LMFDB - Embedded newform 8.21.d.b.3.10

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			3.10
Root			$-13803.2 + 714588. i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.21.d.b.3.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-39.1296 + 1023.25i) q^{2} -61558.6 q^{3} +(-1.04551e6 - 80078.8i) q^{4} -2.85835e6i q^{5} +(2.40876e6 - 6.29900e7i) q^{6} -1.54680e8i q^{7} +(1.22851e8 - 1.06669e9i) q^{8} +3.02682e8 q^{9} +O(q^{10})$	\(q+(-39.1296 + 1023.25i) q^{2} -61558.6 q^{3} +(-1.04551e6 - 80078.8i) q^{4} -2.85835e6i q^{5} +(2.40876e6 - 6.29900e7i) q^{6} -1.54680e8i q^{7} +(1.22851e8 - 1.06669e9i) q^{8} +3.02682e8 q^{9} +(2.92482e9 + 1.11846e8i) q^{10} +1.20777e10 q^{11} +(6.43604e10 + 4.92954e9i) q^{12} +1.32584e10i q^{13} +(1.58276e11 + 6.05255e9i) q^{14} +1.75956e11i q^{15} +(1.08669e12 + 1.67447e11i) q^{16} -1.51710e12 q^{17} +(-1.18438e10 + 3.09720e11i) q^{18} -5.95972e12 q^{19} +(-2.28894e11 + 2.98845e12i) q^{20} +9.52187e12i q^{21} +(-4.72597e11 + 1.23586e13i) q^{22} +5.68078e13i q^{23} +(-7.56256e12 + 6.56640e13i) q^{24} +8.71973e13 q^{25} +(-1.35667e13 - 5.18796e11i) q^{26} +1.96009e14 q^{27} +(-1.23866e13 + 1.61720e14i) q^{28} -9.55289e13i q^{29} +(-1.80048e14 - 6.88509e12i) q^{30} +1.17024e15i q^{31} +(-2.13862e14 + 1.10540e15i) q^{32} -7.43490e14 q^{33} +(5.93636e13 - 1.55238e15i) q^{34} -4.42129e14 q^{35} +(-3.16459e14 - 2.42385e13i) q^{36} -8.09037e15i q^{37} +(2.33201e14 - 6.09830e15i) q^{38} -8.16169e14i q^{39} +(-3.04898e15 - 3.51152e14i) q^{40} +1.78313e16 q^{41} +(-9.74327e15 - 3.72587e14i) q^{42} +2.76012e16 q^{43} +(-1.26275e16 - 9.67172e14i) q^{44} -8.65173e14i q^{45} +(-5.81287e16 - 2.22286e15i) q^{46} -1.55525e16i q^{47} +(-6.68949e16 - 1.03078e16i) q^{48} +5.58665e16 q^{49} +(-3.41199e15 + 8.92248e16i) q^{50} +9.33908e16 q^{51} +(1.06172e15 - 1.38618e16i) q^{52} +2.45574e17i q^{53} +(-7.66975e15 + 2.00567e17i) q^{54} -3.45225e16i q^{55} +(-1.64995e17 - 1.90026e16i) q^{56} +3.66873e17 q^{57} +(9.77501e16 + 3.73800e15i) q^{58} +4.21252e17 q^{59} +(1.40904e16 - 1.83965e17i) q^{60} -5.24046e17i q^{61} +(-1.19745e18 - 4.57910e16i) q^{62} -4.68188e16i q^{63} +(-1.12274e18 - 2.62089e17i) q^{64} +3.78972e16 q^{65} +(2.90924e16 - 7.60777e17i) q^{66} -2.46735e17 q^{67} +(1.58615e18 + 1.21488e17i) q^{68} -3.49701e18i q^{69} +(1.73003e16 - 4.52410e17i) q^{70} +3.30845e18i q^{71} +(3.71849e16 - 3.22869e17i) q^{72} -3.00902e18 q^{73} +(8.27849e18 + 3.16573e17i) q^{74} -5.36774e18 q^{75} +(6.23097e18 + 4.77248e17i) q^{76} -1.86818e18i q^{77} +(8.35147e17 + 3.19364e16i) q^{78} +1.13858e19i q^{79} +(4.78623e17 - 3.10613e18i) q^{80} -1.31214e19 q^{81} +(-6.97730e17 + 1.82459e19i) q^{82} -4.84976e18 q^{83} +(7.62500e17 - 9.95525e18i) q^{84} +4.33641e18i q^{85} +(-1.08002e18 + 2.82430e19i) q^{86} +5.88063e18i q^{87} +(1.48377e18 - 1.28832e19i) q^{88} +1.43860e19 q^{89} +(8.85290e17 + 3.38539e16i) q^{90} +2.05081e18 q^{91} +(4.54910e18 - 5.93933e19i) q^{92} -7.20384e19i q^{93} +(1.59142e19 + 6.08564e17i) q^{94} +1.70350e19i q^{95} +(1.31651e19 - 6.80471e19i) q^{96} +2.08925e18 q^{97} +(-2.18603e18 + 5.71655e19i) q^{98} +3.65572e18 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 $

$2$	−39.1296	+	1023.25i	−0.0382125	+	0.999270i
$2$	−39.1296	+	1023.25i	−0.0382125	+	0.999270i
$3$	−61558.6			−1.04250			−0.521251	−	0.853404i	$-0.674534\pi$
$3$	−61558.6			−1.04250			−0.521251	+	0.853404i	$0.674534\pi$
$4$	−1.04551e6	−	80078.8i	−0.997080	−	0.0763691i
$5$		−	2.85835e6i		−	0.292695i	−0.989233	−	0.146348i	$-0.953248\pi$
$5$		−	2.85835e6i		−	0.292695i	0.989233	−	0.146348i	$-0.0467518\pi$
$6$	2.40876e6	−	6.29900e7i	0.0398365	−	1.04174i
$7$		−	1.54680e8i		−	0.547587i	−0.961789	−	0.273793i	$-0.911722\pi$
$7$		−	1.54680e8i		−	0.547587i	0.961789	−	0.273793i	$-0.0882784\pi$
$8$	1.22851e8	−	1.06669e9i	0.114414	−	0.993433i
$9$	3.02682e8			0.0868085
$10$	2.92482e9	+	1.11846e8i	0.292482	+	0.0111846i
$11$	1.20777e10			0.465649			0.232825	−	0.972519i	$-0.425203\pi$
$11$	1.20777e10			0.465649			0.232825	+	0.972519i	$0.425203\pi$
$12$	6.43604e10	+	4.92954e9i	1.03946	+	0.0796149i
$13$			1.32584e10i			0.0961740i	0.998843	+	0.0480870i	$0.0153125\pi$
$13$			1.32584e10i			0.0961740i	−0.998843	+	0.0480870i	$0.984688\pi$
$14$	1.58276e11	+	6.05255e9i	0.547187	+	0.0209246i
$15$			1.75956e11i			0.305135i
$16$	1.08669e12	+	1.67447e11i	0.988336	+	0.152292i
$17$	−1.51710e12			−0.752533			−0.376267	−	0.926511i	$-0.622792\pi$
$17$	−1.51710e12			−0.752533			−0.376267	+	0.926511i	$0.622792\pi$
$18$	−1.18438e10	+	3.09720e11i	−0.00331717	+	0.0867451i
$19$	−5.95972e12			−0.972053			−0.486027	−	0.873944i	$-0.661554\pi$
$19$	−5.95972e12			−0.972053			−0.486027	+	0.873944i	$0.661554\pi$
$20$	−2.28894e11	+	2.98845e12i	−0.0223529	+	0.291841i
$21$			9.52187e12i			0.570860i
$22$	−4.72597e11	+	1.23586e13i	−0.0177936	+	0.465309i
$23$			5.68078e13i			1.37129i	0.727936	+	0.685645i	$0.240480\pi$
$23$			5.68078e13i			1.37129i	−0.727936	+	0.685645i	$0.759520\pi$
$24$	−7.56256e12	+	6.56640e13i	−0.119277	+	1.03566i
$25$	8.71973e13			0.914329
$26$	−1.35667e13	−	5.18796e11i	−0.0961038	−	0.00367505i
$27$	1.96009e14			0.952003
$28$	−1.23866e13	+	1.61720e14i	−0.0418187	+	0.545987i
$29$		−	9.55289e13i		−	0.227067i	−0.993534	−	0.113534i	$-0.963783\pi$
$29$		−	9.55289e13i		−	0.227067i	0.993534	−	0.113534i	$-0.0362170\pi$
$30$	−1.80048e14	−	6.88509e12i	−0.304912	−	0.0116600i
$31$			1.17024e15i			1.42777i	0.700263	+	0.713885i	$0.253066\pi$
$31$			1.17024e15i			1.42777i	−0.700263	+	0.713885i	$0.746934\pi$
$32$	−2.13862e14	+	1.10540e15i	−0.189948	+	0.981794i
$33$	−7.43490e14			−0.485440
$34$	5.93636e13	−	1.55238e15i	0.0287561	−	0.751983i
$35$	−4.42129e14			−0.160276
$36$	−3.16459e14	−	2.42385e13i	−0.0865550	−	0.00662949i
$37$		−	8.09037e15i		−	1.68249i	−0.540658	−	0.841243i	$-0.681825\pi$
$37$		−	8.09037e15i		−	1.68249i	0.540658	−	0.841243i	$-0.318175\pi$
$38$	2.33201e14	−	6.09830e15i	0.0371446	−	0.971343i
$39$		−	8.16169e14i		−	0.100262i
$40$	−3.04898e15	−	3.51152e14i	−0.290773	−	0.0334885i
$41$	1.78313e16			1.32844			0.664222	−	0.747535i	$-0.268763\pi$
$41$	1.78313e16			1.32844			0.664222	+	0.747535i	$0.268763\pi$
$42$	−9.74327e15	−	3.72587e14i	−0.570443	−	0.0218140i
$43$	2.76012e16			1.27715			0.638577	−	0.769558i	$-0.279523\pi$
$43$	2.76012e16			1.27715			0.638577	+	0.769558i	$0.279523\pi$
$44$	−1.26275e16	−	9.67172e14i	−0.464290	−	0.0355612i
$45$		−	8.65173e14i		−	0.0254084i
$46$	−5.81287e16	−	2.22286e15i	−1.37029	−	0.0524004i
$47$		−	1.55525e16i		−	0.295681i	−0.989011	−	0.147840i	$-0.952768\pi$
$47$		−	1.55525e16i		−	0.295681i	0.989011	−	0.147840i	$-0.0472322\pi$
$48$	−6.68949e16	−	1.03078e16i	−1.03034	−	0.158765i
$49$	5.58665e16			0.700149
$50$	−3.41199e15	+	8.92248e16i	−0.0349388	+	0.913662i
$51$	9.33908e16			0.784517
$52$	1.06172e15	−	1.38618e16i	0.00734472	−	0.0958932i
$53$			2.45574e17i			1.40418i	0.712087	+	0.702092i	$0.247750\pi$
$53$			2.45574e17i			1.40418i	−0.712087	+	0.702092i	$0.752250\pi$
$54$	−7.66975e15	+	2.00567e17i	−0.0363784	+	0.951308i
$55$		−	3.45225e16i		−	0.136293i
$56$	−1.64995e17	−	1.90026e16i	−0.543991	−	0.0626517i
$57$	3.66873e17			1.01337
$58$	9.77501e16	+	3.73800e15i	0.226901	+	0.00867680i
$59$	4.21252e17			0.824179			0.412089	−	0.911143i	$-0.364799\pi$
$59$	4.21252e17			0.824179			0.412089	+	0.911143i	$0.364799\pi$
$60$	1.40904e16	−	1.83965e17i	0.0233029	−	0.304244i
$61$		−	5.24046e17i		−	0.734634i	−0.930096	−	0.367317i	$-0.880276\pi$
$61$		−	5.24046e17i		−	0.734634i	0.930096	−	0.367317i	$-0.119724\pi$
$62$	−1.19745e18	−	4.57910e16i	−1.42673	−	0.0545586i
$63$		−	4.68188e16i		−	0.0475352i
$64$	−1.12274e18	−	2.62089e17i	−0.973819	−	0.227326i
$65$	3.78972e16			0.0281497
$66$	2.90924e16	−	7.60777e17i	0.0185499	−	0.485085i
$67$	−2.46735e17			−0.135357			−0.0676787	−	0.997707i	$-0.521559\pi$
$67$	−2.46735e17			−0.135357			−0.0676787	+	0.997707i	$0.521559\pi$
$68$	1.58615e18	+	1.21488e17i	0.750335	+	0.0574703i
$69$		−	3.49701e18i		−	1.42957i
$70$	1.73003e16	−	4.52410e17i	0.00612454	−	0.160159i
$71$			3.30845e18i			1.01634i	0.861256	+	0.508172i	$0.169679\pi$
$71$			3.30845e18i			1.01634i	−0.861256	+	0.508172i	$0.830321\pi$
$72$	3.71849e16	−	3.22869e17i	0.00993212	−	0.0862384i
$73$	−3.00902e18			−0.700158			−0.350079	−	0.936720i	$-0.613845\pi$
$73$	−3.00902e18			−0.700158			−0.350079	+	0.936720i	$0.613845\pi$
$74$	8.27849e18	+	3.16573e17i	1.68126	+	0.0642919i
$75$	−5.36774e18			−0.953189
$76$	6.23097e18	+	4.77248e17i	0.969215	+	0.0742349i
$77$		−	1.86818e18i		−	0.254983i
$78$	8.35147e17	+	3.19364e16i	0.100188	+	0.00383124i
$79$			1.13858e19i			1.20252i	0.799053	+	0.601261i	$0.205335\pi$
$79$			1.13858e19i			1.20252i	−0.799053	+	0.601261i	$0.794665\pi$
$80$	4.78623e17	−	3.10613e18i	0.0445752	−	0.289281i
$81$	−1.31214e19			−1.07927
$82$	−6.97730e17	+	1.82459e19i	−0.0507632	+	1.32747i
$83$	−4.84976e18			−0.312564			−0.156282	−	0.987712i	$-0.549951\pi$
$83$	−4.84976e18			−0.312564			−0.156282	+	0.987712i	$0.549951\pi$
$84$	7.62500e17	−	9.95525e18i	0.0435961	−	0.569193i
$85$			4.33641e18i			0.220263i
$86$	−1.08002e18	+	2.82430e19i	−0.0488032	+	1.27622i
$87$			5.88063e18i			0.236718i
$88$	1.48377e18	−	1.28832e19i	0.0532769	−	0.462592i
$89$	1.43860e19			0.461359			0.230680	−	0.973030i	$-0.425905\pi$
$89$	1.43860e19			0.461359			0.230680	+	0.973030i	$0.425905\pi$
$90$	8.85290e17	+	3.38539e16i	0.0253899	+	0.000970919i
$91$	2.05081e18			0.0526636
$92$	4.54910e18	−	5.93933e19i	0.104724	−	1.36729i
$93$		−	7.20384e19i		−	1.48845i
$94$	1.59142e19	+	6.08564e17i	0.295465	+	0.0112987i
$95$			1.70350e19i			0.284515i
$96$	1.31651e19	−	6.80471e19i	0.198021	−	1.02352i
$97$	2.08925e18			0.0283317			0.0141659	−	0.999900i	$-0.495491\pi$
$97$	2.08925e18			0.0283317			0.0141659	+	0.999900i	$0.495491\pi$
$98$	−2.18603e18	+	5.71655e19i	−0.0267544	+	0.699637i
$99$	3.65572e18			0.0404223
$100$	−9.11659e19	−	6.98265e18i	−0.911659	−	0.0698265i
$101$		−	1.49716e20i		−	1.35536i	−0.735356	−	0.677681i	$-0.762985\pi$
$101$		−	1.49716e20i		−	1.35536i	0.735356	−	0.677681i	$-0.237015\pi$
$102$	−3.65434e18	+	9.55623e19i	−0.0299783	+	0.783944i
$103$			2.30670e20i			1.71640i	0.513314	+	0.858201i	$0.328418\pi$
$103$			2.30670e20i			1.71640i	−0.513314	+	0.858201i	$0.671582\pi$
$104$	1.41426e19	+	1.62881e18i	0.0955425	+	0.0110037i
$105$	2.72169e19			0.167088
$106$	−2.51284e20	−	9.60921e18i	−1.40316	−	0.0536573i
$107$	2.64324e20			1.34369			0.671843	−	0.740693i	$-0.265503\pi$
$107$	2.64324e20			1.34369			0.671843	+	0.740693i	$0.265503\pi$
$108$	−2.04930e20	−	1.56962e19i	−0.949223	−	0.0727036i
$109$		−	3.50091e20i		−	1.47882i	−0.673254	−	0.739411i	$-0.735104\pi$
$109$		−	3.50091e20i		−	1.47882i	0.673254	−	0.739411i	$-0.264896\pi$
$110$	3.53252e19	+	1.35085e18i	0.136194	+	0.00520811i
$111$			4.98032e20i			1.75399i
$112$	2.59007e19	−	1.68088e20i	0.0833932	−	0.541199i
$113$	4.55419e20			1.34161			0.670805	−	0.741634i	$-0.265949\pi$
$113$	4.55419e20			1.34161			0.670805	+	0.741634i	$0.265949\pi$
$114$	−1.43556e19	+	3.75403e20i	−0.0387232	+	1.01263i
$115$	1.62377e20			0.401370
$116$	−7.64984e18	+	9.98767e19i	−0.0173409	+	0.226404i
$117$			4.01309e18i			0.00834872i
$118$	−1.64834e19	+	4.31047e20i	−0.0314939	+	0.823577i
$119$			2.34665e20i			0.412077i
$120$	1.87691e20	+	2.16165e19i	0.303131	+	0.0349118i
$121$	−5.26878e20			−0.783171
$122$	5.36231e20	+	2.05057e19i	0.734097	+	0.0280722i
$123$	−1.09767e21			−1.38491
$124$	9.37114e19	−	1.22350e21i	0.109037	−	1.42360i
$125$		−	5.21834e20i		−	0.560315i
$126$	4.79075e19	+	1.83200e18i	0.0475004	+	0.00181644i
$127$		−	9.90252e20i		−	0.907212i	−0.891202	−	0.453606i	$-0.850137\pi$
$127$		−	9.90252e20i		−	0.907212i	0.891202	−	0.453606i	$-0.149863\pi$
$128$	3.12115e20	−	1.13859e21i	0.264372	−	0.964421i
$129$	−1.69909e21			−1.33143
$130$	−1.48290e18	+	3.87784e19i	−0.00107567	+	0.0281291i
$131$	−2.19779e20			−0.147664			−0.0738318	−	0.997271i	$-0.523523\pi$
$131$	−2.19779e20			−0.147664			−0.0738318	+	0.997271i	$0.523523\pi$
$132$	7.77329e20	+	5.95378e19i	0.484022	+	0.0370726i
$133$			9.21848e20i			0.532283i
$134$	9.65462e18	−	2.52472e20i	0.00517234	−	0.135259i
$135$		−	5.60263e20i		−	0.278647i
$136$	−1.86378e20	+	1.61828e21i	−0.0861005	+	0.747591i
$137$	1.21346e21			0.520978			0.260489	−	0.965477i	$-0.416116\pi$
$137$	1.21346e21			0.520978			0.260489	+	0.965477i	$0.416116\pi$
$138$	3.57832e21	+	1.36837e20i	1.42853	+	0.0546275i
$139$	7.11775e20			0.264359			0.132180	−	0.991226i	$-0.457802\pi$
$139$	7.11775e20			0.264359			0.132180	+	0.991226i	$0.457802\pi$
$140$	4.62252e20	+	3.54052e19i	0.159808	+	0.0122401i
$141$			9.57394e20i			0.308247i
$142$	−3.38538e21	−	1.29458e20i	−1.01560	−	0.0388370i
$143$			1.60132e20i			0.0447834i
$144$	3.28921e20	+	5.06833e19i	0.0857959	+	0.0132203i
$145$	−2.73055e20			−0.0664615
$146$	1.17742e20	−	3.07898e21i	0.0267548	−	0.699647i
$147$	−3.43906e21			−0.729906
$148$	−6.47867e20	+	8.45859e21i	−0.128490	+	1.67757i
$149$			2.63225e21i			0.488049i	0.969769	+	0.244025i	$0.0784678\pi$
$149$			2.63225e21i			0.488049i	−0.969769	+	0.244025i	$0.921532\pi$
$150$	2.10038e20	−	5.49256e21i	0.0364237	−	0.952493i
$151$			2.44641e21i			0.396973i	0.980104	+	0.198486i	$0.0636025\pi$
$151$			2.44641e21i			0.396973i	−0.980104	+	0.198486i	$0.936397\pi$
$152$	−7.32160e20	+	6.35718e21i	−0.111217	+	0.965670i
$153$	−4.59200e20			−0.0653263
$154$	1.91162e21	+	7.31012e19i	0.254797	+	0.00974355i
$155$	3.34496e21			0.417901
$156$	−6.53579e19	+	8.53316e20i	−0.00765688	+	0.0999687i
$157$			7.85849e21i			0.863660i	0.901955	+	0.431830i	$0.142132\pi$
$157$			7.85849e21i			0.863660i	−0.901955	+	0.431830i	$0.857868\pi$
$158$	−1.16506e22	−	4.45522e20i	−1.20164	−	0.0459514i
$159$		−	1.51172e22i		−	1.46386i
$160$	3.15963e21	+	6.11293e20i	0.287367	+	0.0555968i
$161$	8.78701e21			0.750901
$162$	5.13436e20	−	1.34265e22i	0.0412417	−	1.07848i
$163$	1.75843e22			1.32815			0.664076	−	0.747665i	$-0.268825\pi$
$163$	1.75843e22			1.32815			0.664076	+	0.747665i	$0.268825\pi$
$164$	−1.86428e22	−	1.42791e21i	−1.32457	−	0.101452i
$165$			2.12516e21i			0.142086i
$166$	1.89769e20	−	4.96252e21i	0.0119438	−	0.312336i
$167$		−	2.76153e22i		−	1.63676i	−0.574677	−	0.818381i	$-0.694872\pi$
$167$		−	2.76153e22i		−	1.63676i	0.574677	−	0.818381i	$-0.305128\pi$
$168$	1.01569e22	+	1.16977e21i	0.567111	+	0.0653145i
$169$	1.88292e22			0.990751
$170$	−4.43724e21	−	1.69682e20i	−0.220102	−	0.00841679i
$171$	−1.80390e21			−0.0843825
$172$	−2.88574e22	−	2.21027e21i	−1.27342	−	0.0975351i
$173$			2.24815e22i			0.936190i	0.883678	+	0.468095i	$0.155060\pi$
$173$			2.24815e22i			0.936190i	−0.883678	+	0.468095i	$0.844940\pi$
$174$	−6.01736e21	−	2.30106e20i	−0.236545	−	0.00904558i
$175$		−	1.34876e22i		−	0.500675i
$176$	1.31247e22	+	2.02238e21i	0.460218	+	0.0709148i
$177$	−2.59317e22			−0.859207
$178$	−5.62917e20	+	1.47205e22i	−0.0176297	+	0.461023i
$179$	−2.88938e22			−0.855606			−0.427803	−	0.903872i	$-0.640712\pi$
$179$	−2.88938e22			−0.855606			−0.427803	+	0.903872i	$0.640712\pi$
$180$	−6.92821e19	+	9.04550e20i	−0.00194042	+	0.0253342i
$181$			2.95994e22i			0.784327i	0.919895	+	0.392164i	$0.128273\pi$
$181$			2.95994e22i			0.784327i	−0.919895	+	0.392164i	$0.871727\pi$
$182$	−8.02471e19	+	2.09849e21i	−0.00201241	+	0.0526251i
$183$			3.22595e22i			0.765856i
$184$	6.05964e22	+	6.97891e21i	1.36229	+	0.156895i
$185$	−2.31251e22			−0.492456
$186$	7.37134e22	+	2.81883e21i	1.48736	+	0.0568774i
$187$	−1.83232e22			−0.350417
$188$	−1.24543e21	+	1.62604e22i	−0.0225809	+	0.294817i
$189$		−	3.03186e22i		−	0.521304i
$190$	−1.74311e22	−	6.66572e20i	−0.284308	−	0.0108720i
$191$			4.22015e22i			0.653122i	0.945176	+	0.326561i	$0.105890\pi$
$191$			4.22015e22i			0.653122i	−0.945176	+	0.326561i	$0.894110\pi$
$192$	6.91141e22	+	1.61338e22i	1.01521	+	0.236987i
$193$	−2.84002e22			−0.396048			−0.198024	−	0.980197i	$-0.563452\pi$
$193$	−2.84002e22			−0.396048			−0.198024	+	0.980197i	$0.563452\pi$
$194$	−8.17514e19	+	2.13783e21i	−0.00108263	+	0.0283110i
$195$	−2.33290e21			−0.0293461
$196$	−5.84092e22	−	4.47372e21i	−0.698104	−	0.0534698i
$197$		−	1.41075e23i		−	1.60246i	−0.598354	−	0.801232i	$-0.704178\pi$
$197$		−	1.41075e23i		−	1.60246i	0.598354	−	0.801232i	$-0.295822\pi$
$198$	−1.43047e20	+	3.74073e21i	−0.00154464	+	0.0403928i
$199$			1.25438e23i			1.28795i	0.765047	+	0.643974i	$0.222716\pi$
$199$			1.25438e23i			1.28795i	−0.765047	+	0.643974i	$0.777284\pi$
$200$	1.07123e22	−	9.30125e22i	0.104612	−	0.908325i
$201$	1.51886e22			0.141110
$202$	1.53197e23	+	5.85833e21i	1.35437	+	0.0517917i
$203$	−1.47764e22			−0.124339
$204$	−9.76413e22	−	7.47862e21i	−0.782225	−	0.0599128i
$205$		−	5.09680e22i		−	0.388830i
$206$	−2.36034e23	−	9.02602e21i	−1.71515	−	0.0655879i
$207$			1.71947e22i			0.119040i
$208$	−2.22008e21	+	1.44077e22i	−0.0146466	+	0.0950522i
$209$	−7.19800e22			−0.452636
$210$	−1.06498e21	+	2.78497e22i	−0.00638484	+	0.166966i
$211$	−1.50302e22			−0.0859289			−0.0429644	−	0.999077i	$-0.513680\pi$
$211$	−1.50302e22			−0.0859289			−0.0429644	+	0.999077i	$0.513680\pi$
$212$	1.96653e22	−	2.56751e23i	0.107236	−	1.40008i
$213$		−	2.03664e23i		−	1.05954i
$214$	−1.03429e22	+	2.70470e23i	−0.0513456	+	1.34271i
$215$		−	7.88939e22i		−	0.373817i
$216$	2.40800e22	−	2.09081e23i	0.108923	−	0.945751i
$217$	1.81012e23			0.781827
$218$	3.58231e23	+	1.36989e22i	1.47774	+	0.0565094i
$219$	1.85231e23			0.729916
$220$	−2.76452e21	+	3.60937e22i	−0.0104086	+	0.135895i
$221$		−	2.01144e22i		−	0.0723741i
$222$	−5.09613e23	−	1.94878e22i	−1.75271	−	0.0670244i
$223$			2.87848e23i			0.946486i	0.880932	+	0.473243i	$0.156917\pi$
$223$			2.87848e23i			0.946486i	−0.880932	+	0.473243i	$0.843083\pi$
$224$	1.70983e23	+	3.30801e22i	0.537617	+	0.104013i
$225$	2.63931e22			0.0793715
$226$	−1.78203e22	+	4.66008e23i	−0.0512663	+	1.34063i
$227$	1.98559e23			0.546551			0.273275	−	0.961936i	$-0.411893\pi$
$227$	1.98559e23			0.546551			0.273275	+	0.961936i	$0.411893\pi$
$228$	−3.83570e23	−	2.93787e22i	−1.01041	−	0.0773899i
$229$			6.11210e23i			1.54112i	0.637369	+	0.770559i	$0.280023\pi$
$229$			6.11210e23i			1.54112i	−0.637369	+	0.770559i	$0.719977\pi$
$230$	−6.35373e21	+	1.66152e23i	−0.0153374	+	0.401077i
$231$			1.15003e23i			0.265820i
$232$	−1.01900e23	−	1.17358e22i	−0.225576	−	0.0259797i
$233$	6.49765e23			1.37783			0.688917	−	0.724840i	$-0.258086\pi$
$233$	6.49765e23			1.37783			0.688917	+	0.724840i	$0.258086\pi$
$234$	−4.10640e21	−	1.57030e20i	−0.00834262	−	0.000319025i
$235$	−4.44547e22			−0.0865443
$236$	−4.40424e23	−	3.37333e22i	−0.821772	−	0.0629418i
$237$		−	7.00895e23i		−	1.25363i
$238$	−2.40121e23	−	9.18234e21i	−0.411776	−	0.0157465i
$239$		−	1.77828e23i		−	0.292429i	−0.989253	−	0.146215i	$-0.953291\pi$
$239$		−	1.77828e23i		−	0.292429i	0.989253	−	0.146215i	$-0.0467090\pi$
$240$	−2.94634e22	+	1.91209e23i	−0.0464697	+	0.301576i
$241$	−8.68911e23			−1.31463			−0.657317	−	0.753614i	$-0.728309\pi$
$241$	−8.68911e23			−1.31463			−0.657317	+	0.753614i	$0.728309\pi$
$242$	2.06165e22	−	5.39129e23i	0.0299269	−	0.782599i
$243$	1.24297e23			0.173140
$244$	−4.19650e22	+	5.47897e23i	−0.0561033	+	0.732488i
$245$		−	1.59686e23i		−	0.204930i
$246$	4.29513e22	−	1.12319e24i	0.0529206	−	1.38389i
$247$		−	7.90164e22i		−	0.0934863i
$248$	1.24828e24	+	1.43766e23i	1.41839	+	0.163357i
$249$	2.98544e23			0.325848
$250$	5.33968e23	+	2.04191e22i	0.559906	+	0.0214110i
$251$	−5.29812e23			−0.533807			−0.266904	−	0.963723i	$-0.586001\pi$
$251$	−5.29812e23			−0.533807			−0.266904	+	0.963723i	$0.586001\pi$
$252$	−3.74920e21	+	4.89497e22i	−0.00363022	+	0.0473963i
$253$			6.86110e23i			0.638541i
$254$	1.01328e24	+	3.87481e22i	0.906549	+	0.0346668i
$255$		−	2.66944e23i		−	0.229624i
$256$	1.15285e24	+	3.63925e23i	0.953614	+	0.301032i
$257$	−1.81348e24			−1.44272			−0.721360	−	0.692560i	$-0.756483\pi$
$257$	−1.81348e24			−1.44272			−0.721360	+	0.692560i	$0.756483\pi$
$258$	6.64847e22	−	1.73860e24i	0.0508774	−	1.33046i
$259$	−1.25142e24			−0.921306
$260$	−3.96220e22	−	3.03476e21i	−0.0280675	−	0.00214977i
$261$		−	2.89149e22i		−	0.0197114i
$262$	8.59986e21	−	2.24889e23i	0.00564259	−	0.147556i
$263$		−	2.32082e24i		−	1.46583i	−0.680319	−	0.732916i	$-0.738159\pi$
$263$		−	2.32082e24i		−	1.46583i	0.680319	−	0.732916i	$-0.261841\pi$
$264$	−9.13387e22	+	7.93074e23i	−0.0555412	+	0.482252i
$265$	7.01937e23			0.410998
$266$	−9.43283e23	−	3.60715e22i	−0.531895	−	0.0203399i
$267$	−8.85582e23			−0.480968
$268$	2.57964e23	+	1.97582e22i	0.134962	+	0.0103371i
$269$			3.03348e24i			1.52904i	0.644600	+	0.764520i	$0.277024\pi$
$269$			3.03348e24i			1.52904i	−0.644600	+	0.764520i	$0.722976\pi$
$270$	5.73290e23	+	2.19228e22i	0.278443	+	0.0106478i
$271$		−	8.65982e23i		−	0.405337i	−0.979247	−	0.202668i	$-0.935039\pi$
$271$		−	8.65982e23i		−	0.405337i	0.979247	−	0.202668i	$-0.0649613\pi$
$272$	−1.64861e24	−	2.54034e23i	−0.743755	−	0.114605i
$273$	−1.26245e23			−0.0549019
$274$	−4.74822e22	+	1.24168e24i	−0.0199079	+	0.520598i
$275$	1.05315e24			0.425757
$276$	−2.80037e23	+	3.65617e24i	−0.109175	+	1.42540i
$277$			4.40317e24i			1.65565i	0.560990	+	0.827823i	$0.310421\pi$
$277$			4.40317e24i			1.65565i	−0.560990	+	0.827823i	$0.689579\pi$
$278$	−2.78514e22	+	7.28325e23i	−0.0101018	+	0.264166i
$279$			3.54211e23i			0.123942i
$280$	−5.43161e22	+	4.71615e23i	−0.0183379	+	0.159224i
$281$	3.07116e24			1.00055			0.500276	−	0.865866i	$-0.333232\pi$
$281$	3.07116e24			1.00055			0.500276	+	0.865866i	$0.333232\pi$
$282$	−9.79655e23	−	3.74624e22i	−0.308022	−	0.0117789i
$283$	3.69971e24			1.12280			0.561402	−	0.827543i	$-0.310262\pi$
$283$	3.69971e24			1.12280			0.561402	+	0.827543i	$0.310262\pi$
$284$	2.64937e23	−	3.45903e24i	0.0776173	−	1.01338i
$285$		−	1.04865e24i		−	0.296608i
$286$	−1.63855e23	−	6.26588e21i	−0.0447507	−	0.00171128i
$287$		−	2.75813e24i		−	0.727439i
$288$	−6.47323e22	+	3.34586e23i	−0.0164891	+	0.0852281i
$289$	−1.76263e24			−0.433694
$290$	1.06845e22	−	2.79404e23i	0.00253966	−	0.0664130i
$291$	−1.28611e23			−0.0295359
$292$	3.14597e24	+	2.40959e23i	0.698114	+	0.0534705i
$293$		−	3.10876e24i		−	0.666671i	−0.942808	−	0.333335i	$-0.891826\pi$
$293$		−	3.10876e24i		−	0.666671i	0.942808	−	0.333335i	$-0.108174\pi$
$294$	1.34569e23	−	3.51903e24i	0.0278915	−	0.729373i
$295$		−	1.20409e24i		−	0.241233i
$296$	−8.62992e24	−	9.93913e23i	−1.67144	−	0.192500i
$297$	2.36735e24			0.443300
$298$	−2.69345e24	−	1.02999e23i	−0.487693	−	0.0186496i
$299$	−7.53181e23			−0.131883
$300$	5.61205e24	+	4.29843e23i	0.950406	+	0.0727942i
$301$		−	4.26934e24i		−	0.699352i
$302$	−2.50330e24	−	9.57271e22i	−0.396683	−	0.0151693i
$303$			9.21633e24i			1.41297i
$304$	−6.47635e24	−	9.97938e23i	−0.960715	−	0.148036i
$305$	−1.49791e24			−0.215024
$306$	1.79683e22	−	4.69878e23i	0.00249628	−	0.0652785i
$307$	8.14443e23			0.109516			0.0547579	−	0.998500i	$-0.482561\pi$
$307$	8.14443e23			0.109516			0.0547579	+	0.998500i	$0.482561\pi$
$308$	−1.49602e23	+	1.95321e24i	−0.0194729	+	0.254239i
$309$		−	1.41997e25i		−	1.78935i
$310$	−1.30887e23	+	3.42274e24i	−0.0159690	+	0.417596i
$311$			6.16008e24i			0.727750i	0.931448	+	0.363875i	$0.118547\pi$
$311$			6.16008e24i			0.727750i	−0.931448	+	0.363875i	$0.881453\pi$
$312$	−8.70600e23	−	1.00268e23i	−0.0996031	−	0.0114713i
$313$	1.22170e25			1.35370			0.676848	−	0.736123i	$-0.263345\pi$
$313$	1.22170e25			1.35370			0.676848	+	0.736123i	$0.263345\pi$
$314$	−8.04122e24	−	3.07499e23i	−0.863029	−	0.0330026i
$315$	−1.33825e23			−0.0139133
$316$	9.11763e23	−	1.19040e25i	0.0918356	−	1.19901i
$317$			2.56157e24i			0.249985i	0.992158	+	0.124992i	$0.0398907\pi$
$317$			2.56157e24i			0.249985i	−0.992158	+	0.124992i	$0.960109\pi$
$318$	1.54687e25	+	5.91530e23i	1.46279	+	0.0559378i
$319$		−	1.15377e24i		−	0.105734i
$320$	−7.49142e23	+	3.20918e24i	−0.0665372	+	0.285032i
$321$	−1.62714e25			−1.40080
$322$	−3.43832e23	+	8.99133e24i	−0.0286938	+	0.750352i
$323$	9.04151e24			0.731502
$324$	1.37186e25	+	1.05075e24i	1.07612	+	0.0824231i
$325$			1.15610e24i			0.0879347i
$326$	−6.88064e23	+	1.79931e25i	−0.0507520	+	1.32718i
$327$			2.15511e25i			1.54167i
$328$	2.19059e24	−	1.90204e25i	0.151993	−	1.31972i
$329$	−2.40566e24			−0.161911
$330$	−2.17457e24	−	8.31564e22i	−0.141982	−	0.00542946i
$331$	−1.75257e25			−1.11019			−0.555093	−	0.831788i	$-0.687317\pi$
$331$	−1.75257e25			−1.11019			−0.555093	+	0.831788i	$0.687317\pi$
$332$	5.07049e24	+	3.88363e23i	0.311651	+	0.0238702i
$333$		−	2.44881e24i		−	0.146054i
$334$	2.82574e25	+	1.08058e24i	1.63557	+	0.0625447i
$335$			7.05254e23i			0.0396185i
$336$	−1.59441e24	+	1.03473e25i	−0.0869375	+	0.564201i
$337$	−2.12183e25			−1.12308			−0.561540	−	0.827449i	$-0.689791\pi$
$337$	−2.12183e25			−1.12308			−0.561540	+	0.827449i	$0.689791\pi$
$338$	−7.36778e23	+	1.92670e25i	−0.0378590	+	0.990027i
$339$	−2.80350e25			−1.39863
$340$	3.47255e23	−	4.53378e24i	0.0168213	−	0.219620i
$341$			1.41339e25i			0.664840i
$342$	7.05860e22	−	1.84585e24i	0.00322446	−	0.0843208i
$343$		−	2.09836e25i		−	0.930979i
$344$	3.39084e24	−	2.94419e25i	0.146125	−	1.26877i
$345$	−9.99569e24			−0.418429
$346$	−2.30042e25	−	8.79691e23i	−0.935507	−	0.0357741i
$347$	1.61375e25			0.637592			0.318796	−	0.947823i	$-0.396722\pi$
$347$	1.61375e25			0.637592			0.318796	+	0.947823i	$0.396722\pi$
$348$	4.70914e23	−	6.14828e24i	0.0180779	−	0.236027i
$349$		−	2.24563e25i		−	0.837692i	−0.908057	−	0.418846i	$-0.862435\pi$
$349$		−	2.24563e25i		−	0.837692i	0.908057	−	0.418846i	$-0.137565\pi$
$350$	1.38013e25	+	5.27766e23i	0.500309	+	0.0191320i
$351$			2.59877e24i			0.0915580i
$352$	−2.58297e24	+	1.33508e25i	−0.0884490	+	0.457172i
$353$	5.47178e25			1.82130			0.910650	−	0.413178i	$-0.135581\pi$
$353$	5.47178e25			1.82130			0.910650	+	0.413178i	$0.135581\pi$
$354$	1.01470e24	−	2.65346e25i	0.0328324	−	0.858580i
$355$	9.45671e24			0.297479
$356$	−1.50407e25	−	1.15201e24i	−0.460012	−	0.0352336i
$357$		−	1.44457e25i		−	0.429591i
$358$	1.13060e24	−	2.95656e25i	0.0326948	−	0.854982i
$359$		−	7.27751e24i		−	0.204662i	−0.994750	−	0.102331i	$-0.967370\pi$
$359$		−	7.27751e24i		−	0.204662i	0.994750	−	0.102331i	$-0.0326302\pi$
$360$	−9.22872e23	−	1.06288e23i	−0.0252416	−	0.00290709i
$361$	−2.07167e24			−0.0551122
$362$	−3.02877e25	−	1.15821e24i	−0.783755	−	0.0299711i
$363$	3.24339e25			0.816456
$364$	−2.14415e24	−	1.64226e23i	−0.0525098	−	0.00402187i
$365$			8.60084e24i			0.204933i
$366$	−3.30097e25	−	1.26230e24i	−0.765297	−	0.0292653i
$367$		−	2.03693e25i		−	0.459532i	−0.973246	−	0.229766i	$-0.926204\pi$
$367$		−	2.03693e25i		−	0.459532i	0.973246	−	0.229766i	$-0.0737962\pi$
$368$	−9.51230e24	+	6.17323e25i	−0.208837	+	1.35530i
$369$	5.39721e24			0.115320
$370$	9.04877e23	−	2.36628e25i	0.0188179	−	0.492096i
$371$	3.79853e25			0.768912
$372$	−5.76875e24	+	7.53171e25i	−0.113672	+	1.48410i
$373$			2.39090e25i			0.458642i	0.973351	+	0.229321i	$0.0736505\pi$
$373$			2.39090e25i			0.458642i	−0.973351	+	0.229321i	$0.926349\pi$
$374$	7.16978e23	−	1.87492e25i	0.0133903	−	0.350161i
$375$			3.21234e25i			0.584129i
$376$	−1.65898e25	−	1.91065e24i	−0.293739	−	0.0338301i
$377$	1.26656e24			0.0218380
$378$	3.10236e25	+	1.18635e24i	0.520923	+	0.0199203i
$379$	−5.54765e25			−0.907229			−0.453614	−	0.891198i	$-0.649866\pi$
$379$	−5.54765e25			−0.907229			−0.453614	+	0.891198i	$0.649866\pi$
$380$	1.36414e24	−	1.78103e25i	0.0217282	−	0.283685i
$381$			6.09586e25i			0.945769i
$382$	−4.31828e25	−	1.65133e24i	−0.652645	−	0.0249574i
$383$		−	3.50725e25i		−	0.516391i	−0.966093	−	0.258196i	$-0.916872\pi$
$383$		−	3.50725e25i		−	0.516391i	0.966093	−	0.258196i	$-0.0831279\pi$
$384$	−1.92134e25	+	7.00899e25i	−0.275608	+	1.00541i
$385$	−5.33992e24			−0.0746325
$386$	1.11129e24	−	2.90605e25i	0.0151340	−	0.395759i
$387$	8.35440e24			0.110868
$388$	−2.18434e24	−	1.67305e23i	−0.0282490	−	0.00216367i
$389$			8.84689e25i			1.11505i	0.830160	+	0.557525i	$0.188249\pi$
$389$			8.84689e25i			1.11505i	−0.830160	+	0.557525i	$0.811751\pi$
$390$	9.12854e22	−	2.38715e24i	0.00112139	−	0.0293246i
$391$		−	8.61832e25i		−	1.03194i
$392$	6.86327e24	−	5.95922e25i	0.0801070	−	0.695551i
$393$	1.35293e25			0.153939
$394$	1.44355e26	+	5.52021e24i	1.60129	+	0.0612341i
$395$	3.25447e25			0.351973
$396$	−3.82211e24	−	2.92746e23i	−0.0403043	−	0.00308702i
$397$			2.75841e25i			0.283631i	0.989893	+	0.141815i	$0.0452940\pi$
$397$			2.75841e25i			0.283631i	−0.989893	+	0.141815i	$0.954706\pi$
$398$	−1.28355e26	−	4.90834e24i	−1.28701	−	0.0492157i
$399$		−	5.67477e25i		−	0.554906i
$400$	9.47561e25	+	1.46009e25i	0.903664	+	0.139245i
$401$	1.28179e26			1.19226			0.596132	−	0.802886i	$-0.296703\pi$
$401$	1.28179e26			1.19226			0.596132	+	0.802886i	$0.296703\pi$
$402$	−5.94325e23	+	1.55418e25i	−0.00539217	+	0.141007i
$403$	−1.55155e25			−0.137314
$404$	−1.19891e25	+	1.56530e26i	−0.103508	+	1.35140i
$405$			3.75057e25i			0.315898i
$406$	5.78193e23	−	1.51200e25i	0.00475130	−	0.124248i
$407$		−	9.77135e25i		−	0.783448i
$408$	1.14732e25	−	9.96191e25i	0.0897598	−	0.779365i
$409$	−2.43179e26			−1.85649			−0.928245	−	0.371970i	$-0.878682\pi$
$409$	−2.43179e26			−1.85649			−0.928245	+	0.371970i	$0.878682\pi$
$410$	5.21532e25	+	1.99436e24i	0.388546	+	0.0148581i
$411$	−7.46989e25			−0.543121
$412$	1.84718e25	−	2.41169e26i	0.131080	−	1.71139i
$413$		−	6.51591e25i		−	0.451309i
$414$	−1.75945e25	−	6.72822e23i	−0.118953	−	0.00454880i
$415$			1.38623e25i			0.0914860i
$416$	−1.46559e25	−	2.83547e24i	−0.0944231	−	0.0182680i
$417$	−4.38159e25			−0.275595
$418$	2.81655e24	−	7.36537e25i	0.0172963	−	0.452306i
$419$	−1.28227e26			−0.768847			−0.384424	−	0.923157i	$-0.625600\pi$
$419$	−1.28227e26			−0.768847			−0.384424	+	0.923157i	$0.625600\pi$
$420$	−2.84556e25	−	2.17949e24i	−0.166600	−	0.0127604i
$421$		−	9.55424e25i		−	0.546230i	−0.961981	−	0.273115i	$-0.911946\pi$
$421$		−	9.55424e25i		−	0.546230i	0.961981	−	0.273115i	$-0.0880539\pi$
$422$	5.88124e23	−	1.53796e25i	0.00328355	−	0.0858661i
$423$		−	4.70748e24i		−	0.0256676i
$424$	2.61952e26	+	3.01691e25i	1.39496	+	0.160659i
$425$	−1.32287e26			−0.688063
$426$	2.08399e26	+	7.96927e24i	1.05877	+	0.0404876i
$427$	−8.10592e25			−0.402276
$428$	−2.76354e26	−	2.11667e25i	−1.33976	−	0.102616i
$429$		−	9.85749e24i		−	0.0466867i
$430$	8.07284e25	+	3.08709e24i	0.373544	+	0.0142845i
$431$			4.16737e26i			1.88404i	0.335563	+	0.942018i	$0.391073\pi$
$431$			4.16737e26i			1.88404i	−0.335563	+	0.942018i	$0.608927\pi$
$432$	2.13000e26	+	3.28211e25i	0.940899	+	0.144983i
$433$	1.01631e26			0.438680			0.219340	−	0.975648i	$-0.429610\pi$
$433$	1.01631e26			0.438680			0.219340	+	0.975648i	$0.429610\pi$
$434$	−7.08293e24	+	1.85221e26i	−0.0298756	+	0.781256i
$435$	1.68089e25			0.0692862
$436$	−2.80349e25	+	3.66025e26i	−0.112936	+	1.47450i
$437$		−	3.38559e26i		−	1.33297i
$438$	−7.24801e24	+	1.89538e26i	−0.0278919	+	0.729383i
$439$			4.93500e26i			1.85628i	0.372237	+	0.928138i	$0.378591\pi$
$439$			4.93500e26i			1.85628i	−0.372237	+	0.928138i	$0.621409\pi$
$440$	−3.68248e25	−	4.24113e24i	−0.135398	−	0.0155939i
$441$	1.69098e25			0.0607789
$442$	2.05821e25	+	7.87066e23i	0.0723213	+	0.00276559i
$443$	3.85805e26			1.32535			0.662676	−	0.748906i	$-0.269421\pi$
$443$	3.85805e26			1.32535			0.662676	+	0.748906i	$0.269421\pi$
$444$	3.98818e25	−	5.20700e26i	0.133951	−	1.74887i
$445$		−	4.11202e25i		−	0.135038i
$446$	−2.94541e26	−	1.12634e25i	−0.945795	−	0.0361676i
$447$		−	1.62037e26i		−	0.508792i
$448$	−4.05398e25	+	1.73665e26i	−0.124481	+	0.533250i
$449$	4.60843e26			1.38385			0.691926	−	0.721968i	$-0.256762\pi$
$449$	4.60843e26			1.38385			0.691926	+	0.721968i	$0.256762\pi$
$450$	−1.03275e24	+	2.70068e25i	−0.00303298	+	0.0793136i
$451$	2.15361e26			0.618590
$452$	−4.76147e26	−	3.64694e25i	−1.33769	−	0.102458i
$453$		−	1.50598e26i		−	0.413844i
$454$	−7.76952e24	+	2.03176e26i	−0.0208851	+	0.546152i
$455$		−	5.86193e24i		−	0.0154144i
$456$	4.50708e25	−	3.91339e26i	0.115944	−	1.00671i
$457$	−8.85671e24			−0.0222900			−0.0111450	−	0.999938i	$-0.503548\pi$
$457$	−8.85671e24			−0.0222900			−0.0111450	+	0.999938i	$0.503548\pi$
$458$	−6.25422e26	−	2.39164e25i	−1.53999	−	0.0588899i
$459$	−2.97366e26			−0.716414
$460$	−1.69767e26	−	1.30029e25i	−0.400198	−	0.0306523i
$461$		−	1.59679e26i		−	0.368331i	−0.982895	−	0.184165i	$-0.941042\pi$
$461$		−	1.59679e26i		−	0.368331i	0.982895	−	0.184165i	$-0.0589582\pi$
$462$	−1.17677e26	−	4.50001e24i	−0.265626	−	0.0101577i
$463$			3.46977e26i			0.766462i	0.923653	+	0.383231i	$0.125189\pi$
$463$			3.46977e26i			0.766462i	−0.923653	+	0.383231i	$0.874811\pi$
$464$	1.59960e25	−	1.03810e26i	0.0345806	−	0.224419i
$465$	−2.05911e26			−0.435663
$466$	−2.54250e25	+	6.64873e26i	−0.0526505	+	1.37683i
$467$	6.35479e26			1.28805			0.644025	−	0.765005i	$-0.277263\pi$
$467$	6.35479e26			1.28805			0.644025	+	0.765005i	$0.277263\pi$
$468$	3.21363e23	−	4.19574e24i	0.000637584	−	0.00832434i
$469$			3.81648e25i			0.0741199i
$470$	1.73949e24	−	4.54883e25i	0.00330707	−	0.0864811i
$471$		−	4.83758e26i		−	0.900366i
$472$	5.17513e25	−	4.49345e26i	0.0942978	−	0.818766i
$473$	3.33360e26			0.594706
$474$	7.17193e26	+	2.74257e25i	1.25272	+	0.0479043i
$475$	−5.19672e26			−0.888777
$476$	1.87917e25	−	2.45345e26i	0.0314700	−	0.410874i
$477$			7.43310e25i			0.121895i
$478$	1.81963e26	+	6.95833e24i	0.292216	+	0.0111744i
$479$		−	6.78069e26i		−	1.06640i	−0.845990	−	0.533198i	$-0.820990\pi$
$479$		−	6.78069e26i		−	1.06640i	0.845990	−	0.533198i	$-0.179010\pi$
$480$	−1.94502e26	−	3.76304e25i	−0.299580	−	0.0579597i
$481$	1.07265e26			0.161811
$482$	3.40001e25	−	8.89115e26i	0.0502354	−	1.31367i
$483$	−5.40917e26			−0.782815
$484$	5.50858e26	+	4.21918e25i	0.780883	+	0.0598100i
$485$		−	5.97181e24i		−	0.00829256i
$486$	−4.86368e24	+	1.27187e26i	−0.00661610	+	0.173013i
$487$			1.58063e26i			0.210640i	0.994438	+	0.105320i	$0.0335867\pi$
$487$			1.58063e26i			0.210640i	−0.994438	+	0.105320i	$0.966413\pi$
$488$	−5.58995e26	−	6.43797e25i	−0.729809	−	0.0840525i
$489$	−1.08246e27			−1.38460
$490$	1.63399e26	+	6.24845e24i	0.204781	+	0.00783089i
$491$	8.93462e26			1.09714			0.548569	−	0.836105i	$-0.315173\pi$
$491$	8.93462e26			1.09714			0.548569	+	0.836105i	$0.315173\pi$
$492$	1.14763e27	+	8.79000e25i	1.38086	+	0.105764i
$493$			1.44927e26i			0.170876i
$494$	8.08537e25	+	3.09188e24i	0.0934180	+	0.00357234i
$495$		−	1.04493e25i		−	0.0118314i
$496$	−1.95953e26	+	1.27168e27i	−0.217438	+	1.41111i
$497$	5.11750e26			0.556536
$498$	−1.16819e25	+	3.05486e26i	−0.0124515	+	0.325610i
$499$	−5.36375e26			−0.560354			−0.280177	−	0.959948i	$-0.590393\pi$
$499$	−5.36375e26			−0.560354			−0.280177	+	0.959948i	$0.590393\pi$
$500$	−4.17879e25	+	5.45585e26i	−0.0427908	+	0.558679i
$501$			1.69996e27i			1.70633i
$502$	2.07313e25	−	5.42131e26i	0.0203981	−	0.533417i
$503$			5.79553e26i			0.559002i	0.960145	+	0.279501i	$0.0901691\pi$
$503$			5.79553e26i			0.559002i	−0.960145	+	0.279501i	$0.909831\pi$
$504$	−4.99412e25	−	5.75175e24i	−0.0472230	−	0.00543870i
$505$	−4.27942e26			−0.396708
$506$	−7.02064e26	−	2.68472e25i	−0.638075	−	0.0244002i
$507$	−1.15910e27			−1.03286
$508$	−7.92982e25	+	1.03532e27i	−0.0692829	+	0.904562i
$509$		−	3.79126e26i		−	0.324792i	−0.986726	−	0.162396i	$-0.948078\pi$
$509$		−	3.79126e26i		−	0.324792i	0.986726	−	0.162396i	$-0.0519223\pi$
$510$	2.73151e26	+	1.04454e25i	0.229457	+	0.00877451i
$511$			4.65434e26i			0.383397i
$512$	−4.17497e26	+	1.16541e27i	−0.337252	+	0.941415i
$513$	−1.16816e27			−0.925398
$514$	7.09608e25	−	1.85565e27i	0.0551299	−	1.44167i
$515$	6.59336e26			0.502383
$516$	1.77642e27	+	1.36061e26i	1.32755	+	0.101680i
$517$		−	1.87840e26i		−	0.137684i
$518$	4.89674e25	−	1.28051e27i	0.0352054	−	0.920634i
$519$		−	1.38393e27i		−	0.975979i
$520$	4.65572e24	−	4.04246e25i	0.00322072	−	0.0279648i
$521$	1.82007e27			1.23512			0.617562	−	0.786522i	$-0.288120\pi$
$521$	1.82007e27			1.23512			0.617562	+	0.786522i	$0.288120\pi$
$522$	2.95872e25	+	1.13143e24i	0.0196970	+	0.000753220i
$523$	−9.89424e26			−0.646198			−0.323099	−	0.946365i	$-0.604725\pi$
$523$	−9.89424e26			−0.646198			−0.323099	+	0.946365i	$0.604725\pi$
$524$	2.29782e26	+	1.75996e25i	0.147232	+	0.0112769i
$525$			8.30281e26i			0.521954i
$526$	2.37479e27	+	9.08128e25i	1.46476	+	0.0560131i
$527$		−	1.77537e27i		−	1.07444i
$528$	−8.07940e26	−	1.24495e26i	−0.479778	−	0.0739287i
$529$	−1.51097e27			−0.880439
$530$	−2.74665e25	+	7.18259e26i	−0.0157052	+	0.410698i
$531$	1.27505e26			0.0715457
$532$	7.38205e25	−	9.63805e26i	0.0406500	−	0.530729i
$533$			2.36414e26i			0.127762i
$534$	3.46524e25	−	9.06173e26i	0.0183790	−	0.480616i
$535$		−	7.55530e26i		−	0.393291i
$536$	−3.03117e25	+	2.63189e26i	−0.0154868	+	0.134469i
$537$	1.77866e27			0.891971
$538$	−3.10402e27	−	1.18699e26i	−1.52792	−	0.0584284i
$539$	6.74741e26			0.326024
$540$	−4.48652e25	+	5.85763e26i	−0.0212800	+	0.277833i
$541$			1.20643e27i			0.561732i	0.959747	+	0.280866i	$0.0906216\pi$
$541$			1.20643e27i			0.561732i	−0.959747	+	0.280866i	$0.909378\pi$
$542$	8.86118e26	+	3.38855e25i	0.405041	+	0.0154889i
$543$		−	1.82210e27i		−	0.817662i
$544$	3.24451e26	−	1.67701e27i	0.142942	−	0.738833i
$545$	−1.00068e27			−0.432844
$546$	4.93991e24	−	1.29180e26i	0.00209794	−	0.0548618i
$547$	1.77472e27			0.740042			0.370021	−	0.929023i	$-0.379350\pi$
$547$	1.77472e27			0.740042			0.370021	+	0.929023i	$0.379350\pi$
$548$	−1.26869e27	−	9.71724e25i	−0.519457	−	0.0397867i
$549$		−	1.58619e26i		−	0.0637724i
$550$	−4.12092e25	+	1.07763e27i	−0.0162692	+	0.425446i
$551$			5.69326e26i			0.220722i
$552$	−3.73023e27	−	4.29612e26i	−1.42018	−	0.163563i
$553$	1.76115e27			0.658485
$554$	−4.50555e27	−	1.72294e26i	−1.65444	−	0.0632663i
$555$	1.42355e27			0.513385
$556$	−7.44170e26	−	5.69981e25i	−0.263587	−	0.0201889i
$557$			5.26001e26i			0.182993i	0.995805	+	0.0914965i	$0.0291650\pi$
$557$			5.26001e26i			0.182993i	−0.995805	+	0.0914965i	$0.970835\pi$
$558$	−3.62447e26	−	1.38601e25i	−0.123852	−	0.00473615i
$559$			3.65948e26i			0.122829i
$560$	−4.80456e26	−	7.40332e25i	−0.158407	−	0.0244088i
$561$	1.12795e27			0.365310
$562$	−1.20173e26	+	3.14257e27i	−0.0382336	+	0.999821i
$563$	1.43328e27			0.447968			0.223984	−	0.974593i	$-0.428094\pi$
$563$	1.43328e27			0.447968			0.223984	+	0.974593i	$0.428094\pi$
$564$	7.66670e25	−	1.00097e27i	0.0235406	−	0.307347i
$565$		−	1.30175e27i		−	0.392683i
$566$	−1.44768e26	+	3.78574e27i	−0.0429051	+	1.12198i
$567$			2.02962e27i			0.590995i
$568$	3.52909e27	+	4.06447e26i	1.00967	+	0.116284i
$569$	3.05567e27			0.858980			0.429490	−	0.903072i	$-0.358693\pi$
$569$	3.05567e27			0.858980			0.429490	+	0.903072i	$0.358693\pi$
$570$	1.07303e27	+	4.10333e25i	0.296391	+	0.0113341i
$571$	−1.35768e27			−0.368500			−0.184250	−	0.982879i	$-0.558986\pi$
$571$	−1.35768e27			−0.368500			−0.184250	+	0.982879i	$0.558986\pi$
$572$	1.28232e25	−	1.67420e26i	0.00342007	−	0.0446526i
$573$		−	2.59787e27i		−	0.680880i
$574$	2.82227e27	+	1.07925e26i	0.726907	+	0.0277972i
$575$			4.95348e27i			1.25381i
$576$	−3.39833e26	−	7.93297e25i	−0.0845357	−	0.0197338i
$577$	−2.39151e27			−0.584675			−0.292337	−	0.956315i	$-0.594433\pi$
$577$	−2.39151e27			−0.584675			−0.292337	+	0.956315i	$0.594433\pi$
$578$	6.89710e25	−	1.80362e27i	0.0165725	−	0.433377i
$579$	1.74828e27			0.412880
$580$	2.85483e26	+	2.18659e25i	0.0662674	+	0.00507561i
$581$			7.50159e26i			0.171156i
$582$	5.03251e24	−	1.31602e26i	0.00112864	−	0.0295143i
$583$			2.96598e27i			0.653857i
$584$	−3.69662e26	+	3.20969e27i	−0.0801081	+	0.695560i
$585$	1.14708e25			0.00244363
$586$	3.18105e27	+	1.21645e26i	0.666184	+	0.0254751i
$587$	−8.53021e27			−1.75622			−0.878110	−	0.478459i	$-0.841195\pi$
$587$	−8.53021e27			−1.75622			−0.878110	+	0.478459i	$0.841195\pi$
$588$	3.59559e27	+	2.75396e26i	0.727774	+	0.0557423i
$589$		−	6.97431e27i		−	1.38787i
$590$	1.23208e27	+	4.71153e25i	0.241057	+	0.00921812i
$591$			8.68439e27i			1.67057i
$592$	1.35471e27	−	8.79170e27i	0.256229	−	1.66286i
$593$	−6.78323e27			−1.26151			−0.630753	−	0.775984i	$-0.717254\pi$
$593$	−6.78323e27			−1.26151			−0.630753	+	0.775984i	$0.717254\pi$
$594$	−9.26333e25	+	2.42239e27i	−0.0169396	+	0.442976i
$595$	6.70755e26			0.120613
$596$	2.10787e26	−	2.75205e27i	0.0372719	−	0.486624i
$597$		−	7.72180e27i		−	1.34269i
$598$	2.94716e25	−	7.70694e26i	0.00503956	−	0.131786i
$599$		−	2.14857e27i		−	0.361311i	−0.983546	−	0.180655i	$-0.942178\pi$
$599$		−	2.14857e27i		−	0.361311i	0.983546	−	0.180655i	$-0.0578219\pi$
$600$	−6.59435e26	+	5.72572e27i	−0.109058	+	0.946930i
$601$	−6.28435e27			−1.02215			−0.511076	−	0.859535i	$-0.670753\pi$
$601$	−6.28435e27			−1.02215			−0.511076	+	0.859535i	$0.670753\pi$
$602$	4.36861e27	+	1.67058e26i	0.698842	+	0.0267240i
$603$	−7.46822e25			−0.0117502
$604$	1.95906e26	−	2.55776e27i	0.0303165	−	0.395813i
$605$			1.50600e27i			0.229230i
$606$	−9.43063e27	−	3.60631e26i	−1.41193	−	0.0539929i
$607$		−	7.51691e27i		−	1.10701i	−0.832845	−	0.553506i	$-0.813290\pi$
$607$		−	7.51691e27i		−	1.10701i	0.832845	−	0.553506i	$-0.186710\pi$
$608$	1.27456e27	−	6.58789e27i	0.184639	−	0.954356i
$609$	9.09613e26			0.129624
$610$	5.86125e25	−	1.53274e27i	0.00821659	−	0.214867i
$611$	2.06202e26			0.0284368
$612$	4.80100e26	+	3.67722e25i	0.0651355	+	0.00498891i
$613$		−	7.41418e27i		−	0.989598i	−0.869008	−	0.494799i	$-0.835242\pi$
$613$		−	7.41418e27i		−	0.989598i	0.869008	−	0.494799i	$-0.164758\pi$
$614$	−3.18688e25	+	8.33380e26i	−0.00418487	+	0.109436i
$615$			3.13752e27i			0.405355i
$616$	−1.99277e27	−	2.29509e26i	−0.253309	−	0.0291737i
$617$	3.50634e27			0.438533			0.219266	−	0.975665i	$-0.429634\pi$
$617$	3.50634e27			0.438533			0.219266	+	0.975665i	$0.429634\pi$
$618$	1.45299e28	+	5.55629e26i	1.78804	+	0.0683755i
$619$	−1.01588e27			−0.123009			−0.0615046	−	0.998107i	$-0.519590\pi$
$619$	−1.01588e27			−0.123009			−0.0615046	+	0.998107i	$0.519590\pi$
$620$	−3.49720e27	−	2.67860e26i	−0.416681	−	0.0319148i
$621$			1.11348e28i			1.30547i
$622$	−6.30332e27	−	2.41041e26i	−0.727219	−	0.0278091i
$623$		−	2.22522e27i		−	0.252634i
$624$	1.36665e26	−	8.86920e26i	0.0152690	−	0.0990920i
$625$	6.82419e27			0.750328
$626$	−4.78046e26	+	1.25011e28i	−0.0517281	+	1.35271i
$627$	4.43099e27			0.471874
$628$	6.29299e26	−	8.21616e27i	0.0659570	−	0.861138i
$629$			1.22739e28i			1.26613i
$630$	5.23650e24	−	1.36936e26i	0.000531662	−	0.0139032i
$631$		−	2.41792e27i		−	0.241629i	−0.992675	−	0.120814i	$-0.961449\pi$
$631$		−	2.41792e27i		−	0.241629i	0.992675	−	0.120814i	$-0.0385505\pi$
$632$	1.21451e28	+	1.39876e27i	1.19463	+	0.137586i
$633$	9.25237e26			0.0895810
$634$	−2.62113e27	−	1.00233e26i	−0.249802	−	0.00955254i
$635$	−2.83049e27			−0.265537
$636$	−1.21057e27	+	1.58052e28i	−0.111794	+	1.45959i
$637$			7.40700e26i			0.0673361i
$638$	1.18060e27	+	4.51467e25i	0.105657	+	0.00404035i
$639$			1.00141e27i			0.0882273i
$640$	−3.25448e27	−	8.92135e26i	−0.282281	−	0.0773804i
$641$	−3.65490e27			−0.312101			−0.156050	−	0.987749i	$-0.549876\pi$
$641$	−3.65490e27			−0.312101			−0.156050	+	0.987749i	$0.549876\pi$
$642$	6.36693e26	−	1.66497e28i	0.0535278	−	1.39977i
$643$	2.11566e27			0.175120			0.0875601	−	0.996159i	$-0.472093\pi$
$643$	2.11566e27			0.175120			0.0875601	+	0.996159i	$0.472093\pi$
$644$	−9.18694e27	−	7.03654e26i	−0.748708	−	0.0573456i
$645$			4.85660e27i			0.389705i
$646$	−3.53790e26	+	9.25174e27i	−0.0279525	+	0.730968i
$647$		−	1.51438e28i		−	1.17813i	−0.808087	−	0.589063i	$-0.799497\pi$
$647$		−	1.51438e28i		−	1.17813i	0.808087	−	0.589063i	$-0.200503\pi$
$648$	−1.61199e27	+	1.39965e28i	−0.123484	+	1.07219i
$649$	5.08777e27			0.383778
$650$	−1.18298e27	−	4.52376e25i	−0.0878705	−	0.00336020i
$651$	−1.11429e28			−0.815056
$652$	−1.83846e28	−	1.40813e27i	−1.32427	−	0.101430i
$653$			2.62981e27i			0.186549i	0.995640	+	0.0932744i	$0.0297334\pi$
$653$			2.62981e27i			0.186549i	−0.995640	+	0.0932744i	$0.970267\pi$
$654$	−2.20522e28	−	8.43286e26i	−1.54055	−	0.0589111i
$655$			6.28206e26i			0.0432204i
$656$	1.93770e28	+	2.98579e27i	1.31295	+	0.202312i
$657$	−9.10777e26			−0.0607797
$658$	9.41325e25	−	2.46160e27i	0.00618701	−	0.161793i
$659$	2.62364e28			1.69844			0.849219	−	0.528041i	$-0.177073\pi$
$659$	2.62364e28			1.69844			0.849219	+	0.528041i	$0.177073\pi$
$660$	1.70180e26	−	2.22188e27i	0.0108510	−	0.141671i
$661$			2.11090e28i			1.32573i	0.748741	+	0.662863i	$0.230659\pi$
$661$			2.11090e28i			1.32573i	−0.748741	+	0.662863i	$0.769341\pi$
$662$	6.85773e26	−	1.79332e28i	0.0424229	−	1.10937i
$663$			1.23821e27i			0.0754501i
$664$	−5.95799e26	+	5.17319e27i	−0.0357618	+	0.310511i
$665$	2.63497e27			0.155797
$666$	2.50575e27	+	9.58210e25i	0.145947	+	0.00558108i
$667$	5.42678e27			0.311375
$668$	−2.21140e27	+	2.88722e28i	−0.124998	+	1.63198i
$669$		−	1.77195e28i		−	0.986713i
$670$	−7.21653e26	−	2.75963e25i	−0.0395895	−	0.00151392i
$671$		−	6.32929e27i		−	0.342082i
$672$	−1.05255e28	−	2.03637e27i	−0.560467	−	0.108433i
$673$	2.63180e28			1.38071			0.690354	−	0.723472i	$-0.257455\pi$
$673$	2.63180e28			1.38071			0.690354	+	0.723472i	$0.257455\pi$
$674$	8.30262e26	−	2.17116e28i	0.0429157	−	1.12226i
$675$	1.70914e28			0.870445
$676$	−1.96862e28	−	1.50782e27i	−0.987857	−	0.0756627i
$677$		−	1.07390e28i		−	0.530977i	−0.964114	−	0.265489i	$-0.914467\pi$
$677$		−	1.07390e28i		−	0.530977i	0.964114	−	0.265489i	$-0.0855333\pi$
$678$	1.09700e27	−	2.86868e28i	0.0534451	−	1.39761i
$679$		−	3.23164e26i		−	0.0155141i
$680$	4.62561e27	+	5.32734e26i	0.218816	+	0.0252012i
$681$	−1.22230e28			−0.569780
$682$	−1.44625e28	−	5.53052e26i	−0.664354	−	0.0254052i
$683$	−2.85213e28			−1.29111			−0.645553	−	0.763715i	$-0.723373\pi$
$683$	−2.85213e28			−1.29111			−0.645553	+	0.763715i	$0.723373\pi$
$684$	1.88601e27	+	1.44454e26i	0.0841360	+	0.00644421i
$685$		−	3.46850e27i		−	0.152488i
$686$	2.14716e28	+	8.21081e26i	0.930299	+	0.0355750i
$687$		−	3.76253e28i		−	1.60662i
$688$	2.99938e28	+	4.62174e27i	1.26226	+	0.194501i
$689$	−3.25592e27			−0.135046
$690$	3.91127e26	−	1.02281e28i	0.0159892	−	0.418124i
$691$	3.85730e27			0.155419			0.0777093	−	0.996976i	$-0.475239\pi$
$691$	3.85730e27			0.155419			0.0777093	+	0.996976i	$0.475239\pi$
$692$	1.80029e27	−	2.35047e28i	0.0714960	−	0.933456i
$693$		−	5.65466e26i		−	0.0221347i
$694$	−6.31455e26	+	1.65128e28i	−0.0243639	+	0.637126i
$695$		−	2.03450e27i		−	0.0773767i
$696$	6.27281e27	+	7.22443e26i	0.235163	+	0.0270839i
$697$	−2.70518e28			−0.999699
$698$	2.29785e28	+	8.78706e26i	0.837080	+	0.0320103i
$699$	−3.99986e28			−1.43639
$700$	−1.08007e27	+	1.41015e28i	−0.0382361	+	0.499212i
$701$			4.20975e28i			1.46918i	0.678510	+	0.734592i	$0.262626\pi$
$701$			4.20975e28i			1.46918i	−0.678510	+	0.734592i	$0.737374\pi$
$702$	−2.65919e27	−	1.01689e26i	−0.0914911	−	0.00349866i
$703$			4.82164e28i			1.63547i
$704$	−1.35601e28	−	3.16544e27i	−0.453458	−	0.105854i
$705$	2.73657e27			0.0902226
$706$	−2.14108e27	+	5.59901e28i	−0.0695964	+	1.81997i
$707$	−2.31581e28			−0.742178
$708$	2.71119e28	+	2.07658e27i	0.856698	+	0.0656169i
$709$			5.49936e27i			0.171337i	0.996324	+	0.0856683i	$0.0273025\pi$
$709$			5.49936e27i			0.171337i	−0.996324	+	0.0856683i	$0.972697\pi$
$710$	−3.70037e26	+	9.67660e27i	−0.0113674	+	0.297262i
$711$			3.44629e27i			0.104389i
$712$	1.76734e27	−	1.53454e28i	0.0527861	−	0.458330i
$713$	−6.64788e28			−1.95789
$714$	1.47815e28	+	5.65252e26i	0.429277	+	0.0164157i
$715$	4.57713e26			0.0131079
$716$	3.02088e28	+	2.31378e27i	0.853108	+	0.0653419i
$717$			1.09468e28i			0.304858i
$718$	7.44673e27	+	2.84766e26i	0.204513	+	0.00782066i
$719$		−	2.67767e28i		−	0.725218i	−0.931941	−	0.362609i	$-0.881886\pi$
$719$		−	2.67767e28i		−	0.725218i	0.931941	−	0.362609i	$-0.118114\pi$
$720$	1.44871e26	−	9.40172e26i	0.00386951	−	0.0251121i
$721$	3.56800e28			0.939879
$722$	8.10635e25	−	2.11984e27i	0.00210598	−	0.0550720i
$723$	5.34890e28			1.37051
$724$	2.37029e27	−	3.09466e28i	0.0598984	−	0.782037i
$725$		−	8.32985e27i		−	0.207614i
$726$	−1.26912e27	+	3.31881e28i	−0.0311988	+	0.815860i
$727$			2.83458e28i			0.687297i	0.939098	+	0.343648i	$0.111663\pi$
$727$			2.83458e28i			0.687297i	−0.939098	+	0.343648i	$0.888337\pi$
$728$	2.51944e26	−	2.18758e27i	0.00602547	−	0.0523178i
$729$	3.81001e28			0.898774
$730$	−8.80082e27	−	3.36547e26i	−0.204783	−	0.00783100i
$731$	−4.18738e28			−0.961101
$732$	2.58331e27	−	3.37278e28i	0.0584878	−	0.763620i
$733$		−	7.06691e28i		−	1.57830i	−0.614200	−	0.789150i	$-0.710521\pi$
$733$		−	7.06691e28i		−	1.57830i	0.614200	−	0.789150i	$-0.289479\pi$
$734$	2.08430e28	+	7.97043e26i	0.459197	+	0.0175599i
$735$			9.83006e27i			0.213640i
$736$	−6.27955e28	−	1.21490e28i	−1.34633	−	0.260474i
$737$	−2.98000e27			−0.0630291
$738$	−2.11191e26	+	5.52271e27i	−0.00440667	+	0.115236i
$739$	5.87202e28			1.20877			0.604384	−	0.796693i	$-0.293419\pi$
$739$	5.87202e28			1.20877			0.604384	+	0.796693i	$0.293419\pi$
$740$	2.41776e28	+	1.85183e27i	0.491017	+	0.0376084i
$741$			4.86414e27i			0.0974595i
$742$	−1.48635e27	+	3.88686e28i	−0.0293820	+	0.768351i
$743$			4.35032e28i			0.848463i	0.905554	+	0.424231i	$0.139456\pi$
$743$			4.35032e28i			0.848463i	−0.905554	+	0.424231i	$0.860544\pi$
$744$	−7.68427e28	−	8.85001e27i	−1.47868	−	0.170300i
$745$	7.52389e27			0.142850
$746$	−2.44650e28	−	9.35550e26i	−0.458307	−	0.0175258i
$747$	−1.46794e27			−0.0271332
$748$	1.91571e28	+	1.46730e27i	0.349393	+	0.0267610i
$749$		−	4.08855e28i		−	0.735785i
$750$	−3.28703e28	−	1.25698e27i	−0.583703	−	0.0223210i
$751$			5.79180e28i			1.01488i	0.861687	+	0.507439i	$0.169408\pi$
$751$			5.79180e28i			1.01488i	−0.861687	+	0.507439i	$0.830592\pi$
$752$	2.60423e27	−	1.69007e28i	0.0450299	−	0.292232i
$753$	3.26145e28			0.556495
$754$	−4.95600e25	+	1.29601e27i	−0.000834483	+	0.0218220i
$755$	6.99272e27			0.116192
$756$	−2.42788e27	+	3.16985e28i	−0.0398115	+	0.519782i
$757$		−	1.00773e29i		−	1.63075i	−0.578936	−	0.815373i	$-0.696532\pi$
$757$		−	1.00773e29i		−	1.63075i	0.578936	−	0.815373i	$-0.303468\pi$
$758$	2.17077e27	−	5.67664e28i	0.0346674	−	0.906566i
$759$		−	4.22360e28i		−	0.665680i
$760$	1.81711e28	+	2.09277e27i	0.282647	+	0.0325526i
$761$	−4.50572e28			−0.691699			−0.345850	−	0.938290i	$-0.612409\pi$
$761$	−4.50572e28			−0.691699			−0.345850	+	0.938290i	$0.612409\pi$
$762$	−6.23760e28	−	2.38528e27i	−0.945078	−	0.0361402i
$763$	−5.41519e28			−0.809783
$764$	3.37944e27	−	4.41222e28i	0.0498783	−	0.651214i
$765$			1.31256e27i			0.0191207i
$766$	3.58880e28	+	1.37237e27i	0.516014	+	0.0197326i
$767$			5.58512e27i			0.0792646i
$768$	−7.09678e28	−	2.24027e28i	−0.994144	−	0.313826i
$769$	−1.12133e28			−0.155050			−0.0775250	−	0.996990i	$-0.524702\pi$
$769$	−1.12133e28			−0.155050			−0.0775250	+	0.996990i	$0.524702\pi$
$770$	2.08949e26	−	5.46409e27i	0.00285189	−	0.0745779i
$771$	1.11636e29			1.50404
$772$	2.96928e28	+	2.27425e27i	0.394891	+	0.0302458i
$773$		−	8.64611e28i		−	1.13508i	−0.823347	−	0.567539i	$-0.807896\pi$
$773$		−	8.64611e28i		−	1.13508i	0.823347	−	0.567539i	$-0.192104\pi$
$774$	−3.26904e26	+	8.54865e27i	−0.00423653	+	0.110787i
$775$			1.02042e29i			1.30545i
$776$	2.56667e26	−	2.22858e27i	0.00324155	−	0.0281457i
$777$	7.70355e28			0.960463
$778$	−9.05260e28	−	3.46175e27i	−1.11424	−	0.0426088i
$779$	−1.06269e29			−1.29132
$780$	2.43908e27	+	1.86816e26i	0.0292604	+	0.00224113i
$781$			3.99586e28i			0.473260i
$782$	8.81872e28	+	3.37231e27i	1.03119	+	0.0394330i
$783$		−	1.87245e28i		−	0.216169i
$784$	6.07093e28	+	9.35467e27i	0.691982	+	0.106627i
$785$	2.24623e28			0.252789
$786$	−5.29396e26	+	1.38439e28i	−0.00588241	+	0.153827i
$787$	1.76317e29			1.93440			0.967202	−	0.254009i	$-0.0817492\pi$
$787$	1.76317e29			1.93440			0.967202	+	0.254009i	$0.0817492\pi$
$788$	−1.12971e28	+	1.47496e29i	−0.122379	+	1.59778i
$789$			1.42867e29i			1.52813i
$790$	−1.27346e27	+	3.33014e28i	−0.0134497	+	0.351716i
$791$		−	7.04440e28i		−	0.734648i
$792$	4.49110e26	−	3.89952e27i	0.00462489	−	0.0401569i
$793$	6.94801e27			0.0706527
$794$	−2.82255e28	−	1.07935e27i	−0.283424	−	0.0108382i
$795$	−4.32103e28			−0.428466
$796$	1.00449e28	−	1.31147e29i	0.0983595	−	1.28419i
$797$			1.41048e29i			1.36390i	0.731398	+	0.681950i	$0.238868\pi$
$797$			1.41048e29i			1.36390i	−0.731398	+	0.681950i	$0.761132\pi$
$798$	5.80672e28	+	2.22051e27i	0.554501	+	0.0212043i
$799$			2.35948e28i			0.222509i
$800$	−1.86482e28	+	9.63880e28i	−0.173675	+	0.897683i
$801$	4.35438e27			0.0400499
$802$	−5.01558e27	+	1.31159e29i	−0.0455594	+	1.19139i
$803$	−3.63422e28			−0.326028
$804$	−1.58799e28	−	1.21629e27i	−0.140698	−	0.0107765i
$805$		−	2.51164e28i		−	0.219785i
$806$	6.07115e26	−	1.58763e28i	0.00524712	−	0.137214i
$807$		−	1.86737e29i		−	1.59403i
$808$	−1.59701e29	−	1.83928e28i	−1.34646	−	0.155073i
$809$	−2.55438e28			−0.212716			−0.106358	−	0.994328i	$-0.533919\pi$
$809$	−2.55438e28			−0.212716			−0.106358	+	0.994328i	$0.533919\pi$
$810$	−3.83778e28	−	1.46758e27i	−0.315667	−	0.0120712i
$811$	−1.56820e29			−1.27406			−0.637032	−	0.770837i	$-0.719838\pi$
$811$	−1.56820e29			−1.27406			−0.637032	+	0.770837i	$0.719838\pi$
$812$	1.54489e28	+	1.18327e27i	0.123976	+	0.00949566i
$813$			5.33087e28i			0.422564i
$814$	9.99855e28	+	3.82349e27i	0.782876	+	0.0299375i
$815$		−	5.02620e28i		−	0.388744i
$816$	1.01486e29	+	1.56380e28i	0.775366	+	0.119476i
$817$	−1.64495e29			−1.24146
$818$	9.51548e27	−	2.48833e29i	0.0709410	−	1.85513i
$819$	6.20743e26			0.00457165
$820$	−4.08146e27	+	5.32878e28i	−0.0296946	+	0.387694i
$821$			1.92538e29i			1.38383i	0.721977	+	0.691917i	$0.243234\pi$
$821$			1.92538e29i			1.38383i	−0.721977	+	0.691917i	$0.756766\pi$
$822$	2.92294e27	−	7.64359e28i	0.0207540	−	0.542724i
$823$			6.98818e28i			0.490192i	0.969499	+	0.245096i	$0.0788194\pi$
$823$			6.98818e28i			0.490192i	−0.969499	+	0.245096i	$0.921181\pi$
$824$	2.46054e29	+	2.83381e28i	1.70513	+	0.196381i
$825$	−6.48303e28			−0.443852
$826$	6.66741e28	+	2.54965e27i	0.450980	+	0.0172456i
$827$	−2.28697e28			−0.152829			−0.0764143	−	0.997076i	$-0.524347\pi$
$827$	−2.28697e28			−0.152829			−0.0764143	+	0.997076i	$0.524347\pi$
$828$	1.37693e27	−	1.79773e28i	0.00909096	−	0.118692i
$829$		−	1.82517e29i		−	1.19058i	−0.803512	−	0.595289i	$-0.797038\pi$
$829$		−	1.82517e29i		−	1.19058i	0.803512	−	0.595289i	$-0.202962\pi$
$830$	−1.41846e28	−	5.42426e26i	−0.0914192	−	0.00349591i
$831$		−	2.71053e29i		−	1.72601i
$832$	3.47488e27	−	1.48857e28i	0.0218628	−	0.0936561i
$833$	−8.47551e28			−0.526885
$834$	1.71450e27	−	4.48347e28i	0.0105312	−	0.275394i
$835$	−7.89343e28			−0.479072
$836$	7.52561e28	+	5.76408e27i	0.451314	+	0.0345674i
$837$			2.29378e29i			1.35924i
$838$	5.01748e27	−	1.31209e29i	0.0293795	−	0.768286i
$839$		−	8.14510e28i		−	0.471278i	−0.971841	−	0.235639i	$-0.924282\pi$
$839$		−	8.14510e28i		−	0.471278i	0.971841	−	0.235639i	$-0.0757183\pi$
$840$	3.34363e27	−	2.90320e28i	0.0191172	−	0.165991i
$841$	1.67869e29			0.948440
$842$	9.77640e28	+	3.73853e27i	0.545831	+	0.0208728i
$843$	−1.89057e29			−1.04308
$844$	1.57142e28	+	1.20360e27i	0.0856779	+	0.00656231i
$845$		−	5.38204e28i		−	0.289988i
$846$	4.81694e27	+	1.84202e26i	0.0256488	+	0.000980822i
$847$			8.14973e28i			0.428854i
$848$	−4.11206e28	+	2.66862e29i	−0.213846	+	1.38780i
$849$	−2.27749e29			−1.17052
$850$	5.17634e27	−	1.35363e29i	0.0262926	−	0.687561i
$851$	4.59596e29			2.30718
$852$	−1.63091e28	+	2.12933e29i	−0.0809161	+	1.05645i
$853$		−	3.65625e29i		−	1.79286i	−0.443188	−	0.896429i	$-0.646153\pi$
$853$		−	3.65625e29i		−	1.79286i	0.443188	−	0.896429i	$-0.353847\pi$
$854$	3.17181e27	−	8.29440e28i	0.0153719	−	0.401982i
$855$			5.15619e27i			0.0246984i
$856$	3.24725e28	−	2.81951e29i	0.153737	−	1.33486i
$857$	3.77837e29			1.76806			0.884029	−	0.467432i	$-0.154821\pi$
$857$	3.77837e29			1.76806			0.884029	+	0.467432i	$0.154821\pi$
$858$	1.00867e28	+	3.85719e26i	0.0466526	+	0.00178401i
$859$	−2.04029e29			−0.932739			−0.466370	−	0.884590i	$-0.654438\pi$
$859$	−2.04029e29			−0.932739			−0.466370	+	0.884590i	$0.654438\pi$
$860$	−6.31773e27	+	8.24847e28i	−0.0285481	+	0.372725i
$861$			1.69787e29i			0.758356i
$862$	−4.26427e29	−	1.63067e28i	−1.88266	−	0.0719937i
$863$			2.17377e29i			0.948651i	0.880350	+	0.474325i	$0.157308\pi$
$863$			2.17377e29i			0.948651i	−0.880350	+	0.474325i	$0.842692\pi$
$864$	−4.19189e28	+	2.16669e29i	−0.180831	+	0.934671i
$865$	6.42600e28			0.274019
$866$	−3.97678e27	+	1.03994e29i	−0.0167630	+	0.438360i
$867$	1.08505e29			0.452126
$868$	−1.89251e29	−	1.44953e28i	−0.779544	−	0.0597075i
$869$			1.37515e29i			0.559954i
$870$	−6.57725e26	+	1.71997e28i	−0.00264760	+	0.0692356i
$871$		−	3.27131e27i		−	0.0130179i
$872$	−3.73439e29	−	4.30091e28i	−1.46911	−	0.169198i
$873$	6.32379e26			0.00245943
$874$	3.46431e29	+	1.32477e28i	1.33199	+	0.0509360i
$875$	−8.07172e28			−0.306821
$876$	−1.93662e29	−	1.48331e28i	−0.727784	−	0.0557430i
$877$		−	9.07699e28i		−	0.337245i	−0.985681	−	0.168623i	$-0.946068\pi$
$877$		−	9.07699e28i		−	0.337245i	0.985681	−	0.168623i	$-0.0539319\pi$
$878$	−5.04975e29	−	1.93105e28i	−1.85492	−	0.0709329i
$879$			1.91371e29i			0.695005i
$880$	5.78068e27	−	3.75151e28i	0.0207564	−	0.134704i
$881$	1.53866e29			0.546239			0.273119	−	0.961980i	$-0.411945\pi$
$881$	1.53866e29			0.546239			0.273119	+	0.961980i	$0.411945\pi$
$882$	−6.61673e26	+	1.73030e28i	−0.00232251	+	0.0607345i
$883$	5.75460e29			1.99714			0.998569	−	0.0534855i	$-0.0170331\pi$
$883$	5.75460e29			1.99714			0.998569	+	0.0534855i	$0.0170331\pi$
$884$	−1.61073e27	+	2.10298e28i	−0.00552715	+	0.0721628i
$885$			7.41219e28i			0.251486i
$886$	−1.50964e28	+	3.94776e29i	−0.0506450	+	1.32438i
$887$		−	9.01924e28i		−	0.299181i	−0.988748	−	0.149590i	$-0.952204\pi$
$887$		−	9.01924e28i		−	0.299181i	0.988748	−	0.149590i	$-0.0477955\pi$
$888$	5.31246e29	+	6.11839e28i	1.74247	+	0.200682i
$889$	−1.53172e29			−0.496777
$890$	4.20763e28	+	1.60902e27i	0.134939	+	0.00516013i
$891$	−1.58477e29			−0.502563
$892$	2.30505e28	−	3.00949e29i	0.0722823	−	0.943722i
$893$			9.26889e28i			0.287417i
$894$	1.65805e29	+	6.34046e27i	0.508420	+	0.0194422i
$895$			8.25886e28i			0.250432i
$896$	−1.76116e29	−	4.82779e28i	−0.528104	−	0.144766i
$897$	4.63648e28			0.137488
$898$	−1.80326e28	+	4.71559e29i	−0.0528804	+	1.38284i
$899$	1.11792e29			0.324200
$900$	−2.75943e28	−	2.11353e27i	−0.0791397	−	0.00606153i
$901$		−	3.72561e29i		−	1.05669i
$902$	−8.42700e27	+	2.20369e29i	−0.0236378	+	0.618138i
$903$			2.62815e29i			0.729076i
$904$	5.59488e28	−	4.85791e29i	0.153499	−	1.33280i
$905$	8.46056e28			0.229569
$906$	1.54100e29	+	5.89283e27i	0.413542	+	0.0158140i
$907$	−3.21089e29			−0.852220			−0.426110	−	0.904671i	$-0.640116\pi$
$907$	−3.21089e29			−0.852220			−0.426110	+	0.904671i	$0.640116\pi$
$908$	−2.07596e29	−	1.59004e28i	−0.544955	−	0.0417396i
$909$		−	4.53165e28i		−	0.117657i
$910$	5.99823e27	+	2.29375e26i	0.0154031	+	0.000589022i
$911$		−	6.46468e29i		−	1.64196i	−0.570956	−	0.820981i	$-0.693427\pi$
$911$		−	6.46468e29i		−	1.64196i	0.570956	−	0.820981i	$-0.306573\pi$
$912$	3.98675e29	+	6.14317e28i	1.00155	+	0.154328i
$913$	−5.85741e28			−0.145545
$914$	3.46559e26	−	9.06265e27i	0.000851757	−	0.0222737i
$915$	9.22092e28			0.224163
$916$	4.89450e28	−	6.39029e29i	0.117694	−	1.53662i
$917$			3.39954e28i			0.0808586i
$918$	1.16358e28	−	3.04280e29i	0.0273759	−	0.715891i
$919$			4.36629e29i			1.01615i	0.861313	+	0.508075i	$0.169643\pi$
$919$			4.36629e29i			1.01615i	−0.861313	+	0.508075i	$0.830357\pi$
$920$	1.99482e28	−	1.73206e29i	0.0459225	−	0.398735i
$921$	−5.01360e28			−0.114170
$922$	1.63392e29	+	6.24816e27i	0.368062	+	0.0140748i
$923$	−4.38647e28			−0.0977459
$924$	9.20929e27	−	1.20237e29i	0.0203005	−	0.265044i
$925$		−	7.05458e29i		−	1.53835i
$926$	−3.55045e29	−	1.35770e28i	−0.765902	−	0.0292884i
$927$			6.98198e28i			0.148998i
$928$	1.05598e29	+	2.04300e28i	0.222933	+	0.0431309i
$929$	−3.84815e29			−0.803701			−0.401850	−	0.915705i	$-0.631633\pi$
$929$	−3.84815e29			−0.803701			−0.401850	+	0.915705i	$0.631633\pi$
$930$	8.05721e27	−	2.10699e29i	0.0166477	−	0.435344i
$931$	−3.32949e29			−0.680582
$932$	−6.79338e29	−	5.20324e28i	−1.37381	−	0.105224i
$933$		−	3.79206e29i		−	0.758681i
$934$	−2.48660e28	+	6.50255e29i	−0.0492195	+	1.28711i
$935$			5.23741e28i			0.102565i
$936$	4.28072e27	+	4.93013e26i	0.00829389	+	0.000955212i
$937$	9.96411e28			0.191004			0.0955020	−	0.995429i	$-0.469554\pi$
$937$	9.96411e28			0.191004			0.0955020	+	0.995429i	$0.469554\pi$
$938$	−3.90522e28	−	1.49337e27i	−0.0740658	−	0.00283230i
$939$	−7.52062e29			−1.41123
$940$	4.64780e28	+	3.55988e27i	0.0862916	+	0.00660932i
$941$			2.62280e29i			0.481803i	0.970550	+	0.240902i	$0.0774431\pi$
$941$			2.62280e29i			0.481803i	−0.970550	+	0.240902i	$0.922557\pi$
$942$	4.95007e29	+	1.89293e28i	0.899709	+	0.0344052i
$943$			1.01295e30i			1.82168i
$944$	4.57768e29	+	7.05373e28i	0.814565	+	0.125516i
$945$	−8.66613e28			−0.152583
$946$	−1.30442e28	+	3.41112e29i	−0.0227252	+	0.594272i
$947$	7.23582e29			1.24735			0.623675	−	0.781684i	$-0.285639\pi$
$947$	7.23582e29			1.24735			0.623675	+	0.781684i	$0.285639\pi$
$948$	−5.61269e28	+	7.32796e29i	−0.0957387	+	1.24997i
$949$		−	3.98948e28i		−	0.0673370i
$950$	2.03345e28	−	5.31755e29i	0.0339624	−	0.888128i
$951$		−	1.57687e29i		−	0.260610i
$952$	2.50315e29	+	2.88289e28i	0.409371	+	0.0471475i
$953$	1.29209e29			0.209104			0.104552	−	0.994519i	$-0.466659\pi$
$953$	1.29209e29			0.209104			0.104552	+	0.994519i	$0.466659\pi$
$954$	−7.60593e28	−	2.90854e27i	−0.121806	−	0.00465791i
$955$	1.20627e29			0.191166
$956$	−1.42403e28	+	1.85922e29i	−0.0223326	+	0.291575i
$957$			7.10247e28i			0.110228i
$958$	6.93835e29	+	2.65325e28i	1.06562	+	0.0407496i
$959$		−	1.87698e29i		−	0.285281i
$960$	4.61162e28	−	1.97553e29i	0.0693651	−	0.297146i
$961$	−6.97671e29			−1.03852
$962$	−4.19725e27	+	1.09760e29i	−0.00618321	+	0.161693i
$963$	8.00061e28			0.116643
$964$	9.08459e29	+	6.95814e28i	1.31080	+	0.100397i
$965$			8.11777e28i			0.115921i
$966$	2.11658e28	−	5.53494e29i	0.0299133	−	0.782243i
$967$			5.85806e29i			0.819386i	0.912223	+	0.409693i	$0.134364\pi$
$967$			5.85806e29i			0.819386i	−0.912223	+	0.409693i	$0.865636\pi$
$968$	−6.47277e28	+	5.62016e29i	−0.0896058	+	0.778028i
$969$	−5.56583e29			−0.762592
$970$	6.11067e27	+	2.33674e26i	0.00828651	+	0.000316879i
$971$	−6.43528e29			−0.863725			−0.431862	−	0.901940i	$-0.642143\pi$
$971$	−6.43528e29			−0.863725			−0.431862	+	0.901940i	$0.642143\pi$
$972$	−1.29954e29	−	9.95354e27i	−0.172634	−	0.0132225i
$973$		−	1.10097e29i		−	0.144760i
$974$	−1.61738e29	−	6.18493e27i	−0.210486	−	0.00804907i
$975$		−	7.11677e28i		−	0.0916721i
$976$	8.77499e28	−	5.69473e29i	0.111879	−	0.726065i
$977$	9.80161e29			1.23695			0.618474	−	0.785805i	$-0.287751\pi$
$977$	9.80161e29			1.23695			0.618474	+	0.785805i	$0.287751\pi$
$978$	4.23563e28	−	1.10763e30i	0.0529090	−	1.38359i
$979$	1.73750e29			0.214832
$980$	−1.27875e28	+	1.66954e29i	−0.0156503	+	0.204332i
$981$		−	1.05966e29i		−	0.128374i
$982$	−3.49608e28	+	9.14237e29i	−0.0419243	+	1.09634i
$983$		−	3.23763e29i		−	0.384319i	−0.981364	−	0.192160i	$-0.938451\pi$
$983$		−	3.23763e29i		−	0.384319i	0.981364	−	0.192160i	$-0.0615492\pi$
$984$	−1.34850e29	+	1.17087e30i	−0.158453	+	1.37581i
$985$	−4.03243e29			−0.469034
$986$	−1.48297e29	−	5.67093e27i	−0.170751	−	0.00652958i
$987$	1.48089e29			0.168792
$988$	−6.32754e27	+	8.26128e28i	−0.00713946	+	0.0932133i
$989$			1.56796e30i			1.75135i
$990$	1.06923e28	+	4.08878e26i	0.0118228	+	0.000452108i
$991$		−	7.20297e29i		−	0.788452i	−0.919014	−	0.394226i	$-0.871013\pi$
$991$		−	7.20297e29i		−	0.788452i	0.919014	−	0.394226i	$-0.128987\pi$
$992$	−1.29359e30	−	2.50270e29i	−1.40178	−	0.271201i
$993$	1.07886e30			1.15737
$994$	−2.00245e28	+	5.23649e29i	−0.0212666	+	0.556130i
$995$	3.58546e29			0.376976
$996$	−3.12132e29	−	2.39071e28i	−0.324897	−	0.0248847i
$997$			1.28135e30i			1.32043i	0.751078	+	0.660214i	$0.229534\pi$
$997$			1.28135e30i			1.32043i	−0.751078	+	0.660214i	$0.770466\pi$
$998$	2.09881e28	−	5.48846e29i	0.0214125	−	0.559945i
$999$		−	1.58579e30i		−	1.60173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.21.d.b.3.10	yes	18
3.2	odd	2		72.21.b.b.19.9		18
4.3	odd	2		32.21.d.b.15.13		18
8.3	odd	2	inner	8.21.d.b.3.9	✓	18
8.5	even	2		32.21.d.b.15.14		18
24.11	even	2		72.21.b.b.19.10		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.21.d.b.3.9	✓	18	8.3	odd	2	inner
8.21.d.b.3.10	yes	18	1.1	even	1	trivial
32.21.d.b.15.13		18	4.3	odd	2
32.21.d.b.15.14		18	8.5	even	2
72.21.b.b.19.9		18	3.2	odd	2
72.21.b.b.19.10		18	24.11	even	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)

\(f(q)\)	\(=\)	\(q+(-39.1296 + 1023.25i) q^{2} -61558.6 q^{3} +(-1.04551e6 - 80078.8i) q^{4} -2.85835e6i q^{5} +(2.40876e6 - 6.29900e7i) q^{6} -1.54680e8i q^{7} +(1.22851e8 - 1.06669e9i) q^{8} +3.02682e8 q^{9} +O(q^{10})\)	\(q+(-39.1296 + 1023.25i) q^{2} -61558.6 q^{3} +(-1.04551e6 - 80078.8i) q^{4} -2.85835e6i q^{5} +(2.40876e6 - 6.29900e7i) q^{6} -1.54680e8i q^{7} +(1.22851e8 - 1.06669e9i) q^{8} +3.02682e8 q^{9} +(2.92482e9 + 1.11846e8i) q^{10} +1.20777e10 q^{11} +(6.43604e10 + 4.92954e9i) q^{12} +1.32584e10i q^{13} +(1.58276e11 + 6.05255e9i) q^{14} +1.75956e11i q^{15} +(1.08669e12 + 1.67447e11i) q^{16} -1.51710e12 q^{17} +(-1.18438e10 + 3.09720e11i) q^{18} -5.95972e12 q^{19} +(-2.28894e11 + 2.98845e12i) q^{20} +9.52187e12i q^{21} +(-4.72597e11 + 1.23586e13i) q^{22} +5.68078e13i q^{23} +(-7.56256e12 + 6.56640e13i) q^{24} +8.71973e13 q^{25} +(-1.35667e13 - 5.18796e11i) q^{26} +1.96009e14 q^{27} +(-1.23866e13 + 1.61720e14i) q^{28} -9.55289e13i q^{29} +(-1.80048e14 - 6.88509e12i) q^{30} +1.17024e15i q^{31} +(-2.13862e14 + 1.10540e15i) q^{32} -7.43490e14 q^{33} +(5.93636e13 - 1.55238e15i) q^{34} -4.42129e14 q^{35} +(-3.16459e14 - 2.42385e13i) q^{36} -8.09037e15i q^{37} +(2.33201e14 - 6.09830e15i) q^{38} -8.16169e14i q^{39} +(-3.04898e15 - 3.51152e14i) q^{40} +1.78313e16 q^{41} +(-9.74327e15 - 3.72587e14i) q^{42} +2.76012e16 q^{43} +(-1.26275e16 - 9.67172e14i) q^{44} -8.65173e14i q^{45} +(-5.81287e16 - 2.22286e15i) q^{46} -1.55525e16i q^{47} +(-6.68949e16 - 1.03078e16i) q^{48} +5.58665e16 q^{49} +(-3.41199e15 + 8.92248e16i) q^{50} +9.33908e16 q^{51} +(1.06172e15 - 1.38618e16i) q^{52} +2.45574e17i q^{53} +(-7.66975e15 + 2.00567e17i) q^{54} -3.45225e16i q^{55} +(-1.64995e17 - 1.90026e16i) q^{56} +3.66873e17 q^{57} +(9.77501e16 + 3.73800e15i) q^{58} +4.21252e17 q^{59} +(1.40904e16 - 1.83965e17i) q^{60} -5.24046e17i q^{61} +(-1.19745e18 - 4.57910e16i) q^{62} -4.68188e16i q^{63} +(-1.12274e18 - 2.62089e17i) q^{64} +3.78972e16 q^{65} +(2.90924e16 - 7.60777e17i) q^{66} -2.46735e17 q^{67} +(1.58615e18 + 1.21488e17i) q^{68} -3.49701e18i q^{69} +(1.73003e16 - 4.52410e17i) q^{70} +3.30845e18i q^{71} +(3.71849e16 - 3.22869e17i) q^{72} -3.00902e18 q^{73} +(8.27849e18 + 3.16573e17i) q^{74} -5.36774e18 q^{75} +(6.23097e18 + 4.77248e17i) q^{76} -1.86818e18i q^{77} +(8.35147e17 + 3.19364e16i) q^{78} +1.13858e19i q^{79} +(4.78623e17 - 3.10613e18i) q^{80} -1.31214e19 q^{81} +(-6.97730e17 + 1.82459e19i) q^{82} -4.84976e18 q^{83} +(7.62500e17 - 9.95525e18i) q^{84} +4.33641e18i q^{85} +(-1.08002e18 + 2.82430e19i) q^{86} +5.88063e18i q^{87} +(1.48377e18 - 1.28832e19i) q^{88} +1.43860e19 q^{89} +(8.85290e17 + 3.38539e16i) q^{90} +2.05081e18 q^{91} +(4.54910e18 - 5.93933e19i) q^{92} -7.20384e19i q^{93} +(1.59142e19 + 6.08564e17i) q^{94} +1.70350e19i q^{95} +(1.31651e19 - 6.80471e19i) q^{96} +2.08925e18 q^{97} +(-2.18603e18 + 5.71655e19i) q^{98} +3.65572e18 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more