LMFDB - Embedded newform 8.21.d.b.3.7

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			3.7
Root			$22670.7 - 1.21630e6i$ of defining polynomial
Character	$\chi$	$=$	8.3
Dual form			8.21.d.b.3.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-340.525 - 965.722i) q^{2} +84336.7 q^{3} +(-816662. + 657705. i) q^{4} +4.86521e6i q^{5} +(-2.87188e7 - 8.14458e7i) q^{6} -1.26224e8i q^{7} +(9.13253e8 + 5.64703e8i) q^{8} +3.62590e9 q^{9} +O(q^{10})$	\(q+(-340.525 - 965.722i) q^{2} +84336.7 q^{3} +(-816662. + 657705. i) q^{4} +4.86521e6i q^{5} +(-2.87188e7 - 8.14458e7i) q^{6} -1.26224e8i q^{7} +(9.13253e8 + 5.64703e8i) q^{8} +3.62590e9 q^{9} +(4.69844e9 - 1.65673e9i) q^{10} +1.51387e10 q^{11} +(-6.88746e10 + 5.54687e10i) q^{12} +1.95170e11i q^{13} +(-1.21897e11 + 4.29823e10i) q^{14} +4.10316e11i q^{15} +(2.34361e11 - 1.07424e12i) q^{16} +3.56201e12 q^{17} +(-1.23471e12 - 3.50161e12i) q^{18} +3.48807e12 q^{19} +(-3.19987e12 - 3.97323e12i) q^{20} -1.06453e13i q^{21} +(-5.15512e12 - 1.46198e13i) q^{22} -1.17677e13i q^{23} +(7.70208e13 + 4.76252e13i) q^{24} +7.16971e13 q^{25} +(1.88480e14 - 6.64604e13i) q^{26} +1.17326e13 q^{27} +(8.30179e13 + 1.03082e14i) q^{28} -7.56048e14i q^{29} +(3.96251e14 - 1.39723e14i) q^{30} +1.11233e15i q^{31} +(-1.11723e15 + 1.39479e14i) q^{32} +1.27675e15 q^{33} +(-1.21295e15 - 3.43992e15i) q^{34} +6.14105e14 q^{35} +(-2.96113e15 + 2.38477e15i) q^{36} -7.17444e14i q^{37} +(-1.18778e15 - 3.36851e15i) q^{38} +1.64600e16i q^{39} +(-2.74740e15 + 4.44317e15i) q^{40} +3.23458e15 q^{41} +(-1.02804e16 + 3.62499e15i) q^{42} -1.36789e16 q^{43} +(-1.23632e16 + 9.95682e15i) q^{44} +1.76408e16i q^{45} +(-1.13644e16 + 4.00720e15i) q^{46} -4.28694e16i q^{47} +(1.97652e16 - 9.05983e16i) q^{48} +6.38598e16 q^{49} +(-2.44147e16 - 6.92395e16i) q^{50} +3.00409e17 q^{51} +(-1.28364e17 - 1.59388e17i) q^{52} +3.34779e17i q^{53} +(-3.99524e15 - 1.13304e16i) q^{54} +7.36531e16i q^{55} +(7.12790e16 - 1.15274e17i) q^{56} +2.94173e17 q^{57} +(-7.30133e17 + 2.57453e17i) q^{58} +2.74237e17 q^{59} +(-2.69867e17 - 3.35089e17i) q^{60} +1.49210e17i q^{61} +(1.07420e18 - 3.78775e17i) q^{62} -4.57675e17i q^{63} +(5.15142e17 + 1.03143e18i) q^{64} -9.49545e17 q^{65} +(-4.34766e17 - 1.23299e18i) q^{66} -2.92321e18 q^{67} +(-2.90896e18 + 2.34275e18i) q^{68} -9.92452e17i q^{69} +(-2.09118e17 - 5.93055e17i) q^{70} +3.51233e18i q^{71} +(3.31137e18 + 2.04756e18i) q^{72} +5.45402e17 q^{73} +(-6.92851e17 + 2.44307e17i) q^{74} +6.04670e18 q^{75} +(-2.84858e18 + 2.29412e18i) q^{76} -1.91087e18i q^{77} +(1.58958e19 - 5.60505e18i) q^{78} -1.64097e19i q^{79} +(5.22643e18 + 1.14022e18i) q^{80} -1.16532e19 q^{81} +(-1.10145e18 - 3.12370e18i) q^{82} -1.30232e19 q^{83} +(7.00146e18 + 8.69361e18i) q^{84} +1.73300e19i q^{85} +(4.65801e18 + 1.32100e19i) q^{86} -6.37627e19i q^{87} +(1.38255e19 + 8.54889e18i) q^{88} -2.43956e19 q^{89} +(1.70361e19 - 6.00712e18i) q^{90} +2.46351e19 q^{91} +(7.73969e18 + 9.61025e18i) q^{92} +9.38101e19i q^{93} +(-4.13999e19 + 1.45981e19i) q^{94} +1.69702e19i q^{95} +(-9.42233e19 + 1.17632e19i) q^{96} -7.85794e18 q^{97} +(-2.17459e19 - 6.16708e19i) q^{98} +5.48915e19 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 $

$2$	−340.525	−	965.722i	−0.332544	−	0.943088i
$2$	−340.525	−	965.722i	−0.332544	−	0.943088i
$3$	84336.7			1.42825			0.714125	−	0.700018i	$-0.246825\pi$
$3$	84336.7			1.42825			0.714125	+	0.700018i	$0.246825\pi$
$4$	−816662.	+	657705.i	−0.778829	+	0.627236i
$5$			4.86521e6i			0.498198i	0.968478	+	0.249099i	$0.0801344\pi$
$5$			4.86521e6i			0.498198i	−0.968478	+	0.249099i	$0.919866\pi$
$6$	−2.87188e7	−	8.14458e7i	−0.474956	−	1.34697i
$7$		−	1.26224e8i		−	0.446849i	−0.974721	−	0.223424i	$-0.928276\pi$
$7$		−	1.26224e8i		−	0.446849i	0.974721	−	0.223424i	$-0.0717236\pi$
$8$	9.13253e8	+	5.64703e8i	0.850533	+	0.525921i
$9$	3.62590e9			1.03990
$10$	4.69844e9	−	1.65673e9i	0.469844	−	0.165673i
$11$	1.51387e10			0.583664			0.291832	−	0.956470i	$-0.405735\pi$
$11$	1.51387e10			0.583664			0.291832	+	0.956470i	$0.405735\pi$
$12$	−6.88746e10	+	5.54687e10i	−1.11236	+	0.895850i
$13$			1.95170e11i			1.41573i	0.706348	+	0.707865i	$0.250341\pi$
$13$			1.95170e11i			1.41573i	−0.706348	+	0.707865i	$0.749659\pi$
$14$	−1.21897e11	+	4.29823e10i	−0.421418	+	0.148597i
$15$			4.10316e11i			0.711551i
$16$	2.34361e11	−	1.07424e12i	0.213150	−	0.977019i
$17$	3.56201e12			1.76688			0.883439	−	0.468546i	$-0.155222\pi$
$17$	3.56201e12			1.76688			0.883439	+	0.468546i	$0.155222\pi$
$18$	−1.23471e12	−	3.50161e12i	−0.345812	−	0.980715i
$19$	3.48807e12			0.568918			0.284459	−	0.958688i	$-0.408186\pi$
$19$	3.48807e12			0.568918			0.284459	+	0.958688i	$0.408186\pi$
$20$	−3.19987e12	−	3.97323e12i	−0.312488	−	0.388011i
$21$		−	1.06453e13i		−	0.638212i
$22$	−5.15512e12	−	1.46198e13i	−0.194094	−	0.550446i
$23$		−	1.17677e13i		−	0.284063i	−0.989862	−	0.142031i	$-0.954637\pi$
$23$		−	1.17677e13i		−	0.284063i	0.989862	−	0.142031i	$-0.0453634\pi$
$24$	7.70208e13	+	4.76252e13i	1.21477	+	0.751147i
$25$	7.16971e13			0.751799
$26$	1.88480e14	−	6.64604e13i	1.33516	−	0.470792i
$27$	1.17326e13			0.0569844
$28$	8.30179e13	+	1.03082e14i	0.280280	+	0.348019i
$29$		−	7.56048e14i		−	1.79709i	−0.438882	−	0.898545i	$-0.644625\pi$
$29$		−	7.56048e14i		−	1.79709i	0.438882	−	0.898545i	$-0.355375\pi$
$30$	3.96251e14	−	1.39723e14i	0.671055	−	0.236622i
$31$			1.11233e15i			1.35711i	0.734548	+	0.678557i	$0.237394\pi$
$31$			1.11233e15i			1.35711i	−0.734548	+	0.678557i	$0.762606\pi$
$32$	−1.11723e15	+	1.39479e14i	−0.992297	+	0.123883i
$33$	1.27675e15			0.833618
$34$	−1.21295e15	−	3.43992e15i	−0.587564	−	1.66632i
$35$	6.14105e14			0.222619
$36$	−2.96113e15	+	2.38477e15i	−0.809903	+	0.652261i
$37$		−	7.17444e14i		−	0.149201i	−0.997214	−	0.0746003i	$-0.976232\pi$
$37$		−	7.17444e14i		−	0.149201i	0.997214	−	0.0746003i	$-0.0237681\pi$
$38$	−1.18778e15	−	3.36851e15i	−0.189190	−	0.536540i
$39$			1.64600e16i			2.02202i
$40$	−2.74740e15	+	4.44317e15i	−0.262013	+	0.423734i
$41$	3.23458e15			0.240979			0.120490	−	0.992715i	$-0.461554\pi$
$41$	3.23458e15			0.240979			0.120490	+	0.992715i	$0.461554\pi$
$42$	−1.02804e16	+	3.62499e15i	−0.601890	+	0.212233i
$43$	−1.36789e16			−0.632946			−0.316473	−	0.948602i	$-0.602499\pi$
$43$	−1.36789e16			−0.632946			−0.316473	+	0.948602i	$0.602499\pi$
$44$	−1.23632e16	+	9.95682e15i	−0.454574	+	0.366095i
$45$			1.76408e16i			0.518075i
$46$	−1.13644e16	+	4.00720e15i	−0.267896	+	0.0944633i
$47$		−	4.28694e16i		−	0.815021i	−0.913201	−	0.407510i	$-0.866397\pi$
$47$		−	4.28694e16i		−	0.815021i	0.913201	−	0.407510i	$-0.133603\pi$
$48$	1.97652e16	−	9.05983e16i	0.304431	−	1.39543i
$49$	6.38598e16			0.800326
$50$	−2.44147e16	−	6.92395e16i	−0.250006	−	0.709013i
$51$	3.00409e17			2.52354
$52$	−1.28364e17	−	1.59388e17i	−0.887997	−	1.10261i
$53$			3.34779e17i			1.91425i	0.289671	+	0.957126i	$0.406454\pi$
$53$			3.34779e17i			1.91425i	−0.289671	+	0.957126i	$0.593546\pi$
$54$	−3.99524e15	−	1.13304e16i	−0.0189498	−	0.0537413i
$55$			7.36531e16i			0.290780i
$56$	7.12790e16	−	1.15274e17i	0.235007	−	0.380060i
$57$	2.94173e17			0.812557
$58$	−7.30133e17	+	2.57453e17i	−1.69481	+	0.597611i
$59$	2.74237e17			0.536545			0.268272	−	0.963343i	$-0.413547\pi$
$59$	2.74237e17			0.536545			0.268272	+	0.963343i	$0.413547\pi$
$60$	−2.69867e17	−	3.35089e17i	−0.446310	−	0.554177i
$61$			1.49210e17i			0.209170i	0.994516	+	0.104585i	$0.0333515\pi$
$61$			1.49210e17i			0.209170i	−0.994516	+	0.104585i	$0.966648\pi$
$62$	1.07420e18	−	3.78775e17i	1.27988	−	0.451300i
$63$		−	4.57675e17i		−	0.464677i
$64$	5.15142e17	+	1.03143e18i	0.446814	+	0.894627i
$65$	−9.49545e17			−0.705313
$66$	−4.34766e17	−	1.23299e18i	−0.277214	−	0.786175i
$67$	−2.92321e18			−1.60366			−0.801828	−	0.597555i	$-0.796139\pi$
$67$	−2.92321e18			−1.60366			−0.801828	+	0.597555i	$0.796139\pi$
$68$	−2.90896e18	+	2.34275e18i	−1.37610	+	1.10825i
$69$		−	9.92452e17i		−	0.405712i
$70$	−2.09118e17	−	5.93055e17i	−0.0740306	−	0.209949i
$71$			3.51233e18i			1.07898i	0.841993	+	0.539489i	$0.181382\pi$
$71$			3.51233e18i			1.07898i	−0.841993	+	0.539489i	$0.818618\pi$
$72$	3.31137e18	+	2.04756e18i	0.884468	+	0.546904i
$73$	5.45402e17			0.126908			0.0634539	−	0.997985i	$-0.479788\pi$
$73$	5.45402e17			0.126908			0.0634539	+	0.997985i	$0.479788\pi$
$74$	−6.92851e17	+	2.44307e17i	−0.140709	+	0.0496157i
$75$	6.04670e18			1.07376
$76$	−2.84858e18	+	2.29412e18i	−0.443090	+	0.356846i
$77$		−	1.91087e18i		−	0.260809i
$78$	1.58958e19	−	5.60505e18i	1.90694	−	0.672409i
$79$		−	1.64097e19i		−	1.73312i	−0.499070	−	0.866562i	$-0.666325\pi$
$79$		−	1.64097e19i		−	1.73312i	0.499070	−	0.866562i	$-0.333675\pi$
$80$	5.22643e18	+	1.14022e18i	0.486749	+	0.106191i
$81$	−1.16532e19			−0.958510
$82$	−1.10145e18	−	3.12370e18i	−0.0801361	−	0.227264i
$83$	−1.30232e19			−0.839335			−0.419668	−	0.907678i	$-0.637853\pi$
$83$	−1.30232e19			−0.839335			−0.419668	+	0.907678i	$0.637853\pi$
$84$	7.00146e18	+	8.69361e18i	0.400309	+	0.497058i
$85$			1.73300e19i			0.880254i
$86$	4.65801e18	+	1.32100e19i	0.210482	+	0.596924i
$87$		−	6.37627e19i		−	2.56669i
$88$	1.38255e19	+	8.54889e18i	0.496426	+	0.306961i
$89$	−2.43956e19			−0.782368			−0.391184	−	0.920313i	$-0.627934\pi$
$89$	−2.43956e19			−0.782368			−0.391184	+	0.920313i	$0.627934\pi$
$90$	1.70361e19	−	6.00712e18i	0.488590	−	0.172283i
$91$	2.46351e19			0.632617
$92$	7.73969e18	+	9.61025e18i	0.178174	+	0.221236i
$93$			9.38101e19i			1.93830i
$94$	−4.13999e19	+	1.45981e19i	−0.768636	+	0.271030i
$95$			1.69702e19i			0.283434i
$96$	−9.42233e19	+	1.17632e19i	−1.41725	+	0.176935i
$97$	−7.85794e18			−0.106559			−0.0532796	−	0.998580i	$-0.516967\pi$
$97$	−7.85794e18			−0.106559			−0.0532796	+	0.998580i	$0.516967\pi$
$98$	−2.17459e19	−	6.16708e19i	−0.266143	−	0.754778i
$99$	5.48915e19			0.606951
$100$	−5.85523e19	+	4.71555e19i	−0.585523	+	0.471555i
$101$			1.53362e20i			1.38837i	0.719799	+	0.694183i	$0.244234\pi$
$101$			1.53362e20i			1.38837i	−0.719799	+	0.694183i	$0.755766\pi$
$102$	−1.02297e20	−	2.90111e20i	−0.839189	−	2.37992i
$103$		−	7.06517e19i		−	0.525715i	−0.964835	−	0.262857i	$-0.915335\pi$
$103$		−	7.06517e19i		−	0.525715i	0.964835	−	0.262857i	$-0.0846649\pi$
$104$	−1.10213e20	+	1.78240e20i	−0.744562	+	1.20413i
$105$	5.17916e19			0.317956
$106$	3.23303e20	−	1.14001e20i	1.80531	−	0.636573i
$107$	1.69073e20			0.859483			0.429742	−	0.902952i	$-0.358605\pi$
$107$	1.69073e20			0.859483			0.429742	+	0.902952i	$0.358605\pi$
$108$	−9.58155e18	+	7.71657e18i	−0.0443811	+	0.0357427i
$109$		−	1.46975e20i		−	0.620838i	−0.950600	−	0.310419i	$-0.899531\pi$
$109$		−	1.46975e20i		−	0.620838i	0.950600	−	0.310419i	$-0.100469\pi$
$110$	7.11285e19	−	2.50807e19i	0.274231	−	0.0966971i
$111$		−	6.05069e19i		−	0.213096i
$112$	−1.35595e20	−	2.95819e19i	−0.436580	−	0.0952458i
$113$	1.92152e20			0.566059			0.283029	−	0.959111i	$-0.408661\pi$
$113$	1.92152e20			0.566059			0.283029	+	0.959111i	$0.408661\pi$
$114$	−1.00173e20	−	2.84089e20i	−0.270211	−	0.766313i
$115$	5.72525e19			0.141519
$116$	4.97257e20	+	6.17436e20i	1.12720	+	1.39963i
$117$			7.07668e20i			1.47221i
$118$	−9.33845e19	−	2.64837e20i	−0.178425	−	0.506009i
$119$		−	4.49611e20i		−	0.789527i
$120$	−2.31707e20	+	3.74723e20i	−0.374219	+	0.605198i
$121$	−4.43569e20			−0.659337
$122$	1.44096e20	−	5.08098e19i	0.197266	−	0.0695583i
$123$	2.72794e20			0.344178
$124$	−7.31584e20	−	9.08396e20i	−0.851230	−	1.05696i
$125$			8.12805e20i			0.872742i
$126$	−4.41986e20	+	1.55850e20i	−0.438231	+	0.154526i
$127$		−	1.52243e21i		−	1.39476i	−0.716702	−	0.697379i	$-0.754349\pi$
$127$		−	1.52243e21i		−	1.39476i	0.716702	−	0.697379i	$-0.245651\pi$
$128$	8.20660e20	−	8.48713e20i	0.695126	−	0.718888i
$129$	−1.15363e21			−0.904005
$130$	3.23344e20	+	9.16996e20i	0.234548	+	0.665172i
$131$	−8.13929e20			−0.546857			−0.273428	−	0.961892i	$-0.588158\pi$
$131$	−8.13929e20			−0.546857			−0.273428	+	0.961892i	$0.588158\pi$
$132$	−1.04267e21	+	8.39725e20i	−0.649246	+	0.522875i
$133$		−	4.40278e20i		−	0.254220i
$134$	9.95424e20	+	2.82300e21i	0.533286	+	1.51239i
$135$			5.70815e19i			0.0283895i
$136$	3.25302e21	+	2.01148e21i	1.50279	+	0.929238i
$137$	−1.95796e21			−0.840615			−0.420308	−	0.907382i	$-0.638078\pi$
$137$	−1.95796e21			−0.840615			−0.420308	+	0.907382i	$0.638078\pi$
$138$	−9.58432e20	+	3.37954e20i	−0.382623	+	0.134917i
$139$	−3.33138e21			−1.23731			−0.618653	−	0.785665i	$-0.712321\pi$
$139$	−3.33138e21			−1.23731			−0.618653	+	0.785665i	$0.712321\pi$
$140$	−5.01516e20	+	4.03900e20i	−0.173382	+	0.139635i
$141$		−	3.61546e21i		−	1.16405i
$142$	3.39194e21	−	1.19604e21i	1.01757	−	0.358807i
$143$			2.95463e21i			0.826310i
$144$	8.49769e20	−	3.89510e21i	0.221654	−	1.01600i
$145$	3.67834e21			0.895306
$146$	−1.85723e20	−	5.26707e20i	−0.0422024	−	0.119685i
$147$	5.38573e21			1.14307
$148$	4.71866e20	+	5.85909e20i	0.0935840	+	0.116202i
$149$		−	7.16621e21i		−	1.32870i	−0.747422	−	0.664350i	$-0.768709\pi$
$149$		−	7.16621e21i		−	1.32870i	0.747422	−	0.664350i	$-0.231291\pi$
$150$	−2.05905e21	−	5.83943e21i	−0.357071	−	1.01265i
$151$			4.35389e21i			0.706493i	0.935530	+	0.353246i	$0.114922\pi$
$151$			4.35389e21i			0.706493i	−0.935530	+	0.353246i	$0.885078\pi$
$152$	3.18550e21	+	1.96973e21i	0.483884	+	0.299206i
$153$	1.29155e22			1.83737
$154$	−1.84537e21	+	6.50698e20i	−0.245966	+	0.0867306i
$155$	−5.41171e21			−0.676111
$156$	−1.08258e22	−	1.34423e22i	−1.26828	−	1.57481i
$157$		−	3.66999e21i		−	0.403338i	−0.979454	−	0.201669i	$-0.935364\pi$
$157$		−	3.66999e21i		−	0.403338i	0.979454	−	0.201669i	$-0.0646365\pi$
$158$	−1.58472e22	+	5.58791e21i	−1.63449	+	0.576339i
$159$			2.82342e22i			2.73403i
$160$	−6.78597e20	−	5.43555e21i	−0.0617180	−	0.494360i
$161$	−1.48537e21			−0.126933
$162$	3.96822e21	+	1.12538e22i	0.318747	+	0.903959i
$163$	3.23237e20			0.0244144			0.0122072	−	0.999925i	$-0.496114\pi$
$163$	3.23237e20			0.0244144			0.0122072	+	0.999925i	$0.496114\pi$
$164$	−2.64156e21	+	2.12740e21i	−0.187682	+	0.151151i
$165$			6.21167e21i			0.415306i
$166$	4.43471e21	+	1.25768e22i	0.279116	+	0.791567i
$167$		−	1.38936e22i		−	0.823474i	−0.911303	−	0.411737i	$-0.864922\pi$
$167$		−	1.38936e22i		−	0.823474i	0.911303	−	0.411737i	$-0.135078\pi$
$168$	6.01143e21	−	9.72185e21i	0.335649	−	0.542821i
$169$	−1.90865e22			−1.00429
$170$	1.67359e22	−	5.90128e21i	0.830157	−	0.292723i
$171$	1.26474e22			0.591617
$172$	1.11710e22	−	8.99668e21i	0.492957	−	0.397006i
$173$			4.49412e21i			0.187147i	0.995612	+	0.0935737i	$0.0298291\pi$
$173$			4.49412e21i			0.187147i	−0.995612	+	0.0935737i	$0.970171\pi$
$174$	−6.15770e22	+	2.17128e22i	−2.42062	+	0.853538i
$175$		−	9.04988e21i		−	0.335941i
$176$	3.54793e21	−	1.62627e22i	0.124408	−	0.570251i
$177$	2.31283e22			0.766320
$178$	8.30730e21	+	2.35593e22i	0.260172	+	0.737842i
$179$	−3.47973e22			−1.03042			−0.515211	−	0.857063i	$-0.672286\pi$
$179$	−3.47973e22			−1.03042			−0.515211	+	0.857063i	$0.672286\pi$
$180$	−1.16024e22	−	1.44065e22i	−0.324955	−	0.403492i
$181$		−	2.34167e22i		−	0.620497i	−0.950655	−	0.310248i	$-0.899588\pi$
$181$		−	2.34167e22i		−	0.620497i	0.950655	−	0.310248i	$-0.100412\pi$
$182$	−8.38887e21	−	2.37907e22i	−0.210373	−	0.596613i
$183$			1.25839e22i			0.298748i
$184$	6.64527e21	−	1.07469e22i	0.149395	−	0.241605i
$185$	3.49052e21			0.0743314
$186$	9.05945e22	−	3.19447e22i	1.82798	−	0.644569i
$187$	5.39244e22			1.03126
$188$	2.81954e22	+	3.50098e22i	0.511210	+	0.634762i
$189$		−	1.48093e21i		−	0.0254634i
$190$	1.63885e22	−	5.77878e21i	0.267303	−	0.0942541i
$191$		−	2.58648e22i		−	0.400291i	−0.979766	−	0.200145i	$-0.935859\pi$
$191$		−	2.58648e22i		−	0.400291i	0.979766	−	0.200145i	$-0.0641415\pi$
$192$	4.34454e22	+	8.69878e22i	0.638163	+	1.27775i
$193$	2.68246e22			0.374076			0.187038	−	0.982353i	$-0.440111\pi$
$193$	2.68246e22			0.374076			0.187038	+	0.982353i	$0.440111\pi$
$194$	2.67582e21	+	7.58858e21i	0.0354356	+	0.100495i
$195$	−8.00815e22			−1.00736
$196$	−5.21519e22	+	4.20009e22i	−0.623317	+	0.501993i
$197$		−	4.69360e22i		−	0.533143i	−0.963815	−	0.266572i	$-0.914109\pi$
$197$		−	4.69360e22i		−	0.533143i	0.963815	−	0.266572i	$-0.0858909\pi$
$198$	−1.86919e22	−	5.30100e22i	−0.201838	−	0.572408i
$199$		−	6.01397e22i		−	0.617491i	−0.951145	−	0.308746i	$-0.900091\pi$
$199$		−	6.01397e22i		−	0.617491i	0.951145	−	0.308746i	$-0.0999092\pi$
$200$	6.54777e22	+	4.04876e22i	0.639430	+	0.395387i
$201$	−2.46534e23			−2.29042
$202$	1.48105e23	−	5.22235e22i	1.30935	−	0.461692i
$203$	−9.54313e22			−0.803027
$204$	−2.45332e23	+	1.97580e23i	−1.96541	+	1.58286i
$205$			1.57369e22i			0.120055i
$206$	−6.82299e22	+	2.40587e22i	−0.495795	+	0.174823i
$207$		−	4.26686e22i		−	0.295396i
$208$	2.09661e23	+	4.57403e22i	1.38320	+	0.301763i
$209$	5.28050e22			0.332057
$210$	−1.76363e22	−	5.00163e22i	−0.105734	−	0.299860i
$211$	2.54766e23			1.45652			0.728262	−	0.685299i	$-0.240329\pi$
$211$	2.54766e23			1.45652			0.728262	+	0.685299i	$0.240329\pi$
$212$	−2.20186e23	−	2.73401e23i	−1.20069	−	1.49088i
$213$			2.96219e23i			1.54105i
$214$	−5.75737e22	−	1.63278e23i	−0.285816	−	0.810568i
$215$		−	6.65507e22i		−	0.315332i
$216$	1.07148e22	+	6.62543e21i	0.0484671	+	0.0299693i
$217$	1.40402e23			0.606424
$218$	−1.41937e23	+	5.00486e22i	−0.585505	+	0.206456i
$219$	4.59974e22			0.181256
$220$	−4.84420e22	−	6.01497e22i	−0.182388	−	0.226468i
$221$			6.95200e23i			2.50142i
$222$	−5.84328e22	+	2.06041e22i	−0.200968	+	0.0708637i
$223$		−	3.52305e23i		−	1.15843i	−0.815174	−	0.579216i	$-0.803359\pi$
$223$		−	3.52305e23i		−	1.15843i	0.815174	−	0.579216i	$-0.196641\pi$
$224$	1.76056e22	+	1.41021e23i	0.0553568	+	0.443407i
$225$	2.59967e23			0.781794
$226$	−6.54327e22	−	1.85566e23i	−0.188239	−	0.533843i
$227$	4.23328e23			1.16525			0.582624	−	0.812742i	$-0.302026\pi$
$227$	4.23328e23			1.16525			0.582624	+	0.812742i	$0.302026\pi$
$228$	−2.40240e23	+	1.93479e23i	−0.632843	+	0.509665i
$229$			9.70854e22i			0.244793i	0.992481	+	0.122396i	$0.0390580\pi$
$229$			9.70854e22i			0.244793i	−0.992481	+	0.122396i	$0.960942\pi$
$230$	−1.94959e22	−	5.52900e22i	−0.0470614	−	0.133465i
$231$		−	1.61156e23i		−	0.372501i
$232$	4.26943e23	−	6.90464e23i	0.945127	−	1.52848i
$233$	−4.99591e23			−1.05939			−0.529694	−	0.848189i	$-0.677693\pi$
$233$	−4.99591e23			−1.05939			−0.529694	+	0.848189i	$0.677693\pi$
$234$	6.83411e23	−	2.40979e23i	1.38843	−	0.489576i
$235$	2.08569e23			0.406042
$236$	−2.23959e23	+	1.80367e23i	−0.417877	+	0.336540i
$237$		−	1.38394e24i		−	2.47533i
$238$	−4.34199e23	+	1.53104e23i	−0.744594	+	0.262552i
$239$			4.59439e23i			0.755525i	0.925902	+	0.377763i	$0.123306\pi$
$239$			4.59439e23i			0.755525i	−0.925902	+	0.377763i	$0.876694\pi$
$240$	4.40780e23	+	9.61620e22i	0.695199	+	0.151667i
$241$	6.71339e23			1.01571			0.507857	−	0.861441i	$-0.330438\pi$
$241$	6.71339e23			1.01571			0.507857	+	0.861441i	$0.330438\pi$
$242$	1.51046e23	+	4.28364e23i	0.219258	+	0.621812i
$243$	−1.02371e24			−1.42598
$244$	−9.81363e22	−	1.21854e23i	−0.131199	−	0.162908i
$245$			3.10692e23i			0.398721i
$246$	−9.28931e22	−	2.63443e23i	−0.114454	−	0.324590i
$247$			6.80769e23i			0.805434i
$248$	−6.28136e23	+	1.01584e24i	−0.713734	+	1.15427i
$249$	−1.09833e24			−1.19878
$250$	7.84943e23	−	2.76780e23i	0.823073	−	0.290225i
$251$	−5.67208e23			−0.571486			−0.285743	−	0.958306i	$-0.592240\pi$
$251$	−5.67208e23			−0.571486			−0.285743	+	0.958306i	$0.592240\pi$
$252$	3.01015e23	+	3.73765e23i	0.291462	+	0.361904i
$253$		−	1.78148e23i		−	0.165797i
$254$	−1.47024e24	+	5.18424e23i	−1.31538	+	0.463818i
$255$			1.46155e24i			1.25722i
$256$	−1.09908e24	−	5.03522e23i	−0.909134	−	0.416503i
$257$	1.43742e24			1.14354			0.571770	−	0.820414i	$-0.306257\pi$
$257$	1.43742e24			1.14354			0.571770	+	0.820414i	$0.306257\pi$
$258$	3.92841e23	+	1.11409e24i	0.300621	+	0.852556i
$259$	−9.05584e22			−0.0666701
$260$	7.75457e23	−	6.24520e23i	0.549319	−	0.442398i
$261$		−	2.74136e24i		−	1.86879i
$262$	2.77163e23	+	7.86029e23i	0.181854	+	0.515734i
$263$			4.04959e23i			0.255773i	0.991789	+	0.127886i	$0.0408193\pi$
$263$			4.04959e23i			0.255773i	−0.991789	+	0.127886i	$0.959181\pi$
$264$	1.16600e24	+	7.20986e23i	0.709020	+	0.438417i
$265$	−1.62877e24			−0.953676
$266$	−4.25186e23	+	1.49926e23i	−0.239752	+	0.0845394i
$267$	−2.05744e24			−1.11742
$268$	2.38727e24	−	1.92261e24i	1.24897	−	1.00587i
$269$		−	7.34903e23i		−	0.370431i	−0.982698	−	0.185215i	$-0.940702\pi$
$269$		−	7.34903e23i		−	0.370431i	0.982698	−	0.185215i	$-0.0592983\pi$
$270$	5.51248e22	−	1.94377e22i	0.0267738	−	0.00944075i
$271$		−	4.11047e24i		−	1.92397i	−0.273100	−	0.961986i	$-0.588049\pi$
$271$		−	4.11047e24i		−	1.92397i	0.273100	−	0.961986i	$-0.411951\pi$
$272$	8.34797e23	−	3.82647e24i	0.376610	−	1.72627i
$273$	2.07765e24			0.903535
$274$	6.66733e23	+	1.89084e24i	0.279541	+	0.792774i
$275$	1.08540e24			0.438798
$276$	6.52740e23	+	8.10497e23i	0.254477	+	0.315981i
$277$			6.38513e23i			0.240089i	0.992769	+	0.120044i	$0.0383037\pi$
$277$			6.38513e23i			0.240089i	−0.992769	+	0.120044i	$0.961696\pi$
$278$	1.13442e24	+	3.21719e24i	0.411458	+	1.16689i
$279$			4.03319e24i			1.41126i
$280$	5.60834e23	+	3.46787e23i	0.189345	+	0.117080i
$281$	−4.28449e24			−1.39584			−0.697921	−	0.716175i	$-0.745891\pi$
$281$	−4.28449e24			−1.39584			−0.697921	+	0.716175i	$0.745891\pi$
$282$	−3.49153e24	+	1.23116e24i	−1.09780	+	0.387099i
$283$	4.08346e24			1.23927			0.619633	−	0.784892i	$-0.287282\pi$
$283$	4.08346e24			1.23927			0.619633	+	0.784892i	$0.287282\pi$
$284$	−2.31008e24	−	2.86839e24i	−0.676773	−	0.840339i
$285$			1.43121e24i			0.404814i
$286$	2.85335e24	−	1.00613e24i	0.779283	−	0.274784i
$287$		−	4.08281e23i		−	0.107681i
$288$	−4.05095e24	+	5.05738e23i	−1.03189	+	0.128825i
$289$	8.62372e24			2.12186
$290$	−1.25256e24	−	3.55225e24i	−0.297728	−	0.844352i
$291$	−6.62713e23			−0.152193
$292$	−4.45409e23	+	3.58713e23i	−0.0988394	+	0.0796011i
$293$			2.47467e24i			0.530690i	0.964154	+	0.265345i	$0.0854858\pi$
$293$			2.47467e24i			0.530690i	−0.964154	+	0.265345i	$0.914514\pi$
$294$	−1.83397e24	−	5.20112e24i	−0.380119	−	1.07801i
$295$			1.33422e24i			0.267305i
$296$	4.05143e23	−	6.55208e23i	0.0784677	−	0.126900i
$297$	1.77616e23			0.0332597
$298$	−6.92056e24	+	2.44027e24i	−1.25308	+	0.441851i
$299$	2.29671e24			0.402156
$300$	−4.93811e24	+	3.97694e24i	−0.836273	+	0.673499i
$301$			1.72660e24i			0.282831i
$302$	4.20464e24	−	1.48261e24i	0.666285	−	0.234940i
$303$			1.29340e25i			1.98293i
$304$	8.17468e23	−	3.74704e24i	0.121265	−	0.555844i
$305$	−7.25940e23			−0.104208
$306$	−4.39805e24	−	1.24728e25i	−0.611007	−	1.73280i
$307$	−8.40302e24			−1.12993			−0.564965	−	0.825115i	$-0.691110\pi$
$307$	−8.40302e24			−1.12993			−0.564965	+	0.825115i	$0.691110\pi$
$308$	1.25679e24	+	1.56053e24i	0.163589	+	0.203126i
$309$		−	5.95853e24i		−	0.750852i
$310$	1.84282e24	+	5.22621e24i	0.224836	+	0.637632i
$311$		−	1.49760e25i		−	1.76926i	−0.466292	−	0.884631i	$-0.654410\pi$
$311$		−	1.49760e25i		−	1.76926i	0.466292	−	0.884631i	$-0.345590\pi$
$312$	−9.29503e24	+	1.50322e25i	−1.06342	+	1.71979i
$313$	−1.48295e25			−1.64318			−0.821588	−	0.570081i	$-0.806912\pi$
$313$	−1.48295e25			−1.64318			−0.821588	+	0.570081i	$0.806912\pi$
$314$	−3.54419e24	+	1.24972e24i	−0.380383	+	0.134127i
$315$	2.22668e24			0.231501
$316$	1.07927e25	+	1.34012e25i	1.08708	+	1.34981i
$317$			6.07588e24i			0.592948i	0.955041	+	0.296474i	$0.0958108\pi$
$317$			6.07588e24i			0.592948i	−0.955041	+	0.296474i	$0.904189\pi$
$318$	2.72663e25	−	9.61443e24i	2.57843	−	0.909185i
$319$		−	1.14456e25i		−	1.04890i
$320$	−5.01815e24	+	2.50627e24i	−0.445701	+	0.222602i
$321$	1.42591e25			1.22756
$322$	5.05804e23	+	1.43445e24i	0.0422108	+	0.119709i
$323$	1.24246e25			1.00521
$324$	9.51676e24	−	7.66439e24i	0.746516	−	0.601212i
$325$			1.39932e25i			1.06434i
$326$	−1.10070e23	−	3.12157e23i	−0.00811885	−	0.0230249i
$327$		−	1.23954e25i		−	0.886712i
$328$	2.95399e24	+	1.82658e24i	0.204961	+	0.126736i
$329$	−5.41114e24			−0.364191
$330$	5.99874e24	−	2.11523e24i	0.391670	−	0.138108i
$331$	−8.24033e24			−0.521993			−0.260996	−	0.965340i	$-0.584051\pi$
$331$	−8.24033e24			−0.521993			−0.260996	+	0.965340i	$0.584051\pi$
$332$	1.06355e25	−	8.56539e24i	0.653699	−	0.526461i
$333$		−	2.60138e24i		−	0.155153i
$334$	−1.34173e25	+	4.73111e24i	−0.776608	+	0.273841i
$335$		−	1.42220e25i		−	0.798938i
$336$	−1.14357e25	−	2.49484e24i	−0.623545	−	0.136035i
$337$	−3.21488e25			−1.70163			−0.850815	−	0.525465i	$-0.823891\pi$
$337$	−3.21488e25			−1.70163			−0.850815	+	0.525465i	$0.823891\pi$
$338$	6.49943e24	+	1.84323e25i	0.333970	+	0.947134i
$339$	1.62055e25			0.808473
$340$	−1.13980e25	−	1.41527e25i	−0.552127	−	0.685568i
$341$			1.68392e25i			0.792098i
$342$	−4.30676e24	−	1.22139e25i	−0.196738	−	0.557947i
$343$		−	1.81323e25i		−	0.804474i
$344$	−1.24923e25	−	7.72452e24i	−0.538342	−	0.332880i
$345$	4.82849e24			0.202125
$346$	4.34007e24	−	1.53036e24i	0.176496	−	0.0622347i
$347$	−1.27479e25			−0.503667			−0.251834	−	0.967771i	$-0.581034\pi$
$347$	−1.27479e25			−0.503667			−0.251834	+	0.967771i	$0.581034\pi$
$348$	4.19370e25	+	5.20725e25i	1.60992	+	1.99902i
$349$			1.13915e25i			0.424940i	0.977168	+	0.212470i	$0.0681508\pi$
$349$			1.13915e25i			0.424940i	−0.977168	+	0.212470i	$0.931849\pi$
$350$	−8.73967e24	+	3.08171e24i	−0.316821	+	0.111715i
$351$			2.28985e24i			0.0806745i
$352$	−1.69134e25	+	2.11154e24i	−0.579168	+	0.0723058i
$353$	2.47620e25			0.824211			0.412106	−	0.911136i	$-0.364793\pi$
$353$	2.47620e25			0.824211			0.412106	+	0.911136i	$0.364793\pi$
$354$	−7.87575e24	−	2.23355e25i	−0.254835	−	0.722707i
$355$	−1.70882e25			−0.537544
$356$	1.99229e25	−	1.60451e25i	0.609331	−	0.490729i
$357$		−	3.79187e25i		−	1.12764i
$358$	1.18493e25	+	3.36045e25i	0.342660	+	0.971778i
$359$			4.85328e25i			1.36487i	0.730947	+	0.682434i	$0.239078\pi$
$359$			4.85328e25i			1.36487i	−0.730947	+	0.682434i	$0.760922\pi$
$360$	−9.96180e24	+	1.61105e25i	−0.272466	+	0.440640i
$361$	−2.54233e25			−0.676332
$362$	−2.26140e25	+	7.97396e24i	−0.585183	+	0.206342i
$363$	−3.74091e25			−0.941698
$364$	−2.01186e25	+	1.62026e25i	−0.492701	+	0.396800i
$365$			2.65350e24i			0.0632251i
$366$	1.21526e25	−	4.28513e24i	0.281745	−	0.0993467i
$367$			5.19588e25i			1.17219i	0.810242	+	0.586096i	$0.199336\pi$
$367$			5.19588e25i			1.17219i	−0.810242	+	0.586096i	$0.800664\pi$
$368$	−1.26414e25	−	2.75789e24i	−0.277535	−	0.0605480i
$369$	1.17283e25			0.250594
$370$	−1.18861e24	−	3.37087e24i	−0.0247184	−	0.0701010i
$371$	4.22570e25			0.855382
$372$	−6.16994e25	−	7.66111e25i	−1.21577	−	1.50960i
$373$		−	3.44797e25i		−	0.661417i	−0.943733	−	0.330708i	$-0.892712\pi$
$373$		−	3.44797e25i		−	0.661417i	0.943733	−	0.330708i	$-0.107288\pi$
$374$	−1.83626e25	−	5.20760e25i	−0.342940	−	0.972571i
$375$			6.85493e25i			1.24649i
$376$	2.42085e25	−	3.91506e25i	0.428637	−	0.693203i
$377$	1.47558e26			2.54419
$378$	−1.43017e24	+	5.04294e23i	−0.0240142	+	0.00846770i
$379$	7.98002e25			1.30500			0.652502	−	0.757787i	$-0.273719\pi$
$379$	7.98002e25			1.30500			0.652502	+	0.757787i	$0.273719\pi$
$380$	−1.11614e25	−	1.38589e25i	−0.177780	−	0.220746i
$381$		−	1.28396e26i		−	1.99206i
$382$	−2.49782e25	+	8.80761e24i	−0.377509	+	0.133114i
$383$			3.01797e25i			0.444352i	0.975007	+	0.222176i	$0.0713160\pi$
$383$			3.01797e25i			0.444352i	−0.975007	+	0.222176i	$0.928684\pi$
$384$	6.92118e25	−	7.15777e25i	0.992814	−	1.02675i
$385$	9.29678e24			0.129935
$386$	−9.13445e24	−	2.59051e25i	−0.124397	−	0.352787i
$387$	−4.95983e25			−0.658199
$388$	6.41728e24	−	5.16820e24i	0.0829915	−	0.0668378i
$389$			9.38588e25i			1.18298i	0.806311	+	0.591492i	$0.201461\pi$
$389$			9.38588e25i			1.18298i	−0.806311	+	0.591492i	$0.798539\pi$
$390$	2.72697e25	+	7.73365e25i	0.334992	+	0.950032i
$391$		−	4.19168e25i		−	0.501904i
$392$	5.83202e25	+	3.60619e25i	0.680704	+	0.420908i
$393$	−6.86441e25			−0.781048
$394$	−4.53271e25	+	1.59829e25i	−0.502801	+	0.177293i
$395$	7.98366e25			0.863438
$396$	−4.48278e25	+	3.61024e25i	−0.472711	+	0.380701i
$397$			4.72991e25i			0.486349i	0.969983	+	0.243174i	$0.0781887\pi$
$397$			4.72991e25i			0.486349i	−0.969983	+	0.243174i	$0.921811\pi$
$398$	−5.80783e25	+	2.04791e25i	−0.582348	+	0.205343i
$399$		−	3.71316e25i		−	0.363090i
$400$	1.68030e25	−	7.70203e25i	0.160246	−	0.734522i
$401$	−1.29001e26			−1.19991			−0.599957	−	0.800032i	$-0.704816\pi$
$401$	−1.29001e26			−1.19991			−0.599957	+	0.800032i	$0.704816\pi$
$402$	8.39508e25	+	2.38083e26i	0.761666	+	2.16007i
$403$	−2.17094e26			−1.92131
$404$	−1.00867e26	−	1.25245e26i	−0.870833	−	1.08130i
$405$		−	5.66955e25i		−	0.477527i
$406$	3.24967e25	+	9.21601e25i	0.267042	+	0.757325i
$407$		−	1.08612e25i		−	0.0870830i
$408$	2.74349e26	+	1.69642e26i	2.14636	+	1.32718i
$409$	9.77077e25			0.745926			0.372963	−	0.927846i	$-0.378342\pi$
$409$	9.77077e25			0.745926			0.372963	+	0.927846i	$0.378342\pi$
$410$	1.51975e25	−	5.35881e24i	0.113223	−	0.0399236i
$411$	−1.65128e26			−1.20061
$412$	4.64679e25	+	5.76985e25i	0.329747	+	0.409442i
$413$		−	3.46152e25i		−	0.239754i
$414$	−4.12060e25	+	1.45297e25i	−0.278585	+	0.0982322i
$415$		−	6.33604e25i		−	0.418155i
$416$	−2.72222e25	−	2.18050e26i	−0.175384	−	1.40482i
$417$	−2.80958e26			−1.76718
$418$	−1.79814e25	−	5.09950e25i	−0.110423	−	0.313159i
$419$	1.45698e26			0.873603			0.436801	−	0.899558i	$-0.356111\pi$
$419$	1.45698e26			0.873603			0.436801	+	0.899558i	$0.356111\pi$
$420$	−4.22962e25	+	3.40636e25i	−0.247633	+	0.199433i
$421$		−	1.12181e26i		−	0.641354i	−0.947189	−	0.320677i	$-0.896090\pi$
$421$		−	1.12181e26i		−	0.641354i	0.947189	−	0.320677i	$-0.103910\pi$
$422$	−8.67543e25	−	2.46033e26i	−0.484358	−	1.37363i
$423$		−	1.55440e26i		−	0.847539i
$424$	−1.89051e26	+	3.05738e26i	−1.00675	+	1.62814i
$425$	2.55386e26			1.32834
$426$	2.86065e26	−	1.00870e26i	1.45334	−	0.512466i
$427$	1.88339e25			0.0934676
$428$	−1.38076e26	+	1.11200e26i	−0.669391	+	0.539099i
$429$			2.49184e26i			1.18018i
$430$	−6.42695e25	+	2.26622e25i	−0.297386	+	0.104862i
$431$			1.82538e26i			0.825240i	0.910903	+	0.412620i	$0.135386\pi$
$431$			1.82538e26i			0.825240i	−0.910903	+	0.412620i	$0.864614\pi$
$432$	2.74966e24	−	1.26037e25i	0.0121462	−	0.0556749i
$433$	−2.27223e26			−0.980785			−0.490392	−	0.871502i	$-0.663147\pi$
$433$	−2.27223e26			−0.980785			−0.490392	+	0.871502i	$0.663147\pi$
$434$	−4.78105e25	−	1.35590e26i	−0.201663	−	0.571912i
$435$	3.10219e26			1.27872
$436$	9.66661e25	+	1.20029e26i	0.389412	+	0.483527i
$437$		−	4.10467e25i		−	0.161608i
$438$	−1.56633e25	−	4.44207e25i	−0.0602755	−	0.170940i
$439$			2.33052e26i			0.876614i	0.898825	+	0.438307i	$0.144422\pi$
$439$			2.33052e26i			0.876614i	−0.898825	+	0.438307i	$0.855578\pi$
$440$	−4.15922e25	+	6.72640e25i	−0.152927	+	0.247318i
$441$	2.31549e26			0.832258
$442$	6.71370e26	−	2.36733e26i	2.35906	−	0.831832i
$443$	−1.40927e26			−0.484124			−0.242062	−	0.970261i	$-0.577824\pi$
$443$	−1.40927e26			−0.484124			−0.242062	+	0.970261i	$0.577824\pi$
$444$	3.97956e25	+	4.94136e25i	0.133661	+	0.165965i
$445$		−	1.18690e26i		−	0.389774i
$446$	−3.40229e26	+	1.19969e26i	−1.09250	+	0.385230i
$447$		−	6.04374e26i		−	1.89771i
$448$	1.30191e26	−	6.50231e25i	0.399763	−	0.199658i
$449$	1.40666e26			0.422400			0.211200	−	0.977443i	$-0.432263\pi$
$449$	1.40666e26			0.422400			0.211200	+	0.977443i	$0.432263\pi$
$450$	−8.85251e25	−	2.51056e26i	−0.259981	−	0.737301i
$451$	4.89674e25			0.140651
$452$	−1.56924e26	+	1.26380e26i	−0.440863	+	0.355052i
$453$			3.67193e26i			1.00905i
$454$	−1.44154e26	−	4.08817e26i	−0.387496	−	1.09893i
$455$			1.19855e26i			0.315168i
$456$	2.68654e26	+	1.66120e26i	0.691107	+	0.427341i
$457$	1.27721e26			0.321441			0.160720	−	0.987000i	$-0.448618\pi$
$457$	1.27721e26			0.321441			0.160720	+	0.987000i	$0.448618\pi$
$458$	9.37575e25	−	3.30600e25i	0.230861	−	0.0814044i
$459$	4.17916e25			0.100684
$460$	−4.67559e25	+	3.76552e25i	−0.110219	+	0.0887660i
$461$			3.61599e26i			0.834100i	0.908883	+	0.417050i	$0.136936\pi$
$461$			3.61599e26i			0.834100i	−0.908883	+	0.417050i	$0.863064\pi$
$462$	−1.55632e26	+	5.48777e25i	−0.351301	+	0.123873i
$463$		−	4.74287e26i		−	1.04769i	−0.851815	−	0.523843i	$-0.824498\pi$
$463$		−	4.74287e26i		−	1.04769i	0.851815	−	0.523843i	$-0.175502\pi$
$464$	−8.12181e26	−	1.77188e26i	−1.75579	−	0.383050i
$465$	−4.56406e26			−0.965655
$466$	1.70123e26	+	4.82466e26i	0.352293	+	0.999096i
$467$	3.26188e26			0.661150			0.330575	−	0.943780i	$-0.392757\pi$
$467$	3.26188e26			0.661150			0.330575	+	0.943780i	$0.392757\pi$
$468$	−4.65437e26	−	5.77925e26i	−0.923426	−	1.14660i
$469$			3.68978e26i			0.716592i
$470$	−7.10228e25	−	2.01419e26i	−0.135027	−	0.382933i
$471$		−	3.09515e26i		−	0.576067i
$472$	2.50448e26	+	1.54863e26i	0.456349	+	0.282180i
$473$	−2.07081e26			−0.369428
$474$	−1.33650e27	+	4.71266e26i	−2.33446	+	0.823157i
$475$	2.50085e26			0.427712
$476$	2.95711e26	+	3.67180e26i	0.495220	+	0.614907i
$477$			1.21387e27i			1.99063i
$478$	4.43690e26	−	1.56450e26i	0.712527	−	0.251245i
$479$			9.19723e26i			1.44644i	0.690615	+	0.723222i	$0.257340\pi$
$479$			9.19723e26i			1.44644i	−0.690615	+	0.723222i	$0.742660\pi$
$480$	−5.72306e25	−	4.58416e26i	−0.0881488	−	0.706070i
$481$	1.40024e26			0.211228
$482$	−2.28608e26	−	6.48327e26i	−0.337769	−	0.957907i
$483$	−1.25271e26			−0.181292
$484$	3.62246e26	−	2.91737e26i	0.513511	−	0.413560i
$485$		−	3.82305e25i		−	0.0530876i
$486$	3.48597e26	+	9.88615e26i	0.474200	+	1.34482i
$487$		−	3.19780e26i		−	0.426149i	−0.977036	−	0.213074i	$-0.931652\pi$
$487$		−	3.19780e26i		−	0.426149i	0.977036	−	0.213074i	$-0.0683477\pi$
$488$	−8.42595e25	+	1.36267e26i	−0.110007	+	0.177906i
$489$	2.72608e25			0.0348698
$490$	3.00042e26	−	1.05798e26i	0.376029	−	0.132592i
$491$	7.81706e25			0.0959905			0.0479953	−	0.998848i	$-0.484717\pi$
$491$	7.81706e25			0.0959905			0.0479953	+	0.998848i	$0.484717\pi$
$492$	−2.22780e26	+	1.79418e26i	−0.268056	+	0.215881i
$493$		−	2.69306e27i		−	3.17524i
$494$	6.57433e26	−	2.31819e26i	0.759595	−	0.267842i
$495$			2.67059e26i			0.302381i
$496$	1.19491e27	+	2.60686e26i	1.32593	+	0.289269i
$497$	4.43340e26			0.482140
$498$	3.74009e26	+	1.06068e27i	0.398647	+	1.13056i
$499$	−9.10365e26			−0.951064			−0.475532	−	0.879698i	$-0.657744\pi$
$499$	−9.10365e26			−0.951064			−0.475532	+	0.879698i	$0.657744\pi$
$500$	−5.34585e26	−	6.63786e26i	−0.547415	−	0.679717i
$501$		−	1.17174e27i		−	1.17613i
$502$	1.93149e26	+	5.47766e26i	0.190044	+	0.538961i
$503$			1.52189e26i			0.146792i	0.997303	+	0.0733959i	$0.0233837\pi$
$503$			1.52189e26i			0.146792i	−0.997303	+	0.0733959i	$0.976616\pi$
$504$	2.58450e26	−	4.17973e26i	0.244383	−	0.395224i
$505$	−7.46138e26			−0.691680
$506$	−1.72042e26	+	6.06640e25i	−0.156361	+	0.0551348i
$507$	−1.60969e27			−1.43438
$508$	1.00131e27	+	1.24331e27i	0.874843	+	1.08628i
$509$		−	6.41114e26i		−	0.549234i	−0.961554	−	0.274617i	$-0.911449\pi$
$509$		−	6.41114e26i		−	0.549234i	0.961554	−	0.274617i	$-0.0885510\pi$
$510$	1.41145e27	−	4.97695e26i	1.18567	−	0.418082i
$511$		−	6.88427e25i		−	0.0567086i
$512$	−1.11999e26	+	1.23286e27i	−0.0904724	+	0.995899i
$513$	4.09241e25			0.0324194
$514$	−4.89476e26	−	1.38814e27i	−0.380277	−	1.07846i
$515$	3.43735e26			0.261910
$516$	9.42128e26	−	7.58750e26i	0.704066	−	0.567024i
$517$		−	6.48988e26i		−	0.475698i
$518$	3.08374e25	+	8.74543e25i	0.0221707	+	0.0628758i
$519$			3.79020e26i			0.267293i
$520$	−8.67175e26	−	5.36211e26i	−0.599892	−	0.370939i
$521$	1.33712e27			0.907388			0.453694	−	0.891157i	$-0.350106\pi$
$521$	1.33712e27			0.907388			0.453694	+	0.891157i	$0.350106\pi$
$522$	−2.64739e27	+	9.33500e26i	−1.76243	+	0.621454i
$523$	−4.93173e26			−0.322094			−0.161047	−	0.986947i	$-0.551487\pi$
$523$	−4.93173e26			−0.322094			−0.161047	+	0.986947i	$0.551487\pi$
$524$	6.64705e26	−	5.35325e26i	0.425908	−	0.343008i
$525$		−	7.63237e26i		−	0.479807i
$526$	3.91078e26	−	1.37899e26i	0.241216	−	0.0850556i
$527$			3.96213e27i			2.39785i
$528$	2.99221e26	−	1.37154e27i	0.177686	−	0.814461i
$529$	1.57768e27			0.919308
$530$	5.54637e26	+	1.57294e27i	0.317139	+	0.899400i
$531$	9.94356e26			0.557952
$532$	2.89573e26	+	3.59558e26i	0.159456	+	0.197994i
$533$			6.31294e26i			0.341161i
$534$	7.00610e26	+	1.98692e27i	0.371590	+	1.05382i
$535$			8.22578e26i			0.428192i
$536$	−2.66963e27	−	1.65074e27i	−1.36396	−	0.843396i
$537$	−2.93469e27			−1.47170
$538$	−7.09712e26	+	2.50253e26i	−0.349349	+	0.123184i
$539$	9.66757e26			0.467121
$540$	−3.75428e25	−	4.66163e25i	−0.0178069	−	0.0221106i
$541$			2.72131e27i			1.26708i	0.773709	+	0.633541i	$0.218399\pi$
$541$			2.72131e27i			1.26708i	−0.773709	+	0.633541i	$0.781601\pi$
$542$	−3.96957e27	+	1.39972e27i	−1.81447	+	0.639805i
$543$		−	1.97489e27i		−	0.886225i
$544$	−3.97958e27	+	4.96828e26i	−1.75327	+	0.218885i
$545$	7.15064e26			0.309300
$546$	−7.07490e26	−	2.00643e27i	−0.300465	−	0.852113i
$547$	−3.35783e26			−0.140019			−0.0700093	−	0.997546i	$-0.522303\pi$
$547$	−3.35783e26			−0.140019			−0.0700093	+	0.997546i	$0.522303\pi$
$548$	1.59899e27	−	1.28776e27i	0.654696	−	0.527264i
$549$			5.41022e26i			0.217516i
$550$	−3.69607e26	−	1.04820e27i	−0.145920	−	0.413825i
$551$		−	2.63715e27i		−	1.02240i
$552$	5.60441e26	−	9.06360e26i	0.213373	−	0.345072i
$553$	−2.07129e27			−0.774444
$554$	6.16626e26	−	2.17430e26i	0.226425	−	0.0798401i
$555$	2.94379e26			0.106164
$556$	2.72061e27	−	2.19107e27i	0.963649	−	0.776082i
$557$			1.68401e27i			0.585859i	0.956134	+	0.292929i	$0.0946301\pi$
$557$			1.68401e27i			0.585859i	−0.956134	+	0.292929i	$0.905370\pi$
$558$	3.89494e27	−	1.37340e27i	1.33094	−	0.469306i
$559$		−	2.66972e27i		−	0.896080i
$560$	1.43922e26	−	6.59699e26i	0.0474512	−	0.217503i
$561$	4.54781e27			1.47290
$562$	1.45898e27	+	4.13763e27i	0.464179	+	1.31640i
$563$	1.64929e27			0.515481			0.257741	−	0.966214i	$-0.417022\pi$
$563$	1.64929e27			0.515481			0.257741	+	0.966214i	$0.417022\pi$
$564$	2.37791e27	+	2.95261e27i	0.730136	+	0.906599i
$565$			9.34862e26i			0.282009i
$566$	−1.39052e27	−	3.94349e27i	−0.412110	−	1.16874i
$567$			1.47092e27i			0.428309i
$568$	−1.98343e27	+	3.20765e27i	−0.567457	+	0.917706i
$569$	4.44042e26			0.124825			0.0624125	−	0.998050i	$-0.480121\pi$
$569$	4.44042e26			0.124825			0.0624125	+	0.998050i	$0.480121\pi$
$570$	1.38215e27	−	4.87363e26i	0.381775	−	0.134618i
$571$	1.78241e27			0.483777			0.241889	−	0.970304i	$-0.422233\pi$
$571$	1.78241e27			0.483777			0.241889	+	0.970304i	$0.422233\pi$
$572$	−1.94328e27	−	2.41293e27i	−0.518291	−	0.643554i
$573$		−	2.18135e27i		−	0.571715i
$574$	−3.94286e26	+	1.39030e26i	−0.101553	+	0.0358087i
$575$		−	8.43712e26i		−	0.213558i
$576$	1.86785e27	+	3.73988e27i	0.464641	+	0.930321i
$577$	−5.12768e26			−0.125361			−0.0626805	−	0.998034i	$-0.519965\pi$
$577$	−5.12768e26			−0.125361			−0.0626805	+	0.998034i	$0.519965\pi$
$578$	−2.93659e27	−	8.32811e27i	−0.705610	−	2.00110i
$579$	2.26230e27			0.534275
$580$	−3.00396e27	+	2.41926e27i	−0.697290	+	0.561568i
$581$			1.64383e27i			0.375056i
$582$	2.25670e26	+	6.39996e26i	0.0506109	+	0.143532i
$583$			5.06813e27i			1.11728i
$584$	4.98090e26	+	3.07990e26i	0.107939	+	0.0667434i
$585$	−3.44296e27			−0.733454
$586$	2.38984e27	−	8.42686e26i	0.500487	−	0.176478i
$587$	−4.59426e27			−0.945878			−0.472939	−	0.881095i	$-0.656807\pi$
$587$	−4.59426e27			−0.945878			−0.472939	+	0.881095i	$0.656807\pi$
$588$	−4.39832e27	+	3.54222e27i	−0.890253	+	0.716972i
$589$			3.87988e27i			0.772086i
$590$	1.28849e27	−	4.54336e26i	0.252092	−	0.0888908i
$591$		−	3.95843e27i		−	0.761462i
$592$	−7.70710e26	−	1.68141e26i	−0.145772	−	0.0318021i
$593$	5.91413e27			1.09988			0.549939	−	0.835205i	$-0.314651\pi$
$593$	5.91413e27			1.09988			0.549939	+	0.835205i	$0.314651\pi$
$594$	−6.04828e25	−	1.71528e26i	−0.0110603	−	0.0313668i
$595$	2.18745e27			0.393341
$596$	4.71325e27	+	5.85237e27i	0.833408	+	1.03483i
$597$		−	5.07199e27i		−	0.881932i
$598$	−7.82087e26	−	2.21798e27i	−0.133734	−	0.379268i
$599$		−	8.24036e27i		−	1.38573i	−0.721068	−	0.692864i	$-0.756349\pi$
$599$		−	8.24036e27i		−	1.38573i	0.721068	−	0.692864i	$-0.243651\pi$
$600$	5.52217e27	+	3.41459e27i	0.913266	+	0.564711i
$601$	−8.63115e27			−1.40386			−0.701930	−	0.712246i	$-0.747678\pi$
$601$	−8.63115e27			−1.40386			−0.701930	+	0.712246i	$0.747678\pi$
$602$	1.66742e27	−	5.87951e26i	0.266735	−	0.0940537i
$603$	−1.05993e28			−1.66764
$604$	−2.86357e27	−	3.55565e27i	−0.443138	−	0.550237i
$605$		−	2.15806e27i		−	0.328480i
$606$	1.24907e28	−	4.40436e27i	1.87008	−	0.659412i
$607$		−	3.90613e27i		−	0.575254i	−0.957742	−	0.287627i	$-0.907134\pi$
$607$		−	3.90613e27i		−	0.575254i	0.957742	−	0.287627i	$-0.0928664\pi$
$608$	−3.89697e27	+	4.86514e26i	−0.564536	+	0.0704790i
$609$	−8.04836e27			−1.14692
$610$	2.47200e26	+	7.01056e26i	0.0346538	+	0.0982775i
$611$	8.36683e27			1.15385
$612$	−1.05476e28	+	8.49459e27i	−1.43100	+	1.15247i
$613$			8.78457e27i			1.17251i	0.810127	+	0.586254i	$0.199398\pi$
$613$			8.78457e27i			1.17251i	−0.810127	+	0.586254i	$0.800602\pi$
$614$	2.86144e27	+	8.11498e27i	0.375751	+	1.06562i
$615$			1.32720e27i			0.171469i
$616$	1.07907e27	−	1.74511e27i	0.137165	−	0.221827i
$617$	−9.93663e27			−1.24276			−0.621381	−	0.783509i	$-0.713428\pi$
$617$	−9.93663e27			−1.24276			−0.621381	+	0.783509i	$0.713428\pi$
$618$	−5.75429e27	+	2.02903e27i	−0.708120	+	0.249691i
$619$	−1.10877e28			−1.34256			−0.671281	−	0.741203i	$-0.734256\pi$
$619$	−1.10877e28			−1.34256			−0.671281	+	0.741203i	$0.734256\pi$
$620$	4.41954e27	−	3.55931e27i	0.526575	−	0.424081i
$621$		−	1.38066e26i		−	0.0161871i
$622$	−1.44627e28	+	5.09970e27i	−1.66857	+	0.588357i
$623$			3.07930e27i			0.349600i
$624$	1.76821e28	+	3.85759e27i	1.97555	+	0.430993i
$625$	2.88311e27			0.317001
$626$	5.04983e27	+	1.43212e28i	0.546428	+	1.54966i
$627$	4.45340e27			0.474260
$628$	2.41377e27	+	2.99714e27i	0.252988	+	0.314131i
$629$		−	2.55554e27i		−	0.263619i
$630$	−7.58241e26	−	2.15036e27i	−0.0769843	−	0.218326i
$631$		−	1.33853e28i		−	1.33763i	−0.743429	−	0.668815i	$-0.766802\pi$
$631$		−	1.33853e28i		−	1.33763i	0.743429	−	0.668815i	$-0.233198\pi$
$632$	9.26661e27	−	1.49862e28i	0.911486	−	1.47408i
$633$	2.14862e28			2.08028
$634$	5.86761e27	−	2.06899e27i	0.559202	−	0.197181i
$635$	7.40692e27			0.694865
$636$	−1.85697e28	−	2.30578e28i	−1.71488	−	2.12934i
$637$			1.24635e28i			1.13305i
$638$	−1.10533e28	+	3.89752e27i	−0.989201	+	0.348804i
$639$			1.27354e28i			1.12203i
$640$	4.12917e27	+	3.99269e27i	0.358148	+	0.346310i
$641$	6.17579e27			0.527366			0.263683	−	0.964609i	$-0.415063\pi$
$641$	6.17579e27			0.527366			0.263683	+	0.964609i	$0.415063\pi$
$642$	−4.85558e27	−	1.37703e28i	−0.408216	−	1.15769i
$643$	1.45988e28			1.20839			0.604195	−	0.796837i	$-0.293495\pi$
$643$	1.45988e28			1.20839			0.604195	+	0.796837i	$0.293495\pi$
$644$	1.21304e27	−	9.76932e26i	0.0988592	−	0.0796170i
$645$		−	5.61267e27i		−	0.450373i
$646$	−4.23088e27	−	1.19987e28i	−0.334276	−	0.948000i
$647$			1.88186e27i			0.146401i	0.997317	+	0.0732004i	$0.0233213\pi$
$647$			1.88186e27i			0.146401i	−0.997317	+	0.0732004i	$0.976679\pi$
$648$	−1.06424e28	−	6.58063e27i	−0.815245	−	0.504101i
$649$	4.15160e27			0.313162
$650$	1.35135e28	−	4.76502e27i	1.00377	−	0.353941i
$651$	1.18411e28			0.866126
$652$	−2.63976e26	+	2.12595e26i	−0.0190146	+	0.0153136i
$653$		−	7.52706e27i		−	0.533941i	−0.963705	−	0.266971i	$-0.913977\pi$
$653$		−	7.52706e27i		−	0.533941i	0.963705	−	0.266971i	$-0.0860227\pi$
$654$	−1.19705e28	+	4.22094e27i	−0.836247	+	0.294870i
$655$		−	3.95994e27i		−	0.272443i
$656$	7.58059e26	−	3.47473e27i	0.0513647	−	0.235441i
$657$	1.97757e27			0.131971
$658$	1.84263e27	+	5.22565e27i	0.121110	+	0.343464i
$659$	−2.74243e28			−1.77534			−0.887669	−	0.460482i	$-0.847677\pi$
$659$	−2.74243e28			−1.77534			−0.887669	+	0.460482i	$0.847677\pi$
$660$	−4.08544e27	−	5.07283e27i	−0.260495	−	0.323453i
$661$		−	1.11450e28i		−	0.699950i	−0.936759	−	0.349975i	$-0.886190\pi$
$661$		−	1.11450e28i		−	0.699950i	0.936759	−	0.349975i	$-0.113810\pi$
$662$	2.80604e27	+	7.95786e27i	0.173585	+	0.492285i
$663$			5.86309e28i			3.57265i
$664$	−1.18934e28	−	7.35422e27i	−0.713883	−	0.441424i
$665$	2.14204e27			0.126652
$666$	−2.51221e27	+	8.85834e26i	−0.146323	+	0.0515953i
$667$	−8.89697e27			−0.510486
$668$	9.13788e27	+	1.13464e28i	0.516512	+	0.641345i
$669$		−	2.97123e28i		−	1.65453i
$670$	−1.37345e28	+	4.84295e27i	−0.753469	+	0.265682i
$671$			2.25885e27i			0.122085i
$672$	1.48480e27	+	1.18932e28i	0.0790633	+	0.633296i
$673$	−8.66157e27			−0.454408			−0.227204	−	0.973847i	$-0.572958\pi$
$673$	−8.66157e27			−0.454408			−0.227204	+	0.973847i	$0.572958\pi$
$674$	1.09475e28	+	3.10468e28i	0.565867	+	1.60479i
$675$	8.41193e26			0.0428408
$676$	1.55872e28	−	1.25533e28i	0.782171	−	0.629927i
$677$			6.27182e27i			0.310104i	0.987906	+	0.155052i	$0.0495545\pi$
$677$			6.27182e27i			0.310104i	−0.987906	+	0.155052i	$0.950446\pi$
$678$	−5.51838e27	−	1.56500e28i	−0.268853	−	0.762461i
$679$			9.91858e26i			0.0476159i
$680$	−9.78628e27	+	1.58266e28i	−0.462944	+	0.748686i
$681$	3.57021e28			1.66426
$682$	1.62620e28	−	5.73418e27i	0.747018	−	0.263407i
$683$	−2.46439e28			−1.11559			−0.557793	−	0.829980i	$-0.688352\pi$
$683$	−2.46439e28			−1.11559			−0.557793	+	0.829980i	$0.688352\pi$
$684$	−1.03287e28	+	8.31826e27i	−0.460768	+	0.371083i
$685$		−	9.52587e27i		−	0.418792i
$686$	−1.75108e28	+	6.17450e27i	−0.758689	+	0.267523i
$687$			8.18786e27i			0.349626i
$688$	−3.20580e27	+	1.46945e28i	−0.134912	+	0.618401i
$689$	−6.53389e28			−2.71006
$690$	−1.64422e27	−	4.66298e27i	−0.0672154	−	0.190622i
$691$	3.79505e28			1.52910			0.764552	−	0.644562i	$-0.222960\pi$
$691$	3.79505e28			1.52910			0.764552	+	0.644562i	$0.222960\pi$
$692$	−2.95580e27	−	3.67018e27i	−0.117386	−	0.145756i
$693$		−	6.92862e27i		−	0.271215i
$694$	4.34097e27	+	1.23109e28i	0.167491	+	0.475002i
$695$		−	1.62079e28i		−	0.616422i
$696$	3.60070e28	−	5.82315e28i	1.34988	−	2.18306i
$697$	1.15216e28			0.425780
$698$	1.10010e28	−	3.87910e27i	0.400756	−	0.141311i
$699$	−4.21338e28			−1.51307
$700$	5.95215e27	+	7.39069e27i	0.210714	+	0.261640i
$701$		−	2.03325e27i		−	0.0709596i	−0.999370	−	0.0354798i	$-0.988704\pi$
$701$		−	2.03325e27i		−	0.0709596i	0.999370	−	0.0354798i	$-0.0112959\pi$
$702$	2.21136e27	−	7.79751e26i	0.0760831	−	0.0268278i
$703$		−	2.50250e27i		−	0.0848829i
$704$	7.79860e27	+	1.56146e28i	0.260789	+	0.522161i
$705$	1.75900e28			0.579929
$706$	−8.43208e27	−	2.39132e28i	−0.274086	−	0.777304i
$707$	1.93579e28			0.620389
$708$	−1.88880e28	+	1.52116e28i	−0.596833	+	0.480664i
$709$			3.94725e28i			1.22979i	0.788608	+	0.614896i	$0.210802\pi$
$709$			3.94725e28i			1.22979i	−0.788608	+	0.614896i	$0.789198\pi$
$710$	5.81897e27	+	1.65025e28i	0.178757	+	0.506951i
$711$		−	5.94999e28i		−	1.80227i
$712$	−2.22793e28	−	1.37763e28i	−0.665430	−	0.411464i
$713$	1.30896e28			0.385505
$714$	−3.66189e28	+	1.29123e28i	−1.06347	+	0.374990i
$715$	−1.43749e28			−0.411666
$716$	2.84176e28	−	2.28863e28i	0.802523	−	0.646318i
$717$			3.87476e28i			1.07908i
$718$	4.68692e28	−	1.65266e28i	1.28719	−	0.453878i
$719$		−	2.52527e28i		−	0.683942i	−0.939710	−	0.341971i	$-0.888905\pi$
$719$		−	2.52527e28i		−	0.683942i	0.939710	−	0.341971i	$-0.111095\pi$
$720$	1.89505e28	+	4.13431e27i	0.506169	+	0.110428i
$721$	−8.91792e27			−0.234915
$722$	8.65727e27	+	2.45519e28i	0.224910	+	0.637841i
$723$	5.66185e28			1.45069
$724$	1.54013e28	+	1.91235e28i	0.389198	+	0.483261i
$725$		−	5.42065e28i		−	1.35105i
$726$	1.27387e28	+	3.61268e28i	0.313156	+	0.888103i
$727$		−	6.02907e28i		−	1.46186i	−0.682452	−	0.730931i	$-0.739086\pi$
$727$		−	6.02907e28i		−	1.46186i	0.682452	−	0.730931i	$-0.260914\pi$
$728$	2.24981e28	+	1.39115e28i	0.538062	+	0.332707i
$729$	−4.57036e28			−1.07814
$730$	2.56254e27	−	9.03581e26i	0.0596268	−	0.0210251i
$731$	−4.87244e28			−1.11834
$732$	−8.27649e27	−	1.02768e28i	−0.187385	−	0.232673i
$733$			2.73732e28i			0.611345i	0.952137	+	0.305673i	$0.0988813\pi$
$733$			2.73732e28i			0.611345i	−0.952137	+	0.305673i	$0.901119\pi$
$734$	5.01778e28	−	1.76933e28i	1.10548	−	0.389805i
$735$			2.62027e28i			0.569473i
$736$	1.64136e27	+	1.31472e28i	0.0351904	+	0.281874i
$737$	−4.42536e28			−0.935996
$738$	−3.99376e27	−	1.13262e28i	−0.0833334	−	0.236332i
$739$	8.14966e28			1.67763			0.838813	−	0.544419i	$-0.183250\pi$
$739$	8.14966e28			1.67763			0.838813	+	0.544419i	$0.183250\pi$
$740$	−2.85057e27	+	2.29573e27i	−0.0578915	+	0.0466233i
$741$			5.74138e28i			1.15036i
$742$	−1.43896e28	−	4.08085e28i	−0.284452	−	0.806700i
$743$			4.08224e28i			0.796178i	0.917347	+	0.398089i	$0.130326\pi$
$743$			4.08224e28i			0.796178i	−0.917347	+	0.398089i	$0.869674\pi$
$744$	−5.29749e28	+	8.56724e28i	−1.01939	+	1.64859i
$745$	3.48651e28			0.661955
$746$	−3.32978e28	+	1.17412e28i	−0.623774	+	0.219950i
$747$	−4.72207e28			−0.872823
$748$	−4.40380e28	+	3.54663e28i	−0.803177	+	0.646845i
$749$		−	2.13411e28i		−	0.384059i
$750$	6.61995e28	−	2.33427e28i	1.17555	−	0.414514i
$751$		−	1.72660e28i		−	0.302547i	−0.988492	−	0.151273i	$-0.951663\pi$
$751$		−	1.72660e28i		−	0.302547i	0.988492	−	0.151273i	$-0.0483374\pi$
$752$	−4.60522e28	−	1.00469e28i	−0.796291	−	0.173722i
$753$	−4.78365e28			−0.816225
$754$	−5.02472e28	−	1.42500e29i	−0.846055	−	2.39940i
$755$	−2.11826e28			−0.351973
$756$	9.74015e26	+	1.20942e27i	0.0159716	+	0.0198316i
$757$			6.18361e28i			1.00065i	0.865837	+	0.500326i	$0.166787\pi$
$757$			6.18361e28i			1.00065i	−0.865837	+	0.500326i	$0.833213\pi$
$758$	−2.71739e28	−	7.70648e28i	−0.433971	−	1.23073i
$759$		−	1.50245e28i		−	0.236800i
$760$	−9.58314e27	+	1.54981e28i	−0.149064	+	0.241070i
$761$	6.86927e28			1.05454			0.527271	−	0.849697i	$-0.323215\pi$
$761$	6.86927e28			1.05454			0.527271	+	0.849697i	$0.323215\pi$
$762$	−1.23995e29	+	4.37222e28i	−1.87869	+	0.662448i
$763$	−1.85517e28			−0.277421
$764$	1.70114e28	+	2.11228e28i	0.251077	+	0.311758i
$765$			6.28367e28i			0.915375i
$766$	2.91452e28	−	1.02769e28i	0.419063	−	0.147767i
$767$			5.35230e28i			0.759603i
$768$	−9.26925e28	−	4.24654e28i	−1.29847	−	0.594871i
$769$	1.05970e29			1.46528			0.732638	−	0.680619i	$-0.238289\pi$
$769$	1.05970e29			1.46528			0.732638	+	0.680619i	$0.238289\pi$
$770$	−3.16578e27	−	8.97810e27i	−0.0432090	−	0.122540i
$771$	1.21227e29			1.63326
$772$	−2.19066e28	+	1.76427e28i	−0.291342	+	0.234634i
$773$		−	1.36439e29i		−	1.79120i	−0.444857	−	0.895601i	$-0.646746\pi$
$773$		−	1.36439e29i		−	1.79120i	0.444857	−	0.895601i	$-0.353254\pi$
$774$	1.68895e28	+	4.78982e28i	0.218880	+	0.620740i
$775$			7.97508e28i			1.02028i
$776$	−7.17629e27	−	4.43740e27i	−0.0906322	−	0.0560417i
$777$	−7.63740e27			−0.0952216
$778$	9.06415e28	−	3.19613e28i	1.11566	−	0.393394i
$779$	1.12825e28			0.137097
$780$	6.53995e28	−	5.26700e28i	0.784564	−	0.631855i
$781$			5.31723e28i			0.629760i
$782$	−4.04800e28	+	1.42737e28i	−0.473340	+	0.166905i
$783$		−	8.87040e27i		−	0.102406i
$784$	1.49662e28	−	6.86011e28i	0.170590	−	0.781934i
$785$	1.78553e28			0.200942
$786$	2.33750e28	+	6.62911e28i	0.259733	+	0.736597i
$787$	2.50792e28			0.275148			0.137574	−	0.990492i	$-0.456070\pi$
$787$	2.50792e28			0.275148			0.137574	+	0.990492i	$0.456070\pi$
$788$	3.08700e28	+	3.83308e28i	0.334407	+	0.415228i
$789$			3.41530e28i			0.365307i
$790$	−2.71863e28	−	7.71000e28i	−0.287131	−	0.814298i
$791$		−	2.42542e28i		−	0.252943i
$792$	5.01299e28	+	3.09974e28i	0.516232	+	0.319208i
$793$	−2.91214e28			−0.296129
$794$	4.56778e28	−	1.61065e28i	0.458670	−	0.161732i
$795$	−1.37365e29			−1.36209
$796$	3.95542e28	+	4.91138e28i	0.387313	+	0.480920i
$797$			3.02327e28i			0.292343i	0.989259	+	0.146172i	$0.0466952\pi$
$797$			3.02327e28i			0.292343i	−0.989259	+	0.146172i	$0.953305\pi$
$798$	−3.58588e28	+	1.26442e28i	−0.342426	+	0.120743i
$799$		−	1.52701e29i		−	1.44004i
$800$	−8.01020e28	+	1.00003e28i	−0.746008	+	0.0931348i
$801$	−8.84559e28			−0.813583
$802$	4.39281e28	+	1.24579e29i	0.399024	+	1.13162i
$803$	8.25669e27			0.0740714
$804$	2.01335e29	−	1.62146e29i	1.78385	−	1.43664i
$805$		−	7.22662e27i		−	0.0632378i
$806$	7.39257e28	+	2.09652e29i	0.638918	+	1.81196i
$807$		−	6.19793e28i		−	0.529068i
$808$	−8.66040e28	+	1.40058e29i	−0.730170	+	1.18085i
$809$	−8.70610e28			−0.725001			−0.362500	−	0.931984i	$-0.618077\pi$
$809$	−8.70610e28			−0.725001			−0.362500	+	0.931984i	$0.618077\pi$
$810$	−5.47521e28	+	1.93062e28i	−0.450350	+	0.158799i
$811$	3.36143e28			0.273096			0.136548	−	0.990633i	$-0.456399\pi$
$811$	3.36143e28			0.273096			0.136548	+	0.990633i	$0.456399\pi$
$812$	7.79350e28	−	6.27656e28i	0.625421	−	0.503688i
$813$		−	3.46664e29i		−	2.74791i
$814$	−1.04889e28	+	3.69851e27i	−0.0821269	+	0.0289589i
$815$			1.57262e27i			0.0121632i
$816$	7.04041e28	−	3.22712e29i	0.537893	−	2.46555i
$817$	−4.77130e28			−0.360094
$818$	−3.32719e28	−	9.43585e28i	−0.248053	−	0.703474i
$819$	8.93245e28			0.657857
$820$	−1.03502e28	−	1.28517e28i	−0.0753029	−	0.0935025i
$821$			4.64099e28i			0.333564i	0.985994	+	0.166782i	$0.0533376\pi$
$821$			4.64099e28i			0.333564i	−0.985994	+	0.166782i	$0.946662\pi$
$822$	5.62300e28	+	1.59467e29i	0.399255	+	1.13228i
$823$			1.17639e29i			0.825186i	0.910915	+	0.412593i	$0.135377\pi$
$823$			1.17639e29i			0.825186i	−0.910915	+	0.412593i	$0.864623\pi$
$824$	3.98972e28	−	6.45229e28i	0.276484	−	0.447138i
$825$	9.15394e28			0.626713
$826$	−3.34287e28	+	1.17873e28i	−0.226110	+	0.0797289i
$827$	−2.44978e29			−1.63709			−0.818545	−	0.574442i	$-0.805219\pi$
$827$	−2.44978e29			−1.63709			−0.818545	+	0.574442i	$0.805219\pi$
$828$	2.80633e28	+	3.48458e28i	0.185283	+	0.230063i
$829$			5.12749e28i			0.334472i	0.985917	+	0.167236i	$0.0534841\pi$
$829$			5.12749e28i			0.334472i	−0.985917	+	0.167236i	$0.946516\pi$
$830$	−6.11886e28	+	2.15758e28i	−0.394357	+	0.139055i
$831$			5.38501e28i			0.342907i
$832$	−2.01305e29	+	1.00540e29i	−1.26655	+	0.632568i
$833$	2.27470e29			1.41408
$834$	9.56732e28	+	2.71327e29i	0.587665	+	1.66661i
$835$	6.75952e28			0.410253
$836$	−4.31238e28	+	3.47301e28i	−0.258616	+	0.208278i
$837$			1.30505e28i			0.0773343i
$838$	−4.96139e28	−	1.40704e29i	−0.290511	−	0.823884i
$839$			3.38731e29i			1.95991i	0.199228	+	0.979953i	$0.436157\pi$
$839$			3.38731e29i			1.95991i	−0.199228	+	0.979953i	$0.563843\pi$
$840$	4.72989e28	+	2.92469e28i	0.270432	+	0.167220i
$841$	−3.94615e29			−2.22953
$842$	−1.08336e29	+	3.82004e28i	−0.604853	+	0.213278i
$843$	−3.61340e29			−1.99361
$844$	−2.08058e29	+	1.67561e29i	−1.13438	+	0.913584i
$845$		−	9.28599e28i		−	0.500335i
$846$	−1.50112e29	+	5.29312e28i	−0.799303	+	0.281844i
$847$			5.59889e28i			0.294624i
$848$	3.59634e29	+	7.84591e28i	1.87026	+	0.408023i
$849$	3.44386e29			1.76998
$850$	−8.69654e28	−	2.46632e29i	−0.441730	−	1.25274i
$851$	−8.44268e27			−0.0423823
$852$	−1.94824e29	−	2.41910e29i	−0.966601	−	1.20021i
$853$		−	2.20403e29i		−	1.08076i	−0.841423	−	0.540378i	$-0.818281\pi$
$853$		−	2.20403e29i		−	1.08076i	0.841423	−	0.540378i	$-0.181719\pi$
$854$	−6.41340e27	−	1.81883e28i	−0.0310821	−	0.0881481i
$855$			6.15323e28i			0.294742i
$856$	1.54407e29	+	9.54763e28i	0.731019	+	0.452020i
$857$	−3.05396e27			−0.0142908			−0.00714539	−	0.999974i	$-0.502274\pi$
$857$	−3.05396e27			−0.0142908			−0.00714539	+	0.999974i	$0.502274\pi$
$858$	2.40642e29	−	8.48533e28i	1.11301	−	0.392461i
$859$	−1.31353e29			−0.600494			−0.300247	−	0.953861i	$-0.597069\pi$
$859$	−1.31353e29			−0.600494			−0.300247	+	0.953861i	$0.597069\pi$
$860$	4.37707e28	+	5.43494e28i	0.197788	+	0.245590i
$861$		−	3.44331e28i		−	0.153796i
$862$	1.76281e29	−	6.21587e28i	0.778274	−	0.274428i
$863$			1.63710e29i			0.714441i	0.934020	+	0.357221i	$0.116276\pi$
$863$			1.63710e29i			0.714441i	−0.934020	+	0.357221i	$0.883724\pi$
$864$	−1.31080e28	+	1.63645e27i	−0.0565454	+	0.00705937i
$865$	−2.18649e28			−0.0932364
$866$	7.73751e28	+	2.19434e29i	0.326154	+	0.924966i
$867$	7.27296e29			3.03054
$868$	−1.14661e29	+	9.23432e28i	−0.472301	+	0.380371i
$869$		−	2.48422e29i		−	1.01156i
$870$	−1.05637e29	−	2.99585e29i	−0.425230	−	1.20595i
$871$		−	5.70523e29i		−	2.27034i
$872$	8.29972e28	−	1.34225e29i	0.326512	−	0.528043i
$873$	−2.84921e28			−0.110811
$874$	−3.96397e28	+	1.39774e28i	−0.152411	+	0.0537419i
$875$	1.02595e29			0.389984
$876$	−3.75643e28	+	3.02527e28i	−0.141167	+	0.113690i
$877$			3.08590e29i			1.14653i	0.819370	+	0.573265i	$0.194323\pi$
$877$			3.08590e29i			1.14653i	−0.819370	+	0.573265i	$0.805677\pi$
$878$	2.25064e29	−	7.93602e28i	0.826724	−	0.291513i
$879$			2.08705e29i			0.757957i
$880$	7.91215e28	+	1.72614e28i	0.284098	+	0.0619797i
$881$	2.88421e29			1.02392			0.511962	−	0.859008i	$-0.328919\pi$
$881$	2.88421e29			1.02392			0.511962	+	0.859008i	$0.328919\pi$
$882$	−7.88483e28	−	2.23612e29i	−0.276762	−	0.784892i
$883$	−2.99132e29			−1.03814			−0.519069	−	0.854732i	$-0.673721\pi$
$883$	−2.99132e29			−1.03814			−0.519069	+	0.854732i	$0.673721\pi$
$884$	−4.57236e29	−	5.67743e29i	−1.56898	−	1.94818i
$885$			1.12524e29i			0.381779i
$886$	4.79891e28	+	1.36096e29i	0.160993	+	0.456572i
$887$			5.86956e28i			0.194701i	0.995250	+	0.0973507i	$0.0310368\pi$
$887$			5.86956e28i			0.194701i	−0.995250	+	0.0973507i	$0.968963\pi$
$888$	3.41684e28	−	5.52581e28i	0.112072	−	0.181245i
$889$	−1.92166e29			−0.623246
$890$	−1.14621e29	+	4.04168e28i	−0.367591	+	0.129617i
$891$	−1.76415e29			−0.559448
$892$	2.31713e29	+	2.87714e29i	0.726611	+	0.902221i
$893$		−	1.49532e29i		−	0.463680i
$894$	−5.83658e29	+	2.05805e29i	−1.78971	+	0.631073i
$895$		−	1.69296e29i		−	0.513354i
$896$	−1.07128e29	−	1.03587e29i	−0.321234	−	0.310616i
$897$	1.93697e29			0.574379
$898$	−4.79001e28	−	1.35844e29i	−0.140467	−	0.398361i
$899$	8.40974e29			2.43885
$900$	−2.12305e29	+	1.70981e29i	−0.608884	+	0.490370i
$901$			1.19249e30i			3.38225i
$902$	−1.66746e28	−	4.72889e28i	−0.0467725	−	0.132646i
$903$			1.45616e29i			0.403954i
$904$	1.75484e29	+	1.08509e29i	0.481452	+	0.297702i
$905$	1.13927e29			0.309130
$906$	3.54606e29	−	1.25038e29i	0.951621	−	0.335553i
$907$	1.72537e29			0.457942			0.228971	−	0.973433i	$-0.426464\pi$
$907$	1.72537e29			0.457942			0.228971	+	0.973433i	$0.426464\pi$
$908$	−3.45715e29	+	2.78425e29i	−0.907529	+	0.730885i
$909$			5.56075e29i			1.44376i
$910$	1.15747e29	−	4.08136e28i	0.297231	−	0.104807i
$911$		−	5.22848e29i		−	1.32798i	−0.747741	−	0.663990i	$-0.768862\pi$
$911$		−	5.22848e29i		−	1.32798i	0.747741	−	0.663990i	$-0.231138\pi$
$912$	6.89426e28	−	3.16013e29i	0.173197	−	0.793884i
$913$	−1.97154e29			−0.489890
$914$	−4.34922e28	−	1.23343e29i	−0.106893	−	0.303147i
$915$	−6.12234e28			−0.148835
$916$	−6.38535e28	−	7.92859e28i	−0.153543	−	0.190652i
$917$			1.02737e29i			0.244362i
$918$	−1.42311e28	−	4.03591e28i	−0.0334820	−	0.0949543i
$919$		−	7.80290e29i		−	1.81594i	−0.419038	−	0.907969i	$-0.637632\pi$
$919$		−	7.80290e29i		−	1.81594i	0.419038	−	0.907969i	$-0.362368\pi$
$920$	5.22860e28	+	3.23307e28i	0.120367	+	0.0744280i
$921$	−7.08684e29			−1.61382
$922$	3.49204e29	−	1.23134e29i	0.786630	−	0.277375i
$923$	−6.85503e29			−1.52754
$924$	1.05993e29	+	1.31610e29i	0.233646	+	0.290115i
$925$		−	5.14387e28i		−	0.112169i
$926$	−4.58029e29	+	1.61506e29i	−0.988060	+	0.348401i
$927$		−	2.56176e29i		−	0.546690i
$928$	1.05453e29	+	8.44678e29i	0.222628	+	1.78325i
$929$	−4.97570e29			−1.03920			−0.519598	−	0.854411i	$-0.673918\pi$
$929$	−4.97570e29			−1.03920			−0.519598	+	0.854411i	$0.673918\pi$
$930$	1.55418e29	+	4.40761e29i	0.321123	+	0.910697i
$931$	2.22748e29			0.455320
$932$	4.07997e29	−	3.28583e29i	0.825083	−	0.664486i
$933$		−	1.26303e30i		−	2.52695i
$934$	−1.11075e29	−	3.15007e29i	−0.219861	−	0.623522i
$935$			2.62354e29i			0.513773i
$936$	−3.99623e29	+	6.46280e29i	−0.774268	+	1.25217i
$937$	2.52525e29			0.484070			0.242035	−	0.970268i	$-0.422185\pi$
$937$	2.52525e29			0.484070			0.242035	+	0.970268i	$0.422185\pi$
$938$	3.56330e29	−	1.25646e29i	0.675809	−	0.238298i
$939$	−1.25067e30			−2.34687
$940$	−1.70330e29	+	1.37177e29i	−0.316237	+	0.254684i
$941$			2.37447e29i			0.436185i	0.975928	+	0.218093i	$0.0699835\pi$
$941$			2.37447e29i			0.436185i	−0.975928	+	0.218093i	$0.930017\pi$
$942$	−2.98906e29	+	1.05398e29i	−0.543282	+	0.191568i
$943$		−	3.80636e28i		−	0.0684531i
$944$	6.42705e28	−	2.94598e29i	0.114365	−	0.524215i
$945$	7.20504e27			0.0126858
$946$	7.05163e28	+	1.99983e29i	0.122851	+	0.348403i
$947$	3.70419e29			0.638548			0.319274	−	0.947662i	$-0.396561\pi$
$947$	3.70419e29			0.638548			0.319274	+	0.947662i	$0.396561\pi$
$948$	9.10223e29	+	1.13021e30i	1.55262	+	1.92786i
$949$			1.06446e29i			0.179667i
$950$	−8.51601e28	−	2.41513e29i	−0.142233	−	0.403370i
$951$			5.12420e29i			0.846878i
$952$	2.53897e29	−	4.10609e29i	0.415229	−	0.671519i
$953$	1.08040e29			0.174846			0.0874232	−	0.996171i	$-0.472137\pi$
$953$	1.08040e29			0.174846			0.0874232	+	0.996171i	$0.472137\pi$
$954$	1.17227e30	−	4.13354e29i	1.87734	−	0.661971i
$955$	1.25838e29			0.199424
$956$	−3.02175e29	−	3.75206e29i	−0.473893	−	0.588425i
$957$		−	9.65286e29i		−	1.49809i
$958$	8.88196e29	−	3.13188e29i	1.36412	−	0.481006i
$959$			2.47140e29i			0.375628i
$960$	−4.23214e29	+	2.11371e29i	−0.636572	+	0.317931i
$961$	−5.65484e29			−0.841756
$962$	−4.76816e28	−	1.35224e29i	−0.0702425	−	0.199206i
$963$	6.13043e29			0.893775
$964$	−5.48257e29	+	4.41543e29i	−0.791068	+	0.637092i
$965$			1.30507e29i			0.186364i
$966$	4.26579e28	+	1.20977e29i	0.0602876	+	0.170974i
$967$		−	9.56100e29i		−	1.33733i	−0.743564	−	0.668665i	$-0.766866\pi$
$967$		−	9.56100e29i		−	1.33733i	0.743564	−	0.668665i	$-0.233134\pi$
$968$	−4.05091e29	−	2.50485e29i	−0.560788	−	0.346759i
$969$	1.04785e30			1.43569
$970$	−3.69201e28	+	1.30184e28i	−0.0500662	+	0.0176539i
$971$	4.95486e29			0.665026			0.332513	−	0.943099i	$-0.392103\pi$
$971$	4.95486e29			0.665026			0.332513	+	0.943099i	$0.392103\pi$
$972$	8.36021e29	−	6.73296e29i	1.11059	−	0.894424i
$973$			4.20500e29i			0.552888i
$974$	−3.08818e29	+	1.08893e29i	−0.401896	+	0.141713i
$975$			1.18014e30i			1.52015i
$976$	1.60288e29	+	3.49691e28i	0.204364	+	0.0445847i
$977$	8.15060e29			1.02859			0.514297	−	0.857612i	$-0.328053\pi$
$977$	8.15060e29			1.02859			0.514297	+	0.857612i	$0.328053\pi$
$978$	−9.28297e27	−	2.63263e28i	−0.0115957	−	0.0328853i
$979$	−3.69318e29			−0.456640
$980$	−2.04343e29	−	2.53730e29i	−0.250092	−	0.310535i
$981$		−	5.32916e29i		−	0.645608i
$982$	−2.66190e28	−	7.54910e28i	−0.0319210	−	0.0905275i
$983$			1.10181e30i			1.30789i	0.756542	+	0.653945i	$0.226887\pi$
$983$			1.10181e30i			1.30789i	−0.756542	+	0.653945i	$0.773113\pi$
$984$	2.49130e29	+	1.54048e29i	0.292735	+	0.181011i
$985$	2.28354e29			0.265611
$986$	−2.60074e30	+	9.17052e29i	−2.99453	+	1.05591i
$987$	−4.56357e29			−0.520156
$988$	−4.47745e29	−	5.55958e29i	−0.505197	−	0.627296i
$989$			1.60970e29i			0.179796i
$990$	2.57905e29	−	9.09402e28i	0.285172	−	0.100555i
$991$		−	1.03685e30i		−	1.13496i	−0.823388	−	0.567478i	$-0.807919\pi$
$991$		−	1.03685e30i		−	1.13496i	0.823388	−	0.567478i	$-0.192081\pi$
$992$	−1.55147e29	−	1.24272e30i	−0.168123	−	1.34666i
$993$	−6.94962e29			−0.745536
$994$	−1.50968e29	−	4.28143e29i	−0.160333	−	0.454700i
$995$	2.92593e29			0.307633
$996$	8.96965e29	−	7.22377e29i	0.933646	−	0.751918i
$997$			3.50619e29i			0.361313i	0.983546	+	0.180657i	$0.0578223\pi$
$997$			3.50619e29i			0.361313i	−0.983546	+	0.180657i	$0.942178\pi$
$998$	3.10002e29	+	8.79159e29i	0.316271	+	0.896937i
$999$		−	8.41747e27i		−	0.00850211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8.21.d.b.3.7	✓	18
3.2	odd	2		72.21.b.b.19.12		18
4.3	odd	2		32.21.d.b.15.2		18
8.3	odd	2	inner	8.21.d.b.3.8	yes	18
8.5	even	2		32.21.d.b.15.1		18
24.11	even	2		72.21.b.b.19.11		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8.21.d.b.3.7	✓	18	1.1	even	1	trivial
8.21.d.b.3.8	yes	18	8.3	odd	2	inner
32.21.d.b.15.1		18	8.5	even	2
32.21.d.b.15.2		18	4.3	odd	2
72.21.b.b.19.11		18	24.11	even	2
72.21.b.b.19.12		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8 = 2^{3} \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	8.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-340.525 - 965.722i) q^{2} +84336.7 q^{3} +(-816662. + 657705. i) q^{4} +4.86521e6i q^{5} +(-2.87188e7 - 8.14458e7i) q^{6} -1.26224e8i q^{7} +(9.13253e8 + 5.64703e8i) q^{8} +3.62590e9 q^{9} +O(q^{10})\)	\(q+(-340.525 - 965.722i) q^{2} +84336.7 q^{3} +(-816662. + 657705. i) q^{4} +4.86521e6i q^{5} +(-2.87188e7 - 8.14458e7i) q^{6} -1.26224e8i q^{7} +(9.13253e8 + 5.64703e8i) q^{8} +3.62590e9 q^{9} +(4.69844e9 - 1.65673e9i) q^{10} +1.51387e10 q^{11} +(-6.88746e10 + 5.54687e10i) q^{12} +1.95170e11i q^{13} +(-1.21897e11 + 4.29823e10i) q^{14} +4.10316e11i q^{15} +(2.34361e11 - 1.07424e12i) q^{16} +3.56201e12 q^{17} +(-1.23471e12 - 3.50161e12i) q^{18} +3.48807e12 q^{19} +(-3.19987e12 - 3.97323e12i) q^{20} -1.06453e13i q^{21} +(-5.15512e12 - 1.46198e13i) q^{22} -1.17677e13i q^{23} +(7.70208e13 + 4.76252e13i) q^{24} +7.16971e13 q^{25} +(1.88480e14 - 6.64604e13i) q^{26} +1.17326e13 q^{27} +(8.30179e13 + 1.03082e14i) q^{28} -7.56048e14i q^{29} +(3.96251e14 - 1.39723e14i) q^{30} +1.11233e15i q^{31} +(-1.11723e15 + 1.39479e14i) q^{32} +1.27675e15 q^{33} +(-1.21295e15 - 3.43992e15i) q^{34} +6.14105e14 q^{35} +(-2.96113e15 + 2.38477e15i) q^{36} -7.17444e14i q^{37} +(-1.18778e15 - 3.36851e15i) q^{38} +1.64600e16i q^{39} +(-2.74740e15 + 4.44317e15i) q^{40} +3.23458e15 q^{41} +(-1.02804e16 + 3.62499e15i) q^{42} -1.36789e16 q^{43} +(-1.23632e16 + 9.95682e15i) q^{44} +1.76408e16i q^{45} +(-1.13644e16 + 4.00720e15i) q^{46} -4.28694e16i q^{47} +(1.97652e16 - 9.05983e16i) q^{48} +6.38598e16 q^{49} +(-2.44147e16 - 6.92395e16i) q^{50} +3.00409e17 q^{51} +(-1.28364e17 - 1.59388e17i) q^{52} +3.34779e17i q^{53} +(-3.99524e15 - 1.13304e16i) q^{54} +7.36531e16i q^{55} +(7.12790e16 - 1.15274e17i) q^{56} +2.94173e17 q^{57} +(-7.30133e17 + 2.57453e17i) q^{58} +2.74237e17 q^{59} +(-2.69867e17 - 3.35089e17i) q^{60} +1.49210e17i q^{61} +(1.07420e18 - 3.78775e17i) q^{62} -4.57675e17i q^{63} +(5.15142e17 + 1.03143e18i) q^{64} -9.49545e17 q^{65} +(-4.34766e17 - 1.23299e18i) q^{66} -2.92321e18 q^{67} +(-2.90896e18 + 2.34275e18i) q^{68} -9.92452e17i q^{69} +(-2.09118e17 - 5.93055e17i) q^{70} +3.51233e18i q^{71} +(3.31137e18 + 2.04756e18i) q^{72} +5.45402e17 q^{73} +(-6.92851e17 + 2.44307e17i) q^{74} +6.04670e18 q^{75} +(-2.84858e18 + 2.29412e18i) q^{76} -1.91087e18i q^{77} +(1.58958e19 - 5.60505e18i) q^{78} -1.64097e19i q^{79} +(5.22643e18 + 1.14022e18i) q^{80} -1.16532e19 q^{81} +(-1.10145e18 - 3.12370e18i) q^{82} -1.30232e19 q^{83} +(7.00146e18 + 8.69361e18i) q^{84} +1.73300e19i q^{85} +(4.65801e18 + 1.32100e19i) q^{86} -6.37627e19i q^{87} +(1.38255e19 + 8.54889e18i) q^{88} -2.43956e19 q^{89} +(1.70361e19 - 6.00712e18i) q^{90} +2.46351e19 q^{91} +(7.73969e18 + 9.61025e18i) q^{92} +9.38101e19i q^{93} +(-4.13999e19 + 1.45981e19i) q^{94} +1.69702e19i q^{95} +(-9.42233e19 + 1.17632e19i) q^{96} -7.85794e18 q^{97} +(-2.17459e19 - 6.16708e19i) q^{98} +5.48915e19 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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