LMFDB - Embedded newform 8.21.d.b.3.3

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			3.3
Root			$-20011.7 - 4.20507e6i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.21.d.b.3.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-980.704 - 294.612i) q^{2} -86392.9 q^{3} +(874983. + 577854. i) q^{4} +1.68203e7i q^{5} +(8.47258e7 + 2.54524e7i) q^{6} -3.64653e8i q^{7} +(-6.87856e8 - 8.24485e8i) q^{8} +3.97695e9 q^{9} +O(q^{10})$	\(q+(-980.704 - 294.612i) q^{2} -86392.9 q^{3} +(874983. + 577854. i) q^{4} +1.68203e7i q^{5} +(8.47258e7 + 2.54524e7i) q^{6} -3.64653e8i q^{7} +(-6.87856e8 - 8.24485e8i) q^{8} +3.97695e9 q^{9} +(4.95546e9 - 1.64957e10i) q^{10} +2.95556e10 q^{11} +(-7.55923e10 - 4.99225e10i) q^{12} +1.06510e11i q^{13} +(-1.07431e11 + 3.57616e11i) q^{14} -1.45315e12i q^{15} +(4.31680e11 + 1.01123e12i) q^{16} +2.31198e12 q^{17} +(-3.90021e12 - 1.17166e12i) q^{18} -8.42253e11 q^{19} +(-9.71968e12 + 1.47175e13i) q^{20} +3.15034e13i q^{21} +(-2.89852e13 - 8.70743e12i) q^{22} +2.92728e12i q^{23} +(5.94259e13 + 7.12296e13i) q^{24} -1.87555e14 q^{25} +(3.13790e13 - 1.04454e14i) q^{26} -4.23466e13 q^{27} +(2.10716e14 - 3.19065e14i) q^{28} +2.89106e14i q^{29} +(-4.28117e14 + 1.42511e15i) q^{30} +6.94432e14i q^{31} +(-1.25431e14 - 1.11889e15i) q^{32} -2.55339e15 q^{33} +(-2.26737e15 - 6.81138e14i) q^{34} +6.13357e15 q^{35} +(3.47976e15 + 2.29810e15i) q^{36} -2.39031e15i q^{37} +(8.26001e14 + 2.48138e14i) q^{38} -9.20166e15i q^{39} +(1.38681e16 - 1.15699e16i) q^{40} -8.44047e15 q^{41} +(9.28129e15 - 3.08955e16i) q^{42} -2.60268e16 q^{43} +(2.58606e16 + 1.70788e16i) q^{44} +6.68934e16i q^{45} +(8.62413e14 - 2.87080e15i) q^{46} +4.58565e16i q^{47} +(-3.72941e16 - 8.73627e16i) q^{48} -5.31795e16 q^{49} +(1.83935e17 + 5.52559e16i) q^{50} -1.99739e17 q^{51} +(-6.15470e16 + 9.31941e16i) q^{52} -2.23880e17i q^{53} +(4.15294e16 + 1.24758e16i) q^{54} +4.97133e17i q^{55} +(-3.00651e17 + 2.50829e17i) q^{56} +7.27647e16 q^{57} +(8.51741e16 - 2.83527e17i) q^{58} -3.72686e17 q^{59} +(8.39711e17 - 1.27148e18i) q^{60} +1.14075e18i q^{61} +(2.04588e17 - 6.81032e17i) q^{62} -1.45021e18i q^{63} +(-2.06628e17 + 1.13425e18i) q^{64} -1.79152e18 q^{65} +(2.50412e18 + 7.52260e17i) q^{66} +1.69388e18 q^{67} +(2.02295e18 + 1.33599e18i) q^{68} -2.52896e17i q^{69} +(-6.01521e18 - 1.80702e18i) q^{70} -1.43248e18i q^{71} +(-2.73557e18 - 3.27893e18i) q^{72} +6.55444e17 q^{73} +(-7.04214e17 + 2.34419e18i) q^{74} +1.62034e19 q^{75} +(-7.36958e17 - 4.86700e17i) q^{76} -1.07775e19i q^{77} +(-2.71092e18 + 9.02411e18i) q^{78} +3.74112e18i q^{79} +(-1.70091e19 + 7.26098e18i) q^{80} -1.02083e19 q^{81} +(8.27760e18 + 2.48666e18i) q^{82} -1.51998e19 q^{83} +(-1.82044e19 + 2.75650e19i) q^{84} +3.88882e19i q^{85} +(2.55246e19 + 7.66782e18i) q^{86} -2.49767e19i q^{87} +(-2.03300e19 - 2.43681e19i) q^{88} +2.12767e19 q^{89} +(1.97076e19 - 6.56026e19i) q^{90} +3.88390e19 q^{91} +(-1.69154e18 + 2.56132e18i) q^{92} -5.99940e19i q^{93} +(1.35099e19 - 4.49717e19i) q^{94} -1.41669e19i q^{95} +(1.08363e19 + 9.66643e19i) q^{96} -6.94557e19 q^{97} +(5.21533e19 + 1.56673e19i) q^{98} +1.17541e20 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 $

$2$	−980.704	−	294.612i	−0.957718	−	0.287707i
$2$	−980.704	−	294.612i	−0.957718	−	0.287707i
$3$	−86392.9			−1.46307			−0.731536	−	0.681803i	$-0.761196\pi$
$3$	−86392.9			−1.46307			−0.731536	+	0.681803i	$0.761196\pi$
$4$	874983.	+	577854.i	0.834449	+	0.551085i
$5$			1.68203e7i			1.72240i	0.508269	+	0.861199i	$0.330286\pi$
$5$			1.68203e7i			1.72240i	−0.508269	+	0.861199i	$0.669714\pi$
$6$	8.47258e7	+	2.54524e7i	1.40121	+	0.420936i
$7$		−	3.64653e8i		−	1.29092i	−0.763794	−	0.645460i	$-0.776666\pi$
$7$		−	3.64653e8i		−	1.29092i	0.763794	−	0.645460i	$-0.223334\pi$
$8$	−6.87856e8	−	8.24485e8i	−0.640616	−	0.767861i
$9$	3.97695e9			1.14058
$10$	4.95546e9	−	1.64957e10i	0.495546	−	1.64957i
$11$	2.95556e10			1.13949			0.569747	−	0.821820i	$-0.307041\pi$
$11$	2.95556e10			1.13949			0.569747	+	0.821820i	$0.307041\pi$
$12$	−7.55923e10	−	4.99225e10i	−1.22086	−	0.806276i
$13$			1.06510e11i			0.772600i	0.922373	+	0.386300i	$0.126247\pi$
$13$			1.06510e11i			0.772600i	−0.922373	+	0.386300i	$0.873753\pi$
$14$	−1.07431e11	+	3.57616e11i	−0.371407	+	1.23634i
$15$		−	1.45315e12i		−	2.51999i
$16$	4.31680e11	+	1.01123e12i	0.392611	+	0.919705i
$17$	2.31198e12			1.14682			0.573410	−	0.819269i	$-0.305620\pi$
$17$	2.31198e12			1.14682			0.573410	+	0.819269i	$0.305620\pi$
$18$	−3.90021e12	−	1.17166e12i	−1.09235	−	0.328152i
$19$	−8.42253e11			−0.137375			−0.0686873	−	0.997638i	$-0.521881\pi$
$19$	−8.42253e11			−0.137375			−0.0686873	+	0.997638i	$0.521881\pi$
$20$	−9.71968e12	+	1.47175e13i	−0.949187	+	1.43725i
$21$			3.15034e13i			1.88871i
$22$	−2.89852e13	−	8.70743e12i	−1.09132	−	0.327841i
$23$			2.92728e12i			0.0706621i	0.999376	+	0.0353310i	$0.0112486\pi$
$23$			2.92728e12i			0.0706621i	−0.999376	+	0.0353310i	$0.988751\pi$
$24$	5.94259e13	+	7.12296e13i	0.937267	+	1.12344i
$25$	−1.87555e14			−1.96665
$26$	3.13790e13	−	1.04454e14i	0.222283	−	0.739934i
$27$	−4.23466e13			−0.205675
$28$	2.10716e14	−	3.19065e14i	0.711407	−	1.07721i
$29$			2.89106e14i			0.687190i	0.939118	+	0.343595i	$0.111645\pi$
$29$			2.89106e14i			0.687190i	−0.939118	+	0.343595i	$0.888355\pi$
$30$	−4.28117e14	+	1.42511e15i	−0.725019	+	2.41344i
$31$			6.94432e14i			0.847252i	0.905837	+	0.423626i	$0.139243\pi$
$31$			6.94432e14i			0.847252i	−0.905837	+	0.423626i	$0.860757\pi$
$32$	−1.25431e14	−	1.11889e15i	−0.111405	−	0.993775i
$33$	−2.55339e15			−1.66716
$34$	−2.26737e15	−	6.81138e14i	−1.09833	−	0.329948i
$35$	6.13357e15			2.22348
$36$	3.47976e15	+	2.29810e15i	0.951754	+	0.628555i
$37$		−	2.39031e15i		−	0.497092i	−0.968620	−	0.248546i	$-0.920047\pi$
$37$		−	2.39031e15i		−	0.497092i	0.968620	−	0.248546i	$-0.0799527\pi$
$38$	8.26001e14	+	2.48138e14i	0.131566	+	0.0395237i
$39$		−	9.20166e15i		−	1.13037i
$40$	1.38681e16	−	1.15699e16i	1.32256	−	1.10340i
$41$	−8.44047e15			−0.628822			−0.314411	−	0.949287i	$-0.601807\pi$
$41$	−8.44047e15			−0.628822			−0.314411	+	0.949287i	$0.601807\pi$
$42$	9.28129e15	−	3.08955e16i	0.543395	−	1.80885i
$43$	−2.60268e16			−1.20431			−0.602153	−	0.798381i	$-0.705690\pi$
$43$	−2.60268e16			−1.20431			−0.602153	+	0.798381i	$0.705690\pi$
$44$	2.58606e16	+	1.70788e16i	0.950850	+	0.627958i
$45$			6.68934e16i			1.96453i
$46$	8.62413e14	−	2.87080e15i	0.0203300	−	0.0676744i
$47$			4.58565e16i			0.871811i	0.899992	+	0.435906i	$0.143572\pi$
$47$			4.58565e16i			0.871811i	−0.899992	+	0.435906i	$0.856428\pi$
$48$	−3.72941e16	−	8.73627e16i	−0.574418	−	1.34559i
$49$	−5.31795e16			−0.666475
$50$	1.83935e17	+	5.52559e16i	1.88350	+	0.565820i
$51$	−1.99739e17			−1.67788
$52$	−6.15470e16	+	9.31941e16i	−0.425768	+	0.644696i
$53$		−	2.23880e17i		−	1.28014i	−0.768318	−	0.640068i	$-0.778906\pi$
$53$		−	2.23880e17i		−	1.28014i	0.768318	−	0.640068i	$-0.221094\pi$
$54$	4.15294e16	+	1.24758e16i	0.196978	+	0.0591740i
$55$			4.97133e17i			1.96266i
$56$	−3.00651e17	+	2.50829e17i	−0.991247	+	0.826984i
$57$	7.27647e16			0.200989
$58$	8.51741e16	−	2.83527e17i	0.197710	−	0.658135i
$59$	−3.72686e17			−0.729161			−0.364580	−	0.931172i	$-0.618788\pi$
$59$	−3.72686e17			−0.729161			−0.364580	+	0.931172i	$0.618788\pi$
$60$	8.39711e17	−	1.27148e18i	1.38873	−	2.10280i
$61$			1.14075e18i			1.59917i	0.600556	+	0.799583i	$0.294946\pi$
$61$			1.14075e18i			1.59917i	−0.600556	+	0.799583i	$0.705054\pi$
$62$	2.04588e17	−	6.81032e17i	0.243761	−	0.811429i
$63$		−	1.45021e18i		−	1.47239i
$64$	−2.06628e17	+	1.13425e18i	−0.179222	+	0.983809i
$65$	−1.79152e18			−1.33072
$66$	2.50412e18	+	7.52260e17i	1.59667	+	0.479654i
$67$	1.69388e18			0.929257			0.464628	−	0.885506i	$-0.346188\pi$
$67$	1.69388e18			0.929257			0.464628	+	0.885506i	$0.346188\pi$
$68$	2.02295e18	+	1.33599e18i	0.956963	+	0.631995i
$69$		−	2.52896e17i		−	0.103384i
$70$	−6.01521e18	−	1.80702e18i	−2.12947	−	0.639710i
$71$		−	1.43248e18i		−	0.440054i	−0.975494	−	0.220027i	$-0.929385\pi$
$71$		−	1.43248e18i		−	0.440054i	0.975494	−	0.220027i	$-0.0706146\pi$
$72$	−2.73557e18	−	3.27893e18i	−0.730672	−	0.875805i
$73$	6.55444e17			0.152513			0.0762565	−	0.997088i	$-0.475703\pi$
$73$	6.55444e17			0.152513			0.0762565	+	0.997088i	$0.475703\pi$
$74$	−7.04214e17	+	2.34419e18i	−0.143017	+	0.476074i
$75$	1.62034e19			2.87735
$76$	−7.36958e17	−	4.86700e17i	−0.114632	−	0.0757051i
$77$		−	1.07775e19i		−	1.47100i
$78$	−2.71092e18	+	9.02411e18i	−0.325215	+	1.08258i
$79$			3.74112e18i			0.395121i	0.980291	+	0.197561i	$0.0633019\pi$
$79$			3.74112e18i			0.395121i	−0.980291	+	0.197561i	$0.936698\pi$
$80$	−1.70091e19	+	7.26098e18i	−1.58410	+	0.676232i
$81$	−1.02083e19			−0.839661
$82$	8.27760e18	+	2.48666e18i	0.602235	+	0.180917i
$83$	−1.51998e19			−0.979621			−0.489811	−	0.871829i	$-0.662934\pi$
$83$	−1.51998e19			−0.979621			−0.489811	+	0.871829i	$0.662934\pi$
$84$	−1.82044e19	+	2.75650e19i	−1.04084	+	1.57603i
$85$			3.88882e19i			1.97528i
$86$	2.55246e19	+	7.66782e18i	1.15339	+	0.346488i
$87$		−	2.49767e19i		−	1.00541i
$88$	−2.03300e19	−	2.43681e19i	−0.729979	−	0.874974i
$89$	2.12767e19			0.682346			0.341173	−	0.940000i	$-0.389176\pi$
$89$	2.12767e19			0.682346			0.341173	+	0.940000i	$0.389176\pi$
$90$	1.97076e19	−	6.56026e19i	0.565209	−	1.88146i
$91$	3.88390e19			0.997365
$92$	−1.69154e18	+	2.56132e18i	−0.0389408	+	0.0589639i
$93$		−	5.99940e19i		−	1.23959i
$94$	1.35099e19	−	4.49717e19i	0.250826	−	0.834950i
$95$		−	1.41669e19i		−	0.236614i
$96$	1.08363e19	+	9.66643e19i	0.162993	+	1.45396i
$97$	−6.94557e19			−0.941868			−0.470934	−	0.882168i	$-0.656083\pi$
$97$	−6.94557e19			−0.941868			−0.470934	+	0.882168i	$0.656083\pi$
$98$	5.21533e19	+	1.56673e19i	0.638295	+	0.191750i
$99$	1.17541e20			1.29968
$100$	−1.64107e20	−	1.08379e20i	−1.64107	−	1.08379i
$101$			6.91127e19i			0.625668i	0.949808	+	0.312834i	$0.101278\pi$
$101$			6.91127e19i			0.625668i	−0.949808	+	0.312834i	$0.898722\pi$
$102$	1.95885e20	+	5.88455e19i	1.60694	+	0.482738i
$103$			7.42626e18i			0.0552584i	0.999618	+	0.0276292i	$0.00879576\pi$
$103$			7.42626e18i			0.0552584i	−0.999618	+	0.0276292i	$0.991204\pi$
$104$	8.78155e19	−	7.32633e19i	0.593250	−	0.494940i
$105$	−5.29897e20			−3.25311
$106$	−6.59577e19	+	2.19560e20i	−0.368305	+	1.22601i
$107$	1.94444e20			0.988453			0.494227	−	0.869333i	$-0.335451\pi$
$107$	1.94444e20			0.988453			0.494227	+	0.869333i	$0.335451\pi$
$108$	−3.70525e19	−	2.44701e19i	−0.171625	−	0.113344i
$109$			3.23383e20i			1.36601i	0.730415	+	0.683003i	$0.239327\pi$
$109$			3.23383e20i			1.36601i	−0.730415	+	0.683003i	$0.760673\pi$
$110$	1.46461e20	−	4.87540e20i	0.564672	−	1.87968i
$111$			2.06506e20i			0.727281i
$112$	3.68747e20	−	1.57413e20i	1.18727	−	0.506829i
$113$	−4.42432e20			−1.30335			−0.651677	−	0.758496i	$-0.725934\pi$
$113$	−4.42432e20			−1.30335			−0.651677	+	0.758496i	$0.725934\pi$
$114$	−7.13606e19	−	2.14374e19i	−0.192491	−	0.0578260i
$115$	−4.92377e19			−0.121708
$116$	−1.67061e20	+	2.52963e20i	−0.378700	+	0.573425i
$117$			4.23583e20i			0.881210i
$118$	3.65495e20	+	1.09798e20i	0.698331	+	0.209785i
$119$		−	8.43071e20i		−	1.48045i
$120$	−1.19810e21	+	9.99561e20i	−1.93500	+	1.61435i
$121$	2.00781e20			0.298448
$122$	3.36080e20	−	1.11874e21i	0.460091	−	1.53155i
$123$	7.29196e20			0.920012
$124$	−4.01281e20	+	6.07616e20i	−0.466908	+	0.706989i
$125$		−	1.55061e21i		−	1.66496i
$126$	−4.27248e20	+	1.42222e21i	−0.423618	+	1.41014i
$127$			4.00904e20i			0.367285i	0.982993	+	0.183643i	$0.0587889\pi$
$127$			4.00904e20i			0.367285i	−0.982993	+	0.183643i	$0.941211\pi$
$128$	5.36806e20	−	1.05149e21i	0.454693	−	0.890648i
$129$	2.24853e21			1.76199
$130$	1.75695e21	+	5.27804e20i	1.27446	+	0.382859i
$131$	7.08938e20			0.476316			0.238158	−	0.971226i	$-0.423456\pi$
$131$	7.08938e20			0.476316			0.238158	+	0.971226i	$0.423456\pi$
$132$	−2.23417e21	−	1.47549e21i	−1.39116	−	0.918748i
$133$			3.07130e20i			0.177340i
$134$	−1.66120e21	−	4.99039e20i	−0.889966	−	0.267354i
$135$		−	7.12281e20i		−	0.354253i
$136$	−1.59031e21	−	1.90619e21i	−0.734671	−	0.880598i
$137$	8.38295e20			0.359908			0.179954	−	0.983675i	$-0.442405\pi$
$137$	8.38295e20			0.359908			0.179954	+	0.983675i	$0.442405\pi$
$138$	−7.45063e19	+	2.48016e20i	−0.0297442	+	0.0990124i
$139$	−3.16274e21			−1.17467			−0.587335	−	0.809344i	$-0.699823\pi$
$139$	−3.16274e21			−1.17467			−0.587335	+	0.809344i	$0.699823\pi$
$140$	5.36677e21	+	3.54431e21i	1.85538	+	1.22532i
$141$		−	3.96168e21i		−	1.27552i
$142$	−4.22027e20	+	1.40484e21i	−0.126607	+	0.421448i
$143$			3.14795e21i			0.880374i
$144$	1.71677e21	+	4.02159e21i	0.447803	+	1.04899i
$145$	−4.86284e21			−1.18361
$146$	−6.42796e20	−	1.93102e20i	−0.146064	−	0.0438791i
$147$	4.59433e21			0.975100
$148$	1.38125e21	−	2.09148e21i	0.273940	−	0.414798i
$149$			1.03338e22i			1.91602i	0.286740	+	0.958008i	$0.407428\pi$
$149$			1.03338e22i			1.91602i	−0.286740	+	0.958008i	$0.592572\pi$
$150$	−1.58907e22	−	4.77371e21i	−2.75569	−	0.827835i
$151$		−	8.08356e21i		−	1.31170i	−0.754893	−	0.655848i	$-0.772311\pi$
$151$		−	8.08356e21i		−	1.31170i	0.754893	−	0.655848i	$-0.227689\pi$
$152$	5.79349e20	+	6.94425e20i	0.0880045	+	0.105485i
$153$	9.19463e21			1.30804
$154$	−3.17519e21	+	1.05696e22i	−0.423216	+	1.40880i
$155$	−1.16805e22			−1.45931
$156$	5.31722e21	−	8.05130e21i	0.622929	−	0.943236i
$157$			3.88131e21i			0.426562i	0.976991	+	0.213281i	$0.0684149\pi$
$157$			3.88131e21i			0.426562i	−0.976991	+	0.213281i	$0.931585\pi$
$158$	1.10218e21	−	3.66893e21i	0.113679	−	0.378415i
$159$			1.93416e22i			1.87293i
$160$	1.88201e22	−	2.10978e21i	1.71168	−	0.191884i
$161$	1.06744e21			0.0912191
$162$	1.00113e22	+	3.00749e21i	0.804159	+	0.241576i
$163$	−2.16871e22			−1.63804			−0.819020	−	0.573765i	$-0.805482\pi$
$163$	−2.16871e22			−1.63804			−0.819020	+	0.573765i	$0.805482\pi$
$164$	−7.38527e21	−	4.87736e21i	−0.524720	−	0.346534i
$165$		−	4.29488e22i		−	2.87152i
$166$	1.49065e22	+	4.47806e21i	0.938201	+	0.281844i
$167$		−	1.36722e22i		−	0.810352i	−0.914239	−	0.405176i	$-0.867210\pi$
$167$		−	1.36722e22i		−	0.810352i	0.914239	−	0.405176i	$-0.132790\pi$
$168$	2.59741e22	−	2.16698e22i	1.45027	−	1.20994i
$169$	7.66069e21			0.403089
$170$	1.14569e22	−	3.81378e22i	0.568302	−	1.89176i
$171$	−3.34960e21			−0.156686
$172$	−2.27731e22	−	1.50397e22i	−1.00493	−	0.663675i
$173$			3.92487e22i			1.63442i	0.576339	+	0.817211i	$0.304481\pi$
$173$			3.92487e22i			1.63442i	−0.576339	+	0.817211i	$0.695519\pi$
$174$	−7.35844e21	+	2.44947e22i	−0.289263	+	0.962898i
$175$			6.83923e22i			2.53879i
$176$	1.27585e22	+	2.98873e22i	0.447378	+	1.04800i
$177$	3.21974e22			1.06681
$178$	−2.08662e22	−	6.26838e21i	−0.653496	−	0.196316i
$179$	−4.77271e22			−1.41330			−0.706651	−	0.707562i	$-0.749795\pi$
$179$	−4.77271e22			−1.41330			−0.706651	+	0.707562i	$0.749795\pi$
$180$	−3.86546e22	+	5.85306e22i	−1.08262	+	1.63930i
$181$		−	1.43094e22i		−	0.379171i	−0.981864	−	0.189585i	$-0.939286\pi$
$181$		−	1.43094e22i		−	0.379171i	0.981864	−	0.189585i	$-0.0607144\pi$
$182$	−3.80896e22	−	1.14424e22i	−0.955195	−	0.286949i
$183$		−	9.85530e22i		−	2.33969i
$184$	2.41350e21	−	2.01355e21i	0.0542586	−	0.0452673i
$185$	4.02057e22			0.856190
$186$	−1.76750e22	+	5.88363e22i	−0.356639	+	1.18718i
$187$	6.83319e22			1.30680
$188$	−2.64984e22	+	4.01237e22i	−0.480442	+	0.727482i
$189$			1.54418e22i			0.265509i
$190$	−4.17375e21	+	1.38936e22i	−0.0680755	+	0.226609i
$191$		−	8.04614e22i		−	1.24524i	−0.782524	−	0.622621i	$-0.786068\pi$
$191$		−	8.04614e22i		−	1.24524i	0.782524	−	0.622621i	$-0.213932\pi$
$192$	1.78512e22	−	9.79915e22i	0.262214	−	1.43938i
$193$	−1.11689e23			−1.55753			−0.778766	−	0.627315i	$-0.784154\pi$
$193$	−1.11689e23			−1.55753			−0.778766	+	0.627315i	$0.784154\pi$
$194$	6.81154e22	+	2.04625e22i	0.902045	+	0.270982i
$195$	1.54775e23			1.94694
$196$	−4.65312e22	−	3.07300e22i	−0.556139	−	0.367284i
$197$			1.72505e22i			0.195948i	0.995189	+	0.0979738i	$0.0312361\pi$
$197$			1.72505e22i			0.195948i	−0.995189	+	0.0979738i	$0.968764\pi$
$198$	−1.15273e23	−	3.46290e22i	−1.24473	−	0.373928i
$199$			1.69597e23i			1.74135i	0.491858	+	0.870676i	$0.336318\pi$
$199$			1.69597e23i			1.74135i	−0.491858	+	0.870676i	$0.663682\pi$
$200$	1.29011e23	+	1.54636e23i	1.25987	+	1.51012i
$201$	−1.46340e23			−1.35957
$202$	2.03614e22	−	6.77791e22i	0.180009	−	0.599214i
$203$	1.05423e23			0.887108
$204$	−1.74768e23	−	1.15420e23i	−1.40010	−	0.924654i
$205$		−	1.41971e23i		−	1.08308i
$206$	2.18787e21	−	7.28296e21i	0.0158982	−	0.0529219i
$207$			1.16416e22i			0.0805955i
$208$	−1.07705e23	+	4.59780e22i	−0.710564	+	0.303331i
$209$	−2.48933e22			−0.156538
$210$	5.19672e23	+	1.56114e23i	3.11556	+	0.935942i
$211$	−1.06851e22			−0.0610877			−0.0305439	−	0.999533i	$-0.509724\pi$
$211$	−1.06851e22			−0.0610877			−0.0305439	+	0.999533i	$0.509724\pi$
$212$	1.29370e23	−	1.95891e23i	0.705464	−	1.06821i
$213$			1.23756e23i			0.643831i
$214$	−1.90692e23	−	5.72855e22i	−0.946660	−	0.284385i
$215$		−	4.37779e23i		−	2.07429i
$216$	2.91284e22	+	3.49141e22i	0.131758	+	0.157929i
$217$	2.53227e23			1.09374
$218$	9.52727e22	−	3.17143e23i	0.393010	−	1.30825i
$219$	−5.66257e22			−0.223137
$220$	−2.87270e23	+	4.34983e23i	−1.08159	+	1.63774i
$221$			2.46248e23i			0.886033i
$222$	6.08391e22	−	2.02521e23i	0.209244	−	0.696531i
$223$			6.34169e22i			0.208524i	0.994550	+	0.104262i	$0.0332481\pi$
$223$			6.34169e22i			0.208524i	−0.994550	+	0.104262i	$0.966752\pi$
$224$	−4.08007e23	+	4.57387e22i	−1.28288	+	0.143815i
$225$	−7.45895e23			−2.24312
$226$	4.33895e23	+	1.30346e23i	1.24825	+	0.374984i
$227$	−1.13881e23			−0.313468			−0.156734	−	0.987641i	$-0.550097\pi$
$227$	−1.13881e23			−0.313468			−0.156734	+	0.987641i	$0.550097\pi$
$228$	6.36679e22	+	4.20474e22i	0.167715	+	0.110762i
$229$			3.51437e23i			0.886121i	0.896492	+	0.443060i	$0.146107\pi$
$229$			3.51437e23i			0.886121i	−0.896492	+	0.443060i	$0.853893\pi$
$230$	4.82876e22	+	1.45060e22i	0.116562	+	0.0350163i
$231$			9.31101e23i			2.15217i
$232$	2.38363e23	−	1.98863e23i	0.527667	−	0.440225i
$233$	4.48445e23			0.950933			0.475466	−	0.879734i	$-0.342279\pi$
$233$	4.48445e23			0.950933			0.475466	+	0.879734i	$0.342279\pi$
$234$	1.24793e23	−	4.15409e23i	0.253531	−	0.843951i
$235$	−7.71320e23			−1.50161
$236$	−3.26094e23	−	2.15358e23i	−0.608448	−	0.401830i
$237$		−	3.23206e23i		−	0.578090i
$238$	−2.48379e23	+	8.26803e23i	−0.425937	+	1.41786i
$239$		−	6.35130e22i		−	0.104444i	−0.998635	−	0.0522220i	$-0.983370\pi$
$239$		−	6.35130e22i		−	0.104444i	0.998635	−	0.0522220i	$-0.0166304\pi$
$240$	1.46947e24	−	6.27297e23i	2.31765	−	0.989375i
$241$	−1.20735e24			−1.82668			−0.913338	−	0.407202i	$-0.866504\pi$
$241$	−1.20735e24			−1.82668			−0.913338	+	0.407202i	$0.866504\pi$
$242$	−1.96907e23	−	5.91525e22i	−0.285829	−	0.0858657i
$243$	1.02958e24			1.43416
$244$	−6.59189e23	+	9.98140e23i	−0.881276	+	1.33442i
$245$		−	8.94495e23i		−	1.14793i
$246$	−7.15126e23	−	2.14830e23i	−0.881112	−	0.264694i
$247$		−	8.97080e22i		−	0.106136i
$248$	5.72549e23	−	4.77670e23i	0.650572	−	0.542764i
$249$	1.31316e24			1.43326
$250$	−4.56830e23	+	1.52069e24i	−0.479021	+	1.59456i
$251$	1.33605e24			1.34613			0.673065	−	0.739583i	$-0.264977\pi$
$251$	1.33605e24			1.34613			0.673065	+	0.739583i	$0.264977\pi$
$252$	8.38008e23	−	1.26891e24i	0.811414	−	1.22864i
$253$			8.65175e22i			0.0805190i
$254$	1.18111e23	−	3.93168e23i	0.105671	−	0.351756i
$255$		−	3.35966e24i		−	2.88997i
$256$	−8.36230e23	+	8.73052e23i	−0.691713	+	0.722172i
$257$	1.56338e24			1.24375			0.621875	−	0.783117i	$-0.286371\pi$
$257$	1.56338e24			1.24375			0.621875	+	0.783117i	$0.286371\pi$
$258$	−2.20515e24	−	6.62445e23i	−1.68749	−	0.506936i
$259$	−8.71633e23			−0.641706
$260$	−1.56755e24	−	1.03524e24i	−1.11042	−	0.733342i
$261$			1.14976e24i			0.783794i
$262$	−6.95258e23	−	2.08862e23i	−0.456177	−	0.137040i
$263$			2.63570e24i			1.66471i	0.554244	+	0.832354i	$0.313007\pi$
$263$			2.63570e24i			1.66471i	−0.554244	+	0.832354i	$0.686993\pi$
$264$	1.75637e24	+	2.10523e24i	1.06801	+	1.28015i
$265$	3.76572e24			2.20490
$266$	9.04843e22	−	3.01204e23i	0.0510219	−	0.169842i
$267$	−1.83816e24			−0.998321
$268$	1.48212e24	+	9.78819e23i	0.775418	+	0.512099i
$269$		−	3.33951e24i		−	1.68329i	−0.540027	−	0.841647i	$-0.681586\pi$
$269$		−	3.33951e24i		−	1.68329i	0.540027	−	0.841647i	$-0.318414\pi$
$270$	−2.09847e23	+	6.98537e23i	−0.101921	+	0.339275i
$271$			8.24630e23i			0.385981i	0.981201	+	0.192991i	$0.0618187\pi$
$271$			8.24630e23i			0.385981i	−0.981201	+	0.192991i	$0.938181\pi$
$272$	9.98037e23	+	2.33794e24i	0.450254	+	1.05474i
$273$	−3.35541e24			−1.45922
$274$	−8.22119e23	−	2.46972e23i	−0.344690	−	0.103548i
$275$	−5.54328e24			−2.24099
$276$	1.46137e23	−	2.21280e23i	0.0569732	−	0.0862684i
$277$			1.73553e24i			0.652580i	0.945270	+	0.326290i	$0.105799\pi$
$277$			1.73553e24i			0.652580i	−0.945270	+	0.326290i	$0.894201\pi$
$278$	3.10171e24	+	9.31782e23i	1.12500	+	0.337961i
$279$			2.76172e24i			0.966357i
$280$	−4.21901e24	−	5.05703e24i	−1.42440	−	1.70732i
$281$	2.59074e24			0.844036			0.422018	−	0.906587i	$-0.361322\pi$
$281$	2.59074e24			0.844036			0.422018	+	0.906587i	$0.361322\pi$
$282$	−1.16716e24	+	3.88523e24i	−0.366977	+	1.22159i
$283$	−1.50077e24			−0.455459			−0.227730	−	0.973724i	$-0.573130\pi$
$283$	−1.50077e24			−0.455459			−0.227730	+	0.973724i	$0.573130\pi$
$284$	8.27767e23	−	1.25340e24i	0.242507	−	0.367203i
$285$			1.22392e24i			0.346183i
$286$	9.27424e23	−	3.08720e24i	0.253290	−	0.843150i
$287$			3.07784e24i			0.811759i
$288$	−4.98832e23	−	4.44977e24i	−0.127066	−	1.13348i
$289$	1.28103e24			0.315196
$290$	4.76901e24	+	1.43265e24i	1.13357	+	0.340534i
$291$	6.00047e24			1.37802
$292$	5.73502e23	+	3.78751e23i	0.127264	+	0.0840476i
$293$		−	5.50029e24i		−	1.17953i	−0.807574	−	0.589766i	$-0.799220\pi$
$293$		−	5.50029e24i		−	1.17953i	0.807574	−	0.589766i	$-0.200780\pi$
$294$	−4.50568e24	−	1.35355e24i	−0.933871	−	0.280543i
$295$		−	6.26869e24i		−	1.25590i
$296$	−1.97077e24	+	1.64419e24i	−0.381698	+	0.318445i
$297$	−1.25158e24			−0.234365
$298$	3.04448e24	−	1.01344e25i	0.551252	−	1.83500i
$299$	−3.11783e23			−0.0545935
$300$	1.41777e25	+	9.36320e24i	2.40100	+	1.58567i
$301$			9.49076e24i			1.55466i
$302$	−2.38151e24	+	7.92758e24i	−0.377384	+	1.25624i
$303$		−	5.97084e24i		−	0.915397i
$304$	−3.63584e23	−	8.51709e23i	−0.0539348	−	0.126344i
$305$	−1.91878e25			−2.75440
$306$	−9.01721e24	−	2.70885e24i	−1.25273	−	0.376331i
$307$	−2.32060e24			−0.312044			−0.156022	−	0.987754i	$-0.549867\pi$
$307$	−2.32060e24			−0.312044			−0.156022	+	0.987754i	$0.549867\pi$
$308$	6.22784e24	−	9.43015e24i	0.810644	−	1.22747i
$309$		−	6.41576e23i		−	0.0808469i
$310$	1.14552e25	+	3.44123e24i	1.39760	+	0.419853i
$311$			3.94846e24i			0.466470i	0.972420	+	0.233235i	$0.0749312\pi$
$311$			3.94846e24i			0.466470i	−0.972420	+	0.233235i	$0.925069\pi$
$312$	−7.58663e24	+	6.32942e24i	−0.867967	+	0.724133i
$313$	5.88598e24			0.652192			0.326096	−	0.945337i	$-0.394267\pi$
$313$	5.88598e24			0.652192			0.326096	+	0.945337i	$0.394267\pi$
$314$	1.14348e24	−	3.80642e24i	0.122725	−	0.408526i
$315$	2.43929e25			2.53605
$316$	−2.16182e24	+	3.27341e24i	−0.217745	+	0.329709i
$317$			1.40352e25i			1.36970i	0.728685	+	0.684849i	$0.240132\pi$
$317$			1.40352e25i			1.36970i	−0.728685	+	0.684849i	$0.759868\pi$
$318$	5.69828e24	−	1.89684e25i	0.538856	−	1.79374i
$319$			8.54469e24i			0.783050i
$320$	−1.90785e25	−	3.47555e24i	−1.69451	−	0.308691i
$321$	−1.67986e25			−1.44618
$322$	−1.04684e24	−	3.14481e23i	−0.0873622	−	0.0262444i
$323$	−1.94727e24			−0.157544
$324$	−8.93211e24	−	5.89892e24i	−0.700654	−	0.462724i
$325$		−	1.99763e25i		−	1.51944i
$326$	2.12686e25	+	6.38927e24i	1.56878	+	0.471276i
$327$		−	2.79380e25i		−	1.99857i
$328$	5.80583e24	+	6.95904e24i	0.402834	+	0.482848i
$329$	1.67217e25			1.12544
$330$	−1.26532e25	+	4.21200e25i	−0.826155	+	2.75010i
$331$	−1.16179e25			−0.735951			−0.367976	−	0.929835i	$-0.619949\pi$
$331$	−1.16179e25			−0.735951			−0.367976	+	0.929835i	$0.619949\pi$
$332$	−1.32996e25	−	8.78329e24i	−0.817444	−	0.539854i
$333$		−	9.50613e24i		−	0.566972i
$334$	−4.02799e24	+	1.34084e25i	−0.233144	+	0.776089i
$335$			2.84916e25i			1.60055i
$336$	−3.18571e25	+	1.35994e25i	−1.73705	+	0.741527i
$337$	7.90893e24			0.418619			0.209309	−	0.977849i	$-0.432878\pi$
$337$	7.90893e24			0.418619			0.209309	+	0.977849i	$0.432878\pi$
$338$	−7.51286e24	−	2.25693e24i	−0.386046	−	0.115972i
$339$	3.82230e25			1.90690
$340$	−2.24717e25	+	3.40265e25i	−1.08855	+	1.64827i
$341$			2.05243e25i			0.965440i
$342$	3.28496e24	+	9.86832e23i	0.150062	+	0.0450798i
$343$		−	9.70442e24i		−	0.430555i
$344$	1.79027e25	+	2.14587e25i	0.771498	+	0.924740i
$345$	4.25379e24			0.178068
$346$	1.15631e25	−	3.84913e25i	0.470235	−	1.56532i
$347$	−3.29133e25			−1.30040			−0.650200	−	0.759763i	$-0.725315\pi$
$347$	−3.29133e25			−1.30040			−0.650200	+	0.759763i	$0.725315\pi$
$348$	1.44329e25	−	2.18542e25i	0.554065	−	0.838962i
$349$		−	4.94005e25i		−	1.84279i	−0.388623	−	0.921397i	$-0.627049\pi$
$349$		−	4.94005e25i		−	1.84279i	0.388623	−	0.921397i	$-0.372951\pi$
$350$	2.01492e25	−	6.70726e25i	0.730428	−	2.43145i
$351$		−	4.51031e24i		−	0.158904i
$352$	−3.70718e24	−	3.30695e25i	−0.126945	−	1.13240i
$353$	1.62932e25			0.542326			0.271163	−	0.962534i	$-0.412592\pi$
$353$	1.62932e25			0.542326			0.271163	+	0.962534i	$0.412592\pi$
$354$	−3.15762e25	−	9.48576e24i	−1.02171	−	0.306930i
$355$	2.40948e25			0.757948
$356$	1.86168e25	+	1.22949e25i	0.569383	+	0.376031i
$357$			7.28353e25i			2.16601i
$358$	4.68062e25	+	1.40610e25i	1.35355	+	0.406617i
$359$		−	5.41413e25i		−	1.52259i	−0.648403	−	0.761297i	$-0.724563\pi$
$359$		−	5.41413e25i		−	1.52259i	0.648403	−	0.761297i	$-0.275437\pi$
$360$	5.51526e25	−	4.60130e25i	1.50848	−	1.25851i
$361$	−3.68806e25			−0.981128
$362$	−4.21571e24	+	1.40333e25i	−0.109090	+	0.363139i
$363$	−1.73461e25			−0.436651
$364$	3.39835e25	+	2.24433e25i	0.832251	+	0.549633i
$365$			1.10247e25i			0.262688i
$366$	−2.90349e25	+	9.66513e25i	−0.673146	+	2.24077i
$367$			2.12308e25i			0.478968i	0.970900	+	0.239484i	$0.0769782\pi$
$367$			2.12308e25i			0.478968i	−0.970900	+	0.239484i	$0.923022\pi$
$368$	−2.96014e24	+	1.26365e24i	−0.0649882	+	0.0277427i
$369$	−3.35673e25			−0.717220
$370$	−3.94299e25	−	1.18451e25i	−0.819989	−	0.246332i
$371$	−8.16385e25			−1.65255
$372$	3.46678e25	−	5.24937e25i	0.683120	−	1.03438i
$373$		−	4.08340e25i		−	0.783309i	−0.920112	−	0.391655i	$-0.871903\pi$
$373$		−	4.08340e25i		−	0.783309i	0.920112	−	0.391655i	$-0.128097\pi$
$374$	−6.70134e25	−	2.01314e25i	−1.25154	−	0.375974i
$375$			1.33962e26i			2.43595i
$376$	3.78080e25	−	3.15427e25i	0.669430	−	0.558496i
$377$	−3.07925e25			−0.530923
$378$	4.54934e24	−	1.51438e25i	0.0763890	−	0.254283i
$379$	6.13221e25			1.00282			0.501412	−	0.865209i	$-0.332814\pi$
$379$	6.13221e25			1.00282			0.501412	+	0.865209i	$0.332814\pi$
$380$	8.18643e24	−	1.23958e25i	0.130394	−	0.197442i
$381$		−	3.46353e25i		−	0.537364i
$382$	−2.37049e25	+	7.89087e25i	−0.358265	+	1.19259i
$383$		−	5.66622e24i		−	0.0834268i	−0.999130	−	0.0417134i	$-0.986718\pi$
$383$		−	5.66622e24i		−	0.0834268i	0.999130	−	0.0417134i	$-0.0132816\pi$
$384$	−4.63763e25	+	9.08414e25i	−0.665248	+	1.30308i
$385$	1.81281e26			2.53364
$386$	1.09534e26	+	3.29049e25i	1.49168	+	0.448113i
$387$	−1.03507e26			−1.37360
$388$	−6.07725e25	−	4.01353e25i	−0.785941	−	0.519050i
$389$			2.56636e25i			0.323461i	0.986835	+	0.161730i	$0.0517075\pi$
$389$			2.56636e25i			0.323461i	−0.986835	+	0.161730i	$0.948292\pi$
$390$	−1.51788e26	−	4.55985e25i	−1.86463	−	0.560150i
$391$			6.76782e24i			0.0810366i
$392$	3.65799e25	+	4.38457e25i	0.426954	+	0.511760i
$393$	−6.12472e25			−0.696884
$394$	5.08221e24	−	1.69177e25i	0.0563755	−	0.187663i
$395$	−6.29266e25			−0.680556
$396$	1.02846e26	+	6.79215e25i	1.08452	+	0.716235i
$397$			4.41470e25i			0.453938i	0.973902	+	0.226969i	$0.0728816\pi$
$397$			4.41470e25i			0.453938i	−0.973902	+	0.226969i	$0.927118\pi$
$398$	4.99652e25	−	1.66324e26i	0.500999	−	1.66772i
$399$		−	2.65339e25i		−	0.259461i
$400$	−8.09636e25	−	1.89660e26i	−0.772129	−	1.80874i
$401$	8.39617e25			0.780976			0.390488	−	0.920608i	$-0.372306\pi$
$401$	8.39617e25			0.780976			0.390488	+	0.920608i	$0.372306\pi$
$402$	1.43516e26	+	4.31134e25i	1.30208	+	0.391158i
$403$	−7.39636e25			−0.654587
$404$	−3.99371e25	+	6.04724e25i	−0.344796	+	0.522088i
$405$		−	1.71707e26i		−	1.44623i
$406$	−1.03389e26	−	3.10590e25i	−0.849599	−	0.255227i
$407$		−	7.06469e25i		−	0.566434i
$408$	1.37392e26	+	1.64682e26i	1.07488	+	1.28838i
$409$	1.78278e26			1.36102			0.680508	−	0.732740i	$-0.261759\pi$
$409$	1.78278e26			1.36102			0.680508	+	0.732740i	$0.261759\pi$
$410$	−4.18264e25	+	1.39232e26i	−0.311610	+	1.03729i
$411$	−7.24227e25			−0.526571
$412$	−4.29130e24	+	6.49786e24i	−0.0304520	+	0.0461103i
$413$			1.35901e26i			0.941288i
$414$	3.42977e24	−	1.14170e25i	0.0231879	−	0.0771878i
$415$		−	2.55666e26i		−	1.68730i
$416$	1.19173e26	−	1.33596e25i	0.767791	−	0.0860715i
$417$	2.73238e26			1.71862
$418$	2.44129e25	+	7.33386e24i	0.149919	+	0.0450370i
$419$	2.19481e26			1.31600			0.658000	−	0.753018i	$-0.271403\pi$
$419$	2.19481e26			1.31600			0.658000	+	0.753018i	$0.271403\pi$
$420$	−4.63651e26	−	3.06203e26i	−2.71455	−	1.79274i
$421$		−	2.80463e25i		−	0.160345i	−0.996781	−	0.0801723i	$-0.974453\pi$
$421$		−	2.80463e25i		−	0.160345i	0.996781	−	0.0801723i	$-0.0255471\pi$
$422$	1.04789e25	+	3.14796e24i	0.0585048	+	0.0175754i
$423$			1.82369e26i			0.994368i
$424$	−1.84586e26	+	1.53997e26i	−0.982967	+	0.820076i
$425$	−4.33623e26			−2.25540
$426$	3.64601e25	−	1.21368e26i	0.185235	−	0.616608i
$427$	4.15979e26			2.06439
$428$	1.70135e26	+	1.12360e26i	0.824814	+	0.544722i
$429$		−	2.71960e26i		−	1.28805i
$430$	−1.28975e26	+	4.29331e26i	−0.596789	+	1.98659i
$431$			2.93226e26i			1.32565i	0.748773	+	0.662826i	$0.230643\pi$
$431$			2.93226e26i			1.32565i	−0.748773	+	0.662826i	$0.769357\pi$
$432$	−1.82802e25	−	4.28219e25i	−0.0807501	−	0.189160i
$433$	−3.63565e26			−1.56929			−0.784646	−	0.619945i	$-0.787155\pi$
$433$	−3.63565e26			−1.56929			−0.784646	+	0.619945i	$0.787155\pi$
$434$	−2.48340e26	−	7.46037e25i	−1.04749	−	0.314675i
$435$	4.20115e26			1.73171
$436$	−1.86869e26	+	2.82955e26i	−0.752786	+	1.13986i
$437$		−	2.46551e24i		−	0.00970718i
$438$	5.55330e25	+	1.66826e25i	0.213703	+	0.0641982i
$439$		−	5.58045e24i		−	0.0209906i	−0.999945	−	0.0104953i	$-0.996659\pi$
$439$		−	5.58045e24i		−	0.0209906i	0.999945	−	0.0104953i	$-0.00334081\pi$
$440$	4.09878e26	−	3.41956e26i	1.50705	−	1.25731i
$441$	−2.11492e26			−0.760166
$442$	7.25477e25	−	2.41496e26i	0.254918	−	0.848570i
$443$	−3.86486e26			−1.32769			−0.663845	−	0.747870i	$-0.731077\pi$
$443$	−3.86486e26			−1.32769			−0.663845	+	0.747870i	$0.731077\pi$
$444$	−1.19330e26	+	1.80689e26i	−0.400794	+	0.606879i
$445$			3.57881e26i			1.17527i
$446$	1.86834e25	−	6.21932e25i	0.0599939	−	0.199707i
$447$		−	8.92771e26i		−	2.80327i
$448$	4.13609e26	+	7.53477e25i	1.27002	+	0.231361i
$449$	−2.54008e26			−0.762753			−0.381377	−	0.924420i	$-0.624550\pi$
$449$	−2.54008e26			−0.762753			−0.381377	+	0.924420i	$0.624550\pi$
$450$	7.31502e26	+	2.19750e26i	2.14828	+	0.645361i
$451$	−2.49463e26			−0.716540
$452$	−3.87121e26	−	2.55662e26i	−1.08758	−	0.718259i
$453$			6.98362e26i			1.91910i
$454$	1.11684e26	+	3.35508e25i	0.300214	+	0.0901870i
$455$			6.53283e26i			1.71786i
$456$	−5.00517e25	−	5.99934e25i	−0.128757	−	0.154332i
$457$	−4.82016e26			−1.21311			−0.606554	−	0.795042i	$-0.707449\pi$
$457$	−4.82016e26			−1.21311			−0.606554	+	0.795042i	$0.707449\pi$
$458$	1.03538e26	−	3.44656e26i	0.254943	−	0.848654i
$459$	−9.79045e25			−0.235872
$460$	−4.30822e25	−	2.84522e25i	−0.101559	−	0.0670715i
$461$			4.12032e26i			0.950434i	0.879869	+	0.475217i	$0.157630\pi$
$461$			4.12032e26i			0.950434i	−0.879869	+	0.475217i	$0.842370\pi$
$462$	2.74314e26	−	9.13134e26i	0.619196	−	2.06118i
$463$			2.63607e26i			0.582300i	0.956677	+	0.291150i	$0.0940378\pi$
$463$			2.63607e26i			0.582300i	−0.956677	+	0.291150i	$0.905962\pi$
$464$	−2.92351e26	+	1.24801e26i	−0.632012	+	0.269798i
$465$	1.00912e27			2.13507
$466$	−4.39792e26	−	1.32117e26i	−0.910726	−	0.273590i
$467$	2.33101e26			0.472471			0.236236	−	0.971696i	$-0.424086\pi$
$467$	2.33101e26			0.472471			0.236236	+	0.971696i	$0.424086\pi$
$468$	−2.44769e26	+	3.70628e26i	−0.485622	+	0.735325i
$469$		−	6.17680e26i		−	1.19960i
$470$	7.56436e26	+	2.27240e26i	1.43812	+	0.432023i
$471$		−	3.35318e26i		−	0.624090i
$472$	2.56355e26	+	3.07274e26i	0.467112	+	0.559894i
$473$	−7.69238e26			−1.37230
$474$	−9.52204e25	+	3.16969e26i	−0.166321	+	0.553648i
$475$	1.57968e26			0.270168
$476$	4.87172e26	−	7.37673e26i	0.815855	−	1.23536i
$477$		−	8.90358e26i		−	1.46009i
$478$	−1.87117e25	+	6.22875e25i	−0.0300493	+	0.100028i
$479$		−	3.33329e25i		−	0.0524226i	−0.999656	−	0.0262113i	$-0.991656\pi$
$479$		−	3.33329e25i		−	0.0524226i	0.999656	−	0.0262113i	$-0.00834427\pi$
$480$	−1.62592e27	+	1.82270e26i	−2.50430	+	0.280739i
$481$	2.54591e26			0.384054
$482$	1.18405e27	+	3.55699e26i	1.74944	+	0.525548i
$483$	−9.22194e25			−0.133460
$484$	1.75680e26	+	1.16022e26i	0.249040	+	0.164470i
$485$		−	1.16826e27i		−	1.62227i
$486$	−1.00971e27	−	3.03327e26i	−1.37352	−	0.412618i
$487$		−	5.35339e26i		−	0.713410i	−0.934217	−	0.356705i	$-0.883900\pi$
$487$		−	5.35339e26i		−	0.713410i	0.934217	−	0.356705i	$-0.116100\pi$
$488$	9.40534e26	−	7.84675e26i	1.22794	−	1.02445i
$489$	1.87361e27			2.39657
$490$	−2.63529e26	+	8.77234e26i	−0.330269	+	1.09940i
$491$	−3.93131e26			−0.482750			−0.241375	−	0.970432i	$-0.577598\pi$
$491$	−3.93131e26			−0.482750			−0.241375	+	0.970432i	$0.577598\pi$
$492$	6.38035e26	+	4.21369e26i	0.767703	+	0.507005i
$493$			6.68408e26i			0.788083i
$494$	−2.64291e25	+	8.79770e25i	−0.0305360	+	0.101648i
$495$			1.97707e27i			2.23857i
$496$	−7.02228e26	+	2.99773e26i	−0.779222	+	0.332640i
$497$	−5.22359e26			−0.568075
$498$	−1.28782e27	−	3.86872e26i	−1.37266	−	0.412358i
$499$	3.50826e26			0.366511			0.183255	−	0.983065i	$-0.441336\pi$
$499$	3.50826e26			0.366511			0.183255	+	0.983065i	$0.441336\pi$
$500$	8.96029e26	−	1.35676e27i	0.917534	−	1.38932i
$501$			1.18118e27i			1.18560i
$502$	−1.31027e27	−	3.93618e26i	−1.28921	−	0.387291i
$503$		−	7.83816e26i		−	0.756022i	−0.925801	−	0.378011i	$-0.876608\pi$
$503$		−	7.83816e26i		−	0.756022i	0.925801	−	0.378011i	$-0.123392\pi$
$504$	−1.19567e27	+	9.97533e26i	−1.13059	+	0.943240i
$505$	−1.16250e27			−1.07765
$506$	2.54891e25	−	8.48480e25i	0.0231659	−	0.0771146i
$507$	−6.61829e26			−0.589747
$508$	−2.31664e26	+	3.50785e26i	−0.202405	+	0.306481i
$509$			1.14995e27i			0.985148i	0.870271	+	0.492574i	$0.163944\pi$
$509$			1.14995e27i			0.985148i	−0.870271	+	0.492574i	$0.836056\pi$
$510$	−9.89798e26	+	3.29483e27i	−0.831466	+	2.76778i
$511$		−	2.39009e26i		−	0.196882i
$512$	1.07731e27	−	6.09842e26i	0.870241	−	0.492627i
$513$	3.56665e25			0.0282545
$514$	−1.53321e27	−	4.60590e26i	−1.19116	−	0.357836i
$515$	−1.24912e26			−0.0951768
$516$	1.96743e27	+	1.29933e27i	1.47029	+	0.971004i
$517$			1.35531e27i			0.993424i
$518$	8.54814e26	+	2.56794e26i	0.614574	+	0.184623i
$519$		−	3.39081e27i		−	2.39128i
$520$	1.23231e27	+	1.47708e27i	0.852484	+	1.02181i
$521$	1.79868e27			1.22061			0.610306	−	0.792166i	$-0.291047\pi$
$521$	1.79868e27			1.22061			0.610306	+	0.792166i	$0.291047\pi$
$522$	3.38733e26	−	1.12757e27i	0.225503	−	0.750654i
$523$	1.23394e27			0.805890			0.402945	−	0.915224i	$-0.367987\pi$
$523$	1.23394e27			0.805890			0.402945	+	0.915224i	$0.367987\pi$
$524$	6.20309e26	+	4.09663e26i	0.397461	+	0.262491i
$525$		−	5.90861e27i		−	3.71443i
$526$	7.76509e26	−	2.58484e27i	0.478949	−	1.59432i
$527$			1.60551e27i			0.971646i
$528$	−1.10225e27	−	2.58205e27i	−0.654546	−	1.53330i
$529$	1.70759e27			0.995007
$530$	−3.69306e27	−	1.10943e27i	−2.11168	−	0.634367i
$531$	−1.48215e27			−0.831664
$532$	−1.77477e26	+	2.68734e26i	−0.0977293	+	0.147981i
$533$		−	8.98990e26i		−	0.485828i
$534$	1.80269e27	+	5.41544e26i	0.956111	+	0.287224i
$535$			3.27060e27i			1.70251i
$536$	−1.16515e27	−	1.39658e27i	−0.595297	−	0.713540i
$537$	4.12328e27			2.06776
$538$	−9.83861e26	+	3.27507e27i	−0.484296	+	1.61212i
$539$	−1.57175e27			−0.759444
$540$	4.11595e26	−	6.23234e26i	0.195224	−	0.295606i
$541$			3.90282e26i			0.181721i	0.995864	+	0.0908607i	$0.0289618\pi$
$541$			3.90282e26i			0.181721i	−0.995864	+	0.0908607i	$0.971038\pi$
$542$	2.42946e26	−	8.08718e26i	0.111050	−	0.369662i
$543$			1.23623e27i			0.554754i
$544$	−2.89994e26	−	2.58686e27i	−0.127761	−	1.13968i
$545$	−5.43940e27			−2.35281
$546$	3.29067e27	+	9.88546e26i	1.39752	+	0.419827i
$547$	−5.54597e26			−0.231262			−0.115631	−	0.993292i	$-0.536889\pi$
$547$	−5.54597e26			−0.231262			−0.115631	+	0.993292i	$0.536889\pi$
$548$	7.33494e26	+	4.84412e26i	0.300325	+	0.198340i
$549$			4.53672e27i			1.82397i
$550$	5.43632e27	+	1.63312e27i	2.14624	+	0.644749i
$551$		−	2.43500e26i		−	0.0944026i
$552$	−2.08509e26	+	1.73956e26i	−0.0793843	+	0.0662292i
$553$	1.36421e27			0.510070
$554$	5.11308e26	−	1.70204e27i	0.187752	−	0.624988i
$555$	−3.47349e27			−1.25267
$556$	−2.76735e27	−	1.82760e27i	−0.980202	−	0.647343i
$557$			2.54412e27i			0.885087i	0.896747	+	0.442543i	$0.145924\pi$
$557$			2.54412e27i			0.885087i	−0.896747	+	0.442543i	$0.854076\pi$
$558$	8.13636e26	−	2.70843e27i	0.278028	−	0.925498i
$559$		−	2.77211e27i		−	0.930447i
$560$	2.64774e27	+	6.20242e27i	0.872961	+	2.04494i
$561$	−5.90339e27			−1.91193
$562$	−2.54075e27	−	7.63264e26i	−0.808349	−	0.242835i
$563$	−1.04936e27			−0.327976			−0.163988	−	0.986462i	$-0.552436\pi$
$563$	−1.04936e27			−0.327976			−0.163988	+	0.986462i	$0.552436\pi$
$564$	2.28927e27	−	3.46640e27i	0.702921	−	1.06436i
$565$		−	7.44184e27i		−	2.24489i
$566$	1.47181e27	+	4.42145e26i	0.436202	+	0.131039i
$567$			3.72249e27i			1.08393i
$568$	−1.18106e27	+	9.85343e26i	−0.337900	+	0.281906i
$569$	1.91505e27			0.538340			0.269170	−	0.963093i	$-0.413251\pi$
$569$	1.91505e27			0.538340			0.269170	+	0.963093i	$0.413251\pi$
$570$	3.60583e26	−	1.20031e27i	0.0995993	−	0.331546i
$571$	9.26020e26			0.251339			0.125669	−	0.992072i	$-0.459892\pi$
$571$	9.26020e26			0.251339			0.125669	+	0.992072i	$0.459892\pi$
$572$	−1.81906e27	+	2.75440e27i	−0.485161	+	0.734627i
$573$			6.95129e27i			1.82188i
$574$	9.06769e26	−	3.01845e27i	0.233549	−	0.777437i
$575$		−	5.49025e26i		−	0.138968i
$576$	−8.21750e26	+	4.51087e27i	−0.204416	+	1.12211i
$577$	−8.98956e26			−0.219776			−0.109888	−	0.993944i	$-0.535049\pi$
$577$	−8.98956e26			−0.219776			−0.109888	+	0.993944i	$0.535049\pi$
$578$	−1.25631e27	−	3.77406e26i	−0.301869	−	0.0906840i
$579$	9.64912e27			2.27878
$580$	−4.25491e27	−	2.81002e27i	−0.987666	−	0.652272i
$581$			5.54267e27i			1.26461i
$582$	−5.88469e27	−	1.76781e27i	−1.31976	−	0.396466i
$583$		−	6.61689e27i		−	1.45871i
$584$	−4.50851e26	−	5.40403e26i	−0.0977023	−	0.117109i
$585$	−7.12478e27			−1.51779
$586$	−1.62045e27	+	5.39416e27i	−0.339360	+	1.12966i
$587$	8.28104e26			0.170492			0.0852460	−	0.996360i	$-0.472832\pi$
$587$	8.28104e26			0.170492			0.0852460	+	0.996360i	$0.472832\pi$
$588$	4.01996e27	+	2.65486e27i	0.813671	+	0.537363i
$589$		−	5.84888e26i		−	0.116391i
$590$	−1.84683e27	+	6.14773e27i	−0.361333	+	1.20280i
$591$		−	1.49032e27i		−	0.286685i
$592$	2.41714e27	−	1.03185e27i	0.457178	−	0.195164i
$593$	2.16861e27			0.403306			0.201653	−	0.979457i	$-0.435369\pi$
$593$	2.16861e27			0.403306			0.201653	+	0.979457i	$0.435369\pi$
$594$	1.22743e27	+	3.68730e26i	0.224456	+	0.0674285i
$595$	1.41807e28			2.54993
$596$	−5.97146e27	+	9.04194e27i	−1.05589	+	1.59882i
$597$		−	1.46519e28i		−	2.54772i
$598$	3.05767e26	+	9.18552e25i	0.0522852	+	0.0157069i
$599$			6.16313e26i			0.103641i	0.998656	+	0.0518207i	$0.0165024\pi$
$599$			6.16313e26i			0.103641i	−0.998656	+	0.0518207i	$0.983498\pi$
$600$	−1.11456e28	−	1.33594e28i	−1.84328	−	2.20941i
$601$	−8.17765e26			−0.133010			−0.0665049	−	0.997786i	$-0.521185\pi$
$601$	−8.17765e26			−0.133010			−0.0665049	+	0.997786i	$0.521185\pi$
$602$	2.79609e27	−	9.30763e27i	0.447288	−	1.48893i
$603$	6.73649e27			1.05989
$604$	4.67112e27	−	7.07298e27i	0.722856	−	1.09454i
$605$			3.37719e27i			0.514046i
$606$	−1.75908e27	+	5.85563e27i	−0.263366	+	0.876692i
$607$		−	7.48374e27i		−	1.10213i	−0.834463	−	0.551064i	$-0.814222\pi$
$607$		−	7.48374e27i		−	1.10213i	0.834463	−	0.551064i	$-0.185778\pi$
$608$	1.05645e26	+	9.42390e26i	0.0153042	+	0.136520i
$609$	−9.10783e27			−1.29790
$610$	1.88175e28	+	5.65296e27i	2.63794	+	0.792460i
$611$	−4.88416e27			−0.673562
$612$	8.04515e27	+	5.31316e27i	1.09149	+	0.720839i
$613$			2.92871e27i			0.390906i	0.980713	+	0.195453i	$0.0626177\pi$
$613$			2.92871e27i			0.390906i	−0.980713	+	0.195453i	$0.937382\pi$
$614$	2.27582e27	+	6.83676e26i	0.298850	+	0.0897773i
$615$			1.22653e28i			1.58463i
$616$	−8.88590e27	+	7.41339e27i	−1.12952	+	0.942344i
$617$	1.27218e28			1.59109			0.795547	−	0.605891i	$-0.207183\pi$
$617$	1.27218e28			1.59109			0.795547	+	0.605891i	$0.207183\pi$
$618$	−1.89016e26	+	6.29196e26i	−0.0232602	+	0.0774286i
$619$	−1.60929e28			−1.94863			−0.974314	−	0.225195i	$-0.927698\pi$
$619$	−1.60929e28			−1.94863			−0.974314	+	0.225195i	$0.927698\pi$
$620$	−1.02203e28	−	6.74965e27i	−1.21772	−	0.804201i
$621$		−	1.23960e26i		−	0.0145334i
$622$	1.16326e27	−	3.87227e27i	0.134207	−	0.446747i
$623$		−	7.75862e27i		−	0.880854i
$624$	9.30496e27	−	3.97218e27i	1.03961	−	0.443795i
$625$	8.19518e27			0.901069
$626$	−5.77240e27	−	1.73408e27i	−0.624616	−	0.187640i
$627$	2.15060e27			0.229026
$628$	−2.24283e27	+	3.39608e27i	−0.235072	+	0.355944i
$629$		−	5.52635e27i		−	0.570075i
$630$	−2.39222e28	−	7.18644e27i	−2.42882	−	0.729639i
$631$			9.82154e27i			0.981490i	0.871303	+	0.490745i	$0.163275\pi$
$631$			9.82154e27i			0.981490i	−0.871303	+	0.490745i	$0.836725\pi$
$632$	3.08449e27	−	2.57335e27i	0.303398	−	0.253121i
$633$	9.23116e26			0.0893757
$634$	4.13493e27	−	1.37643e28i	0.394072	−	1.31178i
$635$	−6.74332e27			−0.632611
$636$	−1.11766e28	+	1.69236e28i	−1.03214	+	1.56287i
$637$		−	5.66412e27i		−	0.514918i
$638$	2.51737e27	−	8.37981e27i	0.225289	−	0.749941i
$639$		−	5.69691e27i		−	0.501916i
$640$	1.76864e28	+	9.02924e27i	1.53405	+	0.783161i
$641$	7.29542e27			0.622974			0.311487	−	0.950250i	$-0.399173\pi$
$641$	7.29542e27			0.622974			0.311487	+	0.950250i	$0.399173\pi$
$642$	1.64744e28	+	4.94906e27i	1.38503	+	0.416076i
$643$	−3.08089e26			−0.0255016			−0.0127508	−	0.999919i	$-0.504059\pi$
$643$	−3.08089e26			−0.0255016			−0.0127508	+	0.999919i	$0.504059\pi$
$644$	9.33994e26	+	6.16826e26i	0.0761177	+	0.0502694i
$645$			3.78210e28i			3.03484i
$646$	1.90970e27	+	5.73691e26i	0.150883	+	0.0453265i
$647$			4.11006e27i			0.319746i	0.987138	+	0.159873i	$0.0511085\pi$
$647$			4.11006e27i			0.319746i	−0.987138	+	0.159873i	$0.948891\pi$
$648$	7.02186e27	+	8.41660e27i	0.537900	+	0.644743i
$649$	−1.10150e28			−0.830875
$650$	−5.88527e27	+	1.95909e28i	−0.437153	+	1.45519i
$651$	−2.18770e28			−1.60021
$652$	−1.89758e28	−	1.25320e28i	−1.36686	−	0.902699i
$653$		−	2.18243e28i		−	1.54813i	−0.633105	−	0.774066i	$-0.718220\pi$
$653$		−	2.18243e28i		−	1.54813i	0.633105	−	0.774066i	$-0.281780\pi$
$654$	−8.23088e27	+	2.73989e28i	−0.575001	+	1.91406i
$655$			1.19245e28i			0.820405i
$656$	−3.64358e27	−	8.53522e27i	−0.246882	−	0.578331i
$657$	2.60666e27			0.173953
$658$	−1.63990e28	−	4.92642e27i	−1.07785	−	0.323797i
$659$	−1.03384e28			−0.669265			−0.334632	−	0.942349i	$-0.608612\pi$
$659$	−1.03384e28			−0.669265			−0.334632	+	0.942349i	$0.608612\pi$
$660$	2.48181e28	−	3.75794e28i	1.58245	−	2.39613i
$661$			3.34206e27i			0.209894i	0.994478	+	0.104947i	$0.0334672\pi$
$661$			3.34206e27i			0.209894i	−0.994478	+	0.104947i	$0.966533\pi$
$662$	1.13938e28	+	3.42279e27i	0.704834	+	0.211739i
$663$		−	2.12741e28i		−	1.29633i
$664$	1.04553e28	+	1.25320e28i	0.627561	+	0.752213i
$665$	−5.16602e27			−0.305450
$666$	−2.80062e27	+	9.32270e27i	−0.163122	+	0.543000i
$667$	−8.46295e26			−0.0485583
$668$	7.90054e27	−	1.19629e28i	0.446573	−	0.676197i
$669$		−	5.47877e27i		−	0.305086i
$670$	8.39398e27	−	2.79418e28i	0.460490	−	1.53288i
$671$			3.37156e28i			1.82224i
$672$	3.52489e28	−	3.95150e27i	1.87695	−	0.210412i
$673$	−7.36345e27			−0.386306			−0.193153	−	0.981169i	$-0.561871\pi$
$673$	−7.36345e27			−0.386306			−0.193153	+	0.981169i	$0.561871\pi$
$674$	−7.75632e27	−	2.33007e27i	−0.400919	−	0.120440i
$675$	7.94229e27			0.404490
$676$	6.70297e27	+	4.42676e27i	0.336357	+	0.222136i
$677$		−	1.68918e28i		−	0.835199i	−0.908631	−	0.417600i	$-0.862871\pi$
$677$		−	1.68918e28i		−	0.835199i	0.908631	−	0.417600i	$-0.137129\pi$
$678$	−3.74855e28	−	1.12610e28i	−1.82627	−	0.548629i
$679$			2.53272e28i			1.21588i
$680$	3.20627e28	−	2.67495e28i	1.51674	−	1.26540i
$681$	9.83853e27			0.458626
$682$	6.04672e27	−	2.01283e28i	0.277764	−	0.924619i
$683$	2.83245e28			1.28220			0.641100	−	0.767457i	$-0.278478\pi$
$683$	2.83245e28			1.28220			0.641100	+	0.767457i	$0.278478\pi$
$684$	−2.93084e27	−	1.93558e27i	−0.130747	−	0.0863475i
$685$			1.41004e28i			0.619904i
$686$	−2.85904e27	+	9.51716e27i	−0.123874	+	0.412350i
$687$		−	3.03617e28i		−	1.29646i
$688$	−1.12353e28	−	2.63190e28i	−0.472824	−	1.10761i
$689$	2.38453e28			0.989034
$690$	−4.17171e27	−	1.25322e27i	−0.170539	−	0.0512313i
$691$	9.01687e26			0.0363308			0.0181654	−	0.999835i	$-0.494217\pi$
$691$	9.01687e26			0.0363308			0.0181654	+	0.999835i	$0.494217\pi$
$692$	−2.26800e28	+	3.43420e28i	−0.900705	+	1.36384i
$693$		−	4.28616e28i		−	1.67779i
$694$	3.22782e28	+	9.69666e27i	1.24542	+	0.374134i
$695$		−	5.31982e28i		−	2.02325i
$696$	−2.05929e28	+	1.71804e28i	−0.772014	+	0.644081i
$697$	−1.95142e28			−0.721146
$698$	−1.45540e28	+	4.84472e28i	−0.530185	+	1.76488i
$699$	−3.87425e28			−1.39128
$700$	−3.95208e28	+	5.98422e28i	−1.39909	+	2.11849i
$701$			1.13211e28i			0.395100i	0.980293	+	0.197550i	$0.0632985\pi$
$701$			1.13211e28i			0.395100i	−0.980293	+	0.197550i	$0.936702\pi$
$702$	−1.32879e27	+	4.42328e27i	−0.0457179	+	0.152186i
$703$			2.01325e27i			0.0682879i
$704$	−6.10702e27	+	3.35235e28i	−0.204222	+	1.12104i
$705$	6.66365e28			2.19696
$706$	−1.59788e28	−	4.80018e27i	−0.519395	−	0.156031i
$707$	2.52021e28			0.807687
$708$	2.81722e28	+	1.86054e28i	0.890202	+	0.587905i
$709$			5.95923e28i			1.85664i	0.371783	+	0.928320i	$0.378747\pi$
$709$			5.95923e28i			1.85664i	−0.371783	+	0.928320i	$0.621253\pi$
$710$	−2.36298e28	−	7.09861e27i	−0.725901	−	0.218067i
$711$			1.48782e28i			0.450666i
$712$	−1.46353e28	−	1.75423e28i	−0.437122	−	0.523947i
$713$	−2.03280e27			−0.0598686
$714$	2.14582e28	−	7.14299e28i	0.623176	−	2.07443i
$715$	−5.29494e28			−1.51635
$716$	−4.17604e28	−	2.75793e28i	−1.17933	−	0.778849i
$717$			5.48707e27i			0.152809i
$718$	−1.59507e28	+	5.30966e28i	−0.438061	+	1.45822i
$719$			2.54256e28i			0.688623i	0.938855	+	0.344312i	$0.111888\pi$
$719$			2.54256e28i			0.688623i	−0.938855	+	0.344312i	$0.888112\pi$
$720$	−6.76443e28	+	2.88765e28i	−1.80678	+	0.771295i
$721$	2.70801e27			0.0713341
$722$	3.61689e28	+	1.08655e28i	0.939645	+	0.282278i
$723$	1.04306e29			2.67256
$724$	8.26873e27	−	1.25205e28i	0.208955	−	0.316399i
$725$		−	5.42231e28i		−	1.35146i
$726$	1.70113e28	+	5.11036e27i	0.418189	+	0.125628i
$727$		−	4.74565e28i		−	1.15067i	−0.817917	−	0.575337i	$-0.804871\pi$
$727$		−	4.74565e28i		−	1.15067i	0.817917	−	0.575337i	$-0.195129\pi$
$728$	−2.67157e28	−	3.20222e28i	−0.638928	−	0.765838i
$729$	−5.33541e28			−1.25861
$730$	3.24802e27	−	1.08120e28i	0.0755772	−	0.251581i
$731$	−6.01736e28			−1.38112
$732$	5.69493e28	−	8.62322e28i	1.28937	−	1.95236i
$733$			3.45216e27i			0.0770995i	0.999257	+	0.0385498i	$0.0122738\pi$
$733$			3.45216e27i			0.0770995i	−0.999257	+	0.0385498i	$0.987726\pi$
$734$	6.25486e27	−	2.08211e28i	0.137802	−	0.458716i
$735$			7.72780e28i			1.67951i
$736$	3.27531e27	−	3.67172e26i	0.0702222	−	0.00787211i
$737$	5.00637e28			1.05888
$738$	3.29196e28	+	9.88933e27i	0.686895	+	0.206349i
$739$	6.30447e28			1.29779			0.648895	−	0.760878i	$-0.275232\pi$
$739$	6.30447e28			1.29779			0.648895	+	0.760878i	$0.275232\pi$
$740$	3.51793e28	+	2.32330e28i	0.714447	+	0.471833i
$741$			7.75013e27i			0.155284i
$742$	8.00631e28	+	2.40517e28i	1.58268	+	0.475452i
$743$		−	1.06032e28i		−	0.206799i	−0.994640	−	0.103400i	$-0.967028\pi$
$743$		−	1.06032e28i		−	0.206799i	0.994640	−	0.103400i	$-0.0329721\pi$
$744$	−4.94641e28	+	4.12673e28i	−0.951833	+	0.794102i
$745$	−1.73818e29			−3.30014
$746$	−1.20302e28	+	4.00460e28i	−0.225364	+	0.750190i
$747$	−6.04490e28			−1.11733
$748$	5.97893e28	+	3.94859e28i	1.09045	+	0.720155i
$749$		−	7.09045e28i		−	1.27601i
$750$	3.94668e28	−	1.31377e29i	0.700841	−	2.33296i
$751$		−	1.67963e28i		−	0.294316i	−0.989113	−	0.147158i	$-0.952987\pi$
$751$		−	1.67963e28i		−	0.294316i	0.989113	−	0.147158i	$-0.0470126\pi$
$752$	−4.63713e28	+	1.97953e28i	−0.801809	+	0.342283i
$753$	−1.15426e29			−1.96948
$754$	3.01983e28	+	9.07185e27i	0.508475	+	0.152750i
$755$	1.35968e29			2.25926
$756$	−8.92311e27	+	1.35113e28i	−0.146318	+	0.221554i
$757$			3.68923e28i			0.597003i	0.954409	+	0.298502i	$0.0964868\pi$
$757$			3.68923e28i			0.597003i	−0.954409	+	0.298502i	$0.903513\pi$
$758$	−6.01388e28	−	1.80662e28i	−0.960423	−	0.288520i
$759$		−	7.47449e27i		−	0.117805i
$760$	−1.16804e28	+	9.74482e27i	−0.181687	+	0.151579i
$761$	7.29129e28			1.11933			0.559664	−	0.828719i	$-0.310930\pi$
$761$	7.29129e28			1.11933			0.559664	+	0.828719i	$0.310930\pi$
$762$	−1.02040e28	+	3.39669e28i	−0.154604	+	0.514644i
$763$	1.17923e29			1.76341
$764$	4.64949e28	−	7.04023e28i	0.686234	−	1.03909i
$765$			1.54656e29i			2.25296i
$766$	−1.66934e27	+	5.55688e27i	−0.0240025	+	0.0798994i
$767$		−	3.96946e28i		−	0.563350i
$768$	7.22443e28	−	7.54255e28i	1.01203	−	1.05659i
$769$	1.07688e28			0.148904			0.0744519	−	0.997225i	$-0.476279\pi$
$769$	1.07688e28			0.148904			0.0744519	+	0.997225i	$0.476279\pi$
$770$	−1.77783e29	−	5.34076e28i	−2.42651	−	0.728947i
$771$	−1.35065e29			−1.81969
$772$	−9.77259e28	−	6.45399e28i	−1.29968	−	0.858332i
$773$			1.12471e29i			1.47654i	0.674503	+	0.738272i	$0.264358\pi$
$773$			1.12471e29i			1.47654i	−0.674503	+	0.738272i	$0.735642\pi$
$774$	1.01510e29	+	3.04945e28i	1.31553	+	0.395196i
$775$		−	1.30244e29i		−	1.66625i
$776$	4.77755e28	+	5.72651e28i	0.603376	+	0.723224i
$777$	7.53029e28			0.938862
$778$	7.56081e27	−	2.51684e28i	0.0930620	−	0.309784i
$779$	7.10901e27			0.0863843
$780$	1.35425e29	+	8.94372e28i	1.62463	+	1.07293i
$781$		−	4.23378e28i		−	0.501439i
$782$	1.99388e27	−	6.63723e27i	0.0233148	−	0.0776103i
$783$		−	1.22426e28i		−	0.141338i
$784$	−2.29565e28	−	5.37765e28i	−0.261665	−	0.612960i
$785$	−6.52848e28			−0.734709
$786$	6.00653e28	+	1.80442e28i	0.667419	+	0.200499i
$787$	5.39829e28			0.592255			0.296128	−	0.955148i	$-0.404305\pi$
$787$	5.39829e28			0.592255			0.296128	+	0.955148i	$0.404305\pi$
$788$	−9.96829e27	+	1.50939e28i	−0.107984	+	0.163508i
$789$		−	2.27706e29i		−	2.43559i
$790$	6.17124e28	+	1.85390e28i	0.651781	+	0.195801i
$791$			1.61334e29i			1.68253i
$792$	−8.08513e28	−	9.69107e28i	−0.832597	−	0.997975i
$793$	−1.21501e29			−1.23552
$794$	1.30062e28	−	4.32951e28i	0.130601	−	0.434745i
$795$	−3.25332e29			−3.22593
$796$	−9.80021e28	+	1.48394e29i	−0.959632	+	1.45307i
$797$			7.35071e28i			0.710798i	0.934715	+	0.355399i	$0.115655\pi$
$797$			7.35071e28i			0.710798i	−0.934715	+	0.355399i	$0.884345\pi$
$798$	−7.81720e27	+	2.60219e28i	−0.0746487	+	0.248490i
$799$			1.06019e29i			0.999810i
$800$	2.35251e28	+	2.09853e29i	0.219095	+	1.95441i
$801$	8.46164e28			0.778269
$802$	−8.23416e28	−	2.47361e28i	−0.747955	−	0.224692i
$803$	1.93720e28			0.173788
$804$	−1.28045e29	−	8.45630e28i	−1.13449	−	0.749238i
$805$			1.79547e28i			0.157115i
$806$	7.25364e28	+	2.17906e28i	0.626910	+	0.188330i
$807$			2.88510e29i			2.46278i
$808$	5.69823e28	−	4.75396e28i	0.480426	−	0.400813i
$809$	2.02377e29			1.68529			0.842646	−	0.538468i	$-0.180997\pi$
$809$	2.02377e29			1.68529			0.842646	+	0.538468i	$0.180997\pi$
$810$	−5.05869e28	+	1.68393e29i	−0.416091	+	1.38508i
$811$	−1.16708e28			−0.0948182			−0.0474091	−	0.998876i	$-0.515096\pi$
$811$	−1.16708e28			−0.0948182			−0.0474091	+	0.998876i	$0.515096\pi$
$812$	9.22437e28	+	6.09193e28i	0.740246	+	0.488872i
$813$		−	7.12422e28i		−	0.564718i
$814$	−2.08134e28	+	6.92837e28i	−0.162967	+	0.542484i
$815$		−	3.64783e29i		−	2.82136i
$816$	−8.62233e28	−	2.01981e29i	−0.658753	−	1.54315i
$817$	2.19212e28			0.165441
$818$	−1.74837e29	−	5.25227e28i	−1.30347	−	0.391574i
$819$	1.54461e29			1.13757
$820$	8.20386e28	−	1.24222e29i	0.596870	−	0.903777i
$821$		−	1.11995e29i		−	0.804946i	−0.915432	−	0.402473i	$-0.868151\pi$
$821$		−	1.11995e29i		−	0.804946i	0.915432	−	0.402473i	$-0.131849\pi$
$822$	7.10252e28	+	2.13366e28i	0.504306	+	0.151498i
$823$			1.93588e29i			1.35794i	0.734168	+	0.678968i	$0.237573\pi$
$823$			1.93588e29i			1.35794i	−0.734168	+	0.678968i	$0.762427\pi$
$824$	6.12284e27	−	5.10820e27i	0.0424307	−	0.0353994i
$825$	4.78900e29			3.27873
$826$	4.00381e28	−	1.33279e29i	0.270815	−	0.901489i
$827$	−2.00807e29			−1.34191			−0.670956	−	0.741497i	$-0.734116\pi$
$827$	−2.00807e29			−1.34191			−0.670956	+	0.741497i	$0.734116\pi$
$828$	−6.72718e27	+	1.01862e28i	−0.0444150	+	0.0672529i
$829$		−	1.38032e29i		−	0.900396i	−0.892929	−	0.450198i	$-0.851353\pi$
$829$		−	1.38032e29i		−	0.900396i	0.892929	−	0.450198i	$-0.148647\pi$
$830$	−7.53222e28	+	2.50732e29i	−0.485447	+	1.61596i
$831$		−	1.49937e29i		−	0.954771i
$832$	−1.20809e29	−	2.20079e28i	−0.760091	−	0.138467i
$833$	−1.22950e29			−0.764326
$834$	−2.67966e29	−	8.04993e28i	−1.64596	−	0.494461i
$835$	2.29970e29			1.39575
$836$	−2.17812e28	−	1.43847e28i	−0.130623	−	0.0862656i
$837$		−	2.94068e28i		−	0.174258i
$838$	−2.15245e29	−	6.46616e28i	−1.26036	−	0.378623i
$839$		−	3.34163e29i		−	1.93348i	−0.255767	−	0.966738i	$-0.582328\pi$
$839$		−	3.34163e29i		−	1.93348i	0.255767	−	0.966738i	$-0.417672\pi$
$840$	3.64493e29	+	4.36892e29i	2.08399	+	2.49793i
$841$	9.34124e28			0.527770
$842$	−8.26278e27	+	2.75051e28i	−0.0461323	+	0.153565i
$843$	−2.23822e29			−1.23488
$844$	−9.34928e27	−	6.17443e27i	−0.0509746	−	0.0336645i
$845$			1.28855e29i			0.694279i
$846$	5.37281e28	−	1.78850e29i	0.286087	−	0.952325i
$847$		−	7.32154e28i		−	0.385273i
$848$	2.26393e29	−	9.66445e28i	1.17735	−	0.502596i
$849$	1.29656e29			0.666370
$850$	4.25255e29	+	1.27751e29i	2.16003	+	0.648894i
$851$	6.99711e27			0.0351256
$852$	−7.15132e28	+	1.08285e29i	−0.354805	+	0.537244i
$853$			3.64380e29i			1.78675i	0.449311	+	0.893375i	$0.351669\pi$
$853$			3.64380e29i			1.78675i	−0.449311	+	0.893375i	$0.648331\pi$
$854$	−4.07952e29	−	1.22553e29i	−1.97711	−	0.593941i
$855$		−	5.63412e28i		−	0.269876i
$856$	−1.33749e29	−	1.60316e29i	−0.633219	−	0.758995i
$857$	−1.92262e29			−0.899676			−0.449838	−	0.893110i	$-0.648518\pi$
$857$	−1.92262e29			−0.899676			−0.449838	+	0.893110i	$0.648518\pi$
$858$	−8.01228e28	+	2.66713e29i	−0.370581	+	1.23359i
$859$	3.17854e29			1.45310			0.726551	−	0.687113i	$-0.241122\pi$
$859$	3.17854e29			1.45310			0.726551	+	0.687113i	$0.241122\pi$
$860$	2.52972e29	−	3.83049e29i	1.14311	−	1.73089i
$861$		−	2.65904e29i		−	1.18766i
$862$	8.63879e28	−	2.87568e29i	0.381400	−	1.26960i
$863$			3.79268e29i			1.65515i	0.561353	+	0.827576i	$0.310281\pi$
$863$			3.79268e29i			1.65515i	−0.561353	+	0.827576i	$0.689719\pi$
$864$	5.31157e27	+	4.73812e28i	0.0229132	+	0.204394i
$865$	−6.60174e29			−2.81512
$866$	3.56550e29	+	1.07111e29i	1.50294	+	0.451496i
$867$	−1.10672e29			−0.461154
$868$	2.21569e29	+	1.46328e29i	0.912666	+	0.602741i
$869$			1.10571e29i			0.450239i
$870$	−4.12008e29	−	1.23771e29i	−1.65849	−	0.498226i
$871$			1.80415e29i			0.717944i
$872$	2.66625e29	−	2.22441e29i	1.04890	−	0.875086i
$873$	−2.76221e29			−1.07427
$874$	−7.26370e26	+	2.41794e27i	−0.00279282	+	0.00929674i
$875$	−5.65436e29			−2.14933
$876$	−4.95465e28	−	3.27214e28i	−0.186197	−	0.122968i
$877$		−	2.00911e29i		−	0.746464i	−0.927738	−	0.373232i	$-0.878250\pi$
$877$		−	2.00911e29i		−	0.746464i	0.927738	−	0.373232i	$-0.121750\pi$
$878$	−1.64407e27	+	5.47277e27i	−0.00603914	+	0.0201031i
$879$			4.75186e29i			1.72574i
$880$	−5.02714e29	+	2.14602e29i	−1.80507	+	0.770563i
$881$	1.90398e29			0.675931			0.337966	−	0.941158i	$-0.390261\pi$
$881$	1.90398e29			0.675931			0.337966	+	0.941158i	$0.390261\pi$
$882$	2.07411e29	+	6.23081e28i	0.728025	+	0.218705i
$883$	5.19250e29			1.80206			0.901031	−	0.433755i	$-0.142812\pi$
$883$	5.19250e29			1.80206			0.901031	+	0.433755i	$0.142812\pi$
$884$	−1.42296e29	+	2.15463e29i	−0.488280	+	0.739350i
$885$			5.41570e29i			1.83748i
$886$	3.79028e29	+	1.13864e29i	1.27155	+	0.381986i
$887$			4.92436e29i			1.63348i	0.577007	+	0.816739i	$0.304220\pi$
$887$			4.92436e29i			1.63348i	−0.577007	+	0.816739i	$0.695780\pi$
$888$	1.70261e29	−	1.42046e29i	0.558451	−	0.465908i
$889$	1.46191e29			0.474136
$890$	1.05436e29	−	3.50975e29i	0.338134	−	1.12558i
$891$	−3.01712e29			−0.956789
$892$	−3.66457e28	+	5.54887e28i	−0.114914	+	0.174003i
$893$		−	3.86228e28i		−	0.119765i
$894$	−2.63021e29	+	8.75544e29i	−0.806521	+	2.68474i
$895$		−	8.02784e29i		−	2.43427i
$896$	−3.83430e29	−	1.95748e29i	−1.14976	−	0.586972i
$897$	2.69359e28			0.0798742
$898$	2.49107e29	+	7.48339e28i	0.730503	+	0.219450i
$899$	−2.00764e29			−0.582224
$900$	−6.52645e29	−	4.31019e29i	−1.87177	−	1.23615i
$901$		−	5.17606e29i		−	1.46809i
$902$	2.44649e29	+	7.34948e28i	0.686243	+	0.206154i
$903$		−	8.19935e29i		−	2.27458i
$904$	3.04330e29	+	3.64779e29i	0.834950	+	1.00080i
$905$	2.40688e29			0.653083
$906$	2.05746e29	−	6.84886e29i	0.552140	−	1.83796i
$907$	−4.29545e29			−1.14008			−0.570041	−	0.821617i	$-0.693073\pi$
$907$	−4.29545e29			−1.14008			−0.570041	+	0.821617i	$0.693073\pi$
$908$	−9.96442e28	−	6.58068e28i	−0.261573	−	0.172748i
$909$			2.74857e29i			0.713623i
$910$	1.92465e29	−	6.40677e29i	0.494240	−	1.64523i
$911$			5.20927e29i			1.32310i	0.749900	+	0.661551i	$0.230101\pi$
$911$			5.20927e29i			1.32310i	−0.749900	+	0.661551i	$0.769899\pi$
$912$	3.14111e28	+	7.35816e28i	0.0789104	+	0.184850i
$913$	−4.49240e29			−1.11627
$914$	4.72715e29	+	1.42008e29i	1.16182	+	0.349020i
$915$	1.65769e30			4.02988
$916$	−2.03080e29	+	3.07502e29i	−0.488328	+	0.739423i
$917$		−	2.58516e29i		−	0.614886i
$918$	9.60153e28	+	2.88438e28i	0.225899	+	0.0678620i
$919$		−	7.91946e29i		−	1.84306i	−0.388302	−	0.921532i	$-0.626938\pi$
$919$		−	7.91946e29i		−	1.84306i	0.388302	−	0.921532i	$-0.373062\pi$
$920$	3.38685e28	+	4.05958e28i	0.0779682	+	0.0934549i
$921$	2.00483e29			0.456543
$922$	1.21390e29	−	4.04082e29i	0.273447	−	0.910248i
$923$	1.52573e29			0.339986
$924$	−5.38041e29	+	8.14698e29i	−1.18603	+	1.79588i
$925$			4.48314e29i			0.977607i
$926$	7.76617e28	−	2.58520e29i	0.167532	−	0.557679i
$927$			2.95338e28i			0.0630264i
$928$	3.23478e29	−	3.62628e28i	0.682913	−	0.0765564i
$929$	−1.01853e29			−0.212723			−0.106362	−	0.994328i	$-0.533920\pi$
$929$	−1.01853e29			−0.212723			−0.106362	+	0.994328i	$0.533920\pi$
$930$	−9.89644e29	−	2.97298e29i	−2.04479	−	0.614274i
$931$	4.47906e28			0.0915567
$932$	3.92382e29	+	2.59136e29i	0.793505	+	0.524045i
$933$		−	3.41119e29i		−	0.682479i
$934$	−2.28603e29	−	6.86744e28i	−0.452494	−	0.135933i
$935$			1.14936e30i			2.25082i
$936$	3.49237e29	−	2.91364e29i	0.676647	−	0.564518i
$937$	7.68737e28			0.147361			0.0736804	−	0.997282i	$-0.476526\pi$
$937$	7.68737e28			0.147361			0.0736804	+	0.997282i	$0.476526\pi$
$938$	−1.81976e29	+	6.05761e29i	−0.345132	+	1.14888i
$939$	−5.08507e29			−0.954203
$940$	−6.74892e29	−	4.45710e29i	−1.25301	−	0.827512i
$941$			7.80777e29i			1.43427i	0.696935	+	0.717135i	$0.254547\pi$
$941$			7.80777e29i			1.43427i	−0.696935	+	0.717135i	$0.745453\pi$
$942$	−9.87887e28	+	3.28847e29i	−0.179555	+	0.597703i
$943$		−	2.47076e28i		−	0.0444339i
$944$	−1.60881e29	−	3.76870e29i	−0.286276	−	0.670613i
$945$	−2.59735e29			−0.457313
$946$	7.54394e29	+	2.26627e29i	1.31428	+	0.394821i
$947$	−1.92963e29			−0.332640			−0.166320	−	0.986072i	$-0.553188\pi$
$947$	−1.92963e29			−0.332640			−0.166320	+	0.986072i	$0.553188\pi$
$948$	1.86766e29	−	2.82800e29i	0.318577	−	0.482387i
$949$			6.98110e28i			0.117832i
$950$	−1.54920e29	−	4.65394e28i	−0.258745	−	0.0777293i
$951$		−	1.21254e30i		−	2.00396i
$952$	−6.95099e29	+	5.79912e29i	−1.13678	+	0.948402i
$953$	−9.13861e29			−1.47894			−0.739471	−	0.673188i	$-0.764924\pi$
$953$	−9.13861e29			−1.47894			−0.739471	+	0.673188i	$0.764924\pi$
$954$	−2.62310e29	+	8.73178e29i	−0.420080	+	1.39836i
$955$	1.35338e30			2.14480
$956$	3.67013e28	−	5.55728e28i	0.0575576	−	0.0871533i
$957$		−	7.38200e29i		−	1.14566i
$958$	−9.82029e27	+	3.26897e28i	−0.0150824	+	0.0502061i
$959$		−	3.05687e29i		−	0.464612i
$960$	1.64825e30	+	3.00263e29i	2.47919	+	0.451637i
$961$	1.89555e29			0.282163
$962$	−2.49678e29	−	7.50055e28i	−0.367815	−	0.110495i
$963$	7.73292e29			1.12741
$964$	−1.05641e30	−	6.97671e29i	−1.52427	−	1.00665i
$965$		−	1.87864e30i		−	2.68269i
$966$	9.04399e28	+	2.71690e28i	0.127817	+	0.0383974i
$967$			4.43207e28i			0.0619929i	0.999519	+	0.0309964i	$0.00986805\pi$
$967$			4.43207e28i			0.0619929i	−0.999519	+	0.0309964i	$0.990132\pi$
$968$	−1.38109e29	−	1.65541e29i	−0.191191	−	0.229167i
$969$	1.68231e29			0.230498
$970$	−3.44185e29	+	1.14572e30i	−0.466739	+	1.55368i
$971$	−5.27622e29			−0.708159			−0.354079	−	0.935215i	$-0.615206\pi$
$971$	−5.27622e29			−0.708159			−0.354079	+	0.935215i	$0.615206\pi$
$972$	9.00865e29	+	5.94947e29i	1.19673	+	0.790343i
$973$			1.15330e30i			1.51640i
$974$	−1.57717e29	+	5.25009e29i	−0.205253	+	0.683246i
$975$			1.72581e30i			2.22304i
$976$	−1.15356e30	+	4.92441e29i	−1.47076	+	0.627850i
$977$	6.09552e29			0.769246			0.384623	−	0.923074i	$-0.374331\pi$
$977$	6.09552e29			0.769246			0.384623	+	0.923074i	$0.374331\pi$
$978$	−1.83745e30	−	5.51988e29i	−2.29524	−	0.689510i
$979$	6.28846e29			0.777530
$980$	5.16888e29	−	7.82668e29i	0.632609	−	0.957893i
$981$			1.28608e30i			1.55804i
$982$	3.85545e29	+	1.15821e29i	0.462338	+	0.138891i
$983$		−	7.31189e29i		−	0.867949i	−0.900925	−	0.433975i	$-0.857111\pi$
$983$		−	7.31189e29i		−	0.867949i	0.900925	−	0.433975i	$-0.142889\pi$
$984$	−5.01582e29	−	6.01211e29i	−0.589375	−	0.706441i
$985$	−2.90159e29			−0.337500
$986$	1.96921e29	−	6.55510e29i	0.226737	−	0.754762i
$987$	−1.44464e30			−1.64660
$988$	5.18382e28	−	7.84930e28i	0.0584898	−	0.0885649i
$989$		−	7.61879e28i		−	0.0850987i
$990$	5.82469e29	−	1.93892e30i	0.644052	−	2.14392i
$991$			2.35361e29i			0.257631i	0.991669	+	0.128816i	$0.0411175\pi$
$991$			2.35361e29i			0.257631i	−0.991669	+	0.128816i	$0.958882\pi$
$992$	7.76994e29	−	8.71032e28i	0.841978	−	0.0943881i
$993$	1.00371e30			1.07675
$994$	5.12280e29	+	1.53893e29i	0.544056	+	0.163439i
$995$	−2.85266e30			−2.99930
$996$	1.14899e30	+	7.58814e29i	1.19598	+	0.789845i
$997$			1.40218e30i			1.44494i	0.691400	+	0.722472i	$0.256994\pi$
$997$			1.40218e30i			1.44494i	−0.691400	+	0.722472i	$0.743006\pi$
$998$	−3.44057e29	−	1.03358e29i	−0.351014	−	0.105448i
$999$			1.01221e29i			0.102239i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.21.d.b.3.3	✓	18
3.2	odd	2		72.21.b.b.19.16		18
4.3	odd	2		32.21.d.b.15.16		18
8.3	odd	2	inner	8.21.d.b.3.4	yes	18
8.5	even	2		32.21.d.b.15.15		18
24.11	even	2		72.21.b.b.19.15		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.21.d.b.3.3	✓	18	1.1	even	1	trivial
8.21.d.b.3.4	yes	18	8.3	odd	2	inner
32.21.d.b.15.15		18	8.5	even	2
32.21.d.b.15.16		18	4.3	odd	2
72.21.b.b.19.15		18	24.11	even	2
72.21.b.b.19.16		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)

\(f(q)\)	\(=\)	\(q+(-980.704 - 294.612i) q^{2} -86392.9 q^{3} +(874983. + 577854. i) q^{4} +1.68203e7i q^{5} +(8.47258e7 + 2.54524e7i) q^{6} -3.64653e8i q^{7} +(-6.87856e8 - 8.24485e8i) q^{8} +3.97695e9 q^{9} +O(q^{10})\)	\(q+(-980.704 - 294.612i) q^{2} -86392.9 q^{3} +(874983. + 577854. i) q^{4} +1.68203e7i q^{5} +(8.47258e7 + 2.54524e7i) q^{6} -3.64653e8i q^{7} +(-6.87856e8 - 8.24485e8i) q^{8} +3.97695e9 q^{9} +(4.95546e9 - 1.64957e10i) q^{10} +2.95556e10 q^{11} +(-7.55923e10 - 4.99225e10i) q^{12} +1.06510e11i q^{13} +(-1.07431e11 + 3.57616e11i) q^{14} -1.45315e12i q^{15} +(4.31680e11 + 1.01123e12i) q^{16} +2.31198e12 q^{17} +(-3.90021e12 - 1.17166e12i) q^{18} -8.42253e11 q^{19} +(-9.71968e12 + 1.47175e13i) q^{20} +3.15034e13i q^{21} +(-2.89852e13 - 8.70743e12i) q^{22} +2.92728e12i q^{23} +(5.94259e13 + 7.12296e13i) q^{24} -1.87555e14 q^{25} +(3.13790e13 - 1.04454e14i) q^{26} -4.23466e13 q^{27} +(2.10716e14 - 3.19065e14i) q^{28} +2.89106e14i q^{29} +(-4.28117e14 + 1.42511e15i) q^{30} +6.94432e14i q^{31} +(-1.25431e14 - 1.11889e15i) q^{32} -2.55339e15 q^{33} +(-2.26737e15 - 6.81138e14i) q^{34} +6.13357e15 q^{35} +(3.47976e15 + 2.29810e15i) q^{36} -2.39031e15i q^{37} +(8.26001e14 + 2.48138e14i) q^{38} -9.20166e15i q^{39} +(1.38681e16 - 1.15699e16i) q^{40} -8.44047e15 q^{41} +(9.28129e15 - 3.08955e16i) q^{42} -2.60268e16 q^{43} +(2.58606e16 + 1.70788e16i) q^{44} +6.68934e16i q^{45} +(8.62413e14 - 2.87080e15i) q^{46} +4.58565e16i q^{47} +(-3.72941e16 - 8.73627e16i) q^{48} -5.31795e16 q^{49} +(1.83935e17 + 5.52559e16i) q^{50} -1.99739e17 q^{51} +(-6.15470e16 + 9.31941e16i) q^{52} -2.23880e17i q^{53} +(4.15294e16 + 1.24758e16i) q^{54} +4.97133e17i q^{55} +(-3.00651e17 + 2.50829e17i) q^{56} +7.27647e16 q^{57} +(8.51741e16 - 2.83527e17i) q^{58} -3.72686e17 q^{59} +(8.39711e17 - 1.27148e18i) q^{60} +1.14075e18i q^{61} +(2.04588e17 - 6.81032e17i) q^{62} -1.45021e18i q^{63} +(-2.06628e17 + 1.13425e18i) q^{64} -1.79152e18 q^{65} +(2.50412e18 + 7.52260e17i) q^{66} +1.69388e18 q^{67} +(2.02295e18 + 1.33599e18i) q^{68} -2.52896e17i q^{69} +(-6.01521e18 - 1.80702e18i) q^{70} -1.43248e18i q^{71} +(-2.73557e18 - 3.27893e18i) q^{72} +6.55444e17 q^{73} +(-7.04214e17 + 2.34419e18i) q^{74} +1.62034e19 q^{75} +(-7.36958e17 - 4.86700e17i) q^{76} -1.07775e19i q^{77} +(-2.71092e18 + 9.02411e18i) q^{78} +3.74112e18i q^{79} +(-1.70091e19 + 7.26098e18i) q^{80} -1.02083e19 q^{81} +(8.27760e18 + 2.48666e18i) q^{82} -1.51998e19 q^{83} +(-1.82044e19 + 2.75650e19i) q^{84} +3.88882e19i q^{85} +(2.55246e19 + 7.66782e18i) q^{86} -2.49767e19i q^{87} +(-2.03300e19 - 2.43681e19i) q^{88} +2.12767e19 q^{89} +(1.97076e19 - 6.56026e19i) q^{90} +3.88390e19 q^{91} +(-1.69154e18 + 2.56132e18i) q^{92} -5.99940e19i q^{93} +(1.35099e19 - 4.49717e19i) q^{94} -1.41669e19i q^{95} +(1.08363e19 + 9.66643e19i) q^{96} -6.94557e19 q^{97} +(5.21533e19 + 1.56673e19i) q^{98} +1.17541e20 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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