LMFDB - Embedded newform 22.15.b.a.21.7

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			21.7
Root			$-3417.25 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	22.21
Dual form			22.15.b.a.21.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-90.5097i q^{2} +3731.25 q^{3} -8192.00 q^{4} +97060.9 q^{5} -337715. i q^{6} +769857. i q^{7} +741455. i q^{8} +9.13929e6 q^{9} +O(q^{10})$	\(q-90.5097i q^{2} +3731.25 q^{3} -8192.00 q^{4} +97060.9 q^{5} -337715. i q^{6} +769857. i q^{7} +741455. i q^{8} +9.13929e6 q^{9} -8.78495e6i q^{10} +(9.46666e6 - 1.70333e7i) q^{11} -3.05664e7 q^{12} +4.15528e7i q^{13} +6.96795e7 q^{14} +3.62159e8 q^{15} +6.71089e7 q^{16} +4.49448e8i q^{17} -8.27194e8i q^{18} +4.22818e8i q^{19} -7.95123e8 q^{20} +2.87253e9i q^{21} +(-1.54168e9 - 8.56824e8i) q^{22} -2.43013e9 q^{23} +2.76656e9i q^{24} +3.31730e9 q^{25} +3.76093e9 q^{26} +1.62545e10 q^{27} -6.30667e9i q^{28} -2.14199e10i q^{29} -3.27789e10i q^{30} +3.99333e10 q^{31} -6.07400e9i q^{32} +(3.53225e10 - 6.35554e10i) q^{33} +4.06794e10 q^{34} +7.47230e10i q^{35} -7.48690e10 q^{36} -6.78234e10 q^{37} +3.82691e10 q^{38} +1.55044e11i q^{39} +7.19663e10i q^{40} -2.81930e11i q^{41} +2.59992e11 q^{42} -4.47514e11i q^{43} +(-7.75509e10 + 1.39537e11i) q^{44} +8.87067e11 q^{45} +2.19950e11i q^{46} -4.66235e9 q^{47} +2.50400e11 q^{48} +8.55428e10 q^{49} -3.00248e11i q^{50} +1.67700e12i q^{51} -3.40400e11i q^{52} -1.15695e12 q^{53} -1.47119e12i q^{54} +(9.18843e11 - 1.65326e12i) q^{55} -5.70815e11 q^{56} +1.57764e12i q^{57} -1.93871e12 q^{58} -3.73609e12 q^{59} -2.96681e12 q^{60} +2.74015e12i q^{61} -3.61435e12i q^{62} +7.03595e12i q^{63} -5.49756e11 q^{64} +4.03315e12i q^{65} +(-5.75238e12 - 3.19703e12i) q^{66} +1.12103e13 q^{67} -3.68187e12i q^{68} -9.06744e12 q^{69} +6.76316e12 q^{70} -1.25038e13 q^{71} +6.77637e12i q^{72} -4.18678e12i q^{73} +6.13868e12i q^{74} +1.23777e13 q^{75} -3.46372e12i q^{76} +(1.31132e13 + 7.28798e12i) q^{77} +1.40330e13 q^{78} -2.62836e13i q^{79} +6.51365e12 q^{80} +1.69368e13 q^{81} -2.55174e13 q^{82} +5.26788e13i q^{83} -2.35318e13i q^{84} +4.36238e13i q^{85} -4.05043e13 q^{86} -7.99230e13i q^{87} +(1.26294e13 + 7.01911e12i) q^{88} -3.77123e13 q^{89} -8.02882e13i q^{90} -3.19897e13 q^{91} +1.99076e13 q^{92} +1.49001e14 q^{93} +4.21988e11i q^{94} +4.10391e13i q^{95} -2.26636e13i q^{96} +8.75936e13 q^{97} -7.74245e12i q^{98} +(8.65185e13 - 1.55672e14i) 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
$3$	3731.25			1.70611			0.853053	−	0.521824i	$-0.174748\pi$
$3$	3731.25			1.70611			0.853053	+	0.521824i	$0.174748\pi$
$4$	−8192.00			−0.500000
$5$	97060.9			1.24238			0.621190	−	0.783660i	$-0.286650\pi$
$5$	97060.9			1.24238			0.621190	+	0.783660i	$0.286650\pi$
$6$		−	337715.i		−	1.20640i
$7$			769857.i			0.934811i	0.884043	+	0.467406i	$0.154811\pi$
$7$			769857.i			0.934811i	−0.884043	+	0.467406i	$0.845189\pi$
$8$			741455.i			0.353553i
$9$	9.13929e6			1.91080
$10$		−	8.78495e6i		−	0.878495i
$11$	9.46666e6	−	1.70333e7i	0.485789	−	0.874076i
$11$	9.46666e6	−	1.70333e7i	0.485789	−	0.874076i
$12$	−3.05664e7			−0.853053
$13$			4.15528e7i			0.662212i	0.943594	+	0.331106i	$0.107422\pi$
$13$			4.15528e7i			0.662212i	−0.943594	+	0.331106i	$0.892578\pi$
$14$	6.96795e7			0.661011
$15$	3.62159e8			2.11963
$16$	6.71089e7			0.250000
$17$			4.49448e8i			1.09531i	0.836705	+	0.547654i	$0.184479\pi$
$17$			4.49448e8i			1.09531i	−0.836705	+	0.547654i	$0.815521\pi$
$18$		−	8.27194e8i		−	1.35114i
$19$			4.22818e8i			0.473019i	0.971629	+	0.236509i	$0.0760034\pi$
$19$			4.22818e8i			0.473019i	−0.971629	+	0.236509i	$0.923997\pi$
$20$	−7.95123e8			−0.621190
$21$			2.87253e9i			1.59489i
$22$	−1.54168e9	−	8.56824e8i	−0.618065	−	0.343505i
$23$	−2.43013e9			−0.713732			−0.356866	−	0.934156i	$-0.616155\pi$
$23$	−2.43013e9			−0.713732			−0.356866	+	0.934156i	$0.616155\pi$
$24$			2.76656e9i			0.603200i
$25$	3.31730e9			0.543507
$26$	3.76093e9			0.468254
$27$	1.62545e10			1.55392
$28$		−	6.30667e9i		−	0.467406i
$29$		−	2.14199e10i		−	1.24174i	−0.783913	−	0.620871i	$-0.786779\pi$
$29$		−	2.14199e10i		−	1.24174i	0.783913	−	0.620871i	$-0.213221\pi$
$30$		−	3.27789e10i		−	1.49881i
$31$	3.99333e10			1.45145			0.725727	−	0.687983i	$-0.241503\pi$
$31$	3.99333e10			1.45145			0.725727	+	0.687983i	$0.241503\pi$
$32$		−	6.07400e9i		−	0.176777i
$33$	3.53225e10	−	6.35554e10i	0.828808	−	1.49127i
$34$	4.06794e10			0.774500
$35$			7.47230e10i			1.16139i
$36$	−7.48690e10			−0.955399
$37$	−6.78234e10			−0.714443			−0.357222	−	0.934020i	$-0.616276\pi$
$37$	−6.78234e10			−0.714443			−0.357222	+	0.934020i	$0.616276\pi$
$38$	3.82691e10			0.334475
$39$			1.55044e11i			1.12980i
$40$			7.19663e10i			0.439248i
$41$		−	2.81930e11i		−	1.44762i	−0.689999	−	0.723810i	$-0.742389\pi$
$41$		−	2.81930e11i		−	1.44762i	0.689999	−	0.723810i	$-0.257611\pi$
$42$	2.59992e11			1.12776
$43$		−	4.47514e11i		−	1.64637i	−0.567774	−	0.823184i	$-0.692195\pi$
$43$		−	4.47514e11i		−	1.64637i	0.567774	−	0.823184i	$-0.307805\pi$
$44$	−7.75509e10	+	1.39537e11i	−0.242895	+	0.437038i
$45$	8.87067e11			2.37394
$46$			2.19950e11i			0.504685i
$47$	−4.66235e9			−0.00920280			−0.00460140	−	0.999989i	$-0.501465\pi$
$47$	−4.66235e9			−0.00920280			−0.00460140	+	0.999989i	$0.501465\pi$
$48$	2.50400e11			0.426526
$49$	8.55428e10			0.126128
$50$		−	3.00248e11i		−	0.384318i
$51$			1.67700e12i			1.86871i
$52$		−	3.40400e11i		−	0.331106i
$53$	−1.15695e12			−0.984885			−0.492442	−	0.870345i	$-0.663896\pi$
$53$	−1.15695e12			−0.984885			−0.492442	+	0.870345i	$0.663896\pi$
$54$		−	1.47119e12i		−	1.09879i
$55$	9.18843e11	−	1.65326e12i	0.603535	−	1.08593i
$56$	−5.70815e11			−0.330506
$57$			1.57764e12i			0.807020i
$58$	−1.93871e12			−0.878044
$59$	−3.73609e12			−1.50125			−0.750626	−	0.660727i	$-0.770248\pi$
$59$	−3.73609e12			−1.50125			−0.750626	+	0.660727i	$0.770248\pi$
$60$	−2.96681e12			−1.05982
$61$			2.74015e12i			0.871899i	0.899971	+	0.435950i	$0.143587\pi$
$61$			2.74015e12i			0.871899i	−0.899971	+	0.435950i	$0.856413\pi$
$62$		−	3.61435e12i		−	1.02633i
$63$			7.03595e12i			1.78624i
$64$	−5.49756e11			−0.125000
$65$			4.03315e12i			0.822718i
$66$	−5.75238e12	−	3.19703e12i	−1.05448	−	0.586056i
$67$	1.12103e13			1.84967			0.924835	−	0.380369i	$-0.124203\pi$
$67$	1.12103e13			1.84967			0.924835	+	0.380369i	$0.124203\pi$
$68$		−	3.68187e12i		−	0.547654i
$69$	−9.06744e12			−1.21770
$70$	6.76316e12			0.821227
$71$	−1.25038e13			−1.37478			−0.687388	−	0.726290i	$-0.741243\pi$
$71$	−1.25038e13			−1.37478			−0.687388	+	0.726290i	$0.741243\pi$
$72$			6.77637e12i			0.675569i
$73$		−	4.18678e12i		−	0.378983i	−0.981882	−	0.189492i	$-0.939316\pi$
$73$		−	4.18678e12i		−	0.378983i	0.981882	−	0.189492i	$-0.0606840\pi$
$74$			6.13868e12i			0.505188i
$75$	1.23777e13			0.927281
$76$		−	3.46372e12i		−	0.236509i
$77$	1.31132e13	+	7.28798e12i	0.817096	+	0.454121i
$78$	1.40330e13			0.798891
$79$		−	2.62836e13i		−	1.36866i	−0.729173	−	0.684330i	$-0.760095\pi$
$79$		−	2.62836e13i		−	1.36866i	0.729173	−	0.684330i	$-0.239905\pi$
$80$	6.51365e12			0.310595
$81$	1.69368e13			0.740350
$82$	−2.55174e13			−1.02362
$83$			5.26788e13i			1.94128i	0.240531	+	0.970642i	$0.422679\pi$
$83$			5.26788e13i			1.94128i	−0.240531	+	0.970642i	$0.577321\pi$
$84$		−	2.35318e13i		−	0.797444i
$85$			4.36238e13i			1.36079i
$86$	−4.05043e13			−1.16416
$87$		−	7.99230e13i		−	2.11854i
$88$	1.26294e13	+	7.01911e12i	0.309032	+	0.171752i
$89$	−3.77123e13			−0.852616			−0.426308	−	0.904578i	$-0.640186\pi$
$89$	−3.77123e13			−0.852616			−0.426308	+	0.904578i	$0.640186\pi$
$90$		−	8.02882e13i		−	1.67863i
$91$	−3.19897e13			−0.619043
$92$	1.99076e13			0.356866
$93$	1.49001e14			2.47633
$94$			4.21988e11i			0.00650736i
$95$			4.10391e13i			0.587669i
$96$		−	2.26636e13i		−	0.301600i
$97$	8.75936e13			1.08410			0.542051	−	0.840345i	$-0.317648\pi$
$97$	8.75936e13			1.08410			0.542051	+	0.840345i	$0.317648\pi$
$98$		−	7.74245e12i		−	0.0891859i
$99$	8.65185e13	−	1.55672e14i	0.928245	−	1.67018i
$100$	−2.71754e13			−0.271754
$101$			6.42657e13i			0.599417i	0.954031	+	0.299709i	$0.0968895\pi$
$101$			6.42657e13i			0.599417i	−0.954031	+	0.299709i	$0.903111\pi$
$102$	1.51785e14			1.32138
$103$	−1.51457e14			−1.23148			−0.615741	−	0.787948i	$-0.711143\pi$
$103$	−1.51457e14			−1.23148			−0.615741	+	0.787948i	$0.711143\pi$
$104$	−3.08095e13			−0.234127
$105$			2.78811e14i			1.98146i
$106$			1.04716e14i			0.696419i
$107$		−	2.81112e14i		−	1.75063i	−0.483556	−	0.875314i	$-0.660655\pi$
$107$		−	2.81112e14i		−	1.75063i	0.483556	−	0.875314i	$-0.339345\pi$
$108$	−1.33157e14			−0.776959
$109$			1.99942e14i			1.09375i	0.837214	+	0.546876i	$0.184183\pi$
$109$			1.99942e14i			1.09375i	−0.837214	+	0.546876i	$0.815817\pi$
$110$	−1.49636e14	−	8.31642e13i	−0.767871	−	0.426764i
$111$	−2.53066e14			−1.21892
$112$			5.16642e13i			0.233703i
$113$	5.43120e13			0.230859			0.115429	−	0.993316i	$-0.463176\pi$
$113$	5.43120e13			0.230859			0.115429	+	0.993316i	$0.463176\pi$
$114$	1.42792e14			0.570649
$115$	−2.35871e14			−0.886726
$116$			1.75472e14i			0.620871i
$117$			3.79763e14i			1.26535i
$118$			3.38153e14i			1.06155i
$119$	−3.46011e14			−1.02391
$120$			2.68525e14i			0.749403i
$121$	−2.00514e14	−	3.22496e14i	−0.528017	−	0.849234i
$122$	2.48011e14			0.616526
$123$		−	1.05195e15i		−	2.46979i
$124$	−3.27134e14			−0.725727
$125$	−2.70432e14			−0.567138
$126$	6.36821e14			1.26306
$127$			7.36010e14i			1.38120i	0.723235	+	0.690601i	$0.242654\pi$
$127$			7.36010e14i			1.38120i	−0.723235	+	0.690601i	$0.757346\pi$
$128$			4.97582e13i			0.0883883i
$129$		−	1.66979e15i		−	2.80888i
$130$	3.65039e14			0.581750
$131$			5.63371e14i			0.850933i	0.904974	+	0.425466i	$0.139890\pi$
$131$			5.63371e14i			0.850933i	−0.904974	+	0.425466i	$0.860110\pi$
$132$	−2.89362e14	+	5.20646e14i	−0.414404	+	0.745633i
$133$	−3.25509e14			−0.442183
$134$		−	1.01464e15i		−	1.30791i
$135$	1.57768e15			1.93056
$136$	−3.33245e14			−0.387250
$137$	−5.67357e14			−0.626343			−0.313172	−	0.949697i	$-0.601392\pi$
$137$	−5.67357e14			−0.626343			−0.313172	+	0.949697i	$0.601392\pi$
$138$			8.20691e14i			0.861045i
$139$			3.62493e14i			0.361573i	0.983522	+	0.180786i	$0.0578643\pi$
$139$			3.62493e14i			0.361573i	−0.983522	+	0.180786i	$0.942136\pi$
$140$		−	6.12131e14i		−	0.580695i
$141$	−1.73964e13			−0.0157009
$142$			1.13171e15i			0.972114i
$143$	7.07780e14	+	3.93366e14i	0.578823	+	0.321695i
$144$	6.13327e14			0.477699
$145$		−	2.07903e15i		−	1.54271i
$146$	−3.78944e14			−0.267981
$147$	3.19182e14			0.215187
$148$	5.55610e14			0.357222
$149$			2.78077e14i			0.170554i	0.996357	+	0.0852768i	$0.0271774\pi$
$149$			2.78077e14i			0.170554i	−0.996357	+	0.0852768i	$0.972823\pi$
$150$		−	1.12030e15i		−	0.655686i
$151$			1.07558e15i			0.600905i	0.953797	+	0.300453i	$0.0971377\pi$
$151$			1.07558e15i			0.600905i	−0.953797	+	0.300453i	$0.902862\pi$
$152$	−3.13501e14			−0.167237
$153$			4.10763e15i			2.09291i
$154$	6.59633e14	−	1.18687e15i	0.321112	−	0.577774i
$155$	3.87596e15			1.80326
$156$		−	1.27012e15i		−	0.564902i
$157$	1.04359e15			0.443847			0.221923	−	0.975064i	$-0.428767\pi$
$157$	1.04359e15			0.443847			0.221923	+	0.975064i	$0.428767\pi$
$158$	−2.37892e15			−0.967788
$159$	−4.31689e15			−1.68032
$160$		−	5.89548e14i		−	0.219624i
$161$		−	1.87085e15i		−	0.667204i
$162$		−	1.53295e15i		−	0.523507i
$163$	3.97177e14			0.129919			0.0649593	−	0.997888i	$-0.479308\pi$
$163$	3.97177e14			0.129919			0.0649593	+	0.997888i	$0.479308\pi$
$164$			2.30957e15i			0.723810i
$165$	3.42844e15	−	6.16875e15i	1.02969	−	1.85272i
$166$	4.76794e15			1.37269
$167$		−	1.37211e15i		−	0.378768i	−0.981903	−	0.189384i	$-0.939351\pi$
$167$		−	1.37211e15i		−	0.378768i	0.981903	−	0.189384i	$-0.0606490\pi$
$168$	−2.12985e15			−0.563878
$169$	2.21074e15			0.561476
$170$	3.94837e15			0.962223
$171$			3.86425e15i			0.903843i
$172$			3.66603e15i			0.823184i
$173$		−	2.96466e15i		−	0.639223i	−0.947549	−	0.319611i	$-0.896448\pi$
$173$		−	2.96466e15i		−	0.639223i	0.947549	−	0.319611i	$-0.103552\pi$
$174$	−7.23381e15			−1.49804
$175$			2.55385e15i			0.508077i
$176$	6.35297e14	−	1.14308e15i	0.121447	−	0.218519i
$177$	−1.39403e16			−2.56130
$178$			3.41333e15i			0.602890i
$179$	−6.70143e15			−1.13814			−0.569071	−	0.822288i	$-0.692697\pi$
$179$	−6.70143e15			−1.13814			−0.569071	+	0.822288i	$0.692697\pi$
$180$	−7.26686e15			−1.18697
$181$	−3.89252e15			−0.611618			−0.305809	−	0.952093i	$-0.598927\pi$
$181$	−3.89252e15			−0.611618			−0.305809	+	0.952093i	$0.598927\pi$
$182$			2.89538e15i			0.437729i
$183$			1.02242e16i			1.48755i
$184$		−	1.80183e15i		−	0.252342i
$185$	−6.58300e15			−0.887610
$186$		−	1.34861e16i		−	1.75103i
$187$	7.65556e15	+	4.25477e15i	0.957383	+	0.532089i
$188$	3.81940e13			0.00460140
$189$			1.25137e16i			1.45262i
$190$	3.71443e15			0.415544
$191$	9.59113e15			1.03427			0.517137	−	0.855902i	$-0.326998\pi$
$191$	9.59113e15			1.03427			0.517137	+	0.855902i	$0.326998\pi$
$192$	−2.05128e15			−0.213263
$193$			8.41474e15i			0.843606i	0.906688	+	0.421803i	$0.138603\pi$
$193$			8.41474e15i			0.843606i	−0.906688	+	0.421803i	$0.861397\pi$
$194$		−	7.92807e15i		−	0.766576i
$195$			1.50487e16i			1.40364i
$196$	−7.00767e14			−0.0630639
$197$		−	1.24486e16i		−	1.08107i	−0.841320	−	0.540537i	$-0.818221\pi$
$197$		−	1.24486e16i		−	1.08107i	0.841320	−	0.540537i	$-0.181779\pi$
$198$	−1.40898e16	−	7.83076e15i	−1.18100	−	0.656369i
$199$	4.69534e15			0.379923			0.189961	−	0.981792i	$-0.439164\pi$
$199$	4.69534e15			0.379923			0.189961	+	0.981792i	$0.439164\pi$
$200$			2.45963e15i			0.192159i
$201$	4.18285e16			3.15573
$202$	5.81666e15			0.423852
$203$	1.64903e16			1.16079
$204$		−	1.37380e16i		−	0.934357i
$205$		−	2.73644e16i		−	1.79849i
$206$			1.37083e16i			0.870790i
$207$	−2.22097e16			−1.36380
$208$			2.78856e15i			0.165553i
$209$	7.20197e15	+	4.00267e15i	0.413454	+	0.229787i
$210$	2.52351e16			1.40110
$211$		−	6.66236e15i		−	0.357808i	−0.983866	−	0.178904i	$-0.942745\pi$
$211$		−	6.66236e15i		−	0.357808i	0.983866	−	0.178904i	$-0.0572552\pi$
$212$	9.47777e15			0.492442
$213$	−4.66547e16			−2.34552
$214$	−2.54434e16			−1.23788
$215$		−	4.34361e16i		−	2.04541i
$216$			1.20520e16i			0.549393i
$217$			3.07429e16i			1.35684i
$218$	1.80967e16			0.773399
$219$		−	1.56219e16i		−	0.646585i
$220$	−7.52716e15	+	1.35435e16i	−0.301767	+	0.542967i
$221$	−1.86758e16			−0.725326
$222$			2.29050e16i			0.861904i
$223$	−1.40023e16			−0.510580			−0.255290	−	0.966864i	$-0.582171\pi$
$223$	−1.40023e16			−0.510580			−0.255290	+	0.966864i	$0.582171\pi$
$224$	4.67611e15			0.165253
$225$	3.03178e16			1.03853
$226$		−	4.91576e15i		−	0.163242i
$227$		−	3.45271e16i		−	1.11168i	−0.831290	−	0.555839i	$-0.812397\pi$
$227$		−	3.45271e16i		−	1.11168i	0.831290	−	0.555839i	$-0.187603\pi$
$228$		−	1.29240e16i		−	0.403510i
$229$	−1.74756e16			−0.529157			−0.264579	−	0.964364i	$-0.585233\pi$
$229$	−1.74756e16			−0.529157			−0.264579	+	0.964364i	$0.585233\pi$
$230$			2.13486e16i			0.627010i
$231$	4.89286e16	+	2.71933e16i	1.39405	+	0.774779i
$232$	1.58819e16			0.439022
$233$		−	2.18870e16i		−	0.587076i	−0.955947	−	0.293538i	$-0.905167\pi$
$233$		−	2.18870e16i		−	0.587076i	0.955947	−	0.293538i	$-0.0948327\pi$
$234$	3.43722e16			0.894739
$235$	−4.52532e14			−0.0114334
$236$	3.06061e16			0.750626
$237$		−	9.80708e16i		−	2.33508i
$238$			3.13173e16i			0.724012i
$239$			4.65789e16i			1.04569i	0.852427	+	0.522847i	$0.175130\pi$
$239$			4.65789e16i			1.04569i	−0.852427	+	0.522847i	$0.824870\pi$
$240$	2.43041e16			0.529908
$241$		−	6.62659e16i		−	1.40337i	−0.712490	−	0.701683i	$-0.752432\pi$
$241$		−	6.62659e16i		−	1.40337i	0.712490	−	0.701683i	$-0.247568\pi$
$242$	−2.91890e16	+	1.81485e16i	−0.600499	+	0.373365i
$243$	−1.45493e16			−0.290802
$244$		−	2.24473e16i		−	0.435950i
$245$	8.30286e15			0.156699
$246$	−9.52120e16			−1.74641
$247$	−1.75693e16			−0.313238
$248$			2.96088e16i			0.513167i
$249$			1.96558e17i			3.31203i
$250$			2.44767e16i			0.401027i
$251$	−6.78064e16			−1.08033			−0.540163	−	0.841560i	$-0.681637\pi$
$251$	−6.78064e16			−1.08033			−0.540163	+	0.841560i	$0.681637\pi$
$252$		−	5.76385e16i		−	0.893118i
$253$	−2.30052e16	+	4.13931e16i	−0.346723	+	0.623856i
$254$	6.66160e16			0.976658
$255$			1.62771e17i			2.32165i
$256$	4.50360e15			0.0625000
$257$	6.49673e16			0.877329			0.438665	−	0.898651i	$-0.355452\pi$
$257$	6.49673e16			0.877329			0.438665	+	0.898651i	$0.355452\pi$
$258$	−1.51132e17			−1.98618
$259$		−	5.22144e16i		−	0.667870i
$260$		−	3.30396e16i		−	0.411359i
$261$		−	1.95762e17i		−	2.37272i
$262$	5.09905e16			0.601700
$263$			2.18216e16i			0.250724i	0.992111	+	0.125362i	$0.0400093\pi$
$263$			2.18216e16i			0.250724i	−0.992111	+	0.125362i	$0.959991\pi$
$264$	4.71235e16	+	2.61901e16i	0.527242	+	0.293028i
$265$	−1.12295e17			−1.22360
$266$			2.94618e16i			0.312671i
$267$	−1.40714e17			−1.45465
$268$	−9.18349e16			−0.924835
$269$	−1.26796e16			−0.124406			−0.0622029	−	0.998064i	$-0.519813\pi$
$269$	−1.26796e16			−0.124406			−0.0622029	+	0.998064i	$0.519813\pi$
$270$		−	1.42795e17i		−	1.36511i
$271$			5.76970e16i			0.537487i	0.963212	+	0.268743i	$0.0866084\pi$
$271$			5.76970e16i			0.537487i	−0.963212	+	0.268743i	$0.913392\pi$
$272$			3.01619e16i			0.273827i
$273$	−1.19362e17			−1.05615
$274$			5.13513e16i			0.442892i
$275$	3.14038e16	−	5.65045e16i	0.264030	−	0.475066i
$276$	7.42805e16			0.608851
$277$		−	7.76088e16i		−	0.620230i	−0.950699	−	0.310115i	$-0.899632\pi$
$277$		−	7.76088e16i		−	0.620230i	0.950699	−	0.310115i	$-0.100368\pi$
$278$	3.28091e16			0.255671
$279$	3.64962e17			2.77344
$280$	−5.54038e16			−0.410614
$281$		−	5.28687e16i		−	0.382168i	−0.981574	−	0.191084i	$-0.938800\pi$
$281$		−	5.28687e16i		−	0.382168i	0.981574	−	0.191084i	$-0.0612004\pi$
$282$			1.57454e15i			0.0111022i
$283$			8.34031e16i			0.573690i	0.957977	+	0.286845i	$0.0926065\pi$
$283$			8.34031e16i			0.573690i	−0.957977	+	0.286845i	$0.907394\pi$
$284$	1.02431e17			0.687388
$285$			1.53127e17i			1.00262i
$286$	3.56034e16	−	6.40609e16i	0.227473	−	0.409290i
$287$	2.17046e17			1.35325
$288$		−	5.55120e16i		−	0.337784i
$289$	−3.36253e16			−0.199702
$290$	−1.88173e17			−1.09086
$291$	3.26834e17			1.84959
$292$			3.42981e16i			0.189492i
$293$		−	1.23014e17i		−	0.663562i	−0.943356	−	0.331781i	$-0.892350\pi$
$293$		−	1.23014e17i		−	0.663562i	0.943356	−	0.331781i	$-0.107650\pi$
$294$		−	2.88891e16i		−	0.152161i
$295$	−3.62629e17			−1.86512
$296$		−	5.02880e16i		−	0.252594i
$297$	1.53876e17	−	2.76868e17i	0.754877	−	1.35824i
$298$	2.51686e16			0.120600
$299$		−	1.00979e17i		−	0.472641i
$300$	−1.01398e17			−0.463640
$301$	3.44522e17			1.53904
$302$	9.73508e16			0.424904
$303$			2.39792e17i			1.02267i
$304$			2.83748e16i			0.118255i
$305$			2.65962e17i			1.08323i
$306$	3.71780e17			1.47991
$307$			1.45355e17i			0.565536i	0.959188	+	0.282768i	$0.0912526\pi$
$307$			1.45355e17i			0.565536i	−0.959188	+	0.282768i	$0.908747\pi$
$308$	−1.07423e17	−	5.97031e16i	−0.408548	−	0.227061i
$309$	−5.65124e17			−2.10104
$310$		−	3.50812e17i		−	1.27510i
$311$	4.57229e17			1.62484			0.812421	−	0.583071i	$-0.198149\pi$
$311$	4.57229e17			1.62484			0.812421	+	0.583071i	$0.198149\pi$
$312$	−1.14958e17			−0.399446
$313$	−2.82880e17			−0.961152			−0.480576	−	0.876953i	$-0.659572\pi$
$313$	−2.82880e17			−0.961152			−0.480576	+	0.876953i	$0.659572\pi$
$314$		−	9.44551e16i		−	0.313847i
$315$			6.82915e17i			2.21918i
$316$			2.15315e17i			0.684330i
$317$	3.39512e17			1.05546			0.527728	−	0.849414i	$-0.323044\pi$
$317$	3.39512e17			1.05546			0.527728	+	0.849414i	$0.323044\pi$
$318$			3.90720e17i			1.18816i
$319$	−3.64851e17	−	2.02775e17i	−1.08538	−	0.603225i
$320$	−5.33598e16			−0.155297
$321$		−	1.04890e18i		−	2.98676i
$322$	−1.69330e17			−0.471785
$323$	−1.90035e17			−0.518101
$324$	−1.38747e17			−0.370175
$325$			1.37843e17i			0.359917i
$326$		−	3.59484e16i		−	0.0918663i
$327$			7.46035e17i			1.86606i
$328$	2.09039e17			0.511811
$329$		−	3.58934e15i		−	0.00860288i
$330$	−5.58331e17	−	3.10307e17i	−1.31007	−	0.728104i
$331$	−9.07533e16			−0.208481			−0.104240	−	0.994552i	$-0.533241\pi$
$331$	−9.07533e16			−0.208481			−0.104240	+	0.994552i	$0.533241\pi$
$332$		−	4.31544e17i		−	0.970642i
$333$	−6.19858e17			−1.36516
$334$	−1.24189e17			−0.267829
$335$	1.08808e18			2.29799
$336$			1.92772e17i			0.398722i
$337$		−	3.82518e17i		−	0.774895i	−0.921892	−	0.387448i	$-0.873357\pi$
$337$		−	3.82518e17i		−	0.774895i	0.921892	−	0.387448i	$-0.126643\pi$
$338$		−	2.00094e17i		−	0.397023i
$339$	2.02652e17			0.393870
$340$		−	3.57366e17i		−	0.680395i
$341$	3.78035e17	−	6.80195e17i	0.705101	−	1.26868i
$342$	3.49752e17			0.639113
$343$			5.87991e17i			1.05272i
$344$	3.31811e17			0.582079
$345$	−8.80094e17			−1.51285
$346$	−2.68330e17			−0.451999
$347$			2.91503e17i			0.481212i	0.970623	+	0.240606i	$0.0773462\pi$
$347$			2.91503e17i			0.481212i	−0.970623	+	0.240606i	$0.922654\pi$
$348$			6.54729e17i			1.05927i
$349$		−	2.67054e17i		−	0.423468i	−0.977327	−	0.211734i	$-0.932089\pi$
$349$		−	2.67054e17i		−	0.423468i	0.977327	−	0.211734i	$-0.0679111\pi$
$350$	2.31148e17			0.359264
$351$			6.75421e17i			1.02902i
$352$	−1.03460e17	−	5.75005e16i	−0.154516	−	0.0858762i
$353$	−5.11705e17			−0.749198			−0.374599	−	0.927187i	$-0.622220\pi$
$353$	−5.11705e17			−0.749198			−0.374599	+	0.927187i	$0.622220\pi$
$354$			1.26173e18i			1.81111i
$355$	−1.21363e18			−1.70799
$356$	3.08939e17			0.426308
$357$	−1.29105e18			−1.74689
$358$			6.06544e17i			0.804788i
$359$			7.25258e17i			0.943694i	0.881680	+	0.471847i	$0.156413\pi$
$359$			7.25258e17i			0.943694i	−0.881680	+	0.471847i	$0.843587\pi$
$360$			6.57721e17i			0.839313i
$361$	6.20232e17			0.776253
$362$			3.52310e17i			0.432479i
$363$	−7.48170e17	−	1.20332e18i	−0.900853	−	1.44888i
$364$	2.62060e17			0.309521
$365$		−	4.06372e17i		−	0.470841i
$366$	9.25390e17			1.05186
$367$	1.29022e18			1.43881			0.719403	−	0.694593i	$-0.244415\pi$
$367$	1.29022e18			1.43881			0.719403	+	0.694593i	$0.244415\pi$
$368$	−1.63083e17			−0.178433
$369$		−	2.57664e18i		−	2.76611i
$370$			5.95826e17i			0.627635i
$371$		−	8.90690e17i		−	0.920681i
$372$	−1.22062e18			−1.23817
$373$			9.16964e17i			0.912831i	0.889767	+	0.456416i	$0.150867\pi$
$373$			9.16964e17i			0.912831i	−0.889767	+	0.456416i	$0.849133\pi$
$374$	3.85098e17	−	6.92902e17i	0.376244	−	0.676972i
$375$	−1.00905e18			−0.967597
$376$		−	3.45692e15i		−	0.00325368i
$377$	8.90056e17			0.822295
$378$	1.13261e18			1.02716
$379$	8.50809e17			0.757457			0.378728	−	0.925508i	$-0.376361\pi$
$379$	8.50809e17			0.757457			0.378728	+	0.925508i	$0.376361\pi$
$380$		−	3.36192e17i		−	0.293834i
$381$			2.74624e18i			2.35648i
$382$		−	8.68090e17i		−	0.731343i
$383$	1.30044e18			1.07572			0.537860	−	0.843034i	$-0.319233\pi$
$383$	1.30044e18			1.07572			0.537860	+	0.843034i	$0.319233\pi$
$384$			1.85661e17i			0.150800i
$385$	1.27278e18	+	7.07378e17i	1.01514	+	0.564191i
$386$	7.61615e17			0.596519
$387$		−	4.08995e18i		−	3.14588i
$388$	−7.17567e17			−0.542051
$389$	1.40815e18			1.04473			0.522363	−	0.852723i	$-0.325051\pi$
$389$	1.40815e18			1.04473			0.522363	+	0.852723i	$0.325051\pi$
$390$	1.36205e18			0.992526
$391$		−	1.09222e18i		−	0.781757i
$392$			6.34262e16i			0.0445929i
$393$			2.10208e18i			1.45178i
$394$	−1.12671e18			−0.764435
$395$		−	2.55111e18i		−	1.70039i
$396$	−7.08760e17	+	1.27526e18i	−0.464123	+	0.835091i
$397$	1.83808e18			1.18258			0.591292	−	0.806458i	$-0.298618\pi$
$397$	1.83808e18			1.18258			0.591292	+	0.806458i	$0.298618\pi$
$398$		−	4.24973e17i		−	0.268646i
$399$	−1.21456e18			−0.754411
$400$	2.22620e17			0.135877
$401$	−2.43882e18			−1.46275			−0.731375	−	0.681976i	$-0.761121\pi$
$401$	−2.43882e18			−1.46275			−0.731375	+	0.681976i	$0.761121\pi$
$402$		−	3.78589e18i		−	2.23144i
$403$			1.65934e18i			0.961170i
$404$		−	5.26464e17i		−	0.299709i
$405$	1.64390e18			0.919796
$406$		−	1.49253e18i		−	0.820805i
$407$	−6.42062e17	+	1.15525e18i	−0.347069	+	0.624478i
$408$	−1.24342e18			−0.660690
$409$			2.31353e18i			1.20841i	0.796830	+	0.604203i	$0.206508\pi$
$409$			2.31353e18i			1.20841i	−0.796830	+	0.604203i	$0.793492\pi$
$410$	−2.47674e18			−1.27173
$411$	−2.11695e18			−1.06861
$412$	1.24073e18			0.615741
$413$		−	2.87626e18i		−	1.40339i
$414$			2.01019e18i			0.964350i
$415$			5.11305e18i			2.41181i
$416$	2.52392e17			0.117064
$417$			1.35255e18i			0.616882i
$418$	3.62281e17	−	6.51848e17i	0.162484	−	0.292356i
$419$	1.72428e18			0.760518			0.380259	−	0.924880i	$-0.375835\pi$
$419$	1.72428e18			0.760518			0.380259	+	0.924880i	$0.375835\pi$
$420$		−	2.28402e18i		−	0.990728i
$421$	−1.93522e18			−0.825574			−0.412787	−	0.910828i	$-0.635445\pi$
$421$	−1.93522e18			−0.825574			−0.412787	+	0.910828i	$0.635445\pi$
$422$	−6.03008e17			−0.253009
$423$	−4.26106e16			−0.0175847
$424$		−	8.57830e17i		−	0.348209i
$425$			1.49095e18i			0.595308i
$426$			4.22270e18i			1.65853i
$427$	−2.10953e18			−0.815061
$428$			2.30287e18i			0.875314i
$429$	2.64091e18	+	1.46775e18i	0.987534	+	0.548846i
$430$	−3.93138e18			−1.44633
$431$			2.95529e18i			1.06969i	0.844949	+	0.534847i	$0.179631\pi$
$431$			2.95529e18i			1.06969i	−0.844949	+	0.534847i	$0.820369\pi$
$432$	1.09082e18			0.388479
$433$	−6.12703e17			−0.214701			−0.107351	−	0.994221i	$-0.534237\pi$
$433$	−6.12703e17			−0.214701			−0.107351	+	0.994221i	$0.534237\pi$
$434$	2.78253e18			0.959428
$435$		−	7.75740e18i		−	2.63203i
$436$		−	1.63793e18i		−	0.546876i
$437$		−	1.02750e18i		−	0.337608i
$438$	−1.41394e18			−0.457205
$439$		−	7.28296e16i		−	0.0231770i	−0.999933	−	0.0115885i	$-0.996311\pi$
$439$		−	7.28296e16i		−	0.0231770i	0.999933	−	0.0115885i	$-0.00368881\pi$
$440$	1.22582e18	+	6.81281e17i	0.383936	+	0.213382i
$441$	7.81800e17			0.241005
$442$			1.69034e18i			0.512883i
$443$	4.22331e18			1.26132			0.630662	−	0.776058i	$-0.282784\pi$
$443$	4.22331e18			1.26132			0.630662	+	0.776058i	$0.282784\pi$
$444$	2.07312e18			0.609458
$445$	−3.66039e18			−1.05927
$446$			1.26734e18i			0.361035i
$447$			1.03757e18i			0.290982i
$448$		−	4.23234e17i		−	0.116851i
$449$	−3.14406e18			−0.854606			−0.427303	−	0.904108i	$-0.640536\pi$
$449$	−3.14406e18			−0.854606			−0.427303	+	0.904108i	$0.640536\pi$
$450$		−	2.74405e18i		−	0.734353i
$451$	−4.80219e18	−	2.66894e18i	−1.26533	−	0.703239i
$452$	−4.44924e17			−0.115429
$453$			4.01328e18i			1.02521i
$454$	−3.12503e18			−0.786075
$455$	−3.10495e18			−0.769086
$456$	−1.16975e18			−0.285325
$457$		−	4.06817e18i		−	0.977204i	−0.872507	−	0.488602i	$-0.837507\pi$
$457$		−	4.06817e18i		−	0.977204i	0.872507	−	0.488602i	$-0.162493\pi$
$458$			1.58171e18i			0.374171i
$459$			7.30556e18i			1.70202i
$460$	1.93225e18			0.443363
$461$		−	4.03160e18i		−	0.911109i	−0.890208	−	0.455555i	$-0.849441\pi$
$461$		−	4.03160e18i		−	0.911109i	0.890208	−	0.455555i	$-0.150559\pi$
$462$	2.46126e18	−	4.42851e18i	0.547852	−	0.985744i
$463$	4.83475e18			1.06000			0.530001	−	0.847997i	$-0.322191\pi$
$463$	4.83475e18			1.06000			0.530001	+	0.847997i	$0.322191\pi$
$464$		−	1.43746e18i		−	0.310435i
$465$	1.44622e19			3.07655
$466$	−1.98098e18			−0.415125
$467$	−2.19304e18			−0.452718			−0.226359	−	0.974044i	$-0.572682\pi$
$467$	−2.19304e18			−0.452718			−0.226359	+	0.974044i	$0.572682\pi$
$468$		−	3.11102e18i		−	0.632676i
$469$			8.63034e18i			1.72909i
$470$			4.09585e16i			0.00808461i
$471$	3.89390e18			0.757249
$472$		−	2.77015e18i		−	0.530773i
$473$	−7.62262e18	−	4.23646e18i	−1.43905	−	0.799788i
$474$	−8.87636e18			−1.65115
$475$			1.40262e18i			0.257089i
$476$	2.83452e18			0.511954
$477$	−1.05737e19			−1.88192
$478$	4.21584e18			0.739417
$479$			7.29626e18i			1.26111i	0.776146	+	0.630553i	$0.217172\pi$
$479$			7.29626e18i			1.26111i	−0.776146	+	0.630553i	$0.782828\pi$
$480$		−	2.19975e18i		−	0.374701i
$481$		−	2.81825e18i		−	0.473113i
$482$	−5.99770e18			−0.992329
$483$		−	6.98063e18i		−	1.13832i
$484$	1.64261e18	+	2.64189e18i	0.264009	+	0.424617i
$485$	8.50192e18			1.34687
$486$			1.31685e18i			0.205628i
$487$	−6.28135e18			−0.966830			−0.483415	−	0.875391i	$-0.660604\pi$
$487$	−6.28135e18			−0.966830			−0.483415	+	0.875391i	$0.660604\pi$
$488$	−2.03170e18			−0.308263
$489$	1.48197e18			0.221655
$490$		−	7.51489e17i		−	0.110803i
$491$			2.00811e18i			0.291889i	0.989293	+	0.145944i	$0.0466221\pi$
$491$			2.00811e18i			0.291889i	−0.989293	+	0.145944i	$0.953378\pi$
$492$			8.61760e18i			1.23490i
$493$	9.62712e18			1.36009
$494$			1.59019e18i			0.221493i
$495$	8.39757e18	−	1.51097e19i	1.15323	−	2.07500i
$496$	2.67988e18			0.362864
$497$		−	9.62611e18i		−	1.28516i
$498$	1.77904e19			2.34196
$499$	8.25616e18			1.07170			0.535851	−	0.844313i	$-0.319991\pi$
$499$	8.25616e18			1.07170			0.535851	+	0.844313i	$0.319991\pi$
$500$	2.21538e18			0.283569
$501$		−	5.11968e18i		−	0.646218i
$502$			6.13714e18i			0.763906i
$503$			1.80484e18i			0.221545i	0.993846	+	0.110772i	$0.0353325\pi$
$503$			1.80484e18i			0.221545i	−0.993846	+	0.110772i	$0.964668\pi$
$504$	−5.21684e18			−0.631530
$505$			6.23768e18i			0.744704i
$506$	3.74647e18	+	2.08220e18i	0.441133	+	0.245170i
$507$	8.24884e18			0.957937
$508$		−	6.02939e18i		−	0.690601i
$509$	−6.88843e18			−0.778209			−0.389104	−	0.921194i	$-0.627215\pi$
$509$	−6.88843e18			−0.778209			−0.389104	+	0.921194i	$0.627215\pi$
$510$	1.47324e19			1.64166
$511$	3.22322e18			0.354278
$512$		−	4.07619e17i		−	0.0441942i
$513$			6.87270e18i			0.735032i
$514$		−	5.88017e18i		−	0.620366i
$515$	−1.47005e19			−1.52997
$516$			1.36789e19i			1.40444i
$517$	−4.41369e16	+	7.94151e16i	−0.00447062	+	0.00804394i
$518$	−4.72591e18			−0.472255
$519$		−	1.10619e19i		−	1.09058i
$520$	−2.99040e18			−0.290875
$521$	−7.02523e18			−0.674212			−0.337106	−	0.941467i	$-0.609448\pi$
$521$	−7.02523e18			−0.674212			−0.337106	+	0.941467i	$0.609448\pi$
$522$	−1.77184e19			−1.67776
$523$		−	6.70510e18i		−	0.626460i	−0.949677	−	0.313230i	$-0.898589\pi$
$523$		−	6.70510e18i		−	0.626460i	0.949677	−	0.313230i	$-0.101411\pi$
$524$		−	4.61513e18i		−	0.425466i
$525$			9.52906e18i			0.866832i
$526$	1.97507e18			0.177289
$527$			1.79479e19i			1.58979i
$528$	2.37045e18	−	4.26513e18i	0.207202	−	0.372817i
$529$	−5.68729e18			−0.490587
$530$			1.01638e19i			0.865216i
$531$	−3.41452e19			−2.86859
$532$	2.66657e18			0.221092
$533$	1.17150e19			0.958631
$534$			1.27360e19i			1.02859i
$535$		−	2.72850e19i		−	2.17494i
$536$			8.31194e18i			0.653957i
$537$	−2.50047e19			−1.94179
$538$			1.14763e18i			0.0879682i
$539$	8.09805e17	−	1.45707e18i	0.0612716	−	0.110245i
$540$	−1.29243e19			−0.965278
$541$		−	1.69394e19i		−	1.24887i	−0.781078	−	0.624434i	$-0.785330\pi$
$541$		−	1.69394e19i		−	1.24887i	0.781078	−	0.624434i	$-0.214670\pi$
$542$	5.22213e18			0.380061
$543$	−1.45240e19			−1.04349
$544$	2.72995e18			0.193625
$545$			1.94066e19i			1.35885i
$546$			1.08034e19i			0.746813i
$547$		−	1.10587e19i		−	0.754730i	−0.926065	−	0.377365i	$-0.876830\pi$
$547$		−	1.10587e19i		−	0.754730i	0.926065	−	0.377365i	$-0.123170\pi$
$548$	4.64779e18			0.313172
$549$			2.50431e19i			1.66602i
$550$	−5.11420e18	−	2.84235e18i	−0.335923	−	0.186697i
$551$	9.05671e18			0.587367
$552$		−	6.72310e18i		−	0.430523i
$553$	2.02346e19			1.27944
$554$	−7.02435e18			−0.438569
$555$	−2.45629e19			−1.51436
$556$		−	2.96954e18i		−	0.180786i
$557$			1.43515e19i			0.862800i	0.902161	+	0.431400i	$0.141980\pi$
$557$			1.43515e19i			0.862800i	−0.902161	+	0.431400i	$0.858020\pi$
$558$		−	3.30326e19i		−	1.96112i
$559$	1.85954e19			1.09024
$560$			5.01458e18i			0.290348i
$561$	2.85648e19	+	1.58756e19i	1.63340	+	0.907801i
$562$	−4.78513e18			−0.270234
$563$		−	2.93837e19i		−	1.63888i	−0.573164	−	0.819441i	$-0.694284\pi$
$563$		−	2.93837e19i		−	1.63888i	0.573164	−	0.819441i	$-0.305716\pi$
$564$	1.42511e17			0.00785047
$565$	5.27157e18			0.286814
$566$	7.54879e18			0.405660
$567$			1.30389e19i			0.692088i
$568$		−	9.27098e18i		−	0.486057i
$569$		−	1.68626e19i		−	0.873250i	−0.899644	−	0.436625i	$-0.856174\pi$
$569$		−	1.68626e19i		−	0.873250i	0.899644	−	0.436625i	$-0.143826\pi$
$570$	1.38595e19			0.708963
$571$			5.79458e17i			0.0292799i	0.999893	+	0.0146399i	$0.00466020\pi$
$571$			5.79458e17i			0.0292799i	−0.999893	+	0.0146399i	$0.995340\pi$
$572$	−5.79813e18	−	3.22246e18i	−0.289412	−	0.160848i
$573$	3.57869e19			1.76458
$574$		−	1.96448e19i		−	0.956894i
$575$	−8.06149e18			−0.387918
$576$	−5.02438e18			−0.238850
$577$	2.69896e19			1.26755			0.633775	−	0.773518i	$-0.281505\pi$
$577$	2.69896e19			1.26755			0.633775	+	0.773518i	$0.281505\pi$
$578$			3.04342e18i			0.141210i
$579$			3.13975e19i			1.43928i
$580$			1.70314e19i			0.771357i
$581$	−4.05551e19			−1.81473
$582$		−	2.95816e19i		−	1.30786i
$583$	−1.09525e19	+	1.97067e19i	−0.478447	+	0.860864i
$584$	3.10431e18			0.133991
$585$			3.68601e19i			1.57205i
$586$	−1.11340e19			−0.469209
$587$	1.87930e19			0.782581			0.391291	−	0.920267i	$-0.372029\pi$
$587$	1.87930e19			0.782581			0.391291	+	0.920267i	$0.372029\pi$
$588$	−2.61474e18			−0.107594
$589$			1.68845e19i			0.686565i
$590$			3.28214e19i			1.31884i
$591$		−	4.64487e19i		−	1.84443i
$592$	−4.55155e18			−0.178611
$593$			1.33880e19i			0.519197i	0.965717	+	0.259598i	$0.0835902\pi$
$593$			1.33880e19i			0.519197i	−0.965717	+	0.259598i	$0.916410\pi$
$594$	−2.50592e19	−	1.39273e19i	−0.960422	−	0.533778i
$595$	−3.35841e19			−1.27208
$596$		−	2.27800e18i		−	0.0852768i
$597$	1.75195e19			0.648188
$598$	−9.13955e18			−0.334208
$599$	−3.76132e19			−1.35942			−0.679708	−	0.733483i	$-0.737893\pi$
$599$	−3.76132e19			−1.35942			−0.679708	+	0.733483i	$0.737893\pi$
$600$			9.17751e18i			0.327843i
$601$		−	1.33356e18i		−	0.0470861i	−0.999723	−	0.0235430i	$-0.992505\pi$
$601$		−	1.33356e18i		−	0.0470861i	0.999723	−	0.0235430i	$-0.00749468\pi$
$602$		−	3.11825e19i		−	1.08827i
$603$	1.02454e20			3.53434
$604$		−	8.81119e18i		−	0.300453i
$605$	−1.94621e19	−	3.13018e19i	−0.655998	−	1.05507i
$606$	2.17034e19			0.723137
$607$			3.36221e19i			1.10740i	0.832716	+	0.553700i	$0.186785\pi$
$607$			3.36221e19i			1.10740i	−0.832716	+	0.553700i	$0.813215\pi$
$608$	2.56820e18			0.0836187
$609$	6.15293e19			1.98044
$610$	2.40721e19			0.765959
$611$		−	1.93734e17i		−	0.00609420i
$612$		−	3.36497e19i		−	1.04646i
$613$			2.27256e19i			0.698702i	0.936992	+	0.349351i	$0.113598\pi$
$613$			2.27256e19i			0.698702i	−0.936992	+	0.349351i	$0.886402\pi$
$614$	1.31560e19			0.399894
$615$		−	1.02104e20i		−	3.06842i
$616$	−5.40371e18	+	9.72284e18i	−0.160556	+	0.288887i
$617$	−2.30547e18			−0.0677273			−0.0338636	−	0.999426i	$-0.510781\pi$
$617$	−2.30547e18			−0.0677273			−0.0338636	+	0.999426i	$0.510781\pi$
$618$			5.11492e19i			1.48566i
$619$	−1.26168e18			−0.0362339			−0.0181169	−	0.999836i	$-0.505767\pi$
$619$	−1.26168e18			−0.0362339			−0.0181169	+	0.999836i	$0.505767\pi$
$620$	−3.17519e19			−0.901629
$621$	−3.95006e19			−1.10908
$622$		−	4.13837e19i		−	1.14894i
$623$		−	2.90331e19i		−	0.797035i
$624$			1.04048e19i			0.282451i
$625$	−4.64956e19			−1.24811
$626$			2.56034e19i			0.679637i
$627$	2.68724e19	+	1.49350e19i	0.705397	+	0.392042i
$628$	−8.54910e18			−0.221923
$629$		−	3.04831e19i		−	0.782536i
$630$	6.18104e19			1.56920
$631$	5.48356e19			1.37676			0.688378	−	0.725352i	$-0.258323\pi$
$631$	5.48356e19			1.37676			0.688378	+	0.725352i	$0.258323\pi$
$632$	1.94881e19			0.483894
$633$		−	2.48589e19i		−	0.610459i
$634$		−	3.07291e19i		−	0.746320i
$635$			7.14378e19i			1.71598i
$636$	3.53640e19			0.840159
$637$			3.55454e18i			0.0835233i
$638$	−1.83531e19	+	3.30225e19i	−0.426544	+	0.767477i
$639$	−1.14275e20			−2.62692
$640$			4.82958e18i			0.109812i
$641$	−6.06411e19			−1.36383			−0.681916	−	0.731430i	$-0.738853\pi$
$641$	−6.06411e19			−1.36383			−0.681916	+	0.731430i	$0.738853\pi$
$642$	−9.49358e19			−2.11195
$643$	6.35677e19			1.39881			0.699407	−	0.714724i	$-0.253448\pi$
$643$	6.35677e19			1.39881			0.699407	+	0.714724i	$0.253448\pi$
$644$			1.53260e19i			0.333602i
$645$		−	1.62071e20i		−	3.48969i
$646$			1.72000e19i			0.366353i
$647$	2.90750e19			0.612618			0.306309	−	0.951932i	$-0.400906\pi$
$647$	2.90750e19			0.612618			0.306309	+	0.951932i	$0.400906\pi$
$648$			1.25579e19i			0.261753i
$649$	−3.53683e19	+	6.36379e19i	−0.729292	+	1.31221i
$650$	1.24761e19			0.254499
$651$			1.14710e20i			2.31491i
$652$	−3.25368e18			−0.0649593
$653$	−3.27248e19			−0.646375			−0.323188	−	0.946335i	$-0.604754\pi$
$653$	−3.27248e19			−0.646375			−0.323188	+	0.946335i	$0.604754\pi$
$654$	6.75233e19			1.31950
$655$			5.46813e19i			1.05718i
$656$		−	1.89200e19i		−	0.361905i
$657$		−	3.82641e19i		−	0.724160i
$658$	−3.24870e17			−0.00608315
$659$			2.37134e19i			0.439336i	0.975575	+	0.219668i	$0.0704974\pi$
$659$			2.37134e19i			0.439336i	−0.975575	+	0.219668i	$0.929503\pi$
$660$	−2.80857e19	+	5.05344e19i	−0.514847	+	0.926359i
$661$	5.88657e19			1.06771			0.533854	−	0.845577i	$-0.320743\pi$
$661$	5.88657e19			1.06771			0.533854	+	0.845577i	$0.320743\pi$
$662$			8.21405e18i			0.147418i
$663$	−6.96842e19			−1.23748
$664$	−3.90589e19			−0.686347
$665$	−3.15942e19			−0.549359
$666$			5.61031e19i			0.965311i
$667$			5.20531e19i			0.886270i
$668$			1.12403e19i			0.189384i
$669$	−5.22460e19			−0.871104
$670$		−	9.84820e19i		−	1.62493i
$671$	4.66738e19	+	2.59401e19i	0.762106	+	0.423559i
$672$	1.74478e19			0.281939
$673$			1.33079e19i			0.212815i	0.994323	+	0.106408i	$0.0339349\pi$
$673$			1.33079e19i			0.212815i	−0.994323	+	0.106408i	$0.966065\pi$
$674$	−3.46216e19			−0.547934
$675$	5.39212e19			0.844565
$676$	−1.81104e19			−0.280738
$677$			3.77845e19i			0.579687i	0.957074	+	0.289843i	$0.0936032\pi$
$677$			3.77845e19i			0.579687i	−0.957074	+	0.289843i	$0.906397\pi$
$678$		−	1.83420e19i		−	0.278508i
$679$			6.74346e19i			1.01343i
$680$	−3.23451e19			−0.481112
$681$		−	1.28829e20i		−	1.89664i
$682$	−6.15642e19	−	3.42158e19i	−0.897093	−	0.498582i
$683$	−7.54364e19			−1.08802			−0.544009	−	0.839079i	$-0.683094\pi$
$683$	−7.54364e19			−1.08802			−0.544009	+	0.839079i	$0.683094\pi$
$684$		−	3.16560e19i		−	0.451921i
$685$	−5.50682e19			−0.778156
$686$	5.32188e19			0.744383
$687$	−6.52061e19			−0.902799
$688$		−	3.00321e19i		−	0.411592i
$689$		−	4.80747e19i		−	0.652202i
$690$			7.96570e19i			1.06975i
$691$	3.08617e19			0.410273			0.205137	−	0.978733i	$-0.434236\pi$
$691$	3.08617e19			0.410273			0.205137	+	0.978733i	$0.434236\pi$
$692$			2.42865e19i			0.319611i
$693$	1.19845e20	+	6.66069e19i	1.56131	+	0.867734i
$694$	2.63838e19			0.340268
$695$			3.51839e19i			0.449211i
$696$	5.92593e19			0.749018
$697$	1.26713e20			1.58559
$698$	−2.41709e19			−0.299437
$699$		−	8.16658e19i		−	1.00161i
$700$		−	2.09211e19i		−	0.254038i
$701$		−	1.50855e20i		−	1.81357i	−0.421595	−	0.906784i	$-0.638530\pi$
$701$		−	1.50855e20i		−	1.81357i	0.421595	−	0.906784i	$-0.361470\pi$
$702$	6.11321e19			0.727628
$703$		−	2.86770e19i		−	0.337945i
$704$	−5.20435e18	+	9.36414e18i	−0.0607237	+	0.109259i
$705$	−1.68851e18			−0.0195065
$706$			4.63142e19i			0.529763i
$707$	−4.94754e19			−0.560342
$708$	1.14199e20			1.28065
$709$	−7.11969e19			−0.790565			−0.395283	−	0.918560i	$-0.629353\pi$
$709$	−7.11969e19			−0.790565			−0.395283	+	0.918560i	$0.629353\pi$
$710$			1.09845e20i			1.20773i
$711$		−	2.40213e20i		−	2.61523i
$712$		−	2.79620e19i		−	0.301445i
$713$	−9.70432e19			−1.03595
$714$			1.16853e20i			1.23524i
$715$	6.86977e19	+	3.81805e19i	0.719118	+	0.399668i
$716$	5.48981e19			0.569071
$717$			1.73798e20i			1.78406i
$718$	6.56429e19			0.667293
$719$	7.40505e17			0.00745463			0.00372731	−	0.999993i	$-0.498814\pi$
$719$	7.40505e17			0.00745463			0.00372731	+	0.999993i	$0.498814\pi$
$720$	5.95301e19			0.593484
$721$		−	1.16600e20i		−	1.15120i
$722$		−	5.61370e19i		−	0.548894i
$723$		−	2.47255e20i		−	2.39429i
$724$	3.18875e19			0.305809
$725$		−	7.10563e19i		−	0.674895i
$726$	−1.08912e20	+	6.77167e19i	−1.02451	+	0.637000i
$727$	1.21886e20			1.13557			0.567785	−	0.823177i	$-0.307801\pi$
$727$	1.21886e20			1.13557			0.567785	+	0.823177i	$0.307801\pi$
$728$		−	2.37189e19i		−	0.218865i
$729$	−1.35295e20			−1.23649
$730$	−3.67806e19			−0.332935
$731$	2.01134e20			1.80328
$732$		−	8.37568e19i		−	0.743776i
$733$			8.44485e19i			0.742787i	0.928476	+	0.371393i	$0.121120\pi$
$733$			8.44485e19i			0.742787i	−0.928476	+	0.371393i	$0.878880\pi$
$734$		−	1.16778e20i		−	1.01739i
$735$	3.09801e19			0.267345
$736$			1.47606e19i			0.126171i
$737$	1.06124e20	−	1.90948e20i	0.898550	−	1.61675i
$738$	−2.33211e20			−1.95594
$739$			8.20261e19i			0.681461i	0.940161	+	0.340731i	$0.110674\pi$
$739$			8.20261e19i			0.681461i	−0.940161	+	0.340731i	$0.889326\pi$
$740$	5.39280e19			0.443805
$741$	−6.55554e19			−0.534418
$742$	−8.06161e19			−0.651020
$743$			2.02662e20i			1.62125i	0.585566	+	0.810625i	$0.300872\pi$
$743$			2.02662e20i			1.62125i	−0.585566	+	0.810625i	$0.699128\pi$
$744$			1.10478e20i			0.875517i
$745$			2.69904e19i			0.211892i
$746$	8.29941e19			0.645469
$747$			4.81446e20i			3.70940i
$748$	−6.27144e19	−	3.48551e19i	−0.478692	−	0.266045i
$749$	2.16416e20			1.63651
$750$			9.13289e19i			0.684194i
$751$	−4.15889e19			−0.308672			−0.154336	−	0.988018i	$-0.549324\pi$
$751$	−4.15889e19			−0.308672			−0.154336	+	0.988018i	$0.549324\pi$
$752$	−3.12885e17			−0.00230070
$753$	−2.53003e20			−1.84315
$754$		−	8.05587e19i		−	0.581451i
$755$			1.04397e20i			0.746552i
$756$		−	1.02512e20i		−	0.726310i
$757$	−3.30612e19			−0.232085			−0.116043	−	0.993244i	$-0.537021\pi$
$757$	−3.30612e19			−0.232085			−0.116043	+	0.993244i	$0.537021\pi$
$758$		−	7.70065e19i		−	0.535603i
$759$	−8.58384e19	+	1.54448e20i	−0.591547	+	1.06436i
$760$	−3.04286e19			−0.207772
$761$		−	1.42069e20i		−	0.961186i	−0.876944	−	0.480593i	$-0.840421\pi$
$761$		−	1.42069e20i		−	0.961186i	0.876944	−	0.480593i	$-0.159579\pi$
$762$	2.48561e20			1.66628
$763$	−1.53927e20			−1.02245
$764$	−7.85705e19			−0.517137
$765$			3.98690e20i			2.60019i
$766$		−	1.17703e20i		−	0.760649i
$767$		−	1.55245e20i		−	0.994146i
$768$	1.68041e19			0.106632
$769$		−	1.27357e20i		−	0.800829i	−0.916334	−	0.400414i	$-0.868866\pi$
$769$		−	1.27357e20i		−	0.800829i	0.916334	−	0.400414i	$-0.131134\pi$
$770$	6.40245e19	−	1.15199e20i	0.398943	−	0.717815i
$771$	2.42409e20			1.49682
$772$		−	6.89335e19i		−	0.421803i
$773$	2.92905e20			1.77611			0.888055	−	0.459737i	$-0.152056\pi$
$773$	2.92905e20			1.77611			0.888055	+	0.459737i	$0.152056\pi$
$774$	−3.70180e20			−2.22447
$775$	1.32471e20			0.788876
$776$			6.49468e19i			0.383288i
$777$		−	1.94825e20i		−	1.13946i
$778$		−	1.27451e20i		−	0.738732i
$779$	1.19205e20			0.684751
$780$		−	1.23279e20i		−	0.701822i
$781$	−1.18369e20	+	2.12980e20i	−0.667852	+	1.20166i
$782$	−9.88562e19			−0.552785
$783$		−	3.48170e20i		−	1.92956i
$784$	5.74068e18			0.0315320
$785$	1.01292e20			0.551426
$786$	1.90259e20			1.02656
$787$			2.47042e20i			1.32114i	0.750766	+	0.660568i	$0.229684\pi$
$787$			2.47042e20i			1.32114i	−0.750766	+	0.660568i	$0.770316\pi$
$788$			1.01979e20i			0.540537i
$789$			8.14220e19i			0.427763i
$790$	−2.30900e20			−1.20236
$791$			4.18125e19i			0.215810i
$792$	1.15424e20	+	6.41496e19i	0.590499	+	0.328184i
$793$	−1.13861e20			−0.577382
$794$		−	1.66364e20i		−	0.836213i
$795$	−4.19001e20			−2.08759
$796$	−3.84642e19			−0.189961
$797$	1.18489e19			0.0580058			0.0290029	−	0.999579i	$-0.490767\pi$
$797$	1.18489e19			0.0580058			0.0290029	+	0.999579i	$0.490767\pi$
$798$			1.09929e20i			0.533449i
$799$		−	2.09548e18i		−	0.0100799i
$800$		−	2.01493e19i		−	0.0960794i
$801$	−3.44664e20			−1.62918
$802$			2.20737e20i			1.03432i
$803$	−7.13145e19	−	3.96348e19i	−0.331260	−	0.184106i
$804$	−3.42659e20			−1.57787
$805$		−	1.81587e20i		−	0.828921i
$806$	1.50186e20			0.679650
$807$	−4.73110e19			−0.212250
$808$	−4.76501e19			−0.211926
$809$			2.90561e20i			1.28114i	0.767898	+	0.640572i	$0.221303\pi$
$809$			2.90561e20i			1.28114i	−0.767898	+	0.640572i	$0.778697\pi$
$810$		−	1.48789e20i		−	0.650394i
$811$			2.77182e19i			0.120121i	0.998195	+	0.0600604i	$0.0191293\pi$
$811$			2.77182e19i			0.120121i	−0.998195	+	0.0600604i	$0.980871\pi$
$812$	−1.35088e20			−0.580397
$813$			2.15282e20i			0.917010i
$814$	1.04562e20	+	5.81128e19i	0.441572	+	0.245415i
$815$	3.85504e19			0.161408
$816$			1.12542e20i			0.467178i
$817$	1.89217e20			0.778763
$818$	2.09397e20			0.854472
$819$	−2.92363e20			−1.18287
$820$			2.24169e20i			0.899247i
$821$			1.82037e20i			0.724033i	0.932172	+	0.362017i	$0.117912\pi$
$821$			1.82037e20i			0.724033i	−0.932172	+	0.362017i	$0.882088\pi$
$822$			1.91605e20i			0.755620i
$823$	−1.22557e20			−0.479226			−0.239613	−	0.970868i	$-0.577021\pi$
$823$	−1.22557e20			−0.479226			−0.239613	+	0.970868i	$0.577021\pi$
$824$		−	1.12298e20i		−	0.435395i
$825$	1.17176e20	−	2.10833e20i	0.450463	−	0.810514i
$826$	−2.60329e20			−0.992345
$827$		−	4.81098e20i		−	1.81842i	−0.416334	−	0.909212i	$-0.636685\pi$
$827$		−	4.81098e20i		−	1.81842i	0.416334	−	0.909212i	$-0.363315\pi$
$828$	1.81942e20			0.681898
$829$	−2.94876e20			−1.09587			−0.547934	−	0.836522i	$-0.684585\pi$
$829$	−2.94876e20			−1.09587			−0.547934	+	0.836522i	$0.684585\pi$
$830$	4.62780e20			1.70541
$831$		−	2.89578e20i		−	1.05818i
$832$		−	2.28439e19i		−	0.0827764i
$833$			3.84470e19i			0.138149i
$834$	1.22419e20			0.436201
$835$		−	1.33178e20i		−	0.470573i
$836$	−5.89985e19	−	3.27899e19i	−0.206727	−	0.114894i
$837$	6.49097e20			2.25544
$838$		−	1.56064e20i		−	0.537767i
$839$	−2.90096e20			−0.991306			−0.495653	−	0.868521i	$-0.665071\pi$
$839$	−2.90096e20			−0.991306			−0.495653	+	0.868521i	$0.665071\pi$
$840$	−2.06726e20			−0.700550
$841$	−1.61253e20			−0.541922
$842$			1.75156e20i			0.583769i
$843$		−	1.97267e20i		−	0.652020i
$844$			5.45780e19i			0.178904i
$845$	2.14577e20			0.697566
$846$			3.85667e18i			0.0124343i
$847$	2.48276e20	−	1.54368e20i	0.793873	−	0.493597i
$848$	−7.76419e19			−0.246221
$849$			3.11198e20i			0.978776i
$850$	1.34946e20			0.420946
$851$	1.64820e20			0.509921
$852$	3.82195e20			1.17276
$853$		−	2.66218e20i		−	0.810204i	−0.914271	−	0.405102i	$-0.867236\pi$
$853$		−	2.66218e20i		−	0.810204i	0.914271	−	0.405102i	$-0.132764\pi$
$854$			1.90933e20i			0.576335i
$855$			3.75068e20i			1.12292i
$856$	2.08432e20			0.618940
$857$		−	9.37383e19i		−	0.276090i	−0.990426	−	0.138045i	$-0.955918\pi$
$857$		−	9.37383e19i		−	0.276090i	0.990426	−	0.138045i	$-0.0440819\pi$
$858$	1.32845e20	−	2.39028e20i	0.388093	−	0.698292i
$859$	4.89506e20			1.41842			0.709212	−	0.704996i	$-0.249051\pi$
$859$	4.89506e20			1.41842			0.709212	+	0.704996i	$0.249051\pi$
$860$			3.55828e20i			1.02271i
$861$	8.09854e20			2.30879
$862$	2.67483e20			0.756388
$863$	3.52267e20			0.988090			0.494045	−	0.869436i	$-0.335518\pi$
$863$	3.52267e20			0.988090			0.494045	+	0.869436i	$0.335518\pi$
$864$		−	9.87300e19i		−	0.274696i
$865$		−	2.87753e20i		−	0.794157i
$866$			5.54556e19i			0.151817i
$867$	−1.25465e20			−0.340712
$868$		−	2.51846e20i		−	0.678418i
$869$	−4.47696e20	−	2.48818e20i	−1.19631	−	0.664880i
$870$	−7.02120e20			−1.86113
$871$			4.65820e20i			1.22487i
$872$	−1.48248e20			−0.386700
$873$	8.00543e20			2.07150
$874$	−9.29990e19			−0.238725
$875$		−	2.08194e20i		−	0.530167i
$876$			1.27975e20i			0.323293i
$877$			2.83099e20i			0.709482i	0.934965	+	0.354741i	$0.115431\pi$
$877$			2.83099e20i			0.709482i	−0.934965	+	0.354741i	$0.884569\pi$
$878$	−6.59179e18			−0.0163886
$879$		−	4.58997e20i		−	1.13211i
$880$	6.16625e19	−	1.10949e20i	0.150884	−	0.271484i
$881$	−1.37762e20			−0.334424			−0.167212	−	0.985921i	$-0.553476\pi$
$881$	−1.37762e20			−0.334424			−0.167212	+	0.985921i	$0.553476\pi$
$882$		−	7.07605e19i		−	0.170416i
$883$	−6.84765e20			−1.63613			−0.818063	−	0.575128i	$-0.804952\pi$
$883$	−6.84765e20			−1.63613			−0.818063	+	0.575128i	$0.804952\pi$
$884$	1.52992e20			0.362663
$885$	−1.35306e21			−3.18210
$886$		−	3.82250e20i		−	0.891890i
$887$			6.30950e20i			1.46059i	0.683130	+	0.730297i	$0.260618\pi$
$887$			6.30950e20i			1.46059i	−0.683130	+	0.730297i	$0.739382\pi$
$888$		−	1.87637e20i		−	0.430952i
$889$	−5.66622e20			−1.29116
$890$			3.31301e20i			0.749019i
$891$	1.60335e20	−	2.88490e20i	0.359654	−	0.647122i
$892$	1.14707e20			0.255290
$893$		−	1.97133e18i		−	0.00435309i
$894$	9.39105e19			0.205756
$895$	−6.50447e20			−1.41400
$896$	−3.83067e19			−0.0826264
$897$		−	3.76777e20i		−	0.806376i
$898$			2.84567e20i			0.604298i
$899$		−	8.55367e20i		−	1.80233i
$900$	−2.48363e20			−0.519266
$901$		−	5.19991e20i		−	1.07875i
$902$	−2.41565e20	+	4.34645e20i	−0.497265	+	0.894724i
$903$	1.28550e21			2.62577
$904$			4.02699e19i			0.0816210i
$905$	−3.77811e20			−0.759862
$906$	3.63240e20			0.724931
$907$	−1.98682e20			−0.393467			−0.196734	−	0.980457i	$-0.563033\pi$
$907$	−1.98682e20			−0.393467			−0.196734	+	0.980457i	$0.563033\pi$
$908$			2.82846e20i			0.555839i
$909$			5.87342e20i			1.14537i
$910$			2.81028e20i			0.543826i
$911$	−4.10014e19			−0.0787353			−0.0393677	−	0.999225i	$-0.512534\pi$
$911$	−4.10014e19			−0.0787353			−0.0393677	+	0.999225i	$0.512534\pi$
$912$			1.05874e20i			0.201755i
$913$	8.97291e20	+	4.98692e20i	1.69683	+	0.943055i
$914$	−3.68208e20			−0.690988
$915$			9.92371e20i			1.84810i
$916$	1.43160e20			0.264579
$917$	−4.33715e20			−0.795462
$918$	6.61224e20			1.20351
$919$			1.81150e20i			0.327213i	0.986526	+	0.163607i	$0.0523128\pi$
$919$			1.81150e20i			0.327213i	−0.986526	+	0.163607i	$0.947687\pi$
$920$		−	1.74888e20i		−	0.313505i
$921$			5.42355e20i			0.964864i
$922$	−3.64898e20			−0.644252
$923$		−	5.19566e20i		−	0.910393i
$924$	−4.00823e20	−	2.22767e20i	−0.697026	−	0.387390i
$925$	−2.24991e20			−0.388305
$926$		−	4.37592e20i		−	0.749535i
$927$	−1.38421e21			−2.35311
$928$	−1.30104e20			−0.219511
$929$	−7.67893e20			−1.28585			−0.642926	−	0.765929i	$-0.722280\pi$
$929$	−7.67893e20			−1.28585			−0.642926	+	0.765929i	$0.722280\pi$
$930$		−	1.30897e21i		−	2.17545i
$931$			3.61690e19i			0.0596608i
$932$			1.79298e20i			0.293538i
$933$	1.70604e21			2.77215
$934$			1.98491e20i			0.320120i
$935$	7.43056e20	+	4.12972e20i	1.18943	+	0.661057i
$936$	−2.81577e20			−0.447370
$937$		−	5.59914e20i		−	0.882966i	−0.897270	−	0.441483i	$-0.854453\pi$
$937$		−	5.59914e20i		−	0.882966i	0.897270	−	0.441483i	$-0.145547\pi$
$938$	7.81129e20			1.22265
$939$	−1.05550e21			−1.63983
$940$	3.70714e18			0.00571668
$941$		−	9.77656e20i		−	1.49644i	−0.663452	−	0.748219i	$-0.730909\pi$
$941$		−	9.77656e20i		−	1.49644i	0.663452	−	0.748219i	$-0.269091\pi$
$942$		−	3.52436e20i		−	0.535456i
$943$			6.85128e20i			1.03321i
$944$	−2.50725e20			−0.375313
$945$			1.21459e21i			1.80470i
$946$	−3.83441e20	+	6.89921e20i	−0.565536	+	1.01756i
$947$	−3.97822e20			−0.582423			−0.291212	−	0.956659i	$-0.594058\pi$
$947$	−3.97822e20			−0.582423			−0.291212	+	0.956659i	$0.594058\pi$
$948$			8.03396e20i			1.16754i
$949$	1.73972e20			0.250967
$950$	1.26950e20			0.181789
$951$	1.26680e21			1.80072
$952$		−	2.56551e20i		−	0.362006i
$953$			1.73901e20i			0.243585i	0.992556	+	0.121793i	$0.0388643\pi$
$953$			1.73901e20i			0.243585i	−0.992556	+	0.121793i	$0.961136\pi$
$954$			9.57026e20i			1.33071i
$955$	9.30923e20			1.28496
$956$		−	3.81575e20i		−	0.522847i
$957$	−1.36135e21	−	7.56604e20i	−1.85177	−	1.02917i
$958$	6.60382e20			0.891737
$959$		−	4.36784e20i		−	0.585513i
$960$	−1.99099e20			−0.264954
$961$	8.37725e20			1.10672
$962$	−2.55079e20			−0.334541
$963$		−	2.56917e21i		−	3.34509i
$964$			5.42850e20i			0.701683i
$965$			8.16742e20i			1.04808i
$966$	−6.31815e20			−0.804915
$967$			1.23305e21i			1.55953i	0.626070	+	0.779767i	$0.284662\pi$
$967$			1.23305e21i			1.55953i	−0.626070	+	0.779767i	$0.715338\pi$
$968$	2.39117e20	−	1.48672e20i	0.300249	−	0.186682i
$969$	−7.09067e20			−0.883936
$970$		−	7.69506e20i		−	0.952379i
$971$	−2.94621e20			−0.362017			−0.181008	−	0.983482i	$-0.557936\pi$
$971$	−2.94621e20			−0.362017			−0.181008	+	0.983482i	$0.557936\pi$
$972$	1.19188e20			0.145401
$973$	−2.79068e20			−0.338003
$974$			5.68523e20i			0.683652i
$975$			5.14328e20i			0.614056i
$976$			1.83889e20i			0.217975i
$977$	1.29210e21			1.52067			0.760334	−	0.649532i	$-0.225035\pi$
$977$	1.29210e21			1.52067			0.760334	+	0.649532i	$0.225035\pi$
$978$		−	1.34133e20i		−	0.156734i
$979$	−3.57010e20	+	6.42364e20i	−0.414192	+	0.745251i
$980$	−6.80171e19			−0.0783493
$981$			1.82733e21i			2.08994i
$982$	1.81754e20			0.206397
$983$	−9.28526e20			−1.04693			−0.523467	−	0.852046i	$-0.675362\pi$
$983$	−9.28526e20			−1.04693			−0.523467	+	0.852046i	$0.675362\pi$
$984$	7.79976e20			0.873204
$985$		−	1.20827e21i		−	1.34310i
$986$		−	8.71347e20i		−	0.961729i
$987$		−	1.33928e19i		−	0.0146774i
$988$	1.43927e20			0.156619
$989$			1.08752e21i			1.17507i
$990$	−1.36757e21	−	7.60061e20i	−1.46725	−	0.815459i
$991$	−3.75535e20			−0.400069			−0.200034	−	0.979789i	$-0.564105\pi$
$991$	−3.75535e20			−0.400069			−0.200034	+	0.979789i	$0.564105\pi$
$992$		−	2.42555e20i		−	0.256583i
$993$	−3.38623e20			−0.355691
$994$	−8.71256e20			−0.908743
$995$	4.55733e20			0.472008
$996$		−	1.61020e21i		−	1.65602i
$997$			6.76971e20i			0.691360i	0.938352	+	0.345680i	$0.112352\pi$
$997$			6.76971e20i			0.691360i	−0.938352	+	0.345680i	$0.887648\pi$
$998$		−	7.47262e20i		−	0.757808i
$999$	−1.10244e21			−1.11019

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.15.b.a.21.7	✓	14
4.3	odd	2		176.15.h.e.65.1		14
11.10	odd	2	inner	22.15.b.a.21.14	yes	14
44.43	even	2		176.15.h.e.65.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.15.b.a.21.7	✓	14	1.1	even	1	trivial
22.15.b.a.21.14	yes	14	11.10	odd	2	inner
176.15.h.e.65.1		14	4.3	odd	2
176.15.h.e.65.2		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)

\(f(q)\)	\(=\)	\(q-90.5097i q^{2} +3731.25 q^{3} -8192.00 q^{4} +97060.9 q^{5} -337715. i q^{6} +769857. i q^{7} +741455. i q^{8} +9.13929e6 q^{9} +O(q^{10})\)	\(q-90.5097i q^{2} +3731.25 q^{3} -8192.00 q^{4} +97060.9 q^{5} -337715. i q^{6} +769857. i q^{7} +741455. i q^{8} +9.13929e6 q^{9} -8.78495e6i q^{10} +(9.46666e6 - 1.70333e7i) q^{11} -3.05664e7 q^{12} +4.15528e7i q^{13} +6.96795e7 q^{14} +3.62159e8 q^{15} +6.71089e7 q^{16} +4.49448e8i q^{17} -8.27194e8i q^{18} +4.22818e8i q^{19} -7.95123e8 q^{20} +2.87253e9i q^{21} +(-1.54168e9 - 8.56824e8i) q^{22} -2.43013e9 q^{23} +2.76656e9i q^{24} +3.31730e9 q^{25} +3.76093e9 q^{26} +1.62545e10 q^{27} -6.30667e9i q^{28} -2.14199e10i q^{29} -3.27789e10i q^{30} +3.99333e10 q^{31} -6.07400e9i q^{32} +(3.53225e10 - 6.35554e10i) q^{33} +4.06794e10 q^{34} +7.47230e10i q^{35} -7.48690e10 q^{36} -6.78234e10 q^{37} +3.82691e10 q^{38} +1.55044e11i q^{39} +7.19663e10i q^{40} -2.81930e11i q^{41} +2.59992e11 q^{42} -4.47514e11i q^{43} +(-7.75509e10 + 1.39537e11i) q^{44} +8.87067e11 q^{45} +2.19950e11i q^{46} -4.66235e9 q^{47} +2.50400e11 q^{48} +8.55428e10 q^{49} -3.00248e11i q^{50} +1.67700e12i q^{51} -3.40400e11i q^{52} -1.15695e12 q^{53} -1.47119e12i q^{54} +(9.18843e11 - 1.65326e12i) q^{55} -5.70815e11 q^{56} +1.57764e12i q^{57} -1.93871e12 q^{58} -3.73609e12 q^{59} -2.96681e12 q^{60} +2.74015e12i q^{61} -3.61435e12i q^{62} +7.03595e12i q^{63} -5.49756e11 q^{64} +4.03315e12i q^{65} +(-5.75238e12 - 3.19703e12i) q^{66} +1.12103e13 q^{67} -3.68187e12i q^{68} -9.06744e12 q^{69} +6.76316e12 q^{70} -1.25038e13 q^{71} +6.77637e12i q^{72} -4.18678e12i q^{73} +6.13868e12i q^{74} +1.23777e13 q^{75} -3.46372e12i q^{76} +(1.31132e13 + 7.28798e12i) q^{77} +1.40330e13 q^{78} -2.62836e13i q^{79} +6.51365e12 q^{80} +1.69368e13 q^{81} -2.55174e13 q^{82} +5.26788e13i q^{83} -2.35318e13i q^{84} +4.36238e13i q^{85} -4.05043e13 q^{86} -7.99230e13i q^{87} +(1.26294e13 + 7.01911e12i) q^{88} -3.77123e13 q^{89} -8.02882e13i q^{90} -3.19897e13 q^{91} +1.99076e13 q^{92} +1.49001e14 q^{93} +4.21988e11i q^{94} +4.10391e13i q^{95} -2.26636e13i q^{96} +8.75936e13 q^{97} -7.74245e12i q^{98} +(8.65185e13 - 1.55672e14i) 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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