LMFDB - Embedded newform 354.7.d.a.235.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,7,Mod(235,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("354.235");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	354.d (of order $2$, degree $1$, 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:	$81.4391456014$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			235.3
Character	$\chi$	$=$	354.235
Dual form			354.7.d.a.235.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685i q^{2} +15.5885 q^{3} -32.0000 q^{4} +117.083 q^{5} -88.1816i q^{6} +626.230 q^{7} +181.019i q^{8} +243.000 q^{9} +O(q^{10})$	\(q-5.65685i q^{2} +15.5885 q^{3} -32.0000 q^{4} +117.083 q^{5} -88.1816i q^{6} +626.230 q^{7} +181.019i q^{8} +243.000 q^{9} -662.324i q^{10} -2448.22i q^{11} -498.831 q^{12} +657.581i q^{13} -3542.49i q^{14} +1825.15 q^{15} +1024.00 q^{16} +8454.02 q^{17} -1374.62i q^{18} -5380.68 q^{19} -3746.67 q^{20} +9761.96 q^{21} -13849.2 q^{22} -19941.2i q^{23} +2821.81i q^{24} -1916.48 q^{25} +3719.84 q^{26} +3788.00 q^{27} -20039.4 q^{28} -23410.8 q^{29} -10324.6i q^{30} +1133.12i q^{31} -5792.62i q^{32} -38164.0i q^{33} -47823.1i q^{34} +73321.2 q^{35} -7776.00 q^{36} -14477.3i q^{37} +30437.7i q^{38} +10250.7i q^{39} +21194.4i q^{40} -14137.9 q^{41} -55222.0i q^{42} +115979. i q^{43} +78343.0i q^{44} +28451.3 q^{45} -112805. q^{46} +80048.2i q^{47} +15962.6 q^{48} +274515. q^{49} +10841.2i q^{50} +131785. q^{51} -21042.6i q^{52} +198626. q^{53} -21428.1i q^{54} -286646. i q^{55} +113360. i q^{56} -83876.4 q^{57} +132431. i q^{58} +(-204279. - 21232.5i) q^{59} -58404.8 q^{60} -110067. i q^{61} +6409.88 q^{62} +152174. q^{63} -32768.0 q^{64} +76991.8i q^{65} -215888. q^{66} +290250. i q^{67} -270529. q^{68} -310853. i q^{69} -414767. i q^{70} +243917. q^{71} +43987.7i q^{72} -444431. i q^{73} -81896.2 q^{74} -29874.9 q^{75} +172182. q^{76} -1.53315e6i q^{77} +57986.5 q^{78} -376135. q^{79} +119893. q^{80} +59049.0 q^{81} +79975.8i q^{82} +266953. i q^{83} -312383. q^{84} +989825. q^{85} +656077. q^{86} -364938. q^{87} +443175. q^{88} +117162. i q^{89} -160945. i q^{90} +411797. i q^{91} +638119. i q^{92} +17663.6i q^{93} +452821. q^{94} -629988. q^{95} -90298.0i q^{96} +1.21239e6i q^{97} -1.55289e6i q^{98} -594917. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9}+O(q^{10}) $ 60 * q - 1920 * q^4 + 408 * q^7 + 14580 * q^9	$ 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9} + 4536 q^{15} + 61440 q^{16} - 15840 q^{17} - 5616 q^{19} - 17472 q^{22} + 226260 q^{25} - 34048 q^{26} - 13056 q^{28} - 75392 q^{29} + 278000 q^{35} - 466560 q^{36} + 67376 q^{41} + 209856 q^{46} + 269100 q^{49} - 206064 q^{51} + 490000 q^{53} - 373248 q^{57} - 863472 q^{59} - 145152 q^{60} - 155072 q^{62} + 99144 q^{63} - 1966080 q^{64} - 404352 q^{66} + 506880 q^{68} - 2041856 q^{71} - 2146176 q^{74} + 808704 q^{75} + 179712 q^{76} + 228096 q^{78} + 670248 q^{79} + 3542940 q^{81} + 873408 q^{85} + 1832576 q^{86} - 2568024 q^{87} + 559104 q^{88} + 1049472 q^{94} - 245856 q^{95}+O(q^{100}) $ 60 * q - 1920 * q^4 + 408 * q^7 + 14580 * q^9 + 4536 * q^15 + 61440 * q^16 - 15840 * q^17 - 5616 * q^19 - 17472 * q^22 + 226260 * q^25 - 34048 * q^26 - 13056 * q^28 - 75392 * q^29 + 278000 * q^35 - 466560 * q^36 + 67376 * q^41 + 209856 * q^46 + 269100 * q^49 - 206064 * q^51 + 490000 * q^53 - 373248 * q^57 - 863472 * q^59 - 145152 * q^60 - 155072 * q^62 + 99144 * q^63 - 1966080 * q^64 - 404352 * q^66 + 506880 * q^68 - 2041856 * q^71 - 2146176 * q^74 + 808704 * q^75 + 179712 * q^76 + 228096 * q^78 + 670248 * q^79 + 3542940 * q^81 + 873408 * q^85 + 1832576 * q^86 - 2568024 * q^87 + 559104 * q^88 + 1049472 * q^94 - 245856 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	5.65685i		−	0.707107i
$2$		−	5.65685i		−	0.707107i
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	−32.0000			−0.500000
$5$	117.083			0.936667			0.468334	−	0.883552i	$-0.344855\pi$
$5$	117.083			0.936667			0.468334	+	0.883552i	$0.344855\pi$
$6$		−	88.1816i		−	0.408248i
$7$	626.230			1.82574			0.912872	−	0.408246i	$-0.133859\pi$
$7$	626.230			1.82574			0.912872	+	0.408246i	$0.133859\pi$
$8$			181.019i			0.353553i
$9$	243.000			0.333333
$10$		−	662.324i		−	0.662324i
$11$		−	2448.22i		−	1.83938i	−0.392641	−	0.919692i	$-0.628439\pi$
$11$		−	2448.22i		−	1.83938i	0.392641	−	0.919692i	$-0.371561\pi$
$12$	−498.831			−0.288675
$13$			657.581i			0.299308i	0.988738	+	0.149654i	$0.0478160\pi$
$13$			657.581i			0.299308i	−0.988738	+	0.149654i	$0.952184\pi$
$14$		−	3542.49i		−	1.29100i
$15$	1825.15			0.540785
$16$	1024.00			0.250000
$17$	8454.02			1.72074			0.860372	−	0.509666i	$-0.170231\pi$
$17$	8454.02			1.72074			0.860372	+	0.509666i	$0.170231\pi$
$18$		−	1374.62i		−	0.235702i
$19$	−5380.68			−0.784469			−0.392235	−	0.919865i	$-0.628298\pi$
$19$	−5380.68			−0.784469			−0.392235	+	0.919865i	$0.628298\pi$
$20$	−3746.67			−0.468334
$21$	9761.96			1.05409
$22$	−13849.2			−1.30064
$23$		−	19941.2i		−	1.63896i	−0.573109	−	0.819479i	$-0.694263\pi$
$23$		−	19941.2i		−	1.63896i	0.573109	−	0.819479i	$-0.305737\pi$
$24$			2821.81i			0.204124i
$25$	−1916.48			−0.122655
$26$	3719.84			0.211643
$27$	3788.00			0.192450
$28$	−20039.4			−0.912872
$29$	−23410.8			−0.959891			−0.479945	−	0.877298i	$-0.659344\pi$
$29$	−23410.8			−0.959891			−0.479945	+	0.877298i	$0.659344\pi$
$30$		−	10324.6i		−	0.382393i
$31$			1133.12i			0.0380356i	0.999819	+	0.0190178i	$0.00605391\pi$
$31$			1133.12i			0.0380356i	−0.999819	+	0.0190178i	$0.993946\pi$
$32$		−	5792.62i		−	0.176777i
$33$		−	38164.0i		−	1.06197i
$34$		−	47823.1i		−	1.21675i
$35$	73321.2			1.71011
$36$	−7776.00			−0.166667
$37$		−	14477.3i		−	0.285814i	−0.989736	−	0.142907i	$-0.954355\pi$
$37$		−	14477.3i		−	0.285814i	0.989736	−	0.142907i	$-0.0456450\pi$
$38$			30437.7i			0.554704i
$39$			10250.7i			0.172806i
$40$			21194.4i			0.331162i
$41$	−14137.9			−0.205131			−0.102566	−	0.994726i	$-0.532705\pi$
$41$	−14137.9			−0.205131			−0.102566	+	0.994726i	$0.532705\pi$
$42$		−	55222.0i		−	0.745357i
$43$			115979.i			1.45873i	0.684126	+	0.729364i	$0.260184\pi$
$43$			115979.i			1.45873i	−0.684126	+	0.729364i	$0.739816\pi$
$44$			78343.0i			0.919692i
$45$	28451.3			0.312222
$46$	−112805.			−1.15892
$47$			80048.2i			0.771006i	0.922707	+	0.385503i	$0.125972\pi$
$47$			80048.2i			0.771006i	−0.922707	+	0.385503i	$0.874028\pi$
$48$	15962.6			0.144338
$49$	274515.			2.33334
$50$			10841.2i			0.0867299i
$51$	131785.			0.993472
$52$		−	21042.6i		−	0.149654i
$53$	198626.			1.33416			0.667082	−	0.744984i	$-0.267543\pi$
$53$	198626.			1.33416			0.667082	+	0.744984i	$0.267543\pi$
$54$		−	21428.1i		−	0.136083i
$55$		−	286646.i		−	1.72289i
$56$			113360.i			0.645498i
$57$	−83876.4			−0.452914
$58$			132431.i			0.678745i
$59$	−204279.	−	21232.5i	−0.994642	−	0.103382i
$59$	−204279.	−	21232.5i	−0.994642	−	0.103382i
$60$	−58404.8			−0.270393
$61$		−	110067.i		−	0.484915i	−0.970162	−	0.242458i	$-0.922046\pi$
$61$		−	110067.i		−	0.484915i	0.970162	−	0.242458i	$-0.0779536\pi$
$62$	6409.88			0.0268952
$63$	152174.			0.608581
$64$	−32768.0			−0.125000
$65$			76991.8i			0.280352i
$66$	−215888.			−0.750925
$67$			290250.i			0.965046i	0.875883	+	0.482523i	$0.160279\pi$
$67$			290250.i			0.965046i	−0.875883	+	0.482523i	$0.839721\pi$
$68$	−270529.			−0.860372
$69$		−	310853.i		−	0.946253i
$70$		−	414767.i		−	1.20923i
$71$	243917.			0.681502			0.340751	−	0.940154i	$-0.389319\pi$
$71$	243917.			0.681502			0.340751	+	0.940154i	$0.389319\pi$
$72$			43987.7i			0.117851i
$73$		−	444431.i		−	1.14245i	−0.820795	−	0.571223i	$-0.806469\pi$
$73$		−	444431.i		−	1.14245i	0.820795	−	0.571223i	$-0.193531\pi$
$74$	−81896.2			−0.202101
$75$	−29874.9			−0.0708147
$76$	172182.			0.392235
$77$		−	1.53315e6i		−	3.35824i
$78$	57986.5			0.122192
$79$	−376135.			−0.762890			−0.381445	−	0.924392i	$-0.624573\pi$
$79$	−376135.			−0.762890			−0.381445	+	0.924392i	$0.624573\pi$
$80$	119893.			0.234167
$81$	59049.0			0.111111
$82$			79975.8i			0.145050i
$83$			266953.i			0.466875i	0.972372	+	0.233438i	$0.0749975\pi$
$83$			266953.i			0.466875i	−0.972372	+	0.233438i	$0.925002\pi$
$84$	−312383.			−0.527047
$85$	989825.			1.61176
$86$	656077.			1.03148
$87$	−364938.			−0.554193
$88$	443175.			0.650320
$89$			117162.i			0.166195i	0.996541	+	0.0830974i	$0.0264813\pi$
$89$			117162.i			0.166195i	−0.996541	+	0.0830974i	$0.973519\pi$
$90$		−	160945.i		−	0.220775i
$91$			411797.i			0.546461i
$92$			638119.i			0.819479i
$93$			17663.6i			0.0219599i
$94$	452821.			0.545184
$95$	−629988.			−0.734787
$96$		−	90298.0i		−	0.102062i
$97$			1.21239e6i			1.32840i	0.747555	+	0.664199i	$0.231227\pi$
$97$			1.21239e6i			1.32840i	−0.747555	+	0.664199i	$0.768773\pi$
$98$		−	1.55289e6i		−	1.64992i
$99$		−	594917.i		−	0.613128i
$100$	61327.3			0.0613273
$101$		−	383864.i		−	0.372575i	−0.982495	−	0.186287i	$-0.940354\pi$
$101$		−	383864.i		−	0.372575i	0.982495	−	0.186287i	$-0.0596456\pi$
$102$		−	745489.i		−	0.702491i
$103$			773923.i			0.708250i	0.935198	+	0.354125i	$0.115221\pi$
$103$			773923.i			0.708250i	−0.935198	+	0.354125i	$0.884779\pi$
$104$	−119035.			−0.105822
$105$	1.14296e6			0.987335
$106$		−	1.12360e6i		−	0.943397i
$107$	686959.			0.560763			0.280382	−	0.959889i	$-0.409539\pi$
$107$	686959.			0.560763			0.280382	+	0.959889i	$0.409539\pi$
$108$	−121216.			−0.0962250
$109$			257809.i			0.199076i	0.995034	+	0.0995380i	$0.0317365\pi$
$109$			257809.i			0.199076i	−0.995034	+	0.0995380i	$0.968264\pi$
$110$	−1.62151e6			−1.21827
$111$		−	225679.i		−	0.165015i
$112$	641260.			0.456436
$113$		−	1.56285e6i		−	1.08313i	−0.840659	−	0.541565i	$-0.817832\pi$
$113$		−	1.56285e6i		−	1.08313i	0.840659	−	0.541565i	$-0.182168\pi$
$114$			474477.i			0.320258i
$115$		−	2.33478e6i		−	1.53516i
$116$	749145.			0.479945
$117$			159792.i			0.0997695i
$118$	−120109.	+	1.15557e6i	−0.0731021	+	0.703318i
$119$	5.29416e6			3.14164
$120$			330387.i			0.191196i
$121$	−4.22222e6			−2.38333
$122$	−622631.			−0.342887
$123$	−220387.			−0.118433
$124$		−	36259.8i		−	0.0190178i
$125$	−2.05382e6			−1.05155
$126$		−	860826.i		−	0.430332i
$127$	1.20126e6			0.586443			0.293221	−	0.956045i	$-0.405273\pi$
$127$	1.20126e6			0.586443			0.293221	+	0.956045i	$0.405273\pi$
$128$			185364.i			0.0883883i
$129$			1.80793e6i			0.842197i
$130$	435531.			0.198239
$131$		−	2.92321e6i		−	1.30031i	−0.759804	−	0.650153i	$-0.774705\pi$
$131$		−	2.92321e6i		−	1.30031i	0.759804	−	0.650153i	$-0.225295\pi$
$132$			1.22125e6i			0.530984i
$133$	−3.36954e6			−1.43224
$134$	1.64190e6			0.682390
$135$	443511.			0.180262
$136$			1.53034e6i			0.608375i
$137$	−1.14141e6			−0.443893			−0.221946	−	0.975059i	$-0.571241\pi$
$137$	−1.14141e6			−0.443893			−0.221946	+	0.975059i	$0.571241\pi$
$138$	−1.75845e6			−0.669102
$139$	−4.56066e6			−1.69818			−0.849088	−	0.528251i	$-0.822848\pi$
$139$	−4.56066e6			−1.69818			−0.849088	+	0.528251i	$0.822848\pi$
$140$	−2.34628e6			−0.855057
$141$			1.24783e6i			0.445141i
$142$		−	1.37980e6i		−	0.481895i
$143$	1.60990e6			0.550543
$144$	248832.			0.0833333
$145$	−2.74101e6			−0.899098
$146$	−2.51408e6			−0.807832
$147$	4.27927e6			1.34715
$148$			463275.i			0.142907i
$149$		−	2.82142e6i		−	0.852920i	−0.904506	−	0.426460i	$-0.859760\pi$
$149$		−	2.82142e6i		−	0.852920i	0.904506	−	0.426460i	$-0.140240\pi$
$150$			168998.i			0.0500735i
$151$			1.74960e6i			0.508169i	0.967182	+	0.254085i	$0.0817742\pi$
$151$			1.74960e6i			0.508169i	−0.967182	+	0.254085i	$0.918226\pi$
$152$		−	974006.i		−	0.277352i
$153$	2.05433e6			0.573582
$154$	−8.67280e6			−2.37464
$155$			132669.i			0.0356267i
$156$		−	328021.i		−	0.0864029i
$157$		−	5.81803e6i		−	1.50341i	−0.659500	−	0.751704i	$-0.729232\pi$
$157$		−	5.81803e6i		−	1.50341i	0.659500	−	0.751704i	$-0.270768\pi$
$158$			2.12774e6i			0.539445i
$159$	3.09628e6			0.770280
$160$		−	678219.i		−	0.165581i
$161$		−	1.24878e7i		−	2.99232i
$162$		−	334032.i		−	0.0785674i
$163$	5.84246e6			1.34907			0.674533	−	0.738245i	$-0.264345\pi$
$163$	5.84246e6			1.34907			0.674533	+	0.738245i	$0.264345\pi$
$164$	452411.			0.102566
$165$		−	4.46837e6i		−	0.994711i
$166$	1.51012e6			0.330131
$167$	−5.89974e6			−1.26673			−0.633364	−	0.773854i	$-0.718326\pi$
$167$	−5.89974e6			−1.26673			−0.633364	+	0.773854i	$0.718326\pi$
$168$			1.76710e6i			0.372678i
$169$	4.39440e6			0.910414
$170$		−	5.59930e6i		−	1.13969i
$171$	−1.30750e6			−0.261490
$172$		−	3.71133e6i		−	0.729364i
$173$			8.33462e6i			1.60971i	0.593472	+	0.804855i	$0.297757\pi$
$173$			8.33462e6i			1.60971i	−0.593472	+	0.804855i	$0.702243\pi$
$174$			2.06440e6i			0.391874i
$175$	−1.20016e6			−0.223936
$176$		−	2.50698e6i		−	0.459846i
$177$	−3.18439e6	−	330982.i	−0.574257	−	0.0596876i
$178$	662770.			0.117518
$179$			1.07999e7i			1.88305i	0.336943	+	0.941525i	$0.390607\pi$
$179$			1.07999e7i			1.88305i	−0.336943	+	0.941525i	$0.609393\pi$
$180$	−910440.			−0.156111
$181$	−659045.			−0.111142			−0.0555712	−	0.998455i	$-0.517698\pi$
$181$	−659045.			−0.111142			−0.0555712	+	0.998455i	$0.517698\pi$
$182$	2.32947e6			0.386406
$183$		−	1.71577e6i		−	0.279966i
$184$	3.60974e6			0.579459
$185$		−	1.69506e6i		−	0.267712i
$186$	99920.2			0.0155280
$187$		−	2.06973e7i		−	3.16511i
$188$		−	2.56154e6i		−	0.385503i
$189$	2.37216e6			0.351365
$190$			3.56375e6i			0.519573i
$191$		−	5.50856e6i		−	0.790566i	−0.918559	−	0.395283i	$-0.870646\pi$
$191$		−	5.50856e6i		−	0.790566i	0.918559	−	0.395283i	$-0.129354\pi$
$192$	−510803.			−0.0721688
$193$	−888897.			−0.123646			−0.0618229	−	0.998087i	$-0.519691\pi$
$193$	−888897.			−0.123646			−0.0618229	+	0.998087i	$0.519691\pi$
$194$	6.85834e6			0.939320
$195$			1.20018e6i			0.161862i
$196$	−8.78449e6			−1.16667
$197$	7.16430e6			0.937077			0.468538	−	0.883443i	$-0.344781\pi$
$197$	7.16430e6			0.937077			0.468538	+	0.883443i	$0.344781\pi$
$198$	−3.36536e6			−0.433547
$199$	6.98402e6			0.886229			0.443115	−	0.896465i	$-0.353873\pi$
$199$	6.98402e6			0.886229			0.443115	+	0.896465i	$0.353873\pi$
$200$		−	346920.i		−	0.0433650i
$201$			4.52455e6i			0.557169i
$202$	−2.17146e6			−0.263450
$203$	−1.46605e7			−1.75251
$204$	−4.21712e6			−0.496736
$205$	−1.65531e6			−0.192140
$206$	4.37797e6			0.500808
$207$		−	4.84571e6i		−	0.546319i
$208$			673363.i			0.0748271i
$209$			1.31731e7i			1.44294i
$210$		−	6.46558e6i		−	0.698151i
$211$		−	6.62052e6i		−	0.704765i	−0.935856	−	0.352383i	$-0.885372\pi$
$211$		−	6.62052e6i		−	0.704765i	0.935856	−	0.352383i	$-0.114628\pi$
$212$	−6.35605e6			−0.667082
$213$	3.80229e6			0.393465
$214$		−	3.88603e6i		−	0.396519i
$215$			1.35792e7i			1.36634i
$216$			685700.i			0.0680414i
$217$			709593.i			0.0694432i
$218$	1.45839e6			0.140768
$219$		−	6.92799e6i		−	0.659592i
$220$			9.17267e6i			0.861445i
$221$			5.55920e6i			0.515033i
$222$	−1.27663e6			−0.116683
$223$	−2.04661e6			−0.184553			−0.0922763	−	0.995733i	$-0.529414\pi$
$223$	−2.04661e6			−0.184553			−0.0922763	+	0.995733i	$0.529414\pi$
$224$		−	3.62751e6i		−	0.322749i
$225$	−465704.			−0.0408849
$226$	−8.84079e6			−0.765889
$227$			1.70364e7i			1.45646i	0.685330	+	0.728232i	$0.259658\pi$
$227$			1.70364e7i			1.45646i	−0.685330	+	0.728232i	$0.740342\pi$
$228$	2.68405e6			0.226457
$229$		−	1.03402e7i		−	0.861038i	−0.902582	−	0.430519i	$-0.858331\pi$
$229$		−	1.03402e7i		−	0.861038i	0.902582	−	0.430519i	$-0.141669\pi$
$230$	−1.32075e7			−1.08552
$231$		−	2.38994e7i		−	1.93888i
$232$		−	4.23780e6i		−	0.339373i
$233$		−	5.05020e6i		−	0.399246i	−0.979873	−	0.199623i	$-0.936028\pi$
$233$		−	5.05020e6i		−	0.399246i	0.979873	−	0.199623i	$-0.0639717\pi$
$234$	903921.			0.0705477
$235$			9.37231e6i			0.722176i
$236$	6.53691e6	+	679439.i	0.497321	+	0.0516910i
$237$	−5.86336e6			−0.440455
$238$		−	2.99483e7i		−	2.22147i
$239$	−6.29929e6			−0.461422			−0.230711	−	0.973022i	$-0.574105\pi$
$239$	−6.29929e6			−0.461422			−0.230711	+	0.973022i	$0.574105\pi$
$240$	1.86895e6			0.135196
$241$	7.61877e6			0.544294			0.272147	−	0.962256i	$-0.412266\pi$
$241$	7.61877e6			0.544294			0.272147	+	0.962256i	$0.412266\pi$
$242$			2.38845e7i			1.68527i
$243$	920483.			0.0641500
$244$			3.52213e6i			0.242458i
$245$	3.21412e7			2.18556
$246$			1.24670e6i			0.0837445i
$247$		−	3.53823e6i		−	0.234798i
$248$	−205116.			−0.0134476
$249$			4.16139e6i			0.269551i
$250$			1.16181e7i			0.743561i
$251$	1.50591e7			0.952308			0.476154	−	0.879362i	$-0.342030\pi$
$251$	1.50591e7			0.952308			0.476154	+	0.879362i	$0.342030\pi$
$252$	−4.86957e6			−0.304291
$253$	−4.88205e7			−3.01467
$254$		−	6.79535e6i		−	0.414678i
$255$	1.54298e7			0.930553
$256$	1.04858e6			0.0625000
$257$	2.56607e7			1.51171			0.755857	−	0.654737i	$-0.227221\pi$
$257$	2.56607e7			1.51171			0.755857	+	0.654737i	$0.227221\pi$
$258$	1.02272e7			0.595523
$259$		−	9.06614e6i		−	0.521823i
$260$		−	2.46374e6i		−	0.140176i
$261$	−5.68882e6			−0.319964
$262$	−1.65361e7			−0.919455
$263$	−1.21340e7			−0.667016			−0.333508	−	0.942747i	$-0.608232\pi$
$263$	−1.21340e7			−0.667016			−0.333508	+	0.942747i	$0.608232\pi$
$264$	6.90842e6			0.375463
$265$	2.32559e7			1.24967
$266$			1.90610e7i			1.01275i
$267$			1.82638e6i			0.0959526i
$268$		−	9.28800e6i		−	0.482523i
$269$			2.64537e7i			1.35903i	0.733662	+	0.679515i	$0.237810\pi$
$269$			2.64537e7i			1.35903i	−0.733662	+	0.679515i	$0.762190\pi$
$270$		−	2.50888e6i		−	0.127464i
$271$	2.61362e7			1.31321			0.656605	−	0.754235i	$-0.271992\pi$
$271$	2.61362e7			1.31321			0.656605	+	0.754235i	$0.271992\pi$
$272$	8.65691e6			0.430186
$273$			6.41928e6i			0.315499i
$274$			6.45676e6i			0.313880i
$275$			4.69196e6i			0.225609i
$276$			9.94728e6i			0.473127i
$277$	−8.31876e6			−0.391398			−0.195699	−	0.980664i	$-0.562698\pi$
$277$	−8.31876e6			−0.391398			−0.195699	+	0.980664i	$0.562698\pi$
$278$			2.57990e7i			1.20079i
$279$			275348.i			0.0126785i
$280$			1.32725e7i			0.604617i
$281$	4.36527e7			1.96740			0.983699	−	0.179820i	$-0.0575516\pi$
$281$	4.36527e7			1.96740			0.983699	+	0.179820i	$0.0575516\pi$
$282$	7.05878e6			0.314762
$283$		−	9.41605e6i		−	0.415441i	−0.978188	−	0.207721i	$-0.933396\pi$
$283$		−	9.41605e6i		−	0.415441i	0.978188	−	0.207721i	$-0.0666045\pi$
$284$	−7.80535e6			−0.340751
$285$	−9.82054e6			−0.424229
$286$		−	9.10698e6i		−	0.389293i
$287$	−8.85355e6			−0.374517
$288$		−	1.40761e6i		−	0.0589256i
$289$	4.73329e7			1.96096
$290$			1.55055e7i			0.635758i
$291$			1.88993e7i			0.766951i
$292$			1.42218e7i			0.571223i
$293$	−6.42985e6			−0.255622			−0.127811	−	0.991799i	$-0.540795\pi$
$293$	−6.42985e6			−0.255622			−0.127811	+	0.991799i	$0.540795\pi$
$294$		−	2.42072e7i		−	0.952582i
$295$	−2.39176e7	−	2.48597e6i	−0.931648	−	0.0968345i
$296$	2.62068e6			0.101050
$297$		−	9.27384e6i		−	0.353990i
$298$	−1.59603e7			−0.603106
$299$	1.31130e7			0.490554
$300$	955998.			0.0354073
$301$			7.26296e7i			2.66326i
$302$	9.89724e6			0.359330
$303$		−	5.98385e6i		−	0.215106i
$304$	−5.50981e6			−0.196117
$305$		−	1.28870e7i		−	0.454204i
$306$		−	1.16210e7i		−	0.405583i
$307$	3.68285e6			0.127283			0.0636413	−	0.997973i	$-0.479729\pi$
$307$	3.68285e6			0.127283			0.0636413	+	0.997973i	$0.479729\pi$
$308$			4.90608e7i			1.67912i
$309$			1.20643e7i			0.408908i
$310$	750491.			0.0251919
$311$	3.63411e7			1.20814			0.604070	−	0.796932i	$-0.293545\pi$
$311$	3.63411e7			1.20814			0.604070	+	0.796932i	$0.293545\pi$
$312$	−1.85557e6			−0.0610961
$313$		−	7.68297e6i		−	0.250551i	−0.992122	−	0.125276i	$-0.960019\pi$
$313$		−	7.68297e6i		−	0.250551i	0.992122	−	0.125276i	$-0.0399815\pi$
$314$	−3.29118e7			−1.06307
$315$	1.78170e7			0.570038
$316$	1.20363e7			0.381445
$317$	−3.06323e7			−0.961618			−0.480809	−	0.876825i	$-0.659657\pi$
$317$	−3.06323e7			−0.961618			−0.480809	+	0.876825i	$0.659657\pi$
$318$		−	1.75152e7i		−	0.544670i
$319$			5.73147e7i			1.76561i
$320$	−3.83659e6			−0.117083
$321$	1.07086e7			0.323757
$322$	−7.06416e7			−2.11589
$323$	−4.54883e7			−1.34987
$324$	−1.88957e6			−0.0555556
$325$		−	1.26024e6i		−	0.0367116i
$326$		−	3.30499e7i		−	0.953933i
$327$			4.01885e6i			0.114937i
$328$		−	2.55923e6i		−	0.0725249i
$329$			5.01286e7i			1.40766i
$330$	−2.52769e7			−0.703367
$331$	−1.10379e6			−0.0304370			−0.0152185	−	0.999884i	$-0.504844\pi$
$331$	−1.10379e6			−0.0304370			−0.0152185	+	0.999884i	$0.504844\pi$
$332$		−	8.54251e6i		−	0.233438i
$333$		−	3.51799e6i		−	0.0952713i
$334$			3.33740e7i			0.895712i
$335$			3.39835e7i			0.903927i
$336$	9.99625e6			0.263523
$337$			3.31881e7i			0.867146i	0.901118	+	0.433573i	$0.142747\pi$
$337$			3.31881e7i			0.867146i	−0.901118	+	0.433573i	$0.857253\pi$
$338$		−	2.48585e7i		−	0.643760i
$339$		−	2.43624e7i		−	0.625346i
$340$	−3.16744e7			−0.805882
$341$	2.77412e6			0.0699620
$342$			7.39636e6i			0.184901i
$343$	9.82344e7			2.43434
$344$	−2.09945e7			−0.515738
$345$		−	3.63957e7i		−	0.886324i
$346$	4.71477e7			1.13824
$347$			4.06627e7i			0.973213i	0.873621	+	0.486606i	$0.161765\pi$
$347$			4.06627e7i			0.973213i	−0.873621	+	0.486606i	$0.838235\pi$
$348$	1.16780e7			0.277097
$349$			4.39822e7i			1.03467i	0.855784	+	0.517334i	$0.173075\pi$
$349$			4.39822e7i			1.03467i	−0.855784	+	0.517334i	$0.826925\pi$
$350$			6.78911e6i			0.158347i
$351$			2.49091e6i			0.0576019i
$352$	−1.41816e7			−0.325160
$353$		−	3.03736e7i		−	0.690513i	−0.938508	−	0.345256i	$-0.887792\pi$
$353$		−	3.03736e7i		−	0.690513i	0.938508	−	0.345256i	$-0.112208\pi$
$354$	−1.87231e6	+	1.80136e7i	−0.0422055	+	0.406061i
$355$	2.85586e7			0.638341
$356$		−	3.74919e6i		−	0.0830974i
$357$	8.25278e7			1.81383
$358$	6.10936e7			1.33152
$359$	5.67589e7			1.22673			0.613367	−	0.789798i	$-0.289815\pi$
$359$	5.67589e7			1.22673			0.613367	+	0.789798i	$0.289815\pi$
$360$			5.15023e6i			0.110387i
$361$	−1.80942e7			−0.384608
$362$			3.72812e6i			0.0785895i
$363$	−6.58179e7			−1.37602
$364$		−	1.31775e7i		−	0.273230i
$365$		−	5.20355e7i		−	1.07009i
$366$	−9.70585e6			−0.197966
$367$			8.31785e7i			1.68272i	0.540472	+	0.841362i	$0.318246\pi$
$367$			8.31785e7i			1.68272i	−0.540472	+	0.841362i	$0.681754\pi$
$368$		−	2.04198e7i		−	0.409740i
$369$	−3.43550e6			−0.0683771
$370$	−9.58868e6			−0.189301
$371$	1.24386e8			2.43584
$372$		−	565234.i		−	0.0109799i
$373$	−5.94682e7			−1.14593			−0.572965	−	0.819580i	$-0.694207\pi$
$373$	−5.94682e7			−1.14593			−0.572965	+	0.819580i	$0.694207\pi$
$374$	−1.17082e8			−2.23807
$375$	−3.20158e7			−0.607115
$376$	−1.44903e7			−0.272592
$377$		−	1.53945e7i		−	0.287303i
$378$		−	1.34189e7i		−	0.248452i
$379$	−6.93731e7			−1.27430			−0.637152	−	0.770738i	$-0.719888\pi$
$379$	−6.93731e7			−1.27430			−0.637152	+	0.770738i	$0.719888\pi$
$380$	2.01596e7			0.367393
$381$	1.87258e7			0.338583
$382$	−3.11611e7			−0.559015
$383$	−8.52075e7			−1.51664			−0.758318	−	0.651885i	$-0.773979\pi$
$383$	−8.52075e7			−1.51664			−0.758318	+	0.651885i	$0.773979\pi$
$384$			2.88954e6i			0.0510310i
$385$		−	1.79506e8i		−	3.14556i
$386$			5.02836e6i			0.0874308i
$387$			2.81829e7i			0.486243i
$388$		−	3.87966e7i		−	0.664199i
$389$	7.08718e7			1.20399			0.601997	−	0.798498i	$-0.294372\pi$
$389$	7.08718e7			1.20399			0.601997	+	0.798498i	$0.294372\pi$
$390$	6.78926e6			0.114453
$391$		−	1.68583e8i		−	2.82023i
$392$			4.96926e7i			0.824961i
$393$		−	4.55683e7i		−	0.750732i
$394$		−	4.05274e7i		−	0.662613i
$395$	−4.40391e7			−0.714574
$396$			1.90374e7i			0.306564i
$397$		−	7.51278e7i		−	1.20069i	−0.799743	−	0.600343i	$-0.795031\pi$
$397$		−	7.51278e7i		−	1.20069i	0.799743	−	0.600343i	$-0.204969\pi$
$398$		−	3.95076e7i		−	0.626659i
$399$	−5.25260e7			−0.826904
$400$	−1.96247e6			−0.0306637
$401$		−	960104.i		−	0.0148897i	−0.999972	−	0.00744484i	$-0.997630\pi$
$401$		−	960104.i		−	0.0148897i	0.999972	−	0.00744484i	$-0.00236979\pi$
$402$	2.55947e7			0.393978
$403$	−745116.			−0.0113844
$404$			1.22837e7i			0.186287i
$405$	6.91366e6			0.104074
$406$			8.29325e7i			1.23922i
$407$	−3.54437e7			−0.525721
$408$			2.38557e7i			0.351246i
$409$			3.48161e7i			0.508874i	0.967089	+	0.254437i	$0.0818901\pi$
$409$			3.48161e7i			0.508874i	−0.967089	+	0.254437i	$0.918110\pi$
$410$			9.36384e6i			0.135863i
$411$	−1.77927e7			−0.256282
$412$		−	2.47656e7i		−	0.354125i
$413$	−1.27925e8	−	1.32964e7i	−1.81596	−	0.188749i
$414$	−2.74115e7			−0.386306
$415$			3.12558e7i			0.437307i
$416$	3.80911e6			0.0529108
$417$	−7.10936e7			−0.980443
$418$	7.45182e7			1.02031
$419$			9.15956e7i			1.24518i	0.782548	+	0.622590i	$0.213920\pi$
$419$			9.15956e7i			1.24518i	−0.782548	+	0.622590i	$0.786080\pi$
$420$	−3.65748e7			−0.493667
$421$			4.43807e7i			0.594768i	0.954758	+	0.297384i	$0.0961142\pi$
$421$			4.43807e7i			0.594768i	−0.954758	+	0.297384i	$0.903886\pi$
$422$	−3.74513e7			−0.498344
$423$			1.94517e7i			0.257002i
$424$			3.59552e7i			0.471698i
$425$	−1.62019e7			−0.211057
$426$		−	2.15090e7i		−	0.278222i
$427$		−	6.89270e7i		−	0.885331i
$428$	−2.19827e7			−0.280382
$429$	2.50959e7			0.317856
$430$	7.68157e7			0.966150
$431$			9.58430e7i			1.19709i	0.801087	+	0.598547i	$0.204255\pi$
$431$			9.58430e7i			1.19709i	−0.801087	+	0.598547i	$0.795745\pi$
$432$	3.87891e6			0.0481125
$433$	−9.97571e7			−1.22880			−0.614399	−	0.788996i	$-0.710601\pi$
$433$	−9.97571e7			−1.22880			−0.614399	+	0.788996i	$0.710601\pi$
$434$	4.01406e6			0.0491038
$435$	−4.27282e7			−0.519095
$436$		−	8.24990e6i		−	0.0995380i
$437$			1.07297e8i			1.28571i
$438$	−3.91907e7			−0.466402
$439$	1.30887e8			1.54704			0.773521	−	0.633771i	$-0.218494\pi$
$439$	1.30887e8			1.54704			0.773521	+	0.633771i	$0.218494\pi$
$440$	5.18884e7			0.609134
$441$	6.67072e7			0.777780
$442$	3.14476e7			0.364184
$443$			4.38917e7i			0.504861i	0.967615	+	0.252430i	$0.0812299\pi$
$443$			4.38917e7i			0.504861i	−0.967615	+	0.252430i	$0.918770\pi$
$444$			7.22174e6i			0.0825074i
$445$			1.37178e7i			0.155669i
$446$			1.15774e7i			0.130498i
$447$		−	4.39815e7i		−	0.492434i
$448$	−2.05203e7			−0.228218
$449$	8.97272e7			0.991254			0.495627	−	0.868535i	$-0.334938\pi$
$449$	8.97272e7			0.991254			0.495627	+	0.868535i	$0.334938\pi$
$450$			2.63442e6i			0.0289100i
$451$			3.46126e7i			0.377315i
$452$			5.00111e7i			0.541565i
$453$			2.72736e7i			0.293392i
$454$	9.63724e7			1.02988
$455$			4.82146e7i			0.511852i
$456$		−	1.51833e7i		−	0.160129i
$457$		−	1.77370e8i		−	1.85837i	−0.369617	−	0.929184i	$-0.620511\pi$
$457$		−	1.77370e8i		−	1.85837i	0.369617	−	0.929184i	$-0.379489\pi$
$458$	−5.84930e7			−0.608846
$459$	3.20238e7			0.331157
$460$			7.47131e7i			0.767579i
$461$	6.89053e7			0.703315			0.351657	−	0.936129i	$-0.385618\pi$
$461$	6.89053e7			0.703315			0.351657	+	0.936129i	$0.385618\pi$
$462$	−1.35196e8			−1.37100
$463$			3.42086e7i			0.344661i	0.985039	+	0.172331i	$0.0551297\pi$
$463$			3.42086e7i			0.344661i	−0.985039	+	0.172331i	$0.944870\pi$
$464$	−2.39726e7			−0.239973
$465$			2.06811e6i			0.0205691i
$466$	−2.85682e7			−0.282310
$467$			1.04701e8i			1.02802i	0.857785	+	0.514009i	$0.171840\pi$
$467$			1.04701e8i			1.02802i	−0.857785	+	0.514009i	$0.828160\pi$
$468$		−	5.11335e6i		−	0.0498847i
$469$			1.81763e8i			1.76193i
$470$	5.30178e7			0.510656
$471$		−	9.06941e7i		−	0.867993i
$472$	3.84349e6	−	3.69784e7i	0.0365510	−	0.351659i
$473$	2.83942e8			2.68316
$474$			3.31682e7i			0.311449i
$475$	1.03120e7			0.0962188
$476$	−1.69413e8			−1.57082
$477$	4.82662e7			0.444722
$478$			3.56342e7i			0.326275i
$479$	−1.39074e8			−1.26543			−0.632716	−	0.774384i	$-0.718060\pi$
$479$	−1.39074e8			−1.26543			−0.632716	+	0.774384i	$0.718060\pi$
$480$		−	1.05724e7i		−	0.0955982i
$481$	9.52001e6			0.0855465
$482$		−	4.30983e7i		−	0.384874i
$483$		−	1.94665e8i		−	1.72762i
$484$	1.35111e8			1.19167
$485$			1.41951e8i			1.24427i
$486$		−	5.20704e6i		−	0.0453609i
$487$	−5.17092e7			−0.447694			−0.223847	−	0.974624i	$-0.571862\pi$
$487$	−5.17092e7			−0.447694			−0.223847	+	0.974624i	$0.571862\pi$
$488$	1.99242e7			0.171443
$489$	9.10750e7			0.778883
$490$		−	1.81818e8i		−	1.54543i
$491$	7.53699e7			0.636727			0.318363	−	0.947969i	$-0.396867\pi$
$491$	7.53699e7			0.636727			0.318363	+	0.947969i	$0.396867\pi$
$492$	7.05240e6			0.0592163
$493$	−1.97915e8			−1.65173
$494$	−2.00152e7			−0.166027
$495$		−	6.96549e7i		−	0.574297i
$496$			1.16031e6i			0.00950889i
$497$	1.52748e8			1.24425
$498$	2.35404e7			0.190601
$499$	−7.37094e7			−0.593227			−0.296614	−	0.954998i	$-0.595857\pi$
$499$	−7.37094e7			−0.593227			−0.296614	+	0.954998i	$0.595857\pi$
$500$	6.57221e7			0.525777
$501$	−9.19678e7			−0.731346
$502$		−	8.51871e7i		−	0.673384i
$503$			1.64385e8i			1.29169i	0.763468	+	0.645846i	$0.223495\pi$
$503$			1.64385e8i			1.29169i	−0.763468	+	0.645846i	$0.776505\pi$
$504$			2.75464e7i			0.215166i
$505$		−	4.49441e7i		−	0.348979i
$506$			2.76170e8i			2.13170i
$507$	6.85019e7			0.525628
$508$	−3.84403e7			−0.293221
$509$			1.35583e8i			1.02814i	0.857748	+	0.514070i	$0.171863\pi$
$509$			1.35583e8i			1.02814i	−0.857748	+	0.514070i	$0.828137\pi$
$510$		−	8.72844e7i		−	0.658000i
$511$		−	2.78316e8i		−	2.08581i
$512$		−	5.93164e6i		−	0.0441942i
$513$	−2.03820e7			−0.150971
$514$		−	1.45159e8i		−	1.06894i
$515$			9.06136e7i			0.663394i
$516$		−	5.78539e7i		−	0.421098i
$517$	1.95975e8			1.41818
$518$	−5.12858e7			−0.368985
$519$			1.29924e8i			0.929366i
$520$	−1.39370e7			−0.0991195
$521$	−2.24967e8			−1.59076			−0.795380	−	0.606111i	$-0.792729\pi$
$521$	−2.24967e8			−1.59076			−0.795380	+	0.606111i	$0.792729\pi$
$522$			3.21808e7i			0.226248i
$523$	−5.55339e7			−0.388198			−0.194099	−	0.980982i	$-0.562178\pi$
$523$	−5.55339e7			−0.388198			−0.194099	+	0.980982i	$0.562178\pi$
$524$			9.35426e7i			0.650153i
$525$	−1.87086e7			−0.129289
$526$			6.86401e7i			0.471651i
$527$			9.57940e6i			0.0654495i
$528$		−	3.90799e7i		−	0.265492i
$529$	−2.49616e8			−1.68618
$530$		−	1.31555e8i		−	0.883649i
$531$	−4.96397e7	−	5.15949e6i	−0.331547	−	0.0344606i
$532$	1.07825e8			0.716120
$533$		−	9.29678e6i		−	0.0613975i
$534$	1.03316e7			0.0678488
$535$	8.04315e7			0.525248
$536$	−5.25409e7			−0.341195
$537$			1.68354e8i			1.08718i
$538$	1.49644e8			0.960979
$539$		−	6.72074e8i		−	4.29191i
$540$	−1.41924e7			−0.0901308
$541$		−	1.73413e8i		−	1.09519i	−0.836744	−	0.547595i	$-0.815543\pi$
$541$		−	1.73413e8i		−	1.09519i	0.836744	−	0.547595i	$-0.184457\pi$
$542$		−	1.47849e8i		−	0.928580i
$543$	−1.02735e7			−0.0641681
$544$		−	4.89709e7i		−	0.304188i
$545$			3.01852e7i			0.186468i
$546$	3.63129e7			0.223092
$547$	3.13410e6			0.0191492			0.00957460	−	0.999954i	$-0.496952\pi$
$547$	3.13410e6			0.0191492			0.00957460	+	0.999954i	$0.496952\pi$
$548$	3.65250e7			0.221946
$549$		−	2.67462e7i		−	0.161638i
$550$	2.65417e7			0.159530
$551$	1.25966e8			0.753005
$552$	5.62703e7			0.334551
$553$	−2.35547e8			−1.39284
$554$			4.70580e7i			0.276761i
$555$		−	2.64233e7i		−	0.154564i
$556$	1.45941e8			0.849088
$557$	−2.51736e8			−1.45673			−0.728365	−	0.685190i	$-0.759719\pi$
$557$	−2.51736e8			−1.45673			−0.728365	+	0.685190i	$0.759719\pi$
$558$	1.55760e6			0.00896507
$559$	−7.62656e7			−0.436609
$560$	7.50809e7			0.427529
$561$		−	3.22639e8i		−	1.82738i
$562$		−	2.46937e8i		−	1.39116i
$563$			5.42737e7i			0.304134i	0.988370	+	0.152067i	$0.0485929\pi$
$563$			5.42737e7i			0.304134i	−0.988370	+	0.152067i	$0.951407\pi$
$564$		−	3.99305e7i		−	0.222570i
$565$		−	1.82983e8i		−	1.01453i
$566$	−5.32652e7			−0.293761
$567$	3.69783e7			0.202860
$568$			4.41537e7i			0.240947i
$569$		−	2.86608e8i		−	1.55579i	−0.628394	−	0.777895i	$-0.716287\pi$
$569$		−	2.86608e8i		−	1.55579i	0.628394	−	0.777895i	$-0.283713\pi$
$570$			5.55533e7i			0.299975i
$571$			2.63425e7i			0.141498i	0.997494	+	0.0707489i	$0.0225389\pi$
$571$			2.63425e7i			0.141498i	−0.997494	+	0.0707489i	$0.977461\pi$
$572$	−5.15169e7			−0.275272
$573$		−	8.58700e7i		−	0.456434i
$574$			5.00833e7i			0.264824i
$575$			3.82169e7i			0.201026i
$576$	−7.96262e6			−0.0416667
$577$	−2.41063e7			−0.125488			−0.0627441	−	0.998030i	$-0.519985\pi$
$577$	−2.41063e7			−0.125488			−0.0627441	+	0.998030i	$0.519985\pi$
$578$		−	2.67755e8i		−	1.38661i
$579$	−1.38565e7			−0.0713870
$580$	8.77124e7			0.449549
$581$			1.67174e8i			0.852395i
$582$	1.06911e8			0.542317
$583$		−	4.86281e8i		−	2.45404i
$584$	8.04506e7			0.403916
$585$			1.87090e7i			0.0934508i
$586$			3.63727e7i			0.180752i
$587$		−	2.49986e8i		−	1.23595i	−0.786198	−	0.617975i	$-0.787953\pi$
$587$		−	2.49986e8i		−	1.23595i	0.786198	−	0.617975i	$-0.212047\pi$
$588$	−1.36937e8			−0.673577
$589$		−	6.09694e6i		−	0.0298377i
$590$	−1.40628e7	+	1.35299e8i	−0.0684723	+	0.658775i
$591$	1.11680e8			0.541022
$592$		−	1.48248e7i		−	0.0714535i
$593$	3.33338e8			1.59853			0.799265	−	0.600979i	$-0.205223\pi$
$593$	3.33338e8			1.59853			0.799265	+	0.600979i	$0.205223\pi$
$594$	−5.24608e7			−0.250308
$595$	6.19858e8			2.94267
$596$			9.02853e7i			0.426460i
$597$	1.08870e8			0.511665
$598$		−	7.41781e7i		−	0.346874i
$599$	−3.13374e8			−1.45808			−0.729042	−	0.684469i	$-0.760034\pi$
$599$	−3.13374e8			−1.45808			−0.729042	+	0.684469i	$0.760034\pi$
$600$		−	5.40794e6i		−	0.0250368i
$601$		−	2.12094e8i		−	0.977024i	−0.872557	−	0.488512i	$-0.837540\pi$
$601$		−	2.12094e8i		−	0.977024i	0.872557	−	0.488512i	$-0.162460\pi$
$602$	4.10855e8			1.88321
$603$			7.05308e7i			0.321682i
$604$		−	5.59873e7i		−	0.254085i
$605$	−4.94352e8			−2.23239
$606$	−3.38498e7			−0.152103
$607$	9.55577e7			0.427267			0.213634	−	0.976914i	$-0.431470\pi$
$607$	9.55577e7			0.427267			0.213634	+	0.976914i	$0.431470\pi$
$608$			3.11682e7i			0.138676i
$609$	−2.28535e8			−1.01181
$610$	−7.28997e7			−0.321171
$611$	−5.26381e7			−0.230769
$612$	−6.57384e7			−0.286791
$613$			1.90882e8i			0.828675i	0.910123	+	0.414337i	$0.135987\pi$
$613$			1.90882e8i			0.828675i	−0.910123	+	0.414337i	$0.864013\pi$
$614$		−	2.08334e7i		−	0.0900024i
$615$	−2.58037e7			−0.110932
$616$	2.77530e8			1.18732
$617$	3.86424e8			1.64516			0.822580	−	0.568649i	$-0.192534\pi$
$617$	3.86424e8			1.64516			0.822580	+	0.568649i	$0.192534\pi$
$618$	6.82458e7			0.289142
$619$	−2.65985e8			−1.12146			−0.560731	−	0.827998i	$-0.689480\pi$
$619$	−2.65985e8			−1.12146			−0.560731	+	0.827998i	$0.689480\pi$
$620$		−	4.24542e6i		−	0.0178133i
$621$		−	7.55372e7i		−	0.315418i
$622$		−	2.05576e8i		−	0.854283i
$623$			7.33705e7i			0.303429i
$624$			1.04967e7i			0.0432015i
$625$	−2.10523e8			−0.862301
$626$	−4.34615e7			−0.177166
$627$			2.05348e8i			0.833082i
$628$			1.86177e8i			0.751704i
$629$		−	1.22392e8i		−	0.491813i
$630$		−	1.00788e8i		−	0.403078i
$631$	8.22936e7			0.327550			0.163775	−	0.986498i	$-0.447633\pi$
$631$	8.22936e7			0.327550			0.163775	+	0.986498i	$0.447633\pi$
$632$		−	6.80876e7i		−	0.269722i
$633$		−	1.03204e8i		−	0.406896i
$634$			1.73283e8i			0.679966i
$635$	1.40648e8			0.549302
$636$	−9.90809e7			−0.385140
$637$			1.80516e8i			0.698389i
$638$	3.24221e8			1.24847
$639$	5.92718e7			0.227167
$640$			2.17030e7i			0.0827905i
$641$	2.91404e7			0.110642			0.0553212	−	0.998469i	$-0.482382\pi$
$641$	2.91404e7			0.110642			0.0553212	+	0.998469i	$0.482382\pi$
$642$		−	6.05772e7i		−	0.228931i
$643$	1.42475e7			0.0535927			0.0267964	−	0.999641i	$-0.491469\pi$
$643$	1.42475e7			0.0535927			0.0267964	+	0.999641i	$0.491469\pi$
$644$			3.99609e8i			1.49616i
$645$			2.11679e8i			0.788858i
$646$			2.57321e8i			0.954503i
$647$	−2.31261e8			−0.853865			−0.426932	−	0.904284i	$-0.640406\pi$
$647$	−2.31261e8			−0.853865			−0.426932	+	0.904284i	$0.640406\pi$
$648$			1.06890e7i			0.0392837i
$649$	−5.19818e7	+	5.00119e8i	−0.190159	+	1.82953i
$650$	−7.12899e6			−0.0259590
$651$			1.10615e7i			0.0400931i
$652$	−1.86959e8			−0.674533
$653$	−4.35499e8			−1.56404			−0.782019	−	0.623254i	$-0.785810\pi$
$653$	−4.35499e8			−1.56404			−0.782019	+	0.623254i	$0.785810\pi$
$654$	2.27340e7			0.0812724
$655$		−	3.42259e8i		−	1.21795i
$656$	−1.44772e7			−0.0512828
$657$		−	1.07997e8i		−	0.380815i
$658$	2.83570e8			0.995366
$659$			3.04274e8i			1.06319i	0.847000	+	0.531593i	$0.178406\pi$
$659$			3.04274e8i			1.06319i	−0.847000	+	0.531593i	$0.821594\pi$
$660$			1.42988e8i			0.497356i
$661$	−2.55140e8			−0.883435			−0.441718	−	0.897154i	$-0.645631\pi$
$661$	−2.55140e8			−0.883435			−0.441718	+	0.897154i	$0.645631\pi$
$662$			6.24397e6i			0.0215222i
$663$			8.66593e7i			0.297355i
$664$	−4.83237e7			−0.165065
$665$	−3.94517e8			−1.34153
$666$	−1.99008e7			−0.0673670
$667$			4.66839e8i			1.57322i
$668$	1.88792e8			0.633364
$669$	−3.19035e7			−0.106552
$670$	1.92239e8			0.639173
$671$	−2.69467e8			−0.891945
$672$		−	5.65473e7i		−	0.186339i
$673$			2.80257e8i			0.919415i	0.888071	+	0.459707i	$0.152046\pi$
$673$			2.80257e8i			0.919415i	−0.888071	+	0.459707i	$0.847954\pi$
$674$	1.87740e8			0.613165
$675$	−7.25961e6			−0.0236049
$676$	−1.40621e8			−0.455207
$677$	2.54527e8			0.820291			0.410145	−	0.912020i	$-0.365478\pi$
$677$	2.54527e8			0.820291			0.410145	+	0.912020i	$0.365478\pi$
$678$	−1.37814e8			−0.442186
$679$			7.59238e8i			2.42532i
$680$			1.79177e8i			0.569845i
$681$			2.65571e8i			0.840890i
$682$		−	1.56928e7i		−	0.0494706i
$683$		−	5.66274e8i		−	1.77732i	−0.458571	−	0.888658i	$-0.651639\pi$
$683$		−	5.66274e8i		−	1.77732i	0.458571	−	0.888658i	$-0.348361\pi$
$684$	4.18401e7			0.130745
$685$	−1.33640e8			−0.415780
$686$		−	5.55697e8i		−	1.72134i
$687$		−	1.61188e8i		−	0.497120i
$688$			1.18763e8i			0.364682i
$689$			1.30613e8i			0.399327i
$690$	−2.05885e8			−0.626726
$691$		−	3.34577e8i		−	1.01406i	−0.861930	−	0.507028i	$-0.830744\pi$
$691$		−	3.34577e8i		−	1.01406i	0.861930	−	0.507028i	$-0.169256\pi$
$692$		−	2.66708e8i		−	0.804855i
$693$		−	3.72555e8i		−	1.11941i
$694$	2.30023e8			0.688165
$695$	−5.33977e8			−1.59063
$696$		−	6.60608e7i		−	0.195937i
$697$	−1.19522e8			−0.352979
$698$	2.48801e8			0.731621
$699$		−	7.87248e7i		−	0.230505i
$700$	3.84050e7			0.111968
$701$		−	2.17724e8i		−	0.632050i	−0.948751	−	0.316025i	$-0.897652\pi$
$701$		−	2.17724e8i		−	0.632050i	0.948751	−	0.316025i	$-0.102348\pi$
$702$	1.40907e7			0.0407307
$703$			7.78978e7i			0.224212i
$704$			8.02233e7i			0.229923i
$705$			1.46100e8i			0.416949i
$706$	−1.71819e8			−0.488266
$707$		−	2.40387e8i		−	0.680226i
$708$	1.01900e8	+	1.05914e7i	0.287128	+	0.0298438i
$709$	1.59760e8			0.448259			0.224129	−	0.974559i	$-0.428046\pi$
$709$	1.59760e8			0.448259			0.224129	+	0.974559i	$0.428046\pi$
$710$		−	1.61552e8i		−	0.451375i
$711$	−9.14007e7			−0.254297
$712$	−2.12086e7			−0.0587588
$713$	2.25957e7			0.0623387
$714$		−	4.66848e8i		−	1.28257i
$715$	1.88493e8			0.515676
$716$		−	3.45598e8i		−	0.941525i
$717$	−9.81963e7			−0.266402
$718$		−	3.21077e8i		−	0.867432i
$719$			3.73546e8i			1.00498i	0.864583	+	0.502490i	$0.167582\pi$
$719$			3.73546e8i			1.00498i	−0.864583	+	0.502490i	$0.832418\pi$
$720$	2.91341e7			0.0780556
$721$			4.84654e8i			1.29308i
$722$			1.02356e8i			0.271959i
$723$	1.18765e8			0.314248
$724$	2.10895e7			0.0555712
$725$	4.48663e7			0.117735
$726$			3.72322e8i			0.972991i
$727$	−2.65165e8			−0.690101			−0.345050	−	0.938584i	$-0.612138\pi$
$727$	−2.65165e8			−0.690101			−0.345050	+	0.938584i	$0.612138\pi$
$728$	−7.45432e7			−0.193203
$729$	1.43489e7			0.0370370
$730$	−2.94357e8			−0.756669
$731$			9.80489e8i			2.51010i
$732$			5.49046e7i			0.139983i
$733$	−1.23734e8			−0.314178			−0.157089	−	0.987584i	$-0.550211\pi$
$733$	−1.23734e8			−0.314178			−0.157089	+	0.987584i	$0.550211\pi$
$734$	4.70529e8			1.18987
$735$	5.01031e8			1.26184
$736$	−1.15512e8			−0.289730
$737$	7.10596e8			1.77509
$738$			1.94341e7i			0.0483499i
$739$		−	2.34627e8i		−	0.581358i	−0.956821	−	0.290679i	$-0.906119\pi$
$739$		−	2.34627e8i		−	0.581358i	0.956821	−	0.290679i	$-0.0938812\pi$
$740$			5.42418e7i			0.133856i
$741$		−	5.51555e7i		−	0.135561i
$742$		−	7.03633e8i		−	1.72240i
$743$	−4.76649e8			−1.16207			−0.581034	−	0.813879i	$-0.697352\pi$
$743$	−4.76649e8			−1.16207			−0.581034	+	0.813879i	$0.697352\pi$
$744$	−3.19745e6			−0.00776398
$745$		−	3.30341e8i		−	0.798903i
$746$			3.36403e8i			0.810296i
$747$			6.48697e7i			0.155625i
$748$			6.62313e8i			1.58255i
$749$	4.30194e8			1.02381
$750$			1.81109e8i			0.429295i
$751$			1.25753e8i			0.296891i	0.988921	+	0.148446i	$0.0474270\pi$
$751$			1.25753e8i			0.296891i	−0.988921	+	0.148446i	$0.952573\pi$
$752$			8.19693e7i			0.192752i
$753$	2.34748e8			0.549815
$754$	−8.70843e7			−0.203154
$755$			2.04849e8i			0.475985i
$756$	−7.59090e7			−0.175682
$757$	−3.64141e8			−0.839426			−0.419713	−	0.907657i	$-0.637869\pi$
$757$	−3.64141e8			−0.839426			−0.419713	+	0.907657i	$0.637869\pi$
$758$			3.92433e8i			0.901070i
$759$	−7.61036e8			−1.74052
$760$		−	1.14040e8i		−	0.259786i
$761$	7.02172e8			1.59327			0.796635	−	0.604460i	$-0.206611\pi$
$761$	7.02172e8			1.59327			0.796635	+	0.604460i	$0.206611\pi$
$762$		−	1.05929e8i		−	0.239414i
$763$			1.61448e8i			0.363462i
$764$			1.76274e8i			0.395283i
$765$	2.40528e8			0.537255
$766$			4.82006e8i			1.07242i
$767$	1.39621e7	−	1.34330e8i	0.0309431	−	0.297705i
$768$	1.63457e7			0.0360844
$769$			2.75560e8i			0.605950i	0.952998	+	0.302975i	$0.0979799\pi$
$769$			2.75560e8i			0.605950i	−0.952998	+	0.302975i	$0.902020\pi$
$770$	−1.01544e9			−2.22424
$771$	4.00011e8			0.872788
$772$	2.84447e7			0.0618229
$773$			2.31760e8i			0.501764i	0.968018	+	0.250882i	$0.0807206\pi$
$773$			2.31760e8i			0.501764i	−0.968018	+	0.250882i	$0.919279\pi$
$774$	1.59427e8			0.343825
$775$		−	2.17160e6i		−	0.00466524i
$776$	−2.19467e8			−0.469660
$777$		−	1.41327e8i		−	0.301275i
$778$		−	4.00911e8i		−	0.851352i
$779$	7.60712e7			0.160919
$780$		−	3.84059e7i		−	0.0809308i
$781$		−	5.97162e8i		−	1.25354i
$782$	−9.53651e8			−1.99420
$783$	−8.86799e7			−0.184731
$784$	2.81104e8			0.583335
$785$		−	6.81195e8i		−	1.40819i
$786$	−2.57773e8			−0.530848
$787$	−8.95649e8			−1.83744			−0.918721	−	0.394908i	$-0.870776\pi$
$787$	−8.95649e8			−1.83744			−0.918721	+	0.394908i	$0.870776\pi$
$788$	−2.29258e8			−0.468538
$789$	−1.89150e8			−0.385102
$790$			2.49123e8i			0.505280i
$791$		−	9.78701e8i		−	1.97752i
$792$	1.07692e8			0.216773
$793$	7.23776e7			0.145139
$794$	−4.24987e8			−0.849013
$795$	3.62523e8			0.721496
$796$	−2.23489e8			−0.443115
$797$			4.47371e8i			0.883676i	0.897095	+	0.441838i	$0.145673\pi$
$797$			4.47371e8i			0.883676i	−0.897095	+	0.441838i	$0.854327\pi$
$798$			2.97132e8i			0.584710i
$799$			6.76729e8i			1.32670i
$800$			1.11014e7i			0.0216825i
$801$			2.84704e7i			0.0553983i
$802$	−5.43117e6			−0.0105286
$803$	−1.08806e9			−2.10140
$804$		−	1.44786e8i		−	0.278585i
$805$		−	1.46211e9i		−	2.80281i
$806$			4.21501e6i			0.00804996i
$807$			4.12372e8i			0.784636i
$808$	6.94868e7			0.131725
$809$			9.23404e8i			1.74400i	0.489507	+	0.872000i	$0.337177\pi$
$809$			9.23404e8i			1.74400i	−0.489507	+	0.872000i	$0.662823\pi$
$810$		−	3.91096e7i		−	0.0735915i
$811$			8.16530e8i			1.53077i	0.643574	+	0.765384i	$0.277451\pi$
$811$			8.16530e8i			1.53077i	−0.643574	+	0.765384i	$0.722549\pi$
$812$	4.69137e8			0.876257
$813$	4.07423e8			0.758182
$814$			2.00500e8i			0.371741i
$815$	6.84055e8			1.26363
$816$	1.34948e8			0.248368
$817$		−	6.24046e8i		−	1.14433i
$818$	1.96949e8			0.359828
$819$			1.00067e8i			0.182154i
$820$	5.29699e7			0.0960699
$821$			7.87168e8i			1.42245i	0.702963	+	0.711227i	$0.251860\pi$
$821$			7.87168e8i			1.42245i	−0.702963	+	0.711227i	$0.748140\pi$
$822$			1.00651e8i			0.181218i
$823$		−	1.71767e8i		−	0.308135i	−0.988060	−	0.154067i	$-0.950763\pi$
$823$		−	1.71767e8i		−	0.308135i	0.988060	−	0.154067i	$-0.0492373\pi$
$824$	−1.40095e8			−0.250404
$825$			7.31404e7i			0.130255i
$826$	−7.52159e7	+	7.23655e8i	−0.133466	+	1.28408i
$827$	5.05093e8			0.893008			0.446504	−	0.894782i	$-0.352669\pi$
$827$	5.05093e8			0.893008			0.446504	+	0.894782i	$0.352669\pi$
$828$			1.55063e8i			0.273160i
$829$	2.75561e8			0.483676			0.241838	−	0.970317i	$-0.422250\pi$
$829$	2.75561e8			0.483676			0.241838	+	0.970317i	$0.422250\pi$
$830$	1.76810e8			0.309223
$831$	−1.29677e8			−0.225974
$832$		−	2.15476e7i		−	0.0374136i
$833$	2.32076e9			4.01508
$834$			4.02166e8i			0.693278i
$835$	−6.90761e8			−1.18650
$836$		−	4.21538e8i		−	0.721470i
$837$			4.29224e6i			0.00731995i
$838$	5.18143e8			0.880476
$839$		−	1.13829e8i		−	0.192738i	−0.995346	−	0.0963691i	$-0.969277\pi$
$839$		−	1.13829e8i		−	0.192738i	0.995346	−	0.0963691i	$-0.0307229\pi$
$840$			2.06899e8i			0.349076i
$841$	−4.67589e7			−0.0786097
$842$	2.51055e8			0.420565
$843$	6.80479e8			1.13588
$844$			2.11857e8i			0.352383i
$845$	5.14511e8			0.852755
$846$	1.10035e8			0.181728
$847$	−2.64408e9			−4.35135
$848$	2.03393e8			0.333541
$849$		−	1.46782e8i		−	0.239855i
$850$			9.16520e7i			0.149240i
$851$	−2.88695e8			−0.468437
$852$	−1.21673e8			−0.196733
$853$	9.67947e7			0.155957			0.0779784	−	0.996955i	$-0.475153\pi$
$853$	9.67947e7			0.155957			0.0779784	+	0.996955i	$0.475153\pi$
$854$	−3.89910e8			−0.626024
$855$	−1.53087e8			−0.244929
$856$			1.24353e8i			0.198260i
$857$			2.81411e8i			0.447094i	0.974693	+	0.223547i	$0.0717636\pi$
$857$			2.81411e8i			0.447094i	−0.974693	+	0.223547i	$0.928236\pi$
$858$		−	1.41964e8i		−	0.224758i
$859$			8.67660e8i			1.36890i	0.729062	+	0.684448i	$0.239957\pi$
$859$			8.67660e8i			1.36890i	−0.729062	+	0.684448i	$0.760043\pi$
$860$		−	4.34535e8i		−	0.683171i
$861$	−1.38013e8			−0.216228
$862$	5.42170e8			0.846474
$863$			8.73813e8i			1.35952i	0.733434	+	0.679761i	$0.237916\pi$
$863$			8.73813e8i			1.35952i	−0.733434	+	0.679761i	$0.762084\pi$
$864$		−	2.19424e7i		−	0.0340207i
$865$			9.75846e8i			1.50776i
$866$			5.64312e8i			0.868891i
$867$	7.37846e8			1.13216
$868$		−	2.27070e7i		−	0.0347216i
$869$			9.20860e8i			1.40325i
$870$			2.41707e8i			0.367055i
$871$	−1.90863e8			−0.288846
$872$	−4.66685e7			−0.0703840
$873$			2.94612e8i			0.442800i
$874$	6.06964e8			0.909136
$875$	−1.28616e9			−1.91987
$876$			2.21696e8i			0.329796i
$877$	−1.93143e8			−0.286338			−0.143169	−	0.989698i	$-0.545729\pi$
$877$	−1.93143e8			−0.286338			−0.143169	+	0.989698i	$0.545729\pi$
$878$		−	7.40407e8i		−	1.09392i
$879$	−1.00231e8			−0.147583
$880$		−	2.93525e8i		−	0.430723i
$881$			3.49813e8i			0.511573i	0.966733	+	0.255787i	$0.0823345\pi$
$881$			3.49813e8i			0.511573i	−0.966733	+	0.255787i	$0.917666\pi$
$882$		−	3.77353e8i		−	0.549974i
$883$	−9.17352e7			−0.133246			−0.0666230	−	0.997778i	$-0.521222\pi$
$883$	−9.17352e7			−0.133246			−0.0666230	+	0.997778i	$0.521222\pi$
$884$		−	1.77894e8i		−	0.257517i
$885$	−3.72839e8	−	3.87524e7i	−0.537887	−	0.0559074i
$886$	2.48289e8			0.356990
$887$		−	1.35679e9i		−	1.94420i	−0.234572	−	0.972099i	$-0.575369\pi$
$887$		−	1.35679e9i		−	1.94420i	0.234572	−	0.972099i	$-0.424631\pi$
$888$	4.08523e7			0.0583415
$889$	7.52265e8			1.07069
$890$	7.75993e7			0.110075
$891$		−	1.44565e8i		−	0.204376i
$892$	6.54915e7			0.0922763
$893$		−	4.30713e8i		−	0.604831i
$894$	−2.48797e8			−0.348203
$895$			1.26449e9i			1.76379i
$896$			1.16080e8i			0.161374i
$897$	2.04411e8			0.283222
$898$		−	5.07574e8i		−	0.700923i
$899$		−	2.65272e7i		−	0.0365100i
$900$	1.49025e7			0.0204424
$901$	1.67919e9			2.29576
$902$	1.95798e8			0.266802
$903$			1.13218e9i			1.53764i
$904$	2.82905e8			0.382945
$905$	−7.71633e7			−0.104103
$906$	1.54283e8			0.207459
$907$	5.48952e8			0.735720			0.367860	−	0.929881i	$-0.380091\pi$
$907$	5.48952e8			0.735720			0.367860	+	0.929881i	$0.380091\pi$
$908$		−	5.45165e8i		−	0.728232i
$909$		−	9.32790e7i		−	0.124192i
$910$	2.72743e8			0.361934
$911$	−3.30400e8			−0.437004			−0.218502	−	0.975837i	$-0.570117\pi$
$911$	−3.30400e8			−0.437004			−0.218502	+	0.975837i	$0.570117\pi$
$912$	−8.58895e7			−0.113228
$913$	6.53560e8			0.858763
$914$	−1.00336e9			−1.31406
$915$		−	2.00888e8i		−	0.262235i
$916$			3.30886e8i			0.430519i
$917$		−	1.83060e9i		−	2.37402i
$918$		−	1.81154e8i		−	0.234164i
$919$		−	3.72892e8i		−	0.480437i	−0.970719	−	0.240218i	$-0.922781\pi$
$919$		−	3.72892e8i		−	0.480437i	0.970719	−	0.240218i	$-0.0772191\pi$
$920$	4.22641e8			0.542761
$921$	5.74100e7			0.0734867
$922$		−	3.89787e8i		−	0.497319i
$923$			1.60395e8i			0.203979i
$924$			7.64782e8i			0.969441i
$925$			2.77455e7i			0.0350564i
$926$	1.93513e8			0.243712
$927$			1.88063e8i			0.236083i
$928$			1.35610e8i			0.169686i
$929$		−	3.42159e8i		−	0.426758i	−0.976970	−	0.213379i	$-0.931553\pi$
$929$		−	3.42159e8i		−	0.426758i	0.976970	−	0.213379i	$-0.0684468\pi$
$930$	1.16990e7			0.0145445
$931$	−1.47708e9			−1.83043
$932$			1.61606e8i			0.199623i
$933$	5.66502e8			0.697520
$934$	5.92279e8			0.726919
$935$		−	2.42331e9i		−	2.96465i
$936$	−2.89255e7			−0.0352738
$937$			1.02496e9i			1.24591i	0.782258	+	0.622955i	$0.214068\pi$
$937$			1.02496e9i			1.24591i	−0.782258	+	0.622955i	$0.785932\pi$
$938$	1.02821e9			1.24587
$939$		−	1.19766e8i		−	0.144656i
$940$		−	2.99914e8i		−	0.361088i
$941$		−	1.46817e9i		−	1.76201i	−0.473110	−	0.881004i	$-0.656869\pi$
$941$		−	1.46817e9i		−	1.76201i	0.473110	−	0.881004i	$-0.343131\pi$
$942$	−5.13043e8			−0.613764
$943$			2.81926e8i			0.336202i
$944$	−2.09181e8	−	2.17421e7i	−0.248660	−	0.0258455i
$945$	2.77740e8			0.329112
$946$		−	1.60622e9i		−	1.89728i
$947$	−3.59648e8			−0.423475			−0.211737	−	0.977327i	$-0.567912\pi$
$947$	−3.59648e8			−0.423475			−0.211737	+	0.977327i	$0.567912\pi$
$948$	1.87627e8			0.220227
$949$	2.92249e8			0.341944
$950$		−	5.83332e7i		−	0.0680370i
$951$	−4.77511e8			−0.555190
$952$			9.58346e8i			1.11074i
$953$	3.38000e8			0.390515			0.195258	−	0.980752i	$-0.437446\pi$
$953$	3.38000e8			0.390515			0.195258	+	0.980752i	$0.437446\pi$
$954$		−	2.73035e8i		−	0.314466i
$955$		−	6.44961e8i		−	0.740497i
$956$	2.01577e8			0.230711
$957$			8.93448e8i			1.01937i
$958$			7.86720e8i			0.894796i
$959$	−7.14782e8			−0.810435
$960$	−5.98065e7			−0.0675981
$961$	8.86220e8			0.998553
$962$		−	5.38533e7i		−	0.0604905i
$963$	1.66931e8			0.186921
$964$	−2.43801e8			−0.272147
$965$	−1.04075e8			−0.115815
$966$	−1.10119e9			−1.22161
$967$			1.15571e8i			0.127812i	0.997956	+	0.0639058i	$0.0203557\pi$
$967$			1.15571e8i			0.127812i	−0.997956	+	0.0639058i	$0.979644\pi$
$968$		−	7.64303e8i		−	0.842635i
$969$	−7.09093e8			−0.779349
$970$	8.02997e8			0.879830
$971$	2.55114e8			0.278661			0.139330	−	0.990246i	$-0.455505\pi$
$971$	2.55114e8			0.278661			0.139330	+	0.990246i	$0.455505\pi$
$972$	−2.94555e7			−0.0320750
$973$	−2.85602e9			−3.10044
$974$			2.92511e8i			0.316567i
$975$		−	1.96452e7i		−	0.0211954i
$976$		−	1.12708e8i		−	0.121229i
$977$		−	3.75608e8i		−	0.402764i	−0.979513	−	0.201382i	$-0.935457\pi$
$977$		−	3.75608e8i		−	0.402764i	0.979513	−	0.201382i	$-0.0645433\pi$
$978$		−	5.15198e8i		−	0.550754i
$979$	2.86839e8			0.305696
$980$	−1.02852e9			−1.09278
$981$			6.26476e7i			0.0663587i
$982$		−	4.26356e8i		−	0.450234i
$983$			1.76441e9i			1.85755i	0.370648	+	0.928773i	$0.379136\pi$
$983$			1.76441e9i			1.85755i	−0.370648	+	0.928773i	$0.620864\pi$
$984$		−	3.98944e7i		−	0.0418723i
$985$	8.38821e8			0.877729
$986$			1.11958e9i			1.16795i
$987$			7.81427e8i			0.812713i
$988$			1.13223e8i			0.117399i
$989$	2.31276e9			2.39079
$990$	−3.94028e8			−0.406089
$991$		−	5.99599e8i		−	0.616083i	−0.951373	−	0.308042i	$-0.900326\pi$
$991$		−	5.99599e8i		−	0.616083i	0.951373	−	0.308042i	$-0.0996736\pi$
$992$	6.56372e6			0.00672380
$993$	−1.72064e7			−0.0175728
$994$		−	8.64074e8i		−	0.879816i
$995$	8.17712e8			0.830102
$996$		−	1.33164e8i		−	0.134775i
$997$	3.34106e8			0.337131			0.168566	−	0.985690i	$-0.446087\pi$
$997$	3.34106e8			0.337131			0.168566	+	0.985690i	$0.446087\pi$
$998$			4.16963e8i			0.419475i
$999$		−	5.48401e7i		−	0.0550049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.7.d.a.235.3	✓	60
59.58	odd	2	inner	354.7.d.a.235.4	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.7.d.a.235.3	✓	60	1.1	even	1	trivial
354.7.d.a.235.4	yes	60	59.58	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	354.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.65685i q^{2} +15.5885 q^{3} -32.0000 q^{4} +117.083 q^{5} -88.1816i q^{6} +626.230 q^{7} +181.019i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-5.65685i q^{2} +15.5885 q^{3} -32.0000 q^{4} +117.083 q^{5} -88.1816i q^{6} +626.230 q^{7} +181.019i q^{8} +243.000 q^{9} -662.324i q^{10} -2448.22i q^{11} -498.831 q^{12} +657.581i q^{13} -3542.49i q^{14} +1825.15 q^{15} +1024.00 q^{16} +8454.02 q^{17} -1374.62i q^{18} -5380.68 q^{19} -3746.67 q^{20} +9761.96 q^{21} -13849.2 q^{22} -19941.2i q^{23} +2821.81i q^{24} -1916.48 q^{25} +3719.84 q^{26} +3788.00 q^{27} -20039.4 q^{28} -23410.8 q^{29} -10324.6i q^{30} +1133.12i q^{31} -5792.62i q^{32} -38164.0i q^{33} -47823.1i q^{34} +73321.2 q^{35} -7776.00 q^{36} -14477.3i q^{37} +30437.7i q^{38} +10250.7i q^{39} +21194.4i q^{40} -14137.9 q^{41} -55222.0i q^{42} +115979. i q^{43} +78343.0i q^{44} +28451.3 q^{45} -112805. q^{46} +80048.2i q^{47} +15962.6 q^{48} +274515. q^{49} +10841.2i q^{50} +131785. q^{51} -21042.6i q^{52} +198626. q^{53} -21428.1i q^{54} -286646. i q^{55} +113360. i q^{56} -83876.4 q^{57} +132431. i q^{58} +(-204279. - 21232.5i) q^{59} -58404.8 q^{60} -110067. i q^{61} +6409.88 q^{62} +152174. q^{63} -32768.0 q^{64} +76991.8i q^{65} -215888. q^{66} +290250. i q^{67} -270529. q^{68} -310853. i q^{69} -414767. i q^{70} +243917. q^{71} +43987.7i q^{72} -444431. i q^{73} -81896.2 q^{74} -29874.9 q^{75} +172182. q^{76} -1.53315e6i q^{77} +57986.5 q^{78} -376135. q^{79} +119893. q^{80} +59049.0 q^{81} +79975.8i q^{82} +266953. i q^{83} -312383. q^{84} +989825. q^{85} +656077. q^{86} -364938. q^{87} +443175. q^{88} +117162. i q^{89} -160945. i q^{90} +411797. i q^{91} +638119. i q^{92} +17663.6i q^{93} +452821. q^{94} -629988. q^{95} -90298.0i q^{96} +1.21239e6i q^{97} -1.55289e6i q^{98} -594917. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 60 * q - 1920 * q^4 + 408 * q^7 + 14580 * q^9	\( 60 q - 1920 q^{4} + 408 q^{7} + 14580 q^{9} + 4536 q^{15} + 61440 q^{16} - 15840 q^{17} - 5616 q^{19} - 17472 q^{22} + 226260 q^{25} - 34048 q^{26} - 13056 q^{28} - 75392 q^{29} + 278000 q^{35} - 466560 q^{36} + 67376 q^{41} + 209856 q^{46} + 269100 q^{49} - 206064 q^{51} + 490000 q^{53} - 373248 q^{57} - 863472 q^{59} - 145152 q^{60} - 155072 q^{62} + 99144 q^{63} - 1966080 q^{64} - 404352 q^{66} + 506880 q^{68} - 2041856 q^{71} - 2146176 q^{74} + 808704 q^{75} + 179712 q^{76} + 228096 q^{78} + 670248 q^{79} + 3542940 q^{81} + 873408 q^{85} + 1832576 q^{86} - 2568024 q^{87} + 559104 q^{88} + 1049472 q^{94} - 245856 q^{95}+O(q^{100}) \) 60 * q - 1920 * q^4 + 408 * q^7 + 14580 * q^9 + 4536 * q^15 + 61440 * q^16 - 15840 * q^17 - 5616 * q^19 - 17472 * q^22 + 226260 * q^25 - 34048 * q^26 - 13056 * q^28 - 75392 * q^29 + 278000 * q^35 - 466560 * q^36 + 67376 * q^41 + 209856 * q^46 + 269100 * q^49 - 206064 * q^51 + 490000 * q^53 - 373248 * q^57 - 863472 * q^59 - 145152 * q^60 - 155072 * q^62 + 99144 * q^63 - 1966080 * q^64 - 404352 * q^66 + 506880 * q^68 - 2041856 * q^71 - 2146176 * q^74 + 808704 * q^75 + 179712 * q^76 + 228096 * q^78 + 670248 * q^79 + 3542940 * q^81 + 873408 * q^85 + 1832576 * q^86 - 2568024 * q^87 + 559104 * q^88 + 1049472 * q^94 - 245856 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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