LMFDB - Embedded newform 4.19.b.a.3.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,19,Mod(3,4)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 19, names="a")

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

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 19);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 19 $
Character orbit:	$[\chi]$	$=$	4.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:	$8.21544550839$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3 x^{7} - 10969 x^{6} - 835887 x^{5} + 20786973 x^{4} - 17082875145 x^{3} + \cdots + 71\!\cdots\!30 $ x^8 - 3x^7 - 10969x^6 - 835887x^5 + 20786973x^4 - 17082875145x^3 - 2740871824195x^2 + 109263554839035*x + 71754930984829630
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{56}\cdot 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.4
Root			$54.8957 + 117.008i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.19.b.a.3.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-207.583 + 468.031i) q^{2} +4128.11i q^{3} +(-175963. - 194311. i) q^{4} -1.32216e6 q^{5} +(-1.93208e6 - 856924. i) q^{6} -1.88890e7i q^{7} +(1.27470e8 - 4.20206e7i) q^{8} +3.70379e8 q^{9} +O(q^{10})$	\(q+(-207.583 + 468.031i) q^{2} +4128.11i q^{3} +(-175963. - 194311. i) q^{4} -1.32216e6 q^{5} +(-1.93208e6 - 856924. i) q^{6} -1.88890e7i q^{7} +(1.27470e8 - 4.20206e7i) q^{8} +3.70379e8 q^{9} +(2.74457e8 - 6.18811e8i) q^{10} -2.94158e9i q^{11} +(8.02134e8 - 7.26393e8i) q^{12} +2.06691e9 q^{13} +(8.84066e9 + 3.92104e9i) q^{14} -5.45800e9i q^{15} +(-6.79368e9 + 6.83828e10i) q^{16} -1.59586e11 q^{17} +(-7.68844e10 + 1.73349e11i) q^{18} -3.75156e11i q^{19} +(2.32650e11 + 2.56909e11i) q^{20} +7.79759e10 q^{21} +(1.37675e12 + 6.10621e11i) q^{22} -3.51589e12i q^{23} +(1.73465e11 + 5.26211e11i) q^{24} -2.06660e12 q^{25} +(-4.29055e11 + 9.67380e11i) q^{26} +3.12828e12i q^{27} +(-3.67034e12 + 3.32377e12i) q^{28} +1.15396e12 q^{29} +(2.55452e12 + 1.13299e12i) q^{30} +2.94593e13i q^{31} +(-3.05951e13 - 1.73748e13i) q^{32} +1.21431e13 q^{33} +(3.31273e13 - 7.46912e13i) q^{34} +2.49743e13i q^{35} +(-6.51730e13 - 7.19686e13i) q^{36} +1.43358e14 q^{37} +(1.75585e14 + 7.78760e13i) q^{38} +8.53243e12i q^{39} +(-1.68536e14 + 5.55578e13i) q^{40} -3.41574e14 q^{41} +(-1.61865e13 + 3.64952e13i) q^{42} -1.16170e14i q^{43} +(-5.71580e14 + 5.17608e14i) q^{44} -4.89699e14 q^{45} +(1.64555e15 + 7.29839e14i) q^{46} -1.28500e15i q^{47} +(-2.82292e14 - 2.80450e13i) q^{48} +1.27162e15 q^{49} +(4.28990e14 - 9.67233e14i) q^{50} -6.58787e14i q^{51} +(-3.63700e14 - 4.01623e14i) q^{52} -9.01838e14 q^{53} +(-1.46413e15 - 6.49376e14i) q^{54} +3.88923e15i q^{55} +(-7.93728e14 - 2.40779e15i) q^{56} +1.54868e15 q^{57} +(-2.39543e14 + 5.40091e14i) q^{58} +1.35294e16i q^{59} +(-1.06055e15 + 9.60405e14i) q^{60} +1.92707e15 q^{61} +(-1.37879e16 - 6.11525e15i) q^{62} -6.99610e15i q^{63} +(1.44829e16 - 1.07128e16i) q^{64} -2.73278e15 q^{65} +(-2.52071e15 + 5.68337e15i) q^{66} -3.28116e16i q^{67} +(2.80812e16 + 3.10092e16i) q^{68} +1.45140e16 q^{69} +(-1.16887e16 - 5.18423e15i) q^{70} -1.05678e16i q^{71} +(4.72123e16 - 1.55636e16i) q^{72} -5.27239e16 q^{73} +(-2.97586e16 + 6.70960e16i) q^{74} -8.53114e15i q^{75} +(-7.28968e16 + 6.60135e16i) q^{76} -5.55636e16 q^{77} +(-3.99345e15 - 1.77119e15i) q^{78} +2.46184e16i q^{79} +(8.98231e15 - 9.04128e16i) q^{80} +1.30579e17 q^{81} +(7.09049e16 - 1.59867e17i) q^{82} +1.57512e17i q^{83} +(-1.37209e16 - 1.51515e16i) q^{84} +2.10997e17 q^{85} +(5.43710e16 + 2.41148e16i) q^{86} +4.76368e15i q^{87} +(-1.23607e17 - 3.74964e17i) q^{88} -1.76561e17 q^{89} +(1.01653e17 - 2.29195e17i) q^{90} -3.90420e16i q^{91} +(-6.83175e17 + 6.18666e17i) q^{92} -1.21611e17 q^{93} +(6.01419e17 + 2.66743e17i) q^{94} +4.96015e17i q^{95} +(7.17248e16 - 1.26300e17i) q^{96} +8.50771e16 q^{97} +(-2.63966e17 + 5.95157e17i) q^{98} -1.08950e18i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 84 q^{2} + 352016 q^{4} + 860880 q^{5} + 310944 q^{6} - 154160064 q^{8} - 729541560 q^{9}+O(q^{10}) $ 8 * q + 84 * q^2 + 352016 * q^4 + 860880 * q^5 + 310944 * q^6 - 154160064 * q^8 - 729541560 * q^9	$ 8 q + 84 q^{2} + 352016 q^{4} + 860880 q^{5} + 310944 q^{6} - 154160064 q^{8} - 729541560 q^{9} - 853591160 q^{10} - 2983758720 q^{12} - 6658778288 q^{13} - 3330240576 q^{14} + 35282993408 q^{16} + 213854181648 q^{17} + 197420552436 q^{18} - 421824543840 q^{20} - 771822339072 q^{21} - 586750684320 q^{22} - 3940602195456 q^{24} + 528925732440 q^{25} + 12314194404552 q^{26} - 20860043224320 q^{28} + 11238056568912 q^{29} + 63814514963520 q^{30} - 133632603995136 q^{32} - 21541938424320 q^{33} + 295093712425768 q^{34} - 595880470532208 q^{36} - 158886968816432 q^{37} + 830666716492320 q^{38} - 16\!\cdots\!80 q^{40}+ \cdots + 24\!\cdots\!76 q^{98}+O(q^{100}) $ 8 * q + 84 * q^2 + 352016 * q^4 + 860880 * q^5 + 310944 * q^6 - 154160064 * q^8 - 729541560 * q^9 - 853591160 * q^10 - 2983758720 * q^12 - 6658778288 * q^13 - 3330240576 * q^14 + 35282993408 * q^16 + 213854181648 * q^17 + 197420552436 * q^18 - 421824543840 * q^20 - 771822339072 * q^21 - 586750684320 * q^22 - 3940602195456 * q^24 + 528925732440 * q^25 + 12314194404552 * q^26 - 20860043224320 * q^28 + 11238056568912 * q^29 + 63814514963520 * q^30 - 133632603995136 * q^32 - 21541938424320 * q^33 + 295093712425768 * q^34 - 595880470532208 * q^36 - 158886968816432 * q^37 + 830666716492320 * q^38 - 1609388875268480 * q^40 + 451509984725136 * q^41 + 3247297173265920 * q^42 - 3429204744604800 * q^44 + 394282398204240 * q^45 + 3658225092496704 * q^46 - 6713415182530560 * q^48 - 2251201133570680 * q^49 + 6942506471898780 * q^50 - 6479715597253472 * q^52 + 1216384760086992 * q^53 + 3284600487812928 * q^54 + 7432202560564224 * q^56 + 2661563378188800 * q^57 - 17440122911455928 * q^58 + 36392091128935680 * q^60 + 184592915104336 * q^61 - 42580340982416640 * q^62 + 74097564160495616 * q^64 - 5670291051587040 * q^65 - 140809597617788160 * q^66 + 131212356714741792 * q^68 - 26839260584143872 * q^69 - 153862868594448000 * q^70 + 156072744876684864 * q^72 + 31494366486758032 * q^73 - 108949653815722872 * q^74 + 152098090223483520 * q^76 + 180811187963888640 * q^77 + 14085206442507840 * q^78 - 152292076037383680 * q^80 - 260466732987857784 * q^81 + 335145451981844968 * q^82 - 850166994683553792 * q^84 - 204660361893474400 * q^85 + 950236163482864224 * q^86 - 1369014843355476480 * q^88 + 162001265029847952 * q^89 + 1771450132254688200 * q^90 - 1193579560451823360 * q^92 + 668158876340367360 * q^93 + 1478730179820369024 * q^94 - 2028358051400441856 * q^96 - 1214976752903766512 * q^97 + 2427758859173433876 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

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 $

$2$	−207.583	+	468.031i	−0.405435	+	0.914124i
$2$	−207.583	+	468.031i	−0.405435	+	0.914124i
$3$			4128.11i			0.209729i	0.994486	+	0.104865i	$0.0334410\pi$
$3$			4128.11i			0.209729i	−0.994486	+	0.104865i	$0.966559\pi$
$4$	−175963.	−	194311.i	−0.671245	−	0.741236i
$5$	−1.32216e6			−0.676944			−0.338472	−	0.940976i	$-0.609910\pi$
$5$	−1.32216e6			−0.676944			−0.338472	+	0.940976i	$0.609910\pi$
$6$	−1.93208e6	−	856924.i	−0.191719	−	0.0850317i
$7$		−	1.88890e7i		−	0.468088i	−0.972226	−	0.234044i	$-0.924804\pi$
$7$		−	1.88890e7i		−	0.468088i	0.972226	−	0.234044i	$-0.0751959\pi$
$8$	1.27470e8	−	4.20206e7i	0.949727	−	0.313078i
$9$	3.70379e8			0.956014
$10$	2.74457e8	−	6.18811e8i	0.274457	−	0.618811i
$11$		−	2.94158e9i		−	1.24752i	−0.781617	−	0.623758i	$-0.785605\pi$
$11$		−	2.94158e9i		−	1.24752i	0.781617	−	0.623758i	$-0.214395\pi$
$12$	8.02134e8	−	7.26393e8i	0.155459	−	0.140780i
$13$	2.06691e9			0.194909			0.0974545	−	0.995240i	$-0.468930\pi$
$13$	2.06691e9			0.194909			0.0974545	+	0.995240i	$0.468930\pi$
$14$	8.84066e9	+	3.92104e9i	0.427890	+	0.189779i
$15$		−	5.45800e9i		−	0.141975i
$16$	−6.79368e9	+	6.83828e10i	−0.0988610	+	0.995101i
$17$	−1.59586e11			−1.34572			−0.672859	−	0.739771i	$-0.734934\pi$
$17$	−1.59586e11			−1.34572			−0.672859	+	0.739771i	$0.734934\pi$
$18$	−7.68844e10	+	1.73349e11i	−0.387601	+	0.873915i
$19$		−	3.75156e11i		−	1.16260i	−0.813690	−	0.581299i	$-0.802545\pi$
$19$		−	3.75156e11i		−	1.16260i	0.813690	−	0.581299i	$-0.197455\pi$
$20$	2.32650e11	+	2.56909e11i	0.454395	+	0.501775i
$21$	7.79759e10			0.0981718
$22$	1.37675e12	+	6.10621e11i	1.14038	+	0.505787i
$23$		−	3.51589e12i		−	1.95202i	−0.217716	−	0.976012i	$-0.569861\pi$
$23$		−	3.51589e12i		−	1.95202i	0.217716	−	0.976012i	$-0.430139\pi$
$24$	1.73465e11	+	5.26211e11i	0.0656616	+	0.199186i
$25$	−2.06660e12			−0.541747
$26$	−4.29055e11	+	9.67380e11i	−0.0790230	+	0.178171i
$27$			3.12828e12i			0.410234i
$28$	−3.67034e12	+	3.32377e12i	−0.346963	+	0.314201i
$29$	1.15396e12			0.0795444			0.0397722	−	0.999209i	$-0.487337\pi$
$29$	1.15396e12			0.0795444			0.0397722	+	0.999209i	$0.487337\pi$
$30$	2.55452e12	+	1.13299e12i	0.129783	+	0.0575617i
$31$			2.94593e13i			1.11421i	0.830441	+	0.557106i	$0.188088\pi$
$31$			2.94593e13i			1.11421i	−0.830441	+	0.557106i	$0.811912\pi$
$32$	−3.05951e13	−	1.73748e13i	−0.869564	−	0.493820i
$33$	1.21431e13			0.261641
$34$	3.31273e13	−	7.46912e13i	0.545601	−	1.23015i
$35$			2.49743e13i			0.316869i
$36$	−6.51730e13	−	7.19686e13i	−0.641719	−	0.708631i
$37$	1.43358e14			1.10308			0.551539	−	0.834149i	$-0.314041\pi$
$37$	1.43358e14			1.10308			0.551539	+	0.834149i	$0.314041\pi$
$38$	1.75585e14	+	7.78760e13i	1.06276	+	0.471358i
$39$			8.53243e12i			0.0408782i
$40$	−1.68536e14	+	5.55578e13i	−0.642913	+	0.211936i
$41$	−3.41574e14			−1.04335			−0.521675	−	0.853144i	$-0.674693\pi$
$41$	−3.41574e14			−1.04335			−0.521675	+	0.853144i	$0.674693\pi$
$42$	−1.61865e13	+	3.64952e13i	−0.0398023	+	0.0897412i
$43$		−	1.16170e14i		−	0.231141i	−0.993299	−	0.115570i	$-0.963130\pi$
$43$		−	1.16170e14i		−	0.231141i	0.993299	−	0.115570i	$-0.0368696\pi$
$44$	−5.71580e14	+	5.17608e14i	−0.924704	+	0.837389i
$45$	−4.89699e14			−0.647168
$46$	1.64555e15	+	7.29839e14i	1.78439	+	0.791419i
$47$		−	1.28500e15i		−	1.14821i	−0.818781	−	0.574105i	$-0.805350\pi$
$47$		−	1.28500e15i		−	1.14821i	0.818781	−	0.574105i	$-0.194650\pi$
$48$	−2.82292e14	−	2.80450e13i	−0.208702	−	0.0207341i
$49$	1.27162e15			0.780894
$50$	4.28990e14	−	9.67233e14i	0.219643	−	0.495223i
$51$		−	6.58787e14i		−	0.282237i
$52$	−3.63700e14	−	4.01623e14i	−0.130832	−	0.144474i
$53$	−9.01838e14			−0.273304			−0.136652	−	0.990619i	$-0.543634\pi$
$53$	−9.01838e14			−0.273304			−0.136652	+	0.990619i	$0.543634\pi$
$54$	−1.46413e15	−	6.49376e14i	−0.375004	−	0.166323i
$55$			3.88923e15i			0.844499i
$56$	−7.93728e14	−	2.40779e15i	−0.146548	−	0.444556i
$57$	1.54868e15			0.243831
$58$	−2.39543e14	+	5.40091e14i	−0.0322501	+	0.0727135i
$59$			1.35294e16i			1.56175i	0.624690	+	0.780873i	$0.285225\pi$
$59$			1.35294e16i			1.56175i	−0.624690	+	0.780873i	$0.714775\pi$
$60$	−1.06055e15	+	9.60405e14i	−0.105237	+	0.0953001i
$61$	1.92707e15			0.164790			0.0823948	−	0.996600i	$-0.473743\pi$
$61$	1.92707e15			0.164790			0.0823948	+	0.996600i	$0.473743\pi$
$62$	−1.37879e16	−	6.11525e15i	−1.01853	−	0.451741i
$63$		−	6.99610e15i		−	0.447498i
$64$	1.44829e16	−	1.07128e16i	0.803965	−	0.594677i
$65$	−2.73278e15			−0.131943
$66$	−2.52071e15	+	5.68337e15i	−0.106078	+	0.239172i
$67$		−	3.28116e16i		−	1.20602i	−0.797734	−	0.603009i	$-0.793968\pi$
$67$		−	3.28116e16i		−	1.20602i	0.797734	−	0.603009i	$-0.206032\pi$
$68$	2.80812e16	+	3.10092e16i	0.903306	+	0.997494i
$69$	1.45140e16			0.409397
$70$	−1.16887e16	−	5.18423e15i	−0.289658	−	0.128470i
$71$		−	1.05678e16i		−	0.230493i	−0.993337	−	0.115247i	$-0.963234\pi$
$71$		−	1.05678e16i		−	0.230493i	0.993337	−	0.115247i	$-0.0367659\pi$
$72$	4.72123e16	−	1.55636e16i	0.907952	−	0.299307i
$73$	−5.27239e16			−0.895575			−0.447787	−	0.894140i	$-0.647788\pi$
$73$	−5.27239e16			−0.895575			−0.447787	+	0.894140i	$0.647788\pi$
$74$	−2.97586e16	+	6.70960e16i	−0.447226	+	1.00835i
$75$		−	8.53114e15i		−	0.113620i
$76$	−7.28968e16	+	6.60135e16i	−0.861760	+	0.780388i
$77$	−5.55636e16			−0.583947
$78$	−3.99345e15	−	1.77119e15i	−0.0373677	−	0.0165734i
$79$			2.46184e16i			0.205407i	0.994712	+	0.102703i	$0.0327493\pi$
$79$			2.46184e16i			0.205407i	−0.994712	+	0.102703i	$0.967251\pi$
$80$	8.98231e15	−	9.04128e16i	0.0669234	−	0.673628i
$81$	1.30579e17			0.869975
$82$	7.09049e16	−	1.59867e17i	0.423011	−	0.953752i
$83$			1.57512e17i			0.842577i	0.906927	+	0.421289i	$0.138422\pi$
$83$			1.57512e17i			0.842577i	−0.906927	+	0.421289i	$0.861578\pi$
$84$	−1.37209e16	−	1.51515e16i	−0.0658973	−	0.0727685i
$85$	2.10997e17			0.910976
$86$	5.43710e16	+	2.41148e16i	0.211291	+	0.0937126i
$87$			4.76368e15i			0.0166828i
$88$	−1.23607e17	−	3.74964e17i	−0.390570	−	1.18480i
$89$	−1.76561e17			−0.503947			−0.251974	−	0.967734i	$-0.581080\pi$
$89$	−1.76561e17			−0.503947			−0.251974	+	0.967734i	$0.581080\pi$
$90$	1.01653e17	−	2.29195e17i	0.262385	−	0.591592i
$91$		−	3.90420e16i		−	0.0912345i
$92$	−6.83175e17	+	6.18666e17i	−1.44691	+	1.31029i
$93$	−1.21611e17			−0.233683
$94$	6.01419e17	+	2.66743e17i	1.04961	+	0.465525i
$95$			4.96015e17i			0.787014i
$96$	7.17248e16	−	1.26300e17i	0.103569	−	0.182373i
$97$	8.50771e16			0.111910			0.0559548	−	0.998433i	$-0.482180\pi$
$97$	8.50771e16			0.111910			0.0559548	+	0.998433i	$0.482180\pi$
$98$	−2.63966e17	+	5.95157e17i	−0.316602	+	0.713834i
$99$		−	1.08950e18i		−	1.19264i
$100$	3.63645e17	+	4.01562e17i	0.363645	+	0.401562i
$101$	−9.26693e17			−0.847312			−0.423656	−	0.905823i	$-0.639254\pi$
$101$	−9.26693e17			−0.847312			−0.423656	+	0.905823i	$0.639254\pi$
$102$	3.08333e17	+	1.36753e17i	0.257999	+	0.114429i
$103$		−	1.41521e18i		−	1.08464i	−0.840171	−	0.542321i	$-0.817546\pi$
$103$		−	1.41521e18i		−	1.08464i	0.840171	−	0.542321i	$-0.182454\pi$
$104$	2.63470e17	−	8.68529e16i	0.185110	−	0.0610217i
$105$	−1.03096e17			−0.0664568
$106$	1.87206e17	−	4.22088e17i	0.110807	−	0.249833i
$107$			4.27847e17i			0.232720i	0.993207	+	0.116360i	$0.0371227\pi$
$107$			4.27847e17i			0.232720i	−0.993207	+	0.116360i	$0.962877\pi$
$108$	6.07857e17	−	5.50460e17i	0.304080	−	0.275367i
$109$	3.16310e18			1.45638			0.728191	−	0.685375i	$-0.240362\pi$
$109$	3.16310e18			1.45638			0.728191	+	0.685375i	$0.240362\pi$
$110$	−1.82028e18	−	8.07337e17i	−0.771977	−	0.342389i
$111$			5.91796e17i			0.231348i
$112$	1.29169e18	+	1.28326e17i	0.465795	+	0.0462756i
$113$	−2.43054e18			−0.809089			−0.404544	−	0.914518i	$-0.632570\pi$
$113$	−2.43054e18			−0.809089			−0.404544	+	0.914518i	$0.632570\pi$
$114$	−3.21480e17	+	7.24833e17i	−0.0988577	+	0.222892i
$115$			4.64856e18i			1.32141i
$116$	−2.03055e17	−	2.24227e17i	−0.0533938	−	0.0589612i
$117$	7.65542e17			0.186336
$118$	−6.33218e18	−	2.80847e18i	−1.42763	−	0.633186i
$119$			3.01442e18i			0.629914i
$120$	−2.29348e17	−	6.95733e17i	−0.0444493	−	0.134838i
$121$	−3.09296e18			−0.556297
$122$	−4.00027e17	+	9.01931e17i	−0.0668115	+	0.150638i
$123$		−	1.41005e18i		−	0.218821i
$124$	5.72426e18	−	5.18375e18i	0.825894	−	0.747909i
$125$	7.77600e18			1.04368
$126$	3.27440e18	+	1.45227e18i	0.409069	+	0.181432i
$127$		−	4.71231e18i		−	0.548277i	−0.961690	−	0.274139i	$-0.911607\pi$
$127$		−	4.71231e18i		−	0.548277i	0.961690	−	0.274139i	$-0.0883927\pi$
$128$	2.00750e18	+	9.00225e18i	0.217653	+	0.976026i
$129$	4.79560e17			0.0484770
$130$	5.67279e17	−	1.27903e18i	0.0534941	−	0.120612i
$131$		−	1.55719e19i		−	1.37056i	−0.728278	−	0.685281i	$-0.759679\pi$
$131$		−	1.55719e19i		−	1.37056i	0.728278	−	0.685281i	$-0.240321\pi$
$132$	−2.13674e18	−	2.35954e18i	−0.175625	−	0.193938i
$133$	−7.08634e18			−0.544198
$134$	1.53569e19	+	6.81112e18i	1.10245	+	0.488962i
$135$		−	4.13607e18i		−	0.277705i
$136$	−2.03424e19	+	6.70589e18i	−1.27807	+	0.421314i
$137$	−1.59634e19			−0.938946			−0.469473	−	0.882947i	$-0.655556\pi$
$137$	−1.59634e19			−0.938946			−0.469473	+	0.882947i	$0.655556\pi$
$138$	−3.01285e18	+	6.79300e18i	−0.165984	+	0.374240i
$139$			1.95220e19i			1.00784i	0.863750	+	0.503920i	$0.168109\pi$
$139$			1.95220e19i			1.00784i	−0.863750	+	0.503920i	$0.831891\pi$
$140$	4.85276e18	−	4.39454e18i	0.234875	−	0.212697i
$141$	5.30461e18			0.240814
$142$	4.94605e18	+	2.19369e18i	0.210700	+	0.0934501i
$143$		−	6.07998e18i		−	0.243152i
$144$	−2.51624e18	+	2.53276e19i	−0.0945125	+	0.951330i
$145$	−1.52572e18			−0.0538471
$146$	1.09446e19	−	2.46765e19i	0.363098	−	0.818666i
$147$			5.24937e18i			0.163776i
$148$	−2.52256e19	−	2.78559e19i	−0.740435	−	0.817641i
$149$	5.73830e19			1.58528			0.792641	−	0.609688i	$-0.208705\pi$
$149$	5.73830e19			1.58528			0.792641	+	0.609688i	$0.208705\pi$
$150$	3.99284e18	+	1.77092e18i	0.103863	+	0.0460656i
$151$			4.94237e19i			1.21100i	0.795847	+	0.605498i	$0.207026\pi$
$151$			4.94237e19i			1.21100i	−0.795847	+	0.605498i	$0.792974\pi$
$152$	−1.57643e19	−	4.78213e19i	−0.363984	−	1.10415i
$153$	−5.91073e19			−1.28652
$154$	1.15340e19	−	2.60055e19i	0.236753	−	0.533800i
$155$		−	3.89499e19i		−	0.754259i
$156$	1.65794e18	−	1.50139e18i	0.0303004	−	0.0274393i
$157$	9.09817e19			1.56985			0.784923	−	0.619593i	$-0.212702\pi$
$157$	9.09817e19			1.56985			0.784923	+	0.619593i	$0.212702\pi$
$158$	−1.15222e19	−	5.11035e18i	−0.187767	−	0.0832792i
$159$		−	3.72288e18i		−	0.0573198i
$160$	4.04515e19	+	2.29721e19i	0.588646	+	0.334289i
$161$	−6.64118e19			−0.913719
$162$	−2.71059e19	+	6.11149e19i	−0.352719	+	0.795265i
$163$			9.05626e19i			1.11496i	0.830189	+	0.557482i	$0.188232\pi$
$163$			9.05626e19i			1.11496i	−0.830189	+	0.557482i	$0.811768\pi$
$164$	6.01043e19	+	6.63715e19i	0.700344	+	0.773369i
$165$	−1.60551e19			−0.177116
$166$	−7.37204e19	−	3.26967e19i	−0.770220	−	0.341610i
$167$		−	9.72890e19i		−	0.962976i	−0.876453	−	0.481488i	$-0.840096\pi$
$167$		−	9.72890e19i		−	0.962976i	0.876453	−	0.481488i	$-0.159904\pi$
$168$	9.93961e18	−	3.27659e18i	0.0932365	−	0.0307354i
$169$	−1.08183e20			−0.962010
$170$	−4.37994e19	+	9.87534e19i	−0.369342	+	0.832745i
$171$		−	1.38950e20i		−	1.11146i
$172$	−2.25730e19	+	2.04415e19i	−0.171330	+	0.155152i
$173$	5.20622e19			0.375066			0.187533	−	0.982258i	$-0.439951\pi$
$173$	5.20622e19			0.375066			0.187533	+	0.982258i	$0.439951\pi$
$174$	−2.22955e18	−	9.88858e17i	−0.0152502	−	0.00676380i
$175$			3.90361e19i			0.253585i
$176$	2.01153e20	+	1.99841e19i	1.24140	+	0.123331i
$177$	−5.58508e19			−0.327544
$178$	3.66511e19	−	8.26362e19i	0.204318	−	0.460670i
$179$		−	1.32199e20i		−	0.700732i	−0.936613	−	0.350366i	$-0.886057\pi$
$179$		−	1.32199e20i		−	0.700732i	0.936613	−	0.350366i	$-0.113943\pi$
$180$	8.61689e19	+	9.51537e19i	0.434408	+	0.479704i
$181$	3.29186e20			1.57883			0.789413	−	0.613862i	$-0.210385\pi$
$181$	3.29186e20			1.57883			0.789413	+	0.613862i	$0.210385\pi$
$182$	1.82729e19	+	8.10444e18i	0.0833997	+	0.0369897i
$183$			7.95516e18i			0.0345612i
$184$	−1.47740e20	−	4.48172e20i	−0.611135	−	1.85389i
$185$	−1.89542e20			−0.746722
$186$	2.52444e19	−	5.69179e19i	0.0947433	−	0.213615i
$187$			4.69434e20i			1.67880i
$188$	−2.49689e20	+	2.26112e20i	−0.851095	+	0.770731i
$189$	5.90901e19			0.192025
$190$	−2.32151e20	−	1.02964e20i	−0.719429	−	0.319083i
$191$			1.30143e20i			0.384698i	0.981327	+	0.192349i	$0.0616106\pi$
$191$			1.30143e20i			0.384698i	−0.981327	+	0.192349i	$0.938389\pi$
$192$	4.42234e19	+	5.97871e19i	0.124721	+	0.168615i
$193$	−1.66813e20			−0.448967			−0.224483	−	0.974478i	$-0.572069\pi$
$193$	−1.66813e20			−0.448967			−0.224483	+	0.974478i	$0.572069\pi$
$194$	−1.76605e19	+	3.98188e19i	−0.0453721	+	0.102299i
$195$		−	1.12812e19i		−	0.0276722i
$196$	−2.23757e20	−	2.47089e20i	−0.524171	−	0.578826i
$197$	9.90856e19			0.221725			0.110862	−	0.993836i	$-0.464639\pi$
$197$	9.90856e19			0.221725			0.110862	+	0.993836i	$0.464639\pi$
$198$	5.09920e20	+	2.26161e20i	1.09022	+	0.483539i
$199$			2.60582e20i			0.532435i	0.963913	+	0.266218i	$0.0857740\pi$
$199$			2.60582e20i			0.532435i	−0.963913	+	0.266218i	$0.914226\pi$
$200$	−2.63430e20	+	8.68397e19i	−0.514512	+	0.169609i
$201$	1.35450e20			0.252938
$202$	1.92365e20	−	4.33721e20i	0.343530	−	0.774548i
$203$		−	2.17972e19i		−	0.0372338i
$204$	−1.28009e20	+	1.15922e20i	−0.209204	+	0.189450i
$205$	4.51615e20			0.706290
$206$	6.62364e20	+	2.93774e20i	0.991497	+	0.439752i
$207$		−	1.30221e21i		−	1.86616i
$208$	−1.40419e19	+	1.41341e20i	−0.0192689	+	0.193954i
$209$	−1.10355e21			−1.45036
$210$	2.14010e19	−	4.82523e19i	0.0269439	−	0.0607498i
$211$		−	6.24652e20i		−	0.753522i	−0.926311	−	0.376761i	$-0.877038\pi$
$211$		−	6.24652e20i		−	0.753522i	0.926311	−	0.376761i	$-0.122962\pi$
$212$	1.58690e20	+	1.75237e20i	0.183454	+	0.202582i
$213$	4.36249e19			0.0483413
$214$	−2.00246e20	−	8.88137e19i	−0.212735	−	0.0943530i
$215$			1.53594e20i			0.156469i
$216$	1.31452e20	+	3.98762e20i	0.128435	+	0.389610i
$217$	5.56458e20			0.521549
$218$	−6.56606e20	+	1.48043e21i	−0.590468	+	1.33131i
$219$		−	2.17650e20i		−	0.187828i
$220$	7.55718e20	−	6.84359e20i	0.625973	−	0.566865i
$221$	−3.29850e20			−0.262293
$222$	−2.76979e20	−	1.22847e20i	−0.211481	−	0.0937965i
$223$			2.29245e21i			1.68096i	0.541846	+	0.840478i	$0.317726\pi$
$223$			2.29245e21i			1.68096i	−0.541846	+	0.840478i	$0.682274\pi$
$224$	−3.28192e20	+	5.77911e20i	−0.231151	+	0.407032i
$225$	−7.65425e20			−0.517917
$226$	5.04538e20	−	1.13757e21i	0.328033	−	0.739607i
$227$		−	1.55986e20i		−	0.0974660i	−0.998812	−	0.0487330i	$-0.984482\pi$
$227$		−	1.55986e20i		−	0.0974660i	0.998812	−	0.0487330i	$-0.0155183\pi$
$228$	−2.72511e20	−	3.00926e20i	−0.163670	−	0.180736i
$229$	3.87226e20			0.223586			0.111793	−	0.993731i	$-0.464341\pi$
$229$	3.87226e20			0.223586			0.111793	+	0.993731i	$0.464341\pi$
$230$	−2.17567e21	−	9.64961e20i	−1.20793	−	0.535747i
$231$		−	2.29372e20i		−	0.122471i
$232$	1.47096e20	−	4.84902e19i	0.0755455	−	0.0249036i
$233$	1.02273e21			0.505309			0.252655	−	0.967557i	$-0.418696\pi$
$233$	1.02273e21			0.505309			0.252655	+	0.967557i	$0.418696\pi$
$234$	−1.58913e20	+	3.58297e20i	−0.0755470	+	0.170334i
$235$			1.69897e21i			0.777275i
$236$	2.62890e21	−	2.38067e21i	1.15762	−	1.04831i
$237$	−1.01627e20			−0.0430799
$238$	−1.41084e21	−	6.25742e20i	−0.575820	−	0.255389i
$239$		−	1.60818e21i		−	0.632054i	−0.948750	−	0.316027i	$-0.897651\pi$
$239$		−	1.60818e21i		−	0.632054i	0.948750	−	0.316027i	$-0.102349\pi$
$240$	3.73234e20	+	3.70799e19i	0.141280	+	0.0140358i
$241$	4.24764e21			1.54880			0.774398	−	0.632699i	$-0.218053\pi$
$241$	4.24764e21			1.54880			0.774398	+	0.632699i	$0.218053\pi$
$242$	6.42046e20	−	1.44760e21i	0.225542	−	0.508524i
$243$			1.75100e21i			0.592693i
$244$	−3.39093e20	−	3.74450e20i	−0.110614	−	0.122148i
$245$	−1.68128e21			−0.528622
$246$	6.59950e20	+	2.92703e20i	0.200030	+	0.0887179i
$247$		−	7.75415e20i		−	0.226601i
$248$	1.23790e21	+	3.75519e21i	0.348835	+	1.05820i
$249$	−6.50224e20			−0.176713
$250$	−1.61416e21	+	3.63941e21i	−0.423143	+	0.954049i
$251$		−	3.54195e21i		−	0.895735i	−0.894100	−	0.447867i	$-0.852184\pi$
$251$		−	3.54195e21i		−	0.895735i	0.894100	−	0.447867i	$-0.147816\pi$
$252$	−1.35942e21	+	1.23105e21i	−0.331702	+	0.300381i
$253$	−1.03423e22			−2.43518
$254$	2.20551e21	+	9.78194e20i	0.501193	+	0.222291i
$255$			8.71020e20i			0.191059i
$256$	−4.63006e21	−	9.29142e20i	−0.980453	−	0.196753i
$257$	4.05940e21			0.829973			0.414986	−	0.909828i	$-0.363786\pi$
$257$	4.05940e21			0.829973			0.414986	+	0.909828i	$0.363786\pi$
$258$	−9.95485e19	+	2.24449e20i	−0.0196543	+	0.0443140i
$259$		−	2.70789e21i		−	0.516337i
$260$	4.80868e20	+	5.31008e20i	0.0885657	+	0.0978005i
$261$	4.27404e20			0.0760456
$262$	7.28812e21	+	3.23245e21i	1.25286	+	0.555674i
$263$			9.34762e20i			0.155274i	0.996982	+	0.0776371i	$0.0247375\pi$
$263$			9.34762e20i			0.155274i	−0.996982	+	0.0776371i	$0.975262\pi$
$264$	1.54789e21	−	5.10262e20i	0.248488	−	0.0819140i
$265$	1.19237e21			0.185011
$266$	1.47100e21	−	3.31663e21i	0.220637	−	0.497465i
$267$		−	7.28863e20i		−	0.105693i
$268$	−6.37564e21	+	5.77362e21i	−0.893944	+	0.809534i
$269$	7.70204e21			1.04432			0.522162	−	0.852846i	$-0.325126\pi$
$269$	7.70204e21			1.04432			0.522162	+	0.852846i	$0.325126\pi$
$270$	1.93581e21	+	8.58577e20i	0.253857	+	0.112591i
$271$		−	7.39650e21i		−	0.938216i	−0.883141	−	0.469108i	$-0.844576\pi$
$271$		−	7.39650e21i		−	0.938216i	0.883141	−	0.469108i	$-0.155424\pi$
$272$	1.08417e21	−	1.09129e22i	0.133039	−	1.33913i
$273$	1.61169e20			0.0191346
$274$	3.31373e21	−	7.47138e21i	0.380682	−	0.858313i
$275$			6.07906e21i			0.675838i
$276$	−2.55392e21	−	2.82022e21i	−0.274806	−	0.303460i
$277$	−9.35787e21			−0.974673			−0.487337	−	0.873214i	$-0.662031\pi$
$277$	−9.35787e21			−0.974673			−0.487337	+	0.873214i	$0.662031\pi$
$278$	−9.13692e21	−	4.05244e21i	−0.921291	−	0.408614i
$279$			1.09111e22i			1.06520i
$280$	1.04943e21	+	3.18348e21i	0.0992047	+	0.300940i
$281$	8.27367e21			0.757428			0.378714	−	0.925514i	$-0.376366\pi$
$281$	8.27367e21			0.757428			0.378714	+	0.925514i	$0.376366\pi$
$282$	−1.10114e21	+	2.48272e21i	−0.0976343	+	0.220134i
$283$			9.59464e21i			0.824045i	0.911174	+	0.412022i	$0.135177\pi$
$283$			9.59464e21i			0.824045i	−0.911174	+	0.412022i	$0.864823\pi$
$284$	−2.05343e21	+	1.85954e21i	−0.170850	+	0.154717i
$285$	−2.04760e21			−0.165060
$286$	2.84562e21	+	1.26210e21i	0.222271	+	0.0985824i
$287$			6.45201e21i			0.488380i
$288$	−1.13318e22	−	6.43525e21i	−0.831315	−	0.472099i
$289$	1.14046e22			0.810957
$290$	3.16713e20	−	7.14085e20i	0.0218315	−	0.0492230i
$291$			3.51207e20i			0.0234707i
$292$	9.27745e21	+	1.02448e22i	0.601150	+	0.663832i
$293$	−2.31656e22			−1.45558			−0.727789	−	0.685801i	$-0.759452\pi$
$293$	−2.31656e22			−1.45558			−0.727789	+	0.685801i	$0.759452\pi$
$294$	−2.45687e21	−	1.08968e21i	−0.149712	−	0.0664007i
$295$		−	1.78880e22i		−	1.05721i
$296$	1.82739e22	−	6.02398e21i	1.04762	−	0.345349i
$297$	9.20207e21			0.511773
$298$	−1.19117e22	+	2.68570e22i	−0.642729	+	1.44914i
$299$		−	7.26704e21i		−	0.380467i
$300$	−1.65769e21	+	1.50116e21i	−0.0842194	+	0.0762670i
$301$	−2.19433e21			−0.108194
$302$	−2.31319e22	−	1.02595e22i	−1.10700	−	0.490981i
$303$		−	3.82549e21i		−	0.177706i
$304$	2.56543e22	+	2.54869e21i	1.15690	+	0.114936i
$305$	−2.54789e21			−0.111553
$306$	1.22697e22	−	2.76641e22i	0.521602	−	1.17604i
$307$		−	4.28819e22i		−	1.77023i	−0.465376	−	0.885113i	$-0.654081\pi$
$307$		−	4.28819e22i		−	1.77023i	0.465376	−	0.885113i	$-0.345919\pi$
$308$	9.77712e21	+	1.07966e22i	0.391971	+	0.432843i
$309$	5.84214e21			0.227481
$310$	1.82298e22	+	8.08532e21i	0.689486	+	0.305803i
$311$			1.12377e22i			0.412891i	0.978458	+	0.206446i	$0.0661896\pi$
$311$			1.12377e22i			0.412891i	−0.978458	+	0.206446i	$0.933810\pi$
$312$	3.58538e20	+	1.08763e21i	0.0127980	+	0.0388231i
$313$	−7.11821e21			−0.246872			−0.123436	−	0.992353i	$-0.539391\pi$
$313$	−7.11821e21			−0.246872			−0.123436	+	0.992353i	$0.539391\pi$
$314$	−1.88862e22	+	4.25823e22i	−0.636471	+	1.43503i
$315$			9.24995e21i			0.302931i
$316$	4.78361e21	−	4.33191e21i	0.152255	−	0.137878i
$317$	1.35840e21			0.0420237			0.0210119	−	0.999779i	$-0.493311\pi$
$317$	1.35840e21			0.0420237			0.0210119	+	0.999779i	$0.493311\pi$
$318$	1.74242e21	+	7.72806e20i	0.0523974	+	0.0232395i
$319$		−	3.39447e21i		−	0.0992330i
$320$	−1.91487e22	+	1.41639e22i	−0.544239	+	0.402563i
$321$	−1.76620e21			−0.0488083
$322$	1.37860e22	−	3.10828e22i	0.370454	−	0.835252i
$323$			5.98696e22i			1.56453i
$324$	−2.29770e22	−	2.53728e22i	−0.583966	−	0.644857i
$325$	−4.27148e21			−0.105591
$326$	−4.23861e22	−	1.87992e22i	−1.01921	−	0.452045i
$327$			1.30576e22i			0.305446i
$328$	−4.35406e22	+	1.43531e22i	−0.990899	+	0.326650i
$329$	−2.42724e22			−0.537464
$330$	3.33277e21	−	7.51431e21i	0.0718092	−	0.161906i
$331$		−	7.25887e21i		−	0.152201i	−0.997100	−	0.0761004i	$-0.975753\pi$
$331$		−	7.25887e21i		−	0.152201i	0.997100	−	0.0761004i	$-0.0242469\pi$
$332$	3.06062e22	−	2.77162e22i	0.624548	−	0.565575i
$333$	5.30968e22			1.05456
$334$	4.55343e22	+	2.01955e22i	0.880279	+	0.390424i
$335$			4.33821e22i			0.816407i
$336$	−5.29743e20	+	5.33221e21i	−0.00970536	+	0.0976909i
$337$	−1.00042e22			−0.178448			−0.0892240	−	0.996012i	$-0.528439\pi$
$337$	−1.00042e22			−0.178448			−0.0892240	+	0.996012i	$0.528439\pi$
$338$	2.24570e22	−	5.06332e22i	0.390033	−	0.879397i
$339$		−	1.00335e22i		−	0.169690i
$340$	−3.71277e22	−	4.09990e22i	−0.611488	−	0.675248i
$341$	8.66569e22			1.39000
$342$	6.50330e22	+	2.88437e22i	1.01601	+	0.450625i
$343$		−	5.47788e22i		−	0.833615i
$344$	−4.88152e21	−	1.48082e22i	−0.0723650	−	0.219521i
$345$	−1.91898e22			−0.277139
$346$	−1.08072e22	+	2.43667e22i	−0.152065	+	0.342857i
$347$		−	3.29167e22i		−	0.451285i	−0.974210	−	0.225642i	$-0.927552\pi$
$347$		−	3.29167e22i		−	0.451285i	0.974210	−	0.225642i	$-0.0724480\pi$
$348$	9.25633e20	−	8.38230e20i	0.0123659	−	0.0111983i
$349$	−3.95894e22			−0.515407			−0.257703	−	0.966224i	$-0.582966\pi$
$349$	−3.95894e22			−0.515407			−0.257703	+	0.966224i	$0.582966\pi$
$350$	−1.82701e22	−	8.10321e21i	−0.231808	−	0.102812i
$351$			6.46588e21i			0.0799582i
$352$	−5.11092e22	+	8.99978e22i	−0.616049	+	1.08480i
$353$	−8.55865e22			−1.00562			−0.502809	−	0.864398i	$-0.667700\pi$
$353$	−8.55865e22			−1.00562			−0.502809	+	0.864398i	$0.667700\pi$
$354$	1.15937e22	−	2.61399e22i	0.132798	−	0.299416i
$355$			1.39723e22i			0.156031i
$356$	3.10682e22	+	3.43077e22i	0.338272	+	0.373544i
$357$	−1.24439e22			−0.132112
$358$	6.18735e22	+	2.74423e22i	0.640556	+	0.284102i
$359$		−	9.57626e22i		−	0.966820i	−0.875394	−	0.483410i	$-0.839398\pi$
$359$		−	9.57626e22i		−	0.966820i	0.875394	−	0.483410i	$-0.160602\pi$
$360$	−6.24221e22	+	2.05775e22i	−0.614633	+	0.202614i
$361$	−3.66149e22			−0.351636
$362$	−6.83334e22	+	1.54069e23i	−0.640112	+	1.44324i
$363$		−	1.27681e22i		−	0.116672i
$364$	−7.58627e21	+	6.86993e21i	−0.0676263	+	0.0612407i
$365$	6.97093e22			0.606254
$366$	−3.72326e21	−	1.65135e21i	−0.0315932	−	0.0140123i
$367$			3.89940e22i			0.322852i	0.986885	+	0.161426i	$0.0516093\pi$
$367$			3.89940e22i			0.322852i	−0.986885	+	0.161426i	$0.948391\pi$
$368$	2.40427e23	+	2.38858e22i	1.94246	+	0.192979i
$369$	−1.26512e23			−0.997458
$370$	3.93456e22	−	8.87114e22i	0.302747	−	0.682596i
$371$			1.70348e22i			0.127930i
$372$	2.13991e22	+	2.36303e22i	0.156859	+	0.173214i
$373$	1.63263e23			1.16818			0.584089	−	0.811689i	$-0.301452\pi$
$373$	1.63263e23			1.16818			0.584089	+	0.811689i	$0.301452\pi$
$374$	−2.19710e23	−	9.74465e22i	−1.53464	−	0.680646i
$375$			3.21001e22i			0.218890i
$376$	−5.39964e22	−	1.63799e23i	−0.359479	−	1.09049i
$377$	2.38514e21			0.0155039
$378$	−1.22661e22	+	2.76560e22i	−0.0778538	+	0.175535i
$379$			6.50655e22i			0.403272i	0.979461	+	0.201636i	$0.0646258\pi$
$379$			6.50655e22i			0.403272i	−0.979461	+	0.201636i	$0.935374\pi$
$380$	9.63810e22	−	8.72803e22i	0.583363	−	0.528279i
$381$	1.94529e22			0.114990
$382$	−6.09110e22	−	2.70154e22i	−0.351662	−	0.155970i
$383$		−	1.65551e23i		−	0.933559i	−0.884374	−	0.466779i	$-0.845414\pi$
$383$		−	1.65551e23i		−	0.933559i	0.884374	−	0.466779i	$-0.154586\pi$
$384$	−3.71622e22	+	8.28715e21i	−0.204701	+	0.0456483i
$385$	7.34637e22			0.395300
$386$	3.46275e22	−	7.80737e22i	0.182027	−	0.410411i
$387$		−	4.30268e22i		−	0.220974i
$388$	−1.49704e22	−	1.65314e22i	−0.0751187	−	0.0829514i
$389$	5.13874e22			0.251948			0.125974	−	0.992034i	$-0.459794\pi$
$389$	5.13874e22			0.251948			0.125974	+	0.992034i	$0.459794\pi$
$390$	5.27996e21	+	2.34179e21i	0.0252959	+	0.0112193i
$391$			5.61087e23i			2.62687i
$392$	1.62093e23	−	5.34341e22i	0.741636	−	0.244481i
$393$	6.42823e22			0.287447
$394$	−2.05685e22	+	4.63752e22i	−0.0898951	+	0.202684i
$395$		−	3.25493e22i		−	0.139049i
$396$	−2.11701e23	+	1.91711e23i	−0.884029	+	0.800555i
$397$	−1.82624e21			−0.00745493			−0.00372747	−	0.999993i	$-0.501186\pi$
$397$	−1.82624e21			−0.00745493			−0.00372747	+	0.999993i	$0.501186\pi$
$398$	−1.21961e23	−	5.40924e22i	−0.486712	−	0.215868i
$399$		−	2.92532e22i		−	0.114134i
$400$	1.40398e22	−	1.41320e23i	0.0535576	−	0.539093i
$401$	−2.52344e23			−0.941225			−0.470612	−	0.882340i	$-0.655967\pi$
$401$	−2.52344e23			−0.941225			−0.470612	+	0.882340i	$0.655967\pi$
$402$	−2.81170e22	+	6.33947e22i	−0.102550	+	0.231216i
$403$			6.08899e22i			0.217170i
$404$	1.63063e23	+	1.80066e23i	0.568754	+	0.628058i
$405$	−1.72645e23			−0.588925
$406$	1.02018e22	+	4.52473e21i	0.0340363	+	0.0150959i
$407$		−	4.21698e23i		−	1.37611i
$408$	−2.76826e22	−	8.39758e22i	−0.0883620	−	0.268048i
$409$	−1.37476e23			−0.429256			−0.214628	−	0.976696i	$-0.568854\pi$
$409$	−1.37476e23			−0.429256			−0.214628	+	0.976696i	$0.568854\pi$
$410$	−9.37474e22	+	2.11370e23i	−0.286355	+	0.645637i
$411$		−	6.58987e22i		−	0.196925i
$412$	−2.74991e23	+	2.49025e23i	−0.803976	+	0.728060i
$413$	2.55557e23			0.731034
$414$	6.09477e23	+	2.70317e23i	1.70590	+	0.756607i
$415$		−	2.08255e23i		−	0.570378i
$416$	−6.32373e22	−	3.59121e22i	−0.169486	−	0.0962500i
$417$	−8.05890e22			−0.211374
$418$	2.29078e23	−	5.16497e23i	0.588027	−	1.32581i
$419$		−	1.48352e23i		−	0.372705i	−0.982483	−	0.186353i	$-0.940333\pi$
$419$		−	1.48352e23i		−	0.372705i	0.982483	−	0.186353i	$-0.0596667\pi$
$420$	1.81411e22	+	2.00327e22i	0.0446088	+	0.0492602i
$421$	1.15768e23			0.278645			0.139322	−	0.990247i	$-0.455508\pi$
$421$	1.15768e23			0.278645			0.139322	+	0.990247i	$0.455508\pi$
$422$	2.92357e23	+	1.29667e23i	0.688812	+	0.305504i
$423$		−	4.75937e23i		−	1.09771i
$424$	−1.14957e23	+	3.78957e22i	−0.259564	+	0.0855653i
$425$	3.29800e23			0.729038
$426$	−9.05578e21	+	2.04178e22i	−0.0195992	+	0.0441899i
$427$		−	3.64005e22i		−	0.0771360i
$428$	8.31352e22	−	7.52852e22i	0.172501	−	0.156212i
$429$	2.50988e22			0.0509962
$430$	−7.18870e22	−	3.18836e22i	−0.143032	−	0.0634382i
$431$			9.25008e23i			1.80240i	0.433407	+	0.901198i	$0.357311\pi$
$431$			9.25008e23i			1.80240i	−0.433407	+	0.901198i	$0.642689\pi$
$432$	−2.13920e23	−	2.12525e22i	−0.408224	−	0.0405561i
$433$	4.41197e22			0.0824597			0.0412298	−	0.999150i	$-0.486872\pi$
$433$	4.41197e22			0.0824597			0.0412298	+	0.999150i	$0.486872\pi$
$434$	−1.15511e23	+	2.60440e23i	−0.211454	+	0.476760i
$435$		−	6.29833e21i		−	0.0112933i
$436$	−5.56589e23	−	6.14625e23i	−0.977588	−	1.07952i
$437$	−1.31901e24			−2.26942
$438$	1.01867e23	+	4.51804e22i	0.171698	+	0.0761523i
$439$			2.99800e23i			0.495052i	0.968881	+	0.247526i	$0.0796175\pi$
$439$			2.99800e23i			0.495052i	−0.968881	+	0.247526i	$0.920382\pi$
$440$	1.63428e23	+	4.95761e23i	0.264394	+	0.802044i
$441$	4.70981e23			0.746545
$442$	6.84712e22	−	1.54380e23i	0.106343	−	0.239768i
$443$			1.46363e23i			0.222739i	0.993779	+	0.111370i	$0.0355238\pi$
$443$			1.46363e23i			0.222739i	−0.993779	+	0.111370i	$0.964476\pi$
$444$	1.14992e23	−	1.04134e23i	0.171483	−	0.155291i
$445$	2.33441e23			0.341144
$446$	−1.07294e24	−	4.75873e23i	−1.53660	−	0.681518i
$447$			2.36883e23i			0.332480i
$448$	−2.02353e23	−	2.73569e23i	−0.278361	−	0.376326i
$449$	8.91953e23			1.20261			0.601305	−	0.799019i	$-0.294648\pi$
$449$	8.91953e23			1.20261			0.601305	+	0.799019i	$0.294648\pi$
$450$	1.58889e23	−	3.58243e23i	0.209982	−	0.473440i
$451$			1.00477e24i			1.30160i
$452$	4.27684e23	+	4.72279e23i	0.543097	+	0.599726i
$453$	−2.04026e23			−0.253982
$454$	7.30064e22	+	3.23800e22i	0.0890960	+	0.0395161i
$455$			5.16196e22i			0.0617607i
$456$	1.97411e23	−	6.50766e22i	0.231573	−	0.0763381i
$457$	7.19199e23			0.827186			0.413593	−	0.910462i	$-0.364274\pi$
$457$	7.19199e23			0.827186			0.413593	+	0.910462i	$0.364274\pi$
$458$	−8.03815e22	+	1.81234e23i	−0.0906497	+	0.204386i
$459$		−	4.99229e23i		−	0.552059i
$460$	9.03264e23	−	8.17974e23i	0.979477	−	0.886990i
$461$	−7.57360e23			−0.805367			−0.402684	−	0.915339i	$-0.631922\pi$
$461$	−7.57360e23			−0.805367			−0.402684	+	0.915339i	$0.631922\pi$
$462$	1.07353e23	+	4.76137e22i	0.111954	+	0.0496540i
$463$		−	1.66200e24i		−	1.69982i	−0.526930	−	0.849909i	$-0.676657\pi$
$463$		−	1.66200e24i		−	1.69982i	0.526930	−	0.849909i	$-0.323343\pi$
$464$	−7.83965e21	+	7.89113e22i	−0.00786384	+	0.0791548i
$465$	1.60789e23			0.158190
$466$	−2.12301e23	+	4.78669e23i	−0.204870	+	0.461915i
$467$		−	1.16306e24i		−	1.10091i	−0.834866	−	0.550454i	$-0.814455\pi$
$467$		−	1.16306e24i		−	1.10091i	0.834866	−	0.550454i	$-0.185545\pi$
$468$	−1.34707e23	−	1.48753e23i	−0.125077	−	0.138119i
$469$	−6.19779e23			−0.564523
$470$	−7.95171e23	−	3.52677e23i	−0.710525	−	0.315134i
$471$			3.75582e23i			0.329243i
$472$	5.68513e23	+	1.72460e24i	0.488948	+	1.48323i
$473$	−3.41722e23			−0.288352
$474$	2.10960e22	−	4.75647e22i	0.0174661	−	0.0393804i
$475$			7.75298e23i			0.629834i
$476$	5.85734e23	−	5.30426e23i	0.466915	−	0.422827i
$477$	−3.34022e23			−0.261282
$478$	7.52680e23	+	3.33831e23i	0.577775	+	0.256257i
$479$		−	1.75601e23i		−	0.132284i	−0.997810	−	0.0661419i	$-0.978931\pi$
$479$		−	1.75601e23i		−	0.132284i	0.997810	−	0.0661419i	$-0.0210690\pi$
$480$	−9.48314e22	+	1.66988e23i	−0.0701102	+	0.123456i
$481$	2.96308e23			0.215000
$482$	−8.81737e23	+	1.98803e24i	−0.627936	+	1.41579i
$483$		−	2.74155e23i		−	0.191634i
$484$	5.44246e23	+	6.00995e23i	0.373411	+	0.412347i
$485$	−1.12485e23			−0.0757565
$486$	−8.19523e23	−	3.63478e23i	−0.541795	−	0.240299i
$487$		−	1.08519e24i		−	0.704278i	−0.935948	−	0.352139i	$-0.885454\pi$
$487$		−	1.08519e24i		−	0.704278i	0.935948	−	0.352139i	$-0.114546\pi$
$488$	2.45644e23	−	8.09767e22i	0.156505	−	0.0515919i
$489$	−3.73852e23			−0.233841
$490$	3.49004e23	−	7.86891e23i	0.214322	−	0.483226i
$491$			1.46351e24i			0.882395i	0.897410	+	0.441197i	$0.145446\pi$
$491$			1.46351e24i			0.882395i	−0.897410	+	0.441197i	$0.854554\pi$
$492$	−2.73988e23	+	2.48117e23i	−0.162198	+	0.146883i
$493$	−1.84156e23			−0.107044
$494$	3.62919e23	+	1.60963e23i	0.207141	+	0.0918720i
$495$			1.44049e24i			0.807352i
$496$	−2.01451e24	−	2.00137e23i	−1.10875	−	0.110152i
$497$	−1.99615e23			−0.107891
$498$	1.34975e23	−	3.04325e23i	0.0716458	−	0.161538i
$499$		−	2.30021e24i		−	1.19912i	−0.800329	−	0.599561i	$-0.795342\pi$
$499$		−	2.30021e24i		−	1.19912i	0.800329	−	0.599561i	$-0.204658\pi$
$500$	−1.36829e24	−	1.51096e24i	−0.700562	−	0.773610i
$501$	4.01619e23			0.201964
$502$	1.65775e24	+	7.35249e23i	0.818813	+	0.363162i
$503$			2.20636e24i			1.07045i	0.844710	+	0.535224i	$0.179773\pi$
$503$			2.20636e24i			1.07045i	−0.844710	+	0.535224i	$0.820227\pi$
$504$	−2.93980e23	−	8.91795e23i	−0.140102	−	0.425001i
$505$	1.22523e24			0.573583
$506$	2.14688e24	−	4.84051e24i	0.987308	−	2.22606i
$507$		−	4.46592e23i		−	0.201762i
$508$	−9.15651e23	+	8.29191e23i	−0.406403	+	0.368028i
$509$	2.37760e24			1.03676			0.518382	−	0.855149i	$-0.326535\pi$
$509$	2.37760e24			1.03676			0.518382	+	0.855149i	$0.326535\pi$
$510$	−4.07665e23	−	1.80809e23i	−0.174651	−	0.0774618i
$511$			9.95904e23i			0.419208i
$512$	1.39599e24	−	1.97414e24i	0.577367	−	0.816485i
$513$	1.17359e24			0.476937
$514$	−8.42662e23	+	1.89993e24i	−0.336500	+	0.758698i
$515$			1.87113e24i			0.734242i
$516$	−8.43848e22	−	9.31836e22i	−0.0325400	−	0.0359329i
$517$	−3.77992e24			−1.43241
$518$	1.26738e24	+	5.62112e23i	0.471996	+	0.209341i
$519$			2.14918e23i			0.0786624i
$520$	−3.48348e23	+	1.14833e23i	−0.125309	+	0.0413083i
$521$	4.75233e24			1.68023			0.840113	−	0.542412i	$-0.182489\pi$
$521$	4.75233e24			1.68023			0.840113	+	0.542412i	$0.182489\pi$
$522$	−8.87217e22	+	2.00038e23i	−0.0308315	+	0.0695151i
$523$		−	7.14021e23i		−	0.243891i	−0.992537	−	0.121945i	$-0.961087\pi$
$523$		−	7.14021e23i		−	0.243891i	0.992537	−	0.121945i	$-0.0389133\pi$
$524$	−3.02578e24	+	2.74007e24i	−1.01591	+	0.919983i
$525$	−1.61145e23			−0.0531842
$526$	−4.37498e23	−	1.94040e23i	−0.141940	−	0.0629536i
$527$		−	4.70129e24i		−	1.49941i
$528$	−8.24966e22	+	8.30383e23i	−0.0258661	+	0.260359i
$529$	−9.11736e24			−2.81040
$530$	−2.47516e23	+	5.58067e23i	−0.0750101	+	0.169123i
$531$			5.01101e24i			1.49305i
$532$	1.24693e24	+	1.37695e24i	0.365290	+	0.403379i
$533$	−7.06004e23			−0.203358
$534$	3.41131e23	+	1.51299e23i	0.0966161	+	0.0428515i
$535$		−	5.65681e23i		−	0.157539i
$536$	−1.37876e24	−	4.18250e24i	−0.377578	−	1.14539i
$537$	5.45733e23			0.146964
$538$	−1.59881e24	+	3.60480e24i	−0.423406	+	0.954641i
$539$		−	3.74056e24i		−	0.974178i
$540$	−8.03682e23	+	7.27795e23i	−0.205845	+	0.186408i
$541$	6.25922e24			1.57669			0.788343	−	0.615237i	$-0.210940\pi$
$541$	6.25922e24			1.57669			0.788343	+	0.615237i	$0.210940\pi$
$542$	3.46179e24	+	1.53539e24i	0.857645	+	0.380386i
$543$			1.35892e24i			0.331126i
$544$	4.88254e24	+	2.77276e24i	1.17019	+	0.664543i
$545$	−4.18212e24			−0.985889
$546$	−3.34560e22	+	7.54323e22i	−0.00775783	+	0.0174914i
$547$		−	7.18635e24i		−	1.63916i	−0.572962	−	0.819582i	$-0.694206\pi$
$547$		−	7.18635e24i		−	1.63916i	0.572962	−	0.819582i	$-0.305794\pi$
$548$	2.80897e24	+	3.10186e24i	0.630263	+	0.695981i
$549$	7.13748e23			0.157541
$550$	−2.84519e24	−	1.26191e24i	−0.617799	−	0.274008i
$551$		−	4.32916e23i		−	0.0924783i
$552$	1.85010e24	−	6.09886e23i	0.388816	−	0.128173i
$553$	4.65017e23			0.0961485
$554$	1.94253e24	−	4.37978e24i	0.395167	−	0.890972i
$555$		−	7.82448e23i		−	0.156610i
$556$	3.79333e24	−	3.43515e24i	0.747047	−	0.676507i
$557$	2.99747e24			0.580842			0.290421	−	0.956899i	$-0.406205\pi$
$557$	2.99747e24			0.580842			0.290421	+	0.956899i	$0.406205\pi$
$558$	−5.10675e24	−	2.26496e24i	−0.973726	−	0.431870i
$559$		−	2.40112e23i		−	0.0450514i
$560$	−1.70781e24	−	1.69667e23i	−0.315317	−	0.0313260i
$561$	−1.93787e24			−0.352095
$562$	−1.71747e24	+	3.87234e24i	−0.307088	+	0.692383i
$563$			7.00602e24i			1.23281i	0.787430	+	0.616404i	$0.211411\pi$
$563$			7.00602e24i			1.23281i	−0.787430	+	0.616404i	$0.788589\pi$
$564$	−9.33413e23	−	1.03074e24i	−0.161645	−	0.178500i
$565$	3.21355e24			0.547708
$566$	−4.49059e24	−	1.99168e24i	−0.753279	−	0.334097i
$567$		−	2.46650e24i		−	0.407225i
$568$	−4.44064e23	−	1.34708e24i	−0.0721624	−	0.218906i
$569$	−1.53844e24			−0.246077			−0.123039	−	0.992402i	$-0.539264\pi$
$569$	−1.53844e24			−0.246077			−0.123039	+	0.992402i	$0.539264\pi$
$570$	4.25047e23	−	9.58343e23i	0.0669212	−	0.150885i
$571$			7.86222e24i			1.21848i	0.792984	+	0.609242i	$0.208526\pi$
$571$			7.86222e24i			1.21848i	−0.792984	+	0.609242i	$0.791474\pi$
$572$	−1.18140e24	+	1.06985e24i	−0.180233	+	0.163215i
$573$	−5.37244e23			−0.0806826
$574$	−3.01974e24	−	1.33933e24i	−0.446440	−	0.198006i
$575$			7.26594e24i			1.05750i
$576$	5.36418e24	−	3.96778e24i	0.768601	−	0.568519i
$577$	−2.65233e24			−0.374149			−0.187075	−	0.982346i	$-0.559901\pi$
$577$	−2.65233e24			−0.374149			−0.187075	+	0.982346i	$0.559901\pi$
$578$	−2.36739e24	+	5.33769e24i	−0.328790	+	0.741315i
$579$		−	6.88622e23i		−	0.0941616i
$580$	2.68470e23	+	2.96463e23i	0.0361446	+	0.0399134i
$581$	2.97524e24			0.394400
$582$	−1.64376e23	−	7.29046e22i	−0.0214552	−	0.00951586i
$583$			2.65283e24i			0.340951i
$584$	−6.72073e24	+	2.21549e24i	−0.850552	+	0.280385i
$585$	−1.01217e24			−0.126139
$586$	4.80879e24	−	1.08422e25i	0.590143	−	1.33058i
$587$		−	1.02050e23i		−	0.0123330i	−0.999981	−	0.00616651i	$-0.998037\pi$
$587$		−	1.02050e23i		−	0.0123330i	0.999981	−	0.00616651i	$-0.00196287\pi$
$588$	1.02001e24	−	9.23694e23i	0.121397	−	0.109934i
$589$	1.10519e25			1.29538
$590$	8.37213e24	+	3.71324e24i	0.966425	+	0.428632i
$591$			4.09036e23i			0.0465022i
$592$	−9.73927e23	+	9.80322e24i	−0.109051	+	1.09767i
$593$	−1.41015e25			−1.55515			−0.777576	−	0.628789i	$-0.783551\pi$
$593$	−1.41015e25			−1.55515			−0.777576	+	0.628789i	$0.783551\pi$
$594$	−1.91019e24	+	4.30686e24i	−0.207491	+	0.467824i
$595$		−	3.98554e24i		−	0.426417i
$596$	−1.00973e25	−	1.11501e25i	−1.06411	−	1.17507i
$597$	−1.07571e24			−0.111667
$598$	3.40121e24	+	1.50851e24i	0.347794	+	0.154255i
$599$		−	7.49001e24i		−	0.754468i	−0.926118	−	0.377234i	$-0.876875\pi$
$599$		−	7.49001e24i		−	0.754468i	0.926118	−	0.377234i	$-0.123125\pi$
$600$	−3.58483e23	−	1.08747e24i	−0.0355720	−	0.107908i
$601$	6.10479e24			0.596761			0.298381	−	0.954447i	$-0.403553\pi$
$601$	6.10479e24			0.596761			0.298381	+	0.954447i	$0.403553\pi$
$602$	4.55506e23	−	1.02702e24i	0.0438657	−	0.0989029i
$603$		−	1.21527e25i		−	1.15297i
$604$	9.60355e24	−	8.69674e24i	0.897634	−	0.812875i
$605$	4.08938e24			0.376582
$606$	1.79045e24	+	7.94105e23i	0.162446	+	0.0720484i
$607$		−	9.20261e24i		−	0.822646i	−0.911490	−	0.411323i	$-0.865067\pi$
$607$		−	9.20261e24i		−	0.822646i	0.911490	−	0.411323i	$-0.134933\pi$
$608$	−6.51825e24	+	1.14779e25i	−0.574115	+	1.01095i
$609$	8.99813e22			0.00780902
$610$	5.28898e23	−	1.19249e24i	0.0452276	−	0.101974i
$611$		−	2.65598e24i		−	0.223797i
$612$	1.04007e25	+	1.14852e25i	0.863573	+	0.953618i
$613$	−1.56120e25			−1.27736			−0.638681	−	0.769471i	$-0.720520\pi$
$613$	−1.56120e25			−1.27736			−0.638681	+	0.769471i	$0.720520\pi$
$614$	2.00701e25	+	8.90154e24i	1.61821	+	0.717712i
$615$			1.86431e24i			0.148130i
$616$	−7.08270e24	+	2.33481e24i	−0.554591	+	0.182821i
$617$	2.44611e24			0.188759			0.0943797	−	0.995536i	$-0.469913\pi$
$617$	2.44611e24			0.188759			0.0943797	+	0.995536i	$0.469913\pi$
$618$	−1.21273e24	+	2.73431e24i	−0.0922290	+	0.207946i
$619$			8.45665e24i			0.633844i	0.948452	+	0.316922i	$0.102649\pi$
$619$			8.45665e24i			0.633844i	−0.948452	+	0.316922i	$0.897351\pi$
$620$	−7.56837e24	+	6.85373e24i	−0.559084	+	0.506293i
$621$	1.09987e25			0.800786
$622$	−5.25962e24	−	2.33276e24i	−0.377434	−	0.167401i
$623$			3.33507e24i			0.235892i
$624$	−5.83472e23	−	5.79666e22i	−0.0406779	−	0.00404126i
$625$	−2.39763e24			−0.164764
$626$	1.47762e24	−	3.33155e24i	0.100091	−	0.225672i
$627$		−	4.55558e24i		−	0.304183i
$628$	−1.60094e25	−	1.76787e25i	−1.05375	−	1.16363i
$629$	−2.28779e25			−1.48443
$630$	−4.32927e24	−	1.92013e24i	−0.276917	−	0.122819i
$631$			1.67996e25i			1.05934i	0.848204	+	0.529669i	$0.177684\pi$
$631$			1.67996e25i			1.05934i	−0.848204	+	0.529669i	$0.822316\pi$
$632$	1.03448e24	+	3.13811e24i	0.0643084	+	0.195081i
$633$	2.57863e24			0.158036
$634$	−2.81981e23	+	6.35775e23i	−0.0170379	+	0.0384149i
$635$			6.23041e24i			0.371153i
$636$	−7.23395e23	+	6.55088e23i	−0.0424875	+	0.0384756i
$637$	2.62832e24			0.152203
$638$	1.58872e24	+	7.04634e23i	0.0907112	+	0.0402325i
$639$		−	3.91409e24i		−	0.220355i
$640$	−2.65422e24	−	1.19024e25i	−0.147339	−	0.660715i
$641$	6.60106e24			0.361319			0.180660	−	0.983546i	$-0.442177\pi$
$641$	6.60106e24			0.361319			0.180660	+	0.983546i	$0.442177\pi$
$642$	3.66632e23	−	8.26636e23i	0.0197886	−	0.0446169i
$643$			1.53516e25i			0.817059i	0.912745	+	0.408530i	$0.133958\pi$
$643$			1.53516e25i			0.817059i	−0.912745	+	0.408530i	$0.866042\pi$
$644$	1.16860e25	+	1.29045e25i	0.613329	+	0.677281i
$645$	−6.34054e23			−0.0328162
$646$	−2.80209e25	−	1.24279e25i	−1.43017	−	0.634315i
$647$		−	1.52646e25i		−	0.768330i	−0.923264	−	0.384165i	$-0.874489\pi$
$647$		−	1.52646e25i		−	0.768330i	0.923264	−	0.384165i	$-0.125511\pi$
$648$	1.66449e25	−	5.48699e24i	0.826240	−	0.272370i
$649$	3.97978e25			1.94830
$650$	8.86686e23	−	1.99919e24i	0.0428104	−	0.0965235i
$651$			2.29712e24i			0.109384i
$652$	1.75973e25	−	1.59357e25i	0.826451	−	0.748413i
$653$	2.68162e25			1.24216			0.621082	−	0.783746i	$-0.286693\pi$
$653$	2.68162e25			1.24216			0.621082	+	0.783746i	$0.286693\pi$
$654$	−6.11138e24	−	2.71054e24i	−0.279216	−	0.123839i
$655$			2.05884e25i			0.927795i
$656$	2.32054e24	−	2.33578e25i	0.103147	−	1.03824i
$657$	−1.95278e25			−0.856182
$658$	5.03852e24	−	1.13602e25i	0.217907	−	0.491308i
$659$		−	1.16336e25i		−	0.496300i	−0.968722	−	0.248150i	$-0.920177\pi$
$659$		−	1.16336e25i		−	0.496300i	0.968722	−	0.248150i	$-0.0798227\pi$
$660$	2.82511e24	+	3.11968e24i	0.118888	+	0.131285i
$661$	−3.25671e25			−1.35197			−0.675983	−	0.736917i	$-0.736281\pi$
$661$	−3.25671e25			−1.35197			−0.675983	+	0.736917i	$0.736281\pi$
$662$	3.39738e24	+	1.50682e24i	0.139130	+	0.0617075i
$663$		−	1.36166e24i		−	0.0550105i
$664$	6.61873e24	+	2.00780e25i	0.263792	+	0.800219i
$665$	9.36925e24			0.368392
$666$	−1.10220e25	+	2.48510e25i	−0.427554	+	0.963996i
$667$		−	4.05721e24i		−	0.155273i
$668$	−1.89043e25	+	1.71192e25i	−0.713792	+	0.646393i
$669$	−9.46348e24			−0.352546
$670$	−2.03042e25	−	9.00537e24i	−0.746297	−	0.331000i
$671$		−	5.66863e24i		−	0.205578i
$672$	−2.38568e24	−	1.35481e24i	−0.0853667	−	0.0484792i
$673$	−8.08091e24			−0.285315			−0.142658	−	0.989772i	$-0.545565\pi$
$673$	−8.08091e24			−0.285315			−0.142658	+	0.989772i	$0.545565\pi$
$674$	2.07669e24	−	4.68226e24i	0.0723491	−	0.163124i
$675$		−	6.46489e24i		−	0.222243i
$676$	1.90362e25	+	2.10211e25i	0.645744	+	0.713077i
$677$	−3.47140e25			−1.16200			−0.581001	−	0.813903i	$-0.697339\pi$
$677$	−3.47140e25			−1.16200			−0.581001	+	0.813903i	$0.697339\pi$
$678$	4.69600e24	+	2.08278e24i	0.155117	+	0.0687982i
$679$		−	1.60702e24i		−	0.0523835i
$680$	2.68959e25	−	8.86624e24i	0.865179	−	0.285206i
$681$	6.43927e23			0.0204415
$682$	−1.79885e25	+	4.05582e25i	−0.563554	+	1.27063i
$683$		−	3.69511e25i		−	1.14246i	−0.820790	−	0.571231i	$-0.806466\pi$
$683$		−	3.69511e25i		−	1.14246i	0.820790	−	0.571231i	$-0.193534\pi$
$684$	−2.69995e25	+	2.44500e25i	−0.823854	+	0.746062i
$685$	2.11061e25			0.635614
$686$	2.56382e25	+	1.13711e25i	0.762027	+	0.337977i
$687$			1.59851e24i			0.0468926i
$688$	7.94401e24	+	7.89219e23i	0.230008	+	0.0228508i
$689$	−1.86402e24			−0.0532694
$690$	3.98346e24	−	8.98141e24i	0.112362	−	0.253339i
$691$			3.96605e25i			1.10422i	0.833771	+	0.552110i	$0.186177\pi$
$691$			3.96605e25i			1.10422i	−0.833771	+	0.552110i	$0.813823\pi$
$692$	−9.16101e24	−	1.01162e25i	−0.251761	−	0.278012i
$693$	−2.05796e25			−0.558261
$694$	1.54060e25	+	6.83293e24i	0.412530	+	0.182967i
$695$		−	2.58112e25i		−	0.682251i
$696$	2.00173e23	+	6.07228e23i	0.00522302	+	0.0158441i
$697$	5.45104e25			1.40406
$698$	8.21808e24	−	1.85291e25i	0.208964	−	0.471145i
$699$			4.22193e24i			0.105978i
$700$	7.58512e24	−	6.86889e24i	0.187966	−	0.170218i
$701$	−4.88001e24			−0.119388			−0.0596938	−	0.998217i	$-0.519012\pi$
$701$	−4.88001e24			−0.119388			−0.0596938	+	0.998217i	$0.519012\pi$
$702$	−3.02623e24	−	1.34220e24i	−0.0730917	−	0.0324179i
$703$		−	5.37816e25i		−	1.28244i
$704$	−3.15124e25	−	4.26027e25i	−0.741869	−	1.00296i
$705$	−7.01352e24			−0.163017
$706$	1.77663e25	−	4.00572e25i	0.407713	−	0.919259i
$707$			1.75043e25i			0.396617i
$708$	9.82765e24	+	1.08524e25i	0.219862	+	0.242787i
$709$	−7.10626e25			−1.56973			−0.784865	−	0.619667i	$-0.787268\pi$
$709$	−7.10626e25			−1.56973			−0.784865	+	0.619667i	$0.787268\pi$
$710$	−6.53945e24	−	2.90040e24i	−0.142632	−	0.0632605i
$711$			9.11813e24i			0.196372i
$712$	−2.25063e25	+	7.41920e24i	−0.478613	+	0.157775i
$713$	1.03576e26			2.17497
$714$	2.58313e24	−	5.82411e24i	0.0535627	−	0.120766i
$715$			8.03869e24i			0.164600i
$716$	−2.56877e25	+	2.32622e25i	−0.519408	+	0.470363i
$717$	6.63874e24			0.132560
$718$	4.48199e25	+	1.98787e25i	0.883794	+	0.391983i
$719$			7.52947e25i			1.46624i	0.680101	+	0.733119i	$0.261936\pi$
$719$			7.52947e25i			1.46624i	−0.680101	+	0.733119i	$0.738064\pi$
$720$	3.32686e24	−	3.34870e25i	0.0639797	−	0.643998i
$721$	−2.67320e25			−0.507708
$722$	7.60063e24	−	1.71369e25i	0.142566	−	0.321439i
$723$			1.75347e25i			0.324828i
$724$	−5.79245e25	−	6.39643e25i	−1.05978	−	1.17028i
$725$	−2.38478e24			−0.0430929
$726$	5.97586e24	+	2.65043e24i	0.106652	+	0.0473028i
$727$			6.45592e25i			1.13802i	0.822332	+	0.569008i	$0.192673\pi$
$727$			6.45592e25i			1.13802i	−0.822332	+	0.569008i	$0.807327\pi$
$728$	−1.64057e24	−	4.97669e24i	−0.0285635	−	0.0866479i
$729$	4.33605e25			0.745670
$730$	−1.44704e25	+	3.26261e25i	−0.245797	+	0.554191i
$731$			1.85390e25i			0.311050i
$732$	1.54577e24	−	1.39981e24i	0.0256180	−	0.0231990i
$733$	3.77170e25			0.617450			0.308725	−	0.951151i	$-0.400098\pi$
$733$	3.77170e25			0.617450			0.308725	+	0.951151i	$0.400098\pi$
$734$	−1.82504e25	−	8.09449e24i	−0.295127	−	0.130896i
$735$		−	6.94049e24i		−	0.110868i
$736$	−6.10878e25	+	1.07569e26i	−0.963949	+	1.69741i
$737$	−9.65178e25			−1.50453
$738$	2.62617e25	−	5.92116e25i	0.404404	−	0.911800i
$739$		−	1.11743e26i		−	1.69988i	−0.526878	−	0.849941i	$-0.676638\pi$
$739$		−	1.11743e26i		−	1.69988i	0.526878	−	0.849941i	$-0.323362\pi$
$740$	3.33523e25	+	3.68299e25i	0.501233	+	0.553497i
$741$	3.20100e24			0.0475249
$742$	−7.97284e24	−	3.53614e24i	−0.116944	−	0.0518674i
$743$			3.16522e25i			0.458675i	0.973347	+	0.229337i	$0.0736559\pi$
$743$			3.16522e25i			0.458675i	−0.973347	+	0.229337i	$0.926344\pi$
$744$	−1.55018e25	+	5.11018e24i	−0.221935	+	0.0731610i
$745$	−7.58693e25			−1.07315
$746$	−3.38907e25	+	7.64124e25i	−0.473621	+	1.06786i
$747$			5.83390e25i			0.805515i
$748$	9.12160e25	−	8.26029e25i	1.24439	−	1.12689i
$749$	8.08162e24			0.108934
$750$	−1.50239e25	−	6.66343e24i	−0.200092	−	0.0887456i
$751$		−	1.15621e26i		−	1.52152i	−0.649035	−	0.760758i	$-0.724827\pi$
$751$		−	1.15621e26i		−	1.52152i	0.649035	−	0.760758i	$-0.275173\pi$
$752$	8.78718e25	+	8.72986e24i	1.14259	+	0.113513i
$753$	1.46216e25			0.187862
$754$	−4.95114e23	+	1.11632e24i	−0.00628584	+	0.0141725i
$755$		−	6.53459e25i		−	0.819777i
$756$	−1.03977e25	−	1.14818e25i	−0.128896	−	0.142336i
$757$	5.08490e25			0.622901			0.311451	−	0.950262i	$-0.399185\pi$
$757$	5.08490e25			0.622901			0.311451	+	0.950262i	$0.399185\pi$
$758$	−3.04527e25	−	1.35065e25i	−0.368640	−	0.163501i
$759$		−	4.26940e25i		−	0.510729i
$760$	2.08429e25	+	6.32272e25i	0.246397	+	0.747449i
$761$	3.42609e24			0.0400255			0.0200127	−	0.999800i	$-0.493629\pi$
$761$	3.42609e24			0.0400255			0.0200127	+	0.999800i	$0.493629\pi$
$762$	−4.03809e24	+	9.10457e24i	−0.0466209	+	0.105115i
$763$		−	5.97480e25i		−	0.681714i
$764$	2.52881e25	−	2.29003e25i	0.285152	−	0.258227i
$765$	7.81491e25			0.870905
$766$	7.74828e25	+	3.43654e25i	0.853388	+	0.378497i
$767$			2.79641e25i			0.304398i
$768$	3.83560e24	−	1.91134e25i	0.0412650	−	0.205630i
$769$	−5.67008e25			−0.602910			−0.301455	−	0.953480i	$-0.597472\pi$
$769$	−5.67008e25			−0.602910			−0.301455	+	0.953480i	$0.597472\pi$
$770$	−1.52498e25	+	3.43833e25i	−0.160268	+	0.361353i
$771$			1.67576e25i			0.174070i
$772$	2.93529e25	+	3.24135e25i	0.301367	+	0.332790i
$773$	−2.52060e25			−0.255793			−0.127897	−	0.991788i	$-0.540823\pi$
$773$	−2.52060e25			−0.255793			−0.127897	+	0.991788i	$0.540823\pi$
$774$	2.01379e25	+	8.93163e24i	0.201997	+	0.0895905i
$775$		−	6.08806e25i		−	0.603620i
$776$	1.08448e25	−	3.57499e24i	0.106284	−	0.0350364i
$777$	1.11785e25			0.108291
$778$	−1.06671e25	+	2.40509e25i	−0.102148	+	0.230311i
$779$			1.28144e26i			1.21300i
$780$	−2.19206e24	+	1.98507e24i	−0.0205117	+	0.0185748i
$781$	−3.10859e25			−0.287544
$782$	−2.62606e26	−	1.16472e26i	−2.40129	−	1.06503i
$783$			3.60992e24i			0.0326318i
$784$	−8.63896e24	+	8.69569e25i	−0.0772000	+	0.777068i
$785$	−1.20292e26			−1.06270
$786$	−1.33439e25	+	3.00861e25i	−0.116541	+	0.262763i
$787$			3.30706e25i			0.285541i	0.989756	+	0.142771i	$0.0456012\pi$
$787$			3.30706e25i			0.285541i	−0.989756	+	0.142771i	$0.954399\pi$
$788$	−1.74354e25	−	1.92534e25i	−0.148832	−	0.164350i
$789$	−3.85879e24			−0.0325656
$790$	1.52341e25	+	6.75668e24i	0.127108	+	0.0563754i
$791$			4.59105e25i			0.378725i
$792$	−4.57814e25	−	1.38879e26i	−0.373390	−	1.13269i
$793$	3.98309e24			0.0321190
$794$	3.79096e23	−	8.54738e23i	0.00302249	−	0.00681473i
$795$			4.92223e24i			0.0388023i
$796$	5.06338e25	−	4.58528e25i	0.394660	−	0.357394i
$797$	1.97865e26			1.52491			0.762456	−	0.647040i	$-0.223993\pi$
$797$	1.97865e26			1.52491			0.762456	+	0.647040i	$0.223993\pi$
$798$	1.36914e25	+	6.07245e24i	0.104333	+	0.0462741i
$799$			2.05067e26i			1.54517i
$800$	6.32277e25	+	3.59066e25i	0.471083	+	0.267525i
$801$	−6.53946e25			−0.481780
$802$	5.23822e25	−	1.18105e26i	0.381606	−	0.860396i
$803$			1.55092e26i			1.11724i
$804$	−2.38341e25	−	2.63193e25i	−0.169783	−	0.187486i
$805$	8.78068e25			0.618537
$806$	−2.84984e25	−	1.26397e25i	−0.198520	−	0.0880483i
$807$			3.17948e25i			0.219025i
$808$	−1.18126e26	+	3.89402e25i	−0.804716	+	0.265275i
$809$	1.09597e26			0.738349			0.369175	−	0.929360i	$-0.379640\pi$
$809$	1.09597e26			0.738349			0.369175	+	0.929360i	$0.379640\pi$
$810$	3.58382e25	−	8.08035e25i	0.238771	−	0.538350i
$811$		−	2.91378e26i		−	1.91986i	−0.280241	−	0.959930i	$-0.590414\pi$
$811$		−	2.91378e26i		−	1.91986i	0.280241	−	0.959930i	$-0.409586\pi$
$812$	−4.23543e24	+	3.83550e24i	−0.0275990	+	0.0249930i
$813$	3.05335e25			0.196771
$814$	1.97368e26	+	8.75373e25i	1.25793	+	0.557922i
$815$		−	1.19738e26i		−	0.754768i
$816$	4.50497e25	+	4.47559e24i	0.280854	+	0.0279022i
$817$	−4.35818e25			−0.268724
$818$	2.85376e25	−	6.43430e25i	0.174036	−	0.392393i
$819$		−	1.44603e25i		−	0.0872215i
$820$	−7.94674e25	−	8.77535e25i	−0.474094	−	0.523528i
$821$	−1.57731e26			−0.930742			−0.465371	−	0.885116i	$-0.654079\pi$
$821$	−1.57731e26			−0.930742			−0.465371	+	0.885116i	$0.654079\pi$
$822$	3.08426e25	+	1.36794e25i	0.180014	+	0.0798402i
$823$		−	1.01658e26i		−	0.586869i	−0.955979	−	0.293435i	$-0.905202\pi$
$823$		−	1.01658e26i		−	0.586869i	0.955979	−	0.293435i	$-0.0947983\pi$
$824$	−5.94680e25	−	1.80397e26i	−0.339577	−	1.03011i
$825$	−2.50950e25			−0.141743
$826$	−5.30493e25	+	1.19609e26i	−0.296387	+	0.668255i
$827$			5.85196e25i			0.323409i	0.986839	+	0.161704i	$0.0516991\pi$
$827$			5.85196e25i			0.323409i	−0.986839	+	0.161704i	$0.948301\pi$
$828$	−2.53034e26	+	2.29141e26i	−1.38327	+	1.25265i
$829$	2.42454e26			1.31111			0.655555	−	0.755147i	$-0.272435\pi$
$829$	2.42454e26			1.31111			0.655555	+	0.755147i	$0.272435\pi$
$830$	9.74699e25	+	4.32302e25i	0.521396	+	0.231251i
$831$		−	3.86303e25i		−	0.204418i
$832$	2.99350e25	−	2.21423e25i	0.156700	−	0.115908i
$833$	−2.02932e26			−1.05086
$834$	1.67289e25	−	3.77182e25i	0.0856983	−	0.193222i
$835$			1.28631e26i			0.651881i
$836$	1.94184e26	+	2.14432e26i	0.973547	+	1.07506i
$837$	−9.21570e25			−0.457087
$838$	6.94332e25	+	3.07952e25i	0.340699	+	0.151108i
$839$		−	1.47501e26i		−	0.716042i	−0.933713	−	0.358021i	$-0.883452\pi$
$839$		−	1.47501e26i		−	0.716042i	0.933713	−	0.358021i	$-0.116548\pi$
$840$	−1.31417e25	+	4.33217e24i	−0.0631159	+	0.0208062i
$841$	−2.09126e26			−0.993673
$842$	−2.40315e25	+	5.41832e25i	−0.112972	+	0.254716i
$843$			3.41546e25i			0.158855i
$844$	−1.21376e26	+	1.09915e26i	−0.558537	+	0.505797i
$845$	1.43035e26			0.651227
$846$	2.22753e26	+	9.87962e25i	1.00344	+	0.445048i
$847$			5.84231e25i			0.260396i
$848$	6.12679e24	−	6.16702e25i	0.0270191	−	0.271965i
$849$	−3.96077e25			−0.172826
$850$	−6.84608e25	+	1.54357e26i	−0.295578	+	0.666431i
$851$		−	5.04031e26i		−	2.15323i
$852$	−7.67636e24	−	8.47678e24i	−0.0324488	−	0.0358323i
$853$	−1.85831e26			−0.777277			−0.388639	−	0.921390i	$-0.627055\pi$
$853$	−1.85831e26			−0.777277			−0.388639	+	0.921390i	$0.627055\pi$
$854$	1.70366e25	+	7.55612e24i	0.0705118	+	0.0312736i
$855$			1.83714e26i			0.752397i
$856$	1.79784e25	+	5.45378e25i	0.0728596	+	0.221021i
$857$	2.39288e26			0.959607			0.479803	−	0.877376i	$-0.340708\pi$
$857$	2.39288e26			0.959607			0.479803	+	0.877376i	$0.340708\pi$
$858$	−5.21008e24	+	1.17470e25i	−0.0206756	+	0.0466168i
$859$			3.56929e26i			1.40166i	0.713328	+	0.700831i	$0.247187\pi$
$859$			3.56929e26i			1.40166i	−0.713328	+	0.700831i	$0.752813\pi$
$860$	2.98450e25	−	2.70269e25i	0.115981	−	0.105029i
$861$	−2.66346e25			−0.102428
$862$	−4.32933e26	−	1.92016e26i	−1.64761	−	0.730755i
$863$		−	8.94525e25i		−	0.336896i	−0.985711	−	0.168448i	$-0.946125\pi$
$863$		−	8.94525e25i		−	0.336896i	0.985711	−	0.168448i	$-0.0538755\pi$
$864$	5.43530e25	−	9.57098e25i	0.202582	−	0.356724i
$865$	−6.88344e25			−0.253899
$866$	−9.15850e24	+	2.06494e25i	−0.0334321	+	0.0753784i
$867$			4.70792e25i			0.170082i
$868$	−9.79160e25	−	1.08126e26i	−0.350087	−	0.386591i
$869$	7.24168e25			0.256249
$870$	2.94782e24	+	1.30743e24i	0.0103235	+	0.00457871i
$871$		−	6.78187e25i		−	0.235064i
$872$	4.03202e26	−	1.32916e26i	1.38317	−	0.455961i
$873$	3.15108e25			0.106987
$874$	2.73804e26	−	6.17338e26i	0.920103	−	2.07453i
$875$		−	1.46881e26i		−	0.488532i
$876$	−4.22917e25	+	3.82983e25i	−0.139225	+	0.126079i
$877$	1.58456e26			0.516312			0.258156	−	0.966103i	$-0.416885\pi$
$877$	1.58456e26			0.516312			0.258156	+	0.966103i	$0.416885\pi$
$878$	−1.40316e26	−	6.22333e25i	−0.452538	−	0.200711i
$879$		−	9.56302e25i		−	0.305278i
$880$	−2.65956e26	−	2.64222e25i	−0.840362	−	0.0834880i
$881$	5.28553e26			1.65312			0.826562	−	0.562846i	$-0.190294\pi$
$881$	5.28553e26			1.65312			0.826562	+	0.562846i	$0.190294\pi$
$882$	−9.77675e25	+	2.20434e26i	−0.302676	+	0.682435i
$883$			4.69314e26i			1.43819i	0.694910	+	0.719096i	$0.255444\pi$
$883$			4.69314e26i			1.43819i	−0.694910	+	0.719096i	$0.744556\pi$
$884$	5.80413e25	+	6.40933e25i	0.176063	+	0.194421i
$885$	7.38434e25			0.221729
$886$	−6.85024e25	−	3.03824e25i	−0.203611	−	0.0903064i
$887$			5.43121e26i			1.59803i	0.601314	+	0.799013i	$0.294644\pi$
$887$			5.43121e26i			1.59803i	−0.601314	+	0.799013i	$0.705356\pi$
$888$	2.48676e25	+	7.54364e25i	0.0724299	+	0.219717i
$889$	−8.90109e25			−0.256642
$890$	−4.84584e25	+	1.09258e26i	−0.138312	+	0.311848i
$891$		−	3.84107e26i		−	1.08531i
$892$	4.45447e26	−	4.03386e26i	1.24598	−	1.12833i
$893$	−4.82075e26			−1.33491
$894$	−1.10869e26	−	4.91728e25i	−0.303928	−	0.134799i
$895$			1.74788e26i			0.474357i
$896$	1.70044e26	−	3.79196e25i	0.456866	−	0.101881i
$897$	2.99991e25			0.0797952
$898$	−1.85154e26	+	4.17462e26i	−0.487580	+	1.09933i
$899$			3.39950e25i			0.0886294i
$900$	1.34686e26	+	1.48730e26i	0.347649	+	0.383899i
$901$	1.43921e26			0.367790
$902$	−4.70263e26	−	2.08572e26i	−1.18982	−	0.527713i
$903$		−	9.05843e24i		−	0.0226915i
$904$	−3.09821e26	+	1.02133e26i	−0.768414	+	0.253308i
$905$	−4.35236e26			−1.06878
$906$	4.23524e25	−	9.54907e25i	0.102973	−	0.232171i
$907$			6.98465e25i			0.168143i	0.996460	+	0.0840715i	$0.0267924\pi$
$907$			6.98465e25i			0.168143i	−0.996460	+	0.0840715i	$0.973208\pi$
$908$	−3.03097e25	+	2.74477e25i	−0.0722453	+	0.0654235i
$909$	−3.43228e26			−0.810042
$910$	−2.41596e25	−	1.07153e25i	−0.0564569	−	0.0250400i
$911$		−	1.78736e26i		−	0.413568i	−0.978387	−	0.206784i	$-0.933700\pi$
$911$		−	1.78736e26i		−	0.413568i	0.978387	−	0.206784i	$-0.0662997\pi$
$912$	−1.05213e25	+	1.05903e26i	−0.0241054	+	0.242637i
$913$	4.63333e26			1.05113
$914$	−1.49293e26	+	3.36608e26i	−0.335370	+	0.756150i
$915$		−	1.05180e25i		−	0.0233960i
$916$	−6.81374e25	−	7.52421e25i	−0.150081	−	0.165730i
$917$	−2.94137e26			−0.641544
$918$	2.33655e26	+	1.03631e26i	0.504650	+	0.223824i
$919$		−	3.44364e26i		−	0.736510i	−0.929725	−	0.368255i	$-0.879955\pi$
$919$		−	3.44364e26i		−	0.736510i	0.929725	−	0.368255i	$-0.120045\pi$
$920$	1.95335e26	+	5.92553e26i	0.413705	+	1.25498i
$921$	1.77021e26			0.371269
$922$	1.57215e26	−	3.54468e26i	0.326524	−	0.736205i
$923$		−	2.18427e25i		−	0.0449252i
$924$	−4.45694e25	+	4.03610e25i	−0.0907798	+	0.0822080i
$925$	−2.96263e26			−0.597588
$926$	7.77868e26	+	3.45003e26i	1.55384	+	0.689166i
$927$		−	5.24165e26i		−	1.03693i
$928$	−3.53056e25	−	2.00498e25i	−0.0691690	−	0.0392807i
$929$	3.91574e26			0.759753			0.379877	−	0.925037i	$-0.375966\pi$
$929$	3.91574e26			0.759753			0.379877	+	0.925037i	$0.375966\pi$
$930$	−3.33771e25	+	7.52544e25i	−0.0641359	+	0.144606i
$931$		−	4.77056e26i		−	0.907866i
$932$	−1.79962e26	−	1.98727e26i	−0.339186	−	0.374553i
$933$	−4.63906e25			−0.0865954
$934$	5.44349e26	+	2.41432e26i	1.00637	+	0.446346i
$935$		−	6.20666e26i		−	1.13646i
$936$	9.75838e25	−	3.21685e25i	0.176968	−	0.0583376i
$937$	8.94695e26			1.60701			0.803505	−	0.595297i	$-0.202966\pi$
$937$	8.94695e26			1.60701			0.803505	+	0.595297i	$0.202966\pi$
$938$	1.28655e26	−	2.90076e26i	0.228877	−	0.516044i
$939$		−	2.93847e25i		−	0.0517763i
$940$	3.30127e26	−	2.98955e26i	0.576144	−	0.521742i
$941$	−8.27428e26			−1.43029			−0.715144	−	0.698977i	$-0.753639\pi$
$941$	−8.27428e26			−1.43029			−0.715144	+	0.698977i	$0.753639\pi$
$942$	−1.75784e26	−	7.79644e25i	−0.300969	−	0.133487i
$943$			1.20094e27i			2.03665i
$944$	−9.25178e26	−	9.19143e25i	−1.55409	−	0.154396i
$945$	−7.81264e25			−0.129990
$946$	7.09356e25	−	1.59937e26i	0.116908	−	0.263589i
$947$			1.18000e26i			0.192633i	0.995351	+	0.0963166i	$0.0307061\pi$
$947$			1.18000e26i			0.192633i	−0.995351	+	0.0963166i	$0.969294\pi$
$948$	1.78826e25	+	1.97472e25i	0.0289172	+	0.0319324i
$949$	−1.08976e26			−0.174556
$950$	−3.62864e26	−	1.60938e26i	−0.575746	−	0.255357i
$951$			5.60762e24i			0.00881362i
$952$	1.26668e26	+	3.84249e26i	0.197212	+	0.598247i
$953$	7.92961e25			0.122297			0.0611485	−	0.998129i	$-0.480524\pi$
$953$	7.92961e25			0.122297			0.0611485	+	0.998129i	$0.480524\pi$
$954$	6.93372e25	−	1.56333e26i	0.105933	−	0.238844i
$955$		−	1.72069e26i		−	0.260419i
$956$	−3.12487e26	+	2.82980e26i	−0.468501	+	0.424263i
$957$	1.40127e25			0.0208121
$958$	8.21866e25	+	3.64517e25i	0.120924	+	0.0536325i
$959$			3.01533e26i			0.439509i
$960$	−5.84702e25	−	7.90479e25i	−0.0844294	−	0.114143i
$961$	−1.68799e26			−0.241468
$962$	−6.15085e25	+	1.38682e26i	−0.0871685	+	0.196536i
$963$			1.58466e26i			0.222484i
$964$	−7.47426e26	−	8.25361e26i	−1.03962	−	1.14802i
$965$	2.20553e26			0.303925
$966$	1.28313e26	+	5.69099e25i	0.175177	+	0.0776950i
$967$			2.95296e26i			0.399410i	0.979856	+	0.199705i	$0.0639984\pi$
$967$			2.95296e26i			0.399410i	−0.979856	+	0.199705i	$0.936002\pi$
$968$	−3.94261e26	+	1.29968e26i	−0.528330	+	0.174164i
$969$	−2.47148e26			−0.328128
$970$	2.33500e25	−	5.26466e25i	0.0307144	−	0.0692508i
$971$			1.40971e27i			1.83720i	0.395185	+	0.918601i	$0.370680\pi$
$971$			1.40971e27i			1.83720i	−0.395185	+	0.918601i	$0.629320\pi$
$972$	3.40238e26	−	3.08111e26i	0.439325	−	0.397842i
$973$	3.68752e26			0.471758
$974$	5.07902e26	+	2.25266e26i	0.643798	+	0.285539i
$975$		−	1.76331e25i		−	0.0221456i
$976$	−1.30919e25	+	1.31779e26i	−0.0162913	+	0.163982i
$977$	1.73439e25			0.0213843			0.0106922	−	0.999943i	$-0.496597\pi$
$977$	1.73439e25			0.0213843			0.0106922	+	0.999943i	$0.496597\pi$
$978$	7.76052e25	−	1.74974e26i	0.0948072	−	0.213759i
$979$			5.19368e26i			0.628682i
$980$	2.95842e26	+	3.26690e26i	0.354834	+	0.391833i
$981$	1.17155e27			1.39232
$982$	−6.84969e26	−	3.03800e26i	−0.806618	−	0.357754i
$983$		−	4.98458e26i		−	0.581630i	−0.956779	−	0.290815i	$-0.906074\pi$
$983$		−	4.98458e26i		−	0.581630i	0.956779	−	0.290815i	$-0.0939263\pi$
$984$	−5.92513e25	−	1.79740e26i	−0.0685081	−	0.207821i
$985$	−1.31007e26			−0.150095
$986$	3.82276e25	−	8.61908e25i	0.0433996	−	0.0978518i
$987$		−	1.00199e26i		−	0.112722i
$988$	−1.50671e26	+	1.36444e26i	−0.167965	+	0.152105i
$989$	−4.08440e26			−0.451192
$990$	−6.74194e26	−	2.99021e26i	−0.738020	−	0.327329i
$991$		−	1.10528e27i		−	1.19898i	−0.800383	−	0.599489i	$-0.795371\pi$
$991$		−	1.10528e27i		−	1.19898i	0.800383	−	0.599489i	$-0.204629\pi$
$992$	5.11849e26	−	9.01310e26i	0.550220	−	0.968878i
$993$	2.99654e25			0.0319210
$994$	4.14367e25	−	9.34261e25i	0.0437429	−	0.0986259i
$995$		−	3.44530e26i		−	0.360429i
$996$	1.14415e26	+	1.26345e26i	0.118618	+	0.130986i
$997$	−1.05120e27			−1.08002			−0.540008	−	0.841660i	$-0.681579\pi$
$997$	−1.05120e27			−1.08002			−0.540008	+	0.841660i	$0.681579\pi$
$998$	1.07657e27	+	4.77485e26i	1.09615	+	0.486166i
$999$			4.48463e26i			0.452520i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.19.b.a.3.4	yes	8
3.2	odd	2		36.19.d.c.19.5		8
4.3	odd	2	inner	4.19.b.a.3.3	✓	8
8.3	odd	2		64.19.c.e.63.5		8
8.5	even	2		64.19.c.e.63.4		8
12.11	even	2		36.19.d.c.19.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.19.b.a.3.3	✓	8	4.3	odd	2	inner
4.19.b.a.3.4	yes	8	1.1	even	1	trivial
36.19.d.c.19.5		8	3.2	odd	2
36.19.d.c.19.6		8	12.11	even	2
64.19.c.e.63.4		8	8.5	even	2
64.19.c.e.63.5		8	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 19 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-207.583 + 468.031i) q^{2} +4128.11i q^{3} +(-175963. - 194311. i) q^{4} -1.32216e6 q^{5} +(-1.93208e6 - 856924. i) q^{6} -1.88890e7i q^{7} +(1.27470e8 - 4.20206e7i) q^{8} +3.70379e8 q^{9} +O(q^{10})\)	\(q+(-207.583 + 468.031i) q^{2} +4128.11i q^{3} +(-175963. - 194311. i) q^{4} -1.32216e6 q^{5} +(-1.93208e6 - 856924. i) q^{6} -1.88890e7i q^{7} +(1.27470e8 - 4.20206e7i) q^{8} +3.70379e8 q^{9} +(2.74457e8 - 6.18811e8i) q^{10} -2.94158e9i q^{11} +(8.02134e8 - 7.26393e8i) q^{12} +2.06691e9 q^{13} +(8.84066e9 + 3.92104e9i) q^{14} -5.45800e9i q^{15} +(-6.79368e9 + 6.83828e10i) q^{16} -1.59586e11 q^{17} +(-7.68844e10 + 1.73349e11i) q^{18} -3.75156e11i q^{19} +(2.32650e11 + 2.56909e11i) q^{20} +7.79759e10 q^{21} +(1.37675e12 + 6.10621e11i) q^{22} -3.51589e12i q^{23} +(1.73465e11 + 5.26211e11i) q^{24} -2.06660e12 q^{25} +(-4.29055e11 + 9.67380e11i) q^{26} +3.12828e12i q^{27} +(-3.67034e12 + 3.32377e12i) q^{28} +1.15396e12 q^{29} +(2.55452e12 + 1.13299e12i) q^{30} +2.94593e13i q^{31} +(-3.05951e13 - 1.73748e13i) q^{32} +1.21431e13 q^{33} +(3.31273e13 - 7.46912e13i) q^{34} +2.49743e13i q^{35} +(-6.51730e13 - 7.19686e13i) q^{36} +1.43358e14 q^{37} +(1.75585e14 + 7.78760e13i) q^{38} +8.53243e12i q^{39} +(-1.68536e14 + 5.55578e13i) q^{40} -3.41574e14 q^{41} +(-1.61865e13 + 3.64952e13i) q^{42} -1.16170e14i q^{43} +(-5.71580e14 + 5.17608e14i) q^{44} -4.89699e14 q^{45} +(1.64555e15 + 7.29839e14i) q^{46} -1.28500e15i q^{47} +(-2.82292e14 - 2.80450e13i) q^{48} +1.27162e15 q^{49} +(4.28990e14 - 9.67233e14i) q^{50} -6.58787e14i q^{51} +(-3.63700e14 - 4.01623e14i) q^{52} -9.01838e14 q^{53} +(-1.46413e15 - 6.49376e14i) q^{54} +3.88923e15i q^{55} +(-7.93728e14 - 2.40779e15i) q^{56} +1.54868e15 q^{57} +(-2.39543e14 + 5.40091e14i) q^{58} +1.35294e16i q^{59} +(-1.06055e15 + 9.60405e14i) q^{60} +1.92707e15 q^{61} +(-1.37879e16 - 6.11525e15i) q^{62} -6.99610e15i q^{63} +(1.44829e16 - 1.07128e16i) q^{64} -2.73278e15 q^{65} +(-2.52071e15 + 5.68337e15i) q^{66} -3.28116e16i q^{67} +(2.80812e16 + 3.10092e16i) q^{68} +1.45140e16 q^{69} +(-1.16887e16 - 5.18423e15i) q^{70} -1.05678e16i q^{71} +(4.72123e16 - 1.55636e16i) q^{72} -5.27239e16 q^{73} +(-2.97586e16 + 6.70960e16i) q^{74} -8.53114e15i q^{75} +(-7.28968e16 + 6.60135e16i) q^{76} -5.55636e16 q^{77} +(-3.99345e15 - 1.77119e15i) q^{78} +2.46184e16i q^{79} +(8.98231e15 - 9.04128e16i) q^{80} +1.30579e17 q^{81} +(7.09049e16 - 1.59867e17i) q^{82} +1.57512e17i q^{83} +(-1.37209e16 - 1.51515e16i) q^{84} +2.10997e17 q^{85} +(5.43710e16 + 2.41148e16i) q^{86} +4.76368e15i q^{87} +(-1.23607e17 - 3.74964e17i) q^{88} -1.76561e17 q^{89} +(1.01653e17 - 2.29195e17i) q^{90} -3.90420e16i q^{91} +(-6.83175e17 + 6.18666e17i) q^{92} -1.21611e17 q^{93} +(6.01419e17 + 2.66743e17i) q^{94} +4.96015e17i q^{95} +(7.17248e16 - 1.26300e17i) q^{96} +8.50771e16 q^{97} +(-2.63966e17 + 5.95157e17i) q^{98} -1.08950e18i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 84 q^{2} + 352016 q^{4} + 860880 q^{5} + 310944 q^{6} - 154160064 q^{8} - 729541560 q^{9}+O(q^{10}) \) 8 * q + 84 * q^2 + 352016 * q^4 + 860880 * q^5 + 310944 * q^6 - 154160064 * q^8 - 729541560 * q^9	\( 8 q + 84 q^{2} + 352016 q^{4} + 860880 q^{5} + 310944 q^{6} - 154160064 q^{8} - 729541560 q^{9} - 853591160 q^{10} - 2983758720 q^{12} - 6658778288 q^{13} - 3330240576 q^{14} + 35282993408 q^{16} + 213854181648 q^{17} + 197420552436 q^{18} - 421824543840 q^{20} - 771822339072 q^{21} - 586750684320 q^{22} - 3940602195456 q^{24} + 528925732440 q^{25} + 12314194404552 q^{26} - 20860043224320 q^{28} + 11238056568912 q^{29} + 63814514963520 q^{30} - 133632603995136 q^{32} - 21541938424320 q^{33} + 295093712425768 q^{34} - 595880470532208 q^{36} - 158886968816432 q^{37} + 830666716492320 q^{38} - 16\!\cdots\!80 q^{40}+ \cdots + 24\!\cdots\!76 q^{98}+O(q^{100}) \) 8 * q + 84 * q^2 + 352016 * q^4 + 860880 * q^5 + 310944 * q^6 - 154160064 * q^8 - 729541560 * q^9 - 853591160 * q^10 - 2983758720 * q^12 - 6658778288 * q^13 - 3330240576 * q^14 + 35282993408 * q^16 + 213854181648 * q^17 + 197420552436 * q^18 - 421824543840 * q^20 - 771822339072 * q^21 - 586750684320 * q^22 - 3940602195456 * q^24 + 528925732440 * q^25 + 12314194404552 * q^26 - 20860043224320 * q^28 + 11238056568912 * q^29 + 63814514963520 * q^30 - 133632603995136 * q^32 - 21541938424320 * q^33 + 295093712425768 * q^34 - 595880470532208 * q^36 - 158886968816432 * q^37 + 830666716492320 * q^38 - 1609388875268480 * q^40 + 451509984725136 * q^41 + 3247297173265920 * q^42 - 3429204744604800 * q^44 + 394282398204240 * q^45 + 3658225092496704 * q^46 - 6713415182530560 * q^48 - 2251201133570680 * q^49 + 6942506471898780 * q^50 - 6479715597253472 * q^52 + 1216384760086992 * q^53 + 3284600487812928 * q^54 + 7432202560564224 * q^56 + 2661563378188800 * q^57 - 17440122911455928 * q^58 + 36392091128935680 * q^60 + 184592915104336 * q^61 - 42580340982416640 * q^62 + 74097564160495616 * q^64 - 5670291051587040 * q^65 - 140809597617788160 * q^66 + 131212356714741792 * q^68 - 26839260584143872 * q^69 - 153862868594448000 * q^70 + 156072744876684864 * q^72 + 31494366486758032 * q^73 - 108949653815722872 * q^74 + 152098090223483520 * q^76 + 180811187963888640 * q^77 + 14085206442507840 * q^78 - 152292076037383680 * q^80 - 260466732987857784 * q^81 + 335145451981844968 * q^82 - 850166994683553792 * q^84 - 204660361893474400 * q^85 + 950236163482864224 * q^86 - 1369014843355476480 * q^88 + 162001265029847952 * q^89 + 1771450132254688200 * q^90 - 1193579560451823360 * q^92 + 668158876340367360 * q^93 + 1478730179820369024 * q^94 - 2028358051400441856 * q^96 - 1214976752903766512 * q^97 + 2427758859173433876 * q^98

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