LMFDB - Embedded newform 54.9.f.a.11.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [54,9,Mod(5,54)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(54, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("54.5");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	54.f (of order $18$, degree $6$, 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:	$21.9984449433$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.16
Character	$\chi$	$=$	54.11
Dual form			54.9.f.a.5.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(7.27231 - 8.66680i) q^{2} +(-62.6465 - 51.3460i) q^{3} +(-22.2270 - 126.055i) q^{4} +(-16.8419 + 46.2726i) q^{5} +(-900.591 + 169.541i) q^{6} +(-338.197 + 1918.01i) q^{7} +(-1254.14 - 724.077i) q^{8} +(1288.18 + 6433.30i) q^{9} +O(q^{10})$	\(q+(7.27231 - 8.66680i) q^{2} +(-62.6465 - 51.3460i) q^{3} +(-22.2270 - 126.055i) q^{4} +(-16.8419 + 46.2726i) q^{5} +(-900.591 + 169.541i) q^{6} +(-338.197 + 1918.01i) q^{7} +(-1254.14 - 724.077i) q^{8} +(1288.18 + 6433.30i) q^{9} +(278.556 + 482.474i) q^{10} +(2872.37 + 7891.77i) q^{11} +(-5080.00 + 9038.20i) q^{12} +(2160.72 - 1813.06i) q^{13} +(14163.5 + 16879.4i) q^{14} +(3431.00 - 2034.06i) q^{15} +(-15395.9 + 5603.66i) q^{16} +(5038.37 - 2908.90i) q^{17} +(65124.2 + 35620.5i) q^{18} +(15717.3 - 27223.1i) q^{19} +(6207.26 + 1094.51i) q^{20} +(119669. - 102792. i) q^{21} +(89285.2 + 32497.2i) q^{22} +(247135. - 43576.6i) q^{23} +(41389.0 + 109756. i) q^{24} +(297379. + 249530. i) q^{25} -31911.7i q^{26} +(249624. - 469167. i) q^{27} +249292. q^{28} +(90397.1 - 107731. i) q^{29} +(7322.50 - 44528.1i) q^{30} +(105847. + 600286. i) q^{31} +(-63398.2 + 174185. i) q^{32} +(225267. - 641877. i) q^{33} +(11429.7 - 64821.0i) q^{34} +(-83055.4 - 47952.1i) q^{35} +(782319. - 305375. i) q^{36} +(-271513. - 470275. i) q^{37} +(-121636. - 334193. i) q^{38} +(-228455. + 2637.63i) q^{39} +(54627.0 - 45837.5i) q^{40} +(2.33519e6 + 2.78297e6i) q^{41} +(-20605.0 - 1.78468e6i) q^{42} +(-1.89175e6 + 688539. i) q^{43} +(930956. - 537488. i) q^{44} +(-319381. - 48741.2i) q^{45} +(1.41957e6 - 2.45877e6i) q^{46} +(4.29240e6 + 756865. i) q^{47} +(1.25223e6 + 439469. i) q^{48} +(1.85276e6 + 674350. i) q^{49} +(4.32526e6 - 762660. i) q^{50} +(-464997. - 76467.2i) q^{51} +(-276572. - 232072. i) q^{52} +6.92620e6i q^{53} +(-2.25083e6 - 5.57537e6i) q^{54} -413549. q^{55} +(1.81293e6 - 2.16057e6i) q^{56} +(-2.38243e6 + 898415. i) q^{57} +(-276288. - 1.56691e6i) q^{58} +(-2.87289e6 + 7.89321e6i) q^{59} +(-332665. - 387285. i) q^{60} +(-897172. + 5.08811e6i) q^{61} +(5.97231e6 + 3.44811e6i) q^{62} +(-1.27748e7 + 295021. i) q^{63} +(1.04858e6 + 1.81619e6i) q^{64} +(47504.5 + 130518. i) q^{65} +(-3.92481e6 - 6.62027e6i) q^{66} +(-7.33162e6 + 6.15196e6i) q^{67} +(-478671. - 570457. i) q^{68} +(-1.77196e7 - 9.95946e6i) q^{69} +(-1.01960e6 + 371103. i) q^{70} +(-3.70974e7 + 2.14182e7i) q^{71} +(3.04265e6 - 9.00099e6i) q^{72} +(4.34939e6 - 7.53337e6i) q^{73} +(-6.05031e6 - 1.06683e6i) q^{74} +(-5.81737e6 - 3.09014e7i) q^{75} +(-3.78097e6 - 1.37616e6i) q^{76} +(-1.61079e7 + 2.84026e6i) q^{77} +(-1.63854e6 + 1.99916e6i) q^{78} +(-1.83181e7 - 1.53707e7i) q^{79} -806786. i q^{80} +(-3.97279e7 + 1.65745e7i) q^{81} +4.11016e7 q^{82} +(-2.80636e7 + 3.34449e7i) q^{83} +(-1.56173e7 - 1.28002e7i) q^{84} +(49747.1 + 282130. i) q^{85} +(-7.78993e6 + 2.14027e7i) q^{86} +(-1.11946e7 + 2.10745e6i) q^{87} +(2.11190e6 - 1.19772e7i) q^{88} +(4.04206e7 + 2.33369e7i) q^{89} +(-2.74507e6 + 2.41355e6i) q^{90} +(2.74672e6 + 4.75746e6i) q^{91} +(-1.09861e7 - 3.01841e7i) q^{92} +(2.41913e7 - 4.30406e7i) q^{93} +(3.77752e7 - 3.16972e7i) q^{94} +(994976. + 1.18577e6i) q^{95} +(1.29154e7 - 7.65685e6i) q^{96} +(1.63107e8 - 5.93660e7i) q^{97} +(1.93183e7 - 1.11534e7i) q^{98} +(-4.70700e7 + 2.86448e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) $ 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	7.27231	−	8.66680i	0.454519	−	0.541675i
$2$	7.27231	−	8.66680i	0.454519	−	0.541675i
$3$	−62.6465	−	51.3460i	−0.773414	−	0.633901i
$3$	−62.6465	−	51.3460i	−0.773414	−	0.633901i
$4$	−22.2270	−	126.055i	−0.0868241	−	0.492404i
$5$	−16.8419	+	46.2726i	−0.0269470	+	0.0740362i	−0.952437	−	0.304737i	$-0.901432\pi$
$5$	−16.8419	+	46.2726i	−0.0269470	+	0.0740362i	0.925490	+	0.378773i	$0.123654\pi$
$6$	−900.591	+	169.541i	−0.694900	+	0.130819i
$7$	−338.197	+	1918.01i	−0.140857	+	0.798838i	0.829744	+	0.558143i	$0.188486\pi$
$7$	−338.197	+	1918.01i	−0.140857	+	0.798838i	−0.970601	+	0.240694i	$0.922625\pi$
$8$	−1254.14	−	724.077i	−0.306186	−	0.176777i
$9$	1288.18	+	6433.30i	0.196339	+	0.980536i
$10$	278.556	+	482.474i	0.0278556	+	0.0482474i
$11$	2872.37	+	7891.77i	0.196187	+	0.539019i	0.998308	−	0.0581422i	$-0.0185177\pi$
$11$	2872.37	+	7891.77i	0.196187	+	0.539019i	−0.802122	+	0.597161i	$0.796295\pi$
$12$	−5080.00	+	9038.20i	−0.244984	+	0.435870i
$13$	2160.72	−	1813.06i	0.0756529	−	0.0634803i	−0.604177	−	0.796850i	$-0.706498\pi$
$13$	2160.72	−	1813.06i	0.0756529	−	0.0634803i	0.679830	+	0.733370i	$0.262054\pi$
$14$	14163.5	+	16879.4i	0.368688	+	0.439386i
$15$	3431.00	−	2034.06i	0.0677728	−	0.0401789i
$16$	−15395.9	+	5603.66i	−0.234923	+	0.0855050i
$17$	5038.37	−	2908.90i	0.0603246	−	0.0348284i	−0.469534	−	0.882914i	$-0.655578\pi$
$17$	5038.37	−	2908.90i	0.0603246	−	0.0348284i	0.529859	+	0.848086i	$0.322245\pi$
$18$	65124.2	+	35620.5i	0.620372	+	0.339321i
$19$	15717.3	−	27223.1i	0.120604	−	0.208893i	−0.799402	−	0.600797i	$-0.794850\pi$
$19$	15717.3	−	27223.1i	0.120604	−	0.208893i	0.920006	+	0.391904i	$0.128183\pi$
$20$	6207.26	+	1094.51i	0.0387954	+	0.00684067i
$21$	119669.	−	102792.i	0.615324	−	0.528543i
$22$	89285.2	+	32497.2i	0.381144	+	0.138725i
$23$	247135.	−	43576.6i	0.883126	−	0.155719i	0.286348	−	0.958126i	$-0.407559\pi$
$23$	247135.	−	43576.6i	0.883126	−	0.155719i	0.596778	+	0.802407i	$0.296447\pi$
$24$	41389.0	+	109756.i	0.124750	+	0.330813i
$25$	297379.	+	249530.i	0.761289	+	0.638798i
$26$		−	31911.7i		−	0.0698323i
$27$	249624.	−	469167.i	0.469711	−	0.882820i
$28$	249292.			0.405580
$29$	90397.1	−	107731.i	0.127809	−	0.152317i	−0.698345	−	0.715762i	$-0.746080\pi$
$29$	90397.1	−	107731.i	0.127809	−	0.152317i	0.826154	+	0.563444i	$0.190524\pi$
$30$	7322.50	−	44528.1i	0.00904012	−	0.0549729i
$31$	105847.	+	600286.i	0.114612	+	0.649997i	0.986942	+	0.161079i	$0.0514973\pi$
$31$	105847.	+	600286.i	0.114612	+	0.649997i	−0.872330	+	0.488918i	$0.837392\pi$
$32$	−63398.2	+	174185.i	−0.0604612	+	0.166116i
$33$	225267.	−	641877.i	0.189951	−	0.541248i
$34$	11429.7	−	64821.0i	0.00855301	−	0.0485065i
$35$	−83055.4	−	47952.1i	−0.0553472	−	0.0319547i
$36$	782319.	−	305375.i	0.465773	−	0.181812i
$37$	−271513.	−	470275.i	−0.144872	−	0.250926i	0.784453	−	0.620188i	$-0.212944\pi$
$37$	−271513.	−	470275.i	−0.144872	−	0.250926i	−0.929325	+	0.369262i	$0.879610\pi$
$38$	−121636.	−	334193.i	−0.0583350	−	0.160274i
$39$	−228455.	+	2637.63i	−0.0987513	+	0.00114013i
$40$	54627.0	−	45837.5i	0.0213387	−	0.0179053i
$41$	2.33519e6	+	2.78297e6i	0.826392	+	0.984856i	1.00000		4.09152e-5i	$1.30237e-5\pi$
$41$	2.33519e6	+	2.78297e6i	0.826392	+	0.984856i	−0.173608	+	0.984815i	$0.555543\pi$
$42$	−20605.0	−	1.78468e6i	−0.00662179	−	0.573539i
$43$	−1.89175e6	+	688539.i	−0.553336	+	0.201398i	−0.603528	−	0.797342i	$-0.706239\pi$
$43$	−1.89175e6	+	688539.i	−0.553336	+	0.201398i	0.0501921	+	0.998740i	$0.484017\pi$
$44$	930956.	−	537488.i	0.248381	−	0.143403i
$45$	−319381.	−	48741.2i	−0.0778859	−	0.0118863i
$46$	1.41957e6	−	2.45877e6i	0.317049	−	0.549145i
$47$	4.29240e6	+	756865.i	0.879647	+	0.155105i	0.595192	−	0.803584i	$-0.297076\pi$
$47$	4.29240e6	+	756865.i	0.879647	+	0.155105i	0.284455	+	0.958689i	$0.408187\pi$
$48$	1.25223e6	+	439469.i	0.235895	+	0.0827872i
$49$	1.85276e6	+	674350.i	0.321392	+	0.116977i
$50$	4.32526e6	−	762660.i	0.692042	−	0.122026i
$51$	−464997.	−	76467.2i	−0.0687336	−	0.0113030i
$52$	−276572.	−	232072.i	−0.0378264	−	0.0317402i
$53$			6.92620e6i			0.877792i	0.898538	+	0.438896i	$0.144630\pi$
$53$			6.92620e6i			0.877792i	−0.898538	+	0.438896i	$0.855370\pi$
$54$	−2.25083e6	−	5.57537e6i	−0.264709	−	0.655690i
$55$	−413549.			−0.0451935
$56$	1.81293e6	−	2.16057e6i	0.184344	−	0.219693i
$57$	−2.38243e6	+	898415.i	−0.225694	+	0.0851094i
$58$	−276288.	−	1.56691e6i	−0.0244146	−	0.138462i
$59$	−2.87289e6	+	7.89321e6i	−0.237089	+	0.651397i	0.762899	+	0.646518i	$0.223775\pi$
$59$	−2.87289e6	+	7.89321e6i	−0.237089	+	0.651397i	−0.999988	+	0.00487933i	$0.998447\pi$
$60$	−332665.	−	387285.i	−0.0256686	−	0.0298831i
$61$	−897172.	+	5.08811e6i	−0.0647972	+	0.367483i	0.935116	+	0.354341i	$0.115295\pi$
$61$	−897172.	+	5.08811e6i	−0.0647972	+	0.367483i	−0.999914	+	0.0131426i	$0.995816\pi$
$62$	5.97231e6	+	3.44811e6i	0.404181	+	0.233354i
$63$	−1.27748e7	+	295021.i	−0.810945	+	0.0187280i
$64$	1.04858e6	+	1.81619e6i	0.0625000	+	0.108253i
$65$	47504.5	+	130518.i	0.00266122	+	0.00731165i
$66$	−3.92481e6	−	6.62027e6i	−0.206844	−	0.348899i
$67$	−7.33162e6	+	6.15196e6i	−0.363832	+	0.305291i	−0.806316	−	0.591485i	$-0.798542\pi$
$67$	−7.33162e6	+	6.15196e6i	−0.363832	+	0.305291i	0.442484	+	0.896776i	$0.354097\pi$
$68$	−478671.	−	570457.i	−0.0223873	−	0.0266801i
$69$	−1.77196e7	−	9.95946e6i	−0.781733	−	0.439379i
$70$	−1.01960e6	+	371103.i	−0.0424655	+	0.0154562i
$71$	−3.70974e7	+	2.14182e7i	−1.45986	+	0.842848i	−0.999004	−	0.0446290i	$-0.985789\pi$
$71$	−3.70974e7	+	2.14182e7i	−1.45986	+	0.842848i	−0.460852	+	0.887477i	$0.652456\pi$
$72$	3.04265e6	−	9.00099e6i	0.113220	−	0.334935i
$73$	4.34939e6	−	7.53337e6i	0.153157	−	0.265276i	−0.779229	−	0.626739i	$-0.784389\pi$
$73$	4.34939e6	−	7.53337e6i	0.153157	−	0.265276i	0.932386	+	0.361463i	$0.117723\pi$
$74$	−6.05031e6	−	1.06683e6i	−0.201767	−	0.0355770i
$75$	−5.81737e6	−	3.09014e7i	−0.183858	−	0.976637i
$76$	−3.78097e6	−	1.37616e6i	−0.113331	−	0.0412491i
$77$	−1.61079e7	+	2.84026e6i	−0.458222	+	0.0807970i
$78$	−1.63854e6	+	1.99916e6i	−0.0442668	+	0.0540093i
$79$	−1.83181e7	−	1.53707e7i	−0.470296	−	0.394626i	0.376606	−	0.926373i	$-0.377091\pi$
$79$	−1.83181e7	−	1.53707e7i	−0.470296	−	0.394626i	−0.846903	+	0.531748i	$0.821535\pi$
$80$		−	806786.i		−	0.0196969i
$81$	−3.97279e7	+	1.65745e7i	−0.922902	+	0.385035i
$82$	4.11016e7			0.909083
$83$	−2.80636e7	+	3.34449e7i	−0.591332	+	0.704722i	−0.975861	−	0.218391i	$-0.929919\pi$
$83$	−2.80636e7	+	3.34449e7i	−0.591332	+	0.704722i	0.384529	+	0.923113i	$0.374364\pi$
$84$	−1.56173e7	−	1.28002e7i	−0.313682	−	0.257098i
$85$	49747.1	+	282130.i	0.000952998	+	0.00540472i
$86$	−7.78993e6	+	2.14027e7i	−0.142410	+	0.391268i
$87$	−1.11946e7	+	2.10745e6i	−0.195404	+	0.0367859i
$88$	2.11190e6	−	1.19772e7i	0.0352163	−	0.199721i
$89$	4.04206e7	+	2.33369e7i	0.644233	+	0.371948i	0.786243	−	0.617917i	$-0.212023\pi$
$89$	4.04206e7	+	2.33369e7i	0.644233	+	0.371948i	−0.142010	+	0.989865i	$0.545357\pi$
$90$	−2.74507e6	+	2.41355e6i	−0.0418392	+	0.0367863i
$91$	2.74672e6	+	4.75746e6i	0.0400542	+	0.0693760i
$92$	−1.09861e7	−	3.01841e7i	−0.153353	−	0.421335i
$93$	2.41913e7	−	4.30406e7i	0.323391	−	0.575370i
$94$	3.77752e7	−	3.16972e7i	0.483833	−	0.405984i
$95$	994976.	+	1.18577e6i	0.0122157	+	0.0145581i
$96$	1.29154e7	−	7.65685e6i	0.152062	−	0.0901499i
$97$	1.63107e8	−	5.93660e7i	1.84240	−	0.670580i	0.853687	−	0.520787i	$-0.174361\pi$
$97$	1.63107e8	−	5.93660e7i	1.84240	−	0.670580i	0.988717	−	0.149794i	$-0.0478609\pi$
$98$	1.93183e7	−	1.11534e7i	0.209442	−	0.120922i
$99$	−4.70700e7	+	2.86448e7i	−0.490008	+	0.298199i
$100$	2.48448e7	−	4.30325e7i	0.248448	−	0.430325i
$101$	2.54895e7	+	4.49449e6i	0.244949	+	0.0431912i	0.294775	−	0.955567i	$-0.404755\pi$
$101$	2.54895e7	+	4.49449e6i	0.244949	+	0.0431912i	−0.0498254	+	0.998758i	$0.515866\pi$
$102$	−4.04433e6	+	3.47394e6i	−0.0373633	+	0.0320939i
$103$	2.29937e7	+	8.36903e6i	0.204296	+	0.0743578i	0.442142	−	0.896945i	$-0.354219\pi$
$103$	2.29937e7	+	8.36903e6i	0.204296	+	0.0743578i	−0.237845	+	0.971303i	$0.576441\pi$
$104$	−4.02264e6	+	709300.i	−0.0343857	+	0.00606313i
$105$	2.74099e6	+	7.26859e6i	0.0225502	+	0.0597989i
$106$	6.00280e7	+	5.03695e7i	0.475478	+	0.398974i
$107$			1.79114e8i			1.36645i	0.730208	+	0.683224i	$0.239423\pi$
$107$			1.79114e8i			1.36645i	−0.730208	+	0.683224i	$0.760577\pi$
$108$	−6.46894e7	−	2.10383e7i	−0.475486	−	0.154638i
$109$	1.74708e8			1.23768			0.618839	−	0.785518i	$-0.287603\pi$
$109$	1.74708e8			1.23768			0.618839	+	0.785518i	$0.287603\pi$
$110$	−3.00746e6	+	3.58415e6i	−0.0205413	+	0.0244802i
$111$	−7.13736e6	+	4.34022e7i	−0.0470160	+	0.285904i
$112$	−5.54101e6	−	3.14247e7i	−0.0352142	−	0.199709i
$113$	−6.27460e7	+	1.72393e8i	−0.384833	+	1.05732i	0.584462	+	0.811421i	$0.301305\pi$
$113$	−6.27460e7	+	1.72393e8i	−0.384833	+	1.05732i	−0.969295	+	0.245899i	$0.920917\pi$
$114$	−9.53938e6	+	2.71816e7i	−0.0564808	+	0.160937i
$115$	−2.14581e6	+	1.21695e7i	−0.0122687	+	0.0695794i
$116$	−1.55893e7	−	9.00051e6i	−0.0860986	−	0.0497090i
$117$	1.44474e7	+	1.15650e7i	0.0770984	+	0.0617167i
$118$	4.75163e7	+	8.23007e7i	0.245084	+	0.424498i
$119$	3.87534e6	+	1.06474e7i	0.0193251	+	0.0530953i
$120$	−5.77576e6	+	66684.0i	−0.0278538	+	0.000321586i
$121$	1.10179e8	−	9.24511e7i	0.513993	−	0.431291i
$122$	3.75732e7	+	4.47780e7i	0.169605	+	0.202127i
$123$	−3.39721e6	−	2.94246e8i	−0.0148423	−	1.28555i
$124$	7.33166e7	−	2.66851e7i	0.310110	−	0.112871i
$125$	−3.32131e7	+	1.91756e7i	−0.136041	+	0.0785431i
$126$	−9.03453e7	+	1.12862e8i	−0.358446	+	0.447781i
$127$	1.94753e8	−	3.37322e8i	0.748632	−	1.29667i	−0.199846	−	0.979827i	$-0.564044\pi$
$127$	1.94753e8	−	3.37322e8i	0.748632	−	1.29667i	0.948478	−	0.316842i	$-0.102622\pi$
$128$	2.33661e7	+	4.12008e6i	0.0870455	+	0.0153485i
$129$	1.53865e8	+	5.39989e7i	0.555624	+	0.194996i
$130$	1.47664e6	+	537452.i	0.00517012	+	0.00188177i
$131$	−6.45499e7	+	1.13819e7i	−0.219185	+	0.0386482i	−0.282162	−	0.959367i	$-0.591052\pi$
$131$	−6.45499e7	+	1.13819e7i	−0.219185	+	0.0386482i	0.0629772	+	0.998015i	$0.479940\pi$
$132$	−8.59190e7	−	1.41291e7i	−0.283005	−	0.0465392i
$133$	4.68986e7	+	3.93526e7i	0.149883	+	0.125767i
$134$			1.08281e8i			0.335839i
$135$	1.75054e7	+	1.94524e7i	0.0527033	+	0.0585650i
$136$	−8.42508e6			−0.0246274
$137$	1.02484e8	−	1.22136e8i	0.290920	−	0.346705i	−0.600712	−	0.799465i	$-0.705116\pi$
$137$	1.02484e8	−	1.22136e8i	0.290920	−	0.346705i	0.891632	+	0.452760i	$0.149561\pi$
$138$	−2.15179e8	+	8.11442e7i	−0.593314	+	0.223739i
$139$	−8.62064e7	−	4.88901e8i	−0.230930	−	1.30967i	−0.851018	−	0.525137i	$-0.824014\pi$
$139$	−8.62064e7	−	4.88901e8i	−0.230930	−	1.30967i	0.620088	−	0.784532i	$-0.287097\pi$
$140$	−4.19855e6	+	1.15354e7i	−0.0109292	+	0.0300276i
$141$	−2.30042e8	−	2.67812e8i	−0.582010	−	0.677570i
$142$	−8.41565e7	+	4.77275e8i	−0.206983	+	1.17386i
$143$	2.05147e7	+	1.18441e7i	0.0490592	+	0.0283243i
$144$	−5.58827e7	−	9.18280e7i	−0.129965	−	0.213563i
$145$	3.46255e6	+	5.99730e6i	0.00783292	+	0.0135670i
$146$	−3.36601e7	−	9.24804e7i	−0.0740805	−	0.203535i
$147$	−8.14439e7	−	1.37377e8i	−0.174417	−	0.294202i
$148$	−5.32458e7	+	4.46785e7i	−0.110978	+	0.0931219i
$149$	−1.60506e7	−	1.91283e7i	−0.0325645	−	0.0388089i	0.749516	−	0.661986i	$-0.230286\pi$
$149$	−1.60506e7	−	1.91283e7i	−0.0325645	−	0.0388089i	−0.782081	+	0.623177i	$0.785842\pi$
$150$	−3.10122e8	−	1.74307e8i	−0.612587	−	0.344310i
$151$	3.29411e7	−	1.19896e7i	0.0633622	−	0.0230619i	−0.310145	−	0.950689i	$-0.600377\pi$
$151$	3.29411e7	−	1.19896e7i	0.0633622	−	0.0230619i	0.373507	+	0.927627i	$0.378155\pi$
$152$	−3.94233e7	+	2.27610e7i	−0.0738547	+	0.0426400i
$153$	2.52042e7	+	2.86661e7i	0.0459946	+	0.0523122i
$154$	−9.25258e7	+	1.60259e8i	−0.164505	+	0.284932i
$155$	−2.95595e7	−	5.21213e6i	−0.0512118	−	0.00903001i
$156$	5.41035e6	+	2.87394e7i	0.00913539	+	0.0485265i
$157$	−5.98462e8	−	2.17822e8i	−0.985004	−	0.358512i	−0.201220	−	0.979546i	$-0.564491\pi$
$157$	−5.98462e8	−	2.17822e8i	−0.985004	−	0.358512i	−0.783784	+	0.621034i	$0.786713\pi$
$158$	−2.66430e8	+	4.69787e7i	−0.427518	+	0.0753829i
$159$	3.55633e8	−	4.33903e8i	0.556433	−	0.678897i
$160$	−6.99225e6	−	5.86720e6i	−0.0106693	−	0.00895263i
$161$			4.88744e8i			0.727408i
$162$	−1.45266e8	+	4.64849e8i	−0.210913	+	0.674919i
$163$	−7.67529e8			−1.08729			−0.543644	−	0.839316i	$-0.682956\pi$
$163$	−7.67529e8			−1.08729			−0.543644	+	0.839316i	$0.682956\pi$
$164$	2.98904e8	−	3.56220e8i	0.413196	−	0.492428i
$165$	2.59074e7	+	2.12341e7i	0.0349533	+	0.0286482i
$166$	8.57732e7	+	4.86444e8i	0.112959	+	0.640620i
$167$	−3.57009e8	+	9.80874e8i	−0.459000	+	1.26109i	0.467230	+	0.884136i	$0.345252\pi$
$167$	−3.57009e8	+	9.80874e8i	−0.459000	+	1.26109i	−0.926231	+	0.376958i	$0.876970\pi$
$168$	−2.24510e8	+	4.22654e7i	−0.281838	+	0.0530576i
$169$	−1.40269e8	+	7.95503e8i	−0.171955	+	0.975203i
$170$	2.80694e6	+	1.62059e6i	0.00336076	+	0.00194034i
$171$	1.95381e8	+	6.60456e7i	0.228506	+	0.0772430i
$172$	1.28842e8	+	2.23161e8i	0.147212	+	0.254979i
$173$	−1.71633e8	−	4.71557e8i	−0.191609	−	0.526441i	0.806269	−	0.591549i	$-0.201483\pi$
$173$	−1.71633e8	−	4.71557e8i	−0.191609	−	0.526441i	−0.997878	+	0.0651075i	$0.979261\pi$
$174$	−6.31460e7	+	1.12348e8i	−0.0688888	+	0.122565i
$175$	−5.79174e8	+	4.85984e8i	−0.617528	+	0.518168i
$176$	−8.84456e7	−	1.05405e8i	−0.0921776	−	0.109853i
$177$	5.85262e8	−	3.46971e8i	0.596289	−	0.353509i
$178$	4.96207e8	−	1.80605e8i	0.494291	−	0.179907i
$179$	1.26521e8	−	7.30467e7i	0.123239	−	0.0711522i	−0.437113	−	0.899407i	$-0.643999\pi$
$179$	1.26521e8	−	7.30467e7i	0.123239	−	0.0711522i	0.560352	+	0.828254i	$0.310666\pi$
$180$	954778.	+	4.13430e7i	0.000909521	+	0.0393833i
$181$	−3.84168e8	+	6.65398e8i	−0.357937	+	0.619965i	−0.987616	−	0.156890i	$-0.949853\pi$
$181$	−3.84168e8	+	6.65398e8i	−0.357937	+	0.619965i	0.629679	+	0.776855i	$0.283186\pi$
$182$	6.12069e7	+	1.07924e7i	0.0557847	+	0.00983635i
$183$	3.17459e8	−	2.72687e8i	0.283063	−	0.243142i
$184$	−3.41494e8	−	1.24294e8i	−0.297929	−	0.108437i
$185$	2.63337e7	−	4.64333e6i	0.0224814	−	0.00396408i
$186$	−1.97098e8	−	5.22667e8i	−0.164676	−	0.436690i
$187$	3.74284e7	+	3.14062e7i	0.0306080	+	0.0256832i
$188$		−	5.57903e8i		−	0.446608i
$189$	8.15444e8	+	6.37452e8i	0.639068	+	0.499574i
$190$	1.75126e7			0.0134380
$191$	6.52787e8	−	7.77961e8i	0.490499	−	0.584554i	−0.462845	−	0.886439i	$-0.653172\pi$
$191$	6.52787e8	−	7.77961e8i	0.490499	−	0.584554i	0.953344	+	0.301885i	$0.0976160\pi$
$192$	2.75642e7	−	1.67618e8i	0.0202834	−	0.123343i
$193$	−3.41215e8	−	1.93513e9i	−0.245923	−	1.39470i	−0.818339	−	0.574735i	$-0.805105\pi$
$193$	−3.41215e8	−	1.93513e9i	−0.245923	−	1.39470i	0.572417	−	0.819963i	$-0.306006\pi$
$194$	6.71649e8	−	1.84534e9i	0.474172	−	1.30278i
$195$	3.72556e6	−	1.06156e7i	0.00257664	−	0.00734189i
$196$	4.38242e7	−	2.48539e8i	0.0296954	−	0.168411i
$197$	8.43504e8	+	4.86997e8i	0.560044	+	0.323342i	0.753163	−	0.657834i	$-0.228527\pi$
$197$	8.43504e8	+	4.86997e8i	0.560044	+	0.323342i	−0.193119	+	0.981175i	$0.561860\pi$
$198$	−9.40484e7	+	6.16260e8i	−0.0611914	+	0.400962i
$199$	2.55947e8	+	4.43313e8i	0.163207	+	0.282682i	0.936017	−	0.351955i	$-0.114483\pi$
$199$	2.55947e8	+	4.43313e8i	0.163207	+	0.282682i	−0.772810	+	0.634637i	$0.781150\pi$
$200$	−1.92275e8	−	5.28271e8i	−0.120172	−	0.330169i
$201$	7.75179e8	−	8.94982e6i	0.474917	−	0.00548315i
$202$	2.24321e8	−	1.88227e8i	0.134730	−	0.113052i
$203$	1.76057e8	+	2.09817e8i	0.103674	+	0.123554i
$204$	696366.	+	6.03150e7i	0.000402084	+	0.0348261i
$205$	−1.68104e8	+	6.11849e7i	−0.0951837	+	0.0346440i
$206$	2.39750e8	−	1.38420e8i	0.133134	−	0.0768652i
$207$	5.98695e8	+	1.53376e9i	0.326080	+	0.835363i
$208$	−2.31065e7	+	4.00217e7i	−0.0123447	+	0.0213817i
$209$	2.59984e8	+	4.58422e7i	0.136258	+	0.0240260i
$210$	8.29288e7	+	2.91039e7i	0.0426411	+	0.0149649i
$211$	−3.10685e9	−	1.13080e9i	−1.56744	−	0.570501i	−0.595014	−	0.803715i	$-0.702854\pi$
$211$	−3.10685e9	−	1.13080e9i	−1.56744	−	0.570501i	−0.972425	+	0.233214i	$0.925076\pi$
$212$	8.73085e8	−	1.53948e8i	0.432228	−	0.0762135i
$213$	3.42376e9	+	5.63026e8i	1.66336	+	0.273533i
$214$	1.55234e9	+	1.30257e9i	0.740171	+	0.621078i
$215$		−	9.91323e7i		−	0.0463939i
$216$	−6.52776e8	+	4.07653e8i	−0.299881	+	0.187273i
$217$	−1.18715e9			−0.535386
$218$	1.27053e9	−	1.51416e9i	0.562549	−	0.670420i
$219$	−6.59283e8	+	2.48616e8i	−0.286613	+	0.108082i
$220$	9.19194e6	+	5.21301e7i	0.00392389	+	0.0222535i
$221$	5.61249e6	−	1.54202e7i	0.00235281	−	0.00646429i
$222$	3.24254e8	+	3.77493e8i	0.133497	+	0.155416i
$223$	2.11508e8	−	1.19952e9i	0.0855279	−	0.485053i	−0.911714	−	0.410827i	$-0.865240\pi$
$223$	2.11508e8	−	1.19952e9i	0.0855279	−	0.485053i	0.997241	−	0.0742263i	$-0.0236487\pi$
$224$	−3.12647e8	−	1.80507e8i	−0.124183	−	0.0716972i
$225$	−1.22223e9	+	2.23456e9i	−0.476893	+	0.871892i
$226$	1.03779e9	+	1.79750e9i	0.397810	+	0.689027i
$227$	−1.21867e9	−	3.34828e9i	−0.458970	−	1.26101i	−0.926253	−	0.376901i	$-0.876990\pi$
$227$	−1.21867e9	−	3.34828e9i	−0.458970	−	1.26101i	0.467284	−	0.884107i	$-0.345233\pi$
$228$	1.66204e8	+	2.80349e8i	0.0615039	+	0.103743i
$229$	−5.32816e8	+	4.47086e8i	−0.193747	+	0.162573i	−0.734501	−	0.678608i	$-0.762584\pi$
$229$	−5.32816e8	+	4.47086e8i	−0.193747	+	0.162573i	0.540754	+	0.841181i	$0.318139\pi$
$230$	8.98656e7	+	1.07098e8i	0.0321131	+	0.0382709i
$231$	1.15494e9	+	6.49144e8i	0.405613	+	0.227978i
$232$	−1.91376e8	+	6.96552e7i	−0.0660596	+	0.0240437i
$233$	−3.28484e9	+	1.89650e9i	−1.11453	+	0.643472i	−0.939998	−	0.341181i	$-0.889173\pi$
$233$	−3.28484e9	+	1.89650e9i	−1.11453	+	0.643472i	−0.174528	+	0.984652i	$0.555840\pi$
$234$	2.05297e8	−	4.11080e7i	0.0684731	−	0.0137108i
$235$	−1.07314e8	+	1.85873e8i	−0.0351872	+	0.0609461i
$236$	1.05884e9	+	1.86702e8i	0.341335	+	0.0601867i
$237$	3.58341e8	+	1.90348e9i	0.113580	+	0.603330i
$238$	1.20462e8	+	4.38445e7i	0.0375441	+	0.0136649i
$239$	9.41783e8	−	1.66062e8i	0.288642	−	0.0508954i	−0.0274525	−	0.999623i	$-0.508739\pi$
$239$	9.41783e8	−	1.66062e8i	0.288642	−	0.0508954i	0.316094	+	0.948728i	$0.397628\pi$
$240$	−4.14252e7	+	5.05423e7i	−0.0124859	+	0.0152339i
$241$	7.90975e8	+	6.63707e8i	0.234474	+	0.196747i	0.752452	−	0.658647i	$-0.228871\pi$
$241$	7.90975e8	+	6.63707e8i	0.234474	+	0.196747i	−0.517978	+	0.855394i	$0.673315\pi$
$242$		−	1.62723e9i		−	0.474447i
$243$	3.33985e9	+	1.00153e9i	0.957860	+	0.287237i
$244$	6.61326e8			0.186576
$245$	−6.24078e7	+	7.43748e7i	−0.0173211	+	0.0206425i
$246$	−2.57488e9	−	2.11040e9i	−0.703098	−	0.576269i
$247$	−1.53965e7	−	8.73179e7i	−0.00413651	−	0.0234593i
$248$	3.01907e8	−	8.29483e8i	0.0798117	−	0.219281i
$249$	3.47535e9	−	6.54255e8i	0.904068	−	0.170196i
$250$	−7.53448e7	+	4.27302e8i	−0.0192883	+	0.109389i
$251$	−5.43907e9	−	3.14025e9i	−1.37034	−	0.791168i	−0.379372	−	0.925244i	$-0.623860\pi$
$251$	−5.43907e9	−	3.14025e9i	−1.37034	−	0.791168i	−0.990971	+	0.134076i	$0.957193\pi$
$252$	3.21134e8	+	1.60377e9i	0.0796313	+	0.397686i
$253$	1.05376e9	+	1.82516e9i	0.257193	+	0.445471i
$254$	−1.50720e9	−	4.14099e9i	−0.362106	−	0.994877i
$255$	1.13697e7	−	2.02288e7i	0.00268900	−	0.00478419i
$256$	2.05633e8	−	1.72547e8i	0.0478778	−	0.0401742i
$257$	3.25584e9	+	3.88016e9i	0.746329	+	0.889440i	0.996902	−	0.0786577i	$-0.0250634\pi$
$257$	3.25584e9	+	3.88016e9i	0.746329	+	0.889440i	−0.250573	+	0.968098i	$0.580619\pi$
$258$	1.58695e9	−	9.40821e8i	0.358167	−	0.212338i
$259$	9.93817e8	−	3.61720e8i	0.220855	−	0.0803847i
$260$	1.53966e7	−	8.88921e6i	0.00336923	−	0.00194522i
$261$	8.09514e8	+	4.42775e8i	0.174447	+	0.0954159i
$262$	−3.70782e8	+	6.42214e8i	−0.0786890	+	0.136293i
$263$	−2.47638e9	−	4.36653e8i	−0.517601	−	0.0912670i	−0.0912555	−	0.995828i	$-0.529088\pi$
$263$	−2.47638e9	−	4.36653e8i	−0.517601	−	0.0912670i	−0.426345	+	0.904561i	$0.640199\pi$
$264$	−7.47284e8	+	6.41892e8i	−0.153840	+	0.132144i
$265$	−3.20493e8	−	1.16650e8i	−0.0649884	−	0.0236538i
$266$	6.82123e8	−	1.20277e8i	0.136250	−	0.0240245i
$267$	−1.33396e9	−	3.53741e9i	−0.262481	−	0.696050i
$268$	9.38447e8	+	7.87451e8i	0.181916	+	0.152646i
$269$			5.33259e9i			1.01842i	0.860641	+	0.509212i	$0.170063\pi$
$269$			5.33259e9i			1.01842i	−0.860641	+	0.509212i	$0.829937\pi$
$270$	2.95895e8	−	1.02524e7i	0.0556779	−	0.00192917i
$271$	−1.00008e10			−1.85421			−0.927104	−	0.374803i	$-0.877710\pi$
$271$	−1.00008e10			−1.85421			−0.927104	+	0.374803i	$0.877710\pi$
$272$	−6.12698e7	+	7.30185e7i	−0.0111936	+	0.0133401i
$273$	7.22038e7	−	4.39071e8i	0.0129990	−	0.0790468i
$274$	−3.13231e8	−	1.77642e9i	−0.0555727	−	0.315169i
$275$	−1.11505e9	+	3.06359e9i	−0.194969	+	0.535673i
$276$	−8.61590e8	+	2.45502e9i	−0.148479	+	0.423077i
$277$	1.07107e9	−	6.07432e9i	0.181927	−	1.03176i	−0.747913	−	0.663797i	$-0.768944\pi$
$277$	1.07107e9	−	6.07432e9i	0.181927	−	1.03176i	0.929840	−	0.367964i	$-0.119945\pi$
$278$	−4.86413e9	−	2.80831e9i	−0.814378	−	0.470181i
$279$	−3.72547e9	+	1.45422e9i	−0.614843	+	0.240001i
$280$	6.94420e7	+	1.20277e8i	0.0112977	+	0.0195682i
$281$	−2.01731e9	−	5.54252e9i	−0.323555	−	0.888959i	−0.989703	−	0.143139i	$-0.954280\pi$
$281$	−2.01731e9	−	5.54252e9i	−0.323555	−	0.888959i	0.666148	−	0.745820i	$-0.267942\pi$
$282$	−3.99401e9	+	4.61128e7i	−0.631558	+	0.00729164i
$283$	1.03413e9	−	8.67742e8i	0.161225	−	0.135283i	−0.558606	−	0.829433i	$-0.688664\pi$
$283$	1.03413e9	−	8.67742e8i	0.161225	−	0.135283i	0.719831	+	0.694149i	$0.244219\pi$
$284$	3.52444e9	+	4.20026e9i	0.541772	+	0.645659i
$285$	−1.44748e6	−	1.25372e8i	−0.000219399	−	0.0190030i
$286$	2.51840e8	−	9.16622e7i	0.0376409	−	0.0137002i
$287$	−6.12751e9	+	3.53772e9i	−0.903143	+	0.521430i
$288$	−1.20225e9	−	1.83477e8i	−0.174753	−	0.0266694i
$289$	−3.47096e9	+	6.01187e9i	−0.497574	+	0.861823i
$290$	7.71582e7	+	1.36051e7i	0.0109091	+	0.00192357i
$291$	−1.32663e10	−	4.65580e9i	−1.85002	−	0.649266i
$292$	−1.04630e9	−	3.80821e8i	−0.143921	−	0.0523828i
$293$	9.34842e9	−	1.64838e9i	1.26843	−	0.223659i	0.501372	−	0.865232i	$-0.332829\pi$
$293$	9.34842e9	−	1.64838e9i	1.26843	−	0.223659i	0.767062	+	0.641573i	$0.221718\pi$
$294$	−1.78291e9	−	2.93193e8i	−0.238638	−	0.0392433i
$295$	−3.16855e8	−	2.65873e8i	−0.0418381	−	0.0351064i
$296$			7.86387e8i			0.102440i
$297$	4.41957e9	+	6.22354e8i	0.568008	+	0.0799856i
$298$	−2.82506e8			−0.0358230
$299$	4.54983e8	−	5.42228e8i	0.0569260	−	0.0678417i
$300$	−3.76599e9	+	1.42015e9i	−0.464937	+	0.175328i
$301$	−6.80842e8	−	3.86125e9i	−0.0829431	−	0.470394i
$302$	1.35647e8	−	3.72686e8i	0.0163073	−	0.0448038i
$303$	−1.36606e9	−	1.59035e9i	−0.162068	−	0.188678i
$304$	−8.94329e7	+	5.07199e8i	−0.0104714	+	0.0593860i
$305$	−2.20330e8	−	1.27208e8i	−0.0254610	−	0.0146999i
$306$	4.31736e8	−	9.97054e6i	0.0492417	−	0.00113719i
$307$	8.95811e8	+	1.55159e9i	0.100847	+	0.174672i	0.912034	−	0.410115i	$-0.134511\pi$
$307$	8.95811e8	+	1.55159e9i	0.100847	+	0.174672i	−0.811187	+	0.584787i	$0.801178\pi$
$308$	7.16060e8	+	1.96736e9i	0.0795695	+	0.218615i
$309$	−1.01076e9	−	1.70493e9i	−0.110870	−	0.187013i
$310$	−2.60138e8	+	2.18282e8i	−0.0281681	+	0.0236358i
$311$	5.51357e9	+	6.57082e9i	0.589374	+	0.702389i	0.975486	−	0.220063i	$-0.0706263\pi$
$311$	5.51357e9	+	6.57082e9i	0.589374	+	0.702389i	−0.386111	+	0.922452i	$0.626182\pi$
$312$	2.88424e8	+	1.62111e8i	0.0304378	+	0.0171078i
$313$	1.40191e10	−	5.10252e9i	1.46063	−	0.531627i	0.515094	−	0.857133i	$-0.327757\pi$
$313$	1.40191e10	−	5.10252e9i	1.46063	−	0.531627i	0.945540	+	0.325506i	$0.105535\pi$
$314$	−6.24002e9	+	3.60268e9i	−0.641900	+	0.370601i
$315$	2.01500e8	−	5.96091e8i	0.0204660	−	0.0605439i
$316$	−1.53040e9	+	2.65074e9i	−0.153482	+	0.265839i
$317$	1.64776e10	+	2.90545e9i	1.63176	+	0.287724i	0.913131	−	0.407666i	$-0.133657\pi$
$317$	1.64776e10	+	2.90545e9i	1.63176	+	0.287724i	0.718633	+	0.695390i	$0.244768\pi$
$318$	−1.17428e9	−	6.23767e9i	−0.114832	−	0.609978i
$319$	1.10984e9	+	4.03950e8i	0.107176	+	0.0390090i
$320$	−1.01700e8	+	1.79324e7i	−0.00969884	+	0.00171017i
$321$	9.19676e9	−	1.12208e10i	0.866193	−	1.05683i
$322$	4.23585e9	+	3.55430e9i	0.394019	+	0.330621i
$323$		−	1.82880e8i		−	0.0168018i
$324$	2.97234e9	+	4.63952e9i	0.269723	+	0.421010i
$325$	1.09497e9			0.0981448
$326$	−5.58171e9	+	6.65203e9i	−0.494194	+	0.588957i
$327$	−1.09449e10	−	8.97057e9i	−0.957238	−	0.784565i
$328$	−9.13565e8	−	5.18108e9i	−0.0789303	−	0.447636i
$329$	−2.90335e9	+	7.97688e9i	−0.247808	+	0.680847i
$330$	3.72438e8	−	7.01136e7i	0.0314050	−	0.00591217i
$331$	2.57824e9	−	1.46219e10i	0.214789	−	1.21813i	−0.666484	−	0.745519i	$-0.732202\pi$
$331$	2.57824e9	−	1.46219e10i	0.214789	−	1.21813i	0.881273	−	0.472608i	$-0.156687\pi$
$332$	4.83968e9	+	2.79419e9i	0.398350	+	0.229987i
$333$	2.67566e9	−	2.35253e9i	0.217598	−	0.191319i
$334$	5.90476e9	+	1.02273e10i	0.474478	+	0.821821i
$335$	−1.61189e8	−	4.42864e8i	−0.0127984	−	0.0351634i
$336$	−1.26640e9	+	2.25316e9i	−0.0993609	+	0.176780i
$337$	1.56948e10	−	1.31695e10i	1.21685	−	1.02106i	0.217866	−	0.975979i	$-0.430090\pi$
$337$	1.56948e10	−	1.31695e10i	1.21685	−	1.02106i	0.998983	−	0.0450794i	$-0.0143541\pi$
$338$	5.87439e9	+	7.00083e9i	0.450086	+	0.536392i
$339$	1.27825e10	−	7.57809e9i	0.967872	−	0.573800i
$340$	3.44583e7	−	1.25418e7i	0.00257856	−	0.000938520i
$341$	−4.43329e9	+	2.55956e9i	−0.327875	+	0.189299i
$342$	1.99328e9	−	1.21302e9i	0.145701	−	0.0886676i
$343$	−7.53376e9	+	1.30489e10i	−0.544296	+	0.942749i
$344$	2.87107e9	+	5.06247e8i	0.205026	+	0.0361517i
$345$	7.59282e8	−	6.52198e8i	0.0535953	−	0.0460366i
$346$	−5.33506e9	−	1.94180e9i	−0.372250	−	0.135488i
$347$	1.63776e10	−	2.88782e9i	1.12962	−	0.199183i	0.422560	−	0.906335i	$-0.361132\pi$
$347$	1.63776e10	−	2.88782e9i	1.12962	−	0.199183i	0.707061	+	0.707152i	$0.250020\pi$
$348$	5.14478e8	+	1.36430e9i	0.0350792	+	0.0930236i
$349$	1.76327e10	+	1.47956e10i	1.18855	+	0.997312i	0.999883	+	0.0152709i	$0.00486107\pi$
$349$	1.76327e10	+	1.47956e10i	1.18855	+	0.997312i	0.188667	+	0.982041i	$0.439583\pi$
$350$			8.55382e9i			0.570017i
$351$	−3.11260e8	−	1.46632e9i	−0.0205067	−	0.0966053i
$352$	−1.55673e9			−0.101401
$353$	−3.72871e9	+	4.44370e9i	−0.240137	+	0.286185i	−0.872630	−	0.488382i	$-0.837587\pi$
$353$	−3.72871e9	+	4.44370e9i	−0.240137	+	0.286185i	0.632493	+	0.774566i	$0.282032\pi$
$354$	1.24908e9	−	7.59563e9i	0.0795382	−	0.483672i
$355$	−3.66287e8	−	2.07732e9i	−0.0230626	−	0.130794i
$356$	2.04331e9	−	5.61394e9i	0.127214	−	0.349517i
$357$	3.03925e8	−	8.66007e8i	0.0187109	−	0.0533149i
$358$	2.87016e8	−	1.62775e9i	0.0174733	−	0.0990957i
$359$	−1.64745e9	−	9.51153e8i	−0.0991821	−	0.0572628i	0.449589	−	0.893236i	$-0.351571\pi$
$359$	−1.64745e9	−	9.51153e8i	−0.0991821	−	0.0572628i	−0.548771	+	0.835973i	$0.684904\pi$
$360$	3.65256e8	+	2.92385e8i	0.0217464	+	0.0174078i
$361$	7.99772e9	+	1.38525e10i	0.470909	+	0.815639i
$362$	2.97309e9	+	8.16849e9i	0.173130	+	0.475672i
$363$	−1.16493e10	+	1.34497e8i	−0.670925	+	0.00774616i
$364$	5.38652e8	−	4.51982e8i	0.0306833	−	0.0257464i
$365$	2.75337e8	+	3.28134e8i	0.0155129	+	0.0184876i
$366$	−5.46611e7	−	4.73442e9i	−0.00304617	−	0.263841i
$367$	2.66501e10	−	9.69986e9i	1.46905	−	0.534689i	0.521204	−	0.853432i	$-0.325483\pi$
$367$	2.66501e10	−	9.69986e9i	1.46905	−	0.534689i	0.947841	+	0.318743i	$0.103261\pi$
$368$	−3.56068e9	+	2.05576e9i	−0.194152	+	0.112094i
$369$	−1.48955e10	+	1.86079e10i	−0.803434	+	1.00367i
$370$	1.51264e8	−	2.61996e8i	0.00807101	−	0.0139794i
$371$	−1.32845e10	−	2.34242e9i	−0.701213	−	0.123643i
$372$	−5.96321e9	−	2.09279e9i	−0.311392	−	0.109283i
$373$	−6.59113e9	−	2.39898e9i	−0.340506	−	0.123934i	0.166107	−	0.986108i	$-0.446880\pi$
$373$	−6.59113e9	−	2.39898e9i	−0.340506	−	0.123934i	−0.506613	+	0.862174i	$0.669103\pi$
$374$	5.44383e8	−	9.59894e7i	0.0278239	−	0.00490610i
$375$	3.06527e9	+	5.04074e8i	0.155004	+	0.0254900i
$376$	−4.83523e9	−	4.05724e9i	−0.241917	−	0.202992i
$377$		−	3.96673e8i		−	0.0196366i
$378$	1.14548e10	−	2.43155e9i	0.561076	−	0.119101i
$379$	−1.45505e10			−0.705214			−0.352607	−	0.935772i	$-0.614705\pi$
$379$	−1.45505e10			−0.705214			−0.352607	+	0.935772i	$0.614705\pi$
$380$	1.27357e8	−	1.51778e8i	0.00610785	−	0.00727905i
$381$	−2.95207e10	+	1.11323e10i	−1.40096	+	0.528304i
$382$	−1.99517e9	−	1.13152e10i	−0.0936970	−	0.531382i
$383$	−5.73929e9	+	1.57686e10i	−0.266725	+	0.732820i	0.731950	+	0.681358i	$0.238610\pi$
$383$	−5.73929e9	+	1.57686e10i	−0.266725	+	0.732820i	−0.998675	+	0.0514621i	$0.983612\pi$
$384$	−1.25226e9	−	1.45786e9i	−0.0575928	−	0.0670490i
$385$	1.39861e8	−	7.93190e8i	0.00636581	−	0.0361023i
$386$	−1.92528e10	−	1.11156e10i	−0.867250	−	0.500707i
$387$	−6.86649e9	−	1.12832e10i	−0.306119	−	0.503024i
$388$	−1.11088e10	−	1.92410e10i	−0.490161	−	0.848984i
$389$	−1.09514e10	−	3.00888e10i	−0.478270	−	1.31403i	−0.910961	−	0.412493i	$-0.864658\pi$
$389$	−1.09514e10	−	3.00888e10i	−0.478270	−	1.31403i	0.432691	−	0.901542i	$-0.357564\pi$
$390$	−6.49103e7	−	1.09489e8i	−0.00280579	−	0.00473273i
$391$	1.11840e9	−	9.38446e8i	0.0478508	−	0.0401515i
$392$	−1.83534e9	−	2.18727e9i	−0.0777269	−	0.0926314i
$393$	4.62824e9	+	2.60134e9i	0.194020	+	0.109050i
$394$	1.03549e10	−	3.76889e9i	0.429697	−	0.156397i
$395$	1.01975e9	−	5.88755e8i	0.0418896	−	0.0241850i
$396$	4.65706e9	+	5.29674e9i	0.189379	+	0.215391i
$397$	−7.78128e9	+	1.34776e10i	−0.313248	+	0.542562i	−0.979064	−	0.203554i	$-0.934751\pi$
$397$	−7.78128e9	+	1.34776e10i	−0.313248	+	0.542562i	0.665815	+	0.746117i	$0.268084\pi$
$398$	5.70343e9	+	1.00567e9i	0.227302	+	0.0400796i
$399$	−9.17438e8	−	4.87336e9i	−0.0361980	−	0.192281i
$400$	−5.97670e9	−	2.17534e9i	−0.233465	−	0.0849743i
$401$	−1.50172e10	+	2.64793e9i	−0.580778	+	0.102407i	−0.456316	−	0.889818i	$-0.650832\pi$
$401$	−1.50172e10	+	2.64793e9i	−0.580778	+	0.102407i	−0.124462	+	0.992224i	$0.539720\pi$
$402$	5.55978e9	−	6.78341e9i	0.212889	−	0.259743i
$403$	1.31706e9	+	1.10514e9i	0.0499327	+	0.0418986i
$404$		−	3.31299e9i		−	0.124364i
$405$	−9.78536e7	−	2.11746e9i	−0.00363711	−	0.0787037i
$406$	3.09878e9			0.114048
$407$	2.93142e9	−	3.49353e9i	0.106832	−	0.127317i
$408$	5.27802e8	+	4.32594e8i	0.0190472	+	0.0156113i
$409$	1.17907e9	+	6.68684e9i	0.0421353	+	0.238961i	0.998601	−	0.0528847i	$-0.0168416\pi$
$409$	1.17907e9	+	6.68684e9i	0.0421353	+	0.238961i	−0.956465	+	0.291846i	$0.905730\pi$
$410$	−6.92228e8	+	1.90188e9i	−0.0244970	+	0.0673051i
$411$	−1.26915e10	+	2.38924e9i	−0.444779	+	0.0837321i
$412$	5.43881e8	−	3.08450e9i	0.0188762	−	0.107052i
$413$	−1.41676e10	−	8.17970e9i	−0.486965	−	0.281149i
$414$	1.76467e10	+	5.96519e9i	0.600705	+	0.203059i
$415$	−1.07494e9	−	1.86185e9i	−0.0362403	−	0.0627701i
$416$	1.78822e8	+	4.91310e8i	0.00597102	+	0.0164052i
$417$	−1.97026e10	+	3.50543e10i	−0.651596	+	1.15930i
$418$	2.28799e9	−	1.91985e9i	0.0749462	−	0.0628873i
$419$	1.18526e10	+	1.41254e10i	0.384555	+	0.458295i	0.923247	−	0.384208i	$-0.125525\pi$
$419$	1.18526e10	+	1.41254e10i	0.384555	+	0.458295i	−0.538691	+	0.842503i	$0.681081\pi$
$420$	8.55322e8	−	5.07075e8i	0.0274873	−	0.0162958i
$421$	−6.37176e9	+	2.31913e9i	−0.202829	+	0.0738239i	−0.441437	−	0.897292i	$-0.645531\pi$
$421$	−6.37176e9	+	2.31913e9i	−0.202829	+	0.0738239i	0.238608	+	0.971116i	$0.423309\pi$
$422$	−3.23944e10	+	1.87029e10i	−1.02146	+	0.589739i
$423$	6.60241e8	+	2.85892e10i	0.0206225	+	0.892979i
$424$	5.01511e9	−	8.68642e9i	0.155173	−	0.268768i
$425$	2.22416e9	+	3.92180e8i	0.0681727	+	0.0120207i
$426$	2.97783e10	−	2.55786e10i	0.904194	−	0.776672i
$427$	−9.45563e9	−	3.44157e9i	−0.284432	−	0.103525i
$428$	2.25782e10	−	3.98115e9i	0.672845	−	0.118641i
$429$	−6.77023e8	−	1.79534e9i	−0.0199882	−	0.0530051i
$430$	−8.59160e8	−	7.20921e8i	−0.0251305	−	0.0210870i
$431$		−	1.47980e10i		−	0.428838i	−0.976742	−	0.214419i	$-0.931214\pi$
$431$		−	1.47980e10i		−	0.428838i	0.976742	−	0.214419i	$-0.0687857\pi$
$432$	−1.21414e9	+	8.62206e9i	−0.0348605	+	0.247558i
$433$	1.56023e10			0.443852			0.221926	−	0.975063i	$-0.428766\pi$
$433$	1.56023e10			0.443852			0.221926	+	0.975063i	$0.428766\pi$
$434$	−8.63333e9	+	1.02888e10i	−0.243343	+	0.290005i
$435$	9.10210e7	−	5.53498e8i	0.00254205	−	0.0154582i
$436$	−3.88324e9	−	2.20229e10i	−0.107460	−	0.609438i
$437$	2.69800e9	−	7.41268e9i	0.0739802	−	0.203259i
$438$	−2.63981e9	+	7.52189e9i	−0.0717258	+	0.204376i
$439$	−7.34756e9	+	4.16701e10i	−0.197827	+	1.12193i	0.710509	+	0.703688i	$0.248465\pi$
$439$	−7.34756e9	+	4.16701e10i	−0.197827	+	1.12193i	−0.908335	+	0.418243i	$0.862646\pi$
$440$	5.18648e8	+	2.99441e8i	0.0138376	+	0.00798916i
$441$	−1.95160e9	+	1.27880e10i	−0.0515985	+	0.338103i
$442$	−9.28280e7	−	1.60783e8i	−0.00243215	−	0.00421260i
$443$	−2.61615e10	−	7.18781e10i	−0.679278	−	1.86630i	−0.450334	−	0.892860i	$-0.648695\pi$
$443$	−2.61615e10	−	7.18781e10i	−0.679278	−	1.86630i	−0.228944	−	0.973440i	$-0.573527\pi$
$444$	5.62973e9	−	6.49979e7i	0.144862	−	0.00167251i
$445$	−1.76062e9	+	1.47733e9i	−0.0448977	+	0.0376737i
$446$	−8.85787e9	−	1.05564e10i	−0.223867	−	0.266794i
$447$	2.33502e7	+	2.02245e9i	0.000584872	+	0.0506581i
$448$	−3.83809e9	+	1.39695e9i	−0.0952802	+	0.0346792i
$449$	−4.70970e9	+	2.71914e9i	−0.115880	+	0.0669032i	−0.556820	−	0.830633i	$-0.687979\pi$
$449$	−4.70970e9	+	2.71914e9i	−0.115880	+	0.0669032i	0.440940	+	0.897537i	$0.354645\pi$
$450$	1.04781e10	+	2.68432e10i	0.255525	+	0.654613i
$451$	−1.52550e10	+	2.64225e10i	−0.368728	+	0.638656i
$452$	2.31258e10	+	4.07769e9i	0.554041	+	0.0976924i
$453$	−2.67926e9	−	9.40287e8i	−0.0636242	−	0.0223289i
$454$	−3.78814e10	−	1.37877e10i	−0.891668	−	0.324541i
$455$	−2.66400e8	+	4.69735e7i	−0.00621567	+	0.00109599i
$456$	3.63842e9	+	5.98326e8i	0.0841498	+	0.0138382i
$457$	−3.68291e10	−	3.09033e10i	−0.844358	−	0.708501i	0.114182	−	0.993460i	$-0.463575\pi$
$457$	−3.68291e10	−	3.09033e10i	−0.844358	−	0.708501i	−0.958540	+	0.284959i	$0.908020\pi$
$458$			7.86916e9i			0.178841i
$459$	−1.07064e8	−	3.08997e9i	−0.00241208	−	0.0696150i
$460$	1.58172e9			0.0353264
$461$	2.56213e10	−	3.05343e10i	0.567280	−	0.676058i	−0.403790	−	0.914852i	$-0.632307\pi$
$461$	2.56213e10	−	3.05343e10i	0.567280	−	0.676058i	0.971070	+	0.238793i	$0.0767519\pi$
$462$	1.40251e10	−	5.28887e9i	0.307849	−	0.116090i
$463$	9.78153e9	+	5.54738e10i	0.212855	+	1.20716i	0.884591	+	0.466368i	$0.154438\pi$
$463$	9.78153e9	+	5.54738e10i	0.212855	+	1.20716i	−0.671736	+	0.740790i	$0.734451\pi$
$464$	−7.88059e8	+	2.16517e9i	−0.0170015	+	0.0467112i
$465$	1.58418e9	+	1.84428e9i	0.0338838	+	0.0394471i
$466$	−7.45175e9	+	4.22610e10i	−0.158021	+	0.896181i
$467$	4.64369e10	+	2.68104e10i	0.976329	+	0.563684i	0.901160	−	0.433487i	$-0.142717\pi$
$467$	4.64369e10	+	2.68104e10i	0.976329	+	0.563684i	0.0751690	+	0.997171i	$0.476050\pi$
$468$	1.13671e9	−	2.07822e9i	0.0236956	−	0.0433220i
$469$	−9.31998e9	−	1.61427e10i	−0.192630	−	0.333645i
$470$	8.30507e8	+	2.28180e9i	0.0170197	+	0.0467612i
$471$	2.63073e10	+	4.43744e10i	0.534555	+	0.901673i
$472$	9.31831e9	−	7.81899e9i	0.187745	−	0.157537i
$473$	−1.08676e10	−	1.29515e10i	−0.217114	−	0.258747i
$474$	1.91031e10	+	1.07370e10i	0.378434	+	0.212702i
$475$	1.14670e10	−	4.17363e9i	0.225255	−	0.0819860i
$476$	1.25603e9	−	7.25167e8i	0.0244665	−	0.0141257i
$477$	−4.45583e10	+	8.92220e9i	−0.860707	+	0.172345i
$478$	5.40972e9	−	9.36990e9i	0.103625	−	0.179483i
$479$	5.08128e10	+	8.95967e9i	0.965231	+	0.170196i	0.633983	−	0.773347i	$-0.281419\pi$
$479$	5.08128e10	+	8.95967e9i	0.965231	+	0.170196i	0.331248	+	0.943544i	$0.392530\pi$
$480$	1.36784e8	+	7.26584e8i	0.00257673	+	0.0136874i
$481$	−1.43930e9	−	5.23863e8i	−0.0268888	−	0.00978673i
$482$	1.15044e10	−	2.02854e9i	0.213146	−	0.0375834i
$483$	2.50951e10	−	3.06181e10i	0.461105	−	0.562588i
$484$	−1.41029e10	−	1.18337e10i	−0.256996	−	0.215646i
$485$			8.54721e9i			0.154475i
$486$	3.29685e10	−	2.16624e10i	0.590955	−	0.388294i
$487$	2.69278e9			0.0478724			0.0239362	−	0.999713i	$-0.492380\pi$
$487$	2.69278e9			0.0478724			0.0239362	+	0.999713i	$0.492380\pi$
$488$	4.80937e9	−	5.73158e9i	0.0848025	−	0.101064i
$489$	4.80831e10	+	3.94095e10i	0.840924	+	0.689233i
$490$	1.90742e8	+	1.08175e9i	0.00330874	+	0.0187648i
$491$	1.37117e10	−	3.76727e10i	0.235921	−	0.648187i	−0.764075	−	0.645128i	$-0.776804\pi$
$491$	1.37117e10	−	3.76727e10i	0.235921	−	0.648187i	0.999995	−	0.00305903i	$-0.000973721\pi$
$492$	−3.70158e10	+	6.96843e9i	−0.631722	+	0.118925i
$493$	1.42075e8	−	8.05745e8i	0.00240508	−	0.0136399i
$494$	−8.68735e8	−	5.01565e8i	−0.0145875	−	0.00842207i
$495$	−5.32726e8	−	2.66048e9i	−0.00887325	−	0.0443139i
$496$	−4.99340e9	−	8.64883e9i	−0.0825030	−	0.142899i
$497$	−2.85341e10	−	7.83967e10i	−0.467668	−	1.28491i
$498$	1.96035e10	−	3.48781e10i	0.318726	−	0.567069i
$499$	−2.98747e10	+	2.50679e10i	−0.481839	+	0.404311i	−0.851091	−	0.525018i	$-0.824058\pi$
$499$	−2.98747e10	+	2.50679e10i	−0.481839	+	0.404311i	0.369252	+	0.929329i	$0.379614\pi$
$500$	3.15541e9	+	3.76047e9i	0.0504866	+	0.0601675i
$501$	7.27293e10	−	4.31174e10i	1.15441	−	0.684387i
$502$	−6.67705e10	+	2.43025e10i	−1.05140	+	0.382680i
$503$	8.78769e10	−	5.07358e10i	1.37279	−	0.792578i	0.381508	−	0.924365i	$-0.375405\pi$
$503$	8.78769e10	−	5.07358e10i	1.37279	−	0.792578i	0.991278	+	0.131787i	$0.0420715\pi$
$504$	1.62350e10	+	8.87993e9i	0.251611	+	0.137622i
$505$	−6.37263e8	+	1.10377e9i	−0.00979835	+	0.0169712i
$506$	2.34816e10	+	4.14044e9i	0.358200	+	0.0631603i
$507$	4.96332e10	−	4.26333e10i	0.751174	−	0.645234i
$508$	−4.68500e10	−	1.70520e10i	−0.703484	−	0.256047i
$509$	−7.00551e10	+	1.23526e10i	−1.04368	+	0.184030i	−0.669107	−	0.743166i	$-0.733323\pi$
$509$	−7.00551e10	+	1.23526e10i	−1.04368	+	0.184030i	−0.374577	+	0.927196i	$0.622212\pi$
$510$	−9.26344e7	−	2.45649e8i	−0.00136928	−	0.00363107i
$511$	1.29781e10	+	1.08899e10i	0.190339	+	0.159714i
$512$		−	3.03700e9i		−	0.0441942i
$513$	−8.84877e9	−	1.41696e10i	−0.127765	−	0.204591i
$514$	5.73060e10			0.821009
$515$	−7.74514e8	+	9.23030e8i	−0.0110103	+	0.0131216i
$516$	3.38690e9	−	2.05958e10i	0.0477754	−	0.290522i
$517$	6.35634e9	+	3.60486e10i	0.0889703	+	0.504576i
$518$	4.09239e9	−	1.12438e10i	0.0568405	−	0.156168i
$519$	−1.34604e10	+	3.83541e10i	−0.185518	+	0.528618i
$520$	3.49276e7	−	1.98084e8i	0.000477700	−	0.00270917i
$521$	2.36854e10	+	1.36748e10i	0.321462	+	0.185596i	0.652044	−	0.758181i	$-0.273912\pi$
$521$	2.36854e10	+	1.36748e10i	0.321462	+	0.185596i	−0.330582	+	0.943777i	$0.607245\pi$
$522$	9.72448e9	−	3.79591e9i	0.130974	−	0.0511250i
$523$	1.45372e9	+	2.51791e9i	0.0194300	+	0.0336537i	0.875577	−	0.483079i	$-0.160482\pi$
$523$	1.45372e9	+	2.51791e9i	0.0194300	+	0.0336537i	−0.856147	+	0.516732i	$0.827148\pi$
$524$	2.86950e9	+	7.88388e9i	0.0380610	+	0.104572i
$525$	6.12366e10	−	7.07006e8i	0.806072	−	0.00930649i
$526$	−2.17934e10	+	1.82868e10i	−0.284697	+	0.238889i
$527$	2.27947e9	+	2.71656e9i	0.0295523	+	0.0352190i
$528$	1.28670e8	+	1.11446e10i	0.00165555	+	0.143393i
$529$	−1.44115e10	+	5.24536e9i	−0.184029	+	0.0669812i
$530$	−3.34171e9	+	1.92934e9i	−0.0423512	+	0.0244515i
$531$	−5.44802e10	−	8.31430e9i	−0.685268	−	0.104580i
$532$	3.91819e9	−	6.78651e9i	0.0489147	−	0.0847228i
$533$	1.00914e10	+	1.77938e9i	0.125038	+	0.0220476i
$534$	−4.03590e10	−	1.41640e10i	−0.496335	−	0.174189i
$535$	−8.28805e9	−	3.01660e9i	−0.101167	−	0.0368217i
$536$	1.36494e10	−	2.40675e9i	0.165369	−	0.0291590i
$537$	−1.16767e10	−	1.92020e9i	−0.140418	−	0.0230914i
$538$	4.62165e10	+	3.87802e10i	0.551655	+	0.462894i
$539$			1.65585e10i			0.196186i
$540$	2.06299e9	−	2.63902e9i	0.0242617	−	0.0310362i
$541$	−1.91676e10			−0.223758			−0.111879	−	0.993722i	$-0.535687\pi$
$541$	−1.91676e10			−0.223758			−0.111879	+	0.993722i	$0.535687\pi$
$542$	−7.27291e10	+	8.66752e10i	−0.842774	+	1.00438i
$543$	5.82323e10	−	2.19594e10i	0.669830	−	0.252593i
$544$	1.87264e8	+	1.06203e9i	0.00213825	+	0.0121266i
$545$	−2.94241e9	+	8.08421e9i	−0.0333517	+	0.0916330i
$546$	−3.28025e9	−	3.81884e9i	−0.0369094	−	0.0429695i
$547$	4.61040e9	−	2.61469e10i	0.0514978	−	0.292059i	−0.948172	−	0.317758i	$-0.897070\pi$
$547$	4.61040e9	−	2.61469e10i	0.0514978	−	0.292059i	0.999670	+	0.0256991i	$0.00818119\pi$
$548$	−1.76738e10	−	1.02040e10i	−0.195978	−	0.113148i
$549$	−3.38891e10	+	7.82636e8i	−0.373053	+	0.00861530i
$550$	1.84425e10	+	3.19433e10i	0.201543	+	0.349083i
$551$	−1.51198e9	−	4.15413e9i	−0.0164036	−	0.0450685i
$552$	1.50115e10	+	2.53209e10i	0.161684	+	0.272724i
$553$	3.56762e10	−	2.99359e10i	0.381486	−	0.320105i
$554$	−4.48558e10	−	5.34571e10i	−0.476190	−	0.567501i
$555$	−1.88813e9	−	1.06124e9i	−0.0199003	−	0.0111851i
$556$	−5.97125e10	+	2.17336e10i	−0.624836	+	0.227422i
$557$	8.50253e10	−	4.90894e10i	0.883339	−	0.509996i	0.0115812	−	0.999933i	$-0.496314\pi$
$557$	8.50253e10	−	4.90894e10i	0.883339	−	0.509996i	0.871758	+	0.489937i	$0.162980\pi$
$558$	−1.44893e10	+	4.28634e10i	−0.149455	+	0.442130i
$559$	−2.83917e9	+	4.91759e9i	−0.0290767	+	0.0503623i
$560$	1.54742e9	+	2.72852e8i	0.0157346	+	0.00277444i
$561$	−7.32181e8	−	3.88929e9i	−0.00739209	−	0.0392662i
$562$	−6.27064e10	−	2.28233e10i	−0.628589	−	0.228788i
$563$	−5.77083e10	+	1.01755e10i	−0.574387	+	0.101280i	−0.453294	−	0.891361i	$-0.649751\pi$
$563$	−5.77083e10	+	1.01755e10i	−0.574387	+	0.101280i	−0.121093	+	0.992641i	$0.538640\pi$
$564$	−2.86461e10	+	3.49507e10i	−0.283106	+	0.345413i
$565$	−6.92033e9	−	5.80684e9i	−0.0679099	−	0.0569831i
$566$		−	1.52731e10i		−	0.148820i
$567$	−1.83542e10	−	8.18039e10i	−0.177584	−	0.791483i
$568$	6.20337e10			0.595984
$569$	−9.36498e10	+	1.11607e11i	−0.893424	+	1.06474i	0.104111	+	0.994566i	$0.466800\pi$
$569$	−9.36498e10	+	1.11607e11i	−0.893424	+	1.06474i	−0.997535	+	0.0701757i	$0.977644\pi$
$570$	−1.09710e9	−	8.99201e8i	−0.0103932	−	0.00851838i
$571$	1.83624e10	+	1.04138e11i	0.172737	+	0.979639i	0.940724	+	0.339174i	$0.110147\pi$
$571$	1.83624e10	+	1.04138e11i	0.172737	+	0.979639i	−0.767987	+	0.640465i	$0.778742\pi$
$572$	1.03704e9	−	2.84924e9i	0.00968749	−	0.0266162i
$573$	−8.08400e10	+	1.52186e10i	−0.749908	+	0.141174i
$574$	−1.39004e10	+	7.88333e10i	−0.128050	+	0.726210i
$575$	8.43663e10	+	4.87089e10i	0.771787	+	0.445592i
$576$	−1.03333e10	+	9.08538e9i	−0.0938750	+	0.0825378i
$577$	−8.35675e10	−	1.44743e11i	−0.753936	−	1.30585i	−0.945902	−	0.324453i	$-0.894820\pi$
$577$	−8.35675e10	−	1.44743e11i	−0.753936	−	1.30585i	0.191966	−	0.981402i	$-0.438514\pi$
$578$	2.68618e10	+	7.38023e10i	0.240671	+	0.661239i
$579$	−7.79850e10	+	1.38749e11i	−0.693900	+	1.23457i
$580$	6.79031e8	−	5.69774e8i	0.00600036	−	0.00503490i
$581$	−5.46566e10	−	6.51372e10i	−0.479665	−	0.571643i
$582$	−1.36827e11	+	8.11178e10i	−1.19256	+	0.707008i
$583$	−5.46600e10	+	1.98946e10i	−0.473146	+	0.172211i
$584$	−1.09095e10	+	6.29859e9i	−0.0937892	+	0.0541492i
$585$	−7.78464e8	+	4.73741e8i	−0.00664684	+	0.00404499i
$586$	5.36985e10	−	9.30085e10i	0.455377	−	0.788737i
$587$	8.72869e10	+	1.53910e10i	0.735185	+	0.129633i	0.528690	−	0.848815i	$-0.322683\pi$
$587$	8.72869e10	+	1.53910e10i	0.735185	+	0.129633i	0.206494	+	0.978448i	$0.433794\pi$
$588$	−1.55069e10	+	1.33199e10i	−0.129723	+	0.111428i
$589$	1.80053e10	+	6.55338e9i	0.149602	+	0.0544508i
$590$	−4.60853e9	+	8.12609e8i	−0.0380325	+	0.00670615i
$591$	−2.78373e10	−	7.38192e10i	−0.228179	−	0.605089i
$592$	6.81546e9	+	5.71885e9i	0.0554892	+	0.0465610i
$593$		−	5.17123e9i		−	0.0418191i	−0.999781	−	0.0209096i	$-0.993344\pi$
$593$		−	5.17123e9i		−	0.0418191i	0.999781	−	0.0209096i	$-0.00665620\pi$
$594$	3.75343e10	−	3.37776e10i	0.301497	−	0.271321i
$595$	−5.57952e8			−0.00445173
$596$	−2.05447e9	+	2.44842e9i	−0.0162823	+	0.0194045i
$597$	6.72815e9	−	4.09139e10i	0.0529662	−	0.322087i
$598$	−1.39060e9	−	7.88650e9i	−0.0108742	−	0.0616708i
$599$	−3.22813e10	+	8.86921e10i	−0.250751	+	0.688934i	0.748904	+	0.662679i	$0.230580\pi$
$599$	−3.22813e10	+	8.86921e10i	−0.250751	+	0.688934i	−0.999655	+	0.0262551i	$0.991642\pi$
$600$	−1.50792e10	+	4.29669e10i	−0.116352	+	0.331535i
$601$	3.26169e10	−	1.84979e11i	0.250002	−	1.41783i	−0.558580	−	0.829451i	$-0.688654\pi$
$601$	3.26169e10	−	1.84979e11i	0.250002	−	1.41783i	0.808582	−	0.588383i	$-0.200235\pi$
$602$	−3.84160e10	−	2.21795e10i	−0.292500	−	0.168875i
$603$	−4.90218e10	−	3.92417e10i	−0.370783	−	0.296810i
$604$	−2.24353e9	−	3.88591e9i	−0.0168572	−	0.0291974i
$605$	2.42234e9	+	6.65531e9i	0.0180806	+	0.0496760i
$606$	−2.37176e10	+	2.73832e8i	−0.175866	+	0.00203045i
$607$	1.17126e11	−	9.82801e10i	0.862775	−	0.723954i	−0.0997893	−	0.995009i	$-0.531817\pi$
$607$	1.17126e11	−	9.82801e10i	0.862775	−	0.723954i	0.962564	+	0.271055i	$0.0873724\pi$
$608$	3.74541e9	+	4.46361e9i	0.0274085	+	0.0326642i
$609$	−2.56127e8	−	2.21841e10i	−0.00186202	−	0.161277i
$610$	−2.70480e9	+	9.84465e8i	−0.0195351	+	0.00711019i
$611$	1.06469e10	−	6.14700e9i	0.0763940	−	0.0441061i
$612$	3.05331e9	−	3.81428e9i	0.0217653	−	0.0271899i
$613$	9.69886e10	−	1.67989e11i	0.686876	−	1.18970i	−0.285967	−	0.958240i	$-0.592315\pi$
$613$	9.69886e10	−	1.67989e11i	0.686876	−	1.18970i	0.972843	−	0.231465i	$-0.0743520\pi$
$614$	1.99619e10	+	3.51983e9i	0.140452	+	0.0247656i
$615$	1.36727e10	+	4.79845e9i	0.0955773	+	0.0335429i
$616$	2.22581e10	+	8.10129e9i	0.154584	+	0.0562641i
$617$	−2.49874e11	+	4.40595e10i	−1.72417	+	0.304018i	−0.946031	−	0.324075i	$-0.894947\pi$
$617$	−2.49874e11	+	4.40595e10i	−1.72417	+	0.304018i	−0.778139	+	0.628092i	$0.783836\pi$
$618$	−2.21268e10	−	3.63868e9i	−0.151693	−	0.0249454i
$619$	−6.45714e10	−	5.41819e10i	−0.439823	−	0.369055i	0.395820	−	0.918328i	$-0.370460\pi$
$619$	−6.45714e10	−	5.41819e10i	−0.439823	−	0.369055i	−0.835643	+	0.549273i	$0.814905\pi$
$620$			3.84198e9i			0.0260009i
$621$	4.12461e10	−	1.26825e11i	0.277343	−	0.852784i
$622$	9.70444e10			0.648349
$623$	−5.84304e10	+	6.96346e10i	−0.387870	+	0.462246i
$624$	3.50250e9	−	1.32079e9i	0.0231015	−	0.00871157i
$625$	2.60042e10	+	1.47477e11i	0.170421	+	0.966506i
$626$	5.77284e10	−	1.58608e11i	0.375917	−	1.03282i
$627$	−1.39333e10	−	1.62210e10i	−0.0901538	−	0.104956i
$628$	−1.41557e10	+	8.02809e10i	−0.0910107	+	0.516147i
$629$	−2.73597e9	−	1.57961e9i	−0.0174787	−	0.0100913i
$630$	−3.70084e9	−	6.08132e9i	−0.0234930	−	0.0386043i
$631$	−9.10902e9	−	1.57773e10i	−0.0574585	−	0.0995210i	0.835865	−	0.548934i	$-0.184966\pi$
$631$	−9.10902e9	−	1.57773e10i	−0.0574585	−	0.0995210i	−0.893324	+	0.449413i	$0.851633\pi$
$632$	1.18438e10	+	3.25407e10i	0.0742377	+	0.203966i
$633$	1.36571e11	+	2.30365e11i	0.850639	+	1.43484i
$634$	1.45011e11	−	1.21679e11i	0.897522	−	0.753110i
$635$	1.23288e10	+	1.46928e10i	0.0758271	+	0.0903672i
$636$	−6.26004e10	−	3.51851e10i	−0.382603	−	0.215045i
$637$	5.22594e9	−	1.90209e9i	0.0317400	−	0.0115524i
$638$	1.15721e10	−	6.68114e9i	0.0698439	−	0.0403244i
$639$	−1.85578e11	−	2.11068e11i	−1.11307	−	1.26596i
$640$	−5.84175e8	+	1.01182e9i	−0.00348196	+	0.00603092i
$641$	−1.72048e11	−	3.03367e10i	−1.01910	−	0.179695i	−0.360954	−	0.932584i	$-0.617549\pi$
$641$	−1.72048e11	−	3.03367e10i	−1.01910	−	0.179695i	−0.658148	+	0.752889i	$0.728660\pi$
$642$	−3.03672e10	−	1.61308e11i	−0.178757	−	0.949546i
$643$	2.09323e11	+	7.61874e10i	1.22454	+	0.445697i	0.871725	−	0.489996i	$-0.163002\pi$
$643$	2.09323e11	+	7.61874e10i	1.22454	+	0.445697i	0.352817	+	0.935692i	$0.385224\pi$
$644$	6.16089e10	−	1.08633e10i	0.358179	−	0.0631566i
$645$	−5.09005e9	+	6.21030e9i	−0.0294092	+	0.0358817i
$646$	−1.58498e9	−	1.32996e9i	−0.00910112	−	0.00763675i
$647$			1.02730e11i			0.586247i	0.956075	+	0.293124i	$0.0946948\pi$
$647$			1.02730e11i			0.586247i	−0.956075	+	0.293124i	$0.905305\pi$
$648$	6.18255e10	+	7.97936e9i	0.350645	+	0.0452552i
$649$	−7.05434e10			−0.397629
$650$	7.96294e9	−	9.48986e9i	0.0446087	−	0.0531626i
$651$	7.43709e10	+	6.09554e10i	0.414075	+	0.339382i
$652$	1.70598e10	+	9.67512e10i	0.0944028	+	0.535385i
$653$	−5.29934e10	+	1.45598e11i	−0.291454	+	0.800762i	0.704401	+	0.709802i	$0.251216\pi$
$653$	−5.29934e10	+	1.45598e11i	−0.291454	+	0.800762i	−0.995855	+	0.0909598i	$0.971007\pi$
$654$	−1.57341e11	+	2.96203e10i	−0.860063	+	0.161912i
$655$	5.60470e8	−	3.17858e9i	0.00304500	−	0.0172691i
$656$	−5.15472e10	−	2.97608e10i	−0.278349	−	0.160705i
$657$	5.40672e10	+	1.82766e10i	0.290183	+	0.0980921i
$658$	4.80200e10	+	8.31731e10i	0.256164	+	0.443690i
$659$	7.62706e10	+	2.09552e11i	0.404404	+	1.11109i	0.960088	+	0.279697i	$0.0902341\pi$
$659$	7.62706e10	+	2.09552e11i	0.404404	+	1.11109i	−0.555684	+	0.831393i	$0.687544\pi$
$660$	2.10083e9	−	3.73774e9i	0.0110717	−	0.0196985i
$661$	1.76438e11	−	1.48049e11i	0.924243	−	0.775532i	−0.0505318	−	0.998722i	$-0.516092\pi$
$661$	1.76438e11	−	1.48049e11i	0.924243	−	0.775532i	0.974775	+	0.223190i	$0.0716472\pi$
$662$	−1.07976e11	−	1.28680e11i	−0.562204	−	0.670008i
$663$	−1.14337e9	+	6.77843e8i	−0.00591742	+	0.00350813i
$664$	5.94124e10	−	2.16243e10i	0.305636	−	0.111242i
$665$	−2.61081e9	+	1.50735e9i	−0.0133502	+	0.00770775i
$666$	−9.30638e8	−	4.02977e10i	−0.00473025	−	0.204825i
$667$	1.76457e10	−	3.05633e10i	0.0891531	−	0.154418i
$668$	1.31580e11	+	2.32010e10i	0.660820	+	0.116520i
$669$	−7.48409e10	+	6.42859e10i	−0.373624	+	0.320930i
$670$	−5.01043e9	−	1.82365e9i	−0.0248643	−	0.00904986i
$671$	−4.27312e10	+	7.53467e9i	−0.210793	+	0.0371684i
$672$	1.03180e10	+	2.73613e10i	0.0505961	+	0.134171i
$673$	2.14684e10	+	1.80141e10i	0.104650	+	0.0878118i	0.693611	−	0.720349i	$-0.256019\pi$
$673$	2.14684e10	+	1.80141e10i	0.104650	+	0.0878118i	−0.588961	+	0.808161i	$0.700463\pi$
$674$		−	2.31797e11i		−	1.12323i
$675$	1.91304e11	−	7.72314e10i	0.921529	−	0.372031i
$676$	1.03395e11			0.495123
$677$	−1.70444e11	+	2.03127e11i	−0.811384	+	0.966970i	−0.999886	−	0.0151030i	$-0.995192\pi$
$677$	−1.70444e11	+	2.03127e11i	−0.811384	+	0.966970i	0.188502	+	0.982073i	$0.439637\pi$
$678$	2.72807e10	−	1.65894e11i	0.129103	−	0.785075i
$679$	5.87023e10	+	3.32918e11i	0.276170	+	1.56624i
$680$	1.41894e8	−	3.89851e8i	0.000663634	−	0.00182332i
$681$	−9.55749e10	+	2.72332e11i	−0.444381	+	1.26622i
$682$	−1.00570e10	+	5.70364e10i	−0.0464872	+	0.263642i
$683$	3.24306e11	+	1.87238e11i	1.49029	+	0.860422i	0.999938	−	0.0111006i	$-0.00353352\pi$
$683$	3.24306e11	+	1.87238e11i	1.49029	+	0.860422i	0.490356	+	0.871522i	$0.336867\pi$
$684$	3.98267e9	−	2.60968e10i	0.0181949	−	0.119224i
$685$	3.92552e9	+	6.79920e9i	0.0178293	+	0.0308813i
$686$	5.83040e10	+	1.60189e11i	0.263270	+	0.723329i
$687$	5.63351e10	−	6.50417e8i	0.252902	−	0.00291988i
$688$	2.52668e10	−	2.12014e10i	0.112771	−	0.0946260i
$689$	1.25576e10	+	1.49656e10i	0.0557225	+	0.0664075i
$690$	−1.30736e8	−	1.13235e10i	−0.000576764	−	0.0499558i
$691$	−1.75800e11	+	6.39861e10i	−0.771095	+	0.280656i	−0.697454	−	0.716629i	$-0.745684\pi$
$691$	−1.75800e11	+	6.39861e10i	−0.771095	+	0.280656i	−0.0736406	+	0.997285i	$0.523462\pi$
$692$	−5.56274e10	+	3.21165e10i	−0.242585	+	0.140057i
$693$	−3.90221e10	−	9.99682e10i	−0.169191	−	0.433440i
$694$	9.40750e10	−	1.62943e11i	0.405543	−	0.702420i
$695$	2.40746e10	+	4.24500e9i	0.103186	+	0.0181944i
$696$	1.55656e10	+	5.46274e9i	0.0663328	+	0.0232795i
$697$	1.98609e10	+	7.22878e9i	0.0841527	+	0.0306291i
$698$	2.56461e11	−	4.52210e10i	1.08044	−	0.190510i
$699$	3.03161e11	+	4.98539e10i	1.26989	+	0.208829i
$700$	7.41342e10	+	6.22060e10i	0.308764	+	0.259084i
$701$		−	1.12948e11i		−	0.467742i	−0.972268	−	0.233871i	$-0.924861\pi$
$701$		−	1.12948e11i		−	0.467742i	0.972268	−	0.233871i	$-0.0751394\pi$
$702$	−1.49719e10	−	7.96592e9i	−0.0616494	−	0.0328010i
$703$	−1.70698e10			−0.0698887
$704$	−1.13210e10	+	1.34919e10i	−0.0460888	+	0.0549265i
$705$	1.62667e10	−	6.13418e9i	0.0658481	−	0.0248313i
$706$	1.13964e10	+	6.46320e10i	0.0458720	+	0.260153i
$707$	−1.72409e10	+	4.73691e10i	−0.0690055	+	0.189591i
$708$	−5.67462e10	−	6.60633e10i	−0.225841	−	0.262922i
$709$	7.71577e10	−	4.37583e11i	0.305347	−	1.73171i	−0.316517	−	0.948587i	$-0.602513\pi$
$709$	7.71577e10	−	4.37583e11i	0.305347	−	1.73171i	0.621865	−	0.783125i	$-0.286375\pi$
$710$	−2.06674e10	−	1.19323e10i	−0.0813304	−	0.0469562i
$711$	7.52873e10	−	1.37646e11i	0.294607	−	0.538623i
$712$	−3.37954e10	−	5.85353e10i	−0.131503	−	0.227771i
$713$	5.23168e10	+	1.43739e11i	0.202434	+	0.556182i
$714$	−5.29527e9	−	8.93193e9i	−0.0203749	−	0.0343679i
$715$	−8.93564e8	+	7.49790e8i	−0.00341902	+	0.00286890i
$716$	−1.20201e10	−	1.43250e10i	−0.0457358	−	0.0545058i
$717$	−6.75261e10	−	3.79536e10i	−0.255502	−	0.143607i
$718$	−2.02242e10	+	7.36101e9i	−0.0760981	+	0.0276974i
$719$	2.91184e11	−	1.68115e11i	1.08956	−	0.629059i	0.156103	−	0.987741i	$-0.450107\pi$
$719$	2.91184e11	−	1.68115e11i	1.08956	−	0.629059i	0.933460	+	0.358681i	$0.116774\pi$
$720$	5.19029e9	−	1.03929e9i	0.0193135	−	0.00386727i
$721$	−2.38283e10	+	4.12718e10i	−0.0881762	+	0.152726i
$722$	1.78218e11	+	3.14247e10i	0.655849	+	0.115644i
$723$	−1.54732e10	−	8.21923e10i	−0.0566273	−	0.300800i
$724$	9.24159e10	+	3.36366e10i	0.336351	+	0.122422i
$725$	5.37644e10	−	9.48011e9i	0.194600	−	0.0343132i
$726$	−8.35518e10	+	1.01940e11i	−0.300753	+	0.366944i
$727$	−3.61510e11	−	3.03343e11i	−1.29414	−	1.08592i	−0.991125	−	0.132932i	$-0.957561\pi$
$727$	−3.61510e11	−	3.03343e11i	−1.29414	−	1.08592i	−0.303020	−	0.952984i	$-0.597995\pi$
$728$		−	7.95535e9i		−	0.0283226i
$729$	−1.57805e11	−	2.34230e11i	−0.558742	−	0.829341i
$730$	4.84621e9			0.0170652
$731$	−7.52842e9	+	8.97202e9i	−0.0263654	+	0.0314210i
$732$	−4.14298e10	−	3.39564e10i	−0.144301	−	0.118271i
$733$	5.69866e10	+	3.23187e11i	0.197404	+	1.11954i	0.908953	+	0.416898i	$0.136883\pi$
$733$	5.69866e10	+	3.23187e11i	0.197404	+	1.11954i	−0.711549	+	0.702637i	$0.752006\pi$
$734$	1.09741e11	−	3.01512e11i	0.378082	−	1.03877i
$735$	7.72848e9	−	1.45493e9i	0.0264816	−	0.00498532i
$736$	−8.07752e9	+	4.58099e10i	−0.0275275	+	0.156116i
$737$	−6.96090e10	−	4.01888e10i	−0.235937	−	0.136218i
$738$	5.29463e10	+	2.64419e11i	0.178489	+	0.891389i
$739$	−6.10128e10	−	1.05677e11i	−0.204571	−	0.354327i	0.745425	−	0.666589i	$-0.232246\pi$
$739$	−6.10128e10	−	1.05677e11i	−0.204571	−	0.354327i	−0.949996	+	0.312263i	$0.898913\pi$
$740$	−1.17063e9	−	3.21629e9i	−0.00390386	−	0.0107258i
$741$	−3.51889e9	+	6.26071e9i	−0.0116717	+	0.0207659i
$742$	−1.16910e11	+	9.80995e10i	−0.385689	+	0.323632i
$743$	4.46774e10	+	5.32445e10i	0.146600	+	0.174711i	0.834347	−	0.551239i	$-0.185845\pi$
$743$	4.46774e10	+	5.32445e10i	0.146600	+	0.174711i	−0.687748	+	0.725950i	$0.741400\pi$
$744$	−6.15041e10	+	3.64625e10i	−0.200730	+	0.119002i
$745$	1.15544e9	−	4.20545e8i	0.00375078	−	0.00136517i
$746$	−6.87242e10	+	3.96779e10i	−0.221899	+	0.128113i
$747$	−2.51312e11	−	1.37459e11i	−0.807107	−	0.441458i
$748$	3.12700e9	−	5.41612e9i	0.00998899	−	0.0173014i
$749$	−3.43541e11	−	6.05756e10i	−1.09157	−	0.192473i
$750$	2.66603e10	−	2.29003e10i	0.0842598	−	0.0723763i
$751$	−5.19998e11	−	1.89264e11i	−1.63472	−	0.594988i	−0.648612	−	0.761119i	$-0.724650\pi$
$751$	−5.19998e11	−	1.89264e11i	−1.63472	−	0.594988i	−0.986104	+	0.166131i	$0.946873\pi$
$752$	−7.03266e10	+	1.24005e10i	−0.219912	+	0.0387764i
$753$	1.79500e11	+	4.76000e11i	0.558321	+	1.48056i
$754$	−3.43788e9	−	2.88473e9i	−0.0106367	−	0.00892523i
$755$			1.72620e9i			0.00531254i

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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	54.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(7.27231 - 8.66680i) q^{2} +(-62.6465 - 51.3460i) q^{3} +(-22.2270 - 126.055i) q^{4} +(-16.8419 + 46.2726i) q^{5} +(-900.591 + 169.541i) q^{6} +(-338.197 + 1918.01i) q^{7} +(-1254.14 - 724.077i) q^{8} +(1288.18 + 6433.30i) q^{9} +O(q^{10})\)	\(q+(7.27231 - 8.66680i) q^{2} +(-62.6465 - 51.3460i) q^{3} +(-22.2270 - 126.055i) q^{4} +(-16.8419 + 46.2726i) q^{5} +(-900.591 + 169.541i) q^{6} +(-338.197 + 1918.01i) q^{7} +(-1254.14 - 724.077i) q^{8} +(1288.18 + 6433.30i) q^{9} +(278.556 + 482.474i) q^{10} +(2872.37 + 7891.77i) q^{11} +(-5080.00 + 9038.20i) q^{12} +(2160.72 - 1813.06i) q^{13} +(14163.5 + 16879.4i) q^{14} +(3431.00 - 2034.06i) q^{15} +(-15395.9 + 5603.66i) q^{16} +(5038.37 - 2908.90i) q^{17} +(65124.2 + 35620.5i) q^{18} +(15717.3 - 27223.1i) q^{19} +(6207.26 + 1094.51i) q^{20} +(119669. - 102792. i) q^{21} +(89285.2 + 32497.2i) q^{22} +(247135. - 43576.6i) q^{23} +(41389.0 + 109756. i) q^{24} +(297379. + 249530. i) q^{25} -31911.7i q^{26} +(249624. - 469167. i) q^{27} +249292. q^{28} +(90397.1 - 107731. i) q^{29} +(7322.50 - 44528.1i) q^{30} +(105847. + 600286. i) q^{31} +(-63398.2 + 174185. i) q^{32} +(225267. - 641877. i) q^{33} +(11429.7 - 64821.0i) q^{34} +(-83055.4 - 47952.1i) q^{35} +(782319. - 305375. i) q^{36} +(-271513. - 470275. i) q^{37} +(-121636. - 334193. i) q^{38} +(-228455. + 2637.63i) q^{39} +(54627.0 - 45837.5i) q^{40} +(2.33519e6 + 2.78297e6i) q^{41} +(-20605.0 - 1.78468e6i) q^{42} +(-1.89175e6 + 688539. i) q^{43} +(930956. - 537488. i) q^{44} +(-319381. - 48741.2i) q^{45} +(1.41957e6 - 2.45877e6i) q^{46} +(4.29240e6 + 756865. i) q^{47} +(1.25223e6 + 439469. i) q^{48} +(1.85276e6 + 674350. i) q^{49} +(4.32526e6 - 762660. i) q^{50} +(-464997. - 76467.2i) q^{51} +(-276572. - 232072. i) q^{52} +6.92620e6i q^{53} +(-2.25083e6 - 5.57537e6i) q^{54} -413549. q^{55} +(1.81293e6 - 2.16057e6i) q^{56} +(-2.38243e6 + 898415. i) q^{57} +(-276288. - 1.56691e6i) q^{58} +(-2.87289e6 + 7.89321e6i) q^{59} +(-332665. - 387285. i) q^{60} +(-897172. + 5.08811e6i) q^{61} +(5.97231e6 + 3.44811e6i) q^{62} +(-1.27748e7 + 295021. i) q^{63} +(1.04858e6 + 1.81619e6i) q^{64} +(47504.5 + 130518. i) q^{65} +(-3.92481e6 - 6.62027e6i) q^{66} +(-7.33162e6 + 6.15196e6i) q^{67} +(-478671. - 570457. i) q^{68} +(-1.77196e7 - 9.95946e6i) q^{69} +(-1.01960e6 + 371103. i) q^{70} +(-3.70974e7 + 2.14182e7i) q^{71} +(3.04265e6 - 9.00099e6i) q^{72} +(4.34939e6 - 7.53337e6i) q^{73} +(-6.05031e6 - 1.06683e6i) q^{74} +(-5.81737e6 - 3.09014e7i) q^{75} +(-3.78097e6 - 1.37616e6i) q^{76} +(-1.61079e7 + 2.84026e6i) q^{77} +(-1.63854e6 + 1.99916e6i) q^{78} +(-1.83181e7 - 1.53707e7i) q^{79} -806786. i q^{80} +(-3.97279e7 + 1.65745e7i) q^{81} +4.11016e7 q^{82} +(-2.80636e7 + 3.34449e7i) q^{83} +(-1.56173e7 - 1.28002e7i) q^{84} +(49747.1 + 282130. i) q^{85} +(-7.78993e6 + 2.14027e7i) q^{86} +(-1.11946e7 + 2.10745e6i) q^{87} +(2.11190e6 - 1.19772e7i) q^{88} +(4.04206e7 + 2.33369e7i) q^{89} +(-2.74507e6 + 2.41355e6i) q^{90} +(2.74672e6 + 4.75746e6i) q^{91} +(-1.09861e7 - 3.01841e7i) q^{92} +(2.41913e7 - 4.30406e7i) q^{93} +(3.77752e7 - 3.16972e7i) q^{94} +(994976. + 1.18577e6i) q^{95} +(1.29154e7 - 7.65685e6i) q^{96} +(1.63107e8 - 5.93660e7i) q^{97} +(1.93183e7 - 1.11534e7i) q^{98} +(-4.70700e7 + 2.86448e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9	\( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) 144 * q + 882 * q^5 + 768 * q^6 + 25908 * q^9 - 45756 * q^11 - 21504 * q^12 + 94464 * q^14 - 70002 * q^15 - 182784 * q^18 - 225792 * q^20 - 2071668 * q^21 + 185472 * q^22 + 552996 * q^23 - 1015182 * q^25 - 4137588 * q^27 - 2856132 * q^29 - 861696 * q^30 - 1841490 * q^31 + 10547334 * q^33 - 661248 * q^34 - 12450834 * q^35 - 5104128 * q^36 + 14063616 * q^38 + 4239102 * q^39 - 15673536 * q^41 - 11028480 * q^42 - 4412520 * q^43 - 12558942 * q^45 + 15173838 * q^47 + 3440640 * q^48 - 11347488 * q^49 - 27744768 * q^50 - 3281850 * q^51 + 16379136 * q^54 + 12091392 * q^56 - 13553658 * q^57 - 86547168 * q^59 - 26125056 * q^60 - 34059456 * q^61 + 108329070 * q^63 + 150994944 * q^64 + 22190346 * q^65 + 152091648 * q^66 + 167100948 * q^67 + 13411584 * q^68 - 40190130 * q^69 - 118080000 * q^70 - 251437608 * q^71 - 60948480 * q^72 + 15265278 * q^73 + 41902848 * q^74 + 138868662 * q^75 + 67995648 * q^76 + 564911586 * q^77 + 201203712 * q^78 + 137535768 * q^79 - 23838948 * q^81 - 482857578 * q^83 - 128300544 * q^84 - 343215000 * q^85 - 46237824 * q^86 + 34353810 * q^87 + 47480832 * q^88 + 375969762 * q^89 + 452712960 * q^90 - 155093598 * q^91 + 97042176 * q^92 + 285095622 * q^93 - 70995456 * q^94 - 966996432 * q^95 - 88080384 * q^96 - 484917300 * q^97 - 234233856 * q^98 + 26756370 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more