LMFDB - Embedded newform 20.9.b.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,9,Mod(11,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("20.11");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	20.b (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:	$8.14757220122$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 26 x^{14} - 834 x^{13} + 4390 x^{12} - 61783 x^{11} + 466168 x^{10} + \cdots + 206161212459445 $ x^16 - 5x^15 + 26x^14 - 834x^13 + 4390x^12 - 61783x^11 + 466168x^10 - 1105435x^9 + 46850799x^8 - 116275535x^7 + 626274432x^6 - 8558999923x^5 + 34408048994x^4 - 448299413930x^3 + 1712647133330x^2 + 15986651928135*x + 206161212459445
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{58}\cdot 5^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.3
Root			$6.86496 + 2.82928i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.9.b.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-14.9660 - 5.65855i) q^{2} -25.1248i q^{3} +(191.962 + 169.372i) q^{4} -279.508 q^{5} +(-142.170 + 376.017i) q^{6} +2973.76i q^{7} +(-1914.50 - 3621.04i) q^{8} +5929.74 q^{9} +O(q^{10})$	\(q+(-14.9660 - 5.65855i) q^{2} -25.1248i q^{3} +(191.962 + 169.372i) q^{4} -279.508 q^{5} +(-142.170 + 376.017i) q^{6} +2973.76i q^{7} +(-1914.50 - 3621.04i) q^{8} +5929.74 q^{9} +(4183.12 + 1581.61i) q^{10} -28067.3i q^{11} +(4255.43 - 4823.00i) q^{12} +35637.5 q^{13} +(16827.2 - 44505.2i) q^{14} +7022.60i q^{15} +(8162.50 + 65025.7i) q^{16} +59310.8 q^{17} +(-88744.5 - 33553.8i) q^{18} -146509. i q^{19} +(-53654.9 - 47340.8i) q^{20} +74715.1 q^{21} +(-158820. + 420055. i) q^{22} +309282. i q^{23} +(-90977.9 + 48101.4i) q^{24} +78125.0 q^{25} +(-533351. - 201657. i) q^{26} -313827. i q^{27} +(-503670. + 570847. i) q^{28} +1.02939e6 q^{29} +(39737.7 - 105100. i) q^{30} +162954. i q^{31} +(245791. - 1.01936e6i) q^{32} -705186. q^{33} +(-887645. - 335613. i) q^{34} -831191. i q^{35} +(1.13828e6 + 1.00433e6i) q^{36} +864529. q^{37} +(-829026. + 2.19264e6i) q^{38} -895386. i q^{39} +(535118. + 1.01211e6i) q^{40} +1.51703e6 q^{41} +(-1.11819e6 - 422779. i) q^{42} +2.39249e6i q^{43} +(4.75381e6 - 5.38785e6i) q^{44} -1.65741e6 q^{45} +(1.75009e6 - 4.62871e6i) q^{46} -2.15044e6i q^{47} +(1.63376e6 - 205081. i) q^{48} -3.07844e6 q^{49} +(-1.16922e6 - 442074. i) q^{50} -1.49017e6i q^{51} +(6.84104e6 + 6.03599e6i) q^{52} -9.78137e6 q^{53} +(-1.77581e6 + 4.69674e6i) q^{54} +7.84505e6i q^{55} +(1.07681e7 - 5.69325e6i) q^{56} -3.68100e6 q^{57} +(-1.54058e7 - 5.82483e6i) q^{58} +7.13303e6i q^{59} +(-1.18943e6 + 1.34807e6i) q^{60} -5.43860e6 q^{61} +(922086. - 2.43877e6i) q^{62} +1.76336e7i q^{63} +(-9.44662e6 + 1.38649e7i) q^{64} -9.96100e6 q^{65} +(1.05538e7 + 3.99033e6i) q^{66} -1.02302e7i q^{67} +(1.13854e7 + 1.00456e7i) q^{68} +7.77065e6 q^{69} +(-4.70334e6 + 1.24396e7i) q^{70} -3.55760e7i q^{71} +(-1.13525e7 - 2.14718e7i) q^{72} -3.90536e6 q^{73} +(-1.29385e7 - 4.89198e6i) q^{74} -1.96288e6i q^{75} +(2.48144e7 - 2.81240e7i) q^{76} +8.34654e7 q^{77} +(-5.06659e6 + 1.34003e7i) q^{78} +3.17103e6i q^{79} +(-2.28149e6 - 1.81752e7i) q^{80} +3.10202e7 q^{81} +(-2.27039e7 - 8.58420e6i) q^{82} -4.52697e7i q^{83} +(1.43424e7 + 1.26546e7i) q^{84} -1.65779e7 q^{85} +(1.35380e7 - 3.58059e7i) q^{86} -2.58631e7i q^{87} +(-1.01633e8 + 5.37348e7i) q^{88} +4.70524e7 q^{89} +(2.48048e7 + 9.37856e6i) q^{90} +1.05977e8i q^{91} +(-5.23836e7 + 5.93703e7i) q^{92} +4.09420e6 q^{93} +(-1.21684e7 + 3.21835e7i) q^{94} +4.09504e7i q^{95} +(-2.56113e7 - 6.17546e6i) q^{96} -1.22762e7 q^{97} +(4.60718e7 + 1.74195e7i) q^{98} -1.66432e8i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9}+O(q^{10}) $ 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9	\( 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9} + 8750 q^{10} - 64040 q^{12} + 51392 q^{13} + 68472 q^{14} - 81424 q^{16} + 27552 q^{17} - 616994 q^{18} + 172500 q^{20} + 414496 q^{21} - 389120 q^{22} + 163792 q^{24} + 1250000 q^{25} + 1037124 q^{26} + 1288520 q^{28} + 2764896 q^{29} - 805000 q^{30} - 4379904 q^{32} - 5521600 q^{33} + 3793964 q^{34} - 5468916 q^{36} + 9009472 q^{37} - 3087360 q^{38} + 385000 q^{40} - 8576448 q^{41} - 4067400 q^{42} + 16921200 q^{44} + 1580000 q^{45} - 7974152 q^{46} - 2696640 q^{48} - 32803600 q^{49} + 468750 q^{50} + 6679352 q^{52} + 2452032 q^{53} + 8898704 q^{54} + 34134768 q^{56} + 11957760 q^{57} + 52156572 q^{58} - 24185000 q^{60} + 8371712 q^{61} + 1290000 q^{62} - 47543872 q^{64} + 9060000 q^{65} + 19358000 q^{66} + 16095192 q^{68} + 7527264 q^{69} + 10500000 q^{70} - 42242664 q^{72} + 61907232 q^{73} - 138210876 q^{74} + 2570400 q^{76} - 156997440 q^{77} - 104032400 q^{78} + 37590000 q^{80} + 140586672 q^{81} + 83921012 q^{82} + 69761824 q^{84} - 106960000 q^{85} - 101724672 q^{86} + 44728480 q^{88} + 106647456 q^{89} + 32613750 q^{90} - 13876200 q^{92} + 105563840 q^{93} + 55264632 q^{94} - 453389952 q^{96} + 171851232 q^{97} - 285387714 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9 + 8750 * q^10 - 64040 * q^12 + 51392 * q^13 + 68472 * q^14 - 81424 * q^16 + 27552 * q^17 - 616994 * q^18 + 172500 * q^20 + 414496 * q^21 - 389120 * q^22 + 163792 * q^24 + 1250000 * q^25 + 1037124 * q^26 + 1288520 * q^28 + 2764896 * q^29 - 805000 * q^30 - 4379904 * q^32 - 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 + 9009472 * q^37 - 3087360 * q^38 + 385000 * q^40 - 8576448 * q^41 - 4067400 * q^42 + 16921200 * q^44 + 1580000 * q^45 - 7974152 * q^46 - 2696640 * q^48 - 32803600 * q^49 + 468750 * q^50 + 6679352 * q^52 + 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 + 11957760 * q^57 + 52156572 * q^58 - 24185000 * q^60 + 8371712 * q^61 + 1290000 * q^62 - 47543872 * q^64 + 9060000 * q^65 + 19358000 * q^66 + 16095192 * q^68 + 7527264 * q^69 + 10500000 * q^70 - 42242664 * q^72 + 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 - 156997440 * q^77 - 104032400 * q^78 + 37590000 * q^80 + 140586672 * q^81 + 83921012 * q^82 + 69761824 * q^84 - 106960000 * q^85 - 101724672 * q^86 + 44728480 * q^88 + 106647456 * q^89 + 32613750 * q^90 - 13876200 * q^92 + 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 + 171851232 * q^97 - 285387714 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$1$

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 $

$2$	−14.9660	−	5.65855i	−0.935374	−	0.353659i
$2$	−14.9660	−	5.65855i	−0.935374	−	0.353659i
$3$		−	25.1248i		−	0.310183i	−0.987900	−	0.155091i	$-0.950433\pi$
$3$		−	25.1248i		−	0.310183i	0.987900	−	0.155091i	$-0.0495672\pi$
$4$	191.962	+	169.372i	0.749850	+	0.661608i
$5$	−279.508			−0.447214
$5$	−279.508			−0.447214
$6$	−142.170	+	376.017i	−0.109699	+	0.290137i
$7$			2973.76i			1.23855i	0.785174	+	0.619275i	$0.212573\pi$
$7$			2973.76i			1.23855i	−0.785174	+	0.619275i	$0.787427\pi$
$8$	−1914.50	−	3621.04i	−0.467406	−	0.884043i
$9$	5929.74			0.903787
$10$	4183.12	+	1581.61i	0.418312	+	0.158161i
$11$		−	28067.3i		−	1.91704i	−0.285033	−	0.958518i	$-0.592005\pi$
$11$		−	28067.3i		−	1.91704i	0.285033	−	0.958518i	$-0.407995\pi$
$12$	4255.43	−	4823.00i	0.205219	−	0.232591i
$13$	35637.5			1.24777			0.623885	−	0.781516i	$-0.285553\pi$
$13$	35637.5			1.24777			0.623885	+	0.781516i	$0.285553\pi$
$14$	16827.2	−	44505.2i	0.438025	−	1.15851i
$15$			7022.60i			0.138718i
$16$	8162.50	+	65025.7i	0.124550	+	0.992213i
$17$	59310.8			0.710130			0.355065	−	0.934842i	$-0.384459\pi$
$17$	59310.8			0.710130			0.355065	+	0.934842i	$0.384459\pi$
$18$	−88744.5	−	33553.8i	−0.845379	−	0.319633i
$19$		−	146509.i		−	1.12421i	−0.827065	−	0.562106i	$-0.809991\pi$
$19$		−	146509.i		−	1.12421i	0.827065	−	0.562106i	$-0.190009\pi$
$20$	−53654.9	−	47340.8i	−0.335343	−	0.295880i
$21$	74715.1			0.384177
$22$	−158820.	+	420055.i	−0.677978	+	1.79315i
$23$			309282.i			1.10521i	0.833444	+	0.552603i	$0.186366\pi$
$23$			309282.i			1.10521i	−0.833444	+	0.552603i	$0.813634\pi$
$24$	−90977.9	+	48101.4i	−0.274215	+	0.144981i
$25$	78125.0			0.200000
$26$	−533351.	−	201657.i	−1.16713	−	0.441286i
$27$		−	313827.i		−	0.590522i
$28$	−503670.	+	570847.i	−0.819434	+	0.928726i
$29$	1.02939e6			1.45541			0.727706	−	0.685889i	$-0.240586\pi$
$29$	1.02939e6			1.45541			0.727706	+	0.685889i	$0.240586\pi$
$30$	39737.7	−	105100.i	0.0490589	−	0.129753i
$31$			162954.i			0.176449i	0.996101	+	0.0882245i	$0.0281193\pi$
$31$			162954.i			0.176449i	−0.996101	+	0.0882245i	$0.971881\pi$
$32$	245791.	−	1.01936e6i	0.234405	−	0.972139i
$33$	−705186.			−0.594631
$34$	−887645.	−	335613.i	−0.664238	−	0.251144i
$35$		−	831191.i		−	0.553896i
$36$	1.13828e6	+	1.00433e6i	0.677704	+	0.597952i
$37$	864529.			0.461289			0.230644	−	0.973038i	$-0.425917\pi$
$37$	864529.			0.461289			0.230644	+	0.973038i	$0.425917\pi$
$38$	−829026.	+	2.19264e6i	−0.397588	+	1.05156i
$39$		−	895386.i		−	0.387037i
$40$	535118.	+	1.01211e6i	0.209031	+	0.395356i
$41$	1.51703e6			0.536857			0.268429	−	0.963300i	$-0.413496\pi$
$41$	1.51703e6			0.536857			0.268429	+	0.963300i	$0.413496\pi$
$42$	−1.11819e6	−	422779.i	−0.359349	−	0.135868i
$43$			2.39249e6i			0.699802i	0.936787	+	0.349901i	$0.113785\pi$
$43$			2.39249e6i			0.699802i	−0.936787	+	0.349901i	$0.886215\pi$
$44$	4.75381e6	−	5.38785e6i	1.26833	−	1.43749i
$45$	−1.65741e6			−0.404186
$46$	1.75009e6	−	4.62871e6i	0.390867	−	1.03378i
$47$		−	2.15044e6i		−	0.440694i	−0.975422	−	0.220347i	$-0.929281\pi$
$47$		−	2.15044e6i		−	0.440694i	0.975422	−	0.220347i	$-0.0707189\pi$
$48$	1.63376e6	−	205081.i	0.307767	−	0.0386332i
$49$	−3.07844e6			−0.534006
$50$	−1.16922e6	−	442074.i	−0.187075	−	0.0707319i
$51$		−	1.49017e6i		−	0.220270i
$52$	6.84104e6	+	6.03599e6i	0.935640	+	0.825534i
$53$	−9.78137e6			−1.23964			−0.619821	−	0.784743i	$-0.712795\pi$
$53$	−9.78137e6			−1.23964			−0.619821	+	0.784743i	$0.712795\pi$
$54$	−1.77581e6	+	4.69674e6i	−0.208844	+	0.552359i
$55$			7.84505e6i			0.857324i
$56$	1.07681e7	−	5.69325e6i	1.09493	−	0.578906i
$57$	−3.68100e6			−0.348711
$58$	−1.54058e7	−	5.82483e6i	−1.36136	−	0.514720i
$59$			7.13303e6i			0.588662i	0.955704	+	0.294331i	$0.0950968\pi$
$59$			7.13303e6i			0.588662i	−0.955704	+	0.294331i	$0.904903\pi$
$60$	−1.18943e6	+	1.34807e6i	−0.0917769	+	0.104018i
$61$	−5.43860e6			−0.392796			−0.196398	−	0.980524i	$-0.562925\pi$
$61$	−5.43860e6			−0.392796			−0.196398	+	0.980524i	$0.562925\pi$
$62$	922086.	−	2.43877e6i	0.0624029	−	0.165046i
$63$			1.76336e7i			1.11938i
$64$	−9.44662e6	+	1.38649e7i	−0.563062	+	0.826414i
$65$	−9.96100e6			−0.558020
$66$	1.05538e7	+	3.99033e6i	0.556203	+	0.210297i
$67$		−	1.02302e7i		−	0.507674i	−0.967247	−	0.253837i	$-0.918307\pi$
$67$		−	1.02302e7i		−	0.507674i	0.967247	−	0.253837i	$-0.0816926\pi$
$68$	1.13854e7	+	1.00456e7i	0.532491	+	0.469828i
$69$	7.77065e6			0.342816
$70$	−4.70334e6	+	1.24396e7i	−0.195891	+	0.518100i
$71$		−	3.55760e7i		−	1.39998i	−0.714150	−	0.699992i	$-0.753187\pi$
$71$		−	3.55760e7i		−	1.39998i	0.714150	−	0.699992i	$-0.246813\pi$
$72$	−1.13525e7	−	2.14718e7i	−0.422436	−	0.798986i
$73$	−3.90536e6			−0.137521			−0.0687607	−	0.997633i	$-0.521904\pi$
$73$	−3.90536e6			−0.137521			−0.0687607	+	0.997633i	$0.521904\pi$
$74$	−1.29385e7	−	4.89198e6i	−0.431477	−	0.163139i
$75$		−	1.96288e6i		−	0.0620366i
$76$	2.48144e7	−	2.81240e7i	0.743788	−	0.842991i
$77$	8.34654e7			2.37434
$78$	−5.06659e6	+	1.34003e7i	−0.136879	+	0.362024i
$79$			3.17103e6i			0.0814126i	0.999171	+	0.0407063i	$0.0129608\pi$
$79$			3.17103e6i			0.0814126i	−0.999171	+	0.0407063i	$0.987039\pi$
$80$	−2.28149e6	−	1.81752e7i	−0.0557004	−	0.443731i
$81$	3.10202e7			0.720617
$82$	−2.27039e7	−	8.58420e6i	−0.502163	−	0.189865i
$83$		−	4.52697e7i		−	0.953883i	−0.878935	−	0.476942i	$-0.841745\pi$
$83$		−	4.52697e7i		−	0.953883i	0.878935	−	0.476942i	$-0.158255\pi$
$84$	1.43424e7	+	1.26546e7i	0.288075	+	0.254174i
$85$	−1.65779e7			−0.317580
$86$	1.35380e7	−	3.58059e7i	0.247492	−	0.654577i
$87$		−	2.58631e7i		−	0.451444i
$88$	−1.01633e8	+	5.37348e7i	−1.69474	+	0.896035i
$89$	4.70524e7			0.749932			0.374966	−	0.927038i	$-0.377654\pi$
$89$	4.70524e7			0.749932			0.374966	+	0.927038i	$0.377654\pi$
$90$	2.48048e7	+	9.37856e6i	0.378065	+	0.142944i
$91$			1.05977e8i			1.54542i
$92$	−5.23836e7	+	5.93703e7i	−0.731214	+	0.828739i
$93$	4.09420e6			0.0547315
$94$	−1.21684e7	+	3.21835e7i	−0.155855	+	0.412213i
$95$			4.09504e7i			0.502763i
$96$	−2.56113e7	−	6.17546e6i	−0.301541	−	0.0727084i
$97$	−1.22762e7			−0.138669			−0.0693343	−	0.997593i	$-0.522088\pi$
$97$	−1.22762e7			−0.138669			−0.0693343	+	0.997593i	$0.522088\pi$
$98$	4.60718e7	+	1.74195e7i	0.499495	+	0.188856i
$99$		−	1.66432e8i		−	1.73259i
$100$	1.49970e7	+	1.32322e7i	0.149970	+	0.132322i
$101$	−1.94013e8			−1.86442			−0.932212	−	0.361911i	$-0.882124\pi$
$101$	−1.94013e8			−1.86442			−0.932212	+	0.361911i	$0.882124\pi$
$102$	−8.43222e6	+	2.23019e7i	−0.0779006	+	0.206035i
$103$			1.13205e8i			1.00581i	0.864342	+	0.502904i	$0.167735\pi$
$103$			1.13205e8i			1.00581i	−0.864342	+	0.502904i	$0.832265\pi$
$104$	−6.82280e7	−	1.29045e8i	−0.583216	−	1.10308i
$105$	−2.08835e7			−0.171809
$106$	1.46388e8	+	5.53484e7i	1.15953	+	0.438411i
$107$			7.70868e7i			0.588091i	0.955791	+	0.294046i	$0.0950018\pi$
$107$			7.70868e7i			0.588091i	−0.955791	+	0.294046i	$0.904998\pi$
$108$	5.31535e7	−	6.02428e7i	0.390694	−	0.442803i
$109$	4.31605e7			0.305760			0.152880	−	0.988245i	$-0.451145\pi$
$109$	4.31605e7			0.305760			0.152880	+	0.988245i	$0.451145\pi$
$110$	4.43916e7	−	1.17409e8i	0.303201	−	0.801919i
$111$		−	2.17211e7i		−	0.143084i
$112$	−1.93371e8	+	2.42733e7i	−1.22891	+	0.154261i
$113$	−2.33705e7			−0.143336			−0.0716678	−	0.997429i	$-0.522832\pi$
$113$	−2.33705e7			−0.143336			−0.0716678	+	0.997429i	$0.522832\pi$
$114$	5.50898e7	+	2.08291e7i	0.326176	+	0.123325i
$115$		−	8.64470e7i		−	0.494264i
$116$	1.97603e8	+	1.74349e8i	1.09134	+	0.962913i
$117$	2.11322e8			1.12772
$118$	4.03626e7	−	1.06753e8i	0.208186	−	0.550619i
$119$			1.76376e8i			0.879532i
$120$	2.54291e7	−	1.34447e7i	0.122633	−	0.0648377i
$121$	−5.73415e8			−2.67502
$122$	8.13940e7	+	3.07746e7i	0.367412	+	0.138916i
$123$		−	3.81151e7i		−	0.166524i
$124$	−2.75999e7	+	3.12810e7i	−0.116740	+	0.132310i
$125$	−2.18366e7			−0.0894427
$126$	9.97808e7	−	2.63905e8i	0.395881	−	1.04704i
$127$		−	3.16806e8i		−	1.21781i	−0.793244	−	0.608904i	$-0.791609\pi$
$127$		−	3.16806e8i		−	1.21781i	0.793244	−	0.608904i	$-0.208391\pi$
$128$	2.19833e8	−	1.54048e8i	0.818943	−	0.573874i
$129$	6.01107e7			0.217067
$130$	1.49076e8	+	5.63648e7i	0.521957	+	0.197349i
$131$			4.58741e8i			1.55769i	0.627214	+	0.778847i	$0.284195\pi$
$131$			4.58741e8i			1.55769i	−0.627214	+	0.778847i	$0.715805\pi$
$132$	−1.35369e8	−	1.19438e8i	−0.445884	−	0.393413i
$133$	4.35681e8			1.39239
$134$	−5.78881e7	+	1.53105e8i	−0.179544	+	0.474865i
$135$			8.77175e7i			0.264089i
$136$	−1.13550e8	−	2.14767e8i	−0.331919	−	0.627785i
$137$	2.31251e7			0.0656449			0.0328224	−	0.999461i	$-0.489550\pi$
$137$	2.31251e7			0.0656449			0.0328224	+	0.999461i	$0.489550\pi$
$138$	−1.16296e8	−	4.39707e7i	−0.320661	−	0.121240i
$139$			4.70432e7i			0.126020i	0.998013	+	0.0630098i	$0.0200699\pi$
$139$			4.70432e7i			0.126020i	−0.998013	+	0.0630098i	$0.979930\pi$
$140$	1.40780e8	−	1.59557e8i	0.366462	−	0.415339i
$141$	−5.40295e7			−0.136696
$142$	−2.01308e8	+	5.32429e8i	−0.495118	+	1.30951i
$143$		−	1.00025e9i		−	2.39202i
$144$	4.84015e7	+	3.85586e8i	0.112567	+	0.896749i
$145$	−2.87722e8			−0.650880
$146$	5.84476e7	+	2.20987e7i	0.128634	+	0.0486357i
$147$			7.73451e7i			0.165639i
$148$	1.65956e8	+	1.46427e8i	0.345897	+	0.305192i
$149$	8.05530e7			0.163432			0.0817159	−	0.996656i	$-0.473960\pi$
$149$	8.05530e7			0.163432			0.0817159	+	0.996656i	$0.473960\pi$
$150$	−1.11070e7	+	2.93764e7i	−0.0219398	+	0.0580274i
$151$			3.24540e8i			0.624252i	0.950041	+	0.312126i	$0.101041\pi$
$151$			3.24540e8i			0.624252i	−0.950041	+	0.312126i	$0.898959\pi$
$152$	−5.30513e8	+	2.80490e8i	−0.993852	+	0.525464i
$153$	3.51698e8			0.641806
$154$	−1.24914e9	−	4.72293e8i	−2.22090	−	0.839709i
$155$		−	4.55471e7i		−	0.0789104i
$156$	1.51653e8	−	1.71880e8i	0.256066	−	0.290219i
$157$	8.87303e8			1.46041			0.730203	−	0.683230i	$-0.239426\pi$
$157$	8.87303e8			1.46041			0.730203	+	0.683230i	$0.239426\pi$
$158$	1.79434e7	−	4.74575e7i	0.0287923	−	0.0761512i
$159$			2.45755e8i			0.384516i
$160$	−6.87008e7	+	2.84920e8i	−0.104829	+	0.434754i
$161$	−9.19730e8			−1.36885
$162$	−4.64248e8	−	1.75529e8i	−0.674047	−	0.254853i
$163$			6.99870e8i			0.991441i	0.868482	+	0.495721i	$0.165096\pi$
$163$			6.99870e8i			0.991441i	−0.868482	+	0.495721i	$0.834904\pi$
$164$	2.91212e8	+	2.56942e8i	0.402563	+	0.355189i
$165$	1.97105e8			0.265927
$166$	−2.56161e8	+	6.77506e8i	−0.337350	+	0.892238i
$167$			1.91276e8i			0.245921i	0.992412	+	0.122960i	$0.0392388\pi$
$167$			1.91276e8i			0.245921i	−0.992412	+	0.122960i	$0.960761\pi$
$168$	−1.43042e8	−	2.70546e8i	−0.179567	−	0.339629i
$169$	4.54304e8			0.556929
$170$	2.48104e8	+	9.38067e7i	0.297056	+	0.112315i
$171$		−	8.68758e8i		−	1.01605i
$172$	−4.05219e8	+	4.59265e8i	−0.462995	+	0.524747i
$173$	7.14809e6			0.00798005			0.00399002	−	0.999992i	$-0.498730\pi$
$173$	7.14809e6			0.00798005			0.00399002	+	0.999992i	$0.498730\pi$
$174$	−1.46348e8	+	3.87067e8i	−0.159657	+	0.422269i
$175$			2.32325e8i			0.247710i
$176$	1.82510e9	−	2.29099e8i	1.90211	−	0.238767i
$177$	1.79216e8			0.182593
$178$	−7.04186e8	−	2.66249e8i	−0.701467	−	0.265221i
$179$		−	1.12370e9i		−	1.09455i	−0.836951	−	0.547277i	$-0.815664\pi$
$179$		−	1.12370e9i		−	1.09455i	0.836951	−	0.547277i	$-0.184336\pi$
$180$	−3.18160e8	−	2.80719e8i	−0.303079	−	0.267412i
$181$	7.55106e8			0.703547			0.351774	−	0.936085i	$-0.385579\pi$
$181$	7.55106e8			0.703547			0.351774	+	0.936085i	$0.385579\pi$
$182$	5.99679e8	−	1.58606e9i	0.546554	−	1.44555i
$183$			1.36644e8i			0.121839i
$184$	1.11992e9	−	5.92120e8i	0.977050	−	0.516581i
$185$	−2.41643e8			−0.206295
$186$	−6.12737e7	−	2.31672e7i	−0.0511944	−	0.0193563i
$187$		−	1.66469e9i		−	1.36134i
$188$	3.64224e8	−	4.12803e8i	0.291566	−	0.330454i
$189$	9.33247e8			0.731391
$190$	2.31720e8	−	6.12863e8i	0.177807	−	0.470272i
$191$			6.92682e8i			0.520476i	0.965545	+	0.260238i	$0.0838010\pi$
$191$			6.92682e8i			0.520476i	−0.965545	+	0.260238i	$0.916199\pi$
$192$	3.48354e8	+	2.37344e8i	0.256339	+	0.174652i
$193$	−1.91910e9			−1.38315			−0.691573	−	0.722307i	$-0.743082\pi$
$193$	−1.91910e9			−1.38315			−0.691573	+	0.722307i	$0.743082\pi$
$194$	1.83726e8	+	6.94657e7i	0.129707	+	0.0490415i
$195$			2.50268e8i			0.173088i
$196$	−5.90941e8	−	5.21400e8i	−0.400424	−	0.353302i
$197$	−6.92313e8			−0.459661			−0.229830	−	0.973231i	$-0.573817\pi$
$197$	−6.92313e8			−0.459661			−0.229830	+	0.973231i	$0.573817\pi$
$198$	−9.41764e8	+	2.49082e9i	−0.612747	+	1.62062i
$199$		−	7.25901e6i		−	0.00462876i	−0.999997	−	0.00231438i	$-0.999263\pi$
$199$		−	7.25901e6i		−	0.00462876i	0.999997	−	0.00231438i	$-0.000736691\pi$
$200$	−1.49570e8	−	2.82894e8i	−0.0934813	−	0.176809i
$201$	−2.57032e8			−0.157472
$202$	2.90359e9	+	1.09783e9i	1.74394	+	0.659372i
$203$			3.06114e9i			1.80260i
$204$	2.52393e8	−	2.86056e8i	0.145732	−	0.165170i
$205$	−4.24023e8			−0.240090
$206$	6.40575e8	−	1.69422e9i	0.355714	−	0.940808i
$207$			1.83396e9i			0.998871i
$208$	2.90892e8	+	2.31736e9i	0.155410	+	1.23805i
$209$	−4.11210e9			−2.15516
$210$	3.12542e8	+	1.18170e8i	0.160706	+	0.0607619i
$211$		−	5.70039e8i		−	0.287591i	−0.989607	−	0.143795i	$-0.954069\pi$
$211$		−	5.70039e8i		−	0.287591i	0.989607	−	0.143795i	$-0.0459307\pi$
$212$	−1.87765e9	−	1.65669e9i	−0.929545	−	0.820157i
$213$	−8.93839e8			−0.434251
$214$	4.36200e8	−	1.15368e9i	0.207984	−	0.550086i
$215$		−	6.68720e8i		−	0.312961i
$216$	−1.13638e9	+	6.00822e8i	−0.522046	+	0.276014i
$217$	−4.84587e8			−0.218541
$218$	−6.45940e8	−	2.44226e8i	−0.286000	−	0.108135i
$219$			9.81215e7i			0.0426568i
$220$	−1.32873e9	+	1.50595e9i	−0.567212	+	0.642864i
$221$	2.11369e9			0.886079
$222$	−1.22910e8	+	3.25078e8i	−0.0506029	+	0.133837i
$223$		−	1.74011e9i		−	0.703651i	−0.936066	−	0.351825i	$-0.885561\pi$
$223$		−	1.74011e9i		−	0.703651i	0.936066	−	0.351825i	$-0.114439\pi$
$224$	3.03133e9	+	7.30924e8i	1.20404	+	0.290322i
$225$	4.63261e8			0.180757
$226$	3.49762e8	+	1.32243e8i	0.134072	+	0.0506920i
$227$			3.21593e9i			1.21117i	0.795782	+	0.605583i	$0.207060\pi$
$227$			3.21593e9i			1.21117i	−0.795782	+	0.605583i	$0.792940\pi$
$228$	−7.06610e8	−	6.23457e8i	−0.261481	−	0.230710i
$229$	4.04384e9			1.47045			0.735227	−	0.677821i	$-0.237075\pi$
$229$	4.04384e9			1.47045			0.735227	+	0.677821i	$0.237075\pi$
$230$	−4.89165e8	+	1.29376e9i	−0.174801	+	0.462321i
$231$		−	2.09705e9i		−	0.736480i
$232$	−1.97076e9	−	3.72745e9i	−0.680269	−	1.28665i
$233$	−3.53336e9			−1.19885			−0.599423	−	0.800432i	$-0.704603\pi$
$233$	−3.53336e9			−1.19885			−0.599423	+	0.800432i	$0.704603\pi$
$234$	−3.16264e9	−	1.19577e9i	−1.05484	−	0.398828i
$235$			6.01067e8i			0.197084i
$236$	−1.20813e9	+	1.36927e9i	−0.389463	+	0.441408i
$237$	7.96714e7			0.0252528
$238$	9.98032e8	−	2.63964e9i	0.311055	−	0.822691i
$239$			8.01489e8i			0.245644i	0.992429	+	0.122822i	$0.0391944\pi$
$239$			8.01489e8i			0.245644i	−0.992429	+	0.122822i	$0.960806\pi$
$240$	−4.56649e8	+	5.73220e7i	−0.137638	+	0.0172773i
$241$	5.03262e9			1.49185			0.745926	−	0.666029i	$-0.232007\pi$
$241$	5.03262e9			1.49185			0.745926	+	0.666029i	$0.232007\pi$
$242$	8.58172e9	+	3.24470e9i	2.50215	+	0.946047i
$243$		−	2.83840e9i		−	0.814045i
$244$	−1.04400e9	−	9.21144e8i	−0.294538	−	0.259877i
$245$	8.60449e8			0.238815
$246$	−2.15676e8	+	5.70430e8i	−0.0588928	+	0.155762i
$247$		−	5.22120e9i		−	1.40276i
$248$	5.90064e8	−	3.11976e8i	0.155989	−	0.0824734i
$249$	−1.13739e9			−0.295878
$250$	3.26806e8	+	1.23564e8i	0.0836624	+	0.0316323i
$251$		−	4.06825e9i		−	1.02497i	−0.858695	−	0.512487i	$-0.828724\pi$
$251$		−	4.06825e9i		−	1.02497i	0.858695	−	0.512487i	$-0.171276\pi$
$252$	−2.98664e9	+	3.38498e9i	−0.740594	+	0.839371i
$253$	8.68072e9			2.11872
$254$	−1.79266e9	+	4.74132e9i	−0.430689	+	1.13911i
$255$			4.16516e8i			0.0985078i
$256$	−4.16171e9	+	1.06154e9i	−0.968975	+	0.247160i
$257$	−5.94381e9			−1.36249			−0.681243	−	0.732057i	$-0.738560\pi$
$257$	−5.94381e9			−1.36249			−0.681243	+	0.732057i	$0.738560\pi$
$258$	−8.99616e8	−	3.40140e8i	−0.203039	−	0.0767677i
$259$			2.57090e9i			0.571329i
$260$	−1.91213e9	−	1.68711e9i	−0.418431	−	0.369190i
$261$	6.10399e9			1.31538
$262$	2.59581e9	−	6.86551e9i	0.550893	−	1.45703i
$263$			5.73917e9i			1.19957i	0.800161	+	0.599786i	$0.204747\pi$
$263$			5.73917e9i			1.19957i	−0.800161	+	0.599786i	$0.795253\pi$
$264$	1.35008e9	+	2.55350e9i	0.277934	+	0.525679i
$265$	2.73398e9			0.554385
$266$	−6.52039e9	−	2.46532e9i	−1.30241	−	0.492433i
$267$		−	1.18218e9i		−	0.232616i
$268$	1.73270e9	−	1.96380e9i	0.335881	−	0.380679i
$269$	−5.80678e9			−1.10899			−0.554493	−	0.832188i	$-0.687088\pi$
$269$	−5.80678e9			−1.10899			−0.554493	+	0.832188i	$0.687088\pi$
$270$	4.96354e8	−	1.31278e9i	0.0933977	−	0.247022i
$271$			3.67862e9i			0.682037i	0.940056	+	0.341019i	$0.110772\pi$
$271$			3.67862e9i			0.682037i	−0.940056	+	0.341019i	$0.889228\pi$
$272$	4.84124e8	+	3.85673e9i	0.0884467	+	0.704601i
$273$	2.66266e9			0.479364
$274$	−3.46090e8	−	1.30854e8i	−0.0614025	−	0.0232159i
$275$		−	2.19276e9i		−	0.383407i
$276$	1.49167e9	+	1.31613e9i	0.257061	+	0.226810i
$277$	−1.63959e9			−0.278495			−0.139247	−	0.990258i	$-0.544468\pi$
$277$	−1.63959e9			−0.278495			−0.139247	+	0.990258i	$0.544468\pi$
$278$	2.66197e8	−	7.04049e8i	0.0445680	−	0.117875i
$279$			9.66278e8i			0.159472i
$280$	−3.00977e9	+	1.59131e9i	−0.489668	+	0.258895i
$281$	−1.68401e9			−0.270097			−0.135048	−	0.990839i	$-0.543119\pi$
$281$	−1.68401e9			−0.270097			−0.135048	+	0.990839i	$0.543119\pi$
$282$	8.08605e8	+	3.05729e8i	0.127862	+	0.0483437i
$283$		−	9.98783e9i		−	1.55713i	−0.627563	−	0.778566i	$-0.715947\pi$
$283$		−	9.98783e9i		−	1.55713i	0.627563	−	0.778566i	$-0.284053\pi$
$284$	6.02556e9	−	6.82922e9i	0.926241	−	1.04978i
$285$	1.02887e9			0.155948
$286$	−5.65997e9	+	1.49697e10i	−0.845960	+	2.23743i
$287$			4.51128e9i			0.664925i
$288$	1.45748e9	−	6.04455e9i	0.211852	−	0.878606i
$289$	−3.45799e9			−0.495715
$290$	4.30604e9	+	1.62809e9i	0.608817	+	0.230190i
$291$			3.08438e8i			0.0430126i
$292$	−7.49680e8	−	6.61458e8i	−0.103120	−	0.0909852i
$293$	−6.31006e9			−0.856176			−0.428088	−	0.903737i	$-0.640813\pi$
$293$	−6.31006e9			−0.856176			−0.428088	+	0.903737i	$0.640813\pi$
$294$	4.37661e8	−	1.15755e9i	0.0585799	−	0.154935i
$295$		−	1.99374e9i		−	0.263258i
$296$	−1.65514e9	−	3.13049e9i	−0.215609	−	0.407799i
$297$	−8.80829e9			−1.13205
$298$	−1.20556e9	−	4.55813e8i	−0.152870	−	0.0577992i
$299$			1.10221e10i			1.37904i
$300$	3.32455e8	−	3.76797e8i	0.0410439	−	0.0465181i
$301$	−7.11467e9			−0.866740
$302$	1.83643e9	−	4.85706e9i	0.220773	−	0.583910i
$303$			4.87453e9i			0.578312i
$304$	9.52682e9	−	1.19588e9i	1.11546	−	0.140021i
$305$	1.52013e9			0.175664
$306$	−5.26351e9	−	1.99010e9i	−0.600329	−	0.226981i
$307$			1.73796e10i			1.95653i	0.207370	+	0.978263i	$0.433510\pi$
$307$			1.73796e10i			1.95653i	−0.207370	+	0.978263i	$0.566490\pi$
$308$	1.60221e10	+	1.41367e10i	1.78040	+	1.57088i
$309$	2.84425e9			0.311985
$310$	−2.57731e8	+	6.81658e8i	−0.0279074	+	0.0738108i
$311$			1.22089e8i			0.0130507i	0.999979	+	0.00652537i	$0.00207710\pi$
$311$			1.22089e8i			0.0130507i	−0.999979	+	0.00652537i	$0.997923\pi$
$312$	−3.24223e9	+	1.71421e9i	−0.342157	+	0.180903i
$313$	−2.41043e9			−0.251140			−0.125570	−	0.992085i	$-0.540076\pi$
$313$	−2.41043e9			−0.251140			−0.125570	+	0.992085i	$0.540076\pi$
$314$	−1.32794e10	−	5.02085e9i	−1.36603	−	0.516486i
$315$		−	4.92875e9i		−	0.500604i
$316$	−5.37082e8	+	6.08715e8i	−0.0538632	+	0.0610472i
$317$	−6.16359e9			−0.610375			−0.305187	−	0.952292i	$-0.598719\pi$
$317$	−6.16359e9			−0.610375			−0.305187	+	0.952292i	$0.598719\pi$
$318$	1.39062e9	−	3.67797e9i	0.135988	−	0.359666i
$319$		−	2.88921e10i		−	2.79008i
$320$	2.64041e9	−	3.87537e9i	0.251809	−	0.369584i
$321$	1.93679e9			0.182416
$322$	1.37647e10	+	5.20434e9i	1.28039	+	0.484108i
$323$		−	8.68954e9i		−	0.798337i
$324$	5.95469e9	+	5.25394e9i	0.540355	+	0.476766i
$325$	2.78418e9			0.249554
$326$	3.96025e9	−	1.04742e10i	0.350633	−	0.927369i
$327$		−	1.08440e9i		−	0.0948414i
$328$	−2.90435e9	−	5.49323e9i	−0.250931	−	0.474605i
$329$	6.39490e9			0.545821
$330$	−2.94988e9	−	1.11533e9i	−0.248741	−	0.0940477i
$331$			1.59528e10i			1.32900i	0.747287	+	0.664501i	$0.231356\pi$
$331$			1.59528e10i			1.32900i	−0.747287	+	0.664501i	$0.768644\pi$
$332$	7.66740e9	−	8.69004e9i	0.631097	−	0.715269i
$333$	5.12644e9			0.416906
$334$	1.08235e9	−	2.86264e9i	0.0869722	−	0.230028i
$335$			2.85943e9i			0.227039i
$336$	6.09862e8	+	4.85840e9i	0.0478492	+	0.381185i
$337$	9.96774e9			0.772818			0.386409	−	0.922328i	$-0.373715\pi$
$337$	9.96774e9			0.772818			0.386409	+	0.922328i	$0.373715\pi$
$338$	−6.79911e9	−	2.57070e9i	−0.520937	−	0.196963i
$339$			5.87179e8i			0.0444602i
$340$	−3.18231e9	−	2.80782e9i	−0.238137	−	0.210113i
$341$	4.57369e9			0.338259
$342$	−4.91591e9	+	1.30018e10i	−0.359335	+	0.950385i
$343$			7.98860e9i			0.577157i
$344$	8.66328e9	−	4.58040e9i	0.618655	−	0.327092i
$345$	−2.17196e9			−0.153312
$346$	−1.06978e8	−	4.04478e7i	−0.00746433	−	0.00282222i
$347$		−	2.54624e10i		−	1.75623i	−0.478449	−	0.878115i	$-0.658801\pi$
$347$		−	2.54624e10i		−	1.75623i	0.478449	−	0.878115i	$-0.341199\pi$
$348$	4.38048e9	−	4.96472e9i	0.298679	−	0.338515i
$349$	−9.16614e9			−0.617853			−0.308926	−	0.951086i	$-0.599970\pi$
$349$	−9.16614e9			−0.617853			−0.308926	+	0.951086i	$0.599970\pi$
$350$	1.31462e9	−	3.47697e9i	0.0876050	−	0.231702i
$351$		−	1.11840e10i		−	0.736835i
$352$	−2.86107e10	−	6.89870e9i	−1.86362	−	0.449362i
$353$	8.85659e9			0.570384			0.285192	−	0.958470i	$-0.407943\pi$
$353$	8.85659e9			0.570384			0.285192	+	0.958470i	$0.407943\pi$
$354$	−2.68214e9	−	1.01410e9i	−0.170793	−	0.0645757i
$355$			9.94378e9i			0.626092i
$356$	9.03226e9	+	7.96935e9i	0.562337	+	0.496161i
$357$	4.43141e9			0.272816
$358$	−6.35850e9	+	1.68172e10i	−0.387100	+	1.02382i
$359$			2.43857e10i			1.46811i	0.679091	+	0.734054i	$0.262374\pi$
$359$			2.43857e10i			1.46811i	−0.679091	+	0.734054i	$0.737626\pi$
$360$	3.17311e9	+	6.00156e9i	0.188919	+	0.357317i
$361$	−4.48118e9			−0.263854
$362$	−1.13009e10	−	4.27280e9i	−0.658080	−	0.248816i
$363$			1.44069e10i			0.829746i
$364$	−1.79496e10	+	2.03436e10i	−1.02247	+	1.15884i
$365$	1.09158e9			0.0615014
$366$	7.73205e8	−	2.04501e9i	0.0430894	−	0.113965i
$367$		−	1.67254e9i		−	0.0921958i	−0.998937	−	0.0460979i	$-0.985321\pi$
$367$		−	1.67254e9i		−	0.0921958i	0.998937	−	0.0460979i	$-0.0146786\pi$
$368$	−2.01113e10	+	2.52452e9i	−1.09660	+	0.137653i
$369$	8.99561e9			0.485205
$370$	3.61643e9	+	1.36735e9i	0.192963	+	0.0729580i
$371$		−	2.90874e10i		−	1.53536i
$372$	7.85929e8	+	6.93441e8i	0.0410404	+	0.0362108i
$373$	−1.48837e10			−0.768908			−0.384454	−	0.923144i	$-0.625610\pi$
$373$	−1.48837e10			−0.768908			−0.384454	+	0.923144i	$0.625610\pi$
$374$	−9.41976e9	+	2.49138e10i	−0.481452	+	1.27337i
$375$			5.48640e8i			0.0277436i
$376$	−7.78684e9	+	4.11702e9i	−0.389592	+	0.205983i
$377$	3.66848e10			1.81602
$378$	−1.39670e10	−	5.28083e9i	−0.684124	−	0.258663i
$379$			1.45780e9i			0.0706546i	0.999376	+	0.0353273i	$0.0112474\pi$
$379$			1.45780e9i			0.0706546i	−0.999376	+	0.0353273i	$0.988753\pi$
$380$	−6.93583e9	+	7.86090e9i	−0.332632	+	0.376997i
$381$	−7.95969e9			−0.377743
$382$	3.91958e9	−	1.03667e10i	0.184071	−	0.486839i
$383$		−	1.66897e10i		−	0.775630i	−0.921737	−	0.387815i	$-0.873230\pi$
$383$		−	1.66897e10i		−	0.775630i	0.921737	−	0.387815i	$-0.126770\pi$
$384$	−3.87043e9	−	5.52327e9i	−0.178006	−	0.254022i
$385$	−2.33293e10			−1.06184
$386$	2.87212e10	+	1.08593e10i	1.29376	+	0.489162i
$387$			1.41868e10i			0.632472i
$388$	−2.35657e9	−	2.07925e9i	−0.103981	−	0.0917443i
$389$	−1.67183e9			−0.0730120			−0.0365060	−	0.999333i	$-0.511623\pi$
$389$	−1.67183e9			−0.0730120			−0.0365060	+	0.999333i	$0.511623\pi$
$390$	1.41615e9	−	3.74551e9i	0.0612142	−	0.161902i
$391$			1.83438e10i			0.784841i
$392$	5.89365e9	+	1.11471e10i	0.249598	+	0.472084i
$393$	1.15258e10			0.483170
$394$	1.03611e10	+	3.91749e9i	0.429955	+	0.162563i
$395$		−	8.86329e8i		−	0.0364088i
$396$	2.81889e10	−	3.19485e10i	1.14630	−	1.29918i
$397$	7.22887e8			0.0291010			0.0145505	−	0.999894i	$-0.495368\pi$
$397$	7.22887e8			0.0291010			0.0145505	+	0.999894i	$0.495368\pi$
$398$	−4.10755e7	+	1.08638e8i	−0.00163701	+	0.00432962i
$399$		−	1.09464e10i		−	0.431896i
$400$	6.37695e8	+	5.08013e9i	0.0249100	+	0.198443i
$401$	1.07199e10			0.414584			0.207292	−	0.978279i	$-0.433535\pi$
$401$	1.07199e10			0.414584			0.207292	+	0.978279i	$0.433535\pi$
$402$	3.84673e9	+	1.45443e9i	0.147295	+	0.0556913i
$403$			5.80730e9i			0.220168i
$404$	−3.72430e10	−	3.28603e10i	−1.39804	−	1.23352i
$405$	−8.67041e9			−0.322270
$406$	1.73216e10	−	4.58130e10i	0.637507	−	1.68611i
$407$		−	2.42650e10i		−	0.884306i
$408$	−5.39597e9	+	2.85293e9i	−0.194728	+	0.102956i
$409$	4.25295e10			1.51984			0.759919	−	0.650017i	$-0.225238\pi$
$409$	4.25295e10			1.51984			0.759919	+	0.650017i	$0.225238\pi$
$410$	6.34592e9	+	2.39936e9i	0.224574	+	0.0849101i
$411$		−	5.81013e8i		−	0.0203619i
$412$	−1.91737e10	+	2.17309e10i	−0.665451	+	0.754206i
$413$	−2.12119e10			−0.729087
$414$	1.03776e10	−	2.74471e10i	0.353260	−	0.934318i
$415$			1.26533e10i			0.426590i
$416$	8.75940e9	−	3.63276e10i	0.292483	−	1.21301i
$417$	1.18195e9			0.0390891
$418$	6.15416e10	+	2.32685e10i	2.01588	+	0.762191i
$419$		−	2.75400e10i		−	0.893526i	−0.894652	−	0.446763i	$-0.852577\pi$
$419$		−	2.75400e10i		−	0.893526i	0.894652	−	0.446763i	$-0.147423\pi$
$420$	−4.00883e9	−	3.53707e9i	−0.128831	−	0.113670i
$421$	−4.63614e10			−1.47580			−0.737901	−	0.674909i	$-0.764183\pi$
$421$	−4.63614e10			−1.47580			−0.737901	+	0.674909i	$0.764183\pi$
$422$	−3.22559e9	+	8.53120e9i	−0.101709	+	0.269005i
$423$		−	1.27516e10i		−	0.398293i
$424$	1.87264e10	+	3.54187e10i	0.579417	+	1.09590i
$425$	4.63366e9			0.142026
$426$	1.33772e10	+	5.05783e9i	0.406187	+	0.153577i
$427$		−	1.61731e10i		−	0.486498i
$428$	−1.30563e10	+	1.47977e10i	−0.389086	+	0.440980i
$429$	−2.51311e10			−0.741963
$430$	−3.78399e9	+	1.00081e10i	−0.110682	+	0.292736i
$431$			6.14248e10i			1.78006i	0.455903	+	0.890030i	$0.349317\pi$
$431$			6.14248e10i			1.78006i	−0.455903	+	0.890030i	$0.650683\pi$
$432$	2.04069e10	−	2.56162e9i	0.585924	−	0.0735494i
$433$	−3.85422e10			−1.09644			−0.548220	−	0.836334i	$-0.684694\pi$
$433$	−3.85422e10			−1.09644			−0.548220	+	0.836334i	$0.684694\pi$
$434$	7.25232e9	+	2.74206e9i	0.204418	+	0.0772891i
$435$			7.22896e9i			0.201892i
$436$	8.28516e9	+	7.31016e9i	0.229274	+	0.202293i
$437$	4.53125e10			1.24249
$438$	5.55226e8	−	1.46849e9i	0.0150860	−	0.0399000i
$439$			4.02551e10i			1.08383i	0.840432	+	0.541917i	$0.182301\pi$
$439$			4.02551e10i			1.08383i	−0.840432	+	0.541917i	$0.817699\pi$
$440$	2.84072e10	−	1.50193e10i	0.757911	−	0.400719i
$441$	−1.82543e10			−0.482627
$442$	−3.16335e10	−	1.19604e10i	−0.828815	−	0.313370i
$443$			5.54040e10i			1.43855i	0.694724	+	0.719276i	$0.255527\pi$
$443$			5.54040e10i			1.43855i	−0.694724	+	0.719276i	$0.744473\pi$
$444$	3.67894e9	−	4.16962e9i	0.0946653	−	0.107291i
$445$	−1.31516e10			−0.335380
$446$	−9.84650e9	+	2.60425e10i	−0.248853	+	0.658177i
$447$		−	2.02388e9i		−	0.0506937i
$448$	−4.12310e10	−	2.80920e10i	−1.02356	−	0.697381i
$449$	−9.19597e9			−0.226262			−0.113131	−	0.993580i	$-0.536088\pi$
$449$	−9.19597e9			−0.226262			−0.113131	+	0.993580i	$0.536088\pi$
$450$	−6.93316e9	−	2.62139e9i	−0.169076	−	0.0639265i
$451$		−	4.25790e10i		−	1.02917i
$452$	−4.48623e9	−	3.95830e9i	−0.107480	−	0.0948319i
$453$	8.15400e9			0.193632
$454$	1.81975e10	−	4.81296e10i	0.428340	−	1.13289i
$455$		−	2.96216e10i		−	0.691135i
$456$	7.04726e9	+	1.33290e10i	0.162990	+	0.308276i
$457$	−1.28995e10			−0.295738			−0.147869	−	0.989007i	$-0.547241\pi$
$457$	−1.28995e10			−0.295738			−0.147869	+	0.989007i	$0.547241\pi$
$458$	−6.05200e10	−	2.28823e10i	−1.37543	−	0.520040i
$459$		−	1.86134e10i		−	0.419347i
$460$	1.46417e10	−	1.65945e10i	0.327009	−	0.370624i
$461$	−7.08431e10			−1.56853			−0.784267	−	0.620424i	$-0.786961\pi$
$461$	−7.08431e10			−1.56853			−0.784267	+	0.620424i	$0.786961\pi$
$462$	−1.18663e10	+	3.13844e10i	−0.260463	+	0.688885i
$463$		−	1.90283e9i		−	0.0414073i	−0.999786	−	0.0207037i	$-0.993409\pi$
$463$		−	1.90283e9i		−	0.0414073i	0.999786	−	0.0207037i	$-0.00659065\pi$
$464$	8.40236e9	+	6.69365e10i	0.181271	+	1.44408i
$465$	−1.14436e9			−0.0244767
$466$	5.28802e10	+	1.99937e10i	1.12137	+	0.423984i
$467$			1.05655e10i			0.222138i	0.993813	+	0.111069i	$0.0354274\pi$
$467$			1.05655e10i			0.222138i	−0.993813	+	0.111069i	$0.964573\pi$
$468$	4.05656e10	+	3.57919e10i	0.845619	+	0.746107i
$469$	3.04221e10			0.628779
$470$	3.40117e9	−	8.99557e9i	0.0697007	−	0.184347i
$471$		−	2.22933e10i		−	0.452993i
$472$	2.58290e10	−	1.36562e10i	0.520402	−	0.275144i
$473$	6.71506e10			1.34155
$474$	−1.19236e9	−	4.50825e8i	−0.0236208	−	0.00893088i
$475$		−	1.14460e10i		−	0.224843i
$476$	−2.98731e10	+	3.38574e10i	−0.581905	+	0.659517i
$477$	−5.80010e10			−1.12037
$478$	4.53527e9	−	1.19951e10i	0.0868743	−	0.229769i
$479$		−	1.54560e10i		−	0.293600i	−0.989166	−	0.146800i	$-0.953103\pi$
$479$		−	1.54560e10i		−	0.293600i	0.989166	−	0.146800i	$-0.0468973\pi$
$480$	7.15857e9	+	1.72609e9i	0.134853	+	0.0325162i
$481$	3.08097e10			0.575582
$482$	−7.53181e10	−	2.84773e10i	−1.39544	−	0.527608i
$483$			2.31080e10i			0.424595i
$484$	−1.10074e11	−	9.71202e10i	−2.00587	−	1.76982i
$485$	3.43131e9			0.0620145
$486$	−1.60612e10	+	4.24794e10i	−0.287895	+	0.761436i
$487$			1.21369e10i			0.215771i	0.994163	+	0.107886i	$0.0344080\pi$
$487$			1.21369e10i			0.215771i	−0.994163	+	0.107886i	$0.965592\pi$
$488$	1.04122e10	+	1.96934e10i	0.183596	+	0.347249i
$489$	1.75841e10			0.307528
$490$	−1.28775e10	−	4.86889e9i	−0.223381	−	0.0844590i
$491$			8.96938e10i			1.54325i	0.636077	+	0.771625i	$0.280556\pi$
$491$			8.96938e10i			1.54325i	−0.636077	+	0.771625i	$0.719444\pi$
$492$	6.45562e9	−	7.31664e9i	0.110174	−	0.124868i
$493$	6.10537e10			1.03353
$494$	−2.95445e10	+	7.81405e10i	−0.496099	+	1.31210i
$495$			4.65192e10i			0.774838i
$496$	−1.05962e10	+	1.33012e9i	−0.175075	+	0.0219767i
$497$	1.05794e11			1.73395
$498$	1.70222e10	+	6.43599e9i	0.276757	+	0.104640i
$499$		−	4.65421e10i		−	0.750662i	−0.926891	−	0.375331i	$-0.877529\pi$
$499$		−	4.65421e10i		−	0.750662i	0.926891	−	0.375331i	$-0.122471\pi$
$500$	−4.19179e9	−	3.69850e9i	−0.0670686	−	0.0591760i
$501$	4.80578e9			0.0762803
$502$	−2.30204e10	+	6.08854e10i	−0.362492	+	0.958735i
$503$		−	1.06861e11i		−	1.66935i	−0.550742	−	0.834675i	$-0.685655\pi$
$503$		−	1.06861e11i		−	1.66935i	0.550742	−	0.834675i	$-0.314345\pi$
$504$	6.38520e10	−	3.37595e10i	0.989584	−	0.523208i
$505$	5.42282e10			0.833796
$506$	−1.29916e11	−	4.91203e10i	−1.98180	−	0.749306i
$507$		−	1.14143e10i		−	0.172750i
$508$	5.36580e10	−	6.08146e10i	0.805711	−	0.913173i
$509$	−3.43543e9			−0.0511811			−0.0255906	−	0.999673i	$-0.508147\pi$
$509$	−3.43543e9			−0.0511811			−0.0255906	+	0.999673i	$0.508147\pi$
$510$	2.35688e9	−	6.23357e9i	0.0348382	−	0.0921417i
$511$		−	1.16136e10i		−	0.170327i
$512$	6.82910e10	+	7.66221e9i	0.993764	+	0.111500i
$513$	−4.59784e10			−0.663872
$514$	8.89550e10	+	3.36333e10i	1.27444	+	0.481856i
$515$		−	3.16417e10i		−	0.449811i
$516$	1.15389e10	+	1.01811e10i	0.162767	+	0.143613i
$517$	−6.03572e10			−0.844825
$518$	1.45476e10	−	3.84761e10i	0.202056	−	0.534406i
$519$		−	1.79594e8i		−	0.00247527i
$520$	1.90703e10	+	3.60692e10i	0.260822	+	0.493313i
$521$	8.02756e10			1.08951			0.544757	−	0.838594i	$-0.316622\pi$
$521$	8.02756e10			1.08951			0.544757	+	0.838594i	$0.316622\pi$
$522$	−9.13523e10	−	3.45398e10i	−1.23037	−	0.465198i
$523$		−	1.18432e11i		−	1.58293i	−0.611212	−	0.791467i	$-0.709318\pi$
$523$		−	1.18432e11i		−	1.58293i	0.611212	−	0.791467i	$-0.290682\pi$
$524$	−7.76977e10	+	8.80606e10i	−1.03058	+	1.16804i
$525$	5.83712e9			0.0768354
$526$	3.24754e10	−	8.58923e10i	0.424240	−	1.12205i
$527$			9.66496e9i			0.125302i
$528$	−5.75608e9	−	4.58552e10i	−0.0740613	−	0.590001i
$529$	−1.73445e10			−0.221482
$530$	−4.09167e10	−	1.54703e10i	−0.518557	−	0.196063i
$531$			4.22970e10i			0.532025i
$532$	8.36340e10	+	7.37920e10i	1.04409	+	0.921218i
$533$	5.40633e10			0.669874
$534$	−6.68944e9	+	1.76925e10i	−0.0822669	+	0.217583i
$535$		−	2.15464e10i		−	0.263002i
$536$	−3.70439e10	+	1.95857e10i	−0.448805	+	0.237290i
$537$	−2.82327e10			−0.339512
$538$	8.69042e10	+	3.28579e10i	1.03732	+	0.392203i
$539$			8.64034e10i			1.02371i
$540$	−1.48568e10	+	1.68384e10i	−0.174724	+	0.198027i
$541$	−1.04411e10			−0.121887			−0.0609433	−	0.998141i	$-0.519411\pi$
$541$	−1.04411e10			−0.121887			−0.0609433	+	0.998141i	$0.519411\pi$
$542$	2.08157e10	−	5.50542e10i	0.241209	−	0.637960i
$543$		−	1.89719e10i		−	0.218228i
$544$	1.45781e10	−	6.04591e10i	0.166458	−	0.690345i
$545$	−1.20637e10			−0.136740
$546$	−3.98494e10	−	1.50668e10i	−0.448385	−	0.169532i
$547$			1.22606e11i			1.36950i	0.728780	+	0.684748i	$0.240088\pi$
$547$			1.22606e11i			1.36950i	−0.728780	+	0.684748i	$0.759912\pi$
$548$	4.43913e9	+	3.91673e9i	0.0492238	+	0.0434312i
$549$	−3.22495e10			−0.355004
$550$	−1.24078e10	+	3.28168e10i	−0.135596	+	0.358629i
$551$		−	1.50814e11i		−	1.63619i
$552$	−1.48769e10	−	2.81378e10i	−0.160234	−	0.303064i
$553$	−9.42986e9			−0.100834
$554$	2.45381e10	+	9.27772e9i	0.260497	+	0.0984923i
$555$			6.07124e9i			0.0639890i
$556$	−7.96779e9	+	9.03050e9i	−0.0833756	+	0.0944958i
$557$	−5.92421e10			−0.615474			−0.307737	−	0.951471i	$-0.599572\pi$
$557$	−5.92421e10			−0.615474			−0.307737	+	0.951471i	$0.599572\pi$
$558$	5.46773e9	−	1.44613e10i	0.0563989	−	0.149166i
$559$			8.52623e10i			0.873192i
$560$	5.40487e10	−	6.78459e9i	0.549583	−	0.0689877i
$561$	−4.18251e10			−0.422266
$562$	2.52029e10	+	9.52906e9i	0.252642	+	0.0955223i
$563$			4.07691e10i			0.405786i	0.979201	+	0.202893i	$0.0650344\pi$
$563$			4.07691e10i			0.405786i	−0.979201	+	0.202893i	$0.934966\pi$
$564$	−1.03716e10	−	9.15106e9i	−0.102501	−	0.0904389i
$565$	6.53225e9			0.0641016
$566$	−5.65166e10	+	1.49478e11i	−0.550694	+	1.45650i
$567$			9.22466e10i			0.892520i
$568$	−1.28822e11	+	6.81101e10i	−1.23765	+	0.654362i
$569$	−2.03083e11			−1.93742			−0.968710	−	0.248196i	$-0.920162\pi$
$569$	−2.03083e11			−1.93742			−0.968710	+	0.248196i	$0.920162\pi$
$570$	−1.53981e10	−	5.82191e9i	−0.145870	−	0.0551527i
$571$		−	6.32153e9i		−	0.0594672i	−0.999558	−	0.0297336i	$-0.990534\pi$
$571$		−	6.32153e9i		−	0.0594672i	0.999558	−	0.0297336i	$-0.00946589\pi$
$572$	1.69414e11	−	1.92010e11i	1.58258	−	1.79365i
$573$	1.74035e10			0.161443
$574$	2.55273e10	−	6.75158e10i	0.235157	−	0.621953i
$575$			2.41627e10i			0.221041i
$576$	−5.60160e10	+	8.22155e10i	−0.508888	+	0.746902i
$577$	−2.07819e11			−1.87492			−0.937459	−	0.348095i	$-0.886829\pi$
$577$	−2.07819e11			−1.87492			−0.937459	+	0.348095i	$0.886829\pi$
$578$	5.17522e10	+	1.95672e10i	0.463679	+	0.175314i
$579$			4.82169e10i			0.429028i
$580$	−5.52316e10	−	4.87320e10i	−0.488063	−	0.430628i
$581$	1.34621e11			1.18143
$582$	1.74531e9	−	4.61608e9i	0.0152118	−	0.0402329i
$583$			2.74537e11i			2.37644i
$584$	7.47681e9	+	1.41415e10i	0.0642784	+	0.121575i
$585$	−5.90662e10			−0.504331
$586$	9.44363e10	+	3.57058e10i	0.800845	+	0.302795i
$587$		−	1.85427e11i		−	1.56178i	−0.624669	−	0.780890i	$-0.714766\pi$
$587$		−	1.85427e11i		−	1.56178i	0.624669	−	0.780890i	$-0.285234\pi$
$588$	−1.31001e10	+	1.48473e10i	−0.109588	+	0.124205i
$589$	2.38742e10			0.198366
$590$	−1.12817e10	+	2.98383e10i	−0.0931035	+	0.246244i
$591$			1.73942e10i			0.142579i
$592$	7.05672e9	+	5.62166e10i	0.0574534	+	0.457697i
$593$	−2.29021e11			−1.85207			−0.926035	−	0.377438i	$-0.876805\pi$
$593$	−2.29021e11			−1.85207			−0.926035	+	0.377438i	$0.876805\pi$
$594$	1.31825e11	+	4.98422e10i	1.05889	+	0.400361i
$595$		−	4.92986e10i		−	0.393339i
$596$	1.54631e10	+	1.36434e10i	0.122549	+	0.108128i
$597$	−1.82381e8			−0.00143576
$598$	6.23689e10	−	1.64956e11i	0.487712	−	1.28992i
$599$		−	3.24407e10i		−	0.251990i	−0.992031	−	0.125995i	$-0.959788\pi$
$599$		−	3.24407e10i		−	0.251990i	0.992031	−	0.125995i	$-0.0402124\pi$
$600$	−7.10765e9	+	3.75792e9i	−0.0548430	+	0.0289963i
$601$	1.72826e11			1.32468			0.662339	−	0.749204i	$-0.269564\pi$
$601$	1.72826e11			1.32468			0.662339	+	0.749204i	$0.269564\pi$
$602$	1.06478e11	+	4.02587e10i	0.810726	+	0.306531i
$603$		−	6.06624e10i		−	0.458829i
$604$	−5.49678e10	+	6.22992e10i	−0.413010	+	0.468096i
$605$	1.60274e11			1.19631
$606$	2.75828e10	−	7.29522e10i	0.204526	−	0.540939i
$607$		−	1.39025e11i		−	1.02409i	−0.858958	−	0.512045i	$-0.828888\pi$
$607$		−	1.39025e11i		−	1.02409i	0.858958	−	0.512045i	$-0.171112\pi$
$608$	−1.49345e11	−	3.60105e10i	−1.09289	−	0.263521i
$609$	7.69106e10			0.559136
$610$	−2.27503e10	−	8.60176e9i	−0.164312	−	0.0621252i
$611$		−	7.66366e10i		−	0.549884i
$612$	6.75125e10	+	5.95676e10i	0.481258	+	0.424624i
$613$	2.20690e9			0.0156293			0.00781466	−	0.999969i	$-0.497512\pi$
$613$	2.20690e9			0.0156293			0.00781466	+	0.999969i	$0.497512\pi$
$614$	9.83432e10	−	2.60102e11i	0.691944	−	1.83008i
$615$			1.06535e10i			0.0744718i
$616$	−1.59794e11	−	3.02231e11i	−1.10978	−	2.09902i
$617$	9.75280e10			0.672959			0.336480	−	0.941691i	$-0.390764\pi$
$617$	9.75280e10			0.672959			0.336480	+	0.941691i	$0.390764\pi$
$618$	−4.25669e10	−	1.60943e10i	−0.291822	−	0.110336i
$619$		−	1.62166e11i		−	1.10458i	−0.833652	−	0.552291i	$-0.813754\pi$
$619$		−	1.62166e11i		−	1.10458i	0.833652	−	0.552291i	$-0.186246\pi$
$620$	7.71439e9	−	8.74330e9i	0.0522078	−	0.0591710i
$621$	9.70613e10			0.652649
$622$	6.90847e8	−	1.82718e9i	0.00461552	−	0.0122073i
$623$			1.39923e11i			0.928829i
$624$	5.82231e10	−	7.30859e9i	0.384023	−	0.0482054i
$625$	6.10352e9			0.0400000
$626$	3.60744e10	+	1.36395e10i	0.234910	+	0.0888182i
$627$			1.03316e11i			0.668492i
$628$	1.70328e11	+	1.50284e11i	1.09509	+	0.966216i
$629$	5.12759e10			0.327575
$630$	−2.78896e10	+	7.37636e10i	−0.177043	+	0.468252i
$631$		−	1.15288e11i		−	0.727222i	−0.931551	−	0.363611i	$-0.881544\pi$
$631$		−	1.15288e11i		−	0.727222i	0.931551	−	0.363611i	$-0.118456\pi$
$632$	1.14824e10	−	6.07092e9i	0.0719722	−	0.0380527i
$633$	−1.43221e10			−0.0892056
$634$	9.22442e10	+	3.48770e10i	0.570929	+	0.215865i
$635$			8.85500e10i			0.544620i
$636$	−4.16239e10	+	4.71755e10i	−0.254399	+	0.288329i
$637$	−1.09708e11			−0.666316
$638$	−1.63487e11	+	4.32399e11i	−0.986737	+	2.60977i
$639$		−	2.10956e11i		−	1.26529i
$640$	−6.14453e10	+	4.30578e10i	−0.366243	+	0.256644i
$641$	4.76794e10			0.282422			0.141211	−	0.989980i	$-0.454900\pi$
$641$	4.76794e10			0.282422			0.141211	+	0.989980i	$0.454900\pi$
$642$	−2.89860e10	−	1.09594e10i	−0.170627	−	0.0645131i
$643$		−	5.28167e10i		−	0.308978i	−0.987995	−	0.154489i	$-0.950627\pi$
$643$		−	5.28167e10i		−	0.308978i	0.987995	−	0.154489i	$-0.0493731\pi$
$644$	−1.76553e11	−	1.55776e11i	−1.02643	−	0.905645i
$645$	−1.68015e10			−0.0970752
$646$	−4.91702e10	+	1.30047e11i	−0.282340	+	0.746744i
$647$			2.36573e10i			0.135005i	0.997719	+	0.0675023i	$0.0215030\pi$
$647$			2.36573e10i			0.135005i	−0.997719	+	0.0675023i	$0.978497\pi$
$648$	−5.93881e10	−	1.12325e11i	−0.336821	−	0.637056i
$649$	2.00205e11			1.12849
$650$	−4.16681e10	−	1.57544e10i	−0.233426	−	0.0882571i
$651$			1.21752e10i			0.0677876i
$652$	−1.18538e11	+	1.34348e11i	−0.655945	+	0.743432i
$653$	−2.13122e10			−0.117213			−0.0586064	−	0.998281i	$-0.518666\pi$
$653$	−2.13122e10			−0.117213			−0.0586064	+	0.998281i	$0.518666\pi$
$654$	−6.13613e9	+	1.62291e10i	−0.0335416	+	0.0887122i
$655$		−	1.28222e11i		−	0.696622i
$656$	1.23828e10	+	9.86460e10i	0.0668655	+	0.532677i
$657$	−2.31578e10			−0.124290
$658$	−9.57060e10	−	3.61859e10i	−0.510547	−	0.193035i
$659$			2.55641e11i			1.35547i	0.735307	+	0.677734i	$0.237038\pi$
$659$			2.55641e11i			1.35547i	−0.735307	+	0.677734i	$0.762962\pi$
$660$	3.78367e10	+	3.33841e10i	0.199405	+	0.175940i
$661$	2.42293e11			1.26921			0.634607	−	0.772835i	$-0.281162\pi$
$661$	2.42293e11			1.26921			0.634607	+	0.772835i	$0.281162\pi$
$662$	9.02699e10	−	2.38750e11i	0.470014	−	1.24311i
$663$		−	5.31061e10i		−	0.274846i
$664$	−1.63923e11	+	8.66687e10i	−0.843273	+	0.445851i
$665$	−1.21777e11			−0.622697
$666$	−7.67222e10	−	2.90082e10i	−0.389964	−	0.147443i
$667$			3.18371e11i			1.60853i
$668$	−3.23968e10	+	3.67177e10i	−0.162703	+	0.184404i
$669$	−4.37199e10			−0.218260
$670$	1.61802e10	−	4.27941e10i	0.0802944	−	0.212366i
$671$			1.52647e11i			0.753005i
$672$	1.83643e10	−	7.61617e10i	0.0900529	−	0.373473i
$673$	−2.71463e11			−1.32327			−0.661637	−	0.749824i	$-0.730138\pi$
$673$	−2.71463e11			−1.32327			−0.661637	+	0.749824i	$0.730138\pi$
$674$	−1.49177e11	−	5.64030e10i	−0.722874	−	0.273314i
$675$		−	2.45178e10i		−	0.118104i
$676$	8.72089e10	+	7.69462e10i	0.417613	+	0.368469i
$677$	2.06285e11			0.982002			0.491001	−	0.871159i	$-0.336631\pi$
$677$	2.06285e11			0.982002			0.491001	+	0.871159i	$0.336631\pi$
$678$	3.32258e9	−	8.78771e9i	0.0157238	−	0.0415869i
$679$		−	3.65066e10i		−	0.171748i
$680$	3.17383e10	+	6.00291e10i	0.148439	+	0.280754i
$681$	8.07997e10			0.375683
$682$	−6.84498e10	−	2.58805e10i	−0.316399	−	0.119629i
$683$			7.73768e10i			0.355572i	0.984069	+	0.177786i	$0.0568935\pi$
$683$			7.73768e10i			0.355572i	−0.984069	+	0.177786i	$0.943106\pi$
$684$	1.47143e11	−	1.66768e11i	0.672226	−	0.761884i
$685$	−6.46366e9			−0.0293573
$686$	4.52039e10	−	1.19557e11i	0.204117	−	0.539858i
$687$		−	1.01601e11i		−	0.456110i
$688$	−1.55573e11	+	1.95287e10i	−0.694353	+	0.0871603i
$689$	−3.48584e11			−1.54679
$690$	3.25056e10	+	1.22902e10i	0.143404	+	0.0542203i
$691$		−	2.56757e11i		−	1.12619i	−0.826393	−	0.563093i	$-0.809611\pi$
$691$		−	2.56757e11i		−	1.12619i	0.826393	−	0.563093i	$-0.190389\pi$
$692$	1.37216e9	+	1.21068e9i	0.00598384	+	0.00527966i
$693$	4.94928e11			2.14590
$694$	−1.44080e11	+	3.81070e11i	−0.621108	+	1.64273i
$695$		−	1.31490e10i		−	0.0563577i
$696$	−9.36513e10	+	4.95148e10i	−0.399096	+	0.211008i
$697$	8.99763e10			0.381239
$698$	1.37180e11	+	5.18671e10i	0.577924	+	0.218509i
$699$			8.87749e10i			0.371862i
$700$	−3.93492e10	+	4.45974e10i	−0.163887	+	0.185745i
$701$	−4.26903e11			−1.76790			−0.883950	−	0.467582i	$-0.845125\pi$
$701$	−4.26903e11			−1.76790			−0.883950	+	0.467582i	$0.845125\pi$
$702$	−6.32855e10	+	1.67380e11i	−0.260589	+	0.689217i
$703$		−	1.26661e11i		−	0.518586i
$704$	3.89151e11	+	2.65141e11i	1.58427	+	1.07941i
$705$	1.51017e10			0.0611321
$706$	−1.32548e11	−	5.01155e10i	−0.533523	−	0.201722i
$707$		−	5.76947e11i		−	2.30918i
$708$	3.44026e10	+	3.03541e10i	0.136917	+	0.120805i
$709$	5.42828e10			0.214821			0.107411	−	0.994215i	$-0.465744\pi$
$709$	5.42828e10			0.214821			0.107411	+	0.994215i	$0.465744\pi$
$710$	5.62674e10	−	1.48819e11i	0.221423	−	0.585630i
$711$			1.88034e10i			0.0735796i
$712$	−9.00817e10	−	1.70379e11i	−0.350523	−	0.662972i
$713$	−5.03989e10			−0.195013
$714$	−6.63204e10	−	2.50754e10i	−0.255185	−	0.0964838i
$715$			2.79578e11i			1.06974i
$716$	1.90323e11	−	2.15707e11i	0.724166	−	0.820752i
$717$	2.01373e10			0.0761945
$718$	1.37988e11	−	3.64956e11i	0.519210	−	1.37323i
$719$			3.06039e11i			1.14515i	0.819853	+	0.572574i	$0.194055\pi$
$719$			3.06039e11i			1.14515i	−0.819853	+	0.572574i	$0.805945\pi$
$720$	−1.35286e10	−	1.07774e11i	−0.0503413	−	0.401038i
$721$	−3.36643e11			−1.24574
$722$	6.70653e10	+	2.53570e10i	0.246802	+	0.0933145i
$723$		−	1.26444e11i		−	0.462747i
$724$	1.44951e11	+	1.27893e11i	0.527555	+	0.465473i
$725$	8.04208e10			0.291083
$726$	8.15224e10	−	2.15614e11i	0.293448	−	0.776123i
$727$			4.50991e11i			1.61447i	0.590230	+	0.807235i	$0.299037\pi$
$727$			4.50991e11i			1.61447i	−0.590230	+	0.807235i	$0.700963\pi$
$728$	3.83748e11	−	2.02893e11i	1.36622	−	0.722341i
$729$	1.32209e11			0.468114
$730$	−1.63366e10	−	6.17678e9i	−0.0575268	−	0.0217506i
$731$			1.41900e11i			0.496951i
$732$	−2.31436e10	+	2.62303e10i	−0.0806094	+	0.0913607i
$733$	1.34855e10			0.0467143			0.0233572	−	0.999727i	$-0.492565\pi$
$733$	1.34855e10			0.0467143			0.0233572	+	0.999727i	$0.492565\pi$
$734$	−9.46413e9	+	2.50311e10i	−0.0326059	+	0.0862376i
$735$		−	2.16186e10i		−	0.0740762i
$736$	3.15270e11	+	7.60189e10i	1.07441	+	0.259066i
$737$	−2.87134e11			−0.973228
$738$	−1.34628e11	−	5.09021e10i	−0.453848	−	0.171597i
$739$		−	1.83860e11i		−	0.616468i	−0.951311	−	0.308234i	$-0.900262\pi$
$739$		−	1.83860e11i		−	0.616468i	0.951311	−	0.308234i	$-0.0997379\pi$
$740$	−4.63862e10	−	4.09275e10i	−0.154690	−	0.136486i
$741$	−1.31182e11			−0.435111
$742$	−1.64593e11	+	4.35322e11i	−0.542994	+	1.43613i
$743$		−	1.29363e11i		−	0.424479i	−0.977218	−	0.212239i	$-0.931924\pi$
$743$		−	1.29363e11i		−	0.424479i	0.977218	−	0.212239i	$-0.0680756\pi$
$744$	−7.83833e9	−	1.48252e10i	−0.0255818	−	0.0483849i
$745$	−2.25152e10			−0.0730889
$746$	2.22749e11	+	8.42199e10i	0.719216	+	0.271931i
$747$		−	2.68438e11i		−	0.862107i
$748$	2.81952e11	−	3.19557e11i	0.900676	−	1.02080i
$749$	−2.29237e11			−0.728380
$750$	3.10451e9	−	8.21094e9i	0.00981178	−	0.0259506i
$751$			3.85535e11i			1.21200i	0.795463	+	0.606002i	$0.207228\pi$
$751$			3.85535e11i			1.21200i	−0.795463	+	0.606002i	$0.792772\pi$
$752$	1.39834e11	−	1.75530e10i	0.437262	−	0.0548883i
$753$	−1.02214e11			−0.317929
$754$	−5.49024e11	−	2.07583e11i	−1.69866	−	0.642253i
$755$		−	9.07116e10i		−	0.279174i
$756$	1.79148e11	+	1.58066e11i	0.548433	+	0.483894i
$757$	3.11453e11			0.948438			0.474219	−	0.880407i	$-0.342731\pi$
$757$	3.11453e11			0.948438			0.474219	+	0.880407i	$0.342731\pi$
$758$	8.24902e9	−	2.18174e10i	0.0249877	−	0.0660885i
$759$		−	2.18101e11i		−	0.657191i
$760$	1.48283e11	−	7.83994e10i	0.444464	−	0.234995i
$761$	−3.05630e10			−0.0911290			−0.0455645	−	0.998961i	$-0.514509\pi$
$761$	−3.05630e10			−0.0911290			−0.0455645	+	0.998961i	$0.514509\pi$
$762$	1.19125e11	+	4.50403e10i	0.353331	+	0.133592i
$763$			1.28349e11i			0.378699i
$764$	−1.17321e11	+	1.32968e11i	−0.344351	+	0.390279i
$765$	−9.83025e10			−0.287024
$766$	−9.44398e10	+	2.49779e11i	−0.274309	+	0.725504i
$767$			2.54204e11i			0.734514i
$768$	2.66711e10	+	1.04562e11i	0.0766648	+	0.300559i
$769$	3.15627e11			0.902544			0.451272	−	0.892386i	$-0.350970\pi$
$769$	3.15627e11			0.902544			0.451272	+	0.892386i	$0.350970\pi$
$770$	3.49146e11	+	1.32010e11i	0.993217	+	0.375529i
$771$			1.49337e11i			0.422620i
$772$	−3.68393e11	−	3.25041e11i	−1.03715	−	0.915100i
$773$	5.78869e11			1.62130			0.810649	−	0.585533i	$-0.199115\pi$
$773$	5.78869e11			1.62130			0.810649	+	0.585533i	$0.199115\pi$
$774$	8.02769e10	−	2.12320e11i	0.223680	−	0.591598i
$775$			1.27308e10i			0.0352898i
$776$	2.35028e10	+	4.44527e10i	0.0648146	+	0.122589i
$777$	6.45934e10			0.177216
$778$	2.50206e10	+	9.46015e9i	0.0682935	+	0.0258214i
$779$		−	2.22258e11i		−	0.603542i
$780$	−4.23883e10	+	4.80419e10i	−0.114516	+	0.129790i
$781$	−9.98522e11			−2.68382
$782$	1.03799e11	−	2.74533e11i	0.277566	−	0.734120i
$783$		−	3.23050e11i		−	0.859453i
$784$	−2.51277e10	−	2.00177e11i	−0.0665103	−	0.529847i
$785$	−2.48009e11			−0.653113
$786$	−1.72495e11	−	6.52192e10i	−0.451945	−	0.170878i
$787$			1.55052e11i			0.404184i	0.979367	+	0.202092i	$0.0647740\pi$
$787$			1.55052e11i			0.404184i	−0.979367	+	0.202092i	$0.935226\pi$
$788$	−1.32897e11	−	1.17258e11i	−0.344677	−	0.304115i
$789$	1.44196e11			0.372086
$790$	−5.01534e9	+	1.32648e10i	−0.0128763	+	0.0340559i
$791$		−	6.94981e10i		−	0.177528i
$792$	−6.02657e11	+	3.18633e11i	−1.53168	+	0.809824i
$793$	−1.93818e11			−0.490120
$794$	−1.08187e10	−	4.09049e9i	−0.0272204	−	0.0102919i
$795$		−	6.86906e10i		−	0.171961i
$796$	1.22947e9	−	1.39345e9i	0.00306243	−	0.00347088i
$797$	1.48153e11			0.367179			0.183589	−	0.983003i	$-0.441228\pi$
$797$	1.48153e11			0.367179			0.183589	+	0.983003i	$0.441228\pi$
$798$	−6.19407e10	+	1.63824e11i	−0.152744	+	0.403985i
$799$		−	1.27545e11i		−	0.312950i
$800$	1.92024e10	−	7.96376e10i	0.0468810	−	0.194428i
$801$	2.79009e11			0.677779
$802$	−1.60434e11	−	6.06591e10i	−0.387791	−	0.146622i
$803$			1.09613e11i			0.263633i
$804$	−4.93402e10	−	4.35339e10i	−0.118080	−	0.104184i
$805$	2.57072e11			0.612170
$806$	3.28609e10	−	8.69119e10i	0.0778644	−	0.205939i
$807$			1.45894e11i			0.343988i
$808$	3.71437e11	+	7.02528e11i	0.871444	+	1.64823i
$809$	−1.51376e10			−0.0353397			−0.0176699	−	0.999844i	$-0.505625\pi$
$809$	−1.51376e10			−0.0353397			−0.0176699	+	0.999844i	$0.505625\pi$
$810$	1.29761e11	+	4.90620e10i	0.301443	+	0.113974i
$811$			4.63814e11i			1.07216i	0.844166	+	0.536081i	$0.180096\pi$
$811$			4.63814e11i			1.07216i	−0.844166	+	0.536081i	$0.819904\pi$
$812$	−5.18471e11	+	5.87622e11i	−1.19262	+	1.35168i
$813$	9.24247e10			0.211556
$814$	−1.37305e11	+	3.63150e11i	−0.312743	+	0.827157i
$815$		−	1.95620e11i		−	0.443386i
$816$	9.68995e10	−	1.21635e10i	0.218555	−	0.0274346i
$817$	3.50519e11			0.786727
$818$	−6.36497e11	−	2.40656e11i	−1.42162	−	0.537505i
$819$			6.28419e11i			1.39673i
$820$	−8.13961e10	−	7.18175e10i	−0.180031	−	0.158845i
$821$	−5.46804e11			−1.20354			−0.601768	−	0.798671i	$-0.705537\pi$
$821$	−5.46804e11			−1.20354			−0.601768	+	0.798671i	$0.705537\pi$
$822$	−3.28769e9	+	8.69543e9i	−0.00720118	+	0.0190460i
$823$		−	3.70165e11i		−	0.806855i	−0.915012	−	0.403428i	$-0.867819\pi$
$823$		−	3.70165e11i		−	0.806855i	0.915012	−	0.403428i	$-0.132181\pi$
$824$	4.09918e11	−	2.16730e11i	0.889178	−	0.470122i
$825$	−5.50926e10			−0.118926
$826$	3.17457e11	+	1.20029e11i	0.681969	+	0.257849i
$827$		−	3.48813e10i		−	0.0745712i	−0.999305	−	0.0372856i	$-0.988129\pi$
$827$		−	3.48813e10i		−	0.0745712i	0.999305	−	0.0372856i	$-0.0118711\pi$
$828$	−3.10622e11	+	3.52051e11i	−0.660861	+	0.749004i
$829$	5.96780e11			1.26356			0.631781	−	0.775147i	$-0.282324\pi$
$829$	5.96780e11			1.26356			0.631781	+	0.775147i	$0.282324\pi$
$830$	7.15992e10	−	1.89369e11i	0.150867	−	0.399021i
$831$			4.11944e10i			0.0863842i
$832$	−3.36654e11	+	4.94112e11i	−0.702572	+	1.03117i
$833$	−1.82584e11			−0.379214
$834$	−1.76891e10	−	6.68814e9i	−0.0365629	−	0.0138242i
$835$		−	5.34633e10i		−	0.109979i
$836$	−7.89365e11	−	6.96473e11i	−1.61604	−	1.42587i
$837$	5.11396e10			0.104197
$838$	−1.55836e11	+	4.12163e11i	−0.316004	+	0.835781i
$839$		−	5.39181e10i		−	0.108814i	−0.998519	−	0.0544072i	$-0.982673\pi$
$839$		−	5.39181e10i		−	0.108814i	0.998519	−	0.0544072i	$-0.0173269\pi$
$840$	3.99814e10	+	7.56200e10i	0.0803047	+	0.151887i
$841$	5.59389e11			1.11823
$842$	6.93844e11	+	2.62338e11i	1.38043	+	0.521932i
$843$			4.23104e10i			0.0837793i
$844$	9.65484e10	−	1.09426e11i	0.190272	−	0.215650i
$845$	−1.26982e11			−0.249066
$846$	−7.21555e10	+	1.90840e11i	−0.140860	+	0.372553i
$847$		−	1.70520e12i		−	3.31315i
$848$	−7.98405e10	−	6.36040e11i	−0.154397	−	1.22999i
$849$	−2.50942e11			−0.482995
$850$	−6.93472e10	−	2.62198e10i	−0.132848	−	0.0502289i
$851$			2.67383e11i			0.509819i
$852$	−1.71583e11	−	1.51391e11i	−0.325623	−	0.287304i
$853$	4.92140e11			0.929592			0.464796	−	0.885418i	$-0.346128\pi$
$853$	4.92140e11			0.929592			0.464796	+	0.885418i	$0.346128\pi$
$854$	−9.15162e10	+	2.42046e11i	−0.172055	+	0.455058i
$855$			2.42825e11i			0.454391i
$856$	2.79134e11	−	1.47582e11i	0.519898	−	0.274878i
$857$	1.00404e12			1.86135			0.930673	−	0.365853i	$-0.119223\pi$
$857$	1.00404e12			1.86135			0.930673	+	0.365853i	$0.119223\pi$
$858$	3.76112e11	+	1.42206e11i	0.694013	+	0.262402i
$859$		−	9.99324e11i		−	1.83541i	−0.397259	−	0.917707i	$-0.630038\pi$
$859$		−	9.99324e11i		−	1.83541i	0.397259	−	0.917707i	$-0.369962\pi$
$860$	1.13262e11	−	1.28369e11i	0.207058	−	0.234674i
$861$	1.13345e11			0.206248
$862$	3.47575e11	−	9.19282e11i	0.629535	−	1.66502i
$863$			8.87466e11i			1.59996i	0.600029	+	0.799978i	$0.295156\pi$
$863$			8.87466e11i			1.59996i	−0.600029	+	0.799978i	$0.704844\pi$
$864$	−3.19904e11	−	7.71361e10i	−0.574069	−	0.138421i
$865$	−1.99795e9			−0.00356879
$866$	5.76822e11	+	2.18093e11i	1.02558	+	0.387766i
$867$			8.68813e10i			0.153762i
$868$	−9.30221e10	−	8.20753e10i	−0.163873	−	0.144588i
$869$	8.90022e10			0.156071
$870$	4.09054e10	−	1.08189e11i	0.0714010	−	0.188844i
$871$		−	3.64579e11i		−	0.633460i
$872$	−8.26306e10	−	1.56286e11i	−0.142914	−	0.270305i
$873$	−7.27950e10			−0.125327
$874$	−6.78146e11	−	2.56403e11i	−1.16219	−	0.439417i
$875$		−	6.49368e10i		−	0.110779i
$876$	−1.66190e10	+	1.88356e10i	−0.0282220	+	0.0319862i
$877$	−8.93203e11			−1.50991			−0.754956	−	0.655775i	$-0.772342\pi$
$877$	−8.93203e11			−1.50991			−0.754956	+	0.655775i	$0.772342\pi$
$878$	2.27786e11	−	6.02457e11i	0.383308	−	1.01379i
$879$			1.58539e11i			0.265571i
$880$	−5.10130e11	+	6.40352e10i	−0.850648	+	0.106780i
$881$	1.49474e11			0.248121			0.124060	−	0.992275i	$-0.460408\pi$
$881$	1.49474e11			0.248121			0.124060	+	0.992275i	$0.460408\pi$
$882$	2.73194e11	+	1.03293e11i	0.451437	+	0.170686i
$883$			5.15026e11i			0.847202i	0.905849	+	0.423601i	$0.139234\pi$
$883$			5.15026e11i			0.847202i	−0.905849	+	0.423601i	$0.860766\pi$
$884$	4.05748e11	+	3.57999e11i	0.664426	+	0.586237i
$885$	−5.00924e10			−0.0816580
$886$	3.13506e11	−	8.29175e11i	0.508758	−	1.34559i
$887$			5.23767e11i			0.846142i	0.906096	+	0.423071i	$0.139048\pi$
$887$			5.23767e11i			0.846142i	−0.906096	+	0.423071i	$0.860952\pi$
$888$	−7.86530e10	+	4.15850e10i	−0.126492	+	0.0668783i
$889$	9.42105e11			1.50832
$890$	1.96826e11	+	7.44188e10i	0.313706	+	0.118610i
$891$		−	8.70654e11i		−	1.38145i
$892$	2.94725e11	−	3.34034e11i	0.465541	−	0.527632i
$893$	−3.15058e11			−0.495433
$894$	−1.14522e10	+	3.02893e10i	−0.0179283	+	0.0474176i
$895$			3.14083e11i			0.489500i
$896$	4.58102e11	+	6.53731e11i	0.710772	+	1.01430i
$897$	2.76927e11			0.427756
$898$	1.37627e11	+	5.20359e10i	0.211640	+	0.0800198i
$899$			1.67743e11i			0.256806i
$900$	8.89284e10	+	7.84633e10i	0.135541	+	0.119590i
$901$	−5.80141e11			−0.880307
$902$	−2.40935e11	+	6.37236e11i	−0.363977	+	0.962663i
$903$			1.78755e11i			0.268848i
$904$	4.47427e10	+	8.46254e10i	0.0669959	+	0.126715i
$905$	−2.11058e11			−0.314636
$906$	−1.22033e11	−	4.61398e10i	−0.181119	−	0.0684799i
$907$			7.92940e11i			1.17169i	0.810425	+	0.585843i	$0.199236\pi$
$907$			7.92940e11i			1.17169i	−0.810425	+	0.585843i	$0.800764\pi$
$908$	−5.44688e11	+	6.17336e11i	−0.801317	+	0.908193i
$909$	−1.15045e12			−1.68504
$910$	−1.67615e11	+	4.43316e11i	−0.244426	+	0.646470i
$911$		−	9.15754e11i		−	1.32955i	−0.747043	−	0.664776i	$-0.768527\pi$
$911$		−	9.15754e11i		−	1.32955i	0.747043	−	0.664776i	$-0.231473\pi$
$912$	−3.00461e10	−	2.39359e11i	−0.0434320	−	0.345996i
$913$	−1.27060e12			−1.82863
$914$	1.93053e11	+	7.29923e10i	0.276626	+	0.104590i
$915$		−	3.81931e10i		−	0.0544879i
$916$	7.76261e11	+	6.84911e11i	1.10262	+	0.972864i
$917$	−1.36418e12			−1.92928
$918$	−1.05325e11	+	2.78567e11i	−0.148306	+	0.392247i
$919$			1.22806e12i			1.72170i	0.508862	+	0.860848i	$0.330066\pi$
$919$			1.22806e12i			1.72170i	−0.508862	+	0.860848i	$0.669934\pi$
$920$	−3.13028e11	+	1.65503e11i	−0.436950	+	0.231022i
$921$	4.36658e11			0.606880
$922$	1.06024e12	+	4.00869e11i	1.46717	+	0.554727i
$923$		−	1.26784e12i		−	1.74686i
$924$	3.55181e11	−	4.02553e11i	0.487261	−	0.552250i
$925$	6.75413e10			0.0922577
$926$	−1.07673e10	+	2.84778e10i	−0.0146441	+	0.0387313i
$927$			6.71275e11i			0.909037i
$928$	2.53014e11	−	1.04932e12i	0.341156	−	1.41486i
$929$	−1.01063e12			−1.35684			−0.678420	−	0.734675i	$-0.737335\pi$
$929$	−1.01063e12			−1.35684			−0.678420	+	0.734675i	$0.737335\pi$
$930$	1.71265e10	+	6.47544e9i	0.0228948	+	0.00865640i
$931$			4.51017e11i			0.600336i
$932$	−6.78269e11	−	5.98450e11i	−0.898955	−	0.793167i
$933$	3.06746e9			0.00404811
$934$	5.97854e10	−	1.58123e11i	0.0785611	−	0.207782i
$935$			4.65296e11i			0.608812i
$936$	−4.04574e11	−	7.65203e11i	−0.527102	−	0.996950i
$937$	1.01845e12			1.32123			0.660616	−	0.750724i	$-0.270295\pi$
$937$	1.01845e12			1.32123			0.660616	+	0.750724i	$0.270295\pi$
$938$	−4.55297e11	−	1.72145e11i	−0.588144	−	0.222374i
$939$			6.05615e10i			0.0778994i
$940$	−1.01804e11	+	1.15382e11i	−0.130392	+	0.147784i
$941$	7.42356e11			0.946790			0.473395	−	0.880850i	$-0.343028\pi$
$941$	7.42356e11			0.946790			0.473395	+	0.880850i	$0.343028\pi$
$942$	−1.26148e11	+	3.33642e11i	−0.160205	+	0.423718i
$943$			4.69191e11i			0.593339i
$944$	−4.63830e11	+	5.82234e10i	−0.584078	+	0.0733178i
$945$	−2.60850e11			−0.327088
$946$	−1.00498e12	−	3.79975e11i	−1.25485	−	0.474450i
$947$		−	1.71798e11i		−	0.213609i	−0.994280	−	0.106804i	$-0.965938\pi$
$947$		−	1.71798e11i		−	0.213609i	0.994280	−	0.106804i	$-0.0340619\pi$
$948$	1.52938e10	+	1.34941e10i	0.0189358	+	0.0167074i
$949$	−1.39178e11			−0.171595
$950$	−6.47677e10	+	1.71300e11i	−0.0795177	+	0.210312i
$951$			1.54859e11i			0.189328i
$952$	6.38664e11	−	3.37671e11i	0.777543	−	0.411099i
$953$	−1.48428e11			−0.179947			−0.0899736	−	0.995944i	$-0.528678\pi$
$953$	−1.48428e11			−0.179947			−0.0899736	+	0.995944i	$0.528678\pi$
$954$	8.68043e11	+	3.28202e11i	1.04797	+	0.396230i
$955$		−	1.93610e11i		−	0.232764i
$956$	−1.35750e11	+	1.53855e11i	−0.162520	+	0.184196i
$957$	−7.25908e11			−0.865434
$958$	−8.74587e10	+	2.31315e11i	−0.103834	+	0.274626i
$959$			6.87684e10i			0.0813045i
$960$	−9.73678e10	−	6.63398e10i	−0.114638	−	0.0781069i
$961$	8.26337e11			0.968866
$962$	−4.61097e11	−	1.74338e11i	−0.538384	−	0.203560i
$963$			4.57105e11i			0.531509i
$964$	9.66069e11	+	8.52383e11i	1.11867	+	0.987021i
$965$	5.36404e11			0.618561
$966$	1.30758e11	−	3.45835e11i	0.150162	−	0.397155i
$967$		−	1.23376e12i		−	1.41099i	−0.708714	−	0.705496i	$-0.750724\pi$
$967$		−	1.23376e12i		−	1.41099i	0.708714	−	0.705496i	$-0.249276\pi$
$968$	1.09780e12	+	2.07636e12i	1.25032	+	2.36483i
$969$	−2.18323e11			−0.247631
$970$	−5.13530e10	−	1.94163e10i	−0.0580068	−	0.0219320i
$971$			5.61021e11i			0.631106i	0.948908	+	0.315553i	$0.102190\pi$
$971$			5.61021e11i			0.631106i	−0.948908	+	0.315553i	$0.897810\pi$
$972$	4.80744e11	−	5.44863e11i	0.538578	−	0.610411i
$973$	−1.39895e11			−0.156082
$974$	6.86775e10	−	1.81641e11i	0.0763095	−	0.201827i
$975$		−	6.99521e10i		−	0.0774073i
$976$	−4.43926e10	−	3.53649e11i	−0.0489228	−	0.389738i
$977$	−2.90736e11			−0.319096			−0.159548	−	0.987190i	$-0.551004\pi$
$977$	−2.90736e11			−0.319096			−0.159548	+	0.987190i	$0.551004\pi$
$978$	−2.63163e11	−	9.95005e10i	−0.287654	−	0.108760i
$979$		−	1.32064e12i		−	1.43765i
$980$	1.65173e11	+	1.45736e11i	0.179075	+	0.158002i
$981$	2.55931e11			0.276342
$982$	5.07537e11	−	1.34236e12i	0.545785	−	1.44352i
$983$		−	9.49854e11i		−	1.01729i	−0.860978	−	0.508643i	$-0.830147\pi$
$983$		−	9.49854e11i		−	1.01729i	0.860978	−	0.508643i	$-0.169853\pi$
$984$	−1.38016e11	+	7.29712e10i	−0.147214	+	0.0778344i
$985$	1.93507e11			0.205566
$986$	−9.13729e11	−	3.45475e11i	−0.966740	−	0.365519i
$987$		−	1.60671e11i		−	0.169304i
$988$	8.84324e11	−	1.00227e12i	0.928076	−	1.05186i
$989$	−7.39953e11			−0.773426
$990$	2.63231e11	−	6.96205e11i	0.274029	−	0.724764i
$991$		−	1.23917e11i		−	0.128480i	−0.997934	−	0.0642401i	$-0.979538\pi$
$991$		−	1.23917e11i		−	0.128480i	0.997934	−	0.0642401i	$-0.0204623\pi$
$992$	1.66110e11	+	4.00528e10i	0.171533	+	0.0413605i
$993$	4.00812e11			0.412234
$994$	−1.58332e12	−	5.98643e11i	−1.62189	−	0.613228i
$995$			2.02895e9i			0.00207005i
$996$	−2.18336e11	−	1.92642e11i	−0.221864	−	0.195755i
$997$	−3.60696e11			−0.365057			−0.182529	−	0.983201i	$-0.558428\pi$
$997$	−3.60696e11			−0.365057			−0.182529	+	0.983201i	$0.558428\pi$
$998$	−2.63361e11	+	6.96549e11i	−0.265479	+	0.702150i
$999$		−	2.71313e11i		−	0.272401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.9.b.a.11.3	✓	16
3.2	odd	2		180.9.c.a.91.14		16
4.3	odd	2	inner	20.9.b.a.11.4	yes	16
5.2	odd	4		100.9.d.c.99.19		32
5.3	odd	4		100.9.d.c.99.14		32
5.4	even	2		100.9.b.d.51.14		16
8.3	odd	2		320.9.b.d.191.8		16
8.5	even	2		320.9.b.d.191.9		16
12.11	even	2		180.9.c.a.91.13		16
20.3	even	4		100.9.d.c.99.20		32
20.7	even	4		100.9.d.c.99.13		32
20.19	odd	2		100.9.b.d.51.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.3	✓	16	1.1	even	1	trivial
20.9.b.a.11.4	yes	16	4.3	odd	2	inner
100.9.b.d.51.13		16	20.19	odd	2
100.9.b.d.51.14		16	5.4	even	2
100.9.d.c.99.13		32	20.7	even	4
100.9.d.c.99.14		32	5.3	odd	4
100.9.d.c.99.19		32	5.2	odd	4
100.9.d.c.99.20		32	20.3	even	4
180.9.c.a.91.13		16	12.11	even	2
180.9.c.a.91.14		16	3.2	odd	2
320.9.b.d.191.8		16	8.3	odd	2
320.9.b.d.191.9		16	8.5	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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.9660 - 5.65855i) q^{2} -25.1248i q^{3} +(191.962 + 169.372i) q^{4} -279.508 q^{5} +(-142.170 + 376.017i) q^{6} +2973.76i q^{7} +(-1914.50 - 3621.04i) q^{8} +5929.74 q^{9} +O(q^{10})\)	\(q+(-14.9660 - 5.65855i) q^{2} -25.1248i q^{3} +(191.962 + 169.372i) q^{4} -279.508 q^{5} +(-142.170 + 376.017i) q^{6} +2973.76i q^{7} +(-1914.50 - 3621.04i) q^{8} +5929.74 q^{9} +(4183.12 + 1581.61i) q^{10} -28067.3i q^{11} +(4255.43 - 4823.00i) q^{12} +35637.5 q^{13} +(16827.2 - 44505.2i) q^{14} +7022.60i q^{15} +(8162.50 + 65025.7i) q^{16} +59310.8 q^{17} +(-88744.5 - 33553.8i) q^{18} -146509. i q^{19} +(-53654.9 - 47340.8i) q^{20} +74715.1 q^{21} +(-158820. + 420055. i) q^{22} +309282. i q^{23} +(-90977.9 + 48101.4i) q^{24} +78125.0 q^{25} +(-533351. - 201657. i) q^{26} -313827. i q^{27} +(-503670. + 570847. i) q^{28} +1.02939e6 q^{29} +(39737.7 - 105100. i) q^{30} +162954. i q^{31} +(245791. - 1.01936e6i) q^{32} -705186. q^{33} +(-887645. - 335613. i) q^{34} -831191. i q^{35} +(1.13828e6 + 1.00433e6i) q^{36} +864529. q^{37} +(-829026. + 2.19264e6i) q^{38} -895386. i q^{39} +(535118. + 1.01211e6i) q^{40} +1.51703e6 q^{41} +(-1.11819e6 - 422779. i) q^{42} +2.39249e6i q^{43} +(4.75381e6 - 5.38785e6i) q^{44} -1.65741e6 q^{45} +(1.75009e6 - 4.62871e6i) q^{46} -2.15044e6i q^{47} +(1.63376e6 - 205081. i) q^{48} -3.07844e6 q^{49} +(-1.16922e6 - 442074. i) q^{50} -1.49017e6i q^{51} +(6.84104e6 + 6.03599e6i) q^{52} -9.78137e6 q^{53} +(-1.77581e6 + 4.69674e6i) q^{54} +7.84505e6i q^{55} +(1.07681e7 - 5.69325e6i) q^{56} -3.68100e6 q^{57} +(-1.54058e7 - 5.82483e6i) q^{58} +7.13303e6i q^{59} +(-1.18943e6 + 1.34807e6i) q^{60} -5.43860e6 q^{61} +(922086. - 2.43877e6i) q^{62} +1.76336e7i q^{63} +(-9.44662e6 + 1.38649e7i) q^{64} -9.96100e6 q^{65} +(1.05538e7 + 3.99033e6i) q^{66} -1.02302e7i q^{67} +(1.13854e7 + 1.00456e7i) q^{68} +7.77065e6 q^{69} +(-4.70334e6 + 1.24396e7i) q^{70} -3.55760e7i q^{71} +(-1.13525e7 - 2.14718e7i) q^{72} -3.90536e6 q^{73} +(-1.29385e7 - 4.89198e6i) q^{74} -1.96288e6i q^{75} +(2.48144e7 - 2.81240e7i) q^{76} +8.34654e7 q^{77} +(-5.06659e6 + 1.34003e7i) q^{78} +3.17103e6i q^{79} +(-2.28149e6 - 1.81752e7i) q^{80} +3.10202e7 q^{81} +(-2.27039e7 - 8.58420e6i) q^{82} -4.52697e7i q^{83} +(1.43424e7 + 1.26546e7i) q^{84} -1.65779e7 q^{85} +(1.35380e7 - 3.58059e7i) q^{86} -2.58631e7i q^{87} +(-1.01633e8 + 5.37348e7i) q^{88} +4.70524e7 q^{89} +(2.48048e7 + 9.37856e6i) q^{90} +1.05977e8i q^{91} +(-5.23836e7 + 5.93703e7i) q^{92} +4.09420e6 q^{93} +(-1.21684e7 + 3.21835e7i) q^{94} +4.09504e7i q^{95} +(-2.56113e7 - 6.17546e6i) q^{96} -1.22762e7 q^{97} +(4.60718e7 + 1.74195e7i) q^{98} -1.66432e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9}+O(q^{10}) \) 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9	\( 16 q + 6 q^{2} - 52 q^{4} + 4368 q^{6} - 14184 q^{8} - 38800 q^{9} + 8750 q^{10} - 64040 q^{12} + 51392 q^{13} + 68472 q^{14} - 81424 q^{16} + 27552 q^{17} - 616994 q^{18} + 172500 q^{20} + 414496 q^{21} - 389120 q^{22} + 163792 q^{24} + 1250000 q^{25} + 1037124 q^{26} + 1288520 q^{28} + 2764896 q^{29} - 805000 q^{30} - 4379904 q^{32} - 5521600 q^{33} + 3793964 q^{34} - 5468916 q^{36} + 9009472 q^{37} - 3087360 q^{38} + 385000 q^{40} - 8576448 q^{41} - 4067400 q^{42} + 16921200 q^{44} + 1580000 q^{45} - 7974152 q^{46} - 2696640 q^{48} - 32803600 q^{49} + 468750 q^{50} + 6679352 q^{52} + 2452032 q^{53} + 8898704 q^{54} + 34134768 q^{56} + 11957760 q^{57} + 52156572 q^{58} - 24185000 q^{60} + 8371712 q^{61} + 1290000 q^{62} - 47543872 q^{64} + 9060000 q^{65} + 19358000 q^{66} + 16095192 q^{68} + 7527264 q^{69} + 10500000 q^{70} - 42242664 q^{72} + 61907232 q^{73} - 138210876 q^{74} + 2570400 q^{76} - 156997440 q^{77} - 104032400 q^{78} + 37590000 q^{80} + 140586672 q^{81} + 83921012 q^{82} + 69761824 q^{84} - 106960000 q^{85} - 101724672 q^{86} + 44728480 q^{88} + 106647456 q^{89} + 32613750 q^{90} - 13876200 q^{92} + 105563840 q^{93} + 55264632 q^{94} - 453389952 q^{96} + 171851232 q^{97} - 285387714 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 - 52 * q^4 + 4368 * q^6 - 14184 * q^8 - 38800 * q^9 + 8750 * q^10 - 64040 * q^12 + 51392 * q^13 + 68472 * q^14 - 81424 * q^16 + 27552 * q^17 - 616994 * q^18 + 172500 * q^20 + 414496 * q^21 - 389120 * q^22 + 163792 * q^24 + 1250000 * q^25 + 1037124 * q^26 + 1288520 * q^28 + 2764896 * q^29 - 805000 * q^30 - 4379904 * q^32 - 5521600 * q^33 + 3793964 * q^34 - 5468916 * q^36 + 9009472 * q^37 - 3087360 * q^38 + 385000 * q^40 - 8576448 * q^41 - 4067400 * q^42 + 16921200 * q^44 + 1580000 * q^45 - 7974152 * q^46 - 2696640 * q^48 - 32803600 * q^49 + 468750 * q^50 + 6679352 * q^52 + 2452032 * q^53 + 8898704 * q^54 + 34134768 * q^56 + 11957760 * q^57 + 52156572 * q^58 - 24185000 * q^60 + 8371712 * q^61 + 1290000 * q^62 - 47543872 * q^64 + 9060000 * q^65 + 19358000 * q^66 + 16095192 * q^68 + 7527264 * q^69 + 10500000 * q^70 - 42242664 * q^72 + 61907232 * q^73 - 138210876 * q^74 + 2570400 * q^76 - 156997440 * q^77 - 104032400 * q^78 + 37590000 * q^80 + 140586672 * q^81 + 83921012 * q^82 + 69761824 * q^84 - 106960000 * q^85 - 101724672 * q^86 + 44728480 * q^88 + 106647456 * q^89 + 32613750 * q^90 - 13876200 * q^92 + 105563840 * q^93 + 55264632 * q^94 - 453389952 * q^96 + 171851232 * q^97 - 285387714 * q^98

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