LMFDB - Embedded newform 30.4.c.a.19.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [30,4,Mod(19,30)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("30.19"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(30, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	30.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.77005730017$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	30.19
Dual form			30.4.c.a.19.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +(2.00000 + 11.0000i) q^{5} -6.00000 q^{6} -2.00000i q^{7} -8.00000i q^{8} -9.00000 q^{9} +(-22.0000 + 4.00000i) q^{10} +70.0000 q^{11} -12.0000i q^{12} -54.0000i q^{13} +4.00000 q^{14} +(-33.0000 + 6.00000i) q^{15} +16.0000 q^{16} -22.0000i q^{17} -18.0000i q^{18} -24.0000 q^{19} +(-8.00000 - 44.0000i) q^{20} +6.00000 q^{21} +140.000i q^{22} +100.000i q^{23} +24.0000 q^{24} +(-117.000 + 44.0000i) q^{25} +108.000 q^{26} -27.0000i q^{27} +8.00000i q^{28} -216.000 q^{29} +(-12.0000 - 66.0000i) q^{30} +208.000 q^{31} +32.0000i q^{32} +210.000i q^{33} +44.0000 q^{34} +(22.0000 - 4.00000i) q^{35} +36.0000 q^{36} -254.000i q^{37} -48.0000i q^{38} +162.000 q^{39} +(88.0000 - 16.0000i) q^{40} -206.000 q^{41} +12.0000i q^{42} -292.000i q^{43} -280.000 q^{44} +(-18.0000 - 99.0000i) q^{45} -200.000 q^{46} -320.000i q^{47} +48.0000i q^{48} +339.000 q^{49} +(-88.0000 - 234.000i) q^{50} +66.0000 q^{51} +216.000i q^{52} +402.000i q^{53} +54.0000 q^{54} +(140.000 + 770.000i) q^{55} -16.0000 q^{56} -72.0000i q^{57} -432.000i q^{58} +370.000 q^{59} +(132.000 - 24.0000i) q^{60} -550.000 q^{61} +416.000i q^{62} +18.0000i q^{63} -64.0000 q^{64} +(594.000 - 108.000i) q^{65} -420.000 q^{66} +728.000i q^{67} +88.0000i q^{68} -300.000 q^{69} +(8.00000 + 44.0000i) q^{70} -540.000 q^{71} +72.0000i q^{72} -604.000i q^{73} +508.000 q^{74} +(-132.000 - 351.000i) q^{75} +96.0000 q^{76} -140.000i q^{77} +324.000i q^{78} -792.000 q^{79} +(32.0000 + 176.000i) q^{80} +81.0000 q^{81} -412.000i q^{82} -404.000i q^{83} -24.0000 q^{84} +(242.000 - 44.0000i) q^{85} +584.000 q^{86} -648.000i q^{87} -560.000i q^{88} +938.000 q^{89} +(198.000 - 36.0000i) q^{90} -108.000 q^{91} -400.000i q^{92} +624.000i q^{93} +640.000 q^{94} +(-48.0000 - 264.000i) q^{95} -96.0000 q^{96} +56.0000i q^{97} +678.000i q^{98} -630.000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{4} + 4 q^{5} - 12 q^{6} - 18 q^{9} - 44 q^{10} + 140 q^{11} + 8 q^{14} - 66 q^{15} + 32 q^{16} - 48 q^{19} - 16 q^{20} + 12 q^{21} + 48 q^{24} - 234 q^{25} + 216 q^{26} - 432 q^{29} - 24 q^{30}+ \cdots - 1260 q^{99}+O(q^{100}) $ 2 * q - 8 * q^4 + 4 * q^5 - 12 * q^6 - 18 * q^9 - 44 * q^10 + 140 * q^11 + 8 * q^14 - 66 * q^15 + 32 * q^16 - 48 * q^19 - 16 * q^20 + 12 * q^21 + 48 * q^24 - 234 * q^25 + 216 * q^26 - 432 * q^29 - 24 * q^30 + 416 * q^31 + 88 * q^34 + 44 * q^35 + 72 * q^36 + 324 * q^39 + 176 * q^40 - 412 * q^41 - 560 * q^44 - 36 * q^45 - 400 * q^46 + 678 * q^49 - 176 * q^50 + 132 * q^51 + 108 * q^54 + 280 * q^55 - 32 * q^56 + 740 * q^59 + 264 * q^60 - 1100 * q^61 - 128 * q^64 + 1188 * q^65 - 840 * q^66 - 600 * q^69 + 16 * q^70 - 1080 * q^71 + 1016 * q^74 - 264 * q^75 + 192 * q^76 - 1584 * q^79 + 64 * q^80 + 162 * q^81 - 48 * q^84 + 484 * q^85 + 1168 * q^86 + 1876 * q^89 + 396 * q^90 - 216 * q^91 + 1280 * q^94 - 96 * q^95 - 192 * q^96 - 1260 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/30\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$-1$	$1$

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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$			3.00000i			0.577350i
$3$			3.00000i			0.577350i
$4$	−4.00000			−0.500000
$5$	2.00000	+	11.0000i	0.178885	+	0.983870i
$5$	2.00000	+	11.0000i	0.178885	+	0.983870i
$6$	−6.00000			−0.408248
$7$		−	2.00000i		−	0.107990i	−0.998541	−	0.0539949i	$-0.982805\pi$
$7$		−	2.00000i		−	0.107990i	0.998541	−	0.0539949i	$-0.0171955\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−9.00000			−0.333333
$10$	−22.0000	+	4.00000i	−0.695701	+	0.126491i
$11$	70.0000			1.91871			0.959354	−	0.282204i	$-0.0910657\pi$
$11$	70.0000			1.91871			0.959354	+	0.282204i	$0.0910657\pi$
$12$		−	12.0000i		−	0.288675i
$13$		−	54.0000i		−	1.15207i	−0.817425	−	0.576035i	$-0.804599\pi$
$13$		−	54.0000i		−	1.15207i	0.817425	−	0.576035i	$-0.195401\pi$
$14$	4.00000			0.0763604
$15$	−33.0000	+	6.00000i	−0.568038	+	0.103280i
$16$	16.0000			0.250000
$17$		−	22.0000i		−	0.313870i	−0.987609	−	0.156935i	$-0.949839\pi$
$17$		−	22.0000i		−	0.313870i	0.987609	−	0.156935i	$-0.0501613\pi$
$18$		−	18.0000i		−	0.235702i
$19$	−24.0000			−0.289788			−0.144894	−	0.989447i	$-0.546284\pi$
$19$	−24.0000			−0.289788			−0.144894	+	0.989447i	$0.546284\pi$
$20$	−8.00000	−	44.0000i	−0.0894427	−	0.491935i
$21$	6.00000			0.0623480
$22$			140.000i			1.35673i
$23$			100.000i			0.906584i	0.891362	+	0.453292i	$0.149751\pi$
$23$			100.000i			0.906584i	−0.891362	+	0.453292i	$0.850249\pi$
$24$	24.0000			0.204124
$25$	−117.000	+	44.0000i	−0.936000	+	0.352000i
$26$	108.000			0.814636
$27$		−	27.0000i		−	0.192450i
$28$			8.00000i			0.0539949i
$29$	−216.000			−1.38311			−0.691555	−	0.722324i	$-0.743074\pi$
$29$	−216.000			−1.38311			−0.691555	+	0.722324i	$0.743074\pi$
$30$	−12.0000	−	66.0000i	−0.0730297	−	0.401663i
$31$	208.000			1.20509			0.602547	−	0.798084i	$-0.294153\pi$
$31$	208.000			1.20509			0.602547	+	0.798084i	$0.294153\pi$
$32$			32.0000i			0.176777i
$33$			210.000i			1.10777i
$34$	44.0000			0.221939
$35$	22.0000	−	4.00000i	0.106248	−	0.0193178i
$36$	36.0000			0.166667
$37$		−	254.000i		−	1.12858i	−0.825578	−	0.564288i	$-0.809151\pi$
$37$		−	254.000i		−	1.12858i	0.825578	−	0.564288i	$-0.190849\pi$
$38$		−	48.0000i		−	0.204911i
$39$	162.000			0.665148
$40$	88.0000	−	16.0000i	0.347851	−	0.0632456i
$41$	−206.000			−0.784678			−0.392339	−	0.919821i	$-0.628334\pi$
$41$	−206.000			−0.784678			−0.392339	+	0.919821i	$0.628334\pi$
$42$			12.0000i			0.0440867i
$43$		−	292.000i		−	1.03557i	−0.855510	−	0.517786i	$-0.826756\pi$
$43$		−	292.000i		−	1.03557i	0.855510	−	0.517786i	$-0.173244\pi$
$44$	−280.000			−0.959354
$45$	−18.0000	−	99.0000i	−0.0596285	−	0.327957i
$46$	−200.000			−0.641052
$47$		−	320.000i		−	0.993123i	−0.868001	−	0.496562i	$-0.834596\pi$
$47$		−	320.000i		−	0.993123i	0.868001	−	0.496562i	$-0.165404\pi$
$48$			48.0000i			0.144338i
$49$	339.000			0.988338
$50$	−88.0000	−	234.000i	−0.248902	−	0.661852i
$51$	66.0000			0.181213
$52$			216.000i			0.576035i
$53$			402.000i			1.04187i	0.853597	+	0.520933i	$0.174416\pi$
$53$			402.000i			1.04187i	−0.853597	+	0.520933i	$0.825584\pi$
$54$	54.0000			0.136083
$55$	140.000	+	770.000i	0.343229	+	1.88776i
$56$	−16.0000			−0.0381802
$57$		−	72.0000i		−	0.167309i
$58$		−	432.000i		−	0.978007i
$59$	370.000			0.816439			0.408219	−	0.912884i	$-0.366150\pi$
$59$	370.000			0.816439			0.408219	+	0.912884i	$0.366150\pi$
$60$	132.000	−	24.0000i	0.284019	−	0.0516398i
$61$	−550.000			−1.15443			−0.577215	−	0.816592i	$-0.695861\pi$
$61$	−550.000			−1.15443			−0.577215	+	0.816592i	$0.695861\pi$
$62$			416.000i			0.852130i
$63$			18.0000i			0.0359966i
$64$	−64.0000			−0.125000
$65$	594.000	−	108.000i	1.13349	−	0.206088i
$66$	−420.000			−0.783309
$67$			728.000i			1.32745i	0.747975	+	0.663727i	$0.231026\pi$
$67$			728.000i			1.32745i	−0.747975	+	0.663727i	$0.768974\pi$
$68$			88.0000i			0.156935i
$69$	−300.000			−0.523417
$70$	8.00000	+	44.0000i	0.0136598	+	0.0751287i
$71$	−540.000			−0.902623			−0.451311	−	0.892367i	$-0.649044\pi$
$71$	−540.000			−0.902623			−0.451311	+	0.892367i	$0.649044\pi$
$72$			72.0000i			0.117851i
$73$		−	604.000i		−	0.968395i	−0.874959	−	0.484198i	$-0.839112\pi$
$73$		−	604.000i		−	0.968395i	0.874959	−	0.484198i	$-0.160888\pi$
$74$	508.000			0.798024
$75$	−132.000	−	351.000i	−0.203227	−	0.540400i
$76$	96.0000			0.144894
$77$		−	140.000i		−	0.207201i
$78$			324.000i			0.470330i
$79$	−792.000			−1.12794			−0.563968	−	0.825797i	$-0.690726\pi$
$79$	−792.000			−1.12794			−0.563968	+	0.825797i	$0.690726\pi$
$80$	32.0000	+	176.000i	0.0447214	+	0.245967i
$81$	81.0000			0.111111
$82$		−	412.000i		−	0.554851i
$83$		−	404.000i		−	0.534274i	−0.963659	−	0.267137i	$-0.913922\pi$
$83$		−	404.000i		−	0.534274i	0.963659	−	0.267137i	$-0.0860777\pi$
$84$	−24.0000			−0.0311740
$85$	242.000	−	44.0000i	0.308807	−	0.0561467i
$86$	584.000			0.732260
$87$		−	648.000i		−	0.798539i
$88$		−	560.000i		−	0.678366i
$89$	938.000			1.11717			0.558583	−	0.829449i	$-0.311345\pi$
$89$	938.000			1.11717			0.558583	+	0.829449i	$0.311345\pi$
$90$	198.000	−	36.0000i	0.231900	−	0.0421637i
$91$	−108.000			−0.124412
$92$		−	400.000i		−	0.453292i
$93$			624.000i			0.695761i
$94$	640.000			0.702244
$95$	−48.0000	−	264.000i	−0.0518389	−	0.285114i
$96$	−96.0000			−0.102062
$97$			56.0000i			0.0586179i	0.999570	+	0.0293090i	$0.00933067\pi$
$97$			56.0000i			0.0586179i	−0.999570	+	0.0293090i	$0.990669\pi$
$98$			678.000i			0.698861i
$99$	−630.000			−0.639570
$100$	468.000	−	176.000i	0.468000	−	0.176000i
$101$	−592.000			−0.583230			−0.291615	−	0.956536i	$-0.594193\pi$
$101$	−592.000			−0.583230			−0.291615	+	0.956536i	$0.594193\pi$
$102$			132.000i			0.128137i
$103$		−	62.0000i		−	0.0593111i	−0.999560	−	0.0296555i	$-0.990559\pi$
$103$		−	62.0000i		−	0.0593111i	0.999560	−	0.0296555i	$-0.00944104\pi$
$104$	−432.000			−0.407318
$105$	12.0000	+	66.0000i	0.0111531	+	0.0613423i
$106$	−804.000			−0.736711
$107$			84.0000i			0.0758933i	0.999280	+	0.0379467i	$0.0120817\pi$
$107$			84.0000i			0.0758933i	−0.999280	+	0.0379467i	$0.987918\pi$
$108$			108.000i			0.0962250i
$109$	−370.000			−0.325134			−0.162567	−	0.986698i	$-0.551977\pi$
$109$	−370.000			−0.325134			−0.162567	+	0.986698i	$0.551977\pi$
$110$	−1540.00	+	280.000i	−1.33485	+	0.242700i
$111$	762.000			0.651584
$112$		−	32.0000i		−	0.0269975i
$113$			1746.00i			1.45354i	0.686882	+	0.726769i	$0.258979\pi$
$113$			1746.00i			1.45354i	−0.686882	+	0.726769i	$0.741021\pi$
$114$	144.000			0.118306
$115$	−1100.00	+	200.000i	−0.891961	+	0.162175i
$116$	864.000			0.691555
$117$			486.000i			0.384023i
$118$			740.000i			0.577310i
$119$	−44.0000			−0.0338947
$120$	48.0000	+	264.000i	0.0365148	+	0.200832i
$121$	3569.00			2.68144
$122$		−	1100.00i		−	0.816306i
$123$		−	618.000i		−	0.453034i
$124$	−832.000			−0.602547
$125$	−718.000	−	1199.00i	−0.513759	−	0.857935i
$126$	−36.0000			−0.0254535
$127$			1630.00i			1.13889i	0.822029	+	0.569445i	$0.192842\pi$
$127$			1630.00i			1.13889i	−0.822029	+	0.569445i	$0.807158\pi$
$128$		−	128.000i		−	0.0883883i
$129$	876.000			0.597888
$130$	216.000	+	1188.00i	0.145727	+	0.801496i
$131$	−870.000			−0.580246			−0.290123	−	0.956989i	$-0.593696\pi$
$131$	−870.000			−0.580246			−0.290123	+	0.956989i	$0.593696\pi$
$132$		−	840.000i		−	0.553883i
$133$			48.0000i			0.0312942i
$134$	−1456.00			−0.938651
$135$	297.000	−	54.0000i	0.189346	−	0.0344265i
$136$	−176.000			−0.110970
$137$			918.000i			0.572482i	0.958158	+	0.286241i	$0.0924058\pi$
$137$			918.000i			0.572482i	−0.958158	+	0.286241i	$0.907594\pi$
$138$		−	600.000i		−	0.370112i
$139$	596.000			0.363684			0.181842	−	0.983328i	$-0.441794\pi$
$139$	596.000			0.363684			0.181842	+	0.983328i	$0.441794\pi$
$140$	−88.0000	+	16.0000i	−0.0531240	+	0.00965891i
$141$	960.000			0.573380
$142$		−	1080.00i		−	0.638251i
$143$		−	3780.00i		−	2.21049i
$144$	−144.000			−0.0833333
$145$	−432.000	−	2376.00i	−0.247418	−	1.36080i
$146$	1208.00			0.684759
$147$			1017.00i			0.570617i
$148$			1016.00i			0.564288i
$149$	−1076.00			−0.591606			−0.295803	−	0.955249i	$-0.595587\pi$
$149$	−1076.00			−0.591606			−0.295803	+	0.955249i	$0.595587\pi$
$150$	702.000	−	264.000i	0.382120	−	0.143703i
$151$	−32.0000			−0.0172458			−0.00862292	−	0.999963i	$-0.502745\pi$
$151$	−32.0000			−0.0172458			−0.00862292	+	0.999963i	$0.502745\pi$
$152$			192.000i			0.102456i
$153$			198.000i			0.104623i
$154$	280.000			0.146513
$155$	416.000	+	2288.00i	0.215574	+	1.18566i
$156$	−648.000			−0.332574
$157$		−	2554.00i		−	1.29829i	−0.760665	−	0.649145i	$-0.775127\pi$
$157$		−	2554.00i		−	1.29829i	0.760665	−	0.649145i	$-0.224873\pi$
$158$		−	1584.00i		−	0.797571i
$159$	−1206.00			−0.601522
$160$	−352.000	+	64.0000i	−0.173925	+	0.0316228i
$161$	200.000			0.0979019
$162$			162.000i			0.0785674i
$163$		−	752.000i		−	0.361357i	−0.983542	−	0.180678i	$-0.942171\pi$
$163$		−	752.000i		−	0.361357i	0.983542	−	0.180678i	$-0.0578293\pi$
$164$	824.000			0.392339
$165$	−2310.00	+	420.000i	−1.08990	+	0.198163i
$166$	808.000			0.377789
$167$			2700.00i			1.25109i	0.780188	+	0.625546i	$0.215124\pi$
$167$			2700.00i			1.25109i	−0.780188	+	0.625546i	$0.784876\pi$
$168$		−	48.0000i		−	0.0220433i
$169$	−719.000			−0.327264
$170$	88.0000	+	484.000i	0.0397017	+	0.218359i
$171$	216.000			0.0965961
$172$			1168.00i			0.517786i
$173$			1334.00i			0.586255i	0.956073	+	0.293128i	$0.0946961\pi$
$173$			1334.00i			0.586255i	−0.956073	+	0.293128i	$0.905304\pi$
$174$	1296.00			0.564652
$175$	88.0000	+	234.000i	0.0380124	+	0.101078i
$176$	1120.00			0.479677
$177$			1110.00i			0.471371i
$178$			1876.00i			0.789956i
$179$	1714.00			0.715700			0.357850	−	0.933779i	$-0.383510\pi$
$179$	1714.00			0.715700			0.357850	+	0.933779i	$0.383510\pi$
$180$	72.0000	+	396.000i	0.0298142	+	0.163978i
$181$	−4006.00			−1.64510			−0.822551	−	0.568691i	$-0.807450\pi$
$181$	−4006.00			−1.64510			−0.822551	+	0.568691i	$0.807450\pi$
$182$		−	216.000i		−	0.0879724i
$183$		−	1650.00i		−	0.666511i
$184$	800.000			0.320526
$185$	2794.00	−	508.000i	1.11037	−	0.201886i
$186$	−1248.00			−0.491977
$187$		−	1540.00i		−	0.602224i
$188$			1280.00i			0.496562i
$189$	−54.0000			−0.0207827
$190$	528.000	−	96.0000i	0.201606	−	0.0366556i
$191$	−684.000			−0.259123			−0.129562	−	0.991571i	$-0.541357\pi$
$191$	−684.000			−0.259123			−0.129562	+	0.991571i	$0.541357\pi$
$192$		−	192.000i		−	0.0721688i
$193$			4484.00i			1.67236i	0.548455	+	0.836180i	$0.315216\pi$
$193$			4484.00i			1.67236i	−0.548455	+	0.836180i	$0.684784\pi$
$194$	−112.000			−0.0414491
$195$	324.000	+	1782.00i	0.118985	+	0.654419i
$196$	−1356.00			−0.494169
$197$		−	1058.00i		−	0.382636i	−0.981528	−	0.191318i	$-0.938724\pi$
$197$		−	1058.00i		−	0.382636i	0.981528	−	0.191318i	$-0.0612762\pi$
$198$		−	1260.00i		−	0.452244i
$199$	1128.00			0.401818			0.200909	−	0.979610i	$-0.435610\pi$
$199$	1128.00			0.401818			0.200909	+	0.979610i	$0.435610\pi$
$200$	352.000	+	936.000i	0.124451	+	0.330926i
$201$	−2184.00			−0.766405
$202$		−	1184.00i		−	0.412406i
$203$			432.000i			0.149362i
$204$	−264.000			−0.0906064
$205$	−412.000	−	2266.00i	−0.140367	−	0.772021i
$206$	124.000			0.0419393
$207$		−	900.000i		−	0.302195i
$208$		−	864.000i		−	0.288017i
$209$	−1680.00			−0.556019
$210$	−132.000	+	24.0000i	−0.0433755	+	0.00788646i
$211$	780.000			0.254490			0.127245	−	0.991871i	$-0.459387\pi$
$211$	780.000			0.254490			0.127245	+	0.991871i	$0.459387\pi$
$212$		−	1608.00i		−	0.520933i
$213$		−	1620.00i		−	0.521129i
$214$	−168.000			−0.0536647
$215$	3212.00	−	584.000i	1.01887	−	0.185249i
$216$	−216.000			−0.0680414
$217$		−	416.000i		−	0.130138i
$218$		−	740.000i		−	0.229904i
$219$	1812.00			0.559103
$220$	−560.000	−	3080.00i	−0.171615	−	0.943880i
$221$	−1188.00			−0.361600
$222$			1524.00i			0.460740i
$223$			2570.00i			0.771749i	0.922551	+	0.385874i	$0.126100\pi$
$223$			2570.00i			0.771749i	−0.922551	+	0.385874i	$0.873900\pi$
$224$	64.0000			0.0190901
$225$	1053.00	−	396.000i	0.312000	−	0.117333i
$226$	−3492.00			−1.02781
$227$		−	2836.00i		−	0.829216i	−0.910000	−	0.414608i	$-0.863919\pi$
$227$		−	2836.00i		−	0.829216i	0.910000	−	0.414608i	$-0.136081\pi$
$228$			288.000i			0.0836547i
$229$	610.000			0.176026			0.0880130	−	0.996119i	$-0.471948\pi$
$229$	610.000			0.176026			0.0880130	+	0.996119i	$0.471948\pi$
$230$	−400.000	−	2200.00i	−0.114675	−	0.630712i
$231$	420.000			0.119628
$232$			1728.00i			0.489003i
$233$		−	3514.00i		−	0.988025i	−0.869455	−	0.494012i	$-0.835530\pi$
$233$		−	3514.00i		−	0.988025i	0.869455	−	0.494012i	$-0.164470\pi$
$234$	−972.000			−0.271545
$235$	3520.00	−	640.000i	0.977104	−	0.177655i
$236$	−1480.00			−0.408219
$237$		−	2376.00i		−	0.651214i
$238$		−	88.0000i		−	0.0239672i
$239$	1844.00			0.499073			0.249536	−	0.968365i	$-0.419722\pi$
$239$	1844.00			0.499073			0.249536	+	0.968365i	$0.419722\pi$
$240$	−528.000	+	96.0000i	−0.142009	+	0.0258199i
$241$	982.000			0.262474			0.131237	−	0.991351i	$-0.458105\pi$
$241$	982.000			0.262474			0.131237	+	0.991351i	$0.458105\pi$
$242$			7138.00i			1.89607i
$243$			243.000i			0.0641500i
$244$	2200.00			0.577215
$245$	678.000	+	3729.00i	0.176799	+	0.972396i
$246$	1236.00			0.320343
$247$			1296.00i			0.333856i
$248$		−	1664.00i		−	0.426065i
$249$	1212.00			0.308463
$250$	2398.00	−	1436.00i	0.606651	−	0.363282i
$251$	−3174.00			−0.798172			−0.399086	−	0.916914i	$-0.630672\pi$
$251$	−3174.00			−0.798172			−0.399086	+	0.916914i	$0.630672\pi$
$252$		−	72.0000i		−	0.0179983i
$253$			7000.00i			1.73947i
$254$	−3260.00			−0.805317
$255$	132.000	+	726.000i	0.0324163	+	0.178290i
$256$	256.000			0.0625000
$257$		−	1194.00i		−	0.289804i	−0.989446	−	0.144902i	$-0.953713\pi$
$257$		−	1194.00i		−	0.289804i	0.989446	−	0.144902i	$-0.0462867\pi$
$258$			1752.00i			0.422770i
$259$	−508.000			−0.121875
$260$	−2376.00	+	432.000i	−0.566743	+	0.103044i
$261$	1944.00			0.461037
$262$		−	1740.00i		−	0.410296i
$263$		−	140.000i		−	0.0328242i	−0.999865	−	0.0164121i	$-0.994776\pi$
$263$		−	140.000i		−	0.0328242i	0.999865	−	0.0164121i	$-0.00522437\pi$
$264$	1680.00			0.391655
$265$	−4422.00	+	804.000i	−1.02506	+	0.186375i
$266$	−96.0000			−0.0221283
$267$			2814.00i			0.644996i
$268$		−	2912.00i		−	0.663727i
$269$	−5256.00			−1.19132			−0.595658	−	0.803238i	$-0.703109\pi$
$269$	−5256.00			−1.19132			−0.595658	+	0.803238i	$0.703109\pi$
$270$	108.000	+	594.000i	0.0243432	+	0.133888i
$271$	544.000			0.121940			0.0609698	−	0.998140i	$-0.480581\pi$
$271$	544.000			0.121940			0.0609698	+	0.998140i	$0.480581\pi$
$272$		−	352.000i		−	0.0784674i
$273$		−	324.000i		−	0.0718292i
$274$	−1836.00			−0.404806
$275$	−8190.00	+	3080.00i	−1.79591	+	0.675385i
$276$	1200.00			0.261708
$277$			946.000i			0.205197i	0.994723	+	0.102599i	$0.0327157\pi$
$277$			946.000i			0.205197i	−0.994723	+	0.102599i	$0.967284\pi$
$278$			1192.00i			0.257163i
$279$	−1872.00			−0.401698
$280$	−32.0000	−	176.000i	−0.00682988	−	0.0375643i
$281$	1278.00			0.271313			0.135657	−	0.990756i	$-0.456686\pi$
$281$	1278.00			0.271313			0.135657	+	0.990756i	$0.456686\pi$
$282$			1920.00i			0.405441i
$283$		−	7424.00i		−	1.55940i	−0.626152	−	0.779701i	$-0.715371\pi$
$283$		−	7424.00i		−	1.55940i	0.626152	−	0.779701i	$-0.284629\pi$
$284$	2160.00			0.451311
$285$	792.000	−	144.000i	0.164611	−	0.0299292i
$286$	7560.00			1.56305
$287$			412.000i			0.0847373i
$288$		−	288.000i		−	0.0589256i
$289$	4429.00			0.901486
$290$	4752.00	−	864.000i	0.962231	−	0.174951i
$291$	−168.000			−0.0338431
$292$			2416.00i			0.484198i
$293$			1362.00i			0.271566i	0.990739	+	0.135783i	$0.0433550\pi$
$293$			1362.00i			0.271566i	−0.990739	+	0.135783i	$0.956645\pi$
$294$	−2034.00			−0.403487
$295$	740.000	+	4070.00i	0.146049	+	0.803270i
$296$	−2032.00			−0.399012
$297$		−	1890.00i		−	0.369256i
$298$		−	2152.00i		−	0.418329i
$299$	5400.00			1.04445
$300$	528.000	+	1404.00i	0.101614	+	0.270200i
$301$	−584.000			−0.111831
$302$		−	64.0000i		−	0.0121947i
$303$		−	1776.00i		−	0.336728i
$304$	−384.000			−0.0724471
$305$	−1100.00	−	6050.00i	−0.206511	−	1.13581i
$306$	−396.000			−0.0739798
$307$		−	7740.00i		−	1.43891i	−0.694539	−	0.719455i	$-0.744392\pi$
$307$		−	7740.00i		−	1.43891i	0.694539	−	0.719455i	$-0.255608\pi$
$308$			560.000i			0.103601i
$309$	186.000			0.0342433
$310$	−4576.00	+	832.000i	−0.838385	+	0.152434i
$311$	4980.00			0.908006			0.454003	−	0.891000i	$-0.349996\pi$
$311$	4980.00			0.908006			0.454003	+	0.891000i	$0.349996\pi$
$312$		−	1296.00i		−	0.235165i
$313$		−	604.000i		−	0.109074i	−0.998512	−	0.0545369i	$-0.982632\pi$
$313$		−	604.000i		−	0.109074i	0.998512	−	0.0545369i	$-0.0173683\pi$
$314$	5108.00			0.918029
$315$	−198.000	+	36.0000i	−0.0354160	+	0.00643927i
$316$	3168.00			0.563968
$317$		−	8566.00i		−	1.51771i	−0.651259	−	0.758856i	$-0.725759\pi$
$317$		−	8566.00i		−	1.51771i	0.651259	−	0.758856i	$-0.274241\pi$
$318$		−	2412.00i		−	0.425340i
$319$	−15120.0			−2.65379
$320$	−128.000	−	704.000i	−0.0223607	−	0.122984i
$321$	−252.000			−0.0438170
$322$			400.000i			0.0692271i
$323$			528.000i			0.0909557i
$324$	−324.000			−0.0555556
$325$	2376.00	+	6318.00i	0.405529	+	1.07834i
$326$	1504.00			0.255518
$327$		−	1110.00i		−	0.187716i
$328$			1648.00i			0.277426i
$329$	−640.000			−0.107247
$330$	−840.000	−	4620.00i	−0.140123	−	0.770675i
$331$	3472.00			0.576551			0.288275	−	0.957548i	$-0.406918\pi$
$331$	3472.00			0.576551			0.288275	+	0.957548i	$0.406918\pi$
$332$			1616.00i			0.267137i
$333$			2286.00i			0.376192i
$334$	−5400.00			−0.884655
$335$	−8008.00	+	1456.00i	−1.30604	+	0.237462i
$336$	96.0000			0.0155870
$337$			5668.00i			0.916189i	0.888904	+	0.458094i	$0.151468\pi$
$337$			5668.00i			0.916189i	−0.888904	+	0.458094i	$0.848532\pi$
$338$		−	1438.00i		−	0.231411i
$339$	−5238.00			−0.839201
$340$	−968.000	+	176.000i	−0.154403	+	0.0280734i
$341$	14560.0			2.31222
$342$			432.000i			0.0683038i
$343$		−	1364.00i		−	0.214720i
$344$	−2336.00			−0.366130
$345$	−600.000	−	3300.00i	−0.0936316	−	0.514974i
$346$	−2668.00			−0.414545
$347$			10836.0i			1.67639i	0.545371	+	0.838194i	$0.316389\pi$
$347$			10836.0i			1.67639i	−0.545371	+	0.838194i	$0.683611\pi$
$348$			2592.00i			0.399269i
$349$	8990.00			1.37886			0.689432	−	0.724350i	$-0.257860\pi$
$349$	8990.00			1.37886			0.689432	+	0.724350i	$0.257860\pi$
$350$	−468.000	+	176.000i	−0.0714733	+	0.0268788i
$351$	−1458.00			−0.221716
$352$			2240.00i			0.339183i
$353$			5078.00i			0.765651i	0.923821	+	0.382825i	$0.125049\pi$
$353$			5078.00i			0.765651i	−0.923821	+	0.382825i	$0.874951\pi$
$354$	−2220.00			−0.333310
$355$	−1080.00	−	5940.00i	−0.161466	−	0.888063i
$356$	−3752.00			−0.558583
$357$		−	132.000i		−	0.0195691i
$358$			3428.00i			0.506077i
$359$	3696.00			0.543363			0.271682	−	0.962387i	$-0.412420\pi$
$359$	3696.00			0.543363			0.271682	+	0.962387i	$0.412420\pi$
$360$	−792.000	+	144.000i	−0.115950	+	0.0210819i
$361$	−6283.00			−0.916023
$362$		−	8012.00i		−	1.16326i
$363$			10707.0i			1.54813i
$364$	432.000			0.0622059
$365$	6644.00	−	1208.00i	0.952775	−	0.173232i
$366$	3300.00			0.471294
$367$			286.000i			0.0406787i	0.999793	+	0.0203393i	$0.00647466\pi$
$367$			286.000i			0.0406787i	−0.999793	+	0.0203393i	$0.993525\pi$
$368$			1600.00i			0.226646i
$369$	1854.00			0.261559
$370$	1016.00	+	5588.00i	0.142755	+	0.785152i
$371$	804.000			0.112511
$372$		−	2496.00i		−	0.347881i
$373$		−	8262.00i		−	1.14689i	−0.819244	−	0.573445i	$-0.805607\pi$
$373$		−	8262.00i		−	1.14689i	0.819244	−	0.573445i	$-0.194393\pi$
$374$	3080.00			0.425837
$375$	3597.00	−	2154.00i	0.495329	−	0.296619i
$376$	−2560.00			−0.351122
$377$			11664.0i			1.59344i
$378$		−	108.000i		−	0.0146956i
$379$	2956.00			0.400632			0.200316	−	0.979731i	$-0.435803\pi$
$379$	2956.00			0.400632			0.200316	+	0.979731i	$0.435803\pi$
$380$	192.000	+	1056.00i	0.0259195	+	0.142557i
$381$	−4890.00			−0.657539
$382$		−	1368.00i		−	0.183228i
$383$			5240.00i			0.699090i	0.936920	+	0.349545i	$0.113664\pi$
$383$			5240.00i			0.699090i	−0.936920	+	0.349545i	$0.886336\pi$
$384$	384.000			0.0510310
$385$	1540.00	−	280.000i	0.203859	−	0.0370653i
$386$	−8968.00			−1.18254
$387$			2628.00i			0.345191i
$388$		−	224.000i		−	0.0293090i
$389$	884.000			0.115220			0.0576100	−	0.998339i	$-0.481652\pi$
$389$	884.000			0.115220			0.0576100	+	0.998339i	$0.481652\pi$
$390$	−3564.00	+	648.000i	−0.462744	+	0.0841353i
$391$	2200.00			0.284549
$392$		−	2712.00i		−	0.349430i
$393$		−	2610.00i		−	0.335005i
$394$	2116.00			0.270565
$395$	−1584.00	−	8712.00i	−0.201771	−	1.10974i
$396$	2520.00			0.319785
$397$			3394.00i			0.429068i	0.976717	+	0.214534i	$0.0688233\pi$
$397$			3394.00i			0.429068i	−0.976717	+	0.214534i	$0.931177\pi$
$398$			2256.00i			0.284128i
$399$	−144.000			−0.0180677
$400$	−1872.00	+	704.000i	−0.234000	+	0.0880000i
$401$	−6826.00			−0.850060			−0.425030	−	0.905179i	$-0.639737\pi$
$401$	−6826.00			−0.850060			−0.425030	+	0.905179i	$0.639737\pi$
$402$		−	4368.00i		−	0.541930i
$403$		−	11232.0i		−	1.38835i
$404$	2368.00			0.291615
$405$	162.000	+	891.000i	0.0198762	+	0.109319i
$406$	−864.000			−0.105615
$407$		−	17780.0i		−	2.16541i
$408$		−	528.000i		−	0.0640684i
$409$	−7814.00			−0.944688			−0.472344	−	0.881414i	$-0.656592\pi$
$409$	−7814.00			−0.944688			−0.472344	+	0.881414i	$0.656592\pi$
$410$	4532.00	−	824.000i	0.545901	−	0.0992548i
$411$	−2754.00			−0.330523
$412$			248.000i			0.0296555i
$413$		−	740.000i		−	0.0881671i
$414$	1800.00			0.213684
$415$	4444.00	−	808.000i	0.525656	−	0.0955739i
$416$	1728.00			0.203659
$417$			1788.00i			0.209973i
$418$		−	3360.00i		−	0.393165i
$419$	−8290.00			−0.966570			−0.483285	−	0.875463i	$-0.660557\pi$
$419$	−8290.00			−0.966570			−0.483285	+	0.875463i	$0.660557\pi$
$420$	−48.0000	−	264.000i	−0.00557657	−	0.0306711i
$421$	2110.00			0.244264			0.122132	−	0.992514i	$-0.461027\pi$
$421$	2110.00			0.244264			0.122132	+	0.992514i	$0.461027\pi$
$422$			1560.00i			0.179952i
$423$			2880.00i			0.331041i
$424$	3216.00			0.368356
$425$	968.000	+	2574.00i	0.110482	+	0.293782i
$426$	3240.00			0.368494
$427$			1100.00i			0.124667i
$428$		−	336.000i		−	0.0379467i
$429$	11340.0			1.27622
$430$	1168.00	+	6424.00i	0.130991	+	0.720448i
$431$	−12080.0			−1.35005			−0.675027	−	0.737793i	$-0.735868\pi$
$431$	−12080.0			−1.35005			−0.675027	+	0.737793i	$0.735868\pi$
$432$		−	432.000i		−	0.0481125i
$433$		−	16492.0i		−	1.83038i	−0.403022	−	0.915190i	$-0.632040\pi$
$433$		−	16492.0i		−	1.83038i	0.403022	−	0.915190i	$-0.367960\pi$
$434$	832.000			0.0920214
$435$	7128.00	−	1296.00i	0.785658	−	0.142847i
$436$	1480.00			0.162567
$437$		−	2400.00i		−	0.262718i
$438$			3624.00i			0.395346i
$439$	15048.0			1.63600			0.817998	−	0.575222i	$-0.195084\pi$
$439$	15048.0			1.63600			0.817998	+	0.575222i	$0.195084\pi$
$440$	6160.00	−	1120.00i	0.667424	−	0.121350i
$441$	−3051.00			−0.329446
$442$		−	2376.00i		−	0.255690i
$443$			9876.00i			1.05919i	0.848249	+	0.529597i	$0.177657\pi$
$443$			9876.00i			1.05919i	−0.848249	+	0.529597i	$0.822343\pi$
$444$	−3048.00			−0.325792
$445$	1876.00	+	10318.0i	0.199845	+	1.09915i
$446$	−5140.00			−0.545709
$447$		−	3228.00i		−	0.341564i
$448$			128.000i			0.0134987i
$449$	−17166.0			−1.80426			−0.902131	−	0.431462i	$-0.857998\pi$
$449$	−17166.0			−1.80426			−0.902131	+	0.431462i	$0.857998\pi$
$450$	792.000	+	2106.00i	0.0829672	+	0.220617i
$451$	−14420.0			−1.50557
$452$		−	6984.00i		−	0.726769i
$453$		−	96.0000i		−	0.00995690i
$454$	5672.00			0.586344
$455$	−216.000	−	1188.00i	−0.0222555	−	0.122405i
$456$	−576.000			−0.0591528
$457$			14848.0i			1.51983i	0.650025	+	0.759913i	$0.274758\pi$
$457$			14848.0i			1.51983i	−0.650025	+	0.759913i	$0.725242\pi$
$458$			1220.00i			0.124469i
$459$	−594.000			−0.0604042
$460$	4400.00	−	800.000i	0.445981	−	0.0810874i
$461$	−1260.00			−0.127297			−0.0636486	−	0.997972i	$-0.520274\pi$
$461$	−1260.00			−0.127297			−0.0636486	+	0.997972i	$0.520274\pi$
$462$			840.000i			0.0845895i
$463$			11238.0i			1.12802i	0.825767	+	0.564011i	$0.190742\pi$
$463$			11238.0i			1.12802i	−0.825767	+	0.564011i	$0.809258\pi$
$464$	−3456.00			−0.345778
$465$	−6864.00	+	1248.00i	−0.684538	+	0.124462i
$466$	7028.00			0.698639
$467$			14772.0i			1.46374i	0.681444	+	0.731870i	$0.261352\pi$
$467$			14772.0i			1.46374i	−0.681444	+	0.731870i	$0.738648\pi$
$468$		−	1944.00i		−	0.192012i
$469$	1456.00			0.143351
$470$	1280.00	+	7040.00i	0.125621	+	0.690917i
$471$	7662.00			0.749568
$472$		−	2960.00i		−	0.288655i
$473$		−	20440.0i		−	1.98696i
$474$	4752.00			0.460478
$475$	2808.00	−	1056.00i	0.271242	−	0.102005i
$476$	176.000			0.0169474
$477$		−	3618.00i		−	0.347289i
$478$			3688.00i			0.352898i
$479$	6116.00			0.583397			0.291699	−	0.956510i	$-0.405780\pi$
$479$	6116.00			0.583397			0.291699	+	0.956510i	$0.405780\pi$
$480$	−192.000	−	1056.00i	−0.0182574	−	0.100416i
$481$	−13716.0			−1.30020
$482$			1964.00i			0.185597i
$483$			600.000i			0.0565237i
$484$	−14276.0			−1.34072
$485$	−616.000	+	112.000i	−0.0576724	+	0.0104859i
$486$	−486.000			−0.0453609
$487$			15906.0i			1.48002i	0.672596	+	0.740010i	$0.265179\pi$
$487$			15906.0i			1.48002i	−0.672596	+	0.740010i	$0.734821\pi$
$488$			4400.00i			0.408153i
$489$	2256.00			0.208630
$490$	−7458.00	+	1356.00i	−0.687588	+	0.125016i
$491$	18714.0			1.72006			0.860032	−	0.510241i	$-0.170444\pi$
$491$	18714.0			1.72006			0.860032	+	0.510241i	$0.170444\pi$
$492$			2472.00i			0.226517i
$493$			4752.00i			0.434116i
$494$	−2592.00			−0.236072
$495$	−1260.00	−	6930.00i	−0.114410	−	0.629253i
$496$	3328.00			0.301273
$497$			1080.00i			0.0974741i
$498$			2424.00i			0.218117i
$499$	4056.00			0.363871			0.181935	−	0.983310i	$-0.441764\pi$
$499$	4056.00			0.363871			0.181935	+	0.983310i	$0.441764\pi$
$500$	2872.00	+	4796.00i	0.256879	+	0.428967i
$501$	−8100.00			−0.722318
$502$		−	6348.00i		−	0.564393i
$503$		−	6288.00i		−	0.557392i	−0.960379	−	0.278696i	$-0.910098\pi$
$503$		−	6288.00i		−	0.557392i	0.960379	−	0.278696i	$-0.0899021\pi$
$504$	144.000			0.0127267
$505$	−1184.00	−	6512.00i	−0.104331	−	0.573822i
$506$	−14000.0			−1.22999
$507$		−	2157.00i		−	0.188946i
$508$		−	6520.00i		−	0.569445i
$509$	−2856.00			−0.248703			−0.124352	−	0.992238i	$-0.539685\pi$
$509$	−2856.00			−0.248703			−0.124352	+	0.992238i	$0.539685\pi$
$510$	−1452.00	+	264.000i	−0.126070	+	0.0229218i
$511$	−1208.00			−0.104577
$512$			512.000i			0.0441942i
$513$			648.000i			0.0557698i
$514$	2388.00			0.204922
$515$	682.000	−	124.000i	0.0583544	−	0.0106099i
$516$	−3504.00			−0.298944
$517$		−	22400.0i		−	1.90551i
$518$		−	1016.00i		−	0.0861785i
$519$	−4002.00			−0.338475
$520$	−864.000	−	4752.00i	−0.0728633	−	0.400748i
$521$	17078.0			1.43609			0.718043	−	0.695999i	$-0.245038\pi$
$521$	17078.0			1.43609			0.718043	+	0.695999i	$0.245038\pi$
$522$			3888.00i			0.326002i
$523$			8560.00i			0.715684i	0.933782	+	0.357842i	$0.116487\pi$
$523$			8560.00i			0.715684i	−0.933782	+	0.357842i	$0.883513\pi$
$524$	3480.00			0.290123
$525$	−702.000	+	264.000i	−0.0583577	+	0.0219465i
$526$	280.000			0.0232102
$527$		−	4576.00i		−	0.378242i
$528$			3360.00i			0.276942i
$529$	2167.00			0.178105
$530$	−1608.00	−	8844.00i	−0.131787	−	0.724828i
$531$	−3330.00			−0.272146
$532$		−	192.000i		−	0.0156471i
$533$			11124.0i			0.904004i
$534$	−5628.00			−0.456081
$535$	−924.000	+	168.000i	−0.0746692	+	0.0135762i
$536$	5824.00			0.469326
$537$			5142.00i			0.413210i
$538$		−	10512.0i		−	0.842388i
$539$	23730.0			1.89633
$540$	−1188.00	+	216.000i	−0.0946729	+	0.0172133i
$541$	15970.0			1.26914			0.634569	−	0.772866i	$-0.281178\pi$
$541$	15970.0			1.26914			0.634569	+	0.772866i	$0.281178\pi$
$542$			1088.00i			0.0862244i
$543$		−	12018.0i		−	0.949801i
$544$	704.000			0.0554848
$545$	−740.000	−	4070.00i	−0.0581617	−	0.319889i
$546$	648.000			0.0507909
$547$		−	15524.0i		−	1.21345i	−0.794911	−	0.606726i	$-0.792482\pi$
$547$		−	15524.0i		−	1.21345i	0.794911	−	0.606726i	$-0.207518\pi$
$548$		−	3672.00i		−	0.286241i
$549$	4950.00			0.384810
$550$	−6160.00	−	16380.0i	−0.477570	−	1.26990i
$551$	5184.00			0.400809
$552$			2400.00i			0.185056i
$553$			1584.00i			0.121806i
$554$	−1892.00			−0.145096
$555$	1524.00	+	8382.00i	0.116559	+	0.641074i
$556$	−2384.00			−0.181842
$557$			6774.00i			0.515303i	0.966238	+	0.257651i	$0.0829486\pi$
$557$			6774.00i			0.515303i	−0.966238	+	0.257651i	$0.917051\pi$
$558$		−	3744.00i		−	0.284043i
$559$	−15768.0			−1.19305
$560$	352.000	−	64.0000i	0.0265620	−	0.00482945i
$561$	4620.00			0.347694
$562$			2556.00i			0.191848i
$563$			10484.0i			0.784810i	0.919793	+	0.392405i	$0.128357\pi$
$563$			10484.0i			0.784810i	−0.919793	+	0.392405i	$0.871643\pi$
$564$	−3840.00			−0.286690
$565$	−19206.0	+	3492.00i	−1.43009	+	0.260017i
$566$	14848.0			1.10266
$567$		−	162.000i		−	0.0119989i
$568$			4320.00i			0.319125i
$569$	−23302.0			−1.71682			−0.858410	−	0.512964i	$-0.828547\pi$
$569$	−23302.0			−1.71682			−0.858410	+	0.512964i	$0.828547\pi$
$570$	288.000	+	1584.00i	0.0211631	+	0.116397i
$571$	21520.0			1.57720			0.788602	−	0.614903i	$-0.210805\pi$
$571$	21520.0			1.57720			0.788602	+	0.614903i	$0.210805\pi$
$572$			15120.0i			1.10524i
$573$		−	2052.00i		−	0.149605i
$574$	−824.000			−0.0599183
$575$	−4400.00	−	11700.0i	−0.319118	−	0.848563i
$576$	576.000			0.0416667
$577$			3856.00i			0.278210i	0.990278	+	0.139105i	$0.0444226\pi$
$577$			3856.00i			0.278210i	−0.990278	+	0.139105i	$0.955577\pi$
$578$			8858.00i			0.637447i
$579$	−13452.0			−0.965537
$580$	1728.00	+	9504.00i	0.123709	+	0.680400i
$581$	−808.000			−0.0576962
$582$		−	336.000i		−	0.0239307i
$583$			28140.0i			1.99904i
$584$	−4832.00			−0.342379
$585$	−5346.00	+	972.000i	−0.377829	+	0.0686962i
$586$	−2724.00			−0.192026
$587$		−	26796.0i		−	1.88414i	−0.335418	−	0.942069i	$-0.608878\pi$
$587$		−	26796.0i		−	1.88414i	0.335418	−	0.942069i	$-0.391122\pi$
$588$		−	4068.00i		−	0.285309i
$589$	−4992.00			−0.349222
$590$	−8140.00	+	1480.00i	−0.567997	+	0.103272i
$591$	3174.00			0.220915
$592$		−	4064.00i		−	0.282144i
$593$		−	9870.00i		−	0.683495i	−0.939792	−	0.341747i	$-0.888981\pi$
$593$		−	9870.00i		−	0.683495i	0.939792	−	0.341747i	$-0.111019\pi$
$594$	3780.00			0.261103
$595$	−88.0000	−	484.000i	−0.00606327	−	0.0333480i
$596$	4304.00			0.295803
$597$			3384.00i			0.231990i
$598$			10800.0i			0.738537i
$599$	13296.0			0.906945			0.453472	−	0.891270i	$-0.350185\pi$
$599$	13296.0			0.906945			0.453472	+	0.891270i	$0.350185\pi$
$600$	−2808.00	+	1056.00i	−0.191060	+	0.0718517i
$601$	−9262.00			−0.628627			−0.314314	−	0.949319i	$-0.601774\pi$
$601$	−9262.00			−0.628627			−0.314314	+	0.949319i	$0.601774\pi$
$602$		−	1168.00i		−	0.0790766i
$603$		−	6552.00i		−	0.442484i
$604$	128.000			0.00862292
$605$	7138.00	+	39259.0i	0.479671	+	2.63819i
$606$	3552.00			0.238103
$607$			5498.00i			0.367639i	0.982960	+	0.183820i	$0.0588462\pi$
$607$			5498.00i			0.367639i	−0.982960	+	0.183820i	$0.941154\pi$
$608$		−	768.000i		−	0.0512278i
$609$	−1296.00			−0.0862341
$610$	12100.0	−	2200.00i	0.803139	−	0.146025i
$611$	−17280.0			−1.14415
$612$		−	792.000i		−	0.0523116i
$613$		−	394.000i		−	0.0259600i	−0.999916	−	0.0129800i	$-0.995868\pi$
$613$		−	394.000i		−	0.0259600i	0.999916	−	0.0129800i	$-0.00413179\pi$
$614$	15480.0			1.01746
$615$	6798.00	−	1236.00i	0.445727	−	0.0810412i
$616$	−1120.00			−0.0732566
$617$			7370.00i			0.480883i	0.970664	+	0.240442i	$0.0772923\pi$
$617$			7370.00i			0.480883i	−0.970664	+	0.240442i	$0.922708\pi$
$618$			372.000i			0.0242136i
$619$	−25316.0			−1.64384			−0.821919	−	0.569604i	$-0.807097\pi$
$619$	−25316.0			−1.64384			−0.821919	+	0.569604i	$0.807097\pi$
$620$	−1664.00	−	9152.00i	−0.107787	−	0.592828i
$621$	2700.00			0.174472
$622$			9960.00i			0.642057i
$623$		−	1876.00i		−	0.120643i
$624$	2592.00			0.166287
$625$	11753.0	−	10296.0i	0.752192	−	0.658944i
$626$	1208.00			0.0771268
$627$		−	5040.00i		−	0.321018i
$628$			10216.0i			0.649145i
$629$	−5588.00			−0.354226
$630$	−72.0000	−	396.000i	−0.00455325	−	0.0250429i
$631$	2552.00			0.161004			0.0805020	−	0.996754i	$-0.474348\pi$
$631$	2552.00			0.161004			0.0805020	+	0.996754i	$0.474348\pi$
$632$			6336.00i			0.398786i
$633$			2340.00i			0.146930i
$634$	17132.0			1.07318
$635$	−17930.0	+	3260.00i	−1.12052	+	0.203731i
$636$	4824.00			0.300761
$637$		−	18306.0i		−	1.13863i
$638$		−	30240.0i		−	1.87651i
$639$	4860.00			0.300874
$640$	1408.00	−	256.000i	0.0869626	−	0.0158114i
$641$	8050.00			0.496031			0.248016	−	0.968756i	$-0.420222\pi$
$641$	8050.00			0.496031			0.248016	+	0.968756i	$0.420222\pi$
$642$		−	504.000i		−	0.0309833i
$643$			19368.0i			1.18787i	0.804514	+	0.593934i	$0.202426\pi$
$643$			19368.0i			1.18787i	−0.804514	+	0.593934i	$0.797574\pi$
$644$	−800.000			−0.0489510
$645$	1752.00	+	9636.00i	0.106953	+	0.588244i
$646$	−1056.00			−0.0643154
$647$			9912.00i			0.602289i	0.953579	+	0.301144i	$0.0973686\pi$
$647$			9912.00i			0.602289i	−0.953579	+	0.301144i	$0.902631\pi$
$648$		−	648.000i		−	0.0392837i
$649$	25900.0			1.56651
$650$	−12636.0	+	4752.00i	−0.762500	+	0.286752i
$651$	1248.00			0.0751351
$652$			3008.00i			0.180678i
$653$		−	27986.0i		−	1.67715i	−0.544789	−	0.838573i	$-0.683390\pi$
$653$		−	27986.0i		−	1.67715i	0.544789	−	0.838573i	$-0.316610\pi$
$654$	2220.00			0.132735
$655$	−1740.00	−	9570.00i	−0.103798	−	0.570887i
$656$	−3296.00			−0.196169
$657$			5436.00i			0.322798i
$658$		−	1280.00i		−	0.0758353i
$659$	−7562.00			−0.447001			−0.223501	−	0.974704i	$-0.571748\pi$
$659$	−7562.00			−0.447001			−0.223501	+	0.974704i	$0.571748\pi$
$660$	9240.00	−	1680.00i	0.544949	−	0.0990817i
$661$	20234.0			1.19064			0.595319	−	0.803490i	$-0.297026\pi$
$661$	20234.0			1.19064			0.595319	+	0.803490i	$0.297026\pi$
$662$			6944.00i			0.407683i
$663$		−	3564.00i		−	0.208770i
$664$	−3232.00			−0.188894
$665$	−528.000	+	96.0000i	−0.0307894	+	0.00559808i
$666$	−4572.00			−0.266008
$667$		−	21600.0i		−	1.25391i
$668$		−	10800.0i		−	0.625546i
$669$	−7710.00			−0.445569
$670$	−2912.00	−	16016.0i	−0.167911	−	0.923511i
$671$	−38500.0			−2.21502
$672$			192.000i			0.0110217i
$673$		−	25332.0i		−	1.45093i	−0.688258	−	0.725466i	$-0.741624\pi$
$673$		−	25332.0i		−	1.45093i	0.688258	−	0.725466i	$-0.258376\pi$
$674$	−11336.0			−0.647843
$675$	1188.00	+	3159.00i	0.0677424	+	0.180133i
$676$	2876.00			0.163632
$677$		−	18358.0i		−	1.04218i	−0.853502	−	0.521090i	$-0.825526\pi$
$677$		−	18358.0i		−	1.04218i	0.853502	−	0.521090i	$-0.174474\pi$
$678$		−	10476.0i		−	0.593405i
$679$	112.000			0.00633014
$680$	−352.000	−	1936.00i	−0.0198509	−	0.109180i
$681$	8508.00			0.478748
$682$			29120.0i			1.63499i
$683$			124.000i			0.00694689i	0.999994	+	0.00347345i	$0.00110563\pi$
$683$			124.000i			0.00694689i	−0.999994	+	0.00347345i	$0.998894\pi$
$684$	−864.000			−0.0482980
$685$	−10098.0	+	1836.00i	−0.563248	+	0.102409i
$686$	2728.00			0.151830
$687$			1830.00i			0.101629i
$688$		−	4672.00i		−	0.258893i
$689$	21708.0			1.20030
$690$	6600.00	−	1200.00i	0.364142	−	0.0662076i
$691$	−17456.0			−0.961009			−0.480505	−	0.876992i	$-0.659547\pi$
$691$	−17456.0			−0.961009			−0.480505	+	0.876992i	$0.659547\pi$
$692$		−	5336.00i		−	0.293128i
$693$			1260.00i			0.0690670i
$694$	−21672.0			−1.18539
$695$	1192.00	+	6556.00i	0.0650578	+	0.357818i
$696$	−5184.00			−0.282326
$697$			4532.00i			0.246287i
$698$			17980.0i			0.975004i
$699$	10542.0			0.570436
$700$	−352.000	−	936.000i	−0.0190062	−	0.0505392i
$701$	−17816.0			−0.959916			−0.479958	−	0.877291i	$-0.659348\pi$
$701$	−17816.0			−0.959916			−0.479958	+	0.877291i	$0.659348\pi$
$702$		−	2916.00i		−	0.156777i
$703$			6096.00i			0.327048i
$704$	−4480.00			−0.239839
$705$	1920.00	+	10560.0i	0.102569	+	0.564131i
$706$	−10156.0			−0.541397
$707$			1184.00i			0.0629829i
$708$		−	4440.00i		−	0.235686i
$709$	14298.0			0.757366			0.378683	−	0.925526i	$-0.376377\pi$
$709$	14298.0			0.757366			0.378683	+	0.925526i	$0.376377\pi$
$710$	11880.0	−	2160.00i	0.627956	−	0.114174i
$711$	7128.00			0.375979
$712$		−	7504.00i		−	0.394978i
$713$			20800.0i			1.09252i
$714$	264.000			0.0138375
$715$	41580.0	−	7560.00i	2.17483	−	0.395424i
$716$	−6856.00			−0.357850
$717$			5532.00i			0.288140i
$718$			7392.00i			0.384216i
$719$	18440.0			0.956462			0.478231	−	0.878234i	$-0.341278\pi$
$719$	18440.0			0.956462			0.478231	+	0.878234i	$0.341278\pi$
$720$	−288.000	−	1584.00i	−0.0149071	−	0.0819892i
$721$	−124.000			−0.00640499
$722$		−	12566.0i		−	0.647726i
$723$			2946.00i			0.151539i
$724$	16024.0			0.822551
$725$	25272.0	−	9504.00i	1.29459	−	0.486855i
$726$	−21414.0			−1.09469
$727$			9666.00i			0.493112i	0.969129	+	0.246556i	$0.0792989\pi$
$727$			9666.00i			0.493112i	−0.969129	+	0.246556i	$0.920701\pi$
$728$			864.000i			0.0439862i
$729$	−729.000			−0.0370370
$730$	2416.00	+	13288.0i	0.122493	+	0.673714i
$731$	−6424.00			−0.325035
$732$			6600.00i			0.333255i
$733$			6094.00i			0.307076i	0.988143	+	0.153538i	$0.0490668\pi$
$733$			6094.00i			0.307076i	−0.988143	+	0.153538i	$0.950933\pi$
$734$	−572.000			−0.0287642
$735$	−11187.0	+	2034.00i	−0.561413	+	0.102075i
$736$	−3200.00			−0.160263
$737$			50960.0i			2.54700i
$738$			3708.00i			0.184950i
$739$	−9952.00			−0.495386			−0.247693	−	0.968839i	$-0.579672\pi$
$739$	−9952.00			−0.495386			−0.247693	+	0.968839i	$0.579672\pi$
$740$	−11176.0	+	2032.00i	−0.555186	+	0.100943i
$741$	−3888.00			−0.192752
$742$			1608.00i			0.0795573i
$743$			2208.00i			0.109022i	0.998513	+	0.0545112i	$0.0173601\pi$
$743$			2208.00i			0.109022i	−0.998513	+	0.0545112i	$0.982640\pi$
$744$	4992.00			0.245989
$745$	−2152.00	−	11836.0i	−0.105830	−	0.582064i
$746$	16524.0			0.810974
$747$			3636.00i			0.178091i
$748$			6160.00i			0.301112i
$749$	168.000			0.00819571
$750$	4308.00	+	7194.00i	0.209741	+	0.350250i
$751$	−9400.00			−0.456739			−0.228369	−	0.973575i	$-0.573339\pi$
$751$	−9400.00			−0.456739			−0.228369	+	0.973575i	$0.573339\pi$
$752$		−	5120.00i		−	0.248281i
$753$		−	9522.00i		−	0.460825i
$754$	−23328.0			−1.12673
$755$	−64.0000	−	352.000i	−0.00308503	−	0.0169677i
$756$	216.000			0.0103913
$757$		−	22574.0i		−	1.08384i	−0.840430	−	0.541919i	$-0.817698\pi$
$757$		−	22574.0i		−	1.08384i	0.840430	−	0.541919i	$-0.182302\pi$
$758$			5912.00i			0.283290i
$759$	−21000.0			−1.00428
$760$	−2112.00	+	384.000i	−0.100803	+	0.0183278i
$761$	7278.00			0.346685			0.173343	−	0.984862i	$-0.444543\pi$
$761$	7278.00			0.346685			0.173343	+	0.984862i	$0.444543\pi$
$762$		−	9780.00i		−	0.464950i
$763$			740.000i			0.0351111i
$764$	2736.00			0.129562
$765$	−2178.00	+	396.000i	−0.102936	+	0.0187156i
$766$	−10480.0			−0.494331
$767$		−	19980.0i		−	0.940595i
$768$			768.000i			0.0360844i
$769$	16542.0			0.775708			0.387854	−	0.921721i	$-0.373216\pi$
$769$	16542.0			0.775708			0.387854	+	0.921721i	$0.373216\pi$
$770$	560.000	+	3080.00i	0.0262091	+	0.144150i
$771$	3582.00			0.167319
$772$		−	17936.0i		−	0.836180i
$773$			28926.0i			1.34592i	0.739679	+	0.672960i	$0.234977\pi$
$773$			28926.0i			1.34592i	−0.739679	+	0.672960i	$0.765023\pi$
$774$	−5256.00			−0.244087
$775$	−24336.0	+	9152.00i	−1.12797	+	0.424193i
$776$	448.000			0.0207246
$777$		−	1524.00i		−	0.0703645i
$778$			1768.00i			0.0814728i
$779$	4944.00			0.227390
$780$	−1296.00	−	7128.00i	−0.0594926	−	0.327209i
$781$	−37800.0			−1.73187
$782$			4400.00i			0.201207i
$783$			5832.00i			0.266180i
$784$	5424.00			0.247085
$785$	28094.0	−	5108.00i	1.27735	−	0.232245i
$786$	5220.00			0.236885
$787$			20608.0i			0.933413i	0.884412	+	0.466706i	$0.154560\pi$
$787$			20608.0i			0.933413i	−0.884412	+	0.466706i	$0.845440\pi$
$788$			4232.00i			0.191318i
$789$	420.000			0.0189511
$790$	17424.0	−	3168.00i	0.784706	−	0.142674i
$791$	3492.00			0.156967
$792$			5040.00i			0.226122i
$793$			29700.0i			1.32998i
$794$	−6788.00			−0.303397
$795$	−2412.00	−	13266.0i	−0.107604	−	0.591820i
$796$	−4512.00			−0.200909
$797$		−	41350.0i		−	1.83776i	−0.394541	−	0.918878i	$-0.629096\pi$
$797$		−	41350.0i		−	1.83776i	0.394541	−	0.918878i	$-0.370904\pi$
$798$		−	288.000i		−	0.0127758i
$799$	−7040.00			−0.311711
$800$	−1408.00	−	3744.00i	−0.0622254	−	0.165463i
$801$	−8442.00			−0.372389
$802$		−	13652.0i		−	0.601083i
$803$		−	42280.0i		−	1.85807i
$804$	8736.00			0.383203
$805$	400.000	+	2200.00i	0.0175132	+	0.0963227i
$806$	22464.0			0.981713
$807$		−	15768.0i		−	0.687807i
$808$			4736.00i			0.206203i
$809$	−1794.00			−0.0779650			−0.0389825	−	0.999240i	$-0.512412\pi$
$809$	−1794.00			−0.0779650			−0.0389825	+	0.999240i	$0.512412\pi$
$810$	−1782.00	+	324.000i	−0.0773001	+	0.0140546i
$811$	22756.0			0.985291			0.492646	−	0.870230i	$-0.336030\pi$
$811$	22756.0			0.985291			0.492646	+	0.870230i	$0.336030\pi$
$812$		−	1728.00i		−	0.0746809i
$813$			1632.00i			0.0704019i
$814$	35560.0			1.53118
$815$	8272.00	−	1504.00i	0.355528	−	0.0646415i
$816$	1056.00			0.0453032
$817$			7008.00i			0.300097i
$818$		−	15628.0i		−	0.667995i
$819$	972.000			0.0414706
$820$	1648.00	+	9064.00i	0.0701837	+	0.386011i
$821$	−23632.0			−1.00458			−0.502291	−	0.864698i	$-0.667510\pi$
$821$	−23632.0			−1.00458			−0.502291	+	0.864698i	$0.667510\pi$
$822$		−	5508.00i		−	0.233715i
$823$		−	33210.0i		−	1.40660i	−0.710896	−	0.703298i	$-0.751710\pi$
$823$		−	33210.0i		−	1.40660i	0.710896	−	0.703298i	$-0.248290\pi$
$824$	−496.000			−0.0209696
$825$	−9240.00	−	24570.0i	−0.389934	−	1.03687i
$826$	1480.00			0.0623436
$827$			30476.0i			1.28144i	0.767773	+	0.640722i	$0.221365\pi$
$827$			30476.0i			1.28144i	−0.767773	+	0.640722i	$0.778635\pi$
$828$			3600.00i			0.151097i
$829$	−29802.0			−1.24857			−0.624286	−	0.781196i	$-0.714610\pi$
$829$	−29802.0			−1.24857			−0.624286	+	0.781196i	$0.714610\pi$
$830$	1616.00	+	8888.00i	0.0675809	+	0.371695i
$831$	−2838.00			−0.118471
$832$			3456.00i			0.144009i
$833$		−	7458.00i		−	0.310209i
$834$	−3576.00			−0.148473
$835$	−29700.0	+	5400.00i	−1.23091	+	0.223802i
$836$	6720.00			0.278010
$837$		−	5616.00i		−	0.231920i
$838$		−	16580.0i		−	0.683468i
$839$	28024.0			1.15315			0.576577	−	0.817043i	$-0.304388\pi$
$839$	28024.0			1.15315			0.576577	+	0.817043i	$0.304388\pi$
$840$	528.000	−	96.0000i	0.0216878	−	0.00394323i
$841$	22267.0			0.912994
$842$			4220.00i			0.172721i
$843$			3834.00i			0.156643i
$844$	−3120.00			−0.127245
$845$	−1438.00	−	7909.00i	−0.0585428	−	0.321986i
$846$	−5760.00			−0.234081
$847$		−	7138.00i		−	0.289569i
$848$			6432.00i			0.260467i
$849$	22272.0			0.900322
$850$	−5148.00	+	1936.00i	−0.207735	+	0.0781226i
$851$	25400.0			1.02315
$852$			6480.00i			0.260565i
$853$		−	3938.00i		−	0.158071i	−0.996872	−	0.0790355i	$-0.974816\pi$
$853$		−	3938.00i		−	0.158071i	0.996872	−	0.0790355i	$-0.0251840\pi$
$854$	−2200.00			−0.0881528
$855$	432.000	+	2376.00i	0.0172796	+	0.0950380i
$856$	672.000			0.0268323
$857$		−	8094.00i		−	0.322621i	−0.986904	−	0.161310i	$-0.948428\pi$
$857$		−	8094.00i		−	0.322621i	0.986904	−	0.161310i	$-0.0515720\pi$
$858$			22680.0i			0.902427i
$859$	−9044.00			−0.359229			−0.179614	−	0.983737i	$-0.557485\pi$
$859$	−9044.00			−0.359229			−0.179614	+	0.983737i	$0.557485\pi$
$860$	−12848.0	+	2336.00i	−0.509434	+	0.0926243i
$861$	−1236.00			−0.0489231
$862$		−	24160.0i		−	0.954632i
$863$			6252.00i			0.246606i	0.992369	+	0.123303i	$0.0393486\pi$
$863$			6252.00i			0.246606i	−0.992369	+	0.123303i	$0.960651\pi$
$864$	864.000			0.0340207
$865$	−14674.0	+	2668.00i	−0.576799	+	0.104873i
$866$	32984.0			1.29427
$867$			13287.0i			0.520473i
$868$			1664.00i			0.0650689i
$869$	−55440.0			−2.16418
$870$	2592.00	+	14256.0i	0.101008	+	0.555544i
$871$	39312.0			1.52932
$872$			2960.00i			0.114952i
$873$		−	504.000i		−	0.0195393i
$874$	4800.00			0.185769
$875$	−2398.00	+	1436.00i	−0.0926482	+	0.0554808i
$876$	−7248.00			−0.279552
$877$			40166.0i			1.54653i	0.634081	+	0.773267i	$0.281379\pi$
$877$			40166.0i			1.54653i	−0.634081	+	0.773267i	$0.718621\pi$
$878$			30096.0i			1.15682i
$879$	−4086.00			−0.156789
$880$	2240.00	+	12320.0i	0.0858073	+	0.471940i
$881$	−12834.0			−0.490793			−0.245396	−	0.969423i	$-0.578918\pi$
$881$	−12834.0			−0.490793			−0.245396	+	0.969423i	$0.578918\pi$
$882$		−	6102.00i		−	0.232954i
$883$		−	27192.0i		−	1.03633i	−0.855279	−	0.518167i	$-0.826614\pi$
$883$		−	27192.0i		−	1.03633i	0.855279	−	0.518167i	$-0.173386\pi$
$884$	4752.00			0.180800
$885$	−12210.0	+	2220.00i	−0.463768	+	0.0843215i
$886$	−19752.0			−0.748963
$887$			42060.0i			1.59215i	0.605198	+	0.796075i	$0.293094\pi$
$887$			42060.0i			1.59215i	−0.605198	+	0.796075i	$0.706906\pi$
$888$		−	6096.00i		−	0.230370i
$889$	3260.00			0.122989
$890$	−20636.0	+	3752.00i	−0.777214	+	0.141312i
$891$	5670.00			0.213190
$892$		−	10280.0i		−	0.385874i
$893$			7680.00i			0.287796i
$894$	6456.00			0.241522
$895$	3428.00	+	18854.0i	0.128028	+	0.704156i
$896$	−256.000			−0.00954504
$897$			16200.0i			0.603013i
$898$		−	34332.0i		−	1.27581i
$899$	−44928.0			−1.66678
$900$	−4212.00	+	1584.00i	−0.156000	+	0.0586667i
$901$	8844.00			0.327010
$902$		−	28840.0i		−	1.06460i
$903$		−	1752.00i		−	0.0645658i
$904$	13968.0			0.513904
$905$	−8012.00	−	44066.0i	−0.294285	−	1.61857i
$906$	192.000			0.00704059
$907$			41172.0i			1.50727i	0.657293	+	0.753635i	$0.271701\pi$
$907$			41172.0i			1.50727i	−0.657293	+	0.753635i	$0.728299\pi$
$908$			11344.0i			0.414608i
$909$	5328.00			0.194410
$910$	2376.00	−	432.000i	0.0865534	−	0.0157370i
$911$	−48.0000			−0.00174568			−0.000872838	−	1.00000i	$-0.500278\pi$
$911$	−48.0000			−0.00174568			−0.000872838		1.00000i	$0.500278\pi$
$912$		−	1152.00i		−	0.0418273i
$913$		−	28280.0i		−	1.02512i
$914$	−29696.0			−1.07468
$915$	18150.0	−	3300.00i	0.655760	−	0.119229i
$916$	−2440.00			−0.0880130
$917$			1740.00i			0.0626607i
$918$		−	1188.00i		−	0.0427122i
$919$	34584.0			1.24137			0.620686	−	0.784059i	$-0.286854\pi$
$919$	34584.0			1.24137			0.620686	+	0.784059i	$0.286854\pi$
$920$	1600.00	+	8800.00i	0.0573374	+	0.315356i
$921$	23220.0			0.830755
$922$		−	2520.00i		−	0.0900128i
$923$			29160.0i			1.03988i
$924$	−1680.00			−0.0598138
$925$	11176.0	+	29718.0i	0.397259	+	1.05635i
$926$	−22476.0			−0.797632
$927$			558.000i			0.0197704i
$928$		−	6912.00i		−	0.244502i
$929$	3474.00			0.122689			0.0613446	−	0.998117i	$-0.480461\pi$
$929$	3474.00			0.122689			0.0613446	+	0.998117i	$0.480461\pi$
$930$	−2496.00	−	13728.0i	−0.0880076	−	0.484042i
$931$	−8136.00			−0.286409
$932$			14056.0i			0.494012i
$933$			14940.0i			0.524238i
$934$	−29544.0			−1.03502
$935$	16940.0	−	3080.00i	0.592510	−	0.107729i
$936$	3888.00			0.135773
$937$			44408.0i			1.54829i	0.633009	+	0.774144i	$0.281819\pi$
$937$			44408.0i			1.54829i	−0.633009	+	0.774144i	$0.718181\pi$
$938$			2912.00i			0.101365i
$939$	1812.00			0.0629738
$940$	−14080.0	+	2560.00i	−0.488552	+	0.0888277i
$941$	20188.0			0.699373			0.349686	−	0.936867i	$-0.386288\pi$
$941$	20188.0			0.699373			0.349686	+	0.936867i	$0.386288\pi$
$942$			15324.0i			0.530024i
$943$		−	20600.0i		−	0.711377i
$944$	5920.00			0.204110
$945$	−108.000	−	594.000i	−0.00371771	−	0.0204474i
$946$	40880.0			1.40499
$947$		−	31212.0i		−	1.07102i	−0.844530	−	0.535509i	$-0.820120\pi$
$947$		−	31212.0i		−	1.07102i	0.844530	−	0.535509i	$-0.179880\pi$
$948$			9504.00i			0.325607i
$949$	−32616.0			−1.11566
$950$	2112.00	+	5616.00i	0.0721288	+	0.191797i
$951$	25698.0			0.876251
$952$			352.000i			0.0119836i
$953$		−	20182.0i		−	0.686001i	−0.939335	−	0.343001i	$-0.888557\pi$
$953$		−	20182.0i		−	0.686001i	0.939335	−	0.343001i	$-0.111443\pi$
$954$	7236.00			0.245570
$955$	−1368.00	−	7524.00i	−0.0463533	−	0.254943i
$956$	−7376.00			−0.249536
$957$		−	45360.0i		−	1.53216i
$958$			12232.0i			0.412524i
$959$	1836.00			0.0618222
$960$	2112.00	−	384.000i	0.0710047	−	0.0129099i
$961$	13473.0			0.452251
$962$		−	27432.0i		−	0.919380i
$963$		−	756.000i		−	0.0252978i
$964$	−3928.00			−0.131237
$965$	−49324.0	+	8968.00i	−1.64538	+	0.299161i
$966$	−1200.00			−0.0399683
$967$		−	53722.0i		−	1.78654i	−0.449522	−	0.893269i	$-0.648406\pi$
$967$		−	53722.0i		−	1.78654i	0.449522	−	0.893269i	$-0.351594\pi$
$968$		−	28552.0i		−	0.948033i
$969$	−1584.00			−0.0525133
$970$	−224.000	−	1232.00i	−0.00741465	−	0.0407806i
$971$	22554.0			0.745409			0.372705	−	0.927950i	$-0.378430\pi$
$971$	22554.0			0.745409			0.372705	+	0.927950i	$0.378430\pi$
$972$		−	972.000i		−	0.0320750i
$973$		−	1192.00i		−	0.0392742i
$974$	−31812.0			−1.04653
$975$	−18954.0	+	7128.00i	−0.622578	+	0.234132i
$976$	−8800.00			−0.288608
$977$		−	18126.0i		−	0.593554i	−0.954947	−	0.296777i	$-0.904088\pi$
$977$		−	18126.0i		−	0.593554i	0.954947	−	0.296777i	$-0.0959118\pi$
$978$			4512.00i			0.147523i
$979$	65660.0			2.14352
$980$	−2712.00	−	14916.0i	−0.0883997	−	0.486198i
$981$	3330.00			0.108378
$982$			37428.0i			1.21627i
$983$		−	6232.00i		−	0.202207i	−0.994876	−	0.101104i	$-0.967763\pi$
$983$		−	6232.00i		−	0.202207i	0.994876	−	0.101104i	$-0.0322374\pi$
$984$	−4944.00			−0.160172
$985$	11638.0	−	2116.00i	0.376464	−	0.0684481i
$986$	−9504.00			−0.306967
$987$		−	1920.00i		−	0.0619192i
$988$		−	5184.00i		−	0.166928i
$989$	29200.0			0.938833
$990$	13860.0	−	2520.00i	0.444949	−	0.0808999i
$991$	15184.0			0.486716			0.243358	−	0.969937i	$-0.421751\pi$
$991$	15184.0			0.486716			0.243358	+	0.969937i	$0.421751\pi$
$992$			6656.00i			0.213032i
$993$			10416.0i			0.332872i
$994$	−2160.00			−0.0689246
$995$	2256.00	+	12408.0i	0.0718794	+	0.395337i
$996$	−4848.00			−0.154232
$997$		−	29922.0i		−	0.950491i	−0.879853	−	0.475245i	$-0.842359\pi$
$997$		−	29922.0i		−	0.950491i	0.879853	−	0.475245i	$-0.157641\pi$
$998$			8112.00i			0.257295i
$999$	−6858.00			−0.217195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.4.c.a.19.2	yes	2
3.2	odd	2		90.4.c.a.19.1		2
4.3	odd	2		240.4.f.d.49.1		2
5.2	odd	4		150.4.a.d.1.1		1
5.3	odd	4		150.4.a.f.1.1		1
5.4	even	2	inner	30.4.c.a.19.1	✓	2
8.3	odd	2		960.4.f.d.769.2		2
8.5	even	2		960.4.f.c.769.1		2
12.11	even	2		720.4.f.c.289.1		2
15.2	even	4		450.4.a.p.1.1		1
15.8	even	4		450.4.a.e.1.1		1
15.14	odd	2		90.4.c.a.19.2		2
20.3	even	4		1200.4.a.bc.1.1		1
20.7	even	4		1200.4.a.h.1.1		1
20.19	odd	2		240.4.f.d.49.2		2
40.19	odd	2		960.4.f.d.769.1		2
40.29	even	2		960.4.f.c.769.2		2
60.59	even	2		720.4.f.c.289.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.4.c.a.19.1	✓	2	5.4	even	2	inner
30.4.c.a.19.2	yes	2	1.1	even	1	trivial
90.4.c.a.19.1		2	3.2	odd	2
90.4.c.a.19.2		2	15.14	odd	2
150.4.a.d.1.1		1	5.2	odd	4
150.4.a.f.1.1		1	5.3	odd	4
240.4.f.d.49.1		2	4.3	odd	2
240.4.f.d.49.2		2	20.19	odd	2
450.4.a.e.1.1		1	15.8	even	4
450.4.a.p.1.1		1	15.2	even	4
720.4.f.c.289.1		2	12.11	even	2
720.4.f.c.289.2		2	60.59	even	2
960.4.f.c.769.1		2	8.5	even	2
960.4.f.c.769.2		2	40.29	even	2
960.4.f.d.769.1		2	40.19	odd	2
960.4.f.d.769.2		2	8.3	odd	2
1200.4.a.h.1.1		1	20.7	even	4
1200.4.a.bc.1.1		1	20.3	even	4

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:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	30.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} +3.00000i q^{3} -4.00000 q^{4} +(2.00000 + 11.0000i) q^{5} -6.00000 q^{6} -2.00000i q^{7} -8.00000i q^{8} -9.00000 q^{9} +(-22.0000 + 4.00000i) q^{10} +70.0000 q^{11} -12.0000i q^{12} -54.0000i q^{13} +4.00000 q^{14} +(-33.0000 + 6.00000i) q^{15} +16.0000 q^{16} -22.0000i q^{17} -18.0000i q^{18} -24.0000 q^{19} +(-8.00000 - 44.0000i) q^{20} +6.00000 q^{21} +140.000i q^{22} +100.000i q^{23} +24.0000 q^{24} +(-117.000 + 44.0000i) q^{25} +108.000 q^{26} -27.0000i q^{27} +8.00000i q^{28} -216.000 q^{29} +(-12.0000 - 66.0000i) q^{30} +208.000 q^{31} +32.0000i q^{32} +210.000i q^{33} +44.0000 q^{34} +(22.0000 - 4.00000i) q^{35} +36.0000 q^{36} -254.000i q^{37} -48.0000i q^{38} +162.000 q^{39} +(88.0000 - 16.0000i) q^{40} -206.000 q^{41} +12.0000i q^{42} -292.000i q^{43} -280.000 q^{44} +(-18.0000 - 99.0000i) q^{45} -200.000 q^{46} -320.000i q^{47} +48.0000i q^{48} +339.000 q^{49} +(-88.0000 - 234.000i) q^{50} +66.0000 q^{51} +216.000i q^{52} +402.000i q^{53} +54.0000 q^{54} +(140.000 + 770.000i) q^{55} -16.0000 q^{56} -72.0000i q^{57} -432.000i q^{58} +370.000 q^{59} +(132.000 - 24.0000i) q^{60} -550.000 q^{61} +416.000i q^{62} +18.0000i q^{63} -64.0000 q^{64} +(594.000 - 108.000i) q^{65} -420.000 q^{66} +728.000i q^{67} +88.0000i q^{68} -300.000 q^{69} +(8.00000 + 44.0000i) q^{70} -540.000 q^{71} +72.0000i q^{72} -604.000i q^{73} +508.000 q^{74} +(-132.000 - 351.000i) q^{75} +96.0000 q^{76} -140.000i q^{77} +324.000i q^{78} -792.000 q^{79} +(32.0000 + 176.000i) q^{80} +81.0000 q^{81} -412.000i q^{82} -404.000i q^{83} -24.0000 q^{84} +(242.000 - 44.0000i) q^{85} +584.000 q^{86} -648.000i q^{87} -560.000i q^{88} +938.000 q^{89} +(198.000 - 36.0000i) q^{90} -108.000 q^{91} -400.000i q^{92} +624.000i q^{93} +640.000 q^{94} +(-48.0000 - 264.000i) q^{95} -96.0000 q^{96} +56.0000i q^{97} +678.000i q^{98} -630.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{4} + 4 q^{5} - 12 q^{6} - 18 q^{9} - 44 q^{10} + 140 q^{11} + 8 q^{14} - 66 q^{15} + 32 q^{16} - 48 q^{19} - 16 q^{20} + 12 q^{21} + 48 q^{24} - 234 q^{25} + 216 q^{26} - 432 q^{29} - 24 q^{30}+ \cdots - 1260 q^{99}+O(q^{100}) \) 2 * q - 8 * q^4 + 4 * q^5 - 12 * q^6 - 18 * q^9 - 44 * q^10 + 140 * q^11 + 8 * q^14 - 66 * q^15 + 32 * q^16 - 48 * q^19 - 16 * q^20 + 12 * q^21 + 48 * q^24 - 234 * q^25 + 216 * q^26 - 432 * q^29 - 24 * q^30 + 416 * q^31 + 88 * q^34 + 44 * q^35 + 72 * q^36 + 324 * q^39 + 176 * q^40 - 412 * q^41 - 560 * q^44 - 36 * q^45 - 400 * q^46 + 678 * q^49 - 176 * q^50 + 132 * q^51 + 108 * q^54 + 280 * q^55 - 32 * q^56 + 740 * q^59 + 264 * q^60 - 1100 * q^61 - 128 * q^64 + 1188 * q^65 - 840 * q^66 - 600 * q^69 + 16 * q^70 - 1080 * q^71 + 1016 * q^74 - 264 * q^75 + 192 * q^76 - 1584 * q^79 + 64 * q^80 + 162 * q^81 - 48 * q^84 + 484 * q^85 + 1168 * q^86 + 1876 * q^89 + 396 * q^90 - 216 * q^91 + 1280 * q^94 - 96 * q^95 - 192 * q^96 - 1260 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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