	1.30845e8i	−0.483109	+	0.483109i	−0.906123	−	0.423014i	$-0.860972\pi$
$647$	−1.30845e8	+	1.30845e8i	−0.483109	+	0.483109i	0.423014	+	0.906123i	$0.360972\pi$
$648$		0			0
$649$			2.56360e8i			0.937812i
$650$		0			0
$651$	−5.47945e7			−0.198607
$652$		0			0
$653$	−3.15489e8	−	3.15489e8i	−1.13304	−	1.13304i	−0.989669	−	0.143371i	$-0.954206\pi$
$653$	−3.15489e8	−	3.15489e8i	−1.13304	−	1.13304i	−0.143371	−	0.989669i	$-0.545794\pi$
$654$		0			0
$655$	3.16150e8	−	4.17361e8i	1.12504	−	1.48521i
$656$		0			0
$657$	1.18558e8	−	1.18558e8i	0.418057	−	0.418057i
$658$		0			0
$659$			1.90964e8i			0.667260i	0.942704	+	0.333630i	$0.108274\pi$
$659$			1.90964e8i			0.667260i	−0.942704	+	0.333630i	$0.891726\pi$
$660$		0			0
$661$	4.57014e8			1.58243			0.791216	−	0.611536i	$-0.209448\pi$
$661$	4.57014e8			1.58243			0.791216	+	0.611536i	$0.209448\pi$
$662$		0			0
$663$	−2.08722e8	−	2.08722e8i	−0.716189	−	0.716189i
$664$		0			0
$665$	2.34062e8	−	3.22961e7i	0.795913	−	0.109821i
$666$		0			0
$667$	1.15117e8	−	1.15117e8i	0.387938	−	0.387938i
$668$		0			0
$669$		−	2.17069e8i		−	0.724968i
$670$		0			0
$671$	2.91628e8			0.965299
$672$		0			0
$673$	2.86067e8	+	2.86067e8i	0.938474	+	0.938474i	0.998214	−	0.0597400i	$-0.0190272\pi$
$673$	2.86067e8	+	2.86067e8i	0.938474	+	0.938474i	−0.0597400	+	0.998214i	$0.519027\pi$
$674$		0			0
$675$	−5.16217e7	−	2.89542e7i	−0.167850	−	0.0941458i
$676$		0			0
$677$	2.60104e8	−	2.60104e8i	0.838266	−	0.838266i	−0.150365	−	0.988631i	$-0.548045\pi$
$677$	2.60104e8	−	2.60104e8i	0.838266	−	0.838266i	0.988631	+	0.150365i	$0.0480448\pi$
$678$		0			0
$679$			2.38815e8i			0.762872i
$680$		0			0
$681$	9.87483e6			0.0312672
$682$		0			0
$683$	9.24222e7	+	9.24222e7i	0.290078	+	0.290078i	0.837111	−	0.547033i	$-0.184243\pi$
$683$	9.24222e7	+	9.24222e7i	0.290078	+	0.290078i	−0.547033	+	0.837111i	$0.684243\pi$
$684$		0			0
$685$	−6.05614e6	−	4.38911e7i	−0.0188419	−	0.136554i
$686$		0			0
$687$	2.35208e8	−	2.35208e8i	0.725409	−	0.725409i
$688$		0			0
$689$		−	6.75648e8i		−	2.06568i
$690$		0			0
$691$	−4.54828e8			−1.37852			−0.689261	−	0.724513i	$-0.742065\pi$
$691$	−4.54828e8			−1.37852			−0.689261	+	0.724513i	$0.742065\pi$
$692$		0			0
$693$	3.66562e7	+	3.66562e7i	0.110141	+	0.110141i
$694$		0			0
$695$	−4.89498e8	−	3.70794e8i	−1.45813	−	1.10453i
$696$		0			0
$697$	2.36739e8	−	2.36739e8i	0.699150	−	0.699150i
$698$		0			0
$699$		−	2.63460e7i		−	0.0771406i
$700$		0			0
$701$	−3.98272e8			−1.15618			−0.578090	−	0.815973i	$-0.696202\pi$
$701$	−3.98272e8			−1.15618			−0.578090	+	0.815973i	$0.696202\pi$
$702$		0			0
$703$	1.37438e8	+	1.37438e8i	0.395586	+	0.395586i
$704$		0			0
$705$	−4.29087e7	+	5.66452e7i	−0.122455	+	0.161658i
$706$		0			0
$707$	4.21879e7	−	4.21879e7i	0.119380	−	0.119380i
$708$		0			0
$709$			1.94492e8i			0.545711i	0.962055	+	0.272855i	$0.0879680\pi$
$709$			1.94492e8i			0.545711i	−0.962055	+	0.272855i	$0.912032\pi$
$710$		0			0
$711$	5.39481e7			0.150095
$712$		0			0
$713$	−2.32025e8	−	2.32025e8i	−0.640128	−	0.640128i
$714$		0			0
$715$	−3.68163e8	+	5.07995e7i	−1.00721	+	0.138977i
$716$		0			0
$717$	2.28177e7	−	2.28177e7i	0.0619035	−	0.0619035i
$718$		0			0
$719$		−	5.36699e8i		−	1.44392i	−0.691934	−	0.721961i	$-0.743241\pi$
$719$		−	5.36699e8i		−	1.44392i	0.691934	−	0.721961i	$-0.256759\pi$
$720$		0			0
$721$	8.47977e7			0.226245
$722$		0			0
$723$	−2.59960e8	−	2.59960e8i	−0.687847	−	0.687847i
$724$		0			0
$725$	−1.27522e8	+	3.58744e7i	−0.334636	+	0.0941393i
$726$		0			0
$727$	−6.70897e7	+	6.70897e7i	−0.174603	+	0.174603i	−0.788998	−	0.614395i	$-0.789400\pi$
$727$	−6.70897e7	+	6.70897e7i	−0.174603	+	0.174603i	0.614395	+	0.788998i	$0.289400\pi$
$728$		0			0
$729$		−	1.43489e7i		−	0.0370370i
$730$		0			0
$731$	1.16637e8			0.298596
$732$		0			0
$733$	−2.35707e7	−	2.35707e7i	−0.0598495	−	0.0598495i	0.676549	−	0.736398i	$-0.263475\pi$
$733$	−2.35707e7	−	2.35707e7i	−0.0598495	−	0.0598495i	−0.736398	+	0.676549i	$0.763475\pi$
$734$		0			0
$735$	−2.00653e7	−	1.45420e8i	−0.0505339	−	0.366238i
$736$		0			0
$737$	−3.15636e8	+	3.15636e8i	−0.788467	+	0.788467i
$738$		0			0
$739$		−	5.18563e8i		−	1.28490i	−0.766329	−	0.642448i	$-0.777919\pi$
$739$		−	5.18563e8i		−	1.28490i	0.766329	−	0.642448i	$-0.222081\pi$
$740$		0			0
$741$	−4.10666e8			−1.00933
$742$		0			0
$743$	2.89312e8	+	2.89312e8i	0.705343	+	0.705343i	0.965552	−	0.260209i	$-0.0837916\pi$
$743$	2.89312e8	+	2.89312e8i	0.705343	+	0.705343i	−0.260209	+	0.965552i	$0.583792\pi$
$744$		0			0
$745$	−3.76631e8	−	2.85298e8i	−0.910851	−	0.689968i
$746$		0			0
$747$	1.82046e8	−	1.82046e8i	0.436736	−	0.436736i
$748$		0			0
$749$		−	2.30476e8i		−	0.548504i
$750$		0			0
$751$	−3.00670e8			−0.709857			−0.354928	−	0.934893i	$-0.615495\pi$
$751$	−3.00670e8			−0.709857			−0.354928	+	0.934893i	$0.615495\pi$
$752$		0			0
$753$	−9.73901e7	−	9.73901e7i	−0.228102	−	0.228102i
$754$		0			0
$755$	−9.04319e7	+	1.19382e8i	−0.210126	+	0.277395i
$756$		0			0
$757$	−4.36582e8	+	4.36582e8i	−1.00642	+	1.00642i	−0.00643784	+	0.999979i	$0.502049\pi$
$757$	−4.36582e8	+	4.36582e8i	−1.00642	+	1.00642i	−0.999979	+	0.00643784i	$0.997951\pi$
$758$		0			0
$759$			3.10438e8i			0.709986i
$760$		0			0
$761$	5.85378e8			1.32826			0.664128	−	0.747619i	$-0.268803\pi$
$761$	5.85378e8			1.32826			0.664128	+	0.747619i	$0.268803\pi$
$762$		0			0
$763$	−2.41316e7	−	2.41316e7i	−0.0543267	−	0.0543267i
$764$		0			0
$765$	1.98746e8	−	2.74232e7i	0.443930	−	0.0612540i
$766$		0			0
$767$	5.01089e8	−	5.01089e8i	1.11053	−	1.11053i
$768$		0			0
$769$			10186.9i			2.24008e-5i	1.00000		1.12004e-5i	$3.56520e-6\pi$
$769$			10186.9i			2.24008e-5i	−1.00000		1.12004e-5i	$0.999996\pi$
$770$		0			0
$771$	1.34470e8			0.293402
$772$		0			0
$773$	−1.49946e8	−	1.49946e8i	−0.324636	−	0.324636i	0.525906	−	0.850542i	$-0.323726\pi$
$773$	−1.49946e8	−	1.49946e8i	−0.324636	−	0.324636i	−0.850542	+	0.525906i	$0.823726\pi$
$774$		0			0
$775$	7.23070e7	+	2.57029e8i	0.155337	+	0.552175i
$776$		0			0
$777$	−4.79578e7	+	4.79578e7i	−0.102234	+	0.102234i
$778$		0			0
$779$		−	4.65789e8i		−	0.985319i
$780$		0			0
$781$	−2.99099e8			−0.627858
$782$		0			0
$783$	−2.27091e7	−	2.27091e7i	−0.0473058	−	0.0473058i
$784$		0			0
$785$	−7.10270e7	−	5.14758e8i	−0.146830	−	1.06413i
$786$		0			0
$787$	−3.29898e8	+	3.29898e8i	−0.676793	+	0.676793i	−0.959273	−	0.282481i	$-0.908843\pi$
$787$	−3.29898e8	+	3.29898e8i	−0.676793	+	0.676793i	0.282481	+	0.959273i	$0.408843\pi$
$788$		0			0
$789$		−	9.60487e7i		−	0.195551i
$790$		0			0
$791$	2.18290e8			0.441067
$792$		0			0
$793$	−5.70025e8	−	5.70025e8i	−1.14307	−	1.14307i
$794$		0			0
$795$	3.66063e8	+	2.77292e8i	0.728542	+	0.551869i
$796$		0			0
$797$	−2.30664e8	+	2.30664e8i	−0.455622	+	0.455622i	−0.897215	−	0.441593i	$-0.854413\pi$
$797$	−2.30664e8	+	2.30664e8i	−0.455622	+	0.455622i	0.441593	+	0.897215i	$0.354413\pi$
$798$		0			0
$799$		−	2.40881e8i		−	0.472240i
$800$		0			0
$801$	−1.67621e8			−0.326161
$802$		0			0
$803$	5.05997e8	+	5.05997e8i	0.977241	+	0.977241i
$804$		0			0
$805$	−2.98125e8	+	3.93565e8i	−0.571493	+	0.754448i
$806$		0			0
$807$	−1.50021e8	+	1.50021e8i	−0.285450	+	0.285450i
$808$		0			0
$809$			1.15009e8i			0.217213i	0.994085	+	0.108607i	$0.0346389\pi$
$809$			1.15009e8i			0.217213i	−0.994085	+	0.108607i	$0.965361\pi$
$810$		0			0
$811$	−7.36769e8			−1.38124			−0.690619	−	0.723218i	$-0.742662\pi$
$811$	−7.36769e8			−1.38124			−0.690619	+	0.723218i	$0.742662\pi$
$812$		0			0
$813$	−9.04842e7	−	9.04842e7i	−0.168384	−	0.168384i
$814$		0			0
$815$	−6.36556e8	+	8.78327e7i	−1.17588	+	0.162250i
$816$		0			0
$817$	1.14743e8	−	1.14743e8i	0.210407	−	0.210407i
$818$		0			0
$819$		−	1.43298e8i		−	0.260849i
$820$		0			0
$821$	5.00735e8			0.904854			0.452427	−	0.891802i	$-0.350558\pi$
$821$	5.00735e8			0.904854			0.452427	+	0.891802i	$0.350558\pi$
$822$		0			0
$823$	−6.80752e6	−	6.80752e6i	−0.0122121	−	0.0122121i	0.700974	−	0.713186i	$-0.252749\pi$
$823$	−6.80752e6	−	6.80752e6i	−0.0122121	−	0.0122121i	−0.713186	+	0.700974i	$0.752749\pi$
$824$		0			0
$825$	1.23574e8	−	2.20318e8i	0.220073	−	0.392362i
$826$		0			0
$827$	2.59523e7	−	2.59523e7i	0.0458838	−	0.0458838i	−0.683793	−	0.729676i	$-0.739671\pi$
$827$	2.59523e7	−	2.59523e7i	0.0458838	−	0.0458838i	0.729676	+	0.683793i	$0.239671\pi$
$828$		0			0
$829$			3.24193e8i			0.569037i	0.958671	+	0.284518i	$0.0918337\pi$
$829$			3.24193e8i			0.569037i	−0.958671	+	0.284518i	$0.908166\pi$
$830$		0			0
$831$	−5.65421e8			−0.985300
$832$		0			0
$833$	3.51860e8	+	3.51860e8i	0.608744	+	0.608744i
$834$		0			0
$835$	−1.78410e7	−	1.29300e8i	−0.0306451	−	0.222096i
$836$		0			0
$837$	−4.57715e7	+	4.57715e7i	−0.0780583	+	0.0780583i
$838$		0			0
$839$		−	5.69147e8i		−	0.963692i	−0.876256	−	0.481846i	$-0.839966\pi$
$839$		−	5.69147e8i		−	0.963692i	0.876256	−	0.481846i	$-0.160034\pi$
$840$		0			0
$841$	5.22943e8			0.879157
$842$		0			0
$843$	2.72913e8	+	2.72913e8i	0.455557	+	0.455557i
$844$		0			0
$845$	3.37972e8	+	2.56013e8i	0.560157	+	0.424318i
$846$		0			0
$847$	1.01230e8	−	1.01230e8i	0.166594	−	0.166594i
$848$		0			0
$849$		−	2.21227e8i		−	0.361506i
$850$		0			0
$851$	−4.06151e8			−0.659021
$852$		0			0
$853$	2.70461e7	+	2.70461e7i	0.0435770	+	0.0435770i	0.728560	−	0.684982i	$-0.240190\pi$
$853$	2.70461e7	+	2.70461e7i	0.0435770	+	0.0435770i	−0.684982	+	0.728560i	$0.740190\pi$
$854$		0			0
$855$	1.68541e8	−	2.22497e8i	0.269654	−	0.355980i
$856$		0			0
$857$	1.75013e8	−	1.75013e8i	0.278052	−	0.278052i	−0.554279	−	0.832331i	$-0.687006\pi$
$857$	1.75013e8	−	1.75013e8i	0.278052	−	0.278052i	0.832331	+	0.554279i	$0.187006\pi$
$858$		0			0
$859$			3.42840e8i			0.540894i	0.962735	+	0.270447i	$0.0871716\pi$
$859$			3.42840e8i			0.540894i	−0.962735	+	0.270447i	$0.912828\pi$
$860$		0			0
$861$	1.62533e8			0.254644
$862$		0			0
$863$	−7.99150e8	−	7.99150e8i	−1.24336	−	1.24336i	−0.958600	−	0.284757i	$-0.908087\pi$
$863$	−7.99150e8	−	7.99150e8i	−1.24336	−	1.24336i	−0.284757	−	0.958600i	$-0.591913\pi$
$864$		0			0
$865$	8.78111e8	−	1.21163e8i	1.35675	−	0.187206i
$866$		0			0
$867$	−2.14827e8	+	2.14827e8i	−0.329633	+	0.329633i
$868$		0			0
$869$			2.30247e8i			0.350860i
$870$		0			0
$871$	1.23390e9			1.86735
$872$		0			0
$873$	1.99489e8	+	1.99489e8i	0.299831	+	0.299831i
$874$		0			0
$875$	3.68243e8	−	1.60640e8i	0.549681	−	0.239789i
$876$		0			0
$877$	5.77037e8	−	5.77037e8i	0.855470	−	0.855470i	−0.135331	−	0.990800i	$-0.543210\pi$
$877$	5.77037e8	−	5.77037e8i	0.855470	−	0.855470i	0.990800	+	0.135331i	$0.0432097\pi$
$878$		0			0
$879$		−	4.14961e7i		−	0.0611000i
$880$		0			0
$881$	−2.68153e8			−0.392153			−0.196077	−	0.980589i	$-0.562820\pi$
$881$	−2.68153e8			−0.392153			−0.196077	+	0.980589i	$0.562820\pi$
$882$		0			0
$883$	−4.48535e8	−	4.48535e8i	−0.651499	−	0.651499i	0.301855	−	0.953354i	$-0.402394\pi$
$883$	−4.48535e8	−	4.48535e8i	−0.651499	−	0.651499i	−0.953354	+	0.301855i	$0.902394\pi$
$884$		0			0
$885$	6.58362e7	+	4.77139e8i	0.0949807	+	0.688359i
$886$		0			0
$887$	−4.07398e8	+	4.07398e8i	−0.583779	+	0.583779i	−0.935940	−	0.352161i	$-0.885447\pi$
$887$	−4.07398e8	+	4.07398e8i	−0.583779	+	0.583779i	0.352161	+	0.935940i	$0.385447\pi$
$888$		0			0
$889$		−	1.69616e8i		−	0.241413i
$890$		0			0
$891$	6.12400e7			0.0865770
$892$		0			0
$893$	−2.36970e8	−	2.36970e8i	−0.332766	−	0.332766i
$894$		0			0
$895$	7.74263e8	+	5.86503e8i	1.07999	+	0.818089i
$896$		0			0
$897$	6.06792e8	−	6.06792e8i	0.840741	−	0.840741i
$898$		0			0
$899$			1.44879e8i			0.199401i
$900$		0			0
$901$	−1.55667e9			−2.12825
$902$		0			0
$903$	4.00386e7	+	4.00386e7i	0.0543771	+	0.0543771i
$904$		0			0
$905$	5.26981e8	−	6.95686e8i	0.710967	−	0.938572i
$906$		0			0
$907$	1.38639e8	−	1.38639e8i	0.185808	−	0.185808i	−0.608073	−	0.793881i	$-0.708057\pi$
$907$	1.38639e8	−	1.38639e8i	0.185808	−	0.185808i	0.793881	+	0.608073i	$0.208057\pi$
$908$		0			0
$909$		−	7.04818e7i		−	0.0938394i
$910$		0			0
$911$	−7.12128e8			−0.941896			−0.470948	−	0.882161i	$-0.656088\pi$
$911$	−7.12128e8			−0.941896			−0.470948	+	0.882161i	$0.656088\pi$
$912$		0			0
$913$	7.76957e8	+	7.76957e8i	1.02090	+	1.02090i
$914$		0			0
$915$	5.42781e8	−	7.48935e7i	0.708534	−	0.0977644i
$916$		0			0
$917$	−6.09249e8	+	6.09249e8i	−0.790108	+	0.790108i
$918$		0			0
$919$			4.34345e8i			0.559613i	0.960056	+	0.279807i	$0.0902704\pi$
$919$			4.34345e8i			0.559613i	−0.960056	+	0.279807i	$0.909730\pi$
$920$		0			0
$921$	−7.13575e8			−0.913400
$922$		0			0
$923$	5.84627e8	+	5.84627e8i	0.743488	+	0.743488i
$924$		0			0
$925$	2.88245e8	+	1.61674e8i	0.364197	+	0.204275i
$926$		0			0
$927$	7.08341e7	−	7.08341e7i	0.0889208	−	0.0889208i
$928$		0			0
$929$			3.67090e8i			0.457852i	0.973444	+	0.228926i	$0.0735213\pi$
$929$			3.67090e8i			0.457852i	−0.973444	+	0.228926i	$0.926479\pi$
$930$		0			0
$931$	6.92294e8			0.857909
$932$		0			0
$933$	2.17051e8	+	2.17051e8i	0.267250	+	0.267250i
$934$		0			0
$935$	1.17040e8	+	8.48233e8i	0.143186	+	1.03772i
$936$		0			0
$937$	1.11262e8	−	1.11262e8i	0.135248	−	0.135248i	−0.636242	−	0.771490i	$-0.719512\pi$
$937$	1.11262e8	−	1.11262e8i	0.135248	−	0.135248i	0.771490	+	0.636242i	$0.219512\pi$
$938$		0			0
$939$		−	2.67356e8i		−	0.322919i
$940$		0			0
$941$	−7.63794e8			−0.916659			−0.458329	−	0.888782i	$-0.651552\pi$
$941$	−7.63794e8			−0.916659			−0.458329	+	0.888782i	$0.651552\pi$
$942$		0			0
$943$	6.88241e8	+	6.88241e8i	0.820739	+	0.820739i
$944$		0			0
$945$	7.76385e7	+	5.88110e7i	0.0919987	+	0.0696888i
$946$		0			0
$947$	−1.13872e8	+	1.13872e8i	−0.134081	+	0.134081i	−0.770962	−	0.636881i	$-0.780224\pi$
$947$	−1.13872e8	+	1.13872e8i	−0.134081	+	0.134081i	0.636881	+	0.770962i	$0.280224\pi$
$948$		0			0
$949$		−	1.97807e9i		−	2.31443i
$950$		0			0
$951$	−5.21810e8			−0.606696
$952$		0			0
$953$	9.79865e8	+	9.79865e8i	1.13211	+	1.13211i	0.989826	+	0.142280i	$0.0454434\pi$
$953$	9.79865e8	+	9.79865e8i	1.13211	+	1.13211i	0.142280	+	0.989826i	$0.454557\pi$
$954$		0			0
$955$	−1.32554e8	+	1.74989e8i	−0.152189	+	0.200910i
$956$		0			0
$957$	9.69207e7	−	9.69207e7i	0.110581	−	0.110581i
$958$		0			0
$959$			7.29112e7i			0.0826682i
$960$		0			0
$961$	−5.95491e8			−0.670973
$962$		0			0
$963$	−1.92523e8	−	1.92523e8i	−0.215578	−	0.215578i
$964$		0			0
$965$	−1.48662e9	+	2.05126e8i	−1.65432	+	0.228265i
$966$		0			0
$967$	2.18628e8	−	2.18628e8i	0.241783	−	0.241783i	−0.575804	−	0.817588i	$-0.695311\pi$
$967$	2.18628e8	−	2.18628e8i	0.241783	−	0.241783i	0.817588	+	0.575804i	$0.195311\pi$
$968$		0			0
$969$			9.46159e8i			1.03990i
$970$		0			0
$971$	9.21253e8			1.00628			0.503142	−	0.864203i	$-0.332177\pi$
$971$	9.21253e8			1.00628			0.503142	+	0.864203i	$0.332177\pi$
$972$		0			0
$973$	7.14552e8	+	7.14552e8i	0.775703	+	0.775703i
$974$		0			0
$975$	−6.72181e8	+	1.89097e8i	−0.725225	+	0.204019i
$976$		0			0
$977$	−1.10660e8	+	1.10660e8i	−0.118661	+	0.118661i	−0.763944	−	0.645283i	$-0.776740\pi$
$977$	−1.10660e8	+	1.10660e8i	−0.118661	+	0.118661i	0.645283	+	0.763944i	$0.276740\pi$
$978$		0			0
$979$		−	7.15395e8i		−	0.762426i
$980$		0			0
$981$	−4.03158e7			−0.0427039
$982$		0			0
$983$	5.81692e8	+	5.81692e8i	0.612397	+	0.612397i	0.943570	−	0.331173i	$-0.107445\pi$
$983$	5.81692e8	+	5.81692e8i	0.612397	+	0.612397i	−0.331173	+	0.943570i	$0.607445\pi$
$984$		0			0
$985$	1.71166e8	+	1.24050e9i	0.179106	+	1.29804i
$986$		0			0
$987$	8.26887e7	−	8.26887e7i	0.0859993	−	0.0859993i
$988$		0			0
$989$			3.39084e8i			0.350525i
$990$		0			0
$991$	2.16687e8			0.222644			0.111322	−	0.993784i	$-0.464491\pi$
$991$	2.16687e8			0.222644			0.111322	+	0.993784i	$0.464491\pi$
$992$		0			0
$993$	4.17519e8	+	4.17519e8i	0.426411	+	0.426411i
$994$		0			0
$995$	−2.33468e8	−	1.76852e8i	−0.237005	−	0.179531i
$996$		0			0
$997$	−3.07388e8	+	3.07388e8i	−0.310172	+	0.310172i	−0.844976	−	0.534804i	$-0.820385\pi$
$997$	−3.07388e8	+	3.07388e8i	−0.310172	+	0.310172i	0.534804	+	0.844976i	$0.320385\pi$
$998$		0			0
$999$			8.01213e7i			0.0803621i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.7.bg.b.193.2		8
4.3	odd	2		30.7.f.b.13.4	yes	8
5.2	odd	4	inner	240.7.bg.b.97.2		8
12.11	even	2		90.7.g.f.73.2		8
20.3	even	4		150.7.f.h.7.1		8
20.7	even	4		30.7.f.b.7.4	✓	8
20.19	odd	2		150.7.f.h.43.1		8
60.23	odd	4		450.7.g.r.307.2		8
60.47	odd	4		90.7.g.f.37.2		8
60.59	even	2		450.7.g.r.343.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.7.f.b.7.4	✓	8	20.7	even	4
30.7.f.b.13.4	yes	8	4.3	odd	2
90.7.g.f.37.2		8	60.47	odd	4
90.7.g.f.73.2		8	12.11	even	2
150.7.f.h.7.1		8	20.3	even	4
150.7.f.h.43.1		8	20.19	odd	2
240.7.bg.b.97.2		8	5.2	odd	4	inner
240.7.bg.b.193.2		8	1.1	even	1	trivial
450.7.g.r.307.2		8	60.23	odd	4
450.7.g.r.343.2		8	60.59	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	240.bg (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-11.0227 - 11.0227i) q^{3} +(75.4773 - 99.6402i) q^{5} +(-145.451 + 145.451i) q^{7} +243.000i q^{9} -1037.11 q^{11} +(2027.16 + 2027.16i) q^{13} +(-1930.27 + 266.341i) q^{15} +(4670.49 - 4670.49i) q^{17} -9189.32i q^{19} +3206.54 q^{21} +(13577.9 + 13577.9i) q^{23} +(-4231.35 - 15041.2i) q^{25} +(2678.52 - 2678.52i) q^{27} -8478.24i q^{29} -17088.4 q^{31} +(11431.7 + 11431.7i) q^{33} +(3514.53 + 25471.1i) q^{35} +(-14956.3 + 14956.3i) q^{37} -44689.5i q^{39} +50688.1 q^{41} +(12486.6 + 12486.6i) q^{43} +(24212.6 + 18341.0i) q^{45} +(25787.6 - 25787.6i) q^{47} +75336.8i q^{49} -102963. q^{51} +(-166649. - 166649. i) q^{53} +(-78277.9 + 103337. i) q^{55} +(-101291. + 101291. i) q^{57} -247188. i q^{59} -281194. q^{61} +(-35344.7 - 35344.7i) q^{63} +(354991. - 48982.0i) q^{65} +(304343. - 304343. i) q^{67} -299331. i q^{69} +288398. q^{71} +(-487894. - 487894. i) q^{73} +(-119153. + 212435. i) q^{75} +(150848. - 150848. i) q^{77} -222009. i q^{79} -59049.0 q^{81} +(-749160. - 749160. i) q^{83} +(-112853. - 817885. i) q^{85} +(-93453.1 + 93453.1i) q^{87} +689800. i q^{89} -589705. q^{91} +(188360. + 188360. i) q^{93} +(-915626. - 693585. i) q^{95} +(820944. - 820944. i) q^{97} -252017. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 60 q^{5} - 388 q^{7} + 4192 q^{11} + 7884 q^{13} - 1296 q^{15} - 1372 q^{17} + 4536 q^{21} - 14888 q^{23} + 17932 q^{25} - 2240 q^{31} + 3564 q^{33} + 78232 q^{35} - 69996 q^{37} + 169064 q^{41} - 164136 q^{43}+ \cdots - 854736 q^{97}+O(q^{100}) \) 8 * q + 60 * q^5 - 388 * q^7 + 4192 * q^11 + 7884 * q^13 - 1296 * q^15 - 1372 * q^17 + 4536 * q^21 - 14888 * q^23 + 17932 * q^25 - 2240 * q^31 + 3564 * q^33 + 78232 * q^35 - 69996 * q^37 + 169064 * q^41 - 164136 * q^43 - 44712 * q^45 + 109248 * q^47 - 380376 * q^51 - 480740 * q^53 + 409068 * q^55 - 442584 * q^57 + 266088 * q^61 - 94284 * q^63 + 903396 * q^65 - 92488 * q^67 + 2526032 * q^71 + 324464 * q^73 + 38232 * q^75 + 2822104 * q^77 - 472392 * q^81 - 213264 * q^83 - 1537292 * q^85 + 1707156 * q^87 - 3340176 * q^91 + 1264248 * q^93 - 3084784 * q^95 - 854736 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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