LMFDB - Embedded newform 141.7.d.a.46.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [141,7,Mod(46,141)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(141, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("141.46");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 141 = 3 \cdot 47 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	141.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$32.4376257904$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			46.11
Character	$\chi$	$=$	141.46
Dual form			141.7.d.a.46.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.87833 q^{2} -15.5885 q^{3} +14.8247 q^{4} -243.420i q^{5} +138.399 q^{6} -480.503 q^{7} +436.594 q^{8} +243.000 q^{9} +O(q^{10})$	\(q-8.87833 q^{2} -15.5885 q^{3} +14.8247 q^{4} -243.420i q^{5} +138.399 q^{6} -480.503 q^{7} +436.594 q^{8} +243.000 q^{9} +2161.17i q^{10} +2263.84i q^{11} -231.095 q^{12} -1257.43i q^{13} +4266.06 q^{14} +3794.55i q^{15} -4825.01 q^{16} -4292.10 q^{17} -2157.43 q^{18} +3498.78i q^{19} -3608.64i q^{20} +7490.30 q^{21} -20099.1i q^{22} -5147.01i q^{23} -6805.83 q^{24} -43628.5 q^{25} +11163.9i q^{26} -3788.00 q^{27} -7123.32 q^{28} +22541.9i q^{29} -33689.3i q^{30} +27192.5i q^{31} +14896.0 q^{32} -35289.7i q^{33} +38106.7 q^{34} +116964. i q^{35} +3602.41 q^{36} +51199.0 q^{37} -31063.3i q^{38} +19601.5i q^{39} -106276. i q^{40} -15348.8i q^{41} -66501.3 q^{42} -2776.39i q^{43} +33560.8i q^{44} -59151.2i q^{45} +45696.9i q^{46} +(-92152.1 - 47824.7i) q^{47} +75214.5 q^{48} +113234. q^{49} +387348. q^{50} +66907.2 q^{51} -18641.1i q^{52} +111935. q^{53} +33631.1 q^{54} +551064. q^{55} -209785. q^{56} -54540.6i q^{57} -200134. i q^{58} -288111. q^{59} +56253.1i q^{60} +41272.1 q^{61} -241424. i q^{62} -116762. q^{63} +176549. q^{64} -306085. q^{65} +313314. i q^{66} +94823.3i q^{67} -63629.2 q^{68} +80234.0i q^{69} -1.03845e6i q^{70} +193648. q^{71} +106092. q^{72} -466331. i q^{73} -454561. q^{74} +680101. q^{75} +51868.5i q^{76} -1.08778e6i q^{77} -174028. i q^{78} +646546. q^{79} +1.17451e6i q^{80} +59049.0 q^{81} +136272. i q^{82} +742695. q^{83} +111042. q^{84} +1.04478e6i q^{85} +24649.7i q^{86} -351393. i q^{87} +988379. i q^{88} -89831.8 q^{89} +525164. i q^{90} +604201. i q^{91} -76303.1i q^{92} -423889. i q^{93} +(818157. + 424604. i) q^{94} +851675. q^{95} -232206. q^{96} -1.29801e6 q^{97} -1.00533e6 q^{98} +550113. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 1404 q^{4} + 324 q^{6} - 288 q^{7} - 1932 q^{8} + 11664 q^{9}+O(q^{10}) $ 48 * q + 1404 * q^4 + 324 * q^6 - 288 * q^7 - 1932 * q^8 + 11664 * q^9	$ 48 q + 1404 q^{4} + 324 q^{6} - 288 q^{7} - 1932 q^{8} + 11664 q^{9} + 1944 q^{12} - 18964 q^{14} + 48060 q^{16} - 288 q^{17} + 5184 q^{24} - 187440 q^{25} - 30312 q^{28} - 182548 q^{32} - 109920 q^{34} + 341172 q^{36} - 12096 q^{37} + 215460 q^{42} + 115768 q^{47} + 124416 q^{48} + 779904 q^{49} + 887340 q^{50} - 2592 q^{51} + 63504 q^{53} + 78732 q^{54} + 127248 q^{55} - 2002264 q^{56} + 165216 q^{59} + 955440 q^{61} - 69984 q^{63} + 1815660 q^{64} + 30000 q^{65} + 776648 q^{68} - 1109040 q^{71} - 469476 q^{72} - 376692 q^{74} + 1842912 q^{75} - 1523712 q^{79} + 2834352 q^{81} + 406064 q^{83} - 1423008 q^{84} - 5383968 q^{89} + 5556972 q^{94} + 3809952 q^{95} + 2079432 q^{96} - 2085840 q^{97} - 2907180 q^{98}+O(q^{100}) $ 48 * q + 1404 * q^4 + 324 * q^6 - 288 * q^7 - 1932 * q^8 + 11664 * q^9 + 1944 * q^12 - 18964 * q^14 + 48060 * q^16 - 288 * q^17 + 5184 * q^24 - 187440 * q^25 - 30312 * q^28 - 182548 * q^32 - 109920 * q^34 + 341172 * q^36 - 12096 * q^37 + 215460 * q^42 + 115768 * q^47 + 124416 * q^48 + 779904 * q^49 + 887340 * q^50 - 2592 * q^51 + 63504 * q^53 + 78732 * q^54 + 127248 * q^55 - 2002264 * q^56 + 165216 * q^59 + 955440 * q^61 - 69984 * q^63 + 1815660 * q^64 + 30000 * q^65 + 776648 * q^68 - 1109040 * q^71 - 469476 * q^72 - 376692 * q^74 + 1842912 * q^75 - 1523712 * q^79 + 2834352 * q^81 + 406064 * q^83 - 1423008 * q^84 - 5383968 * q^89 + 5556972 * q^94 + 3809952 * q^95 + 2079432 * q^96 - 2085840 * q^97 - 2907180 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/141\mathbb{Z}\right)^\times$.

$n$	$52$	$95$
$\chi(n)$	$-1$	$1$

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 $

$2$	−8.87833			−1.10979			−0.554896	−	0.831920i	$-0.687242\pi$
$2$	−8.87833			−1.10979			−0.554896	+	0.831920i	$0.687242\pi$
$3$	−15.5885			−0.577350
$3$	−15.5885			−0.577350
$4$	14.8247			0.231636
$5$		−	243.420i		−	1.94736i	−0.227912	−	0.973682i	$-0.573190\pi$
$5$		−	243.420i		−	1.94736i	0.227912	−	0.973682i	$-0.426810\pi$
$6$	138.399			0.640738
$7$	−480.503			−1.40088			−0.700441	−	0.713710i	$-0.747013\pi$
$7$	−480.503			−1.40088			−0.700441	+	0.713710i	$0.747013\pi$
$8$	436.594			0.852723
$9$	243.000			0.333333
$10$			2161.17i			2.16117i
$11$			2263.84i			1.70085i	0.526092	+	0.850427i	$0.323657\pi$
$11$			2263.84i			1.70085i	−0.526092	+	0.850427i	$0.676343\pi$
$12$	−231.095			−0.133735
$13$		−	1257.43i		−	0.572341i	−0.958179	−	0.286171i	$-0.907618\pi$
$13$		−	1257.43i		−	0.572341i	0.958179	−	0.286171i	$-0.0923825\pi$
$14$	4266.06			1.55469
$15$			3794.55i			1.12431i
$16$	−4825.01			−1.17798
$17$	−4292.10			−0.873621			−0.436810	−	0.899554i	$-0.643892\pi$
$17$	−4292.10			−0.873621			−0.436810	+	0.899554i	$0.643892\pi$
$18$	−2157.43			−0.369930
$19$			3498.78i			0.510101i	0.966928	+	0.255051i	$0.0820921\pi$
$19$			3498.78i			0.510101i	−0.966928	+	0.255051i	$0.917908\pi$
$20$		−	3608.64i		−	0.451080i
$21$	7490.30			0.808800
$22$		−	20099.1i		−	1.88759i
$23$		−	5147.01i		−	0.423031i	−0.977375	−	0.211515i	$-0.932160\pi$
$23$		−	5147.01i		−	0.423031i	0.977375	−	0.211515i	$-0.0678398\pi$
$24$	−6805.83			−0.492320
$25$	−43628.5			−2.79223
$26$			11163.9i			0.635179i
$27$	−3788.00			−0.192450
$28$	−7123.32			−0.324495
$29$			22541.9i			0.924265i	0.886811	+	0.462132i	$0.152915\pi$
$29$			22541.9i			0.924265i	−0.886811	+	0.462132i	$0.847085\pi$
$30$		−	33689.3i		−	1.24775i
$31$			27192.5i			0.912776i	0.889781	+	0.456388i	$0.150857\pi$
$31$			27192.5i			0.912776i	−0.889781	+	0.456388i	$0.849143\pi$
$32$	14896.0			0.454590
$33$		−	35289.7i		−	0.981989i
$34$	38106.7			0.969536
$35$			116964.i			2.72803i
$36$	3602.41			0.0772121
$37$	51199.0			1.01078			0.505389	−	0.862891i	$-0.331349\pi$
$37$	51199.0			1.01078			0.505389	+	0.862891i	$0.331349\pi$
$38$		−	31063.3i		−	0.566106i
$39$			19601.5i			0.330442i
$40$		−	106276.i		−	1.66056i
$41$		−	15348.8i		−	0.222702i	−0.993781	−	0.111351i	$-0.964482\pi$
$41$		−	15348.8i		−	0.222702i	0.993781	−	0.111351i	$-0.0355178\pi$
$42$	−66501.3			−0.897599
$43$		−	2776.39i		−	0.0349200i	−0.999848	−	0.0174600i	$-0.994442\pi$
$43$		−	2776.39i		−	0.0349200i	0.999848	−	0.0174600i	$-0.00555797\pi$
$44$			33560.8i			0.393980i
$45$		−	59151.2i		−	0.649121i
$46$			45696.9i			0.469476i
$47$	−92152.1	−	47824.7i	−0.887588	−	0.460637i
$47$	−92152.1	−	47824.7i	−0.887588	−	0.460637i
$48$	75214.5			0.680108
$49$	113234.			0.962472
$50$	387348.			3.09879
$51$	66907.2			0.504385
$52$		−	18641.1i		−	0.132575i
$53$	111935.			0.751865			0.375933	−	0.926647i	$-0.377322\pi$
$53$	111935.			0.751865			0.375933	+	0.926647i	$0.377322\pi$
$54$	33631.1			0.213579
$55$	551064.			3.31218
$56$	−209785.			−1.19457
$57$		−	54540.6i		−	0.294507i
$58$		−	200134.i		−	1.02574i
$59$	−288111.			−1.40283			−0.701413	−	0.712755i	$-0.747447\pi$
$59$	−288111.			−1.40283			−0.701413	+	0.712755i	$0.747447\pi$
$60$			56253.1i			0.260431i
$61$	41272.1			0.181831			0.0909154	−	0.995859i	$-0.471021\pi$
$61$	41272.1			0.181831			0.0909154	+	0.995859i	$0.471021\pi$
$62$		−	241424.i		−	1.01299i
$63$	−116762.			−0.466961
$64$	176549.			0.673481
$65$	−306085.			−1.11456
$66$			313314.i			1.08980i
$67$			94823.3i			0.315276i	0.987497	+	0.157638i	$0.0503879\pi$
$67$			94823.3i			0.315276i	−0.987497	+	0.157638i	$0.949612\pi$
$68$	−63629.2			−0.202362
$69$			80234.0i			0.244237i
$70$		−	1.03845e6i		−	3.02754i
$71$	193648.			0.541051			0.270526	−	0.962713i	$-0.412803\pi$
$71$	193648.			0.541051			0.270526	+	0.962713i	$0.412803\pi$
$72$	106092.			0.284241
$73$		−	466331.i		−	1.19874i	−0.800471	−	0.599371i	$-0.795417\pi$
$73$		−	466331.i		−	1.19874i	0.800471	−	0.599371i	$-0.204583\pi$
$74$	−454561.			−1.12175
$75$	680101.			1.61209
$76$			51868.5i			0.118158i
$77$		−	1.08778e6i		−	2.38270i
$78$		−	174028.i		−	0.366721i
$79$	646546.			1.31135			0.655674	−	0.755044i	$-0.272384\pi$
$79$	646546.			1.31135			0.655674	+	0.755044i	$0.272384\pi$
$80$			1.17451e6i			2.29396i
$81$	59049.0			0.111111
$82$			136272.i			0.247153i
$83$	742695.			1.29890			0.649451	−	0.760403i	$-0.274999\pi$
$83$	742695.			1.29890			0.649451	+	0.760403i	$0.274999\pi$
$84$	111042.			0.187347
$85$			1.04478e6i			1.70126i
$86$			24649.7i			0.0387539i
$87$		−	351393.i		−	0.533624i
$88$			988379.i			1.45036i
$89$	−89831.8			−0.127427			−0.0637133	−	0.997968i	$-0.520294\pi$
$89$	−89831.8			−0.127427			−0.0637133	+	0.997968i	$0.520294\pi$
$90$			525164.i			0.720389i
$91$			604201.i			0.801783i
$92$		−	76303.1i		−	0.0979893i
$93$		−	423889.i		−	0.526991i
$94$	818157.	+	424604.i	0.985038	+	0.511211i
$95$	851675.			0.993352
$96$	−232206.			−0.262457
$97$	−1.29801e6			−1.42221			−0.711103	−	0.703088i	$-0.751804\pi$
$97$	−1.29801e6			−1.42221			−0.711103	+	0.703088i	$0.751804\pi$
$98$	−1.00533e6			−1.06814
$99$			550113.i			0.566952i
$100$	−646781.			−0.646781
$101$	−1.47790e6			−1.43443			−0.717216	−	0.696851i	$-0.754584\pi$
$101$	−1.47790e6			−1.43443			−0.717216	+	0.696851i	$0.754584\pi$
$102$	−594024.			−0.559762
$103$	1.16088e6			1.06237			0.531186	−	0.847256i	$-0.321747\pi$
$103$	1.16088e6			1.06237			0.531186	+	0.847256i	$0.321747\pi$
$104$		−	548989.i		−	0.488049i
$105$		−	1.82329e6i		−	1.57503i
$106$	−993800.			−0.834414
$107$			1.37190e6i			1.11988i	0.828534	+	0.559938i	$0.189175\pi$
$107$			1.37190e6i			1.11988i	−0.828534	+	0.559938i	$0.810825\pi$
$108$	−56156.0			−0.0445784
$109$		−	2.34975e6i		−	1.81444i	−0.420659	−	0.907219i	$-0.638201\pi$
$109$		−	2.34975e6i		−	1.81444i	0.420659	−	0.907219i	$-0.361799\pi$
$110$	−4.89253e6			−3.67583
$111$	−798113.			−0.583573
$112$	2.31843e6			1.65021
$113$		−	664793.i		−	0.460735i	−0.973104	−	0.230367i	$-0.926007\pi$
$113$		−	664793.i		−	0.460735i	0.973104	−	0.230367i	$-0.0739928\pi$
$114$			484230.i			0.326841i
$115$	−1.25289e6			−0.823795
$116$			334177.i			0.214093i
$117$		−	305557.i		−	0.190780i
$118$	2.55794e6			1.55684
$119$	2.06236e6			1.22384
$120$			1.65668e6i			0.958726i
$121$	−3.35340e6			−1.89291
$122$	−366427.			−0.201794
$123$			239265.i			0.128577i
$124$			403121.i			0.211432i
$125$			6.81663e6i			3.49011i
$126$	1.03665e6			0.518229
$127$		−	3.83268e6i		−	1.87108i	−0.353223	−	0.935539i	$-0.614914\pi$
$127$		−	3.83268e6i		−	1.87108i	0.353223	−	0.935539i	$-0.385086\pi$
$128$	−2.52080e6			−1.20201
$129$			43279.6i			0.0201611i
$130$	2.71753e6			1.23693
$131$	−3.57168e6			−1.58876			−0.794380	−	0.607421i	$-0.792204\pi$
$131$	−3.57168e6			−1.58876			−0.794380	+	0.607421i	$0.792204\pi$
$132$		−	523161.i		−	0.227464i
$133$		−	1.68117e6i		−	0.714592i
$134$		−	841873.i		−	0.349890i
$135$			922075.i			0.374770i
$136$	−1.87391e6			−0.744957
$137$		−	541584.i		−	0.210622i	−0.994439	−	0.105311i	$-0.966416\pi$
$137$		−	541584.i		−	0.210622i	0.994439	−	0.105311i	$-0.0335838\pi$
$138$		−	712344.i		−	0.271052i
$139$		−	502757.i		−	0.187204i	−0.995610	−	0.0936018i	$-0.970162\pi$
$139$		−	502757.i		−	0.187204i	0.995610	−	0.0936018i	$-0.0298381\pi$
$140$			1.73396e6i			0.631910i
$141$	1.43651e6	+	745514.i	0.512449	+	0.265949i
$142$	−1.71927e6			−0.600454
$143$	2.84663e6			0.973470
$144$	−1.17248e6			−0.392660
$145$	5.48716e6			1.79988
$146$			4.14024e6i			1.33035i
$147$	−1.76514e6			−0.555684
$148$	759011.			0.234133
$149$	1.26450e6			0.382261			0.191130	−	0.981565i	$-0.438785\pi$
$149$	1.26450e6			0.382261			0.191130	+	0.981565i	$0.438785\pi$
$150$	−6.03816e6			−1.78909
$151$		−	6.39258e6i		−	1.85671i	−0.371689	−	0.928357i	$-0.621221\pi$
$151$		−	6.39258e6i		−	1.85671i	0.371689	−	0.928357i	$-0.378779\pi$
$152$			1.52755e6i			0.434975i
$153$	−1.04298e6			−0.291207
$154$			9.65767e6i			2.64430i
$155$	6.61921e6			1.77751
$156$			290586.i			0.0765423i
$157$	−769041.			−0.198724			−0.0993621	−	0.995051i	$-0.531680\pi$
$157$	−769041.			−0.198724			−0.0993621	+	0.995051i	$0.531680\pi$
$158$	−5.74025e6			−1.45532
$159$	−1.74490e6			−0.434090
$160$		−	3.62599e6i		−	0.885251i
$161$			2.47315e6i			0.592616i
$162$	−524256.			−0.123310
$163$			4.61022e6i			1.06453i	0.846577	+	0.532266i	$0.178660\pi$
$163$			4.61022e6i			1.06453i	−0.846577	+	0.532266i	$0.821340\pi$
$164$		−	227542.i		−	0.0515858i
$165$	−8.59024e6			−1.91229
$166$	−6.59389e6			−1.44151
$167$			3.99227e6i			0.857178i	0.903500	+	0.428589i	$0.140989\pi$
$167$			3.99227e6i			0.857178i	−0.903500	+	0.428589i	$0.859011\pi$
$168$	3.27022e6			0.689682
$169$	3.24567e6			0.672425
$170$		−	9.27594e6i		−	1.88804i
$171$			850204.i			0.170034i
$172$		−	41159.1i		−	0.00808874i
$173$	1.56988e6			0.303199			0.151600	−	0.988442i	$-0.451558\pi$
$173$	1.56988e6			0.303199			0.151600	+	0.988442i	$0.451558\pi$
$174$			3.11978e6i			0.592212i
$175$	2.09636e7			3.91158
$176$		−	1.09230e7i		−	2.00357i
$177$	4.49121e6			0.809922
$178$	797556.			0.141417
$179$			1.06068e6i			0.184937i	0.995716	+	0.0924687i	$0.0294758\pi$
$179$			1.06068e6i			0.184937i	−0.995716	+	0.0924687i	$0.970524\pi$
$180$		−	876900.i		−	0.150360i
$181$		−	857305.i		−	0.144577i	−0.997384	−	0.0722886i	$-0.976970\pi$
$181$		−	857305.i		−	0.144577i	0.997384	−	0.0722886i	$-0.0230303\pi$
$182$		−	5.36429e6i		−	0.889812i
$183$	−643369.			−0.104980
$184$		−	2.24716e6i		−	0.360728i
$185$		−	1.24629e7i		−	1.96835i
$186$			3.76343e6i			0.584850i
$187$		−	9.71661e6i		−	1.48590i
$188$	−1.36613e6	−	708989.i	−0.205598	−	0.106700i
$189$	1.82014e6			0.269600
$190$	−7.56145e6			−1.10241
$191$	1.03532e7			1.48585			0.742927	−	0.669372i	$-0.233437\pi$
$191$	1.03532e7			1.48585			0.742927	+	0.669372i	$0.233437\pi$
$192$	−2.75213e6			−0.388835
$193$			5.78555e6i			0.804772i	0.915470	+	0.402386i	$0.131819\pi$
$193$			5.78555e6i			0.804772i	−0.915470	+	0.402386i	$0.868181\pi$
$194$	1.15242e7			1.57835
$195$	4.77140e6			0.643490
$196$	1.67866e6			0.222943
$197$	9.83855e6			1.28686			0.643432	−	0.765503i	$-0.277510\pi$
$197$	9.83855e6			1.28686			0.643432	+	0.765503i	$0.277510\pi$
$198$		−	4.88408e6i		−	0.629198i
$199$			1.80270e6i			0.228751i	0.993438	+	0.114376i	$0.0364867\pi$
$199$			1.80270e6i			0.228751i	−0.993438	+	0.114376i	$0.963513\pi$
$200$	−1.90480e7			−2.38100
$201$		−	1.47815e6i		−	0.182025i
$202$	1.31213e7			1.59192
$203$		−	1.08314e7i		−	1.29479i
$204$	991880.			0.116834
$205$	−3.73622e6			−0.433682
$206$	−1.03067e7			−1.17901
$207$		−	1.25072e6i		−	0.141010i
$208$			6.06713e6i			0.674207i
$209$	−7.92068e6			−0.867608
$210$			1.61878e7i			1.74795i
$211$			1.78293e7i			1.89796i	0.315331	+	0.948982i	$0.397884\pi$
$211$			1.78293e7i			1.89796i	−0.315331	+	0.948982i	$0.602116\pi$
$212$	1.65941e6			0.174159
$213$	−3.01868e6			−0.312376
$214$		−	1.21802e7i		−	1.24283i
$215$	−675829.			−0.0680020
$216$	−1.65382e6			−0.164107
$217$		−	1.30661e7i		−	1.27869i
$218$			2.08619e7i			2.01365i
$219$			7.26938e6i			0.692094i
$220$	8.16938e6			0.767222
$221$			5.39703e6i			0.500009i
$222$	7.08591e6			0.647645
$223$		−	646403.i		−	0.0582893i	−0.999575	−	0.0291446i	$-0.990722\pi$
$223$		−	646403.i		−	0.0582893i	0.999575	−	0.0291446i	$-0.00927834\pi$
$224$	−7.15756e6			−0.636827
$225$	−1.06017e7			−0.930742
$226$			5.90225e6i			0.511319i
$227$		−	4.80461e6i		−	0.410753i	−0.978683	−	0.205377i	$-0.934158\pi$
$227$		−	4.80461e6i		−	0.410753i	0.978683	−	0.205377i	$-0.0658419\pi$
$228$		−	808550.i		−	0.0682185i
$229$		−	2.21118e7i		−	1.84127i	−0.390419	−	0.920637i	$-0.627670\pi$
$229$		−	2.21118e7i		−	1.84127i	0.390419	−	0.920637i	$-0.372330\pi$
$230$	1.11236e7			0.914240
$231$			1.69568e7i			1.37565i
$232$			9.84166e6i			0.788142i
$233$			1.13334e7i			0.895972i	0.894041	+	0.447986i	$0.147859\pi$
$233$			1.13334e7i			0.895972i	−0.894041	+	0.447986i	$0.852141\pi$
$234$			2.71283e6i			0.211726i
$235$	−1.16415e7	+	2.24317e7i	−0.897028	+	1.72846i
$236$	−4.27117e6			−0.324946
$237$	−1.00787e7			−0.757107
$238$	−1.83104e7			−1.35821
$239$	2.10763e7			1.54383			0.771916	−	0.635725i	$-0.219299\pi$
$239$	2.10763e7			1.54383			0.771916	+	0.635725i	$0.219299\pi$
$240$		−	1.83087e7i		−	1.32442i
$241$	9.61627e6			0.686998			0.343499	−	0.939153i	$-0.388388\pi$
$241$	9.61627e6			0.686998			0.343499	+	0.939153i	$0.388388\pi$
$242$	2.97726e7			2.10073
$243$	−920483.			−0.0641500
$244$	611848.			0.0421186
$245$		−	2.75634e7i		−	1.87428i
$246$		−	2.12427e6i		−	0.142694i
$247$	4.39949e6			0.291952
$248$			1.18721e7i			0.778345i
$249$	−1.15775e7			−0.749922
$250$		−	6.05203e7i		−	3.87330i
$251$	−7.40095e6			−0.468022			−0.234011	−	0.972234i	$-0.575185\pi$
$251$	−7.40095e6			−0.468022			−0.234011	+	0.972234i	$0.575185\pi$
$252$	−1.73097e6			−0.108165
$253$	1.16520e7			0.719514
$254$			3.40278e7i			2.07651i
$255$		−	1.62866e7i		−	0.982221i
$256$	1.10814e7			0.660502
$257$			1.79696e7i			1.05862i	0.848430	+	0.529308i	$0.177548\pi$
$257$			1.79696e7i			1.05862i	−0.848430	+	0.529308i	$0.822452\pi$
$258$		−	384250.i		−	0.0223746i
$259$	−2.46012e7			−1.41598
$260$	−4.53763e6			−0.258172
$261$			5.47768e6i			0.308088i
$262$	3.17105e7			1.76319
$263$	−2.75597e7			−1.51498			−0.757492	−	0.652845i	$-0.773575\pi$
$263$	−2.75597e7			−1.51498			−0.757492	+	0.652845i	$0.773575\pi$
$264$		−	1.54073e7i		−	0.837365i
$265$		−	2.72474e7i		−	1.46416i
$266$			1.49260e7i			0.793048i
$267$	1.40034e6			0.0735698
$268$			1.40573e6i			0.0730294i
$269$	−4.91467e6			−0.252486			−0.126243	−	0.991999i	$-0.540292\pi$
$269$	−4.91467e6			−0.252486			−0.126243	+	0.991999i	$0.540292\pi$
$270$		−	8.18649e6i		−	0.415917i
$271$	−1.85456e7			−0.931820			−0.465910	−	0.884832i	$-0.654273\pi$
$271$	−1.85456e7			−0.931820			−0.465910	+	0.884832i	$0.654273\pi$
$272$	2.07094e7			1.02911
$273$		−	9.41856e6i		−	0.462910i
$274$			4.80836e6i			0.233746i
$275$		−	9.87679e7i		−	4.74917i
$276$			1.18945e6i			0.0565741i
$277$	3.37261e7			1.58682			0.793409	−	0.608689i	$-0.208304\pi$
$277$	3.37261e7			1.58682			0.793409	+	0.608689i	$0.208304\pi$
$278$			4.46365e6i			0.207757i
$279$			6.60778e6i			0.304259i
$280$			5.10659e7i			2.32625i
$281$			1.37809e7i			0.621096i	0.950558	+	0.310548i	$0.100513\pi$
$281$			1.37809e7i			0.621096i	−0.950558	+	0.310548i	$0.899487\pi$
$282$	−1.27538e7	−	6.61892e6i	−0.568712	−	0.295148i
$283$	4.12678e7			1.82076			0.910379	−	0.413776i	$-0.135790\pi$
$283$	4.12678e7			1.82076			0.910379	+	0.413776i	$0.135790\pi$
$284$	2.87078e6			0.125327
$285$	−1.32763e7			−0.573512
$286$	−2.52733e7			−1.08035
$287$			7.37516e6i			0.311979i
$288$	3.61973e6			0.151530
$289$	−5.71547e6			−0.236787
$290$	−4.87168e7			−1.99749
$291$	2.02340e7			0.821111
$292$		−	6.91323e6i		−	0.277672i
$293$			2.84080e7i			1.12938i	0.825305	+	0.564688i	$0.191003\pi$
$293$			2.84080e7i			1.12938i	−0.825305	+	0.564688i	$0.808997\pi$
$294$	1.56715e7			0.616693
$295$			7.01321e7i			2.73181i
$296$	2.23532e7			0.861915
$297$		−	8.57541e6i		−	0.327330i
$298$	−1.12266e7			−0.424230
$299$	−6.47203e6			−0.242118
$300$	1.00823e7			0.373419
$301$			1.33406e6i			0.0489188i
$302$			5.67554e7i			2.06057i
$303$	2.30381e7			0.828170
$304$		−	1.68817e7i		−	0.600889i
$305$		−	1.00465e7i		−	0.354091i
$306$	9.25992e6			0.323179
$307$	−9.52986e6			−0.329361			−0.164680	−	0.986347i	$-0.552659\pi$
$307$	−9.52986e6			−0.329361			−0.164680	+	0.986347i	$0.552659\pi$
$308$		−	1.61260e7i		−	0.551919i
$309$	−1.80964e7			−0.613360
$310$	−5.87675e7			−1.97266
$311$			3.40686e7i			1.13259i	0.824203	+	0.566295i	$0.191624\pi$
$311$			3.40686e7i			1.13259i	−0.824203	+	0.566295i	$0.808376\pi$
$312$			8.55789e6i			0.281775i
$313$		−	4.34628e7i		−	1.41737i	−0.705523	−	0.708687i	$-0.749288\pi$
$313$		−	4.34628e7i		−	1.41737i	0.705523	−	0.708687i	$-0.250712\pi$
$314$	6.82780e6			0.220542
$315$			2.84223e7i			0.909343i
$316$	9.58486e6			0.303756
$317$			1.56253e7i			0.490512i	0.969458	+	0.245256i	$0.0788721\pi$
$317$			1.56253e7i			0.490512i	−0.969458	+	0.245256i	$0.921128\pi$
$318$	1.54918e7			0.481749
$319$	−5.10312e7			−1.57204
$320$		−	4.29757e7i		−	1.31151i
$321$		−	2.13858e7i		−	0.646561i
$322$		−	2.19575e7i		−	0.657680i
$323$		−	1.50171e7i		−	0.445635i
$324$	875385.			0.0257374
$325$			5.48600e7i			1.59811i
$326$		−	4.09311e7i		−	1.18141i
$327$			3.66290e7i			1.04757i
$328$		−	6.70121e6i		−	0.189903i
$329$	4.42793e7	+	2.29799e7i	1.24341	+	0.645299i
$330$	7.62670e7			2.12224
$331$	1.55670e7			0.429259			0.214630	−	0.976696i	$-0.431146\pi$
$331$	1.55670e7			0.429259			0.214630	+	0.976696i	$0.431146\pi$
$332$	1.10103e7			0.300873
$333$	1.24414e7			0.336926
$334$		−	3.54447e7i		−	0.951289i
$335$	2.30819e7			0.613957
$336$	−3.61408e7			−0.952751
$337$	−1.76464e7			−0.461070			−0.230535	−	0.973064i	$-0.574048\pi$
$337$	−1.76464e7			−0.461070			−0.230535	+	0.973064i	$0.574048\pi$
$338$	−2.88161e7			−0.746252
$339$			1.03631e7i			0.266005i
$340$			1.54886e7i			0.394073i
$341$	−6.15594e7			−1.55250
$342$		−	7.54839e6i		−	0.188702i
$343$	2.12148e6			0.0525722
$344$		−	1.21215e6i		−	0.0297771i
$345$	1.95306e7			0.475618
$346$	−1.39379e7			−0.336488
$347$	5.97512e6			0.143007			0.0715037	−	0.997440i	$-0.477220\pi$
$347$	5.97512e6			0.143007			0.0715037	+	0.997440i	$0.477220\pi$
$348$		−	5.20931e6i		−	0.123607i
$349$			1.59760e7i			0.375831i	0.982185	+	0.187915i	$0.0601731\pi$
$349$			1.59760e7i			0.375831i	−0.982185	+	0.187915i	$0.939827\pi$
$350$	−1.86122e8			−4.34104
$351$			4.76315e6i			0.110147i
$352$			3.37221e7i			0.773191i
$353$	4.50608e7			1.02441			0.512206	−	0.858863i	$-0.328828\pi$
$353$	4.50608e7			1.02441			0.512206	+	0.858863i	$0.328828\pi$
$354$	−3.98744e7			−0.898844
$355$		−	4.71379e7i		−	1.05362i
$356$	−1.33173e6			−0.0295166
$357$	−3.21491e7			−0.706584
$358$		−	9.41705e6i		−	0.205242i
$359$		−	4.05678e7i		−	0.876795i	−0.898781	−	0.438397i	$-0.855546\pi$
$359$		−	4.05678e7i		−	0.876795i	0.898781	−	0.438397i	$-0.144454\pi$
$360$		−	2.58251e7i		−	0.553521i
$361$	3.48044e7			0.739797
$362$			7.61144e6i			0.160450i
$363$	5.22743e7			1.09287
$364$			8.95711e6i			0.185722i
$365$	−1.13515e8			−2.33439
$366$	5.71204e6			0.116506
$367$			2.19727e7i			0.444513i	0.974988	+	0.222256i	$0.0713422\pi$
$367$			2.19727e7i			0.444513i	−0.974988	+	0.222256i	$0.928658\pi$
$368$			2.48344e7i			0.498322i
$369$		−	3.72977e6i		−	0.0742340i
$370$			1.10650e8i			2.18446i
$371$	−5.37853e7			−1.05328
$372$		−	6.28404e6i		−	0.122070i
$373$			9.65272e6i			0.186004i	0.995666	+	0.0930022i	$0.0296464\pi$
$373$			9.65272e6i			0.186004i	−0.995666	+	0.0930022i	$0.970354\pi$
$374$			8.62673e7i			1.64904i
$375$		−	1.06261e8i		−	2.01502i
$376$	−4.02331e7	−	2.08800e7i	−0.756867	−	0.392796i
$377$	2.83449e7			0.528995
$378$	−1.61598e7			−0.299200
$379$	8.10146e7			1.48815			0.744073	−	0.668098i	$-0.232891\pi$
$379$	8.10146e7			1.48815			0.744073	+	0.668098i	$0.232891\pi$
$380$	1.26259e7			0.230096
$381$			5.97456e7i			1.08027i
$382$	−9.19195e7			−1.64899
$383$	9.47510e6			0.168650			0.0843252	−	0.996438i	$-0.473127\pi$
$383$	9.47510e6			0.168650			0.0843252	+	0.996438i	$0.473127\pi$
$384$	3.92955e7			0.693983
$385$	−2.64788e8			−4.63998
$386$		−	5.13660e7i		−	0.893129i
$387$		−	674662.i		−	0.0116400i
$388$	−1.92426e7			−0.329435
$389$			8.20924e7i			1.39461i	0.716772	+	0.697307i	$0.245619\pi$
$389$			8.20924e7i			1.39461i	−0.716772	+	0.697307i	$0.754381\pi$
$390$	−4.23620e7			−0.714139
$391$			2.20915e7i			0.369568i
$392$	4.94373e7			0.820722
$393$	5.56769e7			0.917271
$394$	−8.73499e7			−1.42815
$395$		−	1.57383e8i		−	2.55367i
$396$			8.15527e6i			0.131327i
$397$	7.70589e7			1.23155			0.615774	−	0.787923i	$-0.288843\pi$
$397$	7.70589e7			1.23155			0.615774	+	0.787923i	$0.288843\pi$
$398$		−	1.60049e7i		−	0.253866i
$399$			2.62069e7i			0.412570i
$400$	2.10508e8			3.28919
$401$	3.42402e7			0.531010			0.265505	−	0.964109i	$-0.414461\pi$
$401$	3.42402e7			0.531010			0.265505	+	0.964109i	$0.414461\pi$
$402$			1.31235e7i			0.202009i
$403$	3.41928e7			0.522420
$404$	−2.19094e7			−0.332267
$405$		−	1.43737e7i		−	0.216374i
$406$			9.61651e7i			1.43694i
$407$			1.15906e8i			1.71919i
$408$	2.92113e7			0.430101
$409$			6.75868e7i			0.987852i	0.869504	+	0.493926i	$0.164439\pi$
$409$			6.75868e7i			0.987852i	−0.869504	+	0.493926i	$0.835561\pi$
$410$	3.31714e7			0.481296
$411$			8.44245e6i			0.121603i
$412$	1.72097e7			0.246084
$413$	1.38438e8			1.96520
$414$			1.11043e7i			0.156492i
$415$		−	1.80787e8i		−	2.52943i
$416$		−	1.87307e7i		−	0.260180i
$417$			7.83721e6i			0.108082i
$418$	7.03224e7			0.962863
$419$		−	7.41040e7i		−	1.00739i	−0.863880	−	0.503697i	$-0.831973\pi$
$419$		−	7.41040e7i		−	1.00739i	0.863880	−	0.503697i	$-0.168027\pi$
$420$		−	2.70298e7i		−	0.364834i
$421$			8.08895e7i			1.08404i	0.840365	+	0.542021i	$0.182341\pi$
$421$			8.08895e7i			1.08404i	−0.840365	+	0.542021i	$0.817659\pi$
$422$		−	1.58295e8i		−	2.10634i
$423$	−2.23930e7	−	1.16214e7i	−0.295863	−	0.153546i
$424$	4.88704e7			0.641133
$425$	1.87258e8			2.43935
$426$	2.68008e7			0.346672
$427$	−1.98314e7			−0.254723
$428$			2.03380e7i			0.259404i
$429$	−4.43745e7			−0.562033
$430$	6.00023e6			0.0754680
$431$	1.80546e6			0.0225505			0.0112753	−	0.999936i	$-0.496411\pi$
$431$	1.80546e6			0.0225505			0.0112753	+	0.999936i	$0.496411\pi$
$432$	1.82771e7			0.226703
$433$		−	7.59300e7i		−	0.935297i	−0.883915	−	0.467648i	$-0.845101\pi$
$433$		−	7.59300e7i		−	0.935297i	0.883915	−	0.467648i	$-0.154899\pi$
$434$			1.16005e8i			1.41908i
$435$	−8.55363e7			−1.03916
$436$		−	3.48344e7i		−	0.420290i
$437$	1.80083e7			0.215788
$438$		−	6.45400e7i		−	0.768080i
$439$	−1.03268e8			−1.22059			−0.610296	−	0.792174i	$-0.708949\pi$
$439$	−1.03268e8			−1.22059			−0.610296	+	0.792174i	$0.708949\pi$
$440$	2.40592e8			2.82437
$441$	2.75158e7			0.320824
$442$		−	4.79166e7i		−	0.554906i
$443$		−	1.18380e7i		−	0.136165i	−0.997680	−	0.0680827i	$-0.978312\pi$
$443$		−	1.18380e7i		−	0.136165i	0.997680	−	0.0680827i	$-0.0216882\pi$
$444$	−1.18318e7			−0.135177
$445$			2.18669e7i			0.248146i
$446$			5.73898e6i			0.0646889i
$447$	−1.97116e7			−0.220698
$448$	−8.48323e7			−0.943468
$449$		−	2.77402e7i		−	0.306458i	−0.988191	−	0.153229i	$-0.951033\pi$
$449$		−	2.77402e7i		−	0.306458i	0.988191	−	0.153229i	$-0.0489671\pi$
$450$	9.41256e7			1.03293
$451$	3.47473e7			0.378784
$452$		−	9.85537e6i		−	0.106723i
$453$			9.96504e7i			1.07197i
$454$			4.26570e7i			0.455850i
$455$	1.47075e8			1.56136
$456$		−	2.38121e7i		−	0.251133i
$457$	5.59892e7			0.586618			0.293309	−	0.956018i	$-0.405244\pi$
$457$	5.59892e7			0.586618			0.293309	+	0.956018i	$0.405244\pi$
$458$			1.96316e8i			2.04343i
$459$	1.62584e7			0.168128
$460$	−1.85737e7			−0.190821
$461$		−	1.04572e8i		−	1.06736i	−0.845685	−	0.533682i	$-0.820808\pi$
$461$		−	1.04572e8i		−	1.06736i	0.845685	−	0.533682i	$-0.179192\pi$
$462$		−	1.50548e8i		−	1.52669i
$463$		−	3.23303e7i		−	0.325737i	−0.986648	−	0.162868i	$-0.947925\pi$
$463$		−	3.23303e7i		−	0.325737i	0.986648	−	0.162868i	$-0.0520746\pi$
$464$		−	1.08765e8i		−	1.08877i
$465$	−1.03183e8			−1.02624
$466$		−	1.00622e8i		−	0.994341i
$467$		−	3.69268e7i		−	0.362569i	−0.983431	−	0.181285i	$-0.941974\pi$
$467$		−	3.69268e7i		−	0.362569i	0.983431	−	0.181285i	$-0.0580255\pi$
$468$		−	4.52979e6i		−	0.0441917i
$469$		−	4.55629e7i		−	0.441665i
$470$	1.03357e8	−	1.99156e8i	0.995514	−	1.91823i
$471$	1.19882e7			0.114733
$472$	−1.25788e8			−1.19622
$473$	6.28529e6			0.0593939
$474$	8.94816e7			0.840231
$475$		−	1.52647e8i		−	1.42432i
$476$	3.05740e7			0.283486
$477$	2.72003e7			0.250622
$478$	−1.87122e8			−1.71333
$479$	−1.89544e7			−0.172466			−0.0862330	−	0.996275i	$-0.527483\pi$
$479$	−1.89544e7			−0.172466			−0.0862330	+	0.996275i	$0.527483\pi$
$480$			5.65236e7i			0.511100i
$481$		−	6.43793e7i		−	0.578511i
$482$	−8.53764e7			−0.762425
$483$		−	3.85527e7i		−	0.342147i
$484$	−4.97132e7			−0.438466
$485$			3.15962e8i			2.76955i
$486$	8.17235e6			0.0711931
$487$	−8.50620e7			−0.736459			−0.368230	−	0.929735i	$-0.620036\pi$
$487$	−8.50620e7			−0.736459			−0.368230	+	0.929735i	$0.620036\pi$
$488$	1.80192e7			0.155051
$489$		−	7.18663e7i		−	0.614608i
$490$			2.44717e8i			2.08006i
$491$	1.55243e8			1.31150			0.655749	−	0.754979i	$-0.272353\pi$
$491$	1.55243e8			1.31150			0.655749	+	0.754979i	$0.272353\pi$
$492$			3.54703e6i			0.0297831i
$493$		−	9.67520e7i		−	0.807456i
$494$	−3.90601e7			−0.324006
$495$	1.33909e8			1.10406
$496$		−	1.31204e8i		−	1.07523i
$497$	−9.30485e7			−0.757949
$498$	1.02789e8			0.832256
$499$			1.56075e8i			1.25612i	0.778164	+	0.628061i	$0.216151\pi$
$499$			1.56075e8i			1.25612i	−0.778164	+	0.628061i	$0.783849\pi$
$500$			1.01055e8i			0.808437i
$501$		−	6.22334e7i		−	0.494892i
$502$	6.57080e7			0.519406
$503$		−	2.16863e8i		−	1.70405i	−0.523502	−	0.852024i	$-0.675375\pi$
$503$		−	2.16863e8i		−	1.70405i	0.523502	−	0.852024i	$-0.324625\pi$
$504$	−5.09777e7			−0.398188
$505$			3.59750e8i			2.79336i
$506$	−1.03450e8			−0.798510
$507$	−5.05950e7			−0.388225
$508$		−	5.68185e7i		−	0.433410i
$509$			1.53491e8i			1.16394i	0.813212	+	0.581968i	$0.197717\pi$
$509$			1.53491e8i			1.16394i	−0.813212	+	0.581968i	$0.802283\pi$
$510$			1.44598e8i			1.09006i
$511$			2.24073e8i			1.67930i
$512$	6.29473e7			0.468994
$513$		−	1.32534e7i		−	0.0981690i
$514$		−	1.59540e8i		−	1.17484i
$515$		−	2.82582e8i		−	2.06882i
$516$			641608.i			0.00467004i
$517$	1.08267e8	−	2.08617e8i	0.783477	−	1.50966i
$518$	2.18418e8			1.57144
$519$	−2.44720e7			−0.175052
$520$	−1.33635e8			−0.950409
$521$	−1.26936e7			−0.0897575			−0.0448788	−	0.998992i	$-0.514290\pi$
$521$	−1.26936e7			−0.0897575			−0.0448788	+	0.998992i	$0.514290\pi$
$522$		−	4.86326e7i		−	0.341914i
$523$	−1.15577e8			−0.807913			−0.403957	−	0.914778i	$-0.632365\pi$
$523$	−1.15577e8			−0.807913			−0.403957	+	0.914778i	$0.632365\pi$
$524$	−5.29491e7			−0.368015
$525$	−3.26791e8			−2.25835
$526$	2.44684e8			1.68131
$527$		−	1.16713e8i		−	0.797420i
$528$			1.70273e8i			1.15676i
$529$	1.21544e8			0.821045
$530$			2.41911e8i			1.62491i
$531$	−7.00110e7			−0.467609
$532$		−	2.49230e7i		−	0.165525i
$533$	−1.93002e7			−0.127462
$534$	−1.24327e7			−0.0816471
$535$	3.33948e8			2.18081
$536$			4.13993e7i			0.268843i
$537$		−	1.65343e7i		−	0.106774i
$538$	4.36340e7			0.280207
$539$			2.56343e8i			1.63703i
$540$			1.36695e7i			0.0868104i
$541$	1.21553e8			0.767667			0.383833	−	0.923402i	$-0.374604\pi$
$541$	1.21553e8			0.767667			0.383833	+	0.923402i	$0.374604\pi$
$542$	1.64654e8			1.03413
$543$			1.33641e7i			0.0834717i
$544$	−6.39350e7			−0.397139
$545$	−5.71977e8			−3.53337
$546$			8.36210e7i			0.513733i
$547$			8.36527e7i			0.511114i	0.966794	+	0.255557i	$0.0822589\pi$
$547$			8.36527e7i			0.511114i	−0.966794	+	0.255557i	$0.917741\pi$
$548$		−	8.02883e6i		−	0.0487877i
$549$	1.00291e7			0.0606102
$550$			8.76894e8i			5.27059i
$551$	−7.88692e7			−0.471468
$552$			3.50297e7i			0.208266i
$553$	−3.10667e8			−1.83705
$554$	−2.99432e8			−1.76104
$555$			1.94277e8i			1.13643i
$556$		−	7.45324e6i		−	0.0433631i
$557$		−	9.18966e7i		−	0.531782i	−0.964003	−	0.265891i	$-0.914334\pi$
$557$		−	9.18966e7i		−	0.531782i	0.964003	−	0.265891i	$-0.0856661\pi$
$558$		−	5.86660e7i		−	0.337664i
$559$	−3.49112e6			−0.0199862
$560$		−	5.64353e8i		−	3.21356i
$561$			1.51467e8i			0.857886i
$562$		−	1.22351e8i		−	0.689287i
$563$		−	2.57680e8i		−	1.44396i	−0.691912	−	0.721982i	$-0.743231\pi$
$563$		−	2.57680e8i		−	1.44396i	0.691912	−	0.721982i	$-0.256769\pi$
$564$	2.12958e7	+	1.10520e7i	0.118702	+	0.0616035i
$565$	−1.61824e8			−0.897218
$566$	−3.66389e8			−2.02066
$567$	−2.83732e7			−0.155654
$568$	8.45457e7			0.461367
$569$		−	1.51048e8i		−	0.819934i	−0.912100	−	0.409967i	$-0.865540\pi$
$569$		−	1.51048e8i		−	0.819934i	0.912100	−	0.409967i	$-0.134460\pi$
$570$	1.17871e8			0.636479
$571$	−2.88300e7			−0.154859			−0.0774296	−	0.996998i	$-0.524671\pi$
$571$	−2.88300e7			−0.154859			−0.0774296	+	0.996998i	$0.524671\pi$
$572$	4.22005e7			0.225491
$573$	−1.61391e8			−0.857858
$574$		−	6.54791e7i		−	0.346232i
$575$			2.24557e8i			1.18120i
$576$	4.29014e7			0.224494
$577$		−	1.67278e8i		−	0.870788i	−0.900240	−	0.435394i	$-0.856609\pi$
$577$		−	1.67278e8i		−	0.870788i	0.900240	−	0.435394i	$-0.143391\pi$
$578$	5.07438e7			0.262784
$579$		−	9.01878e7i		−	0.464635i
$580$	8.13456e7			0.416917
$581$	−3.56867e8			−1.81961
$582$	−1.79644e8			−0.911262
$583$			2.53404e8i			1.27881i
$584$		−	2.03597e8i		−	1.02220i
$585$	−7.43787e7			−0.371519
$586$		−	2.52216e8i		−	1.25337i
$587$			1.85959e8i			0.919397i	0.888075	+	0.459699i	$0.152043\pi$
$587$			1.85959e8i			0.919397i	−0.888075	+	0.459699i	$0.847957\pi$
$588$	−2.61677e7			−0.128716
$589$	−9.51407e7			−0.465608
$590$		−	6.22656e8i		−	3.03174i
$591$	−1.53368e8			−0.742971
$592$	−2.47036e8			−1.19068
$593$			2.83687e8i			1.36043i	0.733015	+	0.680213i	$0.238113\pi$
$593$			2.83687e8i			1.36043i	−0.733015	+	0.680213i	$0.761887\pi$
$594$			7.61353e7i			0.363268i
$595$		−	5.02022e8i		−	2.38326i
$596$	1.87458e7			0.0885455
$597$		−	2.81013e7i		−	0.132070i
$598$	5.74608e7			0.268700
$599$			3.22335e8i			1.49978i	0.661565	+	0.749888i	$0.269893\pi$
$599$			3.22335e8i			1.49978i	−0.661565	+	0.749888i	$0.730107\pi$
$600$	2.96928e8			1.37467
$601$	9.45547e7			0.435572			0.217786	−	0.975997i	$-0.430117\pi$
$601$	9.45547e7			0.435572			0.217786	+	0.975997i	$0.430117\pi$
$602$		−	1.18442e7i		−	0.0542897i
$603$			2.30421e7i			0.105092i
$604$		−	9.47682e7i		−	0.430082i
$605$			8.16286e8i			3.68618i
$606$	−2.04540e8			−0.919096
$607$			9.14437e7i			0.408872i	0.978880	+	0.204436i	$0.0655361\pi$
$607$			9.14437e7i			0.408872i	−0.978880	+	0.204436i	$0.934464\pi$
$608$			5.21178e7i			0.231887i
$609$			1.68845e8i			0.747545i
$610$			8.91959e7i			0.392967i
$611$	−6.01365e7	+	1.15875e8i	−0.263642	+	0.508004i
$612$	−1.54619e7			−0.0674541
$613$	−2.93931e8			−1.27604			−0.638020	−	0.770020i	$-0.720246\pi$
$613$	−2.93931e8			−1.27604			−0.638020	+	0.770020i	$0.720246\pi$
$614$	8.46093e7			0.365521
$615$	5.82419e7			0.250386
$616$		−	4.74919e8i		−	2.03178i
$617$	2.62121e8			1.11595			0.557977	−	0.829856i	$-0.311578\pi$
$617$	2.62121e8			1.11595			0.557977	+	0.829856i	$0.311578\pi$
$618$	1.60665e8			0.680702
$619$	1.23080e8			0.518937			0.259468	−	0.965752i	$-0.416453\pi$
$619$	1.23080e8			0.518937			0.259468	+	0.965752i	$0.416453\pi$
$620$	9.81280e7			0.411735
$621$			1.94969e7i			0.0814123i
$622$		−	3.02472e8i		−	1.25694i
$623$	4.31644e7			0.178510
$624$		−	9.45772e7i		−	0.389254i
$625$	9.77611e8			4.00430
$626$			3.85877e8i			1.57299i
$627$	1.23471e8			0.500914
$628$	−1.14008e7			−0.0460317
$629$	−2.19751e8			−0.883037
$630$		−	2.52343e8i		−	1.00918i
$631$		−	2.13607e8i		−	0.850214i	−0.905143	−	0.425107i	$-0.860236\pi$
$631$		−	2.13607e8i		−	0.850214i	0.905143	−	0.425107i	$-0.139764\pi$
$632$	2.82278e8			1.11822
$633$		−	2.77932e8i		−	1.09579i
$634$		−	1.38726e8i		−	0.544366i
$635$	−9.32954e8			−3.64367
$636$	−2.58677e7			−0.100551
$637$		−	1.42384e8i		−	0.550863i
$638$	4.53072e8			1.74464
$639$	4.70565e7			0.180350
$640$			6.13615e8i			2.34076i
$641$			5.03945e8i			1.91341i	0.291052	+	0.956707i	$0.405995\pi$
$641$			5.03945e8i			1.91341i	−0.291052	+	0.956707i	$0.594005\pi$
$642$			1.89870e8i			0.717548i
$643$	8.97202e7			0.337487			0.168744	−	0.985660i	$-0.446029\pi$
$643$	8.97202e7			0.337487			0.168744	+	0.985660i	$0.446029\pi$
$644$			3.66638e7i			0.137271i
$645$	1.05351e7			0.0392609
$646$			1.33327e8i			0.494562i
$647$	4.92983e8			1.82020			0.910100	−	0.414388i	$-0.136004\pi$
$647$	4.92983e8			1.82020			0.910100	+	0.414388i	$0.136004\pi$
$648$	2.57805e7			0.0947470
$649$		−	6.52237e8i		−	2.38600i
$650$		−	4.87065e8i		−	1.77356i
$651$			2.03680e8i			0.738253i
$652$			6.83453e7i			0.246584i
$653$	1.42280e7			0.0510982			0.0255491	−	0.999674i	$-0.491867\pi$
$653$	1.42280e7			0.0510982			0.0255491	+	0.999674i	$0.491867\pi$
$654$		−	3.25204e8i		−	1.16258i
$655$			8.69419e8i			3.09389i
$656$			7.40583e7i			0.262339i
$657$		−	1.13318e8i		−	0.399581i
$658$	−3.93127e8	−	2.04023e8i	−1.37992	−	0.716147i
$659$	−1.51707e7			−0.0530090			−0.0265045	−	0.999649i	$-0.508438\pi$
$659$	−1.51707e7			−0.0530090			−0.0265045	+	0.999649i	$0.508438\pi$
$660$	−1.27348e8			−0.442956
$661$	−1.45463e8			−0.503673			−0.251836	−	0.967770i	$-0.581034\pi$
$661$	−1.45463e8			−0.503673			−0.251836	+	0.967770i	$0.581034\pi$
$662$	−1.38209e8			−0.476388
$663$		−	8.41314e7i		−	0.288680i
$664$	3.24257e8			1.10760
$665$	−4.09232e8			−1.39157
$666$	−1.10458e8			−0.373918
$667$	1.16023e8			0.390992
$668$			5.91844e7i			0.198554i
$669$			1.00764e7i			0.0336533i
$670$	−2.04929e8			−0.681364
$671$			9.34334e7i			0.309268i
$672$	1.11575e8			0.367672
$673$		−	2.91464e8i		−	0.956179i	−0.878311	−	0.478090i	$-0.841329\pi$
$673$		−	2.91464e8i		−	0.956179i	0.878311	−	0.478090i	$-0.158671\pi$
$674$	1.56671e8			0.511691
$675$	1.65265e8			0.537364
$676$	4.81161e7			0.155758
$677$			1.10241e8i			0.355284i	0.984095	+	0.177642i	$0.0568469\pi$
$677$			1.10241e8i			0.355284i	−0.984095	+	0.177642i	$0.943153\pi$
$678$		−	9.20070e7i		−	0.295210i
$679$	6.23697e8			1.99234
$680$			4.56147e8i			1.45070i
$681$			7.48965e7i			0.237149i
$682$	5.46545e8			1.72295
$683$	−3.35495e8			−1.05299			−0.526495	−	0.850178i	$-0.676494\pi$
$683$	−3.35495e8			−1.05299			−0.526495	+	0.850178i	$0.676494\pi$
$684$			1.26040e7i			0.0393860i
$685$	−1.31833e8			−0.410158
$686$	−1.88352e7			−0.0583442
$687$			3.44689e8i			1.06306i
$688$			1.33961e7i			0.0411351i
$689$		−	1.40752e8i		−	0.430324i
$690$	−1.73399e8			−0.527837
$691$		−	2.17186e8i		−	0.658261i	−0.944284	−	0.329131i	$-0.893244\pi$
$691$		−	2.17186e8i		−	0.658261i	0.944284	−	0.329131i	$-0.106756\pi$
$692$	2.32730e7			0.0702320
$693$		−	2.64331e8i		−	0.794233i
$694$	−5.30491e7			−0.158708
$695$	−1.22381e8			−0.364553
$696$		−	1.53416e8i		−	0.455034i
$697$			6.58787e7i			0.194557i
$698$		−	1.41840e8i		−	0.417094i
$699$		−	1.76671e8i		−	0.517290i
$700$	3.10780e8			0.906064
$701$		−	5.51910e8i		−	1.60219i	−0.598536	−	0.801096i	$-0.704251\pi$
$701$		−	5.51910e8i		−	1.60219i	0.598536	−	0.801096i	$-0.295749\pi$
$702$		−	4.22889e7i		−	0.122240i
$703$			1.79134e8i			0.515599i
$704$			3.99679e8i			1.14549i
$705$	1.81473e8	−	3.49676e8i	0.517900	−	0.997925i
$706$	−4.00065e8			−1.13688
$707$	7.10134e8			2.00947
$708$	6.65809e7			0.187607
$709$	1.76237e8			0.494492			0.247246	−	0.968953i	$-0.420474\pi$
$709$	1.76237e8			0.494492			0.247246	+	0.968953i	$0.420474\pi$
$710$			4.18506e8i			1.16930i
$711$	1.57111e8			0.437116
$712$	−3.92201e7			−0.108660
$713$	1.39960e8			0.386132
$714$	2.85430e8			0.784161
$715$		−	6.92927e8i		−	1.89570i
$716$			1.57243e7i			0.0428382i
$717$	−3.28546e8			−0.891332
$718$			3.60174e8i			0.973059i
$719$	−2.94259e8			−0.791667			−0.395834	−	0.918322i	$-0.629544\pi$
$719$	−2.94259e8			−0.791667			−0.395834	+	0.918322i	$0.629544\pi$
$720$			2.85405e8i			0.764652i
$721$	−5.57807e8			−1.48826
$722$	−3.09005e8			−0.821020
$723$	−1.49903e8			−0.396639
$724$		−	1.27093e7i		−	0.0334893i
$725$		−	9.83469e8i		−	2.58075i
$726$	−4.64109e8			−1.21286
$727$		−	2.43309e8i		−	0.633221i	−0.948556	−	0.316611i	$-0.897455\pi$
$727$		−	2.43309e8i		−	0.633221i	0.948556	−	0.316611i	$-0.102545\pi$
$728$			2.63791e8i			0.683699i
$729$	1.43489e7			0.0370370
$730$	1.00782e9			2.59068
$731$			1.19165e7i			0.0305068i
$732$	−9.53776e6			−0.0243172
$733$	6.01663e8			1.52771			0.763856	−	0.645387i	$-0.223304\pi$
$733$	6.01663e8			1.52771			0.763856	+	0.645387i	$0.223304\pi$
$734$		−	1.95080e8i		−	0.493316i
$735$			4.29672e8i			1.08212i
$736$		−	7.66699e7i		−	0.192305i
$737$	−2.14665e8			−0.536239
$738$			3.31141e7i			0.0823842i
$739$	−2.79994e8			−0.693771			−0.346885	−	0.937907i	$-0.612761\pi$
$739$	−2.79994e8			−0.693771			−0.346885	+	0.937907i	$0.612761\pi$
$740$		−	1.84759e8i		−	0.455942i
$741$	−6.85813e7			−0.168559
$742$	4.77524e8			1.16892
$743$		−	3.22211e8i		−	0.785549i	−0.919635	−	0.392775i	$-0.871515\pi$
$743$		−	3.22211e8i		−	0.785549i	0.919635	−	0.392775i	$-0.128485\pi$
$744$		−	1.85068e8i		−	0.449378i
$745$		−	3.07805e8i		−	0.744401i
$746$		−	8.57001e7i		−	0.206426i
$747$	1.80475e8			0.432967
$748$		−	1.44046e8i		−	0.344189i
$749$		−	6.59200e8i		−	1.56882i
$750$			9.43418e8i			2.23625i
$751$			2.19432e8i			0.518060i	0.965869	+	0.259030i	$0.0834028\pi$
$751$			2.19432e8i			0.518060i	−0.965869	+	0.259030i	$0.916597\pi$
$752$	4.44635e8	+	2.30755e8i	1.04556	+	0.542622i
$753$	1.15369e8			0.270213
$754$	−2.51656e8			−0.587074
$755$	−1.55608e9			−3.61570
$756$	2.69831e7			0.0624491
$757$		−	4.81514e7i		−	0.111000i	−0.998459	−	0.0554998i	$-0.982325\pi$
$757$		−	4.81514e7i		−	0.111000i	0.998459	−	0.0554998i	$-0.0176752\pi$
$758$	−7.19274e8			−1.65153
$759$	−1.81637e8			−0.415411
$760$	3.71837e8			0.847055
$761$	−5.53824e7			−0.125666			−0.0628330	−	0.998024i	$-0.520014\pi$
$761$	−5.53824e7			−0.125666			−0.0628330	+	0.998024i	$0.520014\pi$
$762$		−	5.30441e8i		−	1.19887i
$763$			1.12906e9i			2.54181i
$764$	1.53484e8			0.344178
$765$			2.53883e8i			0.567086i
$766$	−8.41231e7			−0.187167
$767$			3.62281e8i			0.802896i
$768$	−1.72742e8			−0.381341
$769$	2.11597e7			0.0465298			0.0232649	−	0.999729i	$-0.492594\pi$
$769$	2.11597e7			0.0465298			0.0232649	+	0.999729i	$0.492594\pi$
$770$	2.35087e9			5.14941
$771$		−	2.80118e8i		−	0.611192i
$772$			8.57692e7i			0.186414i
$773$	1.84898e7			0.0400307			0.0200154	−	0.999800i	$-0.493628\pi$
$773$	1.84898e7			0.0400307			0.0200154	+	0.999800i	$0.493628\pi$
$774$			5.98987e6i			0.0129180i
$775$		−	1.18637e9i		−	2.54868i
$776$	−5.66703e8			−1.21275
$777$	3.83496e8			0.817518
$778$		−	7.28844e8i		−	1.54773i
$779$	5.37023e7			0.113600
$780$	7.07346e7			0.149056
$781$			4.38388e8i			0.920249i
$782$		−	1.96135e8i		−	0.410144i
$783$		−	8.53886e7i		−	0.177875i
$784$	−5.46355e8			−1.13377
$785$			1.87200e8i			0.386988i
$786$	−4.94318e8			−1.01798
$787$		−	4.05624e8i		−	0.832145i	−0.909331	−	0.416072i	$-0.863406\pi$
$787$		−	4.05624e8i		−	0.832145i	0.909331	−	0.416072i	$-0.136594\pi$
$788$	1.45854e8			0.298084
$789$	4.29614e8			0.874676
$790$			1.39729e9i			2.83404i
$791$			3.19435e8i			0.645435i
$792$			2.40176e8i			0.483453i
$793$		−	5.18970e7i		−	0.104069i
$794$	−6.84154e8			−1.36676
$795$			4.24745e8i			0.845331i
$796$			2.67245e7i			0.0529871i
$797$		−	2.75904e8i		−	0.544983i	−0.962158	−	0.272492i	$-0.912152\pi$
$797$		−	2.75904e8i		−	0.544983i	0.962158	−	0.272492i	$-0.0878477\pi$
$798$		−	2.32674e8i		−	0.457866i
$799$	3.95526e8	+	2.05268e8i	0.775416	+	0.402422i
$800$	−6.49890e8			−1.26932
$801$	−2.18291e7			−0.0424755
$802$	−3.03996e8			−0.589311
$803$	1.05570e9			2.03889
$804$		−	2.19132e7i		−	0.0421635i
$805$	6.02016e8			1.15404
$806$	−3.03575e8			−0.579777
$807$	7.66121e7			0.145773
$808$	−6.45241e8			−1.22317
$809$			1.08168e8i			0.204293i	0.994769	+	0.102147i	$0.0325711\pi$
$809$			1.08168e8i			0.204293i	−0.994769	+	0.102147i	$0.967429\pi$
$810$			1.27615e8i			0.240130i
$811$	1.19009e8			0.223109			0.111554	−	0.993758i	$-0.464417\pi$
$811$	1.19009e8			0.223109			0.111554	+	0.993758i	$0.464417\pi$
$812$		−	1.60573e8i		−	0.299919i
$813$	2.89097e8			0.537987
$814$		−	1.02905e9i		−	1.90794i
$815$	1.12222e9			2.07303
$816$	−3.22828e8			−0.594156
$817$	9.71397e6			0.0178127
$818$		−	6.00058e8i		−	1.09631i
$819$			1.46821e8i			0.267261i
$820$	−5.53884e7			−0.100456
$821$			1.04538e9i			1.88906i	0.328422	+	0.944531i	$0.393483\pi$
$821$			1.04538e9i			1.88906i	−0.328422	+	0.944531i	$0.606517\pi$
$822$		−	7.49549e7i		−	0.134954i
$823$	2.84805e8			0.510914			0.255457	−	0.966820i	$-0.417774\pi$
$823$	2.84805e8			0.510914			0.255457	+	0.966820i	$0.417774\pi$
$824$	5.06834e8			0.905908
$825$			1.53964e9i			2.74193i
$826$	−1.22910e9			−2.18096
$827$	7.12594e8			1.25987			0.629935	−	0.776648i	$-0.283081\pi$
$827$	7.12594e8			1.25987			0.629935	+	0.776648i	$0.283081\pi$
$828$		−	1.85416e7i		−	0.0326631i
$829$			8.25830e8i			1.44953i	0.688996	+	0.724765i	$0.258052\pi$
$829$			8.25830e8i			1.44953i	−0.688996	+	0.724765i	$0.741948\pi$
$830$			1.60509e9i			2.80714i
$831$	−5.25738e8			−0.916150
$832$		−	2.21999e8i		−	0.385461i
$833$	−4.86011e8			−0.840835
$834$		−	6.95814e7i		−	0.119948i
$835$	9.71801e8			1.66924
$836$	−1.17422e8			−0.200969
$837$		−	1.03005e8i		−	0.175664i
$838$			6.57919e8i			1.11800i
$839$		−	2.35486e8i		−	0.398730i	−0.979925	−	0.199365i	$-0.936112\pi$
$839$		−	2.35486e8i		−	0.398730i	0.979925	−	0.199365i	$-0.0638879\pi$
$840$		−	7.96039e8i		−	1.34306i
$841$	8.66866e7			0.145735
$842$		−	7.18164e8i		−	1.20306i
$843$		−	2.14823e8i		−	0.358590i
$844$			2.64315e8i			0.439637i
$845$		−	7.90062e8i		−	1.30946i
$846$	1.98812e8	+	1.03179e8i	0.328346	+	0.170404i
$847$	1.61132e9			2.65174
$848$	−5.40090e8			−0.885683
$849$	−6.43301e8			−1.05121
$850$	−1.66254e9			−2.70716
$851$		−	2.63522e8i		−	0.427590i
$852$	−4.47510e7			−0.0723576
$853$	−8.91989e8			−1.43718			−0.718592	−	0.695432i	$-0.755213\pi$
$853$	−8.91989e8			−1.43718			−0.718592	+	0.695432i	$0.755213\pi$
$854$	1.76069e8			0.282690
$855$	2.06957e8			0.331117
$856$			5.98962e8i			0.954945i
$857$		−	7.62079e8i		−	1.21076i	−0.795937	−	0.605379i	$-0.793021\pi$
$857$		−	7.62079e8i		−	1.21076i	0.795937	−	0.605379i	$-0.206979\pi$
$858$	3.93972e8			0.623739
$859$		−	7.76072e8i		−	1.22440i	−0.790704	−	0.612199i	$-0.790285\pi$
$859$		−	7.76072e8i		−	1.22440i	0.790704	−	0.612199i	$-0.209715\pi$
$860$	−1.00190e7			−0.0157517
$861$		−	1.14967e8i		−	0.180121i
$862$	−1.60295e7			−0.0250264
$863$	−8.71479e8			−1.35589			−0.677946	−	0.735112i	$-0.737129\pi$
$863$	−8.71479e8			−1.35589			−0.677946	+	0.735112i	$0.737129\pi$
$864$	−5.64259e7			−0.0874858
$865$		−	3.82141e8i		−	0.590439i
$866$			6.74131e8i			1.03798i
$867$	8.90953e7			0.136709
$868$		−	1.93701e8i		−	0.296191i
$869$			1.46368e9i			2.23041i
$870$	7.59419e8			1.15325
$871$	1.19234e8			0.180446
$872$		−	1.02589e9i		−	1.54721i
$873$	−3.15416e8			−0.474069
$874$	−1.59883e8			−0.239480
$875$		−	3.27541e9i		−	4.88924i
$876$			1.07767e8i			0.160314i
$877$		−	8.70101e8i		−	1.28994i	−0.764206	−	0.644972i	$-0.776869\pi$
$877$		−	8.70101e8i		−	1.28994i	0.764206	−	0.644972i	$-0.223131\pi$
$878$	9.16844e8			1.35460
$879$		−	4.42837e8i		−	0.652045i
$880$	−2.65889e9			−3.90169
$881$			7.68661e8i			1.12411i	0.827101	+	0.562053i	$0.189988\pi$
$881$			7.68661e8i			1.12411i	−0.827101	+	0.562053i	$0.810012\pi$
$882$	−2.44295e8			−0.356048
$883$	−1.51815e8			−0.220513			−0.110256	−	0.993903i	$-0.535167\pi$
$883$	−1.51815e8			−0.220513			−0.110256	+	0.993903i	$0.535167\pi$
$884$			8.00095e7i			0.115820i
$885$		−	1.09325e9i		−	1.57721i
$886$			1.05102e8i			0.151115i
$887$			2.72015e8i			0.389782i	0.980825	+	0.194891i	$0.0624353\pi$
$887$			2.72015e8i			0.389782i	−0.980825	+	0.194891i	$0.937565\pi$
$888$	−3.48452e8			−0.497627
$889$			1.84162e9i			2.62116i
$890$		−	1.94142e8i		−	0.275390i
$891$			1.33677e8i			0.188984i
$892$		−	9.58274e6i		−	0.0135019i
$893$	1.67328e8	−	3.22420e8i	0.234972	−	0.452760i
$894$	1.75006e8			0.244929
$895$	2.58191e8			0.360140
$896$	1.21125e9			1.68388
$897$	1.00889e8			0.139787
$898$			2.46286e8i			0.340104i
$899$	−6.12970e8			−0.843646
$900$	−1.57168e8			−0.215594
$901$	−4.80438e8			−0.656845
$902$	−3.08498e8			−0.420371
$903$		−	2.07959e7i		−	0.0282433i
$904$		−	2.90245e8i		−	0.392879i
$905$	−2.08686e8			−0.281544
$906$		−	8.84729e8i		−	1.18967i
$907$	1.12903e9			1.51315			0.756575	−	0.653907i	$-0.226871\pi$
$907$	1.12903e9			1.51315			0.756575	+	0.653907i	$0.226871\pi$
$908$		−	7.12271e7i		−	0.0951454i
$909$	−3.59129e8			−0.478144
$910$	−1.30578e9			−1.73279
$911$	1.25405e9			1.65867			0.829336	−	0.558749i	$-0.188719\pi$
$911$	1.25405e9			1.65867			0.829336	+	0.558749i	$0.188719\pi$
$912$			2.63159e8i			0.346924i
$913$			1.68134e9i			2.20924i
$914$	−4.97090e8			−0.651023
$915$			1.56609e8i			0.204434i
$916$		−	3.27802e8i		−	0.426506i
$917$	1.71620e9			2.22567
$918$	−1.44348e8			−0.186587
$919$			1.01391e9i			1.30633i	0.757216	+	0.653164i	$0.226559\pi$
$919$			1.01391e9i			1.30633i	−0.757216	+	0.653164i	$0.773441\pi$
$920$	−5.47004e8			−0.702469
$921$	1.48556e8			0.190156
$922$			9.28424e8i			1.18455i
$923$		−	2.43500e8i		−	0.309666i
$924$			2.51380e8i			0.318651i
$925$	−2.23374e9			−2.82232
$926$			2.87039e8i			0.361500i
$927$	2.82094e8			0.354124
$928$			3.35784e8i			0.420161i
$929$	−1.98176e7			−0.0247175			−0.0123587	−	0.999924i	$-0.503934\pi$
$929$	−1.98176e7			−0.0247175			−0.0123587	+	0.999924i	$0.503934\pi$
$930$	9.16095e8			1.13892
$931$			3.96181e8i			0.490958i
$932$			1.68015e8i			0.207540i
$933$		−	5.31077e8i		−	0.653901i
$934$			3.27848e8i			0.402376i
$935$	−2.36522e9			−2.89359
$936$		−	1.33404e8i		−	0.162683i
$937$			4.15710e8i			0.505326i	0.967554	+	0.252663i	$0.0813063\pi$
$937$			4.15710e8i			0.505326i	−0.967554	+	0.252663i	$0.918694\pi$
$938$			4.04522e8i			0.490155i
$939$			6.77517e8i			0.818321i
$940$	−1.72582e8	+	3.32544e8i	−0.207784	+	0.400374i
$941$	1.17539e8			0.141063			0.0705315	−	0.997510i	$-0.477530\pi$
$941$	1.17539e8			0.141063			0.0705315	+	0.997510i	$0.477530\pi$
$942$	−1.06435e8			−0.127330
$943$	−7.90007e7			−0.0942097
$944$	1.39014e9			1.65250
$945$		−	4.43060e8i		−	0.525009i
$946$	−5.58028e7			−0.0659148
$947$	1.01799e9			1.19866			0.599329	−	0.800503i	$-0.295434\pi$
$947$	1.01799e9			1.19866			0.599329	+	0.800503i	$0.295434\pi$
$948$	−1.49413e8			−0.175374
$949$	−5.86381e8			−0.686090
$950$			1.35525e9i			1.58069i
$951$		−	2.43574e8i		−	0.283197i
$952$	9.00417e8			1.04360
$953$			1.33609e9i			1.54368i	0.635814	+	0.771842i	$0.280664\pi$
$953$			1.33609e9i			1.54368i	−0.635814	+	0.771842i	$0.719336\pi$
$954$	−2.41493e8			−0.278138
$955$		−	2.52019e9i		−	2.89350i
$956$	3.12450e8			0.357607
$957$	7.95497e8			0.907618
$958$	1.68283e8			0.191401
$959$			2.60232e8i			0.295057i
$960$			6.69924e8i			0.757203i
$961$	1.48071e8			0.166840
$962$			5.71581e8i			0.642026i
$963$			3.33371e8i			0.373292i
$964$	1.42559e8			0.159134
$965$	1.40832e9			1.56718
$966$			3.42283e8i			0.379712i
$967$	1.42961e9			1.58103			0.790513	−	0.612445i	$-0.209814\pi$
$967$	1.42961e9			1.58103			0.790513	+	0.612445i	$0.209814\pi$
$968$	−1.46408e9			−1.61413
$969$			2.34094e8i			0.257287i
$970$		−	2.80521e9i		−	3.07362i
$971$			1.16744e9i			1.27520i	0.770368	+	0.637600i	$0.220073\pi$
$971$			1.16744e9i			1.27520i	−0.770368	+	0.637600i	$0.779927\pi$
$972$	−1.36459e7			−0.0148595
$973$			2.41576e8i			0.262250i
$974$	7.55208e8			0.817316
$975$		−	8.55183e8i		−	0.922667i
$976$	−1.99138e8			−0.214193
$977$	8.83211e8			0.947067			0.473534	−	0.880776i	$-0.342978\pi$
$977$	8.83211e8			0.947067			0.473534	+	0.880776i	$0.342978\pi$
$978$			6.38052e8i			0.682087i
$979$		−	2.03365e8i		−	0.216734i
$980$		−	4.08620e8i		−	0.434152i
$981$		−	5.70989e8i		−	0.604813i
$982$	−1.37830e9			−1.45549
$983$			1.48935e9i			1.56797i	0.620782	+	0.783983i	$0.286815\pi$
$983$			1.48935e9i			1.56797i	−0.620782	+	0.783983i	$0.713185\pi$
$984$			1.04462e8i			0.109641i
$985$		−	2.39490e9i		−	2.50599i
$986$			8.58996e8i			0.896108i
$987$	−6.90247e8	−	3.58221e8i	−0.717882	−	0.372563i
$988$	6.52212e7			0.0676267
$989$	−1.42901e7			−0.0147722
$990$	−1.18888e9			−1.22528
$991$	−1.49117e9			−1.53217			−0.766083	−	0.642741i	$-0.777797\pi$
$991$	−1.49117e9			−1.53217			−0.766083	+	0.642741i	$0.777797\pi$
$992$			4.05059e8i			0.414938i
$993$	−2.42665e8			−0.247833
$994$	8.26115e8			0.841165
$995$	4.38813e8			0.445462
$996$	−1.71633e8			−0.173709
$997$		−	1.86771e9i		−	1.88462i	−0.334738	−	0.942311i	$-0.608648\pi$
$997$		−	1.86771e9i		−	1.88462i	0.334738	−	0.942311i	$-0.391352\pi$
$998$		−	1.38569e9i		−	1.39403i
$999$	−1.93941e8			−0.194524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	141.7.d.a.46.11	✓	48
47.46	odd	2	inner	141.7.d.a.46.12	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
141.7.d.a.46.11	✓	48	1.1	even	1	trivial
141.7.d.a.46.12	yes	48	47.46	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 141 = 3 \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	141.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-8.87833 q^{2} -15.5885 q^{3} +14.8247 q^{4} -243.420i q^{5} +138.399 q^{6} -480.503 q^{7} +436.594 q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-8.87833 q^{2} -15.5885 q^{3} +14.8247 q^{4} -243.420i q^{5} +138.399 q^{6} -480.503 q^{7} +436.594 q^{8} +243.000 q^{9} +2161.17i q^{10} +2263.84i q^{11} -231.095 q^{12} -1257.43i q^{13} +4266.06 q^{14} +3794.55i q^{15} -4825.01 q^{16} -4292.10 q^{17} -2157.43 q^{18} +3498.78i q^{19} -3608.64i q^{20} +7490.30 q^{21} -20099.1i q^{22} -5147.01i q^{23} -6805.83 q^{24} -43628.5 q^{25} +11163.9i q^{26} -3788.00 q^{27} -7123.32 q^{28} +22541.9i q^{29} -33689.3i q^{30} +27192.5i q^{31} +14896.0 q^{32} -35289.7i q^{33} +38106.7 q^{34} +116964. i q^{35} +3602.41 q^{36} +51199.0 q^{37} -31063.3i q^{38} +19601.5i q^{39} -106276. i q^{40} -15348.8i q^{41} -66501.3 q^{42} -2776.39i q^{43} +33560.8i q^{44} -59151.2i q^{45} +45696.9i q^{46} +(-92152.1 - 47824.7i) q^{47} +75214.5 q^{48} +113234. q^{49} +387348. q^{50} +66907.2 q^{51} -18641.1i q^{52} +111935. q^{53} +33631.1 q^{54} +551064. q^{55} -209785. q^{56} -54540.6i q^{57} -200134. i q^{58} -288111. q^{59} +56253.1i q^{60} +41272.1 q^{61} -241424. i q^{62} -116762. q^{63} +176549. q^{64} -306085. q^{65} +313314. i q^{66} +94823.3i q^{67} -63629.2 q^{68} +80234.0i q^{69} -1.03845e6i q^{70} +193648. q^{71} +106092. q^{72} -466331. i q^{73} -454561. q^{74} +680101. q^{75} +51868.5i q^{76} -1.08778e6i q^{77} -174028. i q^{78} +646546. q^{79} +1.17451e6i q^{80} +59049.0 q^{81} +136272. i q^{82} +742695. q^{83} +111042. q^{84} +1.04478e6i q^{85} +24649.7i q^{86} -351393. i q^{87} +988379. i q^{88} -89831.8 q^{89} +525164. i q^{90} +604201. i q^{91} -76303.1i q^{92} -423889. i q^{93} +(818157. + 424604. i) q^{94} +851675. q^{95} -232206. q^{96} -1.29801e6 q^{97} -1.00533e6 q^{98} +550113. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 1404 q^{4} + 324 q^{6} - 288 q^{7} - 1932 q^{8} + 11664 q^{9}+O(q^{10}) \) 48 * q + 1404 * q^4 + 324 * q^6 - 288 * q^7 - 1932 * q^8 + 11664 * q^9	\( 48 q + 1404 q^{4} + 324 q^{6} - 288 q^{7} - 1932 q^{8} + 11664 q^{9} + 1944 q^{12} - 18964 q^{14} + 48060 q^{16} - 288 q^{17} + 5184 q^{24} - 187440 q^{25} - 30312 q^{28} - 182548 q^{32} - 109920 q^{34} + 341172 q^{36} - 12096 q^{37} + 215460 q^{42} + 115768 q^{47} + 124416 q^{48} + 779904 q^{49} + 887340 q^{50} - 2592 q^{51} + 63504 q^{53} + 78732 q^{54} + 127248 q^{55} - 2002264 q^{56} + 165216 q^{59} + 955440 q^{61} - 69984 q^{63} + 1815660 q^{64} + 30000 q^{65} + 776648 q^{68} - 1109040 q^{71} - 469476 q^{72} - 376692 q^{74} + 1842912 q^{75} - 1523712 q^{79} + 2834352 q^{81} + 406064 q^{83} - 1423008 q^{84} - 5383968 q^{89} + 5556972 q^{94} + 3809952 q^{95} + 2079432 q^{96} - 2085840 q^{97} - 2907180 q^{98}+O(q^{100}) \) 48 * q + 1404 * q^4 + 324 * q^6 - 288 * q^7 - 1932 * q^8 + 11664 * q^9 + 1944 * q^12 - 18964 * q^14 + 48060 * q^16 - 288 * q^17 + 5184 * q^24 - 187440 * q^25 - 30312 * q^28 - 182548 * q^32 - 109920 * q^34 + 341172 * q^36 - 12096 * q^37 + 215460 * q^42 + 115768 * q^47 + 124416 * q^48 + 779904 * q^49 + 887340 * q^50 - 2592 * q^51 + 63504 * q^53 + 78732 * q^54 + 127248 * q^55 - 2002264 * q^56 + 165216 * q^59 + 955440 * q^61 - 69984 * q^63 + 1815660 * q^64 + 30000 * q^65 + 776648 * q^68 - 1109040 * q^71 - 469476 * q^72 - 376692 * q^74 + 1842912 * q^75 - 1523712 * q^79 + 2834352 * q^81 + 406064 * q^83 - 1423008 * q^84 - 5383968 * q^89 + 5556972 * q^94 + 3809952 * q^95 + 2079432 * q^96 - 2085840 * q^97 - 2907180 * q^98

Introduction

L-functions

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