LMFDB - Embedded newform 5.18.b.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,18,Mod(4,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	5.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:	$9.16110436723$
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} + 203459x^{6} + 12362849196x^{4} + 237701205446144x^{2} + 1320400799499206656 $ x^8 + 203459x^6 + 12362849196x^4 + 237701205446144*x^2 + 1320400799499206656
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{8}\cdot 5^{12}\cdot 11 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.3
Root			$-137.667i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.18.b.a.4.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-275.335i q^{2} +2990.60i q^{3} +55262.8 q^{4} +(-756669. + 436339. i) q^{5} +823415. q^{6} +2.43909e7i q^{7} -5.13044e7i q^{8} +1.20196e8 q^{9} +O(q^{10})$	\(q-275.335i q^{2} +2990.60i q^{3} +55262.8 q^{4} +(-756669. + 436339. i) q^{5} +823415. q^{6} +2.43909e7i q^{7} -5.13044e7i q^{8} +1.20196e8 q^{9} +(1.20139e8 + 2.08337e8i) q^{10} +8.41139e8 q^{11} +1.65269e8i q^{12} +4.01580e9i q^{13} +6.71566e9 q^{14} +(-1.30491e9 - 2.26289e9i) q^{15} -6.88248e9 q^{16} -8.60868e9i q^{17} -3.30943e10i q^{18} -6.64861e10 q^{19} +(-4.18157e10 + 2.41133e10i) q^{20} -7.29433e10 q^{21} -2.31595e11i q^{22} +5.12783e11i q^{23} +1.53431e11 q^{24} +(3.82157e11 - 6.60328e11i) q^{25} +1.10569e12 q^{26} +7.45665e11i q^{27} +1.34791e12i q^{28} +1.63558e11 q^{29} +(-6.23053e11 + 3.59288e11i) q^{30} -3.12692e12 q^{31} -4.82959e12i q^{32} +2.51551e12i q^{33} -2.37027e12 q^{34} +(-1.06427e13 - 1.84558e13i) q^{35} +6.64240e12 q^{36} +2.41839e12i q^{37} +1.83059e13i q^{38} -1.20096e13 q^{39} +(2.23861e13 + 3.88205e13i) q^{40} +4.43989e13 q^{41} +2.00838e13i q^{42} -7.24471e13i q^{43} +4.64837e13 q^{44} +(-9.09490e13 + 5.24464e13i) q^{45} +1.41187e14 q^{46} -5.71958e13i q^{47} -2.05827e13i q^{48} -3.62285e14 q^{49} +(-1.81811e14 - 1.05221e14i) q^{50} +2.57451e13 q^{51} +2.21925e14i q^{52} -3.35911e14i q^{53} +2.05308e14 q^{54} +(-6.36464e14 + 3.67021e14i) q^{55} +1.25136e15 q^{56} -1.98833e14i q^{57} -4.50331e13i q^{58} -2.43892e14 q^{59} +(-7.21132e13 - 1.25054e14i) q^{60} +2.41050e15 q^{61} +8.60950e14i q^{62} +2.93170e15i q^{63} -2.23185e15 q^{64} +(-1.75225e15 - 3.03863e15i) q^{65} +6.92606e14 q^{66} -2.63132e15i q^{67} -4.75740e14i q^{68} -1.53353e15 q^{69} +(-5.08153e15 + 2.93030e15i) q^{70} +4.51149e15 q^{71} -6.16661e15i q^{72} -2.61026e15i q^{73} +6.65866e14 q^{74} +(1.97477e15 + 1.14288e15i) q^{75} -3.67421e15 q^{76} +2.05161e16i q^{77} +3.30667e15i q^{78} +7.48386e15 q^{79} +(5.20776e15 - 3.00309e15i) q^{80} +1.32922e16 q^{81} -1.22245e16i q^{82} -2.07744e15i q^{83} -4.03105e15 q^{84} +(3.75630e15 + 6.51393e15i) q^{85} -1.99472e16 q^{86} +4.89135e14i q^{87} -4.31541e16i q^{88} +2.77854e15 q^{89} +(1.44403e16 + 2.50414e16i) q^{90} -9.79490e16 q^{91} +2.83378e16i q^{92} -9.35136e15i q^{93} -1.57480e16 q^{94} +(5.03080e16 - 2.90105e16i) q^{95} +1.44434e16 q^{96} -5.77968e16i q^{97} +9.97495e16i q^{98} +1.01102e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 579096 q^{4} + 379200 q^{5} + 357816 q^{6} - 234916344 q^{9}+O(q^{10}) $ 8 * q - 579096 * q^4 + 379200 * q^5 + 357816 * q^6 - 234916344 * q^9	$ 8 q - 579096 q^{4} + 379200 q^{5} + 357816 q^{6} - 234916344 q^{9} + 329570200 q^{10} + 463296576 q^{11} - 29937907992 q^{14} + 30646226400 q^{15} + 30848001568 q^{16} - 20615713280 q^{19} - 47558579400 q^{20} - 75039699024 q^{21} + 1768741136160 q^{24} - 1789249435000 q^{25} - 838901194224 q^{26} - 4079017824720 q^{29} + 2416984007400 q^{30} + 11329328658496 q^{31} - 36406243632832 q^{34} + 4019663899200 q^{35} + 59729752432728 q^{36} + 40318460422272 q^{39} - 209747532172000 q^{40} + 97217252847456 q^{41} - 116357853210912 q^{44} - 366841998003600 q^{45} + 10\!\cdots\!36 q^{46}+ \cdots - 56\!\cdots\!68 q^{99}+O(q^{100}) $ 8 * q - 579096 * q^4 + 379200 * q^5 + 357816 * q^6 - 234916344 * q^9 + 329570200 * q^10 + 463296576 * q^11 - 29937907992 * q^14 + 30646226400 * q^15 + 30848001568 * q^16 - 20615713280 * q^19 - 47558579400 * q^20 - 75039699024 * q^21 + 1768741136160 * q^24 - 1789249435000 * q^25 - 838901194224 * q^26 - 4079017824720 * q^29 + 2416984007400 * q^30 + 11329328658496 * q^31 - 36406243632832 * q^34 + 4019663899200 * q^35 + 59729752432728 * q^36 + 40318460422272 * q^39 - 209747532172000 * q^40 + 97217252847456 * q^41 - 116357853210912 * q^44 - 366841998003600 * q^45 + 1081224261700136 * q^46 - 856574357621656 * q^49 - 1283266301910000 * q^50 + 2468309514424896 * q^51 - 3408409774777680 * q^54 - 2042713226757600 * q^55 + 8363016326678880 * q^56 - 1091409512240640 * q^59 - 11479379108104800 * q^60 + 8064731010774976 * q^61 - 3616160324265856 * q^64 - 11989509557901600 * q^65 + 27318846906958752 * q^66 - 12078989597365008 * q^69 - 13190931213697800 * q^70 + 25241492058140736 * q^71 - 29902523510328912 * q^74 + 3839235716880000 * q^75 + 20767634734678560 * q^76 + 3229852337730880 * q^79 + 1263407265391200 * q^80 - 49353541005202632 * q^81 + 101439947332382688 * q^84 + 25693702369787200 * q^85 - 165112838769552744 * q^86 + 92963987535626640 * q^89 + 206315814421823400 * q^90 - 225591670236809664 * q^91 + 162612564681867848 * q^94 + 204319715505252000 * q^95 - 654303222993538944 * q^96 - 56327331239952768 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	275.335i		−	0.760512i	−0.924881	−	0.380256i	$-0.875836\pi$
$2$		−	275.335i		−	0.760512i	0.924881	−	0.380256i	$-0.124164\pi$
$3$			2990.60i			0.263164i	0.991305	+	0.131582i	$0.0420057\pi$
$3$			2990.60i			0.263164i	−0.991305	+	0.131582i	$0.957994\pi$
$4$	55262.8			0.421622
$5$	−756669.	+	436339.i	−0.866285	+	0.499550i
$5$	−756669.	+	436339.i	−0.866285	+	0.499550i
$6$	823415.			0.200140
$7$			2.43909e7i			1.59917i	0.600554	+	0.799584i	$0.294947\pi$
$7$			2.43909e7i			1.59917i	−0.600554	+	0.799584i	$0.705053\pi$
$8$		−	5.13044e7i		−	1.08116i
$9$	1.20196e8			0.930744
$10$	1.20139e8	+	2.08337e8i	0.379913	+	0.658820i
$11$	8.41139e8			1.18312			0.591561	−	0.806260i	$-0.298512\pi$
$11$	8.41139e8			1.18312			0.591561	+	0.806260i	$0.298512\pi$
$12$			1.65269e8i			0.110956i
$13$			4.01580e9i			1.36538i	0.730707	+	0.682691i	$0.239190\pi$
$13$			4.01580e9i			1.36538i	−0.730707	+	0.682691i	$0.760810\pi$
$14$	6.71566e9			1.21619
$15$	−1.30491e9	−	2.26289e9i	−0.131464	−	0.227975i
$16$	−6.88248e9			−0.400613
$17$		−	8.60868e9i		−	0.299310i	−0.988738	−	0.149655i	$-0.952184\pi$
$17$		−	8.60868e9i		−	0.299310i	0.988738	−	0.149655i	$-0.0478163\pi$
$18$		−	3.30943e10i		−	0.707842i
$19$	−6.64861e10			−0.898101			−0.449051	−	0.893506i	$-0.648238\pi$
$19$	−6.64861e10			−0.898101			−0.449051	+	0.893506i	$0.648238\pi$
$20$	−4.18157e10	+	2.41133e10i	−0.365245	+	0.210621i
$21$	−7.29433e10			−0.420844
$22$		−	2.31595e11i		−	0.899779i
$23$			5.12783e11i			1.36536i	0.730718	+	0.682680i	$0.239186\pi$
$23$			5.12783e11i			1.36536i	−0.730718	+	0.682680i	$0.760814\pi$
$24$	1.53431e11			0.284523
$25$	3.82157e11	−	6.60328e11i	0.500900	−	0.865505i
$26$	1.10569e12			1.03839
$27$			7.45665e11i			0.508103i
$28$			1.34791e12i			0.674244i
$29$	1.63558e11			0.0607139			0.0303570	−	0.999539i	$-0.490336\pi$
$29$	1.63558e11			0.0607139			0.0303570	+	0.999539i	$0.490336\pi$
$30$	−6.23053e11	+	3.59288e11i	−0.173378	+	0.0999797i
$31$	−3.12692e12			−0.658480			−0.329240	−	0.944246i	$-0.606793\pi$
$31$	−3.12692e12			−0.658480			−0.329240	+	0.944246i	$0.606793\pi$
$32$		−	4.82959e12i		−	0.776489i
$33$			2.51551e12i			0.311356i
$34$	−2.37027e12			−0.227629
$35$	−1.06427e13	−	1.84558e13i	−0.798864	−	1.38534i
$36$	6.64240e12			0.392422
$37$			2.41839e12i			0.113191i	0.998397	+	0.0565954i	$0.0180245\pi$
$37$			2.41839e12i			0.113191i	−0.998397	+	0.0565954i	$0.981975\pi$
$38$			1.83059e13i			0.683016i
$39$	−1.20096e13			−0.359320
$40$	2.23861e13	+	3.88205e13i	0.540093	+	0.936593i
$41$	4.43989e13			0.868379			0.434189	−	0.900822i	$-0.357035\pi$
$41$	4.43989e13			0.868379			0.434189	+	0.900822i	$0.357035\pi$
$42$			2.00838e13i			0.320057i
$43$		−	7.24471e13i		−	0.945234i	−0.881268	−	0.472617i	$-0.843309\pi$
$43$		−	7.24471e13i		−	0.945234i	0.881268	−	0.472617i	$-0.156691\pi$
$44$	4.64837e13			0.498830
$45$	−9.09490e13	+	5.24464e13i	−0.806290	+	0.464953i
$46$	1.41187e14			1.03837
$47$		−	5.71958e13i		−	0.350374i	−0.984535	−	0.175187i	$-0.943947\pi$
$47$		−	5.71958e13i		−	0.350374i	0.984535	−	0.175187i	$-0.0560531\pi$
$48$		−	2.05827e13i		−	0.105427i
$49$	−3.62285e14			−1.55734
$50$	−1.81811e14	−	1.05221e14i	−0.658227	−	0.380941i
$51$	2.57451e13			0.0787677
$52$			2.21925e14i			0.575675i
$53$		−	3.35911e14i		−	0.741104i	−0.928812	−	0.370552i	$-0.879168\pi$
$53$		−	3.35911e14i		−	0.741104i	0.928812	−	0.370552i	$-0.120832\pi$
$54$	2.05308e14			0.386418
$55$	−6.36464e14	+	3.67021e14i	−1.02492	+	0.591029i
$56$	1.25136e15			1.72896
$57$		−	1.98833e14i		−	0.236348i
$58$		−	4.50331e13i		−	0.0461736i
$59$	−2.43892e14			−0.216249			−0.108125	−	0.994137i	$-0.534485\pi$
$59$	−2.43892e14			−0.216249			−0.108125	+	0.994137i	$0.534485\pi$
$60$	−7.21132e13	−	1.25054e14i	−0.0554280	−	0.0961194i
$61$	2.41050e15			1.60992			0.804960	−	0.593329i	$-0.202187\pi$
$61$	2.41050e15			1.60992			0.804960	+	0.593329i	$0.202187\pi$
$62$			8.60950e14i			0.500782i
$63$			2.93170e15i			1.48842i
$64$	−2.23185e15			−0.991142
$65$	−1.75225e15	−	3.03863e15i	−0.682076	−	1.18281i
$66$	6.92606e14			0.236790
$67$		−	2.63132e15i		−	0.791659i	−0.918324	−	0.395829i	$-0.870457\pi$
$67$		−	2.63132e15i		−	0.791659i	0.918324	−	0.395829i	$-0.129543\pi$
$68$		−	4.75740e14i		−	0.126196i
$69$	−1.53353e15			−0.359314
$70$	−5.08153e15	+	2.93030e15i	−1.05356	+	0.607546i
$71$	4.51149e15			0.829133			0.414566	−	0.910019i	$-0.363933\pi$
$71$	4.51149e15			0.829133			0.414566	+	0.910019i	$0.363933\pi$
$72$		−	6.16661e15i		−	1.00628i
$73$		−	2.61026e15i		−	0.378826i	−0.981898	−	0.189413i	$-0.939342\pi$
$73$		−	2.61026e15i		−	0.378826i	0.981898	−	0.189413i	$-0.0606585\pi$
$74$	6.65866e14			0.0860830
$75$	1.97477e15	+	1.14288e15i	0.227770	+	0.131819i
$76$	−3.67421e15			−0.378659
$77$			2.05161e16i			1.89201i
$78$			3.30667e15i			0.273267i
$79$	7.48386e15			0.555003			0.277501	−	0.960725i	$-0.410494\pi$
$79$	7.48386e15			0.555003			0.277501	+	0.960725i	$0.410494\pi$
$80$	5.20776e15	−	3.00309e15i	0.347045	−	0.200126i
$81$	1.32922e16			0.797030
$82$		−	1.22245e16i		−	0.660412i
$83$		−	2.07744e15i		−	0.101243i	−0.998718	−	0.0506214i	$-0.983880\pi$
$83$		−	2.07744e15i		−	0.101243i	0.998718	−	0.0506214i	$-0.0161202\pi$
$84$	−4.03105e15			−0.177437
$85$	3.75630e15	+	6.51393e15i	0.149520	+	0.259288i
$86$	−1.99472e16			−0.718862
$87$			4.89135e14i			0.0159777i
$88$		−	4.31541e16i		−	1.27915i
$89$	2.77854e15			0.0748173			0.0374086	−	0.999300i	$-0.488090\pi$
$89$	2.77854e15			0.0748173			0.0374086	+	0.999300i	$0.488090\pi$
$90$	1.44403e16	+	2.50414e16i	0.353602	+	0.613193i
$91$	−9.79490e16			−2.18348
$92$			2.83378e16i			0.575665i
$93$		−	9.35136e15i		−	0.173289i
$94$	−1.57480e16			−0.266464
$95$	5.03080e16	−	2.90105e16i	0.778012	−	0.448646i
$96$	1.44434e16			0.204344
$97$		−	5.77968e16i		−	0.748762i	−0.927275	−	0.374381i	$-0.877855\pi$
$97$		−	5.77968e16i		−	0.748762i	0.927275	−	0.374381i	$-0.122145\pi$
$98$			9.97495e16i			1.18438i
$99$	1.01102e17			1.10119
$100$	2.11190e16	−	3.64916e16i	0.211190	−	0.364916i
$101$	−6.77981e16			−0.622997			−0.311499	−	0.950247i	$-0.600831\pi$
$101$	−6.77981e16			−0.622997			−0.311499	+	0.950247i	$0.600831\pi$
$102$		−	7.08852e15i		−	0.0599038i
$103$			9.15022e16i			0.711729i	0.934537	+	0.355865i	$0.115814\pi$
$103$			9.15022e16i			0.711729i	−0.934537	+	0.355865i	$0.884186\pi$
$104$	2.06029e17			1.47620
$105$	5.51939e16	−	3.18280e16i	0.364571	−	0.210233i
$106$	−9.24880e16			−0.563619
$107$			3.51736e16i			0.197904i	0.995092	+	0.0989519i	$0.0315490\pi$
$107$			3.51736e16i			0.197904i	−0.995092	+	0.0989519i	$0.968451\pi$
$108$			4.12076e16i			0.214227i
$109$	−3.76273e17			−1.80875			−0.904375	−	0.426739i	$-0.859662\pi$
$109$	−3.76273e17			−1.80875			−0.904375	+	0.426739i	$0.859662\pi$
$110$	1.01054e17	+	1.75241e17i	0.449484	+	0.779465i
$111$	−7.23242e15			−0.0297878
$112$		−	1.67870e17i		−	0.640648i
$113$		−	3.30695e17i		−	1.17020i	−0.810960	−	0.585101i	$-0.801055\pi$
$113$		−	3.30695e17i		−	1.17020i	0.810960	−	0.585101i	$-0.198945\pi$
$114$	−5.47456e16			−0.179746
$115$	−2.23747e17	−	3.88007e17i	−0.682065	−	1.18279i
$116$	9.03866e15			0.0255983
$117$			4.82686e17i			1.27082i
$118$			6.71518e16i			0.164460i
$119$	2.09973e17			0.478647
$120$	−1.16096e17	+	6.69478e16i	−0.246478	+	0.142133i
$121$	2.02067e17			0.399779
$122$		−	6.63695e17i		−	1.22436i
$123$			1.32779e17i			0.228526i
$124$	−1.72803e17			−0.277630
$125$	−1.03934e15	+	6.66399e17i	−0.00155963	+	0.999999i
$126$	8.07198e17			1.13196
$127$			7.69744e17i			1.00929i	0.863328	+	0.504643i	$0.168376\pi$
$127$			7.69744e17i			1.00929i	−0.863328	+	0.504643i	$0.831624\pi$
$128$		−	1.85170e16i		−	0.0227136i
$129$	2.16660e17			0.248752
$130$	−8.36642e17	+	4.82455e17i	−0.899541	+	0.518727i
$131$	1.50692e18			1.51804			0.759022	−	0.651065i	$-0.225678\pi$
$131$	1.50692e18			1.51804			0.759022	+	0.651065i	$0.225678\pi$
$132$			1.39014e17i			0.131274i
$133$		−	1.62165e18i		−	1.43621i
$134$	−7.24494e17			−0.602066
$135$	−3.25363e17	−	5.64222e17i	−0.253823	−	0.440162i
$136$	−4.41664e17			−0.323602
$137$		−	3.94985e17i		−	0.271929i	−0.990714	−	0.135965i	$-0.956587\pi$
$137$		−	3.94985e17i		−	0.271929i	0.990714	−	0.135965i	$-0.0434134\pi$
$138$			4.22233e17i			0.273263i
$139$	−7.47149e17			−0.454759			−0.227380	−	0.973806i	$-0.573016\pi$
$139$	−7.47149e17			−0.454759			−0.227380	+	0.973806i	$0.573016\pi$
$140$	−5.88145e17	−	1.01992e18i	−0.336819	−	0.584088i
$141$	1.71050e17			0.0922061
$142$		−	1.24217e18i		−	0.630565i
$143$			3.37785e18i			1.61541i
$144$	−8.27250e17			−0.372869
$145$	−1.23759e17	+	7.13666e16i	−0.0525956	+	0.0303296i
$146$	−7.18695e17			−0.288101
$147$		−	1.08345e18i		−	0.409836i
$148$			1.33647e17i			0.0477237i
$149$	−9.58107e17			−0.323095			−0.161548	−	0.986865i	$-0.551649\pi$
$149$	−9.58107e17			−0.323095			−0.161548	+	0.986865i	$0.551649\pi$
$150$	3.14673e17	−	5.43724e17i	0.100250	−	0.173222i
$151$	3.59671e18			1.08293			0.541466	−	0.840723i	$-0.317870\pi$
$151$	3.59671e18			1.08293			0.541466	+	0.840723i	$0.317870\pi$
$152$			3.41103e18i			0.970991i
$153$		−	1.03473e18i		−	0.278581i
$154$	5.64880e18			1.43890
$155$	2.36605e18	−	1.36440e18i	0.570432	−	0.328944i
$156$	−6.63687e17			−0.151497
$157$			1.64813e18i			0.356323i	0.984001	+	0.178162i	$0.0570150\pi$
$157$			1.64813e18i			0.356323i	−0.984001	+	0.178162i	$0.942985\pi$
$158$		−	2.06057e18i		−	0.422086i
$159$	1.00457e18			0.195032
$160$	2.10734e18	+	3.65440e18i	0.387895	+	0.672661i
$161$	−1.25072e19			−2.18344
$162$		−	3.65981e18i		−	0.606151i
$163$			3.35481e18i			0.527318i	0.964616	+	0.263659i	$0.0849294\pi$
$163$			3.35481e18i			0.527318i	−0.964616	+	0.263659i	$0.915071\pi$
$164$	2.45361e18			0.366127
$165$	−1.09761e18	−	1.90341e18i	−0.155538	−	0.269723i
$166$	−5.71991e17			−0.0769964
$167$		−	5.47912e17i		−	0.0700843i	−0.999386	−	0.0350422i	$-0.988843\pi$
$167$		−	5.47912e17i		−	0.0700843i	0.999386	−	0.0350422i	$-0.0111566\pi$
$168$			3.74231e18i			0.455000i
$169$	−7.47627e18			−0.864267
$170$	1.79351e18	−	1.03424e18i	0.197191	−	0.113712i
$171$	−7.99140e18			−0.835903
$172$		−	4.00363e18i		−	0.398531i
$173$		−	2.01070e19i		−	1.90527i	−0.304121	−	0.952634i	$-0.598363\pi$
$173$		−	2.01070e19i		−	1.90527i	0.304121	−	0.952634i	$-0.401637\pi$
$174$	1.34676e17			0.0121513
$175$	1.61060e19	+	9.32114e18i	1.38409	+	0.801024i
$176$	−5.78912e18			−0.473975
$177$		−	7.29381e17i		−	0.0569091i
$178$		−	7.65029e17i		−	0.0568994i
$179$	4.53989e18			0.321955			0.160977	−	0.986958i	$-0.448535\pi$
$179$	4.53989e18			0.321955			0.160977	+	0.986958i	$0.448535\pi$
$180$	−5.02610e18	+	2.89833e18i	−0.339950	+	0.196034i
$181$	4.15934e18			0.268384			0.134192	−	0.990955i	$-0.457156\pi$
$181$	4.15934e18			0.268384			0.134192	+	0.990955i	$0.457156\pi$
$182$			2.69688e19i			1.66056i
$183$			7.20885e18i			0.423674i
$184$	2.63080e19			1.47617
$185$	−1.05524e18	−	1.82992e18i	−0.0565445	−	0.0980556i
$186$	−2.57475e18			−0.131788
$187$		−	7.24110e18i		−	0.354120i
$188$		−	3.16080e18i		−	0.147725i
$189$	−1.81874e19			−0.812543
$190$	−7.98759e18	−	1.38515e19i	−0.341201	−	0.591687i
$191$	3.00403e19			1.22721			0.613607	−	0.789612i	$-0.289718\pi$
$191$	3.00403e19			1.22721			0.613607	+	0.789612i	$0.289718\pi$
$192$		−	6.67457e18i		−	0.260833i
$193$			4.96197e19i			1.85531i	0.373438	+	0.927655i	$0.378179\pi$
$193$			4.96197e19i			1.85531i	−0.373438	+	0.927655i	$0.621821\pi$
$194$	−1.59135e19			−0.569442
$195$	9.08733e18	−	5.24028e18i	0.311273	−	0.179498i
$196$	−2.00209e19			−0.656608
$197$		−	5.07587e19i		−	1.59422i	−0.603836	−	0.797109i	$-0.706362\pi$
$197$		−	5.07587e19i		−	1.59422i	0.603836	−	0.797109i	$-0.293638\pi$
$198$		−	2.78369e19i		−	0.837464i
$199$	−3.21936e18			−0.0927936			−0.0463968	−	0.998923i	$-0.514774\pi$
$199$	−3.21936e18			−0.0927936			−0.0463968	+	0.998923i	$0.514774\pi$
$200$	−3.38778e19	−	1.96063e19i	−0.935750	−	0.541553i
$201$	7.86922e18			0.208336
$202$			1.86672e19i			0.473797i
$203$			3.98932e18i			0.0970918i
$204$	1.42275e18			0.0332102
$205$	−3.35952e19	+	1.93729e19i	−0.752264	+	0.433798i
$206$	2.51937e19			0.541279
$207$			6.16347e19i			1.27080i
$208$		−	2.76387e19i		−	0.546990i
$209$	−5.59240e19			−1.06256
$210$	−8.76335e18	−	1.51968e19i	−0.159884	−	0.277261i
$211$	9.47490e19			1.66025			0.830126	−	0.557576i	$-0.188269\pi$
$211$	9.47490e19			1.66025			0.830126	+	0.557576i	$0.188269\pi$
$212$		−	1.85634e19i		−	0.312466i
$213$			1.34920e19i			0.218198i
$214$	9.68450e18			0.150508
$215$	3.16115e19	+	5.48185e19i	0.472191	+	0.818842i
$216$	3.82559e19			0.549341
$217$		−	7.62684e19i		−	1.05302i
$218$			1.03601e20i			1.37558i
$219$	7.80624e18			0.0996935
$220$	−3.51728e19	+	2.02826e19i	−0.432129	+	0.249191i
$221$	3.45708e19			0.408672
$222$			1.99134e18i			0.0226540i
$223$		−	1.31328e20i		−	1.43802i	−0.694999	−	0.719011i	$-0.744595\pi$
$223$		−	1.31328e20i		−	1.43802i	0.694999	−	0.719011i	$-0.255405\pi$
$224$	1.17798e20			1.24174
$225$	4.59339e19	−	7.93691e19i	0.466210	−	0.805564i
$226$	−9.10518e19			−0.889953
$227$			1.40184e20i			1.31971i	0.751392	+	0.659856i	$0.229383\pi$
$227$			1.40184e20i			1.31971i	−0.751392	+	0.659856i	$0.770617\pi$
$228$		−	1.09881e19i		−	0.0996496i
$229$	−2.03342e20			−1.77675			−0.888375	−	0.459119i	$-0.848165\pi$
$229$	−2.03342e20			−1.77675			−0.888375	+	0.459119i	$0.848165\pi$
$230$	−1.06832e20	+	6.16053e19i	−0.899526	+	0.518718i
$231$	−6.13554e19			−0.497910
$232$		−	8.39124e18i		−	0.0656415i
$233$		−	1.39686e20i		−	1.05348i	−0.850027	−	0.526740i	$-0.823414\pi$
$233$		−	1.39686e20i		−	1.05348i	0.850027	−	0.526740i	$-0.176586\pi$
$234$	1.32900e20			0.966475
$235$	2.49567e19	+	4.32783e19i	0.175029	+	0.303524i
$236$	−1.34781e19			−0.0911754
$237$			2.23812e19i			0.146057i
$238$		−	5.78130e19i		−	0.364017i
$239$	−7.58670e19			−0.460968			−0.230484	−	0.973076i	$-0.574031\pi$
$239$	−7.58670e19			−0.460968			−0.230484	+	0.973076i	$0.574031\pi$
$240$	8.98104e18	+	1.55743e19i	0.0526661	+	0.0913300i
$241$	−2.19191e20			−1.24073			−0.620365	−	0.784313i	$-0.713016\pi$
$241$	−2.19191e20			−1.24073			−0.620365	+	0.784313i	$0.713016\pi$
$242$		−	5.56362e19i		−	0.304037i
$243$			1.36047e20i			0.717853i
$244$	1.33211e20			0.678777
$245$	2.74130e20	−	1.58079e20i	1.34910	−	0.777969i
$246$	3.65587e19			0.173797
$247$		−	2.66995e20i		−	1.22625i
$248$			1.60425e20i			0.711922i
$249$	6.21278e18			0.0266435
$250$	1.83483e20	+	2.86165e17i	0.760511	+	0.00118611i
$251$	3.03839e19			0.121735			0.0608676	−	0.998146i	$-0.480613\pi$
$251$	3.03839e19			0.121735			0.0608676	+	0.998146i	$0.480613\pi$
$252$			1.62014e20i			0.627549i
$253$			4.31322e20i			1.61539i
$254$	2.11937e20			0.767574
$255$	−1.94805e19	+	1.12336e19i	−0.0682353	+	0.0393484i
$256$	−2.97632e20			−1.00842
$257$			2.96660e20i			0.972361i	0.873858	+	0.486180i	$0.161610\pi$
$257$			2.96660e20i			0.972361i	−0.873858	+	0.486180i	$0.838390\pi$
$258$		−	5.96540e19i		−	0.189179i
$259$	−5.89866e19			−0.181011
$260$	−9.68343e19	−	1.67923e20i	−0.287578	−	0.498698i
$261$	1.96591e19			0.0565091
$262$		−	4.14907e20i		−	1.15449i
$263$		−	3.43830e20i		−	0.926233i	−0.886297	−	0.463116i	$-0.846731\pi$
$263$		−	3.43830e20i		−	0.926233i	0.886297	−	0.463116i	$-0.153269\pi$
$264$	1.29057e20			0.336625
$265$	1.46571e20	+	2.54173e20i	0.370218	+	0.642008i
$266$	−4.46498e20			−1.09226
$267$			8.30950e18i			0.0196892i
$268$		−	1.45414e20i		−	0.333781i
$269$	−1.76686e20			−0.392923			−0.196462	−	0.980511i	$-0.562945\pi$
$269$	−1.76686e20			−0.392923			−0.196462	+	0.980511i	$0.562945\pi$
$270$	−1.55350e20	+	8.95836e19i	−0.334749	+	0.193035i
$271$	1.00224e20			0.209282			0.104641	−	0.994510i	$-0.466631\pi$
$271$	1.00224e20			0.209282			0.104641	+	0.994510i	$0.466631\pi$
$272$			5.92491e19i			0.119907i
$273$		−	2.92926e20i		−	0.574613i
$274$	−1.08753e20			−0.206806
$275$	3.21447e20	−	5.55427e20i	0.592626	−	1.02400i
$276$	−8.47470e19			−0.151495
$277$		−	1.22541e20i		−	0.212424i	−0.994343	−	0.106212i	$-0.966128\pi$
$277$		−	1.22541e20i		−	0.212424i	0.994343	−	0.106212i	$-0.0338722\pi$
$278$			2.05716e20i			0.345850i
$279$	−3.75845e20			−0.612877
$280$	−9.46866e20	+	5.46017e20i	−1.49777	+	0.863700i
$281$	6.75283e20			1.03629			0.518146	−	0.855292i	$-0.326622\pi$
$281$	6.75283e20			1.03629			0.518146	+	0.855292i	$0.326622\pi$
$282$		−	4.70959e19i		−	0.0701238i
$283$			6.87359e20i			0.993114i	0.868004	+	0.496557i	$0.165403\pi$
$283$			6.87359e20i			0.993114i	−0.868004	+	0.496557i	$0.834597\pi$
$284$	2.49318e20			0.349581
$285$	8.67586e19	+	1.50451e20i	0.118068	+	0.204745i
$286$	9.30039e20			1.22854
$287$			1.08293e21i			1.38868i
$288$		−	5.80500e20i		−	0.722713i
$289$	7.53131e20			0.910414
$290$	1.96497e19	+	3.40752e19i	0.0230660	+	0.0399995i
$291$	1.72847e20			0.197047
$292$		−	1.44250e20i		−	0.159721i
$293$		−	1.22015e21i		−	1.31231i	−0.754625	−	0.656156i	$-0.772181\pi$
$293$		−	1.22015e21i		−	1.31231i	0.754625	−	0.656156i	$-0.227819\pi$
$294$	−2.98311e20			−0.311685
$295$	1.84545e20	−	1.06419e20i	0.187334	−	0.108027i
$296$	1.24074e20			0.122377
$297$			6.27208e20i			0.601148i
$298$			2.63800e20i			0.245718i
$299$	−2.05924e21			−1.86424
$300$	1.09132e20	+	6.31585e19i	0.0960328	+	0.0555778i
$301$	1.76705e21			1.51159
$302$		−	9.90299e20i		−	0.823583i
$303$		−	2.02757e20i		−	0.163951i
$304$	4.57589e20			0.359791
$305$	−1.82395e21	+	1.05180e21i	−1.39465	+	0.804235i
$306$	−2.84898e20			−0.211864
$307$		−	1.90026e21i		−	1.37448i	−0.726431	−	0.687239i	$-0.758823\pi$
$307$		−	1.90026e21i		−	1.37448i	0.726431	−	0.687239i	$-0.241177\pi$
$308$			1.13378e21i			0.797714i
$309$	−2.73646e20			−0.187302
$310$	−3.75666e20	−	6.51454e20i	−0.250165	−	0.433820i
$311$	−1.43465e21			−0.929569			−0.464785	−	0.885424i	$-0.653868\pi$
$311$	−1.43465e21			−0.929569			−0.464785	+	0.885424i	$0.653868\pi$
$312$			6.16148e20i			0.388482i
$313$			2.00027e21i			1.22733i	0.789566	+	0.613665i	$0.210306\pi$
$313$			2.00027e21i			1.22733i	−0.789566	+	0.613665i	$0.789694\pi$
$314$	4.53787e20			0.270988
$315$	−1.27921e21	−	2.21833e21i	−0.743538	−	1.28939i
$316$	4.13579e20			0.234001
$317$		−	1.13693e21i		−	0.626226i	−0.949716	−	0.313113i	$-0.898628\pi$
$317$		−	1.13693e21i		−	0.626226i	0.949716	−	0.313113i	$-0.101372\pi$
$318$		−	2.76594e20i		−	0.148324i
$319$	1.37575e20			0.0718320
$320$	1.68877e21	−	9.73844e20i	0.858612	−	0.495125i
$321$	−1.05190e20			−0.0520813
$322$			3.44367e21i			1.66053i
$323$			5.72358e20i			0.268810i
$324$	7.34565e20			0.336045
$325$	2.65175e21	+	1.53467e21i	1.18174	+	0.683920i
$326$	9.23695e20			0.401032
$327$		−	1.12528e21i		−	0.475998i
$328$		−	2.27786e21i		−	0.938856i
$329$	1.39506e21			0.560308
$330$	−5.24074e20	+	3.02211e20i	−0.205127	+	0.118288i
$331$	−1.84600e21			−0.704195			−0.352097	−	0.935963i	$-0.614531\pi$
$331$	−1.84600e21			−0.704195			−0.352097	+	0.935963i	$0.614531\pi$
$332$		−	1.14805e20i		−	0.0426862i
$333$			2.90682e20i			0.105352i
$334$	−1.50859e20			−0.0533000
$335$	1.14815e21	+	1.99104e21i	0.395473	+	0.685802i
$336$	5.02031e20			0.168596
$337$		−	6.86430e20i		−	0.224772i	−0.993665	−	0.112386i	$-0.964151\pi$
$337$		−	6.86430e20i		−	0.224772i	0.993665	−	0.112386i	$-0.0358493\pi$
$338$			2.05848e21i			0.657285i
$339$	9.88975e20			0.307956
$340$	2.07584e20	+	3.59978e20i	0.0630409	+	0.109321i
$341$	−2.63018e21			−0.779063
$342$			2.20031e21i			0.635714i
$343$		−	3.16238e21i		−	0.891280i
$344$	−3.71686e21			−1.02195
$345$	1.16037e21	−	6.69137e20i	0.311268	−	0.179495i
$346$	−5.53616e21			−1.44898
$347$			8.26157e20i			0.210990i	0.994420	+	0.105495i	$0.0336427\pi$
$347$			8.26157e20i			0.210990i	−0.994420	+	0.105495i	$0.966357\pi$
$348$			2.70310e19i			0.00673656i
$349$	3.10029e21			0.754026			0.377013	−	0.926208i	$-0.376951\pi$
$349$	3.10029e21			0.754026			0.377013	+	0.926208i	$0.376951\pi$
$350$	2.56643e21	−	4.43454e21i	0.609188	−	1.05262i
$351$	−2.99445e21			−0.693755
$352$		−	4.06235e21i		−	0.918682i
$353$		−	2.62238e21i		−	0.578909i	−0.957192	−	0.289455i	$-0.906526\pi$
$353$		−	2.62238e21i		−	0.578909i	0.957192	−	0.289455i	$-0.0934739\pi$
$354$	−2.00824e20			−0.0432801
$355$	−3.41371e21	+	1.96854e21i	−0.718266	+	0.414193i
$356$	1.53550e20			0.0315446
$357$			6.27946e20i			0.125963i
$358$		−	1.24999e21i		−	0.244850i
$359$	4.39853e21			0.841403			0.420702	−	0.907199i	$-0.361784\pi$
$359$	4.39853e21			0.841403			0.420702	+	0.907199i	$0.361784\pi$
$360$	2.69073e21	+	4.66609e21i	0.502689	+	0.871729i
$361$	−1.05999e21			−0.193414
$362$		−	1.14521e21i		−	0.204109i
$363$			6.04302e20i			0.105208i
$364$	−5.41294e21			−0.920601
$365$	1.13896e21	+	1.97510e21i	0.189242	+	0.328171i
$366$	1.98485e21			0.322209
$367$			6.17095e21i			0.978793i	0.872061	+	0.489396i	$0.162783\pi$
$367$			6.17095e21i			0.978793i	−0.872061	+	0.489396i	$0.837217\pi$
$368$		−	3.52922e21i		−	0.546981i
$369$	5.33659e21			0.808239
$370$	−5.03840e20	+	2.90543e20i	−0.0745724	+	0.0430027i
$371$	8.19317e21			1.18515
$372$		−	5.16783e20i		−	0.0730622i
$373$			8.48385e21i			1.17238i	0.810174	+	0.586190i	$0.199373\pi$
$373$			8.48385e21i			1.17238i	−0.810174	+	0.586190i	$0.800627\pi$
$374$	−1.99373e21			−0.269313
$375$	−1.99293e21	−	3.10823e18i	−0.263164	−	0.000410438i
$376$	−2.93440e21			−0.378811
$377$			6.56816e20i			0.0828976i
$378$			5.00763e21i			0.617948i
$379$	5.99241e21			0.723050			0.361525	−	0.932362i	$-0.382256\pi$
$379$	5.99241e21			0.723050			0.361525	+	0.932362i	$0.382256\pi$
$380$	2.78016e21	−	1.60320e21i	0.328027	−	0.189159i
$381$	−2.30199e21			−0.265608
$382$		−	8.27113e21i		−	0.933311i
$383$			2.17350e21i			0.239866i	0.992782	+	0.119933i	$0.0382680\pi$
$383$			2.17350e21i			0.239866i	−0.992782	+	0.119933i	$0.961732\pi$
$384$	5.53769e19			0.00597741
$385$	−8.95198e21	−	1.55239e22i	−0.945154	−	1.63902i
$386$	1.36620e22			1.41099
$387$		−	8.70789e21i		−	0.879771i
$388$		−	3.19401e21i		−	0.315694i
$389$	−1.86409e22			−1.80258			−0.901289	−	0.433218i	$-0.857378\pi$
$389$	−1.86409e22			−1.80258			−0.901289	+	0.433218i	$0.857378\pi$
$390$	−1.44283e21	−	2.50206e21i	−0.136510	−	0.236727i
$391$	4.41439e21			0.408665
$392$			1.85868e22i			1.68373i
$393$			4.50659e21i			0.399495i
$394$	−1.39756e22			−1.21242
$395$	−5.66280e21	+	3.26550e21i	−0.480791	+	0.277252i
$396$	5.58718e21			0.464284
$397$		−	7.16091e21i		−	0.582437i	−0.956657	−	0.291218i	$-0.905939\pi$
$397$		−	7.16091e21i		−	0.582437i	0.956657	−	0.291218i	$-0.0940607\pi$
$398$			8.86401e20i			0.0705706i
$399$	4.84971e21			0.377961
$400$	−2.63019e21	+	4.54470e21i	−0.200667	+	0.346733i
$401$	−2.30431e21			−0.172113			−0.0860566	−	0.996290i	$-0.527427\pi$
$401$	−2.30431e21			−0.172113			−0.0860566	+	0.996290i	$0.527427\pi$
$402$		−	2.16667e21i		−	0.158442i
$403$		−	1.25571e22i		−	0.899077i
$404$	−3.74672e21			−0.262669
$405$	−1.00578e22	+	5.79991e21i	−0.690455	+	0.398156i
$406$	1.09840e21			0.0738394
$407$			2.03420e21i			0.133919i
$408$		−	1.32084e21i		−	0.0851605i
$409$	1.97605e22			1.24782			0.623908	−	0.781498i	$-0.285544\pi$
$409$	1.97605e22			1.24782			0.623908	+	0.781498i	$0.285544\pi$
$410$	5.33404e21	+	9.24994e21i	0.329909	+	0.572105i
$411$	1.18124e21			0.0715621
$412$			5.05667e21i			0.300081i
$413$		−	5.94873e21i		−	0.345819i
$414$	1.69702e22			0.966459
$415$	9.06467e20	+	1.57193e21i	0.0505759	+	0.0877052i
$416$	1.93947e22			1.06020
$417$		−	2.23442e21i		−	0.119676i
$418$			1.53978e22i			0.808092i
$419$	−2.45016e21			−0.126001			−0.0630006	−	0.998013i	$-0.520067\pi$
$419$	−2.45016e21			−0.126001			−0.0630006	+	0.998013i	$0.520067\pi$
$420$	3.05017e21	−	1.75890e21i	0.153711	−	0.0886386i
$421$	4.22696e21			0.208752			0.104376	−	0.994538i	$-0.466716\pi$
$421$	4.22696e21			0.208752			0.104376	+	0.994538i	$0.466716\pi$
$422$		−	2.60877e22i		−	1.26264i
$423$		−	6.87473e21i		−	0.326109i
$424$	−1.72337e22			−0.801253
$425$	−5.68456e21	−	3.28986e21i	−0.259054	−	0.149924i
$426$	3.71483e21			0.165942
$427$			5.87943e22i			2.57453i
$428$			1.94379e21i			0.0834406i
$429$	−1.01018e22			−0.425119
$430$	1.50934e22	−	8.70374e21i	0.622739	−	0.359107i
$431$	−2.22344e22			−0.899432			−0.449716	−	0.893172i	$-0.648475\pi$
$431$	−2.22344e22			−0.899432			−0.449716	+	0.893172i	$0.648475\pi$
$432$		−	5.13203e21i		−	0.203553i
$433$		−	2.10672e22i		−	0.819333i	−0.912235	−	0.409667i	$-0.865645\pi$
$433$		−	2.10672e22i		−	0.819333i	0.912235	−	0.409667i	$-0.134355\pi$
$434$	−2.09993e22			−0.800835
$435$	−2.13429e20	−	3.70113e20i	−0.00798167	−	0.0138413i
$436$	−2.07939e22			−0.762608
$437$		−	3.40929e22i		−	1.22623i
$438$		−	2.14933e21i		−	0.0758181i
$439$	4.37524e22			1.51375			0.756874	−	0.653560i	$-0.226725\pi$
$439$	4.37524e22			1.51375			0.756874	+	0.653560i	$0.226725\pi$
$440$	1.88298e22	+	3.26534e22i	0.638997	+	1.10810i
$441$	−4.35454e22			−1.44949
$442$		−	9.51854e21i		−	0.310800i
$443$			2.24729e22i			0.719827i	0.932986	+	0.359914i	$0.117194\pi$
$443$			2.24729e22i			0.719827i	−0.932986	+	0.359914i	$0.882806\pi$
$444$	−3.99684e20			−0.0125592
$445$	−2.10244e21	+	1.21239e21i	−0.0648131	+	0.0373749i
$446$	−3.61591e22			−1.09363
$447$		−	2.86531e21i		−	0.0850272i
$448$		−	5.44369e22i		−	1.58500i
$449$	−2.31598e22			−0.661670			−0.330835	−	0.943689i	$-0.607330\pi$
$449$	−2.31598e22			−0.661670			−0.330835	+	0.943689i	$0.607330\pi$
$450$	−2.18531e22	−	1.26472e22i	−0.612641	−	0.354558i
$451$	3.73456e22			1.02740
$452$		−	1.82751e22i		−	0.493383i
$453$			1.07563e22i			0.284989i
$454$	3.85976e22			1.00366
$455$	7.41150e22	−	4.27389e22i	1.89151	−	1.09075i
$456$	−1.02010e22			−0.255530
$457$			7.37859e22i			1.81420i	0.420912	+	0.907101i	$0.361710\pi$
$457$			7.37859e22i			1.81420i	−0.420912	+	0.907101i	$0.638290\pi$
$458$			5.59872e22i			1.35124i
$459$	6.41920e21			0.152080
$460$	−1.23649e22	−	2.14424e22i	−0.287573	−	0.498690i
$461$	7.16140e21			0.163508			0.0817542	−	0.996653i	$-0.473948\pi$
$461$	7.16140e21			0.163508			0.0817542	+	0.996653i	$0.473948\pi$
$462$			1.68933e22i			0.378667i
$463$			6.96956e22i			1.53379i	0.641771	+	0.766897i	$0.278200\pi$
$463$			6.96956e22i			1.53379i	−0.641771	+	0.766897i	$0.721800\pi$
$464$	−1.12568e21			−0.0243228
$465$	4.08036e21	+	7.07589e21i	0.0865662	+	0.150117i
$466$	−3.84603e22			−0.801184
$467$		−	7.30135e22i		−	1.49352i	−0.665096	−	0.746758i	$-0.731609\pi$
$467$		−	7.30135e22i		−	1.49352i	0.665096	−	0.746758i	$-0.268391\pi$
$468$			2.66746e22i			0.535806i
$469$	6.41802e22			1.26600
$470$	1.19160e22	−	6.87146e21i	0.230834	−	0.133112i
$471$	−4.92889e21			−0.0937716
$472$			1.25127e22i			0.233800i
$473$		−	6.09381e22i		−	1.11833i
$474$	6.16232e21			0.111078
$475$	−2.54081e22	+	4.39026e22i	−0.449859	+	0.777311i
$476$	1.16037e22			0.201808
$477$		−	4.03753e22i		−	0.689779i
$478$			2.08888e22i			0.350572i
$479$	−8.82520e22			−1.45503			−0.727516	−	0.686091i	$-0.759325\pi$
$479$	−8.82520e22			−1.45503			−0.727516	+	0.686091i	$0.759325\pi$
$480$	−1.09288e22	+	6.30219e21i	−0.177020	+	0.102080i
$481$	−9.71177e21			−0.154549
$482$			6.03508e22i			0.943590i
$483$		−	3.74041e22i		−	0.574604i
$484$	1.11668e22			0.168556
$485$	2.52190e22	+	4.37330e22i	0.374044	+	0.648641i
$486$	3.74585e22			0.545936
$487$		−	8.68662e22i		−	1.24410i	−0.782978	−	0.622049i	$-0.786301\pi$
$487$		−	8.68662e22i		−	1.24410i	0.782978	−	0.622049i	$-0.213699\pi$
$488$		−	1.23670e23i		−	1.74058i
$489$	−1.00329e22			−0.138771
$490$	−4.35246e22	−	7.54774e22i	−0.591654	−	1.02601i
$491$	1.69753e22			0.226790			0.113395	−	0.993550i	$-0.463827\pi$
$491$	1.69753e22			0.226790			0.113395	+	0.993550i	$0.463827\pi$
$492$			7.33775e21i			0.0963517i
$493$		−	1.40802e21i		−	0.0181723i
$494$	−7.35130e22			−0.932578
$495$	−7.65007e22	+	4.41147e22i	−0.953940	+	0.550097i
$496$	2.15210e22			0.263796
$497$			1.10039e23i			1.32592i
$498$		−	1.71059e21i		−	0.0202627i
$499$	−8.59451e22			−1.00084			−0.500422	−	0.865781i	$-0.666822\pi$
$499$	−8.59451e22			−1.00084			−0.500422	+	0.865781i	$0.666822\pi$
$500$	−5.74366e19	+	3.68271e22i	−0.000657573	+	0.421621i
$501$	1.63858e21			0.0184437
$502$		−	8.36573e21i		−	0.0925811i
$503$			8.57709e22i			0.933281i	0.884447	+	0.466640i	$0.154536\pi$
$503$			8.57709e22i			0.933281i	−0.884447	+	0.466640i	$0.845464\pi$
$504$	1.50409e23			1.60922
$505$	5.13007e22	−	2.95829e22i	0.539693	−	0.311218i
$506$	1.18758e23			1.22852
$507$		−	2.23585e22i		−	0.227444i
$508$			4.25382e22i			0.425537i
$509$	−1.19520e23			−1.17582			−0.587908	−	0.808928i	$-0.700048\pi$
$509$	−1.19520e23			−1.17582			−0.587908	+	0.808928i	$0.700048\pi$
$510$	3.09300e21	+	5.36366e21i	0.0299249	+	0.0518937i
$511$	6.36666e22			0.605806
$512$			7.95213e22i			0.744199i
$513$		−	4.95764e22i		−	0.456328i
$514$	8.16808e22			0.739492
$515$	−3.99259e22	−	6.92368e22i	−0.355544	−	0.616561i
$516$	1.19732e22			0.104879
$517$		−	4.81096e22i		−	0.414536i
$518$			1.62411e22i			0.137661i
$519$	6.01320e22			0.501398
$520$	−1.55895e23	+	8.98982e22i	−1.27881	+	0.737433i
$521$	2.19068e23			1.76791			0.883953	−	0.467576i	$-0.154872\pi$
$521$	2.19068e23			1.76791			0.883953	+	0.467576i	$0.154872\pi$
$522$		−	5.41282e21i		−	0.0429759i
$523$		−	1.41671e23i		−	1.10667i	−0.832959	−	0.553334i	$-0.813355\pi$
$523$		−	1.41671e23i		−	1.10667i	0.832959	−	0.553334i	$-0.186645\pi$
$524$	8.32767e22			0.640040
$525$	−2.78758e22	+	4.81665e22i	−0.210801	+	0.364243i
$526$	−9.46684e22			−0.704411
$527$			2.69187e22i			0.197090i
$528$		−	1.73129e22i		−	0.124733i
$529$	−1.21896e23			−0.864206
$530$	6.99828e22	−	4.03561e22i	0.488255	−	0.281556i
$531$	−2.93149e22			−0.201273
$532$		−	8.96172e22i		−	0.605540i
$533$			1.78297e23i			1.18567i
$534$	2.28789e21			0.0149739
$535$	−1.53476e22	−	2.66147e22i	−0.0988628	−	0.171441i
$536$	−1.34998e23			−0.855910
$537$			1.35770e22i			0.0847270i
$538$			4.86478e22i			0.298823i
$539$	−3.04732e23			−1.84252
$540$	−1.79805e22	−	3.11805e22i	−0.107017	−	0.185582i
$541$	−8.41450e22			−0.493005			−0.246503	−	0.969142i	$-0.579281\pi$
$541$	−8.41450e22			−0.493005			−0.246503	+	0.969142i	$0.579281\pi$
$542$		−	2.75951e22i		−	0.159161i
$543$			1.24389e22i			0.0706290i
$544$	−4.15764e22			−0.232411
$545$	2.84714e23	−	1.64183e23i	1.56689	−	0.903560i
$546$	−8.06527e22			−0.437000
$547$		−	3.89693e22i		−	0.207889i	−0.994583	−	0.103944i	$-0.966854\pi$
$547$		−	3.89693e22i		−	0.207889i	0.994583	−	0.103944i	$-0.0331464\pi$
$548$		−	2.18280e22i		−	0.114651i
$549$	2.89734e23			1.49842
$550$	−1.52928e23	−	8.85054e22i	−0.778763	−	0.450699i
$551$	−1.08743e22			−0.0545272
$552$			7.86767e22i			0.388476i
$553$			1.82538e23i			0.887543i
$554$	−3.37398e22			−0.161551
$555$	5.47255e21	−	3.15579e21i	0.0258047	−	0.0148805i
$556$	−4.12896e22			−0.191736
$557$		−	2.32989e23i		−	1.06553i	−0.846263	−	0.532766i	$-0.821153\pi$
$557$		−	2.32989e23i		−	1.06553i	0.846263	−	0.532766i	$-0.178847\pi$
$558$			1.03483e23i			0.466100i
$559$	2.90933e23			1.29060
$560$	7.32481e22	+	1.27022e23i	0.320036	+	0.554984i
$561$	2.16552e22			0.0931918
$562$		−	1.85929e23i		−	0.788113i
$563$		−	9.12208e22i		−	0.380866i	−0.981700	−	0.190433i	$-0.939011\pi$
$563$		−	9.12208e22i		−	0.380866i	0.981700	−	0.190433i	$-0.0609892\pi$
$564$	9.45268e21			0.0388761
$565$	1.44295e23	+	2.50227e23i	0.584574	+	1.01373i
$566$	1.89254e23			0.755275
$567$			3.24209e23i			1.27458i
$568$		−	2.31460e23i		−	0.896425i
$569$	−9.35509e22			−0.356939			−0.178469	−	0.983945i	$-0.557115\pi$
$569$	−9.35509e22			−0.356939			−0.178469	+	0.983945i	$0.557115\pi$
$570$	4.14243e22	−	2.38876e22i	0.155711	−	0.0897919i
$571$	−4.28288e23			−1.58609			−0.793047	−	0.609161i	$-0.791506\pi$
$571$	−4.28288e23			−1.58609			−0.793047	+	0.609161i	$0.791506\pi$
$572$			1.86669e23i			0.681094i
$573$			8.98383e22i			0.322959i
$574$	2.98168e23			1.05611
$575$	3.38605e23	+	1.95963e23i	1.18173	+	0.683909i
$576$	−2.68261e23			−0.922500
$577$			2.90787e23i			0.985329i	0.870219	+	0.492664i	$0.163977\pi$
$577$			2.90787e23i			0.985329i	−0.870219	+	0.492664i	$0.836023\pi$
$578$		−	2.07363e23i		−	0.692380i
$579$	−1.48392e23			−0.488252
$580$	−6.83927e21	+	3.94392e21i	−0.0221754	+	0.0127876i
$581$	5.06706e22			0.161904
$582$		−	4.75907e22i		−	0.149857i
$583$		−	2.82548e23i		−	0.876818i
$584$	−1.33918e23			−0.409571
$585$	−2.10614e23	−	3.65233e23i	−0.634838	−	1.10089i
$586$	−3.35948e23			−0.998028
$587$		−	1.26868e23i		−	0.371473i	−0.982600	−	0.185737i	$-0.940533\pi$
$587$		−	1.26868e23i		−	0.371473i	0.982600	−	0.185737i	$-0.0594671\pi$
$588$		−	5.98743e22i		−	0.172796i
$589$	2.07897e23			0.591382
$590$	−2.93009e22	−	5.08117e22i	−0.0821560	−	0.142469i
$591$	1.51799e23			0.419541
$592$		−	1.66445e22i		−	0.0453458i
$593$		−	1.32480e23i		−	0.355784i	−0.984050	−	0.177892i	$-0.943072\pi$
$593$		−	1.32480e23i		−	0.355784i	0.984050	−	0.177892i	$-0.0569278\pi$
$594$	1.72692e23			0.457181
$595$	−1.58880e23	+	9.16195e22i	−0.414645	+	0.239108i
$596$	−5.29477e22			−0.136224
$597$		−	9.62780e21i		−	0.0244200i
$598$			5.66979e23i			1.41777i
$599$	−5.93521e23			−1.46321			−0.731607	−	0.681727i	$-0.761229\pi$
$599$	−5.93521e23			−1.46321			−0.731607	+	0.681727i	$0.761229\pi$
$600$	5.86346e22	−	1.01315e23i	0.142518	−	0.246256i
$601$	−1.72671e21			−0.00413797			−0.00206898	−	0.999998i	$-0.500659\pi$
$601$	−1.72671e21			−0.00413797			−0.00206898	+	0.999998i	$0.500659\pi$
$602$		−	4.86530e23i		−	1.14958i
$603$		−	3.16276e23i		−	0.736832i
$604$	1.98764e23			0.456588
$605$	−1.52898e23	+	8.81698e22i	−0.346323	+	0.199710i
$606$	−5.58260e22			−0.124686
$607$		−	2.08633e23i		−	0.459492i	−0.973251	−	0.229746i	$-0.926210\pi$
$607$		−	2.08633e23i		−	0.459492i	0.973251	−	0.229746i	$-0.0737896\pi$
$608$			3.21101e23i			0.697366i
$609$	−1.19304e22			−0.0255511
$610$	2.89596e23	+	5.02198e23i	0.611630	+	1.06065i
$611$	2.29687e23			0.478395
$612$		−	5.71823e22i		−	0.117456i
$613$		−	1.08017e23i		−	0.218816i	−0.993997	−	0.109408i	$-0.965105\pi$
$613$		−	1.08017e23i		−	0.218816i	0.993997	−	0.109408i	$-0.0348954\pi$
$614$	−5.23209e23			−1.04531
$615$	−5.79367e22	−	1.00470e23i	−0.114160	−	0.197969i
$616$	1.05257e24			2.04557
$617$			9.73966e23i			1.86690i	0.358714	+	0.933448i	$0.383215\pi$
$617$			9.73966e23i			1.86690i	−0.358714	+	0.933448i	$0.616785\pi$
$618$			7.53442e22i			0.142445i
$619$	3.73326e23			0.696174			0.348087	−	0.937462i	$-0.386831\pi$
$619$	3.73326e23			0.696174			0.348087	+	0.937462i	$0.386831\pi$
$620$	1.30754e23	−	7.54004e22i	0.240506	−	0.138690i
$621$	−3.82364e23			−0.693743
$622$			3.95008e23i			0.706948i
$623$			6.77711e22i			0.119645i
$624$	8.26562e22			0.143948
$625$	−2.89989e23	−	5.04697e23i	−0.498198	−	0.867063i
$626$	5.50744e23			0.933400
$627$		−	1.67246e23i		−	0.279629i
$628$			9.10802e22i			0.150234i
$629$	2.08191e22			0.0338791
$630$	−6.10782e23	+	3.52212e23i	−0.980599	+	0.565470i
$631$	1.00811e24			1.59683			0.798417	−	0.602105i	$-0.205671\pi$
$631$	1.00811e24			1.59683			0.798417	+	0.602105i	$0.205671\pi$
$632$		−	3.83955e23i		−	0.600047i
$633$			2.83356e23i			0.436919i
$634$	−3.13037e23			−0.476252
$635$	−3.35869e23	−	5.82441e23i	−0.504189	−	0.874330i
$636$	5.55156e22			0.0822299
$637$		−	1.45486e24i		−	2.12636i
$638$		−	3.78791e22i		−	0.0546291i
$639$	5.42265e23			0.771711
$640$	8.07968e21	+	1.40112e22i	0.0113466	+	0.0196764i
$641$	−9.24099e23			−1.28064			−0.640318	−	0.768110i	$-0.721197\pi$
$641$	−9.24099e23			−1.28064			−0.640318	+	0.768110i	$0.721197\pi$
$642$			2.89624e22i			0.0396084i
$643$			1.41354e24i			1.90772i	0.300245	+	0.953862i	$0.402932\pi$
$643$			1.41354e24i			1.90772i	−0.300245	+	0.953862i	$0.597068\pi$
$644$	−6.91185e23			−0.920586
$645$	−1.63940e23	+	9.45372e22i	−0.215490	+	0.124264i
$646$	1.57590e23			0.204434
$647$			9.10189e23i			1.16532i	0.812716	+	0.582660i	$0.197988\pi$
$647$			9.10189e23i			1.16532i	−0.812716	+	0.582660i	$0.802012\pi$
$648$		−	6.81949e23i		−	0.861717i
$649$	−2.05147e23			−0.255850
$650$	4.22547e23	−	7.30118e23i	0.520129	−	0.898731i
$651$	2.28088e23			0.277118
$652$			1.85396e23i			0.222329i
$653$		−	9.48371e23i		−	1.12258i	−0.827620	−	0.561288i	$-0.810306\pi$
$653$		−	9.48371e23i		−	1.12258i	0.827620	−	0.561288i	$-0.189694\pi$
$654$	−3.09829e23			−0.362002
$655$	−1.14024e24	+	6.57528e23i	−1.31506	+	0.758338i
$656$	−3.05574e23			−0.347884
$657$		−	3.13744e23i		−	0.352590i
$658$		−	3.84107e23i		−	0.426121i
$659$	−1.24301e23			−0.136128			−0.0680641	−	0.997681i	$-0.521682\pi$
$659$	−1.24301e23			−0.136128			−0.0680641	+	0.997681i	$0.521682\pi$
$660$	−6.06572e22	−	1.05188e23i	−0.0655781	−	0.113721i
$661$	−4.05632e23			−0.432932			−0.216466	−	0.976290i	$-0.569453\pi$
$661$	−4.05632e23			−0.432932			−0.216466	+	0.976290i	$0.569453\pi$
$662$			5.08267e23i			0.535548i
$663$			1.03387e23i			0.107548i
$664$	−1.06582e23			−0.109460
$665$	7.07591e23	+	1.22706e24i	0.717461	+	1.24417i
$666$	8.00348e22			0.0801213
$667$			8.38696e22i			0.0828963i
$668$		−	3.02792e22i		−	0.0295491i
$669$	3.92748e23			0.378436
$670$	5.48202e23	−	3.16125e23i	0.521561	−	0.300762i
$671$	2.02757e24			1.90473
$672$			3.52286e23i			0.326781i
$673$		−	1.59557e24i		−	1.46147i	−0.682664	−	0.730733i	$-0.739179\pi$
$673$		−	1.59557e24i		−	1.46147i	0.682664	−	0.730733i	$-0.260821\pi$
$674$	−1.88998e23			−0.170942
$675$	4.92384e23	+	2.84961e23i	0.439766	+	0.254509i
$676$	−4.13160e23			−0.364394
$677$			3.21368e23i			0.279897i	0.990159	+	0.139949i	$0.0446938\pi$
$677$			3.21368e23i			0.279897i	−0.990159	+	0.139949i	$0.955306\pi$
$678$		−	2.72299e23i		−	0.234204i
$679$	1.40971e24			1.19740
$680$	3.34193e23	−	1.92715e23i	0.280332	−	0.161655i
$681$	−4.19234e23			−0.347301
$682$			7.24179e23i			0.592486i
$683$			6.20239e23i			0.501168i	0.968095	+	0.250584i	$0.0806226\pi$
$683$			6.20239e23i			0.501168i	−0.968095	+	0.250584i	$0.919377\pi$
$684$	−4.41627e23			−0.352435
$685$	1.72347e23	+	2.98873e23i	0.135842	+	0.235568i
$686$	−8.70713e23			−0.677829
$687$		−	6.08115e23i		−	0.467577i
$688$			4.98616e23i			0.378673i
$689$	1.34895e24			1.01189
$690$	−1.84237e23	−	3.19491e23i	−0.136508	−	0.236723i
$691$	−2.58392e24			−1.89111			−0.945553	−	0.325468i	$-0.894478\pi$
$691$	−2.58392e24			−1.89111			−0.945553	+	0.325468i	$0.894478\pi$
$692$		−	1.11117e24i		−	0.803302i
$693$			2.46597e24i			1.76098i
$694$	2.27470e23			0.160461
$695$	5.65345e23	−	3.26010e23i	0.393951	−	0.227175i
$696$	2.50948e22			0.0172745
$697$		−	3.82216e23i		−	0.259914i
$698$		−	8.53618e23i		−	0.573446i
$699$	4.17743e23			0.277238
$700$	8.90062e23	+	5.15112e23i	0.583562	+	0.337729i
$701$	−1.45739e24			−0.944002			−0.472001	−	0.881598i	$-0.656468\pi$
$701$	−1.45739e24			−0.944002			−0.472001	+	0.881598i	$0.656468\pi$
$702$			8.24475e23i			0.527609i
$703$		−	1.60789e23i		−	0.101657i
$704$	−1.87730e24			−1.17264
$705$	−1.29428e23	+	7.46355e22i	−0.0798767	+	0.0460615i
$706$	−7.22032e23			−0.440267
$707$		−	1.65366e24i		−	0.996277i
$708$		−	4.03077e22i		−	0.0239941i
$709$	−1.40022e24			−0.823572			−0.411786	−	0.911280i	$-0.635095\pi$
$709$	−1.40022e24			−0.823572			−0.411786	+	0.911280i	$0.635095\pi$
$710$	5.42007e23	+	9.39912e23i	0.314999	+	0.546249i
$711$	8.99533e23			0.516566
$712$		−	1.42552e23i		−	0.0808895i
$713$		−	1.60343e24i		−	0.899062i
$714$	1.72895e23			0.0957962
$715$	−1.47389e24	−	2.55591e24i	−0.806980	−	1.39941i
$716$	2.50887e23			0.135743
$717$		−	2.26888e23i		−	0.121310i
$718$		−	1.21107e24i		−	0.639897i
$719$	2.68849e24			1.40383			0.701913	−	0.712262i	$-0.252329\pi$
$719$	2.68849e24			1.40383			0.701913	+	0.712262i	$0.252329\pi$
$720$	6.25955e23	−	3.60961e23i	0.323011	−	0.186266i
$721$	−2.23182e24			−1.13818
$722$			2.91851e23i			0.147094i
$723$		−	6.55511e23i		−	0.326516i
$724$	2.29857e23			0.113156
$725$	6.25047e22	−	1.08002e23i	0.0304116	−	0.0525482i
$726$	1.66385e23			0.0800117
$727$			3.76032e24i			1.78724i	0.448825	+	0.893620i	$0.351843\pi$
$727$			3.76032e24i			1.78724i	−0.448825	+	0.893620i	$0.648157\pi$
$728$			5.02522e24i			2.36069i
$729$	1.30970e24			0.608116
$730$	5.43814e23	−	3.13595e23i	0.249578	−	0.143921i
$731$	−6.23674e23			−0.282918
$732$			3.98381e23i			0.178630i
$733$			7.16715e23i			0.317660i	0.987306	+	0.158830i	$0.0507722\pi$
$733$			7.16715e23i			0.317660i	−0.987306	+	0.158830i	$0.949228\pi$
$734$	1.69908e24			0.744384
$735$	4.72750e23	+	8.19811e23i	0.204734	+	0.355035i
$736$	2.47653e24			1.06019
$737$		−	2.21331e24i		−	0.936629i
$738$		−	1.46935e24i		−	0.614675i
$739$	−4.16628e24			−1.72294			−0.861471	−	0.507807i	$-0.830456\pi$
$739$	−4.16628e24			−1.72294			−0.861471	+	0.507807i	$0.830456\pi$
$740$	−5.83153e22	−	1.01126e23i	−0.0238404	−	0.0413424i
$741$	7.98475e23			0.322706
$742$		−	2.25586e24i		−	0.901321i
$743$			4.05156e24i			1.60036i	0.599761	+	0.800179i	$0.295262\pi$
$743$			4.05156e24i			1.60036i	−0.599761	+	0.800179i	$0.704738\pi$
$744$	−4.79766e23			−0.187353
$745$	7.24970e23	−	4.18059e23i	0.279893	−	0.161402i
$746$	2.33590e24			0.891608
$747$		−	2.49701e23i		−	0.0942313i
$748$		−	4.00163e23i		−	0.149305i
$749$	−8.57914e23			−0.316482
$750$	−8.55804e20	+	5.48723e23i	−0.000312143	+	0.200139i
$751$	2.96073e24			1.06772			0.533862	−	0.845571i	$-0.320740\pi$
$751$	2.96073e24			1.06772			0.533862	+	0.845571i	$0.320740\pi$
$752$			3.93649e23i			0.140365i
$753$			9.08659e22i			0.0320364i
$754$	1.80844e23			0.0630446
$755$	−2.72152e24	+	1.56938e24i	−0.938128	+	0.540978i
$756$	−1.00509e24			−0.342586
$757$			1.79219e24i			0.604046i	0.953301	+	0.302023i	$0.0976620\pi$
$757$			1.79219e24i			0.604046i	−0.953301	+	0.302023i	$0.902338\pi$
$758$		−	1.64992e24i		−	0.549888i
$759$	−1.28991e24			−0.425113
$760$	−1.48837e24	−	2.58102e24i	−0.485058	−	0.841155i
$761$	5.85997e23			0.188854			0.0944269	−	0.995532i	$-0.469898\pi$
$761$	5.85997e23			0.188854			0.0944269	+	0.995532i	$0.469898\pi$
$762$			6.33818e23i			0.201998i
$763$		−	9.17764e24i		−	2.89249i
$764$	1.66011e24			0.517420
$765$	4.51494e23	+	7.82951e23i	0.139165	+	0.241331i
$766$	5.98439e23			0.182421
$767$		−	9.79421e23i		−	0.295263i
$768$		−	8.90097e23i		−	0.265379i
$769$	−1.30761e23			−0.0385571			−0.0192785	−	0.999814i	$-0.506137\pi$
$769$	−1.30761e23			−0.0385571			−0.0192785	+	0.999814i	$0.506137\pi$
$770$	−4.27427e24	+	2.46479e24i	−1.24650	+	0.718801i
$771$	−8.87190e23			−0.255891
$772$			2.74212e24i			0.782239i
$773$		−	1.87689e24i		−	0.529559i	−0.964309	−	0.264779i	$-0.914701\pi$
$773$		−	1.87689e24i		−	0.529559i	0.964309	−	0.264779i	$-0.0852992\pi$
$774$	−2.39758e24			−0.669076
$775$	−1.19497e24	+	2.06479e24i	−0.329833	+	0.569918i
$776$	−2.96523e24			−0.809532
$777$		−	1.76405e23i		−	0.0476357i
$778$			5.13247e24i			1.37088i
$779$	−2.95191e24			−0.779892
$780$	5.02191e23	−	2.89592e23i	0.131240	−	0.0756803i
$781$	3.79479e24			0.980966
$782$		−	1.21543e24i		−	0.310795i
$783$			1.21959e23i			0.0308489i
$784$	2.49342e24			0.623891
$785$	−7.19142e23	−	1.24709e24i	−0.178001	−	0.308677i
$786$	1.24082e24			0.303821
$787$		−	1.68314e24i		−	0.407694i	−0.979003	−	0.203847i	$-0.934656\pi$
$787$		−	1.68314e24i		−	0.407694i	0.979003	−	0.203847i	$-0.0653445\pi$
$788$		−	2.80507e24i		−	0.672157i
$789$	1.02826e24			0.243751
$790$	8.99105e23	+	1.55917e24i	0.210853	+	0.365647i
$791$	8.06594e24			1.87135
$792$		−	5.18698e24i		−	1.19056i
$793$			9.68011e24i			2.19816i
$794$	−1.97165e24			−0.442950
$795$	−7.60130e23	+	4.38335e23i	−0.168954	+	0.0974283i
$796$	−1.77911e23			−0.0391238
$797$			5.71625e24i			1.24370i	0.783137	+	0.621849i	$0.213618\pi$
$797$			5.71625e24i			1.24370i	−0.783137	+	0.621849i	$0.786382\pi$
$798$		−	1.33529e24i		−	0.287444i
$799$	−4.92381e23			−0.104870
$800$	−3.18911e24	−	1.84566e24i	−0.672055	−	0.388944i
$801$	3.33971e23			0.0696358
$802$			6.34457e23i			0.130894i
$803$		−	2.19559e24i		−	0.448197i
$804$	4.34875e23			0.0878392
$805$	9.46383e24	−	5.45739e24i	1.89148	−	1.09074i
$806$	−3.45741e24			−0.683758
$807$		−	5.28397e23i		−	0.103403i
$808$			3.47834e24i			0.673560i
$809$	9.30965e24			1.78390			0.891951	−	0.452132i	$-0.149337\pi$
$809$	9.30965e24			1.78390			0.891951	+	0.452132i	$0.149337\pi$
$810$	1.59692e24	+	2.76926e24i	0.302802	+	0.525099i
$811$	2.24912e23			0.0422022			0.0211011	−	0.999777i	$-0.493283\pi$
$811$	2.24912e23			0.0422022			0.0211011	+	0.999777i	$0.493283\pi$
$812$			2.20461e23i			0.0409360i
$813$			2.99729e23i			0.0550756i
$814$	5.60086e23			0.101847
$815$	−1.46383e24	−	2.53848e24i	−0.263422	−	0.456808i
$816$	−1.77190e23			−0.0315554
$817$			4.81673e24i			0.848916i
$818$		−	5.44076e24i		−	0.948979i
$819$	−1.17731e25			−2.03226
$820$	−1.85657e24	+	1.07060e24i	−0.317171	+	0.182899i
$821$	−1.06174e25			−1.79515			−0.897575	−	0.440863i	$-0.854673\pi$
$821$	−1.06174e25			−1.79515			−0.897575	+	0.440863i	$0.854673\pi$
$822$		−	3.25237e23i		−	0.0544238i
$823$		−	1.28460e24i		−	0.212750i	−0.994326	−	0.106375i	$-0.966076\pi$
$823$		−	1.28460e24i		−	0.212750i	0.994326	−	0.106375i	$-0.0339244\pi$
$824$	4.69447e24			0.769494
$825$	1.66106e24	+	9.61317e23i	0.269480	+	0.155958i
$826$	−1.63789e24			−0.263000
$827$			4.75685e23i			0.0756001i	0.999285	+	0.0378000i	$0.0120350\pi$
$827$			4.75685e23i			0.0756001i	−0.999285	+	0.0378000i	$0.987965\pi$
$828$			3.40611e24i			0.535797i
$829$	3.03025e23			0.0471808			0.0235904	−	0.999722i	$-0.492490\pi$
$829$	3.03025e23			0.0471808			0.0235904	+	0.999722i	$0.492490\pi$
$830$	4.32808e23	−	2.49582e23i	0.0667008	−	0.0384635i
$831$	3.66471e23			0.0559025
$832$		−	8.96269e24i		−	1.35329i
$833$			3.11879e24i			0.466127i
$834$	−6.15214e23			−0.0910153
$835$	2.39075e23	+	4.14588e23i	0.0350106	+	0.0607130i
$836$	−3.09052e24			−0.448000
$837$		−	2.33164e24i		−	0.334576i
$838$			6.74613e23i			0.0958254i
$839$	−4.13529e24			−0.581473			−0.290736	−	0.956803i	$-0.593900\pi$
$839$	−4.13529e24			−0.581473			−0.290736	+	0.956803i	$0.593900\pi$
$840$	−1.63292e24	−	2.83169e24i	−0.227295	−	0.394160i
$841$	−7.23040e24			−0.996314
$842$		−	1.16383e24i		−	0.158758i
$843$			2.01950e24i			0.272715i
$844$	5.23610e24			0.699998
$845$	5.65706e24	−	3.26219e24i	0.748702	−	0.431744i
$846$	−1.89285e24			−0.248010
$847$			4.92860e24i			0.639315i
$848$			2.31190e24i			0.296896i
$849$	−2.05561e24			−0.261352
$850$	−9.05814e23	+	1.56516e24i	−0.114019	+	0.197014i
$851$	−1.24011e24			−0.154546
$852$			7.45609e23i			0.0919971i
$853$		−	9.48988e24i		−	1.15929i	−0.814868	−	0.579647i	$-0.803190\pi$
$853$		−	9.48988e24i		−	1.15929i	0.814868	−	0.579647i	$-0.196810\pi$
$854$	1.61881e25			1.95796
$855$	6.04684e24	−	3.48696e24i	0.724130	−	0.417575i
$856$	1.80456e24			0.213966
$857$		−	1.28981e25i		−	1.51422i	−0.653287	−	0.757111i	$-0.726610\pi$
$857$		−	1.28981e25i		−	1.51422i	0.653287	−	0.757111i	$-0.273390\pi$
$858$			2.78137e24i			0.323308i
$859$	−4.19527e24			−0.482856			−0.241428	−	0.970419i	$-0.577616\pi$
$859$	−4.19527e24			−0.482856			−0.241428	+	0.970419i	$0.577616\pi$
$860$	1.74694e24	+	3.02942e24i	0.199086	+	0.345242i
$861$	−3.23860e24			−0.365452
$862$			6.12190e24i			0.684029i
$863$			9.87014e24i			1.09202i	0.837778	+	0.546011i	$0.183854\pi$
$863$			9.87014e24i			1.09202i	−0.837778	+	0.546011i	$0.816146\pi$
$864$	3.60126e24			0.394537
$865$	8.77347e24	+	1.52144e25i	0.951776	+	1.65050i
$866$	−5.80054e24			−0.623113
$867$			2.25231e24i			0.239588i
$868$		−	4.21481e24i		−	0.443976i
$869$	6.29496e24			0.656637
$870$	−1.01905e23	+	5.87643e22i	−0.0105265	+	0.00607016i
$871$	1.05669e25			1.08092
$872$			1.93045e25i			1.95555i
$873$		−	6.94697e24i		−	0.696906i
$874$	−9.38697e24			−0.932563
$875$	−1.62541e25	−	2.53503e22i	−1.59917	−	0.00249411i
$876$	4.31395e23			0.0420329
$877$		−	3.25689e23i		−	0.0314272i	−0.999877	−	0.0157136i	$-0.994998\pi$
$877$		−	3.25689e23i		−	0.0314272i	0.999877	−	0.0157136i	$-0.00500200\pi$
$878$		−	1.20466e25i		−	1.15122i
$879$	3.64896e24			0.345354
$880$	4.38045e24	−	2.52602e24i	0.410597	−	0.236774i
$881$	−7.07076e24			−0.656404			−0.328202	−	0.944608i	$-0.606443\pi$
$881$	−7.07076e24			−0.656404			−0.328202	+	0.944608i	$0.606443\pi$
$882$			1.19895e25i			1.10235i
$883$		−	9.90137e24i		−	0.901632i	−0.892617	−	0.450816i	$-0.851133\pi$
$883$		−	9.90137e24i		−	0.901632i	0.892617	−	0.450816i	$-0.148867\pi$
$884$	1.91048e24			0.172305
$885$	3.18257e23	+	5.51900e23i	0.0284289	+	0.0492995i
$886$	6.18758e24			0.547437
$887$		−	1.40069e25i		−	1.22741i	−0.789534	−	0.613706i	$-0.789678\pi$
$887$		−	1.40069e25i		−	1.22741i	0.789534	−	0.613706i	$-0.210322\pi$
$888$			3.71055e23i			0.0322054i
$889$	−1.87747e25			−1.61402
$890$	3.33812e23	+	5.78874e23i	0.0284241	+	0.0492911i
$891$	1.11806e25			0.942984
$892$		−	7.25754e24i		−	0.606301i
$893$			3.80273e24i			0.314672i
$894$	−7.88919e23			−0.0646642
$895$	−3.43519e24	+	1.98093e24i	−0.278904	+	0.160832i
$896$	4.51646e23			0.0363229
$897$		−	6.15834e24i		−	0.490601i
$898$			6.37671e24i			0.503208i
$899$	−5.11432e23			−0.0399789
$900$	2.53844e24	−	4.38616e24i	0.196564	−	0.339643i
$901$	−2.89175e24			−0.221820
$902$		−	1.02825e25i		−	0.781349i
$903$			5.28453e24i			0.397796i
$904$	−1.69661e25			−1.26518
$905$	−3.14724e24	+	1.81488e24i	−0.232497	+	0.134071i
$906$	2.96158e24			0.216738
$907$		−	1.08843e25i		−	0.789111i	−0.918872	−	0.394555i	$-0.870899\pi$
$907$		−	1.08843e25i		−	0.789111i	0.918872	−	0.394555i	$-0.129101\pi$
$908$			7.74697e24i			0.556419i
$909$	−8.14910e24			−0.579851
$910$	−1.17675e25	−	2.04064e25i	−0.829532	−	1.43852i
$911$	8.75509e24			0.611441			0.305720	−	0.952121i	$-0.401103\pi$
$911$	8.75509e24			0.611441			0.305720	+	0.952121i	$0.401103\pi$
$912$			1.36847e24i			0.0946842i
$913$		−	1.74741e24i		−	0.119783i
$914$	2.03158e25			1.37972
$915$	−3.14550e24	−	5.45471e24i	−0.211646	−	0.367022i
$916$	−1.12373e25			−0.749116
$917$			3.67551e25i			2.42761i
$918$		−	1.76743e24i		−	0.115659i
$919$	1.70647e25			1.10641			0.553205	−	0.833045i	$-0.313405\pi$
$919$	1.70647e25			1.10641			0.553205	+	0.833045i	$0.313405\pi$
$920$	−1.99065e25	+	1.14792e25i	−1.27879	+	0.737421i
$921$	5.68292e24			0.361714
$922$		−	1.97178e24i		−	0.124350i
$923$			1.81173e25i			1.13208i
$924$	−3.39067e24			−0.209930
$925$	1.59693e24	+	9.24203e23i	0.0979673	+	0.0566973i
$926$	1.91896e25			1.16647
$927$			1.09982e25i			0.662438i
$928$		−	7.89917e23i		−	0.0471437i
$929$	7.46407e24			0.441410			0.220705	−	0.975341i	$-0.429164\pi$
$929$	7.46407e24			0.441410			0.220705	+	0.975341i	$0.429164\pi$
$930$	1.94824e24	−	1.12346e24i	0.114166	−	0.0658346i
$931$	2.40869e25			1.39865
$932$		−	7.71942e24i		−	0.444170i
$933$		−	4.29045e24i		−	0.244630i
$934$	−2.01032e25			−1.13584
$935$	3.15957e24	+	5.47911e24i	0.176901	+	0.306769i
$936$	2.47639e25			1.37396
$937$		−	1.93663e25i		−	1.06478i	−0.846499	−	0.532391i	$-0.821294\pi$
$937$		−	1.93663e25i		−	1.06478i	0.846499	−	0.532391i	$-0.178706\pi$
$938$		−	1.76710e25i		−	0.962804i
$939$	−5.98200e24			−0.322990
$940$	1.37918e24	+	2.39168e24i	0.0737962	+	0.127972i
$941$	−1.31358e25			−0.696536			−0.348268	−	0.937395i	$-0.613230\pi$
$941$	−1.31358e25			−0.696536			−0.348268	+	0.937395i	$0.613230\pi$
$942$			1.35709e24i			0.0713144i
$943$			2.27670e25i			1.18565i
$944$	1.67858e24			0.0866324
$945$	1.37619e25	−	7.93588e24i	0.703894	−	0.405905i
$946$	−1.67784e25			−0.850501
$947$		−	1.18757e25i		−	0.596602i	−0.954472	−	0.298301i	$-0.903580\pi$
$947$		−	1.18757e25i		−	0.596602i	0.954472	−	0.298301i	$-0.0964200\pi$
$948$			1.23685e24i			0.0615808i
$949$	1.04823e25			0.517242
$950$	1.20879e25	+	6.99573e24i	0.591154	+	0.342123i
$951$	3.40011e24			0.164800
$952$		−	1.07726e25i		−	0.517494i
$953$		−	1.47341e25i		−	0.701509i	−0.936468	−	0.350754i	$-0.885925\pi$
$953$		−	1.47341e25i		−	0.701509i	0.936468	−	0.350754i	$-0.114075\pi$
$954$	−1.11167e25			−0.524585
$955$	−2.27305e25	+	1.31077e25i	−1.06312	+	0.613054i
$956$	−4.19262e24			−0.194354
$957$			4.11431e23i			0.0189036i
$958$			2.42988e25i			1.10657i
$959$	9.63404e24			0.434861
$960$	2.91238e24	+	5.05044e24i	0.130299	+	0.225956i
$961$	−1.27725e25			−0.566404
$962$			2.67399e24i			0.117536i
$963$			4.22774e24i			0.184198i
$964$	−1.21131e25			−0.523119
$965$	−2.16510e25	−	3.75457e25i	−0.926820	−	1.60723i
$966$	−1.02986e25			−0.436993
$967$			1.06729e25i			0.448909i	0.974485	+	0.224455i	$0.0720600\pi$
$967$			1.06729e25i			0.448909i	−0.974485	+	0.224455i	$0.927940\pi$
$968$		−	1.03670e25i		−	0.432226i
$969$	−1.71169e24			−0.0707414
$970$	1.20412e25	−	6.94366e24i	0.493299	−	0.284465i
$971$	1.19457e25			0.485117			0.242559	−	0.970137i	$-0.422013\pi$
$971$	1.19457e25			0.485117			0.242559	+	0.970137i	$0.422013\pi$
$972$			7.51834e24i			0.302663i
$973$		−	1.82236e25i		−	0.727237i
$974$	−2.39173e25			−0.946151
$975$	−4.58957e24	+	7.93031e24i	−0.179983	+	0.310993i
$976$	−1.65903e25			−0.644955
$977$			1.83232e25i			0.706149i	0.935595	+	0.353075i	$0.114864\pi$
$977$			1.83232e25i			0.706149i	−0.935595	+	0.353075i	$0.885136\pi$
$978$			2.76240e24i			0.105537i
$979$	2.33714e24			0.0885180
$980$	1.51492e25	−	8.73588e24i	0.568810	−	0.328008i
$981$	−4.52268e25			−1.68348
$982$		−	4.67388e24i		−	0.172476i
$983$		−	4.53385e25i		−	1.65868i	−0.558746	−	0.829339i	$-0.688717\pi$
$983$		−	4.53385e25i		−	1.65868i	0.558746	−	0.829339i	$-0.311283\pi$
$984$	6.81216e24			0.247074
$985$	2.21480e25	+	3.84075e25i	0.796391	+	1.38105i
$986$	−3.87676e23			−0.0138202
$987$			4.17205e24i			0.147453i
$988$		−	1.47549e25i		−	0.517014i
$989$	3.71496e25			1.29058
$990$	1.21463e25	+	2.10633e25i	0.418355	+	0.725483i
$991$	3.20238e25			1.09357			0.546785	−	0.837273i	$-0.315851\pi$
$991$	3.20238e25			1.09357			0.546785	+	0.837273i	$0.315851\pi$
$992$			1.51017e25i			0.511303i
$993$		−	5.52063e24i		−	0.185319i
$994$	3.02976e25			1.00838
$995$	2.43599e24	−	1.40473e24i	0.0803857	−	0.0463550i
$996$	3.43336e23			0.0112335
$997$		−	2.62226e25i		−	0.850681i	−0.905033	−	0.425341i	$-0.860154\pi$
$997$		−	2.62226e25i		−	0.850681i	0.905033	−	0.425341i	$-0.139846\pi$
$998$			2.36637e25i			0.761154i
$999$	−1.80331e24			−0.0575126

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.18.b.a.4.3	✓	8
3.2	odd	2		45.18.b.b.19.6		8
4.3	odd	2		80.18.c.b.49.4		8
5.2	odd	4		25.18.a.f.1.6		8
5.3	odd	4		25.18.a.f.1.3		8
5.4	even	2	inner	5.18.b.a.4.6	yes	8
15.14	odd	2		45.18.b.b.19.3		8
20.19	odd	2		80.18.c.b.49.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.18.b.a.4.3	✓	8	1.1	even	1	trivial
5.18.b.a.4.6	yes	8	5.4	even	2	inner
25.18.a.f.1.3		8	5.3	odd	4
25.18.a.f.1.6		8	5.2	odd	4
45.18.b.b.19.3		8	15.14	odd	2
45.18.b.b.19.6		8	3.2	odd	2
80.18.c.b.49.4		8	4.3	odd	2
80.18.c.b.49.5		8	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-275.335i q^{2} +2990.60i q^{3} +55262.8 q^{4} +(-756669. + 436339. i) q^{5} +823415. q^{6} +2.43909e7i q^{7} -5.13044e7i q^{8} +1.20196e8 q^{9} +O(q^{10})\)	\(q-275.335i q^{2} +2990.60i q^{3} +55262.8 q^{4} +(-756669. + 436339. i) q^{5} +823415. q^{6} +2.43909e7i q^{7} -5.13044e7i q^{8} +1.20196e8 q^{9} +(1.20139e8 + 2.08337e8i) q^{10} +8.41139e8 q^{11} +1.65269e8i q^{12} +4.01580e9i q^{13} +6.71566e9 q^{14} +(-1.30491e9 - 2.26289e9i) q^{15} -6.88248e9 q^{16} -8.60868e9i q^{17} -3.30943e10i q^{18} -6.64861e10 q^{19} +(-4.18157e10 + 2.41133e10i) q^{20} -7.29433e10 q^{21} -2.31595e11i q^{22} +5.12783e11i q^{23} +1.53431e11 q^{24} +(3.82157e11 - 6.60328e11i) q^{25} +1.10569e12 q^{26} +7.45665e11i q^{27} +1.34791e12i q^{28} +1.63558e11 q^{29} +(-6.23053e11 + 3.59288e11i) q^{30} -3.12692e12 q^{31} -4.82959e12i q^{32} +2.51551e12i q^{33} -2.37027e12 q^{34} +(-1.06427e13 - 1.84558e13i) q^{35} +6.64240e12 q^{36} +2.41839e12i q^{37} +1.83059e13i q^{38} -1.20096e13 q^{39} +(2.23861e13 + 3.88205e13i) q^{40} +4.43989e13 q^{41} +2.00838e13i q^{42} -7.24471e13i q^{43} +4.64837e13 q^{44} +(-9.09490e13 + 5.24464e13i) q^{45} +1.41187e14 q^{46} -5.71958e13i q^{47} -2.05827e13i q^{48} -3.62285e14 q^{49} +(-1.81811e14 - 1.05221e14i) q^{50} +2.57451e13 q^{51} +2.21925e14i q^{52} -3.35911e14i q^{53} +2.05308e14 q^{54} +(-6.36464e14 + 3.67021e14i) q^{55} +1.25136e15 q^{56} -1.98833e14i q^{57} -4.50331e13i q^{58} -2.43892e14 q^{59} +(-7.21132e13 - 1.25054e14i) q^{60} +2.41050e15 q^{61} +8.60950e14i q^{62} +2.93170e15i q^{63} -2.23185e15 q^{64} +(-1.75225e15 - 3.03863e15i) q^{65} +6.92606e14 q^{66} -2.63132e15i q^{67} -4.75740e14i q^{68} -1.53353e15 q^{69} +(-5.08153e15 + 2.93030e15i) q^{70} +4.51149e15 q^{71} -6.16661e15i q^{72} -2.61026e15i q^{73} +6.65866e14 q^{74} +(1.97477e15 + 1.14288e15i) q^{75} -3.67421e15 q^{76} +2.05161e16i q^{77} +3.30667e15i q^{78} +7.48386e15 q^{79} +(5.20776e15 - 3.00309e15i) q^{80} +1.32922e16 q^{81} -1.22245e16i q^{82} -2.07744e15i q^{83} -4.03105e15 q^{84} +(3.75630e15 + 6.51393e15i) q^{85} -1.99472e16 q^{86} +4.89135e14i q^{87} -4.31541e16i q^{88} +2.77854e15 q^{89} +(1.44403e16 + 2.50414e16i) q^{90} -9.79490e16 q^{91} +2.83378e16i q^{92} -9.35136e15i q^{93} -1.57480e16 q^{94} +(5.03080e16 - 2.90105e16i) q^{95} +1.44434e16 q^{96} -5.77968e16i q^{97} +9.97495e16i q^{98} +1.01102e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 579096 q^{4} + 379200 q^{5} + 357816 q^{6} - 234916344 q^{9}+O(q^{10}) \) 8 * q - 579096 * q^4 + 379200 * q^5 + 357816 * q^6 - 234916344 * q^9	\( 8 q - 579096 q^{4} + 379200 q^{5} + 357816 q^{6} - 234916344 q^{9} + 329570200 q^{10} + 463296576 q^{11} - 29937907992 q^{14} + 30646226400 q^{15} + 30848001568 q^{16} - 20615713280 q^{19} - 47558579400 q^{20} - 75039699024 q^{21} + 1768741136160 q^{24} - 1789249435000 q^{25} - 838901194224 q^{26} - 4079017824720 q^{29} + 2416984007400 q^{30} + 11329328658496 q^{31} - 36406243632832 q^{34} + 4019663899200 q^{35} + 59729752432728 q^{36} + 40318460422272 q^{39} - 209747532172000 q^{40} + 97217252847456 q^{41} - 116357853210912 q^{44} - 366841998003600 q^{45} + 10\!\cdots\!36 q^{46}+ \cdots - 56\!\cdots\!68 q^{99}+O(q^{100}) \) 8 * q - 579096 * q^4 + 379200 * q^5 + 357816 * q^6 - 234916344 * q^9 + 329570200 * q^10 + 463296576 * q^11 - 29937907992 * q^14 + 30646226400 * q^15 + 30848001568 * q^16 - 20615713280 * q^19 - 47558579400 * q^20 - 75039699024 * q^21 + 1768741136160 * q^24 - 1789249435000 * q^25 - 838901194224 * q^26 - 4079017824720 * q^29 + 2416984007400 * q^30 + 11329328658496 * q^31 - 36406243632832 * q^34 + 4019663899200 * q^35 + 59729752432728 * q^36 + 40318460422272 * q^39 - 209747532172000 * q^40 + 97217252847456 * q^41 - 116357853210912 * q^44 - 366841998003600 * q^45 + 1081224261700136 * q^46 - 856574357621656 * q^49 - 1283266301910000 * q^50 + 2468309514424896 * q^51 - 3408409774777680 * q^54 - 2042713226757600 * q^55 + 8363016326678880 * q^56 - 1091409512240640 * q^59 - 11479379108104800 * q^60 + 8064731010774976 * q^61 - 3616160324265856 * q^64 - 11989509557901600 * q^65 + 27318846906958752 * q^66 - 12078989597365008 * q^69 - 13190931213697800 * q^70 + 25241492058140736 * q^71 - 29902523510328912 * q^74 + 3839235716880000 * q^75 + 20767634734678560 * q^76 + 3229852337730880 * q^79 + 1263407265391200 * q^80 - 49353541005202632 * q^81 + 101439947332382688 * q^84 + 25693702369787200 * q^85 - 165112838769552744 * q^86 + 92963987535626640 * q^89 + 206315814421823400 * q^90 - 225591670236809664 * q^91 + 162612564681867848 * q^94 + 204319715505252000 * q^95 - 654303222993538944 * q^96 - 56327331239952768 * q^99

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