LMFDB - Embedded newform 22.7.b.a.21.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,7,Mod(21,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("22.21");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	22.b (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:	$5.06118983964$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 1781x^{4} + 14500x^{3} + 786532x^{2} - 11444432x + 42080676 $ x^6 - 2x^5 - 1781x^4 + 14500x^3 + 786532x^2 - 11444432*x + 42080676
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.1
Root			$-32.5131 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.7.b.a.21.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5.65685i q^{2} -41.5131 q^{3} -32.0000 q^{4} +155.573 q^{5} +234.833i q^{6} +562.567i q^{7} +181.019i q^{8} +994.336 q^{9} +O(q^{10})$	\(q-5.65685i q^{2} -41.5131 q^{3} -32.0000 q^{4} +155.573 q^{5} +234.833i q^{6} +562.567i q^{7} +181.019i q^{8} +994.336 q^{9} -880.056i q^{10} +(-1173.59 - 627.888i) q^{11} +1328.42 q^{12} +3272.55i q^{13} +3182.36 q^{14} -6458.33 q^{15} +1024.00 q^{16} -1751.31i q^{17} -5624.81i q^{18} +8806.02i q^{19} -4978.35 q^{20} -23353.9i q^{21} +(-3551.87 + 6638.84i) q^{22} -4919.08 q^{23} -7514.67i q^{24} +8578.08 q^{25} +18512.4 q^{26} -11014.9 q^{27} -18002.1i q^{28} +15064.6i q^{29} +36533.8i q^{30} -4422.42 q^{31} -5792.62i q^{32} +(48719.4 + 26065.6i) q^{33} -9906.88 q^{34} +87520.4i q^{35} -31818.8 q^{36} -27378.8 q^{37} +49814.4 q^{38} -135854. i q^{39} +28161.8i q^{40} -40130.1i q^{41} -132110. q^{42} -13388.3i q^{43} +(37554.9 + 20092.4i) q^{44} +154692. q^{45} +27826.5i q^{46} +125948. q^{47} -42509.4 q^{48} -198832. q^{49} -48524.9i q^{50} +72702.1i q^{51} -104722. i q^{52} +100119. q^{53} +62309.8i q^{54} +(-182580. - 97682.6i) q^{55} -101835. q^{56} -365565. i q^{57} +85218.0 q^{58} -337180. q^{59} +206667. q^{60} -53782.3i q^{61} +25017.0i q^{62} +559380. i q^{63} -32768.0 q^{64} +509122. i q^{65} +(147449. - 275599. i) q^{66} +153989. q^{67} +56041.8i q^{68} +204206. q^{69} +495090. q^{70} +118037. q^{71} +179994. i q^{72} +402389. i q^{73} +154878. i q^{74} -356102. q^{75} -281793. i q^{76} +(353229. - 660224. i) q^{77} -768505. q^{78} -561206. i q^{79} +159307. q^{80} -267608. q^{81} -227010. q^{82} +569941. i q^{83} +747324. i q^{84} -272456. i q^{85} -75735.6 q^{86} -625376. i q^{87} +(113660. - 212443. i) q^{88} +805884. q^{89} -875071. i q^{90} -1.84103e6 q^{91} +157411. q^{92} +183588. q^{93} -712469. i q^{94} +1.36998e6i q^{95} +240469. i q^{96} +1.00183e6 q^{97} +1.12477e6i q^{98} +(-1.16694e6 - 624331. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 52 q^{3} - 192 q^{4} + 368 q^{5} - 346 q^{9}+O(q^{10}) $ 6 * q - 52 * q^3 - 192 * q^4 + 368 * q^5 - 346 * q^9	$ 6 q - 52 q^{3} - 192 q^{4} + 368 q^{5} - 346 q^{9} - 1166 q^{11} + 1664 q^{12} + 2208 q^{14} - 6512 q^{15} + 6144 q^{16} - 11776 q^{20} + 1056 q^{22} + 2156 q^{23} + 59862 q^{25} - 1824 q^{26} - 57472 q^{27} - 78468 q^{31} + 142208 q^{33} + 28704 q^{34} + 11072 q^{36} - 205920 q^{37} + 101472 q^{38} - 344160 q^{42} + 37312 q^{44} + 368716 q^{45} + 493460 q^{47} - 53248 q^{48} - 270762 q^{49} - 531700 q^{53} + 274956 q^{55} - 70656 q^{56} + 509184 q^{58} - 833380 q^{59} + 208384 q^{60} - 196608 q^{64} + 193248 q^{66} + 537420 q^{67} + 398860 q^{69} + 96096 q^{70} - 460372 q^{71} - 211428 q^{75} + 249744 q^{77} - 1866912 q^{78} + 376832 q^{80} + 485654 q^{81} + 428640 q^{82} + 1055808 q^{86} - 33792 q^{88} + 2377952 q^{89} - 5068656 q^{91} - 68992 q^{92} + 699868 q^{93} + 1351632 q^{97} - 2470930 q^{99}+O(q^{100}) $ 6 * q - 52 * q^3 - 192 * q^4 + 368 * q^5 - 346 * q^9 - 1166 * q^11 + 1664 * q^12 + 2208 * q^14 - 6512 * q^15 + 6144 * q^16 - 11776 * q^20 + 1056 * q^22 + 2156 * q^23 + 59862 * q^25 - 1824 * q^26 - 57472 * q^27 - 78468 * q^31 + 142208 * q^33 + 28704 * q^34 + 11072 * q^36 - 205920 * q^37 + 101472 * q^38 - 344160 * q^42 + 37312 * q^44 + 368716 * q^45 + 493460 * q^47 - 53248 * q^48 - 270762 * q^49 - 531700 * q^53 + 274956 * q^55 - 70656 * q^56 + 509184 * q^58 - 833380 * q^59 + 208384 * q^60 - 196608 * q^64 + 193248 * q^66 + 537420 * q^67 + 398860 * q^69 + 96096 * q^70 - 460372 * q^71 - 211428 * q^75 + 249744 * q^77 - 1866912 * q^78 + 376832 * q^80 + 485654 * q^81 + 428640 * q^82 + 1055808 * q^86 - 33792 * q^88 + 2377952 * q^89 - 5068656 * q^91 - 68992 * q^92 + 699868 * q^93 + 1351632 * q^97 - 2470930 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/22\mathbb{Z}\right)^\times$.

$n$	$13$
$\chi(n)$	$-1$

Coefficient data

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

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

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

$2$		−	5.65685i		−	0.707107i
$2$		−	5.65685i		−	0.707107i
$3$	−41.5131			−1.53752			−0.768761	−	0.639536i	$-0.779126\pi$
$3$	−41.5131			−1.53752			−0.768761	+	0.639536i	$0.779126\pi$
$4$	−32.0000			−0.500000
$5$	155.573			1.24459			0.622294	−	0.782784i	$-0.286201\pi$
$5$	155.573			1.24459			0.622294	+	0.782784i	$0.286201\pi$
$6$			234.833i			1.08719i
$7$			562.567i			1.64014i	0.572266	+	0.820068i	$0.306065\pi$
$7$			562.567i			1.64014i	−0.572266	+	0.820068i	$0.693935\pi$
$8$			181.019i			0.353553i
$9$	994.336			1.36397
$10$		−	880.056i		−	0.880056i
$11$	−1173.59	−	627.888i	−0.881737	−	0.471741i
$11$	−1173.59	−	627.888i	−0.881737	−	0.471741i
$12$	1328.42			0.768761
$13$			3272.55i			1.48956i	0.667313	+	0.744778i	$0.267444\pi$
$13$			3272.55i			1.48956i	−0.667313	+	0.744778i	$0.732556\pi$
$14$	3182.36			1.15975
$15$	−6458.33			−1.91358
$16$	1024.00			0.250000
$17$		−	1751.31i		−	0.356463i	−0.983989	−	0.178232i	$-0.942962\pi$
$17$		−	1751.31i		−	0.356463i	0.983989	−	0.178232i	$-0.0570377\pi$
$18$		−	5624.81i		−	0.964474i
$19$			8806.02i			1.28386i	0.766762	+	0.641932i	$0.221867\pi$
$19$			8806.02i			1.28386i	−0.766762	+	0.641932i	$0.778133\pi$
$20$	−4978.35			−0.622294
$21$		−	23353.9i		−	2.52175i
$22$	−3551.87	+	6638.84i	−0.333572	+	0.623482i
$23$	−4919.08			−0.404297			−0.202148	−	0.979355i	$-0.564792\pi$
$23$	−4919.08			−0.404297			−0.202148	+	0.979355i	$0.564792\pi$
$24$		−	7514.67i		−	0.543596i
$25$	8578.08			0.548997
$26$	18512.4			1.05327
$27$	−11014.9			−0.559616
$28$		−	18002.1i		−	0.820068i
$29$			15064.6i			0.617678i	0.951114	+	0.308839i	$0.0999405\pi$
$29$			15064.6i			0.617678i	−0.951114	+	0.308839i	$0.900060\pi$
$30$			36533.8i			1.35310i
$31$	−4422.42			−0.148448			−0.0742240	−	0.997242i	$-0.523648\pi$
$31$	−4422.42			−0.148448			−0.0742240	+	0.997242i	$0.523648\pi$
$32$		−	5792.62i		−	0.176777i
$33$	48719.4	+	26065.6i	1.35569	+	0.725313i
$34$	−9906.88			−0.252058
$35$			87520.4i			2.04129i
$36$	−31818.8			−0.681986
$37$	−27378.8			−0.540517			−0.270259	−	0.962788i	$-0.587109\pi$
$37$	−27378.8			−0.540517			−0.270259	+	0.962788i	$0.587109\pi$
$38$	49814.4			0.907829
$39$		−	135854.i		−	2.29022i
$40$			28161.8i			0.440028i
$41$		−	40130.1i		−	0.582262i	−0.956683	−	0.291131i	$-0.905968\pi$
$41$		−	40130.1i		−	0.582262i	0.956683	−	0.291131i	$-0.0940316\pi$
$42$	−132110.			−1.78314
$43$		−	13388.3i		−	0.168391i	−0.996449	−	0.0841957i	$-0.973168\pi$
$43$		−	13388.3i		−	0.168391i	0.996449	−	0.0841957i	$-0.0268321\pi$
$44$	37554.9	+	20092.4i	0.440868	+	0.235871i
$45$	154692.			1.69758
$46$			27826.5i			0.285881i
$47$	125948.			1.21310			0.606551	−	0.795045i	$-0.292553\pi$
$47$	125948.			1.21310			0.606551	+	0.795045i	$0.292553\pi$
$48$	−42509.4			−0.384380
$49$	−198832.			−1.69005
$50$		−	48524.9i		−	0.388199i
$51$			72702.1i			0.548070i
$52$		−	104722.i		−	0.744778i
$53$	100119.			0.672497			0.336249	−	0.941773i	$-0.390842\pi$
$53$	100119.			0.672497			0.336249	+	0.941773i	$0.390842\pi$
$54$			62309.8i			0.395708i
$55$	−182580.	−	97682.6i	−1.09740	−	0.587123i
$56$	−101835.			−0.579876
$57$		−	365565.i		−	1.97397i
$58$	85218.0			0.436765
$59$	−337180.			−1.64175			−0.820873	−	0.571110i	$-0.806513\pi$
$59$	−337180.			−1.64175			−0.820873	+	0.571110i	$0.806513\pi$
$60$	206667.			0.956790
$61$		−	53782.3i		−	0.236946i	−0.992957	−	0.118473i	$-0.962200\pi$
$61$		−	53782.3i		−	0.236946i	0.992957	−	0.118473i	$-0.0377999\pi$
$62$			25017.0i			0.104969i
$63$			559380.i			2.23710i
$64$	−32768.0			−0.125000
$65$			509122.i			1.85388i
$66$	147449.	−	275599.i	0.512873	−	0.958617i
$67$	153989.			0.511993			0.255997	−	0.966678i	$-0.417596\pi$
$67$	153989.			0.511993			0.255997	+	0.966678i	$0.417596\pi$
$68$			56041.8i			0.178232i
$69$	204206.			0.621615
$70$	495090.			1.44341
$71$	118037.			0.329795			0.164897	−	0.986311i	$-0.447271\pi$
$71$	118037.			0.329795			0.164897	+	0.986311i	$0.447271\pi$
$72$			179994.i			0.482237i
$73$			402389.i			1.03437i	0.855873	+	0.517187i	$0.173021\pi$
$73$			402389.i			1.03437i	−0.855873	+	0.517187i	$0.826979\pi$
$74$			154878.i			0.382203i
$75$	−356102.			−0.844095
$76$		−	281793.i		−	0.641932i
$77$	353229.	−	660224.i	0.773720	−	1.44617i
$78$	−768505.			−1.61943
$79$		−	561206.i		−	1.13826i	−0.822248	−	0.569129i	$-0.807280\pi$
$79$		−	561206.i		−	1.13826i	0.822248	−	0.569129i	$-0.192720\pi$
$80$	159307.			0.311147
$81$	−267608.			−0.503552
$82$	−227010.			−0.411722
$83$			569941.i			0.996771i	0.866955	+	0.498386i	$0.166074\pi$
$83$			569941.i			0.996771i	−0.866955	+	0.498386i	$0.833926\pi$
$84$			747324.i			1.26087i
$85$		−	272456.i		−	0.443650i
$86$	−75735.6			−0.119071
$87$		−	625376.i		−	0.949694i
$88$	113660.	−	212443.i	0.166786	−	0.311741i
$89$	805884.			1.14315			0.571574	−	0.820550i	$-0.306333\pi$
$89$	805884.			1.14315			0.571574	+	0.820550i	$0.306333\pi$
$90$		−	875071.i		−	1.20037i
$91$	−1.84103e6			−2.44307
$92$	157411.			0.202148
$93$	183588.			0.228242
$94$		−	712469.i		−	0.857793i
$95$			1.36998e6i			1.59788i
$96$			240469.i			0.271798i
$97$	1.00183e6			1.09769			0.548844	−	0.835925i	$-0.315068\pi$
$97$	1.00183e6			1.09769			0.548844	+	0.835925i	$0.315068\pi$
$98$			1.12477e6i			1.19504i
$99$	−1.16694e6	−	624331.i	−1.20266	−	0.643442i
$100$	−274498.			−0.274498
$101$		−	320013.i		−	0.310601i	−0.987867	−	0.155301i	$-0.950365\pi$
$101$		−	320013.i		−	0.310601i	0.987867	−	0.155301i	$-0.0496346\pi$
$102$	411265.			0.387544
$103$	1.88724e6			1.72709			0.863547	−	0.504268i	$-0.168238\pi$
$103$	1.88724e6			1.72709			0.863547	+	0.504268i	$0.168238\pi$
$104$	−592395.			−0.526637
$105$		−	3.63324e6i		−	3.13853i
$106$		−	566361.i		−	0.475528i
$107$			1.21527e6i			0.992025i	0.868315	+	0.496012i	$0.165203\pi$
$107$			1.21527e6i			0.992025i	−0.868315	+	0.496012i	$0.834797\pi$
$108$	352477.			0.279808
$109$			747494.i			0.577203i	0.957449	+	0.288601i	$0.0931902\pi$
$109$			747494.i			0.577203i	−0.957449	+	0.288601i	$0.906810\pi$
$110$	−552576.	+	1.03283e6i	−0.415159	+	0.775978i
$111$	1.13658e6			0.831057
$112$			576068.i			0.410034i
$113$	599923.			0.415777			0.207888	−	0.978153i	$-0.433341\pi$
$113$	599923.			0.415777			0.207888	+	0.978153i	$0.433341\pi$
$114$	−2.06795e6			−1.39581
$115$	−765278.			−0.503183
$116$		−	482066.i		−	0.308839i
$117$			3.25402e6i			2.03171i
$118$			1.90738e6i			1.16089i
$119$	985226.			0.584649
$120$		−	1.16908e6i		−	0.676552i
$121$	983075.	+	1.47377e6i	0.554920	+	0.831904i
$122$	−304239.			−0.167546
$123$			1.66592e6i			0.895241i
$124$	141517.			0.0742240
$125$	−1.09631e6			−0.561313
$126$	3.16433e6			1.58187
$127$		−	2.88684e6i		−	1.40933i	−0.709541	−	0.704664i	$-0.751098\pi$
$127$		−	2.88684e6i		−	1.40933i	0.709541	−	0.704664i	$-0.248902\pi$
$128$			185364.i			0.0883883i
$129$			555789.i			0.258905i
$130$	2.88003e6			1.31089
$131$		−	1.00234e6i		−	0.445863i	−0.974834	−	0.222932i	$-0.928437\pi$
$131$		−	1.00234e6i		−	0.445863i	0.974834	−	0.222932i	$-0.0715626\pi$
$132$	−1.55902e6	−	834098.i	−0.677845	−	0.362656i
$133$	−4.95398e6			−2.10571
$134$		−	871091.i		−	0.362034i
$135$	−1.71363e6			−0.696490
$136$	317020.			0.126029
$137$	−415951.			−0.161764			−0.0808818	−	0.996724i	$-0.525774\pi$
$137$	−415951.			−0.161764			−0.0808818	+	0.996724i	$0.525774\pi$
$138$		−	1.15516e6i		−	0.439548i
$139$		−	3.13482e6i		−	1.16726i	−0.812019	−	0.583631i	$-0.801632\pi$
$139$		−	3.13482e6i		−	1.16726i	0.812019	−	0.583631i	$-0.198368\pi$
$140$		−	2.80065e6i		−	1.02065i
$141$	−5.22848e6			−1.86517
$142$		−	667720.i		−	0.233200i
$143$	2.05480e6	−	3.84064e6i	0.702685	−	1.31340i
$144$	1.01820e6			0.340993
$145$			2.34364e6i			0.768755i
$146$	2.27626e6			0.731413
$147$	8.25415e6			2.59849
$148$	876122.			0.270259
$149$			1.12693e6i			0.340675i	0.985386	+	0.170337i	$0.0544857\pi$
$149$			1.12693e6i			0.340675i	−0.985386	+	0.170337i	$0.945514\pi$
$150$			2.01442e6i			0.596865i
$151$			5.47157e6i			1.58921i	0.607127	+	0.794605i	$0.292322\pi$
$151$			5.47157e6i			1.58921i	−0.607127	+	0.794605i	$0.707678\pi$
$152$	−1.59406e6			−0.453914
$153$		−	1.74139e6i		−	0.486206i
$154$	−3.73479e6	−	1.99816e6i	−1.02260	−	0.547103i
$155$	−688010.			−0.184756
$156$			4.34732e6i			1.14511i
$157$	−5.05000e6			−1.30495			−0.652473	−	0.757812i	$-0.726268\pi$
$157$	−5.05000e6			−1.30495			−0.652473	+	0.757812i	$0.726268\pi$
$158$	−3.17466e6			−0.804870
$159$	−4.15627e6			−1.03398
$160$		−	901177.i		−	0.220014i
$161$		−	2.76731e6i		−	0.663102i
$162$			1.51382e6i			0.356065i
$163$	3.61048e6			0.833686			0.416843	−	0.908979i	$-0.363137\pi$
$163$	3.61048e6			0.833686			0.416843	+	0.908979i	$0.363137\pi$
$164$			1.28416e6i			0.291131i
$165$	7.57944e6	+	4.05511e6i	1.68727	+	0.902715i
$166$	3.22407e6			0.704824
$167$		−	8.85321e6i		−	1.90086i	−0.310932	−	0.950432i	$-0.600641\pi$
$167$		−	8.85321e6i		−	1.90086i	0.310932	−	0.950432i	$-0.399359\pi$
$168$	4.22750e6			0.891572
$169$	−5.88279e6			−1.21877
$170$	−1.54125e6			−0.313708
$171$			8.75614e6i			1.75116i
$172$			428425.i			0.0841957i
$173$		−	2.78711e6i		−	0.538290i	−0.963100	−	0.269145i	$-0.913259\pi$
$173$		−	2.78711e6i		−	0.538290i	0.963100	−	0.269145i	$-0.0867410\pi$
$174$	−3.53766e6			−0.671535
$175$			4.82574e6i			0.900430i
$176$	−1.20176e6	−	642957.i	−0.220434	−	0.117935i
$177$	1.39974e7			2.52422
$178$		−	4.55877e6i		−	0.808328i
$179$	2.05899e6			0.359001			0.179501	−	0.983758i	$-0.442552\pi$
$179$	2.05899e6			0.359001			0.179501	+	0.983758i	$0.442552\pi$
$180$	−4.95015e6			−0.848791
$181$	2.44164e6			0.411762			0.205881	−	0.978577i	$-0.433994\pi$
$181$	2.44164e6			0.411762			0.205881	+	0.978577i	$0.433994\pi$
$182$			1.04144e7i			1.72751i
$183$			2.23267e6i			0.364310i
$184$		−	890449.i		−	0.142941i
$185$	−4.25941e6			−0.672720
$186$		−	1.03853e6i		−	0.161391i
$187$	−1.09962e6	+	2.05532e6i	−0.168159	+	0.314307i
$188$	−4.03033e6			−0.606551
$189$		−	6.19663e6i		−	0.917846i
$190$	7.74979e6			1.12987
$191$	1.46170e6			0.209778			0.104889	−	0.994484i	$-0.466551\pi$
$191$	1.46170e6			0.209778			0.104889	+	0.994484i	$0.466551\pi$
$192$	1.36030e6			0.192190
$193$			7.05871e6i			0.981869i	0.871196	+	0.490935i	$0.163345\pi$
$193$			7.05871e6i			0.981869i	−0.871196	+	0.490935i	$0.836655\pi$
$194$		−	5.66721e6i		−	0.776183i
$195$		−	2.11352e7i		−	2.85038i
$196$	6.36264e6			0.845024
$197$			8.27203e6i			1.08197i	0.841034	+	0.540983i	$0.181948\pi$
$197$			8.27203e6i			1.08197i	−0.841034	+	0.540983i	$0.818052\pi$
$198$	−3.53175e6	+	6.60124e6i	−0.454982	+	0.850413i
$199$	−1.24256e6			−0.157673			−0.0788366	−	0.996888i	$-0.525121\pi$
$199$	−1.24256e6			−0.157673			−0.0788366	+	0.996888i	$0.525121\pi$
$200$			1.55280e6i			0.194100i
$201$	−6.39254e6			−0.787201
$202$	−1.81027e6			−0.219628
$203$	−8.47482e6			−1.01308
$204$		−	2.32647e6i		−	0.274035i
$205$		−	6.24318e6i		−	0.724676i
$206$		−	1.06759e7i		−	1.22124i
$207$	−4.89122e6			−0.551450
$208$			3.35109e6i			0.372389i
$209$	5.52919e6	−	1.03347e7i	0.605652	−	1.13203i
$210$	−2.05527e7			−2.21928
$211$			1.63465e7i			1.74011i	0.492953	+	0.870056i	$0.335917\pi$
$211$			1.63465e7i			1.74011i	−0.492953	+	0.870056i	$0.664083\pi$
$212$	−3.20382e6			−0.336249
$213$	−4.90009e6			−0.507067
$214$	6.87462e6			0.701467
$215$		−	2.08286e6i		−	0.209578i
$216$		−	1.99391e6i		−	0.197854i
$217$		−	2.48790e6i		−	0.243475i
$218$	4.22847e6			0.408144
$219$		−	1.67044e7i		−	1.59037i
$220$	5.84255e6	+	3.12584e6i	0.548699	+	0.293562i
$221$	5.73124e6			0.530972
$222$		−	6.42946e6i		−	0.587646i
$223$	1.29219e7			1.16523			0.582615	−	0.812748i	$-0.302030\pi$
$223$	1.29219e7			1.16523			0.582615	+	0.812748i	$0.302030\pi$
$224$	3.25874e6			0.289938
$225$	8.52949e6			0.748817
$226$		−	3.39368e6i		−	0.293998i
$227$		−	4.31943e6i		−	0.369274i	−0.982807	−	0.184637i	$-0.940889\pi$
$227$		−	4.31943e6i		−	0.369274i	0.982807	−	0.184637i	$-0.0591109\pi$
$228$			1.16981e7i			0.986984i
$229$	−1.73096e7			−1.44138			−0.720692	−	0.693255i	$-0.756176\pi$
$229$	−1.73096e7			−1.44138			−0.720692	+	0.693255i	$0.756176\pi$
$230$			4.32907e6i			0.355804i
$231$	−1.46636e7	+	2.74079e7i	−1.18961	+	2.22352i
$232$	−2.72698e6			−0.218382
$233$			1.81640e7i			1.43596i	0.696063	+	0.717981i	$0.254933\pi$
$233$			1.81640e7i			1.43596i	−0.696063	+	0.717981i	$0.745067\pi$
$234$	1.84075e7			1.43664
$235$	1.95941e7			1.50981
$236$	1.07898e7			0.820873
$237$			2.32974e7i			1.75010i
$238$		−	5.57328e6i		−	0.413409i
$239$			1.63745e6i			0.119943i	0.998200	+	0.0599716i	$0.0191010\pi$
$239$			1.63745e6i			0.119943i	−0.998200	+	0.0599716i	$0.980899\pi$
$240$	−6.61333e6			−0.478395
$241$		−	1.08289e7i		−	0.773633i	−0.922157	−	0.386816i	$-0.873575\pi$
$241$		−	1.08289e7i		−	0.773633i	0.922157	−	0.386816i	$-0.126425\pi$
$242$	8.33689e6	−	5.56111e6i	0.588245	−	0.392388i
$243$	1.91391e7			1.33384
$244$			1.72103e6i			0.118473i
$245$	−3.09330e7			−2.10341
$246$	9.42389e6			0.633031
$247$	−2.88182e7			−1.91239
$248$		−	800543.i		−	0.0524843i
$249$		−	2.36600e7i		−	1.53256i
$250$			6.20169e6i			0.396908i
$251$	1.79196e7			1.13320			0.566601	−	0.823993i	$-0.308258\pi$
$251$	1.79196e7			1.13320			0.566601	+	0.823993i	$0.308258\pi$
$252$		−	1.79002e7i		−	1.11855i
$253$	5.77299e6	+	3.08863e6i	0.356484	+	0.190724i
$254$	−1.63304e7			−0.996545
$255$			1.13105e7i			0.682121i
$256$	1.04858e6			0.0625000
$257$	−2.11042e7			−1.24328			−0.621641	−	0.783302i	$-0.713534\pi$
$257$	−2.11042e7			−1.24328			−0.621641	+	0.783302i	$0.713534\pi$
$258$	3.14402e6			0.183074
$259$		−	1.54024e7i		−	0.886522i
$260$		−	1.62919e7i		−	0.926941i
$261$			1.49792e7i			0.842496i
$262$	−5.67010e6			−0.315273
$263$			2.18105e7i			1.19894i	0.800396	+	0.599472i	$0.204623\pi$
$263$			2.18105e7i			1.19894i	−0.800396	+	0.599472i	$0.795377\pi$
$264$	−4.71837e6	+	8.81916e6i	−0.256437	+	0.479309i
$265$	1.55759e7			0.836982
$266$			2.80239e7i			1.48896i
$267$	−3.34547e7			−1.75762
$268$	−4.92764e6			−0.255997
$269$	2.11114e7			1.08458			0.542288	−	0.840192i	$-0.317558\pi$
$269$	2.11114e7			1.08458			0.542288	+	0.840192i	$0.317558\pi$
$270$			9.69374e6i			0.492493i
$271$		−	3.75101e7i		−	1.88469i	−0.334640	−	0.942346i	$-0.608615\pi$
$271$		−	3.75101e7i		−	1.88469i	0.334640	−	0.942346i	$-0.391385\pi$
$272$		−	1.79334e6i		−	0.0891159i
$273$	7.64268e7			3.75628
$274$			2.35298e6i			0.114384i
$275$	−1.00672e7	−	5.38607e6i	−0.484071	−	0.258985i
$276$	−6.53460e6			−0.310808
$277$		−	4.60892e6i		−	0.216850i	−0.994105	−	0.108425i	$-0.965419\pi$
$277$		−	4.60892e6i		−	0.216850i	0.994105	−	0.108425i	$-0.0345808\pi$
$278$	−1.77332e7			−0.825378
$279$	−4.39737e6			−0.202479
$280$	−1.58429e7			−0.721706
$281$		−	2.57781e7i		−	1.16180i	−0.813975	−	0.580900i	$-0.802701\pi$
$281$		−	2.57781e7i		−	1.16180i	0.813975	−	0.580900i	$-0.197299\pi$
$282$			2.95768e7i			1.31887i
$283$			4.26850e6i			0.188328i	0.995557	+	0.0941642i	$0.0300179\pi$
$283$			4.26850e6i			0.188328i	−0.995557	+	0.0941642i	$0.969982\pi$
$284$	−3.77719e6			−0.164897
$285$		−	5.68722e7i		−	2.45678i
$286$	−2.17259e7	−	1.16237e7i	−0.928711	−	0.496873i
$287$	2.25759e7			0.954990
$288$		−	5.75981e6i		−	0.241119i
$289$	2.10705e7			0.872934
$290$	1.32577e7			0.543592
$291$	−4.15891e7			−1.68772
$292$		−	1.28764e7i		−	0.517187i
$293$			2.82205e7i			1.12192i	0.827843	+	0.560959i	$0.189568\pi$
$293$			2.82205e7i			1.12192i	−0.827843	+	0.560959i	$0.810432\pi$
$294$		−	4.66925e7i		−	1.83741i
$295$	−5.24563e7			−2.04330
$296$		−	4.95609e6i		−	0.191102i
$297$	1.29270e7	+	6.91613e6i	0.493434	+	0.263994i
$298$	6.37490e6			0.240893
$299$		−	1.60980e7i		−	0.602223i
$300$	1.13953e7			0.422047
$301$	7.53181e6			0.276185
$302$	3.09519e7			1.12374
$303$			1.32847e7i			0.477556i
$304$			9.01737e6i			0.320966i
$305$		−	8.36709e6i		−	0.294900i
$306$	−9.85076e6			−0.343800
$307$			5.22991e7i			1.80750i	0.428057	+	0.903752i	$0.359198\pi$
$307$			5.22991e7i			1.80750i	−0.428057	+	0.903752i	$0.640802\pi$
$308$	−1.13033e7	+	2.11272e7i	−0.386860	+	0.723085i
$309$	−7.83453e7			−2.65545
$310$			3.89197e6i			0.130643i
$311$	4.28332e7			1.42396			0.711982	−	0.702197i	$-0.247798\pi$
$311$	4.28332e7			1.42396			0.711982	+	0.702197i	$0.247798\pi$
$312$	2.45922e7			0.809716
$313$	3.32457e7			1.08418			0.542091	−	0.840320i	$-0.317633\pi$
$313$	3.32457e7			1.08418			0.542091	+	0.840320i	$0.317633\pi$
$314$			2.85671e7i			0.922736i
$315$			8.70247e7i			2.78427i
$316$			1.79586e7i			0.569129i
$317$	1.49771e7			0.470166			0.235083	−	0.971975i	$-0.424464\pi$
$317$	1.49771e7			0.470166			0.235083	+	0.971975i	$0.424464\pi$
$318$			2.35114e7i			0.731134i
$319$	9.45885e6	−	1.76796e7i	0.291384	−	0.544630i
$320$	−5.09783e6			−0.155573
$321$		−	5.04497e7i		−	1.52526i
$322$	−1.56543e7			−0.468884
$323$	1.54220e7			0.457651
$324$	8.56345e6			0.251776
$325$			2.80722e7i			0.817761i
$326$		−	2.04240e7i		−	0.589505i
$327$		−	3.10308e7i		−	0.887462i
$328$	7.26433e6			0.205861
$329$			7.08541e7i			1.98965i
$330$	2.29391e7	−	4.28758e7i	0.638316	−	1.19308i
$331$	−5.72143e6			−0.157768			−0.0788842	−	0.996884i	$-0.525136\pi$
$331$	−5.72143e6			−0.157768			−0.0788842	+	0.996884i	$0.525136\pi$
$332$		−	1.82381e7i		−	0.498386i
$333$	−2.72237e7			−0.737250
$334$	−5.00813e7			−1.34411
$335$	2.39565e7			0.637220
$336$		−	2.39144e7i		−	0.630436i
$337$		−	3.20214e7i		−	0.836664i	−0.908294	−	0.418332i	$-0.862615\pi$
$337$		−	3.20214e7i		−	0.836664i	0.908294	−	0.418332i	$-0.137385\pi$
$338$			3.32781e7i			0.861804i
$339$	−2.49046e7			−0.639266
$340$			8.71861e6i			0.221825i
$341$	5.19011e6	+	2.77678e6i	0.130892	+	0.0700291i
$342$	4.95322e7			1.23825
$343$		−	4.56711e7i		−	1.13177i
$344$	2.42354e6			0.0595353
$345$	3.17691e7			0.773654
$346$	−1.57663e7			−0.380628
$347$		−	8.53561e6i		−	0.204290i	−0.994770	−	0.102145i	$-0.967429\pi$
$347$		−	8.53561e6i		−	0.204290i	0.994770	−	0.102145i	$-0.0325705\pi$
$348$			2.00120e7i			0.474847i
$349$			1.70635e7i			0.401414i	0.979651	+	0.200707i	$0.0643240\pi$
$349$			1.70635e7i			0.401414i	−0.979651	+	0.200707i	$0.935676\pi$
$350$	2.72985e7			0.636700
$351$		−	3.60469e7i		−	0.833578i
$352$	−3.63711e6	+	6.79817e6i	−0.0833929	+	0.155871i
$353$	−4.60075e7			−1.04594			−0.522968	−	0.852352i	$-0.675175\pi$
$353$	−4.60075e7			−1.04594			−0.522968	+	0.852352i	$0.675175\pi$
$354$		−	7.91812e7i		−	1.78489i
$355$	1.83635e7			0.410459
$356$	−2.57883e7			−0.571574
$357$	−4.08998e7			−0.898910
$358$		−	1.16474e7i		−	0.253852i
$359$			1.15691e7i			0.250043i	0.992154	+	0.125022i	$0.0399001\pi$
$359$			1.15691e7i			0.250043i	−0.992154	+	0.125022i	$0.960100\pi$
$360$			2.80023e7i			0.600186i
$361$	−3.05002e7			−0.648307
$362$		−	1.38120e7i		−	0.291160i
$363$	−4.08105e7	−	6.11807e7i	−0.853202	−	1.27907i
$364$	5.89130e7			1.22154
$365$			6.26010e7i			1.28737i
$366$	1.26299e7			0.257606
$367$	−4.97883e6			−0.100723			−0.0503615	−	0.998731i	$-0.516037\pi$
$367$	−4.97883e6			−0.100723			−0.0503615	+	0.998731i	$0.516037\pi$
$368$	−5.03714e6			−0.101074
$369$		−	3.99028e7i		−	0.794190i
$370$			2.40949e7i			0.475685i
$371$			5.63239e7i			1.10299i
$372$	−5.87482e6			−0.114121
$373$		−	2.36429e7i		−	0.455590i	−0.973709	−	0.227795i	$-0.926848\pi$
$373$		−	2.36429e7i		−	0.455590i	0.973709	−	0.227795i	$-0.0731516\pi$
$374$	1.16266e7	+	6.22041e6i	0.222249	+	0.118906i
$375$	4.55114e7			0.863030
$376$			2.27990e7i			0.428896i
$377$	−4.92996e7			−0.920066
$378$	−3.50534e7			−0.649015
$379$	1.59004e7			0.292072			0.146036	−	0.989279i	$-0.453348\pi$
$379$	1.59004e7			0.292072			0.146036	+	0.989279i	$0.453348\pi$
$380$		−	4.38394e7i		−	0.798940i
$381$			1.19842e8i			2.16687i
$382$		−	8.26865e6i		−	0.148335i
$383$	−5.32888e7			−0.948505			−0.474252	−	0.880389i	$-0.657282\pi$
$383$	−5.32888e7			−0.948505			−0.474252	+	0.880389i	$0.657282\pi$
$384$		−	7.69502e6i		−	0.135899i
$385$	5.49530e7	−	1.02713e8i	0.962962	−	1.79988i
$386$	3.99301e7			0.694286
$387$		−	1.33125e7i		−	0.229681i
$388$	−3.20586e7			−0.548844
$389$	−8.43359e7			−1.43273			−0.716363	−	0.697727i	$-0.754195\pi$
$389$	−8.43359e7			−1.43273			−0.716363	+	0.697727i	$0.754195\pi$
$390$	−1.19559e8			−2.01552
$391$			8.61481e6i			0.144117i
$392$		−	3.59925e7i		−	0.597522i
$393$			4.16102e7i			0.685524i
$394$	4.67937e7			0.765065
$395$		−	8.73087e7i		−	1.41666i
$396$	3.73422e7	+	1.99786e7i	0.601332	+	0.321721i
$397$	1.39558e7			0.223040			0.111520	−	0.993762i	$-0.464428\pi$
$397$	1.39558e7			0.223040			0.111520	+	0.993762i	$0.464428\pi$
$398$			7.02898e6i			0.111492i
$399$	2.05655e8			3.23758
$400$	8.78395e6			0.137249
$401$	5.35293e7			0.830153			0.415077	−	0.909786i	$-0.363755\pi$
$401$	5.35293e7			0.830153			0.415077	+	0.909786i	$0.363755\pi$
$402$			3.61617e7i			0.556635i
$403$		−	1.44726e7i		−	0.221122i
$404$			1.02404e7i			0.155301i
$405$	−4.16327e7			−0.626714
$406$			4.79408e7i			0.716354i
$407$	3.21315e7	+	1.71908e7i	0.476594	+	0.254984i
$408$	−1.31605e7			−0.193772
$409$			6.32419e7i			0.924347i	0.886790	+	0.462173i	$0.152930\pi$
$409$			6.32419e7i			0.924347i	−0.886790	+	0.462173i	$0.847070\pi$
$410$	−3.53167e7			−0.512423
$411$	1.72674e7			0.248715
$412$	−6.03918e7			−0.863547
$413$		−	1.89686e8i		−	2.69269i
$414$			2.76689e7i			0.389934i
$415$			8.86676e7i			1.24057i
$416$	1.89567e7			0.263319
$417$			1.30136e8i			1.79469i
$418$	−5.84618e7	−	3.12778e7i	−0.800466	−	0.428260i
$419$	9.31206e6			0.126591			0.0632956	−	0.997995i	$-0.479839\pi$
$419$	9.31206e6			0.126591			0.0632956	+	0.997995i	$0.479839\pi$
$420$			1.16264e8i			1.56927i
$421$	−2.19313e7			−0.293912			−0.146956	−	0.989143i	$-0.546948\pi$
$421$	−2.19313e7			−0.293912			−0.146956	+	0.989143i	$0.546948\pi$
$422$	9.24697e7			1.23044
$423$	1.25235e8			1.65464
$424$			1.81235e7i			0.237764i
$425$		−	1.50228e7i		−	0.195697i
$426$			2.77191e7i			0.358550i
$427$	3.02561e7			0.388624
$428$		−	3.88887e7i		−	0.496012i
$429$	−8.53009e7	+	1.59437e8i	−1.08039	+	2.01937i
$430$	−1.17824e7			−0.148194
$431$			4.16809e7i			0.520601i	0.965528	+	0.260300i	$0.0838216\pi$
$431$			4.16809e7i			0.520601i	−0.965528	+	0.260300i	$0.916178\pi$
$432$	−1.12793e7			−0.139904
$433$	1.37815e8			1.69760			0.848798	−	0.528718i	$-0.177327\pi$
$433$	1.37815e8			1.69760			0.848798	+	0.528718i	$0.177327\pi$
$434$	−1.40737e7			−0.172163
$435$		−	9.72919e7i		−	1.18198i
$436$		−	2.39198e7i		−	0.288601i
$437$		−	4.33175e7i		−	0.519062i
$438$	−9.44944e7			−1.12456
$439$		−	7.06075e7i		−	0.834559i	−0.908778	−	0.417280i	$-0.862984\pi$
$439$		−	7.06075e7i		−	0.834559i	0.908778	−	0.417280i	$-0.137016\pi$
$440$	1.76824e7	−	3.30504e7i	0.207579	−	0.387989i
$441$	−1.97706e8			−2.30518
$442$		−	3.24208e7i		−	0.375454i
$443$	−4.33504e7			−0.498634			−0.249317	−	0.968422i	$-0.580206\pi$
$443$	−4.33504e7			−0.498634			−0.249317	+	0.968422i	$0.580206\pi$
$444$	−3.63705e7			−0.415528
$445$	1.25374e8			1.42275
$446$		−	7.30973e7i		−	0.823942i
$447$		−	4.67825e7i		−	0.523794i
$448$		−	1.84342e7i		−	0.205017i
$449$	−4.32962e7			−0.478312			−0.239156	−	0.970981i	$-0.576871\pi$
$449$	−4.32962e7			−0.478312			−0.239156	+	0.970981i	$0.576871\pi$
$450$		−	4.82501e7i		−	0.529493i
$451$	−2.51972e7	+	4.70964e7i	−0.274677	+	0.513402i
$452$	−1.91975e7			−0.207888
$453$		−	2.27142e8i		−	2.44344i
$454$	−2.44344e7			−0.261116
$455$	−2.86415e8			−3.04062
$456$	6.61744e7			0.697903
$457$			1.73513e7i			0.181796i	0.995860	+	0.0908980i	$0.0289737\pi$
$457$			1.73513e7i			0.181796i	−0.995860	+	0.0908980i	$0.971026\pi$
$458$			9.79177e7i			1.01921i
$459$			1.92905e7i			0.199483i
$460$	2.44889e7			0.251591
$461$		−	3.21397e7i		−	0.328050i	−0.986456	−	0.164025i	$-0.947552\pi$
$461$		−	3.21397e7i		−	0.328050i	0.986456	−	0.164025i	$-0.0524477\pi$
$462$	1.55043e8	+	8.29499e7i	1.57226	+	0.841182i
$463$	−1.40558e8			−1.41616			−0.708078	−	0.706134i	$-0.750438\pi$
$463$	−1.40558e8			−1.41616			−0.708078	+	0.706134i	$0.750438\pi$
$464$			1.54261e7i			0.154420i
$465$	2.85614e7			0.284067
$466$	1.02751e8			1.01538
$467$	−1.02465e8			−1.00607			−0.503033	−	0.864267i	$-0.667782\pi$
$467$	−1.02465e8			−1.00607			−0.503033	+	0.864267i	$0.667782\pi$
$468$		−	1.04129e8i		−	1.01586i
$469$			8.66289e7i			0.839739i
$470$		−	1.10841e8i		−	1.06760i
$471$	2.09641e8			2.00638
$472$		−	6.10362e7i		−	0.580445i
$473$	−8.40634e6	+	1.57124e7i	−0.0794372	+	0.148477i
$474$	1.31790e8			1.23751
$475$			7.55387e7i			0.704837i
$476$	−3.15272e7			−0.292324
$477$	9.95523e7			0.917268
$478$	9.26284e6			0.0848126
$479$			7.50766e7i			0.683121i	0.939860	+	0.341561i	$0.110955\pi$
$479$			7.50766e7i			0.683121i	−0.939860	+	0.341561i	$0.889045\pi$
$480$			3.74106e7i			0.338276i
$481$		−	8.95986e7i		−	0.805130i
$482$	−6.12577e7			−0.547041
$483$			1.14880e8i			1.01953i
$484$	−3.14584e7	−	4.71606e7i	−0.277460	−	0.415952i
$485$	1.55858e8			1.36617
$486$		−	1.08267e8i		−	0.943165i
$487$	2.45602e7			0.212640			0.106320	−	0.994332i	$-0.466093\pi$
$487$	2.45602e7			0.212640			0.106320	+	0.994332i	$0.466093\pi$
$488$	9.73564e6			0.0837732
$489$	−1.49882e8			−1.28181
$490$			1.74984e8i			1.48734i
$491$		−	1.63937e8i		−	1.38494i	−0.721444	−	0.692472i	$-0.756521\pi$
$491$		−	1.63937e8i		−	1.38494i	0.721444	−	0.692472i	$-0.243479\pi$
$492$		−	5.33096e7i		−	0.447620i
$493$	2.63826e7			0.220180
$494$			1.63020e8i			1.35226i
$495$	−1.81546e8	−	9.71293e7i	−1.49682	−	0.800820i
$496$	−4.52855e6			−0.0371120
$497$			6.64038e7i			0.540909i
$498$	−1.33841e8			−1.08368
$499$	−3.35715e7			−0.270190			−0.135095	−	0.990833i	$-0.543134\pi$
$499$	−3.35715e7			−0.270190			−0.135095	+	0.990833i	$0.543134\pi$
$500$	3.50820e7			0.280656
$501$			3.67524e8i			2.92262i
$502$		−	1.01369e8i		−	0.801294i
$503$		−	4.18394e7i		−	0.328762i	−0.986397	−	0.164381i	$-0.947437\pi$
$503$		−	4.18394e7i		−	0.328762i	0.986397	−	0.164381i	$-0.0525626\pi$
$504$	−1.01259e8			−0.790935
$505$		−	4.97855e7i		−	0.386570i
$506$	1.74719e7	−	3.26570e7i	0.134862	−	0.252072i
$507$	2.44213e8			1.87389
$508$			9.23790e7i			0.704664i
$509$	1.93657e8			1.46852			0.734260	−	0.678868i	$-0.237529\pi$
$509$	1.93657e8			1.46852			0.734260	+	0.678868i	$0.237529\pi$
$510$	6.39819e7			0.482333
$511$	−2.26371e8			−1.69651
$512$		−	5.93164e6i		−	0.0441942i
$513$		−	9.69976e7i		−	0.718470i
$514$			1.19384e8i			0.879134i
$515$	2.93605e8			2.14952
$516$		−	1.77853e7i		−	0.129453i
$517$	−1.47811e8	−	7.90811e7i	−1.06964	−	0.572270i
$518$	−8.71292e7			−0.626866
$519$			1.15702e8i			0.827632i
$520$	−9.21609e7			−0.655446
$521$	4.32733e6			0.0305990			0.0152995	−	0.999883i	$-0.495130\pi$
$521$	4.32733e6			0.0305990			0.0152995	+	0.999883i	$0.495130\pi$
$522$	8.47353e7			0.595735
$523$			1.83961e8i			1.28594i	0.765892	+	0.642969i	$0.222298\pi$
$523$			1.83961e8i			1.28594i	−0.765892	+	0.642969i	$0.777702\pi$
$524$			3.20749e7i			0.222932i
$525$		−	2.00331e8i		−	1.38443i
$526$	1.23379e8			0.847782
$527$			7.74500e6i			0.0529163i
$528$	4.98887e7	+	2.66911e7i	0.338922	+	0.181328i
$529$	−1.23839e8			−0.836544
$530$		−	8.81107e7i		−	0.591835i
$531$	−3.35271e8			−2.23930
$532$	1.58527e8			1.05286
$533$	1.31328e8			0.867312
$534$			1.89249e8i			1.24282i
$535$			1.89064e8i			1.23466i
$536$			2.78749e7i			0.181017i
$537$	−8.54752e7			−0.551972
$538$		−	1.19424e8i		−	0.766912i
$539$	2.33348e8	+	1.24844e8i	1.49018	+	0.797266i
$540$	5.48361e7			0.348245
$541$		−	8.76383e7i		−	0.553480i	−0.960945	−	0.276740i	$-0.910746\pi$
$541$		−	8.76383e7i		−	0.553480i	0.960945	−	0.276740i	$-0.0892541\pi$
$542$	−2.12189e8			−1.33268
$543$	−1.01360e8			−0.633093
$544$	−1.01446e7			−0.0630144
$545$			1.16290e8i			0.718379i
$546$		−	4.32335e8i		−	2.65609i
$547$			4.38238e6i			0.0267762i	0.999910	+	0.0133881i	$0.00426169\pi$
$547$			4.38238e6i			0.0267762i	−0.999910	+	0.0133881i	$0.995738\pi$
$548$	1.33104e7			0.0808818
$549$		−	5.34777e7i		−	0.323188i
$550$	−3.04682e7	+	5.69485e7i	−0.183130	+	0.342290i
$551$	−1.32659e8			−0.793015
$552$			3.69653e7i			0.219774i
$553$	3.15716e8			1.86690
$554$	−2.60720e7			−0.153336
$555$	1.76821e8			1.03432
$556$			1.00314e8i			0.583631i
$557$		−	2.44031e8i		−	1.41214i	−0.708140	−	0.706072i	$-0.750466\pi$
$557$		−	2.44031e8i		−	1.41214i	0.708140	−	0.706072i	$-0.249534\pi$
$558$			2.48753e7i			0.143174i
$559$	4.38139e7			0.250828
$560$			8.96209e7i			0.510323i
$561$	4.56487e7	−	8.53226e7i	0.258547	−	0.483254i
$562$	−1.45823e8			−0.821517
$563$		−	3.18995e8i		−	1.78755i	−0.448511	−	0.893777i	$-0.648045\pi$
$563$		−	3.18995e8i		−	1.78755i	0.448511	−	0.893777i	$-0.351955\pi$
$564$	1.67312e8			0.932585
$565$	9.33320e7			0.517470
$566$	2.41463e7			0.133168
$567$		−	1.50547e8i		−	0.825893i
$568$			2.13670e7i			0.116600i
$569$		−	4.87047e6i		−	0.0264383i	−0.999913	−	0.0132192i	$-0.995792\pi$
$569$		−	4.87047e6i		−	0.0264383i	0.999913	−	0.0132192i	$-0.00420791\pi$
$570$	−3.21718e8			−1.73720
$571$		−	6.19484e7i		−	0.332753i	−0.986062	−	0.166376i	$-0.946793\pi$
$571$		−	6.19484e7i		−	0.332753i	0.986062	−	0.166376i	$-0.0532067\pi$
$572$	−6.57535e7	+	1.22901e8i	−0.351342	+	0.656698i
$573$	−6.06798e7			−0.322538
$574$		−	1.27708e8i		−	0.675280i
$575$	−4.21963e7			−0.221958
$576$	−3.25824e7			−0.170497
$577$	−1.94815e7			−0.101413			−0.0507066	−	0.998714i	$-0.516147\pi$
$577$	−1.94815e7			−0.101413			−0.0507066	+	0.998714i	$0.516147\pi$
$578$		−	1.19193e8i		−	0.617257i
$579$		−	2.93029e8i		−	1.50965i
$580$		−	7.49966e7i		−	0.384377i
$581$	−3.20630e8			−1.63484
$582$			2.35263e8i			1.19340i
$583$	−1.17499e8	−	6.28638e7i	−0.592966	−	0.317245i
$584$	−7.28402e7			−0.365706
$585$			5.06238e8i			2.52864i
$586$	1.59639e8			0.793316
$587$	−2.18801e8			−1.08177			−0.540885	−	0.841097i	$-0.681911\pi$
$587$	−2.18801e8			−1.08177			−0.540885	+	0.841097i	$0.681911\pi$
$588$	−2.64133e8			−1.29924
$589$		−	3.89439e7i		−	0.190587i
$590$			2.96738e8i			1.44483i
$591$		−	3.43397e8i		−	1.66354i
$592$	−2.80359e7			−0.135129
$593$			1.46841e8i			0.704177i	0.935967	+	0.352089i	$0.114528\pi$
$593$			1.46841e8i			0.704177i	−0.935967	+	0.352089i	$0.885472\pi$
$594$	3.91235e7	−	7.31262e7i	0.186672	−	0.348910i
$595$	1.53275e8			0.727646
$596$		−	3.60619e7i		−	0.170337i
$597$	5.15825e7			0.242426
$598$	−9.10638e7			−0.425836
$599$	3.42767e8			1.59485			0.797423	−	0.603421i	$-0.206196\pi$
$599$	3.42767e8			1.59485			0.797423	+	0.603421i	$0.206196\pi$
$600$		−	6.44614e7i		−	0.298433i
$601$		−	3.62306e8i		−	1.66898i	−0.551020	−	0.834492i	$-0.685761\pi$
$601$		−	3.62306e8i		−	1.66898i	0.551020	−	0.834492i	$-0.314239\pi$
$602$		−	4.26063e7i		−	0.195292i
$603$	1.53116e8			0.698345
$604$		−	1.75090e8i		−	0.794605i
$605$	1.52940e8	+	2.29279e8i	0.690646	+	1.03538i
$606$	7.51497e7			0.337683
$607$			2.33328e8i			1.04328i	0.853165	+	0.521640i	$0.174680\pi$
$607$			2.33328e8i			1.04328i	−0.853165	+	0.521640i	$0.825320\pi$
$608$	5.10099e7			0.226957
$609$	3.51816e8			1.55763
$610$	−4.73314e7			−0.208526
$611$			4.12171e8i			1.80698i
$612$			5.57243e7i			0.243103i
$613$			3.55486e8i			1.54327i	0.636066	+	0.771634i	$0.280560\pi$
$613$			3.55486e8i			1.54327i	−0.636066	+	0.771634i	$0.719440\pi$
$614$	2.95848e8			1.27810
$615$			2.59173e8i			1.11421i
$616$	1.19513e8	+	6.39412e7i	0.511298	+	0.273551i
$617$	−2.02737e8			−0.863132			−0.431566	−	0.902081i	$-0.642039\pi$
$617$	−2.02737e8			−0.863132			−0.431566	+	0.902081i	$0.642039\pi$
$618$			4.43188e8i			1.87768i
$619$	−2.08625e8			−0.879618			−0.439809	−	0.898091i	$-0.644954\pi$
$619$	−2.08625e8			−0.879618			−0.439809	+	0.898091i	$0.644954\pi$
$620$	2.20163e7			0.0923782
$621$	5.41833e7			0.226251
$622$		−	2.42301e8i		−	1.00689i
$623$			4.53364e8i			1.87492i
$624$		−	1.39114e8i		−	0.572556i
$625$	−3.04590e8			−1.24760
$626$		−	1.88066e8i		−	0.766632i
$627$	−2.29534e8	+	4.29024e8i	−0.931203	+	1.74052i
$628$	1.61600e8			0.652473
$629$			4.79486e7i			0.192675i
$630$	4.92286e8			1.96877
$631$	−4.31963e8			−1.71933			−0.859663	−	0.510861i	$-0.829327\pi$
$631$	−4.31963e8			−1.71933			−0.859663	+	0.510861i	$0.829327\pi$
$632$	1.01589e8			0.402435
$633$		−	6.78593e8i		−	2.67546i
$634$		−	8.47235e7i		−	0.332458i
$635$		−	4.49116e8i		−	1.75403i
$636$	1.33000e8			0.516990
$637$		−	6.50690e8i		−	2.51742i
$638$	−1.00011e8	−	5.35073e7i	−0.385111	−	0.206040i
$639$	1.17369e8			0.449831
$640$			2.88377e7i			0.110007i
$641$	8.83907e7			0.335608			0.167804	−	0.985820i	$-0.446332\pi$
$641$	8.83907e7			0.335608			0.167804	+	0.985820i	$0.446332\pi$
$642$	−2.85387e8			−1.07852
$643$	−3.44806e8			−1.29701			−0.648503	−	0.761212i	$-0.724605\pi$
$643$	−3.44806e8			−1.29701			−0.648503	+	0.761212i	$0.724605\pi$
$644$			8.85540e7i			0.331551i
$645$			8.64660e7i			0.322230i
$646$		−	8.72402e7i		−	0.323608i
$647$	5.41898e7			0.200081			0.100040	−	0.994983i	$-0.468103\pi$
$647$	5.41898e7			0.200081			0.100040	+	0.994983i	$0.468103\pi$
$648$		−	4.84422e7i		−	0.178032i
$649$	3.95712e8	+	2.11711e8i	1.44759	+	0.774480i
$650$	1.58800e8			0.578245
$651$			1.03281e8i			0.374348i
$652$	−1.15535e8			−0.416843
$653$	5.00498e8			1.79747			0.898737	−	0.438488i	$-0.144486\pi$
$653$	5.00498e8			1.79747			0.898737	+	0.438488i	$0.144486\pi$
$654$	−1.75537e8			−0.627530
$655$		−	1.55938e8i		−	0.554915i
$656$		−	4.10932e7i		−	0.145566i
$657$			4.00110e8i			1.41086i
$658$	4.00811e8			1.40690
$659$			1.49050e7i			0.0520804i	0.999661	+	0.0260402i	$0.00828979\pi$
$659$			1.49050e7i			0.0520804i	−0.999661	+	0.0260402i	$0.991710\pi$
$660$	−2.42542e8	−	1.29763e8i	−0.843637	−	0.451357i
$661$	4.79576e8			1.66056			0.830278	−	0.557350i	$-0.188182\pi$
$661$	4.79576e8			1.66056			0.830278	+	0.557350i	$0.188182\pi$
$662$			3.23653e7i			0.111559i
$663$	−2.37921e8			−0.816381
$664$	−1.03170e8			−0.352412
$665$	−7.70707e8			−2.62074
$666$			1.54001e8i			0.521315i
$667$		−	7.41038e7i		−	0.249726i
$668$			2.83303e8i			0.950432i
$669$	−5.36428e8			−1.79157
$670$		−	1.35519e8i		−	0.450583i
$671$	−3.37692e7	+	6.31185e7i	−0.111777	+	0.208924i
$672$	−1.35280e8			−0.445786
$673$		−	4.12777e8i		−	1.35416i	−0.735908	−	0.677081i	$-0.763245\pi$
$673$		−	4.12777e8i		−	1.35416i	0.735908	−	0.677081i	$-0.236755\pi$
$674$	−1.81141e8			−0.591611
$675$	−9.44868e7			−0.307227
$676$	1.88249e8			0.609387
$677$			1.79192e8i			0.577500i	0.957405	+	0.288750i	$0.0932396\pi$
$677$			1.79192e8i			0.577500i	−0.957405	+	0.288750i	$0.906760\pi$
$678$			1.40882e8i			0.452029i
$679$			5.63596e8i			1.80036i
$680$	4.93199e7			0.156854
$681$			1.79313e8i			0.567766i
$682$	1.57078e7	−	2.93597e7i	0.0495180	−	0.0925547i
$683$	3.83703e8			1.20430			0.602148	−	0.798384i	$-0.294312\pi$
$683$	3.83703e8			1.20430			0.602148	+	0.798384i	$0.294312\pi$
$684$		−	2.80197e8i		−	0.875578i
$685$	−6.47109e7			−0.201329
$686$	−2.58355e8			−0.800284
$687$	7.18573e8			2.21616
$688$		−	1.37096e7i		−	0.0420978i
$689$			3.27646e8i			1.00172i
$690$		−	1.79713e8i		−	0.547056i
$691$	−5.62227e8			−1.70403			−0.852015	−	0.523517i	$-0.824619\pi$
$691$	−5.62227e8			−1.70403			−0.852015	+	0.523517i	$0.824619\pi$
$692$			8.91876e7i			0.269145i
$693$	3.51228e8	−	6.56484e8i	1.05533	−	1.97253i
$694$	−4.82847e7			−0.144455
$695$		−	4.87694e8i		−	1.45276i
$696$	1.13205e8			0.335767
$697$	−7.02801e7			−0.207555
$698$	9.65260e7			0.283843
$699$		−	7.54042e8i		−	2.20782i
$700$		−	1.54424e8i		−	0.450215i
$701$		−	8.52636e7i		−	0.247520i	−0.992312	−	0.123760i	$-0.960505\pi$
$701$		−	8.52636e7i		−	0.247520i	0.992312	−	0.123760i	$-0.0394952\pi$
$702$	−2.03912e8			−0.589429
$703$		−	2.41098e8i		−	0.693950i
$704$	3.84563e7	+	2.05746e7i	0.110217	+	0.0589677i
$705$	−8.13413e8			−2.32137
$706$			2.60258e8i			0.739588i
$707$	1.80029e8			0.509428
$708$	−4.47917e8			−1.26211
$709$	1.23402e8			0.346246			0.173123	−	0.984900i	$-0.444614\pi$
$709$	1.23402e8			0.346246			0.173123	+	0.984900i	$0.444614\pi$
$710$		−	1.03879e8i		−	0.290238i
$711$		−	5.58027e8i		−	1.55255i
$712$			1.45881e8i			0.404164i
$713$	2.17542e7			0.0600171
$714$			2.31364e8i			0.635625i
$715$	3.19672e8	−	5.97502e8i	0.874552	−	1.63464i
$716$	−6.58878e7			−0.179501
$717$		−	6.79758e7i		−	0.184415i
$718$	6.54446e7			0.176807
$719$	4.85475e8			1.30611			0.653056	−	0.757310i	$-0.273487\pi$
$719$	4.85475e8			1.30611			0.653056	+	0.757310i	$0.273487\pi$
$720$	1.58405e8			0.424396
$721$			1.06170e9i			2.83267i
$722$			1.72535e8i			0.458422i
$723$			4.49543e8i			1.18948i
$724$	−7.81326e7			−0.205881
$725$			1.29225e8i			0.339104i
$726$	−3.46090e8	+	2.30859e8i	−0.904439	+	0.603305i
$727$	3.27708e7			0.0852871			0.0426436	−	0.999090i	$-0.486422\pi$
$727$	3.27708e7			0.0852871			0.0426436	+	0.999090i	$0.486422\pi$
$728$		−	3.33262e8i		−	0.863757i
$729$	−5.99437e8			−1.54725
$730$	3.54125e8			0.910307
$731$	−2.34470e7			−0.0600254
$732$		−	7.14454e7i		−	0.182155i
$733$			6.33574e8i			1.60874i	0.594130	+	0.804369i	$0.297496\pi$
$733$			6.33574e8i			1.60874i	−0.594130	+	0.804369i	$0.702504\pi$
$734$			2.81645e7i			0.0712219i
$735$	1.28413e9			3.23404
$736$			2.84944e7i			0.0714703i
$737$	−1.80720e8	−	9.66876e7i	−0.451443	−	0.241528i
$738$	−2.25724e8			−0.561577
$739$			2.55770e8i			0.633747i	0.948468	+	0.316873i	$0.102633\pi$
$739$			2.55770e8i			0.633747i	−0.948468	+	0.316873i	$0.897367\pi$
$740$	1.36301e8			0.336360
$741$	1.19633e9			2.94034
$742$	3.18616e8			0.779930
$743$		−	1.05929e8i		−	0.258254i	−0.991628	−	0.129127i	$-0.958782\pi$
$743$		−	1.05929e8i		−	0.258254i	0.991628	−	0.129127i	$-0.0412175\pi$
$744$			3.32330e7i			0.0806957i
$745$			1.75321e8i			0.423999i
$746$	−1.33744e8			−0.322151
$747$			5.66713e8i			1.35957i
$748$	3.51879e7	−	6.57702e7i	0.0840793	−	0.157154i
$749$	−6.83672e8			−1.62706
$750$		−	2.57451e8i		−	0.610255i
$751$	2.47361e8			0.583999			0.292000	−	0.956418i	$-0.405679\pi$
$751$	2.47361e8			0.583999			0.292000	+	0.956418i	$0.405679\pi$
$752$	1.28971e8			0.303275
$753$	−7.43897e8			−1.74232
$754$			2.78880e8i			0.650585i
$755$			8.51231e8i			1.97791i
$756$			1.98292e8i			0.458923i
$757$	−1.73783e8			−0.400608			−0.200304	−	0.979734i	$-0.564193\pi$
$757$	−1.73783e8			−0.400608			−0.200304	+	0.979734i	$0.564193\pi$
$758$		−	8.99462e7i		−	0.206526i
$759$	−2.39655e8	−	1.28219e8i	−0.548101	−	0.293242i
$760$	−2.47993e8			−0.564936
$761$			1.14915e7i			0.0260748i	0.999915	+	0.0130374i	$0.00415005\pi$
$761$			1.14915e7i			0.0260748i	−0.999915	+	0.0130374i	$0.995850\pi$
$762$	6.77927e8			1.53221
$763$	−4.20516e8			−0.946691
$764$	−4.67745e7			−0.104889
$765$		−	2.70913e8i		−	0.605126i
$766$			3.01447e8i			0.670694i
$767$		−	1.10344e9i		−	2.44547i
$768$	−4.35296e7			−0.0960951
$769$		−	2.40729e8i		−	0.529357i	−0.964337	−	0.264679i	$-0.914734\pi$
$769$		−	2.40729e8i		−	0.529357i	0.964337	−	0.264679i	$-0.0852659\pi$
$770$	−5.81034e8	−	3.10861e8i	−1.27271	−	0.680917i
$771$	8.76101e8			1.91157
$772$		−	2.25879e8i		−	0.490935i
$773$	−3.21248e8			−0.695507			−0.347753	−	0.937586i	$-0.613055\pi$
$773$	−3.21248e8			−0.695507			−0.347753	+	0.937586i	$0.613055\pi$
$774$	−7.53066e7			−0.162409
$775$	−3.79358e7			−0.0814975
$776$			1.81351e8i			0.388091i
$777$			6.39402e8i			1.36305i
$778$			4.77076e8i			1.01309i
$779$	3.53387e8			0.747546
$780$			6.76327e8i			1.42519i
$781$	−1.38528e8	−	7.41141e7i	−0.290792	−	0.155578i
$782$	4.87327e7			0.101906
$783$		−	1.65935e8i		−	0.345662i
$784$	−2.03604e8			−0.422512
$785$	−7.85646e8			−1.62412
$786$	2.35383e8			0.484739
$787$			2.07195e7i			0.0425065i	0.999774	+	0.0212532i	$0.00676562\pi$
$787$			2.07195e7i			0.0425065i	−0.999774	+	0.0212532i	$0.993234\pi$
$788$		−	2.64705e8i		−	0.540983i
$789$		−	9.05422e8i		−	1.84340i
$790$	−4.93893e8			−1.00173
$791$			3.37497e8i			0.681930i
$792$	1.13016e8	−	2.11240e8i	0.227491	−	0.425206i
$793$	1.76005e8			0.352945
$794$		−	7.89458e7i		−	0.157713i
$795$	−6.46604e8			−1.28688
$796$	3.97619e7			0.0788366
$797$	8.52877e8			1.68466			0.842328	−	0.538965i	$-0.181185\pi$
$797$	8.52877e8			1.68466			0.842328	+	0.538965i	$0.181185\pi$
$798$		−	1.16336e9i		−	2.28931i
$799$		−	2.20573e8i		−	0.432427i
$800$		−	4.96895e7i		−	0.0970499i
$801$	8.01320e8			1.55922
$802$		−	3.02807e8i		−	0.587007i
$803$	2.52655e8	−	4.72240e8i	0.487957	−	0.912046i
$804$	2.04561e8			0.393600
$805$		−	4.30520e8i		−	0.825288i
$806$	−8.18693e7			−0.156357
$807$	−8.76400e8			−1.66756
$808$	5.79285e7			0.109814
$809$		−	9.43038e8i		−	1.78108i	−0.454905	−	0.890540i	$-0.650327\pi$
$809$		−	9.43038e8i		−	1.78108i	0.454905	−	0.890540i	$-0.349673\pi$
$810$			2.35510e8i			0.443153i
$811$			9.96885e8i			1.86888i	0.356114	+	0.934442i	$0.384101\pi$
$811$			9.96885e8i			1.86888i	−0.356114	+	0.934442i	$0.615899\pi$
$812$	2.71194e8			0.506538
$813$			1.55716e9i			2.89776i
$814$	9.72460e7	−	1.81763e8i	0.180301	−	0.337003i
$815$	5.61695e8			1.03759
$816$			7.44469e7i			0.137018i
$817$	1.17898e8			0.216192
$818$	3.57750e8			0.653612
$819$	−1.83060e9			−3.33229
$820$			1.99782e8i			0.362338i
$821$		−	7.20740e8i		−	1.30241i	−0.758900	−	0.651207i	$-0.774263\pi$
$821$		−	7.20740e8i		−	1.30241i	0.758900	−	0.651207i	$-0.225737\pi$
$822$		−	9.76793e7i		−	0.175868i
$823$	8.95717e7			0.160683			0.0803417	−	0.996767i	$-0.474399\pi$
$823$	8.95717e7			0.160683			0.0803417	+	0.996767i	$0.474399\pi$
$824$			3.41627e8i			0.610620i
$825$	4.17919e8	+	2.23592e8i	0.744269	+	0.398194i
$826$	−1.07303e9			−1.90402
$827$		−	2.54024e8i		−	0.449115i	−0.974461	−	0.224557i	$-0.927906\pi$
$827$		−	2.54024e8i		−	0.449115i	0.974461	−	0.224557i	$-0.0720937\pi$
$828$	1.56519e8			0.275725
$829$	−2.37655e7			−0.0417141			−0.0208570	−	0.999782i	$-0.506639\pi$
$829$	−2.37655e7			−0.0417141			−0.0208570	+	0.999782i	$0.506639\pi$
$830$	5.01580e8			0.877215
$831$			1.91331e8i			0.333412i
$832$		−	1.07235e8i		−	0.186194i
$833$			3.48216e8i			0.602440i
$834$	7.36160e8			1.26904
$835$		−	1.37732e9i		−	2.36579i
$836$	−1.76934e8	+	3.30710e8i	−0.302826	+	0.566015i
$837$	4.87125e7			0.0830738
$838$		−	5.26770e7i		−	0.0895135i
$839$	−3.05248e8			−0.516853			−0.258427	−	0.966031i	$-0.583204\pi$
$839$	−3.05248e8			−0.516853			−0.258427	+	0.966031i	$0.583204\pi$
$840$	6.57687e8			1.10964
$841$	3.67882e8			0.618473
$842$			1.24062e8i			0.207827i
$843$			1.07013e9i			1.78629i
$844$		−	5.23088e8i		−	0.870056i
$845$	−9.15206e8			−1.51687
$846$		−	7.08433e8i		−	1.17001i
$847$	−8.29093e8	+	5.53045e8i	−1.36444	+	0.910145i
$848$	1.02522e8			0.168124
$849$		−	1.77199e8i		−	0.289559i
$850$	−8.49820e7			−0.138379
$851$	1.34679e8			0.218529
$852$	1.56803e8			0.253533
$853$		−	6.59469e8i		−	1.06254i	−0.847201	−	0.531272i	$-0.821714\pi$
$853$		−	6.59469e8i		−	1.06254i	0.847201	−	0.531272i	$-0.178286\pi$
$854$		−	1.71155e8i		−	0.274799i
$855$			1.36222e9i			2.17946i
$856$	−2.19988e8			−0.350734
$857$		−	2.21289e8i		−	0.351575i	−0.984428	−	0.175788i	$-0.943753\pi$
$857$		−	2.21289e8i		−	0.351575i	0.984428	−	0.175788i	$-0.0562472\pi$
$858$	9.01911e8	+	4.82535e8i	1.42791	+	0.763953i
$859$	1.23094e9			1.94204			0.971021	−	0.238995i	$-0.0768178\pi$
$859$	1.23094e9			1.94204			0.971021	+	0.238995i	$0.0768178\pi$
$860$			6.66516e7i			0.104789i
$861$	−9.37194e8			−1.46832
$862$	2.35783e8			0.368120
$863$	−1.21099e9			−1.88411			−0.942056	−	0.335455i	$-0.891110\pi$
$863$	−1.21099e9			−1.88411			−0.942056	+	0.335455i	$0.891110\pi$
$864$			6.38052e7i			0.0989270i
$865$		−	4.33600e8i		−	0.669948i
$866$		−	7.79602e8i		−	1.20038i
$867$	−8.74701e8			−1.34215
$868$			7.96129e7i			0.121738i
$869$	−3.52374e8	+	6.58627e8i	−0.536964	+	1.00364i
$870$	−5.50366e8			−0.835784
$871$			5.03936e8i			0.762642i
$872$	−1.35311e8			−0.204072
$873$	9.96156e8			1.49722
$874$	−2.45041e8			−0.367032
$875$		−	6.16750e8i		−	0.920629i
$876$			5.34541e8i			0.795186i
$877$			7.23871e8i			1.07315i	0.843851	+	0.536577i	$0.180283\pi$
$877$			7.23871e8i			1.07315i	−0.843851	+	0.536577i	$0.819717\pi$
$878$	−3.99416e8			−0.590123
$879$		−	1.17152e9i		−	1.72497i
$880$	−1.86962e8	−	1.00027e8i	−0.274350	−	0.146781i
$881$	−1.55299e8			−0.227112			−0.113556	−	0.993532i	$-0.536224\pi$
$881$	−1.55299e8			−0.227112			−0.113556	+	0.993532i	$0.536224\pi$
$882$			1.11840e9i			1.63001i
$883$	7.75077e8			1.12580			0.562902	−	0.826524i	$-0.309685\pi$
$883$	7.75077e8			1.12580			0.562902	+	0.826524i	$0.309685\pi$
$884$	−1.83400e8			−0.265486
$885$	2.17762e9			3.14161
$886$			2.45227e8i			0.352587i
$887$		−	2.17717e8i		−	0.311976i	−0.987759	−	0.155988i	$-0.950144\pi$
$887$		−	2.17717e8i		−	0.311976i	0.987759	−	0.155988i	$-0.0498561\pi$
$888$			2.05743e8i			0.293823i
$889$	1.62404e9			2.31149
$890$		−	7.09223e8i		−	1.00603i
$891$	3.14062e8	+	1.68028e8i	0.444000	+	0.237546i
$892$	−4.13501e8			−0.582615
$893$			1.10910e9i			1.55746i
$894$	−2.64642e8			−0.370379
$895$	3.20325e8			0.446808
$896$	−1.04280e8			−0.144969
$897$			6.68276e8i			0.925930i
$898$			2.44920e8i			0.338217i
$899$		−	6.66217e7i		−	0.0916931i
$900$	−2.72944e8			−0.374408
$901$		−	1.75340e8i		−	0.239721i
$902$	2.66417e8	+	1.42537e8i	0.363030	+	0.194226i
$903$	−3.12669e8			−0.424640
$904$			1.08598e8i			0.146999i
$905$	3.79855e8			0.512474
$906$	−1.28491e9			−1.72778
$907$	1.92503e8			0.257998			0.128999	−	0.991645i	$-0.458824\pi$
$907$	1.92503e8			0.257998			0.128999	+	0.991645i	$0.458824\pi$
$908$			1.38222e8i			0.184637i
$909$		−	3.18200e8i		−	0.423651i
$910$			1.62021e9i			2.15004i
$911$	−4.80350e8			−0.635335			−0.317667	−	0.948202i	$-0.602900\pi$
$911$	−4.80350e8			−0.635335			−0.317667	+	0.948202i	$0.602900\pi$
$912$		−	3.74339e8i		−	0.493492i
$913$	3.57859e8	−	6.68878e8i	0.470218	−	0.878890i
$914$	9.81540e7			0.128549
$915$			3.47344e8i			0.453415i
$916$	5.53906e8			0.720692
$917$	5.63884e8			0.731276
$918$	1.09123e8			0.141055
$919$			1.32400e9i			1.70585i	0.522033	+	0.852926i	$0.325174\pi$
$919$			1.32400e9i			1.70585i	−0.522033	+	0.852926i	$0.674826\pi$
$920$		−	1.38530e8i		−	0.177902i
$921$		−	2.17110e9i		−	2.77908i
$922$	−1.81810e8			−0.231966
$923$			3.86283e8i			0.491248i
$924$	4.69236e8	−	8.77054e8i	0.594806	−	1.11176i
$925$	−2.34858e8			−0.296742
$926$			7.95114e8i			1.00137i
$927$	1.87655e9			2.35571
$928$	8.72632e7			0.109191
$929$	−6.17444e8			−0.770106			−0.385053	−	0.922894i	$-0.625817\pi$
$929$	−6.17444e8			−0.770106			−0.385053	+	0.922894i	$0.625817\pi$
$930$		−	1.61568e8i		−	0.200866i
$931$		−	1.75092e9i		−	2.16979i
$932$		−	5.81247e8i		−	0.717981i
$933$	−1.77814e9			−2.18938
$934$			5.79631e8i			0.711396i
$935$	−1.71072e8	+	3.19753e8i	−0.209288	+	0.391182i
$936$	−5.89040e8			−0.718319
$937$		−	6.81980e8i		−	0.828997i	−0.910050	−	0.414498i	$-0.863957\pi$
$937$		−	6.81980e8i		−	0.828997i	0.910050	−	0.414498i	$-0.136043\pi$
$938$	4.90047e8			0.593785
$939$	−1.38013e9			−1.66695
$940$	−6.27012e8			−0.754905
$941$		−	1.58337e9i		−	1.90026i	−0.311852	−	0.950131i	$-0.600949\pi$
$941$		−	1.58337e9i		−	1.90026i	0.311852	−	0.950131i	$-0.399051\pi$
$942$		−	1.18591e9i		−	1.41873i
$943$			1.97403e8i			0.235407i
$944$	−3.45273e8			−0.410437
$945$		−	9.64030e8i		−	1.14234i
$946$	8.88827e7	+	4.75535e7i	0.104989	+	0.0561706i
$947$	2.95359e8			0.347776			0.173888	−	0.984765i	$-0.444367\pi$
$947$	2.95359e8			0.347776			0.173888	+	0.984765i	$0.444367\pi$
$948$		−	7.45516e8i		−	0.875049i
$949$	−1.31684e9			−1.54076
$950$	4.27312e8			0.498395
$951$	−6.21747e8			−0.722890
$952$			1.78345e8i			0.206705i
$953$			1.25203e9i			1.44656i	0.690553	+	0.723282i	$0.257367\pi$
$953$			1.25203e9i			1.44656i	−0.690553	+	0.723282i	$0.742633\pi$
$954$		−	5.63153e8i		−	0.648606i
$955$	2.27402e8			0.261087
$956$		−	5.23985e7i		−	0.0599716i
$957$	−3.92666e8	+	7.33937e8i	−0.448010	+	0.837380i
$958$	4.24697e8			0.483040
$959$		−	2.34000e8i		−	0.265314i
$960$	2.11627e8			0.239197
$961$	−8.67946e8			−0.977963
$962$	−5.06846e8			−0.569313
$963$			1.20839e9i			1.35309i
$964$			3.46526e8i			0.386816i
$965$			1.09815e9i			1.22202i
$966$	6.49857e8			0.720919
$967$			6.73829e8i			0.745195i	0.927993	+	0.372598i	$0.121533\pi$
$967$			6.73829e8i			0.745195i	−0.927993	+	0.372598i	$0.878467\pi$
$968$	−2.66781e8	+	1.77956e8i	−0.294122	+	0.196194i
$969$	−6.40216e8			−0.703648
$970$		−	8.81667e8i		−	0.966027i
$971$	1.46250e9			1.59749			0.798743	−	0.601672i	$-0.205498\pi$
$971$	1.46250e9			1.59749			0.798743	+	0.601672i	$0.205498\pi$
$972$	−6.12451e8			−0.666918
$973$	1.76354e9			1.91447
$974$		−	1.38934e8i		−	0.150359i
$975$		−	1.16536e9i		−	1.25733i
$976$		−	5.50731e7i		−	0.0592366i
$977$	5.82424e8			0.624534			0.312267	−	0.949994i	$-0.398912\pi$
$977$	5.82424e8			0.624534			0.312267	+	0.949994i	$0.398912\pi$
$978$			8.47862e8i			0.906377i
$979$	−9.45779e8	−	5.06005e8i	−1.00796	−	0.539270i
$980$	9.89857e8			1.05171
$981$			7.43260e8i			0.787289i
$982$	−9.27367e8			−0.979304
$983$	−1.22564e9			−1.29033			−0.645165	−	0.764043i	$-0.723212\pi$
$983$	−1.22564e9			−1.29033			−0.645165	+	0.764043i	$0.723212\pi$
$984$	−3.01565e8			−0.316515
$985$			1.28691e9i			1.34660i
$986$		−	1.49243e8i		−	0.155691i
$987$		−	2.94137e9i		−	3.05913i
$988$	9.22182e8			0.956193
$989$			6.58581e7i			0.0680801i
$990$	−5.49447e8	+	1.02698e9i	−0.566265	+	1.05841i
$991$	4.01381e8			0.412416			0.206208	−	0.978508i	$-0.433888\pi$
$991$	4.01381e8			0.412416			0.206208	+	0.978508i	$0.433888\pi$
$992$			2.56174e7i			0.0262422i
$993$	2.37514e8			0.242572
$994$	3.75637e8			0.382480
$995$	−1.93309e8			−0.196238
$996$			7.57120e8i			0.766279i
$997$		−	1.60438e9i		−	1.61891i	−0.587185	−	0.809453i	$-0.699764\pi$
$997$		−	1.60438e9i		−	1.61891i	0.587185	−	0.809453i	$-0.300236\pi$
$998$			1.89909e8i			0.191053i
$999$	3.01575e8			0.302482

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.7.b.a.21.1	✓	6
3.2	odd	2		198.7.d.a.109.5		6
4.3	odd	2		176.7.h.e.65.5		6
11.10	odd	2	inner	22.7.b.a.21.4	yes	6
33.32	even	2		198.7.d.a.109.2		6
44.43	even	2		176.7.h.e.65.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.7.b.a.21.1	✓	6	1.1	even	1	trivial
22.7.b.a.21.4	yes	6	11.10	odd	2	inner
176.7.h.e.65.5		6	4.3	odd	2
176.7.h.e.65.6		6	44.43	even	2
198.7.d.a.109.2		6	33.32	even	2
198.7.d.a.109.5		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	22.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-5.65685i q^{2} -41.5131 q^{3} -32.0000 q^{4} +155.573 q^{5} +234.833i q^{6} +562.567i q^{7} +181.019i q^{8} +994.336 q^{9} +O(q^{10})\)	\(q-5.65685i q^{2} -41.5131 q^{3} -32.0000 q^{4} +155.573 q^{5} +234.833i q^{6} +562.567i q^{7} +181.019i q^{8} +994.336 q^{9} -880.056i q^{10} +(-1173.59 - 627.888i) q^{11} +1328.42 q^{12} +3272.55i q^{13} +3182.36 q^{14} -6458.33 q^{15} +1024.00 q^{16} -1751.31i q^{17} -5624.81i q^{18} +8806.02i q^{19} -4978.35 q^{20} -23353.9i q^{21} +(-3551.87 + 6638.84i) q^{22} -4919.08 q^{23} -7514.67i q^{24} +8578.08 q^{25} +18512.4 q^{26} -11014.9 q^{27} -18002.1i q^{28} +15064.6i q^{29} +36533.8i q^{30} -4422.42 q^{31} -5792.62i q^{32} +(48719.4 + 26065.6i) q^{33} -9906.88 q^{34} +87520.4i q^{35} -31818.8 q^{36} -27378.8 q^{37} +49814.4 q^{38} -135854. i q^{39} +28161.8i q^{40} -40130.1i q^{41} -132110. q^{42} -13388.3i q^{43} +(37554.9 + 20092.4i) q^{44} +154692. q^{45} +27826.5i q^{46} +125948. q^{47} -42509.4 q^{48} -198832. q^{49} -48524.9i q^{50} +72702.1i q^{51} -104722. i q^{52} +100119. q^{53} +62309.8i q^{54} +(-182580. - 97682.6i) q^{55} -101835. q^{56} -365565. i q^{57} +85218.0 q^{58} -337180. q^{59} +206667. q^{60} -53782.3i q^{61} +25017.0i q^{62} +559380. i q^{63} -32768.0 q^{64} +509122. i q^{65} +(147449. - 275599. i) q^{66} +153989. q^{67} +56041.8i q^{68} +204206. q^{69} +495090. q^{70} +118037. q^{71} +179994. i q^{72} +402389. i q^{73} +154878. i q^{74} -356102. q^{75} -281793. i q^{76} +(353229. - 660224. i) q^{77} -768505. q^{78} -561206. i q^{79} +159307. q^{80} -267608. q^{81} -227010. q^{82} +569941. i q^{83} +747324. i q^{84} -272456. i q^{85} -75735.6 q^{86} -625376. i q^{87} +(113660. - 212443. i) q^{88} +805884. q^{89} -875071. i q^{90} -1.84103e6 q^{91} +157411. q^{92} +183588. q^{93} -712469. i q^{94} +1.36998e6i q^{95} +240469. i q^{96} +1.00183e6 q^{97} +1.12477e6i q^{98} +(-1.16694e6 - 624331. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 52 q^{3} - 192 q^{4} + 368 q^{5} - 346 q^{9}+O(q^{10}) \) 6 * q - 52 * q^3 - 192 * q^4 + 368 * q^5 - 346 * q^9	\( 6 q - 52 q^{3} - 192 q^{4} + 368 q^{5} - 346 q^{9} - 1166 q^{11} + 1664 q^{12} + 2208 q^{14} - 6512 q^{15} + 6144 q^{16} - 11776 q^{20} + 1056 q^{22} + 2156 q^{23} + 59862 q^{25} - 1824 q^{26} - 57472 q^{27} - 78468 q^{31} + 142208 q^{33} + 28704 q^{34} + 11072 q^{36} - 205920 q^{37} + 101472 q^{38} - 344160 q^{42} + 37312 q^{44} + 368716 q^{45} + 493460 q^{47} - 53248 q^{48} - 270762 q^{49} - 531700 q^{53} + 274956 q^{55} - 70656 q^{56} + 509184 q^{58} - 833380 q^{59} + 208384 q^{60} - 196608 q^{64} + 193248 q^{66} + 537420 q^{67} + 398860 q^{69} + 96096 q^{70} - 460372 q^{71} - 211428 q^{75} + 249744 q^{77} - 1866912 q^{78} + 376832 q^{80} + 485654 q^{81} + 428640 q^{82} + 1055808 q^{86} - 33792 q^{88} + 2377952 q^{89} - 5068656 q^{91} - 68992 q^{92} + 699868 q^{93} + 1351632 q^{97} - 2470930 q^{99}+O(q^{100}) \) 6 * q - 52 * q^3 - 192 * q^4 + 368 * q^5 - 346 * q^9 - 1166 * q^11 + 1664 * q^12 + 2208 * q^14 - 6512 * q^15 + 6144 * q^16 - 11776 * q^20 + 1056 * q^22 + 2156 * q^23 + 59862 * q^25 - 1824 * q^26 - 57472 * q^27 - 78468 * q^31 + 142208 * q^33 + 28704 * q^34 + 11072 * q^36 - 205920 * q^37 + 101472 * q^38 - 344160 * q^42 + 37312 * q^44 + 368716 * q^45 + 493460 * q^47 - 53248 * q^48 - 270762 * q^49 - 531700 * q^53 + 274956 * q^55 - 70656 * q^56 + 509184 * q^58 - 833380 * q^59 + 208384 * q^60 - 196608 * q^64 + 193248 * q^66 + 537420 * q^67 + 398860 * q^69 + 96096 * q^70 - 460372 * q^71 - 211428 * q^75 + 249744 * q^77 - 1866912 * q^78 + 376832 * q^80 + 485654 * q^81 + 428640 * q^82 + 1055808 * q^86 - 33792 * q^88 + 2377952 * q^89 - 5068656 * q^91 - 68992 * q^92 + 699868 * q^93 + 1351632 * q^97 - 2470930 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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