LMFDB - Embedded newform 22.11.b.a.21.9

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			21.9
Root			$230.003 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.11.b.a.21.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+22.6274i q^{2} +189.131 q^{3} -512.000 q^{4} -1492.29 q^{5} +4279.54i q^{6} -21897.3i q^{7} -11585.2i q^{8} -23278.6 q^{9} +O(q^{10})$	\(q+22.6274i q^{2} +189.131 q^{3} -512.000 q^{4} -1492.29 q^{5} +4279.54i q^{6} -21897.3i q^{7} -11585.2i q^{8} -23278.6 q^{9} -33766.7i q^{10} +(-161000. + 4067.66i) q^{11} -96834.9 q^{12} +49899.0i q^{13} +495479. q^{14} -282238. q^{15} +262144. q^{16} -2.49225e6i q^{17} -526735. i q^{18} -1.02789e6i q^{19} +764053. q^{20} -4.14145e6i q^{21} +(-92040.6 - 3.64301e6i) q^{22} +9.76729e6 q^{23} -2.19112e6i q^{24} -7.53869e6 q^{25} -1.12909e6 q^{26} -1.55707e7 q^{27} +1.12114e7i q^{28} -6.29158e6i q^{29} -6.38632e6i q^{30} +3.66786e6 q^{31} +5.93164e6i q^{32} +(-3.04500e7 + 769319. i) q^{33} +5.63933e7 q^{34} +3.26771e7i q^{35} +1.19186e7 q^{36} -6.77049e7 q^{37} +2.32585e7 q^{38} +9.43744e6i q^{39} +1.72885e7i q^{40} +1.77533e8i q^{41} +9.37102e7 q^{42} +4.27757e7i q^{43} +(8.24318e7 - 2.08264e6i) q^{44} +3.47384e7 q^{45} +2.21009e8i q^{46} -1.23276e8 q^{47} +4.95795e7 q^{48} -1.97015e8 q^{49} -1.70581e8i q^{50} -4.71362e8i q^{51} -2.55483e7i q^{52} -4.18303e8 q^{53} -3.52324e8i q^{54} +(2.40258e8 - 6.07013e6i) q^{55} -2.53685e8 q^{56} -1.94405e8i q^{57} +1.42362e8 q^{58} +5.37998e8 q^{59} +1.44506e8 q^{60} -9.73365e8i q^{61} +8.29942e7i q^{62} +5.09738e8i q^{63} -1.34218e8 q^{64} -7.44639e7i q^{65} +(-1.74077e7 - 6.89004e8i) q^{66} -1.10292e9 q^{67} +1.27603e9i q^{68} +1.84729e9 q^{69} -7.39399e8 q^{70} +2.08250e9 q^{71} +2.69688e8i q^{72} -1.22086e9i q^{73} -1.53199e9i q^{74} -1.42580e9 q^{75} +5.26280e8i q^{76} +(8.90707e7 + 3.52545e9i) q^{77} -2.13545e8 q^{78} +4.55531e9i q^{79} -3.91195e8 q^{80} -1.57031e9 q^{81} -4.01712e9 q^{82} -3.69645e9i q^{83} +2.12042e9i q^{84} +3.71917e9i q^{85} -9.67904e8 q^{86} -1.18993e9i q^{87} +(4.71248e7 + 1.86522e9i) q^{88} +1.01627e10 q^{89} +7.86041e8i q^{90} +1.09265e9 q^{91} -5.00085e9 q^{92} +6.93705e8 q^{93} -2.78941e9i q^{94} +1.53391e9i q^{95} +1.12186e9i q^{96} -3.66369e9 q^{97} -4.45795e9i q^{98} +(3.74785e9 - 9.46894e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	189.131			0.778315			0.389158	−	0.921171i	$-0.372766\pi$
$3$	189.131			0.778315			0.389158	+	0.921171i	$0.372766\pi$
$4$	−512.000			−0.500000
$5$	−1492.29			−0.477533			−0.238767	−	0.971077i	$-0.576743\pi$
$5$	−1492.29			−0.477533			−0.238767	+	0.971077i	$0.576743\pi$
$6$			4279.54i			0.550352i
$7$		−	21897.3i		−	1.30287i	−0.758706	−	0.651433i	$-0.774168\pi$
$7$		−	21897.3i		−	1.30287i	0.758706	−	0.651433i	$-0.225832\pi$
$8$		−	11585.2i		−	0.353553i
$9$	−23278.6			−0.394225
$10$		−	33766.7i		−	0.337667i
$11$	−161000.	+	4067.66i	−0.999681	+	0.0252570i
$11$	−161000.	+	4067.66i	−0.999681	+	0.0252570i
$12$	−96834.9			−0.389158
$13$			49899.0i			0.134393i	0.997740	+	0.0671963i	$0.0214054\pi$
$13$			49899.0i			0.134393i	−0.997740	+	0.0671963i	$0.978595\pi$
$14$	495479.			0.921266
$15$	−282238.			−0.371671
$16$	262144.			0.250000
$17$		−	2.49225e6i		−	1.75529i	−0.479316	−	0.877643i	$-0.659115\pi$
$17$		−	2.49225e6i		−	1.75529i	0.479316	−	0.877643i	$-0.340885\pi$
$18$		−	526735.i		−	0.278759i
$19$		−	1.02789e6i		−	0.415125i	−0.978222	−	0.207562i	$-0.933447\pi$
$19$		−	1.02789e6i		−	0.415125i	0.978222	−	0.207562i	$-0.0665530\pi$
$20$	764053.			0.238767
$21$		−	4.14145e6i		−	1.01404i
$22$	−92040.6	−	3.64301e6i	−0.0178594	−	0.706881i
$23$	9.76729e6			1.51752			0.758761	−	0.651369i	$-0.225805\pi$
$23$	9.76729e6			1.51752			0.758761	+	0.651369i	$0.225805\pi$
$24$		−	2.19112e6i		−	0.275176i
$25$	−7.53869e6			−0.771962
$26$	−1.12909e6			−0.0950299
$27$	−1.55707e7			−1.08515
$28$			1.12114e7i			0.651433i
$29$		−	6.29158e6i		−	0.306740i	−0.988169	−	0.153370i	$-0.950987\pi$
$29$		−	6.29158e6i		−	0.306740i	0.988169	−	0.153370i	$-0.0490126\pi$
$30$		−	6.38632e6i		−	0.262811i
$31$	3.66786e6			0.128116			0.0640581	−	0.997946i	$-0.479596\pi$
$31$	3.66786e6			0.128116			0.0640581	+	0.997946i	$0.479596\pi$
$32$			5.93164e6i			0.176777i
$33$	−3.04500e7	+	769319.i	−0.778067	+	0.0196579i
$34$	5.63933e7			1.24117
$35$			3.26771e7i			0.622162i
$36$	1.19186e7			0.197113
$37$	−6.77049e7			−0.976363			−0.488182	−	0.872742i	$-0.662340\pi$
$37$	−6.77049e7			−0.976363			−0.488182	+	0.872742i	$0.662340\pi$
$38$	2.32585e7			0.293537
$39$			9.43744e6i			0.104600i
$40$			1.72885e7i			0.168833i
$41$			1.77533e8i			1.53236i	0.642627	+	0.766179i	$0.277844\pi$
$41$			1.77533e8i			1.53236i	−0.642627	+	0.766179i	$0.722156\pi$
$42$	9.37102e7			0.717035
$43$			4.27757e7i			0.290975i	0.989360	+	0.145487i	$0.0464750\pi$
$43$			4.27757e7i			0.290975i	−0.989360	+	0.145487i	$0.953525\pi$
$44$	8.24318e7	−	2.08264e6i	0.499840	−	0.0126285i
$45$	3.47384e7			0.188256
$46$			2.21009e8i			1.07305i
$47$	−1.23276e8			−0.537513			−0.268756	−	0.963208i	$-0.586613\pi$
$47$	−1.23276e8			−0.537513			−0.268756	+	0.963208i	$0.586613\pi$
$48$	4.95795e7			0.194579
$49$	−1.97015e8			−0.697461
$50$		−	1.70581e8i		−	0.545860i
$51$		−	4.71362e8i		−	1.36617i
$52$		−	2.55483e7i		−	0.0671963i
$53$	−4.18303e8			−1.00026			−0.500128	−	0.865951i	$-0.666714\pi$
$53$	−4.18303e8			−1.00026			−0.500128	+	0.865951i	$0.666714\pi$
$54$		−	3.52324e8i		−	0.767315i
$55$	2.40258e8	−	6.07013e6i	0.477381	−	0.0120610i
$56$	−2.53685e8			−0.460633
$57$		−	1.94405e8i		−	0.323098i
$58$	1.42362e8			0.216898
$59$	5.37998e8			0.752525			0.376262	−	0.926513i	$-0.377209\pi$
$59$	5.37998e8			0.752525			0.376262	+	0.926513i	$0.377209\pi$
$60$	1.44506e8			0.185836
$61$		−	9.73365e8i		−	1.15246i	−0.817287	−	0.576231i	$-0.804523\pi$
$61$		−	9.73365e8i		−	1.15246i	0.817287	−	0.576231i	$-0.195477\pi$
$62$			8.29942e7i			0.0905919i
$63$			5.09738e8i			0.513623i
$64$	−1.34218e8			−0.125000
$65$		−	7.44639e7i		−	0.0641769i
$66$	−1.74077e7	−	6.89004e8i	−0.0139002	−	0.550177i
$67$	−1.10292e9			−0.816904			−0.408452	−	0.912780i	$-0.633931\pi$
$67$	−1.10292e9			−0.816904			−0.408452	+	0.912780i	$0.633931\pi$
$68$			1.27603e9i			0.877643i
$69$	1.84729e9			1.18111
$70$	−7.39399e8			−0.439935
$71$	2.08250e9			1.15423			0.577115	−	0.816663i	$-0.304178\pi$
$71$	2.08250e9			1.15423			0.577115	+	0.816663i	$0.304178\pi$
$72$			2.69688e8i			0.139380i
$73$		−	1.22086e9i		−	0.588912i	−0.955665	−	0.294456i	$-0.904862\pi$
$73$		−	1.22086e9i		−	0.588912i	0.955665	−	0.294456i	$-0.0951384\pi$
$74$		−	1.53199e9i		−	0.690393i
$75$	−1.42580e9			−0.600830
$76$			5.26280e8i			0.207562i
$77$	8.90707e7	+	3.52545e9i	0.0329065	+	1.30245i
$78$	−2.13545e8			−0.0739633
$79$			4.55531e9i			1.48041i	0.672380	+	0.740206i	$0.265272\pi$
$79$			4.55531e9i			1.48041i	−0.672380	+	0.740206i	$0.734728\pi$
$80$	−3.91195e8			−0.119383
$81$	−1.57031e9			−0.450361
$82$	−4.01712e9			−1.08354
$83$		−	3.69645e9i		−	0.938414i	−0.883088	−	0.469207i	$-0.844540\pi$
$83$		−	3.69645e9i		−	0.938414i	0.883088	−	0.469207i	$-0.155460\pi$
$84$			2.12042e9i			0.507021i
$85$			3.71917e9i			0.838207i
$86$	−9.67904e8			−0.205750
$87$		−	1.18993e9i		−	0.238740i
$88$	4.71248e7	+	1.86522e9i	0.00892969	+	0.353441i
$89$	1.01627e10			1.81995			0.909977	−	0.414658i	$-0.136099\pi$
$89$	1.01627e10			1.81995			0.909977	+	0.414658i	$0.136099\pi$
$90$			7.86041e8i			0.133117i
$91$	1.09265e9			0.175096
$92$	−5.00085e9			−0.758761
$93$	6.93705e8			0.0997149
$94$		−	2.78941e9i		−	0.380079i
$95$			1.53391e9i			0.198236i
$96$			1.12186e9i			0.137588i
$97$	−3.66369e9			−0.426639			−0.213319	−	0.976983i	$-0.568427\pi$
$97$	−3.66369e9			−0.426639			−0.213319	+	0.976983i	$0.568427\pi$
$98$		−	4.45795e9i		−	0.493179i
$99$	3.74785e9	−	9.46894e7i	0.394099	−	0.00995693i
$100$	3.85981e9			0.385981
$101$		−	1.12773e10i		−	1.07300i	−0.843902	−	0.536498i	$-0.819747\pi$
$101$		−	1.12773e10i		−	1.07300i	0.843902	−	0.536498i	$-0.180253\pi$
$102$	1.06657e10			0.966025
$103$	−1.06606e10			−0.919591			−0.459795	−	0.888025i	$-0.652077\pi$
$103$	−1.06606e10			−0.919591			−0.459795	+	0.888025i	$0.652077\pi$
$104$	5.78092e8			0.0475150
$105$			6.18024e9i			0.484238i
$106$		−	9.46511e9i		−	0.707288i
$107$		−	2.21656e10i		−	1.58038i	−0.612865	−	0.790188i	$-0.709983\pi$
$107$		−	2.21656e10i		−	1.58038i	0.612865	−	0.790188i	$-0.290017\pi$
$108$	7.97218e9			0.542573
$109$		−	7.77931e9i		−	0.505602i	−0.967518	−	0.252801i	$-0.918648\pi$
$109$		−	7.77931e9i		−	0.505602i	0.967518	−	0.252801i	$-0.0813518\pi$
$110$	1.37351e8	+	5.43642e9i	0.00852844	+	0.337559i
$111$	−1.28051e10			−0.759919
$112$		−	5.74024e9i		−	0.325717i
$113$	3.73352e9			0.202641			0.101320	−	0.994854i	$-0.467693\pi$
$113$	3.73352e9			0.202641			0.101320	+	0.994854i	$0.467693\pi$
$114$	4.39889e9			0.228465
$115$	−1.45756e10			−0.724667
$116$			3.22129e9i			0.153370i
$117$		−	1.16158e9i		−	0.0529809i
$118$			1.21735e10i			0.532115i
$119$	−5.45736e10			−2.28690
$120$			3.26979e9i			0.131406i
$121$	2.59043e10	−	1.30978e9i	0.998724	−	0.0504978i
$122$	2.20247e10			0.814913
$123$			3.35770e10i			1.19266i
$124$	−1.87794e9			−0.0640581
$125$	2.58231e10			0.846171
$126$	−1.15341e10			−0.363186
$127$			4.33766e10i			1.31292i	0.754362	+	0.656459i	$0.227946\pi$
$127$			4.33766e10i			1.31292i	−0.754362	+	0.656459i	$0.772054\pi$
$128$		−	3.03700e9i		−	0.0883883i
$129$			8.09020e9i			0.226470i
$130$	1.68493e9			0.0453799
$131$		−	1.47399e10i		−	0.382065i	−0.981584	−	0.191032i	$-0.938816\pi$
$131$		−	1.47399e10i		−	0.382065i	0.981584	−	0.191032i	$-0.0611835\pi$
$132$	1.55904e10	−	3.93891e8i	0.389034	−	0.00982894i
$133$	−2.25080e10			−0.540852
$134$		−	2.49563e10i		−	0.577638i
$135$	2.32360e10			0.518194
$136$	−2.88734e10			−0.620587
$137$	5.63721e10			1.16805			0.584025	−	0.811735i	$-0.301477\pi$
$137$	5.63721e10			1.16805			0.584025	+	0.811735i	$0.301477\pi$
$138$			4.17995e10i			0.835172i
$139$		−	6.66444e9i		−	0.128437i	−0.997936	−	0.0642184i	$-0.979545\pi$
$139$		−	6.66444e9i		−	0.128437i	0.997936	−	0.0642184i	$-0.0204554\pi$
$140$		−	1.67307e10i		−	0.311081i
$141$	−2.33152e10			−0.418354
$142$			4.71215e10i			0.816164i
$143$	−2.02972e8	−	8.03373e9i	−0.00339435	−	0.134350i
$144$	−6.10235e9			−0.0985563
$145$			9.38887e9i			0.146478i
$146$	2.76248e10			0.416423
$147$	−3.72617e10			−0.542845
$148$	3.46649e10			0.488182
$149$			8.56636e10i			1.16645i	0.812312	+	0.583224i	$0.198209\pi$
$149$			8.56636e10i			1.16645i	−0.812312	+	0.583224i	$0.801791\pi$
$150$		−	3.22621e10i		−	0.424851i
$151$		−	8.66896e10i		−	1.10429i	−0.833749	−	0.552144i	$-0.813810\pi$
$151$		−	8.66896e10i		−	1.10429i	0.833749	−	0.552144i	$-0.186190\pi$
$152$	−1.19083e10			−0.146769
$153$			5.80162e10i			0.691978i
$154$	−7.97719e10	+	2.01544e9i	−0.920972	+	0.0232684i
$155$	−5.47351e9			−0.0611798
$156$		−	4.83197e9i		−	0.0522999i
$157$	6.11137e10			0.640679			0.320339	−	0.947303i	$-0.396203\pi$
$157$	6.11137e10			0.640679			0.320339	+	0.947303i	$0.396203\pi$
$158$	−1.03075e11			−1.04681
$159$	−7.91139e10			−0.778515
$160$		−	8.85174e9i		−	0.0844167i
$161$		−	2.13877e11i		−	1.97713i
$162$		−	3.55321e10i		−	0.318454i
$163$	7.76171e10			0.674558			0.337279	−	0.941405i	$-0.390493\pi$
$163$	7.76171e10			0.674558			0.337279	+	0.941405i	$0.390493\pi$
$164$		−	9.08970e10i		−	0.766179i
$165$	4.54402e10	−	1.14805e9i	0.371553	−	0.00938729i
$166$	8.36411e10			0.663559
$167$		−	1.34875e11i		−	1.03837i	−0.854663	−	0.519183i	$-0.826236\pi$
$167$		−	1.34875e11i		−	1.03837i	0.854663	−	0.519183i	$-0.173764\pi$
$168$	−4.79796e10			−0.358518
$169$	1.35369e11			0.981939
$170$	−8.41552e10			−0.592702
$171$			2.39278e10i			0.163653i
$172$		−	2.19012e10i		−	0.145487i
$173$		−	1.23093e11i		−	0.794333i	−0.917747	−	0.397166i	$-0.869994\pi$
$173$		−	1.23093e11i		−	0.794333i	0.917747	−	0.397166i	$-0.130006\pi$
$174$	2.69251e10			0.168815
$175$			1.65077e11i			1.00576i
$176$	−4.22051e10	+	1.06631e9i	−0.249920	+	0.00631424i
$177$	1.01752e11			0.585701
$178$			2.29956e11i			1.28690i
$179$	−1.22922e11			−0.668903			−0.334451	−	0.942413i	$-0.608551\pi$
$179$	−1.22922e11			−0.668903			−0.334451	+	0.942413i	$0.608551\pi$
$180$	−1.77861e10			−0.0941278
$181$	6.88791e10			0.354564			0.177282	−	0.984160i	$-0.443270\pi$
$181$	6.88791e10			0.354564			0.177282	+	0.984160i	$0.443270\pi$
$182$			2.47239e10i			0.123811i
$183$		−	1.84093e11i		−	0.896978i
$184$		−	1.13156e11i		−	0.536525i
$185$	1.01035e11			0.466246
$186$			1.56967e10i			0.0705091i
$187$	1.01376e10	+	4.01252e11i	0.0443332	+	1.75473i
$188$	6.31172e10			0.268756
$189$			3.40955e11i			1.41380i
$190$	−3.47084e10			−0.140174
$191$	−4.89388e9			−0.0192525			−0.00962624	−	0.999954i	$-0.503064\pi$
$191$	−4.89388e9			−0.0192525			−0.00962624	+	0.999954i	$0.503064\pi$
$192$	−2.53847e10			−0.0972894
$193$			3.59882e11i			1.34392i	0.740587	+	0.671961i	$0.234548\pi$
$193$			3.59882e11i			1.34392i	−0.740587	+	0.671961i	$0.765452\pi$
$194$		−	8.28999e10i		−	0.301679i
$195$		−	1.40834e10i		−	0.0499499i
$196$	1.00872e11			0.348730
$197$		−	3.71509e11i		−	1.25210i	−0.779783	−	0.626050i	$-0.784671\pi$
$197$		−	3.71509e11i		−	1.25210i	0.779783	−	0.626050i	$-0.215329\pi$
$198$	2.14258e9	+	8.48041e10i	0.00704061	+	0.278670i
$199$	−5.71091e11			−1.82995			−0.914976	−	0.403508i	$-0.867791\pi$
$199$	−5.71091e11			−1.82995			−0.914976	+	0.403508i	$0.867791\pi$
$200$			8.73375e10i			0.272930i
$201$	−2.08596e11			−0.635809
$202$	2.55176e11			0.758722
$203$	−1.37769e11			−0.399641
$204$			2.41337e11i			0.683083i
$205$		−	2.64931e11i		−	0.731752i
$206$		−	2.41221e11i		−	0.650249i
$207$	−2.27369e11			−0.598245
$208$			1.30807e10i			0.0335982i
$209$	4.18111e9	+	1.65490e11i	0.0104848	+	0.414992i
$210$	−1.39843e11			−0.342408
$211$			2.41239e11i			0.576814i	0.957508	+	0.288407i	$0.0931256\pi$
$211$			2.41239e11i			0.576814i	−0.957508	+	0.288407i	$0.906874\pi$
$212$	2.14171e11			0.500128
$213$	3.93864e11			0.898356
$214$	5.01550e11			1.11749
$215$		−	6.38338e10i		−	0.138950i
$216$			1.80390e11i			0.383657i
$217$		−	8.03161e10i		−	0.166918i
$218$	1.76026e11			0.357515
$219$		−	2.30901e11i		−	0.458359i
$220$	−1.23012e11	+	3.10791e9i	−0.238690	+	0.00603052i
$221$	1.24361e11			0.235897
$222$		−	2.89746e11i		−	0.537344i
$223$	−9.19738e11			−1.66778			−0.833892	−	0.551927i	$-0.813893\pi$
$223$	−9.19738e11			−1.66778			−0.833892	+	0.551927i	$0.813893\pi$
$224$	1.29887e11			0.230316
$225$	1.75490e11			0.304327
$226$			8.44800e10i			0.143289i
$227$		−	1.06971e12i		−	1.77474i	−0.461054	−	0.887372i	$-0.652528\pi$
$227$		−	1.06971e12i		−	1.77474i	0.461054	−	0.887372i	$-0.347472\pi$
$228$			9.95356e10i			0.161549i
$229$	5.03739e11			0.799886			0.399943	−	0.916540i	$-0.369030\pi$
$229$	5.03739e11			0.799886			0.399943	+	0.916540i	$0.369030\pi$
$230$		−	3.29809e11i		−	0.512417i
$231$	1.68460e10	+	6.66771e11i	0.0256116	+	1.01372i
$232$	−7.28895e10			−0.108449
$233$			4.82850e11i			0.703125i	0.936164	+	0.351562i	$0.114349\pi$
$233$			4.82850e11i			0.703125i	−0.936164	+	0.351562i	$0.885651\pi$
$234$	2.62835e10			0.0374632
$235$	1.83963e11			0.256680
$236$	−2.75455e11			−0.376262
$237$			8.61549e11i			1.15223i
$238$		−	1.23486e12i		−	1.61708i
$239$		−	1.41011e12i		−	1.80827i	−0.427248	−	0.904135i	$-0.640517\pi$
$239$		−	1.41011e12i		−	1.80827i	0.427248	−	0.904135i	$-0.359483\pi$
$240$	−7.39870e10			−0.0929178
$241$		−	1.38573e12i		−	1.70449i	−0.523145	−	0.852243i	$-0.675242\pi$
$241$		−	1.38573e12i		−	1.70449i	0.523145	−	0.852243i	$-0.324758\pi$
$242$	2.96370e10	+	5.86148e11i	0.0357073	+	0.706205i
$243$	6.22438e11			0.734624
$244$			4.98363e11i			0.576231i
$245$	2.94004e11			0.333061
$246$	−7.59760e11			−0.843337
$247$	5.12907e10			0.0557897
$248$		−	4.24930e10i		−	0.0452959i
$249$		−	6.99112e11i		−	0.730382i
$250$			5.84310e11i			0.598333i
$251$	6.09029e11			0.611321			0.305661	−	0.952141i	$-0.401123\pi$
$251$	6.09029e11			0.611321			0.305661	+	0.952141i	$0.401123\pi$
$252$		−	2.60986e11i		−	0.256811i
$253$	−1.57253e12	+	3.97300e10i	−1.51704	+	0.0383280i
$254$	−9.81501e11			−0.928373
$255$			7.03409e11i			0.652389i
$256$	6.87195e10			0.0625000
$257$	−7.18987e11			−0.641292			−0.320646	−	0.947199i	$-0.603900\pi$
$257$	−7.18987e11			−0.641292			−0.320646	+	0.947199i	$0.603900\pi$
$258$	−1.83060e11			−0.160138
$259$			1.48255e12i			1.27207i
$260$			3.81255e10i			0.0320885i
$261$			1.46459e11i			0.120924i
$262$	3.33525e11			0.270161
$263$			1.95208e12i			1.55138i	0.631113	+	0.775691i	$0.282599\pi$
$263$			1.95208e12i			1.55138i	−0.631113	+	0.775691i	$0.717401\pi$
$264$	8.91274e9	+	3.52770e11i	0.00695011	+	0.275088i
$265$	6.24229e11			0.477656
$266$		−	5.09298e11i		−	0.382440i
$267$	1.92208e12			1.41650
$268$	5.64696e11			0.408452
$269$	−6.77474e11			−0.480985			−0.240492	−	0.970651i	$-0.577309\pi$
$269$	−6.77474e11			−0.480985			−0.240492	+	0.970651i	$0.577309\pi$
$270$			5.25770e11i			0.366418i
$271$			6.75054e11i			0.461840i	0.972973	+	0.230920i	$0.0741736\pi$
$271$			6.75054e11i			0.461840i	−0.972973	+	0.230920i	$0.925826\pi$
$272$		−	6.53329e11i		−	0.438821i
$273$	2.06654e11			0.136280
$274$			1.27556e12i			0.825937i
$275$	1.21373e12	−	3.06648e10i	0.771716	−	0.0194974i
$276$	−9.45815e11			−0.590556
$277$			4.70811e11i			0.288701i	0.989527	+	0.144350i	$0.0461092\pi$
$277$			4.70811e11i			0.288701i	−0.989527	+	0.144350i	$0.953891\pi$
$278$	1.50799e11			0.0908186
$279$	−8.53826e10			−0.0505067
$280$	3.78572e11			0.219967
$281$			2.41153e12i			1.37645i	0.725497	+	0.688225i	$0.241610\pi$
$281$			2.41153e12i			1.37645i	−0.725497	+	0.688225i	$0.758390\pi$
$282$		−	5.27564e11i		−	0.295821i
$283$		−	3.14854e12i		−	1.73451i	−0.497865	−	0.867254i	$-0.665883\pi$
$283$		−	3.14854e12i		−	1.73451i	0.497865	−	0.867254i	$-0.334117\pi$
$284$	−1.06624e12			−0.577115
$285$			2.90110e11i			0.154290i
$286$	1.81782e11	−	4.59274e9i	0.0949996	−	0.00240017i
$287$	3.88749e12			1.99646
$288$		−	1.38080e11i		−	0.0696898i
$289$	−4.19534e12			−2.08103
$290$	−2.12446e11			−0.103576
$291$	−6.92916e11			−0.332059
$292$			6.25078e11i			0.294456i
$293$		−	3.45233e12i		−	1.59872i	−0.600850	−	0.799362i	$-0.705171\pi$
$293$		−	3.45233e12i		−	1.59872i	0.600850	−	0.799362i	$-0.294829\pi$
$294$		−	8.43135e11i		−	0.383849i
$295$	−8.02850e11			−0.359355
$296$			7.84377e11i			0.345197i
$297$	2.50687e12	−	6.33362e10i	1.08480	−	0.0274075i
$298$	−1.93835e12			−0.824803
$299$			4.87379e11i			0.203944i
$300$	7.30008e11			0.300415
$301$	9.36672e11			0.379101
$302$	1.96156e12			0.780850
$303$		−	2.13288e12i		−	0.835129i
$304$		−	2.69455e11i		−	0.103781i
$305$			1.45254e12i			0.550338i
$306$	−1.31276e12			−0.489302
$307$		−	1.51390e11i		−	0.0555142i	−0.999615	−	0.0277571i	$-0.991164\pi$
$307$		−	1.51390e11i		−	0.0555142i	0.999615	−	0.0277571i	$-0.00883649\pi$
$308$	−4.56042e10	−	1.80503e12i	−0.0164532	−	0.651225i
$309$	−2.01624e12			−0.715732
$310$		−	1.23851e11i		−	0.0432606i
$311$	1.00090e12			0.344024			0.172012	−	0.985095i	$-0.444973\pi$
$311$	1.00090e12			0.344024			0.172012	+	0.985095i	$0.444973\pi$
$312$	1.09335e11			0.0369816
$313$	−1.99775e12			−0.664996			−0.332498	−	0.943104i	$-0.607891\pi$
$313$	−1.99775e12			−0.664996			−0.332498	+	0.943104i	$0.607891\pi$
$314$			1.38285e12i			0.453028i
$315$		−	7.60677e11i		−	0.245272i
$316$		−	2.33232e12i		−	0.740206i
$317$	−5.45172e12			−1.70309			−0.851545	−	0.524282i	$-0.824334\pi$
$317$	−5.45172e12			−1.70309			−0.851545	+	0.524282i	$0.824334\pi$
$318$		−	1.79014e12i		−	0.550493i
$319$	2.55920e10	+	1.01294e12i	0.00774731	+	0.306642i
$320$	2.00292e11			0.0596916
$321$		−	4.19219e12i		−	1.23003i
$322$	4.83949e12			1.39804
$323$	−2.56176e12			−0.728662
$324$	8.04000e11			0.225181
$325$		−	3.76173e11i		−	0.103746i
$326$			1.75627e12i			0.476985i
$327$		−	1.47131e12i		−	0.393518i
$328$	2.05676e12			0.541770
$329$			2.69941e12i			0.700307i
$330$	2.59774e10	+	1.02819e12i	0.00663782	+	0.262728i
$331$	1.28630e12			0.323743			0.161872	−	0.986812i	$-0.448247\pi$
$331$	1.28630e12			0.323743			0.161872	+	0.986812i	$0.448247\pi$
$332$			1.89258e12i			0.469207i
$333$	1.57608e12			0.384907
$334$	3.05188e12			0.734235
$335$	1.64588e12			0.390099
$336$		−	1.08566e12i		−	0.253510i
$337$		−	2.75537e11i		−	0.0633913i	−0.999498	−	0.0316957i	$-0.989909\pi$
$337$		−	2.75537e11i		−	0.0633913i	0.999498	−	0.0316957i	$-0.0100907\pi$
$338$			3.06304e12i			0.694335i
$339$	7.06124e11			0.157718
$340$		−	1.90421e12i		−	0.419103i
$341$	−5.90524e11	+	1.49196e10i	−0.128075	+	0.00323583i
$342$	−5.41425e11			−0.115720
$343$		−	1.87134e12i		−	0.394168i
$344$	4.95567e11			0.102875
$345$	−2.75670e12			−0.564020
$346$	2.78528e12			0.561678
$347$			5.68777e12i			1.13056i	0.824898	+	0.565281i	$0.191232\pi$
$347$			5.68777e12i			1.13056i	−0.824898	+	0.565281i	$0.808768\pi$
$348$			6.09245e11i			0.119370i
$349$			5.39293e12i			1.04159i	0.853681	+	0.520796i	$0.174365\pi$
$349$			5.39293e12i			1.04159i	−0.853681	+	0.520796i	$0.825635\pi$
$350$	−3.73526e12			−0.711182
$351$		−	7.76962e11i		−	0.145836i
$352$	−2.41279e10	−	9.54992e11i	−0.00446484	−	0.176720i
$353$	5.62493e12			1.02623			0.513114	−	0.858321i	$-0.328492\pi$
$353$	5.62493e12			1.02623			0.513114	+	0.858321i	$0.328492\pi$
$354$			2.30238e12i			0.414153i
$355$	−3.10769e12			−0.551183
$356$	−5.20332e12			−0.909977
$357$	−1.03215e13			−1.77993
$358$		−	2.78140e12i		−	0.472986i
$359$			7.09363e12i			1.18959i	0.803879	+	0.594794i	$0.202766\pi$
$359$			7.09363e12i			1.18959i	−0.803879	+	0.594794i	$0.797234\pi$
$360$		−	4.02453e11i		−	0.0665584i
$361$	5.07451e12			0.827671
$362$			1.55856e12i			0.250714i
$363$	4.89930e12	−	2.47720e11i	0.777322	−	0.0393032i
$364$	−5.59438e11			−0.0875478
$365$			1.82187e12i			0.281225i
$366$	4.16555e12			0.634259
$367$	−1.71493e12			−0.257582			−0.128791	−	0.991672i	$-0.541110\pi$
$367$	−1.71493e12			−0.257582			−0.128791	+	0.991672i	$0.541110\pi$
$368$	2.56044e12			0.379381
$369$		−	4.13272e12i		−	0.604094i
$370$			2.28617e12i			0.329686i
$371$			9.15969e12i			1.30320i
$372$	−3.55177e11			−0.0498574
$373$		−	6.70536e12i		−	0.928706i	−0.885650	−	0.464353i	$-0.846287\pi$
$373$		−	6.70536e12i		−	0.928706i	0.885650	−	0.464353i	$-0.153713\pi$
$374$	−9.07930e12	+	2.29389e11i	−1.24078	+	0.0313483i
$375$	4.88394e12			0.658588
$376$			1.42818e12i			0.190039i
$377$	3.13944e11			0.0412235
$378$	−7.71494e12			−0.999709
$379$	−2.99725e11			−0.0383290			−0.0191645	−	0.999816i	$-0.506101\pi$
$379$	−2.99725e11			−0.0383290			−0.0191645	+	0.999816i	$0.506101\pi$
$380$		−	7.85362e11i		−	0.0991179i
$381$			8.20385e12i			1.02186i
$382$		−	1.10736e11i		−	0.0136136i
$383$	−1.08063e12			−0.131124			−0.0655621	−	0.997848i	$-0.520884\pi$
$383$	−1.08063e12			−0.131124			−0.0655621	+	0.997848i	$0.520884\pi$
$384$		−	5.74390e11i		−	0.0687940i
$385$	−1.32919e11	−	5.26100e12i	−0.0157139	−	0.621963i
$386$	−8.14321e12			−0.950296
$387$		−	9.95759e11i		−	0.114709i
$388$	1.87581e12			0.213319
$389$	1.21161e13			1.36024			0.680120	−	0.733101i	$-0.261928\pi$
$389$	1.21161e13			1.36024			0.680120	+	0.733101i	$0.261928\pi$
$390$	3.18671e11			0.0353199
$391$		−	2.43426e13i		−	2.66368i
$392$			2.28247e12i			0.246590i
$393$		−	2.78776e12i		−	0.297367i
$394$	8.40630e12			0.885368
$395$		−	6.79785e12i		−	0.706946i
$396$	−1.91890e12	+	4.84810e10i	−0.197050	+	0.00497847i
$397$	3.83697e10			0.00389078			0.00194539	−	0.999998i	$-0.499381\pi$
$397$	3.83697e10			0.00389078			0.00194539	+	0.999998i	$0.499381\pi$
$398$		−	1.29223e13i		−	1.29397i
$399$	−4.25695e12			−0.420953
$400$	−1.97622e12			−0.192991
$401$	3.57065e12			0.344370			0.172185	−	0.985065i	$-0.444917\pi$
$401$	3.57065e12			0.344370			0.172185	+	0.985065i	$0.444917\pi$
$402$		−	4.72000e12i		−	0.449585i
$403$			1.83023e11i			0.0172179i
$404$			5.77397e12i			0.536498i
$405$	2.34336e12			0.215062
$406$		−	3.11735e12i		−	0.282589i
$407$	1.09005e13	−	2.75400e11i	0.976052	−	0.0246600i
$408$	−5.46084e12			−0.483012
$409$			1.25078e13i			1.09286i	0.837504	+	0.546431i	$0.184014\pi$
$409$			1.25078e13i			1.09286i	−0.837504	+	0.546431i	$0.815986\pi$
$410$	5.99471e12			0.517427
$411$	1.06617e13			0.909112
$412$	5.45821e12			0.459795
$413$		−	1.17807e13i		−	0.980439i
$414$		−	5.14477e12i		−	0.423023i
$415$			5.51618e12i			0.448124i
$416$	−2.95983e11			−0.0237575
$417$		−	1.26045e12i		−	0.0999644i
$418$	−3.74461e12	+	9.46076e10i	−0.293444	+	0.00741387i
$419$	−4.74623e12			−0.367518			−0.183759	−	0.982971i	$-0.558827\pi$
$419$	−4.74623e12			−0.367518			−0.183759	+	0.982971i	$0.558827\pi$
$420$		−	3.16428e12i		−	0.242119i
$421$	−2.18650e13			−1.65325			−0.826626	−	0.562752i	$-0.809743\pi$
$421$	−2.18650e13			−1.65325			−0.826626	+	0.562752i	$0.809743\pi$
$422$	−5.45862e12			−0.407869
$423$	2.86969e12			0.211901
$424$			4.84614e12i			0.353644i
$425$			1.87883e13i			1.35501i
$426$			8.91212e12i			0.635233i
$427$	−2.13140e13			−1.50150
$428$			1.13488e13i			0.790188i
$429$	−3.83883e10	−	1.51942e12i	−0.00264187	−	0.104566i
$430$	1.44439e12			0.0982525
$431$		−	1.12483e13i		−	0.756309i	−0.925743	−	0.378154i	$-0.876559\pi$
$431$		−	1.12483e13i		−	0.756309i	0.925743	−	0.378154i	$-0.123441\pi$
$432$	−4.08176e12			−0.271287
$433$	2.41537e13			1.58688			0.793440	−	0.608649i	$-0.208288\pi$
$433$	2.41537e13			1.58688			0.793440	+	0.608649i	$0.208288\pi$
$434$	1.81735e12			0.118029
$435$			1.77572e12i			0.114006i
$436$			3.98301e12i			0.252801i
$437$		−	1.00397e13i		−	0.629961i
$438$	5.22470e12			0.324109
$439$			2.76135e13i			1.69355i	0.531951	+	0.846775i	$0.321459\pi$
$439$			2.76135e13i			1.69355i	−0.531951	+	0.846775i	$0.678541\pi$
$440$	−7.03239e10	−	2.78345e12i	−0.00426422	−	0.168780i
$441$	4.58624e12			0.274957
$442$			2.81397e12i			0.166805i
$443$	−3.07008e13			−1.79941			−0.899707	−	0.436494i	$-0.856220\pi$
$443$	−3.07008e13			−1.79941			−0.899707	+	0.436494i	$0.856220\pi$
$444$	6.55620e12			0.379959
$445$	−1.51658e13			−0.869089
$446$		−	2.08113e13i		−	1.17930i
$447$			1.62016e13i			0.907864i
$448$			2.93900e12i			0.162858i
$449$	1.72051e13			0.942812			0.471406	−	0.881916i	$-0.343747\pi$
$449$	1.72051e13			0.942812			0.471406	+	0.881916i	$0.343747\pi$
$450$			3.97089e12i			0.215192i
$451$	−7.22145e11	−	2.85828e13i	−0.0387027	−	1.53187i
$452$	−1.91156e12			−0.101320
$453$		−	1.63957e13i		−	0.859484i
$454$	2.42047e13			1.25493
$455$	−1.63056e12			−0.0836140
$456$	−2.25223e12			−0.114232
$457$		−	9.73206e12i		−	0.488229i	−0.969746	−	0.244115i	$-0.921503\pi$
$457$		−	9.73206e12i		−	0.488229i	0.969746	−	0.244115i	$-0.0784973\pi$
$458$			1.13983e13i			0.565605i
$459$			3.88061e13i			1.90474i
$460$	7.46273e12			0.362334
$461$			2.58974e13i			1.24380i	0.783095	+	0.621902i	$0.213640\pi$
$461$			2.58974e13i			1.24380i	−0.783095	+	0.621902i	$0.786360\pi$
$462$	−1.50873e13	+	3.81181e11i	−0.716807	+	0.0181101i
$463$	2.05424e12			0.0965486			0.0482743	−	0.998834i	$-0.484628\pi$
$463$	2.05424e12			0.0965486			0.0482743	+	0.998834i	$0.484628\pi$
$464$		−	1.64930e12i		−	0.0766849i
$465$	−1.03521e12			−0.0476171
$466$	−1.09256e13			−0.497184
$467$	−1.07305e13			−0.483098			−0.241549	−	0.970389i	$-0.577655\pi$
$467$	−1.07305e13			−0.483098			−0.241549	+	0.970389i	$0.577655\pi$
$468$			5.94729e11i			0.0264905i
$469$			2.41510e13i			1.06432i
$470$			4.16262e12i			0.181500i
$471$	1.15585e13			0.498650
$472$		−	6.23284e12i		−	0.266058i
$473$	−1.73997e11	−	6.88687e12i	−0.00734913	−	0.290882i
$474$	−1.94946e13			−0.814748
$475$			7.74895e12i			0.320461i
$476$	2.79417e13			1.14345
$477$	9.73750e12			0.394326
$478$	3.19071e13			1.27864
$479$			1.48018e13i			0.587000i	0.955959	+	0.293500i	$0.0948201\pi$
$479$			1.48018e13i			0.587000i	−0.955959	+	0.293500i	$0.905180\pi$
$480$		−	1.67413e12i		−	0.0657028i
$481$		−	3.37841e12i		−	0.131216i
$482$	3.13555e13			1.20525
$483$		−	4.04507e13i		−	1.53883i
$484$	−1.32630e13	+	6.70609e11i	−0.499362	+	0.0252489i
$485$	5.46729e12			0.203734
$486$			1.40842e13i			0.519457i
$487$	−2.63683e13			−0.962580			−0.481290	−	0.876562i	$-0.659832\pi$
$487$	−2.63683e13			−0.962580			−0.481290	+	0.876562i	$0.659832\pi$
$488$	−1.12767e13			−0.407457
$489$	1.46798e13			0.525019
$490$			6.65256e12i			0.235509i
$491$		−	3.58681e13i		−	1.25690i	−0.777849	−	0.628451i	$-0.783689\pi$
$491$		−	3.58681e13i		−	1.25690i	0.777849	−	0.628451i	$-0.216311\pi$
$492$		−	1.71914e13i		−	0.596329i
$493$	−1.56802e13			−0.538416
$494$			1.16058e12i			0.0394493i
$495$	−5.59288e12	+	1.41304e11i	−0.188196	+	0.00475476i
$496$	9.61507e11			0.0320291
$497$		−	4.56010e13i		−	1.50381i
$498$	1.58191e13			0.516458
$499$	−5.18121e13			−1.67467			−0.837334	−	0.546692i	$-0.815887\pi$
$499$	−5.18121e13			−1.67467			−0.837334	+	0.546692i	$0.815887\pi$
$500$	−1.32214e13			−0.423085
$501$		−	2.55091e13i		−	0.808176i
$502$			1.37808e13i			0.432269i
$503$		−	1.59789e13i		−	0.496259i	−0.968727	−	0.248129i	$-0.920184\pi$
$503$		−	1.59789e13i		−	0.496259i	0.968727	−	0.248129i	$-0.0798158\pi$
$504$	5.90544e12			0.181593
$505$			1.68290e13i			0.512391i
$506$	−8.98988e11	−	3.55823e13i	−0.0271020	−	1.07271i
$507$	2.56023e13			0.764258
$508$		−	2.22088e13i		−	0.656459i
$509$	−8.26768e12			−0.241988			−0.120994	−	0.992653i	$-0.538608\pi$
$509$	−8.26768e12			−0.241988			−0.120994	+	0.992653i	$0.538608\pi$
$510$	−1.59163e13			−0.461309
$511$	−2.67334e13			−0.767273
$512$			1.55494e12i			0.0441942i
$513$			1.60049e13i			0.450471i
$514$		−	1.62688e13i		−	0.453462i
$515$	1.59087e13			0.439135
$516$		−	4.14218e12i		−	0.113235i
$517$	1.98474e13	−	5.01444e11i	0.537341	−	0.0135759i
$518$	−3.35463e13			−0.899490
$519$		−	2.32806e13i		−	0.618242i
$520$	−8.62682e11			−0.0226900
$521$	5.89297e13			1.53513			0.767566	−	0.640970i	$-0.221468\pi$
$521$	5.89297e13			1.53513			0.767566	+	0.640970i	$0.221468\pi$
$522$	−3.31399e12			−0.0855065
$523$			1.34146e13i			0.342822i	0.985200	+	0.171411i	$0.0548325\pi$
$523$			1.34146e13i			0.342822i	−0.985200	+	0.171411i	$0.945167\pi$
$524$			7.54681e12i			0.191032i
$525$			3.12211e13i			0.782801i
$526$	−4.41705e13			−1.09699
$527$		−	9.14124e12i		−	0.224881i
$528$	−7.98227e12	+	2.01672e11i	−0.194517	+	0.00491447i
$529$	5.39735e13			1.30287
$530$			1.41247e13i			0.337754i
$531$	−1.25238e13			−0.296664
$532$	1.15241e13			0.270426
$533$	−8.85874e12			−0.205938
$534$			4.34918e13i			1.00162i
$535$			3.30775e13i			0.754681i
$536$			1.27776e13i			0.288819i
$537$	−2.32482e13			−0.520617
$538$		−	1.53295e13i		−	0.340108i
$539$	3.17194e13	−	8.01392e11i	0.697238	−	0.0176157i
$540$	−1.18968e13			−0.259097
$541$			2.11868e13i			0.457172i	0.973524	+	0.228586i	$0.0734102\pi$
$541$			2.11868e13i			0.457172i	−0.973524	+	0.228586i	$0.926590\pi$
$542$	−1.52747e13			−0.326570
$543$	1.30271e13			0.275962
$544$	1.47832e13			0.310294
$545$			1.16090e13i			0.241442i
$546$			4.67605e12i			0.0963642i
$547$			2.00409e13i			0.409243i	0.978841	+	0.204621i	$0.0655963\pi$
$547$			2.00409e13i			0.409243i	−0.978841	+	0.204621i	$0.934404\pi$
$548$	−2.88625e13			−0.584025
$549$			2.26586e13i			0.454329i
$550$	6.93866e11	+	2.74635e13i	0.0137868	+	0.545686i
$551$	−6.46705e12			−0.127335
$552$		−	2.14013e13i		−	0.417586i
$553$	9.97489e13			1.92878
$554$	−1.06532e13			−0.204142
$555$	1.91089e13			0.362886
$556$			3.41219e12i			0.0642184i
$557$		−	8.89359e13i		−	1.65883i	−0.558636	−	0.829413i	$-0.688675\pi$
$557$		−	8.89359e13i		−	1.65883i	0.558636	−	0.829413i	$-0.311325\pi$
$558$		−	1.93199e12i		−	0.0357136i
$559$	−2.13447e12			−0.0391048
$560$			8.56611e12i			0.155540i
$561$	1.91734e12	+	7.58890e13i	0.0345052	+	1.36573i
$562$	−5.45666e13			−0.973297
$563$			3.91922e13i			0.692879i	0.938072	+	0.346440i	$0.112609\pi$
$563$			3.91922e13i			0.692879i	−0.938072	+	0.346440i	$0.887391\pi$
$564$	1.19374e13			0.209177
$565$	−5.57150e12			−0.0967677
$566$	7.12432e13			1.22648
$567$			3.43856e13i			0.586761i
$568$		−	2.41262e13i		−	0.408082i
$569$		−	1.91525e13i		−	0.321118i	−0.987026	−	0.160559i	$-0.948670\pi$
$569$		−	1.91525e13i		−	0.321118i	0.987026	−	0.160559i	$-0.0513298\pi$
$570$	−6.56443e12			−0.109099
$571$		−	3.43740e13i		−	0.566304i	−0.959075	−	0.283152i	$-0.908620\pi$
$571$		−	3.43740e13i		−	0.566304i	0.959075	−	0.283152i	$-0.0913800\pi$
$572$	1.03922e11	+	4.11327e12i	0.00169717	+	0.0671749i
$573$	−9.25583e11			−0.0149845
$574$			8.79639e13i			1.41171i
$575$	−7.36326e13			−1.17147
$576$	3.12440e12			0.0492781
$577$	−9.46742e13			−1.48031			−0.740155	−	0.672436i	$-0.765248\pi$
$577$	−9.46742e13			−1.48031			−0.740155	+	0.672436i	$0.765248\pi$
$578$		−	9.49296e13i		−	1.47151i
$579$			6.80648e13i			1.04600i
$580$		−	4.80710e12i		−	0.0732392i
$581$	−8.09422e13			−1.22263
$582$		−	1.56789e13i		−	0.234802i
$583$	6.73466e13	−	1.70151e12i	0.999937	−	0.0252634i
$584$	−1.41439e13			−0.208212
$585$			1.73342e12i			0.0253002i
$586$	7.81172e13			1.13047
$587$	−3.50164e13			−0.502436			−0.251218	−	0.967931i	$-0.580831\pi$
$587$	−3.50164e13			−0.502436			−0.251218	+	0.967931i	$0.580831\pi$
$588$	1.90780e13			0.271422
$589$		−	3.77016e12i		−	0.0531842i
$590$		−	1.81664e13i		−	0.254103i
$591$		−	7.02638e13i		−	0.974528i
$592$	−1.77484e13			−0.244091
$593$		−	3.02601e13i		−	0.412664i	−0.978482	−	0.206332i	$-0.933847\pi$
$593$		−	3.02601e13i		−	0.412664i	0.978482	−	0.206332i	$-0.0661527\pi$
$594$	1.43313e12	+	5.67240e13i	0.0193800	+	0.767070i
$595$	8.14397e13			1.09207
$596$		−	4.38598e13i		−	0.583224i
$597$	−1.08011e14			−1.42428
$598$	−1.10281e13			−0.144210
$599$	1.14914e13			0.149019			0.0745093	−	0.997220i	$-0.476261\pi$
$599$	1.14914e13			0.149019			0.0745093	+	0.997220i	$0.476261\pi$
$600$			1.65182e13i			0.212425i
$601$		−	4.63649e13i		−	0.591312i	−0.955294	−	0.295656i	$-0.904462\pi$
$601$		−	4.63649e13i		−	0.591312i	0.955294	−	0.295656i	$-0.0955383\pi$
$602$			2.11945e13i			0.268065i
$603$	2.56745e13			0.322044
$604$			4.43851e13i			0.552144i
$605$	−3.86568e13	+	1.95458e12i	−0.476924	+	0.0241144i
$606$	4.82616e13			0.590525
$607$			8.30566e13i			1.00793i	0.863724	+	0.503965i	$0.168126\pi$
$607$			8.30566e13i			1.00793i	−0.863724	+	0.503965i	$0.831874\pi$
$608$	6.09707e12			0.0733844
$609$	−2.60562e13			−0.311047
$610$	−3.28673e13			−0.389148
$611$		−	6.15135e12i		−	0.0722377i
$612$		−	2.97043e13i		−	0.345989i
$613$		−	1.29208e14i		−	1.49275i	−0.665528	−	0.746373i	$-0.731793\pi$
$613$		−	1.29208e14i		−	1.49275i	0.665528	−	0.746373i	$-0.268207\pi$
$614$	3.42555e12			0.0392545
$615$		−	5.01066e13i		−	0.569534i
$616$	4.08432e13	−	1.03190e12i	0.460486	−	0.0116342i
$617$	9.08518e13			1.01603			0.508016	−	0.861347i	$-0.330379\pi$
$617$	9.08518e13			1.01603			0.508016	+	0.861347i	$0.330379\pi$
$618$		−	4.56223e13i		−	0.506099i
$619$	1.28455e14			1.41350			0.706752	−	0.707461i	$-0.250159\pi$
$619$	1.28455e14			1.41350			0.706752	+	0.707461i	$0.250159\pi$
$620$	2.80244e12			0.0305899
$621$	−1.52083e14			−1.64673
$622$			2.26478e13i			0.243262i
$623$		−	2.22536e14i		−	2.37116i
$624$			2.47397e12i			0.0261500i
$625$	3.50845e13			0.367888
$626$		−	4.52039e13i		−	0.470223i
$627$	7.90775e11	+	3.12992e13i	0.00816047	+	0.322995i
$628$	−3.12902e13			−0.320339
$629$			1.68738e14i			1.71380i
$630$	1.72122e13			0.173433
$631$	−9.33854e13			−0.933538			−0.466769	−	0.884379i	$-0.654582\pi$
$631$	−9.33854e13			−0.933538			−0.466769	+	0.884379i	$0.654582\pi$
$632$	5.27744e13			0.523405
$633$			4.56258e13i			0.448943i
$634$		−	1.23358e14i		−	1.20427i
$635$		−	6.47306e13i		−	0.626961i
$636$	4.05063e13			0.389257
$637$		−	9.83088e12i		−	0.0937336i
$638$	−2.29203e13	+	5.79081e11i	−0.216828	+	0.00547818i
$639$	−4.84776e13			−0.455027
$640$			4.53209e12i			0.0422084i
$641$	6.10921e13			0.564540			0.282270	−	0.959335i	$-0.408913\pi$
$641$	6.10921e13			0.564540			0.282270	+	0.959335i	$0.408913\pi$
$642$	9.48584e13			0.869763
$643$	1.06962e14			0.973138			0.486569	−	0.873642i	$-0.338248\pi$
$643$	1.06962e14			0.973138			0.486569	+	0.873642i	$0.338248\pi$
$644$			1.09505e14i			0.988564i
$645$		−	1.20729e13i		−	0.108147i
$646$		−	5.79661e13i		−	0.515242i
$647$	1.36739e14			1.20607			0.603033	−	0.797717i	$-0.293959\pi$
$647$	1.36739e14			1.20607			0.603033	+	0.797717i	$0.293959\pi$
$648$			1.81925e13i			0.159227i
$649$	−8.66175e13	+	2.18839e12i	−0.752285	+	0.0190065i
$650$	8.51183e12			0.0733595
$651$		−	1.51902e13i		−	0.129915i
$652$	−3.97400e13			−0.337279
$653$	−1.99326e14			−1.67880			−0.839398	−	0.543517i	$-0.817092\pi$
$653$	−1.99326e14			−1.67880			−0.839398	+	0.543517i	$0.817092\pi$
$654$	3.32919e13			0.278259
$655$			2.19962e13i			0.182449i
$656$			4.65393e13i			0.383090i
$657$			2.84198e13i			0.232164i
$658$	−6.10806e13			−0.495192
$659$			1.74398e14i			1.40319i	0.712578	+	0.701593i	$0.247527\pi$
$659$			1.74398e14i			1.40319i	−0.712578	+	0.701593i	$0.752473\pi$
$660$	−2.32654e13	+	5.87801e11i	−0.185776	+	0.00469365i
$661$	−8.73288e13			−0.692070			−0.346035	−	0.938222i	$-0.612472\pi$
$661$	−8.73288e13			−0.692070			−0.346035	+	0.938222i	$0.612472\pi$
$662$			2.91056e13i			0.228921i
$663$	2.35205e13			0.183603
$664$	−4.28242e13			−0.331779
$665$	3.35885e13			0.258275
$666$			3.56625e13i			0.272170i
$667$		−	6.14517e13i		−	0.465484i
$668$			6.90562e13i			0.519183i
$669$	−1.73951e14			−1.29806
$670$			3.72420e13i			0.275841i
$671$	3.95932e12	+	1.56711e14i	0.0291077	+	1.15209i
$672$	2.45656e13			0.179259
$673$			3.37631e13i			0.244550i	0.992496	+	0.122275i	$0.0390189\pi$
$673$			3.37631e13i			0.244550i	−0.992496	+	0.122275i	$0.960981\pi$
$674$	6.23468e12			0.0448244
$675$	1.17383e14			0.837692
$676$	−6.93087e13			−0.490969
$677$			2.19078e14i			1.54048i	0.637756	+	0.770239i	$0.279863\pi$
$677$			2.19078e14i			1.54048i	−0.637756	+	0.770239i	$0.720137\pi$
$678$			1.59778e13i			0.111524i
$679$			8.02249e13i			0.555853i
$680$	4.30875e13			0.296351
$681$		−	2.02315e14i		−	1.38131i
$682$	−3.37592e11	−	1.33620e13i	−0.00228808	−	0.0905630i
$683$	−5.28942e13			−0.355881			−0.177940	−	0.984041i	$-0.556943\pi$
$683$	−5.28942e13			−0.355881			−0.177940	+	0.984041i	$0.556943\pi$
$684$		−	1.22511e13i		−	0.0818263i
$685$	−8.41237e13			−0.557783
$686$	4.23435e13			0.278719
$687$	9.52725e13			0.622564
$688$			1.12134e13i			0.0727436i
$689$		−	2.08729e13i		−	0.134427i
$690$		−	6.23770e13i		−	0.398822i
$691$	5.03497e13			0.319600			0.159800	−	0.987149i	$-0.448915\pi$
$691$	5.03497e13			0.319600			0.159800	+	0.987149i	$0.448915\pi$
$692$			6.30236e13i			0.397166i
$693$	−2.07344e12	−	8.20676e13i	−0.0129726	−	0.513459i
$694$	−1.28699e14			−0.799428
$695$			9.94529e12i			0.0613329i
$696$	−1.37856e13			−0.0844074
$697$	4.42458e14			2.68973
$698$	−1.22028e14			−0.736517
$699$			9.13217e13i			0.547253i
$700$		−	8.45193e13i		−	0.502882i
$701$			3.55533e13i			0.210034i	0.994470	+	0.105017i	$0.0334897\pi$
$701$			3.55533e13i			0.210034i	−0.994470	+	0.105017i	$0.966510\pi$
$702$	1.75806e13			0.103121
$703$			6.95932e13i			0.405313i
$704$	2.16090e13	−	5.45952e11i	0.124960	−	0.00315712i
$705$	3.47931e13			0.199778
$706$			1.27278e14i			0.725653i
$707$	−2.46942e14			−1.39797
$708$	−5.20970e13			−0.292851
$709$	7.75048e13			0.432611			0.216306	−	0.976326i	$-0.430599\pi$
$709$	7.75048e13			0.432611			0.216306	+	0.976326i	$0.430599\pi$
$710$		−	7.03190e13i		−	0.389746i
$711$		−	1.06041e14i		−	0.583616i
$712$		−	1.17738e14i		−	0.643451i
$713$	3.58251e13			0.194419
$714$		−	2.33550e14i		−	1.25860i
$715$	3.02894e11	+	1.19887e13i	0.00162091	+	0.0641565i
$716$	6.29359e13			0.334451
$717$		−	2.66695e14i		−	1.40740i
$718$	−1.60510e14			−0.841165
$719$	4.80926e13			0.250284			0.125142	−	0.992139i	$-0.460061\pi$
$719$	4.80926e13			0.250284			0.125142	+	0.992139i	$0.460061\pi$
$720$	9.10648e12			0.0470639
$721$			2.33438e14i			1.19810i
$722$			1.14823e14i			0.585252i
$723$		−	2.62084e14i		−	1.32663i
$724$	−3.52661e13			−0.177282
$725$			4.74303e13i			0.236791i
$726$	5.60527e12	+	1.10859e14i	0.0277916	+	0.549650i
$727$	7.89064e13			0.388544			0.194272	−	0.980948i	$-0.437766\pi$
$727$	7.89064e13			0.388544			0.194272	+	0.980948i	$0.437766\pi$
$728$		−	1.26586e13i		−	0.0619057i
$729$	2.10448e14			1.02213
$730$	−4.12243e13			−0.198856
$731$	1.06608e14			0.510743
$732$			9.42556e13i			0.448489i
$733$		−	1.98215e14i		−	0.936733i	−0.883534	−	0.468367i	$-0.844843\pi$
$733$		−	1.98215e14i		−	0.936733i	0.883534	−	0.468367i	$-0.155157\pi$
$734$		−	3.88044e13i		−	0.182138i
$735$	5.56052e13			0.259226
$736$			5.79361e13i			0.268263i
$737$	1.77570e14	−	4.48631e12i	0.816643	−	0.0206325i
$738$	9.35129e13			0.427159
$739$		−	3.44552e14i		−	1.56326i	−0.623741	−	0.781631i	$-0.714388\pi$
$739$		−	3.44552e14i		−	1.56326i	0.623741	−	0.781631i	$-0.285612\pi$
$740$	−5.17301e13			−0.233123
$741$	9.70065e12			0.0434220
$742$	−2.07260e14			−0.921502
$743$			7.01812e13i			0.309939i	0.987919	+	0.154970i	$0.0495280\pi$
$743$			7.01812e13i			0.309939i	−0.987919	+	0.154970i	$0.950472\pi$
$744$		−	8.03673e12i		−	0.0352545i
$745$		−	1.27835e14i		−	0.557017i
$746$	1.51725e14			0.656694
$747$			8.60482e13i			0.369946i
$748$	−5.19047e12	−	2.05441e14i	−0.0221666	−	0.877363i
$749$	−4.85366e14			−2.05902
$750$			1.10511e14i			0.465692i
$751$	−1.80713e14			−0.756467			−0.378234	−	0.925710i	$-0.623468\pi$
$751$	−1.80713e14			−0.756467			−0.378234	+	0.925710i	$0.623468\pi$
$752$	−3.23160e13			−0.134378
$753$	1.15186e14			0.475801
$754$			7.10374e12i			0.0291494i
$755$			1.29366e14i			0.527334i
$756$		−	1.74569e14i		−	0.706901i
$757$	9.02328e13			0.362982			0.181491	−	0.983393i	$-0.441908\pi$
$757$	9.02328e13			0.362982			0.181491	+	0.983393i	$0.441908\pi$
$758$		−	6.78201e12i		−	0.0271027i
$759$	−2.97414e14	+	7.51417e12i	−1.18073	+	0.0298313i
$760$	1.77707e13			0.0700869
$761$			1.13739e14i			0.445642i	0.974859	+	0.222821i	$0.0715266\pi$
$761$			1.13739e14i			0.445642i	−0.974859	+	0.222821i	$0.928473\pi$
$762$	−1.85632e14			−0.722567
$763$	−1.70346e14			−0.658732
$764$	2.50567e12			0.00962624
$765$		−	8.65770e13i		−	0.330442i
$766$		−	2.44518e13i		−	0.0927188i
$767$			2.68456e13i			0.101134i
$768$	1.29970e13			0.0486447
$769$		−	5.45958e13i		−	0.203015i	−0.994835	−	0.101507i	$-0.967633\pi$
$769$		−	5.45958e13i		−	0.203015i	0.994835	−	0.101507i	$-0.0323666\pi$
$770$	1.19043e14	−	3.00762e12i	0.439795	−	0.0111114i
$771$	−1.35983e14			−0.499127
$772$		−	1.84260e14i		−	0.671961i
$773$	2.88956e14			1.04697			0.523485	−	0.852035i	$-0.324632\pi$
$773$	2.88956e14			1.04697			0.523485	+	0.852035i	$0.324632\pi$
$774$	2.25315e13			0.0811119
$775$	−2.76509e13			−0.0989009
$776$			4.24447e13i			0.150840i
$777$			2.80396e14i			0.990072i
$778$			2.74156e14i			0.961835i
$779$	1.82485e14			0.636120
$780$			7.21070e12i			0.0249749i
$781$	−3.35281e14	+	8.47089e12i	−1.15386	+	0.0291524i
$782$	5.50810e14			1.88351
$783$			9.79642e13i			0.332858i
$784$	−5.16464e13			−0.174365
$785$	−9.11994e13			−0.305945
$786$	6.30798e13			0.210270
$787$		−	4.58395e14i		−	1.51833i	−0.650899	−	0.759164i	$-0.725608\pi$
$787$		−	4.58395e14i		−	1.51833i	0.650899	−	0.759164i	$-0.274392\pi$
$788$			1.90213e14i			0.626050i
$789$			3.69198e14i			1.20746i
$790$	1.53818e14			0.499886
$791$		−	8.17540e13i		−	0.264014i
$792$	−1.09700e12	−	4.34197e13i	−0.00352031	−	0.139335i
$793$	4.85700e13			0.154882
$794$			8.68208e11i			0.00275120i
$795$	1.18061e14			0.371767
$796$	2.92398e14			0.914976
$797$	−1.94195e14			−0.603875			−0.301938	−	0.953328i	$-0.597633\pi$
$797$	−1.94195e14			−0.603875			−0.301938	+	0.953328i	$0.597633\pi$
$798$		−	9.63238e13i		−	0.297659i
$799$			3.07235e14i			0.943488i
$800$		−	4.47168e13i		−	0.136465i
$801$	−2.36574e14			−0.717472
$802$			8.07947e13i			0.243507i
$803$	4.96603e12	+	1.96557e14i	0.0148741	+	0.588724i
$804$	1.06801e14			0.317904
$805$			3.19167e14i			0.944145i
$806$	−4.14133e12			−0.0121749
$807$	−1.28131e14			−0.374358
$808$	−1.30650e14			−0.379361
$809$		−	3.38801e14i		−	0.977693i	−0.872370	−	0.488846i	$-0.837418\pi$
$809$		−	3.38801e14i		−	0.977693i	0.872370	−	0.488846i	$-0.162582\pi$
$810$			5.30243e13i			0.152072i
$811$		−	9.97336e13i		−	0.284274i	−0.989847	−	0.142137i	$-0.954603\pi$
$811$		−	9.97336e13i		−	0.284274i	0.989847	−	0.142137i	$-0.0453974\pi$
$812$	7.05375e13			0.199820
$813$			1.27673e14i			0.359457i
$814$	6.23160e12	+	2.46649e14i	0.0174372	+	0.690173i
$815$	−1.15827e14			−0.322124
$816$		−	1.23565e14i		−	0.341541i
$817$	4.39687e13			0.120791
$818$	−2.83020e14			−0.772770
$819$	−2.54354e13			−0.0690271
$820$			1.35645e14i			0.365876i
$821$		−	2.15175e14i		−	0.576868i	−0.957500	−	0.288434i	$-0.906865\pi$
$821$		−	2.15175e14i		−	0.576868i	0.957500	−	0.288434i	$-0.0931346\pi$
$822$			2.41247e14i			0.642839i
$823$	5.70245e13			0.151030			0.0755149	−	0.997145i	$-0.475940\pi$
$823$	5.70245e13			0.151030			0.0755149	+	0.997145i	$0.475940\pi$
$824$			1.23505e14i			0.325124i
$825$	2.29553e14	−	5.79966e12i	0.600638	−	0.0151751i
$826$	2.66567e14			0.693275
$827$			4.09350e14i			1.05820i	0.848560	+	0.529100i	$0.177470\pi$
$827$			4.09350e14i			1.05820i	−0.848560	+	0.529100i	$0.822530\pi$
$828$	1.16413e14			0.299123
$829$	2.52851e14			0.645790			0.322895	−	0.946435i	$-0.395344\pi$
$829$	2.52851e14			0.645790			0.322895	+	0.946435i	$0.395344\pi$
$830$	−1.24817e14			−0.316871
$831$			8.90448e13i			0.224700i
$832$		−	6.69734e12i		−	0.0167991i
$833$			4.91013e14i			1.22424i
$834$	2.85207e13			0.0706855
$835$			2.01273e14i			0.495854i
$836$	−2.14073e12	−	8.47308e13i	−0.00524240	−	0.207496i
$837$	−5.71110e13			−0.139025
$838$		−	1.07395e14i		−	0.259875i
$839$	8.53952e12			0.0205411			0.0102706	−	0.999947i	$-0.496731\pi$
$839$	8.53952e12			0.0205411			0.0102706	+	0.999947i	$0.496731\pi$
$840$	7.15996e13			0.171204
$841$	3.81123e14			0.905911
$842$		−	4.94749e14i		−	1.16903i
$843$			4.56094e14i			1.07131i
$844$		−	1.23515e14i		−	0.288407i
$845$	−2.02009e14			−0.468908
$846$			6.49337e13i			0.149837i
$847$	−2.86807e13	−	5.67234e14i	−0.0657919	−	1.30120i
$848$	−1.09656e14			−0.250064
$849$		−	5.95485e14i		−	1.34999i
$850$	−4.25132e14			−0.958139
$851$	−6.61294e14			−1.48165
$852$	−2.01658e14			−0.449178
$853$		−	4.56131e14i		−	1.01005i	−0.863104	−	0.505026i	$-0.831483\pi$
$853$		−	4.56131e14i		−	1.01005i	0.863104	−	0.505026i	$-0.168517\pi$
$854$		−	4.82281e14i		−	1.06172i
$855$		−	3.57073e13i		−	0.0781495i
$856$	−2.56793e14			−0.558747
$857$		−	4.46202e14i		−	0.965223i	−0.875834	−	0.482612i	$-0.839688\pi$
$857$		−	4.46202e14i		−	0.965223i	0.875834	−	0.482612i	$-0.160312\pi$
$858$	3.43806e13	−	8.68628e11i	0.0739397	−	0.00186809i
$859$	−7.70597e14			−1.64764			−0.823819	−	0.566853i	$-0.808161\pi$
$859$	−7.70597e14			−1.64764			−0.823819	+	0.566853i	$0.808161\pi$
$860$			3.26829e13i			0.0694750i
$861$	7.35244e14			1.55387
$862$	2.54519e14			0.534791
$863$	8.06578e14			1.68497			0.842485	−	0.538720i	$-0.181092\pi$
$863$	8.06578e14			1.68497			0.842485	+	0.538720i	$0.181092\pi$
$864$		−	9.23596e13i		−	0.191829i
$865$			1.83690e14i			0.379320i
$866$			5.46536e14i			1.12209i
$867$	−7.93467e14			−1.61969
$868$			4.11219e13i			0.0834592i
$869$	−1.85295e13	−	7.33403e14i	−0.0373907	−	1.47994i
$870$	−4.01800e13			−0.0806147
$871$		−	5.50348e13i		−	0.109786i
$872$	−9.01252e13			−0.178757
$873$	8.52856e13			0.168192
$874$	2.27173e14			0.445450
$875$		−	5.65455e14i		−	1.10245i
$876$			1.18221e14i			0.229179i
$877$			2.52922e14i			0.487516i	0.969836	+	0.243758i	$0.0783803\pi$
$877$			2.52922e14i			0.487516i	−0.969836	+	0.243758i	$0.921620\pi$
$878$	−6.24821e14			−1.19752
$879$		−	6.52940e14i		−	1.24431i
$880$	6.29823e13	−	1.59125e12i	0.119345	−	0.00301526i
$881$	−2.00936e14			−0.378598			−0.189299	−	0.981920i	$-0.560621\pi$
$881$	−2.00936e14			−0.378598			−0.189299	+	0.981920i	$0.560621\pi$
$882$			1.03775e14i			0.194424i
$883$	7.73344e14			1.44069			0.720343	−	0.693619i	$-0.243985\pi$
$883$	7.73344e14			1.44069			0.720343	+	0.693619i	$0.243985\pi$
$884$	−6.36729e13			−0.117949
$885$	−1.51843e14			−0.279692
$886$		−	6.94680e14i		−	1.27238i
$887$			2.28417e14i			0.416016i	0.978127	+	0.208008i	$0.0666980\pi$
$887$			2.28417e14i			0.416016i	−0.978127	+	0.208008i	$0.933302\pi$
$888$			1.48350e14i			0.268672i
$889$	9.49830e14			1.71056
$890$		−	3.43162e14i		−	0.614539i
$891$	2.52820e14	−	6.38750e12i	0.450218	−	0.0113748i
$892$	4.70906e14			0.833892
$893$			1.26714e14i			0.223135i
$894$	−3.66601e14			−0.641957
$895$	1.83435e14			0.319423
$896$	−6.65020e13			−0.115158
$897$			9.21782e13i			0.158733i
$898$			3.89306e14i			0.666668i
$899$		−	2.30766e13i		−	0.0392983i
$900$	−8.98510e13			−0.152163
$901$			1.04252e15i			1.75574i
$902$	6.46754e14	−	1.63403e13i	1.08320	−	0.0273670i
$903$	1.77153e14			0.295060
$904$		−	4.32538e13i		−	0.0716443i
$905$	−1.02788e14			−0.169316
$906$	3.70992e14			0.607747
$907$	−7.66416e14			−1.24861			−0.624307	−	0.781179i	$-0.714619\pi$
$907$	−7.66416e14			−1.24861			−0.624307	+	0.781179i	$0.714619\pi$
$908$			5.47690e14i			0.887372i
$909$			2.62519e14i			0.423002i
$910$		−	3.68953e13i		−	0.0591240i
$911$	−1.95634e14			−0.311783			−0.155892	−	0.987774i	$-0.549825\pi$
$911$	−1.95634e14			−0.311783			−0.155892	+	0.987774i	$0.549825\pi$
$912$		−	5.09622e13i		−	0.0807745i
$913$	1.50359e13	+	5.95127e14i	0.0237015	+	0.938114i
$914$	2.20211e14			0.345230
$915$			2.74720e14i			0.428337i
$916$	−2.57914e14			−0.399943
$917$	−3.22763e14			−0.497779
$918$	−8.78081e14			−1.34686
$919$		−	3.35546e14i		−	0.511888i	−0.966692	−	0.255944i	$-0.917614\pi$
$919$		−	3.35546e14i		−	0.511888i	0.966692	−	0.255944i	$-0.0823863\pi$
$920$			1.68862e14i			0.256209i
$921$		−	2.86324e13i		−	0.0432076i
$922$	−5.85991e14			−0.879502
$923$			1.03915e14i			0.155120i
$924$	−8.62515e12	−	3.41387e14i	−0.0128058	−	0.506859i
$925$	5.10406e14			0.753715
$926$			4.64821e13i			0.0682702i
$927$	2.48163e14			0.362526
$928$	3.73194e13			0.0542244
$929$	1.05651e15			1.52685			0.763426	−	0.645895i	$-0.223516\pi$
$929$	1.05651e15			1.52685			0.763426	+	0.645895i	$0.223516\pi$
$930$		−	2.34241e13i		−	0.0336704i
$931$			2.02510e14i			0.289533i
$932$		−	2.47219e14i		−	0.351562i
$933$	1.89301e14			0.267759
$934$		−	2.42803e14i		−	0.341602i
$935$	−1.51283e13	−	5.98785e14i	−0.0211706	−	0.837939i
$936$	−1.34572e13			−0.0187316
$937$		−	4.09856e14i		−	0.567458i	−0.958904	−	0.283729i	$-0.908428\pi$
$937$		−	4.09856e14i		−	0.567458i	0.958904	−	0.283729i	$-0.0915716\pi$
$938$	−5.46475e14			−0.752585
$939$	−3.77835e14			−0.517577
$940$	−9.41893e13			−0.128340
$941$		−	7.93793e14i		−	1.07587i	−0.842987	−	0.537934i	$-0.819205\pi$
$941$		−	7.93793e14i		−	1.07587i	0.842987	−	0.537934i	$-0.180795\pi$
$942$			2.61538e14i			0.352599i
$943$			1.73402e15i			2.32539i
$944$	1.41033e14			0.188131
$945$		−	5.08805e14i		−	0.675137i
$946$	1.55832e14	−	3.93710e12i	0.205684	−	0.00519662i
$947$	8.59888e14			1.12899			0.564497	−	0.825435i	$-0.309070\pi$
$947$	8.59888e14			1.12899			0.564497	+	0.825435i	$0.309070\pi$
$948$		−	4.41113e14i		−	0.576114i
$949$	6.09195e13			0.0791454
$950$	−1.75339e14			−0.226600
$951$	−1.03109e15			−1.32554
$952$			6.32248e14i			0.808542i
$953$			1.55204e15i			1.97442i	0.159439	+	0.987208i	$0.449031\pi$
$953$			1.55204e15i			1.97442i	−0.159439	+	0.987208i	$0.550969\pi$
$954$			2.20335e14i			0.278831i
$955$	7.30309e12			0.00919369
$956$			7.21976e14i			0.904135i
$957$	4.84023e12	+	1.91578e14i	0.00602985	+	0.238664i
$958$	−3.34928e14			−0.415072
$959$		−	1.23440e15i		−	1.52181i
$960$	3.78813e13			0.0464589
$961$	−8.06175e14			−0.983586
$962$	7.64447e13			0.0927837
$963$			5.15984e14i			0.623024i
$964$			7.09494e14i			0.852243i
$965$		−	5.37049e14i		−	0.641767i
$966$	9.15295e14			1.08812
$967$			6.56070e14i			0.775921i	0.921676	+	0.387961i	$0.126820\pi$
$967$			6.56070e14i			0.775921i	−0.921676	+	0.387961i	$0.873180\pi$
$968$	−1.51742e13	−	3.00108e14i	−0.0178537	−	0.353102i
$969$	−4.84508e14			−0.567129
$970$			1.23711e14i			0.144062i
$971$	6.25000e14			0.724076			0.362038	−	0.932163i	$-0.382081\pi$
$971$	6.25000e14			0.724076			0.362038	+	0.932163i	$0.382081\pi$
$972$	−3.18688e14			−0.367312
$973$	−1.45933e14			−0.167336
$974$		−	5.96646e14i		−	0.680647i
$975$		−	7.11459e13i		−	0.0807471i
$976$		−	2.55162e14i		−	0.288115i
$977$	−6.17257e14			−0.693414			−0.346707	−	0.937973i	$-0.612700\pi$
$977$	−6.17257e14			−0.693414			−0.346707	+	0.937973i	$0.612700\pi$
$978$			3.32165e14i			0.371245i
$979$	−1.63620e15	+	4.13385e13i	−1.81937	+	0.0459665i
$980$	−1.50530e14			−0.166530
$981$			1.81092e14i			0.199321i
$982$	8.11603e14			0.888763
$983$	−3.91951e14			−0.427036			−0.213518	−	0.976939i	$-0.568492\pi$
$983$	−3.91951e14			−0.427036			−0.213518	+	0.976939i	$0.568492\pi$
$984$	3.88997e14			0.421668
$985$			5.54400e14i			0.597919i
$986$		−	3.54803e14i		−	0.380717i
$987$			5.10540e14i			0.545060i
$988$	−2.62608e13			−0.0278948
$989$			4.17803e14i			0.441560i
$990$	−3.19735e12	−	1.26552e14i	−0.00336213	−	0.133074i
$991$	2.68869e14			0.281301			0.140651	−	0.990059i	$-0.455081\pi$
$991$	2.68869e14			0.281301			0.140651	+	0.990059i	$0.455081\pi$
$992$			2.17564e13i			0.0226480i
$993$	2.43278e14			0.251975
$994$	1.03183e15			1.06335
$995$	8.52233e14			0.873863
$996$			3.57945e14i			0.365191i
$997$		−	9.50980e14i		−	0.965374i	−0.875793	−	0.482687i	$-0.839661\pi$
$997$		−	9.50980e14i		−	0.965374i	0.875793	−	0.482687i	$-0.160339\pi$
$998$		−	1.17237e15i		−	1.18417i
$999$	1.05421e15			1.05950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.11.b.a.21.9	yes	10
3.2	odd	2		198.11.d.a.109.4		10
4.3	odd	2		176.11.h.e.65.4		10
11.10	odd	2	inner	22.11.b.a.21.4	✓	10
33.32	even	2		198.11.d.a.109.9		10
44.43	even	2		176.11.h.e.65.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.11.b.a.21.4	✓	10	11.10	odd	2	inner
22.11.b.a.21.9	yes	10	1.1	even	1	trivial
176.11.h.e.65.3		10	44.43	even	2
176.11.h.e.65.4		10	4.3	odd	2
198.11.d.a.109.4		10	3.2	odd	2
198.11.d.a.109.9		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)

\(f(q)\)	\(=\)	\(q+22.6274i q^{2} +189.131 q^{3} -512.000 q^{4} -1492.29 q^{5} +4279.54i q^{6} -21897.3i q^{7} -11585.2i q^{8} -23278.6 q^{9} +O(q^{10})\)	\(q+22.6274i q^{2} +189.131 q^{3} -512.000 q^{4} -1492.29 q^{5} +4279.54i q^{6} -21897.3i q^{7} -11585.2i q^{8} -23278.6 q^{9} -33766.7i q^{10} +(-161000. + 4067.66i) q^{11} -96834.9 q^{12} +49899.0i q^{13} +495479. q^{14} -282238. q^{15} +262144. q^{16} -2.49225e6i q^{17} -526735. i q^{18} -1.02789e6i q^{19} +764053. q^{20} -4.14145e6i q^{21} +(-92040.6 - 3.64301e6i) q^{22} +9.76729e6 q^{23} -2.19112e6i q^{24} -7.53869e6 q^{25} -1.12909e6 q^{26} -1.55707e7 q^{27} +1.12114e7i q^{28} -6.29158e6i q^{29} -6.38632e6i q^{30} +3.66786e6 q^{31} +5.93164e6i q^{32} +(-3.04500e7 + 769319. i) q^{33} +5.63933e7 q^{34} +3.26771e7i q^{35} +1.19186e7 q^{36} -6.77049e7 q^{37} +2.32585e7 q^{38} +9.43744e6i q^{39} +1.72885e7i q^{40} +1.77533e8i q^{41} +9.37102e7 q^{42} +4.27757e7i q^{43} +(8.24318e7 - 2.08264e6i) q^{44} +3.47384e7 q^{45} +2.21009e8i q^{46} -1.23276e8 q^{47} +4.95795e7 q^{48} -1.97015e8 q^{49} -1.70581e8i q^{50} -4.71362e8i q^{51} -2.55483e7i q^{52} -4.18303e8 q^{53} -3.52324e8i q^{54} +(2.40258e8 - 6.07013e6i) q^{55} -2.53685e8 q^{56} -1.94405e8i q^{57} +1.42362e8 q^{58} +5.37998e8 q^{59} +1.44506e8 q^{60} -9.73365e8i q^{61} +8.29942e7i q^{62} +5.09738e8i q^{63} -1.34218e8 q^{64} -7.44639e7i q^{65} +(-1.74077e7 - 6.89004e8i) q^{66} -1.10292e9 q^{67} +1.27603e9i q^{68} +1.84729e9 q^{69} -7.39399e8 q^{70} +2.08250e9 q^{71} +2.69688e8i q^{72} -1.22086e9i q^{73} -1.53199e9i q^{74} -1.42580e9 q^{75} +5.26280e8i q^{76} +(8.90707e7 + 3.52545e9i) q^{77} -2.13545e8 q^{78} +4.55531e9i q^{79} -3.91195e8 q^{80} -1.57031e9 q^{81} -4.01712e9 q^{82} -3.69645e9i q^{83} +2.12042e9i q^{84} +3.71917e9i q^{85} -9.67904e8 q^{86} -1.18993e9i q^{87} +(4.71248e7 + 1.86522e9i) q^{88} +1.01627e10 q^{89} +7.86041e8i q^{90} +1.09265e9 q^{91} -5.00085e9 q^{92} +6.93705e8 q^{93} -2.78941e9i q^{94} +1.53391e9i q^{95} +1.12186e9i q^{96} -3.66369e9 q^{97} -4.45795e9i q^{98} +(3.74785e9 - 9.46894e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 106 q^{3} - 5120 q^{4} + 1138 q^{5} + 78044 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more