LMFDB - Embedded newform 10.22.b.a.9.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,22,Mod(9,10)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("10.9");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	10.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:	$27.9477344287$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 124640735 x^{8} + \cdots + 49\!\cdots\!00 $ x^10 + 124640735x^8 + 4978985708344843x^6 + 72834822986364822545965x^4 + 290426118121262728766390623556x^2 + 4921147175535440508379606707124900
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{61}\cdot 3^{4}\cdot 5^{20}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.9
Root			$2500.07i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.22.b.a.9.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1024.00i q^{2} +98402.7i q^{3} -1.04858e6 q^{4} +(1.82310e7 - 1.20195e7i) q^{5} -1.00764e8 q^{6} +3.06895e8i q^{7} -1.07374e9i q^{8} +7.77265e8 q^{9} +(1.23080e10 + 1.86685e10i) q^{10} +1.53366e11 q^{11} -1.03183e11i q^{12} +6.41638e11i q^{13} -3.14260e11 q^{14} +(1.18275e12 + 1.79398e12i) q^{15} +1.09951e12 q^{16} -6.71094e12i q^{17} +7.95920e11i q^{18} +2.37092e13 q^{19} +(-1.91166e13 + 1.26034e13i) q^{20} -3.01993e13 q^{21} +1.57047e14i q^{22} +4.43024e13i q^{23} +1.05659e14 q^{24} +(1.87900e14 - 4.38255e14i) q^{25} -6.57038e14 q^{26} +1.10581e15i q^{27} -3.21803e14i q^{28} -3.74853e15 q^{29} +(-1.83703e15 + 1.21114e15i) q^{30} -1.46763e15 q^{31} +1.12590e15i q^{32} +1.50916e16i q^{33} +6.87200e15 q^{34} +(3.68873e15 + 5.59499e15i) q^{35} -8.15022e14 q^{36} +4.48822e16i q^{37} +2.42783e16i q^{38} -6.31389e16 q^{39} +(-1.29059e16 - 1.95754e16i) q^{40} -1.32967e16 q^{41} -3.09241e16i q^{42} +6.99128e16i q^{43} -1.60816e17 q^{44} +(1.41703e16 - 9.34235e15i) q^{45} -4.53656e16 q^{46} -4.37671e17i q^{47} +1.08195e17i q^{48} +4.64361e17 q^{49} +(4.48773e17 + 1.92409e17i) q^{50} +6.60375e17 q^{51} -6.72807e17i q^{52} -2.21872e17i q^{53} -1.13235e18 q^{54} +(2.79602e18 - 1.84339e18i) q^{55} +3.29526e17 q^{56} +2.33305e18i q^{57} -3.83850e18i q^{58} -4.32602e18 q^{59} +(-1.24021e18 - 1.88112e18i) q^{60} +4.73085e18 q^{61} -1.50285e18i q^{62} +2.38539e17i q^{63} -1.15292e18 q^{64} +(7.71218e18 + 1.16977e19i) q^{65} -1.54538e19 q^{66} +4.73660e18i q^{67} +7.03693e18i q^{68} -4.35947e18 q^{69} +(-5.72927e18 + 3.77726e18i) q^{70} -7.94295e18 q^{71} -8.34582e17i q^{72} +3.02901e19i q^{73} -4.59594e19 q^{74} +(4.31255e19 + 1.84898e19i) q^{75} -2.48609e19 q^{76} +4.70673e19i q^{77} -6.46543e19i q^{78} +1.45817e20 q^{79} +(2.00452e19 - 1.32156e19i) q^{80} -1.00684e20 q^{81} -1.36159e19i q^{82} +9.71136e19i q^{83} +3.16663e19 q^{84} +(-8.06623e19 - 1.22347e20i) q^{85} -7.15907e19 q^{86} -3.68865e20i q^{87} -1.64676e20i q^{88} +3.21590e20 q^{89} +(9.56657e18 + 1.45104e19i) q^{90} -1.96916e20 q^{91} -4.64544e19i q^{92} -1.44419e20i q^{93} +4.48175e20 q^{94} +(4.32243e20 - 2.84974e20i) q^{95} -1.10792e20 q^{96} +6.26501e20i q^{97} +4.75506e20i q^{98} +1.19206e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10485760 q^{4} + 27722150 q^{5} - 230748160 q^{6} - 12711922730 q^{9} - 22426931200 q^{10} - 199435236680 q^{11} - 104903905280 q^{14} - 1714785566200 q^{15} + 10995116277760 q^{16} + 123436918144200 q^{19}+ \cdots + 21\!\cdots\!40 q^{99}+O(q^{100}) $ 10 * q - 10485760 * q^4 + 27722150 * q^5 - 230748160 * q^6 - 12711922730 * q^9 - 22426931200 * q^10 - 199435236680 * q^11 - 104903905280 * q^14 - 1714785566200 * q^15 + 10995116277760 * q^16 + 123436918144200 * q^19 - 29068781158400 * q^20 - 158960071181080 * q^21 + 241956982620160 * q^24 - 753844388658750 * q^25 - 173073038991360 * q^26 + 1774546489874700 * q^29 + 5639638400921600 * q^30 + 10456190999441920 * q^31 - 18958190285946880 * q^34 + 24035281816377400 * q^35 + 13329417088532480 * q^36 + 45468500581785840 * q^39 + 23516341809971200 * q^40 + 93828363171915220 * q^41 + 209123002736967680 * q^44 - 1294878557826950 * q^45 - 453509186534543360 * q^46 - 1584589583512161570 * q^49 + 130953516753920000 * q^50 - 512256548145748480 * q^51 - 3219652987818598400 * q^54 + 8644481518774929800 * q^55 + 109999717382881280 * q^56 - 5722347962825378600 * q^59 + 1798082989863731200 * q^60 - 12650867843198554180 * q^61 - 11529215046068469760 * q^64 + 26346750548743534800 * q^65 - 32504410286103019520 * q^66 + 96951047157018456040 * q^69 + 41090423076705996800 * q^70 - 104781163131643184880 * q^71 + 32904860966761553920 * q^74 + 296606638041153670000 * q^75 - 129432989879972659200 * q^76 + 96531112322635730400 * q^79 + 30480826271950438400 * q^80 - 828031346148584406190 * q^81 + 166681715598772142080 * q^84 + 634500251198792806400 * q^85 - 1012021399291540418560 * q^86 + 1925821863958052788100 * q^89 + 598299873941928857600 * q^90 - 3491972396700191783280 * q^91 + 919679051426714398720 * q^94 + 1154253771449725323000 * q^95 - 253710285007916892160 * q^96 + 2120189706372537680840 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$-1$

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 $

$2$			1024.00i			0.707107i
$2$			1024.00i			0.707107i
$3$			98402.7i			0.962130i	0.876685	+	0.481065i	$0.159750\pi$
$3$			98402.7i			0.962130i	−0.876685	+	0.481065i	$0.840250\pi$
$4$	−1.04858e6			−0.500000
$5$	1.82310e7	−	1.20195e7i	0.834881	−	0.550430i
$5$	1.82310e7	−	1.20195e7i	0.834881	−	0.550430i
$6$	−1.00764e8			−0.680329
$7$			3.06895e8i			0.410639i	0.978695	+	0.205320i	$0.0658234\pi$
$7$			3.06895e8i			0.410639i	−0.978695	+	0.205320i	$0.934177\pi$
$8$		−	1.07374e9i		−	0.353553i
$9$	7.77265e8			0.0743058
$10$	1.23080e10	+	1.86685e10i	0.389213	+	0.590350i
$11$	1.53366e11			1.78282			0.891408	−	0.453202i	$-0.149718\pi$
$11$	1.53366e11			1.78282			0.891408	+	0.453202i	$0.149718\pi$
$12$		−	1.03183e11i		−	0.481065i
$13$			6.41638e11i			1.29088i	0.763812	+	0.645439i	$0.223326\pi$
$13$			6.41638e11i			1.29088i	−0.763812	+	0.645439i	$0.776674\pi$
$14$	−3.14260e11			−0.290366
$15$	1.18275e12	+	1.79398e12i	0.529585	+	0.803264i
$16$	1.09951e12			0.250000
$17$		−	6.71094e12i		−	0.807365i	−0.914899	−	0.403682i	$-0.867730\pi$
$17$		−	6.71094e12i		−	0.807365i	0.914899	−	0.403682i	$-0.132270\pi$
$18$			7.95920e11i			0.0525422i
$19$	2.37092e13			0.887166			0.443583	−	0.896233i	$-0.353707\pi$
$19$	2.37092e13			0.887166			0.443583	+	0.896233i	$0.353707\pi$
$20$	−1.91166e13	+	1.26034e13i	−0.417441	+	0.275215i
$21$	−3.01993e13			−0.395088
$22$			1.57047e14i			1.26064i
$23$			4.43024e13i			0.222990i	0.993765	+	0.111495i	$0.0355638\pi$
$23$			4.43024e13i			0.222990i	−0.993765	+	0.111495i	$0.964436\pi$
$24$	1.05659e14			0.340164
$25$	1.87900e14	−	4.38255e14i	0.394054	−	0.919087i
$26$	−6.57038e14			−0.912789
$27$			1.10581e15i			1.03362i
$28$		−	3.21803e14i		−	0.205320i
$29$	−3.74853e15			−1.65456			−0.827279	−	0.561791i	$-0.810113\pi$
$29$	−3.74853e15			−1.65456			−0.827279	+	0.561791i	$0.810113\pi$
$30$	−1.83703e15	+	1.21114e15i	−0.567994	+	0.374473i
$31$	−1.46763e15			−0.321602			−0.160801	−	0.986987i	$-0.551408\pi$
$31$	−1.46763e15			−0.321602			−0.160801	+	0.986987i	$0.551408\pi$
$32$			1.12590e15i			0.176777i
$33$			1.50916e16i			1.71530i
$34$	6.87200e15			0.570893
$35$	3.68873e15	+	5.59499e15i	0.226028	+	0.342835i
$36$	−8.15022e14			−0.0371529
$37$			4.48822e16i			1.53446i	0.641370	+	0.767232i	$0.278366\pi$
$37$			4.48822e16i			1.53446i	−0.641370	+	0.767232i	$0.721634\pi$
$38$			2.42783e16i			0.627321i
$39$	−6.31389e16			−1.24199
$40$	−1.29059e16	−	1.95754e16i	−0.194606	−	0.295175i
$41$	−1.32967e16			−0.154709			−0.0773543	−	0.997004i	$-0.524647\pi$
$41$	−1.32967e16			−0.154709			−0.0773543	+	0.997004i	$0.524647\pi$
$42$		−	3.09241e16i		−	0.279370i
$43$			6.99128e16i			0.493330i	0.969101	+	0.246665i	$0.0793348\pi$
$43$			6.99128e16i			0.493330i	−0.969101	+	0.246665i	$0.920665\pi$
$44$	−1.60816e17			−0.891408
$45$	1.41703e16	−	9.34235e15i	0.0620366	−	0.0409001i
$46$	−4.53656e16			−0.157677
$47$		−	4.37671e17i		−	1.21373i	−0.794806	−	0.606863i	$-0.792428\pi$
$47$		−	4.37671e17i		−	1.21373i	0.794806	−	0.606863i	$-0.207572\pi$
$48$			1.08195e17i			0.240533i
$49$	4.64361e17			0.831375
$50$	4.48773e17	+	1.92409e17i	0.649893	+	0.278638i
$51$	6.60375e17			0.776790
$52$		−	6.72807e17i		−	0.645439i
$53$		−	2.21872e17i		−	0.174263i	−0.996197	−	0.0871316i	$-0.972230\pi$
$53$		−	2.21872e17i		−	0.174263i	0.996197	−	0.0871316i	$-0.0277701\pi$
$54$	−1.13235e18			−0.730881
$55$	2.79602e18	−	1.84339e18i	1.48844	−	0.981315i
$56$	3.29526e17			0.145183
$57$			2.33305e18i			0.853569i
$58$		−	3.83850e18i		−	1.16995i
$59$	−4.32602e18			−1.10190			−0.550951	−	0.834538i	$-0.685735\pi$
$59$	−4.32602e18			−1.10190			−0.550951	+	0.834538i	$0.685735\pi$
$60$	−1.24021e18	−	1.88112e18i	−0.264793	−	0.401632i
$61$	4.73085e18			0.849134			0.424567	−	0.905397i	$-0.360426\pi$
$61$	4.73085e18			0.849134			0.424567	+	0.905397i	$0.360426\pi$
$62$		−	1.50285e18i		−	0.227407i
$63$			2.38539e17i			0.0305129i
$64$	−1.15292e18			−0.125000
$65$	7.71218e18	+	1.16977e19i	0.710538	+	1.07773i
$66$	−1.54538e19			−1.21290
$67$			4.73660e18i			0.317454i	0.987323	+	0.158727i	$0.0507390\pi$
$67$			4.73660e18i			0.317454i	−0.987323	+	0.158727i	$0.949261\pi$
$68$			7.03693e18i			0.403682i
$69$	−4.35947e18			−0.214545
$70$	−5.72927e18	+	3.77726e18i	−0.242421	+	0.159826i
$71$	−7.94295e18			−0.289581			−0.144790	−	0.989462i	$-0.546251\pi$
$71$	−7.94295e18			−0.289581			−0.144790	+	0.989462i	$0.546251\pi$
$72$		−	8.34582e17i		−	0.0262711i
$73$			3.02901e19i			0.824917i	0.910976	+	0.412458i	$0.135330\pi$
$73$			3.02901e19i			0.824917i	−0.910976	+	0.412458i	$0.864670\pi$
$74$	−4.59594e19			−1.08503
$75$	4.31255e19	+	1.84898e19i	0.884281	+	0.379131i
$76$	−2.48609e19			−0.443583
$77$			4.70673e19i			0.732094i
$78$		−	6.46543e19i		−	0.878221i
$79$	1.45817e20			1.73270			0.866349	−	0.499440i	$-0.166461\pi$
$79$	1.45817e20			1.73270			0.866349	+	0.499440i	$0.166461\pi$
$80$	2.00452e19	−	1.32156e19i	0.208720	−	0.137607i
$81$	−1.00684e20			−0.920173
$82$		−	1.36159e19i		−	0.109395i
$83$			9.71136e19i			0.687006i	0.939152	+	0.343503i	$0.111613\pi$
$83$			9.71136e19i			0.687006i	−0.939152	+	0.343503i	$0.888387\pi$
$84$	3.16663e19			0.197544
$85$	−8.06623e19	−	1.22347e20i	−0.444398	−	0.674054i
$86$	−7.15907e19			−0.348837
$87$		−	3.68865e20i		−	1.59190i
$88$		−	1.64676e20i		−	0.630321i
$89$	3.21590e20			1.09322			0.546609	−	0.837388i	$-0.315918\pi$
$89$	3.21590e20			1.09322			0.546609	+	0.837388i	$0.315918\pi$
$90$	9.56657e18	+	1.45104e19i	0.0289208	+	0.0438665i
$91$	−1.96916e20			−0.530085
$92$		−	4.64544e19i		−	0.111495i
$93$		−	1.44419e20i		−	0.309423i
$94$	4.48175e20			0.858234
$95$	4.32243e20	−	2.84974e20i	0.740678	−	0.488323i
$96$	−1.10792e20			−0.170082
$97$			6.26501e20i			0.862618i	0.902204	+	0.431309i	$0.141948\pi$
$97$			6.26501e20i			0.862618i	−0.902204	+	0.431309i	$0.858052\pi$
$98$			4.75506e20i			0.587871i
$99$	1.19206e20			0.132474
$100$	−1.97027e20	+	4.59544e20i	−0.197027	+	0.459544i
$101$	−8.79588e20			−0.792328			−0.396164	−	0.918180i	$-0.629659\pi$
$101$	−8.79588e20			−0.792328			−0.396164	+	0.918180i	$0.629659\pi$
$102$			6.76224e20i			0.549273i
$103$			6.30864e20i			0.462535i	0.972890	+	0.231267i	$0.0742873\pi$
$103$			6.30864e20i			0.462535i	−0.972890	+	0.231267i	$0.925713\pi$
$104$	6.88954e20			0.456394
$105$	−5.50562e20	+	3.62981e20i	−0.329852	+	0.217468i
$106$	2.27197e20			0.123223
$107$		−	2.68373e21i		−	1.31889i	−0.751752	−	0.659446i	$-0.770791\pi$
$107$		−	2.68373e21i		−	1.31889i	0.751752	−	0.659446i	$-0.229209\pi$
$108$		−	1.15953e21i		−	0.516811i
$109$	−4.33058e21			−1.75214			−0.876068	−	0.482188i	$-0.839842\pi$
$109$	−4.33058e21			−1.75214			−0.876068	+	0.482188i	$0.839842\pi$
$110$	1.88763e21	+	2.86312e21i	0.693895	+	1.05249i
$111$	−4.41653e21			−1.47635
$112$			3.37435e20i			0.102660i
$113$			3.73895e21i			1.03616i	0.855332	+	0.518079i	$0.173353\pi$
$113$			3.73895e21i			1.03616i	−0.855332	+	0.518079i	$0.826647\pi$
$114$	−2.38905e21			−0.603564
$115$	5.32493e20	+	8.07675e20i	0.122740	+	0.186170i
$116$	3.93062e21			0.827279
$117$			4.98723e20i			0.0959198i
$118$		−	4.42985e21i		−	0.779162i
$119$	2.05955e21			0.331536
$120$	1.92627e21	−	1.26997e21i	0.283997	−	0.187237i
$121$	1.61210e22			2.17843
$122$			4.84439e21i			0.600428i
$123$		−	1.30843e21i		−	0.148850i
$124$	1.53892e21			0.160801
$125$	−1.84202e21	−	1.02483e22i	−0.176905	−	0.984228i
$126$	−2.44264e20			−0.0215759
$127$		−	1.59552e22i		−	1.29707i	−0.761184	−	0.648535i	$-0.775382\pi$
$127$		−	1.59552e22i		−	1.29707i	0.761184	−	0.648535i	$-0.224618\pi$
$128$		−	1.18059e21i		−	0.0883883i
$129$	−6.87961e21			−0.474648
$130$	−1.19784e22	+	7.89728e21i	−0.762070	+	0.502426i
$131$	1.05025e21			0.0616516			0.0308258	−	0.999525i	$-0.490186\pi$
$131$	1.05025e21			0.0616516			0.0308258	+	0.999525i	$0.490186\pi$
$132$		−	1.58247e22i		−	0.857650i
$133$			7.27625e21i			0.364305i
$134$	−4.85027e21			−0.224474
$135$	1.32913e22	+	2.01600e22i	0.568936	+	0.862952i
$136$	−7.20582e21			−0.285447
$137$		−	3.93590e22i		−	1.44370i	−0.692047	−	0.721852i	$-0.743291\pi$
$137$		−	3.93590e22i		−	1.44370i	0.692047	−	0.721852i	$-0.256709\pi$
$138$		−	4.46410e21i		−	0.151706i
$139$	1.10059e21			0.0346712			0.0173356	−	0.999850i	$-0.494482\pi$
$139$	1.10059e21			0.0346712			0.0173356	+	0.999850i	$0.494482\pi$
$140$	−3.86791e21	−	5.86678e21i	−0.113014	−	0.171418i
$141$	4.30680e22			1.16776
$142$		−	8.13358e21i		−	0.204764i
$143$			9.84057e22i			2.30140i
$144$	8.54612e20			0.0185765
$145$	−6.83394e22	+	4.50555e22i	−1.38136	+	0.910718i
$146$	−3.10170e22			−0.583304
$147$			4.56944e22i			0.799891i
$148$		−	4.70624e22i		−	0.767232i
$149$	8.30974e22			1.26221			0.631105	−	0.775697i	$-0.282602\pi$
$149$	8.30974e22			1.26221			0.631105	+	0.775697i	$0.282602\pi$
$150$	−1.89336e22	+	4.41605e22i	−0.268086	+	0.625281i
$151$	−6.32403e22			−0.835095			−0.417548	−	0.908655i	$-0.637110\pi$
$151$	−6.32403e22			−0.835095			−0.417548	+	0.908655i	$0.637110\pi$
$152$		−	2.54576e22i		−	0.313660i
$153$		−	5.21618e21i		−	0.0599919i
$154$	−4.81969e22			−0.517669
$155$	−2.67563e22	+	1.76402e22i	−0.268499	+	0.177019i
$156$	6.62060e22			0.620996
$157$		−	1.29254e23i		−	1.13370i	−0.823823	−	0.566848i	$-0.808163\pi$
$157$		−	1.29254e23i		−	1.13370i	0.823823	−	0.566848i	$-0.191837\pi$
$158$			1.49316e23i			1.22520i
$159$	2.18328e22			0.167664
$160$	1.35328e22	+	2.05263e22i	0.0973032	+	0.147588i
$161$	−1.35962e22			−0.0915683
$162$		−	1.03101e23i		−	0.650660i
$163$		−	1.99406e23i		−	1.17969i	−0.807516	−	0.589845i	$-0.799189\pi$
$163$		−	1.99406e23i		−	1.17969i	0.807516	−	0.589845i	$-0.200811\pi$
$164$	1.39426e22			0.0773543
$165$	1.81394e23	+	2.75135e23i	0.944153	+	1.43207i
$166$	−9.94444e22			−0.485786
$167$		−	4.03872e23i		−	1.85234i	−0.377106	−	0.926170i	$-0.623081\pi$
$167$		−	4.03872e23i		−	1.85234i	0.377106	−	0.926170i	$-0.376919\pi$
$168$			3.24262e22i			0.139685i
$169$	−1.64635e23			−0.666366
$170$	1.25283e23	−	8.25982e22i	0.476628	−	0.314237i
$171$	1.84284e22			0.0659216
$172$		−	7.33089e22i		−	0.246665i
$173$		−	3.89942e22i		−	0.123457i	−0.998093	−	0.0617285i	$-0.980339\pi$
$173$		−	3.89942e22i		−	0.123457i	0.998093	−	0.0617285i	$-0.0196613\pi$
$174$	3.77718e23			1.12564
$175$	1.34498e23	+	5.76655e22i	0.377413	+	0.161814i
$176$	1.68628e23			0.445704
$177$		−	4.25692e23i		−	1.06017i
$178$			3.29308e23i			0.773023i
$179$	−3.58700e23			−0.793916			−0.396958	−	0.917837i	$-0.629934\pi$
$179$	−3.58700e23			−0.793916			−0.396958	+	0.917837i	$0.629934\pi$
$180$	−1.48586e22	+	9.79617e21i	−0.0310183	+	0.0204501i
$181$	−5.78011e23			−1.13844			−0.569221	−	0.822184i	$-0.692755\pi$
$181$	−5.78011e23			−1.13844			−0.569221	+	0.822184i	$0.692755\pi$
$182$		−	2.01642e23i		−	0.374827i
$183$			4.65528e23i			0.816977i
$184$	4.75693e22			0.0788387
$185$	5.39463e23	+	8.18247e23i	0.844614	+	1.28109i
$186$	1.47885e23			0.218795
$187$		−	1.02923e24i		−	1.43938i
$188$			4.58932e23i			0.606863i
$189$	−3.39368e23			−0.424446
$190$	2.91813e23	+	4.42616e23i	0.345296	+	0.523739i
$191$	−1.13854e22			−0.0127497			−0.00637483	−	0.999980i	$-0.502029\pi$
$191$	−1.13854e22			−0.0127497			−0.00637483	+	0.999980i	$0.502029\pi$
$192$		−	1.13451e23i		−	0.120266i
$193$			9.10352e23i			0.913814i	0.889514	+	0.456907i	$0.151043\pi$
$193$			9.10352e23i			0.913814i	−0.889514	+	0.456907i	$0.848957\pi$
$194$	−6.41537e23			−0.609963
$195$	−1.15108e24	+	7.58900e23i	−1.03692	+	0.683630i
$196$	−4.86918e23			−0.415688
$197$		−	5.71344e22i		−	0.0462384i	−0.999733	−	0.0231192i	$-0.992640\pi$
$197$		−	5.71344e22i		−	0.0462384i	0.999733	−	0.0231192i	$-0.00735972\pi$
$198$			1.22067e23i			0.0936730i
$199$	4.63450e23			0.337323			0.168662	−	0.985674i	$-0.446056\pi$
$199$	4.63450e23			0.337323			0.168662	+	0.985674i	$0.446056\pi$
$200$	−4.70573e23	−	2.01756e23i	−0.324946	−	0.139319i
$201$	−4.66094e23			−0.305432
$202$		−	9.00698e23i		−	0.560261i
$203$		−	1.15041e24i		−	0.679427i
$204$	−6.92453e23			−0.388395
$205$	−2.42412e23	+	1.59820e23i	−0.129163	+	0.0851562i
$206$	−6.46004e23			−0.327062
$207$			3.44347e22i			0.0165694i
$208$			7.05489e23i			0.322719i
$209$	3.63620e24			1.58165
$210$	−3.71692e23	−	5.63776e23i	−0.153773	−	0.233241i
$211$	3.08641e24			1.21475			0.607377	−	0.794414i	$-0.292222\pi$
$211$	3.08641e24			1.21475			0.607377	+	0.794414i	$0.292222\pi$
$212$			2.32650e23i			0.0871316i
$213$		−	7.81608e23i		−	0.278614i
$214$	2.74814e24			0.932597
$215$	8.40318e23	+	1.27458e24i	0.271544	+	0.411872i
$216$	1.18736e24			0.365441
$217$		−	4.50408e23i		−	0.132062i
$218$		−	4.43451e24i		−	1.23895i
$219$	−2.98062e24			−0.793677
$220$	−2.93183e24	+	1.93293e24i	−0.744220	+	0.490658i
$221$	4.30600e24			1.04221
$222$		−	4.52253e24i		−	1.04394i
$223$			5.22536e24i			1.15058i	0.817951	+	0.575288i	$0.195110\pi$
$223$			5.22536e24i			1.15058i	−0.817951	+	0.575288i	$0.804890\pi$
$224$	−3.45533e23			−0.0725914
$225$	1.46048e23	−	3.40640e23i	0.0292805	−	0.0682935i
$226$	−3.82869e24			−0.732675
$227$		−	9.01909e24i		−	1.64775i	−0.566772	−	0.823875i	$-0.691808\pi$
$227$		−	9.01909e24i		−	1.64775i	0.566772	−	0.823875i	$-0.308192\pi$
$228$		−	2.44638e24i		−	0.426784i
$229$	5.33265e23			0.0888527			0.0444263	−	0.999013i	$-0.485854\pi$
$229$	5.33265e23			0.0888527			0.0444263	+	0.999013i	$0.485854\pi$
$230$	−8.27059e23	+	5.45273e23i	−0.131642	+	0.0867904i
$231$	−4.63155e24			−0.704370
$232$			4.02495e24i			0.584975i
$233$			1.15356e24i			0.160251i	0.996785	+	0.0801256i	$0.0255321\pi$
$233$			1.15356e24i			0.160251i	−0.996785	+	0.0801256i	$0.974468\pi$
$234$	−5.10693e23			−0.0678255
$235$	−5.26060e24	−	7.97918e24i	−0.668071	−	1.01332i
$236$	4.53617e24			0.550951
$237$			1.43488e25i			1.66708i
$238$			2.10898e24i			0.234431i
$239$	−1.16123e25			−1.23520			−0.617602	−	0.786491i	$-0.711896\pi$
$239$	−1.16123e25			−1.23520			−0.617602	+	0.786491i	$0.711896\pi$
$240$	1.30045e24	+	1.97250e24i	0.132396	+	0.200816i
$241$	1.52518e25			1.48642			0.743209	−	0.669059i	$-0.233303\pi$
$241$	1.52518e25			1.48642			0.743209	+	0.669059i	$0.233303\pi$
$242$			1.65079e25i			1.54038i
$243$			1.65957e24i			0.148296i
$244$	−4.96066e24			−0.424567
$245$	8.46576e24	−	5.58140e24i	0.694100	−	0.457614i
$246$	1.33984e24			0.105253
$247$			1.52128e25i			1.14522i
$248$			1.57585e24i			0.113703i
$249$	−9.55624e24			−0.660989
$250$	1.04942e25	−	1.88623e24i	0.695954	−	0.125090i
$251$	−2.91524e25			−1.85396			−0.926981	−	0.375108i	$-0.877606\pi$
$251$	−2.91524e25			−1.85396			−0.926981	+	0.375108i	$0.877606\pi$
$252$		−	2.50126e23i		−	0.0152564i
$253$			6.79449e24i			0.397549i
$254$	1.63381e25			0.917168
$255$	1.20393e25	−	7.93738e24i	0.648527	−	0.427568i
$256$	1.20893e24			0.0625000
$257$		−	1.10459e25i		−	0.548155i	−0.961708	−	0.274078i	$-0.911627\pi$
$257$		−	1.10459e25i		−	0.548155i	0.961708	−	0.274078i	$-0.0883725\pi$
$258$		−	7.04472e24i		−	0.335627i
$259$	−1.37741e25			−0.630111
$260$	−8.08681e24	−	1.22659e25i	−0.355269	−	0.538865i
$261$	−2.91360e24			−0.122943
$262$			1.07546e24i			0.0435943i
$263$		−	4.57055e25i		−	1.78005i	−0.455908	−	0.890027i	$-0.650685\pi$
$263$		−	4.57055e25i		−	1.78005i	0.455908	−	0.890027i	$-0.349315\pi$
$264$	1.62045e25			0.606450
$265$	−2.66679e24	−	4.04494e24i	−0.0959197	−	0.145489i
$266$	−7.45088e24			−0.257603
$267$			3.16453e25i			1.05182i
$268$		−	4.96668e24i		−	0.158727i
$269$	1.86981e25			0.574644			0.287322	−	0.957834i	$-0.407235\pi$
$269$	1.86981e25			0.574644			0.287322	+	0.957834i	$0.407235\pi$
$270$	−2.06439e25	+	1.36103e25i	−0.610199	+	0.402299i
$271$	−1.32012e25			−0.375350			−0.187675	−	0.982231i	$-0.560095\pi$
$271$	−1.32012e25			−0.375350			−0.187675	+	0.982231i	$0.560095\pi$
$272$		−	7.37876e24i		−	0.201841i
$273$		−	1.93770e25i		−	0.510011i
$274$	4.03036e25			1.02085
$275$	2.88175e25	−	6.72135e25i	0.702526	−	1.63856i
$276$	4.57124e24			0.107273
$277$			5.20025e25i			1.17486i	0.809274	+	0.587431i	$0.199861\pi$
$277$			5.20025e25i			1.17486i	−0.809274	+	0.587431i	$0.800139\pi$
$278$			1.12700e24i			0.0245162i
$279$	−1.14074e24			−0.0238969
$280$	6.00758e24	−	3.96074e24i	0.121210	−	0.0799130i
$281$	7.28489e25			1.41581			0.707907	−	0.706305i	$-0.249639\pi$
$281$	7.28489e25			1.41581			0.707907	+	0.706305i	$0.249639\pi$
$282$			4.41017e25i			0.825733i
$283$		−	4.23689e25i		−	0.764345i	−0.924091	−	0.382172i	$-0.875176\pi$
$283$		−	4.23689e25i		−	0.764345i	0.924091	−	0.382172i	$-0.124824\pi$
$284$	8.32879e24			0.144790
$285$	2.80422e25	+	4.25338e25i	0.469830	+	0.712629i
$286$	−1.00767e26			−1.62733
$287$		−	4.08070e24i		−	0.0635294i
$288$			8.75123e23i			0.0131355i
$289$	2.40552e25			0.348162
$290$	−4.61369e25	−	6.99795e25i	−0.643975	−	0.976769i
$291$	−6.16494e25			−0.829950
$292$		−	3.17614e25i		−	0.412458i
$293$			8.82956e25i			1.10619i	0.833119	+	0.553094i	$0.186553\pi$
$293$			8.82956e25i			1.10619i	−0.833119	+	0.553094i	$0.813447\pi$
$294$	−4.67911e25			−0.565609
$295$	−7.88676e25	+	5.19967e25i	−0.919957	+	0.606520i
$296$	4.81919e25			0.542515
$297$			1.69594e26i			1.84276i
$298$			8.50918e25i			0.892518i
$299$	−2.84261e25			−0.287852
$300$	−4.52203e25	−	1.93880e25i	−0.442141	−	0.189566i
$301$	−2.14559e25			−0.202581
$302$		−	6.47581e25i		−	0.590502i
$303$		−	8.65538e25i		−	0.762323i
$304$	2.60686e25			0.221791
$305$	8.62480e25	−	5.68625e25i	0.708926	−	0.467388i
$306$	5.34137e24			0.0424207
$307$			5.86168e25i			0.449851i	0.974376	+	0.224926i	$0.0722139\pi$
$307$			5.86168e25i			0.449851i	−0.974376	+	0.224926i	$0.927786\pi$
$308$		−	4.93537e25i		−	0.366047i
$309$	−6.20787e25			−0.445019
$310$	−1.80635e25	−	2.73984e25i	−0.125171	−	0.189858i
$311$	2.12049e26			1.42053			0.710267	−	0.703933i	$-0.248574\pi$
$311$	2.12049e26			1.42053			0.710267	+	0.703933i	$0.248574\pi$
$312$			6.77949e25i			0.439111i
$313$			1.05454e26i			0.660464i	0.943900	+	0.330232i	$0.107127\pi$
$313$			1.05454e26i			0.660464i	−0.943900	+	0.330232i	$0.892873\pi$
$314$	1.32356e26			0.801644
$315$	2.86712e24	+	4.34879e24i	0.0167952	+	0.0254746i
$316$	−1.52900e26			−0.866349
$317$		−	1.82598e26i		−	1.00086i	−0.865776	−	0.500431i	$-0.833175\pi$
$317$		−	1.82598e26i		−	1.00086i	0.865776	−	0.500431i	$-0.166825\pi$
$318$			2.23568e25i			0.118556i
$319$	−5.74898e26			−2.94977
$320$	−2.10189e25	+	1.38576e25i	−0.104360	+	0.0688037i
$321$	2.64086e26			1.26895
$322$		−	1.39225e25i		−	0.0647486i
$323$		−	1.59111e26i		−	0.716266i
$324$	1.05575e26			0.460086
$325$	2.81201e26	+	1.20564e26i	1.18643	+	0.508676i
$326$	2.04192e26			0.834167
$327$		−	4.26141e26i		−	1.68578i
$328$			1.42773e25i			0.0546977i
$329$	1.34319e26			0.498403
$330$	−2.81739e26	+	1.85748e26i	−1.01263	+	0.667617i
$331$	1.96468e26			0.684066			0.342033	−	0.939688i	$-0.388884\pi$
$331$	1.96468e26			0.684066			0.342033	+	0.939688i	$0.388884\pi$
$332$		−	1.01831e26i		−	0.343503i
$333$			3.48854e25i			0.114020i
$334$	4.13565e26			1.30980
$335$	5.69316e25	+	8.63528e25i	0.174736	+	0.265037i
$336$	−3.32045e25			−0.0987721
$337$		−	5.13442e26i		−	1.48040i	−0.672389	−	0.740198i	$-0.734732\pi$
$337$		−	5.13442e26i		−	1.48040i	0.672389	−	0.740198i	$-0.265268\pi$
$338$		−	1.68587e26i		−	0.471192i
$339$	−3.67923e26			−0.996920
$340$	8.45805e25	+	1.28290e26i	0.222199	+	0.337027i
$341$	−2.25085e26			−0.573357
$342$			1.88706e25i			0.0466136i
$343$			3.13925e26i			0.752035i
$344$	7.50683e25			0.174419
$345$	−7.94774e25	+	5.23987e25i	−0.179120	+	0.118092i
$346$	3.99300e25			0.0872973
$347$			2.36574e26i			0.501772i	0.968017	+	0.250886i	$0.0807220\pi$
$347$			2.36574e26i			0.501772i	−0.968017	+	0.250886i	$0.919278\pi$
$348$			3.86783e26i			0.795950i
$349$	−5.61635e26			−1.12147			−0.560734	−	0.827996i	$-0.689481\pi$
$349$	−5.61635e26			−1.12147			−0.560734	+	0.827996i	$0.689481\pi$
$350$	−5.90494e25	+	1.37726e26i	−0.114420	+	0.266871i
$351$	−7.09531e26			−1.33428
$352$			1.72675e26i			0.315160i
$353$		−	4.90666e26i		−	0.869263i	−0.900608	−	0.434632i	$-0.856879\pi$
$353$		−	4.90666e26i		−	0.869263i	0.900608	−	0.434632i	$-0.143121\pi$
$354$	4.35909e26			0.749655
$355$	−1.44808e26	+	9.54705e25i	−0.241765	+	0.159394i
$356$	−3.37211e26			−0.546609
$357$			2.02666e26i			0.318980i
$358$		−	3.67309e26i		−	0.561384i
$359$	6.93549e26			1.02940			0.514701	−	0.857370i	$-0.327903\pi$
$359$	6.93549e26			1.02940			0.514701	+	0.857370i	$0.327903\pi$
$360$	−1.00313e25	−	1.52152e25i	−0.0144604	−	0.0219332i
$361$	−1.52081e26			−0.212937
$362$		−	5.91884e26i		−	0.805001i
$363$			1.58634e27i			2.09594i
$364$	2.06481e26			0.265043
$365$	3.64072e26	+	5.52217e26i	0.454059	+	0.688708i
$366$	−4.76701e26			−0.577690
$367$		−	6.84618e26i		−	0.806222i	−0.915151	−	0.403111i	$-0.867929\pi$
$367$		−	6.84618e26i		−	0.806222i	0.915151	−	0.403111i	$-0.132071\pi$
$368$			4.87110e25i			0.0557474i
$369$	−1.03351e25			−0.0114957
$370$	−8.37885e26	+	5.52410e26i	−0.905871	+	0.597232i
$371$	6.80914e25			0.0715593
$372$			1.51434e26i			0.154711i
$373$			1.94529e27i			1.93216i	0.258249	+	0.966078i	$0.416854\pi$
$373$			1.94529e27i			1.93216i	−0.258249	+	0.966078i	$0.583146\pi$
$374$	1.05393e27			1.01780
$375$	1.00846e27	−	1.81260e26i	0.946955	−	0.170205i
$376$	−4.69946e26			−0.429117
$377$		−	2.40520e27i		−	2.13583i
$378$		−	3.47513e26i		−	0.300128i
$379$	7.72014e25			0.0648505			0.0324253	−	0.999474i	$-0.489677\pi$
$379$	7.72014e25			0.0648505			0.0324253	+	0.999474i	$0.489677\pi$
$380$	−4.53239e26	+	2.98816e26i	−0.370339	+	0.244161i
$381$	1.57004e27			1.24795
$382$		−	1.16587e25i		−	0.00901537i
$383$		−	2.39780e27i		−	1.80396i	−0.431781	−	0.901979i	$-0.642115\pi$
$383$		−	2.39780e27i		−	1.80396i	0.431781	−	0.901979i	$-0.357885\pi$
$384$	1.16173e26			0.0850411
$385$	5.65727e26	+	8.58083e26i	0.402966	+	0.611212i
$386$	−9.32201e26			−0.646164
$387$			5.43408e25i			0.0366573i
$388$		−	6.56934e26i		−	0.431309i
$389$	−2.46961e27			−1.57818			−0.789091	−	0.614276i	$-0.789448\pi$
$389$	−2.46961e27			−1.57818			−0.789091	+	0.614276i	$0.789448\pi$
$390$	−7.77113e26	−	1.17871e27i	−0.483399	−	0.733211i
$391$	2.97311e26			0.180034
$392$		−	4.98604e26i		−	0.293936i
$393$			1.03347e26i			0.0593168i
$394$	5.85056e25			0.0326955
$395$	2.65838e27	−	1.75265e27i	1.44660	−	0.953728i
$396$	−1.24997e26			−0.0662368
$397$		−	2.13081e26i		−	0.109963i	−0.998487	−	0.0549813i	$-0.982490\pi$
$397$		−	2.13081e26i		−	0.109963i	0.998487	−	0.0549813i	$-0.0175099\pi$
$398$			4.74573e26i			0.238523i
$399$	−7.16002e26			−0.350509
$400$	2.06598e26	−	4.81866e26i	0.0985135	−	0.229772i
$401$	−1.98004e26			−0.0919726			−0.0459863	−	0.998942i	$-0.514643\pi$
$401$	−1.98004e26			−0.0919726			−0.0459863	+	0.998942i	$0.514643\pi$
$402$		−	4.77280e26i		−	0.215973i
$403$		−	9.41687e26i		−	0.415149i
$404$	9.22315e26			0.396164
$405$	−1.83557e27	+	1.21018e27i	−0.768235	+	0.506491i
$406$	1.17802e27			0.480427
$407$			6.88342e27i			2.73567i
$408$		−	7.09072e26i		−	0.274637i
$409$	8.23580e26			0.310893			0.155447	−	0.987844i	$-0.450318\pi$
$409$	8.23580e26			0.310893			0.155447	+	0.987844i	$0.450318\pi$
$410$	−1.63656e26	−	2.48230e26i	−0.0602145	−	0.0913323i
$411$	3.87303e27			1.38903
$412$		−	6.61508e26i		−	0.231267i
$413$		−	1.32764e27i		−	0.452484i
$414$	−3.52611e25			−0.0117164
$415$	1.16726e27	+	1.77048e27i	0.378148	+	0.573568i
$416$	−7.22421e26			−0.228197
$417$			1.08301e26i			0.0333582i
$418$			3.72347e27i			1.11840i
$419$	−2.20495e27			−0.645880			−0.322940	−	0.946419i	$-0.604671\pi$
$419$	−2.20495e27			−0.645880			−0.322940	+	0.946419i	$0.604671\pi$
$420$	5.77307e26	−	3.80613e26i	0.164926	−	0.108734i
$421$	−3.41481e27			−0.951492			−0.475746	−	0.879583i	$-0.657822\pi$
$421$	−3.41481e27			−0.951492			−0.475746	+	0.879583i	$0.657822\pi$
$422$			3.16048e27i			0.858960i
$423$		−	3.40187e26i		−	0.0901869i
$424$	−2.38233e26			−0.0616114
$425$	−2.94110e27	−	1.26098e27i	−0.742039	−	0.318145i
$426$	8.00367e26			0.197010
$427$			1.45187e27i			0.348688i
$428$			2.81410e27i			0.659446i
$429$	−9.68338e27			−2.21424
$430$	−1.30517e27	+	8.60485e26i	−0.291238	+	0.192010i
$431$	1.90658e27			0.415187			0.207594	−	0.978215i	$-0.433437\pi$
$431$	1.90658e27			0.415187			0.207594	+	0.978215i	$0.433437\pi$
$432$			1.21585e27i			0.258405i
$433$		−	7.87835e27i		−	1.63423i	−0.576476	−	0.817114i	$-0.695573\pi$
$433$		−	7.87835e27i		−	1.63423i	0.576476	−	0.817114i	$-0.304427\pi$
$434$	4.61218e26			0.0933821
$435$	−4.43358e27	−	6.72478e27i	−0.876229	−	1.32905i
$436$	4.54094e27			0.876068
$437$			1.05038e27i			0.197829i
$438$		−	3.05216e27i		−	0.561214i
$439$	3.85514e27			0.692091			0.346045	−	0.938218i	$-0.387524\pi$
$439$	3.85514e27			0.692091			0.346045	+	0.938218i	$0.387524\pi$
$440$	−1.97932e27	−	3.00220e27i	−0.346947	−	0.526243i
$441$	3.60932e26			0.0617760
$442$			4.40934e27i			0.736953i
$443$			8.26744e27i			1.34937i	0.738105	+	0.674686i	$0.235721\pi$
$443$			8.26744e27i			1.34937i	−0.738105	+	0.674686i	$0.764279\pi$
$444$	4.63107e27			0.738177
$445$	5.86289e27	−	3.86535e27i	0.912708	−	0.601740i
$446$	−5.35077e27			−0.813579
$447$			8.17701e27i			1.21441i
$448$		−	3.53826e26i		−	0.0513299i
$449$	7.44054e27			1.05443			0.527215	−	0.849732i	$-0.323236\pi$
$449$	7.44054e27			1.05443			0.527215	+	0.849732i	$0.323236\pi$
$450$	3.48816e26	+	1.49553e26i	0.0482908	+	0.0207045i
$451$	−2.03927e27			−0.275817
$452$		−	3.92058e27i		−	0.518079i
$453$		−	6.22302e27i		−	0.803470i
$454$	9.23555e27			1.16513
$455$	−3.58996e27	+	2.36683e27i	−0.442558	+	0.291775i
$456$	2.50510e27			0.301782
$457$		−	7.48813e27i		−	0.881563i	−0.897614	−	0.440782i	$-0.854701\pi$
$457$		−	7.48813e27i		−	0.881563i	0.897614	−	0.440782i	$-0.145299\pi$
$458$			5.46063e26i			0.0628283i
$459$	7.42104e27			0.834510
$460$	−5.58359e26	−	8.46909e26i	−0.0613701	−	0.0930849i
$461$	−3.97848e27			−0.427423			−0.213711	−	0.976897i	$-0.568555\pi$
$461$	−3.97848e27			−0.427423			−0.213711	+	0.976897i	$0.568555\pi$
$462$		−	4.74271e27i		−	0.498065i
$463$		−	1.04945e28i		−	1.07736i	−0.842511	−	0.538679i	$-0.818924\pi$
$463$		−	1.04945e28i		−	1.07736i	0.842511	−	0.538679i	$-0.181076\pi$
$464$	−4.12155e27			−0.413640
$465$	−1.73584e27	−	2.63289e27i	−0.170315	−	0.258331i
$466$	−1.18124e27			−0.113315
$467$			1.03403e28i			0.969857i	0.874554	+	0.484929i	$0.161154\pi$
$467$			1.03403e28i			0.969857i	−0.874554	+	0.484929i	$0.838846\pi$
$468$		−	5.22949e26i		−	0.0479599i
$469$	−1.45364e27			−0.130359
$470$	8.17068e27	−	5.38685e27i	0.716524	−	0.472397i
$471$	1.27189e28			1.09076
$472$			4.64503e27i			0.389581i
$473$			1.07223e28i			0.879517i
$474$	−1.46931e28			−1.17880
$475$	4.45496e27	−	1.03907e28i	0.349591	−	0.815383i
$476$	−2.15960e27			−0.165768
$477$		−	1.72453e26i		−	0.0129488i
$478$		−	1.18910e28i		−	0.873421i
$479$	2.73265e27			0.196364			0.0981820	−	0.995168i	$-0.468697\pi$
$479$	2.73265e27			0.196364			0.0981820	+	0.995168i	$0.468697\pi$
$480$	−2.01984e27	+	1.33166e27i	−0.141998	+	0.0936183i
$481$	−2.87982e28			−1.98080
$482$			1.56178e28i			1.05106i
$483$		−	1.33790e27i		−	0.0881006i
$484$	−1.69040e28			−1.08922
$485$	7.53024e27	+	1.14217e28i	0.474811	+	0.720184i
$486$	−1.69940e27			−0.104861
$487$			1.17348e28i			0.708635i	0.935125	+	0.354318i	$0.115287\pi$
$487$			1.17348e28i			0.708635i	−0.935125	+	0.354318i	$0.884713\pi$
$488$		−	5.07971e27i		−	0.300214i
$489$	1.96221e28			1.13502
$490$	5.71535e27	+	8.66894e27i	0.323582	+	0.490803i
$491$	−1.04161e28			−0.577233			−0.288617	−	0.957445i	$-0.593195\pi$
$491$	−1.04161e28			−0.577233			−0.288617	+	0.957445i	$0.593195\pi$
$492$			1.37199e27i			0.0744249i
$493$			2.51562e28i			1.33583i
$494$	−1.55779e28			−0.809795
$495$	2.17325e27	−	1.43280e27i	0.110600	−	0.0729174i
$496$	−1.61367e27			−0.0804004
$497$		−	2.43765e27i		−	0.118913i
$498$		−	9.78559e27i		−	0.467390i
$499$	−6.52648e27			−0.305227			−0.152614	−	0.988286i	$-0.548769\pi$
$499$	−6.52648e27			−0.305227			−0.152614	+	0.988286i	$0.548769\pi$
$500$	1.93150e27	+	1.07461e28i	0.0884523	+	0.492114i
$501$	3.97421e28			1.78219
$502$		−	2.98521e28i		−	1.31095i
$503$			6.24913e27i			0.268754i	0.990930	+	0.134377i	$0.0429034\pi$
$503$			6.24913e27i			0.268754i	−0.990930	+	0.134377i	$0.957097\pi$
$504$	2.56129e26			0.0107879
$505$	−1.60358e28	+	1.05722e28i	−0.661500	+	0.436121i
$506$	−6.95755e27			−0.281110
$507$		−	1.62006e28i		−	0.641131i
$508$			1.67303e28i			0.648535i
$509$	−1.76857e28			−0.671560			−0.335780	−	0.941940i	$-0.609000\pi$
$509$	−1.76857e28			−0.671560			−0.335780	+	0.941940i	$0.609000\pi$
$510$	8.12788e27	+	1.23282e28i	0.302336	+	0.458578i
$511$	−9.29587e27			−0.338743
$512$			1.23794e27i			0.0441942i
$513$			2.62180e28i			0.916994i
$514$	1.13110e28			0.387604
$515$	7.58268e27	+	1.15013e28i	0.254593	+	0.386162i
$516$	7.21379e27			0.237324
$517$		−	6.71240e28i		−	2.16385i
$518$		−	1.41047e28i		−	0.445556i
$519$	3.83713e27			0.118782
$520$	1.25603e28	−	8.28089e27i	0.381035	−	0.251213i
$521$	−2.50674e28			−0.745269			−0.372635	−	0.927978i	$-0.621546\pi$
$521$	−2.50674e28			−0.745269			−0.372635	+	0.927978i	$0.621546\pi$
$522$		−	2.98353e27i		−	0.0869341i
$523$		−	2.33559e28i		−	0.667005i	−0.942749	−	0.333503i	$-0.891769\pi$
$523$		−	2.33559e28i		−	0.667005i	0.942749	−	0.333503i	$-0.108231\pi$
$524$	−1.10127e27			−0.0308258
$525$	−5.67444e27	+	1.32350e28i	−0.155686	+	0.363121i
$526$	4.68024e28			1.25869
$527$			9.84917e27i			0.259650i
$528$			1.65934e28i			0.428825i
$529$	3.75089e28			0.950276
$530$	4.14202e27	−	2.73080e27i	0.102876	−	0.0678255i
$531$	−3.36247e27			−0.0818777
$532$		−	7.62970e27i		−	0.182153i
$533$		−	8.53169e27i		−	0.199710i
$534$	−3.24048e28			−0.743748
$535$	−3.22571e28	−	4.89270e28i	−0.725957	−	1.10112i
$536$	5.08588e27			0.112237
$537$		−	3.52971e28i		−	0.763851i
$538$			1.91469e28i			0.406335i
$539$	7.12173e28			1.48219
$540$	−1.39370e28	−	2.11393e28i	−0.284468	−	0.431476i
$541$	3.51006e28			0.702657			0.351329	−	0.936252i	$-0.385730\pi$
$541$	3.51006e28			0.702657			0.351329	+	0.936252i	$0.385730\pi$
$542$		−	1.35180e28i		−	0.265412i
$543$		−	5.68779e28i		−	1.09533i
$544$	7.55585e27			0.142723
$545$	−7.89507e28	+	5.20515e28i	−1.46283	+	0.964428i
$546$	1.98421e28			0.360632
$547$		−	3.29031e28i		−	0.586637i	−0.956015	−	0.293319i	$-0.905240\pi$
$547$		−	3.29031e28i		−	0.586637i	0.956015	−	0.293319i	$-0.0947597\pi$
$548$			4.12709e28i			0.721852i
$549$	3.67713e27			0.0630956
$550$	6.88266e28	+	2.95091e28i	1.15864	+	0.496761i
$551$	−8.88748e28			−1.46787
$552$			4.68095e27i			0.0758531i
$553$			4.47504e28i			0.711513i
$554$	−5.32506e28			−0.830753
$555$	−8.05177e28	+	5.30846e28i	−1.23258	+	0.812629i
$556$	−1.15405e27			−0.0173356
$557$		−	5.23337e28i		−	0.771439i	−0.922616	−	0.385720i	$-0.873953\pi$
$557$		−	5.23337e28i		−	0.771439i	0.922616	−	0.385720i	$-0.126047\pi$
$558$		−	1.16811e27i		−	0.0168976i
$559$	−4.48587e28			−0.636829
$560$	4.05580e27	+	6.15176e27i	0.0565070	+	0.0857088i
$561$	1.01279e29			1.38487
$562$			7.45972e28i			1.00113i
$563$			5.83332e28i			0.768382i	0.923254	+	0.384191i	$0.125520\pi$
$563$			5.83332e28i			0.768382i	−0.923254	+	0.384191i	$0.874480\pi$
$564$	−4.51601e28			−0.583881
$565$	4.49404e28	+	6.81648e28i	0.570333	+	0.865070i
$566$	4.33857e28			0.540473
$567$		−	3.08995e28i		−	0.377859i
$568$			8.52868e27i			0.102382i
$569$	1.36923e29			1.61361			0.806804	−	0.590819i	$-0.201195\pi$
$569$	1.36923e29			1.61361			0.806804	+	0.590819i	$0.201195\pi$
$570$	−4.35546e28	+	2.87152e28i	−0.503905	+	0.332220i
$571$	−7.93138e28			−0.900885			−0.450443	−	0.892805i	$-0.648734\pi$
$571$	−7.93138e28			−0.900885			−0.450443	+	0.892805i	$0.648734\pi$
$572$		−	1.03186e29i		−	1.15070i
$573$		−	1.12036e27i		−	0.0122668i
$574$	4.17864e27			0.0449221
$575$	1.94157e28	+	8.32440e27i	0.204947	+	0.0878700i
$576$	−8.96126e26			−0.00928823
$577$			1.84821e29i			1.88107i	0.339699	+	0.940534i	$0.389675\pi$
$577$			1.84821e29i			1.88107i	−0.339699	+	0.940534i	$0.610325\pi$
$578$			2.46325e28i			0.246188i
$579$	−8.95811e28			−0.879208
$580$	7.16590e28	−	4.72441e28i	0.690680	−	0.455359i
$581$	−2.98037e28			−0.282111
$582$		−	6.31289e28i		−	0.586864i
$583$		−	3.40277e28i		−	0.310679i
$584$	3.25237e28			0.291652
$585$	5.99441e27	+	9.09221e27i	0.0527971	+	0.0800816i
$586$	−9.04147e28			−0.782193
$587$			2.97907e28i			0.253152i	0.991957	+	0.126576i	$0.0403988\pi$
$587$			2.97907e28i			0.253152i	−0.991957	+	0.126576i	$0.959601\pi$
$588$		−	4.79141e28i		−	0.399946i
$589$	−3.47964e28			−0.285314
$590$	−5.32446e28	−	8.07605e28i	−0.428874	−	0.650508i
$591$	5.62218e27			0.0444873
$592$			4.93486e28i			0.383616i
$593$		−	1.13427e29i		−	0.866251i	−0.901334	−	0.433125i	$-0.857411\pi$
$593$		−	1.13427e29i		−	0.866251i	0.901334	−	0.433125i	$-0.142589\pi$
$594$	−1.73664e29			−1.30303
$595$	3.75477e28	−	2.47548e28i	0.276793	−	0.182487i
$596$	−8.71340e28			−0.631105
$597$			4.56048e28i			0.324549i
$598$		−	2.91083e28i		−	0.203542i
$599$	5.02899e28			0.345541			0.172770	−	0.984962i	$-0.444728\pi$
$599$	5.02899e28			0.345541			0.172770	+	0.984962i	$0.444728\pi$
$600$	1.98533e28	−	4.63056e28i	0.134043	−	0.312641i
$601$	−4.60057e28			−0.305232			−0.152616	−	0.988286i	$-0.548770\pi$
$601$	−4.60057e28			−0.305232			−0.152616	+	0.988286i	$0.548770\pi$
$602$		−	2.19708e28i		−	0.143246i
$603$			3.68159e27i			0.0235887i
$604$	6.63123e28			0.417548
$605$	2.93901e29	−	1.93766e29i	1.81873	−	1.19907i
$606$	8.86311e28			0.539043
$607$		−	1.11365e29i		−	0.665684i	−0.942983	−	0.332842i	$-0.891992\pi$
$607$		−	1.11365e29i		−	0.665684i	0.942983	−	0.332842i	$-0.108008\pi$
$608$			2.66942e28i			0.156830i
$609$	1.13203e29			0.653697
$610$	5.82272e28	+	8.83180e28i	0.330494	+	0.501286i
$611$	2.80827e29			1.56677
$612$			5.46956e27i			0.0299960i
$613$		−	1.01980e29i		−	0.549770i	−0.961477	−	0.274885i	$-0.911360\pi$
$613$		−	1.01980e29i		−	0.549770i	0.961477	−	0.274885i	$-0.0886397\pi$
$614$	−6.00236e28			−0.318093
$615$	−1.57267e28	−	2.38540e28i	−0.0819313	−	0.124272i
$616$	5.05382e28			0.258834
$617$			4.07000e28i			0.204927i	0.994737	+	0.102464i	$0.0326726\pi$
$617$			4.07000e28i			0.204927i	−0.994737	+	0.102464i	$0.967327\pi$
$618$		−	6.35686e28i		−	0.314676i
$619$	−6.69921e28			−0.326041			−0.163020	−	0.986623i	$-0.552124\pi$
$619$	−6.69921e28			−0.326041			−0.163020	+	0.986623i	$0.552124\pi$
$620$	2.80560e28	−	1.84971e28i	0.134250	−	0.0885096i
$621$	−4.89901e28			−0.230487
$622$			2.17138e29i			1.00447i
$623$			9.86943e28i			0.448919i
$624$	−6.94220e28			−0.310498
$625$	−1.56761e29	−	1.64696e29i	−0.689443	−	0.724340i
$626$	−1.07985e29			−0.467018
$627$			3.57812e29i			1.52176i
$628$			1.35532e29i			0.566848i
$629$	3.01202e29			1.23887
$630$	−4.45317e27	+	2.93593e27i	−0.0180133	+	0.0118760i
$631$	−2.23581e29			−0.889461			−0.444730	−	0.895665i	$-0.646700\pi$
$631$	−2.23581e29			−0.889461			−0.444730	+	0.895665i	$0.646700\pi$
$632$		−	1.56569e29i		−	0.612601i
$633$			3.03711e29i			1.16875i
$634$	1.86981e29			0.707717
$635$	−1.91774e29	−	2.90879e29i	−0.713947	−	1.08290i
$636$	−2.28933e28			−0.0838320
$637$			2.97952e29i			1.07320i
$638$		−	5.88696e29i		−	2.08580i
$639$	−6.17378e27			−0.0215175
$640$	−1.41901e28	−	2.15233e28i	−0.0486516	−	0.0737938i
$641$	−4.52403e29			−1.52587			−0.762933	−	0.646478i	$-0.776241\pi$
$641$	−4.52403e29			−1.52587			−0.762933	+	0.646478i	$0.776241\pi$
$642$			2.70424e29i			0.897280i
$643$		−	2.53157e29i		−	0.826371i	−0.910647	−	0.413185i	$-0.864416\pi$
$643$		−	2.53157e29i		−	0.826371i	0.910647	−	0.413185i	$-0.135584\pi$
$644$	1.42566e28			0.0457841
$645$	−1.25422e29	+	8.26895e28i	−0.396275	+	0.261260i
$646$	1.62930e29			0.506477
$647$		−	9.58702e28i		−	0.293217i	−0.989195	−	0.146608i	$-0.953164\pi$
$647$		−	9.58702e28i		−	0.293217i	0.989195	−	0.146608i	$-0.0468357\pi$
$648$			1.08109e29i			0.325330i
$649$	−6.63466e29			−1.96449
$650$	−1.23457e29	+	2.87950e29i	−0.359688	+	0.838932i
$651$	4.43213e28			0.127061
$652$			2.09092e29i			0.589845i
$653$		−	4.61557e28i		−	0.128126i	−0.997946	−	0.0640630i	$-0.979594\pi$
$653$		−	4.61557e28i		−	0.128126i	0.997946	−	0.0640630i	$-0.0204058\pi$
$654$	4.36368e29			1.19203
$655$	1.91471e28	−	1.26235e28i	0.0514718	−	0.0339349i
$656$	−1.46199e28			−0.0386771
$657$			2.35434e28i			0.0612961i
$658$			1.37543e29i			0.352424i
$659$	1.25629e29			0.316805			0.158402	−	0.987375i	$-0.449366\pi$
$659$	1.25629e29			0.316805			0.158402	+	0.987375i	$0.449366\pi$
$660$	−1.90206e29	−	2.88500e29i	−0.472076	−	0.716036i
$661$	4.78576e28			0.116906			0.0584528	−	0.998290i	$-0.481383\pi$
$661$	4.78576e28			0.116906			0.0584528	+	0.998290i	$0.481383\pi$
$662$			2.01183e29i			0.483708i
$663$			4.23722e29i			1.00274i
$664$	1.04275e29			0.242893
$665$	8.74570e28	+	1.32653e29i	0.200524	+	0.304152i
$666$	−3.57227e28			−0.0806240
$667$		−	1.66069e29i		−	0.368949i
$668$			4.23490e29i			0.926170i
$669$	−5.14189e29			−1.10700
$670$	−8.84252e28	+	5.82980e28i	−0.187409	+	0.123557i
$671$	7.25553e29			1.51385
$672$		−	3.40014e28i		−	0.0698424i
$673$		−	5.16188e29i		−	1.04388i	−0.852983	−	0.521939i	$-0.825209\pi$
$673$		−	5.16188e29i		−	1.04388i	0.852983	−	0.521939i	$-0.174791\pi$
$674$	5.25765e29			1.04680
$675$	4.84628e29	+	2.07782e29i	0.949989	+	0.407303i
$676$	1.72633e29			0.333183
$677$			7.16827e28i			0.136218i	0.997678	+	0.0681088i	$0.0216965\pi$
$677$			7.16827e28i			0.136218i	−0.997678	+	0.0681088i	$0.978303\pi$
$678$		−	3.76753e29i		−	0.704929i
$679$	−1.92270e29			−0.354225
$680$	−1.31369e29	+	8.66104e28i	−0.238314	+	0.157118i
$681$	8.87503e29			1.58535
$682$		−	2.30487e29i		−	0.405424i
$683$		−	8.50027e29i		−	1.47236i	−0.676783	−	0.736182i	$-0.736627\pi$
$683$		−	8.50027e29i		−	1.47236i	0.676783	−	0.736182i	$-0.263373\pi$
$684$	−1.93235e28			−0.0329608
$685$	−4.73076e29	−	7.17553e29i	−0.794658	−	1.20532i
$686$	−3.21459e29			−0.531769
$687$			5.24747e28i			0.0854878i
$688$			7.68699e28i			0.123333i
$689$	1.42362e29			0.224953
$690$	−5.36563e28	−	8.13849e28i	−0.0835036	−	0.126657i
$691$	−4.05349e29			−0.621311			−0.310656	−	0.950523i	$-0.600549\pi$
$691$	−4.05349e29			−0.621311			−0.310656	+	0.950523i	$0.600549\pi$
$692$			4.08884e28i			0.0617285i
$693$			3.65838e28i			0.0543989i
$694$	−2.42251e29			−0.354807
$695$	2.00647e28	−	1.32285e28i	0.0289463	−	0.0190840i
$696$	−3.96066e29			−0.562822
$697$			8.92336e28i			0.124906i
$698$		−	5.75114e29i		−	0.792998i
$699$	−1.13513e29			−0.154182
$700$	−1.41032e29	−	6.04666e28i	−0.188707	−	0.0809070i
$701$	3.43882e29			0.453284			0.226642	−	0.973978i	$-0.427225\pi$
$701$	3.43882e29			0.453284			0.226642	+	0.973978i	$0.427225\pi$
$702$		−	7.26560e29i		−	0.943478i
$703$			1.06412e30i			1.36132i
$704$	−1.76819e29			−0.222852
$705$	7.85172e29	−	5.17657e29i	0.974943	−	0.642771i
$706$	5.02442e29			0.614662
$707$		−	2.69941e29i		−	0.325361i
$708$			4.46371e29i			0.530086i
$709$	−9.26613e29			−1.08421			−0.542104	−	0.840311i	$-0.682372\pi$
$709$	−9.26613e29			−1.08421			−0.542104	+	0.840311i	$0.682372\pi$
$710$	−9.77618e28	−	1.48283e29i	−0.112708	−	0.170954i
$711$	1.13338e29			0.128750
$712$		−	3.45304e29i		−	0.386511i
$713$		−	6.50194e28i		−	0.0717138i
$714$	−2.07530e29			−0.225553
$715$	1.18279e30	+	1.79403e30i	1.26676	+	1.92139i
$716$	3.76124e29			0.396958
$717$		−	1.14268e30i		−	1.18843i
$718$			7.10194e29i			0.727898i
$719$	2.08758e29			0.210857			0.105429	−	0.994427i	$-0.466379\pi$
$719$	2.08758e29			0.210857			0.105429	+	0.994427i	$0.466379\pi$
$720$	1.55804e28	−	1.02720e28i	0.0155091	−	0.0102250i
$721$	−1.93609e29			−0.189935
$722$		−	1.55731e29i		−	0.150569i
$723$			1.50081e30i			1.43013i
$724$	6.06089e29			0.569221
$725$	−7.04347e29	+	1.64281e30i	−0.651985	+	1.52068i
$726$	−1.62442e30			−1.48205
$727$		−	7.93469e29i		−	0.713541i	−0.934192	−	0.356770i	$-0.883878\pi$
$727$		−	7.93469e29i		−	0.713541i	0.934192	−	0.356770i	$-0.116122\pi$
$728$			2.11437e29i			0.187413i
$729$	−1.21650e30			−1.06285
$730$	−5.65471e29	+	3.72810e29i	−0.486990	+	0.321068i
$731$	4.69181e29			0.398297
$732$		−	4.88142e29i		−	0.408488i
$733$		−	5.07371e29i		−	0.418537i	−0.977858	−	0.209268i	$-0.932892\pi$
$733$		−	5.07371e29i		−	0.418537i	0.977858	−	0.209268i	$-0.0671083\pi$
$734$	7.01049e29			0.570085
$735$	5.49225e29	+	8.33053e29i	0.440284	+	0.667814i
$736$	−4.98800e28			−0.0394194
$737$			7.26434e29i			0.565962i
$738$		−	1.05831e28i		−	0.00812872i
$739$	5.16147e29			0.390847			0.195423	−	0.980719i	$-0.437392\pi$
$739$	5.16147e29			0.390847			0.195423	+	0.980719i	$0.437392\pi$
$740$	−5.65668e29	−	8.57994e29i	−0.422307	−	0.640547i
$741$	−1.49698e30			−1.10185
$742$			6.97256e28i			0.0506001i
$743$			9.51771e29i			0.681004i	0.940244	+	0.340502i	$0.110597\pi$
$743$			9.51771e29i			0.681004i	−0.940244	+	0.340502i	$0.889403\pi$
$744$	−1.55068e29			−0.109397
$745$	1.51495e30	−	9.98791e29i	1.05380	−	0.694758i
$746$	−1.99198e30			−1.36624
$747$			7.54831e28i			0.0510485i
$748$			1.07923e30i			0.719691i
$749$	8.23623e29			0.541589
$750$	1.85610e29	+	1.03266e30i	0.120353	+	0.669599i
$751$	7.83348e28			0.0500882			0.0250441	−	0.999686i	$-0.492027\pi$
$751$	7.83348e28			0.0500882			0.0250441	+	0.999686i	$0.492027\pi$
$752$		−	4.81225e29i		−	0.303431i
$753$		−	2.86868e30i		−	1.78375i
$754$	2.46293e30			1.51026
$755$	−1.15293e30	+	7.60118e29i	−0.697206	+	0.459661i
$756$	3.55853e29			0.212223
$757$		−	1.24360e29i		−	0.0731434i	−0.999331	−	0.0365717i	$-0.988356\pi$
$757$		−	1.24360e29i		−	0.0731434i	0.999331	−	0.0365717i	$-0.0116437\pi$
$758$			7.90543e28i			0.0458563i
$759$	−6.68596e29			−0.382494
$760$	−3.05988e29	−	4.64117e29i	−0.172648	−	0.261869i
$761$	−8.88008e29			−0.494172			−0.247086	−	0.968994i	$-0.579473\pi$
$761$	−8.88008e29			−0.494172			−0.247086	+	0.968994i	$0.579473\pi$
$762$			1.60772e30i			0.882435i
$763$		−	1.32903e30i		−	0.719496i
$764$	1.19385e28			0.00637483
$765$	−6.26960e28	−	9.50961e28i	−0.0330213	−	0.0500861i
$766$	2.45535e30			1.27559
$767$		−	2.77574e30i		−	1.42242i
$768$			1.18962e29i			0.0601331i
$769$	−2.24158e29			−0.111771			−0.0558854	−	0.998437i	$-0.517798\pi$
$769$	−2.24158e29			−0.111771			−0.0558854	+	0.998437i	$0.517798\pi$
$770$	−8.78677e29	+	5.79304e29i	−0.432192	+	0.284940i
$771$	1.08695e30			0.527397
$772$		−	9.54574e29i		−	0.456907i
$773$			3.84044e30i			1.81341i	0.421762	+	0.906707i	$0.361412\pi$
$773$			3.84044e30i			1.81341i	−0.421762	+	0.906707i	$0.638588\pi$
$774$	−5.56450e28			−0.0259206
$775$	−2.75767e29	+	6.43196e29i	−0.126728	+	0.295580i
$776$	6.72700e29			0.304981
$777$		−	1.35541e30i		−	0.606248i
$778$		−	2.52888e30i		−	1.11594i
$779$	−3.15255e29			−0.137252
$780$	1.20700e30	−	7.95764e29i	0.518458	−	0.341815i
$781$	−1.21818e30			−0.516269
$782$			3.04446e29i			0.127303i
$783$		−	4.14517e30i		−	1.71019i
$784$	5.10571e29			0.207844
$785$	−1.55357e30	−	2.35642e30i	−0.624020	−	0.946501i
$786$	−1.05828e29			−0.0419433
$787$		−	3.62681e30i		−	1.41837i	−0.705022	−	0.709185i	$-0.749063\pi$
$787$		−	3.62681e30i		−	1.41837i	0.705022	−	0.709185i	$-0.250937\pi$
$788$			5.99098e28i			0.0231192i
$789$	4.49755e30			1.71264
$790$	1.79471e30	+	2.72218e30i	0.674388	+	1.02290i
$791$	−1.14747e30			−0.425487
$792$		−	1.27997e29i		−	0.0468365i
$793$			3.03550e30i			1.09613i
$794$	2.18195e29			0.0777553
$795$	3.98033e29	−	2.62420e29i	0.139979	−	0.0922872i
$796$	−4.85963e29			−0.168662
$797$			4.34951e30i			1.48980i	0.667177	+	0.744900i	$0.267503\pi$
$797$			4.34951e30i			1.48980i	−0.667177	+	0.744900i	$0.732497\pi$
$798$		−	7.33186e29i		−	0.247847i
$799$	−2.93719e30			−0.979919
$800$	4.93431e29	+	2.11556e29i	0.162473	+	0.0696596i
$801$	2.49961e29			0.0812325
$802$		−	2.02756e29i		−	0.0650345i
$803$			4.64547e30i			1.47067i
$804$	4.88735e29			0.152716
$805$	−2.47872e29	+	1.63419e29i	−0.0764487	+	0.0504019i
$806$	9.64287e29			0.293554
$807$			1.83995e30i			0.552882i
$808$			9.44451e29i			0.280130i
$809$	−3.14413e30			−0.920536			−0.460268	−	0.887780i	$-0.652247\pi$
$809$	−3.14413e30			−0.920536			−0.460268	+	0.887780i	$0.652247\pi$
$810$	−1.23922e30	−	1.87963e30i	−0.358143	−	0.543224i
$811$	6.27225e30			1.78939			0.894694	−	0.446679i	$-0.147393\pi$
$811$	6.27225e30			1.78939			0.894694	+	0.446679i	$0.147393\pi$
$812$			1.20629e30i			0.339713i
$813$		−	1.29903e30i		−	0.361135i
$814$	−7.04862e30			−1.93441
$815$	−2.39676e30	−	3.63536e30i	−0.649337	−	0.984902i
$816$	7.26090e29			0.194197
$817$			1.65758e30i			0.437666i
$818$			8.43346e29i			0.219835i
$819$	−1.53056e29			−0.0393884
$820$	2.54188e29	−	1.67584e29i	0.0645817	−	0.0425781i
$821$	−3.78956e29			−0.0950574			−0.0475287	−	0.998870i	$-0.515135\pi$
$821$	−3.78956e29			−0.0950574			−0.0475287	+	0.998870i	$0.515135\pi$
$822$			3.96598e30i			0.982193i
$823$		−	2.40420e30i		−	0.587858i	−0.955827	−	0.293929i	$-0.905037\pi$
$823$		−	2.40420e30i		−	0.587858i	0.955827	−	0.293929i	$-0.0949630\pi$
$824$	6.77385e29			0.163531
$825$	6.61399e30	+	2.83571e30i	1.57651	+	0.675921i
$826$	1.35950e30			0.319955
$827$			6.21040e30i			1.44315i	0.692336	+	0.721576i	$0.256582\pi$
$827$			6.21040e30i			1.44315i	−0.692336	+	0.721576i	$0.743418\pi$
$828$		−	3.61074e28i		−	0.00828471i
$829$	−4.98385e30			−1.12913			−0.564563	−	0.825390i	$-0.690955\pi$
$829$	−4.98385e30			−1.12913			−0.564563	+	0.825390i	$0.690955\pi$
$830$	−1.81297e30	+	1.19527e30i	−0.405574	+	0.267391i
$831$	−5.11719e30			−1.13037
$832$		−	7.39759e29i		−	0.161360i
$833$		−	3.11630e30i		−	0.671223i
$834$	−1.10900e29			−0.0235878
$835$	−4.85435e30	−	7.36298e30i	−1.01958	−	1.54648i
$836$	−3.81283e30			−0.790827
$837$		−	1.62292e30i		−	0.332415i
$838$		−	2.25787e30i		−	0.456706i
$839$	1.80398e30			0.360355			0.180178	−	0.983634i	$-0.442333\pi$
$839$	1.80398e30			0.360355			0.180178	+	0.983634i	$0.442333\pi$
$840$	3.89748e29	+	5.91162e29i	0.0768867	+	0.116620i
$841$	8.91864e30			1.73756
$842$		−	3.49677e30i		−	0.672806i
$843$			7.16852e30i			1.36220i
$844$	−3.23634e30			−0.607377
$845$	−3.00146e30	+	1.97884e30i	−0.556336	+	0.366788i
$846$	3.48351e29			0.0637718
$847$			4.94744e30i			0.894550i
$848$		−	2.43951e29i		−	0.0435658i
$849$	4.16921e30			0.735399
$850$	1.29125e30	−	3.01169e30i	0.224963	−	0.524700i
$851$	−1.98839e30			−0.342169
$852$			8.19575e29i			0.139307i
$853$		−	7.86130e28i		−	0.0131987i	−0.999978	−	0.00659933i	$-0.997899\pi$
$853$		−	7.86130e28i		−	0.0131987i	0.999978	−	0.00659933i	$-0.00210065\pi$
$854$	−1.48672e30			−0.246559
$855$	3.35967e29	−	2.21500e29i	0.0550367	−	0.0362852i
$856$	−2.88163e30			−0.466299
$857$			6.53153e30i			1.04404i	0.852934	+	0.522019i	$0.174821\pi$
$857$			6.53153e30i			1.04404i	−0.852934	+	0.522019i	$0.825179\pi$
$858$		−	9.91578e30i		−	1.56571i
$859$	7.18909e30			1.12136			0.560681	−	0.828032i	$-0.310539\pi$
$859$	7.18909e30			1.12136			0.560681	+	0.828032i	$0.310539\pi$
$860$	−8.81137e29	−	1.33649e30i	−0.135772	−	0.205936i
$861$	4.01552e29			0.0611235
$862$			1.95234e30i			0.293582i
$863$		−	1.15029e31i		−	1.70881i	−0.519607	−	0.854405i	$-0.673922\pi$
$863$		−	1.15029e31i		−	1.70881i	0.519607	−	0.854405i	$-0.326078\pi$
$864$	−1.24503e30			−0.182720
$865$	−4.68691e29	−	7.10902e29i	−0.0679544	−	0.103072i
$866$	8.06743e30			1.15557
$867$			2.36710e30i			0.334977i
$868$			4.72287e29i			0.0660311i
$869$	2.23634e31			3.08908
$870$	6.88617e30	−	4.53999e30i	0.939779	−	0.619588i
$871$	−3.03918e30			−0.409794
$872$			4.64992e30i			0.619474i
$873$			4.86957e29i			0.0640975i
$874$	−1.07558e30			−0.139886
$875$	3.14515e30	−	5.65307e29i	0.404163	−	0.0726440i
$876$	3.12541e30			0.396839
$877$		−	2.73682e30i		−	0.343361i	−0.985153	−	0.171680i	$-0.945080\pi$
$877$		−	2.73682e30i		−	0.343361i	0.985153	−	0.171680i	$-0.0549196\pi$
$878$			3.94767e30i			0.489382i
$879$	−8.68852e30			−1.06430
$880$	3.07425e30	−	2.02683e30i	0.372110	−	0.245329i
$881$	−4.77586e30			−0.571221			−0.285611	−	0.958346i	$-0.592196\pi$
$881$	−4.77586e30			−0.571221			−0.285611	+	0.958346i	$0.592196\pi$
$882$			3.69594e29i			0.0436823i
$883$		−	2.76560e30i		−	0.323000i	−0.986873	−	0.161500i	$-0.948367\pi$
$883$		−	2.76560e30i		−	0.323000i	0.986873	−	0.161500i	$-0.0516331\pi$
$884$	−4.51517e30			−0.521105
$885$	−5.11662e30	−	7.76079e30i	−0.583551	−	0.885119i
$886$	−8.46586e30			−0.954150
$887$		−	3.35525e30i		−	0.373703i	−0.982388	−	0.186852i	$-0.940172\pi$
$887$		−	3.35525e30i		−	0.373703i	0.982388	−	0.186852i	$-0.0598283\pi$
$888$			4.74222e30i			0.521970i
$889$	4.89658e30			0.532628
$890$	3.95812e30	+	6.00360e30i	0.425495	+	0.645382i
$891$	−1.54416e31			−1.64050
$892$		−	5.47918e30i		−	0.575288i
$893$		−	1.03769e31i		−	1.07678i
$894$	−8.37326e30			−0.858718
$895$	−6.53945e30	+	4.31140e30i	−0.662826	+	0.436995i
$896$	3.62318e29			0.0362957
$897$		−	2.79720e30i		−	0.276951i
$898$			7.61911e30i			0.745594i
$899$	5.50145e30			0.532109
$900$	−1.53142e29	+	3.57187e29i	−0.0146403	+	0.0341468i
$901$	−1.48897e30			−0.140694
$902$		−	2.08821e30i		−	0.195032i
$903$		−	2.11132e30i		−	0.194909i
$904$	4.01467e30			0.366338
$905$	−1.05377e31	+	6.94742e30i	−0.950465	+	0.626633i
$906$	6.37237e30			0.568139
$907$			7.57889e29i			0.0667927i	0.999442	+	0.0333964i	$0.0106324\pi$
$907$			7.57889e29i			0.0667927i	−0.999442	+	0.0333964i	$0.989368\pi$
$908$			9.45720e30i			0.823875i
$909$	−6.83673e29			−0.0588746
$910$	−2.42363e30	−	3.67612e30i	−0.206316	−	0.312936i
$911$	−7.94313e30			−0.668419			−0.334209	−	0.942499i	$-0.608469\pi$
$911$	−7.94313e30			−0.668419			−0.334209	+	0.942499i	$0.608469\pi$
$912$			2.56522e30i			0.213392i
$913$			1.48940e31i			1.22480i
$914$	7.66785e30			0.623359
$915$	5.59543e30	+	8.48704e30i	0.449688	+	0.682079i
$916$	−5.59169e29			−0.0444263
$917$			3.22317e29i			0.0253166i
$918$			7.59914e30i			0.590088i
$919$	−8.88197e29			−0.0681862			−0.0340931	−	0.999419i	$-0.510854\pi$
$919$	−8.88197e29			−0.0681862			−0.0340931	+	0.999419i	$0.510854\pi$
$920$	8.67235e29	−	5.71760e29i	0.0658210	−	0.0433952i
$921$	−5.76805e30			−0.432815
$922$		−	4.07397e30i		−	0.302234i
$923$		−	5.09650e30i		−	0.373813i
$924$	4.85653e30			0.352185
$925$	1.96699e31	+	8.43336e30i	1.41031	+	0.604661i
$926$	1.07463e31			0.761807
$927$			4.90348e29i			0.0343690i
$928$		−	4.22047e30i		−	0.292487i
$929$	−1.06608e31			−0.730509			−0.365255	−	0.930908i	$-0.619018\pi$
$929$	−1.06608e31			−0.730509			−0.365255	+	0.930908i	$0.619018\pi$
$930$	2.69608e30	−	1.77750e30i	0.182668	−	0.120431i
$931$	1.10097e31			0.737568
$932$		−	1.20959e30i		−	0.0801256i
$933$			2.08662e31i			1.36674i
$934$	−1.05885e31			−0.685793
$935$	−1.23709e31	−	1.87639e31i	−0.792279	−	1.20171i
$936$	5.35500e29			0.0339128
$937$			1.24893e31i			0.782118i	0.920366	+	0.391059i	$0.127891\pi$
$937$			1.24893e31i			0.782118i	−0.920366	+	0.391059i	$0.872109\pi$
$938$		−	1.48852e30i		−	0.0921778i
$939$	−1.03770e31			−0.635452
$940$	5.51614e30	+	8.36677e30i	0.334035	+	0.506659i
$941$	2.09482e30			0.125446			0.0627228	−	0.998031i	$-0.480022\pi$
$941$	2.09482e30			0.125446			0.0627228	+	0.998031i	$0.480022\pi$
$942$			1.30242e31i			0.771285i
$943$		−	5.89077e29i		−	0.0344984i
$944$	−4.75651e30			−0.275475
$945$	−6.18701e30	+	4.07904e30i	−0.354362	+	0.233628i
$946$	−1.09796e31			−0.621913
$947$		−	1.17811e31i		−	0.659953i	−0.943989	−	0.329976i	$-0.892959\pi$
$947$		−	1.17811e31i		−	0.659953i	0.943989	−	0.329976i	$-0.107041\pi$
$948$		−	1.50458e31i		−	0.833540i
$949$	−1.94353e31			−1.06487
$950$	1.06401e31	+	4.56188e30i	0.576563	+	0.247198i
$951$	1.79682e31			0.962960
$952$		−	2.21143e30i		−	0.117216i
$953$		−	1.50103e31i		−	0.786889i	−0.919348	−	0.393445i	$-0.871283\pi$
$953$		−	1.50103e31i		−	0.786889i	0.919348	−	0.393445i	$-0.128717\pi$
$954$	1.76592e29			0.00915617
$955$	−2.07567e29	+	1.36847e29i	−0.0106445	+	0.00701779i
$956$	1.21763e31			0.617602
$957$		−	5.65715e31i		−	2.83807i
$958$			2.79824e30i			0.138850i
$959$	1.20791e31			0.592841
$960$	−1.36362e30	−	2.06831e30i	−0.0661981	−	0.100408i
$961$	−1.86716e31			−0.896572
$962$		−	2.94893e31i		−	1.40064i
$963$		−	2.08597e30i		−	0.0980014i
$964$	−1.59926e31			−0.743209
$965$	1.09420e31	+	1.65966e31i	0.502990	+	0.762926i
$966$	1.37001e30			0.0622965
$967$			3.56223e30i			0.160230i	0.996786	+	0.0801149i	$0.0255287\pi$
$967$			3.56223e30i			0.160230i	−0.996786	+	0.0801149i	$0.974471\pi$
$968$		−	1.73097e31i		−	0.770192i
$969$	1.56570e31			0.689141
$970$	−1.16958e31	+	7.71096e30i	−0.509247	+	0.335742i
$971$	4.44139e31			1.91301			0.956505	−	0.291715i	$-0.0942258\pi$
$971$	4.44139e31			1.91301			0.956505	+	0.291715i	$0.0942258\pi$
$972$		−	1.74018e30i		−	0.0741480i
$973$			3.37764e29i			0.0142373i
$974$	−1.20165e31			−0.501081
$975$	−1.18638e31	+	2.76710e31i	−0.489412	+	1.14150i
$976$	5.20163e30			0.212283
$977$		−	4.01407e31i		−	1.62066i	−0.585974	−	0.810330i	$-0.699288\pi$
$977$		−	4.01407e31i		−	1.62066i	0.585974	−	0.810330i	$-0.300712\pi$
$978$			2.00930e31i			0.802577i
$979$	4.93210e31			1.94901
$980$	−8.87699e30	+	5.85252e30i	−0.347050	+	0.228807i
$981$	−3.36601e30			−0.130194
$982$		−	1.06661e31i		−	0.408166i
$983$			2.37125e31i			0.897770i	0.893590	+	0.448885i	$0.148179\pi$
$983$			2.37125e31i			0.897770i	−0.893590	+	0.448885i	$0.851821\pi$
$984$	−1.40492e30			−0.0526263
$985$	−6.86728e29	−	1.04162e30i	−0.0254510	−	0.0386035i
$986$	−2.57599e31			−0.944576
$987$			1.32174e31i			0.479529i
$988$		−	1.59517e31i		−	0.572611i
$989$	−3.09730e30			−0.110008
$990$	1.46719e30	+	2.22540e30i	0.0515604	+	0.0782059i
$991$	1.88460e31			0.655307			0.327654	−	0.944798i	$-0.393742\pi$
$991$	1.88460e31			0.655307			0.327654	+	0.944798i	$0.393742\pi$
$992$		−	1.65240e30i		−	0.0568517i
$993$			1.93330e31i			0.658161i
$994$	2.49616e30			0.0840843
$995$	8.44915e30	−	5.57045e30i	0.281625	−	0.185673i
$996$	1.00204e31			0.330494
$997$			9.50841e30i			0.310319i	0.987889	+	0.155160i	$0.0495892\pi$
$997$			9.50841e30i			0.310319i	−0.987889	+	0.155160i	$0.950411\pi$
$998$		−	6.68311e30i		−	0.215828i
$999$	−4.96313e31			−1.58605

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.22.b.a.9.9	yes	10
4.3	odd	2		80.22.c.c.49.3		10
5.2	odd	4		50.22.a.k.1.4		5
5.3	odd	4		50.22.a.l.1.2		5
5.4	even	2	inner	10.22.b.a.9.2	✓	10
20.19	odd	2		80.22.c.c.49.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.22.b.a.9.2	✓	10	5.4	even	2	inner
10.22.b.a.9.9	yes	10	1.1	even	1	trivial
50.22.a.k.1.4		5	5.2	odd	4
50.22.a.l.1.2		5	5.3	odd	4
80.22.c.c.49.3		10	4.3	odd	2
80.22.c.c.49.8		10	20.19	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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1024.00i q^{2} +98402.7i q^{3} -1.04858e6 q^{4} +(1.82310e7 - 1.20195e7i) q^{5} -1.00764e8 q^{6} +3.06895e8i q^{7} -1.07374e9i q^{8} +7.77265e8 q^{9} +(1.23080e10 + 1.86685e10i) q^{10} +1.53366e11 q^{11} -1.03183e11i q^{12} +6.41638e11i q^{13} -3.14260e11 q^{14} +(1.18275e12 + 1.79398e12i) q^{15} +1.09951e12 q^{16} -6.71094e12i q^{17} +7.95920e11i q^{18} +2.37092e13 q^{19} +(-1.91166e13 + 1.26034e13i) q^{20} -3.01993e13 q^{21} +1.57047e14i q^{22} +4.43024e13i q^{23} +1.05659e14 q^{24} +(1.87900e14 - 4.38255e14i) q^{25} -6.57038e14 q^{26} +1.10581e15i q^{27} -3.21803e14i q^{28} -3.74853e15 q^{29} +(-1.83703e15 + 1.21114e15i) q^{30} -1.46763e15 q^{31} +1.12590e15i q^{32} +1.50916e16i q^{33} +6.87200e15 q^{34} +(3.68873e15 + 5.59499e15i) q^{35} -8.15022e14 q^{36} +4.48822e16i q^{37} +2.42783e16i q^{38} -6.31389e16 q^{39} +(-1.29059e16 - 1.95754e16i) q^{40} -1.32967e16 q^{41} -3.09241e16i q^{42} +6.99128e16i q^{43} -1.60816e17 q^{44} +(1.41703e16 - 9.34235e15i) q^{45} -4.53656e16 q^{46} -4.37671e17i q^{47} +1.08195e17i q^{48} +4.64361e17 q^{49} +(4.48773e17 + 1.92409e17i) q^{50} +6.60375e17 q^{51} -6.72807e17i q^{52} -2.21872e17i q^{53} -1.13235e18 q^{54} +(2.79602e18 - 1.84339e18i) q^{55} +3.29526e17 q^{56} +2.33305e18i q^{57} -3.83850e18i q^{58} -4.32602e18 q^{59} +(-1.24021e18 - 1.88112e18i) q^{60} +4.73085e18 q^{61} -1.50285e18i q^{62} +2.38539e17i q^{63} -1.15292e18 q^{64} +(7.71218e18 + 1.16977e19i) q^{65} -1.54538e19 q^{66} +4.73660e18i q^{67} +7.03693e18i q^{68} -4.35947e18 q^{69} +(-5.72927e18 + 3.77726e18i) q^{70} -7.94295e18 q^{71} -8.34582e17i q^{72} +3.02901e19i q^{73} -4.59594e19 q^{74} +(4.31255e19 + 1.84898e19i) q^{75} -2.48609e19 q^{76} +4.70673e19i q^{77} -6.46543e19i q^{78} +1.45817e20 q^{79} +(2.00452e19 - 1.32156e19i) q^{80} -1.00684e20 q^{81} -1.36159e19i q^{82} +9.71136e19i q^{83} +3.16663e19 q^{84} +(-8.06623e19 - 1.22347e20i) q^{85} -7.15907e19 q^{86} -3.68865e20i q^{87} -1.64676e20i q^{88} +3.21590e20 q^{89} +(9.56657e18 + 1.45104e19i) q^{90} -1.96916e20 q^{91} -4.64544e19i q^{92} -1.44419e20i q^{93} +4.48175e20 q^{94} +(4.32243e20 - 2.84974e20i) q^{95} -1.10792e20 q^{96} +6.26501e20i q^{97} +4.75506e20i q^{98} +1.19206e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10485760 q^{4} + 27722150 q^{5} - 230748160 q^{6} - 12711922730 q^{9} - 22426931200 q^{10} - 199435236680 q^{11} - 104903905280 q^{14} - 1714785566200 q^{15} + 10995116277760 q^{16} + 123436918144200 q^{19}+ \cdots + 21\!\cdots\!40 q^{99}+O(q^{100}) \) 10 * q - 10485760 * q^4 + 27722150 * q^5 - 230748160 * q^6 - 12711922730 * q^9 - 22426931200 * q^10 - 199435236680 * q^11 - 104903905280 * q^14 - 1714785566200 * q^15 + 10995116277760 * q^16 + 123436918144200 * q^19 - 29068781158400 * q^20 - 158960071181080 * q^21 + 241956982620160 * q^24 - 753844388658750 * q^25 - 173073038991360 * q^26 + 1774546489874700 * q^29 + 5639638400921600 * q^30 + 10456190999441920 * q^31 - 18958190285946880 * q^34 + 24035281816377400 * q^35 + 13329417088532480 * q^36 + 45468500581785840 * q^39 + 23516341809971200 * q^40 + 93828363171915220 * q^41 + 209123002736967680 * q^44 - 1294878557826950 * q^45 - 453509186534543360 * q^46 - 1584589583512161570 * q^49 + 130953516753920000 * q^50 - 512256548145748480 * q^51 - 3219652987818598400 * q^54 + 8644481518774929800 * q^55 + 109999717382881280 * q^56 - 5722347962825378600 * q^59 + 1798082989863731200 * q^60 - 12650867843198554180 * q^61 - 11529215046068469760 * q^64 + 26346750548743534800 * q^65 - 32504410286103019520 * q^66 + 96951047157018456040 * q^69 + 41090423076705996800 * q^70 - 104781163131643184880 * q^71 + 32904860966761553920 * q^74 + 296606638041153670000 * q^75 - 129432989879972659200 * q^76 + 96531112322635730400 * q^79 + 30480826271950438400 * q^80 - 828031346148584406190 * q^81 + 166681715598772142080 * q^84 + 634500251198792806400 * q^85 - 1012021399291540418560 * q^86 + 1925821863958052788100 * q^89 + 598299873941928857600 * q^90 - 3491972396700191783280 * q^91 + 919679051426714398720 * q^94 + 1154253771449725323000 * q^95 - 253710285007916892160 * q^96 + 2120189706372537680840 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more