LMFDB - Embedded newform 8.21.d.b.3.6

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			3.6
Root			$-2443.39 - 2.11221e6i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.21.d.b.3.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-749.926 + 697.272i) q^{2} -16119.5 q^{3} +(76200.7 - 1.04580e6i) q^{4} +8.44883e6i q^{5} +(1.20885e7 - 1.12397e7i) q^{6} +6.17349e7i q^{7} +(6.72064e8 + 8.37407e8i) q^{8} -3.22694e9 q^{9} +O(q^{10})$	\(q+(-749.926 + 697.272i) q^{2} -16119.5 q^{3} +(76200.7 - 1.04580e6i) q^{4} +8.44883e6i q^{5} +(1.20885e7 - 1.12397e7i) q^{6} +6.17349e7i q^{7} +(6.72064e8 + 8.37407e8i) q^{8} -3.22694e9 q^{9} +(-5.89113e9 - 6.33599e9i) q^{10} -2.72862e10 q^{11} +(-1.22832e9 + 1.68579e10i) q^{12} +6.05890e10i q^{13} +(-4.30460e10 - 4.62966e10i) q^{14} -1.36191e11i q^{15} +(-1.08790e12 - 1.59382e11i) q^{16} -3.07828e11 q^{17} +(2.41997e12 - 2.25006e12i) q^{18} +7.50547e12 q^{19} +(8.83581e12 + 6.43807e11i) q^{20} -9.95139e11i q^{21} +(2.04626e13 - 1.90259e13i) q^{22} -5.30705e13i q^{23} +(-1.08334e13 - 1.34986e13i) q^{24} +2.39847e13 q^{25} +(-4.22470e13 - 4.54372e13i) q^{26} +1.08222e14 q^{27} +(6.45626e13 + 4.70425e12i) q^{28} -5.67356e14i q^{29} +(9.49623e13 + 1.02133e14i) q^{30} +1.32605e14i q^{31} +(9.26975e14 - 6.39036e14i) q^{32} +4.39842e14 q^{33} +(2.30848e14 - 2.14640e14i) q^{34} -5.21588e14 q^{35} +(-2.45895e14 + 3.37475e15i) q^{36} +2.44065e14i q^{37} +(-5.62854e15 + 5.23335e15i) q^{38} -9.76667e14i q^{39} +(-7.07511e15 + 5.67816e15i) q^{40} -1.67160e16 q^{41} +(6.93882e14 + 7.46280e14i) q^{42} -8.85654e14 q^{43} +(-2.07923e15 + 2.85360e16i) q^{44} -2.72639e16i q^{45} +(3.70045e16 + 3.97989e16i) q^{46} -7.52013e16i q^{47} +(1.75364e16 + 2.56916e15i) q^{48} +7.59811e16 q^{49} +(-1.79868e16 + 1.67239e16i) q^{50} +4.96205e15 q^{51} +(6.33642e16 + 4.61693e15i) q^{52} -2.98647e17i q^{53} +(-8.11586e16 + 7.54603e16i) q^{54} -2.30537e17i q^{55} +(-5.16973e16 + 4.14898e16i) q^{56} -1.20985e17 q^{57} +(3.95601e17 + 4.25475e17i) q^{58} -6.61197e16 q^{59} +(-1.42429e17 - 1.03779e16i) q^{60} -1.14850e17i q^{61} +(-9.24618e16 - 9.94440e16i) q^{62} -1.99215e17i q^{63} +(-2.49581e17 + 1.12558e18i) q^{64} -5.11906e17 q^{65} +(-3.29848e17 + 3.06689e17i) q^{66} +1.03362e18 q^{67} +(-2.34567e16 + 3.21928e17i) q^{68} +8.55472e17i q^{69} +(3.91152e17 - 3.63688e17i) q^{70} +4.52275e18i q^{71} +(-2.16871e18 - 2.70227e18i) q^{72} -3.78599e18 q^{73} +(-1.70180e17 - 1.83031e17i) q^{74} -3.86623e17 q^{75} +(5.71922e17 - 7.84925e18i) q^{76} -1.68451e18i q^{77} +(6.81002e17 + 7.32428e17i) q^{78} +9.29391e18i q^{79} +(1.34659e18 - 9.19147e18i) q^{80} +9.50717e18 q^{81} +(1.25357e19 - 1.16556e19i) q^{82} +2.33949e19 q^{83} +(-1.04072e18 - 7.58303e16i) q^{84} -2.60079e18i q^{85} +(6.64174e17 - 6.17541e17i) q^{86} +9.14552e18i q^{87} +(-1.83381e19 - 2.28497e19i) q^{88} -4.76585e19 q^{89} +(1.90103e19 + 2.04459e19i) q^{90} -3.74046e18 q^{91} +(-5.55013e19 - 4.04401e18i) q^{92} -2.13754e18i q^{93} +(5.24358e19 + 5.63954e19i) q^{94} +6.34124e19i q^{95} +(-1.49424e19 + 1.03010e19i) q^{96} -7.53216e19 q^{97} +(-5.69801e19 + 5.29794e19i) q^{98} +8.80512e19 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 $

$2$	−749.926	+	697.272i	−0.732349	+	0.680929i
$2$	−749.926	+	697.272i	−0.732349	+	0.680929i
$3$	−16119.5			−0.272986			−0.136493	−	0.990641i	$-0.543583\pi$
$3$	−16119.5			−0.272986			−0.136493	+	0.990641i	$0.543583\pi$
$4$	76200.7	−	1.04580e6i	0.0726707	−	0.997356i
$5$			8.44883e6i			0.865160i	0.901596	+	0.432580i	$0.142397\pi$
$5$			8.44883e6i			0.865160i	−0.901596	+	0.432580i	$0.857603\pi$
$6$	1.20885e7	−	1.12397e7i	0.199921	−	0.185884i
$7$			6.17349e7i			0.218550i	0.994012	+	0.109275i	$0.0348529\pi$
$7$			6.17349e7i			0.218550i	−0.994012	+	0.109275i	$0.965147\pi$
$8$	6.72064e8	+	8.37407e8i	0.625909	+	0.779896i
$9$	−3.22694e9			−0.925479
$10$	−5.89113e9	−	6.33599e9i	−0.589113	−	0.633599i
$11$	−2.72862e10			−1.05200			−0.526001	−	0.850484i	$-0.676309\pi$
$11$	−2.72862e10			−1.05200			−0.526001	+	0.850484i	$0.676309\pi$
$12$	−1.22832e9	+	1.68579e10i	−0.0198381	+	0.272264i
$13$			6.05890e10i			0.439501i	0.975556	+	0.219751i	$0.0705244\pi$
$13$			6.05890e10i			0.439501i	−0.975556	+	0.219751i	$0.929476\pi$
$14$	−4.30460e10	−	4.62966e10i	−0.148817	−	0.160055i
$15$		−	1.36191e11i		−	0.236176i
$16$	−1.08790e12	−	1.59382e11i	−0.989438	−	0.144957i
$17$	−3.07828e11			−0.152693			−0.0763466	−	0.997081i	$-0.524326\pi$
$17$	−3.07828e11			−0.152693			−0.0763466	+	0.997081i	$0.524326\pi$
$18$	2.41997e12	−	2.25006e12i	0.677774	−	0.630186i
$19$	7.50547e12			1.22417			0.612085	−	0.790792i	$-0.290331\pi$
$19$	7.50547e12			1.22417			0.612085	+	0.790792i	$0.290331\pi$
$20$	8.83581e12	+	6.43807e11i	0.862873	+	0.0628717i
$21$		−	9.95139e11i		−	0.0596610i
$22$	2.04626e13	−	1.90259e13i	0.770433	−	0.716339i
$23$		−	5.30705e13i		−	1.28107i	−0.767927	−	0.640537i	$-0.778712\pi$
$23$		−	5.30705e13i		−	1.28107i	0.767927	−	0.640537i	$-0.221288\pi$
$24$	−1.08334e13	−	1.34986e13i	−0.170864	−	0.212901i
$25$	2.39847e13			0.251498
$26$	−4.22470e13	−	4.54372e13i	−0.299269	−	0.321869i
$27$	1.08222e14			0.525629
$28$	6.45626e13	+	4.70425e12i	0.217972	+	0.0158822i
$29$		−	5.67356e14i		−	1.34858i	−0.738468	−	0.674288i	$-0.764451\pi$
$29$		−	5.67356e14i		−	1.34858i	0.738468	−	0.674288i	$-0.235549\pi$
$30$	9.49623e13	+	1.02133e14i	0.160819	+	0.172964i
$31$			1.32605e14i			0.161787i	0.996723	+	0.0808935i	$0.0257774\pi$
$31$			1.32605e14i			0.161787i	−0.996723	+	0.0808935i	$0.974223\pi$
$32$	9.26975e14	−	6.39036e14i	0.823320	−	0.567578i
$33$	4.39842e14			0.287182
$34$	2.30848e14	−	2.14640e14i	0.111825	−	0.103973i
$35$	−5.21588e14			−0.189081
$36$	−2.45895e14	+	3.37475e15i	−0.0672551	+	0.923032i
$37$			2.44065e14i			0.0507561i	0.999678	+	0.0253781i	$0.00807896\pi$
$37$			2.44065e14i			0.0507561i	−0.999678	+	0.0253781i	$0.991921\pi$
$38$	−5.62854e15	+	5.23335e15i	−0.896520	+	0.833574i
$39$		−	9.76667e14i		−	0.119978i
$40$	−7.07511e15	+	5.67816e15i	−0.674735	+	0.541511i
$41$	−1.67160e16			−1.24535			−0.622677	−	0.782479i	$-0.713955\pi$
$41$	−1.67160e16			−1.24535			−0.622677	+	0.782479i	$0.713955\pi$
$42$	6.93882e14	+	7.46280e14i	0.0406249	+	0.0436927i
$43$	−8.85654e14			−0.0409807			−0.0204904	−	0.999790i	$-0.506523\pi$
$43$	−8.85654e14			−0.0409807			−0.0204904	+	0.999790i	$0.506523\pi$
$44$	−2.07923e15	+	2.85360e16i	−0.0764497	+	1.04922i
$45$		−	2.72639e16i		−	0.800687i
$46$	3.70045e16	+	3.97989e16i	0.872321	+	0.938194i
$47$		−	7.52013e16i		−	1.42971i	−0.699274	−	0.714853i	$-0.746493\pi$
$47$		−	7.52013e16i		−	1.42971i	0.699274	−	0.714853i	$-0.253507\pi$
$48$	1.75364e16	+	2.56916e15i	0.270103	+	0.0395712i
$49$	7.59811e16			0.952236
$50$	−1.79868e16	+	1.67239e16i	−0.184184	+	0.171252i
$51$	4.96205e15			0.0416831
$52$	6.33642e16	+	4.61693e15i	0.438339	+	0.0319389i
$53$		−	2.98647e17i		−	1.70765i	−0.520560	−	0.853825i	$-0.674277\pi$
$53$		−	2.98647e17i		−	1.70765i	0.520560	−	0.853825i	$-0.325723\pi$
$54$	−8.11586e16	+	7.54603e16i	−0.384944	+	0.357916i
$55$		−	2.30537e17i		−	0.910150i
$56$	−5.16973e16	+	4.14898e16i	−0.170446	+	0.136792i
$57$	−1.20985e17			−0.334181
$58$	3.95601e17	+	4.25475e17i	0.918285	+	0.987629i
$59$	−6.61197e16			−0.129363			−0.0646816	−	0.997906i	$-0.520603\pi$
$59$	−6.61197e16			−0.129363			−0.0646816	+	0.997906i	$0.520603\pi$
$60$	−1.42429e17	−	1.03779e16i	−0.235552	−	0.0171631i
$61$		−	1.14850e17i		−	0.161002i	−0.996755	−	0.0805011i	$-0.974348\pi$
$61$		−	1.14850e17i		−	0.161002i	0.996755	−	0.0805011i	$-0.0256520\pi$
$62$	−9.24618e16	−	9.94440e16i	−0.110165	−	0.118485i
$63$		−	1.99215e17i		−	0.202263i
$64$	−2.49581e17	+	1.12558e18i	−0.216477	+	0.976288i
$65$	−5.11906e17			−0.380239
$66$	−3.29848e17	+	3.06689e17i	−0.210317	+	0.195550i
$67$	1.03362e18			0.567041			0.283520	−	0.958966i	$-0.408498\pi$
$67$	1.03362e18			0.567041			0.283520	+	0.958966i	$0.408498\pi$
$68$	−2.34567e16	+	3.21928e17i	−0.0110963	+	0.152289i
$69$			8.55472e17i			0.349715i
$70$	3.91152e17	−	3.63688e17i	0.138473	−	0.128751i
$71$			4.52275e18i			1.38937i	0.719313	+	0.694687i	$0.244457\pi$
$71$			4.52275e18i			1.38937i	−0.719313	+	0.694687i	$0.755543\pi$
$72$	−2.16871e18	−	2.70227e18i	−0.579265	−	0.721778i
$73$	−3.78599e18			−0.880949			−0.440475	−	0.897765i	$-0.645190\pi$
$73$	−3.78599e18			−0.880949			−0.440475	+	0.897765i	$0.645190\pi$
$74$	−1.70180e17	−	1.83031e17i	−0.0345613	−	0.0371712i
$75$	−3.86623e17			−0.0686555
$76$	5.71922e17	−	7.84925e18i	0.0889613	−	1.22093i
$77$		−	1.68451e18i		−	0.229915i
$78$	6.81002e17	+	7.32428e17i	0.0816963	+	0.0878656i
$79$			9.29391e18i			0.981584i	0.871277	+	0.490792i	$0.163293\pi$
$79$			9.29391e18i			0.981584i	−0.871277	+	0.490792i	$0.836707\pi$
$80$	1.34659e18	−	9.19147e18i	0.125411	−	0.856022i
$81$	9.50717e18			0.781990
$82$	1.25357e19	−	1.16556e19i	0.912035	−	0.847998i
$83$	2.33949e19			1.50779			0.753895	−	0.656995i	$-0.228173\pi$
$83$	2.33949e19			1.50779			0.753895	+	0.656995i	$0.228173\pi$
$84$	−1.04072e18	−	7.58303e16i	−0.0595033	−	0.00433561i
$85$		−	2.60079e18i		−	0.132104i
$86$	6.64174e17	−	6.17541e17i	0.0300122	−	0.0279050i
$87$			9.14552e18i			0.368142i
$88$	−1.83381e19	−	2.28497e19i	−0.658457	−	0.820453i
$89$	−4.76585e19			−1.52841			−0.764206	−	0.644972i	$-0.776869\pi$
$89$	−4.76585e19			−1.52841			−0.764206	+	0.644972i	$0.776869\pi$
$90$	1.90103e19	+	2.04459e19i	0.545211	+	0.586383i
$91$	−3.74046e18			−0.0960530
$92$	−5.55013e19	−	4.04401e18i	−1.27769	−	0.0930966i
$93$		−	2.13754e18i		−	0.0441656i
$94$	5.24358e19	+	5.63954e19i	0.973529	+	1.04704i
$95$			6.34124e19i			1.05910i
$96$	−1.49424e19	+	1.03010e19i	−0.224755	+	0.154941i
$97$	−7.53216e19			−1.02142			−0.510708	−	0.859754i	$-0.670617\pi$
$97$	−7.53216e19			−1.02142			−0.510708	+	0.859754i	$0.670617\pi$
$98$	−5.69801e19	+	5.29794e19i	−0.697369	+	0.648405i
$99$	8.80512e19			0.973606
$100$	1.82765e18	−	2.50833e19i	0.0182765	−	0.250833i
$101$		−	1.89365e20i		−	1.71430i	−0.515067	−	0.857150i	$-0.672233\pi$
$101$		−	1.89365e20i		−	1.71430i	0.515067	−	0.857150i	$-0.327767\pi$
$102$	−3.72117e18	+	3.45990e18i	−0.0305266	+	0.0283832i
$103$			1.17747e19i			0.0876148i	0.999040	+	0.0438074i	$0.0139488\pi$
$103$			1.17747e19i			0.0876148i	−0.999040	+	0.0438074i	$0.986051\pi$
$104$	−5.07377e19	+	4.07197e19i	−0.342766	+	0.275088i
$105$	8.40776e18			0.0516163
$106$	2.08238e20	+	2.23963e20i	1.16279	+	1.25060i
$107$	1.12580e20			0.572300			0.286150	−	0.958185i	$-0.407624\pi$
$107$	1.12580e20			0.572300			0.286150	+	0.958185i	$0.407624\pi$
$108$	8.24661e18	−	1.13179e20i	0.0381978	−	0.524239i
$109$		−	4.23608e20i		−	1.78937i	−0.446701	−	0.894683i	$-0.647401\pi$
$109$		−	4.23608e20i		−	1.78937i	0.446701	−	0.894683i	$-0.352599\pi$
$110$	1.60747e20	+	1.72885e20i	0.619748	+	0.666548i
$111$		−	3.93422e18i		−	0.0138557i
$112$	9.83943e18	−	6.71613e19i	0.0316803	−	0.216242i
$113$	−5.17406e20			−1.52422			−0.762109	−	0.647449i	$-0.775836\pi$
$113$	−5.17406e20			−1.52422			−0.762109	+	0.647449i	$0.775836\pi$
$114$	9.07296e19	−	8.43592e19i	0.244737	−	0.227554i
$115$	4.48383e20			1.10833
$116$	−5.93343e20	−	4.32329e19i	−1.34501	−	0.0980019i
$117$		−	1.95517e20i		−	0.406749i
$118$	4.95849e19	−	4.61034e19i	0.0947390	−	0.0880872i
$119$		−	1.90038e19i		−	0.0333711i
$120$	1.14048e20	−	9.15293e19i	0.184193	−	0.147825i
$121$	7.17883e19			0.106709
$122$	8.00815e19	+	8.61288e19i	0.109631	+	0.117910i
$123$	2.69454e20			0.339964
$124$	1.38679e20	+	1.01046e19i	0.161359	+	0.0117572i
$125$			1.00839e21i			1.08275i
$126$	1.38907e20	+	1.49397e20i	0.137727	+	0.148127i
$127$			1.68672e21i			1.54527i	0.634848	+	0.772637i	$0.281063\pi$
$127$			1.68672e21i			1.54527i	−0.634848	+	0.772637i	$0.718937\pi$
$128$	−5.97670e20	−	1.01813e21i	−0.506246	−	0.862389i
$129$	1.42763e19			0.0111872
$130$	3.83891e20	−	3.56938e20i	0.278468	−	0.258916i
$131$	−1.48144e21			−0.995340			−0.497670	−	0.867367i	$-0.665811\pi$
$131$	−1.48144e21			−0.995340			−0.497670	+	0.867367i	$0.665811\pi$
$132$	3.35162e19	−	4.59988e20i	0.0208697	−	0.286422i
$133$			4.63350e20i			0.267542i
$134$	−7.75141e20	+	7.20716e20i	−0.415272	+	0.386115i
$135$			9.14351e20i			0.454753i
$136$	−2.06880e20	−	2.57778e20i	−0.0955719	−	0.119085i
$137$	−5.06132e20			−0.217299			−0.108650	−	0.994080i	$-0.534653\pi$
$137$	−5.06132e20			−0.217299			−0.108650	+	0.994080i	$0.534653\pi$
$138$	−5.96496e20	−	6.41540e20i	−0.238131	−	0.256114i
$139$	8.38666e20			0.311488			0.155744	−	0.987797i	$-0.450223\pi$
$139$	8.38666e20			0.311488			0.155744	+	0.987797i	$0.450223\pi$
$140$	−3.97454e19	+	5.45478e20i	−0.0137406	+	0.188581i
$141$			1.21221e21i			0.390290i
$142$	−3.15358e21	−	3.39172e21i	−0.946065	−	1.01751i
$143$		−	1.65325e21i		−	0.462357i
$144$	3.51059e21	+	5.14317e20i	0.915704	+	0.134155i
$145$	4.79349e21			1.16673
$146$	2.83921e21	−	2.63986e21i	0.645163	−	0.599864i
$147$	−1.22478e21			−0.259947
$148$	2.55244e20	+	1.85979e19i	0.0506219	+	0.00368848i
$149$			2.35561e21i			0.436758i	0.975864	+	0.218379i	$0.0700769\pi$
$149$			2.35561e21i			0.436758i	−0.975864	+	0.218379i	$0.929923\pi$
$150$	2.89938e20	−	2.69581e20i	0.0502798	−	0.0467495i
$151$		−	1.21038e22i		−	1.96405i	−0.188748	−	0.982026i	$-0.560443\pi$
$151$		−	1.21038e22i		−	1.96405i	0.188748	−	0.982026i	$-0.439557\pi$
$152$	5.04416e21	+	6.28514e21i	0.766219	+	0.954726i
$153$	9.93345e20			0.141314
$154$	1.17456e21	+	1.26326e21i	0.156556	+	0.168378i
$155$	−1.12036e21			−0.139972
$156$	−1.02140e21	−	7.44227e19i	−0.119660	−	0.00871886i
$157$		−	3.90370e21i		−	0.429022i	−0.976722	−	0.214511i	$-0.931184\pi$
$157$		−	3.90370e21i		−	0.429022i	0.976722	−	0.214511i	$-0.0688159\pi$
$158$	−6.48038e21	−	6.96974e21i	−0.668389	−	0.718862i
$159$			4.81405e21i			0.466165i
$160$	5.39911e21	+	7.83186e21i	0.491046	+	0.712303i
$161$	3.27630e21			0.279979
$162$	−7.12967e21	+	6.62908e21i	−0.572689	+	0.532480i
$163$	−1.79709e22			−1.35735			−0.678677	−	0.734437i	$-0.737446\pi$
$163$	−1.79709e22			−1.35735			−0.678677	+	0.734437i	$0.737446\pi$
$164$	−1.27377e21	+	1.74816e22i	−0.0905007	+	1.24206i
$165$			3.71615e21i			0.248458i
$166$	−1.75445e22	+	1.63126e22i	−1.10423	+	1.02670i
$167$		−	2.50440e22i		−	1.48436i	−0.670202	−	0.742179i	$-0.733793\pi$
$167$		−	2.50440e22i		−	1.48436i	0.670202	−	0.742179i	$-0.266207\pi$
$168$	8.33337e20	−	6.68797e20i	0.0465294	−	0.0373424i
$169$	1.53339e22			0.806838
$170$	1.81346e21	+	1.95040e21i	0.0899535	+	0.0967462i
$171$	−2.42197e22			−1.13294
$172$	−6.74874e19	+	9.26220e20i	−0.00297809	+	0.0408723i
$173$			1.68015e22i			0.699658i	0.936814	+	0.349829i	$0.113760\pi$
$173$			1.68015e22i			0.699658i	−0.936814	+	0.349829i	$0.886240\pi$
$174$	−6.37691e21	−	6.85846e21i	−0.250679	−	0.269609i
$175$			1.48070e21i			0.0549649i
$176$	2.96846e22	+	4.34893e21i	1.04089	+	0.152495i
$177$	1.06582e21			0.0353143
$178$	3.57404e22	−	3.32309e22i	1.11933	−	1.04074i
$179$	4.08453e22			1.20952			0.604759	−	0.796409i	$-0.293270\pi$
$179$	4.08453e22			1.20952			0.604759	+	0.796409i	$0.293270\pi$
$180$	−2.85127e22	−	2.07753e21i	−0.798570	−	0.0581865i
$181$		−	5.55662e20i		−	0.0147240i	−0.999973	−	0.00736199i	$-0.997657\pi$
$181$		−	5.55662e20i		−	0.0147240i	0.999973	−	0.00736199i	$-0.00234341\pi$
$182$	2.80507e21	−	2.60812e21i	0.0703443	−	0.0654053i
$183$			1.85133e21i			0.0439513i
$184$	4.44416e22	−	3.56668e22i	0.999106	−	0.801836i
$185$	−2.06206e21			−0.0439122
$186$	1.49044e21	+	1.60299e21i	0.0300736	+	0.0323446i
$187$	8.39948e21			0.160634
$188$	−7.86458e22	−	5.73040e21i	−1.42593	−	0.103898i
$189$			6.68109e21i			0.114876i
$190$	−4.42157e22	−	4.75546e22i	−0.721174	−	0.775633i
$191$			5.34999e22i			0.827979i	0.910282	+	0.413989i	$0.135865\pi$
$191$			5.34999e22i			0.827979i	−0.910282	+	0.413989i	$0.864135\pi$
$192$	4.02313e21	−	1.81439e22i	0.0590951	−	0.266513i
$193$	−2.35465e22			−0.328362			−0.164181	−	0.986430i	$-0.552498\pi$
$193$	−2.35465e22			−0.328362			−0.164181	+	0.986430i	$0.552498\pi$
$194$	5.64856e22	−	5.25196e22i	0.748033	−	0.695511i
$195$	8.25169e21			0.103800
$196$	5.78981e21	−	7.94613e22i	0.0691996	−	0.949718i
$197$			3.39087e22i			0.385167i	0.981281	+	0.192583i	$0.0616866\pi$
$197$			3.39087e22i			0.385167i	−0.981281	+	0.192583i	$0.938313\pi$
$198$	−6.60318e22	+	6.13956e22i	−0.713019	+	0.662957i
$199$			7.22475e22i			0.741809i	0.928671	+	0.370904i	$0.120952\pi$
$199$			7.22475e22i			0.741809i	−0.928671	+	0.370904i	$0.879048\pi$
$200$	1.61193e22	+	2.00850e22i	0.157415	+	0.196143i
$201$	−1.66615e22			−0.154794
$202$	1.32039e23	+	1.42010e23i	1.16732	+	1.25547i
$203$	3.50257e22			0.294731
$204$	3.78112e20	−	5.18933e21i	0.00302914	−	0.0415729i
$205$		−	1.41230e23i		−	1.07743i
$206$	−8.21016e21	−	8.83015e21i	−0.0596595	−	0.0641646i
$207$			1.71255e23i			1.18561i
$208$	9.65679e21	−	6.59147e22i	0.0637088	−	0.434859i
$209$	−2.04796e23			−1.28783
$210$	−6.30519e21	+	5.86249e21i	−0.0378012	+	0.0351471i
$211$	1.30256e23			0.744688			0.372344	−	0.928095i	$-0.378554\pi$
$211$	1.30256e23			0.744688			0.372344	+	0.928095i	$0.378554\pi$
$212$	−3.12326e23	−	2.27571e22i	−1.70314	−	0.124096i
$213$		−	7.29046e22i		−	0.379279i
$214$	−8.44266e22	+	7.84988e22i	−0.419123	+	0.389696i
$215$		−	7.48274e21i		−	0.0354549i
$216$	7.27323e22	+	9.06261e22i	0.328995	+	0.409936i
$217$	−8.18637e21			−0.0353585
$218$	2.95370e23	+	3.17675e23i	1.21843	+	1.31044i
$219$	6.10285e22			0.240487
$220$	−2.41096e23	−	1.75671e22i	−0.907744	−	0.0661412i
$221$		−	1.86510e22i		−	0.0671088i
$222$	2.74322e21	+	2.95037e21i	0.00943476	+	0.0101472i
$223$		−	4.41000e23i		−	1.45007i	−0.688710	−	0.725037i	$-0.741823\pi$
$223$		−	4.41000e23i		−	1.45007i	0.688710	−	0.725037i	$-0.258177\pi$
$224$	3.94509e22	+	5.72268e22i	0.124044	+	0.179936i
$225$	−7.73974e22			−0.232756
$226$	3.88016e23	−	3.60772e23i	1.11626	−	1.03788i
$227$	−1.05199e23			−0.289568			−0.144784	−	0.989463i	$-0.546249\pi$
$227$	−1.05199e23			−0.289568			−0.144784	+	0.989463i	$0.546249\pi$
$228$	−9.21912e21	+	1.26526e23i	−0.0242852	+	0.333298i
$229$		−	6.05893e23i		−	1.52771i	−0.645387	−	0.763855i	$-0.723304\pi$
$229$		−	6.05893e23i		−	1.52771i	0.645387	−	0.763855i	$-0.276696\pi$
$230$	−3.36254e23	+	3.12645e23i	−0.811688	+	0.754698i
$231$			2.71536e22i			0.0627636i
$232$	4.75108e23	−	3.81299e23i	1.05175	−	0.844085i
$233$	−1.04700e23			−0.222018			−0.111009	−	0.993819i	$-0.535408\pi$
$233$	−1.04700e23			−0.222018			−0.111009	+	0.993819i	$0.535408\pi$
$234$	1.36329e23	+	1.46623e23i	0.276967	+	0.297882i
$235$	6.35363e23			1.23693
$236$	−5.03837e21	+	6.91482e22i	−0.00940091	+	0.129021i
$237$		−	1.49814e23i		−	0.267959i
$238$	1.32508e22	+	1.42514e22i	0.0227233	+	0.0244393i
$239$			6.86162e22i			0.112836i	0.998407	+	0.0564180i	$0.0179680\pi$
$239$			6.86162e22i			0.112836i	−0.998407	+	0.0564180i	$0.982032\pi$
$240$	−2.17064e22	+	1.48162e23i	−0.0342354	+	0.233682i
$241$	7.40316e23			1.12007			0.560037	−	0.828467i	$-0.310787\pi$
$241$	7.40316e23			1.12007			0.560037	+	0.828467i	$0.310787\pi$
$242$	−5.38359e22	+	5.00560e22i	−0.0781481	+	0.0726611i
$243$	−5.30599e23			−0.739101
$244$	−1.20110e23	−	8.75163e21i	−0.160576	−	0.0117001i
$245$			6.41951e23i			0.823836i
$246$	−2.02070e23	+	1.87883e23i	−0.248973	+	0.231492i
$247$			4.54749e23i			0.538025i
$248$	−1.11045e23	+	8.91192e22i	−0.126177	+	0.101264i
$249$	−3.77116e23			−0.411605
$250$	−7.03119e23	−	7.56214e23i	−0.737274	−	0.792948i
$251$	−1.33787e24			−1.34796			−0.673980	−	0.738750i	$-0.735417\pi$
$251$	−1.33787e24			−1.34796			−0.673980	+	0.738750i	$0.735417\pi$
$252$	−2.08340e23	−	1.51803e22i	−0.201728	−	0.0146986i
$253$			1.44809e24i			1.34769i
$254$	−1.17610e24	−	1.26491e24i	−1.05222	−	1.13168i
$255$			4.19235e22i			0.0360625i
$256$	1.15812e24	+	3.46783e23i	0.957975	+	0.286852i
$257$	−4.81853e23			−0.383339			−0.191670	−	0.981459i	$-0.561390\pi$
$257$	−4.81853e23			−0.383339			−0.191670	+	0.981459i	$0.561390\pi$
$258$	−1.07062e22	+	9.95448e21i	−0.00819290	+	0.00761766i
$259$	−1.50673e22			−0.0110927
$260$	−3.90076e22	+	5.35353e23i	−0.0276322	+	0.379234i
$261$			1.83083e24i			1.24808i
$262$	1.11097e24	−	1.03297e24i	0.728936	−	0.677756i
$263$			5.98683e23i			0.378128i	0.981965	+	0.189064i	$0.0605454\pi$
$263$			5.98683e23i			0.378128i	−0.981965	+	0.189064i	$0.939455\pi$
$264$	2.95602e23	+	3.68327e23i	0.179750	+	0.223972i
$265$	2.52321e24			1.47739
$266$	−3.23081e23	−	3.47478e23i	−0.182177	−	0.195934i
$267$	7.68234e23			0.417235
$268$	7.87629e22	−	1.08097e24i	0.0412072	−	0.565542i
$269$			5.30086e22i			0.0267192i	0.999911	+	0.0133596i	$0.00425262\pi$
$269$			5.30086e22i			0.0267192i	−0.999911	+	0.0133596i	$0.995747\pi$
$270$	−6.37551e23	−	6.85695e23i	−0.309654	−	0.333038i
$271$		−	3.52114e24i		−	1.64812i	−0.566500	−	0.824062i	$-0.691703\pi$
$271$		−	3.52114e24i		−	1.64812i	0.566500	−	0.824062i	$-0.308297\pi$
$272$	3.34886e23	+	4.90623e22i	0.151080	+	0.0221339i
$273$	6.02945e22			0.0262211
$274$	3.79561e23	−	3.52911e23i	0.159139	−	0.147965i
$275$	−6.54453e23			−0.264577
$276$	8.94655e23	+	6.51876e22i	0.348791	+	0.0254140i
$277$		−	6.25325e23i		−	0.235130i	−0.993065	−	0.117565i	$-0.962491\pi$
$277$		−	6.25325e23i		−	0.235130i	0.993065	−	0.117565i	$-0.0375088\pi$
$278$	−6.28937e23	+	5.84778e23i	−0.228118	+	0.212101i
$279$		−	4.27910e23i		−	0.149730i
$280$	−3.50541e23	−	4.36782e23i	−0.118347	−	0.147463i
$281$	4.32696e24			1.40968			0.704838	−	0.709368i	$-0.251020\pi$
$281$	4.32696e24			1.40968			0.704838	+	0.709368i	$0.251020\pi$
$282$	−8.45241e23	−	9.09068e23i	−0.265760	−	0.285828i
$283$	−4.60817e24			−1.39851			−0.699253	−	0.714874i	$-0.746484\pi$
$283$	−4.60817e24			−1.39851			−0.699253	+	0.714874i	$0.746484\pi$
$284$	4.72991e24	+	3.44637e23i	1.38570	+	0.100967i
$285$		−	1.02218e24i		−	0.289120i
$286$	1.15276e24	+	1.23981e24i	0.314832	+	0.338606i
$287$		−	1.03196e24i		−	0.272172i
$288$	−2.99130e24	+	2.06213e24i	−0.761965	+	0.525281i
$289$	−3.96947e24			−0.976685
$290$	−3.59476e24	+	3.34236e24i	−0.854457	+	0.794463i
$291$	1.21415e24			0.278832
$292$	−2.88495e23	+	3.95940e24i	−0.0640192	+	0.878620i
$293$		−	2.84512e24i		−	0.610133i	−0.952331	−	0.305066i	$-0.901321\pi$
$293$		−	2.84512e24i		−	0.610133i	0.952331	−	0.305066i	$-0.0986786\pi$
$294$	9.18494e23	−	8.54004e23i	0.190372	−	0.177006i
$295$		−	5.58634e23i		−	0.111920i
$296$	−2.04382e23	+	1.64027e23i	−0.0395845	+	0.0317687i
$297$	−2.95298e24			−0.552962
$298$	−1.64250e24	−	1.76653e24i	−0.297401	−	0.319859i
$299$	3.21549e24			0.563034
$300$	−2.94609e22	+	4.04332e23i	−0.00498924	+	0.0684739i
$301$		−	5.46758e22i		−	0.00895633i
$302$	8.43965e24	+	9.07696e24i	1.33738	+	1.43837i
$303$			3.05248e24i			0.467980i
$304$	−8.16519e24	−	1.19624e24i	−1.21124	−	0.177452i
$305$	9.70346e23			0.139293
$306$	−7.44935e23	+	6.92631e23i	−0.103491	+	0.0962250i
$307$	5.66512e24			0.761773			0.380887	−	0.924622i	$-0.375619\pi$
$307$	5.66512e24			0.761773			0.380887	+	0.924622i	$0.375619\pi$
$308$	−1.76167e24	−	1.28361e23i	−0.229307	−	0.0167081i
$309$		−	1.89803e23i		−	0.0239176i
$310$	8.40185e23	−	7.81194e23i	0.102508	−	0.0953108i
$311$		−	4.13896e24i		−	0.488975i	−0.969652	−	0.244488i	$-0.921380\pi$
$311$		−	4.13896e24i		−	0.488975i	0.969652	−	0.244488i	$-0.0786198\pi$
$312$	8.17868e23	−	6.56383e23i	0.0935702	−	0.0750951i
$313$	−1.13021e25			−1.25233			−0.626163	−	0.779692i	$-0.715375\pi$
$313$	−1.13021e25			−1.25233			−0.626163	+	0.779692i	$0.715375\pi$
$314$	2.72194e24	+	2.92749e24i	0.292134	+	0.314194i
$315$	1.68314e24			0.174990
$316$	9.71960e24	+	7.08202e23i	0.978989	+	0.0713324i
$317$		−	9.80341e24i		−	0.956720i	−0.878164	−	0.478360i	$-0.841231\pi$
$317$		−	9.80341e24i		−	0.956720i	0.878164	−	0.478360i	$-0.158769\pi$
$318$	−3.35670e24	−	3.61018e24i	−0.317425	−	0.341395i
$319$			1.54810e25i			1.41871i
$320$	−9.50986e24	−	2.10867e24i	−0.844645	−	0.187287i
$321$	−1.81474e24			−0.156230
$322$	−2.45698e24	+	2.28447e24i	−0.205042	+	0.190646i
$323$	−2.31040e24			−0.186922
$324$	7.24453e23	−	9.94263e24i	0.0568277	−	0.779922i
$325$			1.45321e24i			0.110534i
$326$	1.34768e25	−	1.25306e25i	0.994057	−	0.924262i
$327$			6.82837e24i			0.488472i
$328$	−1.12342e25	−	1.39981e25i	−0.779478	−	0.971248i
$329$	4.64255e24			0.312462
$330$	−2.59116e24	−	2.78683e24i	−0.169182	−	0.181958i
$331$	1.53387e25			0.971648			0.485824	−	0.874057i	$-0.338520\pi$
$331$	1.53387e25			0.971648			0.485824	+	0.874057i	$0.338520\pi$
$332$	1.78271e24	−	2.44665e25i	0.109572	−	1.50380i
$333$		−	7.87585e23i		−	0.0469737i
$334$	1.74624e25	+	1.87811e25i	1.01074	+	1.08707i
$335$			8.73291e24i			0.490581i
$336$	−1.58607e23	+	1.08261e24i	−0.00864829	+	0.0590309i
$337$	7.89256e24			0.417752			0.208876	−	0.977942i	$-0.433019\pi$
$337$	7.89256e24			0.417752			0.208876	+	0.977942i	$0.433019\pi$
$338$	−1.14993e25	+	1.06919e25i	−0.590887	+	0.549400i
$339$	8.34035e24			0.416090
$340$	−2.71991e24	−	1.98182e23i	−0.131755	−	0.00960008i
$341$		−	3.61830e24i		−	0.170200i
$342$	1.81630e25	−	1.68877e25i	0.829710	−	0.771455i
$343$			9.61666e24i			0.426661i
$344$	−5.95216e23	−	7.41653e23i	−0.0256502	−	0.0319607i
$345$	−7.22773e24			−0.302560
$346$	−1.17152e25	−	1.25998e25i	−0.476418	−	0.512394i
$347$	1.50298e24			0.0593825			0.0296912	−	0.999559i	$-0.490548\pi$
$347$	1.50298e24			0.0593825			0.0296912	+	0.999559i	$0.490548\pi$
$348$	9.56441e24	+	6.96895e23i	0.367169	+	0.0267531i
$349$			3.33846e25i			1.24535i	0.782480	+	0.622676i	$0.213954\pi$
$349$			3.33846e25i			1.24535i	−0.782480	+	0.622676i	$0.786046\pi$
$350$	−1.03245e24	−	1.11041e24i	−0.0374272	−	0.0402535i
$351$			6.55708e24i			0.231015i
$352$	−2.52937e25	+	1.74369e25i	−0.866134	+	0.597093i
$353$	−4.35082e25			−1.44818			−0.724092	−	0.689703i	$-0.757741\pi$
$353$	−4.35082e25			−1.44818			−0.724092	+	0.689703i	$0.757741\pi$
$354$	−7.99285e23	+	7.43166e23i	−0.0258624	+	0.0240466i
$355$	−3.82119e25			−1.20203
$356$	−3.63161e24	+	4.98415e25i	−0.111071	+	1.52437i
$357$			3.06332e23i			0.00910983i
$358$	−3.06310e25	+	2.84803e25i	−0.885789	+	0.823596i
$359$		−	5.13216e25i		−	1.44330i	−0.692259	−	0.721649i	$-0.743385\pi$
$359$		−	5.13216e25i		−	1.44330i	0.692259	−	0.721649i	$-0.256615\pi$
$360$	2.28310e25	−	1.83231e25i	0.624453	−	0.501157i
$361$	1.87421e25			0.498593
$362$	3.87447e23	+	4.16705e23i	0.0100260	+	0.0107831i
$363$	−1.15720e24			−0.0291300
$364$	−2.85026e23	+	3.91178e24i	−0.00698023	+	0.0957990i
$365$		−	3.19872e25i		−	0.762162i
$366$	−1.29088e24	−	1.38836e24i	−0.0299277	−	0.0321877i
$367$			9.79775e23i			0.0221037i	0.999939	+	0.0110519i	$0.00351799\pi$
$367$			9.79775e23i			0.0221037i	−0.999939	+	0.0110519i	$0.996482\pi$
$368$	−8.45847e24	+	5.77353e25i	−0.185701	+	1.26754i
$369$	5.39415e25			1.15255
$370$	1.54639e24	−	1.43782e24i	0.0321590	−	0.0299011i
$371$	1.84369e25			0.373207
$372$	−2.23544e24	−	1.62882e23i	−0.0440488	−	0.00320954i
$373$		−	1.20006e25i		−	0.230204i	−0.993354	−	0.115102i	$-0.963280\pi$
$373$		−	1.20006e25i		−	0.230204i	0.993354	−	0.115102i	$-0.0367196\pi$
$374$	−6.29898e24	+	5.85672e24i	−0.117640	+	0.109380i
$375$		−	1.62547e25i		−	0.295574i
$376$	6.29742e25	−	5.05401e25i	1.11502	−	0.894866i
$377$	3.43755e25			0.592701
$378$	−4.65854e24	−	5.01032e24i	−0.0782225	−	0.0841294i
$379$	−5.23113e25			−0.855468			−0.427734	−	0.903905i	$-0.640688\pi$
$379$	−5.23113e25			−0.855468			−0.427734	+	0.903905i	$0.640688\pi$
$380$	6.63169e25	+	4.83207e24i	1.05630	+	0.0769657i
$381$		−	2.71892e25i		−	0.421838i
$382$	−3.73039e25	−	4.01209e25i	−0.563795	−	0.606369i
$383$		−	1.18449e26i		−	1.74399i	−0.489515	−	0.871995i	$-0.662826\pi$
$383$		−	1.18449e26i		−	1.74399i	0.489515	−	0.871995i	$-0.337174\pi$
$384$	9.63417e24	+	1.64118e25i	0.138198	+	0.235420i
$385$	1.42322e25			0.198913
$386$	1.76581e25	−	1.64183e25i	0.240476	−	0.223591i
$387$	2.85796e24			0.0379268
$388$	−5.73956e24	+	7.87716e25i	−0.0742269	+	1.01871i
$389$			2.42607e25i			0.305779i	0.988243	+	0.152889i	$0.0488578\pi$
$389$			2.42607e25i			0.305779i	−0.988243	+	0.152889i	$0.951142\pi$
$390$	−6.18816e24	+	5.75367e24i	−0.0760178	+	0.0706804i
$391$			1.63366e25i			0.195611i
$392$	5.10642e25	+	6.36271e25i	0.596013	+	0.742645i
$393$	2.38802e25			0.271714
$394$	−2.36436e25	−	2.54290e25i	−0.262271	−	0.282077i
$395$	−7.85226e25			−0.849227
$396$	6.70956e24	−	9.20842e25i	0.0707526	−	0.971031i
$397$			1.38755e26i			1.42673i	0.700791	+	0.713366i	$0.252830\pi$
$397$			1.38755e26i			1.42673i	−0.700791	+	0.713366i	$0.747170\pi$
$398$	−5.03761e25	−	5.41802e25i	−0.505119	−	0.543263i
$399$		−	7.46899e24i		−	0.0730353i
$400$	−2.60930e25	−	3.82273e24i	−0.248842	−	0.0364564i
$401$	4.99079e25			0.464222			0.232111	−	0.972689i	$-0.425437\pi$
$401$	4.99079e25			0.464222			0.232111	+	0.972689i	$0.425437\pi$
$402$	1.24949e25	−	1.16176e25i	0.113363	−	0.105404i
$403$	−8.03442e24			−0.0711056
$404$	−1.98039e26	−	1.44298e25i	−1.70977	−	0.124579i
$405$			8.03244e25i			0.676546i
$406$	−2.62666e25	+	2.44224e25i	−0.215846	+	0.200691i
$407$		−	6.65962e24i		−	0.0533956i
$408$	3.33482e24	+	4.15526e24i	0.0260898	+	0.0325085i
$409$	−9.92475e25			−0.757682			−0.378841	−	0.925462i	$-0.623677\pi$
$409$	−9.92475e25			−0.757682			−0.378841	+	0.925462i	$0.623677\pi$
$410$	9.84759e25	+	1.05912e26i	0.733654	+	0.789056i
$411$	8.15862e24			0.0593196
$412$	1.23140e25	+	8.97240e23i	0.0873832	+	0.00636703i
$413$		−	4.08190e24i		−	0.0282723i
$414$	−1.19412e26	−	1.28429e26i	−0.807315	−	0.868279i
$415$			1.97660e26i			1.30448i
$416$	3.87186e25	+	5.61645e25i	0.249451	+	0.361850i
$417$	−1.35189e25			−0.0850317
$418$	1.53582e26	−	1.42798e26i	0.943141	−	0.876921i
$419$	8.81396e25			0.528483			0.264241	−	0.964457i	$-0.414878\pi$
$419$	8.81396e25			0.528483			0.264241	+	0.964457i	$0.414878\pi$
$420$	6.40677e23	−	8.79286e24i	0.00375099	−	0.0514799i
$421$			5.58973e25i			0.319573i	0.987152	+	0.159786i	$0.0510805\pi$
$421$			5.58973e25i			0.319573i	−0.987152	+	0.159786i	$0.948919\pi$
$422$	−9.76826e25	+	9.08241e25i	−0.545372	+	0.507080i
$423$			2.42671e26i			1.32316i
$424$	2.50089e26	−	2.00710e26i	1.33179	−	1.06883i
$425$	−7.38318e24			−0.0384020
$426$	5.08343e25	+	5.46731e25i	0.258262	+	0.277765i
$427$	7.09024e24			0.0351870
$428$	8.57868e24	−	1.17737e26i	0.0415894	−	0.570787i
$429$			2.66496e25i			0.126217i
$430$	5.21750e24	+	5.61150e24i	0.0241423	+	0.0259653i
$431$		−	2.02264e26i		−	0.914420i	−0.889359	−	0.457210i	$-0.848849\pi$
$431$		−	2.02264e26i		−	0.914420i	0.889359	−	0.457210i	$-0.151151\pi$
$432$	−1.17735e26	−	1.72487e25i	−0.520077	−	0.0761936i
$433$	9.70735e25			0.419008			0.209504	−	0.977808i	$-0.432815\pi$
$433$	9.70735e25			0.419008			0.209504	+	0.977808i	$0.432815\pi$
$434$	6.13917e24	−	5.70813e24i	0.0258948	−	0.0240767i
$435$	−7.72689e25			−0.318502
$436$	−4.43011e26	−	3.22792e25i	−1.78464	−	0.130034i
$437$		−	3.98319e26i		−	1.56825i
$438$	−4.57668e25	+	4.25534e25i	−0.176120	+	0.163754i
$439$			1.06665e26i			0.401214i	0.979672	+	0.200607i	$0.0642915\pi$
$439$			1.06665e26i			0.401214i	−0.979672	+	0.200607i	$0.935708\pi$
$440$	1.93053e26	−	1.54935e26i	0.709823	−	0.569671i
$441$	−2.45187e26			−0.881274
$442$	1.30048e25	+	1.39869e25i	0.0456964	+	0.0491471i
$443$	3.37450e26			1.15924			0.579618	−	0.814888i	$-0.303202\pi$
$443$	3.37450e26			1.15924			0.579618	+	0.814888i	$0.303202\pi$
$444$	−4.11442e24	−	2.99790e23i	−0.0138191	−	0.00100690i
$445$		−	4.02659e26i		−	1.32232i
$446$	3.07497e26	+	3.30717e26i	0.987398	+	1.06196i
$447$		−	3.79714e25i		−	0.119229i
$448$	−6.94878e25	−	1.54079e25i	−0.213368	−	0.0473110i
$449$	−2.12762e26			−0.638896			−0.319448	−	0.947604i	$-0.603498\pi$
$449$	−2.12762e26			−0.638896			−0.319448	+	0.947604i	$0.603498\pi$
$450$	5.80423e25	−	5.39670e25i	0.170459	−	0.158491i
$451$	4.56116e26			1.31012
$452$	−3.94267e25	+	5.41105e26i	−0.110766	+	1.52019i
$453$			1.95108e26i			0.536158i
$454$	7.88910e25	−	7.33519e25i	0.212065	−	0.197176i
$455$		−	3.16025e25i		−	0.0831012i
$456$	−8.13095e25	−	1.01314e26i	−0.209167	−	0.260627i
$457$	−1.99071e26			−0.501010			−0.250505	−	0.968115i	$-0.580597\pi$
$457$	−1.99071e26			−0.501010			−0.250505	+	0.968115i	$0.580597\pi$
$458$	4.22472e26	+	4.54375e26i	1.04026	+	1.11882i
$459$	−3.33139e25			−0.0802599
$460$	3.41671e25	−	4.68921e26i	0.0805434	−	1.10540i
$461$		−	5.96463e26i		−	1.37586i	−0.725777	−	0.687930i	$-0.758519\pi$
$461$		−	5.96463e26i		−	1.37586i	0.725777	−	0.687930i	$-0.241481\pi$
$462$	−1.89334e25	−	2.03632e25i	−0.0427375	−	0.0459648i
$463$		−	2.47453e26i		−	0.546617i	−0.961926	−	0.273308i	$-0.911882\pi$
$463$		−	2.47453e26i		−	0.546617i	0.961926	−	0.273308i	$-0.0881179\pi$
$464$	−9.04263e25	+	6.17225e26i	−0.195486	+	1.33433i
$465$	1.80597e25			0.0382103
$466$	7.85174e25	−	7.30046e25i	0.162595	−	0.151179i
$467$	−5.31638e26			−1.07757			−0.538787	−	0.842442i	$-0.681117\pi$
$467$	−5.31638e26			−1.07757			−0.538787	+	0.842442i	$0.681117\pi$
$468$	−2.04473e26	−	1.48986e25i	−0.405674	−	0.0295587i
$469$			6.38107e25i			0.123927i
$470$	−4.76475e26	+	4.43021e26i	−0.905861	+	0.842259i
$471$			6.29259e25i			0.117117i
$472$	−4.44367e25	−	5.53691e25i	−0.0809695	−	0.100890i
$473$	2.41662e25			0.0431118
$474$	1.04461e26	+	1.12349e26i	0.182461	+	0.196239i
$475$	1.80017e26			0.307877
$476$	−1.98742e25	−	1.44810e24i	−0.0332828	−	0.00242510i
$477$			9.63716e26i			1.58039i
$478$	−4.78441e25	−	5.14571e25i	−0.0768334	−	0.0826354i
$479$			3.84647e26i			0.604932i	0.953160	+	0.302466i	$0.0978099\pi$
$479$			3.84647e26i			0.604932i	−0.953160	+	0.302466i	$0.902190\pi$
$480$	−8.70311e25	−	1.26246e26i	−0.134049	−	0.194449i
$481$	−1.47877e25			−0.0223074
$482$	−5.55182e26	+	5.16202e26i	−0.820286	+	0.762692i
$483$	−5.28125e25			−0.0764303
$484$	5.47032e24	−	7.50765e25i	0.00775460	−	0.106427i
$485$		−	6.36379e26i		−	0.883688i
$486$	3.97910e26	−	3.69972e26i	0.541280	−	0.503275i
$487$			3.66749e25i			0.0488741i	0.999701	+	0.0244371i	$0.00777934\pi$
$487$			3.66749e25i			0.0488741i	−0.999701	+	0.0244371i	$0.992221\pi$
$488$	9.61760e25	−	7.71864e25i	0.125565	−	0.100773i
$489$	2.89682e26			0.370538
$490$	−4.47614e26	−	4.81415e26i	−0.560974	−	0.603336i
$491$	−7.55878e26			−0.928190			−0.464095	−	0.885785i	$-0.653620\pi$
$491$	−7.55878e26			−0.928190			−0.464095	+	0.885785i	$0.653620\pi$
$492$	2.05326e25	−	2.81796e26i	0.0247054	−	0.339065i
$493$			1.74648e26i			0.205918i
$494$	−3.17084e26	−	3.41028e26i	−0.366357	−	0.394022i
$495$			7.43929e26i			0.842325i
$496$	2.11349e25	−	1.44261e26i	0.0234522	−	0.160078i
$497$	−2.79212e26			−0.303647
$498$	2.82809e26	−	2.62952e26i	0.301439	−	0.280274i
$499$	7.77009e26			0.811746			0.405873	−	0.913929i	$-0.366967\pi$
$499$	7.77009e26			0.811746			0.405873	+	0.913929i	$0.366967\pi$
$500$	1.05457e27	+	7.68397e25i	1.07988	+	0.0786839i
$501$			4.03697e26i			0.405209i
$502$	1.00330e27	−	9.32859e26i	0.987178	−	0.917866i
$503$		−	1.47036e27i		−	1.41822i	−0.705097	−	0.709110i	$-0.749097\pi$
$503$		−	1.47036e27i		−	1.41822i	0.705097	−	0.709110i	$-0.250903\pi$
$504$	1.66824e26	−	1.33885e26i	0.157744	−	0.126598i
$505$	1.59992e27			1.48314
$506$	−1.00971e27	−	1.08596e27i	−0.917684	−	0.986982i
$507$	−2.47176e26			−0.220256
$508$	1.76398e27	+	1.28529e26i	1.54119	+	0.112296i
$509$			8.27692e26i			0.709073i	0.935042	+	0.354536i	$0.115361\pi$
$509$			8.27692e26i			0.709073i	−0.935042	+	0.354536i	$0.884639\pi$
$510$	−2.92321e25	−	3.14395e25i	−0.0245560	−	0.0264104i
$511$		−	2.33728e26i		−	0.192531i
$512$	−1.11031e27	+	5.47463e26i	−0.896898	+	0.442237i
$513$	8.12259e26			0.643459
$514$	3.61354e26	−	3.35982e26i	0.280738	−	0.261027i
$515$	−9.94824e25			−0.0758008
$516$	1.08787e24	−	1.49302e25i	0.000812978	−	0.0111576i
$517$			2.05196e27i			1.50405i
$518$	1.12994e25	−	1.05060e25i	0.00812376	−	0.00755338i
$519$		−	2.70832e26i		−	0.190997i
$520$	−3.44034e26	−	4.28674e26i	−0.237995	−	0.296547i
$521$	−3.49221e26			−0.236986			−0.118493	−	0.992955i	$-0.537806\pi$
$521$	−3.49221e26			−0.236986			−0.118493	+	0.992955i	$0.537806\pi$
$522$	−1.27658e27	−	1.37298e27i	−0.849853	−	0.914029i
$523$	−1.26906e27			−0.828831			−0.414415	−	0.910088i	$-0.636014\pi$
$523$	−1.26906e27			−0.828831			−0.414415	+	0.910088i	$0.636014\pi$
$524$	−1.12887e26	+	1.54930e27i	−0.0723320	+	0.992708i
$525$		−	2.38681e25i		−	0.0150046i
$526$	−4.17444e26	−	4.48967e26i	−0.257479	−	0.276922i
$527$		−	4.08196e25i		−	0.0247038i
$528$	−4.78503e26	−	7.01028e25i	−0.284149	−	0.0416290i
$529$	−1.10032e27			−0.641153
$530$	−1.89222e27	+	1.75937e27i	−1.08197	+	1.00600i
$531$	2.13365e26			0.119723
$532$	4.84573e26	+	3.53076e25i	0.266835	+	0.0194425i
$533$		−	1.01280e27i		−	0.547335i
$534$	−5.76118e26	+	5.35668e26i	−0.305562	+	0.284108i
$535$			9.51169e26i			0.495131i
$536$	6.94662e26	+	8.65564e26i	0.354916	+	0.442233i
$537$	−6.58408e26			−0.330181
$538$	−3.69614e25	−	3.97525e25i	−0.0181939	−	0.0195678i
$539$	−2.07324e27			−1.00175
$540$	9.56232e26	+	6.96742e25i	0.453550	+	0.0330472i
$541$		−	2.64356e26i		−	0.123088i	−0.998104	−	0.0615440i	$-0.980398\pi$
$541$		−	2.64356e26i		−	0.123088i	0.998104	−	0.0615440i	$-0.0196025\pi$
$542$	2.45519e27	+	2.64059e27i	1.12226	+	1.20700i
$543$			8.95702e24i			0.00401944i
$544$	−2.85349e26	+	1.96713e26i	−0.125715	+	0.0866653i
$545$	3.57899e27			1.54809
$546$	−4.52164e25	+	4.20416e25i	−0.0192030	+	0.0178547i
$547$	−7.85407e26			−0.327507			−0.163754	−	0.986501i	$-0.552360\pi$
$547$	−7.85407e26			−0.327507			−0.163754	+	0.986501i	$0.552360\pi$
$548$	−3.85676e25	+	5.29315e26i	−0.0157913	+	0.216725i
$549$			3.70614e26i			0.149004i
$550$	4.90791e26	−	4.56331e26i	0.193762	−	0.180158i
$551$		−	4.25827e27i		−	1.65089i
$552$	−7.16378e26	+	5.74932e26i	−0.272742	+	0.218890i
$553$	−5.73759e26			−0.214525
$554$	4.36021e26	+	4.68947e26i	0.160107	+	0.172197i
$555$	3.32395e25			0.0119874
$556$	6.39069e25	−	8.77080e26i	0.0226360	−	0.310664i
$557$		−	1.79432e27i		−	0.624236i	−0.950043	−	0.312118i	$-0.898962\pi$
$557$		−	1.79432e27i		−	0.624236i	0.950043	−	0.312118i	$-0.101038\pi$
$558$	2.98369e26	+	3.20900e26i	0.101956	+	0.109655i
$559$		−	5.36609e25i		−	0.0180111i
$560$	5.67435e26	+	8.31317e25i	0.187084	+	0.0274086i
$561$	−1.35396e26			−0.0438507
$562$	−3.24490e27	+	3.01706e27i	−1.03238	+	0.959890i
$563$	4.71503e27			1.47367			0.736836	−	0.676071i	$-0.236319\pi$
$563$	4.71503e27			1.47367			0.736836	+	0.676071i	$0.236319\pi$
$564$	1.26774e27	+	9.23714e25i	0.389258	+	0.0283626i
$565$		−	4.37147e27i		−	1.31869i
$566$	3.45579e27	−	3.21315e27i	1.02420	−	0.952284i
$567$			5.86924e26i			0.170904i
$568$	−3.78738e27	+	3.03958e27i	−1.08357	+	0.869621i
$569$	−1.72052e27			−0.483656			−0.241828	−	0.970319i	$-0.577747\pi$
$569$	−1.72052e27			−0.483656			−0.241828	+	0.970319i	$0.577747\pi$
$570$	7.12737e26	+	7.66559e26i	0.196870	+	0.211737i
$571$	1.40979e27			0.382641			0.191321	−	0.981528i	$-0.438723\pi$
$571$	1.40979e27			0.382641			0.191321	+	0.981528i	$0.438723\pi$
$572$	−1.72897e27	−	1.25978e26i	−0.461134	−	0.0335998i
$573$		−	8.62394e26i		−	0.226026i
$574$	7.19556e26	+	7.73893e26i	0.185330	+	0.199325i
$575$		−	1.27288e27i		−	0.322188i
$576$	8.05384e26	−	3.63219e27i	0.200345	−	0.903534i
$577$	−6.12456e27			−1.49733			−0.748663	−	0.662950i	$-0.769304\pi$
$577$	−6.12456e27			−1.49733			−0.748663	+	0.662950i	$0.769304\pi$
$578$	2.97681e27	−	2.76780e27i	0.715274	−	0.665053i
$579$	3.79559e26			0.0896382
$580$	3.65267e26	−	5.01305e27i	0.0847873	−	1.16365i
$581$			1.44428e27i			0.329527i
$582$	−9.10522e26	+	8.46592e26i	−0.204202	+	0.189865i
$583$			8.14894e27i			1.79645i
$584$	−2.54443e27	−	3.17042e27i	−0.551394	−	0.687049i
$585$	1.65189e27			0.351903
$586$	1.98382e27	+	2.13363e27i	0.415457	+	0.446830i
$587$	3.87893e27			0.798604			0.399302	−	0.916820i	$-0.369253\pi$
$587$	3.87893e27			0.798604			0.399302	+	0.916820i	$0.369253\pi$
$588$	−9.33291e25	+	1.28088e27i	−0.0188905	+	0.259260i
$589$			9.95264e26i			0.198055i
$590$	3.89520e26	+	4.18934e26i	0.0762095	+	0.0819644i
$591$		−	5.46593e26i		−	0.105145i
$592$	3.88996e25	−	2.65518e26i	0.00735746	−	0.0502200i
$593$	−5.05296e27			−0.939722			−0.469861	−	0.882740i	$-0.655696\pi$
$593$	−5.05296e27			−0.939722			−0.469861	+	0.882740i	$0.655696\pi$
$594$	2.21451e27	−	2.05903e27i	0.404962	−	0.376528i
$595$	1.60560e26			0.0288713
$596$	2.46351e27	+	1.79499e26i	0.435603	+	0.0317395i
$597$		−	1.16460e27i		−	0.202503i
$598$	−2.41138e27	+	2.24207e27i	−0.412338	+	0.383387i
$599$			6.42777e27i			1.08092i	0.841371	+	0.540459i	$0.181749\pi$
$599$			6.42777e27i			1.08092i	−0.841371	+	0.540459i	$0.818251\pi$
$600$	−2.59835e26	−	3.23761e26i	−0.0429720	−	0.0535441i
$601$	6.13048e27			0.997126			0.498563	−	0.866854i	$-0.333861\pi$
$601$	6.13048e27			0.997126			0.498563	+	0.866854i	$0.333861\pi$
$602$	3.81239e25	+	4.10028e25i	0.00609863	+	0.00655916i
$603$	−3.33545e27			−0.524784
$604$	−1.26582e28	−	9.22319e26i	−1.95886	−	0.142729i
$605$			6.06527e26i			0.0923202i
$606$	−2.12841e27	−	2.28914e27i	−0.318661	−	0.342725i
$607$			8.59036e27i			1.26510i	0.774520	+	0.632549i	$0.217991\pi$
$607$			8.59036e27i			1.26510i	−0.774520	+	0.632549i	$0.782009\pi$
$608$	6.95739e27	−	4.79627e27i	1.00788	−	0.694812i
$609$	−5.64598e26			−0.0804575
$610$	−7.27687e26	+	6.76595e26i	−0.102011	+	0.0948484i
$611$	4.55638e27			0.628358
$612$	7.56936e25	−	1.03884e27i	0.0102694	−	0.140941i
$613$			6.53893e27i			0.872774i	0.899759	+	0.436387i	$0.143742\pi$
$613$			6.53893e27i			0.872774i	−0.899759	+	0.436387i	$0.856258\pi$
$614$	−4.24842e27	+	3.95013e27i	−0.557884	+	0.518714i
$615$			2.27657e27i			0.294124i
$616$	1.41062e27	−	1.13210e27i	0.179310	−	0.143906i
$617$	−4.14779e27			−0.518759			−0.259379	−	0.965776i	$-0.583518\pi$
$617$	−4.14779e27			−0.518759			−0.259379	+	0.965776i	$0.583518\pi$
$618$	1.32344e26	+	1.42338e26i	0.0162862	+	0.0175160i
$619$	−2.89355e27			−0.350368			−0.175184	−	0.984536i	$-0.556052\pi$
$619$	−2.89355e27			−0.350368			−0.175184	+	0.984536i	$0.556052\pi$
$620$	−8.53721e25	+	1.17167e27i	−0.0101718	+	0.139602i
$621$		−	5.74341e27i		−	0.673370i
$622$	2.88598e27	+	3.10391e27i	0.332958	+	0.358101i
$623$		−	2.94220e27i		−	0.334034i
$624$	−1.55663e26	+	1.06251e27i	−0.0173916	+	0.118710i
$625$	−6.23232e27			−0.685250
$626$	8.47576e27	−	7.88066e27i	0.917140	−	0.852745i
$627$	3.30122e27			0.351559
$628$	−4.08250e27	−	2.97465e26i	−0.427888	−	0.0311773i
$629$		−	7.51302e25i		−	0.00775011i
$630$	−1.26223e27	+	1.17360e27i	−0.128154	+	0.119156i
$631$		−	1.13124e28i		−	1.13048i	−0.824928	−	0.565238i	$-0.808784\pi$
$631$		−	1.13124e28i		−	1.13048i	0.824928	−	0.565238i	$-0.191216\pi$
$632$	−7.78279e27	+	6.24610e27i	−0.765534	+	0.614382i
$633$	−2.09967e27			−0.203289
$634$	6.83564e27	+	7.35183e27i	0.651458	+	0.700653i
$635$	−1.42508e28			−1.33691
$636$	5.03455e27	+	3.66834e26i	0.464932	+	0.0338765i
$637$			4.60362e27i			0.418509i
$638$	−1.07945e28	−	1.16096e28i	−0.966038	−	1.03899i
$639$		−	1.45947e28i		−	1.28584i
$640$	8.60200e27	−	5.04961e27i	0.746104	−	0.437984i
$641$	2.31014e28			1.97268			0.986341	−	0.164713i	$-0.0526699\pi$
$641$	2.31014e28			1.97268			0.986341	+	0.164713i	$0.0526699\pi$
$642$	1.36092e27	−	1.26537e27i	0.114415	−	0.106381i
$643$	1.26662e28			1.04843			0.524213	−	0.851587i	$-0.324360\pi$
$643$	1.26662e28			1.04843			0.524213	+	0.851587i	$0.324360\pi$
$644$	2.49657e26	−	3.42637e27i	0.0203462	−	0.279239i
$645$			1.20618e26i			0.00967868i
$646$	1.73263e27	−	1.61097e27i	0.136892	−	0.127281i
$647$		−	3.27969e27i		−	0.255147i	−0.991829	−	0.127573i	$-0.959281\pi$
$647$		−	3.27969e27i		−	0.255147i	0.991829	−	0.127573i	$-0.0407188\pi$
$648$	6.38943e27	+	7.96137e27i	0.489454	+	0.609871i
$649$	1.80416e27			0.136090
$650$	−1.01328e27	−	1.08980e27i	−0.0752657	−	0.0809494i
$651$	1.31961e26			0.00965238
$652$	−1.36939e27	+	1.87940e28i	−0.0986398	+	1.35376i
$653$			2.38862e27i			0.169440i	0.996405	+	0.0847200i	$0.0269996\pi$
$653$			2.38862e27i			0.169440i	−0.996405	+	0.0847200i	$0.973000\pi$
$654$	−4.76123e27	−	5.12077e27i	−0.332615	−	0.357732i
$655$		−	1.25164e28i		−	0.861128i
$656$	1.81853e28	+	2.66422e27i	1.23220	+	0.180523i
$657$	1.22172e28			0.815300
$658$	−3.48157e27	+	3.23712e27i	−0.228832	+	0.212765i
$659$	−3.24782e27			−0.210251			−0.105125	−	0.994459i	$-0.533524\pi$
$659$	−3.24782e27			−0.210251			−0.105125	+	0.994459i	$0.533524\pi$
$660$	3.88636e27	+	2.83173e26i	0.247801	+	0.0180556i
$661$		−	2.77284e28i		−	1.74145i	−0.491774	−	0.870723i	$-0.663651\pi$
$661$		−	2.77284e28i		−	1.74145i	0.491774	−	0.870723i	$-0.336349\pi$
$662$	−1.15029e28	+	1.06952e28i	−0.711585	+	0.661623i
$663$			3.00646e26i			0.0183198i
$664$	1.57229e28	+	1.95911e28i	0.943739	+	1.17592i
$665$	−3.91476e27			−0.231467
$666$	5.49160e26	+	5.90630e26i	0.0319858	+	0.0344012i
$667$	−3.01098e28			−1.72763
$668$	−2.61911e28	−	1.90837e27i	−1.48043	−	0.107869i
$669$			7.10872e27i			0.395850i
$670$	−6.08921e27	−	6.54903e27i	−0.334051	−	0.359277i
$671$			3.13382e27i			0.169375i
$672$	−6.35930e26	−	9.22469e26i	−0.0338623	−	0.0491201i
$673$	−1.45343e28			−0.762504			−0.381252	−	0.924471i	$-0.624507\pi$
$673$	−1.45343e28			−0.762504			−0.381252	+	0.924471i	$0.624507\pi$
$674$	−5.91883e27	+	5.50325e27i	−0.305940	+	0.284460i
$675$	2.59568e27			0.132195
$676$	1.16846e27	−	1.60363e28i	0.0586335	−	0.804705i
$677$			3.77095e28i			1.86451i	0.361807	+	0.932253i	$0.382160\pi$
$677$			3.77095e28i			1.86451i	−0.361807	+	0.932253i	$0.617840\pi$
$678$	−6.25464e27	+	5.81549e27i	−0.304723	+	0.283328i
$679$		−	4.64998e27i		−	0.223230i
$680$	2.17792e27	−	1.74790e27i	0.103027	−	0.0826850i
$681$	1.69575e27			0.0790481
$682$	2.52293e27	+	2.71345e27i	0.115894	+	0.124646i
$683$	−3.81940e28			−1.72897			−0.864487	−	0.502655i	$-0.832357\pi$
$683$	−3.81940e28			−1.72897			−0.864487	+	0.502655i	$0.832357\pi$
$684$	−1.84556e27	+	2.53291e28i	−0.0823318	+	1.12995i
$685$		−	4.27622e27i		−	0.187999i
$686$	−6.70542e27	−	7.21178e27i	−0.290526	−	0.312465i
$687$			9.76672e27i			0.417044i
$688$	9.63501e26	+	1.41157e26i	0.0405479	+	0.00594044i
$689$	1.80947e28			0.750515
$690$	5.42026e27	−	5.03969e27i	0.221579	−	0.206022i
$691$	4.53729e28			1.82817			0.914084	−	0.405526i	$-0.132912\pi$
$691$	4.53729e28			1.82817			0.914084	+	0.405526i	$0.132912\pi$
$692$	1.75710e28	+	1.28028e27i	0.697808	+	0.0508446i
$693$			5.43583e27i			0.212781i
$694$	−1.12712e27	+	1.04798e27i	−0.0434887	+	0.0404353i
$695$			7.08574e27i			0.269487i
$696$	−7.65852e27	+	6.14637e27i	−0.287113	+	0.230423i
$697$	5.14565e27			0.190157
$698$	−2.32781e28	−	2.50360e28i	−0.847996	−	0.912032i
$699$	1.68772e27			0.0606079
$700$	1.54852e27	+	1.12830e26i	0.0548196	+	0.00399434i
$701$			2.44859e28i			0.854545i	0.904123	+	0.427273i	$0.140526\pi$
$701$			2.44859e28i			0.854545i	−0.904123	+	0.427273i	$0.859474\pi$
$702$	−4.57207e27	−	4.91732e27i	−0.157305	−	0.169183i
$703$			1.83182e27i			0.0621342i
$704$	6.81012e27	−	3.07129e28i	0.227734	−	1.02706i
$705$	−1.02418e28			−0.337663
$706$	3.26279e28	−	3.03370e28i	1.06058	−	0.986111i
$707$	1.16905e28			0.374660
$708$	8.12162e25	−	1.11464e27i	0.00256632	−	0.0352210i
$709$		−	2.07454e27i		−	0.0646339i	−0.999478	−	0.0323169i	$-0.989711\pi$
$709$		−	2.07454e27i		−	0.0646339i	0.999478	−	0.0323169i	$-0.0102886\pi$
$710$	2.86561e28	−	2.66441e28i	0.880306	−	0.818497i
$711$		−	2.99909e28i		−	0.908435i
$712$	−3.20296e28	−	3.99096e28i	−0.956647	−	1.19200i
$713$	7.03742e27			0.207261
$714$	−2.13597e26	−	2.29726e26i	−0.00620315	−	0.00667158i
$715$	1.39680e28			0.400012
$716$	3.11244e27	−	4.27162e28i	0.0878964	−	1.20632i
$717$		−	1.10606e27i		−	0.0308026i
$718$	3.57851e28	+	3.84874e28i	0.982783	+	1.05700i
$719$			6.81553e28i			1.84591i	0.384906	+	0.922956i	$0.374234\pi$
$719$			6.81553e28i			1.84591i	−0.384906	+	0.922956i	$0.625766\pi$
$720$	−4.34537e27	+	2.96604e28i	−0.116065	+	0.792230i
$721$	−7.26910e26			−0.0191482
$722$	−1.40552e28	+	1.30683e28i	−0.365144	+	0.339507i
$723$	−1.19336e28			−0.305765
$724$	−5.81113e26	−	4.23418e25i	−0.0146850	−	0.00107000i
$725$		−	1.36079e28i		−	0.339164i
$726$	8.67810e26	−	8.06879e26i	0.0213333	−	0.0198355i
$727$			3.11037e27i			0.0754167i	0.999289	+	0.0377083i	$0.0120058\pi$
$727$			3.11037e27i			0.0754167i	−0.999289	+	0.0377083i	$0.987994\pi$
$728$	−2.51383e27	−	3.13229e27i	−0.0601204	−	0.0749114i
$729$	−2.45964e28			−0.580225
$730$	2.23038e28	+	2.39880e28i	0.518979	+	0.558169i
$731$	2.72629e26			0.00625747
$732$	1.93612e27	+	1.41072e26i	0.0438351	+	0.00319397i
$733$		−	5.70653e28i		−	1.27448i	−0.770667	−	0.637239i	$-0.780077\pi$
$733$		−	5.70653e28i		−	1.27448i	0.770667	−	0.637239i	$-0.219923\pi$
$734$	−6.83170e26	−	7.34759e26i	−0.0150511	−	0.0161877i
$735$		−	1.03480e28i		−	0.224896i
$736$	−3.39139e28	−	4.91950e28i	−0.727110	−	1.05473i
$737$	−2.82037e28			−0.596528
$738$	−4.04521e28	+	3.76119e28i	−0.844069	+	0.784805i
$739$	5.29434e28			1.08985			0.544926	−	0.838484i	$-0.316558\pi$
$739$	5.29434e28			1.08985			0.544926	+	0.838484i	$0.316558\pi$
$740$	−1.57131e26	+	2.15651e27i	−0.00319113	+	0.0437961i
$741$		−	7.33035e27i		−	0.146873i
$742$	−1.38263e28	+	1.28556e28i	−0.273318	+	0.254127i
$743$			3.40637e28i			0.664360i	0.943216	+	0.332180i	$0.107784\pi$
$743$			3.40637e28i			0.664360i	−0.943216	+	0.332180i	$0.892216\pi$
$744$	1.78999e27	−	1.43656e27i	0.0344446	−	0.0276436i
$745$	−1.99022e28			−0.377866
$746$	8.36766e27	+	8.99954e27i	0.156753	+	0.168590i
$747$	−7.54942e28			−1.39543
$748$	6.40046e26	−	8.78420e27i	0.0116733	−	0.160209i
$749$			6.95012e27i			0.125076i
$750$	1.13340e28	+	1.21898e28i	0.201265	+	0.216464i
$751$			1.46366e28i			0.256473i	0.991744	+	0.128236i	$0.0409316\pi$
$751$			1.46366e28i			0.256473i	−0.991744	+	0.128236i	$0.959068\pi$
$752$	−1.19857e28	+	8.18114e28i	−0.207246	+	1.41461i
$753$	2.15659e28			0.367974
$754$	−2.57791e28	+	2.39691e28i	−0.434064	+	0.403588i
$755$	1.02263e29			1.69922
$756$	6.98711e27	+	5.09104e26i	0.114572	+	0.00834812i
$757$		−	7.96001e28i		−	1.28812i	−0.764977	−	0.644058i	$-0.777249\pi$
$757$		−	7.96001e28i		−	1.28812i	0.764977	−	0.644058i	$-0.222751\pi$
$758$	3.92296e28	−	3.64752e28i	0.626501	−	0.582513i
$759$		−	2.33426e28i		−	0.367901i
$760$	−5.31020e28	+	4.26172e28i	−0.825991	+	0.662902i
$761$	−2.73143e28			−0.419318			−0.209659	−	0.977775i	$-0.567235\pi$
$761$	−2.73143e28			−0.419318			−0.209659	+	0.977775i	$0.567235\pi$
$762$	1.89582e28	+	2.03898e28i	0.287242	+	0.308933i
$763$	2.61514e28			0.391066
$764$	5.59504e28	+	4.07673e27i	0.825789	+	0.0601697i
$765$			8.39260e27i			0.122259i
$766$	8.25912e28	+	8.88280e28i	1.18753	+	1.27721i
$767$		−	4.00613e27i		−	0.0568553i
$768$	−1.86684e28	−	5.58998e27i	−0.261514	−	0.0783065i
$769$	−9.32051e28			−1.28877			−0.644387	−	0.764700i	$-0.722887\pi$
$769$	−9.32051e28			−1.28877			−0.644387	+	0.764700i	$0.722887\pi$
$770$	−1.06731e28	+	9.92369e27i	−0.145674	+	0.135446i
$771$	7.76725e27			0.104646
$772$	−1.79426e27	+	2.46250e28i	−0.0238623	+	0.327494i
$773$			5.86801e28i			0.770364i	0.922841	+	0.385182i	$0.125861\pi$
$773$			5.86801e28i			0.770364i	−0.922841	+	0.385182i	$0.874139\pi$
$774$	−2.14325e27	+	1.99277e27i	−0.0277756	+	0.0258254i
$775$			3.18050e27i			0.0406891i
$776$	−5.06210e28	−	6.30749e28i	−0.639313	−	0.796598i
$777$	2.42879e26			0.00302816
$778$	−1.69163e28	−	1.81937e28i	−0.208214	−	0.223937i
$779$	−1.25461e29			−1.52453
$780$	6.28785e26	−	8.62965e27i	0.00754321	−	0.103525i
$781$		−	1.23409e29i		−	1.46162i
$782$	−1.13910e28	−	1.22512e28i	−0.133197	−	0.143256i
$783$		−	6.14005e28i		−	0.708850i
$784$	−8.26597e28	−	1.21100e28i	−0.942178	−	0.138033i
$785$	3.29817e28			0.371173
$786$	−1.79083e28	+	1.66510e28i	−0.198989	+	0.185018i
$787$	1.04151e29			1.14266			0.571328	−	0.820722i	$-0.306429\pi$
$787$	1.04151e29			1.14266			0.571328	+	0.820722i	$0.306429\pi$
$788$	3.54618e28	+	2.58387e27i	0.384148	+	0.0279903i
$789$		−	9.65049e27i		−	0.103224i
$790$	5.88861e28	−	5.47516e28i	0.621931	−	0.578264i
$791$		−	3.19420e28i		−	0.333118i
$792$	5.91760e28	+	7.37347e28i	0.609388	+	0.759312i
$793$	6.95863e27			0.0707607
$794$	−9.67497e28	−	1.04056e29i	−0.971504	−	1.04487i
$795$	−4.06731e28			−0.403307
$796$	7.55567e28	+	5.50531e27i	0.739847	+	0.0539077i
$797$			8.25588e28i			0.798326i	0.916880	+	0.399163i	$0.130699\pi$
$797$			8.25588e28i			0.798326i	−0.916880	+	0.399163i	$0.869301\pi$
$798$	5.20791e27	+	5.60118e27i	0.0497319	+	0.0534873i
$799$			2.31491e28i			0.218306i
$800$	2.22333e28	−	1.53271e28i	0.207063	−	0.142745i
$801$	1.53791e29			1.41451
$802$	−3.74272e28	+	3.47994e28i	−0.339973	+	0.316103i
$803$	1.03305e29			0.926761
$804$	−1.26962e27	+	1.74247e28i	−0.0112490	+	0.154385i
$805$			2.76809e28i			0.242226i
$806$	6.02521e27	−	5.60217e27i	0.0520741	−	0.0484179i
$807$		−	8.54474e26i		−	0.00729396i
$808$	1.58576e29	−	1.27266e29i	1.33698	−	1.07300i
$809$	1.14500e29			0.953495			0.476748	−	0.879040i	$-0.341816\pi$
$809$	1.14500e29			0.953495			0.476748	+	0.879040i	$0.341816\pi$
$810$	−5.60079e28	−	6.02373e28i	−0.460680	−	0.495468i
$811$	−2.20639e29			−1.79256			−0.896279	−	0.443491i	$-0.853740\pi$
$811$	−2.20639e29			−1.79256			−0.896279	+	0.443491i	$0.853740\pi$
$812$	2.66898e27	−	3.66300e28i	0.0214183	−	0.293952i
$813$			5.67591e28i			0.449915i
$814$	4.64356e27	+	4.99422e27i	0.0363586	+	0.0391042i
$815$		−	1.51833e29i		−	1.17433i
$816$	−5.39821e27	−	7.90862e26i	−0.0412428	−	0.00604225i
$817$	−6.64725e27			−0.0501674
$818$	7.44283e28	−	6.92025e28i	0.554887	−	0.515928i
$819$	1.20703e28			0.0888950
$820$	−1.47699e29	−	1.07619e28i	−1.07458	−	0.0782976i
$821$			1.50901e29i			1.08458i	0.840192	+	0.542288i	$0.182442\pi$
$821$			1.50901e29i			1.08458i	−0.840192	+	0.542288i	$0.817558\pi$
$822$	−6.11836e27	+	5.68877e27i	−0.0434427	+	0.0403925i
$823$			2.60574e29i			1.82781i	0.405924	+	0.913907i	$0.366950\pi$
$823$			2.60574e29i			1.82781i	−0.405924	+	0.913907i	$0.633050\pi$
$824$	−9.86022e27	+	7.91336e27i	−0.0683305	+	0.0548389i
$825$	1.05495e28			0.0722257
$826$	2.84619e27	+	3.06112e27i	0.0192514	+	0.0207052i
$827$	−2.63817e29			−1.76298			−0.881491	−	0.472201i	$-0.843460\pi$
$827$	−2.63817e29			−1.76298			−0.881491	+	0.472201i	$0.843460\pi$
$828$	1.79100e29	+	1.30498e28i	1.18247	+	0.0861589i
$829$			1.66562e29i			1.08650i	0.839571	+	0.543250i	$0.182807\pi$
$829$			1.66562e29i			1.08650i	−0.839571	+	0.543250i	$0.817193\pi$
$830$	−1.37823e29	−	1.48230e29i	−0.888258	−	0.955335i
$831$			1.00799e28i			0.0641871i
$832$	−6.81980e28	−	1.51219e28i	−0.429080	−	0.0951419i
$833$	−2.33891e28			−0.145400
$834$	1.01382e28	−	9.42635e27i	0.0622729	−	0.0579006i
$835$	2.11592e29			1.28421
$836$	−1.56056e28	+	2.14176e29i	−0.0935875	+	1.28443i
$837$			1.43508e28i			0.0850399i
$838$	−6.60981e28	+	6.14572e28i	−0.387034	+	0.359859i
$839$		−	2.45841e28i		−	0.142244i	−0.997468	−	0.0711221i	$-0.977342\pi$
$839$		−	2.45841e28i		−	0.142244i	0.997468	−	0.0711221i	$-0.0226580\pi$
$840$	5.65055e27	+	7.04072e27i	0.0323071	+	0.0402554i
$841$	−1.44898e29			−0.818657
$842$	−3.89756e28	−	4.19188e28i	−0.217606	−	0.234039i
$843$	−6.97486e28			−0.384822
$844$	9.92563e27	−	1.36223e29i	0.0541170	−	0.742720i
$845$			1.29554e29i			0.698044i
$846$	−1.69207e29	−	1.81985e29i	−0.900981	−	0.969018i
$847$			4.43185e27i			0.0233212i
$848$	−4.75989e28	+	3.24897e29i	−0.247536	+	1.68961i
$849$	7.42817e28			0.381773
$850$	5.53684e27	−	5.14808e27i	0.0281237	−	0.0261491i
$851$	1.29526e28			0.0650224
$852$	−7.62439e28	−	5.55538e27i	−0.378276	−	0.0275625i
$853$		−	4.10833e28i		−	0.201453i	−0.994914	−	0.100727i	$-0.967883\pi$
$853$		−	4.10833e28i		−	0.201453i	0.994914	−	0.100727i	$-0.0321168\pi$
$854$	−5.31715e27	+	4.94382e27i	−0.0257692	+	0.0239599i
$855$		−	2.04628e29i		−	0.980178i
$856$	7.56610e28	+	9.42753e28i	0.358207	+	0.446334i
$857$	1.78159e29			0.833682			0.416841	−	0.908979i	$-0.363137\pi$
$857$	1.78159e29			0.833682			0.416841	+	0.908979i	$0.363137\pi$
$858$	−1.85820e28	−	1.99852e28i	−0.0859447	−	0.0924348i
$859$	−1.16232e29			−0.531366			−0.265683	−	0.964060i	$-0.585597\pi$
$859$	−1.16232e29			−0.531366			−0.265683	+	0.964060i	$0.585597\pi$
$860$	−7.82547e27	−	5.70190e26i	−0.0353611	−	0.00257653i
$861$			1.66347e28i			0.0742992i
$862$	1.41033e29	+	1.51683e29i	0.622655	+	0.669675i
$863$		−	2.20822e29i		−	0.963683i	−0.876259	−	0.481841i	$-0.839968\pi$
$863$		−	2.20822e29i		−	0.963683i	0.876259	−	0.481841i	$-0.160032\pi$
$864$	1.00319e29	−	6.91579e28i	0.432760	−	0.298335i
$865$	−1.41953e29			−0.605316
$866$	−7.27979e28	+	6.76866e28i	−0.306860	+	0.285315i
$867$	6.39861e28			0.266621
$868$	−6.23807e26	+	8.56134e27i	−0.00256953	+	0.0352650i
$869$		−	2.53596e29i		−	1.03263i
$870$	5.79459e28	−	5.38774e28i	0.233255	−	0.216877i
$871$			6.26262e28i			0.249215i
$872$	3.54733e29	−	2.84692e29i	1.39552	−	1.11998i
$873$	2.43059e29			0.945298
$874$	2.77736e29	+	2.98709e29i	1.06787	+	1.14851i
$875$	−6.22526e28			−0.236634
$876$	4.65041e27	−	6.38238e28i	0.0174763	−	0.239851i
$877$		−	4.03997e29i		−	1.50100i	−0.660868	−	0.750502i	$-0.729812\pi$
$877$		−	4.03997e29i		−	1.50100i	0.660868	−	0.750502i	$-0.270188\pi$
$878$	−7.43744e28	−	7.99908e28i	−0.273199	−	0.293829i
$879$			4.58620e28i			0.166558i
$880$	−3.67434e28	+	2.50800e29i	−0.131933	+	0.900537i
$881$	−1.24285e29			−0.441226			−0.220613	−	0.975361i	$-0.570806\pi$
$881$	−1.24285e29			−0.441226			−0.220613	+	0.975361i	$0.570806\pi$
$882$	1.83872e29	−	1.70962e29i	0.645400	−	0.600085i
$883$	4.93807e29			1.71376			0.856880	−	0.515515i	$-0.172399\pi$
$883$	4.93807e29			1.71376			0.856880	+	0.515515i	$0.172399\pi$
$884$	−1.95053e28	−	1.42122e27i	−0.0669314	−	0.00487684i
$885$			9.00493e27i			0.0305525i
$886$	−2.53062e29	+	2.35294e29i	−0.848966	+	0.789358i
$887$		−	2.63289e29i		−	0.873367i	−0.899615	−	0.436684i	$-0.856153\pi$
$887$		−	2.63289e29i		−	0.873367i	0.899615	−	0.436684i	$-0.143847\pi$
$888$	3.29454e27	−	2.64405e27i	0.0108060	−	0.00867241i
$889$	−1.04130e29			−0.337720
$890$	2.80763e29	+	3.01964e29i	0.900408	+	0.968401i
$891$	−2.59415e29			−0.822655
$892$	−4.61199e29	−	3.36045e28i	−1.44624	−	0.105378i
$893$		−	5.64421e29i		−	1.75021i
$894$	2.64764e28	+	2.84757e28i	0.0811864	+	0.0873171i
$895$			3.45095e29i			1.04643i
$896$	6.28541e28	−	3.68971e28i	0.188475	−	0.110640i
$897$	−5.18322e28			−0.153700
$898$	1.59556e29	−	1.48353e29i	0.467895	−	0.435043i
$899$	7.52343e28			0.218182
$900$	−5.89774e27	+	8.09425e28i	−0.0169145	+	0.232141i
$901$			9.19319e28i			0.260747i
$902$	−3.42053e29	+	3.18037e29i	−0.959462	+	0.892096i
$903$			8.81349e26i			0.00244495i
$904$	−3.47730e29	−	4.33280e29i	−0.954021	−	1.18873i
$905$	4.69469e27			0.0127386
$906$	−1.36043e29	−	1.46316e29i	−0.365086	−	0.392655i
$907$	1.56123e29			0.414376			0.207188	−	0.978301i	$-0.433569\pi$
$907$	1.56123e29			0.414376			0.207188	+	0.978301i	$0.433569\pi$
$908$	−8.01620e27	+	1.10017e29i	−0.0210431	+	0.288803i
$909$			6.11072e29i			1.58655i
$910$	2.20355e28	+	2.36995e28i	0.0565860	+	0.0608591i
$911$			4.36036e28i			0.110749i	0.998466	+	0.0553743i	$0.0176352\pi$
$911$			4.36036e28i			0.110749i	−0.998466	+	0.0553743i	$0.982365\pi$
$912$	1.31619e29	+	1.92828e28i	0.330652	+	0.0484419i
$913$	−6.38359e29			−1.58620
$914$	1.49289e29	−	1.38807e29i	0.366915	−	0.341153i
$915$	−1.56415e28			−0.0380249
$916$	−6.33645e29	−	4.61695e28i	−1.52367	−	0.111020i
$917$		−	9.14567e28i		−	0.217531i
$918$	2.49829e28	−	2.32288e28i	0.0587782	−	0.0546513i
$919$			4.60052e29i			1.07066i	0.844643	+	0.535331i	$0.179813\pi$
$919$			4.60052e29i			1.07066i	−0.844643	+	0.535331i	$0.820187\pi$
$920$	3.01342e29	+	3.75479e29i	0.693716	+	0.864386i
$921$	−9.13192e28			−0.207953
$922$	4.15897e29	+	4.47303e29i	0.936864	+	1.00761i
$923$	−2.74029e29			−0.610632
$924$	2.83973e28	+	2.06912e27i	0.0625976	+	0.00456107i
$925$			5.85384e27i			0.0127651i
$926$	1.72542e29	+	1.85571e29i	0.372207	+	0.400314i
$927$		−	3.79963e28i		−	0.0810857i
$928$	−3.62561e29	−	5.25925e29i	−0.765422	−	1.11031i
$929$	4.28630e29			0.895212			0.447606	−	0.894231i	$-0.352277\pi$
$929$	4.28630e29			0.895212			0.447606	+	0.894231i	$0.352277\pi$
$930$	−1.35434e28	+	1.25925e28i	−0.0279833	+	0.0260185i
$931$	5.70274e29			1.16570
$932$	−7.97824e27	+	1.09496e29i	−0.0161342	+	0.221431i
$933$			6.67181e28i			0.133483i
$934$	3.98689e29	−	3.70696e29i	0.789160	−	0.733751i
$935$			7.09657e28i			0.138974i
$936$	1.63728e29	−	1.31400e29i	0.317222	−	0.254588i
$937$	−7.15749e29			−1.37203			−0.686017	−	0.727585i	$-0.740643\pi$
$937$	−7.15749e29			−1.37203			−0.686017	+	0.727585i	$0.740643\pi$
$938$	−4.44934e28	−	4.78533e28i	−0.0843853	−	0.0907576i
$939$	1.82185e29			0.341867
$940$	4.84151e28	−	6.64465e29i	0.0898882	−	1.23365i
$941$			1.37461e29i			0.252513i	0.991998	+	0.126257i	$0.0402963\pi$
$941$			1.37461e29i			0.252513i	−0.991998	+	0.126257i	$0.959704\pi$
$942$	−4.38764e28	−	4.71897e28i	−0.0797485	−	0.0857706i
$943$			8.87124e29i			1.59539i
$944$	7.19315e28	+	1.05383e28i	0.127997	+	0.0187521i
$945$	−5.64474e28			−0.0993862
$946$	−1.81228e28	+	1.68504e28i	−0.0315729	+	0.0293561i
$947$	7.72513e29			1.33170			0.665849	−	0.746086i	$-0.268069\pi$
$947$	7.72513e29			1.33170			0.665849	+	0.746086i	$0.268069\pi$
$948$	−1.56676e29	−	1.14159e28i	−0.267250	−	0.0194727i
$949$		−	2.29389e29i		−	0.387179i
$950$	−1.34999e29	+	1.25521e29i	−0.225473	+	0.209642i
$951$			1.58027e29i			0.261171i
$952$	1.59139e28	−	1.27718e28i	0.0260260	−	0.0208872i
$953$	1.64663e29			0.266481			0.133241	−	0.991084i	$-0.457462\pi$
$953$	1.64663e29			0.266481			0.133241	+	0.991084i	$0.457462\pi$
$954$	−6.71972e29	−	7.22716e29i	−1.07614	−	1.15740i
$955$	−4.52011e29			−0.716334
$956$	7.17591e28	+	5.22860e27i	0.112538	+	0.00819987i
$957$		−	2.49547e29i		−	0.387286i
$958$	−2.68203e29	−	2.88456e29i	−0.411916	−	0.443022i
$959$		−	3.12460e28i		−	0.0474907i
$960$	1.53295e29	+	3.39907e28i	0.230576	+	0.0511267i
$961$	6.54206e29			0.973825
$962$	1.10896e28	−	1.03110e28i	0.0163368	−	0.0151898i
$963$	−3.63289e29			−0.529651
$964$	5.64126e28	−	7.74226e29i	0.0813966	−	1.11711i
$965$		−	1.98940e29i		−	0.284086i
$966$	3.96054e28	−	3.68247e28i	0.0559736	−	0.0520436i
$967$		−	4.55583e29i		−	0.637240i	−0.947883	−	0.318620i	$-0.896781\pi$
$967$		−	4.55583e29i		−	0.637240i	0.947883	−	0.318620i	$-0.103219\pi$
$968$	4.82464e28	+	6.01161e28i	0.0667899	+	0.0832218i
$969$	3.72425e28			0.0510272
$970$	4.43729e29	+	4.77237e29i	0.601729	+	0.647168i
$971$	−1.41934e30			−1.90500			−0.952501	−	0.304534i	$-0.901499\pi$
$971$	−1.41934e30			−1.90500			−0.952501	+	0.304534i	$0.901499\pi$
$972$	−4.04320e28	+	5.54902e29i	−0.0537109	+	0.737146i
$973$			5.17750e28i			0.0680756i
$974$	−2.55724e28	−	2.75034e28i	−0.0332798	−	0.0357929i
$975$		−	2.34251e28i		−	0.0301742i
$976$	−1.83050e28	+	1.24945e29i	−0.0233384	+	0.159302i
$977$	7.03797e29			0.888182			0.444091	−	0.895982i	$-0.353527\pi$
$977$	7.03797e29			0.888182			0.444091	+	0.895982i	$0.353527\pi$
$978$	−2.17240e29	+	2.01987e29i	−0.271363	+	0.252310i
$979$	1.30042e30			1.60789
$980$	6.71355e29	+	4.89171e28i	0.821658	+	0.0598687i
$981$			1.36696e30i			1.65602i
$982$	5.66852e29	−	5.27052e29i	0.679759	−	0.632032i
$983$		−	1.22719e30i		−	1.45672i	−0.685193	−	0.728362i	$-0.740282\pi$
$983$		−	1.22719e30i		−	1.45672i	0.685193	−	0.728362i	$-0.259718\pi$
$984$	1.81090e29	+	2.25643e29i	0.212787	+	0.265137i
$985$	−2.86489e29			−0.333231
$986$	−1.21777e29	−	1.30973e29i	−0.140216	−	0.150804i
$987$	−7.48358e28			−0.0852978
$988$	4.75578e29	+	3.46522e28i	0.536602	+	0.0390986i
$989$			4.70021e28i			0.0524994i
$990$	−5.18721e29	−	5.57891e29i	−0.573564	−	0.616876i
$991$			7.91296e28i			0.0866168i	0.999062	+	0.0433084i	$0.0137898\pi$
$991$			7.91296e28i			0.0866168i	−0.999062	+	0.0433084i	$0.986210\pi$
$992$	8.47395e28	+	1.22922e29i	0.0918267	+	0.133202i
$993$	−2.47253e29			−0.265246
$994$	2.09388e29	−	1.94686e29i	0.222376	−	0.206762i
$995$	−6.10407e29			−0.641783
$996$	−2.87365e28	+	3.94389e29i	−0.0299116	+	0.410517i
$997$		−	1.33035e30i		−	1.37092i	−0.728109	−	0.685462i	$-0.759600\pi$
$997$		−	1.33035e30i		−	1.37092i	0.728109	−	0.685462i	$-0.240400\pi$
$998$	−5.82699e29	+	5.41786e29i	−0.594482	+	0.552742i
$999$			2.64133e28i			0.0266789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.21.d.b.3.6	yes	18
3.2	odd	2		72.21.b.b.19.13		18
4.3	odd	2		32.21.d.b.15.12		18
8.3	odd	2	inner	8.21.d.b.3.5	✓	18
8.5	even	2		32.21.d.b.15.11		18
24.11	even	2		72.21.b.b.19.14		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.21.d.b.3.5	✓	18	8.3	odd	2	inner
8.21.d.b.3.6	yes	18	1.1	even	1	trivial
32.21.d.b.15.11		18	8.5	even	2
32.21.d.b.15.12		18	4.3	odd	2
72.21.b.b.19.13		18	3.2	odd	2
72.21.b.b.19.14		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)

\(f(q)\)	\(=\)	\(q+(-749.926 + 697.272i) q^{2} -16119.5 q^{3} +(76200.7 - 1.04580e6i) q^{4} +8.44883e6i q^{5} +(1.20885e7 - 1.12397e7i) q^{6} +6.17349e7i q^{7} +(6.72064e8 + 8.37407e8i) q^{8} -3.22694e9 q^{9} +O(q^{10})\)	\(q+(-749.926 + 697.272i) q^{2} -16119.5 q^{3} +(76200.7 - 1.04580e6i) q^{4} +8.44883e6i q^{5} +(1.20885e7 - 1.12397e7i) q^{6} +6.17349e7i q^{7} +(6.72064e8 + 8.37407e8i) q^{8} -3.22694e9 q^{9} +(-5.89113e9 - 6.33599e9i) q^{10} -2.72862e10 q^{11} +(-1.22832e9 + 1.68579e10i) q^{12} +6.05890e10i q^{13} +(-4.30460e10 - 4.62966e10i) q^{14} -1.36191e11i q^{15} +(-1.08790e12 - 1.59382e11i) q^{16} -3.07828e11 q^{17} +(2.41997e12 - 2.25006e12i) q^{18} +7.50547e12 q^{19} +(8.83581e12 + 6.43807e11i) q^{20} -9.95139e11i q^{21} +(2.04626e13 - 1.90259e13i) q^{22} -5.30705e13i q^{23} +(-1.08334e13 - 1.34986e13i) q^{24} +2.39847e13 q^{25} +(-4.22470e13 - 4.54372e13i) q^{26} +1.08222e14 q^{27} +(6.45626e13 + 4.70425e12i) q^{28} -5.67356e14i q^{29} +(9.49623e13 + 1.02133e14i) q^{30} +1.32605e14i q^{31} +(9.26975e14 - 6.39036e14i) q^{32} +4.39842e14 q^{33} +(2.30848e14 - 2.14640e14i) q^{34} -5.21588e14 q^{35} +(-2.45895e14 + 3.37475e15i) q^{36} +2.44065e14i q^{37} +(-5.62854e15 + 5.23335e15i) q^{38} -9.76667e14i q^{39} +(-7.07511e15 + 5.67816e15i) q^{40} -1.67160e16 q^{41} +(6.93882e14 + 7.46280e14i) q^{42} -8.85654e14 q^{43} +(-2.07923e15 + 2.85360e16i) q^{44} -2.72639e16i q^{45} +(3.70045e16 + 3.97989e16i) q^{46} -7.52013e16i q^{47} +(1.75364e16 + 2.56916e15i) q^{48} +7.59811e16 q^{49} +(-1.79868e16 + 1.67239e16i) q^{50} +4.96205e15 q^{51} +(6.33642e16 + 4.61693e15i) q^{52} -2.98647e17i q^{53} +(-8.11586e16 + 7.54603e16i) q^{54} -2.30537e17i q^{55} +(-5.16973e16 + 4.14898e16i) q^{56} -1.20985e17 q^{57} +(3.95601e17 + 4.25475e17i) q^{58} -6.61197e16 q^{59} +(-1.42429e17 - 1.03779e16i) q^{60} -1.14850e17i q^{61} +(-9.24618e16 - 9.94440e16i) q^{62} -1.99215e17i q^{63} +(-2.49581e17 + 1.12558e18i) q^{64} -5.11906e17 q^{65} +(-3.29848e17 + 3.06689e17i) q^{66} +1.03362e18 q^{67} +(-2.34567e16 + 3.21928e17i) q^{68} +8.55472e17i q^{69} +(3.91152e17 - 3.63688e17i) q^{70} +4.52275e18i q^{71} +(-2.16871e18 - 2.70227e18i) q^{72} -3.78599e18 q^{73} +(-1.70180e17 - 1.83031e17i) q^{74} -3.86623e17 q^{75} +(5.71922e17 - 7.84925e18i) q^{76} -1.68451e18i q^{77} +(6.81002e17 + 7.32428e17i) q^{78} +9.29391e18i q^{79} +(1.34659e18 - 9.19147e18i) q^{80} +9.50717e18 q^{81} +(1.25357e19 - 1.16556e19i) q^{82} +2.33949e19 q^{83} +(-1.04072e18 - 7.58303e16i) q^{84} -2.60079e18i q^{85} +(6.64174e17 - 6.17541e17i) q^{86} +9.14552e18i q^{87} +(-1.83381e19 - 2.28497e19i) q^{88} -4.76585e19 q^{89} +(1.90103e19 + 2.04459e19i) q^{90} -3.74046e18 q^{91} +(-5.55013e19 - 4.04401e18i) q^{92} -2.13754e18i q^{93} +(5.24358e19 + 5.63954e19i) q^{94} +6.34124e19i q^{95} +(-1.49424e19 + 1.03010e19i) q^{96} -7.53216e19 q^{97} +(-5.69801e19 + 5.29794e19i) q^{98} +8.80512e19 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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