LMFDB - Embedded newform 8.21.d.b.3.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8,21,Mod(3,8)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 21, names="a")

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

chi := DirichletCharacter("8.3");

S:= CuspForms(chi, 21);

N := Newforms(S);

Level:	$ N $	$=$	$ 8 = 2^{3} $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	8.d (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:	$20.2811012082$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 66008406614424 x^{16} + \cdots + 53\!\cdots\!00 $ x^18 + 66008406614424x^16 - 170362825164232872x^15 + 1756210031321623676418457398x^14 - 8143876994687623666322842711032x^13 + 24350477750271510634494454384791667990404x^12 - 150098892256302975432925342820456817156772440x^11 + 191202710428210659782696002203561503780870353303759377x^10 - 1295069212697340229160215370735662134952032297259046562056x^9 + 870944882856087336674875277000277878990405713083632292121165358076x^8 - 4812915841402167440171875831348280575634953635256498021616060003579520x^7 + 2268474737024234177226752378807914883078144887754356976399017987196241603311520x^6 - 4757172104321022064833287336478952531807855909655138781977813255912131556348455680x^5 + 3199222078336759259493497095495346495581808310744107378246303720899215796326992176238102400x^4 + 8929774272757329376425833321340788600302219356646171490279817057245825930569313705998374604800x^3 + 2186805491439153577309421324561832859804177633153493793273223699303415894069647268007263015677943481600x^2 + 13250359115341501288916746421398415873922554950681918855831714718905060696192946493864164248007740533504000x + 531754461748673811827664952573861209640978431708236170453755006606958174478016712983511620954972201107600928640000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{153}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.17
Root			$-1372.90 - 1.21540e6i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.21.d.b.3.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(979.944 - 297.130i) q^{2} -11837.6 q^{3} +(872004. - 582341. i) q^{4} +4.86160e6i q^{5} +(-1.16002e7 + 3.51730e6i) q^{6} +3.96260e8i q^{7} +(6.81484e8 - 8.29760e8i) q^{8} -3.34666e9 q^{9} +O(q^{10})$	\(q+(979.944 - 297.130i) q^{2} -11837.6 q^{3} +(872004. - 582341. i) q^{4} +4.86160e6i q^{5} +(-1.16002e7 + 3.51730e6i) q^{6} +3.96260e8i q^{7} +(6.81484e8 - 8.29760e8i) q^{8} -3.34666e9 q^{9} +(1.44453e9 + 4.76409e9i) q^{10} +2.78400e10 q^{11} +(-1.03224e10 + 6.89351e9i) q^{12} +1.92255e11i q^{13} +(1.17741e11 + 3.88312e11i) q^{14} -5.75496e10i q^{15} +(4.21269e11 - 1.01561e12i) q^{16} +1.00761e12 q^{17} +(-3.27953e12 + 9.94391e11i) q^{18} +9.04652e11 q^{19} +(2.83111e12 + 4.23933e12i) q^{20} -4.69076e12i q^{21} +(2.72817e13 - 8.27211e12i) q^{22} +5.92847e13i q^{23} +(-8.06712e12 + 9.82235e12i) q^{24} +7.17323e13 q^{25} +(5.71247e13 + 1.88399e14i) q^{26} +8.08914e13 q^{27} +(2.30758e14 + 3.45540e14i) q^{28} +4.75437e14i q^{29} +(-1.70997e13 - 5.63953e13i) q^{30} -5.26254e14i q^{31} +(1.11053e14 - 1.12041e15i) q^{32} -3.29559e14 q^{33} +(9.87399e14 - 2.99390e14i) q^{34} -1.92645e15 q^{35} +(-2.91830e15 + 1.94890e15i) q^{36} -5.41855e15i q^{37} +(8.86508e14 - 2.68799e14i) q^{38} -2.27584e15i q^{39} +(4.03396e15 + 3.31310e15i) q^{40} -1.00310e16 q^{41} +(-1.39376e15 - 4.59668e15i) q^{42} -2.73018e16 q^{43} +(2.42766e16 - 1.62124e16i) q^{44} -1.62701e16i q^{45} +(1.76153e16 + 5.80957e16i) q^{46} -5.52785e16i q^{47} +(-4.98681e15 + 1.20223e16i) q^{48} -7.72294e16 q^{49} +(7.02936e16 - 2.13138e16i) q^{50} -1.19276e16 q^{51} +(1.11958e17 + 1.67647e17i) q^{52} -1.63835e16i q^{53} +(7.92691e16 - 2.40353e16i) q^{54} +1.35347e17i q^{55} +(3.28800e17 + 2.70044e17i) q^{56} -1.07089e16 q^{57} +(1.41266e17 + 4.65901e17i) q^{58} -5.08001e17 q^{59} +(-3.35135e16 - 5.01834e16i) q^{60} -2.76180e17i q^{61} +(-1.56366e17 - 5.15700e17i) q^{62} -1.32614e18i q^{63} +(-2.24081e17 - 1.13094e18i) q^{64} -9.34666e17 q^{65} +(-3.22949e17 + 9.79217e16i) q^{66} -7.08470e17 q^{67} +(8.78638e17 - 5.86772e17i) q^{68} -7.01788e17i q^{69} +(-1.88782e18 + 5.72407e17i) q^{70} +2.20639e18i q^{71} +(-2.28069e18 + 2.77692e18i) q^{72} +8.31823e18 q^{73} +(-1.61001e18 - 5.30988e18i) q^{74} -8.49137e17 q^{75} +(7.88860e17 - 5.26816e17i) q^{76} +1.10319e19i q^{77} +(-6.76218e17 - 2.23019e18i) q^{78} +2.46057e18i q^{79} +(4.93747e18 + 2.04804e18i) q^{80} +1.07115e19 q^{81} +(-9.82981e18 + 2.98051e18i) q^{82} +1.22709e19 q^{83} +(-2.73162e18 - 4.09036e18i) q^{84} +4.89858e18i q^{85} +(-2.67543e19 + 8.11219e18i) q^{86} -5.62802e18i q^{87} +(1.89725e19 - 2.31005e19i) q^{88} +3.83975e19 q^{89} +(-4.83433e18 - 1.59438e19i) q^{90} -7.61829e19 q^{91} +(3.45239e19 + 5.16965e19i) q^{92} +6.22958e18i q^{93} +(-1.64249e19 - 5.41699e19i) q^{94} +4.39805e18i q^{95} +(-1.31460e18 + 1.32629e19i) q^{96} +2.89133e19 q^{97} +(-7.56804e19 + 2.29471e19i) q^{98} -9.31710e19 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9}+O(q^{10}) $ 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9	$ 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9} + 742754160 q^{10} + 27862395020 q^{11} - 212292734088 q^{12} - 431248136928 q^{14} - 958534870512 q^{16} + 4343925139172 q^{17} - 4517494524426 q^{18} - 360681653556 q^{19} - 32520172742880 q^{20} - 66275482922148 q^{22} + 22289322475152 q^{24} - 395727477008910 q^{25} + 154289718058128 q^{26} - 12\!\cdots\!64 q^{27}+ \cdots + 62\!\cdots\!84 q^{99}+O(q^{100}) $ 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9 + 742754160 * q^10 + 27862395020 * q^11 - 212292734088 * q^12 - 431248136928 * q^14 - 958534870512 * q^16 + 4343925139172 * q^17 - 4517494524426 * q^18 - 360681653556 * q^19 - 32520172742880 * q^20 - 66275482922148 * q^22 + 22289322475152 * q^24 - 395727477008910 * q^25 + 154289718058128 * q^26 - 1208398438889064 * q^27 - 394619539621440 * q^28 + 223250517248160 * q^30 - 2833814588985248 * q^32 + 4461969540487176 * q^33 - 939462769526748 * q^34 + 3615863153468160 * q^35 + 1560521174396700 * q^36 + 12905383833568412 * q^38 + 11813880412973760 * q^40 + 16990829756398820 * q^41 + 38127588900300480 * q^42 - 27498466356753396 * q^43 + 33178844343953144 * q^44 - 21739818881100192 * q^46 + 28364131397385312 * q^48 - 252965388018862638 * q^49 + 41705619584456530 * q^50 - 34182574557901800 * q^51 - 44583718369992480 * q^52 - 579400710808894920 * q^54 - 505574909383001472 * q^56 - 522453489061123704 * q^57 - 677523738697093680 * q^58 + 93112194700366220 * q^59 + 1631640690429240000 * q^60 + 1780090172849178240 * q^62 + 175441813011570240 * q^64 + 1575343920200472960 * q^65 + 8001047667731567880 * q^66 - 1452645642074335668 * q^67 + 1153770320813215592 * q^68 - 6151558949299572480 * q^70 - 5306529204268842936 * q^72 + 9882821313863175972 * q^73 - 5642095430673385488 * q^74 + 13414715768769378060 * q^75 - 8416781249057544840 * q^76 - 14599907290310144160 * q^78 - 22104885212702947200 * q^80 - 32315102667184036518 * q^81 + 10320950271478847652 * q^82 - 46425529968268557748 * q^83 + 17095266896298568320 * q^84 + 33555485282446075868 * q^86 + 32344350945394345872 * q^88 - 28075170672250840156 * q^89 - 33204348719592139440 * q^90 + 161045136122144660736 * q^91 - 932896292396925120 * q^92 - 107259275077774974528 * q^94 + 68580843917215697472 * q^96 + 127276645173366650724 * q^97 + 154837385163137764402 * q^98 + 62802542261652714084 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/8\mathbb{Z}\right)^\times$.

$n$	$5$	$7$
$\chi(n)$	$-1$	$-1$

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 $

$2$	979.944	−	297.130i	0.956976	−	0.290166i
$2$	979.944	−	297.130i	0.956976	−	0.290166i
$3$	−11837.6			−0.200471			−0.100235	−	0.994964i	$-0.531960\pi$
$3$	−11837.6			−0.200471			−0.100235	+	0.994964i	$0.531960\pi$
$4$	872004.	−	582341.i	0.831608	−	0.555364i
$5$			4.86160e6i			0.497827i	0.968526	+	0.248914i	$0.0800736\pi$
$5$			4.86160e6i			0.497827i	−0.968526	+	0.248914i	$0.919926\pi$
$6$	−1.16002e7	+	3.51730e6i	−0.191846	+	0.0581697i
$7$			3.96260e8i			1.40281i	0.712762	+	0.701406i	$0.247444\pi$
$7$			3.96260e8i			1.40281i	−0.712762	+	0.701406i	$0.752556\pi$
$8$	6.81484e8	−	8.29760e8i	0.634681	−	0.772774i
$9$	−3.34666e9			−0.959812
$10$	1.44453e9	+	4.76409e9i	0.144453	+	0.476409i
$11$	2.78400e10			1.07335			0.536677	−	0.843788i	$-0.319679\pi$
$11$	2.78400e10			1.07335			0.536677	+	0.843788i	$0.319679\pi$
$12$	−1.03224e10	+	6.89351e9i	−0.166713	+	0.111334i
$13$			1.92255e11i			1.39458i	0.716788	+	0.697291i	$0.245612\pi$
$13$			1.92255e11i			1.39458i	−0.716788	+	0.697291i	$0.754388\pi$
$14$	1.17741e11	+	3.88312e11i	0.407048	+	1.34246i
$15$		−	5.75496e10i		−	0.0997997i
$16$	4.21269e11	−	1.01561e12i	0.383142	−	0.923689i
$17$	1.00761e12			0.499807			0.249904	−	0.968271i	$-0.419601\pi$
$17$	1.00761e12			0.499807			0.249904	+	0.968271i	$0.419601\pi$
$18$	−3.27953e12	+	9.94391e11i	−0.918517	+	0.278505i
$19$	9.04652e11			0.147552			0.0737761	−	0.997275i	$-0.476495\pi$
$19$	9.04652e11			0.147552			0.0737761	+	0.997275i	$0.476495\pi$
$20$	2.83111e12	+	4.23933e12i	0.276475	+	0.413997i
$21$		−	4.69076e12i		−	0.281222i
$22$	2.72817e13	−	8.27211e12i	1.02717	−	0.311451i
$23$			5.92847e13i			1.43108i	0.698571	+	0.715541i	$0.253820\pi$
$23$			5.92847e13i			1.43108i	−0.698571	+	0.715541i	$0.746180\pi$
$24$	−8.06712e12	+	9.82235e12i	−0.127235	+	0.154918i
$25$	7.17323e13			0.752168
$26$	5.71247e13	+	1.88399e14i	0.404660	+	1.33458i
$27$	8.08914e13			0.392884
$28$	2.30758e14	+	3.45540e14i	0.779071	+	1.16659i
$29$			4.75437e14i			1.13009i	0.825060	+	0.565045i	$0.191141\pi$
$29$			4.75437e14i			1.13009i	−0.825060	+	0.565045i	$0.808859\pi$
$30$	−1.70997e13	−	5.63953e13i	−0.0289585	−	0.0955060i
$31$		−	5.26254e14i		−	0.642065i	−0.947068	−	0.321032i	$-0.895970\pi$
$31$		−	5.26254e14i		−	0.642065i	0.947068	−	0.321032i	$-0.104030\pi$
$32$	1.11053e14	−	1.12041e15i	0.0986351	−	0.995124i
$33$	−3.29559e14			−0.215176
$34$	9.87399e14	−	2.99390e14i	0.478304	−	0.145027i
$35$	−1.92645e15			−0.698358
$36$	−2.91830e15	+	1.94890e15i	−0.798187	+	0.533044i
$37$		−	5.41855e15i		−	1.12685i	−0.826167	−	0.563425i	$-0.809483\pi$
$37$		−	5.41855e15i		−	1.12685i	0.826167	−	0.563425i	$-0.190517\pi$
$38$	8.86508e14	−	2.68799e14i	0.141204	−	0.0428146i
$39$		−	2.27584e15i		−	0.279573i
$40$	4.03396e15	+	3.31310e15i	0.384708	+	0.315962i
$41$	−1.00310e16			−0.747318			−0.373659	−	0.927566i	$-0.621897\pi$
$41$	−1.00310e16			−0.747318			−0.373659	+	0.927566i	$0.621897\pi$
$42$	−1.39376e15	−	4.59668e15i	−0.0816011	−	0.269123i
$43$	−2.73018e16			−1.26330			−0.631651	−	0.775253i	$-0.717622\pi$
$43$	−2.73018e16			−1.26330			−0.631651	+	0.775253i	$0.717622\pi$
$44$	2.42766e16	−	1.62124e16i	0.892609	−	0.596102i
$45$		−	1.62701e16i		−	0.477821i
$46$	1.76153e16	+	5.80957e16i	0.415251	+	1.36951i
$47$		−	5.52785e16i		−	1.05094i	−0.850812	−	0.525470i	$-0.823889\pi$
$47$		−	5.52785e16i		−	1.05094i	0.850812	−	0.525470i	$-0.176111\pi$
$48$	−4.98681e15	+	1.20223e16i	−0.0768087	+	0.185172i
$49$	−7.72294e16			−0.967880
$50$	7.02936e16	−	2.13138e16i	0.719807	−	0.218253i
$51$	−1.19276e16			−0.100197
$52$	1.11958e17	+	1.67647e17i	0.774500	+	1.15975i
$53$		−	1.63835e16i		−	0.0936804i	−0.998902	−	0.0468402i	$-0.985085\pi$
$53$		−	1.63835e16i		−	0.0936804i	0.998902	−	0.0468402i	$-0.0149152\pi$
$54$	7.92691e16	−	2.40353e16i	0.375981	−	0.114002i
$55$			1.35347e17i			0.534345i
$56$	3.28800e17	+	2.70044e17i	1.08406	+	0.890338i
$57$	−1.07089e16			−0.0295799
$58$	1.41266e17	+	4.65901e17i	0.327913	+	1.08147i
$59$	−5.08001e17			−0.993904			−0.496952	−	0.867778i	$-0.665548\pi$
$59$	−5.08001e17			−0.993904			−0.496952	+	0.867778i	$0.665548\pi$
$60$	−3.35135e16	−	5.01834e16i	−0.0554251	−	0.0829942i
$61$		−	2.76180e17i		−	0.387164i	−0.981084	−	0.193582i	$-0.937990\pi$
$61$		−	2.76180e17i		−	0.387164i	0.981084	−	0.193582i	$-0.0620105\pi$
$62$	−1.56366e17	−	5.15700e17i	−0.186305	−	0.614441i
$63$		−	1.32614e18i		−	1.34643i
$64$	−2.24081e17	−	1.13094e18i	−0.194359	−	0.980930i
$65$	−9.34666e17			−0.694261
$66$	−3.22949e17	+	9.79217e16i	−0.205918	+	0.0624367i
$67$	−7.08470e17			−0.388663			−0.194332	−	0.980936i	$-0.562254\pi$
$67$	−7.08470e17			−0.388663			−0.194332	+	0.980936i	$0.562254\pi$
$68$	8.78638e17	−	5.86772e17i	0.415643	−	0.277575i
$69$		−	7.01788e17i		−	0.286890i
$70$	−1.88782e18	+	5.72407e17i	−0.668312	+	0.202640i
$71$			2.20639e18i			0.677795i	0.940823	+	0.338898i	$0.110054\pi$
$71$			2.20639e18i			0.677795i	−0.940823	+	0.338898i	$0.889946\pi$
$72$	−2.28069e18	+	2.77692e18i	−0.609174	+	0.741717i
$73$	8.31823e18			1.93554			0.967770	−	0.251835i	$-0.0810342\pi$
$73$	8.31823e18			1.93554			0.967770	+	0.251835i	$0.0810342\pi$
$74$	−1.61001e18	−	5.30988e18i	−0.326973	−	1.07837i
$75$	−8.49137e17			−0.150787
$76$	7.88860e17	−	5.26816e17i	0.122706	−	0.0819451i
$77$			1.10319e19i			1.50571i
$78$	−6.76218e17	−	2.23019e18i	−0.0811224	−	0.267544i
$79$			2.46057e18i			0.259875i	0.991522	+	0.129938i	$0.0414777\pi$
$79$			2.46057e18i			0.259875i	−0.991522	+	0.129938i	$0.958522\pi$
$80$	4.93747e18	+	2.04804e18i	0.459838	+	0.190739i
$81$	1.07115e19			0.881050
$82$	−9.82981e18	+	2.98051e18i	−0.715166	+	0.216846i
$83$	1.22709e19			0.790851			0.395425	−	0.918498i	$-0.370597\pi$
$83$	1.22709e19			0.790851			0.395425	+	0.918498i	$0.370597\pi$
$84$	−2.73162e18	−	4.09036e18i	−0.156181	−	0.233867i
$85$			4.89858e18i			0.248818i
$86$	−2.67543e19	+	8.11219e18i	−1.20895	+	0.366567i
$87$		−	5.62802e18i		−	0.226550i
$88$	1.89725e19	−	2.31005e19i	0.681238	−	0.829460i
$89$	3.83975e19			1.23141			0.615706	−	0.787976i	$-0.288871\pi$
$89$	3.83975e19			1.23141			0.615706	+	0.787976i	$0.288871\pi$
$90$	−4.83433e18	−	1.59438e19i	−0.138647	−	0.457263i
$91$	−7.61829e19			−1.95634
$92$	3.45239e19	+	5.16965e19i	0.794771	+	1.19010i
$93$			6.22958e18i			0.128715i
$94$	−1.64249e19	−	5.41699e19i	−0.304947	−	1.00572i
$95$			4.39805e18i			0.0734555i
$96$	−1.31460e18	+	1.32629e19i	−0.0197734	+	0.199493i
$97$	2.89133e19			0.392085			0.196043	−	0.980595i	$-0.437191\pi$
$97$	2.89133e19			0.392085			0.196043	+	0.980595i	$0.437191\pi$
$98$	−7.56804e19	+	2.29471e19i	−0.926239	+	0.280846i
$99$	−9.31710e19			−1.03022
$100$	6.25508e19	−	4.17727e19i	0.625508	−	0.417727i
$101$		−	9.84179e19i		−	0.890964i	−0.895291	−	0.445482i	$-0.853032\pi$
$101$		−	9.84179e19i		−	0.890964i	0.895291	−	0.445482i	$-0.146968\pi$
$102$	−1.16884e19	+	3.54406e18i	−0.0958858	+	0.0290736i
$103$		−	2.53311e20i		−	1.88487i	−0.334385	−	0.942436i	$-0.608529\pi$
$103$		−	2.53311e20i		−	1.88487i	0.334385	−	0.942436i	$-0.391471\pi$
$104$	1.59525e20	+	1.31019e20i	1.07770	+	0.885115i
$105$	2.28046e19			0.140000
$106$	−4.86803e18	−	1.60549e19i	−0.0271828	−	0.0896499i
$107$	−3.48945e20			−1.77386			−0.886931	−	0.461902i	$-0.847167\pi$
$107$	−3.48945e20			−1.77386			−0.886931	+	0.461902i	$0.847167\pi$
$108$	7.05376e19	−	4.71064e19i	0.326726	−	0.218194i
$109$			4.36494e20i			1.84380i	0.387429	+	0.921899i	$0.373363\pi$
$109$			4.36494e20i			1.84380i	−0.387429	+	0.921899i	$0.626637\pi$
$110$	4.02156e19	+	1.32632e20i	0.155049	+	0.511356i
$111$			6.41426e19i			0.225900i
$112$	4.02444e20	+	1.66932e20i	1.29576	+	0.537477i
$113$	5.39787e20			1.59015			0.795075	−	0.606511i	$-0.207431\pi$
$113$	5.39787e20			1.59015			0.795075	+	0.606511i	$0.207431\pi$
$114$	−1.04941e19	+	3.18193e18i	−0.0283072	+	0.00858307i
$115$	−2.88218e20			−0.712432
$116$	2.76866e20	+	4.14583e20i	0.627611	+	0.939791i
$117$		−	6.43411e20i		−	1.33854i
$118$	−4.97813e20	+	1.50942e20i	−0.951143	+	0.288397i
$119$			3.99274e20i			0.701135i
$120$	−4.77523e19	−	3.92191e19i	−0.0771226	−	0.0633410i
$121$	1.02318e20			0.152089
$122$	−8.20614e19	−	2.70641e20i	−0.112342	−	0.370506i
$123$	1.18743e20			0.149815
$124$	−3.06459e20	−	4.58896e20i	−0.356579	−	0.533946i
$125$			8.12371e20i			0.872277i
$126$	−3.94037e20	−	1.29955e21i	−0.390689	−	1.28851i
$127$		−	1.10768e21i		−	1.01479i	−0.861713	−	0.507396i	$-0.830608\pi$
$127$		−	1.10768e21i		−	1.01479i	0.861713	−	0.507396i	$-0.169392\pi$
$128$	−5.55622e20	−	1.04167e21i	−0.470630	−	0.882331i
$129$	3.23188e20			0.253255
$130$	−9.15920e20	+	2.77717e20i	−0.664392	+	0.201451i
$131$	−2.07719e20			−0.139561			−0.0697804	−	0.997562i	$-0.522230\pi$
$131$	−2.07719e20			−0.139561			−0.0697804	+	0.997562i	$0.522230\pi$
$132$	−2.87377e20	+	1.91916e20i	−0.178942	+	0.119501i
$133$			3.58477e20i			0.206988i
$134$	−6.94261e20	+	2.10508e20i	−0.371942	+	0.112777i
$135$			3.93261e20i			0.195589i
$136$	6.86669e20	−	8.36073e20i	0.317218	−	0.386238i
$137$	7.35146e20			0.315622			0.157811	−	0.987469i	$-0.449556\pi$
$137$	7.35146e20			0.315622			0.157811	+	0.987469i	$0.449556\pi$
$138$	−2.08522e20	−	6.87713e20i	−0.0832456	−	0.274547i
$139$	3.82935e21			1.42225			0.711127	−	0.703064i	$-0.248185\pi$
$139$	3.82935e21			1.42225			0.711127	+	0.703064i	$0.248185\pi$
$140$	−1.67988e21	+	1.12185e21i	−0.580760	+	0.387843i
$141$			6.54364e20i			0.210683i
$142$	6.55584e20	+	2.16214e21i	0.196673	+	0.648634i
$143$			5.35239e21i			1.49688i
$144$	−1.40984e21	+	3.39889e21i	−0.367744	+	0.886568i
$145$	−2.31138e21			−0.562590
$146$	8.15140e21	−	2.47159e21i	1.85227	−	0.561628i
$147$	9.14209e20			0.194031
$148$	−3.15545e21	−	4.72500e21i	−0.625811	−	0.937097i
$149$		−	3.97915e21i		−	0.737781i	−0.929473	−	0.368891i	$-0.879738\pi$
$149$		−	3.97915e21i		−	0.737781i	0.929473	−	0.368891i	$-0.120262\pi$
$150$	−8.32107e20	+	2.52304e20i	−0.144300	+	0.0437534i
$151$		−	3.56951e21i		−	0.579215i	−0.957146	−	0.289607i	$-0.906475\pi$
$151$		−	3.56951e21i		−	0.579215i	0.957146	−	0.289607i	$-0.0935247\pi$
$152$	6.16506e20	−	7.50644e20i	0.0936486	−	0.114024i
$153$	−3.37212e21			−0.479721
$154$	3.27790e21	+	1.08106e22i	0.436907	+	1.44093i
$155$	2.55844e21			0.319637
$156$	−1.32531e21	−	1.98454e21i	−0.155265	−	0.232495i
$157$		−	8.79447e20i		−	0.0966525i	−0.998832	−	0.0483263i	$-0.984611\pi$
$157$		−	8.79447e20i		−	0.0966525i	0.998832	−	0.0483263i	$-0.0153887\pi$
$158$	7.31109e20	+	2.41122e21i	0.0754069	+	0.248694i
$159$			1.93941e20i			0.0187802i
$160$	5.44698e21	+	5.39896e20i	0.495400	+	0.0491033i
$161$	−2.34921e22			−2.00754
$162$	1.04967e22	−	3.18271e21i	0.843144	−	0.255651i
$163$	5.56367e21			0.420228			0.210114	−	0.977677i	$-0.432616\pi$
$163$	5.56367e21			0.420228			0.210114	+	0.977677i	$0.432616\pi$
$164$	−8.74707e21	+	5.84146e21i	−0.621475	+	0.415033i
$165$		−	1.60218e21i		−	0.107120i
$166$	1.20248e22	−	3.64604e21i	0.756826	−	0.229478i
$167$		−	1.51638e22i		−	0.898759i	−0.893341	−	0.449379i	$-0.851645\pi$
$167$		−	1.51638e22i		−	0.898759i	0.893341	−	0.449379i	$-0.148355\pi$
$168$	−3.89220e21	−	3.19667e21i	−0.217321	−	0.178487i
$169$	−1.79570e22			−0.944860
$170$	1.45552e21	+	4.80034e21i	0.0721984	+	0.238113i
$171$	−3.02756e21			−0.141622
$172$	−2.38073e22	+	1.58990e22i	−1.05057	+	0.701592i
$173$		−	4.65103e22i		−	1.93682i	−0.249370	−	0.968408i	$-0.580223\pi$
$173$		−	4.65103e22i		−	1.93682i	0.249370	−	0.968408i	$-0.419777\pi$
$174$	−1.67225e21	−	5.51515e21i	−0.0657370	−	0.216803i
$175$			2.84246e22i			1.05515i
$176$	1.17282e22	−	2.82745e22i	0.411247	−	0.991446i
$177$	6.01351e21			0.199249
$178$	3.76274e22	−	1.14091e22i	1.17843	−	0.357314i
$179$	2.15790e22			0.639001			0.319500	−	0.947586i	$-0.396485\pi$
$179$	2.15790e22			0.639001			0.319500	+	0.947586i	$0.396485\pi$
$180$	−9.47474e21	−	1.41876e22i	−0.265364	−	0.397359i
$181$			6.42549e22i			1.70263i	0.524654	+	0.851316i	$0.324195\pi$
$181$			6.42549e22i			1.70263i	−0.524654	+	0.851316i	$0.675805\pi$
$182$	−7.46550e22	+	2.26362e22i	−1.87217	+	0.567662i
$183$			3.26931e21i			0.0776149i
$184$	4.91921e22	+	4.04016e22i	1.10590	+	0.908281i
$185$	2.63428e22			0.560977
$186$	1.85099e21	+	6.10464e21i	0.0373487	+	0.123177i
$187$	2.80519e22			0.536470
$188$	−3.21910e22	−	4.82031e22i	−0.583654	−	0.873970i
$189$			3.20540e22i			0.551143i
$190$	1.30679e21	+	4.30985e21i	0.0213143	+	0.0702952i
$191$			6.88101e21i			0.106492i	0.998581	+	0.0532462i	$0.0169568\pi$
$191$			6.88101e21i			0.106492i	−0.998581	+	0.0532462i	$0.983043\pi$
$192$	2.65258e21	+	1.33875e22i	0.0389633	+	0.196648i
$193$	1.13196e23			1.57854			0.789272	−	0.614044i	$-0.210458\pi$
$193$	1.13196e23			1.57854			0.789272	+	0.614044i	$0.210458\pi$
$194$	2.83334e22	−	8.59101e21i	0.375216	−	0.113770i
$195$	1.10642e22			0.139179
$196$	−6.73443e22	+	4.49738e22i	−0.804897	+	0.537526i
$197$			1.59402e22i			0.181064i	0.995894	+	0.0905320i	$0.0288567\pi$
$197$			1.59402e22i			0.181064i	−0.995894	+	0.0905320i	$0.971143\pi$
$198$	−9.13024e22	+	2.76839e22i	−0.985894	+	0.298934i
$199$			5.88531e22i			0.604280i	0.953264	+	0.302140i	$0.0977010\pi$
$199$			5.88531e22i			0.604280i	−0.953264	+	0.302140i	$0.902299\pi$
$200$	4.88844e22	−	5.95206e22i	0.477387	−	0.581256i
$201$	8.38658e21			0.0779155
$202$	−2.92429e22	−	9.64440e22i	−0.258527	−	0.852632i
$203$	−1.88396e23			−1.58530
$204$	−1.04010e22	+	6.94596e21i	−0.0833243	+	0.0556456i
$205$		−	4.87667e22i		−	0.372036i
$206$	−7.52663e22	−	2.48231e23i	−0.546926	−	1.80378i
$207$		−	1.98406e23i		−	1.37357i
$208$	1.95256e23	+	8.09912e22i	1.28816	+	0.534324i
$209$	2.51856e22			0.158376
$210$	2.23472e22	−	6.77591e21i	0.133977	−	0.0406233i
$211$	−1.31609e23			−0.752424			−0.376212	−	0.926534i	$-0.622773\pi$
$211$	−1.31609e23			−0.752424			−0.376212	+	0.926534i	$0.622773\pi$
$212$	−9.54080e21	−	1.42865e22i	−0.0520267	−	0.0779053i
$213$		−	2.61183e22i		−	0.135878i
$214$	−3.41947e23	+	1.03682e23i	−1.69754	+	0.514714i
$215$		−	1.32730e23i		−	0.628906i
$216$	5.51262e22	−	6.71205e22i	0.249356	−	0.303611i
$217$	2.08533e23			0.900696
$218$	1.29695e23	+	4.27740e23i	0.535007	+	1.76447i
$219$	−9.84677e22			−0.388019
$220$	7.88181e22	+	1.18023e23i	0.296756	+	0.444365i
$221$			1.93718e23i			0.697022i
$222$	1.90587e22	+	6.28561e22i	0.0655485	+	0.216181i
$223$			2.37547e23i			0.781090i	0.920584	+	0.390545i	$0.127713\pi$
$223$			2.37547e23i			0.781090i	−0.920584	+	0.390545i	$0.872287\pi$
$224$	4.43973e23	+	4.40059e22i	1.39597	+	0.138366i
$225$	−2.40063e23			−0.721939
$226$	5.28961e23	−	1.60387e23i	1.52174	−	0.461407i
$227$	−3.05009e23			−0.839564			−0.419782	−	0.907625i	$-0.637893\pi$
$227$	−3.05009e23			−0.839564			−0.419782	+	0.907625i	$0.637893\pi$
$228$	−9.33820e21	+	6.23623e21i	−0.0245988	+	0.0164276i
$229$		−	2.03839e23i		−	0.513963i	−0.966416	−	0.256981i	$-0.917272\pi$
$229$		−	2.03839e23i		−	0.513963i	0.966416	−	0.256981i	$-0.0827279\pi$
$230$	−2.82438e23	+	8.56383e22i	−0.681781	+	0.206723i
$231$		−	1.30591e23i		−	0.301851i
$232$	3.94498e23	+	3.24003e23i	0.873304	+	0.717247i
$233$	1.55544e23			0.329834			0.164917	−	0.986307i	$-0.447264\pi$
$233$	1.55544e23			0.329834			0.164917	+	0.986307i	$0.447264\pi$
$234$	−1.91177e23	−	6.30507e23i	−0.388398	−	1.28095i
$235$	2.68742e23			0.523187
$236$	−4.42979e23	+	2.95830e23i	−0.826538	+	0.551978i
$237$		−	2.91272e22i		−	0.0520973i
$238$	1.18636e23	+	3.91266e23i	0.203446	+	0.670970i
$239$		−	1.59701e23i		−	0.262620i	−0.991341	−	0.131310i	$-0.958082\pi$
$239$		−	1.59701e23i		−	0.262620i	0.991341	−	0.131310i	$-0.0419184\pi$
$240$	−5.84477e22	−	2.42439e22i	−0.0921839	−	0.0382375i
$241$	−3.71550e22			−0.0562143			−0.0281072	−	0.999605i	$-0.508948\pi$
$241$	−3.71550e22			−0.0562143			−0.0281072	+	0.999605i	$0.508948\pi$
$242$	1.00266e23	−	3.04017e22i	0.145546	−	0.0441310i
$243$	−4.08849e23			−0.569509
$244$	−1.60831e23	−	2.40830e23i	−0.215017	−	0.321968i
$245$		−	3.75458e23i		−	0.481837i
$246$	1.16361e23	−	3.52820e22i	0.143370	−	0.0434713i
$247$			1.73924e23i			0.205774i
$248$	−4.36665e23	−	3.58634e23i	−0.496171	−	0.407506i
$249$	−1.45258e23			−0.158542
$250$	2.41380e23	+	7.96078e23i	0.253105	+	0.834749i
$251$	1.22841e24			1.23768			0.618838	−	0.785519i	$-0.287604\pi$
$251$	1.22841e24			1.23768			0.618838	+	0.785519i	$0.287604\pi$
$252$	−7.72268e23	−	1.15640e24i	−0.747761	−	1.11971i
$253$			1.65049e24i			1.53606i
$254$	−3.29125e23	−	1.08546e24i	−0.294458	−	0.971132i
$255$		−	5.79874e22i		−	0.0498806i
$256$	−8.53990e23	−	8.55689e23i	−0.706404	−	0.707809i
$257$	−1.13022e24			−0.899150			−0.449575	−	0.893242i	$-0.648425\pi$
$257$	−1.13022e24			−0.899150			−0.449575	+	0.893242i	$0.648425\pi$
$258$	3.16706e23	−	9.60287e22i	0.242359	−	0.0734859i
$259$	2.14715e24			1.58076
$260$	−8.15033e23	+	5.44295e23i	−0.577353	+	0.385568i
$261$		−	1.59112e24i		−	1.08467i
$262$	−2.03553e23	+	6.17196e22i	−0.133556	+	0.0404958i
$263$			1.73822e24i			1.09786i	0.835868	+	0.548930i	$0.184965\pi$
$263$			1.73822e24i			1.09786i	−0.835868	+	0.548930i	$0.815035\pi$
$264$	−2.24589e23	+	2.73455e23i	−0.136568	+	0.166282i
$265$	7.96501e22			0.0466367
$266$	1.06514e23	+	3.51287e23i	0.0600608	+	0.198083i
$267$	−4.54534e23			−0.246862
$268$	−6.17789e23	+	4.12571e23i	−0.323215	+	0.215849i
$269$		−	1.91524e24i		−	0.965383i	−0.875790	−	0.482691i	$-0.839659\pi$
$269$		−	1.91524e24i		−	0.965383i	0.875790	−	0.482691i	$-0.160341\pi$
$270$	1.16850e23	+	3.85374e23i	0.0567531	+	0.187174i
$271$			2.24447e23i			0.105056i	0.998619	+	0.0525280i	$0.0167279\pi$
$271$			2.24447e23i			0.105056i	−0.998619	+	0.0525280i	$0.983272\pi$
$272$	4.24475e23	−	1.02333e24i	0.191497	−	0.461667i
$273$	9.01821e23			0.392188
$274$	7.20402e23	−	2.18434e23i	0.302043	−	0.0915829i
$275$	1.99703e24			0.807342
$276$	−4.08680e23	−	6.11962e23i	−0.159328	−	0.238580i
$277$			3.22736e24i			1.21353i	0.794883	+	0.606763i	$0.207532\pi$
$277$			3.22736e24i			1.21353i	−0.794883	+	0.606763i	$0.792468\pi$
$278$	3.75255e24	−	1.13781e24i	1.36106	−	0.412689i
$279$			1.76119e24i			0.616261i
$280$	−1.31285e24	+	1.59849e24i	−0.443235	+	0.539673i
$281$	−4.13828e24			−1.34821			−0.674104	−	0.738636i	$-0.735470\pi$
$281$	−4.13828e24			−1.34821			−0.674104	+	0.738636i	$0.735470\pi$
$282$	1.94431e23	+	6.41240e23i	0.0611329	+	0.201618i
$283$	1.84766e24			0.560735			0.280368	−	0.959893i	$-0.409544\pi$
$283$	1.84766e24			0.560735			0.280368	+	0.959893i	$0.409544\pi$
$284$	1.28487e24	+	1.92398e24i	0.376423	+	0.563660i
$285$		−	5.20623e22i		−	0.0147257i
$286$	1.59035e24	+	5.24504e24i	0.434344	+	1.43248i
$287$		−	3.97488e24i		−	1.04835i
$288$	−3.71657e23	+	3.74963e24i	−0.0946711	+	0.955131i
$289$	−3.04896e24			−0.750193
$290$	−2.26502e24	+	6.86781e23i	−0.538385	+	0.163244i
$291$	−3.42264e23			−0.0786015
$292$	7.25353e24	−	4.84404e24i	1.60961	−	1.07493i
$293$		−	3.50629e22i		−	0.00751919i	−0.999993	−	0.00375960i	$-0.998803\pi$
$293$		−	3.50629e22i		−	0.00751919i	0.999993	−	0.00375960i	$-0.00119672\pi$
$294$	8.95874e23	−	2.71639e23i	0.185684	−	0.0563013i
$295$		−	2.46970e24i		−	0.494793i
$296$	−4.49610e24	−	3.69266e24i	−0.870800	−	0.715190i
$297$	2.25202e24			0.421704
$298$	−1.18232e24	−	3.89934e24i	−0.214079	−	0.706039i
$299$	−1.13978e25			−1.99576
$300$	−7.40451e23	+	4.94487e23i	−0.125396	+	0.0837419i
$301$		−	1.08186e25i		−	1.77217i
$302$	−1.06061e24	−	3.49792e24i	−0.168068	−	0.554295i
$303$			1.16503e24i			0.178612i
$304$	3.81102e23	−	9.18771e23i	0.0565335	−	0.136292i
$305$	1.34268e24			0.192741
$306$	−3.30449e24	+	1.00196e24i	−0.459081	+	0.139199i
$307$	−8.38314e24			−1.12726			−0.563628	−	0.826028i	$-0.690595\pi$
$307$	−8.38314e24			−1.12726			−0.563628	+	0.826028i	$0.690595\pi$
$308$	6.42432e24	+	9.61984e24i	0.836219	+	1.25216i
$309$			2.99859e24i			0.377861i
$310$	2.50712e24	−	7.60188e23i	0.305885	−	0.0927478i
$311$		−	7.29114e24i		−	0.861374i	−0.902501	−	0.430687i	$-0.858271\pi$
$311$		−	7.29114e24i		−	0.861374i	0.902501	−	0.430687i	$-0.141729\pi$
$312$	−1.88840e24	−	1.55094e24i	−0.216046	−	0.177440i
$313$	7.51935e24			0.833177			0.416588	−	0.909095i	$-0.363226\pi$
$313$	7.51935e24			0.833177			0.416588	+	0.909095i	$0.363226\pi$
$314$	−2.61310e23	−	8.61809e23i	−0.0280453	−	0.0924942i
$315$	6.44718e24			0.670292
$316$	1.43289e24	+	2.14563e24i	0.144325	+	0.216114i
$317$			7.43530e24i			0.725615i	0.931864	+	0.362807i	$0.118182\pi$
$317$			7.43530e24i			0.725615i	−0.931864	+	0.362807i	$0.881818\pi$
$318$	5.76257e22	+	1.90052e23i	0.00544936	+	0.0179722i
$319$			1.32362e25i			1.21299i
$320$	5.49815e24	−	1.08939e24i	0.488334	−	0.0967574i
$321$	4.13067e24			0.355607
$322$	−2.30210e25	+	6.98022e24i	−1.92117	+	0.582519i
$323$	9.11535e23			0.0737476
$324$	9.34048e24	−	6.23775e24i	0.732688	−	0.489303i
$325$			1.37909e25i			1.04896i
$326$	5.45209e24	−	1.65313e24i	0.402149	−	0.121936i
$327$		−	5.16704e24i		−	0.369627i
$328$	−6.83596e24	+	8.32332e24i	−0.474309	+	0.577508i
$329$	2.19046e25			1.47427
$330$	−4.76056e23	−	1.57005e24i	−0.0310827	−	0.102512i
$331$	−7.67940e22			−0.00486460			−0.00243230	−	0.999997i	$-0.500774\pi$
$331$	−7.67940e22			−0.00486460			−0.00243230	+	0.999997i	$0.500774\pi$
$332$	1.07002e25	−	7.14583e24i	0.657678	−	0.439210i
$333$			1.81340e25i			1.08156i
$334$	−4.50562e24	−	1.48597e25i	−0.260789	−	0.860091i
$335$		−	3.44430e24i		−	0.193487i
$336$	−4.76396e24	−	1.97607e24i	−0.259762	−	0.107748i
$337$	1.40411e25			0.743196			0.371598	−	0.928394i	$-0.378810\pi$
$337$	1.40411e25			0.743196			0.371598	+	0.928394i	$0.378810\pi$
$338$	−1.75969e25	+	5.33557e24i	−0.904209	+	0.274166i
$339$	−6.38978e24			−0.318778
$340$	2.85265e24	+	4.27158e24i	0.138184	+	0.206919i
$341$		−	1.46509e25i		−	0.689163i
$342$	−2.96684e24	+	8.99578e23i	−0.135529	+	0.0410940i
$343$			1.01557e24i			0.0450579i
$344$	−1.86058e25	+	2.26540e25i	−0.801794	+	0.976247i
$345$	3.41181e24			0.142822
$346$	−1.38196e25	−	4.55775e25i	−0.561998	−	1.85349i
$347$	4.44481e24			0.175614			0.0878068	−	0.996138i	$-0.472014\pi$
$347$	4.44481e24			0.175614			0.0878068	+	0.996138i	$0.472014\pi$
$348$	−3.27743e24	−	4.90766e24i	−0.125817	−	0.188400i
$349$		−	3.02572e25i		−	1.12869i	−0.825539	−	0.564346i	$-0.809129\pi$
$349$		−	3.02572e25i		−	1.12869i	0.825539	−	0.564346i	$-0.190871\pi$
$350$	8.44580e24	+	2.78545e25i	0.306168	+	1.00975i
$351$			1.55518e25i			0.547910i
$352$	3.09173e24	−	3.11922e25i	0.105870	−	1.06812i
$353$	−3.47498e25			−1.15666			−0.578329	−	0.815804i	$-0.696295\pi$
$353$	−3.47498e25			−1.15666			−0.578329	+	0.815804i	$0.696295\pi$
$354$	5.89290e24	−	1.78679e24i	0.190676	−	0.0578151i
$355$	−1.07266e25			−0.337425
$356$	3.34828e25	−	2.23605e25i	1.02405	−	0.683881i
$357$		−	4.72644e24i		−	0.140557i
$358$	2.11462e25	−	6.41177e24i	0.611509	−	0.185416i
$359$			1.38151e25i			0.388516i	0.980950	+	0.194258i	$0.0622300\pi$
$359$			1.38151e25i			0.388516i	−0.980950	+	0.194258i	$0.937770\pi$
$360$	−1.35003e25	−	1.10878e25i	−0.369247	−	0.303264i
$361$	−3.67716e25			−0.978228
$362$	1.90921e25	+	6.29662e25i	0.494045	+	1.62938i
$363$	−1.21120e24			−0.0304894
$364$	−6.64318e25	+	4.43644e25i	−1.62690	+	1.08648i
$365$			4.04399e25i			0.963565i
$366$	9.71409e23	+	3.20374e24i	0.0225212	+	0.0742756i
$367$		−	8.35212e25i		−	1.88424i	−0.335277	−	0.942120i	$-0.608830\pi$
$367$		−	8.35212e25i		−	1.88424i	0.335277	−	0.942120i	$-0.391170\pi$
$368$	6.02100e25	+	2.49749e25i	1.32188	+	0.548308i
$369$	3.35703e25			0.717285
$370$	2.58145e25	−	7.82724e24i	0.536842	−	0.162776i
$371$	6.49213e24			0.131416
$372$	3.62774e24	+	5.43222e24i	0.0714836	+	0.107040i
$373$		−	5.09653e25i		−	0.977656i	−0.872380	−	0.488828i	$-0.837425\pi$
$373$		−	5.09653e25i		−	0.977656i	0.872380	−	0.488828i	$-0.162575\pi$
$374$	2.74892e25	−	8.33504e24i	0.513389	−	0.155665i
$375$		−	9.61652e24i		−	0.174866i
$376$	−4.58679e25	−	3.76714e25i	−0.812139	−	0.667012i
$377$	−9.14051e25			−1.57600
$378$	9.52420e24	+	3.14111e25i	0.159923	+	0.527431i
$379$	2.21704e25			0.362562			0.181281	−	0.983431i	$-0.441976\pi$
$379$	2.21704e25			0.362562			0.181281	+	0.983431i	$0.441976\pi$
$380$	2.56117e24	+	3.83512e24i	0.0407945	+	0.0610862i
$381$			1.31123e25i			0.203436i
$382$	2.04455e24	+	6.74301e24i	0.0309005	+	0.101911i
$383$			1.03560e26i			1.52477i	0.647126	+	0.762383i	$0.275971\pi$
$383$			1.03560e26i			1.52477i	−0.647126	+	0.762383i	$0.724029\pi$
$384$	6.57722e24	+	1.23309e25i	0.0943474	+	0.176881i
$385$	−5.36326e25			−0.749586
$386$	1.10925e26	−	3.36338e25i	1.51063	−	0.458039i
$387$	9.13698e25			1.21253
$388$	2.52125e25	−	1.68374e25i	0.326061	−	0.217750i
$389$		−	7.82150e25i		−	0.985812i	−0.870082	−	0.492906i	$-0.835935\pi$
$389$		−	7.82150e25i		−	0.985812i	0.870082	−	0.492906i	$-0.164065\pi$
$390$	1.08423e25	−	3.28750e24i	0.133191	−	0.0403850i
$391$			5.97358e25i			0.715265i
$392$	−5.26306e25	+	6.40818e25i	−0.614295	+	0.747953i
$393$	2.45889e24			0.0279778
$394$	4.73631e24	+	1.56205e25i	0.0525386	+	0.173274i
$395$	−1.19623e25			−0.129373
$396$	−8.12455e25	+	5.42573e25i	−0.856737	+	0.572145i
$397$			6.91197e25i			0.710718i	0.934730	+	0.355359i	$0.115641\pi$
$397$			6.91197e25i			0.710718i	−0.934730	+	0.355359i	$0.884359\pi$
$398$	1.74870e25	+	5.76727e25i	0.175341	+	0.578282i
$399$		−	4.24350e24i		−	0.0414950i
$400$	3.02186e25	−	7.28518e25i	0.288187	−	0.694769i
$401$	9.67081e24			0.0899537			0.0449768	−	0.998988i	$-0.485679\pi$
$401$	9.67081e24			0.0899537			0.0449768	+	0.998988i	$0.485679\pi$
$402$	8.21837e24	−	2.49190e24i	0.0745633	−	0.0226084i
$403$	1.01175e26			0.895412
$404$	−5.73128e25	−	8.58208e25i	−0.494809	−	0.740933i
$405$			5.20750e25i			0.438611i
$406$	−1.84618e26	+	5.59782e25i	−1.51710	+	0.460001i
$407$		−	1.50853e26i		−	1.20951i
$408$	−8.12850e24	+	9.89708e24i	−0.0635929	+	0.0774293i
$409$	3.70175e25			0.282601			0.141301	−	0.989967i	$-0.454872\pi$
$409$	3.70175e25			0.282601			0.141301	+	0.989967i	$0.454872\pi$
$410$	−1.44900e25	−	4.77886e25i	−0.107952	−	0.356029i
$411$	−8.70235e24			−0.0632730
$412$	−1.47513e26	−	2.20888e26i	−1.04679	−	1.56747i
$413$		−	2.01300e26i		−	1.39426i
$414$	−5.89522e25	−	1.94426e26i	−0.398563	−	1.31447i
$415$			5.96560e25i			0.393707i
$416$	2.15404e26	+	2.13505e25i	1.38778	+	0.137555i
$417$	−4.53302e25			−0.285120
$418$	2.46804e25	−	7.48338e24i	0.151562	−	0.0459552i
$419$	−1.11094e26			−0.666118			−0.333059	−	0.942906i	$-0.608081\pi$
$419$	−1.11094e26			−0.666118			−0.333059	+	0.942906i	$0.608081\pi$
$420$	1.98857e25	−	1.32800e25i	0.116425	−	0.0777510i
$421$			2.76341e26i			1.57988i	0.613183	+	0.789941i	$0.289889\pi$
$421$			2.76341e26i			1.57988i	−0.613183	+	0.789941i	$0.710111\pi$
$422$	−1.28970e26	+	3.91051e25i	−0.720052	+	0.218328i
$423$			1.84998e26i			1.00870i
$424$	−1.35944e25	−	1.11651e25i	−0.0723938	−	0.0594572i
$425$	7.22781e25			0.375939
$426$	−7.76053e24	−	2.55945e25i	−0.0394271	−	0.130032i
$427$	1.09439e26			0.543118
$428$	−3.04282e26	+	2.03205e26i	−1.47516	+	0.985138i
$429$		−	6.33593e25i		−	0.300080i
$430$	−3.94382e25	−	1.30068e26i	−0.182487	−	0.601849i
$431$		−	2.45142e26i		−	1.10827i	−0.832427	−	0.554134i	$-0.813050\pi$
$431$		−	2.45142e26i		−	1.10827i	0.832427	−	0.554134i	$-0.186950\pi$
$432$	3.40771e25	−	8.21539e25i	0.150531	−	0.362903i
$433$	3.48165e26			1.50282			0.751409	−	0.659837i	$-0.229375\pi$
$433$	3.48165e26			1.50282			0.751409	+	0.659837i	$0.229375\pi$
$434$	2.04351e26	−	6.19615e25i	0.861944	−	0.261351i
$435$	2.73612e25			0.112783
$436$	2.54189e26	+	3.80625e26i	1.02398	+	1.53332i
$437$			5.36321e25i			0.211159i
$438$	−9.64928e25	+	2.92577e25i	−0.371325	+	0.112590i
$439$			1.66012e26i			0.624445i	0.950009	+	0.312223i	$0.101073\pi$
$439$			1.66012e26i			0.624445i	−0.950009	+	0.312223i	$0.898927\pi$
$440$	1.12306e26	+	9.22368e25i	0.412928	+	0.339139i
$441$	2.58460e26			0.928983
$442$	5.75593e25	+	1.89833e26i	0.202252	+	0.667034i
$443$	−5.32389e26			−1.82891			−0.914454	−	0.404689i	$-0.867380\pi$
$443$	−5.32389e26			−1.82891			−0.914454	+	0.404689i	$0.867380\pi$
$444$	3.73528e25	+	5.59326e25i	0.125457	+	0.187860i
$445$			1.86673e26i			0.613031i
$446$	7.05823e25	+	2.32783e26i	0.226646	+	0.747485i
$447$			4.71035e25i			0.147903i
$448$	4.48144e26	−	8.87943e25i	1.37606	−	0.272650i
$449$	−2.32273e26			−0.697487			−0.348743	−	0.937218i	$-0.613391\pi$
$449$	−2.32273e26			−0.697487			−0.348743	+	0.937218i	$0.613391\pi$
$450$	−2.35249e26	+	7.13300e25i	−0.690879	+	0.209482i
$451$	−2.79263e26			−0.802137
$452$	4.70697e26	−	3.14340e26i	1.32238	−	0.883112i
$453$			4.22544e25i			0.116115i
$454$	−2.98891e26	+	9.06272e25i	−0.803442	+	0.243613i
$455$		−	3.70370e26i		−	0.973918i
$456$	−7.29794e24	+	8.88581e24i	−0.0187738	+	0.0228586i
$457$	5.64579e25			0.142090			0.0710449	−	0.997473i	$-0.477367\pi$
$457$	5.64579e25			0.142090			0.0710449	+	0.997473i	$0.477367\pi$
$458$	−6.05665e25	−	1.99750e26i	−0.149134	−	0.491850i
$459$	8.15069e25			0.196366
$460$	−2.51328e26	+	1.67841e26i	−0.592464	+	0.395659i
$461$		−	4.09880e26i		−	0.945469i	−0.881205	−	0.472735i	$-0.843267\pi$
$461$		−	4.09880e26i		−	0.945469i	0.881205	−	0.472735i	$-0.156733\pi$
$462$	−3.88024e25	−	1.27972e26i	−0.0875869	−	0.288864i
$463$		−	4.96909e26i		−	1.09766i	−0.835935	−	0.548829i	$-0.815074\pi$
$463$		−	4.96909e26i		−	1.09766i	0.835935	−	0.548829i	$-0.184926\pi$
$464$	4.82857e26	+	2.00287e26i	1.04385	+	0.432985i
$465$	−3.02857e25			−0.0640779
$466$	1.52425e26	−	4.62169e25i	0.315643	−	0.0957064i
$467$	−6.59837e26			−1.33742			−0.668710	−	0.743523i	$-0.733153\pi$
$467$	−6.59837e26			−1.33742			−0.668710	+	0.743523i	$0.733153\pi$
$468$	−3.74685e26	−	5.61057e26i	−0.743374	−	1.11314i
$469$		−	2.80738e26i		−	0.545221i
$470$	2.63352e26	−	7.98512e25i	0.500677	−	0.151811i
$471$			1.04105e25i			0.0193760i
$472$	−3.46195e26	+	4.21519e26i	−0.630812	+	0.768063i
$473$	−7.60084e26			−1.35597
$474$	−8.65456e24	−	2.85430e25i	−0.0151169	−	0.0498559i
$475$	6.48928e25			0.110984
$476$	2.32514e26	+	3.48169e26i	0.389385	+	0.583069i
$477$			5.48300e25i			0.0899155i
$478$	−4.74519e25	−	1.56498e26i	−0.0762034	−	0.251321i
$479$			3.67403e26i			0.577813i	0.957357	+	0.288906i	$0.0932916\pi$
$479$			3.67403e26i			0.577813i	−0.957357	+	0.288906i	$0.906708\pi$
$480$	−6.44791e25	−	6.39107e24i	−0.0993131	−	0.00984376i
$481$	1.04174e27			1.57148
$482$	−3.64098e25	+	1.10399e25i	−0.0537958	+	0.0163115i
$483$	2.78090e26			0.402452
$484$	8.92216e25	−	5.95839e25i	0.126478	−	0.0844647i
$485$			1.40565e26i			0.195191i
$486$	−4.00649e26	+	1.21481e26i	−0.545007	+	0.165252i
$487$			8.25813e26i			1.10051i	0.834998	+	0.550253i	$0.185469\pi$
$487$			8.25813e26i			1.10051i	−0.834998	+	0.550253i	$0.814531\pi$
$488$	−2.29163e26	−	1.88212e26i	−0.299190	−	0.245725i
$489$	−6.58604e25			−0.0842434
$490$	−1.11560e26	−	3.67928e26i	−0.139813	−	0.461107i
$491$	3.79623e26			0.466163			0.233082	−	0.972457i	$-0.425119\pi$
$491$	3.79623e26			0.466163			0.233082	+	0.972457i	$0.425119\pi$
$492$	1.03544e26	−	6.91488e25i	0.124588	−	0.0832020i
$493$			4.79054e26i			0.564827i
$494$	5.16780e25	+	1.70436e26i	0.0597085	+	0.196921i
$495$		−	4.52960e26i		−	0.512871i
$496$	−5.34468e26	−	2.21695e26i	−0.593068	−	0.246002i
$497$	−8.74302e26			−0.950819
$498$	−1.42344e26	+	4.31603e25i	−0.151721	+	0.0460036i
$499$	1.58664e27			1.65757			0.828784	−	0.559568i	$-0.189033\pi$
$499$	1.58664e27			1.65757			0.828784	+	0.559568i	$0.189033\pi$
$500$	4.73077e26	+	7.08391e26i	0.484431	+	0.725392i
$501$			1.79503e26i			0.180175i
$502$	1.20378e27	−	3.64998e26i	1.18443	−	0.359131i
$503$		−	1.42295e27i		−	1.37249i	−0.727372	−	0.686244i	$-0.759258\pi$
$503$		−	1.42295e27i		−	1.37249i	0.727372	−	0.686244i	$-0.240742\pi$
$504$	−1.10038e27	−	9.03746e26i	−1.04049	−	0.854557i
$505$	4.78468e26			0.443547
$506$	4.90410e26	+	1.61739e27i	0.445712	+	1.46997i
$507$	2.12568e26			0.189417
$508$	−6.45047e26	−	9.65901e26i	−0.563579	−	0.843909i
$509$			9.54843e26i			0.818001i	0.912534	+	0.409001i	$0.134123\pi$
$509$			9.54843e26i			0.818001i	−0.912534	+	0.409001i	$0.865877\pi$
$510$	−1.72298e25	−	5.68244e25i	−0.0144737	−	0.0477346i
$511$			3.29618e27i			2.71520i
$512$	−1.09111e27	−	5.84781e26i	−0.881394	−	0.472382i
$513$	7.31786e25			0.0579710
$514$	−1.10755e27	+	3.35823e26i	−0.860466	+	0.260903i
$515$	1.23150e27			0.938342
$516$	2.81821e26	−	1.88205e26i	0.210609	−	0.140649i
$517$		−	1.53896e27i		−	1.12803i
$518$	2.10409e27	−	6.37983e26i	1.51275	−	0.458682i
$519$			5.50570e26i			0.388275i
$520$	−6.36960e26	+	7.75549e26i	−0.440635	+	0.536507i
$521$	−3.59622e26			−0.244044			−0.122022	−	0.992527i	$-0.538938\pi$
$521$	−3.59622e26			−0.244044			−0.122022	+	0.992527i	$0.538938\pi$
$522$	−4.72770e26	−	1.55921e27i	−0.314735	−	1.03801i
$523$	−4.12832e26			−0.269623			−0.134811	−	0.990871i	$-0.543043\pi$
$523$	−4.12832e26			−0.269623			−0.134811	+	0.990871i	$0.543043\pi$
$524$	−1.81132e26	+	1.20963e26i	−0.116060	+	0.0775071i
$525$		−	3.36479e26i		−	0.211526i
$526$	5.16477e26	+	1.70336e27i	0.318562	+	1.05063i
$527$		−	5.30258e26i		−	0.320908i
$528$	−1.38833e26	+	3.34702e26i	−0.0824430	+	0.198756i
$529$	−1.79852e27			−1.04800
$530$	7.80526e25	−	2.36664e25i	0.0446302	−	0.0135324i
$531$	1.70011e27			0.953961
$532$	2.08756e26	+	3.12593e26i	0.114954	+	0.172133i
$533$		−	1.92851e27i		−	1.04220i
$534$	−4.45418e26	+	1.35056e26i	−0.236241	+	0.0716309i
$535$		−	1.69643e27i		−	0.883077i
$536$	−4.82811e26	+	5.87860e26i	−0.246677	+	0.300349i
$537$	−2.55443e26			−0.128101
$538$	−5.69074e26	−	1.87682e27i	−0.280121	−	0.923849i
$539$	−2.15007e27			−1.03888
$540$	2.29012e26	+	3.42925e26i	0.108623	+	0.162653i
$541$			1.95235e27i			0.909045i	0.890735	+	0.454523i	$0.150190\pi$
$541$			1.95235e27i			0.909045i	−0.890735	+	0.454523i	$0.849810\pi$
$542$	6.66899e25	+	2.19946e26i	0.0304837	+	0.100536i
$543$		−	7.60623e26i		−	0.341327i
$544$	1.11898e26	−	1.12893e27i	0.0492985	−	0.497370i
$545$	−2.12206e27			−0.917894
$546$	8.83734e26	−	2.67958e26i	0.375314	−	0.113799i
$547$	−8.12726e26			−0.338899			−0.169450	−	0.985539i	$-0.554199\pi$
$547$	−8.12726e26			−0.338899			−0.169450	+	0.985539i	$0.554199\pi$
$548$	6.41050e26	−	4.28106e26i	0.262474	−	0.175285i
$549$			9.24281e26i			0.371604i
$550$	1.95698e27	−	5.93377e26i	0.772608	−	0.234263i
$551$			4.30105e26i			0.166747i
$552$	−5.82316e26	−	4.78257e26i	−0.221701	−	0.182084i
$553$	−9.75025e26			−0.364556
$554$	9.58944e26	+	3.16263e27i	0.352124	+	1.16132i
$555$	−3.11835e26			−0.112459
$556$	3.33921e27	−	2.22999e27i	1.18276	−	0.789868i
$557$		−	4.65269e27i		−	1.61865i	−0.587364	−	0.809323i	$-0.699834\pi$
$557$		−	4.65269e27i		−	1.61865i	0.587364	−	0.809323i	$-0.300166\pi$
$558$	5.23303e26	+	1.72587e27i	0.178818	+	0.589747i
$559$		−	5.24891e27i		−	1.76178i
$560$	−8.11556e26	+	1.95652e27i	−0.267571	+	0.645066i
$561$	−3.32066e26			−0.107546
$562$	−4.05529e27	+	1.22961e27i	−1.29020	+	0.391204i
$563$	−1.62681e27			−0.508455			−0.254228	−	0.967144i	$-0.581821\pi$
$563$	−1.62681e27			−0.508455			−0.254228	+	0.967144i	$0.581821\pi$
$564$	3.81063e26	+	5.70608e26i	0.117005	+	0.175205i
$565$			2.62423e27i			0.791621i
$566$	1.81060e27	−	5.48995e26i	0.536610	−	0.162706i
$567$			4.24454e27i			1.23595i
$568$	1.83077e27	+	1.50362e27i	0.523782	+	0.430184i
$569$	3.69001e27			1.03730			0.518651	−	0.854986i	$-0.326435\pi$
$569$	3.69001e27			1.03730			0.518651	+	0.854986i	$0.326435\pi$
$570$	−1.54693e25	−	5.10182e25i	−0.00427289	−	0.0140921i
$571$	3.77393e26			0.102431			0.0512156	−	0.998688i	$-0.483690\pi$
$571$	3.77393e26			0.102431			0.0512156	+	0.998688i	$0.483690\pi$
$572$	3.11692e27	+	4.66730e27i	0.831313	+	1.24482i
$573$		−	8.14546e25i		−	0.0213486i
$574$	−1.18105e27	−	3.89516e27i	−0.304194	−	1.00324i
$575$			4.25263e27i			1.07641i
$576$	7.49922e26	+	3.78485e27i	0.186548	+	0.941508i
$577$	5.96875e27			1.45923			0.729617	−	0.683856i	$-0.239698\pi$
$577$	5.96875e27			1.45923			0.729617	+	0.683856i	$0.239698\pi$
$578$	−2.98781e27	+	9.05936e26i	−0.717917	+	0.217680i
$579$	−1.33996e27			−0.316451
$580$	−2.01553e27	+	1.34601e27i	−0.467854	+	0.312442i
$581$			4.86245e27i			1.10941i
$582$	−3.35399e26	+	1.01697e26i	−0.0752198	+	0.0228075i
$583$		−	4.56118e26i		−	0.100552i
$584$	5.66874e27	−	6.90213e27i	1.22845	−	1.49574i
$585$	3.12801e27			0.666360
$586$	−1.04182e25	−	3.43596e25i	−0.00218181	−	0.00719569i
$587$	−5.25622e27			−1.08216			−0.541081	−	0.840970i	$-0.681985\pi$
$587$	−5.25622e27			−1.08216			−0.541081	+	0.840970i	$0.681985\pi$
$588$	7.97194e26	−	5.32381e26i	0.161358	−	0.107758i
$589$		−	4.76077e26i		−	0.0947380i
$590$	−7.33820e26	−	2.42016e27i	−0.143572	−	0.473505i
$591$		−	1.88694e26i		−	0.0362980i
$592$	−5.50312e27	−	2.28267e27i	−1.04086	−	0.431744i
$593$	2.01007e27			0.373821			0.186911	−	0.982377i	$-0.440153\pi$
$593$	2.01007e27			0.373821			0.186911	+	0.982377i	$0.440153\pi$
$594$	2.20685e27	−	6.69142e26i	0.403561	−	0.122364i
$595$	−1.94111e27			−0.349044
$596$	−2.31722e27	−	3.46983e27i	−0.409737	−	0.613545i
$597$		−	6.96678e26i		−	0.121140i
$598$	−1.11692e28	+	3.38662e27i	−1.90990	+	0.579102i
$599$		−	5.36055e27i		−	0.901448i	−0.892663	−	0.450724i	$-0.851166\pi$
$599$		−	5.36055e27i		−	0.901448i	0.892663	−	0.450724i	$-0.148834\pi$
$600$	−5.78673e26	+	7.04580e26i	−0.0957020	+	0.116525i
$601$	6.55184e25			0.0106566			0.00532830	−	0.999986i	$-0.498304\pi$
$601$	6.55184e25			0.0106566			0.00532830	+	0.999986i	$0.498304\pi$
$602$	−3.21453e27	−	1.06016e28i	−0.514225	−	1.69593i
$603$	2.37101e27			0.373044
$604$	−2.07867e27	−	3.11263e27i	−0.321675	−	0.481679i
$605$			4.97428e26i			0.0757141i
$606$	3.46165e26	+	1.14166e27i	0.0518271	+	0.170928i
$607$		−	8.75457e27i		−	1.28928i	−0.764485	−	0.644641i	$-0.777007\pi$
$607$		−	8.75457e27i		−	1.28928i	0.764485	−	0.644641i	$-0.222993\pi$
$608$	1.00465e26	−	1.01358e27i	0.0145538	−	0.146833i
$609$	2.23016e27			0.317806
$610$	1.31575e27	−	3.98949e26i	0.184448	−	0.0559267i
$611$	1.06276e28			1.46562
$612$	−2.94050e27	+	1.96372e27i	−0.398939	+	0.266419i
$613$			3.98007e27i			0.531234i	0.964079	+	0.265617i	$0.0855756\pi$
$613$			3.98007e27i			0.531234i	−0.964079	+	0.265617i	$0.914424\pi$
$614$	−8.21500e27	+	2.49088e27i	−1.07876	+	0.327091i
$615$			5.77279e26i			0.0745822i
$616$	9.15381e27	+	7.51805e27i	1.16358	+	0.955648i
$617$	−1.86653e27			−0.233445			−0.116722	−	0.993165i	$-0.537239\pi$
$617$	−1.86653e27			−0.233445			−0.116722	+	0.993165i	$0.537239\pi$
$618$	8.90971e26	+	2.93845e27i	0.109642	+	0.361605i
$619$	−1.35625e28			−1.64223			−0.821114	−	0.570764i	$-0.806647\pi$
$619$	−1.35625e28			−1.64223			−0.821114	+	0.570764i	$0.806647\pi$
$620$	2.23097e27	−	1.48988e27i	0.265813	−	0.177515i
$621$			4.79563e27i			0.562250i
$622$	−2.16642e27	−	7.14491e27i	−0.249941	−	0.824314i
$623$			1.52154e28i			1.72744i
$624$	−2.31135e27	−	9.58740e26i	−0.258238	−	0.107116i
$625$	2.89150e27			0.317924
$626$	7.36854e27	−	2.23422e27i	0.797330	−	0.241759i
$627$	−2.98136e26			−0.0317497
$628$	−5.12138e26	−	7.66881e26i	−0.0536773	−	0.0803770i
$629$		−	5.45978e27i		−	0.563208i
$630$	6.31787e27	−	1.91565e27i	0.641454	−	0.194496i
$631$			1.05880e28i			1.05808i	0.848597	+	0.529040i	$0.177448\pi$
$631$			1.05880e28i			1.05808i	−0.848597	+	0.529040i	$0.822552\pi$
$632$	2.04168e27	+	1.67684e27i	0.200825	+	0.164938i
$633$	1.55794e27			0.150839
$634$	2.20925e27	+	7.28618e27i	0.210549	+	0.694396i
$635$	5.38509e27			0.505191
$636$	1.12940e26	+	1.69118e26i	0.0104298	+	0.0156177i
$637$		−	1.48477e28i		−	1.34979i
$638$	3.93286e27	+	1.29707e28i	0.351967	+	1.16080i
$639$		−	7.38402e27i		−	0.650556i
$640$	5.06419e27	−	2.70121e27i	0.439248	−	0.234292i
$641$	−4.49180e27			−0.383566			−0.191783	−	0.981437i	$-0.561427\pi$
$641$	−4.49180e27			−0.383566			−0.191783	+	0.981437i	$0.561427\pi$
$642$	4.04783e27	−	1.22735e27i	0.340308	−	0.103185i
$643$	9.22634e27			0.763694			0.381847	−	0.924225i	$-0.375288\pi$
$643$	9.22634e27			0.763694			0.381847	+	0.924225i	$0.375288\pi$
$644$	−2.04852e28	+	1.36804e28i	−1.66948	+	1.11491i
$645$			1.57121e27i			0.126077i
$646$	8.93253e26	−	2.70844e26i	0.0705748	−	0.0213990i
$647$		−	9.33398e27i		−	0.726146i	−0.931761	−	0.363073i	$-0.881728\pi$
$647$		−	9.33398e27i		−	0.726146i	0.931761	−	0.363073i	$-0.118272\pi$
$648$	7.29972e27	−	8.88798e27i	0.559186	−	0.680852i
$649$	−1.41428e28			−1.06681
$650$	4.09769e27	+	1.35143e28i	0.304372	+	1.00383i
$651$	−2.46853e27			−0.180563
$652$	4.85154e27	−	3.23995e27i	0.349465	−	0.233380i
$653$			1.60220e28i			1.13654i	0.822842	+	0.568270i	$0.192387\pi$
$653$			1.60220e28i			1.13654i	−0.822842	+	0.568270i	$0.807613\pi$
$654$	−1.53528e27	−	5.06341e27i	−0.107253	−	0.353725i
$655$		−	1.00985e27i		−	0.0694772i
$656$	−4.22575e27	+	1.01876e28i	−0.286329	+	0.690290i
$657$	−2.78382e28			−1.85775
$658$	2.14653e28	−	6.50852e27i	1.41084	−	0.427783i
$659$	2.39029e28			1.54738			0.773688	−	0.633566i	$-0.218410\pi$
$659$	2.39029e28			1.54738			0.773688	+	0.633566i	$0.218410\pi$
$660$	−9.33016e26	−	1.39711e27i	−0.0594908	−	0.0890822i
$661$		−	1.77129e28i		−	1.11243i	−0.831037	−	0.556217i	$-0.812252\pi$
$661$		−	1.77129e28i		−	1.11243i	0.831037	−	0.556217i	$-0.187748\pi$
$662$	−7.52538e25	+	2.28178e25i	−0.00465531	+	0.00141154i
$663$		−	2.29315e27i		−	0.139732i
$664$	8.36240e27	−	1.01819e28i	0.501938	−	0.611149i
$665$	−1.74277e27			−0.103044
$666$	5.38816e27	+	1.77703e28i	0.313833	+	1.03503i
$667$	−2.81862e28			−1.61725
$668$	−8.83050e27	−	1.32229e28i	−0.499138	−	0.747415i
$669$		−	2.81198e27i		−	0.156586i
$670$	−1.02340e27	−	3.37522e27i	−0.0561434	−	0.185163i
$671$		−	7.68887e27i		−	0.415564i
$672$	−5.25557e27	−	5.20924e26i	−0.279851	−	0.0277384i
$673$	−2.07760e27			−0.108996			−0.0544981	−	0.998514i	$-0.517356\pi$
$673$	−2.07760e27			−0.108996			−0.0544981	+	0.998514i	$0.517356\pi$
$674$	1.37595e28	−	4.17204e27i	0.711221	−	0.215650i
$675$	5.80253e27			0.295515
$676$	−1.56586e28	+	1.04571e28i	−0.785753	+	0.524741i
$677$		−	6.05106e26i		−	0.0299188i	−0.999888	−	0.0149594i	$-0.995238\pi$
$677$		−	6.05106e26i		−	0.0299188i	0.999888	−	0.0149594i	$-0.00476191\pi$
$678$	−6.26162e27	+	1.89859e27i	−0.305063	+	0.0924986i
$679$			1.14572e28i			0.550022i
$680$	4.06465e27	+	3.33831e27i	0.192280	+	0.157920i
$681$	3.61057e27			0.168308
$682$	−4.35323e27	−	1.43571e28i	−0.199971	−	0.659512i
$683$	−2.09376e27			−0.0947809			−0.0473904	−	0.998876i	$-0.515090\pi$
$683$	−2.09376e27			−0.0947809			−0.0473904	+	0.998876i	$0.515090\pi$
$684$	−2.64004e27	+	1.76307e27i	−0.117774	+	0.0786519i
$685$			3.57398e27i			0.157126i
$686$	3.01757e26	+	9.95206e26i	0.0130743	+	0.0431193i
$687$			2.41296e27i			0.103034i
$688$	−1.15014e28	+	2.77279e28i	−0.484025	+	1.16690i
$689$	3.14981e27			0.130645
$690$	3.34338e27	−	1.01375e27i	0.136677	−	0.0414420i
$691$	2.96337e28			1.19400			0.597002	−	0.802240i	$-0.296358\pi$
$691$	2.96337e28			1.19400			0.597002	+	0.802240i	$0.296358\pi$
$692$	−2.70849e28	−	4.05572e28i	−1.07564	−	1.61067i
$693$		−	3.69199e28i		−	1.44520i
$694$	4.35566e27	−	1.32069e27i	0.168058	−	0.0509571i
$695$			1.86168e28i			0.708037i
$696$	−4.66991e27	−	3.83541e27i	−0.175072	−	0.143787i
$697$	−1.01073e28			−0.373515
$698$	−8.99033e27	−	2.96504e28i	−0.327508	−	1.08013i
$699$	−1.84127e27			−0.0661219
$700$	1.65528e28	+	2.47864e28i	0.585992	+	0.877471i
$701$			2.48058e28i			0.865713i	0.901463	+	0.432856i	$0.142494\pi$
$701$			2.48058e28i			0.865713i	−0.901463	+	0.432856i	$0.857506\pi$
$702$	4.62090e27	+	1.52399e28i	0.158985	+	0.524337i
$703$		−	4.90191e27i		−	0.166269i
$704$	−6.23843e27	−	3.14853e28i	−0.208616	−	1.05289i
$705$	−3.18126e27			−0.104884
$706$	−3.40528e28	+	1.03252e28i	−1.10689	+	0.335622i
$707$	3.89990e28			1.24986
$708$	5.24380e27	−	3.50191e27i	0.165697	−	0.110655i
$709$			3.39191e28i			1.05677i	0.849003	+	0.528387i	$0.177203\pi$
$709$			3.39191e28i			1.05677i	−0.849003	+	0.528387i	$0.822797\pi$
$710$	−1.05114e28	+	3.18718e27i	−0.322908	+	0.0979092i
$711$		−	8.23468e27i		−	0.249431i
$712$	2.61673e28	−	3.18607e28i	0.781554	−	0.951603i
$713$	3.11989e28			0.918847
$714$	−1.40437e27	−	4.63165e27i	−0.0407848	−	0.134510i
$715$	−2.60211e28			−0.745188
$716$	1.88170e28	−	1.25663e28i	0.531398	−	0.354878i
$717$			1.89047e27i			0.0526476i
$718$	4.10488e27	+	1.35380e28i	0.112734	+	0.371801i
$719$			4.82927e28i			1.30795i	0.756515	+	0.653977i	$0.226901\pi$
$719$			4.82927e28i			1.30795i	−0.756515	+	0.653977i	$0.773099\pi$
$720$	−1.65240e28	−	6.85409e27i	−0.441358	−	0.183073i
$721$	1.00377e29			2.64412
$722$	−3.60341e28	+	1.09259e28i	−0.936141	+	0.283848i
$723$	4.39826e26			0.0112693
$724$	3.74183e28	+	5.60305e28i	0.945580	+	1.41592i
$725$			3.41042e28i			0.850017i
$726$	−1.18690e27	+	3.59882e26i	−0.0291776	+	0.00884697i
$727$		−	3.90810e28i		−	0.947593i	−0.880634	−	0.473797i	$-0.842883\pi$
$727$		−	3.90810e28i		−	0.947593i	0.880634	−	0.473797i	$-0.157117\pi$
$728$	−5.19174e28	+	6.32135e28i	−1.24165	+	1.51181i
$729$	−3.25089e28			−0.766880
$730$	1.20159e28	+	3.96288e28i	0.279594	+	0.922109i
$731$	−2.75095e28			−0.631407
$732$	1.90385e27	+	2.85085e27i	0.0431045	+	0.0645451i
$733$			2.46670e28i			0.550905i	0.961315	+	0.275452i	$0.0888277\pi$
$733$			2.46670e28i			0.550905i	−0.961315	+	0.275452i	$0.911172\pi$
$734$	−2.48166e28	−	8.18461e28i	−0.546742	−	1.80317i
$735$			4.44452e27i			0.0965942i
$736$	6.64232e28	+	6.58376e27i	1.42410	+	0.141155i
$737$	−1.97238e28			−0.417173
$738$	3.28970e28	−	9.97474e27i	0.686424	−	0.208131i
$739$	−3.59103e28			−0.739221			−0.369611	−	0.929187i	$-0.620509\pi$
$739$	−3.59103e28			−0.739221			−0.369611	+	0.929187i	$0.620509\pi$
$740$	2.29710e28	−	1.53405e28i	0.466513	−	0.311546i
$741$		−	2.05884e27i		−	0.0412516i
$742$	6.36192e27	−	1.92900e27i	0.125762	−	0.0381324i
$743$		−	4.29533e28i		−	0.837739i	−0.908046	−	0.418869i	$-0.862426\pi$
$743$		−	4.29533e28i		−	0.837739i	0.908046	−	0.418869i	$-0.137574\pi$
$744$	5.16905e27	+	4.24536e27i	0.0994676	+	0.0816930i
$745$	1.93450e28			0.367288
$746$	−1.51433e28	−	4.99431e28i	−0.283682	−	0.935594i
$747$	−4.10664e28			−0.759068
$748$	2.44613e28	−	1.63357e28i	0.446133	−	0.297936i
$749$		−	1.38273e29i		−	2.48839i
$750$	−2.85735e27	−	9.42364e27i	−0.0507401	−	0.167343i
$751$			1.61560e28i			0.283096i	0.989931	+	0.141548i	$0.0452080\pi$
$751$			1.61560e28i			0.283096i	−0.989931	+	0.141548i	$0.954792\pi$
$752$	−5.61413e28	−	2.32872e28i	−0.970742	−	0.402660i
$753$	−1.45414e28			−0.248118
$754$	−8.95719e28	+	2.71592e28i	−1.50820	+	0.457302i
$755$	1.73535e28			0.288349
$756$	1.86664e28	+	2.79512e28i	0.306085	+	0.458335i
$757$			3.24624e28i			0.525317i	0.964889	+	0.262659i	$0.0845993\pi$
$757$			3.24624e28i			0.525317i	−0.964889	+	0.262659i	$0.915401\pi$
$758$	2.17258e28	−	6.58750e27i	0.346963	−	0.105203i
$759$		−	1.95378e28i		−	0.307934i
$760$	3.64933e27	+	2.99720e27i	0.0567645	+	0.0466208i
$761$	2.94459e27			0.0452042			0.0226021	−	0.999745i	$-0.492805\pi$
$761$	2.94459e27			0.0452042			0.0226021	+	0.999745i	$0.492805\pi$
$762$	3.89604e27	+	1.28493e28i	0.0590301	+	0.194683i
$763$	−1.72965e29			−2.58650
$764$	4.00710e27	+	6.00027e27i	0.0591420	+	0.0885599i
$765$		−	1.63939e28i		−	0.238818i
$766$	3.07707e28	+	1.01483e29i	0.442435	+	1.45916i
$767$		−	9.76658e28i		−	1.38608i
$768$	1.01092e28	+	1.01293e28i	0.141613	+	0.141895i
$769$	2.27487e28			0.314553			0.157277	−	0.987555i	$-0.449729\pi$
$769$	2.27487e28			0.314553			0.157277	+	0.987555i	$0.449729\pi$
$770$	−5.25569e28	+	1.59358e28i	−0.717336	+	0.217504i
$771$	1.33791e28			0.180253
$772$	9.87070e28	−	6.59184e28i	1.31273	−	0.876665i
$773$			4.97514e28i			0.653147i	0.945172	+	0.326573i	$0.105894\pi$
$773$			4.97514e28i			0.653147i	−0.945172	+	0.326573i	$0.894106\pi$
$774$	8.95373e28	−	2.71487e28i	1.16036	−	0.351835i
$775$		−	3.77494e28i		−	0.482940i
$776$	1.97040e28	−	2.39911e28i	0.248849	−	0.302993i
$777$	−2.54171e28			−0.316895
$778$	−2.32400e28	−	7.66463e28i	−0.286049	−	0.943399i
$779$	−9.07456e27			−0.110268
$780$	9.64802e27	−	6.44313e27i	0.115742	−	0.0772949i
$781$			6.14259e28i			0.727514i
$782$	1.77493e28	+	5.85377e28i	0.207546	+	0.684492i
$783$			3.84588e28i			0.443995i
$784$	−3.25344e28	+	7.84347e28i	−0.370836	+	0.894021i
$785$	4.27552e27			0.0481163
$786$	2.40958e27	−	7.30611e26i	0.0267741	−	0.00811821i
$787$	1.07675e29			1.18132			0.590662	−	0.806919i	$-0.298867\pi$
$787$	1.07675e29			1.18132			0.590662	+	0.806919i	$0.298867\pi$
$788$	9.28264e27	+	1.38999e28i	0.100556	+	0.150574i
$789$		−	2.05763e28i		−	0.220089i
$790$	−1.17224e28	+	3.55436e27i	−0.123807	+	0.0375396i
$791$			2.13896e29i			2.23068i
$792$	−6.34946e28	+	7.73096e28i	−0.653860	+	0.796125i
$793$	5.30971e28			0.539931
$794$	2.05375e28	+	6.77335e28i	0.206226	+	0.680140i
$795$	−9.42864e26			−0.00934928
$796$	3.42725e28	+	5.13201e28i	0.335595	+	0.502524i
$797$			5.01741e27i			0.0485173i	0.999706	+	0.0242586i	$0.00772252\pi$
$797$			5.01741e27i			0.0485173i	−0.999706	+	0.0242586i	$0.992277\pi$
$798$	−1.26087e27	−	4.15839e27i	−0.0120404	−	0.0397097i
$799$		−	5.56991e28i		−	0.525267i
$800$	7.96611e27	−	8.03696e28i	0.0741902	−	0.748500i
$801$	−1.28503e29			−1.18192
$802$	9.47685e27	−	2.87349e27i	0.0860836	−	0.0261015i
$803$	2.31580e29			2.07752
$804$	7.31313e27	−	4.88385e27i	0.0647952	−	0.0432715i
$805$		−	1.14209e29i		−	0.999408i
$806$	9.91459e28	−	3.00621e28i	0.856888	−	0.259818i
$807$			2.26718e28i			0.193531i
$808$	−8.16632e28	−	6.70702e28i	−0.688514	−	0.565478i
$809$	3.71760e28			0.309583			0.154792	−	0.987947i	$-0.450529\pi$
$809$	3.71760e28			0.309583			0.154792	+	0.987947i	$0.450529\pi$
$810$	1.54730e28	+	5.10306e28i	0.127270	+	0.419740i
$811$	−1.24910e29			−1.01482			−0.507408	−	0.861706i	$-0.669396\pi$
$811$	−1.24910e29			−1.01482			−0.507408	+	0.861706i	$0.669396\pi$
$812$	−1.64282e29	+	1.09711e29i	−1.31835	+	0.880420i
$813$		−	2.65691e27i		−	0.0210606i
$814$	−4.48228e28	−	1.47827e29i	−0.350958	−	1.15747i
$815$			2.70483e28i			0.209201i
$816$	−5.02475e27	+	1.21138e28i	−0.0383896	+	0.0925505i
$817$	−2.46987e28			−0.186403
$818$	3.62751e28	−	1.09990e28i	0.270443	−	0.0820012i
$819$	2.54958e29			1.87771
$820$	−2.83988e28	−	4.25247e28i	−0.206615	−	0.309388i
$821$			8.98034e28i			0.645448i	0.946493	+	0.322724i	$0.104599\pi$
$821$			8.98034e28i			0.645448i	−0.946493	+	0.322724i	$0.895401\pi$
$822$	−8.52782e27	+	2.58573e27i	−0.0605508	+	0.0183597i
$823$		−	5.34245e28i		−	0.374751i	−0.982288	−	0.187375i	$-0.940002\pi$
$823$		−	5.34245e28i		−	0.374751i	0.982288	−	0.187375i	$-0.0599980\pi$
$824$	−2.10187e29	−	1.72627e29i	−1.45658	−	1.19629i
$825$	−2.36400e28			−0.161848
$826$	−5.98123e28	−	1.97263e29i	−0.404567	−	1.33427i
$827$	−8.05212e28			−0.538090			−0.269045	−	0.963128i	$-0.586708\pi$
$827$	−8.05212e28			−0.538090			−0.269045	+	0.963128i	$0.586708\pi$
$828$	−1.15540e29	−	1.73010e29i	−0.762830	−	1.14227i
$829$			1.27468e29i			0.831485i	0.909482	+	0.415742i	$0.136478\pi$
$829$			1.27468e29i			0.831485i	−0.909482	+	0.415742i	$0.863522\pi$
$830$	1.77256e28	+	5.84596e28i	0.114240	+	0.376769i
$831$		−	3.82041e28i		−	0.243276i
$832$	2.17428e29	−	4.30807e28i	1.36799	−	0.271050i
$833$	−7.78169e28			−0.483754
$834$	−4.44211e28	+	1.34690e28i	−0.272853	+	0.0827321i
$835$	7.37203e28			0.447427
$836$	2.19619e28	−	1.46666e28i	0.131706	−	0.0879561i
$837$		−	4.25695e28i		−	0.252257i
$838$	−1.08866e29	+	3.30094e28i	−0.637460	+	0.193285i
$839$			1.20820e29i			0.699067i	0.936924	+	0.349533i	$0.113660\pi$
$839$			1.20820e29i			0.699067i	−0.936924	+	0.349533i	$0.886340\pi$
$840$	1.55409e28	−	1.89223e28i	0.0888555	−	0.108189i
$841$	−4.90457e28			−0.277103
$842$	8.21092e28	+	2.70799e29i	0.458428	+	1.51191i
$843$	4.89873e28			0.270276
$844$	−1.14764e29	+	7.66416e28i	−0.625721	+	0.417869i
$845$		−	8.72998e28i		−	0.470377i
$846$	5.49685e28	+	1.81288e29i	0.292692	+	0.965306i
$847$			4.05444e28i			0.213352i
$848$	−1.66392e28	−	6.90188e27i	−0.0865316	−	0.0358929i
$849$	−2.18718e28			−0.112411
$850$	7.08284e28	−	2.14760e28i	0.359765	−	0.109085i
$851$	3.21237e29			1.61261
$852$	−1.52098e28	−	2.27753e28i	−0.0754617	−	0.112997i
$853$		−	2.92906e29i		−	1.43628i	−0.695901	−	0.718138i	$-0.744995\pi$
$853$		−	2.92906e29i		−	1.43628i	0.695901	−	0.718138i	$-0.255005\pi$
$854$	1.07244e29	−	3.25176e28i	0.519751	−	0.157594i
$855$		−	1.47188e28i		−	0.0705035i
$856$	−2.37801e29	+	2.89541e29i	−1.12584	+	1.37079i
$857$	−1.78476e29			−0.835162			−0.417581	−	0.908640i	$-0.637122\pi$
$857$	−1.78476e29			−0.835162			−0.417581	+	0.908640i	$0.637122\pi$
$858$	−1.88259e28	−	6.20886e28i	−0.0870731	−	0.287170i
$859$	−3.54007e29			−1.61838			−0.809189	−	0.587549i	$-0.800093\pi$
$859$	−3.54007e29			−1.61838			−0.809189	+	0.587549i	$0.800093\pi$
$860$	−7.72944e28	−	1.15741e29i	−0.349272	−	0.523003i
$861$			4.70530e28i			0.210163i
$862$	−7.28390e28	−	2.40225e29i	−0.321581	−	1.06059i
$863$			5.98519e28i			0.261198i	0.991435	+	0.130599i	$0.0416900\pi$
$863$			5.98519e28i			0.261198i	−0.991435	+	0.130599i	$0.958310\pi$
$864$	8.98326e27	−	9.06315e28i	0.0387522	−	0.390969i
$865$	2.26115e29			0.964201
$866$	3.41182e29	−	1.03450e29i	1.43816	−	0.436066i
$867$	3.60923e28			0.150392
$868$	1.81842e29	−	1.21437e29i	0.749025	−	0.500214i
$869$			6.85024e28i			0.278938i
$870$	2.68124e28	−	8.12982e27i	0.107930	−	0.0327257i
$871$		−	1.36207e29i		−	0.542023i
$872$	3.62185e29	+	2.97464e29i	1.42484	+	1.17022i
$873$	−9.67629e28			−0.376328
$874$	1.59357e28	+	5.25564e28i	0.0612712	+	0.202074i
$875$	−3.21910e29			−1.22364
$876$	−8.58642e28	+	5.73418e28i	−0.322679	+	0.215492i
$877$			1.41241e29i			0.524765i	0.964964	+	0.262383i	$0.0845083\pi$
$877$			1.41241e29i			0.524765i	−0.964964	+	0.262383i	$0.915492\pi$
$878$	4.93271e28	+	1.62682e29i	0.181193	+	0.597579i
$879$			4.15060e26i			0.00150738i
$880$	1.37459e29	+	5.70176e28i	0.493569	+	0.204730i
$881$	−2.59025e29			−0.919564			−0.459782	−	0.888032i	$-0.652073\pi$
$881$	−2.59025e29			−0.919564			−0.459782	+	0.888032i	$0.652073\pi$
$882$	2.53276e29	−	7.67962e28i	0.889015	−	0.269559i
$883$	−2.78860e29			−0.967785			−0.483892	−	0.875127i	$-0.660777\pi$
$883$	−2.78860e29			−0.967785			−0.483892	+	0.875127i	$0.660777\pi$
$884$	1.12810e29	+	1.68923e29i	0.387101	+	0.579649i
$885$			2.92352e28i			0.0991914i
$886$	−5.21712e29	+	1.58189e29i	−1.75022	+	0.530687i
$887$		−	2.60662e29i		−	0.864652i	−0.901717	−	0.432326i	$-0.857693\pi$
$887$		−	2.60662e29i		−	0.864652i	0.901717	−	0.432326i	$-0.142307\pi$
$888$	5.32229e28	+	4.37121e28i	0.174570	+	0.143375i
$889$	4.38929e29			1.42356
$890$	5.54662e28	+	1.82929e29i	0.177881	+	0.586656i
$891$	2.98209e29			0.945678
$892$	1.38333e29	+	2.07142e29i	0.433789	+	0.649561i
$893$		−	5.00079e28i		−	0.155069i
$894$	1.39959e28	+	4.61588e28i	0.0429165	+	0.141540i
$895$			1.04908e29i			0.318112i
$896$	4.12773e29	−	2.20170e29i	1.23774	−	0.660205i
$897$	1.34922e29			0.400091
$898$	−2.27615e29	+	6.90153e28i	−0.667478	+	0.202387i
$899$	2.50201e29			0.725591
$900$	−2.09336e29	+	1.39799e29i	−0.600370	+	0.400939i
$901$		−	1.65082e28i		−	0.0468221i
$902$	−2.73662e29	+	8.29775e28i	−0.767626	+	0.232753i
$903$			1.28066e29i			0.355269i
$904$	3.67856e29	−	4.47894e29i	1.00924	−	1.22883i
$905$	−3.12381e29			−0.847617
$906$	1.25550e28	+	4.14070e28i	0.0336927	+	0.111120i
$907$	−6.98026e29			−1.85267			−0.926337	−	0.376697i	$-0.877060\pi$
$907$	−6.98026e29			−1.85267			−0.926337	+	0.376697i	$0.877060\pi$
$908$	−2.65969e29	+	1.77619e29i	−0.698187	+	0.466263i
$909$			3.29371e29i			0.855158i
$910$	−1.10048e29	−	3.62942e29i	−0.282598	−	0.932016i
$911$		−	5.98350e29i		−	1.51975i	−0.650071	−	0.759873i	$-0.725261\pi$
$911$		−	5.98350e29i		−	1.51975i	0.650071	−	0.759873i	$-0.274739\pi$
$912$	−4.51133e27	+	1.08760e28i	−0.0113333	+	0.0273226i
$913$	3.41622e29			0.848863
$914$	5.53256e28	−	1.67753e28i	0.135977	−	0.0412296i
$915$	−1.58941e28			−0.0386388
$916$	−1.18704e29	−	1.77748e29i	−0.285436	−	0.427415i
$917$		−	8.23107e28i		−	0.195778i
$918$	7.98721e28	−	2.42181e28i	0.187918	−	0.0569788i
$919$		−	1.14274e29i		−	0.265946i	−0.991120	−	0.132973i	$-0.957548\pi$
$919$		−	1.14274e29i		−	0.265946i	0.991120	−	0.132973i	$-0.0424524\pi$
$920$	−1.96416e29	+	2.39152e29i	−0.452167	+	0.550549i
$921$	9.92361e28			0.225982
$922$	−1.21788e29	−	4.01659e29i	−0.274343	−	0.904792i
$923$	−4.24189e29			−0.945241
$924$	−7.60484e28	−	1.13876e29i	−0.167637	−	0.251022i
$925$		−	3.88685e29i		−	0.847580i
$926$	−1.47646e29	−	4.86943e29i	−0.318503	−	1.05043i
$927$			8.47745e29i			1.80912i
$928$	5.32684e29	+	5.27988e28i	1.12458	+	0.111467i
$929$	7.98293e28			0.166727			0.0833633	−	0.996519i	$-0.473434\pi$
$929$	7.98293e28			0.166727			0.0833633	+	0.996519i	$0.473434\pi$
$930$	−2.96783e28	+	8.99878e27i	−0.0613210	+	0.0185932i
$931$	−6.98657e28			−0.142813
$932$	1.35635e29	−	9.05798e28i	0.274292	−	0.183178i
$933$			8.63095e28i			0.172680i
$934$	−6.46603e29	+	1.96057e29i	−1.27988	+	0.388074i
$935$			1.36377e29i			0.267070i
$936$	−5.33877e29	−	4.38474e29i	−1.03439	−	0.849544i
$937$	1.00786e30			1.93200			0.965998	−	0.258548i	$-0.0832440\pi$
$937$	1.00786e30			1.93200			0.965998	+	0.258548i	$0.0832440\pi$
$938$	−8.34157e28	−	2.75108e29i	−0.158205	−	0.521764i
$939$	−8.90110e28			−0.167027
$940$	2.34344e29	−	1.56499e29i	0.435086	−	0.290559i
$941$		−	7.65693e29i		−	1.40656i	−0.710912	−	0.703281i	$-0.751718\pi$
$941$		−	7.65693e29i		−	1.40656i	0.710912	−	0.703281i	$-0.248282\pi$
$942$	3.09328e27	+	1.02017e28i	0.00562225	+	0.0185424i
$943$		−	5.94685e29i		−	1.06947i
$944$	−2.14005e29	+	5.15930e29i	−0.380807	+	0.918059i
$945$	−1.55834e29			−0.274374
$946$	−7.44840e29	+	2.25844e29i	−1.29763	+	0.393456i
$947$	5.26248e29			0.907174			0.453587	−	0.891212i	$-0.350144\pi$
$947$	5.26248e29			0.907174			0.453587	+	0.891212i	$0.350144\pi$
$948$	−1.69620e28	−	2.53990e28i	−0.0289330	−	0.0433245i
$949$			1.59922e30i			2.69927i
$950$	6.35913e28	−	1.92816e28i	0.106209	−	0.0322038i
$951$		−	8.80160e28i		−	0.145464i
$952$	3.31302e29	+	2.72099e29i	0.541819	+	0.444997i
$953$	−7.28169e27			−0.0117843			−0.00589214	−	0.999983i	$-0.501876\pi$
$953$	−7.28169e27			−0.0117843			−0.00589214	+	0.999983i	$0.501876\pi$
$954$	1.62916e28	+	5.37303e28i	0.0260904	+	0.0860470i
$955$	−3.34527e28			−0.0530148
$956$	−9.30003e28	−	1.39260e29i	−0.145850	−	0.218397i
$957$		−	1.56684e29i		−	0.243168i
$958$	1.09166e29	+	3.60034e29i	0.167662	+	0.552953i
$959$			2.91309e29i			0.442759i
$960$	−6.50848e28	+	1.28958e28i	−0.0978966	+	0.0193970i
$961$	3.94847e29			0.587753
$962$	1.02085e30	−	3.09533e29i	1.50387	−	0.455991i
$963$	1.16780e30			1.70257
$964$	−3.23993e28	+	2.16369e28i	−0.0467483	+	0.0312194i
$965$			5.50311e29i			0.785842i
$966$	2.72513e29	−	8.26289e28i	0.385137	−	0.116778i
$967$			4.20930e29i			0.588769i	0.955687	+	0.294384i	$0.0951146\pi$
$967$			4.20930e29i			0.588769i	−0.955687	+	0.294384i	$0.904885\pi$
$968$	6.97280e28	−	8.48992e28i	0.0965280	−	0.117530i
$969$	−1.07904e28			−0.0147842
$970$	4.17660e28	+	1.37746e29i	0.0566377	+	0.186793i
$971$	−8.64643e29			−1.16050			−0.580249	−	0.814439i	$-0.697045\pi$
$971$	−8.64643e29			−1.16050			−0.580249	+	0.814439i	$0.697045\pi$
$972$	−3.56518e29	+	2.38090e29i	−0.473608	+	0.316285i
$973$			1.51742e30i			1.99515i
$974$	2.45374e29	+	8.09251e29i	0.319329	+	1.05316i
$975$		−	1.63251e29i		−	0.210286i
$976$	−2.80491e29	−	1.16346e29i	−0.357619	−	0.148339i
$977$	−1.01193e30			−1.27704			−0.638519	−	0.769606i	$-0.720453\pi$
$977$	−1.01193e30			−1.27704			−0.638519	+	0.769606i	$0.720453\pi$
$978$	−6.45395e28	+	1.95691e28i	−0.0806190	+	0.0244446i
$979$	1.06899e30			1.32174
$980$	−2.18645e29	−	3.27401e29i	−0.267595	−	0.400700i
$981$		−	1.46080e30i		−	1.76970i
$982$	3.72010e29	−	1.12797e29i	0.446107	−	0.135265i
$983$			2.24923e28i			0.0266992i	0.999911	+	0.0133496i	$0.00424944\pi$
$983$			2.24923e28i			0.0266992i	−0.999911	+	0.0133496i	$0.995751\pi$
$984$	8.09213e28	−	9.85280e28i	0.0950849	−	0.115773i
$985$	−7.74949e28			−0.0901386
$986$	1.42341e29	+	4.69446e29i	0.163893	+	0.540526i
$987$	−2.59298e29			−0.295548
$988$	1.01283e29	+	1.51662e29i	0.114279	+	0.171123i
$989$		−	1.61858e30i		−	1.80789i
$990$	−1.34588e29	−	4.43875e29i	−0.148818	−	0.490805i
$991$			5.02722e29i			0.550290i	0.961403	+	0.275145i	$0.0887259\pi$
$991$			5.02722e29i			0.550290i	−0.961403	+	0.275145i	$0.911274\pi$
$992$	−5.89620e29	−	5.84423e28i	−0.638934	−	0.0633301i
$993$	9.09055e26			0.000975209
$994$	−8.56767e29	+	2.59781e29i	−0.909911	+	0.275895i
$995$	−2.86120e29			−0.300827
$996$	−1.26665e29	+	8.45894e28i	−0.131845	+	0.0880486i
$997$		−	1.53860e30i		−	1.58553i	−0.609527	−	0.792766i	$-0.708640\pi$
$997$		−	1.53860e30i		−	1.58553i	0.609527	−	0.792766i	$-0.291360\pi$
$998$	1.55481e30	−	4.71437e29i	1.58625	−	0.480970i
$999$		−	4.38314e29i		−	0.442722i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.21.d.b.3.17	✓	18
3.2	odd	2		72.21.b.b.19.2		18
4.3	odd	2		32.21.d.b.15.10		18
8.3	odd	2	inner	8.21.d.b.3.18	yes	18
8.5	even	2		32.21.d.b.15.9		18
24.11	even	2		72.21.b.b.19.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.21.d.b.3.17	✓	18	1.1	even	1	trivial
8.21.d.b.3.18	yes	18	8.3	odd	2	inner
32.21.d.b.15.9		18	8.5	even	2
32.21.d.b.15.10		18	4.3	odd	2
72.21.b.b.19.1		18	24.11	even	2
72.21.b.b.19.2		18	3.2	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:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(979.944 - 297.130i) q^{2} -11837.6 q^{3} +(872004. - 582341. i) q^{4} +4.86160e6i q^{5} +(-1.16002e7 + 3.51730e6i) q^{6} +3.96260e8i q^{7} +(6.81484e8 - 8.29760e8i) q^{8} -3.34666e9 q^{9} +O(q^{10})\)	\(q+(979.944 - 297.130i) q^{2} -11837.6 q^{3} +(872004. - 582341. i) q^{4} +4.86160e6i q^{5} +(-1.16002e7 + 3.51730e6i) q^{6} +3.96260e8i q^{7} +(6.81484e8 - 8.29760e8i) q^{8} -3.34666e9 q^{9} +(1.44453e9 + 4.76409e9i) q^{10} +2.78400e10 q^{11} +(-1.03224e10 + 6.89351e9i) q^{12} +1.92255e11i q^{13} +(1.17741e11 + 3.88312e11i) q^{14} -5.75496e10i q^{15} +(4.21269e11 - 1.01561e12i) q^{16} +1.00761e12 q^{17} +(-3.27953e12 + 9.94391e11i) q^{18} +9.04652e11 q^{19} +(2.83111e12 + 4.23933e12i) q^{20} -4.69076e12i q^{21} +(2.72817e13 - 8.27211e12i) q^{22} +5.92847e13i q^{23} +(-8.06712e12 + 9.82235e12i) q^{24} +7.17323e13 q^{25} +(5.71247e13 + 1.88399e14i) q^{26} +8.08914e13 q^{27} +(2.30758e14 + 3.45540e14i) q^{28} +4.75437e14i q^{29} +(-1.70997e13 - 5.63953e13i) q^{30} -5.26254e14i q^{31} +(1.11053e14 - 1.12041e15i) q^{32} -3.29559e14 q^{33} +(9.87399e14 - 2.99390e14i) q^{34} -1.92645e15 q^{35} +(-2.91830e15 + 1.94890e15i) q^{36} -5.41855e15i q^{37} +(8.86508e14 - 2.68799e14i) q^{38} -2.27584e15i q^{39} +(4.03396e15 + 3.31310e15i) q^{40} -1.00310e16 q^{41} +(-1.39376e15 - 4.59668e15i) q^{42} -2.73018e16 q^{43} +(2.42766e16 - 1.62124e16i) q^{44} -1.62701e16i q^{45} +(1.76153e16 + 5.80957e16i) q^{46} -5.52785e16i q^{47} +(-4.98681e15 + 1.20223e16i) q^{48} -7.72294e16 q^{49} +(7.02936e16 - 2.13138e16i) q^{50} -1.19276e16 q^{51} +(1.11958e17 + 1.67647e17i) q^{52} -1.63835e16i q^{53} +(7.92691e16 - 2.40353e16i) q^{54} +1.35347e17i q^{55} +(3.28800e17 + 2.70044e17i) q^{56} -1.07089e16 q^{57} +(1.41266e17 + 4.65901e17i) q^{58} -5.08001e17 q^{59} +(-3.35135e16 - 5.01834e16i) q^{60} -2.76180e17i q^{61} +(-1.56366e17 - 5.15700e17i) q^{62} -1.32614e18i q^{63} +(-2.24081e17 - 1.13094e18i) q^{64} -9.34666e17 q^{65} +(-3.22949e17 + 9.79217e16i) q^{66} -7.08470e17 q^{67} +(8.78638e17 - 5.86772e17i) q^{68} -7.01788e17i q^{69} +(-1.88782e18 + 5.72407e17i) q^{70} +2.20639e18i q^{71} +(-2.28069e18 + 2.77692e18i) q^{72} +8.31823e18 q^{73} +(-1.61001e18 - 5.30988e18i) q^{74} -8.49137e17 q^{75} +(7.88860e17 - 5.26816e17i) q^{76} +1.10319e19i q^{77} +(-6.76218e17 - 2.23019e18i) q^{78} +2.46057e18i q^{79} +(4.93747e18 + 2.04804e18i) q^{80} +1.07115e19 q^{81} +(-9.82981e18 + 2.98051e18i) q^{82} +1.22709e19 q^{83} +(-2.73162e18 - 4.09036e18i) q^{84} +4.89858e18i q^{85} +(-2.67543e19 + 8.11219e18i) q^{86} -5.62802e18i q^{87} +(1.89725e19 - 2.31005e19i) q^{88} +3.83975e19 q^{89} +(-4.83433e18 - 1.59438e19i) q^{90} -7.61829e19 q^{91} +(3.45239e19 + 5.16965e19i) q^{92} +6.22958e18i q^{93} +(-1.64249e19 - 5.41699e19i) q^{94} +4.39805e18i q^{95} +(-1.31460e18 + 1.32629e19i) q^{96} +2.89133e19 q^{97} +(-7.56804e19 + 2.29471e19i) q^{98} -9.31710e19 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9}+O(q^{10}) \) 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9	\( 18 q - 398 q^{2} - 114228 q^{3} + 724980 q^{4} - 91643748 q^{6} - 3105291368 q^{8} + 10197650262 q^{9} + 742754160 q^{10} + 27862395020 q^{11} - 212292734088 q^{12} - 431248136928 q^{14} - 958534870512 q^{16} + 4343925139172 q^{17} - 4517494524426 q^{18} - 360681653556 q^{19} - 32520172742880 q^{20} - 66275482922148 q^{22} + 22289322475152 q^{24} - 395727477008910 q^{25} + 154289718058128 q^{26} - 12\!\cdots\!64 q^{27}+ \cdots + 62\!\cdots\!84 q^{99}+O(q^{100}) \) 18 * q - 398 * q^2 - 114228 * q^3 + 724980 * q^4 - 91643748 * q^6 - 3105291368 * q^8 + 10197650262 * q^9 + 742754160 * q^10 + 27862395020 * q^11 - 212292734088 * q^12 - 431248136928 * q^14 - 958534870512 * q^16 + 4343925139172 * q^17 - 4517494524426 * q^18 - 360681653556 * q^19 - 32520172742880 * q^20 - 66275482922148 * q^22 + 22289322475152 * q^24 - 395727477008910 * q^25 + 154289718058128 * q^26 - 1208398438889064 * q^27 - 394619539621440 * q^28 + 223250517248160 * q^30 - 2833814588985248 * q^32 + 4461969540487176 * q^33 - 939462769526748 * q^34 + 3615863153468160 * q^35 + 1560521174396700 * q^36 + 12905383833568412 * q^38 + 11813880412973760 * q^40 + 16990829756398820 * q^41 + 38127588900300480 * q^42 - 27498466356753396 * q^43 + 33178844343953144 * q^44 - 21739818881100192 * q^46 + 28364131397385312 * q^48 - 252965388018862638 * q^49 + 41705619584456530 * q^50 - 34182574557901800 * q^51 - 44583718369992480 * q^52 - 579400710808894920 * q^54 - 505574909383001472 * q^56 - 522453489061123704 * q^57 - 677523738697093680 * q^58 + 93112194700366220 * q^59 + 1631640690429240000 * q^60 + 1780090172849178240 * q^62 + 175441813011570240 * q^64 + 1575343920200472960 * q^65 + 8001047667731567880 * q^66 - 1452645642074335668 * q^67 + 1153770320813215592 * q^68 - 6151558949299572480 * q^70 - 5306529204268842936 * q^72 + 9882821313863175972 * q^73 - 5642095430673385488 * q^74 + 13414715768769378060 * q^75 - 8416781249057544840 * q^76 - 14599907290310144160 * q^78 - 22104885212702947200 * q^80 - 32315102667184036518 * q^81 + 10320950271478847652 * q^82 - 46425529968268557748 * q^83 + 17095266896298568320 * q^84 + 33555485282446075868 * q^86 + 32344350945394345872 * q^88 - 28075170672250840156 * q^89 - 33204348719592139440 * q^90 + 161045136122144660736 * q^91 - 932896292396925120 * q^92 - 107259275077774974528 * q^94 + 68580843917215697472 * q^96 + 127276645173366650724 * q^97 + 154837385163137764402 * q^98 + 62802542261652714084 * q^99

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