LMFDB - Embedded newform 18.11.d.a.11.1

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			11.1
Root			$0.500000 + 79.2536i$ of defining polynomial
Character	$\chi$	$=$	18.11
Dual form			18.11.d.a.5.1

$q$-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} +(-237.011 + 53.6159i) q^{3} +(256.000 + 443.405i) q^{4} +(-1517.40 + 876.072i) q^{5} +(5251.05 + 1630.82i) q^{6} +(-13322.5 + 23075.2i) q^{7} -11585.2i q^{8} +(53299.7 - 25415.2i) q^{9} +39646.5 q^{10} +(21339.2 + 12320.2i) q^{11} +(-84448.4 - 91366.3i) q^{12} +(-280428. - 485715. i) q^{13} +(522132. - 301453. i) q^{14} +(312670. - 288996. i) q^{15} +(-131072. + 227023. i) q^{16} -1.25314e6i q^{17} +(-1.33200e6 - 104984. i) q^{18} +1.23964e6 q^{19} +(-776910. - 448549. i) q^{20} +(1.92038e6 - 6.18338e6i) q^{21} +(-278775. - 482852. i) q^{22} +(6.66248e6 - 3.84658e6i) q^{23} +(621153. + 2.74583e6i) q^{24} +(-3.34781e6 + 5.79857e6i) q^{25} +1.26907e7i q^{26} +(-1.12700e7 + 8.88139e6i) q^{27} -1.36422e7 q^{28} +(2.22205e7 + 1.28290e7i) q^{29} +(-9.39667e6 + 2.12568e6i) q^{30} +(-1.55202e6 - 2.68819e6i) q^{31} +(5.13695e6 - 2.96582e6i) q^{32} +(-5.71820e6 - 1.77591e6i) q^{33} +(-1.41777e7 + 2.45564e7i) q^{34} -4.66858e7i q^{35} +(2.49139e7 + 1.71271e7i) q^{36} -7.91883e7 q^{37} +(-2.42919e7 - 1.40250e7i) q^{38} +(9.25066e7 + 1.00085e8i) q^{39} +(1.01495e7 + 1.75795e7i) q^{40} +(9.25239e7 - 5.34187e7i) q^{41} +(-1.07588e8 + 9.94424e7i) q^{42} +(1.26396e8 - 2.18925e8i) q^{43} +1.26159e7i q^{44} +(-5.86115e7 + 8.52594e7i) q^{45} -1.74077e8 q^{46} +(1.35084e8 + 7.79908e7i) q^{47} +(1.88935e7 - 6.08346e7i) q^{48} +(-2.13739e8 - 3.70206e8i) q^{49} +(1.31207e8 - 7.57522e7i) q^{50} +(6.71883e7 + 2.97009e8i) q^{51} +(1.43579e8 - 2.48686e8i) q^{52} -7.35338e8i q^{53} +(3.21327e8 - 4.65339e7i) q^{54} -4.31736e7 q^{55} +(2.67332e8 + 1.54344e8i) q^{56} +(-2.93809e8 + 6.64646e7i) q^{57} +(-2.90287e8 - 5.02792e8i) q^{58} +(-1.86013e8 + 1.07395e8i) q^{59} +(2.08186e8 + 6.46564e7i) q^{60} +(-7.44947e8 + 1.29029e9i) q^{61} +7.02366e7i q^{62} +(-1.23624e8 + 1.56849e9i) q^{63} -1.34218e8 q^{64} +(8.51043e8 + 4.91350e8i) q^{65} +(9.19613e7 + 9.94946e7i) q^{66} +(-1.88410e8 - 3.26335e8i) q^{67} +(5.55649e8 - 3.20804e8i) q^{68} +(-1.37284e9 + 1.26890e9i) q^{69} +(-5.28189e8 + 9.14851e8i) q^{70} -2.45358e8i q^{71} +(-2.94441e8 - 6.17489e8i) q^{72} +6.92446e8 q^{73} +(1.55177e9 + 8.95914e8i) q^{74} +(4.82572e8 - 1.55382e9i) q^{75} +(3.17349e8 + 5.49664e8i) q^{76} +(-5.68583e8 + 3.28272e8i) q^{77} +(-6.80424e8 - 3.00784e9i) q^{78} +(6.13200e8 - 1.06209e9i) q^{79} -4.59314e8i q^{80} +(2.19492e9 - 2.70924e9i) q^{81} -2.41745e9 q^{82} +(-2.68014e9 - 1.54738e9i) q^{83} +(3.23336e9 - 7.31440e8i) q^{84} +(1.09784e9 + 1.90152e9i) q^{85} +(-4.95371e9 + 2.86002e9i) q^{86} +(-5.95435e9 - 1.84925e9i) q^{87} +(1.42733e8 - 2.47220e8i) q^{88} -3.69983e9i q^{89} +(2.11315e9 - 1.00762e9i) q^{90} +1.49440e10 q^{91} +(3.41119e9 + 1.96945e9i) q^{92} +(5.11977e8 + 5.53917e8i) q^{93} +(-1.76473e9 - 3.05660e9i) q^{94} +(-1.88104e9 + 1.08602e9i) q^{95} +(-1.05850e9 + 9.78355e8i) q^{96} +(2.45031e9 - 4.24407e9i) q^{97} +9.67271e9i q^{98} +(1.45050e9 + 1.14323e8i) 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
$3$	−237.011	+	53.6159i	−0.975355	+	0.220642i
$3$	−237.011	+	53.6159i	−0.975355	+	0.220642i
$4$	256.000	+	443.405i	0.250000	+	0.433013i
$5$	−1517.40	+	876.072i	−0.485569	+	0.280343i	−0.722734	−	0.691126i	$-0.757115\pi$
$5$	−1517.40	+	876.072i	−0.485569	+	0.280343i	0.237166	+	0.971469i	$0.423782\pi$
$6$	5251.05	+	1630.82i	0.675289	+	0.209725i
$7$	−13322.5	+	23075.2i	−0.792674	+	1.37295i	0.131632	+	0.991299i	$0.457978\pi$
$7$	−13322.5	+	23075.2i	−0.792674	+	1.37295i	−0.924306	+	0.381653i	$0.875355\pi$
$8$		−	11585.2i		−	0.353553i
$9$	53299.7	−	25415.2i	0.902635	−	0.430408i
$10$	39646.5			0.396465
$11$	21339.2	+	12320.2i	0.132500	+	0.0764989i	0.564785	−	0.825238i	$-0.308959\pi$
$11$	21339.2	+	12320.2i	0.132500	+	0.0764989i	−0.432285	+	0.901737i	$0.642293\pi$
$12$	−84448.4	−	91366.3i	−0.339379	−	0.367181i
$13$	−280428.	−	485715.i	−0.755274	−	1.30817i	−0.945238	−	0.326381i	$-0.894171\pi$
$13$	−280428.	−	485715.i	−0.755274	−	1.30817i	0.189965	−	0.981791i	$-0.439163\pi$
$14$	522132.	−	301453.i	0.970823	−	0.560505i
$15$	312670.	−	288996.i	0.411746	−	0.380571i
$16$	−131072.	+	227023.i	−0.125000	+	0.216506i
$17$		−	1.25314e6i		−	0.882583i	−0.897364	−	0.441291i	$-0.854521\pi$
$17$		−	1.25314e6i		−	0.882583i	0.897364	−	0.441291i	$-0.145479\pi$
$18$	−1.33200e6	−	104984.i	−0.704921	−	0.0555596i
$19$	1.23964e6			0.500644			0.250322	−	0.968163i	$-0.419464\pi$
$19$	1.23964e6			0.500644			0.250322	+	0.968163i	$0.419464\pi$
$20$	−776910.	−	448549.i	−0.242784	−	0.140172i
$21$	1.92038e6	−	6.18338e6i	0.470208	−	1.51401i
$22$	−278775.	−	482852.i	−0.0540929	−	0.0936916i
$23$	6.66248e6	−	3.84658e6i	1.03513	−	0.597635i	0.116683	−	0.993169i	$-0.462774\pi$
$23$	6.66248e6	−	3.84658e6i	1.03513	−	0.597635i	0.918451	+	0.395534i	$0.129441\pi$
$24$	621153.	+	2.74583e6i	0.0780086	+	0.344840i
$25$	−3.34781e6	+	5.79857e6i	−0.342815	+	0.593774i
$26$			1.26907e7i			1.06812i
$27$	−1.12700e7	+	8.88139e6i	−0.785423	+	0.618959i
$28$	−1.36422e7			−0.792674
$29$	2.22205e7	+	1.28290e7i	1.08334	+	0.625465i	0.931795	−	0.362985i	$-0.118243\pi$
$29$	2.22205e7	+	1.28290e7i	1.08334	+	0.625465i	0.151543	+	0.988451i	$0.451576\pi$
$30$	−9.39667e6	+	2.12568e6i	−0.386694	+	0.0874767i
$31$	−1.55202e6	−	2.68819e6i	−0.0542113	−	0.0938968i	0.837646	−	0.546213i	$-0.183931\pi$
$31$	−1.55202e6	−	2.68819e6i	−0.0542113	−	0.0938968i	−0.891858	+	0.452316i	$0.850598\pi$
$32$	5.13695e6	−	2.96582e6i	0.153093	−	0.0883883i
$33$	−5.71820e6	−	1.77591e6i	−0.146113	−	0.0453786i
$34$	−1.41777e7	+	2.45564e7i	−0.312040	+	0.540469i
$35$		−	4.66858e7i		−	0.888883i
$36$	2.49139e7	+	1.71271e7i	0.412031	+	0.283250i
$37$	−7.91883e7			−1.14196			−0.570982	−	0.820962i	$-0.693437\pi$
$37$	−7.91883e7			−1.14196			−0.570982	+	0.820962i	$0.693437\pi$
$38$	−2.42919e7	−	1.40250e7i	−0.306580	−	0.177004i
$39$	9.25066e7	+	1.00085e8i	1.02530	+	1.10929i
$40$	1.01495e7	+	1.75795e7i	0.0991163	+	0.171674i
$41$	9.25239e7	−	5.34187e7i	0.798610	−	0.461078i	−0.0443751	−	0.999015i	$-0.514130\pi$
$41$	9.25239e7	−	5.34187e7i	0.798610	−	0.461078i	0.842985	+	0.537937i	$0.180796\pi$
$42$	−1.07588e8	+	9.94424e7i	−0.823227	+	0.760895i
$43$	1.26396e8	−	2.18925e8i	0.859790	−	1.48920i	−0.0123386	−	0.999924i	$-0.503928\pi$
$43$	1.26396e8	−	2.18925e8i	0.859790	−	1.48920i	0.872129	−	0.489276i	$-0.162739\pi$
$44$			1.26159e7i			0.0764989i
$45$	−5.86115e7	+	8.52594e7i	−0.317629	+	0.462040i
$46$	−1.74077e8			−0.845184
$47$	1.35084e8	+	7.79908e7i	0.588999	+	0.340059i	0.764702	−	0.644384i	$-0.222886\pi$
$47$	1.35084e8	+	7.79908e7i	0.588999	+	0.340059i	−0.175702	+	0.984443i	$0.556220\pi$
$48$	1.88935e7	−	6.08346e7i	0.0741490	−	0.238751i
$49$	−2.13739e8	−	3.70206e8i	−0.756664	−	1.31058i
$50$	1.31207e8	−	7.57522e7i	0.419861	−	0.242407i
$51$	6.71883e7	+	2.97009e8i	0.194734	+	0.860831i
$52$	1.43579e8	−	2.48686e8i	0.377637	−	0.654086i
$53$		−	7.35338e8i		−	1.75836i	−0.476489	−	0.879180i	$-0.658091\pi$
$53$		−	7.35338e8i		−	1.75836i	0.476489	−	0.879180i	$-0.341909\pi$
$54$	3.21327e8	−	4.65339e7i	0.699807	−	0.101345i
$55$	−4.31736e7			−0.0857838
$56$	2.67332e8	+	1.54344e8i	0.485412	+	0.280253i
$57$	−2.93809e8	+	6.64646e7i	−0.488305	+	0.110463i
$58$	−2.90287e8	−	5.02792e8i	−0.442271	−	0.766035i
$59$	−1.86013e8	+	1.07395e8i	−0.260185	+	0.150218i	−0.624419	−	0.781090i	$-0.714664\pi$
$59$	−1.86013e8	+	1.07395e8i	−0.260185	+	0.150218i	0.364234	+	0.931308i	$0.381331\pi$
$60$	2.08186e8	+	6.46564e7i	0.267729	+	0.0831487i
$61$	−7.44947e8	+	1.29029e9i	−0.882016	+	1.52770i	−0.0329199	+	0.999458i	$0.510481\pi$
$61$	−7.44947e8	+	1.29029e9i	−0.882016	+	1.52770i	−0.849096	+	0.528238i	$0.822853\pi$
$62$			7.02366e7i			0.0766664i
$63$	−1.23624e8	+	1.56849e9i	−0.124566	+	1.58045i
$64$	−1.34218e8			−0.125000
$65$	8.51043e8	+	4.91350e8i	0.733474	+	0.423472i
$66$	9.19613e7	+	9.94946e7i	0.0734320	+	0.0794474i
$67$	−1.88410e8	−	3.26335e8i	−0.139550	−	0.241707i	0.787776	−	0.615961i	$-0.211232\pi$
$67$	−1.88410e8	−	3.26335e8i	−0.139550	−	0.241707i	−0.927326	+	0.374254i	$0.877899\pi$
$68$	5.55649e8	−	3.20804e8i	0.382169	−	0.220646i
$69$	−1.37284e9	+	1.26890e9i	−0.877760	+	0.811300i
$70$	−5.28189e8	+	9.14851e8i	−0.314268	+	0.544327i
$71$		−	2.45358e8i		−	0.135991i	−0.997686	−	0.0679954i	$-0.978340\pi$
$71$		−	2.45358e8i		−	0.135991i	0.997686	−	0.0679954i	$-0.0216603\pi$
$72$	−2.94441e8	−	6.17489e8i	−0.152172	−	0.319129i
$73$	6.92446e8			0.334020			0.167010	−	0.985955i	$-0.446589\pi$
$73$	6.92446e8			0.334020			0.167010	+	0.985955i	$0.446589\pi$
$74$	1.55177e9	+	8.95914e8i	0.699307	+	0.403745i
$75$	4.82572e8	−	1.55382e9i	0.203355	−	0.654779i
$76$	3.17349e8	+	5.49664e8i	0.125161	+	0.216785i
$77$	−5.68583e8	+	3.28272e8i	−0.210058	+	0.121277i
$78$	−6.80424e8	−	3.00784e9i	−0.235671	−	1.04179i
$79$	6.13200e8	−	1.06209e9i	0.199281	−	0.345166i	−0.749014	−	0.662554i	$-0.769473\pi$
$79$	6.13200e8	−	1.06209e9i	0.199281	−	0.345166i	0.948296	+	0.317388i	$0.102806\pi$
$80$		−	4.59314e8i		−	0.140172i
$81$	2.19492e9	−	2.70924e9i	0.629498	−	0.777002i
$82$	−2.41745e9			−0.652062
$83$	−2.68014e9	−	1.54738e9i	−0.680403	−	0.392831i	0.119604	−	0.992822i	$-0.461838\pi$
$83$	−2.68014e9	−	1.54738e9i	−0.680403	−	0.392831i	−0.800007	+	0.599991i	$0.795171\pi$
$84$	3.23336e9	−	7.31440e8i	0.773138	−	0.174897i
$85$	1.09784e9	+	1.90152e9i	0.247426	+	0.428554i
$86$	−4.95371e9	+	2.86002e9i	−1.05302	+	0.607963i
$87$	−5.95435e9	−	1.84925e9i	−1.19464	−	0.371021i
$88$	1.42733e8	−	2.47220e8i	0.0270464	−	0.0468458i
$89$		−	3.69983e9i		−	0.662571i	−0.943531	−	0.331285i	$-0.892518\pi$
$89$		−	3.69983e9i		−	0.662571i	0.943531	−	0.331285i	$-0.107482\pi$
$90$	2.11315e9	−	1.00762e9i	0.357863	−	0.170642i
$91$	1.49440e10			2.39474
$92$	3.41119e9	+	1.96945e9i	0.517567	+	0.298818i
$93$	5.11977e8	+	5.53917e8i	0.0735928	+	0.0796214i
$94$	−1.76473e9	−	3.05660e9i	−0.240458	−	0.416485i
$95$	−1.88104e9	+	1.08602e9i	−0.243097	+	0.140352i
$96$	−1.05850e9	+	9.78355e8i	−0.129818	+	0.119989i
$97$	2.45031e9	−	4.24407e9i	0.285340	−	0.494224i	−0.687351	−	0.726325i	$-0.741227\pi$
$97$	2.45031e9	−	4.24407e9i	0.285340	−	0.494224i	0.972692	+	0.232101i	$0.0745600\pi$
$98$			9.67271e9i			1.07008i
$99$	1.45050e9	+	1.14323e8i	0.152525	+	0.0120215i
$100$	−3.42815e9			−0.342815
$101$	−1.64361e10	−	9.48939e9i	−1.56384	−	0.902883i	−0.996863	−	0.0791491i	$-0.974780\pi$
$101$	−1.64361e10	−	9.48939e9i	−1.56384	−	0.902883i	−0.566977	−	0.823734i	$-0.691887\pi$
$102$	2.04365e9	−	6.58030e9i	0.185100	−	0.595998i
$103$	5.83959e9	+	1.01145e10i	0.503728	+	0.872482i	0.999991	+	0.00430997i	$0.00137191\pi$
$103$	5.83959e9	+	1.01145e10i	0.503728	+	0.872482i	−0.496263	+	0.868172i	$0.665295\pi$
$104$	−5.62713e9	+	3.24882e9i	−0.462509	+	0.267030i
$105$	2.50310e9	+	1.10651e10i	0.196125	+	0.866976i
$106$	−8.31940e9	+	1.44096e10i	−0.621674	+	1.07677i
$107$		−	2.19686e9i		−	0.156633i	−0.996929	−	0.0783166i	$-0.975045\pi$
$107$		−	2.19686e9i		−	0.156633i	0.996929	−	0.0783166i	$-0.0249545\pi$
$108$	−6.82316e9	−	2.72352e9i	−0.464373	−	0.185358i
$109$	1.52093e10			0.988502			0.494251	−	0.869319i	$-0.335442\pi$
$109$	1.52093e10			0.988502			0.494251	+	0.869319i	$0.335442\pi$
$110$	8.46027e8	+	4.88454e8i	0.0525316	+	0.0303291i
$111$	1.87685e10	−	4.24575e9i	1.11382	−	0.251965i
$112$	−3.49241e9	−	6.04902e9i	−0.198168	−	0.343238i
$113$	−2.48547e10	+	1.43499e10i	−1.34902	+	0.778855i	−0.988110	−	0.153747i	$-0.950866\pi$
$113$	−2.48547e10	+	1.43499e10i	−1.34902	+	0.778855i	−0.360906	+	0.932602i	$0.617532\pi$
$114$	6.50943e9	+	2.02164e9i	0.338079	+	0.104998i
$115$	−6.73977e9	+	1.16736e10i	−0.335086	+	0.580386i
$116$			1.31369e10i			0.625465i
$117$	−2.72912e10	−	1.87613e10i	−1.24478	−	0.855726i
$118$	4.86012e9			0.212440
$119$	2.89165e10	+	1.66949e10i	1.21174	+	0.699600i
$120$	−3.34809e9	−	3.62236e9i	−0.134552	−	0.145574i
$121$	−1.26651e10	−	2.19367e10i	−0.488296	−	0.845753i
$122$	2.91959e10	−	1.68562e10i	1.08024	−	0.623679i
$123$	−1.90651e10	+	1.76216e10i	−0.677195	+	0.625921i
$124$	7.94637e8	−	1.37635e9i	0.0271057	−	0.0469484i
$125$		−	2.88425e10i		−	0.945110i
$126$	2.01680e10	−	2.93374e10i	0.635053	−	0.923781i
$127$	1.60110e10			0.484618			0.242309	−	0.970199i	$-0.422095\pi$
$127$	1.60110e10			0.484618			0.242309	+	0.970199i	$0.422095\pi$
$128$	2.63012e9	+	1.51850e9i	0.0765466	+	0.0441942i
$129$	−1.82195e10	+	5.86646e10i	−0.510021	+	1.64220i
$130$	−1.11180e10	−	1.92569e10i	−0.299440	−	0.518645i
$131$	4.16221e10	−	2.40305e10i	1.07887	−	0.622884i	0.148276	−	0.988946i	$-0.452628\pi$
$131$	4.16221e10	−	2.40305e10i	1.07887	−	0.622884i	0.930590	+	0.366062i	$0.119294\pi$
$132$	−6.76413e8	−	2.99011e9i	−0.0168788	−	0.0746136i
$133$	−1.65151e10	+	2.86050e10i	−0.396847	+	0.687359i
$134$			8.52645e9i			0.197353i
$135$	9.32033e9	−	2.33499e10i	0.207856	−	0.520735i
$136$	−1.45179e10			−0.312040
$137$	−2.56508e10	−	1.48095e10i	−0.531494	−	0.306858i	0.210130	−	0.977673i	$-0.432611\pi$
$137$	−2.56508e10	−	1.48095e10i	−0.531494	−	0.306858i	−0.741625	+	0.670815i	$0.765944\pi$
$138$	4.12581e10	−	9.33327e9i	0.824354	−	0.186483i
$139$	−1.79112e10	−	3.10231e10i	−0.345184	−	0.597877i	0.640203	−	0.768206i	$-0.278850\pi$
$139$	−1.79112e10	−	3.10231e10i	−0.345184	−	0.597877i	−0.985387	+	0.170329i	$0.945517\pi$
$140$	2.07007e10	−	1.19516e10i	0.384898	−	0.222221i
$141$	−3.61980e10	−	1.12420e10i	−0.649514	−	0.201720i
$142$	−2.77591e9	+	4.80802e9i	−0.0480800	+	0.0832770i
$143$		−	1.38197e10i		−	0.231110i
$144$	−1.21626e9	+	1.54315e10i	−0.0196433	+	0.249227i
$145$	−4.49566e10			−0.701380
$146$	−1.35691e10	−	7.83414e9i	−0.204544	−	0.118094i
$147$	7.05075e10	+	7.62833e10i	1.02718	+	1.11133i
$148$	−2.02722e10	−	3.51125e10i	−0.285491	−	0.494485i
$149$	1.02374e11	−	5.91059e10i	1.39399	−	0.804821i	0.400237	−	0.916412i	$-0.368928\pi$
$149$	1.02374e11	−	5.91059e10i	1.39399	−	0.804821i	0.993754	+	0.111590i	$0.0355944\pi$
$150$	−2.70359e10	+	2.49889e10i	−0.356029	+	0.329072i
$151$	−1.48871e10	+	2.57853e10i	−0.189639	+	0.328464i	−0.945130	−	0.326695i	$-0.894065\pi$
$151$	−1.48871e10	+	2.57853e10i	−0.189639	+	0.328464i	0.755491	+	0.655159i	$0.227398\pi$
$152$		−	1.43616e10i		−	0.177004i
$153$	−3.18488e10	−	6.67920e10i	−0.379870	−	0.796649i
$154$	1.48559e10			0.171512
$155$	4.71009e9	+	2.71937e9i	0.0526466	+	0.0303956i
$156$	−2.06963e10	+	6.66395e10i	−0.224011	+	0.721289i
$157$	−7.90926e10	−	1.36992e11i	−0.829158	−	1.43614i	−0.898699	−	0.438565i	$-0.855487\pi$
$157$	−7.90926e10	−	1.36992e11i	−0.829158	−	1.43614i	0.0695413	−	0.997579i	$-0.477846\pi$
$158$	−2.40324e10	+	1.38751e10i	−0.244069	+	0.140913i
$159$	3.94258e10	+	1.74283e11i	0.387968	+	1.71503i
$160$	−5.19655e9	+	9.00068e9i	−0.0495581	+	0.0858372i
$161$			2.04984e11i			1.89492i
$162$	−7.36631e10	+	2.82573e10i	−0.660199	+	0.253253i
$163$	1.42978e11			1.24260			0.621300	−	0.783573i	$-0.286605\pi$
$163$	1.42978e11			1.24260			0.621300	+	0.783573i	$0.286605\pi$
$164$	4.73722e10	+	2.73504e10i	0.399305	+	0.230539i
$165$	1.02326e10	−	2.31479e9i	0.0836696	−	0.0189275i
$166$	3.50131e10	+	6.06445e10i	0.277773	+	0.481118i
$167$	−1.30459e11	+	7.53206e10i	−1.00437	+	0.579871i	−0.909537	−	0.415622i	$-0.863564\pi$
$167$	−1.30459e11	+	7.53206e10i	−1.00437	+	0.579871i	−0.0948292	+	0.995494i	$0.530230\pi$
$168$	−7.16359e10	−	2.22480e10i	−0.535284	−	0.166244i
$169$	−8.83503e10	+	1.53027e11i	−0.640877	+	1.11003i
$170$		−	4.96827e10i		−	0.349913i
$171$	6.60726e10	−	3.15057e10i	0.451898	−	0.215481i
$172$	1.29430e11			0.859790
$173$	−7.41184e10	−	4.27923e10i	−0.478295	−	0.276144i	0.241411	−	0.970423i	$-0.422390\pi$
$173$	−7.41184e10	−	4.27923e10i	−0.478295	−	0.276144i	−0.719706	+	0.694279i	$0.755723\pi$
$174$	9.57591e10	+	1.03603e11i	0.600390	+	0.649573i
$175$	−8.92021e10	−	1.54503e11i	−0.543482	−	0.941338i
$176$	−5.59396e9	+	3.22967e9i	−0.0331250	+	0.0191247i
$177$	3.83291e10	−	3.54270e10i	0.220629	−	0.203924i
$178$	−4.18588e10	+	7.25016e10i	−0.234254	+	0.405740i
$179$		−	2.25435e11i		−	1.22675i	−0.789792	−	0.613374i	$-0.789812\pi$
$179$		−	2.25435e11i		−	1.22675i	0.789792	−	0.613374i	$-0.210188\pi$
$180$	−5.28090e10	−	4.16223e9i	−0.279476	−	0.0220274i
$181$	2.03664e11			1.04839			0.524193	−	0.851599i	$-0.324367\pi$
$181$	2.03664e11			1.04839			0.524193	+	0.851599i	$0.324367\pi$
$182$	−2.92841e11	−	1.69072e11i	−1.46647	−	0.846669i
$183$	1.07381e11	−	3.45754e11i	0.523205	−	1.68466i
$184$	−4.45636e10	−	7.71864e10i	−0.211296	−	0.365975i
$185$	1.20161e11	−	6.93747e10i	0.554502	−	0.320142i
$186$	−3.76580e9	−	1.66469e10i	−0.0169158	−	0.0747770i
$187$	1.54390e10	−	2.67411e10i	0.0675166	−	0.116942i
$188$			7.98626e10i			0.340059i
$189$	−5.47960e10	−	3.78379e11i	−0.227217	−	1.56898i
$190$	4.91475e10			0.198488
$191$	4.21991e11	+	2.43637e11i	1.66011	+	0.958464i	0.972661	+	0.232230i	$0.0746023\pi$
$191$	4.21991e11	+	2.43637e11i	1.66011	+	0.958464i	0.687448	+	0.726234i	$0.258731\pi$
$192$	3.18111e10	−	7.19621e9i	0.121919	−	0.0275802i
$193$	9.86442e10	+	1.70857e11i	0.368371	+	0.638037i	0.989311	−	0.145821i	$-0.0465824\pi$
$193$	9.86442e10	+	1.70857e11i	0.368371	+	0.638037i	−0.620940	+	0.783858i	$0.713249\pi$
$194$	−9.60323e10	+	5.54443e10i	−0.349469	+	0.201766i
$195$	−2.28051e11	−	7.08260e10i	−0.808833	−	0.251200i
$196$	1.09434e11	−	1.89546e11i	0.378332	−	0.655290i
$197$			6.07492e10i			0.204743i	0.994746	+	0.102372i	$0.0326431\pi$
$197$			6.07492e10i			0.204743i	−0.994746	+	0.102372i	$0.967357\pi$
$198$	−2.71304e10	−	1.86508e10i	−0.0891517	−	0.0612873i
$199$	−3.52040e11			−1.12805			−0.564023	−	0.825759i	$-0.690747\pi$
$199$	−3.52040e11			−1.12805			−0.564023	+	0.825759i	$0.690747\pi$
$200$	6.71778e10	+	3.87851e10i	0.209931	+	0.121204i
$201$	6.21520e10	+	6.72433e10i	0.189441	+	0.204960i
$202$	2.14720e11	+	3.71907e11i	0.638435	+	1.10580i
$203$	−5.92064e11	+	3.41828e11i	−1.71747	+	0.991580i
$204$	−1.14495e11	+	1.05826e11i	−0.324067	+	0.299530i
$205$	−9.35973e10	+	1.62115e11i	−0.258520	+	0.447770i
$206$		−	2.64270e11i		−	0.712379i
$207$	2.57346e11	−	3.74350e11i	0.677121	−	0.984976i
$208$	1.47025e11			0.377637
$209$	2.64531e10	+	1.52727e10i	0.0663353	+	0.0382987i
$210$	7.61363e10	−	2.45149e11i	0.186421	−	0.600253i
$211$	1.94433e11	+	3.36769e11i	0.464899	+	0.805229i	0.999197	−	0.0400674i	$-0.0127573\pi$
$211$	1.94433e11	+	3.36769e11i	0.464899	+	0.805229i	−0.534298	+	0.845296i	$0.679424\pi$
$212$	3.26053e11	−	1.88247e11i	0.761392	−	0.439590i
$213$	1.31551e10	+	5.81527e10i	0.0300052	+	0.132639i
$214$	−2.48547e10	+	4.30495e10i	−0.0553782	+	0.0959179i
$215$			4.42930e11i			0.964145i
$216$	1.02893e11	+	1.30565e11i	0.218835	+	0.277689i
$217$	8.27072e10			0.171888
$218$	−2.98041e11	−	1.72074e11i	−0.605332	−	0.349488i
$219$	−1.64118e11	+	3.71262e10i	−0.325788	+	0.0736986i
$220$	−1.10524e10	−	1.91434e10i	−0.0214459	−	0.0371455i
$221$	−6.08670e11	+	3.51416e11i	−1.15457	+	0.666591i
$222$	−4.15822e11	−	1.29142e11i	−0.771156	−	0.239499i
$223$	−1.40716e11	+	2.43728e11i	−0.255164	+	0.441958i	−0.964940	−	0.262470i	$-0.915463\pi$
$223$	−1.40716e11	+	2.43728e11i	−0.255164	+	0.441958i	0.709776	+	0.704428i	$0.248796\pi$
$224$			1.58048e11i			0.280253i
$225$	−3.10654e10	+	3.94147e11i	−0.0538721	+	0.683511i
$226$	6.49402e11			1.10147
$227$	1.52112e11	+	8.78218e10i	0.252368	+	0.145704i	0.620848	−	0.783931i	$-0.286788\pi$
$227$	1.52112e11	+	8.78218e10i	0.252368	+	0.145704i	−0.368480	+	0.929636i	$0.620122\pi$
$228$	−1.04686e11	−	1.13262e11i	−0.169908	−	0.183827i
$229$	−2.08209e11	−	3.60628e11i	−0.330614	−	0.572641i	0.652018	−	0.758203i	$-0.273923\pi$
$229$	−2.08209e11	−	3.60628e11i	−0.330614	−	0.572641i	−0.982632	+	0.185563i	$0.940589\pi$
$230$	2.64144e11	−	1.52504e11i	0.410395	−	0.236941i
$231$	1.17160e11	−	1.08289e11i	0.178123	−	0.164636i
$232$	1.48627e11	−	2.57430e11i	0.221135	−	0.383018i
$233$		−	7.72485e11i		−	1.12489i	−0.826834	−	0.562446i	$-0.809861\pi$
$233$		−	7.72485e11i		−	1.12489i	0.826834	−	0.562446i	$-0.190139\pi$
$234$	3.22536e11	+	6.76411e11i	0.459726	+	0.964120i
$235$	−2.73302e11			−0.381333
$236$	−9.52385e10	−	5.49860e10i	−0.130093	−	0.0751090i
$237$	−8.83902e10	+	2.84606e11i	−0.118212	+	0.380629i
$238$	−3.77763e11	−	6.54305e11i	−0.494692	−	0.856832i
$239$	1.15387e11	−	6.66187e10i	0.147968	−	0.0854292i	−0.424188	−	0.905574i	$-0.639441\pi$
$239$	1.15387e11	−	6.66187e10i	0.147968	−	0.0854292i	0.572156	+	0.820145i	$0.306107\pi$
$240$	2.46266e10	+	1.08863e11i	0.0309277	+	0.136717i
$241$	1.17727e11	−	2.03909e11i	0.144807	−	0.250813i	−0.784494	−	0.620137i	$-0.787077\pi$
$241$	1.17727e11	−	2.03909e11i	0.144807	−	0.250813i	0.929301	+	0.369323i	$0.120411\pi$
$242$			5.73159e11i			0.690555i
$243$	−3.74963e11	+	7.59803e11i	−0.442545	+	0.896746i
$244$	−7.62826e11			−0.882016
$245$	6.48655e11	+	3.74501e11i	0.734824	+	0.424251i
$246$	5.72964e11	−	1.29614e11i	0.635992	−	0.143872i
$247$	−3.47630e11	−	6.02114e11i	−0.378123	−	0.654928i
$248$	−3.11433e10	+	1.79806e10i	−0.0331975	+	0.0191666i
$249$	7.18186e11	+	2.23048e11i	0.750309	+	0.233024i
$250$	−3.26315e11	+	5.65195e11i	−0.334147	+	0.578759i
$251$		−	1.26000e12i		−	1.26474i	−0.774665	−	0.632372i	$-0.782082\pi$
$251$		−	1.26000e12i		−	1.26474i	0.774665	−	0.632372i	$-0.217918\pi$
$252$	−7.27125e11	+	3.46719e11i	−0.715495	+	0.341173i
$253$	1.89563e11			0.182874
$254$	−3.13750e11	−	1.81144e11i	−0.296767	−	0.171338i
$255$	−3.62153e11	−	3.91819e11i	−0.335885	−	0.363400i
$256$	−3.43597e10	−	5.95128e10i	−0.0312500	−	0.0541266i
$257$	1.38027e12	−	7.96900e11i	1.23112	−	0.710785i	0.263853	−	0.964563i	$-0.415007\pi$
$257$	1.38027e12	−	7.96900e11i	1.23112	−	0.710785i	0.967262	+	0.253778i	$0.0816733\pi$
$258$	1.02074e12	−	9.43456e11i	0.892930	−	0.825321i
$259$	1.05498e12	−	1.82729e12i	0.905205	−	1.56786i
$260$			5.03143e11i			0.423472i
$261$	1.51040e12	+	1.19045e11i	1.24706	+	0.0982895i
$262$	−1.08750e12			−0.880891
$263$	−5.52204e11	−	3.18815e11i	−0.438855	−	0.253373i	0.264257	−	0.964452i	$-0.414873\pi$
$263$	−5.52204e11	−	3.18815e11i	−0.438855	−	0.253373i	−0.703112	+	0.711079i	$0.748207\pi$
$264$	−2.05743e10	+	6.62467e10i	−0.0160437	+	0.0516589i
$265$	6.44210e11	+	1.11580e12i	0.492944	+	0.853805i
$266$	6.47257e11	−	3.73694e11i	0.486036	−	0.280613i
$267$	1.98370e11	+	8.76902e11i	0.146191	+	0.646241i
$268$	9.64658e10	−	1.67084e11i	0.0697749	−	0.120854i
$269$		−	1.61700e12i		−	1.14802i	−0.818849	−	0.574009i	$-0.805387\pi$
$269$		−	1.61700e12i		−	1.14802i	0.818849	−	0.574009i	$-0.194613\pi$
$270$	−4.46815e11	+	3.52116e11i	−0.311393	+	0.245396i
$271$	−2.06167e12			−1.41050			−0.705249	−	0.708959i	$-0.749165\pi$
$271$	−2.06167e12			−1.41050			−0.705249	+	0.708959i	$0.749165\pi$
$272$	2.84492e11	+	1.64252e11i	0.191085	+	0.110323i
$273$	−3.54189e12	+	8.01234e11i	−2.33572	+	0.528380i
$274$	3.35101e11	+	5.80412e11i	0.216982	+	0.375823i
$275$	−1.42879e11	+	8.24914e10i	−0.0908460	+	0.0524500i
$276$	−9.14084e11	−	2.83888e11i	−0.570743	−	0.177256i
$277$	2.30665e11	−	3.99524e11i	0.141444	−	0.244988i	−0.786597	−	0.617467i	$-0.788159\pi$
$277$	2.30665e11	−	3.99524e11i	0.141444	−	0.244988i	0.928041	+	0.372479i	$0.121492\pi$
$278$			8.10569e11i			0.488164i
$279$	−1.51043e11	−	1.03834e11i	−0.0893469	−	0.0614215i
$280$	−5.40866e11			−0.314268
$281$	2.00247e12	+	1.15613e12i	1.14297	+	0.659894i	0.947164	−	0.320749i	$-0.103935\pi$
$281$	2.00247e12	+	1.15613e12i	1.14297	+	0.659894i	0.195805	+	0.980643i	$0.437268\pi$
$282$	5.82144e11	+	6.29832e11i	0.326426	+	0.353166i
$283$	−2.87921e11	−	4.98693e11i	−0.158614	−	0.274727i	0.775755	−	0.631034i	$-0.217369\pi$
$283$	−2.87921e11	−	4.98693e11i	−0.158614	−	0.274727i	−0.934369	+	0.356307i	$0.884036\pi$
$284$	1.08793e11	−	6.28118e10i	0.0588857	−	0.0339977i
$285$	3.87599e11	−	3.58252e11i	0.206138	−	0.190530i
$286$	−1.56352e11	+	2.70810e11i	−0.0817098	+	0.141526i
$287$			2.84668e12i			1.46194i
$288$	1.98421e11	−	2.88634e11i	0.100144	−	0.145675i
$289$	4.45631e11			0.221048
$290$	8.80965e11	+	5.08626e11i	0.429506	+	0.247975i
$291$	−3.53202e11	+	1.13727e12i	−0.169262	+	0.545002i
$292$	1.77266e11	+	3.07034e11i	0.0835049	+	0.144635i
$293$	4.99521e11	−	2.88398e11i	0.231321	−	0.133553i	−0.379860	−	0.925044i	$-0.624028\pi$
$293$	4.99521e11	−	2.88398e11i	0.231321	−	0.133553i	0.611181	+	0.791491i	$0.290695\pi$
$294$	−5.18611e11	−	2.29254e12i	−0.236105	−	1.04371i
$295$	1.88171e11	−	3.25921e11i	0.0842252	−	0.145882i
$296$			9.17416e11i			0.403745i
$297$	−3.49913e11	+	5.06737e10i	−0.151418	+	0.0219281i
$298$	−2.67483e12			−1.13819
$299$	−3.73669e12	−	2.15738e12i	−1.56362	−	0.902756i
$300$	8.12511e11	−	1.83804e11i	0.334367	−	0.0756394i
$301$	3.36782e12	+	5.83324e12i	1.36307	+	2.36090i
$302$	5.83454e11	−	3.36858e11i	0.232259	−	0.134095i
$303$	4.40433e12	+	1.36786e12i	1.72451	+	0.535583i
$304$	−1.62483e11	+	2.81428e11i	−0.0625805	+	0.108393i
$305$		−	2.61051e12i		−	0.989069i
$306$	−1.31559e11	+	1.66918e12i	−0.0490359	+	0.622151i
$307$	−8.36379e11			−0.306698			−0.153349	−	0.988172i	$-0.549006\pi$
$307$	−8.36379e11			−0.306698			−0.153349	+	0.988172i	$0.549006\pi$
$308$	−2.91115e11	−	1.68075e11i	−0.105029	−	0.0606387i
$309$	−1.92634e12	−	2.08415e12i	−0.683819	−	0.739837i
$310$	−6.15324e10	−	1.06577e11i	−0.0214929	−	0.0372268i
$311$	−2.78352e12	+	1.60706e12i	−0.956735	+	0.552371i	−0.895167	−	0.445732i	$-0.852944\pi$
$311$	−2.78352e12	+	1.60706e12i	−0.956735	+	0.552371i	−0.0615685	+	0.998103i	$0.519610\pi$
$312$	1.15950e12	−	1.07171e12i	0.392192	−	0.362497i
$313$	−2.68831e10	+	4.65629e10i	−0.00894865	+	0.0154995i	−0.870465	−	0.492230i	$-0.836182\pi$
$313$	−2.68831e10	+	4.65629e10i	−0.00894865	+	0.0154995i	0.861516	+	0.507730i	$0.169515\pi$
$314$			3.57932e12i			1.17261i
$315$	−1.18653e12	−	2.48834e12i	−0.382582	−	0.802336i
$316$	6.27917e11			0.199281
$317$	−1.89495e11	−	1.09405e11i	−0.0591972	−	0.0341775i	0.470109	−	0.882608i	$-0.344214\pi$
$317$	−1.89495e11	−	1.09405e11i	−0.0591972	−	0.0341775i	−0.529306	+	0.848431i	$0.677548\pi$
$318$	1.19921e12	−	3.86130e12i	0.368772	−	1.18740i
$319$	3.16113e11	+	5.47523e11i	0.0956948	+	0.165748i
$320$	2.03662e11	−	1.17584e11i	0.0606961	−	0.0350429i
$321$	1.17787e11	+	5.20681e11i	0.0345598	+	0.152773i
$322$	2.31913e12	−	4.01685e12i	0.669955	−	1.16040i
$323$		−	1.55345e12i		−	0.441859i
$324$	1.76319e12	+	2.79675e11i	0.493826	+	0.0783302i
$325$	3.75527e12			1.03568
$326$	−2.80179e12	−	1.61761e12i	−0.760934	−	0.439325i
$327$	−3.60478e12	+	8.15463e11i	−0.964141	+	0.218105i
$328$	−6.18868e11	−	1.07191e12i	−0.163016	−	0.282351i
$329$	−3.59931e12	+	2.07806e12i	−0.933769	+	0.539112i
$330$	−2.26707e11	−	7.04085e10i	−0.0579288	−	0.0179910i
$331$	2.22479e12	−	3.85345e12i	0.559949	−	0.969860i	−0.437551	−	0.899194i	$-0.644154\pi$
$331$	2.22479e12	−	3.85345e12i	0.559949	−	0.969860i	0.997500	−	0.0706667i	$-0.0225127\pi$
$332$		−	1.58451e12i		−	0.392831i
$333$	−4.22071e12	+	2.01258e12i	−1.03078	+	0.491510i
$334$	3.40862e12			0.820062
$335$	5.71786e11	+	3.30121e11i	0.135522	+	0.0782437i
$336$	1.15206e12	+	1.24644e12i	0.269017	+	0.291055i
$337$	−1.59864e12	−	2.76893e12i	−0.367791	−	0.637033i	0.621429	−	0.783471i	$-0.286553\pi$
$337$	−1.59864e12	−	2.76893e12i	−0.367791	−	0.637033i	−0.989220	+	0.146438i	$0.953219\pi$
$338$	3.46261e12	−	1.99914e12i	0.784910	−	0.453168i
$339$	5.12147e12	−	4.73370e12i	1.14392	−	1.05731i
$340$	−5.62095e11	+	9.73578e11i	−0.123713	+	0.214277i
$341$		−	7.64851e10i		−	0.0165884i
$342$	−1.65120e12	−	1.30142e11i	−0.352914	−	0.0278155i
$343$	3.86358e12			0.813803
$344$	−2.53630e12	−	1.46433e12i	−0.526512	−	0.303982i
$345$	9.71510e11	−	3.12814e12i	0.198770	−	0.640016i
$346$	9.68279e11	+	1.67711e12i	0.195263	+	0.338206i
$347$	−4.84815e12	+	2.79908e12i	−0.963671	+	0.556376i	−0.897301	−	0.441419i	$-0.854475\pi$
$347$	−4.84815e12	+	2.79908e12i	−0.963671	+	0.556376i	−0.0663700	+	0.997795i	$0.521142\pi$
$348$	−7.04347e11	−	3.11359e12i	−0.138004	−	0.610051i
$349$	−1.74422e12	+	3.02108e12i	−0.336880	+	0.583493i	−0.983844	−	0.179027i	$-0.942705\pi$
$349$	−1.74422e12	+	3.02108e12i	−0.336880	+	0.583493i	0.646964	+	0.762520i	$0.276038\pi$
$350$			4.03683e12i			0.768599i
$351$	7.47424e12	+	2.98340e12i	1.40291	+	0.559985i
$352$	1.46158e11			0.0270464
$353$	−6.58504e11	−	3.80188e11i	−0.120139	−	0.0693624i	0.438726	−	0.898621i	$-0.355430\pi$
$353$	−6.58504e11	−	3.80188e11i	−0.120139	−	0.0693624i	−0.558865	+	0.829258i	$0.688763\pi$
$354$	−1.15190e12	+	2.60580e11i	−0.207205	+	0.0468732i
$355$	2.14952e11	+	3.72307e11i	0.0381241	+	0.0660328i
$356$	1.64052e12	−	9.47157e11i	0.286901	−	0.165643i
$357$	−7.74864e12	−	2.40650e12i	−1.33624	−	0.414997i
$358$	−2.55050e12	+	4.41760e12i	−0.433721	+	0.751227i
$359$			5.16502e12i			0.866163i	0.901355	+	0.433082i	$0.142574\pi$
$359$			5.16502e12i			0.866163i	−0.901355	+	0.433082i	$0.857426\pi$
$360$	9.87750e11	+	6.79028e11i	0.163356	+	0.112299i
$361$	−4.59435e12			−0.749356
$362$	−3.99098e12	−	2.30420e12i	−0.642003	−	0.370661i
$363$	4.17793e12	+	4.52018e12i	0.662870	+	0.717171i
$364$	3.82566e12	+	6.62623e12i	0.598686	+	1.03695i
$365$	−1.05072e12	+	6.06633e11i	−0.162189	+	0.0936401i
$366$	−6.01598e12	+	5.56048e12i	−0.916012	+	0.846656i
$367$	−1.98523e12	+	3.43852e12i	−0.298182	+	0.516466i	−0.975720	−	0.219022i	$-0.929713\pi$
$367$	−1.98523e12	+	3.43852e12i	−0.298182	+	0.516466i	0.677538	+	0.735487i	$0.263047\pi$
$368$			2.01672e12i			0.298818i
$369$	3.57385e12	−	5.19871e12i	0.522401	−	0.759912i
$370$	−3.13954e12			−0.452749
$371$	1.69681e13	+	9.79652e12i	2.41414	+	1.39381i
$372$	−1.14543e11	+	3.68816e11i	−0.0160789	+	0.0517720i
$373$	6.46389e11	+	1.11958e12i	0.0895261	+	0.155064i	0.907311	−	0.420460i	$-0.138131\pi$
$373$	6.46389e11	+	1.11958e12i	0.0895261	+	0.155064i	−0.817785	+	0.575524i	$0.804798\pi$
$374$	−6.05082e11	+	3.49344e11i	−0.0826906	+	0.0477414i
$375$	1.54642e12	+	6.83599e12i	0.208531	+	0.921818i
$376$	9.03542e11	−	1.56498e12i	0.120229	−	0.208243i
$377$		−	1.43904e13i		−	1.88959i
$378$	−3.20709e12	+	8.03462e12i	−0.415577	+	1.04113i
$379$	−9.89663e12			−1.26558			−0.632792	−	0.774322i	$-0.718091\pi$
$379$	−9.89663e12			−1.26558			−0.632792	+	0.774322i	$0.718091\pi$
$380$	−9.63091e11	−	5.56041e11i	−0.121548	−	0.0701760i
$381$	−3.79479e12	+	8.58444e11i	−0.472675	+	0.106927i
$382$	−5.51287e12	−	9.54857e12i	−0.677737	−	1.17387i
$383$	8.31726e12	−	4.80197e12i	1.00922	−	0.582674i	0.0982580	−	0.995161i	$-0.468673\pi$
$383$	8.31726e12	−	4.80197e12i	1.00922	−	0.582674i	0.910964	+	0.412487i	$0.135340\pi$
$384$	−7.04784e11	−	2.18885e11i	−0.0844111	−	0.0262156i
$385$	5.75179e11	−	9.96240e11i	0.0679985	−	0.117777i
$386$		−	4.46413e12i		−	0.520955i
$387$	1.17287e12	−	1.48810e13i	0.135113	−	1.71426i
$388$	2.50912e12			0.285340
$389$	2.25570e12	+	1.30233e12i	0.253241	+	0.146209i	0.621247	−	0.783614i	$-0.286626\pi$
$389$	2.25570e12	+	1.30233e12i	0.253241	+	0.146209i	−0.368006	+	0.929823i	$0.619960\pi$
$390$	3.66756e12	+	3.96800e12i	0.406495	+	0.439794i
$391$	−4.82031e12	−	8.34903e12i	−0.527462	−	0.913591i
$392$	−4.28893e12	+	2.47621e12i	−0.463360	+	0.267521i
$393$	−8.57649e12	+	7.92712e12i	−0.914844	+	0.845576i
$394$	6.87299e11	−	1.19044e12i	0.0723876	−	0.125379i
$395$			2.14883e12i			0.223469i
$396$	3.20635e11	+	6.72424e11i	0.0329257	+	0.0690505i
$397$	−3.60275e12			−0.365327			−0.182663	−	0.983176i	$-0.558472\pi$
$397$	−3.60275e12			−0.365327			−0.182663	+	0.983176i	$0.558472\pi$
$398$	6.89855e12	+	3.98288e12i	0.690785	+	0.398825i
$399$	2.38058e12	−	7.66518e12i	0.235407	−	0.757980i
$400$	−8.77607e11	−	1.52006e12i	−0.0857038	−	0.148443i
$401$	8.81130e12	−	5.08721e12i	0.849803	−	0.490634i	−0.0107814	−	0.999942i	$-0.503432\pi$
$401$	8.81130e12	−	5.08721e12i	0.849803	−	0.490634i	0.860584	+	0.509308i	$0.170099\pi$
$402$	−4.57153e11	−	2.02086e12i	−0.0435443	−	0.192489i
$403$	−8.70462e11	+	1.50768e12i	−0.0818888	+	0.141836i
$404$		−	9.71714e12i		−	0.902883i
$405$	−9.57093e11	+	6.03392e12i	−0.0878373	+	0.553763i
$406$	1.54694e13			1.40231
$407$	−1.68982e12	−	9.75618e11i	−0.151310	−	0.0873590i
$408$	3.44091e12	−	7.78393e11i	0.304350	−	0.0688490i
$409$	−1.65885e12	−	2.87321e12i	−0.144941	−	0.251044i	0.784410	−	0.620242i	$-0.212966\pi$
$409$	−1.65885e12	−	2.87321e12i	−0.144941	−	0.251044i	−0.929351	+	0.369198i	$0.879632\pi$
$410$	3.66825e12	−	2.11786e12i	0.316621	−	0.182801i
$411$	6.87356e12	+	2.13473e12i	0.586101	+	0.182026i
$412$	−2.98987e12	+	5.17860e12i	−0.251864	+	0.436241i
$413$		−	5.72304e12i		−	0.476296i
$414$	−9.27822e12	+	4.42418e12i	−0.762892	+	0.363774i
$415$	5.42246e12			0.440510
$416$	−2.88109e12	−	1.66340e12i	−0.231254	−	0.133515i
$417$	5.90850e12	+	6.39251e12i	0.468594	+	0.506980i
$418$	−3.45581e11	−	5.98564e11i	−0.0270813	−	0.0469061i
$419$	−1.29084e13	+	7.45265e12i	−0.999542	+	0.577086i	−0.908113	−	0.418725i	$-0.862477\pi$
$419$	−1.29084e13	+	7.45265e12i	−0.999542	+	0.577086i	−0.0914295	+	0.995812i	$0.529144\pi$
$420$	−4.26551e12	+	3.94254e12i	−0.326381	+	0.301669i
$421$	−8.92356e12	+	1.54561e13i	−0.674726	+	1.16866i	0.301822	+	0.953364i	$0.402405\pi$
$421$	−8.92356e12	+	1.54561e13i	−0.674726	+	1.16866i	−0.976549	+	0.215296i	$0.930928\pi$
$422$		−	8.79905e12i		−	0.657467i
$423$	9.18208e12	+	7.23702e11i	0.678015	+	0.0534390i
$424$	−8.51907e12			−0.621674
$425$	7.26643e12	+	4.19527e12i	0.524054	+	0.302563i
$426$	4.00136e11	−	1.28839e12i	0.0285207	−	0.0918331i
$427$	−1.98491e13	−	3.43796e13i	−1.39830	−	2.42193i
$428$	9.74100e11	−	5.62397e11i	0.0678242	−	0.0391583i
$429$	7.40958e11	+	3.27543e12i	0.0509926	+	0.225415i
$430$	5.01118e12	−	8.67961e12i	0.340877	−	0.590416i
$431$			2.19946e13i			1.47887i	0.673229	+	0.739434i	$0.264907\pi$
$431$			2.19946e13i			1.47887i	−0.673229	+	0.739434i	$0.735093\pi$
$432$	−5.39106e11	−	3.72265e12i	−0.0358307	−	0.247419i
$433$	7.98949e12			0.524904			0.262452	−	0.964945i	$-0.415469\pi$
$433$	7.98949e12			0.524904			0.262452	+	0.964945i	$0.415469\pi$
$434$	−1.62072e12	−	9.35725e11i	−0.105259	−	0.0607715i
$435$	1.06552e13	−	2.41039e12i	0.684094	−	0.154754i
$436$	3.89359e12	+	6.74390e12i	0.247126	+	0.428034i
$437$	8.25910e12	−	4.76839e12i	0.518233	−	0.299202i
$438$	3.63607e12	+	1.12926e12i	0.225560	+	0.0700523i
$439$	6.52586e12	−	1.13031e13i	0.400235	−	0.693228i	−0.593519	−	0.804820i	$-0.702262\pi$
$439$	6.52586e12	−	1.13031e13i	0.400235	−	0.693228i	0.993754	+	0.111592i	$0.0355951\pi$
$440$			5.00177e11i			0.0303291i
$441$	−2.08011e13	−	1.42997e13i	−1.24707	−	0.857301i
$442$	1.59033e13			0.942703
$443$	−7.22063e12	−	4.16883e12i	−0.423210	−	0.244341i	0.273240	−	0.961946i	$-0.411905\pi$
$443$	−7.22063e12	−	4.16883e12i	−0.423210	−	0.244341i	−0.696450	+	0.717605i	$0.745238\pi$
$444$	6.68733e12	+	7.23514e12i	0.387559	+	0.419307i
$445$	3.24132e12	+	5.61413e12i	0.185747	+	0.321723i
$446$	5.51493e12	−	3.18405e12i	0.312511	−	0.180428i
$447$	−2.10949e13	+	1.94977e13i	−1.18206	+	1.09256i
$448$	1.78811e12	−	3.09710e12i	0.0990842	−	0.171619i
$449$			2.29001e12i			0.125489i	0.998030	+	0.0627445i	$0.0199853\pi$
$449$			2.29001e12i			0.125489i	−0.998030	+	0.0627445i	$0.980015\pi$
$450$	5.06802e12	−	7.37221e12i	0.274647	−	0.399517i
$451$	2.63252e12			0.141088
$452$	−1.27256e13	−	7.34715e12i	−0.674508	−	0.389427i
$453$	2.14592e12	−	6.90959e12i	0.112492	−	0.362211i
$454$	−1.98718e12	−	3.44190e12i	−0.103029	−	0.178451i
$455$	−2.26760e13	+	1.30920e13i	−1.16281	+	0.671350i
$456$	7.70008e11	+	3.40385e12i	0.0390545	+	0.172642i
$457$	−1.45156e13	+	2.51418e13i	−0.728207	+	1.26129i	0.229434	+	0.973324i	$0.426313\pi$
$457$	−1.45156e13	+	2.51418e13i	−0.728207	+	1.26129i	−0.957640	+	0.287967i	$0.907021\pi$
$458$			9.42245e12i			0.467559i
$459$	1.11296e13	+	1.41229e13i	0.546283	+	0.693201i
$460$	−6.90153e12			−0.335086
$461$	−1.25299e13	−	7.23412e12i	−0.601785	−	0.347441i	0.167958	−	0.985794i	$-0.446283\pi$
$461$	−1.25299e13	−	7.23412e12i	−0.601785	−	0.347441i	−0.769744	+	0.638353i	$0.779616\pi$
$462$	−3.52101e12	+	7.96511e11i	−0.167285	+	0.0378427i
$463$	1.56310e13	+	2.70737e13i	0.734652	+	1.27245i	0.954876	+	0.297005i	$0.0959877\pi$
$463$	1.56310e13	+	2.70737e13i	0.734652	+	1.27245i	−0.220224	+	0.975449i	$0.570679\pi$
$464$	−5.82497e12	+	3.36305e12i	−0.270834	+	0.156366i
$465$	−1.26215e12	−	3.91986e11i	−0.0580557	−	0.0180304i
$466$	−8.73967e12	+	1.51376e13i	−0.397709	+	0.688852i
$467$		−	1.76520e12i		−	0.0794714i	−0.999210	−	0.0397357i	$-0.987348\pi$
$467$		−	1.76520e12i		−	0.0794714i	0.999210	−	0.0397357i	$-0.0126516\pi$
$468$	1.33232e12	−	1.69040e13i	0.0593442	−	0.752939i
$469$	1.00403e13			0.442470
$470$	5.35561e12	+	3.09206e12i	0.233518	+	0.134821i
$471$	2.60908e13	+	2.82281e13i	1.12560	+	1.21780i
$472$	1.24419e12	+	2.15500e12i	0.0531101	+	0.0919894i
$473$	5.39441e12	−	3.11446e12i	0.227844	−	0.131546i
$474$	4.95203e12	−	4.57709e12i	0.206963	−	0.191292i
$475$	−4.15009e12	+	7.18816e12i	−0.171628	+	0.297269i
$476$			1.70956e13i			0.699600i
$477$	−1.86887e13	−	3.91933e13i	−0.756812	−	1.58716i
$478$	−3.01482e12			−0.120815
$479$	−1.87360e13	−	1.08173e13i	−0.743019	−	0.428982i	0.0801467	−	0.996783i	$-0.474461\pi$
$479$	−1.87360e13	−	1.08173e13i	−0.743019	−	0.428982i	−0.823166	+	0.567801i	$0.807794\pi$
$480$	7.49060e11	−	2.41188e12i	0.0293975	−	0.0946563i
$481$	2.22066e13	+	3.84630e13i	0.862496	+	1.49389i
$482$	−4.61393e12	+	2.66385e12i	−0.177352	+	0.102394i
$483$	−1.09904e13	−	4.85835e13i	−0.418098	−	1.84822i
$484$	6.48455e12	−	1.12316e13i	0.244148	−	0.422877i
$485$			8.58661e12i			0.319973i
$486$	1.59439e13	−	1.06468e13i	0.588050	−	0.392679i
$487$	3.23621e13			1.18139			0.590693	−	0.806897i	$-0.298855\pi$
$487$	3.23621e13			1.18139			0.590693	+	0.806897i	$0.298855\pi$
$488$	1.49483e13	+	8.63039e12i	0.540122	+	0.311840i
$489$	−3.38874e13	+	7.66590e12i	−1.21198	+	0.274169i
$490$	−8.47400e12	−	1.46774e13i	−0.299991	−	0.519599i
$491$	−3.67133e12	+	2.11965e12i	−0.128652	+	0.0742772i	−0.562945	−	0.826495i	$-0.690332\pi$
$491$	−3.67133e12	+	2.11965e12i	−0.128652	+	0.0742772i	0.434293	+	0.900772i	$0.356998\pi$
$492$	−1.26942e13	−	3.94244e12i	−0.440330	−	0.136754i
$493$	1.60766e13	−	2.78454e13i	0.552025	−	0.956135i
$494$			1.57320e13i			0.534747i
$495$	−2.30114e12	+	1.09726e12i	−0.0774314	+	0.0369220i
$496$	8.13708e11			0.0271057
$497$	5.66170e12	+	3.26878e12i	0.186709	+	0.107796i
$498$	−1.15500e13	−	1.24962e13i	−0.377082	−	0.407972i
$499$	−2.96179e13	−	5.12997e13i	−0.957308	−	1.65811i	−0.728996	−	0.684518i	$-0.760013\pi$
$499$	−2.96179e13	−	5.12997e13i	−0.957308	−	1.65811i	−0.228312	−	0.973588i	$-0.573321\pi$
$500$	1.27889e13	−	7.38367e12i	0.409245	−	0.236278i
$501$	2.68819e13	−	2.48465e13i	0.851670	−	0.787185i
$502$	−1.42553e13	+	2.46909e13i	−0.447154	+	0.774494i
$503$		−	1.50892e12i		−	0.0468627i	−0.999725	−	0.0234314i	$-0.992541\pi$
$503$		−	1.50892e12i		−	0.0468627i	0.999725	−	0.0234314i	$-0.00745911\pi$
$504$	1.81714e13	+	1.43221e12i	0.558772	+	0.0440406i
$505$	3.32536e13			1.01247
$506$	−3.71466e12	−	2.14466e12i	−0.111987	−	0.0646556i
$507$	1.27353e13	−	4.10061e13i	0.380163	−	1.22408i
$508$	4.09881e12	+	7.09936e12i	0.121155	+	0.209846i
$509$	4.82293e13	−	2.78452e13i	1.41163	−	0.815007i	0.416091	−	0.909323i	$-0.363400\pi$
$509$	4.82293e13	−	2.78452e13i	1.41163	−	0.815007i	0.995542	+	0.0943159i	$0.0300664\pi$
$510$	2.66378e12	+	1.17754e13i	0.0772054	+	0.341290i
$511$	−9.22510e12	+	1.59783e13i	−0.264769	+	0.458593i
$512$			1.55494e12i			0.0441942i
$513$	−1.39707e13	+	1.10098e13i	−0.393217	+	0.309878i
$514$	−3.60636e13			−1.00520
$515$	−1.77220e13	−	1.02318e13i	−0.489189	−	0.282433i
$516$	−3.06763e13	+	6.93951e12i	−0.838601	+	0.189706i
$517$	1.92173e12	+	3.32853e12i	0.0520282	+	0.0901156i
$518$	−4.13468e13	+	2.38716e13i	−1.10865	+	0.640077i
$519$	1.98612e13	+	6.16833e12i	0.527436	+	0.163806i
$520$	5.69241e12	−	9.85954e12i	0.149720	−	0.259322i
$521$		−	1.96299e13i		−	0.511363i	−0.966761	−	0.255681i	$-0.917700\pi$
$521$		−	1.96299e13i		−	0.511363i	0.966761	−	0.255681i	$-0.0822998\pi$
$522$	−2.82508e13	−	1.94210e13i	−0.728916	−	0.501093i
$523$	2.15578e11			0.00550931			0.00275465	−	0.999996i	$-0.499123\pi$
$523$	2.15578e11			0.00550931			0.00275465	+	0.999996i	$0.499123\pi$
$524$	2.13105e13	+	1.23036e13i	0.539433	+	0.311442i
$525$	2.94257e13	+	3.18362e13i	0.737786	+	0.798224i
$526$	7.21396e12	+	1.24949e13i	0.179162	+	0.310317i
$527$	−3.36868e12	+	1.94491e12i	−0.0828717	+	0.0478460i
$528$	1.15267e12	−	1.06539e12i	0.0280889	−	0.0259621i
$529$	8.87916e12	−	1.53792e13i	0.214335	−	0.371240i
$530$		−	2.91536e13i		−	0.697129i
$531$	−7.18497e12	+	1.04516e13i	−0.170197	+	0.247578i
$532$	−1.69115e13			−0.396847
$533$	−5.18925e13	−	2.99602e13i	−1.20634	−	0.696479i
$534$	6.03377e12	−	1.94280e13i	0.138958	−	0.447427i
$535$	1.92461e12	+	3.33352e12i	0.0439111	+	0.0760562i
$536$	−3.78067e12	+	2.18277e12i	−0.0854564	+	0.0493383i
$537$	1.20869e13	+	5.34306e13i	0.270672	+	1.19652i
$538$	−1.82943e13	+	3.16866e13i	−0.405886	+	0.703015i
$539$		−	1.05332e13i		−	0.231536i
$540$	1.27395e13	−	1.84491e12i	0.277449	−	0.0401796i
$541$	2.73330e13			0.589795			0.294898	−	0.955529i	$-0.404714\pi$
$541$	2.73330e13			0.589795			0.294898	+	0.955529i	$0.404714\pi$
$542$	4.04003e13	+	2.33251e13i	0.863751	+	0.498687i
$543$	−4.82707e13	+	1.09196e13i	−1.02255	+	0.231318i
$544$	−3.71659e12	−	6.43733e12i	−0.0780100	−	0.135117i
$545$	−2.30787e13	+	1.33245e13i	−0.479986	+	0.277120i
$546$	7.84715e13	+	2.43710e13i	1.61714	+	0.502238i
$547$	9.95038e12	−	1.72346e13i	0.203190	−	0.351936i	−0.746364	−	0.665538i	$-0.768202\pi$
$547$	9.95038e12	−	1.72346e13i	0.203190	−	0.351936i	0.949555	+	0.313602i	$0.101536\pi$
$548$		−	1.51649e13i		−	0.306858i
$549$	−6.91261e12	+	8.77048e13i	−0.138605	+	1.75858i
$550$	3.73314e12			0.0741755
$551$	2.75455e13	+	1.59034e13i	0.542366	+	0.313135i
$552$	1.47005e13	+	1.59047e13i	0.286838	+	0.310335i
$553$	1.63387e13	+	2.82994e13i	0.315930	+	0.547208i
$554$	−9.04020e12	+	5.21936e12i	−0.173232	+	0.100016i
$555$	−2.47598e13	+	2.28851e13i	−0.470200	+	0.434598i
$556$	9.17054e12	−	1.58838e13i	0.172592	−	0.298938i
$557$			2.12438e13i			0.396238i	0.980178	+	0.198119i	$0.0634832\pi$
$557$			2.12438e13i			0.396238i	−0.980178	+	0.198119i	$0.936517\pi$
$558$	1.78507e12	+	3.74359e12i	0.0329978	+	0.0692017i
$559$	−1.41780e14			−2.59751
$560$	1.05988e13	+	6.11920e12i	0.192449	+	0.111110i
$561$	−2.22546e12	+	7.16571e12i	−0.0400503	+	0.128957i
$562$	−2.61602e13	−	4.53107e13i	−0.466615	−	0.808201i
$563$	4.51059e13	−	2.60419e13i	0.797428	−	0.460396i	−0.0451427	−	0.998981i	$-0.514374\pi$
$563$	4.51059e13	−	2.60419e13i	0.797428	−	0.460396i	0.842571	+	0.538585i	$0.181041\pi$
$564$	−4.28191e12	−	1.89283e13i	−0.0750312	−	0.331678i
$565$	2.51431e13	−	4.35491e13i	0.436693	−	0.756375i
$566$			1.30298e13i			0.224314i
$567$	3.32744e13	+	8.67421e13i	0.567799	+	1.48018i
$568$	−2.84254e12			−0.0480800
$569$	2.96469e13	+	1.71166e13i	0.497070	+	0.286983i	0.727503	−	0.686105i	$-0.240681\pi$
$569$	2.96469e13	+	1.71166e13i	0.497070	+	0.286983i	−0.230433	+	0.973088i	$0.574014\pi$
$570$	−1.16485e13	+	2.63509e12i	−0.193596	+	0.0437947i
$571$	1.08864e13	+	1.88559e13i	0.179352	+	0.310646i	0.941659	−	0.336569i	$-0.109267\pi$
$571$	1.08864e13	+	1.88559e13i	0.179352	+	0.310646i	−0.762307	+	0.647216i	$0.775933\pi$
$572$	6.12774e12	−	3.53785e12i	0.100074	−	0.0577776i
$573$	−1.13079e14	−	3.51192e13i	−1.83067	−	0.568554i
$574$	3.22065e13	−	5.57832e13i	0.516873	−	0.895250i
$575$			5.15105e13i			0.819514i
$576$	−7.15376e12	+	3.41116e12i	−0.112829	+	0.0538010i
$577$	−3.17642e13			−0.496659			−0.248329	−	0.968676i	$-0.579882\pi$
$577$	−3.17642e13			−0.496659			−0.248329	+	0.968676i	$0.579882\pi$
$578$	−8.73256e12	−	5.04174e12i	−0.135364	−	0.0781523i
$579$	−3.25404e13	−	3.52061e13i	−0.500070	−	0.541034i
$580$	−1.15089e13	−	1.99340e13i	−0.175345	−	0.303706i
$581$	7.14120e13	−	4.12298e13i	1.07868	−	0.622774i
$582$	1.97880e13	−	1.82898e13i	0.296338	−	0.273901i
$583$	9.05953e12	−	1.56916e13i	0.134513	−	0.232983i
$584$		−	8.02216e12i		−	0.118094i
$585$	5.78481e13	+	4.55940e12i	0.844325	+	0.0665470i
$586$	−1.30514e13			−0.188873
$587$	−8.43399e13	−	4.86937e13i	−1.21016	−	0.698686i	−0.247366	−	0.968922i	$-0.579565\pi$
$587$	−8.43399e13	−	4.86937e13i	−1.21016	−	0.698686i	−0.962794	+	0.270236i	$0.912898\pi$
$588$	−1.57745e13	+	5.07919e13i	−0.224424	+	0.722616i
$589$	−1.92396e12	−	3.33239e12i	−0.0271406	−	0.0470088i
$590$	−7.37476e12	+	4.25782e12i	−0.103154	+	0.0595562i
$591$	−3.25712e12	−	1.43982e13i	−0.0451749	−	0.199697i
$592$	1.03794e13	−	1.79776e13i	0.142746	−	0.247243i
$593$		−	1.04993e13i		−	0.143182i	−0.997434	−	0.0715911i	$-0.977192\pi$
$593$		−	1.04993e13i		−	0.143182i	0.997434	−	0.0715911i	$-0.0228077\pi$
$594$	7.43018e12	+	2.96582e12i	0.100477	+	0.0401063i
$595$	−5.85039e13			−0.784513
$596$	5.24157e13	+	3.02622e13i	0.696996	+	0.402411i
$597$	8.34375e13	−	1.88750e13i	1.10025	−	0.248894i
$598$	4.88159e13	+	8.45516e13i	0.638345	+	1.10565i
$599$	7.52937e12	−	4.34708e12i	0.0976393	−	0.0563721i	−0.450385	−	0.892834i	$-0.648713\pi$
$599$	7.52937e12	−	4.34708e12i	0.0976393	−	0.0563721i	0.548025	+	0.836462i	$0.315380\pi$
$600$	−1.80014e13	−	5.59071e12i	−0.231499	−	0.0718970i
$601$	1.59976e13	−	2.77087e13i	0.204025	−	0.353382i	−0.745797	−	0.666174i	$-0.767931\pi$
$601$	1.59976e13	−	2.77087e13i	0.204025	−	0.353382i	0.949822	+	0.312792i	$0.101264\pi$
$602$		−	1.52410e14i		−	1.92767i
$603$	−1.83360e13	−	1.26051e13i	−0.229995	−	0.158110i
$604$	−1.52444e13			−0.189639
$605$	3.84362e13	+	2.21912e13i	0.474202	+	0.273781i
$606$	−7.08313e13	−	7.66336e13i	−0.866686	−	0.937684i
$607$	3.54173e13	+	6.13446e13i	0.429806	+	0.744446i	0.996856	−	0.0792376i	$-0.0252486\pi$
$607$	3.54173e13	+	6.13446e13i	0.429806	+	0.744446i	−0.567050	+	0.823684i	$0.691915\pi$
$608$	6.36799e12	−	3.67656e12i	0.0766451	−	0.0442511i
$609$	1.21998e14	−	1.12761e14i	1.45636	−	1.34609i
$610$	−2.95346e13	+	5.11554e13i	−0.349689	+	0.605678i
$611$		−	8.74832e13i		−	1.02735i
$612$	2.14626e13	−	3.12207e13i	0.249992	−	0.363651i
$613$	−1.29701e14			−1.49845			−0.749225	−	0.662315i	$-0.769574\pi$
$613$	−1.29701e14			−1.49845			−0.749225	+	0.662315i	$0.769574\pi$
$614$	1.63896e13	+	9.46255e12i	0.187814	+	0.108434i
$615$	1.34917e13	−	4.34414e13i	0.153352	−	0.493775i
$616$	3.80310e12	+	6.58717e12i	0.0428780	+	0.0742669i
$617$	−5.68113e13	+	3.28000e13i	−0.635344	+	0.366816i	−0.782819	−	0.622250i	$-0.786219\pi$
$617$	−5.68113e13	+	3.28000e13i	−0.635344	+	0.366816i	0.147475	+	0.989066i	$0.452885\pi$
$618$	1.41691e13	+	6.26349e13i	0.157180	+	0.694822i
$619$	6.02727e13	−	1.04395e14i	0.663235	−	1.14876i	−0.316525	−	0.948584i	$-0.602516\pi$
$619$	6.02727e13	−	1.04395e14i	0.663235	−	1.14876i	0.979761	−	0.200173i	$-0.0641505\pi$
$620$			2.78464e12i			0.0303956i
$621$	−4.09229e13	+	1.02523e14i	−0.443107	+	1.11010i
$622$	7.27274e13			0.781171
$623$	8.53744e13	+	4.92909e13i	0.909677	+	0.525202i
$624$	−3.48466e13	+	7.88288e12i	−0.368330	+	0.0833224i
$625$	−7.42533e12	−	1.28610e13i	−0.0778602	−	0.134858i
$626$	1.05360e12	−	6.08295e11i	0.0109598	−	0.00632765i
$627$	−7.08853e12	−	2.20149e12i	−0.0731507	−	0.0227185i
$628$	4.04954e13	−	7.01401e13i	0.414579	−	0.718072i
$629$			9.92341e13i			1.00788i
$630$	−4.90124e12	+	6.21853e13i	−0.0493860	+	0.626592i
$631$	1.02330e14			1.02296			0.511478	−	0.859296i	$-0.329098\pi$
$631$	1.02330e14			1.02296			0.511478	+	0.859296i	$0.329098\pi$
$632$	−1.23046e13	−	7.10407e12i	−0.122034	−	0.0704566i
$633$	−6.41391e13	−	6.93932e13i	−0.631109	−	0.682808i
$634$	2.47555e12	+	4.28778e12i	0.0241672	+	0.0418587i
$635$	−2.42951e13	+	1.40268e13i	−0.235315	+	0.135859i
$636$	−6.71851e13	+	6.20982e13i	−0.645636	+	0.596751i
$637$	−1.19877e14	+	2.07632e14i	−1.14298	+	1.97969i
$638$		−	1.43056e13i		−	0.135333i
$639$	−6.23582e12	−	1.30775e13i	−0.0585315	−	0.122750i
$640$	−5.32127e12			−0.0495581
$641$	1.25241e13	+	7.23077e12i	0.115732	+	0.0668182i	0.556749	−	0.830681i	$-0.312049\pi$
$641$	1.25241e13	+	7.23077e12i	0.115732	+	0.0668182i	−0.441016	+	0.897499i	$0.645382\pi$
$642$	3.58269e12	−	1.15358e13i	0.0328499	−	0.105773i
$643$	8.42850e12	+	1.45986e13i	0.0766824	+	0.132818i	0.901817	−	0.432119i	$-0.142234\pi$
$643$	8.42850e12	+	1.45986e13i	0.0766824	+	0.132818i	−0.825134	+	0.564937i	$0.808901\pi$
$644$	−9.08909e13	+	5.24759e13i	−0.820524	+	0.473730i
$645$	−2.37481e13	−	1.04979e14i	−0.212731	−	0.940384i
$646$	−1.75753e13	+	3.04412e13i	−0.156221	+	0.270582i
$647$			1.50340e14i			1.32603i	0.748607	+	0.663014i	$0.230723\pi$
$647$			1.50340e14i			1.32603i	−0.748607	+	0.663014i	$0.769277\pi$
$648$	−3.13872e13	−	2.54287e13i	−0.274712	−	0.222561i
$649$	−5.29250e12			−0.0459660
$650$	−7.35880e13	−	4.24861e13i	−0.634220	−	0.366167i
$651$	−1.96025e13	+	4.43442e12i	−0.167651	+	0.0379256i
$652$	3.66024e13	+	6.33972e13i	0.310650	+	0.538062i
$653$	2.15063e13	−	1.24167e13i	0.181134	−	0.104578i	−0.406691	−	0.913566i	$-0.633318\pi$
$653$	2.15063e13	−	1.24167e13i	0.181134	−	0.104578i	0.587825	+	0.808988i	$0.299984\pi$
$654$	7.98649e13	+	2.48037e13i	0.667525	+	0.207314i
$655$	−4.21050e13	+	7.29280e13i	−0.349243	+	0.604906i
$656$			2.80068e13i			0.230539i
$657$	3.69072e13	−	1.75986e13i	0.301498	−	0.143765i
$658$	9.40423e13			0.762419
$659$	−6.30385e13	−	3.63953e13i	−0.507199	−	0.292832i	0.224482	−	0.974478i	$-0.427931\pi$
$659$	−6.30385e13	−	3.63953e13i	−0.507199	−	0.292832i	−0.731682	+	0.681646i	$0.761264\pi$
$660$	3.64595e12	+	3.94461e12i	0.0291132	+	0.0314981i
$661$	−2.85777e13	−	4.94981e13i	−0.226475	−	0.392266i	0.730286	−	0.683142i	$-0.239387\pi$
$661$	−2.85777e13	−	4.94981e13i	−0.226475	−	0.392266i	−0.956761	+	0.290875i	$0.906053\pi$
$662$	−8.71935e13	+	5.03412e13i	−0.685795	+	0.395944i
$663$	1.25420e14	−	1.15924e14i	0.979038	−	0.904909i
$664$	−1.79267e13	+	3.10500e13i	−0.138887	+	0.240559i
$665$		−	5.78737e13i		−	0.445014i
$666$	1.05478e14	+	8.31348e12i	0.804994	+	0.0634471i
$667$	1.97391e14			1.49520
$668$	−6.67951e13	−	3.85642e13i	−0.502183	−	0.289936i
$669$	2.02837e13	−	6.53109e13i	0.151362	−	0.487366i
$670$	−7.46979e12	−	1.29381e13i	−0.0553266	−	0.0958285i
$671$	−3.17932e13	+	1.83558e13i	−0.233734	+	0.134946i
$672$	−8.47390e12	−	3.74592e13i	−0.0618354	−	0.273346i
$673$	8.27819e13	−	1.43382e14i	0.599598	−	1.03853i	−0.393283	−	0.919418i	$-0.628661\pi$
$673$	8.27819e13	−	1.43382e14i	0.599598	−	1.03853i	0.992880	−	0.119116i	$-0.0380060\pi$
$674$			7.23462e13i			0.520135i
$675$	−1.37697e13	−	9.50829e13i	−0.0982666	−	0.678552i
$676$	−9.04707e13			−0.640877
$677$	−2.28508e13	−	1.31929e13i	−0.160678	−	0.0927677i	0.417505	−	0.908675i	$-0.362905\pi$
$677$	−2.28508e13	−	1.31929e13i	−0.160678	−	0.0927677i	−0.578183	+	0.815907i	$0.696238\pi$
$678$	−1.53916e14	+	3.48183e13i	−1.07432	+	0.243030i
$679$	6.52885e13	+	1.13083e14i	0.452364	+	0.783517i
$680$	2.20295e13	−	1.27188e13i	0.151517	−	0.0874783i
$681$	−4.07609e13	−	1.26591e13i	−0.278296	−	0.0864308i
$682$	−8.65331e11	+	1.49880e12i	−0.00586489	+	0.0101583i
$683$			9.85002e13i			0.662725i	0.943503	+	0.331363i	$0.107508\pi$
$683$			9.85002e13i			0.662725i	−0.943503	+	0.331363i	$0.892492\pi$
$684$	3.08844e13	+	2.12314e13i	0.206281	+	0.141807i
$685$	5.18968e13			0.344103
$686$	−7.57104e13	−	4.37114e13i	−0.498350	−	0.287723i
$687$	6.86832e13	+	7.43096e13i	0.448815	+	0.485581i
$688$	3.31341e13	+	5.73899e13i	0.214948	+	0.372300i
$689$	−3.57165e14	+	2.06209e14i	−2.30024	+	1.32804i
$690$	−5.44285e13	+	5.03074e13i	−0.348001	+	0.321652i
$691$	9.30486e12	−	1.61165e13i	0.0590636	−	0.102301i	−0.834982	−	0.550278i	$-0.814522\pi$
$691$	9.30486e12	−	1.61165e13i	0.0590636	−	0.102301i	0.894045	+	0.447977i	$0.147855\pi$
$692$		−	4.38193e13i		−	0.276144i
$693$	−2.19622e13	+	3.19474e13i	−0.137407	+	0.199880i
$694$	1.26672e14			0.786834
$695$	5.43570e13	+	3.13831e13i	0.335221	+	0.193540i
$696$	−2.14240e13	+	6.89825e13i	−0.131176	+	0.422370i
$697$	−6.69412e13	−	1.15945e14i	−0.406939	−	0.704839i
$698$	6.83593e13	−	3.94673e13i	0.412592	−	0.238210i
$699$	4.14175e13	+	1.83088e14i	0.248198	+	1.09717i
$700$	4.56715e13	−	7.91053e13i	0.271741	−	0.470669i
$701$		−	9.40950e13i		−	0.555874i	−0.960599	−	0.277937i	$-0.910349\pi$
$701$		−	9.40950e13i		−	0.555874i	0.960599	−	0.277937i	$-0.0896506\pi$
$702$	−1.12711e14	−	1.43024e14i	−0.661122	−	0.838925i
$703$	−9.81653e13			−0.571717
$704$	−2.86411e12	−	1.65359e12i	−0.0165625	−	0.00956236i
$705$	6.47757e13	−	1.46534e13i	0.371935	−	0.0841379i
$706$	8.60266e12	+	1.49002e13i	0.0490467	+	0.0849513i
$707$	4.37939e14	−	2.52844e14i	2.47923	−	1.43138i
$708$	2.55207e13	+	7.92600e12i	0.143459	+	0.0445541i
$709$	7.26216e13	−	1.25784e14i	0.405354	−	0.702094i	−0.589008	−	0.808127i	$-0.700481\pi$
$709$	7.26216e13	−	1.25784e14i	0.405354	−	0.702094i	0.994363	+	0.106033i	$0.0338148\pi$
$710$		−	9.72761e12i		−	0.0539156i
$711$	5.69009e12	−	7.21938e13i	0.0313163	−	0.397331i
$712$	−4.28634e13			−0.234254
$713$	−2.06807e13	−	1.19400e13i	−0.112232	−	0.0647972i
$714$	1.24615e14	+	1.34824e14i	0.671553	+	0.726565i
$715$	1.21071e13	+	2.09701e13i	0.0647902	+	0.112220i
$716$	9.99589e13	−	5.77113e13i	0.531198	−	0.306687i
$717$	−2.37762e13	+	2.19760e13i	−0.125472	+	0.115972i
$718$	5.84355e13	−	1.01213e14i	0.306235	−	0.530415i
$719$			1.20790e14i			0.628617i	0.949321	+	0.314308i	$0.101773\pi$
$719$			1.20790e14i			0.628617i	−0.949321	+	0.314308i	$0.898227\pi$
$720$	−1.16735e13	−	2.44813e13i	−0.0603310	−	0.126524i
$721$	−3.11191e14			−1.59717
$722$	9.00305e13	+	5.19791e13i	0.458885	+	0.264937i
$723$	−1.69698e13	+	5.46407e13i	−0.0858985	+	0.276582i
$724$	5.21380e13	+	9.03057e13i	0.262097	+	0.453965i
$725$	−1.48780e14	+	8.58981e13i	−0.742770	+	0.428838i
$726$	−3.07304e13	−	1.35845e14i	−0.152365	−	0.673536i
$727$	−8.12798e13	+	1.40781e14i	−0.400231	+	0.693220i	−0.993754	−	0.111597i	$-0.964403\pi$
$727$	−8.12798e13	+	1.40781e14i	−0.400231	+	0.693220i	0.593523	+	0.804817i	$0.297737\pi$
$728$		−	1.73129e14i		−	0.846669i
$729$	4.81330e13	−	2.00186e14i	0.233779	−	0.972290i
$730$	2.74531e13			0.132427
$731$	−2.74344e14	−	1.58393e14i	−1.31434	−	0.758836i
$732$	1.80798e14	−	4.08996e13i	0.860279	−	0.194609i
$733$	−5.22659e13	−	9.05272e13i	−0.247001	−	0.427818i	0.715691	−	0.698417i	$-0.246112\pi$
$733$	−5.22659e13	−	9.05272e13i	−0.247001	−	0.427818i	−0.962692	+	0.270599i	$0.912778\pi$
$734$	7.78049e13	−	4.49207e13i	0.365196	−	0.210846i
$735$	−1.73818e14	−	5.39828e13i	−0.810322	−	0.251663i
$736$	2.28166e13	−	3.95194e13i	0.105648	−	0.182988i
$737$		−	9.28500e12i		−	0.0427016i
$738$	−1.28849e14	+	6.14400e13i	−0.588574	+	0.280653i
$739$	1.60506e14			0.728233			0.364117	−	0.931353i	$-0.381371\pi$
$739$	1.60506e14			0.728233			0.364117	+	0.931353i	$0.381371\pi$
$740$	6.15222e13	+	3.55199e13i	0.277251	+	0.160071i
$741$	1.14675e14	+	1.24069e14i	0.513308	+	0.555358i
$742$	−2.21670e14	−	3.83944e14i	−0.985570	−	1.70706i
$743$	3.47251e14	−	2.00486e14i	1.53356	−	0.885399i	0.534362	−	0.845255i	$-0.320552\pi$
$743$	3.47251e14	−	2.00486e14i	1.53356	−	0.885399i	0.999194	−	0.0401438i	$-0.0127816\pi$
$744$	6.41726e12	−	5.93137e12i	0.0281504	−	0.0260190i
$745$	−1.03562e14	+	1.79375e14i	−0.451252	+	0.781592i
$746$		−	2.92522e13i		−	0.126609i
$747$	−1.82177e14	−	1.43586e13i	−0.783233	−	0.0617319i
$748$	1.58095e13			0.0675166
$749$	5.06930e13	+	2.92676e13i	0.215050	+	0.124159i
$750$	4.70370e13	−	1.51453e14i	0.198213	−	0.638223i
$751$	1.11474e12	+	1.93079e12i	0.00466633	+	0.00808232i	0.868349	−	0.495953i	$-0.165181\pi$
$751$	1.11474e12	+	1.93079e12i	0.00466633	+	0.00808232i	−0.863683	+	0.504036i	$0.831848\pi$
$752$	−3.54115e13	+	2.04448e13i	−0.147250	+	0.0850147i
$753$	6.75561e13	+	2.98635e14i	0.279055	+	1.23357i
$754$	−1.62809e14	+	2.81994e14i	−0.668071	+	1.15713i
$755$		−	5.21689e13i		−	0.212656i
$756$	1.53747e14	−	1.21162e14i	0.622584	−	0.490633i
$757$	3.65647e13			0.147090			0.0735449	−	0.997292i	$-0.476569\pi$
$757$	3.65647e13			0.147090			0.0735449	+	0.997292i	$0.476569\pi$
$758$	1.93934e14	+	1.11968e14i	0.775009	+	0.447452i
$759$	−4.49286e13	+	1.01636e13i	−0.178367	+	0.0403495i
$760$	1.25818e13	+	2.17923e13i	0.0496219	+	0.0859477i
$761$	1.13600e14	−	6.55868e13i	0.445096	−	0.256976i	−0.260661	−	0.965430i	$-0.583940\pi$
$761$	1.13600e14	−	6.55868e13i	0.445096	−	0.256976i	0.705757	+	0.708454i	$0.250607\pi$
$762$	8.40745e13	+	2.61111e13i	0.327257	+	0.101637i
$763$	−2.02626e14	+	3.50958e14i	−0.783560	+	1.35717i
$764$			2.49484e14i			0.958464i
$765$	1.06842e14	+	7.34485e13i	0.407788	+	0.280334i
$766$	−2.17313e14			−0.824026
$767$	1.04326e14	+	6.02328e13i	0.393022	+	0.226911i
$768$	1.13345e13	+	1.22630e13i	0.0424224	+	0.0458976i
$769$	−2.37104e14	−	4.10677e14i	−0.881674	−	1.52710i	−0.849479	−	0.527622i	$-0.823084\pi$
$769$	−2.37104e14	−	4.10677e14i	−0.881674	−	1.52710i	−0.0321947	−	0.999482i	$-0.510250\pi$
$770$	−2.25423e13	+	1.30148e13i	−0.0832809	+	0.0480822i
$771$	−2.84413e14	+	2.62879e14i	−1.04395	+	0.964903i
$772$	−5.05058e13	+	8.74787e13i	−0.184185	+	0.319018i
$773$			4.26133e14i			1.54400i	0.635621	+	0.772001i	$0.280744\pi$
$773$			4.26133e14i			1.54400i	−0.635621	+	0.772001i	$0.719256\pi$
$774$	−1.91343e14	+	2.78338e14i	−0.688823	+	1.00200i
$775$	2.07835e13			0.0743379
$776$	−4.91686e13	−	2.83875e13i	−0.174735	−	0.100883i
$777$	−1.52071e14	+	4.89651e14i	−0.536961	+	1.72895i
$778$	−2.94684e13	−	5.10408e13i	−0.103385	−	0.179069i
$779$	1.14697e14	−	6.62201e13i	0.399819	−	0.230836i
$780$	−2.69765e13	−	1.19250e14i	−0.0934355	−	0.413035i
$781$	3.02287e12	−	5.23577e12i	0.0104031	−	0.0180188i
$782$			2.18142e14i			0.745944i
$783$	−3.64364e14	+	5.27664e13i	−1.23802	+	0.179287i
$784$	1.12061e14			0.378332
$785$	2.40030e14	+	1.38582e14i	0.805226	+	0.464898i
$786$	2.57749e14	−	5.83072e13i	0.859181	−	0.194361i
$787$	1.36958e14	+	2.37218e14i	0.453641	+	0.785730i	0.998609	−	0.0527273i	$-0.0167914\pi$
$787$	1.36958e14	+	2.37218e14i	0.453641	+	0.785730i	−0.544968	+	0.838457i	$0.683458\pi$
$788$	−2.69365e13	+	1.55518e13i	−0.0886564	+	0.0511858i
$789$	1.47972e14	+	4.59558e13i	0.483944	+	0.150299i
$790$	2.43113e13	−	4.21083e13i	0.0790082	−	0.136846i
$791$		−	7.64704e14i		−	2.46951i
$792$	1.32446e12	−	1.68043e13i	0.00425025	−	0.0539256i
$793$	8.35616e14			2.66465
$794$	7.05991e13	+	4.07604e13i	0.223716	+	0.129162i
$795$	−2.12510e14	−	2.29918e14i	−0.669181	−	0.723999i
$796$	−9.01223e13	−	1.56096e14i	−0.282012	−	0.488459i
$797$	−1.80096e14	+	1.03979e14i	−0.560032	+	0.323335i	−0.753159	−	0.657839i	$-0.771471\pi$
$797$	−1.80096e14	+	1.03979e14i	−0.560032	+	0.323335i	0.193126	+	0.981174i	$0.438137\pi$
$798$	−1.33371e14	+	1.23273e14i	−0.412143	+	0.380937i
$799$	9.77335e13	−	1.69279e14i	0.300130	−	0.519840i
$800$			3.97160e13i			0.121204i
$801$	−9.40318e13	−	1.97200e14i	−0.285176	−	0.598059i
$802$	−2.30221e14			−0.693861
$803$	1.47763e13	+	8.53109e12i	0.0442576	+	0.0255521i
$804$	−1.39051e13	+	4.47728e13i	−0.0413899	+	0.133270i
$805$	−1.79581e14	−	3.11043e14i	−0.531228	−	0.920113i
$806$	3.41150e13	−	1.96963e13i	0.100293	−	0.0579041i
$807$	8.66970e13	+	3.83248e14i	0.253301	+	1.11973i
$808$	−1.09937e14	+	1.90416e14i	−0.319217	+	0.552901i
$809$		−	5.06557e14i		−	1.46179i	−0.682489	−	0.730896i	$-0.739102\pi$
$809$		−	5.06557e14i		−	1.46179i	0.682489	−	0.730896i	$-0.260898\pi$
$810$	8.70211e13	−	1.07412e14i	0.249574	−	0.308054i
$811$	−3.62187e14			−1.03235			−0.516177	−	0.856482i	$-0.672645\pi$
$811$	−3.62187e14			−1.03235			−0.516177	+	0.856482i	$0.672645\pi$
$812$	−3.03137e14	−	1.75016e14i	−0.858733	−	0.495790i
$813$	4.88639e14	−	1.10538e14i	1.37574	−	0.311215i
$814$	2.20757e13	+	3.82362e13i	0.0617721	+	0.106992i
$815$	−2.16955e14	+	1.25259e14i	−0.603368	+	0.348354i
$816$	−7.62344e13	−	2.36762e13i	−0.210717	−	0.0654427i
$817$	1.56686e14	−	2.71389e14i	0.430448	−	0.745559i
$818$			7.50708e13i			0.204977i
$819$	7.96508e14	−	3.79803e14i	2.16158	−	1.03072i
$820$	−9.58436e13			−0.258520
$821$	−4.80906e13	−	2.77651e13i	−0.128927	−	0.0744362i	0.434149	−	0.900841i	$-0.357049\pi$
$821$	−4.80906e13	−	2.77651e13i	−0.128927	−	0.0744362i	−0.563077	+	0.826405i	$0.690382\pi$
$822$	−1.10542e14	−	1.19597e14i	−0.294556	−	0.318686i
$823$	1.52870e12	+	2.64779e12i	0.00404877	+	0.00701268i	0.868043	−	0.496490i	$-0.165378\pi$
$823$	1.52870e12	+	2.64779e12i	0.00404877	+	0.00701268i	−0.863994	+	0.503502i	$0.832045\pi$
$824$	1.17178e14	−	6.76530e13i	0.308469	−	0.178095i
$825$	2.94412e13	−	2.72120e13i	0.0770345	−	0.0712018i
$826$	−6.47488e13	+	1.12148e14i	−0.168396	+	0.291670i
$827$		−	1.10267e14i		−	0.285047i	−0.989791	−	0.142524i	$-0.954478\pi$
$827$		−	1.10267e14i		−	0.285047i	0.989791	−	0.142524i	$-0.0455217\pi$
$828$	2.31869e14	+	1.82752e13i	0.595787	+	0.0469580i
$829$	−6.19479e13			−0.158217			−0.0791086	−	0.996866i	$-0.525207\pi$
$829$	−6.19479e13			−0.158217			−0.0791086	+	0.996866i	$0.525207\pi$
$830$	−1.06258e14	−	6.13481e13i	−0.269756	−	0.155744i
$831$	−3.32494e13	+	1.07059e14i	−0.0839033	+	0.270158i
$832$	3.76384e13	+	6.51916e13i	0.0944092	+	0.163522i
$833$	−4.63921e14	+	2.67845e14i	−1.15670	+	0.667818i
$834$	−4.34594e13	−	1.92114e14i	−0.107709	−	0.476134i
$835$	1.31973e14	−	2.28583e14i	0.325126	−	0.563135i
$836$			1.56392e13i			0.0382987i
$837$	4.13661e13	+	1.65116e13i	0.100697	+	0.0401941i
$838$	3.37268e14			0.816123
$839$	−2.68487e14	−	1.55011e14i	−0.645824	−	0.372866i	0.141031	−	0.990005i	$-0.454958\pi$
$839$	−2.68487e14	−	1.55011e14i	−0.645824	−	0.372866i	−0.786854	+	0.617139i	$0.788292\pi$
$840$	1.28191e14	−	2.89990e13i	0.306522	−	0.0693405i
$841$	1.18813e14	+	2.05791e14i	0.282414	+	0.489155i
$842$	3.49731e14	−	2.01917e14i	0.826368	−	0.477104i
$843$	−5.36595e14	−	1.66651e14i	−1.26040	−	0.391444i
$844$	−9.95499e13	+	1.72426e14i	−0.232450	+	0.402614i
$845$		−	3.09605e14i		−	0.718662i
$846$	−1.71744e14	−	1.18065e14i	−0.396304	−	0.272439i
$847$	6.74924e14			1.54824
$848$	1.66939e14	+	9.63823e13i	0.380696	+	0.219795i
$849$	9.49783e13	+	1.02759e14i	0.215321	+	0.232960i
$850$	−9.49282e13	−	1.64420e14i	−0.213944	−	0.370562i
$851$	−5.27591e14	+	3.04605e14i	−1.18209	+	0.682478i
$852$	−2.24175e13	+	2.07201e13i	−0.0499332	+	0.0461525i
$853$	−2.10562e13	+	3.64705e13i	−0.0466268	+	0.0807600i	−0.888397	−	0.459076i	$-0.848180\pi$
$853$	−2.10562e13	+	3.64705e13i	−0.0466268	+	0.0807600i	0.841770	+	0.539836i	$0.181514\pi$
$854$			8.98267e14i			1.97750i
$855$	−7.26573e13	+	1.05691e14i	−0.159019	+	0.231317i
$856$	−2.54512e13			−0.0553782
$857$	2.08014e14	+	1.20097e14i	0.449974	+	0.259793i	0.707819	−	0.706394i	$-0.249679\pi$
$857$	2.08014e14	+	1.20097e14i	0.449974	+	0.259793i	−0.257845	+	0.966186i	$0.583012\pi$
$858$	2.25375e13	−	7.25681e13i	0.0484697	−	0.156066i
$859$	−8.95316e13	−	1.55073e14i	−0.191430	−	0.331567i	0.754294	−	0.656537i	$-0.227979\pi$
$859$	−8.95316e13	−	1.55073e14i	−0.191430	−	0.331567i	−0.945724	+	0.324970i	$0.894646\pi$
$860$	−1.96397e14	+	1.13390e14i	−0.417487	+	0.241036i
$861$	−1.52627e14	−	6.74694e14i	−0.322564	−	1.42591i
$862$	2.48840e14	−	4.31004e14i	0.522859	−	0.905618i
$863$		−	5.73471e13i		−	0.119800i	−0.998204	−	0.0599001i	$-0.980922\pi$
$863$		−	5.73471e13i		−	0.119800i	0.998204	−	0.0599001i	$-0.0190782\pi$
$864$	−3.15527e13	+	7.90480e13i	−0.0655341	+	0.164181i
$865$	1.49957e14			0.309660
$866$	−1.56561e14	−	9.03907e13i	−0.321436	−	0.185581i
$867$	−1.05620e14	+	2.38929e13i	−0.215600	+	0.0487724i
$868$	2.11730e13	+	3.66728e13i	0.0429719	+	0.0744295i
$869$	2.61705e13	−	1.51095e13i	0.0528096	−	0.0304896i
$870$	−2.36069e14	−	7.33162e13i	−0.473634	−	0.147097i
$871$	−1.05671e14	+	1.83027e14i	−0.210797	+	0.365110i
$872$		−	1.76204e14i		−	0.349488i
$873$	2.27373e13	−	2.88483e14i	0.0448402	−	0.568916i
$874$	−2.15793e14			−0.423136
$875$	6.65546e14	+	3.84253e14i	1.29759	+	0.749164i
$876$	−5.84760e13	−	6.32663e13i	−0.113359	−	0.122646i
$877$	4.66682e14	+	8.08318e14i	0.899546	+	1.55806i	0.828075	+	0.560617i	$0.189436\pi$
$877$	4.66682e14	+	8.08318e14i	0.899546	+	1.55806i	0.0714709	+	0.997443i	$0.477231\pi$
$878$	−2.55761e14	+	1.47663e14i	−0.490186	+	0.283009i
$879$	−1.02929e14	+	9.51359e13i	−0.196153	+	0.181301i
$880$	5.65885e12	−	9.80142e12i	0.0107230	−	0.0185727i
$881$			1.10722e14i			0.208618i	0.994545	+	0.104309i	$0.0332632\pi$
$881$			1.10722e14i			0.208618i	−0.994545	+	0.104309i	$0.966737\pi$
$882$	2.45834e14	+	5.15552e14i	0.460573	+	0.965895i
$883$	6.20646e14			1.15622			0.578110	−	0.815959i	$-0.303790\pi$
$883$	6.20646e14			1.15622			0.578110	+	0.815959i	$0.303790\pi$
$884$	−3.11639e14	−	1.79925e14i	−0.577285	−	0.333296i
$885$	−2.71240e13	+	8.73360e13i	−0.0499617	+	0.160871i
$886$	9.43299e13	+	1.63384e14i	0.172775	+	0.299255i
$887$	−2.80344e14	+	1.61857e14i	−0.510591	+	0.294790i	−0.733076	−	0.680146i	$-0.761916\pi$
$887$	−2.80344e14	+	1.61857e14i	−0.510591	+	0.294790i	0.222486	+	0.974936i	$0.428583\pi$
$888$	−4.91881e13	−	2.17438e14i	−0.0890830	−	0.393795i
$889$	−2.13306e14	+	3.69457e14i	−0.384144	+	0.665357i
$890$		−	1.46685e14i		−	0.262686i
$891$	8.02165e13	−	3.07712e13i	0.142848	−	0.0547968i
$892$	−1.44093e14			−0.255164
$893$	1.67456e14	+	9.66808e13i	0.294879	+	0.170248i
$894$	6.33964e14	−	1.43413e14i	1.11014	−	0.251132i
$895$	1.97497e14	+	3.42075e14i	0.343911	+	0.595671i
$896$	−7.00794e13	+	4.04603e13i	−0.121353	+	0.0700631i
$897$	1.00131e15	+	3.10977e14i	1.72427	+	0.535508i
$898$	2.59085e13	−	4.48749e13i	0.0443671	−	0.0768461i
$899$		−	7.96438e13i		−	0.135629i
$900$	−1.82719e14	+	8.71271e13i	−0.309437	+	0.147550i
$901$	−9.21483e14			−1.55190
$902$	−5.15867e13	−	2.97836e13i	−0.0863982	−	0.0498820i
$903$	−1.11097e15	−	1.20198e15i	−1.85039	−	2.00197i
$904$	1.66247e14	+	2.87948e14i	0.275367	+	0.476949i
$905$	−3.09040e14	+	1.78424e14i	−0.509064	+	0.293908i
$906$	−1.20224e14	+	1.11121e14i	−0.196948	+	0.182036i
$907$	−4.76544e14	+	8.25398e14i	−0.776366	+	1.34470i	0.157658	+	0.987494i	$0.449606\pi$
$907$	−4.76544e14	+	8.25398e14i	−0.776366	+	1.34470i	−0.934024	+	0.357211i	$0.883728\pi$
$908$			8.99295e13i			0.145704i
$909$	−1.11721e15	−	8.80552e13i	−1.80018	−	0.141885i
$910$	5.92476e14			0.949432
$911$	−8.83569e14	−	5.10129e14i	−1.40815	−	0.812995i	−0.412939	−	0.910759i	$-0.635498\pi$
$911$	−8.83569e14	−	5.10129e14i	−1.40815	−	0.812995i	−0.995210	+	0.0977642i	$0.968831\pi$
$912$	2.34212e13	−	7.54132e13i	0.0371222	−	0.119529i
$913$	−3.81280e13	−	6.60397e13i	−0.0601022	−	0.104100i
$914$	5.68894e14	−	3.28451e14i	0.891867	−	0.514920i
$915$	1.39965e14	+	6.18721e14i	0.218230	+	0.964693i
$916$	1.06603e14	−	1.84642e14i	0.165307	−	0.286320i
$917$			1.28058e15i			1.97498i
$918$	−5.83135e13	−	4.02668e14i	−0.0894449	−	0.617637i
$919$	−4.07983e14			−0.622393			−0.311196	−	0.950346i	$-0.600730\pi$
$919$	−4.07983e14			−0.622393			−0.311196	+	0.950346i	$0.600730\pi$
$920$	1.35242e14	+	7.80819e13i	0.205197	+	0.118471i
$921$	1.98231e14	−	4.48432e13i	0.299140	−	0.0676704i
$922$	1.63689e14	+	2.83518e14i	0.245678	+	0.425526i
$923$	−1.19174e14	+	6.88053e13i	−0.177899	+	0.102710i
$924$	7.80089e13	+	2.42273e13i	0.115820	+	0.0359704i
$925$	2.65107e14	−	4.59179e14i	0.391483	−	0.678068i
$926$		−	7.07378e14i		−	1.03895i
$927$	5.68309e14	+	3.90683e14i	0.830205	+	0.570724i
$928$	1.52194e14			0.221135
$929$	3.87127e14	+	2.23508e14i	0.559468	+	0.323009i	0.752932	−	0.658099i	$-0.228639\pi$
$929$	3.87127e14	+	2.23508e14i	0.559468	+	0.323009i	−0.193464	+	0.981107i	$0.561972\pi$
$930$	2.02981e13	+	2.19609e13i	0.0291770	+	0.0315671i
$931$	−2.64960e14	−	4.58924e14i	−0.378819	−	0.656134i
$932$	3.42524e14	−	1.97756e14i	0.487092	−	0.281223i
$933$	5.73560e14	−	5.30133e14i	0.811280	−	0.749854i
$934$	−1.99710e13	+	3.45908e13i	−0.0280974	+	0.0486661i
$935$			5.41026e13i			0.0757113i
$936$	−2.17355e14	+	3.16175e14i	−0.302545	+	0.440098i
$937$	−1.26985e15			−1.75814			−0.879072	−	0.476689i	$-0.841837\pi$
$937$	−1.26985e15			−1.75814			−0.879072	+	0.476689i	$0.841837\pi$
$938$	−1.96749e14	−	1.13593e14i	−0.270956	−	0.156437i
$939$	3.87508e12	−	1.24773e13i	0.00530827	−	0.0170920i
$940$	−6.99654e13	−	1.21184e14i	−0.0953332	−	0.165122i
$941$	1.10489e15	−	6.37906e14i	1.49751	−	0.864587i	0.497513	−	0.867457i	$-0.334247\pi$
$941$	1.10489e15	−	6.37906e14i	1.49751	−	0.864587i	0.999996	+	0.00286943i	$0.000913369\pi$
$942$	−1.91909e14	−	8.48339e14i	−0.258726	−	1.14371i
$943$	4.10959e14	−	7.11802e14i	0.551112	−	0.954554i
$944$		−	5.63057e13i		−	0.0751090i
$945$	4.14635e14	+	5.26147e14i	0.550182	+	0.698149i
$946$	−1.40945e14			−0.186034
$947$	6.90521e14	+	3.98673e14i	0.906624	+	0.523440i	0.879343	−	0.476188i	$-0.157982\pi$
$947$	6.90521e14	+	3.98673e14i	0.906624	+	0.523440i	0.0272806	+	0.999628i	$0.491315\pi$
$948$	−1.48823e14	+	3.36664e13i	−0.194370	+	0.0439698i
$949$	−1.94181e14	−	3.36332e14i	−0.252276	−	0.436955i
$950$	1.62649e14	−	9.39057e13i	0.210201	−	0.121360i
$951$	5.07783e13	+	1.57703e13i	0.0652793	+	0.0202738i
$952$	1.93415e14	−	3.35004e14i	0.247346	−	0.428416i
$953$		−	3.64436e14i		−	0.463614i	−0.972762	−	0.231807i	$-0.925536\pi$
$953$		−	3.64436e14i		−	0.463614i	0.972762	−	0.231807i	$-0.0744637\pi$
$954$	−7.71985e13	+	9.79467e14i	−0.0976938	+	1.23950i
$955$	−8.53774e14			−1.07480
$956$	5.90781e13	+	3.41088e13i	0.0739839	+	0.0427146i
$957$	−1.04278e14	−	1.12820e14i	−0.129907	−	0.140549i
$958$	2.44767e14	+	4.23948e14i	0.303336	+	0.525394i
$959$	6.83465e14	−	3.94599e14i	0.842603	−	0.486477i
$960$	−4.19658e13	+	3.87884e13i	−0.0514683	+	0.0475713i
$961$	4.04997e14	−	7.01475e14i	0.494122	−	0.855845i
$962$		−	1.00496e15i		−	1.21975i
$963$	−5.58336e13	−	1.17092e14i	−0.0674162	−	0.141383i
$964$	1.20552e14			0.144807
$965$	−2.99366e14	−	1.72839e14i	−0.357738	−	0.206540i
$966$	−3.34293e14	+	1.07638e15i	−0.397412	+	1.27962i
$967$	−8.44038e13	−	1.46192e14i	−0.0998228	−	0.172898i	0.811788	−	0.583952i	$-0.198494\pi$
$967$	−8.44038e13	−	1.46192e14i	−0.0998228	−	0.172898i	−0.911611	+	0.411054i	$0.865161\pi$
$968$	−2.54141e14	+	1.46729e14i	−0.299019	+	0.172639i
$969$	8.32895e13	+	3.68185e14i	0.0974926	+	0.430970i
$970$	9.71464e13	−	1.68263e14i	0.113128	−	0.195943i
$971$			1.05583e15i			1.22320i	0.791167	+	0.611600i	$0.209474\pi$
$971$			1.05583e15i			1.22320i	−0.791167	+	0.611600i	$0.790526\pi$
$972$	−4.32891e14	+	2.82489e13i	−0.498939	+	0.0325589i
$973$	9.54487e14			1.09447
$974$	−6.34165e14	−	3.66135e14i	−0.723448	−	0.417683i
$975$	−8.90042e14	+	2.01342e14i	−1.01015	+	0.228514i
$976$	−1.95283e14	−	3.38241e14i	−0.220504	−	0.381924i
$977$	−3.94261e14	+	2.27626e14i	−0.442905	+	0.255711i	−0.704829	−	0.709377i	$-0.748976\pi$
$977$	−3.94261e14	+	2.27626e14i	−0.442905	+	0.255711i	0.261924	+	0.965088i	$0.415643\pi$
$978$	7.50785e14	+	2.33172e14i	0.839114	+	0.260604i
$979$	4.55828e13	−	7.89517e13i	0.0506859	−	0.0877906i
$980$			3.83489e14i			0.424251i
$981$	8.10652e14	−	3.86548e14i	0.892256	−	0.425459i
$982$	9.59242e13			0.105044
$983$	1.72844e14	+	9.97916e13i	0.188316	+	0.108724i	0.591194	−	0.806529i	$-0.298657\pi$
$983$	1.72844e14	+	9.97916e13i	0.188316	+	0.108724i	−0.402878	+	0.915254i	$0.631990\pi$
$984$	2.04150e14	+	2.20874e14i	0.221296	+	0.239425i
$985$	−5.32207e13	−	9.21810e13i	−0.0573984	−	0.0994169i
$986$	−6.30070e14	+	3.63771e14i	−0.676089	+	0.390340i
$987$	7.41659e14	−	6.85504e14i	0.791805	−	0.731853i
$988$	1.77987e14	−	3.08282e14i	0.189061	−	0.327464i
$989$		−	1.94478e15i		−	2.05536i
$990$	5.75071e13	+	4.53252e12i	0.0604707	+	0.00476611i
$991$	−1.20407e15			−1.25975			−0.629876	−	0.776696i	$-0.716894\pi$
$991$	−1.20407e15			−1.25975			−0.629876	+	0.776696i	$0.716894\pi$
$992$	−1.59454e13	−	9.20605e12i	−0.0165988	−	0.00958330i
$993$	−3.20694e14	+	1.03259e15i	−0.332158	+	1.06951i
$994$	−7.39641e13	−	1.28110e14i	−0.0762235	−	0.132023i
$995$	5.34187e14	−	3.08413e14i	0.547744	−	0.316240i
$996$	8.49552e13	+	3.75548e14i	0.0866749	+	0.383150i
$997$	−2.99806e13	+	5.19279e13i	−0.0304344	+	0.0527139i	−0.880841	−	0.473411i	$-0.843022\pi$
$997$	−2.99806e13	+	5.19279e13i	−0.0304344	+	0.0527139i	0.850407	+	0.526125i	$0.176356\pi$
$998$			1.34035e15i			1.35384i
$999$	8.92449e14	−	7.03302e14i	0.896925	−	0.706829i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.11.d.a.11.1	yes	20
3.2	odd	2		54.11.d.a.35.8		20
9.2	odd	6		162.11.b.c.161.6		20
9.4	even	3		54.11.d.a.17.8		20
9.5	odd	6	inner	18.11.d.a.5.1	✓	20
9.7	even	3		162.11.b.c.161.15		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.11.d.a.5.1	✓	20	9.5	odd	6	inner
18.11.d.a.11.1	yes	20	1.1	even	1	trivial
54.11.d.a.17.8		20	9.4	even	3
54.11.d.a.35.8		20	3.2	odd	2
162.11.b.c.161.6		20	9.2	odd	6
162.11.b.c.161.15		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} +(-237.011 + 53.6159i) q^{3} +(256.000 + 443.405i) q^{4} +(-1517.40 + 876.072i) q^{5} +(5251.05 + 1630.82i) q^{6} +(-13322.5 + 23075.2i) q^{7} -11585.2i q^{8} +(53299.7 - 25415.2i) q^{9} +39646.5 q^{10} +(21339.2 + 12320.2i) q^{11} +(-84448.4 - 91366.3i) q^{12} +(-280428. - 485715. i) q^{13} +(522132. - 301453. i) q^{14} +(312670. - 288996. i) q^{15} +(-131072. + 227023. i) q^{16} -1.25314e6i q^{17} +(-1.33200e6 - 104984. i) q^{18} +1.23964e6 q^{19} +(-776910. - 448549. i) q^{20} +(1.92038e6 - 6.18338e6i) q^{21} +(-278775. - 482852. i) q^{22} +(6.66248e6 - 3.84658e6i) q^{23} +(621153. + 2.74583e6i) q^{24} +(-3.34781e6 + 5.79857e6i) q^{25} +1.26907e7i q^{26} +(-1.12700e7 + 8.88139e6i) q^{27} -1.36422e7 q^{28} +(2.22205e7 + 1.28290e7i) q^{29} +(-9.39667e6 + 2.12568e6i) q^{30} +(-1.55202e6 - 2.68819e6i) q^{31} +(5.13695e6 - 2.96582e6i) q^{32} +(-5.71820e6 - 1.77591e6i) q^{33} +(-1.41777e7 + 2.45564e7i) q^{34} -4.66858e7i q^{35} +(2.49139e7 + 1.71271e7i) q^{36} -7.91883e7 q^{37} +(-2.42919e7 - 1.40250e7i) q^{38} +(9.25066e7 + 1.00085e8i) q^{39} +(1.01495e7 + 1.75795e7i) q^{40} +(9.25239e7 - 5.34187e7i) q^{41} +(-1.07588e8 + 9.94424e7i) q^{42} +(1.26396e8 - 2.18925e8i) q^{43} +1.26159e7i q^{44} +(-5.86115e7 + 8.52594e7i) q^{45} -1.74077e8 q^{46} +(1.35084e8 + 7.79908e7i) q^{47} +(1.88935e7 - 6.08346e7i) q^{48} +(-2.13739e8 - 3.70206e8i) q^{49} +(1.31207e8 - 7.57522e7i) q^{50} +(6.71883e7 + 2.97009e8i) q^{51} +(1.43579e8 - 2.48686e8i) q^{52} -7.35338e8i q^{53} +(3.21327e8 - 4.65339e7i) q^{54} -4.31736e7 q^{55} +(2.67332e8 + 1.54344e8i) q^{56} +(-2.93809e8 + 6.64646e7i) q^{57} +(-2.90287e8 - 5.02792e8i) q^{58} +(-1.86013e8 + 1.07395e8i) q^{59} +(2.08186e8 + 6.46564e7i) q^{60} +(-7.44947e8 + 1.29029e9i) q^{61} +7.02366e7i q^{62} +(-1.23624e8 + 1.56849e9i) q^{63} -1.34218e8 q^{64} +(8.51043e8 + 4.91350e8i) q^{65} +(9.19613e7 + 9.94946e7i) q^{66} +(-1.88410e8 - 3.26335e8i) q^{67} +(5.55649e8 - 3.20804e8i) q^{68} +(-1.37284e9 + 1.26890e9i) q^{69} +(-5.28189e8 + 9.14851e8i) q^{70} -2.45358e8i q^{71} +(-2.94441e8 - 6.17489e8i) q^{72} +6.92446e8 q^{73} +(1.55177e9 + 8.95914e8i) q^{74} +(4.82572e8 - 1.55382e9i) q^{75} +(3.17349e8 + 5.49664e8i) q^{76} +(-5.68583e8 + 3.28272e8i) q^{77} +(-6.80424e8 - 3.00784e9i) q^{78} +(6.13200e8 - 1.06209e9i) q^{79} -4.59314e8i q^{80} +(2.19492e9 - 2.70924e9i) q^{81} -2.41745e9 q^{82} +(-2.68014e9 - 1.54738e9i) q^{83} +(3.23336e9 - 7.31440e8i) q^{84} +(1.09784e9 + 1.90152e9i) q^{85} +(-4.95371e9 + 2.86002e9i) q^{86} +(-5.95435e9 - 1.84925e9i) q^{87} +(1.42733e8 - 2.47220e8i) q^{88} -3.69983e9i q^{89} +(2.11315e9 - 1.00762e9i) q^{90} +1.49440e10 q^{91} +(3.41119e9 + 1.96945e9i) q^{92} +(5.11977e8 + 5.53917e8i) q^{93} +(-1.76473e9 - 3.05660e9i) q^{94} +(-1.88104e9 + 1.08602e9i) q^{95} +(-1.05850e9 + 9.78355e8i) q^{96} +(2.45031e9 - 4.24407e9i) q^{97} +9.67271e9i q^{98} +(1.45050e9 + 1.14323e8i) 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

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