LMFDB - Embedded newform 22.15.b.a.21.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,15,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, 15, names="a")

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

chi := DirichletCharacter("22.21");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 15 $
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:	$27.3523729934$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 38299509 x^{12} + 1255603312 x^{11} + 548839279225666 x^{10} + \cdots + 61\!\cdots\!00 $ x^14 - 2x^13 - 38299509x^12 + 1255603312x^11 + 548839279225666x^10 - 62614853719962708x^9 - 3647746096331338780406x^8 + 909709401522475794317032x^7 + 11341528896592004854718535645x^6 - 4608641836922062401823748151666x^5 - 14199433672677462467950659880576257x^4 + 7648786246750765008517429480227297240x^3 + 5468207905418692926727112276614665574080x^2 - 3973529610997293170696151713639263984312200*x + 613220922939245616829253347741252697812260300
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{56}\cdot 3^{6}\cdot 11^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			21.12
Root			$-1087.11 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.15.b.a.21.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+90.5097i q^{2} +1401.11 q^{3} -8192.00 q^{4} +44552.9 q^{5} +126814. i q^{6} +500199. i q^{7} -741455. i q^{8} -2.81985e6 q^{9} +O(q^{10})$	\(q+90.5097i q^{2} +1401.11 q^{3} -8192.00 q^{4} +44552.9 q^{5} +126814. i q^{6} +500199. i q^{7} -741455. i q^{8} -2.81985e6 q^{9} +4.03247e6i q^{10} +(1.30821e7 - 1.44432e7i) q^{11} -1.14779e7 q^{12} +8.91038e7i q^{13} -4.52729e7 q^{14} +6.24238e7 q^{15} +6.71089e7 q^{16} +6.36213e8i q^{17} -2.55223e8i q^{18} -3.46812e8i q^{19} -3.64978e8 q^{20} +7.00836e8i q^{21} +(1.30725e9 + 1.18406e9i) q^{22} +5.95600e9 q^{23} -1.03886e9i q^{24} -4.11855e9 q^{25} -8.06476e9 q^{26} -1.06524e10 q^{27} -4.09763e9i q^{28} +3.00582e10i q^{29} +5.64995e9i q^{30} -5.23034e10 q^{31} +6.07400e9i q^{32} +(1.83296e10 - 2.02366e10i) q^{33} -5.75834e10 q^{34} +2.22853e10i q^{35} +2.31002e10 q^{36} -8.18322e10 q^{37} +3.13898e10 q^{38} +1.24845e11i q^{39} -3.30340e10i q^{40} +4.00058e10i q^{41} -6.34324e10 q^{42} +1.82418e11i q^{43} +(-1.07169e11 + 1.18319e11i) q^{44} -1.25632e11 q^{45} +5.39076e11i q^{46} -4.40108e11 q^{47} +9.40272e10 q^{48} +4.28024e11 q^{49} -3.72769e11i q^{50} +8.91407e11i q^{51} -7.29939e11i q^{52} +6.53401e10 q^{53} -9.64147e11i q^{54} +(5.82848e11 - 6.43489e11i) q^{55} +3.70875e11 q^{56} -4.85923e11i q^{57} -2.72056e12 q^{58} +4.65987e12 q^{59} -5.11375e11 q^{60} -2.32275e12i q^{61} -4.73397e12i q^{62} -1.41048e12i q^{63} -5.49756e11 q^{64} +3.96984e12i q^{65} +(1.83161e12 + 1.65900e12i) q^{66} +4.10486e12 q^{67} -5.21186e12i q^{68} +8.34504e12 q^{69} -2.01704e12 q^{70} +9.03565e11 q^{71} +2.09079e12i q^{72} +5.59551e12i q^{73} -7.40660e12i q^{74} -5.77056e12 q^{75} +2.84108e12i q^{76} +(7.22450e12 + 6.54368e12i) q^{77} -1.12997e13 q^{78} +1.73153e13i q^{79} +2.98990e12 q^{80} -1.43801e12 q^{81} -3.62091e12 q^{82} -2.98316e13i q^{83} -5.74125e12i q^{84} +2.83452e13i q^{85} -1.65106e13 q^{86} +4.21150e13i q^{87} +(-1.07090e13 - 9.69983e12i) q^{88} +1.60553e13 q^{89} -1.13710e13i q^{90} -4.45697e13 q^{91} -4.87916e13 q^{92} -7.32831e13 q^{93} -3.98340e13i q^{94} -1.54515e13i q^{95} +8.51037e12i q^{96} +8.05913e13 q^{97} +3.87403e13i q^{98} +(-3.68896e13 + 4.07277e13i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9}+O(q^{10}) $ 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9	\( 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9} + 20143042 q^{11} - 35995648 q^{12} + 62814720 q^{14} - 1359602 q^{15} + 939524096 q^{16} - 571457536 q^{20} - 2107666944 q^{22} - 7305755542 q^{23} + 19291879452 q^{25} - 6388480512 q^{26} + 34093422830 q^{27} - 33569873942 q^{31} + 2885838062 q^{33} + 167764701696 q^{34} - 90247757824 q^{36} + 73167823966 q^{37} + 71236111872 q^{38} - 222695314944 q^{42} - 165011800064 q^{44} + 2000205168616 q^{45} - 1612717386124 q^{47} + 294876348416 q^{48} + 3424602524990 q^{49} - 3530064068164 q^{53} - 3715439610854 q^{55} - 514578186240 q^{56} - 1374208002048 q^{58} - 818496564070 q^{59} + 11137859584 q^{60} - 7696581394432 q^{64} - 5938395621888 q^{66} + 16485465276922 q^{67} - 11394452631206 q^{69} - 392146020864 q^{70} - 19380879179878 q^{71} + 23016770893992 q^{75} + 60534793808304 q^{77} + 17335823992320 q^{78} + 4681380134912 q^{80} - 10394309810662 q^{81} - 79417078012416 q^{82} + 6375532305408 q^{86} + 17266007605248 q^{88} - 117770741987650 q^{89} + 150621364097712 q^{91} + 59848749400064 q^{92} + 27345122803162 q^{93} + 123398138843566 q^{97} + 118861332531788 q^{99}+O(q^{100}) \) 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9 + 20143042 * q^11 - 35995648 * q^12 + 62814720 * q^14 - 1359602 * q^15 + 939524096 * q^16 - 571457536 * q^20 - 2107666944 * q^22 - 7305755542 * q^23 + 19291879452 * q^25 - 6388480512 * q^26 + 34093422830 * q^27 - 33569873942 * q^31 + 2885838062 * q^33 + 167764701696 * q^34 - 90247757824 * q^36 + 73167823966 * q^37 + 71236111872 * q^38 - 222695314944 * q^42 - 165011800064 * q^44 + 2000205168616 * q^45 - 1612717386124 * q^47 + 294876348416 * q^48 + 3424602524990 * q^49 - 3530064068164 * q^53 - 3715439610854 * q^55 - 514578186240 * q^56 - 1374208002048 * q^58 - 818496564070 * q^59 + 11137859584 * q^60 - 7696581394432 * q^64 - 5938395621888 * q^66 + 16485465276922 * q^67 - 11394452631206 * q^69 - 392146020864 * q^70 - 19380879179878 * q^71 + 23016770893992 * q^75 + 60534793808304 * q^77 + 17335823992320 * q^78 + 4681380134912 * q^80 - 10394309810662 * q^81 - 79417078012416 * q^82 + 6375532305408 * q^86 + 17266007605248 * q^88 - 117770741987650 * q^89 + 150621364097712 * q^91 + 59848749400064 * q^92 + 27345122803162 * q^93 + 123398138843566 * q^97 + 118861332531788 * 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 $

$2$			90.5097i			0.707107i
$2$			90.5097i			0.707107i
$3$	1401.11			0.640656			0.320328	−	0.947307i	$-0.396207\pi$
$3$	1401.11			0.640656			0.320328	+	0.947307i	$0.396207\pi$
$4$	−8192.00			−0.500000
$5$	44552.9			0.570278			0.285139	−	0.958486i	$-0.407960\pi$
$5$	44552.9			0.570278			0.285139	+	0.958486i	$0.407960\pi$
$6$			126814.i			0.453012i
$7$			500199.i			0.607375i	0.952772	+	0.303687i	$0.0982178\pi$
$7$			500199.i			0.607375i	−0.952772	+	0.303687i	$0.901782\pi$
$8$		−	741455.i		−	0.353553i
$9$	−2.81985e6			−0.589560
$10$			4.03247e6i			0.403247i
$11$	1.30821e7	−	1.44432e7i	0.671321	−	0.741167i
$11$	1.30821e7	−	1.44432e7i	0.671321	−	0.741167i
$12$	−1.14779e7			−0.320328
$13$			8.91038e7i			1.42002i	0.704194	+	0.710008i	$0.251308\pi$
$13$			8.91038e7i			1.42002i	−0.704194	+	0.710008i	$0.748692\pi$
$14$	−4.52729e7			−0.429479
$15$	6.24238e7			0.365352
$16$	6.71089e7			0.250000
$17$			6.36213e8i			1.55046i	0.631680	+	0.775229i	$0.282366\pi$
$17$			6.36213e8i			1.55046i	−0.631680	+	0.775229i	$0.717634\pi$
$18$		−	2.55223e8i		−	0.416882i
$19$		−	3.46812e8i		−	0.387988i	−0.981003	−	0.193994i	$-0.937856\pi$
$19$		−	3.46812e8i		−	0.387988i	0.981003	−	0.193994i	$-0.0621443\pi$
$20$	−3.64978e8			−0.285139
$21$			7.00836e8i			0.389118i
$22$	1.30725e9	+	1.18406e9i	0.524084	+	0.474696i
$23$	5.95600e9			1.74928			0.874641	−	0.484771i	$-0.161097\pi$
$23$	5.95600e9			1.74928			0.874641	+	0.484771i	$0.161097\pi$
$24$		−	1.03886e9i		−	0.226506i
$25$	−4.11855e9			−0.674784
$26$	−8.06476e9			−1.00410
$27$	−1.06524e10			−1.01836
$28$		−	4.09763e9i		−	0.303687i
$29$			3.00582e10i			1.74252i	0.490824	+	0.871259i	$0.336696\pi$
$29$			3.00582e10i			1.74252i	−0.490824	+	0.871259i	$0.663304\pi$
$30$			5.64995e9i			0.258343i
$31$	−5.23034e10			−1.90107			−0.950535	−	0.310616i	$-0.899465\pi$
$31$	−5.23034e10			−1.90107			−0.950535	+	0.310616i	$0.899465\pi$
$32$			6.07400e9i			0.176777i
$33$	1.83296e10	−	2.02366e10i	0.430086	−	0.474833i
$34$	−5.75834e10			−1.09634
$35$			2.22853e10i			0.346372i
$36$	2.31002e10			0.294780
$37$	−8.18322e10			−0.862010			−0.431005	−	0.902350i	$-0.641841\pi$
$37$	−8.18322e10			−0.862010			−0.431005	+	0.902350i	$0.641841\pi$
$38$	3.13898e10			0.274349
$39$			1.24845e11i			0.909741i
$40$		−	3.30340e10i		−	0.201624i
$41$			4.00058e10i			0.205417i	0.994712	+	0.102708i	$0.0327508\pi$
$41$			4.00058e10i			0.205417i	−0.994712	+	0.102708i	$0.967249\pi$
$42$	−6.34324e10			−0.275148
$43$			1.82418e11i			0.671103i	0.942022	+	0.335552i	$0.108923\pi$
$43$			1.82418e11i			0.671103i	−0.942022	+	0.335552i	$0.891077\pi$
$44$	−1.07169e11	+	1.18319e11i	−0.335660	+	0.370583i
$45$	−1.25632e11			−0.336213
$46$			5.39076e11i			1.23693i
$47$	−4.40108e11			−0.868709			−0.434355	−	0.900742i	$-0.643024\pi$
$47$	−4.40108e11			−0.868709			−0.434355	+	0.900742i	$0.643024\pi$
$48$	9.40272e10			0.160164
$49$	4.28024e11			0.631096
$50$		−	3.72769e11i		−	0.477144i
$51$			8.91407e11i			0.993310i
$52$		−	7.29939e11i		−	0.710008i
$53$	6.53401e10			0.0556223			0.0278111	−	0.999613i	$-0.491146\pi$
$53$	6.53401e10			0.0556223			0.0278111	+	0.999613i	$0.491146\pi$
$54$		−	9.64147e11i		−	0.720090i
$55$	5.82848e11	−	6.43489e11i	0.382839	−	0.422671i
$56$	3.70875e11			0.214739
$57$		−	4.85923e11i		−	0.248567i
$58$	−2.72056e12			−1.23215
$59$	4.65987e12			1.87245			0.936223	−	0.351406i	$-0.114296\pi$
$59$	4.65987e12			1.87245			0.936223	+	0.351406i	$0.114296\pi$
$60$	−5.11375e11			−0.182676
$61$		−	2.32275e12i		−	0.739083i	−0.929214	−	0.369542i	$-0.879515\pi$
$61$		−	2.32275e12i		−	0.739083i	0.929214	−	0.369542i	$-0.120485\pi$
$62$		−	4.73397e12i		−	1.34426i
$63$		−	1.41048e12i		−	0.358084i
$64$	−5.49756e11			−0.125000
$65$			3.96984e12i			0.809803i
$66$	1.83161e12	+	1.65900e12i	0.335758	+	0.304117i
$67$	4.10486e12			0.677290			0.338645	−	0.940914i	$-0.390031\pi$
$67$	4.10486e12			0.677290			0.338645	+	0.940914i	$0.390031\pi$
$68$		−	5.21186e12i		−	0.775229i
$69$	8.34504e12			1.12069
$70$	−2.01704e12			−0.244922
$71$	9.03565e11			0.0993462			0.0496731	−	0.998766i	$-0.484182\pi$
$71$	9.03565e11			0.0993462			0.0496731	+	0.998766i	$0.484182\pi$
$72$			2.09079e12i			0.208441i
$73$			5.59551e12i			0.506500i	0.967401	+	0.253250i	$0.0814995\pi$
$73$			5.59551e12i			0.506500i	−0.967401	+	0.253250i	$0.918500\pi$
$74$		−	7.40660e12i		−	0.609533i
$75$	−5.77056e12			−0.432304
$76$			2.84108e12i			0.193994i
$77$	7.22450e12	+	6.54368e12i	0.450166	+	0.407743i
$78$	−1.12997e13			−0.643284
$79$			1.73153e13i			0.901656i	0.892611	+	0.450828i	$0.148871\pi$
$79$			1.73153e13i			0.901656i	−0.892611	+	0.450828i	$0.851129\pi$
$80$	2.98990e12			0.142569
$81$	−1.43801e12			−0.0628591
$82$	−3.62091e12			−0.145252
$83$		−	2.98316e13i		−	1.09934i	−0.835383	−	0.549668i	$-0.814754\pi$
$83$		−	2.98316e13i		−	1.09934i	0.835383	−	0.549668i	$-0.185246\pi$
$84$		−	5.74125e12i		−	0.194559i
$85$			2.83452e13i			0.884191i
$86$	−1.65106e13			−0.474542
$87$			4.21150e13i			1.11635i
$88$	−1.07090e13	−	9.69983e12i	−0.262042	−	0.237348i
$89$	1.60553e13			0.362985			0.181492	−	0.983392i	$-0.441907\pi$
$89$	1.60553e13			0.362985			0.181492	+	0.983392i	$0.441907\pi$
$90$		−	1.13710e13i		−	0.237738i
$91$	−4.45697e13			−0.862481
$92$	−4.87916e13			−0.874641
$93$	−7.32831e13			−1.21793
$94$		−	3.98340e13i		−	0.614270i
$95$		−	1.54515e13i		−	0.221261i
$96$			8.51037e12i			0.113253i
$97$	8.05913e13			0.997439			0.498719	−	0.866764i	$-0.333804\pi$
$97$	8.05913e13			0.997439			0.498719	+	0.866764i	$0.333804\pi$
$98$			3.87403e13i			0.446252i
$99$	−3.68896e13	+	4.07277e13i	−0.395784	+	0.436962i
$100$	3.37392e13			0.337392
$101$			1.65517e14i			1.54380i	0.635742	+	0.771902i	$0.280694\pi$
$101$			1.65517e14i			1.54380i	−0.635742	+	0.771902i	$0.719306\pi$
$102$	−8.06810e13			−0.702376
$103$	2.27143e13			0.184688			0.0923440	−	0.995727i	$-0.470564\pi$
$103$	2.27143e13			0.184688			0.0923440	+	0.995727i	$0.470564\pi$
$104$	6.60665e13			0.502051
$105$			3.12243e13i			0.221905i
$106$			5.91391e12i			0.0393309i
$107$		−	2.52957e14i		−	1.57529i	−0.616130	−	0.787644i	$-0.711300\pi$
$107$		−	2.52957e14i		−	1.57529i	0.616130	−	0.787644i	$-0.288700\pi$
$108$	8.72646e13			0.509181
$109$		−	1.19731e14i		−	0.654970i	−0.944856	−	0.327485i	$-0.893799\pi$
$109$		−	1.19731e14i		−	0.654970i	0.944856	−	0.327485i	$-0.106201\pi$
$110$	5.82420e13	+	5.27534e13i	0.298873	+	0.270708i
$111$	−1.14656e14			−0.552252
$112$			3.35678e13i			0.151844i
$113$	4.10710e14			1.74576			0.872882	−	0.487931i	$-0.162248\pi$
$113$	4.10710e14			1.74576			0.872882	+	0.487931i	$0.162248\pi$
$114$	4.39807e13			0.175763
$115$	2.65357e14			0.997577
$116$		−	2.46237e14i		−	0.871259i
$117$		−	2.51259e14i		−	0.837184i
$118$			4.21763e14i			1.32402i
$119$	−3.18233e14			−0.941709
$120$		−	4.62844e13i		−	0.129171i
$121$	−3.74648e13	−	3.77897e14i	−0.0986564	−	0.995122i
$122$	2.10231e14			0.522611
$123$			5.60527e13i			0.131601i
$124$	4.28470e14			0.950535
$125$	−4.55423e14			−0.955091
$126$	1.27663e14			0.253203
$127$		−	5.67988e14i		−	1.06589i	−0.846149	−	0.532946i	$-0.821085\pi$
$127$		−	5.67988e14i		−	1.06589i	0.846149	−	0.532946i	$-0.178915\pi$
$128$		−	4.97582e13i		−	0.0883883i
$129$			2.55589e14i			0.429946i
$130$	−3.59309e14			−0.572617
$131$		−	3.77791e14i		−	0.570627i	−0.958434	−	0.285314i	$-0.907902\pi$
$131$		−	3.77791e14i		−	0.570627i	0.958434	−	0.285314i	$-0.0920978\pi$
$132$	−1.50156e14	+	1.65779e14i	−0.215043	+	0.237416i
$133$	1.73475e14			0.235654
$134$			3.71530e14i			0.478916i
$135$	−4.74596e14			−0.580748
$136$	4.71723e14			0.548170
$137$	−1.11497e15			−1.23089			−0.615444	−	0.788181i	$-0.711023\pi$
$137$	−1.11497e15			−1.23089			−0.615444	+	0.788181i	$0.711023\pi$
$138$			7.55307e14i			0.792446i
$139$		−	2.80646e14i		−	0.279934i	−0.990156	−	0.139967i	$-0.955300\pi$
$139$		−	2.80646e14i		−	0.279934i	0.990156	−	0.139967i	$-0.0446996\pi$
$140$		−	1.82561e14i		−	0.173186i
$141$	−6.16642e14			−0.556544
$142$			8.17814e13i			0.0702483i
$143$	1.28695e15	+	1.16567e15i	1.05247	+	0.953286i
$144$	−1.89237e14			−0.147390
$145$			1.33918e15i			0.993719i
$146$	−5.06448e14			−0.358150
$147$	5.99711e14			0.404316
$148$	6.70369e14			0.431005
$149$		−	1.06640e15i		−	0.654058i	−0.945014	−	0.327029i	$-0.893952\pi$
$149$		−	1.06640e15i		−	0.654058i	0.945014	−	0.327029i	$-0.106048\pi$
$150$		−	5.22292e14i		−	0.305685i
$151$			3.30485e15i			1.84634i	0.384387	+	0.923172i	$0.374413\pi$
$151$			3.30485e15i			1.84634i	−0.384387	+	0.923172i	$0.625587\pi$
$152$	−2.57145e14			−0.137175
$153$		−	1.79402e15i		−	0.914088i
$154$	−5.92266e14	+	6.53887e14i	−0.288318	+	0.318315i
$155$	−2.33027e15			−1.08414
$156$		−	1.02273e15i		−	0.454871i
$157$	2.08995e14			0.0888872			0.0444436	−	0.999012i	$-0.485848\pi$
$157$	2.08995e14			0.0888872			0.0444436	+	0.999012i	$0.485848\pi$
$158$	−1.56720e15			−0.637567
$159$	9.15490e13			0.0356347
$160$			2.70615e14i			0.100812i
$161$			2.97919e15i			1.06247i
$162$		−	1.30154e14i		−	0.0444481i
$163$	8.66349e14			0.283387			0.141693	−	0.989911i	$-0.454745\pi$
$163$	8.66349e14			0.283387			0.141693	+	0.989911i	$0.454745\pi$
$164$		−	3.27727e14i		−	0.102708i
$165$	8.16637e14	−	9.01602e14i	0.245268	−	0.270787i
$166$	2.70005e15			0.777348
$167$			1.92780e14i			0.0532165i	0.999646	+	0.0266083i	$0.00847068\pi$
$167$			1.92780e14i			0.0532165i	−0.999646	+	0.0266083i	$0.991529\pi$
$168$	5.19639e14			0.137574
$169$	−4.00212e15			−1.01644
$170$	−2.56551e15			−0.625218
$171$			9.77956e14i			0.228742i
$172$		−	1.49437e15i		−	0.335552i
$173$		−	7.07158e15i		−	1.52473i	−0.647146	−	0.762366i	$-0.724038\pi$
$173$		−	7.07158e15i		−	1.52473i	0.647146	−	0.762366i	$-0.275962\pi$
$174$	−3.81181e15			−0.789382
$175$		−	2.06010e15i		−	0.409846i
$176$	8.77928e14	−	9.69270e14i	0.167830	−	0.185292i
$177$	6.52901e15			1.19959
$178$			1.45316e15i			0.256669i
$179$	9.57242e15			1.62574			0.812869	−	0.582447i	$-0.197905\pi$
$179$	9.57242e15			1.62574			0.812869	+	0.582447i	$0.197905\pi$
$180$	1.02918e15			0.168106
$181$	2.41304e15			0.379152			0.189576	−	0.981866i	$-0.439289\pi$
$181$	2.41304e15			0.379152			0.189576	+	0.981866i	$0.439289\pi$
$182$		−	4.03398e15i		−	0.609866i
$183$		−	3.25444e15i		−	0.473498i
$184$		−	4.41611e15i		−	0.618465i
$185$	−3.64586e15			−0.491585
$186$		−	6.63283e15i		−	0.861208i
$187$	9.18898e15	+	8.32303e15i	1.14915	+	1.04085i
$188$	3.60537e15			0.434355
$189$		−	5.32833e15i		−	0.618527i
$190$	1.39851e15			0.156455
$191$	−5.01318e14			−0.0540604			−0.0270302	−	0.999635i	$-0.508605\pi$
$191$	−5.01318e14			−0.0540604			−0.0270302	+	0.999635i	$0.508605\pi$
$192$	−7.70271e14			−0.0800820
$193$			6.10305e15i			0.611851i	0.952056	+	0.305925i	$0.0989658\pi$
$193$			6.10305e15i			0.611851i	−0.952056	+	0.305925i	$0.901034\pi$
$194$			7.29430e15i			0.705296i
$195$			5.56220e15i			0.518805i
$196$	−3.50637e15			−0.315548
$197$			1.25611e16i			1.09085i	0.838160	+	0.545425i	$0.183632\pi$
$197$			1.25611e16i			1.09085i	−0.838160	+	0.545425i	$0.816368\pi$
$198$	−3.68625e15	−	3.33887e15i	−0.308979	−	0.279862i
$199$	9.55075e15			0.772798			0.386399	−	0.922332i	$-0.373719\pi$
$199$	9.55075e15			0.772798			0.386399	+	0.922332i	$0.373719\pi$
$200$			3.05372e15i			0.238572i
$201$	5.75138e15			0.433910
$202$	−1.49809e16			−1.09163
$203$	−1.50351e16			−1.05836
$204$		−	7.30241e15i		−	0.496655i
$205$			1.78238e15i			0.117145i
$206$			2.05586e15i			0.130594i
$207$	−1.67950e16			−1.03131
$208$			5.97966e15i			0.355004i
$209$	−5.00909e15	−	4.53704e15i	−0.287564	−	0.260465i
$210$	−2.82610e15			−0.156911
$211$		−	1.50220e15i		−	0.0806771i	−0.999186	−	0.0403386i	$-0.987156\pi$
$211$		−	1.50220e15i		−	0.0806771i	0.999186	−	0.0403386i	$-0.0128436\pi$
$212$	−5.35266e14			−0.0278111
$213$	1.26600e15			0.0636467
$214$	2.28951e16			1.11390
$215$			8.12727e15i			0.382715i
$216$			7.89829e15i			0.360045i
$217$		−	2.61621e16i		−	1.15466i
$218$	1.08368e16			0.463134
$219$			7.83995e15i			0.324492i
$220$	−4.77469e15	+	5.27146e15i	−0.191420	+	0.211335i
$221$	−5.66890e16			−2.20167
$222$		−	1.03775e16i		−	0.390501i
$223$	1.08557e16			0.395845			0.197922	−	0.980218i	$-0.436581\pi$
$223$	1.08557e16			0.395845			0.197922	+	0.980218i	$0.436581\pi$
$224$	−3.03821e15			−0.107370
$225$	1.16137e16			0.397825
$226$			3.71732e16i			1.23444i
$227$		−	3.02033e16i		−	0.972462i	−0.873830	−	0.486231i	$-0.838371\pi$
$227$		−	3.02033e16i		−	0.972462i	0.873830	−	0.486231i	$-0.161629\pi$
$228$			3.98068e15i			0.124284i
$229$	−4.99647e16			−1.51292			−0.756458	−	0.654042i	$-0.773072\pi$
$229$	−4.99647e16			−1.51292			−0.756458	+	0.654042i	$0.773072\pi$
$230$			2.40174e16i			0.705393i
$231$	1.01223e16	+	9.16844e15i	0.288401	+	0.261223i
$232$	2.22868e16			0.616073
$233$		−	1.89908e16i		−	0.509390i	−0.967021	−	0.254695i	$-0.918025\pi$
$233$		−	1.89908e16i		−	0.509390i	0.967021	−	0.254695i	$-0.0819751\pi$
$234$	2.27414e16			0.591978
$235$	−1.96081e16			−0.495405
$236$	−3.81736e16			−0.936223
$237$			2.42607e16i			0.577651i
$238$		−	2.88032e16i		−	0.665889i
$239$			3.61451e16i			0.811455i	0.913994	+	0.405727i	$0.132982\pi$
$239$			3.61451e16i			0.811455i	−0.913994	+	0.405727i	$0.867018\pi$
$240$	4.18919e15			0.0913379
$241$		−	1.31732e16i		−	0.278980i	−0.990223	−	0.139490i	$-0.955454\pi$
$241$		−	1.31732e16i		−	0.278980i	0.990223	−	0.139490i	$-0.0445463\pi$
$242$	3.42034e16	−	3.39092e15i	0.703657	−	0.0697606i
$243$	4.89354e16			0.978090
$244$			1.90280e16i			0.369542i
$245$	1.90697e16			0.359900
$246$	−5.07331e15			−0.0930563
$247$	3.09023e16			0.550949
$248$			3.87806e16i			0.672130i
$249$		−	4.17975e16i		−	0.704296i
$250$		−	4.12202e16i		−	0.675352i
$251$	−1.42760e16			−0.227453			−0.113726	−	0.993512i	$-0.536279\pi$
$251$	−1.42760e16			−0.227453			−0.113726	+	0.993512i	$0.536279\pi$
$252$			1.15547e16i			0.179042i
$253$	7.79173e16	−	8.60240e16i	1.17433	−	1.29651i
$254$	5.14084e16			0.753699
$255$			3.97148e16i			0.566462i
$256$	4.50360e15			0.0625000
$257$	3.16361e15			0.0427220			0.0213610	−	0.999772i	$-0.493200\pi$
$257$	3.16361e15			0.0427220			0.0213610	+	0.999772i	$0.493200\pi$
$258$	−2.31333e16			−0.304018
$259$		−	4.09324e16i		−	0.523563i
$260$		−	3.25209e16i		−	0.404901i
$261$		−	8.47596e16i		−	1.02732i
$262$	3.41937e16			0.403494
$263$			1.22750e16i			0.141037i	0.997510	+	0.0705184i	$0.0224653\pi$
$263$			1.22750e16i			0.141037i	−0.997510	+	0.0705184i	$0.977535\pi$
$264$	−1.50046e16	−	1.35906e16i	−0.167879	−	0.152058i
$265$	2.91109e15			0.0317201
$266$			1.57012e16i			0.166633i
$267$	2.24953e16			0.232548
$268$	−3.36270e16			−0.338645
$269$	−4.77504e16			−0.468502			−0.234251	−	0.972176i	$-0.575264\pi$
$269$	−4.77504e16			−0.468502			−0.234251	+	0.972176i	$0.575264\pi$
$270$		−	4.29556e16i		−	0.410651i
$271$			3.07940e16i			0.286867i	0.989660	+	0.143434i	$0.0458143\pi$
$271$			3.07940e16i			0.286867i	−0.989660	+	0.143434i	$0.954186\pi$
$272$			4.26955e16i			0.387615i
$273$	−6.24472e16			−0.552554
$274$		−	1.00915e17i		−	0.870369i
$275$	−5.38795e16	+	5.94852e16i	−0.452996	+	0.500127i
$276$	−6.83626e16			−0.560344
$277$		−	5.20244e16i		−	0.415766i	−0.978154	−	0.207883i	$-0.933343\pi$
$277$		−	5.20244e16i		−	0.415766i	0.978154	−	0.207883i	$-0.0666573\pi$
$278$	2.54012e16			0.197943
$279$	1.47488e17			1.12080
$280$	1.65236e16			0.122461
$281$			2.67661e17i			1.93482i	0.253215	+	0.967410i	$0.418512\pi$
$281$			2.67661e17i			1.93482i	−0.253215	+	0.967410i	$0.581488\pi$
$282$		−	5.58121e16i		−	0.393536i
$283$		−	4.00336e16i		−	0.275372i	−0.990476	−	0.137686i	$-0.956033\pi$
$283$		−	4.00336e16i		−	0.275372i	0.990476	−	0.137686i	$-0.0439665\pi$
$284$	−7.40201e15			−0.0496731
$285$		−	2.16493e16i		−	0.141752i
$286$	−1.05504e17	+	1.16481e17i	−0.674075	+	0.744207i
$287$	−2.00109e16			−0.124765
$288$		−	1.71278e16i		−	0.104220i
$289$	−2.36389e17			−1.40392
$290$	−1.21209e17			−0.702665
$291$	1.12918e17			0.639015
$292$		−	4.58384e16i		−	0.253250i
$293$		−	1.80667e17i		−	0.974553i	−0.873248	−	0.487276i	$-0.837990\pi$
$293$		−	1.80667e17i		−	0.974553i	0.873248	−	0.487276i	$-0.162010\pi$
$294$			5.42796e16i			0.285894i
$295$	2.07611e17			1.06781
$296$			6.06749e16i			0.304766i
$297$	−1.39356e17	+	1.53855e17i	−0.683647	+	0.754775i
$298$	9.65196e16			0.462489
$299$			5.30703e17i			2.48401i
$300$	4.72724e16			0.216152
$301$	−9.12455e16			−0.407611
$302$	−2.99121e17			−1.30556
$303$			2.31908e17i			0.989047i
$304$		−	2.32741e16i		−	0.0969971i
$305$		−	1.03485e17i		−	0.421483i
$306$	1.62376e17			0.646358
$307$		−	2.38140e16i		−	0.0926538i	−0.998926	−	0.0463269i	$-0.985248\pi$
$307$		−	2.38140e16i		−	0.0926538i	0.998926	−	0.0463269i	$-0.0147516\pi$
$308$	−5.91831e16	−	5.36058e16i	−0.225083	−	0.203872i
$309$	3.18253e16			0.118321
$310$		−	2.10912e17i		−	0.766601i
$311$	−5.57514e16			−0.198122			−0.0990611	−	0.995081i	$-0.531584\pi$
$311$	−5.57514e16			−0.198122			−0.0990611	+	0.995081i	$0.531584\pi$
$312$	9.25667e16			0.321642
$313$	2.17904e17			0.740379			0.370189	−	0.928956i	$-0.379293\pi$
$313$	2.17904e17			0.740379			0.370189	+	0.928956i	$0.379293\pi$
$314$			1.89161e16i			0.0628528i
$315$		−	6.28412e16i		−	0.204207i
$316$		−	1.41847e17i		−	0.450828i
$317$	−3.85519e17			−1.19848			−0.599241	−	0.800569i	$-0.704531\pi$
$317$	−3.85519e17			−1.19848			−0.599241	+	0.800569i	$0.704531\pi$
$318$			8.28607e15i			0.0251976i
$319$	4.34138e17	+	3.93226e17i	1.29150	+	1.16979i
$320$	−2.44932e16			−0.0712847
$321$		−	3.54422e17i		−	1.00922i
$322$	−2.69645e17			−0.751280
$323$	2.20646e17			0.601560
$324$	1.17802e16			0.0314295
$325$		−	3.66979e17i		−	0.958203i
$326$			7.84130e16i			0.200385i
$327$		−	1.67757e17i		−	0.419611i
$328$	2.96625e16			0.0726258
$329$		−	2.20142e17i		−	0.527632i
$330$	8.16037e16	+	7.39135e16i	0.191475	+	0.173431i
$331$	−5.06864e17			−1.16438			−0.582191	−	0.813052i	$-0.697804\pi$
$331$	−5.06864e17			−1.16438			−0.582191	+	0.813052i	$0.697804\pi$
$332$			2.44381e17i			0.549668i
$333$	2.30754e17			0.508206
$334$	−1.74485e16			−0.0376298
$335$	1.82884e17			0.386243
$336$			4.70323e16i			0.0972795i
$337$		−	9.27596e17i		−	1.87910i	−0.342413	−	0.939550i	$-0.611244\pi$
$337$		−	9.27596e17i		−	1.87910i	0.342413	−	0.939550i	$-0.388756\pi$
$338$		−	3.62230e17i		−	0.718734i
$339$	5.75451e17			1.11843
$340$		−	2.32203e17i		−	0.442096i
$341$	−6.84241e17	+	7.55431e17i	−1.27623	+	1.40901i
$342$	−8.85145e16			−0.161745
$343$			5.53344e17i			0.990686i
$344$	1.35255e17			0.237271
$345$	3.71796e17			0.639103
$346$	6.40046e17			1.07815
$347$			4.61795e17i			0.762330i	0.924507	+	0.381165i	$0.124477\pi$
$347$			4.61795e17i			0.762330i	−0.924507	+	0.381165i	$0.875523\pi$
$348$		−	3.45006e17i		−	0.558177i
$349$		−	8.73084e17i		−	1.38445i	−0.721680	−	0.692226i	$-0.756630\pi$
$349$		−	8.73084e17i		−	1.38445i	0.721680	−	0.692226i	$-0.243370\pi$
$350$	1.86459e17			0.289805
$351$		−	9.49171e17i		−	1.44609i
$352$	8.77283e16	+	7.94610e16i	0.131021	+	0.118674i
$353$	−2.80817e17			−0.411151			−0.205575	−	0.978641i	$-0.565907\pi$
$353$	−2.80817e17			−0.411151			−0.205575	+	0.978641i	$0.565907\pi$
$354$			5.90938e17i			0.848241i
$355$	4.02565e16			0.0566549
$356$	−1.31525e17			−0.181492
$357$	−4.45881e17			−0.603311
$358$			8.66396e17i			1.14957i
$359$		−	1.00439e17i		−	0.130690i	−0.997863	−	0.0653449i	$-0.979185\pi$
$359$		−	1.00439e17i		−	0.130690i	0.997863	−	0.0653449i	$-0.0208148\pi$
$360$			9.31508e16i			0.118869i
$361$	6.78728e17			0.849465
$362$			2.18403e17i			0.268101i
$363$	−5.24924e16	−	5.29477e17i	−0.0632048	−	0.637531i
$364$	3.65115e17			0.431240
$365$			2.49296e17i			0.288846i
$366$	2.94558e17			0.334814
$367$	8.99975e17			1.00362			0.501808	−	0.864979i	$-0.332668\pi$
$367$	8.99975e17			1.00362			0.501808	+	0.864979i	$0.332668\pi$
$368$	3.99701e17			0.437321
$369$		−	1.12810e17i		−	0.121105i
$370$		−	3.29986e17i		−	0.347603i
$371$			3.26831e16i			0.0337836i
$372$	6.00335e17			0.608966
$373$			7.89739e17i			0.786179i	0.919500	+	0.393090i	$0.128594\pi$
$373$			7.89739e17i			0.786179i	−0.919500	+	0.393090i	$0.871406\pi$
$374$	−7.53315e17	+	8.31691e17i	−0.735996	+	0.812570i
$375$	−6.38100e17			−0.611885
$376$			3.26320e17i			0.307135i
$377$	−2.67830e18			−2.47440
$378$	4.82265e17			0.437364
$379$	−1.33167e18			−1.18555			−0.592776	−	0.805367i	$-0.701968\pi$
$379$	−1.33167e18			−1.18555			−0.592776	+	0.805367i	$0.701968\pi$
$380$			1.26579e17i			0.110631i
$381$		−	7.95816e17i		−	0.682870i
$382$		−	4.53741e16i		−	0.0382265i
$383$	−5.71497e15			−0.00472740			−0.00236370	−	0.999997i	$-0.500752\pi$
$383$	−5.71497e15			−0.00472740			−0.00236370	+	0.999997i	$0.500752\pi$
$384$		−	6.97170e16i		−	0.0566265i
$385$	3.21873e17	+	2.91540e17i	0.256719	+	0.232527i
$386$	−5.52385e17			−0.432644
$387$		−	5.14392e17i		−	0.395656i
$388$	−6.60204e17			−0.498719
$389$	−6.26024e17			−0.464455			−0.232227	−	0.972662i	$-0.574601\pi$
$389$	−6.26024e17			−0.464455			−0.232227	+	0.972662i	$0.574601\pi$
$390$	−5.03433e17			−0.366850
$391$			3.78929e18i			2.71219i
$392$		−	3.17361e17i		−	0.223126i
$393$		−	5.29328e17i		−	0.365576i
$394$	−1.13690e18			−0.771347
$395$			7.71448e17i			0.514194i
$396$	3.02200e17	−	3.33642e17i	0.197892	−	0.218481i
$397$	1.53271e18			0.986114			0.493057	−	0.869997i	$-0.335879\pi$
$397$	1.53271e18			0.986114			0.493057	+	0.869997i	$0.335879\pi$
$398$			8.64435e17i			0.546451i
$399$	2.43058e17			0.150973
$400$	−2.76391e17			−0.168696
$401$	1.51669e17			0.0909677			0.0454839	−	0.998965i	$-0.485517\pi$
$401$	1.51669e17			0.0909677			0.0454839	+	0.998965i	$0.485517\pi$
$402$			5.20555e17i			0.306821i
$403$		−	4.66044e18i		−	2.69955i
$404$		−	1.35591e18i		−	0.771902i
$405$	−6.40678e16			−0.0358471
$406$		−	1.36082e18i		−	0.748374i
$407$	−1.07054e18	+	1.18192e18i	−0.578685	+	0.638893i
$408$	6.60938e17			0.351188
$409$			2.75601e18i			1.43952i	0.694223	+	0.719760i	$0.255748\pi$
$409$			2.75601e18i			1.43952i	−0.694223	+	0.719760i	$0.744252\pi$
$410$	−1.61322e17			−0.0828337
$411$	−1.56220e18			−0.788576
$412$	−1.86075e17			−0.0923440
$413$			2.33086e18i			1.13728i
$414$		−	1.52011e18i		−	0.729244i
$415$		−	1.32909e18i		−	0.626926i
$416$	−5.41217e17			−0.251026
$417$		−	3.93217e17i		−	0.179341i
$418$	4.10646e17	−	4.53371e17i	0.184176	−	0.203339i
$419$	1.86113e18			0.820878			0.410439	−	0.911888i	$-0.365376\pi$
$419$	1.86113e18			0.820878			0.410439	+	0.911888i	$0.365376\pi$
$420$		−	2.55790e17i		−	0.110953i
$421$	4.33538e18			1.84949			0.924747	−	0.380583i	$-0.124277\pi$
$421$	4.33538e18			1.84949			0.924747	+	0.380583i	$0.124277\pi$
$422$	1.35964e17			0.0570473
$423$	1.24104e18			0.512156
$424$		−	4.84468e16i		−	0.0196654i
$425$		−	2.62028e18i		−	1.04622i
$426$			1.14585e17i			0.0450050i
$427$	1.16184e18			0.448900
$428$			2.07222e18i			0.787644i
$429$	1.80316e18	+	1.63324e18i	0.674270	+	0.610728i
$430$	−7.35597e17			−0.270620
$431$		−	1.64854e18i		−	0.596702i	−0.954456	−	0.298351i	$-0.903563\pi$
$431$		−	1.64854e18i		−	0.596702i	0.954456	−	0.298351i	$-0.0964366\pi$
$432$	−7.14872e17			−0.254590
$433$	8.32776e17			0.291819			0.145909	−	0.989298i	$-0.453389\pi$
$433$	8.32776e17			0.291819			0.145909	+	0.989298i	$0.453389\pi$
$434$	2.36793e18			0.816469
$435$			1.87635e18i			0.636632i
$436$			9.80837e17i			0.327485i
$437$		−	2.06561e18i		−	0.678701i
$438$	−7.09591e17			−0.229451
$439$			1.03162e18i			0.328299i	0.986435	+	0.164149i	$0.0524879\pi$
$439$			1.03162e18i			0.328299i	−0.986435	+	0.164149i	$0.947512\pi$
$440$	−4.77118e17	−	4.32156e17i	−0.149437	−	0.135354i
$441$	−1.20696e18			−0.372069
$442$		−	5.13090e18i		−	1.55682i
$443$	−7.21037e17			−0.215343			−0.107672	−	0.994187i	$-0.534340\pi$
$443$	−7.21037e17			−0.215343			−0.107672	+	0.994187i	$0.534340\pi$
$444$	9.39264e17			0.276126
$445$	7.15311e17			0.207002
$446$			9.82548e17i			0.279905i
$447$		−	1.49415e18i		−	0.419026i
$448$		−	2.74987e17i		−	0.0759218i
$449$	1.38619e18			0.376788			0.188394	−	0.982094i	$-0.439672\pi$
$449$	1.38619e18			0.376788			0.188394	+	0.982094i	$0.439672\pi$
$450$			1.05115e18i			0.281305i
$451$	5.77813e17	+	5.23362e17i	0.152248	+	0.137901i
$452$	−3.36453e18			−0.872882
$453$			4.63047e18i			1.18287i
$454$	2.73369e18			0.687635
$455$	−1.98571e18			−0.491854
$456$	−3.60290e17			−0.0878817
$457$			3.45729e18i			0.830467i	0.909715	+	0.415233i	$0.136300\pi$
$457$			3.45729e18i			0.830467i	−0.909715	+	0.415233i	$0.863700\pi$
$458$		−	4.52229e18i		−	1.06979i
$459$		−	6.77720e18i		−	1.57893i
$460$	−2.17381e18			−0.498788
$461$		−	4.51090e18i		−	1.01943i	−0.860344	−	0.509715i	$-0.829751\pi$
$461$		−	4.51090e18i		−	1.01943i	0.860344	−	0.509715i	$-0.170249\pi$
$462$	−8.29833e17	+	9.16170e17i	−0.184713	+	0.203931i
$463$	2.92961e18			0.642308			0.321154	−	0.947027i	$-0.395929\pi$
$463$	2.92961e18			0.642308			0.321154	+	0.947027i	$0.395929\pi$
$464$			2.01717e18i			0.435629i
$465$	−3.26498e18			−0.694559
$466$	1.71885e18			0.360193
$467$	−4.71846e18			−0.974051			−0.487026	−	0.873388i	$-0.661918\pi$
$467$	−4.71846e18			−0.974051			−0.487026	+	0.873388i	$0.661918\pi$
$468$			2.05832e18i			0.418592i
$469$			2.05325e18i			0.411369i
$470$		−	1.77472e18i		−	0.350304i
$471$	2.92827e17			0.0569461
$472$		−	3.45508e18i		−	0.662010i
$473$	2.63471e18	+	2.38642e18i	0.497399	+	0.450526i
$474$	−2.19583e18			−0.408461
$475$			1.42836e18i			0.261808i
$476$	2.60697e18			0.470854
$477$	−1.84249e17			−0.0327927
$478$	−3.27148e18			−0.573785
$479$			6.77631e18i			1.17124i	0.810587	+	0.585618i	$0.199148\pi$
$479$			6.77631e18i			1.17124i	−0.810587	+	0.585618i	$0.800852\pi$
$480$			3.79162e17i			0.0645857i
$481$		−	7.29156e18i		−	1.22407i
$482$	1.19231e18			0.197269
$483$			4.17418e18i			0.680678i
$484$	3.06911e17	+	3.09573e18i	0.0493282	+	0.497561i
$485$	3.59058e18			0.568817
$486$			4.42912e18i			0.691614i
$487$	−7.82487e17			−0.120441			−0.0602205	−	0.998185i	$-0.519180\pi$
$487$	−7.82487e17			−0.120441			−0.0602205	+	0.998185i	$0.519180\pi$
$488$	−1.72221e18			−0.261305
$489$	1.21385e18			0.181554
$490$			1.72599e18i			0.254488i
$491$		−	6.43020e18i		−	0.934661i	−0.884083	−	0.467330i	$-0.845216\pi$
$491$		−	6.43020e18i		−	0.934661i	0.884083	−	0.467330i	$-0.154784\pi$
$492$		−	4.59184e17i		−	0.0658007i
$493$	−1.91234e19			−2.70170
$494$			2.79695e18i			0.389580i
$495$	−1.64354e18	+	1.81454e18i	−0.225707	+	0.249190i
$496$	−3.51002e18			−0.475268
$497$			4.51963e17i			0.0603403i
$498$	3.78308e18			0.498012
$499$	−4.76326e18			−0.618301			−0.309151	−	0.951013i	$-0.600045\pi$
$499$	−4.76326e18			−0.618301			−0.309151	+	0.951013i	$0.600045\pi$
$500$	3.73083e18			0.477546
$501$			2.70107e17i			0.0340935i
$502$		−	1.29212e18i		−	0.160834i
$503$			6.80776e18i			0.835657i	0.908526	+	0.417828i	$0.137209\pi$
$503$			6.80776e18i			0.835657i	−0.908526	+	0.417828i	$0.862791\pi$
$504$	−1.04581e18			−0.126602
$505$			7.37425e18i			0.880397i
$506$	7.78600e18	+	7.05227e18i	0.916771	+	0.830377i
$507$	−5.60743e18			−0.651190
$508$			4.65296e18i			0.532946i
$509$	1.68967e19			1.90887			0.954435	−	0.298420i	$-0.0964596\pi$
$509$	1.68967e19			1.90887			0.954435	+	0.298420i	$0.0964596\pi$
$510$	−3.59457e18			−0.400549
$511$	−2.79887e18			−0.307635
$512$			4.07619e17i			0.0441942i
$513$			3.69438e18i			0.395112i
$514$			2.86337e17i			0.0302090i
$515$	1.01199e18			0.105323
$516$		−	2.09378e18i		−	0.214973i
$517$	−5.75756e18	+	6.35659e18i	−0.583183	+	0.643858i
$518$	3.70478e18			0.370215
$519$		−	9.90809e18i		−	0.976829i
$520$	2.94346e18			0.286308
$521$	−9.17150e18			−0.880190			−0.440095	−	0.897951i	$-0.645055\pi$
$521$	−9.17150e18			−0.880190			−0.440095	+	0.897951i	$0.645055\pi$
$522$	7.67156e18			0.726424
$523$		−	8.42801e18i		−	0.787432i	−0.919232	−	0.393716i	$-0.871189\pi$
$523$		−	8.42801e18i		−	0.787432i	0.919232	−	0.393716i	$-0.128811\pi$
$524$			3.09486e18i			0.285314i
$525$		−	2.88643e18i		−	0.262570i
$526$	−1.11101e18			−0.0997281
$527$		−	3.32761e19i		−	2.94753i
$528$	1.23008e18	−	1.35806e18i	0.107521	−	0.118708i
$529$	2.38811e19			2.05999
$530$			2.63482e17i			0.0224295i
$531$	−1.31401e19			−1.10392
$532$	−1.42111e18			−0.117827
$533$	−3.56467e18			−0.291695
$534$			2.03604e18i			0.164436i
$535$		−	1.12700e19i		−	0.898352i
$536$		−	3.04357e18i		−	0.239458i
$537$	1.34121e19			1.04154
$538$		−	4.32187e18i		−	0.331281i
$539$	5.59947e18	−	6.18205e18i	0.423668	−	0.467748i
$540$	3.88789e18			0.290374
$541$			7.48006e18i			0.551473i	0.961233	+	0.275737i	$0.0889217\pi$
$541$			7.48006e18i			0.551473i	−0.961233	+	0.275737i	$0.911078\pi$
$542$	−2.78715e18			−0.202846
$543$	3.38094e18			0.242906
$544$	−3.86436e18			−0.274085
$545$		−	5.33437e18i		−	0.373515i
$546$		−	5.65207e18i		−	0.390714i
$547$			3.69682e18i			0.252300i	0.992011	+	0.126150i	$0.0402620\pi$
$547$			3.69682e18i			0.252300i	−0.992011	+	0.126150i	$0.959738\pi$
$548$	9.13382e18			0.615444
$549$			6.54980e18i			0.435734i
$550$	−5.38399e18	−	4.87662e18i	−0.353643	−	0.320317i
$551$	1.04245e19			0.676077
$552$		−	6.18747e18i		−	0.396223i
$553$	−8.66111e18			−0.547643
$554$	4.70871e18			0.293991
$555$	−5.10827e18			−0.314937
$556$			2.29905e18i			0.139967i
$557$		−	1.46654e19i		−	0.881676i	−0.897587	−	0.440838i	$-0.854681\pi$
$557$		−	1.46654e19i		−	0.881676i	0.897587	−	0.440838i	$-0.145319\pi$
$558$			1.33491e19i			0.792522i
$559$	−1.62542e19			−0.952976
$560$			1.49554e18i			0.0865930i
$561$	1.28748e19	+	1.16615e19i	0.736208	+	0.666830i
$562$	−2.42259e19			−1.36812
$563$			2.13300e19i			1.18968i	0.803843	+	0.594842i	$0.202785\pi$
$563$			2.13300e19i			1.18968i	−0.803843	+	0.594842i	$0.797215\pi$
$564$	5.05153e18			0.278272
$565$	1.82983e19			0.995570
$566$	3.62343e18			0.194717
$567$		−	7.19293e17i		−	0.0381790i
$568$		−	6.69953e17i		−	0.0351242i
$569$			9.18181e18i			0.475491i	0.971327	+	0.237745i	$0.0764084\pi$
$569$			9.18181e18i			0.475491i	−0.971327	+	0.237745i	$0.923592\pi$
$570$	1.95947e18			0.100234
$571$			6.47840e18i			0.327352i	0.986514	+	0.163676i	$0.0523352\pi$
$571$			6.47840e18i			0.327352i	−0.986514	+	0.163676i	$0.947665\pi$
$572$	−1.05427e19	−	9.54916e18i	−0.526234	−	0.476643i
$573$	−7.02404e17			−0.0346341
$574$		−	1.81118e18i		−	0.0882221i
$575$	−2.45301e19			−1.18039
$576$	1.55023e18			0.0736950
$577$	2.22741e18			0.104609			0.0523046	−	0.998631i	$-0.483343\pi$
$577$	2.22741e18			0.104609			0.0523046	+	0.998631i	$0.483343\pi$
$578$		−	2.13955e19i		−	0.992721i
$579$			8.55107e18i			0.391986i
$580$		−	1.09706e19i		−	0.496859i
$581$	1.49218e19			0.667708
$582$			1.02201e19i			0.451852i
$583$	8.54789e17	−	9.43723e17i	0.0373404	−	0.0412254i
$584$	4.14882e18			0.179075
$585$		−	1.11943e19i		−	0.477427i
$586$	1.63521e19			0.689113
$587$	2.64010e19			1.09939			0.549697	−	0.835364i	$-0.314743\pi$
$587$	2.64010e19			1.09939			0.549697	+	0.835364i	$0.314743\pi$
$588$	−4.91283e18			−0.202158
$589$			1.81394e19i			0.737593i
$590$			1.87908e19i			0.755059i
$591$			1.75996e19i			0.698859i
$592$	−5.49166e18			−0.215502
$593$			1.81210e19i			0.702746i	0.936235	+	0.351373i	$0.114285\pi$
$593$			1.81210e19i			0.702746i	−0.936235	+	0.351373i	$0.885715\pi$
$594$	−1.39254e19	−	1.26131e19i	−0.533707	−	0.483411i
$595$	−1.41782e19			−0.537035
$596$			8.73595e18i			0.327029i
$597$	1.33817e19			0.495098
$598$	−4.80337e19			−1.75646
$599$	1.57659e19			0.569811			0.284905	−	0.958556i	$-0.408038\pi$
$599$	1.57659e19			0.569811			0.284905	+	0.958556i	$0.408038\pi$
$600$			4.27861e18i			0.152843i
$601$			2.80542e19i			0.990550i	0.868736	+	0.495275i	$0.164933\pi$
$601$			2.80542e19i			0.990550i	−0.868736	+	0.495275i	$0.835067\pi$
$602$		−	8.25860e18i		−	0.288224i
$603$	−1.15751e19			−0.399303
$604$		−	2.70733e19i		−	0.923172i
$605$	−1.66916e18	−	1.68364e19i	−0.0562615	−	0.567495i
$606$	−2.09899e19			−0.699362
$607$			2.61380e19i			0.860899i	0.902615	+	0.430449i	$0.141645\pi$
$607$			2.61380e19i			0.860899i	−0.902615	+	0.430449i	$0.858355\pi$
$608$	2.10654e18			0.0685873
$609$	−2.10659e19			−0.678045
$610$	9.36642e18			0.298033
$611$		−	3.92153e19i		−	1.23358i
$612$			1.46966e19i			0.457044i
$613$			2.57086e19i			0.790416i	0.918592	+	0.395208i	$0.129328\pi$
$613$			2.57086e19i			0.790416i	−0.918592	+	0.395208i	$0.870672\pi$
$614$	2.15540e18			0.0655161
$615$			2.49731e18i			0.0750494i
$616$	4.85184e18	−	5.35664e18i	0.144159	−	0.159158i
$617$	−2.82495e19			−0.829877			−0.414939	−	0.909849i	$-0.636197\pi$
$617$	−2.82495e19			−0.829877			−0.414939	+	0.909849i	$0.636197\pi$
$618$			2.88050e18i			0.0836659i
$619$	3.52025e18			0.101097			0.0505486	−	0.998722i	$-0.483903\pi$
$619$	3.52025e18			0.101097			0.0505486	+	0.998722i	$0.483903\pi$
$620$	1.90896e19			0.542069
$621$	−6.34458e19			−1.78140
$622$		−	5.04604e18i		−	0.140094i
$623$			8.03085e18i			0.220468i
$624$			8.37818e18i			0.227435i
$625$	4.84721e18			0.130116
$626$			1.97224e19i			0.523527i
$627$	−7.01831e18	−	6.35692e18i	−0.184230	−	0.166868i
$628$	−1.71209e18			−0.0444436
$629$		−	5.20627e19i		−	1.33651i
$630$	5.68774e18			0.144396
$631$	1.21876e19			0.305994			0.152997	−	0.988227i	$-0.451108\pi$
$631$	1.21876e19			0.305994			0.152997	+	0.988227i	$0.451108\pi$
$632$	1.28385e19			0.318783
$633$		−	2.10475e18i		−	0.0516863i
$634$		−	3.48932e19i		−	0.847454i
$635$		−	2.53055e19i		−	0.607854i
$636$	−7.49969e17			−0.0178174
$637$			3.81386e19i			0.896166i
$638$	−3.55908e19	+	3.92937e19i	−0.827165	+	0.913226i
$639$	−2.54792e18			−0.0585705
$640$		−	2.21687e18i		−	0.0504059i
$641$	−5.82127e19			−1.30922			−0.654609	−	0.755968i	$-0.727167\pi$
$641$	−5.82127e19			−1.30922			−0.654609	+	0.755968i	$0.727167\pi$
$642$	3.20786e19			0.713625
$643$	5.76007e19			1.26751			0.633755	−	0.773534i	$-0.281513\pi$
$643$	5.76007e19			1.26751			0.633755	+	0.773534i	$0.281513\pi$
$644$		−	2.44055e19i		−	0.531235i
$645$			1.13872e19i			0.245189i
$646$			1.99706e19i			0.425367i
$647$	5.89767e19			1.24265			0.621327	−	0.783551i	$-0.286594\pi$
$647$	5.89767e19			1.24265			0.621327	+	0.783551i	$0.286594\pi$
$648$			1.06622e18i			0.0222240i
$649$	6.09611e19	−	6.73036e19i	1.25701	−	1.38780i
$650$	3.32151e19			0.677552
$651$		−	3.66561e19i		−	0.739741i
$652$	−7.09713e18			−0.141693
$653$	6.31059e19			1.24646			0.623229	−	0.782039i	$-0.285820\pi$
$653$	6.31059e19			1.24646			0.623229	+	0.782039i	$0.285820\pi$
$654$	1.51836e19			0.296709
$655$		−	1.68317e19i		−	0.325416i
$656$			2.68474e18i			0.0513542i
$657$		−	1.57785e19i		−	0.298612i
$658$	1.99249e19			0.373092
$659$			1.88508e19i			0.349246i	0.984635	+	0.174623i	$0.0558706\pi$
$659$			1.88508e19i			0.349246i	−0.984635	+	0.174623i	$0.944129\pi$
$660$	−6.68989e18	+	7.38592e18i	−0.122634	+	0.135393i
$661$	6.06817e18			0.110065			0.0550323	−	0.998485i	$-0.482474\pi$
$661$	6.06817e18			0.110065			0.0550323	+	0.998485i	$0.482474\pi$
$662$		−	4.58761e19i		−	0.823343i
$663$	−7.94278e19			−1.41052
$664$	−2.21188e19			−0.388674
$665$	7.72882e18			0.134388
$666$			2.08855e19i			0.359356i
$667$			1.79027e20i			3.04816i
$668$		−	1.57925e18i		−	0.0266083i
$669$	1.52101e19			0.253600
$670$			1.65527e19i			0.273115i
$671$	−3.35480e19	−	3.03865e19i	−0.547784	−	0.496162i
$672$	−4.25688e18			−0.0687870
$673$		−	1.03614e20i		−	1.65696i	−0.560020	−	0.828479i	$-0.689207\pi$
$673$		−	1.03614e20i		−	1.65696i	0.560020	−	0.828479i	$-0.310793\pi$
$674$	8.39564e19			1.32872
$675$	4.38725e19			0.687173
$676$	3.27853e19			0.508221
$677$		−	1.15975e20i		−	1.77928i	−0.456665	−	0.889639i	$-0.650956\pi$
$677$		−	1.15975e20i		−	1.77928i	0.456665	−	0.889639i	$-0.349044\pi$
$678$			5.20839e19i			0.790853i
$679$			4.03117e19i			0.605819i
$680$	2.10167e19			0.312609
$681$		−	4.23182e19i		−	0.623014i
$682$	−6.83738e19	−	6.19304e19i	−0.996321	−	0.902430i
$683$	7.01893e19			1.01234			0.506170	−	0.862434i	$-0.331061\pi$
$683$	7.01893e19			1.01234			0.506170	+	0.862434i	$0.331061\pi$
$684$		−	8.01142e18i		−	0.114371i
$685$	−4.96751e19			−0.701948
$686$	−5.00830e19			−0.700521
$687$	−7.00063e19			−0.969259
$688$			1.22419e19i			0.167776i
$689$			5.82206e18i			0.0789845i
$690$			3.36511e19i			0.451914i
$691$	9.82030e19			1.30550			0.652752	−	0.757571i	$-0.273614\pi$
$691$	9.82030e19			1.30550			0.652752	+	0.757571i	$0.273614\pi$
$692$			5.79304e19i			0.762366i
$693$	−2.03720e19	−	1.84522e19i	−0.265400	−	0.240389i
$694$	−4.17969e19			−0.539049
$695$		−	1.25036e19i		−	0.159640i
$696$	3.12264e19			0.394691
$697$	−2.54522e19			−0.318490
$698$	7.90226e19			0.978956
$699$		−	2.66082e19i		−	0.326344i
$700$			1.68763e19i			0.204923i
$701$			8.99600e19i			1.08149i	0.841186	+	0.540746i	$0.181858\pi$
$701$			8.99600e19i			1.08149i	−0.841186	+	0.540746i	$0.818142\pi$
$702$	8.59092e19			1.02254
$703$			2.83804e19i			0.334450i
$704$	−7.19199e18	+	7.94026e18i	−0.0839151	+	0.0926458i
$705$	−2.74732e19			−0.317384
$706$		−	2.54167e19i		−	0.290727i
$707$	−8.27913e19			−0.937667
$708$	−5.34856e19			−0.599797
$709$	−9.16784e19			−1.01799			−0.508995	−	0.860769i	$-0.669983\pi$
$709$	−9.16784e19			−1.01799			−0.508995	+	0.860769i	$0.669983\pi$
$710$			3.64360e18i			0.0400611i
$711$		−	4.88265e19i		−	0.531580i
$712$		−	1.19043e19i		−	0.128334i
$713$	−3.11519e20			−3.32551
$714$		−	4.03565e19i		−	0.426606i
$715$	5.73373e19	+	5.19340e19i	0.600199	+	0.543638i
$716$	−7.84172e19			−0.812869
$717$			5.06434e19i			0.519863i
$718$	9.09071e18			0.0924116
$719$	2.76111e19			0.277959			0.138980	−	0.990295i	$-0.455618\pi$
$719$	2.76111e19			0.277959			0.138980	+	0.990295i	$0.455618\pi$
$720$	−8.43105e18			−0.0840532
$721$			1.13617e19i			0.112175i
$722$			6.14315e19i			0.600662i
$723$		−	1.84572e19i		−	0.178730i
$724$	−1.97676e19			−0.189576
$725$		−	1.23796e20i		−	1.17582i
$726$	4.79228e19	−	4.75107e18i	0.450802	−	0.0446925i
$727$	5.64446e19			0.525874			0.262937	−	0.964813i	$-0.415309\pi$
$727$	5.64446e19			0.525874			0.262937	+	0.964813i	$0.415309\pi$
$728$			3.30464e19i			0.304933i
$729$	7.54420e19			0.689478
$730$	−2.25637e19			−0.204245
$731$	−1.16057e20			−1.04052
$732$			2.66603e19i			0.236749i
$733$			1.84165e20i			1.61987i	0.586522	+	0.809933i	$0.300497\pi$
$733$			1.84165e20i			1.61987i	−0.586522	+	0.809933i	$0.699503\pi$
$734$			8.14564e19i			0.709664i
$735$	2.67189e19			0.230572
$736$			3.61768e19i			0.309232i
$737$	5.37004e19	−	5.92875e19i	0.454679	−	0.501985i
$738$	1.02104e19			0.0856345
$739$			1.21227e19i			0.100713i	0.998731	+	0.0503566i	$0.0160358\pi$
$739$			1.21227e19i			0.100713i	−0.998731	+	0.0503566i	$0.983964\pi$
$740$	2.98669e19			0.245792
$741$	4.32976e19			0.352969
$742$	−2.95813e18			−0.0238886
$743$			3.16066e19i			0.252846i	0.991976	+	0.126423i	$0.0403497\pi$
$743$			3.16066e19i			0.252846i	−0.991976	+	0.126423i	$0.959650\pi$
$744$			5.43361e19i			0.430604i
$745$		−	4.75113e19i		−	0.372995i
$746$	−7.14790e19			−0.555913
$747$			8.41206e19i			0.648124i
$748$	−7.52761e19	−	6.81823e19i	−0.574574	−	0.520427i
$749$	1.26529e20			0.956790
$750$		−	5.77542e19i		−	0.432668i
$751$	−1.26468e19			−0.0938643			−0.0469322	−	0.998898i	$-0.514944\pi$
$751$	−1.26468e19			−0.0938643			−0.0469322	+	0.998898i	$0.514944\pi$
$752$	−2.95352e19			−0.217177
$753$	−2.00024e19			−0.145719
$754$		−	2.42412e20i		−	1.74967i
$755$			1.47241e20i			1.05293i
$756$			4.36497e19i			0.309263i
$757$	8.53626e19			0.599234			0.299617	−	0.954060i	$-0.403141\pi$
$757$	8.53626e19			0.599234			0.299617	+	0.954060i	$0.403141\pi$
$758$		−	1.20529e20i		−	0.838313i
$759$	1.09171e20	−	1.20529e20i	0.752342	−	0.830617i
$760$	−1.14566e19			−0.0782276
$761$			1.39218e20i			0.941893i	0.882162	+	0.470947i	$0.156088\pi$
$761$			1.39218e20i			0.941893i	−0.882162	+	0.470947i	$0.843912\pi$
$762$	7.20291e19			0.482862
$763$	5.98894e19			0.397812
$764$	4.10680e18			0.0270302
$765$		−	7.99290e19i		−	0.521284i
$766$		−	5.17260e17i		−	0.00334278i
$767$			4.15212e20i			2.65890i
$768$	6.31006e18			0.0400410
$769$		−	9.95937e19i		−	0.626250i	−0.949712	−	0.313125i	$-0.898624\pi$
$769$		−	9.95937e19i		−	0.626250i	0.949712	−	0.313125i	$-0.101376\pi$
$770$	−2.63872e19	+	2.91326e19i	−0.164421	+	0.181528i
$771$	4.43258e18			0.0273701
$772$		−	4.99961e19i		−	0.305925i
$773$	−1.31503e20			−0.797405			−0.398702	−	0.917080i	$-0.630539\pi$
$773$	−1.31503e20			−0.797405			−0.398702	+	0.917080i	$0.630539\pi$
$774$	4.65574e19			0.279771
$775$	2.15414e20			1.28281
$776$		−	5.97549e19i		−	0.352648i
$777$		−	5.73510e19i		−	0.335424i
$778$		−	5.66612e19i		−	0.328419i
$779$	1.38745e19			0.0796993
$780$		−	4.55655e19i		−	0.259402i
$781$	1.18206e19	−	1.30504e19i	0.0666932	−	0.0736321i
$782$	−3.42967e20			−1.91781
$783$		−	3.20193e20i		−	1.77451i
$784$	2.87242e19			0.157774
$785$	9.31136e18			0.0506904
$786$	4.79093e19			0.258501
$787$		−	6.88236e19i		−	0.368056i	−0.982921	−	0.184028i	$-0.941086\pi$
$787$		−	6.88236e19i		−	0.368056i	0.982921	−	0.184028i	$-0.0589138\pi$
$788$		−	1.02901e20i		−	0.545425i
$789$			1.71987e19i			0.0903561i
$790$	−6.98235e19			−0.363590
$791$			2.05437e20i			1.06033i
$792$	3.01978e19	+	2.73520e19i	0.154489	+	0.139931i
$793$	2.06966e20			1.04951
$794$			1.38725e20i			0.697288i
$795$	4.07878e18			0.0203217
$796$	−7.82398e19			−0.386399
$797$	−4.10954e19			−0.201180			−0.100590	−	0.994928i	$-0.532073\pi$
$797$	−4.10954e19			−0.201180			−0.100590	+	0.994928i	$0.532073\pi$
$798$			2.19991e19i			0.106754i
$799$		−	2.80002e20i		−	1.34690i
$800$		−	2.50161e19i		−	0.119286i
$801$	−4.52735e19			−0.214001
$802$			1.37275e19i			0.0643239i
$803$	8.08173e19	+	7.32013e19i	0.375401	+	0.340024i
$804$	−4.71153e19			−0.216955
$805$			1.32732e20i			0.605903i
$806$	4.21815e20			1.90887
$807$	−6.69038e19			−0.300148
$808$	1.22723e20			0.545817
$809$		−	4.12688e20i		−	1.81963i	−0.415017	−	0.909814i	$-0.636224\pi$
$809$		−	4.12688e20i		−	1.81963i	0.415017	−	0.909814i	$-0.363776\pi$
$810$		−	5.79875e18i		−	0.0253477i
$811$		−	2.45584e20i		−	1.06427i	−0.846658	−	0.532137i	$-0.821389\pi$
$811$		−	2.45584e20i		−	1.06427i	0.846658	−	0.532137i	$-0.178611\pi$
$812$	1.23167e20			0.529180
$813$			4.31459e19i			0.183783i
$814$	−1.06975e20	−	9.68943e19i	−0.451765	−	0.409192i
$815$	3.85984e19			0.161609
$816$			5.98213e19i			0.248328i
$817$	6.32648e19			0.260380
$818$	−2.49445e20			−1.01789
$819$	1.25680e20			0.508484
$820$		−	1.46012e19i		−	0.0585723i
$821$			8.53756e19i			0.339572i	0.985481	+	0.169786i	$0.0543076\pi$
$821$			8.53756e19i			0.339572i	−0.985481	+	0.169786i	$0.945692\pi$
$822$		−	1.41394e20i		−	0.557607i
$823$	−2.70456e20			−1.05754			−0.528771	−	0.848765i	$-0.677347\pi$
$823$	−2.70456e20			−1.05754			−0.528771	+	0.848765i	$0.677347\pi$
$824$		−	1.68416e19i		−	0.0652971i
$825$	−7.54913e19	+	8.33456e19i	−0.290215	+	0.320409i
$826$	−2.10965e20			−0.804176
$827$			3.13557e19i			0.118516i	0.998243	+	0.0592582i	$0.0188735\pi$
$827$			3.13557e19i			0.118516i	−0.998243	+	0.0592582i	$0.981126\pi$
$828$	1.37585e20			0.515654
$829$	3.90331e19			0.145061			0.0725306	−	0.997366i	$-0.476892\pi$
$829$	3.90331e19			0.145061			0.0725306	+	0.997366i	$0.476892\pi$
$830$	1.20295e20			0.443304
$831$		−	7.28921e19i		−	0.266363i
$832$		−	4.89854e19i		−	0.177502i
$833$			2.72314e20i			0.978488i
$834$	3.55900e19			0.126813
$835$			8.58891e18i			0.0303482i
$836$	4.10344e19	+	3.71675e19i	0.143782	+	0.130232i
$837$	5.57158e20			1.93598
$838$			1.68450e20i			0.580448i
$839$	−2.47164e20			−0.844601			−0.422301	−	0.906456i	$-0.638777\pi$
$839$	−2.47164e20			−0.844601			−0.422301	+	0.906456i	$0.638777\pi$
$840$	2.31514e19			0.0784554
$841$	−6.05938e20			−2.03637
$842$			3.92394e20i			1.30779i
$843$			3.75024e20i			1.23955i
$844$			1.23060e19i			0.0403386i
$845$	−1.78306e20			−0.579654
$846$			1.12326e20i			0.362149i
$847$	1.89024e20	−	1.87398e19i	0.604412	−	0.0599214i
$848$	4.38490e18			0.0139056
$849$		−	5.60917e19i		−	0.176419i
$850$	2.37160e20			0.739792
$851$	−4.87393e20			−1.50790
$852$	−1.03711e19			−0.0318234
$853$			2.27660e20i			0.692856i	0.938077	+	0.346428i	$0.112605\pi$
$853$			2.27660e20i			0.692856i	−0.938077	+	0.346428i	$0.887395\pi$
$854$			1.05157e20i			0.317421i
$855$			4.35708e19i			0.130447i
$856$	−1.87556e20			−0.556949
$857$		−	1.67588e19i		−	0.0493601i	−0.999695	−	0.0246801i	$-0.992143\pi$
$857$		−	1.67588e19i		−	0.0493601i	0.999695	−	0.0246801i	$-0.00785670\pi$
$858$	−1.47824e20	+	1.63204e20i	−0.431850	+	0.476781i
$859$	4.43619e20			1.28546			0.642730	−	0.766093i	$-0.277802\pi$
$859$	4.43619e20			1.28546			0.642730	+	0.766093i	$0.277802\pi$
$860$		−	6.65786e19i		−	0.191358i
$861$	−2.80375e19			−0.0799314
$862$	1.49208e20			0.421932
$863$	−4.56533e20			−1.28055			−0.640275	−	0.768146i	$-0.721179\pi$
$863$	−4.56533e20			−1.28055			−0.640275	+	0.768146i	$0.721179\pi$
$864$		−	6.47028e19i		−	0.180022i
$865$		−	3.15060e20i		−	0.869521i
$866$			7.53743e19i			0.206347i
$867$	−3.31208e20			−0.899430
$868$			2.14320e20i			0.577331i
$869$	2.50089e20	+	2.26522e20i	0.668277	+	0.605300i
$870$	−1.69828e20			−0.450167
$871$			3.65759e20i			0.961762i
$872$	−8.87752e19			−0.231567
$873$	−2.27255e20			−0.588050
$874$	1.86958e20			0.479914
$875$		−	2.27802e20i		−	0.580098i
$876$		−	6.42249e19i		−	0.162246i
$877$		−	7.77903e19i		−	0.194952i	−0.995238	−	0.0974761i	$-0.968923\pi$
$877$		−	7.77903e19i		−	0.194952i	0.995238	−	0.0974761i	$-0.0310770\pi$
$878$	−9.33719e19			−0.232142
$879$		−	2.53135e20i		−	0.624353i
$880$	3.91143e19	−	4.31838e19i	0.0957098	−	0.105668i
$881$	−2.23289e20			−0.542046			−0.271023	−	0.962573i	$-0.587362\pi$
$881$	−2.23289e20			−0.542046			−0.271023	+	0.962573i	$0.587362\pi$
$882$		−	1.09242e20i		−	0.263093i
$883$	−5.66430e20			−1.35338			−0.676692	−	0.736266i	$-0.736587\pi$
$883$	−5.66430e20			−1.35338			−0.676692	+	0.736266i	$0.736587\pi$
$884$	4.64396e20			1.10084
$885$	2.90886e20			0.684102
$886$		−	6.52608e19i		−	0.152271i
$887$		−	2.55434e20i		−	0.591307i	−0.955295	−	0.295653i	$-0.904463\pi$
$887$		−	2.55434e20i		−	0.591307i	0.955295	−	0.295653i	$-0.0955373\pi$
$888$			8.50125e19i			0.195250i
$889$	2.84107e20			0.647395
$890$			6.47425e19i			0.146373i
$891$	−1.88123e19	+	2.07696e19i	−0.0421986	+	0.0465891i
$892$	−8.89301e19			−0.197922
$893$			1.52635e20i			0.337049i
$894$	1.35235e20			0.296296
$895$	4.26479e20			0.927121
$896$	2.48890e19			0.0536848
$897$			7.43575e20i			1.59139i
$898$			1.25463e20i			0.266429i
$899$		−	1.57215e21i		−	3.31265i
$900$	−9.51393e19			−0.198913
$901$			4.15702e19i			0.0862400i
$902$	−4.73693e19	+	5.22977e19i	−0.0975104	+	0.107656i
$903$	−1.27845e20			−0.261138
$904$		−	3.04523e20i		−	0.617221i
$905$	1.07508e20			0.216222
$906$	−4.19102e20			−0.836416
$907$	−4.84985e20			−0.960455			−0.480228	−	0.877144i	$-0.659446\pi$
$907$	−4.84985e20			−0.960455			−0.480228	+	0.877144i	$0.659446\pi$
$908$			2.47425e20i			0.486231i
$909$		−	4.66732e20i		−	0.910165i
$910$		−	1.79726e20i		−	0.347793i
$911$	9.33181e20			1.79200			0.895998	−	0.444057i	$-0.146461\pi$
$911$	9.33181e20			1.79200			0.895998	+	0.444057i	$0.146461\pi$
$912$		−	3.26097e19i		−	0.0621418i
$913$	−4.30865e20	−	3.90262e20i	−0.814791	−	0.738007i
$914$	−3.12918e20			−0.587229
$915$		−	1.44995e20i		−	0.270025i
$916$	4.09311e20			0.756458
$917$	1.88971e20			0.346584
$918$	6.13403e20			1.11647
$919$			6.57826e20i			1.18823i	0.804378	+	0.594117i	$0.202499\pi$
$919$			6.57826e20i			1.18823i	−0.804378	+	0.594117i	$0.797501\pi$
$920$		−	1.96751e20i		−	0.352697i
$921$		−	3.33661e19i		−	0.0593592i
$922$	4.08280e20			0.720845
$923$			8.05111e19i			0.141073i
$924$	−8.29223e19	−	7.51079e19i	−0.144201	−	0.130612i
$925$	3.37030e20			0.581670
$926$			2.65158e20i			0.454180i
$927$	−6.40508e19			−0.108885
$928$	−1.82574e20			−0.308037
$929$	1.04566e20			0.175098			0.0875492	−	0.996160i	$-0.472097\pi$
$929$	1.04566e20			0.175098			0.0875492	+	0.996160i	$0.472097\pi$
$930$		−	2.95512e20i		−	0.491128i
$931$		−	1.48444e20i		−	0.244858i
$932$			1.55572e20i			0.254695i
$933$	−7.81141e19			−0.126928
$934$		−	4.27066e20i		−	0.688758i
$935$	4.09396e20	+	3.70815e20i	0.655333	+	0.593576i
$936$	−1.86297e20			−0.295989
$937$		−	4.36941e20i		−	0.689042i	−0.938779	−	0.344521i	$-0.888041\pi$
$937$		−	4.36941e20i		−	0.689042i	0.938779	−	0.344521i	$-0.111959\pi$
$938$	−1.85839e20			−0.290882
$939$	3.05308e20			0.474328
$940$	1.60630e20			0.247703
$941$			9.91413e20i			1.51749i	0.651385	+	0.758747i	$0.274188\pi$
$941$			9.91413e20i			1.51749i	−0.651385	+	0.758747i	$0.725812\pi$
$942$			2.65036e19i			0.0402670i
$943$			2.38275e20i			0.359332i
$944$	3.12718e20			0.468112
$945$		−	2.37393e20i		−	0.352732i
$946$	−2.15994e20	+	2.38467e20i	−0.318570	+	0.351714i
$947$	2.93637e20			0.429894			0.214947	−	0.976626i	$-0.431042\pi$
$947$	2.93637e20			0.429894			0.214947	+	0.976626i	$0.431042\pi$
$948$		−	1.98744e20i		−	0.288826i
$949$	−4.98581e20			−0.719238
$950$	−1.29281e20			−0.185126
$951$	−5.40157e20			−0.767814
$952$			2.35956e20i			0.332944i
$953$		−	5.24866e20i		−	0.735188i	−0.929986	−	0.367594i	$-0.880182\pi$
$953$		−	5.24866e20i		−	0.735188i	0.929986	−	0.367594i	$-0.119818\pi$
$954$		−	1.66763e19i		−	0.0231879i
$955$	−2.23352e19			−0.0308295
$956$		−	2.96101e20i		−	0.405727i
$957$	6.08277e20	+	5.50955e20i	0.827405	+	0.749432i
$958$	−6.13322e20			−0.828189
$959$		−	5.57706e20i		−	0.747610i
$960$	−3.43178e19			−0.0456690
$961$	1.97870e21			2.61407
$962$	6.59957e20			0.865546
$963$			7.13300e20i			0.928727i
$964$			1.07915e20i			0.139490i
$965$			2.71909e20i			0.348925i
$966$	−3.77804e20			−0.481312
$967$		−	5.23975e20i		−	0.662712i	−0.943506	−	0.331356i	$-0.892494\pi$
$967$		−	5.23975e20i		−	0.662712i	0.943506	−	0.331356i	$-0.107506\pi$
$968$	−2.80194e20	+	2.77784e19i	−0.351829	+	0.0348803i
$969$	3.09151e20			0.385393
$970$			3.24982e20i			0.402214i
$971$	−5.08668e20			−0.625028			−0.312514	−	0.949913i	$-0.601171\pi$
$971$	−5.08668e20			−0.625028			−0.312514	+	0.949913i	$0.601171\pi$
$972$	−4.00878e20			−0.489045
$973$	1.40379e20			0.170025
$974$		−	7.08226e19i		−	0.0851647i
$975$		−	5.14179e20i		−	0.613878i
$976$		−	1.55877e20i		−	0.184771i
$977$	−7.07023e20			−0.832093			−0.416046	−	0.909343i	$-0.636585\pi$
$977$	−7.07023e20			−0.832093			−0.416046	+	0.909343i	$0.636585\pi$
$978$			1.09866e20i			0.128378i
$979$	2.10038e20	−	2.31891e20i	0.243679	−	0.269032i
$980$	−1.56219e20			−0.179950
$981$			3.37623e20i			0.386144i
$982$	5.81995e20			0.660905
$983$	−1.18159e21			−1.33227			−0.666135	−	0.745832i	$-0.732052\pi$
$983$	−1.18159e21			−1.33227			−0.666135	+	0.745832i	$0.732052\pi$
$984$	4.15606e19			0.0465281
$985$			5.59635e20i			0.622087i
$986$		−	1.73085e21i		−	1.91039i
$987$		−	3.08444e20i		−	0.338030i
$988$	−2.53151e20			−0.275475
$989$			1.08648e21i			1.17395i
$990$	−1.64233e20	−	1.48756e20i	−0.176204	−	0.159599i
$991$	−6.35047e20			−0.676535			−0.338268	−	0.941050i	$-0.609841\pi$
$991$	−6.35047e20			−0.676535			−0.338268	+	0.941050i	$0.609841\pi$
$992$		−	3.17691e20i		−	0.336065i
$993$	−7.10175e20			−0.745968
$994$	−4.09070e19			−0.0426671
$995$	4.25514e20			0.440709
$996$			3.42405e20i			0.352148i
$997$			4.24835e20i			0.433864i	0.976187	+	0.216932i	$0.0696051\pi$
$997$			4.24835e20i			0.433864i	−0.976187	+	0.216932i	$0.930395\pi$
$998$		−	4.31121e20i		−	0.437205i
$999$	8.71710e20			0.877837

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.15.b.a.21.12	yes	14
4.3	odd	2		176.15.h.e.65.5		14
11.10	odd	2	inner	22.15.b.a.21.5	✓	14
44.43	even	2		176.15.h.e.65.6		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.15.b.a.21.5	✓	14	11.10	odd	2	inner
22.15.b.a.21.12	yes	14	1.1	even	1	trivial
176.15.h.e.65.5		14	4.3	odd	2
176.15.h.e.65.6		14	44.43	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:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	22.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+90.5097i q^{2} +1401.11 q^{3} -8192.00 q^{4} +44552.9 q^{5} +126814. i q^{6} +500199. i q^{7} -741455. i q^{8} -2.81985e6 q^{9} +O(q^{10})\)	\(q+90.5097i q^{2} +1401.11 q^{3} -8192.00 q^{4} +44552.9 q^{5} +126814. i q^{6} +500199. i q^{7} -741455. i q^{8} -2.81985e6 q^{9} +4.03247e6i q^{10} +(1.30821e7 - 1.44432e7i) q^{11} -1.14779e7 q^{12} +8.91038e7i q^{13} -4.52729e7 q^{14} +6.24238e7 q^{15} +6.71089e7 q^{16} +6.36213e8i q^{17} -2.55223e8i q^{18} -3.46812e8i q^{19} -3.64978e8 q^{20} +7.00836e8i q^{21} +(1.30725e9 + 1.18406e9i) q^{22} +5.95600e9 q^{23} -1.03886e9i q^{24} -4.11855e9 q^{25} -8.06476e9 q^{26} -1.06524e10 q^{27} -4.09763e9i q^{28} +3.00582e10i q^{29} +5.64995e9i q^{30} -5.23034e10 q^{31} +6.07400e9i q^{32} +(1.83296e10 - 2.02366e10i) q^{33} -5.75834e10 q^{34} +2.22853e10i q^{35} +2.31002e10 q^{36} -8.18322e10 q^{37} +3.13898e10 q^{38} +1.24845e11i q^{39} -3.30340e10i q^{40} +4.00058e10i q^{41} -6.34324e10 q^{42} +1.82418e11i q^{43} +(-1.07169e11 + 1.18319e11i) q^{44} -1.25632e11 q^{45} +5.39076e11i q^{46} -4.40108e11 q^{47} +9.40272e10 q^{48} +4.28024e11 q^{49} -3.72769e11i q^{50} +8.91407e11i q^{51} -7.29939e11i q^{52} +6.53401e10 q^{53} -9.64147e11i q^{54} +(5.82848e11 - 6.43489e11i) q^{55} +3.70875e11 q^{56} -4.85923e11i q^{57} -2.72056e12 q^{58} +4.65987e12 q^{59} -5.11375e11 q^{60} -2.32275e12i q^{61} -4.73397e12i q^{62} -1.41048e12i q^{63} -5.49756e11 q^{64} +3.96984e12i q^{65} +(1.83161e12 + 1.65900e12i) q^{66} +4.10486e12 q^{67} -5.21186e12i q^{68} +8.34504e12 q^{69} -2.01704e12 q^{70} +9.03565e11 q^{71} +2.09079e12i q^{72} +5.59551e12i q^{73} -7.40660e12i q^{74} -5.77056e12 q^{75} +2.84108e12i q^{76} +(7.22450e12 + 6.54368e12i) q^{77} -1.12997e13 q^{78} +1.73153e13i q^{79} +2.98990e12 q^{80} -1.43801e12 q^{81} -3.62091e12 q^{82} -2.98316e13i q^{83} -5.74125e12i q^{84} +2.83452e13i q^{85} -1.65106e13 q^{86} +4.21150e13i q^{87} +(-1.07090e13 - 9.69983e12i) q^{88} +1.60553e13 q^{89} -1.13710e13i q^{90} -4.45697e13 q^{91} -4.87916e13 q^{92} -7.32831e13 q^{93} -3.98340e13i q^{94} -1.54515e13i q^{95} +8.51037e12i q^{96} +8.05913e13 q^{97} +3.87403e13i q^{98} +(-3.68896e13 + 4.07277e13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9}+O(q^{10}) \) 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9	\( 14 q + 4394 q^{3} - 114688 q^{4} + 69758 q^{5} + 11016572 q^{9} + 20143042 q^{11} - 35995648 q^{12} + 62814720 q^{14} - 1359602 q^{15} + 939524096 q^{16} - 571457536 q^{20} - 2107666944 q^{22} - 7305755542 q^{23} + 19291879452 q^{25} - 6388480512 q^{26} + 34093422830 q^{27} - 33569873942 q^{31} + 2885838062 q^{33} + 167764701696 q^{34} - 90247757824 q^{36} + 73167823966 q^{37} + 71236111872 q^{38} - 222695314944 q^{42} - 165011800064 q^{44} + 2000205168616 q^{45} - 1612717386124 q^{47} + 294876348416 q^{48} + 3424602524990 q^{49} - 3530064068164 q^{53} - 3715439610854 q^{55} - 514578186240 q^{56} - 1374208002048 q^{58} - 818496564070 q^{59} + 11137859584 q^{60} - 7696581394432 q^{64} - 5938395621888 q^{66} + 16485465276922 q^{67} - 11394452631206 q^{69} - 392146020864 q^{70} - 19380879179878 q^{71} + 23016770893992 q^{75} + 60534793808304 q^{77} + 17335823992320 q^{78} + 4681380134912 q^{80} - 10394309810662 q^{81} - 79417078012416 q^{82} + 6375532305408 q^{86} + 17266007605248 q^{88} - 117770741987650 q^{89} + 150621364097712 q^{91} + 59848749400064 q^{92} + 27345122803162 q^{93} + 123398138843566 q^{97} + 118861332531788 q^{99}+O(q^{100}) \) 14 * q + 4394 * q^3 - 114688 * q^4 + 69758 * q^5 + 11016572 * q^9 + 20143042 * q^11 - 35995648 * q^12 + 62814720 * q^14 - 1359602 * q^15 + 939524096 * q^16 - 571457536 * q^20 - 2107666944 * q^22 - 7305755542 * q^23 + 19291879452 * q^25 - 6388480512 * q^26 + 34093422830 * q^27 - 33569873942 * q^31 + 2885838062 * q^33 + 167764701696 * q^34 - 90247757824 * q^36 + 73167823966 * q^37 + 71236111872 * q^38 - 222695314944 * q^42 - 165011800064 * q^44 + 2000205168616 * q^45 - 1612717386124 * q^47 + 294876348416 * q^48 + 3424602524990 * q^49 - 3530064068164 * q^53 - 3715439610854 * q^55 - 514578186240 * q^56 - 1374208002048 * q^58 - 818496564070 * q^59 + 11137859584 * q^60 - 7696581394432 * q^64 - 5938395621888 * q^66 + 16485465276922 * q^67 - 11394452631206 * q^69 - 392146020864 * q^70 - 19380879179878 * q^71 + 23016770893992 * q^75 + 60534793808304 * q^77 + 17335823992320 * q^78 + 4681380134912 * q^80 - 10394309810662 * q^81 - 79417078012416 * q^82 + 6375532305408 * q^86 + 17266007605248 * q^88 - 117770741987650 * q^89 + 150621364097712 * q^91 + 59848749400064 * q^92 + 27345122803162 * q^93 + 123398138843566 * q^97 + 118861332531788 * q^99

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