LMFDB - Embedded newform 16.9.f.a.3.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,9,Mod(3,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("16.3");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	16.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.51805776098$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.13
Character	$\chi$	$=$	16.3
Dual form			16.9.f.a.11.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(13.3691 + 8.79011i) q^{2} +(-67.4818 + 67.4818i) q^{3} +(101.468 + 235.033i) q^{4} +(191.722 - 191.722i) q^{5} +(-1495.35 + 309.001i) q^{6} -3935.28 q^{7} +(-709.426 + 4034.10i) q^{8} -2546.60i q^{9} +O(q^{10})$	\(q+(13.3691 + 8.79011i) q^{2} +(-67.4818 + 67.4818i) q^{3} +(101.468 + 235.033i) q^{4} +(191.722 - 191.722i) q^{5} +(-1495.35 + 309.001i) q^{6} -3935.28 q^{7} +(-709.426 + 4034.10i) q^{8} -2546.60i q^{9} +(4248.42 - 877.901i) q^{10} +(-868.992 - 868.992i) q^{11} +(-22707.7 - 9013.20i) q^{12} +(28225.1 + 28225.1i) q^{13} +(-52611.3 - 34591.5i) q^{14} +25875.5i q^{15} +(-44944.6 + 47696.5i) q^{16} +56076.6 q^{17} +(22384.9 - 34045.8i) q^{18} +(-36644.4 + 36644.4i) q^{19} +(64514.6 + 25607.3i) q^{20} +(265560. - 265560. i) q^{21} +(-3979.13 - 19256.2i) q^{22} +469847. q^{23} +(-224355. - 320102. i) q^{24} +317110. i q^{25} +(129244. + 625448. i) q^{26} +(-270899. - 270899. i) q^{27} +(-399304. - 924918. i) q^{28} +(-298908. - 298908. i) q^{29} +(-227449. + 345934. i) q^{30} +1.42640e6i q^{31} +(-1.02013e6 + 242592. i) q^{32} +117282. q^{33} +(749695. + 492919. i) q^{34} +(-754480. + 754480. i) q^{35} +(598533. - 258397. i) q^{36} +(855988. - 855988. i) q^{37} +(-812013. + 167796. i) q^{38} -3.80937e6 q^{39} +(637413. + 909439. i) q^{40} -3.48662e6i q^{41} +(5.88460e6 - 1.21600e6i) q^{42} +(-2.28219e6 - 2.28219e6i) q^{43} +(116067. - 292416. i) q^{44} +(-488239. - 488239. i) q^{45} +(6.28146e6 + 4.13001e6i) q^{46} +2.66106e6i q^{47} +(-185701. - 6.25159e6i) q^{48} +9.72160e6 q^{49} +(-2.78743e6 + 4.23949e6i) q^{50} +(-3.78415e6 + 3.78415e6i) q^{51} +(-3.76988e6 + 9.49777e6i) q^{52} +(-2.55554e6 + 2.55554e6i) q^{53} +(-1.24045e6 - 6.00293e6i) q^{54} -333210. q^{55} +(2.79179e6 - 1.58753e7i) q^{56} -4.94567e6i q^{57} +(-1.36871e6 - 6.62358e6i) q^{58} +(5.04996e6 + 5.04996e6i) q^{59} +(-6.08159e6 + 2.62553e6i) q^{60} +(-5.51371e6 - 5.51371e6i) q^{61} +(-1.25382e7 + 1.90697e7i) q^{62} +1.00216e7i q^{63} +(-1.57706e7 - 5.72379e6i) q^{64} +1.08228e7 q^{65} +(1.56796e6 + 1.03092e6i) q^{66} +(2.78569e7 - 2.78569e7i) q^{67} +(5.68996e6 + 1.31798e7i) q^{68} +(-3.17062e7 + 3.17062e7i) q^{69} +(-1.67187e7 + 3.45478e6i) q^{70} +1.70407e7 q^{71} +(1.02732e7 + 1.80662e6i) q^{72} -4.86929e6i q^{73} +(1.89680e7 - 3.91959e6i) q^{74} +(-2.13992e7 - 2.13992e7i) q^{75} +(-1.23309e7 - 4.89440e6i) q^{76} +(3.41972e6 + 3.41972e6i) q^{77} +(-5.09280e7 - 3.34848e7i) q^{78} +4.23147e7i q^{79} +(527595. + 1.77613e7i) q^{80} +5.32698e7 q^{81} +(3.06478e7 - 4.66131e7i) q^{82} +(2.20460e7 - 2.20460e7i) q^{83} +(8.93609e7 + 3.54694e7i) q^{84} +(1.07511e7 - 1.07511e7i) q^{85} +(-1.04502e7 - 5.05716e7i) q^{86} +4.03418e7 q^{87} +(4.12208e6 - 2.88911e6i) q^{88} +9.93313e7i q^{89} +(-2.23566e6 - 1.08190e7i) q^{90} +(-1.11074e8 - 1.11074e8i) q^{91} +(4.76744e7 + 1.10429e8i) q^{92} +(-9.62560e7 - 9.62560e7i) q^{93} +(-2.33910e7 + 3.55761e7i) q^{94} +1.40511e7i q^{95} +(5.24695e7 - 8.52107e7i) q^{96} -1.23600e8 q^{97} +(1.29969e8 + 8.54540e7i) q^{98} +(-2.21297e6 + 2.21297e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8}+O(q^{10}) $ 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8} - 1860 q^{10} - 19778 q^{11} + 14068 q^{12} - 2 q^{13} - 58900 q^{14} + 245336 q^{16} - 4 q^{17} - 223730 q^{18} + 167550 q^{19} - 135380 q^{20} - 13124 q^{21} + 985700 q^{22} - 845572 q^{23} - 800592 q^{24} - 184760 q^{26} + 38656 q^{27} + 94136 q^{28} + 1066174 q^{29} + 1881700 q^{30} - 3395192 q^{32} - 4 q^{33} + 1634900 q^{34} + 426620 q^{35} + 1877324 q^{36} + 2360254 q^{37} - 3010352 q^{38} - 7650052 q^{39} + 3256936 q^{40} - 3731304 q^{42} + 6314814 q^{43} - 10360940 q^{44} + 794370 q^{45} + 1510780 q^{46} + 4591848 q^{48} + 14823770 q^{49} + 14752710 q^{50} - 28969860 q^{51} + 4335652 q^{52} + 2679358 q^{53} + 18667040 q^{54} + 46326780 q^{55} - 36346408 q^{56} - 1034696 q^{58} - 46004162 q^{59} - 20687200 q^{60} - 24476034 q^{61} - 64043472 q^{62} + 50827456 q^{64} - 14970820 q^{65} + 65035780 q^{66} + 59474558 q^{67} + 74339312 q^{68} + 8623420 q^{69} + 39082496 q^{70} - 79832068 q^{71} + 929812 q^{72} - 168043460 q^{74} + 88519490 q^{75} - 166219388 q^{76} + 35952572 q^{77} + 5059788 q^{78} - 12904856 q^{80} - 66961570 q^{81} + 261305296 q^{82} - 34471682 q^{83} + 456781480 q^{84} - 107741252 q^{85} + 9841444 q^{86} + 149712636 q^{87} - 173775752 q^{88} - 650366536 q^{90} - 76429060 q^{91} - 449169832 q^{92} + 138269056 q^{93} - 239278032 q^{94} + 378359728 q^{96} - 4 q^{97} + 630040554 q^{98} + 184838270 q^{99}+O(q^{100}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8 - 1860 * q^10 - 19778 * q^11 + 14068 * q^12 - 2 * q^13 - 58900 * q^14 + 245336 * q^16 - 4 * q^17 - 223730 * q^18 + 167550 * q^19 - 135380 * q^20 - 13124 * q^21 + 985700 * q^22 - 845572 * q^23 - 800592 * q^24 - 184760 * q^26 + 38656 * q^27 + 94136 * q^28 + 1066174 * q^29 + 1881700 * q^30 - 3395192 * q^32 - 4 * q^33 + 1634900 * q^34 + 426620 * q^35 + 1877324 * q^36 + 2360254 * q^37 - 3010352 * q^38 - 7650052 * q^39 + 3256936 * q^40 - 3731304 * q^42 + 6314814 * q^43 - 10360940 * q^44 + 794370 * q^45 + 1510780 * q^46 + 4591848 * q^48 + 14823770 * q^49 + 14752710 * q^50 - 28969860 * q^51 + 4335652 * q^52 + 2679358 * q^53 + 18667040 * q^54 + 46326780 * q^55 - 36346408 * q^56 - 1034696 * q^58 - 46004162 * q^59 - 20687200 * q^60 - 24476034 * q^61 - 64043472 * q^62 + 50827456 * q^64 - 14970820 * q^65 + 65035780 * q^66 + 59474558 * q^67 + 74339312 * q^68 + 8623420 * q^69 + 39082496 * q^70 - 79832068 * q^71 + 929812 * q^72 - 168043460 * q^74 + 88519490 * q^75 - 166219388 * q^76 + 35952572 * q^77 + 5059788 * q^78 - 12904856 * q^80 - 66961570 * q^81 + 261305296 * q^82 - 34471682 * q^83 + 456781480 * q^84 - 107741252 * q^85 + 9841444 * q^86 + 149712636 * q^87 - 173775752 * q^88 - 650366536 * q^90 - 76429060 * q^91 - 449169832 * q^92 + 138269056 * q^93 - 239278032 * q^94 + 378359728 * q^96 - 4 * q^97 + 630040554 * q^98 + 184838270 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	13.3691	+	8.79011i	0.835571	+	0.549382i
$2$	13.3691	+	8.79011i	0.835571	+	0.549382i
$3$	−67.4818	+	67.4818i	−0.833109	+	0.833109i	−0.987941	−	0.154832i	$-0.950516\pi$
$3$	−67.4818	+	67.4818i	−0.833109	+	0.833109i	0.154832	+	0.987941i	$0.450516\pi$
$4$	101.468	+	235.033i	0.396358	+	0.918096i
$5$	191.722	−	191.722i	0.306756	−	0.306756i	−0.536894	−	0.843650i	$-0.680403\pi$
$5$	191.722	−	191.722i	0.306756	−	0.306756i	0.843650	+	0.536894i	$0.180403\pi$
$6$	−1495.35	+	309.001i	−1.15382	+	0.238427i
$7$	−3935.28			−1.63902			−0.819508	−	0.573068i	$-0.805753\pi$
$7$	−3935.28			−1.63902			−0.819508	+	0.573068i	$0.805753\pi$
$8$	−709.426	+	4034.10i	−0.173200	+	0.984887i
$9$		−	2546.60i		−	0.388141i
$10$	4248.42	−	877.901i	0.424842	−	0.0877901i
$11$	−868.992	−	868.992i	−0.0593533	−	0.0593533i	0.676807	−	0.736160i	$-0.263363\pi$
$11$	−868.992	−	868.992i	−0.0593533	−	0.0593533i	−0.736160	+	0.676807i	$0.763363\pi$
$12$	−22707.7	−	9013.20i	−1.09508	−	0.434664i
$13$	28225.1	+	28225.1i	0.988241	+	0.988241i	0.999932	−	0.0116911i	$-0.00372147\pi$
$13$	28225.1	+	28225.1i	0.988241	+	0.988241i	−0.0116911	+	0.999932i	$0.503721\pi$
$14$	−52611.3	−	34591.5i	−1.36951	−	0.900446i
$15$			25875.5i			0.511122i
$16$	−44944.6	+	47696.5i	−0.685800	+	0.727790i
$17$	56076.6			0.671407			0.335703	−	0.941968i	$-0.391026\pi$
$17$	56076.6			0.671407			0.335703	+	0.941968i	$0.391026\pi$
$18$	22384.9	−	34045.8i	0.213238	−	0.324320i
$19$	−36644.4	+	36644.4i	−0.281186	+	0.281186i	−0.833582	−	0.552396i	$-0.813714\pi$
$19$	−36644.4	+	36644.4i	−0.281186	+	0.281186i	0.552396	+	0.833582i	$0.313714\pi$
$20$	64514.6	+	25607.3i	0.403216	+	0.160046i
$21$	265560.	−	265560.i	1.36548	−	1.36548i
$22$	−3979.13	−	19256.2i	−0.0169863	−	0.0822015i
$23$	469847.			1.67898			0.839490	−	0.543375i	$-0.182854\pi$
$23$	469847.			1.67898			0.839490	+	0.543375i	$0.182854\pi$
$24$	−224355.	−	320102.i	−0.676224	−	0.964812i
$25$			317110.i			0.811802i
$26$	129244.	+	625448.i	0.282824	+	1.36867i
$27$	−270899.	−	270899.i	−0.509745	−	0.509745i
$28$	−399304.	−	924918.i	−0.649638	−	1.50477i
$29$	−298908.	−	298908.i	−0.422616	−	0.422616i	0.463487	−	0.886103i	$-0.346598\pi$
$29$	−298908.	−	298908.i	−0.422616	−	0.422616i	−0.886103	+	0.463487i	$0.846598\pi$
$30$	−227449.	+	345934.i	−0.280801	+	0.427079i
$31$			1.42640e6i			1.54452i	0.635305	+	0.772261i	$0.280874\pi$
$31$			1.42640e6i			1.54452i	−0.635305	+	0.772261i	$0.719126\pi$
$32$	−1.02013e6	+	242592.i	−0.972870	+	0.231354i
$33$	117282.			0.0988955
$34$	749695.	+	492919.i	0.561008	+	0.368859i
$35$	−754480.	+	754480.i	−0.502777	+	0.502777i
$36$	598533.	−	258397.i	0.356351	−	0.153843i
$37$	855988.	−	855988.i	0.456731	−	0.456731i	−0.440850	−	0.897581i	$-0.645323\pi$
$37$	855988.	−	855988.i	0.456731	−	0.456731i	0.897581	+	0.440850i	$0.145323\pi$
$38$	−812013.	+	167796.i	−0.389429	+	0.0804723i
$39$	−3.80937e6			−1.64662
$40$	637413.	+	909439.i	0.248990	+	0.355250i
$41$		−	3.48662e6i		−	1.23387i	−0.787015	−	0.616934i	$-0.788374\pi$
$41$		−	3.48662e6i		−	1.23387i	0.787015	−	0.616934i	$-0.211626\pi$
$42$	5.88460e6	−	1.21600e6i	1.89112	−	0.390785i
$43$	−2.28219e6	−	2.28219e6i	−0.667541	−	0.667541i	0.289605	−	0.957146i	$-0.406476\pi$
$43$	−2.28219e6	−	2.28219e6i	−0.667541	−	0.667541i	−0.957146	+	0.289605i	$0.906476\pi$
$44$	116067.	−	292416.i	0.0309668	−	0.0780172i
$45$	−488239.	−	488239.i	−0.119065	−	0.119065i
$46$	6.28146e6	+	4.13001e6i	1.40291	+	0.922402i
$47$			2.66106e6i			0.545334i	0.962108	+	0.272667i	$0.0879058\pi$
$47$			2.66106e6i			0.545334i	−0.962108	+	0.272667i	$0.912094\pi$
$48$	−185701.	−	6.25159e6i	−0.0349824	−	1.17767i
$49$	9.72160e6			1.68637
$50$	−2.78743e6	+	4.23949e6i	−0.445990	+	0.678318i
$51$	−3.78415e6	+	3.78415e6i	−0.559355	+	0.559355i
$52$	−3.76988e6	+	9.49777e6i	−0.515602	+	1.29900i
$53$	−2.55554e6	+	2.55554e6i	−0.323876	+	0.323876i	−0.850252	−	0.526376i	$-0.823550\pi$
$53$	−2.55554e6	+	2.55554e6i	−0.323876	+	0.323876i	0.526376	+	0.850252i	$0.323550\pi$
$54$	−1.24045e6	−	6.00293e6i	−0.145883	−	0.705973i
$55$	−333210.			−0.0364139
$56$	2.79179e6	−	1.58753e7i	0.283877	−	1.61424i
$57$		−	4.94567e6i		−	0.468517i
$58$	−1.36871e6	−	6.62358e6i	−0.120948	−	0.585303i
$59$	5.04996e6	+	5.04996e6i	0.416754	+	0.416754i	0.884083	−	0.467329i	$-0.154784\pi$
$59$	5.04996e6	+	5.04996e6i	0.416754	+	0.416754i	−0.467329	+	0.884083i	$0.654784\pi$
$60$	−6.08159e6	+	2.62553e6i	−0.469259	+	0.202587i
$61$	−5.51371e6	−	5.51371e6i	−0.398221	−	0.398221i	0.479384	−	0.877605i	$-0.340860\pi$
$61$	−5.51371e6	−	5.51371e6i	−0.398221	−	0.398221i	−0.877605	+	0.479384i	$0.840860\pi$
$62$	−1.25382e7	+	1.90697e7i	−0.848533	+	1.29056i
$63$			1.00216e7i			0.636170i
$64$	−1.57706e7	−	5.72379e6i	−0.940004	−	0.341164i
$65$	1.08228e7			0.606297
$66$	1.56796e6	+	1.03092e6i	0.0826343	+	0.0543314i
$67$	2.78569e7	−	2.78569e7i	1.38240	−	1.38240i	0.542062	−	0.840339i	$-0.317644\pi$
$67$	2.78569e7	−	2.78569e7i	1.38240	−	1.38240i	0.840339	−	0.542062i	$-0.182356\pi$
$68$	5.68996e6	+	1.31798e7i	0.266118	+	0.616416i
$69$	−3.17062e7	+	3.17062e7i	−1.39877	+	1.39877i
$70$	−1.67187e7	+	3.45478e6i	−0.696323	+	0.143889i
$71$	1.70407e7			0.670585			0.335293	−	0.942114i	$-0.391165\pi$
$71$	1.70407e7			0.670585			0.335293	+	0.942114i	$0.391165\pi$
$72$	1.02732e7	+	1.80662e6i	0.382275	+	0.0672260i
$73$		−	4.86929e6i		−	0.171465i	−0.996318	−	0.0857323i	$-0.972677\pi$
$73$		−	4.86929e6i		−	0.171465i	0.996318	−	0.0857323i	$-0.0273230\pi$
$74$	1.89680e7	−	3.91959e6i	0.632551	−	0.130711i
$75$	−2.13992e7	−	2.13992e7i	−0.676320	−	0.676320i
$76$	−1.23309e7	−	4.89440e6i	−0.369606	−	0.146705i
$77$	3.41972e6	+	3.41972e6i	0.0972810	+	0.0972810i
$78$	−5.09280e7	−	3.34848e7i	−1.37587	−	0.904626i
$79$			4.23147e7i			1.08638i	0.839608	+	0.543192i	$0.182784\pi$
$79$			4.23147e7i			1.08638i	−0.839608	+	0.543192i	$0.817216\pi$
$80$	527595.	+	1.77613e7i	0.0128807	+	0.433627i
$81$	5.32698e7			1.23749
$82$	3.06478e7	−	4.66131e7i	0.677865	−	1.03098i
$83$	2.20460e7	−	2.20460e7i	0.464534	−	0.464534i	−0.435604	−	0.900138i	$-0.643465\pi$
$83$	2.20460e7	−	2.20460e7i	0.464534	−	0.464534i	0.900138	+	0.435604i	$0.143465\pi$
$84$	8.93609e7	+	3.54694e7i	1.79486	+	0.712421i
$85$	1.07511e7	−	1.07511e7i	0.205958	−	0.205958i
$86$	−1.04502e7	−	5.05716e7i	−0.191043	−	0.924513i
$87$	4.03418e7			0.704170
$88$	4.12208e6	−	2.88911e6i	0.0687362	−	0.0481763i
$89$			9.93313e7i			1.58316i	0.611063	+	0.791582i	$0.290742\pi$
$89$			9.93313e7i			1.58316i	−0.611063	+	0.791582i	$0.709258\pi$
$90$	−2.23566e6	−	1.08190e7i	−0.0340750	−	0.164899i
$91$	−1.11074e8	−	1.11074e8i	−1.61974	−	1.61974i
$92$	4.76744e7	+	1.10429e8i	0.665478	+	1.54146i
$93$	−9.62560e7	−	9.62560e7i	−1.28676	−	1.28676i
$94$	−2.33910e7	+	3.55761e7i	−0.299597	+	0.455666i
$95$			1.40511e7i			0.172511i
$96$	5.24695e7	−	8.52107e7i	0.617763	−	1.00325i
$97$	−1.23600e8			−1.39615			−0.698077	−	0.716023i	$-0.745961\pi$
$97$	−1.23600e8			−1.39615			−0.698077	+	0.716023i	$0.745961\pi$
$98$	1.29969e8	+	8.54540e7i	1.40908	+	0.926463i
$99$	−2.21297e6	+	2.21297e6i	−0.0230375	+	0.0230375i
$100$	−7.45312e7	+	3.21765e7i	−0.745312	+	0.321765i
$101$	−1.37348e8	+	1.37348e8i	−1.31988	+	1.31988i	−0.406020	+	0.913864i	$0.633084\pi$
$101$	−1.37348e8	+	1.37348e8i	−1.31988	+	1.31988i	−0.913864	+	0.406020i	$0.866916\pi$
$102$	−8.38539e7	+	1.73277e7i	−0.774681	+	0.160081i
$103$	6.43405e7			0.571657			0.285829	−	0.958281i	$-0.407731\pi$
$103$	6.43405e7			0.571657			0.285829	+	0.958281i	$0.407731\pi$
$104$	−1.33887e8	+	9.38393e7i	−1.14447	+	0.802142i
$105$		−	1.01827e8i		−	0.837737i
$106$	−5.66288e7	+	1.17019e7i	−0.448553	+	0.0926898i
$107$	2.67265e7	+	2.67265e7i	0.203895	+	0.203895i	0.801666	−	0.597772i	$-0.203947\pi$
$107$	2.67265e7	+	2.67265e7i	0.203895	+	0.203895i	−0.597772	+	0.801666i	$0.703947\pi$
$108$	3.61826e7	−	9.11577e7i	0.265953	−	0.670036i
$109$	4.36281e7	+	4.36281e7i	0.309072	+	0.309072i	0.844550	−	0.535477i	$-0.179868\pi$
$109$	4.36281e7	+	4.36281e7i	0.309072	+	0.309072i	−0.535477	+	0.844550i	$0.679868\pi$
$110$	−4.45473e6	−	2.92895e6i	−0.0304264	−	0.0200052i
$111$			1.15527e8i			0.761014i
$112$	1.76869e8	−	1.87699e8i	1.12404	−	1.19286i
$113$	2.43000e8			1.49037			0.745183	−	0.666860i	$-0.232362\pi$
$113$	2.43000e8			1.49037			0.745183	+	0.666860i	$0.232362\pi$
$114$	4.34730e7	−	6.61193e7i	0.257395	−	0.391479i
$115$	9.00802e7	−	9.00802e7i	0.515036	−	0.515036i
$116$	3.99236e7	−	1.00583e8i	0.220495	−	0.555509i
$117$	7.18780e7	−	7.18780e7i	0.383577	−	0.383577i
$118$	2.31239e7	+	1.11903e8i	0.119271	+	0.577185i
$119$	−2.20677e8			−1.10045
$120$	−1.04384e8	−	1.83568e7i	−0.503397	−	0.0885262i
$121$		−	2.12849e8i		−	0.992954i
$122$	−2.52474e7	−	1.22180e8i	−0.113967	−	0.551518i
$123$	2.35283e8	+	2.35283e8i	1.02795	+	1.02795i
$124$	−3.35250e8	+	1.44734e8i	−1.41802	+	0.612185i
$125$	1.35689e8	+	1.35689e8i	0.555780	+	0.555780i
$126$	−8.80907e7	+	1.33980e8i	−0.349500	+	0.531565i
$127$		−	6.53597e7i		−	0.251244i	−0.992078	−	0.125622i	$-0.959907\pi$
$127$		−	6.53597e7i		−	0.251244i	0.992078	−	0.125622i	$-0.0400926\pi$
$128$	−1.60527e8	−	2.15148e8i	−0.598010	−	0.801488i
$129$	3.08013e8			1.11227
$130$	1.44691e8	+	9.51334e7i	0.506604	+	0.333089i
$131$	−1.11185e8	+	1.11185e8i	−0.377537	+	0.377537i	−0.870213	−	0.492676i	$-0.836019\pi$
$131$	−1.11185e8	+	1.11185e8i	−0.377537	+	0.377537i	0.492676	+	0.870213i	$0.336019\pi$
$132$	1.19004e7	+	2.75652e7i	0.0391981	+	0.0907956i
$133$	1.44206e8	−	1.44206e8i	0.460868	−	0.460868i
$134$	6.17288e8	−	1.27558e8i	1.91456	−	0.395628i
$135$	−1.03875e8			−0.312734
$136$	−3.97822e7	+	2.26218e8i	−0.116287	+	0.661260i
$137$			1.24919e8i			0.354606i	0.984156	+	0.177303i	$0.0567373\pi$
$137$			1.24919e8i			0.354606i	−0.984156	+	0.177303i	$0.943263\pi$
$138$	−7.02585e8	+	1.45183e8i	−1.93724	+	0.400314i
$139$	−1.65986e8	−	1.65986e8i	−0.444644	−	0.444644i	0.448925	−	0.893569i	$-0.351807\pi$
$139$	−1.65986e8	−	1.65986e8i	−0.444644	−	0.444644i	−0.893569	+	0.448925i	$0.851807\pi$
$140$	−2.53883e8	−	1.00772e8i	−0.660878	−	0.262318i
$141$	−1.79573e8	−	1.79573e8i	−0.454323	−	0.454323i
$142$	2.27819e8	+	1.49790e8i	0.560322	+	0.368408i
$143$		−	4.90548e7i		−	0.117311i
$144$	1.21464e8	+	1.14456e8i	0.282485	+	0.266187i
$145$	−1.14615e8			−0.259280
$146$	4.28016e7	−	6.50982e7i	0.0941996	−	0.143271i
$147$	−6.56032e8	+	6.56032e8i	−1.40493	+	1.40493i
$148$	2.88040e8	+	1.14330e8i	0.600352	+	0.238294i
$149$	3.45982e8	−	3.45982e8i	0.701954	−	0.701954i	−0.262876	−	0.964830i	$-0.584671\pi$
$149$	3.45982e8	−	3.45982e8i	0.701954	−	0.701954i	0.964830	+	0.262876i	$0.0846709\pi$
$150$	−9.79873e7	−	4.74190e8i	−0.193555	−	0.936671i
$151$	−1.37967e8			−0.265380			−0.132690	−	0.991158i	$-0.542362\pi$
$151$	−1.37967e8			−0.265380			−0.132690	+	0.991158i	$0.542362\pi$
$152$	−1.21831e8	−	1.73824e8i	−0.228235	−	0.325638i
$153$		−	1.42804e8i		−	0.260601i
$154$	1.56590e7	+	7.57785e7i	0.0278408	+	0.134730i
$155$	2.73472e8	+	2.73472e8i	0.473791	+	0.473791i
$156$	−3.86528e8	−	8.95325e8i	−0.652654	−	1.51176i
$157$	4.48213e8	+	4.48213e8i	0.737710	+	0.737710i	0.972134	−	0.234424i	$-0.0753204\pi$
$157$	4.48213e8	+	4.48213e8i	0.737710	+	0.737710i	−0.234424	+	0.972134i	$0.575320\pi$
$158$	−3.71951e8	+	5.65712e8i	−0.596840	+	0.907751i
$159$		−	3.44905e8i		−	0.539648i
$160$	−1.49071e8	+	2.42092e8i	−0.227464	+	0.369402i
$161$	−1.84898e9			−2.75187
$162$	7.12171e8	+	4.68248e8i	1.03401	+	0.679854i
$163$	4.14876e8	−	4.14876e8i	0.587716	−	0.587716i	−0.349296	−	0.937012i	$-0.613579\pi$
$163$	4.14876e8	−	4.14876e8i	0.587716	−	0.587716i	0.937012	+	0.349296i	$0.113579\pi$
$164$	8.19468e8	−	3.53779e8i	1.13281	−	0.489054i
$165$	2.24856e7	−	2.24856e7i	0.0303368	−	0.0303368i
$166$	4.88523e8	−	1.00949e8i	0.643358	−	0.132944i
$167$	2.58674e8			0.332573			0.166286	−	0.986078i	$-0.446822\pi$
$167$	2.58674e8			0.332573			0.166286	+	0.986078i	$0.446822\pi$
$168$	8.82898e8	+	1.25969e9i	1.10834	+	1.58134i
$169$			7.77586e8i			0.953239i
$170$	2.38237e8	−	4.92297e7i	0.285242	−	0.0589429i
$171$	9.33185e7	+	9.33185e7i	0.109140	+	0.109140i
$172$	3.04820e8	−	7.67958e8i	0.348281	−	0.877452i
$173$	−3.95927e8	−	3.95927e8i	−0.442008	−	0.442008i	0.450678	−	0.892686i	$-0.351182\pi$
$173$	−3.95927e8	−	3.95927e8i	−0.442008	−	0.442008i	−0.892686	+	0.450678i	$0.851182\pi$
$174$	5.39335e8	+	3.54609e8i	0.588385	+	0.386859i
$175$		−	1.24792e9i		−	1.33056i
$176$	8.05043e7	−	2.39135e6i	0.0839012	−	0.00249226i
$177$	−6.81561e8			−0.694404
$178$	−8.73133e8	+	1.32797e9i	−0.869762	+	1.32285i
$179$	2.18752e8	−	2.18752e8i	0.213079	−	0.213079i	−0.592495	−	0.805574i	$-0.701857\pi$
$179$	2.18752e8	−	2.18752e8i	0.213079	−	0.213079i	0.805574	+	0.592495i	$0.201857\pi$
$180$	6.52115e7	−	1.64293e8i	0.0621204	−	0.156505i
$181$	4.74973e8	−	4.74973e8i	0.442542	−	0.442542i	−0.450323	−	0.892865i	$-0.648691\pi$
$181$	4.74973e8	−	4.74973e8i	0.442542	−	0.442542i	0.892865	+	0.450323i	$0.148691\pi$
$182$	−5.08609e8	−	2.46131e9i	−0.463552	−	2.24327i
$183$	7.44150e8			0.663523
$184$	−3.33322e8	+	1.89541e9i	−0.290799	+	1.65360i
$185$		−	3.28224e8i		−	0.280210i
$186$	−4.40759e8	−	2.13296e9i	−0.368255	−	1.78210i
$187$	−4.87301e7	−	4.87301e7i	−0.0398502	−	0.0398502i
$188$	−6.25435e8	+	2.70012e8i	−0.500669	+	0.216148i
$189$	1.06606e9	+	1.06606e9i	0.835480	+	0.835480i
$190$	−1.23511e8	+	1.87851e8i	−0.0947743	+	0.144145i
$191$			6.95504e7i			0.0522596i	0.999659	+	0.0261298i	$0.00831832\pi$
$191$			6.95504e7i			0.0522596i	−0.999659	+	0.0261298i	$0.991682\pi$
$192$	1.45048e9	−	6.77980e8i	1.06735	−	0.498899i
$193$	6.88621e8			0.496308			0.248154	−	0.968721i	$-0.420176\pi$
$193$	6.88621e8			0.496308			0.248154	+	0.968721i	$0.420176\pi$
$194$	−1.65243e9	−	1.08646e9i	−1.16659	−	0.767022i
$195$	−7.30341e8	+	7.30341e8i	−0.505111	+	0.505111i
$196$	9.86429e8	+	2.28489e9i	0.668408	+	1.54825i
$197$	−4.75933e7	+	4.75933e7i	−0.0315996	+	0.0315996i	−0.722730	−	0.691130i	$-0.757113\pi$
$197$	−4.75933e7	+	4.75933e7i	−0.0315996	+	0.0315996i	0.691130	+	0.722730i	$0.257113\pi$
$198$	−4.90378e7	+	1.01332e7i	−0.0319058	+	0.00659307i
$199$	3.94453e7			0.0251526			0.0125763	−	0.999921i	$-0.495997\pi$
$199$	3.94453e7			0.0251526			0.0125763	+	0.999921i	$0.495997\pi$
$200$	−1.27925e9	−	2.24966e8i	−0.799533	−	0.140604i
$201$			3.75967e9i			2.30338i
$202$	−3.04352e9	+	6.28918e8i	−1.82798	+	0.377736i
$203$	1.17629e9	+	1.17629e9i	0.692674	+	0.692674i
$204$	−1.27337e9	−	5.05429e8i	−0.735247	−	0.291836i
$205$	−6.68462e8	−	6.68462e8i	−0.378496	−	0.378496i
$206$	8.60178e8	+	5.65561e8i	0.477660	+	0.314058i
$207$		−	1.19651e9i		−	0.651682i
$208$	−2.61481e9	+	7.76719e7i	−1.39697	+	0.0414964i
$209$	6.36874e7			0.0333786
$210$	8.95075e8	−	1.36134e9i	0.460238	−	0.699989i
$211$	1.09590e9	−	1.09590e9i	0.552892	−	0.552892i	−0.374383	−	0.927274i	$-0.622145\pi$
$211$	1.09590e9	−	1.09590e9i	0.552892	−	0.552892i	0.927274	+	0.374383i	$0.122145\pi$
$212$	−8.59939e8	−	3.41330e8i	−0.425720	−	0.168978i
$213$	−1.14994e9	+	1.14994e9i	−0.558671	+	0.558671i
$214$	1.22381e8	+	5.92238e8i	0.0583525	+	0.282385i
$215$	−8.75093e8			−0.409544
$216$	1.28502e9	−	9.00651e8i	0.590329	−	0.413753i
$217$		−	5.61328e9i		−	2.53150i
$218$	1.99774e8	+	9.66766e8i	0.0884531	+	0.428051i
$219$	3.28589e8	+	3.28589e8i	0.142849	+	0.142849i
$220$	−3.38101e7	−	7.83152e7i	−0.0144330	−	0.0334315i
$221$	1.58277e9	+	1.58277e9i	0.663511	+	0.663511i
$222$	−1.01550e9	+	1.54450e9i	−0.418087	+	0.635881i
$223$		−	8.94702e8i		−	0.361792i	−0.983502	−	0.180896i	$-0.942100\pi$
$223$		−	8.94702e8i		−	0.361792i	0.983502	−	0.180896i	$-0.0578997\pi$
$224$	4.01448e9	−	9.54669e8i	1.59455	−	0.379193i
$225$	8.07551e8			0.315094
$226$	3.24871e9	+	2.13600e9i	1.24531	+	0.818781i
$227$	1.29515e9	−	1.29515e9i	0.487772	−	0.487772i	−0.419831	−	0.907602i	$-0.637911\pi$
$227$	1.29515e9	−	1.29515e9i	0.487772	−	0.487772i	0.907602	+	0.419831i	$0.137911\pi$
$228$	1.16239e9	−	5.01826e8i	0.430144	−	0.185701i
$229$	−1.62019e9	+	1.62019e9i	−0.589149	+	0.589149i	−0.937401	−	0.348252i	$-0.886775\pi$
$229$	−1.62019e9	+	1.62019e9i	−0.589149	+	0.589149i	0.348252	+	0.937401i	$0.386775\pi$
$230$	1.99611e9	−	4.12479e8i	0.713302	−	0.147398i
$231$	−4.61538e8			−0.162091
$232$	1.41788e9	−	9.93771e8i	0.489426	−	0.343032i
$233$		−	2.08325e9i		−	0.706833i	−0.935466	−	0.353416i	$-0.885020\pi$
$233$		−	2.08325e9i		−	0.706833i	0.935466	−	0.353416i	$-0.114980\pi$
$234$	1.59276e9	−	3.29131e8i	0.531236	−	0.109776i
$235$	5.10184e8	+	5.10184e8i	0.167284	+	0.167284i
$236$	−6.74497e8	+	1.69931e9i	−0.217436	+	0.547804i
$237$	−2.85548e9	−	2.85548e9i	−0.905076	−	0.905076i
$238$	−2.95026e9	−	1.93977e9i	−0.919501	−	0.604566i
$239$			5.97632e9i			1.83165i	0.401579	+	0.915824i	$0.368462\pi$
$239$			5.97632e9i			1.83165i	−0.401579	+	0.915824i	$0.631538\pi$
$240$	−1.23417e9	−	1.16297e9i	−0.371989	−	0.350527i
$241$	2.40939e9			0.714231			0.357115	−	0.934060i	$-0.383760\pi$
$241$	2.40939e9			0.714231			0.357115	+	0.934060i	$0.383760\pi$
$242$	1.87096e9	−	2.84560e9i	0.545511	−	0.829684i
$243$	−1.81737e9	+	1.81737e9i	−0.521217	+	0.521217i
$244$	7.36437e8	−	1.85536e9i	0.207767	−	0.523444i
$245$	1.86385e9	−	1.86385e9i	0.517304	−	0.517304i
$246$	1.07737e9	+	5.21370e9i	0.294187	+	1.42366i
$247$	−2.06859e9			−0.555759
$248$	−5.75423e9	−	1.01192e9i	−1.52118	−	0.267511i
$249$			2.97541e9i			0.774015i
$250$	6.21321e8	+	3.00676e9i	0.159058	+	0.769730i
$251$	−4.31727e9	−	4.31727e9i	−1.08771	−	1.08771i	−0.995764	−	0.0919482i	$-0.970691\pi$
$251$	−4.31727e9	−	4.31727e9i	−1.08771	−	1.08771i	−0.0919482	−	0.995764i	$-0.529309\pi$
$252$	−2.35539e9	+	1.01687e9i	−0.584065	+	0.252151i
$253$	−4.08293e8	−	4.08293e8i	−0.0996530	−	0.0996530i
$254$	5.74519e8	−	8.73803e8i	0.138029	−	0.209932i
$255$			1.45101e9i			0.343171i
$256$	−2.54936e8	−	4.28739e9i	−0.0593569	−	0.998237i
$257$	−2.33955e9			−0.536291			−0.268145	−	0.963378i	$-0.586411\pi$
$257$	−2.33955e9			−0.536291			−0.268145	+	0.963378i	$0.586411\pi$
$258$	4.11787e9	+	2.70747e9i	0.929380	+	0.611061i
$259$	−3.36855e9	+	3.36855e9i	−0.748590	+	0.748590i
$260$	1.09816e9	+	2.54370e9i	0.240311	+	0.556638i
$261$	−7.61199e8	+	7.61199e8i	−0.164035	+	0.164035i
$262$	−2.46377e9	+	5.09117e8i	−0.522871	+	0.108047i
$263$	8.87045e8			0.185406			0.0927028	−	0.995694i	$-0.470449\pi$
$263$	8.87045e8			0.185406			0.0927028	+	0.995694i	$0.470449\pi$
$264$	−8.32031e7	+	4.73128e8i	−0.0171287	+	0.0974009i
$265$			9.79907e8i			0.198702i
$266$	3.19550e9	−	6.60323e8i	0.638281	−	0.131895i
$267$	−6.70305e9	−	6.70305e9i	−1.31895	−	1.31895i
$268$	9.37386e9	+	3.72070e9i	1.81710	+	0.721250i
$269$	−3.12349e9	−	3.12349e9i	−0.596528	−	0.596528i	0.342859	−	0.939387i	$-0.388605\pi$
$269$	−3.12349e9	−	3.12349e9i	−0.596528	−	0.596528i	−0.939387	+	0.342859i	$0.888605\pi$
$270$	−1.38872e9	−	9.13072e8i	−0.261312	−	0.171811i
$271$			4.38139e9i			0.812335i	0.913799	+	0.406167i	$0.133135\pi$
$271$			4.38139e9i			0.812335i	−0.913799	+	0.406167i	$0.866865\pi$
$272$	−2.52034e9	+	2.67465e9i	−0.460451	+	0.488643i
$273$	1.49909e10			2.69884
$274$	−1.09805e9	+	1.67006e9i	−0.194814	+	0.296299i
$275$	2.75566e8	−	2.75566e8i	0.0481831	−	0.0481831i
$276$	−1.06691e10	−	4.23483e9i	−1.83862	−	0.729792i
$277$	5.40612e9	−	5.40612e9i	0.918262	−	0.918262i	−0.0786410	−	0.996903i	$-0.525058\pi$
$277$	5.40612e9	−	5.40612e9i	0.918262	−	0.918262i	0.996903	+	0.0786410i	$0.0250581\pi$
$278$	−7.60054e8	−	3.67813e9i	−0.127252	−	0.615811i
$279$	3.63246e9			0.599493
$280$	−2.50840e9	−	3.57889e9i	−0.408098	−	0.582260i
$281$		−	1.71345e9i		−	0.274818i	−0.990514	−	0.137409i	$-0.956122\pi$
$281$		−	1.71345e9i		−	0.274818i	0.990514	−	0.137409i	$-0.0438775\pi$
$282$	−8.22269e8	−	3.97921e9i	−0.130022	−	0.629216i
$283$	−2.57250e9	−	2.57250e9i	−0.401060	−	0.401060i	0.477546	−	0.878606i	$-0.341526\pi$
$283$	−2.57250e9	−	2.57250e9i	−0.401060	−	0.401060i	−0.878606	+	0.477546i	$0.841526\pi$
$284$	1.72908e9	+	4.00512e9i	0.265792	+	0.615661i
$285$	−9.48194e8	−	9.48194e8i	−0.143720	−	0.143720i
$286$	4.31197e8	−	6.55821e8i	0.0644484	−	0.0980214i
$287$			1.37208e10i			2.02233i
$288$	6.17785e8	+	2.59785e9i	0.0897982	+	0.377611i
$289$	−3.83118e9			−0.549213
$290$	−1.53230e9	−	1.00748e9i	−0.216647	−	0.142444i
$291$	8.34079e9	−	8.34079e9i	1.16315	−	1.16315i
$292$	1.14444e9	−	4.94076e8i	0.157421	−	0.0679614i
$293$	−7.45579e9	+	7.45579e9i	−1.01163	+	1.01163i	−0.0117025	+	0.999932i	$0.503725\pi$
$293$	−7.45579e9	+	7.45579e9i	−1.01163	+	1.01163i	−0.999932	+	0.0117025i	$0.996275\pi$
$294$	−1.45372e10	+	3.00398e9i	−1.94577	+	0.402076i
$295$	1.93638e9			0.255683
$296$	2.84588e9	+	4.06040e9i	0.370723	+	0.528934i
$297$			4.70819e8i			0.0605101i
$298$	7.66671e9	−	1.58426e9i	0.972174	−	0.200892i
$299$	1.32615e10	+	1.32615e10i	1.65924	+	1.65924i
$300$	2.85818e9	−	7.20083e9i	0.352861	−	0.888991i
$301$	8.98105e9	+	8.98105e9i	1.09411	+	1.09411i
$302$	−1.84450e9	−	1.21275e9i	−0.221744	−	0.145795i
$303$		−	1.85369e10i		−	2.19922i
$304$	−1.00841e8	−	3.39478e9i	−0.0118071	−	0.397482i
$305$	−2.11420e9			−0.244313
$306$	1.25527e9	−	1.90917e9i	0.143169	−	0.217751i
$307$	7.48390e9	−	7.48390e9i	0.842508	−	0.842508i	−0.146676	−	0.989185i	$-0.546858\pi$
$307$	7.48390e9	−	7.48390e9i	0.842508	−	0.842508i	0.989185	+	0.146676i	$0.0468575\pi$
$308$	−4.56754e8	+	1.15074e9i	−0.0507551	+	0.127871i
$309$	−4.34182e9	+	4.34182e9i	−0.476253	+	0.476253i
$310$	1.25224e9	+	6.05995e9i	0.135594	+	0.656178i
$311$	6.97853e9			0.745971			0.372986	−	0.927837i	$-0.378334\pi$
$311$	6.97853e9			0.745971			0.372986	+	0.927837i	$0.378334\pi$
$312$	2.70247e9	−	1.53674e10i	0.285195	−	1.62174i
$313$			2.82553e9i			0.294390i	0.989108	+	0.147195i	$0.0470244\pi$
$313$			2.82553e9i			0.294390i	−0.989108	+	0.147195i	$0.952976\pi$
$314$	2.05238e9	+	9.93207e9i	0.211125	+	1.02169i
$315$	1.92136e9	+	1.92136e9i	0.195149	+	0.195149i
$316$	−9.94534e9	+	4.29358e9i	−0.997405	+	0.430598i
$317$	−7.29757e9	−	7.29757e9i	−0.722672	−	0.722672i	0.246477	−	0.969149i	$-0.420727\pi$
$317$	−7.29757e9	−	7.29757e9i	−0.722672	−	0.722672i	−0.969149	+	0.246477i	$0.920727\pi$
$318$	3.03175e9	−	4.61108e9i	0.296473	−	0.450914i
$319$			5.19498e8i			0.0501673i
$320$	−4.12096e9	+	1.92621e9i	−0.393005	+	0.183697i
$321$	−3.60710e9			−0.339733
$322$	−2.47193e10	−	1.62527e10i	−2.29939	−	1.51183i
$323$	−2.05489e9	+	2.05489e9i	−0.188790	+	0.188790i
$324$	5.40517e9	+	1.25201e10i	0.490489	+	1.13613i
$325$	−8.95048e9	+	8.95048e9i	−0.802256	+	0.802256i
$326$	9.19334e9	−	1.89973e9i	0.813960	−	0.168198i
$327$	−5.88821e9			−0.514982
$328$	1.40653e10	+	2.47350e9i	1.21522	+	0.213706i
$329$		−	1.04720e10i		−	0.893812i
$330$	4.98265e8	−	1.02962e8i	0.0420150	−	0.00868205i
$331$	−1.19829e10	−	1.19829e10i	−0.998274	−	0.998274i	0.00172485	−	0.999999i	$-0.499451\pi$
$331$	−1.19829e10	−	1.19829e10i	−0.998274	−	0.998274i	−0.999999	+	0.00172485i	$0.999451\pi$
$332$	7.41848e9	+	2.94457e9i	0.610608	+	0.242365i
$333$	−2.17985e9	−	2.17985e9i	−0.177276	−	0.177276i
$334$	3.45825e9	+	2.27377e9i	0.277888	+	0.182710i
$335$		−	1.06816e10i		−	0.848118i
$336$	7.30786e8	+	2.46017e10i	0.0573367	+	1.93023i
$337$	−1.02168e10			−0.792125			−0.396063	−	0.918224i	$-0.629624\pi$
$337$	−1.02168e10			−0.792125			−0.396063	+	0.918224i	$0.629624\pi$
$338$	−6.83507e9	+	1.03957e10i	−0.523692	+	0.796499i
$339$	−1.63981e10	+	1.63981e10i	−1.24164	+	1.24164i
$340$	3.61776e9	+	1.43597e9i	0.270722	+	0.107456i
$341$	1.23953e9	−	1.23953e9i	0.0916725	−	0.0916725i
$342$	4.27308e8	+	2.06787e9i	0.0312346	+	0.151154i
$343$	−1.55711e10			−1.12498
$344$	1.08256e10	−	7.58753e9i	0.773070	−	0.541834i
$345$			1.21576e10i			0.858163i
$346$	−1.81296e9	−	8.77344e9i	−0.126498	−	0.612161i
$347$	6.62326e9	+	6.62326e9i	0.456829	+	0.456829i	0.897613	−	0.440784i	$-0.145300\pi$
$347$	6.62326e9	+	6.62326e9i	0.456829	+	0.456829i	−0.440784	+	0.897613i	$0.645300\pi$
$348$	4.09339e9	+	9.48162e9i	0.279104	+	0.646496i
$349$	8.24797e9	+	8.24797e9i	0.555963	+	0.555963i	0.928155	−	0.372193i	$-0.121394\pi$
$349$	8.24797e9	+	8.24797e9i	0.555963	+	0.555963i	−0.372193	+	0.928155i	$0.621394\pi$
$350$	1.09693e10	−	1.66836e10i	0.730984	−	1.11177i
$351$		−	1.52923e10i		−	1.00750i
$352$	1.09729e9	+	6.75672e8i	0.0714746	+	0.0440114i
$353$	−4.03532e9			−0.259884			−0.129942	−	0.991522i	$-0.541479\pi$
$353$	−4.03532e9			−0.259884			−0.129942	+	0.991522i	$0.541479\pi$
$354$	−9.11189e9	−	5.99100e9i	−0.580224	−	0.381493i
$355$	3.26708e9	−	3.26708e9i	0.205706	−	0.205706i
$356$	−2.33461e10	+	1.00789e10i	−1.45350	+	0.627500i
$357$	1.48917e10	−	1.48917e10i	0.916792	−	0.916792i
$358$	4.84739e9	−	1.00167e9i	0.295104	−	0.0609809i
$359$	1.09502e10			0.659239			0.329619	−	0.944114i	$-0.393080\pi$
$359$	1.09502e10			0.659239			0.329619	+	0.944114i	$0.393080\pi$
$360$	2.31597e9	−	1.62323e9i	0.137887	−	0.0966432i
$361$			1.42979e10i			0.841869i
$362$	1.05250e10	−	2.17491e9i	0.612900	−	0.126651i
$363$	1.43634e10	+	1.43634e10i	0.827239	+	0.827239i
$364$	1.48355e10	−	3.73763e10i	0.845080	−	2.12908i
$365$	−9.33552e8	−	9.33552e8i	−0.0525977	−	0.0525977i
$366$	9.94865e9	+	6.54117e9i	0.554421	+	0.364528i
$367$			4.25227e9i			0.234399i	0.993108	+	0.117200i	$0.0373918\pi$
$367$			4.25227e9i			0.234399i	−0.993108	+	0.117200i	$0.962608\pi$
$368$	−2.11171e10	+	2.24101e10i	−1.15144	+	1.22194i
$369$	−8.87900e9			−0.478915
$370$	2.88512e9	−	4.38807e9i	0.153942	−	0.234135i
$371$	1.00567e10	−	1.00567e10i	0.530838	−	0.530838i
$372$	1.28564e10	−	3.23902e10i	0.671349	−	1.69138i
$373$	2.45830e9	−	2.45830e9i	0.126999	−	0.126999i	−0.640751	−	0.767749i	$-0.721377\pi$
$373$	2.45830e9	−	2.45830e9i	0.126999	−	0.126999i	0.767749	+	0.640751i	$0.221377\pi$
$374$	−2.23136e8	−	1.07982e9i	−0.0114047	−	0.0551907i
$375$	−1.83130e10			−0.926051
$376$	−1.07350e10	−	1.88782e9i	−0.537093	−	0.0944518i
$377$		−	1.68735e10i		−	0.835293i
$378$	4.88153e9	+	2.36232e10i	0.239105	+	1.15710i
$379$	−3.88450e9	−	3.88450e9i	−0.188269	−	0.188269i	0.606679	−	0.794947i	$-0.292502\pi$
$379$	−3.88450e9	−	3.88450e9i	−0.188269	−	0.188269i	−0.794947	+	0.606679i	$0.792502\pi$
$380$	−3.30247e9	+	1.42573e9i	−0.158381	+	0.0683761i
$381$	4.41059e9	+	4.41059e9i	0.209313	+	0.209313i
$382$	−6.11356e8	+	9.29829e8i	−0.0287105	+	0.0436666i
$383$		−	2.45234e9i		−	0.113969i	−0.998375	−	0.0569843i	$-0.981851\pi$
$383$		−	2.45234e9i		−	0.113969i	0.998375	−	0.0569843i	$-0.0181485\pi$
$384$	2.53512e10	+	3.68590e9i	1.16594	+	0.169519i
$385$	1.31127e9			0.0596830
$386$	9.20627e9	+	6.05306e9i	0.414701	+	0.272663i
$387$	−5.81182e9	+	5.81182e9i	−0.259100	+	0.259100i
$388$	−1.25415e10	−	2.90501e10i	−0.553377	−	1.28180i
$389$	2.93888e10	−	2.93888e10i	1.28346	−	1.28346i	0.344782	−	0.938683i	$-0.387953\pi$
$389$	2.93888e10	−	2.93888e10i	1.28346	−	1.28346i	0.938683	−	0.344782i	$-0.112047\pi$
$390$	−1.61838e10	+	3.34425e9i	−0.699556	+	0.144557i
$391$	2.63474e10			1.12728
$392$	−6.89676e9	+	3.92179e10i	−0.292079	+	1.66089i
$393$		−	1.50059e10i		−	0.629059i
$394$	−1.05463e9	+	2.17931e8i	−0.0437639	+	0.00904345i
$395$	8.11268e9	+	8.11268e9i	0.333254	+	0.333254i
$396$	−7.44665e8	−	2.95575e8i	−0.0302817	−	0.0120195i
$397$	2.11692e10	+	2.11692e10i	0.852201	+	0.852201i	0.990404	−	0.138203i	$-0.0441326\pi$
$397$	2.11692e10	+	2.11692e10i	0.852201	+	0.852201i	−0.138203	+	0.990404i	$0.544133\pi$
$398$	5.27349e8	+	3.46728e8i	0.0210168	+	0.0138184i
$399$			1.94626e10i			0.767907i
$400$	−1.51250e10	−	1.42524e10i	−0.590821	−	0.556734i
$401$	−3.11502e10			−1.20471			−0.602356	−	0.798227i	$-0.705771\pi$
$401$	−3.11502e10			−1.20471			−0.602356	+	0.798227i	$0.705771\pi$
$402$	−3.30479e10	+	5.02636e10i	−1.26544	+	1.92464i
$403$	−4.02603e10	+	4.02603e10i	−1.52636	+	1.52636i
$404$	−4.62175e10	−	1.83448e10i	−1.73493	−	0.688633i
$405$	1.02130e10	−	1.02130e10i	0.379606	−	0.379606i
$406$	5.38625e9	+	2.60656e10i	0.198236	+	0.959322i
$407$	−1.48769e9			−0.0542170
$408$	−1.25810e10	−	1.79502e10i	−0.454021	−	0.647782i
$409$			2.91542e10i			1.04186i	0.853600	+	0.520929i	$0.174414\pi$
$409$			2.91542e10i			1.04186i	−0.853600	+	0.520929i	$0.825586\pi$
$410$	−3.06090e9	−	1.48126e10i	−0.108321	−	0.524199i
$411$	−8.42976e9	−	8.42976e9i	−0.295426	−	0.295426i
$412$	6.52849e9	+	1.51221e10i	0.226581	+	0.524836i
$413$	−1.98730e10	−	1.98730e10i	−0.683067	−	0.683067i
$414$	1.05175e10	−	1.59963e10i	0.358022	−	0.544526i
$415$		−	8.45342e9i		−	0.284997i
$416$	−3.56405e10	−	2.19460e10i	−1.19006	−	0.732796i
$417$	2.24021e10			0.740874
$418$	8.51446e8	+	5.59820e8i	0.0278902	+	0.0183376i
$419$	1.16686e9	−	1.16686e9i	0.0378584	−	0.0378584i	−0.687924	−	0.725783i	$-0.741478\pi$
$419$	1.16686e9	−	1.16686e9i	0.0378584	−	0.0378584i	0.725783	+	0.687924i	$0.241478\pi$
$420$	2.39328e10	−	1.03322e10i	0.769122	−	0.332044i
$421$	1.41848e10	−	1.41848e10i	0.451538	−	0.451538i	−0.444327	−	0.895865i	$-0.646557\pi$
$421$	1.41848e10	−	1.41848e10i	0.451538	−	0.451538i	0.895865	+	0.444327i	$0.146557\pi$
$422$	2.42843e10	−	5.01814e9i	0.765729	−	0.158231i
$423$	6.77664e9			0.211667
$424$	−8.49632e9	−	1.21223e10i	−0.262886	−	0.375076i
$425$			1.77824e10i			0.545049i
$426$	−2.54818e10	+	5.26559e9i	−0.773733	+	0.159885i
$427$	2.16980e10	+	2.16980e10i	0.652691	+	0.652691i
$428$	−3.56971e9	+	8.99346e9i	−0.106380	+	0.268010i
$429$	3.31031e9	+	3.31031e9i	0.0977326	+	0.0977326i
$430$	−1.16992e10	−	7.69217e9i	−0.342203	−	0.224996i
$431$		−	3.33630e10i		−	0.966844i	−0.875388	−	0.483422i	$-0.839394\pi$
$431$		−	3.33630e10i		−	0.966844i	0.875388	−	0.483422i	$-0.160606\pi$
$432$	2.50964e10	−	7.45480e8i	0.720570	−	0.0214043i
$433$	6.21568e9			0.176822			0.0884112	−	0.996084i	$-0.471821\pi$
$433$	6.21568e9			0.176822			0.0884112	+	0.996084i	$0.471821\pi$
$434$	4.93413e10	−	7.50447e10i	1.39076	−	2.11525i
$435$	7.73441e9	−	7.73441e9i	0.216008	−	0.216008i
$436$	−5.82717e9	+	1.46809e10i	−0.161255	+	0.406261i
$437$	−1.72173e10	+	1.72173e10i	−0.472105	+	0.472105i
$438$	1.50462e9	+	7.28128e9i	0.0408817	+	0.197839i
$439$	−2.02377e10			−0.544882			−0.272441	−	0.962173i	$-0.587831\pi$
$439$	−2.02377e10			−0.544882			−0.272441	+	0.962173i	$0.587831\pi$
$440$	2.36388e8	−	1.34420e9i	0.00630688	−	0.0358636i
$441$		−	2.47570e10i		−	0.654551i
$442$	7.24754e9	+	3.50730e10i	0.189890	+	0.918932i
$443$	−1.40622e10	−	1.40622e10i	−0.365123	−	0.365123i	0.500572	−	0.865695i	$-0.333123\pi$
$443$	−1.40622e10	−	1.40622e10i	−0.365123	−	0.365123i	−0.865695	+	0.500572i	$0.833123\pi$
$444$	−2.71527e10	+	1.17223e10i	−0.698684	+	0.301634i
$445$	1.90440e10	+	1.90440e10i	0.485644	+	0.485644i
$446$	7.86453e9	−	1.19614e10i	0.198762	−	0.302303i
$447$			4.66950e10i			1.16961i
$448$	6.20619e10	+	2.25247e10i	1.54068	+	0.559174i
$449$	4.47310e10			1.10058			0.550292	−	0.834973i	$-0.314517\pi$
$449$	4.47310e10			1.10058			0.550292	+	0.834973i	$0.314517\pi$
$450$	1.07963e10	+	7.09847e9i	0.263283	+	0.173107i
$451$	−3.02984e9	+	3.02984e9i	−0.0732341	+	0.0732341i
$452$	2.46567e10	+	5.71130e10i	0.590719	+	1.36830i
$453$	9.31029e9	−	9.31029e9i	0.221091	−	0.221091i
$454$	2.86996e10	−	5.93053e9i	0.675541	−	0.139595i
$455$	−4.25906e10			−0.993730
$456$	1.99513e10	+	3.50859e9i	0.461436	+	0.0811470i
$457$		−	7.25399e10i		−	1.66308i	−0.555467	−	0.831538i	$-0.687461\pi$
$457$		−	7.25399e10i		−	1.66308i	0.555467	−	0.831538i	$-0.312539\pi$
$458$	−3.59023e10	+	7.41891e9i	−0.815944	+	0.168608i
$459$	−1.51911e10	−	1.51911e10i	−0.342246	−	0.342246i
$460$	3.03120e10	+	1.20315e10i	0.676992	+	0.268714i
$461$	−3.46095e10	−	3.46095e10i	−0.766288	−	0.766288i	0.211163	−	0.977451i	$-0.432275\pi$
$461$	−3.46095e10	−	3.46095e10i	−0.766288	−	0.766288i	−0.977451	+	0.211163i	$0.932275\pi$
$462$	−6.17037e9	−	4.05697e9i	−0.135439	−	0.0890501i
$463$		−	4.88290e10i		−	1.06256i	−0.847196	−	0.531281i	$-0.821711\pi$
$463$		−	4.88290e10i		−	1.06256i	0.847196	−	0.531281i	$-0.178289\pi$
$464$	2.76912e10	−	8.22557e8i	0.597406	−	0.0177457i
$465$	−3.69088e10			−0.789439
$466$	1.83120e10	−	2.78512e10i	0.388321	−	0.590609i
$467$	1.04323e10	−	1.04323e10i	0.219337	−	0.219337i	−0.588882	−	0.808219i	$-0.700432\pi$
$467$	1.04323e10	−	1.04323e10i	0.219337	−	0.219337i	0.808219	+	0.588882i	$0.200432\pi$
$468$	2.41870e10	+	9.60037e9i	0.504195	+	0.200127i
$469$	−1.09625e11	+	1.09625e11i	−2.26578	+	2.26578i
$470$	2.33615e9	+	1.13053e10i	0.0478750	+	0.231681i
$471$	−6.04925e10			−1.22919
$472$	−2.39546e10	+	1.67895e10i	−0.482638	+	0.338274i
$473$			3.96641e9i			0.0792415i
$474$	−1.30753e10	−	6.32752e10i	−0.259023	−	1.25349i
$475$	−1.16203e10	−	1.16203e10i	−0.228267	−	0.228267i
$476$	−2.23916e10	−	5.18662e10i	−0.436171	−	1.01032i
$477$	6.50792e9	+	6.50792e9i	0.125710	+	0.125710i
$478$	−5.25325e10	+	7.98983e10i	−1.00628	+	1.53047i
$479$			4.86520e10i			0.924185i	0.886832	+	0.462092i	$0.152901\pi$
$479$			4.86520e10i			0.924185i	−0.886832	+	0.462092i	$0.847099\pi$
$480$	−6.27721e9	−	2.63964e10i	−0.118250	−	0.497255i
$481$	4.83207e10			0.902721
$482$	3.22114e10	+	2.11788e10i	0.596791	+	0.392386i
$483$	1.24773e11	−	1.24773e11i	2.29261	−	2.29261i
$484$	5.00263e10	−	2.15973e10i	0.911627	−	0.393566i
$485$	−2.36970e10	+	2.36970e10i	−0.428278	+	0.428278i
$486$	−4.02716e10	+	8.32179e9i	−0.721862	+	0.149167i
$487$	9.83645e10			1.74873			0.874365	−	0.485270i	$-0.161279\pi$
$487$	9.83645e10			1.74873			0.874365	+	0.485270i	$0.161279\pi$
$488$	2.61544e10	−	1.83313e10i	0.461175	−	0.323231i
$489$			5.59932e10i			0.979263i
$490$	4.13015e10	−	8.53460e9i	0.716442	−	0.148047i
$491$	4.47778e10	+	4.47778e10i	0.770437	+	0.770437i	0.978183	−	0.207746i	$-0.0666127\pi$
$491$	4.47778e10	+	4.47778e10i	0.770437	+	0.770437i	−0.207746	+	0.978183i	$0.566613\pi$
$492$	−3.14256e10	+	7.91729e10i	−0.536318	+	1.35119i
$493$	−1.67618e10	−	1.67618e10i	−0.283747	−	0.283747i
$494$	−2.76552e10	−	1.81831e10i	−0.464376	−	0.305324i
$495$			8.48551e8i			0.0141337i
$496$	−6.80342e10	−	6.41089e10i	−1.12409	−	1.05923i
$497$	−6.70599e10			−1.09910
$498$	−2.61542e10	+	3.97786e10i	−0.425230	+	0.646744i
$499$	−6.13122e10	+	6.13122e10i	−0.988883	+	0.988883i	−0.999939	−	0.0110556i	$-0.996481\pi$
$499$	−6.13122e10	+	6.13122e10i	−0.988883	+	0.988883i	0.0110556	+	0.999939i	$0.496481\pi$
$500$	−1.81232e10	+	4.56592e10i	−0.289971	+	0.730548i
$501$	−1.74558e10	+	1.74558e10i	−0.277069	+	0.277069i
$502$	−1.97689e10	−	9.56674e10i	−0.311291	−	1.50643i
$503$	8.62882e10			1.34797			0.673984	−	0.738746i	$-0.264582\pi$
$503$	8.62882e10			1.34797			0.673984	+	0.738746i	$0.264582\pi$
$504$	−4.04279e10	−	7.10956e9i	−0.626555	−	0.110184i
$505$			5.26652e10i			0.809764i
$506$	−1.86959e9	−	9.04748e9i	−0.0285196	−	0.138015i
$507$	−5.24729e10	−	5.24729e10i	−0.794152	−	0.794152i
$508$	1.53617e10	−	6.63190e9i	0.230666	−	0.0995825i
$509$	−7.89620e10	−	7.89620e10i	−1.17638	−	1.17638i	−0.980660	−	0.195719i	$-0.937296\pi$
$509$	−7.89620e10	−	7.89620e10i	−1.17638	−	1.17638i	−0.195719	−	0.980660i	$-0.562704\pi$
$510$	−1.27546e10	+	1.93988e10i	−0.188532	+	0.286744i
$511$			1.91620e10i			0.281033i
$512$	3.42784e10	−	5.95597e10i	0.498817	−	0.866708i
$513$	1.98539e10			0.286666
$514$	−3.12778e10	−	2.05649e10i	−0.448109	−	0.294628i
$515$	1.23355e10	−	1.23355e10i	0.175359	−	0.175359i
$516$	3.12534e10	+	7.23930e10i	0.440857	+	1.02117i
$517$	2.31244e9	−	2.31244e9i	0.0323674	−	0.0323674i
$518$	−7.46445e10	+	1.54247e10i	−1.03676	+	0.214238i
$519$	5.34357e10			0.736482
$520$	−7.67796e9	+	4.36601e10i	−0.105010	+	0.597134i
$521$			1.92894e10i			0.261798i	0.991396	+	0.130899i	$0.0417864\pi$
$521$			1.92894e10i			0.261798i	−0.991396	+	0.130899i	$0.958214\pi$
$522$	−1.68676e10	+	3.48555e9i	−0.227181	+	0.0469450i
$523$	−7.88179e10	−	7.88179e10i	−1.05346	−	1.05346i	−0.998488	−	0.0549727i	$-0.982493\pi$
$523$	−7.88179e10	−	7.88179e10i	−1.05346	−	1.05346i	−0.0549727	−	0.998488i	$-0.517507\pi$
$524$	−3.74137e10	−	1.48504e10i	−0.496255	−	0.196975i
$525$	8.42117e10	+	8.42117e10i	1.10850	+	1.10850i
$526$	1.18590e10	+	7.79723e9i	0.154920	+	0.101858i
$527$			7.99876e10i			1.03700i
$528$	−5.27120e9	+	5.59395e9i	−0.0678225	+	0.0719752i
$529$	1.42446e11			1.81897
$530$	−8.61349e9	+	1.31005e10i	−0.109163	+	0.166029i
$531$	1.28602e10	−	1.28602e10i	0.161760	−	0.161760i
$532$	4.85254e10	+	1.92608e10i	0.605790	+	0.240452i
$533$	9.84102e10	−	9.84102e10i	1.21936	−	1.21936i
$534$	−3.06935e10	−	1.48535e11i	−0.377469	−	1.82668i
$535$	1.02481e10			0.125092
$536$	9.26151e10	+	1.32140e11i	1.12208	+	1.60094i
$537$			2.95236e10i			0.355036i
$538$	−1.43025e10	−	6.92141e10i	−0.170720	−	0.826163i
$539$	−8.44799e9	−	8.44799e9i	−0.100092	−	0.100092i
$540$	−1.05400e10	−	2.44140e10i	−0.123955	−	0.287120i
$541$	−4.08212e10	−	4.08212e10i	−0.476537	−	0.476537i	0.427485	−	0.904022i	$-0.359400\pi$
$541$	−4.08212e10	−	4.08212e10i	−0.476537	−	0.476537i	−0.904022	+	0.427485i	$0.859400\pi$
$542$	−3.85129e10	+	5.85754e10i	−0.446282	+	0.678763i
$543$			6.41041e10i			0.737372i
$544$	−5.72053e10	+	1.36038e10i	−0.653191	+	0.155333i
$545$	1.67289e10			0.189619
$546$	2.00416e11	+	1.31772e11i	2.25508	+	1.48270i
$547$	1.11138e10	−	1.11138e10i	0.124141	−	0.124141i	−0.642307	−	0.766448i	$-0.722023\pi$
$547$	1.11138e10	−	1.11138e10i	0.124141	−	0.124141i	0.766448	+	0.642307i	$0.222023\pi$
$548$	−2.93600e10	+	1.26753e10i	−0.325562	+	0.140551i
$549$	−1.40412e10	+	1.40412e10i	−0.154566	+	0.154566i
$550$	6.10634e9	−	1.26182e9i	0.0667314	−	0.0137895i
$551$	2.19066e10			0.237667
$552$	−1.05413e11	−	1.50399e11i	−1.13537	−	1.61990i
$553$		−	1.66520e11i		−	1.78060i
$554$	1.19796e11	−	2.47548e10i	1.27175	−	0.262797i
$555$	2.21491e10	+	2.21491e10i	0.233445	+	0.233445i
$556$	2.21699e10	−	5.58544e10i	0.231987	−	0.584464i
$557$	6.67953e10	+	6.67953e10i	0.693945	+	0.693945i	0.963098	−	0.269153i	$-0.0867436\pi$
$557$	6.67953e10	+	6.67953e10i	0.693945	+	0.693945i	−0.269153	+	0.963098i	$0.586744\pi$
$558$	4.85629e10	+	3.19298e10i	0.500919	+	0.329351i
$559$		−	1.28830e11i		−	1.31938i
$560$	−2.07623e9	−	6.98958e10i	−0.0211117	−	0.710721i
$561$	6.57679e9			0.0663991
$562$	1.50614e10	−	2.29073e10i	0.150980	−	0.229630i
$563$	−3.18679e10	+	3.18679e10i	−0.317190	+	0.317190i	−0.847687	−	0.530497i	$-0.822005\pi$
$563$	−3.18679e10	+	3.18679e10i	−0.317190	+	0.317190i	0.530497	+	0.847687i	$0.322005\pi$
$564$	2.39846e10	−	6.04264e10i	0.237037	−	0.597187i
$565$	4.65886e10	−	4.65886e10i	0.457178	−	0.457178i
$566$	−1.17795e10	−	5.70046e10i	−0.114779	−	0.555449i
$567$	−2.09631e11			−2.02826
$568$	−1.20891e10	+	6.87438e10i	−0.116145	+	0.660450i
$569$			9.56596e10i			0.912598i	0.889827	+	0.456299i	$0.150825\pi$
$569$			9.56596e10i			0.912598i	−0.889827	+	0.456299i	$0.849175\pi$
$570$	−4.34181e9	−	2.10113e10i	−0.0411312	−	0.199046i
$571$	−4.99891e10	−	4.99891e10i	−0.470252	−	0.470252i	0.431744	−	0.901996i	$-0.357898\pi$
$571$	−4.99891e10	−	4.99891e10i	−0.470252	−	0.470252i	−0.901996	+	0.431744i	$0.857898\pi$
$572$	1.15295e10	−	4.97748e9i	0.107702	−	0.0464971i
$573$	−4.69339e9	−	4.69339e9i	−0.0435379	−	0.0435379i
$574$	−1.20607e11	+	1.83435e11i	−1.11103	+	1.68980i
$575$			1.48993e11i			1.36300i
$576$	−1.45762e10	+	4.01615e10i	−0.132420	+	0.364854i
$577$	−1.38139e11			−1.24627			−0.623135	−	0.782114i	$-0.714141\pi$
$577$	−1.38139e11			−1.24627			−0.623135	+	0.782114i	$0.714141\pi$
$578$	−5.12195e10	−	3.36765e10i	−0.458906	−	0.301728i
$579$	−4.64694e10	+	4.64694e10i	−0.413479	+	0.413479i
$580$	−1.16297e10	−	2.69382e10i	−0.102768	−	0.238044i
$581$	−8.67571e10	+	8.67571e10i	−0.761378	+	0.761378i
$582$	1.84826e11	−	3.81927e10i	1.61091	−	0.332880i
$583$	4.44148e9			0.0384462
$584$	1.96432e10	+	3.45440e9i	0.168873	+	0.0296976i
$585$		−	2.75612e10i		−	0.235329i
$586$	−1.65215e11	+	3.41403e10i	−1.40107	+	0.289519i
$587$	1.50005e11	+	1.50005e11i	1.26344	+	1.26344i	0.949416	+	0.314022i	$0.101677\pi$
$587$	1.50005e11	+	1.50005e11i	1.26344	+	1.26344i	0.314022	+	0.949416i	$0.398323\pi$
$588$	−2.20755e11	−	8.76227e10i	−1.84672	−	0.733006i
$589$	−5.22696e10	−	5.22696e10i	−0.434298	−	0.434298i
$590$	2.58877e10	+	1.70210e10i	0.213642	+	0.140468i
$591$		−	6.42337e9i		−	0.0526517i
$592$	2.35557e9	+	7.92996e10i	0.0191782	+	0.645631i
$593$	1.21616e11			0.983494			0.491747	−	0.870738i	$-0.336358\pi$
$593$	1.21616e11			0.983494			0.491747	+	0.870738i	$0.336358\pi$
$594$	−4.13855e9	+	6.29444e9i	−0.0332432	+	0.0505605i
$595$	−4.23087e10	+	4.23087e10i	−0.337568	+	0.337568i
$596$	1.16423e11	+	4.62110e10i	0.922687	+	0.366236i
$597$	−2.66184e9	+	2.66184e9i	−0.0209548	+	0.0209548i
$598$	6.07248e10	+	2.93865e11i	0.474855	+	2.29796i
$599$	−1.99719e11			−1.55136			−0.775680	−	0.631127i	$-0.782593\pi$
$599$	−1.99719e11			−1.55136			−0.775680	+	0.631127i	$0.782593\pi$
$600$	1.01507e11	−	7.11452e10i	0.783237	−	0.548960i
$601$		−	2.25035e11i		−	1.72485i	−0.506181	−	0.862427i	$-0.668943\pi$
$601$		−	2.25035e11i		−	1.72485i	0.506181	−	0.862427i	$-0.331057\pi$
$602$	4.11244e10	+	1.99013e11i	0.313122	+	1.51529i
$603$	−7.09403e10	−	7.09403e10i	−0.536567	−	0.536567i
$604$	−1.39992e10	−	3.24268e10i	−0.105186	−	0.243644i
$605$	−4.08078e10	−	4.08078e10i	−0.304594	−	0.304594i
$606$	1.62942e11	−	2.47823e11i	1.20821	−	1.83760i
$607$			4.46281e9i			0.0328741i	0.999865	+	0.0164370i	$0.00523230\pi$
$607$			4.46281e9i			0.0328741i	−0.999865	+	0.0164370i	$0.994768\pi$
$608$	2.84923e10	−	4.62717e10i	0.208504	−	0.338611i
$609$	−1.58756e11			−1.15415
$610$	−2.82650e10	−	1.85841e10i	−0.204141	−	0.134221i
$611$	−7.51087e10	+	7.51087e10i	−0.538922	+	0.538922i
$612$	3.35637e10	−	1.44900e10i	0.239257	−	0.103291i
$613$	6.91952e10	−	6.91952e10i	0.490043	−	0.490043i	−0.418277	−	0.908320i	$-0.637366\pi$
$613$	6.91952e10	−	6.91952e10i	0.490043	−	0.490043i	0.908320	+	0.418277i	$0.137366\pi$
$614$	1.65838e11	−	3.42689e10i	1.16683	−	0.241117i
$615$	9.02181e10			0.630657
$616$	−1.62215e10	+	1.13694e10i	−0.112660	+	0.0789617i
$617$			7.78352e10i			0.537076i	0.963269	+	0.268538i	$0.0865405\pi$
$617$			7.78352e10i			0.537076i	−0.963269	+	0.268538i	$0.913460\pi$
$618$	−9.62114e10	+	1.98813e10i	−0.659588	+	0.136298i
$619$	9.02525e10	+	9.02525e10i	0.614747	+	0.614747i	0.944179	−	0.329432i	$-0.106857\pi$
$619$	9.02525e10	+	9.02525e10i	0.614747	+	0.614747i	−0.329432	+	0.944179i	$0.606857\pi$
$620$	−3.65263e10	+	9.20236e10i	−0.247194	+	0.622777i
$621$	−1.27281e11	−	1.27281e11i	−0.855851	−	0.855851i
$622$	9.32969e10	+	6.13421e10i	0.623312	+	0.409823i
$623$		−	3.90896e11i		−	2.59483i
$624$	1.71210e11	−	1.81693e11i	1.12925	−	1.19840i
$625$	−7.18421e10			−0.470824
$626$	−2.48367e10	+	3.77749e10i	−0.161732	+	0.245983i
$627$	−4.29774e9	+	4.29774e9i	−0.0278080	+	0.0278080i
$628$	−5.98655e10	+	1.50824e11i	−0.384891	+	0.969687i
$629$	4.80009e10	−	4.80009e10i	0.306652	−	0.306652i
$630$	8.79794e9	+	4.25758e10i	0.0558494	+	0.270272i
$631$	1.76853e11			1.11557			0.557784	−	0.829986i	$-0.311652\pi$
$631$	1.76853e11			1.11557			0.557784	+	0.829986i	$0.311652\pi$
$632$	−1.70702e11	−	3.00192e10i	−1.06997	−	0.188161i
$633$			1.47906e11i			0.921238i
$634$	−3.34157e10	−	1.61709e11i	−0.206821	−	1.00087i
$635$	−1.25309e10	−	1.25309e10i	−0.0770704	−	0.0770704i
$636$	8.10638e10	−	3.49967e10i	0.495449	−	0.213894i
$637$	2.74394e11	+	2.74394e11i	1.66654	+	1.66654i
$638$	−4.56644e9	+	6.94523e9i	−0.0275610	+	0.0419184i
$639$		−	4.33958e10i		−	0.260282i
$640$	−7.20253e10	−	1.04720e10i	−0.429304	−	0.0624180i
$641$	1.59560e11			0.945132			0.472566	−	0.881295i	$-0.343328\pi$
$641$	1.59560e11			0.945132			0.472566	+	0.881295i	$0.343328\pi$
$642$	−4.82238e10	−	3.17068e10i	−0.283871	−	0.186643i
$643$	8.91476e10	−	8.91476e10i	0.521514	−	0.521514i	−0.396515	−	0.918028i	$-0.629780\pi$
$643$	8.91476e10	−	8.91476e10i	0.521514	−	0.521514i	0.918028	+	0.396515i	$0.129780\pi$
$644$	−1.87612e11	−	4.34570e11i	−1.09073	−	2.52648i
$645$	5.90529e10	−	5.90529e10i	0.341195	−	0.341195i
$646$	−4.55349e10	+	9.40941e9i	−0.261466	+	0.0540297i
$647$	−1.21988e11			−0.696146			−0.348073	−	0.937467i	$-0.613164\pi$
$647$	−1.21988e11			−0.696146			−0.348073	+	0.937467i	$0.613164\pi$
$648$	−3.77910e10	+	2.14895e11i	−0.214333	+	1.21879i
$649$		−	8.77675e9i		−	0.0494715i
$650$	−1.98336e11	+	4.09845e10i	−1.11109	+	0.229597i
$651$	3.78794e11	+	3.78794e11i	2.10901	+	2.10901i
$652$	1.39606e11	+	5.54128e10i	0.772526	+	0.306633i
$653$	1.69140e11	+	1.69140e11i	0.930237	+	0.930237i	0.997720	−	0.0674833i	$-0.0214969\pi$
$653$	1.69140e11	+	1.69140e11i	0.930237	+	0.930237i	−0.0674833	+	0.997720i	$0.521497\pi$
$654$	−7.87202e10	−	5.17580e10i	−0.430304	−	0.282922i
$655$			4.26331e10i			0.231623i
$656$	1.66299e11	+	1.56705e11i	0.897997	+	0.846187i
$657$	−1.24001e10			−0.0665525
$658$	9.20501e10	−	1.40002e11i	0.491044	−	0.746843i
$659$	−9.61406e10	+	9.61406e10i	−0.509759	+	0.509759i	−0.914453	−	0.404693i	$-0.867378\pi$
$659$	−9.61406e10	+	9.61406e10i	−0.509759	+	0.509759i	0.404693	+	0.914453i	$0.367378\pi$
$660$	7.56642e9	+	3.00329e9i	0.0398763	+	0.0158278i
$661$	9.45167e10	−	9.45167e10i	0.495111	−	0.495111i	−0.414801	−	0.909912i	$-0.636149\pi$
$661$	9.45167e10	−	9.45167e10i	0.495111	−	0.495111i	0.909912	+	0.414801i	$0.136149\pi$
$662$	−5.48700e10	−	2.65532e11i	−0.285695	−	1.38256i
$663$	−2.13616e11			−1.10555
$664$	7.32956e10	+	1.04576e11i	0.377056	+	0.537970i
$665$		−	5.52950e10i		−	0.282748i
$666$	−9.98161e9	−	4.83040e10i	−0.0507345	−	0.245519i
$667$	−1.40441e11	−	1.40441e11i	−0.709564	−	0.709564i
$668$	2.62471e10	+	6.07968e10i	0.131818	+	0.305334i
$669$	6.03761e10	+	6.03761e10i	0.301412	+	0.301412i
$670$	9.38923e10	−	1.42804e11i	0.465941	−	0.708663i
$671$			9.58273e9i			0.0472715i
$672$	−2.06482e11	+	3.35328e11i	−1.01252	+	1.64434i
$673$	−3.32437e11			−1.62050			−0.810251	−	0.586083i	$-0.800669\pi$
$673$	−3.32437e11			−1.62050			−0.810251	+	0.586083i	$0.800669\pi$
$674$	−1.36589e11	−	8.98065e10i	−0.661877	−	0.435179i
$675$	8.59049e10	−	8.59049e10i	0.413812	−	0.413812i
$676$	−1.82758e11	+	7.88999e10i	−0.875165	+	0.377824i
$677$	−5.52097e10	+	5.52097e10i	−0.262821	+	0.262821i	−0.826199	−	0.563378i	$-0.809502\pi$
$677$	−5.52097e10	+	5.52097e10i	−0.262821	+	0.262821i	0.563378	+	0.826199i	$0.309502\pi$
$678$	−3.63370e11	+	7.50873e10i	−1.71961	+	0.355343i
$679$	4.86402e11			2.28832
$680$	3.57439e10	+	5.09982e10i	0.167173	+	0.238517i
$681$			1.74798e11i			0.812734i
$682$	2.74670e10	−	5.67583e9i	0.126962	−	0.0262357i
$683$	−2.40861e11	−	2.40861e11i	−1.10684	−	1.10684i	−0.993564	−	0.113272i	$-0.963867\pi$
$683$	−2.40861e11	−	2.40861e11i	−1.10684	−	1.10684i	−0.113272	−	0.993564i	$-0.536133\pi$
$684$	−1.24641e10	+	3.14017e10i	−0.0569424	+	0.143459i
$685$	2.39498e10	+	2.39498e10i	0.108777	+	0.108777i
$686$	−2.08172e11	−	1.36872e11i	−0.939997	−	0.618041i
$687$		−	2.18667e11i		−	0.981650i
$688$	2.11424e11	−	6.28029e9i	0.943629	−	0.0280302i
$689$	−1.44261e11			−0.640135
$690$	−1.06866e11	+	1.62536e11i	−0.471460	+	0.717056i
$691$	−1.98662e11	+	1.98662e11i	−0.871371	+	0.871371i	−0.992622	−	0.121251i	$-0.961309\pi$
$691$	−1.98662e11	+	1.98662e11i	−0.871371	+	0.871371i	0.121251	+	0.992622i	$0.461309\pi$
$692$	5.28818e10	−	1.33229e11i	0.230612	−	0.580999i
$693$	8.70865e9	−	8.70865e9i	0.0377588	−	0.0377588i
$694$	3.03281e10	+	1.46766e11i	0.130740	+	0.632687i
$695$	−6.36465e10			−0.272794
$696$	−2.86195e10	+	1.62743e11i	−0.121962	+	0.693528i
$697$		−	1.95518e11i		−	0.828428i
$698$	3.77677e10	+	1.82769e11i	0.159110	+	0.769982i
$699$	1.40581e11	+	1.40581e11i	0.588869	+	0.588869i
$700$	2.93301e11	−	1.26623e11i	1.22158	−	0.527377i
$701$	−1.41523e11	−	1.41523e11i	−0.586078	−	0.586078i	0.350489	−	0.936567i	$-0.386015\pi$
$701$	−1.41523e11	−	1.41523e11i	−0.586078	−	0.586078i	−0.936567	+	0.350489i	$0.886015\pi$
$702$	1.34421e11	−	2.04445e11i	0.553503	−	0.841839i
$703$			6.27344e10i			0.256853i
$704$	8.73064e9	+	1.86785e10i	0.0355431	+	0.0760415i
$705$	−6.88563e10			−0.278732
$706$	−5.39488e10	−	3.54710e10i	−0.217152	−	0.142776i
$707$	5.40501e11	−	5.40501e11i	2.16331	−	2.16331i
$708$	−6.91565e10	−	1.60189e11i	−0.275233	−	0.637529i
$709$	−1.56696e11	+	1.56696e11i	−0.620116	+	0.620116i	−0.945561	−	0.325445i	$-0.894486\pi$
$709$	−1.56696e11	+	1.56696e11i	−0.620116	+	0.620116i	0.325445	+	0.945561i	$0.394486\pi$
$710$	7.23961e10	−	1.49600e10i	0.284893	−	0.0588707i
$711$	1.07759e11			0.421671
$712$	−4.00712e11	−	7.04682e10i	−1.55924	−	0.274204i
$713$			6.70190e11i			2.59322i
$714$	3.29988e11	−	6.81894e10i	1.26971	−	0.262376i
$715$	−9.40490e9	−	9.40490e9i	−0.0359857	−	0.0359857i
$716$	7.36102e10	+	2.92176e10i	0.280083	+	0.111171i
$717$	−4.03293e11	−	4.03293e11i	−1.52596	−	1.52596i
$718$	1.46394e11	+	9.62532e10i	0.550841	+	0.362174i
$719$		−	8.70268e10i		−	0.325640i	−0.986656	−	0.162820i	$-0.947941\pi$
$719$		−	8.70268e10i		−	0.325640i	0.986656	−	0.162820i	$-0.0520589\pi$
$720$	4.52310e10	−	1.34357e9i	0.168308	−	0.00499955i
$721$	−2.53198e11			−0.936955
$722$	−1.25680e11	+	1.91151e11i	−0.462508	+	0.703441i
$723$	−1.62590e11	+	1.62590e11i	−0.595032	+	0.595032i
$724$	1.59829e11	+	6.34396e10i	0.581701	+	0.230891i
$725$	9.47868e10	−	9.47868e10i	0.343081	−	0.343081i
$726$	6.57704e10	+	3.18283e11i	0.236747	+	1.14569i
$727$	9.10537e10			0.325957			0.162978	−	0.986630i	$-0.447890\pi$
$727$	9.10537e10			0.325957			0.162978	+	0.986630i	$0.447890\pi$
$728$	5.26881e11	−	3.69284e11i	1.87580	−	1.31472i
$729$			1.04224e11i			0.369026i
$730$	−4.27476e9	−	2.06868e10i	−0.0150529	−	0.0728454i
$731$	−1.27977e11	−	1.27977e11i	−0.448192	−	0.448192i
$732$	7.55073e10	+	1.74900e11i	0.262993	+	0.609178i
$733$	2.31868e11	+	2.31868e11i	0.803204	+	0.803204i	0.983595	−	0.180391i	$-0.0577364\pi$
$733$	2.31868e11	+	2.31868e11i	0.803204	+	0.803204i	−0.180391	+	0.983595i	$0.557736\pi$
$734$	−3.73779e10	+	5.68492e10i	−0.128775	+	0.195857i
$735$			2.51552e11i			0.861942i
$736$	−4.79304e11	+	1.13981e11i	−1.63343	+	0.388439i
$737$	−4.84149e10			−0.164100
$738$	−1.18705e11	−	7.80475e10i	−0.400168	−	0.263108i
$739$	−2.53274e11	+	2.53274e11i	−0.849206	+	0.849206i	−0.990034	−	0.140828i	$-0.955024\pi$
$739$	−2.53274e11	+	2.53274e11i	−0.849206	+	0.849206i	0.140828	+	0.990034i	$0.455024\pi$
$740$	7.71433e10	−	3.33041e10i	0.257259	−	0.111063i
$741$	1.39592e11	−	1.39592e11i	0.463008	−	0.463008i
$742$	2.22850e11	−	4.60501e10i	0.735186	−	0.151920i
$743$	−8.65664e9			−0.0284050			−0.0142025	−	0.999899i	$-0.504521\pi$
$743$	−8.65664e9			−0.0284050			−0.0142025	+	0.999899i	$0.504521\pi$
$744$	4.56593e11	−	3.20020e11i	1.49017	−	1.04444i
$745$		−	1.32665e11i		−	0.430657i
$746$	5.44740e10	−	1.12566e10i	0.175887	−	0.0363456i
$747$	−5.61422e10	−	5.61422e10i	−0.180305	−	0.180305i
$748$	6.50862e9	−	1.63977e10i	0.0207913	−	0.0523813i
$749$	−1.05176e11	−	1.05176e11i	−0.334187	−	0.334187i
$750$	−2.44829e11	−	1.60974e11i	−0.773782	−	0.508756i
$751$		−	7.37909e10i		−	0.231976i	−0.993251	−	0.115988i	$-0.962997\pi$
$751$		−	7.37909e10i		−	0.231976i	0.993251	−	0.115988i	$-0.0370034\pi$
$752$	−1.26923e11	−	1.19600e11i	−0.396889	−	0.373990i
$753$	5.82674e11			1.81237
$754$	1.48320e11	−	2.25584e11i	0.458895	−	0.697946i
$755$	−2.64514e10	+	2.64514e10i	−0.0814069	+	0.0814069i
$756$	−1.42389e11	+	3.58731e11i	−0.435901	+	1.09820i
$757$	−2.71468e11	+	2.71468e11i	−0.826674	+	0.826674i	−0.987055	−	0.160381i	$-0.948728\pi$
$757$	−2.71468e11	+	2.71468e11i	−0.826674	+	0.826674i	0.160381	+	0.987055i	$0.448728\pi$
$758$	−1.77872e10	−	8.60776e10i	−0.0538804	−	0.260743i
$759$	5.51048e10			0.166044
$760$	−5.66835e10	−	9.96822e9i	−0.169903	−	0.0298788i
$761$		−	6.09480e11i		−	1.81728i	−0.417585	−	0.908638i	$-0.637123\pi$
$761$		−	6.09480e11i		−	1.81728i	0.417585	−	0.908638i	$-0.362877\pi$
$762$	2.01962e10	+	9.77354e10i	0.0599032	+	0.289889i
$763$	−1.71689e11	−	1.71689e11i	−0.506574	−	0.506574i
$764$	−1.63466e10	+	7.05712e9i	−0.0479793	+	0.0207135i
$765$	−2.73788e10	−	2.73788e10i	−0.0799408	−	0.0799408i
$766$	2.15563e10	−	3.27857e10i	0.0626124	−	0.0952289i
$767$			2.85072e11i			0.823707i
$768$	3.06525e11	+	2.72118e11i	0.881091	+	0.782189i
$769$	4.10154e11			1.17285			0.586423	−	0.810005i	$-0.300536\pi$
$769$	4.10154e11			1.17285			0.586423	+	0.810005i	$0.300536\pi$
$770$	1.75306e10	+	1.15262e10i	0.0498694	+	0.0327888i
$771$	1.57877e11	−	1.57877e11i	0.446788	−	0.446788i
$772$	6.98729e10	+	1.61848e11i	0.196716	+	0.455658i
$773$	−1.09201e11	+	1.09201e11i	−0.305850	+	0.305850i	−0.843297	−	0.537447i	$-0.819389\pi$
$773$	−1.09201e11	+	1.09201e11i	−0.305850	+	0.305850i	0.537447	+	0.843297i	$0.319389\pi$
$774$	−1.28786e11	+	2.66124e10i	−0.358842	+	0.0741517i
$775$	−4.52326e11			−1.25385
$776$	8.76854e10	−	4.98616e11i	0.241813	−	1.37505i
$777$		−	4.54632e11i		−	1.24731i
$778$	6.51234e11	−	1.34572e11i	1.77754	−	0.367313i
$779$	1.27765e11	+	1.27765e11i	0.346946	+	0.346946i
$780$	−2.45760e11	−	9.75478e10i	−0.663946	−	0.263535i
$781$	−1.48082e10	−	1.48082e10i	−0.0398014	−	0.0398014i
$782$	3.52242e11	+	2.31597e11i	0.941922	+	0.619307i
$783$			1.61948e11i			0.430853i
$784$	−4.36933e11	+	4.63686e11i	−1.15651	+	1.22733i
$785$	1.71865e11			0.452594
$786$	1.31903e11	−	2.00616e11i	0.345594	−	0.525624i
$787$	9.46809e10	−	9.46809e10i	0.246811	−	0.246811i	−0.572850	−	0.819660i	$-0.694162\pi$
$787$	9.46809e10	−	9.46809e10i	0.246811	−	0.246811i	0.819660	+	0.572850i	$0.194162\pi$
$788$	−1.60152e10	−	6.35679e9i	−0.0415362	−	0.0164867i
$789$	−5.98594e10	+	5.98594e10i	−0.154463	+	0.154463i
$790$	3.71482e10	+	1.79771e11i	0.0953738	+	0.461542i
$791$	−9.56273e11			−2.44273
$792$	−7.35740e9	−	1.04973e10i	−0.0186992	−	0.0266794i
$793$		−	3.11250e11i		−	0.787077i
$794$	9.69342e10	+	4.69093e11i	0.243891	+	1.18026i
$795$	−6.61259e10	−	6.61259e10i	−0.165540	−	0.165540i
$796$	4.00242e9	+	9.27092e9i	0.00996944	+	0.0230925i
$797$	4.36519e11	+	4.36519e11i	1.08186	+	1.08186i	0.996336	+	0.0855213i	$0.0272556\pi$
$797$	4.36519e11	+	4.36519e11i	1.08186	+	1.08186i	0.0855213	+	0.996336i	$0.472744\pi$
$798$	−1.71078e11	+	2.60198e11i	−0.421874	+	0.641641i
$799$			1.49223e11i			0.366141i
$800$	−7.69285e10	−	3.23493e11i	−0.187814	−	0.789777i
$801$	2.52957e11			0.614491
$802$	−4.16451e11	−	2.73814e11i	−1.00662	−	0.661847i
$803$	−4.23137e9	+	4.23137e9i	−0.0101770	+	0.0101770i
$804$	−8.83645e11	+	3.81486e11i	−2.11472	+	0.912964i
$805$	−3.54491e11	+	3.54491e11i	−0.844153	+	0.844153i
$806$	−8.92139e11	+	1.84353e11i	−2.11394	+	0.436828i
$807$	4.21557e11			0.993945
$808$	−4.56636e11	−	6.51512e11i	−1.07133	−	1.52854i
$809$			4.04706e11i			0.944813i	0.881381	+	0.472407i	$0.156615\pi$
$809$			4.04706e11i			0.944813i	−0.881381	+	0.472407i	$0.843385\pi$
$810$	2.26313e11	−	4.67656e10i	0.525737	−	0.108639i
$811$	3.55918e11	+	3.55918e11i	0.822746	+	0.822746i	0.986501	−	0.163755i	$-0.0523606\pi$
$811$	3.55918e11	+	3.55918e11i	0.822746	+	0.822746i	−0.163755	+	0.986501i	$0.552361\pi$
$812$	−1.57110e11	+	3.95821e11i	−0.361394	+	0.910489i
$813$	−2.95664e11	−	2.95664e11i	−0.676763	−	0.676763i
$814$	−1.98892e10	−	1.30770e10i	−0.0453022	−	0.0297859i
$815$		−	1.59082e11i		−	0.360570i
$816$	−1.04135e10	−	3.50568e11i	−0.0234874	−	0.790699i
$817$	1.67259e11			0.375406
$818$	−2.56269e11	+	3.89767e11i	−0.572378	+	0.870546i
$819$	−2.82860e11	+	2.82860e11i	−0.628689	+	0.628689i
$820$	8.92830e10	−	2.24938e11i	0.197476	−	0.497516i
$821$	3.40311e11	−	3.40311e11i	0.749037	−	0.749037i	−0.225261	−	0.974298i	$-0.572324\pi$
$821$	3.40311e11	−	3.40311e11i	0.749037	−	0.749037i	0.974298	+	0.225261i	$0.0723236\pi$
$822$	−3.86001e10	−	1.86797e11i	−0.0845476	−	0.409151i
$823$	1.85529e11			0.404402			0.202201	−	0.979344i	$-0.435191\pi$
$823$	1.85529e11			0.404402			0.202201	+	0.979344i	$0.435191\pi$
$824$	−4.56449e10	+	2.59556e11i	−0.0990109	+	0.563018i
$825$			3.71914e10i			0.0802836i
$826$	−9.09990e10	−	4.40371e11i	−0.195486	−	0.946016i
$827$	−3.50880e11	−	3.50880e11i	−0.750130	−	0.750130i	0.224373	−	0.974503i	$-0.427967\pi$
$827$	−3.50880e11	−	3.50880e11i	−0.750130	−	0.750130i	−0.974503	+	0.224373i	$0.927967\pi$
$828$	2.81219e11	−	1.21407e11i	0.598306	−	0.258300i
$829$	−6.11186e10	−	6.11186e10i	−0.129406	−	0.129406i	0.639437	−	0.768843i	$-0.279167\pi$
$829$	−6.11186e10	−	6.11186e10i	−0.129406	−	0.129406i	−0.768843	+	0.639437i	$0.779167\pi$
$830$	7.43065e10	−	1.13015e11i	0.156572	−	0.238135i
$831$			7.29630e11i			1.53002i
$832$	−2.83574e11	−	6.06683e11i	−0.591797	−	1.26610i
$833$	5.45154e11			1.13224
$834$	2.99497e11	+	1.96917e11i	0.619053	+	0.407023i
$835$	4.95935e10	−	4.95935e10i	0.102019	−	0.102019i
$836$	6.46222e9	+	1.49686e10i	0.0132299	+	0.0306448i
$837$	3.86411e11	−	3.86411e11i	0.787313	−	0.787313i
$838$	2.58567e10	−	5.34307e9i	0.0524321	−	0.0108347i
$839$	4.60798e11			0.929956			0.464978	−	0.885322i	$-0.346062\pi$
$839$	4.60798e11			0.929956			0.464978	+	0.885322i	$0.346062\pi$
$840$	4.10782e11	+	7.22390e10i	0.825076	+	0.145096i
$841$		−	3.21554e11i		−	0.642791i
$842$	3.14324e11	−	6.49524e10i	0.625359	−	0.129225i
$843$	1.15627e11	+	1.15627e11i	0.228954	+	0.228954i
$844$	3.68770e11	+	1.46373e11i	0.726751	+	0.288464i
$845$	1.49081e11	+	1.49081e11i	0.292411	+	0.292411i
$846$	9.05978e10	+	5.95674e10i	0.176863	+	0.116286i
$847$			8.37618e11i			1.62747i
$848$	−7.03251e9	−	2.36748e11i	−0.0135996	−	0.457828i
$849$	3.47194e11			0.668253
$850$	−1.56310e11	+	2.37736e11i	−0.299440	+	0.455428i
$851$	4.02184e11	−	4.02184e11i	0.766842	−	0.766842i
$852$	−3.86954e11	−	1.53591e11i	−0.734347	−	0.291479i
$853$	−3.84176e11	+	3.84176e11i	−0.725662	+	0.725662i	−0.969752	−	0.244091i	$-0.921511\pi$
$853$	−3.84176e11	+	3.84176e11i	−0.725662	+	0.725662i	0.244091	+	0.969752i	$0.421511\pi$
$854$	9.93555e10	+	4.80811e11i	0.186793	+	0.903946i
$855$	3.57825e10			0.0669585
$856$	−1.26778e11	+	8.88566e10i	−0.236128	+	0.165499i
$857$			4.53230e11i			0.840225i	0.907472	+	0.420112i	$0.138009\pi$
$857$			4.53230e11i			0.840225i	−0.907472	+	0.420112i	$0.861991\pi$
$858$	1.51580e10	+	7.33540e10i	0.0279700	+	0.135355i
$859$	−2.91488e11	−	2.91488e11i	−0.535363	−	0.535363i	0.386800	−	0.922163i	$-0.373580\pi$
$859$	−2.91488e11	−	2.91488e11i	−0.535363	−	0.535363i	−0.922163	+	0.386800i	$0.873580\pi$
$860$	−8.87938e10	−	2.05675e11i	−0.162326	−	0.376001i
$861$	−9.25905e11	−	9.25905e11i	−1.68482	−	1.68482i
$862$	2.93265e11	−	4.46035e11i	0.531167	−	0.807867i
$863$		−	4.45151e11i		−	0.802536i	−0.915961	−	0.401268i	$-0.868570\pi$
$863$		−	4.45151e11i		−	0.802536i	0.915961	−	0.401268i	$-0.131430\pi$
$864$	3.42070e11	+	2.10634e11i	0.613847	+	0.377984i
$865$	−1.51816e11			−0.271177
$866$	8.30983e10	+	5.46366e10i	0.147748	+	0.0971431i
$867$	2.58535e11	−	2.58535e11i	0.457554	−	0.457554i
$868$	1.31930e12	−	5.69567e11i	2.32416	−	1.00338i
$869$	3.67712e10	−	3.67712e10i	0.0644805	−	0.0644805i
$870$	1.71389e11	−	3.54161e10i	0.299161	−	0.0618192i
$871$	1.57253e12			2.73229
$872$	−2.06951e11	+	1.45049e11i	−0.357932	+	0.250870i
$873$			3.14760e11i			0.541905i
$874$	−3.81522e11	+	7.88384e10i	−0.653844	+	0.135111i
$875$	−5.33972e11	−	5.33972e11i	−0.910933	−	0.910933i
$876$	−4.38879e10	+	1.10570e11i	−0.0745295	+	0.187768i
$877$	2.67375e11	+	2.67375e11i	0.451984	+	0.451984i	0.896013	−	0.444029i	$-0.146451\pi$
$877$	2.67375e11	+	2.67375e11i	0.451984	+	0.451984i	−0.444029	+	0.896013i	$0.646451\pi$
$878$	−2.70560e11	−	1.77891e11i	−0.455288	−	0.299348i
$879$		−	1.00626e12i		−	1.68560i
$880$	1.49760e10	−	1.58929e10i	0.0249727	−	0.0265017i
$881$	−6.54614e11			−1.08663			−0.543315	−	0.839529i	$-0.682831\pi$
$881$	−6.54614e11			−1.08663			−0.543315	+	0.839529i	$0.682831\pi$
$882$	2.17617e11	−	3.30980e11i	0.359599	−	0.546924i
$883$	−5.73913e11	+	5.73913e11i	−0.944068	+	0.944068i	−0.998517	−	0.0544488i	$-0.982660\pi$
$883$	−5.73913e11	+	5.73913e11i	−0.944068	+	0.944068i	0.0544488	+	0.998517i	$0.482660\pi$
$884$	−2.11402e11	+	5.32602e11i	−0.346179	+	0.872156i
$885$	−1.30670e11	+	1.30670e11i	−0.213012	+	0.213012i
$886$	−6.43912e10	−	3.11608e11i	−0.104494	−	0.505678i
$887$	−5.88342e11			−0.950463			−0.475231	−	0.879861i	$-0.657636\pi$
$887$	−5.88342e11			−0.950463			−0.475231	+	0.879861i	$0.657636\pi$
$888$	−4.66048e11	−	8.19581e10i	−0.749512	−	0.131807i
$889$			2.57208e11i			0.411792i
$890$	8.72030e10	+	4.22001e11i	0.138986	+	0.672595i
$891$	−4.62910e10	−	4.62910e10i	−0.0734490	−	0.0734490i
$892$	2.10284e11	−	9.07834e10i	0.332160	−	0.143399i
$893$	−9.75129e10	−	9.75129e10i	−0.153340	−	0.153340i
$894$	−4.10455e11	+	6.24272e11i	−0.642562	+	0.977291i
$895$		−	8.38794e10i		−	0.130726i
$896$	6.31719e11	+	8.46666e11i	0.980149	+	1.31365i
$897$	−1.78982e12			−2.76465
$898$	5.98015e11	+	3.93190e11i	0.919616	+	0.604641i
$899$	4.26363e11	−	4.26363e11i	0.652740	−	0.652740i
$900$	8.19404e10	+	1.89801e11i	0.124890	+	0.289286i
$901$	−1.43306e11	+	1.43306e11i	−0.217453	+	0.217453i
$902$	−6.71390e10	+	1.38737e10i	−0.101426	+	0.0209588i
$903$	−1.21212e12			−1.82303
$904$	−1.72391e11	+	9.80287e11i	−0.258131	+	1.46784i
$905$		−	1.82126e11i		−	0.271505i
$906$	2.06309e11	−	4.26320e10i	0.306200	−	0.0632737i
$907$	9.91716e10	+	9.91716e10i	0.146541	+	0.146541i	0.776571	−	0.630030i	$-0.216957\pi$
$907$	9.91716e10	+	9.91716e10i	0.146541	+	0.146541i	−0.630030	+	0.776571i	$0.716957\pi$
$908$	4.35818e11	+	1.72986e11i	0.641154	+	0.254489i
$909$	3.49769e11	+	3.49769e11i	0.512302	+	0.512302i
$910$	−5.69400e11	−	3.74376e11i	−0.830332	−	0.545937i
$911$			8.98335e11i			1.30426i	0.758106	+	0.652131i	$0.226125\pi$
$911$			8.98335e11i			1.30426i	−0.758106	+	0.652131i	$0.773875\pi$
$912$	2.35891e11	+	2.22281e11i	0.340982	+	0.321309i
$913$	−3.83156e10			−0.0551432
$914$	6.37634e11	−	9.69796e11i	0.913665	−	1.38962i
$915$	1.42670e11	−	1.42670e11i	0.203540	−	0.203540i
$916$	−5.45196e11	−	2.16401e11i	−0.774409	−	0.307381i
$917$	4.37542e11	−	4.37542e11i	0.618789	−	0.618789i
$918$	−6.95605e10	−	3.36624e11i	−0.0979471	−	0.473995i
$919$	−5.32146e11			−0.746051			−0.373026	−	0.927821i	$-0.621680\pi$
$919$	−5.32146e11			−0.746051			−0.373026	+	0.927821i	$0.621680\pi$
$920$	2.99487e11	+	4.27297e11i	0.418048	+	0.596457i
$921$			1.01005e12i			1.40380i
$922$	−1.58478e11	−	7.66921e11i	−0.219303	−	1.06127i
$923$	4.80976e11	+	4.80976e11i	0.662699	+	0.662699i
$924$	−4.68313e10	−	1.08477e11i	−0.0642463	−	0.148815i
$925$	2.71442e11	+	2.71442e11i	0.370775	+	0.370775i
$926$	4.29213e11	−	6.52802e11i	0.583753	−	0.887846i
$927$		−	1.63849e11i		−	0.221884i
$928$	3.77437e11	+	2.32412e11i	0.508924	+	0.313376i
$929$	6.38626e11			0.857400			0.428700	−	0.903447i	$-0.358972\pi$
$929$	6.38626e11			0.857400			0.428700	+	0.903447i	$0.358972\pi$
$930$	−4.93440e11	−	3.24433e11i	−0.659633	−	0.433704i
$931$	−3.56243e11	+	3.56243e11i	−0.474184	+	0.474184i
$932$	4.89630e11	−	2.11382e11i	0.648940	−	0.280159i
$933$	−4.70924e11	+	4.70924e11i	−0.621476	+	0.621476i
$934$	2.31172e11	−	4.77698e10i	0.303772	−	0.0627720i
$935$	−1.86853e10			−0.0244485
$936$	2.38971e11	+	3.40955e11i	0.311345	+	0.444215i
$937$		−	1.48043e12i		−	1.92057i	−0.279015	−	0.960287i	$-0.590008\pi$
$937$		−	1.48043e12i		−	1.92057i	0.279015	−	0.960287i	$-0.409992\pi$
$938$	−2.42920e12	+	5.01974e11i	−3.13799	+	0.648440i
$939$	−1.90672e11	−	1.90672e11i	−0.245259	−	0.245259i
$940$	−6.81426e10	+	1.71677e11i	−0.0872785	+	0.219888i
$941$	3.27255e11	+	3.27255e11i	0.417376	+	0.417376i	0.884298	−	0.466922i	$-0.154637\pi$
$941$	3.27255e11	+	3.27255e11i	0.417376	+	0.417376i	−0.466922	+	0.884298i	$0.654637\pi$
$942$	−8.08732e11	−	5.31736e11i	−1.02707	−	0.675293i
$943$		−	1.63818e12i		−	2.07164i
$944$	−4.67834e11	+	1.38968e10i	−0.589120	+	0.0174996i
$945$	4.08776e11			0.512576
$946$	−3.48652e10	+	5.30275e10i	−0.0435339	+	0.0662119i
$947$	−2.58031e11	+	2.58031e11i	−0.320828	+	0.320828i	−0.849085	−	0.528257i	$-0.822846\pi$
$947$	−2.58031e11	+	2.58031e11i	−0.320828	+	0.320828i	0.528257	+	0.849085i	$0.322846\pi$
$948$	3.81391e11	−	9.60869e11i	0.472212	−	1.18968i
$949$	1.37436e11	−	1.37436e11i	0.169448	−	0.169448i
$950$	−5.32097e10	−	2.57498e11i	−0.0653276	−	0.316140i
$951$	9.84907e11			1.20413
$952$	1.56554e11	−	8.90232e11i	0.190597	−	1.08382i
$953$			9.80476e11i			1.18868i	0.804214	+	0.594340i	$0.202587\pi$
$953$			9.80476e11i			1.18868i	−0.804214	+	0.594340i	$0.797413\pi$
$954$	2.97999e10	+	1.44211e11i	0.0359767	+	0.174102i
$955$	1.33344e10	+	1.33344e10i	0.0160309	+	0.0160309i
$956$	−1.40463e12	+	6.06404e11i	−1.68163	+	0.725990i
$957$	−3.50566e10	−	3.50566e10i	−0.0417948	−	0.0417948i
$958$	−4.27657e11	+	6.50435e11i	−0.507731	+	0.772222i
$959$		−	4.91591e11i		−	0.581205i
$960$	1.48106e11	−	4.08074e11i	0.174376	−	0.480456i
$961$	−1.18172e12			−1.38555
$962$	6.46007e11	+	4.24745e11i	0.754287	+	0.495939i
$963$	6.80615e10	−	6.80615e10i	0.0791400	−	0.0791400i
$964$	2.44475e11	+	5.66285e11i	0.283091	+	0.655732i
$965$	1.32024e11	−	1.32024e11i	0.152245	−	0.152245i
$966$	2.76487e12	−	5.71337e11i	3.17516	−	0.656120i
$967$	3.89769e11			0.445760			0.222880	−	0.974846i	$-0.428454\pi$
$967$	3.89769e11			0.445760			0.222880	+	0.974846i	$0.428454\pi$
$968$	8.58652e11	+	1.51000e11i	0.977948	+	0.171979i
$969$		−	2.77336e11i		−	0.314566i
$970$	−5.25107e11	+	1.08509e11i	−0.593145	+	0.122568i
$971$	1.18394e12	+	1.18394e12i	1.33184	+	1.33184i	0.903720	+	0.428124i	$0.140826\pi$
$971$	1.18394e12	+	1.18394e12i	1.33184	+	1.33184i	0.428124	+	0.903720i	$0.359174\pi$
$972$	−6.11546e11	−	2.42737e11i	−0.685116	−	0.271939i
$973$	6.53201e11	+	6.53201e11i	0.728779	+	0.728779i
$974$	1.31505e12	+	8.64635e11i	1.46119	+	0.960721i
$975$		−	1.20799e12i		−	1.33673i
$976$	5.10796e11	−	1.51730e10i	0.562922	−	0.0167214i
$977$	−1.10476e12			−1.21253			−0.606263	−	0.795264i	$-0.707332\pi$
$977$	−1.10476e12			−1.21253			−0.606263	+	0.795264i	$0.707332\pi$
$978$	−4.92186e11	+	7.48580e11i	−0.537990	+	0.818244i
$979$	8.63180e10	−	8.63180e10i	0.0939660	−	0.0939660i
$980$	6.27185e11	+	2.48944e11i	0.679973	+	0.269897i
$981$	1.11103e11	−	1.11103e11i	0.119964	−	0.119964i
$982$	2.05039e11	+	9.92243e11i	0.220491	+	1.06702i
$983$	5.18977e11			0.555819			0.277910	−	0.960607i	$-0.410358\pi$
$983$	5.18977e11			0.555819			0.277910	+	0.960607i	$0.410358\pi$
$984$	−1.11607e12	+	7.82239e11i	−1.19045	+	0.834371i
$985$			1.82494e10i			0.0193867i
$986$	−7.67525e10	−	3.71428e11i	−0.0812054	−	0.392977i
$987$	7.06670e11	+	7.06670e11i	0.744643	+	0.744643i
$988$	−2.09895e11	−	4.86186e11i	−0.220280	−	0.510240i
$989$	−1.07228e12	−	1.07228e12i	−1.12079	−	1.12079i
$990$	−7.45886e9	+	1.13444e10i	−0.00776483	+	0.0118098i
$991$			4.76993e11i			0.494558i	0.968944	+	0.247279i	$0.0795364\pi$
$991$			4.76993e11i			0.494558i	−0.968944	+	0.247279i	$0.920464\pi$
$992$	−3.46034e11	−	1.45511e12i	−0.357332	−	1.50262i
$993$	1.61725e12			1.66334
$994$	−8.96533e11	−	5.89464e11i	−0.918376	−	0.603826i
$995$	7.56254e9	−	7.56254e9i	0.00771570	−	0.00771570i
$996$	−6.99318e11	+	3.01908e11i	−0.710620	+	0.306787i
$997$	6.51920e11	−	6.51920e11i	0.659802	−	0.659802i	−0.295531	−	0.955333i	$-0.595497\pi$
$997$	6.51920e11	−	6.51920e11i	0.659802	−	0.659802i	0.955333	+	0.295531i	$0.0954966\pi$
$998$	−1.35863e12	+	2.80750e11i	−1.36956	+	0.283008i
$999$	−4.63773e11			−0.465633

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.9.f.a.3.13	✓	30
4.3	odd	2		64.9.f.a.47.12		30
8.3	odd	2		128.9.f.a.95.4		30
8.5	even	2		128.9.f.b.95.12		30
16.3	odd	4		128.9.f.b.31.12		30
16.5	even	4		64.9.f.a.15.12		30
16.11	odd	4	inner	16.9.f.a.11.13	yes	30
16.13	even	4		128.9.f.a.31.4		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.9.f.a.3.13	✓	30	1.1	even	1	trivial
16.9.f.a.11.13	yes	30	16.11	odd	4	inner
64.9.f.a.15.12		30	16.5	even	4
64.9.f.a.47.12		30	4.3	odd	2
128.9.f.a.31.4		30	16.13	even	4
128.9.f.a.95.4		30	8.3	odd	2
128.9.f.b.31.12		30	16.3	odd	4
128.9.f.b.95.12		30	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	16.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(13.3691 + 8.79011i) q^{2} +(-67.4818 + 67.4818i) q^{3} +(101.468 + 235.033i) q^{4} +(191.722 - 191.722i) q^{5} +(-1495.35 + 309.001i) q^{6} -3935.28 q^{7} +(-709.426 + 4034.10i) q^{8} -2546.60i q^{9} +O(q^{10})\)	\(q+(13.3691 + 8.79011i) q^{2} +(-67.4818 + 67.4818i) q^{3} +(101.468 + 235.033i) q^{4} +(191.722 - 191.722i) q^{5} +(-1495.35 + 309.001i) q^{6} -3935.28 q^{7} +(-709.426 + 4034.10i) q^{8} -2546.60i q^{9} +(4248.42 - 877.901i) q^{10} +(-868.992 - 868.992i) q^{11} +(-22707.7 - 9013.20i) q^{12} +(28225.1 + 28225.1i) q^{13} +(-52611.3 - 34591.5i) q^{14} +25875.5i q^{15} +(-44944.6 + 47696.5i) q^{16} +56076.6 q^{17} +(22384.9 - 34045.8i) q^{18} +(-36644.4 + 36644.4i) q^{19} +(64514.6 + 25607.3i) q^{20} +(265560. - 265560. i) q^{21} +(-3979.13 - 19256.2i) q^{22} +469847. q^{23} +(-224355. - 320102. i) q^{24} +317110. i q^{25} +(129244. + 625448. i) q^{26} +(-270899. - 270899. i) q^{27} +(-399304. - 924918. i) q^{28} +(-298908. - 298908. i) q^{29} +(-227449. + 345934. i) q^{30} +1.42640e6i q^{31} +(-1.02013e6 + 242592. i) q^{32} +117282. q^{33} +(749695. + 492919. i) q^{34} +(-754480. + 754480. i) q^{35} +(598533. - 258397. i) q^{36} +(855988. - 855988. i) q^{37} +(-812013. + 167796. i) q^{38} -3.80937e6 q^{39} +(637413. + 909439. i) q^{40} -3.48662e6i q^{41} +(5.88460e6 - 1.21600e6i) q^{42} +(-2.28219e6 - 2.28219e6i) q^{43} +(116067. - 292416. i) q^{44} +(-488239. - 488239. i) q^{45} +(6.28146e6 + 4.13001e6i) q^{46} +2.66106e6i q^{47} +(-185701. - 6.25159e6i) q^{48} +9.72160e6 q^{49} +(-2.78743e6 + 4.23949e6i) q^{50} +(-3.78415e6 + 3.78415e6i) q^{51} +(-3.76988e6 + 9.49777e6i) q^{52} +(-2.55554e6 + 2.55554e6i) q^{53} +(-1.24045e6 - 6.00293e6i) q^{54} -333210. q^{55} +(2.79179e6 - 1.58753e7i) q^{56} -4.94567e6i q^{57} +(-1.36871e6 - 6.62358e6i) q^{58} +(5.04996e6 + 5.04996e6i) q^{59} +(-6.08159e6 + 2.62553e6i) q^{60} +(-5.51371e6 - 5.51371e6i) q^{61} +(-1.25382e7 + 1.90697e7i) q^{62} +1.00216e7i q^{63} +(-1.57706e7 - 5.72379e6i) q^{64} +1.08228e7 q^{65} +(1.56796e6 + 1.03092e6i) q^{66} +(2.78569e7 - 2.78569e7i) q^{67} +(5.68996e6 + 1.31798e7i) q^{68} +(-3.17062e7 + 3.17062e7i) q^{69} +(-1.67187e7 + 3.45478e6i) q^{70} +1.70407e7 q^{71} +(1.02732e7 + 1.80662e6i) q^{72} -4.86929e6i q^{73} +(1.89680e7 - 3.91959e6i) q^{74} +(-2.13992e7 - 2.13992e7i) q^{75} +(-1.23309e7 - 4.89440e6i) q^{76} +(3.41972e6 + 3.41972e6i) q^{77} +(-5.09280e7 - 3.34848e7i) q^{78} +4.23147e7i q^{79} +(527595. + 1.77613e7i) q^{80} +5.32698e7 q^{81} +(3.06478e7 - 4.66131e7i) q^{82} +(2.20460e7 - 2.20460e7i) q^{83} +(8.93609e7 + 3.54694e7i) q^{84} +(1.07511e7 - 1.07511e7i) q^{85} +(-1.04502e7 - 5.05716e7i) q^{86} +4.03418e7 q^{87} +(4.12208e6 - 2.88911e6i) q^{88} +9.93313e7i q^{89} +(-2.23566e6 - 1.08190e7i) q^{90} +(-1.11074e8 - 1.11074e8i) q^{91} +(4.76744e7 + 1.10429e8i) q^{92} +(-9.62560e7 - 9.62560e7i) q^{93} +(-2.33910e7 + 3.55761e7i) q^{94} +1.40511e7i q^{95} +(5.24695e7 - 8.52107e7i) q^{96} -1.23600e8 q^{97} +(1.29969e8 + 8.54540e7i) q^{98} +(-2.21297e6 + 2.21297e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8}+O(q^{10}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8	\( 30 q - 2 q^{2} - 2 q^{3} + 184 q^{4} - 2 q^{5} + 3232 q^{6} - 4 q^{7} - 8732 q^{8} - 1860 q^{10} - 19778 q^{11} + 14068 q^{12} - 2 q^{13} - 58900 q^{14} + 245336 q^{16} - 4 q^{17} - 223730 q^{18} + 167550 q^{19} - 135380 q^{20} - 13124 q^{21} + 985700 q^{22} - 845572 q^{23} - 800592 q^{24} - 184760 q^{26} + 38656 q^{27} + 94136 q^{28} + 1066174 q^{29} + 1881700 q^{30} - 3395192 q^{32} - 4 q^{33} + 1634900 q^{34} + 426620 q^{35} + 1877324 q^{36} + 2360254 q^{37} - 3010352 q^{38} - 7650052 q^{39} + 3256936 q^{40} - 3731304 q^{42} + 6314814 q^{43} - 10360940 q^{44} + 794370 q^{45} + 1510780 q^{46} + 4591848 q^{48} + 14823770 q^{49} + 14752710 q^{50} - 28969860 q^{51} + 4335652 q^{52} + 2679358 q^{53} + 18667040 q^{54} + 46326780 q^{55} - 36346408 q^{56} - 1034696 q^{58} - 46004162 q^{59} - 20687200 q^{60} - 24476034 q^{61} - 64043472 q^{62} + 50827456 q^{64} - 14970820 q^{65} + 65035780 q^{66} + 59474558 q^{67} + 74339312 q^{68} + 8623420 q^{69} + 39082496 q^{70} - 79832068 q^{71} + 929812 q^{72} - 168043460 q^{74} + 88519490 q^{75} - 166219388 q^{76} + 35952572 q^{77} + 5059788 q^{78} - 12904856 q^{80} - 66961570 q^{81} + 261305296 q^{82} - 34471682 q^{83} + 456781480 q^{84} - 107741252 q^{85} + 9841444 q^{86} + 149712636 q^{87} - 173775752 q^{88} - 650366536 q^{90} - 76429060 q^{91} - 449169832 q^{92} + 138269056 q^{93} - 239278032 q^{94} + 378359728 q^{96} - 4 q^{97} + 630040554 q^{98} + 184838270 q^{99}+O(q^{100}) \) 30 * q - 2 * q^2 - 2 * q^3 + 184 * q^4 - 2 * q^5 + 3232 * q^6 - 4 * q^7 - 8732 * q^8 - 1860 * q^10 - 19778 * q^11 + 14068 * q^12 - 2 * q^13 - 58900 * q^14 + 245336 * q^16 - 4 * q^17 - 223730 * q^18 + 167550 * q^19 - 135380 * q^20 - 13124 * q^21 + 985700 * q^22 - 845572 * q^23 - 800592 * q^24 - 184760 * q^26 + 38656 * q^27 + 94136 * q^28 + 1066174 * q^29 + 1881700 * q^30 - 3395192 * q^32 - 4 * q^33 + 1634900 * q^34 + 426620 * q^35 + 1877324 * q^36 + 2360254 * q^37 - 3010352 * q^38 - 7650052 * q^39 + 3256936 * q^40 - 3731304 * q^42 + 6314814 * q^43 - 10360940 * q^44 + 794370 * q^45 + 1510780 * q^46 + 4591848 * q^48 + 14823770 * q^49 + 14752710 * q^50 - 28969860 * q^51 + 4335652 * q^52 + 2679358 * q^53 + 18667040 * q^54 + 46326780 * q^55 - 36346408 * q^56 - 1034696 * q^58 - 46004162 * q^59 - 20687200 * q^60 - 24476034 * q^61 - 64043472 * q^62 + 50827456 * q^64 - 14970820 * q^65 + 65035780 * q^66 + 59474558 * q^67 + 74339312 * q^68 + 8623420 * q^69 + 39082496 * q^70 - 79832068 * q^71 + 929812 * q^72 - 168043460 * q^74 + 88519490 * q^75 - 166219388 * q^76 + 35952572 * q^77 + 5059788 * q^78 - 12904856 * q^80 - 66961570 * q^81 + 261305296 * q^82 - 34471682 * q^83 + 456781480 * q^84 - 107741252 * q^85 + 9841444 * q^86 + 149712636 * q^87 - 173775752 * q^88 - 650366536 * q^90 - 76429060 * q^91 - 449169832 * q^92 + 138269056 * q^93 - 239278032 * q^94 + 378359728 * q^96 - 4 * q^97 + 630040554 * q^98 + 184838270 * q^99

Introduction

L-functions

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