LMFDB - Embedded newform 22.15.b.a.21.6

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			21.6
Root			$-2599.55 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.15.b.a.21.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-90.5097i q^{2} +2913.55 q^{3} -8192.00 q^{4} -75323.6 q^{5} -263704. i q^{6} -867659. i q^{7} +741455. i q^{8} +3.70579e6 q^{9} +O(q^{10})$	\(q-90.5097i q^{2} +2913.55 q^{3} -8192.00 q^{4} -75323.6 q^{5} -263704. i q^{6} -867659. i q^{7} +741455. i q^{8} +3.70579e6 q^{9} +6.81751e6i q^{10} +(-1.56983e7 + 1.15461e7i) q^{11} -2.38678e7 q^{12} +3.47214e7i q^{13} -7.85316e7 q^{14} -2.19459e8 q^{15} +6.71089e7 q^{16} +2.76380e8i q^{17} -3.35409e8i q^{18} -8.30217e8i q^{19} +6.17051e8 q^{20} -2.52797e9i q^{21} +(1.04503e9 + 1.42085e9i) q^{22} -5.71780e9 q^{23} +2.16026e9i q^{24} -4.29878e8 q^{25} +3.14263e9 q^{26} -3.13842e9 q^{27} +7.10787e9i q^{28} +2.61317e10i q^{29} +1.98631e10i q^{30} -1.69092e10 q^{31} -6.07400e9i q^{32} +(-4.57378e10 + 3.36401e10i) q^{33} +2.50151e10 q^{34} +6.53552e10i q^{35} -3.03578e10 q^{36} +7.99862e10 q^{37} -7.51426e10 q^{38} +1.01163e11i q^{39} -5.58490e10i q^{40} -1.95749e11i q^{41} -2.28805e11 q^{42} +2.34553e11i q^{43} +(1.28601e11 - 9.45856e10i) q^{44} -2.79133e11 q^{45} +5.17516e11i q^{46} -6.41052e11 q^{47} +1.95525e11 q^{48} -7.46096e10 q^{49} +3.89081e10i q^{50} +8.05247e11i q^{51} -2.84438e11i q^{52} -1.06181e12 q^{53} +2.84058e11i q^{54} +(1.18245e12 - 8.69693e11i) q^{55} +6.43331e11 q^{56} -2.41888e12i q^{57} +2.36517e12 q^{58} +3.40545e12 q^{59} +1.79781e12 q^{60} -3.58361e12i q^{61} +1.53044e12i q^{62} -3.21536e12i q^{63} -5.49756e11 q^{64} -2.61534e12i q^{65} +(3.04475e12 + 4.13971e12i) q^{66} +4.80232e11 q^{67} -2.26411e12i q^{68} -1.66591e13 q^{69} +5.91528e12 q^{70} +4.31225e11 q^{71} +2.74767e12i q^{72} -4.05979e12i q^{73} -7.23952e12i q^{74} -1.25247e12 q^{75} +6.80113e12i q^{76} +(1.00181e13 + 1.36208e13i) q^{77} +9.15619e12 q^{78} -2.11530e13i q^{79} -5.05488e12 q^{80} -2.68686e13 q^{81} -1.77172e13 q^{82} -4.92388e12i q^{83} +2.07091e13i q^{84} -2.08180e13i q^{85} +2.12293e13 q^{86} +7.61359e13i q^{87} +(-8.56092e12 - 1.16396e13i) q^{88} -7.53865e12 q^{89} +2.52642e13i q^{90} +3.01264e13 q^{91} +4.68402e13 q^{92} -4.92656e13 q^{93} +5.80214e13i q^{94} +6.25349e13i q^{95} -1.76969e13i q^{96} -4.89366e13 q^{97} +6.75289e12i q^{98} +(-5.81746e13 + 4.27874e13i) 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
$3$	2913.55			1.33221			0.666106	−	0.745857i	$-0.267960\pi$
$3$	2913.55			1.33221			0.666106	+	0.745857i	$0.267960\pi$
$4$	−8192.00			−0.500000
$5$	−75323.6			−0.964141			−0.482071	−	0.876132i	$-0.660115\pi$
$5$	−75323.6			−0.964141			−0.482071	+	0.876132i	$0.660115\pi$
$6$		−	263704.i		−	0.942016i
$7$		−	867659.i		−	1.05357i	−0.849999	−	0.526784i	$-0.823397\pi$
$7$		−	867659.i		−	1.05357i	0.849999	−	0.526784i	$-0.176603\pi$
$8$			741455.i			0.353553i
$9$	3.70579e6			0.774788
$10$			6.81751e6i			0.681751i
$11$	−1.56983e7	+	1.15461e7i	−0.805572	+	0.592497i
$11$	−1.56983e7	+	1.15461e7i	−0.805572	+	0.592497i
$12$	−2.38678e7			−0.666106
$13$			3.47214e7i			0.553343i	0.960965	+	0.276671i	$0.0892314\pi$
$13$			3.47214e7i			0.553343i	−0.960965	+	0.276671i	$0.910769\pi$
$14$	−7.85316e7			−0.744986
$15$	−2.19459e8			−1.28444
$16$	6.71089e7			0.250000
$17$			2.76380e8i			0.673542i	0.941587	+	0.336771i	$0.109335\pi$
$17$			2.76380e8i			0.673542i	−0.941587	+	0.336771i	$0.890665\pi$
$18$		−	3.35409e8i		−	0.547858i
$19$		−	8.30217e8i		−	0.928787i	−0.885629	−	0.464394i	$-0.846272\pi$
$19$		−	8.30217e8i		−	0.928787i	0.885629	−	0.464394i	$-0.153728\pi$
$20$	6.17051e8			0.482071
$21$		−	2.52797e9i		−	1.40358i
$22$	1.04503e9	+	1.42085e9i	0.418959	+	0.569626i
$23$	−5.71780e9			−1.67932			−0.839661	−	0.543111i	$-0.817246\pi$
$23$	−5.71780e9			−1.67932			−0.839661	+	0.543111i	$0.817246\pi$
$24$			2.16026e9i			0.471008i
$25$	−4.29878e8			−0.0704312
$26$	3.14263e9			0.391273
$27$	−3.13842e9			−0.300030
$28$			7.10787e9i			0.526784i
$29$			2.61317e10i			1.51489i	0.652898	+	0.757446i	$0.273553\pi$
$29$			2.61317e10i			1.51489i	−0.652898	+	0.757446i	$0.726447\pi$
$30$			1.98631e10i			0.908237i
$31$	−1.69092e10			−0.614597			−0.307298	−	0.951613i	$-0.599425\pi$
$31$	−1.69092e10			−0.614597			−0.307298	+	0.951613i	$0.599425\pi$
$32$		−	6.07400e9i		−	0.176777i
$33$	−4.57378e10	+	3.36401e10i	−1.07319	+	0.789332i
$34$	2.50151e10			0.476266
$35$			6.53552e10i			1.01579i
$36$	−3.03578e10			−0.387394
$37$	7.99862e10			0.842564			0.421282	−	0.906930i	$-0.361580\pi$
$37$	7.99862e10			0.842564			0.421282	+	0.906930i	$0.361580\pi$
$38$	−7.51426e10			−0.656752
$39$			1.01163e11i			0.737170i
$40$		−	5.58490e10i		−	0.340875i
$41$		−	1.95749e11i		−	1.00511i	−0.864546	−	0.502553i	$-0.832394\pi$
$41$		−	1.95749e11i		−	1.00511i	0.864546	−	0.502553i	$-0.167606\pi$
$42$	−2.28805e11			−0.992479
$43$			2.34553e11i			0.862904i	0.902136	+	0.431452i	$0.141998\pi$
$43$			2.34553e11i			0.862904i	−0.902136	+	0.431452i	$0.858002\pi$
$44$	1.28601e11	−	9.45856e10i	0.402786	−	0.296249i
$45$	−2.79133e11			−0.747005
$46$			5.17516e11i			1.18746i
$47$	−6.41052e11			−1.26534			−0.632671	−	0.774421i	$-0.718041\pi$
$47$	−6.41052e11			−1.26534			−0.632671	+	0.774421i	$0.718041\pi$
$48$	1.95525e11			0.333053
$49$	−7.46096e10			−0.110008
$50$			3.89081e10i			0.0498024i
$51$			8.05247e11i			0.897301i
$52$		−	2.84438e11i		−	0.276671i
$53$	−1.06181e12			−0.903891			−0.451946	−	0.892046i	$-0.649270\pi$
$53$	−1.06181e12			−0.903891			−0.451946	+	0.892046i	$0.649270\pi$
$54$			2.84058e11i			0.212153i
$55$	1.18245e12	−	8.69693e11i	0.776686	−	0.571251i
$56$	6.43331e11			0.372493
$57$		−	2.41888e12i		−	1.23734i
$58$	2.36517e12			1.07119
$59$	3.40545e12			1.36839			0.684195	−	0.729299i	$-0.260154\pi$
$59$	3.40545e12			1.36839			0.684195	+	0.729299i	$0.260154\pi$
$60$	1.79781e12			0.642220
$61$		−	3.58361e12i		−	1.14028i	−0.821547	−	0.570140i	$-0.806889\pi$
$61$		−	3.58361e12i		−	1.14028i	0.821547	−	0.570140i	$-0.193111\pi$
$62$			1.53044e12i			0.434586i
$63$		−	3.21536e12i		−	0.816292i
$64$	−5.49756e11			−0.125000
$65$		−	2.61534e12i		−	0.533501i
$66$	3.04475e12	+	4.13971e12i	0.558142	+	0.758862i
$67$	4.80232e11			0.0792370			0.0396185	−	0.999215i	$-0.487386\pi$
$67$	4.80232e11			0.0792370			0.0396185	+	0.999215i	$0.487386\pi$
$68$		−	2.26411e12i		−	0.336771i
$69$	−1.66591e13			−2.23721
$70$	5.91528e12			0.718272
$71$	4.31225e11			0.0474128			0.0237064	−	0.999719i	$-0.492453\pi$
$71$	4.31225e11			0.0474128			0.0237064	+	0.999719i	$0.492453\pi$
$72$			2.74767e12i			0.273929i
$73$		−	4.05979e12i		−	0.367488i	−0.982974	−	0.183744i	$-0.941178\pi$
$73$		−	4.05979e12i		−	0.367488i	0.982974	−	0.183744i	$-0.0588218\pi$
$74$		−	7.23952e12i		−	0.595783i
$75$	−1.25247e12			−0.0938293
$76$			6.80113e12i			0.464394i
$77$	1.00181e13	+	1.36208e13i	0.624237	+	0.848726i
$78$	9.15619e12			0.521258
$79$		−	2.11530e13i		−	1.10149i	−0.834672	−	0.550747i	$-0.814343\pi$
$79$		−	2.11530e13i		−	1.10149i	0.834672	−	0.550747i	$-0.185657\pi$
$80$	−5.05488e12			−0.241035
$81$	−2.68686e13			−1.17449
$82$	−1.77172e13			−0.710718
$83$		−	4.92388e12i		−	0.181452i	−0.995876	−	0.0907258i	$-0.971081\pi$
$83$		−	4.92388e12i		−	0.181452i	0.995876	−	0.0907258i	$-0.0289187\pi$
$84$			2.07091e13i			0.701788i
$85$		−	2.08180e13i		−	0.649390i
$86$	2.12293e13			0.610165
$87$			7.61359e13i			2.01816i
$88$	−8.56092e12	−	1.16396e13i	−0.209479	−	0.284813i
$89$	−7.53865e12			−0.170437			−0.0852185	−	0.996362i	$-0.527159\pi$
$89$	−7.53865e12			−0.170437			−0.0852185	+	0.996362i	$0.527159\pi$
$90$			2.52642e13i			0.528212i
$91$	3.01264e13			0.582985
$92$	4.68402e13			0.839661
$93$	−4.92656e13			−0.818773
$94$			5.80214e13i			0.894732i
$95$			6.25349e13i			0.895482i
$96$		−	1.76969e13i		−	0.235504i
$97$	−4.89366e13			−0.605664			−0.302832	−	0.953044i	$-0.597932\pi$
$97$	−4.89366e13			−0.605664			−0.302832	+	0.953044i	$0.597932\pi$
$98$			6.75289e12i			0.0777871i
$99$	−5.81746e13	+	4.27874e13i	−0.624148	+	0.459060i
$100$	3.52156e12			0.0352156
$101$		−	1.98660e14i		−	1.85294i	−0.376373	−	0.926468i	$-0.622829\pi$
$101$		−	1.98660e14i		−	1.85294i	0.376373	−	0.926468i	$-0.377171\pi$
$102$	7.28826e13			0.634487
$103$	−1.35157e14			−1.09895			−0.549477	−	0.835509i	$-0.685173\pi$
$103$	−1.35157e14			−1.09895			−0.549477	+	0.835509i	$0.685173\pi$
$104$	−2.57444e13			−0.195636
$105$			1.90415e14i			1.35325i
$106$			9.61042e13i			0.639148i
$107$		−	1.67405e14i		−	1.04251i	−0.853400	−	0.521256i	$-0.825464\pi$
$107$		−	1.67405e14i		−	1.04251i	0.853400	−	0.521256i	$-0.174536\pi$
$108$	2.57100e13			0.150015
$109$		−	1.43567e14i		−	0.785362i	−0.919675	−	0.392681i	$-0.871548\pi$
$109$		−	1.43567e14i		−	0.785362i	0.919675	−	0.392681i	$-0.128452\pi$
$110$	−7.87156e13	−	1.07023e14i	−0.403936	−	0.549200i
$111$	2.33044e14			1.12247
$112$		−	5.82276e13i		−	0.263392i
$113$	1.01260e14			0.430416			0.215208	−	0.976568i	$-0.430957\pi$
$113$	1.01260e14			0.430416			0.215208	+	0.976568i	$0.430957\pi$
$114$	−2.18932e14			−0.874932
$115$	4.30685e14			1.61910
$116$		−	2.14071e14i		−	0.757446i
$117$			1.28670e14i			0.428723i
$118$		−	3.08226e14i		−	0.967598i
$119$	2.39804e14			0.709623
$120$		−	1.62719e14i		−	0.454118i
$121$	1.13125e14	−	3.62509e14i	0.297893	−	0.954599i
$122$	−3.24351e14			−0.806300
$123$		−	5.70323e14i		−	1.33901i
$124$	1.38520e14			0.307298
$125$	4.92118e14			1.03205
$126$	−2.91021e14			−0.577206
$127$			1.04866e15i			1.96792i	0.178381	+	0.983962i	$0.442914\pi$
$127$			1.04866e15i			1.96792i	−0.178381	+	0.983962i	$0.557086\pi$
$128$			4.97582e13i			0.0883883i
$129$			6.83382e14i			1.14957i
$130$	−2.36714e14			−0.377242
$131$			1.08808e15i			1.64347i	0.569867	+	0.821737i	$0.306995\pi$
$131$			1.08808e15i			1.64347i	−0.569867	+	0.821737i	$0.693005\pi$
$132$	3.74684e14	−	2.75580e14i	0.536596	−	0.394666i
$133$	−7.20345e14			−0.978541
$134$		−	4.34657e13i		−	0.0560290i
$135$	2.36397e14			0.289272
$136$	−2.04924e14			−0.238133
$137$	9.50193e14			1.04898			0.524491	−	0.851416i	$-0.324256\pi$
$137$	9.50193e14			1.04898			0.524491	+	0.851416i	$0.324256\pi$
$138$			1.50781e15i			1.58195i
$139$		−	1.42444e15i		−	1.42082i	−0.703788	−	0.710410i	$-0.748509\pi$
$139$		−	1.42444e15i		−	1.42082i	0.703788	−	0.710410i	$-0.251491\pi$
$140$		−	5.35390e14i		−	0.507895i
$141$	−1.86773e15			−1.68570
$142$		−	3.90300e13i		−	0.0335259i
$143$	−4.00897e14	−	5.45069e14i	−0.327854	−	0.445758i
$144$	2.48691e14			0.193697
$145$		−	1.96833e15i		−	1.46057i
$146$	−3.67450e14			−0.259854
$147$	−2.17379e14			−0.146553
$148$	−6.55247e14			−0.421282
$149$			2.48573e15i			1.52458i	0.647238	+	0.762288i	$0.275924\pi$
$149$			2.48573e15i			1.52458i	−0.647238	+	0.762288i	$0.724076\pi$
$150$			1.13361e14i			0.0663474i
$151$			8.33993e14i			0.465933i	0.972485	+	0.232967i	$0.0748433\pi$
$151$			8.33993e14i			0.465933i	−0.972485	+	0.232967i	$0.925157\pi$
$152$	6.15568e14			0.328376
$153$			1.02421e15i			0.521852i
$154$	1.23281e15	−	9.06733e14i	0.600140	−	0.441402i
$155$	1.27366e15			0.592558
$156$		−	8.28724e14i		−	0.368585i
$157$	−2.83439e14			−0.120549			−0.0602744	−	0.998182i	$-0.519198\pi$
$157$	−2.83439e14			−0.120549			−0.0602744	+	0.998182i	$0.519198\pi$
$158$	−1.91455e15			−0.778874
$159$	−3.09364e15			−1.20417
$160$			4.57515e14i			0.170438i
$161$			4.96110e15i			1.76928i
$162$			2.43187e15i			0.830491i
$163$	−4.94421e15			−1.61727			−0.808636	−	0.588309i	$-0.799794\pi$
$163$	−4.94421e15			−1.61727			−0.808636	+	0.588309i	$0.799794\pi$
$164$			1.60357e15i			0.502553i
$165$	3.44513e15	−	2.53389e15i	1.03471	−	0.761028i
$166$	−4.45659e14			−0.128306
$167$			4.57889e13i			0.0126399i	0.999980	+	0.00631997i	$0.00201172\pi$
$167$			4.57889e13i			0.0126399i	−0.999980	+	0.00631997i	$0.997988\pi$
$168$	1.87437e15			0.496239
$169$	2.73180e15			0.693812
$170$	−1.88423e15			−0.459188
$171$		−	3.07661e15i		−	0.719613i
$172$		−	1.92146e15i		−	0.431452i
$173$		−	6.39265e15i		−	1.37835i	−0.724597	−	0.689173i	$-0.757974\pi$
$173$		−	6.39265e15i		−	1.37835i	0.724597	−	0.689173i	$-0.242026\pi$
$174$	6.89104e15			1.42705
$175$			3.72988e14i			0.0742042i
$176$	−1.05350e15	+	7.74846e14i	−0.201393	+	0.148124i
$177$	9.92192e15			1.82298
$178$			6.82321e14i			0.120517i
$179$	2.80106e15			0.475719			0.237860	−	0.971300i	$-0.423554\pi$
$179$	2.80106e15			0.475719			0.237860	+	0.971300i	$0.423554\pi$
$180$	2.28666e15			0.373503
$181$	6.02858e14			0.0947251			0.0473626	−	0.998878i	$-0.484918\pi$
$181$	6.02858e14			0.0947251			0.0473626	+	0.998878i	$0.484918\pi$
$182$		−	2.72673e15i		−	0.412233i
$183$		−	1.04410e16i		−	1.51909i
$184$		−	4.23949e15i		−	0.593730i
$185$	−6.02484e15			−0.812351
$186$			4.45902e15i			0.578960i
$187$	−3.19112e15	−	4.33871e15i	−0.399072	−	0.542587i
$188$	5.25149e15			0.632671
$189$			2.72308e15i			0.316103i
$190$	5.66001e15			0.633202
$191$	−1.61123e16			−1.73749			−0.868747	−	0.495257i	$-0.835074\pi$
$191$	−1.61123e16			−1.73749			−0.868747	+	0.495257i	$0.835074\pi$
$192$	−1.60174e15			−0.166526
$193$		−	3.93899e15i		−	0.394897i	−0.980313	−	0.197449i	$-0.936734\pi$
$193$		−	3.93899e15i		−	0.394897i	0.980313	−	0.197449i	$-0.0632656\pi$
$194$			4.42924e15i			0.428269i
$195$		−	7.61992e15i		−	0.710736i
$196$	6.11202e14			0.0550038
$197$			4.74963e15i			0.412474i	0.978502	+	0.206237i	$0.0661218\pi$
$197$			4.74963e15i			0.412474i	−0.978502	+	0.206237i	$0.933878\pi$
$198$	3.87267e15	+	5.26537e15i	0.324604	+	0.441339i
$199$	−1.59379e16			−1.28962			−0.644808	−	0.764345i	$-0.723063\pi$
$199$	−1.59379e16			−1.28962			−0.644808	+	0.764345i	$0.723063\pi$
$200$		−	3.18735e14i		−	0.0249012i
$201$	1.39918e15			0.105560
$202$	−1.79806e16			−1.31022
$203$	2.26734e16			1.59604
$204$		−	6.59658e15i		−	0.448650i
$205$			1.47445e16i			0.969065i
$206$			1.22331e16i			0.777077i
$207$	−2.11889e16			−1.30112
$208$			2.33012e15i			0.138336i
$209$	9.58576e15	+	1.30330e16i	0.550304	+	0.748205i
$210$	1.72344e16			0.956890
$211$			1.73324e16i			0.930854i	0.885086	+	0.465427i	$0.154099\pi$
$211$			1.73324e16i			0.930854i	−0.885086	+	0.465427i	$0.845901\pi$
$212$	8.69836e15			0.451946
$213$	1.25639e15			0.0631639
$214$	−1.51517e16			−0.737167
$215$		−	1.76674e16i		−	0.831961i
$216$		−	2.32700e15i		−	0.106077i
$217$			1.46714e16i			0.647520i
$218$	−1.29942e16			−0.555335
$219$		−	1.18284e16i		−	0.489572i
$220$	−9.68666e15	+	7.12453e15i	−0.388343	+	0.285626i
$221$	−9.59633e15			−0.372700
$222$		−	2.10927e16i		−	0.793709i
$223$	3.42689e16			1.24959			0.624794	−	0.780790i	$-0.285183\pi$
$223$	3.42689e16			1.24959			0.624794	+	0.780790i	$0.285183\pi$
$224$	−5.27016e15			−0.186246
$225$	−1.59304e15			−0.0545693
$226$		−	9.16500e15i		−	0.304350i
$227$			3.10536e16i			0.999840i	0.866072	+	0.499920i	$0.166637\pi$
$227$			3.10536e16i			0.999840i	−0.866072	+	0.499920i	$0.833363\pi$
$228$			1.98154e16i			0.618671i
$229$	−1.49288e16			−0.452039			−0.226019	−	0.974123i	$-0.572571\pi$
$229$	−1.49288e16			−0.452039			−0.226019	+	0.974123i	$0.572571\pi$
$230$		−	3.89812e16i		−	1.14488i
$231$	2.91881e16	+	3.96848e16i	0.831616	+	1.13068i
$232$	−1.93755e16			−0.535595
$233$			4.44002e16i			1.19095i	0.803374	+	0.595475i	$0.203036\pi$
$233$			4.44002e16i			1.19095i	−0.803374	+	0.595475i	$0.796964\pi$
$234$	1.16459e16			0.303153
$235$	4.82863e16			1.21997
$236$	−2.78974e16			−0.684195
$237$		−	6.16302e16i		−	1.46742i
$238$		−	2.17046e16i		−	0.501779i
$239$			5.76683e16i			1.29465i	0.762214	+	0.647325i	$0.224112\pi$
$239$			5.76683e16i			1.29465i	−0.762214	+	0.647325i	$0.775888\pi$
$240$	−1.47276e16			−0.321110
$241$		−	4.57373e16i		−	0.968614i	−0.874898	−	0.484307i	$-0.839072\pi$
$241$		−	4.57373e16i		−	0.968614i	0.874898	−	0.484307i	$-0.160928\pi$
$242$	−3.28106e16	−	1.02389e16i	−0.675004	−	0.210642i
$243$	−6.32720e16			−1.26464
$244$			2.93569e16i			0.570140i
$245$	5.61986e15			0.106063
$246$	−5.16198e16			−0.946826
$247$	2.88263e16			0.513938
$248$		−	1.25374e16i		−	0.217293i
$249$		−	1.43459e16i		−	0.241732i
$250$		−	4.45415e16i		−	0.729768i
$251$	−7.06905e16			−1.12628			−0.563138	−	0.826363i	$-0.690406\pi$
$251$	−7.06905e16			−1.12628			−0.563138	+	0.826363i	$0.690406\pi$
$252$			2.63402e16i			0.408146i
$253$	8.97599e16	−	6.60183e16i	1.35282	−	0.994994i
$254$	9.49138e16			1.39153
$255$		−	6.06541e16i		−	0.865125i
$256$	4.50360e15			0.0625000
$257$	3.76880e16			0.508946			0.254473	−	0.967080i	$-0.418098\pi$
$257$	3.76880e16			0.508946			0.254473	+	0.967080i	$0.418098\pi$
$258$	6.18527e16			0.812869
$259$		−	6.94008e16i		−	0.887699i
$260$			2.14249e16i			0.266750i
$261$			9.68385e16i			1.17372i
$262$	9.84820e16			1.16211
$263$		−	1.52822e17i		−	1.75588i	−0.478769	−	0.877941i	$-0.658917\pi$
$263$		−	1.52822e17i		−	1.75588i	0.478769	−	0.877941i	$-0.341083\pi$
$264$	−2.49426e16	−	3.39125e16i	−0.279071	−	0.379431i
$265$	7.99794e16			0.871479
$266$			6.51982e16i			0.691933i
$267$	−2.19642e16			−0.227058
$268$	−3.93406e15			−0.0396185
$269$	−1.05450e17			−1.03462			−0.517311	−	0.855797i	$-0.673067\pi$
$269$	−1.05450e17			−1.03462			−0.517311	+	0.855797i	$0.673067\pi$
$270$		−	2.13962e16i		−	0.204546i
$271$			4.33967e16i			0.404270i	0.979358	+	0.202135i	$0.0647880\pi$
$271$			4.33967e16i			0.404270i	−0.979358	+	0.202135i	$0.935212\pi$
$272$			1.85476e16i			0.168386i
$273$	8.77746e16			0.776659
$274$		−	8.60017e16i		−	0.741742i
$275$	6.74837e15	−	4.96342e15i	0.0567375	−	0.0417303i
$276$	1.36471e17			1.11861
$277$		−	2.21949e16i		−	0.177376i	−0.996059	−	0.0886879i	$-0.971733\pi$
$277$		−	2.21949e16i		−	0.177376i	0.996059	−	0.0886879i	$-0.0282674\pi$
$278$	−1.28925e17			−1.00467
$279$	−6.26617e16			−0.476182
$280$	−4.84579e16			−0.359136
$281$			2.54163e17i			1.83725i	0.395132	+	0.918624i	$0.370699\pi$
$281$			2.54163e17i			1.83725i	−0.395132	+	0.918624i	$0.629301\pi$
$282$			1.69048e17i			1.19197i
$283$		−	3.93577e16i		−	0.270723i	−0.990796	−	0.135361i	$-0.956780\pi$
$283$		−	3.93577e16i		−	0.270723i	0.990796	−	0.135361i	$-0.0432196\pi$
$284$	−3.53260e15			−0.0237064
$285$			1.82198e17i			1.19297i
$286$	−4.93340e16	+	3.62851e16i	−0.315198	+	0.231828i
$287$	−1.69843e17			−1.05895
$288$		−	2.25089e16i		−	0.136964i
$289$	9.19917e16			0.546341
$290$	−1.78153e17			−1.03278
$291$	−1.42579e17			−0.806873
$292$			3.32578e16i			0.183744i
$293$			7.46259e16i			0.402547i	0.979535	+	0.201273i	$0.0645079\pi$
$293$			7.46259e16i			0.402547i	−0.979535	+	0.201273i	$0.935492\pi$
$294$			1.96749e16i			0.103629i
$295$	−2.56510e17			−1.31932
$296$			5.93062e16i			0.297891i
$297$	4.92680e16	−	3.62365e16i	0.241696	−	0.177767i
$298$	2.24982e17			1.07804
$299$		−	1.98530e17i		−	0.929241i
$300$	1.02602e16			0.0469147
$301$	2.03512e17			0.909128
$302$	7.54844e16			0.329465
$303$		−	5.78805e17i		−	2.46850i
$304$		−	5.57149e16i		−	0.232197i
$305$			2.69930e17i			1.09939i
$306$	9.27006e16			0.369005
$307$			4.23515e17i			1.64778i	0.566747	+	0.823892i	$0.308202\pi$
$307$			4.23515e17i			1.64778i	−0.566747	+	0.823892i	$0.691798\pi$
$308$	−8.20681e16	−	1.11582e17i	−0.312118	−	0.424363i
$309$	−3.93787e17			−1.46404
$310$		−	1.15278e17i		−	0.419002i
$311$	−5.34000e17			−1.89766			−0.948831	−	0.315785i	$-0.897732\pi$
$311$	−5.34000e17			−1.89766			−0.948831	+	0.315785i	$0.897732\pi$
$312$	−7.50075e16			−0.260629
$313$	3.33634e17			1.13360			0.566801	−	0.823855i	$-0.308181\pi$
$313$	3.33634e17			1.13360			0.566801	+	0.823855i	$0.308181\pi$
$314$			2.56540e16i			0.0852408i
$315$			2.42192e17i			0.787021i
$316$			1.73285e17i			0.550747i
$317$	3.20010e17			0.994829			0.497414	−	0.867513i	$-0.334283\pi$
$317$	3.20010e17			0.994829			0.497414	+	0.867513i	$0.334283\pi$
$318$			2.80004e17i			0.851480i
$319$	−3.01719e17	−	4.10224e17i	−0.897569	−	1.22035i
$320$	4.14096e16			0.120518
$321$		−	4.87741e17i		−	1.38885i
$322$	4.49028e17			1.25107
$323$	2.29456e17			0.625577
$324$	2.20108e17			0.587246
$325$		−	1.49260e16i		−	0.0389726i
$326$			4.47498e17i			1.14358i
$327$		−	4.18290e17i		−	1.04627i
$328$	1.45139e17			0.355359
$329$			5.56214e17i			1.33313i
$330$	−2.29342e17	−	3.11818e17i	−0.538128	−	0.731650i
$331$	−2.12757e17			−0.488751			−0.244375	−	0.969681i	$-0.578583\pi$
$331$	−2.12757e17			−0.488751			−0.244375	+	0.969681i	$0.578583\pi$
$332$			4.03364e16i			0.0907258i
$333$	2.96412e17			0.652808
$334$	4.14434e15			0.00893778
$335$	−3.61728e16			−0.0763956
$336$		−	1.69649e17i		−	0.350894i
$337$			3.14484e17i			0.637074i	0.947910	+	0.318537i	$0.103191\pi$
$337$			3.14484e17i			0.637074i	−0.947910	+	0.318537i	$0.896809\pi$
$338$		−	2.47254e17i		−	0.490599i
$339$	2.95025e17			0.573405
$340$			1.70541e17i			0.324695i
$341$	2.65446e17	−	1.95235e17i	0.495102	−	0.364147i
$342$	−2.78463e17			−0.508843
$343$		−	5.23731e17i		−	0.937668i
$344$	−1.73911e17			−0.305082
$345$	1.25482e18			2.15699
$346$	−5.78596e17			−0.974637
$347$			3.11559e17i			0.514321i	0.966369	+	0.257161i	$0.0827870\pi$
$347$			3.11559e17i			0.514321i	−0.966369	+	0.257161i	$0.917213\pi$
$348$		−	6.23705e17i		−	1.00908i
$349$		−	1.05194e16i		−	0.0166807i	−0.999965	−	0.00834036i	$-0.997345\pi$
$349$		−	1.05194e16i		−	0.0166807i	0.999965	−	0.00834036i	$-0.00265485\pi$
$350$	3.37590e16			0.0524703
$351$		−	1.08971e17i		−	0.166020i
$352$	7.01310e16	+	9.53516e16i	0.104740	+	0.142406i
$353$	−8.03740e17			−1.17677			−0.588386	−	0.808580i	$-0.700237\pi$
$353$	−8.03740e17			−1.17677			−0.588386	+	0.808580i	$0.700237\pi$
$354$		−	8.98030e17i		−	1.28904i
$355$	−3.24814e16			−0.0457126
$356$	6.17566e16			0.0852185
$357$	6.98680e17			0.945368
$358$		−	2.53523e17i		−	0.336384i
$359$			1.25415e18i			1.63189i	0.578133	+	0.815943i	$0.303782\pi$
$359$			1.25415e18i			1.63189i	−0.578133	+	0.815943i	$0.696218\pi$
$360$		−	2.06965e17i		−	0.264106i
$361$	1.09747e17			0.137354
$362$		−	5.45645e16i		−	0.0669808i
$363$	3.29595e17	−	1.05619e18i	0.396857	−	1.27173i
$364$	−2.46795e17			−0.291492
$365$			3.05798e17i			0.354311i
$366$	−9.45012e17			−1.07416
$367$	−9.57611e17			−1.06789			−0.533945	−	0.845519i	$-0.679291\pi$
$367$	−9.57611e17			−1.06789			−0.533945	+	0.845519i	$0.679291\pi$
$368$	−3.83715e17			−0.419831
$369$		−	7.25403e17i		−	0.778744i
$370$			5.45307e17i			0.574419i
$371$			9.21290e17i			0.952312i
$372$	4.03584e17			0.409386
$373$		−	8.80613e17i		−	0.876644i	−0.898818	−	0.438322i	$-0.855573\pi$
$373$		−	8.80613e17i		−	0.876644i	0.898818	−	0.438322i	$-0.144427\pi$
$374$	−3.92695e17	+	2.88827e17i	−0.383667	+	0.282187i
$375$	1.43381e18			1.37491
$376$		−	4.75311e17i		−	0.447366i
$377$	−9.07330e17			−0.838254
$378$	2.46465e17			0.223518
$379$	1.16292e18			1.03532			0.517661	−	0.855586i	$-0.326803\pi$
$379$	1.16292e18			1.03532			0.517661	+	0.855586i	$0.326803\pi$
$380$		−	5.12286e17i		−	0.447741i
$381$			3.05532e18i			2.62169i
$382$			1.45832e18i			1.22859i
$383$	−4.81244e17			−0.398083			−0.199042	−	0.979991i	$-0.563783\pi$
$383$	−4.81244e17			−0.398083			−0.199042	+	0.979991i	$0.563783\pi$
$384$			1.44973e17i			0.117752i
$385$	−7.54597e17	−	1.02597e18i	−0.601853	−	0.818292i
$386$	−3.56517e17			−0.279235
$387$			8.69204e17i			0.668567i
$388$	4.00889e17			0.302832
$389$	−1.53981e18			−1.14240			−0.571202	−	0.820810i	$-0.693523\pi$
$389$	−1.53981e18			−1.14240			−0.571202	+	0.820810i	$0.693523\pi$
$390$	−6.89677e17			−0.502566
$391$		−	1.58029e18i		−	1.13109i
$392$		−	5.53197e16i		−	0.0388935i
$393$			3.17018e18i			2.18945i
$394$	4.29888e17			0.291663
$395$			1.59332e18i			1.06200i
$396$	4.76567e17	−	3.50514e17i	0.312074	−	0.229530i
$397$	9.44294e17			0.607538			0.303769	−	0.952746i	$-0.401755\pi$
$397$	9.44294e17			0.607538			0.303769	+	0.952746i	$0.401755\pi$
$398$			1.44254e18i			0.911896i
$399$	−2.09876e18			−1.30362
$400$	−2.88486e16			−0.0176078
$401$	−2.13296e18			−1.27930			−0.639651	−	0.768666i	$-0.720921\pi$
$401$	−2.13296e18			−1.27930			−0.639651	+	0.768666i	$0.720921\pi$
$402$		−	1.26639e17i		−	0.0746425i
$403$		−	5.87111e17i		−	0.340083i
$404$			1.62742e18i			0.926468i
$405$	2.02384e18			1.13238
$406$		−	2.05216e18i		−	1.12857i
$407$	−1.25565e18	+	9.23529e17i	−0.678746	+	0.499217i
$408$	−5.97055e17			−0.317244
$409$		−	1.40285e18i		−	0.732739i	−0.930469	−	0.366369i	$-0.880601\pi$
$409$		−	1.40285e18i		−	0.732739i	0.930469	−	0.366369i	$-0.119399\pi$
$410$	1.33452e18			0.685232
$411$	2.76843e18			1.39747
$412$	1.10721e18			0.549477
$413$		−	2.95477e18i		−	1.44169i
$414$			1.91780e18i			0.920030i
$415$			3.70884e17i			0.174945i
$416$	2.10898e17			0.0978181
$417$		−	4.15016e18i		−	1.89283i
$418$	1.17961e18	−	8.67604e17i	0.529061	−	0.389124i
$419$	3.90588e18			1.72275			0.861373	−	0.507974i	$-0.169605\pi$
$419$	3.90588e18			1.72275			0.861373	+	0.507974i	$0.169605\pi$
$420$		−	1.55988e18i		−	0.676623i
$421$	2.25755e17			0.0963080			0.0481540	−	0.998840i	$-0.484666\pi$
$421$	2.25755e17			0.0963080			0.0481540	+	0.998840i	$0.484666\pi$
$422$	1.56875e18			0.658213
$423$	−2.37560e18			−0.980372
$424$		−	7.87285e17i		−	0.319574i
$425$		−	1.18810e17i		−	0.0474384i
$426$		−	1.13716e17i		−	0.0446636i
$427$	−3.10935e18			−1.20136
$428$			1.37138e18i			0.521256i
$429$	−1.16803e18	−	1.58808e18i	−0.436771	−	0.593844i
$430$	−1.59907e18			−0.588285
$431$		−	2.76525e18i		−	1.00091i	−0.865763	−	0.500454i	$-0.833167\pi$
$431$		−	2.76525e18i		−	1.00091i	0.865763	−	0.500454i	$-0.166833\pi$
$432$	−2.10616e17			−0.0750076
$433$	−1.73403e18			−0.607633			−0.303817	−	0.952731i	$-0.598261\pi$
$433$	−1.73403e18			−0.607633			−0.303817	+	0.952731i	$0.598261\pi$
$434$	1.32790e18			0.457866
$435$		−	5.73483e18i		−	1.94579i
$436$			1.17610e18i			0.392681i
$437$			4.74701e18i			1.55973i
$438$	−1.07058e18			−0.346180
$439$		−	1.38152e18i		−	0.439648i	−0.975540	−	0.219824i	$-0.929452\pi$
$439$		−	1.38152e18i		−	0.439648i	0.975540	−	0.219824i	$-0.0705484\pi$
$440$	6.44839e17	+	8.76736e17i	0.201968	+	0.274600i
$441$	−2.76487e17			−0.0852325
$442$			8.68560e17i			0.263538i
$443$	1.78840e18			0.534121			0.267060	−	0.963680i	$-0.413948\pi$
$443$	1.78840e18			0.534121			0.267060	+	0.963680i	$0.413948\pi$
$444$	−1.90909e18			−0.561237
$445$	5.67838e17			0.164325
$446$		−	3.10167e18i		−	0.883592i
$447$			7.24228e18i			2.03106i
$448$			4.77001e17i			0.131696i
$449$	2.40865e18			0.654710			0.327355	−	0.944901i	$-0.393843\pi$
$449$	2.40865e18			0.654710			0.327355	+	0.944901i	$0.393843\pi$
$450$			1.44185e17i			0.0385863i
$451$	2.26014e18	+	3.07293e18i	0.595523	+	0.809686i
$452$	−8.29521e17			−0.215208
$453$			2.42988e18i			0.620722i
$454$	2.81065e18			0.706993
$455$	−2.26923e18			−0.562080
$456$	1.79349e18			0.437466
$457$		−	4.07586e18i		−	0.979051i	−0.871989	−	0.489526i	$-0.837170\pi$
$457$		−	4.07586e18i		−	0.979051i	0.871989	−	0.489526i	$-0.162830\pi$
$458$			1.35120e18i			0.319640i
$459$		−	8.67398e17i		−	0.202083i
$460$	−3.52817e18			−0.809552
$461$		−	2.96254e18i		−	0.669511i	−0.942305	−	0.334755i	$-0.891346\pi$
$461$		−	2.96254e18i		−	0.669511i	0.942305	−	0.334755i	$-0.108654\pi$
$462$	3.59186e18	−	2.64181e18i	0.799513	−	0.588041i
$463$	−4.04238e18			−0.886278			−0.443139	−	0.896453i	$-0.646135\pi$
$463$	−4.04238e18			−0.886278			−0.443139	+	0.896453i	$0.646135\pi$
$464$			1.75367e18i			0.378723i
$465$	3.71086e18			0.789413
$466$	4.01865e18			0.842129
$467$	5.69967e18			1.17661			0.588304	−	0.808640i	$-0.299796\pi$
$467$	5.69967e18			1.17661			0.588304	+	0.808640i	$0.299796\pi$
$468$		−	1.05407e18i		−	0.214362i
$469$		−	4.16678e17i		−	0.0834816i
$470$		−	4.37038e18i		−	0.862648i
$471$	−8.25814e17			−0.160596
$472$			2.52499e18i			0.483799i
$473$	−2.70818e18	−	3.68209e18i	−0.511268	−	0.695131i
$474$	−5.57813e18			−1.03762
$475$			3.56892e17i			0.0654156i
$476$	−1.96447e18			−0.354811
$477$	−3.93484e18			−0.700324
$478$	5.21954e18			0.915455
$479$		−	7.40327e18i		−	1.27960i	−0.768541	−	0.639801i	$-0.779017\pi$
$479$		−	7.40327e18i		−	1.27960i	0.768541	−	0.639801i	$-0.220983\pi$
$480$			1.33299e18i			0.227059i
$481$			2.77724e18i			0.466227i
$482$	−4.13966e18			−0.684914
$483$			1.44544e19i			2.35706i
$484$	−9.26720e17	+	2.96967e18i	−0.148947	+	0.477300i
$485$	3.68608e18			0.583946
$486$			5.72672e18i			0.894236i
$487$	9.76288e18			1.50271			0.751355	−	0.659898i	$-0.229401\pi$
$487$	9.76288e18			1.50271			0.751355	+	0.659898i	$0.229401\pi$
$488$	2.65709e18			0.403150
$489$	−1.44052e19			−2.15455
$490$		−	5.08652e17i		−	0.0749977i
$491$			6.09802e18i			0.886378i	0.896428	+	0.443189i	$0.146153\pi$
$491$			6.09802e18i			0.886378i	−0.896428	+	0.443189i	$0.853847\pi$
$492$			4.67209e18i			0.669507i
$493$	−7.22229e18			−1.02034
$494$		−	2.60906e18i		−	0.363409i
$495$	4.38192e18	−	3.22290e18i	0.601767	−	0.442599i
$496$	−1.13475e18			−0.153649
$497$		−	3.74156e17i		−	0.0499527i
$498$	−1.29845e18			−0.170930
$499$	−1.40351e19			−1.82185			−0.910924	−	0.412574i	$-0.864630\pi$
$499$	−1.40351e19			−1.82185			−0.910924	+	0.412574i	$0.864630\pi$
$500$	−4.03143e18			−0.516024
$501$			1.33408e17i			0.0168391i
$502$			6.39818e18i			0.796398i
$503$			5.18305e18i			0.636223i	0.948053	+	0.318111i	$0.103049\pi$
$503$			5.18305e18i			0.636223i	−0.948053	+	0.318111i	$0.896951\pi$
$504$	2.38405e18			0.288603
$505$			1.49638e19i			1.78649i
$506$	−5.97529e18	−	8.12414e18i	−0.703567	−	0.956585i
$507$	7.95922e18			0.924304
$508$		−	8.59061e18i		−	0.983962i
$509$	−1.31946e19			−1.49064			−0.745319	−	0.666708i	$-0.767703\pi$
$509$	−1.31946e19			−1.49064			−0.745319	+	0.666708i	$0.767703\pi$
$510$	−5.48978e18			−0.611736
$511$	−3.52251e18			−0.387174
$512$		−	4.07619e17i		−	0.0441942i
$513$			2.60557e18i			0.278664i
$514$		−	3.41113e18i		−	0.359879i
$515$	1.01805e19			1.05955
$516$		−	5.59826e18i		−	0.574785i
$517$	1.00634e19	−	7.40165e18i	1.01932	−	0.749712i
$518$	−6.28144e18			−0.627698
$519$		−	1.86253e19i		−	1.83625i
$520$	1.93916e18			0.188621
$521$	1.02649e19			0.985124			0.492562	−	0.870277i	$-0.336060\pi$
$521$	1.02649e19			0.985124			0.492562	+	0.870277i	$0.336060\pi$
$522$	8.76482e18			0.829945
$523$			8.64600e18i			0.807799i	0.914803	+	0.403900i	$0.132345\pi$
$523$			8.64600e18i			0.807799i	−0.914803	+	0.403900i	$0.867655\pi$
$524$		−	8.91357e18i		−	0.821737i
$525$			1.08672e18i			0.0988557i
$526$	−1.38319e19			−1.24160
$527$		−	4.67336e18i		−	0.413957i
$528$	−3.06941e18	+	2.25755e18i	−0.268298	+	0.197333i
$529$	2.11004e19			1.82012
$530$		−	7.23891e18i		−	0.616229i
$531$	1.26199e19			1.06021
$532$	5.90107e18			0.489271
$533$	6.79668e18			0.556169
$534$			1.98797e18i			0.160554i
$535$			1.26095e19i			1.00513i
$536$			3.56071e17i			0.0280145i
$537$	8.16101e18			0.633759
$538$			9.54427e18i			0.731588i
$539$	1.17125e18	−	8.61450e17i	0.0886190	−	0.0651792i
$540$	−1.93657e18			−0.144636
$541$		−	1.19057e19i		−	0.877757i	−0.898546	−	0.438879i	$-0.855376\pi$
$541$		−	1.19057e19i		−	0.877757i	0.898546	−	0.438879i	$-0.144624\pi$
$542$	3.92782e18			0.285862
$543$	1.75646e18			0.126194
$544$	1.67873e18			0.119067
$545$			1.08140e19i			0.757200i
$546$		−	7.94445e18i		−	0.549181i
$547$		−	1.01805e19i		−	0.694799i	−0.937717	−	0.347400i	$-0.887065\pi$
$547$		−	1.01805e19i		−	0.694799i	0.937717	−	0.347400i	$-0.112935\pi$
$548$	−7.78398e18			−0.524491
$549$		−	1.32801e19i		−	0.883475i
$550$	−4.49237e17	−	6.10793e17i	−0.0295078	−	0.0401194i
$551$	2.16950e19			1.40701
$552$		−	1.23520e19i		−	0.790974i
$553$	−1.83536e19			−1.16050
$554$	−2.00885e18			−0.125424
$555$	−1.75537e19			−1.08222
$556$			1.16690e19i			0.710410i
$557$		−	2.05299e19i		−	1.23424i	−0.786867	−	0.617122i	$-0.788298\pi$
$557$		−	2.05299e19i		−	1.23424i	0.786867	−	0.617122i	$-0.211702\pi$
$558$			5.67149e18i			0.336712i
$559$	−8.14403e18			−0.477482
$560$			4.38591e18i			0.253947i
$561$	−9.29746e18	−	1.26410e19i	−0.531648	−	0.722840i
$562$	2.30042e19			1.29913
$563$			2.56873e19i			1.43272i	0.697733	+	0.716358i	$0.254192\pi$
$563$			2.56873e19i			1.43272i	−0.697733	+	0.716358i	$0.745808\pi$
$564$	1.53005e19			0.842852
$565$	−7.62726e18			−0.414982
$566$	−3.56226e18			−0.191430
$567$			2.33128e19i			1.23741i
$568$			3.19734e17i			0.0167630i
$569$		−	1.26575e19i		−	0.655485i	−0.944767	−	0.327742i	$-0.893712\pi$
$569$		−	1.26575e19i		−	0.655485i	0.944767	−	0.327742i	$-0.106288\pi$
$570$	1.64907e19			0.843559
$571$		−	3.03372e18i		−	0.153293i	−0.997058	−	0.0766466i	$-0.975579\pi$
$571$		−	3.03372e18i		−	0.153293i	0.997058	−	0.0766466i	$-0.0244213\pi$
$572$	3.28415e18	+	4.46520e18i	0.163927	+	0.222879i
$573$	−4.69439e19			−2.31471
$574$			1.53725e19i			0.748790i
$575$	2.45796e18			0.118277
$576$	−2.03728e18			−0.0968485
$577$	−1.75043e19			−0.822082			−0.411041	−	0.911617i	$-0.634835\pi$
$577$	−1.75043e19			−0.822082			−0.411041	+	0.911617i	$0.634835\pi$
$578$		−	8.32614e18i		−	0.386321i
$579$		−	1.14764e19i		−	0.526087i
$580$			1.61246e19i			0.730285i
$581$	−4.27225e18			−0.191172
$582$			1.29048e19i			0.570545i
$583$	1.66687e19	−	1.22598e19i	0.728150	−	0.535553i
$584$	3.01015e18			0.129927
$585$		−	9.69190e18i		−	0.413350i
$586$	6.75436e18			0.284643
$587$	2.01981e17			0.00841092			0.00420546	−	0.999991i	$-0.498661\pi$
$587$	2.01981e17			0.00841092			0.00420546	+	0.999991i	$0.498661\pi$
$588$	1.78077e18			0.0732766
$589$			1.40383e19i			0.570830i
$590$			2.32167e19i			0.932901i
$591$			1.38383e19i			0.549503i
$592$	5.36778e18			0.210641
$593$		−	3.53501e19i		−	1.37091i	−0.728116	−	0.685454i	$-0.759604\pi$
$593$		−	3.53501e19i		−	1.37091i	0.728116	−	0.685454i	$-0.240396\pi$
$594$	−3.27976e18	−	4.45923e18i	−0.125700	−	0.170905i
$595$	−1.80629e19			−0.684177
$596$		−	2.03631e19i		−	0.762288i
$597$	−4.64359e19			−1.71804
$598$	−1.79689e19			−0.657073
$599$	3.03003e19			1.09511			0.547557	−	0.836768i	$-0.315558\pi$
$599$	3.03003e19			1.09511			0.547557	+	0.836768i	$0.315558\pi$
$600$		−	9.28651e17i		−	0.0331737i
$601$			2.23510e19i			0.789181i	0.918857	+	0.394590i	$0.129113\pi$
$601$			2.23510e19i			0.789181i	−0.918857	+	0.394590i	$0.870887\pi$
$602$		−	1.84198e19i		−	0.642851i
$603$	1.77964e18			0.0613918
$604$		−	6.83207e18i		−	0.232967i
$605$	−8.52098e18	+	2.73055e19i	−0.287211	+	0.920369i
$606$	−5.23874e19			−1.74550
$607$			6.83948e18i			0.225269i	0.993636	+	0.112635i	$0.0359290\pi$
$607$			6.83948e18i			0.225269i	−0.993636	+	0.112635i	$0.964071\pi$
$608$	−5.04274e18			−0.164188
$609$	6.60600e19			2.12627
$610$	2.44313e19			0.777387
$611$		−	2.22582e19i		−	0.700168i
$612$		−	8.39030e18i		−	0.260926i
$613$		−	7.18627e18i		−	0.220943i	−0.993879	−	0.110471i	$-0.964764\pi$
$613$		−	7.18627e18i		−	0.220943i	0.993879	−	0.110471i	$-0.0352361\pi$
$614$	3.83322e19			1.16516
$615$			4.29588e19i			1.29100i
$616$	−1.00992e19	+	7.42796e18i	−0.300070	+	0.220701i
$617$	−8.06287e18			−0.236861			−0.118431	−	0.992962i	$-0.537786\pi$
$617$	−8.06287e18			−0.236861			−0.118431	+	0.992962i	$0.537786\pi$
$618$			3.56416e19i			1.03523i
$619$	−2.95921e19			−0.849849			−0.424924	−	0.905229i	$-0.639699\pi$
$619$	−2.95921e19			−0.849849			−0.424924	+	0.905229i	$0.639699\pi$
$620$	−1.04338e19			−0.296279
$621$	1.79449e19			0.503847
$622$			4.83322e19i			1.34185i
$623$			6.54098e18i			0.179567i
$624$			6.78890e18i			0.184292i
$625$	−3.44443e19			−0.924608
$626$		−	3.01971e19i		−	0.801577i
$627$	2.79286e19	+	3.79723e19i	0.733122	+	0.996768i
$628$	2.32194e18			0.0602744
$629$			2.21066e19i			0.567502i
$630$	2.19207e19			0.556508
$631$	5.84818e18			0.146830			0.0734151	−	0.997301i	$-0.476610\pi$
$631$	5.84818e18			0.146830			0.0734151	+	0.997301i	$0.476610\pi$
$632$	1.56840e19			0.389437
$633$			5.04988e19i			1.24009i
$634$		−	2.89640e19i		−	0.703450i
$635$		−	7.89887e19i		−	1.89736i
$636$	2.53431e19			0.602087
$637$		−	2.59055e18i		−	0.0608719i
$638$	−3.71292e19	+	2.73085e19i	−0.862921	+	0.634677i
$639$	1.59803e18			0.0367349
$640$		−	3.74797e18i		−	0.0852189i
$641$	3.07064e19			0.690594			0.345297	−	0.938493i	$-0.387778\pi$
$641$	3.07064e19			0.690594			0.345297	+	0.938493i	$0.387778\pi$
$642$	−4.41453e19			−0.982063
$643$	−3.34635e19			−0.736366			−0.368183	−	0.929753i	$-0.620020\pi$
$643$	−3.34635e19			−0.736366			−0.368183	+	0.929753i	$0.620020\pi$
$644$		−	4.06413e19i		−	0.884641i
$645$		−	5.14747e19i		−	1.10835i
$646$		−	2.07679e19i		−	0.442350i
$647$	−3.22302e19			−0.679098			−0.339549	−	0.940588i	$-0.610275\pi$
$647$	−3.22302e19			−0.679098			−0.339549	+	0.940588i	$0.610275\pi$
$648$		−	1.99219e19i		−	0.415246i
$649$	−5.34598e19	+	3.93196e19i	−1.10234	+	0.810767i
$650$	−1.35095e18			−0.0275578
$651$			4.27458e19i			0.862634i
$652$	4.05029e19			0.808636
$653$	8.05170e19			1.59036			0.795179	−	0.606374i	$-0.207377\pi$
$653$	8.05170e19			1.59036			0.795179	+	0.606374i	$0.207377\pi$
$654$	−3.78593e19			−0.739824
$655$		−	8.19582e19i		−	1.58454i
$656$		−	1.31365e19i		−	0.251277i
$657$		−	1.50447e19i		−	0.284726i
$658$	5.03428e19			0.942662
$659$		−	8.02662e19i		−	1.48708i	−0.668690	−	0.743541i	$-0.733145\pi$
$659$		−	8.02662e19i		−	1.48708i	0.668690	−	0.743541i	$-0.266855\pi$
$660$	−2.82225e19	+	2.07576e19i	−0.517355	+	0.380514i
$661$	4.55001e19			0.825282			0.412641	−	0.910894i	$-0.364606\pi$
$661$	4.55001e19			0.825282			0.412641	+	0.910894i	$0.364606\pi$
$662$			1.92566e19i			0.345599i
$663$	−2.79593e19			−0.496515
$664$	3.65083e18			0.0641528
$665$	5.42590e19			0.943452
$666$		−	2.68281e19i		−	0.461605i
$667$		−	1.49416e20i		−	2.54399i
$668$		−	3.75103e17i		−	0.00631997i
$669$	9.98441e19			1.66471
$670$			3.27399e18i			0.0540199i
$671$	4.13767e19	+	5.62567e19i	0.675613	+	0.918578i
$672$	−1.53549e19			−0.248120
$673$		−	1.46349e19i		−	0.234038i	−0.993130	−	0.117019i	$-0.962666\pi$
$673$		−	1.46349e19i		−	0.234038i	0.993130	−	0.117019i	$-0.0373338\pi$
$674$	2.84639e19			0.450479
$675$	1.34914e18			0.0211315
$676$	−2.23789e19			−0.346906
$677$		−	6.09622e19i		−	0.935276i	−0.883920	−	0.467638i	$-0.845105\pi$
$677$		−	6.09622e19i		−	0.935276i	0.883920	−	0.467638i	$-0.154895\pi$
$678$		−	2.67027e19i		−	0.405459i
$679$			4.24603e19i			0.638109i
$680$	1.54356e19			0.229594
$681$			9.04760e19i			1.33200i
$682$	−1.76706e19	−	2.40254e19i	−0.257491	−	0.350090i
$683$	5.87414e17			0.00847226			0.00423613	−	0.999991i	$-0.498652\pi$
$683$	5.87414e17			0.00847226			0.00423613	+	0.999991i	$0.498652\pi$
$684$			2.52036e19i			0.359807i
$685$	−7.15719e19			−1.01137
$686$	−4.74027e19			−0.663032
$687$	−4.34957e19			−0.602211
$688$			1.57406e19i			0.215726i
$689$		−	3.68676e19i		−	0.500162i
$690$		−	1.13573e20i		−	1.52522i
$691$	−1.07427e20			−1.42812			−0.714062	−	0.700083i	$-0.753147\pi$
$691$	−1.07427e20			−1.42812			−0.714062	+	0.700083i	$0.753147\pi$
$692$			5.23686e19i			0.689173i
$693$	3.71249e19	+	5.04758e19i	0.483651	+	0.657583i
$694$	2.81991e19			0.363680
$695$			1.07294e20i			1.36987i
$696$	−5.64514e19			−0.713526
$697$	5.41011e19			0.676982
$698$	−9.52112e17			−0.0117951
$699$			1.29362e20i			1.58660i
$700$		−	3.05552e18i		−	0.0371021i
$701$			1.14615e20i			1.37789i	0.724812	+	0.688947i	$0.241927\pi$
$701$			1.14615e20i			1.37789i	−0.724812	+	0.688947i	$0.758073\pi$
$702$	−9.86289e18			−0.117394
$703$		−	6.64059e19i		−	0.782563i
$704$	8.63025e18	−	6.34754e18i	0.100697	−	0.0740622i
$705$	1.40684e20			1.62526
$706$			7.27462e19i			0.832104i
$707$	−1.72369e20			−1.95220
$708$	−8.12804e19			−0.911492
$709$	4.19675e19			0.466003			0.233002	−	0.972476i	$-0.425145\pi$
$709$	4.19675e19			0.466003			0.233002	+	0.972476i	$0.425145\pi$
$710$			2.93988e18i			0.0323237i
$711$		−	7.83885e19i		−	0.853424i
$712$		−	5.58957e18i		−	0.0602585i
$713$	9.66832e19			1.03211
$714$		−	6.32373e19i		−	0.668476i
$715$	3.01970e19	+	4.10565e19i	0.316098	+	0.429773i
$716$	−2.29463e19			−0.237860
$717$			1.68019e20i			1.72475i
$718$	1.13513e20			1.15392
$719$	−1.88410e18			−0.0189671			−0.00948356	−	0.999955i	$-0.503019\pi$
$719$	−1.88410e18			−0.0189671			−0.00948356	+	0.999955i	$0.503019\pi$
$720$	−1.87323e19			−0.186751
$721$			1.17271e20i			1.15782i
$722$		−	9.93316e18i		−	0.0971241i
$723$		−	1.33258e20i		−	1.29040i
$724$	−4.93861e18			−0.0473626
$725$		−	1.12334e19i		−	0.106696i
$726$	−9.55951e19	−	2.98315e19i	−0.899248	−	0.280620i
$727$	−2.64591e19			−0.246510			−0.123255	−	0.992375i	$-0.539333\pi$
$727$	−2.64591e19			−0.246510			−0.123255	+	0.992375i	$0.539333\pi$
$728$			2.23374e19i			0.206116i
$729$	−5.58341e19			−0.510278
$730$	2.76777e19			0.250536
$731$	−6.48259e19			−0.581202
$732$			8.55328e19i			0.759547i
$733$			2.62616e19i			0.230990i	0.993308	+	0.115495i	$0.0368454\pi$
$733$			2.62616e19i			0.230990i	−0.993308	+	0.115495i	$0.963155\pi$
$734$			8.66730e19i			0.755112i
$735$	1.63737e19			0.141298
$736$			3.47299e19i			0.296865i
$737$	−7.53884e18	+	5.54481e18i	−0.0638311	+	0.0469477i
$738$	−6.56560e19			−0.550655
$739$		−	2.35064e20i		−	1.95288i	−0.215800	−	0.976438i	$-0.569236\pi$
$739$		−	2.35064e20i		−	1.95288i	0.215800	−	0.976438i	$-0.430764\pi$
$740$	4.93555e19			0.406175
$741$	8.39868e19			0.684674
$742$	8.33857e19			0.673386
$743$			2.17854e20i			1.74279i	0.490584	+	0.871394i	$0.336783\pi$
$743$			2.17854e20i			1.74279i	−0.490584	+	0.871394i	$0.663217\pi$
$744$		−	3.65283e19i		−	0.289480i
$745$		−	1.87234e20i		−	1.46991i
$746$	−7.97040e19			−0.619881
$747$		−	1.82468e19i		−	0.140586i
$748$	2.61416e19	+	3.55427e19i	0.199536	+	0.271293i
$749$	−1.45250e20			−1.09836
$750$		−	1.29774e20i		−	0.972205i
$751$	−7.99894e19			−0.593680			−0.296840	−	0.954927i	$-0.595933\pi$
$751$	−7.99894e19			−0.593680			−0.296840	+	0.954927i	$0.595933\pi$
$752$	−4.30202e19			−0.316336
$753$	−2.05960e20			−1.50044
$754$			8.21221e19i			0.592735i
$755$		−	6.28193e19i		−	0.449226i
$756$		−	2.23075e19i		−	0.158051i
$757$	−1.22053e20			−0.856794			−0.428397	−	0.903591i	$-0.640922\pi$
$757$	−1.22053e20			−0.856794			−0.428397	+	0.903591i	$0.640922\pi$
$758$		−	1.05256e20i		−	0.732083i
$759$	2.61520e20	−	1.92347e20i	1.80224	−	1.32554i
$760$	−4.63668e19			−0.316601
$761$			1.68403e20i			1.13935i	0.821871	+	0.569674i	$0.192930\pi$
$761$			1.68403e20i			1.13935i	−0.821871	+	0.569674i	$0.807070\pi$
$762$	2.76536e20			1.85381
$763$	−1.24567e20			−0.827433
$764$	1.31992e20			0.868747
$765$		−	7.71469e19i		−	0.503139i
$766$			4.35572e19i			0.281487i
$767$			1.18242e20i			0.757189i
$768$	1.31214e19			0.0832632
$769$			4.56302e19i			0.286925i	0.989656	+	0.143462i	$0.0458236\pi$
$769$			4.56302e19i			0.286925i	−0.989656	+	0.143462i	$0.954176\pi$
$770$	−9.28599e19	+	6.82984e19i	−0.578620	+	0.425574i
$771$	1.09806e20			0.678024
$772$			3.22682e19i			0.197449i
$773$	3.35365e19			0.203358			0.101679	−	0.994817i	$-0.467579\pi$
$773$	3.35365e19			0.203358			0.101679	+	0.994817i	$0.467579\pi$
$774$	7.86714e19			0.472748
$775$	7.26888e18			0.0432868
$776$		−	3.62843e19i		−	0.214135i
$777$		−	2.02202e20i		−	1.18260i
$778$			1.39368e20i			0.807801i
$779$	−1.62514e20			−0.933530
$780$			6.24224e19i			0.355368i
$781$	−6.76951e18	+	4.97897e18i	−0.0381944	+	0.0280920i
$782$	−1.43031e20			−0.799804
$783$		−	8.20123e19i		−	0.454513i
$784$	−5.00697e18			−0.0275019
$785$	2.13497e19			0.116226
$786$	2.86932e20			1.54818
$787$			2.81672e20i			1.50633i	0.657831	+	0.753165i	$0.271474\pi$
$787$			2.81672e20i			1.50633i	−0.657831	+	0.753165i	$0.728526\pi$
$788$		−	3.89090e19i		−	0.206237i
$789$		−	4.45254e20i		−	2.33921i
$790$	1.44211e20			0.750944
$791$		−	8.78591e19i		−	0.453473i
$792$	−3.17249e19	−	4.31339e19i	−0.162302	−	0.220670i
$793$	1.24428e20			0.630966
$794$		−	8.54677e19i		−	0.429594i
$795$	2.33024e20			1.16099
$796$	1.30563e20			0.644808
$797$	−2.50971e20			−1.22861			−0.614307	−	0.789067i	$-0.710564\pi$
$797$	−2.50971e20			−1.22861			−0.614307	+	0.789067i	$0.710564\pi$
$798$			1.89958e20i			0.921802i
$799$		−	1.77174e20i		−	0.852261i
$800$			2.61108e18i			0.0124506i
$801$	−2.79366e19			−0.132052
$802$			1.93054e20i			0.904602i
$803$	4.68747e19	+	6.37319e19i	0.217736	+	0.296038i
$804$	−1.14621e19			−0.0527802
$805$		−	3.73688e20i		−	1.70584i
$806$	−5.31392e19			−0.240475
$807$	−3.07234e20			−1.37834
$808$	1.47297e20			0.655112
$809$			1.67113e20i			0.736834i	0.929661	+	0.368417i	$0.120100\pi$
$809$			1.67113e20i			0.736834i	−0.929661	+	0.368417i	$0.879900\pi$
$810$		−	1.83177e20i		−	0.800711i
$811$			8.31549e19i			0.360364i	0.983633	+	0.180182i	$0.0576687\pi$
$811$			8.31549e19i			0.360364i	−0.983633	+	0.180182i	$0.942331\pi$
$812$	−1.85741e20			−0.798021
$813$			1.26438e20i			0.538573i
$814$	8.35883e19	+	1.13648e20i	0.353000	+	0.479946i
$815$	3.72415e20			1.55928
$816$			5.40392e19i			0.224325i
$817$	1.94730e20			0.801454
$818$	−1.26972e20			−0.518125
$819$	1.11642e20			0.451690
$820$		−	1.20787e20i		−	0.484532i
$821$			1.86972e20i			0.743660i	0.928301	+	0.371830i	$0.121270\pi$
$821$			1.86972e20i			0.743660i	−0.928301	+	0.371830i	$0.878730\pi$
$822$		−	2.50570e20i		−	0.988158i
$823$	1.33342e20			0.521397			0.260698	−	0.965420i	$-0.416047\pi$
$823$	1.33342e20			0.521397			0.260698	+	0.965420i	$0.416047\pi$
$824$		−	1.00213e20i		−	0.388539i
$825$	1.96617e19	−	1.44611e19i	0.0755863	−	0.0555936i
$826$	−2.67435e20			−1.01943
$827$			5.37762e19i			0.203260i	0.994822	+	0.101630i	$0.0324057\pi$
$827$			5.37762e19i			0.203260i	−0.994822	+	0.101630i	$0.967594\pi$
$828$	1.73580e20			0.650559
$829$	3.94236e20			1.46512			0.732562	−	0.680700i	$-0.238324\pi$
$829$	3.94236e20			1.46512			0.732562	+	0.680700i	$0.238324\pi$
$830$	3.35686e19			0.123705
$831$		−	6.46658e19i		−	0.236302i
$832$		−	1.90883e19i		−	0.0691679i
$833$		−	2.06206e19i		−	0.0740947i
$834$	−3.75630e20			−1.33844
$835$		−	3.44898e18i		−	0.0121867i
$836$	−7.85266e19	−	1.06766e20i	−0.275152	−	0.374103i
$837$	5.30681e19			0.184398
$838$		−	3.53520e20i		−	1.21816i
$839$	1.55689e19			0.0532015			0.0266007	−	0.999646i	$-0.491532\pi$
$839$	1.55689e19			0.0532015			0.0266007	+	0.999646i	$0.491532\pi$
$840$	−1.41184e20			−0.478445
$841$	−3.85307e20			−1.29490
$842$		−	2.04330e19i		−	0.0681000i
$843$			7.40515e20i			2.44760i
$844$		−	1.41987e20i		−	0.465427i
$845$	−2.05769e20			−0.668933
$846$			2.15015e20i			0.693228i
$847$	−3.14534e20	−	9.81540e19i	−1.00574	−	0.313851i
$848$	−7.12569e19			−0.225973
$849$		−	1.14671e20i		−	0.360660i
$850$	−1.07534e19			−0.0335440
$851$	−4.57345e20			−1.41494
$852$	−1.02924e19			−0.0315819
$853$			5.69284e19i			0.173255i	0.996241	+	0.0866274i	$0.0276090\pi$
$853$			5.69284e19i			0.173255i	−0.996241	+	0.0866274i	$0.972391\pi$
$854$			2.81426e20i			0.849493i
$855$			2.31741e20i			0.693809i
$856$	1.24123e20			0.368584
$857$			1.82987e20i			0.538958i	0.963006	+	0.269479i	$0.0868515\pi$
$857$			1.82987e20i			0.538958i	−0.963006	+	0.269479i	$0.913148\pi$
$858$	−1.43737e20	+	1.05718e20i	−0.419911	+	0.308844i
$859$	3.81449e20			1.10531			0.552655	−	0.833410i	$-0.313615\pi$
$859$	3.81449e20			1.10531			0.552655	+	0.833410i	$0.313615\pi$
$860$			1.44731e20i			0.415981i
$861$	−4.94846e20			−1.41074
$862$	−2.50282e20			−0.707748
$863$	−1.41862e20			−0.397916			−0.198958	−	0.980008i	$-0.563756\pi$
$863$	−1.41862e20			−0.397916			−0.198958	+	0.980008i	$0.563756\pi$
$864$			1.90628e19i			0.0530384i
$865$			4.81517e20i			1.32892i
$866$			1.56947e20i			0.429662i
$867$	2.68022e20			0.727842
$868$		−	1.20188e20i		−	0.323760i
$869$	2.44235e20	+	3.32066e20i	0.652632	+	0.887333i
$870$	−5.19057e20			−1.37588
$871$			1.66744e19i			0.0438452i
$872$	1.06449e20			0.277667
$873$	−1.81349e20			−0.469261
$874$	4.29650e20			1.10290
$875$		−	4.26991e20i		−	1.08733i
$876$			9.68982e19i			0.244786i
$877$		−	4.00254e19i		−	0.100309i	−0.998741	−	0.0501544i	$-0.984029\pi$
$877$		−	4.00254e19i		−	0.100309i	0.998741	−	0.0501544i	$-0.0159713\pi$
$878$	−1.25041e20			−0.310878
$879$			2.17426e20i			0.536277i
$880$	7.93531e19	−	5.83641e19i	0.194171	−	0.142813i
$881$	7.93534e20			1.92634			0.963172	−	0.268885i	$-0.0866552\pi$
$881$	7.93534e20			1.92634			0.963172	+	0.268885i	$0.0866552\pi$
$882$			2.50248e19i			0.0602685i
$883$	−6.32658e20			−1.51162			−0.755812	−	0.654788i	$-0.772758\pi$
$883$	−6.32658e20			−1.51162			−0.755812	+	0.654788i	$0.772758\pi$
$884$	7.86131e19			0.186350
$885$	−7.47355e20			−1.75762
$886$		−	1.61868e20i		−	0.377680i
$887$		−	2.94341e20i		−	0.681373i	−0.940177	−	0.340686i	$-0.889341\pi$
$887$		−	2.94341e20i		−	0.681373i	0.940177	−	0.340686i	$-0.110659\pi$
$888$			1.72791e20i			0.396854i
$889$	9.09878e20			2.07334
$890$		−	5.13948e19i		−	0.116196i
$891$	4.21792e20	−	3.10228e20i	0.946138	−	0.695883i
$892$	−2.80731e20			−0.624794
$893$			5.32212e20i			1.17523i
$894$	6.55496e20			1.43618
$895$	−2.10986e20			−0.458661
$896$	4.31732e19			0.0931232
$897$		−	5.78427e20i		−	1.23795i
$898$		−	2.18006e20i		−	0.462950i
$899$		−	4.41865e20i		−	0.931047i
$900$	1.30502e19			0.0272846
$901$		−	2.93464e20i		−	0.608809i
$902$	2.78130e20	−	2.04564e20i	0.572534	−	0.421098i
$903$	5.92943e20			1.21115
$904$			7.50797e19i			0.152175i
$905$	−4.54094e19			−0.0913284
$906$	2.19927e20			0.438917
$907$	5.43443e20			1.07623			0.538113	−	0.842873i	$-0.319138\pi$
$907$	5.43443e20			1.07623			0.538113	+	0.842873i	$0.319138\pi$
$908$		−	2.54391e20i		−	0.499920i
$909$		−	7.36191e20i		−	1.43563i
$910$			2.05387e20i			0.397451i
$911$	−4.55809e20			−0.875294			−0.437647	−	0.899147i	$-0.644188\pi$
$911$	−4.55809e20			−0.875294			−0.437647	+	0.899147i	$0.644188\pi$
$912$		−	1.62328e20i		−	0.309335i
$913$	5.68516e19	+	7.72966e19i	0.107510	+	0.146172i
$914$	−3.68904e20			−0.692294
$915$			7.86454e20i			1.46462i
$916$	1.22296e20			0.226019
$917$	9.44085e20			1.73151
$918$	−7.85079e19			−0.142894
$919$		−	5.46063e20i		−	0.986356i	−0.869928	−	0.493178i	$-0.835835\pi$
$919$		−	5.46063e20i		−	0.986356i	0.869928	−	0.493178i	$-0.164165\pi$
$920$			3.19334e20i			0.572440i
$921$			1.23393e21i			2.19520i
$922$	−2.68138e20			−0.473416
$923$			1.49728e19i			0.0262355i
$924$	−2.39109e20	−	3.25098e20i	−0.415808	−	0.565341i
$925$	−3.43843e19			−0.0593428
$926$			3.65874e20i			0.626693i
$927$	−5.00865e20			−0.851456
$928$	1.58724e20			0.267798
$929$	−2.23731e20			−0.374641			−0.187321	−	0.982299i	$-0.559980\pi$
$929$	−2.23731e20			−0.374641			−0.187321	+	0.982299i	$0.559980\pi$
$930$		−	3.35869e20i		−	0.558199i
$931$			6.19422e19i			0.102174i
$932$		−	3.63727e20i		−	0.595475i
$933$	−1.55583e21			−2.52809
$934$		−	5.15875e20i		−	0.831987i
$935$	2.40366e20	+	3.26807e20i	0.384762	+	0.523130i
$936$	−9.54032e19			−0.151577
$937$		−	8.55067e20i		−	1.34841i	−0.738543	−	0.674206i	$-0.764486\pi$
$937$		−	8.55067e20i		−	1.34841i	0.738543	−	0.674206i	$-0.235514\pi$
$938$	−3.77134e19			−0.0590304
$939$	9.72059e20			1.51020
$940$	−3.95561e20			−0.609984
$941$		−	9.05540e20i		−	1.38605i	−0.720911	−	0.693027i	$-0.756277\pi$
$941$		−	9.05540e20i		−	1.38605i	0.720911	−	0.693027i	$-0.243723\pi$
$942$			7.47442e19i			0.113559i
$943$			1.11925e21i			1.68790i
$944$	2.28536e20			0.342097
$945$		−	2.05112e20i		−	0.304768i
$946$	−3.33265e20	+	2.45116e20i	−0.491532	+	0.361521i
$947$	−6.85540e20			−1.00365			−0.501826	−	0.864969i	$-0.667338\pi$
$947$	−6.85540e20			−1.00365			−0.501826	+	0.864969i	$0.667338\pi$
$948$			5.04875e20i			0.733711i
$949$	1.40962e20			0.203347
$950$	3.23022e19			0.0462558
$951$	9.32363e20			1.32532
$952$			1.77804e20i			0.250890i
$953$			6.24466e20i			0.874698i	0.899292	+	0.437349i	$0.144083\pi$
$953$			6.24466e20i			0.874698i	−0.899292	+	0.437349i	$0.855917\pi$
$954$			3.56141e20i			0.495204i
$955$	1.21363e21			1.67519
$956$		−	4.72419e20i		−	0.647325i
$957$	−8.79073e20	−	1.19521e21i	−1.19575	−	1.62577i
$958$	−6.70067e20			−0.904815
$959$		−	8.24444e20i		−	1.10517i
$960$	1.20649e20			0.160555
$961$	−4.71024e20			−0.622271
$962$	2.51367e20			0.329672
$963$		−	6.20366e20i		−	0.807726i
$964$			3.74680e20i			0.484307i
$965$			2.96699e20i			0.380737i
$966$	1.30826e21			1.66669
$967$		−	1.81318e20i		−	0.229327i	−0.993404	−	0.114664i	$-0.963421\pi$
$967$		−	1.81318e20i		−	0.229327i	0.993404	−	0.114664i	$-0.0365790\pi$
$968$	2.68784e20	+	8.38771e19i	0.337502	+	0.105321i
$969$	6.68530e20			0.833401
$970$		−	3.33626e20i		−	0.412912i
$971$	−5.19816e20			−0.638726			−0.319363	−	0.947632i	$-0.603469\pi$
$971$	−5.19816e20			−0.638726			−0.319363	+	0.947632i	$0.603469\pi$
$972$	5.18324e20			0.632321
$973$	−1.23593e21			−1.49693
$974$		−	8.83635e20i		−	1.06258i
$975$		−	4.34876e19i		−	0.0519198i
$976$		−	2.40492e20i		−	0.285070i
$977$	3.78331e20			0.445257			0.222628	−	0.974903i	$-0.428536\pi$
$977$	3.78331e20			0.445257			0.222628	+	0.974903i	$0.428536\pi$
$978$			1.30381e21i			1.52350i
$979$	1.18344e20	−	8.70420e19i	0.137299	−	0.100983i
$980$	−4.60379e19			−0.0530314
$981$		−	5.32030e20i		−	0.608489i
$982$	5.51930e20			0.626764
$983$	−7.85688e20			−0.885881			−0.442941	−	0.896551i	$-0.646065\pi$
$983$	−7.85688e20			−0.885881			−0.442941	+	0.896551i	$0.646065\pi$
$984$	4.22869e20			0.473413
$985$		−	3.57759e20i		−	0.397683i
$986$			6.53687e20i			0.721492i
$987$			1.62056e21i			1.77600i
$988$	−2.36145e20			−0.256969
$989$		−	1.34113e21i		−	1.44909i
$990$	−2.91703e20	−	3.96606e20i	−0.312964	−	0.425513i
$991$	−1.09370e21			−1.16515			−0.582574	−	0.812778i	$-0.697954\pi$
$991$	−1.09370e21			−1.16515			−0.582574	+	0.812778i	$0.697954\pi$
$992$			1.02706e20i			0.108646i
$993$	−6.19877e20			−0.651120
$994$	−3.38648e19			−0.0353219
$995$	1.20050e21			1.24337
$996$			1.17522e20i			0.120866i
$997$			1.11125e21i			1.13487i	0.823418	+	0.567435i	$0.192064\pi$
$997$			1.11125e21i			1.13487i	−0.823418	+	0.567435i	$0.807936\pi$
$998$			1.27031e21i			1.28824i
$999$	−2.51030e20			−0.252795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.15.b.a.21.6	✓	14
4.3	odd	2		176.15.h.e.65.4		14
11.10	odd	2	inner	22.15.b.a.21.13	yes	14
44.43	even	2		176.15.h.e.65.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.15.b.a.21.6	✓	14	1.1	even	1	trivial
22.15.b.a.21.13	yes	14	11.10	odd	2	inner
176.15.h.e.65.3		14	44.43	even	2
176.15.h.e.65.4		14	4.3	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:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	22.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-90.5097i q^{2} +2913.55 q^{3} -8192.00 q^{4} -75323.6 q^{5} -263704. i q^{6} -867659. i q^{7} +741455. i q^{8} +3.70579e6 q^{9} +O(q^{10})\)	\(q-90.5097i q^{2} +2913.55 q^{3} -8192.00 q^{4} -75323.6 q^{5} -263704. i q^{6} -867659. i q^{7} +741455. i q^{8} +3.70579e6 q^{9} +6.81751e6i q^{10} +(-1.56983e7 + 1.15461e7i) q^{11} -2.38678e7 q^{12} +3.47214e7i q^{13} -7.85316e7 q^{14} -2.19459e8 q^{15} +6.71089e7 q^{16} +2.76380e8i q^{17} -3.35409e8i q^{18} -8.30217e8i q^{19} +6.17051e8 q^{20} -2.52797e9i q^{21} +(1.04503e9 + 1.42085e9i) q^{22} -5.71780e9 q^{23} +2.16026e9i q^{24} -4.29878e8 q^{25} +3.14263e9 q^{26} -3.13842e9 q^{27} +7.10787e9i q^{28} +2.61317e10i q^{29} +1.98631e10i q^{30} -1.69092e10 q^{31} -6.07400e9i q^{32} +(-4.57378e10 + 3.36401e10i) q^{33} +2.50151e10 q^{34} +6.53552e10i q^{35} -3.03578e10 q^{36} +7.99862e10 q^{37} -7.51426e10 q^{38} +1.01163e11i q^{39} -5.58490e10i q^{40} -1.95749e11i q^{41} -2.28805e11 q^{42} +2.34553e11i q^{43} +(1.28601e11 - 9.45856e10i) q^{44} -2.79133e11 q^{45} +5.17516e11i q^{46} -6.41052e11 q^{47} +1.95525e11 q^{48} -7.46096e10 q^{49} +3.89081e10i q^{50} +8.05247e11i q^{51} -2.84438e11i q^{52} -1.06181e12 q^{53} +2.84058e11i q^{54} +(1.18245e12 - 8.69693e11i) q^{55} +6.43331e11 q^{56} -2.41888e12i q^{57} +2.36517e12 q^{58} +3.40545e12 q^{59} +1.79781e12 q^{60} -3.58361e12i q^{61} +1.53044e12i q^{62} -3.21536e12i q^{63} -5.49756e11 q^{64} -2.61534e12i q^{65} +(3.04475e12 + 4.13971e12i) q^{66} +4.80232e11 q^{67} -2.26411e12i q^{68} -1.66591e13 q^{69} +5.91528e12 q^{70} +4.31225e11 q^{71} +2.74767e12i q^{72} -4.05979e12i q^{73} -7.23952e12i q^{74} -1.25247e12 q^{75} +6.80113e12i q^{76} +(1.00181e13 + 1.36208e13i) q^{77} +9.15619e12 q^{78} -2.11530e13i q^{79} -5.05488e12 q^{80} -2.68686e13 q^{81} -1.77172e13 q^{82} -4.92388e12i q^{83} +2.07091e13i q^{84} -2.08180e13i q^{85} +2.12293e13 q^{86} +7.61359e13i q^{87} +(-8.56092e12 - 1.16396e13i) q^{88} -7.53865e12 q^{89} +2.52642e13i q^{90} +3.01264e13 q^{91} +4.68402e13 q^{92} -4.92656e13 q^{93} +5.80214e13i q^{94} +6.25349e13i q^{95} -1.76969e13i q^{96} -4.89366e13 q^{97} +6.75289e12i q^{98} +(-5.81746e13 + 4.27874e13i) 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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