LMFDB - Embedded newform 18.11.d.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,11,Mod(5,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("18.5");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	18.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.4364305481$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + 63819 x^{18} - 574086 x^{17} + 1685636151 x^{16} - 13472077884 x^{15} + \cdots + 42\!\cdots\!17 $ x^20 - 10x^19 + 63819x^18 - 574086x^17 + 1685636151x^16 - 13472077884x^15 + 23849722149866x^14 - 166712339223788x^13 + 195479019402402405x^12 - 1170707468814910094x^11 + 938326637750627487341x^10 - 4680905675328128110986x^9 + 2551316542474577226379677x^8 - 10177193606819996156162676x^7 + 3644946427174260203987635170x^6 - 10899238750832113741944409252x^5 + 2446510322689300614446071763767x^4 - 4874867111497712925857039900178x^3 + 623192578601325527612865828822963x^2 - 620756959890572838693596656972206*x + 42080692026395342189225080891718217
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{46}\cdot 3^{37} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.2
Root			$0.500000 + 100.759i$ of defining polynomial
Character	$\chi$	$=$	18.11
Dual form			18.11.d.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-19.5959 - 11.3137i) q^{2} +(-196.987 - 142.285i) q^{3} +(256.000 + 443.405i) q^{4} +(3091.89 - 1785.10i) q^{5} +(2250.37 + 5016.87i) q^{6} +(12604.4 - 21831.4i) q^{7} -11585.2i q^{8} +(18558.8 + 56056.7i) q^{9} -80784.5 q^{10} +(-171690. - 99125.1i) q^{11} +(12661.4 - 123770. i) q^{12} +(141992. + 245938. i) q^{13} +(-493988. + 285204. i) q^{14} +(-863055. - 88288.4i) q^{15} +(-131072. + 227023. i) q^{16} -1.47323e6i q^{17} +(270534. - 1.30845e6i) q^{18} -4.67704e6 q^{19} +(1.58305e6 + 913972. i) q^{20} +(-5.58918e6 + 2.50709e6i) q^{21} +(2.24294e6 + 3.88489e6i) q^{22} +(4.51953e6 - 2.60935e6i) q^{23} +(-1.64841e6 + 2.28214e6i) q^{24} +(1.49036e6 - 2.58138e6i) q^{25} -6.42584e6i q^{26} +(4.32022e6 - 1.36831e7i) q^{27} +1.29069e7 q^{28} +(1.64106e6 + 947468. i) q^{29} +(1.59135e7 + 1.14944e7i) q^{30} +(9.25805e6 + 1.60354e7i) q^{31} +(5.13695e6 - 2.96582e6i) q^{32} +(1.97166e7 + 4.39553e7i) q^{33} +(-1.66677e7 + 2.88693e7i) q^{34} -9.00003e7i q^{35} +(-2.01048e7 + 2.25796e7i) q^{36} -9.06055e7 q^{37} +(9.16509e7 + 5.29147e7i) q^{38} +(7.02273e6 - 6.86501e7i) q^{39} +(-2.06808e7 - 3.58202e7i) q^{40} +(-4.27366e6 + 2.46740e6i) q^{41} +(1.37890e8 + 1.41058e7i) q^{42} +(-3.66421e7 + 6.34660e7i) q^{43} -1.01504e8i q^{44} +(1.57449e8 + 1.40192e8i) q^{45} -1.18086e8 q^{46} +(-2.91846e8 - 1.68497e8i) q^{47} +(5.81216e7 - 2.60710e7i) q^{48} +(-1.76502e8 - 3.05711e8i) q^{49} +(-5.84101e7 + 3.37231e7i) q^{50} +(-2.09619e8 + 2.90207e8i) q^{51} +(-7.27001e7 + 1.25920e8i) q^{52} -8.02924e7i q^{53} +(-2.39465e8 + 2.19255e8i) q^{54} -7.07793e8 q^{55} +(-2.52922e8 - 1.46025e8i) q^{56} +(9.21316e8 + 6.65475e8i) q^{57} +(-2.14388e7 - 3.71330e7i) q^{58} +(7.95473e8 - 4.59267e8i) q^{59} +(-1.81795e8 - 4.05285e8i) q^{60} +(3.70068e6 - 6.40977e6i) q^{61} -4.18972e8i q^{62} +(1.45772e9 + 3.01396e8i) q^{63} -1.34218e8 q^{64} +(8.78049e8 + 5.06942e8i) q^{65} +(1.10933e8 - 1.08441e9i) q^{66} +(9.55400e8 + 1.65480e9i) q^{67} +(6.53238e8 - 3.77147e8i) q^{68} +(-1.26156e9 - 1.29055e8i) q^{69} +(-1.01824e9 + 1.76364e9i) q^{70} -2.72418e9i q^{71} +(6.49431e8 - 2.15008e8i) q^{72} +2.42985e9 q^{73} +(1.77550e9 + 1.02508e9i) q^{74} +(-6.60875e8 + 2.96442e8i) q^{75} +(-1.19732e9 - 2.07382e9i) q^{76} +(-4.32808e9 + 2.49882e9i) q^{77} +(-9.14303e8 + 1.26581e9i) q^{78} +(7.42978e8 - 1.28688e9i) q^{79} +9.35907e8i q^{80} +(-2.79793e9 + 2.08069e9i) q^{81} +1.11662e8 q^{82} +(-5.66479e8 - 3.27057e8i) q^{83} +(-2.54249e9 - 1.83646e9i) q^{84} +(-2.62987e9 - 4.55506e9i) q^{85} +(1.43607e9 - 8.29117e8i) q^{86} +(-1.88457e8 - 4.20138e8i) q^{87} +(-1.14839e9 + 1.98907e9i) q^{88} +1.33310e9i q^{89} +(-1.49926e9 - 4.52851e9i) q^{90} +7.15890e9 q^{91} +(2.31400e9 + 1.33599e9i) q^{92} +(4.57889e8 - 4.47605e9i) q^{93} +(3.81266e9 + 6.60372e9i) q^{94} +(-1.44609e10 + 8.34899e9i) q^{95} +(-1.43391e9 - 1.46685e8i) q^{96} +(2.78067e9 - 4.81625e9i) q^{97} +7.98759e9i q^{98} +(2.37028e9 - 1.14640e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 84 q^{3} + 5120 q^{4} - 9918 q^{5} + 12864 q^{6} + 12238 q^{7} + 79248 q^{9} - 327582 q^{11} + 9216 q^{12} - 280550 q^{13} + 175680 q^{14} - 2685042 q^{15} - 2621440 q^{16} + 3925632 q^{18} - 2966240 q^{19}+ \cdots + 41160676842 q^{99}+O(q^{100}) $ 20 * q - 84 * q^3 + 5120 * q^4 - 9918 * q^5 + 12864 * q^6 + 12238 * q^7 + 79248 * q^9 - 327582 * q^11 + 9216 * q^12 - 280550 * q^13 + 175680 * q^14 - 2685042 * q^15 - 2621440 * q^16 + 3925632 * q^18 - 2966240 * q^19 - 5078016 * q^20 - 11895726 * q^21 + 3473472 * q^22 + 10446606 * q^23 + 2752512 * q^24 + 9609944 * q^25 + 2340576 * q^27 + 12531712 * q^28 + 32440806 * q^29 + 37556352 * q^30 - 40069958 * q^31 - 35367930 * q^33 + 30746496 * q^34 - 32695296 * q^36 - 127390400 * q^37 + 370567296 * q^38 + 153125550 * q^39 - 245419398 * q^41 - 344505600 * q^42 - 86593094 * q^43 + 394622766 * q^45 - 366913920 * q^46 + 1094979330 * q^47 + 26738688 * q^48 - 598072056 * q^49 - 456606720 * q^50 - 2329772724 * q^51 + 143641600 * q^52 + 1623484224 * q^54 - 262510308 * q^55 + 89948160 * q^56 + 311135772 * q^57 + 249515904 * q^58 - 2125085130 * q^59 - 2357738496 * q^60 + 312021586 * q^61 + 5475513858 * q^63 - 2684354560 * q^64 + 13076821350 * q^65 + 2185467264 * q^66 - 1200881210 * q^67 - 2610487296 * q^68 - 11765922354 * q^69 + 1138681152 * q^70 + 1554382848 * q^72 + 5213376328 * q^73 + 9118122624 * q^74 + 13244996208 * q^75 - 759357440 * q^76 - 33678720774 * q^77 - 14572366080 * q^78 - 3396212726 * q^79 + 14546869128 * q^81 + 3667214592 * q^82 + 16739541378 * q^83 + 1518514176 * q^84 + 7141101588 * q^85 - 11512304064 * q^86 - 32778228834 * q^87 - 1778417664 * q^88 + 16769410560 * q^90 - 10426841884 * q^91 + 5348662272 * q^92 - 4843832814 * q^93 + 6416128320 * q^94 - 26494427340 * q^95 - 1962934272 * q^96 + 6721893598 * q^97 + 41160676842 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−19.5959	−	11.3137i	−0.612372	−	0.353553i
$2$	−19.5959	−	11.3137i	−0.612372	−	0.353553i
$3$	−196.987	−	142.285i	−0.810646	−	0.585536i
$3$	−196.987	−	142.285i	−0.810646	−	0.585536i
$4$	256.000	+	443.405i	0.250000	+	0.433013i
$5$	3091.89	−	1785.10i	0.989404	−	0.571233i	0.0843077	−	0.996440i	$-0.473132\pi$
$5$	3091.89	−	1785.10i	0.989404	−	0.571233i	0.905096	+	0.425207i	$0.139799\pi$
$6$	2250.37	+	5016.87i	0.289399	+	0.645173i
$7$	12604.4	−	21831.4i	0.749947	−	1.29895i	−0.197900	−	0.980222i	$-0.563412\pi$
$7$	12604.4	−	21831.4i	0.749947	−	1.29895i	0.947847	−	0.318725i	$-0.103255\pi$
$8$		−	11585.2i		−	0.353553i
$9$	18558.8	+	56056.7i	0.314294	+	0.949326i
$10$	−80784.5			−0.807845
$11$	−171690.	−	99125.1i	−1.06606	−	0.615489i	−0.138956	−	0.990299i	$-0.544375\pi$
$11$	−171690.	−	99125.1i	−1.06606	−	0.615489i	−0.927102	+	0.374810i	$0.877708\pi$
$12$	12661.4	−	123770.i	0.0508832	−	0.497404i
$13$	141992.	+	245938.i	0.382427	+	0.662383i	0.991409	−	0.130801i	$-0.0417550\pi$
$13$	141992.	+	245938.i	0.382427	+	0.662383i	−0.608982	+	0.793184i	$0.708422\pi$
$14$	−493988.	+	285204.i	−0.918494	+	0.530293i
$15$	−863055.	−	88288.4i	−1.13653	−	0.116265i
$16$	−131072.	+	227023.i	−0.125000	+	0.216506i
$17$		−	1.47323e6i		−	1.03759i	−0.854899	−	0.518795i	$-0.826381\pi$
$17$		−	1.47323e6i		−	1.03759i	0.854899	−	0.518795i	$-0.173619\pi$
$18$	270534.	−	1.30845e6i	0.143172	−	0.692461i
$19$	−4.67704e6			−1.88888			−0.944438	−	0.328691i	$-0.893393\pi$
$19$	−4.67704e6			−1.88888			−0.944438	+	0.328691i	$0.893393\pi$
$20$	1.58305e6	+	913972.i	0.494702	+	0.285616i
$21$	−5.58918e6	+	2.50709e6i	−1.36852	+	0.613865i
$22$	2.24294e6	+	3.88489e6i	0.435216	+	0.753817i
$23$	4.51953e6	−	2.60935e6i	0.702190	−	0.405409i	−0.105973	−	0.994369i	$-0.533796\pi$
$23$	4.51953e6	−	2.60935e6i	0.702190	−	0.405409i	0.808162	+	0.588960i	$0.200462\pi$
$24$	−1.64841e6	+	2.28214e6i	−0.207018	+	0.286607i
$25$	1.49036e6	−	2.58138e6i	0.152613	−	0.264334i
$26$		−	6.42584e6i		−	0.540833i
$27$	4.32022e6	−	1.36831e7i	0.301083	−	0.953598i
$28$	1.29069e7			0.749947
$29$	1.64106e6	+	947468.i	0.0800083	+	0.0461928i	0.539470	−	0.842005i	$-0.318624\pi$
$29$	1.64106e6	+	947468.i	0.0800083	+	0.0461928i	−0.459462	+	0.888197i	$0.651958\pi$
$30$	1.59135e7	+	1.14944e7i	0.654876	+	0.473023i
$31$	9.25805e6	+	1.60354e7i	0.323378	+	0.560108i	0.981183	−	0.193081i	$-0.0618480\pi$
$31$	9.25805e6	+	1.60354e7i	0.323378	+	0.560108i	−0.657804	+	0.753189i	$0.728515\pi$
$32$	5.13695e6	−	2.96582e6i	0.153093	−	0.0883883i
$33$	1.97166e7	+	4.39553e7i	0.503805	+	1.12316i
$34$	−1.66677e7	+	2.88693e7i	−0.366844	+	0.635392i
$35$		−	9.00003e7i		−	1.71358i
$36$	−2.01048e7	+	2.25796e7i	−0.332497	+	0.373425i
$37$	−9.06055e7			−1.30661			−0.653305	−	0.757095i	$-0.726618\pi$
$37$	−9.06055e7			−1.30661			−0.653305	+	0.757095i	$0.726618\pi$
$38$	9.16509e7	+	5.29147e7i	1.15670	+	0.667818i
$39$	7.02273e6	−	6.86501e7i	0.0778364	−	0.760883i
$40$	−2.06808e7	−	3.58202e7i	−0.201961	−	0.349807i
$41$	−4.27366e6	+	2.46740e6i	−0.0368876	+	0.0212971i	−0.518330	−	0.855180i	$-0.673446\pi$
$41$	−4.27366e6	+	2.46740e6i	−0.0368876	+	0.0212971i	0.481443	+	0.876478i	$0.340113\pi$
$42$	1.37890e8	+	1.41058e7i	1.05508	+	0.107932i
$43$	−3.66421e7	+	6.34660e7i	−0.249252	+	0.431717i	−0.963318	−	0.268361i	$-0.913518\pi$
$43$	−3.66421e7	+	6.34660e7i	−0.249252	+	0.431717i	0.714067	+	0.700078i	$0.246851\pi$
$44$		−	1.01504e8i		−	0.615489i
$45$	1.57449e8	+	1.40192e8i	0.853249	+	0.759731i
$46$	−1.18086e8			−0.573335
$47$	−2.91846e8	−	1.68497e8i	−1.27252	−	0.734689i	−0.297058	−	0.954860i	$-0.596005\pi$
$47$	−2.91846e8	−	1.68497e8i	−1.27252	−	0.734689i	−0.975461	+	0.220170i	$0.929339\pi$
$48$	5.81216e7	−	2.60710e7i	0.228103	−	0.102318i
$49$	−1.76502e8	−	3.05711e8i	−0.624842	−	1.08226i
$50$	−5.84101e7	+	3.37231e7i	−0.186912	+	0.107914i
$51$	−2.09619e8	+	2.90207e8i	−0.607547	+	0.841119i
$52$	−7.27001e7	+	1.25920e8i	−0.191213	+	0.331191i
$53$		−	8.02924e7i		−	0.191997i	−0.995381	−	0.0959986i	$-0.969396\pi$
$53$		−	8.02924e7i		−	0.191997i	0.995381	−	0.0959986i	$-0.0306044\pi$
$54$	−2.39465e8	+	2.19255e8i	−0.521523	+	0.477508i
$55$	−7.07793e8			−1.40635
$56$	−2.52922e8	−	1.46025e8i	−0.459247	−	0.265146i
$57$	9.21316e8	+	6.65475e8i	1.53121	+	1.10601i
$58$	−2.14388e7	−	3.71330e7i	−0.0326633	−	0.0565744i
$59$	7.95473e8	−	4.59267e8i	1.11267	−	0.642399i	0.173149	−	0.984896i	$-0.444606\pi$
$59$	7.95473e8	−	4.59267e8i	1.11267	−	0.642399i	0.939519	+	0.342497i	$0.111273\pi$
$60$	−1.81795e8	−	4.05285e8i	−0.233789	−	0.521200i
$61$	3.70068e6	−	6.40977e6i	0.00438160	−	0.00758915i	−0.863826	−	0.503790i	$-0.831939\pi$
$61$	3.70068e6	−	6.40977e6i	0.00438160	−	0.00758915i	0.868208	+	0.496201i	$0.165272\pi$
$62$		−	4.18972e8i		−	0.457326i
$63$	1.45772e9	+	3.01396e8i	1.46883	+	0.303693i
$64$	−1.34218e8			−0.125000
$65$	8.78049e8	+	5.06942e8i	0.756749	+	0.436909i
$66$	1.10933e8	−	1.08441e9i	0.0885808	−	0.865914i
$67$	9.55400e8	+	1.65480e9i	0.707638	+	1.22566i	0.965731	+	0.259545i	$0.0835724\pi$
$67$	9.55400e8	+	1.65480e9i	0.707638	+	1.22566i	−0.258093	+	0.966120i	$0.583094\pi$
$68$	6.53238e8	−	3.77147e8i	0.449290	−	0.259398i
$69$	−1.26156e9	−	1.29055e8i	−0.806609	−	0.0825141i
$70$	−1.01824e9	+	1.76364e9i	−0.605841	+	1.04935i
$71$		−	2.72418e9i		−	1.50989i	−0.655790	−	0.754943i	$-0.727664\pi$
$71$		−	2.72418e9i		−	1.50989i	0.655790	−	0.754943i	$-0.272336\pi$
$72$	6.49431e8	−	2.15008e8i	0.335637	−	0.111120i
$73$	2.42985e9			1.17210			0.586051	−	0.810274i	$-0.300682\pi$
$73$	2.42985e9			1.17210			0.586051	+	0.810274i	$0.300682\pi$
$74$	1.77550e9	+	1.02508e9i	0.800132	+	0.461956i
$75$	−6.60875e8	+	2.96442e8i	−0.278492	+	0.124921i
$76$	−1.19732e9	−	2.07382e9i	−0.472219	−	0.817907i
$77$	−4.32808e9	+	2.49882e9i	−1.59897	+	0.923168i
$78$	−9.14303e8	+	1.26581e9i	−0.316678	+	0.438424i
$79$	7.42978e8	−	1.28688e9i	0.241457	−	0.418217i	−0.719672	−	0.694314i	$-0.755708\pi$
$79$	7.42978e8	−	1.28688e9i	0.241457	−	0.418217i	0.961130	+	0.276097i	$0.0890412\pi$
$80$			9.35907e8i			0.285616i
$81$	−2.79793e9	+	2.08069e9i	−0.802438	+	0.596735i
$82$	1.11662e8			0.0301186
$83$	−5.66479e8	−	3.27057e8i	−0.143811	−	0.0830295i	0.426368	−	0.904550i	$-0.359793\pi$
$83$	−5.66479e8	−	3.27057e8i	−0.143811	−	0.0830295i	−0.570179	+	0.821520i	$0.693126\pi$
$84$	−2.54249e9	−	1.83646e9i	−0.607942	−	0.439121i
$85$	−2.62987e9	−	4.55506e9i	−0.592705	−	1.02660i
$86$	1.43607e9	−	8.29117e8i	0.305270	−	0.176248i
$87$	−1.88457e8	−	4.20138e8i	−0.0378109	−	0.0842938i
$88$	−1.14839e9	+	1.98907e9i	−0.217608	+	0.376908i
$89$			1.33310e9i			0.238733i	0.992850	+	0.119366i	$0.0380863\pi$
$89$			1.33310e9i			0.238733i	−0.992850	+	0.119366i	$0.961914\pi$
$90$	−1.49926e9	−	4.52851e9i	−0.253901	−	0.766908i
$91$	7.15890e9			1.14720
$92$	2.31400e9	+	1.33599e9i	0.351095	+	0.202705i
$93$	4.57889e8	−	4.47605e9i	0.0658181	−	0.643399i
$94$	3.81266e9	+	6.60372e9i	0.519504	+	0.899807i
$95$	−1.44609e10	+	8.34899e9i	−1.86886	+	1.07899i
$96$	−1.43391e9	−	1.46685e8i	−0.175859	−	0.0179899i
$97$	2.78067e9	−	4.81625e9i	0.323810	−	0.560855i	−0.657461	−	0.753489i	$-0.728370\pi$
$97$	2.78067e9	−	4.81625e9i	0.323810	−	0.560855i	0.981271	+	0.192634i	$0.0617029\pi$
$98$			7.98759e9i			0.883660i
$99$	2.37028e9	−	1.14640e10i	0.249244	−	1.20548i
$100$	1.52613e9			0.152613
$101$	1.81497e9	+	1.04787e9i	0.172688	+	0.0997015i	0.583853	−	0.811860i	$-0.301545\pi$
$101$	1.81497e9	+	1.04787e9i	0.172688	+	0.0997015i	−0.411165	+	0.911561i	$0.634878\pi$
$102$	7.39100e9	−	3.31531e9i	0.669425	−	0.300278i
$103$	−6.89443e9	−	1.19415e10i	−0.594720	−	1.03008i	−0.993586	−	0.113076i	$-0.963930\pi$
$103$	−6.89443e9	−	1.19415e10i	−0.594720	−	1.03008i	0.398867	−	0.917009i	$-0.369404\pi$
$104$	2.84925e9	−	1.64502e9i	0.234188	−	0.135208i
$105$	−1.28057e10	+	1.77289e10i	−1.00336	+	1.38910i
$106$	−9.08405e8	+	1.57340e9i	−0.0678813	+	0.117574i
$107$			2.70745e9i			0.193037i	0.995331	+	0.0965186i	$0.0307707\pi$
$107$			2.70745e9i			0.193037i	−0.995331	+	0.0965186i	$0.969229\pi$
$108$	7.17312e9	−	1.58726e9i	0.488191	−	0.108027i
$109$	2.29489e10			1.49152			0.745760	−	0.666215i	$-0.232087\pi$
$109$	2.29489e10			1.49152			0.745760	+	0.666215i	$0.232087\pi$
$110$	1.38699e10	+	8.00777e9i	0.861209	+	0.497219i
$111$	1.78481e10	+	1.28918e10i	1.05920	+	0.765067i
$112$	3.30416e9	+	5.72297e9i	0.187487	+	0.324737i
$113$	5.53357e9	−	3.19481e9i	0.300340	−	0.173401i	−0.342256	−	0.939607i	$-0.611191\pi$
$113$	5.53357e9	−	3.19481e9i	0.300340	−	0.173401i	0.642596	+	0.766206i	$0.277858\pi$
$114$	−1.05251e10	−	2.34641e10i	−0.546638	−	1.21865i
$115$	9.31592e9	−	1.61357e10i	0.463166	−	0.802227i
$116$			9.70207e8i			0.0461928i
$117$	−1.11513e10	+	1.25239e10i	−0.508622	+	0.571231i
$118$	−2.07840e10			−0.908489
$119$	−3.21627e10	−	1.85691e10i	−1.34777	−	0.778138i
$120$	−1.02284e9	+	9.99870e9i	−0.0411057	+	0.401825i
$121$	6.68286e9	+	1.15750e10i	0.257653	+	0.446268i
$122$	−1.45036e8	+	8.37368e7i	−0.00536634	+	0.00309826i
$123$	1.19293e9	+	1.22034e8i	0.0423730	+	0.00433465i
$124$	−4.74012e9	+	8.21013e9i	−0.161689	+	0.280054i
$125$			2.42235e10i			0.793755i
$126$	−2.51554e10	−	2.23983e10i	−0.792098	−	0.705282i
$127$	2.33830e10			0.707752			0.353876	−	0.935292i	$-0.384863\pi$
$127$	2.33830e10			0.707752			0.353876	+	0.935292i	$0.384863\pi$
$128$	2.63012e9	+	1.51850e9i	0.0765466	+	0.0441942i
$129$	1.62483e10	−	7.28835e9i	0.454841	−	0.204024i
$130$	−1.14708e10	−	1.98680e10i	−0.308942	−	0.535102i
$131$	5.53612e10	−	3.19628e10i	1.43499	−	0.828493i	0.437496	−	0.899221i	$-0.355866\pi$
$131$	5.53612e10	−	3.19628e10i	1.43499	−	0.828493i	0.997496	+	0.0707280i	$0.0225322\pi$
$132$	−1.44425e10	+	1.99950e10i	−0.360391	+	0.498944i
$133$	−5.89511e10	+	1.02106e11i	−1.41656	+	2.45355i
$134$		−	4.32364e10i		−	1.00075i
$135$	−1.10681e10	−	5.00186e10i	−0.246833	−	1.11548i
$136$	−1.70677e10			−0.366844
$137$	−1.92851e10	−	1.11342e10i	−0.399593	−	0.230705i	0.286715	−	0.958016i	$-0.407437\pi$
$137$	−1.92851e10	−	1.11342e10i	−0.399593	−	0.230705i	−0.686309	+	0.727311i	$0.740770\pi$
$138$	2.32614e10	+	1.68019e10i	0.464772	+	0.335709i
$139$	−4.79695e10	−	8.30856e10i	−0.924466	−	1.60122i	−0.792418	−	0.609979i	$-0.791178\pi$
$139$	−4.79695e10	−	8.30856e10i	−0.924466	−	1.60122i	−0.132048	−	0.991243i	$-0.542155\pi$
$140$	3.99066e10	−	2.30401e10i	0.742001	−	0.428394i
$141$	3.35152e10	+	7.47172e10i	0.601375	+	1.34068i
$142$	−3.08206e10	+	5.33828e10i	−0.533825	+	0.924613i
$143$		−	5.63001e10i		−	0.941518i
$144$	−1.51587e10	−	3.13420e9i	−0.244822	−	0.0506190i
$145$	6.76531e9			0.105547
$146$	−4.76152e10	−	2.74906e10i	−0.717763	−	0.414401i
$147$	−8.72953e9	+	8.53348e10i	−0.127176	+	1.24320i
$148$	−2.31950e10	−	4.01749e10i	−0.326652	−	0.565779i
$149$	−6.42829e10	+	3.71137e10i	−0.875314	+	0.505363i	−0.869111	−	0.494618i	$-0.835308\pi$
$149$	−6.42829e10	+	3.71137e10i	−0.875314	+	0.505363i	−0.00620357	+	0.999981i	$0.501975\pi$
$150$	1.63043e10	+	1.66789e9i	0.214707	+	0.0219640i
$151$	−2.26560e10	+	3.92414e10i	−0.288602	+	0.499873i	−0.973476	−	0.228788i	$-0.926524\pi$
$151$	−2.26560e10	+	3.92414e10i	−0.288602	+	0.499873i	0.684875	+	0.728661i	$0.259857\pi$
$152$			5.41846e10i			0.667818i
$153$	8.25845e10	−	2.73413e10i	0.985011	−	0.326109i
$154$	1.13084e11			1.30556
$155$	5.72497e10	+	3.30531e10i	0.639904	+	0.369449i
$156$	3.22376e10	−	1.44605e10i	0.348931	−	0.156517i
$157$	−1.81100e10	−	3.13674e10i	−0.189854	−	0.328837i	0.755347	−	0.655325i	$-0.227468\pi$
$157$	−1.81100e10	−	3.13674e10i	−0.189854	−	0.328837i	−0.945201	+	0.326488i	$0.894135\pi$
$158$	−2.91187e10	+	1.68117e10i	−0.295724	+	0.170736i
$159$	−1.14244e10	+	1.58166e10i	−0.112421	+	0.155642i
$160$	1.05886e10	−	1.83400e10i	0.100981	−	0.174904i
$161$		−	1.31557e11i		−	1.21614i
$162$	7.83683e10	−	9.11800e9i	0.702369	−	0.0817193i
$163$	1.39750e10			0.121455			0.0607273	−	0.998154i	$-0.480658\pi$
$163$	1.39750e10			0.121455			0.0607273	+	0.998154i	$0.480658\pi$
$164$	−2.18811e9	−	1.26331e9i	−0.0184438	−	0.0106485i
$165$	1.39426e11	+	1.00709e11i	1.14005	+	0.823469i
$166$	7.40045e9	+	1.28180e10i	0.0587107	+	0.101690i
$167$	1.29494e11	−	7.47632e10i	0.996933	−	0.575580i	0.0895936	−	0.995978i	$-0.471443\pi$
$167$	1.29494e11	−	7.47632e10i	0.996933	−	0.575580i	0.907339	+	0.420399i	$0.138110\pi$
$168$	2.90452e10	+	6.47520e10i	0.217034	+	0.483846i
$169$	2.86055e10	−	4.95463e10i	0.207499	−	0.359399i
$170$			1.19014e11i			0.838212i
$171$	−8.68001e10	−	2.62180e11i	−0.593662	−	1.79316i
$172$	−3.75215e10			−0.249252
$173$	1.06275e11	+	6.13581e10i	0.685807	+	0.395951i	0.802039	−	0.597271i	$-0.203748\pi$
$173$	1.06275e11	+	6.13581e10i	0.685807	+	0.395951i	−0.116233	+	0.993222i	$0.537082\pi$
$174$	−1.06033e9	+	1.03651e10i	−0.00664804	+	0.0649874i
$175$	−3.75701e10	−	6.50734e10i	−0.228904	−	0.396473i
$176$	4.50074e10	−	2.59850e10i	0.266514	−	0.153872i
$177$	−2.22045e11	−	2.27146e10i	−1.27813	−	0.130749i
$178$	1.50823e10	−	2.61233e10i	0.0844047	−	0.146193i
$179$			2.85929e11i			1.55594i	0.628302	+	0.777969i	$0.283750\pi$
$179$			2.85929e11i			1.55594i	−0.628302	+	0.777969i	$0.716250\pi$
$180$	−2.18549e10	+	1.05703e11i	−0.115661	+	0.559401i
$181$	−1.54643e11			−0.796045			−0.398022	−	0.917376i	$-0.630303\pi$
$181$	−1.54643e11			−0.796045			−0.398022	+	0.917376i	$0.630303\pi$
$182$	−1.40285e11	−	8.09937e10i	−0.702514	−	0.405596i
$183$	−1.64100e9	+	7.36088e8i	−0.00799565	+	0.00358653i
$184$	−3.02300e10	−	5.23599e10i	−0.143334	−	0.248261i
$185$	−2.80142e11	+	1.61740e11i	−1.29276	+	0.746378i
$186$	−5.96135e10	+	8.25320e10i	−0.267781	+	0.370730i
$187$	−1.46034e11	+	2.52938e11i	−0.638625	+	1.10613i
$188$		−	1.72541e11i		−	0.734689i
$189$	−2.44267e11	−	2.66783e11i	−1.01288	−	1.10624i
$190$	3.77832e11			1.52592
$191$	−1.72218e11	−	9.94299e10i	−0.677502	−	0.391156i	0.121411	−	0.992602i	$-0.461258\pi$
$191$	−1.72218e11	−	9.94299e10i	−0.677502	−	0.391156i	−0.798913	+	0.601446i	$0.794591\pi$
$192$	2.64391e10	+	1.90972e10i	0.101331	+	0.0731921i
$193$	7.31637e10	+	1.26723e11i	0.273218	+	0.473227i	0.969684	−	0.244363i	$-0.0785787\pi$
$193$	7.31637e10	+	1.26723e11i	0.273218	+	0.473227i	−0.696466	+	0.717590i	$0.745245\pi$
$194$	−1.08979e11	+	6.29193e10i	−0.396584	+	0.228968i
$195$	−1.00834e11	−	2.24794e11i	−0.357629	−	0.797283i
$196$	9.03692e10	−	1.56524e11i	0.312421	−	0.541129i
$197$		−	1.34679e11i		−	0.453909i	−0.973905	−	0.226955i	$-0.927123\pi$
$197$		−	1.34679e11i		−	0.453909i	0.973905	−	0.226955i	$-0.0728769\pi$
$198$	−1.76148e11	+	1.97831e11i	−0.578832	+	0.650082i
$199$	4.99786e11			1.60147			0.800734	−	0.599020i	$-0.204443\pi$
$199$	4.99786e11			1.60147			0.800734	+	0.599020i	$0.204443\pi$
$200$	−2.99059e10	−	1.72662e10i	−0.0934561	−	0.0539569i
$201$	4.72526e10	−	4.61914e11i	0.144027	−	1.40793i
$202$	−2.37107e10	−	4.10681e10i	−0.0704996	−	0.122109i
$203$	4.13691e10	−	2.38845e10i	0.120004	−	0.0692844i
$204$	−1.82342e11	−	1.86531e10i	−0.516102	−	0.0527959i
$205$	−8.80912e9	+	1.52578e10i	−0.0243312	+	0.0421428i
$206$			3.12006e11i			0.841060i
$207$	2.30149e11	+	2.04924e11i	0.605560	+	0.539189i
$208$	−7.44449e10			−0.191213
$209$	8.03000e11	+	4.63612e11i	2.01365	+	1.16258i
$210$	4.51519e11	−	2.02534e11i	1.10555	−	0.495907i
$211$	−2.75783e10	−	4.77671e10i	−0.0659410	−	0.114213i	0.831170	−	0.556018i	$-0.187672\pi$
$211$	−2.75783e10	−	4.77671e10i	−0.0659410	−	0.114213i	−0.897111	+	0.441805i	$0.854338\pi$
$212$	3.56020e10	−	2.05548e10i	0.0831372	−	0.0479993i
$213$	−3.87611e11	+	5.36628e11i	−0.884093	+	1.22398i
$214$	3.06313e10	−	5.30549e10i	0.0682489	−	0.118211i
$215$			2.61640e11i			0.569523i
$216$	−1.58522e11	−	5.00507e10i	−0.337148	−	0.106449i
$217$	4.66767e11			0.970067
$218$	−4.49704e11	−	2.59637e11i	−0.913366	−	0.527332i
$219$	−4.78649e11	−	3.45732e11i	−0.950160	−	0.686308i
$220$	−1.81195e11	−	3.13839e11i	−0.351587	−	0.608967i
$221$	3.62323e11	−	2.09188e11i	0.687282	−	0.396803i
$222$	−2.03895e11	−	4.54555e11i	−0.378131	−	0.842989i
$223$	−6.13593e10	+	1.06277e11i	−0.111264	+	0.192716i	−0.916280	−	0.400538i	$-0.868823\pi$
$223$	−6.13593e10	+	1.06277e11i	−0.111264	+	0.192716i	0.805016	+	0.593253i	$0.202157\pi$
$224$		−	1.49529e11i		−	0.265146i
$225$	1.72363e11	+	3.56376e10i	0.298904	+	0.0618010i
$226$	−1.44580e11			−0.245226
$227$	5.62176e11	+	3.24573e11i	0.932703	+	0.538496i	0.887665	−	0.460489i	$-0.152326\pi$
$227$	5.62176e11	+	3.24573e11i	0.932703	+	0.538496i	0.0450373	+	0.998985i	$0.485659\pi$
$228$	−5.92177e10	+	5.78878e11i	−0.0961120	+	0.939534i
$229$	3.14128e11	+	5.44085e11i	0.498803	+	0.863951i	0.999999	−	0.00138219i	$-0.000439964\pi$
$229$	3.14128e11	+	5.44085e11i	0.498803	+	0.863951i	−0.501197	+	0.865333i	$0.667107\pi$
$230$	−3.65108e11	+	2.10795e11i	−0.567260	+	0.327508i
$231$	1.20812e12	+	1.23588e11i	1.83675	+	0.187895i
$232$	1.09766e10	−	1.90121e10i	0.0163316	−	0.0282872i
$233$		−	5.57291e11i		−	0.811527i	−0.913978	−	0.405763i	$-0.867006\pi$
$233$		−	5.57291e11i		−	0.811527i	0.913978	−	0.405763i	$-0.132994\pi$
$234$	3.60212e11	−	1.19256e11i	0.513427	−	0.169981i
$235$	−1.20314e12			−1.67871
$236$	4.07282e11	+	2.35145e11i	0.556334	+	0.321199i
$237$	−3.29461e11	+	1.47783e11i	−0.440618	+	0.197644i
$238$	4.20171e11	+	7.27758e11i	0.550227	+	0.953021i
$239$	−1.20254e12	+	6.94289e11i	−1.54210	+	0.890329i	−0.543389	+	0.839481i	$0.682859\pi$
$239$	−1.20254e12	+	6.94289e11i	−1.54210	+	0.890329i	−0.998706	+	0.0508484i	$0.983807\pi$
$240$	1.33166e11	−	1.84362e11i	0.167239	−	0.231534i
$241$	5.39136e11	−	9.33810e11i	0.663152	−	1.14861i	−0.316631	−	0.948549i	$-0.602552\pi$
$241$	5.39136e11	−	9.33810e11i	0.663152	−	1.14861i	0.979783	−	0.200063i	$-0.0641148\pi$
$242$		−	3.02432e11i		−	0.364376i
$243$	8.47207e11	−	1.17638e10i	0.999904	−	0.0138840i
$244$	3.78950e9			0.00438160
$245$	−1.09145e12	−	6.30149e11i	−1.23644	−	0.713860i
$246$	−2.19959e10	−	1.58878e10i	−0.0244155	−	0.0176356i
$247$	−6.64105e11	−	1.15026e12i	−0.722357	−	1.25116i
$248$	1.85774e11	−	1.07257e11i	0.198028	−	0.114332i
$249$	6.50536e10	+	1.45028e11i	0.0679633	+	0.151514i
$250$	2.74057e11	−	4.74681e11i	0.280635	−	0.486073i
$251$		−	1.05338e12i		−	1.05734i	−0.848827	−	0.528670i	$-0.822691\pi$
$251$		−	1.05338e12i		−	1.05734i	0.848827	−	0.528670i	$-0.177309\pi$
$252$	2.39535e11	+	7.23517e11i	0.235704	+	0.711944i
$253$	−1.03461e12			−0.998100
$254$	−4.58211e11	−	2.64548e11i	−0.433408	−	0.250228i
$255$	−1.30069e11	+	1.27148e12i	−0.120635	+	1.17926i
$256$	−3.43597e10	−	5.95128e10i	−0.0312500	−	0.0541266i
$257$	9.27087e10	−	5.35254e10i	0.0826904	−	0.0477413i	−0.458085	−	0.888909i	$-0.651464\pi$
$257$	9.27087e10	−	5.35254e10i	0.0826904	−	0.0477413i	0.540775	+	0.841167i	$0.318131\pi$
$258$	−4.00859e11	−	4.10068e10i	−0.350665	−	0.0358722i
$259$	−1.14202e12	+	1.97804e12i	−0.979888	+	1.69722i
$260$			5.19108e11i			0.436909i
$261$	−2.26559e10	+	1.09576e11i	−0.0187059	+	0.0904721i
$262$	−1.44647e12			−1.17167
$263$	5.25464e11	+	3.03377e11i	0.417603	+	0.241103i	0.694051	−	0.719925i	$-0.255824\pi$
$263$	5.25464e11	+	3.03377e11i	0.417603	+	0.241103i	−0.276448	+	0.961029i	$0.589157\pi$
$264$	5.09232e11	−	2.28421e11i	0.397097	−	0.178122i
$265$	−1.43330e11	−	2.48255e11i	−0.109675	−	0.189963i
$266$	2.31040e12	−	1.33391e12i	1.73492	−	1.00166i
$267$	1.89680e11	−	2.62603e11i	0.139787	−	0.193528i
$268$	−4.89165e11	+	8.47258e11i	−0.353819	+	0.612832i
$269$		−	1.85533e12i		−	1.31722i	−0.752483	−	0.658612i	$-0.771144\pi$
$269$		−	1.85533e12i		−	1.31722i	0.752483	−	0.658612i	$-0.228856\pi$
$270$	−3.49007e11	+	1.10538e12i	−0.243229	+	0.770359i
$271$	5.55952e11			0.380357			0.190178	−	0.981750i	$-0.439093\pi$
$271$	5.55952e11			0.380357			0.190178	+	0.981750i	$0.439093\pi$
$272$	3.34458e11	+	1.93099e11i	0.224645	+	0.129699i
$273$	−1.41021e12	−	1.01861e12i	−0.929973	−	0.671727i
$274$	2.51939e11	+	4.36371e11i	0.163133	+	0.282555i
$275$	−5.11760e11	+	2.95465e11i	−0.325389	+	0.187863i
$276$	−2.65736e11	−	5.92421e11i	−0.165923	−	0.369901i
$277$	1.17734e12	−	2.03922e12i	0.721945	−	1.25045i	−0.238274	−	0.971198i	$-0.576582\pi$
$277$	1.17734e12	−	2.03922e12i	0.721945	−	1.25045i	0.960219	−	0.279248i	$-0.0900851\pi$
$278$			2.17085e12i			1.30739i
$279$	−7.27075e11	+	8.16573e11i	−0.430089	+	0.483030i
$280$	−1.04267e12			−0.605841
$281$	−1.25457e12	−	7.24329e11i	−0.716085	−	0.413432i	0.0972249	−	0.995262i	$-0.469003\pi$
$281$	−1.25457e12	−	7.24329e11i	−0.716085	−	0.413432i	−0.813310	+	0.581830i	$0.802337\pi$
$282$	1.88568e11	−	1.84333e12i	0.105736	−	1.03361i
$283$	1.45881e12	+	2.52673e12i	0.803648	+	1.39196i	0.917200	+	0.398427i	$0.130444\pi$
$283$	1.45881e12	+	2.52673e12i	0.803648	+	1.39196i	−0.113552	+	0.993532i	$0.536223\pi$
$284$	1.20792e12	−	6.97390e11i	0.653800	−	0.377472i
$285$	4.03655e12	+	4.12928e11i	2.14677	+	0.219609i
$286$	−6.36962e11	+	1.10325e12i	−0.332877	+	0.576560i
$287$			1.24400e11i			0.0638868i
$288$	2.61590e11	+	2.32919e11i	0.132026	+	0.117555i
$289$	−1.54413e11			−0.0765942
$290$	−1.32572e11	−	7.65407e10i	−0.0646343	−	0.0373166i
$291$	−1.23304e12	+	5.53091e11i	−0.590896	+	0.265053i
$292$	6.22042e11	+	1.07741e12i	0.293025	+	0.507535i
$293$	1.33675e12	−	7.71772e11i	0.619030	−	0.357397i	−0.157461	−	0.987525i	$-0.550331\pi$
$293$	1.33675e12	−	7.71772e11i	0.619030	−	0.357397i	0.776491	+	0.630128i	$0.216998\pi$
$294$	1.13652e12	−	1.57345e12i	0.517415	−	0.716335i
$295$	1.63968e12	−	2.84000e12i	0.733918	−	1.27118i
$296$			1.04969e12i			0.461956i
$297$	−2.09807e12	+	1.92100e12i	−0.907901	+	0.831277i
$298$	1.67958e12			0.714691
$299$	1.28348e12	+	7.41017e11i	0.537072	+	0.310079i
$300$	−3.00628e11	−	2.17146e11i	−0.123715	−	0.0893606i
$301$	9.23702e11	+	1.59990e12i	0.373852	+	0.647530i
$302$	8.87931e11	−	5.12647e11i	0.353463	−	0.204072i
$303$	−2.08428e11	−	4.64661e11i	−0.0816101	−	0.181938i
$304$	6.13029e11	−	1.06180e12i	0.236109	−	0.408953i
$305$		−	2.64244e10i		−	0.0100116i
$306$	−1.92765e12	−	3.98558e11i	−0.718491	−	0.148554i
$307$	−2.26133e12			−0.829224			−0.414612	−	0.909998i	$-0.636083\pi$
$307$	−2.26133e12			−0.829224			−0.414612	+	0.909998i	$0.636083\pi$
$308$	−2.21598e12	−	1.27939e12i	−0.799487	−	0.461584i
$309$	−3.40988e11	+	3.33330e12i	−0.121045	+	1.18326i
$310$	−7.47907e11	−	1.29541e12i	−0.261240	−	0.452480i
$311$	−1.08915e12	+	6.28821e11i	−0.374357	+	0.216135i	−0.675360	−	0.737488i	$-0.736012\pi$
$311$	−1.08915e12	+	6.28821e11i	−0.374357	+	0.216135i	0.301003	+	0.953623i	$0.402678\pi$
$312$	−7.95327e11	−	8.13600e10i	−0.269013	−	0.0275193i
$313$	1.57235e12	−	2.72340e12i	0.523394	−	0.906545i	−0.476236	−	0.879318i	$-0.657999\pi$
$313$	1.57235e12	−	2.72340e12i	0.523394	−	0.906545i	0.999629	−	0.0272268i	$-0.00866764\pi$
$314$			8.19564e11i			0.268494i
$315$	5.04512e12	−	1.67029e12i	1.62674	−	0.538567i
$316$	7.60810e11			0.241457
$317$	−2.20168e12	−	1.27114e12i	−0.687793	−	0.397097i	0.114992	−	0.993366i	$-0.463316\pi$
$317$	−2.20168e12	−	1.27114e12i	−0.687793	−	0.397097i	−0.802785	+	0.596269i	$0.796649\pi$
$318$	4.02816e11	−	1.80687e11i	0.123871	−	0.0555638i
$319$	−1.87836e11	−	3.25341e11i	−0.0568623	−	0.0984885i
$320$	−4.14986e11	+	2.39592e11i	−0.123675	+	0.0714041i
$321$	3.85230e11	−	5.33332e11i	0.113030	−	0.156485i
$322$	−1.48840e12	+	2.57798e12i	−0.429971	+	0.744732i
$323$			6.89036e12i			1.95988i
$324$	−1.63886e12	−	7.07960e11i	−0.459003	−	0.198282i
$325$	8.46481e11			0.233453
$326$	−2.73853e11	−	1.58109e11i	−0.0743754	−	0.0429407i
$327$	−4.52063e12	−	3.26529e12i	−1.20909	−	0.873339i
$328$	2.85854e10	+	4.95114e10i	0.00752966	+	0.0130417i
$329$	−7.35706e12	+	4.24760e12i	−1.90864	+	1.10196i
$330$	−1.59279e12	−	3.55090e12i	−0.406996	−	0.907338i
$331$	2.79487e12	−	4.84086e12i	0.703432	−	1.21838i	−0.263822	−	0.964571i	$-0.584983\pi$
$331$	2.79487e12	−	4.84086e12i	0.703432	−	1.21838i	0.967254	−	0.253809i	$-0.0816834\pi$
$332$		−	3.34906e11i		−	0.0830295i
$333$	−1.68152e12	−	5.07905e12i	−0.410660	−	1.24040i
$334$	−3.38339e12			−0.813992
$335$	5.90797e12	+	3.41097e12i	1.40028	+	0.808451i
$336$	1.63419e11	−	1.59748e12i	0.0381597	−	0.373027i
$337$	3.41152e12	+	5.90892e12i	0.784871	+	1.35944i	0.929076	+	0.369888i	$0.120604\pi$
$337$	3.41152e12	+	5.90892e12i	0.784871	+	1.35944i	−0.144205	+	0.989548i	$0.546063\pi$
$338$	−1.12110e12	+	6.47270e11i	−0.254134	+	0.146724i
$339$	−1.54461e12	−	1.58010e11i	−0.345002	−	0.0352928i
$340$	1.34649e12	−	2.33219e12i	0.296353	−	0.513298i
$341$		−	3.67082e12i		−	0.796143i
$342$	−1.26530e12	+	6.11968e12i	−0.270434	+	1.30797i
$343$	−1.77796e12			−0.374499
$344$	7.35269e11	+	4.24508e11i	0.152635	+	0.0881239i
$345$	−4.13098e12	+	1.85299e12i	−0.845197	+	0.379122i
$346$	−1.38837e12	−	2.40473e12i	−0.279979	−	0.484939i
$347$	−2.60540e12	+	1.50423e12i	−0.517877	+	0.298996i	−0.736066	−	0.676910i	$-0.763319\pi$
$347$	−2.60540e12	+	1.50423e12i	−0.517877	+	0.298996i	0.218189	+	0.975907i	$0.429985\pi$
$348$	1.38046e11	−	1.91118e11i	0.0270476	−	0.0374460i
$349$	−1.64881e12	+	2.85583e12i	−0.318452	+	0.551575i	−0.980165	−	0.198182i	$-0.936496\pi$
$349$	−1.64881e12	+	2.85583e12i	−0.318452	+	0.551575i	0.661713	+	0.749757i	$0.269830\pi$
$350$			1.70023e12i			0.323719i
$351$	3.97863e12	−	8.80389e11i	0.746789	−	0.165249i
$352$	−1.17595e12			−0.217608
$353$	1.04416e12	+	6.02848e11i	0.190500	+	0.109985i	0.592217	−	0.805779i	$-0.298253\pi$
$353$	1.04416e12	+	6.02848e11i	0.190500	+	0.109985i	−0.401717	+	0.915764i	$0.631586\pi$
$354$	4.09418e12	+	2.95726e12i	0.736463	+	0.531954i
$355$	−4.86294e12	−	8.42286e12i	−0.862496	−	1.49389i
$356$	−5.91102e11	+	3.41273e11i	−0.103374	+	0.0596831i
$357$	3.69351e12	+	8.23416e12i	0.636940	+	1.41997i
$358$	3.23491e12	−	5.60303e12i	0.550107	−	0.952814i
$359$		−	6.75463e12i		−	1.13274i	−0.824152	−	0.566368i	$-0.808348\pi$
$359$		−	6.75463e12i		−	1.13274i	0.824152	−	0.566368i	$-0.191652\pi$
$360$	1.62416e12	−	1.82408e12i	0.268606	−	0.301669i
$361$	1.57437e13			2.56785
$362$	3.03037e12	+	1.74959e12i	0.487476	+	0.281444i
$363$	3.30524e11	−	3.23101e12i	0.0524408	−	0.512631i
$364$	1.83268e12	+	3.17429e12i	0.286800	+	0.496752i
$365$	7.51282e12	−	4.33753e12i	1.15968	−	0.669543i
$366$	4.04848e10	+	4.14150e9i	0.00616434	+	0.000630597i
$367$	−3.78530e12	+	6.55634e12i	−0.568552	+	0.984762i	0.428157	+	0.903704i	$0.359163\pi$
$367$	−3.78530e12	+	6.55634e12i	−0.568552	+	0.984762i	−0.996709	+	0.0810572i	$0.974170\pi$
$368$			1.36805e12i			0.202705i
$369$	−2.17628e11	−	1.93776e11i	−0.0318114	−	0.0283248i
$370$	7.31952e12			1.05554
$371$	−1.75290e12	−	1.01203e12i	−0.249394	−	0.143988i
$372$	2.10192e12	−	9.42839e11i	0.295055	−	0.132350i
$373$	7.23754e11	+	1.25358e12i	0.100241	+	0.173623i	0.911784	−	0.410670i	$-0.134705\pi$
$373$	7.23754e11	+	1.25358e12i	0.100241	+	0.173623i	−0.811543	+	0.584293i	$0.801372\pi$
$374$	5.72334e12	−	3.30437e12i	0.782153	−	0.451576i
$375$	3.44664e12	−	4.77171e12i	0.464772	−	0.643454i
$376$	−1.95208e12	+	3.38110e12i	−0.259752	+	0.449903i
$377$			5.38133e11i			0.0706615i
$378$	1.76834e12	+	7.99143e12i	0.229143	+	1.03554i
$379$	−1.17747e13			−1.50576			−0.752878	−	0.658160i	$-0.771335\pi$
$379$	−1.17747e13			−1.50576			−0.752878	+	0.658160i	$0.771335\pi$
$380$	−7.40397e12	−	4.27469e12i	−0.934430	−	0.539493i
$381$	−4.60614e12	−	3.32706e12i	−0.573737	−	0.414415i
$382$	2.24984e12	+	3.89684e12i	0.276589	+	0.479066i
$383$	4.63483e11	−	2.67592e11i	0.0562393	−	0.0324698i	−0.471617	−	0.881804i	$-0.656329\pi$
$383$	4.63483e11	−	2.67592e11i	0.0562393	−	0.0324698i	0.527856	+	0.849334i	$0.322996\pi$
$384$	−3.02039e11	−	6.73352e11i	−0.0361749	−	0.0806466i
$385$	−8.92129e12	+	1.54521e13i	−1.05469	+	1.82677i
$386$		−	3.31101e12i		−	0.386388i
$387$	−4.23773e12	−	8.76187e11i	−0.488178	−	0.100935i
$388$	2.84740e12			0.323810
$389$	3.75612e12	+	2.16860e12i	0.421688	+	0.243462i	0.695799	−	0.718236i	$-0.255050\pi$
$389$	3.75612e12	+	2.16860e12i	0.421688	+	0.243462i	−0.274111	+	0.961698i	$0.588384\pi$
$390$	−5.67327e11	+	5.54586e12i	−0.0628797	+	0.614675i
$391$	−3.84418e12	−	6.65831e12i	−0.420649	−	0.728585i
$392$	−3.54174e12	+	2.04482e12i	−0.382636	+	0.220915i
$393$	−1.54533e13	−	1.58083e12i	−1.64838	−	0.168625i
$394$	−1.52372e12	+	2.63916e12i	−0.160481	+	0.277962i
$395$		−	5.30517e12i		−	0.551713i
$396$	5.68999e12	−	1.88379e12i	0.584299	−	0.193445i
$397$	−1.37412e13			−1.39339			−0.696694	−	0.717369i	$-0.745346\pi$
$397$	−1.37412e13			−1.39339			−0.696694	+	0.717369i	$0.745346\pi$
$398$	−9.79376e12	−	5.65443e12i	−0.980695	−	0.566204i
$399$	2.61408e13	−	1.17257e13i	2.58497	−	1.15951i
$400$	3.90690e11	+	6.76694e11i	0.0381533	+	0.0660834i
$401$	9.49215e12	−	5.48030e12i	0.915467	−	0.528545i	0.0332811	−	0.999446i	$-0.489404\pi$
$401$	9.49215e12	−	5.48030e12i	0.915467	−	0.528545i	0.882186	+	0.470901i	$0.156071\pi$
$402$	−6.15191e12	+	8.51702e12i	−0.585976	+	0.811255i
$403$	−2.62915e12	+	4.55381e12i	−0.247337	+	0.428401i
$404$			1.07302e12i			0.0997015i
$405$	−4.93664e12	+	1.14278e13i	−0.453061	+	1.04879i
$406$	−1.08089e12			−0.0979829
$407$	1.55560e13	+	8.98128e12i	1.39292	+	0.804204i
$408$	3.36212e12	+	2.42849e12i	0.297380	+	0.214800i
$409$	−3.08338e12	−	5.34057e12i	−0.269408	−	0.466628i	0.699301	−	0.714827i	$-0.253495\pi$
$409$	−3.08338e12	−	5.34057e12i	−0.269408	−	0.466628i	−0.968709	+	0.248199i	$0.920161\pi$
$410$	3.45246e11	−	1.99328e11i	0.0297995	−	0.0172047i
$411$	2.21467e12	+	4.93728e12i	0.188842	+	0.420997i
$412$	3.52995e12	−	6.11405e12i	0.297360	−	0.515042i
$413$		−	2.31551e13i		−	1.92706i
$414$	−2.19153e12	−	6.61951e12i	−0.180196	−	0.544282i
$415$	−2.33532e12			−0.189717
$416$	1.45882e12	+	8.42248e11i	0.117094	+	0.0676042i
$417$	−2.37250e12	+	2.31921e13i	−0.188159	+	1.83933i
$418$	−1.04903e13	−	1.81698e13i	−0.822069	−	1.42387i
$419$	−8.91916e12	+	5.14948e12i	−0.690643	+	0.398743i	−0.803853	−	0.594828i	$-0.797220\pi$
$419$	−8.91916e12	+	5.14948e12i	−0.690643	+	0.398743i	0.113210	+	0.993571i	$0.463887\pi$
$420$	−1.11393e13	−	1.13953e12i	−0.852340	−	0.0871923i
$421$	2.00233e12	−	3.46813e12i	0.151400	−	0.262232i	−0.780343	−	0.625352i	$-0.784955\pi$
$421$	2.00233e12	−	3.46813e12i	0.151400	−	0.262232i	0.931742	+	0.363121i	$0.118289\pi$
$422$			1.24805e12i			0.0932547i
$423$	4.02911e12	−	1.94870e13i	0.297514	−	1.43894i
$424$	−9.30206e11			−0.0678813
$425$	−3.80297e12	−	2.19565e12i	−0.274270	−	0.158350i
$426$	1.36669e13	−	6.13041e12i	0.974138	−	0.436959i
$427$	−9.32894e10	−	1.61582e11i	−0.00657193	−	0.0113829i
$428$	−1.20050e12	+	6.93106e11i	−0.0835875	+	0.0482593i
$429$	−8.01067e12	+	1.10904e13i	−0.551293	+	0.763238i
$430$	2.96012e12	−	5.12707e12i	0.201357	−	0.348760i
$431$			6.89382e12i			0.463526i	0.972772	+	0.231763i	$0.0744493\pi$
$431$			6.89382e12i			0.463526i	−0.972772	+	0.231763i	$0.925551\pi$
$432$	2.54012e12	+	2.77426e12i	0.168825	+	0.184386i
$433$	1.86892e13			1.22787			0.613934	−	0.789357i	$-0.289586\pi$
$433$	1.86892e13			1.22787			0.613934	+	0.789357i	$0.289586\pi$
$434$	−9.14674e12	−	5.28087e12i	−0.594042	−	0.342971i
$435$	−1.33268e12	−	9.62604e11i	−0.0855616	−	0.0618018i
$436$	5.87491e12	+	1.01756e13i	0.372880	+	0.645847i
$437$	−2.11380e13	+	1.22041e13i	−1.32635	+	0.765768i
$438$	5.46805e12	+	1.21902e13i	0.339205	+	0.756208i
$439$	−7.43204e12	+	1.28727e13i	−0.455812	+	0.789489i	−0.998734	−	0.0502935i	$-0.983984\pi$
$439$	−7.43204e12	+	1.28727e13i	−0.455812	+	0.789489i	0.542923	+	0.839783i	$0.317318\pi$
$440$			8.19996e12i			0.497219i
$441$	1.38615e13	−	1.55678e13i	0.831031	−	0.933326i
$442$	−9.46675e12			−0.561164
$443$	−7.48917e12	−	4.32387e12i	−0.438950	−	0.253428i	0.264202	−	0.964467i	$-0.414891\pi$
$443$	−7.48917e12	−	4.32387e12i	−0.438950	−	0.253428i	−0.703152	+	0.711039i	$0.748225\pi$
$444$	−1.14719e12	+	1.12142e13i	−0.0664845	+	0.649913i
$445$	2.37971e12	+	4.12178e12i	0.136372	+	0.236203i
$446$	2.40478e12	−	1.38840e12i	0.136270	−	0.0786758i
$447$	1.79436e13	+	1.83559e12i	1.00548	+	0.102858i
$448$	−1.69173e12	+	2.93016e12i	−0.0937434	+	0.162368i
$449$			2.13962e13i			1.17248i	0.810137	+	0.586241i	$0.199393\pi$
$449$			2.13962e13i			1.17248i	−0.810137	+	0.586241i	$0.800607\pi$
$450$	−2.97442e12	−	2.64842e12i	−0.161191	−	0.143524i
$451$	9.78325e11			0.0524325
$452$	2.83319e12	+	1.63574e12i	0.150170	+	0.0867006i
$453$	1.00464e13	−	4.50642e12i	0.526647	−	0.236233i
$454$	−7.34424e12	−	1.27206e13i	−0.380774	−	0.659520i
$455$	2.21345e13	−	1.27794e13i	1.13504	−	0.655318i
$456$	7.70968e12	−	1.06737e13i	0.391032	−	0.541364i
$457$	8.70254e12	−	1.50732e13i	0.436581	−	0.756181i	−0.560842	−	0.827923i	$-0.689522\pi$
$457$	8.70254e12	−	1.50732e13i	0.436581	−	0.756181i	0.997423	+	0.0717418i	$0.0228558\pi$
$458$		−	1.42158e13i		−	0.705413i
$459$	−2.01583e13	−	6.36468e12i	−0.989444	−	0.312401i
$460$	9.53950e12			0.463166
$461$	9.48716e12	+	5.47741e12i	0.455650	+	0.263070i	0.710214	−	0.703986i	$-0.248598\pi$
$461$	9.48716e12	+	5.47741e12i	0.455650	+	0.263070i	−0.254563	+	0.967056i	$0.581932\pi$
$462$	−2.22760e13	−	1.60901e13i	−1.05834	−	0.764451i
$463$	4.36470e12	+	7.55989e12i	0.205140	+	0.355312i	0.950177	−	0.311710i	$-0.100902\pi$
$463$	4.36470e12	+	7.55989e12i	0.205140	+	0.355312i	−0.745038	+	0.667023i	$0.767568\pi$
$464$	−4.30195e11	+	2.48373e11i	−0.0200021	+	0.0115482i
$465$	−6.57447e12	−	1.46568e13i	−0.302410	−	0.674179i
$466$	−6.30503e12	+	1.09206e13i	−0.286918	+	0.496957i
$467$			3.61030e13i			1.62540i	0.582685	+	0.812698i	$0.302002\pi$
$467$			3.61030e13i			1.62540i	−0.582685	+	0.812698i	$0.697998\pi$
$468$	−8.40790e12	−	1.73841e12i	−0.374506	−	0.0774323i
$469$	4.81688e13			2.12276
$470$	2.35766e13	+	1.36120e13i	1.02800	+	0.593515i
$471$	−8.95691e11	+	8.75575e12i	−0.0386415	+	0.377737i
$472$	−5.32071e12	−	9.21575e12i	−0.227122	−	0.393387i
$473$	1.25822e13	−	7.26431e12i	0.531434	−	0.306824i
$474$	8.12806e12	+	8.31480e11i	0.339700	+	0.0347504i
$475$	−6.97049e12	+	1.20732e13i	−0.288267	+	0.499293i
$476$		−	1.90148e13i		−	0.778138i
$477$	4.50093e12	−	1.49013e12i	0.182268	−	0.0603436i
$478$	3.14199e13			1.25912
$479$	9.53550e12	+	5.50532e12i	0.378152	+	0.218326i	0.677014	−	0.735970i	$-0.263274\pi$
$479$	9.53550e12	+	5.50532e12i	0.378152	+	0.218326i	−0.298862	+	0.954296i	$0.596607\pi$
$480$	−4.69532e12	+	2.10613e12i	−0.184272	+	0.0826570i
$481$	−1.28653e13	−	2.22833e13i	−0.499683	−	0.865476i
$482$	−2.11297e13	+	1.21992e13i	−0.812191	+	0.468919i
$483$	−1.87186e13	+	2.59150e13i	−0.712096	+	0.985861i
$484$	−3.42162e12	+	5.92642e12i	−0.128827	+	0.223134i
$485$		−	1.98551e13i		−	0.739883i
$486$	−1.67349e13	−	9.35453e12i	−0.617222	−	0.345017i
$487$	−6.44905e11			−0.0235424			−0.0117712	−	0.999931i	$-0.503747\pi$
$487$	−6.44905e11			−0.0235424			−0.0117712	+	0.999931i	$0.503747\pi$
$488$	−7.42587e10	−	4.28733e10i	−0.00268317	−	0.00154913i
$489$	−2.75289e12	−	1.98844e12i	−0.0984567	−	0.0711161i
$490$	1.42587e13	+	2.46967e13i	0.504775	+	0.874296i
$491$	−4.31673e12	+	2.49227e12i	−0.151268	+	0.0873348i	−0.573724	−	0.819049i	$-0.694502\pi$
$491$	−4.31673e12	+	2.49227e12i	−0.151268	+	0.0873348i	0.422455	+	0.906384i	$0.361168\pi$
$492$	2.51280e11	+	5.60192e11i	0.00871630	+	0.0194317i
$493$	1.39584e12	−	2.41766e12i	0.0479292	−	0.0830159i
$494$			3.00539e13i			1.02157i
$495$	−1.31358e13	−	3.96766e13i	−0.442007	−	1.33508i
$496$	−4.85389e12			−0.161689
$497$	−5.94727e13	−	3.43366e13i	−1.96126	−	1.13234i
$498$	3.66015e11	−	3.57795e12i	0.0119496	−	0.116812i
$499$	−2.13155e13	−	3.69195e13i	−0.688958	−	1.19331i	−0.972175	−	0.234255i	$-0.924735\pi$
$499$	−2.13155e13	−	3.69195e13i	−0.688958	−	1.19331i	0.283217	−	0.959056i	$-0.408598\pi$
$500$	−1.07408e13	+	6.20121e12i	−0.343706	+	0.198439i
$501$	−3.61463e13	−	3.69767e12i	−1.14518	−	0.117149i
$502$	−1.19176e13	+	2.06419e13i	−0.373826	+	0.647486i
$503$			4.31024e13i			1.33863i	0.742978	+	0.669316i	$0.233413\pi$
$503$			4.31024e13i			1.33863i	−0.742978	+	0.669316i	$0.766587\pi$
$504$	3.49174e12	−	1.68880e13i	0.107372	−	0.519309i
$505$	7.48224e12			0.227811
$506$	2.02741e13	+	1.17053e13i	0.611209	+	0.352882i
$507$	−1.26846e13	+	5.68982e12i	−0.378650	+	0.169847i
$508$	5.98604e12	+	1.03681e13i	0.176938	+	0.306466i
$509$	−3.11764e13	+	1.79997e13i	−0.912509	+	0.526838i	−0.881238	−	0.472673i	$-0.843289\pi$
$509$	−3.11764e13	+	1.79997e13i	−0.912509	+	0.526838i	−0.0312717	+	0.999511i	$0.509956\pi$
$510$	1.69340e13	−	2.34442e13i	0.490804	−	0.679493i
$511$	3.06267e13	−	5.30470e13i	0.879014	−	1.52250i
$512$			1.55494e12i			0.0441942i
$513$	−2.02058e13	+	6.39964e13i	−0.568709	+	1.80123i
$514$	−2.42228e12			−0.0675164
$515$	−4.26336e13	−	2.46145e13i	−1.17684	−	0.679446i
$516$	7.39126e12	+	5.33877e12i	0.202055	+	0.145946i
$517$	3.34046e13	+	5.78585e13i	0.904386	+	1.56644i
$518$	4.47580e13	−	2.58411e13i	1.20011	−	0.692886i
$519$	−1.22045e13	−	2.72082e13i	−0.324103	−	0.722541i
$520$	5.87304e12	−	1.01724e13i	0.154471	−	0.267551i
$521$		−	4.87564e13i		−	1.27011i	−0.772465	−	0.635057i	$-0.780977\pi$
$521$		−	4.87564e13i		−	1.27011i	0.772465	−	0.635057i	$-0.219023\pi$
$522$	1.68368e12	−	1.89093e12i	0.0434417	−	0.0487891i
$523$	−2.95427e13			−0.754992			−0.377496	−	0.926011i	$-0.623215\pi$
$523$	−2.95427e13			−0.754992			−0.377496	+	0.926011i	$0.623215\pi$
$524$	2.83449e13	+	1.63650e13i	0.717496	+	0.414246i
$525$	−1.85816e12	+	1.81643e13i	−0.0465894	+	0.455430i
$526$	−6.86463e12	−	1.18899e13i	−0.170486	−	0.295290i
$527$	2.36239e13	−	1.36392e13i	0.581163	−	0.335534i
$528$	−1.25632e13	−	1.28518e12i	−0.306147	−	0.0313180i
$529$	−7.09580e12	+	1.22903e13i	−0.171287	+	0.296677i
$530$			6.48638e12i			0.155104i
$531$	4.05080e13	+	3.60682e13i	0.959551	+	0.854382i
$532$	−6.03660e13			−1.41656
$533$	−1.21366e12	−	7.00704e11i	−0.0282136	−	0.0162892i
$534$	−6.68797e12	+	2.99996e12i	−0.154024	+	0.0690890i
$535$	4.83307e12	+	8.37112e12i	0.110269	+	0.190992i
$536$	1.91713e13	−	1.10685e13i	0.433338	−	0.250188i
$537$	4.06835e13	−	5.63242e13i	0.911059	−	1.26132i
$538$	−2.09907e13	+	3.63569e13i	−0.465709	+	0.806632i
$539$			6.99833e13i			1.53833i
$540$	1.93451e13	−	1.77124e13i	0.421310	−	0.385752i
$541$	−2.34984e13			−0.507051			−0.253526	−	0.967329i	$-0.581590\pi$
$541$	−2.34984e13			−0.507051			−0.253526	+	0.967329i	$0.581590\pi$
$542$	−1.08944e13	−	6.28988e12i	−0.232920	−	0.134476i
$543$	3.04627e13	+	2.20034e13i	0.645311	+	0.466113i
$544$	−4.36934e12	−	7.56791e12i	−0.0917109	−	0.158848i
$545$	7.09553e13	−	4.09661e13i	1.47572	−	0.852005i
$546$	1.61101e13	+	3.59152e13i	0.331998	+	0.740143i
$547$	1.18795e13	−	2.05759e13i	0.242583	−	0.420167i	−0.718866	−	0.695149i	$-0.755338\pi$
$547$	1.18795e13	−	2.05759e13i	0.242583	−	0.420167i	0.961449	+	0.274982i	$0.0886718\pi$
$548$		−	1.14015e13i		−	0.230705i
$549$	4.27991e11	+	8.84907e10i	0.00858168	+	0.00177434i
$550$	1.33712e13			0.265679
$551$	−7.67532e12	−	4.43135e12i	−0.151126	−	0.0872525i
$552$	−1.49513e12	+	1.46155e13i	−0.0291731	+	0.285179i
$553$	−1.87295e13	−	3.24405e13i	−0.362161	−	0.627281i
$554$	−4.61422e13	+	2.66402e13i	−0.884199	+	0.510492i
$555$	7.81975e13	+	7.99941e12i	1.48501	+	0.151912i
$556$	2.45604e13	−	4.25398e13i	0.462233	−	0.800611i
$557$		−	4.71567e13i		−	0.879564i	−0.898105	−	0.439782i	$-0.855056\pi$
$557$		−	4.71567e13i		−	0.879564i	0.898105	−	0.439782i	$-0.144944\pi$
$558$	2.34862e13	−	7.77559e12i	0.434152	−	0.143735i
$559$	−2.08116e13			−0.381283
$560$	2.04322e13	+	1.17965e13i	0.371000	+	0.214197i
$561$	6.47563e13	−	2.90471e13i	1.16538	−	0.522743i
$562$	1.63897e13	+	2.83878e13i	0.292341	+	0.506349i
$563$	−6.61521e13	+	3.81929e13i	−1.16950	+	0.675213i	−0.953563	−	0.301193i	$-0.902615\pi$
$563$	−6.61521e13	+	3.81929e13i	−1.16950	+	0.675213i	−0.215941	+	0.976406i	$0.569282\pi$
$564$	−2.45501e13	+	3.39884e13i	−0.430187	+	0.595573i
$565$	1.14061e13	−	1.97560e13i	0.198105	−	0.343128i
$566$		−	6.60181e13i		−	1.13653i
$567$	1.01582e13	+	8.73084e13i	0.173341	+	1.48984i
$568$	−3.15603e13			−0.533825
$569$	1.58477e13	+	9.14965e12i	0.265707	+	0.153406i	0.626935	−	0.779071i	$-0.284309\pi$
$569$	1.58477e13	+	9.14965e12i	0.265707	+	0.153406i	−0.361228	+	0.932478i	$0.617642\pi$
$570$	−7.44281e13	−	5.37600e13i	−1.23698	−	0.893480i
$571$	4.54963e13	+	7.88019e13i	0.749542	+	1.29824i	0.948043	+	0.318144i	$0.103059\pi$
$571$	4.54963e13	+	7.88019e13i	0.749542	+	1.29824i	−0.198501	+	0.980101i	$0.563607\pi$
$572$	2.49637e13	−	1.44128e13i	0.407689	−	0.235379i
$573$	1.97772e13	+	4.40904e13i	0.320178	+	0.713791i
$574$	1.40743e12	−	2.43773e12i	0.0225874	−	0.0391225i
$575$		−	1.55555e13i		−	0.247483i
$576$	−2.49091e12	−	7.52381e12i	−0.0392868	−	0.118666i
$577$	1.70116e13			0.265990			0.132995	−	0.991117i	$-0.457541\pi$
$577$	1.70116e13			0.265990			0.132995	+	0.991117i	$0.457541\pi$
$578$	3.02587e12	+	1.74699e12i	0.0469042	+	0.0270801i
$579$	3.61856e12	−	3.53729e13i	0.0556088	−	0.543599i
$580$	1.73192e12	+	2.99977e12i	0.0263868	+	0.0457034i
$581$	−1.42802e13	+	8.24468e12i	−0.215702	+	0.124536i
$582$	3.04200e13	+	3.11189e12i	0.455559	+	0.0466025i
$583$	−7.95899e12	+	1.37854e13i	−0.118172	+	0.204680i
$584$		−	2.81504e13i		−	0.414401i
$585$	−1.21220e13	+	5.86288e13i	−0.176927	+	0.855719i
$586$	−3.49264e13			−0.505436
$587$	2.14336e13	+	1.23747e13i	0.307543	+	0.177560i	0.645826	−	0.763484i	$-0.276513\pi$
$587$	2.14336e13	+	1.23747e13i	0.307543	+	0.177560i	−0.338284	+	0.941044i	$0.609846\pi$
$588$	−4.00726e13	+	1.79750e13i	−0.570114	+	0.255730i
$589$	−4.33003e13	−	7.49983e13i	−0.610822	−	1.05797i
$590$	−6.42619e13	+	3.71016e13i	−0.898863	+	0.518959i
$591$	−1.91629e13	+	2.65300e13i	−0.265780	+	0.367960i
$592$	1.18758e13	−	2.05696e13i	0.163326	−	0.282889i
$593$		−	4.59854e13i		−	0.627114i	−0.949569	−	0.313557i	$-0.898479\pi$
$593$		−	4.59854e13i		−	0.627114i	0.949569	−	0.313557i	$-0.101521\pi$
$594$	6.28474e13	−	1.39068e13i	0.849874	−	0.188060i
$595$	−1.32591e14			−1.77799
$596$	−3.29128e13	−	1.90022e13i	−0.437657	−	0.252681i
$597$	−9.84513e13	−	7.11122e13i	−1.29822	−	0.937718i
$598$	−1.67673e13	−	2.90418e13i	−0.219259	−	0.379767i
$599$	6.72024e13	−	3.87993e13i	0.871467	−	0.503142i	0.00363140	−	0.999993i	$-0.498844\pi$
$599$	6.72024e13	−	3.87993e13i	0.871467	−	0.503142i	0.867835	+	0.496852i	$0.165511\pi$
$600$	3.43435e12	+	7.65640e12i	0.0441661	+	0.0984619i
$601$	−1.96449e13	+	3.40260e13i	−0.250540	+	0.433949i	−0.963675	−	0.267079i	$-0.913942\pi$
$601$	−1.96449e13	+	3.40260e13i	−0.250540	+	0.433949i	0.713134	+	0.701027i	$0.247275\pi$
$602$		−	4.18020e13i		−	0.528706i
$603$	−7.50317e13	+	8.42676e13i	−0.941148	+	1.05700i
$604$	−2.31998e13			−0.288602
$605$	4.13253e13	+	2.38592e13i	0.509846	+	0.294360i
$606$	−1.17269e12	+	1.14636e13i	−0.0143490	+	0.140267i
$607$	5.62568e12	+	9.74396e12i	0.0682702	+	0.118247i	0.898140	−	0.439710i	$-0.144919\pi$
$607$	5.62568e12	+	9.74396e12i	0.0682702	+	0.118247i	−0.829870	+	0.557957i	$0.811585\pi$
$608$	−2.40257e13	+	1.38713e13i	−0.289174	+	0.166955i
$609$	−1.15476e13	−	1.18129e12i	−0.137849	−	0.0141016i
$610$	−2.98958e11	+	5.17810e11i	−0.00353965	+	0.00613085i
$611$		−	9.57014e13i		−	1.12386i
$612$	3.32649e13	+	2.96190e13i	0.387462	+	0.344995i
$613$	−5.33090e12			−0.0615883			−0.0307942	−	0.999526i	$-0.509804\pi$
$613$	−5.33090e12			−0.0615883			−0.0307942	+	0.999526i	$0.509804\pi$
$614$	4.43128e13	+	2.55840e13i	0.507794	+	0.293175i
$615$	3.90625e12	−	1.75219e12i	0.0444001	−	0.0199161i
$616$	2.89494e13	+	5.01418e13i	0.326389	+	0.565323i
$617$	−3.92663e12	+	2.26704e12i	−0.0439131	+	0.0253532i	−0.521796	−	0.853070i	$-0.674738\pi$
$617$	−3.92663e12	+	2.26704e12i	−0.0439131	+	0.0253532i	0.477883	+	0.878424i	$0.341404\pi$
$618$	4.43939e13	−	6.14612e13i	0.492472	−	0.681802i
$619$	−5.70162e13	+	9.87549e13i	−0.627400	+	1.08669i	0.360671	+	0.932693i	$0.382548\pi$
$619$	−5.70162e13	+	9.87549e13i	−0.627400	+	1.08669i	−0.988071	+	0.153996i	$0.950786\pi$
$620$			3.38464e13i			0.369449i
$621$	−1.61786e13	−	7.31141e13i	−0.175180	−	0.791668i
$622$	2.84572e13			0.305661
$623$	2.91034e13	+	1.68028e13i	0.310101	+	0.179037i
$624$	1.46647e13	+	1.05924e13i	0.155006	+	0.111962i
$625$	5.77957e13	+	1.00105e14i	0.606032	+	1.04968i
$626$	−6.16234e13	+	3.55783e13i	−0.641024	+	0.370095i
$627$	−9.22153e13	−	2.05581e14i	−0.951624	−	2.12151i
$628$	9.27231e12	−	1.60601e13i	0.0949270	−	0.164418i
$629$			1.33483e14i			1.35573i
$630$	−1.17761e14	−	2.43481e13i	−1.18658	−	0.245337i
$631$	1.41815e14			1.41767			0.708837	−	0.705372i	$-0.249220\pi$
$631$	1.41815e14			1.41767			0.708837	+	0.705372i	$0.249220\pi$
$632$	−1.49088e13	−	8.60758e12i	−0.147862	−	0.0853681i
$633$	−1.36398e12	+	1.33335e13i	−0.0134212	+	0.131197i
$634$	2.87626e13	+	4.98183e13i	0.280790	+	0.486343i
$635$	7.22975e13	−	4.17410e13i	0.700253	−	0.404291i
$636$	−9.93779e12	−	1.01661e12i	−0.0955002	−	0.00976943i
$637$	5.01240e13	−	8.68173e13i	0.477913	−	0.827769i
$638$			8.50047e12i			0.0804155i
$639$	1.52709e14	−	5.05574e13i	1.43337	−	0.474548i
$640$	1.08427e13			0.100981
$641$	−7.60797e13	−	4.39246e13i	−0.703037	−	0.405899i	0.105440	−	0.994426i	$-0.466375\pi$
$641$	−7.60797e13	−	4.39246e13i	−0.703037	−	0.405899i	−0.808478	+	0.588527i	$0.799708\pi$
$642$	−1.35829e13	+	6.09274e12i	−0.124542	+	0.0558647i
$643$	4.53021e13	+	7.84656e13i	0.412158	+	0.713878i	0.995125	−	0.0986170i	$-0.0314419\pi$
$643$	4.53021e13	+	7.84656e13i	0.412158	+	0.713878i	−0.582968	+	0.812495i	$0.698109\pi$
$644$	5.83330e13	−	3.36786e13i	0.526605	−	0.304036i
$645$	3.72275e13	−	5.15396e13i	0.333477	−	0.461682i
$646$	7.79555e13	−	1.35023e14i	0.692922	−	1.20018i
$647$			9.79400e12i			0.0863851i	0.999067	+	0.0431925i	$0.0137529\pi$
$647$			9.79400e12i			0.0863851i	−0.999067	+	0.0431925i	$0.986247\pi$
$648$	2.41052e13	+	3.24147e13i	0.210978	+	0.283705i
$649$	−1.82099e14			−1.58156
$650$	−1.65876e13	−	9.57684e12i	−0.142960	−	0.0825383i
$651$	−9.19471e13	−	6.64142e13i	−0.786381	−	0.568010i
$652$	3.57760e12	+	6.19659e12i	0.0303636	+	0.0525914i
$653$	−2.99159e13	+	1.72720e13i	−0.251963	+	0.145471i	−0.620663	−	0.784078i	$-0.713136\pi$
$653$	−2.99159e13	+	1.72720e13i	−0.251963	+	0.145471i	0.368700	+	0.929548i	$0.379803\pi$
$654$	5.16434e13	+	1.15131e14i	0.431644	+	0.962288i
$655$	1.14114e14	−	1.97651e14i	0.946524	−	1.63943i
$656$		−	1.29363e12i		−	0.0106485i
$657$	4.50950e13	+	1.36209e14i	0.368385	+	1.11271i
$658$	1.92225e14			1.55840
$659$	−3.63603e13	−	2.09926e13i	−0.292550	−	0.168904i	0.346541	−	0.938035i	$-0.387356\pi$
$659$	−3.63603e13	−	2.09926e13i	−0.292550	−	0.168904i	−0.639091	+	0.769131i	$0.720689\pi$
$660$	−8.96163e12	+	8.76036e13i	−0.0715595	+	0.699524i
$661$	4.07961e13	+	7.06609e13i	0.323304	+	0.559979i	0.981168	−	0.193158i	$-0.0618729\pi$
$661$	4.07961e13	+	7.06609e13i	0.323304	+	0.559979i	−0.657863	+	0.753137i	$0.728540\pi$
$662$	−1.09536e14	+	6.32408e13i	−0.861525	+	0.497402i
$663$	−1.01137e14	−	1.03461e13i	−0.789485	−	0.0807623i
$664$	−3.78903e12	+	6.56279e12i	−0.0293554	+	0.0508450i
$665$			4.20935e14i			3.23673i
$666$	−2.45118e13	+	1.18553e14i	−0.187070	+	0.904776i
$667$	9.88912e12			0.0749080
$668$	6.63007e13	+	3.82787e13i	0.498466	+	0.287790i
$669$	2.72087e13	−	1.22047e13i	0.203038	−	0.0910748i
$670$	−7.71814e13	−	1.33682e14i	−0.571661	−	0.990147i
$671$	−1.27074e12	+	7.33661e11i	−0.00934207	+	0.00539365i
$672$	−2.12758e13	+	2.94553e13i	−0.155253	+	0.214940i
$673$	4.90463e13	−	8.49506e13i	0.355247	−	0.615306i	−0.631913	−	0.775039i	$-0.717730\pi$
$673$	4.90463e13	−	8.49506e13i	0.355247	−	0.615306i	0.987160	+	0.159733i	$0.0510634\pi$
$674$		−	1.54388e14i		−	1.10997i
$675$	−2.88826e13	−	3.15449e13i	−0.206119	−	0.225118i
$676$	2.92921e13			0.207499
$677$	1.66206e14	+	9.59590e13i	1.16870	+	0.674750i	0.953374	−	0.301793i	$-0.0975850\pi$
$677$	1.66206e14	+	9.59590e13i	1.16870	+	0.674750i	0.215327	+	0.976542i	$0.430918\pi$
$678$	2.84805e13	+	2.05717e13i	0.198792	+	0.143589i
$679$	−7.00970e13	−	1.21412e14i	−0.485681	−	0.841223i
$680$	−5.27715e13	+	3.04676e13i	−0.362956	+	0.209553i
$681$	−6.45595e13	−	1.43926e14i	−0.440783	−	0.982661i
$682$	−4.15306e13	+	7.19331e13i	−0.281479	+	0.487536i
$683$		−	6.12781e13i		−	0.412289i	−0.978522	−	0.206145i	$-0.933908\pi$
$683$		−	6.12781e13i		−	0.412289i	0.978522	−	0.206145i	$-0.0660917\pi$
$684$	9.40310e13	−	1.05606e14i	0.628044	−	0.705353i
$685$	−7.95030e13			−0.527146
$686$	3.48407e13	+	2.01153e13i	0.229333	+	0.132405i
$687$	1.55363e13	−	1.51873e14i	0.101523	−	0.992426i
$688$	−9.60552e12	−	1.66372e13i	−0.0623130	−	0.107929i
$689$	1.97470e13	−	1.14009e13i	0.127176	−	0.0734249i
$690$	1.01915e14	+	1.04256e13i	0.651615	+	0.0666586i
$691$	−1.26361e14	+	2.18864e14i	−0.802089	+	1.38926i	0.116149	+	0.993232i	$0.462945\pi$
$691$	−1.26361e14	+	2.18864e14i	−0.802089	+	1.38926i	−0.918239	+	0.396028i	$0.870388\pi$
$692$			6.28307e13i			0.395951i
$693$	−2.20399e14	−	1.96243e14i	−1.37894	−	1.22780i
$694$	6.80736e13			0.422845
$695$	−2.96632e14	−	1.71261e14i	−1.82934	−	1.05617i
$696$	−4.86740e12	+	2.18332e12i	−0.0298024	+	0.0133682i
$697$	3.63505e12	+	6.29609e12i	0.0220977	+	0.0382743i
$698$	6.46200e13	−	3.73084e13i	0.390022	−	0.225180i
$699$	−7.92944e13	+	1.09779e14i	−0.475178	+	0.657861i
$700$	1.92359e13	−	3.33176e13i	0.114452	−	0.198236i
$701$			1.32926e14i			0.785271i	0.919694	+	0.392636i	$0.128437\pi$
$701$			1.32926e14i			0.785271i	−0.919694	+	0.392636i	$0.871563\pi$
$702$	−8.79254e13	−	2.77610e13i	−0.515737	−	0.162836i
$703$	4.23766e14			2.46802
$704$	2.30438e13	+	1.33043e13i	0.133257	+	0.0769361i
$705$	2.37003e14	+	1.71189e14i	1.36084	+	0.982948i
$706$	−1.36409e13	−	2.36267e13i	−0.0777712	−	0.134704i
$707$	4.57531e13	−	2.64155e13i	0.259014	−	0.149542i
$708$	−4.67717e13	−	1.04271e14i	−0.262916	−	0.586133i
$709$	−1.07480e13	+	1.86161e13i	−0.0599924	+	0.103910i	−0.894462	−	0.447144i	$-0.852441\pi$
$709$	−1.07480e13	+	1.86161e13i	−0.0599924	+	0.103910i	0.834469	+	0.551054i	$0.185774\pi$
$710$			2.20072e14i			1.21975i
$711$	8.59268e13	+	1.77661e13i	0.472912	+	0.0977787i
$712$	1.54442e13			0.0844047
$713$	8.36841e13	+	4.83151e13i	0.454146	+	0.262201i
$714$	2.07810e13	−	2.03143e14i	0.111989	−	1.09474i
$715$	−1.00501e14	−	1.74073e14i	−0.537826	−	0.931541i
$716$	−1.26782e14	+	7.31977e13i	−0.673741	+	0.388985i
$717$	3.35673e14	+	3.43385e13i	1.77141	+	0.181211i
$718$	−7.64199e13	+	1.32363e14i	−0.400483	+	0.693657i
$719$		−	2.35028e14i		−	1.22314i	−0.791191	−	0.611569i	$-0.790539\pi$
$719$		−	2.35028e14i		−	1.22314i	0.791191	−	0.611569i	$-0.209461\pi$
$720$	−5.24639e13	+	1.73693e13i	−0.271143	+	0.0897675i
$721$	−3.47600e14			−1.78403
$722$	−3.08511e14	−	1.78119e14i	−1.57248	−	0.907872i
$723$	−2.39070e14	+	1.07237e14i	−1.21014	+	0.542819i
$724$	−3.95886e13	−	6.85695e13i	−0.199011	−	0.344697i
$725$	4.89156e12	−	2.82414e12i	0.0244206	−	0.0140993i
$726$	−4.30316e13	+	5.95751e13i	−0.213356	+	0.295380i
$727$	−9.26722e13	+	1.60513e14i	−0.456328	+	0.790384i	−0.998764	−	0.0497138i	$-0.984169\pi$
$727$	−9.26722e13	+	1.60513e14i	−0.456328	+	0.790384i	0.542435	+	0.840098i	$0.317502\pi$
$728$		−	8.29375e13i		−	0.405596i
$729$	−1.68563e14	−	1.18228e14i	−0.818698	−	0.574225i
$730$	−1.96294e14			−0.946876
$731$	9.35001e13	+	5.39823e13i	0.447945	+	0.258621i
$732$	−7.46482e11	−	5.39190e11i	−0.00355192	−	0.00256558i
$733$	3.96953e13	+	6.87543e13i	0.187594	+	0.324922i	0.944448	−	0.328662i	$-0.106598\pi$
$733$	3.96953e13	+	6.87543e13i	0.187594	+	0.324922i	−0.756854	+	0.653585i	$0.773264\pi$
$734$	1.48353e14	−	8.56517e13i	0.696332	−	0.402027i
$735$	1.25341e14	+	2.79429e14i	0.584326	+	1.30267i
$736$	1.54777e13	−	2.68082e13i	0.0716669	−	0.124131i
$737$		−	3.78816e14i		−	1.74217i
$738$	2.07230e12	+	6.25939e12i	0.00946611	+	0.0285924i
$739$	−1.27528e13			−0.0578607			−0.0289303	−	0.999581i	$-0.509210\pi$
$739$	−1.27528e13			−0.0578607			−0.0289303	+	0.999581i	$0.509210\pi$
$740$	−1.43433e14	−	8.28109e13i	−0.646382	−	0.373189i
$741$	−3.28456e13	+	3.21079e14i	−0.147023	+	1.43721i
$742$	2.28997e13	+	3.96635e13i	0.101815	+	0.176348i
$743$	3.68802e13	−	2.12928e13i	0.162873	−	0.0940349i	−0.416348	−	0.909205i	$-0.636690\pi$
$743$	3.68802e13	−	2.12928e13i	0.162873	−	0.0940349i	0.579221	+	0.815171i	$0.303357\pi$
$744$	−5.18561e13	−	5.30475e12i	−0.227476	−	0.0232702i
$745$	−1.32504e14	+	2.29503e14i	−0.577359	+	1.00002i
$746$		−	3.27534e13i		−	0.141763i
$747$	7.82059e12	−	3.78247e13i	0.0336230	−	0.162620i
$748$	−1.49539e14			−0.638625
$749$	5.91073e13	+	3.41256e13i	0.250745	+	0.144768i
$750$	−1.21526e14	+	5.45117e13i	−0.512109	+	0.229712i
$751$	1.66568e13	+	2.88504e13i	0.0697255	+	0.120768i	0.898780	−	0.438399i	$-0.144454\pi$
$751$	1.66568e13	+	2.88504e13i	0.0697255	+	0.120768i	−0.829055	+	0.559167i	$0.811121\pi$
$752$	7.65057e13	−	4.41706e13i	0.318130	−	0.183672i
$753$	−1.49880e14	+	2.07501e14i	−0.619111	+	0.857129i
$754$	6.08828e12	−	1.05452e13i	0.0249826	−	0.0432712i
$755$			1.61773e14i			0.659435i
$756$	5.57605e13	−	1.76606e14i	0.225797	−	0.715148i
$757$	2.84299e14			1.14366			0.571829	−	0.820373i	$-0.306234\pi$
$757$	2.84299e14			1.14366			0.571829	+	0.820373i	$0.306234\pi$
$758$	2.30737e14	+	1.33216e14i	0.922084	+	0.532365i
$759$	2.03805e14	+	1.47210e14i	0.809106	+	0.584424i
$760$	9.67251e13	+	1.67533e14i	0.381479	+	0.660742i
$761$	−4.08731e13	+	2.35981e13i	−0.160145	+	0.0924600i	−0.577931	−	0.816086i	$-0.696140\pi$
$761$	−4.08731e13	+	2.35981e13i	−0.160145	+	0.0924600i	0.417786	+	0.908546i	$0.362806\pi$
$762$	5.26203e13	+	1.17309e14i	0.204823	+	0.456623i
$763$	2.89256e14	−	5.01006e14i	1.11856	−	1.93740i
$764$		−	1.01816e14i		−	0.391156i
$765$	2.06535e14	−	2.31958e14i	0.788290	−	0.885324i
$766$	−1.21098e13			−0.0459192
$767$	2.25902e14	+	1.30425e14i	0.851028	+	0.491341i
$768$	−1.69938e12	+	1.66121e13i	−0.00636040	+	0.0621755i
$769$	−8.80614e13	−	1.52527e14i	−0.327457	−	0.567172i	0.654550	−	0.756019i	$-0.272858\pi$
$769$	−8.80614e13	−	1.52527e14i	−0.327457	−	0.567172i	−0.982006	+	0.188847i	$0.939525\pi$
$770$	3.49642e14	−	2.01866e14i	1.29172	−	0.745777i
$771$	−2.58783e13	−	2.64728e12i	−0.0949869	−	0.00971692i
$772$	−3.74598e13	+	6.48823e13i	−0.136609	+	0.236614i
$773$		−	4.29604e14i		−	1.55658i	−0.627906	−	0.778289i	$-0.716088\pi$
$773$		−	4.29604e14i		−	1.55658i	0.627906	−	0.778289i	$-0.283912\pi$
$774$	7.31293e13	+	6.51141e13i	0.263261	+	0.234407i
$775$	5.51914e13			0.197407
$776$	−5.57974e13	−	3.22147e13i	−0.198292	−	0.114484i
$777$	5.06411e14	−	2.27156e14i	1.78812	−	0.802081i
$778$	−4.90698e13	−	8.49913e13i	−0.172154	−	0.298179i
$779$	1.99881e13	−	1.15401e13i	0.0696761	−	0.0402275i
$780$	7.38615e13	−	1.02258e14i	0.255826	−	0.354179i
$781$	−2.70035e14	+	4.67714e14i	−0.929318	+	1.60963i
$782$			1.73968e14i			0.594887i
$783$	2.00540e13	−	1.83615e13i	0.0681386	−	0.0623879i
$784$	9.25381e13			0.312421
$785$	−1.11988e14	−	6.46563e13i	−0.375684	−	0.216901i
$786$	2.84936e14	+	2.05812e14i	0.949806	+	0.686053i
$787$	4.99579e13	+	8.65296e13i	0.165474	+	0.286610i	0.936824	−	0.349802i	$-0.113751\pi$
$787$	4.99579e13	+	8.65296e13i	0.165474	+	0.286610i	−0.771349	+	0.636412i	$0.780418\pi$
$788$	5.97174e13	−	3.44779e13i	0.196549	−	0.113477i
$789$	−6.03435e13	−	1.34527e14i	−0.197354	−	0.439971i
$790$	−6.00211e13	+	1.03960e14i	−0.195060	+	0.337854i
$791$		−	1.61074e14i		−	0.520167i
$792$	−1.32813e14	−	2.74603e13i	−0.426202	−	0.0881209i
$793$	2.10187e12			0.00670256
$794$	2.69271e14	+	1.55464e14i	0.853272	+	0.492637i
$795$	−7.08888e12	+	6.92968e13i	−0.0223225	+	0.218211i
$796$	1.27945e14	+	2.21607e14i	0.400367	+	0.693456i
$797$	−1.57786e14	+	9.10975e13i	−0.490654	+	0.283279i	−0.724846	−	0.688911i	$-0.758089\pi$
$797$	−1.57786e14	+	9.10975e13i	−0.490654	+	0.283279i	0.234192	+	0.972190i	$0.424756\pi$
$798$	−6.44916e14	−	6.59732e13i	−1.99291	−	0.203870i
$799$	−2.48235e14	+	4.29956e14i	−0.762307	+	1.32035i
$800$		−	1.76806e13i		−	0.0539569i
$801$	−7.47291e13	+	2.47406e13i	−0.226635	+	0.0750323i
$802$	−2.48010e14			−0.747476
$803$	−4.17180e14	−	2.40859e14i	−1.24953	−	0.721416i
$804$	2.16911e14	−	9.72978e13i	0.645658	−	0.289616i
$805$	−2.34843e14	−	4.06759e14i	−0.694700	−	1.20326i
$806$	1.03041e14	−	5.94908e13i	0.302925	−	0.174894i
$807$	−2.63986e14	+	3.65476e14i	−0.771283	+	1.06780i
$808$	1.21399e13	−	2.10268e13i	0.0352498	−	0.0610545i
$809$			5.53322e14i			1.59674i	0.602164	+	0.798372i	$0.294305\pi$
$809$			5.53322e14i			1.59674i	−0.602164	+	0.798372i	$0.705695\pi$
$810$	2.26029e14	−	1.68087e14i	0.648246	−	0.482069i
$811$	3.72399e14			1.06146			0.530731	−	0.847540i	$-0.321917\pi$
$811$	3.72399e14			1.06146			0.530731	+	0.847540i	$0.321917\pi$
$812$	2.11810e13	+	1.22288e13i	0.0600020	+	0.0346422i
$813$	−1.09515e14	−	7.91039e13i	−0.308335	−	0.222713i
$814$	−2.03223e14	−	3.51993e14i	−0.568658	−	0.984944i
$815$	4.32091e13	−	2.49468e13i	0.120168	−	0.0693788i
$816$	−3.84086e13	−	8.56265e13i	−0.106164	−	0.236678i
$817$	1.71377e14	−	2.96833e14i	0.470806	−	0.815459i
$818$			1.39538e14i			0.381000i
$819$	1.32860e14	+	4.01304e14i	0.360558	+	1.08907i
$820$	−9.02054e12			−0.0243312
$821$	−1.68216e14	−	9.71198e13i	−0.450975	−	0.260370i	0.257267	−	0.966340i	$-0.417178\pi$
$821$	−1.68216e14	−	9.71198e13i	−0.450975	−	0.260370i	−0.708242	+	0.705970i	$0.750511\pi$
$822$	1.24605e13	−	1.21807e14i	0.0332030	−	0.324573i
$823$	−2.13293e14	−	3.69434e14i	−0.564907	−	0.978448i	−0.997058	−	0.0766469i	$-0.975579\pi$
$823$	−2.13293e14	−	3.69434e14i	−0.564907	−	0.978448i	0.432151	−	0.901801i	$-0.357755\pi$
$824$	−1.38345e14	+	7.98736e13i	−0.364190	+	0.210265i
$825$	1.42850e14	+	1.46132e13i	0.373776	+	0.0382364i
$826$	−2.61970e14	+	4.53745e14i	−0.681319	+	1.18008i
$827$		−	3.08388e14i		−	0.797206i	−0.917124	−	0.398603i	$-0.869495\pi$
$827$		−	3.08388e14i		−	0.797206i	0.917124	−	0.398603i	$-0.130505\pi$
$828$	−3.19462e13	+	1.54510e14i	−0.0820857	+	0.397012i
$829$	−1.19874e14			−0.306162			−0.153081	−	0.988214i	$-0.548920\pi$
$829$	−1.19874e14			−0.306162			−0.153081	+	0.988214i	$0.548920\pi$
$830$	4.57627e13	+	2.64211e13i	0.116177	+	0.0670750i
$831$	−5.22072e14	+	2.34181e14i	−1.31742	+	0.590944i
$832$	−1.90579e13	−	3.30093e13i	−0.0478034	−	0.0827979i
$833$	−4.50383e14	+	2.60029e14i	−1.12294	+	0.648330i
$834$	3.08880e14	−	4.27629e14i	0.765526	−	1.05983i
$835$	2.66920e14	−	4.62318e14i	0.657579	−	1.13896i
$836$			4.74739e14i			1.16258i
$837$	2.59411e14	−	5.74022e13i	0.631482	−	0.139734i
$838$	2.33039e14			0.563908
$839$	−4.70910e14	−	2.71880e14i	−1.13273	−	0.653984i	−0.188113	−	0.982147i	$-0.560237\pi$
$839$	−4.70910e14	−	2.71880e14i	−1.13273	−	0.653984i	−0.944621	+	0.328163i	$0.893570\pi$
$840$	2.05393e14	+	1.48357e14i	0.491123	+	0.354742i
$841$	−2.08558e14	−	3.61233e14i	−0.495732	−	0.858634i
$842$	−7.84749e13	+	4.53075e13i	−0.185426	+	0.107056i
$843$	1.44073e14	+	3.21191e14i	0.338412	+	0.754441i
$844$	1.41201e13	−	2.44567e13i	0.0329705	−	0.0571066i
$845$		−	2.04255e14i		−	0.474121i
$846$	−2.99425e14	+	3.36282e14i	−0.690933	+	0.775982i
$847$	3.36933e14			0.772905
$848$	1.82282e13	+	1.05241e13i	0.0415686	+	0.0239997i
$849$	7.21504e13	−	7.05300e14i	0.163569	−	1.59895i
$850$	4.96818e13	+	8.60515e13i	0.111970	+	0.193938i
$851$	−4.09494e14	+	2.36422e14i	−0.917488	+	0.529712i
$852$	−3.37172e14	−	3.44919e13i	−0.751024	−	0.0768278i
$853$	8.41982e13	−	1.45835e14i	0.186448	−	0.322937i	−0.757616	−	0.652701i	$-0.773636\pi$
$853$	8.41982e13	−	1.45835e14i	0.186448	−	0.322937i	0.944063	+	0.329764i	$0.106969\pi$
$854$			4.22180e12i			0.00929412i
$855$	−7.36393e14	−	6.55683e14i	−1.61168	−	1.43504i
$856$	3.13664e13			0.0682489
$857$	6.47931e14	+	3.74083e14i	1.40160	+	0.809215i	0.994557	−	0.104193i	$-0.0332259\pi$
$857$	6.47931e14	+	3.74083e14i	1.40160	+	0.809215i	0.407045	+	0.913408i	$0.366559\pi$
$858$	2.82450e14	−	1.26696e14i	0.607442	−	0.272474i
$859$	3.18902e14	+	5.52355e14i	0.681854	+	1.18101i	0.974414	+	0.224759i	$0.0721595\pi$
$859$	3.18902e14	+	5.52355e14i	0.681854	+	1.18101i	−0.292560	+	0.956247i	$0.594507\pi$
$860$	−1.16012e14	+	6.69798e13i	−0.246611	+	0.142381i
$861$	1.77003e13	−	2.45052e13i	0.0374080	−	0.0517896i
$862$	7.79947e13	−	1.35091e14i	0.163881	−	0.283850i
$863$			3.63404e14i			0.759163i	0.925158	+	0.379582i	$0.123932\pi$
$863$			3.63404e14i			0.759163i	−0.925158	+	0.379582i	$0.876068\pi$
$864$	−1.83888e13	−	8.31024e13i	−0.0381931	−	0.172602i
$865$	4.38121e14			0.904720
$866$	−3.66232e14	−	2.11444e14i	−0.751912	−	0.434117i
$867$	3.04174e13	+	2.19708e13i	0.0620908	+	0.0448487i
$868$	1.19492e14	+	2.06967e14i	0.242517	+	0.420051i
$869$	−2.55123e14	+	1.47296e14i	−0.514815	+	0.297229i
$870$	1.52244e13	+	3.39406e13i	0.0305453	+	0.0680963i
$871$	−2.71319e14	+	4.69938e14i	−0.541239	+	0.937454i
$872$		−	2.65868e14i		−	0.527332i
$873$	3.21589e14	+	6.64913e13i	0.634206	+	0.131127i
$874$	5.52292e14			1.08296
$875$	5.28832e14	+	3.05321e14i	1.03105	+	0.595274i
$876$	3.07652e13	−	3.00743e14i	0.0596403	−	0.583008i
$877$	−1.90373e14	−	3.29736e14i	−0.366951	−	0.635577i	0.622136	−	0.782909i	$-0.286265\pi$
$877$	−1.90373e14	−	3.29736e14i	−0.366951	−	0.635577i	−0.989087	+	0.147332i	$0.952932\pi$
$878$	2.91275e14	−	1.68168e14i	0.558253	−	0.322308i
$879$	−3.73134e14	−	3.81707e13i	−0.711083	−	0.0727420i
$880$	9.27719e13	−	1.60686e14i	0.175794	−	0.304483i
$881$			2.25379e14i			0.424654i	0.977199	+	0.212327i	$0.0681041\pi$
$881$			2.25379e14i			0.424654i	−0.977199	+	0.212327i	$0.931896\pi$
$882$	−4.47758e14	+	1.48240e14i	−0.838881	+	0.277729i
$883$	−1.39909e14			−0.260640			−0.130320	−	0.991472i	$-0.541600\pi$
$883$	−1.39909e14			−0.260640			−0.130320	+	0.991472i	$0.541600\pi$
$884$	1.85510e14	+	1.07104e14i	0.343641	+	0.198401i
$885$	−7.27085e14	+	3.26141e14i	−1.33927	+	0.600744i
$886$	9.78381e13	+	1.69461e14i	0.179201	+	0.310385i
$887$	3.53460e14	−	2.04070e14i	0.643758	−	0.371674i	−0.142303	−	0.989823i	$-0.545451\pi$
$887$	3.53460e14	−	2.04070e14i	0.643758	−	0.371674i	0.786061	+	0.618149i	$0.212117\pi$
$888$	1.49355e14	−	2.06774e14i	0.270492	−	0.374483i
$889$	2.94728e14	−	5.10483e14i	0.530777	−	0.919333i
$890$		−	1.07694e14i		−	0.192859i
$891$	6.86624e14	−	7.98874e13i	1.22273	−	0.142262i
$892$	−6.28319e13			−0.111264
$893$	1.36498e15	+	7.88069e14i	2.40363	+	1.38774i
$894$	−3.30855e14	−	2.38979e14i	−0.579361	−	0.418478i
$895$	5.10412e14	+	8.84059e14i	0.888803	+	1.53945i
$896$	6.63020e13	−	3.82795e13i	0.114812	−	0.0662866i
$897$	−1.47393e14	−	3.28591e14i	−0.253813	−	0.565840i
$898$	2.42071e14	−	4.19279e14i	0.414535	−	0.717995i
$899$			3.50868e13i			0.0597511i
$900$	2.83231e13	+	8.55499e13i	0.0479654	+	0.144880i
$901$	−1.18289e14			−0.199215
$902$	−1.91712e13	−	1.10685e13i	−0.0321082	−	0.0185377i
$903$	4.56849e13	−	4.46588e14i	0.0760910	−	0.743821i
$904$	−3.70126e13	−	6.41077e13i	−0.0613066	−	0.106186i
$905$	−4.78139e14	+	2.76053e14i	−0.787610	+	0.454727i
$906$	−2.47853e14	−	2.53547e13i	−0.406025	−	0.0415354i
$907$	1.18670e14	−	2.05542e14i	0.193332	−	0.334861i	−0.753021	−	0.657997i	$-0.771404\pi$
$907$	1.18670e14	−	2.05542e14i	0.193332	−	0.334861i	0.946352	+	0.323136i	$0.104737\pi$
$908$			3.32362e14i			0.538496i
$909$	−2.50568e13	+	1.21188e14i	−0.0403743	+	0.195273i
$910$	−5.78328e14			−0.926760
$911$	−2.88814e14	−	1.66747e14i	−0.460284	−	0.265745i	0.251880	−	0.967759i	$-0.418951\pi$
$911$	−2.88814e14	−	1.66747e14i	−0.460284	−	0.265745i	−0.712164	+	0.702013i	$0.752285\pi$
$912$	−2.71837e14	+	1.21935e14i	−0.430858	+	0.193266i
$913$	6.48390e13	+	1.12305e14i	0.102207	+	0.177029i
$914$	−3.41069e14	+	1.96916e14i	−0.534701	+	0.308710i
$915$	−3.75980e12	+	5.20526e12i	−0.00586218	+	0.00811590i
$916$	−1.60833e14	+	2.78571e14i	−0.249401	+	0.431976i
$917$		−	1.61148e15i		−	2.48530i
$918$	3.23013e14	+	3.52787e14i	0.495458	+	0.541127i
$919$	−5.90087e14			−0.900199			−0.450100	−	0.892978i	$-0.648611\pi$
$919$	−5.90087e14			−0.900199			−0.450100	+	0.892978i	$0.648611\pi$
$920$	−1.86935e14	−	1.07927e14i	−0.283630	−	0.163754i
$921$	4.45452e14	+	3.21754e14i	0.672207	+	0.485541i
$922$	−1.23940e14	−	2.14670e14i	−0.186018	−	0.322193i
$923$	6.69980e14	−	3.86813e14i	1.00012	−	0.577421i
$924$	2.54479e14	+	5.67325e14i	0.377827	+	0.842310i
$925$	−1.35035e14	+	2.33888e14i	−0.199406	+	0.345381i
$926$		−	1.97524e14i		−	0.290111i
$927$	5.41450e14	−	6.08099e14i	0.790969	−	0.888332i
$928$	1.12401e13			0.0163316
$929$	2.04348e14	+	1.17980e14i	0.295319	+	0.170503i	0.640338	−	0.768093i	$-0.278794\pi$
$929$	2.04348e14	+	1.17980e14i	0.295319	+	0.170503i	−0.345019	+	0.938596i	$0.612128\pi$
$930$	−3.69903e13	+	3.61596e14i	−0.0531708	+	0.519767i
$931$	8.25509e14	+	1.42982e15i	1.18025	+	2.04425i
$932$	2.47106e14	−	1.42667e14i	0.351401	−	0.202882i
$933$	3.04020e14	+	3.11005e13i	0.430026	+	0.0439905i
$934$	4.08459e14	−	7.07472e14i	0.574664	−	0.995348i
$935$			1.04274e15i			1.45921i
$936$	1.45093e14	+	1.29190e14i	0.201961	+	0.179825i
$937$	3.09488e14			0.428494			0.214247	−	0.976779i	$-0.431270\pi$
$937$	3.09488e14			0.428494			0.214247	+	0.976779i	$0.431270\pi$
$938$	−9.43912e14	−	5.44968e14i	−1.29992	−	0.750510i
$939$	−6.97233e14	+	3.12751e14i	−0.955102	+	0.428421i
$940$	−3.08004e14	−	5.33478e14i	−0.419678	−	0.726904i
$941$	−3.49495e14	+	2.01781e14i	−0.473689	+	0.273484i	−0.717783	−	0.696267i	$-0.754843\pi$
$941$	−3.49495e14	+	2.01781e14i	−0.473689	+	0.273484i	0.244094	+	0.969752i	$0.421509\pi$
$942$	1.16612e14	−	1.61443e14i	0.157213	−	0.217654i
$943$	−1.28766e13	+	2.23030e13i	−0.0172681	+	0.0299092i
$944$			2.40788e14i			0.321199i
$945$	−1.23148e15	−	3.88821e14i	−1.63406	−	0.515930i
$946$	−3.28745e14			−0.433914
$947$	−1.19158e15	−	6.87961e14i	−1.56450	−	0.903263i	−0.996792	−	0.0800310i	$-0.974498\pi$
$947$	−1.19158e15	−	6.87961e14i	−1.56450	−	0.903263i	−0.567705	−	0.823232i	$-0.692169\pi$
$948$	−1.49870e14	−	1.08252e14i	−0.195737	−	0.141382i
$949$	3.45020e14	+	5.97593e14i	0.448243	+	0.776380i
$950$	2.73186e14	−	1.57724e14i	0.353054	−	0.203836i
$951$	2.52837e14	+	5.63665e14i	0.325042	+	0.724633i
$952$	−2.15128e14	+	3.72612e14i	−0.275113	+	0.476510i
$953$		−	4.64155e14i		−	0.590471i	−0.955425	−	0.295236i	$-0.904602\pi$
$953$		−	4.64155e14i		−	0.590471i	0.955425	−	0.295236i	$-0.0953981\pi$
$954$	−1.05059e14	−	2.17218e13i	−0.132951	−	0.0274887i
$955$	−7.09970e14			−0.893764
$956$	−6.15702e14	−	3.55476e14i	−0.771048	−	0.445165i
$957$	−9.29007e12	+	9.08142e13i	−0.0115733	+	0.113134i
$958$	−1.24571e14	−	2.15764e14i	−0.154380	−	0.267393i
$959$	−4.86152e14	+	2.80680e14i	−0.599348	+	0.346034i
$960$	1.15837e14	+	1.18499e13i	0.142067	+	0.0145331i
$961$	2.38391e14	−	4.12906e14i	0.290853	−	0.503772i
$962$			5.82217e14i			0.706658i
$963$	−1.51771e14	+	5.02468e13i	−0.183255	+	0.0606705i
$964$	5.52075e14			0.663152
$965$	4.52428e14	+	2.61209e14i	0.540645	+	0.312142i
$966$	6.60004e14	−	2.96051e14i	0.784622	−	0.351950i
$967$	−7.35609e14	−	1.27411e15i	−0.869990	−	1.50687i	−0.862005	−	0.506899i	$-0.830792\pi$
$967$	−7.35609e14	−	1.27411e15i	−0.869990	−	1.50687i	−0.00798486	−	0.999968i	$-0.502542\pi$
$968$	1.34100e14	−	7.74225e13i	0.157780	−	0.0910941i
$969$	9.80397e14	−	1.35731e15i	1.14758	−	1.58877i
$970$	−2.24635e14	+	3.89078e14i	−0.261588	+	0.453084i
$971$		−	5.54464e14i		−	0.642358i	−0.947019	−	0.321179i	$-0.895921\pi$
$971$		−	5.54464e14i		−	0.642358i	0.947019	−	0.321179i	$-0.104079\pi$
$972$	2.22101e14	+	3.72644e14i	0.255988	+	0.429500i
$973$	−2.41850e15			−2.77320
$974$	1.26375e13	+	7.29627e12i	0.0144167	+	0.00832350i
$975$	−1.66746e14	−	1.20442e14i	−0.189248	−	0.136696i
$976$	9.70111e11	+	1.68028e12i	0.00109540	+	0.00189729i
$977$	7.40469e14	−	4.27510e14i	0.831829	−	0.480257i	−0.0226493	−	0.999743i	$-0.507210\pi$
$977$	7.40469e14	−	4.27510e14i	0.831829	−	0.480257i	0.854479	+	0.519487i	$0.173877\pi$
$978$	3.14489e13	+	7.01107e13i	0.0351488	+	0.0783592i
$979$	1.32143e14	−	2.28879e14i	0.146937	−	0.254503i
$980$		−	6.45273e14i		−	0.713860i
$981$	4.25903e14	+	1.28644e15i	0.468776	+	1.41594i
$982$	1.12787e14			0.123510
$983$	1.11054e15	+	6.41171e14i	1.20995	+	0.698564i	0.962748	−	0.270401i	$-0.0871562\pi$
$983$	1.11054e15	+	6.41171e14i	1.20995	+	0.698564i	0.247200	+	0.968964i	$0.420489\pi$
$984$	1.41379e12	−	1.38204e13i	0.00153253	−	0.0149811i
$985$	−2.40416e14	−	4.16413e14i	−0.259288	−	0.449100i
$986$	−5.47055e13	+	3.15842e13i	−0.0587011	+	0.0338911i
$987$	2.05362e15	+	2.10080e14i	2.19247	+	0.224284i
$988$	3.40022e14	−	5.88935e14i	0.361178	−	0.625579i
$989$			3.82449e14i			0.404196i
$990$	−1.91482e14	+	9.26113e14i	−0.201350	+	0.973841i
$991$	−1.67995e15			−1.75763			−0.878815	−	0.477163i	$-0.841665\pi$
$991$	−1.67995e15			−1.75763			−0.878815	+	0.477163i	$0.841665\pi$
$992$	9.51163e13	+	5.49154e13i	0.0990140	+	0.0571658i
$993$	−1.23934e15	+	5.55918e14i	−1.28364	+	0.575790i
$994$	7.76948e14	+	1.34571e15i	0.800682	+	1.38682i
$995$	1.54528e15	−	8.92168e14i	1.58450	−	0.914811i
$996$	−4.76522e13	+	6.59721e13i	−0.0486168	+	0.0673076i
$997$	−8.62492e14	+	1.49388e15i	−0.875547	+	1.51649i	−0.0193683	+	0.999812i	$0.506166\pi$
$997$	−8.62492e14	+	1.49388e15i	−0.875547	+	1.51649i	−0.856179	+	0.516680i	$0.827168\pi$
$998$			9.64630e14i			0.974334i
$999$	−3.91435e14	+	1.23976e15i	−0.393398	+	1.24598i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.11.d.a.11.2	yes	20
3.2	odd	2		54.11.d.a.35.6		20
9.2	odd	6		162.11.b.c.161.2		20
9.4	even	3		54.11.d.a.17.6		20
9.5	odd	6	inner	18.11.d.a.5.2	✓	20
9.7	even	3		162.11.b.c.161.19		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.11.d.a.5.2	✓	20	9.5	odd	6	inner
18.11.d.a.11.2	yes	20	1.1	even	1	trivial
54.11.d.a.17.6		20	9.4	even	3
54.11.d.a.35.6		20	3.2	odd	2
162.11.b.c.161.2		20	9.2	odd	6
162.11.b.c.161.19		20	9.7	even	3

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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	18.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-19.5959 - 11.3137i) q^{2} +(-196.987 - 142.285i) q^{3} +(256.000 + 443.405i) q^{4} +(3091.89 - 1785.10i) q^{5} +(2250.37 + 5016.87i) q^{6} +(12604.4 - 21831.4i) q^{7} -11585.2i q^{8} +(18558.8 + 56056.7i) q^{9} -80784.5 q^{10} +(-171690. - 99125.1i) q^{11} +(12661.4 - 123770. i) q^{12} +(141992. + 245938. i) q^{13} +(-493988. + 285204. i) q^{14} +(-863055. - 88288.4i) q^{15} +(-131072. + 227023. i) q^{16} -1.47323e6i q^{17} +(270534. - 1.30845e6i) q^{18} -4.67704e6 q^{19} +(1.58305e6 + 913972. i) q^{20} +(-5.58918e6 + 2.50709e6i) q^{21} +(2.24294e6 + 3.88489e6i) q^{22} +(4.51953e6 - 2.60935e6i) q^{23} +(-1.64841e6 + 2.28214e6i) q^{24} +(1.49036e6 - 2.58138e6i) q^{25} -6.42584e6i q^{26} +(4.32022e6 - 1.36831e7i) q^{27} +1.29069e7 q^{28} +(1.64106e6 + 947468. i) q^{29} +(1.59135e7 + 1.14944e7i) q^{30} +(9.25805e6 + 1.60354e7i) q^{31} +(5.13695e6 - 2.96582e6i) q^{32} +(1.97166e7 + 4.39553e7i) q^{33} +(-1.66677e7 + 2.88693e7i) q^{34} -9.00003e7i q^{35} +(-2.01048e7 + 2.25796e7i) q^{36} -9.06055e7 q^{37} +(9.16509e7 + 5.29147e7i) q^{38} +(7.02273e6 - 6.86501e7i) q^{39} +(-2.06808e7 - 3.58202e7i) q^{40} +(-4.27366e6 + 2.46740e6i) q^{41} +(1.37890e8 + 1.41058e7i) q^{42} +(-3.66421e7 + 6.34660e7i) q^{43} -1.01504e8i q^{44} +(1.57449e8 + 1.40192e8i) q^{45} -1.18086e8 q^{46} +(-2.91846e8 - 1.68497e8i) q^{47} +(5.81216e7 - 2.60710e7i) q^{48} +(-1.76502e8 - 3.05711e8i) q^{49} +(-5.84101e7 + 3.37231e7i) q^{50} +(-2.09619e8 + 2.90207e8i) q^{51} +(-7.27001e7 + 1.25920e8i) q^{52} -8.02924e7i q^{53} +(-2.39465e8 + 2.19255e8i) q^{54} -7.07793e8 q^{55} +(-2.52922e8 - 1.46025e8i) q^{56} +(9.21316e8 + 6.65475e8i) q^{57} +(-2.14388e7 - 3.71330e7i) q^{58} +(7.95473e8 - 4.59267e8i) q^{59} +(-1.81795e8 - 4.05285e8i) q^{60} +(3.70068e6 - 6.40977e6i) q^{61} -4.18972e8i q^{62} +(1.45772e9 + 3.01396e8i) q^{63} -1.34218e8 q^{64} +(8.78049e8 + 5.06942e8i) q^{65} +(1.10933e8 - 1.08441e9i) q^{66} +(9.55400e8 + 1.65480e9i) q^{67} +(6.53238e8 - 3.77147e8i) q^{68} +(-1.26156e9 - 1.29055e8i) q^{69} +(-1.01824e9 + 1.76364e9i) q^{70} -2.72418e9i q^{71} +(6.49431e8 - 2.15008e8i) q^{72} +2.42985e9 q^{73} +(1.77550e9 + 1.02508e9i) q^{74} +(-6.60875e8 + 2.96442e8i) q^{75} +(-1.19732e9 - 2.07382e9i) q^{76} +(-4.32808e9 + 2.49882e9i) q^{77} +(-9.14303e8 + 1.26581e9i) q^{78} +(7.42978e8 - 1.28688e9i) q^{79} +9.35907e8i q^{80} +(-2.79793e9 + 2.08069e9i) q^{81} +1.11662e8 q^{82} +(-5.66479e8 - 3.27057e8i) q^{83} +(-2.54249e9 - 1.83646e9i) q^{84} +(-2.62987e9 - 4.55506e9i) q^{85} +(1.43607e9 - 8.29117e8i) q^{86} +(-1.88457e8 - 4.20138e8i) q^{87} +(-1.14839e9 + 1.98907e9i) q^{88} +1.33310e9i q^{89} +(-1.49926e9 - 4.52851e9i) q^{90} +7.15890e9 q^{91} +(2.31400e9 + 1.33599e9i) q^{92} +(4.57889e8 - 4.47605e9i) q^{93} +(3.81266e9 + 6.60372e9i) q^{94} +(-1.44609e10 + 8.34899e9i) q^{95} +(-1.43391e9 - 1.46685e8i) q^{96} +(2.78067e9 - 4.81625e9i) q^{97} +7.98759e9i q^{98} +(2.37028e9 - 1.14640e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 84 q^{3} + 5120 q^{4} - 9918 q^{5} + 12864 q^{6} + 12238 q^{7} + 79248 q^{9} - 327582 q^{11} + 9216 q^{12} - 280550 q^{13} + 175680 q^{14} - 2685042 q^{15} - 2621440 q^{16} + 3925632 q^{18} - 2966240 q^{19}+ \cdots + 41160676842 q^{99}+O(q^{100}) \) 20 * q - 84 * q^3 + 5120 * q^4 - 9918 * q^5 + 12864 * q^6 + 12238 * q^7 + 79248 * q^9 - 327582 * q^11 + 9216 * q^12 - 280550 * q^13 + 175680 * q^14 - 2685042 * q^15 - 2621440 * q^16 + 3925632 * q^18 - 2966240 * q^19 - 5078016 * q^20 - 11895726 * q^21 + 3473472 * q^22 + 10446606 * q^23 + 2752512 * q^24 + 9609944 * q^25 + 2340576 * q^27 + 12531712 * q^28 + 32440806 * q^29 + 37556352 * q^30 - 40069958 * q^31 - 35367930 * q^33 + 30746496 * q^34 - 32695296 * q^36 - 127390400 * q^37 + 370567296 * q^38 + 153125550 * q^39 - 245419398 * q^41 - 344505600 * q^42 - 86593094 * q^43 + 394622766 * q^45 - 366913920 * q^46 + 1094979330 * q^47 + 26738688 * q^48 - 598072056 * q^49 - 456606720 * q^50 - 2329772724 * q^51 + 143641600 * q^52 + 1623484224 * q^54 - 262510308 * q^55 + 89948160 * q^56 + 311135772 * q^57 + 249515904 * q^58 - 2125085130 * q^59 - 2357738496 * q^60 + 312021586 * q^61 + 5475513858 * q^63 - 2684354560 * q^64 + 13076821350 * q^65 + 2185467264 * q^66 - 1200881210 * q^67 - 2610487296 * q^68 - 11765922354 * q^69 + 1138681152 * q^70 + 1554382848 * q^72 + 5213376328 * q^73 + 9118122624 * q^74 + 13244996208 * q^75 - 759357440 * q^76 - 33678720774 * q^77 - 14572366080 * q^78 - 3396212726 * q^79 + 14546869128 * q^81 + 3667214592 * q^82 + 16739541378 * q^83 + 1518514176 * q^84 + 7141101588 * q^85 - 11512304064 * q^86 - 32778228834 * q^87 - 1778417664 * q^88 + 16769410560 * q^90 - 10426841884 * q^91 + 5348662272 * q^92 - 4843832814 * q^93 + 6416128320 * q^94 - 26494427340 * q^95 - 1962934272 * q^96 + 6721893598 * q^97 + 41160676842 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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