LMFDB - Embedded newform 22.11.b.a.21.7

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			21.7
Root			$-138.673 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.11.b.a.21.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+22.6274i q^{2} -251.838 q^{3} -512.000 q^{4} +3507.04 q^{5} -5698.45i q^{6} -17033.0i q^{7} -11585.2i q^{8} +4373.51 q^{9} +O(q^{10})$	\(q+22.6274i q^{2} -251.838 q^{3} -512.000 q^{4} +3507.04 q^{5} -5698.45i q^{6} -17033.0i q^{7} -11585.2i q^{8} +4373.51 q^{9} +79355.3i q^{10} +(157855. + 31925.2i) q^{11} +128941. q^{12} +572760. i q^{13} +385413. q^{14} -883207. q^{15} +262144. q^{16} +316651. i q^{17} +98961.1i q^{18} +1.70040e6i q^{19} -1.79561e6 q^{20} +4.28957e6i q^{21} +(-722384. + 3.57185e6i) q^{22} +4.92708e6 q^{23} +2.91761e6i q^{24} +2.53372e6 q^{25} -1.29601e7 q^{26} +1.37694e7 q^{27} +8.72090e6i q^{28} +1.32575e7i q^{29} -1.99847e7i q^{30} +4.47396e7 q^{31} +5.93164e6i q^{32} +(-3.97539e7 - 8.03998e6i) q^{33} -7.16499e6 q^{34} -5.97355e7i q^{35} -2.23923e6 q^{36} -1.38623e7 q^{37} -3.84756e7 q^{38} -1.44243e8i q^{39} -4.06299e7i q^{40} -1.37050e8i q^{41} -9.70618e7 q^{42} +2.64207e8i q^{43} +(-8.08218e7 - 1.63457e7i) q^{44} +1.53381e7 q^{45} +1.11487e8i q^{46} +3.51358e8 q^{47} -6.60179e7 q^{48} -7.64840e6 q^{49} +5.73314e7i q^{50} -7.97448e7i q^{51} -2.93253e8i q^{52} -8.58062e7 q^{53} +3.11566e8i q^{54} +(5.53604e8 + 1.11963e8i) q^{55} -1.97332e8 q^{56} -4.28225e8i q^{57} -2.99984e8 q^{58} +5.57123e7 q^{59} +4.52202e8 q^{60} +1.30182e9i q^{61} +1.01234e9i q^{62} -7.44940e7i q^{63} -1.34218e8 q^{64} +2.00869e9i q^{65} +(1.81924e8 - 8.99529e8i) q^{66} -5.86911e8 q^{67} -1.62125e8i q^{68} -1.24083e9 q^{69} +1.35166e9 q^{70} -1.48291e9 q^{71} -5.06681e7i q^{72} -2.61401e9i q^{73} -3.13668e8i q^{74} -6.38087e8 q^{75} -8.70603e8i q^{76} +(5.43782e8 - 2.68875e9i) q^{77} +3.26385e9 q^{78} -3.81282e9i q^{79} +9.19350e8 q^{80} -3.72591e9 q^{81} +3.10110e9 q^{82} +4.26258e9i q^{83} -2.19626e9i q^{84} +1.11051e9i q^{85} -5.97833e9 q^{86} -3.33876e9i q^{87} +(3.69861e8 - 1.82879e9i) q^{88} +3.96125e9 q^{89} +3.47061e8i q^{90} +9.75584e9 q^{91} -2.52267e9 q^{92} -1.12672e10 q^{93} +7.95034e9i q^{94} +5.96336e9i q^{95} -1.49381e9i q^{96} +2.03909e9 q^{97} -1.73064e8i q^{98} +(6.90380e8 + 1.39625e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−251.838			−1.03637			−0.518186	−	0.855268i	$-0.673392\pi$
$3$	−251.838			−1.03637			−0.518186	+	0.855268i	$0.673392\pi$
$4$	−512.000			−0.500000
$5$	3507.04			1.12225			0.561127	−	0.827730i	$-0.310368\pi$
$5$	3507.04			1.12225			0.561127	+	0.827730i	$0.310368\pi$
$6$		−	5698.45i		−	0.732825i
$7$		−	17033.0i		−	1.01345i	−0.862108	−	0.506724i	$-0.830856\pi$
$7$		−	17033.0i		−	1.01345i	0.862108	−	0.506724i	$-0.169144\pi$
$8$		−	11585.2i		−	0.353553i
$9$	4373.51			0.0740657
$10$			79355.3i			0.793553i
$11$	157855.	+	31925.2i	0.980155	+	0.198230i
$11$	157855.	+	31925.2i	0.980155	+	0.198230i
$12$	128941.			0.518186
$13$			572760.i			1.54261i	0.636466	+	0.771305i	$0.280396\pi$
$13$			572760.i			1.54261i	−0.636466	+	0.771305i	$0.719604\pi$
$14$	385413.			0.716616
$15$	−883207.			−1.16307
$16$	262144.			0.250000
$17$			316651.i			0.223016i	0.993764	+	0.111508i	$0.0355681\pi$
$17$			316651.i			0.223016i	−0.993764	+	0.111508i	$0.964432\pi$
$18$			98961.1i			0.0523724i
$19$			1.70040e6i			0.686724i	0.939203	+	0.343362i	$0.111566\pi$
$19$			1.70040e6i			0.686724i	−0.939203	+	0.343362i	$0.888434\pi$
$20$	−1.79561e6			−0.561127
$21$			4.28957e6i			1.05031i
$22$	−722384.	+	3.57185e6i	−0.140170	+	0.693075i
$23$	4.92708e6			0.765509			0.382755	−	0.923850i	$-0.374975\pi$
$23$	4.92708e6			0.765509			0.382755	+	0.923850i	$0.374975\pi$
$24$			2.91761e6i			0.366413i
$25$	2.53372e6			0.259452
$26$	−1.29601e7			−1.09079
$27$	1.37694e7			0.959612
$28$			8.72090e6i			0.506724i
$29$			1.32575e7i			0.646358i	0.946338	+	0.323179i	$0.104752\pi$
$29$			1.32575e7i			0.646358i	−0.946338	+	0.323179i	$0.895248\pi$
$30$		−	1.99847e7i		−	0.822416i
$31$	4.47396e7			1.56273			0.781365	−	0.624074i	$-0.214524\pi$
$31$	4.47396e7			1.56273			0.781365	+	0.624074i	$0.214524\pi$
$32$			5.93164e6i			0.176777i
$33$	−3.97539e7	−	8.03998e6i	−1.01581	−	0.205440i
$34$	−7.16499e6			−0.157696
$35$		−	5.97355e7i		−	1.13735i
$36$	−2.23923e6			−0.0370328
$37$	−1.38623e7			−0.199906			−0.0999531	−	0.994992i	$-0.531869\pi$
$37$	−1.38623e7			−0.199906			−0.0999531	+	0.994992i	$0.531869\pi$
$38$	−3.84756e7			−0.485587
$39$		−	1.44243e8i		−	1.59872i
$40$		−	4.06299e7i		−	0.396776i
$41$		−	1.37050e8i		−	1.18294i	−0.806329	−	0.591468i	$-0.798549\pi$
$41$		−	1.37050e8i		−	1.18294i	0.806329	−	0.591468i	$-0.201451\pi$
$42$	−9.70618e7			−0.742680
$43$			2.64207e8i			1.79723i	0.438742	+	0.898613i	$0.355424\pi$
$43$			2.64207e8i			1.79723i	−0.438742	+	0.898613i	$0.644576\pi$
$44$	−8.08218e7	−	1.63457e7i	−0.490078	−	0.0991151i
$45$	1.53381e7			0.0831205
$46$			1.11487e8i			0.541297i
$47$	3.51358e8			1.53201			0.766004	−	0.642836i	$-0.222242\pi$
$47$	3.51358e8			1.53201			0.766004	+	0.642836i	$0.222242\pi$
$48$	−6.60179e7			−0.259093
$49$	−7.64840e6			−0.0270764
$50$			5.73314e7i			0.183461i
$51$		−	7.97448e7i		−	0.231128i
$52$		−	2.93253e8i		−	0.771305i
$53$	−8.58062e7			−0.205182			−0.102591	−	0.994724i	$-0.532713\pi$
$53$	−8.58062e7			−0.205182			−0.102591	+	0.994724i	$0.532713\pi$
$54$			3.11566e8i			0.678548i
$55$	5.53604e8	+	1.11963e8i	1.09998	+	0.222465i
$56$	−1.97332e8			−0.358308
$57$		−	4.28225e8i		−	0.711701i
$58$	−2.99984e8			−0.457044
$59$	5.57123e7			0.0779275			0.0389638	−	0.999241i	$-0.487594\pi$
$59$	5.57123e7			0.0779275			0.0389638	+	0.999241i	$0.487594\pi$
$60$	4.52202e8			0.581536
$61$			1.30182e9i			1.54135i	0.637227	+	0.770676i	$0.280081\pi$
$61$			1.30182e9i			1.54135i	−0.637227	+	0.770676i	$0.719919\pi$
$62$			1.01234e9i			1.10502i
$63$		−	7.44940e7i		−	0.0750617i
$64$	−1.34218e8			−0.125000
$65$			2.00869e9i			1.73120i
$66$	1.81924e8	−	8.99529e8i	0.145268	−	0.718283i
$67$	−5.86911e8			−0.434709			−0.217354	−	0.976093i	$-0.569743\pi$
$67$	−5.86911e8			−0.434709			−0.217354	+	0.976093i	$0.569743\pi$
$68$		−	1.62125e8i		−	0.111508i
$69$	−1.24083e9			−0.793352
$70$	1.35166e9			0.804224
$71$	−1.48291e9			−0.821905			−0.410953	−	0.911657i	$-0.634804\pi$
$71$	−1.48291e9			−0.821905			−0.410953	+	0.911657i	$0.634804\pi$
$72$		−	5.06681e7i		−	0.0261862i
$73$		−	2.61401e9i		−	1.26094i	−0.776215	−	0.630468i	$-0.782863\pi$
$73$		−	2.61401e9i		−	1.26094i	0.776215	−	0.630468i	$-0.217137\pi$
$74$		−	3.13668e8i		−	0.141355i
$75$	−6.38087e8			−0.268889
$76$		−	8.70603e8i		−	0.343362i
$77$	5.43782e8	−	2.68875e9i	0.200896	−	0.993336i
$78$	3.26385e9			1.13046
$79$		−	3.81282e9i		−	1.23911i	−0.784952	−	0.619557i	$-0.787312\pi$
$79$		−	3.81282e9i		−	1.23911i	0.784952	−	0.619557i	$-0.212688\pi$
$80$	9.19350e8			0.280563
$81$	−3.72591e9			−1.06858
$82$	3.10110e9			0.836462
$83$			4.26258e9i			1.08214i	0.840979	+	0.541068i	$0.181980\pi$
$83$			4.26258e9i			1.08214i	−0.840979	+	0.541068i	$0.818020\pi$
$84$		−	2.19626e9i		−	0.525154i
$85$			1.11051e9i			0.250281i
$86$	−5.97833e9			−1.27083
$87$		−	3.33876e9i		−	0.669867i
$88$	3.69861e8	−	1.82879e9i	0.0700850	−	0.346537i
$89$	3.96125e9			0.709386			0.354693	−	0.934983i	$-0.384585\pi$
$89$	3.96125e9			0.709386			0.354693	+	0.934983i	$0.384585\pi$
$90$			3.47061e8i			0.0587750i
$91$	9.75584e9			1.56335
$92$	−2.52267e9			−0.382755
$93$	−1.12672e10			−1.61957
$94$			7.95034e9i			1.08329i
$95$			5.96336e9i			0.770678i
$96$		−	1.49381e9i		−	0.183206i
$97$	2.03909e9			0.237453			0.118726	−	0.992927i	$-0.462119\pi$
$97$	2.03909e9			0.237453			0.118726	+	0.992927i	$0.462119\pi$
$98$		−	1.73064e8i		−	0.0191459i
$99$	6.90380e8	+	1.39625e8i	0.0725959	+	0.0146821i
$100$	−1.29726e9			−0.129726
$101$		−	3.18411e9i		−	0.302957i	−0.988461	−	0.151479i	$-0.951597\pi$
$101$		−	3.18411e9i		−	0.302957i	0.988461	−	0.151479i	$-0.0484035\pi$
$102$	1.80442e9			0.163432
$103$	−1.17875e10			−1.01680			−0.508402	−	0.861120i	$-0.669763\pi$
$103$	−1.17875e10			−1.01680			−0.508402	+	0.861120i	$0.669763\pi$
$104$	6.63556e9			0.545395
$105$			1.50437e10i			1.17871i
$106$		−	1.94157e9i		−	0.145086i
$107$			3.16794e8i			0.0225870i	0.999936	+	0.0112935i	$0.00359490\pi$
$107$			3.16794e8i			0.0225870i	−0.999936	+	0.0112935i	$0.996405\pi$
$108$	−7.04992e9			−0.479806
$109$			1.03724e9i			0.0674137i	0.999432	+	0.0337069i	$0.0107313\pi$
$109$			1.03724e9i			0.0674137i	−0.999432	+	0.0337069i	$0.989269\pi$
$110$	−2.53343e9	+	1.25266e10i	−0.157306	+	0.777805i
$111$	3.49105e9			0.207177
$112$		−	4.46510e9i		−	0.253362i
$113$	1.87245e10			1.01629			0.508144	−	0.861272i	$-0.330332\pi$
$113$	1.87245e10			1.01629			0.508144	+	0.861272i	$0.330332\pi$
$114$	9.68962e9			0.503248
$115$	1.72795e10			0.859096
$116$		−	6.78786e9i		−	0.323179i
$117$			2.50497e9i			0.114254i
$118$			1.26063e9i			0.0551031i
$119$	5.39352e9			0.226015
$120$			1.02322e10i			0.411208i
$121$	2.38990e10	+	1.00791e10i	0.921410	+	0.388593i
$122$	−2.94568e10			−1.08990
$123$			3.45145e10i			1.22596i
$124$	−2.29067e10			−0.781365
$125$	−2.53626e10			−0.831082
$126$	1.68561e9			0.0530766
$127$		−	5.83927e10i		−	1.76742i	−0.468035	−	0.883710i	$-0.655038\pi$
$127$		−	5.83927e10i		−	1.76742i	0.468035	−	0.883710i	$-0.344962\pi$
$128$		−	3.03700e9i		−	0.0883883i
$129$		−	6.65375e10i		−	1.86259i
$130$	−4.54516e10			−1.22414
$131$		−	2.61686e10i		−	0.678304i	−0.940732	−	0.339152i	$-0.889860\pi$
$131$		−	2.61686e10i		−	0.678304i	0.940732	−	0.339152i	$-0.110140\pi$
$132$	2.03540e10	+	4.11647e9i	0.507903	+	0.102720i
$133$	2.89629e10			0.695959
$134$		−	1.32803e10i		−	0.307386i
$135$	4.82898e10			1.07693
$136$	3.66848e9			0.0788481
$137$	−5.47181e10			−1.13378			−0.566889	−	0.823794i	$-0.691853\pi$
$137$	−5.47181e10			−1.13378			−0.566889	+	0.823794i	$0.691853\pi$
$138$		−	2.80767e10i		−	0.560985i
$139$		−	6.67916e10i		−	1.28721i	−0.765360	−	0.643603i	$-0.777439\pi$
$139$		−	6.67916e10i		−	1.28721i	0.765360	−	0.643603i	$-0.222561\pi$
$140$			3.05846e10i			0.568673i
$141$	−8.84855e10			−1.58773
$142$		−	3.35543e10i		−	0.581175i
$143$	−1.82855e10	+	9.04131e10i	−0.305792	+	1.51200i
$144$	1.14649e9			0.0185164
$145$			4.64948e10i			0.725377i
$146$	5.91483e10			0.891616
$147$	1.92616e9			0.0280612
$148$	7.09749e9			0.0999531
$149$			8.77588e10i			1.19498i	0.801878	+	0.597488i	$0.203834\pi$
$149$			8.77588e10i			1.19498i	−0.801878	+	0.597488i	$0.796166\pi$
$150$		−	1.44383e10i		−	0.190133i
$151$		−	1.72260e10i		−	0.219432i	−0.993963	−	0.109716i	$-0.965006\pi$
$151$		−	1.72260e10i		−	0.219432i	0.993963	−	0.109716i	$-0.0349942\pi$
$152$	1.96995e10			0.242794
$153$			1.38487e9i			0.0165178i
$154$	6.08394e10	+	1.23044e10i	0.702395	+	0.142055i
$155$	1.56904e11			1.75378
$156$			7.38524e10i			0.799359i
$157$	−1.77458e11			−1.86036			−0.930178	−	0.367108i	$-0.880348\pi$
$157$	−1.77458e11			−1.86036			−0.930178	+	0.367108i	$0.880348\pi$
$158$	8.62744e10			0.876186
$159$	2.16093e10			0.212645
$160$			2.08025e10i			0.198388i
$161$		−	8.39231e10i		−	0.775804i
$162$		−	8.43077e10i		−	0.755600i
$163$	1.65972e11			1.44244			0.721218	−	0.692709i	$-0.243583\pi$
$163$	1.65972e11			1.44244			0.721218	+	0.692709i	$0.243583\pi$
$164$			7.01698e10i			0.591468i
$165$	−1.39419e11	−	2.81966e10i	−1.13999	−	0.230556i
$166$	−9.64512e10			−0.765186
$167$			1.99990e11i			1.53966i	0.638249	+	0.769830i	$0.279659\pi$
$167$			1.99990e11i			1.53966i	−0.638249	+	0.769830i	$0.720341\pi$
$168$	4.96956e10			0.371340
$169$	−1.90196e11			−1.37965
$170$	−2.51279e10			−0.176975
$171$			7.43669e9i			0.0508627i
$172$		−	1.35274e11i		−	0.898613i
$173$			2.56274e11i			1.65377i	0.562375	+	0.826883i	$0.309888\pi$
$173$			2.56274e11i			1.65377i	−0.562375	+	0.826883i	$0.690112\pi$
$174$	7.55474e10			0.473667
$175$		−	4.31568e10i		−	0.262942i
$176$	4.13807e10	+	8.36899e9i	0.245039	+	0.0495576i
$177$	−1.40305e10			−0.0807619
$178$			8.96330e10i			0.501612i
$179$	8.20427e10			0.446452			0.223226	−	0.974767i	$-0.428341\pi$
$179$	8.20427e10			0.446452			0.223226	+	0.974767i	$0.428341\pi$
$180$	−7.85309e9			−0.0415602
$181$	−4.46390e9			−0.0229785			−0.0114892	−	0.999934i	$-0.503657\pi$
$181$	−4.46390e9			−0.0229785			−0.0114892	+	0.999934i	$0.503657\pi$
$182$			2.20749e11i			1.10546i
$183$		−	3.27848e11i		−	1.59741i
$184$		−	5.70814e10i		−	0.270648i
$185$	−4.86156e10			−0.224345
$186$		−	2.54947e11i		−	1.14521i
$187$	−1.01091e10	+	4.99849e10i	−0.0442085	+	0.218590i
$188$	−1.79896e11			−0.766004
$189$		−	2.34534e11i		−	0.972516i
$190$	−1.34935e11			−0.544952
$191$	1.06444e11			0.418748			0.209374	−	0.977836i	$-0.432857\pi$
$191$	1.06444e11			0.418748			0.209374	+	0.977836i	$0.432857\pi$
$192$	3.38012e10			0.129546
$193$			4.43331e11i			1.65555i	0.561062	+	0.827774i	$0.310393\pi$
$193$			4.43331e11i			1.65555i	−0.561062	+	0.827774i	$0.689607\pi$
$194$			4.61393e10i			0.167904i
$195$		−	5.05866e11i		−	1.79417i
$196$	3.91598e9			0.0135382
$197$		−	1.58152e11i		−	0.533019i	−0.963832	−	0.266510i	$-0.914130\pi$
$197$		−	1.58152e11i		−	0.533019i	0.963832	−	0.266510i	$-0.0858704\pi$
$198$	−3.15935e9	+	1.56215e10i	−0.0103818	+	0.0513330i
$199$	2.57831e10			0.0826170			0.0413085	−	0.999146i	$-0.486847\pi$
$199$	2.57831e10			0.0826170			0.0413085	+	0.999146i	$0.486847\pi$
$200$		−	2.93537e10i		−	0.0917303i
$201$	1.47807e11			0.450520
$202$	7.20482e10			0.214223
$203$	2.25816e11			0.655050
$204$			4.08294e10i			0.115564i
$205$		−	4.80641e11i		−	1.32755i
$206$		−	2.66721e11i		−	0.718988i
$207$	2.15486e10			0.0566980
$208$			1.50146e11i			0.385653i
$209$	−5.42855e10	+	2.68416e11i	−0.136129	+	0.673096i
$210$	−3.40400e11			−0.833475
$211$		−	3.49699e11i		−	0.836145i	−0.908414	−	0.418072i	$-0.862706\pi$
$211$		−	3.49699e11i		−	0.836145i	0.908414	−	0.418072i	$-0.137294\pi$
$212$	4.39328e10			0.102591
$213$	3.73452e11			0.851799
$214$	−7.16822e9			−0.0159714
$215$			9.26586e11i			2.01694i
$216$		−	1.59522e11i		−	0.339274i
$217$		−	7.62051e11i		−	1.58375i
$218$	−2.34702e10			−0.0476687
$219$			6.58308e11i			1.30680i
$220$	−2.83445e11	−	5.73250e10i	−0.549991	−	0.111232i
$221$	−1.81365e11			−0.344027
$222$			7.89935e10i			0.146496i
$223$	−1.02566e12			−1.85986			−0.929930	−	0.367737i	$-0.880133\pi$
$223$	−1.02566e12			−1.85986			−0.929930	+	0.367737i	$0.880133\pi$
$224$	1.01034e11			0.179154
$225$	1.10812e10			0.0192165
$226$			4.23686e11i			0.718625i
$227$		−	1.33950e10i		−	0.0222235i	−0.999938	−	0.0111118i	$-0.996463\pi$
$227$		−	1.33950e10i		−	0.0222235i	0.999938	−	0.0111118i	$-0.00353706\pi$
$228$			2.19251e11i			0.355850i
$229$	8.31243e11			1.31993			0.659965	−	0.751297i	$-0.270571\pi$
$229$	8.31243e11			1.31993			0.659965	+	0.751297i	$0.270571\pi$
$230$			3.90990e11i			0.607472i
$231$	−1.36945e11	+	6.77129e11i	−0.208203	+	1.02947i
$232$	1.53592e11			0.228522
$233$			1.07974e12i			1.57232i	0.618022	+	0.786160i	$0.287934\pi$
$233$			1.07974e12i			1.57232i	−0.618022	+	0.786160i	$0.712066\pi$
$234$	−5.66810e10			−0.0807901
$235$	1.23223e12			1.71930
$236$	−2.85247e10			−0.0389638
$237$			9.60215e11i			1.28418i
$238$			1.22041e11i			0.159817i
$239$		−	1.27584e12i		−	1.63608i	−0.575160	−	0.818041i	$-0.695060\pi$
$239$		−	1.27584e12i		−	1.63608i	0.575160	−	0.818041i	$-0.304940\pi$
$240$	−2.31527e11			−0.290768
$241$		−	4.12875e11i		−	0.507848i	−0.967224	−	0.253924i	$-0.918279\pi$
$241$		−	4.12875e11i		−	0.507848i	0.967224	−	0.253924i	$-0.0817213\pi$
$242$	−2.28064e11	+	5.40772e11i	−0.274777	+	0.651535i
$243$	1.25258e11			0.147834
$244$		−	6.66532e11i		−	0.770676i
$245$	−2.68233e10			−0.0303865
$246$	−7.80975e11			−0.866885
$247$	−9.73919e11			−1.05935
$248$		−	5.18319e11i		−	0.552509i
$249$		−	1.07348e12i		−	1.12150i
$250$		−	5.73890e11i		−	0.587664i
$251$	6.81635e11			0.684200			0.342100	−	0.939663i	$-0.388862\pi$
$251$	6.81635e11			0.684200			0.342100	+	0.939663i	$0.388862\pi$
$252$			3.81409e10i			0.0375309i
$253$	7.77765e11	+	1.57298e11i	0.750318	+	0.151747i
$254$	1.32128e12			1.24975
$255$		−	2.79668e11i		−	0.259384i
$256$	6.87195e10			0.0625000
$257$	−1.90164e12			−1.69615			−0.848074	−	0.529878i	$-0.822238\pi$
$257$	−1.90164e12			−1.69615			−0.848074	+	0.529878i	$0.822238\pi$
$258$	1.50557e12			1.31705
$259$			2.36117e11i			0.202595i
$260$		−	1.02845e12i		−	0.865600i
$261$			5.79819e10i			0.0478729i
$262$	5.92128e11			0.479633
$263$		−	4.55728e11i		−	0.362182i	−0.983466	−	0.181091i	$-0.942037\pi$
$263$		−	4.55728e11i		−	0.362182i	0.983466	−	0.181091i	$-0.0579629\pi$
$264$	−9.31451e10	+	4.60559e11i	−0.0726341	+	0.359141i
$265$	−3.00926e11			−0.230266
$266$			6.55355e11i			0.492117i
$267$	−9.97595e11			−0.735187
$268$	3.00499e11			0.217354
$269$	−8.28392e11			−0.588131			−0.294066	−	0.955785i	$-0.595008\pi$
$269$	−8.28392e11			−0.588131			−0.294066	+	0.955785i	$0.595008\pi$
$270$			1.09267e12i			0.761503i
$271$		−	5.63086e11i		−	0.385237i	−0.981274	−	0.192619i	$-0.938302\pi$
$271$		−	5.63086e11i		−	0.385237i	0.981274	−	0.192619i	$-0.0616980\pi$
$272$			8.30082e10i			0.0557540i
$273$	−2.45689e12			−1.62022
$274$		−	1.23813e12i		−	0.801702i
$275$	3.99960e11	+	8.08893e10i	0.254304	+	0.0514313i
$276$	6.35304e11			0.396676
$277$			2.02830e12i			1.24375i	0.783116	+	0.621876i	$0.213629\pi$
$277$			2.02830e12i			1.24375i	−0.783116	+	0.621876i	$0.786371\pi$
$278$	1.51132e12			0.910192
$279$	1.95669e11			0.115745
$280$	−6.92050e11			−0.402112
$281$		−	7.37475e11i		−	0.420936i	−0.977601	−	0.210468i	$-0.932501\pi$
$281$		−	7.37475e11i		−	0.420936i	0.977601	−	0.210468i	$-0.0674987\pi$
$282$		−	2.00220e12i		−	1.12269i
$283$		−	8.65033e11i		−	0.476541i	−0.971199	−	0.238271i	$-0.923419\pi$
$283$		−	8.65033e11i		−	0.476541i	0.971199	−	0.238271i	$-0.0765805\pi$
$284$	7.59248e11			0.410953
$285$		−	1.50180e12i		−	0.798709i
$286$	−2.04581e12	−	4.13753e11i	−1.06914	−	0.216228i
$287$	−2.33438e12			−1.19884
$288$			2.59421e10i			0.0130931i
$289$	1.91573e12			0.950264
$290$	−1.05206e12			−0.512919
$291$	−5.13520e11			−0.246089
$292$			1.33837e12i			0.630468i
$293$		−	3.62491e12i		−	1.67865i	−0.543632	−	0.839324i	$-0.682951\pi$
$293$		−	3.62491e12i		−	1.67865i	0.543632	−	0.839324i	$-0.317049\pi$
$294$			4.35840e10i			0.0198422i
$295$	1.95385e11			0.0874544
$296$			1.60598e11i			0.0706775i
$297$	2.17357e12	+	4.39590e11i	0.940569	+	0.190224i
$298$	−1.98575e12			−0.844976
$299$			2.82204e12i			1.18088i
$300$	3.26700e11			0.134445
$301$	4.50025e12			1.82139
$302$	3.89781e11			0.155162
$303$			8.01881e11i			0.313976i
$304$			4.45749e11i			0.171681i
$305$			4.56554e12i			1.72979i
$306$	−3.13361e10			−0.0116799
$307$			1.38783e12i			0.508914i	0.967084	+	0.254457i	$0.0818967\pi$
$307$			1.38783e12i			0.508914i	−0.967084	+	0.254457i	$0.918103\pi$
$308$	−2.78416e11	+	1.37664e12i	−0.100448	+	0.496668i
$309$	2.96855e12			1.05379
$310$			3.55033e12i			1.24011i
$311$	−4.20610e11			−0.144570			−0.0722849	−	0.997384i	$-0.523029\pi$
$311$	−4.20610e11			−0.144570			−0.0722849	+	0.997384i	$0.523029\pi$
$312$	−1.67109e12			−0.565232
$313$	3.50926e12			1.16814			0.584068	−	0.811705i	$-0.301460\pi$
$313$	3.50926e12			1.16814			0.584068	+	0.811705i	$0.301460\pi$
$314$		−	4.01541e12i		−	1.31547i
$315$		−	2.61253e11i		−	0.0842383i
$316$			1.95217e12i			0.619557i
$317$	−3.64129e12			−1.13752			−0.568760	−	0.822504i	$-0.692577\pi$
$317$	−3.64129e12			−1.13752			−0.568760	+	0.822504i	$0.692577\pi$
$318$			4.88962e11i			0.150363i
$319$	−4.23249e11	+	2.09277e12i	−0.128128	+	0.633531i
$320$	−4.70707e11			−0.140282
$321$		−	7.97808e10i		−	0.0234085i
$322$	1.89896e12			0.548576
$323$	−5.38432e11			−0.153150
$324$	1.90766e12			0.534290
$325$			1.45121e12i			0.400234i
$326$			3.75551e12i			1.01996i
$327$		−	2.61218e11i		−	0.0698657i
$328$	−1.58776e12			−0.418231
$329$		−	5.98470e12i		−	1.55261i
$330$	6.38015e11	−	3.15468e12i	0.163028	−	0.806095i
$331$	−1.46115e11			−0.0367751			−0.0183875	−	0.999831i	$-0.505853\pi$
$331$	−1.46115e11			−0.0367751			−0.0183875	+	0.999831i	$0.505853\pi$
$332$		−	2.18244e12i		−	0.541068i
$333$	−6.06268e10			−0.0148062
$334$	−4.52525e12			−1.08870
$335$	−2.05832e12			−0.487853
$336$			1.12448e12i			0.262577i
$337$			2.78713e12i			0.641222i	0.947211	+	0.320611i	$0.103888\pi$
$337$			2.78713e12i			0.641222i	−0.947211	+	0.320611i	$0.896112\pi$
$338$		−	4.30364e12i		−	0.975557i
$339$	−4.71554e12			−1.05325
$340$		−	5.68580e11i		−	0.125140i
$341$	7.06238e12	+	1.42832e12i	1.53172	+	0.309780i
$342$	−1.68273e11			−0.0359653
$343$		−	4.68113e12i		−	0.986007i
$344$	3.06091e12			0.635415
$345$	−4.35163e12			−0.890342
$346$	−5.79882e12			−1.16939
$347$		−	6.14272e12i		−	1.22099i	−0.792019	−	0.610497i	$-0.790970\pi$
$347$		−	6.14272e12i		−	1.22099i	0.792019	−	0.610497i	$-0.209030\pi$
$348$			1.70944e12i			0.334933i
$349$		−	7.20268e12i		−	1.39113i	−0.718464	−	0.695564i	$-0.755155\pi$
$349$		−	7.20268e12i		−	1.39113i	0.718464	−	0.695564i	$-0.244845\pi$
$350$	9.76527e11			0.185928
$351$			7.88656e12i			1.48031i
$352$	−1.89369e11	+	9.36339e11i	−0.0350425	+	0.173269i
$353$	1.08313e13			1.97610			0.988050	−	0.154133i	$-0.0492585\pi$
$353$	1.08313e13			1.97610			0.988050	+	0.154133i	$0.0492585\pi$
$354$		−	3.17474e11i		−	0.0571073i
$355$	−5.20061e12			−0.922386
$356$	−2.02816e12			−0.354693
$357$	−1.35830e12			−0.234236
$358$			1.85641e12i			0.315689i
$359$		−	2.24946e12i		−	0.377230i	−0.982051	−	0.188615i	$-0.939600\pi$
$359$		−	2.24946e12i		−	0.377230i	0.982051	−	0.188615i	$-0.0603998\pi$
$360$		−	1.77695e11i		−	0.0293875i
$361$	3.23972e12			0.528411
$362$		−	1.01006e11i		−	0.0162482i
$363$	−6.01868e12	−	2.53830e12i	−0.954922	−	0.402727i
$364$	−4.99499e12			−0.781677
$365$		−	9.16744e12i		−	1.41509i
$366$	7.41836e12			1.12954
$367$	5.56623e12			0.836048			0.418024	−	0.908436i	$-0.362723\pi$
$367$	5.56623e12			0.836048			0.418024	+	0.908436i	$0.362723\pi$
$368$	1.29160e12			0.191377
$369$		−	5.99391e11i		−	0.0876149i
$370$		−	1.10005e12i		−	0.158636i
$371$			1.46154e12i			0.207941i
$372$	5.76878e12			0.809784
$373$			1.04265e13i			1.44409i	0.691848	+	0.722043i	$0.256797\pi$
$373$			1.04265e13i			1.44409i	−0.691848	+	0.722043i	$0.743203\pi$
$374$	−1.13103e12	−	2.28744e11i	−0.154567	−	0.0312602i
$375$	6.38727e12			0.861310
$376$		−	4.07057e12i		−	0.541647i
$377$	−7.59339e12			−0.997078
$378$	5.30690e12			0.687673
$379$	−4.96319e12			−0.634695			−0.317347	−	0.948309i	$-0.602792\pi$
$379$	−4.96319e12			−0.634695			−0.317347	+	0.948309i	$0.602792\pi$
$380$		−	3.05324e12i		−	0.385339i
$381$			1.47055e13i			1.83170i
$382$			2.40854e12i			0.296100i
$383$	1.63528e12			0.198426			0.0992128	−	0.995066i	$-0.468368\pi$
$383$	1.63528e12			0.198426			0.0992128	+	0.995066i	$0.468368\pi$
$384$			7.64833e11i			0.0916032i
$385$	1.90707e12	−	9.42955e12i	0.225456	−	1.11478i
$386$	−1.00314e13			−1.17065
$387$			1.15551e12i			0.133113i
$388$	−1.04401e12			−0.118726
$389$	−6.16183e12			−0.691769			−0.345885	−	0.938277i	$-0.612421\pi$
$389$	−6.16183e12			−0.691769			−0.345885	+	0.938277i	$0.612421\pi$
$390$	1.14464e13			1.26867
$391$			1.56017e12i			0.170721i
$392$			8.86086e10i			0.00957294i
$393$			6.59026e12i			0.702975i
$394$	3.57857e12			0.376902
$395$		−	1.33717e13i		−	1.39060i
$396$	−3.53474e11	−	7.14880e10i	−0.0362979	−	0.00734103i
$397$	2.98076e12			0.302255			0.151128	−	0.988514i	$-0.451710\pi$
$397$	2.98076e12			0.302255			0.151128	+	0.988514i	$0.451710\pi$
$398$			5.83405e11i			0.0584191i
$399$	−7.29396e12			−0.721272
$400$	6.64198e11			0.0648631
$401$	−1.19198e13			−1.14960			−0.574801	−	0.818293i	$-0.694921\pi$
$401$	−1.19198e13			−1.14960			−0.574801	+	0.818293i	$0.694921\pi$
$402$			3.34448e12i			0.318566i
$403$			2.56251e13i			2.41068i
$404$			1.63026e12i			0.151479i
$405$	−1.30669e13			−1.19922
$406$			5.10963e12i			0.463190i
$407$	−2.18823e12	−	4.42556e11i	−0.195939	−	0.0396275i
$408$	−9.23863e11			−0.0817159
$409$		−	1.01841e13i		−	0.889825i	−0.895574	−	0.444913i	$-0.853235\pi$
$409$		−	1.01841e13i		−	0.889825i	0.895574	−	0.444913i	$-0.146765\pi$
$410$	1.08757e13			0.938722
$411$	1.37801e13			1.17501
$412$	6.03522e12			0.508402
$413$		−	9.48948e11i		−	0.0789755i
$414$			4.87590e11i			0.0400915i
$415$			1.49490e13i			1.21443i
$416$	−3.39741e12			−0.272698
$417$			1.68207e13i			1.33402i
$418$	−6.07356e12	−	1.22834e12i	−0.475951	−	0.0962580i
$419$	−3.03014e12			−0.234635			−0.117317	−	0.993094i	$-0.537429\pi$
$419$	−3.03014e12			−0.234635			−0.117317	+	0.993094i	$0.537429\pi$
$420$		−	7.70237e12i		−	0.589356i
$421$	4.16824e12			0.315168			0.157584	−	0.987506i	$-0.449630\pi$
$421$	4.16824e12			0.315168			0.157584	+	0.987506i	$0.449630\pi$
$422$	7.91277e12			0.591244
$423$	1.53667e12			0.113469
$424$			9.94085e11i			0.0725428i
$425$			8.02304e11i			0.0578621i
$426$			8.45026e12i			0.602313i
$427$	2.21739e13			1.56208
$428$		−	1.62198e11i		−	0.0112935i
$429$	4.60498e12	−	2.27695e13i	0.316914	−	1.56699i
$430$	−2.09663e13			−1.42619
$431$			4.31809e12i			0.290339i	0.989407	+	0.145169i	$0.0463727\pi$
$431$			4.31809e12i			0.290339i	−0.989407	+	0.145169i	$0.953627\pi$
$432$	3.60956e12			0.239903
$433$	−2.01077e13			−1.32106			−0.660532	−	0.750798i	$-0.729669\pi$
$433$	−2.01077e13			−1.32106			−0.660532	+	0.750798i	$0.729669\pi$
$434$	1.72432e13			1.11988
$435$		−	1.17092e13i		−	0.751760i
$436$		−	5.31069e11i		−	0.0337069i
$437$			8.37799e12i			0.525694i
$438$	−1.48958e13			−0.924045
$439$		−	2.02565e13i		−	1.24234i	−0.783675	−	0.621172i	$-0.786657\pi$
$439$		−	2.02565e13i		−	1.24234i	0.783675	−	0.621172i	$-0.213343\pi$
$440$	1.29712e12	−	6.41364e12i	0.0786531	−	0.388903i
$441$	−3.34503e10			−0.00200543
$442$		−	4.10382e12i		−	0.243264i
$443$	−1.68372e13			−0.986849			−0.493424	−	0.869789i	$-0.664255\pi$
$443$	−1.68372e13			−0.986849			−0.493424	+	0.869789i	$0.664255\pi$
$444$	−1.78742e12			−0.103589
$445$	1.38923e13			0.796111
$446$		−	2.32081e13i		−	1.31512i
$447$		−	2.21010e13i		−	1.23844i
$448$			2.28613e12i			0.126681i
$449$	1.27938e13			0.701080			0.350540	−	0.936548i	$-0.385998\pi$
$449$	1.27938e13			0.701080			0.350540	+	0.936548i	$0.385998\pi$
$450$			2.50739e11i			0.0135881i
$451$	4.37536e12	−	2.16341e13i	0.234494	−	1.15946i
$452$	−9.58692e12			−0.508144
$453$			4.33817e12i			0.227413i
$454$	3.03094e11			0.0157144
$455$	3.42141e13			1.75448
$456$	−4.96109e12			−0.251624
$457$		−	1.88575e13i		−	0.946027i	−0.881055	−	0.473013i	$-0.843166\pi$
$457$		−	1.88575e13i		−	0.946027i	0.881055	−	0.473013i	$-0.156834\pi$
$458$			1.88089e13i			0.933331i
$459$			4.36009e12i			0.214009i
$460$	−8.84709e12			−0.429548
$461$		−	2.51422e12i		−	0.120753i	−0.998176	−	0.0603765i	$-0.980770\pi$
$461$		−	2.51422e12i		−	0.120753i	0.998176	−	0.0603765i	$-0.0192301\pi$
$462$	−1.53217e13	−	3.09871e12i	−0.727942	−	0.147222i
$463$	2.99795e13			1.40903			0.704514	−	0.709690i	$-0.251165\pi$
$463$	2.99795e13			1.40903			0.704514	+	0.709690i	$0.251165\pi$
$464$			3.47539e12i			0.161589i
$465$	−3.95144e13			−1.81757
$466$	−2.44318e13			−1.11180
$467$	−3.48289e13			−1.56803			−0.784016	−	0.620740i	$-0.786832\pi$
$467$	−3.48289e13			−1.56803			−0.784016	+	0.620740i	$0.786832\pi$
$468$		−	1.28254e12i		−	0.0571272i
$469$			9.99687e12i			0.440555i
$470$			2.78822e13i			1.21573i
$471$	4.46906e13			1.92802
$472$		−	6.45440e11i		−	0.0275515i
$473$	−8.43487e12	+	4.17065e13i	−0.356265	+	1.76156i
$474$	−2.17272e13			−0.908054
$475$			4.30832e12i			0.178172i
$476$	−2.76148e12			−0.113008
$477$	−3.75274e11			−0.0151970
$478$	2.88689e13			1.15688
$479$		−	3.01723e13i		−	1.19655i	−0.801291	−	0.598275i	$-0.795853\pi$
$479$		−	3.01723e13i		−	1.19655i	0.801291	−	0.598275i	$-0.204147\pi$
$480$		−	5.23887e12i		−	0.205604i
$481$		−	7.93977e12i		−	0.308377i
$482$	9.34230e12			0.359103
$483$			2.11350e13i			0.804021i
$484$	−1.22363e13	−	5.16050e12i	−0.460705	−	0.194296i
$485$	7.15116e12			0.266482
$486$			2.83426e12i			0.104534i
$487$	6.42921e12			0.234700			0.117350	−	0.993091i	$-0.462560\pi$
$487$	6.42921e12			0.234700			0.117350	+	0.993091i	$0.462560\pi$
$488$	1.50819e13			0.544950
$489$	−4.17980e13			−1.49490
$490$		−	6.06941e11i		−	0.0214865i
$491$			3.83365e13i			1.34340i	0.740823	+	0.671700i	$0.234436\pi$
$491$			3.83365e13i			1.34340i	−0.740823	+	0.671700i	$0.765564\pi$
$492$		−	1.76714e13i		−	0.612980i
$493$	−4.19801e12			−0.144148
$494$		−	2.20373e13i		−	0.749071i
$495$	2.42119e12	+	4.89670e11i	0.0814710	+	0.0164770i
$496$	1.17282e13			0.390683
$497$			2.52584e13i			0.832958i
$498$	2.42901e13			0.793017
$499$	2.31289e13			0.747571			0.373785	−	0.927515i	$-0.378060\pi$
$499$	2.31289e13			0.747571			0.373785	+	0.927515i	$0.378060\pi$
$500$	1.29857e13			0.415541
$501$		−	5.03650e13i		−	1.59566i
$502$			1.54236e13i			0.483803i
$503$			4.99365e13i			1.55088i	0.631421	+	0.775440i	$0.282472\pi$
$503$			4.99365e13i			1.55088i	−0.631421	+	0.775440i	$0.717528\pi$
$504$	−8.63030e11			−0.0265383
$505$		−	1.11668e13i		−	0.339995i
$506$	−3.55925e12	+	1.75988e13i	−0.107301	+	0.530555i
$507$	4.78986e13			1.42983
$508$			2.98970e13i			0.883710i
$509$	−4.05426e12			−0.118665			−0.0593325	−	0.998238i	$-0.518897\pi$
$509$	−4.05426e12			−0.118665			−0.0593325	+	0.998238i	$0.518897\pi$
$510$	6.32817e12			0.183412
$511$	−4.45245e13			−1.27789
$512$			1.55494e12i			0.0441942i
$513$			2.34134e13i			0.658988i
$514$		−	4.30293e13i		−	1.19936i
$515$	−4.13394e13			−1.14111
$516$			3.40672e13i			0.931297i
$517$	5.54637e13	+	1.12172e13i	1.50161	+	0.303690i
$518$	−5.34271e12			−0.143256
$519$		−	6.45396e13i		−	1.71391i
$520$	2.32712e13			0.612071
$521$	−4.97675e13			−1.29645			−0.648227	−	0.761447i	$-0.724489\pi$
$521$	−4.97675e13			−1.29645			−0.648227	+	0.761447i	$0.724489\pi$
$522$	−1.31198e12			−0.0338513
$523$			2.39051e13i			0.610916i	0.952206	+	0.305458i	$0.0988095\pi$
$523$			2.39051e13i			0.610916i	−0.952206	+	0.305458i	$0.901190\pi$
$524$			1.33983e13i			0.339152i
$525$			1.08685e13i			0.272505i
$526$	1.03119e13			0.256101
$527$			1.41669e13i			0.348514i
$528$	−1.04213e13	−	2.10763e12i	−0.253951	−	0.0513600i
$529$	−1.71504e13			−0.413995
$530$		−	6.80918e12i		−	0.162823i
$531$	2.43658e11			0.00577176
$532$	−1.48290e13			−0.347979
$533$	7.84970e13			1.82481
$534$		−	2.25730e13i		−	0.519856i
$535$			1.11101e12i			0.0253483i
$536$			6.79951e12i			0.153693i
$537$	−2.06615e13			−0.462690
$538$		−	1.87444e13i		−	0.415872i
$539$	−1.20734e12	−	2.44177e11i	−0.0265390	−	0.00536736i
$540$	−2.47244e13			−0.538464
$541$		−	1.18234e13i		−	0.255126i	−0.991830	−	0.127563i	$-0.959285\pi$
$541$		−	1.18234e13i		−	0.255126i	0.991830	−	0.127563i	$-0.0407155\pi$
$542$	1.27412e13			0.272404
$543$	1.12418e12			0.0238142
$544$	−1.87826e12			−0.0394241
$545$			3.63766e12i			0.0756553i
$546$		−	5.55931e13i		−	1.14567i
$547$		−	5.62806e13i		−	1.14927i	−0.818410	−	0.574635i	$-0.805144\pi$
$547$		−	5.62806e13i		−	1.14927i	0.818410	−	0.574635i	$-0.194856\pi$
$548$	2.80156e13			0.566889
$549$			5.69352e12i			0.114161i
$550$	−1.83032e12	+	9.05006e12i	−0.0363674	+	0.179820i
$551$	−2.25431e13			−0.443869
$552$			1.43753e13i			0.280492i
$553$	−6.49439e13			−1.25578
$554$	−4.58953e13			−0.879466
$555$	1.22433e13			0.232505
$556$			3.41973e13i			0.643603i
$557$		−	3.46645e13i		−	0.646561i	−0.946303	−	0.323280i	$-0.895214\pi$
$557$		−	3.46645e13i		−	0.646561i	0.946303	−	0.323280i	$-0.104786\pi$
$558$			4.42749e12i			0.0818439i
$559$	−1.51328e14			−2.77242
$560$		−	1.56593e13i		−	0.284336i
$561$	2.54587e12	−	1.25881e13i	0.0458165	−	0.226541i
$562$	1.66872e13			0.297647
$563$			3.45958e13i			0.611619i	0.952093	+	0.305810i	$0.0989271\pi$
$563$			3.45958e13i			0.611619i	−0.952093	+	0.305810i	$0.901073\pi$
$564$	4.53046e13			0.793865
$565$	6.56675e13			1.14053
$566$	1.95735e13			0.336966
$567$			6.34635e13i			1.08295i
$568$			1.71798e13i			0.290587i
$569$		−	6.14224e13i		−	1.02983i	−0.857241	−	0.514915i	$-0.827823\pi$
$569$		−	6.14224e13i		−	1.02983i	0.857241	−	0.514915i	$-0.172177\pi$
$570$	3.39819e13			0.564772
$571$		−	6.89157e13i		−	1.13537i	−0.823246	−	0.567685i	$-0.807839\pi$
$571$		−	6.89157e13i		−	1.13537i	0.823246	−	0.567685i	$-0.192161\pi$
$572$	9.36217e12	−	4.62915e13i	0.152896	−	0.755999i
$573$	−2.68066e13			−0.433978
$574$		−	5.28210e13i		−	0.847710i
$575$	1.24838e13			0.198613
$576$	−5.87002e11			−0.00925821
$577$	−1.81704e13			−0.284110			−0.142055	−	0.989859i	$-0.545371\pi$
$577$	−1.81704e13			−0.284110			−0.142055	+	0.989859i	$0.545371\pi$
$578$			4.33479e13i			0.671938i
$579$		−	1.11648e14i		−	1.71576i
$580$		−	2.38053e13i		−	0.362689i
$581$	7.26046e13			1.09669
$582$		−	1.16196e13i		−	0.174011i
$583$	−1.35449e13	−	2.73938e12i	−0.201110	−	0.0406733i
$584$	−3.02839e13			−0.445808
$585$			8.78504e12i			0.128222i
$586$	8.20224e13			1.18698
$587$	4.08503e13			0.586145			0.293072	−	0.956090i	$-0.405322\pi$
$587$	4.08503e13			0.586145			0.293072	+	0.956090i	$0.405322\pi$
$588$	−9.86194e11			−0.0140306
$589$			7.60751e13i			1.07316i
$590$			4.42106e12i			0.0618396i
$591$			3.98287e13i			0.552406i
$592$	−3.63392e12			−0.0499766
$593$		−	1.38480e13i		−	0.188848i	−0.995532	−	0.0944241i	$-0.969899\pi$
$593$		−	1.38480e13i		−	0.188848i	0.995532	−	0.0944241i	$-0.0301010\pi$
$594$	−9.94679e12	+	4.91822e13i	−0.134509	+	0.665083i
$595$	1.89153e13			0.253646
$596$		−	4.49325e13i		−	0.597488i
$597$	−6.49317e12			−0.0856219
$598$	−6.38554e13			−0.835010
$599$	6.05813e12			0.0785606			0.0392803	−	0.999228i	$-0.487493\pi$
$599$	6.05813e12			0.0785606			0.0392803	+	0.999228i	$0.487493\pi$
$600$			7.39238e12i			0.0950667i
$601$			4.32973e13i			0.552190i	0.961130	+	0.276095i	$0.0890405\pi$
$601$			4.32973e13i			0.552190i	−0.961130	+	0.276095i	$0.910960\pi$
$602$			1.01829e14i			1.28792i
$603$	−2.56686e12			−0.0321970
$604$			8.81973e12i			0.109716i
$605$	8.38148e13	+	3.53478e13i	1.03405	+	0.436100i
$606$	−1.81445e13			−0.222015
$607$			1.27913e13i			0.155229i	0.996983	+	0.0776144i	$0.0247303\pi$
$607$			1.27913e13i			0.155229i	−0.996983	+	0.0776144i	$0.975270\pi$
$608$	−1.00861e13			−0.121397
$609$	−5.68691e13			−0.678875
$610$	−1.03306e14			−1.22314
$611$			2.01244e14i			2.36329i
$612$		−	7.09056e11i		−	0.00825892i
$613$		−	1.04340e13i		−	0.120545i	−0.998182	−	0.0602726i	$-0.980803\pi$
$613$		−	1.04340e13i		−	0.120545i	0.998182	−	0.0602726i	$-0.0191970\pi$
$614$	−3.14030e13			−0.359856
$615$			1.21044e14i			1.37584i
$616$	−3.11498e13	−	6.29985e12i	−0.351197	−	0.0710275i
$617$	1.43404e14			1.60374			0.801870	−	0.597498i	$-0.203838\pi$
$617$	1.43404e14			1.60374			0.801870	+	0.597498i	$0.203838\pi$
$618$			6.71707e13i			0.745139i
$619$	1.43785e14			1.58219			0.791097	−	0.611690i	$-0.209510\pi$
$619$	1.43785e14			1.58219			0.791097	+	0.611690i	$0.209510\pi$
$620$	−8.03347e13			−0.876890
$621$	6.78429e13			0.734592
$622$		−	9.51731e12i		−	0.102226i
$623$		−	6.74721e13i		−	0.718926i
$624$		−	3.78124e13i		−	0.399679i
$625$	−1.13691e14			−1.19214
$626$			7.94054e13i			0.825997i
$627$	1.36712e13	−	6.75974e13i	0.141081	−	0.697577i
$628$	9.08583e13			0.930178
$629$		−	4.38951e12i		−	0.0445823i
$630$	5.91149e12			0.0595654
$631$	2.99445e13			0.299344			0.149672	−	0.988736i	$-0.452178\pi$
$631$	2.99445e13			0.299344			0.149672	+	0.988736i	$0.452178\pi$
$632$	−4.41725e13			−0.438093
$633$			8.80675e13i			0.866557i
$634$		−	8.23930e13i		−	0.804348i
$635$		−	2.04786e14i		−	1.98349i
$636$	−1.10640e13			−0.106322
$637$		−	4.38070e12i		−	0.0417683i
$638$	−4.73540e13	−	9.57704e12i	−0.447974	−	0.0906000i
$639$	−6.48550e12			−0.0608750
$640$		−	1.06509e13i		−	0.0991941i
$641$	−1.08076e14			−0.998710			−0.499355	−	0.866398i	$-0.666430\pi$
$641$	−1.08076e14			−0.998710			−0.499355	+	0.866398i	$0.666430\pi$
$642$	1.80523e12			0.0165523
$643$	−1.19429e14			−1.08656			−0.543279	−	0.839552i	$-0.682818\pi$
$643$	−1.19429e14			−1.08656			−0.543279	+	0.839552i	$0.682818\pi$
$644$			4.29686e13i			0.387902i
$645$		−	2.33350e14i		−	2.09030i
$646$		−	1.21833e13i		−	0.108294i
$647$	−4.96569e13			−0.437984			−0.218992	−	0.975727i	$-0.570277\pi$
$647$	−4.96569e13			−0.437984			−0.218992	+	0.975727i	$0.570277\pi$
$648$			4.31655e13i			0.377800i
$649$	8.79446e12	+	1.77862e12i	0.0763811	+	0.0154476i
$650$	−3.28372e13			−0.283008
$651$			1.91914e14i			1.64135i
$652$	−8.49776e13			−0.721218
$653$	3.61478e11			0.00304450			0.00152225	−	0.999999i	$-0.499515\pi$
$653$	3.61478e11			0.00304450			0.00152225	+	0.999999i	$0.499515\pi$
$654$	5.91068e12			0.0494025
$655$		−	9.17744e13i		−	0.761229i
$656$		−	3.59269e13i		−	0.295734i
$657$		−	1.14324e13i		−	0.0933921i
$658$	1.35418e14			1.09786
$659$		−	7.12158e13i		−	0.572993i	−0.958081	−	0.286497i	$-0.907509\pi$
$659$		−	7.12158e13i		−	0.572993i	0.958081	−	0.286497i	$-0.0924907\pi$
$660$	7.13824e13	+	1.44366e13i	0.569995	+	0.115278i
$661$	9.17572e12			0.0727165			0.0363583	−	0.999339i	$-0.488424\pi$
$661$	9.17572e12			0.0727165			0.0363583	+	0.999339i	$0.488424\pi$
$662$		−	3.30619e12i		−	0.0260039i
$663$	4.56747e13			0.356540
$664$	4.93830e13			0.382593
$665$	1.01574e14			0.781042
$666$		−	1.37183e12i		−	0.0104696i
$667$			6.53210e13i			0.494793i
$668$		−	1.02395e14i		−	0.769830i
$669$	2.58301e14			1.92751
$670$		−	4.65745e13i		−	0.344964i
$671$	−4.15609e13	+	2.05499e14i	−0.305543	+	1.51077i
$672$	−2.54442e13			−0.185670
$673$		−	5.08704e12i		−	0.0368460i	−0.999830	−	0.0184230i	$-0.994135\pi$
$673$		−	5.08704e12i		−	0.0368460i	0.999830	−	0.0184230i	$-0.00586455\pi$
$674$	−6.30656e13			−0.453412
$675$	3.48877e13			0.248974
$676$	9.73803e13			0.689823
$677$		−	2.43029e13i		−	0.170890i	−0.996343	−	0.0854448i	$-0.972769\pi$
$677$		−	2.43029e13i		−	0.170890i	0.996343	−	0.0854448i	$-0.0272311\pi$
$678$		−	1.06700e14i		−	0.744762i
$679$		−	3.47318e13i		−	0.240646i
$680$	1.28655e13			0.0884875
$681$			3.37337e12i			0.0230318i
$682$	−3.23192e13	+	1.59803e14i	−0.219048	+	1.08309i
$683$	−9.28320e13			−0.624589			−0.312294	−	0.949985i	$-0.601098\pi$
$683$	−9.28320e13			−0.624589			−0.312294	+	0.949985i	$0.601098\pi$
$684$		−	3.80759e12i		−	0.0254313i
$685$	−1.91898e14			−1.27239
$686$	1.05922e14			0.697212
$687$	−2.09339e14			−1.36794
$688$			6.92604e13i			0.449306i
$689$		−	4.91464e13i		−	0.316516i
$690$		−	9.84662e13i		−	0.629567i
$691$	−1.42903e14			−0.907092			−0.453546	−	0.891233i	$-0.649841\pi$
$691$	−1.42903e14			−0.907092			−0.453546	+	0.891233i	$0.649841\pi$
$692$		−	1.31212e14i		−	0.826883i
$693$	2.37823e12	−	1.17592e13i	0.0148795	−	0.0735721i
$694$	1.38994e14			0.863373
$695$		−	2.34241e14i		−	1.44457i
$696$	−3.86803e13			−0.236834
$697$	4.33971e13			0.263814
$698$	1.62978e14			0.983676
$699$		−	2.71921e14i		−	1.62951i
$700$			2.20963e13i			0.131471i
$701$		−	1.56090e14i		−	0.922114i	−0.887371	−	0.461057i	$-0.847470\pi$
$701$		−	1.56090e14i		−	0.922114i	0.887371	−	0.461057i	$-0.152530\pi$
$702$	−1.78452e14			−1.04674
$703$		−	2.35714e13i		−	0.137280i
$704$	−2.11869e13	−	4.28493e12i	−0.122519	−	0.0247788i
$705$	−3.10322e14			−1.78183
$706$			2.45085e14i			1.39731i
$707$	−5.42350e13			−0.307031
$708$	7.18361e12			0.0403809
$709$	2.49375e14			1.39195			0.695973	−	0.718068i	$-0.254973\pi$
$709$	2.49375e14			1.39195			0.695973	+	0.718068i	$0.254973\pi$
$710$		−	1.17676e14i		−	0.652225i
$711$		−	1.66754e13i		−	0.0917759i
$712$		−	4.58921e13i		−	0.250806i
$713$	2.20436e14			1.19628
$714$		−	3.07347e13i		−	0.165630i
$715$	−6.41279e13	+	3.17083e14i	−0.343176	+	1.69684i
$716$	−4.20059e13			−0.223226
$717$			3.21304e14i			1.69559i
$718$	5.08995e13			0.266742
$719$	−2.40822e14			−1.25329			−0.626645	−	0.779305i	$-0.715572\pi$
$719$	−2.40822e14			−1.25329			−0.626645	+	0.779305i	$0.715572\pi$
$720$	4.02078e12			0.0207801
$721$			2.00777e14i			1.03048i
$722$			7.33065e13i			0.373643i
$723$			1.03978e14i			0.526319i
$724$	2.28552e12			0.0114892
$725$			3.35908e13i			0.167699i
$726$	5.74352e13	−	1.36187e14i	0.284771	−	0.675232i
$727$	−1.27130e14			−0.626003			−0.313001	−	0.949753i	$-0.601334\pi$
$727$	−1.27130e14			−0.626003			−0.313001	+	0.949753i	$0.601334\pi$
$728$		−	1.13024e14i		−	0.552729i
$729$	1.88466e14			0.915369
$730$	2.07436e14			1.00062
$731$	−8.36615e13			−0.400810
$732$			1.67858e14i			0.798707i
$733$		−	8.33489e13i		−	0.393895i	−0.980414	−	0.196947i	$-0.936897\pi$
$733$		−	8.33489e13i		−	0.393895i	0.980414	−	0.196947i	$-0.0631028\pi$
$734$			1.25949e14i			0.591175i
$735$	6.75512e12			0.0314917
$736$			2.92257e13i			0.135324i
$737$	−9.26469e13	−	1.87373e13i	−0.426082	−	0.0861724i
$738$	1.35627e13			0.0619531
$739$			2.51503e14i			1.14109i	0.821265	+	0.570547i	$0.193269\pi$
$739$			2.51503e14i			1.14109i	−0.821265	+	0.570547i	$0.806731\pi$
$740$	2.48912e13			0.112173
$741$	2.45270e14			1.09788
$742$	−3.30708e13			−0.147037
$743$			1.36480e14i			0.602733i	0.953508	+	0.301366i	$0.0974427\pi$
$743$			1.36480e14i			0.602733i	−0.953508	+	0.301366i	$0.902557\pi$
$744$			1.30533e14i			0.572604i
$745$			3.07774e14i			1.34107i
$746$	−2.35924e14			−1.02112
$747$			1.86424e13i			0.0801492i
$748$	5.17588e12	−	2.55923e13i	0.0221043	−	0.109295i
$749$	5.39595e12			0.0228907
$750$			1.44528e14i			0.609038i
$751$	2.73472e14			1.14476			0.572378	−	0.819990i	$-0.306021\pi$
$751$	2.73472e14			1.14476			0.572378	+	0.819990i	$0.306021\pi$
$752$	9.21065e13			0.383002
$753$	−1.71662e14			−0.709086
$754$		−	1.71819e14i		−	0.705041i
$755$		−	6.04124e13i		−	0.246259i
$756$			1.20081e14i			0.486258i
$757$	3.59616e14			1.44664			0.723319	−	0.690514i	$-0.242616\pi$
$757$	3.59616e14			1.44664			0.723319	+	0.690514i	$0.242616\pi$
$758$		−	1.12304e14i		−	0.448797i
$759$	−1.95871e14	−	3.96136e13i	−0.777608	−	0.157266i
$760$	6.90869e13			0.272476
$761$		−	3.97670e14i		−	1.55812i	−0.626952	−	0.779058i	$-0.715698\pi$
$761$		−	3.97670e14i		−	1.55812i	0.626952	−	0.779058i	$-0.284302\pi$
$762$	−3.32748e14			−1.29521
$763$	1.76674e13			0.0683203
$764$	−5.44991e13			−0.209374
$765$			4.85681e12i			0.0185372i
$766$			3.70021e13i			0.140308i
$767$			3.19098e13i			0.120212i
$768$	−1.73062e13			−0.0647732
$769$		−	3.87504e14i		−	1.44093i	−0.693489	−	0.720467i	$-0.743928\pi$
$769$		−	3.87504e14i		−	1.44093i	0.693489	−	0.720467i	$-0.256072\pi$
$770$	2.13366e14	+	4.31520e13i	0.788265	+	0.159422i
$771$	4.78907e14			1.75784
$772$		−	2.26985e14i		−	0.827774i
$773$	1.63408e13			0.0592072			0.0296036	−	0.999562i	$-0.490576\pi$
$773$	1.63408e13			0.0592072			0.0296036	+	0.999562i	$0.490576\pi$
$774$	−2.61463e13			−0.0941249
$775$	1.13358e14			0.405454
$776$		−	2.36233e13i		−	0.0839522i
$777$		−	5.94632e13i		−	0.209963i
$778$		−	1.39426e14i		−	0.489155i
$779$	2.33040e14			0.812350
$780$			2.59003e14i			0.897083i
$781$	−2.34084e14	−	4.73420e13i	−0.805595	−	0.162926i
$782$	−3.53025e13			−0.120718
$783$			1.82548e14i			0.620253i
$784$	−2.00498e12			−0.00676909
$785$	−6.22351e14			−2.08779
$786$	−1.49121e14			−0.497078
$787$		−	1.35627e14i		−	0.449233i	−0.974447	−	0.224616i	$-0.927887\pi$
$787$		−	1.35627e14i		−	0.449233i	0.974447	−	0.224616i	$-0.0721129\pi$
$788$			8.09737e13i			0.266510i
$789$			1.14770e14i			0.375355i
$790$	3.02568e14			0.983303
$791$		−	3.18934e14i		−	1.02996i
$792$	1.61759e12	−	7.99821e12i	0.00519089	−	0.0256665i
$793$	−7.45631e14			−2.37771
$794$			6.74468e13i			0.213727i
$795$	7.57847e13			0.238641
$796$	−1.32009e13			−0.0413085
$797$	2.16092e14			0.671965			0.335983	−	0.941868i	$-0.390932\pi$
$797$	2.16092e14			0.671965			0.335983	+	0.941868i	$0.390932\pi$
$798$		−	1.65043e14i		−	0.510016i
$799$			1.11258e14i			0.341663i
$800$			1.50291e13i			0.0458652i
$801$	1.73246e13			0.0525412
$802$		−	2.69715e14i		−	0.812892i
$803$	8.34527e13	−	4.12635e14i	0.249956	−	1.23591i
$804$	−7.56770e13			−0.225260
$805$		−	2.94322e14i		−	0.870648i
$806$	−5.79830e14			−1.70461
$807$	2.08621e14			0.609522
$808$	−3.68887e13			−0.107112
$809$			4.08529e14i			1.17891i	0.807802	+	0.589455i	$0.200657\pi$
$809$			4.08529e14i			1.17891i	−0.807802	+	0.589455i	$0.799343\pi$
$810$		−	2.95671e14i		−	0.847975i
$811$		−	2.05159e14i		−	0.584773i	−0.956300	−	0.292386i	$-0.905551\pi$
$811$		−	2.05159e14i		−	0.584773i	0.956300	−	0.292386i	$-0.0944493\pi$
$812$	−1.15618e14			−0.327525
$813$			1.41807e14i			0.399249i
$814$	1.00139e13	−	4.95140e13i	0.0280208	−	0.138550i
$815$	5.82070e14			1.61878
$816$		−	2.09046e13i		−	0.0577819i
$817$	−4.49257e14			−1.23420
$818$	2.30439e14			0.629201
$819$	4.26672e13			0.115791
$820$			2.46088e14i			0.663777i
$821$			3.42794e14i			0.919004i	0.888177	+	0.459502i	$0.151972\pi$
$821$			3.42794e14i			0.919004i	−0.888177	+	0.459502i	$0.848028\pi$
$822$			3.11808e14i			0.830861i
$823$	1.71647e14			0.454607			0.227304	−	0.973824i	$-0.427009\pi$
$823$	1.71647e14			0.454607			0.227304	+	0.973824i	$0.427009\pi$
$824$			1.36561e14i			0.359494i
$825$	−1.00725e14	−	2.03710e13i	−0.263553	−	0.0533020i
$826$	2.14722e13			0.0558441
$827$		−	4.14254e14i		−	1.07088i	−0.844574	−	0.535438i	$-0.820147\pi$
$827$		−	4.14254e14i		−	1.07088i	0.844574	−	0.535438i	$-0.179853\pi$
$828$	−1.10329e13			−0.0283490
$829$	−2.65366e14			−0.677754			−0.338877	−	0.940831i	$-0.610047\pi$
$829$	−2.65366e14			−0.677754			−0.338877	+	0.940831i	$0.610047\pi$
$830$	−3.38258e14			−0.858733
$831$		−	5.10804e14i		−	1.28899i
$832$		−	7.68746e13i		−	0.192826i
$833$		−	2.42187e12i		−	0.00603847i
$834$	−3.80608e14			−0.943296
$835$			7.01372e14i			1.72789i
$836$	2.77942e13	−	1.37429e14i	0.0680647	−	0.336548i
$837$	6.16037e14			1.49961
$838$		−	6.85642e13i		−	0.165912i
$839$	7.27443e14			1.74980			0.874902	−	0.484301i	$-0.160926\pi$
$839$	7.27443e14			1.74980			0.874902	+	0.484301i	$0.160926\pi$
$840$	1.74285e14			0.416738
$841$	2.44945e14			0.582222
$842$			9.43164e13i			0.222857i
$843$			1.85724e14i			0.436246i
$844$			1.79046e14i			0.418072i
$845$	−6.67025e14			−1.54831
$846$			3.47708e13i			0.0802349i
$847$	1.71677e14	−	4.07072e14i	0.393819	−	0.933800i
$848$	−2.24936e13			−0.0512955
$849$			2.17848e14i			0.493874i
$850$	−1.81541e13			−0.0409147
$851$	−6.83006e13			−0.153030
$852$	−1.91208e14			−0.425900
$853$		−	6.89970e14i		−	1.52786i	−0.645297	−	0.763932i	$-0.723266\pi$
$853$		−	6.89970e14i		−	1.52786i	0.645297	−	0.763932i	$-0.276734\pi$
$854$			5.01739e14i			1.10456i
$855$			2.60808e13i			0.0570808i
$856$	3.67013e12			0.00798569
$857$			3.82753e14i			0.827970i	0.910284	+	0.413985i	$0.135863\pi$
$857$			3.82753e14i			0.827970i	−0.910284	+	0.413985i	$0.864137\pi$
$858$	5.15214e14	+	1.04199e14i	1.10803	+	0.224092i
$859$	−3.58849e14			−0.767267			−0.383633	−	0.923485i	$-0.625327\pi$
$859$	−3.58849e14			−0.767267			−0.383633	+	0.923485i	$0.625327\pi$
$860$		−	4.74412e14i		−	1.00847i
$861$	5.87887e14			1.24245
$862$	−9.77072e13			−0.205301
$863$	3.80616e14			0.795121			0.397560	−	0.917576i	$-0.369857\pi$
$863$	3.80616e14			0.795121			0.397560	+	0.917576i	$0.369857\pi$
$864$			8.16750e13i			0.169637i
$865$			8.98763e14i			1.85594i
$866$		−	4.54986e14i		−	0.934133i
$867$	−4.82453e14			−0.984826
$868$			3.90170e14i			0.791873i
$869$	1.21725e14	−	6.01873e14i	0.245630	−	1.21452i
$870$	2.64948e14			0.531575
$871$		−	3.36160e14i		−	0.670586i
$872$	1.20167e13			0.0238344
$873$	8.91796e12			0.0175871
$874$	−1.89572e14			−0.371721
$875$			4.32002e14i			0.842258i
$876$		−	3.37054e14i		−	0.653399i
$877$			2.05434e14i			0.395980i	0.980204	+	0.197990i	$0.0634414\pi$
$877$			2.05434e14i			0.395980i	−0.980204	+	0.197990i	$0.936559\pi$
$878$	4.58352e14			0.878469
$879$			9.12892e14i			1.73970i
$880$	1.45124e14	+	2.93504e13i	0.274996	+	0.0556161i
$881$	−5.81723e14			−1.09607			−0.548033	−	0.836457i	$-0.684623\pi$
$881$	−5.81723e14			−1.09607			−0.548033	+	0.836457i	$0.684623\pi$
$882$		−	7.56895e11i		−	0.00141805i
$883$	9.09212e13			0.169380			0.0846899	−	0.996407i	$-0.473010\pi$
$883$	9.09212e13			0.169380			0.0846899	+	0.996407i	$0.473010\pi$
$884$	9.28590e13			0.172013
$885$	−4.92055e13			−0.0906353
$886$		−	3.80982e14i		−	0.697807i
$887$			6.57821e14i			1.19809i	0.800715	+	0.599045i	$0.204453\pi$
$887$			6.57821e14i			1.19809i	−0.800715	+	0.599045i	$0.795547\pi$
$888$		−	4.04447e13i		−	0.0732482i
$889$	−9.94603e14			−1.79119
$890$			3.14346e14i			0.562935i
$891$	−5.88153e14	−	1.18950e14i	−1.04737	−	0.211825i
$892$	5.25139e14			0.929930
$893$			5.97449e14i			1.05207i
$894$	5.00089e14			0.875708
$895$	2.87727e14			0.501032
$896$	−5.17293e13			−0.0895770
$897$		−	7.10697e14i		−	1.22383i
$898$			2.89491e14i			0.495739i
$899$			5.93138e14i			1.01008i
$900$	−5.67358e12			−0.00960826
$901$		−	2.71706e13i		−	0.0457589i
$902$	4.89524e14	+	9.90031e13i	0.819862	+	0.165812i
$903$	−1.13333e15			−1.88764
$904$		−	2.16927e14i		−	0.359312i
$905$	−1.56551e13			−0.0257877
$906$	−9.81617e13			−0.160806
$907$	−1.02388e12			−0.00166806			−0.000834032	−	1.00000i	$-0.500265\pi$
$907$	−1.02388e12			−0.00166806			−0.000834032		1.00000i	$0.500265\pi$
$908$			6.85824e12i			0.0111118i
$909$		−	1.39257e13i		−	0.0224387i
$910$			7.74177e14i			1.24060i
$911$	5.93081e14			0.945196			0.472598	−	0.881278i	$-0.343316\pi$
$911$	5.93081e14			0.945196			0.472598	+	0.881278i	$0.343316\pi$
$912$		−	1.12257e14i		−	0.177925i
$913$	−1.36084e14	+	6.72870e14i	−0.214512	+	1.06066i
$914$	4.26697e14			0.668942
$915$		−	1.14978e15i		−	1.79270i
$916$	−4.25597e14			−0.659965
$917$	−4.45731e14			−0.687426
$918$	−9.86575e13			−0.151327
$919$			1.69820e14i			0.259067i	0.991575	+	0.129533i	$0.0413479\pi$
$919$			1.69820e14i			0.259067i	−0.991575	+	0.129533i	$0.958652\pi$
$920$		−	2.00187e14i		−	0.303736i
$921$		−	3.49508e14i		−	0.527424i
$922$	5.68903e13			0.0853853
$923$		−	8.49350e14i		−	1.26788i
$924$	7.01159e13	−	3.46690e14i	0.104101	−	0.514733i
$925$	−3.51231e13			−0.0518662
$926$			6.78359e14i			0.996334i
$927$	−5.15528e13			−0.0753102
$928$	−7.86390e13			−0.114261
$929$	4.28073e14			0.618642			0.309321	−	0.950958i	$-0.399898\pi$
$929$	4.28073e14			0.618642			0.309321	+	0.950958i	$0.399898\pi$
$930$		−	8.94108e14i		−	1.28521i
$931$		−	1.30053e13i		−	0.0185940i
$932$		−	5.52829e14i		−	0.786160i
$933$	1.05926e14			0.149828
$934$		−	7.88088e14i		−	1.10877i
$935$	−3.54532e13	+	1.75299e14i	−0.0496132	+	0.245314i
$936$	2.90207e13			0.0403951
$937$		−	4.66801e14i		−	0.646299i	−0.946348	−	0.323150i	$-0.895258\pi$
$937$		−	4.66801e14i		−	0.646299i	0.946348	−	0.323150i	$-0.104742\pi$
$938$	−2.26203e14			−0.311519
$939$	−8.83765e14			−1.21062
$940$	−6.30901e14			−0.859651
$941$		−	8.81140e14i		−	1.19425i	−0.802147	−	0.597127i	$-0.796309\pi$
$941$		−	8.81140e14i		−	1.19425i	0.802147	−	0.597127i	$-0.203691\pi$
$942$			1.01123e15i			1.36332i
$943$		−	6.75258e14i		−	0.905548i
$944$	1.46046e13			0.0194819
$945$		−	8.22521e14i		−	1.09141i
$946$	−9.43710e14	−	1.90859e14i	−1.24561	−	0.251917i
$947$	−7.52110e13			−0.0987487			−0.0493743	−	0.998780i	$-0.515723\pi$
$947$	−7.52110e13			−0.0987487			−0.0493743	+	0.998780i	$0.515723\pi$
$948$		−	4.91630e14i		−	0.642091i
$949$	1.49720e15			1.94513
$950$	−9.74862e13			−0.125987
$951$	9.17016e14			1.17889
$952$		−	6.24852e13i		−	0.0799084i
$953$			5.01720e12i			0.00638259i	0.999995	+	0.00319129i	$0.00101582\pi$
$953$			5.01720e12i			0.00638259i	−0.999995	+	0.00319129i	$0.998984\pi$
$954$		−	8.49148e12i		−	0.0107459i
$955$	3.73302e14			0.469941
$956$			6.53228e14i			0.818041i
$957$	1.06590e14	−	5.27039e14i	0.132788	−	0.656574i
$958$	6.82721e14			0.846089
$959$			9.32014e14i			1.14902i
$960$	1.18542e14			0.145384
$961$	1.18201e15			1.44213
$962$	1.79656e14			0.218056
$963$			1.38550e12i			0.00167292i
$964$			2.11392e14i			0.253924i
$965$			1.55478e15i			1.85794i
$966$	−4.78231e14			−0.568529
$967$		−	8.51010e14i		−	1.00647i	−0.864149	−	0.503237i	$-0.832142\pi$
$967$		−	8.51010e14i		−	1.00647i	0.864149	−	0.503237i	$-0.167858\pi$
$968$	1.16769e14	−	2.76875e14i	0.137388	−	0.325767i
$969$	1.35598e14			0.158721
$970$			1.61812e14i			0.188431i
$971$	−4.07930e14			−0.472595			−0.236298	−	0.971681i	$-0.575934\pi$
$971$	−4.07930e14			−0.472595			−0.236298	+	0.971681i	$0.575934\pi$
$972$	−6.41321e13			−0.0739169
$973$	−1.13766e15			−1.30452
$974$			1.45476e14i			0.165958i
$975$		−	3.65471e14i		−	0.414791i
$976$			3.41264e14i			0.385338i
$977$	−5.75540e13			−0.0646551			−0.0323275	−	0.999477i	$-0.510292\pi$
$977$	−5.75540e13			−0.0646551			−0.0323275	+	0.999477i	$0.510292\pi$
$978$		−	9.45782e14i		−	1.05705i
$979$	6.25304e14	+	1.26464e14i	0.695309	+	0.140622i
$980$	1.37335e13			0.0151933
$981$			4.53639e12i			0.00499305i
$982$	−8.67457e14			−0.949927
$983$	−1.78324e15			−1.94286			−0.971429	−	0.237329i	$-0.923728\pi$
$983$	−1.78324e15			−1.94286			−0.971429	+	0.237329i	$0.923728\pi$
$984$	3.99859e14			0.433442
$985$		−	5.54645e14i		−	0.598183i
$986$		−	9.49902e13i		−	0.101928i
$987$			1.50718e15i			1.60908i
$988$	4.98647e14			0.529674
$989$			1.30177e15i			1.37579i
$990$	−1.10800e13	+	5.47853e13i	−0.0116510	+	0.0576087i
$991$	1.91671e14			0.200534			0.100267	−	0.994961i	$-0.468030\pi$
$991$	1.91671e14			0.200534			0.100267	+	0.994961i	$0.468030\pi$
$992$			2.65380e14i			0.276254i
$993$	3.67972e13			0.0381126
$994$	−5.71531e14			−0.588990
$995$	9.04224e13			0.0927172
$996$			5.49622e14i			0.560748i
$997$		−	6.76413e14i		−	0.686651i	−0.939217	−	0.343325i	$-0.888447\pi$
$997$		−	6.76413e14i		−	0.686651i	0.939217	−	0.343325i	$-0.111553\pi$
$998$			5.23347e14i			0.528612i
$999$	−1.90875e14			−0.191832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.11.b.a.21.7	yes	10
3.2	odd	2		198.11.d.a.109.1		10
4.3	odd	2		176.11.h.e.65.8		10
11.10	odd	2	inner	22.11.b.a.21.2	✓	10
33.32	even	2		198.11.d.a.109.6		10
44.43	even	2		176.11.h.e.65.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.11.b.a.21.2	✓	10	11.10	odd	2	inner
22.11.b.a.21.7	yes	10	1.1	even	1	trivial
176.11.h.e.65.7		10	44.43	even	2
176.11.h.e.65.8		10	4.3	odd	2
198.11.d.a.109.1		10	3.2	odd	2
198.11.d.a.109.6		10	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:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	22.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+22.6274i q^{2} -251.838 q^{3} -512.000 q^{4} +3507.04 q^{5} -5698.45i q^{6} -17033.0i q^{7} -11585.2i q^{8} +4373.51 q^{9} +O(q^{10})\)	\(q+22.6274i q^{2} -251.838 q^{3} -512.000 q^{4} +3507.04 q^{5} -5698.45i q^{6} -17033.0i q^{7} -11585.2i q^{8} +4373.51 q^{9} +79355.3i q^{10} +(157855. + 31925.2i) q^{11} +128941. q^{12} +572760. i q^{13} +385413. q^{14} -883207. q^{15} +262144. q^{16} +316651. i q^{17} +98961.1i q^{18} +1.70040e6i q^{19} -1.79561e6 q^{20} +4.28957e6i q^{21} +(-722384. + 3.57185e6i) q^{22} +4.92708e6 q^{23} +2.91761e6i q^{24} +2.53372e6 q^{25} -1.29601e7 q^{26} +1.37694e7 q^{27} +8.72090e6i q^{28} +1.32575e7i q^{29} -1.99847e7i q^{30} +4.47396e7 q^{31} +5.93164e6i q^{32} +(-3.97539e7 - 8.03998e6i) q^{33} -7.16499e6 q^{34} -5.97355e7i q^{35} -2.23923e6 q^{36} -1.38623e7 q^{37} -3.84756e7 q^{38} -1.44243e8i q^{39} -4.06299e7i q^{40} -1.37050e8i q^{41} -9.70618e7 q^{42} +2.64207e8i q^{43} +(-8.08218e7 - 1.63457e7i) q^{44} +1.53381e7 q^{45} +1.11487e8i q^{46} +3.51358e8 q^{47} -6.60179e7 q^{48} -7.64840e6 q^{49} +5.73314e7i q^{50} -7.97448e7i q^{51} -2.93253e8i q^{52} -8.58062e7 q^{53} +3.11566e8i q^{54} +(5.53604e8 + 1.11963e8i) q^{55} -1.97332e8 q^{56} -4.28225e8i q^{57} -2.99984e8 q^{58} +5.57123e7 q^{59} +4.52202e8 q^{60} +1.30182e9i q^{61} +1.01234e9i q^{62} -7.44940e7i q^{63} -1.34218e8 q^{64} +2.00869e9i q^{65} +(1.81924e8 - 8.99529e8i) q^{66} -5.86911e8 q^{67} -1.62125e8i q^{68} -1.24083e9 q^{69} +1.35166e9 q^{70} -1.48291e9 q^{71} -5.06681e7i q^{72} -2.61401e9i q^{73} -3.13668e8i q^{74} -6.38087e8 q^{75} -8.70603e8i q^{76} +(5.43782e8 - 2.68875e9i) q^{77} +3.26385e9 q^{78} -3.81282e9i q^{79} +9.19350e8 q^{80} -3.72591e9 q^{81} +3.10110e9 q^{82} +4.26258e9i q^{83} -2.19626e9i q^{84} +1.11051e9i q^{85} -5.97833e9 q^{86} -3.33876e9i q^{87} +(3.69861e8 - 1.82879e9i) q^{88} +3.96125e9 q^{89} +3.47061e8i q^{90} +9.75584e9 q^{91} -2.52267e9 q^{92} -1.12672e10 q^{93} +7.95034e9i q^{94} +5.96336e9i q^{95} -1.49381e9i q^{96} +2.03909e9 q^{97} -1.73064e8i q^{98} +(6.90380e8 + 1.39625e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 106 q^{3} - 5120 q^{4} + 1138 q^{5} + 78044 q^{9}+O(q^{10}) \) 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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