LMFDB - Embedded newform 13.10.e.a.4.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [13,10,Mod(4,13)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(13, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("13.4");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$N$	$=$	$13$
Weight:	$k$	$=$	$10$
Character orbit:	$[\chi]$	$=$	13.e (of order $6$ , degree $2$ , 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:	$6.69546587013$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} + 7679 x^{18} + 24599364 x^{16} + 42662336000 x^{14} + 43527566862400 x^{12} + \cdots + 25\!\cdots\!36$ x^20 + 7679x^18 + 24599364x^16 + 42662336000x^14 + 43527566862400x^12 + 26625453181634304x^10 + 9550565219960082432x^8 + 1876223091685443895296x^6 + 172106193081772189679616x^4 + 4841822934658519419322368*x^2 + 25162285487879223389454336
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$2^{22}\cdot 3^{10}\cdot 13^{6}$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.9
Root			$36.6943i$ of defining polynomial
Character	$\chi$	$=$	13.4
Dual form			13.10.e.a.10.9

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(31.7782 + 18.3471i) q^{2} +(65.0132 - 112.606i) q^{3} +(417.236 + 722.673i) q^{4} +1417.57i q^{5} +(4132.00 - 2385.61i) q^{6} +(6502.05 - 3753.96i) q^{7} +11832.9i q^{8} +(1388.07 + 2404.21i) q^{9} +(-26008.3 + 45047.7i) q^{10} +(-37111.4 - 21426.3i) q^{11} +108503. q^{12} +(-100802. + 21057.0i) q^{13} +275498. q^{14} +(159627. + 92160.5i) q^{15} +(-3474.44 + 6017.90i) q^{16} +(-267613. - 463519. i) q^{17} +101868. i q^{18} +(-362845. + 209488. i) q^{19} +(-1.02444e6 + 591459. i) q^{20} -976228. i q^{21} +(-786223. - 1.36178e6i) q^{22} +(147347. - 255212. i) q^{23} +(1.33245e6 + 769291. i) q^{24} -56368.4 q^{25} +(-3.58965e6 - 1.18028e6i) q^{26} +2.92028e6 q^{27} +(5.42577e6 + 3.13257e6i) q^{28} +(-810352. + 1.40357e6i) q^{29} +(3.38176e6 + 5.85739e6i) q^{30} +3.25108e6i q^{31} +(5.02592e6 - 2.90172e6i) q^{32} +(-4.82547e6 + 2.78598e6i) q^{33} -1.96397e7i q^{34} +(5.32149e6 + 9.21709e6i) q^{35} +(-1.15830e6 + 2.00624e6i) q^{36} +(-1.73916e7 - 1.00410e7i) q^{37} -1.53741e7 q^{38} +(-4.18234e6 + 1.27199e7i) q^{39} -1.67738e7 q^{40} +(2.98218e7 + 1.72176e7i) q^{41} +(1.79110e7 - 3.10228e7i) q^{42} +(1.56885e6 + 2.71733e6i) q^{43} -3.57593e7i q^{44} +(-3.40812e6 + 1.96768e6i) q^{45} +(9.36482e6 - 5.40678e6i) q^{46} +5.82844e7i q^{47} +(451768. + 782486. i) q^{48} +(8.00765e6 - 1.38697e7i) q^{49} +(-1.79128e6 - 1.03420e6i) q^{50} -6.95935e7 q^{51} +(-5.72756e7 - 6.40614e7i) q^{52} -2.43962e7 q^{53} +(9.28012e7 + 5.35788e7i) q^{54} +(3.03732e7 - 5.26079e7i) q^{55} +(4.44201e7 + 7.69378e7i) q^{56} +5.44780e7i q^{57} +(-5.15030e7 + 2.97353e7i) q^{58} +(1.40221e8 - 8.09564e7i) q^{59} +1.53811e8i q^{60} +(-4.21753e7 - 7.30498e7i) q^{61} +(-5.96480e7 + 1.03313e8i) q^{62} +(1.80506e7 + 1.04215e7i) q^{63} +2.16511e8 q^{64} +(-2.98496e7 - 1.42894e8i) q^{65} -2.04459e8 q^{66} +(-4.23890e7 - 2.44733e7i) q^{67} +(2.23315e8 - 3.86794e8i) q^{68} +(-1.91589e7 - 3.31843e7i) q^{69} +3.90536e8i q^{70} +(-2.87471e7 + 1.65972e7i) q^{71} +(-2.84486e7 + 1.64248e7i) q^{72} +2.22708e8i q^{73} +(-3.68448e8 - 6.38171e8i) q^{74} +(-3.66469e6 + 6.34742e6i) q^{75} +(-3.02783e8 - 1.74812e8i) q^{76} -3.21734e8 q^{77} +(-3.66282e8 + 3.27483e8i) q^{78} +1.28556e7 q^{79} +(-8.53077e6 - 4.92524e6i) q^{80} +(1.62535e8 - 2.81520e8i) q^{81} +(6.31788e8 + 1.09429e9i) q^{82} -1.32887e8i q^{83} +(7.05494e8 - 4.07317e8i) q^{84} +(6.57069e8 - 3.79359e8i) q^{85} +1.15136e8i q^{86} +(1.05367e8 + 1.82501e8i) q^{87} +(2.53534e8 - 4.39134e8i) q^{88} +(5.06681e8 + 2.92532e8i) q^{89} -1.44405e8 q^{90} +(-5.76375e8 + 5.15321e8i) q^{91} +2.45913e8 q^{92} +(3.66091e8 + 2.11363e8i) q^{93} +(-1.06935e9 + 1.85217e9i) q^{94} +(-2.96964e8 - 5.14356e8i) q^{95} -7.54600e8i q^{96} +(-8.94294e8 + 5.16321e8i) q^{97} +(5.08937e8 - 2.93835e8i) q^{98} -1.18965e8i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q - 3 q^{2} - 163 q^{3} + 2559 q^{4} - 3288 q^{6} + 1023 q^{7} - 64763 q^{9} + 44195 q^{10} - 94599 q^{11} - 427652 q^{12} + 187013 q^{13} + 473556 q^{14} + 754950 q^{15} - 594809 q^{16} - 49656 q^{17}+ \cdots - 1557570597 q^{98}+O(q^{100})$ 20 * q - 3 * q^2 - 163 * q^3 + 2559 * q^4 - 3288 * q^6 + 1023 * q^7 - 64763 * q^9 + 44195 * q^10 - 94599 * q^11 - 427652 * q^12 + 187013 * q^13 + 473556 * q^14 + 754950 * q^15 - 594809 * q^16 - 49656 * q^17 - 3879 * q^19 - 154815 * q^20 + 2536766 * q^22 + 3126189 * q^23 - 6472626 * q^24 - 1529274 * q^25 - 13931889 * q^26 + 18052718 * q^27 + 4918980 * q^28 - 2712414 * q^29 + 15022758 * q^30 - 14390595 * q^32 - 34050309 * q^33 + 7549080 * q^35 + 27039443 * q^36 - 36102006 * q^37 - 39021096 * q^38 - 32365163 * q^39 + 134360674 * q^40 + 30265110 * q^41 - 60800034 * q^42 + 26621029 * q^43 + 31870857 * q^45 + 121485864 * q^46 - 41385538 * q^48 + 7027649 * q^49 - 58518456 * q^50 - 10208934 * q^51 - 109817238 * q^52 - 36429786 * q^53 - 393493974 * q^54 + 65727080 * q^55 + 63636336 * q^56 + 470295633 * q^58 + 3987867 * q^59 - 268212896 * q^61 - 445379898 * q^62 + 506780166 * q^63 + 343337066 * q^64 + 292006563 * q^65 - 445758060 * q^66 - 944780397 * q^67 - 168297045 * q^68 + 541942791 * q^69 + 1318764849 * q^71 + 1409393649 * q^72 - 541934631 * q^74 - 609413441 * q^75 - 594798654 * q^76 - 1470187374 * q^77 - 2076950874 * q^78 + 1556703616 * q^79 - 968911845 * q^80 - 1069563758 * q^81 + 1859661377 * q^82 + 7275171300 * q^84 - 318942363 * q^85 - 644123073 * q^87 - 2054580464 * q^88 - 2287100109 * q^89 - 6489878934 * q^90 - 4972612749 * q^91 + 10148843820 * q^92 - 1470324870 * q^93 - 2447356414 * q^94 + 4625601270 * q^95 + 7273214547 * q^97 - 1557570597 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/13\mathbb{Z}\right)^\times$ .

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	31.7782	+	18.3471i	1.40441	+	0.810837i	0.994841	−	0.101442i	$-0.0323456\pi$
$2$	31.7782	+	18.3471i	1.40441	+	0.810837i	0.409569	+	0.912279i	$0.365679\pi$
$3$	65.0132	−	112.606i	0.463400	−	0.802632i	−0.535728	−	0.844391i	$-0.679963\pi$
$3$	65.0132	−	112.606i	0.463400	−	0.802632i	0.999128	+	0.0417587i	$0.0132961\pi$
$4$	417.236	+	722.673i	0.814913	+	1.41147i
$5$			1417.57i			1.01433i	0.861850	+	0.507164i	$0.169306\pi$
$5$			1417.57i			1.01433i	−0.861850	+	0.507164i	$0.830694\pi$
$6$	4132.00	−	2385.61i	1.30161	−	0.751483i
$7$	6502.05	−	3753.96i	1.02355	−	0.590947i	0.108420	−	0.994105i	$-0.465421\pi$
$7$	6502.05	−	3753.96i	1.02355	−	0.590947i	0.915130	+	0.403158i	$0.132088\pi$
$8$			11832.9i			1.02137i
$9$	1388.07	+	2404.21i	0.0705212	+	0.122146i
$10$	−26008.3	+	45047.7i	−0.822454	+	1.42453i
$11$	−37111.4	−	21426.3i	−0.764259	−	0.441245i	0.0665635	−	0.997782i	$-0.478796\pi$
$11$	−37111.4	−	21426.3i	−0.764259	−	0.441245i	−0.830823	+	0.556537i	$0.812130\pi$
$12$	108503.			1.51052
$13$	−100802.	+	21057.0i	−0.978871	+	0.204480i
$13$	−100802.	+	21057.0i	−0.978871	+	0.204480i
$14$	275498.			1.91665
$15$	159627.	+	92160.5i	0.814132	+	0.470039i
$16$	−3474.44	+	6017.90i	−0.0132539	+	0.0229565i
$17$	−267613.	−	463519.i	−0.777118	−	1.34601i	−0.933596	−	0.358327i	$-0.883347\pi$
$17$	−267613.	−	463519.i	−0.777118	−	1.34601i	0.156478	−	0.987681i	$-0.449986\pi$
$18$			101868.i			0.228725i
$19$	−362845.	+	209488.i	−0.638748	+	0.368781i	−0.784132	−	0.620594i	$-0.786892\pi$
$19$	−362845.	+	209488.i	−0.638748	+	0.368781i	0.145384	+	0.989375i	$0.453558\pi$
$20$	−1.02444e6	+	591459.i	−1.43169	+	0.826589i
$21$		−	976228.i		−	1.09538i
$22$	−786223.	−	1.36178e6i	−0.715556	−	1.23938i
$23$	147347.	−	255212.i	0.109791	−	0.190163i	−0.805895	−	0.592059i	$-0.798315\pi$
$23$	147347.	−	255212.i	0.109791	−	0.190163i	0.915685	+	0.401896i	$0.131649\pi$
$24$	1.33245e6	+	769291.i	0.819787	+	0.473304i
$25$	−56368.4			−0.0288606
$26$	−3.58965e6	−	1.18028e6i	−1.54054	−	0.506531i
$27$	2.92028e6			1.05752
$28$	5.42577e6	+	3.13257e6i	1.66821	+	0.963141i
$29$	−810352.	+	1.40357e6i	−0.212756	+	0.368505i	−0.952576	−	0.304300i	$-0.901577\pi$
$29$	−810352.	+	1.40357e6i	−0.212756	+	0.368505i	0.739820	+	0.672805i	$0.234911\pi$
$30$	3.38176e6	+	5.85739e6i	0.762250	+	1.32026i
$31$			3.25108e6i			0.632265i	0.948715	+	0.316133i	$0.102384\pi$
$31$			3.25108e6i			0.632265i	−0.948715	+	0.316133i	$0.897616\pi$
$32$	5.02592e6	−	2.90172e6i	0.847307	−	0.489193i
$33$	−4.82547e6	+	2.78598e6i	−0.708315	+	0.408946i
$34$		−	1.96397e7i		−	2.52047i
$35$	5.32149e6	+	9.21709e6i	0.599414	+	1.03822i
$36$	−1.15830e6	+	2.00624e6i	−0.114937	+	0.199077i
$37$	−1.73916e7	−	1.00410e7i	−1.52556	−	0.880785i	−0.999540	−	0.0303155i	$-0.990349\pi$
$37$	−1.73916e7	−	1.00410e7i	−1.52556	−	0.880785i	−0.526024	−	0.850470i	$-0.676318\pi$
$38$	−1.53741e7			−1.19609
$39$	−4.18234e6	+	1.27199e7i	−0.289486	+	0.880429i
$40$	−1.67738e7			−1.03601
$41$	2.98218e7	+	1.72176e7i	1.64819	+	0.951580i	0.977793	+	0.209573i	$0.0672074\pi$
$41$	2.98218e7	+	1.72176e7i	1.64819	+	0.951580i	0.670392	+	0.742007i	$0.266126\pi$
$42$	1.79110e7	−	3.10228e7i	0.888174	−	1.53836i
$43$	1.56885e6	+	2.71733e6i	0.0699801	+	0.121209i	0.898892	−	0.438170i	$-0.144373\pi$
$43$	1.56885e6	+	2.71733e6i	0.0699801	+	0.121209i	−0.828912	+	0.559379i	$0.811040\pi$
$44$		−	3.57593e7i		−	1.43831i
$45$	−3.40812e6	+	1.96768e6i	−0.123896	+	0.0715316i
$46$	9.36482e6	−	5.40678e6i	0.308382	−	0.178044i
$47$			5.82844e7i			1.74226i	0.491056	+	0.871128i	$0.336611\pi$
$47$			5.82844e7i			1.74226i	−0.491056	+	0.871128i	$0.663389\pi$
$48$	451768.	+	782486.i	0.0122837	+	0.0212760i
$49$	8.00765e6	−	1.38697e7i	0.198437	−	0.343703i
$50$	−1.79128e6	−	1.03420e6i	−0.0405321	−	0.0234012i
$51$	−6.95935e7			−1.44047
$52$	−5.72756e7	−	6.40614e7i	−1.08631	−	1.21501i
$53$	−2.43962e7			−0.424699			−0.212349	−	0.977194i	$-0.568111\pi$
$53$	−2.43962e7			−0.424699			−0.212349	+	0.977194i	$0.568111\pi$
$54$	9.28012e7	+	5.35788e7i	1.48519	+	0.857474i
$55$	3.03732e7	−	5.26079e7i	0.447567	−	0.775209i
$56$	4.44201e7	+	7.69378e7i	0.603578	+	1.04543i
$57$			5.44780e7i			0.683573i
$58$	−5.15030e7	+	2.97353e7i	−0.597595	+	0.345021i
$59$	1.40221e8	−	8.09564e7i	1.50653	−	0.869795i	0.506559	−	0.862205i	$-0.330917\pi$
$59$	1.40221e8	−	8.09564e7i	1.50653	−	0.869795i	0.999971	−	0.00759004i	$-0.00241601\pi$
$60$			1.53811e8i			1.53216i
$61$	−4.21753e7	−	7.30498e7i	−0.390008	−	0.675514i	0.602442	−	0.798163i	$-0.294195\pi$
$61$	−4.21753e7	−	7.30498e7i	−0.390008	−	0.675514i	−0.992450	+	0.122649i	$0.960861\pi$
$62$	−5.96480e7	+	1.03313e8i	−0.512664	+	0.887960i
$63$	1.80506e7	+	1.04215e7i	0.144364	+	0.0833486i
$64$	2.16511e8			1.61313
$65$	−2.98496e7	−	1.42894e8i	−0.207410	−	0.992896i
$66$	−2.04459e8			−1.32635
$67$	−4.23890e7	−	2.44733e7i	−0.256990	−	0.148373i	0.365971	−	0.930626i	$-0.380737\pi$
$67$	−4.23890e7	−	2.44733e7i	−0.256990	−	0.148373i	−0.622961	+	0.782253i	$0.714070\pi$
$68$	2.23315e8	−	3.86794e8i	1.26657	−	2.19376i
$69$	−1.91589e7	−	3.31843e7i	−0.101754	−	0.176243i
$70$			3.90536e8i			1.94411i
$71$	−2.87471e7	+	1.65972e7i	−0.134256	+	0.0775125i	−0.565623	−	0.824664i	$-0.691364\pi$
$71$	−2.87471e7	+	1.65972e7i	−0.134256	+	0.0775125i	0.431368	+	0.902176i	$0.358031\pi$
$72$	−2.84486e7	+	1.64248e7i	−0.124757	+	0.0720285i
$73$			2.22708e8i			0.917875i	0.888468	+	0.458938i	$0.151770\pi$
$73$			2.22708e8i			0.917875i	−0.888468	+	0.458938i	$0.848230\pi$
$74$	−3.68448e8	−	6.38171e8i	−1.42835	−	2.47397i
$75$	−3.66469e6	+	6.34742e6i	−0.0133740	+	0.0231644i
$76$	−3.02783e8	−	1.74812e8i	−1.04105	−	0.601049i
$77$	−3.21734e8			−1.04301
$78$	−3.66282e8	+	3.27483e8i	−1.12044	+	1.00176i
$79$	1.28556e7			0.0371338			0.0185669	−	0.999828i	$-0.494090\pi$
$79$	1.28556e7			0.0371338			0.0185669	+	0.999828i	$0.494090\pi$
$80$	−8.53077e6	−	4.92524e6i	−0.0232854	−	0.0134438i
$81$	1.62535e8	−	2.81520e8i	0.419532	−	0.726651i
$82$	6.31788e8	+	1.09429e9i	1.54315	+	2.67282i
$83$		−	1.32887e8i		−	0.307348i	−0.988122	−	0.153674i	$-0.950889\pi$
$83$		−	1.32887e8i		−	0.307348i	0.988122	−	0.153674i	$-0.0491105\pi$
$84$	7.05494e8	−	4.07317e8i	1.54610	−	0.892639i
$85$	6.57069e8	−	3.79359e8i	1.36529	−	0.788253i
$86$			1.15136e8i			0.226970i
$87$	1.05367e8	+	1.82501e8i	0.197183	+	0.341530i
$88$	2.53534e8	−	4.39134e8i	0.450676	−	0.780594i
$89$	5.06681e8	+	2.92532e8i	0.856012	+	0.494218i	0.862675	−	0.505759i	$-0.168788\pi$
$89$	5.06681e8	+	2.92532e8i	0.856012	+	0.494218i	−0.00666311	+	0.999978i	$0.502121\pi$
$90$	−1.44405e8			−0.232002
$91$	−5.76375e8	+	5.15321e8i	−0.881087	+	0.787756i
$92$	2.45913e8			0.357879
$93$	3.66091e8	+	2.11363e8i	0.507476	+	0.292992i
$94$	−1.06935e9	+	1.85217e9i	−1.41269	+	2.44684i
$95$	−2.96964e8	−	5.14356e8i	−0.374065	−	0.647900i
$96$		−	7.54600e8i		−	0.906768i
$97$	−8.94294e8	+	5.16321e8i	−1.02567	+	0.592170i	−0.915741	−	0.401769i	$-0.868395\pi$
$97$	−8.94294e8	+	5.16321e8i	−1.02567	+	0.592170i	−0.109928	+	0.993940i	$0.535062\pi$
$98$	5.08937e8	−	2.93835e8i	0.557374	−	0.321800i
$99$		−	1.18965e8i		−	0.124469i
$100$	−2.35189e7	−	4.07359e7i	−0.0235189	−	0.0407359i
$101$	3.67836e8	−	6.37111e8i	0.351729	−	0.609213i	−0.634823	−	0.772657i	$-0.718927\pi$
$101$	3.67836e8	−	6.37111e8i	0.351729	−	0.609213i	0.986553	+	0.163445i	$0.0522605\pi$
$102$	−2.21156e9	−	1.27684e9i	−2.02301	−	1.16798i
$103$	−1.16039e8			−0.101587			−0.0507934	−	0.998709i	$-0.516175\pi$
$103$	−1.16039e8			−0.101587			−0.0507934	+	0.998709i	$0.516175\pi$
$104$	−2.49164e8	−	1.19278e9i	−0.208850	−	0.999792i
$105$	1.38387e9			1.11107
$106$	−7.75267e8	−	4.47601e8i	−0.596451	−	0.344361i
$107$	2.10697e8	−	3.64938e8i	0.155393	−	0.269149i	−0.777809	−	0.628501i	$-0.783669\pi$
$107$	2.10697e8	−	3.64938e8i	0.155393	−	0.269149i	0.933202	+	0.359352i	$0.117002\pi$
$108$	1.21844e9	+	2.11041e9i	0.861785	+	1.49266i
$109$		−	1.30101e9i		−	0.882796i	−0.897311	−	0.441398i	$-0.854483\pi$
$109$		−	1.30101e9i		−	0.882796i	0.897311	−	0.441398i	$-0.145517\pi$
$110$	1.93041e9	−	1.11452e9i	1.25714	−	0.725808i
$111$	−2.26136e9	+	1.30560e9i	−1.41389	+	0.816311i
$112$			5.21716e7i			0.0313295i
$113$	5.12304e8	+	8.87337e8i	0.295580	+	0.511959i	0.975120	−	0.221679i	$-0.0711538\pi$
$113$	5.12304e8	+	8.87337e8i	0.295580	+	0.511959i	−0.679540	+	0.733639i	$0.737820\pi$
$114$	−9.99517e8	+	1.73121e9i	−0.554266	+	0.960017i
$115$	3.61780e8	+	2.08874e8i	0.192887	+	0.111364i
$116$	−1.35243e9			−0.693512
$117$	−1.90546e8	−	2.13121e8i	−0.0940077	−	0.105145i
$118$	5.94128e9			2.82105
$119$	−3.48007e9	−	2.00922e9i	−1.59084	−	0.918472i
$120$	−1.09052e9	+	1.88884e9i	−0.480085	+	0.831532i
$121$	−2.60801e8	−	4.51720e8i	−0.110605	−	0.191574i
$122$		−	3.09519e9i		−	1.26493i
$123$	3.87762e9	−	2.23874e9i	1.52754	−	0.881924i
$124$	−2.34947e9	+	1.35646e9i	−0.892424	+	0.515241i
$125$			2.68878e9i			0.985054i
$126$	3.82410e8	+	6.62354e8i	0.135164	+	0.234111i
$127$	−2.38119e9	+	4.12435e9i	−0.812228	+	1.40682i	0.0990726	+	0.995080i	$0.468412\pi$
$127$	−2.38119e9	+	4.12435e9i	−0.812228	+	1.40682i	−0.911301	+	0.411741i	$0.864921\pi$
$128$	4.30705e9	+	2.48668e9i	1.41819	+	0.818793i
$129$	4.07985e8			0.129715
$130$	1.67313e9	−	5.08857e9i	0.513788	−	1.56261i
$131$	−3.55676e9			−1.05520			−0.527599	−	0.849494i	$-0.676908\pi$
$131$	−3.55676e9			−1.05520			−0.527599	+	0.849494i	$0.676908\pi$
$132$	−4.02671e9	−	2.32482e9i	−1.15443	−	0.666511i
$133$	−1.57282e9	+	2.72421e9i	−0.435860	+	0.754932i
$134$	−8.98030e8	−	1.55543e9i	−0.240613	−	0.416754i
$135$			4.13969e9i			1.07267i
$136$	5.48476e9	−	3.16663e9i	1.37478	−	0.793728i
$137$	4.57722e9	−	2.64266e9i	1.11009	−	0.640913i	0.171240	−	0.985229i	$-0.445223\pi$
$137$	4.57722e9	−	2.64266e9i	1.11009	−	0.640913i	0.938854	+	0.344316i	$0.111889\pi$
$138$		−	1.40605e9i		−	0.330023i
$139$	−4.67395e8	−	8.09552e8i	−0.106198	−	0.183941i	0.808029	−	0.589143i	$-0.200534\pi$
$139$	−4.67395e8	−	8.09552e8i	−0.106198	−	0.183941i	−0.914227	+	0.405202i	$0.867201\pi$
$140$	−4.44063e9	+	7.69139e9i	−0.976941	+	1.69211i
$141$	6.56318e9	+	3.78925e9i	1.39839	+	0.807361i
$142$	−1.21804e9			−0.251400
$143$	4.19209e9	+	1.37837e9i	0.838337	+	0.275646i
$144$	−1.92910e7			−0.00373873
$145$	−1.98965e9	−	1.14873e9i	−0.373785	−	0.215805i
$146$	−4.08606e9	+	7.07727e9i	−0.744247	+	1.28907i
$147$	−1.04121e9	−	1.80342e9i	−0.183911	−	0.318544i
$148$		−	1.67579e10i		−	2.87105i
$149$	5.67412e9	−	3.27595e9i	0.943105	−	0.544502i	0.0521726	−	0.998638i	$-0.483385\pi$
$149$	5.67412e9	−	3.27595e9i	0.943105	−	0.544502i	0.890932	+	0.454136i	$0.150052\pi$
$150$	−2.32914e8	+	1.34473e8i	−0.0375652	+	0.0216883i
$151$		−	1.99924e8i		−	0.0312946i	−0.999878	−	0.0156473i	$-0.995019\pi$
$151$		−	1.99924e8i		−	0.0312946i	0.999878	−	0.0156473i	$-0.00498089\pi$
$152$	−2.47885e9	−	4.29349e9i	−0.376663	−	0.652400i
$153$	7.42931e8	−	1.28679e9i	0.109607	−	0.189844i
$154$	−1.02241e10	−	5.90290e9i	−1.46482	−	0.845712i
$155$	−4.60861e9			−0.641324
$156$	−1.09374e10	+	2.28475e9i	−1.47861	+	0.308872i
$157$	−6.66154e9			−0.875036			−0.437518	−	0.899210i	$-0.644142\pi$
$157$	−6.66154e9			−0.875036			−0.437518	+	0.899210i	$0.644142\pi$
$158$	4.08526e8	+	2.35863e8i	0.0521510	+	0.0301094i
$159$	−1.58607e9	+	2.74716e9i	−0.196805	+	0.340877i
$160$	4.11338e9	+	7.12458e9i	0.496202	+	0.859447i
$161$		−	2.21253e9i		−	0.259522i
$162$	1.03302e10	−	5.96412e9i	1.17839	−	0.680345i
$163$	−5.09312e9	+	2.94051e9i	−0.565118	+	0.326271i	−0.755197	−	0.655498i	$-0.772459\pi$
$163$	−5.09312e9	+	2.94051e9i	−0.565118	+	0.326271i	0.190079	+	0.981769i	$0.439126\pi$
$164$			2.87352e10i			3.10182i
$165$	−3.94932e9	−	6.84042e9i	−0.414805	−	0.718464i
$166$	2.43809e9	−	4.22290e9i	0.249209	−	0.431642i
$167$	−4.43486e9	−	2.56047e9i	−0.441221	−	0.254739i	0.262894	−	0.964825i	$-0.415323\pi$
$167$	−4.43486e9	−	2.56047e9i	−0.441221	−	0.254739i	−0.704115	+	0.710086i	$0.748656\pi$
$168$	1.15516e10			1.11879
$169$	9.71771e9	−	4.24518e9i	0.916376	−	0.400319i
$170$	2.78406e10			2.55658
$171$	−1.00731e9	−	5.81569e8i	−0.0900906	−	0.0520138i
$172$	−1.30916e9	+	2.26754e9i	−0.114055	+	0.197550i
$173$	6.57711e9	+	1.13919e10i	0.558249	+	0.966915i	0.997643	+	0.0686205i	$0.0218598\pi$
$173$	6.57711e9	+	1.13919e10i	0.558249	+	0.966915i	−0.439394	+	0.898294i	$0.644807\pi$
$174$			7.73274e9i			0.639532i
$175$	−3.66510e8	+	2.11605e8i	−0.0295403	+	0.0170551i
$176$	2.57883e8	−	1.48889e8i	0.0202589	−	0.0116965i
$177$		−	2.10529e10i		−	1.61225i
$178$	1.07343e10	+	1.85923e10i	0.801461	+	1.38817i
$179$	5.16800e9	−	8.95124e9i	0.376256	−	0.651695i	−0.614258	−	0.789105i	$-0.710545\pi$
$179$	5.16800e9	−	8.95124e9i	0.376256	−	0.651695i	0.990514	+	0.137410i	$0.0438779\pi$
$180$	−2.84398e9	−	1.64197e9i	−0.201930	−	0.116584i
$181$	−2.73183e9			−0.189191			−0.0945956	−	0.995516i	$-0.530156\pi$
$181$	−2.73183e9			−0.189191			−0.0945956	+	0.995516i	$0.530156\pi$
$182$	−2.77708e10	+	5.80115e9i	−1.87615	+	0.391916i
$183$	−1.09678e10			−0.722919
$184$	3.01988e9	+	1.74353e9i	0.194227	+	0.112137i
$185$	1.42338e10	−	2.46537e10i	0.893405	−	1.54742i
$186$	7.75581e9	+	1.34335e10i	0.475137	+	0.822961i
$187$			2.29358e10i			1.37160i
$188$	−4.21206e10	+	2.43183e10i	−2.45914	+	1.41979i
$189$	1.89878e10	−	1.09626e10i	1.08242	−	0.624937i
$190$		−	2.17937e10i		−	1.21322i
$191$	−5.08137e9	−	8.80119e9i	−0.276268	−	0.478510i	0.694186	−	0.719795i	$-0.255764\pi$
$191$	−5.08137e9	−	8.80119e9i	−0.276268	−	0.478510i	−0.970454	+	0.241285i	$0.922431\pi$
$192$	1.40761e10	−	2.43804e10i	0.747525	−	1.29475i
$193$	−1.25869e10	−	7.26704e9i	−0.652996	−	0.377007i	0.136607	−	0.990625i	$-0.456380\pi$
$193$	−1.25869e10	−	7.26704e9i	−0.652996	−	0.377007i	−0.789603	+	0.613618i	$0.789714\pi$
$194$	−3.78920e10			−1.92061
$195$	−1.80314e10	−	5.92874e9i	−0.893043	−	0.293634i
$196$	1.33643e10			0.646836
$197$	2.12969e9	+	1.22958e9i	0.100744	+	0.0581645i	0.549525	−	0.835477i	$-0.314809\pi$
$197$	2.12969e9	+	1.22958e9i	0.100744	+	0.0581645i	−0.448782	+	0.893641i	$0.648142\pi$
$198$	2.18266e9	−	3.78049e9i	0.100924	−	0.174805i
$199$	1.25051e10	+	2.16594e10i	0.565259	+	0.979058i	0.997026	+	0.0770722i	$0.0245572\pi$
$199$	1.25051e10	+	2.16594e10i	0.565259	+	0.979058i	−0.431766	+	0.901986i	$0.642109\pi$
$200$		−	6.66998e8i		−	0.0294774i
$201$	−5.51168e9	+	3.18217e9i	−0.238178	+	0.137512i
$202$	2.33783e10	−	1.34975e10i	0.987944	−	0.570390i
$203$			1.21681e10i			0.502911i
$204$	−2.90369e10	−	5.02934e10i	−1.17385	−	2.03318i
$205$	−2.44071e10	+	4.22743e10i	−0.965214	+	1.67180i
$206$	−3.68752e9	−	2.12899e9i	−0.142670	−	0.0823704i
$207$	8.18109e8			0.0309703
$208$	2.23512e8	−	6.79779e8i	0.00827974	−	0.0251816i
$209$	1.79543e10			0.650892
$210$	4.39768e10	+	2.53900e10i	1.56040	+	0.900899i
$211$	1.47813e10	−	2.56020e10i	0.513383	−	0.889206i	−0.486496	−	0.873683i	$-0.661725\pi$
$211$	1.47813e10	−	2.56020e10i	0.513383	−	0.889206i	0.999880	−	0.0155231i	$-0.00494135\pi$
$212$	−1.01790e10	−	1.76305e10i	−0.346092	−	0.599450i
$213$			4.31614e9i			0.143677i
$214$	1.33911e10	−	7.73138e9i	0.436471	−	0.251997i
$215$	−3.85200e9	+	2.22395e9i	−0.122946	+	0.0709827i
$216$			3.45552e10i			1.08012i
$217$	1.22044e10	+	2.11387e10i	0.373635	+	0.647155i
$218$	2.38698e10	−	4.13437e10i	0.715804	−	1.23981i
$219$	2.50783e10	+	1.44790e10i	0.736716	+	0.425343i
$220$	5.06911e10			1.45891
$221$	3.67363e10	+	4.10887e10i	1.03593	+	1.15866i
$222$	−9.58159e10			−2.64758
$223$	−3.97704e10	−	2.29614e10i	−1.07693	−	0.621767i	−0.146864	−	0.989157i	$-0.546918\pi$
$223$	−3.97704e10	−	2.29614e10i	−1.07693	−	0.621767i	−0.930067	+	0.367390i	$0.880251\pi$
$224$	2.17859e10	−	3.77342e10i	0.578174	−	1.00143i
$225$	−7.82432e7	−	1.35521e8i	−0.00203529	−	0.00352522i
$226$			3.75973e10i			0.958669i
$227$	−5.28657e9	+	3.05220e9i	−0.132147	+	0.0762952i	−0.564616	−	0.825354i	$-0.690976\pi$
$227$	−5.28657e9	+	3.05220e9i	−0.132147	+	0.0762952i	0.432469	+	0.901649i	$0.357642\pi$
$228$	−3.93698e10	+	2.27302e10i	−0.964843	+	0.557052i
$229$			2.74503e10i			0.659610i	0.944049	+	0.329805i	$0.106983\pi$
$229$			2.74503e10i			0.659610i	−0.944049	+	0.329805i	$0.893017\pi$
$230$	7.66447e9	+	1.32752e10i	0.180595	+	0.312800i
$231$	−2.09170e10	+	3.62292e10i	−0.483331	+	0.837154i
$232$	−1.66082e10	−	9.58877e9i	−0.376381	−	0.217304i
$233$	−2.55024e10			−0.566864			−0.283432	−	0.958992i	$-0.591473\pi$
$233$	−2.55024e10			−0.566864			−0.283432	+	0.958992i	$0.591473\pi$
$234$	−2.14504e9	−	1.02686e10i	−0.0467697	−	0.223892i
$235$	−8.26220e10			−1.76722
$236$	1.17010e11	+	6.75558e10i	2.45538	+	1.41762i
$237$	8.35781e8	−	1.44761e9i	0.0172078	−	0.0298047i
$238$	−7.37268e10	−	1.27699e11i	−1.48946	−	2.57982i
$239$		−	2.55166e10i		−	0.505863i	−0.967484	−	0.252931i	$-0.918605\pi$
$239$		−	2.55166e10i		−	0.505863i	0.967484	−	0.252931i	$-0.0813947\pi$
$240$	−1.10923e9	+	6.40411e8i	−0.0215809	+	0.0124597i
$241$	6.54248e10	−	3.77730e10i	1.24930	−	0.721282i	0.278328	−	0.960486i	$-0.410220\pi$
$241$	6.54248e10	−	3.77730e10i	1.24930	−	0.721282i	0.970969	+	0.239204i	$0.0768864\pi$
$242$		−	1.91398e10i		−	0.358731i
$243$	7.60605e9	+	1.31741e10i	0.139937	+	0.242377i
$244$	3.51941e10	−	6.09579e10i	0.635646	−	1.10097i
$245$	1.96611e10	+	1.13514e10i	0.348627	+	0.201280i
$246$	1.64298e11			2.86039
$247$	3.21644e10	−	2.87573e10i	0.549843	−	0.491600i
$248$	−3.84695e10			−0.645779
$249$	−1.49639e10	−	8.63938e9i	−0.246687	−	0.142425i
$250$	−4.93314e10	+	8.54445e10i	−0.798718	+	1.38342i
$251$	1.83167e10	+	3.17254e10i	0.291283	+	0.504516i	0.974113	−	0.226060i	$-0.0725847\pi$
$251$	1.83167e10	+	3.17254e10i	0.291283	+	0.504516i	−0.682831	+	0.730577i	$0.739251\pi$
$252$			1.73929e10i			0.271688i
$253$	−1.09365e10	+	6.31419e9i	−0.167817	+	0.0968891i
$254$	−1.51340e11	+	8.73763e10i	−2.28140	+	1.31717i
$255$		−	9.86534e10i		−	1.46110i
$256$	3.58200e10	+	6.20421e10i	0.521250	+	0.902832i
$257$	−1.40500e10	+	2.43353e10i	−0.200899	+	0.347967i	−0.948818	−	0.315823i	$-0.897719\pi$
$257$	−1.40500e10	+	2.43353e10i	−0.200899	+	0.347967i	0.747920	+	0.663789i	$0.231053\pi$
$258$	1.29650e10	+	7.48536e9i	0.182173	+	0.105178i
$259$	−1.50774e11			−2.08199
$260$	9.08113e10	−	8.11920e10i	1.23242	−	1.10188i
$261$	−4.49930e9			−0.0600154
$262$	−1.13027e11	−	6.52564e10i	−1.48193	−	0.855594i
$263$	2.03952e10	−	3.53255e10i	0.262861	−	0.455289i	−0.704140	−	0.710061i	$-0.748667\pi$
$263$	2.03952e10	−	3.53255e10i	0.262861	−	0.455289i	0.967001	+	0.254772i	$0.0820005\pi$
$264$	−3.29661e10	−	5.70990e10i	−0.417687	−	0.723454i
$265$		−	3.45832e10i		−	0.430784i
$266$	−9.99629e10	+	5.77136e10i	−1.22425	+	0.706824i
$267$	6.58819e10	−	3.80369e10i	0.793351	−	0.458041i
$268$		−	4.08445e10i		−	0.483645i
$269$	−4.02706e10	−	6.97508e10i	−0.468925	−	0.812201i	0.530444	−	0.847720i	$-0.322025\pi$
$269$	−4.02706e10	−	6.97508e10i	−0.468925	−	0.812201i	−0.999369	+	0.0355183i	$0.988692\pi$
$270$	−7.59515e10	+	1.31552e11i	−0.869760	+	1.50647i
$271$	1.42982e11	+	8.25505e10i	1.61034	+	0.929733i	0.989290	+	0.145966i	$0.0466289\pi$
$271$	1.42982e11	+	8.25505e10i	1.61034	+	0.929733i	0.621055	+	0.783767i	$0.286704\pi$
$272$	3.71922e9			0.0411995
$273$	2.05564e10	+	9.84060e10i	0.223983	+	1.07223i
$274$	1.93941e11			2.07870
$275$	2.09191e9	+	1.20777e9i	0.0220570	+	0.0127346i
$276$	1.59876e10	−	2.76913e10i	0.165841	−	0.287245i
$277$	−4.75113e10	−	8.22920e10i	−0.484884	−	0.839844i	0.514965	−	0.857211i	$-0.327805\pi$
$277$	−4.75113e10	−	8.22920e10i	−0.484884	−	0.839844i	−0.999849	+	0.0173672i	$0.994472\pi$
$278$		−	3.43015e10i		−	0.344438i
$279$	−7.81626e9	+	4.51272e9i	−0.0772289	+	0.0445881i
$280$	−1.09064e11	+	6.29684e10i	−1.06041	+	0.612225i
$281$		−	1.86053e11i		−	1.78016i	−0.455809	−	0.890078i	$-0.650650\pi$
$281$		−	1.86053e11i		−	1.78016i	0.455809	−	0.890078i	$-0.349350\pi$
$282$	1.39044e11	+	2.40831e11i	1.30928	+	2.26773i
$283$	5.18958e10	−	8.98861e10i	0.480942	−	0.833017i	−0.518818	−	0.854884i	$-0.673628\pi$
$283$	5.18958e10	−	8.98861e10i	0.480942	−	0.833017i	0.999761	+	0.0218678i	$0.00696129\pi$
$284$	−2.39887e10	−	1.38499e10i	−0.218813	−	0.126332i
$285$	−7.72262e10			−0.693367
$286$	1.07928e11	+	1.20715e11i	0.953865	+	1.06688i
$287$	2.58537e11			2.24933
$288$	1.39527e10	+	8.05557e9i	0.119506	+	0.0689970i
$289$	−8.39396e10	+	1.45388e11i	−0.707826	+	1.22599i
$290$	−4.21517e10	−	7.30089e10i	−0.349965	−	0.606157i
$291$			1.34271e11i			1.09765i
$292$	−1.60945e11	+	9.29219e10i	−1.29555	+	0.747989i
$293$	−9.35018e10	+	5.39833e10i	−0.741166	+	0.427913i	−0.822493	−	0.568775i	$-0.807418\pi$
$293$	−9.35018e10	+	5.39833e10i	−0.741166	+	0.427913i	0.0813268	+	0.996687i	$0.474084\pi$
$294$		−	7.64126e10i		−	0.596488i
$295$	1.14761e11	+	1.98772e11i	0.882258	+	1.52812i
$296$	1.18814e11	−	2.05792e11i	0.899610	−	1.55817i
$297$	−1.08376e11	−	6.25708e10i	−0.808218	−	0.466625i
$298$	2.40417e11			1.76601
$299$	−9.47889e9	+	2.88286e10i	−0.0685863	+	0.208595i
$300$	−6.11615e9			−0.0435946
$301$	2.04015e10	+	1.17788e10i	0.143256	+	0.0827091i
$302$	3.66804e9	−	6.35322e9i	0.0253748	−	0.0439504i
$303$	−4.78284e10	−	8.28412e10i	−0.325982	−	0.564618i
$304$		−	2.91142e9i		−	0.0195512i
$305$	1.03553e11	−	5.97863e10i	0.685193	−	0.395596i
$306$	4.72180e10	−	2.72613e10i	0.307866	−	0.177746i
$307$		−	1.18337e11i		−	0.760326i	−0.924920	−	0.380163i	$-0.875868\pi$
$307$		−	1.18337e11i		−	0.760326i	0.924920	−	0.380163i	$-0.124132\pi$
$308$	−1.34239e11	−	2.32509e11i	−0.849963	−	1.47218i
$309$	−7.54408e9	+	1.30667e10i	−0.0470753	+	0.0815368i
$310$	−1.46453e11	−	8.45549e10i	−0.900683	−	0.520009i
$311$	−1.19220e11			−0.722647			−0.361323	−	0.932441i	$-0.617675\pi$
$311$	−1.19220e11			−0.722647			−0.361323	+	0.932441i	$0.617675\pi$
$312$	−1.50513e11	−	4.94889e10i	−0.899247	−	0.295674i
$313$	−3.12948e11			−1.84299			−0.921495	−	0.388389i	$-0.873032\pi$
$313$	−3.12948e11			−1.84299			−0.921495	+	0.388389i	$0.873032\pi$
$314$	−2.11692e11	−	1.22220e11i	−1.22891	−	0.709512i
$315$	−1.47732e10	+	2.55879e10i	−0.0845428	+	0.146432i
$316$	5.36379e9	+	9.29036e9i	0.0302608	+	0.0524132i
$317$		−	2.96387e10i		−	0.164851i	−0.996597	−	0.0824257i	$-0.973733\pi$
$317$		−	2.96387e10i		−	0.164851i	0.996597	−	0.0824257i	$-0.0262667\pi$
$318$	−1.00805e11	+	5.81999e10i	−0.552791	+	0.319154i
$319$	6.01467e10	−	3.47257e10i	0.325202	−	0.187756i
$320$			3.06918e11i			1.63624i
$321$	−2.73962e10	−	4.74516e10i	−0.144018	−	0.249447i
$322$	4.05937e10	−	7.03103e10i	0.210430	−	0.364475i
$323$	1.94204e11	+	1.12124e11i	0.992766	+	0.573173i
$324$	2.71262e11			1.36753
$325$	5.68206e9	−	1.18695e9i	0.0282508	−	0.00590141i
$326$	−2.15800e11			−1.05821
$327$	−1.46501e11	−	8.45826e10i	−0.708561	−	0.409088i
$328$	−2.03733e11	+	3.52876e11i	−0.971918	+	1.68341i
$329$	2.18797e11	+	3.78968e11i	1.02958	+	1.78329i
$330$		−	2.89835e11i		−	1.34536i
$331$	3.04109e11	−	1.75577e11i	1.39253	−	0.803976i	0.398932	−	0.916980i	$-0.369381\pi$
$331$	3.04109e11	−	1.75577e11i	1.39253	−	0.803976i	0.993594	+	0.113005i	$0.0360476\pi$
$332$	9.60336e10	−	5.54450e10i	0.433812	−	0.250462i
$333$		−	5.57505e10i		−	0.248456i
$334$	−9.39546e10	−	1.62734e11i	−0.413104	−	0.715517i
$335$	3.46925e10	−	6.00891e10i	0.150499	−	0.260672i
$336$	5.87484e9	+	3.39184e9i	0.0251460	+	0.0145181i
$337$	−5.10205e10			−0.215481			−0.107741	−	0.994179i	$-0.534362\pi$
$337$	−5.10205e10			−0.215481			−0.107741	+	0.994179i	$0.534362\pi$
$338$	3.86698e11	+	4.33880e10i	1.61156	+	0.180819i
$339$	1.33226e11			0.547887
$340$	5.48305e11	+	3.16564e11i	2.22519	+	1.28472i
$341$	6.96585e10	−	1.20652e11i	0.278984	−	0.483215i
$342$	−2.13403e10	−	3.69624e10i	−0.0843495	−	0.146098i
$343$			1.82730e11i			0.712831i
$344$	−3.21538e10	+	1.85640e10i	−0.123800	+	0.0714758i
$345$	4.70409e10	−	2.71591e10i	0.178768	−	0.103212i
$346$			4.82685e11i			1.81059i
$347$	−2.00819e11	−	3.47828e11i	−0.743569	−	1.28790i	−0.950860	−	0.309621i	$-0.899798\pi$
$347$	−2.00819e11	−	3.47828e11i	−0.743569	−	1.28790i	0.207291	−	0.978279i	$-0.433535\pi$
$348$	−8.79258e10	+	1.52292e11i	−0.321373	+	0.556635i
$349$	−1.05697e10	−	6.10240e9i	−0.0381370	−	0.0220184i	0.480810	−	0.876825i	$-0.340343\pi$
$349$	−1.05697e10	−	6.10240e9i	−0.0381370	−	0.0220184i	−0.518947	+	0.854806i	$0.673676\pi$
$350$	−1.55294e10			−0.0553156
$351$	−2.94371e11	+	6.14923e10i	−1.03517	+	0.216241i
$352$	−2.48692e11			−0.863417
$353$	9.44456e10	+	5.45282e10i	0.323739	+	0.186911i	0.653058	−	0.757308i	$-0.273486\pi$
$353$	9.44456e10	+	5.45282e10i	0.323739	+	0.186911i	−0.329319	+	0.944219i	$0.606819\pi$
$354$	3.86261e11	−	6.69024e11i	1.30727	−	2.26426i
$355$	−2.35276e10	−	4.07510e10i	−0.0786230	−	0.136179i
$356$			4.88220e11i			1.61098i
$357$	−4.52501e11	+	2.61251e11i	−1.47439	+	0.851239i
$358$	3.28459e11	−	1.89636e11i	1.05684	−	0.610165i
$359$			1.39991e11i			0.444812i	0.974954	+	0.222406i	$0.0713910\pi$
$359$			1.39991e11i			0.444812i	−0.974954	+	0.222406i	$0.928609\pi$
$360$	−2.32833e10	−	4.03278e10i	−0.0730605	−	0.126545i
$361$	−7.35730e10	+	1.27432e11i	−0.228001	+	0.394909i
$362$	−8.68128e10	−	5.01214e10i	−0.265702	−	0.153403i
$363$	−6.78220e10			−0.205017
$364$	−6.12893e11	−	2.01520e11i	−1.82990	−	0.601675i
$365$	−3.15704e11			−0.931026
$366$	−3.48537e11	−	2.01228e11i	−1.01528	−	0.586170i
$367$	2.57178e11	−	4.45445e11i	0.740008	−	1.28173i	−0.212484	−	0.977165i	$-0.568155\pi$
$367$	2.57178e11	−	4.45445e11i	0.740008	−	1.28173i	0.952491	−	0.304566i	$-0.0985115\pi$
$368$	1.02389e9	+	1.77343e9i	0.00291031	+	0.00504080i
$369$			9.55969e10i			0.268426i
$370$	9.04649e11	−	5.22299e11i	2.50941	−	1.44881i
$371$	−1.58625e11	+	9.15824e10i	−0.434700	+	0.250974i
$372$			3.52752e11i			0.955051i
$373$	1.45294e11	+	2.51656e11i	0.388649	+	0.673159i	0.992268	−	0.124114i	$-0.0396087\pi$
$373$	1.45294e11	+	2.51656e11i	0.388649	+	0.673159i	−0.603619	+	0.797273i	$0.706275\pi$
$374$	−4.20807e11	+	7.28859e11i	−1.11214	+	1.92629i
$375$	3.02773e11	+	1.74806e11i	0.790636	+	0.456474i
$376$	−6.89671e11			−1.77949
$377$	5.21304e10	−	1.58547e11i	0.132909	−	0.404223i
$378$	8.04531e11			2.02689
$379$	3.86896e10	+	2.23375e10i	0.0963203	+	0.0556106i	0.547386	−	0.836880i	$-0.315623\pi$
$379$	3.86896e10	+	2.23375e10i	0.0963203	+	0.0556106i	−0.451066	+	0.892491i	$0.648956\pi$
$380$	2.47808e11	−	4.29215e11i	0.609661	−	1.05596i
$381$	3.09618e11	+	5.36274e11i	0.752773	+	1.30384i
$382$		−	3.72914e11i		−	0.896033i
$383$	−8.26844e10	+	4.77379e10i	−0.196349	+	0.113362i	−0.594951	−	0.803762i	$-0.702829\pi$
$383$	−8.26844e10	+	4.77379e10i	−0.196349	+	0.113362i	0.398602	+	0.917124i	$0.369495\pi$
$384$	5.60030e11	−	3.23333e11i	1.31438	−	0.758857i
$385$		−	4.56079e11i		−	1.05795i
$386$	−2.66659e11	−	4.61867e11i	−0.611383	−	1.05895i
$387$	−4.35536e9	+	7.54370e9i	−0.00987017	+	0.0170956i
$388$	−7.46262e11	−	4.30855e11i	−1.67166	−	0.965135i
$389$	−2.40025e11			−0.531476			−0.265738	−	0.964045i	$-0.585616\pi$
$389$	−2.40025e11			−0.531476			−0.265738	+	0.964045i	$0.585616\pi$
$390$	−4.64228e11	−	5.19228e11i	−1.01611	−	1.13650i
$391$	−1.57728e11			−0.341281
$392$	1.64118e11	+	9.47533e10i	0.351049	+	0.202678i
$393$	−2.31236e11	+	4.00513e11i	−0.488979	+	0.846936i
$394$	4.51185e10	+	7.81476e10i	0.0943239	+	0.163374i
$395$			1.82236e10i			0.0376658i
$396$	8.59727e10	−	4.96363e10i	0.175684	−	0.101431i
$397$	2.77353e11	−	1.60130e11i	0.560371	−	0.323531i	−0.192923	−	0.981214i	$-0.561797\pi$
$397$	2.77353e11	−	1.60130e11i	0.560371	−	0.323531i	0.753295	+	0.657683i	$0.228463\pi$
$398$			9.17730e11i			1.83333i
$399$	2.04508e11	+	3.54219e11i	0.403955	+	0.699671i
$400$	1.95848e8	−	3.39219e8i	0.000382516	−	0.000662537i
$401$	−1.19254e10	−	6.88515e9i	−0.0230316	−	0.0132973i	0.488440	−	0.872597i	$-0.337566\pi$
$401$	−1.19254e10	−	6.88515e9i	−0.0230316	−	0.0132973i	−0.511472	+	0.859300i	$0.670899\pi$
$402$	−2.33535e11			−0.446000
$403$	−6.84578e10	−	3.27716e11i	−0.129286	−	0.618906i
$404$	6.13897e11			1.14651
$405$	3.99073e11	+	2.30405e11i	0.737062	+	0.425543i
$406$	−2.23250e11	+	3.86681e11i	−0.407779	+	0.706294i
$407$	4.30284e11	+	7.45273e11i	0.777285	+	1.34630i
$408$		−	8.23490e11i		−	1.47125i
$409$	−3.92239e11	+	2.26459e11i	−0.693100	+	0.400161i	−0.804772	−	0.593584i	$-0.797713\pi$
$409$	−3.92239e11	+	2.26459e11i	−0.693100	+	0.400161i	0.111672	+	0.993745i	$0.464379\pi$
$410$	−1.55123e12	+	8.95601e11i	−2.71111	+	1.56526i
$411$		−	6.87231e11i		−	1.18800i
$412$	−4.84157e10	−	8.38585e10i	−0.0827845	−	0.143387i
$413$	6.07814e11	−	1.05277e12i	1.02801	−	1.78056i
$414$	2.59980e10	+	1.50100e10i	0.0434950	+	0.0251118i
$415$	1.88376e11			0.311751
$416$	−4.45523e11	+	3.98331e11i	−0.729374	+	0.652114i
$417$	−1.21547e11			−0.196849
$418$	5.70554e11	+	3.29409e11i	0.914120	+	0.527767i
$419$	−4.33353e11	+	7.50590e11i	−0.686877	+	1.18971i	0.285966	+	0.958240i	$0.407686\pi$
$419$	−4.33353e11	+	7.50590e11i	−0.686877	+	1.18971i	−0.972843	+	0.231466i	$0.925648\pi$
$420$	5.77399e11	+	1.00008e12i	0.905428	+	1.56825i
$421$		−	9.07071e11i		−	1.40725i	−0.710570	−	0.703626i	$-0.751563\pi$
$421$		−	9.07071e11i		−	1.40725i	0.710570	−	0.703626i	$-0.248437\pi$
$422$	9.39446e11	−	5.42389e11i	1.44200	−	0.832540i
$423$	−1.40128e11	+	8.09028e10i	−0.212810	+	0.122866i
$424$		−	2.88677e11i		−	0.433776i
$425$	1.50849e10	+	2.61278e10i	0.0224281	+	0.0388466i
$426$	−7.91889e10	+	1.37159e11i	−0.116499	+	0.201782i
$427$	−5.48452e11	−	3.16649e11i	−0.798386	−	0.460949i
$428$	3.51641e11			0.506527
$429$	4.27754e11	−	3.82443e11i	0.609728	−	0.545142i
$430$	−1.63213e11			−0.230222
$431$	1.02681e11	+	5.92831e10i	0.143332	+	0.0827528i	0.569951	−	0.821679i	$-0.306962\pi$
$431$	1.02681e11	+	5.92831e10i	0.143332	+	0.0827528i	−0.426619	+	0.904431i	$0.640295\pi$
$432$	−1.01463e10	+	1.75740e10i	−0.0140163	+	0.0242769i
$433$	−1.32970e11	−	2.30311e11i	−0.181785	−	0.314861i	0.760703	−	0.649100i	$-0.224854\pi$
$433$	−1.32970e11	−	2.30311e11i	−0.181785	−	0.314861i	−0.942488	+	0.334239i	$0.891521\pi$
$434$			8.95664e11i			1.21183i
$435$	−2.58707e11	+	1.49365e11i	−0.346423	+	0.200008i
$436$	9.40203e11	−	5.42827e11i	1.24604	−	0.719402i
$437$			1.23470e11i			0.161955i
$438$	5.31296e11	+	9.20232e11i	0.689768	+	1.19471i
$439$	−3.88144e10	+	6.72285e10i	−0.0498772	+	0.0863899i	−0.889886	−	0.456183i	$-0.849216\pi$
$439$	−3.88144e10	+	6.72285e10i	−0.0498772	+	0.0863899i	0.840009	+	0.542573i	$0.182550\pi$
$440$	6.22502e11	+	3.59402e11i	0.791778	+	0.457133i
$441$	4.44607e10			0.0559761
$442$	4.13554e11	+	1.97973e12i	0.515385	+	2.46721i
$443$	1.22924e12			1.51642			0.758212	−	0.652008i	$-0.226073\pi$
$443$	1.22924e12			1.51642			0.758212	+	0.652008i	$0.226073\pi$
$444$	−1.88704e12	−	1.08948e12i	−2.30440	−	1.33045i
$445$	−4.14684e11	+	7.18254e11i	−0.501299	+	0.868276i
$446$	−8.42554e11	−	1.45935e12i	−1.00830	−	1.74643i
$447$		−	8.51920e11i		−	1.00929i
$448$	1.40776e12	−	8.12773e11i	1.65112	−	0.953275i
$449$	6.70229e11	−	3.86957e11i	0.778243	−	0.449319i	−0.0575645	−	0.998342i	$-0.518333\pi$
$449$	6.70229e11	−	3.86957e11i	0.778243	−	0.449319i	0.835807	+	0.549023i	$0.185000\pi$
$450$		−	5.74216e9i		−	0.00660114i
$451$	−7.37819e11	−	1.27794e12i	−0.839761	−	1.45451i
$452$	−4.27503e11	+	7.40457e11i	−0.481744	+	0.834405i
$453$	−2.25127e10	−	1.29977e10i	−0.0251180	−	0.0145019i
$454$	−2.23997e11			−0.247452
$455$	−7.30502e11	−	8.17049e11i	−0.799043	−	0.893711i
$456$	−6.44631e11			−0.698183
$457$	−3.24952e11	−	1.87611e11i	−0.348495	−	0.201204i	0.315527	−	0.948917i	$-0.397819\pi$
$457$	−3.24952e11	−	1.87611e11i	−0.348495	−	0.201204i	−0.664022	+	0.747713i	$0.731152\pi$
$458$	−5.03634e11	+	8.72320e11i	−0.534836	+	0.926363i
$459$	−7.81505e11	−	1.35361e12i	−0.821817	−	1.42343i
$460$			3.48598e11i			0.363007i
$461$	8.61196e11	−	4.97212e11i	0.888072	−	0.512728i	0.0147604	−	0.999891i	$-0.495301\pi$
$461$	8.61196e11	−	4.97212e11i	0.888072	−	0.512728i	0.873311	+	0.487163i	$0.161968\pi$
$462$	−1.32941e12	+	7.67533e11i	−1.35759	+	0.783805i
$463$			1.76404e12i			1.78400i	0.452038	+	0.891999i	$0.350697\pi$
$463$			1.76404e12i			1.78400i	−0.452038	+	0.891999i	$0.649303\pi$
$464$	−5.63103e9	−	9.75323e9i	−0.00563971	−	0.00976827i
$465$	−2.99621e11	+	5.18958e11i	−0.297190	+	0.514747i
$466$	−8.10419e11	−	4.67896e11i	−0.796110	−	0.459634i
$467$	−7.36402e10			−0.0716455			−0.0358227	−	0.999358i	$-0.511405\pi$
$467$	−7.36402e10			−0.0716455			−0.0358227	+	0.999358i	$0.511405\pi$
$468$	7.45144e10	−	2.26624e11i	0.0718015	−	0.218373i
$469$	−3.67487e11			−0.350723
$470$	−2.62558e12	−	1.51588e12i	−2.48190	−	1.43293i
$471$	−4.33088e11	+	7.50130e11i	−0.405492	+	0.702332i
$472$	9.57945e11	+	1.65921e12i	0.888386	+	1.53873i
$473$		−	1.34459e11i		−	0.123514i
$474$	5.31192e10	−	3.06684e10i	0.0483336	−	0.0279054i
$475$	2.04530e10	−	1.18085e10i	0.0184346	−	0.0106432i
$476$		−	3.35327e12i		−	2.99390i
$477$	−3.38636e10	−	5.86535e10i	−0.0299503	−	0.0518754i
$478$	4.68157e11	−	8.10873e11i	0.410172	−	0.710439i
$479$	1.49367e12	+	8.62369e11i	1.29641	+	0.748485i	0.979783	−	0.200063i	$-0.0641148\pi$
$479$	1.49367e12	+	8.62369e11i	1.29641	+	0.748485i	0.316632	+	0.948549i	$0.397448\pi$
$480$	1.06969e12			0.919760
$481$	1.96454e12	+	6.45944e11i	1.67343	+	0.550227i
$482$	2.77211e12			2.33937
$483$	−2.49145e11	−	1.43844e11i	−0.208300	−	0.120262i
$484$	2.17631e11	−	3.76948e11i	0.180267	−	0.312232i
$485$	−7.31919e11	−	1.26772e12i	−0.600655	−	1.04036i
$486$			5.58197e11i			0.453863i
$487$	−1.65811e12	+	9.57311e11i	−1.33578	+	0.771210i	−0.986178	−	0.165689i	$-0.947015\pi$
$487$	−1.65811e12	+	9.57311e11i	−1.33578	+	0.771210i	−0.349598	+	0.936900i	$0.613682\pi$
$488$	8.64387e11	−	4.99054e11i	0.689952	−	0.398344i
$489$			7.64688e11i			0.604776i
$490$	4.16530e11	+	7.21452e11i	0.326411	+	0.565360i
$491$	−8.98173e11	+	1.55568e12i	−0.697418	+	1.20796i	0.271941	+	0.962314i	$0.412335\pi$
$491$	−8.98173e11	+	1.55568e12i	−0.697418	+	1.20796i	−0.969359	+	0.245650i	$0.920999\pi$
$492$	3.23576e12	+	1.86817e12i	2.48962	+	1.43738i
$493$	8.67443e11			0.661348
$494$	1.54974e12	−	3.23731e11i	1.17081	−	0.244576i
$495$	1.68640e11			0.126252
$496$	−1.95646e10	−	1.12957e10i	−0.0145146	−	0.00838000i
$497$	−1.24610e11	+	2.15831e11i	−0.0916115	+	0.158676i
$498$	−3.17016e11	−	5.49088e11i	−0.230967	−	0.400046i
$499$			1.29654e12i			0.936122i	0.883696	+	0.468061i	$0.155047\pi$
$499$			1.29654e12i			0.936122i	−0.883696	+	0.468061i	$0.844953\pi$
$500$	−1.94311e12	+	1.12185e12i	−1.39037	+	0.802733i
$501$	−5.76649e11	+	3.32929e11i	−0.408923	+	0.236092i
$502$			1.34423e12i			0.944731i
$503$	−5.41388e11	−	9.37711e11i	−0.377097	−	0.653150i	0.613542	−	0.789662i	$-0.289744\pi$
$503$	−5.41388e11	−	9.37711e11i	−0.377097	−	0.653150i	−0.990638	+	0.136512i	$0.956411\pi$
$504$	−1.23316e11	+	2.13590e11i	−0.0851301	+	0.147450i
$505$	9.03147e11	+	5.21432e11i	0.617941	+	0.356769i
$506$	−4.63389e11			−0.314245
$507$	1.53746e11	−	1.37027e12i	0.103340	−	0.921020i
$508$	−3.97408e12			−2.64758
$509$	1.25867e12	+	7.26693e11i	0.831154	+	0.479867i	0.854248	−	0.519866i	$-0.174018\pi$
$509$	1.25867e12	+	7.26693e11i	0.831154	+	0.479867i	−0.0230935	+	0.999733i	$0.507352\pi$
$510$	1.81001e12	−	3.13503e12i	1.18472	−	2.05199i
$511$	8.36039e11	+	1.44806e12i	0.542416	+	0.939492i
$512$			8.24265e10i			0.0530093i
$513$	−1.05961e12	+	6.11765e11i	−0.675487	+	0.389993i
$514$	−8.92966e11	+	5.15554e11i	−0.564288	+	0.325792i
$515$		−	1.64493e11i		−	0.103042i
$516$	1.70226e11	+	2.94840e11i	0.105706	+	0.183089i
$517$	1.24882e12	−	2.16302e12i	0.768762	−	1.33154i
$518$	−4.79134e12	−	2.76628e12i	−2.92397	−	1.68815i
$519$	1.71040e12			1.03477
$520$	1.69084e12	−	3.53206e11i	1.01412	−	0.211843i
$521$	−9.18754e11			−0.546298			−0.273149	−	0.961972i	$-0.588065\pi$
$521$	−9.18754e11			−0.546298			−0.273149	+	0.961972i	$0.588065\pi$
$522$	−1.42980e11	−	8.25493e10i	−0.0842862	−	0.0486627i
$523$	−1.44839e12	+	2.50868e12i	−0.846501	+	1.46618i	0.0378095	+	0.999285i	$0.487962\pi$
$523$	−1.44839e12	+	2.50868e12i	−0.846501	+	1.46618i	−0.884311	+	0.466898i	$0.845371\pi$
$524$	−1.48401e12	−	2.57038e12i	−0.859895	−	1.48938i
$525$			5.50284e10i			0.0316133i
$526$	1.29624e12	−	7.48387e11i	0.738331	−	0.426276i
$527$	1.50694e12	−	8.70030e11i	0.851035	−	0.491345i
$528$		−	3.87189e10i		−	0.0216806i
$529$	8.57154e11	+	1.48463e12i	0.475892	+	0.824269i
$530$	6.34504e11	−	1.09899e12i	0.349295	−	0.604997i
$531$	3.89272e11	+	2.24746e11i	0.212485	+	0.122678i
$532$	−2.62495e12			−1.42075
$533$	−3.36865e12	−	1.10762e12i	−1.80794	−	0.594453i
$534$	2.79148e12			1.48559
$535$	5.17324e11	+	2.98677e11i	0.273005	+	0.157619i
$536$	2.89589e11	−	5.01582e11i	0.151544	−	0.262483i
$537$	−6.71976e11	−	1.16390e12i	−0.348714	−	0.603991i
$538$		−	2.95540e12i		−	1.52089i
$539$	−5.94351e11	+	3.43149e11i	−0.303315	+	0.175119i
$540$	−2.99164e12	+	1.72723e12i	−1.51404	+	0.874133i
$541$			6.88869e11i			0.345739i	0.984945	+	0.172870i	$0.0553039\pi$
$541$			6.88869e11i			0.345739i	−0.984945	+	0.172870i	$0.944696\pi$
$542$	3.02913e12	+	5.24661e12i	1.50772	+	2.61145i
$543$	−1.77605e11	+	3.07621e11i	−0.0876711	+	0.151851i
$544$	−2.69001e12	−	1.55308e12i	−1.31692	−	0.760322i
$545$	1.84426e12			0.895445
$546$	−1.15222e12	+	3.50432e12i	−0.554843	+	1.68747i
$547$	−3.12007e12			−1.49012			−0.745061	−	0.666996i	$-0.767580\pi$
$547$	−3.12007e12			−1.49012			−0.745061	+	0.666996i	$0.767580\pi$
$548$	3.81956e12	+	2.20522e12i	1.80926	+	1.04458i
$549$	1.17085e11	−	2.02796e11i	0.0550077	−	0.0952762i
$550$	4.43181e10	+	7.67612e10i	0.0206514	+	0.0357692i
$551$		−	6.79037e11i		−	0.313842i
$552$	3.92664e11	−	2.26705e11i	0.180010	−	0.103929i
$553$	8.35875e10	−	4.82592e10i	0.0380083	−	0.0219441i
$554$		−	3.48679e12i		−	1.57265i
$555$	−1.85077e12	−	3.20563e12i	−0.828007	−	1.43415i
$556$	3.90028e11	−	6.75548e11i	0.173085	−	0.299792i
$557$	2.29858e12	+	1.32708e12i	1.01184	+	0.584185i	0.911729	−	0.410792i	$-0.134748\pi$
$557$	2.29858e12	+	1.32708e12i	1.01184	+	0.584185i	0.100109	+	0.994977i	$0.468081\pi$
$558$	−3.31182e11			−0.144615
$559$	−2.15363e11	−	2.40878e11i	−0.0932863	−	0.104338i
$560$	−7.39567e10			−0.0317783
$561$	2.58272e12	+	1.49113e12i	1.10089	+	0.635599i
$562$	3.41354e12	−	5.91242e12i	1.44342	−	2.50007i
$563$	6.85251e11	+	1.18689e12i	0.287450	+	0.497878i	0.973200	−	0.229959i	$-0.0738592\pi$
$563$	6.85251e11	+	1.18689e12i	0.287450	+	0.497878i	−0.685750	+	0.727837i	$0.740526\pi$
$564$			6.32405e12i			2.63172i
$565$	−1.25786e12	+	7.26225e11i	−0.519295	+	0.299815i
$566$	3.29831e12	−	1.90428e12i	1.35088	−	0.779932i
$567$		−	2.44061e12i		−	0.991686i
$568$	−1.96392e11	−	3.40161e11i	−0.0791691	−	0.137125i
$569$	1.35627e12	−	2.34912e12i	0.542425	−	0.939508i	−0.456339	−	0.889806i	$-0.650840\pi$
$569$	1.35627e12	−	2.34912e12i	0.542425	−	0.939508i	0.998764	−	0.0497018i	$-0.0158271\pi$
$570$	−2.45411e12	−	1.41688e12i	−0.973772	−	0.562207i
$571$	−3.89232e12			−1.53231			−0.766153	−	0.642658i	$-0.777832\pi$
$571$	−3.89232e12			−1.53231			−0.766153	+	0.642658i	$0.777832\pi$
$572$	7.52982e11	+	3.60462e12i	0.294105	+	1.40792i
$573$	−1.32142e12			−0.512090
$574$	8.21583e12	+	4.74341e12i	3.15899	+	1.82384i
$575$	−8.30569e9	+	1.43859e10i	−0.00316862	+	0.00548821i
$576$	3.00532e11	+	5.20537e11i	0.113760	+	0.197038i
$577$		−	4.61600e12i		−	1.73370i	−0.498567	−	0.866851i	$-0.666140\pi$
$577$		−	4.61600e12i		−	1.73370i	0.498567	−	0.866851i	$-0.333860\pi$
$578$	−5.33490e12	+	3.08010e12i	−1.98816	+	1.14786i
$579$	−1.63663e12	+	9.44908e11i	−0.605197	+	0.349410i
$580$		−	1.91716e12i		−	0.703448i
$581$	−4.98851e11	−	8.64036e11i	−0.181626	−	0.314586i
$582$	−2.46348e12	+	4.26688e12i	−0.890013	+	1.54155i
$583$	9.05378e11	+	5.22720e11i	0.324580	+	0.187396i
$584$	−2.63528e12			−0.937493
$585$	3.02113e11	−	2.70111e11i	0.106652	−	0.0953546i
$586$	−3.96176e12			−1.38787
$587$	−1.29535e12	−	7.47872e11i	−0.450315	−	0.259990i	0.257648	−	0.966239i	$-0.417052\pi$
$587$	−1.29535e12	−	7.47872e11i	−0.450315	−	0.259990i	−0.707963	+	0.706249i	$0.750386\pi$
$588$	8.68856e11	−	1.50490e12i	0.299743	−	0.519171i
$589$	−6.81063e11	−	1.17964e12i	−0.233168	−	0.403858i
$590$			8.42215e12i			2.86147i
$591$	2.76916e11	−	1.59878e11i	0.0933694	−	0.0539069i
$592$	1.20852e11	−	6.97737e10i	0.0404394	−	0.0233477i
$593$			2.12351e12i			0.705192i	0.935776	+	0.352596i	$0.114701\pi$
$593$			2.12351e12i			0.705192i	−0.935776	+	0.352596i	$0.885299\pi$
$594$	−2.29599e12	−	3.97677e12i	−0.756713	−	1.31067i
$595$	2.84820e12	−	4.93323e12i	0.931631	−	1.61363i
$596$	4.73489e12	+	2.73369e12i	1.53710	+	0.887443i
$597$	3.25198e12			1.04776
$598$	−8.30145e11	+	7.42210e11i	−0.265460	+	0.237340i
$599$	1.24442e12			0.394954			0.197477	−	0.980308i	$-0.436725\pi$
$599$	1.24442e12			0.394954			0.197477	+	0.980308i	$0.436725\pi$
$600$	−7.51081e10	−	4.33637e10i	−0.0236595	−	0.0136598i
$601$	−3.62857e11	+	6.28487e11i	−0.113449	+	0.196499i	−0.917159	−	0.398522i	$-0.869523\pi$
$601$	−3.62857e11	+	6.28487e11i	−0.113449	+	0.196499i	0.803710	+	0.595022i	$0.202857\pi$
$602$	4.32216e11	+	7.48620e11i	0.134127	+	0.232315i
$603$		−	1.35882e11i		−	0.0418539i
$604$	1.44480e11	−	8.34154e10i	0.0441714	−	0.0255023i
$605$	6.40343e11	−	3.69702e11i	0.194318	−	0.112190i
$606$		−	3.51006e12i		−	1.05727i
$607$	1.58447e12	+	2.74438e12i	0.473734	+	0.820531i	0.999548	−	0.0300688i	$-0.00957264\pi$
$607$	1.58447e12	+	2.74438e12i	0.473734	+	0.820531i	−0.525814	+	0.850599i	$0.676239\pi$
$608$	−1.21575e12	+	2.10575e12i	−0.360810	+	0.624942i
$609$	1.37020e12	+	7.91088e11i	0.403653	+	0.233049i
$610$	4.38763e12			1.28306
$611$	−1.22729e12	−	5.87520e12i	−0.356256	−	1.70544i
$612$	1.23991e12			0.357280
$613$	7.68172e11	+	4.43504e11i	0.219728	+	0.126860i	0.605824	−	0.795598i	$-0.292843\pi$
$613$	7.68172e11	+	4.43504e11i	0.219728	+	0.126860i	−0.386096	+	0.922459i	$0.626177\pi$
$614$	2.17116e12	−	3.76055e12i	0.616500	−	1.06781i
$615$	3.17357e12	+	5.49678e12i	0.894560	+	1.54942i
$616$		−	3.80703e12i		−	1.06530i
$617$	−1.66139e12	+	9.59203e11i	−0.461517	+	0.266457i	−0.712682	−	0.701487i	$-0.752520\pi$
$617$	−1.66139e12	+	9.59203e11i	−0.461517	+	0.266457i	0.251165	+	0.967944i	$0.419186\pi$
$618$	−4.79475e11	+	2.76825e11i	−0.132226	+	0.0763408i
$619$			3.56519e12i			0.976057i	0.872828	+	0.488028i	$0.162284\pi$
$619$			3.56519e12i			0.976057i	−0.872828	+	0.488028i	$0.837716\pi$
$620$	−1.92288e12	−	3.33052e12i	−0.522624	−	0.905211i
$621$	4.30293e11	−	7.45290e11i	0.116105	−	0.201101i
$622$	−3.78858e12	−	2.18734e12i	−1.01489	−	0.585949i
$623$	4.39262e12			1.16823
$624$	−6.20161e10	−	6.93635e10i	−0.0163747	−	0.0183147i
$625$	−3.92161e12			−1.02803
$626$	−9.94493e12	−	5.74171e12i	−2.58832	−	1.49437i
$627$	1.16726e12	−	2.02176e12i	0.301623	−	0.522427i
$628$	−2.77943e12	−	4.81411e12i	−0.713079	−	1.23509i
$629$			1.07484e13i			2.73790i
$630$	−9.38931e11	+	5.42092e11i	−0.237466	+	0.137101i
$631$	1.05142e12	−	6.07039e11i	0.264025	−	0.152435i	−0.362144	−	0.932122i	$-0.617955\pi$
$631$	1.05142e12	−	6.07039e11i	0.264025	−	0.152435i	0.626169	+	0.779687i	$0.284622\pi$
$632$			1.52118e11i			0.0379274i
$633$	−1.92196e12	−	3.32893e12i	−0.475803	−	0.824115i
$634$	5.43786e11	−	9.41864e11i	0.133668	−	0.231519i
$635$	−5.84654e12	−	3.37550e12i	−1.42698	−	0.823866i
$636$	−2.64707e12			−0.641517
$637$	−5.15136e11	+	1.56671e12i	−0.123964	+	0.377017i
$638$	2.54847e12			0.608957
$639$	−7.98061e10	−	4.60761e10i	−0.0189357	−	0.0109325i
$640$	−3.52503e12	+	6.10553e12i	−0.830525	+	1.43851i
$641$	−1.39060e12	−	2.40858e12i	−0.325342	−	0.563509i	0.656240	−	0.754553i	$-0.272146\pi$
$641$	−1.39060e12	−	2.40858e12i	−0.325342	−	0.563509i	−0.981581	+	0.191044i	$0.938813\pi$
$642$		−	2.01057e12i		−	0.467101i
$643$	4.38888e12	−	2.53392e12i	1.01252	−	0.584580i	0.100593	−	0.994928i	$-0.467926\pi$
$643$	4.38888e12	−	2.53392e12i	1.01252	−	0.584580i	0.911929	+	0.410348i	$0.134593\pi$
$644$	1.59894e12	−	9.23148e11i	0.366307	−	0.211488i
$645$			5.78345e11i			0.131574i
$646$	4.11430e12	+	7.12618e12i	0.929500	+	1.60994i
$647$	−3.29613e12	+	5.70906e12i	−0.739494	+	1.28084i	0.213229	+	0.977002i	$0.431602\pi$
$647$	−3.29613e12	+	5.70906e12i	−0.739494	+	1.28084i	−0.952723	+	0.303840i	$0.901731\pi$
$648$	3.33118e12	+	1.92326e12i	0.742182	+	0.428499i
$649$	−6.93839e12			−1.53517
$650$	2.02343e11	+	6.65306e10i	0.0444608	+	0.0146188i
$651$	3.17379e12			0.692570
$652$	−4.25006e12	−	2.45377e12i	−0.921045	−	0.531766i
$653$	4.45378e11	−	7.71417e11i	0.0958560	−	0.166027i	−0.814110	−	0.580711i	$-0.802775\pi$
$653$	4.45378e11	−	7.71417e11i	0.0958560	−	0.166027i	0.909966	+	0.414684i	$0.136108\pi$
$654$	−3.10370e12	−	5.37577e12i	−0.663407	−	1.14905i
$655$		−	5.04195e12i		−	1.07032i
$656$	−2.07228e11	+	1.19643e11i	−0.0436898	+	0.0252243i
$657$	−5.35437e11	+	3.09135e11i	−0.112115	+	0.0647297i
$658$			1.60572e13i			3.33929i
$659$	6.56775e11	+	1.13757e12i	0.135654	+	0.234960i	0.925847	−	0.377898i	$-0.123353\pi$
$659$	6.56775e11	+	1.13757e12i	0.135654	+	0.234960i	−0.790193	+	0.612858i	$0.790020\pi$
$660$	3.29559e12	−	5.70813e12i	0.676061	−	1.17097i
$661$	3.84713e12	+	2.22114e12i	0.783845	+	0.452553i	0.837791	−	0.545991i	$-0.183847\pi$
$661$	3.84713e12	+	2.22114e12i	0.783845	+	0.452553i	−0.0539463	+	0.998544i	$0.517180\pi$
$662$	1.28854e13			2.60757
$663$	7.01519e12	−	1.46543e12i	1.41003	−	0.294546i
$664$	1.57243e12			0.313917
$665$	−3.86175e12	−	2.22958e12i	−0.765749	−	0.442105i
$666$	1.02286e12	−	1.77165e12i	0.201458	−	0.348935i
$667$	2.38805e11	+	4.13623e11i	0.0467173	+	0.0809167i
$668$		−	4.27328e12i		−	0.830361i
$669$	−5.17120e12	+	2.98559e12i	−0.998099	+	0.576253i
$670$	2.20493e12	−	1.27302e12i	0.422725	−	0.244060i
$671$			3.61464e12i			0.688358i
$672$	−2.83274e12	−	4.90645e12i	−0.535852	−	0.928123i
$673$	2.75973e12	−	4.77998e12i	0.518559	−	0.898170i	−0.481209	−	0.876606i	$-0.659802\pi$
$673$	2.75973e12	−	4.77998e12i	0.518559	−	0.898170i	0.999767	−	0.0215642i	$-0.00686462\pi$
$674$	−1.62134e12	−	9.36080e11i	−0.302624	−	0.174720i
$675$	−1.64611e11			−0.0305206
$676$	7.12245e12	+	5.25149e12i	1.31181	+	0.967213i
$677$	−5.16749e12			−0.945432			−0.472716	−	0.881215i	$-0.656726\pi$
$677$	−5.16749e12			−0.945432			−0.472716	+	0.881215i	$0.656726\pi$
$678$	4.23369e12	+	2.44432e12i	0.769458	+	0.444247i
$679$	−3.87650e12	+	6.71429e12i	−0.699883	+	1.21223i
$680$	4.48890e12	+	7.77500e12i	0.805100	+	1.39447i
$681$			7.93734e11i			0.141421i
$682$	4.42724e12	−	2.55607e12i	0.783617	−	0.452421i
$683$	2.18507e12	−	1.26155e12i	0.384214	−	0.221826i	−0.295436	−	0.955362i	$-0.595465\pi$
$683$	2.18507e12	−	1.26155e12i	0.384214	−	0.221826i	0.679650	+	0.733537i	$0.262132\pi$
$684$		−	9.70605e11i		−	0.169547i
$685$	3.74615e12	+	6.48852e12i	0.650096	+	1.12600i
$686$	−3.35258e12	+	5.80683e12i	−0.577990	+	1.00111i
$687$	3.09107e12	+	1.78463e12i	0.529424	+	0.305663i
$688$	−2.18035e10			−0.00371004
$689$	2.45919e12	−	5.13710e11i	0.415725	−	0.0868423i
$690$	1.99317e12			0.334751
$691$	−9.85501e11	−	5.68979e11i	−0.164439	−	0.0949392i	0.415522	−	0.909583i	$-0.363599\pi$
$691$	−9.85501e11	−	5.68979e11i	−0.164439	−	0.0949392i	−0.579961	+	0.814644i	$0.696932\pi$
$692$	−5.48841e12	+	9.50620e12i	−0.909848	+	1.57590i
$693$	−4.46589e11	−	7.73515e11i	−0.0735544	−	0.127400i
$694$		−	1.47378e13i		−	2.41165i
$695$	1.14759e12	−	6.62563e11i	0.186576	−	0.107720i
$696$	−2.15951e12	+	1.24679e12i	−0.348830	+	0.201397i
$697$		−	1.84306e13i		−	2.95796i
$698$	−2.23923e11	−	3.87846e11i	−0.0357067	−	0.0618458i
$699$	−1.65799e12	+	2.87172e12i	−0.262685	+	0.454983i
$700$	−3.05842e11	−	1.76578e11i	−0.0481455	−	0.0277968i
$701$	−1.08353e13			−1.69476			−0.847382	−	0.530984i	$-0.821822\pi$
$701$	−1.08353e13			−1.69476			−0.847382	+	0.530984i	$0.821822\pi$
$702$	−1.04828e13	−	3.44676e12i	−1.62914	−	0.535665i
$703$	8.41391e12			1.29927
$704$	−8.03503e12	−	4.63903e12i	−1.23285	−	0.711787i
$705$	−5.37152e12	+	9.30374e12i	−0.818929	+	1.41843i
$706$	2.00087e12	+	3.46562e12i	0.303109	+	0.525000i
$707$		−	5.52337e12i		−	0.831413i
$708$	1.52144e13	−	8.78403e12i	2.27565	−	1.31385i
$709$	−3.34154e12	+	1.92924e12i	−0.496636	+	0.286733i	−0.727323	−	0.686295i	$-0.759236\pi$
$709$	−3.34154e12	+	1.92924e12i	−0.496636	+	0.286733i	0.230687	+	0.973028i	$0.425903\pi$
$710$		−	1.72666e12i		−	0.255002i
$711$	1.78444e10	+	3.09074e10i	0.00261872	+	0.00453575i
$712$	−3.46149e12	+	5.99548e12i	−0.504781	+	0.874307i
$713$	8.29713e11	+	4.79035e11i	0.120233	+	0.0694167i
$714$	−1.91729e13			−2.76087
$715$	−1.95392e12	+	5.94257e12i	−0.279596	+	0.850348i
$716$	8.62509e12			1.22646
$717$	−2.87333e12	−	1.65892e12i	−0.406022	−	0.234417i
$718$	−2.56844e12	+	4.44867e12i	−0.360670	+	0.624698i
$719$	1.54615e12	+	2.67802e12i	0.215761	+	0.373709i	0.953508	−	0.301369i	$-0.0974435\pi$
$719$	1.54615e12	+	2.67802e12i	0.215761	+	0.373709i	−0.737747	+	0.675078i	$0.764110\pi$
$720$		−	2.73463e10i		−	0.00379230i
$721$	−7.54493e11	+	4.35607e11i	−0.103979	+	0.0600324i
$722$	−4.67604e12	+	2.69971e12i	−0.640413	+	0.369743i
$723$		−	9.82298e12i		−	1.33697i
$724$	−1.13982e12	−	1.97422e12i	−0.154174	−	0.267038i
$725$	4.56782e10	−	7.91170e10i	0.00614028	−	0.0106353i
$726$	−2.15526e12	−	1.24434e12i	−0.287929	−	0.166236i
$727$	−5.87291e11			−0.0779737			−0.0389869	−	0.999240i	$-0.512413\pi$
$727$	−5.87291e11			−0.0779737			−0.0389869	+	0.999240i	$0.512413\pi$
$728$	−6.09772e12	−	6.82016e12i	−0.804593	−	0.899918i
$729$	8.37634e12			1.09845
$730$	−1.00325e13	−	5.79227e12i	−1.30754	−	0.754911i
$731$	8.39692e11	−	1.45439e12i	0.108766	−	0.188388i
$732$	−4.57616e12	−	7.92614e12i	−0.589116	−	1.02038i
$733$			2.05752e12i			0.263255i	0.991299	+	0.131627i	$0.0420202\pi$
$733$			2.05752e12i			0.263255i	−0.991299	+	0.131627i	$0.957980\pi$
$734$	1.63453e13	−	9.43696e12i	2.07855	−	1.20005i
$735$	2.55647e12	−	1.47598e12i	0.323108	−	0.186546i
$736$		−	1.71023e12i		−	0.214835i
$737$	1.04874e12	+	1.81648e12i	0.130938	+	0.226791i
$738$	−1.75393e12	+	3.03790e12i	−0.217650	+	0.376981i
$739$	−3.10287e11	−	1.79144e11i	−0.0382704	−	0.0220954i	0.480743	−	0.876862i	$-0.340367\pi$
$739$	−3.10287e11	−	1.79144e11i	−0.0382704	−	0.0220954i	−0.519013	+	0.854766i	$0.673700\pi$
$740$	2.37554e13			2.91219
$741$	−1.14714e12	−	5.49151e12i	−0.139777	−	0.669129i
$742$	−6.72110e12			−0.813997
$743$	7.43764e12	+	4.29412e12i	0.895335	+	0.516922i	0.875684	−	0.482885i	$-0.160411\pi$
$743$	7.43764e12	+	4.29412e12i	0.895335	+	0.516922i	0.0196510	+	0.999807i	$0.493744\pi$
$744$	−2.50102e12	+	4.33190e12i	−0.299254	+	0.518323i
$745$	4.64388e12	+	8.04343e12i	0.552303	+	0.956617i
$746$			1.06629e13i			1.26052i
$747$	3.19487e11	−	1.84456e11i	0.0375414	−	0.0216745i
$748$	−1.65751e13	+	9.56965e12i	−1.93597	+	1.11773i
$749$		−	3.16379e12i		−	0.367316i
$750$	6.41438e12	+	1.11100e13i	0.740251	+	1.28215i
$751$	−1.48236e12	+	2.56752e12i	−0.170049	+	0.294533i	−0.938437	−	0.345451i	$-0.887726\pi$
$751$	−1.48236e12	+	2.56752e12i	−0.170049	+	0.294533i	0.768388	+	0.639984i	$0.221059\pi$
$752$	−3.50750e11	−	2.02505e11i	−0.0399960	−	0.0230917i
$753$	4.76330e12			0.539921
$754$	4.56549e12	−	4.08188e12i	0.514418	−	0.459928i
$755$	2.83406e11			0.0317429
$756$	1.58448e13	+	9.14799e12i	1.76416	+	1.01854i
$757$	5.93497e12	−	1.02797e13i	0.656881	−	1.13775i	−0.324538	−	0.945873i	$-0.605209\pi$
$757$	5.93497e12	−	1.02797e13i	0.656881	−	1.13775i	0.981419	−	0.191879i	$-0.0614580\pi$
$758$	8.19657e11	+	1.41969e12i	0.0901822	+	0.156200i
$759$			1.64202e12i			0.179594i
$760$	6.08630e12	−	3.51393e12i	0.661747	−	0.382060i
$761$	−4.40836e12	+	2.54517e12i	−0.476481	+	0.275097i	−0.718949	−	0.695063i	$-0.755376\pi$
$761$	−4.40836e12	+	2.54517e12i	−0.476481	+	0.275097i	0.242468	+	0.970159i	$0.422043\pi$
$762$			2.27224e13i			2.44150i
$763$	−4.88393e12	−	8.45922e12i	−0.521686	−	0.903587i
$764$	4.24025e12	−	7.34434e12i	0.450269	−	0.779888i
$765$	1.82412e12	+	1.05315e12i	0.192564	+	0.111177i
$766$	−3.50341e12			−0.367673
$767$	−1.24299e13	+	1.11132e13i	−1.29684	+	1.15947i
$768$	9.31510e12			0.966189
$769$	3.78254e12	+	2.18385e12i	0.390045	+	0.225192i	0.682180	−	0.731185i	$-0.261032\pi$
$769$	3.78254e12	+	2.18385e12i	0.390045	+	0.225192i	−0.292135	+	0.956377i	$0.594366\pi$
$770$	8.36775e12	−	1.44934e13i	0.857829	−	1.48580i
$771$	1.82687e12	+	3.16423e12i	0.186193	+	0.322495i
$772$		−	1.21283e13i		−	1.22891i
$773$	−1.25195e13	+	7.22811e12i	−1.26118	+	0.728144i	−0.973303	−	0.229523i	$-0.926283\pi$
$773$	−1.25195e13	+	7.22811e12i	−1.26118	+	0.728144i	−0.287879	+	0.957667i	$0.592950\pi$
$774$	−2.76811e11	+	1.59817e11i	−0.0277235	+	0.0160062i
$775$		−	1.83258e11i		−	0.0182476i
$776$	−6.10955e12	−	1.05820e13i	−0.604827	−	1.04759i
$777$	−9.80232e12	+	1.69781e13i	−0.964794	+	1.67107i
$778$	−7.62757e12	−	4.40378e12i	−0.746411	−	0.430940i
$779$	−1.44276e13			−1.40370
$780$	−3.23878e12	−	1.55045e13i	−0.313297	−	1.49979i
$781$	1.42246e12			0.136808
$782$	−5.01230e12	−	2.89385e12i	−0.479299	−	0.276723i
$783$	−2.36645e12	+	4.09882e12i	−0.224994	+	0.389700i
$784$	5.56441e10	+	9.63784e10i	0.00526014	+	0.00911082i
$785$		−	9.44317e12i		−	0.887574i
$786$	−1.46966e13	+	8.48506e12i	−1.37345	+	0.792964i
$787$	1.28655e13	−	7.42792e12i	1.19548	−	0.690209i	0.235934	−	0.971769i	$-0.424185\pi$
$787$	1.28655e13	−	7.42792e12i	1.19548	−	0.690209i	0.959544	+	0.281560i	$0.0908518\pi$
$788$			2.05210e12i			0.189596i
$789$	−2.65191e12	−	4.59325e12i	−0.243620	−	0.421962i
$790$	−3.34351e11	+	5.79113e11i	−0.0305408	+	0.0528982i
$791$	6.66206e12	+	3.84634e12i	0.605082	+	0.349344i
$792$	1.40769e12			0.127129
$793$	5.78957e12	+	6.47550e12i	0.519897	+	0.581492i
$794$	1.17517e13			1.04932
$795$	−3.89428e12	−	2.24837e12i	−0.345761	−	0.199625i
$796$	−1.04351e13	+	1.80742e13i	−0.921274	+	1.59569i
$797$	1.53316e11	+	2.65551e11i	0.0134594	+	0.0233123i	0.872677	−	0.488299i	$-0.162382\pi$
$797$	1.53316e11	+	2.65551e11i	0.0134594	+	0.0233123i	−0.859217	+	0.511611i	$0.829049\pi$
$798$			1.50086e13i			1.31017i
$799$	2.70160e13	−	1.55977e13i	2.34509	−	1.35394i
$800$	−2.83303e11	+	1.63565e11i	−0.0244538	+	0.0141184i
$801$			1.62422e12i			0.139412i
$802$	−2.52646e11	−	4.37595e11i	−0.0215639	−	0.0373498i
$803$	4.77182e12	−	8.26503e12i	0.405008	−	0.701495i
$804$	−4.59934e12	−	2.65543e12i	−0.388189	−	0.224121i
$805$	3.13641e12			0.263240
$806$	3.83719e12	−	1.16702e13i	0.320262	−	0.974028i
$807$	−1.04725e13			−0.869199
$808$	7.53884e12	+	4.35255e12i	0.622234	+	0.359247i
$809$	4.56800e12	−	7.91200e12i	0.374936	−	0.649409i	−0.615381	−	0.788230i	$-0.710998\pi$
$809$	4.56800e12	−	7.91200e12i	0.374936	−	0.649409i	0.990317	+	0.138821i	$0.0443313\pi$
$810$	8.45454e12	+	1.46437e13i	0.690092	+	1.19527i
$811$		−	1.24574e13i		−	1.01119i	−0.862771	−	0.505594i	$-0.831273\pi$
$811$		−	1.24574e13i		−	1.01119i	0.862771	−	0.505594i	$-0.168727\pi$
$812$	−8.79357e12	+	5.07697e12i	−0.709844	+	0.409829i
$813$	1.85914e13	−	1.07337e13i	1.49247	−	0.861676i
$814$			3.15779e13i			2.52100i
$815$	−4.16837e12	−	7.21983e12i	−0.330946	−	0.573215i
$816$	2.41798e11	−	4.18807e11i	0.0190918	−	0.0330680i
$817$	−1.13850e12	−	6.57314e11i	−0.0893993	−	0.0516147i
$818$	−1.66195e13			−1.29786
$819$	−2.03899e12	−	6.70422e11i	−0.158357	−	0.0520680i
$820$	−4.07340e13			−3.14626
$821$	−1.22940e12	−	7.09795e11i	−0.0944386	−	0.0545241i	0.452037	−	0.891999i	$-0.350698\pi$
$821$	−1.22940e12	−	7.09795e11i	−0.0944386	−	0.0545241i	−0.546476	+	0.837475i	$0.684031\pi$
$822$	1.26087e13	−	2.18390e13i	0.963271	−	1.66843i
$823$	−3.45127e12	−	5.97778e12i	−0.262228	−	0.454193i	0.704605	−	0.709599i	$-0.251124\pi$
$823$	−3.45127e12	−	5.97778e12i	−0.262228	−	0.454193i	−0.966834	+	0.255406i	$0.917791\pi$
$824$		−	1.37308e12i		−	0.103758i
$825$	2.72004e11	−	1.57041e11i	0.0204424	−	0.0118024i
$826$	3.86305e13	−	2.23033e13i	2.88749	−	1.66709i
$827$			3.79690e12i			0.282263i	0.989991	+	0.141132i	$0.0450741\pi$
$827$			3.79690e12i			0.282263i	−0.989991	+	0.141132i	$0.954926\pi$
$828$	3.41344e11	+	5.91226e11i	0.0252381	+	0.0437136i
$829$	−4.09678e12	+	7.09583e12i	−0.301264	+	0.521805i	−0.976423	−	0.215868i	$-0.930742\pi$
$829$	−4.09678e12	+	7.09583e12i	−0.301264	+	0.521805i	0.675158	+	0.737673i	$0.264075\pi$
$830$	5.98624e12	+	3.45615e12i	0.437827	+	0.252779i
$831$	−1.23554e13			−0.898781
$832$	−2.18248e13	+	4.55906e12i	−1.57905	+	0.329853i
$833$	−8.57180e12			−0.616836
$834$	−3.86255e12	−	2.23005e12i	−0.276457	−	0.159612i
$835$	3.62963e12	−	6.28671e12i	0.258389	−	0.447543i
$836$	7.49115e12	+	1.29751e13i	0.530421	+	0.918715i
$837$			9.49405e12i			0.668632i
$838$	−2.75424e13	+	1.59016e13i	−1.92932	+	1.11389i
$839$	7.02600e11	−	4.05646e11i	0.0489530	−	0.0282630i	−0.475324	−	0.879811i	$-0.657669\pi$
$839$	7.02600e11	−	4.05646e11i	0.0489530	−	0.0282630i	0.524277	+	0.851548i	$0.324336\pi$
$840$			1.63751e13i			1.13482i
$841$	5.94023e12	+	1.02888e13i	0.409469	+	0.709222i
$842$	1.66422e13	−	2.88251e13i	1.14105	−	1.97636i
$843$	−2.09507e13	−	1.20959e13i	−1.42881	−	0.824924i
$844$	2.46691e13			1.67345
$845$	6.01782e12	+	1.37755e13i	0.406055	+	0.929505i
$846$	−5.93734e12			−0.398497
$847$	−3.39148e12	−	1.95807e12i	−0.226420	−	0.130723i
$848$	8.47630e10	−	1.46814e11i	0.00562892	−	0.00974958i
$849$	−6.74782e12	−	1.16876e13i	−0.445737	−	0.772039i
$850$			1.10706e12i			0.0727422i
$851$	−5.12517e12	+	2.95902e12i	−0.334985	+	0.193404i
$852$	−3.11916e12	+	1.80085e12i	−0.202796	+	0.117084i
$853$		−	1.79193e13i		−	1.15891i	−0.815004	−	0.579455i	$-0.803266\pi$
$853$		−	1.79193e13i		−	1.15891i	0.815004	−	0.579455i	$-0.196734\pi$
$854$	−1.16192e13	−	2.01251e13i	−0.747508	−	1.29472i
$855$	8.24413e11	−	1.42792e12i	0.0527591	−	0.0913814i
$856$	4.31826e12	+	2.49315e12i	0.274901	+	0.158714i
$857$	1.89206e13			1.19818			0.599090	−	0.800681i	$-0.295529\pi$
$857$	1.89206e13			1.19818			0.599090	+	0.800681i	$0.295529\pi$
$858$	2.06100e13	−	4.30530e12i	1.29833	−	0.271213i
$859$	−2.52359e13			−1.58143			−0.790716	−	0.612184i	$-0.790291\pi$
$859$	−2.52359e13			−1.58143			−0.790716	+	0.612184i	$0.790291\pi$
$860$	−3.21438e12	−	1.85583e12i	−0.200380	−	0.115690i
$861$	1.68083e13	−	2.91128e13i	1.04234	−	1.80539i
$862$	2.17535e12	+	3.76782e12i	0.134198	+	0.232438i
$863$			2.98253e13i			1.83036i	0.403048	+	0.915179i	$0.367951\pi$
$863$			2.98253e13i			1.83036i	−0.403048	+	0.915179i	$0.632049\pi$
$864$	1.46771e13	−	8.47383e12i	0.896042	−	0.517330i
$865$	−1.61488e13	+	9.32349e12i	−0.980768	+	0.566247i
$866$		−	9.75848e12i		−	0.589592i
$867$	1.09144e13	+	1.89042e13i	0.656013	+	1.13625i
$868$	−1.01842e13	+	1.76396e13i	−0.608961	+	1.05475i
$869$	−4.77088e11	−	2.75447e11i	−0.0283798	−	0.0163851i
$870$	−1.09617e13			−0.648695
$871$	4.78824e12	+	1.57438e12i	0.281899	+	0.0926889i
$872$	1.53946e13			0.901665
$873$	−2.48268e12	−	1.43338e12i	−0.144663	−	0.0835212i
$874$	−2.26532e12	+	3.92364e12i	−0.131319	+	0.227451i
$875$	1.00936e13	+	1.74826e13i	0.582115	+	1.00825i
$876$			2.41646e13i			1.38647i
$877$	5.08369e12	−	2.93507e12i	0.290189	−	0.167541i	−0.347838	−	0.937555i	$-0.613084\pi$
$877$	5.08369e12	−	2.93507e12i	0.290189	−	0.167541i	0.638027	+	0.770014i	$0.279751\pi$
$878$	−2.46690e12	+	1.42427e12i	−0.140096	+	0.0808846i
$879$			1.40385e13i			0.793179i
$880$	2.11059e11	+	3.65566e11i	0.0118640	+	0.0205491i
$881$	1.03965e13	−	1.80072e13i	0.581426	−	1.00706i	−0.413885	−	0.910329i	$-0.635828\pi$
$881$	1.03965e13	−	1.80072e13i	0.581426	−	1.00706i	0.995311	−	0.0967298i	$-0.0308383\pi$
$882$	1.41288e12	+	8.15727e11i	0.0786134	+	0.0453875i
$883$	−2.40223e13			−1.32981			−0.664907	−	0.746926i	$-0.731529\pi$
$883$	−2.40223e13			−1.32981			−0.664907	+	0.746926i	$0.731529\pi$
$884$	−1.43660e13	+	4.36920e13i	−0.791227	+	2.40640i
$885$	2.98439e13			1.63535
$886$	3.90631e13	+	2.25531e13i	2.12968	+	1.22957i
$887$	1.16870e12	−	2.02425e12i	0.0633938	−	0.109801i	−0.832587	−	0.553895i	$-0.813141\pi$
$887$	1.16870e12	−	2.02425e12i	0.0633938	−	0.109801i	0.895980	+	0.444094i	$0.146474\pi$
$888$	−1.54489e13	−	2.67583e13i	−0.833758	−	1.44411i
$889$			3.57557e13i			1.91994i
$890$	−2.63558e13	+	1.52165e13i	−1.40806	+	0.812944i
$891$	−1.20638e13	+	6.96507e12i	−0.641263	+	0.370233i
$892$		−	3.83213e13i		−	2.02674i
$893$	−1.22099e13	−	2.11482e13i	−0.642511	−	1.11286i
$894$	1.56303e13	−	2.70725e13i	0.818368	−	1.41746i
$895$	1.26890e13	+	7.32598e12i	0.661032	+	0.381647i
$896$	3.73395e13			1.93545
$897$	2.63003e12	+	2.94162e12i	0.135642	+	0.151712i
$898$	2.83982e13			1.45730
$899$	−4.56311e12	−	2.63451e12i	−0.232993	−	0.134518i
$900$	6.52917e10	−	1.13089e11i	0.00331716	−	0.00574549i
$901$	6.52874e12	+	1.13081e13i	0.330041	+	0.571648i
$902$		−	5.41475e13i		−	2.72364i
$903$	2.65274e12	−	1.53156e12i	0.132770	−	0.0766547i
$904$	−1.04997e13	+	6.06202e12i	−0.522902	+	0.301897i
$905$		−	3.87256e12i		−	0.191902i
$906$	−4.76941e11	−	8.26087e11i	−0.0235173	−	0.0407332i
$907$	−9.22298e12	+	1.59747e13i	−0.452520	+	0.783788i	−0.998542	−	0.0539828i	$-0.982808\pi$
$907$	−9.22298e12	+	1.59747e13i	−0.452520	+	0.783788i	0.546021	+	0.837771i	$0.316142\pi$
$908$	−4.41149e12	−	2.54698e12i	−0.215377	−	0.124348i
$909$	2.04233e12			0.0992175
$910$	−8.22351e12	−	3.93670e13i	−0.397531	−	1.90303i
$911$	1.63941e13			0.788595			0.394298	−	0.918983i	$-0.370988\pi$
$911$	1.63941e13			0.788595			0.394298	+	0.918983i	$0.370988\pi$
$912$	−3.27843e11	−	1.89280e11i	−0.0156924	−	0.00906002i
$913$	−2.84727e12	+	4.93162e12i	−0.135616	+	0.234893i
$914$	−6.88426e12	−	1.19239e13i	−0.326287	−	0.565145i
$915$		−	1.55476e13i		−	0.733277i
$916$	−1.98376e13	+	1.14532e13i	−0.931020	+	0.537525i
$917$	−2.31263e13	+	1.33519e13i	−1.08005	+	0.623566i
$918$		−	5.73536e13i		−	2.66544i
$919$	5.58667e12	+	9.67639e12i	0.258365	+	0.447501i	0.965804	−	0.259273i	$-0.0834831\pi$
$919$	5.58667e12	+	9.67639e12i	0.258365	+	0.447501i	−0.707439	+	0.706774i	$0.750150\pi$
$920$	−2.47157e12	+	4.28088e12i	−0.113744	+	0.197010i
$921$	−1.33255e13	−	7.69350e12i	−0.610262	−	0.352335i
$922$	3.64897e13			1.66296
$923$	2.54829e12	−	2.27836e12i	0.115569	−	0.103327i
$924$	−3.49092e13			−1.57549
$925$	9.80333e11	+	5.65996e11i	0.0440287	+	0.0254200i
$926$	−3.23651e13	+	5.60580e13i	−1.44653	+	2.50547i
$927$	−1.61071e11	−	2.78982e11i	−0.00716403	−	0.0124085i
$928$			9.40565e12i			0.416316i
$929$	−2.01335e12	+	1.16241e12i	−0.0886849	+	0.0512022i	−0.543687	−	0.839288i	$-0.682972\pi$
$929$	−2.01335e12	+	1.16241e12i	−0.0886849	+	0.0512022i	0.455002	+	0.890491i	$0.349639\pi$
$930$	−1.90428e13	+	1.09944e13i	−0.834752	+	0.481945i
$931$			6.71004e12i			0.292719i
$932$	−1.06405e13	−	1.84299e13i	−0.461945	−	0.800112i
$933$	−7.75085e12	+	1.34249e13i	−0.334874	+	0.580019i
$934$	−2.34015e12	−	1.35109e12i	−0.100620	−	0.0580928i
$935$	−3.25131e13			−1.39125
$936$	2.52183e12	−	2.25470e12i	0.107393	−	0.0960169i
$937$	−3.73094e12			−0.158121			−0.0790606	−	0.996870i	$-0.525192\pi$
$937$	−3.73094e12			−0.158121			−0.0790606	+	0.996870i	$0.525192\pi$
$938$	−1.16781e13	−	6.74234e12i	−0.492559	−	0.284379i
$939$	−2.03458e13	+	3.52399e13i	−0.854042	+	1.47924i
$940$	−3.44728e13	−	5.97087e13i	−1.44013	−	2.49438i
$941$		−	1.79721e12i		−	0.0747213i	−0.999302	−	0.0373607i	$-0.988105\pi$
$941$		−	1.79721e12i		−	0.0747213i	0.999302	−	0.0373607i	$-0.0118950\pi$
$942$	−2.75255e13	+	1.58919e13i	−1.13895	+	0.657575i
$943$	8.78827e12	−	5.07391e12i	0.361910	−	0.208949i
$944$			1.12511e12i			0.0461128i
$945$	1.55402e13	+	2.69165e13i	0.633891	+	1.09793i
$946$	2.46694e12	−	4.27286e12i	0.100149	−	0.173464i
$947$	2.60766e13	+	1.50554e13i	1.05360	+	0.608298i	0.923656	−	0.383223i	$-0.125186\pi$
$947$	2.60766e13	+	1.50554e13i	1.05360	+	0.608298i	0.129947	+	0.991521i	$0.458519\pi$
$948$	1.39487e12			0.0560914
$949$	−4.68956e12	−	2.24495e13i	−0.187687	−	0.898481i
$950$	8.66611e11			0.0345198
$951$	−3.33750e12	−	1.92691e12i	−0.132315	−	0.0763921i
$952$	2.37748e13	−	4.11791e13i	0.938102	−	1.62484i
$953$	−1.14877e13	−	1.98972e13i	−0.451143	−	0.781402i	0.547315	−	0.836927i	$-0.315650\pi$
$953$	−1.14877e13	−	1.98972e13i	−0.451143	−	0.781402i	−0.998457	+	0.0555248i	$0.982317\pi$
$954$		−	2.48520e12i		−	0.0971392i
$955$	1.24763e13	−	7.20317e12i	0.485366	−	0.280226i
$956$	1.84402e13	−	1.06464e13i	0.714011	−	0.412234i
$957$		−	9.03051e12i		−	0.348024i
$958$	3.16440e13	+	5.48090e13i	1.21380	+	2.10236i
$959$	1.98409e13	−	3.43654e13i	0.757491	−	1.31201i
$960$	3.45609e13	+	1.99537e13i	1.31330	+	0.758235i
$961$	1.58701e13			0.600240
$962$	5.05783e13	+	5.65707e13i	1.90404	+	2.12963i
$963$	1.16985e12			0.0438340
$964$	5.45951e13	+	3.15205e13i	2.03614	+	1.17556i
$965$	1.03015e13	−	1.78427e13i	0.382409	−	0.662352i
$966$	−5.27825e12	−	9.14220e12i	−0.195026	−	0.337795i
$967$			9.41605e11i			0.0346298i	0.999850	+	0.0173149i	$0.00551177\pi$
$967$			9.41605e11i			0.0346298i	−0.999850	+	0.0173149i	$0.994488\pi$
$968$	5.34514e12	−	3.08602e12i	0.195668	−	0.112969i
$969$	2.52516e13	−	1.45790e13i	0.920095	−	0.531217i
$970$		−	5.37145e13i		−	1.94813i
$971$	9.31486e12	+	1.61338e13i	0.336271	+	0.582439i	0.983728	−	0.179663i	$-0.0575008\pi$
$971$	9.31486e12	+	1.61338e13i	0.336271	+	0.582439i	−0.647457	+	0.762102i	$0.724167\pi$
$972$	−6.34703e12	+	1.09934e13i	−0.228072	+	0.395033i
$973$	−6.07805e12	−	3.50916e12i	−0.217399	−	0.125515i
$974$	−7.02557e13			−2.50130
$975$	2.35751e11	−	7.17002e11i	0.00835475	−	0.0254097i
$976$	5.86141e11			0.0206766
$977$	−1.19025e13	−	6.87188e12i	−0.417937	−	0.241296i	0.276257	−	0.961084i	$-0.410906\pi$
$977$	−1.19025e13	−	6.87188e12i	−0.417937	−	0.241296i	−0.694194	+	0.719788i	$0.744239\pi$
$978$	−1.40299e13	+	2.43004e13i	−0.490375	+	0.849354i
$979$	−1.25358e13	−	2.17126e13i	−0.436143	−	0.755422i
$980$			1.89448e13i			0.656103i
$981$	3.12789e12	−	1.80589e12i	0.107830	−	0.0622559i
$982$	−5.70846e13	+	3.29578e13i	−1.95892	+	1.13098i
$983$			2.97895e13i			1.01759i	0.860888	+	0.508794i	$0.169909\pi$
$983$			2.97895e13i			1.01759i	−0.860888	+	0.508794i	$0.830091\pi$
$984$	2.64907e13	+	4.58833e13i	0.900774	+	1.56019i
$985$	−1.74301e12	+	3.01898e12i	−0.0589979	+	0.102187i
$986$	2.75658e13	+	1.59151e13i	0.928804	+	0.536245i
$987$	5.68989e13			1.90843
$988$	3.42023e13	+	1.12458e13i	1.14195	+	0.375476i
$989$	9.24661e11			0.0307326
$990$	5.35909e12	+	3.09407e12i	0.177310	+	0.102370i
$991$	1.47981e13	−	2.56310e13i	0.487387	−	0.844179i	−0.512508	−	0.858683i	$-0.671283\pi$
$991$	1.47981e13	−	2.56310e13i	0.487387	−	0.844179i	0.999895	+	0.0145036i	$0.00461679\pi$
$992$	9.43370e12	+	1.63397e13i	0.309300	+	0.535723i
$993$		−	4.56594e13i		−	1.49025i
$994$	−7.91978e12	+	4.57249e12i	−0.257320	+	0.148564i
$995$	−3.07037e13	+	1.77268e13i	−0.993085	+	0.573358i
$996$		−	1.44186e13i		−	0.464256i
$997$	−6.47622e12	−	1.12171e13i	−0.207584	−	0.359546i	0.743369	−	0.668881i	$-0.233227\pi$
$997$	−6.47622e12	−	1.12171e13i	−0.207584	−	0.359546i	−0.950953	+	0.309336i	$0.899893\pi$
$998$	−2.37878e13	+	4.12016e13i	−0.759043	+	1.31470i
$999$	−5.07882e13	−	2.93226e13i	−1.61331	−	0.931446i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	13.10.e.a.4.9	✓	20
13.6	odd	12		169.10.a.f.1.3		20
13.7	odd	12		169.10.a.f.1.18		20
13.10	even	6	inner	13.10.e.a.10.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.10.e.a.4.9	✓	20	1.1	even	1	trivial
13.10.e.a.10.9	yes	20	13.10	even	6	inner
169.10.a.f.1.3		20	13.6	odd	12
169.10.a.f.1.18		20	13.7	odd	12

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	13.10.e.a.4.9

Level	$13$
Weight	$10$
Character	13.4
Analytic conductor	$6.695$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$