LMFDB - Embedded newform 336.7.bh.f.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,7,Mod(145,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))

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

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

chi := DirichletCharacter("336.145");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	336.bh (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$77.2981720963$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 193x^{6} + 306x^{5} + 29845x^{4} + 16988x^{3} + 1125468x^{2} + 214128x + 35378704 $ x^8 - 2x^7 + 193x^6 + 306x^5 + 29845x^4 + 16988x^3 + 1125468x^2 + 214128*x + 35378704
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{4}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.1
Root			$-5.50376 + 9.53280i$ of defining polynomial
Character	$\chi$	$=$	336.145
Dual form			336.7.bh.f.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.5000 - 7.79423i) q^{3} +(-124.321 - 71.7768i) q^{5} +(-342.924 + 7.21089i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})$	\(q+(13.5000 - 7.79423i) q^{3} +(-124.321 - 71.7768i) q^{5} +(-342.924 + 7.21089i) q^{7} +(121.500 - 210.444i) q^{9} +(9.06867 + 15.7074i) q^{11} +1803.01i q^{13} -2237.78 q^{15} +(4669.87 - 2696.15i) q^{17} +(-10832.2 - 6254.00i) q^{19} +(-4573.27 + 2770.18i) q^{21} +(-5992.48 + 10379.3i) q^{23} +(2491.32 + 4315.10i) q^{25} -3788.00i q^{27} -14985.6 q^{29} +(-39568.1 + 22844.6i) q^{31} +(244.854 + 141.367i) q^{33} +(43150.3 + 23717.5i) q^{35} +(27607.0 - 47816.7i) q^{37} +(14053.1 + 24340.7i) q^{39} -10939.4i q^{41} +52058.1 q^{43} +(-30210.0 + 17441.8i) q^{45} +(74324.8 + 42911.4i) q^{47} +(117545. - 4945.58i) q^{49} +(42028.8 - 72796.0i) q^{51} +(113280. + 196207. i) q^{53} -2603.68i q^{55} -194980. q^{57} +(-128022. + 73913.5i) q^{59} +(337926. + 195102. i) q^{61} +(-40147.8 + 73042.5i) q^{63} +(129415. - 224153. i) q^{65} +(57512.5 + 99614.6i) q^{67} +186827. i q^{69} +302841. q^{71} +(254367. - 146859. i) q^{73} +(67265.7 + 38835.9i) q^{75} +(-3223.13 - 5321.05i) q^{77} +(268149. - 464449. i) q^{79} +(-29524.5 - 51137.9i) q^{81} -779343. i q^{83} -774084. q^{85} +(-202306. + 116802. i) q^{87} +(-465658. - 268848. i) q^{89} +(-13001.3 - 618297. i) q^{91} +(-356113. + 616805. i) q^{93} +(897784. + 1.55501e6i) q^{95} +863823. i q^{97} +4407.37 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 108 q^{3} + 462 q^{5} - 580 q^{7} + 972 q^{9}+O(q^{10}) $ 8 * q + 108 * q^3 + 462 * q^5 - 580 * q^7 + 972 * q^9	$ 8 q + 108 q^{3} + 462 q^{5} - 580 q^{7} + 972 q^{9} - 1806 q^{11} + 8316 q^{15} + 9564 q^{17} - 23022 q^{19} - 1350 q^{21} - 2400 q^{23} + 32762 q^{25} - 2484 q^{29} - 148416 q^{31} - 48762 q^{33} - 11412 q^{35} - 84046 q^{37} + 75222 q^{39} - 92972 q^{43} + 112266 q^{45} + 323124 q^{47} - 8644 q^{49} + 86076 q^{51} + 358086 q^{53} - 414396 q^{57} - 719382 q^{59} + 421536 q^{61} + 104490 q^{63} - 322740 q^{65} - 267010 q^{67} + 464664 q^{71} + 1944486 q^{73} + 884574 q^{75} - 1713498 q^{77} + 685904 q^{79} - 236196 q^{81} - 3876168 q^{85} - 33534 q^{87} + 4130604 q^{89} + 484266 q^{91} - 1335744 q^{93} + 2105232 q^{95} - 877716 q^{99}+O(q^{100}) $ 8 * q + 108 * q^3 + 462 * q^5 - 580 * q^7 + 972 * q^9 - 1806 * q^11 + 8316 * q^15 + 9564 * q^17 - 23022 * q^19 - 1350 * q^21 - 2400 * q^23 + 32762 * q^25 - 2484 * q^29 - 148416 * q^31 - 48762 * q^33 - 11412 * q^35 - 84046 * q^37 + 75222 * q^39 - 92972 * q^43 + 112266 * q^45 + 323124 * q^47 - 8644 * q^49 + 86076 * q^51 + 358086 * q^53 - 414396 * q^57 - 719382 * q^59 + 421536 * q^61 + 104490 * q^63 - 322740 * q^65 - 267010 * q^67 + 464664 * q^71 + 1944486 * q^73 + 884574 * q^75 - 1713498 * q^77 + 685904 * q^79 - 236196 * q^81 - 3876168 * q^85 - 33534 * q^87 + 4130604 * q^89 + 484266 * q^91 - 1335744 * q^93 + 2105232 * q^95 - 877716 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	13.5000	−	7.79423i	0.500000	−	0.288675i
$3$	13.5000	−	7.79423i	0.500000	−	0.288675i
$4$		0			0
$5$	−124.321	−	71.7768i	−0.994569	−	0.574215i	−0.0879320	−	0.996126i	$-0.528026\pi$
$5$	−124.321	−	71.7768i	−0.994569	−	0.574215i	−0.906637	+	0.421912i	$0.861359\pi$
$6$		0			0
$7$	−342.924	+	7.21089i	−0.999779	+	0.0210230i
$7$	−342.924	+	7.21089i	−0.999779	+	0.0210230i
$8$		0			0
$9$	121.500	−	210.444i	0.166667	−	0.288675i
$10$		0			0
$11$	9.06867	+	15.7074i	0.00681343	+	0.0118012i	0.869412	−	0.494088i	$-0.164498\pi$
$11$	9.06867	+	15.7074i	0.00681343	+	0.0118012i	−0.862599	+	0.505889i	$0.831165\pi$
$12$		0			0
$13$			1803.01i			0.820671i	0.911935	+	0.410335i	$0.134588\pi$
$13$			1803.01i			0.820671i	−0.911935	+	0.410335i	$0.865412\pi$
$14$		0			0
$15$	−2237.78			−0.663046
$16$		0			0
$17$	4669.87	−	2696.15i	0.950512	−	0.548779i	0.0572723	−	0.998359i	$-0.481760\pi$
$17$	4669.87	−	2696.15i	0.950512	−	0.548779i	0.893240	+	0.449580i	$0.148426\pi$
$18$		0			0
$19$	−10832.2	−	6254.00i	−1.57927	−	0.911795i	−0.994961	−	0.100267i	$-0.968030\pi$
$19$	−10832.2	−	6254.00i	−1.57927	−	0.911795i	−0.584314	−	0.811528i	$-0.698636\pi$
$20$		0			0
$21$	−4573.27	+	2770.18i	−0.493821	+	0.299123i
$22$		0			0
$23$	−5992.48	+	10379.3i	−0.492519	+	0.853068i	−0.999963	−	0.00861656i	$-0.997257\pi$
$23$	−5992.48	+	10379.3i	−0.492519	+	0.853068i	0.507444	+	0.861685i	$0.330591\pi$
$24$		0			0
$25$	2491.32	+	4315.10i	0.159445	+	0.276166i
$26$		0			0
$27$		−	3788.00i		−	0.192450i
$28$		0			0
$29$	−14985.6			−0.614443			−0.307221	−	0.951638i	$-0.599399\pi$
$29$	−14985.6			−0.614443			−0.307221	+	0.951638i	$0.599399\pi$
$30$		0			0
$31$	−39568.1	+	22844.6i	−1.32819	+	0.766830i	−0.985019	−	0.172443i	$-0.944834\pi$
$31$	−39568.1	+	22844.6i	−1.32819	+	0.766830i	−0.343170	+	0.939273i	$0.611501\pi$
$32$		0			0
$33$	244.854	+	141.367i	0.00681343	+	0.00393373i
$34$		0			0
$35$	43150.3	+	23717.5i	1.00642	+	0.553179i
$36$		0			0
$37$	27607.0	−	47816.7i	0.545021	−	0.944005i	−0.453584	−	0.891213i	$-0.649855\pi$
$37$	27607.0	−	47816.7i	0.545021	−	0.944005i	0.998606	−	0.0527914i	$-0.0168118\pi$
$38$		0			0
$39$	14053.1	+	24340.7i	0.236907	+	0.410335i
$40$		0			0
$41$		−	10939.4i		−	0.158724i	−0.996846	−	0.0793619i	$-0.974712\pi$
$41$		−	10939.4i		−	0.158724i	0.996846	−	0.0793619i	$-0.0252883\pi$
$42$		0			0
$43$	52058.1			0.654762			0.327381	−	0.944892i	$-0.393834\pi$
$43$	52058.1			0.654762			0.327381	+	0.944892i	$0.393834\pi$
$44$		0			0
$45$	−30210.0	+	17441.8i	−0.331523	+	0.191405i
$46$		0			0
$47$	74324.8	+	42911.4i	0.715880	+	0.413313i	0.813234	−	0.581936i	$-0.197705\pi$
$47$	74324.8	+	42911.4i	0.715880	+	0.413313i	−0.0973546	+	0.995250i	$0.531038\pi$
$48$		0			0
$49$	117545.	−	4945.58i	0.999116	−	0.0420367i
$50$		0			0
$51$	42028.8	−	72796.0i	0.316837	−	0.548779i
$52$		0			0
$53$	113280.	+	196207.i	0.760899	+	1.31792i	0.942388	+	0.334523i	$0.108575\pi$
$53$	113280.	+	196207.i	0.760899	+	1.31792i	−0.181488	+	0.983393i	$0.558091\pi$
$54$		0			0
$55$		−	2603.68i		−	0.0156495i
$56$		0			0
$57$	−194980.			−1.05285
$58$		0			0
$59$	−128022.	+	73913.5i	−0.623345	+	0.359888i	−0.778170	−	0.628054i	$-0.783852\pi$
$59$	−128022.	+	73913.5i	−0.623345	+	0.359888i	0.154825	+	0.987942i	$0.450518\pi$
$60$		0			0
$61$	337926.	+	195102.i	1.48878	+	0.859550i	0.999918	−	0.0128082i	$-0.00407709\pi$
$61$	337926.	+	195102.i	1.48878	+	0.859550i	0.488867	+	0.872358i	$0.337410\pi$
$62$		0			0
$63$	−40147.8	+	73042.5i	−0.160561	+	0.292115i
$64$		0			0
$65$	129415.	−	224153.i	0.471241	−	0.816214i
$66$		0			0
$67$	57512.5	+	99614.6i	0.191222	+	0.331206i	0.945655	−	0.325170i	$-0.105422\pi$
$67$	57512.5	+	99614.6i	0.191222	+	0.331206i	−0.754433	+	0.656377i	$0.772088\pi$
$68$		0			0
$69$			186827.i			0.568712i
$70$		0			0
$71$	302841.			0.846134			0.423067	−	0.906098i	$-0.360953\pi$
$71$	302841.			0.846134			0.423067	+	0.906098i	$0.360953\pi$
$72$		0			0
$73$	254367.	−	146859.i	0.653870	−	0.377512i	−0.136067	−	0.990700i	$-0.543446\pi$
$73$	254367.	−	146859.i	0.653870	−	0.377512i	0.789937	+	0.613187i	$0.210113\pi$
$74$		0			0
$75$	67265.7	+	38835.9i	0.159445	+	0.0920554i
$76$		0			0
$77$	−3223.13	−	5321.05i	−0.00706002	−	0.0116554i
$78$		0			0
$79$	268149.	−	464449.i	0.543871	−	0.942012i	−0.454806	−	0.890590i	$-0.650292\pi$
$79$	268149.	−	464449.i	0.543871	−	0.942012i	0.998677	−	0.0514214i	$-0.0163752\pi$
$80$		0			0
$81$	−29524.5	−	51137.9i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	779343.i		−	1.36300i	−0.731820	−	0.681498i	$-0.761329\pi$
$83$		−	779343.i		−	1.36300i	0.731820	−	0.681498i	$-0.238671\pi$
$84$		0			0
$85$	−774084.			−1.26047
$86$		0			0
$87$	−202306.	+	116802.i	−0.307221	+	0.177374i
$88$		0			0
$89$	−465658.	−	268848.i	−0.660537	−	0.381361i	0.131945	−	0.991257i	$-0.457878\pi$
$89$	−465658.	−	268848.i	−0.660537	−	0.381361i	−0.792481	+	0.609896i	$0.791211\pi$
$90$		0			0
$91$	−13001.3	−	618297.i	−0.0172530	−	0.820489i
$92$		0			0
$93$	−356113.	+	616805.i	−0.442730	+	0.766830i
$94$		0			0
$95$	897784.	+	1.55501e6i	1.04713	+	1.81368i
$96$		0			0
$97$			863823.i			0.946476i	0.880935	+	0.473238i	$0.156915\pi$
$97$			863823.i			0.946476i	−0.880935	+	0.473238i	$0.843085\pi$
$98$		0			0
$99$	4407.37			0.00454228
$100$		0			0
$101$	839759.	−	484835.i	0.815062	−	0.470576i	−0.0336485	−	0.999434i	$-0.510713\pi$
$101$	839759.	−	484835.i	0.815062	−	0.470576i	0.848711	+	0.528857i	$0.177379\pi$
$102$		0			0
$103$	1.32954e6	+	767611.i	1.21672	+	0.702473i	0.964215	−	0.265123i	$-0.0854126\pi$
$103$	1.32954e6	+	767611.i	1.21672	+	0.702473i	0.252504	+	0.967596i	$0.418746\pi$
$104$		0			0
$105$	767389.	−	16136.4i	0.662899	−	0.0139392i
$106$		0			0
$107$	−1.02169e6	+	1.76961e6i	−0.833999	+	1.44453i	0.0608432	+	0.998147i	$0.480621\pi$
$107$	−1.02169e6	+	1.76961e6i	−0.833999	+	1.44453i	−0.894843	+	0.446382i	$0.852712\pi$
$108$		0			0
$109$	−402411.	−	696996.i	−0.310735	−	0.538209i	0.667787	−	0.744353i	$-0.267242\pi$
$109$	−402411.	−	696996.i	−0.310735	−	0.538209i	−0.978522	+	0.206144i	$0.933909\pi$
$110$		0			0
$111$		−	860700.i		−	0.629337i
$112$		0			0
$113$	568602.			0.394069			0.197035	−	0.980397i	$-0.436869\pi$
$113$	568602.			0.394069			0.197035	+	0.980397i	$0.436869\pi$
$114$		0			0
$115$	1.48998e6	−	860243.i	0.979689	−	0.565623i
$116$		0			0
$117$	379434.	+	219066.i	0.236907	+	0.136778i
$118$		0			0
$119$	−1.58197e6	+	958249.i	−0.938765	+	0.568640i
$120$		0			0
$121$	885616.	−	1.53393e6i	0.499907	−	0.865865i
$122$		0			0
$123$	−85264.3	−	147682.i	−0.0458196	−	0.0793619i
$124$		0			0
$125$			1.52775e6i			0.782207i
$126$		0			0
$127$	1.38300e6			0.675166			0.337583	−	0.941296i	$-0.390391\pi$
$127$	1.38300e6			0.675166			0.337583	+	0.941296i	$0.390391\pi$
$128$		0			0
$129$	702785.	−	405753.i	0.327381	−	0.189013i
$130$		0			0
$131$	−3.05740e6	−	1.76519e6i	−1.36000	−	0.785196i	−0.370375	−	0.928882i	$-0.620771\pi$
$131$	−3.05740e6	−	1.76519e6i	−1.36000	−	0.785196i	−0.989623	+	0.143687i	$0.954104\pi$
$132$		0			0
$133$	3.75974e6	+	2.06654e6i	1.59809	+	0.878392i
$134$		0			0
$135$	−271890.	+	470928.i	−0.110508	+	0.191405i
$136$		0			0
$137$	737873.	+	1.27803e6i	0.286959	+	0.497027i	0.973082	−	0.230458i	$-0.0740223\pi$
$137$	737873.	+	1.27803e6i	0.286959	+	0.497027i	−0.686123	+	0.727485i	$0.740689\pi$
$138$		0			0
$139$			136322.i			0.0507601i	0.999678	+	0.0253800i	$0.00807958\pi$
$139$			136322.i			0.0507601i	−0.999678	+	0.0253800i	$0.991920\pi$
$140$		0			0
$141$	1.33785e6			0.477253
$142$		0			0
$143$	−28320.7	+	16350.9i	−0.00968490	+	0.00559158i
$144$		0			0
$145$	1.86303e6	+	1.07562e6i	0.611105	+	0.352822i
$146$		0			0
$147$	1.54831e6	−	982938.i	0.487423	−	0.309438i
$148$		0			0
$149$	1.25168e6	−	2.16798e6i	0.378387	−	0.655385i	−0.612441	−	0.790516i	$-0.709812\pi$
$149$	1.25168e6	−	2.16798e6i	0.378387	−	0.655385i	0.990828	+	0.135131i	$0.0431457\pi$
$150$		0			0
$151$	2.48249e6	+	4.29981e6i	0.721037	+	1.24887i	0.960585	+	0.277987i	$0.0896674\pi$
$151$	2.48249e6	+	4.29981e6i	0.721037	+	1.24887i	−0.239548	+	0.970884i	$0.576999\pi$
$152$		0			0
$153$		−	1.31033e6i		−	0.365852i
$154$		0			0
$155$	6.55886e6			1.76130
$156$		0			0
$157$	−4.43406e6	+	2.56001e6i	−1.14578	+	0.661519i	−0.947856	−	0.318698i	$-0.896754\pi$
$157$	−4.43406e6	+	2.56001e6i	−1.14578	+	0.661519i	−0.197928	+	0.980217i	$0.563421\pi$
$158$		0			0
$159$	3.05857e6	+	1.76587e6i	0.760899	+	0.439305i
$160$		0			0
$161$	1.98012e6	−	3.60252e6i	0.474476	−	0.863234i
$162$		0			0
$163$	74722.7	−	129424.i	0.0172540	−	0.0298848i	−0.857269	−	0.514868i	$-0.827841\pi$
$163$	74722.7	−	129424.i	0.0172540	−	0.0298848i	0.874523	+	0.484983i	$0.161174\pi$
$164$		0			0
$165$	−20293.7	−	35149.7i	−0.00451761	−	0.00782474i
$166$		0			0
$167$		−	646098.i		−	0.138723i	−0.997592	−	0.0693616i	$-0.977904\pi$
$167$		−	646098.i		−	0.138723i	0.997592	−	0.0693616i	$-0.0220962\pi$
$168$		0			0
$169$	1.57595e6			0.326499
$170$		0			0
$171$	−2.63224e6	+	1.51972e6i	−0.526425	+	0.303932i
$172$		0			0
$173$	5.32398e6	+	3.07380e6i	1.02825	+	0.593660i	0.916482	−	0.400075i	$-0.131016\pi$
$173$	5.32398e6	+	3.07380e6i	1.02825	+	0.593660i	0.111766	+	0.993735i	$0.464349\pi$
$174$		0			0
$175$	−885451.	−	1.46179e6i	−0.165215	−	0.272753i
$176$		0			0
$177$	−1.15220e6	+	1.99566e6i	−0.207782	+	0.359888i
$178$		0			0
$179$	4.95145e6	+	8.57617e6i	0.863323	+	1.49532i	0.868703	+	0.495334i	$0.164954\pi$
$179$	4.95145e6	+	8.57617e6i	0.863323	+	1.49532i	−0.00537926	+	0.999986i	$0.501712\pi$
$180$		0			0
$181$		−	2.53186e6i		−	0.426976i	−0.976946	−	0.213488i	$-0.931518\pi$
$181$		−	2.53186e6i		−	0.426976i	0.976946	−	0.213488i	$-0.0684824\pi$
$182$		0			0
$183$	6.08267e6			0.992523
$184$		0			0
$185$	−6.86426e6	+	3.96308e6i	−1.08412	+	0.625919i
$186$		0			0
$187$	84699.0	+	48901.0i	0.0129525	+	0.00747813i
$188$		0			0
$189$	27314.8	+	1.29900e6i	0.00404588	+	0.192408i
$190$		0			0
$191$	5.83095e6	−	1.00995e7i	0.836834	−	1.44944i	−0.0556949	−	0.998448i	$-0.517737\pi$
$191$	5.83095e6	−	1.00995e7i	0.836834	−	1.44944i	0.892529	−	0.450991i	$-0.148929\pi$
$192$		0			0
$193$	4.36885e6	+	7.56706e6i	0.607708	+	1.05258i	0.991617	+	0.129210i	$0.0412441\pi$
$193$	4.36885e6	+	7.56706e6i	0.607708	+	1.05258i	−0.383909	+	0.923371i	$0.625423\pi$
$194$		0			0
$195$		−	4.03475e6i		−	0.544142i
$196$		0			0
$197$	−1.00023e7			−1.30828			−0.654139	−	0.756375i	$-0.726969\pi$
$197$	−1.00023e7			−1.30828			−0.654139	+	0.756375i	$0.726969\pi$
$198$		0			0
$199$	−8.65656e6	+	4.99786e6i	−1.09846	+	0.634199i	−0.935817	−	0.352486i	$-0.885337\pi$
$199$	−8.65656e6	+	4.99786e6i	−1.09846	+	0.634199i	−0.162647	+	0.986684i	$0.552003\pi$
$200$		0			0
$201$	1.55284e6	+	896531.i	0.191222	+	0.110402i
$202$		0			0
$203$	5.13894e6	−	108060.i	0.614307	−	0.0129174i
$204$		0			0
$205$	−785196.	+	1.36000e6i	−0.0911416	+	0.157862i
$206$		0			0
$207$	1.45617e6	+	2.52217e6i	0.164173	+	0.284356i
$208$		0			0
$209$		−	226862.i		−	0.0248498i
$210$		0			0
$211$	−4.70945e6			−0.501329			−0.250665	−	0.968074i	$-0.580649\pi$
$211$	−4.70945e6			−0.501329			−0.250665	+	0.968074i	$0.580649\pi$
$212$		0			0
$213$	4.08835e6	−	2.36041e6i	0.423067	−	0.244258i
$214$		0			0
$215$	−6.47193e6	−	3.73657e6i	−0.651206	−	0.375974i
$216$		0			0
$217$	1.34041e7	−	8.11930e6i	1.31177	−	0.794583i
$218$		0			0
$219$	2.28930e6	−	3.96518e6i	0.217957	−	0.377512i
$220$		0			0
$221$	4.86119e6	+	8.41984e6i	0.450367	+	0.780058i
$222$		0			0
$223$			1.42227e7i			1.28253i	0.767320	+	0.641264i	$0.221590\pi$
$223$			1.42227e7i			1.28253i	−0.767320	+	0.641264i	$0.778410\pi$
$224$		0			0
$225$	1.21078e6			0.106296
$226$		0			0
$227$	−1.47096e6	+	849261.i	−0.125755	+	0.0726045i	−0.561558	−	0.827438i	$-0.689798\pi$
$227$	−1.47096e6	+	849261.i	−0.125755	+	0.0726045i	0.435803	+	0.900042i	$0.356464\pi$
$228$		0			0
$229$	−5.72840e6	−	3.30729e6i	−0.477009	−	0.275401i	0.242160	−	0.970236i	$-0.422144\pi$
$229$	−5.72840e6	−	3.30729e6i	−0.477009	−	0.275401i	−0.719169	+	0.694835i	$0.755477\pi$
$230$		0			0
$231$	−84985.8	−	46712.4i	−0.00689462	−	0.00378963i
$232$		0			0
$233$	−2.87935e6	+	4.98718e6i	−0.227629	+	0.394264i	−0.957105	−	0.289742i	$-0.906431\pi$
$233$	−2.87935e6	+	4.98718e6i	−0.227629	+	0.394264i	0.729476	+	0.684006i	$0.239764\pi$
$234$		0			0
$235$	−6.16009e6	−	1.06696e7i	−0.474661	−	0.822137i
$236$		0			0
$237$		−	8.36007e6i		−	0.628008i
$238$		0			0
$239$	−2.48851e7			−1.82283			−0.911416	−	0.411487i	$-0.865010\pi$
$239$	−2.48851e7			−1.82283			−0.911416	+	0.411487i	$0.865010\pi$
$240$		0			0
$241$	−1.26148e7	+	7.28314e6i	−0.901214	+	0.520316i	−0.877594	−	0.479405i	$-0.840853\pi$
$241$	−1.26148e7	+	7.28314e6i	−0.901214	+	0.520316i	−0.0236202	+	0.999721i	$0.507519\pi$
$242$		0			0
$243$	−797162.	−	460241.i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	−1.49683e7	−	7.82217e6i	−1.01783	−	0.531899i
$246$		0			0
$247$	1.12760e7	−	1.95307e7i	0.748283	−	1.29606i
$248$		0			0
$249$	−6.07438e6	−	1.05211e7i	−0.393463	−	0.681498i
$250$		0			0
$251$		−	6.60358e6i		−	0.417598i	−0.977959	−	0.208799i	$-0.933045\pi$
$251$		−	6.60358e6i		−	0.417598i	0.977959	−	0.208799i	$-0.0669554\pi$
$252$		0			0
$253$	−217375.			−0.0134230
$254$		0			0
$255$	−1.04501e7	+	6.03339e6i	−0.630233	+	0.363865i
$256$		0			0
$257$	−473448.	−	273345.i	−0.0278916	−	0.0161032i	0.485989	−	0.873965i	$-0.338459\pi$
$257$	−473448.	−	273345.i	−0.0278916	−	0.0161032i	−0.513881	+	0.857862i	$0.671793\pi$
$258$		0			0
$259$	−9.12230e6	+	1.65966e7i	−0.525055	+	0.955254i
$260$		0			0
$261$	−1.82076e6	+	3.15364e6i	−0.102407	+	0.177374i
$262$		0			0
$263$	−4.14663e6	−	7.18218e6i	−0.227944	−	0.394811i	0.729255	−	0.684243i	$-0.239867\pi$
$263$	−4.14663e6	−	7.18218e6i	−0.227944	−	0.394811i	−0.957199	+	0.289432i	$0.906534\pi$
$264$		0			0
$265$		−	3.25236e7i		−	1.74768i
$266$		0			0
$267$	−8.38184e6			−0.440358
$268$		0			0
$269$	−83937.8	+	48461.5i	−0.00431222	+	0.00248966i	−0.502155	−	0.864778i	$-0.667459\pi$
$269$	−83937.8	+	48461.5i	−0.00431222	+	0.00248966i	0.497842	+	0.867268i	$0.334126\pi$
$270$		0			0
$271$	−14880.3	−	8591.15i	−0.000747660	−	0.000431662i	0.499626	−	0.866241i	$-0.333471\pi$
$271$	−14880.3	−	8591.15i	−0.000747660	−	0.000431662i	−0.500374	+	0.865809i	$0.666804\pi$
$272$		0			0
$273$	−4.99467e6	−	8.24567e6i	−0.245481	−	0.405264i
$274$		0			0
$275$	−45186.0	+	78264.4i	−0.00217273	+	0.00376328i
$276$		0			0
$277$	−820007.	−	1.42029e6i	−0.0385814	−	0.0668250i	0.846090	−	0.533040i	$-0.178951\pi$
$277$	−820007.	−	1.42029e6i	−0.0385814	−	0.0668250i	−0.884671	+	0.466215i	$0.845617\pi$
$278$		0			0
$279$			1.11025e7i			0.511220i
$280$		0			0
$281$	757209.			0.0341269			0.0170634	−	0.999854i	$-0.494568\pi$
$281$	757209.			0.0341269			0.0170634	+	0.999854i	$0.494568\pi$
$282$		0			0
$283$	3.10416e7	−	1.79219e7i	1.36957	−	0.790723i	0.378700	−	0.925520i	$-0.376371\pi$
$283$	3.10416e7	−	1.79219e7i	1.36957	−	0.790723i	0.990873	+	0.134796i	$0.0430380\pi$
$284$		0			0
$285$	2.42402e7	+	1.39951e7i	1.04713	+	0.604562i
$286$		0			0
$287$	78882.9	+	3.75139e6i	0.00333685	+	0.158689i
$288$		0			0
$289$	2.46966e6	−	4.27757e6i	0.102316	−	0.177216i
$290$		0			0
$291$	6.73283e6	+	1.16616e7i	0.273224	+	0.473238i
$292$		0			0
$293$			3.66609e6i			0.145747i	0.997341	+	0.0728736i	$0.0232170\pi$
$293$			3.66609e6i			0.145747i	−0.997341	+	0.0728736i	$0.976783\pi$
$294$		0			0
$295$	2.12211e7			0.826612
$296$		0			0
$297$	59499.6	−	34352.1i	0.00227114	−	0.00131124i
$298$		0			0
$299$	−1.87140e7	−	1.08045e7i	−0.700088	−	0.404196i
$300$		0			0
$301$	−1.78520e7	+	375385.i	−0.654617	+	0.0137651i
$302$		0			0
$303$	7.55783e6	−	1.30906e7i	0.271687	−	0.470576i
$304$		0			0
$305$	−2.80075e7	−	4.85105e7i	−0.987133	−	1.70976i
$306$		0			0
$307$			5.67870e6i			0.196261i	0.995174	+	0.0981305i	$0.0312862\pi$
$307$			5.67870e6i			0.196261i	−0.995174	+	0.0981305i	$0.968714\pi$
$308$		0			0
$309$	2.39317e7			0.811146
$310$		0			0
$311$	−3.71584e7	+	2.14534e7i	−1.23531	+	0.713207i	−0.968132	−	0.250441i	$-0.919425\pi$
$311$	−3.71584e7	+	2.14534e7i	−1.23531	+	0.713207i	−0.267178	+	0.963647i	$0.586091\pi$
$312$		0			0
$313$	1.56327e7	+	9.02555e6i	0.509802	+	0.294334i	0.732752	−	0.680496i	$-0.238235\pi$
$313$	1.56327e7	+	9.02555e6i	0.509802	+	0.294334i	−0.222950	+	0.974830i	$0.571569\pi$
$314$		0			0
$315$	1.02340e7	−	6.19905e6i	0.327426	−	0.198332i
$316$		0			0
$317$	−2.81057e7	+	4.86805e7i	−0.882301	+	1.52819i	−0.0335241	+	0.999438i	$0.510673\pi$
$317$	−2.81057e7	+	4.86805e7i	−0.882301	+	1.52819i	−0.848777	+	0.528752i	$0.822660\pi$
$318$		0			0
$319$	−135900.	−	235385.i	−0.00418646	−	0.00725116i
$320$		0			0
$321$			3.18530e7i			0.963019i
$322$		0			0
$323$	−6.74469e7			−2.00149
$324$		0			0
$325$	−7.78018e6	+	4.49189e6i	−0.226642	+	0.130852i
$326$		0			0
$327$	−1.08651e7	−	6.27297e6i	−0.310735	−	0.179403i
$328$		0			0
$329$	−2.57972e7	−	1.41794e7i	−0.724410	−	0.398172i
$330$		0			0
$331$	1.86546e7	−	3.23107e7i	0.514400	−	0.890968i	−0.485460	−	0.874259i	$-0.661348\pi$
$331$	1.86546e7	−	3.23107e7i	0.514400	−	0.890968i	0.999860	−	0.0167087i	$-0.00531880\pi$
$332$		0			0
$333$	−6.70849e6	−	1.16195e7i	−0.181674	−	0.314668i
$334$		0			0
$335$		−	1.65123e7i		−	0.439210i
$336$		0			0
$337$	1.90332e6			0.0497303			0.0248652	−	0.999691i	$-0.492084\pi$
$337$	1.90332e6			0.0497303			0.0248652	+	0.999691i	$0.492084\pi$
$338$		0			0
$339$	7.67612e6	−	4.43181e6i	0.197035	−	0.113758i
$340$		0			0
$341$	−717660.	−	414341.i	−0.0180990	−	0.0104495i
$342$		0			0
$343$	−4.02734e7	+	2.54356e6i	−0.998012	+	0.0630318i
$344$		0			0
$345$	1.34099e7	−	2.32266e7i	0.326563	−	0.565623i
$346$		0			0
$347$	3.82931e6	+	6.63256e6i	0.0916500	+	0.158742i	0.908206	−	0.418524i	$-0.137453\pi$
$347$	3.82931e6	+	6.63256e6i	0.0916500	+	0.158742i	−0.816556	+	0.577267i	$0.804119\pi$
$348$		0			0
$349$		−	4.53060e7i		−	1.06581i	−0.846175	−	0.532904i	$-0.821101\pi$
$349$		−	4.53060e7i		−	1.06581i	0.846175	−	0.532904i	$-0.178899\pi$
$350$		0			0
$351$	6.82981e6			0.157938
$352$		0			0
$353$	−6.90858e7	+	3.98867e7i	−1.57060	+	0.906784i	−0.574500	+	0.818505i	$0.694803\pi$
$353$	−6.90858e7	+	3.98867e7i	−1.57060	+	0.906784i	−0.996096	+	0.0882793i	$0.971863\pi$
$354$		0			0
$355$	−3.76495e7	−	2.17369e7i	−0.841539	−	0.485863i
$356$		0			0
$357$	−1.38878e7	+	2.52666e7i	−0.305230	+	0.555318i
$358$		0			0
$359$	−3.80493e7	+	6.59033e7i	−0.822362	+	1.42437i	0.0815573	+	0.996669i	$0.474011\pi$
$359$	−3.80493e7	+	6.59033e7i	−0.822362	+	1.42437i	−0.903919	+	0.427704i	$0.859323\pi$
$360$		0			0
$361$	5.47021e7	+	9.47468e7i	1.16274	+	2.01392i
$362$		0			0
$363$		−	2.76108e7i		−	0.577243i
$364$		0			0
$365$	−4.21642e7			−0.867092
$366$		0			0
$367$	3.54625e7	−	2.04743e7i	0.717417	−	0.414201i	−0.0963843	−	0.995344i	$-0.530728\pi$
$367$	3.54625e7	−	2.04743e7i	0.717417	−	0.414201i	0.813801	+	0.581143i	$0.197394\pi$
$368$		0			0
$369$	−2.30213e6	−	1.32914e6i	−0.0458196	−	0.0264540i
$370$		0			0
$371$	−4.02614e7	−	6.64674e7i	−0.788438	−	1.30163i
$372$		0			0
$373$	2.34532e7	−	4.06221e7i	0.451935	−	0.782774i	−0.546572	−	0.837412i	$-0.684067\pi$
$373$	2.34532e7	−	4.06221e7i	0.451935	−	0.782774i	0.998506	+	0.0546388i	$0.0174007\pi$
$374$		0			0
$375$	1.19076e7	+	2.06246e7i	0.225804	+	0.391104i
$376$		0			0
$377$		−	2.70193e7i		−	0.504255i
$378$		0			0
$379$	9.33006e7			1.71383			0.856913	−	0.515462i	$-0.172379\pi$
$379$	9.33006e7			1.71383			0.856913	+	0.515462i	$0.172379\pi$
$380$		0			0
$381$	1.86705e7	−	1.07794e7i	0.337583	−	0.194904i
$382$		0			0
$383$	6.33524e7	+	3.65765e7i	1.12763	+	0.651037i	0.943338	−	0.331834i	$-0.107668\pi$
$383$	6.33524e7	+	3.65765e7i	1.12763	+	0.651037i	0.184292	+	0.982872i	$0.441001\pi$
$384$		0			0
$385$	18774.9	+	892865.i	0.000328999	+	0.0156460i
$386$		0			0
$387$	6.32506e6	−	1.09553e7i	0.109127	−	0.189013i
$388$		0			0
$389$	−5.24716e7	−	9.08835e7i	−0.891407	−	1.54396i	−0.838190	−	0.545378i	$-0.816386\pi$
$389$	−5.24716e7	−	9.08835e7i	−0.891407	−	1.54396i	−0.0532167	−	0.998583i	$-0.516947\pi$
$390$		0			0
$391$			6.46265e7i			1.08114i
$392$		0			0
$393$	−5.50332e7			−0.906666
$394$		0			0
$395$	−6.66733e7	+	3.84938e7i	−1.08183	+	0.624597i
$396$		0			0
$397$	−6.23636e7	−	3.60057e7i	−0.996689	−	0.575439i	−0.0894223	−	0.995994i	$-0.528502\pi$
$397$	−6.23636e7	−	3.60057e7i	−0.996689	−	0.575439i	−0.907267	+	0.420555i	$0.861835\pi$
$398$		0			0
$399$	6.68635e7	−	1.40598e6i	1.05262	−	0.0221341i
$400$		0			0
$401$	−3.70281e7	+	6.41346e7i	−0.574247	+	0.994625i	0.421876	+	0.906654i	$0.361372\pi$
$401$	−3.70281e7	+	6.41346e7i	−0.574247	+	0.994625i	−0.996123	+	0.0879715i	$0.971962\pi$
$402$		0			0
$403$	−4.11892e7	−	7.13418e7i	−0.629315	−	1.09001i
$404$		0			0
$405$			8.47670e6i			0.127603i
$406$		0			0
$407$	1.00143e6			0.0148539
$408$		0			0
$409$	9.72326e6	−	5.61373e6i	0.142116	−	0.0820505i	−0.427256	−	0.904131i	$-0.640520\pi$
$409$	9.72326e6	−	5.61373e6i	0.142116	−	0.0820505i	0.569372	+	0.822080i	$0.307186\pi$
$410$		0			0
$411$	1.99226e7	+	1.15023e7i	0.286959	+	0.165676i
$412$		0			0
$413$	4.33688e7	−	2.62699e7i	0.615641	−	0.372913i
$414$		0			0
$415$	−5.59388e7	+	9.68888e7i	−0.782652	+	1.35559i
$416$		0			0
$417$	1.06253e6	+	1.84035e6i	0.0146532	+	0.0253800i
$418$		0			0
$419$		−	1.55584e7i		−	0.211506i	−0.994392	−	0.105753i	$-0.966275\pi$
$419$		−	1.55584e7i		−	0.211506i	0.994392	−	0.105753i	$-0.0337253\pi$
$420$		0			0
$421$	6.19246e7			0.829883			0.414941	−	0.909848i	$-0.363802\pi$
$421$	6.19246e7			0.829883			0.414941	+	0.909848i	$0.363802\pi$
$422$		0			0
$423$	1.80609e7	−	1.04275e7i	0.238627	−	0.137771i
$424$		0			0
$425$	2.32683e7	+	1.34340e7i	0.303108	+	0.175000i
$426$		0			0
$427$	−1.17290e8	−	6.44683e7i	−1.50653	−	0.828062i
$428$		0			0
$429$	−254886.	+	441475.i	−0.00322830	+	0.00559158i
$430$		0			0
$431$	2.12396e7	+	3.67881e7i	0.265286	+	0.459489i	0.967639	−	0.252340i	$-0.0812002\pi$
$431$	2.12396e7	+	3.67881e7i	0.265286	+	0.459489i	−0.702352	+	0.711829i	$0.747867\pi$
$432$		0			0
$433$			9.66424e7i			1.19043i	0.803566	+	0.595215i	$0.202933\pi$
$433$			9.66424e7i			1.19043i	−0.803566	+	0.595215i	$0.797067\pi$
$434$		0			0
$435$	3.35346e7			0.407404
$436$		0			0
$437$	1.29824e8	−	7.49540e7i	1.55565	−	0.898153i
$438$		0			0
$439$	8.59548e7	+	4.96260e7i	1.01596	+	0.586564i	0.912931	−	0.408114i	$-0.133813\pi$
$439$	8.59548e7	+	4.96260e7i	1.01596	+	0.586564i	0.103028	+	0.994678i	$0.467147\pi$
$440$		0			0
$441$	1.32410e7	−	2.53375e7i	0.154384	−	0.295426i
$442$		0			0
$443$	5.71127e7	−	9.89221e7i	0.656934	−	1.13784i	−0.324472	−	0.945895i	$-0.605186\pi$
$443$	5.71127e7	−	9.89221e7i	0.656934	−	1.13784i	0.981405	−	0.191947i	$-0.0614802\pi$
$444$		0			0
$445$	3.85941e7	+	6.68469e7i	0.437966	+	0.758579i
$446$		0			0
$447$		−	3.90236e7i		−	0.436923i
$448$		0			0
$449$	5.31323e7			0.586975			0.293488	−	0.955963i	$-0.405184\pi$
$449$	5.31323e7			0.586975			0.293488	+	0.955963i	$0.405184\pi$
$450$		0			0
$451$	171830.	−	99205.9i	0.00187313	−	0.00108145i
$452$		0			0
$453$	6.70273e7	+	3.86982e7i	0.721037	+	0.416291i
$454$		0			0
$455$	−4.27631e7	+	7.78006e7i	−0.453978	+	0.825940i
$456$		0			0
$457$	7.90827e7	−	1.36975e8i	0.828577	−	1.43514i	−0.0705775	−	0.997506i	$-0.522484\pi$
$457$	7.90827e7	−	1.36975e8i	0.828577	−	1.43514i	0.899155	−	0.437631i	$-0.144182\pi$
$458$		0			0
$459$	−1.02130e7	−	1.76894e7i	−0.105612	−	0.182926i
$460$		0			0
$461$			1.75859e8i			1.79499i	0.441026	+	0.897494i	$0.354615\pi$
$461$			1.75859e8i			1.79499i	−0.441026	+	0.897494i	$0.645385\pi$
$462$		0			0
$463$	5.63336e7			0.567576			0.283788	−	0.958887i	$-0.408409\pi$
$463$	5.63336e7			0.567576			0.283788	+	0.958887i	$0.408409\pi$
$464$		0			0
$465$	8.85447e7	−	5.11213e7i	0.880650	−	0.508444i
$466$		0			0
$467$	2.41547e7	+	1.39457e7i	0.237165	+	0.136928i	0.613873	−	0.789405i	$-0.289611\pi$
$467$	2.41547e7	+	1.39457e7i	0.237165	+	0.136928i	−0.376708	+	0.926332i	$0.622944\pi$
$468$		0			0
$469$	−2.04407e7	−	3.37455e7i	−0.198143	−	0.327113i
$470$		0			0
$471$	−3.99066e7	+	6.91202e7i	−0.381928	+	0.661519i
$472$		0			0
$473$	472098.	+	817698.i	0.00446117	+	0.00772698i
$474$		0			0
$475$		−	6.23229e7i		−	0.581523i
$476$		0			0
$477$	5.50543e7			0.507266
$478$		0			0
$479$	−4.93664e7	+	2.85017e7i	−0.449185	+	0.259337i	−0.707486	−	0.706727i	$-0.750171\pi$
$479$	−4.93664e7	+	2.85017e7i	−0.449185	+	0.259337i	0.258301	+	0.966064i	$0.416837\pi$
$480$		0			0
$481$	8.62141e7	+	4.97758e7i	0.774717	+	0.447283i
$482$		0			0
$483$	−1.34719e6	−	6.40675e7i	−0.0119560	−	0.568587i
$484$		0			0
$485$	6.20025e7	−	1.07391e8i	0.543480	−	0.941335i
$486$		0			0
$487$	5.53575e7	+	9.58820e7i	0.479280	+	0.830138i	0.999718	−	0.0237622i	$-0.00756447\pi$
$487$	5.53575e7	+	9.58820e7i	0.479280	+	0.830138i	−0.520438	+	0.853900i	$0.674231\pi$
$488$		0			0
$489$		−	2.32962e6i		−	0.0199232i
$490$		0			0
$491$	3.65467e7			0.308748			0.154374	−	0.988012i	$-0.450664\pi$
$491$	3.65467e7			0.308748			0.154374	+	0.988012i	$0.450664\pi$
$492$		0			0
$493$	−6.99810e7	+	4.04035e7i	−0.584035	+	0.337193i
$494$		0			0
$495$	−547930.	−	316347.i	−0.00451761	−	0.00260825i
$496$		0			0
$497$	−1.03851e8	+	2.18375e6i	−0.845947	+	0.0177883i
$498$		0			0
$499$	6.86955e6	−	1.18984e7i	0.0552874	−	0.0957606i	−0.837057	−	0.547116i	$-0.815726\pi$
$499$	6.86955e6	−	1.18984e7i	0.0552874	−	0.0957606i	0.892345	+	0.451355i	$0.149059\pi$
$500$		0			0
$501$	−5.03583e6	−	8.72232e6i	−0.0400459	−	0.0693616i
$502$		0			0
$503$		−	4.78225e7i		−	0.375775i	−0.982191	−	0.187888i	$-0.939836\pi$
$503$		−	4.78225e7i		−	0.375775i	0.982191	−	0.187888i	$-0.0601641\pi$
$504$		0			0
$505$	−1.39200e8			−1.08085
$506$		0			0
$507$	2.12753e7	−	1.22833e7i	0.163250	−	0.0942523i
$508$		0			0
$509$	−1.98161e8	−	1.14408e8i	−1.50268	−	0.867571i	−0.999995	−	0.00309898i	$-0.999014\pi$
$509$	−1.98161e8	−	1.14408e8i	−1.50268	−	0.867571i	−0.502681	−	0.864472i	$-0.667653\pi$
$510$		0			0
$511$	−8.61695e7	+	5.21956e7i	−0.645789	+	0.391175i
$512$		0			0
$513$	−2.36901e7	+	4.10325e7i	−0.175475	+	0.303932i
$514$		0			0
$515$	−1.10193e8	−	1.90860e8i	−0.806740	−	1.39731i
$516$		0			0
$517$			1.55660e6i			0.0112643i
$518$		0			0
$519$	9.58316e7			0.685499
$520$		0			0
$521$	−6.55225e7	+	3.78295e7i	−0.463316	+	0.267496i	−0.713438	−	0.700719i	$-0.752863\pi$
$521$	−6.55225e7	+	3.78295e7i	−0.463316	+	0.267496i	0.250121	+	0.968214i	$0.419529\pi$
$522$		0			0
$523$	1.32740e8	+	7.66375e7i	0.927891	+	0.535718i	0.886144	−	0.463410i	$-0.153374\pi$
$523$	1.32740e8	+	7.66375e7i	0.927891	+	0.535718i	0.0417470	+	0.999128i	$0.486708\pi$
$524$		0			0
$525$	−2.33471e7	−	1.28327e7i	−0.161345	−	0.0886831i
$526$		0			0
$527$	−1.23185e8	+	2.13363e8i	−0.841640	+	1.45776i
$528$		0			0
$529$	2.19826e6	+	3.80750e6i	0.0148495	+	0.0257201i
$530$		0			0
$531$			3.59219e7i			0.239925i
$532$		0			0
$533$	1.97239e7			0.130260
$534$		0			0
$535$	2.54034e8	−	1.46667e8i	1.65894	−	0.957789i
$536$		0			0
$537$	1.33689e8	+	7.71855e7i	0.863323	+	0.498440i
$538$		0			0
$539$	1.14366e6	+	1.80148e6i	0.00730349	+	0.0115044i
$540$		0			0
$541$	−6.40271e7	+	1.10898e8i	−0.404364	+	0.700378i	−0.994247	−	0.107110i	$-0.965840\pi$
$541$	−6.40271e7	+	1.10898e8i	−0.404364	+	0.700378i	0.589883	+	0.807488i	$0.299174\pi$
$542$		0			0
$543$	−1.97339e7	−	3.41800e7i	−0.123257	−	0.213488i
$544$		0			0
$545$			1.15535e8i			0.713715i
$546$		0			0
$547$	1.61523e8			0.986901			0.493451	−	0.869774i	$-0.335735\pi$
$547$	1.61523e8			0.986901			0.493451	+	0.869774i	$0.335735\pi$
$548$		0			0
$549$	8.21160e7	−	4.74097e7i	0.496262	−	0.286517i
$550$		0			0
$551$	1.62328e8	+	9.37202e7i	0.970374	+	0.560245i
$552$		0			0
$553$	−8.86059e7	+	1.61204e8i	−0.523947	+	0.953237i
$554$		0			0
$555$	−6.17783e7	+	1.07003e8i	−0.361374	+	0.625919i
$556$		0			0
$557$	3.22377e7	+	5.58373e7i	0.186551	+	0.323116i	0.944098	−	0.329665i	$-0.106936\pi$
$557$	3.22377e7	+	5.58373e7i	0.186551	+	0.323116i	−0.757547	+	0.652781i	$0.773602\pi$
$558$		0			0
$559$			9.38615e7i			0.537344i
$560$		0			0
$561$	1.52458e6			0.00863500
$562$		0			0
$563$	5.72927e7	−	3.30779e7i	0.321051	−	0.185359i	−0.330810	−	0.943697i	$-0.607322\pi$
$563$	5.72927e7	−	3.30779e7i	0.321051	−	0.185359i	0.651861	+	0.758339i	$0.273989\pi$
$564$		0			0
$565$	−7.06892e7	−	4.08124e7i	−0.391929	−	0.226280i
$566$		0			0
$567$	1.04934e7	+	1.73235e7i	0.0575662	+	0.0950358i
$568$		0			0
$569$	−4.70533e7	+	8.14986e7i	−0.255419	+	0.442398i	−0.965009	−	0.262216i	$-0.915547\pi$
$569$	−4.70533e7	+	8.14986e7i	−0.255419	+	0.442398i	0.709590	+	0.704614i	$0.248880\pi$
$570$		0			0
$571$	2.66234e7	+	4.61132e7i	0.143007	+	0.247695i	0.928627	−	0.371014i	$-0.120990\pi$
$571$	2.66234e7	+	4.61132e7i	0.143007	+	0.247695i	−0.785621	+	0.618708i	$0.787656\pi$
$572$		0			0
$573$		−	1.81791e8i		−	0.966292i
$574$		0			0
$575$	−5.97168e7			−0.314118
$576$		0			0
$577$	1.41079e8	−	8.14519e7i	0.734403	−	0.424008i	−0.0856281	−	0.996327i	$-0.527290\pi$
$577$	1.41079e8	−	8.14519e7i	0.734403	−	0.424008i	0.820031	+	0.572320i	$0.193956\pi$
$578$		0			0
$579$	1.17959e8	+	6.81036e7i	0.607708	+	0.350860i
$580$		0			0
$581$	5.61976e6	+	2.67256e8i	0.0286543	+	1.36269i
$582$		0			0
$583$	−2.05461e6	+	3.55868e6i	−0.0103687	+	0.0179591i
$584$		0			0
$585$	−3.14477e7	−	5.44691e7i	−0.157080	−	0.272071i
$586$		0			0
$587$		−	3.89096e8i		−	1.92372i	−0.273541	−	0.961860i	$-0.588195\pi$
$587$		−	3.89096e8i		−	1.92372i	0.273541	−	0.961860i	$-0.411805\pi$
$588$		0			0
$589$	5.71482e8			2.79677
$590$		0			0
$591$	−1.35031e8	+	7.79600e7i	−0.654139	+	0.377667i
$592$		0			0
$593$	8.59444e7	+	4.96200e7i	0.412148	+	0.237954i	0.691712	−	0.722173i	$-0.256857\pi$
$593$	8.59444e7	+	4.96200e7i	0.412148	+	0.237954i	−0.279564	+	0.960127i	$0.590190\pi$
$594$		0			0
$595$	2.65452e8	−	5.58183e6i	1.26019	−	0.0264988i
$596$		0			0
$597$	−7.79090e7	+	1.34942e8i	−0.366155	+	0.634199i
$598$		0			0
$599$	5.57032e7	+	9.64807e7i	0.259179	+	0.448911i	0.966022	−	0.258459i	$-0.0832148\pi$
$599$	5.57032e7	+	9.64807e7i	0.259179	+	0.448911i	−0.706843	+	0.707370i	$0.749881\pi$
$600$		0			0
$601$		−	3.79725e8i		−	1.74923i	−0.484821	−	0.874613i	$-0.661115\pi$
$601$		−	3.79725e8i		−	1.74923i	0.484821	−	0.874613i	$-0.338885\pi$
$602$		0			0
$603$	2.79511e7			0.127481
$604$		0			0
$605$	−2.20202e8	+	1.27133e8i	−0.994384	+	0.574108i
$606$		0			0
$607$	−2.31004e8	−	1.33370e8i	−1.03289	−	0.596339i	−0.115078	−	0.993356i	$-0.536712\pi$
$607$	−2.31004e8	−	1.33370e8i	−1.03289	−	0.596339i	−0.917811	+	0.397017i	$0.870045\pi$
$608$		0			0
$609$	6.85334e7	−	4.15129e7i	0.303424	−	0.183794i
$610$		0			0
$611$	−7.73699e7	+	1.34009e8i	−0.339194	+	0.587502i
$612$		0			0
$613$	1.13234e8	+	1.96127e8i	0.491581	+	0.851442i	0.999953	−	0.00969481i	$-0.00308600\pi$
$613$	1.13234e8	+	1.96127e8i	0.491581	+	0.851442i	−0.508372	+	0.861137i	$0.669753\pi$
$614$		0			0
$615$			2.44800e7i			0.105241i
$616$		0			0
$617$	4.18551e8			1.78194			0.890969	−	0.454064i	$-0.150026\pi$
$617$	4.18551e8			1.78194			0.890969	+	0.454064i	$0.150026\pi$
$618$		0			0
$619$	−1.61311e8	+	9.31331e7i	−0.680131	+	0.392674i	−0.799905	−	0.600127i	$-0.795117\pi$
$619$	−1.61311e8	+	9.31331e7i	−0.680131	+	0.392674i	0.119773	+	0.992801i	$0.461783\pi$
$620$		0			0
$621$	3.93167e7	+	2.26995e7i	0.164173	+	0.0947854i
$622$		0			0
$623$	1.61624e8	+	8.88366e7i	0.668408	+	0.367390i
$624$		0			0
$625$	1.48584e8	−	2.57355e8i	0.608599	−	1.05413i
$626$		0			0
$627$	−1.76821e6	−	3.06264e6i	−0.00717351	−	0.0124249i
$628$		0			0
$629$		−	2.97730e8i		−	1.19638i
$630$		0			0
$631$	−9.35237e7			−0.372249			−0.186124	−	0.982526i	$-0.559593\pi$
$631$	−9.35237e7			−0.372249			−0.186124	+	0.982526i	$0.559593\pi$
$632$		0			0
$633$	−6.35776e7	+	3.67066e7i	−0.250665	+	0.144721i
$634$		0			0
$635$	−1.71936e8	−	9.92672e7i	−0.671499	−	0.387690i
$636$		0			0
$637$	8.91694e6	+	2.11935e8i	0.0344983	+	0.819945i
$638$		0			0
$639$	3.67951e7	−	6.37311e7i	0.141022	−	0.244258i
$640$		0			0
$641$	1.30617e8	+	2.26235e8i	0.495935	+	0.858985i	0.999989	−	0.00468711i	$-0.00149196\pi$
$641$	1.30617e8	+	2.26235e8i	0.495935	+	0.858985i	−0.504054	+	0.863672i	$0.668159\pi$
$642$		0			0
$643$		−	8.78628e7i		−	0.330501i	−0.986252	−	0.165250i	$-0.947157\pi$
$643$		−	8.78628e7i		−	0.330501i	0.986252	−	0.165250i	$-0.0528432\pi$
$644$		0			0
$645$	−1.16495e8			−0.434137
$646$		0			0
$647$	−1.65500e7	+	9.55514e6i	−0.0611061	+	0.0352797i	−0.530242	−	0.847846i	$-0.677899\pi$
$647$	−1.65500e7	+	9.55514e6i	−0.0611061	+	0.0352797i	0.469136	+	0.883126i	$0.344566\pi$
$648$		0			0
$649$	−2.32198e6	−	1.34059e6i	−0.00849422	−	0.00490414i
$650$		0			0
$651$	1.17672e8	−	2.14085e8i	0.426511	−	0.775968i
$652$		0			0
$653$	−2.04507e8	+	3.54216e8i	−0.734460	+	1.27212i	0.220500	+	0.975387i	$0.429231\pi$
$653$	−2.04507e8	+	3.54216e8i	−0.734460	+	1.27212i	−0.954960	+	0.296735i	$0.904102\pi$
$654$		0			0
$655$	2.53400e8	+	4.38901e8i	0.901741	+	1.56186i
$656$		0			0
$657$		−	7.13733e7i		−	0.251675i
$658$		0			0
$659$	−1.37017e8			−0.478761			−0.239380	−	0.970926i	$-0.576944\pi$
$659$	−1.37017e8			−0.478761			−0.239380	+	0.970926i	$0.576944\pi$
$660$		0			0
$661$	2.96239e8	−	1.71033e8i	1.02574	−	0.592211i	0.109979	−	0.993934i	$-0.464922\pi$
$661$	2.96239e8	−	1.71033e8i	1.02574	−	0.592211i	0.915761	+	0.401723i	$0.131588\pi$
$662$		0			0
$663$	1.31252e8	+	7.57785e7i	0.450367	+	0.260019i
$664$		0			0
$665$	−3.19085e8	−	5.26776e8i	−1.08503	−	1.79127i
$666$		0			0
$667$	8.98012e7	−	1.55540e8i	0.302625	−	0.524162i
$668$		0			0
$669$	1.10855e8	+	1.92006e8i	0.370234	+	0.641264i
$670$		0			0
$671$			7.07725e6i			0.0234259i
$672$		0			0
$673$	−2.20742e7			−0.0724169			−0.0362085	−	0.999344i	$-0.511528\pi$
$673$	−2.20742e7			−0.0724169			−0.0362085	+	0.999344i	$0.511528\pi$
$674$		0			0
$675$	1.63456e7	−	9.43712e6i	0.0531482	−	0.0306851i
$676$		0			0
$677$	−2.67348e8	−	1.54354e8i	−0.861611	−	0.497452i	0.00294015	−	0.999996i	$-0.499064\pi$
$677$	−2.67348e8	−	1.54354e8i	−0.861611	−	0.497452i	−0.864552	+	0.502544i	$0.832397\pi$
$678$		0			0
$679$	−6.22893e6	−	2.96226e8i	−0.0198978	−	0.946267i
$680$		0			0
$681$	−1.32387e7	+	2.29300e7i	−0.0419182	+	0.0726045i
$682$		0			0
$683$	1.38264e8	+	2.39480e8i	0.433956	+	0.751634i	0.997210	−	0.0746501i	$-0.0237840\pi$
$683$	1.38264e8	+	2.39480e8i	0.433956	+	0.751634i	−0.563254	+	0.826284i	$0.690451\pi$
$684$		0			0
$685$		−	2.11849e8i		−	0.659104i
$686$		0			0
$687$	−1.03111e8			−0.318006
$688$		0			0
$689$	−3.53765e8	+	2.04246e8i	−1.08158	+	0.624448i
$690$		0			0
$691$	−4.23565e8	−	2.44545e8i	−1.28377	−	0.741183i	−0.306232	−	0.951957i	$-0.599068\pi$
$691$	−4.23565e8	−	2.44545e8i	−1.28377	−	0.741183i	−0.977535	+	0.210774i	$0.932402\pi$
$692$		0			0
$693$	−1.51140e6	+	31781.1i	−0.00454128	+	9.54925e-5i
$694$		0			0
$695$	9.78477e6	−	1.69477e7i	0.0291472	−	0.0504844i
$696$		0			0
$697$	−2.94943e7	−	5.10856e7i	−0.0871043	−	0.150869i
$698$		0			0
$699$			8.97693e7i			0.262843i
$700$		0			0
$701$	7.76826e6			0.0225512			0.0112756	−	0.999936i	$-0.496411\pi$
$701$	7.76826e6			0.0225512			0.0112756	+	0.999936i	$0.496411\pi$
$702$		0			0
$703$	−5.98091e8	+	3.45308e8i	−1.72148	+	0.993895i
$704$		0			0
$705$	−1.66322e8	−	9.60263e7i	−0.474661	−	0.274046i
$706$		0			0
$707$	−2.84478e8	+	1.72317e8i	−0.804989	+	0.487607i
$708$		0			0
$709$	−1.58830e8	+	2.75101e8i	−0.445649	+	0.771886i	−0.998097	−	0.0616608i	$-0.980360\pi$
$709$	−1.58830e8	+	2.75101e8i	−0.445649	+	0.771886i	0.552448	+	0.833547i	$0.313694\pi$
$710$		0			0
$711$	−6.51603e7	−	1.12861e8i	−0.181290	−	0.314004i
$712$		0			0
$713$		−	5.47584e8i		−	1.51072i
$714$		0			0
$715$	4.69447e6			0.0128431
$716$		0			0
$717$	−3.35950e8	+	1.93961e8i	−0.911416	+	0.526206i
$718$		0			0
$719$	1.04725e8	+	6.04630e7i	0.281750	+	0.162668i	0.634215	−	0.773157i	$-0.281323\pi$
$719$	1.04725e8	+	6.04630e7i	0.281750	+	0.162668i	−0.352466	+	0.935825i	$0.614657\pi$
$720$		0			0
$721$	−4.61467e8	−	2.53645e8i	−1.23122	−	0.676738i
$722$		0			0
$723$	−1.13533e8	+	1.96645e8i	−0.300405	+	0.520316i
$724$		0			0
$725$	−3.73341e7	−	6.46645e7i	−0.0979696	−	0.169688i
$726$		0			0
$727$		−	8.10287e7i		−	0.210880i	−0.994426	−	0.105440i	$-0.966375\pi$
$727$		−	8.10287e7i		−	0.210880i	0.994426	−	0.105440i	$-0.0336251\pi$
$728$		0			0
$729$	−1.43489e7			−0.0370370
$730$		0			0
$731$	2.43105e8	−	1.40357e8i	0.622359	−	0.359319i
$732$		0			0
$733$	−3.34250e8	−	1.92979e8i	−0.848709	−	0.490002i	0.0115059	−	0.999934i	$-0.496337\pi$
$733$	−3.34250e8	−	1.92979e8i	−0.848709	−	0.490002i	−0.860215	+	0.509931i	$0.829671\pi$
$734$		0			0
$735$	−2.63040e8	+	1.10671e7i	−0.662460	+	0.0278723i
$736$		0			0
$737$	−1.04312e6	+	1.80674e6i	−0.00260575	+	0.00451330i
$738$		0			0
$739$	−3.79454e8	−	6.57233e8i	−0.940211	−	1.62849i	−0.765067	−	0.643950i	$-0.777294\pi$
$739$	−3.79454e8	−	6.57233e8i	−0.940211	−	1.62849i	−0.175144	−	0.984543i	$-0.556039\pi$
$740$		0			0
$741$		−	3.51552e8i		−	0.864043i
$742$		0			0
$743$	4.74332e7			0.115642			0.0578211	−	0.998327i	$-0.481585\pi$
$743$	4.74332e7			0.115642			0.0578211	+	0.998327i	$0.481585\pi$
$744$		0			0
$745$	−3.11221e8	+	1.79684e8i	−0.752663	+	0.434550i
$746$		0			0
$747$	−1.64008e8	−	9.46902e7i	−0.393463	−	0.227166i
$748$		0			0
$749$	3.37600e8	−	6.14209e8i	0.803447	−	1.46174i
$750$		0			0
$751$	−2.97712e6	+	5.15652e6i	−0.00702872	+	0.0121741i	−0.869518	−	0.493901i	$-0.835571\pi$
$751$	−2.97712e6	+	5.15652e6i	−0.00702872	+	0.0121741i	0.862490	+	0.506075i	$0.168904\pi$
$752$		0			0
$753$	−5.14698e7	−	8.91483e7i	−0.120550	−	0.208799i
$754$		0			0
$755$		−	7.12742e8i		−	1.65612i
$756$		0			0
$757$	−2.15672e8			−0.497172			−0.248586	−	0.968610i	$-0.579966\pi$
$757$	−2.15672e8			−0.497172			−0.248586	+	0.968610i	$0.579966\pi$
$758$		0			0
$759$	−2.93457e6	+	1.69427e6i	−0.00671149	+	0.00387488i
$760$		0			0
$761$	4.61795e8	+	2.66617e8i	1.04784	+	0.604971i	0.922044	−	0.387085i	$-0.126518\pi$
$761$	4.61795e8	+	2.66617e8i	1.04784	+	0.604971i	0.125796	+	0.992056i	$0.459851\pi$
$762$		0			0
$763$	1.43022e8	+	2.36115e8i	0.321981	+	0.531558i
$764$		0			0
$765$	−9.40512e7	+	1.62901e8i	−0.210078	+	0.363865i
$766$		0			0
$767$	−1.33267e8	−	2.30825e8i	−0.295350	−	0.511561i
$768$		0			0
$769$			4.83062e8i			1.06224i	0.847295	+	0.531122i	$0.178229\pi$
$769$			4.83062e8i			1.06224i	−0.847295	+	0.531122i	$0.821771\pi$
$770$		0			0
$771$	−8.52206e6			−0.0185944
$772$		0			0
$773$	−2.31560e8	+	1.33691e8i	−0.501331	+	0.289444i	−0.729263	−	0.684233i	$-0.760137\pi$
$773$	−2.31560e8	+	1.33691e8i	−0.501331	+	0.289444i	0.227932	+	0.973677i	$0.426804\pi$
$774$		0			0
$775$	−1.97154e8	−	1.13827e8i	−0.423545	−	0.244534i
$776$		0			0
$777$	6.20641e6	+	2.95155e8i	0.0132305	+	0.629197i
$778$		0			0
$779$	−6.84151e7	+	1.18498e8i	−0.144724	+	0.250669i
$780$		0			0
$781$	2.74636e6	+	4.75684e6i	0.00576507	+	0.00998540i
$782$		0			0
$783$			5.67655e7i			0.118250i
$784$		0			0
$785$	7.34997e8			1.51941
$786$		0			0
$787$	−7.82601e7	+	4.51835e7i	−0.160552	+	0.0926948i	−0.578123	−	0.815949i	$-0.696215\pi$
$787$	−7.82601e7	+	4.51835e7i	−0.160552	+	0.0926948i	0.417571	+	0.908644i	$0.362881\pi$
$788$		0			0
$789$	−1.11959e8	−	6.46396e7i	−0.227944	−	0.131604i
$790$		0			0
$791$	−1.94987e8	+	4.10012e6i	−0.393982	+	0.00828452i
$792$		0			0
$793$	−3.51771e8	+	6.09285e8i	−0.705408	+	1.22180i
$794$		0			0
$795$	−2.53497e8	−	4.39069e8i	−0.504511	−	0.873839i
$796$		0			0
$797$		−	2.69704e8i		−	0.532736i	−0.963871	−	0.266368i	$-0.914176\pi$
$797$		−	2.69704e8i		−	0.532736i	0.963871	−	0.266368i	$-0.0858237\pi$
$798$		0			0
$799$	4.62782e8			0.907270
$800$		0			0
$801$	−1.13155e8	+	6.53300e7i	−0.220179	+	0.127120i
$802$		0			0
$803$	4.61353e6	+	2.66363e6i	0.00891019	+	0.00514430i
$804$		0			0
$805$	−5.04748e8	+	3.05742e8i	−0.967581	+	0.586094i
$806$		0			0
$807$	−755440.	+	1.30846e6i	−0.00143741	+	0.00248966i
$808$		0			0
$809$	3.20016e8	+	5.54285e8i	0.604403	+	1.04686i	0.992145	+	0.125089i	$0.0399217\pi$
$809$	3.20016e8	+	5.54285e8i	0.604403	+	1.04686i	−0.387742	+	0.921768i	$0.626745\pi$
$810$		0			0
$811$		−	3.65657e8i		−	0.685507i	−0.939425	−	0.342753i	$-0.888640\pi$
$811$		−	3.65657e8i		−	0.685507i	0.939425	−	0.342753i	$-0.111360\pi$
$812$		0			0
$813$	−267846.			−0.000498440
$814$		0			0
$815$	−1.85792e7	+	1.07267e7i	−0.0343206	+	0.0198150i
$816$		0			0
$817$	−5.63906e8	−	3.25572e8i	−1.03405	−	0.597008i
$818$		0			0
$819$	−1.31697e8	−	7.23870e7i	−0.239730	−	0.131768i
$820$		0			0
$821$	3.64436e7	−	6.31222e7i	0.0658555	−	0.114065i	−0.831218	−	0.555947i	$-0.812356\pi$
$821$	3.64436e7	−	6.31222e7i	0.0658555	−	0.114065i	0.897073	+	0.441882i	$0.145689\pi$
$822$		0			0
$823$	4.25160e8	+	7.36399e8i	0.762699	+	1.32103i	0.941455	+	0.337139i	$0.109459\pi$
$823$	4.25160e8	+	7.36399e8i	0.762699	+	1.32103i	−0.178756	+	0.983893i	$0.557207\pi$
$824$		0			0
$825$			1.40876e6i			0.00250885i
$826$		0			0
$827$	4.62375e8			0.817482			0.408741	−	0.912650i	$-0.365968\pi$
$827$	4.62375e8			0.817482			0.408741	+	0.912650i	$0.365968\pi$
$828$		0			0
$829$	4.09186e8	−	2.36243e8i	0.718219	−	0.414664i	−0.0958780	−	0.995393i	$-0.530566\pi$
$829$	4.09186e8	−	2.36243e8i	0.718219	−	0.414664i	0.814097	+	0.580729i	$0.197233\pi$
$830$		0			0
$831$	−2.21402e7	−	1.27826e7i	−0.0385814	−	0.0222750i
$832$		0			0
$833$	5.35586e8	−	3.40014e8i	0.926603	−	0.588250i
$834$		0			0
$835$	−4.63749e7	+	8.03236e7i	−0.0796568	+	0.137970i
$836$		0			0
$837$	8.65354e7	+	1.49884e8i	0.147577	+	0.255610i
$838$		0			0
$839$		−	2.02085e8i		−	0.342175i	−0.985256	−	0.171088i	$-0.945272\pi$
$839$		−	2.02085e8i		−	0.342175i	0.985256	−	0.171088i	$-0.0547281\pi$
$840$		0			0
$841$	−3.70254e8			−0.622460
$842$		0			0
$843$	1.02223e7	−	5.90186e6i	0.0170634	−	0.00985159i
$844$		0			0
$845$	−1.95924e8	−	1.13117e8i	−0.324726	−	0.187481i
$846$		0			0
$847$	−2.92638e8	+	5.32408e8i	−0.481594	+	0.876183i
$848$		0			0
$849$	2.79375e8	−	4.83891e8i	0.456524	−	0.790723i
$850$		0			0
$851$	3.30869e8	+	5.73081e8i	0.536867	+	0.929881i
$852$		0			0
$853$		−	5.88721e8i		−	0.948555i	−0.880375	−	0.474277i	$-0.842709\pi$
$853$		−	5.88721e8i		−	0.948555i	0.880375	−	0.474277i	$-0.157291\pi$
$854$		0			0
$855$	4.36323e8			0.698088
$856$		0			0
$857$	3.25457e8	−	1.87903e8i	0.517072	−	0.298531i	−0.218664	−	0.975800i	$-0.570170\pi$
$857$	3.25457e8	−	1.87903e8i	0.517072	−	0.298531i	0.735736	+	0.677269i	$0.236837\pi$
$858$		0			0
$859$	−7.63491e8	−	4.40802e8i	−1.20455	−	0.695447i	−0.242986	−	0.970030i	$-0.578127\pi$
$859$	−7.63491e8	−	4.40802e8i	−1.20455	−	0.695447i	−0.961563	+	0.274583i	$0.911460\pi$
$860$		0			0
$861$	3.03041e7	+	5.00289e7i	0.0474779	+	0.0783811i
$862$		0			0
$863$	−3.87828e8	+	6.71738e8i	−0.603402	+	1.04512i	0.388900	+	0.921280i	$0.372855\pi$
$863$	−3.87828e8	+	6.71738e8i	−0.603402	+	1.04512i	−0.992302	+	0.123843i	$0.960478\pi$
$864$		0			0
$865$	−4.41255e8	−	7.64277e8i	−0.681776	−	1.18087i
$866$		0			0
$867$		−	7.69963e7i		−	0.118144i
$868$		0			0
$869$	9.72704e6			0.0148225
$870$		0			0
$871$	−1.79606e8	+	1.03696e8i	−0.271811	+	0.156930i
$872$		0			0
$873$	1.81787e8	+	1.04954e8i	0.273224	+	0.157746i
$874$		0			0
$875$	−1.10164e7	−	5.23902e8i	−0.0164443	−	0.782034i
$876$		0			0
$877$	−5.15223e8	+	8.92392e8i	−0.763829	+	1.32299i	0.177034	+	0.984205i	$0.443350\pi$
$877$	−5.15223e8	+	8.92392e8i	−0.763829	+	1.32299i	−0.940863	+	0.338786i	$0.889984\pi$
$878$		0			0
$879$	2.85744e7	+	4.94922e7i	0.0420736	+	0.0728736i
$880$		0			0
$881$			3.86019e8i			0.564522i	0.959338	+	0.282261i	$0.0910844\pi$
$881$			3.86019e8i			0.564522i	−0.959338	+	0.282261i	$0.908916\pi$
$882$		0			0
$883$	7.92977e8			1.15180			0.575902	−	0.817519i	$-0.304651\pi$
$883$	7.92977e8			1.15180			0.575902	+	0.817519i	$0.304651\pi$
$884$		0			0
$885$	2.86485e8	−	1.65402e8i	0.413306	−	0.238622i
$886$		0			0
$887$	9.71544e8	+	5.60921e8i	1.39217	+	0.803769i	0.993555	−	0.113350i	$-0.0361582\pi$
$887$	9.71544e8	+	5.60921e8i	1.39217	+	0.803769i	0.398613	+	0.917119i	$0.369492\pi$
$888$		0			0
$889$	−4.74264e8	+	9.97265e6i	−0.675017	+	0.0141940i
$890$		0			0
$891$	535496.	−	927506.i	0.000757047	−	0.00131124i
$892$		0			0
$893$	−5.36736e8	−	9.29654e8i	−0.753714	−	1.30547i
$894$		0			0
$895$		−	1.42160e9i		−	1.98293i
$896$		0			0
$897$	−3.36852e8			−0.466726
$898$		0			0
$899$	5.92953e8	−	3.42342e8i	0.816096	−	0.471173i
$900$		0			0
$901$	1.05801e9	+	6.10842e8i	1.44649	+	0.835131i
$902$		0			0
$903$	−2.38076e8	+	1.44210e8i	−0.323335	+	0.195854i
$904$		0			0
$905$	−1.81729e8	+	3.14763e8i	−0.245176	+	0.424657i
$906$		0			0
$907$	4.81942e8	+	8.34748e8i	0.645911	+	1.11875i	0.984090	+	0.177669i	$0.0568556\pi$
$907$	4.81942e8	+	8.34748e8i	0.645911	+	1.11875i	−0.338179	+	0.941082i	$0.609811\pi$
$908$		0			0
$909$		−	2.35630e8i		−	0.313718i
$910$		0			0
$911$	−3.63584e8			−0.480894			−0.240447	−	0.970662i	$-0.577294\pi$
$911$	−3.63584e8			−0.480894			−0.240447	+	0.970662i	$0.577294\pi$
$912$		0			0
$913$	1.22415e7	−	7.06761e6i	0.0160850	−	0.00928667i
$914$		0			0
$915$	−7.56204e8	−	4.36594e8i	−0.987133	−	0.569921i
$916$		0			0
$917$	1.06119e9	+	5.83280e8i	1.37621	+	0.756431i
$918$		0			0
$919$	−1.77327e8	+	3.07139e8i	−0.228469	+	0.395720i	−0.957355	−	0.288915i	$-0.906705\pi$
$919$	−1.77327e8	+	3.07139e8i	−0.228469	+	0.395720i	0.728885	+	0.684636i	$0.240039\pi$
$920$		0			0
$921$	4.42611e7	+	7.66625e7i	0.0566557	+	0.0981305i
$922$		0			0
$923$			5.46026e8i			0.694398i
$924$		0			0
$925$	2.75112e8			0.347603
$926$		0			0
$927$	3.23079e8	−	1.86529e8i	0.405573	−	0.234158i
$928$		0			0
$929$	3.82297e6	+	2.20719e6i	0.00476819	+	0.00275292i	0.502382	−	0.864646i	$-0.332457\pi$
$929$	3.82297e6	+	2.20719e6i	0.00476819	+	0.00275292i	−0.497614	+	0.867399i	$0.665790\pi$
$930$		0			0
$931$	−1.30421e9	−	6.81555e8i	−1.61621	−	0.844601i
$932$		0			0
$933$	−3.34426e8	+	5.79242e8i	−0.411770	+	0.713207i
$934$		0			0
$935$	−7.01991e6	−	1.21588e7i	−0.00858810	−	0.0148750i
$936$		0			0
$937$		−	8.40152e7i		−	0.102127i	−0.998695	−	0.0510633i	$-0.983739\pi$
$937$		−	8.40152e7i		−	0.102127i	0.998695	−	0.0510633i	$-0.0162610\pi$
$938$		0			0
$939$	2.81389e8			0.339868
$940$		0			0
$941$	3.49185e8	−	2.01602e8i	0.419070	−	0.241950i	−0.275609	−	0.961270i	$-0.588880\pi$
$941$	3.49185e8	−	2.01602e8i	0.419070	−	0.241950i	0.694680	+	0.719319i	$0.255546\pi$
$942$		0			0
$943$	1.13543e8	+	6.55542e7i	0.135402	+	0.0781746i
$944$		0			0
$945$	8.98419e7	−	1.63453e8i	0.106459	−	0.193686i
$946$		0			0
$947$	−2.65756e8	+	4.60302e8i	−0.312919	+	0.541992i	−0.978993	−	0.203894i	$-0.934640\pi$
$947$	−2.65756e8	+	4.60302e8i	−0.312919	+	0.541992i	0.666074	+	0.745886i	$0.267974\pi$
$948$		0			0
$949$	2.64788e8	+	4.58627e8i	0.309813	+	0.536612i
$950$		0			0
$951$			8.76249e8i			1.01879i
$952$		0			0
$953$	−6.69633e8			−0.773674			−0.386837	−	0.922148i	$-0.626432\pi$
$953$	−6.69633e8			−0.773674			−0.386837	+	0.922148i	$0.626432\pi$
$954$		0			0
$955$	−1.44982e9	+	8.37054e8i	−1.66458	+	0.961044i
$956$		0			0
$957$	−3.66930e6	−	2.11847e6i	−0.00418646	−	0.00241705i
$958$		0			0
$959$	−2.62250e8	−	4.32948e8i	−0.297345	−	0.490885i
$960$		0			0
$961$	6.00004e8	−	1.03924e9i	0.676058	−	1.17097i
$962$		0			0
$963$	2.48269e8	+	4.30015e8i	0.278000	+	0.481510i
$964$		0			0
$965$		−	1.25433e9i		−	1.39582i
$966$		0			0
$967$	1.00910e8			0.111597			0.0557986	−	0.998442i	$-0.482230\pi$
$967$	1.00910e8			0.111597			0.0557986	+	0.998442i	$0.482230\pi$
$968$		0			0
$969$	−9.10533e8	+	5.25696e8i	−1.00075	+	0.577781i
$970$		0			0
$971$	7.72923e7	+	4.46247e7i	0.0844265	+	0.0487436i	0.541619	−	0.840624i	$-0.317812\pi$
$971$	7.72923e7	+	4.46247e7i	0.0844265	+	0.0487436i	−0.457192	+	0.889368i	$0.651145\pi$
$972$		0			0
$973$	−983004.	−	4.67482e7i	−0.00106713	−	0.0507488i
$974$		0			0
$975$	−7.00216e7	+	1.21281e8i	−0.0755472	+	0.130852i
$976$		0			0
$977$	6.15359e8	+	1.06583e9i	0.659849	+	1.14289i	0.980654	+	0.195747i	$0.0627132\pi$
$977$	6.15359e8	+	1.06583e9i	0.659849	+	1.14289i	−0.320805	+	0.947145i	$0.603953\pi$
$978$		0			0
$979$		−	9.75237e6i		−	0.0103935i
$980$		0			0
$981$	−1.95572e8			−0.207157
$982$		0			0
$983$	3.87371e8	−	2.23649e8i	0.407818	−	0.235454i	−0.282034	−	0.959404i	$-0.591009\pi$
$983$	3.87371e8	−	2.23649e8i	0.407818	−	0.235454i	0.689852	+	0.723951i	$0.257676\pi$
$984$		0			0
$985$	1.24349e9	+	7.17931e8i	1.30117	+	0.751232i
$986$		0			0
$987$	−4.58780e8	+	9.64706e6i	−0.477148	+	0.0100333i
$988$		0			0
$989$	−3.11957e8	+	5.40326e8i	−0.322483	+	0.558557i
$990$		0			0
$991$	4.20298e8	+	7.27977e8i	0.431853	+	0.747992i	0.997033	−	0.0769760i	$-0.0245265\pi$
$991$	4.20298e8	+	7.27977e8i	0.431853	+	0.747992i	−0.565180	+	0.824968i	$0.691193\pi$
$992$		0			0
$993$		−	5.81592e8i		−	0.593978i
$994$		0			0
$995$	1.43492e9			1.45666
$996$		0			0
$997$	−1.40730e8	+	8.12503e7i	−0.142004	+	0.0819860i	−0.569319	−	0.822117i	$-0.692793\pi$
$997$	−1.40730e8	+	8.12503e7i	−0.142004	+	0.0819860i	0.427315	+	0.904103i	$0.359460\pi$
$998$		0			0
$999$	−1.81129e8	−	1.04575e8i	−0.181674	−	0.104889i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.7.bh.f.145.1		8
4.3	odd	2		42.7.g.a.19.1	✓	8
7.3	odd	6	inner	336.7.bh.f.241.1		8
12.11	even	2		126.7.n.a.19.4		8
28.3	even	6		42.7.g.a.31.1	yes	8
28.11	odd	6		294.7.g.d.31.2		8
28.19	even	6		294.7.c.b.97.7		8
28.23	odd	6		294.7.c.b.97.6		8
28.27	even	2		294.7.g.d.19.2		8
84.59	odd	6		126.7.n.a.73.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.7.g.a.19.1	✓	8	4.3	odd	2
42.7.g.a.31.1	yes	8	28.3	even	6
126.7.n.a.19.4		8	12.11	even	2
126.7.n.a.73.4		8	84.59	odd	6
294.7.c.b.97.6		8	28.23	odd	6
294.7.c.b.97.7		8	28.19	even	6
294.7.g.d.19.2		8	28.27	even	2
294.7.g.d.31.2		8	28.11	odd	6
336.7.bh.f.145.1		8	1.1	even	1	trivial
336.7.bh.f.241.1		8	7.3	odd	6	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	336.bh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(13.5000 - 7.79423i) q^{3} +(-124.321 - 71.7768i) q^{5} +(-342.924 + 7.21089i) q^{7} +(121.500 - 210.444i) q^{9} +O(q^{10})\)	\(q+(13.5000 - 7.79423i) q^{3} +(-124.321 - 71.7768i) q^{5} +(-342.924 + 7.21089i) q^{7} +(121.500 - 210.444i) q^{9} +(9.06867 + 15.7074i) q^{11} +1803.01i q^{13} -2237.78 q^{15} +(4669.87 - 2696.15i) q^{17} +(-10832.2 - 6254.00i) q^{19} +(-4573.27 + 2770.18i) q^{21} +(-5992.48 + 10379.3i) q^{23} +(2491.32 + 4315.10i) q^{25} -3788.00i q^{27} -14985.6 q^{29} +(-39568.1 + 22844.6i) q^{31} +(244.854 + 141.367i) q^{33} +(43150.3 + 23717.5i) q^{35} +(27607.0 - 47816.7i) q^{37} +(14053.1 + 24340.7i) q^{39} -10939.4i q^{41} +52058.1 q^{43} +(-30210.0 + 17441.8i) q^{45} +(74324.8 + 42911.4i) q^{47} +(117545. - 4945.58i) q^{49} +(42028.8 - 72796.0i) q^{51} +(113280. + 196207. i) q^{53} -2603.68i q^{55} -194980. q^{57} +(-128022. + 73913.5i) q^{59} +(337926. + 195102. i) q^{61} +(-40147.8 + 73042.5i) q^{63} +(129415. - 224153. i) q^{65} +(57512.5 + 99614.6i) q^{67} +186827. i q^{69} +302841. q^{71} +(254367. - 146859. i) q^{73} +(67265.7 + 38835.9i) q^{75} +(-3223.13 - 5321.05i) q^{77} +(268149. - 464449. i) q^{79} +(-29524.5 - 51137.9i) q^{81} -779343. i q^{83} -774084. q^{85} +(-202306. + 116802. i) q^{87} +(-465658. - 268848. i) q^{89} +(-13001.3 - 618297. i) q^{91} +(-356113. + 616805. i) q^{93} +(897784. + 1.55501e6i) q^{95} +863823. i q^{97} +4407.37 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 108 q^{3} + 462 q^{5} - 580 q^{7} + 972 q^{9}+O(q^{10}) \) 8 * q + 108 * q^3 + 462 * q^5 - 580 * q^7 + 972 * q^9	\( 8 q + 108 q^{3} + 462 q^{5} - 580 q^{7} + 972 q^{9} - 1806 q^{11} + 8316 q^{15} + 9564 q^{17} - 23022 q^{19} - 1350 q^{21} - 2400 q^{23} + 32762 q^{25} - 2484 q^{29} - 148416 q^{31} - 48762 q^{33} - 11412 q^{35} - 84046 q^{37} + 75222 q^{39} - 92972 q^{43} + 112266 q^{45} + 323124 q^{47} - 8644 q^{49} + 86076 q^{51} + 358086 q^{53} - 414396 q^{57} - 719382 q^{59} + 421536 q^{61} + 104490 q^{63} - 322740 q^{65} - 267010 q^{67} + 464664 q^{71} + 1944486 q^{73} + 884574 q^{75} - 1713498 q^{77} + 685904 q^{79} - 236196 q^{81} - 3876168 q^{85} - 33534 q^{87} + 4130604 q^{89} + 484266 q^{91} - 1335744 q^{93} + 2105232 q^{95} - 877716 q^{99}+O(q^{100}) \) 8 * q + 108 * q^3 + 462 * q^5 - 580 * q^7 + 972 * q^9 - 1806 * q^11 + 8316 * q^15 + 9564 * q^17 - 23022 * q^19 - 1350 * q^21 - 2400 * q^23 + 32762 * q^25 - 2484 * q^29 - 148416 * q^31 - 48762 * q^33 - 11412 * q^35 - 84046 * q^37 + 75222 * q^39 - 92972 * q^43 + 112266 * q^45 + 323124 * q^47 - 8644 * q^49 + 86076 * q^51 + 358086 * q^53 - 414396 * q^57 - 719382 * q^59 + 421536 * q^61 + 104490 * q^63 - 322740 * q^65 - 267010 * q^67 + 464664 * q^71 + 1944486 * q^73 + 884574 * q^75 - 1713498 * q^77 + 685904 * q^79 - 236196 * q^81 - 3876168 * q^85 - 33534 * q^87 + 4130604 * q^89 + 484266 * q^91 - 1335744 * q^93 + 2105232 * q^95 - 877716 * q^99

Introduction

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