LMFDB - Embedded newform 22.11.b.a.21.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,11,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, 11, names="a")

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

chi := DirichletCharacter("22.21");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 11 $
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:	$13.9778595588$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 135903 x^{8} - 6427236 x^{7} + 6935435151 x^{6} + 631292713590 x^{5} + \cdots + 88\!\cdots\!36 $ x^10 - 2x^9 - 135903x^8 - 6427236x^7 + 6935435151x^6 + 631292713590x^5 - 146480704240861x^4 - 20333833907647600x^3 + 719974580168244048x^2 + 216833564330959154376*x + 8800385848545417604236
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{24}\cdot 3^{2}\cdot 11^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.5
Root			$-126.950 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.11.b.a.21.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22.6274i q^{2} +380.412 q^{3} -512.000 q^{4} +1511.55 q^{5} -8607.74i q^{6} -14680.5i q^{7} +11585.2i q^{8} +85664.2 q^{9} +O(q^{10})$	\(q-22.6274i q^{2} +380.412 q^{3} -512.000 q^{4} +1511.55 q^{5} -8607.74i q^{6} -14680.5i q^{7} +11585.2i q^{8} +85664.2 q^{9} -34202.4i q^{10} +(155111. - 43335.1i) q^{11} -194771. q^{12} +271268. i q^{13} -332183. q^{14} +575011. q^{15} +262144. q^{16} -495742. i q^{17} -1.93836e6i q^{18} -4.29794e6i q^{19} -773913. q^{20} -5.58465e6i q^{21} +(-980562. - 3.50977e6i) q^{22} +4.13702e6 q^{23} +4.40716e6i q^{24} -7.48085e6 q^{25} +6.13810e6 q^{26} +1.01247e7 q^{27} +7.51644e6i q^{28} +2.43927e7i q^{29} -1.30110e7i q^{30} -2.07233e7 q^{31} -5.93164e6i q^{32} +(5.90061e7 - 1.64852e7i) q^{33} -1.12174e7 q^{34} -2.21903e7i q^{35} -4.38600e7 q^{36} +5.24329e7 q^{37} -9.72513e7 q^{38} +1.03194e8i q^{39} +1.75116e7i q^{40} +1.78250e8i q^{41} -1.26366e8 q^{42} +7.80846e7i q^{43} +(-7.94169e7 + 2.21876e7i) q^{44} +1.29485e8 q^{45} -9.36102e7i q^{46} -1.47552e8 q^{47} +9.97227e7 q^{48} +6.69570e7 q^{49} +1.69272e8i q^{50} -1.88586e8i q^{51} -1.38889e8i q^{52} +4.90199e8 q^{53} -2.29096e8i q^{54} +(2.34458e8 - 6.55031e7i) q^{55} +1.70078e8 q^{56} -1.63499e9i q^{57} +5.51944e8 q^{58} -8.79145e8 q^{59} -2.94406e8 q^{60} +1.62033e9i q^{61} +4.68915e8i q^{62} -1.25760e9i q^{63} -1.34218e8 q^{64} +4.10035e8i q^{65} +(-3.73017e8 - 1.33516e9i) q^{66} -8.20477e8 q^{67} +2.53820e8i q^{68} +1.57377e9 q^{69} -5.02110e8 q^{70} +4.98665e8 q^{71} +9.92440e8i q^{72} +2.54843e9i q^{73} -1.18642e9i q^{74} -2.84580e9 q^{75} +2.20055e9i q^{76} +(-6.36183e8 - 2.27712e9i) q^{77} +2.33500e9 q^{78} -2.84301e9i q^{79} +3.96243e8 q^{80} -1.20682e9 q^{81} +4.03334e9 q^{82} +4.81747e9i q^{83} +2.85934e9i q^{84} -7.49338e8i q^{85} +1.76685e9 q^{86} +9.27927e9i q^{87} +(5.02048e8 + 1.79700e9i) q^{88} -5.79652e9 q^{89} -2.92992e9i q^{90} +3.98236e9 q^{91} -2.11816e9 q^{92} -7.88339e9 q^{93} +3.33873e9i q^{94} -6.49654e9i q^{95} -2.25647e9i q^{96} -1.28477e10 q^{97} -1.51506e9i q^{98} +(1.32875e10 - 3.71227e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 106 q^{3} - 5120 q^{4} + 1138 q^{5} + 78044 q^{9}+O(q^{10}) $ 10 * q - 106 * q^3 - 5120 * q^4 + 1138 * q^5 + 78044 * q^9	$ 10 q - 106 q^{3} - 5120 q^{4} + 1138 q^{5} + 78044 q^{9} + 95414 q^{11} + 54272 q^{12} - 156288 q^{14} + 1441618 q^{15} + 2621440 q^{16} - 582656 q^{20} - 6002304 q^{22} + 17496838 q^{23} - 1494468 q^{25} + 9714816 q^{26} + 54656930 q^{27} - 91050970 q^{31} - 12170158 q^{33} - 6879360 q^{34} - 39958528 q^{36} - 82676974 q^{37} - 55302528 q^{38} - 128221824 q^{42} - 48851968 q^{44} - 124619384 q^{45} + 352507996 q^{47} - 27787264 q^{48} - 374605478 q^{49} + 571129876 q^{53} + 1363103126 q^{55} + 80019456 q^{56} + 1594048512 q^{58} - 1508647610 q^{59} - 738108416 q^{60} - 1342177280 q^{64} + 1288087680 q^{66} + 3146811782 q^{67} + 5332296166 q^{69} - 1491609984 q^{70} - 328577450 q^{71} - 18684358968 q^{75} + 4256837904 q^{77} + 4919767680 q^{78} + 298319872 q^{80} - 16957790722 q^{81} + 4545650304 q^{82} - 12971187456 q^{86} + 3073179648 q^{88} + 17791426978 q^{89} + 40311734544 q^{91} - 8958381056 q^{92} - 11674310138 q^{93} - 62585189614 q^{97} + 48880194572 q^{99}+O(q^{100}) $ 10 * q - 106 * q^3 - 5120 * q^4 + 1138 * q^5 + 78044 * q^9 + 95414 * q^11 + 54272 * q^12 - 156288 * q^14 + 1441618 * q^15 + 2621440 * q^16 - 582656 * q^20 - 6002304 * q^22 + 17496838 * q^23 - 1494468 * q^25 + 9714816 * q^26 + 54656930 * q^27 - 91050970 * q^31 - 12170158 * q^33 - 6879360 * q^34 - 39958528 * q^36 - 82676974 * q^37 - 55302528 * q^38 - 128221824 * q^42 - 48851968 * q^44 - 124619384 * q^45 + 352507996 * q^47 - 27787264 * q^48 - 374605478 * q^49 + 571129876 * q^53 + 1363103126 * q^55 + 80019456 * q^56 + 1594048512 * q^58 - 1508647610 * q^59 - 738108416 * q^60 - 1342177280 * q^64 + 1288087680 * q^66 + 3146811782 * q^67 + 5332296166 * q^69 - 1491609984 * q^70 - 328577450 * q^71 - 18684358968 * q^75 + 4256837904 * q^77 + 4919767680 * q^78 + 298319872 * q^80 - 16957790722 * q^81 + 4545650304 * q^82 - 12971187456 * q^86 + 3073179648 * q^88 + 17791426978 * q^89 + 40311734544 * q^91 - 8958381056 * q^92 - 11674310138 * q^93 - 62585189614 * q^97 + 48880194572 * 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 $

$2$		−	22.6274i		−	0.707107i
$2$		−	22.6274i		−	0.707107i
$3$	380.412			1.56548			0.782740	−	0.622348i	$-0.213821\pi$
$3$	380.412			1.56548			0.782740	+	0.622348i	$0.213821\pi$
$4$	−512.000			−0.500000
$5$	1511.55			0.483695			0.241848	−	0.970314i	$-0.422247\pi$
$5$	1511.55			0.483695			0.241848	+	0.970314i	$0.422247\pi$
$6$		−	8607.74i		−	1.10696i
$7$		−	14680.5i		−	0.873478i	−0.899588	−	0.436739i	$-0.856133\pi$
$7$		−	14680.5i		−	0.873478i	0.899588	−	0.436739i	$-0.143867\pi$
$8$			11585.2i			0.353553i
$9$	85664.2			1.45073
$10$		−	34202.4i		−	0.342024i
$11$	155111.	−	43335.1i	0.963119	−	0.269077i
$11$	155111.	−	43335.1i	0.963119	−	0.269077i
$12$	−194771.			−0.782740
$13$			271268.i			0.730604i	0.930889	+	0.365302i	$0.119034\pi$
$13$			271268.i			0.730604i	−0.930889	+	0.365302i	$0.880966\pi$
$14$	−332183.			−0.617642
$15$	575011.			0.757216
$16$	262144.			0.250000
$17$		−	495742.i		−	0.349149i	−0.984644	−	0.174575i	$-0.944145\pi$
$17$		−	495742.i		−	0.349149i	0.984644	−	0.174575i	$-0.0558550\pi$
$18$		−	1.93836e6i		−	1.02582i
$19$		−	4.29794e6i		−	1.73577i	−0.496764	−	0.867886i	$-0.665479\pi$
$19$		−	4.29794e6i		−	1.73577i	0.496764	−	0.867886i	$-0.334521\pi$
$20$	−773913.			−0.241848
$21$		−	5.58465e6i		−	1.36741i
$22$	−980562.	−	3.50977e6i	−0.190266	−	0.681028i
$23$	4.13702e6			0.642760			0.321380	−	0.946950i	$-0.395853\pi$
$23$	4.13702e6			0.642760			0.321380	+	0.946950i	$0.395853\pi$
$24$			4.40716e6i			0.553481i
$25$	−7.48085e6			−0.766039
$26$	6.13810e6			0.516615
$27$	1.01247e7			0.705609
$28$			7.51644e6i			0.436739i
$29$			2.43927e7i			1.18924i	0.804007	+	0.594620i	$0.202698\pi$
$29$			2.43927e7i			1.18924i	−0.804007	+	0.594620i	$0.797302\pi$
$30$		−	1.30110e7i		−	0.535432i
$31$	−2.07233e7			−0.723853			−0.361927	−	0.932207i	$-0.617881\pi$
$31$	−2.07233e7			−0.723853			−0.361927	+	0.932207i	$0.617881\pi$
$32$		−	5.93164e6i		−	0.176777i
$33$	5.90061e7	−	1.64852e7i	1.50774	−	0.421235i
$34$	−1.12174e7			−0.246886
$35$		−	2.21903e7i		−	0.422497i
$36$	−4.38600e7			−0.725365
$37$	5.24329e7			0.756127			0.378064	−	0.925780i	$-0.376590\pi$
$37$	5.24329e7			0.756127			0.378064	+	0.925780i	$0.376590\pi$
$38$	−9.72513e7			−1.22738
$39$			1.03194e8i			1.14375i
$40$			1.75116e7i			0.171012i
$41$			1.78250e8i			1.53855i	0.638920	+	0.769273i	$0.279382\pi$
$41$			1.78250e8i			1.53855i	−0.638920	+	0.769273i	$0.720618\pi$
$42$	−1.26366e8			−0.966907
$43$			7.80846e7i			0.531157i	0.964089	+	0.265579i	$0.0855630\pi$
$43$			7.80846e7i			0.531157i	−0.964089	+	0.265579i	$0.914437\pi$
$44$	−7.94169e7	+	2.21876e7i	−0.481559	+	0.134539i
$45$	1.29485e8			0.701711
$46$		−	9.36102e7i		−	0.454500i
$47$	−1.47552e8			−0.643365			−0.321682	−	0.946848i	$-0.604248\pi$
$47$	−1.47552e8			−0.643365			−0.321682	+	0.946848i	$0.604248\pi$
$48$	9.97227e7			0.391370
$49$	6.69570e7			0.237037
$50$			1.69272e8i			0.541671i
$51$		−	1.88586e8i		−	0.546586i
$52$		−	1.38889e8i		−	0.365302i
$53$	4.90199e8			1.17218			0.586089	−	0.810247i	$-0.300667\pi$
$53$	4.90199e8			1.17218			0.586089	+	0.810247i	$0.300667\pi$
$54$		−	2.29096e8i		−	0.498941i
$55$	2.34458e8	−	6.55031e7i	0.465856	−	0.130151i
$56$	1.70078e8			0.308821
$57$		−	1.63499e9i		−	2.71732i
$58$	5.51944e8			0.840920
$59$	−8.79145e8			−1.22970			−0.614852	−	0.788643i	$-0.710784\pi$
$59$	−8.79145e8			−1.22970			−0.614852	+	0.788643i	$0.710784\pi$
$60$	−2.94406e8			−0.378608
$61$			1.62033e9i			1.91847i	0.282611	+	0.959234i	$0.408799\pi$
$61$			1.62033e9i			1.91847i	−0.282611	+	0.959234i	$0.591201\pi$
$62$			4.68915e8i			0.511841i
$63$		−	1.25760e9i		−	1.26718i
$64$	−1.34218e8			−0.125000
$65$			4.10035e8i			0.353390i
$66$	−3.73017e8	−	1.33516e9i	−0.297858	−	1.06614i
$67$	−8.20477e8			−0.607704			−0.303852	−	0.952719i	$-0.598273\pi$
$67$	−8.20477e8			−0.607704			−0.303852	+	0.952719i	$0.598273\pi$
$68$			2.53820e8i			0.174575i
$69$	1.57377e9			1.00623
$70$	−5.02110e8			−0.298751
$71$	4.98665e8			0.276386			0.138193	−	0.990405i	$-0.455871\pi$
$71$	4.98665e8			0.276386			0.138193	+	0.990405i	$0.455871\pi$
$72$			9.92440e8i			0.512910i
$73$			2.54843e9i			1.22930i	0.788800	+	0.614650i	$0.210703\pi$
$73$			2.54843e9i			1.22930i	−0.788800	+	0.614650i	$0.789297\pi$
$74$		−	1.18642e9i		−	0.534663i
$75$	−2.84580e9			−1.19922
$76$			2.20055e9i			0.867886i
$77$	−6.36183e8	−	2.27712e9i	−0.235033	−	0.841263i
$78$	2.33500e9			0.808751
$79$		−	2.84301e9i		−	0.923937i	−0.886896	−	0.461969i	$-0.847143\pi$
$79$		−	2.84301e9i		−	0.923937i	0.886896	−	0.461969i	$-0.152857\pi$
$80$	3.96243e8			0.120924
$81$	−1.20682e9			−0.346113
$82$	4.03334e9			1.08792
$83$			4.81747e9i			1.22301i	0.791242	+	0.611503i	$0.209435\pi$
$83$			4.81747e9i			1.22301i	−0.791242	+	0.611503i	$0.790565\pi$
$84$			2.85934e9i			0.683706i
$85$		−	7.49338e8i		−	0.168882i
$86$	1.76685e9			0.375585
$87$			9.27927e9i			1.86173i
$88$	5.02048e8	+	1.79700e9i	0.0951331	+	0.340514i
$89$	−5.79652e9			−1.03805			−0.519024	−	0.854760i	$-0.673704\pi$
$89$	−5.79652e9			−1.03805			−0.519024	+	0.854760i	$0.673704\pi$
$90$		−	2.92992e9i		−	0.496185i
$91$	3.98236e9			0.638166
$92$	−2.11816e9			−0.321380
$93$	−7.88339e9			−1.13318
$94$			3.33873e9i			0.454928i
$95$		−	6.49654e9i		−	0.839584i
$96$		−	2.25647e9i		−	0.276741i
$97$	−1.28477e10			−1.49612			−0.748061	−	0.663630i	$-0.769015\pi$
$97$	−1.28477e10			−1.49612			−0.748061	+	0.663630i	$0.769015\pi$
$98$		−	1.51506e9i		−	0.167610i
$99$	1.32875e10	−	3.71227e9i	1.39723	−	0.390358i
$100$	3.83019e9			0.383019
$101$		−	1.54658e10i		−	1.47151i	−0.677245	−	0.735757i	$-0.736826\pi$
$101$		−	1.54658e10i		−	1.47151i	0.677245	−	0.735757i	$-0.263174\pi$
$102$	−4.26722e9			−0.386495
$103$	1.78053e10			1.53590			0.767951	−	0.640508i	$-0.221276\pi$
$103$	1.78053e10			1.53590			0.767951	+	0.640508i	$0.221276\pi$
$104$	−3.14271e9			−0.258307
$105$		−	8.44147e9i		−	0.661411i
$106$		−	1.10919e10i		−	0.828855i
$107$		−	8.67491e8i		−	0.0618509i	−0.999522	−	0.0309255i	$-0.990155\pi$
$107$		−	8.67491e8i		−	0.0618509i	0.999522	−	0.0309255i	$-0.00984545\pi$
$108$	−5.18386e9			−0.352805
$109$			3.78308e9i			0.245875i	0.992414	+	0.122937i	$0.0392314\pi$
$109$			3.78308e9i			0.245875i	−0.992414	+	0.122937i	$0.960769\pi$
$110$	−1.48217e9	−	5.30518e9i	−0.0920309	−	0.329410i
$111$	1.99461e10			1.18370
$112$		−	3.84842e9i		−	0.218369i
$113$	9.61200e9			0.521701			0.260851	−	0.965379i	$-0.415997\pi$
$113$	9.61200e9			0.521701			0.260851	+	0.965379i	$0.415997\pi$
$114$	−3.69955e10			−1.92143
$115$	6.25331e9			0.310900
$116$		−	1.24891e10i		−	0.594620i
$117$			2.32380e10i			1.05991i
$118$			1.98928e10i			0.869531i
$119$	−7.27776e9			−0.304974
$120$			6.66164e9i			0.267716i
$121$	2.21816e10	−	1.34435e10i	0.855195	−	0.518306i
$122$	3.66639e10			1.35656
$123$			6.78085e10i			2.40857i
$124$	1.06103e10			0.361927
$125$	−2.60689e10			−0.854225
$126$	−2.84561e10			−0.896032
$127$		−	3.07258e10i		−	0.930004i	−0.885310	−	0.465002i	$-0.846054\pi$
$127$		−	3.07258e10i		−	0.930004i	0.885310	−	0.465002i	$-0.153946\pi$
$128$			3.03700e9i			0.0883883i
$129$			2.97043e10i			0.831517i
$130$	9.27803e9			0.249884
$131$		−	6.33366e10i		−	1.64172i	−0.571132	−	0.820858i	$-0.693496\pi$
$131$		−	6.33366e10i		−	1.64172i	0.571132	−	0.820858i	$-0.306504\pi$
$132$	−3.02111e10	+	8.44042e9i	−0.753872	+	0.210617i
$133$	−6.30961e10			−1.51616
$134$			1.85653e10i			0.429712i
$135$	1.53040e10			0.341300
$136$	5.74329e9			0.123443
$137$	1.88550e10			0.390682			0.195341	−	0.980735i	$-0.437419\pi$
$137$	1.88550e10			0.390682			0.195341	+	0.980735i	$0.437419\pi$
$138$		−	3.56104e10i		−	0.711511i
$139$			3.95882e10i			0.762942i	0.924381	+	0.381471i	$0.124582\pi$
$139$			3.95882e10i			0.762942i	−0.924381	+	0.381471i	$0.875418\pi$
$140$			1.13615e10i			0.211249i
$141$	−5.61307e10			−1.00718
$142$		−	1.12835e10i		−	0.195435i
$143$	1.17554e10	+	4.20767e10i	0.196589	+	0.703658i
$144$	2.24563e10			0.362682
$145$			3.68707e10i			0.575230i
$146$	5.76643e10			0.869246
$147$	2.54712e10			0.371077
$148$	−2.68456e10			−0.378064
$149$		−	9.44137e10i		−	1.28559i	−0.766037	−	0.642797i	$-0.777774\pi$
$149$		−	9.44137e10i		−	1.28559i	0.766037	−	0.642797i	$-0.222226\pi$
$150$			6.43932e10i			0.847976i
$151$			8.70838e10i			1.10931i	0.832081	+	0.554655i	$0.187150\pi$
$151$			8.70838e10i			1.10931i	−0.832081	+	0.554655i	$0.812850\pi$
$152$	4.97927e10			0.613688
$153$		−	4.24673e10i		−	0.506521i
$154$	−5.15253e10	+	1.43952e10i	−0.594862	+	0.166193i
$155$	−3.13243e10			−0.350124
$156$		−	5.28351e10i		−	0.571873i
$157$	4.10632e9			0.0430481			0.0215241	−	0.999768i	$-0.493148\pi$
$157$	4.10632e9			0.0430481			0.0215241	+	0.999768i	$0.493148\pi$
$158$	−6.43299e10			−0.653322
$159$	1.86478e11			1.83502
$160$		−	8.96596e9i		−	0.0855061i
$161$		−	6.07337e10i		−	0.561436i
$162$			2.73072e10i			0.244739i
$163$	−1.81548e11			−1.57781			−0.788904	−	0.614516i	$-0.789351\pi$
$163$	−1.81548e11			−1.57781			−0.788904	+	0.614516i	$0.789351\pi$
$164$		−	9.12641e10i		−	0.769273i
$165$	8.91906e10	−	2.49182e10i	0.729289	−	0.203749i
$166$	1.09007e11			0.864795
$167$		−	2.13951e11i		−	1.64715i	−0.567208	−	0.823575i	$-0.691976\pi$
$167$		−	2.13951e11i		−	1.64715i	0.567208	−	0.823575i	$-0.308024\pi$
$168$	6.46995e10			0.483453
$169$	6.42721e10			0.466218
$170$	−1.69556e10			−0.119418
$171$		−	3.68179e11i		−	2.51814i
$172$		−	3.99793e10i		−	0.265579i
$173$			7.84240e10i			0.506079i	0.967456	+	0.253039i	$0.0814303\pi$
$173$			7.84240e10i			0.506079i	−0.967456	+	0.253039i	$0.918570\pi$
$174$	2.09966e11			1.31644
$175$			1.09823e11i			0.669118i
$176$	4.06615e10	−	1.13600e10i	0.240780	−	0.0672693i
$177$	−3.34437e11			−1.92508
$178$			1.31160e11i			0.734010i
$179$	−1.77034e11			−0.963364			−0.481682	−	0.876346i	$-0.659974\pi$
$179$	−1.77034e11			−0.963364			−0.481682	+	0.876346i	$0.659974\pi$
$180$	−6.62966e10			−0.350856
$181$	−3.20260e11			−1.64858			−0.824290	−	0.566168i	$-0.808425\pi$
$181$	−3.20260e11			−1.64858			−0.824290	+	0.566168i	$0.808425\pi$
$182$		−	9.01106e10i		−	0.451252i
$183$			6.16393e11i			3.00333i
$184$			4.79284e10i			0.227250i
$185$	7.92548e10			0.365735
$186$			1.78381e11i			0.801278i
$187$	−2.14830e10	−	7.68951e10i	−0.0939481	−	0.336272i
$188$	7.55469e10			0.321682
$189$		−	1.48636e11i		−	0.616334i
$190$	−1.47000e11			−0.593676
$191$	4.84773e11			1.90709			0.953546	−	0.301247i	$-0.0974029\pi$
$191$	4.84773e11			1.90709			0.953546	+	0.301247i	$0.0974029\pi$
$192$	−5.10580e10			−0.195685
$193$			2.56627e11i			0.958330i	0.877725	+	0.479165i	$0.159061\pi$
$193$			2.56627e11i			0.958330i	−0.877725	+	0.479165i	$0.840939\pi$
$194$			2.90710e11i			1.05792i
$195$			1.55982e11i			0.553225i
$196$	−3.42820e10			−0.118518
$197$			6.87854e10i			0.231828i	0.993259	+	0.115914i	$0.0369796\pi$
$197$			6.87854e10i			0.231828i	−0.993259	+	0.115914i	$0.963020\pi$
$198$	−8.39990e10	−	3.00661e11i	−0.276025	−	0.987987i
$199$	5.02816e11			1.61118			0.805589	−	0.592474i	$-0.201849\pi$
$199$	5.02816e11			1.61118			0.805589	+	0.592474i	$0.201849\pi$
$200$		−	8.66674e10i		−	0.270836i
$201$	−3.12119e11			−0.951349
$202$	−3.49950e11			−1.04052
$203$	3.58098e11			1.03878
$204$			9.65561e10i			0.273293i
$205$			2.69434e11i			0.744188i
$206$		−	4.02888e11i		−	1.08605i
$207$	3.54395e11			0.932471
$208$			7.11113e10i			0.182651i
$209$	−1.86252e11	−	6.66659e11i	−0.467056	−	1.67175i
$210$	−1.91009e11			−0.467688
$211$		−	3.15433e11i		−	0.754215i	−0.926169	−	0.377108i	$-0.876919\pi$
$211$		−	3.15433e11i		−	0.754215i	0.926169	−	0.377108i	$-0.123081\pi$
$212$	−2.50982e11			−0.586089
$213$	1.89698e11			0.432678
$214$	−1.96291e10			−0.0437352
$215$			1.18029e11i			0.256918i
$216$			1.17297e11i			0.249470i
$217$			3.04229e11i			0.632270i
$218$	8.56014e10			0.173860
$219$			9.69451e11i			1.92444i
$220$	−1.20043e11	+	3.35376e10i	−0.232928	+	0.0650757i
$221$	1.34479e11			0.255090
$222$		−	4.51328e11i		−	0.837004i
$223$	1.66818e11			0.302496			0.151248	−	0.988496i	$-0.451671\pi$
$223$	1.66818e11			0.302496			0.151248	+	0.988496i	$0.451671\pi$
$224$	−8.70797e10			−0.154410
$225$	−6.40840e11			−1.11132
$226$		−	2.17495e11i		−	0.368898i
$227$		−	2.14684e11i		−	0.356182i	−0.984014	−	0.178091i	$-0.943008\pi$
$227$		−	2.14684e11i		−	0.356182i	0.984014	−	0.178091i	$-0.0569921\pi$
$228$			8.37114e11i			1.35866i
$229$	2.35658e11			0.374201			0.187100	−	0.982341i	$-0.440091\pi$
$229$	2.35658e11			0.374201			0.187100	+	0.982341i	$0.440091\pi$
$230$		−	1.41496e11i		−	0.219840i
$231$	−2.42012e11	−	8.66242e11i	−0.367939	−	1.31698i
$232$	−2.82595e11			−0.420460
$233$		−	9.71534e11i		−	1.41475i	−0.706840	−	0.707373i	$-0.749880\pi$
$233$		−	9.71534e11i		−	1.41475i	0.706840	−	0.707373i	$-0.250120\pi$
$234$	5.25815e11			0.749469
$235$	−2.23033e11			−0.311193
$236$	4.50122e11			0.614852
$237$		−	1.08151e12i		−	1.44641i
$238$			1.64677e11i			0.215649i
$239$			5.16198e10i			0.0661953i	0.999452	+	0.0330977i	$0.0105372\pi$
$239$			5.16198e10i			0.0661953i	−0.999452	+	0.0330977i	$0.989463\pi$
$240$	1.50736e11			0.189304
$241$		−	1.95239e11i		−	0.240150i	−0.992765	−	0.120075i	$-0.961687\pi$
$241$		−	1.95239e11i		−	0.240150i	0.992765	−	0.120075i	$-0.0383134\pi$
$242$	−3.04192e11	−	5.01911e11i	−0.366498	−	0.604714i
$243$	−1.05694e12			−1.24744
$244$		−	8.29610e11i		−	0.959234i
$245$	1.01209e11			0.114654
$246$	1.53433e12			1.70311
$247$	1.16589e12			1.26816
$248$		−	2.40084e11i		−	0.255921i
$249$			1.83262e12i			1.91459i
$250$			5.89871e11i			0.604028i
$251$	2.83522e11			0.284589			0.142294	−	0.989824i	$-0.454552\pi$
$251$	2.83522e11			0.284589			0.142294	+	0.989824i	$0.454552\pi$
$252$			6.43889e11i			0.633590i
$253$	6.41699e11	−	1.79278e11i	0.619054	−	0.172952i
$254$	−6.95245e11			−0.657612
$255$		−	2.85057e11i		−	0.264381i
$256$	6.87195e10			0.0625000
$257$	−9.22509e11			−0.822820			−0.411410	−	0.911450i	$-0.634964\pi$
$257$	−9.22509e11			−0.822820			−0.411410	+	0.911450i	$0.634964\pi$
$258$	6.72132e11			0.587971
$259$		−	7.69743e11i		−	0.660460i
$260$		−	2.09938e11i		−	0.176695i
$261$			2.08958e12i			1.72527i
$262$	−1.43314e12			−1.16087
$263$		−	1.79871e11i		−	0.142949i	−0.997442	−	0.0714746i	$-0.977230\pi$
$263$		−	1.79871e11i		−	0.142949i	0.997442	−	0.0714746i	$-0.0227705\pi$
$264$	1.90985e11	+	6.83600e11i	0.148929	+	0.533068i
$265$	7.40960e11			0.566977
$266$			1.42770e12i			1.07209i
$267$	−2.20506e12			−1.62504
$268$	4.20084e11			0.303852
$269$	−1.09938e12			−0.780527			−0.390263	−	0.920703i	$-0.627616\pi$
$269$	−1.09938e12			−0.780527			−0.390263	+	0.920703i	$0.627616\pi$
$270$		−	3.46290e11i		−	0.241335i
$271$			2.31921e12i			1.58669i	0.608769	+	0.793347i	$0.291664\pi$
$271$			2.31921e12i			1.58669i	−0.608769	+	0.793347i	$0.708336\pi$
$272$		−	1.29956e11i		−	0.0872873i
$273$	1.51494e12			0.999037
$274$		−	4.26640e11i		−	0.276254i
$275$	−1.16036e12	+	3.24183e11i	−0.737786	+	0.206123i
$276$	−8.05772e11			−0.503114
$277$			1.78109e12i			1.09216i	0.837733	+	0.546080i	$0.183881\pi$
$277$			1.78109e12i			1.09216i	−0.837733	+	0.546080i	$0.816119\pi$
$278$	8.95778e11			0.539481
$279$	−1.77524e12			−1.05012
$280$	2.57080e11			0.149375
$281$		−	1.30723e12i		−	0.746139i	−0.927803	−	0.373070i	$-0.878305\pi$
$281$		−	1.30723e12i		−	0.746139i	0.927803	−	0.373070i	$-0.121695\pi$
$282$			1.27009e12i			0.712180i
$283$		−	1.37385e12i		−	0.756844i	−0.925633	−	0.378422i	$-0.876467\pi$
$283$		−	1.37385e12i		−	0.756844i	0.925633	−	0.378422i	$-0.123533\pi$
$284$	−2.55316e11			−0.138193
$285$		−	2.47136e12i		−	1.31435i
$286$	9.52088e11	−	2.65995e11i	0.497561	−	0.139009i
$287$	2.61681e12			1.34389
$288$		−	5.08129e11i		−	0.256455i
$289$	1.77023e12			0.878095
$290$	8.34289e11			0.406749
$291$	−4.88742e12			−2.34215
$292$		−	1.30479e12i		−	0.614650i
$293$			7.63078e11i			0.353371i	0.984267	+	0.176685i	$0.0565375\pi$
$293$			7.63078e11i			0.353371i	−0.984267	+	0.176685i	$0.943462\pi$
$294$		−	5.76348e11i		−	0.262391i
$295$	−1.32887e12			−0.594802
$296$			6.07447e11i			0.267331i
$297$	1.57046e12	−	4.38756e11i	0.679585	−	0.189863i
$298$	−2.13634e12			−0.909052
$299$			1.12224e12i			0.469603i
$300$	1.45705e12			0.599609
$301$	1.14632e12			0.463954
$302$	1.97048e12			0.784400
$303$		−	5.88336e12i		−	2.30363i
$304$		−	1.12668e12i		−	0.433943i
$305$			2.44921e12i			0.927955i
$306$	−9.60926e11			−0.358165
$307$		−	8.31060e11i		−	0.304748i	−0.988323	−	0.152374i	$-0.951308\pi$
$307$		−	8.31060e11i		−	0.304748i	0.988323	−	0.152374i	$-0.0486918\pi$
$308$	3.25726e11	+	1.16588e12i	0.117516	+	0.420631i
$309$	6.77335e12			2.40443
$310$			7.08787e11i			0.247575i
$311$	−2.02328e12			−0.695429			−0.347715	−	0.937600i	$-0.613042\pi$
$311$	−2.02328e12			−0.695429			−0.347715	+	0.937600i	$0.613042\pi$
$312$	−1.19552e12			−0.404375
$313$	1.70446e12			0.567368			0.283684	−	0.958918i	$-0.408443\pi$
$313$	1.70446e12			0.567368			0.283684	+	0.958918i	$0.408443\pi$
$314$		−	9.29154e10i		−	0.0304396i
$315$		−	1.90092e12i		−	0.612929i
$316$			1.45562e12i			0.461969i
$317$	−2.16515e12			−0.676381			−0.338191	−	0.941078i	$-0.609815\pi$
$317$	−2.16515e12			−0.676381			−0.338191	+	0.941078i	$0.609815\pi$
$318$		−	4.21951e12i		−	1.29756i
$319$	1.05706e12	+	3.78358e12i	0.319997	+	1.14538i
$320$	−2.02877e11			−0.0604619
$321$		−	3.30004e11i		−	0.0968264i
$322$	−1.37425e12			−0.396996
$323$	−2.13067e12			−0.606043
$324$	6.17892e11			0.173056
$325$		−	2.02932e12i		−	0.559671i
$326$			4.10797e12i			1.11568i
$327$			1.43913e12i			0.384912i
$328$	−2.06507e12			−0.543958
$329$			2.16615e12i			0.561965i
$330$	−5.63834e11	−	2.01815e12i	−0.144073	−	0.515685i
$331$	3.45305e12			0.869087			0.434544	−	0.900651i	$-0.356910\pi$
$331$	3.45305e12			0.869087			0.434544	+	0.900651i	$0.356910\pi$
$332$		−	2.46654e12i		−	0.611503i
$333$	4.49162e12			1.09694
$334$	−4.84117e12			−1.16471
$335$	−1.24019e12			−0.293944
$336$		−	1.46398e12i		−	0.341853i
$337$		−	4.01711e12i		−	0.924195i	−0.886829	−	0.462098i	$-0.847097\pi$
$337$		−	4.01711e12i		−	0.924195i	0.886829	−	0.462098i	$-0.152903\pi$
$338$		−	1.45431e12i		−	0.329666i
$339$	3.65652e12			0.816713
$340$			3.83661e11i			0.0844409i
$341$	−3.21442e12	+	8.98047e11i	−0.697156	+	0.194772i
$342$	−8.33095e12			−1.78059
$343$		−	5.12985e12i		−	1.08052i
$344$	−9.04629e11			−0.187793
$345$	2.37883e12			0.486708
$346$	1.77453e12			0.357852
$347$			9.61292e12i			1.91077i	0.295367	+	0.955384i	$0.404558\pi$
$347$			9.61292e12i			1.91077i	−0.295367	+	0.955384i	$0.595442\pi$
$348$		−	4.75099e12i		−	0.930867i
$349$			2.75216e12i			0.531552i	0.964035	+	0.265776i	$0.0856282\pi$
$349$			2.75216e12i			0.531552i	−0.964035	+	0.265776i	$0.914372\pi$
$350$	2.48501e12			0.473138
$351$			2.74651e12i			0.515521i
$352$	−2.57048e11	−	9.20064e11i	−0.0475666	−	0.170257i
$353$	−1.54593e12			−0.282044			−0.141022	−	0.990006i	$-0.545039\pi$
$353$	−1.54593e12			−0.282044			−0.141022	+	0.990006i	$0.545039\pi$
$354$			7.56745e12i			1.36123i
$355$	7.53755e11			0.133687
$356$	2.96782e12			0.519024
$357$	−2.76855e12			−0.477431
$358$			4.00581e12i			0.681201i
$359$			3.03955e12i			0.509727i	0.966977	+	0.254864i	$0.0820306\pi$
$359$			3.03955e12i			0.509727i	−0.966977	+	0.254864i	$0.917969\pi$
$360$			1.50012e12i			0.248092i
$361$	−1.23412e13			−2.01290
$362$			7.24666e12i			1.16572i
$363$	8.43813e12	−	5.11408e12i	1.33879	−	0.811398i
$364$	−2.03897e12			−0.319083
$365$			3.85207e12i			0.594607i
$366$	1.39474e13			2.12367
$367$	−1.79491e12			−0.269595			−0.134797	−	0.990873i	$-0.543038\pi$
$367$	−1.79491e12			−0.269595			−0.134797	+	0.990873i	$0.543038\pi$
$368$	1.08450e12			0.160690
$369$			1.52697e13i			2.23202i
$370$		−	1.79333e12i		−	0.258614i
$371$		−	7.19639e12i		−	1.02387i
$372$	4.03630e12			0.566589
$373$			1.03599e12i			0.143487i	0.997423	+	0.0717434i	$0.0228563\pi$
$373$			1.03599e12i			0.143487i	−0.997423	+	0.0717434i	$0.977144\pi$
$374$	−1.73994e12	+	4.86106e11i	−0.237780	+	0.0664313i
$375$	−9.91691e12			−1.33727
$376$		−	1.70943e12i		−	0.227464i
$377$	−6.61696e12			−0.868864
$378$	−3.36326e12			−0.435814
$379$	4.93735e12			0.631391			0.315695	−	0.948861i	$-0.397762\pi$
$379$	4.93735e12			0.631391			0.315695	+	0.948861i	$0.397762\pi$
$380$			3.32623e12i			0.419792i
$381$		−	1.16885e13i		−	1.45590i
$382$		−	1.09692e13i		−	1.34852i
$383$	1.08016e12			0.131067			0.0655337	−	0.997850i	$-0.479125\pi$
$383$	1.08016e12			0.131067			0.0655337	+	0.997850i	$0.479125\pi$
$384$			1.15531e12i			0.138370i
$385$	−9.61621e11	−	3.44197e12i	−0.113684	−	0.406915i
$386$	5.80680e12			0.677642
$387$			6.68905e12i			0.770566i
$388$	6.57802e12			0.748061
$389$	5.92079e12			0.664710			0.332355	−	0.943154i	$-0.392157\pi$
$389$	5.92079e12			0.664710			0.332355	+	0.943154i	$0.392157\pi$
$390$	3.52947e12			0.391189
$391$		−	2.05090e12i		−	0.224419i
$392$			7.75713e11i			0.0838052i
$393$		−	2.40940e13i		−	2.57008i
$394$	1.55644e12			0.163927
$395$		−	4.29734e12i		−	0.446904i
$396$	−6.80319e12	+	1.90068e12i	−0.698613	+	0.195179i
$397$	1.25689e13			1.27451			0.637257	−	0.770651i	$-0.280069\pi$
$397$	1.25689e13			1.27451			0.637257	+	0.770651i	$0.280069\pi$
$398$		−	1.13774e13i		−	1.13928i
$399$	−2.40025e13			−2.37351
$400$	−1.96106e12			−0.191510
$401$	−1.61777e12			−0.156026			−0.0780128	−	0.996952i	$-0.524857\pi$
$401$	−1.61777e12			−0.156026			−0.0780128	+	0.996952i	$0.524857\pi$
$402$			7.06245e12i			0.672706i
$403$		−	5.62157e12i		−	0.528850i
$404$			7.91847e12i			0.735757i
$405$	−1.82417e12			−0.167413
$406$		−	8.10283e12i		−	0.734525i
$407$	8.13292e12	−	2.27218e12i	0.728240	−	0.203456i
$408$	2.18481e12			0.193247
$409$		−	1.63972e13i		−	1.43269i	−0.697746	−	0.716346i	$-0.745813\pi$
$409$		−	1.63972e13i		−	1.43269i	0.697746	−	0.716346i	$-0.254187\pi$
$410$	6.09659e12			0.526220
$411$	7.17267e12			0.611606
$412$	−9.11632e12			−0.767951
$413$			1.29063e13i			1.07412i
$414$		−	8.01903e12i		−	0.659357i
$415$			7.28183e12i			0.591562i
$416$	1.60907e12			0.129154
$417$			1.50598e13i			1.19437i
$418$	−1.50848e13	+	4.21440e12i	−1.18211	+	0.330259i
$419$	−2.14287e12			−0.165930			−0.0829652	−	0.996552i	$-0.526439\pi$
$419$	−2.14287e12			−0.165930			−0.0829652	+	0.996552i	$0.526439\pi$
$420$			4.32203e12i			0.330706i
$421$	−7.24907e12			−0.548116			−0.274058	−	0.961713i	$-0.588366\pi$
$421$	−7.24907e12			−0.548116			−0.274058	+	0.961713i	$0.588366\pi$
$422$	−7.13744e12			−0.533311
$423$	−1.26400e13			−0.933349
$424$			5.67907e12i			0.414427i
$425$			3.70857e12i			0.267462i
$426$		−	4.29237e12i		−	0.305949i
$427$	2.37873e13			1.67574
$428$			4.44155e11i			0.0309255i
$429$	4.47191e12	+	1.60065e13i	0.307756	+	1.10156i
$430$	2.67068e12			0.181669
$431$		−	1.88975e10i		−	0.00127062i	−1.00000		0.000635312i	$-0.999798\pi$
$431$		−	1.88975e10i		−	0.00127062i	1.00000		0.000635312i	$-0.000202226\pi$
$432$	2.65413e12			0.176402
$433$	1.98073e13			1.30132			0.650662	−	0.759367i	$-0.274491\pi$
$433$	1.98073e13			1.30132			0.650662	+	0.759367i	$0.274491\pi$
$434$	6.88392e12			0.447082
$435$			1.40261e13i			0.900512i
$436$		−	1.93694e12i		−	0.122937i
$437$		−	1.77807e13i		−	1.11568i
$438$	2.19362e13			1.36079
$439$			9.27765e11i			0.0569004i	0.999595	+	0.0284502i	$0.00905720\pi$
$439$			9.27765e11i			0.0569004i	−0.999595	+	0.0284502i	$0.990943\pi$
$440$	7.58869e11	+	2.71625e12i	0.0460154	+	0.164705i
$441$	5.73582e12			0.343876
$442$		−	3.04291e12i		−	0.180376i
$443$	−2.10633e13			−1.23455			−0.617273	−	0.786749i	$-0.711763\pi$
$443$	−2.10633e13			−1.23455			−0.617273	+	0.786749i	$0.711763\pi$
$444$	−1.02124e13			−0.591851
$445$	−8.76172e12			−0.502099
$446$		−	3.77467e12i		−	0.213897i
$447$		−	3.59161e13i		−	2.01257i
$448$			1.97039e12i			0.109185i
$449$	−2.67167e13			−1.46403			−0.732016	−	0.681288i	$-0.761420\pi$
$449$	−2.67167e13			−1.46403			−0.732016	+	0.681288i	$0.761420\pi$
$450$			1.45006e13i			0.785819i
$451$	7.72449e12	+	2.76486e13i	0.413988	+	1.48180i
$452$	−4.92135e12			−0.260851
$453$			3.31277e13i			1.73660i
$454$	−4.85776e12			−0.251858
$455$	6.01953e12			0.308678
$456$	1.89417e13			0.960716
$457$			5.84734e12i			0.293344i	0.989185	+	0.146672i	$0.0468562\pi$
$457$			5.84734e12i			0.293344i	−0.989185	+	0.146672i	$0.953144\pi$
$458$		−	5.33233e12i		−	0.264600i
$459$		−	5.01925e12i		−	0.246363i
$460$	−3.20169e12			−0.155450
$461$		−	3.54308e13i		−	1.70168i	−0.525428	−	0.850838i	$-0.676095\pi$
$461$		−	3.54308e13i		−	1.70168i	0.525428	−	0.850838i	$-0.323905\pi$
$462$	−1.96008e13	+	5.47610e12i	−0.931246	+	0.260172i
$463$	−3.16323e12			−0.148671			−0.0743354	−	0.997233i	$-0.523684\pi$
$463$	−3.16323e12			−0.148671			−0.0743354	+	0.997233i	$0.523684\pi$
$464$			6.39440e12i			0.297310i
$465$	−1.19161e13			−0.548113
$466$	−2.19833e13			−1.00038
$467$	3.21939e13			1.44940			0.724702	−	0.689062i	$-0.241977\pi$
$467$	3.21939e13			1.44940			0.724702	+	0.689062i	$0.241977\pi$
$468$		−	1.18978e13i		−	0.529954i
$469$			1.20450e13i			0.530816i
$470$			5.04665e12i			0.220046i
$471$	1.56209e12			0.0673910
$472$		−	1.01851e13i		−	0.434766i
$473$	3.38381e12	+	1.21118e13i	0.142922	+	0.511568i
$474$	−2.44719e13			−1.02276
$475$			3.21522e13i			1.32967i
$476$	3.72621e12			0.152487
$477$	4.19925e13			1.70051
$478$	1.16802e12			0.0468071
$479$			2.12575e13i			0.843012i	0.906826	+	0.421506i	$0.138498\pi$
$479$			2.12575e13i			0.843012i	−0.906826	+	0.421506i	$0.861502\pi$
$480$		−	3.41076e12i		−	0.133858i
$481$			1.42234e13i			0.552429i
$482$	−4.41776e12			−0.169811
$483$		−	2.31038e13i		−	0.878918i
$484$	−1.13570e13	+	6.88309e12i	−0.427598	+	0.259153i
$485$	−1.94199e13			−0.723667
$486$			2.39159e13i			0.882074i
$487$	2.10217e13			0.767403			0.383701	−	0.923457i	$-0.374649\pi$
$487$	2.10217e13			0.767403			0.383701	+	0.923457i	$0.374649\pi$
$488$	−1.87719e13			−0.678281
$489$	−6.90631e13			−2.47003
$490$		−	2.29009e12i		−	0.0810723i
$491$		−	1.25667e13i		−	0.440367i	−0.975458	−	0.220183i	$-0.929334\pi$
$491$		−	1.25667e13i		−	0.440367i	0.975458	−	0.220183i	$-0.0706656\pi$
$492$		−	3.47179e13i		−	1.20428i
$493$	1.20925e13			0.415222
$494$		−	2.63812e13i		−	0.896725i
$495$	2.00847e13	−	5.61127e12i	0.675831	−	0.188814i
$496$	−5.43249e12			−0.180963
$497$		−	7.32066e12i		−	0.241417i
$498$	4.14675e13			1.35382
$499$	2.09538e13			0.677267			0.338634	−	0.940918i	$-0.390035\pi$
$499$	2.09538e13			0.677267			0.338634	+	0.940918i	$0.390035\pi$
$500$	1.33473e13			0.427112
$501$		−	8.13897e13i		−	2.57858i
$502$		−	6.41536e12i		−	0.201235i
$503$		−	1.56868e13i		−	0.487185i	−0.969878	−	0.243592i	$-0.921674\pi$
$503$		−	1.56868e13i		−	0.487185i	0.969878	−	0.243592i	$-0.0783259\pi$
$504$	1.45695e13			0.448016
$505$		−	2.33772e13i		−	0.711765i
$506$	−4.05661e12	−	1.45200e13i	−0.122295	−	0.437737i
$507$	2.44499e13			0.729855
$508$			1.57316e13i			0.465002i
$509$	1.36539e13			0.399639			0.199819	−	0.979833i	$-0.435964\pi$
$509$	1.36539e13			0.399639			0.199819	+	0.979833i	$0.435964\pi$
$510$	−6.45010e12			−0.186946
$511$	3.74123e13			1.07377
$512$		−	1.55494e12i		−	0.0441942i
$513$		−	4.35154e13i		−	1.22478i
$514$			2.08740e13i			0.581822i
$515$	2.69136e13			0.742909
$516$		−	1.52086e13i		−	0.415758i
$517$	−2.28870e13	+	6.39421e12i	−0.619637	+	0.173115i
$518$	−1.74173e13			−0.467016
$519$			2.98334e13i			0.792257i
$520$	−4.75035e12			−0.124942
$521$	−5.02154e12			−0.130812			−0.0654061	−	0.997859i	$-0.520834\pi$
$521$	−5.02154e12			−0.130812			−0.0654061	+	0.997859i	$0.520834\pi$
$522$	4.72818e13			1.21995
$523$			4.18074e12i			0.106843i	0.998572	+	0.0534213i	$0.0170126\pi$
$523$			4.18074e12i			0.106843i	−0.998572	+	0.0534213i	$0.982987\pi$
$524$			3.24283e13i			0.820858i
$525$			4.17779e13i			1.04749i
$526$	−4.07001e12			−0.101080
$527$			1.02734e13i			0.252733i
$528$	1.54681e13	−	4.32150e12i	0.376936	−	0.105309i
$529$	−2.43115e13			−0.586860
$530$		−	1.67660e13i		−	0.400913i
$531$	−7.53112e13			−1.78397
$532$	3.23052e13			0.758079
$533$	−4.83536e13			−1.12407
$534$			4.98949e13i			1.14908i
$535$		−	1.31125e12i		−	0.0299170i
$536$		−	9.50542e12i		−	0.214856i
$537$	−6.73456e13			−1.50813
$538$			2.48762e13i			0.551916i
$539$	1.03858e13	−	2.90159e12i	0.228295	−	0.0637812i
$540$	−7.83565e12			−0.170650
$541$		−	2.75886e13i		−	0.595311i	−0.954673	−	0.297655i	$-0.903795\pi$
$541$		−	2.75886e13i		−	0.595311i	0.954673	−	0.297655i	$-0.0962046\pi$
$542$	5.24777e13			1.12196
$543$	−1.21831e14			−2.58082
$544$	−2.94056e12			−0.0617215
$545$			5.71831e12i			0.118928i
$546$		−	3.42791e13i		−	0.706426i
$547$			4.33640e13i			0.885508i	0.896643	+	0.442754i	$0.145999\pi$
$547$			4.33640e13i			0.885508i	−0.896643	+	0.442754i	$0.854001\pi$
$548$	−9.65376e12			−0.195341
$549$			1.38804e14i			2.78318i
$550$	7.33543e12	+	2.62560e13i	0.145751	+	0.521694i
$551$	1.04838e14			2.06425
$552$			1.82325e13i			0.355755i
$553$	−4.17369e13			−0.807038
$554$	4.03014e13			0.772274
$555$	3.01495e13			0.572552
$556$		−	2.02691e13i		−	0.381471i
$557$		−	5.48012e12i		−	0.102215i	−0.998693	−	0.0511074i	$-0.983725\pi$
$557$		−	5.48012e12i		−	0.102215i	0.998693	−	0.0511074i	$-0.0162751\pi$
$558$			4.01692e13i			0.742544i
$559$	−2.11819e13			−0.388066
$560$		−	5.81706e12i		−	0.105624i
$561$	−8.17240e12	−	2.92518e13i	−0.147074	−	0.526428i
$562$	−2.95792e13			−0.527600
$563$		−	7.92609e13i		−	1.40125i	−0.713527	−	0.700627i	$-0.752904\pi$
$563$		−	7.92609e13i		−	1.40125i	0.713527	−	0.700627i	$-0.247096\pi$
$564$	2.87389e13			0.503588
$565$	1.45290e13			0.252344
$566$	−3.10866e13			−0.535169
$567$			1.77168e13i			0.302322i
$568$			5.77715e12i			0.0977174i
$569$		−	6.20761e13i		−	1.04079i	−0.853926	−	0.520395i	$-0.825785\pi$
$569$		−	6.20761e13i		−	1.04079i	0.853926	−	0.520395i	$-0.174215\pi$
$570$	−5.59205e13			−0.929388
$571$		−	4.46922e13i		−	0.736294i	−0.929768	−	0.368147i	$-0.879992\pi$
$571$		−	4.46922e13i		−	0.736294i	0.929768	−	0.368147i	$-0.120008\pi$
$572$	−6.01878e12	−	2.15433e13i	−0.0982944	−	0.351829i
$573$	1.84413e14			2.98552
$574$		−	5.92116e13i		−	0.950271i
$575$	−3.09484e13			−0.492379
$576$	−1.14976e13			−0.181341
$577$	−1.23729e14			−1.93461			−0.967304	−	0.253621i	$-0.918378\pi$
$577$	−1.23729e14			−1.93461			−0.967304	+	0.253621i	$0.918378\pi$
$578$		−	4.00558e13i		−	0.620907i
$579$			9.76238e13i			1.50025i
$580$		−	1.88778e13i		−	0.287615i
$581$	7.07230e13			1.06827
$582$			1.10590e14i			1.65615i
$583$	7.60354e13	−	2.12428e13i	1.12895	−	0.315406i
$584$	−2.95241e13			−0.434623
$585$			3.51253e13i			0.512673i
$586$	1.72665e13			0.249871
$587$	−1.19420e14			−1.71351			−0.856757	−	0.515719i	$-0.827525\pi$
$587$	−1.19420e14			−1.71351			−0.856757	+	0.515719i	$0.827525\pi$
$588$	−1.30413e13			−0.185538
$589$			8.90675e13i			1.25644i
$590$			3.00689e13i			0.420588i
$591$			2.61668e13i			0.362922i
$592$	1.37450e13			0.189032
$593$		−	5.54971e13i		−	0.756827i	−0.925637	−	0.378413i	$-0.876470\pi$
$593$		−	5.54971e13i		−	0.756827i	0.925637	−	0.378413i	$-0.123530\pi$
$594$	−9.92791e12	−	3.55354e13i	−0.134254	−	0.480539i
$595$	−1.10007e13			−0.147515
$596$			4.83398e13i			0.642797i
$597$	1.91277e14			2.52227
$598$	2.53934e13			0.332059
$599$	4.01531e13			0.520696			0.260348	−	0.965515i	$-0.416163\pi$
$599$	4.01531e13			0.520696			0.260348	+	0.965515i	$0.416163\pi$
$600$		−	3.29693e13i		−	0.423988i
$601$			1.13804e14i			1.45139i	0.688017	+	0.725695i	$0.258481\pi$
$601$			1.13804e14i			1.45139i	−0.688017	+	0.725695i	$0.741519\pi$
$602$		−	2.59384e13i		−	0.328065i
$603$	−7.02855e13			−0.881615
$604$		−	4.45869e13i		−	0.554655i
$605$	3.35285e13	−	2.03205e13i	0.413654	−	0.250702i
$606$	−1.33125e14			−1.62891
$607$		−	1.63924e14i		−	1.98930i	−0.103315	−	0.994649i	$-0.532945\pi$
$607$		−	1.63924e14i		−	1.98930i	0.103315	−	0.994649i	$-0.467055\pi$
$608$	−2.54938e13			−0.306844
$609$	1.36225e14			1.62618
$610$	5.54193e13			0.656163
$611$		−	4.00263e13i		−	0.470045i
$612$			2.17433e13i			0.253261i
$613$		−	8.74209e13i		−	1.00998i	−0.863125	−	0.504990i	$-0.831496\pi$
$613$		−	8.74209e13i		−	1.00998i	0.863125	−	0.504990i	$-0.168504\pi$
$614$	−1.88047e13			−0.215489
$615$			1.02496e14i			1.16501i
$616$	2.63809e13	−	7.37033e12i	0.297431	−	0.0830966i
$617$	−5.20160e13			−0.581716			−0.290858	−	0.956766i	$-0.593941\pi$
$617$	−5.20160e13			−0.581716			−0.290858	+	0.956766i	$0.593941\pi$
$618$		−	1.53264e14i		−	1.70019i
$619$	−1.66699e14			−1.83434			−0.917172	−	0.398492i	$-0.869534\pi$
$619$	−1.66699e14			−1.83434			−0.917172	+	0.398492i	$0.869534\pi$
$620$	1.60380e13			0.175062
$621$	4.18862e13			0.453537
$622$			4.57815e13i			0.491743i
$623$			8.50960e13i			0.906711i
$624$			2.70516e13i			0.285937i
$625$	3.36508e13			0.352854
$626$		−	3.85675e13i		−	0.401190i
$627$	−7.08524e13	−	2.53605e14i	−0.731167	−	2.61710i
$628$	−2.10243e12			−0.0215241
$629$		−	2.59932e13i		−	0.264001i
$630$	−4.30128e13			−0.433406
$631$	−7.84608e13			−0.784343			−0.392171	−	0.919892i	$-0.628276\pi$
$631$	−7.84608e13			−0.784343			−0.392171	+	0.919892i	$0.628276\pi$
$632$	3.29369e13			0.326661
$633$		−	1.19995e14i		−	1.18071i
$634$			4.89917e13i			0.478274i
$635$		−	4.64435e13i		−	0.449838i
$636$	−9.54765e13			−0.917510
$637$			1.81633e13i			0.173180i
$638$	8.56126e13	−	2.39185e13i	0.809906	−	0.226272i
$639$	4.27177e13			0.400962
$640$			4.59057e12i			0.0427530i
$641$	1.68623e14			1.55822			0.779108	−	0.626889i	$-0.215672\pi$
$641$	1.68623e14			1.55822			0.779108	+	0.626889i	$0.215672\pi$
$642$	−7.46714e12			−0.0684666
$643$	1.28715e13			0.117104			0.0585522	−	0.998284i	$-0.481352\pi$
$643$	1.28715e13			0.117104			0.0585522	+	0.998284i	$0.481352\pi$
$644$			3.10957e13i			0.280718i
$645$			4.48995e13i			0.402201i
$646$			4.82116e13i			0.428537i
$647$	−1.23901e13			−0.109283			−0.0546417	−	0.998506i	$-0.517402\pi$
$647$	−1.23901e13			−0.109283			−0.0546417	+	0.998506i	$0.517402\pi$
$648$		−	1.39813e13i		−	0.122369i
$649$	−1.36365e14	+	3.80978e13i	−1.18435	+	0.330885i
$650$	−4.59182e13			−0.395747
$651$			1.15732e14i			0.989806i
$652$	9.29528e13			0.788904
$653$	8.68969e13			0.731877			0.365939	−	0.930639i	$-0.380748\pi$
$653$	8.68969e13			0.731877			0.365939	+	0.930639i	$0.380748\pi$
$654$	3.25638e13			0.272174
$655$		−	9.57363e13i		−	0.794091i
$656$			4.67272e13i			0.384637i
$657$			2.18309e14i			1.78338i
$658$	4.90144e13			0.397369
$659$			4.68439e13i			0.376900i	0.982083	+	0.188450i	$0.0603464\pi$
$659$			4.68439e13i			0.376900i	−0.982083	+	0.188450i	$0.939654\pi$
$660$	−4.56656e13	+	1.27581e13i	−0.364644	+	0.101875i
$661$	−1.40161e13			−0.111076			−0.0555381	−	0.998457i	$-0.517687\pi$
$661$	−1.40161e13			−0.111076			−0.0555381	+	0.998457i	$0.517687\pi$
$662$		−	7.81337e13i		−	0.614538i
$663$	5.11574e13			0.399338
$664$	−5.58115e13			−0.432398
$665$	−9.53728e13			−0.733358
$666$		−	1.01634e14i		−	0.775651i
$667$			1.00913e14i			0.764396i
$668$			1.09543e14i			0.823575i
$669$	6.34597e13			0.473552
$670$			2.80623e13i			0.207850i
$671$	7.02173e13	+	2.51332e14i	0.516216	+	1.84771i
$672$	−3.31261e13			−0.241727
$673$		−	1.32737e14i		−	0.961431i	−0.876877	−	0.480716i	$-0.840377\pi$
$673$		−	1.32737e14i		−	0.961431i	0.876877	−	0.480716i	$-0.159623\pi$
$674$	−9.08967e13			−0.653505
$675$	−7.57415e13			−0.540524
$676$	−3.29073e13			−0.233109
$677$			1.08680e14i			0.764196i	0.924122	+	0.382098i	$0.124798\pi$
$677$			1.08680e14i			0.764196i	−0.924122	+	0.382098i	$0.875202\pi$
$678$		−	8.27376e13i		−	0.577503i
$679$			1.88611e14i			1.30683i
$680$	8.68126e12			0.0597088
$681$		−	8.16685e13i		−	0.557595i
$682$	2.03205e13	+	7.27339e13i	0.137725	+	0.492964i
$683$	−8.61721e13			−0.579780			−0.289890	−	0.957060i	$-0.593619\pi$
$683$	−8.61721e13			−0.579780			−0.289890	+	0.957060i	$0.593619\pi$
$684$			1.88508e14i			1.25907i
$685$	2.85002e13			0.188971
$686$	−1.16075e14			−0.764046
$687$	8.96471e13			0.585804
$688$			2.04694e13i			0.132789i
$689$			1.32975e14i			0.856397i
$690$		−	5.38268e13i		−	0.344155i
$691$	1.01504e14			0.644304			0.322152	−	0.946688i	$-0.395594\pi$
$691$	1.01504e14			0.644304			0.322152	+	0.946688i	$0.395594\pi$
$692$		−	4.01531e13i		−	0.253039i
$693$	−5.44981e13	−	1.95067e14i	−0.340969	−	1.22044i
$694$	2.17516e14			1.35112
$695$			5.98394e13i			0.369031i
$696$	−1.07503e14			−0.658222
$697$	8.83661e13			0.537182
$698$	6.22742e13			0.375864
$699$		−	3.69583e14i		−	2.21476i
$700$		−	5.62293e13i		−	0.334559i
$701$			3.21464e14i			1.89908i	0.313653	+	0.949538i	$0.398447\pi$
$701$			3.21464e14i			1.89908i	−0.313653	+	0.949538i	$0.601553\pi$
$702$	6.21465e13			0.364528
$703$		−	2.25353e14i		−	1.31246i
$704$	−2.08187e13	+	5.81634e12i	−0.120390	+	0.0336346i
$705$	−8.48443e13			−0.487166
$706$			3.49804e13i			0.199435i
$707$	−2.27046e14			−1.28534
$708$	1.71232e14			0.962538
$709$	−1.16025e14			−0.647619			−0.323810	−	0.946122i	$-0.604964\pi$
$709$	−1.16025e14			−0.647619			−0.323810	+	0.946122i	$0.604964\pi$
$710$		−	1.70555e13i		−	0.0945309i
$711$		−	2.43544e14i		−	1.34038i
$712$		−	6.71540e13i		−	0.367005i
$713$	−8.57328e13			−0.465264
$714$			6.26450e13i			0.337595i
$715$	1.77689e13	+	6.36010e13i	0.0950891	+	0.340356i
$716$	9.06412e13			0.481682
$717$			1.96368e13i			0.103627i
$718$	6.87773e13			0.360431
$719$	−1.97629e14			−1.02850			−0.514251	−	0.857640i	$-0.671930\pi$
$719$	−1.97629e14			−1.02850			−0.514251	+	0.857640i	$0.671930\pi$
$720$	3.39438e13			0.175428
$721$		−	2.61392e14i		−	1.34158i
$722$			2.79250e14i			1.42334i
$723$		−	7.42713e13i		−	0.375950i
$724$	1.63973e14			0.824290
$725$		−	1.82478e14i		−	0.911004i
$726$	−1.15718e14	−	1.90933e14i	−0.573745	−	0.946668i
$727$	−1.38046e14			−0.679754			−0.339877	−	0.940470i	$-0.610385\pi$
$727$	−1.38046e14			−0.679754			−0.339877	+	0.940470i	$0.610385\pi$
$728$			4.61366e13i			0.225626i
$729$	−3.30812e14			−1.60673
$730$	8.71624e13			0.420450
$731$	3.87098e13			0.185453
$732$		−	3.15593e14i		−	1.50166i
$733$			9.68070e12i			0.0457495i	0.999738	+	0.0228748i	$0.00728190\pi$
$733$			9.68070e12i			0.0457495i	−0.999738	+	0.0228748i	$0.992718\pi$
$734$			4.06141e13i			0.190632i
$735$	3.85010e13			0.179488
$736$		−	2.45393e13i		−	0.113625i
$737$	−1.27265e14	+	3.55555e13i	−0.585291	+	0.163519i
$738$	3.45513e14			1.57827
$739$			3.27562e13i			0.148618i	0.997235	+	0.0743090i	$0.0236751\pi$
$739$			3.27562e13i			0.148618i	−0.997235	+	0.0743090i	$0.976325\pi$
$740$	−4.05785e13			−0.182868
$741$	4.43520e14			1.98528
$742$	−1.62836e14			−0.723986
$743$		−	9.82751e13i		−	0.434010i	−0.976171	−	0.217005i	$-0.930371\pi$
$743$		−	9.82751e13i		−	0.434010i	0.976171	−	0.217005i	$-0.0696287\pi$
$744$		−	9.13309e13i		−	0.400639i
$745$		−	1.42711e14i		−	0.621835i
$746$	2.34418e13			0.101460
$747$			4.12684e14i			1.77425i
$748$	1.09993e13	+	3.93703e13i	0.0469740	+	0.168136i
$749$	−1.27352e13			−0.0540254
$750$			2.24394e14i			0.945594i
$751$	3.30396e14			1.38304			0.691521	−	0.722356i	$-0.256941\pi$
$751$	3.30396e14			1.38304			0.691521	+	0.722356i	$0.256941\pi$
$752$	−3.86800e13			−0.160841
$753$	1.07855e14			0.445518
$754$			1.49725e14i			0.614379i
$755$			1.31631e14i			0.536568i
$756$			7.61018e13i			0.308167i
$757$	−1.38157e14			−0.555766			−0.277883	−	0.960615i	$-0.589633\pi$
$757$	−1.38157e14			−0.555766			−0.277883	+	0.960615i	$0.589633\pi$
$758$		−	1.11720e14i		−	0.446461i
$759$	2.44110e14	−	6.81996e13i	0.969117	−	0.270753i
$760$	7.52640e13			0.296838
$761$			2.57500e14i			1.00891i	0.863437	+	0.504456i	$0.168307\pi$
$761$			2.57500e14i			1.00891i	−0.863437	+	0.504456i	$0.831693\pi$
$762$	−2.64480e14			−1.02948
$763$	5.55377e13			0.214766
$764$	−2.48204e14			−0.953546
$765$		−	6.41914e13i		−	0.245002i
$766$		−	2.44413e13i		−	0.0926786i
$767$		−	2.38484e14i		−	0.898426i
$768$	2.61417e13			0.0978425
$769$		−	1.05869e14i		−	0.393673i	−0.980436	−	0.196836i	$-0.936933\pi$
$769$		−	1.05869e14i		−	0.393673i	0.980436	−	0.196836i	$-0.0630668\pi$
$770$	−7.78829e13	+	2.17590e13i	−0.287732	+	0.0803869i
$771$	−3.50933e14			−1.28811
$772$		−	1.31393e14i		−	0.479165i
$773$	−1.30533e14			−0.472959			−0.236479	−	0.971637i	$-0.575994\pi$
$773$	−1.30533e14			−0.472959			−0.236479	+	0.971637i	$0.575994\pi$
$774$	1.51356e14			0.544872
$775$	1.55028e14			0.554500
$776$		−	1.48844e14i		−	0.528959i
$777$		−	2.92819e14i		−	1.03394i
$778$		−	1.33972e14i		−	0.470021i
$779$	7.66109e14			2.67056
$780$		−	7.98628e13i		−	0.276612i
$781$	7.73485e13	−	2.16097e13i	0.266193	−	0.0743692i
$782$	−4.64065e13			−0.158688
$783$			2.46969e14i			0.839139i
$784$	1.75524e13			0.0592592
$785$	6.20690e12			0.0208222
$786$	−5.45185e14			−1.81732
$787$			3.31773e14i			1.09892i	0.835519	+	0.549461i	$0.185167\pi$
$787$			3.31773e14i			1.09892i	−0.835519	+	0.549461i	$0.814833\pi$
$788$		−	3.52181e13i		−	0.115914i
$789$		−	6.84250e13i		−	0.223784i
$790$	−9.72377e13			−0.316009
$791$		−	1.41109e14i		−	0.455694i
$792$	4.30075e13	+	1.53939e14i	0.138012	+	0.493994i
$793$	−4.39544e14			−1.40164
$794$		−	2.84402e14i		−	0.901218i
$795$	2.81870e14			0.887591
$796$	−2.57442e14			−0.805589
$797$	5.80158e14			1.80407			0.902037	−	0.431659i	$-0.142072\pi$
$797$	5.80158e14			1.80407			0.902037	+	0.431659i	$0.142072\pi$
$798$			5.43115e14i			1.67833i
$799$			7.31480e13i			0.224630i
$800$			4.43737e13i			0.135418i
$801$	−4.96554e14			−1.50593
$802$			3.66060e13i			0.110327i
$803$	1.10436e14	+	3.95289e14i	0.330776	+	1.18396i
$804$	1.59805e14			0.475675
$805$		−	9.18020e13i		−	0.271564i
$806$	−1.27202e14			−0.373953
$807$	−4.18218e14			−1.22190
$808$	1.79175e14			0.520259
$809$			3.03972e14i			0.877184i	0.898686	+	0.438592i	$0.144523\pi$
$809$			3.03972e14i			0.877184i	−0.898686	+	0.438592i	$0.855477\pi$
$810$			4.12762e13i			0.118379i
$811$			9.80648e13i			0.279517i	0.990186	+	0.139759i	$0.0446327\pi$
$811$			9.80648e13i			0.279517i	−0.990186	+	0.139759i	$0.955367\pi$
$812$	−1.83346e14			−0.519388
$813$			8.82254e14i			2.48394i
$814$	−5.14137e13	−	1.84027e14i	−0.143865	−	0.514944i
$815$	−2.74419e14			−0.763179
$816$		−	4.94367e13i		−	0.136647i
$817$	3.35603e14			0.921968
$818$	−3.71026e14			−1.01307
$819$	3.41146e14			0.925807
$820$		−	1.37950e14i		−	0.372094i
$821$		−	5.47580e13i		−	0.146802i	−0.997303	−	0.0734010i	$-0.976615\pi$
$821$		−	5.47580e13i		−	0.146802i	0.997303	−	0.0734010i	$-0.0233853\pi$
$822$		−	1.62299e14i		−	0.432470i
$823$	−7.45229e14			−1.97374			−0.986871	−	0.161508i	$-0.948364\pi$
$823$	−7.45229e14			−1.97374			−0.986871	+	0.161508i	$0.948364\pi$
$824$			2.06279e14i			0.543024i
$825$	−4.41416e14	+	1.23323e14i	−1.15499	+	0.322682i
$826$	2.92037e14			0.759516
$827$		−	5.02380e14i		−	1.29869i	−0.760495	−	0.649344i	$-0.775043\pi$
$827$		−	5.02380e14i		−	1.29869i	0.760495	−	0.649344i	$-0.224957\pi$
$828$	−1.81450e14			−0.466236
$829$	6.55083e14			1.67311			0.836554	−	0.547884i	$-0.184567\pi$
$829$	6.55083e14			1.67311			0.836554	+	0.547884i	$0.184567\pi$
$830$	1.64769e14			0.418298
$831$			6.77547e14i			1.70976i
$832$		−	3.64090e13i		−	0.0913255i
$833$		−	3.31934e13i		−	0.0827612i
$834$	3.40765e14			0.844548
$835$		−	3.23398e14i		−	0.796719i
$836$	9.53609e13	+	3.41329e14i	0.233528	+	0.835877i
$837$	−2.09818e14			−0.510757
$838$			4.84876e13i			0.117330i
$839$	−2.97018e12			−0.00714452			−0.00357226	−	0.999994i	$-0.501137\pi$
$839$	−2.97018e12			−0.00714452			−0.00357226	+	0.999994i	$0.501137\pi$
$840$	9.77964e13			0.233844
$841$	−1.74296e14			−0.414293
$842$			1.64028e14i			0.387576i
$843$		−	4.97285e14i		−	1.16807i
$844$			1.61502e14i			0.377108i
$845$	9.71504e13			0.225507
$846$			2.86010e14i			0.659977i
$847$	−1.97358e14	−	3.25637e14i	−0.452729	−	0.746994i
$848$	1.28503e14			0.293044
$849$		−	5.22628e14i		−	1.18482i
$850$	8.39154e13			0.189124
$851$	2.16916e14			0.486008
$852$	−9.71253e13			−0.216339
$853$			6.31445e14i			1.39827i	0.714991	+	0.699134i	$0.246431\pi$
$853$			6.31445e14i			1.39827i	−0.714991	+	0.699134i	$0.753569\pi$
$854$		−	5.38246e14i		−	1.18493i
$855$		−	5.56521e14i		−	1.21801i
$856$	1.00501e13			0.0218676
$857$		−	7.06121e14i		−	1.52748i	−0.645525	−	0.763739i	$-0.723362\pi$
$857$		−	7.06121e14i		−	1.52748i	0.645525	−	0.763739i	$-0.276638\pi$
$858$	3.62185e14	−	1.01188e14i	0.778923	−	0.217616i
$859$	1.68508e14			0.360293			0.180146	−	0.983640i	$-0.442343\pi$
$859$	1.68508e14			0.360293			0.180146	+	0.983640i	$0.442343\pi$
$860$		−	6.04307e13i		−	0.128459i
$861$	9.95465e14			2.10383
$862$	−4.27601e11			−0.000898467
$863$	9.51260e13			0.198722			0.0993609	−	0.995051i	$-0.468320\pi$
$863$	9.51260e13			0.198722			0.0993609	+	0.995051i	$0.468320\pi$
$864$		−	6.00562e13i		−	0.124735i
$865$			1.18542e14i			0.244788i
$866$		−	4.48188e14i		−	0.920176i
$867$	6.73418e14			1.37464
$868$		−	1.55765e14i		−	0.316135i
$869$	−1.23202e14	−	4.40982e14i	−0.248610	−	0.889861i
$870$	3.17374e14			0.636758
$871$		−	2.22569e14i		−	0.443991i
$872$	−4.38279e13			−0.0869298
$873$	−1.10059e15			−2.17047
$874$	−4.02331e14			−0.788908
$875$			3.82705e14i			0.746146i
$876$		−	4.96359e14i		−	0.962222i
$877$		−	6.94779e14i		−	1.33921i	−0.742718	−	0.669605i	$-0.766464\pi$
$877$		−	6.94779e14i		−	1.33921i	0.742718	−	0.669605i	$-0.233536\pi$
$878$	2.09929e13			0.0402347
$879$			2.90284e14i			0.553195i
$880$	6.14618e13	−	1.71713e13i	0.116464	−	0.0325378i
$881$	4.77398e14			0.899501			0.449750	−	0.893154i	$-0.351513\pi$
$881$	4.77398e14			0.899501			0.449750	+	0.893154i	$0.351513\pi$
$882$		−	1.29787e14i		−	0.243157i
$883$	1.27293e14			0.237138			0.118569	−	0.992946i	$-0.462169\pi$
$883$	1.27293e14			0.237138			0.118569	+	0.992946i	$0.462169\pi$
$884$	−6.88532e13			−0.127545
$885$	−5.05518e14			−0.931151
$886$			4.76607e14i			0.872956i
$887$			4.32289e14i			0.787328i	0.919254	+	0.393664i	$0.128793\pi$
$887$			4.32289e14i			0.787328i	−0.919254	+	0.393664i	$0.871207\pi$
$888$			2.31080e14i			0.418502i
$889$	−4.51071e14			−0.812337
$890$			1.98255e14i			0.355037i
$891$	−1.87191e14	+	5.22977e13i	−0.333347	+	0.0931310i
$892$	−8.54111e13			−0.151248
$893$			6.34172e14i			1.11673i
$894$	−8.12688e14			−1.42310
$895$	−2.67595e14			−0.465975
$896$	4.45848e13			0.0772052
$897$			4.26914e14i			0.735154i
$898$			6.04529e14i			1.03523i
$899$		−	5.05497e14i		−	0.860836i
$900$	3.28110e14			0.555658
$901$		−	2.43012e14i		−	0.409265i
$902$	6.25616e14	−	1.74785e14i	1.04779	−	0.292733i
$903$	4.36075e14			0.726311
$904$			1.11357e14i			0.184449i
$905$	−4.84089e14			−0.797411
$906$	7.49595e14			1.22796
$907$	−1.53760e14			−0.250500			−0.125250	−	0.992125i	$-0.539973\pi$
$907$	−1.53760e14			−0.250500			−0.125250	+	0.992125i	$0.539973\pi$
$908$			1.09918e14i			0.178091i
$909$		−	1.32486e15i		−	2.13477i
$910$		−	1.36206e14i		−	0.218268i
$911$	−6.42138e14			−1.02338			−0.511689	−	0.859170i	$-0.670980\pi$
$911$	−6.42138e14			−1.02338			−0.511689	+	0.859170i	$0.670980\pi$
$912$		−	4.28602e14i		−	0.679329i
$913$	2.08766e14	+	7.47243e14i	0.329083	+	1.17790i
$914$	1.32310e14			0.207426
$915$			9.31708e14i			1.45270i
$916$	−1.20657e14			−0.187100
$917$	−9.29815e14			−1.43400
$918$	−1.13573e14			−0.174205
$919$			1.82207e14i			0.277964i	0.990295	+	0.138982i	$0.0443830\pi$
$919$			1.82207e14i			0.277964i	−0.990295	+	0.138982i	$0.955617\pi$
$920$			7.24461e13i			0.109920i
$921$		−	3.16145e14i		−	0.477077i
$922$	−8.01708e14			−1.20327
$923$			1.35272e14i			0.201929i
$924$	1.23910e14	+	4.43516e14i	0.183970	+	0.658490i
$925$	−3.92242e14			−0.579223
$926$			7.15757e13i			0.105126i
$927$	1.52528e15			2.22818
$928$	1.44689e14			0.210230
$929$	4.85204e14			0.701206			0.350603	−	0.936524i	$-0.385977\pi$
$929$	4.85204e14			0.701206			0.350603	+	0.936524i	$0.385977\pi$
$930$			2.69631e14i			0.387574i
$931$		−	2.87777e14i		−	0.411442i
$932$			4.97425e14i			0.707373i
$933$	−7.69678e14			−1.08868
$934$		−	7.28466e14i		−	1.02488i
$935$	−3.24727e13	−	1.16231e14i	−0.0454422	−	0.162653i
$936$	−2.69217e14			−0.374734
$937$			6.87775e14i			0.952244i	0.879379	+	0.476122i	$0.157958\pi$
$937$			6.87775e14i			0.952244i	−0.879379	+	0.476122i	$0.842042\pi$
$938$	2.72548e14			0.375344
$939$	6.48396e14			0.888203
$940$	1.14193e14			0.155596
$941$		−	4.89639e14i		−	0.663633i	−0.943344	−	0.331816i	$-0.892339\pi$
$941$		−	4.89639e14i		−	0.663633i	0.943344	−	0.331816i	$-0.107661\pi$
$942$		−	3.53461e13i		−	0.0476526i
$943$			7.37425e14i			0.988916i
$944$	−2.30463e14			−0.307426
$945$		−	2.24671e14i		−	0.298118i
$946$	2.74059e14	−	7.65668e13i	0.361733	−	0.101061i
$947$	2.48534e14			0.326315			0.163157	−	0.986600i	$-0.447832\pi$
$947$	2.48534e14			0.326315			0.163157	+	0.986600i	$0.447832\pi$
$948$			5.53735e14i			0.723203i
$949$	−6.91307e14			−0.898131
$950$	7.27522e14			0.940217
$951$	−8.23649e14			−1.05886
$952$		−	8.43146e13i		−	0.107825i
$953$		−	8.12309e14i		−	1.03337i	−0.856175	−	0.516686i	$-0.827165\pi$
$953$		−	8.12309e14i		−	1.03337i	0.856175	−	0.516686i	$-0.172835\pi$
$954$		−	9.50182e14i		−	1.20244i
$955$	7.32758e14			0.922452
$956$		−	2.64294e13i		−	0.0330977i
$957$	4.02118e14	+	1.43932e15i	0.500950	+	1.79307i
$958$	4.81001e14			0.596099
$959$		−	2.76802e14i		−	0.341252i
$960$	−7.71766e13			−0.0946520
$961$	−3.90173e14			−0.476037
$962$	3.21838e14			0.390627
$963$		−	7.43129e13i		−	0.0897290i
$964$			9.99625e13i			0.120075i
$965$			3.87904e14i			0.463540i
$966$	−5.22780e14			−0.621489
$967$			5.80716e14i			0.686802i	0.939189	+	0.343401i	$0.111579\pi$
$967$			5.80716e14i			0.686802i	−0.939189	+	0.343401i	$0.888421\pi$
$968$	1.55746e14	+	2.56979e14i	0.183249	+	0.302357i
$969$	−8.10532e14			−0.948749
$970$			4.39423e14i			0.511710i
$971$	−1.03057e15			−1.19394			−0.596970	−	0.802264i	$-0.703629\pi$
$971$	−1.03057e15			−1.19394			−0.596970	+	0.802264i	$0.703629\pi$
$972$	5.41155e14			0.623721
$973$	5.81176e14			0.666413
$974$		−	4.75667e14i		−	0.542636i
$975$		−	7.71975e14i		−	0.876154i
$976$			4.24760e14i			0.479617i
$977$	1.65471e15			1.85886			0.929432	−	0.368992i	$-0.120297\pi$
$977$	1.65471e15			1.85886			0.929432	+	0.368992i	$0.120297\pi$
$978$			1.56272e15i			1.74657i
$979$	−8.99105e14	+	2.51193e14i	−0.999763	+	0.279315i
$980$	−5.18189e13			−0.0573268
$981$			3.24075e14i			0.356698i
$982$	−2.84352e14			−0.311386
$983$	−1.05985e15			−1.15472			−0.577358	−	0.816491i	$-0.695916\pi$
$983$	−1.05985e15			−1.15472			−0.577358	+	0.816491i	$0.695916\pi$
$984$	−7.85577e14			−0.851556
$985$			1.03972e14i			0.112134i
$986$		−	2.73622e14i		−	0.293607i
$987$			8.24029e14i			0.879745i
$988$	−5.96938e14			−0.634081
$989$			3.23038e14i			0.341407i
$990$	−1.26969e14	−	4.54464e14i	−0.133512	−	0.477885i
$991$	1.10833e15			1.15958			0.579792	−	0.814765i	$-0.303134\pi$
$991$	1.10833e15			1.15958			0.579792	+	0.814765i	$0.303134\pi$
$992$			1.22923e14i			0.127960i
$993$	1.31358e15			1.36054
$994$	−1.65648e14			−0.170708
$995$	7.60030e14			0.779320
$996$		−	9.38302e14i		−	0.957296i
$997$			3.29622e14i			0.334611i	0.985905	+	0.167306i	$0.0535067\pi$
$997$			3.29622e14i			0.334611i	−0.985905	+	0.167306i	$0.946493\pi$
$998$		−	4.74130e14i		−	0.478900i
$999$	5.30868e14			0.533530

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.11.b.a.21.5	✓	10
3.2	odd	2		198.11.d.a.109.8		10
4.3	odd	2		176.11.h.e.65.2		10
11.10	odd	2	inner	22.11.b.a.21.10	yes	10
33.32	even	2		198.11.d.a.109.3		10
44.43	even	2		176.11.h.e.65.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.11.b.a.21.5	✓	10	1.1	even	1	trivial
22.11.b.a.21.10	yes	10	11.10	odd	2	inner
176.11.h.e.65.1		10	44.43	even	2
176.11.h.e.65.2		10	4.3	odd	2
198.11.d.a.109.3		10	33.32	even	2
198.11.d.a.109.8		10	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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	22.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-22.6274i q^{2} +380.412 q^{3} -512.000 q^{4} +1511.55 q^{5} -8607.74i q^{6} -14680.5i q^{7} +11585.2i q^{8} +85664.2 q^{9} +O(q^{10})\)	\(q-22.6274i q^{2} +380.412 q^{3} -512.000 q^{4} +1511.55 q^{5} -8607.74i q^{6} -14680.5i q^{7} +11585.2i q^{8} +85664.2 q^{9} -34202.4i q^{10} +(155111. - 43335.1i) q^{11} -194771. q^{12} +271268. i q^{13} -332183. q^{14} +575011. q^{15} +262144. q^{16} -495742. i q^{17} -1.93836e6i q^{18} -4.29794e6i q^{19} -773913. q^{20} -5.58465e6i q^{21} +(-980562. - 3.50977e6i) q^{22} +4.13702e6 q^{23} +4.40716e6i q^{24} -7.48085e6 q^{25} +6.13810e6 q^{26} +1.01247e7 q^{27} +7.51644e6i q^{28} +2.43927e7i q^{29} -1.30110e7i q^{30} -2.07233e7 q^{31} -5.93164e6i q^{32} +(5.90061e7 - 1.64852e7i) q^{33} -1.12174e7 q^{34} -2.21903e7i q^{35} -4.38600e7 q^{36} +5.24329e7 q^{37} -9.72513e7 q^{38} +1.03194e8i q^{39} +1.75116e7i q^{40} +1.78250e8i q^{41} -1.26366e8 q^{42} +7.80846e7i q^{43} +(-7.94169e7 + 2.21876e7i) q^{44} +1.29485e8 q^{45} -9.36102e7i q^{46} -1.47552e8 q^{47} +9.97227e7 q^{48} +6.69570e7 q^{49} +1.69272e8i q^{50} -1.88586e8i q^{51} -1.38889e8i q^{52} +4.90199e8 q^{53} -2.29096e8i q^{54} +(2.34458e8 - 6.55031e7i) q^{55} +1.70078e8 q^{56} -1.63499e9i q^{57} +5.51944e8 q^{58} -8.79145e8 q^{59} -2.94406e8 q^{60} +1.62033e9i q^{61} +4.68915e8i q^{62} -1.25760e9i q^{63} -1.34218e8 q^{64} +4.10035e8i q^{65} +(-3.73017e8 - 1.33516e9i) q^{66} -8.20477e8 q^{67} +2.53820e8i q^{68} +1.57377e9 q^{69} -5.02110e8 q^{70} +4.98665e8 q^{71} +9.92440e8i q^{72} +2.54843e9i q^{73} -1.18642e9i q^{74} -2.84580e9 q^{75} +2.20055e9i q^{76} +(-6.36183e8 - 2.27712e9i) q^{77} +2.33500e9 q^{78} -2.84301e9i q^{79} +3.96243e8 q^{80} -1.20682e9 q^{81} +4.03334e9 q^{82} +4.81747e9i q^{83} +2.85934e9i q^{84} -7.49338e8i q^{85} +1.76685e9 q^{86} +9.27927e9i q^{87} +(5.02048e8 + 1.79700e9i) q^{88} -5.79652e9 q^{89} -2.92992e9i q^{90} +3.98236e9 q^{91} -2.11816e9 q^{92} -7.88339e9 q^{93} +3.33873e9i q^{94} -6.49654e9i q^{95} -2.25647e9i q^{96} -1.28477e10 q^{97} -1.51506e9i q^{98} +(1.32875e10 - 3.71227e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 106 q^{3} - 5120 q^{4} + 1138 q^{5} + 78044 q^{9}+O(q^{10}) \) 10 * q - 106 * q^3 - 5120 * q^4 + 1138 * q^5 + 78044 * q^9	\( 10 q - 106 q^{3} - 5120 q^{4} + 1138 q^{5} + 78044 q^{9} + 95414 q^{11} + 54272 q^{12} - 156288 q^{14} + 1441618 q^{15} + 2621440 q^{16} - 582656 q^{20} - 6002304 q^{22} + 17496838 q^{23} - 1494468 q^{25} + 9714816 q^{26} + 54656930 q^{27} - 91050970 q^{31} - 12170158 q^{33} - 6879360 q^{34} - 39958528 q^{36} - 82676974 q^{37} - 55302528 q^{38} - 128221824 q^{42} - 48851968 q^{44} - 124619384 q^{45} + 352507996 q^{47} - 27787264 q^{48} - 374605478 q^{49} + 571129876 q^{53} + 1363103126 q^{55} + 80019456 q^{56} + 1594048512 q^{58} - 1508647610 q^{59} - 738108416 q^{60} - 1342177280 q^{64} + 1288087680 q^{66} + 3146811782 q^{67} + 5332296166 q^{69} - 1491609984 q^{70} - 328577450 q^{71} - 18684358968 q^{75} + 4256837904 q^{77} + 4919767680 q^{78} + 298319872 q^{80} - 16957790722 q^{81} + 4545650304 q^{82} - 12971187456 q^{86} + 3073179648 q^{88} + 17791426978 q^{89} + 40311734544 q^{91} - 8958381056 q^{92} - 11674310138 q^{93} - 62585189614 q^{97} + 48880194572 q^{99}+O(q^{100}) \) 10 * q - 106 * q^3 - 5120 * q^4 + 1138 * q^5 + 78044 * q^9 + 95414 * q^11 + 54272 * q^12 - 156288 * q^14 + 1441618 * q^15 + 2621440 * q^16 - 582656 * q^20 - 6002304 * q^22 + 17496838 * q^23 - 1494468 * q^25 + 9714816 * q^26 + 54656930 * q^27 - 91050970 * q^31 - 12170158 * q^33 - 6879360 * q^34 - 39958528 * q^36 - 82676974 * q^37 - 55302528 * q^38 - 128221824 * q^42 - 48851968 * q^44 - 124619384 * q^45 + 352507996 * q^47 - 27787264 * q^48 - 374605478 * q^49 + 571129876 * q^53 + 1363103126 * q^55 + 80019456 * q^56 + 1594048512 * q^58 - 1508647610 * q^59 - 738108416 * q^60 - 1342177280 * q^64 + 1288087680 * q^66 + 3146811782 * q^67 + 5332296166 * q^69 - 1491609984 * q^70 - 328577450 * q^71 - 18684358968 * q^75 + 4256837904 * q^77 + 4919767680 * q^78 + 298319872 * q^80 - 16957790722 * q^81 + 4545650304 * q^82 - 12971187456 * q^86 + 3073179648 * q^88 + 17791426978 * q^89 + 40311734544 * q^91 - 8958381056 * q^92 - 11674310138 * q^93 - 62585189614 * q^97 + 48880194572 * q^99

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