LMFDB - Embedded newform 22.9.b.a.21.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,9,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, 9, names="a")

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

chi := DirichletCharacter("22.21");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 9 $
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:	$8.96232942134$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 7944x^{6} + 15215349x^{4} + 1757611988x^{2} + 38177252100 $ x^8 + 7944x^6 + 15215349x^4 + 1757611988*x^2 + 38177252100
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 11^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.7
Root			$-70.2090i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.9.b.a.21.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+11.3137i q^{2} +107.356 q^{3} -128.000 q^{4} -1065.90 q^{5} +1214.60i q^{6} +3358.46i q^{7} -1448.15i q^{8} +4964.40 q^{9} +O(q^{10})$	\(q+11.3137i q^{2} +107.356 q^{3} -128.000 q^{4} -1065.90 q^{5} +1214.60i q^{6} +3358.46i q^{7} -1448.15i q^{8} +4964.40 q^{9} -12059.2i q^{10} +(-5944.35 + 13380.0i) q^{11} -13741.6 q^{12} +18360.6i q^{13} -37996.7 q^{14} -114431. q^{15} +16384.0 q^{16} +3045.27i q^{17} +56165.7i q^{18} -180007. i q^{19} +136435. q^{20} +360553. i q^{21} +(-151377. - 67252.7i) q^{22} +128952. q^{23} -155469. i q^{24} +745509. q^{25} -207726. q^{26} -171406. q^{27} -429883. i q^{28} +803829. i q^{29} -1.29464e6i q^{30} +790758. q^{31} +185364. i q^{32} +(-638164. + 1.43643e6i) q^{33} -34453.3 q^{34} -3.57977e6i q^{35} -635443. q^{36} +1.85903e6 q^{37} +2.03655e6 q^{38} +1.97112e6i q^{39} +1.54358e6i q^{40} -1.91113e6i q^{41} -4.07919e6 q^{42} +5.87142e6i q^{43} +(760877. - 1.71264e6i) q^{44} -5.29153e6 q^{45} +1.45892e6i q^{46} -6.46157e6 q^{47} +1.75893e6 q^{48} -5.51448e6 q^{49} +8.43447e6i q^{50} +326929. i q^{51} -2.35015e6i q^{52} +1.03543e7 q^{53} -1.93923e6i q^{54} +(6.33606e6 - 1.42617e7i) q^{55} +4.86357e6 q^{56} -1.93249e7i q^{57} -9.09429e6 q^{58} -2.46965e6 q^{59} +1.46471e7 q^{60} +1.97635e7i q^{61} +8.94640e6i q^{62} +1.66727e7i q^{63} -2.09715e6 q^{64} -1.95705e7i q^{65} +(-1.62513e7 - 7.22001e6i) q^{66} +1.24402e7 q^{67} -389795. i q^{68} +1.38438e7 q^{69} +4.05005e7 q^{70} -3.54223e7 q^{71} -7.18921e6i q^{72} -1.52941e7i q^{73} +2.10326e7i q^{74} +8.00352e7 q^{75} +2.30409e7i q^{76} +(-4.49361e7 - 1.99639e7i) q^{77} -2.23007e7 q^{78} +3.11795e7i q^{79} -1.74636e7 q^{80} -5.09729e7 q^{81} +2.16220e7 q^{82} -3.73727e7i q^{83} -4.61507e7i q^{84} -3.24594e6i q^{85} -6.64275e7 q^{86} +8.62962e7i q^{87} +(1.93763e7 + 8.60834e6i) q^{88} -4.94298e7 q^{89} -5.98668e7i q^{90} -6.16633e7 q^{91} -1.65058e7 q^{92} +8.48929e7 q^{93} -7.31043e7i q^{94} +1.91869e8i q^{95} +1.99000e7i q^{96} +4.09642e7 q^{97} -6.23892e7i q^{98} +(-2.95101e7 + 6.64235e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 182 q^{3} - 1024 q^{4} - 1410 q^{5} + 44582 q^{9}+O(q^{10}) $ 8 * q + 182 * q^3 - 1024 * q^4 - 1410 * q^5 + 44582 * q^9	$ 8 q + 182 q^{3} - 1024 q^{4} - 1410 q^{5} + 44582 q^{9} + 5808 q^{11} - 23296 q^{12} + 12288 q^{14} + 87958 q^{15} + 131072 q^{16} + 180480 q^{20} + 359040 q^{22} - 802026 q^{23} + 999558 q^{25} - 1321728 q^{26} - 1561354 q^{27} + 196726 q^{31} - 4286722 q^{33} - 701952 q^{34} - 5706496 q^{36} + 8627998 q^{37} + 9288960 q^{38} + 4366848 q^{42} - 743424 q^{44} + 1146988 q^{45} - 14335392 q^{47} + 2981888 q^{48} - 6714712 q^{49} + 55946352 q^{53} - 10078442 q^{55} - 1572864 q^{56} - 23226624 q^{58} + 21793110 q^{59} - 11258624 q^{60} - 16777216 q^{64} - 44242176 q^{66} - 113809034 q^{67} - 171636914 q^{69} + 137817600 q^{70} + 16741974 q^{71} + 346496844 q^{75} - 137074080 q^{77} - 57993216 q^{78} - 23101440 q^{80} + 85282724 q^{81} + 47480832 q^{82} + 49839360 q^{86} - 45957120 q^{88} + 42055422 q^{89} - 146801952 q^{91} + 102659328 q^{92} + 253251118 q^{93} + 100034782 q^{97} - 333541978 q^{99}+O(q^{100}) $ 8 * q + 182 * q^3 - 1024 * q^4 - 1410 * q^5 + 44582 * q^9 + 5808 * q^11 - 23296 * q^12 + 12288 * q^14 + 87958 * q^15 + 131072 * q^16 + 180480 * q^20 + 359040 * q^22 - 802026 * q^23 + 999558 * q^25 - 1321728 * q^26 - 1561354 * q^27 + 196726 * q^31 - 4286722 * q^33 - 701952 * q^34 - 5706496 * q^36 + 8627998 * q^37 + 9288960 * q^38 + 4366848 * q^42 - 743424 * q^44 + 1146988 * q^45 - 14335392 * q^47 + 2981888 * q^48 - 6714712 * q^49 + 55946352 * q^53 - 10078442 * q^55 - 1572864 * q^56 - 23226624 * q^58 + 21793110 * q^59 - 11258624 * q^60 - 16777216 * q^64 - 44242176 * q^66 - 113809034 * q^67 - 171636914 * q^69 + 137817600 * q^70 + 16741974 * q^71 + 346496844 * q^75 - 137074080 * q^77 - 57993216 * q^78 - 23101440 * q^80 + 85282724 * q^81 + 47480832 * q^82 + 49839360 * q^86 - 45957120 * q^88 + 42055422 * q^89 - 146801952 * q^91 + 102659328 * q^92 + 253251118 * q^93 + 100034782 * q^97 - 333541978 * 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 $

$2$			11.3137i			0.707107i
$2$			11.3137i			0.707107i
$3$	107.356			1.32539			0.662694	−	0.748890i	$-0.269413\pi$
$3$	107.356			1.32539			0.662694	+	0.748890i	$0.269413\pi$
$4$	−128.000			−0.500000
$5$	−1065.90			−1.70543			−0.852717	−	0.522374i	$-0.825047\pi$
$5$	−1065.90			−1.70543			−0.852717	+	0.522374i	$0.825047\pi$
$6$			1214.60i			0.937191i
$7$			3358.46i			1.39878i	0.714742	+	0.699388i	$0.246544\pi$
$7$			3358.46i			1.39878i	−0.714742	+	0.699388i	$0.753456\pi$
$8$		−	1448.15i		−	0.353553i
$9$	4964.40			0.756652
$10$		−	12059.2i		−	1.20592i
$11$	−5944.35	+	13380.0i	−0.406007	+	0.913870i
$11$	−5944.35	+	13380.0i	−0.406007	+	0.913870i
$12$	−13741.6			−0.662694
$13$			18360.6i			0.642855i	0.946934	+	0.321427i	$0.104163\pi$
$13$			18360.6i			0.642855i	−0.946934	+	0.321427i	$0.895837\pi$
$14$	−37996.7			−0.989085
$15$	−114431.			−2.26036
$16$	16384.0			0.250000
$17$			3045.27i			0.0364611i	0.999834	+	0.0182306i	$0.00580329\pi$
$17$			3045.27i			0.0364611i	−0.999834	+	0.0182306i	$0.994197\pi$
$18$			56165.7i			0.535034i
$19$		−	180007.i		−	1.38126i	−0.723209	−	0.690629i	$-0.757334\pi$
$19$		−	180007.i		−	1.38126i	0.723209	−	0.690629i	$-0.242666\pi$
$20$	136435.			0.852717
$21$			360553.i			1.85392i
$22$	−151377.	−	67252.7i	−0.646204	−	0.287091i
$23$	128952.			0.460804			0.230402	−	0.973096i	$-0.425996\pi$
$23$	128952.			0.460804			0.230402	+	0.973096i	$0.425996\pi$
$24$		−	155469.i		−	0.468595i
$25$	745509.			1.90850
$26$	−207726.			−0.454567
$27$	−171406.			−0.322530
$28$		−	429883.i		−	0.699388i
$29$			803829.i			1.13651i	0.822854	+	0.568253i	$0.192380\pi$
$29$			803829.i			1.13651i	−0.822854	+	0.568253i	$0.807620\pi$
$30$		−	1.29464e6i		−	1.59832i
$31$	790758.			0.856242			0.428121	−	0.903721i	$-0.359176\pi$
$31$	790758.			0.856242			0.428121	+	0.903721i	$0.359176\pi$
$32$			185364.i			0.176777i
$33$	−638164.	+	1.43643e6i	−0.538117	+	1.21123i
$34$	−34453.3			−0.0257819
$35$		−	3.57977e6i		−	2.38552i
$36$	−635443.			−0.378326
$37$	1.85903e6			0.991929			0.495964	−	0.868343i	$-0.334815\pi$
$37$	1.85903e6			0.991929			0.495964	+	0.868343i	$0.334815\pi$
$38$	2.03655e6			0.976697
$39$			1.97112e6i			0.852032i
$40$			1.54358e6i			0.602962i
$41$		−	1.91113e6i		−	0.676325i	−0.941088	−	0.338163i	$-0.890195\pi$
$41$		−	1.91113e6i		−	0.676325i	0.941088	−	0.338163i	$-0.109805\pi$
$42$	−4.07919e6			−1.31092
$43$			5.87142e6i			1.71739i	0.512486	+	0.858696i	$0.328725\pi$
$43$			5.87142e6i			1.71739i	−0.512486	+	0.858696i	$0.671275\pi$
$44$	760877.	−	1.71264e6i	0.203004	−	0.456935i
$45$	−5.29153e6			−1.29042
$46$			1.45892e6i			0.325838i
$47$	−6.46157e6			−1.32418			−0.662090	−	0.749425i	$-0.730330\pi$
$47$	−6.46157e6			−1.32418			−0.662090	+	0.749425i	$0.730330\pi$
$48$	1.75893e6			0.331347
$49$	−5.51448e6			−0.956577
$50$			8.43447e6i			1.34952i
$51$			326929.i			0.0483251i
$52$		−	2.35015e6i		−	0.321427i
$53$	1.03543e7			1.31225			0.656125	−	0.754652i	$-0.272194\pi$
$53$	1.03543e7			1.31225			0.656125	+	0.754652i	$0.272194\pi$
$54$		−	1.93923e6i		−	0.228063i
$55$	6.33606e6	−	1.42617e7i	0.692419	−	1.55854i
$56$	4.86357e6			0.494542
$57$		−	1.93249e7i		−	1.83070i
$58$	−9.09429e6			−0.803631
$59$	−2.46965e6			−0.203810			−0.101905	−	0.994794i	$-0.532494\pi$
$59$	−2.46965e6			−0.203810			−0.101905	+	0.994794i	$0.532494\pi$
$60$	1.46471e7			1.13018
$61$			1.97635e7i			1.42740i	0.700452	+	0.713700i	$0.252982\pi$
$61$			1.97635e7i			1.42740i	−0.700452	+	0.713700i	$0.747018\pi$
$62$			8.94640e6i			0.605455i
$63$			1.66727e7i			1.05839i
$64$	−2.09715e6			−0.125000
$65$		−	1.95705e7i		−	1.09635i
$66$	−1.62513e7	−	7.22001e6i	−0.856470	−	0.380506i
$67$	1.24402e7			0.617348			0.308674	−	0.951168i	$-0.400115\pi$
$67$	1.24402e7			0.617348			0.308674	+	0.951168i	$0.400115\pi$
$68$		−	389795.i		−	0.0182306i
$69$	1.38438e7			0.610744
$70$	4.05005e7			1.68682
$71$	−3.54223e7			−1.39394			−0.696969	−	0.717102i	$-0.745468\pi$
$71$	−3.54223e7			−1.39394			−0.696969	+	0.717102i	$0.745468\pi$
$72$		−	7.18921e6i		−	0.267517i
$73$		−	1.52941e7i		−	0.538557i	−0.963062	−	0.269278i	$-0.913215\pi$
$73$		−	1.52941e7i		−	0.538557i	0.963062	−	0.269278i	$-0.0867852\pi$
$74$			2.10326e7i			0.701400i
$75$	8.00352e7			2.52951
$76$			2.30409e7i			0.690629i
$77$	−4.49361e7	−	1.99639e7i	−1.27830	−	0.567914i
$78$	−2.23007e7			−0.602477
$79$			3.11795e7i			0.800499i	0.916406	+	0.400250i	$0.131077\pi$
$79$			3.11795e7i			0.800499i	−0.916406	+	0.400250i	$0.868923\pi$
$80$	−1.74636e7			−0.426358
$81$	−5.09729e7			−1.18413
$82$	2.16220e7			0.478234
$83$		−	3.73727e7i		−	0.787485i	−0.919221	−	0.393743i	$-0.871180\pi$
$83$		−	3.73727e7i		−	0.787485i	0.919221	−	0.393743i	$-0.128820\pi$
$84$		−	4.61507e7i		−	0.926961i
$85$		−	3.24594e6i		−	0.0621821i
$86$	−6.64275e7			−1.21438
$87$			8.62962e7i			1.50631i
$88$	1.93763e7	+	8.60834e6i	0.323102	+	0.143545i
$89$	−4.94298e7			−0.787823			−0.393911	−	0.919148i	$-0.628878\pi$
$89$	−4.94298e7			−0.787823			−0.393911	+	0.919148i	$0.628878\pi$
$90$		−	5.98668e7i		−	0.912465i
$91$	−6.16633e7			−0.899210
$92$	−1.65058e7			−0.230402
$93$	8.48929e7			1.13485
$94$		−	7.31043e7i		−	0.936336i
$95$			1.91869e8i			2.35564i
$96$			1.99000e7i			0.234298i
$97$	4.09642e7			0.462719			0.231360	−	0.972868i	$-0.425683\pi$
$97$	4.09642e7			0.462719			0.231360	+	0.972868i	$0.425683\pi$
$98$		−	6.23892e7i		−	0.676402i
$99$	−2.95101e7	+	6.64235e7i	−0.307206	+	0.691482i
$100$	−9.54252e7			−0.954252
$101$			1.18153e8i			1.13542i	0.823227	+	0.567712i	$0.192171\pi$
$101$			1.18153e8i			1.13542i	−0.823227	+	0.567712i	$0.807829\pi$
$102$	−3.69878e6			−0.0341710
$103$	1.55085e8			1.37791			0.688954	−	0.724805i	$-0.258070\pi$
$103$	1.55085e8			1.37791			0.688954	+	0.724805i	$0.258070\pi$
$104$	2.65889e7			0.227283
$105$		−	3.84311e8i		−	3.16174i
$106$			1.17145e8i			0.927901i
$107$		−	1.58572e7i		−	0.120974i	−0.998169	−	0.0604869i	$-0.980735\pi$
$107$		−	1.58572e7i		−	0.120974i	0.998169	−	0.0604869i	$-0.0192653\pi$
$108$	2.19399e7			0.161265
$109$		−	1.63146e8i		−	1.15577i	−0.816118	−	0.577885i	$-0.803878\pi$
$109$		−	1.63146e8i		−	1.15577i	0.816118	−	0.577885i	$-0.196122\pi$
$110$	1.61352e8	+	7.16844e7i	1.10206	+	0.489614i
$111$	1.99579e8			1.31469
$112$			5.50251e7i			0.349694i
$113$	9.10485e6			0.0558417			0.0279209	−	0.999610i	$-0.491111\pi$
$113$	9.10485e6			0.0558417			0.0279209	+	0.999610i	$0.491111\pi$
$114$	2.18636e8			1.29450
$115$	−1.37449e8			−0.785871
$116$		−	1.02890e8i		−	0.568253i
$117$			9.11491e7i			0.486417i
$118$		−	2.79408e7i		−	0.144116i
$119$	−1.02274e7			−0.0510010
$120$			1.65713e8i			0.799158i
$121$	−1.43688e8	−	1.59071e8i	−0.670316	−	0.742076i
$122$	−2.23599e8			−1.00932
$123$		−	2.05172e8i		−	0.896393i
$124$	−1.01217e8			−0.428121
$125$	−3.78270e8			−1.54939
$126$	−1.88631e8			−0.748393
$127$		−	1.11942e8i		−	0.430306i	−0.976580	−	0.215153i	$-0.930975\pi$
$127$		−	1.11942e8i		−	0.430306i	0.976580	−	0.215153i	$-0.0690251\pi$
$128$		−	2.37266e7i		−	0.0883883i
$129$			6.30335e8i			2.27621i
$130$	2.21414e8			0.775234
$131$		−	9.91228e7i		−	0.336580i	−0.985738	−	0.168290i	$-0.946175\pi$
$131$		−	9.91228e7i		−	0.336580i	0.985738	−	0.168290i	$-0.0538245\pi$
$132$	8.16850e7	−	1.83862e8i	0.269059	−	0.605616i
$133$	6.04547e8			1.93207
$134$			1.40745e8i			0.436531i
$135$	1.82701e8			0.550054
$136$	4.41002e6			0.0128910
$137$	4.10441e7			0.116511			0.0582557	−	0.998302i	$-0.481446\pi$
$137$	4.10441e7			0.116511			0.0582557	+	0.998302i	$0.481446\pi$
$138$			1.56625e8i			0.431861i
$139$			3.47447e8i			0.930742i	0.885116	+	0.465371i	$0.154079\pi$
$139$			3.47447e8i			0.930742i	−0.885116	+	0.465371i	$0.845921\pi$
$140$			4.58211e8i			1.19276i
$141$	−6.93691e8			−1.75505
$142$		−	4.00757e8i		−	0.985662i
$143$	−2.45664e8	−	1.09142e8i	−0.587485	−	0.261004i
$144$	8.13367e7			0.189163
$145$		−	8.56798e8i		−	1.93824i
$146$	1.73033e8			0.380817
$147$	−5.92014e8			−1.26784
$148$	−2.37956e8			−0.495964
$149$			1.07915e8i			0.218945i	0.993990	+	0.109473i	$0.0349162\pi$
$149$			1.07915e8i			0.218945i	−0.993990	+	0.109473i	$0.965084\pi$
$150$			9.05495e8i			1.78863i
$151$			5.27667e8i			1.01497i	0.861661	+	0.507484i	$0.169424\pi$
$151$			5.27667e8i			1.01497i	−0.861661	+	0.507484i	$0.830576\pi$
$152$	−2.60678e8			−0.488349
$153$			1.51179e7i			0.0275884i
$154$	2.25866e8	−	5.08394e8i	0.401576	−	0.903895i
$155$	−8.42866e8			−1.46026
$156$		−	2.52304e8i		−	0.426016i
$157$	2.06743e8			0.340277			0.170138	−	0.985420i	$-0.445579\pi$
$157$	2.06743e8			0.340277			0.170138	+	0.985420i	$0.445579\pi$
$158$	−3.52756e8			−0.566038
$159$	1.11160e9			1.73924
$160$		−	1.97579e8i		−	0.301481i
$161$			4.33080e8i			0.644562i
$162$		−	5.76692e8i		−	0.837306i
$163$	1.02174e9			1.44741			0.723705	−	0.690110i	$-0.242438\pi$
$163$	1.02174e9			1.44741			0.723705	+	0.690110i	$0.242438\pi$
$164$			2.44625e8i			0.338163i
$165$	6.80217e8	−	1.53108e9i	0.917723	−	2.06568i
$166$	4.22824e8			0.556836
$167$		−	1.22957e8i		−	0.158084i	−0.996871	−	0.0790422i	$-0.974814\pi$
$167$		−	1.22957e8i		−	0.158084i	0.996871	−	0.0790422i	$-0.0251862\pi$
$168$	5.22136e8			0.655460
$169$	4.78620e8			0.586738
$170$	3.67236e7			0.0439693
$171$		−	8.93626e8i		−	1.04513i
$172$		−	7.51542e8i		−	0.858696i
$173$			3.45610e8i			0.385835i	0.981215	+	0.192918i	$0.0617950\pi$
$173$			3.45610e8i			0.385835i	−0.981215	+	0.192918i	$0.938205\pi$
$174$	−9.76330e8			−1.06512
$175$			2.50377e9i			2.66957i
$176$	−9.73923e7	+	2.19217e8i	−0.101502	+	0.228467i
$177$	−2.65132e8			−0.270128
$178$		−	5.59234e8i		−	0.557075i
$179$	1.26831e9			1.23541			0.617707	−	0.786409i	$-0.288062\pi$
$179$	1.26831e9			1.23541			0.617707	+	0.786409i	$0.288062\pi$
$180$	6.77316e8			0.645210
$181$	−5.10123e8			−0.475292			−0.237646	−	0.971352i	$-0.576376\pi$
$181$	−5.10123e8			−0.475292			−0.237646	+	0.971352i	$0.576376\pi$
$182$		−	6.97641e8i		−	0.635838i
$183$			2.12174e9i			1.89186i
$184$		−	1.86742e8i		−	0.162919i
$185$	−1.98154e9			−1.69167
$186$			9.60454e8i			0.802462i
$187$	−4.07456e7	−	1.81022e7i	−0.0333207	−	0.0148035i
$188$	8.27081e8			0.662090
$189$		−	5.75660e8i		−	0.451148i
$190$	−2.17075e9			−1.66569
$191$	1.27397e9			0.957253			0.478626	−	0.878019i	$-0.341135\pi$
$191$	1.27397e9			0.957253			0.478626	+	0.878019i	$0.341135\pi$
$192$	−2.25143e8			−0.165673
$193$			5.01886e8i			0.361722i	0.983509	+	0.180861i	$0.0578885\pi$
$193$			5.01886e8i			0.361722i	−0.983509	+	0.180861i	$0.942112\pi$
$194$			4.63457e8i			0.327192i
$195$		−	2.10101e9i		−	1.45308i
$196$	7.05853e8			0.478289
$197$		−	5.13021e8i		−	0.340620i	−0.985391	−	0.170310i	$-0.945523\pi$
$197$		−	5.13021e8i		−	0.340620i	0.985391	−	0.170310i	$-0.0544769\pi$
$198$	−7.51496e8	−	3.33869e8i	−0.488951	−	0.217228i
$199$	−2.60295e9			−1.65979			−0.829895	−	0.557920i	$-0.811600\pi$
$199$	−2.60295e9			−1.65979			−0.829895	+	0.557920i	$0.811600\pi$
$200$		−	1.07961e9i		−	0.674758i
$201$	1.33554e9			0.818225
$202$	−1.33675e9			−0.802866
$203$	−2.69963e9			−1.58972
$204$		−	4.18470e7i		−	0.0241626i
$205$			2.03707e9i			1.15343i
$206$			1.75458e9i			0.974328i
$207$	6.40168e8			0.348668
$208$			3.00820e8i			0.160714i
$209$	2.40849e9	+	1.07003e9i	1.26229	+	0.560801i
$210$	4.34799e9			2.23569
$211$		−	9.08887e8i		−	0.458543i	−0.973363	−	0.229271i	$-0.926366\pi$
$211$		−	9.08887e8i		−	0.458543i	0.973363	−	0.229271i	$-0.0736344\pi$
$212$	−1.32535e9			−0.656125
$213$	−3.80281e9			−1.84751
$214$	1.79404e8			0.0855414
$215$		−	6.25832e9i		−	2.92890i
$216$			2.48222e8i			0.114032i
$217$			2.65573e9i			1.19769i
$218$	1.84579e9			0.817252
$219$		−	1.64192e9i		−	0.713796i
$220$	−8.11016e8	+	1.82549e9i	−0.346209	+	0.779272i
$221$	−5.59129e7			−0.0234392
$222$			2.25798e9i			0.929626i
$223$	−2.95821e9			−1.19622			−0.598108	−	0.801415i	$-0.704081\pi$
$223$	−2.95821e9			−1.19622			−0.598108	+	0.801415i	$0.704081\pi$
$224$	−6.22538e8			−0.247271
$225$	3.70100e9			1.44407
$226$			1.03010e8i			0.0394861i
$227$		−	2.51073e9i		−	0.945576i	−0.881176	−	0.472788i	$-0.843248\pi$
$227$		−	2.51073e9i		−	0.945576i	0.881176	−	0.472788i	$-0.156752\pi$
$228$			2.47359e9i			0.915351i
$229$	3.15387e9			1.14684			0.573419	−	0.819262i	$-0.305617\pi$
$229$	3.15387e9			1.14684			0.573419	+	0.819262i	$0.305617\pi$
$230$		−	1.55506e9i		−	0.555694i
$231$	−4.82418e9	−	2.14325e9i	−1.69424	−	0.752706i
$232$	1.16407e9			0.401815
$233$			5.76200e9i			1.95501i	0.210905	+	0.977506i	$0.432359\pi$
$233$			5.76200e9i			1.95501i	−0.210905	+	0.977506i	$0.567641\pi$
$234$	−1.03123e9			−0.343949
$235$	6.88736e9			2.25830
$236$	3.16115e8			0.101905
$237$			3.34732e9i			1.06097i
$238$		−	1.15710e8i		−	0.0360632i
$239$			9.46263e8i			0.290015i	0.989431	+	0.145007i	$0.0463206\pi$
$239$			9.46263e8i			0.290015i	−0.989431	+	0.145007i	$0.953679\pi$
$240$	−1.87483e9			−0.565090
$241$		−	4.91602e9i		−	1.45729i	−0.684892	−	0.728644i	$-0.740151\pi$
$241$		−	4.91602e9i		−	1.45729i	0.684892	−	0.728644i	$-0.259849\pi$
$242$	1.79968e9	−	1.62565e9i	0.524727	−	0.473985i
$243$	−4.34767e9			−1.24690
$244$		−	2.52973e9i		−	0.713700i
$245$	5.87786e9			1.63138
$246$	2.32126e9			0.633846
$247$	3.30503e9			0.887948
$248$		−	1.14514e9i		−	0.302727i
$249$		−	4.01220e9i		−	1.04372i
$250$		−	4.27963e9i		−	1.09559i
$251$	1.92828e9			0.485820			0.242910	−	0.970049i	$-0.421898\pi$
$251$	1.92828e9			0.485820			0.242910	+	0.970049i	$0.421898\pi$
$252$		−	2.13411e9i		−	0.529194i
$253$	−7.66535e8	+	1.72537e9i	−0.187090	+	0.421115i
$254$	1.26648e9			0.304272
$255$		−	3.48473e8i		−	0.0824153i
$256$	2.68435e8			0.0625000
$257$	−1.82805e9			−0.419039			−0.209520	−	0.977804i	$-0.567190\pi$
$257$	−1.82805e9			−0.419039			−0.209520	+	0.977804i	$0.567190\pi$
$258$	−7.13142e9			−1.60952
$259$			6.24350e9i			1.38749i
$260$			2.50502e9i			0.548173i
$261$			3.99052e9i			0.859940i
$262$	1.12145e9			0.237998
$263$		−	8.47338e9i		−	1.77106i	−0.464581	−	0.885531i	$-0.653795\pi$
$263$		−	8.47338e9i		−	1.77106i	0.464581	−	0.885531i	$-0.346205\pi$
$264$	2.08017e9	+	9.24161e8i	0.428235	+	0.190253i
$265$	−1.10366e10			−2.23796
$266$			6.83967e9i			1.36618i
$267$	−5.30660e9			−1.04417
$268$	−1.59235e9			−0.308674
$269$	5.95203e9			1.13673			0.568363	−	0.822778i	$-0.307577\pi$
$269$	5.95203e9			1.13673			0.568363	+	0.822778i	$0.307577\pi$
$270$			2.06702e9i			0.388947i
$271$			6.96805e8i			0.129192i	0.997912	+	0.0645958i	$0.0205758\pi$
$271$			6.96805e8i			0.129192i	−0.997912	+	0.0645958i	$0.979424\pi$
$272$			4.98937e7i			0.00911528i
$273$	−6.61995e9			−1.19180
$274$			4.64361e8i			0.0823860i
$275$	−4.43157e9	+	9.97489e9i	−0.774866	+	1.74412i
$276$	−1.77201e9			−0.305372
$277$		−	3.75478e9i		−	0.637772i	−0.947793	−	0.318886i	$-0.896691\pi$
$277$		−	3.75478e9i		−	0.637772i	0.947793	−	0.318886i	$-0.103309\pi$
$278$	−3.93091e9			−0.658134
$279$	3.92564e9			0.647878
$280$	−5.18406e9			−0.843409
$281$		−	5.93778e9i		−	0.952355i	−0.879349	−	0.476178i	$-0.842022\pi$
$281$		−	5.93778e9i		−	0.952355i	0.879349	−	0.476178i	$-0.157978\pi$
$282$		−	7.84822e9i		−	1.24101i
$283$		−	1.82263e9i		−	0.284154i	−0.989856	−	0.142077i	$-0.954622\pi$
$283$		−	1.82263e9i		−	0.284154i	0.989856	−	0.142077i	$-0.0453781\pi$
$284$	4.53405e9			0.696969
$285$			2.05983e10i			3.12214i
$286$	1.23480e9	−	2.77937e9i	0.184557	−	0.415415i
$287$	6.41847e9			0.946028
$288$			9.20219e8i			0.133758i
$289$	6.96648e9			0.998671
$290$	9.69356e9			1.37054
$291$	4.39777e9			0.613282
$292$			1.95764e9i			0.269278i
$293$		−	4.48121e9i		−	0.608029i	−0.952667	−	0.304015i	$-0.901673\pi$
$293$		−	4.48121e9i		−	0.608029i	0.952667	−	0.304015i	$-0.0983272\pi$
$294$		−	6.69788e9i		−	0.896495i
$295$	2.63238e9			0.347585
$296$		−	2.69217e9i		−	0.350700i
$297$	1.01890e9	−	2.29340e9i	0.130950	−	0.294750i
$298$	−1.22091e9			−0.154818
$299$			2.36763e9i			0.296230i
$300$	−1.02445e10			−1.26475
$301$	−1.97190e10			−2.40225
$302$	−5.96987e9			−0.717691
$303$			1.26845e10i			1.50488i
$304$		−	2.94923e9i		−	0.345315i
$305$		−	2.10659e10i		−	2.43434i
$306$	−1.71040e8			−0.0195079
$307$			1.48030e10i			1.66646i	0.552926	+	0.833230i	$0.313511\pi$
$307$			1.48030e10i			1.66646i	−0.552926	+	0.833230i	$0.686489\pi$
$308$	5.75183e9	+	2.55538e9i	0.639150	+	0.283957i
$309$	1.66493e10			1.82626
$310$		−	9.53594e9i		−	1.03256i
$311$	2.33763e9			0.249882			0.124941	−	0.992164i	$-0.460126\pi$
$311$	2.33763e9			0.249882			0.124941	+	0.992164i	$0.460126\pi$
$312$	2.85449e9			0.301239
$313$	3.98216e9			0.414898			0.207449	−	0.978246i	$-0.433484\pi$
$313$	3.98216e9			0.414898			0.207449	+	0.978246i	$0.433484\pi$
$314$			2.33903e9i			0.240612i
$315$		−	1.77714e10i		−	1.80501i
$316$		−	3.99098e9i		−	0.400250i
$317$	6.72620e9			0.666090			0.333045	−	0.942911i	$-0.391924\pi$
$317$	6.72620e9			0.666090			0.333045	+	0.942911i	$0.391924\pi$
$318$			1.25763e10i			1.22983i
$319$	−1.07552e10	−	4.77824e9i	−1.03862	−	0.461430i
$320$	2.23535e9			0.213179
$321$		−	1.70237e9i		−	0.160337i
$322$	−4.89974e9			−0.455774
$323$	5.48170e8			0.0503623
$324$	6.52453e9			0.592065
$325$			1.36880e10i			1.22689i
$326$			1.15597e10i			1.02347i
$327$		−	1.75148e10i		−	1.53184i
$328$	−2.76762e9			−0.239117
$329$		−	2.17010e10i		−	1.85223i
$330$	1.73222e10	+	7.69577e9i	1.46065	+	0.648928i
$331$	1.67921e9			0.139892			0.0699460	−	0.997551i	$-0.477717\pi$
$331$	1.67921e9			0.139892			0.0699460	+	0.997551i	$0.477717\pi$
$332$			4.78371e9i			0.393743i
$333$	9.22898e9			0.750545
$334$	1.39110e9			0.111782
$335$	−1.32600e10			−1.05285
$336$			5.90729e9i			0.463480i
$337$		−	5.65480e8i		−	0.0438427i	−0.999760	−	0.0219214i	$-0.993022\pi$
$337$		−	5.65480e8i		−	0.0438427i	0.999760	−	0.0219214i	$-0.00697835\pi$
$338$			5.41497e9i			0.414886i
$339$	9.77464e8			0.0740119
$340$			4.15481e8i			0.0310910i
$341$	−4.70054e9	+	1.05803e10i	−0.347641	+	0.782494i
$342$	1.01102e10			0.739020
$343$			8.40706e8i			0.0607390i
$344$	8.50273e9			0.607190
$345$	−1.47561e10			−1.04158
$346$	−3.91013e9			−0.272827
$347$			2.55153e10i			1.75988i	0.475083	+	0.879941i	$0.342418\pi$
$347$			2.55153e10i			1.75988i	−0.475083	+	0.879941i	$0.657582\pi$
$348$		−	1.10459e10i		−	0.753155i
$349$		−	8.37613e9i		−	0.564601i	−0.959326	−	0.282300i	$-0.908903\pi$
$349$		−	8.37613e9i		−	0.564601i	0.959326	−	0.282300i	$-0.0910975\pi$
$350$	−2.83269e10			−1.88767
$351$		−	3.14711e9i		−	0.207340i
$352$	−2.48016e9	−	1.10187e9i	−0.161551	−	0.0717726i
$353$	−2.09179e10			−1.34716			−0.673580	−	0.739114i	$-0.735245\pi$
$353$	−2.09179e10			−1.34716			−0.673580	+	0.739114i	$0.735245\pi$
$354$		−	2.99963e9i		−	0.191009i
$355$	3.77565e10			2.37727
$356$	6.32701e9			0.393911
$357$	−1.09798e9			−0.0675961
$358$			1.43493e10i			0.873569i
$359$		−	5.13471e9i		−	0.309128i	−0.987983	−	0.154564i	$-0.950603\pi$
$359$		−	5.13471e9i		−	0.309128i	0.987983	−	0.154564i	$-0.0493972\pi$
$360$			7.66295e9i			0.456232i
$361$	−1.54190e10			−0.907875
$362$		−	5.77139e9i		−	0.336083i
$363$	−1.54258e10	−	1.70772e10i	−0.888429	−	0.983538i
$364$	7.89290e9			0.449605
$365$			1.63019e10i			0.918473i
$366$	−2.40048e10			−1.33775
$367$	8.84680e9			0.487666			0.243833	−	0.969817i	$-0.421595\pi$
$367$	8.84680e9			0.487666			0.243833	+	0.969817i	$0.421595\pi$
$368$	2.11275e9			0.115201
$369$		−	9.48762e9i		−	0.511743i
$370$		−	2.24185e10i		−	1.19619i
$371$			3.47745e10i			1.83555i
$372$	−1.08663e10			−0.567427
$373$		−	1.42801e10i		−	0.737729i	−0.929483	−	0.368865i	$-0.879747\pi$
$373$		−	1.42801e10i		−	0.737729i	0.929483	−	0.368865i	$-0.120253\pi$
$374$	2.04803e8	−	4.60984e8i	0.0104676	−	0.0235613i
$375$	−4.06097e10			−2.05355
$376$			9.35736e9i			0.468168i
$377$	−1.47588e10			−0.730608
$378$	6.51285e9			0.319010
$379$	5.57885e9			0.270388			0.135194	−	0.990819i	$-0.456834\pi$
$379$	5.57885e9			0.270388			0.135194	+	0.990819i	$0.456834\pi$
$380$		−	2.45592e10i		−	1.17782i
$381$		−	1.20177e10i		−	0.570323i
$382$			1.44134e10i			0.676880i
$383$	1.03414e10			0.480600			0.240300	−	0.970699i	$-0.422754\pi$
$383$	1.03414e10			0.480600			0.240300	+	0.970699i	$0.422754\pi$
$384$		−	2.54720e9i		−	0.117149i
$385$	4.78972e10	+	2.12794e10i	2.18006	+	0.968539i
$386$	−5.67819e9			−0.255776
$387$			2.91481e10i			1.29947i
$388$	−5.24342e9			−0.231360
$389$	−4.04072e10			−1.76466			−0.882329	−	0.470633i	$-0.844026\pi$
$389$	−4.04072e10			−1.76466			−0.882329	+	0.470633i	$0.844026\pi$
$390$	2.37703e10			1.02748
$391$			3.92693e8i			0.0168014i
$392$			7.98581e9i			0.338201i
$393$		−	1.06415e10i		−	0.446099i
$394$	5.80417e9			0.240855
$395$		−	3.32341e10i		−	1.36520i
$396$	3.77730e9	−	8.50220e9i	0.153603	−	0.345741i
$397$	1.92978e10			0.776867			0.388433	−	0.921477i	$-0.373016\pi$
$397$	1.92978e10			0.776867			0.388433	+	0.921477i	$0.373016\pi$
$398$		−	2.94490e10i		−	1.17365i
$399$	6.49020e10			2.56075
$400$	1.22144e10			0.477126
$401$	1.71839e10			0.664576			0.332288	−	0.943178i	$-0.392179\pi$
$401$	1.71839e10			0.664576			0.332288	+	0.943178i	$0.392179\pi$
$402$			1.51099e10i			0.578572i
$403$			1.45188e10i			0.550439i
$404$		−	1.51235e10i		−	0.567712i
$405$	5.43318e10			2.01945
$406$		−	3.05428e10i		−	1.12410i
$407$	−1.10508e10	+	2.48738e10i	−0.402730	+	0.906494i
$408$	4.73444e8			0.0170855
$409$		−	4.43496e10i		−	1.58488i	−0.609950	−	0.792440i	$-0.708810\pi$
$409$		−	4.43496e10i		−	1.58488i	0.609950	−	0.792440i	$-0.291190\pi$
$410$	−2.30468e10			−0.815597
$411$	4.40635e9			0.154423
$412$	−1.98508e10			−0.688954
$413$		−	8.29421e9i		−	0.285085i
$414$			7.24267e9i			0.246546i
$415$			3.98354e10i			1.34300i
$416$	−3.40339e9			−0.113642
$417$			3.73007e10i			1.23359i
$418$	−1.21060e10	+	2.72489e10i	−0.396546	+	0.892574i
$419$	3.48472e10			1.13061			0.565304	−	0.824882i	$-0.308759\pi$
$419$	3.48472e10			1.13061			0.565304	+	0.824882i	$0.308759\pi$
$420$			4.91919e10i			1.58087i
$421$	−4.46769e10			−1.42218			−0.711090	−	0.703101i	$-0.751798\pi$
$421$	−4.46769e10			−1.42218			−0.711090	+	0.703101i	$0.751798\pi$
$422$	1.02829e10			0.324239
$423$	−3.20778e10			−1.00194
$424$		−	1.49946e10i		−	0.463951i
$425$			2.27028e9i			0.0695862i
$426$		−	4.30239e10i		−	1.30638i
$427$	−6.63752e10			−1.99661
$428$			2.02972e9i			0.0604869i
$429$	−2.63736e10	−	1.17171e10i	−0.778646	−	0.345931i
$430$	7.08048e10			2.07104
$431$			2.19637e10i			0.636497i	0.948007	+	0.318248i	$0.103095\pi$
$431$			2.19637e10i			0.636497i	−0.948007	+	0.318248i	$0.896905\pi$
$432$	−2.80831e9			−0.0806325
$433$	2.09111e9			0.0594874			0.0297437	−	0.999558i	$-0.490531\pi$
$433$	2.09111e9			0.0594874			0.0297437	+	0.999558i	$0.490531\pi$
$434$	−3.00462e10			−0.846896
$435$		−	9.19827e10i		−	2.56891i
$436$			2.08827e10i			0.577885i
$437$		−	2.32122e10i		−	0.636489i
$438$	1.85762e10			0.504730
$439$		−	6.24447e9i		−	0.168127i	−0.996460	−	0.0840635i	$-0.973210\pi$
$439$		−	6.24447e9i		−	0.168127i	0.996460	−	0.0840635i	$-0.0267899\pi$
$440$	−2.06531e10	−	9.17560e9i	−0.551029	−	0.244807i
$441$	−2.73760e10			−0.723796
$442$		−	6.32582e8i		−	0.0165740i
$443$	−3.60739e8			−0.00936652			−0.00468326	−	0.999989i	$-0.501491\pi$
$443$	−3.60739e8			−0.00936652			−0.00468326	+	0.999989i	$0.501491\pi$
$444$	−2.55461e10			−0.657345
$445$	5.26870e10			1.34358
$446$		−	3.34683e10i		−	0.845853i
$447$			1.15853e10i			0.290187i
$448$		−	7.04321e9i		−	0.174847i
$449$	1.40883e10			0.346635			0.173317	−	0.984866i	$-0.444551\pi$
$449$	1.40883e10			0.346635			0.173317	+	0.984866i	$0.444551\pi$
$450$			4.18721e10i			1.02111i
$451$	2.55709e10	+	1.13605e10i	0.618073	+	0.274593i
$452$	−1.16542e9			−0.0279209
$453$			5.66484e10i			1.34523i
$454$	2.84057e10			0.668623
$455$	6.57267e10			1.53354
$456$	−2.79854e10			−0.647251
$457$		−	4.48437e10i		−	1.02810i	−0.857760	−	0.514051i	$-0.828144\pi$
$457$		−	4.48437e10i		−	1.02810i	0.857760	−	0.514051i	$-0.171856\pi$
$458$			3.56820e10i			0.810937i
$459$		−	5.21977e8i		−	0.0117598i
$460$	1.75935e10			0.392935
$461$			7.44959e10i			1.64941i	0.565562	+	0.824706i	$0.308659\pi$
$461$			7.44959e10i			1.64941i	−0.565562	+	0.824706i	$0.691341\pi$
$462$	2.42481e10	−	5.45794e10i	0.532243	−	1.19801i
$463$	−6.03013e10			−1.31221			−0.656105	−	0.754670i	$-0.727797\pi$
$463$	−6.03013e10			−1.31221			−0.656105	+	0.754670i	$0.727797\pi$
$464$			1.31699e10i			0.284126i
$465$	−9.04870e10			−1.93542
$466$	−6.51896e10			−1.38240
$467$	−5.22205e10			−1.09793			−0.548963	−	0.835846i	$-0.684977\pi$
$467$	−5.22205e10			−1.09793			−0.548963	+	0.835846i	$0.684977\pi$
$468$		−	1.16671e10i		−	0.243209i
$469$			4.17801e10i			0.863532i
$470$			7.79216e10i			1.59686i
$471$	2.21952e10			0.450998
$472$			3.57643e9i			0.0720579i
$473$	−7.85594e10	−	3.49018e10i	−1.56947	−	0.697274i
$474$	−3.78706e10			−0.750220
$475$		−	1.34197e11i		−	2.63614i
$476$	1.30911e9			0.0255005
$477$	5.14028e10			0.992917
$478$	−1.07057e10			−0.205072
$479$			6.42483e10i			1.22045i	0.792228	+	0.610225i	$0.208921\pi$
$479$			6.42483e10i			1.22045i	−0.792228	+	0.610225i	$0.791079\pi$
$480$		−	2.12113e10i		−	0.399579i
$481$			3.41329e10i			0.637666i
$482$	5.56184e10			1.03046
$483$			4.64939e10i			0.854295i
$484$	1.83921e10	+	2.03610e10i	0.335158	+	0.371038i
$485$	−4.36636e10			−0.789137
$486$		−	4.91883e10i		−	0.881692i
$487$	−3.07857e10			−0.547309			−0.273655	−	0.961828i	$-0.588233\pi$
$487$	−3.07857e10			−0.547309			−0.273655	+	0.961828i	$0.588233\pi$
$488$	2.86207e10			0.504662
$489$	1.09691e11			1.91838
$490$			6.65004e10i			1.15356i
$491$			4.47915e10i			0.770671i	0.922776	+	0.385336i	$0.125914\pi$
$491$			4.47915e10i			0.770671i	−0.922776	+	0.385336i	$0.874086\pi$
$492$			2.62621e10i			0.448197i
$493$	−2.44788e9			−0.0414383
$494$			3.73922e10i			0.627874i
$495$	3.14547e10	−	7.08005e10i	0.523920	−	1.17928i
$496$	1.29558e10			0.214061
$497$		−	1.18964e11i		−	1.94981i
$498$	4.53929e10			0.738024
$499$	3.39394e10			0.547396			0.273698	−	0.961816i	$-0.411753\pi$
$499$	3.39394e10			0.547396			0.273698	+	0.961816i	$0.411753\pi$
$500$	4.84185e10			0.774696
$501$		−	1.32003e10i		−	0.209523i
$502$			2.18160e10i			0.343527i
$503$		−	7.83988e10i		−	1.22472i	−0.790578	−	0.612361i	$-0.790220\pi$
$503$		−	7.83988e10i		−	1.22472i	0.790578	−	0.612361i	$-0.209780\pi$
$504$	2.41447e10			0.374197
$505$		−	1.25939e11i		−	1.93639i
$506$	−1.95204e10	−	8.67236e9i	−0.297773	−	0.132292i
$507$	5.13829e10			0.777655
$508$			1.43286e10i			0.215153i
$509$	7.95844e10			1.18565			0.592825	−	0.805331i	$-0.298013\pi$
$509$	7.95844e10			1.18565			0.592825	+	0.805331i	$0.298013\pi$
$510$	3.94252e9			0.0582764
$511$	5.13645e10			0.753321
$512$			3.03700e9i			0.0441942i
$513$			3.08542e10i			0.445497i
$514$		−	2.06820e10i		−	0.296305i
$515$	−1.65304e11			−2.34993
$516$		−	8.06828e10i		−	1.13810i
$517$	3.84099e10	−	8.64556e10i	0.537626	−	1.21013i
$518$	−7.06371e10			−0.981102
$519$			3.71035e10i			0.511382i
$520$	−2.83411e10			−0.387617
$521$	1.61542e10			0.219247			0.109623	−	0.993973i	$-0.465036\pi$
$521$	1.61542e10			0.219247			0.109623	+	0.993973i	$0.465036\pi$
$522$	−4.51476e10			−0.608069
$523$		−	1.90690e10i		−	0.254872i	−0.991847	−	0.127436i	$-0.959325\pi$
$523$		−	1.90690e10i		−	0.254872i	0.991847	−	0.127436i	$-0.0406747\pi$
$524$			1.26877e10i			0.168290i
$525$			2.68795e11i			3.53822i
$526$	9.58653e10			1.25233
$527$			2.40807e9i			0.0312196i
$528$	−1.04557e10	+	2.35344e10i	−0.134529	+	0.302808i
$529$	−6.16824e10			−0.787660
$530$		−	1.24865e11i		−	1.58247i
$531$	−1.22603e10			−0.154214
$532$	−7.73820e10			−0.966036
$533$	3.50895e10			0.434779
$534$		−	6.00373e10i		−	0.738340i
$535$			1.69021e10i			0.206313i
$536$		−	1.80154e10i		−	0.218265i
$537$	1.36161e11			1.63740
$538$			6.73395e10i			0.803787i
$539$	3.27800e10	−	7.37835e10i	0.388377	−	0.874187i
$540$	−2.33857e10			−0.275027
$541$			1.58088e11i			1.84548i	0.385427	+	0.922739i	$0.374054\pi$
$541$			1.58088e11i			1.84548i	−0.385427	+	0.922739i	$0.625946\pi$
$542$	−7.88345e9			−0.0913523
$543$	−5.47650e10			−0.629947
$544$	−5.64483e8			−0.00644548
$545$			1.73897e11i			1.97109i
$546$		−	7.48962e10i		−	0.842731i
$547$		−	3.30999e10i		−	0.369724i	−0.982764	−	0.184862i	$-0.940816\pi$
$547$		−	3.30999e10i		−	0.369724i	0.982764	−	0.184862i	$-0.0591839\pi$
$548$	−5.25364e9			−0.0582557
$549$			9.81141e10i			1.08005i
$550$	−1.12853e11	−	5.01375e10i	−1.23328	−	0.547913i
$551$	1.44695e11			1.56981
$552$		−	2.00480e10i		−	0.215931i
$553$	−1.04715e11			−1.11972
$554$	4.24805e10			0.450973
$555$	−2.12731e11			−2.24212
$556$		−	4.44732e10i		−	0.465371i
$557$			1.79805e11i			1.86802i	0.357250	+	0.934009i	$0.383715\pi$
$557$			1.79805e11i			1.86802i	−0.357250	+	0.934009i	$0.616285\pi$
$558$			4.44135e10i			0.458119i
$559$	−1.07803e11			−1.10403
$560$		−	5.86510e10i		−	0.596380i
$561$	−4.37430e9	−	1.94338e9i	−0.0441629	−	0.0196204i
$562$	6.71783e10			0.673417
$563$		−	8.00717e10i		−	0.796977i	−0.917173	−	0.398488i	$-0.869535\pi$
$563$		−	8.00717e10i		−	0.796977i	0.917173	−	0.398488i	$-0.130465\pi$
$564$	8.87925e10			0.877525
$565$	−9.70482e9			−0.0952344
$566$	2.06208e10			0.200927
$567$		−	1.71191e11i		−	1.65633i
$568$			5.12969e10i			0.492831i
$569$		−	9.97788e10i		−	0.951896i	−0.879474	−	0.475948i	$-0.842105\pi$
$569$		−	9.97788e10i		−	0.951896i	0.879474	−	0.475948i	$-0.157895\pi$
$570$	−2.33044e11			−2.20769
$571$		−	3.65344e10i		−	0.343683i	−0.985125	−	0.171841i	$-0.945028\pi$
$571$		−	3.65344e10i		−	0.343683i	0.985125	−	0.171841i	$-0.0549717\pi$
$572$	3.14450e10	+	1.39701e10i	0.293743	+	0.130502i
$573$	1.36769e11			1.26873
$574$			7.26167e10i			0.668943i
$575$	9.61348e10			0.879446
$576$	−1.04111e10			−0.0945815
$577$	−1.45081e11			−1.30890			−0.654452	−	0.756103i	$-0.727101\pi$
$577$	−1.45081e11			−1.30890			−0.654452	+	0.756103i	$0.727101\pi$
$578$			7.88168e10i			0.706167i
$579$			5.38806e10i			0.479422i
$580$			1.09670e11i			0.969118i
$581$	1.25515e11			1.10152
$582$			4.97551e10i			0.433656i
$583$	−6.15495e10	+	1.38540e11i	−0.532783	+	1.19923i
$584$	−2.21482e10			−0.190409
$585$		−	9.71555e10i		−	0.829553i
$586$	5.06991e10			0.429942
$587$	5.23812e10			0.441187			0.220594	−	0.975366i	$-0.429201\pi$
$587$	5.23812e10			0.441187			0.220594	+	0.975366i	$0.429201\pi$
$588$	7.57778e10			0.633918
$589$		−	1.42342e11i		−	1.18269i
$590$			2.97820e10i			0.245780i
$591$		−	5.50761e10i		−	0.451453i
$592$	3.04584e10			0.247982
$593$		−	1.47372e11i		−	1.19178i	−0.803066	−	0.595890i	$-0.796799\pi$
$593$		−	1.47372e11i		−	1.19178i	0.803066	−	0.595890i	$-0.203201\pi$
$594$	2.59469e10	+	1.15275e10i	0.208420	+	0.0925953i
$595$	1.09014e10			0.0869788
$596$		−	1.38131e10i		−	0.109473i
$597$	−2.79443e11			−2.19986
$598$	−2.67867e10			−0.209466
$599$	−2.85450e10			−0.221729			−0.110865	−	0.993836i	$-0.535362\pi$
$599$	−2.85450e10			−0.221729			−0.110865	+	0.993836i	$0.535362\pi$
$600$		−	1.15903e11i		−	0.894316i
$601$		−	1.04044e9i		−	0.00797480i	−0.999992	−	0.00398740i	$-0.998731\pi$
$601$		−	1.04044e9i		−	0.00797480i	0.999992	−	0.00398740i	$-0.00126923\pi$
$602$		−	2.23094e11i		−	1.69865i
$603$	6.17583e10			0.467118
$604$		−	6.75414e10i		−	0.507484i
$605$	1.53157e11	+	1.69553e11i	1.14318	+	1.26556i
$606$	−1.43508e11			−1.06411
$607$			6.76881e10i			0.498606i	0.968426	+	0.249303i	$0.0802015\pi$
$607$			6.76881e10i			0.498606i	−0.968426	+	0.249303i	$0.919798\pi$
$608$	3.33668e10			0.244174
$609$	−2.89823e11			−2.10699
$610$	2.38333e11			1.72133
$611$		−	1.18638e11i		−	0.851255i
$612$		−	1.93509e9i		−	0.0137942i
$613$		−	4.18024e10i		−	0.296046i	−0.988984	−	0.148023i	$-0.952709\pi$
$613$		−	4.18024e10i		−	0.296046i	0.988984	−	0.148023i	$-0.0472910\pi$
$614$	−1.67476e11			−1.17837
$615$			2.18692e11i			1.52874i
$616$	−2.89108e10	+	6.50745e10i	−0.200788	+	0.451947i
$617$	2.06804e11			1.42698			0.713492	−	0.700663i	$-0.247112\pi$
$617$	2.06804e11			1.42698			0.713492	+	0.700663i	$0.247112\pi$
$618$			1.88366e11i			1.29136i
$619$	1.05226e11			0.716741			0.358370	−	0.933579i	$-0.383332\pi$
$619$	1.05226e11			0.716741			0.358370	+	0.933579i	$0.383332\pi$
$620$	1.07887e11			0.730132
$621$	−2.21031e10			−0.148623
$622$			2.64473e10i			0.176693i
$623$		−	1.66008e11i		−	1.10199i
$624$			3.22949e10i			0.213008i
$625$	1.11982e11			0.733882
$626$			4.50530e10i			0.293377i
$627$	2.58567e11	+	1.14874e11i	1.67302	+	0.743279i
$628$	−2.64631e10			−0.170138
$629$			5.66126e9i			0.0361669i
$630$	2.01061e11			1.27633
$631$	6.14446e10			0.387584			0.193792	−	0.981043i	$-0.437921\pi$
$631$	6.14446e10			0.387584			0.193792	+	0.981043i	$0.437921\pi$
$632$	4.51528e10			0.283019
$633$		−	9.75748e10i		−	0.607747i
$634$			7.60983e10i			0.470997i
$635$			1.19318e11i			0.733859i
$636$	−1.42285e11			−0.869620
$637$		−	1.01249e11i		−	0.614940i
$638$	5.40597e10	−	1.21681e11i	0.326280	−	0.734414i
$639$	−1.75850e11			−1.05473
$640$			2.52901e10i			0.150740i
$641$	2.29437e11			1.35904			0.679519	−	0.733658i	$-0.262189\pi$
$641$	2.29437e11			1.35904			0.679519	+	0.733658i	$0.262189\pi$
$642$	1.92601e10			0.113376
$643$	9.30078e10			0.544096			0.272048	−	0.962284i	$-0.412299\pi$
$643$	9.30078e10			0.544096			0.272048	+	0.962284i	$0.412299\pi$
$644$		−	5.54343e10i		−	0.322281i
$645$		−	6.71871e11i		−	3.88192i
$646$			6.20184e9i			0.0356115i
$647$	−1.65018e11			−0.941702			−0.470851	−	0.882213i	$-0.656053\pi$
$647$	−1.65018e11			−0.941702			−0.470851	+	0.882213i	$0.656053\pi$
$648$			7.38166e10i			0.418653i
$649$	1.46804e10	−	3.30438e10i	0.0827486	−	0.186256i
$650$	−1.54862e11			−0.867542
$651$			2.85110e11i			1.58741i
$652$	−1.30783e11			−0.723705
$653$	1.43934e11			0.791610			0.395805	−	0.918335i	$-0.370466\pi$
$653$	1.43934e11			0.791610			0.395805	+	0.918335i	$0.370466\pi$
$654$	1.98157e11			1.08318
$655$			1.05655e11i			0.574015i
$656$		−	3.13120e10i		−	0.169081i
$657$		−	7.59258e10i		−	0.407500i
$658$	2.45518e11			1.30973
$659$			1.10006e11i			0.583279i	0.956528	+	0.291640i	$0.0942008\pi$
$659$			1.10006e11i			0.583279i	−0.956528	+	0.291640i	$0.905799\pi$
$660$	−8.70678e10	+	1.95978e11i	−0.458861	+	1.03284i
$661$	−1.14673e11			−0.600695			−0.300348	−	0.953830i	$-0.597103\pi$
$661$	−1.14673e11			−0.600695			−0.300348	+	0.953830i	$0.597103\pi$
$662$			1.89981e10i			0.0989185i
$663$	−6.00261e9			−0.0310660
$664$	−5.41215e10			−0.278418
$665$	−6.44384e11			−3.29502
$666$			1.04414e11i			0.530716i
$667$			1.03655e11i			0.523706i
$668$			1.57385e10i			0.0790422i
$669$	−3.17583e11			−1.58545
$670$		−	1.50020e11i		−	0.744474i
$671$	−2.64436e11	−	1.17482e11i	−1.30446	−	0.579535i
$672$	−6.68334e10			−0.327730
$673$			1.40462e11i			0.684698i	0.939573	+	0.342349i	$0.111223\pi$
$673$			1.40462e11i			0.684698i	−0.939573	+	0.342349i	$0.888777\pi$
$674$	6.39767e9			0.0310015
$675$	−1.27785e11			−0.615550
$676$	−6.12634e10			−0.293369
$677$			1.42844e11i			0.679998i	0.940426	+	0.339999i	$0.110427\pi$
$677$			1.42844e11i			0.679998i	−0.940426	+	0.339999i	$0.889573\pi$
$678$			1.10587e10i			0.0523343i
$679$			1.37577e11i			0.647241i
$680$	−4.70063e9			−0.0219847
$681$		−	2.69543e11i		−	1.25325i
$682$	−1.19703e11	−	5.31806e10i	−0.553307	−	0.245819i
$683$	2.64521e11			1.21556			0.607782	−	0.794104i	$-0.292059\pi$
$683$	2.64521e11			1.21556			0.607782	+	0.794104i	$0.292059\pi$
$684$			1.14384e11i			0.522566i
$685$	−4.37487e10			−0.198702
$686$	−9.51151e9			−0.0429490
$687$	3.38588e11			1.52000
$688$			9.61974e10i			0.429348i
$689$			1.90111e11i			0.843586i
$690$		−	1.66946e11i		−	0.736510i
$691$	1.00992e11			0.442969			0.221484	−	0.975164i	$-0.428910\pi$
$691$	1.00992e11			0.442969			0.221484	+	0.975164i	$0.428910\pi$
$692$		−	4.42381e10i		−	0.192918i
$693$	−2.23081e11	−	9.91087e10i	−0.967229	−	0.429713i
$694$	−2.88673e11			−1.24442
$695$		−	3.70342e11i		−	1.58732i
$696$	1.24970e11			0.532561
$697$	5.81992e9			0.0246596
$698$	9.47651e10			0.399233
$699$			6.18588e11i			2.59115i
$700$		−	3.20482e11i		−	1.33479i
$701$		−	2.91296e10i		−	0.120632i	−0.998179	−	0.0603160i	$-0.980789\pi$
$701$		−	2.91296e10i		−	0.120632i	0.998179	−	0.0603160i	$-0.0192108\pi$
$702$	3.56054e10			0.146611
$703$		−	3.34639e11i		−	1.37011i
$704$	1.24662e10	−	2.80598e10i	0.0507509	−	0.114234i
$705$	7.39402e11			2.99312
$706$		−	2.36659e11i		−	0.952587i
$707$	−3.96812e11			−1.58821
$708$	3.39369e10			0.135064
$709$	2.06523e10			0.0817305			0.0408652	−	0.999165i	$-0.486989\pi$
$709$	2.06523e10			0.0817305			0.0408652	+	0.999165i	$0.486989\pi$
$710$			4.27166e11i			1.68098i
$711$			1.54787e11i			0.605700i
$712$			7.15819e10i			0.278537i
$713$	1.01970e11			0.394560
$714$		−	1.24222e10i		−	0.0477977i
$715$	2.61852e11	+	1.16334e11i	1.00192	+	0.445124i
$716$	−1.62343e11			−0.617707
$717$			1.01587e11i			0.384382i
$718$	5.80926e10			0.218586
$719$	−6.12833e10			−0.229312			−0.114656	−	0.993405i	$-0.536577\pi$
$719$	−6.12833e10			−0.229312			−0.114656	+	0.993405i	$0.536577\pi$
$720$	−8.66964e10			−0.322605
$721$			5.20846e11i			1.92739i
$722$		−	1.74446e11i		−	0.641965i
$723$		−	5.27766e11i		−	1.93147i
$724$	6.52958e10			0.237646
$725$			5.99262e11i			2.16903i
$726$	1.93207e11	−	1.74524e11i	0.695466	−	0.628214i
$727$	−1.89951e11			−0.679994			−0.339997	−	0.940427i	$-0.610426\pi$
$727$	−1.89951e11			−0.679994			−0.339997	+	0.940427i	$0.610426\pi$
$728$			8.92980e10i			0.317919i
$729$	−1.32317e11			−0.468497
$730$	−1.84435e11			−0.649458
$731$	−1.78801e10			−0.0626181
$732$		−	2.71583e11i		−	0.945929i
$733$		−	5.03570e11i		−	1.74439i	−0.489158	−	0.872195i	$-0.662696\pi$
$733$		−	5.03570e11i		−	1.74439i	0.489158	−	0.872195i	$-0.337304\pi$
$734$			1.00090e11i			0.344832i
$735$	6.31026e11			2.16221
$736$			2.39030e10i			0.0814594i
$737$	−7.39492e10	+	1.66450e11i	−0.250648	+	0.564175i
$738$	1.07340e11			0.361857
$739$			3.10991e11i			1.04273i	0.853335	+	0.521363i	$0.174576\pi$
$739$			3.10991e11i			1.04273i	−0.853335	+	0.521363i	$0.825424\pi$
$740$	2.53637e11			0.845834
$741$	3.54816e11			1.17688
$742$	−3.93428e11			−1.29793
$743$			6.45324e10i			0.211750i	0.994379	+	0.105875i	$0.0337643\pi$
$743$			6.45324e10i			0.211750i	−0.994379	+	0.105875i	$0.966236\pi$
$744$		−	1.22938e11i		−	0.401231i
$745$		−	1.15026e11i		−	0.373396i
$746$	1.61561e11			0.521654
$747$		−	1.85533e11i		−	0.595853i
$748$	5.21544e9	+	2.31708e9i	0.0166604	+	0.00740175i
$749$	5.32558e10			0.169215
$750$		−	4.59446e11i		−	1.45208i
$751$	−5.37663e11			−1.69025			−0.845124	−	0.534570i	$-0.820474\pi$
$751$	−5.37663e11			−1.69025			−0.845124	+	0.534570i	$0.820474\pi$
$752$	−1.05866e11			−0.331045
$753$	2.07013e11			0.643900
$754$		−	1.66976e11i		−	0.516618i
$755$		−	5.62438e11i		−	1.73096i
$756$			7.36844e10i			0.225574i
$757$	−3.02429e11			−0.920957			−0.460478	−	0.887671i	$-0.652322\pi$
$757$	−3.02429e11			−0.920957			−0.460478	+	0.887671i	$0.652322\pi$
$758$			6.31175e10i			0.191193i
$759$	−8.22925e10	+	1.85230e11i	−0.247967	+	0.558140i
$760$	2.77856e11			0.832846
$761$		−	1.76863e11i		−	0.527349i	−0.964612	−	0.263675i	$-0.915065\pi$
$761$		−	1.76863e11i		−	0.527349i	0.964612	−	0.263675i	$-0.0849345\pi$
$762$	1.35964e11			0.403279
$763$	5.47921e11			1.61666
$764$	−1.63068e11			−0.478626
$765$		−	1.61141e10i		−	0.0470502i
$766$			1.16999e11i			0.339836i
$767$		−	4.53441e10i		−	0.131021i
$768$	2.88183e10			0.0828367
$769$			1.46197e11i			0.418056i	0.977910	+	0.209028i	$0.0670300\pi$
$769$			1.46197e11i			0.418056i	−0.977910	+	0.209028i	$0.932970\pi$
$770$	−2.40749e11	+	5.41895e11i	−0.684861	+	1.54153i
$771$	−1.96252e11			−0.555389
$772$		−	6.42414e10i		−	0.180861i
$773$	2.18958e11			0.613258			0.306629	−	0.951829i	$-0.400799\pi$
$773$	2.18958e11			0.613258			0.306629	+	0.951829i	$0.400799\pi$
$774$	−3.29773e11			−0.918863
$775$	5.89517e11			1.63414
$776$		−	5.93225e10i		−	0.163596i
$777$			6.70279e11i			1.83896i
$778$		−	4.57155e11i		−	1.24780i
$779$	−3.44017e11			−0.934180
$780$			2.68930e11i			0.726542i
$781$	2.10563e11	−	4.73949e11i	0.565949	−	1.27388i
$782$	−4.44282e9			−0.0118804
$783$		−	1.37781e11i		−	0.366557i
$784$	−9.03492e10			−0.239144
$785$	−2.20366e11			−0.580319
$786$	1.20394e11			0.315440
$787$			3.82192e11i			0.996282i	0.867096	+	0.498141i	$0.165984\pi$
$787$			3.82192e11i			0.996282i	−0.867096	+	0.498141i	$0.834016\pi$
$788$			6.56667e10i			0.170310i
$789$		−	9.09671e11i		−	2.34734i
$790$	3.76001e11			0.965341
$791$			3.05783e10i			0.0781101i
$792$	9.61914e10	+	4.27352e10i	0.244476	+	0.108614i
$793$	−3.62870e11			−0.917610
$794$			2.18330e11i			0.549328i
$795$	−1.18485e12			−2.96616
$796$	3.33177e11			0.829895
$797$	−1.99828e11			−0.495248			−0.247624	−	0.968856i	$-0.579650\pi$
$797$	−1.99828e11			−0.495248			−0.247624	+	0.968856i	$0.579650\pi$
$798$			7.34282e11i			1.81072i
$799$		−	1.96772e10i		−	0.0482811i
$800$			1.38190e11i			0.337379i
$801$	−2.45389e11			−0.596108
$802$			1.94414e11i			0.469927i
$803$	2.04634e11	+	9.09133e10i	0.492171	+	0.218658i
$804$	−1.70949e11			−0.409112
$805$		−	4.61618e11i		−	1.09926i
$806$	−1.64261e11			−0.389219
$807$	6.38989e11			1.50660
$808$	1.71103e11			0.401433
$809$		−	7.04635e11i		−	1.64502i	−0.568754	−	0.822508i	$-0.692574\pi$
$809$		−	7.04635e11i		−	1.64502i	0.568754	−	0.822508i	$-0.307426\pi$
$810$			6.14694e11i			1.42797i
$811$			2.30141e11i			0.531999i	0.963973	+	0.265999i	$0.0857019\pi$
$811$			2.30141e11i			0.531999i	−0.963973	+	0.265999i	$0.914298\pi$
$812$	3.45553e11			0.794859
$813$			7.48065e10i			0.171229i
$814$	−2.81415e11	−	1.25025e11i	−0.640988	−	0.284773i
$815$	−1.08907e12			−2.46846
$816$			5.35641e9i			0.0120813i
$817$	1.05690e12			2.37216
$818$	5.01758e11			1.12068
$819$	−3.06121e11			−0.680390
$820$		−	2.60745e11i		−	0.576714i
$821$			4.32504e11i			0.951957i	0.879457	+	0.475979i	$0.157906\pi$
$821$			4.32504e11i			0.951957i	−0.879457	+	0.475979i	$0.842094\pi$
$822$			4.98521e10i			0.109193i
$823$	−5.60310e8			−0.00122132			−0.000610659	−	1.00000i	$-0.500194\pi$
$823$	−5.60310e8			−0.00122132			−0.000610659		1.00000i	$0.500194\pi$
$824$		−	2.24587e11i		−	0.487164i
$825$	−4.75757e11	+	1.07087e12i	−1.02700	+	2.31164i
$826$	9.38383e10			0.201586
$827$			7.69936e11i			1.64601i	0.568033	+	0.823006i	$0.307704\pi$
$827$			7.69936e11i			1.64601i	−0.568033	+	0.823006i	$0.692296\pi$
$828$	−8.19415e10			−0.174334
$829$	−6.88427e11			−1.45760			−0.728802	−	0.684724i	$-0.759923\pi$
$829$	−6.88427e11			−1.45760			−0.728802	+	0.684724i	$0.759923\pi$
$830$	−4.50687e11			−0.949647
$831$		−	4.03100e11i		−	0.845295i
$832$		−	3.85049e10i		−	0.0803568i
$833$		−	1.67931e10i		−	0.0348779i
$834$	−4.22009e11			−0.872283
$835$			1.31060e11i			0.269602i
$836$	−3.08286e11	−	1.36963e11i	−0.631145	−	0.280401i
$837$	−1.35540e11			−0.276164
$838$			3.94251e11i			0.799461i
$839$	7.23133e11			1.45939			0.729693	−	0.683775i	$-0.239663\pi$
$839$	7.23133e11			1.45939			0.729693	+	0.683775i	$0.239663\pi$
$840$	−5.56542e11			−1.11784
$841$	−1.45895e11			−0.291645
$842$		−	5.05462e11i		−	1.00563i
$843$		−	6.37459e11i		−	1.26224i
$844$			1.16338e11i			0.229271i
$845$	−5.10159e11			−1.00064
$846$		−	3.62919e11i		−	0.708481i
$847$	5.34233e11	−	4.82572e11i	1.03800	−	0.937623i
$848$	1.69645e11			0.328063
$849$		−	1.95671e11i		−	0.376614i
$850$	−2.56853e10			−0.0492049
$851$	2.39726e11			0.457085
$852$	4.86760e11			0.923753
$853$		−	1.84780e11i		−	0.349027i	−0.984655	−	0.174514i	$-0.944165\pi$
$853$		−	1.84780e11i		−	0.349027i	0.984655	−	0.174514i	$-0.0558353\pi$
$854$		−	7.50949e11i		−	1.41182i
$855$			9.52512e11i			1.78240i
$856$	−2.29637e10			−0.0427707
$857$		−	3.73581e11i		−	0.692566i	−0.938130	−	0.346283i	$-0.887444\pi$
$857$		−	3.73581e11i		−	0.692566i	0.938130	−	0.346283i	$-0.112556\pi$
$858$	1.32563e11	−	2.98383e11i	0.244610	−	0.550586i
$859$	7.68889e11			1.41218			0.706091	−	0.708121i	$-0.250457\pi$
$859$	7.68889e11			1.41218			0.706091	+	0.708121i	$0.250457\pi$
$860$			8.01065e11i			1.46445i
$861$	6.89064e11			1.25385
$862$	−2.48491e11			−0.450071
$863$	3.07507e11			0.554386			0.277193	−	0.960814i	$-0.410596\pi$
$863$	3.07507e11			0.554386			0.277193	+	0.960814i	$0.410596\pi$
$864$		−	3.17724e10i		−	0.0570158i
$865$		−	3.68384e11i		−	0.658017i
$866$			2.36582e10i			0.0420639i
$867$	7.47897e11			1.32363
$868$		−	3.39934e11i		−	0.598846i
$869$	−4.17181e11	−	1.85342e11i	−0.731552	−	0.325009i
$870$	1.04067e12			1.81650
$871$			2.28410e11i			0.396865i
$872$	−2.36261e11			−0.408626
$873$	2.03362e11			0.350117
$874$	2.62616e11			0.450066
$875$		−	1.27040e12i		−	2.16725i
$876$			2.10165e11i			0.356898i
$877$			8.14445e11i			1.37678i	0.725342	+	0.688389i	$0.241682\pi$
$877$			8.14445e11i			1.37678i	−0.725342	+	0.688389i	$0.758318\pi$
$878$	7.06481e10			0.118884
$879$		−	4.81086e11i		−	0.805874i
$880$	1.03810e11	−	2.33663e11i	0.173105	−	0.389636i
$881$	6.15951e11			1.02245			0.511226	−	0.859447i	$-0.329192\pi$
$881$	6.15951e11			1.02245			0.511226	+	0.859447i	$0.329192\pi$
$882$		−	3.09725e11i		−	0.511801i
$883$	−7.84739e11			−1.29087			−0.645435	−	0.763815i	$-0.723324\pi$
$883$	−7.84739e11			−1.29087			−0.645435	+	0.763815i	$0.723324\pi$
$884$	7.15685e9			0.0117196
$885$	2.82603e11			0.460685
$886$		−	4.08130e9i		−	0.00662313i
$887$			4.96777e10i			0.0802541i	0.999195	+	0.0401270i	$0.0127763\pi$
$887$			4.96777e10i			0.0802541i	−0.999195	+	0.0401270i	$0.987224\pi$
$888$		−	2.89022e11i		−	0.464813i
$889$	3.75953e11			0.601902
$890$			5.96085e11i			0.950054i
$891$	3.03001e11	−	6.82016e11i	0.480765	−	1.08214i
$892$	3.78651e11			0.598108
$893$			1.16313e12i			1.82903i
$894$	−1.31073e11			−0.205193
$895$	−1.35188e12			−2.10692
$896$	7.96848e10			0.123636
$897$			2.54180e11i			0.392620i
$898$			1.59391e11i			0.245108i
$899$			6.35634e11i			0.973124i
$900$	−4.73728e11			−0.722037
$901$			3.15316e10i			0.0478461i
$902$	−1.28529e11	+	2.89302e11i	−0.194167	+	0.437044i
$903$	−2.11696e12			−3.18391
$904$		−	1.31852e10i		−	0.0197430i
$905$	5.43738e11			0.810580
$906$	−6.40904e11			−0.951218
$907$	−2.72646e11			−0.402875			−0.201438	−	0.979501i	$-0.564561\pi$
$907$	−2.72646e11			−0.402875			−0.201438	+	0.979501i	$0.564561\pi$
$908$			3.21373e11i			0.472788i
$909$			5.86557e11i			0.859122i
$910$			7.43612e11i			1.08438i
$911$	3.22636e11			0.468424			0.234212	−	0.972186i	$-0.424749\pi$
$911$	3.22636e11			0.468424			0.234212	+	0.972186i	$0.424749\pi$
$912$		−	3.16619e11i		−	0.457676i
$913$	5.00046e11	+	2.22157e11i	0.719659	+	0.319725i
$914$	5.07348e11			0.726978
$915$		−	2.26156e12i		−	3.22644i
$916$	−4.03695e11			−0.573419
$917$	3.32900e11			0.470800
$918$	5.90549e9			0.00831544
$919$			8.15014e11i			1.14262i	0.820733	+	0.571311i	$0.193565\pi$
$919$			8.15014e11i			1.14262i	−0.820733	+	0.571311i	$0.806435\pi$
$920$			1.99048e11i			0.277847i
$921$			1.58919e12i			2.20871i
$922$	−8.42825e11			−1.16631
$923$		−	6.50373e11i		−	0.896099i
$924$	6.17495e11	+	2.74336e11i	0.847122	+	0.376353i
$925$	1.38593e12			1.89310
$926$		−	6.82232e11i		−	0.927872i
$927$	7.69902e11			1.04260
$928$	−1.49001e11			−0.200908
$929$	−1.16871e12			−1.56908			−0.784541	−	0.620077i	$-0.787101\pi$
$929$	−1.16871e12			−1.56908			−0.784541	+	0.620077i	$0.787101\pi$
$930$		−	1.02374e12i		−	1.36855i
$931$			9.92644e11i			1.32128i
$932$		−	7.37536e11i		−	0.977506i
$933$	2.50960e11			0.331190
$934$		−	5.90807e11i		−	0.776351i
$935$	4.34306e10	+	1.92950e10i	0.0568263	+	0.0252464i
$936$	1.31998e11			0.171975
$937$			6.97255e11i			0.904552i	0.891878	+	0.452276i	$0.149388\pi$
$937$			6.97255e11i			0.904552i	−0.891878	+	0.452276i	$0.850612\pi$
$938$	−4.72688e11			−0.610609
$939$	4.27511e11			0.549901
$940$	−8.81582e11			−1.12915
$941$		−	1.00973e12i		−	1.28779i	−0.765113	−	0.643896i	$-0.777317\pi$
$941$		−	1.00973e12i		−	1.28779i	0.765113	−	0.643896i	$-0.222683\pi$
$942$			2.51110e11i			0.318904i
$943$		−	2.46444e11i		−	0.311653i
$944$	−4.04627e10			−0.0509526
$945$			6.13593e11i			0.769402i
$946$	3.94869e11	−	8.88798e11i	0.493047	−	1.10978i
$947$	−6.74858e11			−0.839097			−0.419549	−	0.907733i	$-0.637812\pi$
$947$	−6.74858e11			−0.839097			−0.419549	+	0.907733i	$0.637812\pi$
$948$		−	4.28457e11i		−	0.530486i
$949$	2.80808e11			0.346214
$950$	1.51826e12			1.86403
$951$	7.22101e11			0.882827
$952$			1.48109e10i			0.0180316i
$953$			4.22219e11i			0.511878i	0.966693	+	0.255939i	$0.0823846\pi$
$953$			4.22219e11i			0.511878i	−0.966693	+	0.255939i	$0.917615\pi$
$954$			5.81556e11i			0.702099i
$955$	−1.35792e12			−1.63253
$956$		−	1.21122e11i		−	0.145007i
$957$	−1.15464e12	−	5.12975e11i	−1.37657	−	0.611573i
$958$	−7.26887e11			−0.862988
$959$			1.37845e11i			0.162973i
$960$	2.39979e11			0.282545
$961$	−2.27593e11			−0.266849
$962$	−3.86170e11			−0.450898
$963$		−	7.87214e10i		−	0.0915351i
$964$			6.29251e11i			0.728644i
$965$		−	5.34958e11i		−	0.616894i
$966$	−5.26019e11			−0.604077
$967$			1.16711e12i			1.33477i	0.744712	+	0.667386i	$0.232587\pi$
$967$			1.16711e12i			1.33477i	−0.744712	+	0.667386i	$0.767413\pi$
$968$	−2.30359e11	+	2.08083e11i	−0.262363	+	0.236993i
$969$	5.88496e10			0.0667495
$970$		−	4.93997e11i		−	0.558004i
$971$	−3.25447e11			−0.366103			−0.183051	−	0.983103i	$-0.558597\pi$
$971$	−3.25447e11			−0.366103			−0.183051	+	0.983103i	$0.558597\pi$
$972$	5.56502e11			0.623450
$973$	−1.16689e12			−1.30190
$974$		−	3.48300e11i		−	0.387006i
$975$			1.46949e12i			1.62611i
$976$			3.23806e11i			0.356850i
$977$	−2.82408e11			−0.309955			−0.154978	−	0.987918i	$-0.549531\pi$
$977$	−2.82408e11			−0.309955			−0.154978	+	0.987918i	$0.549531\pi$
$978$			1.24101e12i			1.35650i
$979$	2.93828e11	−	6.61369e11i	0.319862	−	0.719967i
$980$	−7.52366e11			−0.815689
$981$		−	8.09923e11i		−	0.874516i
$982$	−5.06758e11			−0.544947
$983$	−1.04658e12			−1.12088			−0.560439	−	0.828196i	$-0.689367\pi$
$983$	−1.04658e12			−1.12088			−0.560439	+	0.828196i	$0.689367\pi$
$984$	−2.97121e11			−0.316923
$985$			5.46827e11i			0.580905i
$986$		−	2.76946e10i		−	0.0293013i
$987$		−	2.32974e12i		−	2.45492i
$988$	−4.23044e11			−0.443974
$989$			7.57131e11i			0.791381i
$990$	8.01016e11	+	3.55870e11i	0.833874	+	0.370467i
$991$	−4.32249e11			−0.448167			−0.224083	−	0.974570i	$-0.571939\pi$
$991$	−4.32249e11			−0.448167			−0.224083	+	0.974570i	$0.571939\pi$
$992$			1.46578e11i			0.151364i
$993$	1.80274e11			0.185411
$994$	1.34593e12			1.37872
$995$	2.77447e12			2.83066
$996$			5.13562e11i			0.521862i
$997$		−	6.50471e11i		−	0.658336i	−0.944271	−	0.329168i	$-0.893232\pi$
$997$		−	6.50471e11i		−	0.658336i	0.944271	−	0.329168i	$-0.106768\pi$
$998$			3.83980e11i			0.387067i
$999$	−3.18649e11			−0.319927

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.9.b.a.21.7	yes	8
3.2	odd	2		198.9.d.a.109.4		8
4.3	odd	2		176.9.h.e.65.3		8
11.10	odd	2	inner	22.9.b.a.21.3	✓	8
33.32	even	2		198.9.d.a.109.8		8
44.43	even	2		176.9.h.e.65.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.9.b.a.21.3	✓	8	11.10	odd	2	inner
22.9.b.a.21.7	yes	8	1.1	even	1	trivial
176.9.h.e.65.3		8	4.3	odd	2
176.9.h.e.65.4		8	44.43	even	2
198.9.d.a.109.4		8	3.2	odd	2
198.9.d.a.109.8		8	33.32	even	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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	22.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+11.3137i q^{2} +107.356 q^{3} -128.000 q^{4} -1065.90 q^{5} +1214.60i q^{6} +3358.46i q^{7} -1448.15i q^{8} +4964.40 q^{9} +O(q^{10})\)	\(q+11.3137i q^{2} +107.356 q^{3} -128.000 q^{4} -1065.90 q^{5} +1214.60i q^{6} +3358.46i q^{7} -1448.15i q^{8} +4964.40 q^{9} -12059.2i q^{10} +(-5944.35 + 13380.0i) q^{11} -13741.6 q^{12} +18360.6i q^{13} -37996.7 q^{14} -114431. q^{15} +16384.0 q^{16} +3045.27i q^{17} +56165.7i q^{18} -180007. i q^{19} +136435. q^{20} +360553. i q^{21} +(-151377. - 67252.7i) q^{22} +128952. q^{23} -155469. i q^{24} +745509. q^{25} -207726. q^{26} -171406. q^{27} -429883. i q^{28} +803829. i q^{29} -1.29464e6i q^{30} +790758. q^{31} +185364. i q^{32} +(-638164. + 1.43643e6i) q^{33} -34453.3 q^{34} -3.57977e6i q^{35} -635443. q^{36} +1.85903e6 q^{37} +2.03655e6 q^{38} +1.97112e6i q^{39} +1.54358e6i q^{40} -1.91113e6i q^{41} -4.07919e6 q^{42} +5.87142e6i q^{43} +(760877. - 1.71264e6i) q^{44} -5.29153e6 q^{45} +1.45892e6i q^{46} -6.46157e6 q^{47} +1.75893e6 q^{48} -5.51448e6 q^{49} +8.43447e6i q^{50} +326929. i q^{51} -2.35015e6i q^{52} +1.03543e7 q^{53} -1.93923e6i q^{54} +(6.33606e6 - 1.42617e7i) q^{55} +4.86357e6 q^{56} -1.93249e7i q^{57} -9.09429e6 q^{58} -2.46965e6 q^{59} +1.46471e7 q^{60} +1.97635e7i q^{61} +8.94640e6i q^{62} +1.66727e7i q^{63} -2.09715e6 q^{64} -1.95705e7i q^{65} +(-1.62513e7 - 7.22001e6i) q^{66} +1.24402e7 q^{67} -389795. i q^{68} +1.38438e7 q^{69} +4.05005e7 q^{70} -3.54223e7 q^{71} -7.18921e6i q^{72} -1.52941e7i q^{73} +2.10326e7i q^{74} +8.00352e7 q^{75} +2.30409e7i q^{76} +(-4.49361e7 - 1.99639e7i) q^{77} -2.23007e7 q^{78} +3.11795e7i q^{79} -1.74636e7 q^{80} -5.09729e7 q^{81} +2.16220e7 q^{82} -3.73727e7i q^{83} -4.61507e7i q^{84} -3.24594e6i q^{85} -6.64275e7 q^{86} +8.62962e7i q^{87} +(1.93763e7 + 8.60834e6i) q^{88} -4.94298e7 q^{89} -5.98668e7i q^{90} -6.16633e7 q^{91} -1.65058e7 q^{92} +8.48929e7 q^{93} -7.31043e7i q^{94} +1.91869e8i q^{95} +1.99000e7i q^{96} +4.09642e7 q^{97} -6.23892e7i q^{98} +(-2.95101e7 + 6.64235e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 182 q^{3} - 1024 q^{4} - 1410 q^{5} + 44582 q^{9}+O(q^{10}) \) 8 * q + 182 * q^3 - 1024 * q^4 - 1410 * q^5 + 44582 * q^9	\( 8 q + 182 q^{3} - 1024 q^{4} - 1410 q^{5} + 44582 q^{9} + 5808 q^{11} - 23296 q^{12} + 12288 q^{14} + 87958 q^{15} + 131072 q^{16} + 180480 q^{20} + 359040 q^{22} - 802026 q^{23} + 999558 q^{25} - 1321728 q^{26} - 1561354 q^{27} + 196726 q^{31} - 4286722 q^{33} - 701952 q^{34} - 5706496 q^{36} + 8627998 q^{37} + 9288960 q^{38} + 4366848 q^{42} - 743424 q^{44} + 1146988 q^{45} - 14335392 q^{47} + 2981888 q^{48} - 6714712 q^{49} + 55946352 q^{53} - 10078442 q^{55} - 1572864 q^{56} - 23226624 q^{58} + 21793110 q^{59} - 11258624 q^{60} - 16777216 q^{64} - 44242176 q^{66} - 113809034 q^{67} - 171636914 q^{69} + 137817600 q^{70} + 16741974 q^{71} + 346496844 q^{75} - 137074080 q^{77} - 57993216 q^{78} - 23101440 q^{80} + 85282724 q^{81} + 47480832 q^{82} + 49839360 q^{86} - 45957120 q^{88} + 42055422 q^{89} - 146801952 q^{91} + 102659328 q^{92} + 253251118 q^{93} + 100034782 q^{97} - 333541978 q^{99}+O(q^{100}) \) 8 * q + 182 * q^3 - 1024 * q^4 - 1410 * q^5 + 44582 * q^9 + 5808 * q^11 - 23296 * q^12 + 12288 * q^14 + 87958 * q^15 + 131072 * q^16 + 180480 * q^20 + 359040 * q^22 - 802026 * q^23 + 999558 * q^25 - 1321728 * q^26 - 1561354 * q^27 + 196726 * q^31 - 4286722 * q^33 - 701952 * q^34 - 5706496 * q^36 + 8627998 * q^37 + 9288960 * q^38 + 4366848 * q^42 - 743424 * q^44 + 1146988 * q^45 - 14335392 * q^47 + 2981888 * q^48 - 6714712 * q^49 + 55946352 * q^53 - 10078442 * q^55 - 1572864 * q^56 - 23226624 * q^58 + 21793110 * q^59 - 11258624 * q^60 - 16777216 * q^64 - 44242176 * q^66 - 113809034 * q^67 - 171636914 * q^69 + 137817600 * q^70 + 16741974 * q^71 + 346496844 * q^75 - 137074080 * q^77 - 57993216 * q^78 - 23101440 * q^80 + 85282724 * q^81 + 47480832 * q^82 + 49839360 * q^86 - 45957120 * q^88 + 42055422 * q^89 - 146801952 * q^91 + 102659328 * q^92 + 253251118 * q^93 + 100034782 * q^97 - 333541978 * q^99

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