LMFDB - Embedded newform 22.11.b.a.21.3

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			21.3
Root			$171.602 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.11.b.a.21.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-22.6274i q^{2} -81.3085 q^{3} -512.000 q^{4} +2188.57 q^{5} +1839.80i q^{6} -24594.3i q^{7} +11585.2i q^{8} -52437.9 q^{9} +O(q^{10})$	\(q-22.6274i q^{2} -81.3085 q^{3} -512.000 q^{4} +2188.57 q^{5} +1839.80i q^{6} -24594.3i q^{7} +11585.2i q^{8} -52437.9 q^{9} -49521.7i q^{10} +(-120428. + 106932. i) q^{11} +41630.0 q^{12} +165935. i q^{13} -556506. q^{14} -177950. q^{15} +262144. q^{16} -244728. i q^{17} +1.18653e6i q^{18} +3.94445e6i q^{19} -1.12055e6 q^{20} +1.99973e6i q^{21} +(2.41959e6 + 2.72498e6i) q^{22} -1.16877e7 q^{23} -941978. i q^{24} -4.97578e6 q^{25} +3.75467e6 q^{26} +9.06484e6 q^{27} +1.25923e7i q^{28} -1.49927e7i q^{29} +4.02654e6i q^{30} -4.11697e7 q^{31} -5.93164e6i q^{32} +(9.79186e6 - 8.69447e6i) q^{33} -5.53757e6 q^{34} -5.38265e7i q^{35} +2.68482e7 q^{36} +8.07883e7 q^{37} +8.92527e7 q^{38} -1.34919e7i q^{39} +2.53551e7i q^{40} +5.19576e7i q^{41} +4.52487e7 q^{42} -2.77041e8i q^{43} +(6.16594e7 - 5.47491e7i) q^{44} -1.14764e8 q^{45} +2.64463e8i q^{46} +1.23943e8 q^{47} -2.13145e7 q^{48} -3.22406e8 q^{49} +1.12589e8i q^{50} +1.98985e7i q^{51} -8.49585e7i q^{52} +5.22133e7 q^{53} -2.05114e8i q^{54} +(-2.63566e8 + 2.34028e8i) q^{55} +2.84931e8 q^{56} -3.20717e8i q^{57} -3.39245e8 q^{58} -9.40486e8 q^{59} +9.11102e7 q^{60} +2.99685e8i q^{61} +9.31564e8i q^{62} +1.28968e9i q^{63} -1.34218e8 q^{64} +3.63160e8i q^{65} +(-1.96733e8 - 2.21564e8i) q^{66} +1.61187e9 q^{67} +1.25301e8i q^{68} +9.50310e8 q^{69} -1.21795e9 q^{70} -7.90862e8 q^{71} -6.07506e8i q^{72} -1.36271e9i q^{73} -1.82803e9i q^{74} +4.04573e8 q^{75} -2.01956e9i q^{76} +(2.62992e9 + 2.96186e9i) q^{77} -3.05287e8 q^{78} -1.52092e9i q^{79} +5.73721e8 q^{80} +2.35936e9 q^{81} +1.17567e9 q^{82} -5.40337e9i q^{83} -1.02386e9i q^{84} -5.35605e8i q^{85} -6.26872e9 q^{86} +1.21903e9i q^{87} +(-1.23883e9 - 1.39519e9i) q^{88} -2.91576e9 q^{89} +2.59682e9i q^{90} +4.08105e9 q^{91} +5.98411e9 q^{92} +3.34745e9 q^{93} -2.80450e9i q^{94} +8.63271e9i q^{95} +4.82293e8i q^{96} -7.67759e9 q^{97} +7.29521e9i q^{98} +(6.31502e9 - 5.60728e9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−81.3085			−0.334603			−0.167301	−	0.985906i	$-0.553505\pi$
$3$	−81.3085			−0.334603			−0.167301	+	0.985906i	$0.553505\pi$
$4$	−512.000			−0.500000
$5$	2188.57			0.700343			0.350172	−	0.936686i	$-0.386123\pi$
$5$	2188.57			0.700343			0.350172	+	0.936686i	$0.386123\pi$
$6$			1839.80i			0.236600i
$7$		−	24594.3i		−	1.46334i	−0.681660	−	0.731669i	$-0.738742\pi$
$7$		−	24594.3i		−	1.46334i	0.681660	−	0.731669i	$-0.261258\pi$
$8$			11585.2i			0.353553i
$9$	−52437.9			−0.888041
$10$		−	49521.7i		−	0.495217i
$11$	−120428.	+	106932.i	−0.747766	+	0.663963i
$11$	−120428.	+	106932.i	−0.747766	+	0.663963i
$12$	41630.0			0.167301
$13$			165935.i			0.446910i	0.974714	+	0.223455i	$0.0717336\pi$
$13$			165935.i			0.446910i	−0.974714	+	0.223455i	$0.928266\pi$
$14$	−556506.			−1.03474
$15$	−177950.			−0.234337
$16$	262144.			0.250000
$17$		−	244728.i		−	0.172361i	−0.996280	−	0.0861806i	$-0.972534\pi$
$17$		−	244728.i		−	0.172361i	0.996280	−	0.0861806i	$-0.0274662\pi$
$18$			1.18653e6i			0.627940i
$19$			3.94445e6i			1.59301i	0.604632	+	0.796505i	$0.293320\pi$
$19$			3.94445e6i			1.59301i	−0.604632	+	0.796505i	$0.706680\pi$
$20$	−1.12055e6			−0.350172
$21$			1.99973e6i			0.489637i
$22$	2.41959e6	+	2.72498e6i	0.469492	+	0.528750i
$23$	−1.16877e7			−1.81589			−0.907946	−	0.419086i	$-0.862351\pi$
$23$	−1.16877e7			−1.81589			−0.907946	+	0.419086i	$0.862351\pi$
$24$		−	941978.i		−	0.118300i
$25$	−4.97578e6			−0.509519
$26$	3.75467e6			0.316013
$27$	9.06484e6			0.631744
$28$			1.25923e7i			0.731669i
$29$		−	1.49927e7i		−	0.730952i	−0.930821	−	0.365476i	$-0.880906\pi$
$29$		−	1.49927e7i		−	0.730952i	0.930821	−	0.365476i	$-0.119094\pi$
$30$			4.02654e6i			0.165701i
$31$	−4.11697e7			−1.43803			−0.719017	−	0.694992i	$-0.755408\pi$
$31$	−4.11697e7			−1.43803			−0.719017	+	0.694992i	$0.755408\pi$
$32$		−	5.93164e6i		−	0.176777i
$33$	9.79186e6	−	8.69447e6i	0.250205	−	0.222164i
$34$	−5.53757e6			−0.121878
$35$		−	5.38265e7i		−	1.02484i
$36$	2.68482e7			0.444020
$37$	8.07883e7			1.16504			0.582519	−	0.812817i	$-0.302067\pi$
$37$	8.07883e7			1.16504			0.582519	+	0.812817i	$0.302067\pi$
$38$	8.92527e7			1.12643
$39$		−	1.34919e7i		−	0.149537i
$40$			2.53551e7i			0.247609i
$41$			5.19576e7i			0.448466i	0.974536	+	0.224233i	$0.0719877\pi$
$41$			5.19576e7i			0.448466i	−0.974536	+	0.224233i	$0.928012\pi$
$42$	4.52487e7			0.346226
$43$		−	2.77041e8i		−	1.88452i	−0.334879	−	0.942261i	$-0.608695\pi$
$43$		−	2.77041e8i		−	1.88452i	0.334879	−	0.942261i	$-0.391305\pi$
$44$	6.16594e7	−	5.47491e7i	0.373883	−	0.331981i
$45$	−1.14764e8			−0.621933
$46$			2.64463e8i			1.28403i
$47$	1.23943e8			0.540420			0.270210	−	0.962801i	$-0.412907\pi$
$47$	1.23943e8			0.540420			0.270210	+	0.962801i	$0.412907\pi$
$48$	−2.13145e7			−0.0836507
$49$	−3.22406e8			−1.14136
$50$			1.12589e8i			0.360285i
$51$			1.98985e7i			0.0576725i
$52$		−	8.49585e7i		−	0.223455i
$53$	5.22133e7			0.124854			0.0624269	−	0.998050i	$-0.480116\pi$
$53$	5.22133e7			0.124854			0.0624269	+	0.998050i	$0.480116\pi$
$54$		−	2.05114e8i		−	0.446710i
$55$	−2.63566e8	+	2.34028e8i	−0.523693	+	0.465002i
$56$	2.84931e8			0.517368
$57$		−	3.20717e8i		−	0.533026i
$58$	−3.39245e8			−0.516861
$59$	−9.40486e8			−1.31550			−0.657752	−	0.753234i	$-0.728493\pi$
$59$	−9.40486e8			−1.31550			−0.657752	+	0.753234i	$0.728493\pi$
$60$	9.11102e7			0.117168
$61$			2.99685e8i			0.354826i	0.984136	+	0.177413i	$0.0567729\pi$
$61$			2.99685e8i			0.354826i	−0.984136	+	0.177413i	$0.943227\pi$
$62$			9.31564e8i			1.01684i
$63$			1.28968e9i			1.29950i
$64$	−1.34218e8			−0.125000
$65$			3.63160e8i			0.312990i
$66$	−1.96733e8	−	2.21564e8i	−0.157094	−	0.176921i
$67$	1.61187e9			1.19387			0.596934	−	0.802290i	$-0.296385\pi$
$67$	1.61187e9			1.19387			0.596934	+	0.802290i	$0.296385\pi$
$68$			1.25301e8i			0.0861806i
$69$	9.50310e8			0.607603
$70$	−1.21795e9			−0.724671
$71$	−7.90862e8			−0.438338			−0.219169	−	0.975687i	$-0.570335\pi$
$71$	−7.90862e8			−0.438338			−0.219169	+	0.975687i	$0.570335\pi$
$72$		−	6.07506e8i		−	0.313970i
$73$		−	1.36271e9i		−	0.657337i	−0.944445	−	0.328668i	$-0.893400\pi$
$73$		−	1.36271e9i		−	0.657337i	0.944445	−	0.328668i	$-0.106600\pi$
$74$		−	1.82803e9i		−	0.823806i
$75$	4.04573e8			0.170487
$76$		−	2.01956e9i		−	0.796505i
$77$	2.62992e9	+	2.96186e9i	0.971602	+	1.09423i
$78$	−3.05287e8			−0.105739
$79$		−	1.52092e9i		−	0.494277i	−0.968980	−	0.247139i	$-0.920510\pi$
$79$		−	1.52092e9i		−	0.494277i	0.968980	−	0.247139i	$-0.0794903\pi$
$80$	5.73721e8			0.175086
$81$	2.35936e9			0.676657
$82$	1.17567e9			0.317114
$83$		−	5.40337e9i		−	1.37175i	−0.727721	−	0.685874i	$-0.759420\pi$
$83$		−	5.40337e9i		−	1.37175i	0.727721	−	0.685874i	$-0.240580\pi$
$84$		−	1.02386e9i		−	0.244819i
$85$		−	5.35605e8i		−	0.120712i
$86$	−6.26872e9			−1.33256
$87$			1.21903e9i			0.244579i
$88$	−1.23883e9	−	1.39519e9i	−0.234746	−	0.264375i
$89$	−2.91576e9			−0.522158			−0.261079	−	0.965317i	$-0.584078\pi$
$89$	−2.91576e9			−0.522158			−0.261079	+	0.965317i	$0.584078\pi$
$90$			2.59682e9i			0.439773i
$91$	4.08105e9			0.653981
$92$	5.98411e9			0.907946
$93$	3.34745e9			0.481170
$94$		−	2.80450e9i		−	0.382135i
$95$			8.63271e9i			1.11565i
$96$			4.82293e8i			0.0591500i
$97$	−7.67759e9			−0.894060			−0.447030	−	0.894519i	$-0.647518\pi$
$97$	−7.67759e9			−0.894060			−0.447030	+	0.894519i	$0.647518\pi$
$98$			7.29521e9i			0.807063i
$99$	6.31502e9	−	5.60728e9i	0.664047	−	0.589626i
$100$	2.54760e9			0.254760
$101$			9.61748e9i			0.915070i	0.889192	+	0.457535i	$0.151268\pi$
$101$			9.61748e9i			0.915070i	−0.889192	+	0.457535i	$0.848732\pi$
$102$	4.50251e8			0.0407806
$103$	−1.75871e10			−1.51708			−0.758540	−	0.651626i	$-0.774087\pi$
$103$	−1.75871e10			−1.51708			−0.758540	+	0.651626i	$0.774087\pi$
$104$	−1.92239e9			−0.158007
$105$			4.37655e9i			0.342914i
$106$		−	1.18145e9i		−	0.0882849i
$107$		−	3.23476e9i		−	0.230634i	−0.993329	−	0.115317i	$-0.963212\pi$
$107$		−	3.23476e9i		−	0.230634i	0.993329	−	0.115317i	$-0.0367884\pi$
$108$	−4.64120e9			−0.315872
$109$			3.98467e9i			0.258976i	0.991581	+	0.129488i	$0.0413334\pi$
$109$			3.98467e9i			0.258976i	−0.991581	+	0.129488i	$0.958667\pi$
$110$	5.29545e9	+	5.96383e9i	0.328806	+	0.370307i
$111$	−6.56878e9			−0.389825
$112$		−	6.44726e9i		−	0.365835i
$113$	1.34896e10			0.732162			0.366081	−	0.930583i	$-0.380699\pi$
$113$	1.34896e10			0.732162			0.366081	+	0.930583i	$0.380699\pi$
$114$	−7.25700e9			−0.376906
$115$	−2.55794e10			−1.27175
$116$			7.67625e9i			0.365476i
$117$		−	8.70127e9i		−	0.396874i
$118$			2.12808e10i			0.930202i
$119$	−6.01892e9			−0.252223
$120$		−	2.06159e9i		−	0.0828506i
$121$	3.06859e9	−	2.57553e10i	0.118307	−	0.992977i
$122$	6.78109e9			0.250900
$123$		−	4.22460e9i		−	0.150058i
$124$	2.10789e10			0.719017
$125$	−3.22626e10			−1.05718
$126$	2.91820e10			0.918888
$127$		−	3.58792e10i		−	1.08598i	−0.839738	−	0.542992i	$-0.817291\pi$
$127$		−	3.58792e10i		−	1.08598i	0.839738	−	0.542992i	$-0.182709\pi$
$128$			3.03700e9i			0.0883883i
$129$			2.25258e10i			0.630567i
$130$	8.21737e9			0.221318
$131$		−	2.16356e10i		−	0.560807i	−0.959882	−	0.280403i	$-0.909532\pi$
$131$		−	2.16356e10i		−	0.560807i	0.959882	−	0.280403i	$-0.0904682\pi$
$132$	−5.01343e9	+	4.45157e9i	−0.125102	+	0.111082i
$133$	9.70111e10			2.33111
$134$		−	3.64725e10i		−	0.844193i
$135$	1.98391e10			0.442438
$136$	2.83523e9			0.0609389
$137$	2.30645e9			0.0477905			0.0238953	−	0.999714i	$-0.492393\pi$
$137$	2.30645e9			0.0477905			0.0238953	+	0.999714i	$0.492393\pi$
$138$		−	2.15031e10i		−	0.429640i
$139$			2.50186e10i			0.482157i	0.970506	+	0.241078i	$0.0775011\pi$
$139$			2.50186e10i			0.482157i	−0.970506	+	0.241078i	$0.922499\pi$
$140$			2.75592e10i			0.512420i
$141$	−1.00776e10			−0.180826
$142$			1.78952e10i			0.309952i
$143$	−1.77437e10	−	1.99832e10i	−0.296732	−	0.334184i
$144$	−1.37463e10			−0.222010
$145$		−	3.28125e10i		−	0.511917i
$146$	−3.08345e10			−0.464807
$147$	2.62143e10			0.381902
$148$	−4.13636e10			−0.582519
$149$			7.14008e10i			0.972235i	0.873893	+	0.486118i	$0.161587\pi$
$149$			7.14008e10i			0.972235i	−0.873893	+	0.486118i	$0.838413\pi$
$150$		−	9.15444e9i		−	0.120552i
$151$		−	2.39649e10i		−	0.305274i	−0.988282	−	0.152637i	$-0.951223\pi$
$151$		−	2.39649e10i		−	0.305274i	0.988282	−	0.152637i	$-0.0487766\pi$
$152$	−4.56974e10			−0.563214
$153$			1.28330e10i			0.153064i
$154$	6.70192e10	−	5.95082e10i	0.773740	−	0.687026i
$155$	−9.01029e10			−1.00712
$156$			6.90785e9i			0.0747687i
$157$	3.85155e10			0.403773			0.201886	−	0.979409i	$-0.435293\pi$
$157$	3.85155e10			0.403773			0.201886	+	0.979409i	$0.435293\pi$
$158$	−3.44145e10			−0.349507
$159$	−4.24538e9			−0.0417764
$160$		−	1.29818e10i		−	0.123804i
$161$			2.87451e11i			2.65727i
$162$		−	5.33862e10i		−	0.478469i
$163$	−1.10987e11			−0.964575			−0.482287	−	0.876013i	$-0.660194\pi$
$163$	−1.10987e11			−0.964575			−0.482287	+	0.876013i	$0.660194\pi$
$164$		−	2.66023e10i		−	0.224233i
$165$	2.14302e10	−	1.90285e10i	0.175229	−	0.155591i
$166$	−1.22264e11			−0.969972
$167$		−	8.50157e10i		−	0.654510i	−0.944936	−	0.327255i	$-0.893876\pi$
$167$		−	8.50157e10i		−	0.654510i	0.944936	−	0.327255i	$-0.106124\pi$
$168$	−2.31673e10			−0.173113
$169$	1.10324e11			0.800271
$170$	−1.21194e10			−0.0853562
$171$		−	2.06839e11i		−	1.41466i
$172$			1.41845e11i			0.942261i
$173$			2.76098e11i			1.78169i	0.454304	+	0.890847i	$0.349888\pi$
$173$			2.76098e11i			1.78169i	−0.454304	+	0.890847i	$0.650112\pi$
$174$	2.75835e10			0.172943
$175$			1.22376e11i			0.745599i
$176$	−3.15696e10	+	2.80315e10i	−0.186941	+	0.165991i
$177$	7.64696e10			0.440172
$178$			6.59761e10i			0.369221i
$179$	−1.91189e11			−1.04039			−0.520197	−	0.854046i	$-0.674142\pi$
$179$	−1.91189e11			−1.04039			−0.520197	+	0.854046i	$0.674142\pi$
$180$	5.87593e10			0.310967
$181$	2.29067e11			1.17915			0.589575	−	0.807713i	$-0.299295\pi$
$181$	2.29067e11			1.17915			0.589575	+	0.807713i	$0.299295\pi$
$182$		−	9.23436e10i		−	0.462434i
$183$		−	2.43669e10i		−	0.118726i
$184$		−	1.35405e11i		−	0.642015i
$185$	1.76811e11			0.815926
$186$		−	7.57441e10i		−	0.340239i
$187$	2.61692e10	+	2.94722e10i	0.114441	+	0.128886i
$188$	−6.34587e10			−0.270210
$189$		−	2.22944e11i		−	0.924455i
$190$	1.95336e11			0.788886
$191$	−1.93638e11			−0.761771			−0.380886	−	0.924622i	$-0.624381\pi$
$191$	−1.93638e11			−0.761771			−0.380886	+	0.924622i	$0.624381\pi$
$192$	1.09130e10			0.0418254
$193$		−	4.69528e11i		−	1.75337i	−0.481061	−	0.876687i	$-0.659749\pi$
$193$		−	4.69528e11i		−	1.75337i	0.481061	−	0.876687i	$-0.340251\pi$
$194$			1.73724e11i			0.632196i
$195$		−	2.95280e10i		−	0.104728i
$196$	1.65072e11			0.570680
$197$			6.25668e10i			0.210869i	0.994426	+	0.105435i	$0.0336234\pi$
$197$			6.25668e10i			0.210869i	−0.994426	+	0.105435i	$0.966377\pi$
$198$	−1.26878e11	−	1.42893e11i	−0.416929	−	0.469552i
$199$	8.33198e10			0.266983			0.133491	−	0.991050i	$-0.457381\pi$
$199$	8.33198e10			0.266983			0.133491	+	0.991050i	$0.457381\pi$
$200$		−	5.76455e10i		−	0.180142i
$201$	−1.31059e11			−0.399472
$202$	2.17619e11			0.647052
$203$	−3.68735e11			−1.06963
$204$		−	1.01880e10i		−	0.0288363i
$205$			1.13713e11i			0.314080i
$206$			3.97951e11i			1.07274i
$207$	6.12879e11			1.61259
$208$			4.34988e10i			0.111728i
$209$	−4.21787e11	−	4.75024e11i	−1.05770	−	1.19120i
$210$	9.90300e10			0.242477
$211$		−	4.42777e11i		−	1.05870i	−0.848404	−	0.529350i	$-0.822436\pi$
$211$		−	4.42777e11i		−	1.05870i	0.848404	−	0.529350i	$-0.177564\pi$
$212$	−2.67332e10			−0.0624269
$213$	6.43038e10			0.146669
$214$	−7.31943e10			−0.163083
$215$		−	6.06324e11i		−	1.31981i
$216$			1.05018e11i			0.223355i
$217$			1.01254e12i			2.10433i
$218$	9.01629e10			0.183124
$219$			1.10800e11i			0.219947i
$220$	1.34946e11	−	1.19822e11i	0.261846	−	0.232501i
$221$	4.06089e10			0.0770299
$222$			1.48634e11i			0.275648i
$223$	−3.30963e11			−0.600144			−0.300072	−	0.953917i	$-0.597011\pi$
$223$	−3.30963e11			−0.600144			−0.300072	+	0.953917i	$0.597011\pi$
$224$	−1.45885e11			−0.258684
$225$	2.60919e11			0.452474
$226$		−	3.05235e11i		−	0.517717i
$227$			1.15527e12i			1.91670i	0.285596	+	0.958350i	$0.407808\pi$
$227$			1.15527e12i			1.91670i	−0.285596	+	0.958350i	$0.592192\pi$
$228$			1.64207e11i			0.266513i
$229$	−7.96977e11			−1.26552			−0.632759	−	0.774349i	$-0.718078\pi$
$229$	−7.96977e11			−1.26552			−0.632759	+	0.774349i	$0.718078\pi$
$230$			5.78796e11i			0.899262i
$231$	−2.13835e11	−	2.40824e11i	−0.325101	−	0.366134i
$232$	1.73694e11			0.258431
$233$			8.70222e11i			1.26722i	0.773654	+	0.633608i	$0.218427\pi$
$233$			8.70222e11i			1.26722i	−0.773654	+	0.633608i	$0.781573\pi$
$234$	−1.96887e11			−0.280633
$235$	2.71258e11			0.378480
$236$	4.81529e11			0.657752
$237$			1.23664e11i			0.165387i
$238$			1.36193e11i			0.178348i
$239$		−	7.74908e10i		−	0.0993713i	−0.998765	−	0.0496856i	$-0.984178\pi$
$239$		−	7.74908e10i		−	0.0993713i	0.998765	−	0.0496856i	$-0.0158219\pi$
$240$	−4.66484e10			−0.0585842
$241$		−	1.04530e12i		−	1.28574i	−0.765974	−	0.642872i	$-0.777743\pi$
$241$		−	1.04530e12i		−	1.28574i	0.765974	−	0.642872i	$-0.222257\pi$
$242$	−5.82775e11	−	6.94342e10i	−0.702141	−	0.0836559i
$243$	−7.27105e11			−0.858156
$244$		−	1.53439e11i		−	0.177413i
$245$	−7.05608e11			−0.799343
$246$	−9.55917e10			−0.106107
$247$	−6.54520e11			−0.711932
$248$		−	4.76961e11i		−	0.508422i
$249$			4.39340e11i			0.458991i
$250$			7.30020e11i			0.747540i
$251$	1.27349e12			1.27828			0.639141	−	0.769090i	$-0.279290\pi$
$251$	1.27349e12			1.27828			0.639141	+	0.769090i	$0.279290\pi$
$252$		−	6.60314e11i		−	0.649752i
$253$	1.40753e12	−	1.24979e12i	1.35786	−	1.20569i
$254$	−8.11853e11			−0.767907
$255$			4.35493e10i			0.0403906i
$256$	6.87195e10			0.0625000
$257$	1.34141e12			1.19645			0.598227	−	0.801326i	$-0.295872\pi$
$257$	1.34141e12			1.19645			0.598227	+	0.801326i	$0.295872\pi$
$258$	5.09700e11			0.445878
$259$		−	1.98693e12i		−	1.70484i
$260$		−	1.85938e11i		−	0.156495i
$261$			7.86184e11i			0.649115i
$262$	−4.89559e11			−0.396550
$263$			1.88382e12i			1.49713i	0.663060	+	0.748567i	$0.269258\pi$
$263$			1.88382e12i			1.49713i	−0.663060	+	0.748567i	$0.730742\pi$
$264$	1.00727e11	+	1.13441e11i	0.0785468	+	0.0884607i
$265$	1.14273e11			0.0874405
$266$		−	2.19511e12i		−	1.64834i
$267$	2.37076e11			0.174715
$268$	−8.25279e11			−0.596934
$269$	−2.79421e11			−0.198380			−0.0991898	−	0.995069i	$-0.531625\pi$
$269$	−2.79421e11			−0.198380			−0.0991898	+	0.995069i	$0.531625\pi$
$270$		−	4.48906e11i		−	0.312851i
$271$			2.74751e12i			1.87972i	0.341559	+	0.939860i	$0.389045\pi$
$271$			2.74751e12i			1.87972i	−0.341559	+	0.939860i	$0.610955\pi$
$272$		−	6.41540e10i		−	0.0430903i
$273$	−3.31824e11			−0.218824
$274$		−	5.21891e10i		−	0.0337930i
$275$	5.99225e11	−	5.32069e11i	0.381001	−	0.338302i
$276$	−4.86559e11			−0.303802
$277$		−	2.01022e12i		−	1.23266i	−0.787487	−	0.616331i	$-0.788618\pi$
$277$		−	2.01022e12i		−	1.23266i	0.787487	−	0.616331i	$-0.211382\pi$
$278$	5.66105e11			0.340936
$279$	2.15885e12			1.27703
$280$	6.23592e11			0.362335
$281$			2.84624e11i			0.162458i	0.996695	+	0.0812288i	$0.0258844\pi$
$281$			2.84624e11i			0.162458i	−0.996695	+	0.0812288i	$0.974116\pi$
$282$			2.28030e11i			0.127863i
$283$		−	1.13770e11i		−	0.0626752i	−0.999509	−	0.0313376i	$-0.990023\pi$
$283$		−	1.13770e11i		−	0.0626752i	0.999509	−	0.0313376i	$-0.00997670\pi$
$284$	4.04921e11			0.219169
$285$		−	7.01913e11i		−	0.373301i
$286$	−4.52169e11	+	4.01494e11i	−0.236304	+	0.209821i
$287$	1.27786e12			0.656258
$288$			3.11043e11i			0.156985i
$289$	1.95610e12			0.970292
$290$	−7.42463e11			−0.361980
$291$	6.24254e11			0.299155
$292$			6.97706e11i			0.328668i
$293$			1.32282e11i			0.0612578i	0.999531	+	0.0306289i	$0.00975100\pi$
$293$			1.32282e11i			0.0612578i	−0.999531	+	0.0306289i	$0.990249\pi$
$294$		−	5.93162e11i		−	0.270046i
$295$	−2.05832e12			−0.921305
$296$			9.35952e11i			0.411903i
$297$	−1.09166e12	+	9.69320e11i	−0.472397	+	0.419454i
$298$	1.61561e12			0.687474
$299$		−	1.93940e12i		−	0.811541i
$300$	−2.07141e11			−0.0852433
$301$	−6.81363e12			−2.75769
$302$	−5.42263e11			−0.215862
$303$		−	7.81983e11i		−	0.306185i
$304$			1.03401e12i			0.398252i
$305$			6.55882e11i			0.248500i
$306$	2.90378e11			0.108232
$307$			1.68602e12i			0.618261i	0.951020	+	0.309130i	$0.100038\pi$
$307$			1.68602e12i			0.618261i	−0.951020	+	0.309130i	$0.899962\pi$
$308$	−1.34652e12	−	1.51647e12i	−0.485801	−	0.547117i
$309$	1.42998e12			0.507620
$310$			2.03879e12i			0.712139i
$311$	−1.74391e12			−0.599408			−0.299704	−	0.954032i	$-0.596888\pi$
$311$	−1.74391e12			−0.599408			−0.299704	+	0.954032i	$0.596888\pi$
$312$	1.56307e11			0.0528695
$313$	−4.64785e12			−1.54714			−0.773571	−	0.633710i	$-0.781531\pi$
$313$	−4.64785e12			−1.54714			−0.773571	+	0.633710i	$0.781531\pi$
$314$		−	8.71505e11i		−	0.285510i
$315$			2.82255e12i			0.910099i
$316$			7.78710e11i			0.247139i
$317$	−1.18831e12			−0.371220			−0.185610	−	0.982623i	$-0.559426\pi$
$317$	−1.18831e12			−0.371220			−0.185610	+	0.982623i	$0.559426\pi$
$318$			9.60620e10i			0.0295404i
$319$	1.60319e12	+	1.80554e12i	0.485325	+	0.546581i
$320$	−2.93745e11			−0.0875429
$321$			2.63014e11i			0.0771708i
$322$	6.50428e12			1.87897
$323$	9.65317e11			0.274573
$324$	−1.20799e12			−0.338329
$325$		−	8.25653e11i		−	0.227709i
$326$			2.51136e12i			0.682057i
$327$		−	3.23988e11i		−	0.0866543i
$328$	−6.01941e11			−0.158557
$329$		−	3.04829e12i		−	0.790818i
$330$	−4.30565e11	−	4.84910e11i	−0.110019	−	0.123906i
$331$	2.33970e12			0.588870			0.294435	−	0.955672i	$-0.404869\pi$
$331$	2.33970e12			0.588870			0.294435	+	0.955672i	$0.404869\pi$
$332$			2.76652e12i			0.685874i
$333$	−4.23637e12			−1.03460
$334$	−1.92368e12			−0.462809
$335$	3.52770e12			0.836118
$336$			5.24217e11i			0.122409i
$337$		−	5.50120e12i		−	1.26563i	−0.774302	−	0.632816i	$-0.781899\pi$
$337$		−	5.50120e12i		−	1.26563i	0.774302	−	0.632816i	$-0.218101\pi$
$338$		−	2.49635e12i		−	0.565877i
$339$	−1.09682e12			−0.244984
$340$			2.74230e11i			0.0603560i
$341$	4.95800e12	−	4.40235e12i	1.07531	−	0.954801i
$342$	−4.68023e12			−1.00031
$343$			9.82062e11i			0.206856i
$344$	3.20958e12			0.666279
$345$	2.07982e12			0.425531
$346$	6.24739e12			1.25985
$347$			5.30731e12i			1.05494i	0.849574	+	0.527469i	$0.176859\pi$
$347$			5.30731e12i			1.05494i	−0.849574	+	0.527469i	$0.823141\pi$
$348$		−	6.24144e11i		−	0.122289i
$349$			1.21310e12i			0.234299i	0.993114	+	0.117150i	$0.0373757\pi$
$349$			1.21310e12i			0.234299i	−0.993114	+	0.117150i	$0.962624\pi$
$350$	2.76905e12			0.527218
$351$			1.50417e12i			0.282333i
$352$	6.34281e11	+	7.14338e11i	0.117373	+	0.132188i
$353$	3.15910e12			0.576355			0.288178	−	0.957577i	$-0.406951\pi$
$353$	3.15910e12			0.576355			0.288178	+	0.957577i	$0.406951\pi$
$354$		−	1.73031e12i		−	0.311248i
$355$	−1.73086e12			−0.306987
$356$	1.49287e12			0.261079
$357$	4.89390e11			0.0843944
$358$			4.32612e12i			0.735670i
$359$		−	1.17477e13i		−	1.97007i	−0.172351	−	0.985036i	$-0.555136\pi$
$359$		−	1.17477e13i		−	1.97007i	0.172351	−	0.985036i	$-0.444864\pi$
$360$		−	1.32957e12i		−	0.219887i
$361$	−9.42761e12			−1.53768
$362$		−	5.18319e12i		−	0.833785i
$363$	−2.49502e11	+	2.09412e12i	−0.0395860	+	0.332253i
$364$	−2.08950e12			−0.326990
$365$		−	2.98238e12i		−	0.460361i
$366$	−5.51361e11			−0.0839519
$367$	4.98060e12			0.748086			0.374043	−	0.927411i	$-0.377971\pi$
$367$	4.98060e12			0.748086			0.374043	+	0.927411i	$0.377971\pi$
$368$	−3.06386e12			−0.453973
$369$		−	2.72455e12i		−	0.398256i
$370$		−	4.00078e12i		−	0.576947i
$371$		−	1.28415e12i		−	0.182703i
$372$	−1.71389e12			−0.240585
$373$			2.23705e12i			0.309835i	0.987927	+	0.154918i	$0.0495112\pi$
$373$			2.23705e12i			0.309835i	−0.987927	+	0.154918i	$0.950489\pi$
$374$	6.66880e11	−	5.92142e11i	0.0911360	−	0.0809222i
$375$	2.62323e12			0.353736
$376$			1.43591e12i			0.191067i
$377$	2.48780e12			0.326670
$378$	−5.04464e12			−0.653689
$379$	−4.90239e12			−0.626920			−0.313460	−	0.949601i	$-0.601488\pi$
$379$	−4.90239e12			−0.626920			−0.313460	+	0.949601i	$0.601488\pi$
$380$		−	4.41995e12i		−	0.557827i
$381$			2.91728e12i			0.363374i
$382$			4.38154e12i			0.538654i
$383$	4.84496e12			0.587890			0.293945	−	0.955822i	$-0.405032\pi$
$383$	4.84496e12			0.587890			0.293945	+	0.955822i	$0.405032\pi$
$384$		−	2.46934e11i		−	0.0295750i
$385$	5.75576e12	+	6.48224e12i	0.680455	+	0.766340i
$386$	−1.06242e13			−1.23982
$387$			1.45274e13i			1.67353i
$388$	3.93093e12			0.447030
$389$	4.85745e12			0.545331			0.272666	−	0.962109i	$-0.412095\pi$
$389$	4.85745e12			0.545331			0.272666	+	0.962109i	$0.412095\pi$
$390$	−6.68142e11			−0.0740535
$391$			2.86031e12i			0.312989i
$392$		−	3.73515e12i		−	0.403531i
$393$			1.75916e12i			0.187648i
$394$	1.41573e12			0.149107
$395$		−	3.32864e12i		−	0.346164i
$396$	−3.23329e12	+	2.87093e12i	−0.332023	+	0.294813i
$397$	−2.04108e11			−0.0206970			−0.0103485	−	0.999946i	$-0.503294\pi$
$397$	−2.04108e11			−0.0206970			−0.0103485	+	0.999946i	$0.503294\pi$
$398$		−	1.88531e12i		−	0.188785i
$399$	−7.88782e12			−0.779997
$400$	−1.30437e12			−0.127380
$401$	−6.80954e12			−0.656744			−0.328372	−	0.944548i	$-0.606500\pi$
$401$	−6.80954e12			−0.656744			−0.328372	+	0.944548i	$0.606500\pi$
$402$			2.96553e12i			0.282469i
$403$		−	6.83148e12i		−	0.642672i
$404$		−	4.92415e12i		−	0.457535i
$405$	5.16363e12			0.473892
$406$			8.34351e12i			0.756343i
$407$	−9.72921e12	+	8.63884e12i	−0.871175	+	0.773541i
$408$	−2.30529e11			−0.0203903
$409$			1.24240e13i			1.08553i	0.839884	+	0.542767i	$0.182623\pi$
$409$			1.24240e13i			1.08553i	−0.839884	+	0.542767i	$0.817377\pi$
$410$	2.57303e12			0.222088
$411$	−1.87534e11			−0.0159908
$412$	9.00461e12			0.758540
$413$			2.31306e13i			1.92503i
$414$		−	1.38679e13i		−	1.14027i
$415$		−	1.18257e13i		−	0.960694i
$416$	9.84265e11			0.0790033
$417$		−	2.03422e12i		−	0.161331i
$418$	−1.07486e13	+	9.54395e12i	−0.842304	+	0.747906i
$419$	2.00890e13			1.55557			0.777783	−	0.628533i	$-0.216344\pi$
$419$	2.00890e13			1.55557			0.777783	+	0.628533i	$0.216344\pi$
$420$		−	2.24079e12i		−	0.171457i
$421$	−1.12895e13			−0.853622			−0.426811	−	0.904341i	$-0.640363\pi$
$421$	−1.12895e13			−0.853622			−0.426811	+	0.904341i	$0.640363\pi$
$422$	−1.00189e13			−0.748614
$423$	−6.49930e12			−0.479915
$424$			6.04903e11i			0.0441425i
$425$			1.21771e12i			0.0878213i
$426$		−	1.45503e12i		−	0.103711i
$427$	7.37055e12			0.519231
$428$			1.65620e12i			0.115317i
$429$	1.44271e12	+	1.62481e12i	0.0992873	+	0.111819i
$430$	−1.37195e13			−0.933248
$431$		−	7.37329e11i		−	0.0495764i	−0.999693	−	0.0247882i	$-0.992109\pi$
$431$		−	7.37329e11i		−	0.0495764i	0.999693	−	0.0247882i	$-0.00789114\pi$
$432$	2.37629e12			0.157936
$433$	2.88124e11			0.0189296			0.00946478	−	0.999955i	$-0.496987\pi$
$433$	2.88124e11			0.0189296			0.00946478	+	0.999955i	$0.496987\pi$
$434$	2.29112e13			1.48799
$435$			2.66794e12i			0.171289i
$436$		−	2.04015e12i		−	0.129488i
$437$		−	4.61016e13i		−	2.89273i
$438$	2.50711e12			0.155526
$439$		−	2.09548e13i		−	1.28517i	−0.766215	−	0.642584i	$-0.777862\pi$
$439$		−	2.09548e13i		−	1.28517i	0.766215	−	0.642584i	$-0.222138\pi$
$440$	−2.71127e12	−	3.05348e12i	−0.164403	−	0.185153i
$441$	1.69063e13			1.01357
$442$		−	9.18874e11i		−	0.0544684i
$443$	−2.82743e13			−1.65719			−0.828597	−	0.559846i	$-0.810860\pi$
$443$	−2.82743e13			−1.65719			−0.828597	+	0.559846i	$0.810860\pi$
$444$	3.36321e12			0.194912
$445$	−6.38135e12			−0.365689
$446$			7.48885e12i			0.424366i
$447$		−	5.80549e12i		−	0.325313i
$448$			3.30099e12i			0.182917i
$449$	2.14888e13			1.17755			0.588776	−	0.808296i	$-0.299610\pi$
$449$	2.14888e13			1.17755			0.588776	+	0.808296i	$0.299610\pi$
$450$		−	5.90393e12i		−	0.319947i
$451$	−5.55592e12	−	6.25717e12i	−0.297765	−	0.335348i
$452$	−6.90669e12			−0.366081
$453$			1.94855e12i			0.102146i
$454$	2.61408e13			1.35531
$455$	8.93167e12			0.458011
$456$	3.71559e12			0.188453
$457$		−	4.11420e12i		−	0.206397i	−0.994661	−	0.103199i	$-0.967092\pi$
$457$		−	4.11420e12i		−	0.206397i	0.994661	−	0.103199i	$-0.0329078\pi$
$458$			1.80335e13i			0.894856i
$459$		−	2.21842e12i		−	0.108888i
$460$	1.30967e13			0.635874
$461$			2.52114e13i			1.21086i	0.795900	+	0.605428i	$0.206998\pi$
$461$			2.52114e13i			1.21086i	−0.795900	+	0.605428i	$0.793002\pi$
$462$	−5.44923e12	+	4.83853e12i	−0.258896	+	0.229881i
$463$	−1.87246e13			−0.880050			−0.440025	−	0.897985i	$-0.645030\pi$
$463$	−1.87246e13			−0.880050			−0.440025	+	0.897985i	$0.645030\pi$
$464$		−	3.93024e12i		−	0.182738i
$465$	7.32613e12			0.336984
$466$	1.96909e13			0.896057
$467$	−1.54963e13			−0.697658			−0.348829	−	0.937186i	$-0.613421\pi$
$467$	−1.54963e13			−0.697658			−0.348829	+	0.937186i	$0.613421\pi$
$468$			4.45505e12i			0.198437i
$469$		−	3.96429e13i		−	1.74703i
$470$		−	6.13786e12i		−	0.267626i
$471$	−3.13164e12			−0.135104
$472$		−	1.08958e13i		−	0.465101i
$473$	2.96245e13	+	3.33636e13i	1.25125	+	1.40918i
$474$	2.79819e12			0.116946
$475$		−	1.96267e13i		−	0.811669i
$476$	3.08169e12			0.126111
$477$	−2.73796e12			−0.110875
$478$	−1.75342e12			−0.0702661
$479$			3.76721e13i			1.49397i	0.664841	+	0.746985i	$0.268499\pi$
$479$			3.76721e13i			1.49397i	−0.664841	+	0.746985i	$0.731501\pi$
$480$			1.05553e12i			0.0414253i
$481$			1.34056e13i			0.520667i
$482$	−2.36524e13			−0.909158
$483$		−	2.33722e13i		−	0.889129i
$484$	−1.57112e12	+	1.31867e13i	−0.0591536	+	0.496489i
$485$	−1.68030e13			−0.626149
$486$			1.64525e13i			0.606808i
$487$	−4.25260e13			−1.55242			−0.776210	−	0.630474i	$-0.782861\pi$
$487$	−4.25260e13			−1.55242			−0.776210	+	0.630474i	$0.782861\pi$
$488$	−3.47192e12			−0.125450
$489$	9.02422e12			0.322749
$490$			1.59661e13i			0.565221i
$491$		−	3.09798e13i		−	1.08560i	−0.839861	−	0.542802i	$-0.817363\pi$
$491$		−	3.09798e13i		−	1.08560i	0.839861	−	0.542802i	$-0.182637\pi$
$492$			2.16299e12i			0.0750291i
$493$	−3.66913e12			−0.125988
$494$			1.48101e13i			0.503412i
$495$	1.38209e13	−	1.22719e13i	0.465060	−	0.412941i
$496$	−1.07924e13			−0.359508
$497$			1.94507e13i			0.641437i
$498$	9.94113e12			0.324555
$499$	4.09280e13			1.32287			0.661435	−	0.750002i	$-0.269948\pi$
$499$	4.09280e13			1.32287			0.661435	+	0.750002i	$0.269948\pi$
$500$	1.65185e13			0.528591
$501$			6.91250e12i			0.219001i
$502$		−	2.88158e13i		−	0.903882i
$503$			3.68476e13i			1.14438i	0.820122	+	0.572189i	$0.193906\pi$
$503$			3.68476e13i			1.14438i	−0.820122	+	0.572189i	$0.806094\pi$
$504$	−1.49412e13			−0.459444
$505$			2.10486e13i			0.640863i
$506$	−2.82795e13	−	3.18488e13i	−0.852548	−	0.960154i
$507$	−8.97030e12			−0.267773
$508$			1.83701e13i			0.542992i
$509$	−2.98781e13			−0.874508			−0.437254	−	0.899338i	$-0.644049\pi$
$509$	−2.98781e13			−0.874508			−0.437254	+	0.899338i	$0.644049\pi$
$510$	9.85407e11			0.0285604
$511$	−3.35148e13			−0.961906
$512$		−	1.55494e12i		−	0.0441942i
$513$			3.57558e13i			1.00637i
$514$		−	3.03527e13i		−	0.846021i
$515$	−3.84907e13			−1.06248
$516$		−	1.15332e13i		−	0.315283i
$517$	−1.49262e13	+	1.32534e13i	−0.404108	+	0.358819i
$518$	−4.49592e13			−1.20551
$519$		−	2.24491e13i		−	0.596160i
$520$	−4.20729e12			−0.110659
$521$	−1.02323e13			−0.266554			−0.133277	−	0.991079i	$-0.542550\pi$
$521$	−1.02323e13			−0.266554			−0.133277	+	0.991079i	$0.542550\pi$
$522$	1.77893e13			0.458994
$523$			5.34658e12i			0.136637i	0.997664	+	0.0683184i	$0.0217634\pi$
$523$			5.34658e12i			0.136637i	−0.997664	+	0.0683184i	$0.978237\pi$
$524$			1.10774e13i			0.280403i
$525$		−	9.95020e12i		−	0.249480i
$526$	4.26260e13			1.05863
$527$			1.00754e13i			0.247861i
$528$	2.56688e12	−	2.27920e12i	0.0625512	−	0.0555410i
$529$	9.51761e13			2.29747
$530$		−	2.58569e12i		−	0.0618297i
$531$	4.93172e13			1.16822
$532$	−4.96697e13			−1.16556
$533$	−8.62157e12			−0.200424
$534$		−	5.36442e12i		−	0.123542i
$535$		−	7.07951e12i		−	0.161523i
$536$			1.86739e13i			0.422096i
$537$	1.55453e13			0.348119
$538$			6.32257e12i			0.140276i
$539$	3.88268e13	−	3.44754e13i	0.853469	−	0.757820i
$540$	−1.01576e13			−0.221219
$541$		−	2.79364e13i		−	0.602816i	−0.953495	−	0.301408i	$-0.902543\pi$
$541$		−	2.79364e13i		−	0.602816i	0.953495	−	0.301408i	$-0.0974566\pi$
$542$	6.21691e13			1.32916
$543$	−1.86251e13			−0.394547
$544$	−1.45164e12			−0.0304694
$545$			8.72075e12i			0.181372i
$546$			7.50832e12i			0.154732i
$547$			3.07757e13i			0.628451i	0.949348	+	0.314226i	$0.101745\pi$
$547$			3.07757e13i			0.628451i	−0.949348	+	0.314226i	$0.898255\pi$
$548$	−1.18090e12			−0.0238953
$549$		−	1.57149e13i		−	0.315100i
$550$	−1.20393e13	−	1.35589e13i	−0.239216	−	0.269409i
$551$	5.91378e13			1.16441
$552$			1.10096e13i			0.214820i
$553$	−3.74060e13			−0.723295
$554$	−4.54860e13			−0.871624
$555$	−1.43762e13			−0.273011
$556$		−	1.28095e13i		−	0.241078i
$557$		−	1.77756e13i		−	0.331550i	−0.986164	−	0.165775i	$-0.946987\pi$
$557$		−	1.77756e13i		−	0.331550i	0.986164	−	0.165775i	$-0.0530126\pi$
$558$		−	4.88493e13i		−	0.902999i
$559$	4.59706e13			0.842212
$560$		−	1.41103e13i		−	0.256210i
$561$	−2.12778e12	−	2.39634e12i	−0.0382924	−	0.0431255i
$562$	6.44031e12			0.114875
$563$			8.38356e13i			1.48213i	0.671433	+	0.741065i	$0.265679\pi$
$563$			8.38356e13i			1.48213i	−0.671433	+	0.741065i	$0.734321\pi$
$564$	5.15973e12			0.0904131
$565$	2.95230e13			0.512765
$566$	−2.57432e12			−0.0443180
$567$		−	5.80268e13i		−	0.990179i
$568$		−	9.16233e12i		−	0.154976i
$569$		−	3.84918e13i		−	0.645367i	−0.946507	−	0.322684i	$-0.895415\pi$
$569$		−	3.84918e13i		−	0.645367i	0.946507	−	0.322684i	$-0.104585\pi$
$570$	−1.58825e13			−0.263964
$571$			3.12194e13i			0.514333i	0.966367	+	0.257166i	$0.0827889\pi$
$571$			3.12194e13i			0.514333i	−0.966367	+	0.257166i	$0.917211\pi$
$572$	9.08477e12	+	1.02314e13i	0.148366	+	0.167092i
$573$	1.57444e13			0.254891
$574$		−	2.89147e13i		−	0.464045i
$575$	5.81554e13			0.925233
$576$	7.03810e12			0.111005
$577$	7.41402e13			1.15924			0.579622	−	0.814886i	$-0.303200\pi$
$577$	7.41402e13			1.15924			0.579622	+	0.814886i	$0.303200\pi$
$578$		−	4.42615e13i		−	0.686100i
$579$			3.81766e13i			0.586684i
$580$			1.68000e13i			0.255959i
$581$	−1.32892e14			−2.00733
$582$		−	1.41253e13i		−	0.211535i
$583$	−6.28796e12	+	5.58326e12i	−0.0933613	+	0.0828982i
$584$	1.57873e13			0.232404
$585$		−	1.90434e13i		−	0.277948i
$586$	2.99319e12			0.0433158
$587$	−7.13433e13			−1.02368			−0.511838	−	0.859082i	$-0.671035\pi$
$587$	−7.13433e13			−1.02368			−0.511838	+	0.859082i	$0.671035\pi$
$588$	−1.34217e13			−0.190951
$589$		−	1.62392e14i		−	2.29080i
$590$			4.65745e13i			0.651461i
$591$		−	5.08722e12i		−	0.0705574i
$592$	2.11782e13			0.291259
$593$			1.76148e13i			0.240217i	0.992761	+	0.120109i	$0.0383243\pi$
$593$			1.76148e13i			0.240217i	−0.992761	+	0.120109i	$0.961676\pi$
$594$	2.19332e13	+	2.47015e13i	0.296599	+	0.334035i
$595$	−1.31729e13			−0.176642
$596$		−	3.65572e13i		−	0.486118i
$597$	−6.77461e12			−0.0893332
$598$	−4.38835e13			−0.573846
$599$	−4.94324e13			−0.641028			−0.320514	−	0.947244i	$-0.603856\pi$
$599$	−4.94324e13			−0.641028			−0.320514	+	0.947244i	$0.603856\pi$
$600$			4.68707e12i			0.0602761i
$601$			1.33325e14i			1.70035i	0.526501	+	0.850174i	$0.323504\pi$
$601$			1.33325e14i			1.70035i	−0.526501	+	0.850174i	$0.676496\pi$
$602$			1.54175e14i			1.94998i
$603$	−8.45232e13			−1.06020
$604$			1.22700e13i			0.152637i
$605$	6.71582e12	−	5.63673e13i	0.0828557	−	0.695425i
$606$	−1.76943e13			−0.216506
$607$		−	3.49751e13i		−	0.424439i	−0.977222	−	0.212220i	$-0.931931\pi$
$607$		−	3.49751e13i		−	0.424439i	0.977222	−	0.212220i	$-0.0680692\pi$
$608$	2.33971e13			0.281607
$609$	2.99813e13			0.357901
$610$	1.48409e13			0.175716
$611$			2.05664e13i			0.241519i
$612$		−	6.57051e12i		−	0.0765319i
$613$			1.07928e14i			1.24689i	0.781865	+	0.623447i	$0.214268\pi$
$613$			1.07928e14i			1.24689i	−0.781865	+	0.623447i	$0.785732\pi$
$614$	3.81503e13			0.437176
$615$		−	9.24583e12i		−	0.105092i
$616$	−3.43138e13	+	3.04682e13i	−0.386870	+	0.343513i
$617$	−1.05107e14			−1.17545			−0.587727	−	0.809059i	$-0.699977\pi$
$617$	−1.05107e14			−1.17545			−0.587727	+	0.809059i	$0.699977\pi$
$618$		−	3.23568e13i		−	0.358941i
$619$	−1.16030e13			−0.127678			−0.0638392	−	0.997960i	$-0.520334\pi$
$619$	−1.16030e13			−0.127678			−0.0638392	+	0.997960i	$0.520334\pi$
$620$	4.61327e13			0.503559
$621$	−1.05947e14			−1.14718
$622$			3.94602e13i			0.423845i
$623$			7.17111e13i			0.764093i
$624$		−	3.53682e12i		−	0.0373844i
$625$	−2.20175e13			−0.230871
$626$			1.05169e14i			1.09399i
$627$	3.42949e13	+	3.86235e13i	0.353909	+	0.398578i
$628$	−1.97199e13			−0.201886
$629$		−	1.97712e13i		−	0.200807i
$630$	6.38670e13			0.643537
$631$	1.30516e14			1.30472			0.652360	−	0.757909i	$-0.273779\pi$
$631$	1.30516e14			1.30472			0.652360	+	0.757909i	$0.273779\pi$
$632$	1.76202e13			0.174753
$633$			3.60016e13i			0.354244i
$634$			2.68883e13i			0.262493i
$635$		−	7.85241e13i		−	0.760562i
$636$	2.17364e12			0.0208882
$637$		−	5.34983e13i		−	0.510085i
$638$	4.08548e13	−	3.62761e13i	0.386491	−	0.343176i
$639$	4.14712e13			0.389262
$640$			6.64670e12i			0.0619022i
$641$	−1.20471e14			−1.11325			−0.556624	−	0.830764i	$-0.687904\pi$
$641$	−1.20471e14			−1.11325			−0.556624	+	0.830764i	$0.687904\pi$
$642$	5.95132e12			0.0545680
$643$	3.82031e12			0.0347571			0.0173786	−	0.999849i	$-0.494468\pi$
$643$	3.82031e12			0.0347571			0.0173786	+	0.999849i	$0.494468\pi$
$644$		−	1.47175e14i		−	1.32863i
$645$			4.92993e13i			0.441613i
$646$		−	2.18426e13i		−	0.194152i
$647$	4.88309e13			0.430699			0.215349	−	0.976537i	$-0.430911\pi$
$647$	4.88309e13			0.430699			0.215349	+	0.976537i	$0.430911\pi$
$648$			2.73337e13i			0.239235i
$649$	1.13261e14	−	1.00568e14i	0.983690	−	0.873446i
$650$	−1.86824e13			−0.161015
$651$		−	8.23282e13i		−	0.704115i
$652$	5.68256e13			0.482287
$653$	−1.03193e14			−0.869127			−0.434564	−	0.900641i	$-0.643097\pi$
$653$	−1.03193e14			−0.869127			−0.434564	+	0.900641i	$0.643097\pi$
$654$	−7.33101e12			−0.0612738
$655$		−	4.73512e13i		−	0.392757i
$656$			1.36204e13i			0.112117i
$657$			7.14575e13i			0.583742i
$658$	−6.89749e13			−0.559193
$659$		−	9.85864e13i		−	0.793213i	−0.917989	−	0.396607i	$-0.870188\pi$
$659$		−	9.85864e13i		−	0.793213i	0.917989	−	0.396607i	$-0.129812\pi$
$660$	−1.09723e13	+	9.74258e12i	−0.0876146	+	0.0777955i
$661$	−1.03572e14			−0.820796			−0.410398	−	0.911907i	$-0.634610\pi$
$661$	−1.03572e14			−0.820796			−0.410398	+	0.911907i	$0.634610\pi$
$662$		−	5.29413e13i		−	0.416394i
$663$	−3.30185e12			−0.0257744
$664$	6.25993e13			0.484986
$665$	2.12316e14			1.63258
$666$			9.58581e13i			0.731573i
$667$			1.75230e14i			1.32733i
$668$			4.35280e13i			0.327255i
$669$	2.69101e13			0.200810
$670$		−	7.98227e13i		−	0.591225i
$671$	−3.20459e13	−	3.60906e13i	−0.235591	−	0.265327i
$672$	1.18617e13			0.0865565
$673$		−	7.25328e13i		−	0.525362i	−0.964883	−	0.262681i	$-0.915393\pi$
$673$		−	7.25328e13i		−	0.525362i	0.964883	−	0.262681i	$-0.0846067\pi$
$674$	−1.24478e14			−0.894937
$675$	−4.51046e13			−0.321886
$676$	−5.64860e13			−0.400136
$677$		−	2.62690e14i		−	1.84714i	−0.383429	−	0.923570i	$-0.625257\pi$
$677$		−	2.62690e14i		−	1.84714i	0.383429	−	0.923570i	$-0.374743\pi$
$678$			2.48182e13i			0.173230i
$679$			1.88825e14i			1.30831i
$680$	6.20511e12			0.0426781
$681$		−	9.39333e13i		−	0.641334i
$682$	−9.96138e13	−	1.12187e14i	−0.675146	−	0.760361i
$683$	2.33668e14			1.57216			0.786080	−	0.618125i	$-0.212108\pi$
$683$	2.33668e14			1.57216			0.786080	+	0.618125i	$0.212108\pi$
$684$			1.05901e14i			0.707329i
$685$	5.04784e12			0.0334698
$686$	2.22215e13			0.146269
$687$	6.48010e13			0.423446
$688$		−	7.26246e13i		−	0.471131i
$689$			8.66399e12i			0.0557984i
$690$		−	4.70610e13i		−	0.300896i
$691$	1.44396e13			0.0916572			0.0458286	−	0.998949i	$-0.485407\pi$
$691$	1.44396e13			0.0916572			0.0458286	+	0.998949i	$0.485407\pi$
$692$		−	1.41362e14i		−	0.890847i
$693$	−1.37907e14	−	1.55314e14i	−0.862822	−	0.971725i
$694$	1.20091e14			0.745954
$695$			5.47549e13i			0.337675i
$696$	−1.41228e13			−0.0864716
$697$	1.27155e13			0.0772982
$698$	2.74494e13			0.165675
$699$		−	7.07565e13i		−	0.424014i
$700$		−	6.26564e13i		−	0.372800i
$701$			5.00062e13i			0.295416i	0.989031	+	0.147708i	$0.0471896\pi$
$701$			5.00062e13i			0.295416i	−0.989031	+	0.147708i	$0.952810\pi$
$702$	3.40355e13			0.199639
$703$			3.18665e14i			1.85591i
$704$	1.61636e13	−	1.43521e13i	0.0934707	−	0.0829953i
$705$	−2.20556e13			−0.126640
$706$		−	7.14823e13i		−	0.407545i
$707$	2.36535e14			1.33906
$708$	−3.91524e13			−0.220086
$709$	−1.68566e14			−0.940892			−0.470446	−	0.882429i	$-0.655907\pi$
$709$	−1.68566e14			−0.940892			−0.470446	+	0.882429i	$0.655907\pi$
$710$			3.91649e13i			0.217073i
$711$			7.97538e13i			0.438938i
$712$		−	3.37798e13i		−	0.184611i
$713$	4.81179e14			2.61132
$714$		−	1.10736e13i		−	0.0596759i
$715$	−3.88334e13	−	4.37348e13i	−0.207814	−	0.234044i
$716$	9.78888e13			0.520197
$717$			6.30066e12i			0.0332499i
$718$	−2.65821e14			−1.39305
$719$	−2.62990e13			−0.136866			−0.0684328	−	0.997656i	$-0.521800\pi$
$719$	−2.62990e13			−0.136866			−0.0684328	+	0.997656i	$0.521800\pi$
$720$	−3.00847e13			−0.155483
$721$			4.32544e14i			2.22000i
$722$			2.13322e14i			1.08730i
$723$			8.49916e13i			0.430214i
$724$	−1.17282e14			−0.589575
$725$			7.46001e13i			0.372434i
$726$	4.73846e13	+	5.64559e12i	0.234938	+	0.0279915i
$727$	−2.92303e14			−1.43933			−0.719666	−	0.694321i	$-0.755705\pi$
$727$	−2.92303e14			−1.43933			−0.719666	+	0.694321i	$0.755705\pi$
$728$			4.72799e13i			0.231217i
$729$	−8.01979e13			−0.389516
$730$	−6.74836e13			−0.325525
$731$	−6.77996e13			−0.324818
$732$			1.24759e13i			0.0593629i
$733$		−	2.67786e14i		−	1.26552i	−0.774350	−	0.632758i	$-0.781923\pi$
$733$		−	2.67786e14i		−	1.26552i	0.774350	−	0.632758i	$-0.218077\pi$
$734$		−	1.12698e14i		−	0.528977i
$735$	5.73720e13			0.267463
$736$			6.93273e13i			0.321008i
$737$	−1.94115e14	+	1.72360e14i	−0.892734	+	0.792684i
$738$	−6.16495e13			−0.281610
$739$		−	1.07683e14i		−	0.488567i	−0.969704	−	0.244283i	$-0.921447\pi$
$739$		−	1.07683e14i		−	0.488567i	0.969704	−	0.244283i	$-0.0785527\pi$
$740$	−9.05272e13			−0.407963
$741$	5.32181e13			0.238215
$742$	−2.90570e13			−0.129191
$743$		−	2.25075e14i		−	0.993995i	−0.867752	−	0.496997i	$-0.834436\pi$
$743$		−	2.25075e14i		−	0.993995i	0.867752	−	0.496997i	$-0.165564\pi$
$744$			3.87810e13i			0.170119i
$745$			1.56266e14i			0.680898i
$746$	5.06186e13			0.219087
$747$			2.83341e14i			1.21817i
$748$	−1.33986e13	−	1.50898e13i	−0.0572207	−	0.0644429i
$749$	−7.95568e13			−0.337495
$750$		−	5.93568e13i		−	0.250129i
$751$	9.09921e13			0.380894			0.190447	−	0.981697i	$-0.439006\pi$
$751$	9.09921e13			0.380894			0.190447	+	0.981697i	$0.439006\pi$
$752$	3.24908e13			0.135105
$753$	−1.03546e14			−0.427717
$754$		−	5.62925e13i		−	0.230990i
$755$		−	5.24489e13i		−	0.213797i
$756$			1.14147e14i			0.462228i
$757$	−8.87103e13			−0.356857			−0.178429	−	0.983953i	$-0.557101\pi$
$757$	−8.87103e13			−0.356857			−0.178429	+	0.983953i	$0.557101\pi$
$758$			1.10928e14i			0.443299i
$759$	−1.14444e14	+	1.01618e14i	−0.454345	+	0.403426i
$760$	−1.00012e14			−0.394443
$761$		−	2.36983e14i		−	0.928527i	−0.885697	−	0.464263i	$-0.846319\pi$
$761$		−	2.36983e14i		−	0.928527i	0.885697	−	0.464263i	$-0.153681\pi$
$762$	6.60105e13			0.256944
$763$	9.80004e13			0.378970
$764$	9.91428e13			0.380886
$765$			2.80860e13i			0.107197i
$766$		−	1.09629e14i		−	0.415701i
$767$		−	1.56059e14i		−	0.587912i
$768$	−5.58748e12			−0.0209127
$769$		−	3.82656e13i		−	0.142291i	−0.997466	−	0.0711454i	$-0.977335\pi$
$769$		−	3.82656e13i		−	0.142291i	0.997466	−	0.0711454i	$-0.0226654\pi$
$770$	1.46676e14	−	1.30238e14i	0.541884	−	0.481154i
$771$	−1.09068e14			−0.400337
$772$			2.40398e14i			0.876687i
$773$	−2.59818e14			−0.941395			−0.470697	−	0.882295i	$-0.655998\pi$
$773$	−2.59818e14			−0.941395			−0.470697	+	0.882295i	$0.655998\pi$
$774$	3.28718e14			1.18337
$775$	2.04851e14			0.732706
$776$		−	8.89468e13i		−	0.316098i
$777$			1.61555e14i			0.570446i
$778$		−	1.09912e14i		−	0.385608i
$779$	−2.04944e14			−0.714411
$780$			1.51183e13i			0.0523638i
$781$	9.52423e13	−	8.45683e13i	0.327774	−	0.291040i
$782$	6.47215e13			0.221317
$783$		−	1.35906e14i		−	0.461775i
$784$	−8.45167e13			−0.285340
$785$	8.42939e13			0.282779
$786$	3.98053e13			0.132687
$787$		−	3.10585e14i		−	1.02874i	−0.857567	−	0.514372i	$-0.828025\pi$
$787$		−	3.10585e14i		−	1.02874i	0.857567	−	0.514372i	$-0.171975\pi$
$788$		−	3.20342e13i		−	0.105435i
$789$		−	1.53171e14i		−	0.500945i
$790$	−7.53185e13			−0.244775
$791$		−	3.31768e14i		−	1.07140i
$792$	6.49617e13	+	7.31610e13i	0.208464	+	0.234776i
$793$	−4.97281e13			−0.158575
$794$			4.61844e12i			0.0146350i
$795$	−9.29133e12			−0.0292578
$796$	−4.26598e13			−0.133491
$797$	3.99049e14			1.24089			0.620446	−	0.784249i	$-0.286952\pi$
$797$	3.99049e14			1.24089			0.620446	+	0.784249i	$0.286952\pi$
$798$			1.78481e14i			0.551541i
$799$		−	3.03323e13i		−	0.0931475i
$800$			2.95145e13i			0.0900712i
$801$	1.52896e14			0.463697
$802$			1.54082e14i			0.464388i
$803$	1.45717e14	+	1.64109e14i	0.436447	+	0.491534i
$804$	6.71022e13			0.199736
$805$			6.29108e14i			1.86100i
$806$	−1.54579e14			−0.454438
$807$	2.27193e13			0.0663784
$808$	−1.11421e14			−0.323526
$809$			2.70848e14i			0.781597i	0.920476	+	0.390799i	$0.127801\pi$
$809$			2.70848e14i			0.781597i	−0.920476	+	0.390799i	$0.872199\pi$
$810$		−	1.16840e14i		−	0.335093i
$811$		−	6.60387e14i		−	1.88232i	−0.337957	−	0.941162i	$-0.609736\pi$
$811$		−	6.60387e14i		−	1.88232i	0.337957	−	0.941162i	$-0.390264\pi$
$812$	1.88792e14			0.534815
$813$		−	2.23396e14i		−	0.628960i
$814$	1.95475e14	+	2.20147e14i	0.546976	+	0.616014i
$815$	−2.42904e14			−0.675533
$816$			5.21627e12i			0.0144181i
$817$	1.09277e15			3.00206
$818$	2.81122e14			0.767588
$819$	−2.14002e14			−0.580762
$820$		−	5.82211e13i		−	0.157040i
$821$		−	6.01731e14i		−	1.61319i	−0.591102	−	0.806597i	$-0.701307\pi$
$821$		−	6.01731e14i		−	1.61319i	0.591102	−	0.806597i	$-0.298693\pi$
$822$			4.24342e12i			0.0113072i
$823$	−2.52352e14			−0.668356			−0.334178	−	0.942510i	$-0.608459\pi$
$823$	−2.52352e14			−0.668356			−0.334178	+	0.942510i	$0.608459\pi$
$824$		−	2.03751e14i		−	0.536369i
$825$	−4.87221e13	+	4.32617e13i	−0.127484	+	0.113197i
$826$	5.23386e14			1.36120
$827$			2.55218e14i			0.659756i	0.944024	+	0.329878i	$0.107008\pi$
$827$			2.55218e14i			0.659756i	−0.944024	+	0.329878i	$0.892992\pi$
$828$	−3.13794e14			−0.806294
$829$	−2.83368e14			−0.723734			−0.361867	−	0.932230i	$-0.617860\pi$
$829$	−2.83368e14			−0.723734			−0.361867	+	0.932230i	$0.617860\pi$
$830$	−2.67584e14			−0.679313
$831$			1.63448e14i			0.412453i
$832$		−	2.22714e13i		−	0.0558638i
$833$			7.89017e13i			0.196726i
$834$	−4.60292e13			−0.114078
$835$		−	1.86063e14i		−	0.458382i
$836$	2.15955e14	+	2.43212e14i	0.528849	+	0.595599i
$837$	−3.73197e14			−0.908469
$838$		−	4.54562e14i		−	1.09995i
$839$	−4.71632e14			−1.13447			−0.567236	−	0.823556i	$-0.691987\pi$
$839$	−4.71632e14			−1.13447			−0.567236	+	0.823556i	$0.691987\pi$
$840$	−5.07034e13			−0.121238
$841$	1.95927e14			0.465709
$842$			2.55453e14i			0.603602i
$843$		−	2.31424e13i		−	0.0543588i
$844$			2.26702e14i			0.529350i
$845$	2.41453e14			0.560465
$846$			1.47062e14i			0.339351i
$847$	−6.33433e14	−	7.54698e13i	−1.45306	−	0.173124i
$848$	1.36874e13			0.0312134
$849$			9.25047e12i			0.0209713i
$850$	2.75537e13			0.0620991
$851$	−9.44230e14			−2.11558
$852$	−3.29236e13			−0.0733346
$853$			2.71566e14i			0.601353i	0.953726	+	0.300677i	$0.0972125\pi$
$853$			2.71566e14i			0.601353i	−0.953726	+	0.300677i	$0.902787\pi$
$854$		−	1.66776e14i		−	0.367152i
$855$		−	4.52681e14i		−	0.990746i
$856$	3.74755e13			0.0815414
$857$		−	3.65436e13i		−	0.0790510i	−0.999219	−	0.0395255i	$-0.987415\pi$
$857$		−	3.65436e13i		−	0.0790510i	0.999219	−	0.0395255i	$-0.0125846\pi$
$858$	3.67652e13	−	3.26449e13i	0.0790680	−	0.0702067i
$859$	6.96661e14			1.48955			0.744776	−	0.667315i	$-0.232556\pi$
$859$	6.96661e14			1.48955			0.744776	+	0.667315i	$0.232556\pi$
$860$			3.10438e14i			0.659906i
$861$	−1.03901e14			−0.219586
$862$	−1.66839e13			−0.0350558
$863$	3.71375e14			0.775817			0.387908	−	0.921698i	$-0.373198\pi$
$863$	3.71375e14			0.775817			0.387908	+	0.921698i	$0.373198\pi$
$864$		−	5.37694e13i		−	0.111678i
$865$			6.04261e14i			1.24780i
$866$		−	6.51951e12i		−	0.0133852i
$867$	−1.59048e14			−0.324662
$868$		−	5.18421e14i		−	1.05217i
$869$	1.62635e14	+	1.83162e14i	0.328181	+	0.369603i
$870$	6.03686e13			0.121120
$871$			2.67465e14i			0.533552i
$872$	−4.61634e13			−0.0915620
$873$	4.02597e14			0.793962
$874$	−1.04316e15			−2.04547
$875$			7.93478e14i			1.54701i
$876$		−	5.67294e13i		−	0.109973i
$877$			7.85911e13i			0.151487i	0.997127	+	0.0757435i	$0.0241330\pi$
$877$			7.85911e13i			0.151487i	−0.997127	+	0.0757435i	$0.975867\pi$
$878$	−4.74152e14			−0.908751
$879$		−	1.07556e13i		−	0.0204970i
$880$	−6.90923e13	+	6.13491e13i	−0.130923	+	0.116250i
$881$	−6.54240e13			−0.123270			−0.0616351	−	0.998099i	$-0.519631\pi$
$881$	−6.54240e13			−0.123270			−0.0616351	+	0.998099i	$0.519631\pi$
$882$		−	3.82546e14i		−	0.716705i
$883$	6.10174e14			1.13671			0.568356	−	0.822783i	$-0.307580\pi$
$883$	6.10174e14			1.13671			0.568356	+	0.822783i	$0.307580\pi$
$884$	−2.07917e13			−0.0385150
$885$	1.67359e14			0.308271
$886$			6.39774e14i			1.17181i
$887$		−	8.18047e14i		−	1.48991i	−0.667115	−	0.744955i	$-0.732471\pi$
$887$		−	8.18047e14i		−	1.48991i	0.667115	−	0.744955i	$-0.267529\pi$
$888$		−	7.61008e13i		−	0.137824i
$889$	−8.82424e14			−1.58916
$890$			1.44393e14i			0.258582i
$891$	−2.84134e14	+	2.52291e14i	−0.505981	+	0.449275i
$892$	1.69453e14			0.300072
$893$			4.88886e14i			0.860895i
$894$	−1.31363e14			−0.230031
$895$	−4.18431e14			−0.728633
$896$	7.46930e13			0.129342
$897$			1.57689e14i			0.271544i
$898$		−	4.86236e14i		−	0.832656i
$899$			6.17243e14i			1.05113i
$900$	−1.33591e14			−0.226237
$901$		−	1.27781e13i		−	0.0215199i
$902$	−1.41584e14	+	1.25716e14i	−0.237127	+	0.210552i
$903$	5.54006e14			0.922732
$904$			1.56280e14i			0.258859i
$905$	5.01329e14			0.825810
$906$	4.40906e13			0.0722279
$907$	4.63655e13			0.0755368			0.0377684	−	0.999287i	$-0.487975\pi$
$907$	4.63655e13			0.0755368			0.0377684	+	0.999287i	$0.487975\pi$
$908$		−	5.91498e14i		−	0.958350i
$909$		−	5.04321e14i		−	0.812620i
$910$		−	2.02101e14i		−	0.323863i
$911$	7.93113e14			1.26399			0.631995	−	0.774973i	$-0.282236\pi$
$911$	7.93113e14			1.26399			0.631995	+	0.774973i	$0.282236\pi$
$912$		−	8.40741e13i		−	0.133256i
$913$	5.77792e14	+	6.50719e14i	0.910789	+	1.02575i
$914$	−9.30937e13			−0.145945
$915$		−	5.33288e13i		−	0.0831489i
$916$	4.08052e14			0.632759
$917$	−5.32114e14			−0.820650
$918$	−5.01971e13			−0.0769955
$919$			8.85357e14i			1.35064i	0.737523	+	0.675322i	$0.235995\pi$
$919$			8.85357e14i			1.35064i	−0.737523	+	0.675322i	$0.764005\pi$
$920$		−	2.96343e14i		−	0.449631i
$921$		−	1.37088e14i		−	0.206872i
$922$	5.70469e14			0.856204
$923$		−	1.31231e14i		−	0.195898i
$924$	1.09483e14	+	1.23302e14i	0.162550	+	0.183067i
$925$	−4.01984e14			−0.593609
$926$			4.23689e14i			0.622290i
$927$	9.22232e14			1.34723
$928$	−8.89311e13			−0.129215
$929$	4.61685e13			0.0667217			0.0333609	−	0.999443i	$-0.489379\pi$
$929$	4.61685e13			0.0667217			0.0333609	+	0.999443i	$0.489379\pi$
$930$		−	1.65771e14i		−	0.238284i
$931$		−	1.27171e15i		−	1.81820i
$932$		−	4.45554e14i		−	0.633608i
$933$	1.41795e14			0.200564
$934$			3.50640e14i			0.493319i
$935$	5.72733e13	+	6.45021e13i	0.0801482	+	0.0902642i
$936$	1.00806e14			0.140316
$937$		−	4.14465e14i		−	0.573839i	−0.957955	−	0.286919i	$-0.907369\pi$
$937$		−	4.14465e14i		−	0.573839i	0.957955	−	0.286919i	$-0.0926311\pi$
$938$	−8.97017e14			−1.23534
$939$	3.77909e14			0.517678
$940$	−1.38884e14			−0.189240
$941$		−	7.31311e14i		−	0.991183i	−0.868556	−	0.495592i	$-0.834951\pi$
$941$		−	7.31311e14i		−	0.991183i	0.868556	−	0.495592i	$-0.165049\pi$
$942$			7.08608e13i			0.0955326i
$943$		−	6.07266e14i		−	0.814367i
$944$	−2.46543e14			−0.328876
$945$		−	4.87928e14i		−	0.647436i
$946$	7.54932e14	−	6.70325e14i	0.996442	−	0.884769i
$947$	−1.39817e15			−1.83574			−0.917869	−	0.396882i	$-0.870092\pi$
$947$	−1.39817e15			−1.83574			−0.917869	+	0.396882i	$0.870092\pi$
$948$		−	6.33158e13i		−	0.0826933i
$949$	2.26120e14			0.293770
$950$	−4.44101e14			−0.573937
$951$	9.66194e13			0.124211
$952$		−	6.97307e13i		−	0.0891742i
$953$			4.71182e14i			0.599410i	0.954032	+	0.299705i	$0.0968882\pi$
$953$			4.71182e14i			0.599410i	−0.954032	+	0.299705i	$0.903112\pi$
$954$			6.19529e13i			0.0784006i
$955$	−4.23792e14			−0.533501
$956$			3.96753e13i			0.0496856i
$957$	−1.30353e14	−	1.46806e14i	−0.162391	−	0.182888i
$958$	8.52422e14			1.05640
$959$		−	5.67257e13i		−	0.0699337i
$960$	2.38840e13			0.0292921
$961$	8.75315e14			1.06794
$962$	3.03333e14			0.368167
$963$			1.69624e14i			0.204812i
$964$			5.35192e14i			0.642872i
$965$		−	1.02760e15i		−	1.22796i
$966$	−5.28853e14			−0.628709
$967$		−	3.76102e14i		−	0.444809i	−0.974955	−	0.222404i	$-0.928610\pi$
$967$		−	3.76102e14i		−	0.444809i	0.974955	−	0.222404i	$-0.0713905\pi$
$968$	2.98381e14	+	3.55503e13i	0.351070	+	0.0418279i
$969$	−7.84885e13			−0.0918729
$970$			3.80208e14i			0.442754i
$971$	1.41963e13			0.0164467			0.00822333	−	0.999966i	$-0.497382\pi$
$971$	1.41963e13			0.0164467			0.00822333	+	0.999966i	$0.497382\pi$
$972$	3.72278e14			0.429078
$973$	6.15314e14			0.705558
$974$			9.62253e14i			1.09773i
$975$			6.71326e13i			0.0761922i
$976$			7.85606e13i			0.0887065i
$977$	−1.30757e15			−1.46890			−0.734448	−	0.678665i	$-0.762559\pi$
$977$	−1.30757e15			−1.46890			−0.734448	+	0.678665i	$0.762559\pi$
$978$		−	2.04195e14i		−	0.228218i
$979$	3.51140e14	−	3.11787e14i	0.390452	−	0.346693i
$980$	3.61271e14			0.399672
$981$		−	2.08948e14i		−	0.229982i
$982$	−7.00994e14			−0.767638
$983$	1.49236e14			0.162595			0.0812974	−	0.996690i	$-0.474094\pi$
$983$	1.49236e14			0.162595			0.0812974	+	0.996690i	$0.474094\pi$
$984$	4.89429e13			0.0530536
$985$			1.36932e14i			0.147681i
$986$			8.30229e13i			0.0890868i
$987$			2.47852e14i			0.264610i
$988$	3.35114e14			0.355966
$989$			3.23797e15i			3.42209i
$990$	−2.77682e14	−	3.12731e14i	−0.291993	−	0.328847i
$991$	−1.57690e15			−1.64982			−0.824908	−	0.565266i	$-0.808773\pi$
$991$	−1.57690e15			−1.64982			−0.824908	+	0.565266i	$0.808773\pi$
$992$			2.44204e14i			0.254211i
$993$	−1.90237e14			−0.197038
$994$	4.40120e14			0.453564
$995$	1.82352e14			0.186979
$996$		−	2.24942e14i		−	0.229495i
$997$		−	1.36658e15i		−	1.38727i	−0.720329	−	0.693633i	$-0.756009\pi$
$997$		−	1.36658e15i		−	1.38727i	0.720329	−	0.693633i	$-0.243991\pi$
$998$		−	9.26094e14i		−	0.935411i
$999$	7.32333e14			0.736005

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.11.b.a.21.3	✓	10
3.2	odd	2		198.11.d.a.109.7		10
4.3	odd	2		176.11.h.e.65.6		10
11.10	odd	2	inner	22.11.b.a.21.8	yes	10
33.32	even	2		198.11.d.a.109.2		10
44.43	even	2		176.11.h.e.65.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.11.b.a.21.3	✓	10	1.1	even	1	trivial
22.11.b.a.21.8	yes	10	11.10	odd	2	inner
176.11.h.e.65.5		10	44.43	even	2
176.11.h.e.65.6		10	4.3	odd	2
198.11.d.a.109.2		10	33.32	even	2
198.11.d.a.109.7		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-22.6274i q^{2} -81.3085 q^{3} -512.000 q^{4} +2188.57 q^{5} +1839.80i q^{6} -24594.3i q^{7} +11585.2i q^{8} -52437.9 q^{9} +O(q^{10})\)	\(q-22.6274i q^{2} -81.3085 q^{3} -512.000 q^{4} +2188.57 q^{5} +1839.80i q^{6} -24594.3i q^{7} +11585.2i q^{8} -52437.9 q^{9} -49521.7i q^{10} +(-120428. + 106932. i) q^{11} +41630.0 q^{12} +165935. i q^{13} -556506. q^{14} -177950. q^{15} +262144. q^{16} -244728. i q^{17} +1.18653e6i q^{18} +3.94445e6i q^{19} -1.12055e6 q^{20} +1.99973e6i q^{21} +(2.41959e6 + 2.72498e6i) q^{22} -1.16877e7 q^{23} -941978. i q^{24} -4.97578e6 q^{25} +3.75467e6 q^{26} +9.06484e6 q^{27} +1.25923e7i q^{28} -1.49927e7i q^{29} +4.02654e6i q^{30} -4.11697e7 q^{31} -5.93164e6i q^{32} +(9.79186e6 - 8.69447e6i) q^{33} -5.53757e6 q^{34} -5.38265e7i q^{35} +2.68482e7 q^{36} +8.07883e7 q^{37} +8.92527e7 q^{38} -1.34919e7i q^{39} +2.53551e7i q^{40} +5.19576e7i q^{41} +4.52487e7 q^{42} -2.77041e8i q^{43} +(6.16594e7 - 5.47491e7i) q^{44} -1.14764e8 q^{45} +2.64463e8i q^{46} +1.23943e8 q^{47} -2.13145e7 q^{48} -3.22406e8 q^{49} +1.12589e8i q^{50} +1.98985e7i q^{51} -8.49585e7i q^{52} +5.22133e7 q^{53} -2.05114e8i q^{54} +(-2.63566e8 + 2.34028e8i) q^{55} +2.84931e8 q^{56} -3.20717e8i q^{57} -3.39245e8 q^{58} -9.40486e8 q^{59} +9.11102e7 q^{60} +2.99685e8i q^{61} +9.31564e8i q^{62} +1.28968e9i q^{63} -1.34218e8 q^{64} +3.63160e8i q^{65} +(-1.96733e8 - 2.21564e8i) q^{66} +1.61187e9 q^{67} +1.25301e8i q^{68} +9.50310e8 q^{69} -1.21795e9 q^{70} -7.90862e8 q^{71} -6.07506e8i q^{72} -1.36271e9i q^{73} -1.82803e9i q^{74} +4.04573e8 q^{75} -2.01956e9i q^{76} +(2.62992e9 + 2.96186e9i) q^{77} -3.05287e8 q^{78} -1.52092e9i q^{79} +5.73721e8 q^{80} +2.35936e9 q^{81} +1.17567e9 q^{82} -5.40337e9i q^{83} -1.02386e9i q^{84} -5.35605e8i q^{85} -6.26872e9 q^{86} +1.21903e9i q^{87} +(-1.23883e9 - 1.39519e9i) q^{88} -2.91576e9 q^{89} +2.59682e9i q^{90} +4.08105e9 q^{91} +5.98411e9 q^{92} +3.34745e9 q^{93} -2.80450e9i q^{94} +8.63271e9i q^{95} +4.82293e8i q^{96} -7.67759e9 q^{97} +7.29521e9i q^{98} +(6.31502e9 - 5.60728e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 106 q^{3} - 5120 q^{4} + 1138 q^{5} + 78044 q^{9}+O(q^{10}) \) 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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