LMFDB - Embedded newform 21.30.c.a.20.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,30,Mod(20,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 30, names="a")

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

chi := DirichletCharacter("21.20");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	21.c (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:	$111.883889004$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			20.20
Character	$\chi$	$=$	21.20
Dual form			21.30.c.a.20.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1646.15i q^{2} +(2.25912e6 + 7.97037e6i) q^{3} +5.34161e8 q^{4} +1.37077e10 q^{5} +(-1.31204e10 + 3.71885e9i) q^{6} +(-1.61859e12 - 7.74652e11i) q^{7} +1.76308e12i q^{8} +(-5.84231e13 + 3.60121e13i) q^{9} +O(q^{10})$	\(q+1646.15i q^{2} +(2.25912e6 + 7.97037e6i) q^{3} +5.34161e8 q^{4} +1.37077e10 q^{5} +(-1.31204e10 + 3.71885e9i) q^{6} +(-1.61859e12 - 7.74652e11i) q^{7} +1.76308e12i q^{8} +(-5.84231e13 + 3.60121e13i) q^{9} +2.25649e13i q^{10} -1.65225e15i q^{11} +(1.20674e15 + 4.25746e15i) q^{12} +7.11308e15i q^{13} +(1.27519e15 - 2.66443e15i) q^{14} +(3.09673e16 + 1.09255e17i) q^{15} +2.83873e17 q^{16} -1.14786e18 q^{17} +(-5.92812e16 - 9.61731e16i) q^{18} +4.19951e18i q^{19} +7.32210e18 q^{20} +(2.51768e18 - 1.46508e19i) q^{21} +2.71985e18 q^{22} -6.01642e19i q^{23} +(-1.40524e19 + 3.98301e18i) q^{24} +1.63560e18 q^{25} -1.17092e19 q^{26} +(-4.19014e20 - 3.84298e20i) q^{27} +(-8.64586e20 - 4.13789e20i) q^{28} -2.75913e21i q^{29} +(-1.79850e20 + 5.09768e19i) q^{30} -2.77443e21i q^{31} +1.41384e21i q^{32} +(1.31691e22 - 3.73264e21i) q^{33} -1.88956e21i q^{34} +(-2.21870e22 - 1.06187e22i) q^{35} +(-3.12074e22 + 1.92362e22i) q^{36} -2.45582e22 q^{37} -6.91302e21 q^{38} +(-5.66939e22 + 1.60693e22i) q^{39} +2.41677e22i q^{40} +2.01845e23 q^{41} +(2.41173e22 + 4.14448e21i) q^{42} -7.28553e23 q^{43} -8.82569e23i q^{44} +(-8.00845e23 + 4.93641e23i) q^{45} +9.90392e22 q^{46} -2.16367e24 q^{47} +(6.41304e23 + 2.26257e24i) q^{48} +(2.01973e24 + 2.50768e24i) q^{49} +2.69244e21i q^{50} +(-2.59317e24 - 9.14890e24i) q^{51} +3.79953e24i q^{52} +1.10372e25i q^{53} +(6.32612e23 - 6.89760e23i) q^{54} -2.26485e25i q^{55} +(1.36577e24 - 2.85369e24i) q^{56} +(-3.34716e25 + 9.48721e24i) q^{57} +4.54195e24 q^{58} +2.77774e25 q^{59} +(1.65415e25 + 5.83598e25i) q^{60} -9.03685e25i q^{61} +4.56713e24 q^{62} +(1.22460e26 - 1.30310e25i) q^{63} +1.50076e26 q^{64} +9.75038e25i q^{65} +(6.14448e24 + 2.16782e25i) q^{66} -2.34833e25 q^{67} -6.13144e26 q^{68} +(4.79530e26 - 1.35918e26i) q^{69} +(1.74799e25 - 3.65232e25i) q^{70} -4.44198e26i q^{71} +(-6.34921e25 - 1.03004e26i) q^{72} +7.29866e25i q^{73} -4.04265e25i q^{74} +(3.69503e24 + 1.30364e25i) q^{75} +2.24322e27i q^{76} +(-1.27992e27 + 2.67431e27i) q^{77} +(-2.64525e25 - 9.33266e25i) q^{78} -4.11080e27 q^{79} +3.89124e27 q^{80} +(2.11639e27 - 4.20787e27i) q^{81} +3.32267e26i q^{82} -7.11680e27 q^{83} +(1.34485e27 - 7.82586e27i) q^{84} -1.57345e28 q^{85} -1.19931e27i q^{86} +(2.19913e28 - 6.23322e27i) q^{87} +2.91305e27 q^{88} -1.23620e28 q^{89} +(-8.12607e26 - 1.31831e27i) q^{90} +(5.51017e27 - 1.15131e28i) q^{91} -3.21374e28i q^{92} +(2.21132e28 - 6.26778e27i) q^{93} -3.56173e27i q^{94} +5.75655e28i q^{95} +(-1.12688e28 + 3.19404e27i) q^{96} +2.43776e28i q^{97} +(-4.12802e27 + 3.32478e27i) q^{98} +(5.95010e28 + 9.65297e28i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9}+O(q^{10}) $ 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9	$ 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9} - 11\!\cdots\!48 q^{15}+ \cdots - 23\!\cdots\!24 q^{99}+O(q^{100}) $ 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9 - 116668222909200048 * q^15 + 4964525139713333892 * q^16 + 1542346202347854996 * q^18 + 33840646982361357348 * q^21 - 9870996616978150672 * q^22 + 3225406746743103424612 * q^25 - 3181907581338093199564 * q^28 + 5113912044496410095244 * q^30 - 85758641407134848258352 * q^36 - 17812771227715200149976 * q^37 + 388095283792424641491696 * q^39 + 804036587819434104664956 * q^42 + 2391536152977907871782320 * q^43 - 1070985628070611677307000 * q^46 - 512656982878691867441540 * q^49 - 961431915936904000664400 * q^51 + 20345422731681279280765248 * q^57 - 40096240109469024574169272 * q^58 - 164991837955115951799442596 * q^60 - 360764839802574990409097184 * q^63 - 1608343949909674725081473028 * q^64 + 483978610969894046870693264 * q^67 - 656026306765550013508448520 * q^70 + 1937172856654554597960695124 * q^72 - 8054141680325499868559088636 * q^78 - 11740735193468750125742145952 * q^79 + 18477545939654446572971367132 * q^81 - 7249045143271847568431965452 * q^84 + 14576359553686844022629140848 * q^85 - 1685535263940707754634995584 * q^88 + 44135166284535829618726469040 * q^91 + 226499776928895503792863540632 * q^93 - 231093384978708762520959066624 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$-1$

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 $

$2$			1646.15i			0.0710451i	0.999369	+	0.0355225i	$0.0113096\pi$
$2$			1646.15i			0.0710451i	−0.999369	+	0.0355225i	$0.988690\pi$
$3$	2.25912e6	+	7.97037e6i	0.272698	+	0.962100i
$3$	2.25912e6	+	7.97037e6i	0.272698	+	0.962100i
$4$	5.34161e8			0.994953
$5$	1.37077e10			1.00438			0.502190	−	0.864757i	$-0.332528\pi$
$5$	1.37077e10			1.00438			0.502190	+	0.864757i	$0.332528\pi$
$6$	−1.31204e10	+	3.71885e9i	−0.0683525	+	0.0193738i
$7$	−1.61859e12	−	7.74652e11i	−0.902016	−	0.431703i
$7$	−1.61859e12	−	7.74652e11i	−0.902016	−	0.431703i
$8$			1.76308e12i			0.141732i
$9$	−5.84231e13	+	3.60121e13i	−0.851272	+	0.524725i
$10$			2.25649e13i			0.0713563i
$11$		−	1.65225e15i		−	1.31184i	−0.754829	−	0.655922i	$-0.772280\pi$
$11$		−	1.65225e15i		−	1.31184i	0.754829	−	0.655922i	$-0.227720\pi$
$12$	1.20674e15	+	4.25746e15i	0.271321	+	0.957244i
$13$			7.11308e15i			0.501048i	0.968110	+	0.250524i	$0.0806029\pi$
$13$			7.11308e15i			0.501048i	−0.968110	+	0.250524i	$0.919397\pi$
$14$	1.27519e15	−	2.66443e15i	0.0306704	−	0.0640838i
$15$	3.09673e16	+	1.09255e17i	0.273892	+	0.966315i
$16$	2.83873e17			0.984883
$17$	−1.14786e18			−1.65341			−0.826706	−	0.562634i	$-0.809788\pi$
$17$	−1.14786e18			−1.65341			−0.826706	+	0.562634i	$0.809788\pi$
$18$	−5.92812e16	−	9.61731e16i	−0.0372791	−	0.0604787i
$19$			4.19951e18i			1.20579i	0.797821	+	0.602895i	$0.205986\pi$
$19$			4.19951e18i			1.20579i	−0.797821	+	0.602895i	$0.794014\pi$
$20$	7.32210e18			0.999311
$21$	2.51768e18	−	1.46508e19i	0.169364	−	0.985554i
$22$	2.71985e18			0.0932001
$23$		−	6.01642e19i		−	1.08214i	−0.840977	−	0.541071i	$-0.818019\pi$
$23$		−	6.01642e19i		−	1.08214i	0.840977	−	0.541071i	$-0.181981\pi$
$24$	−1.40524e19	+	3.98301e18i	−0.136360	+	0.0386499i
$25$	1.63560e18			0.00878107
$26$	−1.17092e19			−0.0355970
$27$	−4.19014e20	−	3.84298e20i	−0.736977	−	0.675917i
$28$	−8.64586e20	−	4.13789e20i	−0.897463	−	0.429524i
$29$		−	2.75913e21i		−	1.72188i	−0.508710	−	0.860938i	$-0.669877\pi$
$29$		−	2.75913e21i		−	1.72188i	0.508710	−	0.860938i	$-0.330123\pi$
$30$	−1.79850e20	+	5.09768e19i	−0.0686519	+	0.0194587i
$31$		−	2.77443e21i		−	0.658309i	−0.944276	−	0.329154i	$-0.893236\pi$
$31$		−	2.77443e21i		−	0.658309i	0.944276	−	0.329154i	$-0.106764\pi$
$32$			1.41384e21i			0.211703i
$33$	1.31691e22	−	3.73264e21i	1.26212	−	0.357737i
$34$		−	1.88956e21i		−	0.117467i
$35$	−2.21870e22	−	1.06187e22i	−0.905967	−	0.433594i
$36$	−3.12074e22	+	1.92362e22i	−0.846975	+	0.522076i
$37$	−2.45582e22			−0.447994			−0.223997	−	0.974590i	$-0.571911\pi$
$37$	−2.45582e22			−0.447994			−0.223997	+	0.974590i	$0.571911\pi$
$38$	−6.91302e21			−0.0856654
$39$	−5.66939e22	+	1.60693e22i	−0.482058	+	0.136635i
$40$			2.41677e22i			0.142353i
$41$	2.01845e23			0.831099			0.415549	−	0.909571i	$-0.363589\pi$
$41$	2.01845e23			0.831099			0.415549	+	0.909571i	$0.363589\pi$
$42$	2.41173e22	+	4.14448e21i	0.0700187	+	0.0120325i
$43$	−7.28553e23			−1.50373			−0.751863	−	0.659320i	$-0.770844\pi$
$43$	−7.28553e23			−1.50373			−0.751863	+	0.659320i	$0.770844\pi$
$44$		−	8.82569e23i		−	1.30522i
$45$	−8.00845e23	+	4.93641e23i	−0.855001	+	0.527024i
$46$	9.90392e22			0.0768809
$47$	−2.16367e24			−1.22962			−0.614812	−	0.788674i	$-0.710768\pi$
$47$	−2.16367e24			−1.22962			−0.614812	+	0.788674i	$0.710768\pi$
$48$	6.41304e23	+	2.26257e24i	0.268575	+	0.947556i
$49$	2.01973e24	+	2.50768e24i	0.627265	+	0.778806i
$50$			2.69244e21i			0.000623852i
$51$	−2.59317e24	−	9.14890e24i	−0.450882	−	1.59075i
$52$			3.79953e24i			0.498519i
$53$			1.10372e25i			1.09865i	0.835609	+	0.549325i	$0.185115\pi$
$53$			1.10372e25i			1.09865i	−0.835609	+	0.549325i	$0.814885\pi$
$54$	6.32612e23	−	6.89760e23i	0.0480206	−	0.0523586i
$55$		−	2.26485e25i		−	1.31759i
$56$	1.36577e24	−	2.85369e24i	0.0611860	−	0.127844i
$57$	−3.34716e25	+	9.48721e24i	−1.16009	+	0.328816i
$58$	4.54195e24			0.122331
$59$	2.77774e25			0.583898			0.291949	−	0.956434i	$-0.405696\pi$
$59$	2.77774e25			0.583898			0.291949	+	0.956434i	$0.405696\pi$
$60$	1.65415e25	+	5.83598e25i	0.272510	+	0.961437i
$61$		−	9.03685e25i		−	1.17148i	−0.810500	−	0.585739i	$-0.800804\pi$
$61$		−	9.03685e25i		−	1.17148i	0.810500	−	0.585739i	$-0.199196\pi$
$62$	4.56713e24			0.0467696
$63$	1.22460e26	−	1.30310e25i	0.994386	−	0.105813i
$64$	1.50076e26			0.969843
$65$			9.75038e25i			0.503243i
$66$	6.14448e24	+	2.16782e25i	0.0254154	+	0.0896678i
$67$	−2.34833e25			−0.0781043			−0.0390521	−	0.999237i	$-0.512434\pi$
$67$	−2.34833e25			−0.0781043			−0.0390521	+	0.999237i	$0.512434\pi$
$68$	−6.13144e26			−1.64507
$69$	4.79530e26	−	1.35918e26i	1.04113	−	0.295098i
$70$	1.74799e25	−	3.65232e25i	0.0308048	−	0.0643645i
$71$		−	4.44198e26i		−	0.637280i	−0.947876	−	0.318640i	$-0.896774\pi$
$71$		−	4.44198e26i		−	0.637280i	0.947876	−	0.318640i	$-0.103226\pi$
$72$	−6.34921e25	−	1.03004e26i	−0.0743701	−	0.120652i
$73$			7.29866e25i			0.0699942i	0.999387	+	0.0349971i	$0.0111422\pi$
$73$			7.29866e25i			0.0699942i	−0.999387	+	0.0349971i	$0.988858\pi$
$74$		−	4.04265e25i		−	0.0318278i
$75$	3.69503e24	+	1.30364e25i	0.00239458	+	0.00844827i
$76$			2.24322e27i			1.19970i
$77$	−1.27992e27	+	2.67431e27i	−0.566327	+	1.18330i
$78$	−2.64525e25	−	9.33266e25i	−0.00970722	−	0.0342479i
$79$	−4.11080e27			−1.25410			−0.627052	−	0.778978i	$-0.715739\pi$
$79$	−4.11080e27			−1.25410			−0.627052	+	0.778978i	$0.715739\pi$
$80$	3.89124e27			0.989198
$81$	2.11639e27	−	4.20787e27i	0.449328	−	0.893367i
$82$			3.32267e26i			0.0590455i
$83$	−7.11680e27			−1.06085			−0.530423	−	0.847733i	$-0.677967\pi$
$83$	−7.11680e27			−1.06085			−0.530423	+	0.847733i	$0.677967\pi$
$84$	1.34485e27	−	7.82586e27i	0.168509	−	0.980579i
$85$	−1.57345e28			−1.66066
$86$		−	1.19931e27i		−	0.106832i
$87$	2.19913e28	−	6.23322e27i	1.65662	−	0.469552i
$88$	2.91305e27			0.185930
$89$	−1.23620e28			−0.669784			−0.334892	−	0.942256i	$-0.608700\pi$
$89$	−1.23620e28			−0.669784			−0.334892	+	0.942256i	$0.608700\pi$
$90$	−8.12607e26	−	1.31831e27i	−0.0374424	−	0.0607436i
$91$	5.51017e27	−	1.15131e28i	0.216304	−	0.451953i
$92$		−	3.21374e28i		−	1.07668i
$93$	2.21132e28	−	6.26778e27i	0.633359	−	0.179519i
$94$		−	3.56173e27i		−	0.0873588i
$95$			5.75655e28i			1.21107i
$96$	−1.12688e28	+	3.19404e27i	−0.203679	+	0.0577308i
$97$			2.43776e28i			0.379142i	0.981867	+	0.189571i	$0.0607097\pi$
$97$			2.43776e28i			0.379142i	−0.981867	+	0.189571i	$0.939290\pi$
$98$	−4.12802e27	+	3.32478e27i	−0.0553304	+	0.0445641i
$99$	5.95010e28	+	9.65297e28i	0.688357	+	1.11674i
$100$	8.73675e26			0.00873675
$101$	1.37010e29			1.18602			0.593010	−	0.805195i	$-0.297940\pi$
$101$	1.37010e29			1.18602			0.593010	+	0.805195i	$0.297940\pi$
$102$	1.50604e28	−	4.26874e27i	0.113015	−	0.0320329i
$103$		−	1.06328e29i		−	0.692643i	−0.938116	−	0.346321i	$-0.887431\pi$
$103$		−	1.06328e29i		−	0.692643i	0.938116	−	0.346321i	$-0.112569\pi$
$104$	−1.25409e28			−0.0710143
$105$	3.45115e28	−	2.00828e29i	0.170106	−	0.989871i
$106$	−1.81689e28			−0.0780537
$107$			3.85749e28i			0.144624i	0.997382	+	0.0723119i	$0.0230377\pi$
$107$			3.85749e28i			0.144624i	−0.997382	+	0.0723119i	$0.976962\pi$
$108$	−2.23821e29	−	2.05277e29i	−0.733258	−	0.672506i
$109$	−5.36212e29			−1.53692			−0.768461	−	0.639896i	$-0.778977\pi$
$109$	−5.36212e29			−1.53692			−0.768461	+	0.639896i	$0.778977\pi$
$110$	3.72828e28			0.0936084
$111$	−5.54800e28	−	1.95738e29i	−0.122167	−	0.431015i
$112$	−4.59473e29	−	2.19903e29i	−0.888380	−	0.425177i
$113$		−	2.88250e29i		−	0.489927i	−0.969532	−	0.244964i	$-0.921224\pi$
$113$		−	2.88250e29i		−	0.489927i	0.969532	−	0.244964i	$-0.0787761\pi$
$114$	−1.56174e28	−	5.50993e28i	−0.0233608	−	0.0824187i
$115$		−	8.24710e29i		−	1.08688i
$116$		−	1.47382e30i		−	1.71319i
$117$	−2.56157e29	−	4.15568e29i	−0.262912	−	0.426528i
$118$			4.57257e28i			0.0414831i
$119$	1.85792e30	+	8.89196e29i	1.49140	+	0.713783i
$120$	−1.92625e29	+	5.45977e28i	−0.136957	+	0.0388192i
$121$	−1.14363e30			−0.720935
$122$	1.48760e29			0.0832278
$123$	4.55993e29	+	1.60878e30i	0.226639	+	0.799600i
$124$		−	1.48199e30i		−	0.654986i
$125$	−2.53083e30			−0.995561
$126$	2.14510e28	+	2.01587e29i	0.00751751	+	0.0706462i
$127$	−1.21450e30			−0.379528			−0.189764	−	0.981830i	$-0.560772\pi$
$127$	−1.21450e30			−0.379528			−0.189764	+	0.981830i	$0.560772\pi$
$128$			1.00610e30i			0.280605i
$129$	−1.64589e30	−	5.80684e30i	−0.410063	−	1.44673i
$130$	−1.60506e29			−0.0357529
$131$	6.54668e30			1.30493			0.652465	−	0.757819i	$-0.273735\pi$
$131$	6.54668e30			1.30493			0.652465	+	0.757819i	$0.273735\pi$
$132$	7.03439e30	−	1.99383e30i	1.25575	−	0.355931i
$133$	3.25316e30	−	6.79727e30i	0.520543	−	1.08764i
$134$		−	3.86570e28i		−	0.00554892i
$135$	−5.74371e30	−	5.26783e30i	−0.740206	−	0.678878i
$136$		−	2.02377e30i		−	0.234341i
$137$			5.00608e30i			0.521254i	0.965440	+	0.260627i	$0.0839293\pi$
$137$			5.00608e30i			0.521254i	−0.965440	+	0.260627i	$0.916071\pi$
$138$	2.23742e29	+	7.89378e29i	0.0209652	+	0.0739671i
$139$		−	2.24857e31i		−	1.89755i	−0.315958	−	0.948773i	$-0.602326\pi$
$139$		−	2.24857e31i		−	1.89755i	0.315958	−	0.948773i	$-0.397674\pi$
$140$	−1.18514e31	−	5.67208e30i	−0.901395	−	0.431406i
$141$	−4.88800e30	−	1.72453e31i	−0.335316	−	1.18302i
$142$	7.31216e29			0.0452756
$143$	1.17526e31			0.657297
$144$	−1.65848e31	+	1.02229e31i	−0.838403	+	0.516793i
$145$		−	3.78213e31i		−	1.72942i
$146$	−1.20147e29			−0.00497274
$147$	−1.54243e31	+	2.17632e31i	−0.578235	+	0.815870i
$148$	−1.31180e31			−0.445732
$149$		−	8.53378e30i		−	0.262991i	−0.991317	−	0.131495i	$-0.958022\pi$
$149$		−	8.53378e30i		−	0.262991i	0.991317	−	0.131495i	$-0.0419779\pi$
$150$	−2.14598e28	+	6.08256e27i	−0.000600208	+	0.000170123i
$151$	−1.60350e31			−0.407289			−0.203644	−	0.979045i	$-0.565279\pi$
$151$	−1.60350e31			−0.407289			−0.203644	+	0.979045i	$0.565279\pi$
$152$	−7.40407e30			−0.170898
$153$	6.70618e31	−	4.13370e31i	1.40750	−	0.867586i
$154$	−4.40231e30	−	2.10694e30i	−0.0840679	−	0.0402348i
$155$		−	3.80310e31i		−	0.661193i
$156$	−3.02837e31	+	8.58361e30i	−0.479625	+	0.135945i
$157$			1.56917e31i			0.226530i	0.993565	+	0.113265i	$0.0361309\pi$
$157$			1.56917e31i			0.226530i	−0.993565	+	0.113265i	$0.963869\pi$
$158$		−	6.76698e30i		−	0.0890979i
$159$	−8.79707e31	+	2.49344e31i	−1.05701	+	0.299600i
$160$			1.93805e31i			0.212630i
$161$	−4.66063e31	+	9.73809e31i	−0.467164	+	0.976109i
$162$	6.92678e30	+	3.48390e30i	0.0634693	+	0.0319225i
$163$	7.51416e31			0.629739			0.314869	−	0.949135i	$-0.398039\pi$
$163$	7.51416e31			0.629739			0.314869	+	0.949135i	$0.398039\pi$
$164$	1.07818e32			0.826904
$165$	1.80517e32	−	5.11658e31i	1.26765	−	0.359304i
$166$		−	1.17153e31i		−	0.0753679i
$167$	−1.08713e32			−0.641051			−0.320526	−	0.947240i	$-0.603860\pi$
$167$	−1.08713e32			−0.641051			−0.320526	+	0.947240i	$0.603860\pi$
$168$	2.58304e31	+	4.43887e30i	0.139684	+	0.0240042i
$169$	1.50942e32			0.748951
$170$		−	2.59014e31i		−	0.117981i
$171$	−1.51233e32	−	2.45349e32i	−0.632708	−	1.02645i
$172$	−3.89165e32			−1.49614
$173$	4.41231e32			1.55954			0.779771	−	0.626065i	$-0.215335\pi$
$173$	4.41231e32			1.55954			0.779771	+	0.626065i	$0.215335\pi$
$174$	1.02608e31	+	3.62010e31i	0.0333593	+	0.117694i
$175$	−2.64736e30	−	1.26702e30i	−0.00792067	−	0.00379082i
$176$		−	4.69030e32i		−	1.29201i
$177$	6.27524e31	+	2.21396e32i	0.159228	+	0.561768i
$178$		−	2.03498e31i		−	0.0475849i
$179$			9.16633e32i			1.97618i	0.153878	+	0.988090i	$0.450824\pi$
$179$			9.16633e32i			1.97618i	−0.153878	+	0.988090i	$0.549176\pi$
$180$	−4.27780e32	+	2.63684e32i	−0.850686	+	0.524363i
$181$			6.74836e32i			1.23839i	0.785235	+	0.619197i	$0.212542\pi$
$181$			6.74836e32i			1.23839i	−0.785235	+	0.619197i	$0.787458\pi$
$182$	1.89523e31	+	9.07055e30i	0.0321091	+	0.0153673i
$183$	7.20270e32	−	2.04153e32i	1.12708	−	0.319459i
$184$	1.06074e32			0.153374
$185$	−3.36636e32			−0.449956
$186$	1.03177e31	+	3.64017e31i	0.0127540	+	0.0449970i
$187$			1.89656e33i			2.16902i
$188$	−1.15575e33			−1.22342
$189$	3.80513e32	+	9.46610e32i	0.372970	+	0.927844i
$190$	−9.47614e31			−0.0860407
$191$		−	1.63445e33i		−	1.37527i	−0.726059	−	0.687633i	$-0.758650\pi$
$191$		−	1.63445e33i		−	1.37527i	0.726059	−	0.687633i	$-0.241350\pi$
$192$	3.39040e32	+	1.19616e33i	0.264474	+	0.933086i
$193$	2.33949e32			0.169255			0.0846273	−	0.996413i	$-0.473030\pi$
$193$	2.33949e32			0.169255			0.0846273	+	0.996413i	$0.473030\pi$
$194$	−4.01292e31			−0.0269362
$195$	−7.77141e32	+	2.20273e32i	−0.484170	+	0.137233i
$196$	1.07886e33	+	1.33951e33i	0.624099	+	0.774875i
$197$		−	2.64605e32i		−	0.142180i	−0.997470	−	0.0710899i	$-0.977352\pi$
$197$		−	2.64605e32i		−	0.142180i	0.997470	−	0.0710899i	$-0.0226477\pi$
$198$	−1.58902e32	+	9.79475e31i	−0.0793386	+	0.0489044i
$199$		−	2.12781e33i		−	0.987558i	−0.869587	−	0.493779i	$-0.835615\pi$
$199$		−	2.12781e33i		−	0.987558i	0.869587	−	0.493779i	$-0.164385\pi$
$200$			2.88369e30i			0.00124456i
$201$	−5.30517e31	−	1.87171e32i	−0.0212989	−	0.0751441i
$202$			2.25539e32i			0.0842609i
$203$	−2.13737e33	+	4.46590e33i	−0.743339	+	1.55316i
$204$	−1.38517e33	−	4.88699e33i	−0.448606	−	1.58272i
$205$	2.76683e33			0.834740
$206$	1.75032e32			0.0492089
$207$	2.16664e33	+	3.51498e33i	0.567827	+	0.921197i
$208$			2.01921e33i			0.493474i
$209$	6.93865e33			1.58181
$210$	3.30592e32	+	5.68111e31i	0.0703255	+	0.0120852i
$211$	1.53466e33			0.304731			0.152366	−	0.988324i	$-0.451311\pi$
$211$	1.53466e33			0.304731			0.152366	+	0.988324i	$0.451311\pi$
$212$			5.89565e33i			1.09311i
$213$	3.54042e33	−	1.00350e33i	0.613127	−	0.173785i
$214$	−6.35000e31			−0.0102748
$215$	−9.98676e33			−1.51031
$216$	6.77547e32	−	7.38755e32i	0.0957988	−	0.104453i
$217$	−2.14922e33	+	4.49066e33i	−0.284194	+	0.593805i
$218$		−	8.82684e32i		−	0.109191i
$219$	−5.81730e32	+	1.64886e32i	−0.0673414	+	0.0190873i
$220$		−	1.20980e34i		−	1.31094i
$221$		−	8.16485e33i		−	0.828439i
$222$	3.22214e32	−	9.13283e31i	0.0306215	−	0.00867936i
$223$		−	4.39028e33i		−	0.390905i	−0.980713	−	0.195453i	$-0.937382\pi$
$223$		−	4.39028e33i		−	0.390905i	0.980713	−	0.195453i	$-0.0626176\pi$
$224$	1.09524e33	−	2.28843e33i	0.0913927	−	0.190959i
$225$	−9.55570e31	+	5.89014e31i	−0.00747508	+	0.00460765i
$226$	4.74502e32			0.0348069
$227$	7.33316e33			0.504564			0.252282	−	0.967654i	$-0.418819\pi$
$227$	7.33316e33			0.504564			0.252282	+	0.967654i	$0.418819\pi$
$228$	−1.78793e34	+	5.06770e33i	−1.15423	+	0.327156i
$229$			8.31384e33i			0.503717i	0.967764	+	0.251859i	$0.0810418\pi$
$229$			8.31384e33i			0.503717i	−0.967764	+	0.251859i	$0.918958\pi$
$230$	1.35760e33			0.0772177
$231$	−2.42067e34	−	4.15984e33i	−1.29289	−	0.222179i
$232$	4.86457e33			0.244044
$233$		−	3.48244e34i		−	1.64143i	−0.571337	−	0.820716i	$-0.693575\pi$
$233$		−	3.48244e34i		−	1.64143i	0.571337	−	0.820716i	$-0.306425\pi$
$234$	6.84087e32	−	4.21672e32i	0.0303027	−	0.0186786i
$235$	−2.96589e34			−1.23501
$236$	1.48376e34			0.580951
$237$	−9.28679e33	−	3.27646e34i	−0.341991	−	1.20657i
$238$	−1.46375e33	+	3.05841e33i	−0.0507108	+	0.105957i
$239$			2.34983e34i			0.766067i	0.923734	+	0.383033i	$0.125121\pi$
$239$			2.34983e34i			0.766067i	−0.923734	+	0.383033i	$0.874879\pi$
$240$	8.79079e33	+	3.10146e34i	0.269752	+	0.951707i
$241$		−	6.85561e34i		−	1.98061i	−0.138912	−	0.990305i	$-0.544361\pi$
$241$		−	6.85561e34i		−	1.98061i	0.138912	−	0.990305i	$-0.455639\pi$
$242$		−	1.88258e33i		−	0.0512189i
$243$	3.83195e34	+	7.36232e33i	0.982039	+	0.188679i
$244$		−	4.82713e34i		−	1.16557i
$245$	2.76858e34	+	3.43745e34i	0.630013	+	0.782218i
$246$	−2.64829e33	+	7.50632e32i	−0.0568077	+	0.0161016i
$247$	−2.98715e34			−0.604158
$248$	4.89154e33			0.0933031
$249$	−1.60777e34	−	5.67235e34i	−0.289290	−	1.02064i
$250$		−	4.16612e33i		−	0.0707298i
$251$	4.08692e34			0.654828			0.327414	−	0.944881i	$-0.393823\pi$
$251$	4.08692e34			0.654828			0.327414	+	0.944881i	$0.393823\pi$
$252$	6.54132e34	−	6.96066e33i	0.989367	−	0.105279i
$253$	−9.94063e34			−1.41960
$254$		−	1.99925e33i		−	0.0269636i
$255$	−3.55462e34	−	1.25410e35i	−0.452857	−	1.59772i
$256$	7.89152e34			0.949907
$257$	−8.50905e34			−0.967945			−0.483972	−	0.875083i	$-0.660806\pi$
$257$	−8.50905e34			−0.967945			−0.483972	+	0.875083i	$0.660806\pi$
$258$	9.55891e33	−	2.70938e33i	0.102783	−	0.0291329i
$259$	3.97496e34	+	1.90241e34i	0.404097	+	0.193400i
$260$			5.20827e34i			0.500703i
$261$	9.93621e34	+	1.61197e35i	0.903511	+	1.46578i
$262$			1.07768e34i			0.0927089i
$263$		−	1.53828e35i		−	1.25221i	−0.779740	−	0.626103i	$-0.784649\pi$
$263$		−	1.53828e35i		−	1.25221i	0.779740	−	0.626103i	$-0.215351\pi$
$264$	6.58093e33	+	2.32181e34i	0.0507026	+	0.178883i
$265$			1.51295e35i			1.10346i
$266$	1.11893e34	+	5.35519e33i	0.0772716	+	0.0369820i
$267$	−2.79274e34	−	9.85300e34i	−0.182649	−	0.644399i
$268$	−1.25439e34			−0.0777100
$269$	6.38364e34			0.374680			0.187340	−	0.982295i	$-0.440013\pi$
$269$	6.38364e34			0.374680			0.187340	+	0.982295i	$0.440013\pi$
$270$	8.67163e33	−	9.45500e33i	0.0482310	−	0.0525880i
$271$			1.91619e35i			1.01015i	0.863076	+	0.505074i	$0.168535\pi$
$271$			1.91619e35i			1.01015i	−0.863076	+	0.505074i	$0.831465\pi$
$272$	−3.25848e35			−1.62842
$273$	1.04212e35	+	1.79085e34i	0.493810	+	0.0848594i
$274$	−8.24075e33			−0.0370325
$275$		−	2.70243e33i		−	0.0115194i
$276$	2.56147e35	−	7.26022e34i	1.03587	−	0.293608i
$277$	−4.75727e35			−1.82558			−0.912791	−	0.408427i	$-0.866077\pi$
$277$	−4.75727e35			−1.82558			−0.912791	+	0.408427i	$0.866077\pi$
$278$	3.70149e34			0.134811
$279$	9.99130e34	+	1.62091e35i	0.345431	+	0.560400i
$280$	1.87216e34	−	3.91175e34i	0.0614540	−	0.128404i
$281$			5.51041e35i			1.71768i	0.512245	+	0.858839i	$0.328814\pi$
$281$			5.51041e35i			1.71768i	−0.512245	+	0.858839i	$0.671186\pi$
$282$	2.83883e34	−	8.04637e33i	0.0840479	−	0.0238225i
$283$			1.66431e35i			0.468092i	0.972226	+	0.234046i	$0.0751966\pi$
$283$			1.66431e35i			0.468092i	−0.972226	+	0.234046i	$0.924803\pi$
$284$		−	2.37273e35i		−	0.634064i
$285$	−4.58818e35	+	1.30047e35i	−1.16517	+	0.330257i
$286$			1.93465e34i			0.0466977i
$287$	−3.26704e35	−	1.56360e35i	−0.749664	−	0.358788i
$288$	−5.09154e34	−	8.26011e34i	−0.111086	−	0.180217i
$289$	8.35624e35			1.73377
$290$	6.22595e34			0.122867
$291$	−1.94299e35	+	5.50721e34i	−0.364772	+	0.103391i
$292$			3.89866e34i			0.0696409i
$293$	4.84366e35			0.823366			0.411683	−	0.911327i	$-0.364941\pi$
$293$	4.84366e35			0.823366			0.411683	+	0.911327i	$0.364941\pi$
$294$	−3.58254e34	−	2.53907e34i	−0.0579636	−	0.0410808i
$295$	3.80763e35			0.586456
$296$		−	4.32981e34i		−	0.0634949i
$297$	−6.34957e35	+	6.92317e35i	−0.886698	+	0.966800i
$298$	1.40479e34			0.0186842
$299$	4.27953e35			0.542205
$300$	1.97374e33	+	6.96351e33i	0.00238249	+	0.00840563i
$301$	1.17923e36	+	5.64375e35i	1.35638	+	0.649163i
$302$		−	2.63959e34i		−	0.0289359i
$303$	3.09522e35	+	1.09202e36i	0.323425	+	1.14107i
$304$			1.19213e36i			1.18756i
$305$		−	1.23874e36i		−	1.17661i
$306$	6.80468e34	+	1.10394e35i	0.0616378	+	0.0999962i
$307$		−	4.14891e35i		−	0.358449i	−0.983808	−	0.179224i	$-0.942641\pi$
$307$		−	4.14891e35i		−	0.358449i	0.983808	−	0.179224i	$-0.0573588\pi$
$308$	−6.83684e35	+	1.42851e36i	−0.563469	+	1.17733i
$309$	8.47476e35	−	2.40209e35i	0.666391	−	0.188882i
$310$	6.26047e34			0.0469745
$311$	−7.22914e35			−0.517680			−0.258840	−	0.965920i	$-0.583340\pi$
$311$	−7.22914e35			−0.517680			−0.258840	+	0.965920i	$0.583340\pi$
$312$	−2.83315e34	−	9.99557e34i	−0.0193654	−	0.0683229i
$313$		−	6.81116e35i		−	0.444455i	−0.974995	−	0.222228i	$-0.928667\pi$
$313$		−	6.81116e35i		−	0.444455i	0.974995	−	0.222228i	$-0.0713328\pi$
$314$	−2.58309e34			−0.0160938
$315$	1.67864e36	−	1.78625e35i	0.998742	−	0.106277i
$316$	−2.19583e36			−1.24777
$317$			1.68810e36i			0.916300i	0.888875	+	0.458150i	$0.151488\pi$
$317$			1.68810e36i			0.916300i	−0.888875	+	0.458150i	$0.848512\pi$
$318$	−4.10458e34	−	1.44813e35i	−0.0212851	−	0.0750955i
$319$	−4.55878e36			−2.25883
$320$	2.05719e36			0.974092
$321$	−3.07456e35	+	8.71454e34i	−0.139143	+	0.0394386i
$322$	−1.60303e35	−	7.67209e34i	−0.0693478	−	0.0331897i
$323$		−	4.82047e36i		−	1.99367i
$324$	1.13049e36	−	2.24768e36i	0.447060	−	0.888858i
$325$			1.16342e34i			0.00439974i
$326$			1.23694e35i			0.0447398i
$327$	−1.21137e36	−	4.27380e36i	−0.419115	−	1.47867i
$328$			3.55869e35i			0.117793i
$329$	3.50209e36	+	1.67609e36i	1.10914	+	0.530833i
$330$	8.42264e34	+	2.97158e35i	0.0255268	+	0.0900606i
$331$	4.91857e34			0.0142670			0.00713350	−	0.999975i	$-0.497729\pi$
$331$	4.91857e34			0.0142670			0.00713350	+	0.999975i	$0.497729\pi$
$332$	−3.80152e36			−1.05549
$333$	1.43477e36	−	8.84392e35i	0.381364	−	0.235073i
$334$		−	1.78958e35i		−	0.0455435i
$335$	−3.21901e35			−0.0784464
$336$	7.14702e35	−	4.15896e36i	0.166804	−	0.970655i
$337$	−3.67526e36			−0.821589			−0.410794	−	0.911728i	$-0.634749\pi$
$337$	−3.67526e36			−0.821589			−0.410794	+	0.911728i	$0.634749\pi$
$338$			2.48473e35i			0.0532093i
$339$	2.29746e36	−	6.51192e35i	0.471359	−	0.133602i
$340$	−8.40478e36			−1.65227
$341$	−4.58406e36			−0.863598
$342$	4.03880e35	−	2.48952e35i	0.0729246	−	0.0449508i
$343$	−1.32653e36	−	5.62349e36i	−0.229590	−	0.973288i
$344$		−	1.28450e36i		−	0.213125i
$345$	6.57324e36	−	1.86312e36i	1.04569	−	0.296390i
$346$			7.26331e35i			0.110798i
$347$			6.02613e36i			0.881579i	0.897610	+	0.440790i	$0.145302\pi$
$347$			6.02613e36i			0.881579i	−0.897610	+	0.440790i	$0.854698\pi$
$348$	1.17469e37	−	3.32954e36i	1.64826	−	0.467182i
$349$			2.04744e36i			0.275576i	0.990462	+	0.137788i	$0.0439993\pi$
$349$			2.04744e36i			0.275576i	−0.990462	+	0.137788i	$0.956001\pi$
$350$	2.08571e33	−	4.35795e33i	0.000269319	−	0.000562725i
$351$	2.73354e36	−	2.98048e36i	0.338667	−	0.369261i
$352$	2.33602e36			0.277721
$353$	1.26440e37			1.44262			0.721308	−	0.692614i	$-0.243541\pi$
$353$	1.26440e37			1.44262			0.721308	+	0.692614i	$0.243541\pi$
$354$	−3.64450e35	+	1.03300e35i	−0.0399109	+	0.0113123i
$355$		−	6.08892e36i		−	0.640072i
$356$	−6.60332e36			−0.666404
$357$	−2.88996e36	+	1.68171e37i	−0.280028	+	1.62953i
$358$	−1.50891e36			−0.140398
$359$			4.98569e36i			0.445508i	0.974875	+	0.222754i	$0.0715047\pi$
$359$			4.98569e36i			0.445508i	−0.974875	+	0.222754i	$0.928495\pi$
$360$	−8.70328e35	−	1.41195e36i	−0.0746959	−	0.121181i
$361$	−5.50607e36			−0.453929
$362$	−1.11088e36			−0.0879819
$363$	−2.58359e36	−	9.11512e36i	−0.196597	−	0.693611i
$364$	2.94332e36	−	6.14987e36i	0.215212	−	0.449672i
$365$			1.00048e36i			0.0703008i
$366$	3.36067e35	+	1.18567e36i	0.0226960	+	0.0800734i
$367$			1.86060e37i			1.20780i	0.797059	+	0.603901i	$0.206388\pi$
$367$			1.86060e37i			1.20780i	−0.797059	+	0.603901i	$0.793612\pi$
$368$		−	1.70790e37i		−	1.06578i
$369$	−1.17924e37	+	7.26886e36i	−0.707491	+	0.436098i
$370$		−	5.54153e35i		−	0.0319672i
$371$	8.55001e36	−	1.78647e37i	0.474291	−	0.991000i
$372$	1.18120e37	−	3.34800e36i	0.630162	−	0.178613i
$373$	−2.32369e37			−1.19234			−0.596169	−	0.802859i	$-0.703311\pi$
$373$	−2.32369e37			−1.19234			−0.596169	+	0.802859i	$0.703311\pi$
$374$	−3.12202e36			−0.154098
$375$	−5.71746e36	−	2.01717e37i	−0.271487	−	0.957829i
$376$		−	3.81472e36i		−	0.174277i
$377$	1.96260e37			0.862743
$378$	−1.55826e36	+	6.26381e35i	−0.0659187	+	0.0264977i
$379$	−8.33717e36			−0.339430			−0.169715	−	0.985493i	$-0.554285\pi$
$379$	−8.33717e36			−0.339430			−0.169715	+	0.985493i	$0.554285\pi$
$380$			3.07493e37i			1.20496i
$381$	−2.74370e36	−	9.68001e36i	−0.103496	−	0.365144i
$382$	2.69054e36			0.0977059
$383$	−1.59429e37			−0.557424			−0.278712	−	0.960375i	$-0.589907\pi$
$383$	−1.59429e37			−0.557424			−0.278712	+	0.960375i	$0.589907\pi$
$384$	−8.01897e36	+	2.27290e36i	−0.269970	+	0.0765204i
$385$	−1.75447e37	+	3.66586e37i	−0.568808	+	1.18849i
$386$			3.85115e35i			0.0120247i
$387$	4.25643e37	−	2.62367e37i	1.28008	−	0.789042i
$388$			1.30216e37i			0.377228i
$389$			4.83465e36i			0.134926i	0.997722	+	0.0674630i	$0.0214905\pi$
$389$			4.83465e36i			0.134926i	−0.997722	+	0.0674630i	$0.978510\pi$
$390$	−3.62602e35	−	1.27929e36i	−0.00974975	−	0.0343979i
$391$			6.90603e37i			1.78923i
$392$	−4.42124e36	+	3.56095e36i	−0.110381	+	0.0889032i
$393$	1.47897e37	+	5.21794e37i	0.355852	+	1.25547i
$394$	4.35579e35			0.0101012
$395$	−5.63494e37			−1.25960
$396$	3.17831e37	+	5.15624e37i	0.684883	+	1.11110i
$397$			8.92922e37i			1.85503i	0.373786	+	0.927515i	$0.378060\pi$
$397$			8.92922e37i			1.85503i	−0.373786	+	0.927515i	$0.621940\pi$
$398$	3.50269e36			0.0701612
$399$	6.15260e37	+	1.05730e37i	1.18837	+	0.204217i
$400$	4.64304e35			0.00864833
$401$		−	2.41874e37i		−	0.434505i	−0.976115	−	0.217253i	$-0.930290\pi$
$401$		−	2.41874e37i		−	0.434505i	0.976115	−	0.217253i	$-0.0697095\pi$
$402$	3.08111e35	−	8.73309e34i	0.00533862	−	0.00151318i
$403$	1.97348e37			0.329844
$404$	7.31853e37			1.18003
$405$	2.90108e37	−	5.76801e37i	0.451296	−	0.897281i
$406$	−7.35153e36	−	3.51843e36i	−0.110344	−	0.0528106i
$407$			4.05764e37i			0.587698i
$408$	1.61302e37	−	4.57195e36i	0.225459	−	0.0639042i
$409$		−	6.27784e37i		−	0.846881i	−0.905924	−	0.423441i	$-0.860822\pi$
$409$		−	6.27784e37i		−	0.846881i	0.905924	−	0.423441i	$-0.139178\pi$
$410$			4.55461e36i			0.0593042i
$411$	−3.99003e37	+	1.13093e37i	−0.501498	+	0.142145i
$412$		−	5.67965e37i		−	0.689147i
$413$	−4.49600e37	−	2.15178e37i	−0.526685	−	0.252070i
$414$	−5.78618e36	+	3.56660e36i	−0.0654465	+	0.0403413i
$415$	−9.75547e37			−1.06549
$416$	−1.00568e37			−0.106073
$417$	1.79220e38	−	5.07980e37i	1.82563	−	0.517457i
$418$			1.14220e37i			0.112380i
$419$	−1.17454e38			−1.11626			−0.558130	−	0.829754i	$-0.688481\pi$
$419$	−1.17454e38			−1.11626			−0.558130	+	0.829754i	$0.688481\pi$
$420$	1.84347e37	−	1.07274e38i	0.169247	−	0.984875i
$421$	−1.73657e38			−1.54029			−0.770145	−	0.637869i	$-0.779816\pi$
$421$	−1.73657e38			−1.54029			−0.770145	+	0.637869i	$0.779816\pi$
$422$			2.52628e36i			0.0216496i
$423$	1.26408e38	−	7.79183e37i	1.04674	−	0.645214i
$424$	−1.94595e37			−0.155714
$425$	−1.87745e36			−0.0145187
$426$	1.65191e36	+	5.82806e36i	0.0123466	+	0.0435597i
$427$	−7.00041e37	+	1.46269e38i	−0.505731	+	1.05669i
$428$			2.06052e37i			0.143894i
$429$	2.65506e37	+	9.36726e37i	0.179243	+	0.632385i
$430$		−	1.64397e37i		−	0.107300i
$431$			3.99375e37i			0.252034i	0.992028	+	0.126017i	$0.0402195\pi$
$431$			3.99375e37i			0.252034i	−0.992028	+	0.126017i	$0.959781\pi$
$432$	−1.18947e38	−	1.09092e38i	−0.725837	−	0.665700i
$433$		−	2.69975e37i		−	0.159312i	−0.996822	−	0.0796562i	$-0.974618\pi$
$433$		−	2.69975e37i		−	0.159312i	0.996822	−	0.0796562i	$-0.0253822\pi$
$434$	−7.39229e36	−	3.53794e36i	−0.0421869	−	0.0201906i
$435$	3.01450e38	−	8.54429e37i	1.66387	−	0.471609i
$436$	−2.86423e38			−1.52917
$437$	2.52660e38			1.30484
$438$	−2.71426e35	−	9.57615e35i	−0.00135606	−	0.00478427i
$439$			2.22268e38i			1.07434i	0.843475	+	0.537169i	$0.180506\pi$
$439$			2.22268e38i			1.07434i	−0.843475	+	0.537169i	$0.819494\pi$
$440$	3.99311e37			0.186744
$441$	−2.08306e38	−	7.37718e37i	−0.942632	−	0.333834i
$442$	1.34406e37			0.0588565
$443$		−	1.84884e38i		−	0.783509i	−0.920070	−	0.391755i	$-0.871868\pi$
$443$		−	1.84884e38i		−	0.783509i	0.920070	−	0.391755i	$-0.128132\pi$
$444$	−2.96353e37	−	1.04556e38i	−0.121550	−	0.428839i
$445$	−1.69455e38			−0.672719
$446$	7.22705e36			0.0277719
$447$	6.80174e37	−	1.92788e37i	0.253023	−	0.0717170i
$448$	−2.42911e38	−	1.16257e38i	−0.874813	−	0.418684i
$449$			2.08938e38i			0.728525i	0.931296	+	0.364263i	$0.118679\pi$
$449$			2.08938e38i			0.728525i	−0.931296	+	0.364263i	$0.881321\pi$
$450$	−9.69605e34	−	1.57301e35i	−0.000327351	−	0.000531068i
$451$		−	3.33499e38i		−	1.09027i
$452$		−	1.53972e38i		−	0.487455i
$453$	−3.62249e37	−	1.27805e38i	−0.111067	−	0.391852i
$454$			1.20715e37i			0.0358468i
$455$	7.55315e37	−	1.57818e38i	0.217252	−	0.453933i
$456$	−1.67267e37	−	5.90131e37i	−0.0466036	−	0.164421i
$457$	−1.08516e38			−0.292892			−0.146446	−	0.989219i	$-0.546783\pi$
$457$	−1.08516e38			−0.292892			−0.146446	+	0.989219i	$0.546783\pi$
$458$	−1.36858e37			−0.0357867
$459$	4.80971e38	+	4.41122e38i	1.21853	+	1.11757i
$460$		−	4.40528e38i		−	1.08140i
$461$	−2.64900e36			−0.00630114			−0.00315057	−	0.999995i	$-0.501003\pi$
$461$	−2.64900e36			−0.00630114			−0.00315057	+	0.999995i	$0.501003\pi$
$462$	6.84772e36	−	3.98479e37i	0.0157847	−	0.0918537i
$463$	2.91043e38			0.650179			0.325089	−	0.945683i	$-0.394606\pi$
$463$	2.91043e38			0.650179			0.325089	+	0.945683i	$0.394606\pi$
$464$		−	7.83245e38i		−	1.69585i
$465$	3.03121e38	−	8.59166e37i	0.636133	−	0.180306i
$466$	5.73261e37			0.116616
$467$	1.17358e38			0.231430			0.115715	−	0.993282i	$-0.463084\pi$
$467$	1.17358e38			0.231430			0.115715	+	0.993282i	$0.463084\pi$
$468$	−1.36829e38	−	2.21981e38i	−0.261585	−	0.424375i
$469$	3.80098e37	+	1.81914e37i	0.0704513	+	0.0337179i
$470$		−	4.88229e37i		−	0.0877415i
$471$	−1.25069e38	+	3.54495e37i	−0.217944	+	0.0617742i
$472$			4.89736e37i			0.0827568i
$473$			1.20375e39i			1.97265i
$474$	5.39353e37	−	1.52874e37i	0.0857211	−	0.0242968i
$475$			6.86873e36i			0.0105881i
$476$	9.92427e38	+	4.74974e38i	1.48388	+	0.710181i
$477$	−3.97473e38	−	6.44829e38i	−0.576489	−	0.935251i
$478$	−3.86817e37			−0.0544253
$479$	−1.15260e39			−1.57331			−0.786654	−	0.617394i	$-0.788188\pi$
$479$	−1.15260e39			−1.57331			−0.786654	+	0.617394i	$0.788188\pi$
$480$	−1.54470e38	+	4.37829e37i	−0.204571	+	0.0579838i
$481$		−	1.74685e38i		−	0.224466i
$482$	1.12853e38			0.140713
$483$	−8.81451e38	−	1.51474e38i	−1.06651	−	0.183276i
$484$	−6.10880e38			−0.717296
$485$			3.34161e38i			0.380803i
$486$	−1.21195e37	+	6.30796e37i	−0.0134047	+	0.0697690i
$487$	1.01199e39			1.08644			0.543219	−	0.839591i	$-0.317205\pi$
$487$	1.01199e39			1.08644			0.543219	+	0.839591i	$0.317205\pi$
$488$	1.59327e38			0.166035
$489$	1.69754e38	+	5.98906e38i	0.171728	+	0.605871i
$490$	−5.65855e37	+	4.55750e37i	−0.0555728	+	0.0447593i
$491$		−	1.37756e39i		−	1.31350i	−0.754109	−	0.656749i	$-0.771931\pi$
$491$		−	1.37756e39i		−	1.31350i	0.754109	−	0.656749i	$-0.228069\pi$
$492$	2.43574e38	+	8.59348e38i	0.225495	+	0.795564i
$493$			3.16711e39i			2.84697i
$494$		−	4.91729e37i		−	0.0429225i
$495$	8.15620e38	+	1.32320e39i	0.691373	+	1.12163i
$496$		−	7.87587e38i		−	0.648357i
$497$	−3.44099e38	+	7.18972e38i	−0.275116	+	0.574837i
$498$	9.33753e37	−	2.64663e37i	0.0725115	−	0.0205527i
$499$	−3.04074e38			−0.229362			−0.114681	−	0.993402i	$-0.536585\pi$
$499$	−3.04074e38			−0.229362			−0.114681	+	0.993402i	$0.536585\pi$
$500$	−1.35187e39			−0.990536
$501$	−2.45596e38	−	8.66483e38i	−0.174813	−	0.616755i
$502$			6.72768e37i			0.0465223i
$503$	−1.49463e39			−1.00415			−0.502073	−	0.864825i	$-0.667429\pi$
$503$	−1.49463e39			−1.00415			−0.502073	+	0.864825i	$0.667429\pi$
$504$	2.29747e37	+	2.15906e38i	0.0149971	+	0.140936i
$505$	1.87809e39			1.19122
$506$		−	1.63638e38i		−	0.100856i
$507$	3.40997e38	+	1.20306e39i	0.204237	+	0.720566i
$508$	−6.48739e38			−0.377612
$509$	−4.02828e37			−0.0227883			−0.0113941	−	0.999935i	$-0.503627\pi$
$509$	−4.02828e37			−0.0227883			−0.0113941	+	0.999935i	$0.503627\pi$
$510$	2.06444e38	−	5.85144e37i	0.113510	−	0.0321733i
$511$	5.65393e37	−	1.18135e38i	0.0302167	−	0.0631359i
$512$			6.70051e38i			0.348092i
$513$	1.61386e39	−	1.75966e39i	0.815014	−	0.888640i
$514$		−	1.40072e38i		−	0.0687677i
$515$		−	1.45751e39i		−	0.695677i
$516$	−8.79171e38	−	3.10179e39i	−0.407993	−	1.43943i
$517$			3.57493e39i			1.61308i
$518$	−3.13165e37	+	6.54337e37i	−0.0137401	+	0.0287091i
$519$	9.96794e38	+	3.51677e39i	0.425284	+	1.50043i
$520$	−1.71907e38			−0.0713254
$521$	3.08072e38			0.124310			0.0621550	−	0.998067i	$-0.480203\pi$
$521$	3.08072e38			0.124310			0.0621550	+	0.998067i	$0.480203\pi$
$522$	−2.65355e38	+	1.63565e38i	−0.104137	+	0.0641900i
$523$		−	4.34830e38i		−	0.165976i	−0.996551	−	0.0829880i	$-0.973554\pi$
$523$		−	4.34830e38i		−	0.165976i	0.996551	−	0.0829880i	$-0.0264463\pi$
$524$	3.49698e39			1.29834
$525$	4.11792e36	−	2.39628e37i	0.00148720	−	0.00865422i
$526$	2.53223e38			0.0889632
$527$			3.18467e39i			1.08846i
$528$	3.73834e39	−	1.05960e39i	1.24305	−	0.352329i
$529$	−5.28669e38			−0.171032
$530$	−2.49053e38			−0.0783957
$531$	−1.62284e39	+	1.00032e39i	−0.497056	+	0.306386i
$532$	1.73771e39	−	3.63084e39i	0.517916	−	1.08215i
$533$			1.43574e39i			0.416420i
$534$	1.62195e38	−	4.59726e37i	0.0457814	−	0.0129763i
$535$			5.28772e38i			0.145257i
$536$		−	4.14029e37i		−	0.0110698i
$537$	−7.30590e39	+	2.07079e39i	−1.90128	+	0.538900i
$538$			1.05084e38i			0.0266192i
$539$	4.14332e39	−	3.33711e39i	1.02167	−	0.822874i
$540$	−3.06807e39	−	2.81387e39i	−0.736470	−	0.675452i
$541$	2.94250e39			0.687632			0.343816	−	0.939037i	$-0.388280\pi$
$541$	2.94250e39			0.687632			0.343816	+	0.939037i	$0.388280\pi$
$542$	−3.15434e38			−0.0717660
$543$	−5.37869e39	+	1.52454e39i	−1.19146	+	0.337707i
$544$		−	1.62290e39i		−	0.350032i
$545$	−7.35021e39			−1.54366
$546$	−2.94800e37	+	1.71549e38i	−0.00602885	+	0.0350828i
$547$	4.86226e38			0.0968326			0.0484163	−	0.998827i	$-0.484583\pi$
$547$	4.86226e38			0.0968326			0.0484163	+	0.998827i	$0.484583\pi$
$548$			2.67405e39i			0.518623i
$549$	3.25435e39	+	5.27961e39i	0.614704	+	0.997247i
$550$	4.44860e36			0.000818397
$551$	1.15870e40			2.07622
$552$	2.39634e38	+	8.45450e38i	0.0418247	+	0.147561i
$553$	6.65368e39	+	3.18444e39i	1.13122	+	0.541400i
$554$		−	7.83118e38i		−	0.129699i
$555$	−7.60502e38	−	2.68311e39i	−0.122702	−	0.432903i
$556$		−	1.20110e40i		−	1.88797i
$557$		−	9.72938e39i		−	1.49000i	−0.667067	−	0.744998i	$-0.732450\pi$
$557$		−	9.72938e39i		−	1.49000i	0.667067	−	0.744998i	$-0.267550\pi$
$558$	−2.66826e38	+	1.64472e38i	−0.0398136	+	0.0245412i
$559$		−	5.18226e39i		−	0.753439i
$560$	−6.29831e39	−	3.01436e39i	−0.892272	−	0.427040i
$561$	−1.51163e40	+	4.28456e39i	−2.08681	+	0.591487i
$562$	−9.07095e38			−0.122033
$563$	−8.04726e39			−1.05506			−0.527529	−	0.849537i	$-0.676881\pi$
$563$	−8.04726e39			−1.05506			−0.527529	+	0.849537i	$0.676881\pi$
$564$	−2.61098e39	−	9.21175e39i	−0.333623	−	1.17705i
$565$		−	3.95123e39i		−	0.492074i
$566$	−2.73970e38			−0.0332556
$567$	−6.68520e39	+	5.17134e39i	−0.790970	+	0.611855i
$568$	7.83155e38			0.0903227
$569$			4.92946e39i			0.554206i	0.960840	+	0.277103i	$0.0893744\pi$
$569$			4.92946e39i			0.554206i	−0.960840	+	0.277103i	$0.910626\pi$
$570$	−2.14077e38	−	7.55283e38i	−0.0234631	−	0.0827798i
$571$	−3.01134e39			−0.321763			−0.160881	−	0.986974i	$-0.551434\pi$
$571$	−3.01134e39			−0.321763			−0.160881	+	0.986974i	$0.551434\pi$
$572$	6.27778e39			0.653979
$573$	1.30271e40	−	3.69241e39i	1.32314	−	0.375032i
$574$	2.57392e38	−	5.37803e38i	0.0254901	−	0.0532600i
$575$		−	9.84047e37i		−	0.00950237i
$576$	−8.76790e39	+	5.40454e39i	−0.825600	+	0.508901i
$577$		−	1.29813e40i		−	1.19198i	−0.802990	−	0.595992i	$-0.796759\pi$
$577$		−	1.29813e40i		−	1.19198i	0.802990	−	0.595992i	$-0.203241\pi$
$578$			1.37556e39i			0.123176i
$579$	5.28520e38	+	1.86466e39i	0.0461554	+	0.162840i
$580$		−	2.02027e40i		−	1.72069i
$581$	1.15192e40	+	5.51305e39i	0.956900	+	0.457971i
$582$	−9.06568e37	−	3.19845e38i	−0.00734543	−	0.0259153i
$583$	1.82363e40			1.44126
$584$	−1.28681e38			−0.00992039
$585$	−3.51131e39	−	5.69647e39i	−0.264064	−	0.428397i
$586$			7.97338e38i			0.0584961i
$587$	3.87385e38			0.0277262			0.0138631	−	0.999904i	$-0.495587\pi$
$587$	3.87385e38			0.0277262			0.0138631	+	0.999904i	$0.495587\pi$
$588$	−8.23907e39	+	1.16250e40i	−0.575317	+	0.811752i
$589$	1.16513e40			0.793782
$590$			6.26792e38i			0.0416648i
$591$	2.10900e39	−	5.97775e38i	0.136791	−	0.0387721i
$592$	−6.97142e39			−0.441221
$593$	−1.25692e40			−0.776274			−0.388137	−	0.921602i	$-0.626881\pi$
$593$	−1.25692e40			−0.776274			−0.388137	+	0.921602i	$0.626881\pi$
$594$	−1.13966e39	−	1.04523e39i	−0.0686864	−	0.0629956i
$595$	2.54677e40	+	1.21888e40i	1.49794	+	0.716910i
$596$		−	4.55841e39i		−	0.261663i
$597$	1.69594e40	−	4.80698e39i	0.950130	−	0.269305i
$598$			7.04474e38i			0.0385210i
$599$			2.11358e40i			1.12805i	0.825756	+	0.564027i	$0.190749\pi$
$599$			2.11358e40i			1.12805i	−0.825756	+	0.564027i	$0.809251\pi$
$600$	−2.29841e37	+	6.51462e36i	−0.00119739	+	0.000339387i
$601$			2.64978e40i			1.34750i	0.738957	+	0.673752i	$0.235318\pi$
$601$			2.64978e40i			1.34750i	−0.738957	+	0.673752i	$0.764682\pi$
$602$	−9.29046e38	+	1.94118e39i	−0.0461199	+	0.0963644i
$603$	1.37197e39	−	8.45683e38i	0.0664880	−	0.0409832i
$604$	−8.56525e39			−0.405233
$605$	−1.56764e40			−0.724093
$606$	−1.79763e39	+	5.09519e38i	−0.0810674	+	0.0229777i
$607$			5.48665e39i			0.241586i	0.992678	+	0.120793i	$0.0385437\pi$
$607$			5.48665e39i			0.241586i	−0.992678	+	0.120793i	$0.961456\pi$
$608$	−5.93745e39			−0.255269
$609$	−4.04234e40	−	6.94662e39i	−1.69700	−	0.291624i
$610$	2.03915e39			0.0835924
$611$		−	1.53904e40i		−	0.616101i
$612$	3.58218e40	−	2.20806e40i	1.40040	−	0.863207i
$613$	−7.35368e38			−0.0280755			−0.0140378	−	0.999901i	$-0.504469\pi$
$613$	−7.35368e38			−0.0280755			−0.0140378	+	0.999901i	$0.504469\pi$
$614$	6.82972e38			0.0254660
$615$	6.25060e39	+	2.20526e40i	0.227632	+	0.803103i
$616$	−4.71502e39	−	2.25660e39i	−0.167712	−	0.0802665i
$617$		−	1.29963e40i		−	0.451530i	−0.974182	−	0.225765i	$-0.927512\pi$
$617$		−	1.29963e40i		−	0.451530i	0.974182	−	0.225765i	$-0.0724881\pi$
$618$	3.95419e38	+	1.39507e39i	0.0134191	+	0.0473438i
$619$			1.74106e40i			0.577164i	0.957455	+	0.288582i	$0.0931838\pi$
$619$			1.74106e40i			0.577164i	−0.957455	+	0.288582i	$0.906816\pi$
$620$		−	2.03147e40i		−	0.657855i
$621$	−2.31210e40	+	2.52096e40i	−0.731439	+	0.797514i
$622$		−	1.19002e39i		−	0.0367786i
$623$	2.00090e40	+	9.57628e39i	0.604156	+	0.289148i
$624$	−1.60939e40	+	4.56165e39i	−0.474771	+	0.134569i
$625$	−3.49964e40			−1.00870
$626$	1.12122e39			0.0315764
$627$	1.56753e40	+	5.53036e40i	0.431355	+	1.52186i
$628$			8.38191e39i			0.225387i
$629$	2.81895e40			0.740718
$630$	2.94043e38	+	2.76328e39i	0.00755045	+	0.0709557i
$631$	5.93501e40			1.48935			0.744673	−	0.667429i	$-0.232605\pi$
$631$	5.93501e40			1.48935			0.744673	+	0.667429i	$0.232605\pi$
$632$		−	7.24766e39i		−	0.177746i
$633$	3.46699e39	+	1.22318e40i	0.0830995	+	0.293182i
$634$	−2.77886e39			−0.0650987
$635$	−1.66480e40			−0.381190
$636$	−4.69905e40	+	1.33190e40i	−1.05168	+	0.298087i
$637$	−1.78374e40	+	1.43665e40i	−0.390219	+	0.314290i
$638$		−	7.50444e39i		−	0.160479i
$639$	1.59965e40	+	2.59514e40i	0.334397	+	0.542499i
$640$			1.37913e40i			0.281835i
$641$			1.93964e39i			0.0387507i	0.999812	+	0.0193753i	$0.00616774\pi$
$641$			1.93964e39i			0.0387507i	−0.999812	+	0.0193753i	$0.993832\pi$
$642$	−1.43454e38	−	5.06118e38i	−0.00280192	−	0.00988540i
$643$			3.24762e40i			0.620164i	0.950710	+	0.310082i	$0.100357\pi$
$643$			3.24762e40i			0.620164i	−0.950710	+	0.310082i	$0.899643\pi$
$644$	−2.48953e40	+	5.20171e40i	−0.464806	+	0.971182i
$645$	−2.25613e40	−	7.95982e40i	−0.411859	−	1.45307i
$646$	7.93521e39			0.141640
$647$	−1.25775e40			−0.219525			−0.109762	−	0.993958i	$-0.535009\pi$
$647$	−1.25775e40			−0.219525			−0.109762	+	0.993958i	$0.535009\pi$
$648$	7.41881e39	+	3.73136e39i	0.126618	+	0.0636839i
$649$		−	4.58952e40i		−	0.765983i
$650$	−1.91516e37			−0.000312580
$651$	−4.06475e40	−	6.98513e39i	−0.648798	−	0.111494i
$652$	4.01377e40			0.626560
$653$		−	2.19281e40i		−	0.334780i	−0.985891	−	0.167390i	$-0.946466\pi$
$653$		−	2.19281e40i		−	0.334780i	0.985891	−	0.167390i	$-0.0535339\pi$
$654$	7.03532e39	−	1.99409e39i	0.105052	−	0.0297761i
$655$	8.97397e40			1.31065
$656$	5.72985e40			0.818535
$657$	−2.62840e39	−	4.26411e39i	−0.0367277	−	0.0595841i
$658$	−2.75910e39	+	5.76496e39i	−0.0377131	+	0.0787990i
$659$			9.04042e40i			1.20879i	0.796686	+	0.604394i	$0.206585\pi$
$659$			9.04042e40i			1.20879i	−0.796686	+	0.604394i	$0.793415\pi$
$660$	9.64251e40	−	2.73308e40i	1.26126	−	0.357491i
$661$			9.58277e39i			0.122622i	0.998119	+	0.0613112i	$0.0195282\pi$
$661$			9.58277e39i			0.122622i	−0.998119	+	0.0613112i	$0.980472\pi$
$662$			8.09670e37i			0.00101360i
$663$	6.50769e40	−	1.84454e40i	0.797041	−	0.225913i
$664$		−	1.25475e40i		−	0.150355i
$665$	4.45932e40	−	9.31747e40i	0.522824	−	1.09241i
$666$	1.45584e39	+	2.36184e39i	0.0167008	+	0.0270941i
$667$	−1.66001e41			−1.86331
$668$	−5.80703e40			−0.637816
$669$	3.49921e40	−	9.91817e39i	0.376090	−	0.106599i
$670$		−	5.29898e38i		−	0.00557323i
$671$	−1.49311e41			−1.53680
$672$	2.07139e40	+	3.55960e39i	0.208644	+	0.0358548i
$673$	−7.68644e40			−0.757717			−0.378858	−	0.925455i	$-0.623683\pi$
$673$	−7.68644e40			−0.757717			−0.378858	+	0.925455i	$0.623683\pi$
$674$		−	6.05003e39i		−	0.0583699i
$675$	−6.85341e38	−	6.28559e38i	−0.00647145	−	0.00593528i
$676$	8.06274e40			0.745171
$677$	9.98234e40			0.903018			0.451509	−	0.892266i	$-0.350886\pi$
$677$	9.98234e40			0.903018			0.451509	+	0.892266i	$0.350886\pi$
$678$	1.07196e39	+	3.78196e39i	0.00949177	+	0.0334878i
$679$	1.88842e40	−	3.94573e40i	0.163677	−	0.341992i
$680$		−	2.77412e40i		−	0.235367i
$681$	1.65665e40	+	5.84480e40i	0.137594	+	0.485441i
$682$		−	7.54604e39i		−	0.0613544i
$683$			2.16857e41i			1.72613i	0.505092	+	0.863065i	$0.331459\pi$
$683$			2.16857e41i			1.72613i	−0.505092	+	0.863065i	$0.668541\pi$
$684$	−8.07828e40	−	1.31056e41i	−0.629514	−	1.02127i
$685$			6.86216e40i			0.523538i
$686$	9.25710e39	−	2.18367e39i	0.0691473	−	0.0163112i
$687$	−6.62643e40	+	1.87820e40i	−0.484626	+	0.137363i
$688$	−2.06817e41			−1.48099
$689$	−7.85087e40			−0.550477
$690$	3.06697e39	+	1.08205e40i	0.0210571	+	0.0742911i
$691$		−	2.37839e41i		−	1.59901i	−0.600657	−	0.799507i	$-0.705094\pi$
$691$		−	2.37839e41i		−	1.59901i	0.600657	−	0.799507i	$-0.294906\pi$
$692$	2.35688e41			1.55167
$693$	−2.15305e40	−	2.02334e41i	−0.138810	−	1.30448i
$694$	−9.91991e39			−0.0626319
$695$		−	3.08227e41i		−	1.90586i
$696$	1.09897e40	+	3.87724e40i	0.0665503	+	0.234795i
$697$	−2.31691e41			−1.37415
$698$	−3.37038e39			−0.0195783
$699$	2.77563e41	−	7.86726e40i	1.57922	−	0.447615i
$700$	−1.41412e39	−	6.76795e38i	−0.00788069	−	0.00377168i
$701$			1.20046e41i			0.655293i	0.944800	+	0.327647i	$0.106256\pi$
$701$			1.20046e41i			0.655293i	−0.944800	+	0.327647i	$0.893744\pi$
$702$	4.90632e39	+	4.49982e39i	0.0262342	+	0.0240606i
$703$		−	1.03133e41i		−	0.540186i
$704$		−	2.47963e41i		−	1.27228i
$705$	−6.70031e40	−	2.36392e41i	−0.336785	−	1.18820i
$706$			2.08139e40i			0.102491i
$707$	−2.21762e41	−	1.06135e41i	−1.06981	−	0.512008i
$708$	3.35199e40	+	1.18261e41i	0.158424	+	0.558932i
$709$	−2.47898e41			−1.14790			−0.573948	−	0.818892i	$-0.694589\pi$
$709$	−2.47898e41			−1.14790			−0.573948	+	0.818892i	$0.694589\pi$
$710$	1.00233e40			0.0454740
$711$	2.40166e41	−	1.48038e41i	1.06758	−	0.658059i
$712$		−	2.17952e40i		−	0.0949296i
$713$	−1.66921e41			−0.712384
$714$	−2.76834e40	−	4.75730e39i	−0.115770	−	0.0198946i
$715$	1.61101e41			0.660176
$716$			4.89630e41i			1.96621i
$717$	−1.87290e41	+	5.30855e40i	−0.737033	+	0.208905i
$718$	−8.20719e39			−0.0316512
$719$	1.70882e41			0.645843			0.322921	−	0.946426i	$-0.395335\pi$
$719$	1.70882e41			0.645843			0.322921	+	0.946426i	$0.395335\pi$
$720$	−2.27338e41	+	1.40132e41i	−0.842076	+	0.519057i
$721$	−8.23675e40	+	1.72102e41i	−0.299016	+	0.624775i
$722$		−	9.06382e39i		−	0.0322494i
$723$	5.46417e41	−	1.54877e41i	1.90554	−	0.540108i
$724$			3.60471e41i			1.23214i
$725$		−	4.51285e39i		−	0.0151199i
$726$	1.50048e40	−	4.25297e39i	0.0492777	−	0.0139673i
$727$		−	1.00781e41i		−	0.324437i	−0.986755	−	0.162219i	$-0.948135\pi$
$727$		−	1.00781e41i		−	0.324437i	0.986755	−	0.162219i	$-0.0518650\pi$
$728$	2.02986e40	+	9.71485e39i	0.0640560	+	0.0306571i
$729$	2.78880e40	+	3.22053e41i	0.0862716	+	0.996272i
$730$	−1.64693e39			−0.00499453
$731$	8.36280e41			2.48628
$732$	3.84740e41	−	1.09051e41i	1.12139	−	0.317847i
$733$			2.15111e39i			0.00614689i	0.999995	+	0.00307345i	$0.000978310\pi$
$733$			2.15111e39i			0.00614689i	−0.999995	+	0.00307345i	$0.999022\pi$
$734$	−3.06283e40			−0.0858084
$735$	−2.11431e41	+	2.98322e41i	−0.580769	+	0.819444i
$736$	8.50627e40			0.229092
$737$			3.88003e40i			0.102461i
$738$	−1.19656e40	−	1.94121e40i	−0.0309826	−	0.0502638i
$739$	−3.98177e41			−1.01095			−0.505477	−	0.862840i	$-0.668684\pi$
$739$	−3.98177e41			−1.01095			−0.505477	+	0.862840i	$0.668684\pi$
$740$	−1.79818e41			−0.447685
$741$	−6.74833e40	−	2.38087e41i	−0.164753	−	0.581261i
$742$	2.94079e40	+	1.40746e40i	0.0704057	+	0.0336960i
$743$		−	2.27165e40i		−	0.0533338i	−0.999644	−	0.0266669i	$-0.991511\pi$
$743$		−	2.27165e40i		−	0.0533338i	0.999644	−	0.0266669i	$-0.00848935\pi$
$744$	1.10506e40	+	3.89874e40i	0.0254435	+	0.0897669i
$745$		−	1.16978e41i		−	0.264143i
$746$		−	3.82513e40i		−	0.0847098i
$747$	4.15786e41	−	2.56291e41i	0.903069	−	0.556652i
$748$			1.01307e42i			2.15807i
$749$	2.98821e40	−	6.24368e40i	0.0624346	−	0.130453i
$750$	3.32055e40	−	9.41178e39i	0.0680491	−	0.0192878i
$751$	−4.42565e41			−0.889606			−0.444803	−	0.895628i	$-0.646726\pi$
$751$	−4.42565e41			−0.889606			−0.444803	+	0.895628i	$0.646726\pi$
$752$	−6.14209e41			−1.21104
$753$	9.23286e40	+	3.25743e41i	0.178570	+	0.630010i
$754$			3.23072e40i			0.0612936i
$755$	−2.19802e41			−0.409073
$756$	2.03255e41	+	5.05642e41i	0.371087	+	0.923160i
$757$	−6.37836e41			−1.14240			−0.571201	−	0.820810i	$-0.693522\pi$
$757$	−6.37836e41			−1.14240			−0.571201	+	0.820810i	$0.693522\pi$
$758$		−	1.37242e40i		−	0.0241148i
$759$	−2.24571e41	−	7.92305e41i	−0.387122	−	1.36580i
$760$	−1.01492e41			−0.171647
$761$	−6.94568e41			−1.15249			−0.576245	−	0.817277i	$-0.695483\pi$
$761$	−6.94568e41			−1.15249			−0.576245	+	0.817277i	$0.695483\pi$
$762$	1.59347e40	−	4.51654e39i	0.0259417	−	0.00735291i
$763$	8.67905e41	+	4.15378e41i	1.38633	+	0.663494i
$764$		−	8.73057e41i		−	1.36832i
$765$	9.19261e41	−	5.66633e41i	1.41367	−	0.871387i
$766$		−	2.62444e40i		−	0.0396022i
$767$			1.97583e41i			0.292561i
$768$	1.78279e41	+	6.28983e41i	0.259038	+	0.913905i
$769$			9.66671e41i			1.37831i	0.724614	+	0.689155i	$0.242018\pi$
$769$			9.66671e41i			1.37831i	−0.724614	+	0.689155i	$0.757982\pi$
$770$	−6.03454e40	−	2.88812e40i	−0.0844362	−	0.0404110i
$771$	−1.92230e41	−	6.78202e41i	−0.263956	−	0.931259i
$772$	1.24967e41			0.168400
$773$	5.03598e41			0.666011			0.333005	−	0.942925i	$-0.391937\pi$
$773$	5.03598e41			0.666011			0.333005	+	0.942925i	$0.391937\pi$
$774$	4.31895e40	+	7.00672e40i	0.0560576	+	0.0909434i
$775$		−	4.53787e39i		−	0.00578066i
$776$	−4.29797e40			−0.0537364
$777$	−6.18297e40	+	3.59796e41i	−0.0758740	+	0.441522i
$778$	−7.95855e39			−0.00958583
$779$			8.47651e41i			1.00213i
$780$	−4.15118e41	+	1.17661e41i	−0.481726	+	0.136541i
$781$	−7.33927e41			−0.836012
$782$	−1.13684e41			−0.127116
$783$	−1.06033e42	+	1.15612e42i	−1.16385	+	1.26898i
$784$	5.73348e41	+	7.11864e41i	0.617783	+	0.767033i
$785$			2.15097e41i			0.227522i
$786$	−8.58951e40	+	2.43461e40i	−0.0891952	+	0.0252815i
$787$		−	1.30227e42i		−	1.32760i	−0.747910	−	0.663800i	$-0.768943\pi$
$787$		−	1.30227e42i		−	1.32760i	0.747910	−	0.663800i	$-0.231057\pi$
$788$		−	1.41342e41i		−	0.141462i
$789$	1.22606e42	−	3.47515e41i	1.20475	−	0.341474i
$790$		−	9.27596e40i		−	0.0894882i
$791$	−2.23293e41	+	4.66557e41i	−0.211503	+	0.441922i
$792$	−1.70189e41	+	1.04905e41i	−0.158277	+	0.0975620i
$793$	6.42798e41			0.586967
$794$	−1.46988e41			−0.131791
$795$	−1.20587e42	+	3.41793e41i	−1.06164	+	0.300912i
$796$		−	1.13659e42i		−	0.982574i
$797$	8.91144e41			0.756489			0.378244	−	0.925706i	$-0.376528\pi$
$797$	8.91144e41			0.756489			0.378244	+	0.925706i	$0.376528\pi$
$798$	−1.74048e40	+	1.01281e41i	−0.0145086	+	0.0844279i
$799$	2.48360e42			2.03308
$800$			2.31249e39i			0.00185898i
$801$	7.22229e41	−	4.45182e41i	0.570169	−	0.351452i
$802$	3.98160e40			0.0308695
$803$	1.20592e41			0.0918215
$804$	−2.83381e40	−	9.99793e40i	−0.0211913	−	0.0747648i
$805$	−6.38864e41	+	1.33486e42i	−0.469211	+	0.980386i
$806$			3.24864e40i			0.0234338i
$807$	1.44214e41	+	5.08800e41i	0.102174	+	0.360480i
$808$			2.41559e41i			0.168096i
$809$		−	3.84262e41i		−	0.262648i	−0.991339	−	0.131324i	$-0.958077\pi$
$809$		−	3.84262e41i		−	0.262648i	0.991339	−	0.131324i	$-0.0419228\pi$
$810$	9.49501e40	+	4.77561e40i	0.0637474	+	0.0320624i
$811$		−	2.60021e42i		−	1.71477i	−0.514677	−	0.857384i	$-0.672088\pi$
$811$		−	2.60021e42i		−	1.71477i	0.514677	−	0.857384i	$-0.327912\pi$
$812$	−1.14170e42	+	2.38551e42i	−0.739587	+	1.54532i
$813$	−1.52728e42	+	4.32892e41i	−0.971863	+	0.275465i
$814$	−6.67947e40			−0.0417531
$815$	1.03002e42			0.632497
$816$	−7.36130e41	−	2.59713e42i	−0.444066	−	1.56670i
$817$		−	3.05957e42i		−	1.81318i
$818$	1.03343e41			0.0601667
$819$	9.26906e40	+	8.71066e41i	0.0530175	+	0.498235i
$820$	1.47793e42			0.830526
$821$		−	1.56827e42i		−	0.865852i	−0.901429	−	0.432926i	$-0.857481\pi$
$821$		−	1.56827e42i		−	0.865852i	0.901429	−	0.432926i	$-0.142519\pi$
$822$	−1.86169e40	−	6.56818e40i	−0.0100987	−	0.0356290i
$823$	−1.49843e42			−0.798616			−0.399308	−	0.916817i	$-0.630750\pi$
$823$	−1.49843e42			−0.798616			−0.399308	+	0.916817i	$0.630750\pi$
$824$	1.87465e41			0.0981693
$825$	2.15393e40	−	6.10511e39i	0.0110828	−	0.00314131i
$826$	3.54215e40	−	7.40109e40i	0.0179084	−	0.0374184i
$827$		−	2.87755e42i		−	1.42953i	−0.699365	−	0.714765i	$-0.746534\pi$
$827$		−	2.87755e42i		−	1.42953i	0.699365	−	0.714765i	$-0.253466\pi$
$828$	1.15733e42	+	1.87756e42i	0.564961	+	0.916548i
$829$		−	2.26722e42i		−	1.08756i	−0.839227	−	0.543781i	$-0.816992\pi$
$829$		−	2.26722e42i		−	1.08756i	0.839227	−	0.543781i	$-0.183008\pi$
$830$		−	1.60590e41i		−	0.0756981i
$831$	−1.07473e42	−	3.79172e42i	−0.497832	−	1.75639i
$832$			1.06750e42i			0.485938i
$833$	−2.31838e42	−	2.87848e42i	−1.03713	−	1.28769i
$834$	8.36211e40	+	2.95022e41i	0.0367628	+	0.129702i
$835$	−1.49020e42			−0.643860
$836$	3.70636e42			1.57382
$837$	−1.06621e42	+	1.16253e42i	−0.444962	+	0.485159i
$838$		−	1.93347e41i		−	0.0793048i
$839$	1.16752e42			0.470669			0.235335	−	0.971914i	$-0.424381\pi$
$839$	1.16752e42			0.470669			0.235335	+	0.971914i	$0.424381\pi$
$840$	3.54075e41	+	6.08465e40i	0.140296	+	0.0241094i
$841$	−5.04514e42			−1.96486
$842$		−	2.85866e41i		−	0.109430i
$843$	−4.39200e42	+	1.24487e42i	−1.65258	+	0.468407i
$844$	8.19756e41			0.303193
$845$	2.06906e42			0.752232
$846$	1.28265e41	+	2.08087e41i	0.0458393	+	0.0743661i
$847$	1.85106e42	+	8.85912e41i	0.650295	+	0.311230i
$848$			3.13317e42i			1.08204i
$849$	−1.32652e42	+	3.75988e41i	−0.450351	+	0.127648i
$850$		−	3.09056e39i		−	0.00103149i
$851$			1.47752e42i			0.484793i
$852$	1.89115e42	−	5.36029e41i	0.610032	−	0.172908i
$853$			5.10638e42i			1.61939i	0.586848	+	0.809697i	$0.300369\pi$
$853$			5.10638e42i			1.61939i	−0.586848	+	0.809697i	$0.699631\pi$
$854$	−2.40781e41	−	1.15237e41i	−0.0750728	−	0.0359297i
$855$	−2.07305e42	−	3.36316e42i	−0.635480	−	1.03095i
$856$	−6.80105e40			−0.0204978
$857$	5.00930e41			0.148442			0.0742208	−	0.997242i	$-0.476353\pi$
$857$	5.00930e41			0.148442			0.0742208	+	0.997242i	$0.476353\pi$
$858$	−1.54199e41	+	4.37062e40i	−0.0449279	+	0.0127344i
$859$		−	5.99895e42i		−	1.71860i	−0.511474	−	0.859299i	$-0.670900\pi$
$859$		−	5.99895e42i		−	1.71860i	0.511474	−	0.859299i	$-0.329100\pi$
$860$	−5.33454e42			−1.50269
$861$	5.08182e41	−	2.95719e42i	0.140758	−	0.819092i
$862$	−6.57430e40			−0.0179058
$863$		−	3.24682e41i		−	0.0869563i	−0.999054	−	0.0434782i	$-0.986156\pi$
$863$		−	3.24682e41i		−	0.0869563i	0.999054	−	0.0434782i	$-0.0138439\pi$
$864$	5.43337e41	−	5.92420e41i	0.143094	−	0.156020i
$865$	6.04824e42			1.56637
$866$	4.44419e40			0.0113184
$867$	1.88778e42	+	6.66023e42i	0.472796	+	1.66806i
$868$	−1.14803e42	+	2.39873e42i	−0.282759	+	0.590808i
$869$			6.79207e42i			1.64519i
$870$	1.40652e41	+	4.96231e41i	0.0335055	+	0.118210i
$871$		−	1.67039e41i		−	0.0391340i
$872$		−	9.45383e41i		−	0.217831i
$873$	−8.77889e41	−	1.42422e42i	−0.198945	−	0.322753i
$874$			4.15916e41i			0.0927022i
$875$	4.09637e42	+	1.96051e42i	0.898012	+	0.429787i
$876$	−3.10738e41	+	8.80755e40i	−0.0670015	+	0.0189909i
$877$	4.47941e42			0.950007			0.475003	−	0.879984i	$-0.342447\pi$
$877$	4.47941e42			0.950007			0.475003	+	0.879984i	$0.342447\pi$
$878$	−3.65886e41			−0.0763264
$879$	1.09424e42	+	3.86057e42i	0.224530	+	0.792160i
$880$		−	6.42931e42i		−	1.29767i
$881$	−5.93686e42			−1.17871			−0.589354	−	0.807875i	$-0.700618\pi$
$881$	−5.93686e42			−1.17871			−0.589354	+	0.807875i	$0.700618\pi$
$882$	1.21439e41	−	3.42902e41i	0.0237173	−	0.0669694i
$883$	8.97460e42			1.72419			0.862094	−	0.506748i	$-0.169153\pi$
$883$	8.97460e42			1.72419			0.862094	+	0.506748i	$0.169153\pi$
$884$		−	4.36135e42i		−	0.824257i
$885$	8.60190e41	+	3.03482e42i	0.159925	+	0.564229i
$886$	3.04346e41			0.0556645
$887$	2.15017e42			0.386884			0.193442	−	0.981112i	$-0.438035\pi$
$887$	2.15017e42			0.386884			0.193442	+	0.981112i	$0.438035\pi$
$888$	3.45101e41	−	9.78156e40i	0.0610884	−	0.0173149i
$889$	1.96577e42	+	9.40815e41i	0.342340	+	0.163843i
$890$		−	2.78948e41i		−	0.0477934i
$891$	−6.95247e42	−	3.49681e42i	−1.17196	−	0.589448i
$892$		−	2.34511e42i		−	0.388932i
$893$		−	9.08636e42i		−	1.48267i
$894$	3.17359e40	+	1.11967e41i	0.00509514	+	0.0179761i
$895$			1.25649e43i			1.98484i
$896$	7.79376e41	−	1.62846e42i	0.121138	−	0.253110i
$897$	9.66797e41	+	3.41094e42i	0.147858	+	0.521655i
$898$	−3.43942e41			−0.0517582
$899$	−7.65503e42			−1.13353
$900$	−5.10428e40	+	3.14628e40i	−0.00743735	+	0.00458439i
$901$		−	1.26692e43i		−	1.81652i
$902$	5.48989e41			0.0774585
$903$	−1.83426e42	+	1.06739e43i	−0.254677	+	1.48200i
$904$	5.08207e41			0.0694382
$905$			9.25043e42i			1.24382i
$906$	2.10385e41	−	5.96316e40i	0.0278392	−	0.00789074i
$907$	6.97609e42			0.908461			0.454231	−	0.890884i	$-0.349914\pi$
$907$	6.97609e42			0.908461			0.454231	+	0.890884i	$0.349914\pi$
$908$	3.91709e42			0.502018
$909$	−8.00454e42	+	4.93401e42i	−1.00963	+	0.622334i
$910$	2.59792e41	+	1.24336e41i	0.0322497	+	0.0154347i
$911$			9.01807e42i			1.10179i	0.834576	+	0.550893i	$0.185713\pi$
$911$			9.01807e42i			1.10179i	−0.834576	+	0.550893i	$0.814287\pi$
$912$	−9.50171e42	+	2.69316e42i	−1.14255	+	0.323845i
$913$			1.17587e43i			1.39167i
$914$		−	1.78633e41i		−	0.0208085i
$915$	9.87322e42	−	2.79847e42i	1.13202	−	0.320859i
$916$			4.44093e42i			0.501175i
$917$	−1.05964e43	−	5.07140e42i	−1.17707	−	0.563343i
$918$	−7.26152e41	+	7.91750e41i	−0.0793979	+	0.0865704i
$919$	1.24267e43			1.33746			0.668729	−	0.743506i	$-0.266838\pi$
$919$	1.24267e43			1.33746			0.668729	+	0.743506i	$0.266838\pi$
$920$	1.45403e42			0.154046
$921$	3.30683e42	−	9.37289e41i	0.344864	−	0.0977482i
$922$		−	4.36066e39i		−	0.000447665i
$923$	3.15962e42			0.319308
$924$	−1.29303e43	−	2.22203e42i	−1.28637	−	0.221058i
$925$	−4.01675e40			−0.00393387
$926$			4.79100e41i			0.0461920i
$927$	3.82910e42	+	6.21203e42i	0.363447	+	0.589627i
$928$	3.90098e42			0.364526
$929$	−2.01687e42			−0.185546			−0.0927728	−	0.995687i	$-0.529573\pi$
$929$	−2.01687e42			−0.185546			−0.0927728	+	0.995687i	$0.529573\pi$
$930$	1.41432e41	+	4.98982e41i	0.0128098	+	0.0451941i
$931$	−1.05310e43	+	8.48189e42i	−0.939076	+	0.756349i
$932$		−	1.86018e43i		−	1.63315i
$933$	−1.63315e42	−	5.76189e42i	−0.141170	−	0.498059i
$934$			1.93189e41i			0.0164419i
$935$			2.59974e43i			2.17852i
$936$	7.32680e41	−	4.51624e41i	0.0604525	−	0.0372630i
$937$			8.46691e42i			0.687861i	0.938995	+	0.343931i	$0.111759\pi$
$937$			8.46691e42i			0.687861i	−0.938995	+	0.343931i	$0.888241\pi$
$938$	−2.99458e40	+	6.25697e40i	−0.00239549	+	0.00500522i
$939$	5.42874e42	−	1.53872e42i	0.427610	−	0.121202i
$940$	−1.58426e43			−1.22878
$941$	8.42086e42			0.643142			0.321571	−	0.946886i	$-0.395789\pi$
$941$	8.42086e42			0.643142			0.321571	+	0.946886i	$0.395789\pi$
$942$	−5.83552e40	−	2.05882e41i	−0.00438875	−	0.0154839i
$943$		−	1.21439e43i		−	0.899367i
$944$	7.88525e42			0.575071
$945$	5.21595e42	+	1.29758e43i	0.374604	+	0.931908i
$946$	−1.98156e42			−0.140147
$947$		−	2.00844e43i		−	1.39889i	−0.714686	−	0.699446i	$-0.753430\pi$
$947$		−	2.00844e43i		−	1.39889i	0.714686	−	0.699446i	$-0.246570\pi$
$948$	−4.96064e42	−	1.75016e43i	−0.340265	−	1.20048i
$949$	−5.19160e41			−0.0350704
$950$	−1.13070e40			−0.000752235
$951$	−1.34547e43	+	3.81362e42i	−0.881572	+	0.249873i
$952$	−1.56772e42	+	3.27565e42i	−0.101166	+	0.211379i
$953$		−	1.10066e43i		−	0.699532i	−0.936837	−	0.349766i	$-0.886261\pi$
$953$		−	1.10066e43i		−	0.699532i	0.936837	−	0.349766i	$-0.113739\pi$
$954$	1.06148e42	−	6.54300e41i	0.0664450	−	0.0409567i
$955$		−	2.24044e43i		−	1.38129i
$956$			1.25519e43i			0.762200i
$957$	−1.02988e43	−	3.63352e43i	−0.615979	−	2.17322i
$958$		−	1.89735e42i		−	0.111776i
$959$	3.87797e42	−	8.10277e42i	0.225027	−	0.470179i
$960$	4.64744e42	+	1.63966e43i	0.265633	+	0.937173i
$961$	1.00644e43			0.566630
$962$	2.87557e41			0.0159472
$963$	−1.38916e42	−	2.25367e42i	−0.0758877	−	0.123114i
$964$		−	3.66200e43i		−	1.97061i
$965$	3.20690e42			0.169996
$966$	2.49349e41	−	1.45100e42i	0.0130208	−	0.0757702i
$967$	−2.47113e43			−1.27119			−0.635596	−	0.772022i	$-0.719246\pi$
$967$	−2.47113e43			−1.27119			−0.635596	+	0.772022i	$0.719246\pi$
$968$		−	2.01630e42i		−	0.102179i
$969$	3.84209e43	−	1.08900e43i	1.91811	−	0.543669i
$970$	−5.50078e41			−0.0270542
$971$	1.78850e43			0.866585			0.433293	−	0.901253i	$-0.357352\pi$
$971$	1.78850e43			0.866585			0.433293	+	0.901253i	$0.357352\pi$
$972$	2.04688e43	+	3.93266e42i	0.977082	+	0.187727i
$973$	−1.74186e43	+	3.63951e43i	−0.819177	+	1.71162i
$974$			1.66588e42i			0.0771861i
$975$	−9.27287e40	+	2.62830e40i	−0.00423299	+	0.00119980i
$976$		−	2.56532e43i		−	1.15377i
$977$		−	9.02248e42i		−	0.399811i	−0.979815	−	0.199905i	$-0.935936\pi$
$977$		−	9.02248e42i		−	0.399811i	0.979815	−	0.199905i	$-0.0640635\pi$
$978$	−9.85889e41	+	2.79440e41i	−0.0430442	+	0.0122005i
$979$			2.04252e43i			0.878653i
$980$	1.47887e43	+	1.83615e43i	0.626833	+	0.778270i
$981$	3.13272e43	−	1.93101e43i	1.30834	−	0.806462i
$982$	2.26767e42			0.0933176
$983$	−4.43159e43			−1.79694			−0.898470	−	0.439035i	$-0.855321\pi$
$983$	−4.43159e43			−1.79694			−0.898470	+	0.439035i	$0.855321\pi$
$984$	−2.83641e42	+	8.03951e41i	−0.113329	+	0.0321219i
$985$		−	3.62712e42i		−	0.142803i
$986$	−5.21354e42			−0.202263
$987$	−5.44743e42	+	3.16994e43i	−0.208254	+	1.21186i
$988$	−1.59562e43			−0.601109
$989$			4.38328e43i			1.62724i
$990$	−2.17818e42	+	1.34263e42i	−0.0796862	+	0.0491186i
$991$	1.15255e42			0.0415521			0.0207761	−	0.999784i	$-0.493386\pi$
$991$	1.15255e42			0.0415521			0.0207761	+	0.999784i	$0.493386\pi$
$992$	3.92261e42			0.139366
$993$	1.11116e41	+	3.92028e41i	0.00389058	+	0.0137263i
$994$	−1.18354e42	−	5.66438e41i	−0.0408393	−	0.0195456i
$995$		−	2.91673e43i		−	0.991885i
$996$	−8.58809e42	−	3.02995e43i	−0.287830	−	1.01549i
$997$		−	2.62939e43i		−	0.868510i	−0.900790	−	0.434255i	$-0.857012\pi$
$997$		−	2.62939e43i		−	0.868510i	0.900790	−	0.434255i	$-0.142988\pi$
$998$		−	5.00552e41i		−	0.0162951i
$999$	1.02902e43	+	9.43768e42i	0.330161	+	0.302807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.30.c.a.20.20	yes	76
3.2	odd	2	inner	21.30.c.a.20.57	yes	76
7.6	odd	2	inner	21.30.c.a.20.58	yes	76
21.20	even	2	inner	21.30.c.a.20.19	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.30.c.a.20.19	✓	76	21.20	even	2	inner
21.30.c.a.20.20	yes	76	1.1	even	1	trivial
21.30.c.a.20.57	yes	76	3.2	odd	2	inner
21.30.c.a.20.58	yes	76	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	21.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1646.15i q^{2} +(2.25912e6 + 7.97037e6i) q^{3} +5.34161e8 q^{4} +1.37077e10 q^{5} +(-1.31204e10 + 3.71885e9i) q^{6} +(-1.61859e12 - 7.74652e11i) q^{7} +1.76308e12i q^{8} +(-5.84231e13 + 3.60121e13i) q^{9} +O(q^{10})\)	\(q+1646.15i q^{2} +(2.25912e6 + 7.97037e6i) q^{3} +5.34161e8 q^{4} +1.37077e10 q^{5} +(-1.31204e10 + 3.71885e9i) q^{6} +(-1.61859e12 - 7.74652e11i) q^{7} +1.76308e12i q^{8} +(-5.84231e13 + 3.60121e13i) q^{9} +2.25649e13i q^{10} -1.65225e15i q^{11} +(1.20674e15 + 4.25746e15i) q^{12} +7.11308e15i q^{13} +(1.27519e15 - 2.66443e15i) q^{14} +(3.09673e16 + 1.09255e17i) q^{15} +2.83873e17 q^{16} -1.14786e18 q^{17} +(-5.92812e16 - 9.61731e16i) q^{18} +4.19951e18i q^{19} +7.32210e18 q^{20} +(2.51768e18 - 1.46508e19i) q^{21} +2.71985e18 q^{22} -6.01642e19i q^{23} +(-1.40524e19 + 3.98301e18i) q^{24} +1.63560e18 q^{25} -1.17092e19 q^{26} +(-4.19014e20 - 3.84298e20i) q^{27} +(-8.64586e20 - 4.13789e20i) q^{28} -2.75913e21i q^{29} +(-1.79850e20 + 5.09768e19i) q^{30} -2.77443e21i q^{31} +1.41384e21i q^{32} +(1.31691e22 - 3.73264e21i) q^{33} -1.88956e21i q^{34} +(-2.21870e22 - 1.06187e22i) q^{35} +(-3.12074e22 + 1.92362e22i) q^{36} -2.45582e22 q^{37} -6.91302e21 q^{38} +(-5.66939e22 + 1.60693e22i) q^{39} +2.41677e22i q^{40} +2.01845e23 q^{41} +(2.41173e22 + 4.14448e21i) q^{42} -7.28553e23 q^{43} -8.82569e23i q^{44} +(-8.00845e23 + 4.93641e23i) q^{45} +9.90392e22 q^{46} -2.16367e24 q^{47} +(6.41304e23 + 2.26257e24i) q^{48} +(2.01973e24 + 2.50768e24i) q^{49} +2.69244e21i q^{50} +(-2.59317e24 - 9.14890e24i) q^{51} +3.79953e24i q^{52} +1.10372e25i q^{53} +(6.32612e23 - 6.89760e23i) q^{54} -2.26485e25i q^{55} +(1.36577e24 - 2.85369e24i) q^{56} +(-3.34716e25 + 9.48721e24i) q^{57} +4.54195e24 q^{58} +2.77774e25 q^{59} +(1.65415e25 + 5.83598e25i) q^{60} -9.03685e25i q^{61} +4.56713e24 q^{62} +(1.22460e26 - 1.30310e25i) q^{63} +1.50076e26 q^{64} +9.75038e25i q^{65} +(6.14448e24 + 2.16782e25i) q^{66} -2.34833e25 q^{67} -6.13144e26 q^{68} +(4.79530e26 - 1.35918e26i) q^{69} +(1.74799e25 - 3.65232e25i) q^{70} -4.44198e26i q^{71} +(-6.34921e25 - 1.03004e26i) q^{72} +7.29866e25i q^{73} -4.04265e25i q^{74} +(3.69503e24 + 1.30364e25i) q^{75} +2.24322e27i q^{76} +(-1.27992e27 + 2.67431e27i) q^{77} +(-2.64525e25 - 9.33266e25i) q^{78} -4.11080e27 q^{79} +3.89124e27 q^{80} +(2.11639e27 - 4.20787e27i) q^{81} +3.32267e26i q^{82} -7.11680e27 q^{83} +(1.34485e27 - 7.82586e27i) q^{84} -1.57345e28 q^{85} -1.19931e27i q^{86} +(2.19913e28 - 6.23322e27i) q^{87} +2.91305e27 q^{88} -1.23620e28 q^{89} +(-8.12607e26 - 1.31831e27i) q^{90} +(5.51017e27 - 1.15131e28i) q^{91} -3.21374e28i q^{92} +(2.21132e28 - 6.26778e27i) q^{93} -3.56173e27i q^{94} +5.75655e28i q^{95} +(-1.12688e28 + 3.19404e27i) q^{96} +2.43776e28i q^{97} +(-4.12802e27 + 3.32478e27i) q^{98} +(5.95010e28 + 9.65297e28i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9}+O(q^{10}) \) 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9	\( 76 q - 20401094660 q^{4} + 1962751543872 q^{7} - 89581451225964 q^{9} - 11\!\cdots\!48 q^{15}+ \cdots - 23\!\cdots\!24 q^{99}+O(q^{100}) \) 76 * q - 20401094660 * q^4 + 1962751543872 * q^7 - 89581451225964 * q^9 - 116668222909200048 * q^15 + 4964525139713333892 * q^16 + 1542346202347854996 * q^18 + 33840646982361357348 * q^21 - 9870996616978150672 * q^22 + 3225406746743103424612 * q^25 - 3181907581338093199564 * q^28 + 5113912044496410095244 * q^30 - 85758641407134848258352 * q^36 - 17812771227715200149976 * q^37 + 388095283792424641491696 * q^39 + 804036587819434104664956 * q^42 + 2391536152977907871782320 * q^43 - 1070985628070611677307000 * q^46 - 512656982878691867441540 * q^49 - 961431915936904000664400 * q^51 + 20345422731681279280765248 * q^57 - 40096240109469024574169272 * q^58 - 164991837955115951799442596 * q^60 - 360764839802574990409097184 * q^63 - 1608343949909674725081473028 * q^64 + 483978610969894046870693264 * q^67 - 656026306765550013508448520 * q^70 + 1937172856654554597960695124 * q^72 - 8054141680325499868559088636 * q^78 - 11740735193468750125742145952 * q^79 + 18477545939654446572971367132 * q^81 - 7249045143271847568431965452 * q^84 + 14576359553686844022629140848 * q^85 - 1685535263940707754634995584 * q^88 + 44135166284535829618726469040 * q^91 + 226499776928895503792863540632 * q^93 - 231093384978708762520959066624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more